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 either not funny or kind is brave or not quiet and vice versa. Everyone who is calm or not happy is either not creative or not strong and vice versa. Everyone who is both wise and creative is not generous. If alice is both not generous and wise then someone is both not happy and not funny and vice versa. If someone is generous or not humble then fred is not brave or not wise and vice versa. Everyone who is rich is both happy and not tall. Everyone who is either generous or not patient is generous. Everyone who is both not creative and not wise is not rich and vice versa. Everyone who is wise or not humble is not happy. Everyone who is patient or wise is both strong and generous and vice versa. Everyone who is both not funny and not wise is either creative or patient and vice versa. If someone is either not happy or creative then john is both rich and not calm and vice versa. Everyone who is either not tall or old is not tall or generous. If susan is either tall or humble then paul is either rich or not patient and vice versa. Everyone who is either calm or not rich is both not brave and generous and vice versa. Someone is funny or not curious. Paul is either not old or not creative. Someone is not brave or not curious. Fred is either humble or not kind. Someone is either not humble or calm. | Fred is wise. | contradiction | (![X]:((~funny(X)<~>kind(X))<=>(brave(X)|~quiet(X))))&
(![X]:((calm(X)|~happy(X))<=>(~creative(X)<~>~strong(X))))&
(![X]:((wise(X)&creative(X))=>~generous(X)))&
(((~generous(alice)&wise(alice)))<=>(?[X]:((~happy(X)&~funny(X)))))&
((?[X]:((generous(X)|~humble(X))))<=>((~brave(fred)|~wise(fred))))&
(![X]:(rich(X)=>(happy(X)&~tall(X))))&
(![X]:((generous(X)<~>~patient(X))=>generous(X)))&
(![X]:((~creative(X)&~wise(X))<=>~rich(X)))&
(![X]:((wise(X)|~humble(X))=>~happy(X)))&
(![X]:((patient(X)|wise(X))<=>(strong(X)&generous(X))))&
(![X]:((~funny(X)&~wise(X))<=>(creative(X)<~>patient(X))))&
((?[X]:((~happy(X)<~>creative(X))))<=>((rich(john)&~calm(john))))&
(![X]:((~tall(X)<~>old(X))=>(~tall(X)|generous(X))))&
(((tall(susan)<~>humble(susan)))<=>((rich(paul)<~>~patient(paul))))&
(![X]:((calm(X)<~>~rich(X))<=>(~brave(X)&generous(X))))&
(?[X]:((funny(X)|~curious(X))))&
((~old(paul)<~>~creative(paul)))&
(?[X]:((~brave(X)|~curious(X))))&
((humble(fred)<~>~kind(fred)))&
(?[X]:((~humble(X)<~>calm(X)))) | wise(fred) | [
"p5",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2810002383556521848754910
% SZS output start Proof for 2810002383556521848754910
6. ! [X0] : (rich(X0) => (~tall(X0) & happy(X0))) [input p5]
8. ! [X0] : ((~wise(X0) & ~creative(X0)) <=> ~rich(X0)) [input p7]
9. ! [X0] : ((~humble(X0) | wise(X0)) => ~happy(X0)) [input p8]
21. wise(fred) [input hypothesis]
26. ! [X0] : ((~tall(X0) & happy(X0)) | ~rich(X0)) [ennf transformation 6]
28. ! [X0] : (~happy(X0) | (humble(X0) & ~wise(X0))) [ennf transformation 9]
46. ! [X0] : (((~wise(X0) & ~creative(X0)) | rich(X0)) & (~rich(X0) | (wise(X0) | creative(X0)))) [nnf transformation 8]
47. ! [X0] : (((~wise(X0) & ~creative(X0)) | rich(X0)) & (~rich(X0) | wise(X0) | creative(X0))) [flattening 46]
87. ~rich(X0) | happy(X0) [cnf transformation 26]
93. ~wise(X0) | rich(X0) [cnf transformation 47]
94. ~wise(X0) | ~happy(X0) [cnf transformation 28]
135. wise(fred) [cnf transformation 21]
162. 6 <=> wise(fred) [avatar definition]
164. wise(fred) <- (6) [avatar component clause 162]
273. 6 [avatar split clause 135,162]
278. rich(fred) <- (6) [resolution 93,164]
281. ~happy(fred) <- (6) [resolution 94,164]
285. happy(fred) <- (6) [resolution 278,87]
286. $false <- (6) [subsumption resolution 285,281]
287. ~6 [avatar contradiction clause 286]
288. $false [avatar sat refutation 273,287]
% SZS output end Proof for 2810002383556521848754910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then mary is calm and vice versa.
If mary is not creative or not quiet then fred is not quiet and vice versa.
If someone is happy or not tall then alice is wise or old and vice versa.
Everyone who is not curious or curious is not humble and vice versa.
If someone is either wise or not wise then alice is not humble and vice versa.
Everyone who is creative or not generous is curious and vice versa.
If paul is both humble and not funny then someone is not kind or calm and vice versa.
Everyone who is either not creative or old is either not funny or not humble and vice versa.
If someone is not rich then john is curious or not brave.
If someone is either kind or not calm then someone is either quiet or not funny and vice versa.
If someone is wise or not kind then fred is either not creative or funny.
Everyone who is both generous and not calm is not tall or not kind.
Everyone who is either kind or not tall is generous.
Everyone who is not quiet is either not brave or not generous and vice versa.
Everyone who is rich or not brave is either brave or not creative.
Everyone who is both tall and not patient is both kind and old.
Someone is both not curious and not quiet.
Someone is curious or funny.
Alice is either not brave or not strong.
Someone is either not calm or not happy.
Alice is either not curious or not strong. | Alice is not curious. | neutral | ((brave(lucy))<=>(calm(mary)))&
(((~creative(mary)|~quiet(mary)))<=>(~quiet(fred)))&
((?[X]:((happy(X)|~tall(X))))<=>((wise(alice)|old(alice))))&
(![X]:((~curious(X)|curious(X))<=>~humble(X)))&
((?[X]:((wise(X)<~>~wise(X))))<=>(~humble(alice)))&
(![X]:((creative(X)|~generous(X))<=>curious(X)))&
(((humble(paul)&~funny(paul)))<=>(?[X]:((~kind(X)|calm(X)))))&
(![X]:((~creative(X)<~>old(X))<=>(~funny(X)<~>~humble(X))))&
((?[X]:(~rich(X)))=>((curious(john)|~brave(john))))&
((?[X]:((kind(X)<~>~calm(X))))<=>(?[X]:((quiet(X)<~>~funny(X)))))&
((?[X]:((wise(X)|~kind(X))))=>((~creative(fred)<~>funny(fred))))&
(![X]:((generous(X)&~calm(X))=>(~tall(X)|~kind(X))))&
(![X]:((kind(X)<~>~tall(X))=>generous(X)))&
(![X]:(~quiet(X)<=>(~brave(X)<~>~generous(X))))&
(![X]:((rich(X)|~brave(X))=>(brave(X)<~>~creative(X))))&
(![X]:((tall(X)&~patient(X))=>(kind(X)&old(X))))&
(?[X]:((~curious(X)&~quiet(X))))&
(?[X]:((curious(X)|funny(X))))&
((~brave(alice)<~>~strong(alice)))&
(?[X]:((~calm(X)<~>~happy(X))))&
((~curious(alice)<~>~strong(alice))) | ~curious(alice) | [] | null | 0 |
Everyone who is strong is not humble or creative. If paul is not calm or not old then someone is not strong or patient. Everyone who is humble is both not brave and not happy. Everyone who is not creative or tall is either not patient or old and vice versa. Everyone who is creative is not rich and vice versa. If someone is both not patient and rich then lucy is either happy or funny. Everyone who is strong or not tall is happy and vice versa. If alice is not brave or curious then someone is patient and vice versa. Everyone who is either not calm or kind is either not curious or not patient. Everyone who is either patient or not old is both patient and not patient. Everyone who is not funny is both happy and not calm. If someone is either not kind or kind then someone is both strong and not old and vice versa. If someone is either not patient or brave then fred is either kind or not humble. If someone is either not wise or not humble then john is not humble and vice versa. If paul is either not rich or happy then someone is either kind or not happy. If lucy is not calm then susan is old. Someone is either creative or old. John is both happy and quiet. Someone is both not curious and wise. Alice is either humble or happy. Fred is curious. Lucy is happy. Someone is either humble or not generous. | Alice is not happy. | contradiction | (![X]:(strong(X)=>(~humble(X)|creative(X))))&
(((~calm(paul)|~old(paul)))=>(?[X]:((~strong(X)|patient(X)))))&
(![X]:(humble(X)=>(~brave(X)&~happy(X))))&
(![X]:((~creative(X)|tall(X))<=>(~patient(X)<~>old(X))))&
(![X]:(creative(X)<=>~rich(X)))&
((?[X]:((~patient(X)&rich(X))))=>((happy(lucy)<~>funny(lucy))))&
(![X]:((strong(X)|~tall(X))<=>happy(X)))&
(((~brave(alice)|curious(alice)))<=>(?[X]:(patient(X))))&
(![X]:((~calm(X)<~>kind(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((patient(X)<~>~old(X))=>(patient(X)&~patient(X))))&
(![X]:(~funny(X)=>(happy(X)&~calm(X))))&
((?[X]:((~kind(X)<~>kind(X))))<=>(?[X]:((strong(X)&~old(X)))))&
((?[X]:((~patient(X)<~>brave(X))))=>((kind(fred)<~>~humble(fred))))&
((?[X]:((~wise(X)<~>~humble(X))))<=>(~humble(john)))&
(((~rich(paul)<~>happy(paul)))=>(?[X]:((kind(X)<~>~happy(X)))))&
((~calm(lucy))=>(old(susan)))&
(?[X]:((creative(X)<~>old(X))))&
((happy(john)&quiet(john)))&
(?[X]:((~curious(X)&wise(X))))&
((humble(alice)<~>happy(alice)))&
(curious(fred))&
(happy(lucy))&
(?[X]:((humble(X)<~>~generous(X)))) | ~happy(alice) | [
"p3",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 372987864871576562989770
% SZS output start Proof for 372987864871576562989770
4. ! [X0] : ((tall(X0) | ~creative(X0)) <=> (~patient(X0) <~> old(X0))) [input p3]
7. ! [X0] : ((~tall(X0) | strong(X0)) <=> happy(X0)) [input p6]
10. ! [X0] : ((patient(X0) <~> ~old(X0)) => (~patient(X0) & patient(X0))) [input p9]
24. ~happy(alice) [input hypothesis]
33. ! [X0] : ((~patient(X0) & patient(X0)) | (patient(X0) <=> ~old(X0))) [ennf transformation 10]
40. ! [X0] : (((tall(X0) | ~creative(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (~tall(X0) & creative(X0)))) [nnf transformation 4]
41. ! [X0] : ((tall(X0) | ~creative(X0) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (~tall(X0) & creative(X0)))) [flattening 40]
44. ! [X0] : (((~tall(X0) | strong(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~strong(X0)))) [nnf transformation 7]
45. ! [X0] : ((~tall(X0) | strong(X0) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~strong(X0)))) [flattening 44]
52. ! [X0] : ((~patient(X0) & patient(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) [nnf transformation 33]
81. ~tall(X0) | ~patient(X0) | old(X0) [cnf transformation 41]
83. ~tall(X0) | patient(X0) | ~old(X0) [cnf transformation 41]
91. tall(X0) | happy(X0) [cnf transformation 45]
101. patient(X0) | patient(X0) | old(X0) [cnf transformation 52]
102. ~patient(X0) | ~old(X0) | ~patient(X0) [cnf transformation 52]
136. ~happy(alice) [cnf transformation 24]
141. patient(X0) | old(X0) [duplicate literal removal 101]
142. ~patient(X0) | ~old(X0) [duplicate literal removal 102]
294. 34 <=> happy(alice) [avatar definition]
295. ~happy(alice) <- (~34) [avatar component clause 294]
309. ~34 [avatar split clause 136,294]
360. ~patient(X0) | old(X0) | happy(X0) [resolution 81,91]
361. old(X0) | happy(X0) [subsumption resolution 360,141]
366. patient(X0) | ~old(X0) | happy(X0) [resolution 83,91]
367. ~old(X0) | happy(X0) [subsumption resolution 366,142]
368. happy(X0) [subsumption resolution 367,361]
370. $false <- (~34) [resolution 368,295]
372. 34 [avatar contradiction clause 370]
374. $false [avatar sat refutation 309,372]
% SZS output end Proof for 372987864871576562989770
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is not calm or not curious. Everyone who is either not brave or humble is both not patient and not creative. Everyone who is brave or rich is both not funny and old and vice versa. If someone is not funny then lucy is not quiet or calm and vice versa. If alice is creative then alice is either old or not rich and vice versa. Everyone who is not funny or generous is humble. If someone is funny or not humble then someone is either humble or not funny. If someone is not strong then someone is kind and vice versa. If someone is happy or not humble then someone is either tall or not creative and vice versa. Everyone who is calm or not strong is not calm or happy and vice versa. Everyone who is patient is creative or not generous. Everyone who is both not funny and not happy is funny or curious and vice versa. Everyone who is both patient and not brave is not humble or creative and vice versa. If alice is not curious or not old then susan is kind or funny and vice versa. If someone is not kind or kind then alice is both curious and not tall and vice versa. Everyone who is either funny or not funny is either not wise or wise and vice versa. Lucy is both not kind and not old. Alice is not old. Susan is both kind and not funny. Fred is old. Someone is rich. Someone is not wise. Someone is brave. | Lucy is not generous. | neutral | (![X]:(~brave(X)=>(~calm(X)|~curious(X))))&
(![X]:((~brave(X)<~>humble(X))=>(~patient(X)&~creative(X))))&
(![X]:((brave(X)|rich(X))<=>(~funny(X)&old(X))))&
((?[X]:(~funny(X)))<=>((~quiet(lucy)|calm(lucy))))&
((creative(alice))<=>((old(alice)<~>~rich(alice))))&
(![X]:((~funny(X)|generous(X))=>humble(X)))&
((?[X]:((funny(X)|~humble(X))))=>(?[X]:((humble(X)<~>~funny(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:(kind(X))))&
((?[X]:((happy(X)|~humble(X))))<=>(?[X]:((tall(X)<~>~creative(X)))))&
(![X]:((calm(X)|~strong(X))<=>(~calm(X)|happy(X))))&
(![X]:(patient(X)=>(creative(X)|~generous(X))))&
(![X]:((~funny(X)&~happy(X))<=>(funny(X)|curious(X))))&
(![X]:((patient(X)&~brave(X))<=>(~humble(X)|creative(X))))&
(((~curious(alice)|~old(alice)))<=>((kind(susan)|funny(susan))))&
((?[X]:((~kind(X)|kind(X))))<=>((curious(alice)&~tall(alice))))&
(![X]:((funny(X)<~>~funny(X))<=>(~wise(X)<~>wise(X))))&
((~kind(lucy)&~old(lucy)))&
(~old(alice))&
((kind(susan)&~funny(susan)))&
(old(fred))&
(?[X]:(rich(X)))&
(?[X]:(~wise(X)))&
(?[X]:(brave(X))) | ~generous(lucy) | [] | null | 0 |
If mary is either tall or not kind then someone is old.
Everyone who is strong or generous is old and vice versa.
Everyone who is both not old and wise is both humble and funny and vice versa.
Everyone who is both generous and not quiet is not happy or not quiet.
If alice is either tall or not humble then alice is either not funny or funny and vice versa.
Everyone who is creative or tall is both generous and not funny and vice versa.
Everyone who is both not kind and not wise is either not funny or not tall and vice versa.
If someone is curious then lucy is not funny.
Everyone who is either happy or not quiet is both quiet and not rich.
Everyone who is happy is not happy or not kind and vice versa.
If someone is both kind and generous then someone is both wise and not tall and vice versa.
Everyone who is not creative or not rich is wise or not happy.
Everyone who is either not funny or humble is patient.
If paul is either not tall or humble then someone is either happy or not humble.
Everyone who is curious or not patient is both not humble and quiet.
Someone is strong or brave.
Someone is brave.
Someone is either old or humble. | Paul is tall. | entailment | (((tall(mary)<~>~kind(mary)))=>(?[X]:(old(X))))&
(![X]:((strong(X)|generous(X))<=>old(X)))&
(![X]:((~old(X)&wise(X))<=>(humble(X)&funny(X))))&
(![X]:((generous(X)&~quiet(X))=>(~happy(X)|~quiet(X))))&
(((tall(alice)<~>~humble(alice)))<=>((~funny(alice)<~>funny(alice))))&
(![X]:((creative(X)|tall(X))<=>(generous(X)&~funny(X))))&
(![X]:((~kind(X)&~wise(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:(curious(X)))=>(~funny(lucy)))&
(![X]:((happy(X)<~>~quiet(X))=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:((curious(X)|~patient(X))=>(~humble(X)&quiet(X))))&
(?[X]:((strong(X)|brave(X))))&
(?[X]:(brave(X)))&
(?[X]:((old(X)<~>humble(X)))) | tall(paul) | [
"p5",
"p6",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7865273243082612809240816
% SZS output start Proof for 7865273243082612809240816
6. ! [X0] : ((tall(X0) | creative(X0)) <=> (~funny(X0) & generous(X0))) [input p5]
7. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p6]
10. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p9]
11. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X0] : (~tall(X0) & wise(X0)) [input p10]
12. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~happy(X0) | wise(X0))) [input p11]
19. ~tall(paul) [input hypothesis]
20. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X1] : (~tall(X1) & wise(X1)) [rectify 11]
31. ! [X0] : ((~happy(X0) | wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 12]
32. ! [X0] : (~happy(X0) | wise(X0) | (rich(X0) & creative(X0))) [flattening 31]
42. ! [X0] : (((tall(X0) | creative(X0)) | (funny(X0) | ~generous(X0))) & ((~funny(X0) & generous(X0)) | (~tall(X0) & ~creative(X0)))) [nnf transformation 6]
43. ! [X0] : ((tall(X0) | creative(X0) | funny(X0) | ~generous(X0)) & ((~funny(X0) & generous(X0)) | (~tall(X0) & ~creative(X0)))) [flattening 42]
44. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (wise(X0) | kind(X0)))) [nnf transformation 7]
45. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | wise(X0) | kind(X0))) [flattening 44]
47. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 10]
48. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 47]
49. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X1] : (~tall(X1) & wise(X1)) | ! [X0] : (~generous(X0) | ~kind(X0))) [nnf transformation 20]
50. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X2] : (~tall(X2) & wise(X2)) | ! [X3] : (~generous(X3) | ~kind(X3))) [rectify 49]
51. ? [X0] : (generous(X0) & kind(X0)) => (generous(sK1) & kind(sK1)) [choice axiom]
52. ? [X2] : (~tall(X2) & wise(X2)) => (~tall(sK2) & wise(sK2)) [choice axiom]
53. ((generous(sK1) & kind(sK1)) | ! [X1] : (tall(X1) | ~wise(X1))) & ((~tall(sK2) & wise(sK2)) | ! [X3] : (~generous(X3) | ~kind(X3))) [skolemisation 50,52,51]
80. ~creative(X0) | ~funny(X0) [cnf transformation 43]
81. ~funny(X0) | ~tall(X0) [cnf transformation 43]
84. funny(X0) | tall(X0) | wise(X0) | kind(X0) [cnf transformation 45]
87. ~wise(X0) | ~tall(X0) | funny(X0) [cnf transformation 45]
93. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 48]
94. happy(X0) | happy(X0) [cnf transformation 48]
98. kind(sK1) | tall(X1) | ~wise(X1) [cnf transformation 53]
100. ~happy(X0) | wise(X0) | creative(X0) [cnf transformation 32]
108. ~tall(paul) [cnf transformation 19]
109. ~kind(X0) | ~happy(X0) [duplicate literal removal 93]
110. happy(X0) [duplicate literal removal 94]
147. ~wise(X0) | ~tall(X0) [subsumption resolution 87,81]
150. ~kind(X0) [subsumption resolution 109,110]
153. 7 <=> ! [X1] : ~wise(X1) [avatar definition]
154. ~wise(X1) <- (7) [avatar component clause 153]
160. tall(X1) | ~wise(X1) [subsumption resolution 98,150]
161. ~wise(X1) [subsumption resolution 160,147]
162. 7 [avatar split clause 161,153]
164. creative(X0) | wise(X0) [subsumption resolution 100,110]
171. 10 <=> tall(paul) [avatar definition]
173. ~tall(paul) <- (~10) [avatar component clause 171]
191. ~10 [avatar split clause 108,171]
194. wise(X0) | ~funny(X0) [resolution 164,80]
196. ~funny(X0) <- (7) [subsumption resolution 194,154]
213. tall(X2) | wise(X2) | kind(X2) <- (7) [resolution 84,196]
220. tall(X2) | kind(X2) <- (7) [subsumption resolution 213,154]
221. tall(X2) <- (7) [subsumption resolution 220,150]
223. $false <- (7, ~10) [resolution 221,173]
225. ~7 | 10 [avatar contradiction clause 223]
227. $false [avatar sat refutation 162,191,225]
% SZS output end Proof for 7865273243082612809240816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is kind or generous. If john is either not wise or not calm then alice is either not curious or calm and vice versa. Everyone who is both not patient and creative is not wise or brave. If mary is both generous and quiet then someone is either strong or not kind and vice versa. Everyone who is both tall and generous is curious and vice versa. If lucy is not creative then fred is both humble and happy. If someone is either strong or not kind then someone is either not wise or kind. If someone is either calm or not rich then someone is not calm. Everyone who is tall is quiet or brave. Everyone who is kind is not kind. If susan is both not patient and not humble then lucy is both not brave and tall and vice versa. If someone is either not curious or patient then susan is not rich. Everyone who is creative or not generous is both not wise and wise. Everyone who is not brave is not patient. If someone is not wise then someone is either curious or wise. Everyone who is both tall and not kind is both not curious and not calm. Susan is both quiet and not kind. Susan is happy or old. Lucy is not quiet. Someone is not funny. Fred is either not funny or calm. Fred is not creative or curious. Someone is not kind. | Lucy is tall. | contradiction | (![X]:(funny(X)=>(kind(X)|generous(X))))&
(((~wise(john)<~>~calm(john)))<=>((~curious(alice)<~>calm(alice))))&
(![X]:((~patient(X)&creative(X))=>(~wise(X)|brave(X))))&
(((generous(mary)&quiet(mary)))<=>(?[X]:((strong(X)<~>~kind(X)))))&
(![X]:((tall(X)&generous(X))<=>curious(X)))&
((~creative(lucy))=>((humble(fred)&happy(fred))))&
((?[X]:((strong(X)<~>~kind(X))))=>(?[X]:((~wise(X)<~>kind(X)))))&
((?[X]:((calm(X)<~>~rich(X))))=>(?[X]:(~calm(X))))&
(![X]:(tall(X)=>(quiet(X)|brave(X))))&
(![X]:(kind(X)=>~kind(X)))&
(((~patient(susan)&~humble(susan)))<=>((~brave(lucy)&tall(lucy))))&
((?[X]:((~curious(X)<~>patient(X))))=>(~rich(susan)))&
(![X]:((creative(X)|~generous(X))=>(~wise(X)&wise(X))))&
(![X]:(~brave(X)=>~patient(X)))&
((?[X]:(~wise(X)))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((tall(X)&~kind(X))=>(~curious(X)&~calm(X))))&
((quiet(susan)&~kind(susan)))&
((happy(susan)|old(susan)))&
(~quiet(lucy))&
(?[X]:(~funny(X)))&
((~funny(fred)<~>calm(fred)))&
((~creative(fred)|curious(fred)))&
(?[X]:(~kind(X))) | tall(lucy) | [
"p4",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7761295019845270315276635
% SZS output start Proof for 7761295019845270315276635
5. ! [X0] : ((generous(X0) & tall(X0)) <=> curious(X0)) [input p4]
10. ! [X0] : (kind(X0) => ~kind(X0)) [input p9]
13. ! [X0] : ((~generous(X0) | creative(X0)) => (wise(X0) & ~wise(X0))) [input p12]
16. ! [X0] : ((~kind(X0) & tall(X0)) => (~calm(X0) & ~curious(X0))) [input p15]
24. tall(lucy) [input hypothesis]
39. ! [X0] : (~kind(X0) | ~kind(X0)) [ennf transformation 10]
41. ! [X0] : ((wise(X0) & ~wise(X0)) | (generous(X0) & ~creative(X0))) [ennf transformation 13]
44. ! [X0] : ((~calm(X0) & ~curious(X0)) | (kind(X0) | ~tall(X0))) [ennf transformation 16]
45. ! [X0] : ((~calm(X0) & ~curious(X0)) | kind(X0) | ~tall(X0)) [flattening 44]
52. ! [X0] : (((generous(X0) & tall(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) | ~tall(X0)))) [nnf transformation 5]
53. ! [X0] : (((generous(X0) & tall(X0)) | ~curious(X0)) & (curious(X0) | ~generous(X0) | ~tall(X0))) [flattening 52]
90. ~tall(X0) | ~generous(X0) | curious(X0) [cnf transformation 53]
91. ~curious(X0) | tall(X0) [cnf transformation 53]
101. ~kind(X0) | ~kind(X0) [cnf transformation 39]
109. ~wise(X0) | generous(X0) [cnf transformation 41]
111. wise(X0) | generous(X0) [cnf transformation 41]
115. ~curious(X0) | kind(X0) | ~tall(X0) [cnf transformation 45]
125. tall(lucy) [cnf transformation 24]
126. ~kind(X0) [duplicate literal removal 101]
217. 19 <=> tall(lucy) [avatar definition]
218. tall(lucy) <- (19) [avatar component clause 217]
244. generous(X0) [subsumption resolution 109,111]
260. ~curious(X0) | ~tall(X0) [subsumption resolution 115,126]
261. ~curious(X0) [subsumption resolution 260,91]
272. 19 [avatar split clause 125,217]
283. ~generous(lucy) | curious(lucy) <- (19) [resolution 90,218]
284. curious(lucy) <- (19) [subsumption resolution 283,244]
285. $false <- (19) [subsumption resolution 284,261]
286. ~19 [avatar contradiction clause 285]
287. $false [avatar sat refutation 272,286]
% SZS output end Proof for 7761295019845270315276635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not generous and strong then someone is both not brave and not rich. If someone is either not funny or not patient then someone is both wise and not old and vice versa. Everyone who is either not wise or kind is both happy and humble and vice versa. Everyone who is either not brave or not humble is brave or not happy and vice versa. Everyone who is not happy is not humble. If lucy is kind then someone is not strong or wise and vice versa. Everyone who is not patient or not funny is not old. If susan is either not wise or generous then john is either quiet or generous. If mary is both generous and happy then someone is kind. Everyone who is either not happy or humble is not wise or not creative and vice versa. If someone is not brave then susan is either not generous or not kind. Everyone who is quiet is creative or humble. If john is not curious or not quiet then alice is humble and vice versa. If mary is either creative or wise then alice is not rich and vice versa. Everyone who is humble is both funny and not rich. Everyone who is not brave or not patient is both old and funny and vice versa. Someone is either not brave or curious. Lucy is not kind or creative. Someone is not old or tall. Lucy is both generous and funny. Someone is creative or not patient. | Susan is not curious. | neutral | (((~generous(susan)&strong(susan)))=>(?[X]:((~brave(X)&~rich(X)))))&
((?[X]:((~funny(X)<~>~patient(X))))<=>(?[X]:((wise(X)&~old(X)))))&
(![X]:((~wise(X)<~>kind(X))<=>(happy(X)&humble(X))))&
(![X]:((~brave(X)<~>~humble(X))<=>(brave(X)|~happy(X))))&
(![X]:(~happy(X)=>~humble(X)))&
((kind(lucy))<=>(?[X]:((~strong(X)|wise(X)))))&
(![X]:((~patient(X)|~funny(X))=>~old(X)))&
(((~wise(susan)<~>generous(susan)))=>((quiet(john)<~>generous(john))))&
(((generous(mary)&happy(mary)))=>(?[X]:(kind(X))))&
(![X]:((~happy(X)<~>humble(X))<=>(~wise(X)|~creative(X))))&
((?[X]:(~brave(X)))=>((~generous(susan)<~>~kind(susan))))&
(![X]:(quiet(X)=>(creative(X)|humble(X))))&
(((~curious(john)|~quiet(john)))<=>(humble(alice)))&
(((creative(mary)<~>wise(mary)))<=>(~rich(alice)))&
(![X]:(humble(X)=>(funny(X)&~rich(X))))&
(![X]:((~brave(X)|~patient(X))<=>(old(X)&funny(X))))&
(?[X]:((~brave(X)<~>curious(X))))&
((~kind(lucy)|creative(lucy)))&
(?[X]:((~old(X)|tall(X))))&
((generous(lucy)&funny(lucy)))&
(?[X]:((creative(X)|~patient(X)))) | ~curious(susan) | [] | null | 0 |
If someone is both funny and not calm then someone is both brave and not funny and vice versa.
Everyone who is not humble is either not funny or not humble.
Everyone who is both not brave and quiet is tall and vice versa.
If paul is not curious then someone is not strong or generous and vice versa.
Everyone who is both not rich and calm is not curious.
If fred is either not old or kind then someone is not funny and vice versa.
If alice is both not creative and strong then paul is old or curious and vice versa.
If mary is curious or not quiet then fred is both not creative and not funny.
Everyone who is either not brave or curious is patient and vice versa.
Everyone who is either not humble or quiet is not strong.
If someone is both not quiet and old then someone is brave or quiet.
Everyone who is brave is not quiet.
Everyone who is either not generous or not brave is either not funny or strong.
Everyone who is either not funny or creative is not rich and vice versa.
If someone is either not humble or strong then someone is both not tall and old and vice versa.
Everyone who is not quiet is either not kind or rich and vice versa.
Someone is either rich or not generous.
Mary is wise or not rich.
Someone is brave or not funny.
Someone is generous.
Someone is tall or humble.
Paul is either not happy or not humble.
Paul is both brave and not wise.
Alice is either patient or not tall. | Paul is not patient. | entailment | ((?[X]:((funny(X)&~calm(X))))<=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:(~humble(X)=>(~funny(X)<~>~humble(X))))&
(![X]:((~brave(X)&quiet(X))<=>tall(X)))&
((~curious(paul))<=>(?[X]:((~strong(X)|generous(X)))))&
(![X]:((~rich(X)&calm(X))=>~curious(X)))&
(((~old(fred)<~>kind(fred)))<=>(?[X]:(~funny(X))))&
(((~creative(alice)&strong(alice)))<=>((old(paul)|curious(paul))))&
(((curious(mary)|~quiet(mary)))=>((~creative(fred)&~funny(fred))))&
(![X]:((~brave(X)<~>curious(X))<=>patient(X)))&
(![X]:((~humble(X)<~>quiet(X))=>~strong(X)))&
((?[X]:((~quiet(X)&old(X))))=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:(brave(X)=>~quiet(X)))&
(![X]:((~generous(X)<~>~brave(X))=>(~funny(X)<~>strong(X))))&
(![X]:((~funny(X)<~>creative(X))<=>~rich(X)))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:((~tall(X)&old(X)))))&
(![X]:(~quiet(X)<=>(~kind(X)<~>rich(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
((wise(mary)|~rich(mary)))&
(?[X]:((brave(X)|~funny(X))))&
(?[X]:(generous(X)))&
(?[X]:((tall(X)|humble(X))))&
((~happy(paul)<~>~humble(paul)))&
((brave(paul)&~wise(paul)))&
((patient(alice)<~>~tall(alice))) | ~patient(paul) | [
"p3",
"p8",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1680736355196441769291754
% SZS output start Proof for 1680736355196441769291754
4. ~curious(paul) <=> ? [X0] : (generous(X0) | ~strong(X0)) [input p3]
9. ! [X0] : ((~brave(X0) <~> curious(X0)) <=> patient(X0)) [input p8]
20. ? [X0] : generous(X0) [input p19]
23. ~wise(paul) & brave(paul) [input p22]
25. patient(paul) [input hypothesis]
45. (~curious(paul) | ! [X0] : (~generous(X0) & strong(X0))) & (? [X0] : (generous(X0) | ~strong(X0)) | curious(paul)) [nnf transformation 4]
46. (~curious(paul) | ! [X0] : (~generous(X0) & strong(X0))) & (? [X1] : (generous(X1) | ~strong(X1)) | curious(paul)) [rectify 45]
47. ? [X1] : (generous(X1) | ~strong(X1)) => (generous(sK2) | ~strong(sK2)) [choice axiom]
48. (~curious(paul) | ! [X0] : (~generous(X0) & strong(X0))) & ((generous(sK2) | ~strong(sK2)) | curious(paul)) [skolemisation 46,47]
55. ! [X0] : ((((~curious(X0) | brave(X0)) & (curious(X0) | ~brave(X0))) | ~patient(X0)) & (patient(X0) | ((~brave(X0) | ~curious(X0)) & (curious(X0) | brave(X0))))) [nnf transformation 9]
73. ? [X0] : generous(X0) => generous(sK9) [choice axiom]
74. generous(sK9) [skolemisation 20,73]
90. ~curious(paul) | ~generous(X0) [cnf transformation 48]
107. ~patient(X0) | ~brave(X0) | curious(X0) [cnf transformation 55]
135. generous(sK9) [cnf transformation 74]
139. brave(paul) [cnf transformation 23]
143. patient(paul) [cnf transformation 25]
172. 7 <=> ! [X0] : ~generous(X0) [avatar definition]
173. ~generous(X0) <- (7) [avatar component clause 172]
175. 8 <=> curious(paul) [avatar definition]
178. 7 | ~8 [avatar split clause 90,175,172]
377. ~brave(paul) | curious(paul) [resolution 107,143]
381. curious(paul) [subsumption resolution 377,139]
384. 8 [avatar split clause 381,175]
385. $false <- (7) [resolution 173,135]
386. ~7 [avatar contradiction clause 385]
387. $false [avatar sat refutation 178,384,386]
% SZS output end Proof for 1680736355196441769291754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or brave is not brave or humble and vice versa.
If alice is not rich then someone is old.
If alice is not funny or calm then john is generous and vice versa.
Everyone who is not happy or not calm is either generous or creative and vice versa.
Everyone who is both creative and not strong is both rich and humble.
If someone is funny or not calm then fred is funny.
Everyone who is either not tall or humble is both tall and curious.
If alice is both patient and not brave then mary is both not old and brave.
If fred is both not patient and not wise then someone is both funny and happy.
Everyone who is funny is creative and vice versa.
Everyone who is both rich and tall is either funny or not happy and vice versa.
If someone is either quiet or curious then susan is not brave or old.
Everyone who is calm or strong is either humble or funny and vice versa.
If someone is either not quiet or not kind then john is either brave or not brave.
If someone is not patient then someone is brave and vice versa.
Everyone who is calm or not patient is not old.
Someone is not tall.
Someone is kind or not wise.
Susan is not brave or not calm.
Someone is rich or not funny.
Someone is either not patient or old.
Someone is either humble or not old.
Someone is both generous and not quiet.
Someone is both not kind and quiet. | Susan is not brave. | neutral | (![X]:((~curious(X)|brave(X))<=>(~brave(X)|humble(X))))&
((~rich(alice))=>(?[X]:(old(X))))&
(((~funny(alice)|calm(alice)))<=>(generous(john)))&
(![X]:((~happy(X)|~calm(X))<=>(generous(X)<~>creative(X))))&
(![X]:((creative(X)&~strong(X))=>(rich(X)&humble(X))))&
((?[X]:((funny(X)|~calm(X))))=>(funny(fred)))&
(![X]:((~tall(X)<~>humble(X))=>(tall(X)&curious(X))))&
(((patient(alice)&~brave(alice)))=>((~old(mary)&brave(mary))))&
(((~patient(fred)&~wise(fred)))=>(?[X]:((funny(X)&happy(X)))))&
(![X]:(funny(X)<=>creative(X)))&
(![X]:((rich(X)&tall(X))<=>(funny(X)<~>~happy(X))))&
((?[X]:((quiet(X)<~>curious(X))))=>((~brave(susan)|old(susan))))&
(![X]:((calm(X)|strong(X))<=>(humble(X)<~>funny(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>((brave(john)<~>~brave(john))))&
((?[X]:(~patient(X)))<=>(?[X]:(brave(X))))&
(![X]:((calm(X)|~patient(X))=>~old(X)))&
(?[X]:(~tall(X)))&
(?[X]:((kind(X)|~wise(X))))&
((~brave(susan)|~calm(susan)))&
(?[X]:((rich(X)|~funny(X))))&
(?[X]:((~patient(X)<~>old(X))))&
(?[X]:((humble(X)<~>~old(X))))&
(?[X]:((generous(X)&~quiet(X))))&
(?[X]:((~kind(X)&quiet(X)))) | ~brave(susan) | [] | null | 0 |
Everyone who is both not tall and not kind is funny or brave and vice versa.
If john is quiet then john is either humble or curious and vice versa.
Everyone who is generous is either tall or quiet.
If someone is either not wise or kind then john is both brave and not strong.
Everyone who is not brave is both brave and not brave.
Everyone who is both calm and not quiet is not brave.
If someone is not old or curious then mary is both calm and humble.
Everyone who is either patient or not old is both happy and curious and vice versa.
Everyone who is both not curious and not happy is not happy and vice versa.
Everyone who is either quiet or not kind is not kind and vice versa.
Everyone who is not quiet or not brave is either humble or happy and vice versa.
Everyone who is not happy or not curious is either not calm or humble.
If someone is curious or not wise then someone is not strong or not generous and vice versa.
Everyone who is not generous or not funny is not generous.
Someone is not funny or happy.
Lucy is not old or brave.
Paul is not quiet or rich. | Mary is humble. | contradiction | (![X]:((~tall(X)&~kind(X))<=>(funny(X)|brave(X))))&
((quiet(john))<=>((humble(john)<~>curious(john))))&
(![X]:(generous(X)=>(tall(X)<~>quiet(X))))&
((?[X]:((~wise(X)<~>kind(X))))=>((brave(john)&~strong(john))))&
(![X]:(~brave(X)=>(brave(X)&~brave(X))))&
(![X]:((calm(X)&~quiet(X))=>~brave(X)))&
((?[X]:((~old(X)|curious(X))))=>((calm(mary)&humble(mary))))&
(![X]:((patient(X)<~>~old(X))<=>(happy(X)&curious(X))))&
(![X]:((~curious(X)&~happy(X))<=>~happy(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~kind(X)))&
(![X]:((~quiet(X)|~brave(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
(![X]:((~generous(X)|~funny(X))=>~generous(X)))&
(?[X]:((~funny(X)|happy(X))))&
((~old(lucy)|brave(lucy)))&
((~quiet(paul)|rich(paul))) | humble(mary) | [
"p4",
"p5",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8699759104346626021860225
% SZS output start Proof for 8699759104346626021860225
5. ! [X0] : (~brave(X0) => (~brave(X0) & brave(X0))) [input p4]
6. ! [X0] : ((~quiet(X0) & calm(X0)) => ~brave(X0)) [input p5]
10. ! [X0] : ((quiet(X0) <~> ~kind(X0)) <=> ~kind(X0)) [input p9]
11. ! [X0] : ((~brave(X0) | ~quiet(X0)) <=> (humble(X0) <~> happy(X0))) [input p10]
12. ! [X0] : ((~curious(X0) | ~happy(X0)) => (~calm(X0) <~> humble(X0))) [input p11]
18. humble(mary) [input hypothesis]
23. ! [X0] : ((~brave(X0) & brave(X0)) | brave(X0)) [ennf transformation 5]
24. ! [X0] : (~brave(X0) | (quiet(X0) | ~calm(X0))) [ennf transformation 6]
25. ! [X0] : (~brave(X0) | quiet(X0) | ~calm(X0)) [flattening 24]
27. ! [X0] : ((~calm(X0) <~> humble(X0)) | (curious(X0) & happy(X0))) [ennf transformation 12]
38. ! [X0] : ((((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | kind(X0)) & (~kind(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0))))) [nnf transformation 10]
39. ! [X0] : (((~brave(X0) | ~quiet(X0)) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0)))) & (((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (brave(X0) & quiet(X0)))) [nnf transformation 11]
40. ! [X0] : ((~brave(X0) | ~quiet(X0) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0)))) & (((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (brave(X0) & quiet(X0)))) [flattening 39]
41. ! [X0] : (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | (curious(X0) & happy(X0))) [nnf transformation 27]
64. brave(X0) | brave(X0) [cnf transformation 23]
66. ~brave(X0) | quiet(X0) | ~calm(X0) [cnf transformation 25]
80. ~kind(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 38]
83. kind(X0) | ~quiet(X0) | kind(X0) [cnf transformation 38]
86. ~happy(X0) | ~humble(X0) | quiet(X0) [cnf transformation 40]
92. ~humble(X0) | calm(X0) | happy(X0) [cnf transformation 41]
102. humble(mary) [cnf transformation 18]
103. ~kind(X0) | ~quiet(X0) [duplicate literal removal 80]
104. ~quiet(X0) | kind(X0) [duplicate literal removal 83]
105. brave(X0) [duplicate literal removal 64]
140. ~calm(X0) | quiet(X0) [subsumption resolution 66,105]
145. 9 <=> humble(mary) [avatar definition]
147. humble(mary) <- (9) [avatar component clause 145]
154. 11 <=> calm(mary) [avatar definition]
156. calm(mary) <- (11) [avatar component clause 154]
159. ~quiet(X0) [subsumption resolution 103,104]
160. ~happy(X0) | ~humble(X0) [subsumption resolution 86,159]
162. ~humble(X0) | calm(X0) [subsumption resolution 92,160]
201. 9 [avatar split clause 102,145]
209. calm(mary) <- (9) [resolution 162,147]
210. 11 | ~9 [avatar split clause 209,145,154]
211. quiet(mary) <- (11) [resolution 156,140]
212. $false <- (11) [subsumption resolution 211,159]
213. ~11 [avatar contradiction clause 212]
214. $false [avatar sat refutation 201,210,213]
% SZS output end Proof for 8699759104346626021860225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or strong is either humble or happy.
Everyone who is both funny and humble is rich.
Everyone who is both happy and not wise is rich and vice versa.
If someone is quiet or not curious then fred is both not rich and old and vice versa.
If someone is either old or not humble then john is both not quiet and not brave.
Everyone who is tall is kind or not curious and vice versa.
Everyone who is either wise or tall is both creative and strong.
Everyone who is both not curious and happy is tall or wise.
Everyone who is strong or not generous is either tall or not curious and vice versa.
Everyone who is either not kind or not old is both not happy and not patient.
Everyone who is both brave and not funny is both rich and not happy and vice versa.
Everyone who is not strong or not calm is both curious and creative.
If fred is not quiet then susan is both calm and not funny and vice versa.
If someone is not strong or not brave then fred is both not curious and not wise and vice versa.
If lucy is both rich and not strong then paul is not curious or curious.
Everyone who is both rich and brave is not strong.
Someone is creative.
Someone is either not kind or not quiet.
Fred is either not strong or not calm.
Someone is either not old or not quiet.
Someone is wise.
Susan is not patient.
Alice is either happy or not old. | Alice is wise. | entailment | (![X]:((quiet(X)|strong(X))=>(humble(X)<~>happy(X))))&
(![X]:((funny(X)&humble(X))=>rich(X)))&
(![X]:((happy(X)&~wise(X))<=>rich(X)))&
((?[X]:((quiet(X)|~curious(X))))<=>((~rich(fred)&old(fred))))&
((?[X]:((old(X)<~>~humble(X))))=>((~quiet(john)&~brave(john))))&
(![X]:(tall(X)<=>(kind(X)|~curious(X))))&
(![X]:((wise(X)<~>tall(X))=>(creative(X)&strong(X))))&
(![X]:((~curious(X)&happy(X))=>(tall(X)|wise(X))))&
(![X]:((strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~happy(X)&~patient(X))))&
(![X]:((brave(X)&~funny(X))<=>(rich(X)&~happy(X))))&
(![X]:((~strong(X)|~calm(X))=>(curious(X)&creative(X))))&
((~quiet(fred))<=>((calm(susan)&~funny(susan))))&
((?[X]:((~strong(X)|~brave(X))))<=>((~curious(fred)&~wise(fred))))&
(((rich(lucy)&~strong(lucy)))=>((~curious(paul)|curious(paul))))&
(![X]:((rich(X)&brave(X))=>~strong(X)))&
(?[X]:(creative(X)))&
(?[X]:((~kind(X)<~>~quiet(X))))&
((~strong(fred)<~>~calm(fred)))&
(?[X]:((~old(X)<~>~quiet(X))))&
(?[X]:(wise(X)))&
(~patient(susan))&
((happy(alice)<~>~old(alice))) | wise(alice) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p10",
"p11",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 605109225788806403771248
% SZS output start Proof for 605109225788806403771248
2. ! [X0] : ((humble(X0) & funny(X0)) => rich(X0)) [input p1]
3. ! [X0] : ((~wise(X0) & happy(X0)) <=> rich(X0)) [input p2]
5. ? [X0] : (old(X0) <~> ~humble(X0)) => (~brave(john) & ~quiet(john)) [input p4]
6. ! [X0] : (tall(X0) <=> (~curious(X0) | kind(X0))) [input p5]
9. ! [X0] : ((~generous(X0) | strong(X0)) <=> (tall(X0) <~> ~curious(X0))) [input p8]
11. ! [X0] : ((~funny(X0) & brave(X0)) <=> (~happy(X0) & rich(X0))) [input p10]
12. ! [X0] : ((~calm(X0) | ~strong(X0)) => (creative(X0) & curious(X0))) [input p11]
14. ? [X0] : (~brave(X0) | ~strong(X0)) <=> (~wise(fred) & ~curious(fred)) [input p13]
16. ! [X0] : ((brave(X0) & rich(X0)) => ~strong(X0)) [input p15]
23. happy(alice) <~> ~old(alice) [input p22]
24. ~wise(alice) [input hypothesis]
29. ! [X0] : ((~calm(X0) | ~strong(X0)) => curious(X0)) [pure predicate removal 12]
31. ! [X0] : (rich(X0) | (~humble(X0) | ~funny(X0))) [ennf transformation 2]
32. ! [X0] : (rich(X0) | ~humble(X0) | ~funny(X0)) [flattening 31]
33. (~brave(john) & ~quiet(john)) | ! [X0] : (old(X0) <=> ~humble(X0)) [ennf transformation 5]
38. ! [X0] : (curious(X0) | (calm(X0) & strong(X0))) [ennf transformation 29]
41. ! [X0] : (~strong(X0) | (~brave(X0) | ~rich(X0))) [ennf transformation 16]
42. ! [X0] : (~strong(X0) | ~brave(X0) | ~rich(X0)) [flattening 41]
44. ! [X0] : (((~wise(X0) & happy(X0)) | ~rich(X0)) & (rich(X0) | (wise(X0) | ~happy(X0)))) [nnf transformation 3]
45. ! [X0] : (((~wise(X0) & happy(X0)) | ~rich(X0)) & (rich(X0) | wise(X0) | ~happy(X0))) [flattening 44]
51. (~brave(john) & ~quiet(john)) | ! [X0] : ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0))) [nnf transformation 33]
52. ! [X0] : ((tall(X0) | (curious(X0) & ~kind(X0))) & ((~curious(X0) | kind(X0)) | ~tall(X0))) [nnf transformation 6]
53. ! [X0] : ((tall(X0) | (curious(X0) & ~kind(X0))) & (~curious(X0) | kind(X0) | ~tall(X0))) [flattening 52]
55. ! [X0] : (((~generous(X0) | strong(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (generous(X0) & ~strong(X0)))) [nnf transformation 9]
56. ! [X0] : ((~generous(X0) | strong(X0) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (generous(X0) & ~strong(X0)))) [flattening 55]
58. ! [X0] : (((~funny(X0) & brave(X0)) | (happy(X0) | ~rich(X0))) & ((~happy(X0) & rich(X0)) | (funny(X0) | ~brave(X0)))) [nnf transformation 11]
59. ! [X0] : (((~funny(X0) & brave(X0)) | happy(X0) | ~rich(X0)) & ((~happy(X0) & rich(X0)) | funny(X0) | ~brave(X0))) [flattening 58]
62. (? [X0] : (~brave(X0) | ~strong(X0)) | (wise(fred) | curious(fred))) & ((~wise(fred) & ~curious(fred)) | ! [X0] : (brave(X0) & strong(X0))) [nnf transformation 14]
63. (? [X0] : (~brave(X0) | ~strong(X0)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X0] : (brave(X0) & strong(X0))) [flattening 62]
64. (? [X0] : (~brave(X0) | ~strong(X0)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X1] : (brave(X1) & strong(X1))) [rectify 63]
65. ? [X0] : (~brave(X0) | ~strong(X0)) => (~brave(sK1) | ~strong(sK1)) [choice axiom]
66. ((~brave(sK1) | ~strong(sK1)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X1] : (brave(X1) & strong(X1))) [skolemisation 64,65]
76. (old(alice) | ~happy(alice)) & (~old(alice) | happy(alice)) [nnf transformation 23]
81. ~funny(X0) | ~humble(X0) | rich(X0) [cnf transformation 32]
82. ~happy(X0) | wise(X0) | rich(X0) [cnf transformation 45]
83. ~rich(X0) | happy(X0) [cnf transformation 45]
93. ~brave(john) | old(X0) | humble(X0) [cnf transformation 51]
96. tall(X0) | curious(X0) [cnf transformation 53]
102. curious(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 56]
108. ~brave(X0) | funny(X0) | rich(X0) [cnf transformation 59]
109. ~brave(X0) | funny(X0) | ~happy(X0) [cnf transformation 59]
112. curious(X0) | strong(X0) [cnf transformation 38]
117. ~curious(fred) | strong(X1) [cnf transformation 66]
118. ~curious(fred) | brave(X1) [cnf transformation 66]
123. ~brave(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 42]
131. ~old(alice) | happy(alice) [cnf transformation 76]
133. ~wise(alice) [cnf transformation 24]
152. 5 <=> ! [X1] : curious(X1) [avatar definition]
153. curious(X1) <- (5) [avatar component clause 152]
162. 7 <=> ! [X0] : (old(X0) | humble(X0)) [avatar definition]
163. old(X0) | humble(X0) <- (7) [avatar component clause 162]
165. 8 <=> brave(john) [avatar definition]
167. ~brave(john) <- (~8) [avatar component clause 165]
168. 7 | ~8 [avatar split clause 93,165,162]
180. ~strong(X0) | curious(X0) [subsumption resolution 102,96]
183. curious(X0) [subsumption resolution 112,180]
184. 5 [avatar split clause 183,152]
201. 14 <=> curious(fred) [avatar definition]
202. ~curious(fred) <- (~14) [avatar component clause 201]
218. 18 <=> ! [X1] : brave(X1) [avatar definition]
219. brave(X1) <- (18) [avatar component clause 218]
222. 19 <=> ! [X1] : strong(X1) [avatar definition]
223. strong(X1) <- (19) [avatar component clause 222]
225. 18 | ~14 [avatar split clause 118,201,218]
226. 19 | ~14 [avatar split clause 117,201,222]
258. 26 <=> happy(alice) [avatar definition]
259. happy(alice) <- (26) [avatar component clause 258]
262. 27 <=> old(alice) [avatar definition]
263. ~old(alice) <- (~27) [avatar component clause 262]
266. 26 | ~27 [avatar split clause 131,262,258]
269. $false <- (5, ~14) [resolution 202,153]
270. ~5 | 14 [avatar contradiction clause 269]
271. $false <- (~8, 18) [resolution 219,167]
274. 8 | ~18 [avatar contradiction clause 271]
279. humble(alice) <- (7, ~27) [resolution 163,263]
315. rich(X0) | funny(X0) <- (18) [resolution 108,219]
316. funny(X0) | ~happy(X0) <- (18) [resolution 109,219]
318. funny(X0) | happy(X0) <- (18) [resolution 315,83]
320. funny(X0) <- (18) [subsumption resolution 318,316]
321. ~strong(X0) | ~rich(X0) <- (18) [resolution 123,219]
322. ~rich(X0) <- (18, 19) [subsumption resolution 321,223]
338. ~humble(X0) | rich(X0) <- (18) [resolution 320,81]
340. ~humble(X0) <- (18, 19) [subsumption resolution 338,322]
343. $false <- (7, 18, 19, ~27) [resolution 340,279]
344. ~7 | ~18 | ~19 | 27 [avatar contradiction clause 343]
348. wise(alice) | rich(alice) <- (26) [resolution 259,82]
351. rich(alice) <- (26) [subsumption resolution 348,133]
352. $false <- (18, 19, 26) [subsumption resolution 351,322]
353. ~18 | ~19 | ~26 [avatar contradiction clause 352]
354. $false [avatar sat refutation 168,184,225,226,266,270,274,344,353]
% SZS output end Proof for 605109225788806403771248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or wise is either not funny or kind and vice versa.
Everyone who is both not calm and creative is both not happy and not patient and vice versa.
Everyone who is not tall or not calm is either not strong or curious and vice versa.
If alice is strong or happy then someone is not tall or not humble and vice versa.
If paul is both not creative and not generous then someone is quiet or not creative.
Everyone who is rich or patient is both humble and not humble.
If john is either not happy or not humble then paul is either brave or not quiet.
If someone is rich or not calm then someone is either not happy or patient.
Everyone who is both not brave and not strong is either not calm or not generous.
Everyone who is either not funny or quiet is humble or not creative and vice versa.
Everyone who is not funny or not calm is both kind and not strong.
Everyone who is either not brave or happy is either not brave or curious.
If someone is both rich and not humble then mary is both wise and not funny and vice versa.
Everyone who is creative or funny is both happy and not humble and vice versa.
If someone is both brave and humble then fred is not rich and vice versa.
Someone is either not tall or not calm.
Paul is old.
Someone is not brave or not humble.
Mary is quiet or old.
Mary is creative or rich.
Someone is humble.
Susan is old or tall.
Someone is either not calm or not tall. | Paul is happy. | entailment | (![X]:((~curious(X)<~>wise(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(~happy(X)&~patient(X))))&
(![X]:((~tall(X)|~calm(X))<=>(~strong(X)<~>curious(X))))&
(((strong(alice)|happy(alice)))<=>(?[X]:((~tall(X)|~humble(X)))))&
(((~creative(paul)&~generous(paul)))=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:((rich(X)|patient(X))=>(humble(X)&~humble(X))))&
(((~happy(john)<~>~humble(john)))=>((brave(paul)<~>~quiet(paul))))&
((?[X]:((rich(X)|~calm(X))))=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:((~brave(X)&~strong(X))=>(~calm(X)<~>~generous(X))))&
(![X]:((~funny(X)<~>quiet(X))<=>(humble(X)|~creative(X))))&
(![X]:((~funny(X)|~calm(X))=>(kind(X)&~strong(X))))&
(![X]:((~brave(X)<~>happy(X))=>(~brave(X)<~>curious(X))))&
((?[X]:((rich(X)&~humble(X))))<=>((wise(mary)&~funny(mary))))&
(![X]:((creative(X)|funny(X))<=>(happy(X)&~humble(X))))&
((?[X]:((brave(X)&humble(X))))<=>(~rich(fred)))&
(?[X]:((~tall(X)<~>~calm(X))))&
(old(paul))&
(?[X]:((~brave(X)|~humble(X))))&
((quiet(mary)|old(mary)))&
((creative(mary)|rich(mary)))&
(?[X]:(humble(X)))&
((old(susan)|tall(susan)))&
(?[X]:((~calm(X)<~>~tall(X)))) | happy(paul) | [
"p1",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 921675032931918508846781
% SZS output start Proof for 921675032931918508846781
2. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (~patient(X0) & ~happy(X0))) [input p1]
6. ! [X0] : ((patient(X0) | rich(X0)) => (~humble(X0) & humble(X0))) [input p5]
14. ! [X0] : ((funny(X0) | creative(X0)) <=> (~humble(X0) & happy(X0))) [input p13]
24. ~happy(paul) [input hypothesis]
31. ! [X0] : ((~humble(X0) & humble(X0)) | (~patient(X0) & ~rich(X0))) [ennf transformation 6]
39. ! [X0] : (((creative(X0) & ~calm(X0)) | (patient(X0) | happy(X0))) & ((~patient(X0) & ~happy(X0)) | (~creative(X0) | calm(X0)))) [nnf transformation 2]
40. ! [X0] : (((creative(X0) & ~calm(X0)) | patient(X0) | happy(X0)) & ((~patient(X0) & ~happy(X0)) | ~creative(X0) | calm(X0))) [flattening 39]
64. ! [X0] : (((funny(X0) | creative(X0)) | (humble(X0) | ~happy(X0))) & ((~humble(X0) & happy(X0)) | (~funny(X0) & ~creative(X0)))) [nnf transformation 14]
65. ! [X0] : ((funny(X0) | creative(X0) | humble(X0) | ~happy(X0)) & ((~humble(X0) & happy(X0)) | (~funny(X0) & ~creative(X0)))) [flattening 64]
91. patient(X0) | creative(X0) | happy(X0) [cnf transformation 40]
104. humble(X0) | ~patient(X0) [cnf transformation 31]
106. ~humble(X0) | ~patient(X0) [cnf transformation 31]
135. ~creative(X0) | happy(X0) [cnf transformation 65]
150. ~happy(paul) [cnf transformation 24]
196. ~patient(X0) [subsumption resolution 104,106]
295. creative(X1) | happy(X1) [resolution 91,196]
296. happy(X1) [subsumption resolution 295,135]
317. $false [resolution 296,150]
% SZS output end Proof for 921675032931918508846781
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both creative and not creative then someone is either strong or humble.
Everyone who is both tall and not kind is either wise or kind and vice versa.
If someone is not old or not kind then someone is either funny or not curious.
Everyone who is not curious is not strong or not happy.
Everyone who is either not kind or brave is either not patient or strong and vice versa.
Everyone who is both not calm and not rich is both funny and patient.
Everyone who is not patient is either not tall or not calm.
If john is not strong or not patient then mary is not rich or not humble.
Everyone who is strong is old.
Everyone who is both not curious and not generous is not brave or not happy.
If lucy is both strong and not wise then someone is both not patient and curious and vice versa.
If someone is creative or not old then mary is generous or not tall.
If mary is both old and not curious then someone is funny or quiet and vice versa.
If someone is kind then john is not rich or not kind.
If fred is both not wise and tall then john is both wise and not humble.
If someone is not humble or not calm then someone is both not old and not curious.
Someone is either not kind or funny.
Someone is either not generous or strong.
Someone is both not kind and not brave.
Mary is not wise.
Someone is both wise and not strong.
Someone is not wise or not curious.
Someone is quiet or funny.
Fred is not brave. | Mary is curious. | contradiction | (((creative(paul)&~creative(paul)))=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((tall(X)&~kind(X))<=>(wise(X)<~>kind(X))))&
((?[X]:((~old(X)|~kind(X))))=>(?[X]:((funny(X)<~>~curious(X)))))&
(![X]:(~curious(X)=>(~strong(X)|~happy(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(~patient(X)<~>strong(X))))&
(![X]:((~calm(X)&~rich(X))=>(funny(X)&patient(X))))&
(![X]:(~patient(X)=>(~tall(X)<~>~calm(X))))&
(((~strong(john)|~patient(john)))=>((~rich(mary)|~humble(mary))))&
(![X]:(strong(X)=>old(X)))&
(![X]:((~curious(X)&~generous(X))=>(~brave(X)|~happy(X))))&
(((strong(lucy)&~wise(lucy)))<=>(?[X]:((~patient(X)&curious(X)))))&
((?[X]:((creative(X)|~old(X))))=>((generous(mary)|~tall(mary))))&
(((old(mary)&~curious(mary)))<=>(?[X]:((funny(X)|quiet(X)))))&
((?[X]:(kind(X)))=>((~rich(john)|~kind(john))))&
(((~wise(fred)&tall(fred)))=>((wise(john)&~humble(john))))&
((?[X]:((~humble(X)|~calm(X))))=>(?[X]:((~old(X)&~curious(X)))))&
(?[X]:((~kind(X)<~>funny(X))))&
(?[X]:((~generous(X)<~>strong(X))))&
(?[X]:((~kind(X)&~brave(X))))&
(~wise(mary))&
(?[X]:((wise(X)&~strong(X))))&
(?[X]:((~wise(X)|~curious(X))))&
(?[X]:((quiet(X)|funny(X))))&
(~brave(fred)) | curious(mary) | [
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1545243300528177274507981
% SZS output start Proof for 1545243300528177274507981
13. (~curious(mary) & old(mary)) <=> ? [X0] : (quiet(X0) | funny(X0)) [input p12]
23. ? [X0] : (funny(X0) | quiet(X0)) [input p22]
25. curious(mary) [input hypothesis]
62. ((~curious(mary) & old(mary)) | ! [X0] : (~quiet(X0) & ~funny(X0))) & (? [X0] : (quiet(X0) | funny(X0)) | (curious(mary) | ~old(mary))) [nnf transformation 13]
63. ((~curious(mary) & old(mary)) | ! [X0] : (~quiet(X0) & ~funny(X0))) & (? [X0] : (quiet(X0) | funny(X0)) | curious(mary) | ~old(mary)) [flattening 62]
64. ((~curious(mary) & old(mary)) | ! [X0] : (~quiet(X0) & ~funny(X0))) & (? [X1] : (quiet(X1) | funny(X1)) | curious(mary) | ~old(mary)) [rectify 63]
65. ? [X1] : (quiet(X1) | funny(X1)) => (quiet(sK3) | funny(sK3)) [choice axiom]
66. ((~curious(mary) & old(mary)) | ! [X0] : (~quiet(X0) & ~funny(X0))) & ((quiet(sK3) | funny(sK3)) | curious(mary) | ~old(mary)) [skolemisation 64,65]
82. ? [X0] : (funny(X0) | quiet(X0)) => (funny(sK10) | quiet(sK10)) [choice axiom]
83. funny(sK10) | quiet(sK10) [skolemisation 23,82]
120. ~curious(mary) | ~funny(X0) [cnf transformation 66]
121. ~curious(mary) | ~quiet(X0) [cnf transformation 66]
139. funny(sK10) | quiet(sK10) [cnf transformation 83]
141. curious(mary) [cnf transformation 25]
218. 17 <=> ! [X0] : ~quiet(X0) [avatar definition]
219. ~quiet(X0) <- (17) [avatar component clause 218]
221. 18 <=> curious(mary) [avatar definition]
224. 17 | ~18 [avatar split clause 121,221,218]
226. 19 <=> ! [X0] : ~funny(X0) [avatar definition]
227. ~funny(X0) <- (19) [avatar component clause 226]
228. 19 | ~18 [avatar split clause 120,221,226]
304. 36 <=> quiet(sK10) [avatar definition]
306. quiet(sK10) <- (36) [avatar component clause 304]
308. 37 <=> funny(sK10) [avatar definition]
310. funny(sK10) <- (37) [avatar component clause 308]
311. 36 | 37 [avatar split clause 139,308,304]
312. 18 [avatar split clause 141,221]
313. $false <- (17, 36) [resolution 306,219]
314. ~17 | ~36 [avatar contradiction clause 313]
315. $false <- (19, 37) [subsumption resolution 310,227]
316. ~19 | ~37 [avatar contradiction clause 315]
317. $false [avatar sat refutation 224,228,311,312,314,316]
% SZS output end Proof for 1545243300528177274507981
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not curious or not happy then alice is both kind and humble. If someone is both not tall and not patient then someone is both strong and tall and vice versa. If someone is not generous or not strong then john is either strong or tall. If paul is not kind then someone is not happy or patient. If someone is both quiet and not brave then someone is either calm or not calm and vice versa. If someone is both not tall and not happy then someone is both strong and not brave. Everyone who is both not tall and humble is not generous or not kind and vice versa. If mary is not brave or tall then lucy is both not kind and not quiet and vice versa. Everyone who is either wise or not strong is not calm or calm and vice versa. If someone is both kind and not generous then someone is not tall or patient. Everyone who is not brave is both strong and quiet and vice versa. Everyone who is not creative is brave and vice versa. If someone is either generous or quiet then someone is either not calm or not brave. Everyone who is both not tall and strong is not tall. If lucy is not brave then someone is not wise or not happy. If someone is either humble or creative then john is not kind or not curious. Paul is either curious or not kind. John is both old and humble. Someone is either not patient or tall. Someone is patient or generous. Alice is both not kind and funny. Paul is not creative. Fred is both generous and not patient. Lucy is not rich or calm. | John is curious. | entailment | ((?[X]:((~curious(X)|~happy(X))))=>((kind(alice)&humble(alice))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:((strong(X)&tall(X)))))&
((?[X]:((~generous(X)|~strong(X))))=>((strong(john)<~>tall(john))))&
((~kind(paul))=>(?[X]:((~happy(X)|patient(X)))))&
((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((calm(X)<~>~calm(X)))))&
((?[X]:((~tall(X)&~happy(X))))=>(?[X]:((strong(X)&~brave(X)))))&
(![X]:((~tall(X)&humble(X))<=>(~generous(X)|~kind(X))))&
(((~brave(mary)|tall(mary)))<=>((~kind(lucy)&~quiet(lucy))))&
(![X]:((wise(X)<~>~strong(X))<=>(~calm(X)|calm(X))))&
((?[X]:((kind(X)&~generous(X))))=>(?[X]:((~tall(X)|patient(X)))))&
(![X]:(~brave(X)<=>(strong(X)&quiet(X))))&
(![X]:(~creative(X)<=>brave(X)))&
((?[X]:((generous(X)<~>quiet(X))))=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:((~tall(X)&strong(X))=>~tall(X)))&
((~brave(lucy))=>(?[X]:((~wise(X)|~happy(X)))))&
((?[X]:((humble(X)<~>creative(X))))=>((~kind(john)|~curious(john))))&
((curious(paul)<~>~kind(paul)))&
((old(john)&humble(john)))&
(?[X]:((~patient(X)<~>tall(X))))&
(?[X]:((patient(X)|generous(X))))&
((~kind(alice)&funny(alice)))&
(~creative(paul))&
((generous(fred)&~patient(fred)))&
((~rich(lucy)|calm(lucy))) | curious(john) | [
"p0",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5010564090110222616747365
% SZS output start Proof for 5010564090110222616747365
1. ? [X0] : (~happy(X0) | ~curious(X0)) => (humble(alice) & kind(alice)) [input p0]
21. funny(alice) & ~kind(alice) [input p20]
25. ~curious(john) [input hypothesis]
32. ~kind(alice) [pure predicate removal 21]
34. (humble(alice) & kind(alice)) | ! [X0] : (happy(X0) & curious(X0)) [ennf transformation 1]
86. kind(alice) | curious(X0) [cnf transformation 34]
143. ~kind(alice) [cnf transformation 32]
147. ~curious(john) [cnf transformation 25]
161. 3 <=> ! [X0] : curious(X0) [avatar definition]
162. curious(X0) <- (3) [avatar component clause 161]
165. 4 <=> kind(alice) [avatar definition]
169. 3 | 4 [avatar split clause 86,165,161]
332. 41 <=> curious(john) [avatar definition]
334. ~curious(john) <- (~41) [avatar component clause 332]
365. ~4 [avatar split clause 143,165]
366. ~41 [avatar split clause 147,332]
375. $false <- (3, ~41) [resolution 334,162]
376. ~3 | 41 [avatar contradiction clause 375]
377. $false [avatar sat refutation 169,365,366,376]
% SZS output end Proof for 5010564090110222616747365
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich or curious then alice is either brave or funny and vice versa.
Everyone who is not humble is both humble and not patient and vice versa.
If lucy is either not rich or not generous then fred is either not kind or patient.
If lucy is either not rich or generous then lucy is not generous or brave.
Everyone who is not curious is either old or not tall.
If someone is not humble then susan is creative.
Everyone who is either generous or humble is creative or not patient.
If mary is humble or funny then someone is either not old or not curious.
If alice is not strong then alice is both kind and funny.
If john is not patient or quiet then john is patient or tall and vice versa.
Everyone who is either not humble or strong is both kind and not calm.
Everyone who is not curious or not brave is not rich or not tall and vice versa.
Everyone who is strong is generous and vice versa.
If someone is not humble or wise then someone is not quiet and vice versa.
Everyone who is funny or not strong is either patient or old.
If mary is either strong or creative then susan is funny or not calm and vice versa.
Susan is tall.
Someone is not brave.
Someone is patient or happy.
Alice is humble or not strong.
Mary is not happy or old.
Susan is humble or not strong.
Someone is both not quiet and calm. | Susan is happy. | neutral | ((?[X]:((~rich(X)|curious(X))))<=>((brave(alice)<~>funny(alice))))&
(![X]:(~humble(X)<=>(humble(X)&~patient(X))))&
(((~rich(lucy)<~>~generous(lucy)))=>((~kind(fred)<~>patient(fred))))&
(((~rich(lucy)<~>generous(lucy)))=>((~generous(lucy)|brave(lucy))))&
(![X]:(~curious(X)=>(old(X)<~>~tall(X))))&
((?[X]:(~humble(X)))=>(creative(susan)))&
(![X]:((generous(X)<~>humble(X))=>(creative(X)|~patient(X))))&
(((humble(mary)|funny(mary)))=>(?[X]:((~old(X)<~>~curious(X)))))&
((~strong(alice))=>((kind(alice)&funny(alice))))&
(((~patient(john)|quiet(john)))<=>((patient(john)|tall(john))))&
(![X]:((~humble(X)<~>strong(X))=>(kind(X)&~calm(X))))&
(![X]:((~curious(X)|~brave(X))<=>(~rich(X)|~tall(X))))&
(![X]:(strong(X)<=>generous(X)))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)|~strong(X))=>(patient(X)<~>old(X))))&
(((strong(mary)<~>creative(mary)))<=>((funny(susan)|~calm(susan))))&
(tall(susan))&
(?[X]:(~brave(X)))&
(?[X]:((patient(X)|happy(X))))&
((humble(alice)|~strong(alice)))&
((~happy(mary)|old(mary)))&
((humble(susan)|~strong(susan)))&
(?[X]:((~quiet(X)&calm(X)))) | happy(susan) | [] | null | 0 |
If alice is both curious and not funny then fred is generous and vice versa.
Everyone who is both not generous and not tall is both humble and not happy.
If alice is both rich and not generous then john is both calm and not kind.
If fred is both calm and not generous then someone is either rich or not curious and vice versa.
Everyone who is either not old or happy is either not curious or creative and vice versa.
Everyone who is tall or not rich is not kind.
If someone is patient then susan is either rich or strong.
If fred is both not strong and not patient then alice is either not calm or not generous and vice versa.
Everyone who is either old or tall is not humble and vice versa.
If someone is old then someone is not happy and vice versa.
Everyone who is creative or quiet is not strong.
Everyone who is not happy is either not generous or kind and vice versa.
Everyone who is either not wise or generous is both not calm and not wise and vice versa.
Everyone who is both humble and not funny is either humble or rich.
If someone is both patient and not creative then fred is happy and vice versa.
Everyone who is quiet or not old is both not generous and not quiet and vice versa.
Someone is curious or rich.
Mary is both not funny and not tall.
Someone is happy.
Someone is not rich or not brave.
Lucy is funny.
Someone is calm.
Someone is not tall.
Someone is both kind and not funny. | Mary is patient. | neutral | (((curious(alice)&~funny(alice)))<=>(generous(fred)))&
(![X]:((~generous(X)&~tall(X))=>(humble(X)&~happy(X))))&
(((rich(alice)&~generous(alice)))=>((calm(john)&~kind(john))))&
(((calm(fred)&~generous(fred)))<=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:((~old(X)<~>happy(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((tall(X)|~rich(X))=>~kind(X)))&
((?[X]:(patient(X)))=>((rich(susan)<~>strong(susan))))&
(((~strong(fred)&~patient(fred)))<=>((~calm(alice)<~>~generous(alice))))&
(![X]:((old(X)<~>tall(X))<=>~humble(X)))&
((?[X]:(old(X)))<=>(?[X]:(~happy(X))))&
(![X]:((creative(X)|quiet(X))=>~strong(X)))&
(![X]:(~happy(X)<=>(~generous(X)<~>kind(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(~calm(X)&~wise(X))))&
(![X]:((humble(X)&~funny(X))=>(humble(X)<~>rich(X))))&
((?[X]:((patient(X)&~creative(X))))<=>(happy(fred)))&
(![X]:((quiet(X)|~old(X))<=>(~generous(X)&~quiet(X))))&
(?[X]:((curious(X)|rich(X))))&
((~funny(mary)&~tall(mary)))&
(?[X]:(happy(X)))&
(?[X]:((~rich(X)|~brave(X))))&
(funny(lucy))&
(?[X]:(calm(X)))&
(?[X]:(~tall(X)))&
(?[X]:((kind(X)&~funny(X)))) | patient(mary) | [] | null | 0 |
If someone is old then someone is either curious or not patient. Everyone who is not calm or generous is not humble or not wise and vice versa. Everyone who is both rich and not curious is old or creative and vice versa. If someone is not old then fred is both old and patient. Everyone who is both not tall and not happy is not tall or strong. If fred is either wise or generous then someone is either old or calm and vice versa. If someone is not wise or not creative then someone is both happy and not old. If someone is not strong or not funny then fred is brave or not rich. Everyone who is both calm and not tall is funny and vice versa. If someone is either happy or tall then someone is both curious and not calm. If john is both not kind and humble then john is patient or not rich. Everyone who is either not generous or strong is not brave or quiet and vice versa. Everyone who is either generous or strong is not old or not tall. If someone is calm or not rich then someone is quiet or generous and vice versa. Everyone who is either calm or not brave is both old and not curious and vice versa. Everyone who is not patient is either not humble or not patient and vice versa. Susan is happy. Someone is both not happy and not curious. Someone is not happy. John is either patient or not old. Someone is either not tall or creative. Someone is creative or not calm. Someone is kind or not funny. Lucy is either calm or not brave. | Fred is not curious. | entailment | ((?[X]:(old(X)))=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:((~calm(X)|generous(X))<=>(~humble(X)|~wise(X))))&
(![X]:((rich(X)&~curious(X))<=>(old(X)|creative(X))))&
((?[X]:(~old(X)))=>((old(fred)&patient(fred))))&
(![X]:((~tall(X)&~happy(X))=>(~tall(X)|strong(X))))&
(((wise(fred)<~>generous(fred)))<=>(?[X]:((old(X)<~>calm(X)))))&
((?[X]:((~wise(X)|~creative(X))))=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:((~strong(X)|~funny(X))))=>((brave(fred)|~rich(fred))))&
(![X]:((calm(X)&~tall(X))<=>funny(X)))&
((?[X]:((happy(X)<~>tall(X))))=>(?[X]:((curious(X)&~calm(X)))))&
(((~kind(john)&humble(john)))=>((patient(john)|~rich(john))))&
(![X]:((~generous(X)<~>strong(X))<=>(~brave(X)|quiet(X))))&
(![X]:((generous(X)<~>strong(X))=>(~old(X)|~tall(X))))&
((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((calm(X)<~>~brave(X))<=>(old(X)&~curious(X))))&
(![X]:(~patient(X)<=>(~humble(X)<~>~patient(X))))&
(happy(susan))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:(~happy(X)))&
((patient(john)<~>~old(john)))&
(?[X]:((~tall(X)<~>creative(X))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((kind(X)|~funny(X))))&
((calm(lucy)<~>~brave(lucy))) | ~curious(fred) | [
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 699049799678436495761474
% SZS output start Proof for 699049799678436495761474
3. ! [X0] : ((~curious(X0) & rich(X0)) <=> (creative(X0) | old(X0))) [input p2]
4. ? [X0] : ~old(X0) => (patient(fred) & old(fred)) [input p3]
25. curious(fred) [input hypothesis]
34. (patient(fred) & old(fred)) | ! [X0] : old(X0) [ennf transformation 4]
50. ! [X0] : (((~curious(X0) & rich(X0)) | (~creative(X0) & ~old(X0))) & ((creative(X0) | old(X0)) | (curious(X0) | ~rich(X0)))) [nnf transformation 3]
51. ! [X0] : (((~curious(X0) & rich(X0)) | (~creative(X0) & ~old(X0))) & (creative(X0) | old(X0) | curious(X0) | ~rich(X0))) [flattening 50]
94. ~curious(X0) | ~old(X0) [cnf transformation 51]
96. old(fred) | old(X0) [cnf transformation 34]
152. curious(fred) [cnf transformation 25]
169. 4 <=> ! [X0] : old(X0) [avatar definition]
170. old(X0) <- (4) [avatar component clause 169]
177. 6 <=> old(fred) [avatar definition]
178. ~old(fred) <- (~6) [avatar component clause 177]
180. 4 | 6 [avatar split clause 96,177,169]
347. ~old(fred) [resolution 94,152]
350. ~6 [avatar split clause 347,177]
355. $false <- (4, ~6) [resolution 178,170]
356. ~4 | 6 [avatar contradiction clause 355]
357. $false [avatar sat refutation 180,350,356]
% SZS output end Proof for 699049799678436495761474
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is generous then someone is either not patient or brave and vice versa.
Everyone who is either not kind or not quiet is happy.
Everyone who is kind or not curious is tall and vice versa.
Everyone who is both not calm and patient is not tall or strong.
Everyone who is both quiet and not generous is either happy or not wise.
Everyone who is either generous or old is both old and not rich and vice versa.
Everyone who is both not generous and not brave is happy and vice versa.
If someone is wise or not quiet then lucy is either not quiet or rich and vice versa.
If paul is not brave then someone is both strong and curious.
If someone is not patient then mary is not creative.
If paul is both patient and not tall then paul is both not funny and not wise and vice versa.
Everyone who is either not brave or not kind is both not strong and not tall and vice versa.
If mary is funny then fred is not strong or not patient and vice versa.
If someone is either not kind or rich then someone is not patient.
Everyone who is both not rich and not calm is creative or strong and vice versa.
Mary is happy or not curious.
Someone is either funny or old.
Lucy is either not strong or not generous.
Lucy is rich.
John is generous or creative.
Mary is rich or calm.
Someone is either not kind or not strong. | Mary is not patient. | neutral | ((?[X]:(generous(X)))<=>(?[X]:((~patient(X)<~>brave(X)))))&
(![X]:((~kind(X)<~>~quiet(X))=>happy(X)))&
(![X]:((kind(X)|~curious(X))<=>tall(X)))&
(![X]:((~calm(X)&patient(X))=>(~tall(X)|strong(X))))&
(![X]:((quiet(X)&~generous(X))=>(happy(X)<~>~wise(X))))&
(![X]:((generous(X)<~>old(X))<=>(old(X)&~rich(X))))&
(![X]:((~generous(X)&~brave(X))<=>happy(X)))&
((?[X]:((wise(X)|~quiet(X))))<=>((~quiet(lucy)<~>rich(lucy))))&
((~brave(paul))=>(?[X]:((strong(X)&curious(X)))))&
((?[X]:(~patient(X)))=>(~creative(mary)))&
(((patient(paul)&~tall(paul)))<=>((~funny(paul)&~wise(paul))))&
(![X]:((~brave(X)<~>~kind(X))<=>(~strong(X)&~tall(X))))&
((funny(mary))<=>((~strong(fred)|~patient(fred))))&
((?[X]:((~kind(X)<~>rich(X))))=>(?[X]:(~patient(X))))&
(![X]:((~rich(X)&~calm(X))<=>(creative(X)|strong(X))))&
((happy(mary)|~curious(mary)))&
(?[X]:((funny(X)<~>old(X))))&
((~strong(lucy)<~>~generous(lucy)))&
(rich(lucy))&
((generous(john)|creative(john)))&
((rich(mary)|calm(mary)))&
(?[X]:((~kind(X)<~>~strong(X)))) | ~patient(mary) | [] | null | 0 |
Everyone who is both old and not quiet is either not kind or not curious and vice versa.
Everyone who is both curious and not curious is either generous or quiet and vice versa.
Everyone who is not happy is both not calm and not tall.
If john is either not wise or not humble then someone is strong or not calm.
If alice is both not funny and humble then lucy is both old and not tall and vice versa.
Everyone who is either not patient or brave is both humble and not happy and vice versa.
Everyone who is tall or not creative is either not brave or not creative.
Everyone who is not quiet or not curious is happy and vice versa.
If paul is both funny and rich then fred is not rich.
Everyone who is both not strong and happy is both not creative and not kind and vice versa.
Everyone who is funny or creative is not wise and vice versa.
Everyone who is brave or funny is rich or not tall and vice versa.
Everyone who is either not creative or not quiet is either happy or not kind and vice versa.
Everyone who is not funny is either not humble or not strong and vice versa.
If paul is calm then mary is humble or kind.
Everyone who is funny or not humble is either happy or not brave and vice versa.
Mary is either not happy or wise.
Someone is not strong or not quiet.
Someone is either brave or not kind.
John is either generous or not happy.
Someone is both not old and not strong.
Someone is either generous or not kind.
Fred is not happy or not creative. | Mary is not humble. | neutral | (![X]:((old(X)&~quiet(X))<=>(~kind(X)<~>~curious(X))))&
(![X]:((curious(X)&~curious(X))<=>(generous(X)<~>quiet(X))))&
(![X]:(~happy(X)=>(~calm(X)&~tall(X))))&
(((~wise(john)<~>~humble(john)))=>(?[X]:((strong(X)|~calm(X)))))&
(((~funny(alice)&humble(alice)))<=>((old(lucy)&~tall(lucy))))&
(![X]:((~patient(X)<~>brave(X))<=>(humble(X)&~happy(X))))&
(![X]:((tall(X)|~creative(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~curious(X))<=>happy(X)))&
(((funny(paul)&rich(paul)))=>(~rich(fred)))&
(![X]:((~strong(X)&happy(X))<=>(~creative(X)&~kind(X))))&
(![X]:((funny(X)|creative(X))<=>~wise(X)))&
(![X]:((brave(X)|funny(X))<=>(rich(X)|~tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(happy(X)<~>~kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)<~>~strong(X))))&
((calm(paul))=>((humble(mary)|kind(mary))))&
(![X]:((funny(X)|~humble(X))<=>(happy(X)<~>~brave(X))))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:((brave(X)<~>~kind(X))))&
((generous(john)<~>~happy(john)))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:((generous(X)<~>~kind(X))))&
((~happy(fred)|~creative(fred))) | ~humble(mary) | [] | null | 0 |
If someone is not happy or not wise then alice is not quiet or not brave and vice versa. Everyone who is curious or strong is either not generous or old and vice versa. Everyone who is both funny and not happy is not humble or not curious and vice versa. Everyone who is both not brave and calm is not tall or curious. If alice is both old and not humble then mary is either rich or not tall. If someone is wise or quiet then mary is either not funny or tall and vice versa. If john is either not strong or not brave then someone is generous or brave and vice versa. Everyone who is not strong or not happy is old or patient and vice versa. If mary is not patient then alice is old and vice versa. If someone is kind or not calm then fred is either not generous or not patient and vice versa. If someone is both not brave and not old then john is not tall or brave. If someone is both old and strong then paul is either not funny or not old and vice versa. Everyone who is rich or not old is not wise. If fred is both happy and patient then fred is not quiet or patient. Everyone who is not creative or creative is both not brave and old and vice versa. Everyone who is both not humble and not creative is brave and vice versa. Fred is both not funny and quiet. Susan is either old or not funny. Paul is quiet. Someone is not brave. Someone is strong or quiet. Someone is old. Someone is not creative or rich. | Paul is humble. | entailment | ((?[X]:((~happy(X)|~wise(X))))<=>((~quiet(alice)|~brave(alice))))&
(![X]:((curious(X)|strong(X))<=>(~generous(X)<~>old(X))))&
(![X]:((funny(X)&~happy(X))<=>(~humble(X)|~curious(X))))&
(![X]:((~brave(X)&calm(X))=>(~tall(X)|curious(X))))&
(((old(alice)&~humble(alice)))=>((rich(mary)<~>~tall(mary))))&
((?[X]:((wise(X)|quiet(X))))<=>((~funny(mary)<~>tall(mary))))&
(((~strong(john)<~>~brave(john)))<=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~strong(X)|~happy(X))<=>(old(X)|patient(X))))&
((~patient(mary))<=>(old(alice)))&
((?[X]:((kind(X)|~calm(X))))<=>((~generous(fred)<~>~patient(fred))))&
((?[X]:((~brave(X)&~old(X))))=>((~tall(john)|brave(john))))&
((?[X]:((old(X)&strong(X))))<=>((~funny(paul)<~>~old(paul))))&
(![X]:((rich(X)|~old(X))=>~wise(X)))&
(((happy(fred)&patient(fred)))=>((~quiet(fred)|patient(fred))))&
(![X]:((~creative(X)|creative(X))<=>(~brave(X)&old(X))))&
(![X]:((~humble(X)&~creative(X))<=>brave(X)))&
((~funny(fred)&quiet(fred)))&
((old(susan)<~>~funny(susan)))&
(quiet(paul))&
(?[X]:(~brave(X)))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:(old(X)))&
(?[X]:((~creative(X)|rich(X)))) | humble(paul) | [
"p1",
"p2",
"p6",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3445689616350349337423661
% SZS output start Proof for 3445689616350349337423661
2. ! [X0] : ((strong(X0) | curious(X0)) <=> (~generous(X0) <~> old(X0))) [input p1]
3. ! [X0] : ((~happy(X0) & funny(X0)) <=> (~curious(X0) | ~humble(X0))) [input p2]
7. (~strong(john) <~> ~brave(john)) <=> ? [X0] : (brave(X0) | generous(X0)) [input p6]
12. ? [X0] : (strong(X0) & old(X0)) <=> (~funny(paul) <~> ~old(paul)) [input p11]
15. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (old(X0) & ~brave(X0))) [input p14]
17. quiet(fred) & ~funny(fred) [input p16]
24. ~humble(paul) [input hypothesis]
39. ! [X0] : (((strong(X0) | curious(X0)) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) & (((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | (~strong(X0) & ~curious(X0)))) [nnf transformation 2]
40. ! [X0] : ((strong(X0) | curious(X0) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) & (((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | (~strong(X0) & ~curious(X0)))) [flattening 39]
41. ! [X0] : (((~happy(X0) & funny(X0)) | (curious(X0) & humble(X0))) & ((~curious(X0) | ~humble(X0)) | (happy(X0) | ~funny(X0)))) [nnf transformation 3]
42. ! [X0] : (((~happy(X0) & funny(X0)) | (curious(X0) & humble(X0))) & (~curious(X0) | ~humble(X0) | happy(X0) | ~funny(X0))) [flattening 41]
48. (((brave(john) | strong(john)) & (~brave(john) | ~strong(john))) | ! [X0] : (~brave(X0) & ~generous(X0))) & (? [X0] : (brave(X0) | generous(X0)) | ((~strong(john) | brave(john)) & (~brave(john) | strong(john)))) [nnf transformation 7]
49. (((brave(john) | strong(john)) & (~brave(john) | ~strong(john))) | ! [X0] : (~brave(X0) & ~generous(X0))) & (? [X1] : (brave(X1) | generous(X1)) | ((~strong(john) | brave(john)) & (~brave(john) | strong(john)))) [rectify 48]
50. ? [X1] : (brave(X1) | generous(X1)) => (brave(sK2) | generous(sK2)) [choice axiom]
51. (((brave(john) | strong(john)) & (~brave(john) | ~strong(john))) | ! [X0] : (~brave(X0) & ~generous(X0))) & ((brave(sK2) | generous(sK2)) | ((~strong(john) | brave(john)) & (~brave(john) | strong(john)))) [skolemisation 49,50]
59. (? [X0] : (strong(X0) & old(X0)) | ((~funny(paul) | old(paul)) & (~old(paul) | funny(paul)))) & (((old(paul) | funny(paul)) & (~old(paul) | ~funny(paul))) | ! [X0] : (~strong(X0) | ~old(X0))) [nnf transformation 12]
60. (? [X0] : (strong(X0) & old(X0)) | ((~funny(paul) | old(paul)) & (~old(paul) | funny(paul)))) & (((old(paul) | funny(paul)) & (~old(paul) | ~funny(paul))) | ! [X1] : (~strong(X1) | ~old(X1))) [rectify 59]
61. ? [X0] : (strong(X0) & old(X0)) => (strong(sK4) & old(sK4)) [choice axiom]
62. ((strong(sK4) & old(sK4)) | ((~funny(paul) | old(paul)) & (~old(paul) | funny(paul)))) & (((old(paul) | funny(paul)) & (~old(paul) | ~funny(paul))) | ! [X1] : (~strong(X1) | ~old(X1))) [skolemisation 60,61]
63. ! [X0] : (((creative(X0) | ~creative(X0)) | (~old(X0) | brave(X0))) & ((old(X0) & ~brave(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 15]
64. ! [X0] : ((creative(X0) | ~creative(X0) | ~old(X0) | brave(X0)) & ((old(X0) & ~brave(X0)) | (~creative(X0) & creative(X0)))) [flattening 63]
82. ~old(X0) | generous(X0) | ~curious(X0) [cnf transformation 40]
87. humble(X0) | funny(X0) [cnf transformation 42]
88. funny(X0) | curious(X0) [cnf transformation 42]
104. brave(john) | strong(john) | ~generous(X0) [cnf transformation 51]
119. ~old(paul) | ~funny(paul) | ~strong(X1) | ~old(X1) [cnf transformation 62]
128. ~brave(X0) | creative(X0) [cnf transformation 64]
129. ~creative(X0) | ~brave(X0) [cnf transformation 64]
130. old(X0) | creative(X0) [cnf transformation 64]
131. ~creative(X0) | old(X0) [cnf transformation 64]
136. ~funny(fred) [cnf transformation 17]
145. ~humble(paul) [cnf transformation 24]
215. 16 <=> ! [X0] : ~brave(X0) [avatar definition]
216. ~brave(X0) <- (16) [avatar component clause 215]
218. 17 <=> strong(john) [avatar definition]
220. strong(john) <- (17) [avatar component clause 218]
222. 18 <=> brave(john) [avatar definition]
224. brave(john) <- (18) [avatar component clause 222]
227. 19 <=> ! [X0] : ~generous(X0) [avatar definition]
228. ~generous(X0) <- (19) [avatar component clause 227]
229. 19 | 17 | 18 [avatar split clause 104,222,218,227]
285. 31 <=> old(paul) [avatar definition]
286. ~old(paul) <- (~31) [avatar component clause 285]
289. 32 <=> funny(paul) [avatar definition]
305. 35 <=> ! [X1] : (~strong(X1) | ~old(X1)) [avatar definition]
306. ~strong(X1) | ~old(X1) <- (35) [avatar component clause 305]
308. 35 | ~32 | ~31 [avatar split clause 119,285,289,305]
309. old(X0) [subsumption resolution 130,131]
310. ~brave(X0) [subsumption resolution 128,129]
311. 16 [avatar split clause 310,215]
331. funny(paul) [resolution 87,145]
334. 32 [avatar split clause 331,289]
335. $false <- (~31) [subsumption resolution 286,309]
336. 31 [avatar contradiction clause 335]
337. ~strong(X1) <- (35) [subsumption resolution 306,309]
342. curious(fred) [resolution 88,136]
346. generous(X0) | ~curious(X0) [resolution 82,309]
347. ~curious(X0) <- (19) [subsumption resolution 346,228]
349. $false <- (19) [resolution 347,342]
352. ~19 [avatar contradiction clause 349]
355. $false <- (17, 35) [subsumption resolution 220,337]
356. ~17 | ~35 [avatar contradiction clause 355]
357. $false <- (16, 18) [subsumption resolution 224,216]
358. ~16 | ~18 [avatar contradiction clause 357]
359. $false [avatar sat refutation 229,308,311,334,336,352,356,358]
% SZS output end Proof for 3445689616350349337423661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not quiet then fred is either not wise or strong. If lucy is rich then alice is either rich or not humble. If alice is both brave and generous then someone is not kind. If someone is both brave and calm then fred is both not strong and not creative and vice versa. Everyone who is not curious or not creative is either old or funny. Everyone who is old is generous. If alice is both not calm and happy then susan is not wise and vice versa. Everyone who is both calm and not patient is not old or humble. If someone is quiet or not creative then someone is both rich and creative and vice versa. If lucy is not funny then alice is both rich and not calm and vice versa. Everyone who is kind or not strong is both not generous and not wise and vice versa. Everyone who is not calm or not wise is both not wise and not calm. If john is funny then fred is not creative or not funny and vice versa. If fred is either not strong or humble then someone is both creative and not creative. Everyone who is strong or calm is not humble and vice versa. If fred is generous then someone is both strong and not happy and vice versa. Fred is not quiet or not patient. Alice is generous or not brave. Paul is both not rich and creative. Someone is humble or not calm. Someone is both humble and curious. Someone is either not calm or brave. Someone is either not generous or not funny. Someone is either not strong or rich. | Fred is creative. | neutral | ((?[X]:((~curious(X)|~quiet(X))))=>((~wise(fred)<~>strong(fred))))&
((rich(lucy))=>((rich(alice)<~>~humble(alice))))&
(((brave(alice)&generous(alice)))=>(?[X]:(~kind(X))))&
((?[X]:((brave(X)&calm(X))))<=>((~strong(fred)&~creative(fred))))&
(![X]:((~curious(X)|~creative(X))=>(old(X)<~>funny(X))))&
(![X]:(old(X)=>generous(X)))&
(((~calm(alice)&happy(alice)))<=>(~wise(susan)))&
(![X]:((calm(X)&~patient(X))=>(~old(X)|humble(X))))&
((?[X]:((quiet(X)|~creative(X))))<=>(?[X]:((rich(X)&creative(X)))))&
((~funny(lucy))<=>((rich(alice)&~calm(alice))))&
(![X]:((kind(X)|~strong(X))<=>(~generous(X)&~wise(X))))&
(![X]:((~calm(X)|~wise(X))=>(~wise(X)&~calm(X))))&
((funny(john))<=>((~creative(fred)|~funny(fred))))&
(((~strong(fred)<~>humble(fred)))=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((strong(X)|calm(X))<=>~humble(X)))&
((generous(fred))<=>(?[X]:((strong(X)&~happy(X)))))&
((~quiet(fred)|~patient(fred)))&
((generous(alice)|~brave(alice)))&
((~rich(paul)&creative(paul)))&
(?[X]:((humble(X)|~calm(X))))&
(?[X]:((humble(X)&curious(X))))&
(?[X]:((~calm(X)<~>brave(X))))&
(?[X]:((~generous(X)<~>~funny(X))))&
(?[X]:((~strong(X)<~>rich(X)))) | creative(fred) | [] | null | 0 |
If susan is calm then fred is quiet.
If susan is either patient or not humble then someone is either not brave or not tall and vice versa.
If lucy is funny or tall then someone is kind and vice versa.
If someone is calm then someone is quiet.
If mary is either not kind or not generous then someone is patient or humble and vice versa.
If someone is both not rich and generous then fred is not rich and vice versa.
Everyone who is curious or not humble is both not calm and not curious and vice versa.
If john is either not old or quiet then paul is not calm.
If alice is either generous or creative then susan is brave or not happy and vice versa.
If lucy is both not funny and tall then john is calm.
Everyone who is generous is either not wise or not brave and vice versa.
If someone is old or not generous then someone is generous and vice versa.
If someone is creative then john is either strong or humble and vice versa.
Everyone who is creative is tall or not creative and vice versa.
Everyone who is humble or calm is both not brave and not strong.
If alice is both not wise and quiet then someone is either not happy or happy and vice versa.
Paul is either generous or not kind.
Someone is both rich and funny.
Paul is either tall or calm.
Someone is happy.
Paul is either quiet or strong.
Someone is either kind or not patient.
Someone is both creative and not patient.
Susan is both not humble and strong. | Alice is curious. | contradiction | ((calm(susan))=>(quiet(fred)))&
(((patient(susan)<~>~humble(susan)))<=>(?[X]:((~brave(X)<~>~tall(X)))))&
(((funny(lucy)|tall(lucy)))<=>(?[X]:(kind(X))))&
((?[X]:(calm(X)))=>(?[X]:(quiet(X))))&
(((~kind(mary)<~>~generous(mary)))<=>(?[X]:((patient(X)|humble(X)))))&
((?[X]:((~rich(X)&generous(X))))<=>(~rich(fred)))&
(![X]:((curious(X)|~humble(X))<=>(~calm(X)&~curious(X))))&
(((~old(john)<~>quiet(john)))=>(~calm(paul)))&
(((generous(alice)<~>creative(alice)))<=>((brave(susan)|~happy(susan))))&
(((~funny(lucy)&tall(lucy)))=>(calm(john)))&
(![X]:(generous(X)<=>(~wise(X)<~>~brave(X))))&
((?[X]:((old(X)|~generous(X))))<=>(?[X]:(generous(X))))&
((?[X]:(creative(X)))<=>((strong(john)<~>humble(john))))&
(![X]:(creative(X)<=>(tall(X)|~creative(X))))&
(![X]:((humble(X)|calm(X))=>(~brave(X)&~strong(X))))&
(((~wise(alice)&quiet(alice)))<=>(?[X]:((~happy(X)<~>happy(X)))))&
((generous(paul)<~>~kind(paul)))&
(?[X]:((rich(X)&funny(X))))&
((tall(paul)<~>calm(paul)))&
(?[X]:(happy(X)))&
((quiet(paul)<~>strong(paul)))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((creative(X)&~patient(X))))&
((~humble(susan)&strong(susan))) | curious(alice) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6313761590892809960304183
% SZS output start Proof for 6313761590892809960304183
7. ! [X0] : ((~humble(X0) | curious(X0)) <=> (~curious(X0) & ~calm(X0))) [input p6]
25. curious(alice) [input hypothesis]
54. ! [X0] : (((~humble(X0) | curious(X0)) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | (humble(X0) & ~curious(X0)))) [nnf transformation 7]
55. ! [X0] : ((~humble(X0) | curious(X0) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | (humble(X0) & ~curious(X0)))) [flattening 54]
112. ~curious(X0) | ~curious(X0) [cnf transformation 55]
163. curious(alice) [cnf transformation 25]
170. ~curious(X0) [duplicate literal removal 112]
419. $false [subsumption resolution 163,170]
% SZS output end Proof for 6313761590892809960304183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or generous is quiet or strong and vice versa.
Everyone who is either not patient or old is both not kind and not old and vice versa.
If someone is both not humble and not tall then alice is kind.
Everyone who is both not rich and humble is not old.
Everyone who is not curious or not old is funny.
Everyone who is not happy or not tall is not happy or patient and vice versa.
Everyone who is not kind or not curious is not generous or not calm.
If someone is both kind and funny then mary is tall and vice versa.
Everyone who is patient is humble and vice versa.
If someone is not old then someone is not happy and vice versa.
Everyone who is either not quiet or patient is both creative and kind.
Everyone who is generous is not brave or curious.
Everyone who is both funny and curious is not funny and vice versa.
Everyone who is both not quiet and not funny is not funny or calm and vice versa.
Everyone who is both quiet and rich is either generous or not patient and vice versa.
Everyone who is both not brave and not patient is either calm or not humble and vice versa.
John is curious or tall.
Someone is either curious or not old.
Someone is curious or rich.
Paul is either curious or patient.
Fred is quiet.
Someone is either strong or not wise.
Alice is either calm or kind. | John is not strong. | neutral | (![X]:((wise(X)<~>generous(X))<=>(quiet(X)|strong(X))))&
(![X]:((~patient(X)<~>old(X))<=>(~kind(X)&~old(X))))&
((?[X]:((~humble(X)&~tall(X))))=>(kind(alice)))&
(![X]:((~rich(X)&humble(X))=>~old(X)))&
(![X]:((~curious(X)|~old(X))=>funny(X)))&
(![X]:((~happy(X)|~tall(X))<=>(~happy(X)|patient(X))))&
(![X]:((~kind(X)|~curious(X))=>(~generous(X)|~calm(X))))&
((?[X]:((kind(X)&funny(X))))<=>(tall(mary)))&
(![X]:(patient(X)<=>humble(X)))&
((?[X]:(~old(X)))<=>(?[X]:(~happy(X))))&
(![X]:((~quiet(X)<~>patient(X))=>(creative(X)&kind(X))))&
(![X]:(generous(X)=>(~brave(X)|curious(X))))&
(![X]:((funny(X)&curious(X))<=>~funny(X)))&
(![X]:((~quiet(X)&~funny(X))<=>(~funny(X)|calm(X))))&
(![X]:((quiet(X)&rich(X))<=>(generous(X)<~>~patient(X))))&
(![X]:((~brave(X)&~patient(X))<=>(calm(X)<~>~humble(X))))&
((curious(john)|tall(john)))&
(?[X]:((curious(X)<~>~old(X))))&
(?[X]:((curious(X)|rich(X))))&
((curious(paul)<~>patient(paul)))&
(quiet(fred))&
(?[X]:((strong(X)<~>~wise(X))))&
((calm(alice)<~>kind(alice))) | ~strong(john) | [] | null | 0 |
Everyone who is brave is not funny or not kind and vice versa.
If someone is not patient or happy then someone is both tall and not calm.
If someone is not kind or not generous then someone is not rich and vice versa.
If someone is brave or curious then someone is humble or not humble.
Everyone who is brave is either strong or old and vice versa.
Everyone who is both brave and not patient is tall.
Everyone who is tall or not patient is either happy or not patient and vice versa.
Everyone who is calm or not patient is either old or not calm and vice versa.
If lucy is either generous or old then alice is either not creative or not quiet and vice versa.
If lucy is both not strong and not creative then someone is both happy and not quiet and vice versa.
If mary is both not patient and patient then fred is not funny or not tall.
Everyone who is not calm is either not funny or not old and vice versa.
If someone is creative or not humble then mary is both not calm and creative and vice versa.
If someone is either not strong or not curious then someone is not rich or tall and vice versa.
If john is both tall and not humble then mary is old and vice versa.
If someone is both not rich and happy then lucy is not rich or strong and vice versa.
Someone is curious or rich.
Someone is either not kind or not rich.
Mary is both funny and not generous.
Someone is not kind.
Mary is either generous or kind.
Someone is both curious and not tall.
Someone is not funny or wise.
Someone is both not calm and not brave. | Mary is not brave. | entailment | (![X]:(brave(X)<=>(~funny(X)|~kind(X))))&
((?[X]:((~patient(X)|happy(X))))=>(?[X]:((tall(X)&~calm(X)))))&
((?[X]:((~kind(X)|~generous(X))))<=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)|curious(X))))=>(?[X]:((humble(X)|~humble(X)))))&
(![X]:(brave(X)<=>(strong(X)<~>old(X))))&
(![X]:((brave(X)&~patient(X))=>tall(X)))&
(![X]:((tall(X)|~patient(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((calm(X)|~patient(X))<=>(old(X)<~>~calm(X))))&
(((generous(lucy)<~>old(lucy)))<=>((~creative(alice)<~>~quiet(alice))))&
(((~strong(lucy)&~creative(lucy)))<=>(?[X]:((happy(X)&~quiet(X)))))&
(((~patient(mary)&patient(mary)))=>((~funny(fred)|~tall(fred))))&
(![X]:(~calm(X)<=>(~funny(X)<~>~old(X))))&
((?[X]:((creative(X)|~humble(X))))<=>((~calm(mary)&creative(mary))))&
((?[X]:((~strong(X)<~>~curious(X))))<=>(?[X]:((~rich(X)|tall(X)))))&
(((tall(john)&~humble(john)))<=>(old(mary)))&
((?[X]:((~rich(X)&happy(X))))<=>((~rich(lucy)|strong(lucy))))&
(?[X]:((curious(X)|rich(X))))&
(?[X]:((~kind(X)<~>~rich(X))))&
((funny(mary)&~generous(mary)))&
(?[X]:(~kind(X)))&
((generous(mary)<~>kind(mary)))&
(?[X]:((curious(X)&~tall(X))))&
(?[X]:((~funny(X)|wise(X))))&
(?[X]:((~calm(X)&~brave(X)))) | ~brave(mary) | [
"p0",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1132900021959481014522938
% SZS output start Proof for 1132900021959481014522938
1. ! [X0] : (brave(X0) <=> (~kind(X0) | ~funny(X0))) [input p0]
19. ~generous(mary) & funny(mary) [input p18]
21. generous(mary) <~> kind(mary) [input p20]
25. brave(mary) [input hypothesis]
37. ! [X0] : ((brave(X0) | (kind(X0) & funny(X0))) & ((~kind(X0) | ~funny(X0)) | ~brave(X0))) [nnf transformation 1]
38. ! [X0] : ((brave(X0) | (kind(X0) & funny(X0))) & (~kind(X0) | ~funny(X0) | ~brave(X0))) [flattening 37]
86. (~kind(mary) | ~generous(mary)) & (kind(mary) | generous(mary)) [nnf transformation 21]
91. ~kind(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 38]
159. funny(mary) [cnf transformation 19]
160. ~generous(mary) [cnf transformation 19]
162. kind(mary) | generous(mary) [cnf transformation 86]
168. brave(mary) [cnf transformation 25]
376. kind(mary) [subsumption resolution 162,160]
393. ~funny(mary) | ~brave(mary) [resolution 91,376]
396. ~brave(mary) [subsumption resolution 393,159]
397. $false [subsumption resolution 396,168]
% SZS output end Proof for 1132900021959481014522938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not old and patient is either humble or not happy.
Everyone who is not quiet is both kind and not calm.
If someone is funny then someone is not curious.
Everyone who is both creative and tall is happy or not tall and vice versa.
Everyone who is creative is generous and vice versa.
Everyone who is not patient or not creative is not quiet.
If someone is both not generous and not quiet then someone is happy or funny and vice versa.
Everyone who is both not tall and quiet is not happy.
If someone is either tall or not old then alice is either strong or creative and vice versa.
If fred is not creative then someone is creative.
Everyone who is both funny and generous is kind.
Everyone who is either not wise or not quiet is funny.
If paul is both not curious and calm then someone is happy and vice versa.
If fred is both not calm and quiet then susan is not tall or not curious and vice versa.
If fred is either wise or patient then paul is either humble or rich.
If john is not humble or not curious then lucy is generous or rich.
John is strong or not curious.
Lucy is rich or not patient.
Paul is both tall and quiet.
Someone is not calm.
Someone is either creative or not patient.
John is brave.
Susan is generous or happy.
Someone is either brave or not calm. | Lucy is not patient. | neutral | (![X]:((~old(X)&patient(X))=>(humble(X)<~>~happy(X))))&
(![X]:(~quiet(X)=>(kind(X)&~calm(X))))&
((?[X]:(funny(X)))=>(?[X]:(~curious(X))))&
(![X]:((creative(X)&tall(X))<=>(happy(X)|~tall(X))))&
(![X]:(creative(X)<=>generous(X)))&
(![X]:((~patient(X)|~creative(X))=>~quiet(X)))&
((?[X]:((~generous(X)&~quiet(X))))<=>(?[X]:((happy(X)|funny(X)))))&
(![X]:((~tall(X)&quiet(X))=>~happy(X)))&
((?[X]:((tall(X)<~>~old(X))))<=>((strong(alice)<~>creative(alice))))&
((~creative(fred))=>(?[X]:(creative(X))))&
(![X]:((funny(X)&generous(X))=>kind(X)))&
(![X]:((~wise(X)<~>~quiet(X))=>funny(X)))&
(((~curious(paul)&calm(paul)))<=>(?[X]:(happy(X))))&
(((~calm(fred)&quiet(fred)))<=>((~tall(susan)|~curious(susan))))&
(((wise(fred)<~>patient(fred)))=>((humble(paul)<~>rich(paul))))&
(((~humble(john)|~curious(john)))=>((generous(lucy)|rich(lucy))))&
((strong(john)|~curious(john)))&
((rich(lucy)|~patient(lucy)))&
((tall(paul)&quiet(paul)))&
(?[X]:(~calm(X)))&
(?[X]:((creative(X)<~>~patient(X))))&
(brave(john))&
((generous(susan)|happy(susan)))&
(?[X]:((brave(X)<~>~calm(X)))) | ~patient(lucy) | [] | null | 0 |
If mary is tall or patient then someone is either not strong or not generous and vice versa. Everyone who is either strong or not tall is rich or brave and vice versa. Everyone who is either tall or not humble is not patient. Everyone who is not patient is curious or not strong. Everyone who is tall or not creative is both not brave and strong and vice versa. If someone is either not rich or old then someone is either humble or not patient and vice versa. If someone is either rich or patient then fred is happy or kind. Everyone who is both generous and not wise is not happy or not old. Everyone who is either not brave or kind is not patient or happy. If someone is either wise or not brave then someone is not calm or not generous. Everyone who is both not tall and kind is not happy or quiet. If paul is patient or not creative then lucy is brave or tall. If someone is either not wise or generous then someone is tall or wise and vice versa. If lucy is happy or not quiet then mary is patient and vice versa. Everyone who is curious or not kind is either old or not patient and vice versa. If someone is either brave or strong then john is not creative. Someone is both strong and quiet. Someone is calm or not tall. Someone is both old and not brave. Lucy is happy or not happy. Someone is quiet. Lucy is either patient or not old. | Fred is not quiet. | neutral | (((tall(mary)|patient(mary)))<=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((strong(X)<~>~tall(X))<=>(rich(X)|brave(X))))&
(![X]:((tall(X)<~>~humble(X))=>~patient(X)))&
(![X]:(~patient(X)=>(curious(X)|~strong(X))))&
(![X]:((tall(X)|~creative(X))<=>(~brave(X)&strong(X))))&
((?[X]:((~rich(X)<~>old(X))))<=>(?[X]:((humble(X)<~>~patient(X)))))&
((?[X]:((rich(X)<~>patient(X))))=>((happy(fred)|kind(fred))))&
(![X]:((generous(X)&~wise(X))=>(~happy(X)|~old(X))))&
(![X]:((~brave(X)<~>kind(X))=>(~patient(X)|happy(X))))&
((?[X]:((wise(X)<~>~brave(X))))=>(?[X]:((~calm(X)|~generous(X)))))&
(![X]:((~tall(X)&kind(X))=>(~happy(X)|quiet(X))))&
(((patient(paul)|~creative(paul)))=>((brave(lucy)|tall(lucy))))&
((?[X]:((~wise(X)<~>generous(X))))<=>(?[X]:((tall(X)|wise(X)))))&
(((happy(lucy)|~quiet(lucy)))<=>(patient(mary)))&
(![X]:((curious(X)|~kind(X))<=>(old(X)<~>~patient(X))))&
((?[X]:((brave(X)<~>strong(X))))=>(~creative(john)))&
(?[X]:((strong(X)&quiet(X))))&
(?[X]:((calm(X)|~tall(X))))&
(?[X]:((old(X)&~brave(X))))&
((happy(lucy)|~happy(lucy)))&
(?[X]:(quiet(X)))&
((patient(lucy)<~>~old(lucy))) | ~quiet(fred) | [] | null | 0 |
Everyone who is not tall or not happy is either tall or creative and vice versa.
If lucy is not tall or not wise then someone is both quiet and brave.
Everyone who is both brave and tall is generous or funny and vice versa.
Everyone who is not wise or creative is both quiet and not old and vice versa.
If someone is not old or not rich then john is either not creative or not curious.
Everyone who is either tall or not kind is wise.
Everyone who is brave is both old and creative.
If someone is either not patient or happy then susan is not tall or old and vice versa.
Everyone who is either not wise or not calm is rich and vice versa.
Everyone who is both not generous and not brave is not quiet.
If paul is not humble then susan is not generous or not wise.
If fred is both not quiet and calm then mary is either not old or rich and vice versa.
Everyone who is creative or old is brave and vice versa.
If lucy is not tall then paul is humble.
Everyone who is brave or not rich is either creative or old.
Someone is not calm.
Alice is not calm.
Fred is not strong or not patient. | Paul is kind. | neutral | (![X]:((~tall(X)|~happy(X))<=>(tall(X)<~>creative(X))))&
(((~tall(lucy)|~wise(lucy)))=>(?[X]:((quiet(X)&brave(X)))))&
(![X]:((brave(X)&tall(X))<=>(generous(X)|funny(X))))&
(![X]:((~wise(X)|creative(X))<=>(quiet(X)&~old(X))))&
((?[X]:((~old(X)|~rich(X))))=>((~creative(john)<~>~curious(john))))&
(![X]:((tall(X)<~>~kind(X))=>wise(X)))&
(![X]:(brave(X)=>(old(X)&creative(X))))&
((?[X]:((~patient(X)<~>happy(X))))<=>((~tall(susan)|old(susan))))&
(![X]:((~wise(X)<~>~calm(X))<=>rich(X)))&
(![X]:((~generous(X)&~brave(X))=>~quiet(X)))&
((~humble(paul))=>((~generous(susan)|~wise(susan))))&
(((~quiet(fred)&calm(fred)))<=>((~old(mary)<~>rich(mary))))&
(![X]:((creative(X)|old(X))<=>brave(X)))&
((~tall(lucy))=>(humble(paul)))&
(![X]:((brave(X)|~rich(X))=>(creative(X)<~>old(X))))&
(?[X]:(~calm(X)))&
(~calm(alice))&
((~strong(fred)|~patient(fred))) | kind(paul) | [] | null | 0 |
Everyone who is patient or old is both not quiet and not kind. Everyone who is creative is rich and vice versa. Everyone who is not old is not kind and vice versa. Everyone who is not funny is kind and vice versa. If someone is wise or not generous then john is both kind and not brave and vice versa. If someone is both funny and not quiet then alice is not curious or not patient and vice versa. If fred is wise then lucy is not happy. If john is not humble or not quiet then paul is both not old and not creative and vice versa. If lucy is quiet then someone is both quiet and not happy. Everyone who is either not strong or strong is funny. Everyone who is creative or wise is both brave and not generous and vice versa. If mary is both curious and not quiet then someone is old or not strong. If lucy is either not tall or tall then mary is either calm or strong and vice versa. If paul is both happy and not kind then someone is both creative and wise and vice versa. Someone is quiet or kind. Paul is strong. Someone is calm or not old. Susan is both not strong and patient. Mary is humble or strong. Someone is not strong. Someone is happy. | Alice is not funny. | contradiction | (![X]:((patient(X)|old(X))=>(~quiet(X)&~kind(X))))&
(![X]:(creative(X)<=>rich(X)))&
(![X]:(~old(X)<=>~kind(X)))&
(![X]:(~funny(X)<=>kind(X)))&
((?[X]:((wise(X)|~generous(X))))<=>((kind(john)&~brave(john))))&
((?[X]:((funny(X)&~quiet(X))))<=>((~curious(alice)|~patient(alice))))&
((wise(fred))=>(~happy(lucy)))&
(((~humble(john)|~quiet(john)))<=>((~old(paul)&~creative(paul))))&
((quiet(lucy))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:((~strong(X)<~>strong(X))=>funny(X)))&
(![X]:((creative(X)|wise(X))<=>(brave(X)&~generous(X))))&
(((curious(mary)&~quiet(mary)))=>(?[X]:((old(X)|~strong(X)))))&
(((~tall(lucy)<~>tall(lucy)))<=>((calm(mary)<~>strong(mary))))&
(((happy(paul)&~kind(paul)))<=>(?[X]:((creative(X)&wise(X)))))&
(?[X]:((quiet(X)|kind(X))))&
(strong(paul))&
(?[X]:((calm(X)|~old(X))))&
((~strong(susan)&patient(susan)))&
((humble(mary)|strong(mary)))&
(?[X]:(~strong(X)))&
(?[X]:(happy(X))) | ~funny(alice) | [
"p0",
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7485062649146379123250768
% SZS output start Proof for 7485062649146379123250768
1. ! [X0] : ((old(X0) | patient(X0)) => (~kind(X0) & ~quiet(X0))) [input p0]
3. ! [X0] : (~old(X0) <=> ~kind(X0)) [input p2]
4. ! [X0] : (~funny(X0) <=> kind(X0)) [input p3]
22. ~funny(alice) [input hypothesis]
23. ! [X0] : ((~kind(X0) & ~quiet(X0)) | (~old(X0) & ~patient(X0))) [ennf transformation 1]
30. ! [X0] : ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0))) [nnf transformation 3]
31. ! [X0] : ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))) [nnf transformation 4]
68. ~kind(X0) | ~old(X0) [cnf transformation 23]
71. ~kind(X0) | old(X0) [cnf transformation 30]
72. ~old(X0) | kind(X0) [cnf transformation 30]
73. kind(X0) | funny(X0) [cnf transformation 31]
121. ~funny(alice) [cnf transformation 22]
128. ~old(X0) [subsumption resolution 72,68]
129. ~kind(X0) [subsumption resolution 71,128]
130. funny(X0) [subsumption resolution 73,129]
261. $false [subsumption resolution 121,130]
% SZS output end Proof for 7485062649146379123250768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not patient is patient or not creative and vice versa. If lucy is not calm or happy then someone is both not wise and not generous and vice versa. Everyone who is humble or not generous is both not calm and not rich and vice versa. Everyone who is both generous and not quiet is both old and creative and vice versa. If fred is curious then someone is not brave. If someone is both not creative and rich then someone is both patient and quiet and vice versa. If someone is both happy and quiet then alice is not brave and vice versa. If susan is either not curious or kind then fred is both humble and curious and vice versa. Everyone who is either not rich or not generous is either not generous or happy. Everyone who is either kind or not humble is both not wise and not curious and vice versa. If someone is both patient and not patient then paul is either happy or kind and vice versa. Everyone who is either quiet or calm is either rich or not generous. If someone is not tall then john is brave. If someone is wise then someone is funny. Everyone who is both curious and not tall is rich and vice versa. If someone is not old or generous then someone is either patient or old and vice versa. John is either not wise or wise. Someone is curious. Paul is creative or strong. John is not generous or rich. Someone is both not quiet and not kind. Someone is both rich and not brave. | Fred is not patient. | entailment | (![X]:((brave(X)&~patient(X))<=>(patient(X)|~creative(X))))&
(((~calm(lucy)|happy(lucy)))<=>(?[X]:((~wise(X)&~generous(X)))))&
(![X]:((humble(X)|~generous(X))<=>(~calm(X)&~rich(X))))&
(![X]:((generous(X)&~quiet(X))<=>(old(X)&creative(X))))&
((curious(fred))=>(?[X]:(~brave(X))))&
((?[X]:((~creative(X)&rich(X))))<=>(?[X]:((patient(X)&quiet(X)))))&
((?[X]:((happy(X)&quiet(X))))<=>(~brave(alice)))&
(((~curious(susan)<~>kind(susan)))<=>((humble(fred)&curious(fred))))&
(![X]:((~rich(X)<~>~generous(X))=>(~generous(X)<~>happy(X))))&
(![X]:((kind(X)<~>~humble(X))<=>(~wise(X)&~curious(X))))&
((?[X]:((patient(X)&~patient(X))))<=>((happy(paul)<~>kind(paul))))&
(![X]:((quiet(X)<~>calm(X))=>(rich(X)<~>~generous(X))))&
((?[X]:(~tall(X)))=>(brave(john)))&
((?[X]:(wise(X)))=>(?[X]:(funny(X))))&
(![X]:((curious(X)&~tall(X))<=>rich(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((patient(X)<~>old(X)))))&
((~wise(john)<~>wise(john)))&
(?[X]:(curious(X)))&
((creative(paul)|strong(paul)))&
((~generous(john)|rich(john)))&
(?[X]:((~quiet(X)&~kind(X))))&
(?[X]:((rich(X)&~brave(X)))) | ~patient(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 4753824948844776224139701
% SZS output start Proof for 4753824948844776224139701
1. ! [X0] : ((~patient(X0) & brave(X0)) <=> (~creative(X0) | patient(X0))) [input p0]
23. patient(fred) [input hypothesis]
33. ! [X0] : (((~patient(X0) & brave(X0)) | (creative(X0) & ~patient(X0))) & ((~creative(X0) | patient(X0)) | (patient(X0) | ~brave(X0)))) [nnf transformation 1]
34. ! [X0] : (((~patient(X0) & brave(X0)) | (creative(X0) & ~patient(X0))) & (~creative(X0) | patient(X0) | patient(X0) | ~brave(X0))) [flattening 33]
82. ~patient(X0) | ~patient(X0) [cnf transformation 34]
150. patient(fred) [cnf transformation 23]
154. ~patient(X0) [duplicate literal removal 82]
292. $false [subsumption resolution 150,154]
% SZS output end Proof for 4753824948844776224139701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is happy or not rich.
If someone is tall or not creative then paul is not tall or brave and vice versa.
If alice is either not patient or curious then someone is either calm or rich and vice versa.
Everyone who is either not patient or creative is either not old or wise.
Everyone who is either not kind or brave is brave and vice versa.
Everyone who is either calm or not old is not funny.
If fred is both patient and tall then john is old or calm and vice versa.
Everyone who is rich is wise or old and vice versa.
Everyone who is both humble and not generous is not patient and vice versa.
If someone is creative or generous then lucy is not humble or funny.
Everyone who is not humble or not brave is both not patient and generous and vice versa.
If fred is both not generous and tall then someone is not brave or not funny and vice versa.
If john is either creative or wise then someone is either humble or curious.
If someone is wise then someone is funny or patient and vice versa.
Everyone who is not creative is both not generous and tall and vice versa.
If lucy is either not calm or not tall then john is either not kind or funny.
Someone is either not quiet or not happy.
Fred is kind or not funny.
Someone is either not curious or generous.
Paul is humble or creative.
Someone is generous or creative.
Paul is both not old and humble.
Susan is either not generous or not tall.
Someone is either not generous or not tall. | Lucy is brave. | entailment | (![X]:(~kind(X)=>(happy(X)|~rich(X))))&
((?[X]:((tall(X)|~creative(X))))<=>((~tall(paul)|brave(paul))))&
(((~patient(alice)<~>curious(alice)))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~patient(X)<~>creative(X))=>(~old(X)<~>wise(X))))&
(![X]:((~kind(X)<~>brave(X))<=>brave(X)))&
(![X]:((calm(X)<~>~old(X))=>~funny(X)))&
(((patient(fred)&tall(fred)))<=>((old(john)|calm(john))))&
(![X]:(rich(X)<=>(wise(X)|old(X))))&
(![X]:((humble(X)&~generous(X))<=>~patient(X)))&
((?[X]:((creative(X)|generous(X))))=>((~humble(lucy)|funny(lucy))))&
(![X]:((~humble(X)|~brave(X))<=>(~patient(X)&generous(X))))&
(((~generous(fred)&tall(fred)))<=>(?[X]:((~brave(X)|~funny(X)))))&
(((creative(john)<~>wise(john)))=>(?[X]:((humble(X)<~>curious(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((funny(X)|patient(X)))))&
(![X]:(~creative(X)<=>(~generous(X)&tall(X))))&
(((~calm(lucy)<~>~tall(lucy)))=>((~kind(john)<~>funny(john))))&
(?[X]:((~quiet(X)<~>~happy(X))))&
((kind(fred)|~funny(fred)))&
(?[X]:((~curious(X)<~>generous(X))))&
((humble(paul)|creative(paul)))&
(?[X]:((generous(X)|creative(X))))&
((~old(paul)&humble(paul)))&
((~generous(susan)<~>~tall(susan)))&
(?[X]:((~generous(X)<~>~tall(X)))) | brave(lucy) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 603430983076204791958906
% SZS output start Proof for 603430983076204791958906
9. ! [X0] : ((~generous(X0) & humble(X0)) <=> ~patient(X0)) [input p8]
11. ! [X0] : ((~brave(X0) | ~humble(X0)) <=> (generous(X0) & ~patient(X0))) [input p10]
25. ~brave(lucy) [input hypothesis]
51. ! [X0] : (((~generous(X0) & humble(X0)) | patient(X0)) & (~patient(X0) | (generous(X0) | ~humble(X0)))) [nnf transformation 9]
52. ! [X0] : (((~generous(X0) & humble(X0)) | patient(X0)) & (~patient(X0) | generous(X0) | ~humble(X0))) [flattening 51]
53. ! [X0] : (((~brave(X0) | ~humble(X0)) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | (brave(X0) & humble(X0)))) [nnf transformation 11]
54. ! [X0] : ((~brave(X0) | ~humble(X0) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | (brave(X0) & humble(X0)))) [flattening 53]
116. ~generous(X0) | patient(X0) [cnf transformation 52]
120. ~patient(X0) | brave(X0) [cnf transformation 54]
122. generous(X0) | brave(X0) [cnf transformation 54]
156. ~brave(lucy) [cnf transformation 25]
259. 22 <=> ! [X0] : brave(X0) [avatar definition]
260. brave(X0) <- (22) [avatar component clause 259]
396. brave(X0) | patient(X0) [resolution 122,116]
400. brave(X0) [subsumption resolution 396,120]
401. 22 [avatar split clause 400,259]
403. $false <- (22) [resolution 260,156]
406. ~22 [avatar contradiction clause 403]
407. $false [avatar sat refutation 401,406]
% SZS output end Proof for 603430983076204791958906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is rich or not calm and vice versa.
Everyone who is both curious and quiet is not tall and vice versa.
Everyone who is either happy or old is happy or quiet and vice versa.
Everyone who is either wise or creative is both not patient and not happy.
Everyone who is both not curious and not strong is not old and vice versa.
If someone is patient then someone is either funny or not brave and vice versa.
Everyone who is not patient or rich is either calm or old.
Everyone who is patient is either old or calm and vice versa.
If alice is both happy and not rich then someone is both rich and funny and vice versa.
If someone is rich or patient then someone is humble.
If mary is happy or not wise then fred is not curious or old and vice versa.
If mary is either not rich or not patient then susan is curious or quiet and vice versa.
If john is not tall then john is not wise or not tall and vice versa.
Everyone who is both funny and not calm is either not funny or not quiet.
Everyone who is both not quiet and wise is either not curious or not creative and vice versa.
If someone is both funny and not creative then someone is either curious or not tall.
Someone is both happy and wise.
Someone is either not funny or curious.
Fred is curious.
Someone is not curious.
Someone is old or tall.
Someone is both wise and patient.
Someone is either not quiet or not creative.
Mary is strong. | John is wise. | entailment | (![X]:(~kind(X)<=>(rich(X)|~calm(X))))&
(![X]:((curious(X)&quiet(X))<=>~tall(X)))&
(![X]:((happy(X)<~>old(X))<=>(happy(X)|quiet(X))))&
(![X]:((wise(X)<~>creative(X))=>(~patient(X)&~happy(X))))&
(![X]:((~curious(X)&~strong(X))<=>~old(X)))&
((?[X]:(patient(X)))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:((~patient(X)|rich(X))=>(calm(X)<~>old(X))))&
(![X]:(patient(X)<=>(old(X)<~>calm(X))))&
(((happy(alice)&~rich(alice)))<=>(?[X]:((rich(X)&funny(X)))))&
((?[X]:((rich(X)|patient(X))))=>(?[X]:(humble(X))))&
(((happy(mary)|~wise(mary)))<=>((~curious(fred)|old(fred))))&
(((~rich(mary)<~>~patient(mary)))<=>((curious(susan)|quiet(susan))))&
((~tall(john))<=>((~wise(john)|~tall(john))))&
(![X]:((funny(X)&~calm(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:((~quiet(X)&wise(X))<=>(~curious(X)<~>~creative(X))))&
((?[X]:((funny(X)&~creative(X))))=>(?[X]:((curious(X)<~>~tall(X)))))&
(?[X]:((happy(X)&wise(X))))&
(?[X]:((~funny(X)<~>curious(X))))&
(curious(fred))&
(?[X]:(~curious(X)))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((wise(X)&patient(X))))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(strong(mary)) | wise(john) | [
"p1",
"p3",
"p6",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7485005117777665184921955
% SZS output start Proof for 7485005117777665184921955
2. ! [X0] : ((quiet(X0) & curious(X0)) <=> ~tall(X0)) [input p1]
4. ! [X0] : ((wise(X0) <~> creative(X0)) => (~happy(X0) & ~patient(X0))) [input p3]
7. ! [X0] : ((rich(X0) | ~patient(X0)) => (calm(X0) <~> old(X0))) [input p6]
8. ! [X0] : (patient(X0) <=> (old(X0) <~> calm(X0))) [input p7]
13. ~tall(john) <=> (~tall(john) | ~wise(john)) [input p12]
15. ! [X0] : ((wise(X0) & ~quiet(X0)) <=> (~curious(X0) <~> ~creative(X0))) [input p14]
25. ~wise(john) [input hypothesis]
30. ! [X0] : ((~happy(X0) & ~patient(X0)) | (wise(X0) <=> creative(X0))) [ennf transformation 4]
31. ! [X0] : ((calm(X0) <~> old(X0)) | (~rich(X0) & patient(X0))) [ennf transformation 7]
35. ! [X0] : (((quiet(X0) & curious(X0)) | tall(X0)) & (~tall(X0) | (~quiet(X0) | ~curious(X0)))) [nnf transformation 2]
36. ! [X0] : (((quiet(X0) & curious(X0)) | tall(X0)) & (~tall(X0) | ~quiet(X0) | ~curious(X0))) [flattening 35]
39. ! [X0] : ((~happy(X0) & ~patient(X0)) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0)))) [nnf transformation 30]
47. ! [X0] : (((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | (~rich(X0) & patient(X0))) [nnf transformation 31]
48. ! [X0] : ((patient(X0) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) & (((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | ~patient(X0))) [nnf transformation 8]
58. (~tall(john) | (tall(john) & wise(john))) & ((~tall(john) | ~wise(john)) | tall(john)) [nnf transformation 13]
59. (~tall(john) | (tall(john) & wise(john))) & (~tall(john) | ~wise(john) | tall(john)) [flattening 58]
61. ! [X0] : (((wise(X0) & ~quiet(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | (~wise(X0) | quiet(X0)))) [nnf transformation 15]
62. ! [X0] : (((wise(X0) & ~quiet(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | ~wise(X0) | quiet(X0))) [flattening 61]
82. tall(X0) | curious(X0) [cnf transformation 36]
83. tall(X0) | quiet(X0) [cnf transformation 36]
91. ~patient(X0) | wise(X0) | ~creative(X0) [cnf transformation 39]
101. patient(X0) | calm(X0) | old(X0) [cnf transformation 47]
103. ~old(X0) | ~calm(X0) | patient(X0) [cnf transformation 47]
107. patient(X0) | calm(X0) | ~old(X0) [cnf transformation 48]
108. patient(X0) | old(X0) | ~calm(X0) [cnf transformation 48]
124. ~tall(john) | wise(john) [cnf transformation 59]
131. ~quiet(X0) | ~curious(X0) | creative(X0) [cnf transformation 62]
148. ~wise(john) [cnf transformation 25]
178. patient(X0) | old(X0) [subsumption resolution 108,101]
179. patient(X0) | ~old(X0) [subsumption resolution 107,103]
180. patient(X0) [subsumption resolution 179,178]
243. 19 <=> wise(john) [avatar definition]
244. ~wise(john) <- (~19) [avatar component clause 243]
247. 20 <=> tall(john) [avatar definition]
249. ~tall(john) <- (~20) [avatar component clause 247]
250. 19 | ~20 [avatar split clause 124,247,243]
296. ~19 [avatar split clause 148,243]
297. curious(john) <- (~20) [resolution 82,249]
298. quiet(john) <- (~20) [resolution 83,249]
353. ~creative(X1) | wise(X1) [resolution 91,180]
422. ~curious(john) | creative(john) <- (~20) [resolution 131,298]
433. creative(john) <- (~20) [subsumption resolution 422,297]
502. wise(john) <- (~20) [resolution 353,433]
505. $false <- (~19, ~20) [subsumption resolution 502,244]
506. 19 | 20 [avatar contradiction clause 505]
507. $false [avatar sat refutation 250,296,506]
% SZS output end Proof for 7485005117777665184921955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or calm is rich or not calm.
Everyone who is not calm or generous is either not happy or kind and vice versa.
If someone is humble then paul is either not wise or calm.
Everyone who is not brave or happy is not happy and vice versa.
If someone is both not strong and not brave then susan is not patient and vice versa.
If someone is not strong or calm then someone is not kind and vice versa.
Everyone who is both not humble and funny is both not brave and calm.
Everyone who is curious or strong is curious and vice versa.
If fred is both funny and not rich then paul is funny and vice versa.
If someone is generous or not kind then susan is both not strong and not quiet and vice versa.
Everyone who is not curious is happy or not kind.
If alice is not quiet or humble then someone is either not wise or not curious and vice versa.
Everyone who is both not kind and not old is not rich or brave and vice versa.
If someone is either not quiet or tall then someone is either not calm or not rich and vice versa.
If someone is either rich or not funny then someone is both brave and generous.
Everyone who is not old or happy is humble or not happy and vice versa.
Alice is not brave.
Someone is both not wise and rich.
Someone is brave or generous.
Someone is quiet.
Someone is both patient and calm.
Someone is calm or patient.
Alice is both wise and not humble.
Paul is tall or not generous. | Susan is not funny. | neutral | (![X]:((~quiet(X)|calm(X))=>(rich(X)|~calm(X))))&
(![X]:((~calm(X)|generous(X))<=>(~happy(X)<~>kind(X))))&
((?[X]:(humble(X)))=>((~wise(paul)<~>calm(paul))))&
(![X]:((~brave(X)|happy(X))<=>~happy(X)))&
((?[X]:((~strong(X)&~brave(X))))<=>(~patient(susan)))&
((?[X]:((~strong(X)|calm(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)&funny(X))=>(~brave(X)&calm(X))))&
(![X]:((curious(X)|strong(X))<=>curious(X)))&
(((funny(fred)&~rich(fred)))<=>(funny(paul)))&
((?[X]:((generous(X)|~kind(X))))<=>((~strong(susan)&~quiet(susan))))&
(![X]:(~curious(X)=>(happy(X)|~kind(X))))&
(((~quiet(alice)|humble(alice)))<=>(?[X]:((~wise(X)<~>~curious(X)))))&
(![X]:((~kind(X)&~old(X))<=>(~rich(X)|brave(X))))&
((?[X]:((~quiet(X)<~>tall(X))))<=>(?[X]:((~calm(X)<~>~rich(X)))))&
((?[X]:((rich(X)<~>~funny(X))))=>(?[X]:((brave(X)&generous(X)))))&
(![X]:((~old(X)|happy(X))<=>(humble(X)|~happy(X))))&
(~brave(alice))&
(?[X]:((~wise(X)&rich(X))))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:(quiet(X)))&
(?[X]:((patient(X)&calm(X))))&
(?[X]:((calm(X)|patient(X))))&
((wise(alice)&~humble(alice)))&
((tall(paul)|~generous(paul))) | ~funny(susan) | [] | null | 0 |
If someone is not strong then someone is both happy and creative.
If mary is not humble or funny then john is curious and vice versa.
If paul is strong or not funny then someone is either funny or creative and vice versa.
Everyone who is either not funny or not generous is kind or not funny and vice versa.
If susan is both not strong and not quiet then someone is both old and generous and vice versa.
If someone is quiet or not quiet then someone is either kind or generous.
Everyone who is tall is not calm or humble.
If alice is not quiet then someone is either not wise or not funny.
If someone is either kind or not curious then john is both not brave and quiet.
Everyone who is either generous or wise is not tall or not happy.
Everyone who is both not wise and not kind is not humble and vice versa.
If susan is wise then someone is either patient or generous.
Everyone who is not quiet is not funny or not brave and vice versa.
Everyone who is not patient or not tall is not kind or kind and vice versa.
Everyone who is rich or not happy is not generous or happy and vice versa.
Everyone who is both not quiet and not calm is generous or humble.
Mary is either brave or strong.
Someone is not creative.
Alice is curious or not tall.
Someone is not quiet or not curious.
Lucy is both rich and funny.
Someone is humble.
Alice is both not wise and not creative. | Mary is not humble. | neutral | ((?[X]:(~strong(X)))=>(?[X]:((happy(X)&creative(X)))))&
(((~humble(mary)|funny(mary)))<=>(curious(john)))&
(((strong(paul)|~funny(paul)))<=>(?[X]:((funny(X)<~>creative(X)))))&
(![X]:((~funny(X)<~>~generous(X))<=>(kind(X)|~funny(X))))&
(((~strong(susan)&~quiet(susan)))<=>(?[X]:((old(X)&generous(X)))))&
((?[X]:((quiet(X)|~quiet(X))))=>(?[X]:((kind(X)<~>generous(X)))))&
(![X]:(tall(X)=>(~calm(X)|humble(X))))&
((~quiet(alice))=>(?[X]:((~wise(X)<~>~funny(X)))))&
((?[X]:((kind(X)<~>~curious(X))))=>((~brave(john)&quiet(john))))&
(![X]:((generous(X)<~>wise(X))=>(~tall(X)|~happy(X))))&
(![X]:((~wise(X)&~kind(X))<=>~humble(X)))&
((wise(susan))=>(?[X]:((patient(X)<~>generous(X)))))&
(![X]:(~quiet(X)<=>(~funny(X)|~brave(X))))&
(![X]:((~patient(X)|~tall(X))<=>(~kind(X)|kind(X))))&
(![X]:((rich(X)|~happy(X))<=>(~generous(X)|happy(X))))&
(![X]:((~quiet(X)&~calm(X))=>(generous(X)|humble(X))))&
((brave(mary)<~>strong(mary)))&
(?[X]:(~creative(X)))&
((curious(alice)|~tall(alice)))&
(?[X]:((~quiet(X)|~curious(X))))&
((rich(lucy)&funny(lucy)))&
(?[X]:(humble(X)))&
((~wise(alice)&~creative(alice))) | ~humble(mary) | [] | null | 0 |
If someone is either humble or not tall then fred is either not creative or wise. Everyone who is not generous or not quiet is not generous. If susan is either not happy or calm then lucy is not tall or kind. If someone is either not rich or calm then susan is not kind. Everyone who is humble or not patient is happy or curious. Everyone who is not kind or curious is humble. Everyone who is calm is either not old or not tall. If someone is either calm or creative then paul is both generous and not generous and vice versa. Everyone who is both calm and not kind is either not funny or not humble and vice versa. If lucy is not quiet or not funny then lucy is either rich or strong and vice versa. If john is not creative then someone is old or not kind. If someone is humble or not curious then someone is happy and vice versa. If paul is patient then susan is either not patient or funny and vice versa. Everyone who is curious is not curious. If lucy is not strong or not tall then someone is not creative. Someone is either strong or creative. Fred is either funny or not wise. Mary is strong or not tall. Fred is patient. Susan is both rich and generous. Paul is both not funny and not brave. Alice is not happy or curious. John is either not happy or not wise. | Alice is not happy. | entailment | ((?[X]:((humble(X)<~>~tall(X))))=>((~creative(fred)<~>wise(fred))))&
(![X]:((~generous(X)|~quiet(X))=>~generous(X)))&
(((~happy(susan)<~>calm(susan)))=>((~tall(lucy)|kind(lucy))))&
((?[X]:((~rich(X)<~>calm(X))))=>(~kind(susan)))&
(![X]:((humble(X)|~patient(X))=>(happy(X)|curious(X))))&
(![X]:((~kind(X)|curious(X))=>humble(X)))&
(![X]:(calm(X)=>(~old(X)<~>~tall(X))))&
((?[X]:((calm(X)<~>creative(X))))<=>((generous(paul)&~generous(paul))))&
(![X]:((calm(X)&~kind(X))<=>(~funny(X)<~>~humble(X))))&
(((~quiet(lucy)|~funny(lucy)))<=>((rich(lucy)<~>strong(lucy))))&
((~creative(john))=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((humble(X)|~curious(X))))<=>(?[X]:(happy(X))))&
((patient(paul))<=>((~patient(susan)<~>funny(susan))))&
(![X]:(curious(X)=>~curious(X)))&
(((~strong(lucy)|~tall(lucy)))=>(?[X]:(~creative(X))))&
(?[X]:((strong(X)<~>creative(X))))&
((funny(fred)<~>~wise(fred)))&
((strong(mary)|~tall(mary)))&
(patient(fred))&
((rich(susan)&generous(susan)))&
((~funny(paul)&~brave(paul)))&
((~happy(alice)|curious(alice)))&
((~happy(john)<~>~wise(john))) | ~happy(alice) | [
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2189520340429199186911641
% SZS output start Proof for 2189520340429199186911641
14. ! [X0] : (curious(X0) => ~curious(X0)) [input p13]
22. curious(alice) | ~happy(alice) [input p21]
24. happy(alice) [input hypothesis]
37. ! [X0] : (~curious(X0) | ~curious(X0)) [ennf transformation 14]
109. ~curious(X0) | ~curious(X0) [cnf transformation 37]
121. curious(alice) | ~happy(alice) [cnf transformation 22]
124. happy(alice) [cnf transformation 24]
125. ~curious(X0) [duplicate literal removal 109]
284. ~happy(alice) [subsumption resolution 121,125]
295. $false [subsumption resolution 124,284]
% SZS output end Proof for 2189520340429199186911641
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and happy then someone is brave or not strong and vice versa.
If someone is not old then lucy is either quiet or not generous.
Everyone who is both tall and not funny is either rich or not creative and vice versa.
If someone is both not generous and not funny then someone is both not patient and not quiet.
If someone is not calm then someone is tall.
Everyone who is either wise or calm is not calm or patient and vice versa.
Everyone who is not kind or happy is both not humble and happy.
Everyone who is kind is humble and vice versa.
Everyone who is both not wise and not patient is either not happy or not quiet.
Everyone who is strong or not quiet is not old.
If fred is both not strong and curious then someone is not humble or kind and vice versa.
Everyone who is either old or not kind is both funny and not happy and vice versa.
Everyone who is not happy is curious or not wise and vice versa.
Everyone who is both calm and funny is quiet or not calm and vice versa.
Everyone who is both not funny and calm is generous or not happy.
Susan is not curious.
Someone is not humble or not brave.
Someone is either patient or humble.
Someone is either not happy or creative.
Someone is either happy or calm.
Someone is rich.
Someone is not kind or strong.
Someone is not wise or not quiet. | Fred is happy. | contradiction | ((?[X]:((wise(X)&happy(X))))<=>(?[X]:((brave(X)|~strong(X)))))&
((?[X]:(~old(X)))=>((quiet(lucy)<~>~generous(lucy))))&
(![X]:((tall(X)&~funny(X))<=>(rich(X)<~>~creative(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:((~patient(X)&~quiet(X)))))&
((?[X]:(~calm(X)))=>(?[X]:(tall(X))))&
(![X]:((wise(X)<~>calm(X))<=>(~calm(X)|patient(X))))&
(![X]:((~kind(X)|happy(X))=>(~humble(X)&happy(X))))&
(![X]:(kind(X)<=>humble(X)))&
(![X]:((~wise(X)&~patient(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((strong(X)|~quiet(X))=>~old(X)))&
(((~strong(fred)&curious(fred)))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((old(X)<~>~kind(X))<=>(funny(X)&~happy(X))))&
(![X]:(~happy(X)<=>(curious(X)|~wise(X))))&
(![X]:((calm(X)&funny(X))<=>(quiet(X)|~calm(X))))&
(![X]:((~funny(X)&calm(X))=>(generous(X)|~happy(X))))&
(~curious(susan))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:((~happy(X)<~>creative(X))))&
(?[X]:((happy(X)<~>calm(X))))&
(?[X]:(rich(X)))&
(?[X]:((~kind(X)|strong(X))))&
(?[X]:((~wise(X)|~quiet(X)))) | happy(fred) | [
"p6",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6644265671402454707501751
% SZS output start Proof for 6644265671402454707501751
7. ! [X0] : ((happy(X0) | ~kind(X0)) => (happy(X0) & ~humble(X0))) [input p6]
11. (curious(fred) & ~strong(fred)) <=> ? [X0] : (kind(X0) | ~humble(X0)) [input p10]
13. ! [X0] : (~happy(X0) <=> (~wise(X0) | curious(X0))) [input p12]
24. happy(fred) [input hypothesis]
31. ! [X0] : ((happy(X0) & ~humble(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 7]
55. ((curious(fred) & ~strong(fred)) | ! [X0] : (~kind(X0) & humble(X0))) & (? [X0] : (kind(X0) | ~humble(X0)) | (~curious(fred) | strong(fred))) [nnf transformation 11]
56. ((curious(fred) & ~strong(fred)) | ! [X0] : (~kind(X0) & humble(X0))) & (? [X0] : (kind(X0) | ~humble(X0)) | ~curious(fred) | strong(fred)) [flattening 55]
57. ((curious(fred) & ~strong(fred)) | ! [X0] : (~kind(X0) & humble(X0))) & (? [X1] : (kind(X1) | ~humble(X1)) | ~curious(fred) | strong(fred)) [rectify 56]
58. ? [X1] : (kind(X1) | ~humble(X1)) => (kind(sK4) | ~humble(sK4)) [choice axiom]
59. ((curious(fred) & ~strong(fred)) | ! [X0] : (~kind(X0) & humble(X0))) & ((kind(sK4) | ~humble(sK4)) | ~curious(fred) | strong(fred)) [skolemisation 57,58]
62. ! [X0] : ((~happy(X0) | (wise(X0) & ~curious(X0))) & ((~wise(X0) | curious(X0)) | happy(X0))) [nnf transformation 13]
63. ! [X0] : ((~happy(X0) | (wise(X0) & ~curious(X0))) & (~wise(X0) | curious(X0) | happy(X0))) [flattening 62]
105. ~humble(X0) | kind(X0) [cnf transformation 31]
118. curious(fred) | humble(X0) [cnf transformation 59]
119. curious(fred) | ~kind(X0) [cnf transformation 59]
127. ~curious(X0) | ~happy(X0) [cnf transformation 63]
146. happy(fred) [cnf transformation 24]
217. 16 <=> ! [X0] : ~kind(X0) [avatar definition]
218. ~kind(X0) <- (16) [avatar component clause 217]
220. 17 <=> curious(fred) [avatar definition]
222. curious(fred) <- (17) [avatar component clause 220]
223. 16 | 17 [avatar split clause 119,220,217]
225. 18 <=> ! [X0] : humble(X0) [avatar definition]
226. humble(X0) <- (18) [avatar component clause 225]
227. 18 | 17 [avatar split clause 118,220,225]
299. ~happy(fred) <- (17) [resolution 127,222]
300. $false <- (17) [subsumption resolution 299,146]
301. ~17 [avatar contradiction clause 300]
305. kind(X1) <- (18) [resolution 226,105]
309. $false <- (16, 18) [subsumption resolution 305,218]
310. ~16 | ~18 [avatar contradiction clause 309]
311. $false [avatar sat refutation 223,227,301,310]
% SZS output end Proof for 6644265671402454707501751
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or kind is both not rich and curious and vice versa. If alice is generous then fred is both not generous and not wise. Everyone who is either creative or brave is rich or not rich and vice versa. Everyone who is both not tall and wise is quiet and vice versa. If someone is either rich or humble then someone is both not tall and calm. Everyone who is calm is not brave. If susan is both old and patient then someone is rich. Everyone who is tall is either calm or kind. If john is wise or calm then someone is not tall and vice versa. Everyone who is creative is either not generous or kind. If lucy is tall or not generous then someone is either curious or not kind. Everyone who is not curious or not wise is not rich and vice versa. If someone is not rich then mary is both not calm and happy. If someone is not strong then alice is not wise or tall. If lucy is brave or not patient then mary is not tall or not kind and vice versa. Everyone who is both not generous and not wise is both funny and not rich and vice versa. John is not old or not quiet. Fred is both funny and kind. Alice is both not wise and strong. Someone is quiet or not quiet. Someone is not old or generous. Someone is creative or not happy. Susan is both not old and not brave. Lucy is either quiet or not strong. | Susan is brave. | contradiction | (![X]:((~kind(X)|kind(X))<=>(~rich(X)&curious(X))))&
((generous(alice))=>((~generous(fred)&~wise(fred))))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)|~rich(X))))&
(![X]:((~tall(X)&wise(X))<=>quiet(X)))&
((?[X]:((rich(X)<~>humble(X))))=>(?[X]:((~tall(X)&calm(X)))))&
(![X]:(calm(X)=>~brave(X)))&
(((old(susan)&patient(susan)))=>(?[X]:(rich(X))))&
(![X]:(tall(X)=>(calm(X)<~>kind(X))))&
(((wise(john)|calm(john)))<=>(?[X]:(~tall(X))))&
(![X]:(creative(X)=>(~generous(X)<~>kind(X))))&
(((tall(lucy)|~generous(lucy)))=>(?[X]:((curious(X)<~>~kind(X)))))&
(![X]:((~curious(X)|~wise(X))<=>~rich(X)))&
((?[X]:(~rich(X)))=>((~calm(mary)&happy(mary))))&
((?[X]:(~strong(X)))=>((~wise(alice)|tall(alice))))&
(((brave(lucy)|~patient(lucy)))<=>((~tall(mary)|~kind(mary))))&
(![X]:((~generous(X)&~wise(X))<=>(funny(X)&~rich(X))))&
((~old(john)|~quiet(john)))&
((funny(fred)&kind(fred)))&
((~wise(alice)&strong(alice)))&
(?[X]:((quiet(X)|~quiet(X))))&
(?[X]:((~old(X)|generous(X))))&
(?[X]:((creative(X)|~happy(X))))&
((~old(susan)&~brave(susan)))&
((quiet(lucy)<~>~strong(lucy))) | brave(susan) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3655742273375887939496541
% SZS output start Proof for 3655742273375887939496541
23. ~brave(susan) & ~old(susan) [input p22]
25. brave(susan) [input hypothesis]
30. ~brave(susan) [pure predicate removal 23]
123. ~brave(susan) [cnf transformation 30]
126. brave(susan) [cnf transformation 25]
239. $false [subsumption resolution 126,123]
% SZS output end Proof for 3655742273375887939496541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not tall then someone is both rich and not old and vice versa. If someone is funny then someone is both not curious and not patient and vice versa. If someone is either strong or kind then susan is not calm and vice versa. If john is creative then paul is both brave and curious and vice versa. If someone is either creative or humble then lucy is either creative or calm and vice versa. If susan is kind then someone is not rich or not funny and vice versa. If alice is wise or humble then someone is both not tall and not calm. If mary is funny then john is either quiet or creative and vice versa. If mary is not tall then mary is both calm and funny. Everyone who is tall or kind is tall. Everyone who is either quiet or not strong is not humble. Everyone who is not quiet or calm is either not brave or brave and vice versa. Everyone who is both not brave and brave is not tall or curious and vice versa. If someone is both not patient and not generous then lucy is both not rich and funny. If paul is kind or not generous then alice is either not humble or wise. Everyone who is both not wise and strong is generous or not happy. Someone is either not generous or rich. Someone is rich or not happy. Paul is wise. Lucy is not quiet. Paul is both funny and wise. Someone is either funny or not happy. Someone is either quiet or not rich. Someone is not kind or curious. | Susan is curious. | contradiction | ((?[X]:((creative(X)|~tall(X))))<=>(?[X]:((rich(X)&~old(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((~curious(X)&~patient(X)))))&
((?[X]:((strong(X)<~>kind(X))))<=>(~calm(susan)))&
((creative(john))<=>((brave(paul)&curious(paul))))&
((?[X]:((creative(X)<~>humble(X))))<=>((creative(lucy)<~>calm(lucy))))&
((kind(susan))<=>(?[X]:((~rich(X)|~funny(X)))))&
(((wise(alice)|humble(alice)))=>(?[X]:((~tall(X)&~calm(X)))))&
((funny(mary))<=>((quiet(john)<~>creative(john))))&
((~tall(mary))=>((calm(mary)&funny(mary))))&
(![X]:((tall(X)|kind(X))=>tall(X)))&
(![X]:((quiet(X)<~>~strong(X))=>~humble(X)))&
(![X]:((~quiet(X)|calm(X))<=>(~brave(X)<~>brave(X))))&
(![X]:((~brave(X)&brave(X))<=>(~tall(X)|curious(X))))&
((?[X]:((~patient(X)&~generous(X))))=>((~rich(lucy)&funny(lucy))))&
(((kind(paul)|~generous(paul)))=>((~humble(alice)<~>wise(alice))))&
(![X]:((~wise(X)&strong(X))=>(generous(X)|~happy(X))))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:((rich(X)|~happy(X))))&
(wise(paul))&
(~quiet(lucy))&
((funny(paul)&wise(paul)))&
(?[X]:((funny(X)<~>~happy(X))))&
(?[X]:((quiet(X)<~>~rich(X))))&
(?[X]:((~kind(X)|curious(X)))) | curious(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7677432599324161626555893
% SZS output start Proof for 7677432599324161626555893
13. ! [X0] : ((brave(X0) & ~brave(X0)) <=> (curious(X0) | ~tall(X0))) [input p12]
25. curious(susan) [input hypothesis]
66. ! [X0] : (((brave(X0) & ~brave(X0)) | (~curious(X0) & tall(X0))) & ((curious(X0) | ~tall(X0)) | (~brave(X0) | brave(X0)))) [nnf transformation 13]
67. ! [X0] : (((brave(X0) & ~brave(X0)) | (~curious(X0) & tall(X0))) & (curious(X0) | ~tall(X0) | ~brave(X0) | brave(X0))) [flattening 66]
130. ~brave(X0) | ~curious(X0) [cnf transformation 67]
132. brave(X0) | ~curious(X0) [cnf transformation 67]
152. curious(susan) [cnf transformation 25]
337. ~curious(X0) [subsumption resolution 130,132]
405. $false [subsumption resolution 152,337]
% SZS output end Proof for 7677432599324161626555893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or tall then susan is generous or not quiet.
Everyone who is not wise is not patient or tall.
Everyone who is not quiet or humble is either generous or not quiet and vice versa.
If someone is both not old and not creative then someone is both not happy and brave and vice versa.
Everyone who is tall or happy is not kind.
Everyone who is not old or curious is either funny or generous.
If someone is either not calm or not humble then alice is strong or not kind.
If someone is creative or not strong then someone is not wise.
If alice is both quiet and not creative then susan is both not curious and not creative and vice versa.
If lucy is both curious and not generous then someone is either not generous or not old and vice versa.
Everyone who is both kind and old is either not funny or strong and vice versa.
Everyone who is either brave or rich is either not old or humble and vice versa.
Everyone who is either not happy or patient is generous or not happy and vice versa.
Everyone who is not strong is happy or not rich and vice versa.
Everyone who is both not calm and not wise is both patient and not wise.
Everyone who is not generous is not old.
Someone is brave or old.
Paul is either old or not tall.
Susan is both not humble and not happy.
Someone is tall or generous.
Susan is brave.
John is both not strong and rich.
Someone is happy or not patient. | Susan is not patient. | entailment | ((?[X]:((~wise(X)|tall(X))))=>((generous(susan)|~quiet(susan))))&
(![X]:(~wise(X)=>(~patient(X)|tall(X))))&
(![X]:((~quiet(X)|humble(X))<=>(generous(X)<~>~quiet(X))))&
((?[X]:((~old(X)&~creative(X))))<=>(?[X]:((~happy(X)&brave(X)))))&
(![X]:((tall(X)|happy(X))=>~kind(X)))&
(![X]:((~old(X)|curious(X))=>(funny(X)<~>generous(X))))&
((?[X]:((~calm(X)<~>~humble(X))))=>((strong(alice)|~kind(alice))))&
((?[X]:((creative(X)|~strong(X))))=>(?[X]:(~wise(X))))&
(((quiet(alice)&~creative(alice)))<=>((~curious(susan)&~creative(susan))))&
(((curious(lucy)&~generous(lucy)))<=>(?[X]:((~generous(X)<~>~old(X)))))&
(![X]:((kind(X)&old(X))<=>(~funny(X)<~>strong(X))))&
(![X]:((brave(X)<~>rich(X))<=>(~old(X)<~>humble(X))))&
(![X]:((~happy(X)<~>patient(X))<=>(generous(X)|~happy(X))))&
(![X]:(~strong(X)<=>(happy(X)|~rich(X))))&
(![X]:((~calm(X)&~wise(X))=>(patient(X)&~wise(X))))&
(![X]:(~generous(X)=>~old(X)))&
(?[X]:((brave(X)|old(X))))&
((old(paul)<~>~tall(paul)))&
((~humble(susan)&~happy(susan)))&
(?[X]:((tall(X)|generous(X))))&
(brave(susan))&
((~strong(john)&rich(john)))&
(?[X]:((happy(X)|~patient(X)))) | ~patient(susan) | [
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7592729315997760123843453
% SZS output start Proof for 7592729315997760123843453
13. ! [X0] : ((~happy(X0) <~> patient(X0)) <=> (~happy(X0) | generous(X0))) [input p12]
19. ~happy(susan) & ~humble(susan) [input p18]
24. patient(susan) [input hypothesis]
61. ! [X0] : ((((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | (happy(X0) & ~generous(X0))) & ((~happy(X0) | generous(X0)) | ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))))) [nnf transformation 13]
62. ! [X0] : ((((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | (happy(X0) & ~generous(X0))) & (~happy(X0) | generous(X0) | ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))))) [flattening 61]
124. ~patient(X0) | happy(X0) | happy(X0) [cnf transformation 62]
135. ~happy(susan) [cnf transformation 19]
141. patient(susan) [cnf transformation 24]
143. ~patient(X0) | happy(X0) [duplicate literal removal 124]
294. happy(susan) [resolution 143,141]
295. $false [subsumption resolution 294,135]
% SZS output end Proof for 7592729315997760123843453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or funny is not wise and vice versa.
Everyone who is not old or curious is either strong or not happy and vice versa.
Everyone who is either not calm or not patient is creative or wise and vice versa.
Everyone who is not calm is both not old and generous.
Everyone who is not old is both kind and old.
Everyone who is both not strong and not kind is not brave.
If someone is both brave and calm then someone is curious and vice versa.
Everyone who is not creative is either not funny or humble.
Everyone who is patient or quiet is either happy or humble.
If someone is not old or not patient then someone is either not curious or not strong and vice versa.
If john is calm then someone is curious or not wise.
Everyone who is quiet is either rich or not happy and vice versa.
Everyone who is both not generous and rich is both not rich and kind.
If someone is both calm and not generous then someone is not funny and vice versa.
Everyone who is both not old and old is funny or rich and vice versa.
If someone is not calm or tall then someone is either not rich or tall.
Someone is both wise and not creative.
Someone is kind or not kind.
Someone is either humble or creative.
John is both not creative and patient.
John is either funny or patient.
Someone is strong or funny. | John is calm. | entailment | (![X]:((~kind(X)|funny(X))<=>~wise(X)))&
(![X]:((~old(X)|curious(X))<=>(strong(X)<~>~happy(X))))&
(![X]:((~calm(X)<~>~patient(X))<=>(creative(X)|wise(X))))&
(![X]:(~calm(X)=>(~old(X)&generous(X))))&
(![X]:(~old(X)=>(kind(X)&old(X))))&
(![X]:((~strong(X)&~kind(X))=>~brave(X)))&
((?[X]:((brave(X)&calm(X))))<=>(?[X]:(curious(X))))&
(![X]:(~creative(X)=>(~funny(X)<~>humble(X))))&
(![X]:((patient(X)|quiet(X))=>(happy(X)<~>humble(X))))&
((?[X]:((~old(X)|~patient(X))))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
((calm(john))=>(?[X]:((curious(X)|~wise(X)))))&
(![X]:(quiet(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((~generous(X)&rich(X))=>(~rich(X)&kind(X))))&
((?[X]:((calm(X)&~generous(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)&old(X))<=>(funny(X)|rich(X))))&
((?[X]:((~calm(X)|tall(X))))=>(?[X]:((~rich(X)<~>tall(X)))))&
(?[X]:((wise(X)&~creative(X))))&
(?[X]:((kind(X)|~kind(X))))&
(?[X]:((humble(X)<~>creative(X))))&
((~creative(john)&patient(john)))&
((funny(john)<~>patient(john)))&
(?[X]:((strong(X)|funny(X)))) | calm(john) | [
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 911707724735513563445629
% SZS output start Proof for 911707724735513563445629
4. ! [X0] : (~calm(X0) => (generous(X0) & ~old(X0))) [input p3]
5. ! [X0] : (~old(X0) => (old(X0) & kind(X0))) [input p4]
23. ~calm(john) [input hypothesis]
29. ! [X0] : ((generous(X0) & ~old(X0)) | calm(X0)) [ennf transformation 4]
30. ! [X0] : ((old(X0) & kind(X0)) | old(X0)) [ennf transformation 5]
97. ~old(X0) | calm(X0) [cnf transformation 29]
100. old(X0) | old(X0) [cnf transformation 30]
144. ~calm(john) [cnf transformation 23]
146. old(X0) [duplicate literal removal 100]
196. 12 <=> calm(john) [avatar definition]
198. ~calm(john) <- (~12) [avatar component clause 196]
243. 22 <=> ! [X1] : calm(X1) [avatar definition]
244. calm(X1) <- (22) [avatar component clause 243]
257. ~12 [avatar split clause 144,196]
264. calm(X0) [resolution 97,146]
265. 22 [avatar split clause 264,243]
266. $false <- (~12, 22) [resolution 244,198]
267. 12 | ~22 [avatar contradiction clause 266]
268. $false [avatar sat refutation 257,265,267]
% SZS output end Proof for 911707724735513563445629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or curious is funny.
If john is both strong and not quiet then mary is not humble.
If paul is both not old and old then someone is kind or not brave and vice versa.
If lucy is happy or generous then someone is not creative or not generous.
If someone is not quiet then john is both not funny and not wise and vice versa.
If paul is not happy then mary is calm.
If fred is not calm or quiet then john is not quiet.
If mary is creative or brave then alice is not calm and vice versa.
If susan is not kind or quiet then mary is both funny and not rich.
If someone is both strong and curious then someone is not old.
If someone is both not rich and patient then someone is calm.
If someone is either not old or not funny then fred is either kind or not rich.
If someone is both not kind and not strong then someone is either funny or not humble and vice versa.
Everyone who is calm is both curious and calm and vice versa.
If mary is not patient or not calm then john is either happy or not strong.
If john is not humble or not old then lucy is not brave or not patient and vice versa.
Someone is both not quiet and not wise.
Susan is both not humble and quiet.
Paul is not strong.
Someone is both not patient and happy.
Fred is either not happy or not rich.
Someone is not happy or happy.
Someone is either brave or kind.
Mary is either brave or not generous. | John is not funny. | entailment | (![X]:((old(X)|curious(X))=>funny(X)))&
(((strong(john)&~quiet(john)))=>(~humble(mary)))&
(((~old(paul)&old(paul)))<=>(?[X]:((kind(X)|~brave(X)))))&
(((happy(lucy)|generous(lucy)))=>(?[X]:((~creative(X)|~generous(X)))))&
((?[X]:(~quiet(X)))<=>((~funny(john)&~wise(john))))&
((~happy(paul))=>(calm(mary)))&
(((~calm(fred)|quiet(fred)))=>(~quiet(john)))&
(((creative(mary)|brave(mary)))<=>(~calm(alice)))&
(((~kind(susan)|quiet(susan)))=>((funny(mary)&~rich(mary))))&
((?[X]:((strong(X)&curious(X))))=>(?[X]:(~old(X))))&
((?[X]:((~rich(X)&patient(X))))=>(?[X]:(calm(X))))&
((?[X]:((~old(X)<~>~funny(X))))=>((kind(fred)<~>~rich(fred))))&
((?[X]:((~kind(X)&~strong(X))))<=>(?[X]:((funny(X)<~>~humble(X)))))&
(![X]:(calm(X)<=>(curious(X)&calm(X))))&
(((~patient(mary)|~calm(mary)))=>((happy(john)<~>~strong(john))))&
(((~humble(john)|~old(john)))<=>((~brave(lucy)|~patient(lucy))))&
(?[X]:((~quiet(X)&~wise(X))))&
((~humble(susan)&quiet(susan)))&
(~strong(paul))&
(?[X]:((~patient(X)&happy(X))))&
((~happy(fred)<~>~rich(fred)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((brave(mary)<~>~generous(mary))) | ~funny(john) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6995530208594998173367700
% SZS output start Proof for 6995530208594998173367700
5. ? [X0] : ~quiet(X0) <=> (~wise(john) & ~funny(john)) [input p4]
7. (quiet(fred) | ~calm(fred)) => ~quiet(john) [input p6]
25. funny(john) [input hypothesis]
34. ~quiet(john) | (~quiet(fred) & calm(fred)) [ennf transformation 7]
47. (? [X0] : ~quiet(X0) | (wise(john) | funny(john))) & ((~wise(john) & ~funny(john)) | ! [X0] : quiet(X0)) [nnf transformation 5]
48. (? [X0] : ~quiet(X0) | wise(john) | funny(john)) & ((~wise(john) & ~funny(john)) | ! [X0] : quiet(X0)) [flattening 47]
49. (? [X0] : ~quiet(X0) | wise(john) | funny(john)) & ((~wise(john) & ~funny(john)) | ! [X1] : quiet(X1)) [rectify 48]
50. ? [X0] : ~quiet(X0) => ~quiet(sK2) [choice axiom]
51. (~quiet(sK2) | wise(john) | funny(john)) & ((~wise(john) & ~funny(john)) | ! [X1] : quiet(X1)) [skolemisation 49,50]
92. ~funny(john) | quiet(X1) [cnf transformation 51]
97. ~quiet(john) | ~quiet(fred) [cnf transformation 34]
142. funny(john) [cnf transformation 25]
148. 2 <=> quiet(john) [avatar definition]
149. ~quiet(john) <- (~2) [avatar component clause 148]
189. 11 <=> funny(john) [avatar definition]
202. 14 <=> ! [X1] : quiet(X1) [avatar definition]
203. quiet(X1) <- (14) [avatar component clause 202]
205. 14 | ~11 [avatar split clause 92,189,202]
216. 17 <=> quiet(fred) [avatar definition]
218. ~quiet(fred) <- (~17) [avatar component clause 216]
219. ~17 | ~2 [avatar split clause 97,148,216]
375. 11 [avatar split clause 142,189]
376. $false <- (~2, 14) [subsumption resolution 149,203]
377. 2 | ~14 [avatar contradiction clause 376]
378. $false <- (14, ~17) [subsumption resolution 218,203]
379. ~14 | 17 [avatar contradiction clause 378]
380. $false [avatar sat refutation 205,219,375,377,379]
% SZS output end Proof for 6995530208594998173367700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both humble and not creative then paul is either not rich or happy and vice versa. If someone is kind then john is not strong or not quiet. Everyone who is quiet is either old or not funny. If someone is both quiet and not kind then paul is either not wise or patient and vice versa. Everyone who is either generous or patient is strong or old. If mary is either quiet or funny then someone is not strong and vice versa. If someone is both not rich and not happy then paul is either curious or kind and vice versa. If someone is not wise then fred is not quiet and vice versa. If someone is both not tall and rich then alice is not humble or humble and vice versa. Everyone who is creative or not quiet is not rich. If someone is either tall or strong then paul is not strong and vice versa. Everyone who is both kind and rich is not strong. Everyone who is both old and curious is both wise and not strong. If someone is both not generous and humble then someone is funny and vice versa. If someone is not curious or old then someone is not funny or happy and vice versa. Everyone who is either funny or tall is both tall and not creative and vice versa. Someone is not tall or not kind. Mary is both not old and not generous. Someone is both patient and not brave. Someone is not calm or curious. John is both happy and curious. Fred is creative. Susan is generous or not generous. Lucy is both not curious and not humble. | Paul is brave. | neutral | (((humble(john)&~creative(john)))<=>((~rich(paul)<~>happy(paul))))&
((?[X]:(kind(X)))=>((~strong(john)|~quiet(john))))&
(![X]:(quiet(X)=>(old(X)<~>~funny(X))))&
((?[X]:((quiet(X)&~kind(X))))<=>((~wise(paul)<~>patient(paul))))&
(![X]:((generous(X)<~>patient(X))=>(strong(X)|old(X))))&
(((quiet(mary)<~>funny(mary)))<=>(?[X]:(~strong(X))))&
((?[X]:((~rich(X)&~happy(X))))<=>((curious(paul)<~>kind(paul))))&
((?[X]:(~wise(X)))<=>(~quiet(fred)))&
((?[X]:((~tall(X)&rich(X))))<=>((~humble(alice)|humble(alice))))&
(![X]:((creative(X)|~quiet(X))=>~rich(X)))&
((?[X]:((tall(X)<~>strong(X))))<=>(~strong(paul)))&
(![X]:((kind(X)&rich(X))=>~strong(X)))&
(![X]:((old(X)&curious(X))=>(wise(X)&~strong(X))))&
((?[X]:((~generous(X)&humble(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~curious(X)|old(X))))<=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((funny(X)<~>tall(X))<=>(tall(X)&~creative(X))))&
(?[X]:((~tall(X)|~kind(X))))&
((~old(mary)&~generous(mary)))&
(?[X]:((patient(X)&~brave(X))))&
(?[X]:((~calm(X)|curious(X))))&
((happy(john)&curious(john)))&
(creative(fred))&
((generous(susan)|~generous(susan)))&
((~curious(lucy)&~humble(lucy))) | brave(paul) | [] | null | 0 |
Everyone who is not humble is either humble or not funny.
Everyone who is curious or not curious is not wise.
Everyone who is generous or funny is not strong.
If fred is both not creative and not generous then someone is both not strong and not humble and vice versa.
Everyone who is not wise is tall or not creative and vice versa.
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
Everyone who is old or not quiet is both curious and not brave.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
If alice is curious then someone is either not humble or not creative and vice versa.
Everyone who is both creative and not creative is both not strong and strong.
Someone is happy.
Lucy is generous or not brave.
Susan is not creative.
Lucy is both funny and not wise.
Someone is calm or not quiet.
Alice is either not humble or funny. | Fred is kind. | neutral | (![X]:(~humble(X)=>(humble(X)<~>~funny(X))))&
(![X]:((curious(X)|~curious(X))=>~wise(X)))&
(![X]:((generous(X)|funny(X))=>~strong(X)))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((curious(alice))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:((creative(X)&~creative(X))=>(~strong(X)&strong(X))))&
(?[X]:(happy(X)))&
((generous(lucy)|~brave(lucy)))&
(~creative(susan))&
((funny(lucy)&~wise(lucy)))&
(?[X]:((calm(X)|~quiet(X))))&
((~humble(alice)<~>funny(alice))) | kind(fred) | [] | null | 0 |
If susan is both not patient and curious then alice is curious.
If fred is either not generous or not patient then susan is old or not rich and vice versa.
Everyone who is both strong and quiet is not tall and vice versa.
If mary is humble then someone is either not strong or not quiet.
Everyone who is not strong or not generous is not old or wise and vice versa.
Everyone who is not brave is either not tall or not creative and vice versa.
Everyone who is not humble is not generous or not curious.
Everyone who is tall or not generous is not strong or creative and vice versa.
Everyone who is not strong or not tall is rich.
If someone is either not brave or quiet then mary is both creative and not brave and vice versa.
Everyone who is wise is both not curious and not funny.
If someone is not patient then someone is funny or not rich and vice versa.
Everyone who is not happy or not patient is quiet or generous and vice versa.
If someone is old or patient then mary is not curious or not brave and vice versa.
Everyone who is brave is either strong or not strong.
Everyone who is wise is either not patient or not tall and vice versa.
Someone is both creative and calm.
Fred is curious or wise.
Someone is not funny.
Alice is patient or rich.
Someone is not brave.
Someone is not creative.
Someone is both not kind and not old. | Alice is happy. | neutral | (((~patient(susan)&curious(susan)))=>(curious(alice)))&
(((~generous(fred)<~>~patient(fred)))<=>((old(susan)|~rich(susan))))&
(![X]:((strong(X)&quiet(X))<=>~tall(X)))&
((humble(mary))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((~strong(X)|~generous(X))<=>(~old(X)|wise(X))))&
(![X]:(~brave(X)<=>(~tall(X)<~>~creative(X))))&
(![X]:(~humble(X)=>(~generous(X)|~curious(X))))&
(![X]:((tall(X)|~generous(X))<=>(~strong(X)|creative(X))))&
(![X]:((~strong(X)|~tall(X))=>rich(X)))&
((?[X]:((~brave(X)<~>quiet(X))))<=>((creative(mary)&~brave(mary))))&
(![X]:(wise(X)=>(~curious(X)&~funny(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((funny(X)|~rich(X)))))&
(![X]:((~happy(X)|~patient(X))<=>(quiet(X)|generous(X))))&
((?[X]:((old(X)|patient(X))))<=>((~curious(mary)|~brave(mary))))&
(![X]:(brave(X)=>(strong(X)<~>~strong(X))))&
(![X]:(wise(X)<=>(~patient(X)<~>~tall(X))))&
(?[X]:((creative(X)&calm(X))))&
((curious(fred)|wise(fred)))&
(?[X]:(~funny(X)))&
((patient(alice)|rich(alice)))&
(?[X]:(~brave(X)))&
(?[X]:(~creative(X)))&
(?[X]:((~kind(X)&~old(X)))) | happy(alice) | [] | null | 0 |
If fred is both kind and not calm then paul is both funny and strong.
Everyone who is both not happy and not curious is both rich and not patient.
Everyone who is humble or not tall is brave or not patient and vice versa.
Everyone who is old or not old is either strong or not humble and vice versa.
If someone is both calm and generous then john is either not wise or generous and vice versa.
If someone is not kind or kind then someone is either creative or not wise and vice versa.
Everyone who is not brave or not old is both not generous and humble.
If fred is not kind then someone is either creative or humble.
Everyone who is old or not creative is generous and vice versa.
If someone is either not strong or not generous then someone is curious and vice versa.
If paul is not strong or not funny then john is both not rich and happy and vice versa.
If someone is curious or funny then fred is both not quiet and not strong.
If lucy is both patient and generous then someone is either old or funny and vice versa.
If someone is not brave then alice is either happy or not humble.
Everyone who is either quiet or not strong is both not generous and generous.
If someone is both not calm and not humble then fred is both strong and creative and vice versa.
Someone is both old and not tall.
Alice is not wise.
Someone is wise or not brave.
Paul is not quiet or wise. | Fred is creative. | contradiction | (((kind(fred)&~calm(fred)))=>((funny(paul)&strong(paul))))&
(![X]:((~happy(X)&~curious(X))=>(rich(X)&~patient(X))))&
(![X]:((humble(X)|~tall(X))<=>(brave(X)|~patient(X))))&
(![X]:((old(X)|~old(X))<=>(strong(X)<~>~humble(X))))&
((?[X]:((calm(X)&generous(X))))<=>((~wise(john)<~>generous(john))))&
((?[X]:((~kind(X)|kind(X))))<=>(?[X]:((creative(X)<~>~wise(X)))))&
(![X]:((~brave(X)|~old(X))=>(~generous(X)&humble(X))))&
((~kind(fred))=>(?[X]:((creative(X)<~>humble(X)))))&
(![X]:((old(X)|~creative(X))<=>generous(X)))&
((?[X]:((~strong(X)<~>~generous(X))))<=>(?[X]:(curious(X))))&
(((~strong(paul)|~funny(paul)))<=>((~rich(john)&happy(john))))&
((?[X]:((curious(X)|funny(X))))=>((~quiet(fred)&~strong(fred))))&
(((patient(lucy)&generous(lucy)))<=>(?[X]:((old(X)<~>funny(X)))))&
((?[X]:(~brave(X)))=>((happy(alice)<~>~humble(alice))))&
(![X]:((quiet(X)<~>~strong(X))=>(~generous(X)&generous(X))))&
((?[X]:((~calm(X)&~humble(X))))<=>((strong(fred)&creative(fred))))&
(?[X]:((old(X)&~tall(X))))&
(~wise(alice))&
(?[X]:((wise(X)|~brave(X))))&
((~quiet(paul)|wise(paul))) | creative(fred) | [
"p3",
"p6",
"p8",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 468958449610270674726414
% SZS output start Proof for 468958449610270674726414
4. ! [X0] : ((~old(X0) | old(X0)) <=> (strong(X0) <~> ~humble(X0))) [input p3]
7. ! [X0] : ((~old(X0) | ~brave(X0)) => (humble(X0) & ~generous(X0))) [input p6]
9. ! [X0] : ((~creative(X0) | old(X0)) <=> generous(X0)) [input p8]
10. ? [X0] : (~strong(X0) <~> ~generous(X0)) <=> ? [X0] : curious(X0) [input p9]
12. ? [X0] : (funny(X0) | curious(X0)) => (~strong(fred) & ~quiet(fred)) [input p11]
15. ! [X0] : ((quiet(X0) <~> ~strong(X0)) => (generous(X0) & ~generous(X0))) [input p14]
16. ? [X0] : (~humble(X0) & ~calm(X0)) <=> (creative(fred) & strong(fred)) [input p15]
21. creative(fred) [input hypothesis]
23. ? [X0] : (~strong(X0) <~> ~generous(X0)) <=> ? [X1] : curious(X1) [rectify 10]
28. ! [X0] : ((humble(X0) & ~generous(X0)) | (old(X0) & brave(X0))) [ennf transformation 7]
30. (~strong(fred) & ~quiet(fred)) | ! [X0] : (~funny(X0) & ~curious(X0)) [ennf transformation 12]
32. ! [X0] : ((generous(X0) & ~generous(X0)) | (quiet(X0) <=> ~strong(X0))) [ennf transformation 15]
35. ! [X0] : (((~old(X0) | old(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (old(X0) & ~old(X0)))) [nnf transformation 4]
36. ! [X0] : ((~old(X0) | old(X0) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (old(X0) & ~old(X0)))) [flattening 35]
49. ! [X0] : (((~creative(X0) | old(X0)) | ~generous(X0)) & (generous(X0) | (creative(X0) & ~old(X0)))) [nnf transformation 9]
50. ! [X0] : ((~creative(X0) | old(X0) | ~generous(X0)) & (generous(X0) | (creative(X0) & ~old(X0)))) [flattening 49]
51. (? [X0] : ((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0)))) [nnf transformation 23]
52. (? [X0] : ((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : ((~strong(X3) | generous(X3)) & (~generous(X3) | strong(X3)))) [rectify 51]
53. ? [X0] : ((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) => ((generous(sK4) | strong(sK4)) & (~generous(sK4) | ~strong(sK4))) [choice axiom]
54. ? [X2] : curious(X2) => curious(sK5) [choice axiom]
55. (((generous(sK4) | strong(sK4)) & (~generous(sK4) | ~strong(sK4))) | ! [X1] : ~curious(X1)) & (curious(sK5) | ! [X3] : ((~strong(X3) | generous(X3)) & (~generous(X3) | strong(X3)))) [skolemisation 52,54,53]
64. ! [X0] : ((generous(X0) & ~generous(X0)) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) [nnf transformation 32]
65. (? [X0] : (~humble(X0) & ~calm(X0)) | (~creative(fred) | ~strong(fred))) & ((creative(fred) & strong(fred)) | ! [X0] : (humble(X0) | calm(X0))) [nnf transformation 16]
66. (? [X0] : (~humble(X0) & ~calm(X0)) | ~creative(fred) | ~strong(fred)) & ((creative(fred) & strong(fred)) | ! [X0] : (humble(X0) | calm(X0))) [flattening 65]
67. (? [X0] : (~humble(X0) & ~calm(X0)) | ~creative(fred) | ~strong(fred)) & ((creative(fred) & strong(fred)) | ! [X1] : (humble(X1) | calm(X1))) [rectify 66]
68. ? [X0] : (~humble(X0) & ~calm(X0)) => (~humble(sK7) & ~calm(sK7)) [choice axiom]
69. ((~humble(sK7) & ~calm(sK7)) | ~creative(fred) | ~strong(fred)) & ((creative(fred) & strong(fred)) | ! [X1] : (humble(X1) | calm(X1))) [skolemisation 67,68]
82. ~humble(X0) | strong(X0) | ~old(X0) [cnf transformation 36]
83. ~humble(X0) | strong(X0) | old(X0) [cnf transformation 36]
84. humble(X0) | ~strong(X0) | ~old(X0) [cnf transformation 36]
85. ~strong(X0) | humble(X0) | old(X0) [cnf transformation 36]
103. old(X0) | humble(X0) [cnf transformation 28]
106. ~old(X0) | generous(X0) [cnf transformation 50]
109. curious(sK5) | ~generous(X3) | strong(X3) [cnf transformation 55]
118. ~quiet(fred) | ~curious(X0) [cnf transformation 30]
120. ~strong(fred) | ~curious(X0) [cnf transformation 30]
131. ~generous(X0) | quiet(X0) | strong(X0) [cnf transformation 64]
133. quiet(X0) | generous(X0) | strong(X0) [cnf transformation 64]
137. ~humble(sK7) | ~creative(fred) | ~strong(fred) [cnf transformation 69]
143. creative(fred) [cnf transformation 21]
162. ~strong(X0) | humble(X0) [subsumption resolution 84,85]
163. ~humble(X0) | strong(X0) [subsumption resolution 82,83]
218. 16 <=> ! [X1] : ~curious(X1) [avatar definition]
219. ~curious(X1) <- (16) [avatar component clause 218]
234. 20 <=> curious(sK5) [avatar definition]
236. curious(sK5) <- (20) [avatar component clause 234]
239. 21 <=> ! [X3] : (~generous(X3) | strong(X3)) [avatar definition]
240. ~generous(X3) | strong(X3) <- (21) [avatar component clause 239]
241. 21 | 20 [avatar split clause 109,234,239]
259. 25 <=> strong(fred) [avatar definition]
261. ~strong(fred) <- (~25) [avatar component clause 259]
263. 16 | ~25 [avatar split clause 120,259,218]
265. 26 <=> quiet(fred) [avatar definition]
267. ~quiet(fred) <- (~26) [avatar component clause 265]
269. 16 | ~26 [avatar split clause 118,265,218]
311. quiet(X0) | strong(X0) [subsumption resolution 131,133]
314. 36 <=> creative(fred) [avatar definition]
318. 37 <=> humble(sK7) [avatar definition]
320. ~humble(sK7) <- (~37) [avatar component clause 318]
321. ~25 | ~36 | ~37 [avatar split clause 137,318,314,259]
350. 36 [avatar split clause 143,314]
353. $false <- (16, 20) [resolution 236,219]
354. ~16 | ~20 [avatar contradiction clause 353]
360. generous(X0) | humble(X0) [resolution 106,103]
391. strong(fred) <- (~26) [resolution 311,267]
392. $false <- (~25, ~26) [subsumption resolution 391,261]
393. 25 | 26 [avatar contradiction clause 392]
456. humble(X0) | strong(X0) <- (21) [resolution 360,240]
459. strong(X0) <- (21) [subsumption resolution 456,163]
507. humble(X2) <- (21) [resolution 459,162]
508. $false <- (21, ~25) [resolution 459,261]
509. ~21 | 25 [avatar contradiction clause 508]
512. $false <- (21, ~37) [subsumption resolution 320,507]
513. ~21 | 37 [avatar contradiction clause 512]
514. $false [avatar sat refutation 241,263,269,321,350,354,393,509,513]
% SZS output end Proof for 468958449610270674726414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet or strong is both funny and not quiet.
Everyone who is both curious and brave is both old and wise.
If alice is not humble then someone is not tall and vice versa.
Everyone who is not humble is either strong or quiet and vice versa.
If someone is both creative and generous then someone is both old and quiet and vice versa.
Everyone who is generous is not patient or quiet and vice versa.
If someone is either not calm or tall then someone is both patient and not calm and vice versa.
Everyone who is patient or not tall is both not quiet and not curious.
If paul is quiet or not happy then john is either creative or humble and vice versa.
If paul is either not rich or kind then someone is calm or wise and vice versa.
If someone is both generous and tall then susan is not wise or patient.
Everyone who is either not quiet or brave is either not curious or generous.
If someone is not old or not wise then fred is not humble and vice versa.
Everyone who is not humble or creative is not wise or calm and vice versa.
Everyone who is not rich or rich is creative or wise.
If someone is wise then someone is happy.
Lucy is both not strong and wise.
Alice is either not curious or wise.
Someone is old or generous.
Someone is strong or calm.
Someone is not creative.
Someone is both not patient and old.
Someone is not happy or calm.
Someone is not tall or not quiet. | Lucy is wise. | entailment | (![X]:((~quiet(X)<~>strong(X))=>(funny(X)&~quiet(X))))&
(![X]:((curious(X)&brave(X))=>(old(X)&wise(X))))&
((~humble(alice))<=>(?[X]:(~tall(X))))&
(![X]:(~humble(X)<=>(strong(X)<~>quiet(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:((old(X)&quiet(X)))))&
(![X]:(generous(X)<=>(~patient(X)|quiet(X))))&
((?[X]:((~calm(X)<~>tall(X))))<=>(?[X]:((patient(X)&~calm(X)))))&
(![X]:((patient(X)|~tall(X))=>(~quiet(X)&~curious(X))))&
(((quiet(paul)|~happy(paul)))<=>((creative(john)<~>humble(john))))&
(((~rich(paul)<~>kind(paul)))<=>(?[X]:((calm(X)|wise(X)))))&
((?[X]:((generous(X)&tall(X))))=>((~wise(susan)|patient(susan))))&
(![X]:((~quiet(X)<~>brave(X))=>(~curious(X)<~>generous(X))))&
((?[X]:((~old(X)|~wise(X))))<=>(~humble(fred)))&
(![X]:((~humble(X)|creative(X))<=>(~wise(X)|calm(X))))&
(![X]:((~rich(X)|rich(X))=>(creative(X)|wise(X))))&
((?[X]:(wise(X)))=>(?[X]:(happy(X))))&
((~strong(lucy)&wise(lucy)))&
((~curious(alice)<~>wise(alice)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~patient(X)&old(X))))&
(?[X]:((~happy(X)|calm(X))))&
(?[X]:((~tall(X)|~quiet(X)))) | wise(lucy) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 399964938386055304543721
% SZS output start Proof for 399964938386055304543721
17. wise(lucy) & ~strong(lucy) [input p16]
25. ~wise(lucy) [input hypothesis]
142. wise(lucy) [cnf transformation 17]
152. ~wise(lucy) [cnf transformation 25]
355. $false [subsumption resolution 152,142]
% SZS output end Proof for 399964938386055304543721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then mary is patient.
Everyone who is both not quiet and not wise is both rich and not old.
If someone is both not brave and funny then someone is not strong.
Everyone who is either not funny or not generous is wise and vice versa.
Everyone who is both calm and not wise is both not quiet and rich and vice versa.
If someone is not kind or kind then someone is not kind or quiet and vice versa.
Everyone who is both not old and not kind is not strong.
Everyone who is not happy is brave and vice versa.
Everyone who is either curious or not curious is both kind and wise and vice versa.
Everyone who is not strong is not rich and vice versa.
If someone is not generous then someone is not generous or calm and vice versa.
If john is either not brave or creative then someone is not wise.
Everyone who is both not brave and not curious is not happy or tall.
If someone is either not creative or not kind then mary is both not curious and creative.
Everyone who is not quiet is kind.
Everyone who is not rich is not brave or generous.
Someone is quiet or not strong.
Someone is not quiet.
Someone is either old or not rich.
Paul is brave or not curious.
Someone is not creative.
Someone is both not strong and patient.
Someone is calm.
Paul is either humble or wise. | Mary is not wise. | contradiction | ((?[X]:(creative(X)))=>(patient(mary)))&
(![X]:((~quiet(X)&~wise(X))=>(rich(X)&~old(X))))&
((?[X]:((~brave(X)&funny(X))))=>(?[X]:(~strong(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>wise(X)))&
(![X]:((calm(X)&~wise(X))<=>(~quiet(X)&rich(X))))&
((?[X]:((~kind(X)|kind(X))))<=>(?[X]:((~kind(X)|quiet(X)))))&
(![X]:((~old(X)&~kind(X))=>~strong(X)))&
(![X]:(~happy(X)<=>brave(X)))&
(![X]:((curious(X)<~>~curious(X))<=>(kind(X)&wise(X))))&
(![X]:(~strong(X)<=>~rich(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)|calm(X)))))&
(((~brave(john)<~>creative(john)))=>(?[X]:(~wise(X))))&
(![X]:((~brave(X)&~curious(X))=>(~happy(X)|tall(X))))&
((?[X]:((~creative(X)<~>~kind(X))))=>((~curious(mary)&creative(mary))))&
(![X]:(~quiet(X)=>kind(X)))&
(![X]:(~rich(X)=>(~brave(X)|generous(X))))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((old(X)<~>~rich(X))))&
((brave(paul)|~curious(paul)))&
(?[X]:(~creative(X)))&
(?[X]:((~strong(X)&patient(X))))&
(?[X]:(calm(X)))&
((humble(paul)<~>wise(paul))) | ~wise(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3275478911998899625465342
% SZS output start Proof for 3275478911998899625465342
9. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (wise(X0) & kind(X0))) [input p8]
25. ~wise(mary) [input hypothesis]
57. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (~wise(X0) | ~kind(X0))) & ((wise(X0) & kind(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 9]
58. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ~wise(X0) | ~kind(X0)) & ((wise(X0) & kind(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 57]
100. wise(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 58]
101. wise(X0) | curious(X0) | curious(X0) [cnf transformation 58]
126. ~wise(mary) [cnf transformation 25]
129. wise(X0) | ~curious(X0) [duplicate literal removal 100]
130. wise(X0) | curious(X0) [duplicate literal removal 101]
155. wise(X0) [subsumption resolution 129,130]
238. $false [subsumption resolution 126,155]
% SZS output end Proof for 3275478911998899625465342
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not calm is not kind or not old. Everyone who is not curious is old and vice versa. If someone is not patient or rich then someone is both curious and brave. If john is either not old or not quiet then mary is both not old and not creative and vice versa. If alice is not wise or not kind then someone is not creative and vice versa. Everyone who is both tall and generous is both not kind and not generous. Everyone who is tall or happy is either patient or tall and vice versa. Everyone who is both not happy and quiet is either not patient or kind and vice versa. If susan is not wise or generous then someone is either wise or curious. Everyone who is old is kind or not rich. Everyone who is either not wise or not calm is old or calm. If someone is funny then mary is either curious or brave. Everyone who is not strong or kind is either not wise or not generous and vice versa. Everyone who is not tall is both not rich and not patient. If alice is kind then someone is both not patient and not calm. If john is tall then paul is either not quiet or not kind and vice versa. Fred is not patient. Someone is not tall. John is both generous and funny. Someone is both not patient and funny. Someone is old or not curious. Fred is either funny or creative. Someone is both curious and wise. Alice is not brave. | John is happy. | contradiction | (![X]:((~wise(X)&~calm(X))=>(~kind(X)|~old(X))))&
(![X]:(~curious(X)<=>old(X)))&
((?[X]:((~patient(X)|rich(X))))=>(?[X]:((curious(X)&brave(X)))))&
(((~old(john)<~>~quiet(john)))<=>((~old(mary)&~creative(mary))))&
(((~wise(alice)|~kind(alice)))<=>(?[X]:(~creative(X))))&
(![X]:((tall(X)&generous(X))=>(~kind(X)&~generous(X))))&
(![X]:((tall(X)|happy(X))<=>(patient(X)<~>tall(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~patient(X)<~>kind(X))))&
(((~wise(susan)|generous(susan)))=>(?[X]:((wise(X)<~>curious(X)))))&
(![X]:(old(X)=>(kind(X)|~rich(X))))&
(![X]:((~wise(X)<~>~calm(X))=>(old(X)|calm(X))))&
((?[X]:(funny(X)))=>((curious(mary)<~>brave(mary))))&
(![X]:((~strong(X)|kind(X))<=>(~wise(X)<~>~generous(X))))&
(![X]:(~tall(X)=>(~rich(X)&~patient(X))))&
((kind(alice))=>(?[X]:((~patient(X)&~calm(X)))))&
((tall(john))<=>((~quiet(paul)<~>~kind(paul))))&
(~patient(fred))&
(?[X]:(~tall(X)))&
((generous(john)&funny(john)))&
(?[X]:((~patient(X)&funny(X))))&
(?[X]:((old(X)|~curious(X))))&
((funny(fred)<~>creative(fred)))&
(?[X]:((curious(X)&wise(X))))&
(~brave(alice)) | happy(john) | [
"p5",
"p6",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 569487647662912642272734
% SZS output start Proof for 569487647662912642272734
6. ! [X0] : ((generous(X0) & tall(X0)) => (~generous(X0) & ~kind(X0))) [input p5]
7. ! [X0] : ((happy(X0) | tall(X0)) <=> (patient(X0) <~> tall(X0))) [input p6]
14. ! [X0] : (~tall(X0) => (~patient(X0) & ~rich(X0))) [input p13]
19. funny(john) & generous(john) [input p18]
25. happy(john) [input hypothesis]
29. ! [X0] : (~tall(X0) => ~patient(X0)) [pure predicate removal 14]
33. ! [X0] : ((~generous(X0) & ~kind(X0)) | (~generous(X0) | ~tall(X0))) [ennf transformation 6]
34. ! [X0] : ((~generous(X0) & ~kind(X0)) | ~generous(X0) | ~tall(X0)) [flattening 33]
39. ! [X0] : (~patient(X0) | tall(X0)) [ennf transformation 29]
52. ! [X0] : (((happy(X0) | tall(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (~happy(X0) & ~tall(X0)))) [nnf transformation 7]
53. ! [X0] : ((happy(X0) | tall(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (~happy(X0) & ~tall(X0)))) [flattening 52]
90. ~generous(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 34]
92. ~happy(X0) | patient(X0) | tall(X0) [cnf transformation 53]
93. ~tall(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 53]
117. ~patient(X0) | tall(X0) [cnf transformation 39]
126. generous(john) [cnf transformation 19]
136. happy(john) [cnf transformation 25]
138. ~tall(X0) | ~patient(X0) [duplicate literal removal 93]
140. ~generous(X0) | ~tall(X0) [duplicate literal removal 90]
227. ~patient(X0) [subsumption resolution 117,138]
242. 22 <=> tall(john) [avatar definition]
273. ~tall(john) [resolution 140,126]
274. patient(john) | tall(john) [resolution 92,136]
275. tall(john) [subsumption resolution 274,227]
278. 22 [avatar split clause 275,242]
279. ~22 [avatar split clause 273,242]
280. $false [avatar sat refutation 278,279]
% SZS output end Proof for 569487647662912642272734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either funny or not kind then alice is strong and vice versa.
If someone is both not old and brave then someone is not happy.
If john is either generous or happy then fred is tall and vice versa.
If someone is creative then mary is strong and vice versa.
If alice is either happy or not rich then mary is either not generous or not funny.
Everyone who is not creative is not funny or tall and vice versa.
If someone is both not rich and humble then lucy is kind.
Everyone who is both kind and brave is either strong or wise.
Everyone who is calm or generous is tall and vice versa.
If mary is kind or not tall then susan is not tall or happy and vice versa.
If lucy is either not generous or not quiet then someone is old and vice versa.
Everyone who is brave or tall is not wise or quiet.
Everyone who is calm or curious is either not creative or strong and vice versa.
Everyone who is not happy is both not old and not kind.
Everyone who is happy or creative is happy or not patient and vice versa.
If someone is not generous or strong then lucy is not brave or quiet.
Fred is happy.
Someone is both not rich and old.
Paul is wise.
Paul is either rich or not happy.
Someone is generous or rich.
John is curious.
Someone is either old or strong. | Lucy is not tall. | neutral | ((?[X]:((funny(X)<~>~kind(X))))<=>(strong(alice)))&
((?[X]:((~old(X)&brave(X))))=>(?[X]:(~happy(X))))&
(((generous(john)<~>happy(john)))<=>(tall(fred)))&
((?[X]:(creative(X)))<=>(strong(mary)))&
(((happy(alice)<~>~rich(alice)))=>((~generous(mary)<~>~funny(mary))))&
(![X]:(~creative(X)<=>(~funny(X)|tall(X))))&
((?[X]:((~rich(X)&humble(X))))=>(kind(lucy)))&
(![X]:((kind(X)&brave(X))=>(strong(X)<~>wise(X))))&
(![X]:((calm(X)|generous(X))<=>tall(X)))&
(((kind(mary)|~tall(mary)))<=>((~tall(susan)|happy(susan))))&
(((~generous(lucy)<~>~quiet(lucy)))<=>(?[X]:(old(X))))&
(![X]:((brave(X)|tall(X))=>(~wise(X)|quiet(X))))&
(![X]:((calm(X)|curious(X))<=>(~creative(X)<~>strong(X))))&
(![X]:(~happy(X)=>(~old(X)&~kind(X))))&
(![X]:((happy(X)|creative(X))<=>(happy(X)|~patient(X))))&
((?[X]:((~generous(X)|strong(X))))=>((~brave(lucy)|quiet(lucy))))&
(happy(fred))&
(?[X]:((~rich(X)&old(X))))&
(wise(paul))&
((rich(paul)<~>~happy(paul)))&
(?[X]:((generous(X)|rich(X))))&
(curious(john))&
(?[X]:((old(X)<~>strong(X)))) | ~tall(lucy) | [] | null | 0 |
Everyone who is either not patient or not quiet is both not patient and kind.
Everyone who is not wise or not calm is either calm or humble and vice versa.
Everyone who is not tall or not calm is either quiet or not creative.
Everyone who is not calm or calm is not creative or curious.
Everyone who is not quiet or rich is both patient and kind.
Everyone who is strong or funny is generous and vice versa.
If paul is strong or not happy then john is not brave or not wise.
Everyone who is not happy is generous or not brave.
If someone is either not brave or patient then susan is either wise or not brave.
Everyone who is not funny or creative is both not strong and not calm and vice versa.
If susan is not strong then someone is rich and vice versa.
If john is both not kind and not rich then someone is either not curious or humble and vice versa.
Everyone who is either brave or old is both not quiet and not brave.
If someone is both quiet and tall then someone is not quiet or strong and vice versa.
Everyone who is both not happy and not quiet is both creative and kind and vice versa.
Everyone who is not kind or not generous is both not generous and strong.
Susan is not generous or not wise.
Someone is not curious.
Susan is either tall or not rich. | Susan is brave. | contradiction | (![X]:((~patient(X)<~>~quiet(X))=>(~patient(X)&kind(X))))&
(![X]:((~wise(X)|~calm(X))<=>(calm(X)<~>humble(X))))&
(![X]:((~tall(X)|~calm(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((~calm(X)|calm(X))=>(~creative(X)|curious(X))))&
(![X]:((~quiet(X)|rich(X))=>(patient(X)&kind(X))))&
(![X]:((strong(X)|funny(X))<=>generous(X)))&
(((strong(paul)|~happy(paul)))=>((~brave(john)|~wise(john))))&
(![X]:(~happy(X)=>(generous(X)|~brave(X))))&
((?[X]:((~brave(X)<~>patient(X))))=>((wise(susan)<~>~brave(susan))))&
(![X]:((~funny(X)|creative(X))<=>(~strong(X)&~calm(X))))&
((~strong(susan))<=>(?[X]:(rich(X))))&
(((~kind(john)&~rich(john)))<=>(?[X]:((~curious(X)<~>humble(X)))))&
(![X]:((brave(X)<~>old(X))=>(~quiet(X)&~brave(X))))&
((?[X]:((quiet(X)&tall(X))))<=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:((~happy(X)&~quiet(X))<=>(creative(X)&kind(X))))&
(![X]:((~kind(X)|~generous(X))=>(~generous(X)&strong(X))))&
((~generous(susan)|~wise(susan)))&
(?[X]:(~curious(X)))&
((tall(susan)<~>~rich(susan))) | brave(susan) | [
"p0",
"p2",
"p4",
"p5",
"p8",
"p14",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4844378739886973780703311
% SZS output start Proof for 4844378739886973780703311
1. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) => (kind(X0) & ~patient(X0))) [input p0]
3. ! [X0] : ((~calm(X0) | ~tall(X0)) => (quiet(X0) <~> ~creative(X0))) [input p2]
5. ! [X0] : ((rich(X0) | ~quiet(X0)) => (kind(X0) & patient(X0))) [input p4]
6. ! [X0] : ((funny(X0) | strong(X0)) <=> generous(X0)) [input p5]
9. ? [X0] : (~brave(X0) <~> patient(X0)) => (wise(susan) <~> ~brave(susan)) [input p8]
15. ! [X0] : ((~quiet(X0) & ~happy(X0)) <=> (kind(X0) & creative(X0))) [input p14]
16. ! [X0] : ((~generous(X0) | ~kind(X0)) => (strong(X0) & ~generous(X0))) [input p15]
17. ~wise(susan) | ~generous(susan) [input p16]
19. tall(susan) <~> ~rich(susan) [input p18]
20. brave(susan) [input hypothesis]
22. ! [X0] : ((kind(X0) & ~patient(X0)) | (~patient(X0) <=> ~quiet(X0))) [ennf transformation 1]
23. ! [X0] : ((quiet(X0) <~> ~creative(X0)) | (calm(X0) & tall(X0))) [ennf transformation 3]
26. ! [X0] : ((kind(X0) & patient(X0)) | (~rich(X0) & quiet(X0))) [ennf transformation 5]
31. (wise(susan) <~> ~brave(susan)) | ! [X0] : (~brave(X0) <=> patient(X0)) [ennf transformation 9]
33. ! [X0] : ((strong(X0) & ~generous(X0)) | (generous(X0) & kind(X0))) [ennf transformation 16]
34. ! [X0] : ((kind(X0) & ~patient(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) [nnf transformation 22]
37. ! [X0] : (((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) | (calm(X0) & tall(X0))) [nnf transformation 23]
38. ! [X0] : (((funny(X0) | strong(X0)) | ~generous(X0)) & (generous(X0) | (~funny(X0) & ~strong(X0)))) [nnf transformation 6]
39. ! [X0] : ((funny(X0) | strong(X0) | ~generous(X0)) & (generous(X0) | (~funny(X0) & ~strong(X0)))) [flattening 38]
40. ((brave(susan) | ~wise(susan)) & (~brave(susan) | wise(susan))) | ! [X0] : ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))) [nnf transformation 31]
58. ! [X0] : (((~quiet(X0) & ~happy(X0)) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | (quiet(X0) | happy(X0)))) [nnf transformation 15]
59. ! [X0] : (((~quiet(X0) & ~happy(X0)) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | quiet(X0) | happy(X0))) [flattening 58]
62. (rich(susan) | ~tall(susan)) & (~rich(susan) | tall(susan)) [nnf transformation 19]
64. ~patient(X0) | ~patient(X0) | quiet(X0) [cnf transformation 34]
75. ~quiet(X0) | creative(X0) | tall(X0) [cnf transformation 37]
79. patient(X0) | quiet(X0) [cnf transformation 26]
80. ~rich(X0) | patient(X0) [cnf transformation 26]
83. ~strong(X0) | generous(X0) [cnf transformation 39]
90. ~brave(susan) | wise(susan) | ~brave(X0) | ~patient(X0) [cnf transformation 40]
118. ~quiet(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 59]
119. ~generous(X0) | kind(X0) [cnf transformation 33]
122. strong(X0) | generous(X0) [cnf transformation 33]
123. ~wise(susan) | ~generous(susan) [cnf transformation 17]
126. rich(susan) | ~tall(susan) [cnf transformation 62]
127. brave(susan) [cnf transformation 20]
131. ~patient(X0) | quiet(X0) [duplicate literal removal 64]
133. quiet(X0) [subsumption resolution 79,131]
153. 5 <=> ! [X0] : (~brave(X0) | ~patient(X0)) [avatar definition]
154. ~brave(X0) | ~patient(X0) <- (5) [avatar component clause 153]
156. 6 <=> wise(susan) [avatar definition]
160. 7 <=> brave(susan) [avatar definition]
162. brave(susan) <- (7) [avatar component clause 160]
168. 5 | 6 | ~7 [avatar split clause 90,160,156,153]
232. ~creative(X0) | ~kind(X0) [subsumption resolution 118,133]
233. generous(X0) [subsumption resolution 122,83]
234. kind(X0) [subsumption resolution 119,233]
235. ~wise(susan) [subsumption resolution 123,233]
236. ~6 [avatar split clause 235,156]
238. 22 <=> tall(susan) [avatar definition]
240. ~tall(susan) <- (~22) [avatar component clause 238]
242. 23 <=> rich(susan) [avatar definition]
244. rich(susan) <- (23) [avatar component clause 242]
245. ~22 | 23 [avatar split clause 126,242,238]
247. 7 [avatar split clause 127,160]
265. ~patient(susan) <- (5, 7) [resolution 154,162]
292. creative(X0) | tall(X0) [resolution 75,133]
317. tall(X3) | ~kind(X3) [resolution 292,232]
322. tall(X3) [subsumption resolution 317,234]
325. $false <- (~22) [resolution 322,240]
326. 22 [avatar contradiction clause 325]
328. patient(susan) <- (23) [resolution 244,80]
329. $false <- (5, 7, 23) [subsumption resolution 328,265]
330. ~5 | ~7 | ~23 [avatar contradiction clause 329]
331. $false [avatar sat refutation 168,236,245,247,326,330]
% SZS output end Proof for 4844378739886973780703311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious and rich is either strong or not generous and vice versa. If someone is both rich and not calm then lucy is either strong or curious. If mary is not wise then someone is not tall or kind. Everyone who is not humble is tall or not happy. If someone is both strong and quiet then susan is happy and vice versa. Everyone who is quiet is not wise or not rich. Everyone who is both not rich and tall is not generous. Everyone who is brave is patient and vice versa. Everyone who is either patient or not strong is both not calm and brave and vice versa. Everyone who is not strong is kind or not calm and vice versa. If susan is old or not tall then someone is quiet. If someone is both quiet and happy then fred is happy or generous and vice versa. Everyone who is not wise or not rich is both not happy and not brave. Everyone who is either not curious or not brave is curious or funny and vice versa. Everyone who is not curious or not calm is not calm and vice versa. Everyone who is either rich or curious is brave or not quiet and vice versa. Paul is both not humble and not generous. Someone is either not funny or not wise. Someone is either not brave or not funny. Alice is both calm and not tall. Susan is not funny or funny. Someone is both not tall and not wise. | Paul is happy. | contradiction | (![X]:((~curious(X)&rich(X))<=>(strong(X)<~>~generous(X))))&
((?[X]:((rich(X)&~calm(X))))=>((strong(lucy)<~>curious(lucy))))&
((~wise(mary))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:(~humble(X)=>(tall(X)|~happy(X))))&
((?[X]:((strong(X)&quiet(X))))<=>(happy(susan)))&
(![X]:(quiet(X)=>(~wise(X)|~rich(X))))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((~humble(paul)&~generous(paul)))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((~brave(X)<~>~funny(X))))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X)))) | happy(paul) | [
"p1",
"p5",
"p7",
"p8",
"p9",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1344220764610962091970668
% SZS output start Proof for 1344220764610962091970668
2. ? [X0] : (~calm(X0) & rich(X0)) => (strong(lucy) <~> curious(lucy)) [input p1]
6. ! [X0] : (quiet(X0) => (~rich(X0) | ~wise(X0))) [input p5]
8. ! [X0] : (brave(X0) <=> patient(X0)) [input p7]
9. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p8]
10. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p9]
13. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p12]
14. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (funny(X0) | curious(X0))) [input p13]
15. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p14]
16. ! [X0] : ((rich(X0) <~> curious(X0)) <=> (~quiet(X0) | brave(X0))) [input p15]
23. happy(paul) [input hypothesis]
25. (strong(lucy) <~> curious(lucy)) | ! [X0] : (calm(X0) | ~rich(X0)) [ennf transformation 2]
29. ! [X0] : ((~rich(X0) | ~wise(X0)) | ~quiet(X0)) [ennf transformation 6]
30. ! [X0] : (~rich(X0) | ~wise(X0) | ~quiet(X0)) [flattening 29]
34. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 13]
37. ((~curious(lucy) | ~strong(lucy)) & (curious(lucy) | strong(lucy))) | ! [X0] : (calm(X0) | ~rich(X0)) [nnf transformation 25]
44. ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))) [nnf transformation 8]
45. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 9]
46. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 45]
47. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 10]
48. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 47]
56. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 14]
57. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 56]
58. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 15]
59. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 58]
60. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (quiet(X0) & ~brave(X0))) & ((~quiet(X0) | brave(X0)) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [nnf transformation 16]
61. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (quiet(X0) & ~brave(X0))) & (~quiet(X0) | brave(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [flattening 60]
76. curious(lucy) | strong(lucy) | calm(X0) | ~rich(X0) [cnf transformation 37]
77. ~curious(lucy) | ~strong(lucy) | calm(X0) | ~rich(X0) [cnf transformation 37]
83. ~quiet(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 30]
85. ~brave(X0) | patient(X0) [cnf transformation 44]
86. ~patient(X0) | brave(X0) [cnf transformation 44]
90. brave(X0) | patient(X0) | strong(X0) [cnf transformation 46]
95. ~strong(X0) | calm(X0) [cnf transformation 48]
102. ~happy(X0) | wise(X0) [cnf transformation 34]
103. ~happy(X0) | rich(X0) [cnf transformation 34]
108. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 57]
112. ~calm(X0) | curious(X0) [cnf transformation 59]
120. ~rich(X0) | ~curious(X0) | quiet(X0) [cnf transformation 61]
132. happy(paul) [cnf transformation 23]
134. ~brave(X0) | ~curious(X0) [duplicate literal removal 108]
136. 1 <=> ! [X0] : (calm(X0) | ~rich(X0)) [avatar definition]
137. ~rich(X0) | calm(X0) <- (1) [avatar component clause 136]
139. 2 <=> strong(lucy) [avatar definition]
140. strong(lucy) <- (2) [avatar component clause 139]
141. ~strong(lucy) <- (~2) [avatar component clause 139]
143. 3 <=> curious(lucy) [avatar definition]
144. curious(lucy) <- (3) [avatar component clause 143]
145. ~curious(lucy) <- (~3) [avatar component clause 143]
146. 1 | ~2 | ~3 [avatar split clause 77,143,139,136]
147. 1 | 2 | 3 [avatar split clause 76,143,139,136]
180. patient(X0) | strong(X0) [subsumption resolution 90,85]
228. calm(lucy) <- (2) [resolution 95,140]
230. wise(paul) [resolution 102,132]
233. rich(paul) [resolution 103,132]
237. curious(lucy) <- (2) [resolution 112,228]
239. $false <- (2, ~3) [subsumption resolution 237,145]
240. ~2 | 3 [avatar contradiction clause 239]
241. calm(paul) <- (1) [resolution 233,137]
242. brave(X0) | strong(X0) [resolution 180,86]
271. curious(paul) <- (1) [resolution 241,112]
359. ~curious(paul) | quiet(paul) [resolution 120,233]
362. quiet(paul) <- (1) [subsumption resolution 359,271]
416. ~curious(X2) | strong(X2) [resolution 242,134]
490. ~wise(paul) | ~rich(paul) <- (1) [resolution 362,83]
493. ~rich(paul) <- (1) [subsumption resolution 490,230]
494. $false <- (1) [subsumption resolution 493,233]
495. ~1 [avatar contradiction clause 494]
621. strong(lucy) <- (3) [resolution 416,144]
627. $false <- (~2, 3) [subsumption resolution 621,141]
628. 2 | ~3 [avatar contradiction clause 627]
631. $false [avatar sat refutation 146,147,240,495,628]
% SZS output end Proof for 1344220764610962091970668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not kind and not wise is strong.
Everyone who is not calm or rich is both not tall and not rich and vice versa.
Everyone who is either old or funny is both brave and not quiet.
If mary is either creative or patient then someone is both rich and funny and vice versa.
Everyone who is rich is either rich or patient and vice versa.
If someone is tall or not humble then paul is either not rich or rich.
Everyone who is not calm is patient or not funny.
If mary is not patient then fred is curious and vice versa.
If someone is both patient and not tall then paul is not generous.
If someone is both not curious and not wise then lucy is curious or not rich and vice versa.
Everyone who is either not generous or curious is either wise or happy and vice versa.
Everyone who is both not old and not happy is either kind or not generous and vice versa.
Everyone who is both not kind and not quiet is both not generous and calm.
Everyone who is either funny or not humble is not tall or not generous.
Everyone who is not patient is both old and not tall and vice versa.
If someone is either not creative or wise then john is not creative and vice versa.
Someone is either creative or happy.
Fred is not old or not rich.
Someone is curious or wise.
Mary is not happy.
Mary is tall or not creative.
Paul is both old and not strong. | John is funny. | contradiction | (![X]:((~kind(X)&~wise(X))=>strong(X)))&
(![X]:((~calm(X)|rich(X))<=>(~tall(X)&~rich(X))))&
(![X]:((old(X)<~>funny(X))=>(brave(X)&~quiet(X))))&
(((creative(mary)<~>patient(mary)))<=>(?[X]:((rich(X)&funny(X)))))&
(![X]:(rich(X)<=>(rich(X)<~>patient(X))))&
((?[X]:((tall(X)|~humble(X))))=>((~rich(paul)<~>rich(paul))))&
(![X]:(~calm(X)=>(patient(X)|~funny(X))))&
((~patient(mary))<=>(curious(fred)))&
((?[X]:((patient(X)&~tall(X))))=>(~generous(paul)))&
((?[X]:((~curious(X)&~wise(X))))<=>((curious(lucy)|~rich(lucy))))&
(![X]:((~generous(X)<~>curious(X))<=>(wise(X)<~>happy(X))))&
(![X]:((~old(X)&~happy(X))<=>(kind(X)<~>~generous(X))))&
(![X]:((~kind(X)&~quiet(X))=>(~generous(X)&calm(X))))&
(![X]:((funny(X)<~>~humble(X))=>(~tall(X)|~generous(X))))&
(![X]:(~patient(X)<=>(old(X)&~tall(X))))&
((?[X]:((~creative(X)<~>wise(X))))<=>(~creative(john)))&
(?[X]:((creative(X)<~>happy(X))))&
((~old(fred)|~rich(fred)))&
(?[X]:((curious(X)|wise(X))))&
(~happy(mary))&
((tall(mary)|~creative(mary)))&
((old(paul)&~strong(paul))) | funny(john) | [
"p1",
"p4",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8945793731668323663488826
% SZS output start Proof for 8945793731668323663488826
2. ! [X0] : ((rich(X0) | ~calm(X0)) <=> (~rich(X0) & ~tall(X0))) [input p1]
5. ! [X0] : (rich(X0) <=> (rich(X0) <~> patient(X0))) [input p4]
7. ! [X0] : (~calm(X0) => (~funny(X0) | patient(X0))) [input p6]
15. ! [X0] : (~patient(X0) <=> (~tall(X0) & old(X0))) [input p14]
23. funny(john) [input hypothesis]
29. ! [X0] : ((~funny(X0) | patient(X0)) | calm(X0)) [ennf transformation 7]
30. ! [X0] : (~funny(X0) | patient(X0) | calm(X0)) [flattening 29]
36. ! [X0] : (((rich(X0) | ~calm(X0)) | (rich(X0) | tall(X0))) & ((~rich(X0) & ~tall(X0)) | (~rich(X0) & calm(X0)))) [nnf transformation 2]
37. ! [X0] : ((rich(X0) | ~calm(X0) | rich(X0) | tall(X0)) & ((~rich(X0) & ~tall(X0)) | (~rich(X0) & calm(X0)))) [flattening 36]
43. ! [X0] : ((rich(X0) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | ~rich(X0))) [nnf transformation 5]
55. ! [X0] : ((~patient(X0) | (tall(X0) | ~old(X0))) & ((~tall(X0) & old(X0)) | patient(X0))) [nnf transformation 15]
56. ! [X0] : ((~patient(X0) | tall(X0) | ~old(X0)) & ((~tall(X0) & old(X0)) | patient(X0))) [flattening 55]
70. ~rich(X0) | ~rich(X0) [cnf transformation 37]
71. rich(X0) | ~calm(X0) | rich(X0) | tall(X0) [cnf transformation 37]
83. rich(X0) | rich(X0) | ~patient(X0) [cnf transformation 43]
88. ~funny(X0) | patient(X0) | calm(X0) [cnf transformation 30]
116. ~tall(X0) | patient(X0) [cnf transformation 56]
130. funny(john) [cnf transformation 23]
132. rich(X0) | ~patient(X0) [duplicate literal removal 83]
133. ~rich(X0) [duplicate literal removal 70]
134. ~calm(X0) | rich(X0) | tall(X0) [duplicate literal removal 71]
153. ~patient(X0) [subsumption resolution 132,133]
154. ~funny(X0) | calm(X0) [subsumption resolution 88,153]
158. ~tall(X0) [subsumption resolution 116,153]
203. calm(john) [resolution 154,130]
224. rich(john) | tall(john) [resolution 134,203]
225. tall(john) [subsumption resolution 224,133]
226. $false [subsumption resolution 225,158]
% SZS output end Proof for 8945793731668323663488826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or calm is both not patient and old. Everyone who is either kind or not tall is both calm and not creative and vice versa. Everyone who is either not wise or curious is both quiet and humble and vice versa. If someone is both not brave and not wise then susan is both not happy and not patient and vice versa. Everyone who is not creative or creative is quiet or wise and vice versa. If paul is both funny and tall then someone is either not funny or old and vice versa. Everyone who is not generous or calm is both not quiet and not calm and vice versa. If someone is kind then someone is not curious. If lucy is both calm and kind then susan is not calm or not generous. Everyone who is either not tall or not happy is not humble or not old. Everyone who is not happy is humble and vice versa. Everyone who is either not old or not kind is both not happy and curious. Everyone who is brave or not quiet is not patient or curious and vice versa. Everyone who is both not funny and curious is not happy and vice versa. Everyone who is either not calm or creative is not creative. If someone is not strong then someone is not creative or not strong. Alice is not humble or old. Someone is humble or tall. Alice is either humble or not patient. Alice is both not brave and happy. Someone is patient or quiet. Fred is humble. Alice is quiet or not kind. Mary is either calm or not rich. | Susan is humble. | contradiction | (![X]:((quiet(X)<~>calm(X))=>(~patient(X)&old(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(calm(X)&~creative(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(quiet(X)&humble(X))))&
((?[X]:((~brave(X)&~wise(X))))<=>((~happy(susan)&~patient(susan))))&
(![X]:((~creative(X)|creative(X))<=>(quiet(X)|wise(X))))&
(((funny(paul)&tall(paul)))<=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((~generous(X)|calm(X))<=>(~quiet(X)&~calm(X))))&
((?[X]:(kind(X)))=>(?[X]:(~curious(X))))&
(((calm(lucy)&kind(lucy)))=>((~calm(susan)|~generous(susan))))&
(![X]:((~tall(X)<~>~happy(X))=>(~humble(X)|~old(X))))&
(![X]:(~happy(X)<=>humble(X)))&
(![X]:((~old(X)<~>~kind(X))=>(~happy(X)&curious(X))))&
(![X]:((brave(X)|~quiet(X))<=>(~patient(X)|curious(X))))&
(![X]:((~funny(X)&curious(X))<=>~happy(X)))&
(![X]:((~calm(X)<~>creative(X))=>~creative(X)))&
((?[X]:(~strong(X)))=>(?[X]:((~creative(X)|~strong(X)))))&
((~humble(alice)|old(alice)))&
(?[X]:((humble(X)|tall(X))))&
((humble(alice)<~>~patient(alice)))&
((~brave(alice)&happy(alice)))&
(?[X]:((patient(X)|quiet(X))))&
(humble(fred))&
((quiet(alice)|~kind(alice)))&
((calm(mary)<~>~rich(mary))) | humble(susan) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6207617928529430407167372
% SZS output start Proof for 6207617928529430407167372
1. ! [X0] : ((quiet(X0) <~> calm(X0)) => (old(X0) & ~patient(X0))) [input p0]
3. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (humble(X0) & quiet(X0))) [input p2]
4. ? [X0] : (~wise(X0) & ~brave(X0)) <=> (~patient(susan) & ~happy(susan)) [input p3]
5. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (wise(X0) | quiet(X0))) [input p4]
7. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (~calm(X0) & ~quiet(X0))) [input p6]
11. ! [X0] : (~happy(X0) <=> humble(X0)) [input p10]
13. ! [X0] : ((~quiet(X0) | brave(X0)) <=> (curious(X0) | ~patient(X0))) [input p12]
14. ! [X0] : ((curious(X0) & ~funny(X0)) <=> ~happy(X0)) [input p13]
25. humble(susan) [input hypothesis]
28. ! [X0] : ((old(X0) & ~patient(X0)) | (quiet(X0) <=> calm(X0))) [ennf transformation 1]
37. ! [X0] : ((old(X0) & ~patient(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) [nnf transformation 28]
40. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 3]
41. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [flattening 40]
42. (? [X0] : (~wise(X0) & ~brave(X0)) | (patient(susan) | happy(susan))) & ((~patient(susan) & ~happy(susan)) | ! [X0] : (wise(X0) | brave(X0))) [nnf transformation 4]
43. (? [X0] : (~wise(X0) & ~brave(X0)) | patient(susan) | happy(susan)) & ((~patient(susan) & ~happy(susan)) | ! [X0] : (wise(X0) | brave(X0))) [flattening 42]
44. (? [X0] : (~wise(X0) & ~brave(X0)) | patient(susan) | happy(susan)) & ((~patient(susan) & ~happy(susan)) | ! [X1] : (wise(X1) | brave(X1))) [rectify 43]
45. ? [X0] : (~wise(X0) & ~brave(X0)) => (~wise(sK0) & ~brave(sK0)) [choice axiom]
46. ((~wise(sK0) & ~brave(sK0)) | patient(susan) | happy(susan)) & ((~patient(susan) & ~happy(susan)) | ! [X1] : (wise(X1) | brave(X1))) [skolemisation 44,45]
47. ! [X0] : (((creative(X0) | ~creative(X0)) | (~wise(X0) & ~quiet(X0))) & ((wise(X0) | quiet(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 5]
48. ! [X0] : ((creative(X0) | ~creative(X0) | (~wise(X0) & ~quiet(X0))) & (wise(X0) | quiet(X0) | (~creative(X0) & creative(X0)))) [flattening 47]
54. ! [X0] : (((calm(X0) | ~generous(X0)) | (calm(X0) | quiet(X0))) & ((~calm(X0) & ~quiet(X0)) | (~calm(X0) & generous(X0)))) [nnf transformation 7]
55. ! [X0] : ((calm(X0) | ~generous(X0) | calm(X0) | quiet(X0)) & ((~calm(X0) & ~quiet(X0)) | (~calm(X0) & generous(X0)))) [flattening 54]
60. ! [X0] : ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))) [nnf transformation 11]
62. ! [X0] : (((~quiet(X0) | brave(X0)) | (~curious(X0) & patient(X0))) & ((curious(X0) | ~patient(X0)) | (quiet(X0) & ~brave(X0)))) [nnf transformation 13]
63. ! [X0] : ((~quiet(X0) | brave(X0) | (~curious(X0) & patient(X0))) & (curious(X0) | ~patient(X0) | (quiet(X0) & ~brave(X0)))) [flattening 62]
64. ! [X0] : (((curious(X0) & ~funny(X0)) | happy(X0)) & (~happy(X0) | (~curious(X0) | funny(X0)))) [nnf transformation 14]
65. ! [X0] : (((curious(X0) & ~funny(X0)) | happy(X0)) & (~happy(X0) | ~curious(X0) | funny(X0))) [flattening 64]
76. ~patient(X0) | calm(X0) | ~quiet(X0) [cnf transformation 37]
87. ~curious(X0) | ~wise(X0) | quiet(X0) [cnf transformation 41]
88. humble(X0) | curious(X0) | wise(X0) [cnf transformation 41]
94. ~brave(sK0) | patient(susan) | happy(susan) [cnf transformation 46]
95. ~wise(sK0) | patient(susan) | happy(susan) [cnf transformation 46]
96. wise(X0) | quiet(X0) | creative(X0) [cnf transformation 48]
97. ~creative(X0) | quiet(X0) | wise(X0) [cnf transformation 48]
109. ~calm(X0) | ~calm(X0) [cnf transformation 55]
116. ~happy(X0) | ~humble(X0) [cnf transformation 60]
124. ~curious(X0) | brave(X0) | ~quiet(X0) [cnf transformation 63]
127. happy(X0) | curious(X0) [cnf transformation 65]
142. humble(susan) [cnf transformation 25]
144. ~calm(X0) [duplicate literal removal 109]
147. 1 <=> happy(susan) [avatar definition]
149. happy(susan) <- (1) [avatar component clause 147]
151. 2 <=> patient(susan) [avatar definition]
153. patient(susan) <- (2) [avatar component clause 151]
155. 3 <=> wise(sK0) [avatar definition]
158. 1 | 2 | ~3 [avatar split clause 95,155,151,147]
160. 4 <=> brave(sK0) [avatar definition]
162. ~brave(sK0) <- (~4) [avatar component clause 160]
163. 1 | 2 | ~4 [avatar split clause 94,160,151,147]
165. 5 <=> ! [X1] : (wise(X1) | brave(X1)) [avatar definition]
166. brave(X1) | wise(X1) <- (5) [avatar component clause 165]
169. wise(X0) | quiet(X0) [subsumption resolution 96,97]
265. ~humble(X0) | curious(X0) [resolution 127,116]
278. curious(susan) [resolution 265,142]
300. curious(X1) | wise(X1) | curious(X1) [resolution 88,265]
301. curious(X1) | wise(X1) [duplicate literal removal 300]
358. ~humble(susan) <- (1) [resolution 149,116]
360. $false <- (1) [subsumption resolution 358,142]
361. ~1 [avatar contradiction clause 360]
366. calm(susan) | ~quiet(susan) <- (2) [resolution 153,76]
367. ~quiet(susan) <- (2) [subsumption resolution 366,144]
394. wise(sK0) <- (~4, 5) [resolution 166,162]
464. ~wise(susan) | quiet(susan) [resolution 278,87]
465. ~wise(susan) <- (2) [subsumption resolution 464,367]
592. wise(X1) | brave(X1) | ~quiet(X1) [resolution 301,124]
606. quiet(susan) <- (2) [resolution 465,169]
607. $false <- (2) [subsumption resolution 606,367]
608. ~2 [avatar contradiction clause 607]
613. 3 | 4 | ~5 [avatar split clause 394,165,160,155]
614. wise(X1) | brave(X1) [subsumption resolution 592,169]
615. 5 [avatar split clause 614,165]
616. $false [avatar sat refutation 158,163,361,608,613,615]
% SZS output end Proof for 6207617928529430407167372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not calm or tall then someone is both not curious and old and vice versa. Everyone who is either tall or brave is both not creative and not curious and vice versa. Everyone who is both not curious and patient is patient or not humble. Everyone who is both not generous and old is generous or brave and vice versa. Everyone who is not tall is funny and vice versa. Everyone who is both not patient and tall is not creative and vice versa. If paul is not brave or calm then susan is either wise or not humble. If someone is old then someone is not humble. If someone is not curious or wise then alice is humble or happy and vice versa. Everyone who is not quiet or not humble is either tall or not rich and vice versa. Everyone who is not generous is not patient or not old and vice versa. Everyone who is curious or not tall is wise or not calm. If someone is both wise and calm then lucy is either not patient or not happy and vice versa. If paul is not generous then someone is either not curious or not rich. If alice is happy then someone is either curious or not creative and vice versa. If susan is both patient and not calm then someone is not quiet. Someone is either not brave or quiet. Someone is either not patient or not calm. Paul is strong or happy. Fred is quiet. Lucy is wise. Lucy is either not old or humble. | Alice is not curious. | neutral | ((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~curious(X)&old(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(~creative(X)&~curious(X))))&
(![X]:((~curious(X)&patient(X))=>(patient(X)|~humble(X))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)|brave(X))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~patient(X)&tall(X))<=>~creative(X)))&
(((~brave(paul)|calm(paul)))=>((wise(susan)<~>~humble(susan))))&
((?[X]:(old(X)))=>(?[X]:(~humble(X))))&
((?[X]:((~curious(X)|wise(X))))<=>((humble(alice)|happy(alice))))&
(![X]:((~quiet(X)|~humble(X))<=>(tall(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(~patient(X)|~old(X))))&
(![X]:((curious(X)|~tall(X))=>(wise(X)|~calm(X))))&
((?[X]:((wise(X)&calm(X))))<=>((~patient(lucy)<~>~happy(lucy))))&
((~generous(paul))=>(?[X]:((~curious(X)<~>~rich(X)))))&
((happy(alice))<=>(?[X]:((curious(X)<~>~creative(X)))))&
(((patient(susan)&~calm(susan)))=>(?[X]:(~quiet(X))))&
(?[X]:((~brave(X)<~>quiet(X))))&
(?[X]:((~patient(X)<~>~calm(X))))&
((strong(paul)|happy(paul)))&
(quiet(fred))&
(wise(lucy))&
((~old(lucy)<~>humble(lucy))) | ~curious(alice) | [] | null | 0 |
Everyone who is either not rich or not curious is either not funny or wise. If susan is either strong or not wise then someone is either happy or not quiet and vice versa. If mary is not brave then someone is both strong and humble. Everyone who is not tall is both tall and not rich and vice versa. If mary is brave or kind then fred is not rich or generous and vice versa. Everyone who is not tall or wise is not patient and vice versa. Everyone who is both funny and not brave is either not kind or curious and vice versa. Everyone who is either humble or calm is not funny and vice versa. Everyone who is both humble and not happy is funny or wise. Everyone who is not calm or patient is either not calm or patient and vice versa. Everyone who is both old and brave is either not quiet or not funny and vice versa. If someone is funny or happy then lucy is brave and vice versa. Everyone who is not kind is either curious or not wise. Everyone who is both not curious and not rich is not old and vice versa. If someone is both not strong and not calm then john is not strong or not rich and vice versa. Everyone who is not curious is funny or not calm and vice versa. Someone is humble. Someone is either old or not humble. Paul is quiet or humble. Someone is either tall or creative. Susan is either quiet or not wise. Fred is not strong or rich. Alice is either patient or strong. | John is not patient. | entailment | (![X]:((~rich(X)<~>~curious(X))=>(~funny(X)<~>wise(X))))&
(((strong(susan)<~>~wise(susan)))<=>(?[X]:((happy(X)<~>~quiet(X)))))&
((~brave(mary))=>(?[X]:((strong(X)&humble(X)))))&
(![X]:(~tall(X)<=>(tall(X)&~rich(X))))&
(((brave(mary)|kind(mary)))<=>((~rich(fred)|generous(fred))))&
(![X]:((~tall(X)|wise(X))<=>~patient(X)))&
(![X]:((funny(X)&~brave(X))<=>(~kind(X)<~>curious(X))))&
(![X]:((humble(X)<~>calm(X))<=>~funny(X)))&
(![X]:((humble(X)&~happy(X))=>(funny(X)|wise(X))))&
(![X]:((~calm(X)|patient(X))<=>(~calm(X)<~>patient(X))))&
(![X]:((old(X)&brave(X))<=>(~quiet(X)<~>~funny(X))))&
((?[X]:((funny(X)|happy(X))))<=>(brave(lucy)))&
(![X]:(~kind(X)=>(curious(X)<~>~wise(X))))&
(![X]:((~curious(X)&~rich(X))<=>~old(X)))&
((?[X]:((~strong(X)&~calm(X))))<=>((~strong(john)|~rich(john))))&
(![X]:(~curious(X)<=>(funny(X)|~calm(X))))&
(?[X]:(humble(X)))&
(?[X]:((old(X)<~>~humble(X))))&
((quiet(paul)|humble(paul)))&
(?[X]:((tall(X)<~>creative(X))))&
((quiet(susan)<~>~wise(susan)))&
((~strong(fred)|rich(fred)))&
((patient(alice)<~>strong(alice))) | ~patient(john) | [
"p0",
"p3",
"p5",
"p6",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5495644703504969172436673
% SZS output start Proof for 5495644703504969172436673
1. ! [X0] : ((~rich(X0) <~> ~curious(X0)) => (~funny(X0) <~> wise(X0))) [input p0]
4. ! [X0] : (~tall(X0) <=> (~rich(X0) & tall(X0))) [input p3]
6. ! [X0] : ((wise(X0) | ~tall(X0)) <=> ~patient(X0)) [input p5]
7. ! [X0] : ((~brave(X0) & funny(X0)) <=> (~kind(X0) <~> curious(X0))) [input p6]
10. ! [X0] : ((patient(X0) | ~calm(X0)) <=> (~calm(X0) <~> patient(X0))) [input p9]
13. ! [X0] : (~kind(X0) => (curious(X0) <~> ~wise(X0))) [input p12]
16. ! [X0] : (~curious(X0) <=> (~calm(X0) | funny(X0))) [input p15]
24. patient(john) [input hypothesis]
25. ! [X0] : ((~funny(X0) <~> wise(X0)) | (~rich(X0) <=> ~curious(X0))) [ennf transformation 1]
29. ! [X0] : ((curious(X0) <~> ~wise(X0)) | kind(X0)) [ennf transformation 13]
30. ! [X0] : (((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | ((~rich(X0) | curious(X0)) & (~curious(X0) | rich(X0)))) [nnf transformation 25]
37. ! [X0] : ((~tall(X0) | (rich(X0) | ~tall(X0))) & ((~rich(X0) & tall(X0)) | tall(X0))) [nnf transformation 4]
38. ! [X0] : ((~tall(X0) | rich(X0) | ~tall(X0)) & ((~rich(X0) & tall(X0)) | tall(X0))) [flattening 37]
41. ! [X0] : (((wise(X0) | ~tall(X0)) | patient(X0)) & (~patient(X0) | (~wise(X0) & tall(X0)))) [nnf transformation 6]
42. ! [X0] : ((wise(X0) | ~tall(X0) | patient(X0)) & (~patient(X0) | (~wise(X0) & tall(X0)))) [flattening 41]
43. ! [X0] : (((~brave(X0) & funny(X0)) | ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0)))) & (((~curious(X0) | kind(X0)) & (curious(X0) | ~kind(X0))) | (brave(X0) | ~funny(X0)))) [nnf transformation 7]
44. ! [X0] : (((~brave(X0) & funny(X0)) | ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0)))) & (((~curious(X0) | kind(X0)) & (curious(X0) | ~kind(X0))) | brave(X0) | ~funny(X0))) [flattening 43]
46. ! [X0] : (((patient(X0) | ~calm(X0)) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0)))) & (((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | (~patient(X0) & calm(X0)))) [nnf transformation 10]
47. ! [X0] : ((patient(X0) | ~calm(X0) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0)))) & (((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | (~patient(X0) & calm(X0)))) [flattening 46]
54. ! [X0] : (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | kind(X0)) [nnf transformation 29]
62. ! [X0] : ((~curious(X0) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | curious(X0))) [nnf transformation 16]
63. ! [X0] : ((~curious(X0) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | curious(X0))) [flattening 62]
75. ~funny(X0) | wise(X0) | ~rich(X0) | curious(X0) [cnf transformation 30]
88. tall(X0) | tall(X0) [cnf transformation 38]
90. ~tall(X0) | rich(X0) | ~tall(X0) [cnf transformation 38]
96. ~patient(X0) | ~wise(X0) [cnf transformation 42]
101. ~kind(X0) | funny(X0) | ~curious(X0) [cnf transformation 44]
112. ~patient(X0) | calm(X0) | ~patient(X0) [cnf transformation 47]
125. ~curious(X0) | wise(X0) | kind(X0) [cnf transformation 54]
134. ~calm(X0) | funny(X0) | curious(X0) [cnf transformation 63]
135. ~funny(X0) | ~curious(X0) [cnf transformation 63]
148. patient(john) [cnf transformation 24]
150. ~patient(X0) | calm(X0) [duplicate literal removal 112]
153. tall(X0) [duplicate literal removal 88]
154. ~tall(X0) | rich(X0) [duplicate literal removal 90]
302. ~wise(john) [resolution 96,148]
305. calm(john) [resolution 150,148]
307. rich(X0) [resolution 154,153]
422. 44 <=> funny(john) [avatar definition]
423. ~funny(john) <- (~44) [avatar component clause 422]
424. funny(john) <- (44) [avatar component clause 422]
498. funny(john) | curious(john) [resolution 134,305]
502. curious(john) <- (~44) [subsumption resolution 498,423]
772. wise(john) | kind(john) <- (~44) [resolution 502,125]
775. kind(john) <- (~44) [subsumption resolution 772,302]
894. funny(john) | ~curious(john) <- (~44) [resolution 775,101]
896. ~curious(john) <- (~44) [subsumption resolution 894,423]
897. $false <- (~44) [subsumption resolution 896,502]
898. 44 [avatar contradiction clause 897]
900. wise(john) | ~rich(john) | curious(john) <- (44) [resolution 424,75]
904. ~curious(john) <- (44) [resolution 424,135]
907. ~rich(john) | curious(john) <- (44) [subsumption resolution 900,302]
908. curious(john) <- (44) [subsumption resolution 907,307]
924. $false <- (44) [subsumption resolution 904,908]
925. ~44 [avatar contradiction clause 924]
926. $false [avatar sat refutation 898,925]
% SZS output end Proof for 5495644703504969172436673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient then susan is both not tall and not generous. Everyone who is generous is both creative and old. If someone is either tall or not happy then someone is not strong or kind. Everyone who is not quiet or not brave is both not patient and not strong and vice versa. Everyone who is not tall or not strong is either calm or generous. Everyone who is both not brave and not funny is happy and vice versa. If john is either kind or funny then lucy is not patient or not tall. If paul is not quiet or not humble then someone is brave or not happy. Everyone who is both quiet and not kind is either not brave or not rich and vice versa. If alice is not rich or creative then someone is either generous or funny and vice versa. If someone is not wise or creative then someone is either not brave or not funny and vice versa. Everyone who is calm is not brave and vice versa. If paul is either not rich or not quiet then john is funny and vice versa. Everyone who is curious is happy. Everyone who is either generous or not curious is curious and vice versa. Everyone who is either not wise or not brave is not creative or not kind. Alice is humble. Someone is calm or old. Fred is both patient and strong. Someone is both tall and rich. Someone is not funny or not humble. | Lucy is generous. | entailment | ((?[X]:(~patient(X)))=>((~tall(susan)&~generous(susan))))&
(![X]:(generous(X)=>(creative(X)&old(X))))&
((?[X]:((tall(X)<~>~happy(X))))=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:((~quiet(X)|~brave(X))<=>(~patient(X)&~strong(X))))&
(![X]:((~tall(X)|~strong(X))=>(calm(X)<~>generous(X))))&
(![X]:((~brave(X)&~funny(X))<=>happy(X)))&
(((kind(john)<~>funny(john)))=>((~patient(lucy)|~tall(lucy))))&
(((~quiet(paul)|~humble(paul)))=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(~brave(X)<~>~rich(X))))&
(((~rich(alice)|creative(alice)))<=>(?[X]:((generous(X)<~>funny(X)))))&
((?[X]:((~wise(X)|creative(X))))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(![X]:(calm(X)<=>~brave(X)))&
(((~rich(paul)<~>~quiet(paul)))<=>(funny(john)))&
(![X]:(curious(X)=>happy(X)))&
(![X]:((generous(X)<~>~curious(X))<=>curious(X)))&
(![X]:((~wise(X)<~>~brave(X))=>(~creative(X)|~kind(X))))&
(humble(alice))&
(?[X]:((calm(X)|old(X))))&
((patient(fred)&strong(fred)))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:((~funny(X)|~humble(X)))) | generous(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 807325646192599239167907
% SZS output start Proof for 807325646192599239167907
15. ! [X0] : ((generous(X0) <~> ~curious(X0)) <=> curious(X0)) [input p14]
22. ~generous(lucy) [input hypothesis]
63. ! [X0] : ((((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | ~curious(X0)) & (curious(X0) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0))))) [nnf transformation 15]
116. curious(X0) | generous(X0) | curious(X0) [cnf transformation 63]
117. ~curious(X0) | generous(X0) | ~curious(X0) [cnf transformation 63]
127. ~generous(lucy) [cnf transformation 22]
128. curious(X0) | generous(X0) [duplicate literal removal 116]
129. ~curious(X0) | generous(X0) [duplicate literal removal 117]
263. generous(X0) [subsumption resolution 128,129]
273. $false [subsumption resolution 127,263]
% SZS output end Proof for 807325646192599239167907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and not calm then lucy is both not patient and not wise and vice versa.
Everyone who is not calm is either not quiet or not curious and vice versa.
If paul is both strong and happy then someone is old or quiet and vice versa.
If lucy is either tall or calm then john is both not humble and funny.
If someone is either tall or funny then someone is both generous and not quiet and vice versa.
Everyone who is not patient or not curious is both not rich and patient.
Everyone who is both not creative and curious is both not generous and not quiet and vice versa.
If susan is either funny or not funny then someone is either not creative or not strong and vice versa.
Everyone who is not rich is either funny or happy and vice versa.
If paul is both not generous and old then fred is not tall or funny.
If mary is not tall then fred is either not wise or not creative.
If someone is not wise then mary is either kind or not wise and vice versa.
Everyone who is both not patient and tall is humble.
If fred is either funny or not generous then someone is either not brave or not rich.
Everyone who is funny or calm is both not funny and generous.
If someone is not wise then someone is both tall and patient and vice versa.
Susan is not rich or not curious.
Someone is either kind or rich.
Someone is either curious or not wise.
Lucy is both patient and not rich.
Someone is either not old or quiet.
John is not calm.
Paul is not rich or not happy. | Fred is not tall. | neutral | ((?[X]:((tall(X)&~calm(X))))<=>((~patient(lucy)&~wise(lucy))))&
(![X]:(~calm(X)<=>(~quiet(X)<~>~curious(X))))&
(((strong(paul)&happy(paul)))<=>(?[X]:((old(X)|quiet(X)))))&
(((tall(lucy)<~>calm(lucy)))=>((~humble(john)&funny(john))))&
((?[X]:((tall(X)<~>funny(X))))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~patient(X)|~curious(X))=>(~rich(X)&patient(X))))&
(![X]:((~creative(X)&curious(X))<=>(~generous(X)&~quiet(X))))&
(((funny(susan)<~>~funny(susan)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:(~rich(X)<=>(funny(X)<~>happy(X))))&
(((~generous(paul)&old(paul)))=>((~tall(fred)|funny(fred))))&
((~tall(mary))=>((~wise(fred)<~>~creative(fred))))&
((?[X]:(~wise(X)))<=>((kind(mary)<~>~wise(mary))))&
(![X]:((~patient(X)&tall(X))=>humble(X)))&
(((funny(fred)<~>~generous(fred)))=>(?[X]:((~brave(X)<~>~rich(X)))))&
(![X]:((funny(X)|calm(X))=>(~funny(X)&generous(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((tall(X)&patient(X)))))&
((~rich(susan)|~curious(susan)))&
(?[X]:((kind(X)<~>rich(X))))&
(?[X]:((curious(X)<~>~wise(X))))&
((patient(lucy)&~rich(lucy)))&
(?[X]:((~old(X)<~>quiet(X))))&
(~calm(john))&
((~rich(paul)|~happy(paul))) | ~tall(fred) | [] | null | 0 |
Everyone who is creative is not humble or patient and vice versa.
If someone is creative or wise then alice is both not tall and not rich.
Everyone who is either creative or not generous is either not curious or strong and vice versa.
If mary is both not curious and not strong then mary is not humble and vice versa.
If lucy is both old and not humble then someone is patient or curious and vice versa.
If john is both not quiet and rich then someone is either not wise or humble.
Everyone who is either not brave or not creative is both funny and patient.
Everyone who is either not calm or strong is happy and vice versa.
If someone is happy then fred is both not creative and old.
Everyone who is not curious or not old is not quiet or curious and vice versa.
If someone is not funny then alice is not generous or not patient and vice versa.
Everyone who is both not kind and not strong is either not patient or brave.
If mary is both not humble and not funny then someone is patient and vice versa.
Everyone who is wise or not rich is not humble or rich and vice versa.
Everyone who is both generous and not humble is not rich and vice versa.
Everyone who is either patient or happy is not curious and vice versa.
Alice is not quiet.
Someone is not happy or not old.
Paul is strong or not brave.
Paul is either not funny or strong.
Someone is not patient.
Someone is quiet.
Paul is not old.
Fred is either funny or calm. | Alice is not creative. | contradiction | (![X]:(creative(X)<=>(~humble(X)|patient(X))))&
((?[X]:((creative(X)|wise(X))))=>((~tall(alice)&~rich(alice))))&
(![X]:((creative(X)<~>~generous(X))<=>(~curious(X)<~>strong(X))))&
(((~curious(mary)&~strong(mary)))<=>(~humble(mary)))&
(((old(lucy)&~humble(lucy)))<=>(?[X]:((patient(X)|curious(X)))))&
(((~quiet(john)&rich(john)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((~brave(X)<~>~creative(X))=>(funny(X)&patient(X))))&
(![X]:((~calm(X)<~>strong(X))<=>happy(X)))&
((?[X]:(happy(X)))=>((~creative(fred)&old(fred))))&
(![X]:((~curious(X)|~old(X))<=>(~quiet(X)|curious(X))))&
((?[X]:(~funny(X)))<=>((~generous(alice)|~patient(alice))))&
(![X]:((~kind(X)&~strong(X))=>(~patient(X)<~>brave(X))))&
(((~humble(mary)&~funny(mary)))<=>(?[X]:(patient(X))))&
(![X]:((wise(X)|~rich(X))<=>(~humble(X)|rich(X))))&
(![X]:((generous(X)&~humble(X))<=>~rich(X)))&
(![X]:((patient(X)<~>happy(X))<=>~curious(X)))&
(~quiet(alice))&
(?[X]:((~happy(X)|~old(X))))&
((strong(paul)|~brave(paul)))&
((~funny(paul)<~>strong(paul)))&
(?[X]:(~patient(X)))&
(?[X]:(quiet(X)))&
(~old(paul))&
((funny(fred)<~>calm(fred))) | ~creative(alice) | [
"p0",
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8896710835580502577936529
% SZS output start Proof for 8896710835580502577936529
1. ! [X0] : (creative(X0) <=> (patient(X0) | ~humble(X0))) [input p0]
2. ? [X0] : (wise(X0) | creative(X0)) => (~rich(alice) & ~tall(alice)) [input p1]
14. ! [X0] : ((~rich(X0) | wise(X0)) <=> (rich(X0) | ~humble(X0))) [input p13]
25. ~creative(alice) [input hypothesis]
27. ? [X0] : (wise(X0) | creative(X0)) => ~rich(alice) [pure predicate removal 2]
28. ~rich(alice) | ! [X0] : (~wise(X0) & ~creative(X0)) [ennf transformation 27]
33. ! [X0] : ((creative(X0) | (~patient(X0) & humble(X0))) & ((patient(X0) | ~humble(X0)) | ~creative(X0))) [nnf transformation 1]
34. ! [X0] : ((creative(X0) | (~patient(X0) & humble(X0))) & (patient(X0) | ~humble(X0) | ~creative(X0))) [flattening 33]
60. ! [X0] : (((~rich(X0) | wise(X0)) | (~rich(X0) & humble(X0))) & ((rich(X0) | ~humble(X0)) | (rich(X0) & ~wise(X0)))) [nnf transformation 14]
61. ! [X0] : ((~rich(X0) | wise(X0) | (~rich(X0) & humble(X0))) & (rich(X0) | ~humble(X0) | (rich(X0) & ~wise(X0)))) [flattening 60]
74. humble(X0) | creative(X0) [cnf transformation 34]
77. ~rich(alice) | ~wise(X0) [cnf transformation 28]
117. rich(X0) | ~humble(X0) | rich(X0) [cnf transformation 61]
119. ~rich(X0) | wise(X0) | ~rich(X0) [cnf transformation 61]
137. ~creative(alice) [cnf transformation 25]
138. ~humble(X0) | rich(X0) [duplicate literal removal 117]
139. ~rich(X0) | wise(X0) [duplicate literal removal 119]
143. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
144. ~wise(X0) <- (1) [avatar component clause 143]
146. 2 <=> rich(alice) [avatar definition]
147. rich(alice) <- (2) [avatar component clause 146]
148. ~rich(alice) <- (~2) [avatar component clause 146]
149. 1 | ~2 [avatar split clause 77,146,143]
295. rich(X0) | creative(X0) [resolution 138,74]
321. creative(alice) <- (~2) [resolution 295,148]
324. $false <- (~2) [subsumption resolution 321,137]
325. 2 [avatar contradiction clause 324]
328. wise(alice) <- (2) [resolution 147,139]
329. $false <- (1, 2) [subsumption resolution 328,144]
330. ~1 | ~2 [avatar contradiction clause 329]
331. $false [avatar sat refutation 149,325,330]
% SZS output end Proof for 8896710835580502577936529
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and generous is happy or not old.
Everyone who is both rich and not tall is kind.
If someone is both patient and brave then someone is both not kind and happy and vice versa.
Everyone who is not patient is not calm or not old and vice versa.
Everyone who is either not happy or funny is rich.
Everyone who is generous or kind is not old or not quiet and vice versa.
Everyone who is quiet or happy is not calm.
Everyone who is humble or not wise is either patient or not old and vice versa.
Everyone who is both creative and patient is either not curious or not patient and vice versa.
If john is not rich or not generous then fred is both not happy and not humble and vice versa.
Everyone who is both strong and creative is both not rich and not funny.
If someone is either not curious or creative then someone is tall and vice versa.
Everyone who is either not brave or not curious is either quiet or old and vice versa.
Everyone who is both not strong and not creative is wise or creative.
Everyone who is both not humble and not strong is strong or brave and vice versa.
Everyone who is both not quiet and calm is both not happy and not old and vice versa.
Mary is either not old or not generous.
Someone is either not creative or not patient.
Someone is either kind or not quiet.
Lucy is either happy or not patient.
Fred is calm.
Mary is both kind and calm.
Alice is both not patient and not kind.
Susan is not old. | John is not rich. | contradiction | (![X]:((patient(X)&generous(X))=>(happy(X)|~old(X))))&
(![X]:((rich(X)&~tall(X))=>kind(X)))&
((?[X]:((patient(X)&brave(X))))<=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:(~patient(X)<=>(~calm(X)|~old(X))))&
(![X]:((~happy(X)<~>funny(X))=>rich(X)))&
(![X]:((generous(X)|kind(X))<=>(~old(X)|~quiet(X))))&
(![X]:((quiet(X)|happy(X))=>~calm(X)))&
(![X]:((humble(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:((creative(X)&patient(X))<=>(~curious(X)<~>~patient(X))))&
(((~rich(john)|~generous(john)))<=>((~happy(fred)&~humble(fred))))&
(![X]:((strong(X)&creative(X))=>(~rich(X)&~funny(X))))&
((?[X]:((~curious(X)<~>creative(X))))<=>(?[X]:(tall(X))))&
(![X]:((~brave(X)<~>~curious(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~strong(X)&~creative(X))=>(wise(X)|creative(X))))&
(![X]:((~humble(X)&~strong(X))<=>(strong(X)|brave(X))))&
(![X]:((~quiet(X)&calm(X))<=>(~happy(X)&~old(X))))&
((~old(mary)<~>~generous(mary)))&
(?[X]:((~creative(X)<~>~patient(X))))&
(?[X]:((kind(X)<~>~quiet(X))))&
((happy(lucy)<~>~patient(lucy)))&
(calm(fred))&
((kind(mary)&calm(mary)))&
((~patient(alice)&~kind(alice)))&
(~old(susan)) | ~rich(john) | [
"p2",
"p3",
"p6",
"p8",
"p9",
"p12",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 750275454164449853065569
% SZS output start Proof for 750275454164449853065569
3. ? [X0] : (brave(X0) & patient(X0)) <=> ? [X0] : (happy(X0) & ~kind(X0)) [input p2]
4. ! [X0] : (~patient(X0) <=> (~old(X0) | ~calm(X0))) [input p3]
7. ! [X0] : ((happy(X0) | quiet(X0)) => ~calm(X0)) [input p6]
9. ! [X0] : ((patient(X0) & creative(X0)) <=> (~curious(X0) <~> ~patient(X0))) [input p8]
10. (~generous(john) | ~rich(john)) <=> (~humble(fred) & ~happy(fred)) [input p9]
13. ! [X0] : ((~brave(X0) <~> ~curious(X0)) <=> (quiet(X0) <~> old(X0))) [input p12]
15. ! [X0] : ((~strong(X0) & ~humble(X0)) <=> (brave(X0) | strong(X0))) [input p14]
16. ! [X0] : ((calm(X0) & ~quiet(X0)) <=> (~old(X0) & ~happy(X0))) [input p15]
21. calm(fred) [input p20]
25. ~rich(john) [input hypothesis]
26. ? [X0] : (brave(X0) & patient(X0)) <=> ? [X1] : (happy(X1) & ~kind(X1)) [rectify 3]
33. ! [X0] : (~calm(X0) | (~happy(X0) & ~quiet(X0))) [ennf transformation 7]
38. (? [X0] : (brave(X0) & patient(X0)) | ! [X1] : (~happy(X1) | kind(X1))) & (? [X1] : (happy(X1) & ~kind(X1)) | ! [X0] : (~brave(X0) | ~patient(X0))) [nnf transformation 26]
39. (? [X0] : (brave(X0) & patient(X0)) | ! [X1] : (~happy(X1) | kind(X1))) & (? [X2] : (happy(X2) & ~kind(X2)) | ! [X3] : (~brave(X3) | ~patient(X3))) [rectify 38]
40. ? [X0] : (brave(X0) & patient(X0)) => (brave(sK0) & patient(sK0)) [choice axiom]
41. ? [X2] : (happy(X2) & ~kind(X2)) => (happy(sK1) & ~kind(sK1)) [choice axiom]
42. ((brave(sK0) & patient(sK0)) | ! [X1] : (~happy(X1) | kind(X1))) & ((happy(sK1) & ~kind(sK1)) | ! [X3] : (~brave(X3) | ~patient(X3))) [skolemisation 39,41,40]
43. ! [X0] : ((~patient(X0) | (old(X0) & calm(X0))) & ((~old(X0) | ~calm(X0)) | patient(X0))) [nnf transformation 4]
44. ! [X0] : ((~patient(X0) | (old(X0) & calm(X0))) & (~old(X0) | ~calm(X0) | patient(X0))) [flattening 43]
50. ! [X0] : (((patient(X0) & creative(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | (~patient(X0) | ~creative(X0)))) [nnf transformation 9]
51. ! [X0] : (((patient(X0) & creative(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | ~patient(X0) | ~creative(X0))) [flattening 50]
52. ((~generous(john) | ~rich(john)) | (humble(fred) | happy(fred))) & ((~humble(fred) & ~happy(fred)) | (generous(john) & rich(john))) [nnf transformation 10]
53. (~generous(john) | ~rich(john) | humble(fred) | happy(fred)) & ((~humble(fred) & ~happy(fred)) | (generous(john) & rich(john))) [flattening 52]
59. ! [X0] : ((((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0)))) & (((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))))) [nnf transformation 13]
60. ! [X0] : (((~strong(X0) & ~humble(X0)) | (~brave(X0) & ~strong(X0))) & ((brave(X0) | strong(X0)) | (strong(X0) | humble(X0)))) [nnf transformation 15]
61. ! [X0] : (((~strong(X0) & ~humble(X0)) | (~brave(X0) & ~strong(X0))) & (brave(X0) | strong(X0) | strong(X0) | humble(X0))) [flattening 60]
62. ! [X0] : (((calm(X0) & ~quiet(X0)) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | (~calm(X0) | quiet(X0)))) [nnf transformation 16]
63. ! [X0] : (((calm(X0) & ~quiet(X0)) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | ~calm(X0) | quiet(X0))) [flattening 62]
74. ~kind(sK1) | ~brave(X3) | ~patient(X3) [cnf transformation 42]
75. happy(sK1) | ~brave(X3) | ~patient(X3) [cnf transformation 42]
76. patient(sK0) | ~happy(X1) | kind(X1) [cnf transformation 42]
79. ~patient(X0) | calm(X0) [cnf transformation 44]
80. ~patient(X0) | old(X0) [cnf transformation 44]
87. ~quiet(X0) | ~calm(X0) [cnf transformation 33]
100. patient(X0) | ~curious(X0) | patient(X0) [cnf transformation 51]
103. ~humble(fred) | rich(john) [cnf transformation 53]
113. ~brave(X0) | quiet(X0) | old(X0) | curious(X0) [cnf transformation 59]
121. brave(X0) | strong(X0) | strong(X0) | humble(X0) [cnf transformation 61]
124. ~strong(X0) | ~strong(X0) [cnf transformation 61]
127. ~old(X0) | ~calm(X0) | quiet(X0) [cnf transformation 63]
138. calm(fred) [cnf transformation 21]
144. ~rich(john) [cnf transformation 25]
145. brave(X0) | strong(X0) | humble(X0) [duplicate literal removal 121]
146. ~strong(X0) [duplicate literal removal 124]
149. ~curious(X0) | patient(X0) [duplicate literal removal 100]
151. 1 <=> ! [X1] : (~happy(X1) | kind(X1)) [avatar definition]
152. ~happy(X1) | kind(X1) <- (1) [avatar component clause 151]
159. 3 <=> patient(sK0) [avatar definition]
161. patient(sK0) <- (3) [avatar component clause 159]
162. 1 | 3 [avatar split clause 76,159,151]
164. 4 <=> ! [X3] : (~brave(X3) | ~patient(X3)) [avatar definition]
165. ~brave(X3) | ~patient(X3) <- (4) [avatar component clause 164]
167. 5 <=> happy(sK1) [avatar definition]
169. happy(sK1) <- (5) [avatar component clause 167]
170. 4 | 5 [avatar split clause 75,167,164]
172. 6 <=> kind(sK1) [avatar definition]
174. ~kind(sK1) <- (~6) [avatar component clause 172]
175. 4 | ~6 [avatar split clause 74,172,164]
184. 8 <=> humble(fred) [avatar definition]
185. ~humble(fred) <- (~8) [avatar component clause 184]
188. 9 <=> rich(john) [avatar definition]
197. 9 | ~8 [avatar split clause 103,184,188]
223. humble(X0) | brave(X0) [subsumption resolution 145,146]
224. ~calm(X0) | ~old(X0) [subsumption resolution 127,87]
265. ~9 [avatar split clause 144,188]
266. calm(sK0) <- (3) [resolution 79,161]
267. old(sK0) <- (3) [resolution 80,161]
283. brave(fred) <- (~8) [resolution 223,185]
285. ~patient(fred) <- (4, ~8) [resolution 283,165]
286. ~old(fred) [resolution 224,138]
288. ~old(sK0) <- (3) [resolution 224,266]
291. $false <- (3) [subsumption resolution 288,267]
292. ~3 [avatar contradiction clause 291]
357. quiet(fred) | old(fred) | curious(fred) <- (~8) [resolution 113,283]
358. quiet(fred) | curious(fred) <- (~8) [subsumption resolution 357,286]
360. 30 <=> curious(fred) [avatar definition]
362. curious(fred) <- (30) [avatar component clause 360]
364. 31 <=> quiet(fred) [avatar definition]
366. quiet(fred) <- (31) [avatar component clause 364]
367. 30 | 31 | 8 [avatar split clause 358,184,364,360]
374. ~calm(fred) <- (31) [resolution 366,87]
378. $false <- (31) [subsumption resolution 374,138]
379. ~31 [avatar contradiction clause 378]
385. patient(fred) <- (30) [resolution 362,149]
386. $false <- (4, ~8, 30) [subsumption resolution 385,285]
387. ~4 | 8 | ~30 [avatar contradiction clause 386]
388. kind(sK1) <- (1, 5) [resolution 169,152]
389. $false <- (1, 5, ~6) [subsumption resolution 388,174]
390. ~1 | ~5 | 6 [avatar contradiction clause 389]
391. $false [avatar sat refutation 162,170,175,197,265,292,367,379,387,390]
% SZS output end Proof for 750275454164449853065569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or happy then fred is either not tall or not wise and vice versa.
If someone is either strong or not creative then fred is both brave and not generous and vice versa.
If susan is not strong then susan is patient or not happy and vice versa.
If someone is either not wise or not old then john is not kind or curious and vice versa.
If someone is not generous then someone is not quiet and vice versa.
If susan is not calm then susan is either not quiet or not patient.
Everyone who is both funny and old is both not funny and strong.
Everyone who is not creative is not curious or humble and vice versa.
If paul is both rich and not curious then someone is brave or not tall and vice versa.
Everyone who is wise is not generous or creative and vice versa.
If susan is not generous or not rich then fred is tall or not curious.
If fred is either not brave or not humble then mary is rich.
Everyone who is not generous or generous is both brave and old and vice versa.
If mary is funny then paul is happy and vice versa.
If paul is brave or wise then lucy is both not generous and not funny.
John is either creative or not calm.
Lucy is either not wise or not curious.
Someone is old.
Fred is either happy or not tall.
Fred is creative or not wise.
Susan is patient.
Someone is either brave or calm. | Lucy is not creative. | entailment | ((?[X]:((~kind(X)|happy(X))))<=>((~tall(fred)<~>~wise(fred))))&
((?[X]:((strong(X)<~>~creative(X))))<=>((brave(fred)&~generous(fred))))&
((~strong(susan))<=>((patient(susan)|~happy(susan))))&
((?[X]:((~wise(X)<~>~old(X))))<=>((~kind(john)|curious(john))))&
((?[X]:(~generous(X)))<=>(?[X]:(~quiet(X))))&
((~calm(susan))=>((~quiet(susan)<~>~patient(susan))))&
(![X]:((funny(X)&old(X))=>(~funny(X)&strong(X))))&
(![X]:(~creative(X)<=>(~curious(X)|humble(X))))&
(((rich(paul)&~curious(paul)))<=>(?[X]:((brave(X)|~tall(X)))))&
(![X]:(wise(X)<=>(~generous(X)|creative(X))))&
(((~generous(susan)|~rich(susan)))=>((tall(fred)|~curious(fred))))&
(((~brave(fred)<~>~humble(fred)))=>(rich(mary)))&
(![X]:((~generous(X)|generous(X))<=>(brave(X)&old(X))))&
((funny(mary))<=>(happy(paul)))&
(((brave(paul)|wise(paul)))=>((~generous(lucy)&~funny(lucy))))&
((creative(john)<~>~calm(john)))&
((~wise(lucy)<~>~curious(lucy)))&
(?[X]:(old(X)))&
((happy(fred)<~>~tall(fred)))&
((creative(fred)|~wise(fred)))&
(patient(susan))&
(?[X]:((brave(X)<~>calm(X)))) | ~creative(lucy) | [
"p7",
"p9",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4918144667837819287916332
% SZS output start Proof for 4918144667837819287916332
8. ! [X0] : (~creative(X0) <=> (humble(X0) | ~curious(X0))) [input p7]
10. ! [X0] : (wise(X0) <=> (creative(X0) | ~generous(X0))) [input p9]
13. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (old(X0) & brave(X0))) [input p12]
15. (wise(paul) | brave(paul)) => (~funny(lucy) & ~generous(lucy)) [input p14]
17. ~wise(lucy) <~> ~curious(lucy) [input p16]
23. creative(lucy) [input hypothesis]
31. (~funny(lucy) & ~generous(lucy)) | (~wise(paul) & ~brave(paul)) [ennf transformation 15]
54. ! [X0] : ((~creative(X0) | (~humble(X0) & curious(X0))) & ((humble(X0) | ~curious(X0)) | creative(X0))) [nnf transformation 8]
55. ! [X0] : ((~creative(X0) | (~humble(X0) & curious(X0))) & (humble(X0) | ~curious(X0) | creative(X0))) [flattening 54]
61. ! [X0] : ((wise(X0) | (~creative(X0) & generous(X0))) & ((creative(X0) | ~generous(X0)) | ~wise(X0))) [nnf transformation 10]
62. ! [X0] : ((wise(X0) | (~creative(X0) & generous(X0))) & (creative(X0) | ~generous(X0) | ~wise(X0))) [flattening 61]
64. ! [X0] : (((generous(X0) | ~generous(X0)) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | (~generous(X0) & generous(X0)))) [nnf transformation 13]
65. ! [X0] : ((generous(X0) | ~generous(X0) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | (~generous(X0) & generous(X0)))) [flattening 64]
68. (curious(lucy) | wise(lucy)) & (~curious(lucy) | ~wise(lucy)) [nnf transformation 17]
103. ~creative(X0) | curious(X0) [cnf transformation 55]
111. generous(X0) | wise(X0) [cnf transformation 62]
117. brave(X0) | generous(X0) [cnf transformation 65]
118. brave(X0) | ~generous(X0) [cnf transformation 65]
124. ~generous(lucy) | ~brave(paul) [cnf transformation 31]
130. ~curious(lucy) | ~wise(lucy) [cnf transformation 68]
139. creative(lucy) [cnf transformation 23]
318. brave(X0) [subsumption resolution 117,118]
341. 43 <=> generous(lucy) [avatar definition]
343. ~generous(lucy) <- (~43) [avatar component clause 341]
345. ~generous(lucy) [subsumption resolution 124,318]
346. ~43 [avatar split clause 345,341]
358. 46 <=> wise(lucy) [avatar definition]
359. ~wise(lucy) <- (~46) [avatar component clause 358]
362. 47 <=> curious(lucy) [avatar definition]
366. ~46 | ~47 [avatar split clause 130,362,358]
390. curious(lucy) [resolution 103,139]
393. 47 [avatar split clause 390,362]
397. wise(lucy) <- (~43) [resolution 111,343]
398. $false <- (~43, ~46) [subsumption resolution 397,359]
399. 43 | 46 [avatar contradiction clause 398]
400. $false [avatar sat refutation 346,366,393,399]
% SZS output end Proof for 4918144667837819287916332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or brave is both not tall and not rich and vice versa.
Everyone who is either not old or not rich is calm or funny and vice versa.
Everyone who is either brave or humble is either patient or old and vice versa.
Everyone who is both creative and not tall is both not old and patient.
If someone is not generous then someone is both not generous and not rich and vice versa.
If someone is humble then alice is curious and vice versa.
If mary is not old then someone is humble and vice versa.
If someone is both funny and not generous then alice is either rich or funny.
Everyone who is not rich or curious is tall or not rich and vice versa.
Everyone who is either rich or old is not humble.
Everyone who is tall or not creative is quiet.
Everyone who is both generous and not patient is not calm or funny.
Everyone who is either humble or strong is both creative and funny.
Everyone who is not humble or not funny is both strong and not funny and vice versa.
Everyone who is old is not strong or tall and vice versa.
If someone is either old or curious then someone is kind or not rich and vice versa.
Someone is not wise.
Lucy is not tall or not strong.
Someone is either not kind or not generous.
Fred is both not rich and not brave.
Someone is both patient and not rich.
Someone is either generous or not funny. | Lucy is not rich. | entailment | (![X]:((~wise(X)|brave(X))<=>(~tall(X)&~rich(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(calm(X)|funny(X))))&
(![X]:((brave(X)<~>humble(X))<=>(patient(X)<~>old(X))))&
(![X]:((creative(X)&~tall(X))=>(~old(X)&patient(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)&~rich(X)))))&
((?[X]:(humble(X)))<=>(curious(alice)))&
((~old(mary))<=>(?[X]:(humble(X))))&
((?[X]:((funny(X)&~generous(X))))=>((rich(alice)<~>funny(alice))))&
(![X]:((~rich(X)|curious(X))<=>(tall(X)|~rich(X))))&
(![X]:((rich(X)<~>old(X))=>~humble(X)))&
(![X]:((tall(X)|~creative(X))=>quiet(X)))&
(![X]:((generous(X)&~patient(X))=>(~calm(X)|funny(X))))&
(![X]:((humble(X)<~>strong(X))=>(creative(X)&funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(strong(X)&~funny(X))))&
(![X]:(old(X)<=>(~strong(X)|tall(X))))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:((kind(X)|~rich(X)))))&
(?[X]:(~wise(X)))&
((~tall(lucy)|~strong(lucy)))&
(?[X]:((~kind(X)<~>~generous(X))))&
((~rich(fred)&~brave(fred)))&
(?[X]:((patient(X)&~rich(X))))&
(?[X]:((generous(X)<~>~funny(X)))) | ~rich(lucy) | [
"p1",
"p9",
"p12",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1148983354455522664711202
% SZS output start Proof for 1148983354455522664711202
2. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (funny(X0) | calm(X0))) [input p1]
10. ! [X0] : ((rich(X0) <~> old(X0)) => ~humble(X0)) [input p9]
13. ! [X0] : ((humble(X0) <~> strong(X0)) => (funny(X0) & creative(X0))) [input p12]
14. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (~funny(X0) & strong(X0))) [input p13]
15. ! [X0] : (old(X0) <=> (tall(X0) | ~strong(X0))) [input p14]
18. ~strong(lucy) | ~tall(lucy) [input p17]
23. rich(lucy) [input hypothesis]
30. ! [X0] : (~humble(X0) | (rich(X0) <=> old(X0))) [ennf transformation 10]
33. ! [X0] : ((funny(X0) & creative(X0)) | (humble(X0) <=> strong(X0))) [ennf transformation 13]
36. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 2]
37. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 36]
55. ! [X0] : (~humble(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) [nnf transformation 30]
56. ! [X0] : ((funny(X0) & creative(X0)) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0)))) [nnf transformation 33]
57. ! [X0] : (((~funny(X0) | ~humble(X0)) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 14]
58. ! [X0] : ((~funny(X0) | ~humble(X0) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [flattening 57]
59. ! [X0] : ((old(X0) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ~old(X0))) [nnf transformation 15]
60. ! [X0] : ((old(X0) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ~old(X0))) [flattening 59]
84. ~funny(X0) | ~old(X0) | ~rich(X0) [cnf transformation 37]
110. ~humble(X0) | old(X0) | ~rich(X0) [cnf transformation 55]
116. ~strong(X0) | humble(X0) | funny(X0) [cnf transformation 56]
118. strong(X0) | funny(X0) [cnf transformation 58]
119. ~funny(X0) | humble(X0) [cnf transformation 58]
122. ~strong(X0) | tall(X0) | ~old(X0) [cnf transformation 60]
123. strong(X0) | old(X0) [cnf transformation 60]
132. ~strong(lucy) | ~tall(lucy) [cnf transformation 18]
141. rich(lucy) [cnf transformation 23]
234. 22 <=> tall(lucy) [avatar definition]
236. ~tall(lucy) <- (~22) [avatar component clause 234]
238. 23 <=> strong(lucy) [avatar definition]
239. strong(lucy) <- (23) [avatar component clause 238]
240. ~strong(lucy) <- (~23) [avatar component clause 238]
241. ~22 | ~23 [avatar split clause 132,238,234]
267. funny(lucy) <- (~23) [resolution 118,240]
269. old(lucy) <- (~23) [resolution 123,240]
271. ~old(lucy) | ~rich(lucy) <- (~23) [resolution 84,267]
272. ~rich(lucy) <- (~23) [subsumption resolution 271,269]
273. $false <- (~23) [subsumption resolution 272,141]
274. 23 [avatar contradiction clause 273]
348. humble(X1) | funny(X1) | funny(X1) [resolution 116,118]
352. humble(X1) | funny(X1) [duplicate literal removal 348]
354. humble(X1) [subsumption resolution 352,119]
358. tall(lucy) | ~old(lucy) <- (23) [resolution 122,239]
359. ~old(lucy) <- (~22, 23) [subsumption resolution 358,236]
406. ~rich(X3) | old(X3) [resolution 354,110]
521. old(lucy) [resolution 406,141]
523. $false <- (~22, 23) [subsumption resolution 521,359]
524. 22 | ~23 [avatar contradiction clause 523]
525. $false [avatar sat refutation 241,274,524]
% SZS output end Proof for 1148983354455522664711202
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either rich or not wise is not quiet and vice versa.
Everyone who is either not funny or not creative is rich and vice versa.
Everyone who is either generous or not tall is either tall or happy and vice versa.
If mary is not tall then alice is generous or happy and vice versa.
Everyone who is both funny and wise is both rich and generous and vice versa.
Everyone who is both not rich and brave is either not creative or not curious.
If susan is either not strong or funny then lucy is strong.
If someone is both strong and tall then john is kind or not brave.
If lucy is both quiet and tall then susan is both patient and not old.
Everyone who is not curious is not kind or not generous and vice versa.
Everyone who is happy is not humble and vice versa.
If someone is not wise or not creative then someone is both funny and not quiet.
If john is either not strong or kind then someone is not wise.
Everyone who is both not creative and creative is not brave and vice versa.
If paul is either generous or kind then someone is both happy and not strong and vice versa.
Everyone who is both not funny and not happy is both not brave and not old and vice versa.
Fred is either brave or tall.
Fred is both patient and strong.
Lucy is tall.
Fred is not happy.
Someone is not kind or patient.
Someone is kind or funny.
Susan is not quiet or curious.
Fred is not rich. | Fred is tall. | contradiction | (![X]:((rich(X)<~>~wise(X))<=>~quiet(X)))&
(![X]:((~funny(X)<~>~creative(X))<=>rich(X)))&
(![X]:((generous(X)<~>~tall(X))<=>(tall(X)<~>happy(X))))&
((~tall(mary))<=>((generous(alice)|happy(alice))))&
(![X]:((funny(X)&wise(X))<=>(rich(X)&generous(X))))&
(![X]:((~rich(X)&brave(X))=>(~creative(X)<~>~curious(X))))&
(((~strong(susan)<~>funny(susan)))=>(strong(lucy)))&
((?[X]:((strong(X)&tall(X))))=>((kind(john)|~brave(john))))&
(((quiet(lucy)&tall(lucy)))=>((patient(susan)&~old(susan))))&
(![X]:(~curious(X)<=>(~kind(X)|~generous(X))))&
(![X]:(happy(X)<=>~humble(X)))&
((?[X]:((~wise(X)|~creative(X))))=>(?[X]:((funny(X)&~quiet(X)))))&
(((~strong(john)<~>kind(john)))=>(?[X]:(~wise(X))))&
(![X]:((~creative(X)&creative(X))<=>~brave(X)))&
(((generous(paul)<~>kind(paul)))<=>(?[X]:((happy(X)&~strong(X)))))&
(![X]:((~funny(X)&~happy(X))<=>(~brave(X)&~old(X))))&
((brave(fred)<~>tall(fred)))&
((patient(fred)&strong(fred)))&
(tall(lucy))&
(~happy(fred))&
(?[X]:((~kind(X)|patient(X))))&
(?[X]:((kind(X)|funny(X))))&
((~quiet(susan)|curious(susan)))&
(~rich(fred)) | tall(fred) | [
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5408880761512724391522171
% SZS output start Proof for 5408880761512724391522171
14. ! [X0] : ((creative(X0) & ~creative(X0)) <=> ~brave(X0)) [input p13]
17. brave(fred) <~> tall(fred) [input p16]
25. tall(fred) [input hypothesis]
59. ! [X0] : (((creative(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | (~creative(X0) | creative(X0)))) [nnf transformation 14]
60. ! [X0] : (((creative(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | ~creative(X0) | creative(X0))) [flattening 59]
67. (~tall(fred) | ~brave(fred)) & (tall(fred) | brave(fred)) [nnf transformation 17]
109. ~creative(X0) | brave(X0) [cnf transformation 60]
110. creative(X0) | brave(X0) [cnf transformation 60]
122. ~tall(fred) | ~brave(fred) [cnf transformation 67]
129. tall(fred) [cnf transformation 25]
217. brave(X0) [subsumption resolution 109,110]
244. ~tall(fred) [subsumption resolution 122,217]
264. $false [subsumption resolution 129,244]
% SZS output end Proof for 5408880761512724391522171
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is either not brave or not strong and vice versa.
If someone is both not rich and generous then mary is not curious.
Everyone who is either humble or not generous is either strong or not kind and vice versa.
If someone is not patient then someone is not wise.
Everyone who is curious is both not kind and not tall.
Everyone who is both curious and not quiet is either generous or strong and vice versa.
Everyone who is both not wise and not humble is either brave or not curious and vice versa.
Everyone who is either not generous or not funny is not happy or happy.
If mary is not creative or not wise then someone is either quiet or not rich.
Everyone who is either not funny or old is both not humble and not funny and vice versa.
If someone is curious then lucy is not rich and vice versa.
If paul is both happy and not strong then paul is both not kind and kind and vice versa.
Everyone who is either happy or brave is not kind and vice versa.
Everyone who is both not tall and not patient is both happy and creative and vice versa.
Everyone who is both creative and wise is not curious and vice versa.
Everyone who is not old is either quiet or strong and vice versa.
Someone is not kind or not curious.
Someone is both not humble and not quiet.
Someone is not rich.
Someone is either patient or brave.
John is not generous or brave.
Someone is not strong.
Mary is generous or not kind.
Someone is rich. | Mary is humble. | contradiction | (![X]:(old(X)<=>(~brave(X)<~>~strong(X))))&
((?[X]:((~rich(X)&generous(X))))=>(~curious(mary)))&
(![X]:((humble(X)<~>~generous(X))<=>(strong(X)<~>~kind(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~wise(X))))&
(![X]:(curious(X)=>(~kind(X)&~tall(X))))&
(![X]:((curious(X)&~quiet(X))<=>(generous(X)<~>strong(X))))&
(![X]:((~wise(X)&~humble(X))<=>(brave(X)<~>~curious(X))))&
(![X]:((~generous(X)<~>~funny(X))=>(~happy(X)|happy(X))))&
(((~creative(mary)|~wise(mary)))=>(?[X]:((quiet(X)<~>~rich(X)))))&
(![X]:((~funny(X)<~>old(X))<=>(~humble(X)&~funny(X))))&
((?[X]:(curious(X)))<=>(~rich(lucy)))&
(((happy(paul)&~strong(paul)))<=>((~kind(paul)&kind(paul))))&
(![X]:((happy(X)<~>brave(X))<=>~kind(X)))&
(![X]:((~tall(X)&~patient(X))<=>(happy(X)&creative(X))))&
(![X]:((creative(X)&wise(X))<=>~curious(X)))&
(![X]:(~old(X)<=>(quiet(X)<~>strong(X))))&
(?[X]:((~kind(X)|~curious(X))))&
(?[X]:((~humble(X)&~quiet(X))))&
(?[X]:(~rich(X)))&
(?[X]:((patient(X)<~>brave(X))))&
((~generous(john)|brave(john)))&
(?[X]:(~strong(X)))&
((generous(mary)|~kind(mary)))&
(?[X]:(rich(X))) | humble(mary) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p6",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6142465193401535454594659
% SZS output start Proof for 6142465193401535454594659
1. ! [X0] : (old(X0) <=> (~brave(X0) <~> ~strong(X0))) [input p0]
3. ! [X0] : ((humble(X0) <~> ~generous(X0)) <=> (strong(X0) <~> ~kind(X0))) [input p2]
4. ? [X0] : ~patient(X0) => ? [X0] : ~wise(X0) [input p3]
5. ! [X0] : (curious(X0) => (~tall(X0) & ~kind(X0))) [input p4]
6. ! [X0] : ((~quiet(X0) & curious(X0)) <=> (generous(X0) <~> strong(X0))) [input p5]
7. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (brave(X0) <~> ~curious(X0))) [input p6]
13. ! [X0] : ((happy(X0) <~> brave(X0)) <=> ~kind(X0)) [input p12]
14. ! [X0] : ((~patient(X0) & ~tall(X0)) <=> (creative(X0) & happy(X0))) [input p13]
15. ! [X0] : ((wise(X0) & creative(X0)) <=> ~curious(X0)) [input p14]
16. ! [X0] : (~old(X0) <=> (quiet(X0) <~> strong(X0))) [input p15]
25. humble(mary) [input hypothesis]
26. ? [X0] : ~patient(X0) => ? [X1] : ~wise(X1) [rectify 4]
28. ? [X1] : ~wise(X1) | ! [X0] : patient(X0) [ennf transformation 26]
29. ! [X0] : ((~tall(X0) & ~kind(X0)) | ~curious(X0)) [ennf transformation 5]
33. ! [X0] : ((old(X0) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0)))) & (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | ~old(X0))) [nnf transformation 1]
34. ! [X0] : ((((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))))) [nnf transformation 3]
35. ? [X0] : ~wise(X0) | ! [X1] : patient(X1) [rectify 28]
36. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
37. ~wise(sK0) | ! [X1] : patient(X1) [skolemisation 35,36]
38. ! [X0] : (((~quiet(X0) & curious(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0)))) & (((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (quiet(X0) | ~curious(X0)))) [nnf transformation 6]
39. ! [X0] : (((~quiet(X0) & curious(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0)))) & (((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | quiet(X0) | ~curious(X0))) [flattening 38]
40. ! [X0] : (((~humble(X0) & ~wise(X0)) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0)))) & (((curious(X0) | ~brave(X0)) & (~curious(X0) | brave(X0))) | (humble(X0) | wise(X0)))) [nnf transformation 7]
41. ! [X0] : (((~humble(X0) & ~wise(X0)) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0)))) & (((curious(X0) | ~brave(X0)) & (~curious(X0) | brave(X0))) | humble(X0) | wise(X0))) [flattening 40]
54. ! [X0] : ((((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | kind(X0)) & (~kind(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0))))) [nnf transformation 13]
55. ! [X0] : (((~patient(X0) & ~tall(X0)) | (~creative(X0) | ~happy(X0))) & ((creative(X0) & happy(X0)) | (patient(X0) | tall(X0)))) [nnf transformation 14]
56. ! [X0] : (((~patient(X0) & ~tall(X0)) | ~creative(X0) | ~happy(X0)) & ((creative(X0) & happy(X0)) | patient(X0) | tall(X0))) [flattening 55]
57. ! [X0] : (((wise(X0) & creative(X0)) | curious(X0)) & (~curious(X0) | (~wise(X0) | ~creative(X0)))) [nnf transformation 15]
58. ! [X0] : (((wise(X0) & creative(X0)) | curious(X0)) & (~curious(X0) | ~wise(X0) | ~creative(X0))) [flattening 57]
59. ! [X0] : ((~old(X0) | ((quiet(X0) | ~strong(X0)) & (strong(X0) | ~quiet(X0)))) & (((~strong(X0) | ~quiet(X0)) & (strong(X0) | quiet(X0))) | old(X0))) [nnf transformation 16]
73. ~strong(X0) | ~brave(X0) | ~old(X0) [cnf transformation 33]
74. ~old(X0) | brave(X0) | strong(X0) [cnf transformation 33]
75. ~strong(X0) | old(X0) | brave(X0) [cnf transformation 33]
76. ~brave(X0) | old(X0) | strong(X0) [cnf transformation 33]
80. ~humble(X0) | ~strong(X0) | ~generous(X0) | kind(X0) [cnf transformation 34]
81. ~strong(X0) | kind(X0) | humble(X0) | generous(X0) [cnf transformation 34]
83. ~generous(X0) | humble(X0) | strong(X0) | kind(X0) [cnf transformation 34]
85. ~humble(X0) | generous(X0) | strong(X0) | kind(X0) [cnf transformation 34]
86. ~wise(sK0) | patient(X1) [cnf transformation 37]
87. ~kind(X0) | ~curious(X0) [cnf transformation 29]
89. ~curious(X0) | generous(X0) | quiet(X0) | strong(X0) [cnf transformation 39]
90. ~curious(X0) | ~generous(X0) | quiet(X0) | ~strong(X0) [cnf transformation 39]
91. ~generous(X0) | strong(X0) | curious(X0) [cnf transformation 39]
92. ~strong(X0) | generous(X0) | curious(X0) [cnf transformation 39]
93. ~quiet(X0) | strong(X0) | ~generous(X0) [cnf transformation 39]
94. ~quiet(X0) | generous(X0) | ~strong(X0) [cnf transformation 39]
95. ~curious(X0) | brave(X0) | humble(X0) | wise(X0) [cnf transformation 41]
98. ~wise(X0) | brave(X0) | curious(X0) [cnf transformation 41]
99. ~humble(X0) | ~curious(X0) | ~brave(X0) [cnf transformation 41]
120. ~kind(X0) | happy(X0) | ~brave(X0) [cnf transformation 54]
121. happy(X0) | brave(X0) | kind(X0) [cnf transformation 54]
126. ~creative(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 56]
128. creative(X0) | curious(X0) [cnf transformation 58]
129. wise(X0) | curious(X0) [cnf transformation 58]
130. quiet(X0) | strong(X0) | old(X0) [cnf transformation 59]
131. ~quiet(X0) | ~strong(X0) | old(X0) [cnf transformation 59]
132. ~quiet(X0) | strong(X0) | ~old(X0) [cnf transformation 59]
133. ~strong(X0) | quiet(X0) | ~old(X0) [cnf transformation 59]
144. humble(mary) [cnf transformation 25]
151. 2 <=> curious(mary) [avatar definition]
153. ~curious(mary) <- (~2) [avatar component clause 151]
156. 3 <=> ! [X1] : patient(X1) [avatar definition]
157. patient(X1) <- (3) [avatar component clause 156]
159. 4 <=> wise(sK0) [avatar definition]
161. ~wise(sK0) <- (~4) [avatar component clause 159]
162. 3 | ~4 [avatar split clause 86,159,156]
230. 19 <=> generous(mary) [avatar definition]
231. ~generous(mary) <- (~19) [avatar component clause 230]
232. generous(mary) <- (19) [avatar component clause 230]
234. 20 <=> kind(mary) [avatar definition]
235. kind(mary) <- (20) [avatar component clause 234]
236. ~kind(mary) <- (~20) [avatar component clause 234]
238. curious(sK0) <- (~4) [resolution 129,161]
240. brave(X0) | curious(X0) | curious(X0) [resolution 98,129]
241. curious(X0) | brave(X0) [duplicate literal removal 240]
242. ~curious(mary) | ~brave(mary) [resolution 99,144]
247. 21 <=> strong(mary) [avatar definition]
249. strong(mary) <- (21) [avatar component clause 247]
251. 22 <=> old(mary) [avatar definition]
252. ~old(mary) <- (~22) [avatar component clause 251]
253. old(mary) <- (22) [avatar component clause 251]
256. 23 <=> brave(mary) [avatar definition]
259. ~23 | ~2 [avatar split clause 242,151,256]
266. brave(mary) | strong(mary) <- (22) [resolution 253,74]
269. generous(mary) | curious(mary) <- (21) [resolution 249,92]
333. ~happy(X1) | ~patient(X1) | curious(X1) [resolution 126,128]
342. strong(X1) | old(X1) | strong(X1) | ~generous(X1) [resolution 130,93]
343. ~generous(X1) | old(X1) | strong(X1) [duplicate literal removal 342]
451. 45 <=> happy(mary) [avatar definition]
452. happy(mary) <- (45) [avatar component clause 451]
453. ~happy(mary) <- (~45) [avatar component clause 451]
460. 2 | 19 | ~21 [avatar split clause 269,247,230,151]
464. ~strong(mary) | ~generous(mary) | kind(mary) [resolution 80,144]
485. generous(mary) | strong(mary) | kind(mary) [resolution 85,144]
495. generous(sK0) | quiet(sK0) | strong(sK0) <- (~4) [resolution 89,238]
498. 48 <=> strong(sK0) [avatar definition]
499. ~strong(sK0) <- (~48) [avatar component clause 498]
500. strong(sK0) <- (48) [avatar component clause 498]
502. 49 <=> quiet(sK0) [avatar definition]
504. quiet(sK0) <- (49) [avatar component clause 502]
506. 50 <=> generous(sK0) [avatar definition]
507. ~generous(sK0) <- (~50) [avatar component clause 506]
508. generous(sK0) <- (50) [avatar component clause 506]
509. 48 | 49 | 50 | 4 [avatar split clause 495,159,506,502,498]
537. ~generous(sK0) | quiet(sK0) | ~strong(sK0) <- (~4) [resolution 90,238]
539. ~generous(sK0) | quiet(sK0) <- (~4, 48) [subsumption resolution 537,500]
540. 49 | ~50 | 4 | ~48 [avatar split clause 539,498,159,506,502]
566. ~curious(mary) <- (20) [resolution 235,87]
567. brave(X0) | humble(X0) | wise(X0) | brave(X0) [resolution 95,241]
568. wise(X0) | humble(X0) | brave(X0) [duplicate literal removal 567]
570. brave(mary) | kind(mary) <- (~45) [resolution 453,121]
686. quiet(sK0) | ~old(sK0) <- (48) [resolution 500,133]
692. 57 <=> humble(sK0) [avatar definition]
694. humble(sK0) <- (57) [avatar component clause 692]
696. 58 <=> kind(sK0) [avatar definition]
697. ~kind(sK0) <- (~58) [avatar component clause 696]
698. kind(sK0) <- (58) [avatar component clause 696]
701. 59 <=> old(sK0) [avatar definition]
702. old(sK0) <- (59) [avatar component clause 701]
703. ~old(sK0) <- (~59) [avatar component clause 701]
704. ~59 | 49 | ~48 [avatar split clause 686,498,502,701]
713. old(sK0) | strong(sK0) <- (50) [resolution 508,343]
714. humble(sK0) | strong(sK0) | kind(sK0) <- (50) [resolution 508,83]
741. ~2 | ~20 [avatar split clause 566,234,151]
758. brave(mary) <- (~20, ~45) [subsumption resolution 570,236]
759. 23 | 20 | 45 [avatar split clause 758,451,234,256]
760. 21 | 23 | ~22 [avatar split clause 266,251,256,247]
773. ~patient(mary) | curious(mary) <- (45) [resolution 452,333]
838. quiet(mary) | ~old(mary) <- (21) [resolution 249,133]
842. quiet(mary) <- (21, 22) [subsumption resolution 838,253]
864. generous(mary) | ~strong(mary) <- (21, 22) [resolution 842,94]
866. ~strong(mary) <- (~19, 21, 22) [subsumption resolution 864,231]
867. $false <- (~19, 21, 22) [subsumption resolution 866,249]
868. 19 | ~21 | ~22 [avatar contradiction clause 867]
879. generous(mary) | strong(mary) <- (~20) [subsumption resolution 485,236]
880. 21 | 19 | 20 [avatar split clause 879,234,230,247]
883. old(mary) | strong(mary) <- (19) [resolution 232,343]
886. strong(mary) | curious(mary) <- (19) [resolution 232,91]
887. strong(mary) <- (19, ~22) [subsumption resolution 883,252]
890. 2 | 21 | ~19 [avatar split clause 886,230,247,151]
891. curious(mary) <- (3, 45) [subsumption resolution 773,157]
892. 2 | ~3 | ~45 [avatar split clause 891,451,156,151]
894. ~strong(mary) | kind(mary) <- (19) [subsumption resolution 464,232]
895. 20 | ~21 | ~19 [avatar split clause 894,230,247,234]
897. 21 | ~19 | 22 [avatar split clause 887,251,230,247]
917. 65 <=> brave(sK0) [avatar definition]
919. brave(sK0) <- (65) [avatar component clause 917]
922. 66 <=> curious(sK0) [avatar definition]
924. curious(sK0) <- (66) [avatar component clause 922]
926. 58 | 48 | 57 | ~50 [avatar split clause 714,506,692,498,696]
929. old(sK0) <- (~48, 50) [subsumption resolution 713,499]
930. 59 | 48 | ~50 [avatar split clause 929,506,498,701]
931. brave(mary) <- (~2) [resolution 153,241]
932. humble(sK0) | brave(sK0) <- (~4) [resolution 161,568]
933. curious(sK0) <- (~4) [resolution 161,129]
942. happy(mary) | ~brave(mary) <- (20) [resolution 235,120]
951. old(mary) | brave(mary) <- (21) [resolution 249,75]
957. ~curious(sK0) | ~brave(sK0) <- (57) [resolution 694,99]
958. ~brave(sK0) <- (57, 66) [subsumption resolution 957,924]
959. ~65 | ~57 | ~66 [avatar split clause 958,922,692,917]
961. brave(sK0) | strong(sK0) <- (59) [resolution 702,74]
970. 65 | 57 | 4 [avatar split clause 932,159,692,917]
971. brave(sK0) <- (~48, 59) [subsumption resolution 961,499]
972. 65 | 48 | ~59 [avatar split clause 971,701,498,917]
973. kind(sK0) | humble(sK0) | generous(sK0) <- (48) [resolution 500,81]
982. ~curious(sK0) <- (58) [resolution 698,87]
988. ~66 | ~58 [avatar split clause 982,696,922]
991. 66 | 4 [avatar split clause 933,159,922]
992. kind(sK0) | humble(sK0) <- (48, ~50) [subsumption resolution 973,507]
993. 57 | 58 | ~48 | 50 [avatar split clause 992,506,498,696,692]
996. strong(sK0) | ~old(sK0) <- (49) [resolution 504,132]
997. ~strong(sK0) | old(sK0) <- (49) [resolution 504,131]
998. generous(sK0) | ~strong(sK0) <- (49) [resolution 504,94]
999. strong(sK0) | ~generous(sK0) <- (49) [resolution 504,93]
1014. old(sK0) | strong(sK0) <- (65) [resolution 919,76]
1025. strong(sK0) <- (~59, 65) [subsumption resolution 1014,703]
1026. $false <- (~48, ~59, 65) [subsumption resolution 1025,499]
1027. 48 | 59 | ~65 [avatar contradiction clause 1026]
1028. generous(sK0) | strong(sK0) | kind(sK0) <- (57) [resolution 694,85]
1033. strong(sK0) | kind(sK0) <- (~50, 57) [subsumption resolution 1028,507]
1034. kind(sK0) <- (~48, ~50, 57) [subsumption resolution 1033,499]
1035. $false <- (~48, ~50, 57, ~58) [subsumption resolution 1034,697]
1036. 48 | 50 | ~57 | 58 [avatar contradiction clause 1035]
1041. strong(sK0) <- (49, 59) [subsumption resolution 996,702]
1042. 48 | ~49 | ~59 [avatar split clause 1041,701,502,498]
1043. ~48 | 50 | ~49 [avatar split clause 998,502,506,498]
1044. ~50 | 48 | ~49 [avatar split clause 999,502,498,506]
1048. old(sK0) | brave(sK0) <- (48) [resolution 500,75]
1049. ~brave(sK0) | ~old(sK0) <- (48) [resolution 500,73]
1061. ~strong(sK0) | ~generous(sK0) | kind(sK0) <- (57) [resolution 694,80]
1065. ~generous(sK0) | kind(sK0) <- (48, 57) [subsumption resolution 1061,500]
1066. kind(sK0) <- (48, 50, 57) [subsumption resolution 1065,508]
1067. $false <- (48, 50, 57, ~58) [subsumption resolution 1066,697]
1068. ~48 | ~50 | ~57 | 58 [avatar contradiction clause 1067]
1072. 23 | 22 | ~21 [avatar split clause 951,247,251,256]
1078. 23 | 2 [avatar split clause 931,151,256]
1079. ~23 | 45 | ~20 [avatar split clause 942,234,451,256]
1081. ~59 | ~65 | ~48 [avatar split clause 1049,498,917,701]
1082. 65 | 59 | ~48 [avatar split clause 1048,498,701,917]
1083. old(sK0) <- (48, 49) [subsumption resolution 997,500]
1084. 59 | ~48 | ~49 [avatar split clause 1083,502,498,701]
1085. $false [avatar sat refutation 162,259,460,509,540,704,741,759,760,868,880,890,892,895,897,926,930,959,970,972,988,991,993,1027,1036,1042,1043,1044,1068,1072,1078,1079,1081,1082,1084]
% SZS output end Proof for 6142465193401535454594659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not rich then lucy is either creative or calm and vice versa. Everyone who is both not curious and not humble is not strong or not patient and vice versa. If someone is both not happy and old then john is humble or happy. If mary is kind or creative then someone is not calm or not curious. If someone is either not kind or not curious then someone is not tall and vice versa. Everyone who is not humble is not quiet or not kind and vice versa. Everyone who is strong or curious is either patient or not rich. Everyone who is either happy or strong is both calm and not funny. Everyone who is either not patient or not humble is either not happy or generous and vice versa. Everyone who is wise is both not humble and humble. If someone is strong or not calm then someone is either not funny or not wise and vice versa. Everyone who is either curious or not generous is humble or brave and vice versa. Everyone who is both not happy and kind is brave or not tall and vice versa. Everyone who is not humble is both kind and calm. Everyone who is either kind or not tall is not patient and vice versa. Everyone who is not humble is either not funny or not brave. Someone is old or not creative. Mary is both calm and not old. John is not wise. John is either kind or happy. | Lucy is not tall. | entailment | ((~rich(paul))<=>((creative(lucy)<~>calm(lucy))))&
(![X]:((~curious(X)&~humble(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((~happy(X)&old(X))))=>((humble(john)|happy(john))))&
(((kind(mary)|creative(mary)))=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((~kind(X)<~>~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:(~humble(X)<=>(~quiet(X)|~kind(X))))&
(![X]:((strong(X)|curious(X))=>(patient(X)<~>~rich(X))))&
(![X]:((happy(X)<~>strong(X))=>(calm(X)&~funny(X))))&
(![X]:((~patient(X)<~>~humble(X))<=>(~happy(X)<~>generous(X))))&
(![X]:(wise(X)=>(~humble(X)&humble(X))))&
((?[X]:((strong(X)|~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:((curious(X)<~>~generous(X))<=>(humble(X)|brave(X))))&
(![X]:((~happy(X)&kind(X))<=>(brave(X)|~tall(X))))&
(![X]:(~humble(X)=>(kind(X)&calm(X))))&
(![X]:((kind(X)<~>~tall(X))<=>~patient(X)))&
(![X]:(~humble(X)=>(~funny(X)<~>~brave(X))))&
(?[X]:((old(X)|~creative(X))))&
((calm(mary)&~old(mary)))&
(~wise(john))&
((kind(john)<~>happy(john))) | ~tall(lucy) | [
"p1",
"p5",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 248291617975048976232385
% SZS output start Proof for 248291617975048976232385
2. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> (~patient(X0) | ~strong(X0))) [input p1]
6. ! [X0] : (~humble(X0) <=> (~kind(X0) | ~quiet(X0))) [input p5]
8. ! [X0] : ((happy(X0) <~> strong(X0)) => (~funny(X0) & calm(X0))) [input p7]
9. ! [X0] : ((~patient(X0) <~> ~humble(X0)) <=> (~happy(X0) <~> generous(X0))) [input p8]
10. ! [X0] : (wise(X0) => (humble(X0) & ~humble(X0))) [input p9]
11. ? [X0] : (~calm(X0) | strong(X0)) <=> ? [X0] : (~funny(X0) <~> ~wise(X0)) [input p10]
12. ! [X0] : ((curious(X0) <~> ~generous(X0)) <=> (brave(X0) | humble(X0))) [input p11]
13. ! [X0] : ((kind(X0) & ~happy(X0)) <=> (~tall(X0) | brave(X0))) [input p12]
14. ! [X0] : (~humble(X0) => (calm(X0) & kind(X0))) [input p13]
15. ! [X0] : ((kind(X0) <~> ~tall(X0)) <=> ~patient(X0)) [input p14]
16. ! [X0] : (~humble(X0) => (~funny(X0) <~> ~brave(X0))) [input p15]
21. tall(lucy) [input hypothesis]
23. ? [X0] : (~calm(X0) | strong(X0)) <=> ? [X1] : (~funny(X1) <~> ~wise(X1)) [rectify 11]
28. ! [X0] : ((~funny(X0) & calm(X0)) | (happy(X0) <=> strong(X0))) [ennf transformation 8]
29. ! [X0] : ((humble(X0) & ~humble(X0)) | ~wise(X0)) [ennf transformation 10]
30. ! [X0] : ((calm(X0) & kind(X0)) | humble(X0)) [ennf transformation 14]
31. ! [X0] : ((~funny(X0) <~> ~brave(X0)) | humble(X0)) [ennf transformation 16]
33. ! [X0] : (((~humble(X0) & ~curious(X0)) | (patient(X0) & strong(X0))) & ((~patient(X0) | ~strong(X0)) | (humble(X0) | curious(X0)))) [nnf transformation 2]
34. ! [X0] : (((~humble(X0) & ~curious(X0)) | (patient(X0) & strong(X0))) & (~patient(X0) | ~strong(X0) | humble(X0) | curious(X0))) [flattening 33]
42. ! [X0] : ((~humble(X0) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | humble(X0))) [nnf transformation 6]
43. ! [X0] : ((~humble(X0) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | humble(X0))) [flattening 42]
45. ! [X0] : ((~funny(X0) & calm(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) [nnf transformation 28]
46. ! [X0] : ((((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0))))) [nnf transformation 9]
47. (? [X0] : (~calm(X0) | strong(X0)) | ! [X1] : ((~funny(X1) | wise(X1)) & (~wise(X1) | funny(X1)))) & (? [X1] : ((wise(X1) | funny(X1)) & (~wise(X1) | ~funny(X1))) | ! [X0] : (calm(X0) & ~strong(X0))) [nnf transformation 23]
48. (? [X0] : (~calm(X0) | strong(X0)) | ! [X1] : ((~funny(X1) | wise(X1)) & (~wise(X1) | funny(X1)))) & (? [X2] : ((wise(X2) | funny(X2)) & (~wise(X2) | ~funny(X2))) | ! [X3] : (calm(X3) & ~strong(X3))) [rectify 47]
49. ? [X0] : (~calm(X0) | strong(X0)) => (~calm(sK3) | strong(sK3)) [choice axiom]
50. ? [X2] : ((wise(X2) | funny(X2)) & (~wise(X2) | ~funny(X2))) => ((wise(sK4) | funny(sK4)) & (~wise(sK4) | ~funny(sK4))) [choice axiom]
51. ((~calm(sK3) | strong(sK3)) | ! [X1] : ((~funny(X1) | wise(X1)) & (~wise(X1) | funny(X1)))) & (((wise(sK4) | funny(sK4)) & (~wise(sK4) | ~funny(sK4))) | ! [X3] : (calm(X3) & ~strong(X3))) [skolemisation 48,50,49]
52. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [nnf transformation 12]
53. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [flattening 52]
54. ! [X0] : (((kind(X0) & ~happy(X0)) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | (~kind(X0) | happy(X0)))) [nnf transformation 13]
55. ! [X0] : (((kind(X0) & ~happy(X0)) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | ~kind(X0) | happy(X0))) [flattening 54]
56. ! [X0] : ((((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | patient(X0)) & (~patient(X0) | ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0))))) [nnf transformation 15]
57. ! [X0] : (((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | humble(X0)) [nnf transformation 31]
66. ~curious(X0) | strong(X0) [cnf transformation 34]
67. ~curious(X0) | patient(X0) [cnf transformation 34]
68. ~humble(X0) | strong(X0) [cnf transformation 34]
69. ~humble(X0) | patient(X0) [cnf transformation 34]
79. ~humble(X0) | kind(X0) [cnf transformation 43]
86. ~funny(X0) | strong(X0) | ~happy(X0) [cnf transformation 45]
87. ~funny(X0) | happy(X0) | ~strong(X0) [cnf transformation 45]
91. ~generous(X0) | happy(X0) | ~patient(X0) | humble(X0) [cnf transformation 46]
94. humble(X0) | patient(X0) | generous(X0) | happy(X0) [cnf transformation 46]
95. humble(X0) | patient(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 46]
96. ~humble(X0) | ~wise(X0) [cnf transformation 29]
97. ~wise(X0) | humble(X0) [cnf transformation 29]
100. wise(sK4) | funny(sK4) | ~strong(X3) [cnf transformation 51]
105. brave(X0) | humble(X0) | curious(X0) | generous(X0) [cnf transformation 53]
106. ~generous(X0) | curious(X0) | ~humble(X0) [cnf transformation 53]
107. ~brave(X0) | curious(X0) | ~generous(X0) [cnf transformation 53]
110. ~tall(X0) | brave(X0) | ~kind(X0) | happy(X0) [cnf transformation 55]
111. ~brave(X0) | ~happy(X0) [cnf transformation 55]
112. ~happy(X0) | tall(X0) [cnf transformation 55]
115. kind(X0) | humble(X0) [cnf transformation 30]
117. ~patient(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 56]
120. tall(X0) | ~kind(X0) | patient(X0) [cnf transformation 56]
121. ~brave(X0) | ~funny(X0) | humble(X0) [cnf transformation 57]
122. brave(X0) | funny(X0) | humble(X0) [cnf transformation 57]
129. tall(lucy) [cnf transformation 21]
202. ~generous(X0) | ~happy(X0) | patient(X0) [subsumption resolution 95,69]
203. generous(X0) | patient(X0) | happy(X0) [subsumption resolution 94,69]
206. ~wise(X0) [subsumption resolution 96,97]
225. 21 <=> funny(sK4) [avatar definition]
227. funny(sK4) <- (21) [avatar component clause 225]
229. funny(sK4) | ~strong(X3) [subsumption resolution 100,206]
231. 22 <=> ! [X3] : ~strong(X3) [avatar definition]
232. ~strong(X3) <- (22) [avatar component clause 231]
233. 22 | 21 [avatar split clause 229,225,231]
234. kind(X0) [subsumption resolution 115,79]
235. tall(X0) | patient(X0) [subsumption resolution 120,234]
236. ~tall(X0) | ~patient(X0) [subsumption resolution 117,234]
256. ~patient(lucy) [resolution 236,129]
282. 27 <=> happy(sK4) [avatar definition]
283. happy(sK4) <- (27) [avatar component clause 282]
284. ~happy(sK4) <- (~27) [avatar component clause 282]
286. 28 <=> strong(sK4) [avatar definition]
287. ~strong(sK4) <- (~28) [avatar component clause 286]
299. funny(X2) | humble(X2) | curious(X2) | ~generous(X2) [resolution 122,107]
301. ~happy(X4) | humble(X4) | funny(X4) [resolution 122,111]
304. ~generous(X2) | curious(X2) | funny(X2) [subsumption resolution 299,106]
342. curious(X0) | funny(X0) | patient(X0) | happy(X0) [resolution 304,203]
343. funny(X0) | patient(X0) | happy(X0) [subsumption resolution 342,67]
348. humble(X0) | curious(X0) | generous(X0) | ~funny(X0) | humble(X0) [resolution 105,121]
355. ~funny(X0) | curious(X0) | generous(X0) | humble(X0) [duplicate literal removal 348]
376. brave(X1) | ~kind(X1) | happy(X1) | patient(X1) [resolution 110,235]
380. 32 <=> happy(lucy) [avatar definition]
381. ~happy(lucy) <- (~32) [avatar component clause 380]
382. happy(lucy) <- (32) [avatar component clause 380]
389. humble(lucy) | funny(lucy) <- (32) [resolution 382,301]
414. 36 <=> humble(lucy) [avatar definition]
416. humble(lucy) <- (36) [avatar component clause 414]
419. 37 <=> funny(lucy) [avatar definition]
421. funny(lucy) <- (37) [avatar component clause 419]
422. 37 | 36 | ~32 [avatar split clause 389,380,414,419]
423. brave(X1) | happy(X1) | patient(X1) [subsumption resolution 376,234]
446. happy(X0) | patient(X0) | ~funny(X0) | humble(X0) [resolution 423,121]
451. happy(X0) | patient(X0) | ~funny(X0) [subsumption resolution 446,69]
452. happy(X0) | patient(X0) [subsumption resolution 451,343]
457. patient(lucy) <- (36) [resolution 416,69]
460. $false <- (36) [subsumption resolution 457,256]
461. ~36 [avatar contradiction clause 460]
465. 40 <=> humble(sK4) [avatar definition]
467. humble(sK4) <- (40) [avatar component clause 465]
469. 41 <=> generous(sK4) [avatar definition]
471. generous(sK4) <- (41) [avatar component clause 469]
473. 42 <=> curious(sK4) [avatar definition]
475. curious(sK4) <- (42) [avatar component clause 473]
480. strong(lucy) | ~happy(lucy) <- (37) [resolution 421,86]
496. happy(sK4) | ~patient(sK4) | humble(sK4) <- (41) [resolution 471,91]
505. ~patient(sK4) | humble(sK4) <- (~27, 41) [subsumption resolution 496,284]
507. 45 <=> patient(sK4) [avatar definition]
509. ~patient(sK4) <- (~45) [avatar component clause 507]
510. 40 | ~45 | 27 | ~41 [avatar split clause 505,469,282,507,465]
532. patient(sK4) <- (~27) [resolution 452,284]
538. 45 | 27 [avatar split clause 532,282,507]
544. strong(sK4) <- (40) [resolution 467,68]
548. $false <- (~28, 40) [subsumption resolution 544,287]
549. 28 | ~40 [avatar contradiction clause 548]
556. ~happy(lucy) <- (22, 37) [subsumption resolution 480,232]
557. ~32 | ~22 | ~37 [avatar split clause 556,419,231,380]
561. patient(lucy) <- (~32) [resolution 381,452]
563. $false <- (~32) [subsumption resolution 561,256]
564. 32 [avatar contradiction clause 563]
568. curious(sK4) | generous(sK4) | humble(sK4) <- (21) [resolution 227,355]
569. happy(sK4) | ~strong(sK4) <- (21) [resolution 227,87]
603. patient(sK4) <- (42) [resolution 475,67]
604. strong(sK4) <- (42) [resolution 475,66]
608. 28 | ~42 [avatar split clause 604,473,286]
609. ~28 | 27 | ~21 [avatar split clause 569,225,282,286]
614. tall(sK4) <- (27) [resolution 283,112]
647. ~patient(sK4) <- (27) [resolution 614,236]
653. ~45 | ~27 [avatar split clause 647,282,507]
656. 45 | ~42 [avatar split clause 603,473,507]
659. 40 | 41 | 42 | ~21 [avatar split clause 568,225,473,469,465]
664. patient(sK4) <- (40) [resolution 467,69]
666. $false <- (40, ~45) [subsumption resolution 664,509]
667. ~40 | 45 [avatar contradiction clause 666]
673. ~happy(sK4) | patient(sK4) <- (41) [resolution 471,202]
675. patient(sK4) <- (27, 41) [subsumption resolution 673,283]
676. $false <- (27, 41, ~45) [subsumption resolution 675,509]
677. ~27 | ~41 | 45 [avatar contradiction clause 676]
678. $false [avatar sat refutation 233,422,461,510,538,549,557,564,608,609,653,656,659,667,677]
% SZS output end Proof for 248291617975048976232385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not tall and not creative then fred is not rich or not kind and vice versa. Everyone who is patient is not funny and vice versa. If lucy is both not patient and old then fred is not brave. If someone is not kind then john is both wise and old. Everyone who is not quiet or strong is quiet or not creative and vice versa. Everyone who is not humble is strong and vice versa. Everyone who is not strong or old is not kind and vice versa. Everyone who is not patient or not brave is either funny or happy and vice versa. Everyone who is both not humble and kind is both kind and rich and vice versa. If john is strong or quiet then someone is not patient. Everyone who is creative is both not rich and wise and vice versa. Everyone who is funny or tall is tall and vice versa. Everyone who is not old or not funny is both not humble and not quiet. If lucy is humble then alice is either not generous or tall and vice versa. If someone is both not calm and funny then someone is not funny or brave and vice versa. If mary is tall or not humble then someone is either wise or funny. Mary is either wise or not quiet. John is quiet. Fred is not generous. Someone is not happy. Someone is tall. Someone is both not generous and not funny. Someone is either not curious or not strong. Someone is either rich or wise. | John is happy. | contradiction | (((~tall(lucy)&~creative(lucy)))<=>((~rich(fred)|~kind(fred))))&
(![X]:(patient(X)<=>~funny(X)))&
(((~patient(lucy)&old(lucy)))=>(~brave(fred)))&
((?[X]:(~kind(X)))=>((wise(john)&old(john))))&
(![X]:((~quiet(X)|strong(X))<=>(quiet(X)|~creative(X))))&
(![X]:(~humble(X)<=>strong(X)))&
(![X]:((~strong(X)|old(X))<=>~kind(X)))&
(![X]:((~patient(X)|~brave(X))<=>(funny(X)<~>happy(X))))&
(![X]:((~humble(X)&kind(X))<=>(kind(X)&rich(X))))&
(((strong(john)|quiet(john)))=>(?[X]:(~patient(X))))&
(![X]:(creative(X)<=>(~rich(X)&wise(X))))&
(![X]:((funny(X)|tall(X))<=>tall(X)))&
(![X]:((~old(X)|~funny(X))=>(~humble(X)&~quiet(X))))&
((humble(lucy))<=>((~generous(alice)<~>tall(alice))))&
((?[X]:((~calm(X)&funny(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(((tall(mary)|~humble(mary)))=>(?[X]:((wise(X)<~>funny(X)))))&
((wise(mary)<~>~quiet(mary)))&
(quiet(john))&
(~generous(fred))&
(?[X]:(~happy(X)))&
(?[X]:(tall(X)))&
(?[X]:((~generous(X)&~funny(X))))&
(?[X]:((~curious(X)<~>~strong(X))))&
(?[X]:((rich(X)<~>wise(X)))) | happy(john) | [
"p1",
"p7",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1083778664073333402528200
% SZS output start Proof for 1083778664073333402528200
2. ! [X0] : (patient(X0) <=> ~funny(X0)) [input p1]
8. ! [X0] : ((~brave(X0) | ~patient(X0)) <=> (funny(X0) <~> happy(X0))) [input p7]
13. ! [X0] : ((~funny(X0) | ~old(X0)) => (~quiet(X0) & ~humble(X0))) [input p12]
18. quiet(john) [input p17]
25. happy(john) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & ~humble(X0)) | (funny(X0) & old(X0))) [ennf transformation 13]
35. ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))) [nnf transformation 2]
41. ! [X0] : (((~brave(X0) | ~patient(X0)) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (brave(X0) & patient(X0)))) [nnf transformation 8]
42. ! [X0] : ((~brave(X0) | ~patient(X0) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (brave(X0) & patient(X0)))) [flattening 41]
78. ~funny(X0) | ~patient(X0) [cnf transformation 35]
79. funny(X0) | patient(X0) [cnf transformation 35]
94. ~happy(X0) | ~funny(X0) | patient(X0) [cnf transformation 42]
113. ~quiet(X0) | funny(X0) [cnf transformation 31]
129. quiet(john) [cnf transformation 18]
139. happy(john) [cnf transformation 25]
190. ~happy(X0) | patient(X0) [subsumption resolution 94,79]
192. 11 <=> quiet(john) [avatar definition]
193. quiet(john) <- (11) [avatar component clause 192]
281. 11 [avatar split clause 129,192]
327. funny(john) <- (11) [resolution 113,193]
329. ~patient(john) <- (11) [resolution 327,78]
332. patient(john) [resolution 190,139]
333. $false <- (11) [subsumption resolution 332,329]
334. ~11 [avatar contradiction clause 333]
335. $false [avatar sat refutation 281,334]
% SZS output end Proof for 1083778664073333402528200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is either generous or not brave then someone is not quiet. If alice is both wise and not quiet then someone is generous and vice versa. Everyone who is kind or quiet is both quiet and funny. Everyone who is both funny and strong is not calm and vice versa. Everyone who is both calm and not wise is both quiet and patient and vice versa. If susan is not curious then someone is both brave and kind. If someone is not quiet or curious then fred is either patient or not curious. If someone is both not wise and tall then someone is either humble or quiet. Everyone who is not curious or not brave is not generous and vice versa. Everyone who is both not quiet and not funny is both not strong and kind. Everyone who is either not generous or wise is both patient and not curious and vice versa. If someone is either tall or generous then someone is both not humble and wise and vice versa. Everyone who is rich is not wise or not tall. If mary is both not old and generous then someone is both tall and strong and vice versa. If paul is either humble or happy then fred is not patient or not creative and vice versa. Everyone who is both brave and curious is both not happy and quiet and vice versa. Paul is either brave or tall. Someone is not curious or not strong. John is both strong and funny. Fred is rich or not generous. Fred is both quiet and not strong. Fred is not funny or not rich. Paul is either not rich or not happy. Mary is quiet. | John is not calm. | entailment | (((generous(mary)<~>~brave(mary)))=>(?[X]:(~quiet(X))))&
(((wise(alice)&~quiet(alice)))<=>(?[X]:(generous(X))))&
(![X]:((kind(X)|quiet(X))=>(quiet(X)&funny(X))))&
(![X]:((funny(X)&strong(X))<=>~calm(X)))&
(![X]:((calm(X)&~wise(X))<=>(quiet(X)&patient(X))))&
((~curious(susan))=>(?[X]:((brave(X)&kind(X)))))&
((?[X]:((~quiet(X)|curious(X))))=>((patient(fred)<~>~curious(fred))))&
((?[X]:((~wise(X)&tall(X))))=>(?[X]:((humble(X)<~>quiet(X)))))&
(![X]:((~curious(X)|~brave(X))<=>~generous(X)))&
(![X]:((~quiet(X)&~funny(X))=>(~strong(X)&kind(X))))&
(![X]:((~generous(X)<~>wise(X))<=>(patient(X)&~curious(X))))&
((?[X]:((tall(X)<~>generous(X))))<=>(?[X]:((~humble(X)&wise(X)))))&
(![X]:(rich(X)=>(~wise(X)|~tall(X))))&
(((~old(mary)&generous(mary)))<=>(?[X]:((tall(X)&strong(X)))))&
(((humble(paul)<~>happy(paul)))<=>((~patient(fred)|~creative(fred))))&
(![X]:((brave(X)&curious(X))<=>(~happy(X)&quiet(X))))&
((brave(paul)<~>tall(paul)))&
(?[X]:((~curious(X)|~strong(X))))&
((strong(john)&funny(john)))&
((rich(fred)|~generous(fred)))&
((quiet(fred)&~strong(fred)))&
((~funny(fred)|~rich(fred)))&
((~rich(paul)<~>~happy(paul)))&
(quiet(mary)) | ~calm(john) | [
"p2",
"p3",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8087033326622834125259986
% SZS output start Proof for 8087033326622834125259986
3. ! [X0] : ((quiet(X0) | kind(X0)) => (funny(X0) & quiet(X0))) [input p2]
4. ! [X0] : ((strong(X0) & funny(X0)) <=> ~calm(X0)) [input p3]
10. ! [X0] : ((~funny(X0) & ~quiet(X0)) => (kind(X0) & ~strong(X0))) [input p9]
19. funny(john) & strong(john) [input p18]
25. calm(john) [input hypothesis]
29. ! [X0] : ((funny(X0) & quiet(X0)) | (~quiet(X0) & ~kind(X0))) [ennf transformation 3]
33. ! [X0] : ((kind(X0) & ~strong(X0)) | (funny(X0) | quiet(X0))) [ennf transformation 10]
34. ! [X0] : ((kind(X0) & ~strong(X0)) | funny(X0) | quiet(X0)) [flattening 33]
45. ! [X0] : (((strong(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | (~strong(X0) | ~funny(X0)))) [nnf transformation 4]
46. ! [X0] : (((strong(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | ~strong(X0) | ~funny(X0))) [flattening 45]
85. ~kind(X0) | funny(X0) [cnf transformation 29]
86. ~quiet(X0) | funny(X0) [cnf transformation 29]
87. ~calm(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 46]
106. kind(X0) | funny(X0) | quiet(X0) [cnf transformation 34]
137. strong(john) [cnf transformation 19]
146. calm(john) [cnf transformation 25]
224. kind(X0) | funny(X0) [subsumption resolution 106,86]
225. funny(X0) [subsumption resolution 224,85]
341. ~strong(john) | ~funny(john) [resolution 87,146]
344. ~funny(john) [subsumption resolution 341,137]
345. $false [subsumption resolution 344,225]
% SZS output end Proof for 8087033326622834125259986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and funny is either kind or wise and vice versa.
If someone is brave then susan is tall and vice versa.
Everyone who is funny is brave.
Everyone who is either not funny or patient is both kind and not curious.
If someone is both not wise and generous then someone is not brave and vice versa.
Everyone who is not calm or not wise is not generous or not happy and vice versa.
If someone is both humble and old then someone is either curious or not old.
Everyone who is not calm is both calm and not calm and vice versa.
Everyone who is not brave or not patient is not wise.
Everyone who is either not quiet or humble is either not humble or wise.
Everyone who is both not funny and not old is wise or old.
Everyone who is not kind or not curious is not happy and vice versa.
If someone is either not humble or not generous then fred is either tall or calm and vice versa.
Everyone who is not calm or not rich is tall or humble and vice versa.
Everyone who is both not curious and tall is not kind.
Everyone who is either not creative or old is creative or funny.
Someone is wise or not wise.
Someone is both not creative and not patient.
Someone is funny or curious.
John is strong or not creative.
Paul is either not humble or not wise.
John is wise.
Susan is both curious and funny.
Someone is not quiet or funny. | Paul is generous. | neutral | (![X]:((happy(X)&funny(X))<=>(kind(X)<~>wise(X))))&
((?[X]:(brave(X)))<=>(tall(susan)))&
(![X]:(funny(X)=>brave(X)))&
(![X]:((~funny(X)<~>patient(X))=>(kind(X)&~curious(X))))&
((?[X]:((~wise(X)&generous(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~calm(X)|~wise(X))<=>(~generous(X)|~happy(X))))&
((?[X]:((humble(X)&old(X))))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:(~calm(X)<=>(calm(X)&~calm(X))))&
(![X]:((~brave(X)|~patient(X))=>~wise(X)))&
(![X]:((~quiet(X)<~>humble(X))=>(~humble(X)<~>wise(X))))&
(![X]:((~funny(X)&~old(X))=>(wise(X)|old(X))))&
(![X]:((~kind(X)|~curious(X))<=>~happy(X)))&
((?[X]:((~humble(X)<~>~generous(X))))<=>((tall(fred)<~>calm(fred))))&
(![X]:((~calm(X)|~rich(X))<=>(tall(X)|humble(X))))&
(![X]:((~curious(X)&tall(X))=>~kind(X)))&
(![X]:((~creative(X)<~>old(X))=>(creative(X)|funny(X))))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:((~creative(X)&~patient(X))))&
(?[X]:((funny(X)|curious(X))))&
((strong(john)|~creative(john)))&
((~humble(paul)<~>~wise(paul)))&
(wise(john))&
((curious(susan)&funny(susan)))&
(?[X]:((~quiet(X)|funny(X)))) | generous(paul) | [] | null | 0 |
If someone is both not patient and funny then john is not kind or not curious. If someone is both quiet and old then someone is both strong and not strong. Everyone who is not kind or patient is both not quiet and creative. If john is not strong then someone is either rich or not humble and vice versa. If someone is either creative or kind then mary is both patient and not old. Everyone who is wise is kind and vice versa. Everyone who is either not quiet or not calm is not strong or not calm and vice versa. Everyone who is creative is not quiet or kind and vice versa. If someone is kind then someone is tall. If alice is either not creative or patient then someone is either creative or not happy. If john is both quiet and not tall then someone is both not strong and not tall. If alice is both not calm and calm then someone is either tall or happy. Everyone who is both not funny and not calm is either happy or not funny and vice versa. Everyone who is either not creative or happy is not happy or old and vice versa. Everyone who is both wise and humble is not old and vice versa. Everyone who is either wise or not quiet is not quiet. Someone is not patient or not quiet. Susan is either patient or humble. Fred is strong or rich. Mary is either not funny or curious. | Fred is kind. | entailment | ((?[X]:((~patient(X)&funny(X))))=>((~kind(john)|~curious(john))))&
((?[X]:((quiet(X)&old(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~kind(X)|patient(X))=>(~quiet(X)&creative(X))))&
((~strong(john))<=>(?[X]:((rich(X)<~>~humble(X)))))&
((?[X]:((creative(X)<~>kind(X))))=>((patient(mary)&~old(mary))))&
(![X]:(wise(X)<=>kind(X)))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~strong(X)|~calm(X))))&
(![X]:(creative(X)<=>(~quiet(X)|kind(X))))&
((?[X]:(kind(X)))=>(?[X]:(tall(X))))&
(((~creative(alice)<~>patient(alice)))=>(?[X]:((creative(X)<~>~happy(X)))))&
(((quiet(john)&~tall(john)))=>(?[X]:((~strong(X)&~tall(X)))))&
(((~calm(alice)&calm(alice)))=>(?[X]:((tall(X)<~>happy(X)))))&
(![X]:((~funny(X)&~calm(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(~happy(X)|old(X))))&
(![X]:((wise(X)&humble(X))<=>~old(X)))&
(![X]:((wise(X)<~>~quiet(X))=>~quiet(X)))&
(?[X]:((~patient(X)|~quiet(X))))&
((patient(susan)<~>humble(susan)))&
((strong(fred)|rich(fred)))&
((~funny(mary)<~>curious(mary))) | kind(fred) | [
"p1",
"p2",
"p4",
"p7",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3533812425810481961204592
% SZS output start Proof for 3533812425810481961204592
2. ? [X0] : (old(X0) & quiet(X0)) => ? [X0] : (~strong(X0) & strong(X0)) [input p1]
3. ! [X0] : ((patient(X0) | ~kind(X0)) => (creative(X0) & ~quiet(X0))) [input p2]
5. ? [X0] : (creative(X0) <~> kind(X0)) => (~old(mary) & patient(mary)) [input p4]
8. ! [X0] : (creative(X0) <=> (kind(X0) | ~quiet(X0))) [input p7]
14. ! [X0] : ((~creative(X0) <~> happy(X0)) <=> (old(X0) | ~happy(X0))) [input p13]
15. ! [X0] : ((humble(X0) & wise(X0)) <=> ~old(X0)) [input p14]
16. ! [X0] : ((wise(X0) <~> ~quiet(X0)) => ~quiet(X0)) [input p15]
21. ~kind(fred) [input hypothesis]
22. ? [X0] : (old(X0) & quiet(X0)) => ? [X1] : (~strong(X1) & strong(X1)) [rectify 2]
26. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : (~old(X0) | ~quiet(X0)) [ennf transformation 22]
27. ! [X0] : ((creative(X0) & ~quiet(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 3]
28. (~old(mary) & patient(mary)) | ! [X0] : (creative(X0) <=> kind(X0)) [ennf transformation 5]
35. ! [X0] : (~quiet(X0) | (wise(X0) <=> ~quiet(X0))) [ennf transformation 16]
36. ? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : (~old(X1) | ~quiet(X1)) [rectify 26]
37. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK0) & strong(sK0)) [choice axiom]
38. (~strong(sK0) & strong(sK0)) | ! [X1] : (~old(X1) | ~quiet(X1)) [skolemisation 36,37]
43. (~old(mary) & patient(mary)) | ! [X0] : ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))) [nnf transformation 28]
47. ! [X0] : ((creative(X0) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | ~creative(X0))) [nnf transformation 8]
48. ! [X0] : ((creative(X0) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ~creative(X0))) [flattening 47]
62. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~old(X0) & happy(X0))) & ((old(X0) | ~happy(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [nnf transformation 14]
63. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~old(X0) & happy(X0))) & (old(X0) | ~happy(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [flattening 62]
64. ! [X0] : (((humble(X0) & wise(X0)) | old(X0)) & (~old(X0) | (~humble(X0) | ~wise(X0)))) [nnf transformation 15]
65. ! [X0] : (((humble(X0) & wise(X0)) | old(X0)) & (~old(X0) | ~humble(X0) | ~wise(X0))) [flattening 64]
66. ! [X0] : (~quiet(X0) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 35]
72. strong(sK0) | ~old(X1) | ~quiet(X1) [cnf transformation 38]
73. ~strong(sK0) | ~old(X1) | ~quiet(X1) [cnf transformation 38]
76. creative(X0) | kind(X0) [cnf transformation 27]
84. ~old(mary) | kind(X0) | ~creative(X0) [cnf transformation 43]
95. creative(X0) | quiet(X0) [cnf transformation 48]
113. old(X0) | ~happy(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 63]
114. happy(X0) | ~creative(X0) | happy(X0) [cnf transformation 63]
119. wise(X0) | old(X0) [cnf transformation 65]
121. ~quiet(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 66]
129. ~kind(fred) [cnf transformation 21]
130. ~wise(X0) | ~quiet(X0) [duplicate literal removal 121]
131. old(X0) | ~happy(X0) | ~creative(X0) [duplicate literal removal 113]
132. ~creative(X0) | happy(X0) [duplicate literal removal 114]
150. 4 <=> ! [X1] : (~old(X1) | ~quiet(X1)) [avatar definition]
151. ~old(X1) | ~quiet(X1) <- (4) [avatar component clause 150]
153. 5 <=> strong(sK0) [avatar definition]
156. 4 | ~5 [avatar split clause 73,153,150]
157. 4 | 5 [avatar split clause 72,153,150]
185. 12 <=> old(mary) [avatar definition]
187. ~old(mary) <- (~12) [avatar component clause 185]
189. ~old(mary) | kind(X0) [subsumption resolution 84,76]
191. 13 <=> ! [X0] : kind(X0) [avatar definition]
192. kind(X0) <- (13) [avatar component clause 191]
193. 13 | ~12 [avatar split clause 189,185,191]
256. ~creative(X0) | old(X0) [subsumption resolution 131,132]
296. $false <- (13) [resolution 192,129]
298. ~13 [avatar contradiction clause 296]
301. ~quiet(X0) | old(X0) [resolution 130,119]
302. ~quiet(X0) <- (4) [subsumption resolution 301,151]
316. old(X0) | quiet(X0) [resolution 256,95]
319. old(X0) <- (4) [subsumption resolution 316,302]
320. $false <- (4, ~12) [resolution 319,187]
322. ~4 | 12 [avatar contradiction clause 320]
323. $false [avatar sat refutation 156,157,193,298,322]
% SZS output end Proof for 3533812425810481961204592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either wise or creative then someone is brave. If lucy is both funny and calm then someone is both not tall and wise. Everyone who is rich or not brave is brave or not patient. If someone is not old then paul is both patient and not rich and vice versa. If fred is not old then paul is either happy or creative. If susan is happy then someone is both not calm and not generous and vice versa. Everyone who is funny or not happy is both quiet and not brave. Everyone who is both calm and curious is either creative or calm and vice versa. Everyone who is both old and creative is not funny or not tall. Everyone who is not funny is old. Everyone who is either rich or curious is either calm or not funny and vice versa. Everyone who is both patient and brave is either not curious or not patient. Everyone who is funny is not wise or rich. Everyone who is not generous or kind is generous and vice versa. If someone is patient or old then someone is either patient or tall and vice versa. If someone is humble or curious then someone is both rich and humble and vice versa. Alice is both not old and not strong. Fred is tall. Fred is not creative. Mary is not kind or not happy. Someone is either brave or not kind. Someone is quiet or not brave. Lucy is tall. | Paul is curious. | contradiction | (((wise(fred)<~>creative(fred)))=>(?[X]:(brave(X))))&
(((funny(lucy)&calm(lucy)))=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((rich(X)|~brave(X))=>(brave(X)|~patient(X))))&
((?[X]:(~old(X)))<=>((patient(paul)&~rich(paul))))&
((~old(fred))=>((happy(paul)<~>creative(paul))))&
((happy(susan))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((funny(X)|~happy(X))=>(quiet(X)&~brave(X))))&
(![X]:((calm(X)&curious(X))<=>(creative(X)<~>calm(X))))&
(![X]:((old(X)&creative(X))=>(~funny(X)|~tall(X))))&
(![X]:(~funny(X)=>old(X)))&
(![X]:((rich(X)<~>curious(X))<=>(calm(X)<~>~funny(X))))&
(![X]:((patient(X)&brave(X))=>(~curious(X)<~>~patient(X))))&
(![X]:(funny(X)=>(~wise(X)|rich(X))))&
(![X]:((~generous(X)|kind(X))<=>generous(X)))&
((?[X]:((patient(X)|old(X))))<=>(?[X]:((patient(X)<~>tall(X)))))&
((?[X]:((humble(X)|curious(X))))<=>(?[X]:((rich(X)&humble(X)))))&
((~old(alice)&~strong(alice)))&
(tall(fred))&
(~creative(fred))&
((~kind(mary)|~happy(mary)))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(tall(lucy)) | curious(paul) | [
"p2",
"p3",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2346270534941838688331891
% SZS output start Proof for 2346270534941838688331891
3. ! [X0] : ((~brave(X0) | rich(X0)) => (~patient(X0) | brave(X0))) [input p2]
4. ? [X0] : ~old(X0) <=> (~rich(paul) & patient(paul)) [input p3]
12. ! [X0] : ((brave(X0) & patient(X0)) => (~curious(X0) <~> ~patient(X0))) [input p11]
17. ~strong(alice) & ~old(alice) [input p16]
24. curious(paul) [input hypothesis]
27. ~old(alice) [pure predicate removal 17]
33. ! [X0] : ((~patient(X0) | brave(X0)) | (brave(X0) & ~rich(X0))) [ennf transformation 3]
34. ! [X0] : (~patient(X0) | brave(X0) | (brave(X0) & ~rich(X0))) [flattening 33]
40. ! [X0] : ((~curious(X0) <~> ~patient(X0)) | (~brave(X0) | ~patient(X0))) [ennf transformation 12]
41. ! [X0] : ((~curious(X0) <~> ~patient(X0)) | ~brave(X0) | ~patient(X0)) [flattening 40]
49. (? [X0] : ~old(X0) | (rich(paul) | ~patient(paul))) & ((~rich(paul) & patient(paul)) | ! [X0] : old(X0)) [nnf transformation 4]
50. (? [X0] : ~old(X0) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X0] : old(X0)) [flattening 49]
51. (? [X0] : ~old(X0) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X1] : old(X1)) [rectify 50]
52. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
53. (~old(sK2) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X1] : old(X1)) [skolemisation 51,52]
62. ! [X0] : (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | ~brave(X0) | ~patient(X0)) [nnf transformation 41]
83. ~patient(X0) | brave(X0) | brave(X0) [cnf transformation 34]
84. patient(paul) | old(X1) [cnf transformation 53]
110. ~patient(X0) | ~curious(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 62]
127. ~old(alice) [cnf transformation 27]
134. curious(paul) [cnf transformation 24]
137. ~patient(X0) | ~curious(X0) | ~brave(X0) [duplicate literal removal 110]
140. ~patient(X0) | brave(X0) [duplicate literal removal 83]
174. 8 <=> patient(paul) [avatar definition]
175. patient(paul) <- (8) [avatar component clause 174]
187. 11 <=> ! [X1] : old(X1) [avatar definition]
188. old(X1) <- (11) [avatar component clause 187]
190. 11 | 8 [avatar split clause 84,174,187]
224. ~curious(X0) | ~patient(X0) [subsumption resolution 137,140]
327. $false <- (11) [resolution 188,127]
330. ~11 [avatar contradiction clause 327]
334. ~patient(paul) [resolution 224,134]
335. $false <- (8) [subsumption resolution 334,175]
336. ~8 [avatar contradiction clause 335]
337. $false [avatar sat refutation 190,330,336]
% SZS output end Proof for 2346270534941838688331891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either not creative or creative then someone is both not quiet and humble.
Everyone who is not quiet is calm and vice versa.
If someone is creative or not old then someone is not calm or not kind.
Everyone who is both not quiet and not kind is not wise or quiet.
If someone is not creative then someone is not quiet or not humble and vice versa.
If someone is not calm or not curious then john is either not happy or not brave and vice versa.
Everyone who is either kind or humble is both patient and not old and vice versa.
Everyone who is happy is not funny and vice versa.
If someone is both not humble and strong then susan is not creative.
Everyone who is either rich or funny is brave or humble and vice versa.
If someone is creative then mary is either tall or not strong and vice versa.
If someone is either not wise or not rich then someone is either not generous or kind.
If fred is both not kind and not rich then lucy is calm or tall.
Everyone who is both not old and happy is both not calm and curious and vice versa.
If someone is either not brave or not rich then someone is both not old and funny.
Lucy is wise or not creative.
Someone is brave or quiet.
Susan is both not humble and not brave.
Mary is old.
Someone is not brave or patient.
Someone is wise or not kind.
Someone is not funny. | Susan is not creative. | neutral | (((~creative(mary)<~>creative(mary)))=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:(~quiet(X)<=>calm(X)))&
((?[X]:((creative(X)|~old(X))))=>(?[X]:((~calm(X)|~kind(X)))))&
(![X]:((~quiet(X)&~kind(X))=>(~wise(X)|quiet(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
((?[X]:((~calm(X)|~curious(X))))<=>((~happy(john)<~>~brave(john))))&
(![X]:((kind(X)<~>humble(X))<=>(patient(X)&~old(X))))&
(![X]:(happy(X)<=>~funny(X)))&
((?[X]:((~humble(X)&strong(X))))=>(~creative(susan)))&
(![X]:((rich(X)<~>funny(X))<=>(brave(X)|humble(X))))&
((?[X]:(creative(X)))<=>((tall(mary)<~>~strong(mary))))&
((?[X]:((~wise(X)<~>~rich(X))))=>(?[X]:((~generous(X)<~>kind(X)))))&
(((~kind(fred)&~rich(fred)))=>((calm(lucy)|tall(lucy))))&
(![X]:((~old(X)&happy(X))<=>(~calm(X)&curious(X))))&
((?[X]:((~brave(X)<~>~rich(X))))=>(?[X]:((~old(X)&funny(X)))))&
((wise(lucy)|~creative(lucy)))&
(?[X]:((brave(X)|quiet(X))))&
((~humble(susan)&~brave(susan)))&
(old(mary))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((wise(X)|~kind(X))))&
(?[X]:(~funny(X))) | ~creative(susan) | [] | null | 0 |
If fred is either not creative or not brave then someone is either not rich or not patient and vice versa. Everyone who is both not old and patient is either not happy or rich. Everyone who is either not tall or quiet is both kind and not wise and vice versa. If paul is both rich and not quiet then someone is both not curious and not brave and vice versa. Everyone who is either wise or creative is not tall and vice versa. If mary is not brave or happy then someone is not calm and vice versa. Everyone who is either strong or not creative is either not calm or not strong and vice versa. If alice is not generous then alice is both curious and not strong and vice versa. If alice is either not brave or not wise then lucy is old. Everyone who is not generous or not humble is not curious or patient and vice versa. Everyone who is both humble and not curious is not tall and vice versa. Everyone who is not kind is strong and vice versa. Everyone who is tall or not quiet is both not creative and not curious and vice versa. Everyone who is tall is both rich and not quiet and vice versa. If someone is either not creative or not strong then john is either generous or strong and vice versa. Everyone who is either happy or curious is either kind or tall. Someone is not brave. Lucy is not tall. Paul is either curious or not brave. Someone is not happy. Fred is either not generous or humble. Someone is both generous and not humble. Lucy is both strong and not old. | Paul is not brave. | entailment | (((~creative(fred)<~>~brave(fred)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
(![X]:((~old(X)&patient(X))=>(~happy(X)<~>rich(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(kind(X)&~wise(X))))&
(((rich(paul)&~quiet(paul)))<=>(?[X]:((~curious(X)&~brave(X)))))&
(![X]:((wise(X)<~>creative(X))<=>~tall(X)))&
(((~brave(mary)|happy(mary)))<=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>~creative(X))<=>(~calm(X)<~>~strong(X))))&
((~generous(alice))<=>((curious(alice)&~strong(alice))))&
(((~brave(alice)<~>~wise(alice)))=>(old(lucy)))&
(![X]:((~generous(X)|~humble(X))<=>(~curious(X)|patient(X))))&
(![X]:((humble(X)&~curious(X))<=>~tall(X)))&
(![X]:(~kind(X)<=>strong(X)))&
(![X]:((tall(X)|~quiet(X))<=>(~creative(X)&~curious(X))))&
(![X]:(tall(X)<=>(rich(X)&~quiet(X))))&
((?[X]:((~creative(X)<~>~strong(X))))<=>((generous(john)<~>strong(john))))&
(![X]:((happy(X)<~>curious(X))=>(kind(X)<~>tall(X))))&
(?[X]:(~brave(X)))&
(~tall(lucy))&
((curious(paul)<~>~brave(paul)))&
(?[X]:(~happy(X)))&
((~generous(fred)<~>humble(fred)))&
(?[X]:((generous(X)&~humble(X))))&
((strong(lucy)&~old(lucy))) | ~brave(paul) | [
"p10",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7556566004839636161501690
% SZS output start Proof for 7556566004839636161501690
11. ! [X0] : ((~curious(X0) & humble(X0)) <=> ~tall(X0)) [input p10]
13. ! [X0] : ((~quiet(X0) | tall(X0)) <=> (~curious(X0) & ~creative(X0))) [input p12]
19. curious(paul) <~> ~brave(paul) [input p18]
24. brave(paul) [input hypothesis]
53. ! [X0] : (((~curious(X0) & humble(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) | ~humble(X0)))) [nnf transformation 11]
54. ! [X0] : (((~curious(X0) & humble(X0)) | tall(X0)) & (~tall(X0) | curious(X0) | ~humble(X0))) [flattening 53]
56. ! [X0] : (((~quiet(X0) | tall(X0)) | (curious(X0) | creative(X0))) & ((~curious(X0) & ~creative(X0)) | (quiet(X0) & ~tall(X0)))) [nnf transformation 13]
57. ! [X0] : ((~quiet(X0) | tall(X0) | curious(X0) | creative(X0)) & ((~curious(X0) & ~creative(X0)) | (quiet(X0) & ~tall(X0)))) [flattening 56]
67. (brave(paul) | ~curious(paul)) & (~brave(paul) | curious(paul)) [nnf transformation 19]
119. ~curious(X0) | tall(X0) [cnf transformation 54]
124. ~curious(X0) | ~tall(X0) [cnf transformation 57]
144. ~brave(paul) | curious(paul) [cnf transformation 67]
153. brave(paul) [cnf transformation 24]
261. ~curious(X0) [subsumption resolution 124,119]
294. ~brave(paul) [subsumption resolution 144,261]
306. $false [subsumption resolution 153,294]
% SZS output end Proof for 7556566004839636161501690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not strong is not wise or quiet and vice versa.
If paul is both patient and not funny then susan is either not patient or not happy.
Everyone who is kind or not quiet is either calm or not kind and vice versa.
If paul is both not old and not humble then fred is rich.
Everyone who is not tall or wise is not quiet.
Everyone who is either humble or creative is happy.
If john is either not funny or not wise then someone is either not funny or not brave.
Everyone who is both tall and not humble is not wise or not strong and vice versa.
Everyone who is not strong or not brave is not brave.
If lucy is not funny then lucy is either patient or not funny and vice versa.
Everyone who is both rich and not brave is either quiet or generous.
Everyone who is generous or wise is both not brave and not happy and vice versa.
If someone is either brave or rich then alice is either quiet or happy.
Everyone who is generous or strong is not happy or not humble and vice versa.
Everyone who is happy or old is either happy or kind and vice versa.
Everyone who is curious or not creative is patient.
Someone is either not patient or not strong.
Alice is not curious.
Someone is either not creative or not curious.
John is either generous or wise.
Someone is not generous.
Susan is strong or old.
Someone is generous or not creative. | Lucy is not wise. | contradiction | (![X]:((~tall(X)|~strong(X))<=>(~wise(X)|quiet(X))))&
(((patient(paul)&~funny(paul)))=>((~patient(susan)<~>~happy(susan))))&
(![X]:((kind(X)|~quiet(X))<=>(calm(X)<~>~kind(X))))&
(((~old(paul)&~humble(paul)))=>(rich(fred)))&
(![X]:((~tall(X)|wise(X))=>~quiet(X)))&
(![X]:((humble(X)<~>creative(X))=>happy(X)))&
(((~funny(john)<~>~wise(john)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((tall(X)&~humble(X))<=>(~wise(X)|~strong(X))))&
(![X]:((~strong(X)|~brave(X))=>~brave(X)))&
((~funny(lucy))<=>((patient(lucy)<~>~funny(lucy))))&
(![X]:((rich(X)&~brave(X))=>(quiet(X)<~>generous(X))))&
(![X]:((generous(X)|wise(X))<=>(~brave(X)&~happy(X))))&
((?[X]:((brave(X)<~>rich(X))))=>((quiet(alice)<~>happy(alice))))&
(![X]:((generous(X)|strong(X))<=>(~happy(X)|~humble(X))))&
(![X]:((happy(X)|old(X))<=>(happy(X)<~>kind(X))))&
(![X]:((curious(X)|~creative(X))=>patient(X)))&
(?[X]:((~patient(X)<~>~strong(X))))&
(~curious(alice))&
(?[X]:((~creative(X)<~>~curious(X))))&
((generous(john)<~>wise(john)))&
(?[X]:(~generous(X)))&
((strong(susan)|old(susan)))&
(?[X]:((generous(X)|~creative(X)))) | ~wise(lucy) | [
"p0",
"p5",
"p7",
"p9",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9114024058426848447746026
% SZS output start Proof for 9114024058426848447746026
1. ! [X0] : ((~strong(X0) | ~tall(X0)) <=> (quiet(X0) | ~wise(X0))) [input p0]
6. ! [X0] : ((humble(X0) <~> creative(X0)) => happy(X0)) [input p5]
8. ! [X0] : ((~humble(X0) & tall(X0)) <=> (~strong(X0) | ~wise(X0))) [input p7]
10. ~funny(lucy) <=> (patient(lucy) <~> ~funny(lucy)) [input p9]
12. ! [X0] : ((wise(X0) | generous(X0)) <=> (~happy(X0) & ~brave(X0))) [input p11]
14. ! [X0] : ((strong(X0) | generous(X0)) <=> (~humble(X0) | ~happy(X0))) [input p13]
16. ! [X0] : ((~creative(X0) | curious(X0)) => patient(X0)) [input p15]
24. ~wise(lucy) [input hypothesis]
30. ! [X0] : (happy(X0) | (humble(X0) <=> creative(X0))) [ennf transformation 6]
36. ! [X0] : (patient(X0) | (creative(X0) & ~curious(X0))) [ennf transformation 16]
37. ! [X0] : (((~strong(X0) | ~tall(X0)) | (~quiet(X0) & wise(X0))) & ((quiet(X0) | ~wise(X0)) | (strong(X0) & tall(X0)))) [nnf transformation 1]
38. ! [X0] : ((~strong(X0) | ~tall(X0) | (~quiet(X0) & wise(X0))) & (quiet(X0) | ~wise(X0) | (strong(X0) & tall(X0)))) [flattening 37]
42. ! [X0] : (happy(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) [nnf transformation 30]
46. ! [X0] : (((~humble(X0) & tall(X0)) | (strong(X0) & wise(X0))) & ((~strong(X0) | ~wise(X0)) | (humble(X0) | ~tall(X0)))) [nnf transformation 8]
47. ! [X0] : (((~humble(X0) & tall(X0)) | (strong(X0) & wise(X0))) & (~strong(X0) | ~wise(X0) | humble(X0) | ~tall(X0))) [flattening 46]
48. (~funny(lucy) | ((patient(lucy) | funny(lucy)) & (~funny(lucy) | ~patient(lucy)))) & (((funny(lucy) | ~patient(lucy)) & (~funny(lucy) | patient(lucy))) | funny(lucy)) [nnf transformation 10]
50. ! [X0] : (((wise(X0) | generous(X0)) | (happy(X0) | brave(X0))) & ((~happy(X0) & ~brave(X0)) | (~wise(X0) & ~generous(X0)))) [nnf transformation 12]
51. ! [X0] : ((wise(X0) | generous(X0) | happy(X0) | brave(X0)) & ((~happy(X0) & ~brave(X0)) | (~wise(X0) & ~generous(X0)))) [flattening 50]
53. ! [X0] : (((strong(X0) | generous(X0)) | (humble(X0) & happy(X0))) & ((~humble(X0) | ~happy(X0)) | (~strong(X0) & ~generous(X0)))) [nnf transformation 14]
54. ! [X0] : ((strong(X0) | generous(X0) | (humble(X0) & happy(X0))) & (~humble(X0) | ~happy(X0) | (~strong(X0) & ~generous(X0)))) [flattening 53]
70. ~strong(X0) | ~tall(X0) | wise(X0) [cnf transformation 38]
84. ~creative(X0) | humble(X0) | happy(X0) [cnf transformation 42]
90. wise(X0) | tall(X0) [cnf transformation 47]
93. ~humble(X0) | strong(X0) [cnf transformation 47]
97. funny(lucy) | ~patient(lucy) | funny(lucy) [cnf transformation 48]
98. ~funny(lucy) | ~funny(lucy) | ~patient(lucy) [cnf transformation 48]
104. ~generous(X0) | ~happy(X0) [cnf transformation 51]
114. strong(X0) | generous(X0) | humble(X0) [cnf transformation 54]
122. creative(X0) | patient(X0) [cnf transformation 36]
133. ~wise(lucy) [cnf transformation 24]
136. funny(lucy) | ~patient(lucy) [duplicate literal removal 97]
137. ~funny(lucy) | ~patient(lucy) [duplicate literal removal 98]
193. 12 <=> patient(lucy) [avatar definition]
195. ~patient(lucy) <- (~12) [avatar component clause 193]
197. 13 <=> funny(lucy) [avatar definition]
200. ~12 | ~13 [avatar split clause 137,197,193]
201. ~12 | 13 [avatar split clause 136,197,193]
220. generous(X0) | strong(X0) [subsumption resolution 114,93]
268. tall(lucy) [resolution 90,133]
274. ~happy(X0) | strong(X0) [resolution 220,104]
297. humble(X0) | happy(X0) | patient(X0) [resolution 84,122]
420. happy(X2) | patient(X2) | strong(X2) [resolution 297,93]
424. patient(X2) | strong(X2) [subsumption resolution 420,274]
467. strong(lucy) <- (~12) [resolution 424,195]
489. ~tall(lucy) | wise(lucy) <- (~12) [resolution 467,70]
491. wise(lucy) <- (~12) [subsumption resolution 489,268]
492. $false <- (~12) [subsumption resolution 491,133]
493. 12 [avatar contradiction clause 492]
494. $false [avatar sat refutation 200,201,493]
% SZS output end Proof for 9114024058426848447746026
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or curious then someone is either not funny or rich.
If someone is funny or not patient then john is not calm or old.
If someone is tall then paul is not happy.
If mary is either old or kind then someone is quiet or not calm and vice versa.
Everyone who is wise or not tall is not strong and vice versa.
Everyone who is both kind and generous is both not calm and not tall and vice versa.
Everyone who is quiet or wise is either not humble or rich and vice versa.
If susan is not generous or not wise then someone is not kind or creative and vice versa.
Everyone who is not tall or strong is both tall and humble and vice versa.
Everyone who is both creative and not tall is not wise or funny and vice versa.
If fred is either not generous or wise then someone is both not wise and not curious and vice versa.
Everyone who is brave or humble is either not quiet or humble and vice versa.
If someone is either not humble or rich then john is wise.
If someone is both rich and not tall then alice is not quiet.
If fred is creative or funny then fred is not old or not tall.
Everyone who is brave or quiet is either not tall or not kind.
Susan is either not curious or not kind.
Mary is not kind or generous.
Lucy is either not happy or not patient.
John is wise or not kind.
John is either not tall or not kind. | Mary is not kind. | entailment | ((?[X]:((~brave(X)|curious(X))))=>(?[X]:((~funny(X)<~>rich(X)))))&
((?[X]:((funny(X)|~patient(X))))=>((~calm(john)|old(john))))&
((?[X]:(tall(X)))=>(~happy(paul)))&
(((old(mary)<~>kind(mary)))<=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:((wise(X)|~tall(X))<=>~strong(X)))&
(![X]:((kind(X)&generous(X))<=>(~calm(X)&~tall(X))))&
(![X]:((quiet(X)|wise(X))<=>(~humble(X)<~>rich(X))))&
(((~generous(susan)|~wise(susan)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~tall(X)|strong(X))<=>(tall(X)&humble(X))))&
(![X]:((creative(X)&~tall(X))<=>(~wise(X)|funny(X))))&
(((~generous(fred)<~>wise(fred)))<=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:((brave(X)|humble(X))<=>(~quiet(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>rich(X))))=>(wise(john)))&
((?[X]:((rich(X)&~tall(X))))=>(~quiet(alice)))&
(((creative(fred)|funny(fred)))=>((~old(fred)|~tall(fred))))&
(![X]:((brave(X)|quiet(X))=>(~tall(X)<~>~kind(X))))&
((~curious(susan)<~>~kind(susan)))&
((~kind(mary)|generous(mary)))&
((~happy(lucy)<~>~patient(lucy)))&
((wise(john)|~kind(john)))&
((~tall(john)<~>~kind(john))) | ~kind(mary) | [
"p5",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3770155695430611635727298
% SZS output start Proof for 3770155695430611635727298
6. ! [X0] : ((generous(X0) & kind(X0)) <=> (~tall(X0) & ~calm(X0))) [input p5]
9. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (humble(X0) & tall(X0))) [input p8]
18. generous(mary) | ~kind(mary) [input p17]
22. kind(mary) [input hypothesis]
43. ! [X0] : (((generous(X0) & kind(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~generous(X0) | ~kind(X0)))) [nnf transformation 6]
44. ! [X0] : (((generous(X0) & kind(X0)) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | ~generous(X0) | ~kind(X0))) [flattening 43]
52. ! [X0] : (((strong(X0) | ~tall(X0)) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | (~strong(X0) & tall(X0)))) [nnf transformation 9]
53. ! [X0] : ((strong(X0) | ~tall(X0) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | (~strong(X0) & tall(X0)))) [flattening 52]
84. ~generous(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 44]
97. tall(X0) | tall(X0) [cnf transformation 53]
130. generous(mary) | ~kind(mary) [cnf transformation 18]
136. kind(mary) [cnf transformation 22]
139. tall(X0) [duplicate literal removal 97]
191. 13 <=> kind(mary) [avatar definition]
192. kind(mary) <- (13) [avatar component clause 191]
282. 30 <=> generous(mary) [avatar definition]
284. generous(mary) <- (30) [avatar component clause 282]
285. ~13 | 30 [avatar split clause 130,282,191]
297. 13 [avatar split clause 136,191]
305. ~tall(mary) | ~kind(mary) <- (30) [resolution 84,284]
306. ~kind(mary) <- (30) [subsumption resolution 305,139]
307. $false <- (13, 30) [subsumption resolution 306,192]
308. ~13 | ~30 [avatar contradiction clause 307]
309. $false [avatar sat refutation 285,297,308]
% SZS output end Proof for 3770155695430611635727298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both humble and not rich then someone is both creative and not rich and vice versa. If susan is creative or not curious then someone is not quiet and vice versa. Everyone who is not humble or not calm is both calm and quiet. If john is wise then mary is both not happy and humble and vice versa. If fred is either rich or kind then john is both not creative and happy. If john is both not old and not strong then lucy is both not funny and happy. Everyone who is not strong is calm or creative. If someone is both old and calm then someone is either brave or not calm. If lucy is strong then alice is kind. If susan is either curious or not old then someone is not patient or not quiet. If someone is both brave and curious then alice is both not humble and not wise. Everyone who is strong or not brave is tall or not tall. If fred is not curious then someone is both generous and happy and vice versa. Everyone who is not strong is both rich and kind and vice versa. If paul is patient then fred is not brave and vice versa. If someone is not wise or not curious then paul is not strong and vice versa. Someone is happy. John is either happy or not kind. Someone is funny or quiet. Susan is both not wise and kind. John is either not strong or not rich. Someone is generous. Fred is not strong. Someone is strong. | Paul is not kind. | contradiction | (((humble(susan)&~rich(susan)))<=>(?[X]:((creative(X)&~rich(X)))))&
(((creative(susan)|~curious(susan)))<=>(?[X]:(~quiet(X))))&
(![X]:((~humble(X)|~calm(X))=>(calm(X)&quiet(X))))&
((wise(john))<=>((~happy(mary)&humble(mary))))&
(((rich(fred)<~>kind(fred)))=>((~creative(john)&happy(john))))&
(((~old(john)&~strong(john)))=>((~funny(lucy)&happy(lucy))))&
(![X]:(~strong(X)=>(calm(X)|creative(X))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:((brave(X)<~>~calm(X)))))&
((strong(lucy))=>(kind(alice)))&
(((curious(susan)<~>~old(susan)))=>(?[X]:((~patient(X)|~quiet(X)))))&
((?[X]:((brave(X)&curious(X))))=>((~humble(alice)&~wise(alice))))&
(![X]:((strong(X)|~brave(X))=>(tall(X)|~tall(X))))&
((~curious(fred))<=>(?[X]:((generous(X)&happy(X)))))&
(![X]:(~strong(X)<=>(rich(X)&kind(X))))&
((patient(paul))<=>(~brave(fred)))&
((?[X]:((~wise(X)|~curious(X))))<=>(~strong(paul)))&
(?[X]:(happy(X)))&
((happy(john)<~>~kind(john)))&
(?[X]:((funny(X)|quiet(X))))&
((~wise(susan)&kind(susan)))&
((~strong(john)<~>~rich(john)))&
(?[X]:(generous(X)))&
(~strong(fred))&
(?[X]:(strong(X))) | ~kind(paul) | [
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4319777248846220521977214
% SZS output start Proof for 4319777248846220521977214
14. ! [X0] : (~strong(X0) <=> (kind(X0) & rich(X0))) [input p13]
16. ? [X0] : (~curious(X0) | ~wise(X0)) <=> ~strong(paul) [input p15]
20. kind(susan) & ~wise(susan) [input p19]
25. ~kind(paul) [input hypothesis]
63. ! [X0] : ((~strong(X0) | (~kind(X0) | ~rich(X0))) & ((kind(X0) & rich(X0)) | strong(X0))) [nnf transformation 14]
64. ! [X0] : ((~strong(X0) | ~kind(X0) | ~rich(X0)) & ((kind(X0) & rich(X0)) | strong(X0))) [flattening 63]
66. (? [X0] : (~curious(X0) | ~wise(X0)) | strong(paul)) & (~strong(paul) | ! [X0] : (curious(X0) & wise(X0))) [nnf transformation 16]
67. (? [X0] : (~curious(X0) | ~wise(X0)) | strong(paul)) & (~strong(paul) | ! [X1] : (curious(X1) & wise(X1))) [rectify 66]
68. ? [X0] : (~curious(X0) | ~wise(X0)) => (~curious(sK5) | ~wise(sK5)) [choice axiom]
69. ((~curious(sK5) | ~wise(sK5)) | strong(paul)) & (~strong(paul) | ! [X1] : (curious(X1) & wise(X1))) [skolemisation 67,68]
114. strong(X0) | kind(X0) [cnf transformation 64]
118. ~strong(paul) | wise(X1) [cnf transformation 69]
125. ~wise(susan) [cnf transformation 20]
132. ~kind(paul) [cnf transformation 25]
303. 37 <=> strong(paul) [avatar definition]
304. ~strong(paul) <- (~37) [avatar component clause 303]
320. 41 <=> ! [X1] : wise(X1) [avatar definition]
321. wise(X1) <- (41) [avatar component clause 320]
322. 41 | ~37 [avatar split clause 118,303,320]
354. kind(paul) <- (~37) [resolution 114,304]
355. $false <- (~37) [subsumption resolution 354,132]
356. 37 [avatar contradiction clause 355]
359. $false <- (41) [resolution 321,125]
366. ~41 [avatar contradiction clause 359]
367. $false [avatar sat refutation 322,356,366]
% SZS output end Proof for 4319777248846220521977214
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and kind is generous. Everyone who is not rich is either curious or not patient and vice versa. If john is not brave or generous then alice is not wise or not kind. If susan is either quiet or curious then someone is both not humble and not calm. Everyone who is patient or calm is curious or rich. If john is either not tall or not old then someone is strong or not quiet. If mary is either not kind or old then mary is both not wise and not quiet and vice versa. Everyone who is creative is rich and vice versa. If lucy is both humble and not creative then someone is not humble and vice versa. Everyone who is calm is curious or funny. If john is both calm and happy then fred is not kind or curious and vice versa. Everyone who is both not creative and funny is calm and vice versa. If someone is happy or rich then fred is both not generous and kind and vice versa. Everyone who is both rich and strong is quiet. Everyone who is both not quiet and curious is either strong or not quiet and vice versa. If someone is both not funny and curious then someone is humble and vice versa. Someone is either happy or patient. Someone is strong or rich. Lucy is both not tall and old. Susan is not wise. Mary is humble. Susan is both not humble and tall. Someone is both generous and tall. | Fred is calm. | contradiction | (![X]:((~generous(X)&kind(X))=>generous(X)))&
(![X]:(~rich(X)<=>(curious(X)<~>~patient(X))))&
(((~brave(john)|generous(john)))=>((~wise(alice)|~kind(alice))))&
(((quiet(susan)<~>curious(susan)))=>(?[X]:((~humble(X)&~calm(X)))))&
(![X]:((patient(X)|calm(X))=>(curious(X)|rich(X))))&
(((~tall(john)<~>~old(john)))=>(?[X]:((strong(X)|~quiet(X)))))&
(((~kind(mary)<~>old(mary)))<=>((~wise(mary)&~quiet(mary))))&
(![X]:(creative(X)<=>rich(X)))&
(((humble(lucy)&~creative(lucy)))<=>(?[X]:(~humble(X))))&
(![X]:(calm(X)=>(curious(X)|funny(X))))&
(((calm(john)&happy(john)))<=>((~kind(fred)|curious(fred))))&
(![X]:((~creative(X)&funny(X))<=>calm(X)))&
((?[X]:((happy(X)|rich(X))))<=>((~generous(fred)&kind(fred))))&
(![X]:((rich(X)&strong(X))=>quiet(X)))&
(![X]:((~quiet(X)&curious(X))<=>(strong(X)<~>~quiet(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:(humble(X))))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((strong(X)|rich(X))))&
((~tall(lucy)&old(lucy)))&
(~wise(susan))&
(humble(mary))&
((~humble(susan)&tall(susan)))&
(?[X]:((generous(X)&tall(X)))) | calm(fred) | [
"p0",
"p4",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1707240845600399719127038
% SZS output start Proof for 1707240845600399719127038
1. ! [X0] : ((kind(X0) & ~generous(X0)) => generous(X0)) [input p0]
5. ! [X0] : ((calm(X0) | patient(X0)) => (rich(X0) | curious(X0))) [input p4]
11. (happy(john) & calm(john)) <=> (curious(fred) | ~kind(fred)) [input p10]
13. ? [X0] : (rich(X0) | happy(X0)) <=> (kind(fred) & ~generous(fred)) [input p12]
24. calm(fred) [input hypothesis]
27. ! [X0] : (generous(X0) | (~kind(X0) | generous(X0))) [ennf transformation 1]
28. ! [X0] : (generous(X0) | ~kind(X0) | generous(X0)) [flattening 27]
32. ! [X0] : ((rich(X0) | curious(X0)) | (~calm(X0) & ~patient(X0))) [ennf transformation 5]
33. ! [X0] : (rich(X0) | curious(X0) | (~calm(X0) & ~patient(X0))) [flattening 32]
54. ((happy(john) & calm(john)) | (~curious(fred) & kind(fred))) & ((curious(fred) | ~kind(fred)) | (~happy(john) | ~calm(john))) [nnf transformation 11]
55. ((happy(john) & calm(john)) | (~curious(fred) & kind(fred))) & (curious(fred) | ~kind(fred) | ~happy(john) | ~calm(john)) [flattening 54]
58. (? [X0] : (rich(X0) | happy(X0)) | (~kind(fred) | generous(fred))) & ((kind(fred) & ~generous(fred)) | ! [X0] : (~rich(X0) & ~happy(X0))) [nnf transformation 13]
59. (? [X0] : (rich(X0) | happy(X0)) | ~kind(fred) | generous(fred)) & ((kind(fred) & ~generous(fred)) | ! [X0] : (~rich(X0) & ~happy(X0))) [flattening 58]
60. (? [X0] : (rich(X0) | happy(X0)) | ~kind(fred) | generous(fred)) & ((kind(fred) & ~generous(fred)) | ! [X1] : (~rich(X1) & ~happy(X1))) [rectify 59]
61. ? [X0] : (rich(X0) | happy(X0)) => (rich(sK3) | happy(sK3)) [choice axiom]
62. ((rich(sK3) | happy(sK3)) | ~kind(fred) | generous(fred)) & ((kind(fred) & ~generous(fred)) | ! [X1] : (~rich(X1) & ~happy(X1))) [skolemisation 60,61]
77. generous(X0) | ~kind(X0) | generous(X0) [cnf transformation 28]
88. ~calm(X0) | curious(X0) | rich(X0) [cnf transformation 33]
106. happy(john) | kind(fred) [cnf transformation 55]
107. happy(john) | ~curious(fred) [cnf transformation 55]
111. ~generous(fred) | ~happy(X1) [cnf transformation 62]
112. ~generous(fred) | ~rich(X1) [cnf transformation 62]
113. kind(fred) | ~happy(X1) [cnf transformation 62]
137. calm(fred) [cnf transformation 24]
140. ~kind(X0) | generous(X0) [duplicate literal removal 77]
233. 20 <=> curious(fred) [avatar definition]
235. ~curious(fred) <- (~20) [avatar component clause 233]
237. 21 <=> happy(john) [avatar definition]
239. happy(john) <- (21) [avatar component clause 237]
240. ~20 | 21 [avatar split clause 107,237,233]
242. 22 <=> kind(fred) [avatar definition]
244. kind(fred) <- (22) [avatar component clause 242]
245. 22 | 21 [avatar split clause 106,237,242]
254. 24 <=> ! [X1] : ~rich(X1) [avatar definition]
255. ~rich(X1) <- (24) [avatar component clause 254]
258. 25 <=> ! [X1] : ~happy(X1) [avatar definition]
259. ~happy(X1) <- (25) [avatar component clause 258]
260. 25 | 22 [avatar split clause 113,242,258]
262. 26 <=> generous(fred) [avatar definition]
264. ~generous(fred) <- (~26) [avatar component clause 262]
265. 24 | ~26 [avatar split clause 112,262,254]
266. 25 | ~26 [avatar split clause 111,262,258]
314. generous(fred) <- (22) [resolution 140,244]
315. $false <- (22, ~26) [subsumption resolution 314,264]
316. ~22 | 26 [avatar contradiction clause 315]
317. $false <- (21, 25) [subsumption resolution 239,259]
318. ~21 | ~25 [avatar contradiction clause 317]
335. curious(fred) | rich(fred) [resolution 88,137]
337. rich(fred) <- (~20) [subsumption resolution 335,235]
338. $false <- (~20, 24) [subsumption resolution 337,255]
339. 20 | ~24 [avatar contradiction clause 338]
341. $false [avatar sat refutation 240,245,260,265,266,316,318,339]
% SZS output end Proof for 1707240845600399719127038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not funny is curious or funny and vice versa. If mary is not brave then john is not rich and vice versa. Everyone who is either quiet or not tall is either not tall or not quiet. If someone is not curious then someone is wise and vice versa. If someone is generous or happy then someone is both old and tall and vice versa. Everyone who is happy or not old is both not generous and not strong and vice versa. Everyone who is both not funny and not calm is either not tall or kind and vice versa. Everyone who is both not wise and brave is both rich and not humble. Everyone who is either not humble or strong is either not creative or not calm and vice versa. Everyone who is either not happy or creative is either not happy or strong. Everyone who is generous is not happy or calm. Everyone who is both not happy and happy is either not humble or not generous and vice versa. If someone is brave or not patient then fred is not rich or old. If alice is both strong and not brave then someone is either not tall or not generous and vice versa. If paul is both happy and kind then lucy is not rich. If lucy is both not old and creative then someone is both not tall and happy. John is strong. Someone is generous. Someone is either old or not generous. Someone is either strong or kind. Susan is both not humble and not tall. John is not generous. Someone is kind. Alice is both not funny and not creative. | John is not kind. | contradiction | (![X]:((patient(X)|~funny(X))<=>(curious(X)|funny(X))))&
((~brave(mary))<=>(~rich(john)))&
(![X]:((quiet(X)<~>~tall(X))=>(~tall(X)<~>~quiet(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(wise(X))))&
((?[X]:((generous(X)|happy(X))))<=>(?[X]:((old(X)&tall(X)))))&
(![X]:((happy(X)|~old(X))<=>(~generous(X)&~strong(X))))&
(![X]:((~funny(X)&~calm(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((~wise(X)&brave(X))=>(rich(X)&~humble(X))))&
(![X]:((~humble(X)<~>strong(X))<=>(~creative(X)<~>~calm(X))))&
(![X]:((~happy(X)<~>creative(X))=>(~happy(X)<~>strong(X))))&
(![X]:(generous(X)=>(~happy(X)|calm(X))))&
(![X]:((~happy(X)&happy(X))<=>(~humble(X)<~>~generous(X))))&
((?[X]:((brave(X)|~patient(X))))=>((~rich(fred)|old(fred))))&
(((strong(alice)&~brave(alice)))<=>(?[X]:((~tall(X)<~>~generous(X)))))&
(((happy(paul)&kind(paul)))=>(~rich(lucy)))&
(((~old(lucy)&creative(lucy)))=>(?[X]:((~tall(X)&happy(X)))))&
(strong(john))&
(?[X]:(generous(X)))&
(?[X]:((old(X)<~>~generous(X))))&
(?[X]:((strong(X)<~>kind(X))))&
((~humble(susan)&~tall(susan)))&
(~generous(john))&
(?[X]:(kind(X)))&
((~funny(alice)&~creative(alice))) | ~kind(john) | [
"p2",
"p5",
"p6",
"p8",
"p9",
"p11",
"p13",
"p16",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 29646582372107301412162
% SZS output start Proof for 29646582372107301412162
3. ! [X0] : ((quiet(X0) <~> ~tall(X0)) => (~tall(X0) <~> ~quiet(X0))) [input p2]
6. ! [X0] : ((~old(X0) | happy(X0)) <=> (~strong(X0) & ~generous(X0))) [input p5]
7. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> (~tall(X0) <~> kind(X0))) [input p6]
9. ! [X0] : ((~humble(X0) <~> strong(X0)) <=> (~creative(X0) <~> ~calm(X0))) [input p8]
10. ! [X0] : ((~happy(X0) <~> creative(X0)) => (~happy(X0) <~> strong(X0))) [input p9]
12. ! [X0] : ((happy(X0) & ~happy(X0)) <=> (~humble(X0) <~> ~generous(X0))) [input p11]
14. (~brave(alice) & strong(alice)) <=> ? [X0] : (~tall(X0) <~> ~generous(X0)) [input p13]
17. strong(john) [input p16]
22. ~generous(john) [input p21]
24. ~creative(alice) & ~funny(alice) [input p23]
25. ~kind(john) [input hypothesis]
28. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) | (quiet(X0) <=> ~tall(X0))) [ennf transformation 3]
31. ! [X0] : ((~happy(X0) <~> strong(X0)) | (~happy(X0) <=> creative(X0))) [ennf transformation 10]
43. ! [X0] : (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0)))) [nnf transformation 28]
54. ! [X0] : (((~old(X0) | happy(X0)) | (strong(X0) | generous(X0))) & ((~strong(X0) & ~generous(X0)) | (old(X0) & ~happy(X0)))) [nnf transformation 6]
55. ! [X0] : ((~old(X0) | happy(X0) | strong(X0) | generous(X0)) & ((~strong(X0) & ~generous(X0)) | (old(X0) & ~happy(X0)))) [flattening 54]
56. ! [X0] : (((~calm(X0) & ~funny(X0)) | ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0)))) & (((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | (calm(X0) | funny(X0)))) [nnf transformation 7]
57. ! [X0] : (((~calm(X0) & ~funny(X0)) | ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0)))) & (((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | calm(X0) | funny(X0))) [flattening 56]
58. ! [X0] : ((((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0))))) [nnf transformation 9]
59. ! [X0] : (((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) [nnf transformation 31]
60. ! [X0] : (((happy(X0) & ~happy(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) & (((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (~happy(X0) | happy(X0)))) [nnf transformation 12]
61. ! [X0] : (((happy(X0) & ~happy(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) & (((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | ~happy(X0) | happy(X0))) [flattening 60]
62. ((~brave(alice) & strong(alice)) | ! [X0] : ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0)))) & (? [X0] : ((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (brave(alice) | ~strong(alice))) [nnf transformation 14]
63. ((~brave(alice) & strong(alice)) | ! [X0] : ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0)))) & (? [X0] : ((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | brave(alice) | ~strong(alice)) [flattening 62]
64. ((~brave(alice) & strong(alice)) | ! [X0] : ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0)))) & (? [X1] : ((generous(X1) | tall(X1)) & (~generous(X1) | ~tall(X1))) | brave(alice) | ~strong(alice)) [rectify 63]
65. ? [X1] : ((generous(X1) | tall(X1)) & (~generous(X1) | ~tall(X1))) => ((generous(sK4) | tall(sK4)) & (~generous(sK4) | ~tall(sK4))) [choice axiom]
66. ((~brave(alice) & strong(alice)) | ! [X0] : ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0)))) & (((generous(sK4) | tall(sK4)) & (~generous(sK4) | ~tall(sK4))) | brave(alice) | ~strong(alice)) [skolemisation 64,65]
85. ~quiet(X0) | ~tall(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 43]
88. quiet(X0) | tall(X0) | quiet(X0) | tall(X0) [cnf transformation 43]
98. ~strong(X0) | ~happy(X0) [cnf transformation 55]
105. ~calm(X0) | kind(X0) | tall(X0) [cnf transformation 57]
116. ~creative(X0) | humble(X0) | ~strong(X0) | calm(X0) [cnf transformation 58]
119. ~strong(X0) | happy(X0) | creative(X0) | happy(X0) [cnf transformation 59]
125. ~happy(X0) | ~humble(X0) | generous(X0) [cnf transformation 61]
127. ~humble(X0) | happy(X0) | generous(X0) [cnf transformation 61]
133. strong(alice) | ~tall(X0) | generous(X0) [cnf transformation 66]
139. strong(john) [cnf transformation 17]
147. ~generous(john) [cnf transformation 22]
150. ~creative(alice) [cnf transformation 24]
151. ~kind(john) [cnf transformation 25]
153. ~strong(X0) | happy(X0) | creative(X0) [duplicate literal removal 119]
154. ~tall(X0) | ~quiet(X0) [duplicate literal removal 85]
155. tall(X0) | quiet(X0) [duplicate literal removal 88]
214. ~strong(X0) | creative(X0) [subsumption resolution 153,98]
217. ~humble(X0) | generous(X0) [subsumption resolution 125,127]
235. 18 <=> ! [X0] : (~tall(X0) | generous(X0)) [avatar definition]
236. ~tall(X0) | generous(X0) <- (18) [avatar component clause 235]
247. 21 <=> strong(alice) [avatar definition]
249. strong(alice) <- (21) [avatar component clause 247]
250. 18 | 21 [avatar split clause 133,247,235]
332. creative(john) [resolution 214,139]
340. generous(X0) | quiet(X0) <- (18) [resolution 236,155]
469. creative(alice) <- (21) [resolution 249,214]
472. $false <- (21) [subsumption resolution 469,150]
473. ~21 [avatar contradiction clause 472]
516. 58 <=> humble(john) [avatar definition]
517. humble(john) <- (58) [avatar component clause 516]
520. 59 <=> calm(john) [avatar definition]
521. calm(john) <- (59) [avatar component clause 520]
631. humble(john) | ~strong(john) | calm(john) [resolution 116,332]
644. humble(john) | calm(john) [subsumption resolution 631,139]
645. 59 | 58 [avatar split clause 644,516,520]
654. quiet(john) <- (18) [resolution 340,147]
773. generous(john) <- (58) [resolution 517,217]
786. $false <- (58) [subsumption resolution 773,147]
787. ~58 [avatar contradiction clause 786]
789. kind(john) | tall(john) <- (59) [resolution 521,105]
790. tall(john) <- (59) [subsumption resolution 789,151]
851. ~quiet(john) <- (59) [resolution 790,154]
854. $false <- (18, 59) [subsumption resolution 851,654]
855. ~18 | ~59 [avatar contradiction clause 854]
856. $false [avatar sat refutation 250,473,645,787,855]
% SZS output end Proof for 29646582372107301412162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and kind then someone is happy or not wise and vice versa.
Everyone who is happy is both generous and not curious and vice versa.
If someone is both humble and happy then john is happy or funny and vice versa.
If john is both not humble and not curious then paul is not quiet and vice versa.
Everyone who is not calm or old is creative or kind and vice versa.
Everyone who is either strong or quiet is not quiet or creative.
If susan is funny then fred is both rich and brave.
If susan is brave then paul is not patient or not strong and vice versa.
Everyone who is not old or not wise is humble or not funny and vice versa.
If someone is either not patient or patient then someone is either kind or not funny and vice versa.
If someone is both happy and not calm then susan is not tall.
Everyone who is either not rich or kind is strong.
If susan is not tall then susan is not strong and vice versa.
Everyone who is not happy is not creative and vice versa.
Everyone who is not brave or not old is either strong or old.
Everyone who is either generous or wise is not generous or not patient and vice versa.
John is either not creative or funny.
Susan is both quiet and not tall.
Paul is both not creative and wise.
John is both not funny and quiet.
Someone is not kind or not patient.
Alice is not quiet or not strong.
Mary is not strong.
Someone is either kind or humble. | Alice is not strong. | neutral | ((?[X]:((humble(X)&kind(X))))<=>(?[X]:((happy(X)|~wise(X)))))&
(![X]:(happy(X)<=>(generous(X)&~curious(X))))&
((?[X]:((humble(X)&happy(X))))<=>((happy(john)|funny(john))))&
(((~humble(john)&~curious(john)))<=>(~quiet(paul)))&
(![X]:((~calm(X)|old(X))<=>(creative(X)|kind(X))))&
(![X]:((strong(X)<~>quiet(X))=>(~quiet(X)|creative(X))))&
((funny(susan))=>((rich(fred)&brave(fred))))&
((brave(susan))<=>((~patient(paul)|~strong(paul))))&
(![X]:((~old(X)|~wise(X))<=>(humble(X)|~funny(X))))&
((?[X]:((~patient(X)<~>patient(X))))<=>(?[X]:((kind(X)<~>~funny(X)))))&
((?[X]:((happy(X)&~calm(X))))=>(~tall(susan)))&
(![X]:((~rich(X)<~>kind(X))=>strong(X)))&
((~tall(susan))<=>(~strong(susan)))&
(![X]:(~happy(X)<=>~creative(X)))&
(![X]:((~brave(X)|~old(X))=>(strong(X)<~>old(X))))&
(![X]:((generous(X)<~>wise(X))<=>(~generous(X)|~patient(X))))&
((~creative(john)<~>funny(john)))&
((quiet(susan)&~tall(susan)))&
((~creative(paul)&wise(paul)))&
((~funny(john)&quiet(john)))&
(?[X]:((~kind(X)|~patient(X))))&
((~quiet(alice)|~strong(alice)))&
(~strong(mary))&
(?[X]:((kind(X)<~>humble(X)))) | ~strong(alice) | [] | null | 0 |
Everyone who is either not creative or humble is strong.
Everyone who is both not wise and not curious is wise or kind.
Everyone who is not patient or not happy is kind or not brave and vice versa.
If lucy is not rich or generous then someone is old or not wise and vice versa.
Everyone who is funny is calm or old.
Everyone who is either calm or not funny is both not calm and strong.
If john is not calm then john is both humble and not funny and vice versa.
If someone is creative then someone is creative or quiet and vice versa.
Everyone who is both kind and not quiet is both not curious and not quiet.
Everyone who is not kind is either generous or not patient.
If paul is not funny or brave then someone is tall and vice versa.
Everyone who is funny is either not quiet or not rich.
Everyone who is not quiet is not happy and vice versa.
Everyone who is not patient or not quiet is not quiet or not rich.
If someone is curious then john is not humble.
Everyone who is not wise is not curious or not tall.
Lucy is either patient or brave.
Someone is either not old or curious.
Lucy is not wise or funny.
Someone is happy or not old.
Someone is both not strong and humble.
Someone is not funny or strong.
Someone is both not wise and not kind.
Someone is not wise or not kind. | Paul is rich. | neutral | (![X]:((~creative(X)<~>humble(X))=>strong(X)))&
(![X]:((~wise(X)&~curious(X))=>(wise(X)|kind(X))))&
(![X]:((~patient(X)|~happy(X))<=>(kind(X)|~brave(X))))&
(((~rich(lucy)|generous(lucy)))<=>(?[X]:((old(X)|~wise(X)))))&
(![X]:(funny(X)=>(calm(X)|old(X))))&
(![X]:((calm(X)<~>~funny(X))=>(~calm(X)&strong(X))))&
((~calm(john))<=>((humble(john)&~funny(john))))&
((?[X]:(creative(X)))<=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:((kind(X)&~quiet(X))=>(~curious(X)&~quiet(X))))&
(![X]:(~kind(X)=>(generous(X)<~>~patient(X))))&
(((~funny(paul)|brave(paul)))<=>(?[X]:(tall(X))))&
(![X]:(funny(X)=>(~quiet(X)<~>~rich(X))))&
(![X]:(~quiet(X)<=>~happy(X)))&
(![X]:((~patient(X)|~quiet(X))=>(~quiet(X)|~rich(X))))&
((?[X]:(curious(X)))=>(~humble(john)))&
(![X]:(~wise(X)=>(~curious(X)|~tall(X))))&
((patient(lucy)<~>brave(lucy)))&
(?[X]:((~old(X)<~>curious(X))))&
((~wise(lucy)|funny(lucy)))&
(?[X]:((happy(X)|~old(X))))&
(?[X]:((~strong(X)&humble(X))))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:((~wise(X)&~kind(X))))&
(?[X]:((~wise(X)|~kind(X)))) | rich(paul) | [] | null | 0 |
Everyone who is either not kind or humble is both strong and tall and vice versa. Everyone who is both not strong and not patient is not funny and vice versa. If john is not curious then lucy is not creative and vice versa. Everyone who is either not tall or not rich is both strong and not kind. Everyone who is not humble or not quiet is not happy and vice versa. If someone is not tall or quiet then someone is not calm. If john is happy then fred is either calm or not kind. If lucy is not curious or not funny then someone is either not quiet or not strong. If susan is either happy or not old then susan is both not tall and not old and vice versa. Everyone who is not curious or not brave is not generous and vice versa. Everyone who is either not funny or not generous is either not tall or not wise. Everyone who is not curious is either not rich or not patient and vice versa. If someone is not curious or not creative then someone is either strong or rich and vice versa. Everyone who is not brave or not humble is brave or curious and vice versa. Everyone who is not funny is humble or patient and vice versa. If someone is both not happy and not curious then someone is both not generous and patient and vice versa. Fred is either creative or not quiet. Fred is strong or not quiet. Someone is either not tall or not funny. Someone is not humble or patient. Someone is both tall and not calm. Someone is either happy or not old. Someone is wise or quiet. | Susan is not rich. | entailment | (![X]:((~kind(X)<~>humble(X))<=>(strong(X)&tall(X))))&
(![X]:((~strong(X)&~patient(X))<=>~funny(X)))&
((~curious(john))<=>(~creative(lucy)))&
(![X]:((~tall(X)<~>~rich(X))=>(strong(X)&~kind(X))))&
(![X]:((~humble(X)|~quiet(X))<=>~happy(X)))&
((?[X]:((~tall(X)|quiet(X))))=>(?[X]:(~calm(X))))&
((happy(john))=>((calm(fred)<~>~kind(fred))))&
(((~curious(lucy)|~funny(lucy)))=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(((happy(susan)<~>~old(susan)))<=>((~tall(susan)&~old(susan))))&
(![X]:((~curious(X)|~brave(X))<=>~generous(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~tall(X)<~>~wise(X))))&
(![X]:(~curious(X)<=>(~rich(X)<~>~patient(X))))&
((?[X]:((~curious(X)|~creative(X))))<=>(?[X]:((strong(X)<~>rich(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(brave(X)|curious(X))))&
(![X]:(~funny(X)<=>(humble(X)|patient(X))))&
((?[X]:((~happy(X)&~curious(X))))<=>(?[X]:((~generous(X)&patient(X)))))&
((creative(fred)<~>~quiet(fred)))&
((strong(fred)|~quiet(fred)))&
(?[X]:((~tall(X)<~>~funny(X))))&
(?[X]:((~humble(X)|patient(X))))&
(?[X]:((tall(X)&~calm(X))))&
(?[X]:((happy(X)<~>~old(X))))&
(?[X]:((wise(X)|quiet(X)))) | ~rich(susan) | [
"p1",
"p4",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 565806066178135619276257
% SZS output start Proof for 565806066178135619276257
2. ! [X0] : ((~patient(X0) & ~strong(X0)) <=> ~funny(X0)) [input p1]
5. ! [X0] : ((~quiet(X0) | ~humble(X0)) <=> ~happy(X0)) [input p4]
12. ! [X0] : (~curious(X0) <=> (~rich(X0) <~> ~patient(X0))) [input p11]
14. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> (curious(X0) | brave(X0))) [input p13]
15. ! [X0] : (~funny(X0) <=> (patient(X0) | humble(X0))) [input p14]
16. ? [X0] : (~curious(X0) & ~happy(X0)) <=> ? [X0] : (patient(X0) & ~generous(X0)) [input p15]
24. rich(susan) [input hypothesis]
27. ? [X0] : (~curious(X0) & ~happy(X0)) <=> ? [X1] : (patient(X1) & ~generous(X1)) [rectify 16]
35. ! [X0] : (((~patient(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | (patient(X0) | strong(X0)))) [nnf transformation 2]
36. ! [X0] : (((~patient(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | patient(X0) | strong(X0))) [flattening 35]
39. ! [X0] : (((~quiet(X0) | ~humble(X0)) | happy(X0)) & (~happy(X0) | (quiet(X0) & humble(X0)))) [nnf transformation 5]
40. ! [X0] : ((~quiet(X0) | ~humble(X0) | happy(X0)) & (~happy(X0) | (quiet(X0) & humble(X0)))) [flattening 39]
53. ! [X0] : ((~curious(X0) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0)))) & (((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | curious(X0))) [nnf transformation 12]
59. ! [X0] : (((~humble(X0) | ~brave(X0)) | (~curious(X0) & ~brave(X0))) & ((curious(X0) | brave(X0)) | (humble(X0) & brave(X0)))) [nnf transformation 14]
60. ! [X0] : ((~humble(X0) | ~brave(X0) | (~curious(X0) & ~brave(X0))) & (curious(X0) | brave(X0) | (humble(X0) & brave(X0)))) [flattening 59]
61. ! [X0] : ((~funny(X0) | (~patient(X0) & ~humble(X0))) & ((patient(X0) | humble(X0)) | funny(X0))) [nnf transformation 15]
62. ! [X0] : ((~funny(X0) | (~patient(X0) & ~humble(X0))) & (patient(X0) | humble(X0) | funny(X0))) [flattening 61]
63. (? [X0] : (~curious(X0) & ~happy(X0)) | ! [X1] : (~patient(X1) | generous(X1))) & (? [X1] : (patient(X1) & ~generous(X1)) | ! [X0] : (curious(X0) | happy(X0))) [nnf transformation 27]
64. (? [X0] : (~curious(X0) & ~happy(X0)) | ! [X1] : (~patient(X1) | generous(X1))) & (? [X2] : (patient(X2) & ~generous(X2)) | ! [X3] : (curious(X3) | happy(X3))) [rectify 63]
65. ? [X0] : (~curious(X0) & ~happy(X0)) => (~curious(sK4) & ~happy(sK4)) [choice axiom]
66. ? [X2] : (patient(X2) & ~generous(X2)) => (patient(sK5) & ~generous(sK5)) [choice axiom]
67. ((~curious(sK4) & ~happy(sK4)) | ! [X1] : (~patient(X1) | generous(X1))) & ((patient(sK5) & ~generous(sK5)) | ! [X3] : (curious(X3) | happy(X3))) [skolemisation 64,66,65]
89. ~patient(X0) | funny(X0) [cnf transformation 36]
96. ~happy(X0) | humble(X0) [cnf transformation 40]
123. ~rich(X0) | ~curious(X0) | patient(X0) [cnf transformation 53]
130. curious(X0) | brave(X0) | brave(X0) [cnf transformation 60]
132. ~humble(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
136. ~funny(X0) | ~patient(X0) [cnf transformation 62]
138. patient(sK5) | curious(X3) | happy(X3) [cnf transformation 67]
152. rich(susan) [cnf transformation 24]
153. brave(X0) | curious(X0) [duplicate literal removal 130]
154. ~brave(X0) | ~humble(X0) [duplicate literal removal 132]
258. 23 <=> ! [X3] : curious(X3) [avatar definition]
259. curious(X3) <- (23) [avatar component clause 258]
263. ~patient(X0) [subsumption resolution 136,89]
265. happy(X3) | curious(X3) [subsumption resolution 138,263]
313. ~humble(X0) | curious(X0) [resolution 154,153]
317. curious(X1) | humble(X1) [resolution 265,96]
321. curious(X1) [subsumption resolution 317,313]
322. 23 [avatar split clause 321,258]
450. ~curious(susan) | patient(susan) [resolution 123,152]
454. patient(susan) <- (23) [subsumption resolution 450,259]
455. $false <- (23) [subsumption resolution 454,263]
456. ~23 [avatar contradiction clause 455]
463. $false [avatar sat refutation 322,456]
% SZS output end Proof for 565806066178135619276257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not rich then paul is either generous or calm and vice versa.
Everyone who is both old and wise is not happy or funny.
If susan is both not generous and not calm then john is not brave and vice versa.
Everyone who is not humble is either rich or not happy and vice versa.
Everyone who is either brave or not tall is both not kind and patient and vice versa.
If susan is either not generous or strong then mary is either not quiet or not kind and vice versa.
If mary is calm or not patient then someone is old or creative and vice versa.
Everyone who is not strong is both not tall and not old and vice versa.
Everyone who is both kind and funny is not strong and vice versa.
If someone is humble or patient then someone is not kind or humble.
Everyone who is both not brave and not patient is not quiet or not kind.
Everyone who is not patient is not generous or creative.
Everyone who is either tall or generous is either not strong or not rich and vice versa.
Everyone who is brave or not patient is either kind or not curious and vice versa.
Everyone who is either calm or quiet is old or not kind and vice versa.
If paul is not creative then susan is either strong or old.
Alice is either not quiet or not wise.
John is both not humble and brave.
Someone is both not kind and curious.
John is not humble or old.
John is either not old or not humble.
Someone is wise or tall.
Someone is either not tall or not quiet.
Lucy is both kind and happy. | John is brave. | entailment | ((?[X]:(~rich(X)))<=>((generous(paul)<~>calm(paul))))&
(![X]:((old(X)&wise(X))=>(~happy(X)|funny(X))))&
(((~generous(susan)&~calm(susan)))<=>(~brave(john)))&
(![X]:(~humble(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(~kind(X)&patient(X))))&
(((~generous(susan)<~>strong(susan)))<=>((~quiet(mary)<~>~kind(mary))))&
(((calm(mary)|~patient(mary)))<=>(?[X]:((old(X)|creative(X)))))&
(![X]:(~strong(X)<=>(~tall(X)&~old(X))))&
(![X]:((kind(X)&funny(X))<=>~strong(X)))&
((?[X]:((humble(X)|patient(X))))=>(?[X]:((~kind(X)|humble(X)))))&
(![X]:((~brave(X)&~patient(X))=>(~quiet(X)|~kind(X))))&
(![X]:(~patient(X)=>(~generous(X)|creative(X))))&
(![X]:((tall(X)<~>generous(X))<=>(~strong(X)<~>~rich(X))))&
(![X]:((brave(X)|~patient(X))<=>(kind(X)<~>~curious(X))))&
(![X]:((calm(X)<~>quiet(X))<=>(old(X)|~kind(X))))&
((~creative(paul))=>((strong(susan)<~>old(susan))))&
((~quiet(alice)<~>~wise(alice)))&
((~humble(john)&brave(john)))&
(?[X]:((~kind(X)&curious(X))))&
((~humble(john)|old(john)))&
((~old(john)<~>~humble(john)))&
(?[X]:((wise(X)|tall(X))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
((kind(lucy)&happy(lucy))) | brave(john) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6041290928180096505174564
% SZS output start Proof for 6041290928180096505174564
18. brave(john) & ~humble(john) [input p17]
25. ~brave(john) [input hypothesis]
137. brave(john) [cnf transformation 18]
148. ~brave(john) [cnf transformation 25]
169. 5 <=> brave(john) [avatar definition]
271. 5 [avatar split clause 137,169]
292. ~5 [avatar split clause 148,169]
293. $false [avatar sat refutation 271,292]
% SZS output end Proof for 6041290928180096505174564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either not creative or not humble then alice is both not happy and strong and vice versa.
If someone is either brave or not brave then someone is both not curious and patient.
Everyone who is either generous or not curious is either not strong or strong.
If alice is both calm and creative then alice is not quiet and vice versa.
Everyone who is both strong and not tall is brave or tall.
Everyone who is both curious and not kind is both not calm and happy and vice versa.
If someone is both not calm and patient then paul is not quiet and vice versa.
Everyone who is both not wise and not old is either patient or not tall.
Everyone who is both not quiet and not generous is either tall or not quiet.
Everyone who is calm is both not generous and not old and vice versa.
If someone is both not kind and not wise then paul is either not patient or not curious and vice versa.
Everyone who is brave is both curious and not generous.
If lucy is both not calm and not wise then someone is creative or strong and vice versa.
If paul is both not curious and not kind then someone is curious or not happy and vice versa.
If john is either calm or rich then alice is both not wise and curious.
Everyone who is both brave and not old is not kind or not rich and vice versa.
Mary is either wise or quiet.
Paul is curious or not strong.
Paul is not patient or wise.
John is quiet.
Paul is funny or not funny.
Someone is patient or creative. | Paul is quiet. | entailment | (((~creative(fred)<~>~humble(fred)))<=>((~happy(alice)&strong(alice))))&
((?[X]:((brave(X)<~>~brave(X))))=>(?[X]:((~curious(X)&patient(X)))))&
(![X]:((generous(X)<~>~curious(X))=>(~strong(X)<~>strong(X))))&
(((calm(alice)&creative(alice)))<=>(~quiet(alice)))&
(![X]:((strong(X)&~tall(X))=>(brave(X)|tall(X))))&
(![X]:((curious(X)&~kind(X))<=>(~calm(X)&happy(X))))&
((?[X]:((~calm(X)&patient(X))))<=>(~quiet(paul)))&
(![X]:((~wise(X)&~old(X))=>(patient(X)<~>~tall(X))))&
(![X]:((~quiet(X)&~generous(X))=>(tall(X)<~>~quiet(X))))&
(![X]:(calm(X)<=>(~generous(X)&~old(X))))&
((?[X]:((~kind(X)&~wise(X))))<=>((~patient(paul)<~>~curious(paul))))&
(![X]:(brave(X)=>(curious(X)&~generous(X))))&
(((~calm(lucy)&~wise(lucy)))<=>(?[X]:((creative(X)|strong(X)))))&
(((~curious(paul)&~kind(paul)))<=>(?[X]:((curious(X)|~happy(X)))))&
(((calm(john)<~>rich(john)))=>((~wise(alice)&curious(alice))))&
(![X]:((brave(X)&~old(X))<=>(~kind(X)|~rich(X))))&
((wise(mary)<~>quiet(mary)))&
((curious(paul)|~strong(paul)))&
((~patient(paul)|wise(paul)))&
(quiet(john))&
((funny(paul)|~funny(paul)))&
(?[X]:((patient(X)|creative(X)))) | quiet(paul) | [
"p5",
"p6",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8973513009504358482271304
% SZS output start Proof for 8973513009504358482271304
6. ! [X0] : ((~kind(X0) & curious(X0)) <=> (happy(X0) & ~calm(X0))) [input p5]
7. ? [X0] : (patient(X0) & ~calm(X0)) <=> ~quiet(paul) [input p6]
12. ! [X0] : (brave(X0) => (~generous(X0) & curious(X0))) [input p11]
14. (~kind(paul) & ~curious(paul)) <=> ? [X0] : (~happy(X0) | curious(X0)) [input p13]
16. ! [X0] : ((~old(X0) & brave(X0)) <=> (~rich(X0) | ~kind(X0))) [input p15]
23. ~quiet(paul) [input hypothesis]
33. ! [X0] : ((~generous(X0) & curious(X0)) | ~brave(X0)) [ennf transformation 12]
44. ! [X0] : (((~kind(X0) & curious(X0)) | (~happy(X0) | calm(X0))) & ((happy(X0) & ~calm(X0)) | (kind(X0) | ~curious(X0)))) [nnf transformation 6]
45. ! [X0] : (((~kind(X0) & curious(X0)) | ~happy(X0) | calm(X0)) & ((happy(X0) & ~calm(X0)) | kind(X0) | ~curious(X0))) [flattening 44]
46. (? [X0] : (patient(X0) & ~calm(X0)) | quiet(paul)) & (~quiet(paul) | ! [X0] : (~patient(X0) | calm(X0))) [nnf transformation 7]
47. (? [X0] : (patient(X0) & ~calm(X0)) | quiet(paul)) & (~quiet(paul) | ! [X1] : (~patient(X1) | calm(X1))) [rectify 46]
48. ? [X0] : (patient(X0) & ~calm(X0)) => (patient(sK1) & ~calm(sK1)) [choice axiom]
49. ((patient(sK1) & ~calm(sK1)) | quiet(paul)) & (~quiet(paul) | ! [X1] : (~patient(X1) | calm(X1))) [skolemisation 47,48]
63. ((~kind(paul) & ~curious(paul)) | ! [X0] : (happy(X0) & ~curious(X0))) & (? [X0] : (~happy(X0) | curious(X0)) | (kind(paul) | curious(paul))) [nnf transformation 14]
64. ((~kind(paul) & ~curious(paul)) | ! [X0] : (happy(X0) & ~curious(X0))) & (? [X0] : (~happy(X0) | curious(X0)) | kind(paul) | curious(paul)) [flattening 63]
65. ((~kind(paul) & ~curious(paul)) | ! [X0] : (happy(X0) & ~curious(X0))) & (? [X1] : (~happy(X1) | curious(X1)) | kind(paul) | curious(paul)) [rectify 64]
66. ? [X1] : (~happy(X1) | curious(X1)) => (~happy(sK4) | curious(sK4)) [choice axiom]
67. ((~kind(paul) & ~curious(paul)) | ! [X0] : (happy(X0) & ~curious(X0))) & ((~happy(sK4) | curious(sK4)) | kind(paul) | curious(paul)) [skolemisation 65,66]
69. ! [X0] : (((~old(X0) & brave(X0)) | (rich(X0) & kind(X0))) & ((~rich(X0) | ~kind(X0)) | (old(X0) | ~brave(X0)))) [nnf transformation 16]
70. ! [X0] : (((~old(X0) & brave(X0)) | (rich(X0) & kind(X0))) & (~rich(X0) | ~kind(X0) | old(X0) | ~brave(X0))) [flattening 69]
94. ~happy(X0) | curious(X0) | calm(X0) [cnf transformation 45]
97. ~calm(sK1) | quiet(paul) [cnf transformation 49]
112. ~brave(X0) | curious(X0) [cnf transformation 33]
120. ~curious(paul) | ~curious(X0) [cnf transformation 67]
121. ~curious(paul) | happy(X0) [cnf transformation 67]
122. ~kind(paul) | ~curious(X0) [cnf transformation 67]
123. ~kind(paul) | happy(X0) [cnf transformation 67]
129. kind(X0) | brave(X0) [cnf transformation 70]
140. ~quiet(paul) [cnf transformation 23]
203. 12 <=> quiet(paul) [avatar definition]
212. 14 <=> calm(sK1) [avatar definition]
214. ~calm(sK1) <- (~14) [avatar component clause 212]
215. 12 | ~14 [avatar split clause 97,212,203]
221. 16 <=> curious(paul) [avatar definition]
222. ~curious(paul) <- (~16) [avatar component clause 221]
273. 27 <=> ! [X0] : happy(X0) [avatar definition]
274. happy(X0) <- (27) [avatar component clause 273]
276. 28 <=> kind(paul) [avatar definition]
278. ~kind(paul) <- (~28) [avatar component clause 276]
279. 27 | ~28 [avatar split clause 123,276,273]
281. 29 <=> ! [X0] : ~curious(X0) [avatar definition]
282. ~curious(X0) <- (29) [avatar component clause 281]
283. 29 | ~28 [avatar split clause 122,276,281]
284. 27 | ~16 [avatar split clause 121,221,273]
285. 29 | ~16 [avatar split clause 120,221,281]
344. ~12 [avatar split clause 140,203]
345. brave(paul) <- (~28) [resolution 129,278]
347. curious(paul) <- (~28) [resolution 345,112]
348. $false <- (~16, ~28) [subsumption resolution 347,222]
349. 16 | 28 [avatar contradiction clause 348]
358. curious(X0) | calm(X0) <- (27) [resolution 94,274]
359. calm(X0) <- (27, 29) [subsumption resolution 358,282]
363. $false <- (~14, 27, 29) [resolution 359,214]
366. 14 | ~27 | ~29 [avatar contradiction clause 363]
367. $false [avatar sat refutation 215,279,283,284,285,344,349,366]
% SZS output end Proof for 8973513009504358482271304
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not quiet is both not curious and funny.
If someone is both not brave and not strong then fred is patient or not quiet and vice versa.
Everyone who is creative is both not old and creative and vice versa.
Everyone who is both happy and not quiet is either not quiet or not creative and vice versa.
Everyone who is both funny and happy is happy or patient and vice versa.
Everyone who is calm is either not brave or wise and vice versa.
If mary is both not generous and not calm then john is not kind or not brave.
If someone is either humble or funny then alice is humble.
If susan is happy or funny then someone is either funny or brave and vice versa.
Everyone who is not tall is not old and vice versa.
Everyone who is either tall or not kind is not kind or not creative.
If someone is creative then someone is not kind.
If john is not curious then someone is wise or happy.
Everyone who is funny or not humble is quiet and vice versa.
Everyone who is kind is either not brave or patient and vice versa.
If someone is both not creative and old then someone is both not generous and creative and vice versa.
Alice is rich.
Someone is not tall or calm.
John is not quiet or not creative.
Someone is tall or not rich.
Alice is both not tall and generous.
Paul is humble or not tall.
Alice is either funny or brave. | Paul is kind. | neutral | (![X]:((wise(X)&~quiet(X))=>(~curious(X)&funny(X))))&
((?[X]:((~brave(X)&~strong(X))))<=>((patient(fred)|~quiet(fred))))&
(![X]:(creative(X)<=>(~old(X)&creative(X))))&
(![X]:((happy(X)&~quiet(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((funny(X)&happy(X))<=>(happy(X)|patient(X))))&
(![X]:(calm(X)<=>(~brave(X)<~>wise(X))))&
(((~generous(mary)&~calm(mary)))=>((~kind(john)|~brave(john))))&
((?[X]:((humble(X)<~>funny(X))))=>(humble(alice)))&
(((happy(susan)|funny(susan)))<=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:(~tall(X)<=>~old(X)))&
(![X]:((tall(X)<~>~kind(X))=>(~kind(X)|~creative(X))))&
((?[X]:(creative(X)))=>(?[X]:(~kind(X))))&
((~curious(john))=>(?[X]:((wise(X)|happy(X)))))&
(![X]:((funny(X)|~humble(X))<=>quiet(X)))&
(![X]:(kind(X)<=>(~brave(X)<~>patient(X))))&
((?[X]:((~creative(X)&old(X))))<=>(?[X]:((~generous(X)&creative(X)))))&
(rich(alice))&
(?[X]:((~tall(X)|calm(X))))&
((~quiet(john)|~creative(john)))&
(?[X]:((tall(X)|~rich(X))))&
((~tall(alice)&generous(alice)))&
((humble(paul)|~tall(paul)))&
((funny(alice)<~>brave(alice))) | kind(paul) | [] | null | 0 |
Everyone who is either old or curious is humble. Everyone who is either humble or creative is creative and vice versa. Everyone who is not old is rich. If someone is either curious or tall then john is either rich or kind. Everyone who is not quiet or not tall is both old and wise and vice versa. Everyone who is both not brave and old is not humble and vice versa. Everyone who is both old and brave is funny or not strong. If someone is brave then susan is either strong or wise and vice versa. If mary is not brave or not happy then susan is curious. Everyone who is not kind is not creative or not patient and vice versa. If someone is both not calm and not brave then someone is kind and vice versa. If someone is either strong or not old then susan is funny or not calm and vice versa. Everyone who is either not tall or old is both funny and calm. If someone is wise then lucy is not funny or rich and vice versa. Everyone who is kind is not funny and vice versa. Everyone who is either not kind or not creative is happy or old. Mary is both kind and rich. Paul is not strong or not tall. Susan is both not generous and not strong. Someone is either not brave or not tall. Mary is happy or old. Lucy is not brave. Someone is creative or brave. John is either calm or generous. | Mary is tall. | contradiction | (![X]:((old(X)<~>curious(X))=>humble(X)))&
(![X]:((humble(X)<~>creative(X))<=>creative(X)))&
(![X]:(~old(X)=>rich(X)))&
((?[X]:((curious(X)<~>tall(X))))=>((rich(john)<~>kind(john))))&
(![X]:((~quiet(X)|~tall(X))<=>(old(X)&wise(X))))&
(![X]:((~brave(X)&old(X))<=>~humble(X)))&
(![X]:((old(X)&brave(X))=>(funny(X)|~strong(X))))&
((?[X]:(brave(X)))<=>((strong(susan)<~>wise(susan))))&
(((~brave(mary)|~happy(mary)))=>(curious(susan)))&
(![X]:(~kind(X)<=>(~creative(X)|~patient(X))))&
((?[X]:((~calm(X)&~brave(X))))<=>(?[X]:(kind(X))))&
((?[X]:((strong(X)<~>~old(X))))<=>((funny(susan)|~calm(susan))))&
(![X]:((~tall(X)<~>old(X))=>(funny(X)&calm(X))))&
((?[X]:(wise(X)))<=>((~funny(lucy)|rich(lucy))))&
(![X]:(kind(X)<=>~funny(X)))&
(![X]:((~kind(X)<~>~creative(X))=>(happy(X)|old(X))))&
((kind(mary)&rich(mary)))&
((~strong(paul)|~tall(paul)))&
((~generous(susan)&~strong(susan)))&
(?[X]:((~brave(X)<~>~tall(X))))&
((happy(mary)|old(mary)))&
(~brave(lucy))&
(?[X]:((creative(X)|brave(X))))&
((calm(john)<~>generous(john))) | tall(mary) | [
"p1",
"p5",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7968030472257702410248668
% SZS output start Proof for 7968030472257702410248668
2. ! [X0] : ((humble(X0) <~> creative(X0)) <=> creative(X0)) [input p1]
6. ! [X0] : ((old(X0) & ~brave(X0)) <=> ~humble(X0)) [input p5]
13. ! [X0] : ((~tall(X0) <~> old(X0)) => (calm(X0) & funny(X0))) [input p12]
15. ! [X0] : (kind(X0) <=> ~funny(X0)) [input p14]
17. rich(mary) & kind(mary) [input p16]
25. tall(mary) [input hypothesis]
36. ! [X0] : ((calm(X0) & funny(X0)) | (~tall(X0) <=> old(X0))) [ennf transformation 13]
38. ! [X0] : ((((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | ~creative(X0)) & (creative(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))))) [nnf transformation 2]
42. ! [X0] : (((old(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | (~old(X0) | brave(X0)))) [nnf transformation 6]
43. ! [X0] : (((old(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | ~old(X0) | brave(X0))) [flattening 42]
60. ! [X0] : ((calm(X0) & funny(X0)) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0)))) [nnf transformation 36]
66. ! [X0] : ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0))) [nnf transformation 15]
75. creative(X0) | creative(X0) | ~humble(X0) [cnf transformation 38]
78. ~creative(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 38]
91. old(X0) | humble(X0) [cnf transformation 43]
111. funny(X0) | ~tall(X0) | ~old(X0) [cnf transformation 60]
117. ~funny(X0) | ~kind(X0) [cnf transformation 66]
119. kind(mary) [cnf transformation 17]
130. tall(mary) [cnf transformation 25]
131. creative(X0) | ~humble(X0) [duplicate literal removal 75]
132. ~creative(X0) | ~humble(X0) [duplicate literal removal 78]
133. ~humble(X0) [subsumption resolution 131,132]
152. old(X0) [subsumption resolution 91,133]
206. ~tall(X0) | funny(X0) [subsumption resolution 111,152]
274. funny(mary) [resolution 206,130]
279. ~kind(mary) [resolution 274,117]
280. $false [subsumption resolution 279,119]
% SZS output end Proof for 7968030472257702410248668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or happy then alice is curious.
If mary is wise or not patient then lucy is either not funny or kind.
If mary is either wise or humble then john is either not quiet or old.
If someone is either funny or not happy then someone is either humble or not humble.
Everyone who is both humble and patient is both wise and not generous.
Everyone who is not calm is both not tall and brave.
Everyone who is rich or not wise is not funny or not kind and vice versa.
Everyone who is curious is not calm or not rich.
Everyone who is not patient is both patient and not generous and vice versa.
Everyone who is not brave or humble is creative.
If someone is both not calm and not humble then someone is humble or not patient.
Everyone who is old is both not kind and kind and vice versa.
If someone is curious or wise then john is humble or not strong.
If someone is not happy or curious then lucy is both creative and old and vice versa.
Everyone who is not curious or brave is either not quiet or not wise and vice versa.
Someone is happy or wise.
John is happy.
Mary is either strong or not generous.
Someone is not curious.
Someone is happy or rich.
Someone is either not happy or rich. | John is patient. | entailment | (((rich(alice)<~>happy(alice)))=>(curious(alice)))&
(((wise(mary)|~patient(mary)))=>((~funny(lucy)<~>kind(lucy))))&
(((wise(mary)<~>humble(mary)))=>((~quiet(john)<~>old(john))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((humble(X)&patient(X))=>(wise(X)&~generous(X))))&
(![X]:(~calm(X)=>(~tall(X)&brave(X))))&
(![X]:((rich(X)|~wise(X))<=>(~funny(X)|~kind(X))))&
(![X]:(curious(X)=>(~calm(X)|~rich(X))))&
(![X]:(~patient(X)<=>(patient(X)&~generous(X))))&
(![X]:((~brave(X)|humble(X))=>creative(X)))&
((?[X]:((~calm(X)&~humble(X))))=>(?[X]:((humble(X)|~patient(X)))))&
(![X]:(old(X)<=>(~kind(X)&kind(X))))&
((?[X]:((curious(X)|wise(X))))=>((humble(john)|~strong(john))))&
((?[X]:((~happy(X)|curious(X))))<=>((creative(lucy)&old(lucy))))&
(![X]:((~curious(X)|brave(X))<=>(~quiet(X)<~>~wise(X))))&
(?[X]:((happy(X)|wise(X))))&
(happy(john))&
((strong(mary)<~>~generous(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:((~happy(X)<~>rich(X)))) | patient(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2185719525243393696642691
% SZS output start Proof for 2185719525243393696642691
9. ! [X0] : (~patient(X0) <=> (~generous(X0) & patient(X0))) [input p8]
22. ~patient(john) [input hypothesis]
48. ! [X0] : ((~patient(X0) | (generous(X0) | ~patient(X0))) & ((~generous(X0) & patient(X0)) | patient(X0))) [nnf transformation 9]
49. ! [X0] : ((~patient(X0) | generous(X0) | ~patient(X0)) & ((~generous(X0) & patient(X0)) | patient(X0))) [flattening 48]
94. patient(X0) | patient(X0) [cnf transformation 49]
124. ~patient(john) [cnf transformation 22]
125. patient(X0) [duplicate literal removal 94]
222. $false [subsumption resolution 124,125]
% SZS output end Proof for 2185719525243393696642691
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and brave is either patient or brave and vice versa.
Everyone who is strong or old is not calm.
Everyone who is both curious and not wise is calm.
Everyone who is not calm or not generous is not creative.
If someone is wise then john is either patient or not patient.
If susan is not strong then someone is both funny and patient and vice versa.
If mary is not funny then john is humble or quiet.
If someone is humble or patient then someone is not strong or funny and vice versa.
Everyone who is kind is not quiet and vice versa.
Everyone who is patient is funny or not wise.
If alice is both rich and not calm then someone is not humble.
Everyone who is happy is humble.
Everyone who is both not quiet and not wise is creative.
If someone is not brave then someone is either tall or old.
Everyone who is either kind or curious is both generous and curious.
Everyone who is not creative or happy is either funny or not patient and vice versa.
John is rich or not quiet.
Mary is either not brave or not patient.
Someone is either not wise or creative.
Alice is not calm.
Susan is not happy or not calm.
Someone is both not patient and humble.
Someone is strong. | Mary is wise. | contradiction | (![X]:((~wise(X)&brave(X))<=>(patient(X)<~>brave(X))))&
(![X]:((strong(X)|old(X))=>~calm(X)))&
(![X]:((curious(X)&~wise(X))=>calm(X)))&
(![X]:((~calm(X)|~generous(X))=>~creative(X)))&
((?[X]:(wise(X)))=>((patient(john)<~>~patient(john))))&
((~strong(susan))<=>(?[X]:((funny(X)&patient(X)))))&
((~funny(mary))=>((humble(john)|quiet(john))))&
((?[X]:((humble(X)|patient(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:(kind(X)<=>~quiet(X)))&
(![X]:(patient(X)=>(funny(X)|~wise(X))))&
(((rich(alice)&~calm(alice)))=>(?[X]:(~humble(X))))&
(![X]:(happy(X)=>humble(X)))&
(![X]:((~quiet(X)&~wise(X))=>creative(X)))&
((?[X]:(~brave(X)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((kind(X)<~>curious(X))=>(generous(X)&curious(X))))&
(![X]:((~creative(X)|happy(X))<=>(funny(X)<~>~patient(X))))&
((rich(john)|~quiet(john)))&
((~brave(mary)<~>~patient(mary)))&
(?[X]:((~wise(X)<~>creative(X))))&
(~calm(alice))&
((~happy(susan)|~calm(susan)))&
(?[X]:((~patient(X)&humble(X))))&
(?[X]:(strong(X))) | wise(mary) | [
"p0",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6433330320979590046299516
% SZS output start Proof for 6433330320979590046299516
1. ! [X0] : ((brave(X0) & ~wise(X0)) <=> (patient(X0) <~> brave(X0))) [input p0]
18. ~brave(mary) <~> ~patient(mary) [input p17]
24. wise(mary) [input hypothesis]
45. ! [X0] : (((brave(X0) & ~wise(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~brave(X0) | wise(X0)))) [nnf transformation 1]
46. ! [X0] : (((brave(X0) & ~wise(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | ~brave(X0) | wise(X0))) [flattening 45]
67. (patient(mary) | brave(mary)) & (~patient(mary) | ~brave(mary)) [nnf transformation 18]
78. ~brave(X0) | patient(X0) | ~wise(X0) [cnf transformation 46]
79. brave(X0) | brave(X0) | ~patient(X0) [cnf transformation 46]
112. ~patient(mary) | ~brave(mary) [cnf transformation 67]
113. patient(mary) | brave(mary) [cnf transformation 67]
121. wise(mary) [cnf transformation 24]
124. ~patient(X0) | brave(X0) [duplicate literal removal 79]
223. brave(mary) [subsumption resolution 113,124]
224. ~patient(mary) [subsumption resolution 112,223]
252. patient(mary) | ~wise(mary) [resolution 78,223]
267. ~wise(mary) [subsumption resolution 252,224]
268. $false [subsumption resolution 267,121]
% SZS output end Proof for 6433330320979590046299516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is generous then paul is not old and vice versa.
If someone is funny then someone is either happy or quiet and vice versa.
If someone is either not curious or quiet then someone is both not calm and not brave and vice versa.
Everyone who is not rich is both kind and not tall.
Everyone who is not patient is either wise or not calm and vice versa.
Everyone who is not quiet is strong or happy and vice versa.
Everyone who is either kind or not humble is either rich or creative.
Everyone who is both not generous and strong is either not funny or funny and vice versa.
Everyone who is both not strong and rich is not brave and vice versa.
Everyone who is both wise and not kind is not curious and vice versa.
If someone is both rich and not happy then someone is both funny and curious.
If alice is wise or happy then mary is both not patient and happy.
If someone is either quiet or generous then someone is both calm and humble.
Everyone who is either generous or old is either not wise or not generous and vice versa.
If someone is not happy then john is patient or brave and vice versa.
If john is either tall or not happy then someone is either patient or not rich and vice versa.
John is kind or tall.
Someone is not kind.
Lucy is humble or not funny.
Mary is either not funny or not kind.
Someone is either not wise or brave.
Fred is strong or not old. | Paul is happy. | neutral | ((generous(fred))<=>(~old(paul)))&
((?[X]:(funny(X)))<=>(?[X]:((happy(X)<~>quiet(X)))))&
((?[X]:((~curious(X)<~>quiet(X))))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:(~rich(X)=>(kind(X)&~tall(X))))&
(![X]:(~patient(X)<=>(wise(X)<~>~calm(X))))&
(![X]:(~quiet(X)<=>(strong(X)|happy(X))))&
(![X]:((kind(X)<~>~humble(X))=>(rich(X)<~>creative(X))))&
(![X]:((~generous(X)&strong(X))<=>(~funny(X)<~>funny(X))))&
(![X]:((~strong(X)&rich(X))<=>~brave(X)))&
(![X]:((wise(X)&~kind(X))<=>~curious(X)))&
((?[X]:((rich(X)&~happy(X))))=>(?[X]:((funny(X)&curious(X)))))&
(((wise(alice)|happy(alice)))=>((~patient(mary)&happy(mary))))&
((?[X]:((quiet(X)<~>generous(X))))=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((generous(X)<~>old(X))<=>(~wise(X)<~>~generous(X))))&
((?[X]:(~happy(X)))<=>((patient(john)|brave(john))))&
(((tall(john)<~>~happy(john)))<=>(?[X]:((patient(X)<~>~rich(X)))))&
((kind(john)|tall(john)))&
(?[X]:(~kind(X)))&
((humble(lucy)|~funny(lucy)))&
((~funny(mary)<~>~kind(mary)))&
(?[X]:((~wise(X)<~>brave(X))))&
((strong(fred)|~old(fred))) | happy(paul) | [] | null | 0 |
Everyone who is happy is patient.
Everyone who is either not calm or calm is wise or kind and vice versa.
If someone is either generous or rich then someone is both patient and generous.
If john is both kind and quiet then someone is both tall and not creative.
Everyone who is either old or not wise is not curious and vice versa.
Everyone who is patient is either tall or happy and vice versa.
Everyone who is not quiet is creative.
Everyone who is both not quiet and humble is wise or creative.
If someone is not generous or not creative then mary is not brave or wise and vice versa.
If someone is either not funny or brave then alice is not tall or not patient.
Everyone who is either calm or not rich is either old or calm and vice versa.
Everyone who is both strong and not old is either funny or calm and vice versa.
If alice is either generous or not funny then paul is not funny or not rich and vice versa.
Everyone who is either not tall or old is either creative or calm and vice versa.
Everyone who is tall or strong is not old or not brave and vice versa.
Everyone who is brave is not strong or not tall and vice versa.
Alice is not wise.
Lucy is both not creative and not brave.
Lucy is not generous.
Someone is both not humble and not calm.
Fred is both not old and not creative.
Someone is both not brave and old.
Someone is both not tall and not patient.
Alice is both not brave and rich. | Mary is quiet. | entailment | (![X]:(happy(X)=>patient(X)))&
(![X]:((~calm(X)<~>calm(X))<=>(wise(X)|kind(X))))&
((?[X]:((generous(X)<~>rich(X))))=>(?[X]:((patient(X)&generous(X)))))&
(((kind(john)&quiet(john)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((old(X)<~>~wise(X))<=>~curious(X)))&
(![X]:(patient(X)<=>(tall(X)<~>happy(X))))&
(![X]:(~quiet(X)=>creative(X)))&
(![X]:((~quiet(X)&humble(X))=>(wise(X)|creative(X))))&
((?[X]:((~generous(X)|~creative(X))))<=>((~brave(mary)|wise(mary))))&
((?[X]:((~funny(X)<~>brave(X))))=>((~tall(alice)|~patient(alice))))&
(![X]:((calm(X)<~>~rich(X))<=>(old(X)<~>calm(X))))&
(![X]:((strong(X)&~old(X))<=>(funny(X)<~>calm(X))))&
(((generous(alice)<~>~funny(alice)))<=>((~funny(paul)|~rich(paul))))&
(![X]:((~tall(X)<~>old(X))<=>(creative(X)<~>calm(X))))&
(![X]:((tall(X)|strong(X))<=>(~old(X)|~brave(X))))&
(![X]:(brave(X)<=>(~strong(X)|~tall(X))))&
(~wise(alice))&
((~creative(lucy)&~brave(lucy)))&
(~generous(lucy))&
(?[X]:((~humble(X)&~calm(X))))&
((~old(fred)&~creative(fred)))&
(?[X]:((~brave(X)&old(X))))&
(?[X]:((~tall(X)&~patient(X))))&
((~brave(alice)&rich(alice))) | quiet(mary) | [
"p0",
"p5",
"p6",
"p9",
"p10",
"p11",
"p13",
"p14",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5280292067772269106314974
% SZS output start Proof for 5280292067772269106314974
1. ! [X0] : (happy(X0) => patient(X0)) [input p0]
6. ! [X0] : (patient(X0) <=> (tall(X0) <~> happy(X0))) [input p5]
7. ! [X0] : (~quiet(X0) => creative(X0)) [input p6]
10. ? [X0] : (~funny(X0) <~> brave(X0)) => (~patient(alice) | ~tall(alice)) [input p9]
11. ! [X0] : ((calm(X0) <~> ~rich(X0)) <=> (old(X0) <~> calm(X0))) [input p10]
12. ! [X0] : ((~old(X0) & strong(X0)) <=> (funny(X0) <~> calm(X0))) [input p11]
14. ! [X0] : ((~tall(X0) <~> old(X0)) <=> (creative(X0) <~> calm(X0))) [input p13]
15. ! [X0] : ((strong(X0) | tall(X0)) <=> (~brave(X0) | ~old(X0))) [input p14]
16. ! [X0] : (brave(X0) <=> (~tall(X0) | ~strong(X0))) [input p15]
24. rich(alice) & ~brave(alice) [input p23]
25. ~quiet(mary) [input hypothesis]
29. ! [X0] : (patient(X0) | ~happy(X0)) [ennf transformation 1]
33. ! [X0] : (creative(X0) | quiet(X0)) [ennf transformation 7]
34. (~patient(alice) | ~tall(alice)) | ! [X0] : (~funny(X0) <=> brave(X0)) [ennf transformation 10]
35. ~patient(alice) | ~tall(alice) | ! [X0] : (~funny(X0) <=> brave(X0)) [flattening 34]
44. ! [X0] : ((patient(X0) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0)))) & (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | ~patient(X0))) [nnf transformation 6]
50. ~patient(alice) | ~tall(alice) | ! [X0] : ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))) [nnf transformation 35]
51. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) & (((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [nnf transformation 11]
52. ! [X0] : (((~old(X0) & strong(X0)) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0)))) & (((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | (old(X0) | ~strong(X0)))) [nnf transformation 12]
53. ! [X0] : (((~old(X0) & strong(X0)) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0)))) & (((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | old(X0) | ~strong(X0))) [flattening 52]
56. ! [X0] : ((((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0))))) [nnf transformation 14]
57. ! [X0] : (((strong(X0) | tall(X0)) | (brave(X0) & old(X0))) & ((~brave(X0) | ~old(X0)) | (~strong(X0) & ~tall(X0)))) [nnf transformation 15]
58. ! [X0] : ((strong(X0) | tall(X0) | (brave(X0) & old(X0))) & (~brave(X0) | ~old(X0) | (~strong(X0) & ~tall(X0)))) [flattening 57]
59. ! [X0] : ((brave(X0) | (tall(X0) & strong(X0))) & ((~tall(X0) | ~strong(X0)) | ~brave(X0))) [nnf transformation 16]
60. ! [X0] : ((brave(X0) | (tall(X0) & strong(X0))) & (~tall(X0) | ~strong(X0) | ~brave(X0))) [flattening 59]
67. ~happy(X0) | patient(X0) [cnf transformation 29]
82. patient(X0) | happy(X0) | ~tall(X0) [cnf transformation 44]
84. creative(X0) | quiet(X0) [cnf transformation 33]
89. ~patient(alice) | ~tall(alice) | brave(X0) | funny(X0) [cnf transformation 50]
90. ~patient(alice) | ~tall(alice) | ~funny(X0) | ~brave(X0) [cnf transformation 50]
92. calm(X0) | old(X0) | calm(X0) | rich(X0) [cnf transformation 51]
93. ~calm(X0) | ~old(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 51]
95. ~rich(X0) | calm(X0) | calm(X0) | ~old(X0) [cnf transformation 51]
98. rich(X0) | ~calm(X0) | old(X0) | ~calm(X0) [cnf transformation 51]
99. ~strong(X0) | funny(X0) | old(X0) | calm(X0) [cnf transformation 53]
100. ~strong(X0) | ~funny(X0) | old(X0) | ~calm(X0) [cnf transformation 53]
102. ~calm(X0) | funny(X0) | strong(X0) [cnf transformation 53]
103. ~funny(X0) | calm(X0) | ~old(X0) [cnf transformation 53]
104. ~old(X0) | funny(X0) | ~calm(X0) [cnf transformation 53]
113. ~creative(X0) | ~calm(X0) | old(X0) | tall(X0) [cnf transformation 56]
114. ~old(X0) | ~creative(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 56]
115. ~creative(X0) | ~tall(X0) | calm(X0) | old(X0) [cnf transformation 56]
117. ~old(X0) | tall(X0) | calm(X0) | ~creative(X0) [cnf transformation 56]
119. ~brave(X0) | ~old(X0) | ~tall(X0) [cnf transformation 58]
121. strong(X0) | tall(X0) | old(X0) [cnf transformation 58]
123. ~strong(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 60]
124. strong(X0) | brave(X0) [cnf transformation 60]
125. brave(X0) | tall(X0) [cnf transformation 60]
137. ~brave(alice) [cnf transformation 24]
139. ~quiet(mary) [cnf transformation 25]
140. calm(X0) | old(X0) | rich(X0) [duplicate literal removal 92]
141. ~calm(X0) | ~old(X0) | ~rich(X0) [duplicate literal removal 93]
142. ~old(X0) | calm(X0) | ~rich(X0) [duplicate literal removal 95]
143. ~calm(X0) | rich(X0) | old(X0) [duplicate literal removal 98]
183. ~tall(X0) | patient(X0) [subsumption resolution 82,67]
199. 12 <=> brave(mary) [avatar definition]
200. ~brave(mary) <- (~12) [avatar component clause 199]
201. brave(mary) <- (12) [avatar component clause 199]
211. ~tall(alice) | ~funny(X0) | ~brave(X0) [subsumption resolution 90,183]
213. 15 <=> ! [X0] : (~funny(X0) | ~brave(X0)) [avatar definition]
214. ~funny(X0) | ~brave(X0) <- (15) [avatar component clause 213]
216. 16 <=> tall(alice) [avatar definition]
219. 15 | ~16 [avatar split clause 211,216,213]
220. ~tall(alice) | brave(X0) | funny(X0) [subsumption resolution 89,183]
222. 17 <=> ! [X0] : (brave(X0) | funny(X0)) [avatar definition]
223. funny(X0) | brave(X0) <- (17) [avatar component clause 222]
224. 17 | ~16 [avatar split clause 220,216,222]
225. ~old(X0) | ~rich(X0) [subsumption resolution 141,142]
226. old(X0) | rich(X0) [subsumption resolution 140,143]
253. tall(alice) [resolution 125,137]
258. 16 [avatar split clause 253,216]
298. ~old(X0) | calm(X0) | brave(X0) <- (17) [resolution 103,223]
306. ~calm(X0) | funny(X0) | rich(X0) [resolution 104,226]
332. brave(X0) | calm(X0) | rich(X0) <- (17) [resolution 298,226]
339. funny(X1) | old(X1) | calm(X1) | tall(X1) | old(X1) [resolution 99,121]
342. funny(X1) | old(X1) | calm(X1) | tall(X1) [duplicate literal removal 339]
348. ~funny(X2) | old(X2) | ~calm(X2) | brave(X2) [resolution 100,124]
351. ~calm(X2) | old(X2) | brave(X2) <- (17) [subsumption resolution 348,223]
382. ~calm(X0) | old(X0) | tall(X0) | quiet(X0) [resolution 113,84]
385. ~creative(X1) | ~tall(X1) | ~calm(X1) | rich(X1) [resolution 114,226]
389. ~tall(X0) | calm(X0) | old(X0) | quiet(X0) [resolution 115,84]
397. 31 <=> calm(mary) [avatar definition]
398. calm(mary) <- (31) [avatar component clause 397]
405. 33 <=> old(mary) [avatar definition]
406. ~old(mary) <- (~33) [avatar component clause 405]
407. old(mary) <- (33) [avatar component clause 405]
424. ~creative(X1) | calm(X1) | tall(X1) | rich(X1) [resolution 117,226]
432. calm(X0) | rich(X0) | ~old(X0) | ~tall(X0) <- (17) [resolution 332,119]
437. ~old(X0) | calm(X0) | ~tall(X0) <- (17) [subsumption resolution 432,225]
442. old(X2) | calm(X2) | tall(X2) | ~brave(X2) <- (15) [resolution 342,214]
445. old(X2) | calm(X2) | tall(X2) <- (15) [subsumption resolution 442,125]
478. calm(X2) | ~tall(X2) | rich(X2) <- (17) [resolution 437,226]
486. ~tall(X0) | ~calm(X0) | rich(X0) | quiet(X0) [resolution 385,84]
487. ~tall(X0) | rich(X0) | quiet(X0) <- (17) [subsumption resolution 486,478]
505. 36 <=> tall(mary) [avatar definition]
506. tall(mary) <- (36) [avatar component clause 505]
509. calm(mary) | tall(mary) <- (15, ~33) [resolution 406,445]
518. 36 | 31 | ~15 | 33 [avatar split clause 509,405,213,397,505]
519. calm(X0) | tall(X0) | rich(X0) | quiet(X0) [resolution 424,84]
520. quiet(X0) | rich(X0) | calm(X0) <- (17) [subsumption resolution 519,478]
521. old(mary) | tall(mary) | quiet(mary) <- (31) [resolution 398,382]
527. tall(mary) | quiet(mary) <- (31, ~33) [subsumption resolution 521,406]
528. tall(mary) <- (31, ~33) [subsumption resolution 527,139]
529. 36 | ~31 | 33 [avatar split clause 528,405,397,505]
531. 37 <=> strong(mary) [avatar definition]
533. strong(mary) <- (37) [avatar component clause 531]
535. 38 <=> funny(mary) [avatar definition]
537. funny(mary) <- (38) [avatar component clause 535]
550. rich(mary) | calm(mary) <- (17) [resolution 520,139]
566. calm(mary) | old(mary) | quiet(mary) <- (36) [resolution 506,389]
567. rich(mary) | quiet(mary) <- (17, 36) [resolution 506,487]
579. 41 <=> rich(mary) [avatar definition]
583. rich(mary) <- (17, 36) [subsumption resolution 567,139]
584. 41 | ~17 | ~36 [avatar split clause 583,505,222,579]
585. calm(mary) | quiet(mary) <- (~33, 36) [subsumption resolution 566,406]
586. calm(mary) <- (~33, 36) [subsumption resolution 585,139]
587. 31 | 33 | ~36 [avatar split clause 586,505,405,397]
588. 31 | 41 | ~17 [avatar split clause 550,222,579,397]
589. funny(mary) | strong(mary) <- (31) [resolution 398,102]
592. funny(mary) | rich(mary) <- (31) [resolution 398,306]
593. old(mary) | brave(mary) <- (17, 31) [resolution 398,351]
608. ~tall(mary) | ~brave(mary) <- (37) [resolution 533,123]
613. ~brave(mary) <- (36, 37) [subsumption resolution 608,506]
616. ~12 | ~36 | ~37 [avatar split clause 613,531,505,199]
619. 37 | 38 | ~31 [avatar split clause 589,397,535,531]
627. ~brave(mary) <- (15, 38) [resolution 537,214]
628. $false <- (12, 15, 38) [subsumption resolution 627,201]
629. ~12 | ~15 | ~38 [avatar contradiction clause 628]
630. 12 | 33 | ~17 | ~31 [avatar split clause 593,397,222,405,199]
632. tall(mary) <- (~12) [resolution 200,125]
639. ~rich(mary) <- (33) [resolution 407,225]
652. 36 | 12 [avatar split clause 632,199,505]
653. ~41 | ~33 [avatar split clause 639,405,579]
656. 41 | 38 | ~31 [avatar split clause 592,397,535,579]
657. $false [avatar sat refutation 219,224,258,518,529,584,587,588,616,619,629,630,652,653,656]
% SZS output end Proof for 5280292067772269106314974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not happy is both quiet and not funny and vice versa.
Everyone who is kind is either strong or not wise.
Everyone who is not calm or humble is old or not tall and vice versa.
Everyone who is curious is not quiet or funny and vice versa.
Everyone who is either wise or quiet is either curious or calm and vice versa.
If alice is either happy or calm then someone is not creative or not kind.
Everyone who is either not funny or not humble is either creative or kind.
Everyone who is both patient and old is not generous or kind.
If someone is not strong or strong then someone is either tall or generous and vice versa.
If fred is either not generous or creative then someone is not quiet and vice versa.
Everyone who is quiet or not strong is both not creative and not rich and vice versa.
If someone is happy or not strong then susan is strong or not generous.
If someone is humble then someone is not old or wise and vice versa.
Everyone who is both quiet and not patient is either brave or not wise and vice versa.
Everyone who is either not curious or wise is either not rich or not wise and vice versa.
If paul is both rich and patient then someone is either brave or old and vice versa.
John is both funny and generous.
Paul is both tall and not kind.
Susan is not creative or curious.
Someone is not old.
John is not quiet or not strong.
Mary is quiet.
Someone is not happy.
Someone is either not funny or not calm. | John is rich. | contradiction | (![X]:((wise(X)&~happy(X))<=>(quiet(X)&~funny(X))))&
(![X]:(kind(X)=>(strong(X)<~>~wise(X))))&
(![X]:((~calm(X)|humble(X))<=>(old(X)|~tall(X))))&
(![X]:(curious(X)<=>(~quiet(X)|funny(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(curious(X)<~>calm(X))))&
(((happy(alice)<~>calm(alice)))=>(?[X]:((~creative(X)|~kind(X)))))&
(![X]:((~funny(X)<~>~humble(X))=>(creative(X)<~>kind(X))))&
(![X]:((patient(X)&old(X))=>(~generous(X)|kind(X))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((tall(X)<~>generous(X)))))&
(((~generous(fred)<~>creative(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)|~strong(X))<=>(~creative(X)&~rich(X))))&
((?[X]:((happy(X)|~strong(X))))=>((strong(susan)|~generous(susan))))&
((?[X]:(humble(X)))<=>(?[X]:((~old(X)|wise(X)))))&
(![X]:((quiet(X)&~patient(X))<=>(brave(X)<~>~wise(X))))&
(![X]:((~curious(X)<~>wise(X))<=>(~rich(X)<~>~wise(X))))&
(((rich(paul)&patient(paul)))<=>(?[X]:((brave(X)<~>old(X)))))&
((funny(john)&generous(john)))&
((tall(paul)&~kind(paul)))&
((~creative(susan)|curious(susan)))&
(?[X]:(~old(X)))&
((~quiet(john)|~strong(john)))&
(quiet(mary))&
(?[X]:(~happy(X)))&
(?[X]:((~funny(X)<~>~calm(X)))) | rich(john) | [
"p3",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2329343692925795010513981
% SZS output start Proof for 2329343692925795010513981
4. ! [X0] : (curious(X0) <=> (funny(X0) | ~quiet(X0))) [input p3]
15. ! [X0] : ((~curious(X0) <~> wise(X0)) <=> (~rich(X0) <~> ~wise(X0))) [input p14]
17. generous(john) & funny(john) [input p16]
25. rich(john) [input hypothesis]
40. ! [X0] : ((curious(X0) | (~funny(X0) & quiet(X0))) & ((funny(X0) | ~quiet(X0)) | ~curious(X0))) [nnf transformation 4]
41. ! [X0] : ((curious(X0) | (~funny(X0) & quiet(X0))) & (funny(X0) | ~quiet(X0) | ~curious(X0))) [flattening 40]
65. ! [X0] : ((((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0))))) [nnf transformation 15]
90. ~funny(X0) | curious(X0) [cnf transformation 41]
133. ~wise(X0) | ~rich(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 65]
137. wise(X0) | ~curious(X0) | ~rich(X0) | wise(X0) [cnf transformation 65]
146. funny(john) [cnf transformation 17]
157. rich(john) [cnf transformation 25]
158. ~wise(X0) | ~rich(X0) | ~curious(X0) [duplicate literal removal 133]
160. wise(X0) | ~curious(X0) | ~rich(X0) [duplicate literal removal 137]
259. ~rich(X0) | ~curious(X0) [subsumption resolution 158,160]
316. curious(john) [resolution 90,146]
325. ~curious(john) [resolution 259,157]
327. $false [subsumption resolution 325,316]
% SZS output end Proof for 2329343692925795010513981
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is rich then lucy is wise and vice versa.
Everyone who is old is not creative.
If someone is brave or rich then paul is either not creative or old.
Everyone who is both not creative and not rich is both not curious and generous and vice versa.
Everyone who is either funny or creative is either not funny or not curious.
Everyone who is either not old or not curious is humble and vice versa.
If john is either not rich or not old then someone is not quiet or wise and vice versa.
Everyone who is either calm or tall is not happy.
If someone is both not curious and strong then lucy is either creative or not calm and vice versa.
If susan is happy then john is both not old and not quiet.
If someone is both funny and not old then paul is curious and vice versa.
Everyone who is not curious or tall is both brave and not calm and vice versa.
Everyone who is humble or not funny is happy or humble.
Everyone who is both happy and calm is not tall or not funny.
Everyone who is both wise and funny is not creative or not funny and vice versa.
Everyone who is not curious is not rich.
Someone is either humble or not patient.
Lucy is kind.
Someone is not wise.
Paul is not old.
Lucy is old or funny.
Someone is not patient or not curious.
Susan is not curious or not patient.
Someone is not tall or creative. | Susan is creative. | entailment | ((rich(paul))<=>(wise(lucy)))&
(![X]:(old(X)=>~creative(X)))&
((?[X]:((brave(X)|rich(X))))=>((~creative(paul)<~>old(paul))))&
(![X]:((~creative(X)&~rich(X))<=>(~curious(X)&generous(X))))&
(![X]:((funny(X)<~>creative(X))=>(~funny(X)<~>~curious(X))))&
(![X]:((~old(X)<~>~curious(X))<=>humble(X)))&
(((~rich(john)<~>~old(john)))<=>(?[X]:((~quiet(X)|wise(X)))))&
(![X]:((calm(X)<~>tall(X))=>~happy(X)))&
((?[X]:((~curious(X)&strong(X))))<=>((creative(lucy)<~>~calm(lucy))))&
((happy(susan))=>((~old(john)&~quiet(john))))&
((?[X]:((funny(X)&~old(X))))<=>(curious(paul)))&
(![X]:((~curious(X)|tall(X))<=>(brave(X)&~calm(X))))&
(![X]:((humble(X)|~funny(X))=>(happy(X)|humble(X))))&
(![X]:((happy(X)&calm(X))=>(~tall(X)|~funny(X))))&
(![X]:((wise(X)&funny(X))<=>(~creative(X)|~funny(X))))&
(![X]:(~curious(X)=>~rich(X)))&
(?[X]:((humble(X)<~>~patient(X))))&
(kind(lucy))&
(?[X]:(~wise(X)))&
(~old(paul))&
((old(lucy)|funny(lucy)))&
(?[X]:((~patient(X)|~curious(X))))&
((~curious(susan)|~patient(susan)))&
(?[X]:((~tall(X)|creative(X)))) | creative(susan) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8033286531787355646578615
% SZS output start Proof for 8033286531787355646578615
1. rich(paul) <=> wise(lucy) [input p0]
2. ! [X0] : (old(X0) => ~creative(X0)) [input p1]
3. ? [X0] : (rich(X0) | brave(X0)) => (~creative(paul) <~> old(paul)) [input p2]
5. ! [X0] : ((funny(X0) <~> creative(X0)) => (~funny(X0) <~> ~curious(X0))) [input p4]
7. (~rich(john) <~> ~old(john)) <=> ? [X0] : (wise(X0) | ~quiet(X0)) [input p6]
11. ? [X0] : (~old(X0) & funny(X0)) <=> curious(paul) [input p10]
12. ! [X0] : ((tall(X0) | ~curious(X0)) <=> (~calm(X0) & brave(X0))) [input p11]
15. ! [X0] : ((funny(X0) & wise(X0)) <=> (~funny(X0) | ~creative(X0))) [input p14]
16. ! [X0] : (~curious(X0) => ~rich(X0)) [input p15]
25. ~creative(susan) [input hypothesis]
27. ! [X0] : (~creative(X0) | ~old(X0)) [ennf transformation 2]
28. (~creative(paul) <~> old(paul)) | ! [X0] : (~rich(X0) & ~brave(X0)) [ennf transformation 3]
29. ! [X0] : ((~funny(X0) <~> ~curious(X0)) | (funny(X0) <=> creative(X0))) [ennf transformation 5]
36. ! [X0] : (~rich(X0) | curious(X0)) [ennf transformation 16]
37. (rich(paul) | ~wise(lucy)) & (wise(lucy) | ~rich(paul)) [nnf transformation 1]
38. ((~old(paul) | creative(paul)) & (old(paul) | ~creative(paul))) | ! [X0] : (~rich(X0) & ~brave(X0)) [nnf transformation 28]
41. ! [X0] : (((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) [nnf transformation 29]
43. (((old(john) | rich(john)) & (~old(john) | ~rich(john))) | ! [X0] : (~wise(X0) & quiet(X0))) & (? [X0] : (wise(X0) | ~quiet(X0)) | ((~rich(john) | old(john)) & (~old(john) | rich(john)))) [nnf transformation 7]
44. (((old(john) | rich(john)) & (~old(john) | ~rich(john))) | ! [X0] : (~wise(X0) & quiet(X0))) & (? [X1] : (wise(X1) | ~quiet(X1)) | ((~rich(john) | old(john)) & (~old(john) | rich(john)))) [rectify 43]
45. ? [X1] : (wise(X1) | ~quiet(X1)) => (wise(sK0) | ~quiet(sK0)) [choice axiom]
46. (((old(john) | rich(john)) & (~old(john) | ~rich(john))) | ! [X0] : (~wise(X0) & quiet(X0))) & ((wise(sK0) | ~quiet(sK0)) | ((~rich(john) | old(john)) & (~old(john) | rich(john)))) [skolemisation 44,45]
52. (? [X0] : (~old(X0) & funny(X0)) | ~curious(paul)) & (curious(paul) | ! [X0] : (old(X0) | ~funny(X0))) [nnf transformation 11]
53. (? [X0] : (~old(X0) & funny(X0)) | ~curious(paul)) & (curious(paul) | ! [X1] : (old(X1) | ~funny(X1))) [rectify 52]
54. ? [X0] : (~old(X0) & funny(X0)) => (~old(sK2) & funny(sK2)) [choice axiom]
55. ((~old(sK2) & funny(sK2)) | ~curious(paul)) & (curious(paul) | ! [X1] : (old(X1) | ~funny(X1))) [skolemisation 53,54]
56. ! [X0] : (((tall(X0) | ~curious(X0)) | (calm(X0) | ~brave(X0))) & ((~calm(X0) & brave(X0)) | (~tall(X0) & curious(X0)))) [nnf transformation 12]
57. ! [X0] : ((tall(X0) | ~curious(X0) | calm(X0) | ~brave(X0)) & ((~calm(X0) & brave(X0)) | (~tall(X0) & curious(X0)))) [flattening 56]
58. ! [X0] : (((funny(X0) & wise(X0)) | (funny(X0) & creative(X0))) & ((~funny(X0) | ~creative(X0)) | (~funny(X0) | ~wise(X0)))) [nnf transformation 15]
59. ! [X0] : (((funny(X0) & wise(X0)) | (funny(X0) & creative(X0))) & (~funny(X0) | ~creative(X0) | ~funny(X0) | ~wise(X0))) [flattening 58]
70. rich(paul) | ~wise(lucy) [cnf transformation 37]
71. ~creative(X0) | ~old(X0) [cnf transformation 27]
72. old(paul) | ~creative(paul) | ~brave(X0) [cnf transformation 38]
73. old(paul) | ~creative(paul) | ~rich(X0) [cnf transformation 38]
80. ~curious(X0) | ~funny(X0) | creative(X0) | ~funny(X0) [cnf transformation 41]
93. old(john) | rich(john) | ~wise(X0) [cnf transformation 46]
104. curious(paul) | old(X1) | ~funny(X1) [cnf transformation 55]
107. curious(X0) | brave(X0) [cnf transformation 57]
116. creative(X0) | wise(X0) [cnf transformation 59]
119. funny(X0) | funny(X0) [cnf transformation 59]
120. ~rich(X0) | curious(X0) [cnf transformation 36]
129. ~creative(susan) [cnf transformation 25]
131. funny(X0) [duplicate literal removal 119]
132. ~funny(X0) | ~curious(X0) | creative(X0) [duplicate literal removal 80]
135. 1 <=> wise(lucy) [avatar definition]
139. 2 <=> rich(paul) [avatar definition]
141. rich(paul) <- (2) [avatar component clause 139]
142. ~1 | 2 [avatar split clause 70,139,135]
146. 3 <=> ! [X0] : ~rich(X0) [avatar definition]
147. ~rich(X0) <- (3) [avatar component clause 146]
155. 5 <=> ! [X0] : ~brave(X0) [avatar definition]
156. ~brave(X0) <- (5) [avatar component clause 155]
158. ~creative(paul) | ~rich(X0) [subsumption resolution 73,71]
160. 6 <=> creative(paul) [avatar definition]
162. ~creative(paul) <- (~6) [avatar component clause 160]
163. 3 | ~6 [avatar split clause 158,160,146]
164. ~creative(paul) | ~brave(X0) [subsumption resolution 72,71]
165. 5 | ~6 [avatar split clause 164,160,155]
167. 7 <=> ! [X0] : ~wise(X0) [avatar definition]
168. ~wise(X0) <- (7) [avatar component clause 167]
170. 8 <=> rich(john) [avatar definition]
172. rich(john) <- (8) [avatar component clause 170]
174. 9 <=> old(john) [avatar definition]
176. old(john) <- (9) [avatar component clause 174]
177. 7 | 8 | 9 [avatar split clause 93,174,170,167]
199. 14 <=> creative(lucy) [avatar definition]
200. ~creative(lucy) <- (~14) [avatar component clause 199]
201. creative(lucy) <- (14) [avatar component clause 199]
230. 20 <=> curious(paul) [avatar definition]
231. curious(paul) <- (20) [avatar component clause 230]
244. 23 <=> ! [X1] : (old(X1) | ~funny(X1)) [avatar definition]
245. old(X1) | ~funny(X1) <- (23) [avatar component clause 244]
246. 23 | 20 [avatar split clause 104,230,244]
290. wise(lucy) <- (~14) [resolution 116,200]
291. wise(susan) [resolution 116,129]
294. 1 | 14 [avatar split clause 290,199,135]
296. curious(paul) <- (2) [resolution 120,141]
314. ~curious(X0) | creative(X0) [resolution 132,131]
315. creative(paul) <- (20) [resolution 314,231]
318. $false <- (~6, 20) [subsumption resolution 315,162]
319. 6 | ~20 [avatar contradiction clause 318]
320. 20 | ~2 [avatar split clause 296,139,230]
321. old(X1) <- (23) [subsumption resolution 245,131]
322. $false <- (3, 8) [resolution 147,172]
325. ~3 | ~8 [avatar contradiction clause 322]
332. $false <- (7) [resolution 168,291]
333. ~7 [avatar contradiction clause 332]
339. ~old(lucy) <- (14) [resolution 201,71]
340. $false <- (14, 23) [subsumption resolution 339,321]
341. ~14 | ~23 [avatar contradiction clause 340]
345. 32 <=> curious(john) [avatar definition]
346. ~curious(john) <- (~32) [avatar component clause 345]
347. curious(john) <- (32) [avatar component clause 345]
386. creative(john) <- (32) [resolution 347,314]
429. ~old(john) <- (32) [resolution 386,71]
432. $false <- (9, 32) [subsumption resolution 429,176]
433. ~9 | ~32 [avatar contradiction clause 432]
434. brave(john) <- (~32) [resolution 346,107]
435. $false <- (5, ~32) [subsumption resolution 434,156]
436. ~5 | 32 [avatar contradiction clause 435]
437. $false [avatar sat refutation 142,163,165,177,246,294,319,320,325,333,341,433,436]
% SZS output end Proof for 8033286531787355646578615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not calm and curious then someone is either kind or patient.
Everyone who is not quiet is either not happy or curious and vice versa.
Everyone who is not kind or not strong is not kind or strong.
Everyone who is either not curious or funny is either not kind or not patient.
Everyone who is not patient or not strong is both not strong and not curious.
Everyone who is not curious is not creative or brave.
If paul is strong or not patient then someone is not patient or funny.
Everyone who is both not quiet and not generous is calm or wise.
If john is both old and strong then someone is both not kind and not tall and vice versa.
If someone is not kind or kind then john is wise or creative and vice versa.
If someone is tall or not patient then someone is old or not strong.
Everyone who is not calm is not curious and vice versa.
If john is both not funny and not curious then mary is either not curious or old and vice versa.
Everyone who is not humble is not kind or rich.
Everyone who is either calm or not calm is happy or tall.
Everyone who is rich or calm is not old and vice versa.
Someone is both not wise and not rich.
Lucy is not rich.
Mary is both not calm and not humble.
Someone is either patient or not patient.
Someone is either rich or curious.
Someone is not kind or kind.
Someone is not rich or not strong.
Mary is both not rich and wise. | Paul is creative. | neutral | (((~calm(john)&curious(john)))=>(?[X]:((kind(X)<~>patient(X)))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>curious(X))))&
(![X]:((~kind(X)|~strong(X))=>(~kind(X)|strong(X))))&
(![X]:((~curious(X)<~>funny(X))=>(~kind(X)<~>~patient(X))))&
(![X]:((~patient(X)|~strong(X))=>(~strong(X)&~curious(X))))&
(![X]:(~curious(X)=>(~creative(X)|brave(X))))&
(((strong(paul)|~patient(paul)))=>(?[X]:((~patient(X)|funny(X)))))&
(![X]:((~quiet(X)&~generous(X))=>(calm(X)|wise(X))))&
(((old(john)&strong(john)))<=>(?[X]:((~kind(X)&~tall(X)))))&
((?[X]:((~kind(X)|kind(X))))<=>((wise(john)|creative(john))))&
((?[X]:((tall(X)|~patient(X))))=>(?[X]:((old(X)|~strong(X)))))&
(![X]:(~calm(X)<=>~curious(X)))&
(((~funny(john)&~curious(john)))<=>((~curious(mary)<~>old(mary))))&
(![X]:(~humble(X)=>(~kind(X)|rich(X))))&
(![X]:((calm(X)<~>~calm(X))=>(happy(X)|tall(X))))&
(![X]:((rich(X)|calm(X))<=>~old(X)))&
(?[X]:((~wise(X)&~rich(X))))&
(~rich(lucy))&
((~calm(mary)&~humble(mary)))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:((rich(X)<~>curious(X))))&
(?[X]:((~kind(X)|kind(X))))&
(?[X]:((~rich(X)|~strong(X))))&
((~rich(mary)&wise(mary))) | creative(paul) | [] | null | 0 |
Everyone who is either not curious or curious is not creative or rich and vice versa.
Everyone who is both not happy and generous is either happy or tall.
If mary is either not quiet or not funny then someone is both not generous and rich and vice versa.
If john is both not happy and not quiet then paul is both tall and not curious and vice versa.
Everyone who is both rich and quiet is either funny or creative.
Everyone who is both not patient and not creative is either old or not creative.
Everyone who is both generous and not old is patient.
Everyone who is rich or quiet is both rich and not funny.
If susan is tall then someone is both humble and calm.
If john is strong then someone is not patient.
If someone is either creative or not wise then fred is not curious.
Everyone who is both quiet and funny is both not creative and not quiet.
Everyone who is either not curious or rich is curious and vice versa.
Everyone who is calm is both not strong and not curious and vice versa.
If lucy is brave then john is both not strong and not curious and vice versa.
Everyone who is creative or not tall is either not curious or not funny and vice versa.
Mary is creative or not quiet.
Lucy is humble or generous.
Fred is both wise and not strong.
Lucy is not humble.
Someone is either not kind or wise.
Someone is not wise or humble.
Someone is both not old and not brave.
Someone is either old or not humble. | Mary is not wise. | neutral | (![X]:((~curious(X)<~>curious(X))<=>(~creative(X)|rich(X))))&
(![X]:((~happy(X)&generous(X))=>(happy(X)<~>tall(X))))&
(((~quiet(mary)<~>~funny(mary)))<=>(?[X]:((~generous(X)&rich(X)))))&
(((~happy(john)&~quiet(john)))<=>((tall(paul)&~curious(paul))))&
(![X]:((rich(X)&quiet(X))=>(funny(X)<~>creative(X))))&
(![X]:((~patient(X)&~creative(X))=>(old(X)<~>~creative(X))))&
(![X]:((generous(X)&~old(X))=>patient(X)))&
(![X]:((rich(X)|quiet(X))=>(rich(X)&~funny(X))))&
((tall(susan))=>(?[X]:((humble(X)&calm(X)))))&
((strong(john))=>(?[X]:(~patient(X))))&
((?[X]:((creative(X)<~>~wise(X))))=>(~curious(fred)))&
(![X]:((quiet(X)&funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((~curious(X)<~>rich(X))<=>curious(X)))&
(![X]:(calm(X)<=>(~strong(X)&~curious(X))))&
((brave(lucy))<=>((~strong(john)&~curious(john))))&
(![X]:((creative(X)|~tall(X))<=>(~curious(X)<~>~funny(X))))&
((creative(mary)|~quiet(mary)))&
((humble(lucy)|generous(lucy)))&
((wise(fred)&~strong(fred)))&
(~humble(lucy))&
(?[X]:((~kind(X)<~>wise(X))))&
(?[X]:((~wise(X)|humble(X))))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((old(X)<~>~humble(X)))) | ~wise(mary) | [] | null | 0 |
If someone is both tall and not patient then john is not strong.
If mary is not humble then someone is both brave and not patient and vice versa.
Everyone who is not calm or not humble is both old and funny.
If someone is humble or wise then someone is both tall and creative.
If susan is patient or not curious then someone is not happy or funny and vice versa.
Everyone who is rich or not calm is humble.
Everyone who is happy is humble.
Everyone who is both not quiet and not wise is creative.
If someone is not brave then someone is either tall or old.
Everyone who is either kind or curious is both generous and curious.
Everyone who is not creative or happy is either funny or not patient and vice versa.
If someone is both not happy and not tall then someone is either not generous or kind and vice versa.
If someone is both not creative and wise then john is not old.
If susan is either brave or not calm then john is both not tall and tall.
Everyone who is not tall or wise is both funny and not brave.
Everyone who is not creative or not rich is either quiet or happy and vice versa.
Alice is humble.
John is not old.
John is strong or tall.
Someone is not strong or not rich.
Someone is either patient or funny.
Someone is both not curious and calm.
Mary is either not curious or not calm. | Alice is not old. | neutral | ((?[X]:((tall(X)&~patient(X))))=>(~strong(john)))&
((~humble(mary))<=>(?[X]:((brave(X)&~patient(X)))))&
(![X]:((~calm(X)|~humble(X))=>(old(X)&funny(X))))&
((?[X]:((humble(X)|wise(X))))=>(?[X]:((tall(X)&creative(X)))))&
(((patient(susan)|~curious(susan)))<=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:((rich(X)|~calm(X))=>humble(X)))&
(![X]:(happy(X)=>humble(X)))&
(![X]:((~quiet(X)&~wise(X))=>creative(X)))&
((?[X]:(~brave(X)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((kind(X)<~>curious(X))=>(generous(X)&curious(X))))&
(![X]:((~creative(X)|happy(X))<=>(funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~tall(X))))<=>(?[X]:((~generous(X)<~>kind(X)))))&
((?[X]:((~creative(X)&wise(X))))=>(~old(john)))&
(((brave(susan)<~>~calm(susan)))=>((~tall(john)&tall(john))))&
(![X]:((~tall(X)|wise(X))=>(funny(X)&~brave(X))))&
(![X]:((~creative(X)|~rich(X))<=>(quiet(X)<~>happy(X))))&
(humble(alice))&
(~old(john))&
((strong(john)|tall(john)))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((patient(X)<~>funny(X))))&
(?[X]:((~curious(X)&calm(X))))&
((~curious(mary)<~>~calm(mary))) | ~old(alice) | [] | null | 0 |
Everyone who is funny or not kind is both not wise and brave.
Everyone who is not curious or not quiet is either not patient or humble.
If paul is not wise or generous then fred is either not strong or not tall.
Everyone who is both brave and generous is either rich or kind and vice versa.
If fred is both not calm and not rich then someone is not strong or quiet and vice versa.
Everyone who is not calm or not creative is not tall.
Everyone who is wise is either not strong or calm.
Everyone who is not brave or creative is either humble or not creative.
If someone is not funny then john is humble or tall and vice versa.
Everyone who is both rich and not creative is funny or not tall.
If someone is quiet then lucy is tall.
Everyone who is not calm is not quiet or happy.
Everyone who is tall is curious and vice versa.
Everyone who is either tall or humble is curious and vice versa.
If paul is not happy or wise then paul is either humble or not strong and vice versa.
If lucy is either not kind or not funny then fred is both wise and not rich and vice versa.
Alice is not funny or calm.
Someone is brave.
Someone is both brave and not kind.
Susan is not generous or not funny.
Susan is rich or not generous.
Someone is not humble or not tall. | Alice is humble. | contradiction | (![X]:((funny(X)|~kind(X))=>(~wise(X)&brave(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~patient(X)<~>humble(X))))&
(((~wise(paul)|generous(paul)))=>((~strong(fred)<~>~tall(fred))))&
(![X]:((brave(X)&generous(X))<=>(rich(X)<~>kind(X))))&
(((~calm(fred)&~rich(fred)))<=>(?[X]:((~strong(X)|quiet(X)))))&
(![X]:((~calm(X)|~creative(X))=>~tall(X)))&
(![X]:(wise(X)=>(~strong(X)<~>calm(X))))&
(![X]:((~brave(X)|creative(X))=>(humble(X)<~>~creative(X))))&
((?[X]:(~funny(X)))<=>((humble(john)|tall(john))))&
(![X]:((rich(X)&~creative(X))=>(funny(X)|~tall(X))))&
((?[X]:(quiet(X)))=>(tall(lucy)))&
(![X]:(~calm(X)=>(~quiet(X)|happy(X))))&
(![X]:(tall(X)<=>curious(X)))&
(![X]:((tall(X)<~>humble(X))<=>curious(X)))&
(((~happy(paul)|wise(paul)))<=>((humble(paul)<~>~strong(paul))))&
(((~kind(lucy)<~>~funny(lucy)))<=>((wise(fred)&~rich(fred))))&
((~funny(alice)|calm(alice)))&
(?[X]:(brave(X)))&
(?[X]:((brave(X)&~kind(X))))&
((~generous(susan)|~funny(susan)))&
((rich(susan)|~generous(susan)))&
(?[X]:((~humble(X)|~tall(X)))) | humble(alice) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8431065962888121039290721
% SZS output start Proof for 8431065962888121039290721
13. ! [X0] : (tall(X0) <=> curious(X0)) [input p12]
14. ! [X0] : ((tall(X0) <~> humble(X0)) <=> curious(X0)) [input p13]
23. humble(alice) [input hypothesis]
51. ! [X0] : ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0))) [nnf transformation 13]
52. ! [X0] : ((((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ~curious(X0)) & (curious(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))))) [nnf transformation 14]
100. ~tall(X0) | curious(X0) [cnf transformation 51]
101. ~curious(X0) | tall(X0) [cnf transformation 51]
103. curious(X0) | tall(X0) | ~humble(X0) [cnf transformation 52]
105. ~humble(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 52]
125. humble(alice) [cnf transformation 23]
199. ~tall(X0) | ~humble(X0) [subsumption resolution 105,100]
200. ~humble(X0) | curious(X0) [subsumption resolution 103,199]
270. curious(alice) [resolution 200,125]
272. tall(alice) [resolution 270,101]
288. ~humble(alice) [resolution 272,199]
292. $false [subsumption resolution 288,125]
% SZS output end Proof for 8431065962888121039290721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and generous is both humble and tall and vice versa. Everyone who is rich or not old is both not curious and not wise and vice versa. Everyone who is both not kind and not strong is either kind or not funny. Everyone who is not happy is brave. Everyone who is happy is not humble and vice versa. Everyone who is both not wise and generous is not calm. Everyone who is brave or rich is not patient or happy and vice versa. If someone is kind then paul is both not funny and not strong and vice versa. If lucy is calm or kind then someone is old or creative. Everyone who is strong or kind is not kind or not generous and vice versa. Everyone who is not wise is either not curious or not creative. Everyone who is both not curious and wise is not wise or not funny and vice versa. If someone is quiet or not kind then lucy is not generous or not wise and vice versa. Everyone who is either not strong or not patient is either not wise or not humble. Everyone who is either humble or not wise is strong. Everyone who is both happy and not generous is either generous or not rich. Someone is both happy and curious. John is happy. Someone is not humble. Mary is creative or funny. Mary is brave or generous. Paul is curious or not tall. Mary is patient or not generous. Someone is old. | Mary is strong. | neutral | (![X]:((tall(X)&generous(X))<=>(humble(X)&tall(X))))&
(![X]:((rich(X)|~old(X))<=>(~curious(X)&~wise(X))))&
(![X]:((~kind(X)&~strong(X))=>(kind(X)<~>~funny(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:(happy(X)<=>~humble(X)))&
(![X]:((~wise(X)&generous(X))=>~calm(X)))&
(![X]:((brave(X)|rich(X))<=>(~patient(X)|happy(X))))&
((?[X]:(kind(X)))<=>((~funny(paul)&~strong(paul))))&
(((calm(lucy)|kind(lucy)))=>(?[X]:((old(X)|creative(X)))))&
(![X]:((strong(X)|kind(X))<=>(~kind(X)|~generous(X))))&
(![X]:(~wise(X)=>(~curious(X)<~>~creative(X))))&
(![X]:((~curious(X)&wise(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~generous(lucy)|~wise(lucy))))&
(![X]:((~strong(X)<~>~patient(X))=>(~wise(X)<~>~humble(X))))&
(![X]:((humble(X)<~>~wise(X))=>strong(X)))&
(![X]:((happy(X)&~generous(X))=>(generous(X)<~>~rich(X))))&
(?[X]:((happy(X)&curious(X))))&
(happy(john))&
(?[X]:(~humble(X)))&
((creative(mary)|funny(mary)))&
((brave(mary)|generous(mary)))&
((curious(paul)|~tall(paul)))&
((patient(mary)|~generous(mary)))&
(?[X]:(old(X))) | strong(mary) | [] | null | 0 |
If susan is old then someone is either rich or not old.
Everyone who is either not old or kind is not generous or calm and vice versa.
Everyone who is both old and not humble is both not tall and patient and vice versa.
If someone is both not wise and not happy then someone is either not strong or tall.
Everyone who is calm or humble is both brave and happy.
If lucy is not humble or strong then susan is wise.
If someone is both not old and old then someone is both brave and humble.
Everyone who is either not tall or not calm is both not kind and not calm and vice versa.
Everyone who is either not calm or quiet is both happy and not funny.
Everyone who is both rich and kind is either not patient or happy.
Everyone who is either brave or not quiet is both brave and patient.
If alice is creative then paul is either not calm or strong.
Everyone who is not patient is both rich and not happy and vice versa.
If someone is both kind and not generous then alice is both wise and funny.
If someone is both not old and quiet then someone is both funny and happy.
Everyone who is brave is either not strong or not old and vice versa.
Lucy is both not wise and not quiet.
Susan is humble.
Fred is strong.
Susan is either not calm or calm.
Someone is not humble or not rich.
John is both not brave and not strong.
Someone is not patient.
Fred is either funny or not quiet. | Fred is strong. | entailment | ((old(susan))=>(?[X]:((rich(X)<~>~old(X)))))&
(![X]:((~old(X)<~>kind(X))<=>(~generous(X)|calm(X))))&
(![X]:((old(X)&~humble(X))<=>(~tall(X)&patient(X))))&
((?[X]:((~wise(X)&~happy(X))))=>(?[X]:((~strong(X)<~>tall(X)))))&
(![X]:((calm(X)|humble(X))=>(brave(X)&happy(X))))&
(((~humble(lucy)|strong(lucy)))=>(wise(susan)))&
((?[X]:((~old(X)&old(X))))=>(?[X]:((brave(X)&humble(X)))))&
(![X]:((~tall(X)<~>~calm(X))<=>(~kind(X)&~calm(X))))&
(![X]:((~calm(X)<~>quiet(X))=>(happy(X)&~funny(X))))&
(![X]:((rich(X)&kind(X))=>(~patient(X)<~>happy(X))))&
(![X]:((brave(X)<~>~quiet(X))=>(brave(X)&patient(X))))&
((creative(alice))=>((~calm(paul)<~>strong(paul))))&
(![X]:(~patient(X)<=>(rich(X)&~happy(X))))&
((?[X]:((kind(X)&~generous(X))))=>((wise(alice)&funny(alice))))&
((?[X]:((~old(X)&quiet(X))))=>(?[X]:((funny(X)&happy(X)))))&
(![X]:(brave(X)<=>(~strong(X)<~>~old(X))))&
((~wise(lucy)&~quiet(lucy)))&
(humble(susan))&
(strong(fred))&
((~calm(susan)<~>calm(susan)))&
(?[X]:((~humble(X)|~rich(X))))&
((~brave(john)&~strong(john)))&
(?[X]:(~patient(X)))&
((funny(fred)<~>~quiet(fred))) | strong(fred) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4870558147101296715384476
% SZS output start Proof for 4870558147101296715384476
19. strong(fred) [input p18]
25. ~strong(fred) [input hypothesis]
124. strong(fred) [cnf transformation 19]
133. ~strong(fred) [cnf transformation 25]
224. $false [subsumption resolution 133,124]
% SZS output end Proof for 4870558147101296715384476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and calm then someone is not quiet or tall and vice versa. If someone is rich or wise then john is not strong. If someone is both quiet and not humble then someone is not old and vice versa. If john is wise then someone is patient or not old. If mary is not creative then paul is both not patient and not strong and vice versa. Everyone who is both not strong and not humble is either calm or strong. If paul is both generous and not strong then paul is either not calm or brave. Everyone who is both funny and creative is either old or wise and vice versa. If john is not rich or not patient then lucy is both curious and not quiet and vice versa. If someone is generous or not patient then paul is either not curious or not creative. Everyone who is brave or not patient is not brave or brave. Everyone who is both brave and humble is not calm and vice versa. If someone is not humble or humble then mary is either not rich or not happy. Everyone who is both not patient and funny is both calm and not kind and vice versa. If alice is both not kind and not wise then mary is either not quiet or humble and vice versa. Everyone who is not humble is not generous. Someone is both not strong and not generous. Someone is both wise and not strong. Someone is humble. Alice is happy. Someone is both not calm and not quiet. Fred is either not happy or strong. Alice is both not tall and not wise. Lucy is both strong and not quiet. | John is not strong. | entailment | ((?[X]:((wise(X)&calm(X))))<=>(?[X]:((~quiet(X)|tall(X)))))&
((?[X]:((rich(X)|wise(X))))=>(~strong(john)))&
((?[X]:((quiet(X)&~humble(X))))<=>(?[X]:(~old(X))))&
((wise(john))=>(?[X]:((patient(X)|~old(X)))))&
((~creative(mary))<=>((~patient(paul)&~strong(paul))))&
(![X]:((~strong(X)&~humble(X))=>(calm(X)<~>strong(X))))&
(((generous(paul)&~strong(paul)))=>((~calm(paul)<~>brave(paul))))&
(![X]:((funny(X)&creative(X))<=>(old(X)<~>wise(X))))&
(((~rich(john)|~patient(john)))<=>((curious(lucy)&~quiet(lucy))))&
((?[X]:((generous(X)|~patient(X))))=>((~curious(paul)<~>~creative(paul))))&
(![X]:((brave(X)|~patient(X))=>(~brave(X)|brave(X))))&
(![X]:((brave(X)&humble(X))<=>~calm(X)))&
((?[X]:((~humble(X)|humble(X))))=>((~rich(mary)<~>~happy(mary))))&
(![X]:((~patient(X)&funny(X))<=>(calm(X)&~kind(X))))&
(((~kind(alice)&~wise(alice)))<=>((~quiet(mary)<~>humble(mary))))&
(![X]:(~humble(X)=>~generous(X)))&
(?[X]:((~strong(X)&~generous(X))))&
(?[X]:((wise(X)&~strong(X))))&
(?[X]:(humble(X)))&
(happy(alice))&
(?[X]:((~calm(X)&~quiet(X))))&
((~happy(fred)<~>strong(fred)))&
((~tall(alice)&~wise(alice)))&
((strong(lucy)&~quiet(lucy))) | ~strong(john) | [
"p0",
"p1",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3448421340705827655445789
% SZS output start Proof for 3448421340705827655445789
1. ? [X0] : (calm(X0) & wise(X0)) <=> ? [X0] : (tall(X0) | ~quiet(X0)) [input p0]
2. ? [X0] : (wise(X0) | rich(X0)) => ~strong(john) [input p1]
21. ? [X0] : (~quiet(X0) & ~calm(X0)) [input p20]
25. strong(john) [input hypothesis]
26. ? [X0] : (calm(X0) & wise(X0)) <=> ? [X1] : (tall(X1) | ~quiet(X1)) [rectify 1]
32. ~strong(john) | ! [X0] : (~wise(X0) & ~rich(X0)) [ennf transformation 2]
40. (? [X0] : (calm(X0) & wise(X0)) | ! [X1] : (~tall(X1) & quiet(X1))) & (? [X1] : (tall(X1) | ~quiet(X1)) | ! [X0] : (~calm(X0) | ~wise(X0))) [nnf transformation 26]
41. (? [X0] : (calm(X0) & wise(X0)) | ! [X1] : (~tall(X1) & quiet(X1))) & (? [X2] : (tall(X2) | ~quiet(X2)) | ! [X3] : (~calm(X3) | ~wise(X3))) [rectify 40]
42. ? [X0] : (calm(X0) & wise(X0)) => (calm(sK0) & wise(sK0)) [choice axiom]
43. ? [X2] : (tall(X2) | ~quiet(X2)) => (tall(sK1) | ~quiet(sK1)) [choice axiom]
44. ((calm(sK0) & wise(sK0)) | ! [X1] : (~tall(X1) & quiet(X1))) & ((tall(sK1) | ~quiet(sK1)) | ! [X3] : (~calm(X3) | ~wise(X3))) [skolemisation 41,43,42]
73. ? [X0] : (~quiet(X0) & ~calm(X0)) => (~quiet(sK8) & ~calm(sK8)) [choice axiom]
74. ~quiet(sK8) & ~calm(sK8) [skolemisation 21,73]
77. wise(sK0) | quiet(X1) [cnf transformation 44]
82. ~strong(john) | ~wise(X0) [cnf transformation 32]
130. ~quiet(sK8) [cnf transformation 74]
137. strong(john) [cnf transformation 25]
149. 3 <=> ! [X1] : quiet(X1) [avatar definition]
150. quiet(X1) <- (3) [avatar component clause 149]
153. 4 <=> wise(sK0) [avatar definition]
155. wise(sK0) <- (4) [avatar component clause 153]
157. 3 | 4 [avatar split clause 77,153,149]
171. 8 <=> ! [X0] : ~wise(X0) [avatar definition]
172. ~wise(X0) <- (8) [avatar component clause 171]
174. 9 <=> strong(john) [avatar definition]
177. 8 | ~9 [avatar split clause 82,174,171]
317. 9 [avatar split clause 137,174]
322. $false <- (4, 8) [subsumption resolution 155,172]
323. ~4 | ~8 [avatar contradiction clause 322]
324. $false <- (3) [resolution 150,130]
325. ~3 [avatar contradiction clause 324]
326. $false [avatar sat refutation 157,177,317,323,325]
% SZS output end Proof for 3448421340705827655445789
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is either not brave or humble and vice versa.
If someone is either quiet or kind then alice is both generous and not quiet.
Everyone who is not old or tall is either not old or not kind.
If someone is either not kind or brave then someone is both creative and generous and vice versa.
If someone is quiet then someone is both brave and not brave.
If someone is humble then alice is either not humble or not wise.
If john is not quiet or not strong then fred is not strong or not brave and vice versa.
Everyone who is either not calm or creative is not strong and vice versa.
Everyone who is either rich or strong is both not old and not rich.
Everyone who is either not old or not funny is both calm and quiet.
Everyone who is either not generous or funny is not curious.
Everyone who is both not tall and not curious is both not generous and not strong and vice versa.
Everyone who is either not generous or calm is kind or creative and vice versa.
Everyone who is either funny or kind is both old and funny.
If alice is not happy then mary is both not creative and not funny.
Lucy is not patient.
Susan is not quiet or strong.
Someone is not tall.
Susan is either not tall or curious.
Someone is both wise and rich.
Someone is not generous or strong.
Someone is not wise. | Fred is not strong. | neutral | (![X]:(funny(X)<=>(~brave(X)<~>humble(X))))&
((?[X]:((quiet(X)<~>kind(X))))=>((generous(alice)&~quiet(alice))))&
(![X]:((~old(X)|tall(X))=>(~old(X)<~>~kind(X))))&
((?[X]:((~kind(X)<~>brave(X))))<=>(?[X]:((creative(X)&generous(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((brave(X)&~brave(X)))))&
((?[X]:(humble(X)))=>((~humble(alice)<~>~wise(alice))))&
(((~quiet(john)|~strong(john)))<=>((~strong(fred)|~brave(fred))))&
(![X]:((~calm(X)<~>creative(X))<=>~strong(X)))&
(![X]:((rich(X)<~>strong(X))=>(~old(X)&~rich(X))))&
(![X]:((~old(X)<~>~funny(X))=>(calm(X)&quiet(X))))&
(![X]:((~generous(X)<~>funny(X))=>~curious(X)))&
(![X]:((~tall(X)&~curious(X))<=>(~generous(X)&~strong(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(kind(X)|creative(X))))&
(![X]:((funny(X)<~>kind(X))=>(old(X)&funny(X))))&
((~happy(alice))=>((~creative(mary)&~funny(mary))))&
(~patient(lucy))&
((~quiet(susan)|strong(susan)))&
(?[X]:(~tall(X)))&
((~tall(susan)<~>curious(susan)))&
(?[X]:((wise(X)&rich(X))))&
(?[X]:((~generous(X)|strong(X))))&
(?[X]:(~wise(X))) | ~strong(fred) | [] | null | 0 |
If mary is quiet then someone is not happy. Everyone who is kind is tall or not tall and vice versa. Everyone who is curious is both humble and not kind and vice versa. If someone is quiet or tall then someone is not creative and vice versa. Everyone who is either patient or not patient is not brave and vice versa. Everyone who is brave or strong is not calm. If someone is not wise or patient then someone is not rich. Everyone who is either old or brave is not funny. Everyone who is not rich or curious is wise or kind and vice versa. Everyone who is not happy or rich is not patient or rich and vice versa. Everyone who is happy or not strong is either not curious or not patient. If someone is both happy and brave then someone is not brave. Everyone who is wise is not creative and vice versa. If fred is both humble and brave then alice is either not creative or not curious and vice versa. Everyone who is either happy or curious is either old or strong. If someone is either strong or not quiet then someone is both humble and happy and vice versa. Someone is strong. Lucy is old. Someone is generous or brave. Someone is not wise or not calm. Someone is not humble or curious. Alice is quiet or creative. | Mary is patient. | neutral | ((quiet(mary))=>(?[X]:(~happy(X))))&
(![X]:(kind(X)<=>(tall(X)|~tall(X))))&
(![X]:(curious(X)<=>(humble(X)&~kind(X))))&
((?[X]:((quiet(X)|tall(X))))<=>(?[X]:(~creative(X))))&
(![X]:((patient(X)<~>~patient(X))<=>~brave(X)))&
(![X]:((brave(X)|strong(X))=>~calm(X)))&
((?[X]:((~wise(X)|patient(X))))=>(?[X]:(~rich(X))))&
(![X]:((old(X)<~>brave(X))=>~funny(X)))&
(![X]:((~rich(X)|curious(X))<=>(wise(X)|kind(X))))&
(![X]:((~happy(X)|rich(X))<=>(~patient(X)|rich(X))))&
(![X]:((happy(X)|~strong(X))=>(~curious(X)<~>~patient(X))))&
((?[X]:((happy(X)&brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(wise(X)<=>~creative(X)))&
(((humble(fred)&brave(fred)))<=>((~creative(alice)<~>~curious(alice))))&
(![X]:((happy(X)<~>curious(X))=>(old(X)<~>strong(X))))&
((?[X]:((strong(X)<~>~quiet(X))))<=>(?[X]:((humble(X)&happy(X)))))&
(?[X]:(strong(X)))&
(old(lucy))&
(?[X]:((generous(X)|brave(X))))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((~humble(X)|curious(X))))&
((quiet(alice)|creative(alice))) | patient(mary) | [] | null | 0 |
If someone is either old or funny then someone is either not tall or not wise and vice versa.
If someone is both not wise and strong then paul is generous or curious.
Everyone who is both not rich and funny is either not happy or creative and vice versa.
If susan is not kind then someone is happy or calm and vice versa.
Everyone who is either not creative or creative is either quiet or calm and vice versa.
Everyone who is not patient is not happy or rich and vice versa.
Everyone who is not funny is either generous or not funny.
Everyone who is either kind or not creative is not generous and vice versa.
Everyone who is both old and not funny is both happy and patient and vice versa.
If someone is both not funny and patient then john is not old or not rich.
If paul is both brave and kind then someone is both wise and not wise and vice versa.
If john is both wise and quiet then someone is both not patient and rich.
If someone is either strong or generous then mary is both not happy and funny and vice versa.
Everyone who is not strong is both happy and not calm and vice versa.
Everyone who is not strong or not humble is both not strong and humble.
Everyone who is kind is not funny.
Lucy is rich.
Alice is not old or old.
John is either not tall or not patient.
Someone is both happy and not rich.
Lucy is old or wise.
John is not tall. | John is not happy. | contradiction | ((?[X]:((old(X)<~>funny(X))))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((~wise(X)&strong(X))))=>((generous(paul)|curious(paul))))&
(![X]:((~rich(X)&funny(X))<=>(~happy(X)<~>creative(X))))&
((~kind(susan))<=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((~creative(X)<~>creative(X))<=>(quiet(X)<~>calm(X))))&
(![X]:(~patient(X)<=>(~happy(X)|rich(X))))&
(![X]:(~funny(X)=>(generous(X)<~>~funny(X))))&
(![X]:((kind(X)<~>~creative(X))<=>~generous(X)))&
(![X]:((old(X)&~funny(X))<=>(happy(X)&patient(X))))&
((?[X]:((~funny(X)&patient(X))))=>((~old(john)|~rich(john))))&
(((brave(paul)&kind(paul)))<=>(?[X]:((wise(X)&~wise(X)))))&
(((wise(john)&quiet(john)))=>(?[X]:((~patient(X)&rich(X)))))&
((?[X]:((strong(X)<~>generous(X))))<=>((~happy(mary)&funny(mary))))&
(![X]:(~strong(X)<=>(happy(X)&~calm(X))))&
(![X]:((~strong(X)|~humble(X))=>(~strong(X)&humble(X))))&
(![X]:(kind(X)=>~funny(X)))&
(rich(lucy))&
((~old(alice)|old(alice)))&
((~tall(john)<~>~patient(john)))&
(?[X]:((happy(X)&~rich(X))))&
((old(lucy)|wise(lucy)))&
(~tall(john)) | ~happy(john) | [
"p5",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5266356355241536356767942
% SZS output start Proof for 5266356355241536356767942
6. ! [X0] : (~patient(X0) <=> (rich(X0) | ~happy(X0))) [input p5]
19. ~tall(john) <~> ~patient(john) [input p18]
22. ~tall(john) [input p21]
23. ~happy(john) [input hypothesis]
46. ! [X0] : ((~patient(X0) | (~rich(X0) & happy(X0))) & ((rich(X0) | ~happy(X0)) | patient(X0))) [nnf transformation 6]
47. ! [X0] : ((~patient(X0) | (~rich(X0) & happy(X0))) & (rich(X0) | ~happy(X0) | patient(X0))) [flattening 46]
66. (patient(john) | tall(john)) & (~patient(john) | ~tall(john)) [nnf transformation 19]
95. ~patient(X0) | happy(X0) [cnf transformation 47]
128. patient(john) | tall(john) [cnf transformation 66]
132. ~tall(john) [cnf transformation 22]
133. ~happy(john) [cnf transformation 23]
274. 30 <=> tall(john) [avatar definition]
278. 31 <=> patient(john) [avatar definition]
280. patient(john) <- (31) [avatar component clause 278]
281. 30 | 31 [avatar split clause 128,278,274]
292. ~30 [avatar split clause 132,274]
295. happy(john) <- (31) [resolution 95,280]
296. $false <- (31) [subsumption resolution 295,133]
297. ~31 [avatar contradiction clause 296]
298. $false [avatar sat refutation 281,292,297]
% SZS output end Proof for 5266356355241536356767942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious is curious or generous and vice versa.
If someone is both not patient and not creative then someone is both strong and not wise and vice versa.
Everyone who is either rich or humble is either kind or not funny.
If someone is either not kind or tall then someone is not generous.
If mary is wise or brave then someone is either strong or tall.
Everyone who is either tall or not brave is either tall or not curious.
Everyone who is not creative or curious is both not generous and patient.
If someone is both patient and humble then someone is either not kind or kind and vice versa.
If someone is either not funny or rich then someone is curious or not tall and vice versa.
Everyone who is curious or calm is not creative and vice versa.
Everyone who is both not curious and humble is either not quiet or happy.
If someone is both humble and not kind then lucy is rich or wise.
Everyone who is both not funny and curious is rich or tall.
Everyone who is either not happy or brave is either happy or kind and vice versa.
Everyone who is not wise or not brave is not patient and vice versa.
If mary is not old or calm then alice is happy and vice versa.
Lucy is not curious.
Someone is either kind or rich.
Paul is either rich or patient.
Someone is not brave.
Someone is old or tall.
Someone is brave or not strong.
Someone is strong. | Alice is not calm. | entailment | (![X]:((calm(X)&~curious(X))<=>(curious(X)|generous(X))))&
((?[X]:((~patient(X)&~creative(X))))<=>(?[X]:((strong(X)&~wise(X)))))&
(![X]:((rich(X)<~>humble(X))=>(kind(X)<~>~funny(X))))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:(~generous(X))))&
(((wise(mary)|brave(mary)))=>(?[X]:((strong(X)<~>tall(X)))))&
(![X]:((tall(X)<~>~brave(X))=>(tall(X)<~>~curious(X))))&
(![X]:((~creative(X)|curious(X))=>(~generous(X)&patient(X))))&
((?[X]:((patient(X)&humble(X))))<=>(?[X]:((~kind(X)<~>kind(X)))))&
((?[X]:((~funny(X)<~>rich(X))))<=>(?[X]:((curious(X)|~tall(X)))))&
(![X]:((curious(X)|calm(X))<=>~creative(X)))&
(![X]:((~curious(X)&humble(X))=>(~quiet(X)<~>happy(X))))&
((?[X]:((humble(X)&~kind(X))))=>((rich(lucy)|wise(lucy))))&
(![X]:((~funny(X)&curious(X))=>(rich(X)|tall(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(happy(X)<~>kind(X))))&
(![X]:((~wise(X)|~brave(X))<=>~patient(X)))&
(((~old(mary)|calm(mary)))<=>(happy(alice)))&
(~curious(lucy))&
(?[X]:((kind(X)<~>rich(X))))&
((rich(paul)<~>patient(paul)))&
(?[X]:(~brave(X)))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((brave(X)|~strong(X))))&
(?[X]:(strong(X))) | ~calm(alice) | [
"p0",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7189684597859834878683942
% SZS output start Proof for 7189684597859834878683942
1. ! [X0] : ((~curious(X0) & calm(X0)) <=> (generous(X0) | curious(X0))) [input p0]
7. ! [X0] : ((curious(X0) | ~creative(X0)) => (patient(X0) & ~generous(X0))) [input p6]
10. ! [X0] : ((calm(X0) | curious(X0)) <=> ~creative(X0)) [input p9]
24. calm(alice) [input hypothesis]
33. ! [X0] : ((patient(X0) & ~generous(X0)) | (~curious(X0) & creative(X0))) [ennf transformation 7]
40. ! [X0] : (((~curious(X0) & calm(X0)) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | (curious(X0) | ~calm(X0)))) [nnf transformation 1]
41. ! [X0] : (((~curious(X0) & calm(X0)) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | curious(X0) | ~calm(X0))) [flattening 40]
66. ! [X0] : (((calm(X0) | curious(X0)) | creative(X0)) & (~creative(X0) | (~calm(X0) & ~curious(X0)))) [nnf transformation 10]
67. ! [X0] : ((calm(X0) | curious(X0) | creative(X0)) & (~creative(X0) | (~calm(X0) & ~curious(X0)))) [flattening 66]
86. generous(X0) | curious(X0) | curious(X0) | ~calm(X0) [cnf transformation 41]
89. ~curious(X0) | ~curious(X0) [cnf transformation 41]
109. ~generous(X0) | creative(X0) [cnf transformation 33]
126. ~creative(X0) | ~calm(X0) [cnf transformation 67]
155. calm(alice) [cnf transformation 24]
166. generous(X0) | curious(X0) | ~calm(X0) [duplicate literal removal 86]
167. ~curious(X0) [duplicate literal removal 89]
168. ~calm(X0) | generous(X0) [subsumption resolution 166,167]
350. generous(alice) [resolution 168,155]
351. creative(alice) [resolution 350,109]
388. ~calm(alice) [resolution 351,126]
389. $false [subsumption resolution 388,155]
% SZS output end Proof for 7189684597859834878683942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or not curious then someone is either strong or not old and vice versa. If someone is not humble or not creative then lucy is both not creative and rich. Everyone who is funny or kind is both not quiet and old. If someone is happy or not calm then someone is not quiet. Everyone who is creative is not wise or not happy. If someone is both not quiet and kind then lucy is either happy or not patient. Everyone who is funny or not humble is humble and vice versa. Everyone who is either quiet or calm is brave or not patient. Everyone who is either not strong or funny is kind and vice versa. Everyone who is both happy and creative is both not rich and brave. Everyone who is not creative or humble is not old or not creative and vice versa. If someone is quiet then someone is both funny and not quiet. If fred is not generous then someone is not strong or not curious. Everyone who is both not happy and not creative is either not quiet or creative. If someone is not old then fred is not quiet or wise. Everyone who is wise is funny or humble. Someone is not strong or not humble. Someone is both generous and not wise. Someone is not wise. Lucy is not quiet. Someone is funny. | Fred is rich. | neutral | ((?[X]:((~calm(X)<~>~curious(X))))<=>(?[X]:((strong(X)<~>~old(X)))))&
((?[X]:((~humble(X)|~creative(X))))=>((~creative(lucy)&rich(lucy))))&
(![X]:((funny(X)|kind(X))=>(~quiet(X)&old(X))))&
((?[X]:((happy(X)|~calm(X))))=>(?[X]:(~quiet(X))))&
(![X]:(creative(X)=>(~wise(X)|~happy(X))))&
((?[X]:((~quiet(X)&kind(X))))=>((happy(lucy)<~>~patient(lucy))))&
(![X]:((funny(X)|~humble(X))<=>humble(X)))&
(![X]:((quiet(X)<~>calm(X))=>(brave(X)|~patient(X))))&
(![X]:((~strong(X)<~>funny(X))<=>kind(X)))&
(![X]:((happy(X)&creative(X))=>(~rich(X)&brave(X))))&
(![X]:((~creative(X)|humble(X))<=>(~old(X)|~creative(X))))&
((?[X]:(quiet(X)))=>(?[X]:((funny(X)&~quiet(X)))))&
((~generous(fred))=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:((~happy(X)&~creative(X))=>(~quiet(X)<~>creative(X))))&
((?[X]:(~old(X)))=>((~quiet(fred)|wise(fred))))&
(![X]:(wise(X)=>(funny(X)|humble(X))))&
(?[X]:((~strong(X)|~humble(X))))&
(?[X]:((generous(X)&~wise(X))))&
(?[X]:(~wise(X)))&
(~quiet(lucy))&
(?[X]:(funny(X))) | rich(fred) | [] | null | 0 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.