premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If someone is either kind or not creative then someone is creative or not strong.
Everyone who is wise or not happy is not generous.
If susan is either funny or not creative then lucy is not wise or not strong.
If john is both not happy and humble then paul is not rich.
If john is both tall and not old then someone is both not funny and calm and vice versa.
If someone is generous or not happy then someone is both not creative and not humble and vice versa.
Everyone who is curious or not rich is either brave or kind and vice versa.
Everyone who is either rich or quiet is quiet.
Everyone who is both not brave and not humble is not generous or tall and vice versa.
If susan is both patient and happy then someone is either creative or not generous and vice versa.
If lucy is both generous and patient then susan is not kind or funny and vice versa.
If someone is either not old or not generous then someone is not strong.
If someone is either not wise or tall then fred is either not strong or wise and vice versa.
If alice is either not curious or not creative then susan is either old or not curious.
Everyone who is either brave or wise is both not humble and not funny and vice versa.
If someone is either curious or creative then someone is not quiet or old.
Someone is either brave or wise.
Someone is both not kind and not strong.
Someone is both not wise and not kind.
Mary is either generous or not brave.
Someone is not tall or creative.
Alice is either not quiet or not happy.
Someone is either tall or calm.
Someone is not funny or quiet. | Alice is not rich. | neutral | ((?[X]:((kind(X)<~>~creative(X))))=>(?[X]:((creative(X)|~strong(X)))))&
(![X]:((wise(X)|~happy(X))=>~generous(X)))&
(((funny(susan)<~>~creative(susan)))=>((~wise(lucy)|~strong(lucy))))&
(((~happy(john)&humble(john)))=>(~rich(paul)))&
(((tall(john)&~old(john)))<=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:((generous(X)|~happy(X))))<=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((curious(X)|~rich(X))<=>(brave(X)<~>kind(X))))&
(![X]:((rich(X)<~>quiet(X))=>quiet(X)))&
(![X]:((~brave(X)&~humble(X))<=>(~generous(X)|tall(X))))&
(((patient(susan)&happy(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(((generous(lucy)&patient(lucy)))<=>((~kind(susan)|funny(susan))))&
((?[X]:((~old(X)<~>~generous(X))))=>(?[X]:(~strong(X))))&
((?[X]:((~wise(X)<~>tall(X))))<=>((~strong(fred)<~>wise(fred))))&
(((~curious(alice)<~>~creative(alice)))=>((old(susan)<~>~curious(susan))))&
(![X]:((brave(X)<~>wise(X))<=>(~humble(X)&~funny(X))))&
((?[X]:((curious(X)<~>creative(X))))=>(?[X]:((~quiet(X)|old(X)))))&
(?[X]:((brave(X)<~>wise(X))))&
(?[X]:((~kind(X)&~strong(X))))&
(?[X]:((~wise(X)&~kind(X))))&
((generous(mary)<~>~brave(mary)))&
(?[X]:((~tall(X)|creative(X))))&
((~quiet(alice)<~>~happy(alice)))&
(?[X]:((tall(X)<~>calm(X))))&
(?[X]:((~funny(X)|quiet(X)))) | ~rich(alice) | [] | null | 0 |
If susan is not quiet or not generous then someone is both patient and not curious.
Everyone who is either not calm or not happy is either not old or not wise and vice versa.
If paul is curious or not creative then paul is both not funny and not old and vice versa.
Everyone who is not brave is brave or not tall.
Everyone who is both not curious and happy is not tall and vice versa.
If someone is both not brave and not wise then someone is both not wise and not tall and vice versa.
If mary is both not rich and patient then someone is not humble.
Everyone who is creative or old is either brave or tall.
Everyone who is generous or happy is not wise and vice versa.
Everyone who is both funny and strong is both not calm and tall and vice versa.
Everyone who is brave is either kind or wise.
If someone is curious then susan is both not tall and not rich and vice versa.
Everyone who is either quiet or strong is either creative or tall.
Everyone who is not brave is both tall and not patient.
Everyone who is both old and not humble is both not happy and not humble and vice versa.
If mary is not wise or funny then fred is both not patient and not tall and vice versa.
Someone is either old or quiet.
Someone is not tall or not rich.
Someone is curious or patient.
Paul is rich.
Lucy is generous or not happy. | Lucy is old. | contradiction | (((~quiet(susan)|~generous(susan)))=>(?[X]:((patient(X)&~curious(X)))))&
(![X]:((~calm(X)<~>~happy(X))<=>(~old(X)<~>~wise(X))))&
(((curious(paul)|~creative(paul)))<=>((~funny(paul)&~old(paul))))&
(![X]:(~brave(X)=>(brave(X)|~tall(X))))&
(![X]:((~curious(X)&happy(X))<=>~tall(X)))&
((?[X]:((~brave(X)&~wise(X))))<=>(?[X]:((~wise(X)&~tall(X)))))&
(((~rich(mary)&patient(mary)))=>(?[X]:(~humble(X))))&
(![X]:((creative(X)|old(X))=>(brave(X)<~>tall(X))))&
(![X]:((generous(X)|happy(X))<=>~wise(X)))&
(![X]:((funny(X)&strong(X))<=>(~calm(X)&tall(X))))&
(![X]:(brave(X)=>(kind(X)<~>wise(X))))&
((?[X]:(curious(X)))<=>((~tall(susan)&~rich(susan))))&
(![X]:((quiet(X)<~>strong(X))=>(creative(X)<~>tall(X))))&
(![X]:(~brave(X)=>(tall(X)&~patient(X))))&
(![X]:((old(X)&~humble(X))<=>(~happy(X)&~humble(X))))&
(((~wise(mary)|funny(mary)))<=>((~patient(fred)&~tall(fred))))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul))&
((generous(lucy)|~happy(lucy))) | old(lucy) | [
"p3",
"p4",
"p5",
"p7",
"p8",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5209765187895968186892853
% SZS output start Proof for 5209765187895968186892853
4. ! [X0] : (~brave(X0) => (~tall(X0) | brave(X0))) [input p3]
5. ! [X0] : ((happy(X0) & ~curious(X0)) <=> ~tall(X0)) [input p4]
6. ? [X0] : (~wise(X0) & ~brave(X0)) <=> ? [X0] : (~tall(X0) & ~wise(X0)) [input p5]
8. ! [X0] : ((old(X0) | creative(X0)) => (brave(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((happy(X0) | generous(X0)) <=> ~wise(X0)) [input p8]
14. ! [X0] : (~brave(X0) => (~patient(X0) & tall(X0))) [input p13]
21. ~happy(lucy) | generous(lucy) [input p20]
22. old(lucy) [input hypothesis]
23. ? [X0] : (~wise(X0) & ~brave(X0)) <=> ? [X1] : (~tall(X1) & ~wise(X1)) [rectify 6]
25. ! [X0] : ((~tall(X0) | brave(X0)) | brave(X0)) [ennf transformation 4]
26. ! [X0] : (~tall(X0) | brave(X0) | brave(X0)) [flattening 25]
29. ! [X0] : ((brave(X0) <~> tall(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 8]
32. ! [X0] : ((~patient(X0) & tall(X0)) | brave(X0)) [ennf transformation 14]
38. ! [X0] : (((happy(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | (~happy(X0) | curious(X0)))) [nnf transformation 5]
39. ! [X0] : (((happy(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | ~happy(X0) | curious(X0))) [flattening 38]
40. (? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : (tall(X1) | wise(X1))) & (? [X1] : (~tall(X1) & ~wise(X1)) | ! [X0] : (wise(X0) | brave(X0))) [nnf transformation 23]
41. (? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : (tall(X1) | wise(X1))) & (? [X2] : (~tall(X2) & ~wise(X2)) | ! [X3] : (wise(X3) | brave(X3))) [rectify 40]
42. ? [X0] : (~wise(X0) & ~brave(X0)) => (~wise(sK1) & ~brave(sK1)) [choice axiom]
43. ? [X2] : (~tall(X2) & ~wise(X2)) => (~tall(sK2) & ~wise(sK2)) [choice axiom]
44. ((~wise(sK1) & ~brave(sK1)) | ! [X1] : (tall(X1) | wise(X1))) & ((~tall(sK2) & ~wise(sK2)) | ! [X3] : (wise(X3) | brave(X3))) [skolemisation 41,43,42]
47. ! [X0] : (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | (~old(X0) & ~creative(X0))) [nnf transformation 29]
48. ! [X0] : (((happy(X0) | generous(X0)) | wise(X0)) & (~wise(X0) | (~happy(X0) & ~generous(X0)))) [nnf transformation 9]
49. ! [X0] : ((happy(X0) | generous(X0) | wise(X0)) & (~wise(X0) | (~happy(X0) & ~generous(X0)))) [flattening 48]
87. ~tall(X0) | brave(X0) | brave(X0) [cnf transformation 26]
90. tall(X0) | happy(X0) [cnf transformation 39]
93. ~brave(sK1) | tall(X1) | wise(X1) [cnf transformation 44]
99. ~tall(X0) | ~brave(X0) | ~old(X0) [cnf transformation 47]
100. ~wise(X0) | ~generous(X0) [cnf transformation 49]
116. tall(X0) | brave(X0) [cnf transformation 32]
132. ~happy(lucy) | generous(lucy) [cnf transformation 21]
133. old(lucy) [cnf transformation 22]
134. ~tall(X0) | brave(X0) [duplicate literal removal 87]
177. 9 <=> ! [X1] : (tall(X1) | wise(X1)) [avatar definition]
178. tall(X1) | wise(X1) <- (9) [avatar component clause 177]
185. 11 <=> brave(sK1) [avatar definition]
187. ~brave(sK1) <- (~11) [avatar component clause 185]
188. 9 | ~11 [avatar split clause 93,185,177]
215. ~tall(X0) | ~old(X0) [subsumption resolution 99,134]
237. brave(X0) [subsumption resolution 116,134]
288. 32 <=> generous(lucy) [avatar definition]
292. 33 <=> happy(lucy) [avatar definition]
294. ~happy(lucy) <- (~33) [avatar component clause 292]
295. 32 | ~33 [avatar split clause 132,292,288]
296. $false <- (~11) [subsumption resolution 187,237]
297. 11 [avatar contradiction clause 296]
316. ~old(X0) | wise(X0) <- (9) [resolution 215,178]
317. ~old(X1) | happy(X1) [resolution 215,90]
395. wise(lucy) <- (9) [resolution 316,133]
401. ~generous(lucy) <- (9) [resolution 395,100]
402. ~32 | ~9 [avatar split clause 401,177,288]
445. happy(lucy) [resolution 317,133]
450. $false <- (~33) [subsumption resolution 445,294]
451. 33 [avatar contradiction clause 450]
456. $false [avatar sat refutation 188,295,297,402,451]
% SZS output end Proof for 5209765187895968186892853
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or kind then someone is either generous or humble and vice versa. If susan is either not wise or not quiet then someone is either tall or generous and vice versa. If alice is not rich or not humble then someone is both tall and not kind and vice versa. Everyone who is tall or not kind is both curious and humble and vice versa. Everyone who is wise or not happy is either brave or not strong. If someone is both strong and not old then alice is both tall and not strong. If someone is not tall then someone is either kind or not creative. If john is either not calm or not kind then susan is happy or not generous. Everyone who is either not funny or calm is not generous and vice versa. If paul is either not creative or not brave then someone is not creative or not generous and vice versa. If someone is not wise then someone is happy and vice versa. Everyone who is not funny is both curious and not patient and vice versa. If someone is not funny then someone is not old. If alice is quiet or patient then someone is strong or quiet and vice versa. If mary is either not creative or not humble then fred is either not quiet or strong and vice versa. Someone is both not curious and brave. Lucy is either calm or curious. Alice is both brave and rich. Someone is both patient and not old. Lucy is both not funny and strong. Lucy is either not funny or brave. Someone is either kind or tall. Someone is old. | Lucy is brave. | contradiction | ((?[X]:((~wise(X)|kind(X))))<=>(?[X]:((generous(X)<~>humble(X)))))&
(((~wise(susan)<~>~quiet(susan)))<=>(?[X]:((tall(X)<~>generous(X)))))&
(((~rich(alice)|~humble(alice)))<=>(?[X]:((tall(X)&~kind(X)))))&
(![X]:((tall(X)|~kind(X))<=>(curious(X)&humble(X))))&
(![X]:((wise(X)|~happy(X))=>(brave(X)<~>~strong(X))))&
((?[X]:((strong(X)&~old(X))))=>((tall(alice)&~strong(alice))))&
((?[X]:(~tall(X)))=>(?[X]:((kind(X)<~>~creative(X)))))&
(((~calm(john)<~>~kind(john)))=>((happy(susan)|~generous(susan))))&
(![X]:((~funny(X)<~>calm(X))<=>~generous(X)))&
(((~creative(paul)<~>~brave(paul)))<=>(?[X]:((~creative(X)|~generous(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:(happy(X))))&
(![X]:(~funny(X)<=>(curious(X)&~patient(X))))&
((?[X]:(~funny(X)))=>(?[X]:(~old(X))))&
(((quiet(alice)|patient(alice)))<=>(?[X]:((strong(X)|quiet(X)))))&
(((~creative(mary)<~>~humble(mary)))<=>((~quiet(fred)<~>strong(fred))))&
(?[X]:((~curious(X)&brave(X))))&
((calm(lucy)<~>curious(lucy)))&
((brave(alice)&rich(alice)))&
(?[X]:((patient(X)&~old(X))))&
((~funny(lucy)&strong(lucy)))&
((~funny(lucy)<~>brave(lucy)))&
(?[X]:((kind(X)<~>tall(X))))&
(?[X]:(old(X))) | brave(lucy) | [
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2433416625433114217758714
% SZS output start Proof for 2433416625433114217758714
20. strong(lucy) & ~funny(lucy) [input p19]
21. ~funny(lucy) <~> brave(lucy) [input p20]
24. brave(lucy) [input hypothesis]
83. (~brave(lucy) | funny(lucy)) & (brave(lucy) | ~funny(lucy)) [nnf transformation 21]
159. ~funny(lucy) [cnf transformation 20]
162. ~brave(lucy) | funny(lucy) [cnf transformation 83]
166. brave(lucy) [cnf transformation 24]
409. ~brave(lucy) [subsumption resolution 162,159]
420. $false [subsumption resolution 166,409]
% SZS output end Proof for 2433416625433114217758714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or humble is both not rich and tall and vice versa.
If someone is both not kind and funny then someone is not wise and vice versa.
Everyone who is tall 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.
Everyone who is generous or not rich is either tall or not patient and vice versa.
If someone is humble or tall then someone is not humble or not strong.
Someone is either not happy or not humble.
Someone is patient or not humble.
Someone is humble.
Fred is curious or not creative.
Alice is either not brave or not wise.
Lucy is either funny or calm. | Alice is old. | neutral | (![X]:((~creative(X)|humble(X))<=>(~rich(X)&tall(X))))&
((?[X]:((~kind(X)&funny(X))))<=>(?[X]:(~wise(X))))&
(![X]:(tall(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]:((generous(X)|~rich(X))<=>(tall(X)<~>~patient(X))))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(?[X]:((~happy(X)<~>~humble(X))))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:(humble(X)))&
((curious(fred)|~creative(fred)))&
((~brave(alice)<~>~wise(alice)))&
((funny(lucy)<~>calm(lucy))) | old(alice) | [] | null | 0 |
Everyone who is both calm and not kind is both not old and not patient.
If someone is not curious or happy then someone is curious.
Everyone who is either not humble or not patient is humble and vice versa.
Everyone who is either not patient or not rich is not patient or wise and vice versa.
Everyone who is rich or kind is either tall or funny and vice versa.
If someone is quiet then paul is both curious and rich.
Everyone who is not calm or patient is humble or patient and vice versa.
If fred is kind then someone is both tall and not quiet.
If someone is either not strong or wise then lucy is wise and vice versa.
If someone is not tall then someone is either not creative or not funny.
Everyone who is either not curious or curious is humble or patient.
Everyone who is strong is rich.
Everyone who is both humble and creative is either funny or not rich and vice versa.
If susan is not strong or not wise then someone is either not old or old.
Everyone who is not quiet or not tall is either generous or not wise.
If someone is not quiet then alice is patient and vice versa.
Paul is curious or rich.
Someone is not curious or not creative.
Someone is patient or rich.
Someone is either not humble or rich.
Someone is either curious or humble.
Someone is both not brave and not patient. | Lucy is brave. | neutral | (![X]:((calm(X)&~kind(X))=>(~old(X)&~patient(X))))&
((?[X]:((~curious(X)|happy(X))))=>(?[X]:(curious(X))))&
(![X]:((~humble(X)<~>~patient(X))<=>humble(X)))&
(![X]:((~patient(X)<~>~rich(X))<=>(~patient(X)|wise(X))))&
(![X]:((rich(X)|kind(X))<=>(tall(X)<~>funny(X))))&
((?[X]:(quiet(X)))=>((curious(paul)&rich(paul))))&
(![X]:((~calm(X)|patient(X))<=>(humble(X)|patient(X))))&
((kind(fred))=>(?[X]:((tall(X)&~quiet(X)))))&
((?[X]:((~strong(X)<~>wise(X))))<=>(wise(lucy)))&
((?[X]:(~tall(X)))=>(?[X]:((~creative(X)<~>~funny(X)))))&
(![X]:((~curious(X)<~>curious(X))=>(humble(X)|patient(X))))&
(![X]:(strong(X)=>rich(X)))&
(![X]:((humble(X)&creative(X))<=>(funny(X)<~>~rich(X))))&
(((~strong(susan)|~wise(susan)))=>(?[X]:((~old(X)<~>old(X)))))&
(![X]:((~quiet(X)|~tall(X))=>(generous(X)<~>~wise(X))))&
((?[X]:(~quiet(X)))<=>(patient(alice)))&
((curious(paul)|rich(paul)))&
(?[X]:((~curious(X)|~creative(X))))&
(?[X]:((patient(X)|rich(X))))&
(?[X]:((~humble(X)<~>rich(X))))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((~brave(X)&~patient(X)))) | brave(lucy) | [] | null | 0 |
If someone is both not wise and quiet then susan is both not happy and not humble and vice versa.
Everyone who is happy is either quiet or not creative.
If someone is either not strong or not humble then someone is not brave.
Everyone who is not creative is humble or strong.
If someone is both not wise and humble then mary is both funny and not happy.
Everyone who is not rich or not wise is both not old and kind.
If fred is either creative or humble then alice is either happy or not happy and vice versa.
If lucy is both not creative and not happy then someone is not generous or patient and vice versa.
Everyone who is not curious or kind is curious and vice versa.
Everyone who is not happy or tall is both not wise and not generous.
If john is both wise and brave then someone is both not strong and not patient and vice versa.
Everyone who is either not strong or kind is not rich or not humble and vice versa.
Everyone who is brave or strong is not tall or not brave and vice versa.
If susan is not creative or patient then someone is both not rich and not quiet.
Everyone who is both not creative and not funny is both not quiet and not kind.
Everyone who is not kind or not tall is both brave and not strong and vice versa.
Someone is both old and quiet.
Someone is either happy or not kind.
Someone is humble.
Lucy is humble or not wise.
Someone is both quiet and happy. | Lucy is not funny. | contradiction | ((?[X]:((~wise(X)&quiet(X))))<=>((~happy(susan)&~humble(susan))))&
(![X]:(happy(X)=>(quiet(X)<~>~creative(X))))&
((?[X]:((~strong(X)<~>~humble(X))))=>(?[X]:(~brave(X))))&
(![X]:(~creative(X)=>(humble(X)|strong(X))))&
((?[X]:((~wise(X)&humble(X))))=>((funny(mary)&~happy(mary))))&
(![X]:((~rich(X)|~wise(X))=>(~old(X)&kind(X))))&
(((creative(fred)<~>humble(fred)))<=>((happy(alice)<~>~happy(alice))))&
(((~creative(lucy)&~happy(lucy)))<=>(?[X]:((~generous(X)|patient(X)))))&
(![X]:((~curious(X)|kind(X))<=>curious(X)))&
(![X]:((~happy(X)|tall(X))=>(~wise(X)&~generous(X))))&
(((wise(john)&brave(john)))<=>(?[X]:((~strong(X)&~patient(X)))))&
(![X]:((~strong(X)<~>kind(X))<=>(~rich(X)|~humble(X))))&
(![X]:((brave(X)|strong(X))<=>(~tall(X)|~brave(X))))&
(((~creative(susan)|patient(susan)))=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((~creative(X)&~funny(X))=>(~quiet(X)&~kind(X))))&
(![X]:((~kind(X)|~tall(X))<=>(brave(X)&~strong(X))))&
(?[X]:((old(X)&quiet(X))))&
(?[X]:((happy(X)<~>~kind(X))))&
(?[X]:(humble(X)))&
((humble(lucy)|~wise(lucy)))&
(?[X]:((quiet(X)&happy(X)))) | ~funny(lucy) | [
"p2",
"p4",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3855227593671313174929709
% SZS output start Proof for 3855227593671313174929709
3. ? [X0] : (~strong(X0) <~> ~humble(X0)) => ? [X0] : ~brave(X0) [input p2]
5. ? [X0] : (humble(X0) & ~wise(X0)) => (~happy(mary) & funny(mary)) [input p4]
8. (~happy(lucy) & ~creative(lucy)) <=> ? [X0] : (patient(X0) | ~generous(X0)) [input p7]
9. ! [X0] : ((kind(X0) | ~curious(X0)) <=> curious(X0)) [input p8]
10. ! [X0] : ((tall(X0) | ~happy(X0)) => (~generous(X0) & ~wise(X0))) [input p9]
11. (brave(john) & wise(john)) <=> ? [X0] : (~patient(X0) & ~strong(X0)) [input p10]
12. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (~humble(X0) | ~rich(X0))) [input p11]
13. ! [X0] : ((strong(X0) | brave(X0)) <=> (~brave(X0) | ~tall(X0))) [input p12]
15. ! [X0] : ((~funny(X0) & ~creative(X0)) => (~kind(X0) & ~quiet(X0))) [input p14]
16. ! [X0] : ((~tall(X0) | ~kind(X0)) <=> (~strong(X0) & brave(X0))) [input p15]
22. ~funny(lucy) [input hypothesis]
23. ? [X0] : (~strong(X0) <~> ~humble(X0)) => ? [X1] : ~brave(X1) [rectify 3]
25. ? [X1] : ~brave(X1) | ! [X0] : (~strong(X0) <=> ~humble(X0)) [ennf transformation 23]
28. (~happy(mary) & funny(mary)) | ! [X0] : (~humble(X0) | wise(X0)) [ennf transformation 5]
30. ! [X0] : ((~generous(X0) & ~wise(X0)) | (~tall(X0) & happy(X0))) [ennf transformation 10]
32. ! [X0] : ((~kind(X0) & ~quiet(X0)) | (funny(X0) | creative(X0))) [ennf transformation 15]
33. ! [X0] : ((~kind(X0) & ~quiet(X0)) | funny(X0) | creative(X0)) [flattening 32]
40. ? [X1] : ~brave(X1) | ! [X0] : ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))) [nnf transformation 25]
41. ? [X0] : ~brave(X0) | ! [X1] : ((~strong(X1) | humble(X1)) & (~humble(X1) | strong(X1))) [rectify 40]
42. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
43. ~brave(sK1) | ! [X1] : ((~strong(X1) | humble(X1)) & (~humble(X1) | strong(X1))) [skolemisation 41,42]
45. ((~happy(lucy) & ~creative(lucy)) | ! [X0] : (~patient(X0) & generous(X0))) & (? [X0] : (patient(X0) | ~generous(X0)) | (happy(lucy) | creative(lucy))) [nnf transformation 8]
46. ((~happy(lucy) & ~creative(lucy)) | ! [X0] : (~patient(X0) & generous(X0))) & (? [X0] : (patient(X0) | ~generous(X0)) | happy(lucy) | creative(lucy)) [flattening 45]
47. ((~happy(lucy) & ~creative(lucy)) | ! [X0] : (~patient(X0) & generous(X0))) & (? [X1] : (patient(X1) | ~generous(X1)) | happy(lucy) | creative(lucy)) [rectify 46]
48. ? [X1] : (patient(X1) | ~generous(X1)) => (patient(sK2) | ~generous(sK2)) [choice axiom]
49. ((~happy(lucy) & ~creative(lucy)) | ! [X0] : (~patient(X0) & generous(X0))) & ((patient(sK2) | ~generous(sK2)) | happy(lucy) | creative(lucy)) [skolemisation 47,48]
50. ! [X0] : (((kind(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~kind(X0) & curious(X0)))) [nnf transformation 9]
51. ! [X0] : ((kind(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~kind(X0) & curious(X0)))) [flattening 50]
52. ((brave(john) & wise(john)) | ! [X0] : (patient(X0) | strong(X0))) & (? [X0] : (~patient(X0) & ~strong(X0)) | (~brave(john) | ~wise(john))) [nnf transformation 11]
53. ((brave(john) & wise(john)) | ! [X0] : (patient(X0) | strong(X0))) & (? [X0] : (~patient(X0) & ~strong(X0)) | ~brave(john) | ~wise(john)) [flattening 52]
54. ((brave(john) & wise(john)) | ! [X0] : (patient(X0) | strong(X0))) & (? [X1] : (~patient(X1) & ~strong(X1)) | ~brave(john) | ~wise(john)) [rectify 53]
55. ? [X1] : (~patient(X1) & ~strong(X1)) => (~patient(sK3) & ~strong(sK3)) [choice axiom]
56. ((brave(john) & wise(john)) | ! [X0] : (patient(X0) | strong(X0))) & ((~patient(sK3) & ~strong(sK3)) | ~brave(john) | ~wise(john)) [skolemisation 54,55]
57. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (humble(X0) & rich(X0))) & ((~humble(X0) | ~rich(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 12]
58. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (humble(X0) & rich(X0))) & (~humble(X0) | ~rich(X0) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [flattening 57]
59. ! [X0] : (((strong(X0) | brave(X0)) | (brave(X0) & tall(X0))) & ((~brave(X0) | ~tall(X0)) | (~strong(X0) & ~brave(X0)))) [nnf transformation 13]
60. ! [X0] : ((strong(X0) | brave(X0) | (brave(X0) & tall(X0))) & (~brave(X0) | ~tall(X0) | (~strong(X0) & ~brave(X0)))) [flattening 59]
63. ! [X0] : (((~tall(X0) | ~kind(X0)) | (strong(X0) | ~brave(X0))) & ((~strong(X0) & brave(X0)) | (tall(X0) & kind(X0)))) [nnf transformation 16]
64. ! [X0] : ((~tall(X0) | ~kind(X0) | strong(X0) | ~brave(X0)) & ((~strong(X0) & brave(X0)) | (tall(X0) & kind(X0)))) [flattening 63]
80. ~brave(sK1) | ~humble(X1) | strong(X1) [cnf transformation 43]
81. ~brave(sK1) | ~strong(X1) | humble(X1) [cnf transformation 43]
84. ~happy(mary) | ~humble(X0) | wise(X0) [cnf transformation 28]
98. ~creative(lucy) | generous(X0) [cnf transformation 49]
102. curious(X0) | curious(X0) [cnf transformation 51]
104. kind(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 51]
107. ~generous(X0) | happy(X0) [cnf transformation 30]
108. ~tall(X0) | ~generous(X0) [cnf transformation 30]
109. ~strong(sK3) | ~brave(john) | ~wise(john) [cnf transformation 56]
118. ~kind(X0) | strong(X0) | humble(X0) [cnf transformation 58]
122. strong(X0) | brave(X0) | brave(X0) [cnf transformation 60]
128. ~kind(X0) | funny(X0) | creative(X0) [cnf transformation 33]
130. tall(X0) | brave(X0) [cnf transformation 64]
132. ~strong(X0) | tall(X0) [cnf transformation 64]
142. ~funny(lucy) [cnf transformation 22]
144. brave(X0) | strong(X0) [duplicate literal removal 122]
145. curious(X0) [duplicate literal removal 102]
146. ~curious(X0) | kind(X0) [duplicate literal removal 104]
175. 6 <=> ! [X1] : (~strong(X1) | humble(X1)) [avatar definition]
176. ~strong(X1) | humble(X1) <- (6) [avatar component clause 175]
178. 7 <=> brave(sK1) [avatar definition]
180. ~brave(sK1) <- (~7) [avatar component clause 178]
181. 6 | ~7 [avatar split clause 81,178,175]
183. 8 <=> ! [X1] : (~humble(X1) | strong(X1)) [avatar definition]
184. ~humble(X1) | strong(X1) <- (8) [avatar component clause 183]
185. 8 | ~7 [avatar split clause 80,178,183]
187. 9 <=> ! [X0] : (~humble(X0) | wise(X0)) [avatar definition]
188. ~humble(X0) | wise(X0) <- (9) [avatar component clause 187]
190. 10 <=> happy(mary) [avatar definition]
192. ~happy(mary) <- (~10) [avatar component clause 190]
193. 9 | ~10 [avatar split clause 84,190,187]
224. 17 <=> ! [X0] : generous(X0) [avatar definition]
225. generous(X0) <- (17) [avatar component clause 224]
228. 18 <=> creative(lucy) [avatar definition]
232. 17 | ~18 [avatar split clause 98,228,224]
246. 22 <=> brave(john) [avatar definition]
247. ~brave(john) <- (~22) [avatar component clause 246]
251. 23 <=> wise(john) [avatar definition]
252. ~wise(john) <- (~23) [avatar component clause 251]
261. 25 <=> strong(sK3) [avatar definition]
263. ~strong(sK3) <- (~25) [avatar component clause 261]
264. ~23 | ~22 | ~25 [avatar split clause 109,261,246,251]
318. ~generous(X0) | brave(X0) [resolution 130,108]
321. strong(sK1) <- (~7) [resolution 144,180]
322. kind(X0) [resolution 146,145]
323. tall(sK1) <- (~7) [resolution 321,132]
383. strong(X0) | humble(X0) [resolution 118,322]
392. ~generous(sK1) <- (~7) [resolution 323,108]
406. funny(X0) | creative(X0) [resolution 128,322]
435. creative(lucy) [resolution 406,142]
438. 18 [avatar split clause 435,228]
440. brave(X0) <- (17) [resolution 225,318]
441. happy(X1) <- (17) [resolution 225,107]
442. $false <- (~7, 17) [resolution 225,392]
447. 7 | ~17 [avatar contradiction clause 442]
460. humble(X1) <- (6) [subsumption resolution 176,383]
461. strong(X1) <- (6, 8) [subsumption resolution 184,460]
462. $false <- (6, 8, ~25) [subsumption resolution 263,461]
463. ~6 | ~8 | 25 [avatar contradiction clause 462]
464. $false <- (17, ~22) [subsumption resolution 247,440]
465. ~17 | 22 [avatar contradiction clause 464]
467. wise(X1) <- (6, 9) [resolution 460,188]
482. $false <- (6, 9, ~23) [resolution 467,252]
483. ~6 | ~9 | 23 [avatar contradiction clause 482]
485. $false <- (~10, 17) [subsumption resolution 192,441]
486. 10 | ~17 [avatar contradiction clause 485]
487. $false [avatar sat refutation 181,185,193,232,264,438,447,463,465,483,486]
% SZS output end Proof for 3855227593671313174929709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or funny is not kind.
If someone is humble then someone is wise.
If alice is either brave or not happy then someone is not generous or calm and vice versa.
Everyone who is not creative is both not humble and humble and vice versa.
Everyone who is not calm or not funny is not happy or not tall.
If someone is not wise then susan is both not strong and patient.
If someone is either not humble or not funny then someone is either strong or not rich.
If someone is both tall and not curious then paul is strong and vice versa.
Everyone who is creative is old or generous and vice versa.
Everyone who is not happy is both not creative and not calm.
If someone is strong or tall then someone is either old or happy and vice versa.
If someone is both happy and not brave then alice is both not curious and strong and vice versa.
If alice is both not old and patient then someone is either not generous or happy.
Everyone who is not happy or not humble is happy and vice versa.
Everyone who is either not humble or not quiet is both not strong and strong and vice versa.
Mary is either strong or not humble.
Someone is either quiet or not calm.
Lucy is both old and patient.
Susan is both creative and old.
Someone is not kind or not old.
Someone is either wise or not strong.
Someone is both not rich and not strong. | Lucy is quiet. | contradiction | (![X]:((~wise(X)|funny(X))=>~kind(X)))&
((?[X]:(humble(X)))=>(?[X]:(wise(X))))&
(((brave(alice)<~>~happy(alice)))<=>(?[X]:((~generous(X)|calm(X)))))&
(![X]:(~creative(X)<=>(~humble(X)&humble(X))))&
(![X]:((~calm(X)|~funny(X))=>(~happy(X)|~tall(X))))&
((?[X]:(~wise(X)))=>((~strong(susan)&patient(susan))))&
((?[X]:((~humble(X)<~>~funny(X))))=>(?[X]:((strong(X)<~>~rich(X)))))&
((?[X]:((tall(X)&~curious(X))))<=>(strong(paul)))&
(![X]:(creative(X)<=>(old(X)|generous(X))))&
(![X]:(~happy(X)=>(~creative(X)&~calm(X))))&
((?[X]:((strong(X)|tall(X))))<=>(?[X]:((old(X)<~>happy(X)))))&
((?[X]:((happy(X)&~brave(X))))<=>((~curious(alice)&strong(alice))))&
(((~old(alice)&patient(alice)))=>(?[X]:((~generous(X)<~>happy(X)))))&
(![X]:((~happy(X)|~humble(X))<=>happy(X)))&
(![X]:((~humble(X)<~>~quiet(X))<=>(~strong(X)&strong(X))))&
((strong(mary)<~>~humble(mary)))&
(?[X]:((quiet(X)<~>~calm(X))))&
((old(lucy)&patient(lucy)))&
((creative(susan)&old(susan)))&
(?[X]:((~kind(X)|~old(X))))&
(?[X]:((wise(X)<~>~strong(X))))&
(?[X]:((~rich(X)&~strong(X)))) | quiet(lucy) | [
"p3",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7478899213324146792153990
% SZS output start Proof for 7478899213324146792153990
4. ! [X0] : (~creative(X0) <=> (humble(X0) & ~humble(X0))) [input p3]
10. ! [X0] : (~happy(X0) => (~calm(X0) & ~creative(X0))) [input p9]
14. ! [X0] : ((~humble(X0) | ~happy(X0)) <=> happy(X0)) [input p13]
15. ! [X0] : ((~humble(X0) <~> ~quiet(X0)) <=> (strong(X0) & ~strong(X0))) [input p14]
23. quiet(lucy) [input hypothesis]
34. ! [X0] : ((~calm(X0) & ~creative(X0)) | happy(X0)) [ennf transformation 10]
44. ! [X0] : ((~creative(X0) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | creative(X0))) [nnf transformation 4]
45. ! [X0] : ((~creative(X0) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | creative(X0))) [flattening 44]
69. ! [X0] : (((~humble(X0) | ~happy(X0)) | ~happy(X0)) & (happy(X0) | (humble(X0) & happy(X0)))) [nnf transformation 14]
70. ! [X0] : ((~humble(X0) | ~happy(X0) | ~happy(X0)) & (happy(X0) | (humble(X0) & happy(X0)))) [flattening 69]
71. ! [X0] : ((((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))))) [nnf transformation 15]
72. ! [X0] : ((((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))))) [flattening 71]
89. ~humble(X0) | creative(X0) [cnf transformation 45]
90. creative(X0) | humble(X0) [cnf transformation 45]
106. ~creative(X0) | happy(X0) [cnf transformation 34]
122. ~humble(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 70]
123. ~strong(X0) | ~quiet(X0) | humble(X0) [cnf transformation 72]
125. strong(X0) | ~quiet(X0) | humble(X0) [cnf transformation 72]
141. quiet(lucy) [cnf transformation 23]
143. ~humble(X0) | ~happy(X0) [duplicate literal removal 122]
145. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
146. ~humble(X1) <- (1) [avatar component clause 145]
180. creative(X0) [subsumption resolution 89,90]
231. happy(X0) [subsumption resolution 106,180]
293. ~humble(X0) [subsumption resolution 143,231]
294. 1 [avatar split clause 293,145]
296. ~quiet(X0) | humble(X0) [subsumption resolution 123,125]
334. humble(lucy) [resolution 296,141]
335. $false <- (1) [subsumption resolution 334,146]
336. ~1 [avatar contradiction clause 335]
337. $false [avatar sat refutation 294,336]
% SZS output end Proof for 7478899213324146792153990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then someone is either creative or old and vice versa. Everyone who is not curious is either rich or not curious and vice versa. Everyone who is not calm is either not brave or not humble and vice versa. If someone is either not rich or brave then someone is both not happy and not generous. If someone is either happy or strong then lucy is both not generous and quiet and vice versa. If someone is either creative or not calm then someone is either not creative or not generous. If fred is both not rich and curious then alice is both not wise and not happy and vice versa. If alice is not tall then someone is not patient or strong and vice versa. Everyone who is either strong or brave is either brave or not brave and vice versa. Everyone who is curious or not quiet is creative or old. Everyone who is both not strong and not humble is both old and not calm and vice versa. If someone is not generous or not curious then alice is tall or not wise and vice versa. Everyone who is not happy is either patient or kind and vice versa. If someone is wise then paul is both not patient and wise and vice versa. If alice is both not kind and not funny then someone is not creative or funny and vice versa. Everyone who is both not kind and tall is both generous and not tall and vice versa. Someone is either not generous or rich. Paul is strong or calm. Lucy is both not wise and not happy. John is either not funny or not strong. Mary is either not old or creative. Someone is not funny. Someone is not quiet. Mary is both not creative and patient. | Alice is not tall. | entailment | ((?[X]:(kind(X)))<=>(?[X]:((creative(X)<~>old(X)))))&
(![X]:(~curious(X)<=>(rich(X)<~>~curious(X))))&
(![X]:(~calm(X)<=>(~brave(X)<~>~humble(X))))&
((?[X]:((~rich(X)<~>brave(X))))=>(?[X]:((~happy(X)&~generous(X)))))&
((?[X]:((happy(X)<~>strong(X))))<=>((~generous(lucy)&quiet(lucy))))&
((?[X]:((creative(X)<~>~calm(X))))=>(?[X]:((~creative(X)<~>~generous(X)))))&
(((~rich(fred)&curious(fred)))<=>((~wise(alice)&~happy(alice))))&
((~tall(alice))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((strong(X)<~>brave(X))<=>(brave(X)<~>~brave(X))))&
(![X]:((curious(X)|~quiet(X))=>(creative(X)|old(X))))&
(![X]:((~strong(X)&~humble(X))<=>(old(X)&~calm(X))))&
((?[X]:((~generous(X)|~curious(X))))<=>((tall(alice)|~wise(alice))))&
(![X]:(~happy(X)<=>(patient(X)<~>kind(X))))&
((?[X]:(wise(X)))<=>((~patient(paul)&wise(paul))))&
(((~kind(alice)&~funny(alice)))<=>(?[X]:((~creative(X)|funny(X)))))&
(![X]:((~kind(X)&tall(X))<=>(generous(X)&~tall(X))))&
(?[X]:((~generous(X)<~>rich(X))))&
((strong(paul)|calm(paul)))&
((~wise(lucy)&~happy(lucy)))&
((~funny(john)<~>~strong(john)))&
((~old(mary)<~>creative(mary)))&
(?[X]:(~funny(X)))&
(?[X]:(~quiet(X)))&
((~creative(mary)&patient(mary))) | ~tall(alice) | [
"p7",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6203158788231885364645854
% SZS output start Proof for 6203158788231885364645854
8. ~tall(alice) <=> ? [X0] : (strong(X0) | ~patient(X0)) [input p7]
15. (~funny(alice) & ~kind(alice)) <=> ? [X0] : (funny(X0) | ~creative(X0)) [input p14]
16. ! [X0] : ((tall(X0) & ~kind(X0)) <=> (~tall(X0) & generous(X0))) [input p15]
20. ~funny(john) <~> ~strong(john) [input p19]
25. tall(alice) [input hypothesis]
55. (~tall(alice) | ! [X0] : (~strong(X0) & patient(X0))) & (? [X0] : (strong(X0) | ~patient(X0)) | tall(alice)) [nnf transformation 8]
56. (~tall(alice) | ! [X0] : (~strong(X0) & patient(X0))) & (? [X1] : (strong(X1) | ~patient(X1)) | tall(alice)) [rectify 55]
57. ? [X1] : (strong(X1) | ~patient(X1)) => (strong(sK5) | ~patient(sK5)) [choice axiom]
58. (~tall(alice) | ! [X0] : (~strong(X0) & patient(X0))) & ((strong(sK5) | ~patient(sK5)) | tall(alice)) [skolemisation 56,57]
73. ((~funny(alice) & ~kind(alice)) | ! [X0] : (~funny(X0) & creative(X0))) & (? [X0] : (funny(X0) | ~creative(X0)) | (funny(alice) | kind(alice))) [nnf transformation 15]
74. ((~funny(alice) & ~kind(alice)) | ! [X0] : (~funny(X0) & creative(X0))) & (? [X0] : (funny(X0) | ~creative(X0)) | funny(alice) | kind(alice)) [flattening 73]
75. ((~funny(alice) & ~kind(alice)) | ! [X0] : (~funny(X0) & creative(X0))) & (? [X1] : (funny(X1) | ~creative(X1)) | funny(alice) | kind(alice)) [rectify 74]
76. ? [X1] : (funny(X1) | ~creative(X1)) => (funny(sK8) | ~creative(sK8)) [choice axiom]
77. ((~funny(alice) & ~kind(alice)) | ! [X0] : (~funny(X0) & creative(X0))) & ((funny(sK8) | ~creative(sK8)) | funny(alice) | kind(alice)) [skolemisation 75,76]
78. ! [X0] : (((tall(X0) & ~kind(X0)) | (tall(X0) | ~generous(X0))) & ((~tall(X0) & generous(X0)) | (~tall(X0) | kind(X0)))) [nnf transformation 16]
79. ! [X0] : (((tall(X0) & ~kind(X0)) | tall(X0) | ~generous(X0)) & ((~tall(X0) & generous(X0)) | ~tall(X0) | kind(X0))) [flattening 78]
83. (strong(john) | funny(john)) & (~strong(john) | ~funny(john)) [nnf transformation 20]
121. ~tall(alice) | ~strong(X0) [cnf transformation 58]
149. ~kind(alice) | ~funny(X0) [cnf transformation 77]
153. ~tall(X0) | ~tall(X0) | kind(X0) [cnf transformation 79]
162. strong(john) | funny(john) [cnf transformation 83]
169. tall(alice) [cnf transformation 25]
170. ~tall(X0) | kind(X0) [duplicate literal removal 153]
287. 23 <=> ! [X0] : ~strong(X0) [avatar definition]
288. ~strong(X0) <- (23) [avatar component clause 287]
290. 24 <=> tall(alice) [avatar definition]
291. tall(alice) <- (24) [avatar component clause 290]
293. 23 | ~24 [avatar split clause 121,290,287]
344. 36 <=> ! [X0] : ~funny(X0) [avatar definition]
345. ~funny(X0) <- (36) [avatar component clause 344]
356. 39 <=> kind(alice) [avatar definition]
359. 36 | ~39 [avatar split clause 149,356,344]
381. 44 <=> funny(john) [avatar definition]
383. funny(john) <- (44) [avatar component clause 381]
385. 45 <=> strong(john) [avatar definition]
387. strong(john) <- (45) [avatar component clause 385]
388. 44 | 45 [avatar split clause 162,385,381]
401. 24 [avatar split clause 169,290]
414. kind(alice) <- (24) [resolution 170,291]
417. 39 | ~24 [avatar split clause 414,290,356]
418. $false <- (36, 44) [resolution 345,383]
419. ~36 | ~44 [avatar contradiction clause 418]
420. $false <- (23, 45) [subsumption resolution 387,288]
421. ~23 | ~45 [avatar contradiction clause 420]
422. $false [avatar sat refutation 293,359,388,401,417,419,421]
% SZS output end Proof for 6203158788231885364645854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or kind is not happy or not strong and vice versa.
Everyone who is not happy is either old or brave.
If paul is either curious or quiet then someone is both humble and not brave and vice versa.
If lucy is either rich or not creative then someone is not tall.
If someone is not patient or not tall then someone is not wise and vice versa.
If mary is either humble or brave then alice is not strong or not tall and vice versa.
If alice is either not strong or generous then someone is both not old and rich.
Everyone who is both not generous and not creative is humble and vice versa.
Everyone who is brave or not strong is both old and not patient and vice versa.
If someone is both not old and tall then someone is both not tall and not brave.
Everyone who is rich is not wise and vice versa.
Everyone who is strong is both not tall and not strong and vice versa.
Everyone who is old or quiet is either humble or creative and vice versa.
If susan is either not curious or not creative then susan is both patient and wise.
Everyone who is not quiet is both not old and not brave.
If john is tall or not patient then someone is rich or tall.
Mary is curious or not strong.
Someone is old or tall.
Fred is not strong.
Alice is not old or happy.
John is not wise or not quiet.
Someone is rich.
Paul is not creative or generous.
Someone is either curious or not wise. | Mary is tall. | entailment | (![X]:((~wise(X)|kind(X))<=>(~happy(X)|~strong(X))))&
(![X]:(~happy(X)=>(old(X)<~>brave(X))))&
(((curious(paul)<~>quiet(paul)))<=>(?[X]:((humble(X)&~brave(X)))))&
(((rich(lucy)<~>~creative(lucy)))=>(?[X]:(~tall(X))))&
((?[X]:((~patient(X)|~tall(X))))<=>(?[X]:(~wise(X))))&
(((humble(mary)<~>brave(mary)))<=>((~strong(alice)|~tall(alice))))&
(((~strong(alice)<~>generous(alice)))=>(?[X]:((~old(X)&rich(X)))))&
(![X]:((~generous(X)&~creative(X))<=>humble(X)))&
(![X]:((brave(X)|~strong(X))<=>(old(X)&~patient(X))))&
((?[X]:((~old(X)&tall(X))))=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:(rich(X)<=>~wise(X)))&
(![X]:(strong(X)<=>(~tall(X)&~strong(X))))&
(![X]:((old(X)|quiet(X))<=>(humble(X)<~>creative(X))))&
(((~curious(susan)<~>~creative(susan)))=>((patient(susan)&wise(susan))))&
(![X]:(~quiet(X)=>(~old(X)&~brave(X))))&
(((tall(john)|~patient(john)))=>(?[X]:((rich(X)|tall(X)))))&
((curious(mary)|~strong(mary)))&
(?[X]:((old(X)|tall(X))))&
(~strong(fred))&
((~old(alice)|happy(alice)))&
((~wise(john)|~quiet(john)))&
(?[X]:(rich(X)))&
((~creative(paul)|generous(paul)))&
(?[X]:((curious(X)<~>~wise(X)))) | tall(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 594259313890058935259733
% SZS output start Proof for 594259313890058935259733
12. ! [X0] : (strong(X0) <=> (~strong(X0) & ~tall(X0))) [input p11]
25. ~tall(mary) [input hypothesis]
63. ! [X0] : ((strong(X0) | (strong(X0) | tall(X0))) & ((~strong(X0) & ~tall(X0)) | ~strong(X0))) [nnf transformation 12]
64. ! [X0] : ((strong(X0) | strong(X0) | tall(X0)) & ((~strong(X0) & ~tall(X0)) | ~strong(X0))) [flattening 63]
117. ~strong(X0) | ~strong(X0) [cnf transformation 64]
118. strong(X0) | strong(X0) | tall(X0) [cnf transformation 64]
142. ~tall(mary) [cnf transformation 25]
143. ~strong(X0) [duplicate literal removal 117]
144. tall(X0) | strong(X0) [duplicate literal removal 118]
362. strong(mary) [resolution 144,142]
367. $false [subsumption resolution 362,143]
% SZS output end Proof for 594259313890058935259733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is curious or calm then mary is not creative and vice versa.
If paul is strong then susan is either generous or quiet.
If someone is not rich then someone is calm.
Everyone who is wise is old or calm.
If someone is either not creative or not wise then john is not tall.
Everyone who is not strong or not tall is creative or not quiet.
Everyone who is kind is patient or not strong and vice versa.
Everyone who is not rich is not curious or not calm and vice versa.
If alice is not creative or not quiet then someone is either generous or curious.
If someone is not rich then someone is tall.
Everyone who is either curious or tall is either generous or creative and vice versa.
Everyone who is old or creative is not old or not tall.
Everyone who is not humble or not wise is not curious.
If someone is either not funny or humble then someone is strong and vice versa.
If paul is not kind or not creative then someone is tall or happy and vice versa.
If someone is old or not curious then someone is humble.
Someone is not generous.
Mary is kind or not tall.
John is not funny.
John is humble.
Mary is either strong or funny.
Someone is not curious or quiet.
Mary is either old or not quiet. | Susan is generous. | neutral | (((curious(paul)|calm(paul)))<=>(~creative(mary)))&
((strong(paul))=>((generous(susan)<~>quiet(susan))))&
((?[X]:(~rich(X)))=>(?[X]:(calm(X))))&
(![X]:(wise(X)=>(old(X)|calm(X))))&
((?[X]:((~creative(X)<~>~wise(X))))=>(~tall(john)))&
(![X]:((~strong(X)|~tall(X))=>(creative(X)|~quiet(X))))&
(![X]:(kind(X)<=>(patient(X)|~strong(X))))&
(![X]:(~rich(X)<=>(~curious(X)|~calm(X))))&
(((~creative(alice)|~quiet(alice)))=>(?[X]:((generous(X)<~>curious(X)))))&
((?[X]:(~rich(X)))=>(?[X]:(tall(X))))&
(![X]:((curious(X)<~>tall(X))<=>(generous(X)<~>creative(X))))&
(![X]:((old(X)|creative(X))=>(~old(X)|~tall(X))))&
(![X]:((~humble(X)|~wise(X))=>~curious(X)))&
((?[X]:((~funny(X)<~>humble(X))))<=>(?[X]:(strong(X))))&
(((~kind(paul)|~creative(paul)))<=>(?[X]:((tall(X)|happy(X)))))&
((?[X]:((old(X)|~curious(X))))=>(?[X]:(humble(X))))&
(?[X]:(~generous(X)))&
((kind(mary)|~tall(mary)))&
(~funny(john))&
(humble(john))&
((strong(mary)<~>funny(mary)))&
(?[X]:((~curious(X)|quiet(X))))&
((old(mary)<~>~quiet(mary))) | generous(susan) | [] | null | 0 |
If lucy is not patient or wise then someone is both curious and not curious. Everyone who is both old and kind is either not old or creative and vice versa. Everyone who is both not calm and calm is not quiet or not kind and vice versa. Everyone who is both generous and curious is both creative and tall and vice versa. Everyone who is old is either not humble or calm. Everyone who is creative is both humble and not happy. Everyone who is not wise or not generous is funny and vice versa. Everyone who is tall or not humble is quiet or not old and vice versa. If fred is not wise then someone is not happy and vice versa. Everyone who is either not kind or humble is either wise or quiet. Everyone who is not funny or not calm is both not tall and curious and vice versa. Everyone who is either not brave or quiet is creative and vice versa. Everyone who is either quiet or strong is both not quiet and tall and vice versa. Everyone who is either brave or humble is either not wise or tall and vice versa. Someone is not rich or generous. Alice is patient. Paul is either rich or old. Someone is calm or curious. | Paul is not wise. | entailment | (((~patient(lucy)|wise(lucy)))=>(?[X]:((curious(X)&~curious(X)))))&
(![X]:((old(X)&kind(X))<=>(~old(X)<~>creative(X))))&
(![X]:((~calm(X)&calm(X))<=>(~quiet(X)|~kind(X))))&
(![X]:((generous(X)&curious(X))<=>(creative(X)&tall(X))))&
(![X]:(old(X)=>(~humble(X)<~>calm(X))))&
(![X]:(creative(X)=>(humble(X)&~happy(X))))&
(![X]:((~wise(X)|~generous(X))<=>funny(X)))&
(![X]:((tall(X)|~humble(X))<=>(quiet(X)|~old(X))))&
((~wise(fred))<=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)<~>humble(X))=>(wise(X)<~>quiet(X))))&
(![X]:((~funny(X)|~calm(X))<=>(~tall(X)&curious(X))))&
(![X]:((~brave(X)<~>quiet(X))<=>creative(X)))&
(![X]:((quiet(X)<~>strong(X))<=>(~quiet(X)&tall(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~wise(X)<~>tall(X))))&
(?[X]:((~rich(X)|generous(X))))&
(patient(alice))&
((rich(paul)<~>old(paul)))&
(?[X]:((calm(X)|curious(X)))) | ~wise(paul) | [
"p1",
"p2",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 327966897168739328394362
% SZS output start Proof for 327966897168739328394362
2. ! [X0] : ((kind(X0) & old(X0)) <=> (~old(X0) <~> creative(X0))) [input p1]
3. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (~kind(X0) | ~quiet(X0))) [input p2]
6. ! [X0] : (creative(X0) => (~happy(X0) & humble(X0))) [input p5]
10. ! [X0] : ((~kind(X0) <~> humble(X0)) => (wise(X0) <~> quiet(X0))) [input p9]
19. wise(paul) [input hypothesis]
24. ! [X0] : ((~happy(X0) & humble(X0)) | ~creative(X0)) [ennf transformation 6]
25. ! [X0] : ((wise(X0) <~> quiet(X0)) | (~kind(X0) <=> humble(X0))) [ennf transformation 10]
28. ! [X0] : (((kind(X0) & old(X0)) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0)))) & (((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | (~kind(X0) | ~old(X0)))) [nnf transformation 2]
29. ! [X0] : (((kind(X0) & old(X0)) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0)))) & (((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | ~kind(X0) | ~old(X0))) [flattening 28]
30. ! [X0] : (((calm(X0) & ~calm(X0)) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 3]
31. ! [X0] : (((calm(X0) & ~calm(X0)) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | ~calm(X0) | calm(X0))) [flattening 30]
43. ! [X0] : (((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0)))) [nnf transformation 25]
57. creative(X0) | ~old(X0) | ~kind(X0) | ~old(X0) [cnf transformation 29]
59. old(X0) | creative(X0) | old(X0) [cnf transformation 29]
64. ~calm(X0) | quiet(X0) [cnf transformation 31]
65. ~calm(X0) | kind(X0) [cnf transformation 31]
66. quiet(X0) | calm(X0) [cnf transformation 31]
67. calm(X0) | kind(X0) [cnf transformation 31]
74. ~creative(X0) | humble(X0) [cnf transformation 24]
88. ~quiet(X0) | ~wise(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 43]
116. wise(paul) [cnf transformation 19]
119. creative(X0) | ~old(X0) | ~kind(X0) [duplicate literal removal 57]
120. creative(X0) | old(X0) [duplicate literal removal 59]
131. ~kind(X0) | creative(X0) [subsumption resolution 119,120]
132. kind(X0) [subsumption resolution 65,67]
133. quiet(X0) [subsumption resolution 64,66]
148. ~wise(X0) | ~kind(X0) | ~humble(X0) [subsumption resolution 88,133]
149. ~humble(X0) | ~wise(X0) [subsumption resolution 148,132]
179. creative(X0) [resolution 131,132]
180. humble(X0) [resolution 179,74]
182. ~wise(X0) [resolution 149,180]
188. $false [resolution 182,116]
% SZS output end Proof for 327966897168739328394362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or generous then someone is wise and vice versa.
Everyone who is kind is not patient and vice versa.
Everyone who is either not patient or calm is old and vice versa.
If someone is not patient then mary is brave or not happy.
If someone is not humble or humble then paul is quiet or rich.
Everyone who is either not quiet or creative is curious.
If someone is both not calm and patient then someone is quiet and vice versa.
If alice is both not happy and quiet then someone is either not quiet or funny.
If mary is either not strong or not wise then someone is patient.
If someone is both not patient and wise then someone is either quiet or strong and vice versa.
If lucy is both not humble and not wise then someone is both creative and not kind.
If someone is not patient then someone is patient and vice versa.
Everyone who is both not funny and quiet is both strong and happy.
Everyone who is either tall or patient is not old or kind and vice versa.
If someone is both wise and creative then lucy is patient.
Everyone who is both not strong and not brave is either wise or old and vice versa.
Someone is both not generous and not happy.
Someone is both curious and not tall.
Someone is both not patient and strong.
Someone is both kind and wise.
Alice is not old or not funny.
Mary is either not wise or wise.
Someone is not calm.
Lucy is generous or old. | Lucy is patient. | neutral | ((?[X]:((brave(X)<~>generous(X))))<=>(?[X]:(wise(X))))&
(![X]:(kind(X)<=>~patient(X)))&
(![X]:((~patient(X)<~>calm(X))<=>old(X)))&
((?[X]:(~patient(X)))=>((brave(mary)|~happy(mary))))&
((?[X]:((~humble(X)|humble(X))))=>((quiet(paul)|rich(paul))))&
(![X]:((~quiet(X)<~>creative(X))=>curious(X)))&
((?[X]:((~calm(X)&patient(X))))<=>(?[X]:(quiet(X))))&
(((~happy(alice)&quiet(alice)))=>(?[X]:((~quiet(X)<~>funny(X)))))&
(((~strong(mary)<~>~wise(mary)))=>(?[X]:(patient(X))))&
((?[X]:((~patient(X)&wise(X))))<=>(?[X]:((quiet(X)<~>strong(X)))))&
(((~humble(lucy)&~wise(lucy)))=>(?[X]:((creative(X)&~kind(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)&quiet(X))=>(strong(X)&happy(X))))&
(![X]:((tall(X)<~>patient(X))<=>(~old(X)|kind(X))))&
((?[X]:((wise(X)&creative(X))))=>(patient(lucy)))&
(![X]:((~strong(X)&~brave(X))<=>(wise(X)<~>old(X))))&
(?[X]:((~generous(X)&~happy(X))))&
(?[X]:((curious(X)&~tall(X))))&
(?[X]:((~patient(X)&strong(X))))&
(?[X]:((kind(X)&wise(X))))&
((~old(alice)|~funny(alice)))&
((~wise(mary)<~>wise(mary)))&
(?[X]:(~calm(X)))&
((generous(lucy)|old(lucy))) | patient(lucy) | [] | null | 0 |
Everyone who is both patient and rich is strong or not strong and vice versa. Everyone who is humble is creative or not patient and vice versa. If paul is either humble or generous then someone is either brave or not quiet and vice versa. If someone is both old and tall then someone is either humble or not quiet. Everyone who is not tall or wise is not creative. If mary is either quiet or not humble then someone is both not humble and strong and vice versa. If susan is not tall then someone is strong or not patient and vice versa. If someone is curious or old then lucy is both not old and rich and vice versa. Everyone who is not rich or not brave is funny and vice versa. If someone is not generous then mary is both curious and not happy and vice versa. Everyone who is either not strong or strong is creative or calm. Everyone who is both not quiet and funny is not brave or generous. Everyone who is not tall or not generous is strong or not rich and vice versa. If someone is not calm then someone is rich or kind. If alice is either not humble or patient then someone is calm or not happy. Everyone who is not humble or not tall is both old and not humble and vice versa. Someone is brave or not curious. Someone is either funny or tall. Lucy is funny. Someone is happy or not tall. Susan is not strong or not old. Someone is both not happy and kind. | Alice is not strong. | entailment | (![X]:((patient(X)&rich(X))<=>(strong(X)|~strong(X))))&
(![X]:(humble(X)<=>(creative(X)|~patient(X))))&
(((humble(paul)<~>generous(paul)))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
((?[X]:((old(X)&tall(X))))=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
(((quiet(mary)<~>~humble(mary)))<=>(?[X]:((~humble(X)&strong(X)))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((curious(X)|old(X))))<=>((~old(lucy)&rich(lucy))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)|calm(X))))&
(![X]:((~quiet(X)&funny(X))=>(~brave(X)|generous(X))))&
(![X]:((~tall(X)|~generous(X))<=>(strong(X)|~rich(X))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(((~humble(alice)<~>patient(alice)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((~humble(X)|~tall(X))<=>(old(X)&~humble(X))))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X))))&
(funny(lucy))&
(?[X]:((happy(X)|~tall(X))))&
((~strong(susan)|~old(susan)))&
(?[X]:((~happy(X)&kind(X)))) | ~strong(alice) | [
"p0",
"p6",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1352943039669695067437320
% SZS output start Proof for 1352943039669695067437320
1. ! [X0] : ((rich(X0) & patient(X0)) <=> (~strong(X0) | strong(X0))) [input p0]
7. ~tall(susan) <=> ? [X0] : (~patient(X0) | strong(X0)) [input p6]
13. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~rich(X0) | strong(X0))) [input p12]
16. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~humble(X0) & old(X0))) [input p15]
21. ~old(susan) | ~strong(susan) [input p20]
23. strong(alice) [input hypothesis]
35. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~rich(X0) | ~patient(X0)))) [nnf transformation 1]
36. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~rich(X0) | ~patient(X0))) [flattening 35]
51. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | tall(susan)) [nnf transformation 7]
52. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X1] : (~patient(X1) | strong(X1)) | tall(susan)) [rectify 51]
53. ? [X1] : (~patient(X1) | strong(X1)) => (~patient(sK3) | strong(sK3)) [choice axiom]
54. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & ((~patient(sK3) | strong(sK3)) | tall(susan)) [skolemisation 52,53]
67. ! [X0] : (((~generous(X0) | ~tall(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 13]
68. ! [X0] : ((~generous(X0) | ~tall(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | (generous(X0) & tall(X0)))) [flattening 67]
69. ! [X0] : (((~tall(X0) | ~humble(X0)) | (humble(X0) | ~old(X0))) & ((~humble(X0) & old(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 16]
70. ! [X0] : ((~tall(X0) | ~humble(X0) | humble(X0) | ~old(X0)) & ((~humble(X0) & old(X0)) | (tall(X0) & humble(X0)))) [flattening 69]
83. rich(X0) | ~strong(X0) [cnf transformation 36]
84. strong(X0) | rich(X0) [cnf transformation 36]
106. ~tall(susan) | ~strong(X0) [cnf transformation 54]
120. ~rich(X0) | strong(X0) | tall(X0) [cnf transformation 68]
125. tall(X0) | old(X0) [cnf transformation 70]
134. ~old(susan) | ~strong(susan) [cnf transformation 21]
136. strong(alice) [cnf transformation 23]
137. rich(X0) [subsumption resolution 83,84]
209. 15 <=> ! [X0] : ~strong(X0) [avatar definition]
210. ~strong(X0) <- (15) [avatar component clause 209]
212. 16 <=> tall(susan) [avatar definition]
214. ~tall(susan) <- (~16) [avatar component clause 212]
215. 15 | ~16 [avatar split clause 106,212,209]
264. tall(X0) | strong(X0) [subsumption resolution 120,137]
294. 33 <=> strong(susan) [avatar definition]
296. ~strong(susan) <- (~33) [avatar component clause 294]
298. 34 <=> old(susan) [avatar definition]
301. ~33 | ~34 [avatar split clause 134,298,294]
302. $false <- (15) [resolution 210,136]
303. ~15 [avatar contradiction clause 302]
306. old(susan) <- (~16) [resolution 125,214]
311. 34 | 16 [avatar split clause 306,212,298]
333. strong(susan) <- (~16) [resolution 264,214]
336. $false <- (~16, ~33) [subsumption resolution 333,296]
337. 16 | 33 [avatar contradiction clause 336]
338. $false [avatar sat refutation 215,301,303,311,337]
% SZS output end Proof for 1352943039669695067437320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or not happy and vice versa.
If someone is either not curious or not calm then lucy is both not kind and not old.
Everyone who is both not curious and creative is not funny or patient and vice versa.
Everyone who is tall or not strong is either patient or not old and vice versa.
If someone is not rich or not wise then someone is humble or not kind and vice versa.
If fred is not humble then someone is calm.
If someone is not curious then someone is not brave.
Everyone who is both not funny and rich is wise and vice versa.
If someone is funny then susan is both generous and not creative and vice versa.
If alice is either tall or not happy then susan is not patient or not tall.
Everyone who is either patient or rich is either patient or curious.
Everyone who is not generous or patient is not tall.
Everyone who is either not curious or not old is both not generous and wise and vice versa.
If susan is either not wise or patient then someone is either not rich or not generous.
Everyone who is both creative and not kind is wise or not old and vice versa.
Everyone who is either not generous or not calm is both not tall and not curious and vice versa.
Someone is patient or creative.
Fred is not tall or calm.
Alice is both not generous and curious.
Paul is both not strong and not curious.
Someone is not patient.
Fred is tall.
John is both old and happy. | Fred is funny. | contradiction | (![X]:(tall(X)<=>(wise(X)<~>~happy(X))))&
((?[X]:((~curious(X)<~>~calm(X))))=>((~kind(lucy)&~old(lucy))))&
(![X]:((~curious(X)&creative(X))<=>(~funny(X)|patient(X))))&
(![X]:((tall(X)|~strong(X))<=>(patient(X)<~>~old(X))))&
((?[X]:((~rich(X)|~wise(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
((~humble(fred))=>(?[X]:(calm(X))))&
((?[X]:(~curious(X)))=>(?[X]:(~brave(X))))&
(![X]:((~funny(X)&rich(X))<=>wise(X)))&
((?[X]:(funny(X)))<=>((generous(susan)&~creative(susan))))&
(((tall(alice)<~>~happy(alice)))=>((~patient(susan)|~tall(susan))))&
(![X]:((patient(X)<~>rich(X))=>(patient(X)<~>curious(X))))&
(![X]:((~generous(X)|patient(X))=>~tall(X)))&
(![X]:((~curious(X)<~>~old(X))<=>(~generous(X)&wise(X))))&
(((~wise(susan)<~>patient(susan)))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:((creative(X)&~kind(X))<=>(wise(X)|~old(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(~tall(X)&~curious(X))))&
(?[X]:((patient(X)|creative(X))))&
((~tall(fred)|calm(fred)))&
((~generous(alice)&curious(alice)))&
((~strong(paul)&~curious(paul)))&
(?[X]:(~patient(X)))&
(tall(fred))&
((old(john)&happy(john))) | funny(fred) | [
"p2",
"p3",
"p11",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8975919739032884913302516
% SZS output start Proof for 8975919739032884913302516
3. ! [X0] : ((creative(X0) & ~curious(X0)) <=> (patient(X0) | ~funny(X0))) [input p2]
4. ! [X0] : ((~strong(X0) | tall(X0)) <=> (patient(X0) <~> ~old(X0))) [input p3]
12. ! [X0] : ((patient(X0) | ~generous(X0)) => ~tall(X0)) [input p11]
13. ! [X0] : ((~curious(X0) <~> ~old(X0)) <=> (wise(X0) & ~generous(X0))) [input p12]
15. ! [X0] : ((~kind(X0) & creative(X0)) <=> (~old(X0) | wise(X0))) [input p14]
22. tall(fred) [input p21]
24. funny(fred) [input hypothesis]
33. ! [X0] : (~tall(X0) | (~patient(X0) & generous(X0))) [ennf transformation 12]
37. ! [X0] : (((creative(X0) & ~curious(X0)) | (~patient(X0) & funny(X0))) & ((patient(X0) | ~funny(X0)) | (~creative(X0) | curious(X0)))) [nnf transformation 3]
38. ! [X0] : (((creative(X0) & ~curious(X0)) | (~patient(X0) & funny(X0))) & (patient(X0) | ~funny(X0) | ~creative(X0) | curious(X0))) [flattening 37]
39. ! [X0] : (((~strong(X0) | tall(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (strong(X0) & ~tall(X0)))) [nnf transformation 4]
40. ! [X0] : ((~strong(X0) | tall(X0) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (strong(X0) & ~tall(X0)))) [flattening 39]
57. ! [X0] : ((((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (~wise(X0) | generous(X0))) & ((wise(X0) & ~generous(X0)) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))))) [nnf transformation 13]
58. ! [X0] : ((((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | ~wise(X0) | generous(X0)) & ((wise(X0) & ~generous(X0)) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))))) [flattening 57]
62. ! [X0] : (((~kind(X0) & creative(X0)) | (old(X0) & ~wise(X0))) & ((~old(X0) | wise(X0)) | (kind(X0) | ~creative(X0)))) [nnf transformation 15]
63. ! [X0] : (((~kind(X0) & creative(X0)) | (old(X0) & ~wise(X0))) & (~old(X0) | wise(X0) | kind(X0) | ~creative(X0))) [flattening 62]
78. ~funny(X0) | patient(X0) | ~creative(X0) | curious(X0) [cnf transformation 38]
83. ~old(X0) | patient(X0) | ~tall(X0) [cnf transformation 40]
106. ~tall(X0) | generous(X0) [cnf transformation 33]
107. ~patient(X0) | ~tall(X0) [cnf transformation 33]
109. ~generous(X0) | ~curious(X0) | old(X0) [cnf transformation 58]
120. creative(X0) | old(X0) [cnf transformation 63]
136. tall(fred) [cnf transformation 22]
139. funny(fred) [cnf transformation 24]
274. generous(fred) [resolution 106,136]
326. 32 <=> curious(fred) [avatar definition]
330. 33 <=> old(fred) [avatar definition]
331. old(fred) <- (33) [avatar component clause 330]
345. ~curious(fred) | old(fred) [resolution 109,274]
387. patient(fred) | ~creative(fred) | curious(fred) [resolution 78,139]
393. 38 <=> creative(fred) [avatar definition]
395. ~creative(fred) <- (~38) [avatar component clause 393]
397. 39 <=> patient(fred) [avatar definition]
399. patient(fred) <- (39) [avatar component clause 397]
414. old(fred) <- (~38) [resolution 395,120]
417. 33 | 38 [avatar split clause 414,393,330]
418. 33 | ~32 [avatar split clause 345,326,330]
435. patient(fred) | ~tall(fred) <- (33) [resolution 331,83]
441. patient(fred) <- (33) [subsumption resolution 435,136]
442. 39 | ~33 [avatar split clause 441,330,397]
443. 32 | ~38 | 39 [avatar split clause 387,397,393,326]
477. ~tall(fred) <- (39) [resolution 399,107]
485. $false <- (39) [subsumption resolution 477,136]
486. ~39 [avatar contradiction clause 485]
487. $false [avatar sat refutation 417,418,442,443,486]
% SZS output end Proof for 8975919739032884913302516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is quiet then fred is not humble.
Everyone who is either happy or not tall is not humble or not old and vice versa.
If susan is either strong or not calm then paul is both creative and curious and vice versa.
If susan is wise then someone is humble and vice versa.
Everyone who is not calm is not curious or not tall and vice versa.
Everyone who is curious or wise is either not humble or not quiet and vice versa.
If someone is either not quiet or humble then john is patient and vice versa.
If paul is either not funny or wise then someone is not curious and vice versa.
Everyone who is both not calm and generous is not strong and vice versa.
If fred is both not creative and not generous then someone is both not strong and not humble and vice versa.
Everyone who is not wise is tall or not creative and vice versa.
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
Everyone who is old or not quiet is both curious and not brave.
If paul is either wise or not old then fred is tall.
Mary is both not funny and old.
Lucy is brave or creative.
Someone is wise or funny.
Alice is both happy and wise.
Someone is either not strong or not generous.
Alice is not wise or generous. | Lucy is not curious. | contradiction | ((quiet(alice))=>(~humble(fred)))&
(![X]:((happy(X)<~>~tall(X))<=>(~humble(X)|~old(X))))&
(((strong(susan)<~>~calm(susan)))<=>((creative(paul)&curious(paul))))&
((wise(susan))<=>(?[X]:(humble(X))))&
(![X]:(~calm(X)<=>(~curious(X)|~tall(X))))&
(![X]:((curious(X)|wise(X))<=>(~humble(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(patient(john)))&
(((~funny(paul)<~>wise(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((~calm(X)&generous(X))<=>~strong(X)))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
((~funny(mary)&old(mary)))&
((brave(lucy)|creative(lucy)))&
(?[X]:((wise(X)|funny(X))))&
((happy(alice)&wise(alice)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((~wise(alice)|generous(alice))) | ~curious(lucy) | [
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 600663910014528556050821
% SZS output start Proof for 600663910014528556050821
13. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p12]
15. ! [X0] : ((~quiet(X0) | old(X0)) => (~brave(X0) & curious(X0))) [input p14]
23. ~curious(lucy) [input hypothesis]
28. ! [X0] : ((~brave(X0) & curious(X0)) | (quiet(X0) & ~old(X0))) [ennf transformation 15]
63. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 13]
64. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 63]
119. ~patient(X0) | ~patient(X0) [cnf transformation 64]
121. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 64]
124. curious(X0) | quiet(X0) [cnf transformation 28]
138. ~curious(lucy) [cnf transformation 23]
139. ~patient(X0) [duplicate literal removal 119]
140. ~quiet(X0) | patient(X0) [duplicate literal removal 121]
333. quiet(lucy) [resolution 124,138]
349. patient(lucy) [resolution 333,140]
350. $false [subsumption resolution 349,139]
% SZS output end Proof for 600663910014528556050821
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and curious is either patient or not calm and vice versa. If paul is both not wise and not brave then someone is kind or not creative and vice versa. Everyone who is both calm and patient is not calm or funny. If someone is both old and not curious then someone is either not funny or not rich and vice versa. If someone is not happy or not wise then alice is both tall and generous. Everyone who is not wise or quiet is both not tall and not wise and vice versa. Everyone who is both curious and brave is both curious and not creative and vice versa. Everyone who is not generous is both not happy and not calm and vice versa. Everyone who is patient is not brave or not old and vice versa. Everyone who is kind is curious. If fred is not patient or brave then susan is both not rich and rich. If fred is both not rich and tall then someone is both quiet and not strong and vice versa. If someone is not tall or not creative then someone is not generous and vice versa. Everyone who is either humble or not kind is either happy or tall and vice versa. Everyone who is both not quiet and not strong is both not kind and not patient. If lucy is both creative and strong then john is not brave or not funny and vice versa. Someone is kind. Fred is both generous and not quiet. Lucy is both humble and brave. Someone is not funny or rich. Fred is either not kind or funny. Someone is not happy or funny. Fred is both not old and not humble. | Alice is quiet. | contradiction | (![X]:((~curious(X)&curious(X))<=>(patient(X)<~>~calm(X))))&
(((~wise(paul)&~brave(paul)))<=>(?[X]:((kind(X)|~creative(X)))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)|funny(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:((~funny(X)<~>~rich(X)))))&
((?[X]:((~happy(X)|~wise(X))))=>((tall(alice)&generous(alice))))&
(![X]:((~wise(X)|quiet(X))<=>(~tall(X)&~wise(X))))&
(![X]:((curious(X)&brave(X))<=>(curious(X)&~creative(X))))&
(![X]:(~generous(X)<=>(~happy(X)&~calm(X))))&
(![X]:(patient(X)<=>(~brave(X)|~old(X))))&
(![X]:(kind(X)=>curious(X)))&
(((~patient(fred)|brave(fred)))=>((~rich(susan)&rich(susan))))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)&~strong(X)))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:(~generous(X))))&
(![X]:((humble(X)<~>~kind(X))<=>(happy(X)<~>tall(X))))&
(![X]:((~quiet(X)&~strong(X))=>(~kind(X)&~patient(X))))&
(((creative(lucy)&strong(lucy)))<=>((~brave(john)|~funny(john))))&
(?[X]:(kind(X)))&
((generous(fred)&~quiet(fred)))&
((humble(lucy)&brave(lucy)))&
(?[X]:((~funny(X)|rich(X))))&
((~kind(fred)<~>funny(fred)))&
(?[X]:((~happy(X)|funny(X))))&
((~old(fred)&~humble(fred))) | quiet(alice) | [
"p1",
"p4",
"p5",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8997923833731341659251978
% SZS output start Proof for 8997923833731341659251978
2. (~brave(paul) & ~wise(paul)) <=> ? [X0] : (~creative(X0) | kind(X0)) [input p1]
5. ? [X0] : (~wise(X0) | ~happy(X0)) => (generous(alice) & tall(alice)) [input p4]
6. ! [X0] : ((quiet(X0) | ~wise(X0)) <=> (~wise(X0) & ~tall(X0))) [input p5]
17. ? [X0] : kind(X0) [input p16]
24. quiet(alice) [input hypothesis]
29. (generous(alice) & tall(alice)) | ! [X0] : (wise(X0) & happy(X0)) [ennf transformation 5]
36. ((~brave(paul) & ~wise(paul)) | ! [X0] : (creative(X0) & ~kind(X0))) & (? [X0] : (~creative(X0) | kind(X0)) | (brave(paul) | wise(paul))) [nnf transformation 2]
37. ((~brave(paul) & ~wise(paul)) | ! [X0] : (creative(X0) & ~kind(X0))) & (? [X0] : (~creative(X0) | kind(X0)) | brave(paul) | wise(paul)) [flattening 36]
38. ((~brave(paul) & ~wise(paul)) | ! [X0] : (creative(X0) & ~kind(X0))) & (? [X1] : (~creative(X1) | kind(X1)) | brave(paul) | wise(paul)) [rectify 37]
39. ? [X1] : (~creative(X1) | kind(X1)) => (~creative(sK0) | kind(sK0)) [choice axiom]
40. ((~brave(paul) & ~wise(paul)) | ! [X0] : (creative(X0) & ~kind(X0))) & ((~creative(sK0) | kind(sK0)) | brave(paul) | wise(paul)) [skolemisation 38,39]
46. ! [X0] : (((quiet(X0) | ~wise(X0)) | (wise(X0) | tall(X0))) & ((~wise(X0) & ~tall(X0)) | (~quiet(X0) & wise(X0)))) [nnf transformation 6]
47. ! [X0] : ((quiet(X0) | ~wise(X0) | wise(X0) | tall(X0)) & ((~wise(X0) & ~tall(X0)) | (~quiet(X0) & wise(X0)))) [flattening 46]
67. ? [X0] : kind(X0) => kind(sK6) [choice axiom]
68. kind(sK6) [skolemisation 17,67]
81. ~wise(paul) | ~kind(X0) [cnf transformation 40]
93. tall(alice) | wise(X0) [cnf transformation 29]
97. ~quiet(X0) | ~tall(X0) [cnf transformation 47]
138. kind(sK6) [cnf transformation 68]
149. quiet(alice) [cnf transformation 24]
162. 3 <=> ! [X0] : ~kind(X0) [avatar definition]
163. ~kind(X0) <- (3) [avatar component clause 162]
166. 4 <=> wise(paul) [avatar definition]
168. ~wise(paul) <- (~4) [avatar component clause 166]
170. 3 | ~4 [avatar split clause 81,166,162]
212. 14 <=> ! [X0] : wise(X0) [avatar definition]
213. wise(X0) <- (14) [avatar component clause 212]
224. 17 <=> tall(alice) [avatar definition]
226. tall(alice) <- (17) [avatar component clause 224]
227. 14 | 17 [avatar split clause 93,224,212]
338. $false <- (~4, 14) [subsumption resolution 168,213]
339. 4 | ~14 [avatar contradiction clause 338]
340. $false <- (3) [resolution 163,138]
341. ~3 [avatar contradiction clause 340]
347. ~tall(alice) [resolution 97,149]
348. $false <- (17) [subsumption resolution 347,226]
349. ~17 [avatar contradiction clause 348]
350. $false [avatar sat refutation 170,227,339,341,349]
% SZS output end Proof for 8997923833731341659251978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or patient is both not generous and old and vice versa.
Everyone who is not quiet or not wise is both not kind and quiet and vice versa.
Everyone who is either rich or happy is not strong and vice versa.
If mary is wise or creative then fred is both curious and not curious and vice versa.
Everyone who is not happy or kind is not creative or not happy and vice versa.
If someone is not rich or happy then john is both not old and patient and vice versa.
Everyone who is both humble and not happy is either not creative or brave and vice versa.
Everyone who is both brave and tall is either not strong or kind.
Everyone who is both curious and brave is not patient and vice versa.
If someone is both calm and not old then john is rich or not brave.
Everyone who is either curious or brave is not happy and vice versa.
Everyone who is both wise and not old is either generous or not quiet and vice versa.
Everyone who is strong is both patient and not generous.
Everyone who is happy is either not creative or not curious.
Everyone who is not calm is both old and brave.
Everyone who is either humble or calm is both happy and quiet.
John is rich or not happy.
Someone is both not calm and not funny.
Lucy is not brave.
Someone is either brave or not tall.
Someone is not wise. | Fred is not old. | contradiction | (![X]:((~old(X)|patient(X))<=>(~generous(X)&old(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~kind(X)&quiet(X))))&
(![X]:((rich(X)<~>happy(X))<=>~strong(X)))&
(((wise(mary)|creative(mary)))<=>((curious(fred)&~curious(fred))))&
(![X]:((~happy(X)|kind(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((~old(john)&patient(john))))&
(![X]:((humble(X)&~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((brave(X)&tall(X))=>(~strong(X)<~>kind(X))))&
(![X]:((curious(X)&brave(X))<=>~patient(X)))&
((?[X]:((calm(X)&~old(X))))=>((rich(john)|~brave(john))))&
(![X]:((curious(X)<~>brave(X))<=>~happy(X)))&
(![X]:((wise(X)&~old(X))<=>(generous(X)<~>~quiet(X))))&
(![X]:(strong(X)=>(patient(X)&~generous(X))))&
(![X]:(happy(X)=>(~creative(X)<~>~curious(X))))&
(![X]:(~calm(X)=>(old(X)&brave(X))))&
(![X]:((humble(X)<~>calm(X))=>(happy(X)&quiet(X))))&
((rich(john)|~happy(john)))&
(?[X]:((~calm(X)&~funny(X))))&
(~brave(lucy))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:(~wise(X))) | ~old(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 5160045855043132197539281
% SZS output start Proof for 5160045855043132197539281
1. ! [X0] : ((patient(X0) | ~old(X0)) <=> (old(X0) & ~generous(X0))) [input p0]
22. ~old(fred) [input hypothesis]
32. ! [X0] : (((patient(X0) | ~old(X0)) | (~old(X0) | generous(X0))) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [nnf transformation 1]
33. ! [X0] : ((patient(X0) | ~old(X0) | ~old(X0) | generous(X0)) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [flattening 32]
65. old(X0) | old(X0) [cnf transformation 33]
129. ~old(fred) [cnf transformation 22]
132. old(X0) [duplicate literal removal 65]
187. $false [subsumption resolution 129,132]
% SZS output end Proof for 5160045855043132197539281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or not strong is patient and vice versa.
If someone is both funny and not strong then someone is not happy or old and vice versa.
If mary is quiet then someone is either strong or not strong and vice versa.
Everyone who is curious or not tall is humble or funny.
If someone is calm or rich then someone is both wise and not old.
If someone is either calm or generous then someone is both wise and creative.
Everyone who is either not strong or not funny is not tall and vice versa.
If someone is funny then fred is humble or curious and vice versa.
Everyone who is either not creative or not curious is quiet or patient and vice versa.
Everyone who is humble is not humble.
Everyone who is both calm and creative is both not creative and strong.
Everyone who is not quiet is quiet or brave.
If someone is not old or not wise then alice is quiet.
If alice is either happy or creative then alice is kind or old and vice versa.
If someone is both happy and not funny then someone is not strong or quiet.
If mary is either calm or curious then someone is either not curious or not brave.
Someone is not kind or creative.
Mary is either curious or creative.
Alice is either calm or generous.
Fred is either strong or not curious.
Someone is not happy or strong.
John is not calm.
Someone is happy or patient.
Someone is not generous. | Mary is wise. | neutral | (![X]:((rich(X)|~strong(X))<=>patient(X)))&
((?[X]:((funny(X)&~strong(X))))<=>(?[X]:((~happy(X)|old(X)))))&
((quiet(mary))<=>(?[X]:((strong(X)<~>~strong(X)))))&
(![X]:((curious(X)|~tall(X))=>(humble(X)|funny(X))))&
((?[X]:((calm(X)|rich(X))))=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:((calm(X)<~>generous(X))))=>(?[X]:((wise(X)&creative(X)))))&
(![X]:((~strong(X)<~>~funny(X))<=>~tall(X)))&
((?[X]:(funny(X)))<=>((humble(fred)|curious(fred))))&
(![X]:((~creative(X)<~>~curious(X))<=>(quiet(X)|patient(X))))&
(![X]:(humble(X)=>~humble(X)))&
(![X]:((calm(X)&creative(X))=>(~creative(X)&strong(X))))&
(![X]:(~quiet(X)=>(quiet(X)|brave(X))))&
((?[X]:((~old(X)|~wise(X))))=>(quiet(alice)))&
(((happy(alice)<~>creative(alice)))<=>((kind(alice)|old(alice))))&
((?[X]:((happy(X)&~funny(X))))=>(?[X]:((~strong(X)|quiet(X)))))&
(((calm(mary)<~>curious(mary)))=>(?[X]:((~curious(X)<~>~brave(X)))))&
(?[X]:((~kind(X)|creative(X))))&
((curious(mary)<~>creative(mary)))&
((calm(alice)<~>generous(alice)))&
((strong(fred)<~>~curious(fred)))&
(?[X]:((~happy(X)|strong(X))))&
(~calm(john))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:(~generous(X))) | wise(mary) | [] | null | 0 |
Everyone who is both kind and funny is either not strong or creative. If fred is generous then paul is both old and patient. Everyone who is both not happy and wise is brave. Everyone who is either kind or not strong is either curious or funny and vice versa. If someone is tall or not strong then john is both not humble and curious. If someone is either not calm or not quiet then paul is both tall and not kind and vice versa. Everyone who is both generous and not strong is not patient or not humble and vice versa. If susan is not brave then paul is patient and vice versa. If alice is both not humble and quiet then someone is old and vice versa. Everyone who is old or strong is both not creative and not strong and vice versa. Everyone who is either funny or not rich is both not curious and generous and vice versa. If alice is not quiet or not funny then someone is not calm or quiet and vice versa. If someone is wise then lucy is either brave or quiet. If someone is both not humble and not tall then someone is either not tall or not quiet. Everyone who is both not kind and kind is not tall. If mary is either not curious or old then someone is both not brave and not quiet and vice versa. Someone is both generous and not strong. Alice is both not strong and not patient. Someone is not curious or not creative. Susan is either rich or not old. Someone is either patient or not generous. Paul is rich. Paul is curious. | Susan is curious. | neutral | (![X]:((kind(X)&funny(X))=>(~strong(X)<~>creative(X))))&
((generous(fred))=>((old(paul)&patient(paul))))&
(![X]:((~happy(X)&wise(X))=>brave(X)))&
(![X]:((kind(X)<~>~strong(X))<=>(curious(X)<~>funny(X))))&
((?[X]:((tall(X)|~strong(X))))=>((~humble(john)&curious(john))))&
((?[X]:((~calm(X)<~>~quiet(X))))<=>((tall(paul)&~kind(paul))))&
(![X]:((generous(X)&~strong(X))<=>(~patient(X)|~humble(X))))&
((~brave(susan))<=>(patient(paul)))&
(((~humble(alice)&quiet(alice)))<=>(?[X]:(old(X))))&
(![X]:((old(X)|strong(X))<=>(~creative(X)&~strong(X))))&
(![X]:((funny(X)<~>~rich(X))<=>(~curious(X)&generous(X))))&
(((~quiet(alice)|~funny(alice)))<=>(?[X]:((~calm(X)|quiet(X)))))&
((?[X]:(wise(X)))=>((brave(lucy)<~>quiet(lucy))))&
((?[X]:((~humble(X)&~tall(X))))=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(![X]:((~kind(X)&kind(X))=>~tall(X)))&
(((~curious(mary)<~>old(mary)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
(?[X]:((generous(X)&~strong(X))))&
((~strong(alice)&~patient(alice)))&
(?[X]:((~curious(X)|~creative(X))))&
((rich(susan)<~>~old(susan)))&
(?[X]:((patient(X)<~>~generous(X))))&
(rich(paul))&
(curious(paul)) | curious(susan) | [] | null | 0 |
Everyone who is both not curious and strong is not funny and vice versa.
Everyone who is both not creative and calm is not brave or not kind.
If alice is generous or not calm then someone is both not funny and quiet and vice versa.
Everyone who is not strong or curious is either kind or happy and vice versa.
Everyone who is both happy and not humble is not brave or not humble and vice versa.
Everyone who is both curious and rich is generous.
Everyone who is either patient or not curious is both humble and happy and vice versa.
Everyone who is not strong is either creative or calm.
If alice is both humble and curious then someone is both not happy and not old and vice versa.
Everyone who is either not old or not quiet is not kind and vice versa.
Everyone who is both not strong and not humble is either funny or not wise.
Everyone who is not old or not kind is either quiet or not calm and vice versa.
If fred is both rich and not calm then someone is patient and vice versa.
Everyone who is either humble or creative is patient.
If alice is funny or patient then alice is happy.
If john is strong or not generous then alice is not funny and vice versa.
Fred is either funny or not brave.
John is not wise or generous.
Someone is both not creative and curious.
Susan is not old.
Someone is both curious and not rich.
Someone is generous or calm.
Mary is patient or funny.
Someone is either wise or not rich. | Alice is not patient. | neutral | (![X]:((~curious(X)&strong(X))<=>~funny(X)))&
(![X]:((~creative(X)&calm(X))=>(~brave(X)|~kind(X))))&
(((generous(alice)|~calm(alice)))<=>(?[X]:((~funny(X)&quiet(X)))))&
(![X]:((~strong(X)|curious(X))<=>(kind(X)<~>happy(X))))&
(![X]:((happy(X)&~humble(X))<=>(~brave(X)|~humble(X))))&
(![X]:((curious(X)&rich(X))=>generous(X)))&
(![X]:((patient(X)<~>~curious(X))<=>(humble(X)&happy(X))))&
(![X]:(~strong(X)=>(creative(X)<~>calm(X))))&
(((humble(alice)&curious(alice)))<=>(?[X]:((~happy(X)&~old(X)))))&
(![X]:((~old(X)<~>~quiet(X))<=>~kind(X)))&
(![X]:((~strong(X)&~humble(X))=>(funny(X)<~>~wise(X))))&
(![X]:((~old(X)|~kind(X))<=>(quiet(X)<~>~calm(X))))&
(((rich(fred)&~calm(fred)))<=>(?[X]:(patient(X))))&
(![X]:((humble(X)<~>creative(X))=>patient(X)))&
(((funny(alice)|patient(alice)))=>(happy(alice)))&
(((strong(john)|~generous(john)))<=>(~funny(alice)))&
((funny(fred)<~>~brave(fred)))&
((~wise(john)|generous(john)))&
(?[X]:((~creative(X)&curious(X))))&
(~old(susan))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((generous(X)|calm(X))))&
((patient(mary)|funny(mary)))&
(?[X]:((wise(X)<~>~rich(X)))) | ~patient(alice) | [] | null | 0 |
If lucy is both not funny and wise then someone is not rich or not wise and vice versa. Everyone who is wise or old is tall or not tall and vice versa. If someone is strong then alice is not curious. If john is calm then alice is funny or not happy. Everyone who is quiet is kind or patient and vice versa. Everyone who is either strong or not patient is not happy and vice versa. Everyone who is either rich or humble is not creative or humble and vice versa. Everyone who is kind or not happy is either strong or happy. If lucy is not funny or not humble then susan is both not humble and not calm and vice versa. If someone is creative or kind then paul is either generous or curious and vice versa. Everyone who is curious is either not wise or not creative and vice versa. If mary is not quiet or tall then mary is not creative or not tall and vice versa. If someone is patient or not curious then paul is not happy and vice versa. Everyone who is generous or not funny is kind or not patient. If someone is either not generous or not funny then lucy is curious. If someone is not funny or not calm then fred is curious. Someone is either not generous or not wise. Someone is generous. Someone is strong or wise. Someone is both rich and not generous. Alice is either brave or not brave. Susan is wise or not patient. | Lucy is not calm. | neutral | (((~funny(lucy)&wise(lucy)))<=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:((wise(X)|old(X))<=>(tall(X)|~tall(X))))&
((?[X]:(strong(X)))=>(~curious(alice)))&
((calm(john))=>((funny(alice)|~happy(alice))))&
(![X]:(quiet(X)<=>(kind(X)|patient(X))))&
(![X]:((strong(X)<~>~patient(X))<=>~happy(X)))&
(![X]:((rich(X)<~>humble(X))<=>(~creative(X)|humble(X))))&
(![X]:((kind(X)|~happy(X))=>(strong(X)<~>happy(X))))&
(((~funny(lucy)|~humble(lucy)))<=>((~humble(susan)&~calm(susan))))&
((?[X]:((creative(X)|kind(X))))<=>((generous(paul)<~>curious(paul))))&
(![X]:(curious(X)<=>(~wise(X)<~>~creative(X))))&
(((~quiet(mary)|tall(mary)))<=>((~creative(mary)|~tall(mary))))&
((?[X]:((patient(X)|~curious(X))))<=>(~happy(paul)))&
(![X]:((generous(X)|~funny(X))=>(kind(X)|~patient(X))))&
((?[X]:((~generous(X)<~>~funny(X))))=>(curious(lucy)))&
((?[X]:((~funny(X)|~calm(X))))=>(curious(fred)))&
(?[X]:((~generous(X)<~>~wise(X))))&
(?[X]:(generous(X)))&
(?[X]:((strong(X)|wise(X))))&
(?[X]:((rich(X)&~generous(X))))&
((brave(alice)<~>~brave(alice)))&
((wise(susan)|~patient(susan))) | ~calm(lucy) | [] | null | 0 |
Everyone who is strong or not calm is not strong and vice versa. If someone is not happy then susan is not quiet and vice versa. Everyone who is brave is both not generous and not patient. Everyone who is either not old or generous is both calm and not strong. If paul is both strong and not calm then alice is not rich. Everyone who is both funny and patient is both generous and not kind. If mary is both not kind and brave then susan is tall and vice versa. Everyone who is both happy and not calm is either not tall or wise and vice versa. Everyone who is not quiet or not brave is patient or wise. If someone is not humble then someone is strong or not patient. Everyone who is both not patient and quiet is not rich or not wise and vice versa. Everyone who is either not rich or not funny is both calm and not funny and vice versa. If someone is either rich or calm then fred is happy and vice versa. Everyone who is both not generous and not rich is curious and vice versa. If fred is either not kind or quiet then someone is both rich and old and vice versa. Everyone who is not patient is either not humble or rich and vice versa. John is patient. John is strong or quiet. Someone is patient. Someone is both rich and wise. Paul is not funny. Susan is both rich and not generous. Someone is either kind or quiet. | Paul is quiet. | entailment | (![X]:((strong(X)|~calm(X))<=>~strong(X)))&
((?[X]:(~happy(X)))<=>(~quiet(susan)))&
(![X]:(brave(X)=>(~generous(X)&~patient(X))))&
(![X]:((~old(X)<~>generous(X))=>(calm(X)&~strong(X))))&
(((strong(paul)&~calm(paul)))=>(~rich(alice)))&
(![X]:((funny(X)&patient(X))=>(generous(X)&~kind(X))))&
(((~kind(mary)&brave(mary)))<=>(tall(susan)))&
(![X]:((happy(X)&~calm(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~quiet(X)|~brave(X))=>(patient(X)|wise(X))))&
((?[X]:(~humble(X)))=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~patient(X)&quiet(X))<=>(~rich(X)|~wise(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(calm(X)&~funny(X))))&
((?[X]:((rich(X)<~>calm(X))))<=>(happy(fred)))&
(![X]:((~generous(X)&~rich(X))<=>curious(X)))&
(((~kind(fred)<~>quiet(fred)))<=>(?[X]:((rich(X)&old(X)))))&
(![X]:(~patient(X)<=>(~humble(X)<~>rich(X))))&
(patient(john))&
((strong(john)|quiet(john)))&
(?[X]:(patient(X)))&
(?[X]:((rich(X)&wise(X))))&
(~funny(paul))&
((rich(susan)&~generous(susan)))&
(?[X]:((kind(X)<~>quiet(X)))) | quiet(paul) | [
"p0",
"p10",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8025032169113280901838973
% SZS output start Proof for 8025032169113280901838973
1. ! [X0] : ((~calm(X0) | strong(X0)) <=> ~strong(X0)) [input p0]
11. ! [X0] : ((quiet(X0) & ~patient(X0)) <=> (~wise(X0) | ~rich(X0))) [input p10]
12. ! [X0] : ((~rich(X0) <~> ~funny(X0)) <=> (~funny(X0) & calm(X0))) [input p11]
21. ~funny(paul) [input p20]
24. ~quiet(paul) [input hypothesis]
35. ! [X0] : (((~calm(X0) | strong(X0)) | strong(X0)) & (~strong(X0) | (calm(X0) & ~strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((~calm(X0) | strong(X0) | strong(X0)) & (~strong(X0) | (calm(X0) & ~strong(X0)))) [flattening 35]
49. ! [X0] : (((quiet(X0) & ~patient(X0)) | (wise(X0) & rich(X0))) & ((~wise(X0) | ~rich(X0)) | (~quiet(X0) | patient(X0)))) [nnf transformation 11]
50. ! [X0] : (((quiet(X0) & ~patient(X0)) | (wise(X0) & rich(X0))) & (~wise(X0) | ~rich(X0) | ~quiet(X0) | patient(X0))) [flattening 49]
51. ! [X0] : ((((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0))))) [nnf transformation 12]
52. ! [X0] : ((((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0))))) [flattening 51]
69. ~strong(X0) | ~strong(X0) [cnf transformation 36]
71. ~calm(X0) | strong(X0) | strong(X0) [cnf transformation 36]
98. rich(X0) | quiet(X0) [cnf transformation 50]
101. ~rich(X0) | calm(X0) | funny(X0) [cnf transformation 52]
125. ~funny(paul) [cnf transformation 21]
130. ~quiet(paul) [cnf transformation 24]
133. ~strong(X0) [duplicate literal removal 69]
134. ~calm(X0) | strong(X0) [duplicate literal removal 71]
322. funny(X0) | calm(X0) | quiet(X0) [resolution 101,98]
515. calm(paul) | quiet(paul) [resolution 322,125]
517. calm(paul) [subsumption resolution 515,130]
530. strong(paul) [resolution 517,134]
541. $false [subsumption resolution 530,133]
% SZS output end Proof for 8025032169113280901838973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is both brave and not kind and vice versa.
Everyone who is both not rich and not brave is not old or old and vice versa.
Everyone who is either not calm or humble is not old or funny.
If john is old then alice is either rich or not brave.
If alice is either old or not kind then alice is not happy or happy.
If fred is either rich or old then john is both not humble and funny.
If susan is both not patient and not wise then alice is both not humble and curious.
If someone is not patient then someone is brave or not generous and vice versa.
If paul is tall or not humble then someone is not rich or not quiet and vice versa.
Everyone who is happy or not kind is both tall and not strong.
Everyone who is either not generous or not funny is humble or not calm.
If mary is either brave or not strong then lucy is happy and vice versa.
If someone is generous or humble then paul is not old and vice versa.
If paul is old then someone is both rich and not creative.
If fred is kind or not old then fred is both not brave and creative.
Everyone who is both not brave and not humble is brave.
Lucy is either not quiet or creative.
Someone is either not strong or rich.
Someone is either not quiet or creative.
Fred is either brave or quiet.
Someone is both old and not funny. | Fred is not happy. | neutral | (![X]:(~creative(X)<=>(brave(X)&~kind(X))))&
(![X]:((~rich(X)&~brave(X))<=>(~old(X)|old(X))))&
(![X]:((~calm(X)<~>humble(X))=>(~old(X)|funny(X))))&
((old(john))=>((rich(alice)<~>~brave(alice))))&
(((old(alice)<~>~kind(alice)))=>((~happy(alice)|happy(alice))))&
(((rich(fred)<~>old(fred)))=>((~humble(john)&funny(john))))&
(((~patient(susan)&~wise(susan)))=>((~humble(alice)&curious(alice))))&
((?[X]:(~patient(X)))<=>(?[X]:((brave(X)|~generous(X)))))&
(((tall(paul)|~humble(paul)))<=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((happy(X)|~kind(X))=>(tall(X)&~strong(X))))&
(![X]:((~generous(X)<~>~funny(X))=>(humble(X)|~calm(X))))&
(((brave(mary)<~>~strong(mary)))<=>(happy(lucy)))&
((?[X]:((generous(X)|humble(X))))<=>(~old(paul)))&
((old(paul))=>(?[X]:((rich(X)&~creative(X)))))&
(((kind(fred)|~old(fred)))=>((~brave(fred)&creative(fred))))&
(![X]:((~brave(X)&~humble(X))=>brave(X)))&
((~quiet(lucy)<~>creative(lucy)))&
(?[X]:((~strong(X)<~>rich(X))))&
(?[X]:((~quiet(X)<~>creative(X))))&
((brave(fred)<~>quiet(fred)))&
(?[X]:((old(X)&~funny(X)))) | ~happy(fred) | [] | null | 0 |
Everyone who is not wise is both not wise and not happy and vice versa.
If someone is tall then paul is not funny or not old.
If someone is rich then john is both not humble and old and vice versa.
If someone is either not strong or not curious then someone is both rich and not patient and vice versa.
Everyone who is creative is both not happy and not patient and vice versa.
Everyone who is either curious or not kind is both quiet and rich and vice versa.
If mary is both not humble and not wise then someone is wise or kind.
If someone is not generous then someone is not kind and vice versa.
If paul is either quiet or wise then lucy is both not wise and wise.
If someone is either not humble or not creative then someone is both strong and not strong.
Everyone who is not happy or not patient is both humble and creative.
If someone is brave then fred is either happy or kind and vice versa.
If someone is not generous or old then someone is rich or happy.
Everyone who is not kind or not strong is happy or not funny.
If someone is kind then paul is not quiet.
Everyone who is not rich is generous and vice versa.
Alice is not funny or not patient.
Alice is both not generous and not quiet.
Someone is both wise and not strong.
Susan is wise or not rich.
Alice is either not creative or not strong.
Someone is both old and not curious.
Mary is tall.
Alice is tall or not brave. | Alice is funny. | contradiction | (![X]:(~wise(X)<=>(~wise(X)&~happy(X))))&
((?[X]:(tall(X)))=>((~funny(paul)|~old(paul))))&
((?[X]:(rich(X)))<=>((~humble(john)&old(john))))&
((?[X]:((~strong(X)<~>~curious(X))))<=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:(creative(X)<=>(~happy(X)&~patient(X))))&
(![X]:((curious(X)<~>~kind(X))<=>(quiet(X)&rich(X))))&
(((~humble(mary)&~wise(mary)))=>(?[X]:((wise(X)|kind(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:(~kind(X))))&
(((quiet(paul)<~>wise(paul)))=>((~wise(lucy)&wise(lucy))))&
((?[X]:((~humble(X)<~>~creative(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~happy(X)|~patient(X))=>(humble(X)&creative(X))))&
((?[X]:(brave(X)))<=>((happy(fred)<~>kind(fred))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((~kind(X)|~strong(X))=>(happy(X)|~funny(X))))&
((?[X]:(kind(X)))=>(~quiet(paul)))&
(![X]:(~rich(X)<=>generous(X)))&
((~funny(alice)|~patient(alice)))&
((~generous(alice)&~quiet(alice)))&
(?[X]:((wise(X)&~strong(X))))&
((wise(susan)|~rich(susan)))&
((~creative(alice)<~>~strong(alice)))&
(?[X]:((old(X)&~curious(X))))&
(tall(mary))&
((tall(alice)|~brave(alice))) | funny(alice) | [
"p4",
"p9",
"p10",
"p13",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7347314522225654321492190
% SZS output start Proof for 7347314522225654321492190
5. ! [X0] : (creative(X0) <=> (~patient(X0) & ~happy(X0))) [input p4]
10. ? [X0] : (~humble(X0) <~> ~creative(X0)) => ? [X0] : (~strong(X0) & strong(X0)) [input p9]
11. ! [X0] : ((~patient(X0) | ~happy(X0)) => (creative(X0) & humble(X0))) [input p10]
14. ! [X0] : ((~strong(X0) | ~kind(X0)) => (~funny(X0) | happy(X0))) [input p13]
17. ~patient(alice) | ~funny(alice) [input p16]
21. ~creative(alice) <~> ~strong(alice) [input p20]
25. funny(alice) [input hypothesis]
28. ? [X0] : (~humble(X0) <~> ~creative(X0)) => ? [X1] : (~strong(X1) & strong(X1)) [rectify 10]
35. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : (~humble(X0) <=> ~creative(X0)) [ennf transformation 28]
36. ! [X0] : ((creative(X0) & humble(X0)) | (patient(X0) & happy(X0))) [ennf transformation 11]
38. ! [X0] : ((~funny(X0) | happy(X0)) | (strong(X0) & kind(X0))) [ennf transformation 14]
39. ! [X0] : (~funny(X0) | happy(X0) | (strong(X0) & kind(X0))) [flattening 38]
53. ! [X0] : ((creative(X0) | (patient(X0) | happy(X0))) & ((~patient(X0) & ~happy(X0)) | ~creative(X0))) [nnf transformation 5]
54. ! [X0] : ((creative(X0) | patient(X0) | happy(X0)) & ((~patient(X0) & ~happy(X0)) | ~creative(X0))) [flattening 53]
65. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0))) [nnf transformation 35]
66. ? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : ((~humble(X1) | creative(X1)) & (~creative(X1) | humble(X1))) [rectify 65]
67. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK6) & strong(sK6)) [choice axiom]
68. (~strong(sK6) & strong(sK6)) | ! [X1] : ((~humble(X1) | creative(X1)) & (~creative(X1) | humble(X1))) [skolemisation 66,67]
79. (strong(alice) | creative(alice)) & (~strong(alice) | ~creative(alice)) [nnf transformation 21]
95. ~creative(X0) | ~happy(X0) [cnf transformation 54]
112. strong(sK6) | ~humble(X1) | creative(X1) [cnf transformation 68]
114. ~strong(sK6) | ~humble(X1) | creative(X1) [cnf transformation 68]
116. patient(X0) | humble(X0) [cnf transformation 36]
126. ~funny(X0) | happy(X0) | strong(X0) [cnf transformation 39]
130. ~patient(alice) | ~funny(alice) [cnf transformation 17]
136. ~strong(alice) | ~creative(alice) [cnf transformation 79]
142. funny(alice) [cnf transformation 25]
254. 26 <=> ! [X1] : (~humble(X1) | creative(X1)) [avatar definition]
255. ~humble(X1) | creative(X1) <- (26) [avatar component clause 254]
257. 27 <=> strong(sK6) [avatar definition]
260. 26 | ~27 [avatar split clause 114,257,254]
265. 26 | 27 [avatar split clause 112,257,254]
304. 37 <=> funny(alice) [avatar definition]
305. funny(alice) <- (37) [avatar component clause 304]
308. 38 <=> patient(alice) [avatar definition]
310. ~patient(alice) <- (~38) [avatar component clause 308]
311. ~37 | ~38 [avatar split clause 130,308,304]
322. 41 <=> creative(alice) [avatar definition]
324. creative(alice) <- (41) [avatar component clause 322]
326. 42 <=> strong(alice) [avatar definition]
327. ~strong(alice) <- (~42) [avatar component clause 326]
330. ~41 | ~42 [avatar split clause 136,326,322]
340. 37 [avatar split clause 142,304]
355. ~happy(alice) <- (41) [resolution 95,324]
360. humble(alice) <- (~38) [resolution 116,310]
379. creative(alice) <- (26, ~38) [resolution 255,360]
448. happy(alice) | strong(alice) <- (37) [resolution 126,305]
449. strong(alice) <- (37, 41) [subsumption resolution 448,355]
450. $false <- (37, 41, ~42) [subsumption resolution 449,327]
451. ~37 | ~41 | 42 [avatar contradiction clause 450]
457. 41 | ~26 | 38 [avatar split clause 379,308,254,322]
458. $false [avatar sat refutation 260,265,311,330,340,451,457]
% SZS output end Proof for 7347314522225654321492190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not tall is either not kind or wise. Everyone who is both not humble and not quiet is kind and vice versa. If someone is either wise or brave then lucy is calm or not calm. Everyone who is either funny or not happy is not kind and vice versa. Everyone who is wise or not rich is curious. Everyone who is either creative or patient is both curious and not tall and vice versa. Everyone who is generous or not strong is rich. Everyone who is both not rich and not quiet is not tall or patient. If someone is both not kind and generous then mary is both not happy and not generous and vice versa. If lucy is not generous then mary is calm and vice versa. Everyone who is funny is rich or not calm and vice versa. If mary is not rich or not strong then alice is both not wise and brave. Everyone who is not kind or not strong is either funny or quiet and vice versa. If fred is both not generous and not tall then paul is not strong. Everyone who is both old and rich is both not old and not curious. Everyone who is both calm and kind is old or not rich and vice versa. Mary is both funny and not happy. Alice is not quiet or wise. Someone is both not kind and strong. Someone is both not rich and tall. John is both not quiet and not funny. Mary is not creative or not patient. Someone is curious. | John is not humble. | entailment | (![X]:((~generous(X)|~tall(X))=>(~kind(X)<~>wise(X))))&
(![X]:((~humble(X)&~quiet(X))<=>kind(X)))&
((?[X]:((wise(X)<~>brave(X))))=>((calm(lucy)|~calm(lucy))))&
(![X]:((funny(X)<~>~happy(X))<=>~kind(X)))&
(![X]:((wise(X)|~rich(X))=>curious(X)))&
(![X]:((creative(X)<~>patient(X))<=>(curious(X)&~tall(X))))&
(![X]:((generous(X)|~strong(X))=>rich(X)))&
(![X]:((~rich(X)&~quiet(X))=>(~tall(X)|patient(X))))&
((?[X]:((~kind(X)&generous(X))))<=>((~happy(mary)&~generous(mary))))&
((~generous(lucy))<=>(calm(mary)))&
(![X]:(funny(X)<=>(rich(X)|~calm(X))))&
(((~rich(mary)|~strong(mary)))=>((~wise(alice)&brave(alice))))&
(![X]:((~kind(X)|~strong(X))<=>(funny(X)<~>quiet(X))))&
(((~generous(fred)&~tall(fred)))=>(~strong(paul)))&
(![X]:((old(X)&rich(X))=>(~old(X)&~curious(X))))&
(![X]:((calm(X)&kind(X))<=>(old(X)|~rich(X))))&
((funny(mary)&~happy(mary)))&
((~quiet(alice)|wise(alice)))&
(?[X]:((~kind(X)&strong(X))))&
(?[X]:((~rich(X)&tall(X))))&
((~quiet(john)&~funny(john)))&
((~creative(mary)|~patient(mary)))&
(?[X]:(curious(X))) | ~humble(john) | [
"p1",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1659399507740196337535121
% SZS output start Proof for 1659399507740196337535121
2. ! [X0] : ((~quiet(X0) & ~humble(X0)) <=> kind(X0)) [input p1]
13. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> (funny(X0) <~> quiet(X0))) [input p12]
21. ~funny(john) & ~quiet(john) [input p20]
24. humble(john) [input hypothesis]
38. ! [X0] : (((~quiet(X0) & ~humble(X0)) | ~kind(X0)) & (kind(X0) | (quiet(X0) | humble(X0)))) [nnf transformation 2]
39. ! [X0] : (((~quiet(X0) & ~humble(X0)) | ~kind(X0)) & (kind(X0) | quiet(X0) | humble(X0))) [flattening 38]
52. ! [X0] : (((~strong(X0) | ~kind(X0)) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) & (((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | (strong(X0) & kind(X0)))) [nnf transformation 13]
53. ! [X0] : ((~strong(X0) | ~kind(X0) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) & (((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | (strong(X0) & kind(X0)))) [flattening 52]
67. ~humble(X0) | ~kind(X0) [cnf transformation 39]
99. funny(X0) | quiet(X0) | kind(X0) [cnf transformation 53]
120. ~quiet(john) [cnf transformation 21]
121. ~funny(john) [cnf transformation 21]
124. humble(john) [cnf transformation 24]
210. ~kind(john) [resolution 67,124]
345. quiet(john) | kind(john) [resolution 99,121]
351. kind(john) [subsumption resolution 345,120]
352. $false [subsumption resolution 351,210]
% SZS output end Proof for 1659399507740196337535121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both kind and not tall. If someone is either not generous or not curious then someone is either not funny or not wise and vice versa. If fred is either not kind or not humble then someone is both curious and patient. If someone is both not generous and not rich then someone is either not generous or not strong. Everyone who is old or brave is both strong and not old and vice versa. If mary is both funny and not brave then someone is tall. Everyone who is both tall and not funny is rich or not rich and vice versa. Everyone who is either not kind or creative is either not patient or not creative and vice versa. Everyone who is both quiet and rich is both not creative and rich and vice versa. Everyone who is either not happy or humble is not humble. If alice is either not wise or calm then someone is both wise and patient and vice versa. Everyone who is either calm or rich is either curious or not quiet. Everyone who is strong or humble is either wise or not creative and vice versa. Everyone who is not quiet or creative is either patient or creative. If alice is either not tall or not funny then someone is not curious or not humble and vice versa. Everyone who is both wise and tall is either generous or calm and vice versa. Alice is both wise and patient. Someone is either kind or patient. Lucy is not humble or not funny. Someone is both brave and creative. John is both quiet and not creative. | John is not rich. | neutral | (![X]:(~wise(X)=>(kind(X)&~tall(X))))&
((?[X]:((~generous(X)<~>~curious(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(((~kind(fred)<~>~humble(fred)))=>(?[X]:((curious(X)&patient(X)))))&
((?[X]:((~generous(X)&~rich(X))))=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((old(X)|brave(X))<=>(strong(X)&~old(X))))&
(((funny(mary)&~brave(mary)))=>(?[X]:(tall(X))))&
(![X]:((tall(X)&~funny(X))<=>(rich(X)|~rich(X))))&
(![X]:((~kind(X)<~>creative(X))<=>(~patient(X)<~>~creative(X))))&
(![X]:((quiet(X)&rich(X))<=>(~creative(X)&rich(X))))&
(![X]:((~happy(X)<~>humble(X))=>~humble(X)))&
(((~wise(alice)<~>calm(alice)))<=>(?[X]:((wise(X)&patient(X)))))&
(![X]:((calm(X)<~>rich(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((strong(X)|humble(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((~quiet(X)|creative(X))=>(patient(X)<~>creative(X))))&
(((~tall(alice)<~>~funny(alice)))<=>(?[X]:((~curious(X)|~humble(X)))))&
(![X]:((wise(X)&tall(X))<=>(generous(X)<~>calm(X))))&
((wise(alice)&patient(alice)))&
(?[X]:((kind(X)<~>patient(X))))&
((~humble(lucy)|~funny(lucy)))&
(?[X]:((brave(X)&creative(X))))&
((quiet(john)&~creative(john))) | ~rich(john) | [] | null | 0 |
Everyone who is both rich and happy is quiet.
If someone is not happy or not calm then someone is patient or tall.
Everyone who is funny is rich or strong and vice versa.
If lucy is not wise or generous then paul is not patient or not happy and vice versa.
Everyone who is calm is either patient or not strong.
If someone is not kind or not calm then someone is not tall or quiet.
If paul is patient or tall then susan is both not generous and patient and vice versa.
Everyone who is not generous is humble or kind and vice versa.
Everyone who is both not curious and not patient is either not generous or not strong and vice versa.
If fred is either generous or not funny then someone is both calm and not funny and vice versa.
If susan is both not rich and not brave then someone is both brave and rich and vice versa.
Everyone who is quiet is not curious.
If someone is either not strong or rich then fred is both old and wise.
If lucy is both not quiet and not happy then someone is either not brave or rich and vice versa.
Everyone who is both wise and not brave is both not humble and quiet.
If someone is generous or calm then mary is both generous and old and vice versa.
Mary is not creative.
Someone is rich or not tall.
Alice is either brave or not strong.
Someone is either calm or not calm.
Alice is both not humble and not curious.
Susan is either not happy or not calm.
Someone is either not wise or not curious. | Lucy is not happy. | neutral | (![X]:((rich(X)&happy(X))=>quiet(X)))&
((?[X]:((~happy(X)|~calm(X))))=>(?[X]:((patient(X)|tall(X)))))&
(![X]:(funny(X)<=>(rich(X)|strong(X))))&
(((~wise(lucy)|generous(lucy)))<=>((~patient(paul)|~happy(paul))))&
(![X]:(calm(X)=>(patient(X)<~>~strong(X))))&
((?[X]:((~kind(X)|~calm(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
(((patient(paul)|tall(paul)))<=>((~generous(susan)&patient(susan))))&
(![X]:(~generous(X)<=>(humble(X)|kind(X))))&
(![X]:((~curious(X)&~patient(X))<=>(~generous(X)<~>~strong(X))))&
(((generous(fred)<~>~funny(fred)))<=>(?[X]:((calm(X)&~funny(X)))))&
(((~rich(susan)&~brave(susan)))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:(quiet(X)=>~curious(X)))&
((?[X]:((~strong(X)<~>rich(X))))=>((old(fred)&wise(fred))))&
(((~quiet(lucy)&~happy(lucy)))<=>(?[X]:((~brave(X)<~>rich(X)))))&
(![X]:((wise(X)&~brave(X))=>(~humble(X)&quiet(X))))&
((?[X]:((generous(X)|calm(X))))<=>((generous(mary)&old(mary))))&
(~creative(mary))&
(?[X]:((rich(X)|~tall(X))))&
((brave(alice)<~>~strong(alice)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~humble(alice)&~curious(alice)))&
((~happy(susan)<~>~calm(susan)))&
(?[X]:((~wise(X)<~>~curious(X)))) | ~happy(lucy) | [] | null | 0 |
Everyone who is both not happy and old is strong.
Everyone who is humble or not generous is not brave or humble and vice versa.
Everyone who is both not wise and curious is rich or creative and vice versa.
If susan is both not brave and not wise then someone is both strong and funny.
Everyone who is either funny or old is either not old or not humble.
If someone is not humble or strong then lucy is not patient and vice versa.
If someone is rich then fred is kind and vice versa.
If someone is kind then someone is either not funny or old and vice versa.
If someone is either happy or not brave then someone is either generous or not quiet and vice versa.
If lucy is either not rich or old then someone is generous.
Everyone who is not brave or not calm is both not humble and curious and vice versa.
If someone is both tall and curious then fred is both strong and not happy and vice versa.
Everyone who is both calm and not patient is happy or rich and vice versa.
If mary is not humble or humble then lucy is either rich or kind.
If lucy is both patient and old then mary is tall or not rich and vice versa.
Everyone who is both old and generous is kind.
Someone is not funny or strong.
Alice is old or not kind.
Susan is wise.
Paul is not tall or humble.
Susan is not brave.
Mary is both not generous and not brave.
Someone is kind. | Alice is old. | neutral | (![X]:((~happy(X)&old(X))=>strong(X)))&
(![X]:((humble(X)|~generous(X))<=>(~brave(X)|humble(X))))&
(![X]:((~wise(X)&curious(X))<=>(rich(X)|creative(X))))&
(((~brave(susan)&~wise(susan)))=>(?[X]:((strong(X)&funny(X)))))&
(![X]:((funny(X)<~>old(X))=>(~old(X)<~>~humble(X))))&
((?[X]:((~humble(X)|strong(X))))<=>(~patient(lucy)))&
((?[X]:(rich(X)))<=>(kind(fred)))&
((?[X]:(kind(X)))<=>(?[X]:((~funny(X)<~>old(X)))))&
((?[X]:((happy(X)<~>~brave(X))))<=>(?[X]:((generous(X)<~>~quiet(X)))))&
(((~rich(lucy)<~>old(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~humble(X)&curious(X))))&
((?[X]:((tall(X)&curious(X))))<=>((strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~patient(X))<=>(happy(X)|rich(X))))&
(((~humble(mary)|humble(mary)))=>((rich(lucy)<~>kind(lucy))))&
(((patient(lucy)&old(lucy)))<=>((tall(mary)|~rich(mary))))&
(![X]:((old(X)&generous(X))=>kind(X)))&
(?[X]:((~funny(X)|strong(X))))&
((old(alice)|~kind(alice)))&
(wise(susan))&
((~tall(paul)|humble(paul)))&
(~brave(susan))&
((~generous(mary)&~brave(mary)))&
(?[X]:(kind(X))) | old(alice) | [] | null | 0 |
If someone is either not old or not humble then alice is not calm or humble. If susan is not wise then someone is both not patient and old. If someone is not strong or quiet then someone is happy. If someone is not kind or strong then someone is both happy and not rich and vice versa. Everyone who is either humble or not humble is both happy and brave. If someone is both not strong and creative then mary is creative and vice versa. If susan is either not humble or not funny then alice is both strong and quiet and vice versa. Everyone who is not old or not tall is wise. Everyone who is creative is both humble and not patient. Everyone who is not brave is both not quiet and not happy. Everyone who is either not tall or not strong is humble. Everyone who is not creative is both patient and not happy and vice versa. Everyone who is either not generous or funny is both calm and brave. If someone is not old or not brave then someone is both brave and not calm. If someone is both not generous and creative then mary is both kind and not funny and vice versa. Someone is creative or not happy. Mary is not funny or tall. Someone is not humble or not kind. Lucy is either rich or patient. Someone is either not kind or brave. Someone is curious. Someone is either not kind or not funny. Paul is either generous or not strong. | Alice is happy. | entailment | ((?[X]:((~old(X)<~>~humble(X))))=>((~calm(alice)|humble(alice))))&
((~wise(susan))=>(?[X]:((~patient(X)&old(X)))))&
((?[X]:((~strong(X)|quiet(X))))=>(?[X]:(happy(X))))&
((?[X]:((~kind(X)|strong(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((humble(X)<~>~humble(X))=>(happy(X)&brave(X))))&
((?[X]:((~strong(X)&creative(X))))<=>(creative(mary)))&
(((~humble(susan)<~>~funny(susan)))<=>((strong(alice)&quiet(alice))))&
(![X]:((~old(X)|~tall(X))=>wise(X)))&
(![X]:(creative(X)=>(humble(X)&~patient(X))))&
(![X]:(~brave(X)=>(~quiet(X)&~happy(X))))&
(![X]:((~tall(X)<~>~strong(X))=>humble(X)))&
(![X]:(~creative(X)<=>(patient(X)&~happy(X))))&
(![X]:((~generous(X)<~>funny(X))=>(calm(X)&brave(X))))&
((?[X]:((~old(X)|~brave(X))))=>(?[X]:((brave(X)&~calm(X)))))&
((?[X]:((~generous(X)&creative(X))))<=>((kind(mary)&~funny(mary))))&
(?[X]:((creative(X)|~happy(X))))&
((~funny(mary)|tall(mary)))&
(?[X]:((~humble(X)|~kind(X))))&
((rich(lucy)<~>patient(lucy)))&
(?[X]:((~kind(X)<~>brave(X))))&
(?[X]:(curious(X)))&
(?[X]:((~kind(X)<~>~funny(X))))&
((generous(paul)<~>~strong(paul))) | happy(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6966321096230331943141970
% SZS output start Proof for 6966321096230331943141970
5. ! [X0] : ((humble(X0) <~> ~humble(X0)) => (brave(X0) & happy(X0))) [input p4]
24. ~happy(alice) [input hypothesis]
34. ! [X0] : ((brave(X0) & happy(X0)) | (humble(X0) <=> ~humble(X0))) [ennf transformation 5]
49. ! [X0] : ((brave(X0) & happy(X0)) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) [nnf transformation 34]
89. happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 49]
90. happy(X0) | humble(X0) | humble(X0) [cnf transformation 49]
134. ~happy(alice) [cnf transformation 24]
135. happy(X0) | ~humble(X0) [duplicate literal removal 89]
136. happy(X0) | humble(X0) [duplicate literal removal 90]
198. happy(X0) [subsumption resolution 135,136]
313. $false [subsumption resolution 134,198]
% SZS output end Proof for 6966321096230331943141970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is either curious or happy. Everyone who is not patient is tall or quiet and vice versa. If someone is not brave then someone is not calm or creative. If lucy is humble or strong then someone is both curious and not strong and vice versa. Everyone who is rich or not funny is either funny or strong. If someone is either happy or not patient then someone is brave or creative. If someone is both funny and not rich then lucy is both not patient and wise. If alice is creative or not creative then someone is not tall or tall and vice versa. Everyone who is not kind or creative is either not kind or not tall and vice versa. If lucy is both not humble and not curious then someone is not humble. Everyone who is not funny is either not generous or brave. Everyone who is not funny or not rich is both not wise and not generous. If someone is both humble and calm then someone is both not brave and tall. Everyone who is patient or wise is creative or old and vice versa. If john is both curious and not happy then mary is not brave and vice versa. If alice is not patient then someone is not wise and vice versa. John is not funny. Someone is generous or not rich. Susan is either not creative or not generous. Someone is quiet or not wise. Paul is both not patient and not brave. John is both not wise and tall. Lucy is not rich. Someone is either not funny or not patient. | John is not creative. | entailment | (![X]:(~tall(X)=>(curious(X)<~>happy(X))))&
(![X]:(~patient(X)<=>(tall(X)|quiet(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~calm(X)|creative(X)))))&
(((humble(lucy)|strong(lucy)))<=>(?[X]:((curious(X)&~strong(X)))))&
(![X]:((rich(X)|~funny(X))=>(funny(X)<~>strong(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((brave(X)|creative(X)))))&
((?[X]:((funny(X)&~rich(X))))=>((~patient(lucy)&wise(lucy))))&
(((creative(alice)|~creative(alice)))<=>(?[X]:((~tall(X)|tall(X)))))&
(![X]:((~kind(X)|creative(X))<=>(~kind(X)<~>~tall(X))))&
(((~humble(lucy)&~curious(lucy)))=>(?[X]:(~humble(X))))&
(![X]:(~funny(X)=>(~generous(X)<~>brave(X))))&
(![X]:((~funny(X)|~rich(X))=>(~wise(X)&~generous(X))))&
((?[X]:((humble(X)&calm(X))))=>(?[X]:((~brave(X)&tall(X)))))&
(![X]:((patient(X)|wise(X))<=>(creative(X)|old(X))))&
(((curious(john)&~happy(john)))<=>(~brave(mary)))&
((~patient(alice))<=>(?[X]:(~wise(X))))&
(~funny(john))&
(?[X]:((generous(X)|~rich(X))))&
((~creative(susan)<~>~generous(susan)))&
(?[X]:((quiet(X)|~wise(X))))&
((~patient(paul)&~brave(paul)))&
((~wise(john)&tall(john)))&
(~rich(lucy))&
(?[X]:((~funny(X)<~>~patient(X)))) | ~creative(john) | [
"p1",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 923541185927404556638693
% SZS output start Proof for 923541185927404556638693
2. ! [X0] : (~patient(X0) <=> (quiet(X0) | tall(X0))) [input p1]
14. ! [X0] : ((wise(X0) | patient(X0)) <=> (old(X0) | creative(X0))) [input p13]
22. tall(john) & ~wise(john) [input p21]
25. creative(john) [input hypothesis]
40. ! [X0] : ((~patient(X0) | (~quiet(X0) & ~tall(X0))) & ((quiet(X0) | tall(X0)) | patient(X0))) [nnf transformation 2]
41. ! [X0] : ((~patient(X0) | (~quiet(X0) & ~tall(X0))) & (quiet(X0) | tall(X0) | patient(X0))) [flattening 40]
62. ! [X0] : (((wise(X0) | patient(X0)) | (~old(X0) & ~creative(X0))) & ((old(X0) | creative(X0)) | (~wise(X0) & ~patient(X0)))) [nnf transformation 14]
63. ! [X0] : ((wise(X0) | patient(X0) | (~old(X0) & ~creative(X0))) & (old(X0) | creative(X0) | (~wise(X0) & ~patient(X0)))) [flattening 62]
81. ~patient(X0) | ~tall(X0) [cnf transformation 41]
115. ~creative(X0) | patient(X0) | wise(X0) [cnf transformation 63]
129. ~wise(john) [cnf transformation 22]
130. tall(john) [cnf transformation 22]
134. creative(john) [cnf transformation 25]
309. patient(john) | wise(john) [resolution 115,134]
312. patient(john) [subsumption resolution 309,129]
332. ~tall(john) [resolution 312,81]
333. $false [subsumption resolution 332,130]
% SZS output end Proof for 923541185927404556638693
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not rich is generous or not kind. If someone is calm or not creative then fred is both brave and tall and vice versa. If someone is either funny or not curious then paul is either not happy or not strong. If lucy is both not generous and not strong then fred is kind or calm and vice versa. Everyone who is brave or not rich is not calm or not rich. If alice is tall then john is both rich and not patient and vice versa. If alice is both happy and not kind then someone is either strong or not funny. If someone is not wise or happy then fred is not funny or not rich. If fred is not quiet or kind then someone is creative. Everyone who is either not old or quiet is happy. If paul is either not tall or not rich then someone is either not funny or quiet and vice versa. If someone is not quiet or happy then someone is either funny or brave. Everyone who is happy is both not old and rich. Everyone who is not tall is not funny or quiet and vice versa. If fred is both generous and kind then someone is both generous and not tall. Everyone who is old or not creative is not rich. Alice is both not happy and generous. Mary is either tall or not quiet. Someone is not brave. Mary is creative or brave. Alice is happy or tall. Someone is patient or not brave. Someone is brave or patient. | John is rich. | entailment | (![X]:((happy(X)&~rich(X))=>(generous(X)|~kind(X))))&
((?[X]:((calm(X)|~creative(X))))<=>((brave(fred)&tall(fred))))&
((?[X]:((funny(X)<~>~curious(X))))=>((~happy(paul)<~>~strong(paul))))&
(((~generous(lucy)&~strong(lucy)))<=>((kind(fred)|calm(fred))))&
(![X]:((brave(X)|~rich(X))=>(~calm(X)|~rich(X))))&
((tall(alice))<=>((rich(john)&~patient(john))))&
(((happy(alice)&~kind(alice)))=>(?[X]:((strong(X)<~>~funny(X)))))&
((?[X]:((~wise(X)|happy(X))))=>((~funny(fred)|~rich(fred))))&
(((~quiet(fred)|kind(fred)))=>(?[X]:(creative(X))))&
(![X]:((~old(X)<~>quiet(X))=>happy(X)))&
(((~tall(paul)<~>~rich(paul)))<=>(?[X]:((~funny(X)<~>quiet(X)))))&
((?[X]:((~quiet(X)|happy(X))))=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:(happy(X)=>(~old(X)&rich(X))))&
(![X]:(~tall(X)<=>(~funny(X)|quiet(X))))&
(((generous(fred)&kind(fred)))=>(?[X]:((generous(X)&~tall(X)))))&
(![X]:((old(X)|~creative(X))=>~rich(X)))&
((~happy(alice)&generous(alice)))&
((tall(mary)<~>~quiet(mary)))&
(?[X]:(~brave(X)))&
((creative(mary)|brave(mary)))&
((happy(alice)|tall(alice)))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:((brave(X)|patient(X)))) | rich(john) | [
"p5",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9159953203886915466104034
% SZS output start Proof for 9159953203886915466104034
6. tall(alice) <=> (~patient(john) & rich(john)) [input p5]
17. generous(alice) & ~happy(alice) [input p16]
21. tall(alice) | happy(alice) [input p20]
24. ~rich(john) [input hypothesis]
51. (tall(alice) | (patient(john) | ~rich(john))) & ((~patient(john) & rich(john)) | ~tall(alice)) [nnf transformation 6]
52. (tall(alice) | patient(john) | ~rich(john)) & ((~patient(john) & rich(john)) | ~tall(alice)) [flattening 51]
95. rich(john) | ~tall(alice) [cnf transformation 52]
126. ~happy(alice) [cnf transformation 17]
132. tall(alice) | happy(alice) [cnf transformation 21]
135. ~rich(john) [cnf transformation 24]
203. 15 <=> rich(john) [avatar definition]
211. 17 <=> tall(alice) [avatar definition]
216. ~17 | 15 [avatar split clause 95,203,211]
218. 18 <=> happy(alice) [avatar definition]
316. ~18 [avatar split clause 126,218]
328. 18 | 17 [avatar split clause 132,211,218]
347. ~15 [avatar split clause 135,203]
348. $false [avatar sat refutation 216,316,328,347]
% SZS output end Proof for 9159953203886915466104034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and calm is both not tall and calm.
If someone is either funny or happy then paul is either not tall or not humble.
If someone is either not calm or wise then john is calm or wise and vice versa.
If someone is not creative or not quiet then mary is both not generous and patient.
If someone is not patient or not old then someone is both not wise and not kind and vice versa.
Everyone who is humble is both humble and not strong.
Everyone who is tall is not funny.
Everyone who is either generous or wise is quiet or not kind and vice versa.
Everyone who is strong is humble and vice versa.
Everyone who is both quiet and not patient is either brave or old and vice versa.
Everyone who is not generous is quiet or creative and vice versa.
If someone is both happy and not tall then someone is either old or creative and vice versa.
Everyone who is either quiet or not patient is not wise.
If someone is not funny then someone is both not kind and strong and vice versa.
If someone is not generous or creative then alice is not kind or happy and vice versa.
If someone is rich then susan is both funny and kind.
Lucy is kind or not strong.
Lucy is not tall or kind.
Someone is either not funny or not brave.
Someone is rich.
Someone is not patient or not tall.
Mary is quiet or kind.
Mary is generous or calm. | Paul is not happy. | contradiction | (![X]:((kind(X)&calm(X))=>(~tall(X)&calm(X))))&
((?[X]:((funny(X)<~>happy(X))))=>((~tall(paul)<~>~humble(paul))))&
((?[X]:((~calm(X)<~>wise(X))))<=>((calm(john)|wise(john))))&
((?[X]:((~creative(X)|~quiet(X))))=>((~generous(mary)&patient(mary))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(humble(X)=>(humble(X)&~strong(X))))&
(![X]:(tall(X)=>~funny(X)))&
(![X]:((generous(X)<~>wise(X))<=>(quiet(X)|~kind(X))))&
(![X]:(strong(X)<=>humble(X)))&
(![X]:((quiet(X)&~patient(X))<=>(brave(X)<~>old(X))))&
(![X]:(~generous(X)<=>(quiet(X)|creative(X))))&
((?[X]:((happy(X)&~tall(X))))<=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:((quiet(X)<~>~patient(X))=>~wise(X)))&
((?[X]:(~funny(X)))<=>(?[X]:((~kind(X)&strong(X)))))&
((?[X]:((~generous(X)|creative(X))))<=>((~kind(alice)|happy(alice))))&
((?[X]:(rich(X)))=>((funny(susan)&kind(susan))))&
((kind(lucy)|~strong(lucy)))&
((~tall(lucy)|kind(lucy)))&
(?[X]:((~funny(X)<~>~brave(X))))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)|~tall(X))))&
((quiet(mary)|kind(mary)))&
((generous(mary)|calm(mary))) | ~happy(paul) | [
"p1",
"p5",
"p6",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7212201365593203473712973
% SZS output start Proof for 7212201365593203473712973
2. ? [X0] : (funny(X0) <~> happy(X0)) => (~tall(paul) <~> ~humble(paul)) [input p1]
6. ! [X0] : (humble(X0) => (~strong(X0) & humble(X0))) [input p5]
7. ! [X0] : (tall(X0) => ~funny(X0)) [input p6]
9. ! [X0] : (strong(X0) <=> humble(X0)) [input p8]
14. ? [X0] : ~funny(X0) <=> ? [X0] : (strong(X0) & ~kind(X0)) [input p13]
24. ~happy(paul) [input hypothesis]
27. ? [X0] : ~funny(X0) <=> ? [X1] : (strong(X1) & ~kind(X1)) [rectify 14]
30. (~tall(paul) <~> ~humble(paul)) | ! [X0] : (funny(X0) <=> happy(X0)) [ennf transformation 2]
32. ! [X0] : ((~strong(X0) & humble(X0)) | ~humble(X0)) [ennf transformation 6]
33. ! [X0] : (~funny(X0) | ~tall(X0)) [ennf transformation 7]
36. ((humble(paul) | tall(paul)) & (~humble(paul) | ~tall(paul))) | ! [X0] : ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0))) [nnf transformation 30]
49. ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))) [nnf transformation 9]
60. (? [X0] : ~funny(X0) | ! [X1] : (~strong(X1) | kind(X1))) & (? [X1] : (strong(X1) & ~kind(X1)) | ! [X0] : funny(X0)) [nnf transformation 27]
61. (? [X0] : ~funny(X0) | ! [X1] : (~strong(X1) | kind(X1))) & (? [X2] : (strong(X2) & ~kind(X2)) | ! [X3] : funny(X3)) [rectify 60]
62. ? [X0] : ~funny(X0) => ~funny(sK5) [choice axiom]
63. ? [X2] : (strong(X2) & ~kind(X2)) => (strong(sK6) & ~kind(sK6)) [choice axiom]
64. (~funny(sK5) | ! [X1] : (~strong(X1) | kind(X1))) & ((strong(sK6) & ~kind(sK6)) | ! [X3] : funny(X3)) [skolemisation 61,63,62]
81. humble(paul) | tall(paul) | happy(X0) | ~funny(X0) [cnf transformation 36]
99. ~strong(X0) | ~humble(X0) [cnf transformation 32]
100. ~funny(X0) | ~tall(X0) [cnf transformation 33]
107. humble(X0) | ~strong(X0) [cnf transformation 49]
108. strong(X0) | ~humble(X0) [cnf transformation 49]
127. strong(sK6) | funny(X3) [cnf transformation 64]
143. ~happy(paul) [cnf transformation 24]
148. 2 <=> tall(paul) [avatar definition]
150. tall(paul) <- (2) [avatar component clause 148]
152. 3 <=> humble(paul) [avatar definition]
154. humble(paul) <- (3) [avatar component clause 152]
157. 4 <=> ! [X0] : (happy(X0) | ~funny(X0)) [avatar definition]
158. happy(X0) | ~funny(X0) <- (4) [avatar component clause 157]
159. 4 | 2 | 3 [avatar split clause 81,152,148,157]
238. ~humble(X0) [subsumption resolution 108,99]
239. ~strong(X0) [subsumption resolution 107,238]
271. funny(X3) [subsumption resolution 127,239]
339. ~tall(X0) [resolution 100,271]
347. $false <- (2) [resolution 339,150]
348. ~2 [avatar contradiction clause 347]
349. happy(X0) <- (4) [subsumption resolution 158,271]
350. $false <- (4) [resolution 349,143]
351. ~4 [avatar contradiction clause 350]
352. $false <- (3) [subsumption resolution 154,238]
353. ~3 [avatar contradiction clause 352]
354. $false [avatar sat refutation 159,348,351,353]
% SZS output end Proof for 7212201365593203473712973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is generous or not rich and vice versa.
If john is not quiet then paul is curious and vice versa.
If someone is both not patient and not quiet then someone is either not kind or not calm and vice versa.
Everyone who is not generous is not humble.
If someone is rich or not funny then alice is not happy.
Everyone who is both patient and not humble is not curious or not creative.
Everyone who is both not tall and not happy is both old and not happy and vice versa.
Everyone who is both not old and not calm is calm and vice versa.
If susan is strong then alice is not patient and vice versa.
Everyone who is either not humble or not patient is quiet or tall and vice versa.
If susan is not quiet then someone is both not funny and not creative.
Everyone who is old is both funny and brave and vice versa.
If someone is either patient or not calm then mary is both creative and not brave and vice versa.
Everyone who is both not generous and rich is not brave.
Everyone who is not old is both not rich and happy.
If john is strong or quiet then mary is both kind and old and vice versa.
Someone is either creative or strong.
Someone is either funny or not patient.
Paul is not creative.
Paul is rich.
Someone is both not wise and generous. | Mary is not rich. | neutral | (![X]:(~creative(X)<=>(generous(X)|~rich(X))))&
((~quiet(john))<=>(curious(paul)))&
((?[X]:((~patient(X)&~quiet(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:(~generous(X)=>~humble(X)))&
((?[X]:((rich(X)|~funny(X))))=>(~happy(alice)))&
(![X]:((patient(X)&~humble(X))=>(~curious(X)|~creative(X))))&
(![X]:((~tall(X)&~happy(X))<=>(old(X)&~happy(X))))&
(![X]:((~old(X)&~calm(X))<=>calm(X)))&
((strong(susan))<=>(~patient(alice)))&
(![X]:((~humble(X)<~>~patient(X))<=>(quiet(X)|tall(X))))&
((~quiet(susan))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:(old(X)<=>(funny(X)&brave(X))))&
((?[X]:((patient(X)<~>~calm(X))))<=>((creative(mary)&~brave(mary))))&
(![X]:((~generous(X)&rich(X))=>~brave(X)))&
(![X]:(~old(X)=>(~rich(X)&happy(X))))&
(((strong(john)|quiet(john)))<=>((kind(mary)&old(mary))))&
(?[X]:((creative(X)<~>strong(X))))&
(?[X]:((funny(X)<~>~patient(X))))&
(~creative(paul))&
(rich(paul))&
(?[X]:((~wise(X)&generous(X)))) | ~rich(mary) | [] | null | 0 |
If susan is either not happy or creative then lucy is not tall or not wise and vice versa.
If mary is either not funny or humble then susan is not patient or funny and vice versa.
If someone is either not calm or kind then someone is either rich or not funny and vice versa.
Everyone who is both not strong and not generous is happy.
Everyone who is either not wise or strong is funny or not patient and vice versa.
If someone is happy then someone is either not curious or not patient and vice versa.
If alice is not creative then someone is generous.
If someone is not patient or not quiet then paul is strong or not patient.
Everyone who is either patient or not quiet is both creative and not generous and vice versa.
Everyone who is not curious is either tall or not generous.
Everyone who is not tall is happy or curious and vice versa.
If mary is either not humble or strong then john is tall.
Everyone who is not rich or wise is rich and vice versa.
If alice is not old then someone is not patient.
If paul is strong or not curious then john is rich or old.
If someone is both rich and quiet then someone is wise.
Susan is not kind.
Susan is tall or humble.
Paul is calm or quiet.
John is creative or not brave.
Paul is not creative or not curious.
John is either not generous or not strong.
Lucy is creative.
Someone is either quiet or tall. | Susan is not curious. | neutral | (((~happy(susan)<~>creative(susan)))<=>((~tall(lucy)|~wise(lucy))))&
(((~funny(mary)<~>humble(mary)))<=>((~patient(susan)|funny(susan))))&
((?[X]:((~calm(X)<~>kind(X))))<=>(?[X]:((rich(X)<~>~funny(X)))))&
(![X]:((~strong(X)&~generous(X))=>happy(X)))&
(![X]:((~wise(X)<~>strong(X))<=>(funny(X)|~patient(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)<~>~patient(X)))))&
((~creative(alice))=>(?[X]:(generous(X))))&
((?[X]:((~patient(X)|~quiet(X))))=>((strong(paul)|~patient(paul))))&
(![X]:((patient(X)<~>~quiet(X))<=>(creative(X)&~generous(X))))&
(![X]:(~curious(X)=>(tall(X)<~>~generous(X))))&
(![X]:(~tall(X)<=>(happy(X)|curious(X))))&
(((~humble(mary)<~>strong(mary)))=>(tall(john)))&
(![X]:((~rich(X)|wise(X))<=>rich(X)))&
((~old(alice))=>(?[X]:(~patient(X))))&
(((strong(paul)|~curious(paul)))=>((rich(john)|old(john))))&
((?[X]:((rich(X)&quiet(X))))=>(?[X]:(wise(X))))&
(~kind(susan))&
((tall(susan)|humble(susan)))&
((calm(paul)|quiet(paul)))&
((creative(john)|~brave(john)))&
((~creative(paul)|~curious(paul)))&
((~generous(john)<~>~strong(john)))&
(creative(lucy))&
(?[X]:((quiet(X)<~>tall(X)))) | ~curious(susan) | [] | null | 0 |
Everyone who is funny is not curious and vice versa. If paul is patient then john is not quiet and vice versa. If someone is brave or not quiet then alice is not happy. Everyone who is both not kind and not rich is tall and vice versa. Everyone who is humble or kind is both not calm and patient. If someone is both patient and not curious then alice is patient and vice versa. Everyone who is both not old and not generous is not patient. If someone is either not humble or tall then susan is either old or not brave. Everyone who is either not kind or not rich is both not old and funny. Everyone who is either calm or strong is not strong and vice versa. Everyone who is strong is not creative or not funny and vice versa. If someone is not brave then someone is either not happy or not strong. Everyone who is not happy or not funny is both happy and kind and vice versa. If alice is not quiet then someone is either not tall or not brave. If fred is both not curious and patient then john is patient. Alice is either brave or creative. Someone is brave or tall. Alice is wise. Someone is rich or not wise. Someone is either not wise or rich. Fred is either not patient or rich. John is both rich and creative. | John is humble. | contradiction | (![X]:(funny(X)<=>~curious(X)))&
((patient(paul))<=>(~quiet(john)))&
((?[X]:((brave(X)|~quiet(X))))=>(~happy(alice)))&
(![X]:((~kind(X)&~rich(X))<=>tall(X)))&
(![X]:((humble(X)|kind(X))=>(~calm(X)&patient(X))))&
((?[X]:((patient(X)&~curious(X))))<=>(patient(alice)))&
(![X]:((~old(X)&~generous(X))=>~patient(X)))&
((?[X]:((~humble(X)<~>tall(X))))=>((old(susan)<~>~brave(susan))))&
(![X]:((~kind(X)<~>~rich(X))=>(~old(X)&funny(X))))&
(![X]:((calm(X)<~>strong(X))<=>~strong(X)))&
(![X]:(strong(X)<=>(~creative(X)|~funny(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((~happy(X)|~funny(X))<=>(happy(X)&kind(X))))&
((~quiet(alice))=>(?[X]:((~tall(X)<~>~brave(X)))))&
(((~curious(fred)&patient(fred)))=>(patient(john)))&
((brave(alice)<~>creative(alice)))&
(?[X]:((brave(X)|tall(X))))&
(wise(alice))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~wise(X)<~>rich(X))))&
((~patient(fred)<~>rich(fred)))&
((rich(john)&creative(john))) | humble(john) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7025644501011427005432308
% SZS output start Proof for 7025644501011427005432308
5. ! [X0] : ((kind(X0) | humble(X0)) => (patient(X0) & ~calm(X0))) [input p4]
10. ! [X0] : ((calm(X0) <~> strong(X0)) <=> ~strong(X0)) [input p9]
23. humble(john) [input hypothesis]
27. ! [X0] : ((patient(X0) & ~calm(X0)) | (~kind(X0) & ~humble(X0))) [ennf transformation 5]
44. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | strong(X0)) & (~strong(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [nnf transformation 10]
74. ~calm(X0) | ~humble(X0) [cnf transformation 27]
90. ~strong(X0) | calm(X0) | ~strong(X0) [cnf transformation 44]
91. strong(X0) | calm(X0) | strong(X0) [cnf transformation 44]
117. humble(john) [cnf transformation 23]
120. ~strong(X0) | calm(X0) [duplicate literal removal 90]
121. strong(X0) | calm(X0) [duplicate literal removal 91]
180. calm(X0) [subsumption resolution 120,121]
283. ~humble(X0) [resolution 74,180]
284. $false [resolution 283,117]
% SZS output end Proof for 7025644501011427005432308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or tall then fred is not brave or not happy and vice versa.
Everyone who is not generous is not happy or strong.
Everyone who is both humble and not patient is not tall and vice versa.
Everyone who is not old is not rich and vice versa.
If someone is both strong and not calm then someone is strong and vice versa.
If susan is both not kind and not calm then someone is kind or funny and vice versa.
Everyone who is either not quiet or quiet is strong.
Everyone who is generous is old or not rich and vice versa.
If lucy is either quiet or kind then fred is not quiet or not brave and vice versa.
Everyone who is old is both humble and not happy and vice versa.
Everyone who is not calm or humble is both strong and not happy and vice versa.
If someone is either not old or not calm then paul is not strong or brave.
If someone is either not creative or tall then alice is not generous or not strong and vice versa.
If someone is not kind then someone is either not kind or quiet and vice versa.
Everyone who is brave or rich is both not brave and not patient.
Everyone who is either humble or creative is old or brave and vice versa.
Someone is creative or patient.
Someone is either not curious or old.
John is both not brave and not calm. | Fred is rich. | contradiction | ((?[X]:((quiet(X)<~>tall(X))))<=>((~brave(fred)|~happy(fred))))&
(![X]:(~generous(X)=>(~happy(X)|strong(X))))&
(![X]:((humble(X)&~patient(X))<=>~tall(X)))&
(![X]:(~old(X)<=>~rich(X)))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:(strong(X))))&
(((~kind(susan)&~calm(susan)))<=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((~quiet(X)<~>quiet(X))=>strong(X)))&
(![X]:(generous(X)<=>(old(X)|~rich(X))))&
(((quiet(lucy)<~>kind(lucy)))<=>((~quiet(fred)|~brave(fred))))&
(![X]:(old(X)<=>(humble(X)&~happy(X))))&
(![X]:((~calm(X)|humble(X))<=>(strong(X)&~happy(X))))&
((?[X]:((~old(X)<~>~calm(X))))=>((~strong(paul)|brave(paul))))&
((?[X]:((~creative(X)<~>tall(X))))<=>((~generous(alice)|~strong(alice))))&
((?[X]:(~kind(X)))<=>(?[X]:((~kind(X)<~>quiet(X)))))&
(![X]:((brave(X)|rich(X))=>(~brave(X)&~patient(X))))&
(![X]:((humble(X)<~>creative(X))<=>(old(X)|brave(X))))&
(?[X]:((creative(X)|patient(X))))&
(?[X]:((~curious(X)<~>old(X))))&
((~brave(john)&~calm(john))) | rich(fred) | [
"p2",
"p3",
"p6",
"p7",
"p9",
"p10",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1698599580178282026961566
% SZS output start Proof for 1698599580178282026961566
3. ! [X0] : ((~patient(X0) & humble(X0)) <=> ~tall(X0)) [input p2]
4. ! [X0] : (~old(X0) <=> ~rich(X0)) [input p3]
7. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => strong(X0)) [input p6]
8. ! [X0] : (generous(X0) <=> (~rich(X0) | old(X0))) [input p7]
10. ! [X0] : (old(X0) <=> (~happy(X0) & humble(X0))) [input p9]
11. ! [X0] : ((humble(X0) | ~calm(X0)) <=> (~happy(X0) & strong(X0))) [input p10]
13. ? [X0] : (~creative(X0) <~> tall(X0)) <=> (~strong(alice) | ~generous(alice)) [input p12]
15. ! [X0] : ((rich(X0) | brave(X0)) => (~patient(X0) & ~brave(X0))) [input p14]
16. ! [X0] : ((humble(X0) <~> creative(X0)) <=> (brave(X0) | old(X0))) [input p15]
20. rich(fred) [input hypothesis]
25. ! [X0] : (strong(X0) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 7]
28. ! [X0] : ((~patient(X0) & ~brave(X0)) | (~rich(X0) & ~brave(X0))) [ennf transformation 15]
34. ! [X0] : (((~patient(X0) & humble(X0)) | tall(X0)) & (~tall(X0) | (patient(X0) | ~humble(X0)))) [nnf transformation 3]
35. ! [X0] : (((~patient(X0) & humble(X0)) | tall(X0)) & (~tall(X0) | patient(X0) | ~humble(X0))) [flattening 34]
36. ! [X0] : ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))) [nnf transformation 4]
47. ! [X0] : (strong(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 25]
48. ! [X0] : ((generous(X0) | (rich(X0) & ~old(X0))) & ((~rich(X0) | old(X0)) | ~generous(X0))) [nnf transformation 8]
49. ! [X0] : ((generous(X0) | (rich(X0) & ~old(X0))) & (~rich(X0) | old(X0) | ~generous(X0))) [flattening 48]
52. ! [X0] : ((old(X0) | (happy(X0) | ~humble(X0))) & ((~happy(X0) & humble(X0)) | ~old(X0))) [nnf transformation 10]
53. ! [X0] : ((old(X0) | happy(X0) | ~humble(X0)) & ((~happy(X0) & humble(X0)) | ~old(X0))) [flattening 52]
54. ! [X0] : (((humble(X0) | ~calm(X0)) | (happy(X0) | ~strong(X0))) & ((~happy(X0) & strong(X0)) | (~humble(X0) & calm(X0)))) [nnf transformation 11]
55. ! [X0] : ((humble(X0) | ~calm(X0) | happy(X0) | ~strong(X0)) & ((~happy(X0) & strong(X0)) | (~humble(X0) & calm(X0)))) [flattening 54]
57. (? [X0] : ((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | (strong(alice) & generous(alice))) & ((~strong(alice) | ~generous(alice)) | ! [X0] : ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) [nnf transformation 13]
58. (? [X0] : ((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | (strong(alice) & generous(alice))) & (~strong(alice) | ~generous(alice) | ! [X0] : ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) [flattening 57]
59. (? [X0] : ((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | (strong(alice) & generous(alice))) & (~strong(alice) | ~generous(alice) | ! [X1] : ((~creative(X1) | ~tall(X1)) & (tall(X1) | creative(X1)))) [rectify 58]
60. ? [X0] : ((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) => ((~tall(sK4) | creative(sK4)) & (tall(sK4) | ~creative(sK4))) [choice axiom]
61. (((~tall(sK4) | creative(sK4)) & (tall(sK4) | ~creative(sK4))) | (strong(alice) & generous(alice))) & (~strong(alice) | ~generous(alice) | ! [X1] : ((~creative(X1) | ~tall(X1)) & (tall(X1) | creative(X1)))) [skolemisation 59,60]
67. ! [X0] : ((((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~brave(X0) & ~old(X0))) & ((brave(X0) | old(X0)) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))))) [nnf transformation 16]
68. ! [X0] : ((((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~brave(X0) & ~old(X0))) & (brave(X0) | old(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))))) [flattening 67]
81. ~humble(X0) | patient(X0) | ~tall(X0) [cnf transformation 35]
82. humble(X0) | tall(X0) [cnf transformation 35]
84. ~rich(X0) | old(X0) [cnf transformation 36]
94. strong(X0) | quiet(X0) | quiet(X0) [cnf transformation 47]
95. strong(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 47]
97. ~old(X0) | generous(X0) [cnf transformation 49]
98. rich(X0) | generous(X0) [cnf transformation 49]
105. ~old(X0) | humble(X0) [cnf transformation 53]
107. ~humble(X0) | happy(X0) | old(X0) [cnf transformation 53]
111. ~humble(X0) | ~happy(X0) [cnf transformation 55]
115. ~strong(alice) | ~generous(alice) | tall(X1) | creative(X1) [cnf transformation 61]
128. ~rich(X0) | ~patient(X0) [cnf transformation 28]
133. ~creative(X0) | ~humble(X0) | ~old(X0) [cnf transformation 68]
140. rich(fred) [cnf transformation 20]
142. strong(X0) | quiet(X0) [duplicate literal removal 94]
143. ~quiet(X0) | strong(X0) [duplicate literal removal 95]
220. strong(X0) [subsumption resolution 142,143]
255. 24 <=> generous(alice) [avatar definition]
256. ~generous(alice) <- (~24) [avatar component clause 255]
273. ~generous(alice) | tall(X1) | creative(X1) [subsumption resolution 115,220]
275. 28 <=> ! [X1] : (tall(X1) | creative(X1)) [avatar definition]
276. creative(X1) | tall(X1) <- (28) [avatar component clause 275]
277. 28 | ~24 [avatar split clause 273,255,275]
303. ~creative(X0) | ~old(X0) [subsumption resolution 133,105]
334. old(fred) [resolution 84,140]
337. generous(X0) | old(X0) [resolution 98,84]
338. generous(X0) [subsumption resolution 337,97]
339. $false <- (~24) [resolution 338,256]
340. 24 [avatar contradiction clause 339]
341. humble(fred) [resolution 105,334]
344. ~happy(X0) | tall(X0) [resolution 111,82]
348. ~patient(fred) [resolution 128,140]
367. ~old(X0) | tall(X0) <- (28) [resolution 303,276]
374. patient(fred) | ~tall(fred) [resolution 81,341]
376. ~tall(fred) [subsumption resolution 374,348]
379. happy(X0) | old(X0) | tall(X0) [resolution 107,82]
383. old(X0) | tall(X0) [subsumption resolution 379,344]
384. tall(X0) <- (28) [subsumption resolution 383,367]
418. $false <- (28) [resolution 376,384]
419. ~28 [avatar contradiction clause 418]
420. $false [avatar sat refutation 277,340,419]
% SZS output end Proof for 1698599580178282026961566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is tall. Everyone who is quiet or curious is both not kind and not humble. Everyone who is not tall is both not creative and not brave and vice versa. Everyone who is both happy and patient is both old and brave. Everyone who is both not patient and brave is not rich or not brave and vice versa. Everyone who is not brave or not wise is both not happy and strong. Everyone who is creative is both not generous and not curious and vice versa. Everyone who is not rich is brave and vice versa. Everyone who is strong or not creative is not calm or not wise. If someone is not curious or humble then someone is both calm and not creative and vice versa. If someone is wise then john is either patient or not patient. If susan is not strong then someone is both funny and patient and vice versa. If mary is not funny then john is humble or quiet. If someone is humble or patient then someone is not strong or funny and vice versa. Everyone who is kind is not quiet and vice versa. Everyone who is patient is funny or not wise. Someone is either not humble or kind. Susan is humble. Someone is either happy or wise. Someone is either wise or funny. Someone is either creative or not old. Someone is either not funny or not strong. Someone is old or patient. Someone is old or not happy. | Mary is not curious. | neutral | (![X]:(~calm(X)=>tall(X)))&
(![X]:((quiet(X)|curious(X))=>(~kind(X)&~humble(X))))&
(![X]:(~tall(X)<=>(~creative(X)&~brave(X))))&
(![X]:((happy(X)&patient(X))=>(old(X)&brave(X))))&
(![X]:((~patient(X)&brave(X))<=>(~rich(X)|~brave(X))))&
(![X]:((~brave(X)|~wise(X))=>(~happy(X)&strong(X))))&
(![X]:(creative(X)<=>(~generous(X)&~curious(X))))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:((strong(X)|~creative(X))=>(~calm(X)|~wise(X))))&
((?[X]:((~curious(X)|humble(X))))<=>(?[X]:((calm(X)&~creative(X)))))&
((?[X]:(wise(X)))=>((patient(john)<~>~patient(john))))&
((~strong(susan))<=>(?[X]:((funny(X)&patient(X)))))&
((~funny(mary))=>((humble(john)|quiet(john))))&
((?[X]:((humble(X)|patient(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:(kind(X)<=>~quiet(X)))&
(![X]:(patient(X)=>(funny(X)|~wise(X))))&
(?[X]:((~humble(X)<~>kind(X))))&
(humble(susan))&
(?[X]:((happy(X)<~>wise(X))))&
(?[X]:((wise(X)<~>funny(X))))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:((~funny(X)<~>~strong(X))))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((old(X)|~happy(X)))) | ~curious(mary) | [] | null | 0 |
Everyone who is either not quiet or not funny is either creative or not curious and vice versa.
If someone is either curious or not wise then lucy is both old and generous and vice versa.
If someone is both not calm and not curious then fred is not wise or not creative and vice versa.
If someone is either not kind or happy then john is brave and vice versa.
Everyone who is both not calm and not funny is not quiet and vice versa.
Everyone who is both old and not humble is both not tall and happy and vice versa.
Everyone who is old or kind is either not curious or patient and vice versa.
Everyone who is not patient or not wise is not happy.
Everyone who is both curious and patient is old or not curious.
If susan is not tall then susan is generous or old.
Everyone who is both patient and not brave is kind or quiet and vice versa.
If fred is both curious and calm then john is both humble and not happy.
If mary is either not funny or humble then mary is both not humble and curious.
Everyone who is not wise or not rich is generous or creative.
If someone is brave or old then fred is either not curious or brave.
Everyone who is either not curious or not patient is either not curious or not kind and vice versa.
Someone is not quiet or not happy.
Susan is both not creative and patient.
Someone is not brave or funny.
Someone is humble or not quiet.
Someone is either happy or patient.
Someone is either not calm or not patient.
Someone is not patient.
Someone is not kind or not wise. | John is not calm. | entailment | (![X]:((~quiet(X)<~>~funny(X))<=>(creative(X)<~>~curious(X))))&
((?[X]:((curious(X)<~>~wise(X))))<=>((old(lucy)&generous(lucy))))&
((?[X]:((~calm(X)&~curious(X))))<=>((~wise(fred)|~creative(fred))))&
((?[X]:((~kind(X)<~>happy(X))))<=>(brave(john)))&
(![X]:((~calm(X)&~funny(X))<=>~quiet(X)))&
(![X]:((old(X)&~humble(X))<=>(~tall(X)&happy(X))))&
(![X]:((old(X)|kind(X))<=>(~curious(X)<~>patient(X))))&
(![X]:((~patient(X)|~wise(X))=>~happy(X)))&
(![X]:((curious(X)&patient(X))=>(old(X)|~curious(X))))&
((~tall(susan))=>((generous(susan)|old(susan))))&
(![X]:((patient(X)&~brave(X))<=>(kind(X)|quiet(X))))&
(((curious(fred)&calm(fred)))=>((humble(john)&~happy(john))))&
(((~funny(mary)<~>humble(mary)))=>((~humble(mary)&curious(mary))))&
(![X]:((~wise(X)|~rich(X))=>(generous(X)|creative(X))))&
((?[X]:((brave(X)|old(X))))=>((~curious(fred)<~>brave(fred))))&
(![X]:((~curious(X)<~>~patient(X))<=>(~curious(X)<~>~kind(X))))&
(?[X]:((~quiet(X)|~happy(X))))&
((~creative(susan)&patient(susan)))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((humble(X)|~quiet(X))))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((~calm(X)<~>~patient(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~kind(X)|~wise(X)))) | ~calm(john) | [
"p3",
"p4",
"p7",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1498766547402326970986178
% SZS output start Proof for 1498766547402326970986178
4. ? [X0] : (~kind(X0) <~> happy(X0)) <=> brave(john) [input p3]
5. ! [X0] : ((~funny(X0) & ~calm(X0)) <=> ~quiet(X0)) [input p4]
8. ! [X0] : ((~wise(X0) | ~patient(X0)) => ~happy(X0)) [input p7]
11. ! [X0] : ((~brave(X0) & patient(X0)) <=> (quiet(X0) | kind(X0))) [input p10]
23. ? [X0] : ~patient(X0) [input p22]
25. calm(john) [input hypothesis]
27. ! [X0] : (~happy(X0) | (wise(X0) & patient(X0))) [ennf transformation 8]
49. (? [X0] : ((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) | ~brave(john)) & (brave(john) | ! [X0] : ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) [nnf transformation 4]
50. (? [X0] : ((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) | ~brave(john)) & (brave(john) | ! [X1] : ((~kind(X1) | ~happy(X1)) & (happy(X1) | kind(X1)))) [rectify 49]
51. ? [X0] : ((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) => ((~happy(sK2) | kind(sK2)) & (happy(sK2) | ~kind(sK2))) [choice axiom]
52. (((~happy(sK2) | kind(sK2)) & (happy(sK2) | ~kind(sK2))) | ~brave(john)) & (brave(john) | ! [X1] : ((~kind(X1) | ~happy(X1)) & (happy(X1) | kind(X1)))) [skolemisation 50,51]
53. ! [X0] : (((~funny(X0) & ~calm(X0)) | quiet(X0)) & (~quiet(X0) | (funny(X0) | calm(X0)))) [nnf transformation 5]
54. ! [X0] : (((~funny(X0) & ~calm(X0)) | quiet(X0)) & (~quiet(X0) | funny(X0) | calm(X0))) [flattening 53]
59. ! [X0] : (((~brave(X0) & patient(X0)) | (~quiet(X0) & ~kind(X0))) & ((quiet(X0) | kind(X0)) | (brave(X0) | ~patient(X0)))) [nnf transformation 11]
60. ! [X0] : (((~brave(X0) & patient(X0)) | (~quiet(X0) & ~kind(X0))) & (quiet(X0) | kind(X0) | brave(X0) | ~patient(X0))) [flattening 59]
76. ? [X0] : ~patient(X0) => ~patient(sK8) [choice axiom]
77. ~patient(sK8) [skolemisation 23,76]
99. brave(john) | happy(X1) | kind(X1) [cnf transformation 52]
104. ~calm(X0) | quiet(X0) [cnf transformation 54]
116. ~happy(X0) | patient(X0) [cnf transformation 27]
121. ~kind(X0) | patient(X0) [cnf transformation 60]
124. ~brave(X0) | ~quiet(X0) [cnf transformation 60]
153. ~patient(sK8) [cnf transformation 77]
155. calm(john) [cnf transformation 25]
215. 12 <=> brave(john) [avatar definition]
216. brave(john) <- (12) [avatar component clause 215]
233. 16 <=> ! [X1] : (happy(X1) | kind(X1)) [avatar definition]
234. happy(X1) | kind(X1) <- (16) [avatar component clause 233]
235. 16 | 12 [avatar split clause 99,215,233]
345. quiet(john) [resolution 104,155]
352. ~quiet(john) <- (12) [resolution 124,216]
353. $false <- (12) [subsumption resolution 352,345]
354. ~12 [avatar contradiction clause 353]
362. kind(X2) | patient(X2) <- (16) [resolution 234,116]
366. patient(X2) <- (16) [subsumption resolution 362,121]
378. $false <- (16) [resolution 366,153]
380. ~16 [avatar contradiction clause 378]
381. $false [avatar sat refutation 235,354,380]
% SZS output end Proof for 1498766547402326970986178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and old then someone is either not patient or curious and vice versa.
If fred is quiet then paul is kind or not funny.
If fred is not wise then someone is either brave or not happy and vice versa.
Everyone who is both rich and brave is not rich.
If fred is rich then someone is either funny or not strong.
Everyone who is either not funny or old is both old and not kind.
If john is wise or curious then lucy is both not brave and brave and vice versa.
If susan is either not tall or not funny then someone is old or not kind and vice versa.
Everyone who is brave is both generous and not wise and vice versa.
Everyone who is either not curious or rich is not calm or not wise.
Everyone who is quiet or not quiet is strong and vice versa.
Everyone who is funny or calm is happy or funny and vice versa.
If someone is either not strong or not creative then someone is either not strong or not quiet.
If fred is both strong and generous then paul is either not generous or tall.
Everyone who is not rich or brave is not humble and vice versa.
Everyone who is not funny or tall is both wise and not wise and vice versa.
Someone is not creative.
Alice is either kind or not strong.
Someone is patient.
Alice is either humble or not curious.
John is either not humble or kind.
John is both generous and not wise.
Someone is either rich or funny.
Lucy is kind or calm. | Susan is tall. | contradiction | ((?[X]:((humble(X)&old(X))))<=>(?[X]:((~patient(X)<~>curious(X)))))&
((quiet(fred))=>((kind(paul)|~funny(paul))))&
((~wise(fred))<=>(?[X]:((brave(X)<~>~happy(X)))))&
(![X]:((rich(X)&brave(X))=>~rich(X)))&
((rich(fred))=>(?[X]:((funny(X)<~>~strong(X)))))&
(![X]:((~funny(X)<~>old(X))=>(old(X)&~kind(X))))&
(((wise(john)|curious(john)))<=>((~brave(lucy)&brave(lucy))))&
(((~tall(susan)<~>~funny(susan)))<=>(?[X]:((old(X)|~kind(X)))))&
(![X]:(brave(X)<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)<~>rich(X))=>(~calm(X)|~wise(X))))&
(![X]:((quiet(X)|~quiet(X))<=>strong(X)))&
(![X]:((funny(X)|calm(X))<=>(happy(X)|funny(X))))&
((?[X]:((~strong(X)<~>~creative(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(((strong(fred)&generous(fred)))=>((~generous(paul)<~>tall(paul))))&
(![X]:((~rich(X)|brave(X))<=>~humble(X)))&
(![X]:((~funny(X)|tall(X))<=>(wise(X)&~wise(X))))&
(?[X]:(~creative(X)))&
((kind(alice)<~>~strong(alice)))&
(?[X]:(patient(X)))&
((humble(alice)<~>~curious(alice)))&
((~humble(john)<~>kind(john)))&
((generous(john)&~wise(john)))&
(?[X]:((rich(X)<~>funny(X))))&
((kind(lucy)|calm(lucy))) | tall(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8568357779696893203240970
% SZS output start Proof for 8568357779696893203240970
16. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (~wise(X0) & wise(X0))) [input p15]
25. tall(susan) [input hypothesis]
72. ! [X0] : (((tall(X0) | ~funny(X0)) | (wise(X0) | ~wise(X0))) & ((~wise(X0) & wise(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 16]
73. ! [X0] : ((tall(X0) | ~funny(X0) | wise(X0) | ~wise(X0)) & ((~wise(X0) & wise(X0)) | (~tall(X0) & funny(X0)))) [flattening 72]
135. wise(X0) | ~tall(X0) [cnf transformation 73]
137. ~wise(X0) | ~tall(X0) [cnf transformation 73]
152. tall(susan) [cnf transformation 25]
307. ~tall(X0) [subsumption resolution 135,137]
341. $false [subsumption resolution 152,307]
% SZS output end Proof for 8568357779696893203240970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is old or not generous then lucy is not creative or not generous.
Everyone who is strong or not funny is rich or not kind and vice versa.
Everyone who is either patient or brave is creative or strong and vice versa.
If paul is either creative or not brave then alice is either creative or not strong.
Everyone who is both wise and patient is both happy and not tall and vice versa.
Everyone who is curious or not happy is not generous or funny.
If someone is wise then lucy is both not quiet and happy.
Everyone who is not quiet is funny.
If alice is either not tall or not strong then paul is both tall and creative and vice versa.
Everyone who is both not strong and happy is calm or quiet and vice versa.
If fred is not kind then lucy is either wise or strong.
If mary is either curious or quiet then mary is rich.
Everyone who is either patient or curious is both not humble and rich.
Everyone who is old is old or kind and vice versa.
Everyone who is not generous is not kind.
Everyone who is wise is both generous and not strong and vice versa.
Lucy is either not strong or not quiet.
Paul is either funny or not generous.
Susan is not quiet.
Someone is rich.
John is either quiet or not brave.
Someone is both wise and not curious.
John is humble or rich. | John is not calm. | neutral | (((old(john)|~generous(john)))=>((~creative(lucy)|~generous(lucy))))&
(![X]:((strong(X)|~funny(X))<=>(rich(X)|~kind(X))))&
(![X]:((patient(X)<~>brave(X))<=>(creative(X)|strong(X))))&
(((creative(paul)<~>~brave(paul)))=>((creative(alice)<~>~strong(alice))))&
(![X]:((wise(X)&patient(X))<=>(happy(X)&~tall(X))))&
(![X]:((curious(X)|~happy(X))=>(~generous(X)|funny(X))))&
((?[X]:(wise(X)))=>((~quiet(lucy)&happy(lucy))))&
(![X]:(~quiet(X)=>funny(X)))&
(((~tall(alice)<~>~strong(alice)))<=>((tall(paul)&creative(paul))))&
(![X]:((~strong(X)&happy(X))<=>(calm(X)|quiet(X))))&
((~kind(fred))=>((wise(lucy)<~>strong(lucy))))&
(((curious(mary)<~>quiet(mary)))=>(rich(mary)))&
(![X]:((patient(X)<~>curious(X))=>(~humble(X)&rich(X))))&
(![X]:(old(X)<=>(old(X)|kind(X))))&
(![X]:(~generous(X)=>~kind(X)))&
(![X]:(wise(X)<=>(generous(X)&~strong(X))))&
((~strong(lucy)<~>~quiet(lucy)))&
((funny(paul)<~>~generous(paul)))&
(~quiet(susan))&
(?[X]:(rich(X)))&
((quiet(john)<~>~brave(john)))&
(?[X]:((wise(X)&~curious(X))))&
((humble(john)|rich(john))) | ~calm(john) | [] | null | 0 |
If mary is both not wise and not curious then someone is either not strong or not generous.
Everyone who is funny or not curious is wise and vice versa.
Everyone who is rich is not wise or not patient.
Everyone who is humble is either not rich or not old.
Everyone who is either not creative or old is humble or funny and vice versa.
Everyone who is both not humble and not curious is both tall and not strong and vice versa.
If lucy is not quiet then someone is wise and vice versa.
Everyone who is either strong or not funny is not calm and vice versa.
If someone is either not humble or brave then someone is not creative or quiet.
If fred is patient then lucy is calm or not creative and vice versa.
Everyone who is either not generous or not old is both kind and curious.
Everyone who is not rich or old is either not tall or creative.
If susan is both not tall and funny then someone is both not curious and kind and vice versa.
Everyone who is either rich or not brave is either happy or not curious and vice versa.
Everyone who is not tall or humble is tall or calm and vice versa.
Everyone who is rich or not rich is either tall or patient and vice versa.
Susan is not funny or brave.
Fred is funny or humble.
Fred is either not creative or not patient.
Someone is quiet or brave.
Mary is either not kind or not strong.
Susan is both kind and old.
Someone is strong.
Someone is both not curious and rich. | Mary is not tall. | neutral | (((~wise(mary)&~curious(mary)))=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((funny(X)|~curious(X))<=>wise(X)))&
(![X]:(rich(X)=>(~wise(X)|~patient(X))))&
(![X]:(humble(X)=>(~rich(X)<~>~old(X))))&
(![X]:((~creative(X)<~>old(X))<=>(humble(X)|funny(X))))&
(![X]:((~humble(X)&~curious(X))<=>(tall(X)&~strong(X))))&
((~quiet(lucy))<=>(?[X]:(wise(X))))&
(![X]:((strong(X)<~>~funny(X))<=>~calm(X)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((~creative(X)|quiet(X)))))&
((patient(fred))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~generous(X)<~>~old(X))=>(kind(X)&curious(X))))&
(![X]:((~rich(X)|old(X))=>(~tall(X)<~>creative(X))))&
(((~tall(susan)&funny(susan)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((rich(X)<~>~brave(X))<=>(happy(X)<~>~curious(X))))&
(![X]:((~tall(X)|humble(X))<=>(tall(X)|calm(X))))&
(![X]:((rich(X)|~rich(X))<=>(tall(X)<~>patient(X))))&
((~funny(susan)|brave(susan)))&
((funny(fred)|humble(fred)))&
((~creative(fred)<~>~patient(fred)))&
(?[X]:((quiet(X)|brave(X))))&
((~kind(mary)<~>~strong(mary)))&
((kind(susan)&old(susan)))&
(?[X]:(strong(X)))&
(?[X]:((~curious(X)&rich(X)))) | ~tall(mary) | [] | null | 0 |
Everyone who is not strong is both not generous and not rich.
If lucy is both curious and not calm then lucy is strong.
Everyone who is both curious and rich is both not brave and funny.
If fred is generous or strong then fred is creative or quiet and vice versa.
Everyone who is both humble and old is rich.
Everyone who is either rich or funny is not brave and vice versa.
If someone is kind then someone is both not funny and strong and vice versa.
Everyone who is both calm and brave is brave or not brave.
If paul is either not quiet or tall then someone is both calm and not creative.
If someone is both wise and generous then someone is both tall and patient.
Everyone who is brave is not calm or not strong and vice versa.
If fred is both not generous and rich then alice is either not curious or not generous and vice versa.
If susan is not funny or not wise then someone is old or not humble and vice versa.
Everyone who is both not strong and rich is either not calm or not kind.
Everyone who is not old or not strong is generous and vice versa.
If alice is not kind then lucy is either not creative or strong.
Fred is either quiet or not brave.
Someone is either generous or not rich.
Someone is both not brave and kind.
Paul is rich or not tall.
Someone is not tall.
Someone is both not curious and creative.
Lucy is both not humble and rich.
Lucy is either not brave or not tall. | Paul is not funny. | neutral | (![X]:(~strong(X)=>(~generous(X)&~rich(X))))&
(((curious(lucy)&~calm(lucy)))=>(strong(lucy)))&
(![X]:((curious(X)&rich(X))=>(~brave(X)&funny(X))))&
(((generous(fred)|strong(fred)))<=>((creative(fred)|quiet(fred))))&
(![X]:((humble(X)&old(X))=>rich(X)))&
(![X]:((rich(X)<~>funny(X))<=>~brave(X)))&
((?[X]:(kind(X)))<=>(?[X]:((~funny(X)&strong(X)))))&
(![X]:((calm(X)&brave(X))=>(brave(X)|~brave(X))))&
(((~quiet(paul)<~>tall(paul)))=>(?[X]:((calm(X)&~creative(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((tall(X)&patient(X)))))&
(![X]:(brave(X)<=>(~calm(X)|~strong(X))))&
(((~generous(fred)&rich(fred)))<=>((~curious(alice)<~>~generous(alice))))&
(((~funny(susan)|~wise(susan)))<=>(?[X]:((old(X)|~humble(X)))))&
(![X]:((~strong(X)&rich(X))=>(~calm(X)<~>~kind(X))))&
(![X]:((~old(X)|~strong(X))<=>generous(X)))&
((~kind(alice))=>((~creative(lucy)<~>strong(lucy))))&
((quiet(fred)<~>~brave(fred)))&
(?[X]:((generous(X)<~>~rich(X))))&
(?[X]:((~brave(X)&kind(X))))&
((rich(paul)|~tall(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((~curious(X)&creative(X))))&
((~humble(lucy)&rich(lucy)))&
((~brave(lucy)<~>~tall(lucy))) | ~funny(paul) | [] | null | 0 |
Everyone who is either curious or calm is not kind or not curious and vice versa.
Everyone who is either curious or quiet is not curious or not old and vice versa.
Everyone who is not old is both strong and creative and vice versa.
If mary is not funny or kind then alice is both not calm and tall.
Everyone who is old is both rich and brave and vice versa.
Everyone who is curious or generous is both not rich and calm.
If john is not generous then fred is not wise or not funny.
Everyone who is either not happy or old is both not tall and tall.
If mary is not wise then lucy is either old or not funny and vice versa.
If mary is quiet or not kind then someone is old and vice versa.
If someone is not strong or not old then someone is either funny or not curious and vice versa.
Everyone who is not quiet or not happy is both not curious and kind.
If someone is kind or not patient then someone is both funny and not curious.
Everyone who is not old or not humble is strong.
Everyone who is not kind or old is quiet or not rich.
Everyone who is both not old and not strong is both not curious and not patient and vice versa.
Mary is either not curious or not happy.
Someone is either not generous or not funny.
Someone is not funny.
Fred is either quiet or not tall.
John is happy.
Fred is either creative or calm.
Alice is not wise. | Lucy is patient. | entailment | (![X]:((curious(X)<~>calm(X))<=>(~kind(X)|~curious(X))))&
(![X]:((curious(X)<~>quiet(X))<=>(~curious(X)|~old(X))))&
(![X]:(~old(X)<=>(strong(X)&creative(X))))&
(((~funny(mary)|kind(mary)))=>((~calm(alice)&tall(alice))))&
(![X]:(old(X)<=>(rich(X)&brave(X))))&
(![X]:((curious(X)|generous(X))=>(~rich(X)&calm(X))))&
((~generous(john))=>((~wise(fred)|~funny(fred))))&
(![X]:((~happy(X)<~>old(X))=>(~tall(X)&tall(X))))&
((~wise(mary))<=>((old(lucy)<~>~funny(lucy))))&
(((quiet(mary)|~kind(mary)))<=>(?[X]:(old(X))))&
((?[X]:((~strong(X)|~old(X))))<=>(?[X]:((funny(X)<~>~curious(X)))))&
(![X]:((~quiet(X)|~happy(X))=>(~curious(X)&kind(X))))&
((?[X]:((kind(X)|~patient(X))))=>(?[X]:((funny(X)&~curious(X)))))&
(![X]:((~old(X)|~humble(X))=>strong(X)))&
(![X]:((~kind(X)|old(X))=>(quiet(X)|~rich(X))))&
(![X]:((~old(X)&~strong(X))<=>(~curious(X)&~patient(X))))&
((~curious(mary)<~>~happy(mary)))&
(?[X]:((~generous(X)<~>~funny(X))))&
(?[X]:(~funny(X)))&
((quiet(fred)<~>~tall(fred)))&
(happy(john))&
((creative(fred)<~>calm(fred)))&
(~wise(alice)) | patient(lucy) | [
"p1",
"p2",
"p4",
"p5",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3347447593807103159525358
% SZS output start Proof for 3347447593807103159525358
2. ! [X0] : ((curious(X0) <~> quiet(X0)) <=> (~old(X0) | ~curious(X0))) [input p1]
3. ! [X0] : (~old(X0) <=> (creative(X0) & strong(X0))) [input p2]
5. ! [X0] : (old(X0) <=> (brave(X0) & rich(X0))) [input p4]
6. ! [X0] : ((generous(X0) | curious(X0)) => (calm(X0) & ~rich(X0))) [input p5]
12. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (kind(X0) & ~curious(X0))) [input p11]
16. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (~patient(X0) & ~curious(X0))) [input p15]
24. ~patient(lucy) [input hypothesis]
29. ! [X0] : ((calm(X0) & ~rich(X0)) | (~generous(X0) & ~curious(X0))) [ennf transformation 6]
33. ! [X0] : ((kind(X0) & ~curious(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 12]
40. ! [X0] : ((((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (old(X0) & curious(X0))) & ((~old(X0) | ~curious(X0)) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0))))) [nnf transformation 2]
41. ! [X0] : ((((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (old(X0) & curious(X0))) & (~old(X0) | ~curious(X0) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0))))) [flattening 40]
42. ! [X0] : ((~old(X0) | (~creative(X0) | ~strong(X0))) & ((creative(X0) & strong(X0)) | old(X0))) [nnf transformation 3]
43. ! [X0] : ((~old(X0) | ~creative(X0) | ~strong(X0)) & ((creative(X0) & strong(X0)) | old(X0))) [flattening 42]
44. ! [X0] : ((old(X0) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | ~old(X0))) [nnf transformation 5]
45. ! [X0] : ((old(X0) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | ~old(X0))) [flattening 44]
61. ! [X0] : (((~strong(X0) & ~old(X0)) | (patient(X0) | curious(X0))) & ((~patient(X0) & ~curious(X0)) | (strong(X0) | old(X0)))) [nnf transformation 16]
62. ! [X0] : (((~strong(X0) & ~old(X0)) | patient(X0) | curious(X0)) & ((~patient(X0) & ~curious(X0)) | strong(X0) | old(X0))) [flattening 61]
79. quiet(X0) | curious(X0) | curious(X0) [cnf transformation 41]
82. ~quiet(X0) | ~curious(X0) | old(X0) [cnf transformation 41]
83. strong(X0) | old(X0) [cnf transformation 43]
90. ~old(X0) | rich(X0) [cnf transformation 45]
93. ~rich(X0) | ~curious(X0) [cnf transformation 29]
115. ~curious(X0) | quiet(X0) [cnf transformation 33]
128. ~old(X0) | patient(X0) | curious(X0) [cnf transformation 62]
129. ~strong(X0) | patient(X0) | curious(X0) [cnf transformation 62]
141. ~patient(lucy) [cnf transformation 24]
143. quiet(X0) | curious(X0) [duplicate literal removal 79]
189. 9 <=> old(lucy) [avatar definition]
191. old(lucy) <- (9) [avatar component clause 189]
248. quiet(X0) [subsumption resolution 115,143]
323. ~curious(X2) | old(X2) [resolution 82,248]
342. patient(X0) | curious(X0) | old(X0) [resolution 129,83]
344. patient(X0) | old(X0) [subsumption resolution 342,323]
369. old(lucy) [resolution 344,141]
372. 9 [avatar split clause 369,189]
373. patient(lucy) | curious(lucy) <- (9) [resolution 191,128]
377. rich(lucy) <- (9) [resolution 191,90]
378. curious(lucy) <- (9) [subsumption resolution 373,141]
380. ~curious(lucy) <- (9) [resolution 377,93]
381. $false <- (9) [subsumption resolution 380,378]
382. ~9 [avatar contradiction clause 381]
383. $false [avatar sat refutation 372,382]
% SZS output end Proof for 3347447593807103159525358
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or not humble then someone is both curious and not calm.
If someone is not wise then paul is curious.
If mary is not old or not rich then someone is patient.
Everyone who is funny or not happy is not curious or not tall.
If someone is rich or calm then someone is both not brave and not kind and vice versa.
If someone is not calm then someone is both rich and not patient.
If someone is both not strong and not calm then someone is either quiet or wise.
If someone is wise or not rich then someone is either quiet or not creative and vice versa.
Everyone who is strong is not rich.
Everyone who is both not curious and happy is both patient and curious.
Everyone who is both funny and not humble is not creative or wise.
Everyone who is not humble or rich is not brave and vice versa.
If someone is either creative or happy then someone is either not strong or not old.
Everyone who is both humble and not patient is both wise and kind.
Everyone who is quiet or not patient is either not kind or curious and vice versa.
If alice is either not curious or wise then susan is either tall or brave and vice versa.
Lucy is not curious or not funny.
Mary is either not kind or old.
Lucy is not humble.
Lucy is both calm and not tall.
Alice is either not rich or not funny.
Paul is kind or patient.
Someone is not tall.
Susan is both patient and not creative. | Lucy is curious. | neutral | ((?[X]:((quiet(X)|~humble(X))))=>(?[X]:((curious(X)&~calm(X)))))&
((?[X]:(~wise(X)))=>(curious(paul)))&
(((~old(mary)|~rich(mary)))=>(?[X]:(patient(X))))&
(![X]:((funny(X)|~happy(X))=>(~curious(X)|~tall(X))))&
((?[X]:((rich(X)|calm(X))))<=>(?[X]:((~brave(X)&~kind(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)&~patient(X)))))&
((?[X]:((~strong(X)&~calm(X))))=>(?[X]:((quiet(X)<~>wise(X)))))&
((?[X]:((wise(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>~creative(X)))))&
(![X]:(strong(X)=>~rich(X)))&
(![X]:((~curious(X)&happy(X))=>(patient(X)&curious(X))))&
(![X]:((funny(X)&~humble(X))=>(~creative(X)|wise(X))))&
(![X]:((~humble(X)|rich(X))<=>~brave(X)))&
((?[X]:((creative(X)<~>happy(X))))=>(?[X]:((~strong(X)<~>~old(X)))))&
(![X]:((humble(X)&~patient(X))=>(wise(X)&kind(X))))&
(![X]:((quiet(X)|~patient(X))<=>(~kind(X)<~>curious(X))))&
(((~curious(alice)<~>wise(alice)))<=>((tall(susan)<~>brave(susan))))&
((~curious(lucy)|~funny(lucy)))&
((~kind(mary)<~>old(mary)))&
(~humble(lucy))&
((calm(lucy)&~tall(lucy)))&
((~rich(alice)<~>~funny(alice)))&
((kind(paul)|patient(paul)))&
(?[X]:(~tall(X)))&
((patient(susan)&~creative(susan))) | curious(lucy) | [] | null | 0 |
If susan is either not happy or creative then lucy is not tall or not wise and vice versa.
If mary is either not funny or humble then susan is not patient or funny and vice versa.
If someone is either not calm or kind then someone is either rich or not funny and vice versa.
Everyone who is both not strong and not generous is happy.
Everyone who is either not wise or strong is funny or not patient and vice versa.
If someone is happy then someone is either not curious or not patient and vice versa.
If alice is not creative then someone is generous.
If someone is not patient or not quiet then paul is strong or not patient.
Everyone who is either patient or not quiet is both creative and not generous and vice versa.
Everyone who is not curious is either tall or not generous.
Everyone who is not tall is happy or curious and vice versa.
If mary is either not humble or strong then john is tall.
Everyone who is not rich or wise is rich and vice versa.
If alice is not old then someone is not patient.
If paul is strong or not curious then john is rich or old.
If someone is both rich and quiet then someone is wise.
Susan is not kind.
Susan is tall or humble.
Paul is calm or quiet.
John is creative or not brave.
Paul is not creative or not curious.
John is either not generous or not strong.
Lucy is creative.
Someone is either quiet or tall. | John is rich. | entailment | (((~happy(susan)<~>creative(susan)))<=>((~tall(lucy)|~wise(lucy))))&
(((~funny(mary)<~>humble(mary)))<=>((~patient(susan)|funny(susan))))&
((?[X]:((~calm(X)<~>kind(X))))<=>(?[X]:((rich(X)<~>~funny(X)))))&
(![X]:((~strong(X)&~generous(X))=>happy(X)))&
(![X]:((~wise(X)<~>strong(X))<=>(funny(X)|~patient(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)<~>~patient(X)))))&
((~creative(alice))=>(?[X]:(generous(X))))&
((?[X]:((~patient(X)|~quiet(X))))=>((strong(paul)|~patient(paul))))&
(![X]:((patient(X)<~>~quiet(X))<=>(creative(X)&~generous(X))))&
(![X]:(~curious(X)=>(tall(X)<~>~generous(X))))&
(![X]:(~tall(X)<=>(happy(X)|curious(X))))&
(((~humble(mary)<~>strong(mary)))=>(tall(john)))&
(![X]:((~rich(X)|wise(X))<=>rich(X)))&
((~old(alice))=>(?[X]:(~patient(X))))&
(((strong(paul)|~curious(paul)))=>((rich(john)|old(john))))&
((?[X]:((rich(X)&quiet(X))))=>(?[X]:(wise(X))))&
(~kind(susan))&
((tall(susan)|humble(susan)))&
((calm(paul)|quiet(paul)))&
((creative(john)|~brave(john)))&
((~creative(paul)|~curious(paul)))&
((~generous(john)<~>~strong(john)))&
(creative(lucy))&
(?[X]:((quiet(X)<~>tall(X)))) | rich(john) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2757517877314076507634537
% SZS output start Proof for 2757517877314076507634537
13. ! [X0] : ((wise(X0) | ~rich(X0)) <=> rich(X0)) [input p12]
25. ~rich(john) [input hypothesis]
64. ! [X0] : (((wise(X0) | ~rich(X0)) | ~rich(X0)) & (rich(X0) | (~wise(X0) & rich(X0)))) [nnf transformation 13]
65. ! [X0] : ((wise(X0) | ~rich(X0) | ~rich(X0)) & (rich(X0) | (~wise(X0) & rich(X0)))) [flattening 64]
120. rich(X0) | rich(X0) [cnf transformation 65]
133. ~rich(john) [cnf transformation 25]
134. rich(X0) [duplicate literal removal 120]
332. $false [subsumption resolution 133,134]
% SZS output end Proof for 2757517877314076507634537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not creative is rich and vice versa.
Everyone who is generous is patient or humble and vice versa.
Everyone who is not strong or not humble is creative or kind and vice versa.
Everyone who is creative or not funny is not humble or old and vice versa.
Everyone who is both curious and not humble is either not quiet or not strong and vice versa.
If lucy is not calm or not wise then someone is not brave or funny.
Everyone who is either generous or not generous is curious or not generous.
Everyone who is funny or curious is calm.
If someone is not brave or not patient then someone is either not curious or creative and vice versa.
If alice is either happy or not rich then john is either old or not funny.
If susan is rich then someone is either happy or not tall.
If paul is rich then someone is both humble and happy.
Everyone who is brave or not quiet is both not curious and calm and vice versa.
Everyone who is either not funny or curious is either not funny or creative and vice versa.
Everyone who is both wise and not brave is old or not rich and vice versa.
If mary is generous or strong then alice is both calm and kind and vice versa.
Susan is generous or not creative.
Someone is both not calm and kind.
Someone is either wise or not happy.
Susan is both generous and not rich.
Fred is either brave or creative.
Paul is curious.
Lucy is either patient or brave.
Someone is rich or strong. | Susan is creative. | entailment | (![X]:((strong(X)&~creative(X))<=>rich(X)))&
(![X]:(generous(X)<=>(patient(X)|humble(X))))&
(![X]:((~strong(X)|~humble(X))<=>(creative(X)|kind(X))))&
(![X]:((creative(X)|~funny(X))<=>(~humble(X)|old(X))))&
(![X]:((curious(X)&~humble(X))<=>(~quiet(X)<~>~strong(X))))&
(((~calm(lucy)|~wise(lucy)))=>(?[X]:((~brave(X)|funny(X)))))&
(![X]:((generous(X)<~>~generous(X))=>(curious(X)|~generous(X))))&
(![X]:((funny(X)|curious(X))=>calm(X)))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((~curious(X)<~>creative(X)))))&
(((happy(alice)<~>~rich(alice)))=>((old(john)<~>~funny(john))))&
((rich(susan))=>(?[X]:((happy(X)<~>~tall(X)))))&
((rich(paul))=>(?[X]:((humble(X)&happy(X)))))&
(![X]:((brave(X)|~quiet(X))<=>(~curious(X)&calm(X))))&
(![X]:((~funny(X)<~>curious(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((wise(X)&~brave(X))<=>(old(X)|~rich(X))))&
(((generous(mary)|strong(mary)))<=>((calm(alice)&kind(alice))))&
((generous(susan)|~creative(susan)))&
(?[X]:((~calm(X)&kind(X))))&
(?[X]:((wise(X)<~>~happy(X))))&
((generous(susan)&~rich(susan)))&
((brave(fred)<~>creative(fred)))&
(curious(paul))&
((patient(lucy)<~>brave(lucy)))&
(?[X]:((rich(X)|strong(X)))) | creative(susan) | [
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1026101951364456597314556
% SZS output start Proof for 1026101951364456597314556
7. ! [X0] : ((generous(X0) <~> ~generous(X0)) => (~generous(X0) | curious(X0))) [input p6]
14. ! [X0] : ((~funny(X0) <~> curious(X0)) <=> (~funny(X0) <~> creative(X0))) [input p13]
20. ~rich(susan) & generous(susan) [input p19]
25. ~creative(susan) [input hypothesis]
28. ! [X0] : ((~generous(X0) | curious(X0)) | (generous(X0) <=> ~generous(X0))) [ennf transformation 7]
29. ! [X0] : (~generous(X0) | curious(X0) | (generous(X0) <=> ~generous(X0))) [flattening 28]
46. ! [X0] : (~generous(X0) | curious(X0) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) [nnf transformation 29]
60. ! [X0] : ((((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0)))) & (((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0))))) [nnf transformation 14]
96. ~generous(X0) | curious(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 46]
120. creative(X0) | ~funny(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 60]
125. ~curious(X0) | funny(X0) | creative(X0) | funny(X0) [cnf transformation 60]
142. generous(susan) [cnf transformation 20]
150. ~creative(susan) [cnf transformation 25]
151. creative(X0) | ~funny(X0) | ~curious(X0) [duplicate literal removal 120]
154. ~curious(X0) | funny(X0) | creative(X0) [duplicate literal removal 125]
155. ~generous(X0) | curious(X0) [duplicate literal removal 96]
258. ~curious(X0) | creative(X0) [subsumption resolution 151,154]
281. 27 <=> generous(susan) [avatar definition]
283. generous(susan) <- (27) [avatar component clause 281]
285. 28 <=> creative(susan) [avatar definition]
287. ~creative(susan) <- (~28) [avatar component clause 285]
300. 27 [avatar split clause 142,281]
322. ~28 [avatar split clause 150,285]
337. curious(susan) <- (27) [resolution 155,283]
342. creative(susan) <- (27) [resolution 258,337]
343. $false <- (27, ~28) [subsumption resolution 342,287]
344. ~27 | 28 [avatar contradiction clause 343]
345. $false [avatar sat refutation 300,322,344]
% SZS output end Proof for 1026101951364456597314556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or strong is not happy or calm.
If fred is brave then lucy is both not old and wise.
If lucy is not kind or rich then someone is both old and not creative and vice versa.
Everyone who is either not generous or not curious is either tall or calm and vice versa.
Everyone who is not calm or not rich is tall or humble and vice versa.
Everyone who is both not curious and tall is not kind.
Everyone who is either not creative or old is creative or funny.
Everyone who is both not curious and funny is either curious or not patient and vice versa.
Everyone who is both not patient and not brave is strong or not creative and vice versa.
If someone is tall or not calm then someone is both not happy and happy and vice versa.
Everyone who is either funny or not brave is funny and vice versa.
Everyone who is not wise or not curious is not rich.
Everyone who is either strong or wise is not humble or not happy.
Everyone who is not generous is either not brave or not humble and vice versa.
If someone is kind or not funny then alice is not rich.
Susan is not curious.
Alice is not strong or not calm.
Someone is kind or patient.
Someone is not tall or not rich.
John is either funny or not strong.
Paul is either brave or not happy.
Paul is both patient and not strong.
John is old or not kind. | Paul is curious. | contradiction | (![X]:((~wise(X)<~>strong(X))=>(~happy(X)|calm(X))))&
((brave(fred))=>((~old(lucy)&wise(lucy))))&
(((~kind(lucy)|rich(lucy)))<=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((~generous(X)<~>~curious(X))<=>(tall(X)<~>calm(X))))&
(![X]:((~calm(X)|~rich(X))<=>(tall(X)|humble(X))))&
(![X]:((~curious(X)&tall(X))=>~kind(X)))&
(![X]:((~creative(X)<~>old(X))=>(creative(X)|funny(X))))&
(![X]:((~curious(X)&funny(X))<=>(curious(X)<~>~patient(X))))&
(![X]:((~patient(X)&~brave(X))<=>(strong(X)|~creative(X))))&
((?[X]:((tall(X)|~calm(X))))<=>(?[X]:((~happy(X)&happy(X)))))&
(![X]:((funny(X)<~>~brave(X))<=>funny(X)))&
(![X]:((~wise(X)|~curious(X))=>~rich(X)))&
(![X]:((strong(X)<~>wise(X))=>(~humble(X)|~happy(X))))&
(![X]:(~generous(X)<=>(~brave(X)<~>~humble(X))))&
((?[X]:((kind(X)|~funny(X))))=>(~rich(alice)))&
(~curious(susan))&
((~strong(alice)|~calm(alice)))&
(?[X]:((kind(X)|patient(X))))&
(?[X]:((~tall(X)|~rich(X))))&
((funny(john)<~>~strong(john)))&
((brave(paul)<~>~happy(paul)))&
((patient(paul)&~strong(paul)))&
((old(john)|~kind(john))) | curious(paul) | [
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2389493843747643643460911
% SZS output start Proof for 2389493843747643643460911
8. ! [X0] : ((funny(X0) & ~curious(X0)) <=> (curious(X0) <~> ~patient(X0))) [input p7]
22. ~strong(paul) & patient(paul) [input p21]
24. curious(paul) [input hypothesis]
47. ! [X0] : (((funny(X0) & ~curious(X0)) | ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0)))) & (((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | (~funny(X0) | curious(X0)))) [nnf transformation 8]
48. ! [X0] : (((funny(X0) & ~curious(X0)) | ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0)))) & (((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | ~funny(X0) | curious(X0))) [flattening 47]
91. ~curious(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 48]
127. patient(paul) [cnf transformation 22]
130. curious(paul) [cnf transformation 24]
134. ~patient(X0) | ~curious(X0) [duplicate literal removal 91]
261. ~curious(paul) [resolution 134,127]
262. $false [subsumption resolution 261,130]
% SZS output end Proof for 2389493843747643643460911
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not rich or tall then someone is both funny and creative and vice versa. Everyone who is both not funny and not wise is either not funny or creative and vice versa. If paul is either not calm or tall then fred is both creative and quiet. If lucy is either humble or not curious then susan is either not brave or rich and vice versa. Everyone who is both not patient and old is both tall and humble. Everyone who is strong is not quiet. Everyone who is either creative or not kind is both calm and not happy and vice versa. Everyone who is brave is not humble. Everyone who is either not old or not patient is both not calm and not quiet and vice versa. If susan is both happy and not brave then someone is either not funny or not wise and vice versa. Everyone who is quiet is rich and vice versa. If fred is happy or not happy then susan is not patient or not rich and vice versa. If someone is either patient or not tall then alice is curious or not old. Everyone who is either old or not old is old or not old and vice versa. Everyone who is humble is both not humble and not happy and vice versa. Someone is both not calm and not strong. Susan is not curious or not creative. John is not rich. Fred is not humble or not tall. Paul is not tall. Alice is either not creative or not tall. Lucy is both not calm and strong. Mary is kind. | John is not happy. | contradiction | (((~rich(alice)<~>tall(alice)))<=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((~funny(X)&~wise(X))<=>(~funny(X)<~>creative(X))))&
(((~calm(paul)<~>tall(paul)))=>((creative(fred)&quiet(fred))))&
(((humble(lucy)<~>~curious(lucy)))<=>((~brave(susan)<~>rich(susan))))&
(![X]:((~patient(X)&old(X))=>(tall(X)&humble(X))))&
(![X]:(strong(X)=>~quiet(X)))&
(![X]:((creative(X)<~>~kind(X))<=>(calm(X)&~happy(X))))&
(![X]:(brave(X)=>~humble(X)))&
(![X]:((~old(X)<~>~patient(X))<=>(~calm(X)&~quiet(X))))&
(((happy(susan)&~brave(susan)))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:(quiet(X)<=>rich(X)))&
(((happy(fred)|~happy(fred)))<=>((~patient(susan)|~rich(susan))))&
((?[X]:((patient(X)<~>~tall(X))))=>((curious(alice)|~old(alice))))&
(![X]:((old(X)<~>~old(X))<=>(old(X)|~old(X))))&
(![X]:(humble(X)<=>(~humble(X)&~happy(X))))&
(?[X]:((~calm(X)&~strong(X))))&
((~curious(susan)|~creative(susan)))&
(~rich(john))&
((~humble(fred)|~tall(fred)))&
(~tall(paul))&
((~creative(alice)<~>~tall(alice)))&
((~calm(lucy)&strong(lucy)))&
(kind(mary)) | ~happy(john) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 320595427185705900281000
% SZS output start Proof for 320595427185705900281000
15. ! [X0] : (humble(X0) <=> (~happy(X0) & ~humble(X0))) [input p14]
24. ~happy(john) [input hypothesis]
55. ! [X0] : ((humble(X0) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | ~humble(X0))) [nnf transformation 15]
56. ! [X0] : ((humble(X0) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ~humble(X0))) [flattening 55]
120. ~humble(X0) | ~humble(X0) [cnf transformation 56]
122. humble(X0) | happy(X0) | humble(X0) [cnf transformation 56]
134. ~happy(john) [cnf transformation 24]
135. ~humble(X0) [duplicate literal removal 120]
136. happy(X0) | humble(X0) [duplicate literal removal 122]
282. humble(john) [resolution 136,134]
285. $false [subsumption resolution 282,135]
% SZS output end Proof for 320595427185705900281000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall or rich then someone is both not humble and wise and vice versa. Everyone who is both quiet and not patient is both wise and brave and vice versa. Everyone who is either not kind or not funny is either not strong or not creative. If paul is both old and not calm then susan is humble. Everyone who is either funny or not brave is not curious and vice versa. If someone is both not generous and not wise then someone is either not humble or humble and vice versa. If someone is strong or not quiet then someone is both old and quiet. If someone is not quiet or calm then paul is brave. Everyone who is both curious and funny is either patient or generous and vice versa. If paul is tall then someone is both not brave and not generous. If someone is both not creative and wise then susan is either funny or rich and vice versa. If someone is both curious and not generous then lucy is kind or patient. Everyone who is both humble and not kind is both calm and old. If someone is creative then john is calm and vice versa. Everyone who is calm is either not tall or curious and vice versa. If mary is either not generous or not wise then susan is old. Someone is both not calm and not happy. Fred is not tall or rich. Alice is not creative. Paul is both not generous and patient. Someone is both not old and not wise. Someone is strong or old. Someone is quiet or wise. | Alice is not quiet. | contradiction | (((~tall(fred)|rich(fred)))<=>(?[X]:((~humble(X)&wise(X)))))&
(![X]:((quiet(X)&~patient(X))<=>(wise(X)&brave(X))))&
(![X]:((~kind(X)<~>~funny(X))=>(~strong(X)<~>~creative(X))))&
(((old(paul)&~calm(paul)))=>(humble(susan)))&
(![X]:((funny(X)<~>~brave(X))<=>~curious(X)))&
((?[X]:((~generous(X)&~wise(X))))<=>(?[X]:((~humble(X)<~>humble(X)))))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((old(X)&quiet(X)))))&
((?[X]:((~quiet(X)|calm(X))))=>(brave(paul)))&
(![X]:((curious(X)&funny(X))<=>(patient(X)<~>generous(X))))&
((tall(paul))=>(?[X]:((~brave(X)&~generous(X)))))&
((?[X]:((~creative(X)&wise(X))))<=>((funny(susan)<~>rich(susan))))&
((?[X]:((curious(X)&~generous(X))))=>((kind(lucy)|patient(lucy))))&
(![X]:((humble(X)&~kind(X))=>(calm(X)&old(X))))&
((?[X]:(creative(X)))<=>(calm(john)))&
(![X]:(calm(X)<=>(~tall(X)<~>curious(X))))&
(((~generous(mary)<~>~wise(mary)))=>(old(susan)))&
(?[X]:((~calm(X)&~happy(X))))&
((~tall(fred)|rich(fred)))&
(~creative(alice))&
((~generous(paul)&patient(paul)))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:((strong(X)|old(X))))&
(?[X]:((quiet(X)|wise(X)))) | ~quiet(alice) | [
"p4",
"p7",
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7873646584045663324832761
% SZS output start Proof for 7873646584045663324832761
5. ! [X0] : ((funny(X0) <~> ~brave(X0)) <=> ~curious(X0)) [input p4]
8. ? [X0] : (calm(X0) | ~quiet(X0)) => brave(paul) [input p7]
9. ! [X0] : ((funny(X0) & curious(X0)) <=> (patient(X0) <~> generous(X0))) [input p8]
20. patient(paul) & ~generous(paul) [input p19]
24. ~quiet(alice) [input hypothesis]
32. brave(paul) | ! [X0] : (~calm(X0) & quiet(X0)) [ennf transformation 8]
47. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | curious(X0)) & (~curious(X0) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [nnf transformation 5]
56. ! [X0] : (((funny(X0) & curious(X0)) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0)))) & (((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | (~funny(X0) | ~curious(X0)))) [nnf transformation 9]
57. ! [X0] : (((funny(X0) & curious(X0)) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0)))) & (((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | ~funny(X0) | ~curious(X0))) [flattening 56]
92. ~curious(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 47]
106. brave(paul) | quiet(X0) [cnf transformation 32]
110. ~patient(X0) | generous(X0) | curious(X0) [cnf transformation 57]
112. ~patient(X0) | generous(X0) | funny(X0) [cnf transformation 57]
136. ~generous(paul) [cnf transformation 20]
137. patient(paul) [cnf transformation 20]
142. ~quiet(alice) [cnf transformation 24]
203. 13 <=> ! [X1] : quiet(X1) [avatar definition]
204. quiet(X1) <- (13) [avatar component clause 203]
224. 18 <=> brave(paul) [avatar definition]
226. brave(paul) <- (18) [avatar component clause 224]
228. 13 | 18 [avatar split clause 106,224,203]
326. $false <- (13) [resolution 204,142]
327. ~13 [avatar contradiction clause 326]
378. 47 <=> curious(paul) [avatar definition]
380. curious(paul) <- (47) [avatar component clause 378]
382. 48 <=> funny(paul) [avatar definition]
383. ~funny(paul) <- (~48) [avatar component clause 382]
396. ~brave(paul) | ~funny(paul) <- (47) [resolution 380,92]
398. ~funny(paul) <- (18, 47) [subsumption resolution 396,226]
399. ~48 | ~18 | ~47 [avatar split clause 398,378,224,382]
402. generous(paul) | curious(paul) [resolution 110,137]
404. curious(paul) [subsumption resolution 402,136]
417. 47 [avatar split clause 404,378]
420. generous(paul) | funny(paul) [resolution 112,137]
422. funny(paul) [subsumption resolution 420,136]
423. $false <- (~48) [subsumption resolution 422,383]
424. 48 [avatar contradiction clause 423]
430. $false [avatar sat refutation 228,327,399,417,424]
% SZS output end Proof for 7873646584045663324832761
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not funny or brave then someone is either tall or not humble and vice versa.
Everyone who is both not kind and calm is either tall or quiet and vice versa.
Everyone who is not kind is creative.
Everyone who is generous is either not tall or strong and vice versa.
If someone is both strong and not calm then someone is not tall or wise.
If someone is both not happy and brave then someone is either not happy or not wise and vice versa.
Everyone who is both tall and brave is both curious and generous.
If someone is not calm or rich then someone is either not quiet or generous.
Everyone who is both not patient and old is not happy and vice versa.
Everyone who is not generous or not humble is either not tall or not humble and vice versa.
Everyone who is either not creative or not strong is not calm or patient and vice versa.
Everyone who is both not wise and generous is either not strong or not funny.
If someone is not kind or not brave then susan is not creative or not funny and vice versa.
If mary is not quiet or not strong then someone is not creative or humble and vice versa.
Everyone who is old or not kind is both kind and strong and vice versa.
Everyone who is both not old and brave is happy or not happy.
John is not wise or rich.
Mary is not humble.
Paul is not quiet or tall.
Someone is either not generous or not quiet.
Alice is not curious or not creative.
Someone is either not quiet or not wise.
Someone is both quiet and not rich. | Alice is not happy. | neutral | (((~funny(mary)|brave(mary)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:((~kind(X)&calm(X))<=>(tall(X)<~>quiet(X))))&
(![X]:(~kind(X)=>creative(X)))&
(![X]:(generous(X)<=>(~tall(X)<~>strong(X))))&
((?[X]:((strong(X)&~calm(X))))=>(?[X]:((~tall(X)|wise(X)))))&
((?[X]:((~happy(X)&brave(X))))<=>(?[X]:((~happy(X)<~>~wise(X)))))&
(![X]:((tall(X)&brave(X))=>(curious(X)&generous(X))))&
((?[X]:((~calm(X)|rich(X))))=>(?[X]:((~quiet(X)<~>generous(X)))))&
(![X]:((~patient(X)&old(X))<=>~happy(X)))&
(![X]:((~generous(X)|~humble(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((~creative(X)<~>~strong(X))<=>(~calm(X)|patient(X))))&
(![X]:((~wise(X)&generous(X))=>(~strong(X)<~>~funny(X))))&
((?[X]:((~kind(X)|~brave(X))))<=>((~creative(susan)|~funny(susan))))&
(((~quiet(mary)|~strong(mary)))<=>(?[X]:((~creative(X)|humble(X)))))&
(![X]:((old(X)|~kind(X))<=>(kind(X)&strong(X))))&
(![X]:((~old(X)&brave(X))=>(happy(X)|~happy(X))))&
((~wise(john)|rich(john)))&
(~humble(mary))&
((~quiet(paul)|tall(paul)))&
(?[X]:((~generous(X)<~>~quiet(X))))&
((~curious(alice)|~creative(alice)))&
(?[X]:((~quiet(X)<~>~wise(X))))&
(?[X]:((quiet(X)&~rich(X)))) | ~happy(alice) | [] | null | 0 |
Everyone who is either not strong or happy is either not strong or tall and vice versa.
Everyone who is both creative and not funny is calm and vice versa.
If paul is old or not funny then lucy is not funny or not tall.
If paul is either not patient or strong then fred is patient.
If fred is both brave and not quiet then someone is humble.
If paul is not quiet then someone is strong or rich and vice versa.
If someone is both not quiet and not generous then lucy is either not kind or quiet and vice versa.
If someone is generous then susan is calm.
Everyone who is not kind or not generous is both not old and not quiet.
Everyone who is either creative or tall is both happy and humble.
Everyone who is not patient or brave is either not calm or not happy and vice versa.
Everyone who is either generous or not funny is both not strong and quiet and vice versa.
Everyone who is old or strong is not patient or strong.
Everyone who is both kind and old is both humble and not rich.
Everyone who is either not generous or not tall is either tall or calm and vice versa.
Everyone who is humble is both not quiet and creative and vice versa.
Mary is not curious or tall.
John is not happy.
Lucy is not strong or not old.
Alice is quiet.
Someone is both kind and not funny.
Lucy is both quiet and not old.
Susan is not happy or not quiet. | John is creative. | contradiction | (![X]:((~strong(X)<~>happy(X))<=>(~strong(X)<~>tall(X))))&
(![X]:((creative(X)&~funny(X))<=>calm(X)))&
(((old(paul)|~funny(paul)))=>((~funny(lucy)|~tall(lucy))))&
(((~patient(paul)<~>strong(paul)))=>(patient(fred)))&
(((brave(fred)&~quiet(fred)))=>(?[X]:(humble(X))))&
((~quiet(paul))<=>(?[X]:((strong(X)|rich(X)))))&
((?[X]:((~quiet(X)&~generous(X))))<=>((~kind(lucy)<~>quiet(lucy))))&
((?[X]:(generous(X)))=>(calm(susan)))&
(![X]:((~kind(X)|~generous(X))=>(~old(X)&~quiet(X))))&
(![X]:((creative(X)<~>tall(X))=>(happy(X)&humble(X))))&
(![X]:((~patient(X)|brave(X))<=>(~calm(X)<~>~happy(X))))&
(![X]:((generous(X)<~>~funny(X))<=>(~strong(X)&quiet(X))))&
(![X]:((old(X)|strong(X))=>(~patient(X)|strong(X))))&
(![X]:((kind(X)&old(X))=>(humble(X)&~rich(X))))&
(![X]:((~generous(X)<~>~tall(X))<=>(tall(X)<~>calm(X))))&
(![X]:(humble(X)<=>(~quiet(X)&creative(X))))&
((~curious(mary)|tall(mary)))&
(~happy(john))&
((~strong(lucy)|~old(lucy)))&
(quiet(alice))&
(?[X]:((kind(X)&~funny(X))))&
((quiet(lucy)&~old(lucy)))&
((~happy(susan)|~quiet(susan))) | creative(john) | [
"p0",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8170054510848225476284265
% SZS output start Proof for 8170054510848225476284265
1. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> (~strong(X0) <~> tall(X0))) [input p0]
10. ! [X0] : ((creative(X0) <~> tall(X0)) => (humble(X0) & happy(X0))) [input p9]
18. ~happy(john) [input p17]
24. creative(john) [input hypothesis]
40. ! [X0] : ((humble(X0) & happy(X0)) | (creative(X0) <=> tall(X0))) [ennf transformation 10]
44. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) & (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 1]
58. ! [X0] : ((humble(X0) & happy(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) [nnf transformation 40]
67. tall(X0) | ~strong(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 44]
68. ~tall(X0) | strong(X0) | happy(X0) | strong(X0) [cnf transformation 44]
71. happy(X0) | ~strong(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 44]
72. ~happy(X0) | strong(X0) | tall(X0) | strong(X0) [cnf transformation 44]
93. happy(X0) | tall(X0) | ~creative(X0) [cnf transformation 58]
120. ~happy(john) [cnf transformation 18]
126. creative(john) [cnf transformation 24]
131. tall(X0) | ~strong(X0) | ~happy(X0) [duplicate literal removal 67]
132. ~tall(X0) | strong(X0) | happy(X0) [duplicate literal removal 68]
133. happy(X0) | ~strong(X0) | ~tall(X0) [duplicate literal removal 71]
134. ~happy(X0) | strong(X0) | tall(X0) [duplicate literal removal 72]
135. ~tall(X0) | happy(X0) [subsumption resolution 132,133]
136. ~happy(X0) | tall(X0) [subsumption resolution 131,134]
231. ~creative(X0) | tall(X0) [subsumption resolution 93,136]
262. tall(john) [resolution 231,126]
266. happy(john) [resolution 262,135]
267. $false [subsumption resolution 266,120]
% SZS output end Proof for 8170054510848225476284265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not tall is generous. If fred is either not generous or quiet then lucy is not strong. Everyone who is either not creative or humble is either quiet or not patient and vice versa. If someone is either strong or not curious then john is not strong and vice versa. If someone is not kind or not patient then lucy is both not rich and tall. If someone is either not tall or not creative then someone is not curious. Everyone who is both kind and not calm is not funny or brave and vice versa. Everyone who is not happy is not rich. If susan is not wise then paul is brave and vice versa. Everyone who is both wise and brave is either not funny or happy. Everyone who is happy is both creative and not tall and vice versa. Everyone who is both not creative and wise is either brave or calm and vice versa. If mary is both not old and not wise then someone is tall and vice versa. Everyone who is patient is either not creative or old and vice versa. Everyone who is not strong or not quiet is rich or patient and vice versa. Everyone who is humble or quiet is both generous and old. Someone is not brave. Someone is either not creative or not tall. Someone is not humble or kind. Lucy is not funny. Paul is not rich or not generous. Someone is humble. Susan is not humble. Someone is generous or curious. | Lucy is kind. | entailment | (![X]:((strong(X)&~tall(X))=>generous(X)))&
(((~generous(fred)<~>quiet(fred)))=>(~strong(lucy)))&
(![X]:((~creative(X)<~>humble(X))<=>(quiet(X)<~>~patient(X))))&
((?[X]:((strong(X)<~>~curious(X))))<=>(~strong(john)))&
((?[X]:((~kind(X)|~patient(X))))=>((~rich(lucy)&tall(lucy))))&
((?[X]:((~tall(X)<~>~creative(X))))=>(?[X]:(~curious(X))))&
(![X]:((kind(X)&~calm(X))<=>(~funny(X)|brave(X))))&
(![X]:(~happy(X)=>~rich(X)))&
((~wise(susan))<=>(brave(paul)))&
(![X]:((wise(X)&brave(X))=>(~funny(X)<~>happy(X))))&
(![X]:(happy(X)<=>(creative(X)&~tall(X))))&
(![X]:((~creative(X)&wise(X))<=>(brave(X)<~>calm(X))))&
(((~old(mary)&~wise(mary)))<=>(?[X]:(tall(X))))&
(![X]:(patient(X)<=>(~creative(X)<~>old(X))))&
(![X]:((~strong(X)|~quiet(X))<=>(rich(X)|patient(X))))&
(![X]:((humble(X)|quiet(X))=>(generous(X)&old(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~creative(X)<~>~tall(X))))&
(?[X]:((~humble(X)|kind(X))))&
(~funny(lucy))&
((~rich(paul)|~generous(paul)))&
(?[X]:(humble(X)))&
(~humble(susan))&
(?[X]:((generous(X)|curious(X)))) | kind(lucy) | [
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 306736462754671161153137
% SZS output start Proof for 306736462754671161153137
7. ! [X0] : ((~calm(X0) & kind(X0)) <=> (brave(X0) | ~funny(X0))) [input p6]
20. ~funny(lucy) [input p19]
25. ~kind(lucy) [input hypothesis]
46. ! [X0] : (((~calm(X0) & kind(X0)) | (~brave(X0) & funny(X0))) & ((brave(X0) | ~funny(X0)) | (calm(X0) | ~kind(X0)))) [nnf transformation 7]
47. ! [X0] : (((~calm(X0) & kind(X0)) | (~brave(X0) & funny(X0))) & (brave(X0) | ~funny(X0) | calm(X0) | ~kind(X0))) [flattening 46]
95. funny(X0) | kind(X0) [cnf transformation 47]
132. ~funny(lucy) [cnf transformation 20]
137. ~kind(lucy) [cnf transformation 25]
277. kind(lucy) [resolution 95,132]
278. $false [subsumption resolution 277,137]
% SZS output end Proof for 306736462754671161153137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is either tall or not rich.
Everyone who is humble or not creative is both strong and not old and vice versa.
Everyone who is either old or not old is both curious and not tall.
Everyone who is either not quiet or not generous is either calm or humble and vice versa.
If someone is both not humble and not funny then paul is either kind or curious.
If someone is both happy and brave then john is not funny.
If someone is funny then someone is both not patient and not quiet.
Everyone who is both funny and not old is both rich and not happy and vice versa.
If someone is not rich then john is both humble and not creative.
If someone is either patient or tall then lucy is not rich and vice versa.
Everyone who is not rich or not old is generous and vice versa.
If alice is both curious and not rich then paul is not patient or creative.
Everyone who is both generous and humble is both generous and wise and vice versa.
If mary is either patient or not happy then mary is both happy and creative.
Everyone who is kind or not brave is either not quiet or not curious and vice versa.
Everyone who is both happy and not wise is both not generous and not brave and vice versa.
Mary is not happy.
Someone is both humble and happy.
Lucy is creative.
Paul is both not old and wise.
Mary is not tall.
Paul is not brave or calm.
Paul is not kind or creative.
Susan is not creative. | Lucy is not generous. | contradiction | (![X]:(creative(X)=>(tall(X)<~>~rich(X))))&
(![X]:((humble(X)|~creative(X))<=>(strong(X)&~old(X))))&
(![X]:((old(X)<~>~old(X))=>(curious(X)&~tall(X))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(calm(X)<~>humble(X))))&
((?[X]:((~humble(X)&~funny(X))))=>((kind(paul)<~>curious(paul))))&
((?[X]:((happy(X)&brave(X))))=>(~funny(john)))&
((?[X]:(funny(X)))=>(?[X]:((~patient(X)&~quiet(X)))))&
(![X]:((funny(X)&~old(X))<=>(rich(X)&~happy(X))))&
((?[X]:(~rich(X)))=>((humble(john)&~creative(john))))&
((?[X]:((patient(X)<~>tall(X))))<=>(~rich(lucy)))&
(![X]:((~rich(X)|~old(X))<=>generous(X)))&
(((curious(alice)&~rich(alice)))=>((~patient(paul)|creative(paul))))&
(![X]:((generous(X)&humble(X))<=>(generous(X)&wise(X))))&
(((patient(mary)<~>~happy(mary)))=>((happy(mary)&creative(mary))))&
(![X]:((kind(X)|~brave(X))<=>(~quiet(X)<~>~curious(X))))&
(![X]:((happy(X)&~wise(X))<=>(~generous(X)&~brave(X))))&
(~happy(mary))&
(?[X]:((humble(X)&happy(X))))&
(creative(lucy))&
((~old(paul)&wise(paul)))&
(~tall(mary))&
((~brave(paul)|calm(paul)))&
((~kind(paul)|creative(paul)))&
(~creative(susan)) | ~generous(lucy) | [
"p2",
"p9",
"p10",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3521385101770173310713180
% SZS output start Proof for 3521385101770173310713180
3. ! [X0] : ((old(X0) <~> ~old(X0)) => (~tall(X0) & curious(X0))) [input p2]
10. ? [X0] : (patient(X0) <~> tall(X0)) <=> ~rich(lucy) [input p9]
11. ! [X0] : ((~old(X0) | ~rich(X0)) <=> generous(X0)) [input p10]
14. (patient(mary) <~> ~happy(mary)) => (creative(mary) & happy(mary)) [input p13]
17. ~happy(mary) [input p16]
25. ~generous(lucy) [input hypothesis]
28. ! [X0] : ((~tall(X0) & curious(X0)) | (old(X0) <=> ~old(X0))) [ennf transformation 3]
35. (creative(mary) & happy(mary)) | (patient(mary) <=> ~happy(mary)) [ennf transformation 14]
39. ! [X0] : ((~tall(X0) & curious(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 28]
47. (? [X0] : ((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | rich(lucy)) & (~rich(lucy) | ! [X0] : ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) [nnf transformation 10]
48. (? [X0] : ((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | rich(lucy)) & (~rich(lucy) | ! [X1] : ((patient(X1) | ~tall(X1)) & (tall(X1) | ~patient(X1)))) [rectify 47]
49. ? [X0] : ((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) => ((~tall(sK1) | ~patient(sK1)) & (tall(sK1) | patient(sK1))) [choice axiom]
50. (((~tall(sK1) | ~patient(sK1)) & (tall(sK1) | patient(sK1))) | rich(lucy)) & (~rich(lucy) | ! [X1] : ((patient(X1) | ~tall(X1)) & (tall(X1) | ~patient(X1)))) [skolemisation 48,49]
51. ! [X0] : (((~old(X0) | ~rich(X0)) | ~generous(X0)) & (generous(X0) | (old(X0) & rich(X0)))) [nnf transformation 11]
52. ! [X0] : ((~old(X0) | ~rich(X0) | ~generous(X0)) & (generous(X0) | (old(X0) & rich(X0)))) [flattening 51]
55. (creative(mary) & happy(mary)) | ((patient(mary) | happy(mary)) & (~happy(mary) | ~patient(mary))) [nnf transformation 35]
71. ~tall(X0) | ~old(X0) | ~old(X0) [cnf transformation 39]
72. ~tall(X0) | old(X0) | old(X0) [cnf transformation 39]
92. ~rich(lucy) | tall(X1) | ~patient(X1) [cnf transformation 50]
96. generous(X0) | rich(X0) [cnf transformation 52]
105. happy(mary) | patient(mary) | happy(mary) [cnf transformation 55]
118. ~happy(mary) [cnf transformation 17]
128. ~generous(lucy) [cnf transformation 25]
129. happy(mary) | patient(mary) [duplicate literal removal 105]
132. ~tall(X0) | ~old(X0) [duplicate literal removal 71]
133. ~tall(X0) | old(X0) [duplicate literal removal 72]
134. ~tall(X0) [subsumption resolution 132,133]
181. 11 <=> rich(lucy) [avatar definition]
189. ~rich(lucy) | ~patient(X1) [subsumption resolution 92,134]
191. 13 <=> ! [X1] : ~patient(X1) [avatar definition]
192. ~patient(X1) <- (13) [avatar component clause 191]
193. 13 | ~11 [avatar split clause 189,181,191]
209. 17 <=> happy(mary) [avatar definition]
213. 18 <=> patient(mary) [avatar definition]
215. patient(mary) <- (18) [avatar component clause 213]
222. 18 | 17 [avatar split clause 129,209,213]
226. ~17 [avatar split clause 118,209]
241. rich(lucy) [resolution 96,128]
244. 11 [avatar split clause 241,181]
246. $false <- (13, 18) [resolution 192,215]
247. ~13 | ~18 [avatar contradiction clause 246]
249. $false [avatar sat refutation 193,222,226,244,247]
% SZS output end Proof for 3521385101770173310713180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is both not calm and not curious and vice versa.
If someone is tall then someone is not happy.
If someone is not humble then paul is both brave and not tall.
If someone is not humble then someone is both patient and not curious and vice versa.
Everyone who is not generous or kind is not brave and vice versa.
Everyone who is kind or wise is old and vice versa.
Everyone who is not curious or not rich is not brave or wise.
Everyone who is both not brave and not old is not brave and vice versa.
Everyone who is happy is either not brave or not kind and vice versa.
Everyone who is both not old and not generous is not generous and vice versa.
If mary is both generous and strong then paul is both not quiet and creative.
Everyone who is both not wise and humble is funny.
Everyone who is not creative or not tall is kind.
Everyone who is either tall or not curious is either not tall or not brave.
Everyone who is kind or not curious is both not tall and calm.
Everyone who is happy is either tall or kind.
Someone is calm.
Someone is not generous.
John is not old.
Fred is either not happy or not quiet.
Mary is not rich. | Fred is curious. | entailment | (![X]:(~calm(X)<=>(~calm(X)&~curious(X))))&
((?[X]:(tall(X)))=>(?[X]:(~happy(X))))&
((?[X]:(~humble(X)))=>((brave(paul)&~tall(paul))))&
((?[X]:(~humble(X)))<=>(?[X]:((patient(X)&~curious(X)))))&
(![X]:((~generous(X)|kind(X))<=>~brave(X)))&
(![X]:((kind(X)|wise(X))<=>old(X)))&
(![X]:((~curious(X)|~rich(X))=>(~brave(X)|wise(X))))&
(![X]:((~brave(X)&~old(X))<=>~brave(X)))&
(![X]:(happy(X)<=>(~brave(X)<~>~kind(X))))&
(![X]:((~old(X)&~generous(X))<=>~generous(X)))&
(((generous(mary)&strong(mary)))=>((~quiet(paul)&creative(paul))))&
(![X]:((~wise(X)&humble(X))=>funny(X)))&
(![X]:((~creative(X)|~tall(X))=>kind(X)))&
(![X]:((tall(X)<~>~curious(X))=>(~tall(X)<~>~brave(X))))&
(![X]:((kind(X)|~curious(X))=>(~tall(X)&calm(X))))&
(![X]:(happy(X)=>(tall(X)<~>kind(X))))&
(?[X]:(calm(X)))&
(?[X]:(~generous(X)))&
(~old(john))&
((~happy(fred)<~>~quiet(fred)))&
(~rich(mary)) | curious(fred) | [
"p4",
"p5",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5795747433674582155667326
% SZS output start Proof for 5795747433674582155667326
5. ! [X0] : ((kind(X0) | ~generous(X0)) <=> ~brave(X0)) [input p4]
6. ! [X0] : ((wise(X0) | kind(X0)) <=> old(X0)) [input p5]
8. ! [X0] : ((~old(X0) & ~brave(X0)) <=> ~brave(X0)) [input p7]
13. ! [X0] : ((~tall(X0) | ~creative(X0)) => kind(X0)) [input p12]
15. ! [X0] : ((~curious(X0) | kind(X0)) => (calm(X0) & ~tall(X0))) [input p14]
22. ~curious(fred) [input hypothesis]
27. ! [X0] : (~tall(X0) => kind(X0)) [pure predicate removal 13]
33. ! [X0] : (kind(X0) | tall(X0)) [ennf transformation 27]
35. ! [X0] : ((calm(X0) & ~tall(X0)) | (curious(X0) & ~kind(X0))) [ennf transformation 15]
47. ! [X0] : (((kind(X0) | ~generous(X0)) | brave(X0)) & (~brave(X0) | (~kind(X0) & generous(X0)))) [nnf transformation 5]
48. ! [X0] : ((kind(X0) | ~generous(X0) | brave(X0)) & (~brave(X0) | (~kind(X0) & generous(X0)))) [flattening 47]
49. ! [X0] : (((wise(X0) | kind(X0)) | ~old(X0)) & (old(X0) | (~wise(X0) & ~kind(X0)))) [nnf transformation 6]
50. ! [X0] : ((wise(X0) | kind(X0) | ~old(X0)) & (old(X0) | (~wise(X0) & ~kind(X0)))) [flattening 49]
51. ! [X0] : (((~old(X0) & ~brave(X0)) | brave(X0)) & (~brave(X0) | (old(X0) | brave(X0)))) [nnf transformation 8]
52. ! [X0] : (((~old(X0) & ~brave(X0)) | brave(X0)) & (~brave(X0) | old(X0) | brave(X0))) [flattening 51]
73. ~kind(X0) | ~brave(X0) [cnf transformation 48]
75. ~kind(X0) | old(X0) [cnf transformation 50]
82. ~old(X0) | brave(X0) [cnf transformation 52]
90. kind(X0) | tall(X0) [cnf transformation 33]
96. ~tall(X0) | curious(X0) [cnf transformation 35]
107. ~curious(fred) [cnf transformation 22]
164. old(X0) | tall(X0) [resolution 90,75]
165. tall(X1) | ~brave(X1) [resolution 90,73]
170. tall(X1) | brave(X1) [resolution 164,82]
171. tall(X1) [subsumption resolution 170,165]
174. curious(X0) [resolution 171,96]
186. $false [resolution 174,107]
% SZS output end Proof for 5795747433674582155667326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not calm is rich.
If someone is both not quiet and not strong then someone is creative or generous and vice versa.
Everyone who is either not brave or happy is curious or not old.
If lucy is not funny or not humble then someone is both not kind and creative.
Everyone who is creative or not tall is quiet or not kind and vice versa.
Everyone who is both not strong and creative is both not calm and not humble and vice versa.
Everyone who is not tall or not happy is not creative or calm.
Everyone who is old or not quiet is calm.
Everyone who is not generous is either not strong or not rich.
If alice is both not happy and not brave then alice is not happy.
If alice is both not humble and curious then someone is either not quiet or funny and vice versa.
If alice is both creative and not funny then lucy is creative.
Everyone who is not humble or not strong is not happy.
If someone is both brave and not calm then someone is generous and vice versa.
Everyone who is both not kind and not generous is not brave and vice versa.
Everyone who is quiet is not strong or brave and vice versa.
Someone is calm.
Someone is not happy or not curious.
Fred is both not brave and not strong.
Someone is not curious.
Someone is either happy or not curious.
Someone is funny or not strong.
Alice is both kind and not happy. | Fred is not tall. | entailment | (![X]:((brave(X)|~calm(X))=>rich(X)))&
((?[X]:((~quiet(X)&~strong(X))))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~brave(X)<~>happy(X))=>(curious(X)|~old(X))))&
(((~funny(lucy)|~humble(lucy)))=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((creative(X)|~tall(X))<=>(quiet(X)|~kind(X))))&
(![X]:((~strong(X)&creative(X))<=>(~calm(X)&~humble(X))))&
(![X]:((~tall(X)|~happy(X))=>(~creative(X)|calm(X))))&
(![X]:((old(X)|~quiet(X))=>calm(X)))&
(![X]:(~generous(X)=>(~strong(X)<~>~rich(X))))&
(((~happy(alice)&~brave(alice)))=>(~happy(alice)))&
(((~humble(alice)&curious(alice)))<=>(?[X]:((~quiet(X)<~>funny(X)))))&
(((creative(alice)&~funny(alice)))=>(creative(lucy)))&
(![X]:((~humble(X)|~strong(X))=>~happy(X)))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:(generous(X))))&
(![X]:((~kind(X)&~generous(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(~strong(X)|brave(X))))&
(?[X]:(calm(X)))&
(?[X]:((~happy(X)|~curious(X))))&
((~brave(fred)&~strong(fred)))&
(?[X]:(~curious(X)))&
(?[X]:((happy(X)<~>~curious(X))))&
(?[X]:((funny(X)|~strong(X))))&
((kind(alice)&~happy(alice))) | ~tall(fred) | [
"p1",
"p4",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1936108892301456079165432
% SZS output start Proof for 1936108892301456079165432
2. ? [X0] : (~strong(X0) & ~quiet(X0)) <=> ? [X0] : (generous(X0) | creative(X0)) [input p1]
5. ! [X0] : ((~tall(X0) | creative(X0)) <=> (~kind(X0) | quiet(X0))) [input p4]
16. ! [X0] : (quiet(X0) <=> (brave(X0) | ~strong(X0))) [input p15]
19. ~strong(fred) & ~brave(fred) [input p18]
24. tall(fred) [input hypothesis]
25. ? [X0] : (~strong(X0) & ~quiet(X0)) <=> ? [X1] : (generous(X1) | creative(X1)) [rectify 2]
40. (? [X0] : (~strong(X0) & ~quiet(X0)) | ! [X1] : (~generous(X1) & ~creative(X1))) & (? [X1] : (generous(X1) | creative(X1)) | ! [X0] : (strong(X0) | quiet(X0))) [nnf transformation 25]
41. (? [X0] : (~strong(X0) & ~quiet(X0)) | ! [X1] : (~generous(X1) & ~creative(X1))) & (? [X2] : (generous(X2) | creative(X2)) | ! [X3] : (strong(X3) | quiet(X3))) [rectify 40]
42. ? [X0] : (~strong(X0) & ~quiet(X0)) => (~strong(sK0) & ~quiet(sK0)) [choice axiom]
43. ? [X2] : (generous(X2) | creative(X2)) => (generous(sK1) | creative(sK1)) [choice axiom]
44. ((~strong(sK0) & ~quiet(sK0)) | ! [X1] : (~generous(X1) & ~creative(X1))) & ((generous(sK1) | creative(sK1)) | ! [X3] : (strong(X3) | quiet(X3))) [skolemisation 41,43,42]
47. ! [X0] : (((~tall(X0) | creative(X0)) | (kind(X0) & ~quiet(X0))) & ((~kind(X0) | quiet(X0)) | (tall(X0) & ~creative(X0)))) [nnf transformation 5]
48. ! [X0] : ((~tall(X0) | creative(X0) | (kind(X0) & ~quiet(X0))) & (~kind(X0) | quiet(X0) | (tall(X0) & ~creative(X0)))) [flattening 47]
64. ! [X0] : ((quiet(X0) | (~brave(X0) & strong(X0))) & ((brave(X0) | ~strong(X0)) | ~quiet(X0))) [nnf transformation 16]
65. ! [X0] : ((quiet(X0) | (~brave(X0) & strong(X0))) & (brave(X0) | ~strong(X0) | ~quiet(X0))) [flattening 64]
80. ~quiet(sK0) | ~creative(X1) [cnf transformation 44]
82. ~strong(sK0) | ~creative(X1) [cnf transformation 44]
90. ~tall(X0) | creative(X0) | ~quiet(X0) [cnf transformation 48]
118. quiet(X0) | strong(X0) [cnf transformation 65]
123. ~strong(fred) [cnf transformation 19]
130. tall(fred) [cnf transformation 24]
135. 2 <=> strong(sK0) [avatar definition]
137. ~strong(sK0) <- (~2) [avatar component clause 135]
140. 3 <=> ! [X1] : ~creative(X1) [avatar definition]
141. ~creative(X1) <- (3) [avatar component clause 140]
142. 3 | ~2 [avatar split clause 82,135,140]
144. 4 <=> quiet(sK0) [avatar definition]
146. ~quiet(sK0) <- (~4) [avatar component clause 144]
148. 3 | ~4 [avatar split clause 80,144,140]
150. 5 <=> ! [X3] : (strong(X3) | quiet(X3)) [avatar definition]
151. strong(X3) | quiet(X3) <- (5) [avatar component clause 150]
240. 5 [avatar split clause 118,150]
276. quiet(fred) <- (5) [resolution 151,123]
277. quiet(sK0) <- (~2, 5) [resolution 151,137]
279. $false <- (~2, ~4, 5) [subsumption resolution 277,146]
280. 2 | 4 | ~5 [avatar contradiction clause 279]
290. creative(fred) | ~quiet(fred) [resolution 90,130]
291. ~quiet(fred) <- (3) [subsumption resolution 290,141]
292. $false <- (3, 5) [subsumption resolution 291,276]
293. ~3 | ~5 [avatar contradiction clause 292]
294. $false [avatar sat refutation 142,148,240,280,293]
% SZS output end Proof for 1936108892301456079165432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not creative is wise or tall.
Everyone who is both not patient and rich is humble.
Everyone who is either calm or humble is both not generous and not old and vice versa.
If someone is either not strong or not patient then someone is both not patient and not curious and vice versa.
If susan is kind or not strong then susan is not wise or generous and vice versa.
Everyone who is not curious is both calm and not kind.
If someone is not strong then paul is rich or not kind.
Everyone who is both not generous and strong is patient and vice versa.
If someone is both not creative and strong then someone is either not quiet or old.
If lucy is strong then john is either curious or rich and vice versa.
Everyone who is rich or tall is not curious or not brave.
Everyone who is not patient or not humble is brave.
If someone is old then paul is not creative or generous.
Everyone who is humble is not brave.
Everyone who is both not happy and brave is either not old or humble.
Everyone who is both not calm and quiet is not patient or not happy and vice versa.
Someone is curious or humble.
Someone is not quiet or humble.
Someone is both old and quiet.
Someone is not generous or not brave.
John is both not happy and creative.
Lucy is not rich.
Fred is not happy or calm. | John is not old. | entailment | (![X]:((quiet(X)<~>~creative(X))=>(wise(X)|tall(X))))&
(![X]:((~patient(X)&rich(X))=>humble(X)))&
(![X]:((calm(X)<~>humble(X))<=>(~generous(X)&~old(X))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>(?[X]:((~patient(X)&~curious(X)))))&
(((kind(susan)|~strong(susan)))<=>((~wise(susan)|generous(susan))))&
(![X]:(~curious(X)=>(calm(X)&~kind(X))))&
((?[X]:(~strong(X)))=>((rich(paul)|~kind(paul))))&
(![X]:((~generous(X)&strong(X))<=>patient(X)))&
((?[X]:((~creative(X)&strong(X))))=>(?[X]:((~quiet(X)<~>old(X)))))&
((strong(lucy))<=>((curious(john)<~>rich(john))))&
(![X]:((rich(X)|tall(X))=>(~curious(X)|~brave(X))))&
(![X]:((~patient(X)|~humble(X))=>brave(X)))&
((?[X]:(old(X)))=>((~creative(paul)|generous(paul))))&
(![X]:(humble(X)=>~brave(X)))&
(![X]:((~happy(X)&brave(X))=>(~old(X)<~>humble(X))))&
(![X]:((~calm(X)&quiet(X))<=>(~patient(X)|~happy(X))))&
(?[X]:((curious(X)|humble(X))))&
(?[X]:((~quiet(X)|humble(X))))&
(?[X]:((old(X)&quiet(X))))&
(?[X]:((~generous(X)|~brave(X))))&
((~happy(john)&creative(john)))&
(~rich(lucy))&
((~happy(fred)|calm(fred))) | ~old(john) | [
"p2",
"p11",
"p13",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4874256060700960707500140
% SZS output start Proof for 4874256060700960707500140
3. ! [X0] : ((calm(X0) <~> humble(X0)) <=> (~old(X0) & ~generous(X0))) [input p2]
12. ! [X0] : ((~humble(X0) | ~patient(X0)) => brave(X0)) [input p11]
14. ! [X0] : (humble(X0) => ~brave(X0)) [input p13]
15. ! [X0] : ((brave(X0) & ~happy(X0)) => (~old(X0) <~> humble(X0))) [input p14]
16. ! [X0] : ((quiet(X0) & ~calm(X0)) <=> (~happy(X0) | ~patient(X0))) [input p15]
21. creative(john) & ~happy(john) [input p20]
24. old(john) [input hypothesis]
37. ! [X0] : (brave(X0) | (humble(X0) & patient(X0))) [ennf transformation 12]
40. ! [X0] : (~brave(X0) | ~humble(X0)) [ennf transformation 14]
41. ! [X0] : ((~old(X0) <~> humble(X0)) | (~brave(X0) | happy(X0))) [ennf transformation 15]
42. ! [X0] : ((~old(X0) <~> humble(X0)) | ~brave(X0) | happy(X0)) [flattening 41]
44. ! [X0] : ((((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0))))) [nnf transformation 3]
45. ! [X0] : ((((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0))))) [flattening 44]
60. ! [X0] : (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | ~brave(X0) | happy(X0)) [nnf transformation 42]
61. ! [X0] : (((quiet(X0) & ~calm(X0)) | (happy(X0) & patient(X0))) & ((~happy(X0) | ~patient(X0)) | (~quiet(X0) | calm(X0)))) [nnf transformation 16]
62. ! [X0] : (((quiet(X0) & ~calm(X0)) | (happy(X0) & patient(X0))) & (~happy(X0) | ~patient(X0) | ~quiet(X0) | calm(X0))) [flattening 61]
77. ~old(X0) | calm(X0) | ~humble(X0) [cnf transformation 45]
105. brave(X0) | humble(X0) [cnf transformation 37]
107. ~brave(X0) | ~humble(X0) [cnf transformation 40]
108. humble(X0) | ~old(X0) | ~brave(X0) | happy(X0) [cnf transformation 60]
112. ~calm(X0) | happy(X0) [cnf transformation 62]
120. ~happy(john) [cnf transformation 21]
124. old(john) [cnf transformation 24]
230. ~brave(X0) | ~old(X0) | happy(X0) [subsumption resolution 108,107]
302. 34 <=> calm(john) [avatar definition]
303. calm(john) <- (34) [avatar component clause 302]
306. 35 <=> humble(john) [avatar definition]
307. ~humble(john) <- (~35) [avatar component clause 306]
311. calm(john) | ~humble(john) [resolution 77,124]
323. ~old(X0) | happy(X0) | humble(X0) [resolution 230,105]
391. ~35 | 34 [avatar split clause 311,302,306]
394. happy(john) <- (34) [resolution 303,112]
396. $false <- (34) [subsumption resolution 394,120]
397. ~34 [avatar contradiction clause 396]
431. happy(john) | humble(john) [resolution 323,124]
435. humble(john) [subsumption resolution 431,120]
436. $false <- (~35) [subsumption resolution 435,307]
437. 35 [avatar contradiction clause 436]
439. $false [avatar sat refutation 391,397,437]
% SZS output end Proof for 4874256060700960707500140
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not patient is either curious or not patient. Everyone who is rich is both rich and not strong. Everyone who is not strong is not curious or not brave and vice versa. Everyone who is either not funny or old is both tall and patient. Everyone who is generous is not funny and vice versa. If someone is not patient then someone is old and vice versa. Everyone who is both not brave and not kind is either creative or kind and vice versa. If someone is patient then someone is either not quiet or quiet. Everyone who is either kind or brave is both brave and curious. Everyone who is either brave or not old is either not funny or not rich. Everyone who is both humble and not funny is both not curious and brave and vice versa. Everyone who is happy or quiet is generous or not creative and vice versa. If someone is humble then lucy is either not kind or creative. Everyone who is either not happy or not funny is both kind and not generous and vice versa. Everyone who is both not tall and generous is quiet or happy and vice versa. Everyone who is either quiet or brave is both not generous and happy and vice versa. Someone is rich. Someone is not rich or not calm. Someone is not happy. Someone is not tall or curious. | Lucy is not kind. | contradiction | (![X]:((~brave(X)|~patient(X))=>(curious(X)<~>~patient(X))))&
(![X]:(rich(X)=>(rich(X)&~strong(X))))&
(![X]:(~strong(X)<=>(~curious(X)|~brave(X))))&
(![X]:((~funny(X)<~>old(X))=>(tall(X)&patient(X))))&
(![X]:(generous(X)<=>~funny(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(old(X))))&
(![X]:((~brave(X)&~kind(X))<=>(creative(X)<~>kind(X))))&
((?[X]:(patient(X)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((kind(X)<~>brave(X))=>(brave(X)&curious(X))))&
(![X]:((brave(X)<~>~old(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((humble(X)&~funny(X))<=>(~curious(X)&brave(X))))&
(![X]:((happy(X)|quiet(X))<=>(generous(X)|~creative(X))))&
((?[X]:(humble(X)))=>((~kind(lucy)<~>creative(lucy))))&
(![X]:((~happy(X)<~>~funny(X))<=>(kind(X)&~generous(X))))&
(![X]:((~tall(X)&generous(X))<=>(quiet(X)|happy(X))))&
(![X]:((quiet(X)<~>brave(X))<=>(~generous(X)&happy(X))))&
(?[X]:(rich(X)))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)|curious(X)))) | ~kind(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p8",
"p9",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7628750380518898342676618
% SZS output start Proof for 7628750380518898342676618
2. ! [X0] : (rich(X0) => (~strong(X0) & rich(X0))) [input p1]
3. ! [X0] : (~strong(X0) <=> (~brave(X0) | ~curious(X0))) [input p2]
4. ! [X0] : ((~funny(X0) <~> old(X0)) => (patient(X0) & tall(X0))) [input p3]
5. ! [X0] : (generous(X0) <=> ~funny(X0)) [input p4]
9. ! [X0] : ((kind(X0) <~> brave(X0)) => (curious(X0) & brave(X0))) [input p8]
10. ! [X0] : ((brave(X0) <~> ~old(X0)) => (~funny(X0) <~> ~rich(X0))) [input p9]
12. ! [X0] : ((quiet(X0) | happy(X0)) <=> (~creative(X0) | generous(X0))) [input p11]
14. ! [X0] : ((~happy(X0) <~> ~funny(X0)) <=> (~generous(X0) & kind(X0))) [input p13]
15. ! [X0] : ((generous(X0) & ~tall(X0)) <=> (happy(X0) | quiet(X0))) [input p14]
16. ! [X0] : ((quiet(X0) <~> brave(X0)) <=> (happy(X0) & ~generous(X0))) [input p15]
21. ~kind(lucy) [input hypothesis]
24. ! [X0] : (~strong(X0) => (~brave(X0) | ~curious(X0))) [unused predicate definition removal 3]
27. ! [X0] : ((~strong(X0) & rich(X0)) | ~rich(X0)) [ennf transformation 2]
28. ! [X0] : ((~brave(X0) | ~curious(X0)) | strong(X0)) [ennf transformation 24]
29. ! [X0] : (~brave(X0) | ~curious(X0) | strong(X0)) [flattening 28]
30. ! [X0] : ((patient(X0) & tall(X0)) | (~funny(X0) <=> old(X0))) [ennf transformation 4]
32. ! [X0] : ((curious(X0) & brave(X0)) | (kind(X0) <=> brave(X0))) [ennf transformation 9]
33. ! [X0] : ((~funny(X0) <~> ~rich(X0)) | (brave(X0) <=> ~old(X0))) [ennf transformation 10]
36. ! [X0] : ((patient(X0) & tall(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) [nnf transformation 30]
37. ! [X0] : ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))) [nnf transformation 5]
49. ! [X0] : ((curious(X0) & brave(X0)) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) [nnf transformation 32]
50. ! [X0] : (((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) [nnf transformation 33]
53. ! [X0] : (((quiet(X0) | happy(X0)) | (creative(X0) & ~generous(X0))) & ((~creative(X0) | generous(X0)) | (~quiet(X0) & ~happy(X0)))) [nnf transformation 12]
54. ! [X0] : ((quiet(X0) | happy(X0) | (creative(X0) & ~generous(X0))) & (~creative(X0) | generous(X0) | (~quiet(X0) & ~happy(X0)))) [flattening 53]
56. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (generous(X0) | ~kind(X0))) & ((~generous(X0) & kind(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [nnf transformation 14]
57. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | generous(X0) | ~kind(X0)) & ((~generous(X0) & kind(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [flattening 56]
58. ! [X0] : (((generous(X0) & ~tall(X0)) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | (~generous(X0) | tall(X0)))) [nnf transformation 15]
59. ! [X0] : (((generous(X0) & ~tall(X0)) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~generous(X0) | tall(X0))) [flattening 58]
60. ! [X0] : ((((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | (~happy(X0) | generous(X0))) & ((happy(X0) & ~generous(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0))))) [nnf transformation 16]
61. ! [X0] : ((((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ~happy(X0) | generous(X0)) & ((happy(X0) & ~generous(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0))))) [flattening 60]
73. ~strong(X0) | ~rich(X0) [cnf transformation 27]
74. ~curious(X0) | ~brave(X0) | strong(X0) [cnf transformation 29]
75. tall(X0) | old(X0) | funny(X0) [cnf transformation 36]
79. ~generous(X0) | ~funny(X0) [cnf transformation 37]
80. generous(X0) | funny(X0) [cnf transformation 37]
91. brave(X0) | brave(X0) | ~kind(X0) [cnf transformation 49]
94. ~brave(X0) | kind(X0) | curious(X0) [cnf transformation 49]
97. ~old(X0) | funny(X0) | rich(X0) | ~brave(X0) [cnf transformation 50]
104. ~quiet(X0) | generous(X0) | ~creative(X0) [cnf transformation 54]
105. ~generous(X0) | happy(X0) | quiet(X0) [cnf transformation 54]
106. happy(X0) | quiet(X0) | creative(X0) [cnf transformation 54]
109. ~funny(X0) | kind(X0) | happy(X0) [cnf transformation 57]
112. ~generous(X0) | ~happy(X0) | funny(X0) [cnf transformation 57]
116. ~quiet(X0) | ~tall(X0) [cnf transformation 59]
118. ~quiet(X0) | generous(X0) [cnf transformation 59]
119. generous(X0) | ~happy(X0) [cnf transformation 59]
122. happy(X0) | brave(X0) | ~quiet(X0) [cnf transformation 61]
123. happy(X0) | quiet(X0) | ~brave(X0) [cnf transformation 61]
129. ~kind(lucy) [cnf transformation 21]
130. ~kind(X0) | brave(X0) [duplicate literal removal 91]
155. 6 <=> kind(lucy) [avatar definition]
156. ~kind(lucy) <- (~6) [avatar component clause 155]
164. ~happy(X0) | ~generous(X0) [subsumption resolution 112,79]
165. ~happy(X0) [subsumption resolution 119,164]
166. ~brave(X0) | quiet(X0) [subsumption resolution 123,165]
167. ~quiet(X0) | brave(X0) [subsumption resolution 122,165]
177. ~6 [avatar split clause 129,155]
217. happy(X0) | quiet(X0) | funny(X0) [resolution 105,80]
218. quiet(X0) | funny(X0) [subsumption resolution 217,165]
220. funny(X1) | brave(X1) [resolution 218,167]
225. quiet(X2) | creative(X2) [resolution 106,165]
228. creative(X2) | generous(X2) [resolution 225,118]
265. brave(X0) | kind(X0) | happy(X0) [resolution 220,109]
268. brave(X0) | kind(X0) [subsumption resolution 265,165]
269. brave(X0) [subsumption resolution 268,130]
273. kind(X1) | curious(X1) [resolution 269,94]
274. quiet(X2) [resolution 269,166]
295. generous(X0) | ~creative(X0) [resolution 274,104]
298. ~tall(X3) [resolution 274,116]
299. generous(X0) [subsumption resolution 295,228]
312. old(X0) | funny(X0) [resolution 298,75]
329. ~funny(X2) [resolution 299,79]
350. curious(lucy) <- (~6) [resolution 273,156]
355. ~brave(lucy) | strong(lucy) <- (~6) [resolution 350,74]
357. strong(lucy) <- (~6) [subsumption resolution 355,269]
361. ~rich(lucy) <- (~6) [resolution 357,73]
362. funny(X0) | funny(X0) | rich(X0) | ~brave(X0) [resolution 312,97]
366. funny(X0) | rich(X0) | ~brave(X0) [duplicate literal removal 362]
367. rich(X0) | ~brave(X0) [subsumption resolution 366,329]
368. rich(X0) [subsumption resolution 367,269]
370. $false <- (~6) [resolution 368,361]
371. 6 [avatar contradiction clause 370]
372. $false [avatar sat refutation 177,371]
% SZS output end Proof for 7628750380518898342676618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not humble or calm then someone is either creative or not strong. If someone is both not tall and not strong then someone is either generous or wise. Everyone who is old is both humble and happy and vice versa. If someone is both generous and not funny then someone is either calm or generous. If someone is either wise or not old then someone is tall or not generous and vice versa. Everyone who is both not wise and old is both brave and not quiet and vice versa. Everyone who is not old or not brave is not curious or not creative and vice versa. Everyone who is not quiet is both not tall and not generous. Everyone who is not creative or not rich is both wise and not wise. If mary is curious then susan is either not tall or quiet. If someone is either kind or wise then susan is either not calm or generous. Everyone who is either curious or not wise is not rich and vice versa. Everyone who is both rich and curious is both generous and not funny. If someone is both not quiet and kind then someone is not funny or rich and vice versa. If paul is not tall then someone is both not creative and patient. Everyone who is both not tall and patient is not kind or not creative and vice versa. Someone is curious or funny. Someone is either patient or generous. Someone is either curious or quiet. Someone is not rich or not strong. | Susan is not tall. | neutral | (((~humble(alice)|calm(alice)))=>(?[X]:((creative(X)<~>~strong(X)))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:((generous(X)<~>wise(X)))))&
(![X]:(old(X)<=>(humble(X)&happy(X))))&
((?[X]:((generous(X)&~funny(X))))=>(?[X]:((calm(X)<~>generous(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:((~wise(X)&old(X))<=>(brave(X)&~quiet(X))))&
(![X]:((~old(X)|~brave(X))<=>(~curious(X)|~creative(X))))&
(![X]:(~quiet(X)=>(~tall(X)&~generous(X))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)&~wise(X))))&
((curious(mary))=>((~tall(susan)<~>quiet(susan))))&
((?[X]:((kind(X)<~>wise(X))))=>((~calm(susan)<~>generous(susan))))&
(![X]:((curious(X)<~>~wise(X))<=>~rich(X)))&
(![X]:((rich(X)&curious(X))=>(generous(X)&~funny(X))))&
((?[X]:((~quiet(X)&kind(X))))<=>(?[X]:((~funny(X)|rich(X)))))&
((~tall(paul))=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:((~tall(X)&patient(X))<=>(~kind(X)|~creative(X))))&
(?[X]:((curious(X)|funny(X))))&
(?[X]:((patient(X)<~>generous(X))))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((~rich(X)|~strong(X)))) | ~tall(susan) | [] | null | 0 |
If someone is not old or calm then mary is either not patient or not quiet.
If someone is not tall then mary is not creative or not rich.
Everyone who is both humble and rich is either old or patient.
Everyone who is not happy or not tall is either strong or quiet and vice versa.
If paul is generous then fred is either not wise or patient and vice versa.
If mary is either not humble or generous then someone is not quiet.
Everyone who is both not patient and generous is not generous or not happy and vice versa.
Everyone who is brave or not creative is not creative.
Everyone who is creative or wise is not curious or not patient and vice versa.
If someone is either rich or generous then someone is both humble and rich and vice versa.
If someone is either rich or kind then someone is both wise and calm.
Everyone who is either tall or not creative is both curious and funny and vice versa.
Everyone who is not humble or kind is creative or not generous.
If someone is either not rich or not wise then someone is both strong and not quiet and vice versa.
Everyone who is not happy is either not humble or curious.
If john is not kind or curious then paul is not calm or not brave and vice versa.
Mary is creative or patient.
John is both quiet and rich.
Someone is strong or not tall.
Someone is both not old and rich.
Alice is either not generous or tall.
Someone is tall.
Someone is not brave. | Mary is not rich. | neutral | ((?[X]:((~old(X)|calm(X))))=>((~patient(mary)<~>~quiet(mary))))&
((?[X]:(~tall(X)))=>((~creative(mary)|~rich(mary))))&
(![X]:((humble(X)&rich(X))=>(old(X)<~>patient(X))))&
(![X]:((~happy(X)|~tall(X))<=>(strong(X)<~>quiet(X))))&
((generous(paul))<=>((~wise(fred)<~>patient(fred))))&
(((~humble(mary)<~>generous(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((~patient(X)&generous(X))<=>(~generous(X)|~happy(X))))&
(![X]:((brave(X)|~creative(X))=>~creative(X)))&
(![X]:((creative(X)|wise(X))<=>(~curious(X)|~patient(X))))&
((?[X]:((rich(X)<~>generous(X))))<=>(?[X]:((humble(X)&rich(X)))))&
((?[X]:((rich(X)<~>kind(X))))=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((tall(X)<~>~creative(X))<=>(curious(X)&funny(X))))&
(![X]:((~humble(X)|kind(X))=>(creative(X)|~generous(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:(~happy(X)=>(~humble(X)<~>curious(X))))&
(((~kind(john)|curious(john)))<=>((~calm(paul)|~brave(paul))))&
((creative(mary)|patient(mary)))&
((quiet(john)&rich(john)))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((~old(X)&rich(X))))&
((~generous(alice)<~>tall(alice)))&
(?[X]:(tall(X)))&
(?[X]:(~brave(X))) | ~rich(mary) | [] | null | 0 |
Everyone who is both not rich and not happy is tall or not generous.
Everyone who is not rich is both not generous and old and vice versa.
Everyone who is old or generous is either old or not quiet and vice versa.
If someone is both rich and generous then someone is both patient and tall and vice versa.
If someone is not calm then someone is rich or quiet.
If someone is both not quiet and not wise then lucy is happy and vice versa.
Everyone who is either not calm or wise is old.
Everyone who is both humble and not wise is either humble or not funny.
If someone is both not calm and kind then someone is either not old or not quiet and vice versa.
Everyone who is not kind is either tall or rich and vice versa.
Everyone who is both quiet and not happy is either brave or not tall and vice versa.
If someone is either not brave or strong then paul is either brave or kind and vice versa.
Everyone who is not patient is not happy or rich and vice versa.
Everyone who is both not old and humble is both not brave and not tall and vice versa.
Everyone who is either not calm or not brave is tall or not kind.
Everyone who is either not wise or not patient is both not generous and not strong.
Someone is either not curious or happy.
Paul is both wise and not funny.
Someone is creative.
John is either funny or not calm.
Someone is either not rich or quiet.
Someone is not quiet.
Susan is rich or wise. | Susan is kind. | neutral | (![X]:((~rich(X)&~happy(X))=>(tall(X)|~generous(X))))&
(![X]:(~rich(X)<=>(~generous(X)&old(X))))&
(![X]:((old(X)|generous(X))<=>(old(X)<~>~quiet(X))))&
((?[X]:((rich(X)&generous(X))))<=>(?[X]:((patient(X)&tall(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|quiet(X)))))&
((?[X]:((~quiet(X)&~wise(X))))<=>(happy(lucy)))&
(![X]:((~calm(X)<~>wise(X))=>old(X)))&
(![X]:((humble(X)&~wise(X))=>(humble(X)<~>~funny(X))))&
((?[X]:((~calm(X)&kind(X))))<=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:(~kind(X)<=>(tall(X)<~>rich(X))))&
(![X]:((quiet(X)&~happy(X))<=>(brave(X)<~>~tall(X))))&
((?[X]:((~brave(X)<~>strong(X))))<=>((brave(paul)<~>kind(paul))))&
(![X]:(~patient(X)<=>(~happy(X)|rich(X))))&
(![X]:((~old(X)&humble(X))<=>(~brave(X)&~tall(X))))&
(![X]:((~calm(X)<~>~brave(X))=>(tall(X)|~kind(X))))&
(![X]:((~wise(X)<~>~patient(X))=>(~generous(X)&~strong(X))))&
(?[X]:((~curious(X)<~>happy(X))))&
((wise(paul)&~funny(paul)))&
(?[X]:(creative(X)))&
((funny(john)<~>~calm(john)))&
(?[X]:((~rich(X)<~>quiet(X))))&
(?[X]:(~quiet(X)))&
((rich(susan)|wise(susan))) | kind(susan) | [] | null | 0 |
Everyone who is either funny or curious is both creative and not old and vice versa. Everyone who is both old and kind is both generous and not curious. If someone is not calm then fred is calm or not humble. Everyone who is both not calm and wise is brave or not wise. If someone is not happy then someone is either wise or old and vice versa. Everyone who is both not rich and patient is both not generous and generous and vice versa. If someone is either not curious or not happy then alice is both patient and funny. Everyone who is both not quiet and brave is both humble and tall and vice versa. If someone is both not humble and rich then someone is patient or generous. Everyone who is either not brave or not old is not creative. Everyone who is not old or patient is both not curious and not creative and vice versa. Everyone who is both strong and old is quiet or not humble. Everyone who is either curious or calm is both not brave and not quiet. Everyone who is not old or brave is both curious and old and vice versa. Everyone who is not quiet is both curious and not old. If mary is not old or not generous then paul is strong or curious. Someone is either not kind or not creative. Someone is wise or curious. Someone is either quiet or not quiet. Someone is not patient. Mary is not rich. Paul is tall or not rich. Someone is brave or humble. | Paul is old. | entailment | (![X]:((funny(X)<~>curious(X))<=>(creative(X)&~old(X))))&
(![X]:((old(X)&kind(X))=>(generous(X)&~curious(X))))&
((?[X]:(~calm(X)))=>((calm(fred)|~humble(fred))))&
(![X]:((~calm(X)&wise(X))=>(brave(X)|~wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((~rich(X)&patient(X))<=>(~generous(X)&generous(X))))&
((?[X]:((~curious(X)<~>~happy(X))))=>((patient(alice)&funny(alice))))&
(![X]:((~quiet(X)&brave(X))<=>(humble(X)&tall(X))))&
((?[X]:((~humble(X)&rich(X))))=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~brave(X)<~>~old(X))=>~creative(X)))&
(![X]:((~old(X)|patient(X))<=>(~curious(X)&~creative(X))))&
(![X]:((strong(X)&old(X))=>(quiet(X)|~humble(X))))&
(![X]:((curious(X)<~>calm(X))=>(~brave(X)&~quiet(X))))&
(![X]:((~old(X)|brave(X))<=>(curious(X)&old(X))))&
(![X]:(~quiet(X)=>(curious(X)&~old(X))))&
(((~old(mary)|~generous(mary)))=>((strong(paul)|curious(paul))))&
(?[X]:((~kind(X)<~>~creative(X))))&
(?[X]:((wise(X)|curious(X))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
(?[X]:(~patient(X)))&
(~rich(mary))&
((tall(paul)|~rich(paul)))&
(?[X]:((brave(X)|humble(X)))) | old(paul) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5262385271663670322116992
% SZS output start Proof for 5262385271663670322116992
14. ! [X0] : ((brave(X0) | ~old(X0)) <=> (old(X0) & curious(X0))) [input p13]
24. ~old(paul) [input hypothesis]
61. ! [X0] : (((brave(X0) | ~old(X0)) | (~old(X0) | ~curious(X0))) & ((old(X0) & curious(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 14]
62. ! [X0] : ((brave(X0) | ~old(X0) | ~old(X0) | ~curious(X0)) & ((old(X0) & curious(X0)) | (~brave(X0) & old(X0)))) [flattening 61]
116. old(X0) | old(X0) [cnf transformation 62]
132. ~old(paul) [cnf transformation 24]
133. old(X0) [duplicate literal removal 116]
256. $false [subsumption resolution 132,133]
% SZS output end Proof for 5262385271663670322116992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or not happy then someone is not patient or not rich.
Everyone who is both kind and calm is happy and vice versa.
Everyone who is quiet is both funny and patient.
If fred is either not creative or not rich then paul is funny.
If someone is generous or not kind then susan is both not strong and not quiet and vice versa.
Everyone who is not curious is happy or not kind.
If alice is not quiet or humble then someone is either not wise or not curious and vice versa.
Everyone who is both not kind and not old is not rich or brave and vice versa.
If someone is either not quiet or tall then someone is either not calm or not rich and vice versa.
If someone is either rich or not funny then someone is both brave and generous.
Everyone who is not old or happy is humble or not happy and vice versa.
Everyone who is either happy or not wise is both not generous and humble and vice versa.
If paul is either not generous or not kind then alice is both wise and humble and vice versa.
If someone is both not kind and patient then lucy is either not happy or not humble and vice versa.
If someone is tall or creative then susan is old.
Everyone who is either not humble or not curious is happy or not funny and vice versa.
Someone is both not creative and not strong.
Alice is not humble.
Someone is either not quiet or not humble.
Someone is not patient.
Susan is both not wise and not funny.
Paul is humble or not rich.
Someone is rich.
Someone is not rich or creative. | Susan is not curious. | entailment | ((?[X]:((~funny(X)|~happy(X))))=>(?[X]:((~patient(X)|~rich(X)))))&
(![X]:((kind(X)&calm(X))<=>happy(X)))&
(![X]:(quiet(X)=>(funny(X)&patient(X))))&
(((~creative(fred)<~>~rich(fred)))=>(funny(paul)))&
((?[X]:((generous(X)|~kind(X))))<=>((~strong(susan)&~quiet(susan))))&
(![X]:(~curious(X)=>(happy(X)|~kind(X))))&
(((~quiet(alice)|humble(alice)))<=>(?[X]:((~wise(X)<~>~curious(X)))))&
(![X]:((~kind(X)&~old(X))<=>(~rich(X)|brave(X))))&
((?[X]:((~quiet(X)<~>tall(X))))<=>(?[X]:((~calm(X)<~>~rich(X)))))&
((?[X]:((rich(X)<~>~funny(X))))=>(?[X]:((brave(X)&generous(X)))))&
(![X]:((~old(X)|happy(X))<=>(humble(X)|~happy(X))))&
(![X]:((happy(X)<~>~wise(X))<=>(~generous(X)&humble(X))))&
(((~generous(paul)<~>~kind(paul)))<=>((wise(alice)&humble(alice))))&
((?[X]:((~kind(X)&patient(X))))<=>((~happy(lucy)<~>~humble(lucy))))&
((?[X]:((tall(X)|creative(X))))=>(old(susan)))&
(![X]:((~humble(X)<~>~curious(X))<=>(happy(X)|~funny(X))))&
(?[X]:((~creative(X)&~strong(X))))&
(~humble(alice))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:(~patient(X)))&
((~wise(susan)&~funny(susan)))&
((humble(paul)|~rich(paul)))&
(?[X]:(rich(X)))&
(?[X]:((~rich(X)|creative(X)))) | ~curious(susan) | [
"p10",
"p11",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2052778347558703932195357
% SZS output start Proof for 2052778347558703932195357
11. ! [X0] : ((happy(X0) | ~old(X0)) <=> (~happy(X0) | humble(X0))) [input p10]
12. ! [X0] : ((happy(X0) <~> ~wise(X0)) <=> (humble(X0) & ~generous(X0))) [input p11]
16. ! [X0] : ((~humble(X0) <~> ~curious(X0)) <=> (~funny(X0) | happy(X0))) [input p15]
21. ~funny(susan) & ~wise(susan) [input p20]
25. curious(susan) [input hypothesis]
63. ! [X0] : (((happy(X0) | ~old(X0)) | (happy(X0) & ~humble(X0))) & ((~happy(X0) | humble(X0)) | (~happy(X0) & old(X0)))) [nnf transformation 11]
64. ! [X0] : ((happy(X0) | ~old(X0) | (happy(X0) & ~humble(X0))) & (~happy(X0) | humble(X0) | (~happy(X0) & old(X0)))) [flattening 63]
65. ! [X0] : ((((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | (~humble(X0) | generous(X0))) & ((humble(X0) & ~generous(X0)) | ((happy(X0) | wise(X0)) & (~wise(X0) | ~happy(X0))))) [nnf transformation 12]
66. ! [X0] : ((((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | ~humble(X0) | generous(X0)) & ((humble(X0) & ~generous(X0)) | ((happy(X0) | wise(X0)) & (~wise(X0) | ~happy(X0))))) [flattening 65]
73. ! [X0] : ((((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | (funny(X0) & ~happy(X0))) & ((~funny(X0) | happy(X0)) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0))))) [nnf transformation 16]
74. ! [X0] : ((((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | (funny(X0) & ~happy(X0))) & (~funny(X0) | happy(X0) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0))))) [flattening 73]
125. ~happy(X0) | humble(X0) | ~happy(X0) [cnf transformation 64]
131. humble(X0) | happy(X0) | wise(X0) [cnf transformation 66]
151. ~humble(X0) | ~curious(X0) | funny(X0) [cnf transformation 74]
160. ~wise(susan) [cnf transformation 21]
161. ~funny(susan) [cnf transformation 21]
165. curious(susan) [cnf transformation 25]
166. ~happy(X0) | humble(X0) [duplicate literal removal 125]
308. wise(X0) | humble(X0) [subsumption resolution 131,166]
418. humble(susan) [resolution 308,160]
444. ~curious(susan) | funny(susan) [resolution 151,418]
454. funny(susan) [subsumption resolution 444,165]
455. $false [subsumption resolution 454,161]
% SZS output end Proof for 2052778347558703932195357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not patient or kind then someone is both kind and not wise. Everyone who is wise or not happy is not old or patient. If lucy is both calm and rich then someone is old or quiet and vice versa. If paul is kind or rich then lucy is both not strong and happy and vice versa. Everyone who is patient is both not brave and not curious. Everyone who is both calm and tall is either not wise or wise. If lucy is both not strong and strong then paul is funny or not rich and vice versa. If someone is brave then alice is either old or not quiet. If susan is wise then susan is funny or not curious and vice versa. Everyone who is either rich or humble is not brave and vice versa. If someone is either wise or not brave then susan is not funny. Everyone who is not calm or wise is not quiet or not old. If mary is either not funny or humble then paul is tall and vice versa. If fred is both funny and not calm then someone is both not kind and not happy. Everyone who is calm is both kind and patient. Everyone who is calm or not happy is rich or patient and vice versa. John is not calm. Someone is either not strong or calm. John is either kind or creative. Lucy is not curious or wise. Susan is both not calm and not quiet. Someone is either not happy or not rich. | Susan is not creative. | neutral | (((~patient(lucy)|kind(lucy)))=>(?[X]:((kind(X)&~wise(X)))))&
(![X]:((wise(X)|~happy(X))=>(~old(X)|patient(X))))&
(((calm(lucy)&rich(lucy)))<=>(?[X]:((old(X)|quiet(X)))))&
(((kind(paul)|rich(paul)))<=>((~strong(lucy)&happy(lucy))))&
(![X]:(patient(X)=>(~brave(X)&~curious(X))))&
(![X]:((calm(X)&tall(X))=>(~wise(X)<~>wise(X))))&
(((~strong(lucy)&strong(lucy)))<=>((funny(paul)|~rich(paul))))&
((?[X]:(brave(X)))=>((old(alice)<~>~quiet(alice))))&
((wise(susan))<=>((funny(susan)|~curious(susan))))&
(![X]:((rich(X)<~>humble(X))<=>~brave(X)))&
((?[X]:((wise(X)<~>~brave(X))))=>(~funny(susan)))&
(![X]:((~calm(X)|wise(X))=>(~quiet(X)|~old(X))))&
(((~funny(mary)<~>humble(mary)))<=>(tall(paul)))&
(((funny(fred)&~calm(fred)))=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:(calm(X)=>(kind(X)&patient(X))))&
(![X]:((calm(X)|~happy(X))<=>(rich(X)|patient(X))))&
(~calm(john))&
(?[X]:((~strong(X)<~>calm(X))))&
((kind(john)<~>creative(john)))&
((~curious(lucy)|wise(lucy)))&
((~calm(susan)&~quiet(susan)))&
(?[X]:((~happy(X)<~>~rich(X)))) | ~creative(susan) | [] | null | 0 |
If someone is not humble or funny then john is brave and vice versa.
If lucy is calm then someone is both quiet and not patient.
Everyone who is either kind or not tall is not tall or not creative.
Everyone who is not quiet or kind is both humble and quiet and vice versa.
Everyone who is not happy is generous.
Everyone who is creative or not patient is kind.
Everyone who is both curious and not funny is both not generous and brave.
If lucy is not happy or humble then paul is wise.
If someone is not rich or not brave then fred is both not creative and not happy and vice versa.
If susan is curious then someone is either curious or humble and vice versa.
Everyone who is either not patient or not old is not happy or not humble.
Everyone who is happy or tall is either creative or not kind and vice versa.
Everyone who is both calm and not curious is not happy or not generous and vice versa.
If paul is strong or brave then lucy is tall and vice versa.
Everyone who is wise or not strong is not calm or not humble.
If someone is not rich or not creative then lucy is either not tall or patient and vice versa.
Someone is both not happy and not curious.
Someone is both not patient and quiet.
Someone is patient or not quiet.
Someone is either not curious or not quiet.
Someone is not wise or rich.
Lucy is both creative and not curious.
Alice is both not rich and curious.
Someone is not patient. | Lucy is not old. | entailment | ((?[X]:((~humble(X)|funny(X))))<=>(brave(john)))&
((calm(lucy))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((kind(X)<~>~tall(X))=>(~tall(X)|~creative(X))))&
(![X]:((~quiet(X)|kind(X))<=>(humble(X)&quiet(X))))&
(![X]:(~happy(X)=>generous(X)))&
(![X]:((creative(X)|~patient(X))=>kind(X)))&
(![X]:((curious(X)&~funny(X))=>(~generous(X)&brave(X))))&
(((~happy(lucy)|humble(lucy)))=>(wise(paul)))&
((?[X]:((~rich(X)|~brave(X))))<=>((~creative(fred)&~happy(fred))))&
((curious(susan))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((~patient(X)<~>~old(X))=>(~happy(X)|~humble(X))))&
(![X]:((happy(X)|tall(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((calm(X)&~curious(X))<=>(~happy(X)|~generous(X))))&
(((strong(paul)|brave(paul)))<=>(tall(lucy)))&
(![X]:((wise(X)|~strong(X))=>(~calm(X)|~humble(X))))&
((?[X]:((~rich(X)|~creative(X))))<=>((~tall(lucy)<~>patient(lucy))))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:((~patient(X)&quiet(X))))&
(?[X]:((patient(X)|~quiet(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:((~wise(X)|rich(X))))&
((creative(lucy)&~curious(lucy)))&
((~rich(alice)&curious(alice)))&
(?[X]:(~patient(X))) | ~old(lucy) | [
"p2",
"p3",
"p5",
"p10",
"p11",
"p15",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 128942449611634145266594
% SZS output start Proof for 128942449611634145266594
3. ! [X0] : ((kind(X0) <~> ~tall(X0)) => (~creative(X0) | ~tall(X0))) [input p2]
4. ! [X0] : ((kind(X0) | ~quiet(X0)) <=> (quiet(X0) & humble(X0))) [input p3]
6. ! [X0] : ((~patient(X0) | creative(X0)) => kind(X0)) [input p5]
11. ! [X0] : ((~patient(X0) <~> ~old(X0)) => (~humble(X0) | ~happy(X0))) [input p10]
12. ! [X0] : ((tall(X0) | happy(X0)) <=> (creative(X0) <~> ~kind(X0))) [input p11]
16. ? [X0] : (~creative(X0) | ~rich(X0)) <=> (~tall(lucy) <~> patient(lucy)) [input p15]
22. ~curious(lucy) & creative(lucy) [input p21]
23. curious(alice) & ~rich(alice) [input p22]
25. old(lucy) [input hypothesis]
27. ! [X0] : ((~creative(X0) | ~tall(X0)) | (kind(X0) <=> ~tall(X0))) [ennf transformation 3]
28. ! [X0] : (~creative(X0) | ~tall(X0) | (kind(X0) <=> ~tall(X0))) [flattening 27]
30. ! [X0] : (kind(X0) | (patient(X0) & ~creative(X0))) [ennf transformation 6]
34. ! [X0] : ((~humble(X0) | ~happy(X0)) | (~patient(X0) <=> ~old(X0))) [ennf transformation 11]
35. ! [X0] : (~humble(X0) | ~happy(X0) | (~patient(X0) <=> ~old(X0))) [flattening 34]
44. ! [X0] : (~creative(X0) | ~tall(X0) | ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0)))) [nnf transformation 28]
45. ! [X0] : (((kind(X0) | ~quiet(X0)) | (~quiet(X0) | ~humble(X0))) & ((quiet(X0) & humble(X0)) | (~kind(X0) & quiet(X0)))) [nnf transformation 4]
46. ! [X0] : ((kind(X0) | ~quiet(X0) | ~quiet(X0) | ~humble(X0)) & ((quiet(X0) & humble(X0)) | (~kind(X0) & quiet(X0)))) [flattening 45]
56. ! [X0] : (~humble(X0) | ~happy(X0) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) [nnf transformation 35]
57. ! [X0] : (((tall(X0) | happy(X0)) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (~tall(X0) & ~happy(X0)))) [nnf transformation 12]
58. ! [X0] : ((tall(X0) | happy(X0) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (~tall(X0) & ~happy(X0)))) [flattening 57]
63. (? [X0] : (~creative(X0) | ~rich(X0)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X0] : (creative(X0) & rich(X0))) [nnf transformation 16]
64. (? [X0] : (~creative(X0) | ~rich(X0)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X1] : (creative(X1) & rich(X1))) [rectify 63]
65. ? [X0] : (~creative(X0) | ~rich(X0)) => (~creative(sK4) | ~rich(sK4)) [choice axiom]
66. ((~creative(sK4) | ~rich(sK4)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X1] : (creative(X1) & rich(X1))) [skolemisation 64,65]
85. ~creative(X0) | ~tall(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 44]
88. ~kind(X0) | humble(X0) [cnf transformation 46]
93. ~creative(X0) | kind(X0) [cnf transformation 30]
108. ~old(X0) | ~happy(X0) | ~humble(X0) | patient(X0) [cnf transformation 56]
111. ~kind(X0) | creative(X0) | ~tall(X0) [cnf transformation 58]
114. tall(X0) | happy(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 58]
128. ~patient(lucy) | tall(lucy) | rich(X1) [cnf transformation 66]
140. creative(lucy) [cnf transformation 22]
142. ~rich(alice) [cnf transformation 23]
145. old(lucy) [cnf transformation 25]
148. ~creative(X0) | ~tall(X0) | ~kind(X0) [duplicate literal removal 85]
185. 9 <=> humble(lucy) [avatar definition]
186. humble(lucy) <- (9) [avatar component clause 185]
194. 11 <=> happy(lucy) [avatar definition]
196. happy(lucy) <- (11) [avatar component clause 194]
220. 17 <=> ! [X1] : rich(X1) [avatar definition]
221. rich(X1) <- (17) [avatar component clause 220]
248. ~creative(X0) | happy(X0) | tall(X0) [subsumption resolution 114,93]
249. ~tall(X0) | ~kind(X0) [subsumption resolution 111,148]
251. 23 <=> tall(lucy) [avatar definition]
252. tall(lucy) <- (23) [avatar component clause 251]
253. ~tall(lucy) <- (~23) [avatar component clause 251]
266. 26 <=> patient(lucy) [avatar definition]
268. ~patient(lucy) <- (~26) [avatar component clause 266]
283. 17 | 23 | ~26 [avatar split clause 128,266,251,220]
299. kind(lucy) [resolution 93,140]
303. humble(lucy) [resolution 299,88]
304. 9 [avatar split clause 303,185]
428. $false <- (17) [resolution 221,142]
431. ~17 [avatar contradiction clause 428]
434. ~kind(lucy) <- (23) [resolution 252,249]
435. $false <- (23) [subsumption resolution 434,299]
436. ~23 [avatar contradiction clause 435]
442. happy(lucy) | tall(lucy) [resolution 248,140]
443. happy(lucy) <- (~23) [subsumption resolution 442,253]
444. 11 | 23 [avatar split clause 443,251,194]
446. ~happy(lucy) | ~humble(lucy) | patient(lucy) [resolution 108,145]
447. ~humble(lucy) | patient(lucy) <- (11) [subsumption resolution 446,196]
448. patient(lucy) <- (9, 11) [subsumption resolution 447,186]
449. $false <- (9, 11, ~26) [subsumption resolution 448,268]
450. ~9 | ~11 | 26 [avatar contradiction clause 449]
451. $false [avatar sat refutation 283,304,431,436,444,450]
% SZS output end Proof for 128942449611634145266594
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or brave then someone is both not wise and humble.
Everyone who is both not funny and strong is wise or quiet and vice versa.
If paul is brave or not tall then someone is brave or happy.
Everyone who is not curious is patient and vice versa.
Everyone who is not generous is curious and vice versa.
Everyone who is not strong or old is both funny and not tall.
Everyone who is not creative or not brave is both tall and curious and vice versa.
Everyone who is both funny and not patient is either rich or not calm and vice versa.
If someone is not generous or funny then someone is funny and vice versa.
Everyone who is either not old or not calm is not strong or strong and vice versa.
Everyone who is both curious and tall is both not patient and creative.
Everyone who is either not quiet or generous is rich or creative and vice versa.
Everyone who is either not patient or not rich is both quiet and calm.
Everyone who is either not brave or not wise is either not funny or curious.
Everyone who is funny is either not brave or wise and vice versa.
Everyone who is both patient and strong is strong and vice versa.
Lucy is not patient or not tall.
Fred is either humble or strong.
Susan is wise or quiet.
Lucy is either curious or not rich.
Fred is both not happy and not rich. | Lucy is not quiet. | contradiction | ((?[X]:((~strong(X)<~>brave(X))))=>(?[X]:((~wise(X)&humble(X)))))&
(![X]:((~funny(X)&strong(X))<=>(wise(X)|quiet(X))))&
(((brave(paul)|~tall(paul)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:(~curious(X)<=>patient(X)))&
(![X]:(~generous(X)<=>curious(X)))&
(![X]:((~strong(X)|old(X))=>(funny(X)&~tall(X))))&
(![X]:((~creative(X)|~brave(X))<=>(tall(X)&curious(X))))&
(![X]:((funny(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(~strong(X)|strong(X))))&
(![X]:((curious(X)&tall(X))=>(~patient(X)&creative(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(quiet(X)&calm(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~funny(X)<~>curious(X))))&
(![X]:(funny(X)<=>(~brave(X)<~>wise(X))))&
(![X]:((patient(X)&strong(X))<=>strong(X)))&
((~patient(lucy)|~tall(lucy)))&
((humble(fred)<~>strong(fred)))&
((wise(susan)|quiet(susan)))&
((curious(lucy)<~>~rich(lucy)))&
((~happy(fred)&~rich(fred))) | ~quiet(lucy) | [
"p1",
"p3",
"p5",
"p6",
"p8",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2847163711787545137965720
% SZS output start Proof for 2847163711787545137965720
2. ! [X0] : ((strong(X0) & ~funny(X0)) <=> (quiet(X0) | wise(X0))) [input p1]
4. ! [X0] : (~curious(X0) <=> patient(X0)) [input p3]
6. ! [X0] : ((old(X0) | ~strong(X0)) => (~tall(X0) & funny(X0))) [input p5]
7. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (curious(X0) & tall(X0))) [input p6]
9. ? [X0] : (funny(X0) | ~generous(X0)) <=> ? [X0] : funny(X0) [input p8]
11. ! [X0] : ((tall(X0) & curious(X0)) => (creative(X0) & ~patient(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) <~> generous(X0)) <=> (creative(X0) | rich(X0))) [input p11]
14. ! [X0] : ((~brave(X0) <~> ~wise(X0)) => (~funny(X0) <~> curious(X0))) [input p13]
15. ! [X0] : (funny(X0) <=> (~brave(X0) <~> wise(X0))) [input p14]
16. ! [X0] : ((strong(X0) & patient(X0)) <=> strong(X0)) [input p15]
22. ~quiet(lucy) [input hypothesis]
24. ? [X0] : (funny(X0) | ~generous(X0)) <=> ? [X1] : funny(X1) [rectify 9]
27. ! [X0] : ((~tall(X0) & funny(X0)) | (~old(X0) & strong(X0))) [ennf transformation 6]
28. ! [X0] : ((creative(X0) & ~patient(X0)) | (~tall(X0) | ~curious(X0))) [ennf transformation 11]
29. ! [X0] : ((creative(X0) & ~patient(X0)) | ~tall(X0) | ~curious(X0)) [flattening 28]
31. ! [X0] : ((~funny(X0) <~> curious(X0)) | (~brave(X0) <=> ~wise(X0))) [ennf transformation 14]
36. ! [X0] : (((strong(X0) & ~funny(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (~strong(X0) | funny(X0)))) [nnf transformation 2]
37. ! [X0] : (((strong(X0) & ~funny(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | ~strong(X0) | funny(X0))) [flattening 36]
40. ! [X0] : ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))) [nnf transformation 4]
42. ! [X0] : (((~brave(X0) | ~creative(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [nnf transformation 7]
43. ! [X0] : ((~brave(X0) | ~creative(X0) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [flattening 42]
46. (? [X0] : (funny(X0) | ~generous(X0)) | ! [X1] : ~funny(X1)) & (? [X1] : funny(X1) | ! [X0] : (~funny(X0) & generous(X0))) [nnf transformation 24]
47. (? [X0] : (funny(X0) | ~generous(X0)) | ! [X1] : ~funny(X1)) & (? [X2] : funny(X2) | ! [X3] : (~funny(X3) & generous(X3))) [rectify 46]
48. ? [X0] : (funny(X0) | ~generous(X0)) => (funny(sK2) | ~generous(sK2)) [choice axiom]
49. ? [X2] : funny(X2) => funny(sK3) [choice axiom]
50. ((funny(sK2) | ~generous(sK2)) | ! [X1] : ~funny(X1)) & (funny(sK3) | ! [X3] : (~funny(X3) & generous(X3))) [skolemisation 47,49,48]
53. ! [X0] : ((((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (~creative(X0) & ~rich(X0))) & ((creative(X0) | rich(X0)) | ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0))))) [nnf transformation 12]
54. ! [X0] : ((((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (~creative(X0) & ~rich(X0))) & (creative(X0) | rich(X0) | ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0))))) [flattening 53]
56. ! [X0] : (((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) [nnf transformation 31]
57. ! [X0] : ((funny(X0) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ~funny(X0))) [nnf transformation 15]
58. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | (~strong(X0) | ~patient(X0)))) [nnf transformation 16]
59. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | ~strong(X0) | ~patient(X0))) [flattening 58]
67. ~funny(X0) | ~wise(X0) [cnf transformation 37]
74. ~patient(X0) | ~curious(X0) [cnf transformation 40]
77. funny(X0) | strong(X0) [cnf transformation 27]
79. ~tall(X0) | strong(X0) [cnf transformation 27]
81. creative(X0) | tall(X0) [cnf transformation 43]
82. tall(X0) | brave(X0) [cnf transformation 43]
83. creative(X0) | curious(X0) [cnf transformation 43]
84. curious(X0) | brave(X0) [cnf transformation 43]
92. funny(sK3) | generous(X3) [cnf transformation 50]
102. creative(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 29]
108. ~generous(X0) | quiet(X0) | ~creative(X0) [cnf transformation 54]
114. curious(X0) | ~funny(X0) | ~brave(X0) | wise(X0) [cnf transformation 56]
115. ~curious(X0) | funny(X0) | ~wise(X0) | brave(X0) [cnf transformation 56]
117. wise(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 57]
120. funny(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 57]
122. ~strong(X0) | patient(X0) [cnf transformation 59]
132. ~quiet(lucy) [cnf transformation 22]
142. 3 <=> ! [X1] : (brave(X1) | strong(X1)) [avatar definition]
143. brave(X1) | strong(X1) <- (3) [avatar component clause 142]
182. 12 <=> funny(sK3) [avatar definition]
184. funny(sK3) <- (12) [avatar component clause 182]
187. 13 <=> ! [X3] : generous(X3) [avatar definition]
188. generous(X3) <- (13) [avatar component clause 187]
189. 13 | 12 [avatar split clause 92,182,187]
192. creative(X0) | ~tall(X0) [subsumption resolution 102,83]
193. creative(X0) [subsumption resolution 192,81]
194. ~generous(X0) | quiet(X0) [subsumption resolution 108,193]
196. funny(X0) | ~wise(X0) | brave(X0) [subsumption resolution 115,84]
197. ~wise(X0) | brave(X0) [subsumption resolution 196,67]
198. curious(X0) | ~funny(X0) | ~brave(X0) [subsumption resolution 114,67]
199. ~funny(X0) | curious(X0) [subsumption resolution 198,84]
200. funny(X0) | ~wise(X0) [subsumption resolution 120,197]
201. ~wise(X0) [subsumption resolution 200,67]
203. ~funny(X0) | ~brave(X0) [subsumption resolution 117,201]
244. brave(X0) | strong(X0) [resolution 82,79]
245. 3 [avatar split clause 244,142]
265. curious(sK3) <- (12) [resolution 199,184]
272. ~brave(X1) | strong(X1) [resolution 203,77]
273. strong(X1) <- (3) [subsumption resolution 272,143]
281. patient(X0) <- (3) [resolution 273,122]
283. ~curious(X0) <- (3) [resolution 281,74]
289. $false <- (3, 12) [resolution 283,265]
290. ~3 | ~12 [avatar contradiction clause 289]
296. quiet(X0) <- (13) [resolution 188,194]
298. $false <- (13) [resolution 296,132]
302. ~13 [avatar contradiction clause 298]
303. $false [avatar sat refutation 189,245,290,302]
% SZS output end Proof for 2847163711787545137965720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or strong is either not happy or happy and vice versa.
Everyone who is either not kind or not creative is both not tall and funny and vice versa.
Everyone who is not humble or not calm is both old and calm.
Everyone who is either strong or not patient is not patient or not kind.
Everyone who is either not humble or not tall is both not patient and not wise.
If mary is old then someone is either not rich or not brave.
If lucy is old then someone is either generous or patient and vice versa.
If fred is either not rich or not calm then someone is not patient.
Everyone who is old is either not happy or not humble and vice versa.
Everyone who is not tall or not old is calm or rich.
Everyone who is either not happy or tall is tall.
If someone is not quiet then john is both not calm and curious.
Everyone who is either not rich or not old is either quiet or rich and vice versa.
If someone is generous or not funny then john is not strong.
Everyone who is not kind is not quiet and vice versa.
Everyone who is not wise or not calm is either not generous or not patient.
Lucy is patient.
John is not funny.
Someone is both rich and not wise.
Paul is happy or funny.
Alice is either tall or generous.
Someone is both patient and not curious. | Lucy is humble. | entailment | (![X]:((~happy(X)<~>strong(X))<=>(~happy(X)<~>happy(X))))&
(![X]:((~kind(X)<~>~creative(X))<=>(~tall(X)&funny(X))))&
(![X]:((~humble(X)|~calm(X))=>(old(X)&calm(X))))&
(![X]:((strong(X)<~>~patient(X))=>(~patient(X)|~kind(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(~patient(X)&~wise(X))))&
((old(mary))=>(?[X]:((~rich(X)<~>~brave(X)))))&
((old(lucy))<=>(?[X]:((generous(X)<~>patient(X)))))&
(((~rich(fred)<~>~calm(fred)))=>(?[X]:(~patient(X))))&
(![X]:(old(X)<=>(~happy(X)<~>~humble(X))))&
(![X]:((~tall(X)|~old(X))=>(calm(X)|rich(X))))&
(![X]:((~happy(X)<~>tall(X))=>tall(X)))&
((?[X]:(~quiet(X)))=>((~calm(john)&curious(john))))&
(![X]:((~rich(X)<~>~old(X))<=>(quiet(X)<~>rich(X))))&
((?[X]:((generous(X)|~funny(X))))=>(~strong(john)))&
(![X]:(~kind(X)<=>~quiet(X)))&
(![X]:((~wise(X)|~calm(X))=>(~generous(X)<~>~patient(X))))&
(patient(lucy))&
(~funny(john))&
(?[X]:((rich(X)&~wise(X))))&
((happy(paul)|funny(paul)))&
((tall(alice)<~>generous(alice)))&
(?[X]:((patient(X)&~curious(X)))) | humble(lucy) | [
"p0",
"p2",
"p3",
"p8",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3538234068074484778218258
% SZS output start Proof for 3538234068074484778218258
1. ! [X0] : ((~happy(X0) <~> strong(X0)) <=> (~happy(X0) <~> happy(X0))) [input p0]
3. ! [X0] : ((~calm(X0) | ~humble(X0)) => (calm(X0) & old(X0))) [input p2]
4. ! [X0] : ((strong(X0) <~> ~patient(X0)) => (~kind(X0) | ~patient(X0))) [input p3]
9. ! [X0] : (old(X0) <=> (~happy(X0) <~> ~humble(X0))) [input p8]
12. ? [X0] : ~quiet(X0) => (curious(john) & ~calm(john)) [input p11]
15. ! [X0] : (~kind(X0) <=> ~quiet(X0)) [input p14]
17. patient(lucy) [input p16]
23. ~humble(lucy) [input hypothesis]
24. ! [X0] : ((calm(X0) & old(X0)) | (calm(X0) & humble(X0))) [ennf transformation 3]
25. ! [X0] : ((~kind(X0) | ~patient(X0)) | (strong(X0) <=> ~patient(X0))) [ennf transformation 4]
26. ! [X0] : (~kind(X0) | ~patient(X0) | (strong(X0) <=> ~patient(X0))) [flattening 25]
33. (curious(john) & ~calm(john)) | ! [X0] : quiet(X0) [ennf transformation 12]
36. ! [X0] : ((((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))))) [nnf transformation 1]
39. ! [X0] : (~kind(X0) | ~patient(X0) | ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0)))) [nnf transformation 26]
51. ! [X0] : ((old(X0) | ((~happy(X0) | humble(X0)) & (~humble(X0) | happy(X0)))) & (((humble(X0) | happy(X0)) & (~humble(X0) | ~happy(X0))) | ~old(X0))) [nnf transformation 9]
54. ! [X0] : ((~kind(X0) | quiet(X0)) & (~quiet(X0) | kind(X0))) [nnf transformation 15]
66. strong(X0) | ~happy(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 36]
75. old(X0) | humble(X0) [cnf transformation 24]
78. calm(X0) | calm(X0) [cnf transformation 24]
79. ~kind(X0) | ~patient(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 39]
94. humble(X0) | happy(X0) | ~old(X0) [cnf transformation 51]
95. old(X0) | ~humble(X0) | happy(X0) [cnf transformation 51]
101. ~calm(john) | quiet(X0) [cnf transformation 33]
113. ~quiet(X0) | kind(X0) [cnf transformation 54]
119. patient(lucy) [cnf transformation 17]
128. ~humble(lucy) [cnf transformation 23]
134. ~patient(X0) | ~kind(X0) | ~strong(X0) [duplicate literal removal 79]
135. calm(X0) [duplicate literal removal 78]
141. ~happy(X0) | strong(X0) [duplicate literal removal 66]
190. old(X0) | happy(X0) [subsumption resolution 95,75]
191. humble(X0) | happy(X0) [subsumption resolution 94,190]
193. 11 <=> ! [X0] : quiet(X0) [avatar definition]
194. quiet(X0) <- (11) [avatar component clause 193]
200. quiet(X0) [subsumption resolution 101,135]
201. 11 [avatar split clause 200,193]
239. kind(X0) <- (11) [resolution 113,194]
249. happy(lucy) [resolution 191,128]
252. strong(lucy) [resolution 249,141]
322. ~kind(lucy) | ~strong(lucy) [resolution 134,119]
324. ~strong(lucy) <- (11) [subsumption resolution 322,239]
325. $false <- (11) [subsumption resolution 324,252]
326. ~11 [avatar contradiction clause 325]
330. $false [avatar sat refutation 201,326]
% SZS output end Proof for 3538234068074484778218258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or tall then someone is not kind and vice versa.
Everyone who is both strong and patient is both not strong and calm and vice versa.
If susan is not happy then someone is both happy and curious.
Everyone who is not strong or not rich is either curious or calm.
If fred is either rich or not quiet then paul is both curious and rich and vice versa.
Everyone who is not tall or creative is not tall and vice versa.
If someone is calm or not kind then mary is both quiet and not wise and vice versa.
If someone is either curious or not brave then someone is kind.
Everyone who is both rich and not calm is funny.
Everyone who is not creative or not rich is either not funny or kind and vice versa.
If someone is either wise or old then someone is either brave or generous and vice versa.
Everyone who is curious is generous.
If someone is either curious or not rich then someone is generous.
Everyone who is not calm or humble is both brave and not creative and vice versa.
Everyone who is both humble and not generous is both not curious and not strong.
If someone is both not old and happy then someone is both quiet and funny.
Lucy is not curious.
Lucy is both not creative and rich.
Paul is not generous.
Lucy is either calm or tall.
Someone is either creative or not brave.
Lucy is not calm or strong.
John is either brave or not rich.
Alice is both kind and not brave. | Alice is not patient. | entailment | ((?[X]:((patient(X)<~>tall(X))))<=>(?[X]:(~kind(X))))&
(![X]:((strong(X)&patient(X))<=>(~strong(X)&calm(X))))&
((~happy(susan))=>(?[X]:((happy(X)&curious(X)))))&
(![X]:((~strong(X)|~rich(X))=>(curious(X)<~>calm(X))))&
(((rich(fred)<~>~quiet(fred)))<=>((curious(paul)&rich(paul))))&
(![X]:((~tall(X)|creative(X))<=>~tall(X)))&
((?[X]:((calm(X)|~kind(X))))<=>((quiet(mary)&~wise(mary))))&
((?[X]:((curious(X)<~>~brave(X))))=>(?[X]:(kind(X))))&
(![X]:((rich(X)&~calm(X))=>funny(X)))&
(![X]:((~creative(X)|~rich(X))<=>(~funny(X)<~>kind(X))))&
((?[X]:((wise(X)<~>old(X))))<=>(?[X]:((brave(X)<~>generous(X)))))&
(![X]:(curious(X)=>generous(X)))&
((?[X]:((curious(X)<~>~rich(X))))=>(?[X]:(generous(X))))&
(![X]:((~calm(X)|humble(X))<=>(brave(X)&~creative(X))))&
(![X]:((humble(X)&~generous(X))=>(~curious(X)&~strong(X))))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:((quiet(X)&funny(X)))))&
(~curious(lucy))&
((~creative(lucy)&rich(lucy)))&
(~generous(paul))&
((calm(lucy)<~>tall(lucy)))&
(?[X]:((creative(X)<~>~brave(X))))&
((~calm(lucy)|strong(lucy)))&
((brave(john)<~>~rich(john)))&
((kind(alice)&~brave(alice))) | ~patient(alice) | [
"p1",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7725338953054099246811148
% SZS output start Proof for 7725338953054099246811148
2. ! [X0] : ((patient(X0) & strong(X0)) <=> (calm(X0) & ~strong(X0))) [input p1]
14. ! [X0] : ((humble(X0) | ~calm(X0)) <=> (~creative(X0) & brave(X0))) [input p13]
24. ~brave(alice) & kind(alice) [input p23]
25. patient(alice) [input hypothesis]
46. ! [X0] : (((patient(X0) & strong(X0)) | (~calm(X0) | strong(X0))) & ((calm(X0) & ~strong(X0)) | (~patient(X0) | ~strong(X0)))) [nnf transformation 2]
47. ! [X0] : (((patient(X0) & strong(X0)) | ~calm(X0) | strong(X0)) & ((calm(X0) & ~strong(X0)) | ~patient(X0) | ~strong(X0))) [flattening 46]
75. ! [X0] : (((humble(X0) | ~calm(X0)) | (creative(X0) | ~brave(X0))) & ((~creative(X0) & brave(X0)) | (~humble(X0) & calm(X0)))) [nnf transformation 14]
76. ! [X0] : ((humble(X0) | ~calm(X0) | creative(X0) | ~brave(X0)) & ((~creative(X0) & brave(X0)) | (~humble(X0) & calm(X0)))) [flattening 75]
89. ~strong(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 47]
91. strong(X0) | ~calm(X0) | strong(X0) [cnf transformation 47]
133. brave(X0) | calm(X0) [cnf transformation 76]
154. ~brave(alice) [cnf transformation 24]
155. patient(alice) [cnf transformation 25]
156. ~strong(X0) | ~patient(X0) [duplicate literal removal 89]
157. ~calm(X0) | strong(X0) [duplicate literal removal 91]
350. calm(alice) [resolution 133,154]
355. strong(alice) [resolution 157,350]
373. ~patient(alice) [resolution 355,156]
374. $false [subsumption resolution 373,155]
% SZS output end Proof for 7725338953054099246811148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either strong or not kind then john is not calm and vice versa. Everyone who is not brave is not kind or not humble and vice versa. Everyone who is funny is strong or rich and vice versa. If lucy is old or happy then susan is kind and vice versa. Everyone who is not curious is not strong and vice versa. Everyone who is wise or not humble is not creative and vice versa. Everyone who is either not brave or patient is quiet and vice versa. If lucy is not brave or strong then someone is both humble and brave. Everyone who is both tall and not tall is humble. If someone is old then someone is brave or strong and vice versa. Everyone who is both not quiet and kind is either quiet or patient and vice versa. If alice is humble or curious then lucy is both not humble and tall. Everyone who is either brave or not rich is both not tall and funny and vice versa. Everyone who is brave or kind is generous. Everyone who is both not brave and brave is not wise. If susan is either creative or not tall then paul is not funny or strong. Fred is both tall and not old. Susan is not curious or not brave. Alice is not tall or not quiet. Susan is wise. Someone is either brave or generous. Fred is not strong or not generous. Someone is curious. | Susan is not generous. | contradiction | (((strong(alice)<~>~kind(alice)))<=>(~calm(john)))&
(![X]:(~brave(X)<=>(~kind(X)|~humble(X))))&
(![X]:(funny(X)<=>(strong(X)|rich(X))))&
(((old(lucy)|happy(lucy)))<=>(kind(susan)))&
(![X]:(~curious(X)<=>~strong(X)))&
(![X]:((wise(X)|~humble(X))<=>~creative(X)))&
(![X]:((~brave(X)<~>patient(X))<=>quiet(X)))&
(((~brave(lucy)|strong(lucy)))=>(?[X]:((humble(X)&brave(X)))))&
(![X]:((tall(X)&~tall(X))=>humble(X)))&
((?[X]:(old(X)))<=>(?[X]:((brave(X)|strong(X)))))&
(![X]:((~quiet(X)&kind(X))<=>(quiet(X)<~>patient(X))))&
(((humble(alice)|curious(alice)))=>((~humble(lucy)&tall(lucy))))&
(![X]:((brave(X)<~>~rich(X))<=>(~tall(X)&funny(X))))&
(![X]:((brave(X)|kind(X))=>generous(X)))&
(![X]:((~brave(X)&brave(X))=>~wise(X)))&
(((creative(susan)<~>~tall(susan)))=>((~funny(paul)|strong(paul))))&
((tall(fred)&~old(fred)))&
((~curious(susan)|~brave(susan)))&
((~tall(alice)|~quiet(alice)))&
(wise(susan))&
(?[X]:((brave(X)<~>generous(X))))&
((~strong(fred)|~generous(fred)))&
(?[X]:(curious(X))) | ~generous(susan) | [
"p1",
"p6",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5359198843143486579888593
% SZS output start Proof for 5359198843143486579888593
2. ! [X0] : (~brave(X0) <=> (~humble(X0) | ~kind(X0))) [input p1]
7. ! [X0] : ((~brave(X0) <~> patient(X0)) <=> quiet(X0)) [input p6]
11. ! [X0] : ((kind(X0) & ~quiet(X0)) <=> (quiet(X0) <~> patient(X0))) [input p10]
14. ! [X0] : ((kind(X0) | brave(X0)) => generous(X0)) [input p13]
24. ~generous(susan) [input hypothesis]
30. ! [X0] : (generous(X0) | (~kind(X0) & ~brave(X0))) [ennf transformation 14]
36. ! [X0] : ((~brave(X0) | (humble(X0) & kind(X0))) & ((~humble(X0) | ~kind(X0)) | brave(X0))) [nnf transformation 2]
37. ! [X0] : ((~brave(X0) | (humble(X0) & kind(X0))) & (~humble(X0) | ~kind(X0) | brave(X0))) [flattening 36]
45. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | ~quiet(X0)) & (quiet(X0) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [nnf transformation 7]
53. ! [X0] : (((kind(X0) & ~quiet(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) & (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (~kind(X0) | quiet(X0)))) [nnf transformation 11]
54. ! [X0] : (((kind(X0) & ~quiet(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) & (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | ~kind(X0) | quiet(X0))) [flattening 53]
68. ~brave(X0) | kind(X0) [cnf transformation 37]
81. quiet(X0) | patient(X0) | brave(X0) [cnf transformation 45]
84. ~quiet(X0) | brave(X0) | ~patient(X0) [cnf transformation 45]
93. patient(X0) | quiet(X0) | ~kind(X0) | quiet(X0) [cnf transformation 54]
95. ~quiet(X0) | patient(X0) | ~quiet(X0) [cnf transformation 54]
97. ~quiet(X0) | patient(X0) | kind(X0) [cnf transformation 54]
98. ~patient(X0) | quiet(X0) | kind(X0) [cnf transformation 54]
110. ~kind(X0) | generous(X0) [cnf transformation 30]
123. ~generous(susan) [cnf transformation 24]
124. patient(X0) | quiet(X0) | ~kind(X0) [duplicate literal removal 93]
125. ~quiet(X0) | patient(X0) [duplicate literal removal 95]
201. ~kind(X0) | patient(X0) [subsumption resolution 124,125]
337. patient(X0) | brave(X0) | patient(X0) [resolution 81,125]
338. patient(X0) | brave(X0) [duplicate literal removal 337]
399. brave(X0) | quiet(X0) | kind(X0) [resolution 338,98]
401. quiet(X0) | kind(X0) [subsumption resolution 399,68]
413. kind(X0) | patient(X0) | kind(X0) [resolution 401,97]
414. kind(X1) | brave(X1) | ~patient(X1) [resolution 401,84]
417. kind(X0) | patient(X0) [duplicate literal removal 413]
418. patient(X0) [subsumption resolution 417,201]
419. kind(X1) | brave(X1) [subsumption resolution 414,418]
420. kind(X1) [subsumption resolution 419,68]
432. generous(X1) [resolution 420,110]
466. $false [resolution 432,123]
% SZS output end Proof for 5359198843143486579888593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise then someone is not tall or rich.
Everyone who is creative is both not tall and not brave.
If someone is both not wise and funny then someone is both not strong and not old.
Everyone who is both not kind and happy is not strong and vice versa.
Everyone who is not generous is both not old and not strong and vice versa.
If fred is brave then mary is patient or not generous and vice versa.
If john is both not wise and rich then alice is either calm or kind.
If someone is both creative and not old then someone is humble or not tall.
Everyone who is either humble or not calm is not strong or not tall.
Everyone who is both humble and not tall is not generous and vice versa.
Everyone who is not creative or not patient is both strong and tall and vice versa.
Everyone who is both strong and calm is either not strong or not tall and vice versa.
If someone is not calm or calm then someone is either curious or rich and vice versa.
Everyone who is not creative is either kind or not kind.
Everyone who is both curious and rich is both not humble and humble and vice versa.
Everyone who is both not strong and brave is patient or funny and vice versa.
Lucy is not calm.
Someone is both kind and rich.
Someone is either happy or quiet.
Mary is not funny or not old.
Someone is old or not generous. | Mary is not old. | neutral | ((?[X]:(wise(X)))=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:(creative(X)=>(~tall(X)&~brave(X))))&
((?[X]:((~wise(X)&funny(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:((~kind(X)&happy(X))<=>~strong(X)))&
(![X]:(~generous(X)<=>(~old(X)&~strong(X))))&
((brave(fred))<=>((patient(mary)|~generous(mary))))&
(((~wise(john)&rich(john)))=>((calm(alice)<~>kind(alice))))&
((?[X]:((creative(X)&~old(X))))=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((humble(X)<~>~calm(X))=>(~strong(X)|~tall(X))))&
(![X]:((humble(X)&~tall(X))<=>~generous(X)))&
(![X]:((~creative(X)|~patient(X))<=>(strong(X)&tall(X))))&
(![X]:((strong(X)&calm(X))<=>(~strong(X)<~>~tall(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:(~creative(X)=>(kind(X)<~>~kind(X))))&
(![X]:((curious(X)&rich(X))<=>(~humble(X)&humble(X))))&
(![X]:((~strong(X)&brave(X))<=>(patient(X)|funny(X))))&
(~calm(lucy))&
(?[X]:((kind(X)&rich(X))))&
(?[X]:((happy(X)<~>quiet(X))))&
((~funny(mary)|~old(mary)))&
(?[X]:((old(X)|~generous(X)))) | ~old(mary) | [] | null | 0 |
Everyone who is strong is either kind or not generous and vice versa. Everyone who is not brave is not creative and vice versa. Everyone who is either not calm or happy is brave and vice versa. If mary is not patient or not creative then someone is both not curious and not humble. If alice is not brave or not funny then lucy is either not patient or curious. Everyone who is creative or funny is both humble and strong and vice versa. Everyone who is brave or not curious is both tall and not curious and vice versa. If someone is calm then someone is both not curious and not calm. If someone is both wise and generous then someone is either happy or not strong. Everyone who is humble is either not patient or wise. If someone is not kind then susan is both tall and not funny and vice versa. Everyone who is either strong or not brave is kind. If someone is happy then lucy is humble or not creative. If mary is not brave or not funny then fred is either happy or wise and vice versa. If someone is either wise or not funny then susan is not humble or not curious. If someone is brave then susan is both old and not quiet and vice versa. Susan is not kind. Someone is both not brave and kind. Someone is both happy and not calm. Someone is both not generous and not calm. Someone is both not old and not patient. John is generous. Someone is either not funny or not curious. John is not calm. | Susan is not creative. | entailment | (![X]:(strong(X)<=>(kind(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((~calm(X)<~>happy(X))<=>brave(X)))&
(((~patient(mary)|~creative(mary)))=>(?[X]:((~curious(X)&~humble(X)))))&
(((~brave(alice)|~funny(alice)))=>((~patient(lucy)<~>curious(lucy))))&
(![X]:((creative(X)|funny(X))<=>(humble(X)&strong(X))))&
(![X]:((brave(X)|~curious(X))<=>(tall(X)&~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(humble(X)=>(~patient(X)<~>wise(X))))&
((?[X]:(~kind(X)))<=>((tall(susan)&~funny(susan))))&
(![X]:((strong(X)<~>~brave(X))=>kind(X)))&
((?[X]:(happy(X)))=>((humble(lucy)|~creative(lucy))))&
(((~brave(mary)|~funny(mary)))<=>((happy(fred)<~>wise(fred))))&
((?[X]:((wise(X)<~>~funny(X))))=>((~humble(susan)|~curious(susan))))&
((?[X]:(brave(X)))<=>((old(susan)&~quiet(susan))))&
(~kind(susan))&
(?[X]:((~brave(X)&kind(X))))&
(?[X]:((happy(X)&~calm(X))))&
(?[X]:((~generous(X)&~calm(X))))&
(?[X]:((~old(X)&~patient(X))))&
(generous(john))&
(?[X]:((~funny(X)<~>~curious(X))))&
(~calm(john)) | ~creative(susan) | [
"p1",
"p5",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 541861977778458195570389
% SZS output start Proof for 541861977778458195570389
2. ! [X0] : (~brave(X0) <=> ~creative(X0)) [input p1]
6. ! [X0] : ((funny(X0) | creative(X0)) <=> (strong(X0) & humble(X0))) [input p5]
12. ! [X0] : ((strong(X0) <~> ~brave(X0)) => kind(X0)) [input p11]
17. ~kind(susan) [input p16]
25. creative(susan) [input hypothesis]
33. ! [X0] : (kind(X0) | (strong(X0) <=> ~brave(X0))) [ennf transformation 12]
39. ! [X0] : ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))) [nnf transformation 2]
44. ! [X0] : (((funny(X0) | creative(X0)) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | (~funny(X0) & ~creative(X0)))) [nnf transformation 6]
45. ! [X0] : ((funny(X0) | creative(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | (~funny(X0) & ~creative(X0)))) [flattening 44]
61. ! [X0] : (kind(X0) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) [nnf transformation 33]
85. ~creative(X0) | brave(X0) [cnf transformation 39]
101. ~creative(X0) | strong(X0) [cnf transformation 45]
118. ~brave(X0) | kind(X0) | ~strong(X0) [cnf transformation 61]
132. ~kind(susan) [cnf transformation 17]
145. creative(susan) [cnf transformation 25]
296. brave(susan) [resolution 85,145]
306. strong(susan) [resolution 101,145]
416. kind(susan) | ~strong(susan) [resolution 118,296]
418. ~strong(susan) [subsumption resolution 416,132]
419. $false [subsumption resolution 418,306]
% SZS output end Proof for 541861977778458195570389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or humble then mary is either kind or curious and vice versa.
If mary is quiet then lucy is generous.
Everyone who is either not strong or brave is either patient or quiet and vice versa.
If someone is not creative then someone is not curious.
Everyone who is both humble and not rich is not patient.
If someone is rich or funny then alice is not strong or generous and vice versa.
If someone is both patient and brave then alice is calm and vice versa.
Everyone who is kind is not creative and vice versa.
Everyone who is either strong or humble is not calm and vice versa.
Everyone who is both not patient and kind is both not funny and old.
If lucy is funny then someone is either not old or not calm and vice versa.
Everyone who is not quiet or not creative is both strong and humble.
If paul is humble then susan is not generous and vice versa.
Everyone who is not wise is either not wise or not kind and vice versa.
Everyone who is either wise or tall is both creative and not funny.
Everyone who is humble is either not patient or rich.
Lucy is not quiet or not humble.
Paul is not humble or rich.
Someone is both not curious and happy.
Susan is either not rich or kind.
Fred is both not creative and humble.
John is either brave or calm. | John is not brave. | entailment | ((?[X]:((~old(X)|humble(X))))<=>((kind(mary)<~>curious(mary))))&
((quiet(mary))=>(generous(lucy)))&
(![X]:((~strong(X)<~>brave(X))<=>(patient(X)<~>quiet(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~curious(X))))&
(![X]:((humble(X)&~rich(X))=>~patient(X)))&
((?[X]:((rich(X)|funny(X))))<=>((~strong(alice)|generous(alice))))&
((?[X]:((patient(X)&brave(X))))<=>(calm(alice)))&
(![X]:(kind(X)<=>~creative(X)))&
(![X]:((strong(X)<~>humble(X))<=>~calm(X)))&
(![X]:((~patient(X)&kind(X))=>(~funny(X)&old(X))))&
((funny(lucy))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:((~quiet(X)|~creative(X))=>(strong(X)&humble(X))))&
((humble(paul))<=>(~generous(susan)))&
(![X]:(~wise(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((wise(X)<~>tall(X))=>(creative(X)&~funny(X))))&
(![X]:(humble(X)=>(~patient(X)<~>rich(X))))&
((~quiet(lucy)|~humble(lucy)))&
((~humble(paul)|rich(paul)))&
(?[X]:((~curious(X)&happy(X))))&
((~rich(susan)<~>kind(susan)))&
((~creative(fred)&humble(fred)))&
((brave(john)<~>calm(john))) | ~brave(john) | [
"p7",
"p8",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 552761658018157525319452
% SZS output start Proof for 552761658018157525319452
8. ! [X0] : (kind(X0) <=> ~creative(X0)) [input p7]
9. ! [X0] : ((strong(X0) <~> humble(X0)) <=> ~calm(X0)) [input p8]
12. ! [X0] : ((~creative(X0) | ~quiet(X0)) => (humble(X0) & strong(X0))) [input p11]
14. ! [X0] : (~wise(X0) <=> (~wise(X0) <~> ~kind(X0))) [input p13]
22. brave(john) <~> calm(john) [input p21]
23. brave(john) [input hypothesis]
32. ! [X0] : ((humble(X0) & strong(X0)) | (creative(X0) & quiet(X0))) [ennf transformation 12]
52. ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))) [nnf transformation 8]
53. ! [X0] : ((((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | calm(X0)) & (~calm(X0) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))))) [nnf transformation 9]
59. ! [X0] : ((~wise(X0) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0)))) & (((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | wise(X0))) [nnf transformation 14]
65. (~calm(john) | ~brave(john)) & (calm(john) | brave(john)) [nnf transformation 22]
90. ~creative(X0) | ~kind(X0) [cnf transformation 52]
95. ~strong(X0) | ~humble(X0) | calm(X0) [cnf transformation 53]
103. creative(X0) | strong(X0) [cnf transformation 32]
105. creative(X0) | humble(X0) [cnf transformation 32]
109. kind(X0) | wise(X0) | wise(X0) [cnf transformation 59]
111. ~wise(X0) | ~wise(X0) | kind(X0) [cnf transformation 59]
126. ~calm(john) | ~brave(john) [cnf transformation 65]
127. brave(john) [cnf transformation 23]
128. kind(X0) | wise(X0) [duplicate literal removal 109]
129. ~wise(X0) | kind(X0) [duplicate literal removal 111]
251. kind(X0) [subsumption resolution 128,129]
268. 31 <=> brave(john) [avatar definition]
272. 32 <=> calm(john) [avatar definition]
274. ~calm(john) <- (~32) [avatar component clause 272]
275. ~31 | ~32 [avatar split clause 126,272,268]
277. 31 [avatar split clause 127,268]
282. strong(X0) | ~kind(X0) [resolution 103,90]
283. strong(X0) [subsumption resolution 282,251]
288. humble(X0) | ~kind(X0) [resolution 105,90]
289. humble(X0) [subsumption resolution 288,251]
309. ~humble(X0) | calm(X0) [resolution 95,283]
312. calm(X0) [subsumption resolution 309,289]
313. $false <- (~32) [resolution 312,274]
317. 32 [avatar contradiction clause 313]
319. $false [avatar sat refutation 275,277,317]
% SZS output end Proof for 552761658018157525319452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is either not creative or tall.
Everyone who is both not strong and generous is both creative and quiet.
Everyone who is both not tall and kind is both not curious and not rich.
Everyone who is not strong is humble or curious.
If someone is not old or not tall then john is either not generous or not curious.
If someone is both creative and rich then susan is both old and kind.
Everyone who is humble is either not brave or not rich and vice versa.
Everyone who is generous or not funny is not old and vice versa.
If someone is rich or kind then alice is both curious and humble.
Everyone who is strong is both rich and not old and vice versa.
If susan is not curious or brave then someone is both wise and not quiet.
Everyone who is either not humble or rich is patient or wise.
If someone is both quiet and not tall then someone is kind and vice versa.
If paul is creative or not quiet then someone is wise or calm and vice versa.
If someone is both not brave and not patient then john is both generous and not generous.
Everyone who is not funny is generous or not funny.
Paul is funny or kind.
Alice is both curious and happy.
Lucy is wise.
Someone is not calm or not strong.
Someone is either happy or not kind.
Someone is both not creative and tall.
Mary is both quiet and brave.
Susan is not old. | John is not brave. | neutral | (![X]:(strong(X)=>(~creative(X)<~>tall(X))))&
(![X]:((~strong(X)&generous(X))=>(creative(X)&quiet(X))))&
(![X]:((~tall(X)&kind(X))=>(~curious(X)&~rich(X))))&
(![X]:(~strong(X)=>(humble(X)|curious(X))))&
((?[X]:((~old(X)|~tall(X))))=>((~generous(john)<~>~curious(john))))&
((?[X]:((creative(X)&rich(X))))=>((old(susan)&kind(susan))))&
(![X]:(humble(X)<=>(~brave(X)<~>~rich(X))))&
(![X]:((generous(X)|~funny(X))<=>~old(X)))&
((?[X]:((rich(X)|kind(X))))=>((curious(alice)&humble(alice))))&
(![X]:(strong(X)<=>(rich(X)&~old(X))))&
(((~curious(susan)|brave(susan)))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:((~humble(X)<~>rich(X))=>(patient(X)|wise(X))))&
((?[X]:((quiet(X)&~tall(X))))<=>(?[X]:(kind(X))))&
(((creative(paul)|~quiet(paul)))<=>(?[X]:((wise(X)|calm(X)))))&
((?[X]:((~brave(X)&~patient(X))))=>((generous(john)&~generous(john))))&
(![X]:(~funny(X)=>(generous(X)|~funny(X))))&
((funny(paul)|kind(paul)))&
((curious(alice)&happy(alice)))&
(wise(lucy))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:((happy(X)<~>~kind(X))))&
(?[X]:((~creative(X)&tall(X))))&
((quiet(mary)&brave(mary)))&
(~old(susan)) | ~brave(john) | [] | null | 0 |
Everyone who is not tall or humble is not generous and vice versa. Everyone who is not kind is patient or not quiet and vice versa. If someone is not generous then fred is either not patient or not kind and vice versa. If someone is not generous then paul is both calm and not tall. Everyone who is not old is calm or not rich and vice versa. If someone is not patient then alice is creative or not funny and vice versa. If someone is either old or creative then fred is old. Everyone who is both humble and wise is curious or creative and vice versa. Everyone who is funny is not tall or not rich and vice versa. Everyone who is not wise or not patient is both generous and kind. If susan is either happy or not creative then someone is generous. If paul is creative then someone is patient or not wise. If someone is kind then someone is brave. If someone is brave then someone is either not strong or not kind. Everyone who is not patient or not wise is not generous. If paul is both not strong and not curious then john is not rich or rich and vice versa. Alice is either rich or patient. Someone is either calm or not generous. Paul is either not quiet or patient. Fred is not happy or kind. Someone is both funny and not rich. John is either creative or not happy. Someone is either not quiet or not brave. | Paul is quiet. | entailment | (![X]:((~tall(X)|humble(X))<=>~generous(X)))&
(![X]:(~kind(X)<=>(patient(X)|~quiet(X))))&
((?[X]:(~generous(X)))<=>((~patient(fred)<~>~kind(fred))))&
((?[X]:(~generous(X)))=>((calm(paul)&~tall(paul))))&
(![X]:(~old(X)<=>(calm(X)|~rich(X))))&
((?[X]:(~patient(X)))<=>((creative(alice)|~funny(alice))))&
((?[X]:((old(X)<~>creative(X))))=>(old(fred)))&
(![X]:((humble(X)&wise(X))<=>(curious(X)|creative(X))))&
(![X]:(funny(X)<=>(~tall(X)|~rich(X))))&
(![X]:((~wise(X)|~patient(X))=>(generous(X)&kind(X))))&
(((happy(susan)<~>~creative(susan)))=>(?[X]:(generous(X))))&
((creative(paul))=>(?[X]:((patient(X)|~wise(X)))))&
((?[X]:(kind(X)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~wise(X))=>~generous(X)))&
(((~strong(paul)&~curious(paul)))<=>((~rich(john)|rich(john))))&
((rich(alice)<~>patient(alice)))&
(?[X]:((calm(X)<~>~generous(X))))&
((~quiet(paul)<~>patient(paul)))&
((~happy(fred)|kind(fred)))&
(?[X]:((funny(X)&~rich(X))))&
((creative(john)<~>~happy(john)))&
(?[X]:((~quiet(X)<~>~brave(X)))) | quiet(paul) | [
"p9",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 285830968762874329630916
% SZS output start Proof for 285830968762874329630916
10. ! [X0] : ((~patient(X0) | ~wise(X0)) => (kind(X0) & generous(X0))) [input p9]
15. ! [X0] : ((~wise(X0) | ~patient(X0)) => ~generous(X0)) [input p14]
19. ~quiet(paul) <~> patient(paul) [input p18]
24. ~quiet(paul) [input hypothesis]
29. ! [X0] : ((kind(X0) & generous(X0)) | (patient(X0) & wise(X0))) [ennf transformation 10]
34. ! [X0] : (~generous(X0) | (wise(X0) & patient(X0))) [ennf transformation 15]
73. (~patient(paul) | quiet(paul)) & (patient(paul) | ~quiet(paul)) [nnf transformation 19]
109. generous(X0) | patient(X0) [cnf transformation 29]
118. ~generous(X0) | patient(X0) [cnf transformation 34]
130. ~patient(paul) | quiet(paul) [cnf transformation 73]
138. ~quiet(paul) [cnf transformation 24]
184. 10 <=> ! [X1] : patient(X1) [avatar definition]
185. patient(X1) <- (10) [avatar component clause 184]
248. patient(X0) [subsumption resolution 118,109]
249. 10 [avatar split clause 248,184]
287. 32 <=> quiet(paul) [avatar definition]
291. 33 <=> patient(paul) [avatar definition]
293. ~patient(paul) <- (~33) [avatar component clause 291]
294. 32 | ~33 [avatar split clause 130,291,287]
321. ~32 [avatar split clause 138,287]
332. $false <- (10, ~33) [resolution 293,185]
333. ~10 | 33 [avatar contradiction clause 332]
334. $false [avatar sat refutation 249,294,321,333]
% SZS output end Proof for 285830968762874329630916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both not kind and not rich then mary is either creative or kind and vice versa.
If someone is either not curious or patient then someone is not old and vice versa.
If mary is both humble and calm then someone is not kind.
Everyone who is not curious is not kind and vice versa.
Everyone who is not patient or not curious is both curious and funny.
Everyone who is curious or old is both kind and not funny and vice versa.
If john is not brave then someone is tall or brave.
If paul is patient or not tall then fred is not quiet.
If someone is either tall or wise then someone is not strong and vice versa.
If paul is strong or not old then someone is either not creative or not brave.
Everyone who is both old and happy is both not wise and curious and vice versa.
Everyone who is both not curious and humble is either tall or humble.
Everyone who is humble or not brave is both patient and quiet.
Everyone who is either curious or tall is not patient.
Everyone who is either not old or not generous is either not old or not humble.
Mary is not generous or not kind.
John is creative.
Susan is both generous and curious.
Paul is either not old or kind.
Someone is both not wise and not brave.
Fred is both generous and patient.
Susan is old or not generous. | Mary is not tall. | contradiction | (((~kind(john)&~rich(john)))<=>((creative(mary)<~>kind(mary))))&
((?[X]:((~curious(X)<~>patient(X))))<=>(?[X]:(~old(X))))&
(((humble(mary)&calm(mary)))=>(?[X]:(~kind(X))))&
(![X]:(~curious(X)<=>~kind(X)))&
(![X]:((~patient(X)|~curious(X))=>(curious(X)&funny(X))))&
(![X]:((curious(X)|old(X))<=>(kind(X)&~funny(X))))&
((~brave(john))=>(?[X]:((tall(X)|brave(X)))))&
(((patient(paul)|~tall(paul)))=>(~quiet(fred)))&
((?[X]:((tall(X)<~>wise(X))))<=>(?[X]:(~strong(X))))&
(((strong(paul)|~old(paul)))=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((old(X)&happy(X))<=>(~wise(X)&curious(X))))&
(![X]:((~curious(X)&humble(X))=>(tall(X)<~>humble(X))))&
(![X]:((humble(X)|~brave(X))=>(patient(X)&quiet(X))))&
(![X]:((curious(X)<~>tall(X))=>~patient(X)))&
(![X]:((~old(X)<~>~generous(X))=>(~old(X)<~>~humble(X))))&
((~generous(mary)|~kind(mary)))&
(creative(john))&
((generous(susan)&curious(susan)))&
((~old(paul)<~>kind(paul)))&
(?[X]:((~wise(X)&~brave(X))))&
((generous(fred)&patient(fred)))&
((old(susan)|~generous(susan))) | ~tall(mary) | [
"p4",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 270683207946326002575533
% SZS output start Proof for 270683207946326002575533
5. ! [X0] : ((~curious(X0) | ~patient(X0)) => (funny(X0) & curious(X0))) [input p4]
6. ! [X0] : ((old(X0) | curious(X0)) <=> (~funny(X0) & kind(X0))) [input p5]
14. ! [X0] : ((curious(X0) <~> tall(X0)) => ~patient(X0)) [input p13]
23. ~tall(mary) [input hypothesis]
27. ! [X0] : ((funny(X0) & curious(X0)) | (curious(X0) & patient(X0))) [ennf transformation 5]
34. ! [X0] : (~patient(X0) | (curious(X0) <=> tall(X0))) [ennf transformation 14]
44. ! [X0] : (((old(X0) | curious(X0)) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | (~old(X0) & ~curious(X0)))) [nnf transformation 6]
45. ! [X0] : ((old(X0) | curious(X0) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | (~old(X0) & ~curious(X0)))) [flattening 44]
59. ! [X0] : (~patient(X0) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) [nnf transformation 34]
77. curious(X0) | curious(X0) [cnf transformation 27]
78. funny(X0) | patient(X0) [cnf transformation 27]
82. ~funny(X0) | ~curious(X0) [cnf transformation 45]
106. ~patient(X0) | tall(X0) | ~curious(X0) [cnf transformation 59]
123. ~tall(mary) [cnf transformation 23]
127. curious(X0) [duplicate literal removal 77]
175. ~funny(X0) [subsumption resolution 82,127]
250. ~patient(X0) | tall(X0) [subsumption resolution 106,127]
277. patient(X0) [resolution 78,175]
290. tall(X0) [resolution 250,277]
314. $false [resolution 290,123]
% SZS output end Proof for 270683207946326002575533
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is not generous or not old and vice versa.
If someone is not wise or calm then alice is rich or creative.
Everyone who is both not funny and happy is both strong and brave and vice versa.
If alice is not curious or calm then someone is not curious or not happy.
Everyone who is both not happy and happy is humble or old and vice versa.
Everyone who is patient is calm or kind and vice versa.
If paul is both not creative and wise then someone is either humble or not generous.
If lucy is either not generous or happy then lucy is patient and vice versa.
Everyone who is patient or generous is either strong or brave and vice versa.
If mary is happy or not strong then someone is not calm.
If someone is both rich and not humble then someone is generous or brave.
Everyone who is both not wise and not creative is either not patient or humble and vice versa.
Everyone who is both old and brave is curious or creative and vice versa.
Everyone who is both not humble and not kind is either rich or not curious.
If lucy is not strong or not generous then alice is not tall.
Someone is not strong.
Lucy is not funny or not wise.
Someone is either not wise or rich.
Someone is both not happy and wise.
Susan is either strong or calm.
Paul is not humble.
Someone is not brave or not happy. | Susan is wise. | entailment | (![X]:(~strong(X)<=>(~generous(X)|~old(X))))&
((?[X]:((~wise(X)|calm(X))))=>((rich(alice)|creative(alice))))&
(![X]:((~funny(X)&happy(X))<=>(strong(X)&brave(X))))&
(((~curious(alice)|calm(alice)))=>(?[X]:((~curious(X)|~happy(X)))))&
(![X]:((~happy(X)&happy(X))<=>(humble(X)|old(X))))&
(![X]:(patient(X)<=>(calm(X)|kind(X))))&
(((~creative(paul)&wise(paul)))=>(?[X]:((humble(X)<~>~generous(X)))))&
(((~generous(lucy)<~>happy(lucy)))<=>(patient(lucy)))&
(![X]:((patient(X)|generous(X))<=>(strong(X)<~>brave(X))))&
(((happy(mary)|~strong(mary)))=>(?[X]:(~calm(X))))&
((?[X]:((rich(X)&~humble(X))))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~wise(X)&~creative(X))<=>(~patient(X)<~>humble(X))))&
(![X]:((old(X)&brave(X))<=>(curious(X)|creative(X))))&
(![X]:((~humble(X)&~kind(X))=>(rich(X)<~>~curious(X))))&
(((~strong(lucy)|~generous(lucy)))=>(~tall(alice)))&
(?[X]:(~strong(X)))&
((~funny(lucy)|~wise(lucy)))&
(?[X]:((~wise(X)<~>rich(X))))&
(?[X]:((~happy(X)&wise(X))))&
((strong(susan)<~>calm(susan)))&
(~humble(paul))&
(?[X]:((~brave(X)|~happy(X)))) | wise(susan) | [
"p0",
"p4",
"p5",
"p11",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8807821186008725924597297
% SZS output start Proof for 8807821186008725924597297
1. ! [X0] : (~strong(X0) <=> (~old(X0) | ~generous(X0))) [input p0]
5. ! [X0] : ((happy(X0) & ~happy(X0)) <=> (old(X0) | humble(X0))) [input p4]
6. ! [X0] : (patient(X0) <=> (kind(X0) | calm(X0))) [input p5]
12. ! [X0] : ((~creative(X0) & ~wise(X0)) <=> (~patient(X0) <~> humble(X0))) [input p11]
13. ! [X0] : ((brave(X0) & old(X0)) <=> (creative(X0) | curious(X0))) [input p12]
20. strong(susan) <~> calm(susan) [input p19]
23. ~wise(susan) [input hypothesis]
35. ! [X0] : ((~strong(X0) | (old(X0) & generous(X0))) & ((~old(X0) | ~generous(X0)) | strong(X0))) [nnf transformation 1]
36. ! [X0] : ((~strong(X0) | (old(X0) & generous(X0))) & (~old(X0) | ~generous(X0) | strong(X0))) [flattening 35]
41. ! [X0] : (((happy(X0) & ~happy(X0)) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | (~happy(X0) | happy(X0)))) [nnf transformation 5]
42. ! [X0] : (((happy(X0) & ~happy(X0)) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | ~happy(X0) | happy(X0))) [flattening 41]
43. ! [X0] : ((patient(X0) | (~kind(X0) & ~calm(X0))) & ((kind(X0) | calm(X0)) | ~patient(X0))) [nnf transformation 6]
44. ! [X0] : ((patient(X0) | (~kind(X0) & ~calm(X0))) & (kind(X0) | calm(X0) | ~patient(X0))) [flattening 43]
56. ! [X0] : (((~creative(X0) & ~wise(X0)) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0)))) & (((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (creative(X0) | wise(X0)))) [nnf transformation 12]
57. ! [X0] : (((~creative(X0) & ~wise(X0)) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0)))) & (((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | creative(X0) | wise(X0))) [flattening 56]
58. ! [X0] : (((brave(X0) & old(X0)) | (~creative(X0) & ~curious(X0))) & ((creative(X0) | curious(X0)) | (~brave(X0) | ~old(X0)))) [nnf transformation 13]
59. ! [X0] : (((brave(X0) & old(X0)) | (~creative(X0) & ~curious(X0))) & (creative(X0) | curious(X0) | ~brave(X0) | ~old(X0))) [flattening 58]
68. (~calm(susan) | ~strong(susan)) & (calm(susan) | strong(susan)) [nnf transformation 20]
73. ~strong(X0) | old(X0) [cnf transformation 36]
83. ~happy(X0) | ~humble(X0) [cnf transformation 42]
84. ~happy(X0) | ~old(X0) [cnf transformation 42]
85. ~humble(X0) | happy(X0) [cnf transformation 42]
86. ~old(X0) | happy(X0) [cnf transformation 42]
88. ~calm(X0) | patient(X0) [cnf transformation 44]
105. humble(X0) | ~patient(X0) | creative(X0) | wise(X0) [cnf transformation 57]
113. old(X0) | ~creative(X0) [cnf transformation 59]
124. calm(susan) | strong(susan) [cnf transformation 68]
128. ~wise(susan) [cnf transformation 23]
163. ~old(X0) [subsumption resolution 84,86]
164. ~humble(X0) [subsumption resolution 83,85]
226. ~patient(X0) | creative(X0) | wise(X0) [subsumption resolution 105,164]
227. ~creative(X0) [subsumption resolution 113,163]
251. 25 <=> strong(susan) [avatar definition]
252. strong(susan) <- (25) [avatar component clause 251]
255. 26 <=> calm(susan) [avatar definition]
256. calm(susan) <- (26) [avatar component clause 255]
259. 25 | 26 [avatar split clause 124,255,251]
272. old(susan) <- (25) [resolution 73,252]
273. $false <- (25) [subsumption resolution 272,163]
274. ~25 [avatar contradiction clause 273]
275. patient(susan) <- (26) [resolution 88,256]
376. creative(susan) | wise(susan) <- (26) [resolution 226,275]
378. wise(susan) <- (26) [subsumption resolution 376,227]
379. $false <- (26) [subsumption resolution 378,128]
380. ~26 [avatar contradiction clause 379]
381. $false [avatar sat refutation 259,274,380]
% SZS output end Proof for 8807821186008725924597297
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is patient then john is either not old or happy and vice versa.
If someone is happy or wise then mary is both not generous and humble and vice versa.
Everyone who is either not quiet or not creative is either creative or not tall and vice versa.
Everyone who is either calm or generous is not old and vice versa.
Everyone who is happy is not calm.
Everyone who is both not tall and not happy is not strong or humble.
If john is either not curious or wise then lucy is both not happy and not patient.
Everyone who is not calm is either not brave or rich and vice versa.
If alice is rich then alice is creative.
Everyone who is not tall or old is either not strong or not kind.
Everyone who is kind is both happy and not humble.
Everyone who is not brave is either not curious or not quiet.
Everyone who is both calm and tall is both not calm and quiet.
If someone is generous or not wise then lucy is both happy and not calm and vice versa.
Everyone who is either funny or kind is creative and vice versa.
Everyone who is both not kind and not humble is curious or not tall and vice versa.
Fred is kind or not humble.
John is wise or not curious.
Fred is either generous or tall.
Someone is not calm or not kind.
Susan is either not old or curious.
Someone is not quiet.
Someone is not patient or calm. | Mary is generous. | contradiction | ((patient(susan))<=>((~old(john)<~>happy(john))))&
((?[X]:((happy(X)|wise(X))))<=>((~generous(mary)&humble(mary))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(creative(X)<~>~tall(X))))&
(![X]:((calm(X)<~>generous(X))<=>~old(X)))&
(![X]:(happy(X)=>~calm(X)))&
(![X]:((~tall(X)&~happy(X))=>(~strong(X)|humble(X))))&
(((~curious(john)<~>wise(john)))=>((~happy(lucy)&~patient(lucy))))&
(![X]:(~calm(X)<=>(~brave(X)<~>rich(X))))&
((rich(alice))=>(creative(alice)))&
(![X]:((~tall(X)|old(X))=>(~strong(X)<~>~kind(X))))&
(![X]:(kind(X)=>(happy(X)&~humble(X))))&
(![X]:(~brave(X)=>(~curious(X)<~>~quiet(X))))&
(![X]:((calm(X)&tall(X))=>(~calm(X)&quiet(X))))&
((?[X]:((generous(X)|~wise(X))))<=>((happy(lucy)&~calm(lucy))))&
(![X]:((funny(X)<~>kind(X))<=>creative(X)))&
(![X]:((~kind(X)&~humble(X))<=>(curious(X)|~tall(X))))&
((kind(fred)|~humble(fred)))&
((wise(john)|~curious(john)))&
((generous(fred)<~>tall(fred)))&
(?[X]:((~calm(X)|~kind(X))))&
((~old(susan)<~>curious(susan)))&
(?[X]:(~quiet(X)))&
(?[X]:((~patient(X)|calm(X)))) | generous(mary) | [
"p1",
"p6",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 555626828205233306416958
% SZS output start Proof for 555626828205233306416958
2. ? [X0] : (wise(X0) | happy(X0)) <=> (humble(mary) & ~generous(mary)) [input p1]
7. (~curious(john) <~> wise(john)) => (~patient(lucy) & ~happy(lucy)) [input p6]
14. ? [X0] : (~wise(X0) | generous(X0)) <=> (~calm(lucy) & happy(lucy)) [input p13]
18. ~curious(john) | wise(john) [input p17]
24. generous(mary) [input hypothesis]
28. (~patient(lucy) & ~happy(lucy)) | (~curious(john) <=> wise(john)) [ennf transformation 7]
36. (? [X0] : (wise(X0) | happy(X0)) | (~humble(mary) | generous(mary))) & ((humble(mary) & ~generous(mary)) | ! [X0] : (~wise(X0) & ~happy(X0))) [nnf transformation 2]
37. (? [X0] : (wise(X0) | happy(X0)) | ~humble(mary) | generous(mary)) & ((humble(mary) & ~generous(mary)) | ! [X0] : (~wise(X0) & ~happy(X0))) [flattening 36]
38. (? [X0] : (wise(X0) | happy(X0)) | ~humble(mary) | generous(mary)) & ((humble(mary) & ~generous(mary)) | ! [X1] : (~wise(X1) & ~happy(X1))) [rectify 37]
39. ? [X0] : (wise(X0) | happy(X0)) => (wise(sK0) | happy(sK0)) [choice axiom]
40. ((wise(sK0) | happy(sK0)) | ~humble(mary) | generous(mary)) & ((humble(mary) & ~generous(mary)) | ! [X1] : (~wise(X1) & ~happy(X1))) [skolemisation 38,39]
43. (~patient(lucy) & ~happy(lucy)) | ((~curious(john) | ~wise(john)) & (wise(john) | curious(john))) [nnf transformation 28]
47. (? [X0] : (~wise(X0) | generous(X0)) | (calm(lucy) | ~happy(lucy))) & ((~calm(lucy) & happy(lucy)) | ! [X0] : (wise(X0) & ~generous(X0))) [nnf transformation 14]
48. (? [X0] : (~wise(X0) | generous(X0)) | calm(lucy) | ~happy(lucy)) & ((~calm(lucy) & happy(lucy)) | ! [X0] : (wise(X0) & ~generous(X0))) [flattening 47]
49. (? [X0] : (~wise(X0) | generous(X0)) | calm(lucy) | ~happy(lucy)) & ((~calm(lucy) & happy(lucy)) | ! [X1] : (wise(X1) & ~generous(X1))) [rectify 48]
50. ? [X0] : (~wise(X0) | generous(X0)) => (~wise(sK1) | generous(sK1)) [choice axiom]
51. ((~wise(sK1) | generous(sK1)) | calm(lucy) | ~happy(lucy)) & ((~calm(lucy) & happy(lucy)) | ! [X1] : (wise(X1) & ~generous(X1))) [skolemisation 49,50]
68. ~generous(mary) | ~wise(X1) [cnf transformation 40]
86. ~happy(lucy) | wise(john) | curious(john) [cnf transformation 43]
106. happy(lucy) | wise(X1) [cnf transformation 51]
120. ~curious(john) | wise(john) [cnf transformation 18]
128. generous(mary) [cnf transformation 24]
151. 4 <=> generous(mary) [avatar definition]
168. 8 <=> ! [X1] : ~wise(X1) [avatar definition]
169. ~wise(X1) <- (8) [avatar component clause 168]
175. 8 | ~4 [avatar split clause 68,151,168]
180. 10 <=> wise(john) [avatar definition]
181. wise(john) <- (10) [avatar component clause 180]
184. 11 <=> curious(john) [avatar definition]
194. 13 <=> happy(lucy) [avatar definition]
198. 11 | 10 | ~13 [avatar split clause 86,194,180,184]
220. 18 <=> ! [X1] : wise(X1) [avatar definition]
221. wise(X1) <- (18) [avatar component clause 220]
231. 18 | 13 [avatar split clause 106,194,220]
234. 10 | ~11 [avatar split clause 120,184,180]
273. 4 [avatar split clause 128,151]
274. $false <- (8, 10) [resolution 181,169]
275. ~8 | ~10 [avatar contradiction clause 274]
276. $false <- (8, 18) [subsumption resolution 221,169]
277. ~8 | ~18 [avatar contradiction clause 276]
278. $false [avatar sat refutation 175,198,231,234,273,275,277]
% SZS output end Proof for 555626828205233306416958
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or creative is not quiet or quiet and vice versa. Everyone who is not rich is happy and vice versa. Everyone who is either not happy or not humble is both not kind and not creative. Everyone who is either not calm or tall is both creative and calm and vice versa. Everyone who is either not wise or not generous is either old or not brave and vice versa. Everyone who is both not curious and brave is kind and vice versa. Everyone who is not curious is either not wise or not generous. Everyone who is both not brave and tall is creative or strong. Everyone who is either patient or kind is funny or not brave. If john is both not happy and not brave then someone is not patient or not wise. If lucy is not rich or creative then lucy is rich or not old and vice versa. Everyone who is both calm and tall is both not calm and strong and vice versa. Everyone who is not patient or creative is tall or not strong and vice versa. If john is both not calm and curious then someone is either not creative or not strong and vice versa. Everyone who is curious or calm is not creative and vice versa. Everyone who is curious is either not funny or calm and vice versa. Fred is not kind. Someone is calm or not strong. Someone is not creative. Someone is both not old and not humble. Paul is either not generous or not wise. Someone is both not rich and not quiet. Someone is funny or not calm. | Paul is not patient. | neutral | (![X]:((old(X)|creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~rich(X)<=>happy(X)))&
(![X]:((~happy(X)<~>~humble(X))=>(~kind(X)&~creative(X))))&
(![X]:((~calm(X)<~>tall(X))<=>(creative(X)&calm(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>(old(X)<~>~brave(X))))&
(![X]:((~curious(X)&brave(X))<=>kind(X)))&
(![X]:(~curious(X)=>(~wise(X)<~>~generous(X))))&
(![X]:((~brave(X)&tall(X))=>(creative(X)|strong(X))))&
(![X]:((patient(X)<~>kind(X))=>(funny(X)|~brave(X))))&
(((~happy(john)&~brave(john)))=>(?[X]:((~patient(X)|~wise(X)))))&
(((~rich(lucy)|creative(lucy)))<=>((rich(lucy)|~old(lucy))))&
(![X]:((calm(X)&tall(X))<=>(~calm(X)&strong(X))))&
(![X]:((~patient(X)|creative(X))<=>(tall(X)|~strong(X))))&
(((~calm(john)&curious(john)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:((curious(X)|calm(X))<=>~creative(X)))&
(![X]:(curious(X)<=>(~funny(X)<~>calm(X))))&
(~kind(fred))&
(?[X]:((calm(X)|~strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~old(X)&~humble(X))))&
((~generous(paul)<~>~wise(paul)))&
(?[X]:((~rich(X)&~quiet(X))))&
(?[X]:((funny(X)|~calm(X)))) | ~patient(paul) | [] | null | 0 |
If paul is either kind or strong then lucy is both quiet and not happy. If someone is calm then someone is strong or humble and vice versa. If someone is both calm and humble then someone is either rich or not quiet. If someone is both kind and not patient then someone is both tall and not old. If someone is not generous or generous then fred is either rich or not patient and vice versa. Everyone who is both not old and not strong is not rich or strong and vice versa. If someone is wise then john is not tall or not strong and vice versa. Everyone who is not humble is both not old and wise and vice versa. Everyone who is either not rich or creative is both calm and kind and vice versa. If susan is both calm and not humble then fred is either not old or tall and vice versa. Everyone who is not funny or happy is both funny and humble. Everyone who is curious is either not old or old. Everyone who is not brave is both not calm and not brave. Everyone who is calm or not humble is either not brave or not calm. Everyone who is both rich and not rich is either curious or happy and vice versa. If someone is not calm or calm then someone is both brave and not patient. Someone is wise. Alice is either wise or quiet. Lucy is quiet or not kind. Susan is creative or not creative. John is either not curious or generous. Fred is tall. | Alice is wise. | entailment | (((kind(paul)<~>strong(paul)))=>((quiet(lucy)&~happy(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((strong(X)|humble(X)))))&
((?[X]:((calm(X)&humble(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
((?[X]:((kind(X)&~patient(X))))=>(?[X]:((tall(X)&~old(X)))))&
((?[X]:((~generous(X)|generous(X))))<=>((rich(fred)<~>~patient(fred))))&
(![X]:((~old(X)&~strong(X))<=>(~rich(X)|strong(X))))&
((?[X]:(wise(X)))<=>((~tall(john)|~strong(john))))&
(![X]:(~humble(X)<=>(~old(X)&wise(X))))&
(![X]:((~rich(X)<~>creative(X))<=>(calm(X)&kind(X))))&
(((calm(susan)&~humble(susan)))<=>((~old(fred)<~>tall(fred))))&
(![X]:((~funny(X)|happy(X))=>(funny(X)&humble(X))))&
(![X]:(curious(X)=>(~old(X)<~>old(X))))&
(![X]:(~brave(X)=>(~calm(X)&~brave(X))))&
(![X]:((calm(X)|~humble(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((rich(X)&~rich(X))<=>(curious(X)<~>happy(X))))&
((?[X]:((~calm(X)|calm(X))))=>(?[X]:((brave(X)&~patient(X)))))&
(?[X]:(wise(X)))&
((wise(alice)<~>quiet(alice)))&
((quiet(lucy)|~kind(lucy)))&
((creative(susan)|~creative(susan)))&
((~curious(john)<~>generous(john)))&
(tall(fred)) | wise(alice) | [
"p1",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 341542083021815539128415
% SZS output start Proof for 341542083021815539128415
2. ? [X0] : calm(X0) <=> ? [X0] : (humble(X0) | strong(X0)) [input p1]
8. ! [X0] : (~humble(X0) <=> (wise(X0) & ~old(X0))) [input p7]
13. ! [X0] : (~brave(X0) => (~brave(X0) & ~calm(X0))) [input p12]
14. ! [X0] : ((~humble(X0) | calm(X0)) => (~brave(X0) <~> ~calm(X0))) [input p13]
23. ~wise(alice) [input hypothesis]
24. ? [X0] : calm(X0) <=> ? [X1] : (humble(X1) | strong(X1)) [rectify 2]
34. ! [X0] : ((~brave(X0) & ~calm(X0)) | brave(X0)) [ennf transformation 13]
35. ! [X0] : ((~brave(X0) <~> ~calm(X0)) | (humble(X0) & ~calm(X0))) [ennf transformation 14]
38. (? [X0] : calm(X0) | ! [X1] : (~humble(X1) & ~strong(X1))) & (? [X1] : (humble(X1) | strong(X1)) | ! [X0] : ~calm(X0)) [nnf transformation 24]
39. (? [X0] : calm(X0) | ! [X1] : (~humble(X1) & ~strong(X1))) & (? [X2] : (humble(X2) | strong(X2)) | ! [X3] : ~calm(X3)) [rectify 38]
40. ? [X0] : calm(X0) => calm(sK0) [choice axiom]
41. ? [X2] : (humble(X2) | strong(X2)) => (humble(sK1) | strong(sK1)) [choice axiom]
42. (calm(sK0) | ! [X1] : (~humble(X1) & ~strong(X1))) & ((humble(sK1) | strong(sK1)) | ! [X3] : ~calm(X3)) [skolemisation 39,41,40]
61. ! [X0] : ((~humble(X0) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | humble(X0))) [nnf transformation 8]
62. ! [X0] : ((~humble(X0) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | humble(X0))) [flattening 61]
68. ! [X0] : (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (humble(X0) & ~calm(X0))) [nnf transformation 35]
84. calm(sK0) | ~humble(X1) [cnf transformation 42]
104. wise(X0) | humble(X0) [cnf transformation 62]
121. ~calm(X0) | brave(X0) [cnf transformation 34]
123. ~calm(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 68]
145. ~wise(alice) [cnf transformation 23]
146. ~calm(X0) | ~brave(X0) [duplicate literal removal 123]
170. 5 <=> ! [X1] : ~humble(X1) [avatar definition]
171. ~humble(X1) <- (5) [avatar component clause 170]
173. 6 <=> calm(sK0) [avatar definition]
175. calm(sK0) <- (6) [avatar component clause 173]
176. 5 | 6 [avatar split clause 84,173,170]
182. 8 <=> ! [X3] : ~calm(X3) [avatar definition]
183. ~calm(X3) <- (8) [avatar component clause 182]
280. ~calm(X0) [subsumption resolution 146,121]
281. 8 [avatar split clause 280,182]
300. 32 <=> wise(alice) [avatar definition]
302. ~wise(alice) <- (~32) [avatar component clause 300]
325. ~32 [avatar split clause 145,300]
330. humble(alice) <- (~32) [resolution 104,302]
331. $false <- (5, ~32) [subsumption resolution 330,171]
332. ~5 | 32 [avatar contradiction clause 331]
333. $false <- (6, 8) [subsumption resolution 175,183]
334. ~6 | ~8 [avatar contradiction clause 333]
335. $false [avatar sat refutation 176,281,325,332,334]
% SZS output end Proof for 341542083021815539128415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If 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. | Lucy is not rich. | 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))) | ~rich(lucy) | [] | null | 0 |
If paul is both wise and generous then fred is both not funny and not curious.
If mary is quiet then someone is either not patient or not tall and vice versa.
Everyone who is both not happy and not brave is either not calm or old and vice versa.
If someone is both old and strong then someone is either not strong or rich and vice versa.
If alice is kind then susan is either not humble or humble and vice versa.
If someone is calm or not curious then someone is creative and vice versa.
If lucy is calm or not strong then someone is both rich and wise and vice versa.
If someone is not happy then someone is both not creative and tall and vice versa.
Everyone who is either not quiet or not calm is tall or not old.
Everyone who is not calm is both patient and not wise.
Everyone who is either not rich or happy is brave or strong and vice versa.
Everyone who is either not wise or kind is either not kind or creative and vice versa.
Everyone who is not calm is not generous.
Everyone who is either not funny or strong is both brave and old and vice versa.
If someone is not humble or old then alice is either kind or strong.
If paul is rich then alice is not calm.
Alice is either not strong or not wise.
Lucy is both not old and funny.
Someone is creative or not curious.
Someone is rich or not creative.
Alice is either not tall or not strong.
Alice is old.
Someone is either humble or curious.
Someone is rich or not generous. | Alice is rich. | entailment | (((wise(paul)&generous(paul)))=>((~funny(fred)&~curious(fred))))&
((quiet(mary))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:((~happy(X)&~brave(X))<=>(~calm(X)<~>old(X))))&
((?[X]:((old(X)&strong(X))))<=>(?[X]:((~strong(X)<~>rich(X)))))&
((kind(alice))<=>((~humble(susan)<~>humble(susan))))&
((?[X]:((calm(X)|~curious(X))))<=>(?[X]:(creative(X))))&
(((calm(lucy)|~strong(lucy)))<=>(?[X]:((rich(X)&wise(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:((~quiet(X)<~>~calm(X))=>(tall(X)|~old(X))))&
(![X]:(~calm(X)=>(patient(X)&~wise(X))))&
(![X]:((~rich(X)<~>happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(~kind(X)<~>creative(X))))&
(![X]:(~calm(X)=>~generous(X)))&
(![X]:((~funny(X)<~>strong(X))<=>(brave(X)&old(X))))&
((?[X]:((~humble(X)|old(X))))=>((kind(alice)<~>strong(alice))))&
((rich(paul))=>(~calm(alice)))&
((~strong(alice)<~>~wise(alice)))&
((~old(lucy)&funny(lucy)))&
(?[X]:((creative(X)|~curious(X))))&
(?[X]:((rich(X)|~creative(X))))&
((~tall(alice)<~>~strong(alice)))&
(old(alice))&
(?[X]:((humble(X)<~>curious(X))))&
(?[X]:((rich(X)|~generous(X)))) | rich(alice) | [
"p2",
"p4",
"p9",
"p10",
"p14",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4773173681456912399570687
% SZS output start Proof for 4773173681456912399570687
3. ! [X0] : ((~brave(X0) & ~happy(X0)) <=> (~calm(X0) <~> old(X0))) [input p2]
5. kind(alice) <=> (~humble(susan) <~> humble(susan)) [input p4]
10. ! [X0] : (~calm(X0) => (~wise(X0) & patient(X0))) [input p9]
11. ! [X0] : ((~rich(X0) <~> happy(X0)) <=> (strong(X0) | brave(X0))) [input p10]
15. ? [X0] : (old(X0) | ~humble(X0)) => (kind(alice) <~> strong(alice)) [input p14]
17. ~strong(alice) <~> ~wise(alice) [input p16]
22. old(alice) [input p21]
25. ~rich(alice) [input hypothesis]
34. ! [X0] : ((~wise(X0) & patient(X0)) | calm(X0)) [ennf transformation 10]
35. (kind(alice) <~> strong(alice)) | ! [X0] : (~old(X0) & humble(X0)) [ennf transformation 15]
41. ! [X0] : (((~brave(X0) & ~happy(X0)) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | (brave(X0) | happy(X0)))) [nnf transformation 3]
42. ! [X0] : (((~brave(X0) & ~happy(X0)) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | brave(X0) | happy(X0))) [flattening 41]
48. (kind(alice) | ((~humble(susan) | ~humble(susan)) & (humble(susan) | humble(susan)))) & (((~humble(susan) | humble(susan)) & (humble(susan) | ~humble(susan))) | ~kind(alice)) [nnf transformation 5]
65. ! [X0] : ((((~happy(X0) | rich(X0)) & (happy(X0) | ~rich(X0))) | (~strong(X0) & ~brave(X0))) & ((strong(X0) | brave(X0)) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0))))) [nnf transformation 11]
66. ! [X0] : ((((~happy(X0) | rich(X0)) & (happy(X0) | ~rich(X0))) | (~strong(X0) & ~brave(X0))) & (strong(X0) | brave(X0) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0))))) [flattening 65]
70. ((~strong(alice) | ~kind(alice)) & (strong(alice) | kind(alice))) | ! [X0] : (~old(X0) & humble(X0)) [nnf transformation 35]
71. (wise(alice) | strong(alice)) & (~wise(alice) | ~strong(alice)) [nnf transformation 17]
87. ~old(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 42]
89. ~old(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 42]
98. kind(alice) | humble(susan) | humble(susan) [cnf transformation 48]
99. kind(alice) | ~humble(susan) | ~humble(susan) [cnf transformation 48]
114. ~wise(X0) | calm(X0) [cnf transformation 34]
115. rich(X0) | brave(X0) | happy(X0) | strong(X0) [cnf transformation 66]
138. ~strong(alice) | ~kind(alice) | ~old(X0) [cnf transformation 70]
141. wise(alice) | strong(alice) [cnf transformation 71]
148. old(alice) [cnf transformation 22]
151. ~rich(alice) [cnf transformation 25]
156. kind(alice) | humble(susan) [duplicate literal removal 98]
157. kind(alice) | ~humble(susan) [duplicate literal removal 99]
212. 13 <=> humble(susan) [avatar definition]
216. 14 <=> kind(alice) [avatar definition]
219. ~13 | 14 [avatar split clause 157,216,212]
220. 13 | 14 [avatar split clause 156,216,212]
293. 31 <=> ! [X0] : ~old(X0) [avatar definition]
294. ~old(X0) <- (31) [avatar component clause 293]
296. 32 <=> strong(alice) [avatar definition]
298. ~strong(alice) <- (~32) [avatar component clause 296]
299. 31 | ~14 | ~32 [avatar split clause 138,296,216,293]
311. 35 <=> calm(alice) [avatar definition]
312. calm(alice) <- (35) [avatar component clause 311]
316. 36 <=> wise(alice) [avatar definition]
318. wise(alice) <- (36) [avatar component clause 316]
319. 32 | 36 [avatar split clause 141,316,296]
357. $false <- (31) [resolution 294,148]
358. ~31 [avatar contradiction clause 357]
360. calm(alice) <- (36) [resolution 114,318]
361. 35 | ~36 [avatar split clause 360,316,311]
377. ~calm(alice) | ~happy(alice) [resolution 87,148]
379. ~happy(alice) <- (35) [subsumption resolution 377,312]
406. ~calm(alice) | ~brave(alice) [resolution 89,148]
408. ~brave(alice) <- (35) [subsumption resolution 406,312]
573. brave(alice) | happy(alice) | strong(alice) [resolution 115,151]
590. happy(alice) | strong(alice) <- (35) [subsumption resolution 573,408]
591. strong(alice) <- (35) [subsumption resolution 590,379]
592. $false <- (~32, 35) [subsumption resolution 591,298]
593. 32 | ~35 [avatar contradiction clause 592]
596. $false [avatar sat refutation 219,220,299,319,358,361,593]
% SZS output end Proof for 4773173681456912399570687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either tall or kind then someone is either not funny or calm. If mary is not patient or strong then someone is either strong or not strong. If paul is not strong or tall then someone is both old and tall. If someone is either not curious or not old then mary is both generous and humble. Everyone who is both creative and tall is old or funny. If someone is either patient or not humble then someone is either not curious or not kind. If mary is not brave then alice is patient. If someone is not brave or not quiet then someone is not curious and vice versa. Everyone who is not funny is both generous and not wise and vice versa. If john is either not happy or not brave then susan is either not generous or not happy. If paul is either happy or humble then someone is old and vice versa. Everyone who is not strong is wise or not creative and vice versa. Everyone who is both funny and strong is strong and vice versa. If someone is both strong and generous then lucy is not brave. If someone is both old and happy then alice is happy. Everyone who is not quiet or calm is both kind and brave. John is happy. John is both old and quiet. Someone is tall. Mary is not patient or wise. Mary is not patient. Someone is either funny or quiet. Paul is either not curious or not rich. Paul is not funny. | John is happy. | entailment | (((tall(lucy)<~>kind(lucy)))=>(?[X]:((~funny(X)<~>calm(X)))))&
(((~patient(mary)|strong(mary)))=>(?[X]:((strong(X)<~>~strong(X)))))&
(((~strong(paul)|tall(paul)))=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~curious(X)<~>~old(X))))=>((generous(mary)&humble(mary))))&
(![X]:((creative(X)&tall(X))=>(old(X)|funny(X))))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((~curious(X)<~>~kind(X)))))&
((~brave(mary))=>(patient(alice)))&
((?[X]:((~brave(X)|~quiet(X))))<=>(?[X]:(~curious(X))))&
(![X]:(~funny(X)<=>(generous(X)&~wise(X))))&
(((~happy(john)<~>~brave(john)))=>((~generous(susan)<~>~happy(susan))))&
(((happy(paul)<~>humble(paul)))<=>(?[X]:(old(X))))&
(![X]:(~strong(X)<=>(wise(X)|~creative(X))))&
(![X]:((funny(X)&strong(X))<=>strong(X)))&
((?[X]:((strong(X)&generous(X))))=>(~brave(lucy)))&
((?[X]:((old(X)&happy(X))))=>(happy(alice)))&
(![X]:((~quiet(X)|calm(X))=>(kind(X)&brave(X))))&
(happy(john))&
((old(john)&quiet(john)))&
(?[X]:(tall(X)))&
((~patient(mary)|wise(mary)))&
(~patient(mary))&
(?[X]:((funny(X)<~>quiet(X))))&
((~curious(paul)<~>~rich(paul)))&
(~funny(paul)) | happy(john) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8123740975260984005320867
% SZS output start Proof for 8123740975260984005320867
17. happy(john) [input p16]
25. ~happy(john) [input hypothesis]
123. happy(john) [cnf transformation 17]
134. ~happy(john) [cnf transformation 25]
249. 26 <=> happy(john) [avatar definition]
299. 26 [avatar split clause 123,249]
330. ~26 [avatar split clause 134,249]
331. $false [avatar sat refutation 299,330]
% SZS output end Proof for 8123740975260984005320867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not happy is both not old and not brave.
Everyone who is both not strong and quiet is wise or not happy.
If lucy is either old or not tall then someone is strong and vice versa.
If alice is not brave then paul is quiet or curious and vice versa.
If someone is both not quiet and creative then mary is brave and vice versa.
Everyone who is not old is both humble and kind and vice versa.
If someone is not strong then someone is generous or old and vice versa.
Everyone who is kind or not curious is both not old and not humble and vice versa.
If someone is both quiet and strong then someone is both patient and not generous.
Everyone who is not kind is either not brave or kind and vice versa.
If someone is humble or not brave then someone is not kind and vice versa.
Everyone who is not calm is either not old or wise and vice versa.
Everyone who is both not wise and not tall is either not quiet or not brave.
Everyone who is wise or not quiet is brave or creative and vice versa.
Everyone who is not brave is both tall and not rich and vice versa.
If someone is not brave then fred is patient.
Lucy is funny.
Mary is not brave or generous.
John is both curious and patient.
Paul is either not brave or not funny.
Alice is not kind.
Lucy is patient or not brave. | Fred is tall. | entailment | (![X]:((rich(X)|~happy(X))=>(~old(X)&~brave(X))))&
(![X]:((~strong(X)&quiet(X))=>(wise(X)|~happy(X))))&
(((old(lucy)<~>~tall(lucy)))<=>(?[X]:(strong(X))))&
((~brave(alice))<=>((quiet(paul)|curious(paul))))&
((?[X]:((~quiet(X)&creative(X))))<=>(brave(mary)))&
(![X]:(~old(X)<=>(humble(X)&kind(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((generous(X)|old(X)))))&
(![X]:((kind(X)|~curious(X))<=>(~old(X)&~humble(X))))&
((?[X]:((quiet(X)&strong(X))))=>(?[X]:((patient(X)&~generous(X)))))&
(![X]:(~kind(X)<=>(~brave(X)<~>kind(X))))&
((?[X]:((humble(X)|~brave(X))))<=>(?[X]:(~kind(X))))&
(![X]:(~calm(X)<=>(~old(X)<~>wise(X))))&
(![X]:((~wise(X)&~tall(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((wise(X)|~quiet(X))<=>(brave(X)|creative(X))))&
(![X]:(~brave(X)<=>(tall(X)&~rich(X))))&
((?[X]:(~brave(X)))=>(patient(fred)))&
(funny(lucy))&
((~brave(mary)|generous(mary)))&
((curious(john)&patient(john)))&
((~brave(paul)<~>~funny(paul)))&
(~kind(alice))&
((patient(lucy)|~brave(lucy))) | tall(fred) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6101734369870585331744532
% SZS output start Proof for 6101734369870585331744532
10. ! [X0] : (~kind(X0) <=> (~brave(X0) <~> kind(X0))) [input p9]
15. ! [X0] : (~brave(X0) <=> (~rich(X0) & tall(X0))) [input p14]
23. ~tall(fred) [input hypothesis]
59. ! [X0] : ((~kind(X0) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0)))) & (((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | kind(X0))) [nnf transformation 10]
68. ! [X0] : ((~brave(X0) | (rich(X0) | ~tall(X0))) & ((~rich(X0) & tall(X0)) | brave(X0))) [nnf transformation 15]
69. ! [X0] : ((~brave(X0) | rich(X0) | ~tall(X0)) & ((~rich(X0) & tall(X0)) | brave(X0))) [flattening 68]
98. kind(X0) | ~brave(X0) | kind(X0) [cnf transformation 59]
101. ~kind(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 59]
111. tall(X0) | brave(X0) [cnf transformation 69]
120. ~tall(fred) [cnf transformation 23]
121. kind(X0) | ~brave(X0) [duplicate literal removal 98]
122. ~kind(X0) | ~brave(X0) [duplicate literal removal 101]
207. ~brave(X0) [subsumption resolution 121,122]
213. tall(X0) [subsumption resolution 111,207]
215. $false [subsumption resolution 120,213]
% SZS output end Proof for 6101734369870585331744532
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny or quiet then someone is not generous or old. If fred is both not old and not happy then john is not brave or not curious and vice versa. If someone is not brave or wise then fred is not strong or happy. If lucy is not humble or not curious then someone is calm and vice versa. Everyone who is either strong or not wise is happy or not brave. Everyone who is not quiet or not funny is either not strong or creative. Everyone who is not calm or old is not old and vice versa. If fred is both happy and not happy then someone is not quiet or rich. Everyone who is both brave and not brave is either not patient or not happy and vice versa. Everyone who is either not brave or tall is funny. Everyone who is either not happy or strong is not curious or tall. Everyone who is both not quiet and tall is either old or not happy and vice versa. If someone is not kind or not brave then john is not funny and vice versa. Everyone who is not tall is funny or brave and vice versa. Everyone who is not rich or not brave is creative. Everyone who is both not patient and wise is quiet or brave. Lucy is either not creative or not tall. Alice is not humble. Someone is not kind or not creative. Lucy is both not strong and not kind. Someone is kind. Someone is both strong and not old. | Lucy is not happy. | contradiction | (((~funny(mary)|quiet(mary)))=>(?[X]:((~generous(X)|old(X)))))&
(((~old(fred)&~happy(fred)))<=>((~brave(john)|~curious(john))))&
((?[X]:((~brave(X)|wise(X))))=>((~strong(fred)|happy(fred))))&
(((~humble(lucy)|~curious(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((strong(X)<~>~wise(X))=>(happy(X)|~brave(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~strong(X)<~>creative(X))))&
(![X]:((~calm(X)|old(X))<=>~old(X)))&
(((happy(fred)&~happy(fred)))=>(?[X]:((~quiet(X)|rich(X)))))&
(![X]:((brave(X)&~brave(X))<=>(~patient(X)<~>~happy(X))))&
(![X]:((~brave(X)<~>tall(X))=>funny(X)))&
(![X]:((~happy(X)<~>strong(X))=>(~curious(X)|tall(X))))&
(![X]:((~quiet(X)&tall(X))<=>(old(X)<~>~happy(X))))&
((?[X]:((~kind(X)|~brave(X))))<=>(~funny(john)))&
(![X]:(~tall(X)<=>(funny(X)|brave(X))))&
(![X]:((~rich(X)|~brave(X))=>creative(X)))&
(![X]:((~patient(X)&wise(X))=>(quiet(X)|brave(X))))&
((~creative(lucy)<~>~tall(lucy)))&
(~humble(alice))&
(?[X]:((~kind(X)|~creative(X))))&
((~strong(lucy)&~kind(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((strong(X)&~old(X)))) | ~happy(lucy) | [
"p6",
"p11",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 243740948057339563699854
% SZS output start Proof for 243740948057339563699854
7. ! [X0] : ((old(X0) | ~calm(X0)) <=> ~old(X0)) [input p6]
12. ! [X0] : ((tall(X0) & ~quiet(X0)) <=> (old(X0) <~> ~happy(X0))) [input p11]
14. ! [X0] : (~tall(X0) <=> (brave(X0) | funny(X0))) [input p13]
15. ! [X0] : ((~brave(X0) | ~rich(X0)) => creative(X0)) [input p14]
17. ~creative(lucy) <~> ~tall(lucy) [input p16]
23. ~happy(lucy) [input hypothesis]
25. ! [X0] : (~brave(X0) => creative(X0)) [pure predicate removal 15]
35. ! [X0] : (creative(X0) | brave(X0)) [ennf transformation 25]
47. ! [X0] : (((old(X0) | ~calm(X0)) | old(X0)) & (~old(X0) | (~old(X0) & calm(X0)))) [nnf transformation 7]
48. ! [X0] : ((old(X0) | ~calm(X0) | old(X0)) & (~old(X0) | (~old(X0) & calm(X0)))) [flattening 47]
53. ! [X0] : (((tall(X0) & ~quiet(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | (~tall(X0) | quiet(X0)))) [nnf transformation 12]
54. ! [X0] : (((tall(X0) & ~quiet(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | ~tall(X0) | quiet(X0))) [flattening 53]
59. ! [X0] : ((~tall(X0) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | tall(X0))) [nnf transformation 14]
60. ! [X0] : ((~tall(X0) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | tall(X0))) [flattening 59]
61. (tall(lucy) | creative(lucy)) & (~tall(lucy) | ~creative(lucy)) [nnf transformation 17]
85. ~old(X0) | ~old(X0) [cnf transformation 48]
102. tall(X0) | old(X0) | happy(X0) [cnf transformation 54]
108. ~tall(X0) | ~brave(X0) [cnf transformation 60]
109. creative(X0) | brave(X0) [cnf transformation 35]
111. ~tall(lucy) | ~creative(lucy) [cnf transformation 61]
120. ~happy(lucy) [cnf transformation 23]
121. ~old(X0) [duplicate literal removal 85]
176. tall(X0) | happy(X0) [subsumption resolution 102,121]
198. 16 <=> creative(lucy) [avatar definition]
199. ~creative(lucy) <- (~16) [avatar component clause 198]
202. 17 <=> tall(lucy) [avatar definition]
203. ~tall(lucy) <- (~17) [avatar component clause 202]
204. tall(lucy) <- (17) [avatar component clause 202]
206. ~16 | ~17 [avatar split clause 111,202,198]
217. happy(lucy) <- (~17) [resolution 176,203]
220. $false <- (~17) [subsumption resolution 217,120]
221. 17 [avatar contradiction clause 220]
222. brave(lucy) <- (~16) [resolution 199,109]
223. ~brave(lucy) <- (17) [resolution 204,108]
225. $false <- (~16, 17) [subsumption resolution 223,222]
226. 16 | ~17 [avatar contradiction clause 225]
227. $false [avatar sat refutation 206,221,226]
% SZS output end Proof for 243740948057339563699854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is old. If someone is humble then lucy is not quiet or not old and vice versa. If someone is not tall then lucy is both wise and not tall. If lucy is either not old or not strong then paul is not happy. If susan is wise then someone is happy or wise. Everyone who is both not old and old is kind or wise and vice versa. Everyone who is either not curious or strong is either patient or not generous and vice versa. Everyone who is either calm or generous is not calm or kind and vice versa. If someone is happy or not tall then someone is wise or not generous. Everyone who is not tall or not strong is not rich or not calm and vice versa. Everyone who is either not quiet or not tall is either funny or not brave. If lucy is patient or rich then paul is not patient. If someone is not patient or patient then john is both not funny and not wise. Everyone who is either not generous or not funny is not rich and vice versa. If someone is strong then someone is both not tall and happy and vice versa. Fred is calm or not generous. Someone is funny. Alice is humble or quiet. Someone is either funny or not quiet. Someone is either brave or funny. John is curious. Someone is either quiet or creative. | Susan is kind. | contradiction | (![X]:(kind(X)=>old(X)))&
((?[X]:(humble(X)))<=>((~quiet(lucy)|~old(lucy))))&
((?[X]:(~tall(X)))=>((wise(lucy)&~tall(lucy))))&
(((~old(lucy)<~>~strong(lucy)))=>(~happy(paul)))&
((wise(susan))=>(?[X]:((happy(X)|wise(X)))))&
(![X]:((~old(X)&old(X))<=>(kind(X)|wise(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~calm(X)|kind(X))))&
((?[X]:((happy(X)|~tall(X))))=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:((~tall(X)|~strong(X))<=>(~rich(X)|~calm(X))))&
(![X]:((~quiet(X)<~>~tall(X))=>(funny(X)<~>~brave(X))))&
(((patient(lucy)|rich(lucy)))=>(~patient(paul)))&
((?[X]:((~patient(X)|patient(X))))=>((~funny(john)&~wise(john))))&
(![X]:((~generous(X)<~>~funny(X))<=>~rich(X)))&
((?[X]:(strong(X)))<=>(?[X]:((~tall(X)&happy(X)))))&
((calm(fred)|~generous(fred)))&
(?[X]:(funny(X)))&
((humble(alice)|quiet(alice)))&
(?[X]:((funny(X)<~>~quiet(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(curious(john))&
(?[X]:((quiet(X)<~>creative(X)))) | kind(susan) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6940088984946200266510212
% SZS output start Proof for 6940088984946200266510212
1. ! [X0] : (kind(X0) => old(X0)) [input p0]
6. ! [X0] : ((old(X0) & ~old(X0)) <=> (wise(X0) | kind(X0))) [input p5]
23. kind(susan) [input hypothesis]
26. ! [X0] : (old(X0) | ~kind(X0)) [ennf transformation 1]
42. ! [X0] : (((old(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & ((wise(X0) | kind(X0)) | (~old(X0) | old(X0)))) [nnf transformation 6]
43. ! [X0] : (((old(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & (wise(X0) | kind(X0) | ~old(X0) | old(X0))) [flattening 42]
70. old(X0) | ~kind(X0) [cnf transformation 26]
80. ~old(X0) | ~kind(X0) [cnf transformation 43]
131. kind(susan) [cnf transformation 23]
189. ~kind(X0) [subsumption resolution 80,70]
266. $false [subsumption resolution 131,189]
% SZS output end Proof for 6940088984946200266510212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is rich or not happy and vice versa.
Everyone who is either not patient or wise is brave or rich.
Everyone who is humble is not wise or old and vice versa.
If someone is either creative or not happy then susan is either not rich or not patient and vice versa.
If someone is both not tall and not humble then someone is not tall or not strong and vice versa.
Everyone who is both kind and not funny is rich and vice versa.
If someone is either brave or not happy then john is either not quiet or strong.
Everyone who is both rich and old is both not rich and kind and vice versa.
Everyone who is patient or not happy is not humble.
Everyone who is either happy or humble is wise and vice versa.
If susan is either not quiet or not funny then someone is kind or wise.
Everyone who is not funny is not rich.
If mary is either quiet or not brave then lucy is not quiet or not rich.
Everyone who is funny or generous is both calm and patient and vice versa.
Everyone who is both kind and not happy is either not patient or not brave.
Everyone who is not kind is either not patient or kind and vice versa.
Someone is tall or not strong.
Fred is both not old and not patient.
Someone is wise.
Fred is not old.
Susan is either not brave or not patient. | Lucy is not old. | entailment | (![X]:(~wise(X)<=>(rich(X)|~happy(X))))&
(![X]:((~patient(X)<~>wise(X))=>(brave(X)|rich(X))))&
(![X]:(humble(X)<=>(~wise(X)|old(X))))&
((?[X]:((creative(X)<~>~happy(X))))<=>((~rich(susan)<~>~patient(susan))))&
((?[X]:((~tall(X)&~humble(X))))<=>(?[X]:((~tall(X)|~strong(X)))))&
(![X]:((kind(X)&~funny(X))<=>rich(X)))&
((?[X]:((brave(X)<~>~happy(X))))=>((~quiet(john)<~>strong(john))))&
(![X]:((rich(X)&old(X))<=>(~rich(X)&kind(X))))&
(![X]:((patient(X)|~happy(X))=>~humble(X)))&
(![X]:((happy(X)<~>humble(X))<=>wise(X)))&
(((~quiet(susan)<~>~funny(susan)))=>(?[X]:((kind(X)|wise(X)))))&
(![X]:(~funny(X)=>~rich(X)))&
(((quiet(mary)<~>~brave(mary)))=>((~quiet(lucy)|~rich(lucy))))&
(![X]:((funny(X)|generous(X))<=>(calm(X)&patient(X))))&
(![X]:((kind(X)&~happy(X))=>(~patient(X)<~>~brave(X))))&
(![X]:(~kind(X)<=>(~patient(X)<~>kind(X))))&
(?[X]:((tall(X)|~strong(X))))&
((~old(fred)&~patient(fred)))&
(?[X]:(wise(X)))&
(~old(fred))&
((~brave(susan)<~>~patient(susan))) | ~old(lucy) | [
"p0",
"p2",
"p5",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5525955567237630277530794
% SZS output start Proof for 5525955567237630277530794
1. ! [X0] : (~wise(X0) <=> (~happy(X0) | rich(X0))) [input p0]
3. ! [X0] : (humble(X0) <=> (old(X0) | ~wise(X0))) [input p2]
6. ! [X0] : ((~funny(X0) & kind(X0)) <=> rich(X0)) [input p5]
9. ! [X0] : ((~happy(X0) | patient(X0)) => ~humble(X0)) [input p8]
10. ! [X0] : ((happy(X0) <~> humble(X0)) <=> wise(X0)) [input p9]
12. ! [X0] : (~funny(X0) => ~rich(X0)) [input p11]
22. old(lucy) [input hypothesis]
27. ! [X0] : (~humble(X0) | (happy(X0) & ~patient(X0))) [ennf transformation 9]
29. ! [X0] : (~rich(X0) | funny(X0)) [ennf transformation 12]
34. ! [X0] : ((~wise(X0) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | wise(X0))) [nnf transformation 1]
35. ! [X0] : ((~wise(X0) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | wise(X0))) [flattening 34]
37. ! [X0] : ((humble(X0) | (~old(X0) & wise(X0))) & ((old(X0) | ~wise(X0)) | ~humble(X0))) [nnf transformation 3]
38. ! [X0] : ((humble(X0) | (~old(X0) & wise(X0))) & (old(X0) | ~wise(X0) | ~humble(X0))) [flattening 37]
48. ! [X0] : (((~funny(X0) & kind(X0)) | ~rich(X0)) & (rich(X0) | (funny(X0) | ~kind(X0)))) [nnf transformation 6]
49. ! [X0] : (((~funny(X0) & kind(X0)) | ~rich(X0)) & (rich(X0) | funny(X0) | ~kind(X0))) [flattening 48]
53. ! [X0] : ((((~humble(X0) | ~happy(X0)) & (humble(X0) | happy(X0))) | ~wise(X0)) & (wise(X0) | ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0))))) [nnf transformation 10]
67. ~happy(X0) | rich(X0) | wise(X0) [cnf transformation 35]
69. ~wise(X0) | happy(X0) [cnf transformation 35]
73. humble(X0) | wise(X0) [cnf transformation 38]
74. ~old(X0) | humble(X0) [cnf transformation 38]
90. ~funny(X0) | ~rich(X0) [cnf transformation 49]
100. ~humble(X0) | happy(X0) [cnf transformation 27]
104. ~humble(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 53]
107. ~rich(X0) | funny(X0) [cnf transformation 29]
128. old(lucy) [cnf transformation 22]
212. ~humble(X0) | ~wise(X0) [subsumption resolution 104,100]
231. ~rich(X0) [subsumption resolution 107,90]
248. humble(lucy) [resolution 74,128]
251. happy(X0) | wise(X0) [resolution 100,73]
253. happy(X0) [subsumption resolution 251,69]
260. ~wise(lucy) [resolution 212,248]
263. rich(X0) | wise(X0) [resolution 67,253]
264. wise(X0) [subsumption resolution 263,231]
268. $false [resolution 264,260]
% SZS output end Proof for 5525955567237630277530794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is wise or curious then someone is both happy and not creative. Everyone who is either not old or happy is humble and vice versa. Everyone who is both not patient and not humble is strong or not quiet and vice versa. If someone is old or wise then someone is brave or not brave and vice versa. Everyone who is wise or tall is both happy and not brave and vice versa. Everyone who is either not curious or wise is not strong or strong and vice versa. Everyone who is quiet is not tall or quiet and vice versa. Everyone who is not curious or brave is quiet. If someone is curious then paul is both not old and not tall and vice versa. Everyone who is not calm is either patient or wise. Everyone who is either humble or not generous is not calm and vice versa. Everyone who is either not tall or tall is both happy and brave and vice versa. If someone is not strong then john is not happy or rich. Everyone who is both strong and not tall is either quiet or not curious and vice versa. If mary is either curious or not rich then someone is either not curious or kind and vice versa. Someone is old. Someone is either not patient or wise. Lucy is both not generous and rich. Paul is both not wise and not tall. Someone is either not calm or not generous. Paul is either not rich or strong. Lucy is either not strong or creative. | Paul is humble. | entailment | (((wise(lucy)|curious(lucy)))=>(?[X]:((happy(X)&~creative(X)))))&
(![X]:((~old(X)<~>happy(X))<=>humble(X)))&
(![X]:((~patient(X)&~humble(X))<=>(strong(X)|~quiet(X))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((wise(X)|tall(X))<=>(happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>wise(X))<=>(~strong(X)|strong(X))))&
(![X]:(quiet(X)<=>(~tall(X)|quiet(X))))&
(![X]:((~curious(X)|brave(X))=>quiet(X)))&
((?[X]:(curious(X)))<=>((~old(paul)&~tall(paul))))&
(![X]:(~calm(X)=>(patient(X)<~>wise(X))))&
(![X]:((humble(X)<~>~generous(X))<=>~calm(X)))&
(![X]:((~tall(X)<~>tall(X))<=>(happy(X)&brave(X))))&
((?[X]:(~strong(X)))=>((~happy(john)|rich(john))))&
(![X]:((strong(X)&~tall(X))<=>(quiet(X)<~>~curious(X))))&
(((curious(mary)<~>~rich(mary)))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(?[X]:(old(X)))&
(?[X]:((~patient(X)<~>wise(X))))&
((~generous(lucy)&rich(lucy)))&
((~wise(paul)&~tall(paul)))&
(?[X]:((~calm(X)<~>~generous(X))))&
((~rich(paul)<~>strong(paul)))&
((~strong(lucy)<~>creative(lucy))) | humble(paul) | [
"p1",
"p4",
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 374965881822679006179332
% SZS output start Proof for 374965881822679006179332
2. ! [X0] : ((~old(X0) <~> happy(X0)) <=> humble(X0)) [input p1]
5. ! [X0] : ((tall(X0) | wise(X0)) <=> (~brave(X0) & happy(X0))) [input p4]
6. ! [X0] : ((~curious(X0) <~> wise(X0)) <=> (strong(X0) | ~strong(X0))) [input p5]
9. ? [X0] : curious(X0) <=> (~tall(paul) & ~old(paul)) [input p8]
12. ! [X0] : ((~tall(X0) <~> tall(X0)) <=> (brave(X0) & happy(X0))) [input p11]
23. ~humble(paul) [input hypothesis]
32. ! [X0] : ((((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | ~humble(X0)) & (humble(X0) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))))) [nnf transformation 2]
40. ! [X0] : (((tall(X0) | wise(X0)) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | (~tall(X0) & ~wise(X0)))) [nnf transformation 5]
41. ! [X0] : ((tall(X0) | wise(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | (~tall(X0) & ~wise(X0)))) [flattening 40]
42. ! [X0] : ((((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | (~strong(X0) & strong(X0))) & ((strong(X0) | ~strong(X0)) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0))))) [nnf transformation 6]
43. ! [X0] : ((((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | (~strong(X0) & strong(X0))) & (strong(X0) | ~strong(X0) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0))))) [flattening 42]
46. (? [X0] : curious(X0) | (tall(paul) | old(paul))) & ((~tall(paul) & ~old(paul)) | ! [X0] : ~curious(X0)) [nnf transformation 9]
47. (? [X0] : curious(X0) | tall(paul) | old(paul)) & ((~tall(paul) & ~old(paul)) | ! [X0] : ~curious(X0)) [flattening 46]
48. (? [X0] : curious(X0) | tall(paul) | old(paul)) & ((~tall(paul) & ~old(paul)) | ! [X1] : ~curious(X1)) [rectify 47]
49. ? [X0] : curious(X0) => curious(sK3) [choice axiom]
50. (curious(sK3) | tall(paul) | old(paul)) & ((~tall(paul) & ~old(paul)) | ! [X1] : ~curious(X1)) [skolemisation 48,49]
53. ! [X0] : ((((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | (~brave(X0) | ~happy(X0))) & ((brave(X0) & happy(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))))) [nnf transformation 12]
54. ! [X0] : ((((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ~brave(X0) | ~happy(X0)) & ((brave(X0) & happy(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))))) [flattening 53]
76. ~old(X0) | humble(X0) | ~happy(X0) [cnf transformation 32]
90. ~brave(X0) | ~wise(X0) [cnf transformation 41]
91. ~tall(X0) | ~brave(X0) [cnf transformation 41]
95. wise(X0) | ~curious(X0) | strong(X0) [cnf transformation 43]
96. wise(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 43]
106. curious(sK3) | tall(paul) | old(paul) [cnf transformation 50]
113. happy(X0) | tall(X0) | tall(X0) [cnf transformation 54]
115. brave(X0) | tall(X0) | tall(X0) [cnf transformation 54]
116. brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 54]
147. ~humble(paul) [cnf transformation 23]
148. happy(X0) | tall(X0) [duplicate literal removal 113]
150. brave(X0) | tall(X0) [duplicate literal removal 115]
151. brave(X0) | ~tall(X0) [duplicate literal removal 116]
173. 5 <=> ! [X1] : brave(X1) [avatar definition]
174. brave(X1) <- (5) [avatar component clause 173]
189. ~curious(X0) | wise(X0) [subsumption resolution 95,96]
191. 9 <=> old(paul) [avatar definition]
193. old(paul) <- (9) [avatar component clause 191]
195. 10 <=> tall(paul) [avatar definition]
197. tall(paul) <- (10) [avatar component clause 195]
199. 11 <=> curious(sK3) [avatar definition]
201. curious(sK3) <- (11) [avatar component clause 199]
202. 9 | 10 | 11 [avatar split clause 106,199,195,191]
208. ~tall(X0) [subsumption resolution 151,91]
209. brave(X0) [subsumption resolution 150,208]
210. 5 [avatar split clause 209,173]
211. happy(X0) [subsumption resolution 148,208]
295. ~wise(X0) <- (5) [resolution 90,174]
300. wise(sK3) <- (11) [resolution 189,201]
301. $false <- (5, 11) [subsumption resolution 300,295]
302. ~5 | ~11 [avatar contradiction clause 301]
303. $false <- (10) [subsumption resolution 197,208]
304. ~10 [avatar contradiction clause 303]
309. humble(paul) | ~happy(paul) <- (9) [resolution 76,193]
312. ~happy(paul) <- (9) [subsumption resolution 309,147]
313. $false <- (9) [subsumption resolution 312,211]
314. ~9 [avatar contradiction clause 313]
315. $false [avatar sat refutation 202,210,302,304,314]
% SZS output end Proof for 374965881822679006179332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not calm and kind then someone is old.
Everyone who is not tall is old or strong and vice versa.
Everyone who is not strong is not creative or rich and vice versa.
If someone is either not strong or calm then someone is not wise or happy.
Everyone who is humble or tall is either rich or happy.
If paul is funny then fred is both not rich and not curious and vice versa.
If someone is both not happy and not curious then paul is not kind or quiet and vice versa.
If susan is both not curious and not kind then paul is both generous and rich and vice versa.
Everyone who is both humble and old is funny.
Everyone who is either not tall or tall is not curious and vice versa.
If paul is curious or not happy then someone is either not humble or humble and vice versa.
If someone is kind or not kind then john is not funny and vice versa.
If someone is either strong or not kind then mary is humble and vice versa.
Everyone who is either brave or not curious is not brave and vice versa.
If someone is either tall or not kind then someone is both rich and not patient.
Everyone who is not kind is either not patient or not tall.
Someone is not funny.
Someone is both not calm and not old.
Mary is either patient or creative.
Lucy is either not quiet or patient.
Mary is funny or old.
Someone is not calm or not rich.
Someone is quiet.
Mary is both not kind and patient. | Mary is curious. | contradiction | (((~calm(alice)&kind(alice)))=>(?[X]:(old(X))))&
(![X]:(~tall(X)<=>(old(X)|strong(X))))&
(![X]:(~strong(X)<=>(~creative(X)|rich(X))))&
((?[X]:((~strong(X)<~>calm(X))))=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((humble(X)|tall(X))=>(rich(X)<~>happy(X))))&
((funny(paul))<=>((~rich(fred)&~curious(fred))))&
((?[X]:((~happy(X)&~curious(X))))<=>((~kind(paul)|quiet(paul))))&
(((~curious(susan)&~kind(susan)))<=>((generous(paul)&rich(paul))))&
(![X]:((humble(X)&old(X))=>funny(X)))&
(![X]:((~tall(X)<~>tall(X))<=>~curious(X)))&
(((curious(paul)|~happy(paul)))<=>(?[X]:((~humble(X)<~>humble(X)))))&
((?[X]:((kind(X)|~kind(X))))<=>(~funny(john)))&
((?[X]:((strong(X)<~>~kind(X))))<=>(humble(mary)))&
(![X]:((brave(X)<~>~curious(X))<=>~brave(X)))&
((?[X]:((tall(X)<~>~kind(X))))=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:(~kind(X)=>(~patient(X)<~>~tall(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~calm(X)&~old(X))))&
((patient(mary)<~>creative(mary)))&
((~quiet(lucy)<~>patient(lucy)))&
((funny(mary)|old(mary)))&
(?[X]:((~calm(X)|~rich(X))))&
(?[X]:(quiet(X)))&
((~kind(mary)&patient(mary))) | curious(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8195025117567996220750338
% SZS output start Proof for 8195025117567996220750338
10. ! [X0] : ((~tall(X0) <~> tall(X0)) <=> ~curious(X0)) [input p9]
25. curious(mary) [input hypothesis]
52. ! [X0] : ((((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | curious(X0)) & (~curious(X0) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))))) [nnf transformation 10]
106. ~curious(X0) | tall(X0) | tall(X0) [cnf transformation 52]
107. ~curious(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 52]
145. curious(mary) [cnf transformation 25]
150. ~curious(X0) | tall(X0) [duplicate literal removal 106]
151. ~curious(X0) | ~tall(X0) [duplicate literal removal 107]
224. ~curious(X0) [subsumption resolution 150,151]
330. $false [subsumption resolution 145,224]
% SZS output end Proof for 8195025117567996220750338
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall and quiet is not humble or wise. Everyone who is both not rich and tall is funny or not strong and vice versa. Everyone who is quiet or old is either wise or not quiet and vice versa. If john is both not brave and not happy then susan is not calm and vice versa. Everyone who is brave is quiet or not patient. If susan is either tall or wise then someone is funny or humble and vice versa. Everyone who is kind or not old is either not quiet or not creative. If someone is either strong or not rich then someone is both not rich and not generous. If lucy is both calm and tall then someone is either kind or strong and vice versa. Everyone who is not patient is either old or not happy and vice versa. If john is not creative then mary is rich or kind. If someone is both not old and not curious then lucy is funny or not old and vice versa. If paul is either brave or not humble then someone is not brave. Everyone who is both not humble and not brave is both not old and happy and vice versa. Everyone who is both not strong and wise is both kind and not tall and vice versa. Everyone who is either brave or rich is either not tall or not old and vice versa. Someone is both funny and not old. Someone is both old and not rich. Fred is both not strong and not kind. Someone is humble or not funny. Alice is not quiet or not curious. Someone is funny. Alice is either patient or calm. Someone is old. | Susan is calm. | neutral | (![X]:((~tall(X)&quiet(X))=>(~humble(X)|wise(X))))&
(![X]:((~rich(X)&tall(X))<=>(funny(X)|~strong(X))))&
(![X]:((quiet(X)|old(X))<=>(wise(X)<~>~quiet(X))))&
(((~brave(john)&~happy(john)))<=>(~calm(susan)))&
(![X]:(brave(X)=>(quiet(X)|~patient(X))))&
(((tall(susan)<~>wise(susan)))<=>(?[X]:((funny(X)|humble(X)))))&
(![X]:((kind(X)|~old(X))=>(~quiet(X)<~>~creative(X))))&
((?[X]:((strong(X)<~>~rich(X))))=>(?[X]:((~rich(X)&~generous(X)))))&
(((calm(lucy)&tall(lucy)))<=>(?[X]:((kind(X)<~>strong(X)))))&
(![X]:(~patient(X)<=>(old(X)<~>~happy(X))))&
((~creative(john))=>((rich(mary)|kind(mary))))&
((?[X]:((~old(X)&~curious(X))))<=>((funny(lucy)|~old(lucy))))&
(((brave(paul)<~>~humble(paul)))=>(?[X]:(~brave(X))))&
(![X]:((~humble(X)&~brave(X))<=>(~old(X)&happy(X))))&
(![X]:((~strong(X)&wise(X))<=>(kind(X)&~tall(X))))&
(![X]:((brave(X)<~>rich(X))<=>(~tall(X)<~>~old(X))))&
(?[X]:((funny(X)&~old(X))))&
(?[X]:((old(X)&~rich(X))))&
((~strong(fred)&~kind(fred)))&
(?[X]:((humble(X)|~funny(X))))&
((~quiet(alice)|~curious(alice)))&
(?[X]:(funny(X)))&
((patient(alice)<~>calm(alice)))&
(?[X]:(old(X))) | calm(susan) | [] | null | 0 |
Everyone who is both not patient and not happy is both not wise and quiet. Everyone who is not generous or not brave is either old or not strong and vice versa. If someone is either humble or generous then lucy is either calm or not funny and vice versa. Everyone who is both not calm and not creative is either not old or curious and vice versa. Everyone who is either kind or not wise is not patient or patient and vice versa. If someone is not creative then someone is both not kind and not calm and vice versa. Everyone who is either rich or not calm is old and vice versa. If someone is not creative or not tall then someone is not tall or calm. Everyone who is not strong or humble is either calm or not curious. Everyone who is both kind and creative is either not quiet or kind and vice versa. Everyone who is either quiet or rich is either not generous or not humble and vice versa. If paul is either humble or happy then susan is either not brave or curious. Everyone who is either not old or old is either funny or creative. Everyone who is not wise or not generous is not funny. If alice is patient or humble then susan is either not brave or patient and vice versa. Everyone who is rich or brave is generous or not rich and vice versa. Lucy is either creative or not generous. Paul is strong. Someone is both rich and wise. Susan is both not curious and not rich. Someone is both tall and kind. John is both rich and not creative. Someone is both not creative and strong. Someone is not old. | Susan is not funny. | entailment | (![X]:((~patient(X)&~happy(X))=>(~wise(X)&quiet(X))))&
(![X]:((~generous(X)|~brave(X))<=>(old(X)<~>~strong(X))))&
((?[X]:((humble(X)<~>generous(X))))<=>((calm(lucy)<~>~funny(lucy))))&
(![X]:((~calm(X)&~creative(X))<=>(~old(X)<~>curious(X))))&
(![X]:((kind(X)<~>~wise(X))<=>(~patient(X)|patient(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~kind(X)&~calm(X)))))&
(![X]:((rich(X)<~>~calm(X))<=>old(X)))&
((?[X]:((~creative(X)|~tall(X))))=>(?[X]:((~tall(X)|calm(X)))))&
(![X]:((~strong(X)|humble(X))=>(calm(X)<~>~curious(X))))&
(![X]:((kind(X)&creative(X))<=>(~quiet(X)<~>kind(X))))&
(![X]:((quiet(X)<~>rich(X))<=>(~generous(X)<~>~humble(X))))&
(((humble(paul)<~>happy(paul)))=>((~brave(susan)<~>curious(susan))))&
(![X]:((~old(X)<~>old(X))=>(funny(X)<~>creative(X))))&
(![X]:((~wise(X)|~generous(X))=>~funny(X)))&
(((patient(alice)|humble(alice)))<=>((~brave(susan)<~>patient(susan))))&
(![X]:((rich(X)|brave(X))<=>(generous(X)|~rich(X))))&
((creative(lucy)<~>~generous(lucy)))&
(strong(paul))&
(?[X]:((rich(X)&wise(X))))&
((~curious(susan)&~rich(susan)))&
(?[X]:((tall(X)&kind(X))))&
((rich(john)&~creative(john)))&
(?[X]:((~creative(X)&strong(X))))&
(?[X]:(~old(X))) | ~funny(susan) | [
"p3",
"p6",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4874258353068853177374480
% SZS output start Proof for 4874258353068853177374480
4. ! [X0] : ((~creative(X0) & ~calm(X0)) <=> (~old(X0) <~> curious(X0))) [input p3]
7. ! [X0] : ((rich(X0) <~> ~calm(X0)) <=> old(X0)) [input p6]
13. ! [X0] : ((~old(X0) <~> old(X0)) => (funny(X0) <~> creative(X0))) [input p12]
20. ~rich(susan) & ~curious(susan) [input p19]
25. funny(susan) [input hypothesis]
33. ! [X0] : ((funny(X0) <~> creative(X0)) | (~old(X0) <=> old(X0))) [ennf transformation 13]
41. ! [X0] : (((~creative(X0) & ~calm(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (creative(X0) | calm(X0)))) [nnf transformation 4]
42. ! [X0] : (((~creative(X0) & ~calm(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | creative(X0) | calm(X0))) [flattening 41]
50. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | ~old(X0)) & (old(X0) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [nnf transformation 7]
59. ! [X0] : (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 33]
89. ~old(X0) | curious(X0) | creative(X0) | calm(X0) [cnf transformation 42]
91. ~calm(X0) | curious(X0) | old(X0) [cnf transformation 42]
105. rich(X0) | old(X0) | calm(X0) [cnf transformation 50]
106. ~calm(X0) | rich(X0) | ~old(X0) [cnf transformation 50]
134. ~creative(X0) | ~funny(X0) | old(X0) | old(X0) [cnf transformation 59]
135. ~creative(X0) | ~funny(X0) | ~old(X0) | ~old(X0) [cnf transformation 59]
153. ~curious(susan) [cnf transformation 20]
154. ~rich(susan) [cnf transformation 20]
162. funny(susan) [cnf transformation 25]
167. ~creative(X0) | ~funny(X0) | old(X0) [duplicate literal removal 134]
168. ~creative(X0) | ~funny(X0) | ~old(X0) [duplicate literal removal 135]
251. 18 <=> curious(susan) [avatar definition]
253. ~curious(susan) <- (~18) [avatar component clause 251]
258. ~creative(X0) | ~funny(X0) [subsumption resolution 167,168]
288. ~18 [avatar split clause 153,251]
442. old(susan) | calm(susan) [resolution 105,154]
447. 42 <=> calm(susan) [avatar definition]
448. ~calm(susan) <- (~42) [avatar component clause 447]
449. calm(susan) <- (42) [avatar component clause 447]
451. 43 <=> old(susan) [avatar definition]
453. old(susan) <- (43) [avatar component clause 451]
454. 42 | 43 [avatar split clause 442,451,447]
471. rich(susan) | ~old(susan) <- (42) [resolution 449,106]
472. curious(susan) | old(susan) <- (42) [resolution 449,91]
475. ~old(susan) <- (42) [subsumption resolution 471,154]
476. ~43 | ~42 [avatar split clause 475,447,451]
477. old(susan) <- (~18, 42) [subsumption resolution 472,253]
478. 43 | 18 | ~42 [avatar split clause 477,447,251,451]
489. 44 <=> creative(susan) [avatar definition]
491. creative(susan) <- (44) [avatar component clause 489]
539. curious(susan) | creative(susan) | calm(susan) <- (43) [resolution 89,453]
554. creative(susan) | calm(susan) <- (~18, 43) [subsumption resolution 539,253]
555. creative(susan) <- (~18, ~42, 43) [subsumption resolution 554,448]
556. 44 | 18 | 42 | ~43 [avatar split clause 555,451,447,251,489]
1114. ~funny(susan) <- (44) [resolution 491,258]
1119. $false <- (44) [subsumption resolution 1114,162]
1120. ~44 [avatar contradiction clause 1119]
1123. $false [avatar sat refutation 288,454,476,478,556,1120]
% SZS output end Proof for 4874258353068853177374480
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not brave or not wise and vice versa. If someone is either generous or not curious then someone is brave. If someone is strong then mary is both happy and patient and vice versa. If someone is not curious or not funny then someone is both not happy and creative and vice versa. If fred is not funny or not old then someone is funny or rich. If lucy is wise then someone is rich. Everyone who is not calm is either not kind or not strong. Everyone who is old is brave or humble and vice versa. If fred is not creative then someone is tall and vice versa. If susan is both not humble and wise then someone is both quiet and not creative. If lucy is both not quiet and not brave then paul is either not creative or not generous. Everyone who is either tall or not tall is rich. If mary is humble then mary is rich. Everyone who is old is old or calm and vice versa. If someone is not creative then someone is not old or humble and vice versa. Everyone who is brave is not happy or calm and vice versa. Someone is calm or not patient. Mary is both not patient and not strong. Someone is not creative or not patient. Someone is both not tall and not funny. John is either not tall or quiet. Someone is not wise. Someone is old or creative. Someone is both calm and not curious. | Fred is rich. | entailment | (![X]:(~patient(X)<=>(~brave(X)|~wise(X))))&
((?[X]:((generous(X)<~>~curious(X))))=>(?[X]:(brave(X))))&
((?[X]:(strong(X)))<=>((happy(mary)&patient(mary))))&
((?[X]:((~curious(X)|~funny(X))))<=>(?[X]:((~happy(X)&creative(X)))))&
(((~funny(fred)|~old(fred)))=>(?[X]:((funny(X)|rich(X)))))&
((wise(lucy))=>(?[X]:(rich(X))))&
(![X]:(~calm(X)=>(~kind(X)<~>~strong(X))))&
(![X]:(old(X)<=>(brave(X)|humble(X))))&
((~creative(fred))<=>(?[X]:(tall(X))))&
(((~humble(susan)&wise(susan)))=>(?[X]:((quiet(X)&~creative(X)))))&
(((~quiet(lucy)&~brave(lucy)))=>((~creative(paul)<~>~generous(paul))))&
(![X]:((tall(X)<~>~tall(X))=>rich(X)))&
((humble(mary))=>(rich(mary)))&
(![X]:(old(X)<=>(old(X)|calm(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~old(X)|humble(X)))))&
(![X]:(brave(X)<=>(~happy(X)|calm(X))))&
(?[X]:((calm(X)|~patient(X))))&
((~patient(mary)&~strong(mary)))&
(?[X]:((~creative(X)|~patient(X))))&
(?[X]:((~tall(X)&~funny(X))))&
((~tall(john)<~>quiet(john)))&
(?[X]:(~wise(X)))&
(?[X]:((old(X)|creative(X))))&
(?[X]:((calm(X)&~curious(X)))) | rich(fred) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1257118447066637196151729
% SZS output start Proof for 1257118447066637196151729
12. ! [X0] : ((tall(X0) <~> ~tall(X0)) => rich(X0)) [input p11]
25. ~rich(fred) [input hypothesis]
37. ! [X0] : (rich(X0) | (tall(X0) <=> ~tall(X0))) [ennf transformation 12]
69. ! [X0] : (rich(X0) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) [nnf transformation 37]
119. rich(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 69]
120. rich(X0) | tall(X0) | tall(X0) [cnf transformation 69]
143. ~rich(fred) [cnf transformation 25]
144. rich(X0) | ~tall(X0) [duplicate literal removal 119]
145. rich(X0) | tall(X0) [duplicate literal removal 120]
282. rich(X0) [subsumption resolution 144,145]
345. $false [subsumption resolution 143,282]
% SZS output end Proof for 1257118447066637196151729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not curious or humble then john is both not tall and not brave. Everyone who is either curious or rich is not quiet or strong and vice versa. If someone is not generous then someone is brave or not quiet. Everyone who is funny is either not strong or not curious and vice versa. If someone is not kind then someone is patient. If mary is either not wise or not happy then susan is either generous or not creative. If someone is both old and quiet then john is not happy. If lucy is either creative or not creative then someone is either not happy or not wise and vice versa. If someone is not creative then someone is both wise and not quiet. Everyone who is not humble is either not funny or happy and vice versa. If someone is calm or not strong then someone is not wise. Everyone who is either tall or curious is patient or tall and vice versa. If john is either generous or not funny then mary is both not curious and kind. Everyone who is not kind is both not funny and creative and vice versa. If fred is not kind then someone is quiet or rich. Everyone who is both strong and old is humble or not happy. Someone is happy or wise. Someone is not happy or patient. Someone is creative or quiet. John is not tall or tall. Susan is both curious and rich. Someone is not quiet or not generous. Mary is both wise and funny. Alice is not quiet or not creative. | Mary is not kind. | contradiction | (((~curious(john)<~>humble(john)))=>((~tall(john)&~brave(john))))&
(![X]:((curious(X)<~>rich(X))<=>(~quiet(X)|strong(X))))&
((?[X]:(~generous(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:(funny(X)<=>(~strong(X)<~>~curious(X))))&
((?[X]:(~kind(X)))=>(?[X]:(patient(X))))&
(((~wise(mary)<~>~happy(mary)))=>((generous(susan)<~>~creative(susan))))&
((?[X]:((old(X)&quiet(X))))=>(~happy(john)))&
(((creative(lucy)<~>~creative(lucy)))<=>(?[X]:((~happy(X)<~>~wise(X)))))&
((?[X]:(~creative(X)))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:(~humble(X)<=>(~funny(X)<~>happy(X))))&
((?[X]:((calm(X)|~strong(X))))=>(?[X]:(~wise(X))))&
(![X]:((tall(X)<~>curious(X))<=>(patient(X)|tall(X))))&
(((generous(john)<~>~funny(john)))=>((~curious(mary)&kind(mary))))&
(![X]:(~kind(X)<=>(~funny(X)&creative(X))))&
((~kind(fred))=>(?[X]:((quiet(X)|rich(X)))))&
(![X]:((strong(X)&old(X))=>(humble(X)|~happy(X))))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((~happy(X)|patient(X))))&
(?[X]:((creative(X)|quiet(X))))&
((~tall(john)|tall(john)))&
((curious(susan)&rich(susan)))&
(?[X]:((~quiet(X)|~generous(X))))&
((wise(mary)&funny(mary)))&
((~quiet(alice)|~creative(alice))) | ~kind(mary) | [
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5830255695909335776588973
% SZS output start Proof for 5830255695909335776588973
14. ! [X0] : (~kind(X0) <=> (creative(X0) & ~funny(X0))) [input p13]
23. funny(mary) & wise(mary) [input p22]
25. ~kind(mary) [input hypothesis]
66. ! [X0] : ((~kind(X0) | (~creative(X0) | funny(X0))) & ((creative(X0) & ~funny(X0)) | kind(X0))) [nnf transformation 14]
67. ! [X0] : ((~kind(X0) | ~creative(X0) | funny(X0)) & ((creative(X0) & ~funny(X0)) | kind(X0))) [flattening 66]
123. ~funny(X0) | kind(X0) [cnf transformation 67]
135. funny(mary) [cnf transformation 23]
137. ~kind(mary) [cnf transformation 25]
251. 24 <=> kind(mary) [avatar definition]
252. ~kind(mary) <- (~24) [avatar component clause 251]
321. ~24 [avatar split clause 137,251]
328. kind(mary) [resolution 123,135]
330. $false <- (~24) [subsumption resolution 328,252]
331. 24 [avatar contradiction clause 330]
332. $false [avatar sat refutation 321,331]
% SZS output end Proof for 5830255695909335776588973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not wise is old and vice versa.
Everyone who is quiet or not tall is not creative or brave.
If someone is curious or not rich then someone is funny.
Everyone who is not generous or happy is either strong or not patient and vice versa.
Everyone who is not brave is not old or not wise and vice versa.
Everyone who is kind is happy and vice versa.
If someone is kind or strong then someone is both calm and not strong and vice versa.
Everyone who is both calm and not generous is not generous and vice versa.
Everyone who is brave or not creative is wise.
Everyone who is old is either not kind or kind.
Everyone who is both happy and humble is both humble and not kind.
If lucy is not kind then someone is not tall.
If paul is tall or not old then someone is not happy.
Everyone who is kind is either funny or not happy.
If paul is humble then paul is both quiet and not curious and vice versa.
Everyone who is not brave is both not strong and not calm.
Paul is either old or wise.
Someone is either patient or not strong.
Someone is either not wise or strong.
Fred is not humble or kind.
Mary is patient or wise.
Paul is strong or curious.
Someone is both not old and generous.
Someone is not wise or funny. | Mary is not creative. | neutral | (![X]:((~patient(X)<~>~wise(X))<=>old(X)))&
(![X]:((quiet(X)|~tall(X))=>(~creative(X)|brave(X))))&
((?[X]:((curious(X)|~rich(X))))=>(?[X]:(funny(X))))&
(![X]:((~generous(X)|happy(X))<=>(strong(X)<~>~patient(X))))&
(![X]:(~brave(X)<=>(~old(X)|~wise(X))))&
(![X]:(kind(X)<=>happy(X)))&
((?[X]:((kind(X)|strong(X))))<=>(?[X]:((calm(X)&~strong(X)))))&
(![X]:((calm(X)&~generous(X))<=>~generous(X)))&
(![X]:((brave(X)|~creative(X))=>wise(X)))&
(![X]:(old(X)=>(~kind(X)<~>kind(X))))&
(![X]:((happy(X)&humble(X))=>(humble(X)&~kind(X))))&
((~kind(lucy))=>(?[X]:(~tall(X))))&
(((tall(paul)|~old(paul)))=>(?[X]:(~happy(X))))&
(![X]:(kind(X)=>(funny(X)<~>~happy(X))))&
((humble(paul))<=>((quiet(paul)&~curious(paul))))&
(![X]:(~brave(X)=>(~strong(X)&~calm(X))))&
((old(paul)<~>wise(paul)))&
(?[X]:((patient(X)<~>~strong(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
((~humble(fred)|kind(fred)))&
((patient(mary)|wise(mary)))&
((strong(paul)|curious(paul)))&
(?[X]:((~old(X)&generous(X))))&
(?[X]:((~wise(X)|funny(X)))) | ~creative(mary) | [] | null | 0 |
If someone is either kind or not strong then mary is either tall or not kind. Everyone who is old is not happy or calm and vice versa. If fred is not calm or not curious then someone is both humble and not creative. If john is not strong then lucy is not old or not generous. Everyone who is happy is either not strong or not funny and vice versa. Everyone who is curious or not old is curious. Everyone who is not happy or happy is strong. If someone is not strong or not quiet then someone is both not funny and patient. Everyone who is not tall or kind is curious and vice versa. Everyone who is both brave and not quiet is both quiet and not rich and vice versa. Everyone who is happy is not happy or not kind and vice versa. If someone is both kind and generous then someone is both wise and not tall and vice versa. Everyone who is not creative or not rich is wise or not happy. Everyone who is either not funny or humble is patient. If paul is either not tall or humble then someone is either happy or not humble. If lucy is not wise then lucy is either not kind or rich and vice versa. Lucy is not funny or not strong. Fred is both happy and not tall. Someone is happy. Paul is either funny or not curious. Someone is not generous or not happy. Fred is not old. Someone is either generous or wise. Someone is creative. | Fred is not strong. | contradiction | ((?[X]:((kind(X)<~>~strong(X))))=>((tall(mary)<~>~kind(mary))))&
(![X]:(old(X)<=>(~happy(X)|calm(X))))&
(((~calm(fred)|~curious(fred)))=>(?[X]:((humble(X)&~creative(X)))))&
((~strong(john))=>((~old(lucy)|~generous(lucy))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
((~wise(lucy))<=>((~kind(lucy)<~>rich(lucy))))&
((~funny(lucy)|~strong(lucy)))&
((happy(fred)&~tall(fred)))&
(?[X]:(happy(X)))&
((funny(paul)<~>~curious(paul)))&
(?[X]:((~generous(X)|~happy(X))))&
(~old(fred))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:(creative(X))) | ~strong(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1682329363166582307820074
% SZS output start Proof for 1682329363166582307820074
7. ! [X0] : ((happy(X0) | ~happy(X0)) => strong(X0)) [input p6]
25. ~strong(fred) [input hypothesis]
35. ! [X0] : (strong(X0) | (~happy(X0) & happy(X0))) [ennf transformation 7]
92. strong(X0) | happy(X0) [cnf transformation 35]
93. strong(X0) | ~happy(X0) [cnf transformation 35]
131. ~strong(fred) [cnf transformation 25]
187. strong(X0) [subsumption resolution 92,93]
251. $false [subsumption resolution 131,187]
% SZS output end Proof for 1682329363166582307820074
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is not strong and vice versa.
If lucy is both creative and not calm then someone is not generous or not funny and vice versa.
Everyone who is either not tall or brave is creative or not creative.
If fred is either wise or happy then paul is both not tall and not humble.
Everyone who is either not quiet or rich is either not funny or not wise.
Everyone who is both not rich and kind is not generous.
Everyone who is both wise and patient is either not generous or not tall.
If john is either not calm or creative then mary is old or patient and vice versa.
Everyone who is either not rich or humble is either creative or not rich and vice versa.
If someone is either strong or not calm then someone is either rich or humble and vice versa.
If alice is quiet then alice is creative or quiet and vice versa.
Everyone who is either not curious or curious is both happy and wise.
If someone is both not funny and wise then john is not rich and vice versa.
If someone is either not patient or not tall then someone is both not tall and brave.
Everyone who is not quiet is not creative and vice versa.
If someone is either humble or not generous then mary is strong and vice versa.
Paul is not funny.
Mary is both not generous and rich.
Someone is not tall or not curious.
Alice is not funny or kind.
Someone is either not rich or old.
Someone is both not funny and not brave.
Someone is calm. | Alice is funny. | neutral | (![X]:(patient(X)<=>~strong(X)))&
(((creative(lucy)&~calm(lucy)))<=>(?[X]:((~generous(X)|~funny(X)))))&
(![X]:((~tall(X)<~>brave(X))=>(creative(X)|~creative(X))))&
(((wise(fred)<~>happy(fred)))=>((~tall(paul)&~humble(paul))))&
(![X]:((~quiet(X)<~>rich(X))=>(~funny(X)<~>~wise(X))))&
(![X]:((~rich(X)&kind(X))=>~generous(X)))&
(![X]:((wise(X)&patient(X))=>(~generous(X)<~>~tall(X))))&
(((~calm(john)<~>creative(john)))<=>((old(mary)|patient(mary))))&
(![X]:((~rich(X)<~>humble(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((strong(X)<~>~calm(X))))<=>(?[X]:((rich(X)<~>humble(X)))))&
((quiet(alice))<=>((creative(alice)|quiet(alice))))&
(![X]:((~curious(X)<~>curious(X))=>(happy(X)&wise(X))))&
((?[X]:((~funny(X)&wise(X))))<=>(~rich(john)))&
((?[X]:((~patient(X)<~>~tall(X))))=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:(~quiet(X)<=>~creative(X)))&
((?[X]:((humble(X)<~>~generous(X))))<=>(strong(mary)))&
(~funny(paul))&
((~generous(mary)&rich(mary)))&
(?[X]:((~tall(X)|~curious(X))))&
((~funny(alice)|kind(alice)))&
(?[X]:((~rich(X)<~>old(X))))&
(?[X]:((~funny(X)&~brave(X))))&
(?[X]:(calm(X))) | funny(alice) | [] | null | 0 |
Everyone who is both brave and not creative is not generous and vice versa.
If mary is both not generous and not rich then alice is not curious and vice versa.
If mary is not quiet then someone is not humble or funny.
If lucy is either calm or wise then someone is both kind and funny and vice versa.
Everyone who is either humble or wise is both generous and not quiet.
Everyone who is not rich is either strong or curious.
Everyone who is both happy and not brave is either creative or not kind and vice versa.
Everyone who is old or tall is either not creative or generous and vice versa.
If someone is happy or not calm then lucy is quiet or not rich.
Everyone who is either happy or not wise is strong and vice versa.
If mary is happy then lucy is both happy and generous.
Everyone who is both not creative and not tall is creative or curious.
If someone is either not brave or not happy then someone is either not tall or wise and vice versa.
If john is either creative or generous then someone is not tall or old and vice versa.
Everyone who is either not humble or not kind is brave or tall.
Everyone who is not patient or not quiet is both old and creative.
Alice is quiet.
Fred is not generous or not funny.
Someone is not old or wise.
Someone is both not calm and not generous.
Someone is funny.
Alice is both tall and curious. | Fred is not humble. | neutral | (![X]:((brave(X)&~creative(X))<=>~generous(X)))&
(((~generous(mary)&~rich(mary)))<=>(~curious(alice)))&
((~quiet(mary))=>(?[X]:((~humble(X)|funny(X)))))&
(((calm(lucy)<~>wise(lucy)))<=>(?[X]:((kind(X)&funny(X)))))&
(![X]:((humble(X)<~>wise(X))=>(generous(X)&~quiet(X))))&
(![X]:(~rich(X)=>(strong(X)<~>curious(X))))&
(![X]:((happy(X)&~brave(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((old(X)|tall(X))<=>(~creative(X)<~>generous(X))))&
((?[X]:((happy(X)|~calm(X))))=>((quiet(lucy)|~rich(lucy))))&
(![X]:((happy(X)<~>~wise(X))<=>strong(X)))&
((happy(mary))=>((happy(lucy)&generous(lucy))))&
(![X]:((~creative(X)&~tall(X))=>(creative(X)|curious(X))))&
((?[X]:((~brave(X)<~>~happy(X))))<=>(?[X]:((~tall(X)<~>wise(X)))))&
(((creative(john)<~>generous(john)))<=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((~humble(X)<~>~kind(X))=>(brave(X)|tall(X))))&
(![X]:((~patient(X)|~quiet(X))=>(old(X)&creative(X))))&
(quiet(alice))&
((~generous(fred)|~funny(fred)))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:((~calm(X)&~generous(X))))&
(?[X]:(funny(X)))&
((tall(alice)&curious(alice))) | ~humble(fred) | [] | null | 0 |
Everyone who is either not quiet or not old is either tall or kind and vice versa.
If someone is strong or generous then lucy is not funny and vice versa.
If someone is both humble and curious then someone is both curious and tall and vice versa.
Everyone who is kind or generous is both rich and creative and vice versa.
If fred is creative then someone is either not generous or old.
If someone is both funny and not patient then someone is either not happy or strong.
Everyone who is generous is either wise or not happy and vice versa.
Everyone who is both happy and not patient is either not old or not quiet.
Everyone who is not patient or calm is generous.
If fred is both kind and funny then someone is rich.
Everyone who is either brave or not kind is rich and vice versa.
Everyone who is both happy and rich is tall.
If fred is not curious or kind then alice is either curious or not old.
If someone is either not tall or funny then susan is not wise.
If fred is either rich or creative then someone is either funny or not creative.
If alice is either generous or curious then mary is creative and vice versa.
Mary is happy.
Someone is both kind and patient.
Lucy is not funny.
Someone is not strong.
Paul is either not creative or quiet.
Fred is not rich.
Someone is both not strong and not old.
Someone is either kind or not creative. | Fred is not curious. | neutral | (![X]:((~quiet(X)<~>~old(X))<=>(tall(X)<~>kind(X))))&
((?[X]:((strong(X)|generous(X))))<=>(~funny(lucy)))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((curious(X)&tall(X)))))&
(![X]:((kind(X)|generous(X))<=>(rich(X)&creative(X))))&
((creative(fred))=>(?[X]:((~generous(X)<~>old(X)))))&
((?[X]:((funny(X)&~patient(X))))=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:(generous(X)<=>(wise(X)<~>~happy(X))))&
(![X]:((happy(X)&~patient(X))=>(~old(X)<~>~quiet(X))))&
(![X]:((~patient(X)|calm(X))=>generous(X)))&
(((kind(fred)&funny(fred)))=>(?[X]:(rich(X))))&
(![X]:((brave(X)<~>~kind(X))<=>rich(X)))&
(![X]:((happy(X)&rich(X))=>tall(X)))&
(((~curious(fred)|kind(fred)))=>((curious(alice)<~>~old(alice))))&
((?[X]:((~tall(X)<~>funny(X))))=>(~wise(susan)))&
(((rich(fred)<~>creative(fred)))=>(?[X]:((funny(X)<~>~creative(X)))))&
(((generous(alice)<~>curious(alice)))<=>(creative(mary)))&
(happy(mary))&
(?[X]:((kind(X)&patient(X))))&
(~funny(lucy))&
(?[X]:(~strong(X)))&
((~creative(paul)<~>quiet(paul)))&
(~rich(fred))&
(?[X]:((~strong(X)&~old(X))))&
(?[X]:((kind(X)<~>~creative(X)))) | ~curious(fred) | [] | null | 0 |
If mary is either patient or strong then someone is old or not wise and vice versa.
Everyone who is kind or not generous is humble or kind and vice versa.
If mary is not creative or not funny then paul is either not curious or not patient.
Everyone who is not humble is either patient or wise.
Everyone who is either humble or generous is both rich and not rich and vice versa.
If someone is both not quiet and not creative then john is not strong and vice versa.
Everyone who is either quiet or creative is both calm and not rich.
If someone is tall or happy then alice is not creative or humble.
Everyone who is both not kind and not creative is generous or calm and vice versa.
Everyone who is humble or not kind is either not funny or brave and vice versa.
Everyone who is funny or happy is both not wise and calm and vice versa.
If lucy is not creative then susan is not curious or kind and vice versa.
Everyone who is both patient and rich is patient or not old.
Everyone who is either wise or calm is both kind and not kind.
If john is either tall or not generous then john is either not kind or curious.
Someone is either not quiet or patient.
Someone is patient.
Paul is strong or not wise.
Susan is both quiet and not old.
Fred is curious or not quiet. | John is funny. | contradiction | (((patient(mary)<~>strong(mary)))<=>(?[X]:((old(X)|~wise(X)))))&
(![X]:((kind(X)|~generous(X))<=>(humble(X)|kind(X))))&
(((~creative(mary)|~funny(mary)))=>((~curious(paul)<~>~patient(paul))))&
(![X]:(~humble(X)=>(patient(X)<~>wise(X))))&
(![X]:((humble(X)<~>generous(X))<=>(rich(X)&~rich(X))))&
((?[X]:((~quiet(X)&~creative(X))))<=>(~strong(john)))&
(![X]:((quiet(X)<~>creative(X))=>(calm(X)&~rich(X))))&
((?[X]:((tall(X)|happy(X))))=>((~creative(alice)|humble(alice))))&
(![X]:((~kind(X)&~creative(X))<=>(generous(X)|calm(X))))&
(![X]:((humble(X)|~kind(X))<=>(~funny(X)<~>brave(X))))&
(![X]:((funny(X)|happy(X))<=>(~wise(X)&calm(X))))&
((~creative(lucy))<=>((~curious(susan)|kind(susan))))&
(![X]:((patient(X)&rich(X))=>(patient(X)|~old(X))))&
(![X]:((wise(X)<~>calm(X))=>(kind(X)&~kind(X))))&
(((tall(john)<~>~generous(john)))=>((~kind(john)<~>curious(john))))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:(patient(X)))&
((strong(paul)|~wise(paul)))&
((quiet(susan)&~old(susan)))&
((curious(fred)|~quiet(fred))) | funny(john) | [
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8185166305377062239519107
% SZS output start Proof for 8185166305377062239519107
9. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (calm(X0) | generous(X0))) [input p8]
11. ! [X0] : ((happy(X0) | funny(X0)) <=> (calm(X0) & ~wise(X0))) [input p10]
14. ! [X0] : ((wise(X0) <~> calm(X0)) => (~kind(X0) & kind(X0))) [input p13]
21. funny(john) [input hypothesis]
29. ! [X0] : ((~kind(X0) & kind(X0)) | (wise(X0) <=> calm(X0))) [ennf transformation 14]
46. ! [X0] : (((~creative(X0) & ~kind(X0)) | (~calm(X0) & ~generous(X0))) & ((calm(X0) | generous(X0)) | (creative(X0) | kind(X0)))) [nnf transformation 9]
47. ! [X0] : (((~creative(X0) & ~kind(X0)) | (~calm(X0) & ~generous(X0))) & (calm(X0) | generous(X0) | creative(X0) | kind(X0))) [flattening 46]
50. ! [X0] : (((happy(X0) | funny(X0)) | (~calm(X0) | wise(X0))) & ((calm(X0) & ~wise(X0)) | (~happy(X0) & ~funny(X0)))) [nnf transformation 11]
51. ! [X0] : ((happy(X0) | funny(X0) | ~calm(X0) | wise(X0)) & ((calm(X0) & ~wise(X0)) | (~happy(X0) & ~funny(X0)))) [flattening 50]
54. ! [X0] : ((~kind(X0) & kind(X0)) | ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0)))) [nnf transformation 29]
94. ~calm(X0) | ~kind(X0) [cnf transformation 47]
103. ~funny(X0) | ~wise(X0) [cnf transformation 51]
105. ~funny(X0) | calm(X0) [cnf transformation 51]
113. kind(X0) | wise(X0) | ~calm(X0) [cnf transformation 54]
127. funny(john) [cnf transformation 21]
228. ~calm(X0) | wise(X0) [subsumption resolution 113,94]
279. ~wise(john) [resolution 103,127]
280. calm(john) [resolution 105,127]
283. wise(john) [resolution 228,280]
284. $false [subsumption resolution 283,279]
% SZS output end Proof for 8185166305377062239519107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or rich is both curious and old and vice versa.
If someone is not old or generous then someone is either not old or strong and vice versa.
If lucy is either curious or generous then someone is not tall.
If paul is quiet or not kind then someone is either wise or not kind and vice versa.
Everyone who is both patient and not wise is strong.
Everyone who is both rich and not quiet is not old or creative and vice versa.
Everyone who is both happy and not kind is not humble or not tall and vice versa.
Everyone who is both calm and tall is humble or old and vice versa.
Everyone who is not funny is rich and vice versa.
Everyone who is both not kind and not quiet is both strong and not rich and vice versa.
Everyone who is curious is both rich and not curious.
If someone is both not quiet and wise then fred is not strong or kind and vice versa.
Everyone who is both kind and not humble is not curious or not tall.
Everyone who is either not brave or curious is not happy or strong.
Everyone who is either calm or not funny is either not strong or funny.
Everyone who is both not old and humble is both humble and patient.
Susan is both not brave and not generous.
Paul is not humble.
Someone is quiet or not quiet.
John is curious or tall.
Someone is patient. | Lucy is not happy. | neutral | (![X]:((creative(X)|rich(X))<=>(curious(X)&old(X))))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((~old(X)<~>strong(X)))))&
(((curious(lucy)<~>generous(lucy)))=>(?[X]:(~tall(X))))&
(((quiet(paul)|~kind(paul)))<=>(?[X]:((wise(X)<~>~kind(X)))))&
(![X]:((patient(X)&~wise(X))=>strong(X)))&
(![X]:((rich(X)&~quiet(X))<=>(~old(X)|creative(X))))&
(![X]:((happy(X)&~kind(X))<=>(~humble(X)|~tall(X))))&
(![X]:((calm(X)&tall(X))<=>(humble(X)|old(X))))&
(![X]:(~funny(X)<=>rich(X)))&
(![X]:((~kind(X)&~quiet(X))<=>(strong(X)&~rich(X))))&
(![X]:(curious(X)=>(rich(X)&~curious(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((~strong(fred)|kind(fred))))&
(![X]:((kind(X)&~humble(X))=>(~curious(X)|~tall(X))))&
(![X]:((~brave(X)<~>curious(X))=>(~happy(X)|strong(X))))&
(![X]:((calm(X)<~>~funny(X))=>(~strong(X)<~>funny(X))))&
(![X]:((~old(X)&humble(X))=>(humble(X)&patient(X))))&
((~brave(susan)&~generous(susan)))&
(~humble(paul))&
(?[X]:((quiet(X)|~quiet(X))))&
((curious(john)|tall(john)))&
(?[X]:(patient(X))) | ~happy(lucy) | [] | null | 0 |
If susan is calm then someone is not patient or quiet.
Everyone who is both quiet and not calm is either funny or happy and vice versa.
If john is funny then someone is rich or generous and vice versa.
Everyone who is either creative or not funny is not rich or humble and vice versa.
Everyone who is either strong or tall is both strong and old and vice versa.
If someone is either generous or brave then someone is either kind or wise and vice versa.
If someone is either generous or not calm then someone is happy or creative and vice versa.
Everyone who is not funny is both not kind and old and vice versa.
If paul is generous or not calm then lucy is not old or generous.
Everyone who is both not calm and creative is not creative.
If alice is either funny or not tall then someone is either calm or not generous and vice versa.
Everyone who is either not old or wise is not patient or rich and vice versa.
Everyone who is either humble or not creative is not calm or happy and vice versa.
Everyone who is rich or not happy is not generous and vice versa.
If john is quiet then lucy is not tall.
If someone is creative then susan is generous or not rich.
Someone is not funny.
John is both humble and old.
Someone is not creative.
Someone is generous.
Someone is both not brave and rich.
Alice is either not brave or not calm.
Someone is strong or not tall.
Someone is both not humble and happy. | Paul is not brave. | neutral | ((calm(susan))=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((quiet(X)&~calm(X))<=>(funny(X)<~>happy(X))))&
((funny(john))<=>(?[X]:((rich(X)|generous(X)))))&
(![X]:((creative(X)<~>~funny(X))<=>(~rich(X)|humble(X))))&
(![X]:((strong(X)<~>tall(X))<=>(strong(X)&old(X))))&
((?[X]:((generous(X)<~>brave(X))))<=>(?[X]:((kind(X)<~>wise(X)))))&
((?[X]:((generous(X)<~>~calm(X))))<=>(?[X]:((happy(X)|creative(X)))))&
(![X]:(~funny(X)<=>(~kind(X)&old(X))))&
(((generous(paul)|~calm(paul)))=>((~old(lucy)|generous(lucy))))&
(![X]:((~calm(X)&creative(X))=>~creative(X)))&
(((funny(alice)<~>~tall(alice)))<=>(?[X]:((calm(X)<~>~generous(X)))))&
(![X]:((~old(X)<~>wise(X))<=>(~patient(X)|rich(X))))&
(![X]:((humble(X)<~>~creative(X))<=>(~calm(X)|happy(X))))&
(![X]:((rich(X)|~happy(X))<=>~generous(X)))&
((quiet(john))=>(~tall(lucy)))&
((?[X]:(creative(X)))=>((generous(susan)|~rich(susan))))&
(?[X]:(~funny(X)))&
((humble(john)&old(john)))&
(?[X]:(~creative(X)))&
(?[X]:(generous(X)))&
(?[X]:((~brave(X)&rich(X))))&
((~brave(alice)<~>~calm(alice)))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((~humble(X)&happy(X)))) | ~brave(paul) | [] | null | 0 |
Everyone who is either not calm or kind is either not humble or not quiet and vice versa. Everyone who is rich or strong is both not curious and not humble and vice versa. If susan is both humble and quiet then mary is creative or kind and vice versa. Everyone who is either brave or not brave is both not strong and generous. Everyone who is both not old and not curious is not happy or curious and vice versa. Everyone who is either happy or generous is either funny or not patient. If someone is either not kind or brave then susan is either humble or creative. Everyone who is both funny and not creative is either rich or not patient and vice versa. Everyone who is both generous and not patient is both not kind and humble. If someone is either strong or tall then alice is humble. Everyone who is both not calm and not curious is old or rich and vice versa. If someone is funny or not brave then someone is not curious or not kind and vice versa. If someone is not wise or not old then lucy is curious or not calm and vice versa. Everyone who is not calm is old. If alice is both not humble and funny then someone is not curious and vice versa. If susan is not strong then someone is not happy or curious and vice versa. Mary is happy or not calm. Lucy is not strong. Someone is either calm or brave. Someone is either happy or funny. Someone is not quiet or strong. Lucy is not calm or brave. Mary is old. Lucy is either not rich or quiet. | Alice is happy. | entailment | (![X]:((~calm(X)<~>kind(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((rich(X)|strong(X))<=>(~curious(X)&~humble(X))))&
(((humble(susan)&quiet(susan)))<=>((creative(mary)|kind(mary))))&
(![X]:((brave(X)<~>~brave(X))=>(~strong(X)&generous(X))))&
(![X]:((~old(X)&~curious(X))<=>(~happy(X)|curious(X))))&
(![X]:((happy(X)<~>generous(X))=>(funny(X)<~>~patient(X))))&
((?[X]:((~kind(X)<~>brave(X))))=>((humble(susan)<~>creative(susan))))&
(![X]:((funny(X)&~creative(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(![X]:(~calm(X)=>old(X)))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((~strong(susan))<=>(?[X]:((~happy(X)|curious(X)))))&
((happy(mary)|~calm(mary)))&
(~strong(lucy))&
(?[X]:((calm(X)<~>brave(X))))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy)))&
(old(mary))&
((~rich(lucy)<~>quiet(lucy))) | happy(alice) | [
"p1",
"p3",
"p4",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2409375930488560706909224
% SZS output start Proof for 2409375930488560706909224
2. ! [X0] : ((strong(X0) | rich(X0)) <=> (~humble(X0) & ~curious(X0))) [input p1]
4. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (generous(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((~curious(X0) & ~old(X0)) <=> (curious(X0) | ~happy(X0))) [input p4]
11. ! [X0] : ((~curious(X0) & ~calm(X0)) <=> (rich(X0) | old(X0))) [input p10]
14. ! [X0] : (~calm(X0) => old(X0)) [input p13]
15. (funny(alice) & ~humble(alice)) <=> ? [X0] : ~curious(X0) [input p14]
25. ~happy(alice) [input hypothesis]
27. ! [X0] : ((generous(X0) & ~strong(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 4]
33. ! [X0] : (old(X0) | calm(X0)) [ennf transformation 14]
35. ! [X0] : (((strong(X0) | rich(X0)) | (humble(X0) | curious(X0))) & ((~humble(X0) & ~curious(X0)) | (~strong(X0) & ~rich(X0)))) [nnf transformation 2]
36. ! [X0] : ((strong(X0) | rich(X0) | humble(X0) | curious(X0)) & ((~humble(X0) & ~curious(X0)) | (~strong(X0) & ~rich(X0)))) [flattening 35]
39. ! [X0] : ((generous(X0) & ~strong(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 27]
40. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | (curious(X0) | old(X0)))) [nnf transformation 5]
41. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | curious(X0) | old(X0))) [flattening 40]
47. ! [X0] : (((~curious(X0) & ~calm(X0)) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | (curious(X0) | calm(X0)))) [nnf transformation 11]
48. ! [X0] : (((~curious(X0) & ~calm(X0)) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | curious(X0) | calm(X0))) [flattening 47]
59. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~funny(alice) | humble(alice))) [nnf transformation 15]
60. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ~funny(alice) | humble(alice)) [flattening 59]
61. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ~funny(alice) | humble(alice)) [rectify 60]
62. ? [X1] : ~curious(X1) => ~curious(sK3) [choice axiom]
63. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (~curious(sK3) | ~funny(alice) | humble(alice)) [skolemisation 61,62]
89. curious(X0) | rich(X0) | humble(X0) | strong(X0) [cnf transformation 36]
95. ~strong(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 39]
96. ~strong(X0) | brave(X0) | brave(X0) [cnf transformation 39]
100. ~old(X0) | happy(X0) [cnf transformation 41]
103. ~curious(X0) | ~curious(X0) [cnf transformation 41]
124. ~rich(X0) | ~calm(X0) [cnf transformation 48]
135. old(X0) | calm(X0) [cnf transformation 33]
137. ~humble(alice) | curious(X0) [cnf transformation 63]
153. ~happy(alice) [cnf transformation 25]
155. ~curious(X0) [duplicate literal removal 103]
156. ~strong(X0) | ~brave(X0) [duplicate literal removal 95]
157. ~strong(X0) | brave(X0) [duplicate literal removal 96]
182. ~strong(X0) [subsumption resolution 156,157]
207. 9 <=> humble(alice) [avatar definition]
208. ~humble(alice) <- (~9) [avatar component clause 207]
250. ~humble(alice) [subsumption resolution 137,155]
251. ~9 [avatar split clause 250,207]
304. happy(X1) | calm(X1) [resolution 135,100]
309. calm(alice) [resolution 304,153]
432. rich(X2) | humble(X2) | strong(X2) [resolution 89,155]
433. rich(X2) | humble(X2) [subsumption resolution 432,182]
446. 37 <=> rich(alice) [avatar definition]
447. ~rich(alice) <- (~37) [avatar component clause 446]
448. rich(alice) <- (37) [avatar component clause 446]
479. humble(alice) <- (~37) [resolution 447,433]
480. $false <- (~9, ~37) [subsumption resolution 479,208]
481. 9 | 37 [avatar contradiction clause 480]
483. ~calm(alice) <- (37) [resolution 448,124]
485. $false <- (37) [subsumption resolution 483,309]
486. ~37 [avatar contradiction clause 485]
487. $false [avatar sat refutation 251,481,486]
% SZS output end Proof for 2409375930488560706909224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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