premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is not calm is either not creative or kind.
Everyone who is calm is both funny and humble and vice versa.
Everyone who is both brave and not wise is either calm or not tall.
If someone is not strong then susan is both rich and old and vice versa.
If fred is either tall or not calm then someone is either not calm or not funny and vice versa.
If susan is either not happy or quiet then someone is happy or kind and vice versa.
Everyone who is not curious is both not tall and not curious.
If someone is either happy or patient then someone is both not humble and not quiet and vice versa.
If someone is not kind then someone is either brave or curious and vice versa.
If lucy is not generous or patient then someone is either not strong or quiet and vice versa.
Everyone who is both humble and not curious is either not curious or not brave.
If someone is not quiet or wise then someone is both brave and not curious and vice versa.
Everyone who is old or wise is both calm and not quiet and vice versa.
Everyone who is both curious and not quiet is either quiet or not calm and vice versa.
If alice is both curious and not brave then alice is either not humble or humble and vice versa.
If mary is either wise or not calm then someone is either not funny or not brave.
Someone is either tall or not rich.
Someone is either brave or not tall.
Someone is not strong or wise.
John is not happy.
Mary is old.
Someone is both not wise and not brave.
John is patient or not strong. | Fred is not calm. | neutral | (![X]:(~calm(X)=>(~creative(X)<~>kind(X))))&
(![X]:(calm(X)<=>(funny(X)&humble(X))))&
(![X]:((brave(X)&~wise(X))=>(calm(X)<~>~tall(X))))&
((?[X]:(~strong(X)))<=>((rich(susan)&old(susan))))&
(((tall(fred)<~>~calm(fred)))<=>(?[X]:((~calm(X)<~>~funny(X)))))&
(((~happy(susan)<~>quiet(susan)))<=>(?[X]:((happy(X)|kind(X)))))&
(![X]:(~curious(X)=>(~tall(X)&~curious(X))))&
((?[X]:((happy(X)<~>patient(X))))<=>(?[X]:((~humble(X)&~quiet(X)))))&
((?[X]:(~kind(X)))<=>(?[X]:((brave(X)<~>curious(X)))))&
(((~generous(lucy)|patient(lucy)))<=>(?[X]:((~strong(X)<~>quiet(X)))))&
(![X]:((humble(X)&~curious(X))=>(~curious(X)<~>~brave(X))))&
((?[X]:((~quiet(X)|wise(X))))<=>(?[X]:((brave(X)&~curious(X)))))&
(![X]:((old(X)|wise(X))<=>(calm(X)&~quiet(X))))&
(![X]:((curious(X)&~quiet(X))<=>(quiet(X)<~>~calm(X))))&
(((curious(alice)&~brave(alice)))<=>((~humble(alice)<~>humble(alice))))&
(((wise(mary)<~>~calm(mary)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(?[X]:((tall(X)<~>~rich(X))))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:((~strong(X)|wise(X))))&
(~happy(john))&
(old(mary))&
(?[X]:((~wise(X)&~brave(X))))&
((patient(john)|~strong(john))) | ~calm(fred) | [] | null | 0 |
Everyone who is calm or not quiet is generous or not funny and vice versa.
If susan is both not curious and humble then mary is either not curious or happy.
Everyone who is wise or not generous is both brave and not wise and vice versa.
Everyone who is either rich or not strong is both not generous and not wise and vice versa.
Everyone who is both funny and kind is not calm and vice versa.
Everyone who is strong is either calm or generous and vice versa.
If someone is curious then john is patient.
If alice is not happy or not tall then paul is tall or strong and vice versa.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Someone is either not old or not kind.
Susan is not wise.
Someone is either funny or not funny.
Fred is not strong or not creative.
Someone is generous or not kind. | Alice is not rich. | contradiction | (![X]:((calm(X)|~quiet(X))<=>(generous(X)|~funny(X))))&
(((~curious(susan)&humble(susan)))=>((~curious(mary)<~>happy(mary))))&
(![X]:((wise(X)|~generous(X))<=>(brave(X)&~wise(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(~generous(X)&~wise(X))))&
(![X]:((funny(X)&kind(X))<=>~calm(X)))&
(![X]:(strong(X)<=>(calm(X)<~>generous(X))))&
((?[X]:(curious(X)))=>(patient(john)))&
(((~happy(alice)|~tall(alice)))<=>((tall(paul)|strong(paul))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
((~strong(fred)|~creative(fred)))&
(?[X]:((generous(X)|~kind(X)))) | ~rich(alice) | [
"p2",
"p3",
"p4",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5835130562381806736841021
% SZS output start Proof for 5835130562381806736841021
3. ! [X0] : ((~generous(X0) | wise(X0)) <=> (~wise(X0) & brave(X0))) [input p2]
4. ! [X0] : ((rich(X0) <~> ~strong(X0)) <=> (~wise(X0) & ~generous(X0))) [input p3]
5. ! [X0] : ((kind(X0) & funny(X0)) <=> ~calm(X0)) [input p4]
6. ! [X0] : (strong(X0) <=> (calm(X0) <~> generous(X0))) [input p5]
10. ! [X0] : ((~rich(X0) | rich(X0)) <=> ~funny(X0)) [input p9]
22. ~rich(alice) [input hypothesis]
33. ! [X0] : (((~generous(X0) | wise(X0)) | (wise(X0) | ~brave(X0))) & ((~wise(X0) & brave(X0)) | (generous(X0) & ~wise(X0)))) [nnf transformation 3]
34. ! [X0] : ((~generous(X0) | wise(X0) | wise(X0) | ~brave(X0)) & ((~wise(X0) & brave(X0)) | (generous(X0) & ~wise(X0)))) [flattening 33]
35. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (wise(X0) | generous(X0))) & ((~wise(X0) & ~generous(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [nnf transformation 4]
36. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | wise(X0) | generous(X0)) & ((~wise(X0) & ~generous(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [flattening 35]
37. ! [X0] : (((kind(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | (~kind(X0) | ~funny(X0)))) [nnf transformation 5]
38. ! [X0] : (((kind(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | ~kind(X0) | ~funny(X0))) [flattening 37]
39. ! [X0] : ((strong(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ~strong(X0))) [nnf transformation 6]
42. ! [X0] : (((~rich(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [nnf transformation 10]
43. ! [X0] : ((~rich(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [flattening 42]
66. ~wise(X0) | ~wise(X0) [cnf transformation 34]
70. ~generous(X0) | rich(X0) | strong(X0) [cnf transformation 36]
73. ~strong(X0) | rich(X0) | wise(X0) | generous(X0) [cnf transformation 36]
76. funny(X0) | calm(X0) [cnf transformation 38]
79. ~strong(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 39]
80. ~calm(X0) | generous(X0) | strong(X0) [cnf transformation 39]
89. ~funny(X0) | ~rich(X0) [cnf transformation 43]
90. ~funny(X0) | rich(X0) [cnf transformation 43]
114. ~rich(alice) [cnf transformation 22]
115. ~wise(X0) [duplicate literal removal 66]
136. ~strong(X0) | rich(X0) | generous(X0) [subsumption resolution 73,115]
165. ~funny(X0) [subsumption resolution 89,90]
214. calm(X0) [resolution 76,165]
236. strong(X0) | generous(X0) [resolution 80,214]
264. rich(X0) | generous(X0) | generous(X0) [resolution 136,236]
265. rich(X0) | generous(X0) [duplicate literal removal 264]
281. generous(alice) [resolution 265,114]
291. rich(alice) | strong(alice) [resolution 281,70]
293. strong(alice) [subsumption resolution 291,114]
305. ~calm(alice) | ~generous(alice) [resolution 293,79]
308. ~generous(alice) [subsumption resolution 305,214]
309. $false [subsumption resolution 308,281]
% SZS output end Proof for 5835130562381806736841021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both rich and old then john is not kind or not calm and vice versa.
If someone is curious then lucy is both kind and not humble.
Everyone who is both old and funny is not creative and vice versa.
Everyone who is both brave and not curious is not patient and vice versa.
If susan is both happy and quiet then alice is not generous or quiet and vice versa.
Everyone who is not kind is both rich and curious.
If paul is not strong then alice is old or not strong and vice versa.
Everyone who is not curious or not quiet is either strong or not wise and vice versa.
If someone is both wise and patient then someone is funny.
Everyone who is either not quiet or not creative is not generous or tall.
Everyone who is either not generous or curious is creative.
Everyone who is both calm and quiet is creative.
Everyone who is not calm is either not old or funny and vice versa.
If someone is either calm or strong then someone is old or creative.
Everyone who is either generous or not wise is not tall or not funny.
If paul is either not brave or not creative then lucy is either not kind or quiet and vice versa.
Someone is wise.
Susan is rich.
Lucy is either not happy or curious.
Someone is both creative and patient.
Lucy is not patient.
Paul is not calm or old.
Alice is either calm or brave.
Susan is curious. | Paul is strong. | neutral | (((rich(mary)&old(mary)))<=>((~kind(john)|~calm(john))))&
((?[X]:(curious(X)))=>((kind(lucy)&~humble(lucy))))&
(![X]:((old(X)&funny(X))<=>~creative(X)))&
(![X]:((brave(X)&~curious(X))<=>~patient(X)))&
(((happy(susan)&quiet(susan)))<=>((~generous(alice)|quiet(alice))))&
(![X]:(~kind(X)=>(rich(X)&curious(X))))&
((~strong(paul))<=>((old(alice)|~strong(alice))))&
(![X]:((~curious(X)|~quiet(X))<=>(strong(X)<~>~wise(X))))&
((?[X]:((wise(X)&patient(X))))=>(?[X]:(funny(X))))&
(![X]:((~quiet(X)<~>~creative(X))=>(~generous(X)|tall(X))))&
(![X]:((~generous(X)<~>curious(X))=>creative(X)))&
(![X]:((calm(X)&quiet(X))=>creative(X)))&
(![X]:(~calm(X)<=>(~old(X)<~>funny(X))))&
((?[X]:((calm(X)<~>strong(X))))=>(?[X]:((old(X)|creative(X)))))&
(![X]:((generous(X)<~>~wise(X))=>(~tall(X)|~funny(X))))&
(((~brave(paul)<~>~creative(paul)))<=>((~kind(lucy)<~>quiet(lucy))))&
(?[X]:(wise(X)))&
(rich(susan))&
((~happy(lucy)<~>curious(lucy)))&
(?[X]:((creative(X)&patient(X))))&
(~patient(lucy))&
((~calm(paul)|old(paul)))&
((calm(alice)<~>brave(alice)))&
(curious(susan)) | strong(paul) | [] | null | 0 |
If john is not patient then susan is patient or not strong. Everyone who is not tall is funny and vice versa. Everyone who is both curious and not kind is either not strong or not quiet. Everyone who is funny is both not brave and not happy. If lucy is either not quiet or calm then john is not creative. Everyone who is both not funny and not wise is both tall and quiet and vice versa. If alice is not curious then someone is not calm or patient. If paul is both not quiet and curious then someone is not tall and vice versa. Everyone who is not funny is either not patient or curious. Everyone who is not kind or strong is both funny and not quiet and vice versa. Everyone who is either humble or not brave is either old or humble. Everyone who is not calm is both quiet and not rich. If susan is either not wise or not humble then alice is creative or kind and vice versa. If mary is wise or not quiet then someone is both not humble and patient and vice versa. Everyone who is quiet is either not wise or not curious and vice versa. If lucy is both brave and not calm then someone is patient and vice versa. Someone is either happy or humble. Someone is either patient or quiet. Someone is either not creative or not tall. Fred is both patient and brave. Someone is brave or not wise. Someone is not kind or not tall. Fred is both not rich and generous. Mary is not rich. | Lucy is not wise. | entailment | ((~patient(john))=>((patient(susan)|~strong(susan))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((curious(X)&~kind(X))=>(~strong(X)<~>~quiet(X))))&
(![X]:(funny(X)=>(~brave(X)&~happy(X))))&
(((~quiet(lucy)<~>calm(lucy)))=>(~creative(john)))&
(![X]:((~funny(X)&~wise(X))<=>(tall(X)&quiet(X))))&
((~curious(alice))=>(?[X]:((~calm(X)|patient(X)))))&
(((~quiet(paul)&curious(paul)))<=>(?[X]:(~tall(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>curious(X))))&
(![X]:((~kind(X)|strong(X))<=>(funny(X)&~quiet(X))))&
(![X]:((humble(X)<~>~brave(X))=>(old(X)<~>humble(X))))&
(![X]:(~calm(X)=>(quiet(X)&~rich(X))))&
(((~wise(susan)<~>~humble(susan)))<=>((creative(alice)|kind(alice))))&
(((wise(mary)|~quiet(mary)))<=>(?[X]:((~humble(X)&patient(X)))))&
(![X]:(quiet(X)<=>(~wise(X)<~>~curious(X))))&
(((brave(lucy)&~calm(lucy)))<=>(?[X]:(patient(X))))&
(?[X]:((happy(X)<~>humble(X))))&
(?[X]:((patient(X)<~>quiet(X))))&
(?[X]:((~creative(X)<~>~tall(X))))&
((patient(fred)&brave(fred)))&
(?[X]:((brave(X)|~wise(X))))&
(?[X]:((~kind(X)|~tall(X))))&
((~rich(fred)&generous(fred)))&
(~rich(mary)) | ~wise(lucy) | [
"p1",
"p3",
"p5",
"p11",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4305442468749216035627668
% SZS output start Proof for 4305442468749216035627668
2. ! [X0] : (~tall(X0) <=> funny(X0)) [input p1]
4. ! [X0] : (funny(X0) => (~happy(X0) & ~brave(X0))) [input p3]
6. ! [X0] : ((~wise(X0) & ~funny(X0)) <=> (quiet(X0) & tall(X0))) [input p5]
12. ! [X0] : (~calm(X0) => (~rich(X0) & quiet(X0))) [input p11]
16. (~calm(lucy) & brave(lucy)) <=> ? [X0] : patient(X0) [input p15]
20. brave(fred) & patient(fred) [input p19]
25. wise(lucy) [input hypothesis]
29. ! [X0] : (~calm(X0) => quiet(X0)) [pure predicate removal 12]
34. ! [X0] : ((~happy(X0) & ~brave(X0)) | ~funny(X0)) [ennf transformation 4]
39. ! [X0] : (quiet(X0) | calm(X0)) [ennf transformation 29]
40. ! [X0] : ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))) [nnf transformation 2]
43. ! [X0] : (((~wise(X0) & ~funny(X0)) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | (wise(X0) | funny(X0)))) [nnf transformation 6]
44. ! [X0] : (((~wise(X0) & ~funny(X0)) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | wise(X0) | funny(X0))) [flattening 43]
64. ((~calm(lucy) & brave(lucy)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (calm(lucy) | ~brave(lucy))) [nnf transformation 16]
65. ((~calm(lucy) & brave(lucy)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | calm(lucy) | ~brave(lucy)) [flattening 64]
66. ((~calm(lucy) & brave(lucy)) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | calm(lucy) | ~brave(lucy)) [rectify 65]
67. ? [X1] : patient(X1) => patient(sK3) [choice axiom]
68. ((~calm(lucy) & brave(lucy)) | ! [X0] : ~patient(X0)) & (patient(sK3) | calm(lucy) | ~brave(lucy)) [skolemisation 66,67]
83. funny(X0) | tall(X0) [cnf transformation 40]
87. ~brave(X0) | ~funny(X0) [cnf transformation 34]
94. ~wise(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 44]
110. calm(X0) | quiet(X0) [cnf transformation 39]
127. brave(lucy) | ~patient(X0) [cnf transformation 68]
128. ~calm(lucy) | ~patient(X0) [cnf transformation 68]
135. patient(fred) [cnf transformation 20]
139. wise(lucy) [cnf transformation 25]
156. 4 <=> calm(lucy) [avatar definition]
158. ~calm(lucy) <- (~4) [avatar component clause 156]
160. 5 <=> quiet(lucy) [avatar definition]
161. quiet(lucy) <- (5) [avatar component clause 160]
247. 23 <=> ! [X0] : ~patient(X0) [avatar definition]
248. ~patient(X0) <- (23) [avatar component clause 247]
249. 23 | ~4 [avatar split clause 128,156,247]
251. 24 <=> brave(lucy) [avatar definition]
253. brave(lucy) <- (24) [avatar component clause 251]
254. 23 | 24 [avatar split clause 127,251,247]
310. $false <- (23) [resolution 248,135]
311. ~23 [avatar contradiction clause 310]
314. ~funny(lucy) <- (24) [resolution 87,253]
319. tall(lucy) <- (24) [resolution 314,83]
327. quiet(lucy) <- (~4) [resolution 110,158]
328. 5 | 4 [avatar split clause 327,156,160]
361. ~quiet(lucy) | ~tall(lucy) [resolution 94,139]
368. ~tall(lucy) <- (5) [subsumption resolution 361,161]
369. $false <- (5, 24) [subsumption resolution 368,319]
370. ~5 | ~24 [avatar contradiction clause 369]
376. $false [avatar sat refutation 249,254,311,328,370]
% SZS output end Proof for 4305442468749216035627668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either not calm or not curious then alice is strong or not funny and vice versa. Everyone who is not patient is not quiet or old. Everyone who is strong is happy or old. If lucy is not calm or not humble then john is both not happy and patient. If susan is not rich then someone is either quiet or not old and vice versa. If someone is either not humble or humble then paul is wise or quiet and vice versa. Everyone who is not kind or curious is both quiet and not curious. Everyone who is old or patient is both patient and strong. Everyone who is tall is not strong and vice versa. Everyone who is either not curious or not happy is both not patient and tall and vice versa. Everyone who is either humble or old is either not kind or old. If someone is not funny or not patient then someone is both wise and not brave. If lucy is not rich or funny then mary is not patient or generous and vice versa. If susan is not happy then alice is either not funny or not strong and vice versa. If someone is funny then someone is both not old and kind. If someone is either not old or funny then john is either calm or not creative. Alice is not generous or not wise. Someone is strong or not generous. Someone is rich or creative. Alice is both wise and strong. Susan is not rich. Lucy is not tall or not patient. Someone is rich. Paul is not tall. | Alice is wise. | entailment | (((~calm(fred)<~>~curious(fred)))<=>((strong(alice)|~funny(alice))))&
(![X]:(~patient(X)=>(~quiet(X)|old(X))))&
(![X]:(strong(X)=>(happy(X)|old(X))))&
(((~calm(lucy)|~humble(lucy)))=>((~happy(john)&patient(john))))&
((~rich(susan))<=>(?[X]:((quiet(X)<~>~old(X)))))&
((?[X]:((~humble(X)<~>humble(X))))<=>((wise(paul)|quiet(paul))))&
(![X]:((~kind(X)|curious(X))=>(quiet(X)&~curious(X))))&
(![X]:((old(X)|patient(X))=>(patient(X)&strong(X))))&
(![X]:(tall(X)<=>~strong(X)))&
(![X]:((~curious(X)<~>~happy(X))<=>(~patient(X)&tall(X))))&
(![X]:((humble(X)<~>old(X))=>(~kind(X)<~>old(X))))&
((?[X]:((~funny(X)|~patient(X))))=>(?[X]:((wise(X)&~brave(X)))))&
(((~rich(lucy)|funny(lucy)))<=>((~patient(mary)|generous(mary))))&
((~happy(susan))<=>((~funny(alice)<~>~strong(alice))))&
((?[X]:(funny(X)))=>(?[X]:((~old(X)&kind(X)))))&
((?[X]:((~old(X)<~>funny(X))))=>((calm(john)<~>~creative(john))))&
((~generous(alice)|~wise(alice)))&
(?[X]:((strong(X)|~generous(X))))&
(?[X]:((rich(X)|creative(X))))&
((wise(alice)&strong(alice)))&
(~rich(susan))&
((~tall(lucy)|~patient(lucy)))&
(?[X]:(rich(X)))&
(~tall(paul)) | wise(alice) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8270200989540925304342810
% SZS output start Proof for 8270200989540925304342810
20. strong(alice) & wise(alice) [input p19]
25. ~wise(alice) [input hypothesis]
132. wise(alice) [cnf transformation 20]
138. ~wise(alice) [cnf transformation 25]
303. 34 <=> wise(alice) [avatar definition]
326. 34 [avatar split clause 132,303]
337. ~34 [avatar split clause 138,303]
338. $false [avatar sat refutation 326,337]
% SZS output end Proof for 8270200989540925304342810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is kind then someone is humble or not curious.
Everyone who is both funny and not happy is creative.
Everyone who is patient is both wise and patient.
Everyone who is either happy or brave is both not generous and rich and vice versa.
If lucy is not tall then lucy is humble and vice versa.
Everyone who is either not strong or not creative is not creative and vice versa.
If paul is not strong then someone is quiet.
Everyone who is not curious is not strong and vice versa.
Everyone who is strong is both creative and not quiet and vice versa.
Everyone who is both not curious and strong is either strong or rich.
Everyone who is both quiet and not calm is both curious and not strong.
If susan is either not quiet or tall then someone is either brave or not strong.
Everyone who is not patient is quiet.
If someone is either not strong or brave then someone is either not strong or calm and vice versa.
If someone is either wise or quiet then someone is not happy or not creative and vice versa.
Someone is both not old and not kind.
Someone is rich.
Lucy is generous or creative.
Alice is not tall.
Susan is strong or happy.
Someone is not tall or not rich.
John is rich. | John is wise. | entailment | ((kind(alice))=>(?[X]:((humble(X)|~curious(X)))))&
(![X]:((funny(X)&~happy(X))=>creative(X)))&
(![X]:(patient(X)=>(wise(X)&patient(X))))&
(![X]:((happy(X)<~>brave(X))<=>(~generous(X)&rich(X))))&
((~tall(lucy))<=>(humble(lucy)))&
(![X]:((~strong(X)<~>~creative(X))<=>~creative(X)))&
((~strong(paul))=>(?[X]:(quiet(X))))&
(![X]:(~curious(X)<=>~strong(X)))&
(![X]:(strong(X)<=>(creative(X)&~quiet(X))))&
(![X]:((~curious(X)&strong(X))=>(strong(X)<~>rich(X))))&
(![X]:((quiet(X)&~calm(X))=>(curious(X)&~strong(X))))&
(((~quiet(susan)<~>tall(susan)))=>(?[X]:((brave(X)<~>~strong(X)))))&
(![X]:(~patient(X)=>quiet(X)))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:((~happy(X)|~creative(X)))))&
(?[X]:((~old(X)&~kind(X))))&
(?[X]:(rich(X)))&
((generous(lucy)|creative(lucy)))&
(~tall(alice))&
((strong(susan)|happy(susan)))&
(?[X]:((~tall(X)|~rich(X))))&
(rich(john)) | wise(john) | [
"p2",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3598039960568060276886572
% SZS output start Proof for 3598039960568060276886572
3. ! [X0] : (patient(X0) => (patient(X0) & wise(X0))) [input p2]
6. ! [X0] : ((~strong(X0) <~> ~creative(X0)) <=> ~creative(X0)) [input p5]
9. ! [X0] : (strong(X0) <=> (~quiet(X0) & creative(X0))) [input p8]
13. ! [X0] : (~patient(X0) => quiet(X0)) [input p12]
23. ~wise(john) [input hypothesis]
31. ! [X0] : ((patient(X0) & wise(X0)) | ~patient(X0)) [ennf transformation 3]
39. ! [X0] : (quiet(X0) | patient(X0)) [ennf transformation 13]
43. ! [X0] : ((((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | creative(X0)) & (~creative(X0) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))))) [nnf transformation 6]
46. ! [X0] : ((strong(X0) | (quiet(X0) | ~creative(X0))) & ((~quiet(X0) & creative(X0)) | ~strong(X0))) [nnf transformation 9]
47. ! [X0] : ((strong(X0) | quiet(X0) | ~creative(X0)) & ((~quiet(X0) & creative(X0)) | ~strong(X0))) [flattening 46]
66. ~patient(X0) | wise(X0) [cnf transformation 31]
76. ~creative(X0) | ~creative(X0) | strong(X0) [cnf transformation 43]
79. creative(X0) | strong(X0) | creative(X0) [cnf transformation 43]
83. ~quiet(X0) | ~strong(X0) [cnf transformation 47]
93. quiet(X0) | patient(X0) [cnf transformation 39]
114. ~wise(john) [cnf transformation 23]
116. ~creative(X0) | strong(X0) [duplicate literal removal 76]
117. creative(X0) | strong(X0) [duplicate literal removal 79]
128. strong(X0) [subsumption resolution 116,117]
129. ~quiet(X0) [subsumption resolution 83,128]
143. patient(X0) [subsumption resolution 93,129]
194. wise(X0) [resolution 66,143]
195. $false [resolution 194,114]
% SZS output end Proof for 3598039960568060276886572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not strong is not happy. Everyone who is both patient and not rich is not happy. Everyone who is either not kind or not curious is either not patient or not old. If alice is kind or not humble then lucy is patient. If someone is either kind or patient then someone is either not kind or tall. Everyone who is both old and curious is both not patient and not funny. Everyone who is not happy is both wise and kind and vice versa. If lucy is happy or brave then lucy is rich and vice versa. If someone is either not kind or not creative then susan is old and vice versa. Everyone who is either funny or not brave is either tall or not calm and vice versa. Everyone who is either brave or patient is curious or quiet. Everyone who is both funny and not generous is not brave and vice versa. If fred is both old and not wise then paul is either quiet or wise. If someone is happy then someone is both not generous and creative and vice versa. Everyone who is not kind is not patient and vice versa. Everyone who is both not kind and curious is both patient and not generous and vice versa. Mary is both not tall and humble. Fred is not quiet. Mary is kind or not happy. Someone is both not strong and not tall. Lucy is patient or not generous. | Susan is curious. | neutral | (![X]:((creative(X)|~strong(X))=>~happy(X)))&
(![X]:((patient(X)&~rich(X))=>~happy(X)))&
(![X]:((~kind(X)<~>~curious(X))=>(~patient(X)<~>~old(X))))&
(((kind(alice)|~humble(alice)))=>(patient(lucy)))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:((~kind(X)<~>tall(X)))))&
(![X]:((old(X)&curious(X))=>(~patient(X)&~funny(X))))&
(![X]:(~happy(X)<=>(wise(X)&kind(X))))&
(((happy(lucy)|brave(lucy)))<=>(rich(lucy)))&
((?[X]:((~kind(X)<~>~creative(X))))<=>(old(susan)))&
(![X]:((funny(X)<~>~brave(X))<=>(tall(X)<~>~calm(X))))&
(![X]:((brave(X)<~>patient(X))=>(curious(X)|quiet(X))))&
(![X]:((funny(X)&~generous(X))<=>~brave(X)))&
(((old(fred)&~wise(fred)))=>((quiet(paul)<~>wise(paul))))&
((?[X]:(happy(X)))<=>(?[X]:((~generous(X)&creative(X)))))&
(![X]:(~kind(X)<=>~patient(X)))&
(![X]:((~kind(X)&curious(X))<=>(patient(X)&~generous(X))))&
((~tall(mary)&humble(mary)))&
(~quiet(fred))&
((kind(mary)|~happy(mary)))&
(?[X]:((~strong(X)&~tall(X))))&
((patient(lucy)|~generous(lucy))) | curious(susan) | [] | null | 0 |
Everyone who is not generous or not calm is not curious.
If someone is curious or not strong then paul is not patient.
If someone is either tall or brave then alice is not tall or patient and vice versa.
Everyone who is rich or tall is funny or not quiet and vice versa.
Everyone who is both not patient and rich is curious or quiet and vice versa.
If someone is both not generous and not quiet then someone is tall or patient.
If someone is either old or not patient then alice is either rich or brave and vice versa.
Everyone who is both not kind and not calm is either funny or not wise.
Everyone who is strong or not creative is not creative.
If susan is either happy or not calm then someone is tall and vice versa.
If someone is either happy or creative then fred is either creative or not calm.
Everyone who is either not strong or not patient is either not tall or kind.
Everyone who is patient is both not patient and creative and vice versa.
Everyone who is creative is creative or not curious and vice versa.
If susan is funny or humble then susan is not humble and vice versa.
Everyone who is both curious and not curious is either not humble or not old.
Paul is not calm or not quiet.
Mary is either funny or not kind.
Someone is not old.
Someone is either not wise or humble. | Alice is not creative. | entailment | (![X]:((~generous(X)|~calm(X))=>~curious(X)))&
((?[X]:((curious(X)|~strong(X))))=>(~patient(paul)))&
((?[X]:((tall(X)<~>brave(X))))<=>((~tall(alice)|patient(alice))))&
(![X]:((rich(X)|tall(X))<=>(funny(X)|~quiet(X))))&
(![X]:((~patient(X)&rich(X))<=>(curious(X)|quiet(X))))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:((tall(X)|patient(X)))))&
((?[X]:((old(X)<~>~patient(X))))<=>((rich(alice)<~>brave(alice))))&
(![X]:((~kind(X)&~calm(X))=>(funny(X)<~>~wise(X))))&
(![X]:((strong(X)|~creative(X))=>~creative(X)))&
(((happy(susan)<~>~calm(susan)))<=>(?[X]:(tall(X))))&
((?[X]:((happy(X)<~>creative(X))))=>((creative(fred)<~>~calm(fred))))&
(![X]:((~strong(X)<~>~patient(X))=>(~tall(X)<~>kind(X))))&
(![X]:(patient(X)<=>(~patient(X)&creative(X))))&
(![X]:(creative(X)<=>(creative(X)|~curious(X))))&
(((funny(susan)|humble(susan)))<=>(~humble(susan)))&
(![X]:((curious(X)&~curious(X))=>(~humble(X)<~>~old(X))))&
((~calm(paul)|~quiet(paul)))&
((funny(mary)<~>~kind(mary)))&
(?[X]:(~old(X)))&
(?[X]:((~wise(X)<~>humble(X)))) | ~creative(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3173573772502860012284669
% SZS output start Proof for 3173573772502860012284669
13. ! [X0] : (patient(X0) <=> (creative(X0) & ~patient(X0))) [input p12]
21. creative(alice) [input hypothesis]
54. ! [X0] : ((patient(X0) | (~creative(X0) | patient(X0))) & ((creative(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 13]
55. ! [X0] : ((patient(X0) | ~creative(X0) | patient(X0)) & ((creative(X0) & ~patient(X0)) | ~patient(X0))) [flattening 54]
109. ~patient(X0) | ~patient(X0) [cnf transformation 55]
111. patient(X0) | ~creative(X0) | patient(X0) [cnf transformation 55]
126. creative(alice) [cnf transformation 21]
129. ~patient(X0) [duplicate literal removal 109]
130. ~creative(X0) | patient(X0) [duplicate literal removal 111]
288. patient(alice) [resolution 130,126]
291. $false [subsumption resolution 288,129]
% SZS output end Proof for 3173573772502860012284669
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not curious or not creative then someone is both not patient and not generous and vice versa.
Everyone who is either not brave or funny is happy or generous.
Everyone who is not generous is either not funny or kind and vice versa.
Everyone who is not curious or not tall is either not curious or tall and vice versa.
If someone is both not calm and not rich then someone is both wise and not old.
Everyone who is both old and not brave is either wise or not curious and vice versa.
Everyone who is strong is either happy or generous and vice versa.
Everyone who is wise or generous is both old and not rich and vice versa.
If someone is both tall and not generous then someone is either curious or tall.
Everyone who is either not kind or not quiet is generous and vice versa.
Everyone who is curious is not curious or not patient.
If john is funny then someone is both not humble and tall and vice versa.
Everyone who is creative or not kind is not old and vice versa.
If john is both creative and not humble then someone is not strong and vice versa.
If paul is quiet or tall then lucy is tall and vice versa.
Everyone who is curious or not tall is strong or generous and vice versa.
Someone is either tall or rich.
Mary is either not happy or not strong.
Someone is either not creative or creative.
Fred is not strong or not rich.
Alice is both old and not quiet. | Fred is not patient. | neutral | (((~curious(susan)|~creative(susan)))<=>(?[X]:((~patient(X)&~generous(X)))))&
(![X]:((~brave(X)<~>funny(X))=>(happy(X)|generous(X))))&
(![X]:(~generous(X)<=>(~funny(X)<~>kind(X))))&
(![X]:((~curious(X)|~tall(X))<=>(~curious(X)<~>tall(X))))&
((?[X]:((~calm(X)&~rich(X))))=>(?[X]:((wise(X)&~old(X)))))&
(![X]:((old(X)&~brave(X))<=>(wise(X)<~>~curious(X))))&
(![X]:(strong(X)<=>(happy(X)<~>generous(X))))&
(![X]:((wise(X)|generous(X))<=>(old(X)&~rich(X))))&
((?[X]:((tall(X)&~generous(X))))=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((~kind(X)<~>~quiet(X))<=>generous(X)))&
(![X]:(curious(X)=>(~curious(X)|~patient(X))))&
((funny(john))<=>(?[X]:((~humble(X)&tall(X)))))&
(![X]:((creative(X)|~kind(X))<=>~old(X)))&
(((creative(john)&~humble(john)))<=>(?[X]:(~strong(X))))&
(((quiet(paul)|tall(paul)))<=>(tall(lucy)))&
(![X]:((curious(X)|~tall(X))<=>(strong(X)|generous(X))))&
(?[X]:((tall(X)<~>rich(X))))&
((~happy(mary)<~>~strong(mary)))&
(?[X]:((~creative(X)<~>creative(X))))&
((~strong(fred)|~rich(fred)))&
((old(alice)&~quiet(alice))) | ~patient(fred) | [] | null | 0 |
If mary is either not strong or not tall then susan is either not calm or not wise. Everyone who is either not rich or not wise is not quiet and vice versa. If mary is either not curious or happy then mary is both brave and humble and vice versa. Everyone who is not old is not patient or not curious. Everyone who is either not funny or not happy is not rich or brave and vice versa. If someone is either calm or not funny then john is not calm or not funny and vice versa. Everyone who is not generous is not happy or not kind and vice versa. If lucy is both not brave and generous then alice is not humble. Everyone who is not generous is either curious or not kind and vice versa. Everyone who is either not quiet or tall is not patient or not curious and vice versa. Everyone who is funny or rich is either strong or not old and vice versa. If john is either patient or not humble then someone is curious. Everyone who is patient or not brave is either not curious or not brave and vice versa. If someone is both not humble and not rich then fred is both patient and not quiet. If someone is happy or kind then someone is either not old or creative and vice versa. Everyone who is either curious or not generous is both old and kind. Paul is not rich or generous. Someone is either not quiet or not funny. Mary is wise. Lucy is both happy and not curious. Paul is not happy. John is not happy or patient. Someone is patient. Someone is either not brave or strong. | Alice is kind. | entailment | (((~strong(mary)<~>~tall(mary)))=>((~calm(susan)<~>~wise(susan))))&
(![X]:((~rich(X)<~>~wise(X))<=>~quiet(X)))&
(((~curious(mary)<~>happy(mary)))<=>((brave(mary)&humble(mary))))&
(![X]:(~old(X)=>(~patient(X)|~curious(X))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~rich(X)|brave(X))))&
((?[X]:((calm(X)<~>~funny(X))))<=>((~calm(john)|~funny(john))))&
(![X]:(~generous(X)<=>(~happy(X)|~kind(X))))&
(((~brave(lucy)&generous(lucy)))=>(~humble(alice)))&
(![X]:(~generous(X)<=>(curious(X)<~>~kind(X))))&
(![X]:((~quiet(X)<~>tall(X))<=>(~patient(X)|~curious(X))))&
(![X]:((funny(X)|rich(X))<=>(strong(X)<~>~old(X))))&
(((patient(john)<~>~humble(john)))=>(?[X]:(curious(X))))&
(![X]:((patient(X)|~brave(X))<=>(~curious(X)<~>~brave(X))))&
((?[X]:((~humble(X)&~rich(X))))=>((patient(fred)&~quiet(fred))))&
((?[X]:((happy(X)|kind(X))))<=>(?[X]:((~old(X)<~>creative(X)))))&
(![X]:((curious(X)<~>~generous(X))=>(old(X)&kind(X))))&
((~rich(paul)|generous(paul)))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(wise(mary))&
((happy(lucy)&~curious(lucy)))&
(~happy(paul))&
((~happy(john)|patient(john)))&
(?[X]:(patient(X)))&
(?[X]:((~brave(X)<~>strong(X)))) | kind(alice) | [
"p6",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 684010427287225822206186
% SZS output start Proof for 684010427287225822206186
7. ! [X0] : (~generous(X0) <=> (~kind(X0) | ~happy(X0))) [input p6]
9. ! [X0] : (~generous(X0) <=> (curious(X0) <~> ~kind(X0))) [input p8]
16. ! [X0] : ((curious(X0) <~> ~generous(X0)) => (kind(X0) & old(X0))) [input p15]
25. ~kind(alice) [input hypothesis]
34. ! [X0] : ((kind(X0) & old(X0)) | (curious(X0) <=> ~generous(X0))) [ennf transformation 16]
46. ! [X0] : ((~generous(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | generous(X0))) [nnf transformation 7]
47. ! [X0] : ((~generous(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | generous(X0))) [flattening 46]
48. ! [X0] : ((~generous(X0) | ((curious(X0) | kind(X0)) & (~kind(X0) | ~curious(X0)))) & (((kind(X0) | ~curious(X0)) & (~kind(X0) | curious(X0))) | generous(X0))) [nnf transformation 9]
63. ! [X0] : ((kind(X0) & old(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) [nnf transformation 34]
101. ~generous(X0) | kind(X0) [cnf transformation 47]
104. kind(X0) | ~curious(X0) | generous(X0) [cnf transformation 48]
138. kind(X0) | curious(X0) | generous(X0) [cnf transformation 63]
150. ~kind(alice) [cnf transformation 25]
237. kind(X0) | ~curious(X0) [subsumption resolution 104,101]
299. kind(X0) | curious(X0) [subsumption resolution 138,101]
300. kind(X0) [subsumption resolution 299,237]
335. $false [subsumption resolution 150,300]
% SZS output end Proof for 684010427287225822206186
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or humble is humble and vice versa.
Everyone who is not tall or not generous is not tall.
If someone is either not quiet or not creative then alice is not calm or not tall and vice versa.
Everyone who is both not funny and not curious is not generous or generous.
Everyone who is not calm is either funny or quiet.
Everyone who is either old or not tall is funny or old and vice versa.
If lucy is both not humble and not creative then mary is not rich or patient.
If paul is both not creative and funny then someone is humble or calm.
Everyone who is not calm is rich and vice versa.
Everyone who is either quiet or not generous is both not curious and not wise.
If fred is both quiet and happy then john is either generous or not wise.
Everyone who is tall is not kind or patient.
Everyone who is not tall or calm is calm.
Everyone who is not kind is both not calm and calm and vice versa.
If paul is not calm then someone is either creative or not calm.
Everyone who is either quiet or not rich is both rich and generous and vice versa.
Someone is wise or not rich.
Someone is either tall or not patient.
Paul is either not kind or patient.
John is both not rich and not funny.
Paul is both rich and patient.
Someone is not calm.
Someone is both tall and not strong. | John is curious. | contradiction | (![X]:((funny(X)|humble(X))<=>humble(X)))&
(![X]:((~tall(X)|~generous(X))=>~tall(X)))&
((?[X]:((~quiet(X)<~>~creative(X))))<=>((~calm(alice)|~tall(alice))))&
(![X]:((~funny(X)&~curious(X))=>(~generous(X)|generous(X))))&
(![X]:(~calm(X)=>(funny(X)<~>quiet(X))))&
(![X]:((old(X)<~>~tall(X))<=>(funny(X)|old(X))))&
(((~humble(lucy)&~creative(lucy)))=>((~rich(mary)|patient(mary))))&
(((~creative(paul)&funny(paul)))=>(?[X]:((humble(X)|calm(X)))))&
(![X]:(~calm(X)<=>rich(X)))&
(![X]:((quiet(X)<~>~generous(X))=>(~curious(X)&~wise(X))))&
(((quiet(fred)&happy(fred)))=>((generous(john)<~>~wise(john))))&
(![X]:(tall(X)=>(~kind(X)|patient(X))))&
(![X]:((~tall(X)|calm(X))=>calm(X)))&
(![X]:(~kind(X)<=>(~calm(X)&calm(X))))&
((~calm(paul))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>(rich(X)&generous(X))))&
(?[X]:((wise(X)|~rich(X))))&
(?[X]:((tall(X)<~>~patient(X))))&
((~kind(paul)<~>patient(paul)))&
((~rich(john)&~funny(john)))&
((rich(paul)&patient(paul)))&
(?[X]:(~calm(X)))&
(?[X]:((tall(X)&~strong(X)))) | curious(john) | [
"p1",
"p5",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2479154237883029148732084
% SZS output start Proof for 2479154237883029148732084
2. ! [X0] : ((~generous(X0) | ~tall(X0)) => ~tall(X0)) [input p1]
6. ! [X0] : ((old(X0) <~> ~tall(X0)) <=> (old(X0) | funny(X0))) [input p5]
10. ! [X0] : ((quiet(X0) <~> ~generous(X0)) => (~wise(X0) & ~curious(X0))) [input p9]
16. ! [X0] : ((quiet(X0) <~> ~rich(X0)) <=> (generous(X0) & rich(X0))) [input p15]
20. ~funny(john) & ~rich(john) [input p19]
24. curious(john) [input hypothesis]
27. ! [X0] : (~tall(X0) | (generous(X0) & tall(X0))) [ennf transformation 2]
35. ! [X0] : ((~wise(X0) & ~curious(X0)) | (quiet(X0) <=> ~generous(X0))) [ennf transformation 10]
48. ! [X0] : ((((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0))))) [nnf transformation 6]
49. ! [X0] : ((((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0))))) [flattening 48]
53. ! [X0] : ((~wise(X0) & ~curious(X0)) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) [nnf transformation 35]
59. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | (~generous(X0) | ~rich(X0))) & ((generous(X0) & rich(X0)) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [nnf transformation 16]
60. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | ~generous(X0) | ~rich(X0)) & ((generous(X0) & rich(X0)) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [flattening 59]
75. ~tall(X0) | generous(X0) [cnf transformation 27]
86. old(X0) | funny(X0) | old(X0) | tall(X0) [cnf transformation 49]
90. tall(X0) | ~old(X0) | ~old(X0) [cnf transformation 49]
95. ~curious(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 53]
108. rich(X0) | quiet(X0) | rich(X0) [cnf transformation 60]
118. ~rich(john) [cnf transformation 20]
119. ~funny(john) [cnf transformation 20]
124. curious(john) [cnf transformation 24]
125. rich(X0) | quiet(X0) [duplicate literal removal 108]
127. old(X0) | funny(X0) | tall(X0) [duplicate literal removal 86]
128. ~old(X0) | tall(X0) [duplicate literal removal 90]
157. tall(X0) | funny(X0) [subsumption resolution 127,128]
239. quiet(john) [resolution 125,118]
245. generous(X0) | funny(X0) [resolution 157,75]
300. ~generous(john) | ~quiet(john) [resolution 95,124]
301. ~generous(john) [subsumption resolution 300,239]
334. funny(john) [resolution 245,301]
335. $false [subsumption resolution 334,119]
% SZS output end Proof for 2479154237883029148732084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is creative.
Everyone who is either tall or funny is not generous.
Everyone who is quiet is both patient and not rich and vice versa.
Everyone who is either quiet or not old is strong or not humble.
Everyone who is patient or curious is both curious and strong and vice versa.
Everyone who is not kind or not patient is not humble and vice versa.
Everyone who is not calm is not creative or wise.
If someone is either not calm or creative then susan is both tall and not humble.
Everyone who is either not creative or not funny is not strong.
If someone is both curious and not creative then fred is curious or not funny and vice versa.
Everyone who is patient or not rich is not creative.
Everyone who is rich is quiet or patient and vice versa.
Everyone who is both not old and not patient is both wise and not brave and vice versa.
If someone is not patient then someone is generous or not patient and vice versa.
If someone is either kind or not funny then someone is both patient and rich and vice versa.
If lucy is both not patient and patient then mary is not strong and vice versa.
Mary is either not calm or not curious.
Someone is both not old and not happy.
Mary is humble.
Someone is not happy.
Someone is either not tall or patient.
Alice is creative or tall.
Someone is kind or not funny. | Mary is quiet. | contradiction | (![X]:(~rich(X)=>creative(X)))&
(![X]:((tall(X)<~>funny(X))=>~generous(X)))&
(![X]:(quiet(X)<=>(patient(X)&~rich(X))))&
(![X]:((quiet(X)<~>~old(X))=>(strong(X)|~humble(X))))&
(![X]:((patient(X)|curious(X))<=>(curious(X)&strong(X))))&
(![X]:((~kind(X)|~patient(X))<=>~humble(X)))&
(![X]:(~calm(X)=>(~creative(X)|wise(X))))&
((?[X]:((~calm(X)<~>creative(X))))=>((tall(susan)&~humble(susan))))&
(![X]:((~creative(X)<~>~funny(X))=>~strong(X)))&
((?[X]:((curious(X)&~creative(X))))<=>((curious(fred)|~funny(fred))))&
(![X]:((patient(X)|~rich(X))=>~creative(X)))&
(![X]:(rich(X)<=>(quiet(X)|patient(X))))&
(![X]:((~old(X)&~patient(X))<=>(wise(X)&~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((generous(X)|~patient(X)))))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((patient(X)&rich(X)))))&
(((~patient(lucy)&patient(lucy)))<=>(~strong(mary)))&
((~calm(mary)<~>~curious(mary)))&
(?[X]:((~old(X)&~happy(X))))&
(humble(mary))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)<~>patient(X))))&
((creative(alice)|tall(alice)))&
(?[X]:((kind(X)|~funny(X)))) | quiet(mary) | [
"p0",
"p2",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 47738588634161517935037
% SZS output start Proof for 47738588634161517935037
1. ! [X0] : (~rich(X0) => creative(X0)) [input p0]
3. ! [X0] : (quiet(X0) <=> (~rich(X0) & patient(X0))) [input p2]
11. ! [X0] : ((~rich(X0) | patient(X0)) => ~creative(X0)) [input p10]
24. quiet(mary) [input hypothesis]
29. ! [X0] : (creative(X0) | rich(X0)) [ennf transformation 1]
37. ! [X0] : (~creative(X0) | (rich(X0) & ~patient(X0))) [ennf transformation 11]
39. ! [X0] : ((quiet(X0) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | ~quiet(X0))) [nnf transformation 3]
40. ! [X0] : ((quiet(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | ~quiet(X0))) [flattening 39]
77. creative(X0) | rich(X0) [cnf transformation 29]
81. ~quiet(X0) | ~rich(X0) [cnf transformation 40]
106. ~creative(X0) | rich(X0) [cnf transformation 37]
134. quiet(mary) [cnf transformation 24]
177. rich(X0) [subsumption resolution 106,77]
228. ~rich(mary) [resolution 81,134]
229. $false [subsumption resolution 228,177]
% SZS output end Proof for 47738588634161517935037
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not old and strong then fred is either not tall or not kind and vice versa. Everyone who is not strong is both brave and old. If someone is not strong or not calm then someone is not tall. If someone is not creative then someone is not strong and vice versa. Everyone who is not curious or tall is either humble or kind and vice versa. If someone is tall or creative then someone is both not humble and not calm and vice versa. If lucy is both not humble and patient then mary is either not strong or patient and vice versa. If alice is brave then someone is brave. If susan is quiet or kind then lucy is either strong or creative and vice versa. If someone is either not rich or tall then susan is not wise or not quiet. Everyone who is either rich or quiet is both happy and not old and vice versa. Everyone who is either strong or not strong is either not kind or not funny and vice versa. If susan is either funny or not brave then john is either patient or not brave. Everyone who is both not patient and tall is both not kind and not humble. If someone is calm or not patient then someone is not happy or not calm and vice versa. If someone is either not tall or tall then mary is either not funny or humble. Susan is creative or not kind. John is either not humble or calm. Someone is both not quiet and not rich. Paul is tall. Someone is either not strong or not happy. Paul is both brave and kind. Someone is creative or curious. Someone is not tall. | Paul is not humble. | entailment | (((~old(john)&strong(john)))<=>((~tall(fred)<~>~kind(fred))))&
(![X]:(~strong(X)=>(brave(X)&old(X))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:(~tall(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)|tall(X))<=>(humble(X)<~>kind(X))))&
((?[X]:((tall(X)|creative(X))))<=>(?[X]:((~humble(X)&~calm(X)))))&
(((~humble(lucy)&patient(lucy)))<=>((~strong(mary)<~>patient(mary))))&
((brave(alice))=>(?[X]:(brave(X))))&
(((quiet(susan)|kind(susan)))<=>((strong(lucy)<~>creative(lucy))))&
((?[X]:((~rich(X)<~>tall(X))))=>((~wise(susan)|~quiet(susan))))&
(![X]:((rich(X)<~>quiet(X))<=>(happy(X)&~old(X))))&
(![X]:((strong(X)<~>~strong(X))<=>(~kind(X)<~>~funny(X))))&
(((funny(susan)<~>~brave(susan)))=>((patient(john)<~>~brave(john))))&
(![X]:((~patient(X)&tall(X))=>(~kind(X)&~humble(X))))&
((?[X]:((calm(X)|~patient(X))))<=>(?[X]:((~happy(X)|~calm(X)))))&
((?[X]:((~tall(X)<~>tall(X))))=>((~funny(mary)<~>humble(mary))))&
((creative(susan)|~kind(susan)))&
((~humble(john)<~>calm(john)))&
(?[X]:((~quiet(X)&~rich(X))))&
(tall(paul))&
(?[X]:((~strong(X)<~>~happy(X))))&
((brave(paul)&kind(paul)))&
(?[X]:((creative(X)|curious(X))))&
(?[X]:(~tall(X))) | ~humble(paul) | [
"p4",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 709671506838837676950060
% SZS output start Proof for 709671506838837676950060
5. ! [X0] : ((tall(X0) | ~curious(X0)) <=> (humble(X0) <~> kind(X0))) [input p4]
20. tall(paul) [input p19]
22. kind(paul) & brave(paul) [input p21]
25. humble(paul) [input hypothesis]
48. ! [X0] : (((tall(X0) | ~curious(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) & (((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~tall(X0) & curious(X0)))) [nnf transformation 5]
49. ! [X0] : ((tall(X0) | ~curious(X0) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) & (((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~tall(X0) & curious(X0)))) [flattening 48]
96. ~humble(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 49]
150. tall(paul) [cnf transformation 20]
154. kind(paul) [cnf transformation 22]
157. humble(paul) [cnf transformation 25]
461. ~kind(paul) | ~tall(paul) [resolution 96,157]
464. ~tall(paul) [subsumption resolution 461,154]
465. $false [subsumption resolution 464,150]
% SZS output end Proof for 709671506838837676950060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or not happy is both not generous and humble and vice versa.
If someone is not creative then mary is either old or tall.
Everyone who is both curious and not creative is either not brave or not quiet.
Everyone who is either not old or not kind is both not rich and brave and vice versa.
If someone is either not creative or quiet then someone is not generous and vice versa.
Everyone who is either not quiet or kind is either not strong or brave.
If someone is old then paul is both funny and rich.
If paul is not brave then someone is not happy or old and vice versa.
If someone is not tall or creative then paul is both not brave and strong and vice versa.
Everyone who is patient or calm is kind or brave and vice versa.
Everyone who is not curious or not tall is both generous and not strong.
If someone is both not calm and humble then someone is not happy and vice versa.
Everyone who is kind or not brave is not tall.
Everyone who is both creative and patient is either old or not old.
If someone is both not wise and not humble then someone is both strong and not generous.
If mary is not patient or old then someone is brave and vice versa.
Susan is not curious or quiet.
Mary is not rich or wise.
Someone is generous.
Mary is either creative or not patient. | Susan is quiet. | entailment | (![X]:((calm(X)<~>~happy(X))<=>(~generous(X)&humble(X))))&
((?[X]:(~creative(X)))=>((old(mary)<~>tall(mary))))&
(![X]:((curious(X)&~creative(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(~rich(X)&brave(X))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)<~>kind(X))=>(~strong(X)<~>brave(X))))&
((?[X]:(old(X)))=>((funny(paul)&rich(paul))))&
((~brave(paul))<=>(?[X]:((~happy(X)|old(X)))))&
((?[X]:((~tall(X)|creative(X))))<=>((~brave(paul)&strong(paul))))&
(![X]:((patient(X)|calm(X))<=>(kind(X)|brave(X))))&
(![X]:((~curious(X)|~tall(X))=>(generous(X)&~strong(X))))&
((?[X]:((~calm(X)&humble(X))))<=>(?[X]:(~happy(X))))&
(![X]:((kind(X)|~brave(X))=>~tall(X)))&
(![X]:((creative(X)&patient(X))=>(old(X)<~>~old(X))))&
((?[X]:((~wise(X)&~humble(X))))=>(?[X]:((strong(X)&~generous(X)))))&
(((~patient(mary)|old(mary)))<=>(?[X]:(brave(X))))&
((~curious(susan)|quiet(susan)))&
((~rich(mary)|wise(mary)))&
(?[X]:(generous(X)))&
((creative(mary)<~>~patient(mary))) | quiet(susan) | [
"p5",
"p8",
"p10",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 891038432964613657717843
% SZS output start Proof for 891038432964613657717843
6. ! [X0] : ((~quiet(X0) <~> kind(X0)) => (~strong(X0) <~> brave(X0))) [input p5]
9. ? [X0] : (creative(X0) | ~tall(X0)) <=> (strong(paul) & ~brave(paul)) [input p8]
11. ! [X0] : ((~tall(X0) | ~curious(X0)) => (~strong(X0) & generous(X0))) [input p10]
13. ! [X0] : ((~brave(X0) | kind(X0)) => ~tall(X0)) [input p12]
17. quiet(susan) | ~curious(susan) [input p16]
21. ~quiet(susan) [input hypothesis]
31. ! [X0] : ((~strong(X0) <~> brave(X0)) | (~quiet(X0) <=> kind(X0))) [ennf transformation 6]
33. ! [X0] : ((~strong(X0) & generous(X0)) | (tall(X0) & curious(X0))) [ennf transformation 11]
34. ! [X0] : (~tall(X0) | (brave(X0) & ~kind(X0))) [ennf transformation 13]
48. ! [X0] : (((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0)))) [nnf transformation 31]
53. (? [X0] : (creative(X0) | ~tall(X0)) | (~strong(paul) | brave(paul))) & ((strong(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & tall(X0))) [nnf transformation 9]
54. (? [X0] : (creative(X0) | ~tall(X0)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & tall(X0))) [flattening 53]
55. (? [X0] : (creative(X0) | ~tall(X0)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X1] : (~creative(X1) & tall(X1))) [rectify 54]
56. ? [X0] : (creative(X0) | ~tall(X0)) => (creative(sK3) | ~tall(sK3)) [choice axiom]
57. ((creative(sK3) | ~tall(sK3)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X1] : (~creative(X1) & tall(X1))) [skolemisation 55,56]
96. ~brave(X0) | strong(X0) | kind(X0) | quiet(X0) [cnf transformation 48]
102. ~brave(paul) | tall(X1) [cnf transformation 57]
104. strong(paul) | tall(X1) [cnf transformation 57]
113. ~strong(X0) | curious(X0) [cnf transformation 33]
114. ~strong(X0) | tall(X0) [cnf transformation 33]
118. ~kind(X0) | ~tall(X0) [cnf transformation 34]
119. ~tall(X0) | brave(X0) [cnf transformation 34]
125. quiet(susan) | ~curious(susan) [cnf transformation 17]
129. ~quiet(susan) [cnf transformation 21]
177. 12 <=> brave(paul) [avatar definition]
179. ~brave(paul) <- (~12) [avatar component clause 177]
195. 16 <=> strong(paul) [avatar definition]
196. strong(paul) <- (16) [avatar component clause 195]
212. 20 <=> ! [X1] : tall(X1) [avatar definition]
213. tall(X1) <- (20) [avatar component clause 212]
214. 20 | 16 [avatar split clause 104,195,212]
216. 20 | ~12 [avatar split clause 102,177,212]
250. 28 <=> curious(susan) [avatar definition]
252. ~curious(susan) <- (~28) [avatar component clause 250]
254. 29 <=> quiet(susan) [avatar definition]
255. ~quiet(susan) <- (~29) [avatar component clause 254]
257. ~28 | 29 [avatar split clause 125,254,250]
264. ~29 [avatar split clause 129,254]
275. tall(paul) <- (16) [resolution 114,196]
277. brave(paul) <- (16) [resolution 275,119]
278. $false <- (~12, 16) [subsumption resolution 277,179]
279. 12 | ~16 [avatar contradiction clause 278]
282. brave(X0) <- (20) [resolution 213,119]
384. strong(X1) | kind(X1) | quiet(X1) <- (20) [resolution 96,282]
388. kind(X3) | quiet(X3) | curious(X3) <- (20) [resolution 384,113]
406. quiet(X4) | curious(X4) | ~tall(X4) <- (20) [resolution 388,118]
408. quiet(X4) | curious(X4) <- (20) [subsumption resolution 406,213]
413. curious(susan) <- (20, ~29) [resolution 408,255]
415. $false <- (20, ~28, ~29) [subsumption resolution 413,252]
416. ~20 | 28 | 29 [avatar contradiction clause 415]
417. $false [avatar sat refutation 214,216,257,264,279,416]
% SZS output end Proof for 891038432964613657717843
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or tall is not generous and vice versa.
Everyone who is humble or brave is kind.
If someone is not strong then alice is quiet.
Everyone who is not strong is both not creative and curious and vice versa.
Everyone who is not calm is old or not creative and vice versa.
If paul is funny or not tall then paul is rich or happy.
If someone is either not happy or brave then paul is either tall or not kind.
Everyone who is both creative and brave is not curious.
If someone is funny or not funny then paul is not strong or happy and vice versa.
If susan is curious then lucy is either patient or old.
If someone is both not quiet and kind then someone is tall or not strong.
Everyone who is not brave is not calm or not kind.
Everyone who is not generous is either old or tall and vice versa.
If someone is creative then alice is either happy or not old and vice versa.
Everyone who is not curious or generous is either happy or tall and vice versa.
Everyone who is generous is both strong and not strong.
Susan is strong or not brave.
Someone is either not patient or not rich.
Someone is not strong or not kind.
Alice is quiet or old.
Someone is not curious or not patient.
Mary is either not creative or tall.
Susan is curious or strong.
Someone is not kind or generous. | Paul is not humble. | neutral | (![X]:((~patient(X)|tall(X))<=>~generous(X)))&
(![X]:((humble(X)|brave(X))=>kind(X)))&
((?[X]:(~strong(X)))=>(quiet(alice)))&
(![X]:(~strong(X)<=>(~creative(X)&curious(X))))&
(![X]:(~calm(X)<=>(old(X)|~creative(X))))&
(((funny(paul)|~tall(paul)))=>((rich(paul)|happy(paul))))&
((?[X]:((~happy(X)<~>brave(X))))=>((tall(paul)<~>~kind(paul))))&
(![X]:((creative(X)&brave(X))=>~curious(X)))&
((?[X]:((funny(X)|~funny(X))))<=>((~strong(paul)|happy(paul))))&
((curious(susan))=>((patient(lucy)<~>old(lucy))))&
((?[X]:((~quiet(X)&kind(X))))=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:(~brave(X)=>(~calm(X)|~kind(X))))&
(![X]:(~generous(X)<=>(old(X)<~>tall(X))))&
((?[X]:(creative(X)))<=>((happy(alice)<~>~old(alice))))&
(![X]:((~curious(X)|generous(X))<=>(happy(X)<~>tall(X))))&
(![X]:(generous(X)=>(strong(X)&~strong(X))))&
((strong(susan)|~brave(susan)))&
(?[X]:((~patient(X)<~>~rich(X))))&
(?[X]:((~strong(X)|~kind(X))))&
((quiet(alice)|old(alice)))&
(?[X]:((~curious(X)|~patient(X))))&
((~creative(mary)<~>tall(mary)))&
((curious(susan)|strong(susan)))&
(?[X]:((~kind(X)|generous(X)))) | ~humble(paul) | [] | null | 0 |
If fred is rich then someone is not kind and vice versa.
Everyone who is patient is either wise or not funny.
If someone is either strong or not funny then someone is both rich and funny and vice versa.
If someone is not funny or happy then someone is not tall.
Everyone who is either not calm or brave is not brave.
Everyone who is both not tall and not rich is both patient and rich.
Everyone who is not brave or happy is both not kind and funny.
Everyone who is both not kind and happy is creative or not kind.
Everyone who is either strong or not brave is either not old or not wise and vice versa.
If someone is either old or not tall then someone is both generous and patient and vice versa.
If susan is funny then someone is not rich or not wise and vice versa.
Everyone who is both not patient and rich is happy or humble.
Everyone who is both not strong and quiet is either curious or not strong.
Everyone who is wise is both patient and quiet and vice versa.
If john is quiet then paul is either creative or calm and vice versa.
Everyone who is brave is both not creative and rich and vice versa.
Someone is either not happy or not funny.
John is both not rich and not kind.
Someone is quiet or not quiet.
John is either not rich or quiet.
Someone is either rich or kind.
Mary is curious or not rich.
Someone is not creative or generous. | John is not patient. | entailment | ((rich(fred))<=>(?[X]:(~kind(X))))&
(![X]:(patient(X)=>(wise(X)<~>~funny(X))))&
((?[X]:((strong(X)<~>~funny(X))))<=>(?[X]:((rich(X)&funny(X)))))&
((?[X]:((~funny(X)|happy(X))))=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)<~>brave(X))=>~brave(X)))&
(![X]:((~tall(X)&~rich(X))=>(patient(X)&rich(X))))&
(![X]:((~brave(X)|happy(X))=>(~kind(X)&funny(X))))&
(![X]:((~kind(X)&happy(X))=>(creative(X)|~kind(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(~old(X)<~>~wise(X))))&
((?[X]:((old(X)<~>~tall(X))))<=>(?[X]:((generous(X)&patient(X)))))&
((funny(susan))<=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:((~patient(X)&rich(X))=>(happy(X)|humble(X))))&
(![X]:((~strong(X)&quiet(X))=>(curious(X)<~>~strong(X))))&
(![X]:(wise(X)<=>(patient(X)&quiet(X))))&
((quiet(john))<=>((creative(paul)<~>calm(paul))))&
(![X]:(brave(X)<=>(~creative(X)&rich(X))))&
(?[X]:((~happy(X)<~>~funny(X))))&
((~rich(john)&~kind(john)))&
(?[X]:((quiet(X)|~quiet(X))))&
((~rich(john)<~>quiet(john)))&
(?[X]:((rich(X)<~>kind(X))))&
((curious(mary)|~rich(mary)))&
(?[X]:((~creative(X)|generous(X)))) | ~patient(john) | [
"p1",
"p6",
"p13",
"p15",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3079586257759729997182151
% SZS output start Proof for 3079586257759729997182151
2. ! [X0] : (patient(X0) => (wise(X0) <~> ~funny(X0))) [input p1]
7. ! [X0] : ((happy(X0) | ~brave(X0)) => (funny(X0) & ~kind(X0))) [input p6]
14. ! [X0] : (wise(X0) <=> (quiet(X0) & patient(X0))) [input p13]
16. ! [X0] : (brave(X0) <=> (rich(X0) & ~creative(X0))) [input p15]
18. ~kind(john) & ~rich(john) [input p17]
20. ~rich(john) <~> quiet(john) [input p19]
24. patient(john) [input hypothesis]
29. ! [X0] : ((wise(X0) <~> ~funny(X0)) | ~patient(X0)) [ennf transformation 2]
34. ! [X0] : ((funny(X0) & ~kind(X0)) | (~happy(X0) & brave(X0))) [ennf transformation 7]
43. ! [X0] : (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | ~patient(X0)) [nnf transformation 29]
64. ! [X0] : ((wise(X0) | (~quiet(X0) | ~patient(X0))) & ((quiet(X0) & patient(X0)) | ~wise(X0))) [nnf transformation 14]
65. ! [X0] : ((wise(X0) | ~quiet(X0) | ~patient(X0)) & ((quiet(X0) & patient(X0)) | ~wise(X0))) [flattening 64]
67. ! [X0] : ((brave(X0) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | ~brave(X0))) [nnf transformation 16]
68. ! [X0] : ((brave(X0) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | ~brave(X0))) [flattening 67]
74. (~quiet(john) | rich(john)) & (quiet(john) | ~rich(john)) [nnf transformation 20]
82. ~funny(X0) | wise(X0) | ~patient(X0) [cnf transformation 43]
98. brave(X0) | funny(X0) [cnf transformation 34]
121. ~wise(X0) | quiet(X0) [cnf transformation 65]
128. ~brave(X0) | rich(X0) [cnf transformation 68]
132. ~rich(john) [cnf transformation 18]
136. ~quiet(john) | rich(john) [cnf transformation 74]
141. patient(john) [cnf transformation 24]
262. 28 <=> quiet(john) [avatar definition]
263. ~quiet(john) <- (~28) [avatar component clause 262]
271. ~quiet(john) [subsumption resolution 136,132]
272. ~28 [avatar split clause 271,262]
301. funny(X0) | rich(X0) [resolution 128,98]
473. ~patient(X0) | wise(X0) | rich(X0) [resolution 301,82]
535. wise(john) | rich(john) [resolution 473,141]
537. wise(john) [subsumption resolution 535,132]
552. quiet(john) [resolution 537,121]
574. $false <- (~28) [subsumption resolution 552,263]
575. 28 [avatar contradiction clause 574]
576. $false [avatar sat refutation 272,575]
% SZS output end Proof for 3079586257759729997182151
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is either calm or strong and vice versa.
Everyone who is brave is either happy or not generous.
Everyone who is curious is kind.
If mary is not brave then someone is either humble or brave and vice versa.
Everyone who is either humble or happy is either not rich or not humble and vice versa.
If alice is both tall and kind then someone is creative and vice versa.
Everyone who is either quiet or not tall is generous or not tall and vice versa.
Everyone who is both not calm and not rich is both old and generous.
If someone is both quiet and strong then mary is not curious or not calm and vice versa.
Everyone who is calm is wise and vice versa.
If someone is either not generous or not humble then john is not rich and vice versa.
If lucy is either not curious or not humble then fred is not curious or not happy and vice versa.
If someone is rich or strong then alice is both generous and not patient and vice versa.
Everyone who is patient is not wise or not funny and vice versa.
Someone is humble.
Someone is generous.
Someone is not rich or not strong.
Someone is either funny or quiet.
Fred is either not wise or not strong.
Someone is old or not funny.
Someone is quiet or tall.
Mary is either not generous or not funny. | Lucy is not brave. | neutral | (![X]:(calm(X)<=>(calm(X)<~>strong(X))))&
(![X]:(brave(X)=>(happy(X)<~>~generous(X))))&
(![X]:(curious(X)=>kind(X)))&
((~brave(mary))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:((humble(X)<~>happy(X))<=>(~rich(X)<~>~humble(X))))&
(((tall(alice)&kind(alice)))<=>(?[X]:(creative(X))))&
(![X]:((quiet(X)<~>~tall(X))<=>(generous(X)|~tall(X))))&
(![X]:((~calm(X)&~rich(X))=>(old(X)&generous(X))))&
((?[X]:((quiet(X)&strong(X))))<=>((~curious(mary)|~calm(mary))))&
(![X]:(calm(X)<=>wise(X)))&
((?[X]:((~generous(X)<~>~humble(X))))<=>(~rich(john)))&
(((~curious(lucy)<~>~humble(lucy)))<=>((~curious(fred)|~happy(fred))))&
((?[X]:((rich(X)|strong(X))))<=>((generous(alice)&~patient(alice))))&
(![X]:(patient(X)<=>(~wise(X)|~funny(X))))&
(?[X]:(humble(X)))&
(?[X]:(generous(X)))&
(?[X]:((~rich(X)|~strong(X))))&
(?[X]:((funny(X)<~>quiet(X))))&
((~wise(fred)<~>~strong(fred)))&
(?[X]:((old(X)|~funny(X))))&
(?[X]:((quiet(X)|tall(X))))&
((~generous(mary)<~>~funny(mary))) | ~brave(lucy) | [] | null | 0 |
Everyone who is not tall is both brave and quiet and vice versa. Everyone who is both not happy and strong is either creative or patient and vice versa. If alice is either not rich or strong then paul is both kind and humble. Everyone who is either not curious or not rich is either wise or not wise and vice versa. If someone is not wise or not calm then susan is both humble and strong. Everyone who is not old or curious is both not old and not quiet and vice versa. If fred is either not wise or humble then alice is both not humble and wise. Everyone who is either not brave or not kind is either strong or not calm. Everyone who is funny or not tall is calm or humble. Everyone who is either not tall or not strong is either rich or not humble and vice versa. Everyone who is either not strong or creative is old and vice versa. Everyone who is not rich or not patient is both not rich and not funny. Everyone who is both not kind and patient is not old or happy and vice versa. If someone is brave or not strong then someone is not calm or not brave. Everyone who is both humble and tall is either rich or not tall and vice versa. Everyone who is tall or not calm is not happy and vice versa. Susan is quiet or not generous. Someone is both not tall and creative. John is old or not happy. Someone is old. Someone is creative. Someone is both not happy and not old. | Fred is humble. | neutral | (![X]:(~tall(X)<=>(brave(X)&quiet(X))))&
(![X]:((~happy(X)&strong(X))<=>(creative(X)<~>patient(X))))&
(((~rich(alice)<~>strong(alice)))=>((kind(paul)&humble(paul))))&
(![X]:((~curious(X)<~>~rich(X))<=>(wise(X)<~>~wise(X))))&
((?[X]:((~wise(X)|~calm(X))))=>((humble(susan)&strong(susan))))&
(![X]:((~old(X)|curious(X))<=>(~old(X)&~quiet(X))))&
(((~wise(fred)<~>humble(fred)))=>((~humble(alice)&wise(alice))))&
(![X]:((~brave(X)<~>~kind(X))=>(strong(X)<~>~calm(X))))&
(![X]:((funny(X)|~tall(X))=>(calm(X)|humble(X))))&
(![X]:((~tall(X)<~>~strong(X))<=>(rich(X)<~>~humble(X))))&
(![X]:((~strong(X)<~>creative(X))<=>old(X)))&
(![X]:((~rich(X)|~patient(X))=>(~rich(X)&~funny(X))))&
(![X]:((~kind(X)&patient(X))<=>(~old(X)|happy(X))))&
((?[X]:((brave(X)|~strong(X))))=>(?[X]:((~calm(X)|~brave(X)))))&
(![X]:((humble(X)&tall(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((tall(X)|~calm(X))<=>~happy(X)))&
((quiet(susan)|~generous(susan)))&
(?[X]:((~tall(X)&creative(X))))&
((old(john)|~happy(john)))&
(?[X]:(old(X)))&
(?[X]:(creative(X)))&
(?[X]:((~happy(X)&~old(X)))) | humble(fred) | [] | null | 0 |
If someone is humble then fred is not patient or not happy and vice versa. If someone is not brave then fred is both rich and quiet and vice versa. Everyone who is either quiet or not curious is rich or not rich and vice versa. Everyone who is both generous and creative is either not old or old and vice versa. If fred is humble or not patient then someone is either not tall or not kind and vice versa. If someone is happy then alice is either happy or brave. If someone is strong then someone is either quiet or not happy and vice versa. If john is not quiet or not curious then someone is not brave or rich and vice versa. If someone is wise or not patient then someone is not quiet or not calm. If someone is both not strong and not curious then someone is both not patient and not happy. Everyone who is both happy and humble is both not old and not brave and vice versa. Everyone who is curious or rich is both old and not humble and vice versa. If mary is tall or creative then someone is either not tall or kind and vice versa. Everyone who is both curious and not old is either curious or not wise and vice versa. If someone is wise then mary is not quiet and vice versa. Everyone who is not creative is calm or not old. Lucy is wise. Someone is curious. Someone is both strong and wise. Lucy is either not tall or brave. Lucy is either strong or not brave. Someone is not wise. | Mary is old. | neutral | ((?[X]:(humble(X)))<=>((~patient(fred)|~happy(fred))))&
((?[X]:(~brave(X)))<=>((rich(fred)&quiet(fred))))&
(![X]:((quiet(X)<~>~curious(X))<=>(rich(X)|~rich(X))))&
(![X]:((generous(X)&creative(X))<=>(~old(X)<~>old(X))))&
(((humble(fred)|~patient(fred)))<=>(?[X]:((~tall(X)<~>~kind(X)))))&
((?[X]:(happy(X)))=>((happy(alice)<~>brave(alice))))&
((?[X]:(strong(X)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
(((~quiet(john)|~curious(john)))<=>(?[X]:((~brave(X)|rich(X)))))&
((?[X]:((wise(X)|~patient(X))))=>(?[X]:((~quiet(X)|~calm(X)))))&
((?[X]:((~strong(X)&~curious(X))))=>(?[X]:((~patient(X)&~happy(X)))))&
(![X]:((happy(X)&humble(X))<=>(~old(X)&~brave(X))))&
(![X]:((curious(X)|rich(X))<=>(old(X)&~humble(X))))&
(((tall(mary)|creative(mary)))<=>(?[X]:((~tall(X)<~>kind(X)))))&
(![X]:((curious(X)&~old(X))<=>(curious(X)<~>~wise(X))))&
((?[X]:(wise(X)))<=>(~quiet(mary)))&
(![X]:(~creative(X)=>(calm(X)|~old(X))))&
(wise(lucy))&
(?[X]:(curious(X)))&
(?[X]:((strong(X)&wise(X))))&
((~tall(lucy)<~>brave(lucy)))&
((strong(lucy)<~>~brave(lucy)))&
(?[X]:(~wise(X))) | old(mary) | [] | null | 0 |
Everyone who is not rich or tall is both calm and not old and vice versa.
If someone is either not calm or not generous then john is either rich or calm.
Everyone who is either generous or not patient is either not happy or not curious and vice versa.
Everyone who is calm is not wise or not calm.
If someone is both tall and generous then someone is both not creative and generous and vice versa.
If mary is both not kind and not wise then john is not calm.
Everyone who is either not strong or not tall is not tall and vice versa.
Everyone who is quiet or not generous is patient or not kind and vice versa.
If someone is not humble or not tall then someone is not funny or not happy.
If susan is both patient and happy then mary is both tall and not brave and vice versa.
If someone is generous or brave then lucy is either not generous or not strong.
If fred is both not creative and not rich then susan is not quiet or not rich.
Everyone who is not kind is happy and vice versa.
Everyone who is either tall or not old is either not brave or funny.
Everyone who is kind is rich or strong and vice versa.
Everyone who is not humble is both generous and old and vice versa.
Someone is either not old or funny.
Lucy is not generous.
Susan is either strong or not wise.
Susan is both not calm and patient.
Someone is calm.
Mary is either not patient or not strong.
Susan is either not brave or old. | Mary is curious. | contradiction | (![X]:((~rich(X)|tall(X))<=>(calm(X)&~old(X))))&
((?[X]:((~calm(X)<~>~generous(X))))=>((rich(john)<~>calm(john))))&
(![X]:((generous(X)<~>~patient(X))<=>(~happy(X)<~>~curious(X))))&
(![X]:(calm(X)=>(~wise(X)|~calm(X))))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((~creative(X)&generous(X)))))&
(((~kind(mary)&~wise(mary)))=>(~calm(john)))&
(![X]:((~strong(X)<~>~tall(X))<=>~tall(X)))&
(![X]:((quiet(X)|~generous(X))<=>(patient(X)|~kind(X))))&
((?[X]:((~humble(X)|~tall(X))))=>(?[X]:((~funny(X)|~happy(X)))))&
(((patient(susan)&happy(susan)))<=>((tall(mary)&~brave(mary))))&
((?[X]:((generous(X)|brave(X))))=>((~generous(lucy)<~>~strong(lucy))))&
(((~creative(fred)&~rich(fred)))=>((~quiet(susan)|~rich(susan))))&
(![X]:(~kind(X)<=>happy(X)))&
(![X]:((tall(X)<~>~old(X))=>(~brave(X)<~>funny(X))))&
(![X]:(kind(X)<=>(rich(X)|strong(X))))&
(![X]:(~humble(X)<=>(generous(X)&old(X))))&
(?[X]:((~old(X)<~>funny(X))))&
(~generous(lucy))&
((strong(susan)<~>~wise(susan)))&
((~calm(susan)&patient(susan)))&
(?[X]:(calm(X)))&
((~patient(mary)<~>~strong(mary)))&
((~brave(susan)<~>old(susan))) | curious(mary) | [
"p2",
"p6",
"p7",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3392823923980134844874423
% SZS output start Proof for 3392823923980134844874423
3. ! [X0] : ((generous(X0) <~> ~patient(X0)) <=> (~happy(X0) <~> ~curious(X0))) [input p2]
7. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> ~tall(X0)) [input p6]
8. ! [X0] : ((~generous(X0) | quiet(X0)) <=> (~kind(X0) | patient(X0))) [input p7]
13. ! [X0] : (~kind(X0) <=> happy(X0)) [input p12]
15. ! [X0] : (kind(X0) <=> (strong(X0) | rich(X0))) [input p14]
22. ~patient(mary) <~> ~strong(mary) [input p21]
24. curious(mary) [input hypothesis]
43. ! [X0] : ((((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0)))) & (((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0))))) [nnf transformation 3]
49. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | tall(X0)) & (~tall(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 7]
50. ! [X0] : (((~generous(X0) | quiet(X0)) | (kind(X0) & ~patient(X0))) & ((~kind(X0) | patient(X0)) | (generous(X0) & ~quiet(X0)))) [nnf transformation 8]
51. ! [X0] : ((~generous(X0) | quiet(X0) | (kind(X0) & ~patient(X0))) & (~kind(X0) | patient(X0) | (generous(X0) & ~quiet(X0)))) [flattening 50]
58. ! [X0] : ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0))) [nnf transformation 13]
60. ! [X0] : ((kind(X0) | (~strong(X0) & ~rich(X0))) & ((strong(X0) | rich(X0)) | ~kind(X0))) [nnf transformation 15]
61. ! [X0] : ((kind(X0) | (~strong(X0) & ~rich(X0))) & (strong(X0) | rich(X0) | ~kind(X0))) [flattening 60]
68. (strong(mary) | patient(mary)) & (~strong(mary) | ~patient(mary)) [nnf transformation 22]
85. ~curious(X0) | ~generous(X0) | patient(X0) | happy(X0) [cnf transformation 43]
93. ~tall(X0) | ~tall(X0) | strong(X0) [cnf transformation 49]
96. tall(X0) | strong(X0) | tall(X0) [cnf transformation 49]
98. ~kind(X0) | patient(X0) | generous(X0) [cnf transformation 51]
112. kind(X0) | happy(X0) [cnf transformation 58]
113. ~kind(X0) | ~happy(X0) [cnf transformation 58]
120. kind(X0) | ~strong(X0) [cnf transformation 61]
130. ~strong(mary) | ~patient(mary) [cnf transformation 68]
134. curious(mary) [cnf transformation 24]
135. ~tall(X0) | strong(X0) [duplicate literal removal 93]
136. strong(X0) | tall(X0) [duplicate literal removal 96]
189. strong(X0) [subsumption resolution 135,136]
257. kind(X0) [subsumption resolution 120,189]
271. ~patient(mary) [subsumption resolution 130,189]
287. ~happy(X1) [resolution 113,257]
289. patient(X0) | generous(X0) | happy(X0) [resolution 98,112]
291. patient(X0) | generous(X0) [subsumption resolution 289,287]
292. generous(mary) [resolution 291,271]
325. ~generous(mary) | patient(mary) | happy(mary) [resolution 85,134]
328. patient(mary) | happy(mary) [subsumption resolution 325,292]
329. happy(mary) [subsumption resolution 328,271]
330. $false [subsumption resolution 329,287]
% SZS output end Proof for 3392823923980134844874423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then someone is generous.
If paul is both quiet and creative then susan is not funny.
Everyone who is both brave and funny is happy or tall.
Everyone who is either not funny or not rich is both not rich and not tall.
Everyone who is either not brave or wise is humble and vice versa.
If someone is both brave and not patient then lucy is either brave or not kind and vice versa.
Everyone who is either not rich or not happy is not curious and vice versa.
Everyone who is both curious and not rich is brave and vice versa.
If someone is both creative and old then lucy is humble or happy.
If someone is both strong and kind then mary is either not wise or not happy.
Everyone who is not happy or not generous is old.
Everyone who is either not strong or not funny is both not old and curious and vice versa.
Everyone who is not patient or not curious is rich.
Everyone who is both curious and not patient is both not curious and generous.
Everyone who is quiet is both calm and not tall.
If lucy is not kind or tall then paul is not tall or not kind and vice versa.
Paul is either not happy or not wise.
Lucy is rich.
Susan is either not creative or not brave.
Someone is both not strong and patient.
John is both not curious and rich.
John is not happy.
Someone is either rich or happy.
Someone is either not strong or not generous. | John is strong. | entailment | ((?[X]:(old(X)))=>(?[X]:(generous(X))))&
(((quiet(paul)&creative(paul)))=>(~funny(susan)))&
(![X]:((brave(X)&funny(X))=>(happy(X)|tall(X))))&
(![X]:((~funny(X)<~>~rich(X))=>(~rich(X)&~tall(X))))&
(![X]:((~brave(X)<~>wise(X))<=>humble(X)))&
((?[X]:((brave(X)&~patient(X))))<=>((brave(lucy)<~>~kind(lucy))))&
(![X]:((~rich(X)<~>~happy(X))<=>~curious(X)))&
(![X]:((curious(X)&~rich(X))<=>brave(X)))&
((?[X]:((creative(X)&old(X))))=>((humble(lucy)|happy(lucy))))&
((?[X]:((strong(X)&kind(X))))=>((~wise(mary)<~>~happy(mary))))&
(![X]:((~happy(X)|~generous(X))=>old(X)))&
(![X]:((~strong(X)<~>~funny(X))<=>(~old(X)&curious(X))))&
(![X]:((~patient(X)|~curious(X))=>rich(X)))&
(![X]:((curious(X)&~patient(X))=>(~curious(X)&generous(X))))&
(![X]:(quiet(X)=>(calm(X)&~tall(X))))&
(((~kind(lucy)|tall(lucy)))<=>((~tall(paul)|~kind(paul))))&
((~happy(paul)<~>~wise(paul)))&
(rich(lucy))&
((~creative(susan)<~>~brave(susan)))&
(?[X]:((~strong(X)&patient(X))))&
((~curious(john)&rich(john)))&
(~happy(john))&
(?[X]:((rich(X)<~>happy(X))))&
(?[X]:((~strong(X)<~>~generous(X)))) | strong(john) | [
"p3",
"p10",
"p11",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4966996487215415447164039
% SZS output start Proof for 4966996487215415447164039
4. ! [X0] : ((~funny(X0) <~> ~rich(X0)) => (~tall(X0) & ~rich(X0))) [input p3]
11. ! [X0] : ((~generous(X0) | ~happy(X0)) => old(X0)) [input p10]
12. ! [X0] : ((~strong(X0) <~> ~funny(X0)) <=> (curious(X0) & ~old(X0))) [input p11]
21. rich(john) & ~curious(john) [input p20]
22. ~happy(john) [input p21]
25. ~strong(john) [input hypothesis]
34. ! [X0] : ((~tall(X0) & ~rich(X0)) | (~funny(X0) <=> ~rich(X0))) [ennf transformation 4]
39. ! [X0] : (old(X0) | (generous(X0) & happy(X0))) [ennf transformation 11]
46. ! [X0] : ((~tall(X0) & ~rich(X0)) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0)))) [nnf transformation 34]
56. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | (~curious(X0) | old(X0))) & ((curious(X0) & ~old(X0)) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [nnf transformation 12]
57. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ~curious(X0) | old(X0)) & ((curious(X0) & ~old(X0)) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [flattening 56]
72. ~rich(X0) | ~rich(X0) | funny(X0) [cnf transformation 46]
94. happy(X0) | old(X0) [cnf transformation 39]
96. ~funny(X0) | ~old(X0) | strong(X0) [cnf transformation 57]
118. rich(john) [cnf transformation 21]
119. ~happy(john) [cnf transformation 22]
124. ~strong(john) [cnf transformation 25]
126. ~rich(X0) | funny(X0) [duplicate literal removal 72]
245. old(john) [resolution 94,119]
257. funny(john) [resolution 126,118]
305. ~old(john) | strong(john) [resolution 96,257]
308. strong(john) [subsumption resolution 305,245]
309. $false [subsumption resolution 308,124]
% SZS output end Proof for 4966996487215415447164039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and wise is either not curious or not calm and vice versa. If someone is happy or not kind then someone is either tall or kind. Everyone who is strong is both not kind and old and vice versa. Everyone who is creative or not strong is not calm or not happy. If someone is either not kind or patient then susan is both not happy and wise. Everyone who is old is both not strong and strong. Everyone who is happy is either not humble or not happy. If lucy is not funny or not brave then lucy is either funny or not curious and vice versa. Everyone who is both curious and brave is both not patient and old and vice versa. If someone is either curious or funny then mary is both not funny and not old. Everyone who is not funny or not brave is not wise. Everyone who is both not happy and brave is either not calm or strong and vice versa. Everyone who is both not generous and not wise is either not kind or not generous. Everyone who is both not tall and generous is brave or not brave and vice versa. If paul is not wise or not calm then fred is either not wise or not brave and vice versa. Everyone who is both kind and quiet is rich and vice versa. John is both humble and not wise. Lucy is not funny. Fred is not patient or not old. Someone is either quiet or wise. Lucy is brave. Someone is happy or not happy. | Fred is kind. | neutral | (![X]:((~generous(X)&wise(X))<=>(~curious(X)<~>~calm(X))))&
((?[X]:((happy(X)|~kind(X))))=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:(strong(X)<=>(~kind(X)&old(X))))&
(![X]:((creative(X)|~strong(X))=>(~calm(X)|~happy(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>((~happy(susan)&wise(susan))))&
(![X]:(old(X)=>(~strong(X)&strong(X))))&
(![X]:(happy(X)=>(~humble(X)<~>~happy(X))))&
(((~funny(lucy)|~brave(lucy)))<=>((funny(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&brave(X))<=>(~patient(X)&old(X))))&
((?[X]:((curious(X)<~>funny(X))))=>((~funny(mary)&~old(mary))))&
(![X]:((~funny(X)|~brave(X))=>~wise(X)))&
(![X]:((~happy(X)&brave(X))<=>(~calm(X)<~>strong(X))))&
(![X]:((~generous(X)&~wise(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~tall(X)&generous(X))<=>(brave(X)|~brave(X))))&
(((~wise(paul)|~calm(paul)))<=>((~wise(fred)<~>~brave(fred))))&
(![X]:((kind(X)&quiet(X))<=>rich(X)))&
((humble(john)&~wise(john)))&
(~funny(lucy))&
((~patient(fred)|~old(fred)))&
(?[X]:((quiet(X)<~>wise(X))))&
(brave(lucy))&
(?[X]:((happy(X)|~happy(X)))) | kind(fred) | [] | null | 0 |
Everyone who is either tall or humble is either not brave or curious.
If someone is either patient or not kind then mary is either curious or calm and vice versa.
Everyone who is either not funny or not brave is either happy or strong and vice versa.
If someone is kind or calm then john is either rich or curious.
If someone is tall or kind then alice is not creative.
If paul is both not creative and quiet then someone is not humble and vice versa.
Everyone who is kind or not creative is not strong.
Everyone who is not strong is creative or strong and vice versa.
Everyone who is not brave or rich is either curious or not funny.
Everyone who is both not brave and strong is both not kind and funny and vice versa.
Everyone who is not tall or not generous is generous or not humble and vice versa.
Everyone who is either happy or kind is not tall or not strong and vice versa.
If fred is either not brave or not kind then paul is both creative and patient and vice versa.
Everyone who is either not generous or not humble is either funny or not creative and vice versa.
Everyone who is wise is either creative or not humble.
Someone is both curious and brave.
Lucy is generous or old.
Someone is not creative or happy.
Lucy is generous or not happy.
Susan is both old and not quiet.
Someone is both quiet and not kind. | Mary is not funny. | entailment | (![X]:((tall(X)<~>humble(X))=>(~brave(X)<~>curious(X))))&
((?[X]:((patient(X)<~>~kind(X))))<=>((curious(mary)<~>calm(mary))))&
(![X]:((~funny(X)<~>~brave(X))<=>(happy(X)<~>strong(X))))&
((?[X]:((kind(X)|calm(X))))=>((rich(john)<~>curious(john))))&
((?[X]:((tall(X)|kind(X))))=>(~creative(alice)))&
(((~creative(paul)&quiet(paul)))<=>(?[X]:(~humble(X))))&
(![X]:((kind(X)|~creative(X))=>~strong(X)))&
(![X]:(~strong(X)<=>(creative(X)|strong(X))))&
(![X]:((~brave(X)|rich(X))=>(curious(X)<~>~funny(X))))&
(![X]:((~brave(X)&strong(X))<=>(~kind(X)&funny(X))))&
(![X]:((~tall(X)|~generous(X))<=>(generous(X)|~humble(X))))&
(![X]:((happy(X)<~>kind(X))<=>(~tall(X)|~strong(X))))&
(((~brave(fred)<~>~kind(fred)))<=>((creative(paul)&patient(paul))))&
(![X]:((~generous(X)<~>~humble(X))<=>(funny(X)<~>~creative(X))))&
(![X]:(wise(X)=>(creative(X)<~>~humble(X))))&
(?[X]:((curious(X)&brave(X))))&
((generous(lucy)|old(lucy)))&
(?[X]:((~creative(X)|happy(X))))&
((generous(lucy)|~happy(lucy)))&
((old(susan)&~quiet(susan)))&
(?[X]:((quiet(X)&~kind(X)))) | ~funny(mary) | [
"p4",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3988013242508600361963782
% SZS output start Proof for 3988013242508600361963782
5. ? [X0] : (kind(X0) | tall(X0)) => ~creative(alice) [input p4]
8. ! [X0] : (~strong(X0) <=> (strong(X0) | creative(X0))) [input p7]
10. ! [X0] : ((strong(X0) & ~brave(X0)) <=> (funny(X0) & ~kind(X0))) [input p9]
22. funny(mary) [input hypothesis]
28. ~creative(alice) | ! [X0] : (~kind(X0) & ~tall(X0)) [ennf transformation 5]
43. ! [X0] : ((~strong(X0) | (~strong(X0) & ~creative(X0))) & ((strong(X0) | creative(X0)) | strong(X0))) [nnf transformation 8]
44. ! [X0] : ((~strong(X0) | (~strong(X0) & ~creative(X0))) & (strong(X0) | creative(X0) | strong(X0))) [flattening 43]
46. ! [X0] : (((strong(X0) & ~brave(X0)) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | (~strong(X0) | brave(X0)))) [nnf transformation 10]
47. ! [X0] : (((strong(X0) & ~brave(X0)) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | ~strong(X0) | brave(X0))) [flattening 46]
86. ~creative(alice) | ~kind(X0) [cnf transformation 28]
92. strong(X0) | creative(X0) | strong(X0) [cnf transformation 44]
94. ~strong(X0) | ~strong(X0) [cnf transformation 44]
102. strong(X0) | ~funny(X0) | kind(X0) [cnf transformation 47]
134. funny(mary) [cnf transformation 22]
137. strong(X0) | creative(X0) [duplicate literal removal 92]
138. ~strong(X0) [duplicate literal removal 94]
182. 10 <=> ! [X0] : ~kind(X0) [avatar definition]
183. ~kind(X0) <- (10) [avatar component clause 182]
188. 11 <=> creative(alice) [avatar definition]
190. ~creative(alice) <- (~11) [avatar component clause 188]
191. 10 | ~11 [avatar split clause 86,188,182]
214. creative(X0) [subsumption resolution 137,138]
215. ~funny(X0) | kind(X0) [subsumption resolution 102,138]
251. $false <- (~11) [subsumption resolution 190,214]
252. 11 [avatar contradiction clause 251]
255. kind(mary) [resolution 215,134]
256. $false <- (10) [subsumption resolution 255,183]
257. ~10 [avatar contradiction clause 256]
258. $false [avatar sat refutation 191,252,257]
% SZS output end Proof for 3988013242508600361963782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is not strong.
Everyone who is either old or kind is patient or not happy and vice versa.
Everyone who is both not brave and not rich is not wise.
If someone is both not patient and not curious then someone is not brave and vice versa.
If someone is brave or not tall then someone is either not wise or generous.
Everyone who is both strong and generous is not kind.
If john is both rich and wise then alice is both kind and not brave and vice versa.
If someone is both generous and not kind then someone is both not creative and calm and vice versa.
Everyone who is either not strong or strong is not creative.
Everyone who is kind or calm is either brave or not rich and vice versa.
Everyone who is both kind and not generous is not quiet or rich and vice versa.
If john is not patient then someone is humble and vice versa.
If fred is not humble then john is brave and vice versa.
If susan is both wise and not tall then someone is both creative and strong and vice versa.
If someone is creative then lucy is either old or not wise and vice versa.
If someone is either strong or happy then mary is both humble and not rich and vice versa.
Someone is both not wise and not kind.
Someone is either not humble or not calm.
Fred is either happy or quiet.
Alice is kind or not quiet.
Someone is either not strong or brave.
Lucy is not old.
Someone is not strong.
John is both not old and happy. | Alice is not generous. | entailment | (![X]:(~old(X)=>~strong(X)))&
(![X]:((old(X)<~>kind(X))<=>(patient(X)|~happy(X))))&
(![X]:((~brave(X)&~rich(X))=>~wise(X)))&
((?[X]:((~patient(X)&~curious(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((brave(X)|~tall(X))))=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((strong(X)&generous(X))=>~kind(X)))&
(((rich(john)&wise(john)))<=>((kind(alice)&~brave(alice))))&
((?[X]:((generous(X)&~kind(X))))<=>(?[X]:((~creative(X)&calm(X)))))&
(![X]:((~strong(X)<~>strong(X))=>~creative(X)))&
(![X]:((kind(X)|calm(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((kind(X)&~generous(X))<=>(~quiet(X)|rich(X))))&
((~patient(john))<=>(?[X]:(humble(X))))&
((~humble(fred))<=>(brave(john)))&
(((wise(susan)&~tall(susan)))<=>(?[X]:((creative(X)&strong(X)))))&
((?[X]:(creative(X)))<=>((old(lucy)<~>~wise(lucy))))&
((?[X]:((strong(X)<~>happy(X))))<=>((humble(mary)&~rich(mary))))&
(?[X]:((~wise(X)&~kind(X))))&
(?[X]:((~humble(X)<~>~calm(X))))&
((happy(fred)<~>quiet(fred)))&
((kind(alice)|~quiet(alice)))&
(?[X]:((~strong(X)<~>brave(X))))&
(~old(lucy))&
(?[X]:(~strong(X)))&
((~old(john)&happy(john))) | ~generous(alice) | [
"p0",
"p1",
"p6",
"p9",
"p10",
"p11",
"p15",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2419540996511286312747086
% SZS output start Proof for 2419540996511286312747086
1. ! [X0] : (~old(X0) => ~strong(X0)) [input p0]
2. ! [X0] : ((old(X0) <~> kind(X0)) <=> (~happy(X0) | patient(X0))) [input p1]
7. (wise(john) & rich(john)) <=> (~brave(alice) & kind(alice)) [input p6]
10. ! [X0] : ((calm(X0) | kind(X0)) <=> (brave(X0) <~> ~rich(X0))) [input p9]
11. ! [X0] : ((~generous(X0) & kind(X0)) <=> (rich(X0) | ~quiet(X0))) [input p10]
12. ~patient(john) <=> ? [X0] : humble(X0) [input p11]
16. ? [X0] : (strong(X0) <~> happy(X0)) <=> (~rich(mary) & humble(mary)) [input p15]
20. ~quiet(alice) | kind(alice) [input p19]
24. happy(john) & ~old(john) [input p23]
25. generous(alice) [input hypothesis]
29. ! [X0] : (~strong(X0) | old(X0)) [ennf transformation 1]
36. ! [X0] : ((((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | (happy(X0) & ~patient(X0))) & ((~happy(X0) | patient(X0)) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0))))) [nnf transformation 2]
37. ! [X0] : ((((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | (happy(X0) & ~patient(X0))) & (~happy(X0) | patient(X0) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0))))) [flattening 36]
47. ((wise(john) & rich(john)) | (brave(alice) | ~kind(alice))) & ((~brave(alice) & kind(alice)) | (~wise(john) | ~rich(john))) [nnf transformation 7]
48. ((wise(john) & rich(john)) | brave(alice) | ~kind(alice)) & ((~brave(alice) & kind(alice)) | ~wise(john) | ~rich(john)) [flattening 47]
55. ! [X0] : (((calm(X0) | kind(X0)) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) & (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | (~calm(X0) & ~kind(X0)))) [nnf transformation 10]
56. ! [X0] : ((calm(X0) | kind(X0) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) & (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | (~calm(X0) & ~kind(X0)))) [flattening 55]
57. ! [X0] : (((~generous(X0) & kind(X0)) | (~rich(X0) & quiet(X0))) & ((rich(X0) | ~quiet(X0)) | (generous(X0) | ~kind(X0)))) [nnf transformation 11]
58. ! [X0] : (((~generous(X0) & kind(X0)) | (~rich(X0) & quiet(X0))) & (rich(X0) | ~quiet(X0) | generous(X0) | ~kind(X0))) [flattening 57]
59. (~patient(john) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | patient(john)) [nnf transformation 12]
60. (~patient(john) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | patient(john)) [rectify 59]
61. ? [X1] : humble(X1) => humble(sK5) [choice axiom]
62. (~patient(john) | ! [X0] : ~humble(X0)) & (humble(sK5) | patient(john)) [skolemisation 60,61]
73. (? [X0] : ((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | (rich(mary) | ~humble(mary))) & ((~rich(mary) & humble(mary)) | ! [X0] : ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0)))) [nnf transformation 16]
74. (? [X0] : ((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | rich(mary) | ~humble(mary)) & ((~rich(mary) & humble(mary)) | ! [X0] : ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0)))) [flattening 73]
75. (? [X0] : ((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | rich(mary) | ~humble(mary)) & ((~rich(mary) & humble(mary)) | ! [X1] : ((strong(X1) | ~happy(X1)) & (happy(X1) | ~strong(X1)))) [rectify 74]
76. ? [X0] : ((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) => ((~happy(sK8) | ~strong(sK8)) & (happy(sK8) | strong(sK8))) [choice axiom]
77. (((~happy(sK8) | ~strong(sK8)) & (happy(sK8) | strong(sK8))) | rich(mary) | ~humble(mary)) & ((~rich(mary) & humble(mary)) | ! [X1] : ((strong(X1) | ~happy(X1)) & (happy(X1) | ~strong(X1)))) [skolemisation 75,76]
89. ~strong(X0) | old(X0) [cnf transformation 29]
91. ~happy(X0) | patient(X0) | old(X0) | ~kind(X0) [cnf transformation 37]
107. rich(john) | brave(alice) | ~kind(alice) [cnf transformation 48]
117. ~brave(X0) | rich(X0) | ~kind(X0) [cnf transformation 56]
122. quiet(X0) | kind(X0) [cnf transformation 58]
123. ~rich(X0) | kind(X0) [cnf transformation 58]
125. ~generous(X0) | ~rich(X0) [cnf transformation 58]
127. ~patient(john) | ~humble(X0) [cnf transformation 62]
139. humble(mary) | strong(X1) | ~happy(X1) [cnf transformation 77]
150. ~quiet(alice) | kind(alice) [cnf transformation 20]
155. ~old(john) [cnf transformation 24]
156. happy(john) [cnf transformation 24]
157. generous(alice) [cnf transformation 25]
200. 10 <=> kind(alice) [avatar definition]
201. kind(alice) <- (10) [avatar component clause 200]
204. 11 <=> brave(alice) [avatar definition]
206. brave(alice) <- (11) [avatar component clause 204]
213. 13 <=> rich(john) [avatar definition]
215. rich(john) <- (13) [avatar component clause 213]
216. ~10 | 11 | 13 [avatar split clause 107,213,204,200]
247. 20 <=> ! [X0] : ~humble(X0) [avatar definition]
248. ~humble(X0) <- (20) [avatar component clause 247]
250. 21 <=> patient(john) [avatar definition]
253. 20 | ~21 [avatar split clause 127,250,247]
297. 30 <=> humble(mary) [avatar definition]
298. humble(mary) <- (30) [avatar component clause 297]
315. 34 <=> ! [X1] : (strong(X1) | ~happy(X1)) [avatar definition]
316. ~happy(X1) | strong(X1) <- (34) [avatar component clause 315]
322. 34 | 30 [avatar split clause 139,297,315]
344. kind(alice) [subsumption resolution 150,122]
345. 10 [avatar split clause 344,200]
358. $false <- (20, 30) [resolution 298,248]
359. ~20 | ~30 [avatar contradiction clause 358]
363. ~rich(alice) [resolution 125,157]
389. rich(alice) | ~kind(alice) <- (11) [resolution 117,206]
392. ~kind(alice) <- (11) [subsumption resolution 389,363]
393. $false <- (10, 11) [subsumption resolution 392,201]
394. ~10 | ~11 [avatar contradiction clause 393]
402. 47 <=> kind(john) [avatar definition]
403. kind(john) <- (47) [avatar component clause 402]
408. kind(john) <- (13) [resolution 215,123]
409. 47 | ~13 [avatar split clause 408,213,402]
415. patient(john) | old(john) | ~kind(john) [resolution 91,156]
433. patient(john) | ~kind(john) [subsumption resolution 415,155]
434. patient(john) <- (47) [subsumption resolution 433,403]
435. 21 | ~47 [avatar split clause 434,402,250]
480. strong(john) <- (34) [resolution 316,156]
509. old(john) <- (34) [resolution 480,89]
510. $false <- (34) [subsumption resolution 509,155]
511. ~34 [avatar contradiction clause 510]
512. $false [avatar sat refutation 216,253,322,345,359,394,409,435,511]
% SZS output end Proof for 2419540996511286312747086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If lucy is wise then fred is either kind or brave and vice versa.
Everyone who is either not calm or strong is both wise and not happy and vice versa.
Everyone who is creative is both creative and not strong and vice versa.
Everyone who is happy or curious is brave.
If mary is not curious then paul is not tall.
Everyone who is both not curious and not happy is either not curious or old.
Everyone who is happy is strong.
If susan is not funny then alice is tall and vice versa.
Everyone who is either not strong or curious is either old or calm and vice versa.
Everyone who is tall or generous is calm and vice versa.
Everyone who is either patient or not creative is not rich and vice versa.
If paul is funny or kind then someone is old or not curious.
Everyone who is not brave or not humble is either not happy or not humble.
Everyone who is either not strong or wise is both not kind and generous.
If someone is both funny and quiet then lucy is not rich.
Everyone who is not kind is either not happy or not old.
Paul is not old.
Alice is either not quiet or not funny.
Someone is both humble and not happy.
Susan is old.
Fred is strong or patient.
Alice is both not tall and old.
Paul is either not wise or calm. | Paul is tall. | contradiction | ((wise(lucy))<=>((kind(fred)<~>brave(fred))))&
(![X]:((~calm(X)<~>strong(X))<=>(wise(X)&~happy(X))))&
(![X]:(creative(X)<=>(creative(X)&~strong(X))))&
(![X]:((happy(X)|curious(X))=>brave(X)))&
((~curious(mary))=>(~tall(paul)))&
(![X]:((~curious(X)&~happy(X))=>(~curious(X)<~>old(X))))&
(![X]:(happy(X)=>strong(X)))&
((~funny(susan))<=>(tall(alice)))&
(![X]:((~strong(X)<~>curious(X))<=>(old(X)<~>calm(X))))&
(![X]:((tall(X)|generous(X))<=>calm(X)))&
(![X]:((patient(X)<~>~creative(X))<=>~rich(X)))&
(((funny(paul)|kind(paul)))=>(?[X]:((old(X)|~curious(X)))))&
(![X]:((~brave(X)|~humble(X))=>(~happy(X)<~>~humble(X))))&
(![X]:((~strong(X)<~>wise(X))=>(~kind(X)&generous(X))))&
((?[X]:((funny(X)&quiet(X))))=>(~rich(lucy)))&
(![X]:(~kind(X)=>(~happy(X)<~>~old(X))))&
(~old(paul))&
((~quiet(alice)<~>~funny(alice)))&
(?[X]:((humble(X)&~happy(X))))&
(old(susan))&
((strong(fred)|patient(fred)))&
((~tall(alice)&old(alice)))&
((~wise(paul)<~>calm(paul))) | tall(paul) | [
"p1",
"p6",
"p9",
"p13",
"p15",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7393205512134638707375557
% SZS output start Proof for 7393205512134638707375557
2. ! [X0] : ((~calm(X0) <~> strong(X0)) <=> (~happy(X0) & wise(X0))) [input p1]
7. ! [X0] : (happy(X0) => strong(X0)) [input p6]
10. ! [X0] : ((generous(X0) | tall(X0)) <=> calm(X0)) [input p9]
14. ! [X0] : ((~strong(X0) <~> wise(X0)) => (generous(X0) & ~kind(X0))) [input p13]
16. ! [X0] : (~kind(X0) => (~happy(X0) <~> ~old(X0))) [input p15]
17. ~old(paul) [input p16]
23. ~wise(paul) <~> calm(paul) [input p22]
24. tall(paul) [input hypothesis]
30. ! [X0] : (strong(X0) | ~happy(X0)) [ennf transformation 7]
34. ! [X0] : ((generous(X0) & ~kind(X0)) | (~strong(X0) <=> wise(X0))) [ennf transformation 14]
36. ! [X0] : ((~happy(X0) <~> ~old(X0)) | kind(X0)) [ennf transformation 16]
38. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (happy(X0) | ~wise(X0))) & ((~happy(X0) & wise(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | happy(X0) | ~wise(X0)) & ((~happy(X0) & wise(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [flattening 38]
45. ! [X0] : (((generous(X0) | tall(X0)) | ~calm(X0)) & (calm(X0) | (~generous(X0) & ~tall(X0)))) [nnf transformation 10]
46. ! [X0] : ((generous(X0) | tall(X0) | ~calm(X0)) & (calm(X0) | (~generous(X0) & ~tall(X0)))) [flattening 45]
51. ! [X0] : ((generous(X0) & ~kind(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) [nnf transformation 34]
52. ! [X0] : (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | kind(X0)) [nnf transformation 36]
56. (~calm(paul) | wise(paul)) & (calm(paul) | ~wise(paul)) [nnf transformation 23]
64. ~happy(X0) | ~calm(X0) | ~strong(X0) [cnf transformation 39]
65. ~calm(X0) | strong(X0) | happy(X0) | ~wise(X0) [cnf transformation 39]
75. ~happy(X0) | strong(X0) [cnf transformation 30]
86. ~tall(X0) | calm(X0) [cnf transformation 46]
98. ~strong(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 51]
103. old(X0) | happy(X0) | kind(X0) [cnf transformation 52]
104. ~old(paul) [cnf transformation 17]
114. ~calm(paul) | wise(paul) [cnf transformation 56]
115. tall(paul) [cnf transformation 24]
139. 5 <=> tall(paul) [avatar definition]
140. tall(paul) <- (5) [avatar component clause 139]
154. 8 <=> kind(paul) [avatar definition]
200. 18 <=> wise(paul) [avatar definition]
202. wise(paul) <- (18) [avatar component clause 200]
204. 19 <=> calm(paul) [avatar definition]
205. calm(paul) <- (19) [avatar component clause 204]
207. 18 | ~19 [avatar split clause 114,204,200]
209. 5 [avatar split clause 115,139]
211. calm(paul) <- (5) [resolution 86,140]
214. 19 | ~5 [avatar split clause 211,139,204]
258. happy(paul) | kind(paul) [resolution 103,104]
262. 27 <=> happy(paul) [avatar definition]
264. happy(paul) <- (27) [avatar component clause 262]
265. 8 | 27 [avatar split clause 258,262,154]
273. strong(paul) | happy(paul) | ~wise(paul) <- (19) [resolution 65,205]
274. strong(paul) | happy(paul) <- (18, 19) [subsumption resolution 273,202]
275. strong(paul) <- (18, 19) [subsumption resolution 274,75]
304. ~kind(paul) | ~wise(paul) <- (18, 19) [resolution 275,98]
310. ~kind(paul) <- (18, 19) [subsumption resolution 304,202]
311. ~8 | ~18 | ~19 [avatar split clause 310,204,200,154]
312. ~calm(paul) | ~strong(paul) <- (27) [resolution 264,64]
316. ~strong(paul) <- (19, 27) [subsumption resolution 312,205]
317. $false <- (18, 19, 27) [subsumption resolution 316,275]
318. ~18 | ~19 | ~27 [avatar contradiction clause 317]
319. $false [avatar sat refutation 207,209,214,265,311,318]
% SZS output end Proof for 7393205512134638707375557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not funny is either generous or wise. If someone is funny or not brave then lucy is rich and vice versa. Everyone who is either not creative or not happy is rich and vice versa. Everyone who is either patient or not old is both generous and humble and vice versa. Everyone who is not rich is either patient or not happy and vice versa. If someone is not happy then someone is not calm and vice versa. Everyone who is either funny or old is either not old or rich and vice versa. Everyone who is not strong or calm is funny or not calm. If someone is not patient then fred is funny. Everyone who is quiet or kind is tall. Everyone who is either quiet or funny is not curious or creative and vice versa. Everyone who is not curious is curious. If someone is patient or rich then lucy is both not patient and not tall and vice versa. If susan is wise or strong then someone is not tall or not strong and vice versa. Everyone who is either not strong or old is not brave. If someone is both curious and not creative then lucy is not curious or old. Lucy is both wise and not funny. Susan is not calm or strong. Someone is old. Someone is not creative or not rich. Someone is both humble and generous. Someone is not patient or not rich. Susan is both not calm and not rich. | Fred is not quiet. | neutral | (![X]:((~strong(X)<~>~funny(X))=>(generous(X)<~>wise(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(rich(lucy)))&
(![X]:((~creative(X)<~>~happy(X))<=>rich(X)))&
(![X]:((patient(X)<~>~old(X))<=>(generous(X)&humble(X))))&
(![X]:(~rich(X)<=>(patient(X)<~>~happy(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(~calm(X))))&
(![X]:((funny(X)<~>old(X))<=>(~old(X)<~>rich(X))))&
(![X]:((~strong(X)|calm(X))=>(funny(X)|~calm(X))))&
((?[X]:(~patient(X)))=>(funny(fred)))&
(![X]:((quiet(X)|kind(X))=>tall(X)))&
(![X]:((quiet(X)<~>funny(X))<=>(~curious(X)|creative(X))))&
(![X]:(~curious(X)=>curious(X)))&
((?[X]:((patient(X)|rich(X))))<=>((~patient(lucy)&~tall(lucy))))&
(((wise(susan)|strong(susan)))<=>(?[X]:((~tall(X)|~strong(X)))))&
(![X]:((~strong(X)<~>old(X))=>~brave(X)))&
((?[X]:((curious(X)&~creative(X))))=>((~curious(lucy)|old(lucy))))&
((wise(lucy)&~funny(lucy)))&
((~calm(susan)|strong(susan)))&
(?[X]:(old(X)))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:((humble(X)&generous(X))))&
(?[X]:((~patient(X)|~rich(X))))&
((~calm(susan)&~rich(susan))) | ~quiet(fred) | [] | null | 0 |
Everyone who is creative or not creative is not humble or happy.
Everyone who is either not humble or wise is not kind and vice versa.
Everyone who is not generous or happy is not creative.
If lucy is both generous and strong then someone is wise or quiet and vice versa.
If john is happy or not creative then mary is brave.
Everyone who is curious or strong is not generous.
If someone is happy then susan is both not patient and not creative and vice versa.
If paul is both rich and kind then alice is tall or not old and vice versa.
If john is not funny then someone is both not tall and not rich.
Everyone who is both brave and happy is either not happy or old and vice versa.
Everyone who is both tall and not generous is both not brave and not curious.
If lucy is strong then fred is rich or humble.
Everyone who is either calm or patient is funny.
Everyone who is not calm or not tall is both not kind and humble.
Everyone who is both patient and not calm is not generous and vice versa.
Everyone who is both brave and funny is either not tall or not kind and vice versa.
Fred is both creative and brave.
Someone is not humble.
Someone is not calm or tall.
Someone is both kind and old.
Lucy is not curious.
Someone is wise or kind.
Someone is patient.
Lucy is both not rich and brave. | Fred is not humble. | entailment | (![X]:((creative(X)|~creative(X))=>(~humble(X)|happy(X))))&
(![X]:((~humble(X)<~>wise(X))<=>~kind(X)))&
(![X]:((~generous(X)|happy(X))=>~creative(X)))&
(((generous(lucy)&strong(lucy)))<=>(?[X]:((wise(X)|quiet(X)))))&
(((happy(john)|~creative(john)))=>(brave(mary)))&
(![X]:((curious(X)|strong(X))=>~generous(X)))&
((?[X]:(happy(X)))<=>((~patient(susan)&~creative(susan))))&
(((rich(paul)&kind(paul)))<=>((tall(alice)|~old(alice))))&
((~funny(john))=>(?[X]:((~tall(X)&~rich(X)))))&
(![X]:((brave(X)&happy(X))<=>(~happy(X)<~>old(X))))&
(![X]:((tall(X)&~generous(X))=>(~brave(X)&~curious(X))))&
((strong(lucy))=>((rich(fred)|humble(fred))))&
(![X]:((calm(X)<~>patient(X))=>funny(X)))&
(![X]:((~calm(X)|~tall(X))=>(~kind(X)&humble(X))))&
(![X]:((patient(X)&~calm(X))<=>~generous(X)))&
(![X]:((brave(X)&funny(X))<=>(~tall(X)<~>~kind(X))))&
((creative(fred)&brave(fred)))&
(?[X]:(~humble(X)))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:((kind(X)&old(X))))&
(~curious(lucy))&
(?[X]:((wise(X)|kind(X))))&
(?[X]:(patient(X)))&
((~rich(lucy)&brave(lucy))) | ~humble(fred) | [
"p0",
"p2",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3771681764267805936356046
% SZS output start Proof for 3771681764267805936356046
1. ! [X0] : ((~creative(X0) | creative(X0)) => (happy(X0) | ~humble(X0))) [input p0]
3. ! [X0] : ((happy(X0) | ~generous(X0)) => ~creative(X0)) [input p2]
17. brave(fred) & creative(fred) [input p16]
25. humble(fred) [input hypothesis]
29. ! [X0] : ((happy(X0) | ~humble(X0)) | (creative(X0) & ~creative(X0))) [ennf transformation 1]
30. ! [X0] : (happy(X0) | ~humble(X0) | (creative(X0) & ~creative(X0))) [flattening 29]
31. ! [X0] : (~creative(X0) | (~happy(X0) & generous(X0))) [ennf transformation 3]
73. happy(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 30]
74. ~humble(X0) | happy(X0) | creative(X0) [cnf transformation 30]
80. ~happy(X0) | ~creative(X0) [cnf transformation 31]
122. creative(fred) [cnf transformation 17]
132. humble(fred) [cnf transformation 25]
135. ~humble(X0) | happy(X0) [subsumption resolution 73,74]
236. 22 <=> humble(fred) [avatar definition]
238. humble(fred) <- (22) [avatar component clause 236]
260. 22 [avatar split clause 132,236]
282. happy(fred) <- (22) [resolution 135,238]
292. ~creative(fred) <- (22) [resolution 282,80]
293. $false <- (22) [subsumption resolution 292,122]
294. ~22 [avatar contradiction clause 293]
295. $false [avatar sat refutation 260,294]
% SZS output end Proof for 3771681764267805936356046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and tall is both not happy and wise.
Everyone who is both kind and not kind is either not curious or not tall.
Everyone who is not happy or strong is not generous and vice versa.
If mary is not funny then someone is both funny and not generous.
Everyone who is not strong or not funny is both not creative and patient and vice versa.
Everyone who is both not old and not strong is not rich or not kind.
Everyone who is either not strong or not creative is creative and vice versa.
Everyone who is both not happy and funny is both creative and kind and vice versa.
If someone is rich then susan is wise or not kind.
Everyone who is not kind is either not calm or patient and vice versa.
If someone is either not creative or not humble then someone is both old and not old and vice versa.
If someone is both not humble and patient then someone is patient.
Everyone who is both happy and generous is either strong or calm and vice versa.
Everyone who is wise is either not creative or not strong.
If someone is not wise then fred is generous.
Someone is not funny or not curious.
Susan is both brave and curious.
Someone is not happy.
Susan is not creative or not patient.
Someone is not humble.
Someone is happy or not tall.
Alice is not patient or not wise. | Fred is not kind. | entailment | (![X]:((humble(X)&tall(X))=>(~happy(X)&wise(X))))&
(![X]:((kind(X)&~kind(X))=>(~curious(X)<~>~tall(X))))&
(![X]:((~happy(X)|strong(X))<=>~generous(X)))&
((~funny(mary))=>(?[X]:((funny(X)&~generous(X)))))&
(![X]:((~strong(X)|~funny(X))<=>(~creative(X)&patient(X))))&
(![X]:((~old(X)&~strong(X))=>(~rich(X)|~kind(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>creative(X)))&
(![X]:((~happy(X)&funny(X))<=>(creative(X)&kind(X))))&
((?[X]:(rich(X)))=>((wise(susan)|~kind(susan))))&
(![X]:(~kind(X)<=>(~calm(X)<~>patient(X))))&
((?[X]:((~creative(X)<~>~humble(X))))<=>(?[X]:((old(X)&~old(X)))))&
((?[X]:((~humble(X)&patient(X))))=>(?[X]:(patient(X))))&
(![X]:((happy(X)&generous(X))<=>(strong(X)<~>calm(X))))&
(![X]:(wise(X)=>(~creative(X)<~>~strong(X))))&
((?[X]:(~wise(X)))=>(generous(fred)))&
(?[X]:((~funny(X)|~curious(X))))&
((brave(susan)&curious(susan)))&
(?[X]:(~happy(X)))&
((~creative(susan)|~patient(susan)))&
(?[X]:(~humble(X)))&
(?[X]:((happy(X)|~tall(X))))&
((~patient(alice)|~wise(alice))) | ~kind(fred) | [
"p2",
"p4",
"p6",
"p9",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 825660738369625558203995
% SZS output start Proof for 825660738369625558203995
3. ! [X0] : ((strong(X0) | ~happy(X0)) <=> ~generous(X0)) [input p2]
5. ! [X0] : ((~funny(X0) | ~strong(X0)) <=> (patient(X0) & ~creative(X0))) [input p4]
7. ! [X0] : ((~strong(X0) <~> ~creative(X0)) <=> creative(X0)) [input p6]
10. ! [X0] : (~kind(X0) <=> (~calm(X0) <~> patient(X0))) [input p9]
13. ! [X0] : ((generous(X0) & happy(X0)) <=> (strong(X0) <~> calm(X0))) [input p12]
14. ! [X0] : (wise(X0) => (~creative(X0) <~> ~strong(X0))) [input p13]
15. ? [X0] : ~wise(X0) => generous(fred) [input p14]
23. kind(fred) [input hypothesis]
35. ! [X0] : ((~creative(X0) <~> ~strong(X0)) | ~wise(X0)) [ennf transformation 14]
36. generous(fred) | ! [X0] : wise(X0) [ennf transformation 15]
38. ! [X0] : (((strong(X0) | ~happy(X0)) | generous(X0)) & (~generous(X0) | (~strong(X0) & happy(X0)))) [nnf transformation 3]
39. ! [X0] : ((strong(X0) | ~happy(X0) | generous(X0)) & (~generous(X0) | (~strong(X0) & happy(X0)))) [flattening 38]
42. ! [X0] : (((~funny(X0) | ~strong(X0)) | (~patient(X0) | creative(X0))) & ((patient(X0) & ~creative(X0)) | (funny(X0) & strong(X0)))) [nnf transformation 5]
43. ! [X0] : ((~funny(X0) | ~strong(X0) | ~patient(X0) | creative(X0)) & ((patient(X0) & ~creative(X0)) | (funny(X0) & strong(X0)))) [flattening 42]
44. ! [X0] : ((((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | ~creative(X0)) & (creative(X0) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))))) [nnf transformation 7]
47. ! [X0] : ((~kind(X0) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0)))) & (((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | kind(X0))) [nnf transformation 10]
56. ! [X0] : (((generous(X0) & happy(X0)) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) & (((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | (~generous(X0) | ~happy(X0)))) [nnf transformation 13]
57. ! [X0] : (((generous(X0) & happy(X0)) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) & (((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | ~generous(X0) | ~happy(X0))) [flattening 56]
58. ! [X0] : (((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | ~wise(X0)) [nnf transformation 35]
71. ~generous(X0) | happy(X0) [cnf transformation 39]
76. ~creative(X0) | strong(X0) [cnf transformation 43]
78. patient(X0) | strong(X0) [cnf transformation 43]
82. creative(X0) | ~strong(X0) | creative(X0) [cnf transformation 44]
83. ~creative(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 44]
92. ~calm(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 47]
100. calm(X0) | strong(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 57]
107. strong(X0) | creative(X0) | ~wise(X0) [cnf transformation 58]
108. generous(fred) | wise(X0) [cnf transformation 36]
116. kind(fred) [cnf transformation 23]
117. creative(X0) | ~strong(X0) [duplicate literal removal 82]
118. ~creative(X0) | ~strong(X0) [duplicate literal removal 83]
133. ~creative(X0) [subsumption resolution 118,76]
134. ~strong(X0) [subsumption resolution 117,133]
157. calm(X0) | ~generous(X0) | ~happy(X0) [subsumption resolution 100,134]
158. ~generous(X0) | calm(X0) [subsumption resolution 157,71]
159. creative(X0) | ~wise(X0) [subsumption resolution 107,134]
160. ~wise(X0) [subsumption resolution 159,133]
161. generous(fred) [subsumption resolution 108,160]
189. calm(fred) [resolution 158,161]
226. ~kind(fred) | ~patient(fred) [resolution 92,189]
228. ~patient(fred) [subsumption resolution 226,116]
232. strong(fred) [resolution 228,78]
233. $false [subsumption resolution 232,134]
% SZS output end Proof for 825660738369625558203995
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is happy or not old then fred is either not quiet or kind and vice versa. Everyone who is wise is not generous or not quiet. If someone is either not creative or not quiet then fred is either funny or quiet. If someone is quiet or not kind then paul is not rich or not creative and vice versa. If susan is not funny or brave then someone is tall or quiet and vice versa. If john is either funny or calm then someone is both kind and not funny. If alice is either rich or calm then someone is both not humble and patient. If someone is both patient and strong then paul is not tall or not wise and vice versa. Everyone who is either not old or not humble is not old and vice versa. Everyone who is both patient and not patient is either not curious or not quiet. Everyone who is not creative is both not kind and rich. Everyone who is old is either not creative or not strong. Everyone who is patient or curious is not rich and vice versa. If someone is not humble then someone is not patient or not wise and vice versa. If susan is not brave then john is calm or patient. If alice is either not patient or tall then susan is both not old and not brave. Fred is either not calm or creative. Fred is both humble and strong. John is not calm or patient. John is calm or old. Mary is either not patient or not tall. | Fred is humble. | entailment | (((happy(mary)|~old(mary)))<=>((~quiet(fred)<~>kind(fred))))&
(![X]:(wise(X)=>(~generous(X)|~quiet(X))))&
((?[X]:((~creative(X)<~>~quiet(X))))=>((funny(fred)<~>quiet(fred))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~rich(paul)|~creative(paul))))&
(((~funny(susan)|brave(susan)))<=>(?[X]:((tall(X)|quiet(X)))))&
(((funny(john)<~>calm(john)))=>(?[X]:((kind(X)&~funny(X)))))&
(((rich(alice)<~>calm(alice)))=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((patient(X)&strong(X))))<=>((~tall(paul)|~wise(paul))))&
(![X]:((~old(X)<~>~humble(X))<=>~old(X)))&
(![X]:((patient(X)&~patient(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:(~creative(X)=>(~kind(X)&rich(X))))&
(![X]:(old(X)=>(~creative(X)<~>~strong(X))))&
(![X]:((patient(X)|curious(X))<=>~rich(X)))&
((?[X]:(~humble(X)))<=>(?[X]:((~patient(X)|~wise(X)))))&
((~brave(susan))=>((calm(john)|patient(john))))&
(((~patient(alice)<~>tall(alice)))=>((~old(susan)&~brave(susan))))&
((~calm(fred)<~>creative(fred)))&
((humble(fred)&strong(fred)))&
((~calm(john)|patient(john)))&
((calm(john)|old(john)))&
((~patient(mary)<~>~tall(mary))) | humble(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 360764644194268554864382
% SZS output start Proof for 360764644194268554864382
9. ! [X0] : ((~old(X0) <~> ~humble(X0)) <=> ~old(X0)) [input p8]
22. ~humble(fred) [input hypothesis]
59. ! [X0] : ((((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | old(X0)) & (~old(X0) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0))))) [nnf transformation 9]
104. ~old(X0) | ~old(X0) | humble(X0) [cnf transformation 59]
106. humble(X0) | old(X0) | old(X0) [cnf transformation 59]
132. ~humble(fred) [cnf transformation 22]
133. ~old(X0) | humble(X0) [duplicate literal removal 104]
134. humble(X0) | old(X0) [duplicate literal removal 106]
284. humble(X0) [subsumption resolution 133,134]
315. $false [subsumption resolution 132,284]
% SZS output end Proof for 360764644194268554864382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is curious and vice versa.
Everyone who is not curious or wise is both not creative and not calm.
If mary is either patient or not quiet then lucy is generous or not brave and vice versa.
Everyone who is either calm or quiet is not curious and vice versa.
Everyone who is not rich is old.
Everyone who is not quiet or not strong is both not patient and not curious and vice versa.
If lucy is either humble or not humble then lucy is either not wise or not rich.
If someone is not wise or not quiet then someone is not curious and vice versa.
If someone is wise or humble then lucy is either not kind or tall and vice versa.
Everyone who is both old and wise is either not strong or humble and vice versa.
Everyone who is not old or tall is both humble and not old.
If someone is either quiet or patient then susan is either not humble or tall.
Everyone who is happy is either not curious or creative.
Everyone who is either not kind or wise is not humble or not kind.
If alice is quiet then someone is both rich and not patient.
Someone is either not happy or not curious.
Someone is either not brave or wise.
Someone is not generous.
Mary is either not old or funny.
John is both not kind and patient.
Someone is not calm.
Paul is either not creative or creative.
Someone is either quiet or not quiet. | Lucy is kind. | contradiction | (![X]:(humble(X)<=>curious(X)))&
(![X]:((~curious(X)|wise(X))=>(~creative(X)&~calm(X))))&
(((patient(mary)<~>~quiet(mary)))<=>((generous(lucy)|~brave(lucy))))&
(![X]:((calm(X)<~>quiet(X))<=>~curious(X)))&
(![X]:(~rich(X)=>old(X)))&
(![X]:((~quiet(X)|~strong(X))<=>(~patient(X)&~curious(X))))&
(((humble(lucy)<~>~humble(lucy)))=>((~wise(lucy)<~>~rich(lucy))))&
((?[X]:((~wise(X)|~quiet(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|humble(X))))<=>((~kind(lucy)<~>tall(lucy))))&
(![X]:((old(X)&wise(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((~old(X)|tall(X))=>(humble(X)&~old(X))))&
((?[X]:((quiet(X)<~>patient(X))))=>((~humble(susan)<~>tall(susan))))&
(![X]:(happy(X)=>(~curious(X)<~>creative(X))))&
(![X]:((~kind(X)<~>wise(X))=>(~humble(X)|~kind(X))))&
((quiet(alice))=>(?[X]:((rich(X)&~patient(X)))))&
(?[X]:((~happy(X)<~>~curious(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:(~generous(X)))&
((~old(mary)<~>funny(mary)))&
((~kind(john)&patient(john)))&
(?[X]:(~calm(X)))&
((~creative(paul)<~>creative(paul)))&
(?[X]:((quiet(X)<~>~quiet(X)))) | kind(lucy) | [
"p0",
"p1",
"p3",
"p5",
"p8",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6061955739238082830518868
% SZS output start Proof for 6061955739238082830518868
1. ! [X0] : (humble(X0) <=> curious(X0)) [input p0]
2. ! [X0] : ((wise(X0) | ~curious(X0)) => (~calm(X0) & ~creative(X0))) [input p1]
4. ! [X0] : ((calm(X0) <~> quiet(X0)) <=> ~curious(X0)) [input p3]
6. ! [X0] : ((~strong(X0) | ~quiet(X0)) <=> (~curious(X0) & ~patient(X0))) [input p5]
9. ? [X0] : (humble(X0) | wise(X0)) <=> (~kind(lucy) <~> tall(lucy)) [input p8]
10. ! [X0] : ((wise(X0) & old(X0)) <=> (~strong(X0) <~> humble(X0))) [input p9]
11. ! [X0] : ((tall(X0) | ~old(X0)) => (~old(X0) & humble(X0))) [input p10]
15. quiet(alice) => ? [X0] : (~patient(X0) & rich(X0)) [input p14]
24. kind(lucy) [input hypothesis]
26. ! [X0] : ((~calm(X0) & ~creative(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 2]
29. ! [X0] : ((~old(X0) & humble(X0)) | (~tall(X0) & old(X0))) [ennf transformation 11]
34. ? [X0] : (~patient(X0) & rich(X0)) | ~quiet(alice) [ennf transformation 15]
35. ! [X0] : ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))) [nnf transformation 1]
38. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | curious(X0)) & (~curious(X0) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [nnf transformation 4]
39. ! [X0] : (((~strong(X0) | ~quiet(X0)) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | (strong(X0) & quiet(X0)))) [nnf transformation 6]
40. ! [X0] : ((~strong(X0) | ~quiet(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | (strong(X0) & quiet(X0)))) [flattening 39]
47. (? [X0] : (humble(X0) | wise(X0)) | ((~kind(lucy) | ~tall(lucy)) & (tall(lucy) | kind(lucy)))) & (((~tall(lucy) | kind(lucy)) & (tall(lucy) | ~kind(lucy))) | ! [X0] : (~humble(X0) & ~wise(X0))) [nnf transformation 9]
48. (? [X0] : (humble(X0) | wise(X0)) | ((~kind(lucy) | ~tall(lucy)) & (tall(lucy) | kind(lucy)))) & (((~tall(lucy) | kind(lucy)) & (tall(lucy) | ~kind(lucy))) | ! [X1] : (~humble(X1) & ~wise(X1))) [rectify 47]
49. ? [X0] : (humble(X0) | wise(X0)) => (humble(sK2) | wise(sK2)) [choice axiom]
50. ((humble(sK2) | wise(sK2)) | ((~kind(lucy) | ~tall(lucy)) & (tall(lucy) | kind(lucy)))) & (((~tall(lucy) | kind(lucy)) & (tall(lucy) | ~kind(lucy))) | ! [X1] : (~humble(X1) & ~wise(X1))) [skolemisation 48,49]
51. ! [X0] : (((wise(X0) & old(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | (~wise(X0) | ~old(X0)))) [nnf transformation 10]
52. ! [X0] : (((wise(X0) & old(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | ~wise(X0) | ~old(X0))) [flattening 51]
56. ? [X0] : (~patient(X0) & rich(X0)) => (~patient(sK3) & rich(sK3)) [choice axiom]
57. (~patient(sK3) & rich(sK3)) | ~quiet(alice) [skolemisation 34,56]
73. ~humble(X0) | curious(X0) [cnf transformation 35]
74. ~curious(X0) | humble(X0) [cnf transformation 35]
77. ~calm(X0) | curious(X0) [cnf transformation 26]
87. quiet(X0) | calm(X0) | curious(X0) [cnf transformation 38]
92. ~curious(X0) | quiet(X0) [cnf transformation 40]
93. ~curious(X0) | strong(X0) [cnf transformation 40]
94. ~strong(X0) | ~quiet(X0) | curious(X0) | patient(X0) [cnf transformation 40]
102. tall(lucy) | ~kind(lucy) | ~wise(X1) [cnf transformation 50]
103. tall(lucy) | ~kind(lucy) | ~humble(X1) [cnf transformation 50]
111. ~strong(X0) | old(X0) | ~humble(X0) [cnf transformation 52]
112. strong(X0) | humble(X0) | wise(X0) [cnf transformation 52]
115. ~tall(X0) | humble(X0) [cnf transformation 29]
117. ~tall(X0) | ~old(X0) [cnf transformation 29]
127. ~patient(sK3) | ~quiet(alice) [cnf transformation 57]
142. kind(lucy) [cnf transformation 24]
170. quiet(X0) | curious(X0) [subsumption resolution 87,77]
172. ~strong(X0) | curious(X0) | patient(X0) [subsumption resolution 94,170]
173. quiet(X0) [subsumption resolution 92,170]
175. 5 <=> humble(lucy) [avatar definition]
177. humble(lucy) <- (5) [avatar component clause 175]
208. 12 <=> tall(lucy) [avatar definition]
209. tall(lucy) <- (12) [avatar component clause 208]
212. 13 <=> kind(lucy) [avatar definition]
226. 16 <=> ! [X1] : ~humble(X1) [avatar definition]
227. ~humble(X1) <- (16) [avatar component clause 226]
230. 17 <=> ! [X1] : ~wise(X1) [avatar definition]
231. ~wise(X1) <- (17) [avatar component clause 230]
233. 16 | ~13 | 12 [avatar split clause 103,208,212,226]
234. 17 | ~13 | 12 [avatar split clause 102,208,212,230]
248. ~patient(sK3) [subsumption resolution 127,173]
280. 13 [avatar split clause 142,212]
283. curious(lucy) <- (5) [resolution 73,177]
287. strong(lucy) <- (5) [resolution 93,283]
300. ~old(lucy) <- (12) [resolution 209,117]
301. humble(lucy) <- (12) [resolution 209,115]
314. old(lucy) | ~humble(lucy) <- (5) [resolution 111,287]
320. ~humble(lucy) <- (5, 12) [subsumption resolution 314,300]
321. $false <- (5, 12) [subsumption resolution 320,177]
322. ~5 | ~12 [avatar contradiction clause 321]
325. 5 | ~12 [avatar split clause 301,208,175]
333. curious(X0) | patient(X0) | humble(X0) | wise(X0) [resolution 172,112]
336. curious(X0) | patient(X0) | wise(X0) <- (16) [subsumption resolution 333,227]
337. patient(X0) | curious(X0) <- (16, 17) [subsumption resolution 336,231]
339. curious(sK3) <- (16, 17) [resolution 337,248]
359. humble(sK3) <- (16, 17) [resolution 339,74]
360. $false <- (16, 17) [subsumption resolution 359,227]
361. ~16 | ~17 [avatar contradiction clause 360]
362. $false [avatar sat refutation 233,234,280,322,325,361]
% SZS output end Proof for 6061955739238082830518868
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not tall is either rich or patient.
If someone is either not happy or not creative then someone is not funny and vice versa.
Everyone who is both not curious and kind is both tall and not generous.
Everyone who is happy or not generous is either not tall or not funny and vice versa.
If someone is both not strong and rich then paul is both old and patient.
If someone is kind or happy then alice is both happy and not happy and vice versa.
Everyone who is not brave or not rich is not brave or not tall and vice versa.
Everyone who is either not wise or not happy is not generous.
If alice is not quiet then mary is either brave or funny and vice versa.
If someone is creative or not rich then someone is not tall or old.
Everyone who is both wise and brave is either not rich or patient and vice versa.
Everyone who is both not patient and kind is not wise and vice versa.
Everyone who is not funny is curious.
If paul is curious then lucy is not tall.
Everyone who is both not tall and funny is wise and vice versa.
Everyone who is both not tall and happy is either not quiet or humble.
Someone is not tall or not strong.
Someone is not quiet.
Someone is not rich or brave.
Lucy is brave or not strong.
Someone is both not creative and not humble.
Someone is not quiet or wise.
Paul is old. | Lucy is strong. | contradiction | (![X]:((~strong(X)<~>~tall(X))=>(rich(X)<~>patient(X))))&
((?[X]:((~happy(X)<~>~creative(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)&kind(X))=>(tall(X)&~generous(X))))&
(![X]:((happy(X)|~generous(X))<=>(~tall(X)<~>~funny(X))))&
((?[X]:((~strong(X)&rich(X))))=>((old(paul)&patient(paul))))&
((?[X]:((kind(X)|happy(X))))<=>((happy(alice)&~happy(alice))))&
(![X]:((~brave(X)|~rich(X))<=>(~brave(X)|~tall(X))))&
(![X]:((~wise(X)<~>~happy(X))=>~generous(X)))&
((~quiet(alice))<=>((brave(mary)<~>funny(mary))))&
((?[X]:((creative(X)|~rich(X))))=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((wise(X)&brave(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((~patient(X)&kind(X))<=>~wise(X)))&
(![X]:(~funny(X)=>curious(X)))&
((curious(paul))=>(~tall(lucy)))&
(![X]:((~tall(X)&funny(X))<=>wise(X)))&
(![X]:((~tall(X)&happy(X))=>(~quiet(X)<~>humble(X))))&
(?[X]:((~tall(X)|~strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~rich(X)|brave(X))))&
((brave(lucy)|~strong(lucy)))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:((~quiet(X)|wise(X))))&
(old(paul)) | strong(lucy) | [
"p0",
"p5",
"p6",
"p10",
"p11",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2720623191015763918317807
% SZS output start Proof for 2720623191015763918317807
1. ! [X0] : ((~strong(X0) <~> ~tall(X0)) => (rich(X0) <~> patient(X0))) [input p0]
6. ? [X0] : (happy(X0) | kind(X0)) <=> (~happy(alice) & happy(alice)) [input p5]
7. ! [X0] : ((~rich(X0) | ~brave(X0)) <=> (~tall(X0) | ~brave(X0))) [input p6]
11. ! [X0] : ((brave(X0) & wise(X0)) <=> (~rich(X0) <~> patient(X0))) [input p10]
12. ! [X0] : ((kind(X0) & ~patient(X0)) <=> ~wise(X0)) [input p11]
15. ! [X0] : ((funny(X0) & ~tall(X0)) <=> wise(X0)) [input p14]
20. ~strong(lucy) | brave(lucy) [input p19]
24. strong(lucy) [input hypothesis]
30. ! [X0] : ((rich(X0) <~> patient(X0)) | (~strong(X0) <=> ~tall(X0))) [ennf transformation 1]
39. ! [X0] : (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0)))) [nnf transformation 30]
47. (? [X0] : (happy(X0) | kind(X0)) | (happy(alice) | ~happy(alice))) & ((~happy(alice) & happy(alice)) | ! [X0] : (~happy(X0) & ~kind(X0))) [nnf transformation 6]
48. (? [X0] : (happy(X0) | kind(X0)) | happy(alice) | ~happy(alice)) & ((~happy(alice) & happy(alice)) | ! [X0] : (~happy(X0) & ~kind(X0))) [flattening 47]
49. (? [X0] : (happy(X0) | kind(X0)) | happy(alice) | ~happy(alice)) & ((~happy(alice) & happy(alice)) | ! [X1] : (~happy(X1) & ~kind(X1))) [rectify 48]
50. ? [X0] : (happy(X0) | kind(X0)) => (happy(sK2) | kind(sK2)) [choice axiom]
51. ((happy(sK2) | kind(sK2)) | happy(alice) | ~happy(alice)) & ((~happy(alice) & happy(alice)) | ! [X1] : (~happy(X1) & ~kind(X1))) [skolemisation 49,50]
52. ! [X0] : (((~rich(X0) | ~brave(X0)) | (tall(X0) & brave(X0))) & ((~tall(X0) | ~brave(X0)) | (rich(X0) & brave(X0)))) [nnf transformation 7]
53. ! [X0] : ((~rich(X0) | ~brave(X0) | (tall(X0) & brave(X0))) & (~tall(X0) | ~brave(X0) | (rich(X0) & brave(X0)))) [flattening 52]
56. ! [X0] : (((brave(X0) & wise(X0)) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0)))) & (((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | (~brave(X0) | ~wise(X0)))) [nnf transformation 11]
57. ! [X0] : (((brave(X0) & wise(X0)) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0)))) & (((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | ~brave(X0) | ~wise(X0))) [flattening 56]
58. ! [X0] : (((kind(X0) & ~patient(X0)) | wise(X0)) & (~wise(X0) | (~kind(X0) | patient(X0)))) [nnf transformation 12]
59. ! [X0] : (((kind(X0) & ~patient(X0)) | wise(X0)) & (~wise(X0) | ~kind(X0) | patient(X0))) [flattening 58]
60. ! [X0] : (((funny(X0) & ~tall(X0)) | ~wise(X0)) & (wise(X0) | (~funny(X0) | tall(X0)))) [nnf transformation 15]
61. ! [X0] : (((funny(X0) & ~tall(X0)) | ~wise(X0)) & (wise(X0) | ~funny(X0) | tall(X0))) [flattening 60]
74. ~strong(X0) | rich(X0) | patient(X0) | tall(X0) [cnf transformation 39]
90. happy(alice) | ~kind(X1) [cnf transformation 51]
92. ~happy(alice) | ~kind(X1) [cnf transformation 51]
98. ~brave(X0) | ~rich(X0) | tall(X0) [cnf transformation 53]
106. ~wise(X0) | rich(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 57]
113. wise(X0) | kind(X0) [cnf transformation 59]
116. ~funny(X0) | wise(X0) | tall(X0) [cnf transformation 61]
117. ~wise(X0) | ~tall(X0) [cnf transformation 61]
118. ~wise(X0) | funny(X0) [cnf transformation 61]
124. ~strong(lucy) | brave(lucy) [cnf transformation 20]
128. strong(lucy) [cnf transformation 24]
130. 1 <=> ! [X1] : funny(X1) [avatar definition]
131. funny(X1) <- (1) [avatar component clause 130]
166. 10 <=> happy(alice) [avatar definition]
171. 11 <=> ! [X1] : ~kind(X1) [avatar definition]
172. ~kind(X1) <- (11) [avatar component clause 171]
173. 11 | ~10 [avatar split clause 92,166,171]
175. 11 | 10 [avatar split clause 90,166,171]
220. 21 <=> brave(lucy) [avatar definition]
222. brave(lucy) <- (21) [avatar component clause 220]
224. 22 <=> strong(lucy) [avatar definition]
225. strong(lucy) <- (22) [avatar component clause 224]
227. 21 | ~22 [avatar split clause 124,224,220]
237. 22 [avatar split clause 128,224]
243. ~tall(X0) | kind(X0) [resolution 117,113]
244. ~tall(X0) <- (11) [subsumption resolution 243,172]
245. funny(X0) | kind(X0) [resolution 118,113]
246. funny(X0) <- (11) [subsumption resolution 245,172]
247. 1 | ~11 [avatar split clause 246,171,130]
261. ~rich(lucy) | tall(lucy) <- (21) [resolution 98,222]
262. ~rich(lucy) <- (11, 21) [subsumption resolution 261,244]
293. wise(X0) | tall(X0) <- (1) [resolution 116,131]
296. wise(X0) <- (1, 11) [subsumption resolution 293,244]
301. rich(lucy) | patient(lucy) | tall(lucy) <- (22) [resolution 74,225]
302. patient(lucy) | tall(lucy) <- (11, 21, 22) [subsumption resolution 301,262]
303. patient(lucy) <- (11, 21, 22) [subsumption resolution 302,244]
321. ~brave(X0) | rich(X0) | ~patient(X0) <- (1, 11) [resolution 106,296]
325. rich(lucy) | ~patient(lucy) <- (1, 11, 21) [resolution 321,222]
329. ~patient(lucy) <- (1, 11, 21) [subsumption resolution 325,262]
330. $false <- (1, 11, 21, 22) [subsumption resolution 329,303]
331. ~1 | ~11 | ~21 | ~22 [avatar contradiction clause 330]
334. $false [avatar sat refutation 173,175,227,237,247,331]
% SZS output end Proof for 2720623191015763918317807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not old or wise then someone is both tall and not calm and vice versa.
Everyone who is not strong is not quiet.
Everyone who is not old is generous.
If susan is rich then someone is both curious and not kind.
If lucy is both curious and not funny then susan is either not generous or happy.
Everyone who is not tall or kind is both not calm and quiet.
If someone is both old and creative then someone is both not calm and strong and vice versa.
Everyone who is tall is not quiet.
Everyone who is not patient or funny is brave or not patient and vice versa.
Everyone who is either not rich or not strong is not tall or quiet.
Everyone who is old or creative is not tall.
Everyone who is not patient or not curious is either not rich or not humble and vice versa.
Everyone who is either rich or not calm is not wise and vice versa.
Everyone who is not old is both not happy and not funny and vice versa.
Everyone who is both not rich and not quiet is rich and vice versa.
Everyone who is kind or not curious is either not generous or not patient.
Susan is both not humble and old.
Someone is either generous or not curious.
Someone is not calm or not happy.
Someone is either old or calm.
Someone is both not calm and old.
Paul is funny. | Lucy is not wise. | entailment | (((~old(mary)|wise(mary)))<=>(?[X]:((tall(X)&~calm(X)))))&
(![X]:(~strong(X)=>~quiet(X)))&
(![X]:(~old(X)=>generous(X)))&
((rich(susan))=>(?[X]:((curious(X)&~kind(X)))))&
(((curious(lucy)&~funny(lucy)))=>((~generous(susan)<~>happy(susan))))&
(![X]:((~tall(X)|kind(X))=>(~calm(X)&quiet(X))))&
((?[X]:((old(X)&creative(X))))<=>(?[X]:((~calm(X)&strong(X)))))&
(![X]:(tall(X)=>~quiet(X)))&
(![X]:((~patient(X)|funny(X))<=>(brave(X)|~patient(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(~tall(X)|quiet(X))))&
(![X]:((old(X)|creative(X))=>~tall(X)))&
(![X]:((~patient(X)|~curious(X))<=>(~rich(X)<~>~humble(X))))&
(![X]:((rich(X)<~>~calm(X))<=>~wise(X)))&
(![X]:(~old(X)<=>(~happy(X)&~funny(X))))&
(![X]:((~rich(X)&~quiet(X))<=>rich(X)))&
(![X]:((kind(X)|~curious(X))=>(~generous(X)<~>~patient(X))))&
((~humble(susan)&old(susan)))&
(?[X]:((generous(X)<~>~curious(X))))&
(?[X]:((~calm(X)|~happy(X))))&
(?[X]:((old(X)<~>calm(X))))&
(?[X]:((~calm(X)&old(X))))&
(funny(paul)) | ~wise(lucy) | [
"p5",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3763015953543042961139506
% SZS output start Proof for 3763015953543042961139506
6. ! [X0] : ((kind(X0) | ~tall(X0)) => (quiet(X0) & ~calm(X0))) [input p5]
8. ! [X0] : (tall(X0) => ~quiet(X0)) [input p7]
13. ! [X0] : ((rich(X0) <~> ~calm(X0)) <=> ~wise(X0)) [input p12]
15. ! [X0] : ((~quiet(X0) & ~rich(X0)) <=> rich(X0)) [input p14]
23. wise(lucy) [input hypothesis]
25. ! [X0] : (~tall(X0) => (quiet(X0) & ~calm(X0))) [pure predicate removal 6]
33. ! [X0] : ((quiet(X0) & ~calm(X0)) | tall(X0)) [ennf transformation 25]
34. ! [X0] : (~quiet(X0) | ~tall(X0)) [ennf transformation 8]
57. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | wise(X0)) & (~wise(X0) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [nnf transformation 13]
60. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~rich(X0)) & (rich(X0) | (quiet(X0) | rich(X0)))) [nnf transformation 15]
61. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~rich(X0)) & (rich(X0) | quiet(X0) | rich(X0))) [flattening 60]
83. ~calm(X0) | tall(X0) [cnf transformation 33]
89. ~quiet(X0) | ~tall(X0) [cnf transformation 34]
105. ~wise(X0) | rich(X0) | calm(X0) [cnf transformation 57]
111. rich(X0) | quiet(X0) | rich(X0) [cnf transformation 61]
112. ~rich(X0) | ~rich(X0) [cnf transformation 61]
126. wise(lucy) [cnf transformation 23]
127. rich(X0) | quiet(X0) [duplicate literal removal 111]
128. ~rich(X0) [duplicate literal removal 112]
208. quiet(X0) [subsumption resolution 127,128]
242. ~tall(X1) [resolution 89,208]
283. rich(lucy) | calm(lucy) [resolution 105,126]
284. calm(lucy) [subsumption resolution 283,128]
285. tall(lucy) [resolution 284,83]
286. $false [subsumption resolution 285,242]
% SZS output end Proof for 3763015953543042961139506
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or patient is old or calm and vice versa. Everyone who is quiet or happy is curious and vice versa. If someone is tall or old then someone is either not funny or curious. Everyone who is not strong or not calm is both calm and quiet. If fred is both not curious and patient then lucy is either not brave or generous. Everyone who is either rich or wise is curious. If fred is patient or not humble then susan is both not curious and not funny and vice versa. Everyone who is both generous and wise is not quiet or not generous and vice versa. If someone is not calm or calm then mary is not strong and vice versa. Everyone who is kind or not wise is either not wise or kind. If fred is not generous then fred is either not tall or patient and vice versa. Everyone who is not creative is happy. Everyone who is both happy and not brave is either not wise or strong and vice versa. If fred is rich or not generous then paul is not curious or tall. If someone is either not rich or quiet then paul is either not generous or not quiet and vice versa. If lucy is both not creative and not tall then someone is both generous and not rich and vice versa. Alice is either not curious or calm. Someone is both not quiet and curious. John is humble or not humble. Paul is creative. Someone is either tall or not calm. Someone is not happy. | Susan is not creative. | neutral | (![X]:((quiet(X)|patient(X))<=>(old(X)|calm(X))))&
(![X]:((quiet(X)|happy(X))<=>curious(X)))&
((?[X]:((tall(X)|old(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~strong(X)|~calm(X))=>(calm(X)&quiet(X))))&
(((~curious(fred)&patient(fred)))=>((~brave(lucy)<~>generous(lucy))))&
(![X]:((rich(X)<~>wise(X))=>curious(X)))&
(((patient(fred)|~humble(fred)))<=>((~curious(susan)&~funny(susan))))&
(![X]:((generous(X)&wise(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(~strong(mary)))&
(![X]:((kind(X)|~wise(X))=>(~wise(X)<~>kind(X))))&
((~generous(fred))<=>((~tall(fred)<~>patient(fred))))&
(![X]:(~creative(X)=>happy(X)))&
(![X]:((happy(X)&~brave(X))<=>(~wise(X)<~>strong(X))))&
(((rich(fred)|~generous(fred)))=>((~curious(paul)|tall(paul))))&
((?[X]:((~rich(X)<~>quiet(X))))<=>((~generous(paul)<~>~quiet(paul))))&
(((~creative(lucy)&~tall(lucy)))<=>(?[X]:((generous(X)&~rich(X)))))&
((~curious(alice)<~>calm(alice)))&
(?[X]:((~quiet(X)&curious(X))))&
((humble(john)|~humble(john)))&
(creative(paul))&
(?[X]:((tall(X)<~>~calm(X))))&
(?[X]:(~happy(X))) | ~creative(susan) | [] | null | 0 |
Everyone who is both not patient and not creative is patient and vice versa.
Everyone who is either not quiet or not rich is either rich or wise and vice versa.
Everyone who is calm is either kind or not generous.
If paul is either happy or not happy then lucy is both not funny and generous and vice versa.
Everyone who is not happy or funny is not creative or kind.
If alice is not tall then someone is either not curious or not old.
If someone is either kind or funny then susan is either tall or not humble and vice versa.
Everyone who is kind or not happy is brave.
If someone is both not kind and not quiet then someone is both not tall and not generous.
Everyone who is both quiet and not calm is both generous and not creative.
If someone is not brave then someone is both curious and not curious and vice versa.
If someone is either not kind or tall then someone is not rich.
If someone is either calm or strong then mary is rich or curious.
Everyone who is curious is not tall and vice versa.
Everyone who is not happy is not wise or not kind and vice versa.
If someone is calm or kind then someone is rich.
Someone is not rich or not patient.
Someone is strong or not calm.
Someone is both not generous and tall.
Alice is not funny.
Mary is not tall.
Someone is either tall or rich.
Lucy is not creative or not strong.
Someone is both not wise and not strong. | Lucy is creative. | entailment | (![X]:((~patient(X)&~creative(X))<=>patient(X)))&
(![X]:((~quiet(X)<~>~rich(X))<=>(rich(X)<~>wise(X))))&
(![X]:(calm(X)=>(kind(X)<~>~generous(X))))&
(((happy(paul)<~>~happy(paul)))<=>((~funny(lucy)&generous(lucy))))&
(![X]:((~happy(X)|funny(X))=>(~creative(X)|kind(X))))&
((~tall(alice))=>(?[X]:((~curious(X)<~>~old(X)))))&
((?[X]:((kind(X)<~>funny(X))))<=>((tall(susan)<~>~humble(susan))))&
(![X]:((kind(X)|~happy(X))=>brave(X)))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((quiet(X)&~calm(X))=>(generous(X)&~creative(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((curious(X)&~curious(X)))))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:(~rich(X))))&
((?[X]:((calm(X)<~>strong(X))))=>((rich(mary)|curious(mary))))&
(![X]:(curious(X)<=>~tall(X)))&
(![X]:(~happy(X)<=>(~wise(X)|~kind(X))))&
((?[X]:((calm(X)|kind(X))))=>(?[X]:(rich(X))))&
(?[X]:((~rich(X)|~patient(X))))&
(?[X]:((strong(X)|~calm(X))))&
(?[X]:((~generous(X)&tall(X))))&
(~funny(alice))&
(~tall(mary))&
(?[X]:((tall(X)<~>rich(X))))&
((~creative(lucy)|~strong(lucy)))&
(?[X]:((~wise(X)&~strong(X)))) | creative(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8033278811905599977459664
% SZS output start Proof for 8033278811905599977459664
1. ! [X0] : ((~creative(X0) & ~patient(X0)) <=> patient(X0)) [input p0]
25. ~creative(lucy) [input hypothesis]
42. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~patient(X0)) & (patient(X0) | (creative(X0) | patient(X0)))) [nnf transformation 1]
43. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~patient(X0)) & (patient(X0) | creative(X0) | patient(X0))) [flattening 42]
85. patient(X0) | creative(X0) | patient(X0) [cnf transformation 43]
86. ~patient(X0) | ~patient(X0) [cnf transformation 43]
147. ~creative(lucy) [cnf transformation 25]
156. patient(X0) | creative(X0) [duplicate literal removal 85]
157. ~patient(X0) [duplicate literal removal 86]
158. creative(X0) [subsumption resolution 156,157]
296. $false [subsumption resolution 147,158]
% SZS output end Proof for 8033278811905599977459664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either wise or old then someone is creative and vice versa. If susan is both generous and wise then someone is not happy or not brave and vice versa. Everyone who is old is not funny or not creative and vice versa. If fred is either generous or tall then someone is calm. Everyone who is both brave and funny is old and vice versa. If fred is either old or not creative then susan is quiet or old and vice versa. Everyone who is either tall or not wise is either wise or brave. If someone is either not wise or happy then fred is not curious or old. If someone is not happy then someone is strong. Everyone who is either quiet or not happy is brave or not tall. Everyone who is not happy is either curious or not rich. If someone is both quiet and humble then susan is kind or funny. Everyone who is either funny or strong is either not old or not wise and vice versa. If fred is not curious then paul is both not wise and not quiet. Someone is either not happy or not humble. Lucy is both rich and kind. Alice is either brave or not strong. Someone is either quiet or not kind. Paul is strong. Someone is kind or generous. Someone is generous or creative. | Susan is not wise. | contradiction | (((wise(mary)<~>old(mary)))<=>(?[X]:(creative(X))))&
(((generous(susan)&wise(susan)))<=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:(old(X)<=>(~funny(X)|~creative(X))))&
(((generous(fred)<~>tall(fred)))=>(?[X]:(calm(X))))&
(![X]:((brave(X)&funny(X))<=>old(X)))&
(((old(fred)<~>~creative(fred)))<=>((quiet(susan)|old(susan))))&
(![X]:((tall(X)<~>~wise(X))=>(wise(X)<~>brave(X))))&
((?[X]:((~wise(X)<~>happy(X))))=>((~curious(fred)|old(fred))))&
((?[X]:(~happy(X)))=>(?[X]:(strong(X))))&
(![X]:((quiet(X)<~>~happy(X))=>(brave(X)|~tall(X))))&
(![X]:(~happy(X)=>(curious(X)<~>~rich(X))))&
((?[X]:((quiet(X)&humble(X))))=>((kind(susan)|funny(susan))))&
(![X]:((funny(X)<~>strong(X))<=>(~old(X)<~>~wise(X))))&
((~curious(fred))=>((~wise(paul)&~quiet(paul))))&
(?[X]:((~happy(X)<~>~humble(X))))&
((rich(lucy)&kind(lucy)))&
((brave(alice)<~>~strong(alice)))&
(?[X]:((quiet(X)<~>~kind(X))))&
(strong(paul))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((generous(X)|creative(X)))) | ~wise(susan) | [
"p1",
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1102264114984900215640206
% SZS output start Proof for 1102264114984900215640206
2. (wise(susan) & generous(susan)) <=> ? [X0] : (~brave(X0) | ~happy(X0)) [input p1]
3. ! [X0] : (old(X0) <=> (~creative(X0) | ~funny(X0))) [input p2]
5. ! [X0] : ((funny(X0) & brave(X0)) <=> old(X0)) [input p4]
6. (old(fred) <~> ~creative(fred)) <=> (old(susan) | quiet(susan)) [input p5]
22. ~wise(susan) [input hypothesis]
39. ((wise(susan) & generous(susan)) | ! [X0] : (brave(X0) & happy(X0))) & (? [X0] : (~brave(X0) | ~happy(X0)) | (~wise(susan) | ~generous(susan))) [nnf transformation 2]
40. ((wise(susan) & generous(susan)) | ! [X0] : (brave(X0) & happy(X0))) & (? [X0] : (~brave(X0) | ~happy(X0)) | ~wise(susan) | ~generous(susan)) [flattening 39]
41. ((wise(susan) & generous(susan)) | ! [X0] : (brave(X0) & happy(X0))) & (? [X1] : (~brave(X1) | ~happy(X1)) | ~wise(susan) | ~generous(susan)) [rectify 40]
42. ? [X1] : (~brave(X1) | ~happy(X1)) => (~brave(sK1) | ~happy(sK1)) [choice axiom]
43. ((wise(susan) & generous(susan)) | ! [X0] : (brave(X0) & happy(X0))) & ((~brave(sK1) | ~happy(sK1)) | ~wise(susan) | ~generous(susan)) [skolemisation 41,42]
44. ! [X0] : ((old(X0) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | ~old(X0))) [nnf transformation 3]
45. ! [X0] : ((old(X0) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~old(X0))) [flattening 44]
46. ! [X0] : (((funny(X0) & brave(X0)) | ~old(X0)) & (old(X0) | (~funny(X0) | ~brave(X0)))) [nnf transformation 5]
47. ! [X0] : (((funny(X0) & brave(X0)) | ~old(X0)) & (old(X0) | ~funny(X0) | ~brave(X0))) [flattening 46]
48. (((creative(fred) | ~old(fred)) & (~creative(fred) | old(fred))) | (~old(susan) & ~quiet(susan))) & ((old(susan) | quiet(susan)) | ((old(fred) | creative(fred)) & (~creative(fred) | ~old(fred)))) [nnf transformation 6]
49. (((creative(fred) | ~old(fred)) & (~creative(fred) | old(fred))) | (~old(susan) & ~quiet(susan))) & (old(susan) | quiet(susan) | ((old(fred) | creative(fred)) & (~creative(fred) | ~old(fred)))) [flattening 48]
77. wise(susan) | brave(X0) [cnf transformation 43]
78. ~funny(X0) | ~creative(X0) | ~old(X0) [cnf transformation 45]
79. funny(X0) | old(X0) [cnf transformation 45]
80. creative(X0) | old(X0) [cnf transformation 45]
81. old(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 47]
83. funny(X0) | ~old(X0) [cnf transformation 47]
89. creative(fred) | ~old(fred) | ~old(susan) [cnf transformation 49]
123. ~wise(susan) [cnf transformation 22]
127. 1 <=> ! [X0] : ~creative(X0) [avatar definition]
128. ~creative(X0) <- (1) [avatar component clause 127]
146. 5 <=> ! [X0] : brave(X0) [avatar definition]
147. brave(X0) <- (5) [avatar component clause 146]
149. 6 <=> wise(susan) [avatar definition]
152. 5 | 6 [avatar split clause 77,149,146]
172. funny(X0) [subsumption resolution 83,79]
173. ~brave(X0) | old(X0) [subsumption resolution 81,172]
174. creative(fred) | ~old(susan) [subsumption resolution 89,80]
176. 11 <=> old(susan) [avatar definition]
178. ~old(susan) <- (~11) [avatar component clause 176]
180. 12 <=> creative(fred) [avatar definition]
182. creative(fred) <- (12) [avatar component clause 180]
183. ~11 | 12 [avatar split clause 174,180,176]
278. ~6 [avatar split clause 123,149]
281. old(X0) <- (5) [resolution 173,147]
284. $false <- (5, ~11) [resolution 281,178]
287. ~5 | 11 [avatar contradiction clause 284]
293. ~creative(X1) | ~old(X1) [resolution 78,172]
294. ~creative(X1) <- (5) [subsumption resolution 293,281]
295. 1 | ~5 [avatar split clause 294,146,127]
296. $false <- (1, 12) [resolution 128,182]
298. ~1 | ~12 [avatar contradiction clause 296]
299. $false [avatar sat refutation 152,183,278,287,295,298]
% SZS output end Proof for 1102264114984900215640206
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not generous and vice versa.
Everyone who is either funny or wise is not funny and vice versa.
Everyone who is not happy or quiet is both not calm and tall and vice versa.
If someone is old or curious then john is both kind and patient and vice versa.
Everyone who is brave or old is both wise and not brave.
If someone is wise or calm then someone is either creative or not kind.
If someone is either not kind or not rich then someone is quiet or wise and vice versa.
If someone is rich then someone is not old.
If someone is quiet then john is not happy or humble.
Everyone who is both calm and humble is not patient or not rich.
Everyone who is both not curious and strong is both patient and not generous and vice versa.
Everyone who is curious is old or tall and vice versa.
Everyone who is both wise and not brave is both kind and funny and vice versa.
If someone is both not wise and rich then someone is not curious or humble and vice versa.
Everyone who is not creative or not strong is both funny and curious.
Someone is either not tall or brave.
Fred is not happy.
Susan is old or not happy.
Susan is both not old and rich.
Someone is not curious or wise.
Someone is either not rich or not quiet. | John is quiet. | neutral | (![X]:(brave(X)<=>~generous(X)))&
(![X]:((funny(X)<~>wise(X))<=>~funny(X)))&
(![X]:((~happy(X)|quiet(X))<=>(~calm(X)&tall(X))))&
((?[X]:((old(X)|curious(X))))<=>((kind(john)&patient(john))))&
(![X]:((brave(X)|old(X))=>(wise(X)&~brave(X))))&
((?[X]:((wise(X)|calm(X))))=>(?[X]:((creative(X)<~>~kind(X)))))&
((?[X]:((~kind(X)<~>~rich(X))))<=>(?[X]:((quiet(X)|wise(X)))))&
((?[X]:(rich(X)))=>(?[X]:(~old(X))))&
((?[X]:(quiet(X)))=>((~happy(john)|humble(john))))&
(![X]:((calm(X)&humble(X))=>(~patient(X)|~rich(X))))&
(![X]:((~curious(X)&strong(X))<=>(patient(X)&~generous(X))))&
(![X]:(curious(X)<=>(old(X)|tall(X))))&
(![X]:((wise(X)&~brave(X))<=>(kind(X)&funny(X))))&
((?[X]:((~wise(X)&rich(X))))<=>(?[X]:((~curious(X)|humble(X)))))&
(![X]:((~creative(X)|~strong(X))=>(funny(X)&curious(X))))&
(?[X]:((~tall(X)<~>brave(X))))&
(~happy(fred))&
((old(susan)|~happy(susan)))&
((~old(susan)&rich(susan)))&
(?[X]:((~curious(X)|wise(X))))&
(?[X]:((~rich(X)<~>~quiet(X)))) | quiet(john) | [] | null | 0 |
If john is both not wise and not humble then alice is patient.
If someone is both not generous and calm then someone is both tall and not creative.
If someone is not wise or not curious then paul is not humble or patient and vice versa.
Everyone who is either not calm or generous is strong.
Everyone who is tall is strong.
If someone is either not calm or not quiet then alice is both not tall and happy.
If mary is not rich or brave then john is brave or not kind.
If someone is happy then mary is quiet.
If someone is happy or creative then someone is happy.
If paul is both brave and not funny then someone is both rich and not curious and vice versa.
If mary is both not strong and not generous then someone is both wise and not rich.
If someone is not humble then someone is both generous and not brave and vice versa.
If someone is either humble or not wise then alice is both not tall and not patient.
If someone is both humble and not curious then fred is old and vice versa.
If someone is either not funny or not calm then someone is brave or not quiet and vice versa.
Everyone who is both wise and rich is not wise or not kind and vice versa.
Fred is old.
Someone is either not generous or quiet.
Paul is not creative.
Lucy is funny or not creative.
Someone is either not happy or curious.
Lucy is tall.
Someone is both funny and brave. | Alice is not patient. | entailment | (((~wise(john)&~humble(john)))=>(patient(alice)))&
((?[X]:((~generous(X)&calm(X))))=>(?[X]:((tall(X)&~creative(X)))))&
((?[X]:((~wise(X)|~curious(X))))<=>((~humble(paul)|patient(paul))))&
(![X]:((~calm(X)<~>generous(X))=>strong(X)))&
(![X]:(tall(X)=>strong(X)))&
((?[X]:((~calm(X)<~>~quiet(X))))=>((~tall(alice)&happy(alice))))&
(((~rich(mary)|brave(mary)))=>((brave(john)|~kind(john))))&
((?[X]:(happy(X)))=>(quiet(mary)))&
((?[X]:((happy(X)|creative(X))))=>(?[X]:(happy(X))))&
(((brave(paul)&~funny(paul)))<=>(?[X]:((rich(X)&~curious(X)))))&
(((~strong(mary)&~generous(mary)))=>(?[X]:((wise(X)&~rich(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((humble(X)<~>~wise(X))))=>((~tall(alice)&~patient(alice))))&
((?[X]:((humble(X)&~curious(X))))<=>(old(fred)))&
((?[X]:((~funny(X)<~>~calm(X))))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((wise(X)&rich(X))<=>(~wise(X)|~kind(X))))&
(old(fred))&
(?[X]:((~generous(X)<~>quiet(X))))&
(~creative(paul))&
((funny(lucy)|~creative(lucy)))&
(?[X]:((~happy(X)<~>curious(X))))&
(tall(lucy))&
(?[X]:((funny(X)&brave(X)))) | ~patient(alice) | [
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1777071911640237446358075
% SZS output start Proof for 1777071911640237446358075
13. ? [X0] : (humble(X0) <~> ~wise(X0)) => (~patient(alice) & ~tall(alice)) [input p12]
14. ? [X0] : (~curious(X0) & humble(X0)) <=> old(fred) [input p13]
16. ! [X0] : ((rich(X0) & wise(X0)) <=> (~kind(X0) | ~wise(X0))) [input p15]
17. old(fred) [input p16]
24. patient(alice) [input hypothesis]
44. (~patient(alice) & ~tall(alice)) | ! [X0] : (humble(X0) <=> ~wise(X0)) [ennf transformation 13]
67. (~patient(alice) & ~tall(alice)) | ! [X0] : ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0))) [nnf transformation 44]
68. (? [X0] : (~curious(X0) & humble(X0)) | ~old(fred)) & (old(fred) | ! [X0] : (curious(X0) | ~humble(X0))) [nnf transformation 14]
69. (? [X0] : (~curious(X0) & humble(X0)) | ~old(fred)) & (old(fred) | ! [X1] : (curious(X1) | ~humble(X1))) [rectify 68]
70. ? [X0] : (~curious(X0) & humble(X0)) => (~curious(sK6) & humble(sK6)) [choice axiom]
71. ((~curious(sK6) & humble(sK6)) | ~old(fred)) & (old(fred) | ! [X1] : (curious(X1) | ~humble(X1))) [skolemisation 69,70]
77. ! [X0] : (((rich(X0) & wise(X0)) | (kind(X0) & wise(X0))) & ((~kind(X0) | ~wise(X0)) | (~rich(X0) | ~wise(X0)))) [nnf transformation 16]
78. ! [X0] : (((rich(X0) & wise(X0)) | (kind(X0) & wise(X0))) & (~kind(X0) | ~wise(X0) | ~rich(X0) | ~wise(X0))) [flattening 77]
110. ~patient(alice) | ~wise(X0) | ~humble(X0) [cnf transformation 67]
113. humble(sK6) | ~old(fred) [cnf transformation 71]
122. wise(X0) | wise(X0) [cnf transformation 78]
126. old(fred) [cnf transformation 17]
134. patient(alice) [cnf transformation 24]
136. wise(X0) [duplicate literal removal 122]
146. 3 <=> patient(alice) [avatar definition]
181. 11 <=> ! [X1] : wise(X1) [avatar definition]
182. wise(X1) <- (11) [avatar component clause 181]
282. 34 <=> ! [X0] : (~wise(X0) | ~humble(X0)) [avatar definition]
283. ~humble(X0) | ~wise(X0) <- (34) [avatar component clause 282]
284. 34 | ~3 [avatar split clause 110,146,282]
288. 35 <=> old(fred) [avatar definition]
297. 37 <=> humble(sK6) [avatar definition]
299. humble(sK6) <- (37) [avatar component clause 297]
300. ~35 | 37 [avatar split clause 113,297,288]
339. 11 [avatar split clause 136,181]
340. 35 [avatar split clause 126,288]
361. 3 [avatar split clause 134,146]
374. ~wise(sK6) <- (34, 37) [resolution 283,299]
377. $false <- (11, 34, 37) [subsumption resolution 374,182]
378. ~11 | ~34 | ~37 [avatar contradiction clause 377]
379. $false [avatar sat refutation 284,300,339,340,361,378]
% SZS output end Proof for 1777071911640237446358075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is both kind and strong.
Everyone who is both not happy and kind is either not humble or brave and vice versa.
Everyone who is both happy and patient is not brave.
Everyone who is brave or rich is not creative and vice versa.
If alice is either not generous or not brave then someone is both wise and not brave and vice versa.
If paul is brave or curious then lucy is not curious or quiet and vice versa.
Everyone who is either not strong or rich is not rich or not calm.
If someone is quiet then someone is both quiet and not happy.
Everyone who is not happy is both old and not old.
If fred is not humble then mary is either not quiet or not humble.
Everyone who is brave or humble is creative.
If mary is wise then fred is kind and vice versa.
Everyone who is humble or wise is either not brave or old and vice versa.
Everyone who is generous or funny is both not funny and not quiet.
If susan is kind or wise then someone is either generous or old and vice versa.
Everyone who is both quiet and calm is both not happy and patient and vice versa.
Paul is both not strong and not brave.
Fred is not generous.
John is curious.
Lucy is both wise and not strong.
Fred is both calm and patient.
Someone is either happy or not strong.
Susan is either tall or kind. | Mary is not old. | entailment | (![X]:(tall(X)=>(kind(X)&strong(X))))&
(![X]:((~happy(X)&kind(X))<=>(~humble(X)<~>brave(X))))&
(![X]:((happy(X)&patient(X))=>~brave(X)))&
(![X]:((brave(X)|rich(X))<=>~creative(X)))&
(((~generous(alice)<~>~brave(alice)))<=>(?[X]:((wise(X)&~brave(X)))))&
(((brave(paul)|curious(paul)))<=>((~curious(lucy)|quiet(lucy))))&
(![X]:((~strong(X)<~>rich(X))=>(~rich(X)|~calm(X))))&
((?[X]:(quiet(X)))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:(~happy(X)=>(old(X)&~old(X))))&
((~humble(fred))=>((~quiet(mary)<~>~humble(mary))))&
(![X]:((brave(X)|humble(X))=>creative(X)))&
((wise(mary))<=>(kind(fred)))&
(![X]:((humble(X)|wise(X))<=>(~brave(X)<~>old(X))))&
(![X]:((generous(X)|funny(X))=>(~funny(X)&~quiet(X))))&
(((kind(susan)|wise(susan)))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((quiet(X)&calm(X))<=>(~happy(X)&patient(X))))&
((~strong(paul)&~brave(paul)))&
(~generous(fred))&
(curious(john))&
((wise(lucy)&~strong(lucy)))&
((calm(fred)&patient(fred)))&
(?[X]:((happy(X)<~>~strong(X))))&
((tall(susan)<~>kind(susan))) | ~old(mary) | [
"p1",
"p3",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 434760979495496907515548
% SZS output start Proof for 434760979495496907515548
2. ! [X0] : ((kind(X0) & ~happy(X0)) <=> (~humble(X0) <~> brave(X0))) [input p1]
4. ! [X0] : ((rich(X0) | brave(X0)) <=> ~creative(X0)) [input p3]
9. ! [X0] : (~happy(X0) => (~old(X0) & old(X0))) [input p8]
11. ! [X0] : ((humble(X0) | brave(X0)) => creative(X0)) [input p10]
13. ! [X0] : ((wise(X0) | humble(X0)) <=> (~brave(X0) <~> old(X0))) [input p12]
24. old(mary) [input hypothesis]
26. ! [X0] : ((rich(X0) | brave(X0)) => ~creative(X0)) [unused predicate definition removal 4]
31. ! [X0] : (~creative(X0) | (~rich(X0) & ~brave(X0))) [ennf transformation 26]
35. ! [X0] : ((~old(X0) & old(X0)) | happy(X0)) [ennf transformation 9]
37. ! [X0] : (creative(X0) | (~humble(X0) & ~brave(X0))) [ennf transformation 11]
39. ! [X0] : (((kind(X0) & ~happy(X0)) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0)))) & (((~brave(X0) | humble(X0)) & (brave(X0) | ~humble(X0))) | (~kind(X0) | happy(X0)))) [nnf transformation 2]
40. ! [X0] : (((kind(X0) & ~happy(X0)) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0)))) & (((~brave(X0) | humble(X0)) & (brave(X0) | ~humble(X0))) | ~kind(X0) | happy(X0))) [flattening 39]
53. ! [X0] : (((wise(X0) | humble(X0)) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) & (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | (~wise(X0) & ~humble(X0)))) [nnf transformation 13]
54. ! [X0] : ((wise(X0) | humble(X0) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) & (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | (~wise(X0) & ~humble(X0)))) [flattening 53]
70. ~happy(X0) | brave(X0) | humble(X0) [cnf transformation 40]
75. ~creative(X0) | ~brave(X0) [cnf transformation 31]
91. old(X0) | happy(X0) [cnf transformation 35]
92. ~old(X0) | happy(X0) [cnf transformation 35]
95. creative(X0) | ~brave(X0) [cnf transformation 37]
101. ~old(X0) | brave(X0) | ~humble(X0) [cnf transformation 54]
128. old(mary) [cnf transformation 24]
188. happy(X0) [subsumption resolution 91,92]
198. 15 <=> humble(mary) [avatar definition]
199. ~humble(mary) <- (~15) [avatar component clause 198]
203. ~brave(X0) [subsumption resolution 95,75]
216. ~old(X0) | ~humble(X0) [subsumption resolution 101,203]
257. ~humble(mary) [resolution 216,128]
258. ~15 [avatar split clause 257,198]
260. brave(X0) | humble(X0) [resolution 70,188]
261. humble(X0) [subsumption resolution 260,203]
263. $false <- (~15) [resolution 261,199]
264. 15 [avatar contradiction clause 263]
265. $false [avatar sat refutation 258,264]
% SZS output end Proof for 434760979495496907515548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not tall is not creative.
Everyone who is not kind or old is happy and vice versa.
Everyone who is both not patient and brave is not tall or curious and vice versa.
Everyone who is either quiet or not brave is both not strong and funny and vice versa.
Everyone who is either not calm or not tall is both not funny and not happy and vice versa.
If fred is either not brave or not wise then someone is either creative or brave and vice versa.
If susan is either curious or kind then mary is not creative and vice versa.
Everyone who is humble or creative is both not tall and not old and vice versa.
Everyone who is not generous is funny.
Everyone who is not patient or calm is not tall and vice versa.
If mary is either quiet or not curious then someone is both not kind and not strong.
If someone is either not patient or not strong then someone is creative or humble.
Everyone who is both quiet and not kind is both calm and happy and vice versa.
Everyone who is not happy or happy is both not wise and not brave and vice versa.
Everyone who is both not strong and kind is both not kind and rich.
Everyone who is either happy or not old is both quiet and not humble and vice versa.
Alice is either not curious or curious.
Alice is either humble or tall.
Mary is either strong or creative.
Someone is either calm or patient.
Mary is either not funny or calm. | Fred is not kind. | contradiction | (![X]:((~funny(X)&~tall(X))=>~creative(X)))&
(![X]:((~kind(X)|old(X))<=>happy(X)))&
(![X]:((~patient(X)&brave(X))<=>(~tall(X)|curious(X))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)&funny(X))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~funny(X)&~happy(X))))&
(((~brave(fred)<~>~wise(fred)))<=>(?[X]:((creative(X)<~>brave(X)))))&
(((curious(susan)<~>kind(susan)))<=>(~creative(mary)))&
(![X]:((humble(X)|creative(X))<=>(~tall(X)&~old(X))))&
(![X]:(~generous(X)=>funny(X)))&
(![X]:((~patient(X)|calm(X))<=>~tall(X)))&
(((quiet(mary)<~>~curious(mary)))=>(?[X]:((~kind(X)&~strong(X)))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:((creative(X)|humble(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(calm(X)&happy(X))))&
(![X]:((~happy(X)|happy(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~strong(X)&kind(X))=>(~kind(X)&rich(X))))&
(![X]:((happy(X)<~>~old(X))<=>(quiet(X)&~humble(X))))&
((~curious(alice)<~>curious(alice)))&
((humble(alice)<~>tall(alice)))&
((strong(mary)<~>creative(mary)))&
(?[X]:((calm(X)<~>patient(X))))&
((~funny(mary)<~>calm(mary))) | ~kind(fred) | [
"p1",
"p2",
"p4",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7994635036682912812516241
% SZS output start Proof for 7994635036682912812516241
2. ! [X0] : ((old(X0) | ~kind(X0)) <=> happy(X0)) [input p1]
3. ! [X0] : ((brave(X0) & ~patient(X0)) <=> (curious(X0) | ~tall(X0))) [input p2]
5. ! [X0] : ((~calm(X0) <~> ~tall(X0)) <=> (~happy(X0) & ~funny(X0))) [input p4]
10. ! [X0] : ((calm(X0) | ~patient(X0)) <=> ~tall(X0)) [input p9]
14. ! [X0] : ((happy(X0) | ~happy(X0)) <=> (~brave(X0) & ~wise(X0))) [input p13]
22. ~kind(fred) [input hypothesis]
32. ! [X0] : (((old(X0) | ~kind(X0)) | ~happy(X0)) & (happy(X0) | (~old(X0) & kind(X0)))) [nnf transformation 2]
33. ! [X0] : ((old(X0) | ~kind(X0) | ~happy(X0)) & (happy(X0) | (~old(X0) & kind(X0)))) [flattening 32]
34. ! [X0] : (((brave(X0) & ~patient(X0)) | (~curious(X0) & tall(X0))) & ((curious(X0) | ~tall(X0)) | (~brave(X0) | patient(X0)))) [nnf transformation 3]
35. ! [X0] : (((brave(X0) & ~patient(X0)) | (~curious(X0) & tall(X0))) & (curious(X0) | ~tall(X0) | ~brave(X0) | patient(X0))) [flattening 34]
38. ! [X0] : ((((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0))))) [nnf transformation 5]
39. ! [X0] : ((((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0))))) [flattening 38]
47. ! [X0] : (((calm(X0) | ~patient(X0)) | tall(X0)) & (~tall(X0) | (~calm(X0) & patient(X0)))) [nnf transformation 10]
48. ! [X0] : ((calm(X0) | ~patient(X0) | tall(X0)) & (~tall(X0) | (~calm(X0) & patient(X0)))) [flattening 47]
58. ! [X0] : (((happy(X0) | ~happy(X0)) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | (~happy(X0) & happy(X0)))) [nnf transformation 14]
59. ! [X0] : ((happy(X0) | ~happy(X0) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | (~happy(X0) & happy(X0)))) [flattening 58]
70. happy(X0) | kind(X0) [cnf transformation 33]
76. brave(X0) | tall(X0) [cnf transformation 35]
86. ~happy(X0) | ~tall(X0) | calm(X0) [cnf transformation 39]
108. ~calm(X0) | ~tall(X0) [cnf transformation 48]
122. ~brave(X0) | happy(X0) [cnf transformation 59]
123. ~brave(X0) | ~happy(X0) [cnf transformation 59]
142. ~kind(fred) [cnf transformation 22]
226. ~brave(X0) [subsumption resolution 122,123]
275. tall(X0) [resolution 76,226]
317. ~tall(X0) | calm(X0) | kind(X0) [resolution 86,70]
318. calm(X0) | kind(X0) [subsumption resolution 317,275]
322. kind(X2) | ~tall(X2) [resolution 318,108]
324. kind(X2) [subsumption resolution 322,275]
332. $false [resolution 324,142]
% SZS output end Proof for 7994635036682912812516241
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or curious then someone is either not curious or rich.
Everyone who is either rich or wise is happy and vice versa.
If someone is both creative and not wise then lucy is tall or creative and vice versa.
Everyone who is happy is not creative and vice versa.
If someone is quiet or not old then someone is not creative or not funny.
If lucy is both not happy and not generous then paul is either not calm or funny.
If someone is either not happy or generous then john is either funny or humble and vice versa.
Everyone who is patient is both quiet and calm and vice versa.
If susan is not humble then someone is not rich or not curious.
Everyone who is patient or calm is not wise or rich and vice versa.
If someone is both not patient and not happy then someone is not rich or not brave and vice versa.
If someone is both not calm and not wise then john is either strong or funny and vice versa.
Everyone who is both rich and kind is either not creative or generous and vice versa.
Everyone who is calm or kind is not humble.
If john is not wise then fred is rich and vice versa.
Everyone who is both humble and not funny is either not brave or not strong and vice versa.
Someone is either not rich or not happy.
John is tall.
Someone is either generous or tall.
Paul is either not wise or not tall.
John is either humble or not strong.
John is not patient or tall. | Fred is not humble. | entailment | ((?[X]:((kind(X)|curious(X))))=>(?[X]:((~curious(X)<~>rich(X)))))&
(![X]:((rich(X)<~>wise(X))<=>happy(X)))&
((?[X]:((creative(X)&~wise(X))))<=>((tall(lucy)|creative(lucy))))&
(![X]:(happy(X)<=>~creative(X)))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~creative(X)|~funny(X)))))&
(((~happy(lucy)&~generous(lucy)))=>((~calm(paul)<~>funny(paul))))&
((?[X]:((~happy(X)<~>generous(X))))<=>((funny(john)<~>humble(john))))&
(![X]:(patient(X)<=>(quiet(X)&calm(X))))&
((~humble(susan))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((patient(X)|calm(X))<=>(~wise(X)|rich(X))))&
((?[X]:((~patient(X)&~happy(X))))<=>(?[X]:((~rich(X)|~brave(X)))))&
((?[X]:((~calm(X)&~wise(X))))<=>((strong(john)<~>funny(john))))&
(![X]:((rich(X)&kind(X))<=>(~creative(X)<~>generous(X))))&
(![X]:((calm(X)|kind(X))=>~humble(X)))&
((~wise(john))<=>(rich(fred)))&
(![X]:((humble(X)&~funny(X))<=>(~brave(X)<~>~strong(X))))&
(?[X]:((~rich(X)<~>~happy(X))))&
(tall(john))&
(?[X]:((generous(X)<~>tall(X))))&
((~wise(paul)<~>~tall(paul)))&
((humble(john)<~>~strong(john)))&
((~patient(john)|tall(john))) | ~humble(fred) | [
"p3",
"p6",
"p7",
"p9",
"p11",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2172524121998451423642407
% SZS output start Proof for 2172524121998451423642407
4. ! [X0] : (happy(X0) <=> ~creative(X0)) [input p3]
7. ? [X0] : (~happy(X0) <~> generous(X0)) <=> (funny(john) <~> humble(john)) [input p6]
8. ! [X0] : (patient(X0) <=> (calm(X0) & quiet(X0))) [input p7]
10. ! [X0] : ((calm(X0) | patient(X0)) <=> (rich(X0) | ~wise(X0))) [input p9]
12. ? [X0] : (~wise(X0) & ~calm(X0)) <=> (strong(john) <~> funny(john)) [input p11]
13. ! [X0] : ((kind(X0) & rich(X0)) <=> (~creative(X0) <~> generous(X0))) [input p12]
14. ! [X0] : ((kind(X0) | calm(X0)) => ~humble(X0)) [input p13]
21. humble(john) <~> ~strong(john) [input p20]
23. humble(fred) [input hypothesis]
33. ! [X0] : (~humble(X0) | (~kind(X0) & ~calm(X0))) [ennf transformation 14]
44. ! [X0] : ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))) [nnf transformation 4]
49. (? [X0] : ((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((funny(john) | ~humble(john)) & (humble(john) | ~funny(john)))) & (((~humble(john) | ~funny(john)) & (humble(john) | funny(john))) | ! [X0] : ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) [nnf transformation 7]
50. (? [X0] : ((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((funny(john) | ~humble(john)) & (humble(john) | ~funny(john)))) & (((~humble(john) | ~funny(john)) & (humble(john) | funny(john))) | ! [X1] : ((~happy(X1) | ~generous(X1)) & (generous(X1) | happy(X1)))) [rectify 49]
51. ? [X0] : ((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) => ((~generous(sK3) | happy(sK3)) & (generous(sK3) | ~happy(sK3))) [choice axiom]
52. (((~generous(sK3) | happy(sK3)) & (generous(sK3) | ~happy(sK3))) | ((funny(john) | ~humble(john)) & (humble(john) | ~funny(john)))) & (((~humble(john) | ~funny(john)) & (humble(john) | funny(john))) | ! [X1] : ((~happy(X1) | ~generous(X1)) & (generous(X1) | happy(X1)))) [skolemisation 50,51]
53. ! [X0] : ((patient(X0) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | ~patient(X0))) [nnf transformation 8]
54. ! [X0] : ((patient(X0) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | ~patient(X0))) [flattening 53]
57. ! [X0] : (((calm(X0) | patient(X0)) | (~rich(X0) & wise(X0))) & ((rich(X0) | ~wise(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 10]
58. ! [X0] : ((calm(X0) | patient(X0) | (~rich(X0) & wise(X0))) & (rich(X0) | ~wise(X0) | (~calm(X0) & ~patient(X0)))) [flattening 57]
64. (? [X0] : (~wise(X0) & ~calm(X0)) | ((strong(john) | ~funny(john)) & (funny(john) | ~strong(john)))) & (((~funny(john) | ~strong(john)) & (funny(john) | strong(john))) | ! [X0] : (wise(X0) | calm(X0))) [nnf transformation 12]
65. (? [X0] : (~wise(X0) & ~calm(X0)) | ((strong(john) | ~funny(john)) & (funny(john) | ~strong(john)))) & (((~funny(john) | ~strong(john)) & (funny(john) | strong(john))) | ! [X1] : (wise(X1) | calm(X1))) [rectify 64]
66. ? [X0] : (~wise(X0) & ~calm(X0)) => (~wise(sK7) & ~calm(sK7)) [choice axiom]
67. ((~wise(sK7) & ~calm(sK7)) | ((strong(john) | ~funny(john)) & (funny(john) | ~strong(john)))) & (((~funny(john) | ~strong(john)) & (funny(john) | strong(john))) | ! [X1] : (wise(X1) | calm(X1))) [skolemisation 65,66]
68. ! [X0] : (((kind(X0) & rich(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) & (((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (~kind(X0) | ~rich(X0)))) [nnf transformation 13]
69. ! [X0] : (((kind(X0) & rich(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) & (((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | ~kind(X0) | ~rich(X0))) [flattening 68]
80. (strong(john) | ~humble(john)) & (~strong(john) | humble(john)) [nnf transformation 21]
94. ~creative(X0) | ~happy(X0) [cnf transformation 44]
95. creative(X0) | happy(X0) [cnf transformation 44]
99. humble(john) | funny(john) | generous(X1) | happy(X1) [cnf transformation 52]
100. humble(john) | funny(john) | ~happy(X1) | ~generous(X1) [cnf transformation 52]
101. ~humble(john) | ~funny(john) | generous(X1) | happy(X1) [cnf transformation 52]
102. ~humble(john) | ~funny(john) | ~happy(X1) | ~generous(X1) [cnf transformation 52]
108. ~patient(X0) | calm(X0) [cnf transformation 54]
113. calm(X0) | patient(X0) | wise(X0) [cnf transformation 58]
114. calm(X0) | patient(X0) | ~rich(X0) [cnf transformation 58]
122. ~calm(sK7) | funny(john) | ~strong(john) [cnf transformation 67]
123. ~calm(sK7) | strong(john) | ~funny(john) [cnf transformation 67]
124. ~wise(sK7) | funny(john) | ~strong(john) [cnf transformation 67]
125. ~wise(sK7) | strong(john) | ~funny(john) [cnf transformation 67]
128. generous(X0) | rich(X0) | creative(X0) [cnf transformation 69]
129. ~generous(X0) | ~creative(X0) | rich(X0) [cnf transformation 69]
132. ~humble(X0) | ~calm(X0) [cnf transformation 33]
149. ~strong(john) | humble(john) [cnf transformation 80]
150. strong(john) | ~humble(john) [cnf transformation 80]
152. humble(fred) [cnf transformation 23]
226. 17 <=> humble(john) [avatar definition]
230. 18 <=> funny(john) [avatar definition]
246. 21 <=> ! [X1] : (~happy(X1) | ~generous(X1)) [avatar definition]
247. ~generous(X1) | ~happy(X1) <- (21) [avatar component clause 246]
248. 21 | ~18 | ~17 [avatar split clause 102,226,230,246]
250. 22 <=> ! [X1] : (generous(X1) | happy(X1)) [avatar definition]
251. generous(X1) | happy(X1) <- (22) [avatar component clause 250]
252. 22 | ~18 | ~17 [avatar split clause 101,226,230,250]
253. 21 | 18 | 17 [avatar split clause 100,226,230,246]
254. 22 | 18 | 17 [avatar split clause 99,226,230,250]
268. ~rich(X0) | calm(X0) [subsumption resolution 114,108]
269. calm(X0) | wise(X0) [subsumption resolution 113,108]
279. 28 <=> ! [X1] : rich(X1) [avatar definition]
280. rich(X1) <- (28) [avatar component clause 279]
301. 33 <=> strong(john) [avatar definition]
305. 34 <=> wise(sK7) [avatar definition]
308. ~18 | 33 | ~34 [avatar split clause 125,305,301,230]
309. ~33 | 18 | ~34 [avatar split clause 124,305,230,301]
311. 35 <=> calm(sK7) [avatar definition]
313. ~calm(sK7) <- (~35) [avatar component clause 311]
314. ~18 | 33 | ~35 [avatar split clause 123,311,301,230]
315. ~33 | 18 | ~35 [avatar split clause 122,311,230,301]
317. 36 <=> rich(fred) [avatar definition]
318. rich(fred) <- (36) [avatar component clause 317]
319. ~rich(fred) <- (~36) [avatar component clause 317]
356. ~17 | 33 [avatar split clause 150,301,226]
357. 17 | ~33 [avatar split clause 149,301,226]
362. ~calm(fred) [resolution 132,152]
364. calm(fred) <- (36) [resolution 268,318]
366. $false <- (36) [subsumption resolution 364,362]
367. ~36 [avatar contradiction clause 366]
369. wise(sK7) <- (~35) [resolution 269,313]
373. 34 | 35 [avatar split clause 369,311,305]
461. rich(X0) | creative(X0) | ~happy(X0) <- (21) [resolution 128,247]
463. rich(X0) | ~happy(X0) <- (21) [subsumption resolution 461,94]
475. ~creative(X1) | rich(X1) | happy(X1) <- (22) [resolution 129,251]
486. rich(X1) | happy(X1) <- (22) [subsumption resolution 475,95]
487. rich(X1) <- (21, 22) [subsumption resolution 486,463]
488. 28 | ~21 | ~22 [avatar split clause 487,250,246,279]
491. $false <- (28, ~36) [resolution 280,319]
496. ~28 | 36 [avatar contradiction clause 491]
497. $false [avatar sat refutation 248,252,253,254,308,309,314,315,356,357,367,373,488,496]
% SZS output end Proof for 2172524121998451423642407
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not humble then someone is not rich or strong.
If john is curious then paul is rich or not strong and vice versa.
If someone is not brave then someone is either not humble or happy.
Everyone who is happy is wise and vice versa.
Everyone who is either not creative or old is both not rich and tall.
Everyone who is not kind is quiet or not old and vice versa.
If susan is both not patient and not creative then john is old and vice versa.
Everyone who is both not wise and wise is both not funny and generous and vice versa.
If susan is not old then someone is either happy or not happy and vice versa.
If someone is humble then paul is strong or patient.
If john is both rich and not old then susan is either not funny or happy and vice versa.
Everyone who is not creative is kind and vice versa.
If someone is creative then someone is not quiet or happy.
Everyone who is not creative is not happy or kind.
Everyone who is not generous or not happy is not creative.
If someone is rich then someone is both not quiet and rich and vice versa.
Mary is both old and not kind.
Mary is happy.
Someone is humble.
Someone is both not rich and patient.
Lucy is both not generous and not creative.
Susan is humble or brave. | John is not creative. | contradiction | ((?[X]:((creative(X)<~>~humble(X))))=>(?[X]:((~rich(X)|strong(X)))))&
((curious(john))<=>((rich(paul)|~strong(paul))))&
((?[X]:(~brave(X)))=>(?[X]:((~humble(X)<~>happy(X)))))&
(![X]:(happy(X)<=>wise(X)))&
(![X]:((~creative(X)<~>old(X))=>(~rich(X)&tall(X))))&
(![X]:(~kind(X)<=>(quiet(X)|~old(X))))&
(((~patient(susan)&~creative(susan)))<=>(old(john)))&
(![X]:((~wise(X)&wise(X))<=>(~funny(X)&generous(X))))&
((~old(susan))<=>(?[X]:((happy(X)<~>~happy(X)))))&
((?[X]:(humble(X)))=>((strong(paul)|patient(paul))))&
(((rich(john)&~old(john)))<=>((~funny(susan)<~>happy(susan))))&
(![X]:(~creative(X)<=>kind(X)))&
((?[X]:(creative(X)))=>(?[X]:((~quiet(X)|happy(X)))))&
(![X]:(~creative(X)=>(~happy(X)|kind(X))))&
(![X]:((~generous(X)|~happy(X))=>~creative(X)))&
((?[X]:(rich(X)))<=>(?[X]:((~quiet(X)&rich(X)))))&
((old(mary)&~kind(mary)))&
(happy(mary))&
(?[X]:(humble(X)))&
(?[X]:((~rich(X)&patient(X))))&
((~generous(lucy)&~creative(lucy)))&
((humble(susan)|brave(susan))) | ~creative(john) | [
"p5",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8796732425133953672615456
% SZS output start Proof for 8796732425133953672615456
6. ! [X0] : (~kind(X0) <=> (~old(X0) | quiet(X0))) [input p5]
7. (~creative(susan) & ~patient(susan)) <=> old(john) [input p6]
9. ~old(susan) <=> ? [X0] : (happy(X0) <~> ~happy(X0)) [input p8]
12. ! [X0] : (~creative(X0) <=> kind(X0)) [input p11]
23. ~creative(john) [input hypothesis]
47. ! [X0] : ((~kind(X0) | (old(X0) & ~quiet(X0))) & ((~old(X0) | quiet(X0)) | kind(X0))) [nnf transformation 6]
48. ! [X0] : ((~kind(X0) | (old(X0) & ~quiet(X0))) & (~old(X0) | quiet(X0) | kind(X0))) [flattening 47]
49. ((~creative(susan) & ~patient(susan)) | ~old(john)) & (old(john) | (creative(susan) | patient(susan))) [nnf transformation 7]
50. ((~creative(susan) & ~patient(susan)) | ~old(john)) & (old(john) | creative(susan) | patient(susan)) [flattening 49]
53. (~old(susan) | ! [X0] : ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (? [X0] : ((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | old(susan)) [nnf transformation 9]
54. (~old(susan) | ! [X0] : ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (? [X1] : ((happy(X1) | ~happy(X1)) & (~happy(X1) | happy(X1))) | old(susan)) [rectify 53]
55. ? [X1] : ((happy(X1) | ~happy(X1)) & (~happy(X1) | happy(X1))) => ((happy(sK1) | ~happy(sK1)) & (~happy(sK1) | happy(sK1))) [choice axiom]
56. (~old(susan) | ! [X0] : ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (((happy(sK1) | ~happy(sK1)) & (~happy(sK1) | happy(sK1))) | old(susan)) [skolemisation 54,55]
59. ! [X0] : ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))) [nnf transformation 12]
83. ~kind(X0) | old(X0) [cnf transformation 48]
86. ~creative(susan) | ~old(john) [cnf transformation 50]
93. ~old(susan) | ~happy(X0) | ~happy(X0) [cnf transformation 56]
94. ~old(susan) | happy(X0) | happy(X0) [cnf transformation 56]
102. kind(X0) | creative(X0) [cnf transformation 59]
119. ~creative(john) [cnf transformation 23]
120. ~old(susan) | ~happy(X0) [duplicate literal removal 93]
121. ~old(susan) | happy(X0) [duplicate literal removal 94]
154. 8 <=> old(john) [avatar definition]
156. ~old(john) <- (~8) [avatar component clause 154]
158. 9 <=> creative(susan) [avatar definition]
161. ~8 | ~9 [avatar split clause 86,158,154]
170. 11 <=> ! [X0] : happy(X0) [avatar definition]
171. happy(X0) <- (11) [avatar component clause 170]
173. 12 <=> old(susan) [avatar definition]
175. ~old(susan) <- (~12) [avatar component clause 173]
176. 11 | ~12 [avatar split clause 121,173,170]
178. 13 <=> ! [X0] : ~happy(X0) [avatar definition]
179. ~happy(X0) <- (13) [avatar component clause 178]
180. 13 | ~12 [avatar split clause 120,173,178]
245. old(X0) | creative(X0) [resolution 102,83]
250. creative(susan) <- (~12) [resolution 245,175]
253. 9 | 12 [avatar split clause 250,173,158]
254. creative(john) <- (~8) [resolution 156,245]
255. $false <- (~8) [subsumption resolution 254,119]
256. 8 [avatar contradiction clause 255]
257. $false <- (11, 13) [subsumption resolution 171,179]
258. ~11 | ~13 [avatar contradiction clause 257]
259. $false [avatar sat refutation 161,176,180,253,256,258]
% SZS output end Proof for 8796732425133953672615456
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not old is funny.
Everyone who is curious or funny is both not tall and not calm and vice versa.
Everyone who is both strong and not strong is curious and vice versa.
Everyone who is curious or not old is not tall.
If fred is not wise then someone is both kind and not old and vice versa.
Everyone who is either not rich or not happy is tall or curious and vice versa.
If alice is both brave and wise then fred is not rich or kind and vice versa.
Everyone who is either humble or kind is either not funny or not patient and vice versa.
If alice is not brave then someone is strong.
Everyone who is not wise or not funny is both not wise and not generous and vice versa.
Everyone who is not brave or quiet is creative and vice versa.
If alice is either not strong or rich then someone is curious and vice versa.
If someone is both not humble and not tall then alice is kind and vice versa.
Everyone who is either generous or not wise is either generous or not humble and vice versa.
Everyone who is calm is both kind and quiet.
Everyone who is either kind or not tall is both strong and brave.
Someone is not funny.
Someone is quiet or not curious.
Paul is both not quiet and kind.
Someone is not quiet.
Susan is humble or generous.
John is both not wise and not kind.
Mary is either not wise or not creative.
John is either not patient or patient. | Fred is not wise. | neutral | (![X]:((calm(X)|~old(X))=>funny(X)))&
(![X]:((curious(X)|funny(X))<=>(~tall(X)&~calm(X))))&
(![X]:((strong(X)&~strong(X))<=>curious(X)))&
(![X]:((curious(X)|~old(X))=>~tall(X)))&
((~wise(fred))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((~rich(X)<~>~happy(X))<=>(tall(X)|curious(X))))&
(((brave(alice)&wise(alice)))<=>((~rich(fred)|kind(fred))))&
(![X]:((humble(X)<~>kind(X))<=>(~funny(X)<~>~patient(X))))&
((~brave(alice))=>(?[X]:(strong(X))))&
(![X]:((~wise(X)|~funny(X))<=>(~wise(X)&~generous(X))))&
(![X]:((~brave(X)|quiet(X))<=>creative(X)))&
(((~strong(alice)<~>rich(alice)))<=>(?[X]:(curious(X))))&
((?[X]:((~humble(X)&~tall(X))))<=>(kind(alice)))&
(![X]:((generous(X)<~>~wise(X))<=>(generous(X)<~>~humble(X))))&
(![X]:(calm(X)=>(kind(X)&quiet(X))))&
(![X]:((kind(X)<~>~tall(X))=>(strong(X)&brave(X))))&
(?[X]:(~funny(X)))&
(?[X]:((quiet(X)|~curious(X))))&
((~quiet(paul)&kind(paul)))&
(?[X]:(~quiet(X)))&
((humble(susan)|generous(susan)))&
((~wise(john)&~kind(john)))&
((~wise(mary)<~>~creative(mary)))&
((~patient(john)<~>patient(john))) | ~wise(fred) | [] | null | 0 |
Everyone who is not wise or curious is kind.
Everyone who is not humble or curious is generous.
Everyone who is not quiet is not strong and vice versa.
Everyone who is not happy is both not kind and not calm and vice versa.
If john is not curious or not humble then someone is both calm and not quiet.
Everyone who is not calm or funny is not funny and vice versa.
If paul is not creative or funny then someone is not calm or not happy.
Everyone who is not calm or old is either not patient or tall.
Everyone who is patient or not tall is patient or funny.
If someone is either curious or not funny then susan is either not quiet or not old and vice versa.
If someone is strong then someone is not funny and vice versa.
If someone is either not happy or creative then susan is not wise or generous and vice versa.
If someone is both tall and not curious then someone is not tall and vice versa.
Everyone who is either creative or not tall is humble or not creative.
If paul is not generous then someone is not old.
Everyone who is both creative and not quiet is either not old or creative and vice versa.
Paul is strong.
Mary is either strong or not quiet.
Susan is calm or not brave.
Mary is either calm or not quiet.
Lucy is either wise or creative. | Lucy is not curious. | contradiction | (![X]:((~wise(X)|curious(X))=>kind(X)))&
(![X]:((~humble(X)|curious(X))=>generous(X)))&
(![X]:(~quiet(X)<=>~strong(X)))&
(![X]:(~happy(X)<=>(~kind(X)&~calm(X))))&
(((~curious(john)|~humble(john)))=>(?[X]:((calm(X)&~quiet(X)))))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(((~creative(paul)|funny(paul)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~calm(X)|old(X))=>(~patient(X)<~>tall(X))))&
(![X]:((patient(X)|~tall(X))=>(patient(X)|funny(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>((~quiet(susan)<~>~old(susan))))&
((?[X]:(strong(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~happy(X)<~>creative(X))))<=>((~wise(susan)|generous(susan))))&
((?[X]:((tall(X)&~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>~tall(X))=>(humble(X)|~creative(X))))&
((~generous(paul))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)<~>creative(X))))&
(strong(paul))&
((strong(mary)<~>~quiet(mary)))&
((calm(susan)|~brave(susan)))&
((calm(mary)<~>~quiet(mary)))&
((wise(lucy)<~>creative(lucy))) | ~curious(lucy) | [
"p5",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6775695226423590696918983
% SZS output start Proof for 6775695226423590696918983
6. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p5]
8. ! [X0] : ((old(X0) | ~calm(X0)) => (~patient(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((~tall(X0) | patient(X0)) => (funny(X0) | patient(X0))) [input p8]
13. ? [X0] : (~curious(X0) & tall(X0)) <=> ? [X0] : ~tall(X0) [input p12]
22. ~curious(lucy) [input hypothesis]
24. ? [X0] : (~curious(X0) & tall(X0)) <=> ? [X1] : ~tall(X1) [rectify 13]
33. ! [X0] : ((~patient(X0) <~> tall(X0)) | (~old(X0) & calm(X0))) [ennf transformation 8]
34. ! [X0] : ((funny(X0) | patient(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 9]
35. ! [X0] : (funny(X0) | patient(X0) | (tall(X0) & ~patient(X0))) [flattening 34]
42. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 6]
43. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 42]
46. ! [X0] : (((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | (~old(X0) & calm(X0))) [nnf transformation 33]
61. (? [X0] : (~curious(X0) & tall(X0)) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : (curious(X0) | ~tall(X0))) [nnf transformation 24]
62. (? [X0] : (~curious(X0) & tall(X0)) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : (curious(X3) | ~tall(X3))) [rectify 61]
63. ? [X0] : (~curious(X0) & tall(X0)) => (~curious(sK6) & tall(sK6)) [choice axiom]
64. ? [X2] : ~tall(X2) => ~tall(sK7) [choice axiom]
65. ((~curious(sK6) & tall(sK6)) | ! [X1] : tall(X1)) & (~tall(sK7) | ! [X3] : (curious(X3) | ~tall(X3))) [skolemisation 62,64,63]
84. ~funny(X0) | ~funny(X0) [cnf transformation 43]
85. funny(X0) | ~calm(X0) | funny(X0) [cnf transformation 43]
88. ~patient(X0) | tall(X0) | calm(X0) [cnf transformation 46]
93. funny(X0) | patient(X0) | tall(X0) [cnf transformation 35]
110. ~tall(sK7) | curious(X3) | ~tall(X3) [cnf transformation 65]
111. tall(sK6) | tall(X1) [cnf transformation 65]
112. ~curious(sK6) | tall(X1) [cnf transformation 65]
127. ~curious(lucy) [cnf transformation 22]
130. ~funny(X0) [duplicate literal removal 84]
131. ~calm(X0) | funny(X0) [duplicate literal removal 85]
156. tall(X0) | patient(X0) [subsumption resolution 93,130]
175. 9 <=> ! [X1] : curious(X1) [avatar definition]
176. curious(X1) <- (9) [avatar component clause 175]
210. 16 <=> ! [X1] : tall(X1) [avatar definition]
211. tall(X1) <- (16) [avatar component clause 210]
213. 17 <=> curious(sK6) [avatar definition]
215. ~curious(sK6) <- (~17) [avatar component clause 213]
216. 16 | ~17 [avatar split clause 112,213,210]
218. 18 <=> tall(sK6) [avatar definition]
220. tall(sK6) <- (18) [avatar component clause 218]
221. 16 | 18 [avatar split clause 111,218,210]
223. 19 <=> ! [X3] : (curious(X3) | ~tall(X3)) [avatar definition]
224. ~tall(X3) | curious(X3) <- (19) [avatar component clause 223]
226. 20 <=> tall(sK7) [avatar definition]
228. ~tall(sK7) <- (~20) [avatar component clause 226]
229. 19 | ~20 [avatar split clause 110,226,223]
301. curious(X0) <- (16, 19) [resolution 224,211]
304. 9 | ~16 | ~19 [avatar split clause 301,223,210,175]
307. $false <- (9) [resolution 176,127]
312. ~9 [avatar contradiction clause 307]
313. curious(sK6) <- (18, 19) [resolution 220,224]
315. $false <- (~17, 18, 19) [subsumption resolution 313,215]
316. 17 | ~18 | ~19 [avatar contradiction clause 315]
317. patient(sK7) <- (~20) [resolution 228,156]
334. tall(sK7) | calm(sK7) <- (~20) [resolution 317,88]
336. calm(sK7) <- (~20) [subsumption resolution 334,228]
345. funny(sK7) <- (~20) [resolution 336,131]
347. $false <- (~20) [subsumption resolution 345,130]
348. 20 [avatar contradiction clause 347]
349. $false [avatar sat refutation 216,221,229,304,312,316,348]
% SZS output end Proof for 6775695226423590696918983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is creative.
Everyone who is either tall or funny is not generous.
Everyone who is quiet is both patient and not rich and vice versa.
Everyone who is either quiet or not old is strong or not humble.
Everyone who is patient or curious is both curious and strong and vice versa.
Everyone who is not kind or not patient is not humble and vice versa.
Everyone who is not calm is not creative or wise.
If someone is either not calm or creative then susan is both tall and not humble.
Everyone who is either not creative or not funny is not strong.
If someone is both curious and not creative then fred is curious or not funny and vice versa.
Everyone who is patient or not rich is not creative.
Everyone who is rich is quiet or patient and vice versa.
Everyone who is both not old and not patient is both wise and not brave and vice versa.
If someone is not patient then someone is generous or not patient and vice versa.
If someone is either kind or not funny then someone is both patient and rich and vice versa.
If lucy is both not patient and patient then mary is not strong and vice versa.
Mary is either not calm or not curious.
Someone is both not old and not happy.
Mary is humble.
Someone is not happy.
Someone is either not tall or patient.
Alice is creative or tall.
Someone is kind or not funny. | Lucy is quiet. | contradiction | (![X]:(~rich(X)=>creative(X)))&
(![X]:((tall(X)<~>funny(X))=>~generous(X)))&
(![X]:(quiet(X)<=>(patient(X)&~rich(X))))&
(![X]:((quiet(X)<~>~old(X))=>(strong(X)|~humble(X))))&
(![X]:((patient(X)|curious(X))<=>(curious(X)&strong(X))))&
(![X]:((~kind(X)|~patient(X))<=>~humble(X)))&
(![X]:(~calm(X)=>(~creative(X)|wise(X))))&
((?[X]:((~calm(X)<~>creative(X))))=>((tall(susan)&~humble(susan))))&
(![X]:((~creative(X)<~>~funny(X))=>~strong(X)))&
((?[X]:((curious(X)&~creative(X))))<=>((curious(fred)|~funny(fred))))&
(![X]:((patient(X)|~rich(X))=>~creative(X)))&
(![X]:(rich(X)<=>(quiet(X)|patient(X))))&
(![X]:((~old(X)&~patient(X))<=>(wise(X)&~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((generous(X)|~patient(X)))))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((patient(X)&rich(X)))))&
(((~patient(lucy)&patient(lucy)))<=>(~strong(mary)))&
((~calm(mary)<~>~curious(mary)))&
(?[X]:((~old(X)&~happy(X))))&
(humble(mary))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)<~>patient(X))))&
((creative(alice)|tall(alice)))&
(?[X]:((kind(X)|~funny(X)))) | quiet(lucy) | [
"p0",
"p2",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 423761901350547774437173
% SZS output start Proof for 423761901350547774437173
1. ! [X0] : (~rich(X0) => creative(X0)) [input p0]
3. ! [X0] : (quiet(X0) <=> (~rich(X0) & patient(X0))) [input p2]
11. ! [X0] : ((~rich(X0) | patient(X0)) => ~creative(X0)) [input p10]
24. quiet(lucy) [input hypothesis]
29. ! [X0] : (creative(X0) | rich(X0)) [ennf transformation 1]
37. ! [X0] : (~creative(X0) | (rich(X0) & ~patient(X0))) [ennf transformation 11]
39. ! [X0] : ((quiet(X0) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | ~quiet(X0))) [nnf transformation 3]
40. ! [X0] : ((quiet(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | ~quiet(X0))) [flattening 39]
77. creative(X0) | rich(X0) [cnf transformation 29]
81. ~quiet(X0) | ~rich(X0) [cnf transformation 40]
106. ~creative(X0) | rich(X0) [cnf transformation 37]
134. quiet(lucy) [cnf transformation 24]
177. rich(X0) [subsumption resolution 106,77]
228. ~rich(lucy) [resolution 81,134]
229. $false [subsumption resolution 228,177]
% SZS output end Proof for 423761901350547774437173
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either patient or wise then someone is not brave.
Everyone who is either strong or not strong is not brave and vice versa.
Everyone who is not funny is strong.
Everyone who is not generous or not calm is not strong or not rich and vice versa.
If someone is both not wise and not strong then someone is either not old or not happy.
If lucy is creative or strong then mary is either not wise or not humble and vice versa.
If alice is either not humble or kind then susan is not creative or quiet.
If someone is both happy and not quiet then john is either not old or not happy.
Everyone who is creative or brave is either not rich or not old and vice versa.
Everyone who is either not brave or brave is both not quiet and not rich and vice versa.
If susan is not strong then alice is both not brave and not calm.
If someone is brave or not funny then lucy is either funny or calm.
If someone is not funny then someone is kind and vice versa.
Everyone who is not funny or tall is both generous and funny and vice versa.
Everyone who is either not curious or happy is both brave and calm.
If mary is not wise or not patient then alice is quiet or kind and vice versa.
Someone is either not funny or old.
Someone is either generous or not brave.
Someone is both not generous and not brave.
Someone is both happy and funny.
John is happy or not happy.
Mary is both not creative and not humble.
Someone is not patient or not curious. | Susan is rich. | contradiction | (((patient(fred)<~>wise(fred)))=>(?[X]:(~brave(X))))&
(![X]:((strong(X)<~>~strong(X))<=>~brave(X)))&
(![X]:(~funny(X)=>strong(X)))&
(![X]:((~generous(X)|~calm(X))<=>(~strong(X)|~rich(X))))&
((?[X]:((~wise(X)&~strong(X))))=>(?[X]:((~old(X)<~>~happy(X)))))&
(((creative(lucy)|strong(lucy)))<=>((~wise(mary)<~>~humble(mary))))&
(((~humble(alice)<~>kind(alice)))=>((~creative(susan)|quiet(susan))))&
((?[X]:((happy(X)&~quiet(X))))=>((~old(john)<~>~happy(john))))&
(![X]:((creative(X)|brave(X))<=>(~rich(X)<~>~old(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(~quiet(X)&~rich(X))))&
((~strong(susan))=>((~brave(alice)&~calm(alice))))&
((?[X]:((brave(X)|~funny(X))))=>((funny(lucy)<~>calm(lucy))))&
((?[X]:(~funny(X)))<=>(?[X]:(kind(X))))&
(![X]:((~funny(X)|tall(X))<=>(generous(X)&funny(X))))&
(![X]:((~curious(X)<~>happy(X))=>(brave(X)&calm(X))))&
(((~wise(mary)|~patient(mary)))<=>((quiet(alice)|kind(alice))))&
(?[X]:((~funny(X)<~>old(X))))&
(?[X]:((generous(X)<~>~brave(X))))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:((happy(X)&funny(X))))&
((happy(john)|~happy(john)))&
((~creative(mary)&~humble(mary)))&
(?[X]:((~patient(X)|~curious(X)))) | rich(susan) | [
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3787561163279894291938618
% SZS output start Proof for 3787561163279894291938618
2. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> ~brave(X0)) [input p1]
10. ! [X0] : ((~brave(X0) <~> brave(X0)) <=> (~rich(X0) & ~quiet(X0))) [input p9]
24. rich(susan) [input hypothesis]
39. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | brave(X0)) & (~brave(X0) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 2]
52. ! [X0] : ((((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | (rich(X0) | quiet(X0))) & ((~rich(X0) & ~quiet(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0))))) [nnf transformation 10]
53. ! [X0] : ((((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | rich(X0) | quiet(X0)) & ((~rich(X0) & ~quiet(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0))))) [flattening 52]
79. ~brave(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 39]
80. ~brave(X0) | strong(X0) | strong(X0) [cnf transformation 39]
108. ~rich(X0) | brave(X0) | brave(X0) [cnf transformation 53]
145. rich(susan) [cnf transformation 24]
150. ~rich(X0) | brave(X0) [duplicate literal removal 108]
152. ~brave(X0) | ~strong(X0) [duplicate literal removal 79]
153. ~brave(X0) | strong(X0) [duplicate literal removal 80]
168. ~brave(X0) [subsumption resolution 152,153]
237. ~rich(X0) [subsumption resolution 150,168]
307. $false [subsumption resolution 145,237]
% SZS output end Proof for 3787561163279894291938618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is patient then someone is not happy. If john is calm then someone is either patient or brave and vice versa. If john is quiet then alice is either not generous or not old. If john is strong then someone is kind or not brave. Everyone who is calm or creative is both not curious and not brave and vice versa. Everyone who is either creative or quiet is both happy and tall and vice versa. Everyone who is either patient or not curious is either rich or brave. If mary is both not humble and not creative then mary is strong. Everyone who is either brave or not creative is brave or not wise and vice versa. Everyone who is either strong or not kind is either kind or wise. If someone is calm or funny then someone is not humble. If someone is happy then someone is not tall and vice versa. Everyone who is creative is either calm or humble and vice versa. If fred is generous or not funny then susan is both not brave and not strong. Everyone who is either not calm or humble is generous or not calm and vice versa. Everyone who is either not humble or brave is either creative or not happy. Mary is not old. Alice is not humble. Mary is not kind. Someone is creative or kind. Mary is not rich or not calm. | Alice is quiet. | neutral | ((patient(fred))=>(?[X]:(~happy(X))))&
((calm(john))<=>(?[X]:((patient(X)<~>brave(X)))))&
((quiet(john))=>((~generous(alice)<~>~old(alice))))&
((strong(john))=>(?[X]:((kind(X)|~brave(X)))))&
(![X]:((calm(X)|creative(X))<=>(~curious(X)&~brave(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(happy(X)&tall(X))))&
(![X]:((patient(X)<~>~curious(X))=>(rich(X)<~>brave(X))))&
(((~humble(mary)&~creative(mary)))=>(strong(mary)))&
(![X]:((brave(X)<~>~creative(X))<=>(brave(X)|~wise(X))))&
(![X]:((strong(X)<~>~kind(X))=>(kind(X)<~>wise(X))))&
((?[X]:((calm(X)|funny(X))))=>(?[X]:(~humble(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~tall(X))))&
(![X]:(creative(X)<=>(calm(X)<~>humble(X))))&
(((generous(fred)|~funny(fred)))=>((~brave(susan)&~strong(susan))))&
(![X]:((~calm(X)<~>humble(X))<=>(generous(X)|~calm(X))))&
(![X]:((~humble(X)<~>brave(X))=>(creative(X)<~>~happy(X))))&
(~old(mary))&
(~humble(alice))&
(~kind(mary))&
(?[X]:((creative(X)|kind(X))))&
((~rich(mary)|~calm(mary))) | quiet(alice) | [] | null | 0 |
If someone is not calm or not happy then lucy is either not humble or quiet.
If john is not wise then someone is either tall or not creative.
Everyone who is both curious and kind is both rich and not kind and vice versa.
Everyone who is not brave is not humble or not brave.
If someone is both wise and not old then lucy is both calm and happy and vice versa.
If someone is either humble or not funny then lucy is calm or patient and vice versa.
If susan is either not patient or not rich then someone is not kind or not tall.
If someone is patient then lucy is humble.
Everyone who is not tall or not funny is both not old and not curious.
Everyone who is calm or not strong is tall.
If john is tall or not old then paul is humble or quiet.
If fred is rich then someone is happy.
If someone is humble then john is both generous and not creative.
Everyone who is not strong is not quiet or not curious and vice versa.
If someone is patient or not patient then someone is not old or not curious.
Everyone who is both rich and not calm is curious or not patient.
Lucy is either tall or not humble.
Someone is either not tall or wise.
Someone is wise.
Fred is not generous.
Fred is kind or not old.
Someone is both strong and not calm.
Someone is not patient.
Someone is both not generous and kind. | Lucy is humble. | entailment | ((?[X]:((~calm(X)|~happy(X))))=>((~humble(lucy)<~>quiet(lucy))))&
((~wise(john))=>(?[X]:((tall(X)<~>~creative(X)))))&
(![X]:((curious(X)&kind(X))<=>(rich(X)&~kind(X))))&
(![X]:(~brave(X)=>(~humble(X)|~brave(X))))&
((?[X]:((wise(X)&~old(X))))<=>((calm(lucy)&happy(lucy))))&
((?[X]:((humble(X)<~>~funny(X))))<=>((calm(lucy)|patient(lucy))))&
(((~patient(susan)<~>~rich(susan)))=>(?[X]:((~kind(X)|~tall(X)))))&
((?[X]:(patient(X)))=>(humble(lucy)))&
(![X]:((~tall(X)|~funny(X))=>(~old(X)&~curious(X))))&
(![X]:((calm(X)|~strong(X))=>tall(X)))&
(((tall(john)|~old(john)))=>((humble(paul)|quiet(paul))))&
((rich(fred))=>(?[X]:(happy(X))))&
((?[X]:(humble(X)))=>((generous(john)&~creative(john))))&
(![X]:(~strong(X)<=>(~quiet(X)|~curious(X))))&
((?[X]:((patient(X)|~patient(X))))=>(?[X]:((~old(X)|~curious(X)))))&
(![X]:((rich(X)&~calm(X))=>(curious(X)|~patient(X))))&
((tall(lucy)<~>~humble(lucy)))&
(?[X]:((~tall(X)<~>wise(X))))&
(?[X]:(wise(X)))&
(~generous(fred))&
((kind(fred)|~old(fred)))&
(?[X]:((strong(X)&~calm(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~generous(X)&kind(X)))) | humble(lucy) | [
"p8",
"p9",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2305385631624064652342433
% SZS output start Proof for 2305385631624064652342433
9. ! [X0] : ((~funny(X0) | ~tall(X0)) => (~curious(X0) & ~old(X0))) [input p8]
10. ! [X0] : ((~strong(X0) | calm(X0)) => tall(X0)) [input p9]
14. ! [X0] : (~strong(X0) <=> (~curious(X0) | ~quiet(X0))) [input p13]
17. tall(lucy) <~> ~humble(lucy) [input p16]
25. ~humble(lucy) [input hypothesis]
27. ! [X0] : ((~curious(X0) | ~quiet(X0)) => ~strong(X0)) [unused predicate definition removal 14]
34. ! [X0] : ((~curious(X0) & ~old(X0)) | (funny(X0) & tall(X0))) [ennf transformation 9]
35. ! [X0] : (tall(X0) | (strong(X0) & ~calm(X0))) [ennf transformation 10]
40. ! [X0] : (~strong(X0) | (curious(X0) & quiet(X0))) [ennf transformation 27]
68. (humble(lucy) | ~tall(lucy)) & (~humble(lucy) | tall(lucy)) [nnf transformation 17]
106. ~curious(X0) | tall(X0) [cnf transformation 34]
109. strong(X0) | tall(X0) [cnf transformation 35]
116. ~strong(X0) | curious(X0) [cnf transformation 40]
121. humble(lucy) | ~tall(lucy) [cnf transformation 68]
132. ~humble(lucy) [cnf transformation 25]
139. 2 <=> humble(lucy) [avatar definition]
290. 35 <=> tall(lucy) [avatar definition]
292. ~tall(lucy) <- (~35) [avatar component clause 290]
293. ~35 | 2 [avatar split clause 121,139,290]
314. ~2 [avatar split clause 132,139]
331. curious(X0) | tall(X0) [resolution 116,109]
332. tall(X0) [subsumption resolution 331,106]
336. $false <- (~35) [resolution 332,292]
343. 35 [avatar contradiction clause 336]
344. $false [avatar sat refutation 293,314,343]
% SZS output end Proof for 2305385631624064652342433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or not curious then paul is not brave or not happy and vice versa.
If fred is strong then alice is not kind and vice versa.
Everyone who is either patient or brave is both humble and curious and vice versa.
Everyone who is brave is both tall and humble.
If susan is both happy and curious then john is not happy or not patient.
Everyone who is not brave or not curious is not quiet or calm.
Everyone who is both calm and kind is curious.
If lucy is not funny then someone is both not wise and brave and vice versa.
Everyone who is patient is not calm or not strong and vice versa.
If fred is both not tall and not wise then someone is either curious or not tall and vice versa.
Everyone who is not humble or not happy is both not creative and not old and vice versa.
If someone is calm then susan is both creative and not humble.
If someone is not wise or calm then john is both not calm and not funny and vice versa.
If someone is not old then someone is not tall and vice versa.
Everyone who is either not kind or wise is either not brave or not creative and vice versa.
Everyone who is both rich and calm is both not quiet and not funny and vice versa.
Someone is both wise and not old.
John is either not generous or funny.
Someone is both not calm and rich.
Alice is both not old and tall.
Someone is strong.
Someone is brave or not curious.
Someone is either not calm or tall. | Fred is funny. | entailment | ((?[X]:((wise(X)<~>~curious(X))))<=>((~brave(paul)|~happy(paul))))&
((strong(fred))<=>(~kind(alice)))&
(![X]:((patient(X)<~>brave(X))<=>(humble(X)&curious(X))))&
(![X]:(brave(X)=>(tall(X)&humble(X))))&
(((happy(susan)&curious(susan)))=>((~happy(john)|~patient(john))))&
(![X]:((~brave(X)|~curious(X))=>(~quiet(X)|calm(X))))&
(![X]:((calm(X)&kind(X))=>curious(X)))&
((~funny(lucy))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:(patient(X)<=>(~calm(X)|~strong(X))))&
(((~tall(fred)&~wise(fred)))<=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((~humble(X)|~happy(X))<=>(~creative(X)&~old(X))))&
((?[X]:(calm(X)))=>((creative(susan)&~humble(susan))))&
((?[X]:((~wise(X)|calm(X))))<=>((~calm(john)&~funny(john))))&
((?[X]:(~old(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~kind(X)<~>wise(X))<=>(~brave(X)<~>~creative(X))))&
(![X]:((rich(X)&calm(X))<=>(~quiet(X)&~funny(X))))&
(?[X]:((wise(X)&~old(X))))&
((~generous(john)<~>funny(john)))&
(?[X]:((~calm(X)&rich(X))))&
((~old(alice)&tall(alice)))&
(?[X]:(strong(X)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((~calm(X)<~>tall(X)))) | funny(fred) | [
"p3",
"p5",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3371508036876970093166603
% SZS output start Proof for 3371508036876970093166603
4. ! [X0] : (brave(X0) => (humble(X0) & tall(X0))) [input p3]
6. ! [X0] : ((~curious(X0) | ~brave(X0)) => (calm(X0) | ~quiet(X0))) [input p5]
10. (~wise(fred) & ~tall(fred)) <=> ? [X0] : (curious(X0) <~> ~tall(X0)) [input p9]
11. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> (~old(X0) & ~creative(X0))) [input p10]
12. ? [X0] : calm(X0) => (~humble(susan) & creative(susan)) [input p11]
16. ! [X0] : ((calm(X0) & rich(X0)) <=> (~funny(X0) & ~quiet(X0))) [input p15]
24. ~funny(fred) [input hypothesis]
26. ! [X0] : ((humble(X0) & tall(X0)) | ~brave(X0)) [ennf transformation 4]
29. ! [X0] : ((calm(X0) | ~quiet(X0)) | (curious(X0) & brave(X0))) [ennf transformation 6]
30. ! [X0] : (calm(X0) | ~quiet(X0) | (curious(X0) & brave(X0))) [flattening 29]
33. (~humble(susan) & creative(susan)) | ! [X0] : ~calm(X0) [ennf transformation 12]
48. ((~wise(fred) & ~tall(fred)) | ! [X0] : ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0)))) & (? [X0] : ((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (wise(fred) | tall(fred))) [nnf transformation 10]
49. ((~wise(fred) & ~tall(fred)) | ! [X0] : ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0)))) & (? [X0] : ((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | wise(fred) | tall(fred)) [flattening 48]
50. ((~wise(fred) & ~tall(fred)) | ! [X0] : ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0)))) & (? [X1] : ((tall(X1) | ~curious(X1)) & (~tall(X1) | curious(X1))) | wise(fred) | tall(fred)) [rectify 49]
51. ? [X1] : ((tall(X1) | ~curious(X1)) & (~tall(X1) | curious(X1))) => ((tall(sK2) | ~curious(sK2)) & (~tall(sK2) | curious(sK2))) [choice axiom]
52. ((~wise(fred) & ~tall(fred)) | ! [X0] : ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0)))) & (((tall(sK2) | ~curious(sK2)) & (~tall(sK2) | curious(sK2))) | wise(fred) | tall(fred)) [skolemisation 50,51]
53. ! [X0] : (((~happy(X0) | ~humble(X0)) | (old(X0) | creative(X0))) & ((~old(X0) & ~creative(X0)) | (happy(X0) & humble(X0)))) [nnf transformation 11]
54. ! [X0] : ((~happy(X0) | ~humble(X0) | old(X0) | creative(X0)) & ((~old(X0) & ~creative(X0)) | (happy(X0) & humble(X0)))) [flattening 53]
66. ! [X0] : (((calm(X0) & rich(X0)) | (funny(X0) | quiet(X0))) & ((~funny(X0) & ~quiet(X0)) | (~calm(X0) | ~rich(X0)))) [nnf transformation 16]
67. ! [X0] : (((calm(X0) & rich(X0)) | funny(X0) | quiet(X0)) & ((~funny(X0) & ~quiet(X0)) | ~calm(X0) | ~rich(X0))) [flattening 66]
94. ~brave(X0) | tall(X0) [cnf transformation 26]
97. ~quiet(X0) | calm(X0) | brave(X0) [cnf transformation 30]
98. ~quiet(X0) | calm(X0) | curious(X0) [cnf transformation 30]
108. ~tall(fred) | ~tall(X0) | ~curious(X0) [cnf transformation 52]
112. ~creative(X0) | humble(X0) [cnf transformation 54]
117. creative(susan) | ~calm(X0) [cnf transformation 33]
118. ~humble(susan) | ~calm(X0) [cnf transformation 33]
137. funny(X0) | calm(X0) | quiet(X0) [cnf transformation 67]
150. ~funny(fred) [cnf transformation 24]
233. 19 <=> ! [X0] : (~tall(X0) | ~curious(X0)) [avatar definition]
234. ~tall(X0) | ~curious(X0) <- (19) [avatar component clause 233]
237. 20 <=> tall(fred) [avatar definition]
238. tall(fred) <- (20) [avatar component clause 237]
241. 19 | ~20 [avatar split clause 108,237,233]
253. 23 <=> ! [X0] : ~calm(X0) [avatar definition]
254. ~calm(X0) <- (23) [avatar component clause 253]
256. 24 <=> humble(susan) [avatar definition]
258. ~humble(susan) <- (~24) [avatar component clause 256]
259. 23 | ~24 [avatar split clause 118,256,253]
261. 25 <=> creative(susan) [avatar definition]
263. creative(susan) <- (25) [avatar component clause 261]
264. 23 | 25 [avatar split clause 117,261,253]
376. calm(fred) | quiet(fred) [resolution 137,150]
379. quiet(fred) <- (23) [subsumption resolution 376,254]
382. calm(fred) | curious(fred) <- (23) [resolution 379,98]
383. calm(fred) | brave(fred) <- (23) [resolution 379,97]
384. brave(fred) <- (23) [subsumption resolution 383,254]
404. tall(fred) <- (23) [resolution 384,94]
407. 20 | ~23 [avatar split clause 404,253,237]
408. curious(fred) <- (23) [subsumption resolution 382,254]
409. ~curious(fred) <- (19, 20) [resolution 238,234]
410. $false <- (19, 20, 23) [subsumption resolution 409,408]
411. ~19 | ~20 | ~23 [avatar contradiction clause 410]
436. humble(susan) <- (25) [resolution 263,112]
439. $false <- (~24, 25) [subsumption resolution 436,258]
440. 24 | ~25 [avatar contradiction clause 439]
441. $false [avatar sat refutation 241,259,264,407,411,440]
% SZS output end Proof for 3371508036876970093166603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is kind then someone is either funny or calm and vice versa. If paul is creative then someone is not curious and vice versa. If someone is either not kind or tall then someone is wise or not tall and vice versa. Everyone who is rich is either not strong or not generous. If mary is both not happy and not wise then someone is either rich or quiet and vice versa. Everyone who is not old is either not humble or not happy. If paul is either generous or not quiet then mary is happy or kind and vice versa. If alice is both humble and happy then susan is both not strong and happy and vice versa. If someone is not funny or patient then someone is not kind and vice versa. If someone is not generous then someone is either not brave or not old. Everyone who is humble or kind is either wise or not humble and vice versa. Everyone who is patient or rich is both not strong and kind and vice versa. Everyone who is not brave is both tall and old. Everyone who is not quiet is both wise and not creative. If someone is brave then alice is not quiet or old. Everyone who is kind is both not kind and not happy. Someone is generous or not tall. Someone is either rich or not happy. Someone is either tall or old. Someone is not kind. Paul is patient or old. Alice is old. Mary is creative or not patient. Someone is tall or funny. | Susan is creative. | contradiction | ((kind(lucy))<=>(?[X]:((funny(X)<~>calm(X)))))&
((creative(paul))<=>(?[X]:(~curious(X))))&
((?[X]:((~kind(X)<~>tall(X))))<=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(rich(X)=>(~strong(X)<~>~generous(X))))&
(((~happy(mary)&~wise(mary)))<=>(?[X]:((rich(X)<~>quiet(X)))))&
(![X]:(~old(X)=>(~humble(X)<~>~happy(X))))&
(((generous(paul)<~>~quiet(paul)))<=>((happy(mary)|kind(mary))))&
(((humble(alice)&happy(alice)))<=>((~strong(susan)&happy(susan))))&
((?[X]:((~funny(X)|patient(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((humble(X)|kind(X))<=>(wise(X)<~>~humble(X))))&
(![X]:((patient(X)|rich(X))<=>(~strong(X)&kind(X))))&
(![X]:(~brave(X)=>(tall(X)&old(X))))&
(![X]:(~quiet(X)=>(wise(X)&~creative(X))))&
((?[X]:(brave(X)))=>((~quiet(alice)|old(alice))))&
(![X]:(kind(X)=>(~kind(X)&~happy(X))))&
(?[X]:((generous(X)|~tall(X))))&
(?[X]:((rich(X)<~>~happy(X))))&
(?[X]:((tall(X)<~>old(X))))&
(?[X]:(~kind(X)))&
((patient(paul)|old(paul)))&
(old(alice))&
((creative(mary)|~patient(mary)))&
(?[X]:((tall(X)|funny(X)))) | creative(susan) | [
"p4",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6814162809633926008892672
% SZS output start Proof for 6814162809633926008892672
5. (~wise(mary) & ~happy(mary)) <=> ? [X0] : (rich(X0) <~> quiet(X0)) [input p4]
11. ! [X0] : ((kind(X0) | humble(X0)) <=> (wise(X0) <~> ~humble(X0))) [input p10]
12. ! [X0] : ((rich(X0) | patient(X0)) <=> (kind(X0) & ~strong(X0))) [input p11]
14. ! [X0] : (~quiet(X0) => (~creative(X0) & wise(X0))) [input p13]
16. ! [X0] : (kind(X0) => (~happy(X0) & ~kind(X0))) [input p15]
25. creative(susan) [input hypothesis]
33. ! [X0] : ((~creative(X0) & wise(X0)) | quiet(X0)) [ennf transformation 14]
36. ! [X0] : ((~happy(X0) & ~kind(X0)) | ~kind(X0)) [ennf transformation 16]
51. ((~wise(mary) & ~happy(mary)) | ! [X0] : ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) & (? [X0] : ((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (wise(mary) | happy(mary))) [nnf transformation 5]
52. ((~wise(mary) & ~happy(mary)) | ! [X0] : ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) & (? [X0] : ((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | wise(mary) | happy(mary)) [flattening 51]
53. ((~wise(mary) & ~happy(mary)) | ! [X0] : ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) & (? [X1] : ((~quiet(X1) | ~rich(X1)) & (quiet(X1) | rich(X1))) | wise(mary) | happy(mary)) [rectify 52]
54. ? [X1] : ((~quiet(X1) | ~rich(X1)) & (quiet(X1) | rich(X1))) => ((~quiet(sK4) | ~rich(sK4)) & (quiet(sK4) | rich(sK4))) [choice axiom]
55. ((~wise(mary) & ~happy(mary)) | ! [X0] : ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) & (((~quiet(sK4) | ~rich(sK4)) & (quiet(sK4) | rich(sK4))) | wise(mary) | happy(mary)) [skolemisation 53,54]
70. ! [X0] : (((kind(X0) | humble(X0)) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0)))) & (((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | (~kind(X0) & ~humble(X0)))) [nnf transformation 11]
71. ! [X0] : ((kind(X0) | humble(X0) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0)))) & (((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | (~kind(X0) & ~humble(X0)))) [flattening 70]
72. ! [X0] : (((rich(X0) | patient(X0)) | (~kind(X0) | strong(X0))) & ((kind(X0) & ~strong(X0)) | (~rich(X0) & ~patient(X0)))) [nnf transformation 12]
73. ! [X0] : ((rich(X0) | patient(X0) | ~kind(X0) | strong(X0)) & ((kind(X0) & ~strong(X0)) | (~rich(X0) & ~patient(X0)))) [flattening 72]
105. ~wise(mary) | rich(X0) | ~quiet(X0) [cnf transformation 55]
123. ~humble(X0) | wise(X0) | ~humble(X0) [cnf transformation 71]
128. kind(X0) | humble(X0) | wise(X0) | humble(X0) [cnf transformation 71]
132. ~rich(X0) | kind(X0) [cnf transformation 73]
137. ~creative(X0) | quiet(X0) [cnf transformation 33]
139. ~kind(X0) | ~kind(X0) [cnf transformation 36]
151. creative(susan) [cnf transformation 25]
152. ~kind(X0) [duplicate literal removal 139]
153. ~humble(X0) | wise(X0) [duplicate literal removal 123]
154. humble(X0) | kind(X0) | wise(X0) [duplicate literal removal 128]
225. 17 <=> ! [X0] : (rich(X0) | ~quiet(X0)) [avatar definition]
226. ~quiet(X0) | rich(X0) <- (17) [avatar component clause 225]
228. 18 <=> wise(mary) [avatar definition]
230. ~wise(mary) <- (~18) [avatar component clause 228]
231. 17 | ~18 [avatar split clause 105,228,225]
405. quiet(susan) [resolution 137,151]
412. rich(susan) <- (17) [resolution 226,405]
414. kind(susan) <- (17) [resolution 412,132]
415. $false <- (17) [subsumption resolution 414,152]
416. ~17 [avatar contradiction clause 415]
431. kind(X2) | wise(X2) | wise(X2) [resolution 154,153]
432. kind(X2) | wise(X2) [duplicate literal removal 431]
436. wise(X2) [subsumption resolution 432,152]
437. $false <- (~18) [resolution 436,230]
439. 18 [avatar contradiction clause 437]
440. $false [avatar sat refutation 231,416,439]
% SZS output end Proof for 6814162809633926008892672
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both happy and not generous then someone is humble and vice versa.
If someone is not strong or not creative then john is both not rich and not strong.
If someone is both not quiet and kind then lucy is either calm or not generous.
If someone is not wise or not calm then john is both happy and not creative and vice versa.
If someone is generous then someone is both not tall and not wise.
If susan is not funny or old then someone is either not wise or not calm.
If lucy is either not funny or not humble then paul is happy and vice versa.
Everyone who is not brave or not kind is patient and vice versa.
If john is calm or old then someone is either not brave or not funny and vice versa.
If someone is both not patient and not kind then someone is not rich and vice versa.
Everyone who is both not old and strong is rich or creative.
If lucy is either not curious or not humble then paul is rich.
Everyone who is both not generous and happy is both rich and not kind and vice versa.
Everyone who is either tall or funny is kind or tall and vice versa.
Everyone who is both tall and happy is either not calm or not quiet.
Everyone who is generous or funny is both strong and patient and vice versa.
Lucy is kind.
Fred is not tall.
John is kind or not generous.
Someone is both creative and not funny.
Someone is creative or not tall. | Lucy is not brave. | contradiction | (((happy(paul)&~generous(paul)))<=>(?[X]:(humble(X))))&
((?[X]:((~strong(X)|~creative(X))))=>((~rich(john)&~strong(john))))&
((?[X]:((~quiet(X)&kind(X))))=>((calm(lucy)<~>~generous(lucy))))&
((?[X]:((~wise(X)|~calm(X))))<=>((happy(john)&~creative(john))))&
((?[X]:(generous(X)))=>(?[X]:((~tall(X)&~wise(X)))))&
(((~funny(susan)|old(susan)))=>(?[X]:((~wise(X)<~>~calm(X)))))&
(((~funny(lucy)<~>~humble(lucy)))<=>(happy(paul)))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
(![X]:((tall(X)<~>funny(X))<=>(kind(X)|tall(X))))&
(![X]:((tall(X)&happy(X))=>(~calm(X)<~>~quiet(X))))&
(![X]:((generous(X)|funny(X))<=>(strong(X)&patient(X))))&
(kind(lucy))&
(~tall(fred))&
((kind(john)|~generous(john)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((creative(X)|~tall(X)))) | ~brave(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p7",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7206569251105397302843779
% SZS output start Proof for 7206569251105397302843779
1. (~generous(paul) & happy(paul)) <=> ? [X0] : humble(X0) [input p0]
2. ? [X0] : (~creative(X0) | ~strong(X0)) => (~strong(john) & ~rich(john)) [input p1]
4. ? [X0] : (~calm(X0) | ~wise(X0)) <=> (~creative(john) & happy(john)) [input p3]
5. ? [X0] : generous(X0) => ? [X0] : (~wise(X0) & ~tall(X0)) [input p4]
7. (~funny(lucy) <~> ~humble(lucy)) <=> happy(paul) [input p6]
8. ! [X0] : ((~kind(X0) | ~brave(X0)) <=> patient(X0)) [input p7]
10. ? [X0] : (~kind(X0) & ~patient(X0)) <=> ? [X0] : ~rich(X0) [input p9]
13. ! [X0] : ((happy(X0) & ~generous(X0)) <=> (~kind(X0) & rich(X0))) [input p12]
14. ! [X0] : ((tall(X0) <~> funny(X0)) <=> (tall(X0) | kind(X0))) [input p13]
16. ! [X0] : ((funny(X0) | generous(X0)) <=> (patient(X0) & strong(X0))) [input p15]
22. ~brave(lucy) [input hypothesis]
23. ? [X0] : generous(X0) => ? [X1] : (~wise(X1) & ~tall(X1)) [rectify 5]
24. ? [X0] : (~kind(X0) & ~patient(X0)) <=> ? [X1] : ~rich(X1) [rectify 10]
25. (~strong(john) & ~rich(john)) | ! [X0] : (creative(X0) & strong(X0)) [ennf transformation 2]
27. ? [X1] : (~wise(X1) & ~tall(X1)) | ! [X0] : ~generous(X0) [ennf transformation 23]
34. ((~generous(paul) & happy(paul)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (generous(paul) | ~happy(paul))) [nnf transformation 1]
35. ((~generous(paul) & happy(paul)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | generous(paul) | ~happy(paul)) [flattening 34]
36. ((~generous(paul) & happy(paul)) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | generous(paul) | ~happy(paul)) [rectify 35]
37. ? [X1] : humble(X1) => humble(sK0) [choice axiom]
38. ((~generous(paul) & happy(paul)) | ! [X0] : ~humble(X0)) & (humble(sK0) | generous(paul) | ~happy(paul)) [skolemisation 36,37]
40. (? [X0] : (~calm(X0) | ~wise(X0)) | (creative(john) | ~happy(john))) & ((~creative(john) & happy(john)) | ! [X0] : (calm(X0) & wise(X0))) [nnf transformation 4]
41. (? [X0] : (~calm(X0) | ~wise(X0)) | creative(john) | ~happy(john)) & ((~creative(john) & happy(john)) | ! [X0] : (calm(X0) & wise(X0))) [flattening 40]
42. (? [X0] : (~calm(X0) | ~wise(X0)) | creative(john) | ~happy(john)) & ((~creative(john) & happy(john)) | ! [X1] : (calm(X1) & wise(X1))) [rectify 41]
43. ? [X0] : (~calm(X0) | ~wise(X0)) => (~calm(sK1) | ~wise(sK1)) [choice axiom]
44. ((~calm(sK1) | ~wise(sK1)) | creative(john) | ~happy(john)) & ((~creative(john) & happy(john)) | ! [X1] : (calm(X1) & wise(X1))) [skolemisation 42,43]
45. ? [X0] : (~wise(X0) & ~tall(X0)) | ! [X1] : ~generous(X1) [rectify 27]
46. ? [X0] : (~wise(X0) & ~tall(X0)) => (~wise(sK2) & ~tall(sK2)) [choice axiom]
47. (~wise(sK2) & ~tall(sK2)) | ! [X1] : ~generous(X1) [skolemisation 45,46]
51. (((humble(lucy) | funny(lucy)) & (~humble(lucy) | ~funny(lucy))) | ~happy(paul)) & (happy(paul) | ((~funny(lucy) | humble(lucy)) & (~humble(lucy) | funny(lucy)))) [nnf transformation 7]
52. ! [X0] : (((~kind(X0) | ~brave(X0)) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [nnf transformation 8]
53. ! [X0] : ((~kind(X0) | ~brave(X0) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [flattening 52]
59. (? [X0] : (~kind(X0) & ~patient(X0)) | ! [X1] : rich(X1)) & (? [X1] : ~rich(X1) | ! [X0] : (kind(X0) | patient(X0))) [nnf transformation 24]
60. (? [X0] : (~kind(X0) & ~patient(X0)) | ! [X1] : rich(X1)) & (? [X2] : ~rich(X2) | ! [X3] : (kind(X3) | patient(X3))) [rectify 59]
61. ? [X0] : (~kind(X0) & ~patient(X0)) => (~kind(sK5) & ~patient(sK5)) [choice axiom]
62. ? [X2] : ~rich(X2) => ~rich(sK6) [choice axiom]
63. ((~kind(sK5) & ~patient(sK5)) | ! [X1] : rich(X1)) & (~rich(sK6) | ! [X3] : (kind(X3) | patient(X3))) [skolemisation 60,62,61]
65. ! [X0] : (((happy(X0) & ~generous(X0)) | (kind(X0) | ~rich(X0))) & ((~kind(X0) & rich(X0)) | (~happy(X0) | generous(X0)))) [nnf transformation 13]
66. ! [X0] : (((happy(X0) & ~generous(X0)) | kind(X0) | ~rich(X0)) & ((~kind(X0) & rich(X0)) | ~happy(X0) | generous(X0))) [flattening 65]
67. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (~tall(X0) & ~kind(X0))) & ((tall(X0) | kind(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [nnf transformation 14]
68. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (~tall(X0) & ~kind(X0))) & (tall(X0) | kind(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [flattening 67]
70. ! [X0] : (((funny(X0) | generous(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [nnf transformation 16]
71. ! [X0] : ((funny(X0) | generous(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [flattening 70]
77. happy(paul) | ~humble(X0) [cnf transformation 38]
79. ~rich(john) | strong(X0) [cnf transformation 25]
80. ~rich(john) | creative(X0) [cnf transformation 25]
87. ~creative(john) | wise(X1) [cnf transformation 44]
91. ~wise(sK2) | ~generous(X1) [cnf transformation 47]
97. happy(paul) | ~funny(lucy) | humble(lucy) [cnf transformation 51]
100. patient(X0) | brave(X0) [cnf transformation 53]
101. patient(X0) | kind(X0) [cnf transformation 53]
110. ~patient(sK5) | rich(X1) [cnf transformation 63]
111. ~kind(sK5) | rich(X1) [cnf transformation 63]
116. ~kind(X0) | ~happy(X0) | generous(X0) [cnf transformation 66]
120. tall(X0) | kind(X0) | tall(X0) | ~funny(X0) [cnf transformation 68]
124. ~funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 68]
131. ~patient(X0) | generous(X0) | funny(X0) | ~strong(X0) [cnf transformation 71]
138. ~brave(lucy) [cnf transformation 22]
139. tall(X0) | kind(X0) | ~funny(X0) [duplicate literal removal 120]
140. ~funny(X0) | ~tall(X0) [duplicate literal removal 124]
142. 1 <=> ! [X0] : ~humble(X0) [avatar definition]
143. ~humble(X0) <- (1) [avatar component clause 142]
150. 3 <=> happy(paul) [avatar definition]
152. happy(paul) <- (3) [avatar component clause 150]
153. 1 | 3 [avatar split clause 77,150,142]
160. 5 <=> ! [X0] : creative(X0) [avatar definition]
161. creative(X0) <- (5) [avatar component clause 160]
168. 7 <=> ! [X0] : strong(X0) [avatar definition]
169. strong(X0) <- (7) [avatar component clause 168]
172. 8 <=> rich(john) [avatar definition]
174. ~rich(john) <- (~8) [avatar component clause 172]
175. 5 | ~8 [avatar split clause 80,172,160]
176. 7 | ~8 [avatar split clause 79,172,168]
195. 13 <=> creative(john) [avatar definition]
196. ~creative(john) <- (~13) [avatar component clause 195]
212. 17 <=> ! [X1] : wise(X1) [avatar definition]
213. wise(X1) <- (17) [avatar component clause 212]
214. 17 | ~13 [avatar split clause 87,195,212]
218. 18 <=> ! [X1] : ~generous(X1) [avatar definition]
219. ~generous(X1) <- (18) [avatar component clause 218]
221. 19 <=> wise(sK2) [avatar definition]
223. ~wise(sK2) <- (~19) [avatar component clause 221]
224. 18 | ~19 [avatar split clause 91,221,218]
251. 25 <=> funny(lucy) [avatar definition]
255. 26 <=> humble(lucy) [avatar definition]
257. humble(lucy) <- (26) [avatar component clause 255]
260. 26 | ~25 | 3 [avatar split clause 97,150,251,255]
291. 33 <=> ! [X1] : rich(X1) [avatar definition]
292. rich(X1) <- (33) [avatar component clause 291]
294. 34 <=> kind(sK5) [avatar definition]
297. 33 | ~34 [avatar split clause 111,294,291]
299. 35 <=> patient(sK5) [avatar definition]
301. ~patient(sK5) <- (~35) [avatar component clause 299]
302. 33 | ~35 [avatar split clause 110,299,291]
313. ~funny(X0) | kind(X0) [subsumption resolution 139,140]
333. kind(sK5) <- (~35) [resolution 101,301]
336. 34 | 35 [avatar split clause 333,299,294]
337. $false <- (~8, 33) [resolution 292,174]
338. 8 | ~33 [avatar contradiction clause 337]
339. $false <- (5, ~13) [resolution 161,196]
340. ~5 | 13 [avatar contradiction clause 339]
352. $false <- (17, ~19) [resolution 213,223]
353. ~17 | 19 [avatar contradiction clause 352]
403. generous(X0) | funny(X0) | ~strong(X0) | kind(X0) [resolution 131,101]
404. generous(X1) | funny(X1) | ~strong(X1) | brave(X1) [resolution 131,100]
407. funny(X0) | ~strong(X0) | kind(X0) <- (18) [subsumption resolution 403,219]
408. funny(X0) | kind(X0) <- (7, 18) [subsumption resolution 407,169]
409. kind(X0) <- (7, 18) [subsumption resolution 408,313]
410. funny(X1) | ~strong(X1) | brave(X1) <- (18) [subsumption resolution 404,219]
411. brave(X1) | funny(X1) <- (7, 18) [subsumption resolution 410,169]
415. ~happy(X1) | generous(X1) <- (7, 18) [resolution 409,116]
419. ~happy(X1) <- (7, 18) [subsumption resolution 415,219]
424. funny(lucy) <- (7, 18) [resolution 411,138]
429. 25 | ~7 | ~18 [avatar split clause 424,218,168,251]
430. $false <- (3, 7, 18) [subsumption resolution 152,419]
431. ~3 | ~7 | ~18 [avatar contradiction clause 430]
434. $false <- (1, 26) [subsumption resolution 257,143]
435. ~1 | ~26 [avatar contradiction clause 434]
436. $false [avatar sat refutation 153,175,176,214,224,260,297,302,336,338,340,353,429,431,435]
% SZS output end Proof for 7206569251105397302843779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or rich is both quiet and not calm.
If someone is not generous or not tall then someone is either not creative or not generous and vice versa.
If alice is either not patient or creative then someone is both not old and not tall.
If someone is not calm or humble then someone is both kind and quiet and vice versa.
Everyone who is either generous or strong is both not rich and not kind.
If fred is wise or not brave then someone is not funny.
If lucy is either tall or curious then lucy is not humble or not rich.
Everyone who is not wise or not patient is either not wise or wise.
Everyone who is either not patient or not calm is both funny and not generous.
Everyone who is curious is both not tall and old and vice versa.
If someone is happy then fred is humble.
Everyone who is either strong or not quiet is not wise.
If someone is not generous then someone is either not wise or tall.
Everyone who is either not quiet or not strong is not strong or not happy.
If alice is both curious and calm then john is both tall and creative.
If someone is not creative or brave then someone is quiet or not strong.
Mary is funny.
Lucy is rich.
Someone is both humble and not funny.
Fred is not wise or rich.
Paul is both not kind and curious.
Someone is either not funny or funny.
Someone is not tall.
Someone is both not kind and not calm. | Lucy is not calm. | entailment | (![X]:((old(X)|rich(X))=>(quiet(X)&~calm(X))))&
((?[X]:((~generous(X)|~tall(X))))<=>(?[X]:((~creative(X)<~>~generous(X)))))&
(((~patient(alice)<~>creative(alice)))=>(?[X]:((~old(X)&~tall(X)))))&
((?[X]:((~calm(X)|humble(X))))<=>(?[X]:((kind(X)&quiet(X)))))&
(![X]:((generous(X)<~>strong(X))=>(~rich(X)&~kind(X))))&
(((wise(fred)|~brave(fred)))=>(?[X]:(~funny(X))))&
(((tall(lucy)<~>curious(lucy)))=>((~humble(lucy)|~rich(lucy))))&
(![X]:((~wise(X)|~patient(X))=>(~wise(X)<~>wise(X))))&
(![X]:((~patient(X)<~>~calm(X))=>(funny(X)&~generous(X))))&
(![X]:(curious(X)<=>(~tall(X)&old(X))))&
((?[X]:(happy(X)))=>(humble(fred)))&
(![X]:((strong(X)<~>~quiet(X))=>~wise(X)))&
((?[X]:(~generous(X)))=>(?[X]:((~wise(X)<~>tall(X)))))&
(![X]:((~quiet(X)<~>~strong(X))=>(~strong(X)|~happy(X))))&
(((curious(alice)&calm(alice)))=>((tall(john)&creative(john))))&
((?[X]:((~creative(X)|brave(X))))=>(?[X]:((quiet(X)|~strong(X)))))&
(funny(mary))&
(rich(lucy))&
(?[X]:((humble(X)&~funny(X))))&
((~wise(fred)|rich(fred)))&
((~kind(paul)&curious(paul)))&
(?[X]:((~funny(X)<~>funny(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~kind(X)&~calm(X)))) | ~calm(lucy) | [
"p0",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 632072004193952959141733
% SZS output start Proof for 632072004193952959141733
1. ! [X0] : ((rich(X0) | old(X0)) => (~calm(X0) & quiet(X0))) [input p0]
18. rich(lucy) [input p17]
25. calm(lucy) [input hypothesis]
32. ! [X0] : ((~calm(X0) & quiet(X0)) | (~rich(X0) & ~old(X0))) [ennf transformation 1]
86. ~calm(X0) | ~rich(X0) [cnf transformation 32]
130. rich(lucy) [cnf transformation 18]
141. calm(lucy) [cnf transformation 25]
255. 26 <=> rich(lucy) [avatar definition]
256. rich(lucy) <- (26) [avatar component clause 255]
304. 26 [avatar split clause 130,255]
319. ~rich(lucy) [resolution 86,141]
321. $false <- (26) [subsumption resolution 319,256]
322. ~26 [avatar contradiction clause 321]
323. $false [avatar sat refutation 304,322]
% SZS output end Proof for 632072004193952959141733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or creative is generous or not brave.
If mary is both old and not creative then john is not humble or not funny and vice versa.
Everyone who is both brave and not patient is not curious and vice versa.
If susan is patient or not curious then someone is not strong or tall and vice versa.
Everyone who is rich is either not tall or curious.
Everyone who is both not wise and not happy is both not generous and not strong.
Everyone who is either not brave or generous is not rich or not humble.
If susan is either not generous or quiet then someone is quiet or rich and vice versa.
Everyone who is either funny or not tall is not generous or generous and vice versa.
If someone is not rich or not generous then someone is both funny and not wise.
Everyone who is both funny and old is both not creative and patient.
Everyone who is either not patient or not curious is patient and vice versa.
If someone is both not rich and quiet then someone is generous and vice versa.
If someone is not rich or not humble then someone is both generous and kind.
Everyone who is both curious and not quiet is not brave and vice versa.
Everyone who is either not curious or kind is either not patient or creative.
Someone is not rich.
Someone is either funny or not patient.
Paul is tall.
Someone is either not generous or happy.
Susan is either tall or humble.
Someone is either quiet or not curious.
Someone is both not happy and not calm. | Susan is not brave. | contradiction | (![X]:((generous(X)<~>creative(X))=>(generous(X)|~brave(X))))&
(((old(mary)&~creative(mary)))<=>((~humble(john)|~funny(john))))&
(![X]:((brave(X)&~patient(X))<=>~curious(X)))&
(((patient(susan)|~curious(susan)))<=>(?[X]:((~strong(X)|tall(X)))))&
(![X]:(rich(X)=>(~tall(X)<~>curious(X))))&
(![X]:((~wise(X)&~happy(X))=>(~generous(X)&~strong(X))))&
(![X]:((~brave(X)<~>generous(X))=>(~rich(X)|~humble(X))))&
(((~generous(susan)<~>quiet(susan)))<=>(?[X]:((quiet(X)|rich(X)))))&
(![X]:((funny(X)<~>~tall(X))<=>(~generous(X)|generous(X))))&
((?[X]:((~rich(X)|~generous(X))))=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((funny(X)&old(X))=>(~creative(X)&patient(X))))&
(![X]:((~patient(X)<~>~curious(X))<=>patient(X)))&
((?[X]:((~rich(X)&quiet(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~rich(X)|~humble(X))))=>(?[X]:((generous(X)&kind(X)))))&
(![X]:((curious(X)&~quiet(X))<=>~brave(X)))&
(![X]:((~curious(X)<~>kind(X))=>(~patient(X)<~>creative(X))))&
(?[X]:(~rich(X)))&
(?[X]:((funny(X)<~>~patient(X))))&
(tall(paul))&
(?[X]:((~generous(X)<~>happy(X))))&
((tall(susan)<~>humble(susan)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((~happy(X)&~calm(X)))) | ~brave(susan) | [
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1794573440562492926345256
% SZS output start Proof for 1794573440562492926345256
3. ! [X0] : ((~patient(X0) & brave(X0)) <=> ~curious(X0)) [input p2]
12. ! [X0] : ((~patient(X0) <~> ~curious(X0)) <=> patient(X0)) [input p11]
24. ~brave(susan) [input hypothesis]
44. ! [X0] : (((~patient(X0) & brave(X0)) | curious(X0)) & (~curious(X0) | (patient(X0) | ~brave(X0)))) [nnf transformation 3]
45. ! [X0] : (((~patient(X0) & brave(X0)) | curious(X0)) & (~curious(X0) | patient(X0) | ~brave(X0))) [flattening 44]
62. ! [X0] : ((((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0))))) [nnf transformation 12]
96. curious(X0) | brave(X0) [cnf transformation 45]
97. ~patient(X0) | curious(X0) [cnf transformation 45]
126. patient(X0) | ~curious(X0) | patient(X0) [cnf transformation 62]
128. ~curious(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 62]
155. ~brave(susan) [cnf transformation 24]
156. patient(X0) | ~curious(X0) [duplicate literal removal 126]
157. ~curious(X0) | ~patient(X0) [duplicate literal removal 128]
254. ~patient(X0) [subsumption resolution 157,97]
255. ~curious(X0) [subsumption resolution 156,254]
330. brave(X0) [resolution 96,255]
331. $false [resolution 330,155]
% SZS output end Proof for 1794573440562492926345256
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or patient is old or calm and vice versa. Everyone who is quiet or happy is curious and vice versa. If someone is tall or old then someone is either not funny or curious. Everyone who is not strong or not calm is both calm and quiet. If fred is both not curious and patient then lucy is either not brave or generous. Everyone who is either rich or wise is curious. If fred is patient or not humble then susan is both not curious and not funny and vice versa. Everyone who is both generous and wise is not quiet or not generous and vice versa. If someone is not calm or calm then mary is not strong and vice versa. Everyone who is kind or not wise is either not wise or kind. If fred is not generous then fred is either not tall or patient and vice versa. Everyone who is not creative is happy. Everyone who is both happy and not brave is either not wise or strong and vice versa. If fred is rich or not generous then paul is not curious or tall. If someone is either not rich or quiet then paul is either not generous or not quiet and vice versa. If lucy is both not creative and not tall then someone is both generous and not rich and vice versa. Alice is either not curious or calm. Someone is both not quiet and curious. John is humble or not humble. Paul is creative. Someone is either tall or not calm. Someone is not happy. | Susan is not creative. | neutral | (![X]:((quiet(X)|patient(X))<=>(old(X)|calm(X))))&
(![X]:((quiet(X)|happy(X))<=>curious(X)))&
((?[X]:((tall(X)|old(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~strong(X)|~calm(X))=>(calm(X)&quiet(X))))&
(((~curious(fred)&patient(fred)))=>((~brave(lucy)<~>generous(lucy))))&
(![X]:((rich(X)<~>wise(X))=>curious(X)))&
(((patient(fred)|~humble(fred)))<=>((~curious(susan)&~funny(susan))))&
(![X]:((generous(X)&wise(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(~strong(mary)))&
(![X]:((kind(X)|~wise(X))=>(~wise(X)<~>kind(X))))&
((~generous(fred))<=>((~tall(fred)<~>patient(fred))))&
(![X]:(~creative(X)=>happy(X)))&
(![X]:((happy(X)&~brave(X))<=>(~wise(X)<~>strong(X))))&
(((rich(fred)|~generous(fred)))=>((~curious(paul)|tall(paul))))&
((?[X]:((~rich(X)<~>quiet(X))))<=>((~generous(paul)<~>~quiet(paul))))&
(((~creative(lucy)&~tall(lucy)))<=>(?[X]:((generous(X)&~rich(X)))))&
((~curious(alice)<~>calm(alice)))&
(?[X]:((~quiet(X)&curious(X))))&
((humble(john)|~humble(john)))&
(creative(paul))&
(?[X]:((tall(X)<~>~calm(X))))&
(?[X]:(~happy(X))) | ~creative(susan) | [] | null | 0 |
Everyone who is not strong or not curious is both not rich and not creative.
Everyone who is not rich or happy is either not creative or not kind and vice versa.
Everyone who is both not brave and wise is both not old and not curious and vice versa.
If someone is either not humble or calm then someone is not calm or humble.
Everyone who is not calm is either not kind or rich and vice versa.
If someone is both generous and not creative then someone is rich and vice versa.
Everyone who is rich is happy or humble.
If fred is old then john is both not wise and not curious and vice versa.
Everyone who is not funny is both quiet and not kind and vice versa.
Everyone who is both not quiet and not rich is either not creative or patient and vice versa.
If paul is either strong or not wise then fred is wise or humble.
If someone is curious or not humble then someone is not quiet or kind.
If someone is both funny and not kind then alice is both not curious and kind and vice versa.
Everyone who is both tall and not rich is both quiet and humble.
If someone is either happy or calm then someone is either not funny or not happy and vice versa.
If lucy is both not patient and not strong then lucy is both humble and not kind.
Someone is both not happy and funny.
Someone is old.
Lucy is quiet.
Alice is either strong or old.
Susan is both wise and happy.
John is humble.
Lucy is both kind and tall.
John is both generous and not calm. | John is not rich. | neutral | (![X]:((~strong(X)|~curious(X))=>(~rich(X)&~creative(X))))&
(![X]:((~rich(X)|happy(X))<=>(~creative(X)<~>~kind(X))))&
(![X]:((~brave(X)&wise(X))<=>(~old(X)&~curious(X))))&
((?[X]:((~humble(X)<~>calm(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:(~calm(X)<=>(~kind(X)<~>rich(X))))&
((?[X]:((generous(X)&~creative(X))))<=>(?[X]:(rich(X))))&
(![X]:(rich(X)=>(happy(X)|humble(X))))&
((old(fred))<=>((~wise(john)&~curious(john))))&
(![X]:(~funny(X)<=>(quiet(X)&~kind(X))))&
(![X]:((~quiet(X)&~rich(X))<=>(~creative(X)<~>patient(X))))&
(((strong(paul)<~>~wise(paul)))=>((wise(fred)|humble(fred))))&
((?[X]:((curious(X)|~humble(X))))=>(?[X]:((~quiet(X)|kind(X)))))&
((?[X]:((funny(X)&~kind(X))))<=>((~curious(alice)&kind(alice))))&
(![X]:((tall(X)&~rich(X))=>(quiet(X)&humble(X))))&
((?[X]:((happy(X)<~>calm(X))))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(((~patient(lucy)&~strong(lucy)))=>((humble(lucy)&~kind(lucy))))&
(?[X]:((~happy(X)&funny(X))))&
(?[X]:(old(X)))&
(quiet(lucy))&
((strong(alice)<~>old(alice)))&
((wise(susan)&happy(susan)))&
(humble(john))&
((kind(lucy)&tall(lucy)))&
((generous(john)&~calm(john))) | ~rich(john) | [] | null | 0 |
Everyone who is not happy is either kind or not brave and vice versa.
Everyone who is not funny is tall and vice versa.
Everyone who is both not patient and not curious is either generous or not generous and vice versa.
If alice is either not strong or not old then alice is not quiet and vice versa.
Everyone who is either calm or tall is wise or kind and vice versa.
If mary is either not kind or patient then someone is both brave and not funny.
Everyone who is both not creative and not curious is both not funny and not curious.
Everyone who is either not generous or kind is both not old and not rich and vice versa.
Everyone who is both brave and old is brave or old and vice versa.
Everyone who is brave or kind is either not kind or quiet.
Everyone who is both not quiet and not happy is creative or not brave.
Everyone who is either not tall or calm is both not happy and not rich and vice versa.
Everyone who is either not quiet or wise is both rich and calm and vice versa.
If someone is old then fred is both humble and not rich and vice versa.
If someone is either not generous or strong then mary is not humble.
If lucy is either tall or not funny then someone is tall and vice versa.
Someone is not calm or not humble.
John is both happy and not generous.
Susan is both not generous and rich.
Someone is not generous.
Someone is either generous or wise. | John is not wise. | contradiction | (![X]:(~happy(X)<=>(kind(X)<~>~brave(X))))&
(![X]:(~funny(X)<=>tall(X)))&
(![X]:((~patient(X)&~curious(X))<=>(generous(X)<~>~generous(X))))&
(((~strong(alice)<~>~old(alice)))<=>(~quiet(alice)))&
(![X]:((calm(X)<~>tall(X))<=>(wise(X)|kind(X))))&
(((~kind(mary)<~>patient(mary)))=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:((~creative(X)&~curious(X))=>(~funny(X)&~curious(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(~old(X)&~rich(X))))&
(![X]:((brave(X)&old(X))<=>(brave(X)|old(X))))&
(![X]:((brave(X)|kind(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((~quiet(X)&~happy(X))=>(creative(X)|~brave(X))))&
(![X]:((~tall(X)<~>calm(X))<=>(~happy(X)&~rich(X))))&
(![X]:((~quiet(X)<~>wise(X))<=>(rich(X)&calm(X))))&
((?[X]:(old(X)))<=>((humble(fred)&~rich(fred))))&
((?[X]:((~generous(X)<~>strong(X))))=>(~humble(mary)))&
(((tall(lucy)<~>~funny(lucy)))<=>(?[X]:(tall(X))))&
(?[X]:((~calm(X)|~humble(X))))&
((happy(john)&~generous(john)))&
((~generous(susan)&rich(susan)))&
(?[X]:(~generous(X)))&
(?[X]:((generous(X)<~>wise(X)))) | ~wise(john) | [
"p0",
"p1",
"p4",
"p7",
"p8",
"p9",
"p11",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6084704798483351935994744
% SZS output start Proof for 6084704798483351935994744
1. ! [X0] : (~happy(X0) <=> (kind(X0) <~> ~brave(X0))) [input p0]
2. ! [X0] : (~funny(X0) <=> tall(X0)) [input p1]
5. ! [X0] : ((calm(X0) <~> tall(X0)) <=> (kind(X0) | wise(X0))) [input p4]
8. ! [X0] : ((~generous(X0) <~> kind(X0)) <=> (~rich(X0) & ~old(X0))) [input p7]
9. ! [X0] : ((old(X0) & brave(X0)) <=> (old(X0) | brave(X0))) [input p8]
10. ! [X0] : ((kind(X0) | brave(X0)) => (~kind(X0) <~> quiet(X0))) [input p9]
12. ! [X0] : ((~tall(X0) <~> calm(X0)) <=> (~rich(X0) & ~happy(X0))) [input p11]
13. ! [X0] : ((~quiet(X0) <~> wise(X0)) <=> (calm(X0) & rich(X0))) [input p12]
16. (tall(lucy) <~> ~funny(lucy)) <=> ? [X0] : tall(X0) [input p15]
18. ~generous(john) & happy(john) [input p17]
22. ~wise(john) [input hypothesis]
26. ! [X0] : ((~kind(X0) <~> quiet(X0)) | (~kind(X0) & ~brave(X0))) [ennf transformation 10]
28. ! [X0] : ((~happy(X0) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | happy(X0))) [nnf transformation 1]
29. ! [X0] : ((~funny(X0) | ~tall(X0)) & (tall(X0) | funny(X0))) [nnf transformation 2]
33. ! [X0] : ((((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | ((calm(X0) | ~tall(X0)) & (tall(X0) | ~calm(X0))))) [nnf transformation 5]
34. ! [X0] : ((((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ((calm(X0) | ~tall(X0)) & (tall(X0) | ~calm(X0))))) [flattening 33]
38. ! [X0] : ((((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (rich(X0) | old(X0))) & ((~rich(X0) & ~old(X0)) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))))) [nnf transformation 8]
39. ! [X0] : ((((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | rich(X0) | old(X0)) & ((~rich(X0) & ~old(X0)) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))))) [flattening 38]
40. ! [X0] : (((old(X0) & brave(X0)) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | (~old(X0) | ~brave(X0)))) [nnf transformation 9]
41. ! [X0] : (((old(X0) & brave(X0)) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ~old(X0) | ~brave(X0))) [flattening 40]
42. ! [X0] : (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | (~kind(X0) & ~brave(X0))) [nnf transformation 26]
43. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | (rich(X0) | happy(X0))) & ((~rich(X0) & ~happy(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [nnf transformation 12]
44. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | rich(X0) | happy(X0)) & ((~rich(X0) & ~happy(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [flattening 43]
45. ! [X0] : ((((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | (~calm(X0) | ~rich(X0))) & ((calm(X0) & rich(X0)) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))))) [nnf transformation 13]
46. ! [X0] : ((((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~calm(X0) | ~rich(X0)) & ((calm(X0) & rich(X0)) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))))) [flattening 45]
53. (((funny(lucy) | ~tall(lucy)) & (~funny(lucy) | tall(lucy))) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | ((tall(lucy) | funny(lucy)) & (~funny(lucy) | ~tall(lucy)))) [nnf transformation 16]
54. (((funny(lucy) | ~tall(lucy)) & (~funny(lucy) | tall(lucy))) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | ((tall(lucy) | funny(lucy)) & (~funny(lucy) | ~tall(lucy)))) [rectify 53]
55. ? [X1] : tall(X1) => tall(sK2) [choice axiom]
56. (((funny(lucy) | ~tall(lucy)) & (~funny(lucy) | tall(lucy))) | ! [X0] : ~tall(X0)) & (tall(sK2) | ((tall(lucy) | funny(lucy)) & (~funny(lucy) | ~tall(lucy)))) [skolemisation 54,55]
66. ~brave(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 28]
68. tall(X0) | funny(X0) [cnf transformation 29]
69. ~tall(X0) | ~funny(X0) [cnf transformation 29]
80. ~calm(X0) | wise(X0) | tall(X0) | kind(X0) [cnf transformation 34]
83. ~kind(X0) | calm(X0) | tall(X0) [cnf transformation 34]
95. ~kind(X0) | generous(X0) | rich(X0) | old(X0) [cnf transformation 39]
98. ~old(X0) | brave(X0) [cnf transformation 41]
102. quiet(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
105. ~happy(X0) | calm(X0) | tall(X0) [cnf transformation 44]
115. ~rich(X0) | ~quiet(X0) | ~calm(X0) | wise(X0) [cnf transformation 46]
124. ~funny(lucy) | tall(lucy) | ~tall(X0) [cnf transformation 56]
125. funny(lucy) | ~tall(lucy) | ~tall(X0) [cnf transformation 56]
127. happy(john) [cnf transformation 18]
128. ~generous(john) [cnf transformation 18]
134. ~wise(john) [cnf transformation 22]
135. ~kind(X0) | quiet(X0) [duplicate literal removal 102]
204. ~tall(lucy) | ~tall(X0) [subsumption resolution 125,69]
206. 14 <=> ! [X0] : ~tall(X0) [avatar definition]
207. ~tall(X0) <- (14) [avatar component clause 206]
209. 15 <=> tall(lucy) [avatar definition]
211. ~tall(lucy) <- (~15) [avatar component clause 209]
212. 14 | ~15 [avatar split clause 204,209,206]
213. ~funny(lucy) | ~tall(X0) [subsumption resolution 124,69]
215. 16 <=> funny(lucy) [avatar definition]
217. ~funny(lucy) <- (~16) [avatar component clause 215]
218. 14 | ~16 [avatar split clause 213,215,206]
238. funny(lucy) <- (~15) [resolution 68,211]
239. $false <- (~15, ~16) [subsumption resolution 238,217]
240. 15 | 16 [avatar contradiction clause 239]
277. 25 <=> brave(john) [avatar definition]
278. ~brave(john) <- (~25) [avatar component clause 277]
279. brave(john) <- (25) [avatar component clause 277]
281. 26 <=> kind(john) [avatar definition]
282. ~kind(john) <- (~26) [avatar component clause 281]
283. kind(john) <- (26) [avatar component clause 281]
288. ~happy(john) | ~kind(john) <- (25) [resolution 279,66]
291. ~kind(john) <- (25) [subsumption resolution 288,127]
292. ~26 | ~25 [avatar split clause 291,277,281]
295. calm(john) | tall(john) <- (26) [resolution 283,83]
297. quiet(john) <- (26) [resolution 283,135]
298. calm(john) <- (14, 26) [subsumption resolution 295,207]
331. calm(john) | tall(john) [resolution 105,127]
421. generous(john) | rich(john) | old(john) <- (26) [resolution 95,283]
433. rich(john) | old(john) <- (26) [subsumption resolution 421,128]
493. 40 <=> old(john) [avatar definition]
495. old(john) <- (40) [avatar component clause 493]
497. 41 <=> rich(john) [avatar definition]
499. rich(john) <- (41) [avatar component clause 497]
500. 40 | 41 | ~26 [avatar split clause 433,281,497,493]
557. ~quiet(john) | ~calm(john) | wise(john) <- (41) [resolution 499,115]
562. ~calm(john) | wise(john) <- (26, 41) [subsumption resolution 557,297]
563. wise(john) <- (14, 26, 41) [subsumption resolution 562,298]
564. $false <- (14, 26, 41) [subsumption resolution 563,134]
565. ~14 | ~26 | ~41 [avatar contradiction clause 564]
568. brave(john) <- (40) [resolution 495,98]
569. $false <- (~25, 40) [subsumption resolution 568,278]
570. 25 | ~40 [avatar contradiction clause 569]
572. calm(john) <- (14) [subsumption resolution 331,207]
578. wise(john) | tall(john) | kind(john) <- (14) [resolution 572,80]
581. tall(john) | kind(john) <- (14) [subsumption resolution 578,134]
582. kind(john) <- (14) [subsumption resolution 581,207]
583. $false <- (14, ~26) [subsumption resolution 582,282]
584. ~14 | 26 [avatar contradiction clause 583]
585. $false [avatar sat refutation 212,218,240,292,500,565,570,584]
% SZS output end Proof for 6084704798483351935994744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is either quiet or not generous and vice versa. Everyone who is both creative and not tall is either not funny or not strong. Everyone who is either wise or patient is patient and vice versa. Everyone who is happy or not quiet is both generous and not old and vice versa. If susan is both wise and rich then lucy is either tall or not brave and vice versa. If someone is generous or wise then someone is not calm and vice versa. Everyone who is either strong or not kind is both not curious and strong. If fred is either patient or not wise then susan is either not curious or tall. If paul is strong or not rich then someone is not patient. Everyone who is either not calm or quiet is both curious and kind and vice versa. Everyone who is not quiet is kind and vice versa. Everyone who is both rich and creative is both curious and not old and vice versa. If susan is not quiet or calm then someone is both old and tall and vice versa. If someone is both not funny and not calm then someone is funny. If someone is generous or tall then someone is wise or not funny. Susan is not humble. Susan is kind or not humble. Paul is either not funny or rich. Lucy is either not humble or happy. Someone is either not wise or not humble. | Fred is old. | neutral | (![X]:(generous(X)<=>(quiet(X)<~>~generous(X))))&
(![X]:((creative(X)&~tall(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((wise(X)<~>patient(X))<=>patient(X)))&
(![X]:((happy(X)|~quiet(X))<=>(generous(X)&~old(X))))&
(((wise(susan)&rich(susan)))<=>((tall(lucy)<~>~brave(lucy))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>~kind(X))=>(~curious(X)&strong(X))))&
(((patient(fred)<~>~wise(fred)))=>((~curious(susan)<~>tall(susan))))&
(((strong(paul)|~rich(paul)))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(curious(X)&kind(X))))&
(![X]:(~quiet(X)<=>kind(X)))&
(![X]:((rich(X)&creative(X))<=>(curious(X)&~old(X))))&
(((~quiet(susan)|calm(susan)))<=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~funny(X)&~calm(X))))=>(?[X]:(funny(X))))&
((?[X]:((generous(X)|tall(X))))=>(?[X]:((wise(X)|~funny(X)))))&
(~humble(susan))&
((kind(susan)|~humble(susan)))&
((~funny(paul)<~>rich(paul)))&
((~humble(lucy)<~>happy(lucy)))&
(?[X]:((~wise(X)<~>~humble(X)))) | old(fred) | [] | null | 0 |
If lucy is both curious and wise then lucy is not curious and vice versa. Everyone who is quiet or not funny is patient or not humble and vice versa. Everyone who is both happy and calm is wise or not brave and vice versa. If lucy is both happy and not old then someone is both not wise and not strong. If someone is both funny and not rich then lucy is not tall. Everyone who is either rich or not funny is patient and vice versa. Everyone who is both not funny and rich is not wise or strong and vice versa. If susan is either curious or tall then someone is both not strong and calm. If someone is both not curious and funny then susan is both happy and not kind and vice versa. Everyone who is rich or not strong is generous and vice versa. Everyone who is not quiet or humble is brave or not calm. Everyone who is not tall is either not calm or humble and vice versa. Everyone who is either calm or humble is both creative and generous and vice versa. Everyone who is both not funny and not brave is not funny or strong and vice versa. If someone is not wise then someone is either funny or not tall. Everyone who is either not patient or not tall is both tall and not brave and vice versa. Mary is not brave. Alice is not wise or not rich. John is either wise or quiet. Someone is quiet or not wise. Someone is either calm or curious. Someone is either not old or not patient. Mary is patient or curious. Someone is either old or not old. | Alice is not tall. | contradiction | (((curious(lucy)&wise(lucy)))<=>(~curious(lucy)))&
(![X]:((quiet(X)|~funny(X))<=>(patient(X)|~humble(X))))&
(![X]:((happy(X)&calm(X))<=>(wise(X)|~brave(X))))&
(((happy(lucy)&~old(lucy)))=>(?[X]:((~wise(X)&~strong(X)))))&
((?[X]:((funny(X)&~rich(X))))=>(~tall(lucy)))&
(![X]:((rich(X)<~>~funny(X))<=>patient(X)))&
(![X]:((~funny(X)&rich(X))<=>(~wise(X)|strong(X))))&
(((curious(susan)<~>tall(susan)))=>(?[X]:((~strong(X)&calm(X)))))&
((?[X]:((~curious(X)&funny(X))))<=>((happy(susan)&~kind(susan))))&
(![X]:((rich(X)|~strong(X))<=>generous(X)))&
(![X]:((~quiet(X)|humble(X))=>(brave(X)|~calm(X))))&
(![X]:(~tall(X)<=>(~calm(X)<~>humble(X))))&
(![X]:((calm(X)<~>humble(X))<=>(creative(X)&generous(X))))&
(![X]:((~funny(X)&~brave(X))<=>(~funny(X)|strong(X))))&
((?[X]:(~wise(X)))=>(?[X]:((funny(X)<~>~tall(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>(tall(X)&~brave(X))))&
(~brave(mary))&
((~wise(alice)|~rich(alice)))&
((wise(john)<~>quiet(john)))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((calm(X)<~>curious(X))))&
(?[X]:((~old(X)<~>~patient(X))))&
((patient(mary)|curious(mary)))&
(?[X]:((old(X)<~>~old(X)))) | ~tall(alice) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p10",
"p11",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 813761410020270955292906
% SZS output start Proof for 813761410020270955292906
1. (wise(lucy) & curious(lucy)) <=> ~curious(lucy) [input p0]
2. ! [X0] : ((~funny(X0) | quiet(X0)) <=> (~humble(X0) | patient(X0))) [input p1]
3. ! [X0] : ((calm(X0) & happy(X0)) <=> (~brave(X0) | wise(X0))) [input p2]
5. ? [X0] : (~rich(X0) & funny(X0)) => ~tall(lucy) [input p4]
7. ! [X0] : ((rich(X0) & ~funny(X0)) <=> (strong(X0) | ~wise(X0))) [input p6]
11. ! [X0] : ((humble(X0) | ~quiet(X0)) => (~calm(X0) | brave(X0))) [input p10]
12. ! [X0] : (~tall(X0) <=> (~calm(X0) <~> humble(X0))) [input p11]
14. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> (strong(X0) | ~funny(X0))) [input p13]
16. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> (~brave(X0) & tall(X0))) [input p15]
18. ~rich(alice) | ~wise(alice) [input p17]
25. ~tall(alice) [input hypothesis]
29. ~tall(lucy) | ! [X0] : (rich(X0) | ~funny(X0)) [ennf transformation 5]
31. ! [X0] : ((~calm(X0) | brave(X0)) | (~humble(X0) & quiet(X0))) [ennf transformation 11]
32. ! [X0] : (~calm(X0) | brave(X0) | (~humble(X0) & quiet(X0))) [flattening 31]
34. ((wise(lucy) & curious(lucy)) | curious(lucy)) & (~curious(lucy) | (~wise(lucy) | ~curious(lucy))) [nnf transformation 1]
35. ((wise(lucy) & curious(lucy)) | curious(lucy)) & (~curious(lucy) | ~wise(lucy) | ~curious(lucy)) [flattening 34]
36. ! [X0] : (((~funny(X0) | quiet(X0)) | (humble(X0) & ~patient(X0))) & ((~humble(X0) | patient(X0)) | (funny(X0) & ~quiet(X0)))) [nnf transformation 2]
37. ! [X0] : ((~funny(X0) | quiet(X0) | (humble(X0) & ~patient(X0))) & (~humble(X0) | patient(X0) | (funny(X0) & ~quiet(X0)))) [flattening 36]
38. ! [X0] : (((calm(X0) & happy(X0)) | (brave(X0) & ~wise(X0))) & ((~brave(X0) | wise(X0)) | (~calm(X0) | ~happy(X0)))) [nnf transformation 3]
39. ! [X0] : (((calm(X0) & happy(X0)) | (brave(X0) & ~wise(X0))) & (~brave(X0) | wise(X0) | ~calm(X0) | ~happy(X0))) [flattening 38]
43. ! [X0] : (((rich(X0) & ~funny(X0)) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | (~rich(X0) | funny(X0)))) [nnf transformation 7]
44. ! [X0] : (((rich(X0) & ~funny(X0)) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | ~rich(X0) | funny(X0))) [flattening 43]
55. ! [X0] : ((~tall(X0) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | tall(X0))) [nnf transformation 12]
58. ! [X0] : (((~brave(X0) & ~funny(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (brave(X0) | funny(X0)))) [nnf transformation 14]
59. ! [X0] : (((~brave(X0) & ~funny(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | brave(X0) | funny(X0))) [flattening 58]
64. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | (brave(X0) | ~tall(X0))) & ((~brave(X0) & tall(X0)) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 16]
65. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | brave(X0) | ~tall(X0)) & ((~brave(X0) & tall(X0)) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [flattening 64]
78. ~curious(lucy) | ~wise(lucy) | ~curious(lucy) [cnf transformation 35]
79. curious(lucy) | curious(lucy) [cnf transformation 35]
82. ~humble(X0) | patient(X0) | funny(X0) [cnf transformation 37]
89. brave(X0) | calm(X0) [cnf transformation 39]
92. ~tall(lucy) | rich(X0) | ~funny(X0) [cnf transformation 29]
98. ~funny(X0) | wise(X0) [cnf transformation 44]
114. ~calm(X0) | brave(X0) | ~humble(X0) [cnf transformation 32]
115. ~calm(X0) | humble(X0) | tall(X0) [cnf transformation 55]
128. ~brave(X0) | funny(X0) [cnf transformation 59]
133. tall(X0) | ~patient(X0) | tall(X0) [cnf transformation 65]
136. ~tall(X0) | ~patient(X0) | brave(X0) | ~tall(X0) [cnf transformation 65]
139. ~rich(alice) | ~wise(alice) [cnf transformation 18]
150. ~tall(alice) [cnf transformation 25]
151. ~patient(X0) | tall(X0) [duplicate literal removal 133]
152. ~tall(X0) | ~patient(X0) | brave(X0) [duplicate literal removal 136]
153. ~curious(lucy) | ~wise(lucy) [duplicate literal removal 78]
154. curious(lucy) [duplicate literal removal 79]
156. 1 <=> curious(lucy) [avatar definition]
160. 2 <=> wise(lucy) [avatar definition]
161. ~wise(lucy) <- (~2) [avatar component clause 160]
164. 1 [avatar split clause 154,156]
165. ~2 | ~1 [avatar split clause 153,156,160]
185. 7 <=> ! [X0] : (rich(X0) | ~funny(X0)) [avatar definition]
186. ~funny(X0) | rich(X0) <- (7) [avatar component clause 185]
188. 8 <=> tall(lucy) [avatar definition]
190. ~tall(lucy) <- (~8) [avatar component clause 188]
191. 7 | ~8 [avatar split clause 92,188,185]
235. ~humble(X0) | brave(X0) [subsumption resolution 114,89]
251. 21 <=> wise(alice) [avatar definition]
255. 22 <=> rich(alice) [avatar definition]
257. ~rich(alice) <- (~22) [avatar component clause 255]
258. ~21 | ~22 [avatar split clause 139,255,251]
319. calm(X0) | funny(X0) [resolution 128,89]
342. 35 <=> funny(alice) [avatar definition]
344. funny(alice) <- (35) [avatar component clause 342]
354. 37 <=> humble(alice) [avatar definition]
356. humble(alice) <- (37) [avatar component clause 354]
380. 41 <=> humble(lucy) [avatar definition]
382. humble(lucy) <- (41) [avatar component clause 380]
390. tall(X0) | humble(X0) | funny(X0) [resolution 115,319]
414. patient(alice) | funny(alice) <- (37) [resolution 356,82]
563. humble(X0) | funny(X0) | ~patient(X0) | brave(X0) [resolution 390,152]
567. humble(lucy) | funny(lucy) <- (~8) [resolution 390,190]
569. humble(alice) | funny(alice) [resolution 390,150]
572. funny(X0) | ~patient(X0) | brave(X0) [subsumption resolution 563,235]
573. funny(X0) | ~patient(X0) [subsumption resolution 572,128]
575. 55 <=> funny(lucy) [avatar definition]
576. ~funny(lucy) <- (~55) [avatar component clause 575]
577. funny(lucy) <- (55) [avatar component clause 575]
578. 55 | 41 | 8 [avatar split clause 567,188,380,575]
594. wise(lucy) <- (55) [resolution 577,98]
595. $false <- (~2, 55) [subsumption resolution 594,161]
596. 2 | ~55 [avatar contradiction clause 595]
606. 59 <=> patient(lucy) [avatar definition]
607. patient(lucy) <- (59) [avatar component clause 606]
608. ~patient(lucy) <- (~59) [avatar component clause 606]
622. rich(alice) <- (7, 35) [resolution 186,344]
624. $false <- (7, ~22, 35) [subsumption resolution 622,257]
625. ~7 | 22 | ~35 [avatar contradiction clause 624]
633. funny(alice) <- (37) [subsumption resolution 414,573]
634. 35 | ~37 [avatar split clause 633,354,342]
650. 35 | 37 [avatar split clause 569,354,342]
659. wise(alice) <- (35) [resolution 344,98]
662. 21 | ~35 [avatar split clause 659,342,251]
693. tall(lucy) <- (59) [resolution 607,151]
696. $false <- (~8, 59) [subsumption resolution 693,190]
697. 8 | ~59 [avatar contradiction clause 696]
726. patient(lucy) | funny(lucy) <- (41) [resolution 382,82]
729. funny(lucy) <- (41, ~59) [subsumption resolution 726,608]
730. $false <- (41, ~55, ~59) [subsumption resolution 729,576]
731. ~41 | 55 | 59 [avatar contradiction clause 730]
737. $false [avatar sat refutation 164,165,191,258,578,596,625,634,650,662,697,731]
% SZS output end Proof for 813761410020270955292906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.048 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not patient or patient then someone is strong or kind.
Everyone who is not wise or not quiet is either humble or not curious.
Everyone who is both not tall and humble is either not calm or kind and vice versa.
If someone is calm or not old then someone is either rich or not happy.
Everyone who is both not rich and brave is either not humble or calm and vice versa.
Everyone who is either not tall or humble is wise.
Everyone who is funny or strong is not quiet and vice versa.
If someone is not old or kind then someone is both wise and not brave and vice versa.
Everyone who is both rich and quiet is rich or quiet and vice versa.
Everyone who is either calm or not brave is either not old or kind.
If someone is either funny or not strong then someone is not strong and vice versa.
If someone is brave or humble then susan is rich and vice versa.
Everyone who is not funny is either wise or humble and vice versa.
If fred is either wise or curious then someone is either funny or not quiet.
If lucy is not tall then susan is either not wise or not tall.
If someone is either happy or patient then fred is funny and vice versa.
Someone is curious or not calm.
Alice is not wise.
Alice is either patient or not curious.
Someone is both not kind and not creative.
Mary is generous.
John is either not generous or funny.
Paul is not funny.
Alice is both patient and strong. | Susan is not rich. | contradiction | (((~patient(lucy)|patient(lucy)))=>(?[X]:((strong(X)|kind(X)))))&
(![X]:((~wise(X)|~quiet(X))=>(humble(X)<~>~curious(X))))&
(![X]:((~tall(X)&humble(X))<=>(~calm(X)<~>kind(X))))&
((?[X]:((calm(X)|~old(X))))=>(?[X]:((rich(X)<~>~happy(X)))))&
(![X]:((~rich(X)&brave(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((~tall(X)<~>humble(X))=>wise(X)))&
(![X]:((funny(X)|strong(X))<=>~quiet(X)))&
((?[X]:((~old(X)|kind(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((rich(X)&quiet(X))<=>(rich(X)|quiet(X))))&
(![X]:((calm(X)<~>~brave(X))=>(~old(X)<~>kind(X))))&
((?[X]:((funny(X)<~>~strong(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((brave(X)|humble(X))))<=>(rich(susan)))&
(![X]:(~funny(X)<=>(wise(X)<~>humble(X))))&
(((wise(fred)<~>curious(fred)))=>(?[X]:((funny(X)<~>~quiet(X)))))&
((~tall(lucy))=>((~wise(susan)<~>~tall(susan))))&
((?[X]:((happy(X)<~>patient(X))))<=>(funny(fred)))&
(?[X]:((curious(X)|~calm(X))))&
(~wise(alice))&
((patient(alice)<~>~curious(alice)))&
(?[X]:((~kind(X)&~creative(X))))&
(generous(mary))&
((~generous(john)<~>funny(john)))&
(~funny(paul))&
((patient(alice)&strong(alice))) | ~rich(susan) | [
"p1",
"p11",
"p17",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7595671519324327855469012
% SZS output start Proof for 7595671519324327855469012
2. ! [X0] : ((~quiet(X0) | ~wise(X0)) => (humble(X0) <~> ~curious(X0))) [input p1]
12. ? [X0] : (humble(X0) | brave(X0)) <=> rich(susan) [input p11]
18. ~wise(alice) [input p17]
19. patient(alice) <~> ~curious(alice) [input p18]
24. strong(alice) & patient(alice) [input p23]
25. ~rich(susan) [input hypothesis]
31. ! [X0] : ((humble(X0) <~> ~curious(X0)) | (quiet(X0) & wise(X0))) [ennf transformation 2]
39. ! [X0] : (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (quiet(X0) & wise(X0))) [nnf transformation 31]
64. (? [X0] : (humble(X0) | brave(X0)) | ~rich(susan)) & (rich(susan) | ! [X0] : (~humble(X0) & ~brave(X0))) [nnf transformation 12]
65. (? [X0] : (humble(X0) | brave(X0)) | ~rich(susan)) & (rich(susan) | ! [X1] : (~humble(X1) & ~brave(X1))) [rectify 64]
66. ? [X0] : (humble(X0) | brave(X0)) => (humble(sK6) | brave(sK6)) [choice axiom]
67. ((humble(sK6) | brave(sK6)) | ~rich(susan)) & (rich(susan) | ! [X1] : (~humble(X1) & ~brave(X1))) [skolemisation 65,66]
79. (curious(alice) | ~patient(alice)) & (~curious(alice) | patient(alice)) [nnf transformation 19]
85. ~curious(X0) | humble(X0) | wise(X0) [cnf transformation 39]
129. rich(susan) | ~humble(X1) [cnf transformation 67]
146. ~wise(alice) [cnf transformation 18]
148. curious(alice) | ~patient(alice) [cnf transformation 79]
154. patient(alice) [cnf transformation 24]
156. ~rich(susan) [cnf transformation 25]
242. 20 <=> rich(susan) [avatar definition]
255. 23 <=> ! [X1] : ~humble(X1) [avatar definition]
256. ~humble(X1) <- (23) [avatar component clause 255]
257. 23 | 20 [avatar split clause 129,242,255]
332. 39 <=> patient(alice) [avatar definition]
336. 40 <=> curious(alice) [avatar definition]
338. curious(alice) <- (40) [avatar component clause 336]
339. ~39 | 40 [avatar split clause 148,336,332]
351. 39 [avatar split clause 154,332]
352. ~20 [avatar split clause 156,242]
357. humble(alice) | wise(alice) <- (40) [resolution 85,338]
358. wise(alice) <- (23, 40) [subsumption resolution 357,256]
359. $false <- (23, 40) [subsumption resolution 358,146]
360. ~23 | ~40 [avatar contradiction clause 359]
361. $false [avatar sat refutation 257,339,351,352,360]
% SZS output end Proof for 7595671519324327855469012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or happy then someone is either strong or not rich.
If someone is either not calm or not strong then someone is brave.
If mary is either not creative or not generous then paul is not creative or not quiet and vice versa.
Everyone who is wise is calm or curious and vice versa.
If someone is both happy and not kind then alice is either kind or not generous and vice versa.
Everyone who is either not curious or wise is both patient and strong and vice versa.
If someone is both tall and not patient then someone is creative and vice versa.
If someone is old or not creative then mary is both old and humble.
Everyone who is both calm and not humble is creative.
Everyone who is calm is not brave.
Everyone who is both generous and kind is not generous and vice versa.
Everyone who is curious or kind is both brave and not wise.
Everyone who is both not quiet and not humble is either not creative or not brave and vice versa.
Everyone who is not quiet is either brave or generous.
Everyone who is not funny is both patient and rich and vice versa.
Everyone who is creative or not rich is either not strong or not rich.
Someone is not strong or not quiet.
Someone is either generous or not generous.
Someone is quiet or not tall.
Someone is both funny and not patient.
Lucy is not brave or not funny.
Alice is not brave or not creative.
Someone is either creative or kind.
Someone is either not funny or quiet. | Alice is curious. | contradiction | ((?[X]:((~rich(X)<~>happy(X))))=>(?[X]:((strong(X)<~>~rich(X)))))&
((?[X]:((~calm(X)<~>~strong(X))))=>(?[X]:(brave(X))))&
(((~creative(mary)<~>~generous(mary)))<=>((~creative(paul)|~quiet(paul))))&
(![X]:(wise(X)<=>(calm(X)|curious(X))))&
((?[X]:((happy(X)&~kind(X))))<=>((kind(alice)<~>~generous(alice))))&
(![X]:((~curious(X)<~>wise(X))<=>(patient(X)&strong(X))))&
((?[X]:((tall(X)&~patient(X))))<=>(?[X]:(creative(X))))&
((?[X]:((old(X)|~creative(X))))=>((old(mary)&humble(mary))))&
(![X]:((calm(X)&~humble(X))=>creative(X)))&
(![X]:(calm(X)=>~brave(X)))&
(![X]:((generous(X)&kind(X))<=>~generous(X)))&
(![X]:((curious(X)|kind(X))=>(brave(X)&~wise(X))))&
(![X]:((~quiet(X)&~humble(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:(~quiet(X)=>(brave(X)<~>generous(X))))&
(![X]:(~funny(X)<=>(patient(X)&rich(X))))&
(![X]:((creative(X)|~rich(X))=>(~strong(X)<~>~rich(X))))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:((quiet(X)|~tall(X))))&
(?[X]:((funny(X)&~patient(X))))&
((~brave(lucy)|~funny(lucy)))&
((~brave(alice)|~creative(alice)))&
(?[X]:((creative(X)<~>kind(X))))&
(?[X]:((~funny(X)<~>quiet(X)))) | curious(alice) | [
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7240431889383811758715259
% SZS output start Proof for 7240431889383811758715259
4. ! [X0] : (wise(X0) <=> (curious(X0) | calm(X0))) [input p3]
12. ! [X0] : ((kind(X0) | curious(X0)) => (~wise(X0) & brave(X0))) [input p11]
25. curious(alice) [input hypothesis]
35. ! [X0] : ((~wise(X0) & brave(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 12]
48. ! [X0] : ((wise(X0) | (~curious(X0) & ~calm(X0))) & ((curious(X0) | calm(X0)) | ~wise(X0))) [nnf transformation 4]
49. ! [X0] : ((wise(X0) | (~curious(X0) & ~calm(X0))) & (curious(X0) | calm(X0) | ~wise(X0))) [flattening 48]
98. wise(X0) | ~curious(X0) [cnf transformation 49]
125. ~wise(X0) | ~curious(X0) [cnf transformation 35]
154. curious(alice) [cnf transformation 25]
279. ~curious(X0) [subsumption resolution 125,98]
328. $false [subsumption resolution 154,279]
% SZS output end Proof for 7240431889383811758715259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is funny then someone is not curious.
If mary is not patient or not kind then paul is either not old or not kind.
If lucy is tall or strong then mary is generous or kind.
Everyone who is either not funny or tall is tall.
Everyone who is tall or not rich is either not strong or happy and vice versa.
If susan is generous or not strong then someone is kind or strong and vice versa.
Everyone who is both not patient and creative is either not brave or patient and vice versa.
Everyone who is calm or kind is not happy or strong and vice versa.
If someone is calm then susan is either patient or not generous and vice versa.
If fred is curious then fred is strong and vice versa.
Everyone who is both not generous and rich is either rich or not calm.
If fred is both humble and calm then paul is both not rich and wise and vice versa.
If someone is rich then john is both not brave and not generous.
Everyone who is either patient or not brave is either generous or not calm and vice versa.
If someone is both not kind and not quiet then susan is patient or happy and vice versa.
Everyone who is not brave is calm and vice versa.
Someone is both not tall and generous.
Someone is brave or quiet.
Someone is tall.
Someone is not kind or not wise.
Alice is not humble.
Someone is both funny and curious. | Alice is not generous. | contradiction | ((funny(lucy))=>(?[X]:(~curious(X))))&
(((~patient(mary)|~kind(mary)))=>((~old(paul)<~>~kind(paul))))&
(((tall(lucy)|strong(lucy)))=>((generous(mary)|kind(mary))))&
(![X]:((~funny(X)<~>tall(X))=>tall(X)))&
(![X]:((tall(X)|~rich(X))<=>(~strong(X)<~>happy(X))))&
(((generous(susan)|~strong(susan)))<=>(?[X]:((kind(X)|strong(X)))))&
(![X]:((~patient(X)&creative(X))<=>(~brave(X)<~>patient(X))))&
(![X]:((calm(X)|kind(X))<=>(~happy(X)|strong(X))))&
((?[X]:(calm(X)))<=>((patient(susan)<~>~generous(susan))))&
((curious(fred))<=>(strong(fred)))&
(![X]:((~generous(X)&rich(X))=>(rich(X)<~>~calm(X))))&
(((humble(fred)&calm(fred)))<=>((~rich(paul)&wise(paul))))&
((?[X]:(rich(X)))=>((~brave(john)&~generous(john))))&
(![X]:((patient(X)<~>~brave(X))<=>(generous(X)<~>~calm(X))))&
((?[X]:((~kind(X)&~quiet(X))))<=>((patient(susan)|happy(susan))))&
(![X]:(~brave(X)<=>calm(X)))&
(?[X]:((~tall(X)&generous(X))))&
(?[X]:((brave(X)|quiet(X))))&
(?[X]:(tall(X)))&
(?[X]:((~kind(X)|~wise(X))))&
(~humble(alice))&
(?[X]:((funny(X)&curious(X)))) | ~generous(alice) | [
"p6",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2060106649431889074143008
% SZS output start Proof for 2060106649431889074143008
7. ! [X0] : ((creative(X0) & ~patient(X0)) <=> (~brave(X0) <~> patient(X0))) [input p6]
9. ? [X0] : calm(X0) <=> (patient(susan) <~> ~generous(susan)) [input p8]
14. ! [X0] : ((patient(X0) <~> ~brave(X0)) <=> (generous(X0) <~> ~calm(X0))) [input p13]
16. ! [X0] : (~brave(X0) <=> calm(X0)) [input p15]
23. ~generous(alice) [input hypothesis]
43. ! [X0] : (((creative(X0) & ~patient(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) & (((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (~creative(X0) | patient(X0)))) [nnf transformation 7]
44. ! [X0] : (((creative(X0) & ~patient(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) & (((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | ~creative(X0) | patient(X0))) [flattening 43]
47. (? [X0] : calm(X0) | ((patient(susan) | generous(susan)) & (~generous(susan) | ~patient(susan)))) & (((generous(susan) | ~patient(susan)) & (~generous(susan) | patient(susan))) | ! [X0] : ~calm(X0)) [nnf transformation 9]
48. (? [X0] : calm(X0) | ((patient(susan) | generous(susan)) & (~generous(susan) | ~patient(susan)))) & (((generous(susan) | ~patient(susan)) & (~generous(susan) | patient(susan))) | ! [X1] : ~calm(X1)) [rectify 47]
49. ? [X0] : calm(X0) => calm(sK2) [choice axiom]
50. (calm(sK2) | ((patient(susan) | generous(susan)) & (~generous(susan) | ~patient(susan)))) & (((generous(susan) | ~patient(susan)) & (~generous(susan) | patient(susan))) | ! [X1] : ~calm(X1)) [skolemisation 48,49]
55. ! [X0] : ((((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) & (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))))) [nnf transformation 14]
61. ! [X0] : ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0))) [nnf transformation 16]
91. patient(X0) | ~brave(X0) | ~creative(X0) | patient(X0) [cnf transformation 44]
94. ~patient(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 44]
95. brave(X0) | patient(X0) | creative(X0) [cnf transformation 44]
101. ~generous(susan) | patient(susan) | ~calm(X1) [cnf transformation 50]
102. generous(susan) | ~patient(susan) | ~calm(X1) [cnf transformation 50]
116. ~calm(X0) | generous(X0) | patient(X0) | brave(X0) [cnf transformation 55]
120. ~brave(X0) | patient(X0) | generous(X0) | calm(X0) [cnf transformation 55]
121. brave(X0) | ~patient(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 55]
122. brave(X0) | ~patient(X0) | generous(X0) | calm(X0) [cnf transformation 55]
128. calm(X0) | brave(X0) [cnf transformation 61]
129. ~calm(X0) | ~brave(X0) [cnf transformation 61]
138. ~generous(alice) [cnf transformation 23]
140. patient(X0) | ~brave(X0) | ~creative(X0) [duplicate literal removal 91]
141. ~brave(X0) | ~patient(X0) [duplicate literal removal 94]
190. 11 <=> generous(susan) [avatar definition]
191. ~generous(susan) <- (~11) [avatar component clause 190]
192. generous(susan) <- (11) [avatar component clause 190]
212. ~brave(X0) | ~creative(X0) [subsumption resolution 140,141]
214. 16 <=> patient(susan) [avatar definition]
215. ~patient(susan) <- (~16) [avatar component clause 214]
216. patient(susan) <- (16) [avatar component clause 214]
224. 18 <=> ! [X1] : ~calm(X1) [avatar definition]
225. ~calm(X1) <- (18) [avatar component clause 224]
226. 18 | ~16 | 11 [avatar split clause 102,190,214,224]
227. 18 | 16 | ~11 [avatar split clause 101,190,214,224]
271. ~patient(X0) | generous(X0) | calm(X0) [subsumption resolution 122,141]
272. ~calm(X0) | ~patient(X0) | ~generous(X0) [subsumption resolution 121,141]
273. ~brave(X0) | generous(X0) | calm(X0) [subsumption resolution 120,271]
403. ~patient(X1) | ~generous(X1) | brave(X1) [resolution 272,128]
406. ~generous(X1) | ~patient(X1) [subsumption resolution 403,141]
408. generous(X0) | calm(X0) | patient(X0) | creative(X0) [resolution 273,95]
411. calm(X0) | generous(X0) | creative(X0) [subsumption resolution 408,271]
472. generous(X1) | patient(X1) | brave(X1) | brave(X1) [resolution 116,128]
476. brave(X1) | patient(X1) | generous(X1) [duplicate literal removal 472]
479. ~patient(susan) <- (11) [resolution 406,192]
481. $false <- (11, 16) [subsumption resolution 479,216]
482. ~11 | ~16 [avatar contradiction clause 481]
500. generous(X4) | creative(X4) | ~brave(X4) [resolution 411,129]
502. ~brave(X4) | generous(X4) [subsumption resolution 500,212]
504. patient(X1) | generous(X1) | generous(X1) | calm(X1) [resolution 476,273]
511. patient(X1) | generous(X1) | calm(X1) [duplicate literal removal 504]
512. calm(X1) | generous(X1) [subsumption resolution 511,271]
541. generous(X0) | patient(X0) | generous(X0) [resolution 502,476]
544. generous(X0) | patient(X0) [duplicate literal removal 541]
557. patient(susan) <- (~11) [resolution 544,191]
559. $false <- (~11, ~16) [subsumption resolution 557,215]
560. 11 | 16 [avatar contradiction clause 559]
569. generous(X0) <- (18) [resolution 225,512]
631. $false <- (18) [resolution 569,138]
635. ~18 [avatar contradiction clause 631]
636. $false [avatar sat refutation 226,227,482,560,635]
% SZS output end Proof for 2060106649431889074143008
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old and funny is either patient or wise and vice versa. Everyone who is not brave is not rich or strong. If alice is funny or kind then someone is not happy and vice versa. Everyone who is funny or not old is either quiet or curious. Everyone who is either not happy or not brave is wise or not generous and vice versa. If someone is not curious then someone is not brave or not calm and vice versa. Everyone who is both old and not funny is happy. Everyone who is humble is patient and vice versa. Everyone who is either calm or not funny is either not brave or not tall. If lucy is either rich or not tall then someone is either not rich or happy and vice versa. Everyone who is both not kind and strong is both not happy and not patient. If susan is not brave then someone is both not quiet and curious. Everyone who is not old is both not humble and brave and vice versa. Everyone who is happy is either not happy or quiet and vice versa. If john is wise or calm then someone is either quiet or wise. If mary is both brave and not wise then john is creative and vice versa. Alice is both humble and not strong. John is not creative or strong. John is not humble. Someone is either curious or not tall. Someone is either rich or not quiet. Someone is kind. Susan is both not generous and not humble. | Alice is not funny. | neutral | (![X]:((~old(X)&funny(X))<=>(patient(X)<~>wise(X))))&
(![X]:(~brave(X)=>(~rich(X)|strong(X))))&
(((funny(alice)|kind(alice)))<=>(?[X]:(~happy(X))))&
(![X]:((funny(X)|~old(X))=>(quiet(X)<~>curious(X))))&
(![X]:((~happy(X)<~>~brave(X))<=>(wise(X)|~generous(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~brave(X)|~calm(X)))))&
(![X]:((old(X)&~funny(X))=>happy(X)))&
(![X]:(humble(X)<=>patient(X)))&
(![X]:((calm(X)<~>~funny(X))=>(~brave(X)<~>~tall(X))))&
(((rich(lucy)<~>~tall(lucy)))<=>(?[X]:((~rich(X)<~>happy(X)))))&
(![X]:((~kind(X)&strong(X))=>(~happy(X)&~patient(X))))&
((~brave(susan))=>(?[X]:((~quiet(X)&curious(X)))))&
(![X]:(~old(X)<=>(~humble(X)&brave(X))))&
(![X]:(happy(X)<=>(~happy(X)<~>quiet(X))))&
(((wise(john)|calm(john)))=>(?[X]:((quiet(X)<~>wise(X)))))&
(((brave(mary)&~wise(mary)))<=>(creative(john)))&
((humble(alice)&~strong(alice)))&
((~creative(john)|strong(john)))&
(~humble(john))&
(?[X]:((curious(X)<~>~tall(X))))&
(?[X]:((rich(X)<~>~quiet(X))))&
(?[X]:(kind(X)))&
((~generous(susan)&~humble(susan))) | ~funny(alice) | [] | null | 0 |
Everyone who is both not humble and not curious is not patient or kind and vice versa.
If paul is either patient or not strong then someone is funny or not strong and vice versa.
If someone is either wise or not old then someone is either not generous or patient.
If lucy is either not wise or curious then someone is either strong or not happy and vice versa.
Everyone who is both not wise and tall is either strong or not patient and vice versa.
Everyone who is wise is creative and vice versa.
If fred is generous or rich then someone is not curious.
If fred is not old or curious then fred is not calm or rich and vice versa.
If someone is both not happy and wise then someone is not old and vice versa.
If someone is both patient and happy then susan is humble or funny.
Everyone who is both funny and happy is not humble.
If alice is not tall or not strong then someone is curious or happy and vice versa.
Everyone who is either not kind or not tall is happy or funny and vice versa.
If someone is generous or calm then paul is both happy and not curious and vice versa.
Everyone who is either not strong or old is not curious or not calm and vice versa.
Everyone who is either not old or not quiet is both not quiet and not strong.
Paul is quiet.
Paul is not creative.
Someone is either not calm or not creative.
Someone is not rich or quiet.
Fred is either not rich or not tall.
Someone is both not old and not wise.
John is not kind.
Mary is not rich or quiet. | Paul is old. | entailment | (![X]:((~humble(X)&~curious(X))<=>(~patient(X)|kind(X))))&
(((patient(paul)<~>~strong(paul)))<=>(?[X]:((funny(X)|~strong(X)))))&
((?[X]:((wise(X)<~>~old(X))))=>(?[X]:((~generous(X)<~>patient(X)))))&
(((~wise(lucy)<~>curious(lucy)))<=>(?[X]:((strong(X)<~>~happy(X)))))&
(![X]:((~wise(X)&tall(X))<=>(strong(X)<~>~patient(X))))&
(![X]:(wise(X)<=>creative(X)))&
(((generous(fred)|rich(fred)))=>(?[X]:(~curious(X))))&
(((~old(fred)|curious(fred)))<=>((~calm(fred)|rich(fred))))&
((?[X]:((~happy(X)&wise(X))))<=>(?[X]:(~old(X))))&
((?[X]:((patient(X)&happy(X))))=>((humble(susan)|funny(susan))))&
(![X]:((funny(X)&happy(X))=>~humble(X)))&
(((~tall(alice)|~strong(alice)))<=>(?[X]:((curious(X)|happy(X)))))&
(![X]:((~kind(X)<~>~tall(X))<=>(happy(X)|funny(X))))&
((?[X]:((generous(X)|calm(X))))<=>((happy(paul)&~curious(paul))))&
(![X]:((~strong(X)<~>old(X))<=>(~curious(X)|~calm(X))))&
(![X]:((~old(X)<~>~quiet(X))=>(~quiet(X)&~strong(X))))&
(quiet(paul))&
(~creative(paul))&
(?[X]:((~calm(X)<~>~creative(X))))&
(?[X]:((~rich(X)|quiet(X))))&
((~rich(fred)<~>~tall(fred)))&
(?[X]:((~old(X)&~wise(X))))&
(~kind(john))&
((~rich(mary)|quiet(mary))) | old(paul) | [
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8527432247225444986221726
% SZS output start Proof for 8527432247225444986221726
16. ! [X0] : ((~old(X0) <~> ~quiet(X0)) => (~strong(X0) & ~quiet(X0))) [input p15]
17. quiet(paul) [input p16]
25. ~old(paul) [input hypothesis]
34. ! [X0] : ((~strong(X0) & ~quiet(X0)) | (~old(X0) <=> ~quiet(X0))) [ennf transformation 16]
75. ! [X0] : ((~strong(X0) & ~quiet(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0)))) [nnf transformation 34]
147. ~quiet(X0) | ~quiet(X0) | old(X0) [cnf transformation 75]
151. quiet(paul) [cnf transformation 17]
162. ~old(paul) [cnf transformation 25]
163. ~quiet(X0) | old(X0) [duplicate literal removal 147]
401. old(paul) [resolution 163,151]
402. $false [subsumption resolution 401,162]
% SZS output end Proof for 8527432247225444986221726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not rich then lucy is both wise and generous. Everyone who is not humble is not quiet and vice versa. Everyone who is either not strong or wise is either not humble or not calm. Everyone who is quiet is not kind or humble and vice versa. Everyone who is quiet or not rich is old or not humble. Everyone who is not funny or kind is both quiet and not creative. Everyone who is not kind is wise and vice versa. Everyone who is either funny or calm is not brave or quiet. If someone is not happy then alice is either not rich or not quiet. Everyone who is both not humble and not generous is either not rich or not old and vice versa. If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa. If someone is generous or tall then alice is strong and vice versa. Everyone who is not happy is brave or humble. Everyone who is not happy or not funny is both creative and quiet. Everyone who is not patient is both not kind and happy and vice versa. Someone is brave or wise. Susan is both brave and not strong. Someone is kind or happy. Someone is both not kind and not creative. Alice is not tall or not old. Someone is not calm or funny. Mary is not rich or curious. | Alice is not tall. | entailment | ((~rich(susan))=>((wise(lucy)&generous(lucy))))&
(![X]:(~humble(X)<=>~quiet(X)))&
(![X]:((~strong(X)<~>wise(X))=>(~humble(X)<~>~calm(X))))&
(![X]:(quiet(X)<=>(~kind(X)|humble(X))))&
(![X]:((quiet(X)|~rich(X))=>(old(X)|~humble(X))))&
(![X]:((~funny(X)|kind(X))=>(quiet(X)&~creative(X))))&
(![X]:(~kind(X)<=>wise(X)))&
(![X]:((funny(X)<~>calm(X))=>(~brave(X)|quiet(X))))&
((?[X]:(~happy(X)))=>((~rich(alice)<~>~quiet(alice))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
(?[X]:((brave(X)|wise(X))))&
((brave(susan)&~strong(susan)))&
(?[X]:((kind(X)|happy(X))))&
(?[X]:((~kind(X)&~creative(X))))&
((~tall(alice)|~old(alice)))&
(?[X]:((~calm(X)|funny(X))))&
((~rich(mary)|curious(mary))) | ~tall(alice) | [
"p1",
"p3",
"p4",
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2943214902827119334333904
% SZS output start Proof for 2943214902827119334333904
2. ! [X0] : (~humble(X0) <=> ~quiet(X0)) [input p1]
4. ! [X0] : (quiet(X0) <=> (humble(X0) | ~kind(X0))) [input p3]
5. ! [X0] : ((~rich(X0) | quiet(X0)) => (~humble(X0) | old(X0))) [input p4]
6. ! [X0] : ((kind(X0) | ~funny(X0)) => (~creative(X0) & quiet(X0))) [input p5]
20. ~old(alice) | ~tall(alice) [input p19]
23. tall(alice) [input hypothesis]
32. ! [X0] : ((~humble(X0) | old(X0)) | (rich(X0) & ~quiet(X0))) [ennf transformation 5]
33. ! [X0] : (~humble(X0) | old(X0) | (rich(X0) & ~quiet(X0))) [flattening 32]
34. ! [X0] : ((~creative(X0) & quiet(X0)) | (~kind(X0) & funny(X0))) [ennf transformation 6]
38. ! [X0] : ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))) [nnf transformation 2]
40. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ~quiet(X0))) [nnf transformation 4]
41. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ~quiet(X0))) [flattening 40]
63. ~quiet(X0) | humble(X0) [cnf transformation 38]
70. kind(X0) | quiet(X0) [cnf transformation 41]
72. ~humble(X0) | old(X0) | ~quiet(X0) [cnf transformation 33]
75. quiet(X0) | ~kind(X0) [cnf transformation 34]
102. ~old(alice) | ~tall(alice) [cnf transformation 20]
104. tall(alice) [cnf transformation 23]
119. ~quiet(X0) | old(X0) [subsumption resolution 72,63]
120. quiet(X0) [subsumption resolution 75,70]
156. 11 <=> tall(alice) [avatar definition]
160. 12 <=> old(alice) [avatar definition]
162. ~old(alice) <- (~12) [avatar component clause 160]
163. ~11 | ~12 [avatar split clause 102,160,156]
164. 11 [avatar split clause 104,156]
171. old(X0) [resolution 119,120]
173. $false <- (~12) [resolution 171,162]
174. 12 [avatar contradiction clause 173]
175. $false [avatar sat refutation 163,164,174]
% SZS output end Proof for 2943214902827119334333904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not curious is funny and vice versa. Everyone who is generous is not humble. Everyone who is creative or not creative is not humble and vice versa. If someone is not happy then fred is not tall. If someone is not happy then lucy is either not calm or tall and vice versa. If someone is both not rich and not curious then someone is old or quiet and vice versa. If someone is both funny and rich then someone is kind and vice versa. If someone is either not tall or quiet then alice is not kind or rich. Everyone who is wise or not funny is either creative or not rich and vice versa. Everyone who is not patient or not happy is not funny. Everyone who is either calm or not tall is strong or humble. If mary is not wise or not funny then someone is either creative or not generous. Everyone who is calm is not patient or not quiet. Everyone who is either wise or funny is either happy or not rich and vice versa. Everyone who is not generous is not wise or not happy and vice versa. Everyone who is either not creative or not wise is not tall or not humble. Paul is calm. Paul is not quiet. Someone is either not funny or funny. Lucy is not humble or tall. Someone is either not brave or not wise. John is not rich. | Paul is not old. | entailment | (![X]:((~generous(X)&~curious(X))<=>funny(X)))&
(![X]:(generous(X)=>~humble(X)))&
(![X]:((creative(X)|~creative(X))<=>~humble(X)))&
((?[X]:(~happy(X)))=>(~tall(fred)))&
((?[X]:(~happy(X)))<=>((~calm(lucy)<~>tall(lucy))))&
((?[X]:((~rich(X)&~curious(X))))<=>(?[X]:((old(X)|quiet(X)))))&
((?[X]:((funny(X)&rich(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~tall(X)<~>quiet(X))))=>((~kind(alice)|rich(alice))))&
(![X]:((wise(X)|~funny(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((~patient(X)|~happy(X))=>~funny(X)))&
(![X]:((calm(X)<~>~tall(X))=>(strong(X)|humble(X))))&
(((~wise(mary)|~funny(mary)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(calm(X)=>(~patient(X)|~quiet(X))))&
(![X]:((wise(X)<~>funny(X))<=>(happy(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(~wise(X)|~happy(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(~tall(X)|~humble(X))))&
(calm(paul))&
(~quiet(paul))&
(?[X]:((~funny(X)<~>funny(X))))&
((~humble(lucy)|tall(lucy)))&
(?[X]:((~brave(X)<~>~wise(X))))&
(~rich(john)) | ~old(paul) | [
"p0",
"p5",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 846284132264275344330383
% SZS output start Proof for 846284132264275344330383
1. ! [X0] : ((~curious(X0) & ~generous(X0)) <=> funny(X0)) [input p0]
6. ? [X0] : (~curious(X0) & ~rich(X0)) <=> ? [X0] : (quiet(X0) | old(X0)) [input p5]
10. ! [X0] : ((~happy(X0) | ~patient(X0)) => ~funny(X0)) [input p9]
14. ! [X0] : ((wise(X0) <~> funny(X0)) <=> (happy(X0) <~> ~rich(X0))) [input p13]
15. ! [X0] : (~generous(X0) <=> (~happy(X0) | ~wise(X0))) [input p14]
23. old(paul) [input hypothesis]
24. ? [X0] : (~curious(X0) & ~rich(X0)) <=> ? [X1] : (quiet(X1) | old(X1)) [rectify 6]
34. ! [X0] : (~funny(X0) | (happy(X0) & patient(X0))) [ennf transformation 10]
40. ! [X0] : (((~curious(X0) & ~generous(X0)) | ~funny(X0)) & (funny(X0) | (curious(X0) | generous(X0)))) [nnf transformation 1]
41. ! [X0] : (((~curious(X0) & ~generous(X0)) | ~funny(X0)) & (funny(X0) | curious(X0) | generous(X0))) [flattening 40]
46. (? [X0] : (~curious(X0) & ~rich(X0)) | ! [X1] : (~quiet(X1) & ~old(X1))) & (? [X1] : (quiet(X1) | old(X1)) | ! [X0] : (curious(X0) | rich(X0))) [nnf transformation 24]
47. (? [X0] : (~curious(X0) & ~rich(X0)) | ! [X1] : (~quiet(X1) & ~old(X1))) & (? [X2] : (quiet(X2) | old(X2)) | ! [X3] : (curious(X3) | rich(X3))) [rectify 46]
48. ? [X0] : (~curious(X0) & ~rich(X0)) => (~curious(sK1) & ~rich(sK1)) [choice axiom]
49. ? [X2] : (quiet(X2) | old(X2)) => (quiet(sK2) | old(sK2)) [choice axiom]
50. ((~curious(sK1) & ~rich(sK1)) | ! [X1] : (~quiet(X1) & ~old(X1))) & ((quiet(sK2) | old(sK2)) | ! [X3] : (curious(X3) | rich(X3))) [skolemisation 47,49,48]
62. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) & (((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 14]
63. ! [X0] : ((~generous(X0) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | generous(X0))) [nnf transformation 15]
64. ! [X0] : ((~generous(X0) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | generous(X0))) [flattening 63]
72. funny(X0) | curious(X0) | generous(X0) [cnf transformation 41]
73. ~funny(X0) | ~generous(X0) [cnf transformation 41]
83. ~rich(sK1) | ~old(X1) [cnf transformation 50]
85. ~curious(sK1) | ~old(X1) [cnf transformation 50]
99. ~funny(X0) | happy(X0) [cnf transformation 34]
107. ~wise(X0) | ~happy(X0) | funny(X0) | rich(X0) [cnf transformation 62]
108. rich(X0) | ~happy(X0) | wise(X0) | ~funny(X0) [cnf transformation 62]
113. ~wise(X0) | ~happy(X0) | generous(X0) [cnf transformation 64]
114. ~generous(X0) | wise(X0) [cnf transformation 64]
115. ~generous(X0) | happy(X0) [cnf transformation 64]
126. old(paul) [cnf transformation 23]
155. 7 <=> curious(sK1) [avatar definition]
157. ~curious(sK1) <- (~7) [avatar component clause 155]
160. 8 <=> ! [X1] : ~old(X1) [avatar definition]
161. ~old(X1) <- (8) [avatar component clause 160]
162. 8 | ~7 [avatar split clause 85,155,160]
164. 9 <=> rich(sK1) [avatar definition]
166. ~rich(sK1) <- (~9) [avatar component clause 164]
168. 8 | ~9 [avatar split clause 83,164,160]
240. ~funny(X0) | wise(X0) | rich(X0) [subsumption resolution 108,99]
262. $false <- (8) [resolution 161,126]
263. ~8 [avatar contradiction clause 262]
264. curious(X0) | generous(X0) | happy(X0) [resolution 72,99]
268. happy(X0) | curious(X0) [subsumption resolution 264,115]
300. wise(X0) | rich(X0) | curious(X0) | generous(X0) [resolution 240,72]
301. wise(X0) | rich(X0) | curious(X0) [subsumption resolution 300,114]
311. rich(X0) | curious(X0) | ~happy(X0) | funny(X0) | rich(X0) [resolution 301,107]
314. rich(X3) | curious(X3) | ~happy(X3) | generous(X3) [resolution 301,113]
318. rich(X0) | curious(X0) | ~happy(X0) | funny(X0) [duplicate literal removal 311]
319. rich(X0) | curious(X0) | funny(X0) [subsumption resolution 318,268]
320. rich(X3) | curious(X3) | generous(X3) [subsumption resolution 314,268]
341. curious(sK1) | funny(sK1) <- (~9) [resolution 319,166]
355. funny(sK1) <- (~7, ~9) [subsumption resolution 341,157]
361. curious(sK1) | generous(sK1) <- (~9) [resolution 320,166]
372. generous(sK1) <- (~7, ~9) [subsumption resolution 361,157]
399. ~generous(sK1) <- (~7, ~9) [resolution 355,73]
412. $false <- (~7, ~9) [subsumption resolution 399,372]
413. 7 | 9 [avatar contradiction clause 412]
414. $false [avatar sat refutation 162,168,263,413]
% SZS output end Proof for 846284132264275344330383
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or quiet then paul is either not happy or rich and vice versa. If paul is either not curious or quiet then someone is either happy or not wise and vice versa. Everyone who is old or quiet is tall and vice versa. If fred is calm or not tall then someone is not happy. If someone is both happy and not tall then someone is either calm or not wise. Everyone who is creative is not old or patient and vice versa. Everyone who is both not tall and happy is not old and vice versa. If someone is kind then someone is either curious or not curious. If someone is calm or not creative then mary is creative or not funny. Everyone who is not kind is not old or patient and vice versa. If john is either not humble or funny then mary is curious or calm. Everyone who is either not brave or not wise is both curious and wise and vice versa. Everyone who is both not patient and quiet is not brave. If someone is both patient and not creative then someone is generous. If john is brave then john is both rich and wise and vice versa. Everyone who is both kind and calm is calm and vice versa. John is tall or quiet. Alice is quiet or old. Someone is not generous. John is both not patient and not funny. Someone is not quiet. Alice is either brave or quiet. Fred is both funny and not quiet. Someone is either not generous or humble. | Mary is humble. | neutral | ((?[X]:((~curious(X)|quiet(X))))<=>((~happy(paul)<~>rich(paul))))&
(((~curious(paul)<~>quiet(paul)))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((old(X)|quiet(X))<=>tall(X)))&
(((calm(fred)|~tall(fred)))=>(?[X]:(~happy(X))))&
((?[X]:((happy(X)&~tall(X))))=>(?[X]:((calm(X)<~>~wise(X)))))&
(![X]:(creative(X)<=>(~old(X)|patient(X))))&
(![X]:((~tall(X)&happy(X))<=>~old(X)))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)<~>~curious(X)))))&
((?[X]:((calm(X)|~creative(X))))=>((creative(mary)|~funny(mary))))&
(![X]:(~kind(X)<=>(~old(X)|patient(X))))&
(((~humble(john)<~>funny(john)))=>((curious(mary)|calm(mary))))&
(![X]:((~brave(X)<~>~wise(X))<=>(curious(X)&wise(X))))&
(![X]:((~patient(X)&quiet(X))=>~brave(X)))&
((?[X]:((patient(X)&~creative(X))))=>(?[X]:(generous(X))))&
((brave(john))<=>((rich(john)&wise(john))))&
(![X]:((kind(X)&calm(X))<=>calm(X)))&
((tall(john)|quiet(john)))&
((quiet(alice)|old(alice)))&
(?[X]:(~generous(X)))&
((~patient(john)&~funny(john)))&
(?[X]:(~quiet(X)))&
((brave(alice)<~>quiet(alice)))&
((funny(fred)&~quiet(fred)))&
(?[X]:((~generous(X)<~>humble(X)))) | humble(mary) | [] | null | 0 |
Everyone who is either patient or not quiet is either humble or not kind and vice versa.
Everyone who is creative is not patient or funny.
If alice is either not humble or not old then susan is either wise or patient.
Everyone who is not humble is not quiet.
If alice is rich then someone is wise and vice versa.
If someone is both not patient and not wise then paul is both happy and funny.
Everyone who is not kind or funny is both not curious and not tall.
Everyone who is both not brave and curious is either not wise or patient and vice versa.
If mary is quiet or not kind then paul is brave and vice versa.
Everyone who is creative or quiet is both not wise and generous.
If mary is either generous or not rich then someone is patient and vice versa.
Everyone who is both patient and not generous is both not tall and not curious.
Everyone who is not quiet or not old is not patient or tall.
Everyone who is not strong is both strong and tall and vice versa.
Everyone who is either not rich or not quiet is not brave or humble and vice versa.
Everyone who is either strong or generous is rich or not happy and vice versa.
Lucy is either not generous or not quiet.
Someone is strong or quiet.
John is either creative or not kind.
Alice is brave or not generous.
Someone is either not curious or generous.
Someone is old or not generous. | John is not funny. | neutral | (![X]:((patient(X)<~>~quiet(X))<=>(humble(X)<~>~kind(X))))&
(![X]:(creative(X)=>(~patient(X)|funny(X))))&
(((~humble(alice)<~>~old(alice)))=>((wise(susan)<~>patient(susan))))&
(![X]:(~humble(X)=>~quiet(X)))&
((rich(alice))<=>(?[X]:(wise(X))))&
((?[X]:((~patient(X)&~wise(X))))=>((happy(paul)&funny(paul))))&
(![X]:((~kind(X)|funny(X))=>(~curious(X)&~tall(X))))&
(![X]:((~brave(X)&curious(X))<=>(~wise(X)<~>patient(X))))&
(((quiet(mary)|~kind(mary)))<=>(brave(paul)))&
(![X]:((creative(X)|quiet(X))=>(~wise(X)&generous(X))))&
(((generous(mary)<~>~rich(mary)))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~generous(X))=>(~tall(X)&~curious(X))))&
(![X]:((~quiet(X)|~old(X))=>(~patient(X)|tall(X))))&
(![X]:(~strong(X)<=>(strong(X)&tall(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(~brave(X)|humble(X))))&
(![X]:((strong(X)<~>generous(X))<=>(rich(X)|~happy(X))))&
((~generous(lucy)<~>~quiet(lucy)))&
(?[X]:((strong(X)|quiet(X))))&
((creative(john)<~>~kind(john)))&
((brave(alice)|~generous(alice)))&
(?[X]:((~curious(X)<~>generous(X))))&
(?[X]:((old(X)|~generous(X)))) | ~funny(john) | [] | null | 0 |
If someone is either not tall or not wise then someone is both wise and brave and vice versa. Everyone who is either not curious or brave is not happy or not rich and vice versa. If mary is not funny or creative then someone is wise or creative. Everyone who is not generous is not old and vice versa. Everyone who is both calm and not funny is quiet. If someone is calm then someone is not humble and vice versa. If someone is both not happy and old then mary is either not rich or strong and vice versa. Everyone who is not curious is strong. Everyone who is generous or not creative is not patient or strong. Everyone who is strong or funny is strong or wise and vice versa. Everyone who is either old or strong is not calm and vice versa. Everyone who is not funny is either not calm or not humble and vice versa. Everyone who is not funny is either not old or not generous and vice versa. If someone is both not curious and generous then lucy is not generous or old and vice versa. Everyone who is either not quiet or not rich is funny or not funny. Everyone who is wise is either quiet or humble and vice versa. Fred is not quiet or not humble. Someone is quiet or calm. Paul is not wise or funny. Someone is both not calm and kind. Fred is either humble or kind. Someone is either quiet or not curious. Someone is humble or wise. | Paul is old. | neutral | ((?[X]:((~tall(X)<~>~wise(X))))<=>(?[X]:((wise(X)&brave(X)))))&
(![X]:((~curious(X)<~>brave(X))<=>(~happy(X)|~rich(X))))&
(((~funny(mary)|creative(mary)))=>(?[X]:((wise(X)|creative(X)))))&
(![X]:(~generous(X)<=>~old(X)))&
(![X]:((calm(X)&~funny(X))=>quiet(X)))&
((?[X]:(calm(X)))<=>(?[X]:(~humble(X))))&
((?[X]:((~happy(X)&old(X))))<=>((~rich(mary)<~>strong(mary))))&
(![X]:(~curious(X)=>strong(X)))&
(![X]:((generous(X)|~creative(X))=>(~patient(X)|strong(X))))&
(![X]:((strong(X)|funny(X))<=>(strong(X)|wise(X))))&
(![X]:((old(X)<~>strong(X))<=>~calm(X)))&
(![X]:(~funny(X)<=>(~calm(X)<~>~humble(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>~generous(X))))&
((?[X]:((~curious(X)&generous(X))))<=>((~generous(lucy)|old(lucy))))&
(![X]:((~quiet(X)<~>~rich(X))=>(funny(X)|~funny(X))))&
(![X]:(wise(X)<=>(quiet(X)<~>humble(X))))&
((~quiet(fred)|~humble(fred)))&
(?[X]:((quiet(X)|calm(X))))&
((~wise(paul)|funny(paul)))&
(?[X]:((~calm(X)&kind(X))))&
((humble(fred)<~>kind(fred)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((humble(X)|wise(X)))) | old(paul) | [] | null | 0 |
Everyone who is not brave is both not patient and not kind and vice versa. If someone is not humble or wise then someone is both not patient and not brave. Everyone who is not humble or not kind is both generous and rich and vice versa. If paul is both not old and not kind then someone is either not creative or not humble and vice versa. If someone is either old or kind then someone is quiet. Everyone who is both patient and creative is not curious. If someone is either calm or quiet then someone is either kind or tall. Everyone who is strong is not rich and vice versa. Everyone who is either not rich or creative is both curious and not calm. If susan is both not curious and not rich then someone is wise or not humble and vice versa. Everyone who is both wise and curious is either not quiet or not wise and vice versa. Everyone who is both not quiet and tall is both kind and brave. If someone is either not quiet or funny then mary is quiet or not tall. Everyone who is both not tall and strong is tall or not humble. Everyone who is strong is not patient and vice versa. If someone is not curious then someone is old or not creative and vice versa. Lucy is both not happy and not creative. Alice is both not quiet and generous. Fred is not humble or not tall. Lucy is both not happy and generous. Someone is both not creative and not strong. | Mary is not brave. | contradiction | (![X]:(~brave(X)<=>(~patient(X)&~kind(X))))&
((?[X]:((~humble(X)|wise(X))))=>(?[X]:((~patient(X)&~brave(X)))))&
(![X]:((~humble(X)|~kind(X))<=>(generous(X)&rich(X))))&
(((~old(paul)&~kind(paul)))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
((?[X]:((old(X)<~>kind(X))))=>(?[X]:(quiet(X))))&
(![X]:((patient(X)&creative(X))=>~curious(X)))&
((?[X]:((calm(X)<~>quiet(X))))=>(?[X]:((kind(X)<~>tall(X)))))&
(![X]:(strong(X)<=>~rich(X)))&
(![X]:((~rich(X)<~>creative(X))=>(curious(X)&~calm(X))))&
(((~curious(susan)&~rich(susan)))<=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:((wise(X)&curious(X))<=>(~quiet(X)<~>~wise(X))))&
(![X]:((~quiet(X)&tall(X))=>(kind(X)&brave(X))))&
((?[X]:((~quiet(X)<~>funny(X))))=>((quiet(mary)|~tall(mary))))&
(![X]:((~tall(X)&strong(X))=>(tall(X)|~humble(X))))&
(![X]:(strong(X)<=>~patient(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((old(X)|~creative(X)))))&
((~happy(lucy)&~creative(lucy)))&
((~quiet(alice)&generous(alice)))&
((~humble(fred)|~tall(fred)))&
((~happy(lucy)&generous(lucy)))&
(?[X]:((~creative(X)&~strong(X)))) | ~brave(mary) | [
"p0",
"p2",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8365280963739954104913921
% SZS output start Proof for 8365280963739954104913921
1. ! [X0] : (~brave(X0) <=> (~kind(X0) & ~patient(X0))) [input p0]
3. ! [X0] : ((~kind(X0) | ~humble(X0)) <=> (rich(X0) & generous(X0))) [input p2]
8. ! [X0] : (strong(X0) <=> ~rich(X0)) [input p7]
15. ! [X0] : (strong(X0) <=> ~patient(X0)) [input p14]
22. ~brave(mary) [input hypothesis]
41. ! [X0] : ((~brave(X0) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | brave(X0))) [nnf transformation 1]
42. ! [X0] : ((~brave(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | brave(X0))) [flattening 41]
46. ! [X0] : (((~kind(X0) | ~humble(X0)) | (~rich(X0) | ~generous(X0))) & ((rich(X0) & generous(X0)) | (kind(X0) & humble(X0)))) [nnf transformation 3]
47. ! [X0] : ((~kind(X0) | ~humble(X0) | ~rich(X0) | ~generous(X0)) & ((rich(X0) & generous(X0)) | (kind(X0) & humble(X0)))) [flattening 46]
61. ! [X0] : ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0))) [nnf transformation 8]
71. ! [X0] : ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0))) [nnf transformation 15]
79. ~patient(X0) | brave(X0) [cnf transformation 42]
80. ~kind(X0) | brave(X0) [cnf transformation 42]
89. rich(X0) | kind(X0) [cnf transformation 47]
104. ~strong(X0) | ~rich(X0) [cnf transformation 61]
127. strong(X0) | patient(X0) [cnf transformation 71]
138. ~brave(mary) [cnf transformation 22]
299. ~rich(X1) | patient(X1) [resolution 127,104]
309. kind(X0) | patient(X0) [resolution 299,89]
312. patient(X0) | brave(X0) [resolution 309,80]
313. brave(X0) [subsumption resolution 312,79]
340. $false [resolution 313,138]
% SZS output end Proof for 8365280963739954104913921
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and calm is not calm and vice versa. If someone is rich then mary is either rich or creative. Everyone who is either wise or not strong is humble or strong and vice versa. If lucy is humble or curious then someone is either not rich or old. Everyone who is both wise and tall is not wise or generous and vice versa. If someone is not old or not patient then someone is either not quiet or not rich and vice versa. Everyone who is both old and not old is brave or rich and vice versa. Everyone who is funny is not generous or rich. Everyone who is either not curious or not generous is either happy or strong. If someone is either generous or not funny then someone is not tall and vice versa. If alice is both not kind and not funny then someone is either not quiet or not humble. If lucy is not generous then paul is either not funny or not rich and vice versa. Everyone who is both not old and not curious is not rich or generous and vice versa. Everyone who is both not old and not curious is not kind or not quiet. If fred is not brave or humble then alice is not wise or humble. Everyone who is not rich or not quiet is not patient. Someone is tall or quiet. Someone is either curious or tall. Someone is either not quiet or not humble. Mary is not brave. Fred is generous or not brave. | Mary is not tall. | neutral | (![X]:((creative(X)&calm(X))<=>~calm(X)))&
((?[X]:(rich(X)))=>((rich(mary)<~>creative(mary))))&
(![X]:((wise(X)<~>~strong(X))<=>(humble(X)|strong(X))))&
(((humble(lucy)|curious(lucy)))=>(?[X]:((~rich(X)<~>old(X)))))&
(![X]:((wise(X)&tall(X))<=>(~wise(X)|generous(X))))&
((?[X]:((~old(X)|~patient(X))))<=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(![X]:((old(X)&~old(X))<=>(brave(X)|rich(X))))&
(![X]:(funny(X)=>(~generous(X)|rich(X))))&
(![X]:((~curious(X)<~>~generous(X))=>(happy(X)<~>strong(X))))&
((?[X]:((generous(X)<~>~funny(X))))<=>(?[X]:(~tall(X))))&
(((~kind(alice)&~funny(alice)))=>(?[X]:((~quiet(X)<~>~humble(X)))))&
((~generous(lucy))<=>((~funny(paul)<~>~rich(paul))))&
(![X]:((~old(X)&~curious(X))<=>(~rich(X)|generous(X))))&
(![X]:((~old(X)&~curious(X))=>(~kind(X)|~quiet(X))))&
(((~brave(fred)|humble(fred)))=>((~wise(alice)|humble(alice))))&
(![X]:((~rich(X)|~quiet(X))=>~patient(X)))&
(?[X]:((tall(X)|quiet(X))))&
(?[X]:((curious(X)<~>tall(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(~brave(mary))&
((generous(fred)|~brave(fred))) | ~tall(mary) | [] | null | 0 |
Everyone who is creative or not patient is not patient and vice versa.
If paul is not generous then fred is either kind or not rich.
Everyone who is not curious or rich is either funny or generous and vice versa.
Everyone who is either brave or not strong is not quiet and vice versa.
If lucy is both calm and not humble then mary is brave and vice versa.
If lucy is both patient and not quiet then someone is humble.
If lucy is both not old and not strong then someone is tall and vice versa.
Everyone who is not humble is both tall and calm.
Everyone who is either quiet or funny is happy or brave and vice versa.
Everyone who is both not tall and not humble is both not generous and not old and vice versa.
Everyone who is either creative or brave is both generous and not humble and vice versa.
If someone is both not happy and patient then someone is both not funny and quiet.
If mary is either strong or not patient then paul is both funny and creative.
Everyone who is humble or funny is either tall or not strong.
Everyone who is strong or not kind is both happy and brave and vice versa.
If someone is either humble or tall then lucy is brave.
Alice is either not strong or generous.
Susan is both not curious and quiet.
Someone is curious or calm.
John is both not funny and not tall.
Fred is generous or wise.
Fred is not funny.
Someone is both not happy and not humble.
Someone is either not wise or humble. | John is humble. | entailment | (![X]:((creative(X)|~patient(X))<=>~patient(X)))&
((~generous(paul))=>((kind(fred)<~>~rich(fred))))&
(![X]:((~curious(X)|rich(X))<=>(funny(X)<~>generous(X))))&
(![X]:((brave(X)<~>~strong(X))<=>~quiet(X)))&
(((calm(lucy)&~humble(lucy)))<=>(brave(mary)))&
(((patient(lucy)&~quiet(lucy)))=>(?[X]:(humble(X))))&
(((~old(lucy)&~strong(lucy)))<=>(?[X]:(tall(X))))&
(![X]:(~humble(X)=>(tall(X)&calm(X))))&
(![X]:((quiet(X)<~>funny(X))<=>(happy(X)|brave(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~generous(X)&~old(X))))&
(![X]:((creative(X)<~>brave(X))<=>(generous(X)&~humble(X))))&
((?[X]:((~happy(X)&patient(X))))=>(?[X]:((~funny(X)&quiet(X)))))&
(((strong(mary)<~>~patient(mary)))=>((funny(paul)&creative(paul))))&
(![X]:((humble(X)|funny(X))=>(tall(X)<~>~strong(X))))&
(![X]:((strong(X)|~kind(X))<=>(happy(X)&brave(X))))&
((?[X]:((humble(X)<~>tall(X))))=>(brave(lucy)))&
((~strong(alice)<~>generous(alice)))&
((~curious(susan)&quiet(susan)))&
(?[X]:((curious(X)|calm(X))))&
((~funny(john)&~tall(john)))&
((generous(fred)|wise(fred)))&
(~funny(fred))&
(?[X]:((~happy(X)&~humble(X))))&
(?[X]:((~wise(X)<~>humble(X)))) | humble(john) | [
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7913711134478547045944668
% SZS output start Proof for 7913711134478547045944668
8. ! [X0] : (~humble(X0) => (calm(X0) & tall(X0))) [input p7]
20. ~tall(john) & ~funny(john) [input p19]
25. ~humble(john) [input hypothesis]
30. ! [X0] : ((calm(X0) & tall(X0)) | humble(X0)) [ennf transformation 8]
94. tall(X0) | humble(X0) [cnf transformation 30]
135. ~tall(john) [cnf transformation 20]
142. ~humble(john) [cnf transformation 25]
290. humble(john) [resolution 94,135]
292. $false [subsumption resolution 290,142]
% SZS output end Proof for 7913711134478547045944668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both not tall and not creative and vice versa.
If someone is calm or not creative then mary is patient or strong.
If paul is not tall or patient then someone is either not funny or humble.
Everyone who is not wise is either not brave or not humble and vice versa.
Everyone who is humble is either not creative or not wise.
Everyone who is either not generous or kind is both not old and calm.
If someone is creative or not rich then someone is not wise.
Everyone who is not kind is either strong or not brave.
Everyone who is either quiet or not quiet is either generous or tall.
Everyone who is funny is rich or happy.
If someone is both quiet and not kind then someone is not tall or not creative and vice versa.
Everyone who is not strong or kind is either old or not wise and vice versa.
If alice is wise or not creative then mary is either not wise or not curious.
Everyone who is both not curious and not old is old or not calm.
If someone is not patient or not quiet then alice is rich.
Everyone who is strong or patient is both kind and not tall.
Someone is either not tall or brave.
Mary is both not curious and rich.
Susan is not wise.
Paul is calm or not patient.
Someone is both kind and tall. | Paul is not calm. | entailment | (![X]:(~humble(X)<=>(~tall(X)&~creative(X))))&
((?[X]:((calm(X)|~creative(X))))=>((patient(mary)|strong(mary))))&
(((~tall(paul)|patient(paul)))=>(?[X]:((~funny(X)<~>humble(X)))))&
(![X]:(~wise(X)<=>(~brave(X)<~>~humble(X))))&
(![X]:(humble(X)=>(~creative(X)<~>~wise(X))))&
(![X]:((~generous(X)<~>kind(X))=>(~old(X)&calm(X))))&
((?[X]:((creative(X)|~rich(X))))=>(?[X]:(~wise(X))))&
(![X]:(~kind(X)=>(strong(X)<~>~brave(X))))&
(![X]:((quiet(X)<~>~quiet(X))=>(generous(X)<~>tall(X))))&
(![X]:(funny(X)=>(rich(X)|happy(X))))&
((?[X]:((quiet(X)&~kind(X))))<=>(?[X]:((~tall(X)|~creative(X)))))&
(![X]:((~strong(X)|kind(X))<=>(old(X)<~>~wise(X))))&
(((wise(alice)|~creative(alice)))=>((~wise(mary)<~>~curious(mary))))&
(![X]:((~curious(X)&~old(X))=>(old(X)|~calm(X))))&
((?[X]:((~patient(X)|~quiet(X))))=>(rich(alice)))&
(![X]:((strong(X)|patient(X))=>(kind(X)&~tall(X))))&
(?[X]:((~tall(X)<~>brave(X))))&
((~curious(mary)&rich(mary)))&
(~wise(susan))&
((calm(paul)|~patient(paul)))&
(?[X]:((kind(X)&tall(X)))) | ~calm(paul) | [
"p1",
"p5",
"p8",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5626169316901117702725497
% SZS output start Proof for 5626169316901117702725497
2. ? [X0] : (~creative(X0) | calm(X0)) => (strong(mary) | patient(mary)) [input p1]
6. ! [X0] : ((~generous(X0) <~> kind(X0)) => (calm(X0) & ~old(X0))) [input p5]
9. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) => (generous(X0) <~> tall(X0))) [input p8]
14. ! [X0] : ((~old(X0) & ~curious(X0)) => (~calm(X0) | old(X0))) [input p13]
16. ! [X0] : ((patient(X0) | strong(X0)) => (~tall(X0) & kind(X0))) [input p15]
18. rich(mary) & ~curious(mary) [input p17]
22. calm(paul) [input hypothesis]
26. ~curious(mary) [pure predicate removal 18]
29. (strong(mary) | patient(mary)) | ! [X0] : (creative(X0) & ~calm(X0)) [ennf transformation 2]
30. strong(mary) | patient(mary) | ! [X0] : (creative(X0) & ~calm(X0)) [flattening 29]
33. ! [X0] : ((calm(X0) & ~old(X0)) | (~generous(X0) <=> kind(X0))) [ennf transformation 6]
36. ! [X0] : ((generous(X0) <~> tall(X0)) | (quiet(X0) <=> ~quiet(X0))) [ennf transformation 9]
38. ! [X0] : ((~calm(X0) | old(X0)) | (old(X0) | curious(X0))) [ennf transformation 14]
39. ! [X0] : (~calm(X0) | old(X0) | old(X0) | curious(X0)) [flattening 38]
40. ! [X0] : ((~tall(X0) & kind(X0)) | (~patient(X0) & ~strong(X0))) [ennf transformation 16]
48. ! [X0] : ((calm(X0) & ~old(X0)) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) [nnf transformation 33]
53. ! [X0] : (((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) [nnf transformation 36]
70. strong(mary) | patient(mary) | ~calm(X0) [cnf transformation 30]
83. ~old(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 48]
85. ~kind(X0) | ~generous(X0) | calm(X0) [cnf transformation 48]
89. tall(X0) | generous(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 53]
90. tall(X0) | generous(X0) | quiet(X0) | quiet(X0) [cnf transformation 53]
108. ~calm(X0) | old(X0) | old(X0) | curious(X0) [cnf transformation 39]
109. ~strong(X0) | kind(X0) [cnf transformation 40]
110. ~patient(X0) | kind(X0) [cnf transformation 40]
111. ~strong(X0) | ~tall(X0) [cnf transformation 40]
112. ~patient(X0) | ~tall(X0) [cnf transformation 40]
115. ~curious(mary) [cnf transformation 26]
120. calm(paul) [cnf transformation 22]
121. ~calm(X0) | old(X0) | curious(X0) [duplicate literal removal 108]
122. tall(X0) | generous(X0) | ~quiet(X0) [duplicate literal removal 89]
123. quiet(X0) | generous(X0) | tall(X0) [duplicate literal removal 90]
130. 2 <=> patient(mary) [avatar definition]
132. patient(mary) <- (2) [avatar component clause 130]
134. 3 <=> strong(mary) [avatar definition]
136. strong(mary) <- (3) [avatar component clause 134]
139. 4 <=> ! [X0] : ~calm(X0) [avatar definition]
140. ~calm(X0) <- (4) [avatar component clause 139]
141. 4 | 2 | 3 [avatar split clause 70,134,130,139]
172. generous(X0) | tall(X0) [subsumption resolution 122,123]
209. 19 <=> curious(mary) [avatar definition]
210. ~curious(mary) <- (~19) [avatar component clause 209]
230. ~19 [avatar split clause 115,209]
232. 23 <=> calm(paul) [avatar definition]
234. calm(paul) <- (23) [avatar component clause 232]
236. 23 [avatar split clause 120,232]
304. $false <- (4, 23) [resolution 140,234]
305. ~4 | ~23 [avatar contradiction clause 304]
310. ~tall(mary) <- (2) [resolution 132,112]
311. kind(mary) <- (2) [resolution 132,110]
359. ~generous(mary) | calm(mary) <- (2) [resolution 311,85]
361. 34 <=> calm(mary) [avatar definition]
362. ~calm(mary) <- (~34) [avatar component clause 361]
363. calm(mary) <- (34) [avatar component clause 361]
365. 35 <=> generous(mary) [avatar definition]
366. generous(mary) <- (35) [avatar component clause 365]
367. ~generous(mary) <- (~35) [avatar component clause 365]
368. 34 | ~35 | ~2 [avatar split clause 359,130,365,361]
373. 36 <=> old(mary) [avatar definition]
375. old(mary) <- (36) [avatar component clause 373]
432. tall(mary) <- (~35) [resolution 367,172]
433. $false <- (2, ~35) [subsumption resolution 432,310]
434. ~2 | 35 [avatar contradiction clause 433]
435. old(mary) | curious(mary) <- (34) [resolution 363,121]
436. old(mary) <- (~19, 34) [subsumption resolution 435,210]
437. 36 | 19 | ~34 [avatar split clause 436,361,209,373]
443. ~generous(mary) | ~kind(mary) <- (36) [resolution 375,83]
450. ~kind(mary) <- (35, 36) [subsumption resolution 443,366]
451. $false <- (2, 35, 36) [subsumption resolution 450,311]
452. ~2 | ~35 | ~36 [avatar contradiction clause 451]
455. ~tall(mary) <- (3) [resolution 136,111]
456. kind(mary) <- (3) [resolution 136,109]
458. $false <- (3, 35, 36) [subsumption resolution 456,450]
459. ~3 | ~35 | ~36 [avatar contradiction clause 458]
461. ~generous(mary) | calm(mary) <- (3) [resolution 456,85]
465. ~generous(mary) <- (3, ~34) [subsumption resolution 461,362]
466. ~35 | ~3 | 34 [avatar split clause 465,361,134,365]
467. tall(mary) <- (~35) [resolution 367,172]
468. $false <- (3, ~35) [subsumption resolution 467,455]
469. ~3 | 35 [avatar contradiction clause 468]
470. $false [avatar sat refutation 141,230,236,305,368,434,437,452,459,466,469]
% SZS output end Proof for 5626169316901117702725497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and creative is not humble. Everyone who is both quiet and humble is either rich or tall. Everyone who is either not patient or brave is both not calm and patient. If fred is not happy or not curious then someone is both not kind and not calm and vice versa. If lucy is either not strong or strong then someone is both humble and quiet. If lucy is either not humble or creative then someone is both happy and curious. If someone is both not funny and not tall then paul is not patient. If someone is either not generous or not brave then susan is tall and vice versa. If someone is not old then someone is not curious or not patient and vice versa. Everyone who is both wise and patient is not brave or not humble and vice versa. If alice is both tall and curious then someone is either happy or not tall and vice versa. Everyone who is not wise or not humble is either rich or quiet and vice versa. Everyone who is both generous and not brave is strong. If susan is either not generous or not calm then susan is not creative or kind. If someone is not kind then paul is both funny and calm. Everyone who is both brave and not rich is either humble or not brave and vice versa. Someone is happy or not strong. Someone is either not brave or not funny. Someone is both not humble and not strong. Mary is not patient or not generous. Alice is brave. Lucy is not creative. Fred is both not curious and generous. | Mary is patient. | neutral | (![X]:((kind(X)&creative(X))=>~humble(X)))&
(![X]:((quiet(X)&humble(X))=>(rich(X)<~>tall(X))))&
(![X]:((~patient(X)<~>brave(X))=>(~calm(X)&patient(X))))&
(((~happy(fred)|~curious(fred)))<=>(?[X]:((~kind(X)&~calm(X)))))&
(((~strong(lucy)<~>strong(lucy)))=>(?[X]:((humble(X)&quiet(X)))))&
(((~humble(lucy)<~>creative(lucy)))=>(?[X]:((happy(X)&curious(X)))))&
((?[X]:((~funny(X)&~tall(X))))=>(~patient(paul)))&
((?[X]:((~generous(X)<~>~brave(X))))<=>(tall(susan)))&
((?[X]:(~old(X)))<=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:((wise(X)&patient(X))<=>(~brave(X)|~humble(X))))&
(((tall(alice)&curious(alice)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
(![X]:((~wise(X)|~humble(X))<=>(rich(X)<~>quiet(X))))&
(![X]:((generous(X)&~brave(X))=>strong(X)))&
(((~generous(susan)<~>~calm(susan)))=>((~creative(susan)|kind(susan))))&
((?[X]:(~kind(X)))=>((funny(paul)&calm(paul))))&
(![X]:((brave(X)&~rich(X))<=>(humble(X)<~>~brave(X))))&
(?[X]:((happy(X)|~strong(X))))&
(?[X]:((~brave(X)<~>~funny(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~patient(mary)|~generous(mary)))&
(brave(alice))&
(~creative(lucy))&
((~curious(fred)&generous(fred))) | patient(mary) | [] | null | 0 |
If someone is both not brave and not kind then lucy is both not generous and rich.
If someone is both tall and not patient then someone is either not funny or not kind.
If someone is quiet then someone is not old or not generous.
Everyone who is either not wise or curious is both not rich and not brave and vice versa.
If paul is not rich or funny then someone is either quiet or not kind.
Everyone who is both quiet and not calm is not generous or not old and vice versa.
If someone is curious then someone is both old and not funny and vice versa.
If alice is either funny or not kind then alice is not kind and vice versa.
If john is not kind or creative then susan is either quiet or not funny and vice versa.
Everyone who is either not strong or curious is not patient and vice versa.
Everyone who is either kind or patient is either quiet or brave and vice versa.
Everyone who is wise or happy is both not patient and humble.
If lucy is not tall then fred is either brave or not wise.
If john is either brave or wise then someone is strong or not creative.
If someone is not patient or strong then someone is both curious and old and vice versa.
Everyone who is rich is kind and vice versa.
Lucy is humble.
Someone is both curious and not wise.
Someone is quiet.
Someone is both humble and curious.
Fred is tall.
Someone is either not calm or not brave.
Mary is not curious or brave.
Mary is not old or quiet. | John is wise. | neutral | ((?[X]:((~brave(X)&~kind(X))))=>((~generous(lucy)&rich(lucy))))&
((?[X]:((tall(X)&~patient(X))))=>(?[X]:((~funny(X)<~>~kind(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((~old(X)|~generous(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~rich(X)&~brave(X))))&
(((~rich(paul)|funny(paul)))=>(?[X]:((quiet(X)<~>~kind(X)))))&
(![X]:((quiet(X)&~calm(X))<=>(~generous(X)|~old(X))))&
((?[X]:(curious(X)))<=>(?[X]:((old(X)&~funny(X)))))&
(((funny(alice)<~>~kind(alice)))<=>(~kind(alice)))&
(((~kind(john)|creative(john)))<=>((quiet(susan)<~>~funny(susan))))&
(![X]:((~strong(X)<~>curious(X))<=>~patient(X)))&
(![X]:((kind(X)<~>patient(X))<=>(quiet(X)<~>brave(X))))&
(![X]:((wise(X)|happy(X))=>(~patient(X)&humble(X))))&
((~tall(lucy))=>((brave(fred)<~>~wise(fred))))&
(((brave(john)<~>wise(john)))=>(?[X]:((strong(X)|~creative(X)))))&
((?[X]:((~patient(X)|strong(X))))<=>(?[X]:((curious(X)&old(X)))))&
(![X]:(rich(X)<=>kind(X)))&
(humble(lucy))&
(?[X]:((curious(X)&~wise(X))))&
(?[X]:(quiet(X)))&
(?[X]:((humble(X)&curious(X))))&
(tall(fred))&
(?[X]:((~calm(X)<~>~brave(X))))&
((~curious(mary)|brave(mary)))&
((~old(mary)|quiet(mary))) | wise(john) | [] | null | 0 |
Everyone who is brave or not old is both not funny and wise.
If someone is brave then susan is quiet.
Everyone who is either curious or strong is not quiet and vice versa.
If someone is either old or not strong then alice is either humble or calm and vice versa.
If lucy is tall or not tall then someone is not strong or happy.
Everyone who is either wise or patient is either humble or calm and vice versa.
Everyone who is generous is either not strong or not tall.
Everyone who is either kind or not old is not patient or wise and vice versa.
If john is either not curious or not tall then someone is both funny and not strong.
Everyone who is funny or calm is not brave and vice versa.
If someone is either happy or not happy then susan is brave and vice versa.
Everyone who is both patient and happy is both rich and curious and vice versa.
Everyone who is not happy is not happy or humble.
Everyone who is old or tall is either not kind or not patient and vice versa.
Everyone who is both not brave and quiet is both not quiet and curious and vice versa.
Everyone who is not old is both kind and not wise.
Alice is both kind and tall.
Someone is both not calm and rich.
Someone is generous.
Someone is both not calm and patient.
John is tall or not happy.
Mary is generous.
Lucy is either humble or rich. | Susan is not humble. | contradiction | (![X]:((brave(X)|~old(X))=>(~funny(X)&wise(X))))&
((?[X]:(brave(X)))=>(quiet(susan)))&
(![X]:((curious(X)<~>strong(X))<=>~quiet(X)))&
((?[X]:((old(X)<~>~strong(X))))<=>((humble(alice)<~>calm(alice))))&
(((tall(lucy)|~tall(lucy)))=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:((wise(X)<~>patient(X))<=>(humble(X)<~>calm(X))))&
(![X]:(generous(X)=>(~strong(X)<~>~tall(X))))&
(![X]:((kind(X)<~>~old(X))<=>(~patient(X)|wise(X))))&
(((~curious(john)<~>~tall(john)))=>(?[X]:((funny(X)&~strong(X)))))&
(![X]:((funny(X)|calm(X))<=>~brave(X)))&
((?[X]:((happy(X)<~>~happy(X))))<=>(brave(susan)))&
(![X]:((patient(X)&happy(X))<=>(rich(X)&curious(X))))&
(![X]:(~happy(X)=>(~happy(X)|humble(X))))&
(![X]:((old(X)|tall(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~brave(X)&quiet(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~old(X)=>(kind(X)&~wise(X))))&
((kind(alice)&tall(alice)))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)&patient(X))))&
((tall(john)|~happy(john)))&
(generous(mary))&
((humble(lucy)<~>rich(lucy))) | ~humble(susan) | [
"p0",
"p5",
"p7",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7315225176778340683906265
% SZS output start Proof for 7315225176778340683906265
1. ! [X0] : ((~old(X0) | brave(X0)) => (wise(X0) & ~funny(X0))) [input p0]
6. ! [X0] : ((wise(X0) <~> patient(X0)) <=> (humble(X0) <~> calm(X0))) [input p5]
8. ! [X0] : ((kind(X0) <~> ~old(X0)) <=> (wise(X0) | ~patient(X0))) [input p7]
10. ! [X0] : ((calm(X0) | funny(X0)) <=> ~brave(X0)) [input p9]
11. ? [X0] : (happy(X0) <~> ~happy(X0)) <=> brave(susan) [input p10]
14. ! [X0] : ((tall(X0) | old(X0)) <=> (~kind(X0) <~> ~patient(X0))) [input p13]
16. ! [X0] : (~old(X0) => (~wise(X0) & kind(X0))) [input p15]
24. ~humble(susan) [input hypothesis]
25. ! [X0] : ((wise(X0) & ~funny(X0)) | (old(X0) & ~brave(X0))) [ennf transformation 1]
32. ! [X0] : ((~wise(X0) & kind(X0)) | old(X0)) [ennf transformation 16]
40. ! [X0] : ((((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) & (((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))))) [nnf transformation 6]
42. ! [X0] : ((((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0))))) [nnf transformation 8]
43. ! [X0] : ((((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0))))) [flattening 42]
47. ! [X0] : (((calm(X0) | funny(X0)) | brave(X0)) & (~brave(X0) | (~calm(X0) & ~funny(X0)))) [nnf transformation 10]
48. ! [X0] : ((calm(X0) | funny(X0) | brave(X0)) & (~brave(X0) | (~calm(X0) & ~funny(X0)))) [flattening 47]
49. (? [X0] : ((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | ~brave(susan)) & (brave(susan) | ! [X0] : ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 11]
50. (? [X0] : ((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | ~brave(susan)) & (brave(susan) | ! [X1] : ((happy(X1) | happy(X1)) & (~happy(X1) | ~happy(X1)))) [rectify 49]
51. ? [X0] : ((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) => ((happy(sK3) | ~happy(sK3)) & (~happy(sK3) | happy(sK3))) [choice axiom]
52. (((happy(sK3) | ~happy(sK3)) & (~happy(sK3) | happy(sK3))) | ~brave(susan)) & (brave(susan) | ! [X1] : ((happy(X1) | happy(X1)) & (~happy(X1) | ~happy(X1)))) [skolemisation 50,51]
55. ! [X0] : (((tall(X0) | old(X0)) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (~tall(X0) & ~old(X0)))) [nnf transformation 14]
56. ! [X0] : ((tall(X0) | old(X0) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (~tall(X0) & ~old(X0)))) [flattening 55]
68. ~brave(X0) | wise(X0) [cnf transformation 25]
69. wise(X0) | old(X0) [cnf transformation 25]
85. ~wise(X0) | humble(X0) | patient(X0) | calm(X0) [cnf transformation 40]
98. ~wise(X0) | kind(X0) | ~old(X0) [cnf transformation 43]
100. old(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 43]
106. ~calm(X0) | ~brave(X0) [cnf transformation 48]
108. brave(susan) | ~happy(X1) | ~happy(X1) [cnf transformation 52]
109. brave(susan) | happy(X1) | happy(X1) [cnf transformation 52]
117. ~patient(X0) | ~kind(X0) | ~old(X0) [cnf transformation 56]
128. ~wise(X0) | old(X0) [cnf transformation 32]
140. ~humble(susan) [cnf transformation 24]
143. brave(susan) | ~happy(X1) [duplicate literal removal 108]
144. brave(susan) | happy(X1) [duplicate literal removal 109]
197. ~kind(X0) | old(X0) [subsumption resolution 100,69]
220. 16 <=> ! [X1] : happy(X1) [avatar definition]
221. happy(X1) <- (16) [avatar component clause 220]
223. 17 <=> brave(susan) [avatar definition]
225. brave(susan) <- (17) [avatar component clause 223]
226. 16 | 17 [avatar split clause 144,223,220]
228. 18 <=> ! [X1] : ~happy(X1) [avatar definition]
229. ~happy(X1) <- (18) [avatar component clause 228]
230. 18 | 17 [avatar split clause 143,223,228]
232. ~kind(X0) | ~patient(X0) [subsumption resolution 117,197]
233. old(X0) [subsumption resolution 128,69]
251. wise(susan) <- (17) [resolution 68,225]
304. kind(susan) | ~old(susan) <- (17) [resolution 98,251]
306. kind(susan) <- (17) [subsumption resolution 304,233]
364. ~patient(susan) <- (17) [resolution 306,232]
371. 37 <=> patient(susan) [avatar definition]
373. ~patient(susan) <- (~37) [avatar component clause 371]
375. ~37 | ~17 [avatar split clause 364,223,371]
392. humble(susan) | patient(susan) | calm(susan) <- (17) [resolution 85,251]
394. patient(susan) | calm(susan) <- (17) [subsumption resolution 392,140]
395. calm(susan) <- (17, ~37) [subsumption resolution 394,373]
464. ~brave(susan) <- (17, ~37) [resolution 395,106]
465. $false <- (17, ~37) [subsumption resolution 464,225]
466. ~17 | 37 [avatar contradiction clause 465]
473. $false <- (16, 18) [subsumption resolution 221,229]
474. ~16 | ~18 [avatar contradiction clause 473]
475. $false [avatar sat refutation 226,230,375,466,474]
% SZS output end Proof for 7315225176778340683906265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either rich or happy then someone is not wise or kind and vice versa.
Everyone who is not quiet is both not quiet and humble and vice versa.
Everyone who is both not generous and brave is both rich and not kind.
Everyone who is either wise or old is either not old or curious.
If lucy is quiet or rich then someone is not happy or strong.
If someone is not quiet or calm then someone is both not calm and brave and vice versa.
If someone is either not strong or strong then mary is both not rich and quiet.
Everyone who is happy is both not patient and rich and vice versa.
Everyone who is not brave is not tall.
If mary is not calm then someone is quiet.
If susan is not quiet or curious then someone is both not quiet and rich.
Everyone who is kind is both not brave and not curious.
If someone is both not creative and funny then someone is both calm and not kind.
If susan is both kind and funny then paul is both not humble and rich.
Everyone who is both not happy and calm is humble or not strong and vice versa.
If someone is either strong or not patient then someone is wise or calm.
Susan is not patient.
Someone is not generous or not patient.
Susan is curious.
Lucy is generous.
Someone is funny or not generous.
Susan is not patient or tall. | Mary is old. | neutral | (((rich(mary)<~>happy(mary)))<=>(?[X]:((~wise(X)|kind(X)))))&
(![X]:(~quiet(X)<=>(~quiet(X)&humble(X))))&
(![X]:((~generous(X)&brave(X))=>(rich(X)&~kind(X))))&
(![X]:((wise(X)<~>old(X))=>(~old(X)<~>curious(X))))&
(((quiet(lucy)|rich(lucy)))=>(?[X]:((~happy(X)|strong(X)))))&
((?[X]:((~quiet(X)|calm(X))))<=>(?[X]:((~calm(X)&brave(X)))))&
((?[X]:((~strong(X)<~>strong(X))))=>((~rich(mary)&quiet(mary))))&
(![X]:(happy(X)<=>(~patient(X)&rich(X))))&
(![X]:(~brave(X)=>~tall(X)))&
((~calm(mary))=>(?[X]:(quiet(X))))&
(((~quiet(susan)|curious(susan)))=>(?[X]:((~quiet(X)&rich(X)))))&
(![X]:(kind(X)=>(~brave(X)&~curious(X))))&
((?[X]:((~creative(X)&funny(X))))=>(?[X]:((calm(X)&~kind(X)))))&
(((kind(susan)&funny(susan)))=>((~humble(paul)&rich(paul))))&
(![X]:((~happy(X)&calm(X))<=>(humble(X)|~strong(X))))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((wise(X)|calm(X)))))&
(~patient(susan))&
(?[X]:((~generous(X)|~patient(X))))&
(curious(susan))&
(generous(lucy))&
(?[X]:((funny(X)|~generous(X))))&
((~patient(susan)|tall(susan))) | old(mary) | [] | null | 0 |
If alice is both not rich and creative then alice is not old or calm. Everyone who is either not rich or not wise is not kind and vice versa. If someone is either calm or not tall then alice is not tall and vice versa. Everyone who is both not curious and not brave is both not tall and brave and vice versa. Everyone who is either not calm or brave is not wise or brave and vice versa. If someone is not funny or humble then someone is both kind and not wise. Everyone who is humble is funny or humble and vice versa. Everyone who is old or not wise is quiet or not quiet and vice versa. If susan is either not tall or not brave then alice is either tall or not funny and vice versa. Everyone who is happy or strong is both strong and humble and vice versa. Everyone who is not patient or tall is funny. Everyone who is either not creative or not patient is quiet or kind. Everyone who is both not kind and not generous is both strong and not strong and vice versa. If someone is quiet or creative then someone is both not funny and not brave. If someone is old then john is either creative or tall and vice versa. If john is not tall or tall then lucy is either not creative or not generous and vice versa. Someone is either not quiet or tall. Someone is curious. Someone is either not old or brave. Susan is either happy or not old. Susan is either not strong or tall. Someone is strong or not calm. Someone is either patient or not funny. Lucy is not happy or not creative. | John is not happy. | neutral | (((~rich(alice)&creative(alice)))=>((~old(alice)|calm(alice))))&
(![X]:((~rich(X)<~>~wise(X))<=>~kind(X)))&
((?[X]:((calm(X)<~>~tall(X))))<=>(~tall(alice)))&
(![X]:((~curious(X)&~brave(X))<=>(~tall(X)&brave(X))))&
(![X]:((~calm(X)<~>brave(X))<=>(~wise(X)|brave(X))))&
((?[X]:((~funny(X)|humble(X))))=>(?[X]:((kind(X)&~wise(X)))))&
(![X]:(humble(X)<=>(funny(X)|humble(X))))&
(![X]:((old(X)|~wise(X))<=>(quiet(X)|~quiet(X))))&
(((~tall(susan)<~>~brave(susan)))<=>((tall(alice)<~>~funny(alice))))&
(![X]:((happy(X)|strong(X))<=>(strong(X)&humble(X))))&
(![X]:((~patient(X)|tall(X))=>funny(X)))&
(![X]:((~creative(X)<~>~patient(X))=>(quiet(X)|kind(X))))&
(![X]:((~kind(X)&~generous(X))<=>(strong(X)&~strong(X))))&
((?[X]:((quiet(X)|creative(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
((?[X]:(old(X)))<=>((creative(john)<~>tall(john))))&
(((~tall(john)|tall(john)))<=>((~creative(lucy)<~>~generous(lucy))))&
(?[X]:((~quiet(X)<~>tall(X))))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)<~>brave(X))))&
((happy(susan)<~>~old(susan)))&
((~strong(susan)<~>tall(susan)))&
(?[X]:((strong(X)|~calm(X))))&
(?[X]:((patient(X)<~>~funny(X))))&
((~happy(lucy)|~creative(lucy))) | ~happy(john) | [] | null | 0 |
Everyone who is either wise or not creative is not old.
Everyone who is both not wise and wise is happy or rich.
If paul is both not rich and not quiet then someone is either not brave or not quiet.
Everyone who is happy is either not funny or not humble.
Everyone who is generous is old or not wise.
If lucy is old then someone is not happy and vice versa.
Everyone who is happy or not strong is either tall or calm and vice versa.
Everyone who is not old or not strong is not humble or funny.
If someone is not tall then someone is not patient.
Everyone who is not brave is creative or strong.
If susan is quiet or not humble then someone is not wise or patient and vice versa.
If someone is either not tall or not wise then someone is not brave and vice versa.
If someone is tall then mary is both strong and not humble and vice versa.
Everyone who is happy or not brave is both funny and rich.
Everyone who is not funny is not humble or generous and vice versa.
Everyone who is both kind and brave is both not patient and quiet.
Someone is brave or wise.
Lucy is both wise and brave.
Lucy is either rich or not creative.
Fred is not brave.
Someone is both quiet and not strong.
Someone is both not strong and creative.
Susan is either funny or not rich. | Fred is calm. | neutral | (![X]:((wise(X)<~>~creative(X))=>~old(X)))&
(![X]:((~wise(X)&wise(X))=>(happy(X)|rich(X))))&
(((~rich(paul)&~quiet(paul)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:(happy(X)=>(~funny(X)<~>~humble(X))))&
(![X]:(generous(X)=>(old(X)|~wise(X))))&
((old(lucy))<=>(?[X]:(~happy(X))))&
(![X]:((happy(X)|~strong(X))<=>(tall(X)<~>calm(X))))&
(![X]:((~old(X)|~strong(X))=>(~humble(X)|funny(X))))&
((?[X]:(~tall(X)))=>(?[X]:(~patient(X))))&
(![X]:(~brave(X)=>(creative(X)|strong(X))))&
(((quiet(susan)|~humble(susan)))<=>(?[X]:((~wise(X)|patient(X)))))&
((?[X]:((~tall(X)<~>~wise(X))))<=>(?[X]:(~brave(X))))&
((?[X]:(tall(X)))<=>((strong(mary)&~humble(mary))))&
(![X]:((happy(X)|~brave(X))=>(funny(X)&rich(X))))&
(![X]:(~funny(X)<=>(~humble(X)|generous(X))))&
(![X]:((kind(X)&brave(X))=>(~patient(X)&quiet(X))))&
(?[X]:((brave(X)|wise(X))))&
((wise(lucy)&brave(lucy)))&
((rich(lucy)<~>~creative(lucy)))&
(~brave(fred))&
(?[X]:((quiet(X)&~strong(X))))&
(?[X]:((~strong(X)&creative(X))))&
((funny(susan)<~>~rich(susan))) | calm(fred) | [] | null | 0 |
If someone is strong or not curious then lucy is not generous or tall and vice versa.
Everyone who is not patient or not brave is generous.
If alice is kind then john is not humble or not patient and vice versa.
Everyone who is either calm or happy is brave.
If someone is not old then someone is both not kind and not strong and vice versa.
Everyone who is not funny is funny or not humble and vice versa.
If john is kind or not humble then paul is either funny or not rich and vice versa.
Everyone who is either wise or not calm is brave and vice versa.
Everyone who is happy or funny is strong or tall.
Everyone who is either not creative or generous is either not funny or not calm.
Everyone who is either strong or generous is either kind or not brave and vice versa.
Everyone who is not rich or creative is both not quiet and not generous.
Everyone who is either not creative or not humble is either funny or not rich and vice versa.
If lucy is rich then someone is both not creative and not kind.
Everyone who is happy is either kind or not kind and vice versa.
Everyone who is both not calm and not patient is generous or strong and vice versa.
Someone is both generous and happy.
Someone is either kind or not calm.
Someone is both not humble and not funny.
Mary is not curious or tall.
Lucy is patient or tall.
John is either not generous or generous. | John is creative. | neutral | ((?[X]:((strong(X)|~curious(X))))<=>((~generous(lucy)|tall(lucy))))&
(![X]:((~patient(X)|~brave(X))=>generous(X)))&
((kind(alice))<=>((~humble(john)|~patient(john))))&
(![X]:((calm(X)<~>happy(X))=>brave(X)))&
((?[X]:(~old(X)))<=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:(~funny(X)<=>(funny(X)|~humble(X))))&
(((kind(john)|~humble(john)))<=>((funny(paul)<~>~rich(paul))))&
(![X]:((wise(X)<~>~calm(X))<=>brave(X)))&
(![X]:((happy(X)|funny(X))=>(strong(X)|tall(X))))&
(![X]:((~creative(X)<~>generous(X))=>(~funny(X)<~>~calm(X))))&
(![X]:((strong(X)<~>generous(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~rich(X)|creative(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~creative(X)<~>~humble(X))<=>(funny(X)<~>~rich(X))))&
((rich(lucy))=>(?[X]:((~creative(X)&~kind(X)))))&
(![X]:(happy(X)<=>(kind(X)<~>~kind(X))))&
(![X]:((~calm(X)&~patient(X))<=>(generous(X)|strong(X))))&
(?[X]:((generous(X)&happy(X))))&
(?[X]:((kind(X)<~>~calm(X))))&
(?[X]:((~humble(X)&~funny(X))))&
((~curious(mary)|tall(mary)))&
((patient(lucy)|tall(lucy)))&
((~generous(john)<~>generous(john))) | creative(john) | [] | null | 0 |
If someone is either not creative or kind then someone is not rich. If someone is tall then paul is happy. Everyone who is both tall and not old is either patient or calm and vice versa. If someone is both creative and rich then someone is either not funny or rich and vice versa. Everyone who is both not strong and happy is both not calm and not brave and vice versa. If someone is both kind and not generous then fred is either patient or curious and vice versa. Everyone who is either brave or patient is both patient and strong and vice versa. If someone is humble then someone is not creative. Everyone who is both brave and tall is either not calm or curious and vice versa. Everyone who is either not patient or wise is not calm. Everyone who is either not brave or calm is both not generous and generous. If lucy is both not brave and not tall then john is rich. If susan is calm then someone is both creative and not old and vice versa. Everyone who is both not brave and not curious is both quiet and not tall. If someone is either wise or curious then paul is both not generous and not calm and vice versa. If john is both strong and not curious then paul is both not funny and creative and vice versa. Someone is both not calm and brave. Someone is either not tall or humble. Someone is patient. Someone is either not rich or not strong. Someone is either not happy or not tall. | Paul is brave. | contradiction | ((?[X]:((~creative(X)<~>kind(X))))=>(?[X]:(~rich(X))))&
((?[X]:(tall(X)))=>(happy(paul)))&
(![X]:((tall(X)&~old(X))<=>(patient(X)<~>calm(X))))&
((?[X]:((creative(X)&rich(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((~strong(X)&happy(X))<=>(~calm(X)&~brave(X))))&
((?[X]:((kind(X)&~generous(X))))<=>((patient(fred)<~>curious(fred))))&
(![X]:((brave(X)<~>patient(X))<=>(patient(X)&strong(X))))&
((?[X]:(humble(X)))=>(?[X]:(~creative(X))))&
(![X]:((brave(X)&tall(X))<=>(~calm(X)<~>curious(X))))&
(![X]:((~patient(X)<~>wise(X))=>~calm(X)))&
(![X]:((~brave(X)<~>calm(X))=>(~generous(X)&generous(X))))&
(((~brave(lucy)&~tall(lucy)))=>(rich(john)))&
((calm(susan))<=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((~brave(X)&~curious(X))=>(quiet(X)&~tall(X))))&
((?[X]:((wise(X)<~>curious(X))))<=>((~generous(paul)&~calm(paul))))&
(((strong(john)&~curious(john)))<=>((~funny(paul)&creative(paul))))&
(?[X]:((~calm(X)&brave(X))))&
(?[X]:((~tall(X)<~>humble(X))))&
(?[X]:(patient(X)))&
(?[X]:((~rich(X)<~>~strong(X))))&
(?[X]:((~happy(X)<~>~tall(X)))) | brave(paul) | [
"p1",
"p2",
"p4",
"p6",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9092124822438071309391241
% SZS output start Proof for 9092124822438071309391241
2. ? [X0] : tall(X0) => happy(paul) [input p1]
3. ! [X0] : ((~old(X0) & tall(X0)) <=> (patient(X0) <~> calm(X0))) [input p2]
5. ! [X0] : ((happy(X0) & ~strong(X0)) <=> (~brave(X0) & ~calm(X0))) [input p4]
7. ! [X0] : ((brave(X0) <~> patient(X0)) <=> (strong(X0) & patient(X0))) [input p6]
11. ! [X0] : ((~brave(X0) <~> calm(X0)) => (generous(X0) & ~generous(X0))) [input p10]
17. ? [X0] : (brave(X0) & ~calm(X0)) [input p16]
22. brave(paul) [input hypothesis]
28. happy(paul) | ! [X0] : ~tall(X0) [ennf transformation 2]
31. ! [X0] : ((generous(X0) & ~generous(X0)) | (~brave(X0) <=> calm(X0))) [ennf transformation 11]
40. ! [X0] : (((~old(X0) & tall(X0)) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0)))) & (((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | (old(X0) | ~tall(X0)))) [nnf transformation 3]
41. ! [X0] : (((~old(X0) & tall(X0)) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0)))) & (((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | old(X0) | ~tall(X0))) [flattening 40]
47. ! [X0] : (((happy(X0) & ~strong(X0)) | (brave(X0) | calm(X0))) & ((~brave(X0) & ~calm(X0)) | (~happy(X0) | strong(X0)))) [nnf transformation 5]
48. ! [X0] : (((happy(X0) & ~strong(X0)) | brave(X0) | calm(X0)) & ((~brave(X0) & ~calm(X0)) | ~happy(X0) | strong(X0))) [flattening 47]
53. ! [X0] : ((((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | (~strong(X0) | ~patient(X0))) & ((strong(X0) & patient(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))))) [nnf transformation 7]
54. ! [X0] : ((((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~strong(X0) | ~patient(X0)) & ((strong(X0) & patient(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))))) [flattening 53]
61. ! [X0] : ((generous(X0) & ~generous(X0)) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) [nnf transformation 31]
73. ? [X0] : (brave(X0) & ~calm(X0)) => (brave(sK7) & ~calm(sK7)) [choice axiom]
74. brave(sK7) & ~calm(sK7) [skolemisation 17,73]
88. happy(paul) | ~tall(X0) [cnf transformation 28]
91. ~patient(X0) | calm(X0) | tall(X0) [cnf transformation 41]
101. ~calm(X0) | ~happy(X0) | strong(X0) [cnf transformation 48]
102. ~brave(X0) | ~happy(X0) | strong(X0) [cnf transformation 48]
111. patient(X0) | patient(X0) | ~brave(X0) [cnf transformation 54]
116. ~patient(X0) | ~brave(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 54]
126. ~generous(X0) | calm(X0) | brave(X0) [cnf transformation 61]
128. generous(X0) | calm(X0) | brave(X0) [cnf transformation 61]
145. ~calm(sK7) [cnf transformation 74]
146. brave(sK7) [cnf transformation 74]
154. brave(paul) [cnf transformation 22]
155. ~brave(X0) | patient(X0) [duplicate literal removal 111]
156. ~brave(X0) | ~patient(X0) | ~strong(X0) [duplicate literal removal 116]
170. 4 <=> ! [X0] : ~tall(X0) [avatar definition]
171. ~tall(X0) <- (4) [avatar component clause 170]
173. 5 <=> happy(paul) [avatar definition]
175. happy(paul) <- (5) [avatar component clause 173]
176. 4 | 5 [avatar split clause 88,173,170]
242. brave(X0) | calm(X0) [subsumption resolution 126,128]
352. patient(sK7) [resolution 155,146]
353. patient(paul) [resolution 155,154]
363. calm(sK7) | tall(sK7) [resolution 91,352]
371. tall(sK7) [subsumption resolution 363,145]
372. $false <- (4) [subsumption resolution 371,171]
373. ~4 [avatar contradiction clause 372]
404. ~happy(X0) | strong(X0) | calm(X0) [resolution 102,242]
408. ~happy(X0) | strong(X0) [subsumption resolution 404,101]
458. strong(paul) <- (5) [resolution 408,175]
544. ~patient(paul) | ~strong(paul) [resolution 156,154]
550. ~strong(paul) [subsumption resolution 544,353]
551. $false <- (5) [subsumption resolution 550,458]
552. ~5 [avatar contradiction clause 551]
557. $false [avatar sat refutation 176,373,552]
% SZS output end Proof for 9092124822438071309391241
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not humble is both quiet and not curious. Everyone who is not patient or not rich is both not strong and strong and vice versa. If someone is both patient and not brave then paul is either not funny or not brave and vice versa. Everyone who is funny or not kind is calm and vice versa. Everyone who is either not old or patient is not rich and vice versa. Everyone who is both kind and not calm is both wise and humble and vice versa. Everyone who is kind or old is creative or not creative and vice versa. Everyone who is both not quiet and not wise is both rich and not funny and vice versa. If alice is both curious and not happy then alice is not happy and vice versa. If someone is either not funny or not happy then alice is either strong or not wise and vice versa. If someone is not rich or calm then mary is either not quiet or funny and vice versa. If someone is kind or calm then susan is humble and vice versa. Everyone who is not kind is not calm. Everyone who is patient is not generous or quiet. If someone is either not rich or quiet then someone is either not brave or not old and vice versa. If susan is wise or not curious then john is calm. Someone is quiet or wise. Someone is not creative or not generous. Lucy is not strong or quiet. Susan is either humble or curious. Someone is either rich or strong. Paul is not curious or not calm. | Mary is not patient. | contradiction | (![X]:((~funny(X)<~>~humble(X))=>(quiet(X)&~curious(X))))&
(![X]:((~patient(X)|~rich(X))<=>(~strong(X)&strong(X))))&
((?[X]:((patient(X)&~brave(X))))<=>((~funny(paul)<~>~brave(paul))))&
(![X]:((funny(X)|~kind(X))<=>calm(X)))&
(![X]:((~old(X)<~>patient(X))<=>~rich(X)))&
(![X]:((kind(X)&~calm(X))<=>(wise(X)&humble(X))))&
(![X]:((kind(X)|old(X))<=>(creative(X)|~creative(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(rich(X)&~funny(X))))&
(((curious(alice)&~happy(alice)))<=>(~happy(alice)))&
((?[X]:((~funny(X)<~>~happy(X))))<=>((strong(alice)<~>~wise(alice))))&
((?[X]:((~rich(X)|calm(X))))<=>((~quiet(mary)<~>funny(mary))))&
((?[X]:((kind(X)|calm(X))))<=>(humble(susan)))&
(![X]:(~kind(X)=>~calm(X)))&
(![X]:(patient(X)=>(~generous(X)|quiet(X))))&
((?[X]:((~rich(X)<~>quiet(X))))<=>(?[X]:((~brave(X)<~>~old(X)))))&
(((wise(susan)|~curious(susan)))=>(calm(john)))&
(?[X]:((quiet(X)|wise(X))))&
(?[X]:((~creative(X)|~generous(X))))&
((~strong(lucy)|quiet(lucy)))&
((humble(susan)<~>curious(susan)))&
(?[X]:((rich(X)<~>strong(X))))&
((~curious(paul)|~calm(paul))) | ~patient(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 8857543987704506782725941
% SZS output start Proof for 8857543987704506782725941
2. ! [X0] : ((~rich(X0) | ~patient(X0)) <=> (strong(X0) & ~strong(X0))) [input p1]
23. ~patient(mary) [input hypothesis]
31. ! [X0] : (((~rich(X0) | ~patient(X0)) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | (rich(X0) & patient(X0)))) [nnf transformation 2]
32. ! [X0] : ((~rich(X0) | ~patient(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | (rich(X0) & patient(X0)))) [flattening 31]
75. ~strong(X0) | patient(X0) [cnf transformation 32]
77. strong(X0) | patient(X0) [cnf transformation 32]
143. ~patient(mary) [cnf transformation 23]
145. patient(X0) [subsumption resolution 75,77]
308. $false [subsumption resolution 143,145]
% SZS output end Proof for 8857543987704506782725941
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not wise and not tall then paul is tall.
If susan is not rich then someone is not creative or not kind and vice versa.
If susan is brave or tall then someone is both not quiet and patient and vice versa.
Everyone who is kind is either brave or tall.
Everyone who is either patient or not strong is happy and vice versa.
If susan is not generous then someone is both humble and not curious.
Everyone who is either happy or wise is both tall and not calm.
Everyone who is either rich or not brave is quiet.
Everyone who is wise or strong is both calm and not patient and vice versa.
If fred is both calm and strong then susan is either humble or kind and vice versa.
If someone is not tall or rich then mary is either not patient or not calm.
Everyone who is old is either not creative or curious and vice versa.
If someone is generous or quiet then john is humble or not happy and vice versa.
Everyone who is not happy is either wise or not strong.
Everyone who is either not strong or quiet is both generous and not tall.
Everyone who is generous is either tall or not quiet.
Someone is not old or curious.
John is curious.
Someone is either generous or quiet.
Someone is either generous or strong.
Alice is not old.
Someone is either not happy or rich.
Someone is not creative.
Mary is calm. | Mary is patient. | contradiction | ((?[X]:((~wise(X)&~tall(X))))=>(tall(paul)))&
((~rich(susan))<=>(?[X]:((~creative(X)|~kind(X)))))&
(((brave(susan)|tall(susan)))<=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(kind(X)=>(brave(X)<~>tall(X))))&
(![X]:((patient(X)<~>~strong(X))<=>happy(X)))&
((~generous(susan))=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:((happy(X)<~>wise(X))=>(tall(X)&~calm(X))))&
(![X]:((rich(X)<~>~brave(X))=>quiet(X)))&
(![X]:((wise(X)|strong(X))<=>(calm(X)&~patient(X))))&
(((calm(fred)&strong(fred)))<=>((humble(susan)<~>kind(susan))))&
((?[X]:((~tall(X)|rich(X))))=>((~patient(mary)<~>~calm(mary))))&
(![X]:(old(X)<=>(~creative(X)<~>curious(X))))&
((?[X]:((generous(X)|quiet(X))))<=>((humble(john)|~happy(john))))&
(![X]:(~happy(X)=>(wise(X)<~>~strong(X))))&
(![X]:((~strong(X)<~>quiet(X))=>(generous(X)&~tall(X))))&
(![X]:(generous(X)=>(tall(X)<~>~quiet(X))))&
(?[X]:((~old(X)|curious(X))))&
(curious(john))&
(?[X]:((generous(X)<~>quiet(X))))&
(?[X]:((generous(X)<~>strong(X))))&
(~old(alice))&
(?[X]:((~happy(X)<~>rich(X))))&
(?[X]:(~creative(X)))&
(calm(mary)) | patient(mary) | [
"p2",
"p8",
"p10",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8298518498101135171732645
% SZS output start Proof for 8298518498101135171732645
3. (tall(susan) | brave(susan)) <=> ? [X0] : (patient(X0) & ~quiet(X0)) [input p2]
9. ! [X0] : ((strong(X0) | wise(X0)) <=> (~patient(X0) & calm(X0))) [input p8]
11. ? [X0] : (rich(X0) | ~tall(X0)) => (~patient(mary) <~> ~calm(mary)) [input p10]
15. ! [X0] : ((~strong(X0) <~> quiet(X0)) => (~tall(X0) & generous(X0))) [input p14]
24. calm(mary) [input p23]
25. patient(mary) [input hypothesis]
32. (~patient(mary) <~> ~calm(mary)) | ! [X0] : (~rich(X0) & tall(X0)) [ennf transformation 11]
35. ! [X0] : ((~tall(X0) & generous(X0)) | (~strong(X0) <=> quiet(X0))) [ennf transformation 15]
41. ((tall(susan) | brave(susan)) | ! [X0] : (~patient(X0) | quiet(X0))) & (? [X0] : (patient(X0) & ~quiet(X0)) | (~tall(susan) & ~brave(susan))) [nnf transformation 3]
42. (tall(susan) | brave(susan) | ! [X0] : (~patient(X0) | quiet(X0))) & (? [X0] : (patient(X0) & ~quiet(X0)) | (~tall(susan) & ~brave(susan))) [flattening 41]
43. (tall(susan) | brave(susan) | ! [X0] : (~patient(X0) | quiet(X0))) & (? [X1] : (patient(X1) & ~quiet(X1)) | (~tall(susan) & ~brave(susan))) [rectify 42]
44. ? [X1] : (patient(X1) & ~quiet(X1)) => (patient(sK1) & ~quiet(sK1)) [choice axiom]
45. (tall(susan) | brave(susan) | ! [X0] : (~patient(X0) | quiet(X0))) & ((patient(sK1) & ~quiet(sK1)) | (~tall(susan) & ~brave(susan))) [skolemisation 43,44]
52. ! [X0] : (((strong(X0) | wise(X0)) | (patient(X0) | ~calm(X0))) & ((~patient(X0) & calm(X0)) | (~strong(X0) & ~wise(X0)))) [nnf transformation 9]
53. ! [X0] : ((strong(X0) | wise(X0) | patient(X0) | ~calm(X0)) & ((~patient(X0) & calm(X0)) | (~strong(X0) & ~wise(X0)))) [flattening 52]
56. ((calm(mary) | patient(mary)) & (~calm(mary) | ~patient(mary))) | ! [X0] : (~rich(X0) & tall(X0)) [nnf transformation 32]
64. ! [X0] : ((~tall(X0) & generous(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0)))) [nnf transformation 35]
84. ~quiet(sK1) | ~tall(susan) [cnf transformation 45]
86. patient(sK1) | ~tall(susan) [cnf transformation 45]
105. ~strong(X0) | ~patient(X0) [cnf transformation 53]
113. ~calm(mary) | ~patient(mary) | tall(X0) [cnf transformation 56]
127. ~tall(X0) | quiet(X0) | strong(X0) [cnf transformation 64]
141. calm(mary) [cnf transformation 24]
142. patient(mary) [cnf transformation 25]
173. 8 <=> ! [X0] : (~patient(X0) | quiet(X0)) [avatar definition]
174. ~patient(X0) | quiet(X0) <- (8) [avatar component clause 173]
180. 10 <=> tall(susan) [avatar definition]
181. ~tall(susan) <- (~10) [avatar component clause 180]
185. 11 <=> patient(sK1) [avatar definition]
187. patient(sK1) <- (11) [avatar component clause 185]
188. ~10 | 11 [avatar split clause 86,185,180]
191. 12 <=> quiet(sK1) [avatar definition]
193. ~quiet(sK1) <- (~12) [avatar component clause 191]
194. ~10 | ~12 [avatar split clause 84,191,180]
238. 21 <=> patient(mary) [avatar definition]
242. 22 <=> calm(mary) [avatar definition]
247. 23 <=> ! [X0] : tall(X0) [avatar definition]
248. tall(X0) <- (23) [avatar component clause 247]
251. 23 | ~21 | ~22 [avatar split clause 113,242,238,247]
317. 22 [avatar split clause 141,242]
318. 21 [avatar split clause 142,238]
319. $false <- (~10, 23) [subsumption resolution 181,248]
320. 10 | ~23 [avatar contradiction clause 319]
323. quiet(sK1) <- (8, 11) [resolution 174,187]
325. $false <- (8, 11, ~12) [subsumption resolution 323,193]
326. ~8 | ~11 | 12 [avatar contradiction clause 325]
420. strong(X0) | quiet(X0) <- (23) [resolution 127,248]
445. quiet(X4) | ~patient(X4) <- (23) [resolution 420,105]
451. 8 | ~23 [avatar split clause 445,247,173]
452. $false [avatar sat refutation 188,194,251,317,318,320,326,451]
% SZS output end Proof for 8298518498101135171732645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not old is kind.
If mary is both humble and not creative then someone is not creative.
If mary is either tall or not patient then lucy is curious or humble and vice versa.
If someone is both not generous and tall then lucy is patient or not curious.
If someone is not patient then lucy is strong and vice versa.
If someone is not brave or generous then lucy is tall or not old and vice versa.
Everyone who is both curious and not funny is funny or tall and vice versa.
Everyone who is both generous and not funny is both humble and generous.
Everyone who is not wise or not curious is not kind and vice versa.
Everyone who is funny is both old and funny.
If lucy is either not happy or creative then someone is either generous or strong.
Everyone who is not funny or curious is both not strong and not brave.
Everyone who is not calm is not creative or creative and vice versa.
If susan is either calm or not generous then someone is either creative or not humble.
If someone is not calm or happy then susan is either not creative or wise and vice versa.
If susan is funny or not creative then someone is wise or not kind.
Alice is either not humble or not wise.
Someone is either quiet or not curious.
Someone is not calm or calm.
Someone is both quiet and rich.
Mary is old.
Lucy is not curious or creative.
Someone is not calm. | Lucy is not strong. | entailment | (![X]:((~curious(X)<~>~old(X))=>kind(X)))&
(((humble(mary)&~creative(mary)))=>(?[X]:(~creative(X))))&
(((tall(mary)<~>~patient(mary)))<=>((curious(lucy)|humble(lucy))))&
((?[X]:((~generous(X)&tall(X))))=>((patient(lucy)|~curious(lucy))))&
((?[X]:(~patient(X)))<=>(strong(lucy)))&
((?[X]:((~brave(X)|generous(X))))<=>((tall(lucy)|~old(lucy))))&
(![X]:((curious(X)&~funny(X))<=>(funny(X)|tall(X))))&
(![X]:((generous(X)&~funny(X))=>(humble(X)&generous(X))))&
(![X]:((~wise(X)|~curious(X))<=>~kind(X)))&
(![X]:(funny(X)=>(old(X)&funny(X))))&
(((~happy(lucy)<~>creative(lucy)))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:((~funny(X)|curious(X))=>(~strong(X)&~brave(X))))&
(![X]:(~calm(X)<=>(~creative(X)|creative(X))))&
(((calm(susan)<~>~generous(susan)))=>(?[X]:((creative(X)<~>~humble(X)))))&
((?[X]:((~calm(X)|happy(X))))<=>((~creative(susan)<~>wise(susan))))&
(((funny(susan)|~creative(susan)))=>(?[X]:((wise(X)|~kind(X)))))&
((~humble(alice)<~>~wise(alice)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((quiet(X)&rich(X))))&
(old(mary))&
((~curious(lucy)|creative(lucy)))&
(?[X]:(~calm(X))) | ~strong(lucy) | [
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 736854848603025938616899
% SZS output start Proof for 736854848603025938616899
7. ! [X0] : ((~funny(X0) & curious(X0)) <=> (tall(X0) | funny(X0))) [input p6]
12. ! [X0] : ((curious(X0) | ~funny(X0)) => (~brave(X0) & ~strong(X0))) [input p11]
24. strong(lucy) [input hypothesis]
35. ! [X0] : ((~brave(X0) & ~strong(X0)) | (~curious(X0) & funny(X0))) [ennf transformation 12]
52. ! [X0] : (((~funny(X0) & curious(X0)) | (~tall(X0) & ~funny(X0))) & ((tall(X0) | funny(X0)) | (funny(X0) | ~curious(X0)))) [nnf transformation 7]
53. ! [X0] : (((~funny(X0) & curious(X0)) | (~tall(X0) & ~funny(X0))) & (tall(X0) | funny(X0) | funny(X0) | ~curious(X0))) [flattening 52]
99. ~funny(X0) | ~funny(X0) [cnf transformation 53]
112. ~strong(X0) | funny(X0) [cnf transformation 35]
140. strong(lucy) [cnf transformation 24]
142. ~funny(X0) [duplicate literal removal 99]
248. ~strong(X0) [subsumption resolution 112,142]
304. $false [subsumption resolution 140,248]
% SZS output end Proof for 736854848603025938616899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and patient is old or calm and vice versa. If someone is generous then lucy is either happy or tall and vice versa. Everyone who is either old or not happy is both quiet and not old. Everyone who is either old or not old is both funny and not happy. Everyone who is either curious or old is brave and vice versa. Everyone who is either not quiet or not humble is not rich. If john is both not quiet and brave then someone is either not wise or quiet and vice versa. If someone is both not wise and not strong then fred is both not old and not kind. Everyone who is quiet is both not curious and not patient. Everyone who is kind is wise. Everyone who is quiet or old is either strong or not quiet and vice versa. Everyone who is not curious is not happy. Everyone who is not rich is both tall and generous. If john is both not happy and not rich then susan is either not quiet or wise. Someone is not curious or not rich. Someone is either brave or not wise. Lucy is either not kind or creative. Someone is not humble or rich. Someone is both creative and tall. John is not tall. | Susan is not patient. | entailment | (![X]:((~patient(X)&patient(X))<=>(old(X)|calm(X))))&
((?[X]:(generous(X)))<=>((happy(lucy)<~>tall(lucy))))&
(![X]:((old(X)<~>~happy(X))=>(quiet(X)&~old(X))))&
(![X]:((old(X)<~>~old(X))=>(funny(X)&~happy(X))))&
(![X]:((curious(X)<~>old(X))<=>brave(X)))&
(![X]:((~quiet(X)<~>~humble(X))=>~rich(X)))&
(((~quiet(john)&brave(john)))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
((?[X]:((~wise(X)&~strong(X))))=>((~old(fred)&~kind(fred))))&
(![X]:(quiet(X)=>(~curious(X)&~patient(X))))&
(![X]:(kind(X)=>wise(X)))&
(![X]:((quiet(X)|old(X))<=>(strong(X)<~>~quiet(X))))&
(![X]:(~curious(X)=>~happy(X)))&
(![X]:(~rich(X)=>(tall(X)&generous(X))))&
(((~happy(john)&~rich(john)))=>((~quiet(susan)<~>wise(susan))))&
(?[X]:((~curious(X)|~rich(X))))&
(?[X]:((brave(X)<~>~wise(X))))&
((~kind(lucy)<~>creative(lucy)))&
(?[X]:((~humble(X)|rich(X))))&
(?[X]:((creative(X)&tall(X))))&
(~tall(john)) | ~patient(susan) | [
"p0",
"p2",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5066381400859297583570135
% SZS output start Proof for 5066381400859297583570135
1. ! [X0] : ((patient(X0) & ~patient(X0)) <=> (calm(X0) | old(X0))) [input p0]
3. ! [X0] : ((old(X0) <~> ~happy(X0)) => (~old(X0) & quiet(X0))) [input p2]
4. ! [X0] : ((old(X0) <~> ~old(X0)) => (~happy(X0) & funny(X0))) [input p3]
9. ! [X0] : (quiet(X0) => (~patient(X0) & ~curious(X0))) [input p8]
21. patient(susan) [input hypothesis]
22. ! [X0] : ((old(X0) <~> ~old(X0)) => ~happy(X0)) [pure predicate removal 4]
23. ! [X0] : ((~old(X0) & quiet(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 3]
24. ! [X0] : (~happy(X0) | (old(X0) <=> ~old(X0))) [ennf transformation 22]
27. ! [X0] : ((~patient(X0) & ~curious(X0)) | ~quiet(X0)) [ennf transformation 9]
33. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & ((calm(X0) | old(X0)) | (~patient(X0) | patient(X0)))) [nnf transformation 1]
34. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & (calm(X0) | old(X0) | ~patient(X0) | patient(X0))) [flattening 33]
39. ! [X0] : ((~old(X0) & quiet(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 23]
40. ! [X0] : (~happy(X0) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 24]
62. ~patient(X0) | ~old(X0) [cnf transformation 34]
64. ~old(X0) | patient(X0) [cnf transformation 34]
71. quiet(X0) | old(X0) | happy(X0) [cnf transformation 39]
75. ~happy(X0) | old(X0) | old(X0) [cnf transformation 40]
91. ~quiet(X0) | ~patient(X0) [cnf transformation 27]
113. patient(susan) [cnf transformation 21]
117. ~happy(X0) | old(X0) [duplicate literal removal 75]
120. ~old(X0) [subsumption resolution 62,64]
140. quiet(X0) | happy(X0) [subsumption resolution 71,120]
141. ~happy(X0) [subsumption resolution 117,120]
242. happy(X0) | ~patient(X0) [resolution 140,91]
246. ~patient(X0) [subsumption resolution 242,141]
257. $false [resolution 246,113]
% SZS output end Proof for 5066381400859297583570135
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or patient is not brave or humble and vice versa.
If lucy is either not kind or not rich then susan is tall and vice versa.
If someone is not patient or quiet then someone is not happy or not brave and vice versa.
Everyone who is not happy is both not brave and not rich and vice versa.
Everyone who is not old or not kind is not strong.
If lucy is not patient or not humble then paul is both humble and happy.
If someone is either brave or not rich then someone is not rich or not old.
If someone is either not creative or not tall then someone is not old and vice versa.
If mary is both kind and not creative then someone is both tall and wise and vice versa.
If someone is not generous or patient then john is patient or not wise and vice versa.
Everyone who is both funny and not rich is humble.
If fred is either humble or brave then someone is not tall or old and vice versa.
Everyone who is both wise and happy is both strong and calm.
Everyone who is both kind and not brave is both kind and not patient and vice versa.
Everyone who is both not funny and not rich is either brave or happy and vice versa.
If someone is not funny then someone is either funny or not generous and vice versa.
Someone is both kind and quiet.
Paul is wise.
Mary is tall or strong.
Paul is both not generous and funny.
Alice is both generous and not curious.
Someone is patient.
Someone is either not curious or funny.
Fred is wise. | John is generous. | neutral | (![X]:((~tall(X)|patient(X))<=>(~brave(X)|humble(X))))&
(((~kind(lucy)<~>~rich(lucy)))<=>(tall(susan)))&
((?[X]:((~patient(X)|quiet(X))))<=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:(~happy(X)<=>(~brave(X)&~rich(X))))&
(![X]:((~old(X)|~kind(X))=>~strong(X)))&
(((~patient(lucy)|~humble(lucy)))=>((humble(paul)&happy(paul))))&
((?[X]:((brave(X)<~>~rich(X))))=>(?[X]:((~rich(X)|~old(X)))))&
((?[X]:((~creative(X)<~>~tall(X))))<=>(?[X]:(~old(X))))&
(((kind(mary)&~creative(mary)))<=>(?[X]:((tall(X)&wise(X)))))&
((?[X]:((~generous(X)|patient(X))))<=>((patient(john)|~wise(john))))&
(![X]:((funny(X)&~rich(X))=>humble(X)))&
(((humble(fred)<~>brave(fred)))<=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((wise(X)&happy(X))=>(strong(X)&calm(X))))&
(![X]:((kind(X)&~brave(X))<=>(kind(X)&~patient(X))))&
(![X]:((~funny(X)&~rich(X))<=>(brave(X)<~>happy(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((funny(X)<~>~generous(X)))))&
(?[X]:((kind(X)&quiet(X))))&
(wise(paul))&
((tall(mary)|strong(mary)))&
((~generous(paul)&funny(paul)))&
((generous(alice)&~curious(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~curious(X)<~>funny(X))))&
(wise(fred)) | generous(john) | [] | null | 0 |
Everyone who is rich or patient is either curious or not curious. If lucy is kind or not rich then someone is either tall or kind and vice versa. Everyone who is either not curious or humble is both funny and curious. Everyone who is not generous or funny is both not creative and not quiet. Everyone who is brave or curious is not humble or not tall and vice versa. Everyone who is not patient is old or happy. If john is strong or not brave then someone is either not happy or not strong. Everyone who is not quiet is patient. If someone is curious then alice is both creative and generous. Everyone who is not funny is both not wise and patient and vice versa. If someone is either calm or quiet then mary is curious or not creative. Everyone who is both not patient and not rich is both tall and creative. If john is not happy then someone is happy and vice versa. Everyone who is both creative and wise is not funny or strong and vice versa. Everyone who is either creative or brave is either rich or not happy and vice versa. Alice is either not patient or not old. John is not calm. Lucy is wise. Paul is either rich or not brave. Someone is calm. | Alice is kind. | neutral | (![X]:((rich(X)|patient(X))=>(curious(X)<~>~curious(X))))&
(((kind(lucy)|~rich(lucy)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
((~patient(alice)<~>~old(alice)))&
(~calm(john))&
(wise(lucy))&
((rich(paul)<~>~brave(paul)))&
(?[X]:(calm(X))) | kind(alice) | [] | null | 0 |
If alice is both not rich and creative then alice is not old or calm. Everyone who is either not rich or not wise is not kind and vice versa. If someone is either calm or not tall then alice is not tall and vice versa. Everyone who is both not curious and not brave is both not tall and brave and vice versa. Everyone who is either not calm or brave is not wise or brave and vice versa. If someone is not funny or humble then someone is both kind and not wise. Everyone who is humble is funny or humble and vice versa. Everyone who is old or not wise is quiet or not quiet and vice versa. If susan is either not tall or not brave then alice is either tall or not funny and vice versa. Everyone who is happy or strong is both strong and humble and vice versa. Everyone who is not patient or tall is funny. Everyone who is either not creative or not patient is quiet or kind. Everyone who is both not kind and not generous is both strong and not strong and vice versa. If someone is quiet or creative then someone is both not funny and not brave. If someone is old then john is either creative or tall and vice versa. If john is not tall or tall then lucy is either not creative or not generous and vice versa. Someone is either not quiet or tall. Someone is curious. Someone is either not old or brave. Susan is either happy or not old. Susan is either not strong or tall. Someone is strong or not calm. Someone is either patient or not funny. Lucy is not happy or not creative. | Susan is not calm. | neutral | (((~rich(alice)&creative(alice)))=>((~old(alice)|calm(alice))))&
(![X]:((~rich(X)<~>~wise(X))<=>~kind(X)))&
((?[X]:((calm(X)<~>~tall(X))))<=>(~tall(alice)))&
(![X]:((~curious(X)&~brave(X))<=>(~tall(X)&brave(X))))&
(![X]:((~calm(X)<~>brave(X))<=>(~wise(X)|brave(X))))&
((?[X]:((~funny(X)|humble(X))))=>(?[X]:((kind(X)&~wise(X)))))&
(![X]:(humble(X)<=>(funny(X)|humble(X))))&
(![X]:((old(X)|~wise(X))<=>(quiet(X)|~quiet(X))))&
(((~tall(susan)<~>~brave(susan)))<=>((tall(alice)<~>~funny(alice))))&
(![X]:((happy(X)|strong(X))<=>(strong(X)&humble(X))))&
(![X]:((~patient(X)|tall(X))=>funny(X)))&
(![X]:((~creative(X)<~>~patient(X))=>(quiet(X)|kind(X))))&
(![X]:((~kind(X)&~generous(X))<=>(strong(X)&~strong(X))))&
((?[X]:((quiet(X)|creative(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
((?[X]:(old(X)))<=>((creative(john)<~>tall(john))))&
(((~tall(john)|tall(john)))<=>((~creative(lucy)<~>~generous(lucy))))&
(?[X]:((~quiet(X)<~>tall(X))))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)<~>brave(X))))&
((happy(susan)<~>~old(susan)))&
((~strong(susan)<~>tall(susan)))&
(?[X]:((strong(X)|~calm(X))))&
(?[X]:((patient(X)<~>~funny(X))))&
((~happy(lucy)|~creative(lucy))) | ~calm(susan) | [] | null | 0 |
If john is rich then john is either not calm or generous. If fred is either not generous or brave then paul is humble or rich and vice versa. Everyone who is not creative or humble is strong and vice versa. If lucy is both wise and not rich then alice is either not funny or humble. If lucy is both strong and not creative then susan is either patient or not wise and vice versa. If alice is both not generous and strong then someone is either generous or not brave. Everyone who is not tall or calm is both strong and funny and vice versa. If someone is either not generous or not kind then alice is both not old and not generous and vice versa. Everyone who is both not tall and old is both wise and not quiet. Everyone who is happy or humble is both not tall and patient. If someone is both wise and tall then someone is either quiet or not tall. Everyone who is happy is generous and vice versa. If fred is both old and quiet then someone is both not funny and not quiet and vice versa. If alice is either not happy or not patient then susan is either creative or happy and vice versa. Everyone who is either happy or strong is not patient. If someone is both not kind and tall then alice is both not tall and not strong and vice versa. Susan is both patient and not generous. Someone is not old. Paul is both not tall and not kind. Someone is curious or kind. Alice is both not funny and brave. Lucy is quiet. Someone is not funny or old. | Susan is not kind. | contradiction | ((rich(john))=>((~calm(john)<~>generous(john))))&
(((~generous(fred)<~>brave(fred)))<=>((humble(paul)|rich(paul))))&
(![X]:((~creative(X)|humble(X))<=>strong(X)))&
(((wise(lucy)&~rich(lucy)))=>((~funny(alice)<~>humble(alice))))&
(((strong(lucy)&~creative(lucy)))<=>((patient(susan)<~>~wise(susan))))&
(((~generous(alice)&strong(alice)))=>(?[X]:((generous(X)<~>~brave(X)))))&
(![X]:((~tall(X)|calm(X))<=>(strong(X)&funny(X))))&
((?[X]:((~generous(X)<~>~kind(X))))<=>((~old(alice)&~generous(alice))))&
(![X]:((~tall(X)&old(X))=>(wise(X)&~quiet(X))))&
(![X]:((happy(X)|humble(X))=>(~tall(X)&patient(X))))&
((?[X]:((wise(X)&tall(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:(happy(X)<=>generous(X)))&
(((old(fred)&quiet(fred)))<=>(?[X]:((~funny(X)&~quiet(X)))))&
(((~happy(alice)<~>~patient(alice)))<=>((creative(susan)<~>happy(susan))))&
(![X]:((happy(X)<~>strong(X))=>~patient(X)))&
((?[X]:((~kind(X)&tall(X))))<=>((~tall(alice)&~strong(alice))))&
((patient(susan)&~generous(susan)))&
(?[X]:(~old(X)))&
((~tall(paul)&~kind(paul)))&
(?[X]:((curious(X)|kind(X))))&
((~funny(alice)&brave(alice)))&
(quiet(lucy))&
(?[X]:((~funny(X)|old(X)))) | ~kind(susan) | [
"p6",
"p11",
"p14",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2117888441385966470207740
% SZS output start Proof for 2117888441385966470207740
7. ! [X0] : ((calm(X0) | ~tall(X0)) <=> (funny(X0) & strong(X0))) [input p6]
12. ! [X0] : (happy(X0) <=> generous(X0)) [input p11]
15. ! [X0] : ((happy(X0) <~> strong(X0)) => ~patient(X0)) [input p14]
16. ? [X0] : (tall(X0) & ~kind(X0)) <=> (~strong(alice) & ~tall(alice)) [input p15]
17. ~generous(susan) & patient(susan) [input p16]
21. brave(alice) & ~funny(alice) [input p20]
24. ~kind(susan) [input hypothesis]
36. ! [X0] : (~patient(X0) | (happy(X0) <=> strong(X0))) [ennf transformation 15]
48. ! [X0] : (((calm(X0) | ~tall(X0)) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | (~calm(X0) & tall(X0)))) [nnf transformation 7]
49. ! [X0] : ((calm(X0) | ~tall(X0) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | (~calm(X0) & tall(X0)))) [flattening 48]
59. ! [X0] : ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0))) [nnf transformation 12]
66. ! [X0] : (~patient(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) [nnf transformation 36]
67. (? [X0] : (tall(X0) & ~kind(X0)) | (strong(alice) | tall(alice))) & ((~strong(alice) & ~tall(alice)) | ! [X0] : (~tall(X0) | kind(X0))) [nnf transformation 16]
68. (? [X0] : (tall(X0) & ~kind(X0)) | strong(alice) | tall(alice)) & ((~strong(alice) & ~tall(alice)) | ! [X0] : (~tall(X0) | kind(X0))) [flattening 67]
69. (? [X0] : (tall(X0) & ~kind(X0)) | strong(alice) | tall(alice)) & ((~strong(alice) & ~tall(alice)) | ! [X1] : (~tall(X1) | kind(X1))) [rectify 68]
70. ? [X0] : (tall(X0) & ~kind(X0)) => (tall(sK4) & ~kind(sK4)) [choice axiom]
71. ((tall(sK4) & ~kind(sK4)) | strong(alice) | tall(alice)) & ((~strong(alice) & ~tall(alice)) | ! [X1] : (~tall(X1) | kind(X1))) [skolemisation 69,70]
97. tall(X0) | strong(X0) [cnf transformation 49]
99. tall(X0) | funny(X0) [cnf transformation 49]
116. ~happy(X0) | generous(X0) [cnf transformation 59]
131. ~patient(X0) | happy(X0) | ~strong(X0) [cnf transformation 66]
132. ~tall(alice) | ~tall(X1) | kind(X1) [cnf transformation 71]
136. patient(susan) [cnf transformation 17]
137. ~generous(susan) [cnf transformation 17]
141. ~funny(alice) [cnf transformation 21]
145. ~kind(susan) [cnf transformation 24]
191. 10 <=> funny(alice) [avatar definition]
192. ~funny(alice) <- (~10) [avatar component clause 191]
205. 13 <=> patient(susan) [avatar definition]
207. patient(susan) <- (13) [avatar component clause 205]
304. 33 <=> happy(susan) [avatar definition]
305. happy(susan) <- (33) [avatar component clause 304]
330. 37 <=> ! [X1] : (~tall(X1) | kind(X1)) [avatar definition]
331. ~tall(X1) | kind(X1) <- (37) [avatar component clause 330]
334. 38 <=> tall(alice) [avatar definition]
336. ~tall(alice) <- (~38) [avatar component clause 334]
337. 37 | ~38 [avatar split clause 132,334,330]
338. 13 [avatar split clause 136,205]
339. ~10 [avatar split clause 141,191]
358. funny(alice) <- (~38) [resolution 99,336]
359. $false <- (~10, ~38) [subsumption resolution 358,192]
360. 10 | 38 [avatar contradiction clause 359]
373. kind(X1) | strong(X1) <- (37) [resolution 331,97]
405. happy(susan) | ~strong(susan) <- (13) [resolution 131,207]
412. 46 <=> strong(susan) [avatar definition]
414. ~strong(susan) <- (~46) [avatar component clause 412]
415. ~46 | 33 | ~13 [avatar split clause 405,205,304,412]
417. generous(susan) <- (33) [resolution 305,116]
421. $false <- (33) [subsumption resolution 417,137]
422. ~33 [avatar contradiction clause 421]
449. strong(susan) <- (37) [resolution 373,145]
451. $false <- (37, ~46) [subsumption resolution 449,414]
452. ~37 | 46 [avatar contradiction clause 451]
453. $false [avatar sat refutation 337,338,339,360,415,422,452]
% SZS output end Proof for 2117888441385966470207740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or happy is either rich or patient.
Everyone who is both not generous and curious is humble.
Everyone who is quiet is humble.
Everyone who is not funny or not patient is not patient or not curious and vice versa.
Everyone who is strong is either old or rich and vice versa.
If susan is not calm then john is brave.
Everyone who is not quiet or creative is either not tall or not creative and vice versa.
If someone is not funny then alice is calm and vice versa.
Everyone who is both creative and old is both not calm and not curious.
If john is either not old or not tall then someone is not curious or old.
Everyone who is both not brave and curious is not tall and vice versa.
If fred is creative then mary is generous and vice versa.
Everyone who is not tall or not quiet is either happy or not calm and vice versa.
Everyone who is either patient or curious is generous or wise.
If someone is both kind and rich then someone is both rich and not generous and vice versa.
Everyone who is strong or not strong is patient or not tall and vice versa.
Lucy is both not patient and not generous.
Fred is calm or tall.
Someone is either not brave or not wise.
Alice is either quiet or not calm.
Mary is either old or brave.
Someone is either not old or not generous.
Someone is not old or not strong. | Mary is generous. | neutral | (![X]:((creative(X)<~>happy(X))=>(rich(X)<~>patient(X))))&
(![X]:((~generous(X)&curious(X))=>humble(X)))&
(![X]:(quiet(X)=>humble(X)))&
(![X]:((~funny(X)|~patient(X))<=>(~patient(X)|~curious(X))))&
(![X]:(strong(X)<=>(old(X)<~>rich(X))))&
((~calm(susan))=>(brave(john)))&
(![X]:((~quiet(X)|creative(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:(~funny(X)))<=>(calm(alice)))&
(![X]:((creative(X)&old(X))=>(~calm(X)&~curious(X))))&
(((~old(john)<~>~tall(john)))=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((~brave(X)&curious(X))<=>~tall(X)))&
((creative(fred))<=>(generous(mary)))&
(![X]:((~tall(X)|~quiet(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((patient(X)<~>curious(X))=>(generous(X)|wise(X))))&
((?[X]:((kind(X)&rich(X))))<=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((strong(X)|~strong(X))<=>(patient(X)|~tall(X))))&
((~patient(lucy)&~generous(lucy)))&
((calm(fred)|tall(fred)))&
(?[X]:((~brave(X)<~>~wise(X))))&
((quiet(alice)<~>~calm(alice)))&
((old(mary)<~>brave(mary)))&
(?[X]:((~old(X)<~>~generous(X))))&
(?[X]:((~old(X)|~strong(X)))) | generous(mary) | [] | null | 0 |
Everyone who is not creative is not humble or patient.
Everyone who is not funny or not happy is either not kind or quiet and vice versa.
Everyone who is both brave and not calm is both not curious and not creative.
Everyone who is both rich and not kind is both generous and quiet and vice versa.
If someone is rich then someone is not patient.
Everyone who is old is either not funny or quiet.
If paul is not happy then fred is both not creative and not funny and vice versa.
Everyone who is either not old or tall is either not generous or happy and vice versa.
Everyone who is not quiet is either not wise or wise and vice versa.
Everyone who is either not tall or not humble is wise or not happy and vice versa.
If fred is both quiet and tall then someone is either tall or not creative and vice versa.
If someone is not funny then someone is rich.
Everyone who is either not curious or not old is funny or not brave.
If mary is quiet or not generous then alice is either humble or quiet and vice versa.
If someone is both humble and not humble then someone is either tall or not creative and vice versa.
Everyone who is both not generous and old is either not quiet or not creative and vice versa.
Susan is either not old or not generous.
Someone is not curious.
Alice is patient.
Someone is either creative or not kind.
Someone is both not happy and not creative.
Alice is not brave.
Alice is old.
Someone is patient or not happy. | Paul is calm. | neutral | (![X]:(~creative(X)=>(~humble(X)|patient(X))))&
(![X]:((~funny(X)|~happy(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:((brave(X)&~calm(X))=>(~curious(X)&~creative(X))))&
(![X]:((rich(X)&~kind(X))<=>(generous(X)&quiet(X))))&
((?[X]:(rich(X)))=>(?[X]:(~patient(X))))&
(![X]:(old(X)=>(~funny(X)<~>quiet(X))))&
((~happy(paul))<=>((~creative(fred)&~funny(fred))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)<~>happy(X))))&
(![X]:(~quiet(X)<=>(~wise(X)<~>wise(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(wise(X)|~happy(X))))&
(((quiet(fred)&tall(fred)))<=>(?[X]:((tall(X)<~>~creative(X)))))&
((?[X]:(~funny(X)))=>(?[X]:(rich(X))))&
(![X]:((~curious(X)<~>~old(X))=>(funny(X)|~brave(X))))&
(((quiet(mary)|~generous(mary)))<=>((humble(alice)<~>quiet(alice))))&
((?[X]:((humble(X)&~humble(X))))<=>(?[X]:((tall(X)<~>~creative(X)))))&
(![X]:((~generous(X)&old(X))<=>(~quiet(X)<~>~creative(X))))&
((~old(susan)<~>~generous(susan)))&
(?[X]:(~curious(X)))&
(patient(alice))&
(?[X]:((creative(X)<~>~kind(X))))&
(?[X]:((~happy(X)&~creative(X))))&
(~brave(alice))&
(old(alice))&
(?[X]:((patient(X)|~happy(X)))) | calm(paul) | [] | null | 0 |
Everyone who is brave is both not wise and not kind. If paul is calm or kind then fred is not humble. If susan is patient or generous then someone is both not brave and not quiet. If alice is either happy or calm then susan is both not quiet and quiet. If john is either humble or not humble then someone is not generous and vice versa. Everyone who is not old is both funny and not patient. Everyone who is not kind or not generous is both tall and kind and vice versa. If someone is either tall or calm then mary is creative or not strong and vice versa. Everyone who is quiet is not generous or not kind and vice versa. If someone is either brave or not humble then mary is creative and vice versa. Everyone who is either old or curious is either calm or curious and vice versa. Everyone who is rich is either not brave or wise. If someone is tall or not wise then susan is either brave or not quiet. If someone is either tall or calm then fred is either not strong or not patient and vice versa. If lucy is not brave then john is both wise and calm and vice versa. Everyone who is not generous is either curious or rich and vice versa. Fred is both not rich and not quiet. Someone is either old or brave. Someone is not happy or tall. Someone is strong. Someone is tall or patient. Alice is either not generous or humble. | Alice is not brave. | entailment | (![X]:(brave(X)=>(~wise(X)&~kind(X))))&
(((calm(paul)|kind(paul)))=>(~humble(fred)))&
(((patient(susan)|generous(susan)))=>(?[X]:((~brave(X)&~quiet(X)))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:((old(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(![X]:(rich(X)=>(~brave(X)<~>wise(X))))&
((?[X]:((tall(X)|~wise(X))))=>((brave(susan)<~>~quiet(susan))))&
((?[X]:((tall(X)<~>calm(X))))<=>((~strong(fred)<~>~patient(fred))))&
((~brave(lucy))<=>((wise(john)&calm(john))))&
(![X]:(~generous(X)<=>(curious(X)<~>rich(X))))&
((~rich(fred)&~quiet(fred)))&
(?[X]:((old(X)<~>brave(X))))&
(?[X]:((~happy(X)|tall(X))))&
(?[X]:(strong(X)))&
(?[X]:((tall(X)|patient(X))))&
((~generous(alice)<~>humble(alice))) | ~brave(alice) | [
"p0",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2213014708690918120233004
% SZS output start Proof for 2213014708690918120233004
1. ! [X0] : (brave(X0) => (~kind(X0) & ~wise(X0))) [input p0]
7. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p6]
23. brave(alice) [input hypothesis]
25. ! [X0] : ((~kind(X0) & ~wise(X0)) | ~brave(X0)) [ennf transformation 1]
39. ! [X0] : (((~generous(X0) | ~kind(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 7]
40. ! [X0] : ((~generous(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [flattening 39]
73. ~kind(X0) | ~brave(X0) [cnf transformation 25]
91. kind(X0) | kind(X0) [cnf transformation 40]
145. brave(alice) [cnf transformation 23]
150. kind(X0) [duplicate literal removal 91]
357. ~brave(X0) [resolution 73,150]
358. $false [resolution 357,145]
% SZS output end Proof for 2213014708690918120233004
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not funny is not rich and vice versa. Everyone who is not rich is not quiet or not tall and vice versa. Everyone who is humble is kind or rich. If someone is both humble and not quiet then mary is funny or not generous. Everyone who is either humble or quiet is not rich and vice versa. If someone is funny then mary is both not curious and curious. Everyone who is happy or not rich is not patient. If someone is brave then fred is both not brave and not humble. If fred is tall or rich then mary is either not patient or creative and vice versa. Everyone who is not curious or not quiet is humble. Everyone who is not wise is either not creative or generous and vice versa. Everyone who is either old or not happy is either not generous or happy and vice versa. If someone is both not curious and happy then someone is either not brave or curious. Everyone who is curious is not funny or brave and vice versa. If alice is either not rich or wise then someone is rich. If mary is tall then alice is old. Susan is either generous or calm. Susan is rich or wise. Someone is not strong or quiet. John is either not tall or quiet. Someone is either kind or not rich. Someone is not strong. Someone is old or creative. | Susan is not humble. | contradiction | (![X]:((~brave(X)<~>~funny(X))<=>~rich(X)))&
(![X]:(~rich(X)<=>(~quiet(X)|~tall(X))))&
(![X]:(humble(X)=>(kind(X)|rich(X))))&
((?[X]:((humble(X)&~quiet(X))))=>((funny(mary)|~generous(mary))))&
(![X]:((humble(X)<~>quiet(X))<=>~rich(X)))&
((?[X]:(funny(X)))=>((~curious(mary)&curious(mary))))&
(![X]:((happy(X)|~rich(X))=>~patient(X)))&
((?[X]:(brave(X)))=>((~brave(fred)&~humble(fred))))&
(((tall(fred)|rich(fred)))<=>((~patient(mary)<~>creative(mary))))&
(![X]:((~curious(X)|~quiet(X))=>humble(X)))&
(![X]:(~wise(X)<=>(~creative(X)<~>generous(X))))&
(![X]:((old(X)<~>~happy(X))<=>(~generous(X)<~>happy(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~brave(X)<~>curious(X)))))&
(![X]:(curious(X)<=>(~funny(X)|brave(X))))&
(((~rich(alice)<~>wise(alice)))=>(?[X]:(rich(X))))&
((tall(mary))=>(old(alice)))&
((generous(susan)<~>calm(susan)))&
((rich(susan)|wise(susan)))&
(?[X]:((~strong(X)|quiet(X))))&
((~tall(john)<~>quiet(john)))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:(~strong(X)))&
(?[X]:((old(X)|creative(X)))) | ~humble(susan) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6530678772788443169961600
% SZS output start Proof for 6530678772788443169961600
1. ! [X0] : ((~brave(X0) <~> ~funny(X0)) <=> ~rich(X0)) [input p0]
2. ! [X0] : (~rich(X0) <=> (~tall(X0) | ~quiet(X0))) [input p1]
5. ! [X0] : ((humble(X0) <~> quiet(X0)) <=> ~rich(X0)) [input p4]
6. ? [X0] : funny(X0) => (curious(mary) & ~curious(mary)) [input p5]
8. ? [X0] : brave(X0) => (~humble(fred) & ~brave(fred)) [input p7]
24. ~humble(susan) [input hypothesis]
32. (curious(mary) & ~curious(mary)) | ! [X0] : ~funny(X0) [ennf transformation 6]
34. (~humble(fred) & ~brave(fred)) | ! [X0] : ~brave(X0) [ennf transformation 8]
39. ! [X0] : ((((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | rich(X0)) & (~rich(X0) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0))))) [nnf transformation 1]
40. ! [X0] : ((~rich(X0) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | rich(X0))) [nnf transformation 2]
41. ! [X0] : ((~rich(X0) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | rich(X0))) [flattening 40]
42. ! [X0] : ((((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | rich(X0)) & (~rich(X0) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0))))) [nnf transformation 5]
66. rich(X0) | brave(X0) | funny(X0) [cnf transformation 39]
68. ~rich(X0) | quiet(X0) [cnf transformation 41]
73. ~rich(X0) | humble(X0) | ~quiet(X0) [cnf transformation 42]
74. quiet(X0) | humble(X0) | rich(X0) [cnf transformation 42]
76. ~curious(mary) | ~funny(X0) [cnf transformation 32]
77. curious(mary) | ~funny(X0) [cnf transformation 32]
80. ~brave(fred) | ~brave(X0) [cnf transformation 34]
81. ~humble(fred) | ~brave(X0) [cnf transformation 34]
118. ~humble(susan) [cnf transformation 24]
135. humble(X0) | quiet(X0) [subsumption resolution 74,68]
136. ~rich(X0) | humble(X0) [subsumption resolution 73,135]
138. 4 <=> ! [X0] : ~funny(X0) [avatar definition]
139. ~funny(X0) <- (4) [avatar component clause 138]
141. 5 <=> curious(mary) [avatar definition]
144. 4 | 5 [avatar split clause 77,141,138]
145. 4 | ~5 [avatar split clause 76,141,138]
147. 6 <=> ! [X0] : ~brave(X0) [avatar definition]
148. ~brave(X0) <- (6) [avatar component clause 147]
150. 7 <=> humble(fred) [avatar definition]
153. 6 | ~7 [avatar split clause 81,150,147]
155. 8 <=> brave(fred) [avatar definition]
157. ~brave(fred) <- (~8) [avatar component clause 155]
158. 6 | ~8 [avatar split clause 80,155,147]
176. 12 <=> rich(fred) [avatar definition]
177. rich(fred) <- (12) [avatar component clause 176]
178. ~rich(fred) <- (~12) [avatar component clause 176]
232. 23 <=> rich(susan) [avatar definition]
233. ~rich(susan) <- (~23) [avatar component clause 232]
234. rich(susan) <- (23) [avatar component clause 232]
278. humble(susan) <- (23) [resolution 136,234]
279. $false <- (23) [subsumption resolution 278,118]
280. ~23 [avatar contradiction clause 279]
290. brave(fred) | funny(fred) <- (~12) [resolution 66,178]
292. brave(susan) | funny(susan) <- (~23) [resolution 66,233]
299. funny(fred) <- (~8, ~12) [subsumption resolution 290,157]
300. $false <- (4, ~8, ~12) [subsumption resolution 299,139]
301. ~4 | 8 | 12 [avatar contradiction clause 300]
303. brave(susan) <- (4, ~23) [subsumption resolution 292,139]
307. humble(fred) <- (12) [resolution 177,136]
312. 7 | ~12 [avatar split clause 307,176,150]
328. $false <- (4, 6, ~23) [resolution 303,148]
330. ~4 | ~6 | 23 [avatar contradiction clause 328]
331. $false [avatar sat refutation 144,145,153,158,280,301,312,330]
% SZS output end Proof for 6530678772788443169961600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not happy then someone is quiet or humble and vice versa. Everyone who is not funny or not kind is either not tall or humble. Everyone who is either rich or funny is not calm or not funny. If someone is both not old and not quiet then john is not tall and vice versa. If fred is both not patient and not wise then someone is either not funny or not brave and vice versa. 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. Everyone who is not tall or quiet is either not patient or not strong. If someone is not funny or not happy then someone is not tall. John is either generous or wise. Someone is not generous. Susan is strong or old. Someone is generous or not creative. Alice is either calm or not patient. Someone is curious. Paul is tall or happy. Someone is either humble or not happy. | Alice is quiet. | neutral | (((~patient(fred)<~>~happy(fred)))<=>(?[X]:((quiet(X)|humble(X)))))&
(![X]:((~funny(X)|~kind(X))=>(~tall(X)<~>humble(X))))&
(![X]:((rich(X)<~>funny(X))=>(~calm(X)|~funny(X))))&
((?[X]:((~old(X)&~quiet(X))))<=>(~tall(john)))&
(((~patient(fred)&~wise(fred)))<=>(?[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]:((~tall(X)|quiet(X))=>(~patient(X)<~>~strong(X))))&
((?[X]:((~funny(X)|~happy(X))))=>(?[X]:(~tall(X))))&
((generous(john)<~>wise(john)))&
(?[X]:(~generous(X)))&
((strong(susan)|old(susan)))&
(?[X]:((generous(X)|~creative(X))))&
((calm(alice)<~>~patient(alice)))&
(?[X]:(curious(X)))&
((tall(paul)|happy(paul)))&
(?[X]:((humble(X)<~>~happy(X)))) | quiet(alice) | [] | null | 0 |
If someone is not generous then paul is not strong.
If someone is either calm or happy then paul is both not generous and not old.
Everyone who is both not tall and tall is not kind and vice versa.
If fred is either not kind or happy then someone is both not creative and wise.
If someone is brave then someone is rich or generous and vice versa.
Everyone who is not calm is old.
If someone is kind or not generous then someone is either tall or old.
Everyone who is both patient and rich is calm or not kind and vice versa.
If someone is both brave and kind then paul is both old and quiet.
If susan is patient then someone is both not strong and happy.
If lucy is both not patient and not wise then mary is creative.
Everyone who is both not tall and not wise is both quiet and strong.
Everyone who is not rich is either not happy or calm and vice versa.
Everyone who is both not rich and not wise is old.
If john is either not generous or not calm then someone is both not wise and kind and vice versa.
If alice is not old or not kind then someone is both not strong and not funny and vice versa.
Someone is not quiet.
Fred is both not curious and tall.
John is both not funny and not calm.
Alice is either not funny or not strong.
Mary is either not quiet or brave.
John is not creative or calm.
Paul is either not quiet or brave.
Fred is happy or not happy. | Lucy is not calm. | entailment | ((?[X]:(~generous(X)))=>(~strong(paul)))&
((?[X]:((calm(X)<~>happy(X))))=>((~generous(paul)&~old(paul))))&
(![X]:((~tall(X)&tall(X))<=>~kind(X)))&
(((~kind(fred)<~>happy(fred)))=>(?[X]:((~creative(X)&wise(X)))))&
((?[X]:(brave(X)))<=>(?[X]:((rich(X)|generous(X)))))&
(![X]:(~calm(X)=>old(X)))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((patient(X)&rich(X))<=>(calm(X)|~kind(X))))&
((?[X]:((brave(X)&kind(X))))=>((old(paul)&quiet(paul))))&
((patient(susan))=>(?[X]:((~strong(X)&happy(X)))))&
(((~patient(lucy)&~wise(lucy)))=>(creative(mary)))&
(![X]:((~tall(X)&~wise(X))=>(quiet(X)&strong(X))))&
(![X]:(~rich(X)<=>(~happy(X)<~>calm(X))))&
(![X]:((~rich(X)&~wise(X))=>old(X)))&
(((~generous(john)<~>~calm(john)))<=>(?[X]:((~wise(X)&kind(X)))))&
(((~old(alice)|~kind(alice)))<=>(?[X]:((~strong(X)&~funny(X)))))&
(?[X]:(~quiet(X)))&
((~curious(fred)&tall(fred)))&
((~funny(john)&~calm(john)))&
((~funny(alice)<~>~strong(alice)))&
((~quiet(mary)<~>brave(mary)))&
((~creative(john)|calm(john)))&
((~quiet(paul)<~>brave(paul)))&
((happy(fred)|~happy(fred))) | ~calm(lucy) | [
"p1",
"p2",
"p4",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7601793192478579826341772
% SZS output start Proof for 7601793192478579826341772
2. ? [X0] : (calm(X0) <~> happy(X0)) => (~old(paul) & ~generous(paul)) [input p1]
3. ! [X0] : ((tall(X0) & ~tall(X0)) <=> ~kind(X0)) [input p2]
5. ? [X0] : brave(X0) <=> ? [X0] : (generous(X0) | rich(X0)) [input p4]
8. ! [X0] : ((rich(X0) & patient(X0)) <=> (~kind(X0) | calm(X0))) [input p7]
9. ? [X0] : (kind(X0) & brave(X0)) => (quiet(paul) & old(paul)) [input p8]
13. ! [X0] : (~rich(X0) <=> (~happy(X0) <~> calm(X0))) [input p12]
25. calm(lucy) [input hypothesis]
26. ? [X0] : brave(X0) <=> ? [X1] : (generous(X1) | rich(X1)) [rectify 5]
30. (~old(paul) & ~generous(paul)) | ! [X0] : (calm(X0) <=> happy(X0)) [ennf transformation 2]
34. (quiet(paul) & old(paul)) | ! [X0] : (~kind(X0) | ~brave(X0)) [ennf transformation 9]
42. (~old(paul) & ~generous(paul)) | ! [X0] : ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))) [nnf transformation 30]
43. ! [X0] : (((tall(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | (~tall(X0) | tall(X0)))) [nnf transformation 3]
44. ! [X0] : (((tall(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | ~tall(X0) | tall(X0))) [flattening 43]
48. (? [X0] : brave(X0) | ! [X1] : (~generous(X1) & ~rich(X1))) & (? [X1] : (generous(X1) | rich(X1)) | ! [X0] : ~brave(X0)) [nnf transformation 26]
49. (? [X0] : brave(X0) | ! [X1] : (~generous(X1) & ~rich(X1))) & (? [X2] : (generous(X2) | rich(X2)) | ! [X3] : ~brave(X3)) [rectify 48]
50. ? [X0] : brave(X0) => brave(sK1) [choice axiom]
51. ? [X2] : (generous(X2) | rich(X2)) => (generous(sK2) | rich(sK2)) [choice axiom]
52. (brave(sK1) | ! [X1] : (~generous(X1) & ~rich(X1))) & ((generous(sK2) | rich(sK2)) | ! [X3] : ~brave(X3)) [skolemisation 49,51,50]
57. ! [X0] : (((rich(X0) & patient(X0)) | (kind(X0) & ~calm(X0))) & ((~kind(X0) | calm(X0)) | (~rich(X0) | ~patient(X0)))) [nnf transformation 8]
58. ! [X0] : (((rich(X0) & patient(X0)) | (kind(X0) & ~calm(X0))) & (~kind(X0) | calm(X0) | ~rich(X0) | ~patient(X0))) [flattening 57]
61. ! [X0] : ((~rich(X0) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0)))) & (((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | rich(X0))) [nnf transformation 13]
79. ~old(paul) | happy(X0) | ~calm(X0) [cnf transformation 42]
82. ~tall(X0) | kind(X0) [cnf transformation 44]
83. kind(X0) | tall(X0) [cnf transformation 44]
89. brave(sK1) | ~rich(X1) [cnf transformation 52]
99. ~calm(X0) | rich(X0) [cnf transformation 58]
101. old(paul) | ~kind(X0) | ~brave(X0) [cnf transformation 34]
111. ~rich(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 61]
136. calm(lucy) [cnf transformation 25]
149. 4 <=> old(paul) [avatar definition]
154. 5 <=> ! [X0] : (happy(X0) | ~calm(X0)) [avatar definition]
155. happy(X0) | ~calm(X0) <- (5) [avatar component clause 154]
156. 5 | ~4 [avatar split clause 79,149,154]
163. kind(X0) [subsumption resolution 82,83]
184. 11 <=> brave(sK1) [avatar definition]
186. brave(sK1) <- (11) [avatar component clause 184]
189. 12 <=> ! [X1] : ~rich(X1) [avatar definition]
190. ~rich(X1) <- (12) [avatar component clause 189]
191. 12 | 11 [avatar split clause 89,184,189]
193. 13 <=> ! [X3] : ~brave(X3) [avatar definition]
194. ~brave(X3) <- (13) [avatar component clause 193]
225. old(paul) | ~brave(X0) [subsumption resolution 101,163]
226. 13 | 4 [avatar split clause 225,149,193]
254. ~happy(X0) | ~calm(X0) [subsumption resolution 111,99]
328. $false <- (11, 13) [subsumption resolution 186,194]
329. ~11 | ~13 [avatar contradiction clause 328]
339. rich(lucy) [resolution 99,136]
341. $false <- (12) [subsumption resolution 339,190]
342. ~12 [avatar contradiction clause 341]
345. ~calm(X0) <- (5) [subsumption resolution 155,254]
347. $false <- (5) [resolution 345,136]
348. ~5 [avatar contradiction clause 347]
349. $false [avatar sat refutation 156,191,226,329,342,348]
% SZS output end Proof for 7601793192478579826341772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or funny then someone is not funny and vice versa.
Everyone who is not patient is both brave and not brave.
If someone is both not calm and not kind then someone is either not tall or old and vice versa.
Everyone who is not brave is not tall and vice versa.
Everyone who is happy is not patient.
If paul is old or not creative then lucy is either not wise or not calm and vice versa.
If lucy is both not happy and not patient then susan is both not brave and happy.
If fred is either not rich or not strong then someone is not humble.
Everyone who is either not happy or rich is both old and not old and vice versa.
If fred is either quiet or strong then someone is both old and not quiet and vice versa.
If someone is happy or strong then someone is either kind or happy.
Everyone who is both calm and not brave is not funny or not brave.
Everyone who is not creative is not patient.
Everyone who is both funny and not tall is both kind and not brave.
If someone is both rich and not creative then paul is both not calm and wise and vice versa.
If paul is not funny or old then fred is not rich and vice versa.
Lucy is either not patient or calm.
John is both not old and not quiet.
Someone is both generous and strong.
John is generous.
Someone is not funny.
Alice is both wise and not calm.
Lucy is both not brave and creative. | Lucy is not wise. | contradiction | ((?[X]:((~funny(X)|funny(X))))<=>(?[X]:(~funny(X))))&
(![X]:(~patient(X)=>(brave(X)&~brave(X))))&
((?[X]:((~calm(X)&~kind(X))))<=>(?[X]:((~tall(X)<~>old(X)))))&
(![X]:(~brave(X)<=>~tall(X)))&
(![X]:(happy(X)=>~patient(X)))&
(((old(paul)|~creative(paul)))<=>((~wise(lucy)<~>~calm(lucy))))&
(((~happy(lucy)&~patient(lucy)))=>((~brave(susan)&happy(susan))))&
(((~rich(fred)<~>~strong(fred)))=>(?[X]:(~humble(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(old(X)&~old(X))))&
(((quiet(fred)<~>strong(fred)))<=>(?[X]:((old(X)&~quiet(X)))))&
((?[X]:((happy(X)|strong(X))))=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((calm(X)&~brave(X))=>(~funny(X)|~brave(X))))&
(![X]:(~creative(X)=>~patient(X)))&
(![X]:((funny(X)&~tall(X))=>(kind(X)&~brave(X))))&
((?[X]:((rich(X)&~creative(X))))<=>((~calm(paul)&wise(paul))))&
(((~funny(paul)|old(paul)))<=>(~rich(fred)))&
((~patient(lucy)<~>calm(lucy)))&
((~old(john)&~quiet(john)))&
(?[X]:((generous(X)&strong(X))))&
(generous(john))&
(?[X]:(~funny(X)))&
((wise(alice)&~calm(alice)))&
((~brave(lucy)&creative(lucy))) | ~wise(lucy) | [
"p1",
"p4",
"p5",
"p8",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6627389395490073835175692
% SZS output start Proof for 6627389395490073835175692
2. ! [X0] : (~patient(X0) => (~brave(X0) & brave(X0))) [input p1]
5. ! [X0] : (happy(X0) => ~patient(X0)) [input p4]
6. (~creative(paul) | old(paul)) <=> (~wise(lucy) <~> ~calm(lucy)) [input p5]
9. ! [X0] : ((~happy(X0) <~> rich(X0)) <=> (~old(X0) & old(X0))) [input p8]
13. ! [X0] : (~creative(X0) => ~patient(X0)) [input p12]
16. (old(paul) | ~funny(paul)) <=> ~rich(fred) [input p15]
17. ~patient(lucy) <~> calm(lucy) [input p16]
24. ~wise(lucy) [input hypothesis]
31. ! [X0] : ((~brave(X0) & brave(X0)) | patient(X0)) [ennf transformation 2]
32. ! [X0] : (~patient(X0) | ~happy(X0)) [ennf transformation 5]
38. ! [X0] : (~patient(X0) | creative(X0)) [ennf transformation 13]
52. ((~creative(paul) | old(paul)) | ((~wise(lucy) | calm(lucy)) & (~calm(lucy) | wise(lucy)))) & (((calm(lucy) | wise(lucy)) & (~calm(lucy) | ~wise(lucy))) | (creative(paul) & ~old(paul))) [nnf transformation 6]
53. (~creative(paul) | old(paul) | ((~wise(lucy) | calm(lucy)) & (~calm(lucy) | wise(lucy)))) & (((calm(lucy) | wise(lucy)) & (~calm(lucy) | ~wise(lucy))) | (creative(paul) & ~old(paul))) [flattening 52]
54. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (old(X0) | ~old(X0))) & ((~old(X0) & old(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | old(X0) | ~old(X0)) & ((~old(X0) & old(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [flattening 54]
69. ((old(paul) | ~funny(paul)) | rich(fred)) & (~rich(fred) | (~old(paul) & funny(paul))) [nnf transformation 16]
70. (old(paul) | ~funny(paul) | rich(fred)) & (~rich(fred) | (~old(paul) & funny(paul))) [flattening 69]
71. (~calm(lucy) | patient(lucy)) & (calm(lucy) | ~patient(lucy)) [nnf transformation 17]
79. brave(X0) | patient(X0) [cnf transformation 31]
80. ~brave(X0) | patient(X0) [cnf transformation 31]
89. ~patient(X0) | ~happy(X0) [cnf transformation 32]
94. ~creative(paul) | old(paul) | ~calm(lucy) | wise(lucy) [cnf transformation 53]
98. old(X0) | rich(X0) | happy(X0) [cnf transformation 55]
100. ~old(X0) | rich(X0) | happy(X0) [cnf transformation 55]
115. ~patient(X0) | creative(X0) [cnf transformation 38]
123. ~rich(fred) | ~old(paul) [cnf transformation 70]
125. calm(lucy) | ~patient(lucy) [cnf transformation 71]
135. ~wise(lucy) [cnf transformation 24]
148. patient(X0) [subsumption resolution 79,80]
180. ~happy(X0) [subsumption resolution 89,148]
182. 11 <=> calm(lucy) [avatar definition]
186. 12 <=> wise(lucy) [avatar definition]
190. 13 <=> old(paul) [avatar definition]
194. 14 <=> creative(paul) [avatar definition]
196. ~creative(paul) <- (~14) [avatar component clause 194]
198. 12 | ~11 | 13 | ~14 [avatar split clause 94,194,190,182,186]
203. ~old(X0) | rich(X0) [subsumption resolution 100,180]
204. old(X0) | rich(X0) [subsumption resolution 98,180]
205. rich(X0) [subsumption resolution 204,203]
240. creative(X0) [subsumption resolution 115,148]
251. ~old(paul) [subsumption resolution 123,205]
252. ~13 [avatar split clause 251,190]
254. calm(lucy) [subsumption resolution 125,148]
255. 11 [avatar split clause 254,182]
256. ~12 [avatar split clause 135,186]
257. $false <- (~14) [subsumption resolution 196,240]
258. 14 [avatar contradiction clause 257]
259. $false [avatar sat refutation 198,252,255,256,258]
% SZS output end Proof for 6627389395490073835175692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not rich then someone is rich and vice versa. Everyone who is not happy or happy is not kind and vice versa. Everyone who is both creative and not curious is either kind or humble. Everyone who is strong is both not wise and curious. If john is both wise and generous then someone is happy. If someone is both quiet and rich then someone is creative and vice versa. If fred is either humble or calm then someone is either kind or happy and vice versa. Everyone who is both not kind and not rich is both not creative and generous and vice versa. Everyone who is either wise or not happy is not wise. Everyone who is strong is not quiet. Everyone who is both not funny and not wise is funny or not funny and vice versa. If someone is either not kind or not happy then someone is either not wise or wise. Everyone who is not quiet or happy is not tall and vice versa. If someone is both strong and calm then someone is generous or not strong. If someone is either not creative or not old then someone is either humble or wise. Alice is either not calm or creative. Fred is patient or not rich. Someone is either calm or not wise. Paul is both not curious and not quiet. Fred is not wise. | John is not generous. | contradiction | ((?[X]:((creative(X)&~rich(X))))<=>(?[X]:(rich(X))))&
(![X]:((~happy(X)|happy(X))<=>~kind(X)))&
(![X]:((creative(X)&~curious(X))=>(kind(X)<~>humble(X))))&
(![X]:(strong(X)=>(~wise(X)&curious(X))))&
(((wise(john)&generous(john)))=>(?[X]:(happy(X))))&
((?[X]:((quiet(X)&rich(X))))<=>(?[X]:(creative(X))))&
(((humble(fred)<~>calm(fred)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(~creative(X)&generous(X))))&
(![X]:((wise(X)<~>~happy(X))=>~wise(X)))&
(![X]:(strong(X)=>~quiet(X)))&
(![X]:((~funny(X)&~wise(X))<=>(funny(X)|~funny(X))))&
((?[X]:((~kind(X)<~>~happy(X))))=>(?[X]:((~wise(X)<~>wise(X)))))&
(![X]:((~quiet(X)|happy(X))<=>~tall(X)))&
((?[X]:((strong(X)&calm(X))))=>(?[X]:((generous(X)|~strong(X)))))&
((?[X]:((~creative(X)<~>~old(X))))=>(?[X]:((humble(X)<~>wise(X)))))&
((~calm(alice)<~>creative(alice)))&
((patient(fred)|~rich(fred)))&
(?[X]:((calm(X)<~>~wise(X))))&
((~curious(paul)&~quiet(paul)))&
(~wise(fred)) | ~generous(john) | [
"p0",
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3986790317244807612434849
% SZS output start Proof for 3986790317244807612434849
1. ? [X0] : (~rich(X0) & creative(X0)) <=> ? [X0] : rich(X0) [input p0]
2. ! [X0] : ((happy(X0) | ~happy(X0)) <=> ~kind(X0)) [input p1]
8. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (generous(X0) & ~creative(X0))) [input p7]
21. ~generous(john) [input hypothesis]
22. ? [X0] : (~rich(X0) & creative(X0)) <=> ? [X1] : rich(X1) [rectify 1]
38. (? [X0] : (~rich(X0) & creative(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (rich(X0) | ~creative(X0))) [nnf transformation 22]
39. (? [X0] : (~rich(X0) & creative(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (rich(X3) | ~creative(X3))) [rectify 38]
40. ? [X0] : (~rich(X0) & creative(X0)) => (~rich(sK0) & creative(sK0)) [choice axiom]
41. ? [X2] : rich(X2) => rich(sK1) [choice axiom]
42. ((~rich(sK0) & creative(sK0)) | ! [X1] : ~rich(X1)) & (rich(sK1) | ! [X3] : (rich(X3) | ~creative(X3))) [skolemisation 39,41,40]
43. ! [X0] : (((happy(X0) | ~happy(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) & happy(X0)))) [nnf transformation 2]
44. ! [X0] : ((happy(X0) | ~happy(X0) | kind(X0)) & (~kind(X0) | (~happy(X0) & happy(X0)))) [flattening 43]
57. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~generous(X0) | creative(X0))) & ((generous(X0) & ~creative(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 8]
58. ! [X0] : (((~rich(X0) & ~kind(X0)) | ~generous(X0) | creative(X0)) & ((generous(X0) & ~creative(X0)) | rich(X0) | kind(X0))) [flattening 57]
75. creative(sK0) | ~rich(X1) [cnf transformation 42]
76. ~rich(sK0) | ~rich(X1) [cnf transformation 42]
77. ~kind(X0) | happy(X0) [cnf transformation 44]
78. ~kind(X0) | ~happy(X0) [cnf transformation 44]
94. ~creative(X0) | rich(X0) | kind(X0) [cnf transformation 58]
95. generous(X0) | rich(X0) | kind(X0) [cnf transformation 58]
120. ~generous(john) [cnf transformation 21]
125. 1 <=> ! [X1] : ~rich(X1) [avatar definition]
126. ~rich(X1) <- (1) [avatar component clause 125]
128. 2 <=> rich(sK0) [avatar definition]
130. ~rich(sK0) <- (~2) [avatar component clause 128]
131. 1 | ~2 [avatar split clause 76,128,125]
133. 3 <=> creative(sK0) [avatar definition]
135. creative(sK0) <- (3) [avatar component clause 133]
136. 1 | 3 [avatar split clause 75,133,125]
138. 4 <=> ! [X3] : (rich(X3) | ~creative(X3)) [avatar definition]
139. ~creative(X3) | rich(X3) <- (4) [avatar component clause 138]
145. ~kind(X0) [subsumption resolution 77,78]
152. 7 <=> generous(john) [avatar definition]
154. ~generous(john) <- (~7) [avatar component clause 152]
204. generous(X0) | rich(X0) [subsumption resolution 95,145]
205. ~creative(X0) | rich(X0) [subsumption resolution 94,145]
206. 4 [avatar split clause 205,138]
233. ~7 [avatar split clause 120,152]
236. rich(sK0) <- (3, 4) [resolution 139,135]
237. $false <- (~2, 3, 4) [subsumption resolution 236,130]
238. 2 | ~3 | ~4 [avatar contradiction clause 237]
242. rich(john) <- (~7) [resolution 204,154]
243. $false <- (1, ~7) [subsumption resolution 242,126]
244. ~1 | 7 [avatar contradiction clause 243]
245. $false [avatar sat refutation 131,136,206,233,238,244]
% SZS output end Proof for 3986790317244807612434849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or creative is either old or not curious.
If alice is both not brave and funny then someone is either not rich or brave and vice versa.
Everyone who is both old and not kind is quiet or wise.
Everyone who is humble or curious is both not calm and old and vice versa.
If fred is either happy or not patient then fred is either brave or not strong.
Everyone who is either old or not generous is either strong or old.
If mary is not strong or not quiet then john is not patient.
Everyone who is both not patient and patient is old or calm and vice versa.
If someone is generous then lucy is either happy or tall and vice versa.
Everyone who is either old or not happy is both quiet and not old.
Everyone who is either old or not old is both funny and not happy.
Everyone who is either curious or old is brave and vice versa.
Everyone who is either not quiet or not humble is not rich.
If john is both not quiet and brave then someone is either not wise or quiet and vice versa.
If someone is both not wise and not strong then fred is both not old and not kind.
Everyone who is quiet is both not curious and not patient.
Lucy is kind.
Fred is either wise or quiet.
Mary is not kind.
Paul is quiet or not humble.
Someone is both strong and not generous.
Susan is quiet or not patient.
Mary is patient or not brave. | John is not wise. | entailment | (![X]:((generous(X)|creative(X))=>(old(X)<~>~curious(X))))&
(((~brave(alice)&funny(alice)))<=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((old(X)&~kind(X))=>(quiet(X)|wise(X))))&
(![X]:((humble(X)|curious(X))<=>(~calm(X)&old(X))))&
(((happy(fred)<~>~patient(fred)))=>((brave(fred)<~>~strong(fred))))&
(![X]:((old(X)<~>~generous(X))=>(strong(X)<~>old(X))))&
(((~strong(mary)|~quiet(mary)))=>(~patient(john)))&
(![X]:((~patient(X)&patient(X))<=>(old(X)|calm(X))))&
((?[X]:(generous(X)))<=>((happy(lucy)<~>tall(lucy))))&
(![X]:((old(X)<~>~happy(X))=>(quiet(X)&~old(X))))&
(![X]:((old(X)<~>~old(X))=>(funny(X)&~happy(X))))&
(![X]:((curious(X)<~>old(X))<=>brave(X)))&
(![X]:((~quiet(X)<~>~humble(X))=>~rich(X)))&
(((~quiet(john)&brave(john)))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
((?[X]:((~wise(X)&~strong(X))))=>((~old(fred)&~kind(fred))))&
(![X]:(quiet(X)=>(~curious(X)&~patient(X))))&
(kind(lucy))&
((wise(fred)<~>quiet(fred)))&
(~kind(mary))&
((quiet(paul)|~humble(paul)))&
(?[X]:((strong(X)&~generous(X))))&
((quiet(susan)|~patient(susan)))&
((patient(mary)|~brave(mary))) | ~wise(john) | [
"p7",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 866084565851434034785726
% SZS output start Proof for 866084565851434034785726
8. ! [X0] : ((patient(X0) & ~patient(X0)) <=> (calm(X0) | old(X0))) [input p7]
10. ! [X0] : ((old(X0) <~> ~happy(X0)) => (~old(X0) & quiet(X0))) [input p9]
11. ! [X0] : ((old(X0) <~> ~old(X0)) => (~happy(X0) & funny(X0))) [input p10]
14. (brave(john) & ~quiet(john)) <=> ? [X0] : (~wise(X0) <~> quiet(X0)) [input p13]
24. wise(john) [input hypothesis]
32. ! [X0] : ((~old(X0) & quiet(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 10]
33. ! [X0] : ((~happy(X0) & funny(X0)) | (old(X0) <=> ~old(X0))) [ennf transformation 11]
47. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & ((calm(X0) | old(X0)) | (~patient(X0) | patient(X0)))) [nnf transformation 8]
48. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & (calm(X0) | old(X0) | ~patient(X0) | patient(X0))) [flattening 47]
53. ! [X0] : ((~old(X0) & quiet(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 32]
54. ! [X0] : ((~happy(X0) & funny(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 33]
57. ((brave(john) & ~quiet(john)) | ! [X0] : ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (? [X0] : ((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | (~brave(john) | quiet(john))) [nnf transformation 14]
58. ((brave(john) & ~quiet(john)) | ! [X0] : ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (? [X0] : ((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | ~brave(john) | quiet(john)) [flattening 57]
59. ((brave(john) & ~quiet(john)) | ! [X0] : ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (? [X1] : ((~quiet(X1) | wise(X1)) & (quiet(X1) | ~wise(X1))) | ~brave(john) | quiet(john)) [rectify 58]
60. ? [X1] : ((~quiet(X1) | wise(X1)) & (quiet(X1) | ~wise(X1))) => ((~quiet(sK2) | wise(sK2)) & (quiet(sK2) | ~wise(sK2))) [choice axiom]
61. ((brave(john) & ~quiet(john)) | ! [X0] : ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(sK2) | wise(sK2)) & (quiet(sK2) | ~wise(sK2))) | ~brave(john) | quiet(john)) [skolemisation 59,60]
90. ~patient(X0) | ~old(X0) [cnf transformation 48]
92. ~old(X0) | patient(X0) [cnf transformation 48]
99. quiet(X0) | old(X0) | happy(X0) [cnf transformation 53]
105. ~happy(X0) | old(X0) | old(X0) [cnf transformation 54]
115. ~quiet(john) | ~wise(X0) | ~quiet(X0) [cnf transformation 61]
131. wise(john) [cnf transformation 24]
135. ~happy(X0) | old(X0) [duplicate literal removal 105]
202. ~old(X0) [subsumption resolution 90,92]
222. happy(X0) | quiet(X0) [subsumption resolution 99,202]
223. ~happy(X0) [subsumption resolution 135,202]
227. 18 <=> ! [X0] : (~wise(X0) | ~quiet(X0)) [avatar definition]
228. ~wise(X0) | ~quiet(X0) <- (18) [avatar component clause 227]
239. 21 <=> quiet(john) [avatar definition]
241. ~quiet(john) <- (~21) [avatar component clause 239]
242. 18 | ~21 [avatar split clause 115,239,227]
291. quiet(X0) [resolution 222,223]
294. $false <- (~21) [resolution 291,241]
297. 21 [avatar contradiction clause 294]
299. ~wise(X0) <- (18) [subsumption resolution 228,291]
300. $false <- (18) [resolution 299,131]
301. ~18 [avatar contradiction clause 300]
302. $false [avatar sat refutation 242,297,301]
% SZS output end Proof for 866084565851434034785726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or quiet is not rich or not generous and vice versa.
Everyone who is either quiet or tall is both not generous and funny.
Everyone who is not old is either not tall or not patient.
Everyone who is not old or not funny is either not wise or creative.
Everyone who is strong is not humble and vice versa.
If someone is not curious then mary is not strong or not creative.
If fred is both quiet and not wise then lucy is old and vice versa.
If mary is not happy or humble then susan is not quiet and vice versa.
If lucy is not brave or not creative then someone is strong or not happy and vice versa.
Everyone who is both kind and not calm is either not creative or not calm and vice versa.
Everyone who is both wise and old is not generous.
If susan is both not curious and not happy then lucy is either generous or not calm and vice versa.
Everyone who is both quiet and funny is either not rich or not generous.
Everyone who is both humble and not quiet is not quiet.
If someone is not curious then paul is either creative or kind and vice versa.
If paul is old or rich then alice is both not rich and creative.
Lucy is humble or calm.
Someone is not humble or not calm.
Mary is calm or not quiet.
Fred is both strong and patient.
Someone is rich.
Someone is happy or quiet.
Paul is both not kind and not funny.
Someone is creative or curious. | Mary is not happy. | neutral | (![X]:((~generous(X)|quiet(X))<=>(~rich(X)|~generous(X))))&
(![X]:((quiet(X)<~>tall(X))=>(~generous(X)&funny(X))))&
(![X]:(~old(X)=>(~tall(X)<~>~patient(X))))&
(![X]:((~old(X)|~funny(X))=>(~wise(X)<~>creative(X))))&
(![X]:(strong(X)<=>~humble(X)))&
((?[X]:(~curious(X)))=>((~strong(mary)|~creative(mary))))&
(((quiet(fred)&~wise(fred)))<=>(old(lucy)))&
(((~happy(mary)|humble(mary)))<=>(~quiet(susan)))&
(((~brave(lucy)|~creative(lucy)))<=>(?[X]:((strong(X)|~happy(X)))))&
(![X]:((kind(X)&~calm(X))<=>(~creative(X)<~>~calm(X))))&
(![X]:((wise(X)&old(X))=>~generous(X)))&
(((~curious(susan)&~happy(susan)))<=>((generous(lucy)<~>~calm(lucy))))&
(![X]:((quiet(X)&funny(X))=>(~rich(X)<~>~generous(X))))&
(![X]:((humble(X)&~quiet(X))=>~quiet(X)))&
((?[X]:(~curious(X)))<=>((creative(paul)<~>kind(paul))))&
(((old(paul)|rich(paul)))=>((~rich(alice)&creative(alice))))&
((humble(lucy)|calm(lucy)))&
(?[X]:((~humble(X)|~calm(X))))&
((calm(mary)|~quiet(mary)))&
((strong(fred)&patient(fred)))&
(?[X]:(rich(X)))&
(?[X]:((happy(X)|quiet(X))))&
((~kind(paul)&~funny(paul)))&
(?[X]:((creative(X)|curious(X)))) | ~happy(mary) | [] | null | 0 |
Everyone who is both creative and funny is both strong and rich and vice versa.
Everyone who is not humble is either rich or patient.
If alice is happy or curious then someone is kind and vice versa.
If mary is either strong or creative then mary is not tall or wise.
Everyone who is rich is generous.
If mary is both not patient and not brave then someone is both not quiet and not strong and vice versa.
Everyone who is creative or not quiet is either not wise or not happy.
If someone is not rich or humble then someone is not calm.
Everyone who is creative is not patient.
Everyone who is wise is old.
Everyone who is both not kind and wise is rich and vice versa.
Everyone who is not funny or not tall is either not calm or strong and vice versa.
If paul is either not wise or not funny then someone is not brave or wise and vice versa.
If someone is not tall or curious then lucy is not tall or not strong.
If someone is both calm and not humble then someone is brave or old.
If someone is either not curious or not brave then someone is both kind and not strong.
Someone is not funny or happy.
Mary is not rich.
Mary is both wise and not calm.
Paul is not wise or patient.
Someone is brave.
Someone is both generous and not funny.
Someone is both not patient and not calm.
Someone is patient. | Mary is wise. | entailment | (![X]:((creative(X)&funny(X))<=>(strong(X)&rich(X))))&
(![X]:(~humble(X)=>(rich(X)<~>patient(X))))&
(((happy(alice)|curious(alice)))<=>(?[X]:(kind(X))))&
(((strong(mary)<~>creative(mary)))=>((~tall(mary)|wise(mary))))&
(![X]:(rich(X)=>generous(X)))&
(((~patient(mary)&~brave(mary)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((creative(X)|~quiet(X))=>(~wise(X)<~>~happy(X))))&
((?[X]:((~rich(X)|humble(X))))=>(?[X]:(~calm(X))))&
(![X]:(creative(X)=>~patient(X)))&
(![X]:(wise(X)=>old(X)))&
(![X]:((~kind(X)&wise(X))<=>rich(X)))&
(![X]:((~funny(X)|~tall(X))<=>(~calm(X)<~>strong(X))))&
(((~wise(paul)<~>~funny(paul)))<=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((~tall(X)|curious(X))))=>((~tall(lucy)|~strong(lucy))))&
((?[X]:((calm(X)&~humble(X))))=>(?[X]:((brave(X)|old(X)))))&
((?[X]:((~curious(X)<~>~brave(X))))=>(?[X]:((kind(X)&~strong(X)))))&
(?[X]:((~funny(X)|happy(X))))&
(~rich(mary))&
((wise(mary)&~calm(mary)))&
((~wise(paul)|patient(paul)))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)&~funny(X))))&
(?[X]:((~patient(X)&~calm(X))))&
(?[X]:(patient(X))) | wise(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3804080255699786168123753
% SZS output start Proof for 3804080255699786168123753
19. ~calm(mary) & wise(mary) [input p18]
25. ~wise(mary) [input hypothesis]
127. wise(mary) [cnf transformation 19]
135. ~wise(mary) [cnf transformation 25]
167. 8 <=> wise(mary) [avatar definition]
278. 8 [avatar split clause 127,167]
284. ~8 [avatar split clause 135,167]
285. $false [avatar sat refutation 278,284]
% SZS output end Proof for 3804080255699786168123753
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not patient is not brave or not patient. Everyone who is humble or creative is not curious or patient. Everyone who is both brave and strong is either curious or creative and vice versa. Everyone who is both kind and brave is either not generous or quiet and vice versa. Everyone who is rich is tall or generous and vice versa. If someone is not kind or not tall then someone is either generous or curious. If lucy is both curious and old then someone is not creative and vice versa. Everyone who is not happy is not old. If someone is either quiet or calm then someone is not generous or not kind and vice versa. Everyone who is creative is not quiet and vice versa. Everyone who is not patient or generous is not kind. If someone is either not rich or funny then someone is both not old and not quiet and vice versa. If mary is either not calm or happy then paul is calm. Everyone who is either not wise or not old is both patient and rich and vice versa. Everyone who is generous or not creative is either not curious or not brave and vice versa. Everyone who is wise is not calm or funny and vice versa. Lucy is both kind and not wise. Mary is kind or quiet. Someone is either not curious or rich. Mary is not funny or not wise. Mary is either not humble or humble. Someone is either rich or humble. Someone is both not brave and patient. John is not kind or not rich. | Lucy is strong. | contradiction | (![X]:((~old(X)<~>~patient(X))=>(~brave(X)|~patient(X))))&
(![X]:((humble(X)|creative(X))=>(~curious(X)|patient(X))))&
(![X]:((brave(X)&strong(X))<=>(curious(X)<~>creative(X))))&
(![X]:((kind(X)&brave(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:(rich(X)<=>(tall(X)|generous(X))))&
((?[X]:((~kind(X)|~tall(X))))=>(?[X]:((generous(X)<~>curious(X)))))&
(((curious(lucy)&old(lucy)))<=>(?[X]:(~creative(X))))&
(![X]:(~happy(X)=>~old(X)))&
((?[X]:((quiet(X)<~>calm(X))))<=>(?[X]:((~generous(X)|~kind(X)))))&
(![X]:(creative(X)<=>~quiet(X)))&
(![X]:((~patient(X)|generous(X))=>~kind(X)))&
((?[X]:((~rich(X)<~>funny(X))))<=>(?[X]:((~old(X)&~quiet(X)))))&
(((~calm(mary)<~>happy(mary)))=>(calm(paul)))&
(![X]:((~wise(X)<~>~old(X))<=>(patient(X)&rich(X))))&
(![X]:((generous(X)|~creative(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:(wise(X)<=>(~calm(X)|funny(X))))&
((kind(lucy)&~wise(lucy)))&
((kind(mary)|quiet(mary)))&
(?[X]:((~curious(X)<~>rich(X))))&
((~funny(mary)|~wise(mary)))&
((~humble(mary)<~>humble(mary)))&
(?[X]:((rich(X)<~>humble(X))))&
(?[X]:((~brave(X)&patient(X))))&
((~kind(john)|~rich(john))) | strong(lucy) | [
"p2",
"p3",
"p6",
"p9",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4360833189578511333433979
% SZS output start Proof for 4360833189578511333433979
3. ! [X0] : ((strong(X0) & brave(X0)) <=> (curious(X0) <~> creative(X0))) [input p2]
4. ! [X0] : ((brave(X0) & kind(X0)) <=> (~generous(X0) <~> quiet(X0))) [input p3]
7. (old(lucy) & curious(lucy)) <=> ? [X0] : ~creative(X0) [input p6]
10. ! [X0] : (creative(X0) <=> ~quiet(X0)) [input p9]
11. ! [X0] : ((generous(X0) | ~patient(X0)) => ~kind(X0)) [input p10]
15. ! [X0] : ((~creative(X0) | generous(X0)) <=> (~curious(X0) <~> ~brave(X0))) [input p14]
17. ~wise(lucy) & kind(lucy) [input p16]
25. strong(lucy) [input hypothesis]
35. ! [X0] : (~kind(X0) | (~generous(X0) & patient(X0))) [ennf transformation 11]
38. ! [X0] : (((strong(X0) & brave(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~strong(X0) | ~brave(X0)))) [nnf transformation 3]
39. ! [X0] : (((strong(X0) & brave(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | ~strong(X0) | ~brave(X0))) [flattening 38]
40. ! [X0] : (((brave(X0) & kind(X0)) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0)))) & (((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | (~brave(X0) | ~kind(X0)))) [nnf transformation 4]
41. ! [X0] : (((brave(X0) & kind(X0)) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0)))) & (((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | ~brave(X0) | ~kind(X0))) [flattening 40]
48. ((old(lucy) & curious(lucy)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | (~old(lucy) | ~curious(lucy))) [nnf transformation 7]
49. ((old(lucy) & curious(lucy)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | ~old(lucy) | ~curious(lucy)) [flattening 48]
50. ((old(lucy) & curious(lucy)) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | ~old(lucy) | ~curious(lucy)) [rectify 49]
51. ? [X1] : ~creative(X1) => ~creative(sK1) [choice axiom]
52. ((old(lucy) & curious(lucy)) | ! [X0] : creative(X0)) & (~creative(sK1) | ~old(lucy) | ~curious(lucy)) [skolemisation 50,51]
58. ! [X0] : ((creative(X0) | quiet(X0)) & (~quiet(X0) | ~creative(X0))) [nnf transformation 10]
67. ! [X0] : (((~creative(X0) | generous(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) & (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (creative(X0) & ~generous(X0)))) [nnf transformation 15]
68. ! [X0] : ((~creative(X0) | generous(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) & (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (creative(X0) & ~generous(X0)))) [flattening 67]
85. ~strong(X0) | ~curious(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 39]
86. ~curious(X0) | creative(X0) | brave(X0) [cnf transformation 39]
87. ~creative(X0) | curious(X0) | brave(X0) [cnf transformation 39]
91. ~quiet(X0) | generous(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 41]
93. ~quiet(X0) | ~generous(X0) | kind(X0) [cnf transformation 41]
94. quiet(X0) | brave(X0) | generous(X0) [cnf transformation 41]
104. curious(lucy) | creative(X0) [cnf transformation 52]
113. ~quiet(X0) | ~creative(X0) [cnf transformation 58]
114. quiet(X0) | creative(X0) [cnf transformation 58]
116. ~generous(X0) | ~kind(X0) [cnf transformation 35]
134. brave(X0) | curious(X0) | creative(X0) [cnf transformation 68]
135. ~creative(X0) | generous(X0) | ~brave(X0) | curious(X0) [cnf transformation 68]
140. kind(lucy) [cnf transformation 17]
153. strong(lucy) [cnf transformation 25]
174. 5 <=> ! [X0] : creative(X0) [avatar definition]
175. creative(X0) <- (5) [avatar component clause 174]
182. 7 <=> curious(lucy) [avatar definition]
183. ~curious(lucy) <- (~7) [avatar component clause 182]
185. 5 | 7 [avatar split clause 104,182,174]
268. ~creative(X0) | generous(X0) | curious(X0) [subsumption resolution 135,87]
269. creative(X0) | brave(X0) [subsumption resolution 134,86]
367. ~generous(X2) | kind(X2) | creative(X2) [resolution 93,114]
372. ~generous(X2) | creative(X2) [subsumption resolution 367,116]
375. brave(X1) | generous(X1) | ~creative(X1) [resolution 94,113]
376. generous(X1) | brave(X1) [subsumption resolution 375,269]
435. 44 <=> generous(lucy) [avatar definition]
436. ~generous(lucy) <- (~44) [avatar component clause 435]
437. generous(lucy) <- (44) [avatar component clause 435]
542. ~curious(lucy) | ~creative(lucy) | ~brave(lucy) [resolution 85,153]
550. generous(X3) | ~brave(X3) | ~kind(X3) | creative(X3) [resolution 91,114]
557. generous(X3) | ~kind(X3) | creative(X3) [subsumption resolution 550,269]
558. ~kind(X3) | creative(X3) [subsumption resolution 557,372]
588. ~kind(lucy) <- (44) [resolution 437,116]
590. $false <- (44) [subsumption resolution 588,140]
591. ~44 [avatar contradiction clause 590]
716. creative(lucy) [resolution 558,140]
815. brave(lucy) <- (~44) [resolution 436,376]
818. ~curious(lucy) | ~brave(lucy) [subsumption resolution 542,716]
819. ~curious(lucy) <- (~44) [subsumption resolution 818,815]
820. ~7 | 44 [avatar split clause 819,435,182]
823. generous(X2) | curious(X2) <- (5) [resolution 175,268]
884. curious(lucy) <- (5, ~44) [resolution 823,436]
891. $false <- (5, ~7, ~44) [subsumption resolution 884,183]
892. ~5 | 7 | 44 [avatar contradiction clause 891]
894. $false [avatar sat refutation 185,591,820,892]
% SZS output end Proof for 4360833189578511333433979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or kind is either not brave or not funny and vice versa.
If someone is kind or not curious then alice is both humble and kind.
If susan is not calm then someone is either not curious or not brave.
If someone is either not kind or strong then john is kind or not strong and vice versa.
Everyone who is either happy or rich is both not humble and not curious.
If alice is both funny and rich then someone is not curious or quiet.
Everyone who is both old and calm is happy or not old.
Everyone who is both brave and happy is either not brave or generous.
Everyone who is both not curious and not old is curious and vice versa.
Everyone who is not generous is not creative and vice versa.
Everyone who is patient is not strong or rich.
If someone is both patient and not quiet then mary is both not strong and not tall.
Everyone who is calm is both humble and not patient and vice versa.
If someone is calm then someone is funny.
If someone is brave or generous then someone is both not patient and not calm.
Everyone who is wise is patient or not rich and vice versa.
Someone is both not rich and not curious.
Someone is either not kind or humble.
Someone is both wise and not generous.
John is not calm or not wise.
Susan is both happy and old.
Someone is happy or wise.
Someone is not quiet.
Susan is either not creative or not calm. | Alice is not old. | contradiction | (![X]:((wise(X)|kind(X))<=>(~brave(X)<~>~funny(X))))&
((?[X]:((kind(X)|~curious(X))))=>((humble(alice)&kind(alice))))&
((~calm(susan))=>(?[X]:((~curious(X)<~>~brave(X)))))&
((?[X]:((~kind(X)<~>strong(X))))<=>((kind(john)|~strong(john))))&
(![X]:((happy(X)<~>rich(X))=>(~humble(X)&~curious(X))))&
(((funny(alice)&rich(alice)))=>(?[X]:((~curious(X)|quiet(X)))))&
(![X]:((old(X)&calm(X))=>(happy(X)|~old(X))))&
(![X]:((brave(X)&happy(X))=>(~brave(X)<~>generous(X))))&
(![X]:((~curious(X)&~old(X))<=>curious(X)))&
(![X]:(~generous(X)<=>~creative(X)))&
(![X]:(patient(X)=>(~strong(X)|rich(X))))&
((?[X]:((patient(X)&~quiet(X))))=>((~strong(mary)&~tall(mary))))&
(![X]:(calm(X)<=>(humble(X)&~patient(X))))&
((?[X]:(calm(X)))=>(?[X]:(funny(X))))&
((?[X]:((brave(X)|generous(X))))=>(?[X]:((~patient(X)&~calm(X)))))&
(![X]:(wise(X)<=>(patient(X)|~rich(X))))&
(?[X]:((~rich(X)&~curious(X))))&
(?[X]:((~kind(X)<~>humble(X))))&
(?[X]:((wise(X)&~generous(X))))&
((~calm(john)|~wise(john)))&
((happy(susan)&old(susan)))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:(~quiet(X)))&
((~creative(susan)<~>~calm(susan))) | ~old(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8400112427077098282966319
% SZS output start Proof for 8400112427077098282966319
9. ! [X0] : ((~old(X0) & ~curious(X0)) <=> curious(X0)) [input p8]
25. ~old(alice) [input hypothesis]
57. ! [X0] : (((~old(X0) & ~curious(X0)) | ~curious(X0)) & (curious(X0) | (old(X0) | curious(X0)))) [nnf transformation 9]
58. ! [X0] : (((~old(X0) & ~curious(X0)) | ~curious(X0)) & (curious(X0) | old(X0) | curious(X0))) [flattening 57]
108. curious(X0) | old(X0) | curious(X0) [cnf transformation 58]
109. ~curious(X0) | ~curious(X0) [cnf transformation 58]
139. ~old(alice) [cnf transformation 25]
140. curious(X0) | old(X0) [duplicate literal removal 108]
141. ~curious(X0) [duplicate literal removal 109]
221. old(X0) [subsumption resolution 140,141]
290. $false [subsumption resolution 139,221]
% SZS output end Proof for 8400112427077098282966319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
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