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 both not curious and not brave then someone is tall or not humble.
Everyone who is both quiet and not funny is not kind.
Everyone who is either creative or not quiet is curious.
If mary is both not strong and not rich then someone is generous.
Everyone who is not curious or happy is not curious.
Everyone who is patient is creative.
Everyone who is both happy and not creative is not quiet or patient and vice versa.
If mary is either wise or generous then susan is not patient and vice versa.
Everyone who is either not brave or not curious is not brave and vice versa.
If someone is either funny or not curious then susan is not patient or humble and vice versa.
Everyone who is old or wise is old or not kind and vice versa.
Everyone who is both not patient and creative is either patient or not humble.
Everyone who is brave or patient is kind or rich and vice versa.
Everyone who is not curious is tall and vice versa.
Everyone who is both happy and kind is creative or not curious and vice versa.
If someone is both not old and not strong then paul is either not generous or calm and vice versa.
Someone is either not funny or calm.
Lucy is brave.
Someone is either curious or generous.
Someone is either patient or not happy.
Someone is either not wise or brave.
Lucy is humble or not rich. | Paul is tall. | contradiction | ((?[X]:((~curious(X)&~brave(X))))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((quiet(X)&~funny(X))=>~kind(X)))&
(![X]:((creative(X)<~>~quiet(X))=>curious(X)))&
(((~strong(mary)&~rich(mary)))=>(?[X]:(generous(X))))&
(![X]:((~curious(X)|happy(X))=>~curious(X)))&
(![X]:(patient(X)=>creative(X)))&
(![X]:((happy(X)&~creative(X))<=>(~quiet(X)|patient(X))))&
(((wise(mary)<~>generous(mary)))<=>(~patient(susan)))&
(![X]:((~brave(X)<~>~curious(X))<=>~brave(X)))&
((?[X]:((funny(X)<~>~curious(X))))<=>((~patient(susan)|humble(susan))))&
(![X]:((old(X)|wise(X))<=>(old(X)|~kind(X))))&
(![X]:((~patient(X)&creative(X))=>(patient(X)<~>~humble(X))))&
(![X]:((brave(X)|patient(X))<=>(kind(X)|rich(X))))&
(![X]:(~curious(X)<=>tall(X)))&
(![X]:((happy(X)&kind(X))<=>(creative(X)|~curious(X))))&
((?[X]:((~old(X)&~strong(X))))<=>((~generous(paul)<~>calm(paul))))&
(?[X]:((~funny(X)<~>calm(X))))&
(brave(lucy))&
(?[X]:((curious(X)<~>generous(X))))&
(?[X]:((patient(X)<~>~happy(X))))&
(?[X]:((~wise(X)<~>brave(X))))&
((humble(lucy)|~rich(lucy))) | tall(paul) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7953666818204858263359714
% SZS output start Proof for 7953666818204858263359714
9. ! [X0] : ((~brave(X0) <~> ~curious(X0)) <=> ~brave(X0)) [input p8]
14. ! [X0] : (~curious(X0) <=> tall(X0)) [input p13]
23. tall(paul) [input hypothesis]
44. ! [X0] : ((((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | brave(X0)) & (~brave(X0) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))))) [nnf transformation 9]
55. ! [X0] : ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0))) [nnf transformation 14]
92. ~brave(X0) | ~brave(X0) | curious(X0) [cnf transformation 44]
94. curious(X0) | brave(X0) | brave(X0) [cnf transformation 44]
112. ~tall(X0) | ~curious(X0) [cnf transformation 55]
134. tall(paul) [cnf transformation 23]
136. ~brave(X0) | curious(X0) [duplicate literal removal 92]
137. curious(X0) | brave(X0) [duplicate literal removal 94]
139. 1 <=> ! [X1] : (brave(X1) | curious(X1)) [avatar definition]
140. brave(X1) | curious(X1) <- (1) [avatar component clause 139]
177. 1 [avatar split clause 137,139]
264. curious(X1) <- (1) [subsumption resolution 140,136]
270. ~curious(paul) [resolution 112,134]
272. $false <- (1) [subsumption resolution 270,264]
273. ~1 [avatar contradiction clause 272]
274. $false [avatar sat refutation 177,273]
% SZS output end Proof for 7953666818204858263359714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and strong then someone is both creative and tall.
If fred is not strong or not calm then paul is either not humble or strong and vice versa.
Everyone who is either not generous or old is both happy and not funny and vice versa.
Everyone who is not curious is both not generous and not quiet and vice versa.
If someone is both funny and wise then someone is either wise or rich.
Everyone who is both not rich and patient is either not kind or strong.
If someone is both not kind and not rich then someone is strong or curious and vice versa.
If someone is not generous or old then someone is either kind or not brave.
If someone is both not happy and not generous then someone is brave or not creative and vice versa.
Everyone who is both funny and happy is both not humble and calm and vice versa.
If susan is generous or kind then paul is not creative or not generous.
Everyone who is humble is either rich or not happy and vice versa.
Everyone who is wise or calm is both brave and not wise.
Everyone who is not strong is patient or not tall.
Someone is rich or not happy.
Someone is either happy or not tall.
Susan is calm or kind.
Someone is generous or brave.
Susan is either not rich or not kind. | Fred is not brave. | neutral | ((?[X]:((~tall(X)&strong(X))))=>(?[X]:((creative(X)&tall(X)))))&
(((~strong(fred)|~calm(fred)))<=>((~humble(paul)<~>strong(paul))))&
(![X]:((~generous(X)<~>old(X))<=>(happy(X)&~funny(X))))&
(![X]:(~curious(X)<=>(~generous(X)&~quiet(X))))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((~rich(X)&patient(X))=>(~kind(X)<~>strong(X))))&
((?[X]:((~kind(X)&~rich(X))))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((funny(X)&happy(X))<=>(~humble(X)&calm(X))))&
(((generous(susan)|kind(susan)))=>((~creative(paul)|~generous(paul))))&
(![X]:(humble(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((wise(X)|calm(X))=>(brave(X)&~wise(X))))&
(![X]:(~strong(X)=>(patient(X)|~tall(X))))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:((happy(X)<~>~tall(X))))&
((calm(susan)|kind(susan)))&
(?[X]:((generous(X)|brave(X))))&
((~rich(susan)<~>~kind(susan))) | ~brave(fred) | [] | null | 0 |
Everyone who is not patient or not brave is generous.
If alice is kind then john is not humble or not patient and vice versa.
Everyone who is either calm or happy is brave.
If someone is not old then someone is both not kind and not strong and vice versa.
Everyone who is not funny is funny or not humble and vice versa.
If john is kind or not humble then paul is either funny or not rich and vice versa.
Everyone who is either wise or not calm is brave and vice versa.
Everyone who is happy or funny is strong or tall.
Everyone who is either not creative or generous is either not funny or not calm.
Everyone who is either strong or generous is either kind or not brave and vice versa.
Everyone who is not rich or creative is both not quiet and not generous.
Everyone who is either not creative or not humble is either funny or not rich and vice versa.
If lucy is rich then someone is both not creative and not kind.
Everyone who is happy is either kind or not kind and vice versa.
Everyone who is both not calm and not patient is generous or strong and vice versa.
If mary is generous then susan is not kind or happy and vice versa.
Someone is rich.
John is not patient.
Paul is curious.
Someone is happy.
Someone is not humble or not tall.
Someone is both not kind and not strong. | John is not funny. | entailment | (![X]:((~patient(X)|~brave(X))=>generous(X)))&
((kind(alice))<=>((~humble(john)|~patient(john))))&
(![X]:((calm(X)<~>happy(X))=>brave(X)))&
((?[X]:(~old(X)))<=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:(~funny(X)<=>(funny(X)|~humble(X))))&
(((kind(john)|~humble(john)))<=>((funny(paul)<~>~rich(paul))))&
(![X]:((wise(X)<~>~calm(X))<=>brave(X)))&
(![X]:((happy(X)|funny(X))=>(strong(X)|tall(X))))&
(![X]:((~creative(X)<~>generous(X))=>(~funny(X)<~>~calm(X))))&
(![X]:((strong(X)<~>generous(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~rich(X)|creative(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~creative(X)<~>~humble(X))<=>(funny(X)<~>~rich(X))))&
((rich(lucy))=>(?[X]:((~creative(X)&~kind(X)))))&
(![X]:(happy(X)<=>(kind(X)<~>~kind(X))))&
(![X]:((~calm(X)&~patient(X))<=>(generous(X)|strong(X))))&
((generous(mary))<=>((~kind(susan)|happy(susan))))&
(?[X]:(rich(X)))&
(~patient(john))&
(curious(paul))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)|~tall(X))))&
(?[X]:((~kind(X)&~strong(X)))) | ~funny(john) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 661547195036776237229343
% SZS output start Proof for 661547195036776237229343
5. ! [X0] : (~funny(X0) <=> (~humble(X0) | funny(X0))) [input p4]
23. funny(john) [input hypothesis]
42. ! [X0] : ((~funny(X0) | (humble(X0) & ~funny(X0))) & ((~humble(X0) | funny(X0)) | funny(X0))) [nnf transformation 5]
43. ! [X0] : ((~funny(X0) | (humble(X0) & ~funny(X0))) & (~humble(X0) | funny(X0) | funny(X0))) [flattening 42]
76. ~funny(X0) | ~funny(X0) [cnf transformation 43]
132. funny(john) [cnf transformation 23]
136. ~funny(X0) [duplicate literal removal 76]
203. $false [subsumption resolution 132,136]
% SZS output end Proof for 661547195036776237229343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either calm or not patient then fred is both humble and strong.
If someone is both rich and old then someone is both brave and quiet and vice versa.
Everyone who is either kind or not tall is either generous or old and vice versa.
Everyone who is either funny or not rich is both not wise and not calm.
Everyone who is creative or old is both not creative and not brave.
Everyone who is both patient and kind is either strong or wise.
Everyone who is rich is both not rich and not brave.
Everyone who is both kind and curious is tall or not wise.
If mary is not generous then someone is either kind or not rich.
If fred is both kind and not patient then someone is curious and vice versa.
Everyone who is tall or not curious is not strong.
Everyone who is both rich and creative is both wise and kind and vice versa.
Everyone who is both not humble and not wise is both not curious and happy.
Everyone who is either not wise or not generous is either not patient or not old and vice versa.
Everyone who is either funny or not generous is both not creative and rich and vice versa.
Everyone who is not rich is generous and vice versa.
Someone is quiet.
Someone is strong.
Someone is not calm.
Susan is either kind or not kind.
Lucy is curious.
Susan is old or generous. | Lucy is funny. | contradiction | (((calm(lucy)<~>~patient(lucy)))=>((humble(fred)&strong(fred))))&
((?[X]:((rich(X)&old(X))))<=>(?[X]:((brave(X)&quiet(X)))))&
(![X]:((kind(X)<~>~tall(X))<=>(generous(X)<~>old(X))))&
(![X]:((funny(X)<~>~rich(X))=>(~wise(X)&~calm(X))))&
(![X]:((creative(X)|old(X))=>(~creative(X)&~brave(X))))&
(![X]:((patient(X)&kind(X))=>(strong(X)<~>wise(X))))&
(![X]:(rich(X)=>(~rich(X)&~brave(X))))&
(![X]:((kind(X)&curious(X))=>(tall(X)|~wise(X))))&
((~generous(mary))=>(?[X]:((kind(X)<~>~rich(X)))))&
(((kind(fred)&~patient(fred)))<=>(?[X]:(curious(X))))&
(![X]:((tall(X)|~curious(X))=>~strong(X)))&
(![X]:((rich(X)&creative(X))<=>(wise(X)&kind(X))))&
(![X]:((~humble(X)&~wise(X))=>(~curious(X)&happy(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~creative(X)&rich(X))))&
(![X]:(~rich(X)<=>generous(X)))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X)))&
(?[X]:(~calm(X)))&
((kind(susan)<~>~kind(susan)))&
(curious(lucy))&
((old(susan)|generous(susan))) | funny(lucy) | [
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 277142854359155066637216
% SZS output start Proof for 277142854359155066637216
7. ! [X0] : (rich(X0) => (~brave(X0) & ~rich(X0))) [input p6]
15. ! [X0] : ((funny(X0) <~> ~generous(X0)) <=> (rich(X0) & ~creative(X0))) [input p14]
16. ! [X0] : (~rich(X0) <=> generous(X0)) [input p15]
23. funny(lucy) [input hypothesis]
33. ! [X0] : ((~brave(X0) & ~rich(X0)) | ~rich(X0)) [ennf transformation 7]
58. ! [X0] : ((((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0))))) [nnf transformation 15]
59. ! [X0] : ((((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0))))) [flattening 58]
60. ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))) [nnf transformation 16]
92. ~rich(X0) | ~rich(X0) [cnf transformation 33]
116. rich(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 59]
120. generous(X0) | rich(X0) [cnf transformation 60]
129. funny(lucy) [cnf transformation 23]
130. ~rich(X0) [duplicate literal removal 92]
202. ~funny(X0) | ~generous(X0) [subsumption resolution 116,130]
203. generous(X0) [subsumption resolution 120,130]
208. ~generous(lucy) [resolution 202,129]
210. $false [subsumption resolution 208,203]
% SZS output end Proof for 277142854359155066637216
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not tall is either happy or not tall. If someone is not old or funny then someone is brave or patient and vice versa. Everyone who is not old or not wise is either generous or brave and vice versa. Everyone who is either kind or generous is not funny or not kind. Everyone who is patient or brave is quiet or curious. Everyone who is not curious is generous or not generous and vice versa. If lucy is either not tall or not patient then someone is not humble and vice versa. Everyone who is both not patient and not happy is not creative and vice versa. Everyone who is both not creative and tall is both wise and happy. Everyone who is not calm is either humble or calm. If someone is brave or not wise then someone is not kind or quiet. If susan is happy then susan is not brave and vice versa. If someone is either not creative or not patient then john is generous or brave and vice versa. Everyone who is kind or not creative is both tall and not tall. Everyone who is happy is either not generous or patient and vice versa. Everyone who is both humble and not wise is happy and vice versa. Mary is not humble or wise. Someone is both old and not funny. Someone is both not brave and strong. Fred is tall or not calm. Paul is not kind. Someone is creative or brave. Someone is both not calm and old. Someone is either tall or quiet. | Mary is happy. | contradiction | (![X]:((humble(X)|~tall(X))=>(happy(X)<~>~tall(X))))&
((?[X]:((~old(X)|funny(X))))<=>(?[X]:((brave(X)|patient(X)))))&
(![X]:((~old(X)|~wise(X))<=>(generous(X)<~>brave(X))))&
(![X]:((kind(X)<~>generous(X))=>(~funny(X)|~kind(X))))&
(![X]:((patient(X)|brave(X))=>(quiet(X)|curious(X))))&
(![X]:(~curious(X)<=>(generous(X)|~generous(X))))&
(((~tall(lucy)<~>~patient(lucy)))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)&~happy(X))<=>~creative(X)))&
(![X]:((~creative(X)&tall(X))=>(wise(X)&happy(X))))&
(![X]:(~calm(X)=>(humble(X)<~>calm(X))))&
((?[X]:((brave(X)|~wise(X))))=>(?[X]:((~kind(X)|quiet(X)))))&
((happy(susan))<=>(~brave(susan)))&
((?[X]:((~creative(X)<~>~patient(X))))<=>((generous(john)|brave(john))))&
(![X]:((kind(X)|~creative(X))=>(tall(X)&~tall(X))))&
(![X]:(happy(X)<=>(~generous(X)<~>patient(X))))&
(![X]:((humble(X)&~wise(X))<=>happy(X)))&
((~humble(mary)|wise(mary)))&
(?[X]:((old(X)&~funny(X))))&
(?[X]:((~brave(X)&strong(X))))&
((tall(fred)|~calm(fred)))&
(~kind(paul))&
(?[X]:((creative(X)|brave(X))))&
(?[X]:((~calm(X)&old(X))))&
(?[X]:((tall(X)<~>quiet(X)))) | happy(mary) | [
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8849486219320241035459151
% SZS output start Proof for 8849486219320241035459151
16. ! [X0] : ((~wise(X0) & humble(X0)) <=> happy(X0)) [input p15]
17. wise(mary) | ~humble(mary) [input p16]
25. happy(mary) [input hypothesis]
67. ! [X0] : (((~wise(X0) & humble(X0)) | ~happy(X0)) & (happy(X0) | (wise(X0) | ~humble(X0)))) [nnf transformation 16]
68. ! [X0] : (((~wise(X0) & humble(X0)) | ~happy(X0)) & (happy(X0) | wise(X0) | ~humble(X0))) [flattening 67]
130. ~happy(X0) | humble(X0) [cnf transformation 68]
131. ~wise(X0) | ~happy(X0) [cnf transformation 68]
132. wise(mary) | ~humble(mary) [cnf transformation 17]
143. happy(mary) [cnf transformation 25]
254. 23 <=> humble(mary) [avatar definition]
258. 24 <=> wise(mary) [avatar definition]
260. wise(mary) <- (24) [avatar component clause 258]
261. ~23 | 24 [avatar split clause 132,258,254]
284. humble(mary) [resolution 130,143]
287. 23 [avatar split clause 284,254]
288. ~happy(mary) <- (24) [resolution 131,260]
289. $false <- (24) [subsumption resolution 288,143]
290. ~24 [avatar contradiction clause 289]
291. $false [avatar sat refutation 261,287,290]
% SZS output end Proof for 8849486219320241035459151
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not brave or not patient then alice is both not wise and not creative and vice versa.
Everyone who is not wise or curious is either not old or kind.
If someone is not generous then someone is not curious or old.
Everyone who is not creative is humble and vice versa.
Everyone who is both not quiet and not rich is strong or rich.
Everyone who is both not wise and brave is not kind and vice versa.
If someone is either patient or creative then someone is both funny and not funny.
Everyone who is not tall or humble is patient and vice versa.
If someone is not kind then someone is both creative and not calm.
If someone is kind or creative then susan is patient and vice versa.
If someone is strong or not happy then alice is both tall and not patient and vice versa.
If mary is rich or not patient then alice is not happy.
Everyone who is both not humble and not curious is both not kind and not tall and vice versa.
Everyone who is not curious is either happy or brave.
Fred is either funny or quiet.
Someone is not happy or curious.
Someone is rich.
Someone is not generous or funny.
Alice is either humble or wise. | Mary is quiet. | entailment | (((~brave(alice)<~>~patient(alice)))<=>((~wise(alice)&~creative(alice))))&
(![X]:((~wise(X)|curious(X))=>(~old(X)<~>kind(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~curious(X)|old(X)))))&
(![X]:(~creative(X)<=>humble(X)))&
(![X]:((~quiet(X)&~rich(X))=>(strong(X)|rich(X))))&
(![X]:((~wise(X)&brave(X))<=>~kind(X)))&
((?[X]:((patient(X)<~>creative(X))))=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((~tall(X)|humble(X))<=>patient(X)))&
((?[X]:(~kind(X)))=>(?[X]:((creative(X)&~calm(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(patient(susan)))&
((?[X]:((strong(X)|~happy(X))))<=>((tall(alice)&~patient(alice))))&
(((rich(mary)|~patient(mary)))=>(~happy(alice)))&
(![X]:((~humble(X)&~curious(X))<=>(~kind(X)&~tall(X))))&
(![X]:(~curious(X)=>(happy(X)<~>brave(X))))&
((funny(fred)<~>quiet(fred)))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:(rich(X)))&
(?[X]:((~generous(X)|funny(X))))&
((humble(alice)<~>wise(alice))) | quiet(mary) | [
"p3",
"p4",
"p6",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8845731448346202812861395
% SZS output start Proof for 8845731448346202812861395
4. ! [X0] : (~creative(X0) <=> humble(X0)) [input p3]
5. ! [X0] : ((~rich(X0) & ~quiet(X0)) => (rich(X0) | strong(X0))) [input p4]
7. ? [X0] : (patient(X0) <~> creative(X0)) => ? [X0] : (~funny(X0) & funny(X0)) [input p6]
8. ! [X0] : ((humble(X0) | ~tall(X0)) <=> patient(X0)) [input p7]
11. ? [X0] : (~happy(X0) | strong(X0)) <=> (~patient(alice) & tall(alice)) [input p10]
12. (~patient(mary) | rich(mary)) => ~happy(alice) [input p11]
20. ~quiet(mary) [input hypothesis]
22. ? [X0] : (patient(X0) <~> creative(X0)) => ? [X1] : (~funny(X1) & funny(X1)) [rectify 7]
27. ! [X0] : ((rich(X0) | strong(X0)) | (rich(X0) | quiet(X0))) [ennf transformation 5]
28. ! [X0] : (rich(X0) | strong(X0) | rich(X0) | quiet(X0)) [flattening 27]
29. ? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : (patient(X0) <=> creative(X0)) [ennf transformation 22]
31. ~happy(alice) | (patient(mary) & ~rich(mary)) [ennf transformation 12]
39. ! [X0] : ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))) [nnf transformation 4]
42. ? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))) [nnf transformation 29]
43. ? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1))) [rectify 42]
44. ? [X0] : (~funny(X0) & funny(X0)) => (~funny(sK1) & funny(sK1)) [choice axiom]
45. (~funny(sK1) & funny(sK1)) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1))) [skolemisation 43,44]
46. ! [X0] : (((humble(X0) | ~tall(X0)) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [nnf transformation 8]
47. ! [X0] : ((humble(X0) | ~tall(X0) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [flattening 46]
55. (? [X0] : (~happy(X0) | strong(X0)) | (patient(alice) | ~tall(alice))) & ((~patient(alice) & tall(alice)) | ! [X0] : (happy(X0) & ~strong(X0))) [nnf transformation 11]
56. (? [X0] : (~happy(X0) | strong(X0)) | patient(alice) | ~tall(alice)) & ((~patient(alice) & tall(alice)) | ! [X0] : (happy(X0) & ~strong(X0))) [flattening 55]
57. (? [X0] : (~happy(X0) | strong(X0)) | patient(alice) | ~tall(alice)) & ((~patient(alice) & tall(alice)) | ! [X1] : (happy(X1) & ~strong(X1))) [rectify 56]
58. ? [X0] : (~happy(X0) | strong(X0)) => (~happy(sK4) | strong(sK4)) [choice axiom]
59. ((~happy(sK4) | strong(sK4)) | patient(alice) | ~tall(alice)) & ((~patient(alice) & tall(alice)) | ! [X1] : (happy(X1) & ~strong(X1))) [skolemisation 57,58]
82. humble(X0) | creative(X0) [cnf transformation 39]
84. rich(X0) | strong(X0) | rich(X0) | quiet(X0) [cnf transformation 28]
88. funny(sK1) | creative(X1) | ~patient(X1) [cnf transformation 45]
89. funny(sK1) | patient(X1) | ~creative(X1) [cnf transformation 45]
90. ~funny(sK1) | creative(X1) | ~patient(X1) [cnf transformation 45]
91. ~funny(sK1) | patient(X1) | ~creative(X1) [cnf transformation 45]
93. ~humble(X0) | patient(X0) [cnf transformation 47]
101. ~patient(alice) | ~strong(X1) [cnf transformation 59]
102. ~patient(alice) | happy(X1) [cnf transformation 59]
104. ~happy(alice) | ~rich(mary) [cnf transformation 31]
119. ~quiet(mary) [cnf transformation 20]
120. strong(X0) | rich(X0) | quiet(X0) [duplicate literal removal 84]
134. 4 <=> patient(alice) [avatar definition]
135. ~patient(alice) <- (~4) [avatar component clause 134]
156. 8 <=> ! [X1] : (patient(X1) | ~creative(X1)) [avatar definition]
157. ~creative(X1) | patient(X1) <- (8) [avatar component clause 156]
159. 9 <=> funny(sK1) [avatar definition]
162. 8 | ~9 [avatar split clause 91,159,156]
164. 10 <=> ! [X1] : (creative(X1) | ~patient(X1)) [avatar definition]
165. ~patient(X1) | creative(X1) <- (10) [avatar component clause 164]
166. 10 | ~9 [avatar split clause 90,159,164]
167. 8 | 9 [avatar split clause 89,159,156]
168. 10 | 9 [avatar split clause 88,159,164]
209. 20 <=> ! [X1] : happy(X1) [avatar definition]
210. happy(X1) <- (20) [avatar component clause 209]
211. 20 | ~4 [avatar split clause 102,134,209]
213. 21 <=> ! [X1] : ~strong(X1) [avatar definition]
214. ~strong(X1) <- (21) [avatar component clause 213]
215. 21 | ~4 [avatar split clause 101,134,213]
227. 24 <=> happy(alice) [avatar definition]
229. ~happy(alice) <- (~24) [avatar component clause 227]
232. 25 <=> rich(mary) [avatar definition]
234. ~rich(mary) <- (~25) [avatar component clause 232]
235. ~25 | ~24 [avatar split clause 104,227,232]
275. patient(X0) | creative(X0) [resolution 93,82]
278. creative(X0) <- (10) [subsumption resolution 275,165]
281. $false <- (20, ~24) [resolution 210,229]
282. ~20 | 24 [avatar contradiction clause 281]
290. patient(X0) <- (8, 10) [resolution 157,278]
291. $false <- (~4, 8, 10) [resolution 290,135]
292. 4 | ~8 | ~10 [avatar contradiction clause 291]
339. rich(X0) | quiet(X0) <- (21) [resolution 120,214]
340. quiet(mary) <- (21, ~25) [resolution 339,234]
341. $false <- (21, ~25) [subsumption resolution 340,119]
342. ~21 | 25 [avatar contradiction clause 341]
343. $false [avatar sat refutation 162,166,167,168,211,215,235,282,292,342]
% SZS output end Proof for 8845731448346202812861395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is calm or not curious and vice versa.
Everyone who is not old or not kind is not old or wise.
Everyone who is either strong or not old is not funny.
If mary is either not rich or calm then mary is happy.
If fred is both not happy and kind then someone is both not humble and not old and vice versa.
Everyone who is curious is either humble or calm.
Everyone who is not generous is calm.
If susan is old or strong then someone is generous or not creative.
If john is not kind or not generous then paul is not generous and vice versa.
If someone is quiet or not happy then alice is not wise.
If someone is both quiet and not patient then alice is either patient or brave.
If someone is kind then mary is either rich or not humble.
If someone is both not rich and not humble then someone is patient or not calm.
If fred is calm or not humble then susan is either rich or not generous and vice versa.
Everyone who is kind or not patient is either old or not patient and vice versa.
Everyone who is not old is both strong and not strong.
Someone is both not creative and tall.
Paul is funny or not wise.
Someone is either not humble or not curious.
Someone is not creative.
Someone is creative or quiet.
John is not calm. | Paul is not patient. | contradiction | (![X]:(brave(X)<=>(calm(X)|~curious(X))))&
(![X]:((~old(X)|~kind(X))=>(~old(X)|wise(X))))&
(![X]:((strong(X)<~>~old(X))=>~funny(X)))&
(((~rich(mary)<~>calm(mary)))=>(happy(mary)))&
(((~happy(fred)&kind(fred)))<=>(?[X]:((~humble(X)&~old(X)))))&
(![X]:(curious(X)=>(humble(X)<~>calm(X))))&
(![X]:(~generous(X)=>calm(X)))&
(((old(susan)|strong(susan)))=>(?[X]:((generous(X)|~creative(X)))))&
(((~kind(john)|~generous(john)))<=>(~generous(paul)))&
((?[X]:((quiet(X)|~happy(X))))=>(~wise(alice)))&
((?[X]:((quiet(X)&~patient(X))))=>((patient(alice)<~>brave(alice))))&
((?[X]:(kind(X)))=>((rich(mary)<~>~humble(mary))))&
((?[X]:((~rich(X)&~humble(X))))=>(?[X]:((patient(X)|~calm(X)))))&
(((calm(fred)|~humble(fred)))<=>((rich(susan)<~>~generous(susan))))&
(![X]:((kind(X)|~patient(X))<=>(old(X)<~>~patient(X))))&
(![X]:(~old(X)=>(strong(X)&~strong(X))))&
(?[X]:((~creative(X)&tall(X))))&
((funny(paul)|~wise(paul)))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:(~creative(X)))&
(?[X]:((creative(X)|quiet(X))))&
(~calm(john)) | ~patient(paul) | [
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1573962589652579382689816
% SZS output start Proof for 1573962589652579382689816
15. ! [X0] : ((~patient(X0) | kind(X0)) <=> (old(X0) <~> ~patient(X0))) [input p14]
16. ! [X0] : (~old(X0) => (~strong(X0) & strong(X0))) [input p15]
23. ~patient(paul) [input hypothesis]
37. ! [X0] : ((~strong(X0) & strong(X0)) | old(X0)) [ennf transformation 16]
59. ! [X0] : (((~patient(X0) | kind(X0)) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) & (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | (patient(X0) & ~kind(X0)))) [nnf transformation 15]
60. ! [X0] : ((~patient(X0) | kind(X0) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) & (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | (patient(X0) & ~kind(X0)))) [flattening 59]
107. patient(X0) | ~old(X0) | patient(X0) [cnf transformation 60]
110. strong(X0) | old(X0) [cnf transformation 37]
111. ~strong(X0) | old(X0) [cnf transformation 37]
119. ~patient(paul) [cnf transformation 23]
120. ~old(X0) | patient(X0) [duplicate literal removal 107]
260. old(X0) [subsumption resolution 110,111]
296. patient(X0) [resolution 120,260]
298. $false [resolution 296,119]
% SZS output end Proof for 1573962589652579382689816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either tall or not generous. Everyone who is curious is not old. If paul is not kind then someone is both not creative and creative and vice versa. If lucy is not quiet or not funny then someone is not happy or not calm and vice versa. Everyone who is not creative is not old or not funny and vice versa. If someone is either not calm or calm then paul is not generous and vice versa. Everyone who is either not brave or wise is both not calm and not humble. Everyone who is either happy or not tall is either not patient or not wise. Everyone who is both not curious and not patient is either old or wise. Everyone who is tall or calm is strong and vice versa. Everyone who is both wise and not calm is not strong or not humble and vice versa. If someone is not brave then someone is brave. Everyone who is both wise and happy is both creative and not brave. Everyone who is either quiet or old is either patient or not strong. If fred is strong then someone is both happy and not creative and vice versa. Everyone who is either not curious or not quiet is both funny and not quiet and vice versa. Someone is not funny. Paul is either not kind or curious. Alice is not brave. Someone is brave or wise. John is either not patient or tall. John is brave. | Alice is not creative. | entailment | (![X]:(~patient(X)=>(tall(X)<~>~generous(X))))&
(![X]:(curious(X)=>~old(X)))&
((~kind(paul))<=>(?[X]:((~creative(X)&creative(X)))))&
(((~quiet(lucy)|~funny(lucy)))<=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:(~creative(X)<=>(~old(X)|~funny(X))))&
((?[X]:((~calm(X)<~>calm(X))))<=>(~generous(paul)))&
(![X]:((~brave(X)<~>wise(X))=>(~calm(X)&~humble(X))))&
(![X]:((happy(X)<~>~tall(X))=>(~patient(X)<~>~wise(X))))&
(![X]:((~curious(X)&~patient(X))=>(old(X)<~>wise(X))))&
(![X]:((tall(X)|calm(X))<=>strong(X)))&
(![X]:((wise(X)&~calm(X))<=>(~strong(X)|~humble(X))))&
((?[X]:(~brave(X)))=>(?[X]:(brave(X))))&
(![X]:((wise(X)&happy(X))=>(creative(X)&~brave(X))))&
(![X]:((quiet(X)<~>old(X))=>(patient(X)<~>~strong(X))))&
((strong(fred))<=>(?[X]:((happy(X)&~creative(X)))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(funny(X)&~quiet(X))))&
(?[X]:(~funny(X)))&
((~kind(paul)<~>curious(paul)))&
(~brave(alice))&
(?[X]:((brave(X)|wise(X))))&
((~patient(john)<~>tall(john)))&
(brave(john)) | ~creative(alice) | [
"p1",
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5584607857840471024452991
% SZS output start Proof for 5584607857840471024452991
2. ! [X0] : (curious(X0) => ~old(X0)) [input p1]
5. ! [X0] : (~creative(X0) <=> (~funny(X0) | ~old(X0))) [input p4]
16. ! [X0] : ((~curious(X0) <~> ~quiet(X0)) <=> (~quiet(X0) & funny(X0))) [input p15]
23. creative(alice) [input hypothesis]
26. ! [X0] : (~old(X0) | ~curious(X0)) [ennf transformation 2]
45. ! [X0] : ((~creative(X0) | (funny(X0) & old(X0))) & ((~funny(X0) | ~old(X0)) | creative(X0))) [nnf transformation 5]
46. ! [X0] : ((~creative(X0) | (funny(X0) & old(X0))) & (~funny(X0) | ~old(X0) | creative(X0))) [flattening 45]
66. ! [X0] : ((((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | (quiet(X0) | ~funny(X0))) & ((~quiet(X0) & funny(X0)) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0))))) [nnf transformation 16]
67. ! [X0] : ((((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | quiet(X0) | ~funny(X0)) & ((~quiet(X0) & funny(X0)) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0))))) [flattening 66]
76. ~old(X0) | ~curious(X0) [cnf transformation 26]
85. ~creative(X0) | old(X0) [cnf transformation 46]
86. ~creative(X0) | funny(X0) [cnf transformation 46]
121. ~quiet(X0) | ~quiet(X0) | curious(X0) [cnf transformation 67]
124. quiet(X0) | curious(X0) | quiet(X0) | ~funny(X0) [cnf transformation 67]
133. creative(alice) [cnf transformation 23]
134. ~quiet(X0) | curious(X0) [duplicate literal removal 121]
135. ~funny(X0) | curious(X0) | quiet(X0) [duplicate literal removal 124]
237. old(alice) [resolution 85,133]
238. funny(alice) [resolution 86,133]
239. ~curious(alice) [resolution 237,76]
277. curious(alice) | quiet(alice) [resolution 135,238]
278. quiet(alice) [subsumption resolution 277,239]
290. curious(alice) [resolution 278,134]
291. $false [subsumption resolution 290,239]
% SZS output end Proof for 5584607857840471024452991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and curious then lucy is kind or not calm.
Everyone who is not generous is curious.
Everyone who is both not curious and not tall is either not old or not strong.
Everyone who is not kind is both not quiet and not rich.
If paul is not quiet or patient then john is not creative or happy and vice versa.
Everyone who is not tall or wise is either not happy or humble.
If mary is not calm or not happy then someone is either not kind or strong.
Everyone who is either not curious or creative is both not creative and not strong.
Everyone who is not brave or not strong is both not humble and not tall.
If someone is both not quiet and not curious then susan is not quiet or not kind and vice versa.
If fred is not patient then john is old or not rich.
Everyone who is calm is not curious or curious and vice versa.
If paul is not humble or not patient then paul is either brave or not quiet.
If someone is happy then mary is humble or patient.
If someone is strong or quiet then alice is either quiet or kind and vice versa.
If someone is kind or curious then mary is either not wise or strong.
Someone is not wise or curious.
Susan is not funny or funny.
Susan is either generous or not strong.
Someone is both humble and not patient.
Mary is patient or not wise.
Someone is both not brave and kind. | Lucy is brave. | neutral | ((?[X]:((~patient(X)&curious(X))))=>((kind(lucy)|~calm(lucy))))&
(![X]:(~generous(X)=>curious(X)))&
(![X]:((~curious(X)&~tall(X))=>(~old(X)<~>~strong(X))))&
(![X]:(~kind(X)=>(~quiet(X)&~rich(X))))&
(((~quiet(paul)|patient(paul)))<=>((~creative(john)|happy(john))))&
(![X]:((~tall(X)|wise(X))=>(~happy(X)<~>humble(X))))&
(((~calm(mary)|~happy(mary)))=>(?[X]:((~kind(X)<~>strong(X)))))&
(![X]:((~curious(X)<~>creative(X))=>(~creative(X)&~strong(X))))&
(![X]:((~brave(X)|~strong(X))=>(~humble(X)&~tall(X))))&
((?[X]:((~quiet(X)&~curious(X))))<=>((~quiet(susan)|~kind(susan))))&
((~patient(fred))=>((old(john)|~rich(john))))&
(![X]:(calm(X)<=>(~curious(X)|curious(X))))&
(((~humble(paul)|~patient(paul)))=>((brave(paul)<~>~quiet(paul))))&
((?[X]:(happy(X)))=>((humble(mary)|patient(mary))))&
((?[X]:((strong(X)|quiet(X))))<=>((quiet(alice)<~>kind(alice))))&
((?[X]:((kind(X)|curious(X))))=>((~wise(mary)<~>strong(mary))))&
(?[X]:((~wise(X)|curious(X))))&
((~funny(susan)|funny(susan)))&
((generous(susan)<~>~strong(susan)))&
(?[X]:((humble(X)&~patient(X))))&
((patient(mary)|~wise(mary)))&
(?[X]:((~brave(X)&kind(X)))) | brave(lucy) | [] | null | 0 |
If someone is curious then someone is not brave.
Everyone who is either not generous or curious is both not old and rich.
If someone is both not calm and kind then paul is not tall and vice versa.
If susan is both not curious and not calm then susan is not humble and vice versa.
If someone is happy or not creative then alice is not curious or generous and vice versa.
Everyone who is rich is not brave or creative and vice versa.
If mary is not brave or not patient then fred is humble and vice versa.
Everyone who is not calm is either rich or not rich.
Everyone who is both brave and rich is not tall or not rich.
Everyone who is either not kind or quiet is not funny or not patient and vice versa.
If susan is either not wise or not rich then someone is both tall and not wise and vice versa.
Everyone who is either brave or not brave is both curious and not tall.
If alice is patient or old then someone is either funny or not quiet and vice versa.
If alice is both happy and curious then paul is rich or not strong.
If susan is both not generous and not tall then someone is both tall and not brave and vice versa.
Everyone who is both not rich and not generous is wise.
Someone is not rich.
Someone is either tall or brave.
Someone is not strong.
Someone is not quiet.
Susan is either curious or patient.
Paul is either not wise or not kind.
Mary is either not brave or generous.
Someone is humble or creative. | Mary is not rich. | contradiction | ((?[X]:(curious(X)))=>(?[X]:(~brave(X))))&
(![X]:((~generous(X)<~>curious(X))=>(~old(X)&rich(X))))&
((?[X]:((~calm(X)&kind(X))))<=>(~tall(paul)))&
(((~curious(susan)&~calm(susan)))<=>(~humble(susan)))&
((?[X]:((happy(X)|~creative(X))))<=>((~curious(alice)|generous(alice))))&
(![X]:(rich(X)<=>(~brave(X)|creative(X))))&
(((~brave(mary)|~patient(mary)))<=>(humble(fred)))&
(![X]:(~calm(X)=>(rich(X)<~>~rich(X))))&
(![X]:((brave(X)&rich(X))=>(~tall(X)|~rich(X))))&
(![X]:((~kind(X)<~>quiet(X))<=>(~funny(X)|~patient(X))))&
(((~wise(susan)<~>~rich(susan)))<=>(?[X]:((tall(X)&~wise(X)))))&
(![X]:((brave(X)<~>~brave(X))=>(curious(X)&~tall(X))))&
(((patient(alice)|old(alice)))<=>(?[X]:((funny(X)<~>~quiet(X)))))&
(((happy(alice)&curious(alice)))=>((rich(paul)|~strong(paul))))&
(((~generous(susan)&~tall(susan)))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((~rich(X)&~generous(X))=>wise(X)))&
(?[X]:(~rich(X)))&
(?[X]:((tall(X)<~>brave(X))))&
(?[X]:(~strong(X)))&
(?[X]:(~quiet(X)))&
((curious(susan)<~>patient(susan)))&
((~wise(paul)<~>~kind(paul)))&
((~brave(mary)<~>generous(mary)))&
(?[X]:((humble(X)|creative(X)))) | ~rich(mary) | [
"p1",
"p5",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 26961005514383152849405
% SZS output start Proof for 26961005514383152849405
2. ! [X0] : ((~generous(X0) <~> curious(X0)) => (rich(X0) & ~old(X0))) [input p1]
6. ! [X0] : (rich(X0) <=> (creative(X0) | ~brave(X0))) [input p5]
12. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (~tall(X0) & curious(X0))) [input p11]
23. ~brave(mary) <~> generous(mary) [input p22]
25. ~rich(mary) [input hypothesis]
30. ! [X0] : ((rich(X0) & ~old(X0)) | (~generous(X0) <=> curious(X0))) [ennf transformation 2]
34. ! [X0] : ((~tall(X0) & curious(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 12]
40. ! [X0] : ((rich(X0) & ~old(X0)) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) [nnf transformation 30]
52. ! [X0] : ((rich(X0) | (~creative(X0) & brave(X0))) & ((creative(X0) | ~brave(X0)) | ~rich(X0))) [nnf transformation 6]
53. ! [X0] : ((rich(X0) | (~creative(X0) & brave(X0))) & (creative(X0) | ~brave(X0) | ~rich(X0))) [flattening 52]
63. ! [X0] : ((~tall(X0) & curious(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 34]
83. (~generous(mary) | brave(mary)) & (generous(mary) | ~brave(mary)) [nnf transformation 23]
90. ~generous(X0) | rich(X0) | ~curious(X0) [cnf transformation 40]
102. rich(X0) | brave(X0) [cnf transformation 53]
122. curious(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 63]
123. curious(X0) | brave(X0) | brave(X0) [cnf transformation 63]
145. generous(mary) | ~brave(mary) [cnf transformation 83]
148. ~rich(mary) [cnf transformation 25]
149. curious(X0) | ~brave(X0) [duplicate literal removal 122]
150. brave(X0) | curious(X0) [duplicate literal removal 123]
226. 17 <=> brave(mary) [avatar definition]
262. curious(X0) [subsumption resolution 149,150]
317. 34 <=> generous(mary) [avatar definition]
318. generous(mary) <- (34) [avatar component clause 317]
321. ~17 | 34 [avatar split clause 145,317,226]
336. brave(mary) [resolution 102,148]
340. 17 [avatar split clause 336,226]
347. rich(mary) | ~curious(mary) <- (34) [resolution 90,318]
352. ~curious(mary) <- (34) [subsumption resolution 347,148]
353. $false <- (34) [subsumption resolution 352,262]
354. ~34 [avatar contradiction clause 353]
355. $false [avatar sat refutation 321,340,354]
% SZS output end Proof for 26961005514383152849405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or not wise then someone is either happy or not brave and vice versa.
Everyone who is not kind is generous.
Everyone who is either old or funny is not generous or tall.
If someone is either not tall or kind then someone is not curious and vice versa.
Everyone who is both strong and not brave is both not happy and not patient.
If john is either not rich or creative then someone is either kind or patient.
Everyone who is not kind or not generous is humble or not quiet and vice versa.
Everyone who is either generous or creative is either not creative or not strong and vice versa.
If someone is not kind then someone is either curious or calm and vice versa.
Everyone who is both happy and not curious is either kind or not calm.
Everyone who is either not kind or not humble is either not calm or not curious and vice versa.
If someone is not strong or not kind then susan is both funny and not humble and vice versa.
If mary is not wise then lucy is tall.
Everyone who is both creative and not quiet is either rich or not strong and vice versa.
John is wise or curious.
Someone is not funny.
Someone is both not happy and creative.
Alice is brave or not old.
Susan is not generous or tall. | Susan is not brave. | neutral | ((?[X]:((quiet(X)<~>~wise(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:(~kind(X)=>generous(X)))&
(![X]:((old(X)<~>funny(X))=>(~generous(X)|tall(X))))&
((?[X]:((~tall(X)<~>kind(X))))<=>(?[X]:(~curious(X))))&
(![X]:((strong(X)&~brave(X))=>(~happy(X)&~patient(X))))&
(((~rich(john)<~>creative(john)))=>(?[X]:((kind(X)<~>patient(X)))))&
(![X]:((~kind(X)|~generous(X))<=>(humble(X)|~quiet(X))))&
(![X]:((generous(X)<~>creative(X))<=>(~creative(X)<~>~strong(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((happy(X)&~curious(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~calm(X)<~>~curious(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>((funny(susan)&~humble(susan))))&
((~wise(mary))=>(tall(lucy)))&
(![X]:((creative(X)&~quiet(X))<=>(rich(X)<~>~strong(X))))&
((wise(john)|curious(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~happy(X)&creative(X))))&
((brave(alice)|~old(alice)))&
((~generous(susan)|tall(susan))) | ~brave(susan) | [] | null | 0 |
Everyone who is not strong or strong is both wise and rich and vice versa.
If alice is not creative then someone is generous and vice versa.
Everyone who is both curious and not strong is not wise.
If someone is either not patient or old then someone is not rich and vice versa.
Everyone who is not curious is kind or patient.
If fred is both not strong and not creative then someone is not calm or not wise.
Everyone who is curious or not happy is not humble and vice versa.
If alice is tall or strong then someone is not kind or curious.
If mary is funny then someone is not calm and vice versa.
If someone is not tall or not creative then someone is both not patient and not old and vice versa.
If john is both strong and patient then someone is not calm or not wise.
Everyone who is both quiet and curious is not creative and vice versa.
If lucy is either not old or not generous then mary is both wise and calm and vice versa.
If fred is brave then someone is either tall or quiet and vice versa.
If someone is not calm then susan is both not brave and not patient and vice versa.
Everyone who is either humble or not happy is rich or not funny.
Paul is not tall or not quiet.
Alice is strong.
Someone is not kind or not happy.
Susan is both not old and not brave.
Paul is both tall and calm.
Someone is either not tall or funny. | Susan is not wise. | contradiction | (![X]:((~strong(X)|strong(X))<=>(wise(X)&rich(X))))&
((~creative(alice))<=>(?[X]:(generous(X))))&
(![X]:((curious(X)&~strong(X))=>~wise(X)))&
((?[X]:((~patient(X)<~>old(X))))<=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)=>(kind(X)|patient(X))))&
(((~strong(fred)&~creative(fred)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((curious(X)|~happy(X))<=>~humble(X)))&
(((tall(alice)|strong(alice)))=>(?[X]:((~kind(X)|curious(X)))))&
((funny(mary))<=>(?[X]:(~calm(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(((strong(john)&patient(john)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((quiet(X)&curious(X))<=>~creative(X)))&
(((~old(lucy)<~>~generous(lucy)))<=>((wise(mary)&calm(mary))))&
((brave(fred))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))<=>((~brave(susan)&~patient(susan))))&
(![X]:((humble(X)<~>~happy(X))=>(rich(X)|~funny(X))))&
((~tall(paul)|~quiet(paul)))&
(strong(alice))&
(?[X]:((~kind(X)|~happy(X))))&
((~old(susan)&~brave(susan)))&
((tall(paul)&calm(paul)))&
(?[X]:((~tall(X)<~>funny(X)))) | ~wise(susan) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 6688650779212372307551162
% SZS output start Proof for 6688650779212372307551162
1. ! [X0] : ((strong(X0) | ~strong(X0)) <=> (rich(X0) & wise(X0))) [input p0]
23. ~wise(susan) [input hypothesis]
37. ! [X0] : (((strong(X0) | ~strong(X0)) | (~rich(X0) | ~wise(X0))) & ((rich(X0) & wise(X0)) | (~strong(X0) & strong(X0)))) [nnf transformation 1]
38. ! [X0] : ((strong(X0) | ~strong(X0) | ~rich(X0) | ~wise(X0)) & ((rich(X0) & wise(X0)) | (~strong(X0) & strong(X0)))) [flattening 37]
84. wise(X0) | strong(X0) [cnf transformation 38]
85. wise(X0) | ~strong(X0) [cnf transformation 38]
138. ~wise(susan) [cnf transformation 23]
140. wise(X0) [subsumption resolution 84,85]
320. $false [subsumption resolution 138,140]
% SZS output end Proof for 6688650779212372307551162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or kind then john is either rich or not curious and vice versa. If someone is rich or not patient then someone is both not happy and not old. Everyone who is patient is either patient or kind. Everyone who is either creative or wise is not tall. Everyone who is both generous and strong is not quiet. If john is both not funny and happy then fred is both not wise and not creative and vice versa. Everyone who is not funny is calm or patient and vice versa. If fred is either rich or not brave then alice is not patient. Everyone who is not creative or not patient is both brave and quiet. If someone is not generous then someone is kind or not brave and vice versa. Everyone who is not rich is not happy or not generous. Everyone who is either generous or not curious is not kind and vice versa. If someone is either not patient or not generous then alice is funny. Everyone who is either old or funny is both not wise and not curious. If mary is either brave or not strong then someone is both not rich and not tall. Everyone who is either not quiet or calm is either happy or not calm and vice versa. Someone is not kind or rich. Someone is either not old or happy. Someone is either not curious or not rich. Fred is generous. Someone is not wise or not generous. Someone is not strong or strong. Someone is both not rich and calm. Someone is both creative and not rich. | Mary is not strong. | neutral | ((?[X]:((~creative(X)|kind(X))))<=>((rich(john)<~>~curious(john))))&
((?[X]:((rich(X)|~patient(X))))=>(?[X]:((~happy(X)&~old(X)))))&
(![X]:(patient(X)=>(patient(X)<~>kind(X))))&
(![X]:((creative(X)<~>wise(X))=>~tall(X)))&
(![X]:((generous(X)&strong(X))=>~quiet(X)))&
(((~funny(john)&happy(john)))<=>((~wise(fred)&~creative(fred))))&
(![X]:(~funny(X)<=>(calm(X)|patient(X))))&
(((rich(fred)<~>~brave(fred)))=>(~patient(alice)))&
(![X]:((~creative(X)|~patient(X))=>(brave(X)&quiet(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((kind(X)|~brave(X)))))&
(![X]:(~rich(X)=>(~happy(X)|~generous(X))))&
(![X]:((generous(X)<~>~curious(X))<=>~kind(X)))&
((?[X]:((~patient(X)<~>~generous(X))))=>(funny(alice)))&
(![X]:((old(X)<~>funny(X))=>(~wise(X)&~curious(X))))&
(((brave(mary)<~>~strong(mary)))=>(?[X]:((~rich(X)&~tall(X)))))&
(![X]:((~quiet(X)<~>calm(X))<=>(happy(X)<~>~calm(X))))&
(?[X]:((~kind(X)|rich(X))))&
(?[X]:((~old(X)<~>happy(X))))&
(?[X]:((~curious(X)<~>~rich(X))))&
(generous(fred))&
(?[X]:((~wise(X)|~generous(X))))&
(?[X]:((~strong(X)|strong(X))))&
(?[X]:((~rich(X)&calm(X))))&
(?[X]:((creative(X)&~rich(X)))) | ~strong(mary) | [] | null | 0 |
If paul is not creative then lucy is either tall or not rich.
Everyone who is either funny or tall is not calm or not creative and vice versa.
Everyone who is not humble or not curious is not kind or not brave and vice versa.
Everyone who is either not calm or wise is not calm or happy and vice versa.
Everyone who is not kind or not calm is either creative or kind.
If susan is generous or not curious then alice is kind.
Everyone who is patient is not old.
If someone is strong then john is either tall or curious.
If someone is not humble then someone is rich and vice versa.
If lucy is both not wise and not rich then someone is humble and vice versa.
Everyone who is either tall or generous is wise and vice versa.
Everyone who is either generous or not old is not humble or not quiet and vice versa.
Everyone who is both not wise and not generous is not old or not rich.
Everyone who is not rich is generous.
If someone is both brave and old then someone is not generous and vice versa.
If john is both brave and kind then someone is humble or not brave and vice versa.
Mary is quiet or not patient.
Alice is both not strong and not creative.
Someone is not funny.
Fred is both not generous and not calm.
John is both brave and strong.
Fred is not kind or tall.
Someone is quiet.
Someone is not creative or strong. | John is brave. | entailment | ((~creative(paul))=>((tall(lucy)<~>~rich(lucy))))&
(![X]:((funny(X)<~>tall(X))<=>(~calm(X)|~creative(X))))&
(![X]:((~humble(X)|~curious(X))<=>(~kind(X)|~brave(X))))&
(![X]:((~calm(X)<~>wise(X))<=>(~calm(X)|happy(X))))&
(![X]:((~kind(X)|~calm(X))=>(creative(X)<~>kind(X))))&
(((generous(susan)|~curious(susan)))=>(kind(alice)))&
(![X]:(patient(X)=>~old(X)))&
((?[X]:(strong(X)))=>((tall(john)<~>curious(john))))&
((?[X]:(~humble(X)))<=>(?[X]:(rich(X))))&
(((~wise(lucy)&~rich(lucy)))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)<~>generous(X))<=>wise(X)))&
(![X]:((generous(X)<~>~old(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((~wise(X)&~generous(X))=>(~old(X)|~rich(X))))&
(![X]:(~rich(X)=>generous(X)))&
((?[X]:((brave(X)&old(X))))<=>(?[X]:(~generous(X))))&
(((brave(john)&kind(john)))<=>(?[X]:((humble(X)|~brave(X)))))&
((quiet(mary)|~patient(mary)))&
((~strong(alice)&~creative(alice)))&
(?[X]:(~funny(X)))&
((~generous(fred)&~calm(fred)))&
((brave(john)&strong(john)))&
((~kind(fred)|tall(fred)))&
(?[X]:(quiet(X)))&
(?[X]:((~creative(X)|strong(X)))) | brave(john) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3515355253633047438929028
% SZS output start Proof for 3515355253633047438929028
21. strong(john) & brave(john) [input p20]
25. ~brave(john) [input hypothesis]
131. brave(john) [cnf transformation 21]
136. ~brave(john) [cnf transformation 25]
243. 24 <=> brave(john) [avatar definition]
257. 24 [avatar split clause 131,243]
276. ~24 [avatar split clause 136,243]
277. $false [avatar sat refutation 257,276]
% SZS output end Proof for 3515355253633047438929028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and calm is either not humble or curious.
Everyone who is either not generous or tall is generous and vice versa.
If john is not old then someone is either not patient or not generous and vice versa.
If someone is both not strong and not tall then paul is either wise or funny and vice versa.
Everyone who is both curious and not happy is either brave or creative.
Everyone who is funny or brave is not wise and vice versa.
If someone is either not generous or not calm then mary is either not strong or quiet and vice versa.
Everyone who is not old or old is both brave and not creative.
If someone is both not funny and not brave then lucy is tall.
Everyone who is both old and patient is either rich or brave and vice versa.
If lucy is not rich or not funny then someone is quiet and vice versa.
Everyone who is brave is generous or kind.
If someone is wise then someone is strong.
Everyone who is either not creative or creative is brave or creative and vice versa.
Everyone who is both curious and funny is both brave and not happy.
Everyone who is both humble and not kind is not patient and vice versa.
Fred is both funny and tall.
John is both tall and happy.
Someone is both not wise and calm.
Someone is either quiet or funny.
Someone is both not curious and not quiet.
Susan is not generous or old.
Someone is both not funny and kind.
Paul is both kind and not humble. | Fred is rich. | neutral | (![X]:((generous(X)&calm(X))=>(~humble(X)<~>curious(X))))&
(![X]:((~generous(X)<~>tall(X))<=>generous(X)))&
((~old(john))<=>(?[X]:((~patient(X)<~>~generous(X)))))&
((?[X]:((~strong(X)&~tall(X))))<=>((wise(paul)<~>funny(paul))))&
(![X]:((curious(X)&~happy(X))=>(brave(X)<~>creative(X))))&
(![X]:((funny(X)|brave(X))<=>~wise(X)))&
((?[X]:((~generous(X)<~>~calm(X))))<=>((~strong(mary)<~>quiet(mary))))&
(![X]:((~old(X)|old(X))=>(brave(X)&~creative(X))))&
((?[X]:((~funny(X)&~brave(X))))=>(tall(lucy)))&
(![X]:((old(X)&patient(X))<=>(rich(X)<~>brave(X))))&
(((~rich(lucy)|~funny(lucy)))<=>(?[X]:(quiet(X))))&
(![X]:(brave(X)=>(generous(X)|kind(X))))&
((?[X]:(wise(X)))=>(?[X]:(strong(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)|creative(X))))&
(![X]:((curious(X)&funny(X))=>(brave(X)&~happy(X))))&
(![X]:((humble(X)&~kind(X))<=>~patient(X)))&
((funny(fred)&tall(fred)))&
((tall(john)&happy(john)))&
(?[X]:((~wise(X)&calm(X))))&
(?[X]:((quiet(X)<~>funny(X))))&
(?[X]:((~curious(X)&~quiet(X))))&
((~generous(susan)|old(susan)))&
(?[X]:((~funny(X)&kind(X))))&
((kind(paul)&~humble(paul))) | rich(fred) | [] | null | 0 |
Everyone who is both happy and not generous is both quiet and humble and vice versa.
If alice is either creative or brave then mary is both wise and funny.
If john is old then alice is both happy and calm.
If alice is either not wise or generous then susan is calm or wise.
If john is funny then someone is strong and vice versa.
Everyone who is old or funny is both not wise and not strong.
Everyone who is happy or kind is both not kind and curious.
Everyone who is either not generous or not kind is both not patient and patient and vice versa.
Everyone who is not kind is either kind or not creative and vice versa.
If someone is both not patient and not happy then someone is both generous and calm.
If lucy is either not humble or tall then lucy is not curious or quiet and vice versa.
If lucy is both not tall and strong then someone is not brave and vice versa.
Everyone who is both not calm and not old is not old or funny.
Everyone who is both brave and tall is both not rich and not tall.
Everyone who is either not kind or not humble is either wise or generous and vice versa.
Everyone who is either not tall or wise is either not happy or strong and vice versa.
Someone is both patient and funny.
John is not tall or not kind.
Fred is not old or kind. | Alice is rich. | neutral | (![X]:((happy(X)&~generous(X))<=>(quiet(X)&humble(X))))&
(((creative(alice)<~>brave(alice)))=>((wise(mary)&funny(mary))))&
((old(john))=>((happy(alice)&calm(alice))))&
(((~wise(alice)<~>generous(alice)))=>((calm(susan)|wise(susan))))&
((funny(john))<=>(?[X]:(strong(X))))&
(![X]:((old(X)|funny(X))=>(~wise(X)&~strong(X))))&
(![X]:((happy(X)|kind(X))=>(~kind(X)&curious(X))))&
(![X]:((~generous(X)<~>~kind(X))<=>(~patient(X)&patient(X))))&
(![X]:(~kind(X)<=>(kind(X)<~>~creative(X))))&
((?[X]:((~patient(X)&~happy(X))))=>(?[X]:((generous(X)&calm(X)))))&
(((~humble(lucy)<~>tall(lucy)))<=>((~curious(lucy)|quiet(lucy))))&
(((~tall(lucy)&strong(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~calm(X)&~old(X))=>(~old(X)|funny(X))))&
(![X]:((brave(X)&tall(X))=>(~rich(X)&~tall(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>(wise(X)<~>generous(X))))&
(![X]:((~tall(X)<~>wise(X))<=>(~happy(X)<~>strong(X))))&
(?[X]:((patient(X)&funny(X))))&
((~tall(john)|~kind(john)))&
((~old(fred)|kind(fred))) | rich(alice) | [] | null | 0 |
Everyone who is creative or not happy is rich.
Everyone who is not quiet is wise.
If john is generous or not rich then mary is either quiet or patient.
If someone is not quiet or strong then john is old or not wise.
If someone is quiet or patient then paul is not humble and vice versa.
If someone is both humble and happy then someone is both curious and not patient and vice versa.
Everyone who is both not strong and humble is both not creative and curious and vice versa.
If someone is old or kind then someone is both not brave and not creative and vice versa.
Everyone who is both funny and calm is not humble and vice versa.
If someone is either not brave or not tall then alice is not quiet or brave.
Everyone who is not curious is both calm and not strong and vice versa.
Everyone who is calm or creative is quiet or strong.
Everyone who is both not brave and tall is either creative or brave and vice versa.
Everyone who is quiet or humble is both not calm and not tall and vice versa.
Everyone who is both kind and humble is either not curious or not tall.
Susan is both not old and not kind.
Someone is not humble or patient. | Susan is not curious. | contradiction | (![X]:((creative(X)|~happy(X))=>rich(X)))&
(![X]:(~quiet(X)=>wise(X)))&
(((generous(john)|~rich(john)))=>((quiet(mary)<~>patient(mary))))&
((?[X]:((~quiet(X)|strong(X))))=>((old(john)|~wise(john))))&
((?[X]:((quiet(X)|patient(X))))<=>(~humble(paul)))&
((?[X]:((humble(X)&happy(X))))<=>(?[X]:((curious(X)&~patient(X)))))&
(![X]:((~strong(X)&humble(X))<=>(~creative(X)&curious(X))))&
((?[X]:((old(X)|kind(X))))<=>(?[X]:((~brave(X)&~creative(X)))))&
(![X]:((funny(X)&calm(X))<=>~humble(X)))&
((?[X]:((~brave(X)<~>~tall(X))))=>((~quiet(alice)|brave(alice))))&
(![X]:(~curious(X)<=>(calm(X)&~strong(X))))&
(![X]:((calm(X)|creative(X))=>(quiet(X)|strong(X))))&
(![X]:((~brave(X)&tall(X))<=>(creative(X)<~>brave(X))))&
(![X]:((quiet(X)|humble(X))<=>(~calm(X)&~tall(X))))&
(![X]:((kind(X)&humble(X))=>(~curious(X)<~>~tall(X))))&
((~old(susan)&~kind(susan)))&
(?[X]:((~humble(X)|patient(X)))) | ~curious(susan) | [
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9039279345339530765557578
% SZS output start Proof for 9039279345339530765557578
11. ! [X0] : (~curious(X0) <=> (~strong(X0) & calm(X0))) [input p10]
12. ! [X0] : ((creative(X0) | calm(X0)) => (strong(X0) | quiet(X0))) [input p11]
14. ! [X0] : ((humble(X0) | quiet(X0)) <=> (~tall(X0) & ~calm(X0))) [input p13]
18. ~curious(susan) [input hypothesis]
29. ! [X0] : ((strong(X0) | quiet(X0)) | (~creative(X0) & ~calm(X0))) [ennf transformation 12]
30. ! [X0] : (strong(X0) | quiet(X0) | (~creative(X0) & ~calm(X0))) [flattening 29]
52. ! [X0] : ((~curious(X0) | (strong(X0) | ~calm(X0))) & ((~strong(X0) & calm(X0)) | curious(X0))) [nnf transformation 11]
53. ! [X0] : ((~curious(X0) | strong(X0) | ~calm(X0)) & ((~strong(X0) & calm(X0)) | curious(X0))) [flattening 52]
56. ! [X0] : (((humble(X0) | quiet(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~humble(X0) & ~quiet(X0)))) [nnf transformation 14]
57. ! [X0] : ((humble(X0) | quiet(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | (~humble(X0) & ~quiet(X0)))) [flattening 56]
85. calm(X0) | curious(X0) [cnf transformation 53]
86. ~strong(X0) | curious(X0) [cnf transformation 53]
88. ~calm(X0) | quiet(X0) | strong(X0) [cnf transformation 30]
96. ~calm(X0) | ~quiet(X0) [cnf transformation 57]
106. ~curious(susan) [cnf transformation 18]
233. ~quiet(X0) | curious(X0) [resolution 96,85]
283. quiet(X0) | strong(X0) | curious(X0) [resolution 88,85]
285. strong(X0) | curious(X0) [subsumption resolution 283,233]
286. curious(X0) [subsumption resolution 285,86]
288. $false [resolution 286,106]
% SZS output end Proof for 9039279345339530765557578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and curious is patient and vice versa. Everyone who is both tall and not calm is both not rich and not wise and vice versa. If someone is either not generous or not funny then paul is strong or generous. If someone is strong or funny then someone is both curious and brave. If mary is not kind then paul is either not happy or brave. If someone is either wise or kind then mary is calm. Everyone who is not humble is either not brave or humble. Everyone who is curious is either tall or funny. Everyone who is either curious or not brave is either not quiet or not humble and vice versa. If paul is both not happy and not generous then mary is either kind or not funny and vice versa. Everyone who is not wise or not strong is either not generous or humble. If someone is curious then someone is both creative and patient and vice versa. Everyone who is either not patient or old is either creative or patient and vice versa. Everyone who is either brave or not strong is both not kind and brave and vice versa. Everyone who is wise is kind. Paul is not patient. Paul is either not humble or happy. Mary is both not old and quiet. Someone is not creative or not curious. | Paul is not creative. | neutral | (![X]:((~patient(X)&curious(X))<=>patient(X)))&
(![X]:((tall(X)&~calm(X))<=>(~rich(X)&~wise(X))))&
((?[X]:((~generous(X)<~>~funny(X))))=>((strong(paul)|generous(paul))))&
((?[X]:((strong(X)|funny(X))))=>(?[X]:((curious(X)&brave(X)))))&
((~kind(mary))=>((~happy(paul)<~>brave(paul))))&
((?[X]:((wise(X)<~>kind(X))))=>(calm(mary)))&
(![X]:(~humble(X)=>(~brave(X)<~>humble(X))))&
(![X]:(curious(X)=>(tall(X)<~>funny(X))))&
(![X]:((curious(X)<~>~brave(X))<=>(~quiet(X)<~>~humble(X))))&
(((~happy(paul)&~generous(paul)))<=>((kind(mary)<~>~funny(mary))))&
(![X]:((~wise(X)|~strong(X))=>(~generous(X)<~>humble(X))))&
((?[X]:(curious(X)))<=>(?[X]:((creative(X)&patient(X)))))&
(![X]:((~patient(X)<~>old(X))<=>(creative(X)<~>patient(X))))&
(![X]:((brave(X)<~>~strong(X))<=>(~kind(X)&brave(X))))&
(![X]:(wise(X)=>kind(X)))&
(~patient(paul))&
((~humble(paul)<~>happy(paul)))&
((~old(mary)&quiet(mary)))&
(?[X]:((~creative(X)|~curious(X)))) | ~creative(paul) | [] | null | 0 |
Everyone who is both not rich and creative is either not tall or not humble and vice versa.
If susan is both not brave and not curious then someone is humble and vice versa.
If alice is either not creative or quiet then paul is both calm and humble.
Everyone who is not rich or not funny is either not kind or not old.
If john is not old or quiet then alice is either not happy or not calm and vice versa.
If someone is brave or not humble then someone is calm and vice versa.
If paul is both humble and calm then paul is not humble or rich.
Everyone who is kind is either humble or rich.
Everyone who is both tall and not humble is not patient or patient and vice versa.
Everyone who is either not humble or humble is both curious and calm and vice versa.
If fred is not happy or not curious then alice is generous or calm and vice versa.
If someone is either generous or rich then someone is not humble or old and vice versa.
Everyone who is old is generous.
Everyone who is both not calm and kind is both humble and not old.
If someone is funny then lucy is curious or not strong and vice versa.
If someone is either not patient or quiet then someone is both curious and creative and vice versa.
Someone is not patient or not wise.
Someone is both not brave and not funny.
Mary is brave.
Lucy is both not funny and not wise.
Fred is strong or not humble.
Someone is old or not curious.
Someone is not quiet. | Alice is quiet. | contradiction | (![X]:((~rich(X)&creative(X))<=>(~tall(X)<~>~humble(X))))&
(((~brave(susan)&~curious(susan)))<=>(?[X]:(humble(X))))&
(((~creative(alice)<~>quiet(alice)))=>((calm(paul)&humble(paul))))&
(![X]:((~rich(X)|~funny(X))=>(~kind(X)<~>~old(X))))&
(((~old(john)|quiet(john)))<=>((~happy(alice)<~>~calm(alice))))&
((?[X]:((brave(X)|~humble(X))))<=>(?[X]:(calm(X))))&
(((humble(paul)&calm(paul)))=>((~humble(paul)|rich(paul))))&
(![X]:(kind(X)=>(humble(X)<~>rich(X))))&
(![X]:((tall(X)&~humble(X))<=>(~patient(X)|patient(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(curious(X)&calm(X))))&
(((~happy(fred)|~curious(fred)))<=>((generous(alice)|calm(alice))))&
((?[X]:((generous(X)<~>rich(X))))<=>(?[X]:((~humble(X)|old(X)))))&
(![X]:(old(X)=>generous(X)))&
(![X]:((~calm(X)&kind(X))=>(humble(X)&~old(X))))&
((?[X]:(funny(X)))<=>((curious(lucy)|~strong(lucy))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((curious(X)&creative(X)))))&
(?[X]:((~patient(X)|~wise(X))))&
(?[X]:((~brave(X)&~funny(X))))&
(brave(mary))&
((~funny(lucy)&~wise(lucy)))&
((strong(fred)|~humble(fred)))&
(?[X]:((old(X)|~curious(X))))&
(?[X]:(~quiet(X))) | quiet(alice) | [
"p0",
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1503873093692053103351504
% SZS output start Proof for 1503873093692053103351504
1. ! [X0] : ((creative(X0) & ~rich(X0)) <=> (~tall(X0) <~> ~humble(X0))) [input p0]
3. (~creative(alice) <~> quiet(alice)) => (humble(paul) & calm(paul)) [input p2]
9. ! [X0] : ((~humble(X0) & tall(X0)) <=> (patient(X0) | ~patient(X0))) [input p8]
24. quiet(alice) [input hypothesis]
30. (humble(paul) & calm(paul)) | (~creative(alice) <=> quiet(alice)) [ennf transformation 3]
38. ! [X0] : (((creative(X0) & ~rich(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) & (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (~creative(X0) | rich(X0)))) [nnf transformation 1]
39. ! [X0] : (((creative(X0) & ~rich(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) & (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ~creative(X0) | rich(X0))) [flattening 38]
45. (humble(paul) & calm(paul)) | ((~creative(alice) | ~quiet(alice)) & (quiet(alice) | creative(alice))) [nnf transformation 30]
55. ! [X0] : (((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0))) & ((patient(X0) | ~patient(X0)) | (humble(X0) | ~tall(X0)))) [nnf transformation 9]
56. ! [X0] : (((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0))) & (patient(X0) | ~patient(X0) | humble(X0) | ~tall(X0))) [flattening 55]
87. ~tall(X0) | creative(X0) | humble(X0) [cnf transformation 39]
94. humble(paul) | ~creative(alice) | ~quiet(alice) [cnf transformation 45]
112. tall(X0) | patient(X0) [cnf transformation 56]
113. ~patient(X0) | tall(X0) [cnf transformation 56]
114. ~humble(X0) | patient(X0) [cnf transformation 56]
115. ~patient(X0) | ~humble(X0) [cnf transformation 56]
151. quiet(alice) [cnf transformation 24]
158. 1 <=> ! [X0] : ~humble(X0) [avatar definition]
159. ~humble(X0) <- (1) [avatar component clause 158]
176. 5 <=> quiet(alice) [avatar definition]
180. 6 <=> creative(alice) [avatar definition]
182. ~creative(alice) <- (~6) [avatar component clause 180]
184. 7 <=> humble(paul) [avatar definition]
186. humble(paul) <- (7) [avatar component clause 184]
187. ~5 | ~6 | 7 [avatar split clause 94,184,180,176]
246. ~humble(X0) [subsumption resolution 114,115]
247. 1 [avatar split clause 246,158]
248. tall(X0) [subsumption resolution 112,113]
332. 5 [avatar split clause 151,176]
344. creative(X0) | humble(X0) [resolution 87,248]
345. creative(X0) <- (1) [subsumption resolution 344,159]
346. $false <- (1, ~6) [resolution 345,182]
347. ~1 | 6 [avatar contradiction clause 346]
350. $false <- (1, 7) [subsumption resolution 186,159]
351. ~1 | ~7 [avatar contradiction clause 350]
352. $false [avatar sat refutation 187,247,332,347,351]
% SZS output end Proof for 1503873093692053103351504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious then someone is quiet or tall and vice versa.
If lucy is either wise or calm then paul is quiet and vice versa.
If susan is not wise then someone is not happy or patient and vice versa.
Everyone who is not strong or brave is generous or curious.
If someone is both not generous and creative then mary is both not strong and not curious.
If paul is not funny then someone is calm and vice versa.
Everyone who is strong is not happy or humble and vice versa.
Everyone who is not quiet or not humble is tall or patient and vice versa.
If someone is not wise or brave then fred is either not humble or not brave and vice versa.
Everyone who is either not generous or creative is both humble and not funny and vice versa.
If someone is both generous and not wise then mary is wise or curious and vice versa.
Everyone who is either not patient or humble is not brave.
Everyone who is curious is not wise and vice versa.
Everyone who is either not wise or not happy is both humble and kind and vice versa.
Everyone who is old or kind is both not creative and strong and vice versa.
Everyone who is either creative or kind is both curious and not generous and vice versa.
Fred is calm or not generous.
Lucy is both calm and not brave.
Mary is not wise.
Paul is both not happy and generous.
Someone is not curious.
Lucy is either not patient or not creative. | Lucy is not happy. | contradiction | ((~curious(paul))<=>(?[X]:((quiet(X)|tall(X)))))&
(((wise(lucy)<~>calm(lucy)))<=>(quiet(paul)))&
((~wise(susan))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~strong(X)|brave(X))=>(generous(X)|curious(X))))&
((?[X]:((~generous(X)&creative(X))))=>((~strong(mary)&~curious(mary))))&
((~funny(paul))<=>(?[X]:(calm(X))))&
(![X]:(strong(X)<=>(~happy(X)|humble(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(tall(X)|patient(X))))&
((?[X]:((~wise(X)|brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~generous(X)<~>creative(X))<=>(humble(X)&~funny(X))))&
((?[X]:((generous(X)&~wise(X))))<=>((wise(mary)|curious(mary))))&
(![X]:((~patient(X)<~>humble(X))=>~brave(X)))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((~wise(X)<~>~happy(X))<=>(humble(X)&kind(X))))&
(![X]:((old(X)|kind(X))<=>(~creative(X)&strong(X))))&
(![X]:((creative(X)<~>kind(X))<=>(curious(X)&~generous(X))))&
((calm(fred)|~generous(fred)))&
((calm(lucy)&~brave(lucy)))&
(~wise(mary))&
((~happy(paul)&generous(paul)))&
(?[X]:(~curious(X)))&
((~patient(lucy)<~>~creative(lucy))) | ~happy(lucy) | [
"p0",
"p1",
"p12",
"p13",
"p14",
"p15",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7250385722364686739264927
% SZS output start Proof for 7250385722364686739264927
1. ~curious(paul) <=> ? [X0] : (tall(X0) | quiet(X0)) [input p0]
2. (wise(lucy) <~> calm(lucy)) <=> quiet(paul) [input p1]
13. ! [X0] : (curious(X0) <=> ~wise(X0)) [input p12]
14. ! [X0] : ((~wise(X0) <~> ~happy(X0)) <=> (kind(X0) & humble(X0))) [input p13]
15. ! [X0] : ((kind(X0) | old(X0)) <=> (strong(X0) & ~creative(X0))) [input p14]
16. ! [X0] : ((creative(X0) <~> kind(X0)) <=> (~generous(X0) & curious(X0))) [input p15]
18. ~brave(lucy) & calm(lucy) [input p17]
20. generous(paul) & ~happy(paul) [input p19]
23. ~happy(lucy) [input hypothesis]
28. (~curious(paul) | ! [X0] : (~tall(X0) & ~quiet(X0))) & (? [X0] : (tall(X0) | quiet(X0)) | curious(paul)) [nnf transformation 1]
29. (~curious(paul) | ! [X0] : (~tall(X0) & ~quiet(X0))) & (? [X1] : (tall(X1) | quiet(X1)) | curious(paul)) [rectify 28]
30. ? [X1] : (tall(X1) | quiet(X1)) => (tall(sK0) | quiet(sK0)) [choice axiom]
31. (~curious(paul) | ! [X0] : (~tall(X0) & ~quiet(X0))) & ((tall(sK0) | quiet(sK0)) | curious(paul)) [skolemisation 29,30]
32. (((~calm(lucy) | ~wise(lucy)) & (calm(lucy) | wise(lucy))) | ~quiet(paul)) & (quiet(paul) | ((wise(lucy) | ~calm(lucy)) & (calm(lucy) | ~wise(lucy)))) [nnf transformation 2]
57. ! [X0] : ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))) [nnf transformation 13]
58. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (~kind(X0) | ~humble(X0))) & ((kind(X0) & humble(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [nnf transformation 14]
59. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | ~kind(X0) | ~humble(X0)) & ((kind(X0) & humble(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [flattening 58]
60. ! [X0] : (((kind(X0) | old(X0)) | (~strong(X0) | creative(X0))) & ((strong(X0) & ~creative(X0)) | (~kind(X0) & ~old(X0)))) [nnf transformation 15]
61. ! [X0] : ((kind(X0) | old(X0) | ~strong(X0) | creative(X0)) & ((strong(X0) & ~creative(X0)) | (~kind(X0) & ~old(X0)))) [flattening 60]
62. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | (generous(X0) | ~curious(X0))) & ((~generous(X0) & curious(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [nnf transformation 16]
63. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | generous(X0) | ~curious(X0)) & ((~generous(X0) & curious(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [flattening 62]
68. ~curious(paul) | ~quiet(X0) [cnf transformation 31]
71. quiet(paul) | wise(lucy) | ~calm(lucy) [cnf transformation 32]
109. ~wise(X0) | ~curious(X0) [cnf transformation 57]
110. wise(X0) | curious(X0) [cnf transformation 57]
114. ~wise(X0) | kind(X0) | happy(X0) [cnf transformation 59]
118. ~kind(X0) | ~creative(X0) [cnf transformation 61]
123. curious(X0) | creative(X0) | ~kind(X0) [cnf transformation 63]
129. calm(lucy) [cnf transformation 18]
132. ~happy(paul) [cnf transformation 20]
137. ~happy(lucy) [cnf transformation 23]
142. 2 <=> curious(paul) [avatar definition]
147. 3 <=> ! [X0] : ~quiet(X0) [avatar definition]
148. ~quiet(X0) <- (3) [avatar component clause 147]
149. 3 | ~2 [avatar split clause 68,142,147]
160. 6 <=> quiet(paul) [avatar definition]
161. quiet(paul) <- (6) [avatar component clause 160]
164. 7 <=> wise(lucy) [avatar definition]
165. wise(lucy) <- (7) [avatar component clause 164]
168. 8 <=> calm(lucy) [avatar definition]
173. ~8 | 7 | 6 [avatar split clause 71,160,164,168]
272. ~kind(X0) | curious(X0) [subsumption resolution 123,118]
283. 8 [avatar split clause 129,168]
354. kind(X0) | happy(X0) | curious(X0) [resolution 114,110]
355. happy(X0) | curious(X0) [subsumption resolution 354,272]
358. curious(paul) [resolution 355,132]
359. curious(lucy) [resolution 355,137]
363. 2 [avatar split clause 358,142]
365. $false <- (3, 6) [resolution 148,161]
366. ~3 | ~6 [avatar contradiction clause 365]
370. ~curious(lucy) <- (7) [resolution 165,109]
373. $false <- (7) [subsumption resolution 370,359]
374. ~7 [avatar contradiction clause 373]
375. $false [avatar sat refutation 149,173,283,363,366,374]
% SZS output end Proof for 7250385722364686739264927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both quiet and wise is both not funny and quiet. If susan is not brave or humble then someone is not wise or happy. Everyone who is either not creative or kind is either funny or not kind and vice versa. If john is both not kind and not happy then paul is quiet. Everyone who is strong is creative or patient and vice versa. Everyone who is both not calm and not old is both patient and not quiet and vice versa. If mary is not strong then someone is both not brave and not funny. If susan is both strong and wise then someone is both calm and funny and vice versa. Everyone who is both not wise and not funny is both not rich and kind. If someone is not creative then john is not happy. Everyone who is funny or not creative is tall or not creative and vice versa. If someone is not creative then mary is both patient and humble. If someone is both not generous and not strong then someone is either not tall or not happy. Everyone who is quiet is both creative and funny and vice versa. Everyone who is funny is either humble or generous and vice versa. If paul is either happy or quiet then fred is both not curious and strong. Someone is not happy. Someone is patient. Fred is creative. Paul is not humble or not creative. Someone is both tall and not wise. Someone is not patient. Someone is not patient or happy. Someone is both curious and patient. | Fred is not curious. | neutral | (![X]:((quiet(X)&wise(X))=>(~funny(X)&quiet(X))))&
(((~brave(susan)|humble(susan)))=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((~creative(X)<~>kind(X))<=>(funny(X)<~>~kind(X))))&
(((~kind(john)&~happy(john)))=>(quiet(paul)))&
(![X]:(strong(X)<=>(creative(X)|patient(X))))&
(![X]:((~calm(X)&~old(X))<=>(patient(X)&~quiet(X))))&
((~strong(mary))=>(?[X]:((~brave(X)&~funny(X)))))&
(((strong(susan)&wise(susan)))<=>(?[X]:((calm(X)&funny(X)))))&
(![X]:((~wise(X)&~funny(X))=>(~rich(X)&kind(X))))&
((?[X]:(~creative(X)))=>(~happy(john)))&
(![X]:((funny(X)|~creative(X))<=>(tall(X)|~creative(X))))&
((?[X]:(~creative(X)))=>((patient(mary)&humble(mary))))&
((?[X]:((~generous(X)&~strong(X))))=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:(quiet(X)<=>(creative(X)&funny(X))))&
(![X]:(funny(X)<=>(humble(X)<~>generous(X))))&
(((happy(paul)<~>quiet(paul)))=>((~curious(fred)&strong(fred))))&
(?[X]:(~happy(X)))&
(?[X]:(patient(X)))&
(creative(fred))&
((~humble(paul)|~creative(paul)))&
(?[X]:((tall(X)&~wise(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~patient(X)|happy(X))))&
(?[X]:((curious(X)&patient(X)))) | ~curious(fred) | [] | null | 0 |
Everyone who is either not kind or not patient is both not happy and patient. If susan is both not funny and old then paul is either brave or not kind. Everyone who is both not wise and patient is either not patient or creative. Everyone who is both not patient and not calm is both not calm and not wise. If someone is quiet or not happy then someone is not calm. If susan is tall or not funny then alice is either not kind or humble and vice versa. Everyone who is both not quiet and not brave is either curious or generous. If someone is tall or not happy then someone is either strong or not rich and vice versa. Everyone who is both not curious and tall is either brave or not wise. Everyone who is not kind or quiet is both not wise and patient. If someone is rich then someone is both humble and rich and vice versa. If someone is not old then susan is not kind or humble and vice versa. Everyone who is either not calm or not funny is either not old or strong and vice versa. Everyone who is brave or not funny is not humble or humble. If paul is not rich or not happy then someone is rich or not old and vice versa. Everyone who is curious or not quiet is both calm and curious and vice versa. Someone is not funny. Fred is calm. Someone is quiet. Fred is both tall and brave. Lucy is not quiet. Someone is generous or not humble. Alice is quiet or not generous. Alice is either generous or not quiet. | Lucy is curious. | entailment | (![X]:((~kind(X)<~>~patient(X))=>(~happy(X)&patient(X))))&
(((~funny(susan)&old(susan)))=>((brave(paul)<~>~kind(paul))))&
(![X]:((~wise(X)&patient(X))=>(~patient(X)<~>creative(X))))&
(![X]:((~patient(X)&~calm(X))=>(~calm(X)&~wise(X))))&
((?[X]:((quiet(X)|~happy(X))))=>(?[X]:(~calm(X))))&
(((tall(susan)|~funny(susan)))<=>((~kind(alice)<~>humble(alice))))&
(![X]:((~quiet(X)&~brave(X))=>(curious(X)<~>generous(X))))&
((?[X]:((tall(X)|~happy(X))))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(![X]:((~curious(X)&tall(X))=>(brave(X)<~>~wise(X))))&
(![X]:((~kind(X)|quiet(X))=>(~wise(X)&patient(X))))&
((?[X]:(rich(X)))<=>(?[X]:((humble(X)&rich(X)))))&
((?[X]:(~old(X)))<=>((~kind(susan)|humble(susan))))&
(![X]:((~calm(X)<~>~funny(X))<=>(~old(X)<~>strong(X))))&
(![X]:((brave(X)|~funny(X))=>(~humble(X)|humble(X))))&
(((~rich(paul)|~happy(paul)))<=>(?[X]:((rich(X)|~old(X)))))&
(![X]:((curious(X)|~quiet(X))<=>(calm(X)&curious(X))))&
(?[X]:(~funny(X)))&
(calm(fred))&
(?[X]:(quiet(X)))&
((tall(fred)&brave(fred)))&
(~quiet(lucy))&
(?[X]:((generous(X)|~humble(X))))&
((quiet(alice)|~generous(alice)))&
((generous(alice)<~>~quiet(alice))) | curious(lucy) | [
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3525541400986879976353218
% SZS output start Proof for 3525541400986879976353218
16. ! [X0] : ((~quiet(X0) | curious(X0)) <=> (curious(X0) & calm(X0))) [input p15]
21. ~quiet(lucy) [input p20]
25. ~curious(lucy) [input hypothesis]
75. ! [X0] : (((~quiet(X0) | curious(X0)) | (~curious(X0) | ~calm(X0))) & ((curious(X0) & calm(X0)) | (quiet(X0) & ~curious(X0)))) [nnf transformation 16]
76. ! [X0] : ((~quiet(X0) | curious(X0) | ~curious(X0) | ~calm(X0)) & ((curious(X0) & calm(X0)) | (quiet(X0) & ~curious(X0)))) [flattening 75]
139. curious(X0) | quiet(X0) [cnf transformation 76]
146. ~quiet(lucy) [cnf transformation 21]
151. ~curious(lucy) [cnf transformation 25]
319. quiet(lucy) [resolution 139,151]
321. $false [subsumption resolution 319,146]
% SZS output end Proof for 3525541400986879976353218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and brave is both not funny and not old and vice versa.
Everyone who is either not brave or rich is not brave.
If someone is either quiet or not calm then someone is both brave and not old and vice versa.
If lucy is either strong or tall then someone is strong and vice versa.
Everyone who is both not creative and not happy is either tall or strong and vice versa.
If mary is humble then mary is both patient and not funny and vice versa.
If someone is either not humble or curious then susan is calm.
If someone is generous then someone is not curious or calm.
If mary is both funny and not creative then alice is old.
If someone is patient or not brave then lucy is calm.
Everyone who is either not humble or not funny is not brave or not rich.
If someone is either not kind or not calm then alice is brave and vice versa.
If alice is not funny then lucy is both old and rich.
Everyone who is strong or calm is either not generous or rich and vice versa.
Everyone who is happy or wise is not happy.
If susan is not calm then lucy is both humble and not happy.
Someone is not wise.
Mary is both not tall and strong.
Lucy is either not funny or not strong.
Someone is patient.
Someone is kind or not brave.
Mary is not old.
Someone is either tall or rich.
Fred is both not tall and generous. | Fred is not tall. | entailment | (![X]:((~rich(X)&brave(X))<=>(~funny(X)&~old(X))))&
(![X]:((~brave(X)<~>rich(X))=>~brave(X)))&
((?[X]:((quiet(X)<~>~calm(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(((strong(lucy)<~>tall(lucy)))<=>(?[X]:(strong(X))))&
(![X]:((~creative(X)&~happy(X))<=>(tall(X)<~>strong(X))))&
((humble(mary))<=>((patient(mary)&~funny(mary))))&
((?[X]:((~humble(X)<~>curious(X))))=>(calm(susan)))&
((?[X]:(generous(X)))=>(?[X]:((~curious(X)|calm(X)))))&
(((funny(mary)&~creative(mary)))=>(old(alice)))&
((?[X]:((patient(X)|~brave(X))))=>(calm(lucy)))&
(![X]:((~humble(X)<~>~funny(X))=>(~brave(X)|~rich(X))))&
((?[X]:((~kind(X)<~>~calm(X))))<=>(brave(alice)))&
((~funny(alice))=>((old(lucy)&rich(lucy))))&
(![X]:((strong(X)|calm(X))<=>(~generous(X)<~>rich(X))))&
(![X]:((happy(X)|wise(X))=>~happy(X)))&
((~calm(susan))=>((humble(lucy)&~happy(lucy))))&
(?[X]:(~wise(X)))&
((~tall(mary)&strong(mary)))&
((~funny(lucy)<~>~strong(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((kind(X)|~brave(X))))&
(~old(mary))&
(?[X]:((tall(X)<~>rich(X))))&
((~tall(fred)&generous(fred))) | ~tall(fred) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8289264514392064025693304
% SZS output start Proof for 8289264514392064025693304
24. generous(fred) & ~tall(fred) [input p23]
25. tall(fred) [input hypothesis]
133. ~tall(fred) [cnf transformation 24]
135. tall(fred) [cnf transformation 25]
314. $false [subsumption resolution 135,133]
% SZS output end Proof for 8289264514392064025693304
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and not creative is kind and vice versa. Everyone who is not humble is either not patient or not happy and vice versa. If fred is both brave and curious then susan is not funny and vice versa. If john is both not creative and humble then susan is either wise or calm and vice versa. If someone is kind then someone is wise or patient. Everyone who is both not humble and rich is not patient or humble and vice versa. Everyone who is calm or rich is not patient or not happy. Everyone who is both not brave and strong is happy or humble. Everyone who is patient is not brave or not humble and vice versa. Everyone who is both not happy and not tall is not humble. Everyone who is not kind or not creative is both not strong and generous and vice versa. Everyone who is both calm and patient is either tall or not funny and vice versa. Everyone who is both not creative and kind is either not strong or rich. If mary is either brave or tall then john is quiet. Everyone who is not kind is both not brave and old. If alice is creative or brave then someone is either not rich or calm and vice versa. Someone is generous. Mary is both not tall and not funny. John is not brave or not wise. Fred is not quiet. Mary is kind or not happy. Someone is both not kind and not calm. Someone is both not strong and not tall. | Fred is generous. | entailment | (![X]:((~patient(X)&~creative(X))<=>kind(X)))&
(![X]:(~humble(X)<=>(~patient(X)<~>~happy(X))))&
(((brave(fred)&curious(fred)))<=>(~funny(susan)))&
(((~creative(john)&humble(john)))<=>((wise(susan)<~>calm(susan))))&
((?[X]:(kind(X)))=>(?[X]:((wise(X)|patient(X)))))&
(![X]:((~humble(X)&rich(X))<=>(~patient(X)|humble(X))))&
(![X]:((calm(X)|rich(X))=>(~patient(X)|~happy(X))))&
(![X]:((~brave(X)&strong(X))=>(happy(X)|humble(X))))&
(![X]:(patient(X)<=>(~brave(X)|~humble(X))))&
(![X]:((~happy(X)&~tall(X))=>~humble(X)))&
(![X]:((~kind(X)|~creative(X))<=>(~strong(X)&generous(X))))&
(![X]:((calm(X)&patient(X))<=>(tall(X)<~>~funny(X))))&
(![X]:((~creative(X)&kind(X))=>(~strong(X)<~>rich(X))))&
(((brave(mary)<~>tall(mary)))=>(quiet(john)))&
(![X]:(~kind(X)=>(~brave(X)&old(X))))&
(((creative(alice)|brave(alice)))<=>(?[X]:((~rich(X)<~>calm(X)))))&
(?[X]:(generous(X)))&
((~tall(mary)&~funny(mary)))&
((~brave(john)|~wise(john)))&
(~quiet(fred))&
((kind(mary)|~happy(mary)))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((~strong(X)&~tall(X)))) | generous(fred) | [
"p0",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8043489246238423575569822
% SZS output start Proof for 8043489246238423575569822
1. ! [X0] : ((~creative(X0) & ~patient(X0)) <=> kind(X0)) [input p0]
6. ! [X0] : ((rich(X0) & ~humble(X0)) <=> (humble(X0) | ~patient(X0))) [input p5]
9. ! [X0] : (patient(X0) <=> (~humble(X0) | ~brave(X0))) [input p8]
11. ! [X0] : ((~creative(X0) | ~kind(X0)) <=> (generous(X0) & ~strong(X0))) [input p10]
24. ~generous(fred) [input hypothesis]
38. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~kind(X0)) & (kind(X0) | (creative(X0) | patient(X0)))) [nnf transformation 1]
39. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~kind(X0)) & (kind(X0) | creative(X0) | patient(X0))) [flattening 38]
48. ! [X0] : (((rich(X0) & ~humble(X0)) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | (~rich(X0) | humble(X0)))) [nnf transformation 6]
49. ! [X0] : (((rich(X0) & ~humble(X0)) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | ~rich(X0) | humble(X0))) [flattening 48]
50. ! [X0] : ((patient(X0) | (humble(X0) & brave(X0))) & ((~humble(X0) | ~brave(X0)) | ~patient(X0))) [nnf transformation 9]
51. ! [X0] : ((patient(X0) | (humble(X0) & brave(X0))) & (~humble(X0) | ~brave(X0) | ~patient(X0))) [flattening 50]
52. ! [X0] : (((~creative(X0) | ~kind(X0)) | (~generous(X0) | strong(X0))) & ((generous(X0) & ~strong(X0)) | (creative(X0) & kind(X0)))) [nnf transformation 11]
53. ! [X0] : ((~creative(X0) | ~kind(X0) | ~generous(X0) | strong(X0)) & ((generous(X0) & ~strong(X0)) | (creative(X0) & kind(X0)))) [flattening 52]
70. ~kind(X0) | ~patient(X0) [cnf transformation 39]
88. ~humble(X0) | ~humble(X0) [cnf transformation 49]
96. patient(X0) | humble(X0) [cnf transformation 51]
100. generous(X0) | kind(X0) [cnf transformation 53]
130. ~generous(fred) [cnf transformation 24]
132. ~humble(X0) [duplicate literal removal 88]
184. patient(X0) [subsumption resolution 96,132]
250. kind(fred) [resolution 100,130]
254. ~patient(fred) [resolution 250,70]
255. $false [subsumption resolution 254,184]
% SZS output end Proof for 8043489246238423575569822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both quiet and not quiet then someone is both not kind and kind and vice versa.
If john is either rich or not strong then someone is both happy and not humble.
Everyone who is brave or not quiet is not funny and vice versa.
Everyone who is strong or curious is either not humble or brave and vice versa.
Everyone who is not happy is both not tall and wise.
If paul is not old or not funny then alice is quiet and vice versa.
Everyone who is both funny and strong is either funny or not tall.
If alice is both old and not kind then someone is both patient and not old.
Everyone who is wise or not patient is not strong and vice versa.
If someone is either not brave or brave then someone is both not patient and not old and vice versa.
Everyone who is either calm or humble is not rich or not brave and vice versa.
If susan is either not happy or funny then someone is not calm or humble and vice versa.
If someone is rich then mary is both not rich and strong and vice versa.
If someone is both tall and not funny then someone is either curious or not old.
Everyone who is both curious and not happy is not humble.
Everyone who is not patient or generous is not wise.
John is both old and generous.
Someone is either not creative or humble.
John is rich.
Someone is both not brave and tall.
Mary is both not generous and not creative.
Someone is funny or not humble.
Someone is either not funny or calm.
Fred is either not brave or tall. | Mary is creative. | contradiction | (((quiet(susan)&~quiet(susan)))<=>(?[X]:((~kind(X)&kind(X)))))&
(((rich(john)<~>~strong(john)))=>(?[X]:((happy(X)&~humble(X)))))&
(![X]:((brave(X)|~quiet(X))<=>~funny(X)))&
(![X]:((strong(X)|curious(X))<=>(~humble(X)<~>brave(X))))&
(![X]:(~happy(X)=>(~tall(X)&wise(X))))&
(((~old(paul)|~funny(paul)))<=>(quiet(alice)))&
(![X]:((funny(X)&strong(X))=>(funny(X)<~>~tall(X))))&
(((old(alice)&~kind(alice)))=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((wise(X)|~patient(X))<=>~strong(X)))&
((?[X]:((~brave(X)<~>brave(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(![X]:((calm(X)<~>humble(X))<=>(~rich(X)|~brave(X))))&
(((~happy(susan)<~>funny(susan)))<=>(?[X]:((~calm(X)|humble(X)))))&
((?[X]:(rich(X)))<=>((~rich(mary)&strong(mary))))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((curious(X)&~happy(X))=>~humble(X)))&
(![X]:((~patient(X)|generous(X))=>~wise(X)))&
((old(john)&generous(john)))&
(?[X]:((~creative(X)<~>humble(X))))&
(rich(john))&
(?[X]:((~brave(X)&tall(X))))&
((~generous(mary)&~creative(mary)))&
(?[X]:((funny(X)|~humble(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
((~brave(fred)<~>tall(fred))) | creative(mary) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 448460239770923053825138
% SZS output start Proof for 448460239770923053825138
21. ~creative(mary) & ~generous(mary) [input p20]
25. creative(mary) [input hypothesis]
151. ~creative(mary) [cnf transformation 21]
157. creative(mary) [cnf transformation 25]
333. $false [subsumption resolution 157,151]
% SZS output end Proof for 448460239770923053825138
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not brave then someone is not curious or not rich and vice versa.
If alice is both not strong and strong then alice is strong.
If someone is either humble or not curious then paul is both creative and not curious and vice versa.
Everyone who is not happy or not funny is both not old and not strong.
Everyone who is either quiet or wise is either strong or not kind and vice versa.
Everyone who is not creative is not humble or kind.
If someone is not rich then mary is humble or not old and vice versa.
Everyone who is not patient or rich is not generous or kind.
Everyone who is both not generous and not happy is both not humble and wise.
Everyone who is both not strong and humble is old.
Everyone who is not funny or generous is not funny or tall.
Everyone who is not creative is either creative or not generous and vice versa.
Everyone who is both wise and rich is either curious or not funny and vice versa.
If someone is calm then paul is either not quiet or patient.
Everyone who is not wise is either patient or calm.
Everyone who is wise or strong is either happy or not happy.
Mary is humble or tall.
John is both kind and not calm.
Paul is not calm or old.
Someone is not quiet.
Someone is not creative or not quiet.
Fred is both tall and not patient.
Alice is not humble or happy.
Alice is either kind or not creative. | Alice is kind. | neutral | (((~curious(fred)|~brave(fred)))<=>(?[X]:((~curious(X)|~rich(X)))))&
(((~strong(alice)&strong(alice)))=>(strong(alice)))&
((?[X]:((humble(X)<~>~curious(X))))<=>((creative(paul)&~curious(paul))))&
(![X]:((~happy(X)|~funny(X))=>(~old(X)&~strong(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(strong(X)<~>~kind(X))))&
(![X]:(~creative(X)=>(~humble(X)|kind(X))))&
((?[X]:(~rich(X)))<=>((humble(mary)|~old(mary))))&
(![X]:((~patient(X)|rich(X))=>(~generous(X)|kind(X))))&
(![X]:((~generous(X)&~happy(X))=>(~humble(X)&wise(X))))&
(![X]:((~strong(X)&humble(X))=>old(X)))&
(![X]:((~funny(X)|generous(X))=>(~funny(X)|tall(X))))&
(![X]:(~creative(X)<=>(creative(X)<~>~generous(X))))&
(![X]:((wise(X)&rich(X))<=>(curious(X)<~>~funny(X))))&
((?[X]:(calm(X)))=>((~quiet(paul)<~>patient(paul))))&
(![X]:(~wise(X)=>(patient(X)<~>calm(X))))&
(![X]:((wise(X)|strong(X))=>(happy(X)<~>~happy(X))))&
((humble(mary)|tall(mary)))&
((kind(john)&~calm(john)))&
((~calm(paul)|old(paul)))&
(?[X]:(~quiet(X)))&
(?[X]:((~creative(X)|~quiet(X))))&
((tall(fred)&~patient(fred)))&
((~humble(alice)|happy(alice)))&
((kind(alice)<~>~creative(alice))) | kind(alice) | [] | null | 0 |
Everyone who is both not brave and not curious is both rich and funny. Everyone who is not old is either not brave or generous and vice versa. If lucy is not kind then someone is either not brave or not strong. Everyone who is both not wise and tall is humble and vice versa. If someone is rich then fred is both generous and curious. Everyone who is generous is not humble and vice versa. Everyone who is both calm and not calm is either old or patient. Everyone who is either not kind or wise is quiet or not wise and vice versa. If someone is curious or not tall then someone is both old and generous. Everyone who is curious is either strong or humble and vice versa. If someone is not quiet then someone is both generous and not quiet and vice versa. Everyone who is not tall or tall is either patient or not happy. Everyone who is either curious or happy is both brave and not brave and vice versa. Everyone who is both not happy and old is happy or quiet and vice versa. If mary is not creative then mary is either brave or tall and vice versa. Everyone who is not creative is generous. Paul is both strong and not kind. Someone is generous. Someone is not quiet. Someone is both not happy and not strong. Someone is not humble or not creative. | Lucy is kind. | contradiction | (![X]:((~brave(X)&~curious(X))=>(rich(X)&funny(X))))&
(![X]:(~old(X)<=>(~brave(X)<~>generous(X))))&
((~kind(lucy))=>(?[X]:((~brave(X)<~>~strong(X)))))&
(![X]:((~wise(X)&tall(X))<=>humble(X)))&
((?[X]:(rich(X)))=>((generous(fred)&curious(fred))))&
(![X]:(generous(X)<=>~humble(X)))&
(![X]:((calm(X)&~calm(X))=>(old(X)<~>patient(X))))&
(![X]:((~kind(X)<~>wise(X))<=>(quiet(X)|~wise(X))))&
((?[X]:((curious(X)|~tall(X))))=>(?[X]:((old(X)&generous(X)))))&
(![X]:(curious(X)<=>(strong(X)<~>humble(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~tall(X)|tall(X))=>(patient(X)<~>~happy(X))))&
(![X]:((curious(X)<~>happy(X))<=>(brave(X)&~brave(X))))&
(![X]:((~happy(X)&old(X))<=>(happy(X)|quiet(X))))&
((~creative(mary))<=>((brave(mary)<~>tall(mary))))&
(![X]:(~creative(X)=>generous(X)))&
((strong(paul)&~kind(paul)))&
(?[X]:(generous(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((~happy(X)&~strong(X))))&
(?[X]:((~humble(X)|~creative(X)))) | kind(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5905916642176622038974067
% SZS output start Proof for 5905916642176622038974067
1. ! [X0] : ((~curious(X0) & ~brave(X0)) => (funny(X0) & rich(X0))) [input p0]
2. ! [X0] : (~old(X0) <=> (~brave(X0) <~> generous(X0))) [input p1]
4. ! [X0] : ((tall(X0) & ~wise(X0)) <=> humble(X0)) [input p3]
5. ? [X0] : rich(X0) => (curious(fred) & generous(fred)) [input p4]
6. ! [X0] : (generous(X0) <=> ~humble(X0)) [input p5]
8. ! [X0] : ((~kind(X0) <~> wise(X0)) <=> (~wise(X0) | quiet(X0))) [input p7]
13. ! [X0] : ((curious(X0) <~> happy(X0)) <=> (~brave(X0) & brave(X0))) [input p12]
14. ! [X0] : ((old(X0) & ~happy(X0)) <=> (quiet(X0) | happy(X0))) [input p13]
22. kind(lucy) [input hypothesis]
25. ! [X0] : ((~curious(X0) & ~brave(X0)) => rich(X0)) [pure predicate removal 1]
26. ! [X0] : (rich(X0) | (curious(X0) | brave(X0))) [ennf transformation 25]
27. ! [X0] : (rich(X0) | curious(X0) | brave(X0)) [flattening 26]
29. (curious(fred) & generous(fred)) | ! [X0] : ~rich(X0) [ennf transformation 5]
35. ! [X0] : ((~old(X0) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0)))) & (((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | old(X0))) [nnf transformation 2]
39. ! [X0] : (((tall(X0) & ~wise(X0)) | ~humble(X0)) & (humble(X0) | (~tall(X0) | wise(X0)))) [nnf transformation 4]
40. ! [X0] : (((tall(X0) & ~wise(X0)) | ~humble(X0)) & (humble(X0) | ~tall(X0) | wise(X0))) [flattening 39]
41. ! [X0] : ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))) [nnf transformation 6]
43. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (wise(X0) & ~quiet(X0))) & ((~wise(X0) | quiet(X0)) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [nnf transformation 8]
44. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (wise(X0) & ~quiet(X0))) & (~wise(X0) | quiet(X0) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [flattening 43]
55. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [nnf transformation 13]
56. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [flattening 55]
57. ! [X0] : (((old(X0) & ~happy(X0)) | (~quiet(X0) & ~happy(X0))) & ((quiet(X0) | happy(X0)) | (~old(X0) | happy(X0)))) [nnf transformation 14]
58. ! [X0] : (((old(X0) & ~happy(X0)) | (~quiet(X0) & ~happy(X0))) & (quiet(X0) | happy(X0) | ~old(X0) | happy(X0))) [flattening 57]
68. rich(X0) | curious(X0) | brave(X0) [cnf transformation 27]
72. ~generous(X0) | ~brave(X0) | ~old(X0) [cnf transformation 35]
76. ~humble(X0) | ~wise(X0) [cnf transformation 40]
79. curious(fred) | ~rich(X0) [cnf transformation 29]
81. humble(X0) | generous(X0) [cnf transformation 41]
85. ~wise(X0) | quiet(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 44]
87. wise(X0) | ~kind(X0) | wise(X0) [cnf transformation 44]
105. brave(X0) | happy(X0) | ~curious(X0) [cnf transformation 56]
107. ~curious(X0) | happy(X0) | ~brave(X0) [cnf transformation 56]
112. ~happy(X0) | ~happy(X0) [cnf transformation 58]
115. ~quiet(X0) | old(X0) [cnf transformation 58]
128. kind(lucy) [cnf transformation 22]
130. ~happy(X0) [duplicate literal removal 112]
131. ~wise(X0) | quiet(X0) | ~kind(X0) [duplicate literal removal 85]
132. ~kind(X0) | wise(X0) [duplicate literal removal 87]
134. 1 <=> kind(lucy) [avatar definition]
136. kind(lucy) <- (1) [avatar component clause 134]
148. 4 <=> ! [X0] : ~rich(X0) [avatar definition]
149. ~rich(X0) <- (4) [avatar component clause 148]
151. 5 <=> curious(fred) [avatar definition]
153. curious(fred) <- (5) [avatar component clause 151]
154. 4 | 5 [avatar split clause 79,151,148]
160. ~kind(X0) | quiet(X0) [subsumption resolution 131,132]
203. ~curious(X0) | happy(X0) [subsumption resolution 105,107]
230. 1 [avatar split clause 128,134]
237. ~wise(X2) | generous(X2) [resolution 81,76]
241. wise(lucy) <- (1) [resolution 132,136]
242. quiet(lucy) <- (1) [resolution 160,136]
249. old(lucy) <- (1) [resolution 242,115]
257. curious(X0) | brave(X0) <- (4) [resolution 149,68]
310. 30 <=> generous(lucy) [avatar definition]
312. generous(lucy) <- (30) [avatar component clause 310]
368. generous(lucy) <- (1) [resolution 237,241]
369. 30 | ~1 [avatar split clause 368,134,310]
372. brave(X2) | happy(X2) <- (4) [resolution 257,203]
374. brave(X2) <- (4) [subsumption resolution 372,130]
412. ~brave(lucy) | ~old(lucy) <- (30) [resolution 312,72]
417. ~old(lucy) <- (4, 30) [subsumption resolution 412,374]
418. $false <- (1, 4, 30) [subsumption resolution 417,249]
419. ~1 | ~4 | ~30 [avatar contradiction clause 418]
438. happy(fred) <- (5) [resolution 153,203]
450. $false <- (5) [subsumption resolution 438,130]
451. ~5 [avatar contradiction clause 450]
452. $false [avatar sat refutation 154,230,369,419,451]
% SZS output end Proof for 5905916642176622038974067
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not funny or funny then someone is both quiet and not strong and vice versa.
Everyone who is not rich or not wise is either not tall or generous and vice versa.
Everyone who is either humble or not humble is old and vice versa.
If someone is both generous and strong then someone is either not generous or not wise and vice versa.
If someone is humble or not creative then alice is not tall and vice versa.
If someone is funny then someone is funny or quiet and vice versa.
Everyone who is either curious or not generous is both not rich and not humble.
Everyone who is both brave and humble is either not rich or not funny and vice versa.
Everyone who is both kind and happy is curious and vice versa.
Everyone who is patient or not rich is creative.
If lucy is both strong and wise then someone is not humble or not generous.
If paul is either strong or tall then alice is either curious or not patient and vice versa.
If someone is either rich or wise then someone is both old and quiet and vice versa.
Everyone who is either tall or happy is either not creative or not happy.
Everyone who is either patient or not generous is both not patient and not rich and vice versa.
Everyone who is either not tall or happy is both happy and wise.
Someone is either rich or creative.
Someone is funny.
Someone is not old or humble.
Fred is quiet or not strong.
Lucy is creative or brave.
Someone is either not curious or not wise.
Someone is humble or quiet. | Paul is rich. | entailment | ((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:((quiet(X)&~strong(X)))))&
(![X]:((~rich(X)|~wise(X))<=>(~tall(X)<~>generous(X))))&
(![X]:((humble(X)<~>~humble(X))<=>old(X)))&
((?[X]:((generous(X)&strong(X))))<=>(?[X]:((~generous(X)<~>~wise(X)))))&
((?[X]:((humble(X)|~creative(X))))<=>(~tall(alice)))&
((?[X]:(funny(X)))<=>(?[X]:((funny(X)|quiet(X)))))&
(![X]:((curious(X)<~>~generous(X))=>(~rich(X)&~humble(X))))&
(![X]:((brave(X)&humble(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:((kind(X)&happy(X))<=>curious(X)))&
(![X]:((patient(X)|~rich(X))=>creative(X)))&
(((strong(lucy)&wise(lucy)))=>(?[X]:((~humble(X)|~generous(X)))))&
(((strong(paul)<~>tall(paul)))<=>((curious(alice)<~>~patient(alice))))&
((?[X]:((rich(X)<~>wise(X))))<=>(?[X]:((old(X)&quiet(X)))))&
(![X]:((tall(X)<~>happy(X))=>(~creative(X)<~>~happy(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(~patient(X)&~rich(X))))&
(![X]:((~tall(X)<~>happy(X))=>(happy(X)&wise(X))))&
(?[X]:((rich(X)<~>creative(X))))&
(?[X]:(funny(X)))&
(?[X]:((~old(X)|humble(X))))&
((quiet(fred)|~strong(fred)))&
((creative(lucy)|brave(lucy)))&
(?[X]:((~curious(X)<~>~wise(X))))&
(?[X]:((humble(X)|quiet(X)))) | rich(paul) | [
"p1",
"p9",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4690597484189498947837642
% SZS output start Proof for 4690597484189498947837642
2. ! [X0] : ((~wise(X0) | ~rich(X0)) <=> (~tall(X0) <~> generous(X0))) [input p1]
10. ! [X0] : ((~rich(X0) | patient(X0)) => creative(X0)) [input p9]
14. ! [X0] : ((tall(X0) <~> happy(X0)) => (~creative(X0) <~> ~happy(X0))) [input p13]
15. ! [X0] : ((patient(X0) <~> ~generous(X0)) <=> (~rich(X0) & ~patient(X0))) [input p14]
16. ! [X0] : ((~tall(X0) <~> happy(X0)) => (wise(X0) & happy(X0))) [input p15]
24. ~rich(paul) [input hypothesis]
30. ! [X0] : (creative(X0) | (rich(X0) & ~patient(X0))) [ennf transformation 10]
33. ! [X0] : ((~creative(X0) <~> ~happy(X0)) | (tall(X0) <=> happy(X0))) [ennf transformation 14]
34. ! [X0] : ((wise(X0) & happy(X0)) | (~tall(X0) <=> happy(X0))) [ennf transformation 16]
40. ! [X0] : (((~wise(X0) | ~rich(X0)) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0)))) & (((~generous(X0) | tall(X0)) & (generous(X0) | ~tall(X0))) | (wise(X0) & rich(X0)))) [nnf transformation 2]
41. ! [X0] : ((~wise(X0) | ~rich(X0) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0)))) & (((~generous(X0) | tall(X0)) & (generous(X0) | ~tall(X0))) | (wise(X0) & rich(X0)))) [flattening 40]
70. ! [X0] : (((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0)))) [nnf transformation 33]
71. ! [X0] : ((((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | (rich(X0) | patient(X0))) & ((~rich(X0) & ~patient(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0))))) [nnf transformation 15]
72. ! [X0] : ((((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | rich(X0) | patient(X0)) & ((~rich(X0) & ~patient(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0))))) [flattening 71]
73. ! [X0] : ((wise(X0) & happy(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) [nnf transformation 34]
92. ~tall(X0) | generous(X0) | rich(X0) [cnf transformation 41]
128. creative(X0) | rich(X0) [cnf transformation 30]
145. ~happy(X0) | ~creative(X0) | tall(X0) | ~happy(X0) [cnf transformation 70]
148. ~patient(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 72]
152. ~generous(X0) | patient(X0) | rich(X0) | patient(X0) [cnf transformation 72]
154. happy(X0) | happy(X0) | tall(X0) [cnf transformation 73]
167. ~rich(paul) [cnf transformation 24]
168. happy(X0) | tall(X0) [duplicate literal removal 154]
169. ~patient(X0) | ~generous(X0) [duplicate literal removal 148]
170. ~generous(X0) | patient(X0) | rich(X0) [duplicate literal removal 152]
171. ~happy(X0) | ~creative(X0) | tall(X0) [duplicate literal removal 145]
298. 28 <=> tall(paul) [avatar definition]
299. tall(paul) <- (28) [avatar component clause 298]
300. ~tall(paul) <- (~28) [avatar component clause 298]
673. ~creative(X1) | tall(X1) | tall(X1) [resolution 171,168]
674. ~creative(X1) | tall(X1) [duplicate literal removal 673]
753. tall(X0) | rich(X0) [resolution 674,128]
1006. rich(paul) <- (~28) [resolution 753,300]
1013. $false <- (~28) [subsumption resolution 1006,167]
1014. 28 [avatar contradiction clause 1013]
1020. generous(paul) | rich(paul) <- (28) [resolution 299,92]
1135. generous(paul) <- (28) [subsumption resolution 1020,167]
1155. patient(paul) | rich(paul) <- (28) [resolution 1135,170]
1158. patient(paul) <- (28) [subsumption resolution 1155,167]
1177. ~generous(paul) <- (28) [resolution 1158,169]
1179. $false <- (28) [subsumption resolution 1177,1135]
1180. ~28 [avatar contradiction clause 1179]
1181. $false [avatar sat refutation 1014,1180]
% SZS output end Proof for 4690597484189498947837642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5628
% Time elapsed: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or humble then john is curious.
Everyone who is not creative is either not calm or old.
Everyone who is generous is both happy and not kind and vice versa.
If someone is creative or not calm then someone is either not rich or not strong.
Everyone who is both not kind and tall is both not funny and not kind.
If john is not strong then fred is both not patient and curious.
Everyone who is either not old or not calm is either creative or not humble and vice versa.
If someone is wise or not quiet then paul is not quiet.
Everyone who is humble or not rich is not patient and vice versa.
Everyone who is calm is humble and vice versa.
If lucy is either not happy or calm then fred is kind or creative.
Everyone who is creative or quiet is either rich or not calm and vice versa.
Everyone who is not wise is both not kind and old and vice versa.
Everyone who is not tall is not rich and vice versa.
Everyone who is not rich or generous is not generous or tall and vice versa.
If someone is old then someone is patient and vice versa.
Someone is not tall or not curious.
Someone is either brave or strong.
Lucy is both curious and not patient.
Someone is old or kind.
Someone is not calm or quiet.
Paul is either not curious or not old.
Lucy is both not old and not kind. | Paul is not happy. | neutral | ((?[X]:((~kind(X)<~>humble(X))))=>(curious(john)))&
(![X]:(~creative(X)=>(~calm(X)<~>old(X))))&
(![X]:(generous(X)<=>(happy(X)&~kind(X))))&
((?[X]:((creative(X)|~calm(X))))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((~kind(X)&tall(X))=>(~funny(X)&~kind(X))))&
((~strong(john))=>((~patient(fred)&curious(fred))))&
(![X]:((~old(X)<~>~calm(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:((wise(X)|~quiet(X))))=>(~quiet(paul)))&
(![X]:((humble(X)|~rich(X))<=>~patient(X)))&
(![X]:(calm(X)<=>humble(X)))&
(((~happy(lucy)<~>calm(lucy)))=>((kind(fred)|creative(fred))))&
(![X]:((creative(X)|quiet(X))<=>(rich(X)<~>~calm(X))))&
(![X]:(~wise(X)<=>(~kind(X)&old(X))))&
(![X]:(~tall(X)<=>~rich(X)))&
(![X]:((~rich(X)|generous(X))<=>(~generous(X)|tall(X))))&
((?[X]:(old(X)))<=>(?[X]:(patient(X))))&
(?[X]:((~tall(X)|~curious(X))))&
(?[X]:((brave(X)<~>strong(X))))&
((curious(lucy)&~patient(lucy)))&
(?[X]:((old(X)|kind(X))))&
(?[X]:((~calm(X)|quiet(X))))&
((~curious(paul)<~>~old(paul)))&
((~old(lucy)&~kind(lucy))) | ~happy(paul) | [] | null | 0 |
If someone is strong then someone is not humble or brave and vice versa.
Everyone who is calm is not brave.
Everyone who is patient or tall is creative.
Everyone who is not tall or not strong is both not funny and happy and vice versa.
Everyone who is both not old and not brave is both brave and creative.
Everyone who is generous is both not funny and generous.
If fred is strong then someone is calm.
If someone is both not quiet and not strong then alice is either rich or not patient and vice versa.
If someone is creative or not strong then someone is not patient and vice versa.
Everyone who is kind is humble or not tall and vice versa.
If fred is both not generous and not calm then someone is either strong or not creative.
Everyone who is funny or wise is either humble or not humble.
Everyone who is not wise is both not brave and kind.
If someone is either generous or brave then someone is either not calm or patient.
Everyone who is both patient and not patient is not creative or brave and vice versa.
If someone is either not creative or funny then mary is both not curious and not calm and vice versa.
Someone is humble.
John is both strong and not kind.
Someone is rich.
Paul is not generous.
Someone is both not funny and humble.
Someone is patient.
Someone is both kind and not curious.
Someone is both not quiet and old. | John is not brave. | entailment | ((?[X]:(strong(X)))<=>(?[X]:((~humble(X)|brave(X)))))&
(![X]:(calm(X)=>~brave(X)))&
(![X]:((patient(X)|tall(X))=>creative(X)))&
(![X]:((~tall(X)|~strong(X))<=>(~funny(X)&happy(X))))&
(![X]:((~old(X)&~brave(X))=>(brave(X)&creative(X))))&
(![X]:(generous(X)=>(~funny(X)&generous(X))))&
((strong(fred))=>(?[X]:(calm(X))))&
((?[X]:((~quiet(X)&~strong(X))))<=>((rich(alice)<~>~patient(alice))))&
((?[X]:((creative(X)|~strong(X))))<=>(?[X]:(~patient(X))))&
(![X]:(kind(X)<=>(humble(X)|~tall(X))))&
(((~generous(fred)&~calm(fred)))=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((funny(X)|wise(X))=>(humble(X)<~>~humble(X))))&
(![X]:(~wise(X)=>(~brave(X)&kind(X))))&
((?[X]:((generous(X)<~>brave(X))))=>(?[X]:((~calm(X)<~>patient(X)))))&
(![X]:((patient(X)&~patient(X))<=>(~creative(X)|brave(X))))&
((?[X]:((~creative(X)<~>funny(X))))<=>((~curious(mary)&~calm(mary))))&
(?[X]:(humble(X)))&
((strong(john)&~kind(john)))&
(?[X]:(rich(X)))&
(~generous(paul))&
(?[X]:((~funny(X)&humble(X))))&
(?[X]:(patient(X)))&
(?[X]:((kind(X)&~curious(X))))&
(?[X]:((~quiet(X)&old(X)))) | ~brave(john) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4029211205648738125801628
% SZS output start Proof for 4029211205648738125801628
15. ! [X0] : ((~patient(X0) & patient(X0)) <=> (brave(X0) | ~creative(X0))) [input p14]
25. brave(john) [input hypothesis]
68. ! [X0] : (((~patient(X0) & patient(X0)) | (~brave(X0) & creative(X0))) & ((brave(X0) | ~creative(X0)) | (patient(X0) | ~patient(X0)))) [nnf transformation 15]
69. ! [X0] : (((~patient(X0) & patient(X0)) | (~brave(X0) & creative(X0))) & (brave(X0) | ~creative(X0) | patient(X0) | ~patient(X0))) [flattening 68]
127. patient(X0) | ~brave(X0) [cnf transformation 69]
129. ~patient(X0) | ~brave(X0) [cnf transformation 69]
147. brave(john) [cnf transformation 25]
149. 1 <=> ! [X1] : ~brave(X1) [avatar definition]
150. ~brave(X1) <- (1) [avatar component clause 149]
266. ~brave(X0) [subsumption resolution 127,129]
267. 1 [avatar split clause 266,149]
292. $false <- (1) [resolution 150,147]
293. ~1 [avatar contradiction clause 292]
294. $false [avatar sat refutation 267,293]
% SZS output end Proof for 4029211205648738125801628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or not humble then lucy is not strong and vice versa.
If someone is both not kind and not creative then fred is either not humble or not patient.
If fred is either humble or not curious then mary is old or calm.
If someone is not brave then lucy is either not rich or brave.
Everyone who is both kind and humble is quiet or humble and vice versa.
Everyone who is either funny or humble is either not funny or patient and vice versa.
Everyone who is both curious and patient is not patient or not quiet and vice versa.
Everyone who is either strong or not creative is tall or not tall.
If someone is not brave then someone is not curious or strong.
Everyone who is either not humble or quiet is old.
If mary is both not happy and curious then someone is either not tall or patient.
If paul is both calm and not humble then someone is both quiet and wise and vice versa.
If lucy is strong then alice is not brave and vice versa.
Everyone who is not humble is either wise or not creative.
If lucy is either not generous or not quiet then someone is not quiet or wise and vice versa.
If susan is either not quiet or wise then lucy is either generous or not rich and vice versa.
Someone is old.
Alice is not wise.
Fred is either patient or not wise.
Someone is either not kind or not quiet.
Paul is not wise.
Paul is not humble or not quiet.
Someone is patient.
Someone is both not humble and not tall. | Mary is not curious. | contradiction | ((?[X]:((~strong(X)<~>~humble(X))))<=>(~strong(lucy)))&
((?[X]:((~kind(X)&~creative(X))))=>((~humble(fred)<~>~patient(fred))))&
(((humble(fred)<~>~curious(fred)))=>((old(mary)|calm(mary))))&
((?[X]:(~brave(X)))=>((~rich(lucy)<~>brave(lucy))))&
(![X]:((kind(X)&humble(X))<=>(quiet(X)|humble(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((curious(X)&patient(X))<=>(~patient(X)|~quiet(X))))&
(![X]:((strong(X)<~>~creative(X))=>(tall(X)|~tall(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:((~humble(X)<~>quiet(X))=>old(X)))&
(((~happy(mary)&curious(mary)))=>(?[X]:((~tall(X)<~>patient(X)))))&
(((calm(paul)&~humble(paul)))<=>(?[X]:((quiet(X)&wise(X)))))&
((strong(lucy))<=>(~brave(alice)))&
(![X]:(~humble(X)=>(wise(X)<~>~creative(X))))&
(((~generous(lucy)<~>~quiet(lucy)))<=>(?[X]:((~quiet(X)|wise(X)))))&
(((~quiet(susan)<~>wise(susan)))<=>((generous(lucy)<~>~rich(lucy))))&
(?[X]:(old(X)))&
(~wise(alice))&
((patient(fred)<~>~wise(fred)))&
(?[X]:((~kind(X)<~>~quiet(X))))&
(~wise(paul))&
((~humble(paul)|~quiet(paul)))&
(?[X]:(patient(X)))&
(?[X]:((~humble(X)&~tall(X)))) | ~curious(mary) | [
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 318004994795194496010813
% SZS output start Proof for 318004994795194496010813
5. ! [X0] : ((humble(X0) & kind(X0)) <=> (humble(X0) | quiet(X0))) [input p4]
6. ! [X0] : ((funny(X0) <~> humble(X0)) <=> (~funny(X0) <~> patient(X0))) [input p5]
7. ! [X0] : ((patient(X0) & curious(X0)) <=> (~quiet(X0) | ~patient(X0))) [input p6]
25. ~curious(mary) [input hypothesis]
43. ! [X0] : (((humble(X0) & kind(X0)) | (~humble(X0) & ~quiet(X0))) & ((humble(X0) | quiet(X0)) | (~humble(X0) | ~kind(X0)))) [nnf transformation 5]
44. ! [X0] : (((humble(X0) & kind(X0)) | (~humble(X0) & ~quiet(X0))) & (humble(X0) | quiet(X0) | ~humble(X0) | ~kind(X0))) [flattening 43]
45. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [nnf transformation 6]
46. ! [X0] : (((patient(X0) & curious(X0)) | (quiet(X0) & patient(X0))) & ((~quiet(X0) | ~patient(X0)) | (~patient(X0) | ~curious(X0)))) [nnf transformation 7]
47. ! [X0] : (((patient(X0) & curious(X0)) | (quiet(X0) & patient(X0))) & (~quiet(X0) | ~patient(X0) | ~patient(X0) | ~curious(X0))) [flattening 46]
83. ~quiet(X0) | humble(X0) [cnf transformation 44]
88. ~patient(X0) | funny(X0) | funny(X0) | ~humble(X0) [cnf transformation 45]
92. ~humble(X0) | ~funny(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 45]
95. quiet(X0) | curious(X0) [cnf transformation 47]
96. patient(X0) | patient(X0) [cnf transformation 47]
133. ~curious(mary) [cnf transformation 25]
135. patient(X0) [duplicate literal removal 96]
137. ~patient(X0) | funny(X0) | ~humble(X0) [duplicate literal removal 88]
139. ~humble(X0) | ~funny(X0) | ~patient(X0) [duplicate literal removal 92]
188. ~patient(X0) | ~humble(X0) [subsumption resolution 137,139]
277. curious(X0) | humble(X0) [resolution 95,83]
291. ~humble(X0) [resolution 188,135]
303. humble(mary) [resolution 277,133]
304. $false [subsumption resolution 303,291]
% SZS output end Proof for 318004994795194496010813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either humble or not curious then lucy is not rich or old and vice versa.
If someone is not brave or not humble then someone is not creative or rich and vice versa.
Everyone who is either not patient or humble is either old or curious and vice versa.
If john is both not brave and not funny then alice is either funny or patient and vice versa.
If someone is calm or wise then someone is not strong or calm.
Everyone who is both not happy and creative is wise or brave and vice versa.
Everyone who is either brave or not patient is either brave or wise.
Everyone who is happy or not wise is both brave and not brave and vice versa.
Everyone who is either funny or not kind is kind and vice versa.
Everyone who is not generous or quiet is both strong and not tall.
Everyone who is not rich or not tall is quiet or patient and vice versa.
If john is not generous then paul is both quiet and old and vice versa.
If someone is both funny and not humble then alice is both not quiet and tall and vice versa.
If susan is both happy and brave then someone is either calm or happy.
John is not happy.
Paul is either not quiet or old.
John is not calm or quiet.
Someone is not curious or generous.
Someone is either brave or strong.
Susan is either not kind or quiet. | John is happy. | contradiction | (((humble(susan)<~>~curious(susan)))<=>((~rich(lucy)|old(lucy))))&
((?[X]:((~brave(X)|~humble(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(old(X)<~>curious(X))))&
(((~brave(john)&~funny(john)))<=>((funny(alice)<~>patient(alice))))&
((?[X]:((calm(X)|wise(X))))=>(?[X]:((~strong(X)|calm(X)))))&
(![X]:((~happy(X)&creative(X))<=>(wise(X)|brave(X))))&
(![X]:((brave(X)<~>~patient(X))=>(brave(X)<~>wise(X))))&
(![X]:((happy(X)|~wise(X))<=>(brave(X)&~brave(X))))&
(![X]:((funny(X)<~>~kind(X))<=>kind(X)))&
(![X]:((~generous(X)|quiet(X))=>(strong(X)&~tall(X))))&
(![X]:((~rich(X)|~tall(X))<=>(quiet(X)|patient(X))))&
((~generous(john))<=>((quiet(paul)&old(paul))))&
((?[X]:((funny(X)&~humble(X))))<=>((~quiet(alice)&tall(alice))))&
(((happy(susan)&brave(susan)))=>(?[X]:((calm(X)<~>happy(X)))))&
(~happy(john))&
((~quiet(paul)<~>old(paul)))&
((~calm(john)|quiet(john)))&
(?[X]:((~curious(X)|generous(X))))&
(?[X]:((brave(X)<~>strong(X))))&
((~kind(susan)<~>quiet(susan))) | happy(john) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8703533418041489230183561
% SZS output start Proof for 8703533418041489230183561
6. ! [X0] : ((creative(X0) & ~happy(X0)) <=> (brave(X0) | wise(X0))) [input p5]
8. ! [X0] : ((~wise(X0) | happy(X0)) <=> (~brave(X0) & brave(X0))) [input p7]
21. happy(john) [input hypothesis]
42. ! [X0] : (((creative(X0) & ~happy(X0)) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | (~creative(X0) | happy(X0)))) [nnf transformation 6]
43. ! [X0] : (((creative(X0) & ~happy(X0)) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | ~creative(X0) | happy(X0))) [flattening 42]
45. ! [X0] : (((~wise(X0) | happy(X0)) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 8]
46. ! [X0] : ((~wise(X0) | happy(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [flattening 45]
95. ~happy(X0) | ~brave(X0) [cnf transformation 43]
102. brave(X0) | ~happy(X0) [cnf transformation 46]
137. happy(john) [cnf transformation 21]
235. ~happy(X0) [subsumption resolution 102,95]
310. $false [subsumption resolution 137,235]
% SZS output end Proof for 8703533418041489230183561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is brave then susan is both brave and not quiet. If alice is not humble then someone is either not happy or rich. If someone is both curious and patient then paul is curious or kind and vice versa. Everyone who is old or calm is not generous or generous. Everyone who is happy is not curious and vice versa. If fred is not curious or patient then someone is both not happy and wise and vice versa. If alice is humble or brave then someone is both not brave and not wise. Everyone who is both calm and strong is not patient or not kind and vice versa. Everyone who is either rich or calm is not patient. Everyone who is both not rich and wise is both not wise and not old. Everyone who is rich is both humble and quiet. Everyone who is either not rich or calm is either not creative or not brave. If mary is either humble or curious then someone is either curious or not brave and vice versa. If paul is both not patient and not old then someone is either kind or not calm and vice versa. Everyone who is both tall and not kind is old or not wise. John is not rich or kind. Lucy is either calm or happy. Someone is either funny or not humble. Fred is either generous or not brave. Susan is both not quiet and funny. John is not funny. Someone is patient. Someone is brave or not curious. | Susan is wise. | contradiction | ((?[X]:(brave(X)))=>((brave(susan)&~quiet(susan))))&
((~humble(alice))=>(?[X]:((~happy(X)<~>rich(X)))))&
((?[X]:((curious(X)&patient(X))))<=>((curious(paul)|kind(paul))))&
(![X]:((old(X)|calm(X))=>(~generous(X)|generous(X))))&
(![X]:(happy(X)<=>~curious(X)))&
(((~curious(fred)|patient(fred)))<=>(?[X]:((~happy(X)&wise(X)))))&
(((humble(alice)|brave(alice)))=>(?[X]:((~brave(X)&~wise(X)))))&
(![X]:((calm(X)&strong(X))<=>(~patient(X)|~kind(X))))&
(![X]:((rich(X)<~>calm(X))=>~patient(X)))&
(![X]:((~rich(X)&wise(X))=>(~wise(X)&~old(X))))&
(![X]:(rich(X)=>(humble(X)&quiet(X))))&
(![X]:((~rich(X)<~>calm(X))=>(~creative(X)<~>~brave(X))))&
(((humble(mary)<~>curious(mary)))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(((~patient(paul)&~old(paul)))<=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:((tall(X)&~kind(X))=>(old(X)|~wise(X))))&
((~rich(john)|kind(john)))&
((calm(lucy)<~>happy(lucy)))&
(?[X]:((funny(X)<~>~humble(X))))&
((generous(fred)<~>~brave(fred)))&
((~quiet(susan)&funny(susan)))&
(~funny(john))&
(?[X]:(patient(X)))&
(?[X]:((brave(X)|~curious(X)))) | wise(susan) | [
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6565212851809936274595306
% SZS output start Proof for 6565212851809936274595306
10. ! [X0] : ((wise(X0) & ~rich(X0)) => (~old(X0) & ~wise(X0))) [input p9]
11. ! [X0] : (rich(X0) => (quiet(X0) & humble(X0))) [input p10]
20. funny(susan) & ~quiet(susan) [input p19]
24. wise(susan) [input hypothesis]
32. ! [X0] : ((~old(X0) & ~wise(X0)) | (~wise(X0) | rich(X0))) [ennf transformation 10]
33. ! [X0] : ((~old(X0) & ~wise(X0)) | ~wise(X0) | rich(X0)) [flattening 32]
34. ! [X0] : ((quiet(X0) & humble(X0)) | ~rich(X0)) [ennf transformation 11]
103. ~wise(X0) | ~wise(X0) | rich(X0) [cnf transformation 33]
106. ~rich(X0) | quiet(X0) [cnf transformation 34]
132. ~quiet(susan) [cnf transformation 20]
137. wise(susan) [cnf transformation 24]
138. ~wise(X0) | rich(X0) [duplicate literal removal 103]
143. 2 <=> quiet(susan) [avatar definition]
145. ~quiet(susan) <- (~2) [avatar component clause 143]
329. ~2 [avatar split clause 132,143]
345. rich(susan) [resolution 138,137]
346. quiet(susan) [resolution 345,106]
348. $false <- (~2) [subsumption resolution 346,145]
349. 2 [avatar contradiction clause 348]
350. $false [avatar sat refutation 329,349]
% SZS output end Proof for 6565212851809936274595306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and humble then someone is not kind or not funny.
Everyone who is either not generous or not tall is not creative or not curious and vice versa.
If someone is both happy and not generous then susan is both generous and not curious.
If someone is either not curious or not quiet then susan is both not curious and not generous and vice versa.
Everyone who is not happy is not creative or brave and vice versa.
If someone is either not curious or not quiet then fred is both not funny and not humble and vice versa.
If someone is both wise and not happy then alice is either calm or not wise.
If fred is both calm and creative then fred is wise and vice versa.
Everyone who is not strong or not creative is generous and vice versa.
If someone is strong or not wise then lucy is both quiet and strong.
If john is not rich then someone is humble or not creative and vice versa.
Everyone who is either not rich or quiet is tall or curious and vice versa.
Everyone who is either patient or not patient is not rich or funny and vice versa.
If someone is both wise and kind then john is either generous or old.
Everyone who is both not rich and curious is either not happy or not wise and vice versa.
If susan is quiet or kind then someone is not kind or calm.
Someone is either not wise or not happy.
Someone is either not old or funny.
Mary is kind or not generous.
Susan is either brave or not humble.
Alice is either tall or humble.
Someone is not wise or not rich.
Lucy is tall or not quiet.
Someone is both not funny and not wise. | Fred is not rich. | entailment | ((?[X]:((tall(X)&humble(X))))=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:((~generous(X)<~>~tall(X))<=>(~creative(X)|~curious(X))))&
((?[X]:((happy(X)&~generous(X))))=>((generous(susan)&~curious(susan))))&
((?[X]:((~curious(X)<~>~quiet(X))))<=>((~curious(susan)&~generous(susan))))&
(![X]:(~happy(X)<=>(~creative(X)|brave(X))))&
((?[X]:((~curious(X)<~>~quiet(X))))<=>((~funny(fred)&~humble(fred))))&
((?[X]:((wise(X)&~happy(X))))=>((calm(alice)<~>~wise(alice))))&
(((calm(fred)&creative(fred)))<=>(wise(fred)))&
(![X]:((~strong(X)|~creative(X))<=>generous(X)))&
((?[X]:((strong(X)|~wise(X))))=>((quiet(lucy)&strong(lucy))))&
((~rich(john))<=>(?[X]:((humble(X)|~creative(X)))))&
(![X]:((~rich(X)<~>quiet(X))<=>(tall(X)|curious(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~rich(X)|funny(X))))&
((?[X]:((wise(X)&kind(X))))=>((generous(john)<~>old(john))))&
(![X]:((~rich(X)&curious(X))<=>(~happy(X)<~>~wise(X))))&
(((quiet(susan)|kind(susan)))=>(?[X]:((~kind(X)|calm(X)))))&
(?[X]:((~wise(X)<~>~happy(X))))&
(?[X]:((~old(X)<~>funny(X))))&
((kind(mary)|~generous(mary)))&
((brave(susan)<~>~humble(susan)))&
((tall(alice)<~>humble(alice)))&
(?[X]:((~wise(X)|~rich(X))))&
((tall(lucy)|~quiet(lucy)))&
(?[X]:((~funny(X)&~wise(X)))) | ~rich(fred) | [
"p1",
"p5",
"p8",
"p9",
"p12",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4793831165541214550379228
% SZS output start Proof for 4793831165541214550379228
2. ! [X0] : ((~generous(X0) <~> ~tall(X0)) <=> (~curious(X0) | ~creative(X0))) [input p1]
6. ? [X0] : (~curious(X0) <~> ~quiet(X0)) <=> (~humble(fred) & ~funny(fred)) [input p5]
9. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> generous(X0)) [input p8]
10. ? [X0] : (~wise(X0) | strong(X0)) => (strong(lucy) & quiet(lucy)) [input p9]
13. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> (funny(X0) | ~rich(X0))) [input p12]
23. ~quiet(lucy) | tall(lucy) [input p22]
24. ? [X0] : (~wise(X0) & ~funny(X0)) [input p23]
25. rich(fred) [input hypothesis]
30. (strong(lucy) & quiet(lucy)) | ! [X0] : (wise(X0) & ~strong(X0)) [ennf transformation 10]
36. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (curious(X0) & creative(X0))) & ((~curious(X0) | ~creative(X0)) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [nnf transformation 2]
37. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (curious(X0) & creative(X0))) & (~curious(X0) | ~creative(X0) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [flattening 36]
45. (? [X0] : ((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | (humble(fred) | funny(fred))) & ((~humble(fred) & ~funny(fred)) | ! [X0] : ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) [nnf transformation 6]
46. (? [X0] : ((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | humble(fred) | funny(fred)) & ((~humble(fred) & ~funny(fred)) | ! [X0] : ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) [flattening 45]
47. (? [X0] : ((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | humble(fred) | funny(fred)) & ((~humble(fred) & ~funny(fred)) | ! [X1] : ((~curious(X1) | quiet(X1)) & (~quiet(X1) | curious(X1)))) [rectify 46]
48. ? [X0] : ((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) => ((quiet(sK2) | curious(sK2)) & (~quiet(sK2) | ~curious(sK2))) [choice axiom]
49. (((quiet(sK2) | curious(sK2)) & (~quiet(sK2) | ~curious(sK2))) | humble(fred) | funny(fred)) & ((~humble(fred) & ~funny(fred)) | ! [X1] : ((~curious(X1) | quiet(X1)) & (~quiet(X1) | curious(X1)))) [skolemisation 47,48]
53. ! [X0] : (((~creative(X0) | ~strong(X0)) | ~generous(X0)) & (generous(X0) | (creative(X0) & strong(X0)))) [nnf transformation 9]
54. ! [X0] : ((~creative(X0) | ~strong(X0) | ~generous(X0)) & (generous(X0) | (creative(X0) & strong(X0)))) [flattening 53]
61. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (~funny(X0) & rich(X0))) & ((funny(X0) | ~rich(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 13]
62. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (~funny(X0) & rich(X0))) & (funny(X0) | ~rich(X0) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [flattening 61]
78. ? [X0] : (~wise(X0) & ~funny(X0)) => (~wise(sK8) & ~funny(sK8)) [choice axiom]
79. ~wise(sK8) & ~funny(sK8) [skolemisation 24,78]
81. ~curious(X0) | ~creative(X0) | ~tall(X0) | generous(X0) [cnf transformation 37]
83. ~generous(X0) | ~tall(X0) | creative(X0) [cnf transformation 37]
98. ~funny(fred) | ~quiet(X1) | curious(X1) [cnf transformation 49]
110. creative(X0) | generous(X0) [cnf transformation 54]
111. ~strong(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 54]
113. quiet(lucy) | wise(X0) [cnf transformation 30]
115. strong(lucy) | wise(X0) [cnf transformation 30]
125. funny(X0) | ~rich(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 62]
126. funny(X0) | ~rich(X0) | patient(X0) | patient(X0) [cnf transformation 62]
151. ~quiet(lucy) | tall(lucy) [cnf transformation 23]
153. ~wise(sK8) [cnf transformation 79]
154. rich(fred) [cnf transformation 25]
155. funny(X0) | ~rich(X0) | ~patient(X0) [duplicate literal removal 125]
156. ~rich(X0) | funny(X0) | patient(X0) [duplicate literal removal 126]
197. 10 <=> ! [X1] : (~quiet(X1) | curious(X1)) [avatar definition]
198. ~quiet(X1) | curious(X1) <- (10) [avatar component clause 197]
203. 11 <=> funny(fred) [avatar definition]
223. 10 | ~11 [avatar split clause 98,203,197]
253. 21 <=> ! [X0] : wise(X0) [avatar definition]
254. wise(X0) <- (21) [avatar component clause 253]
256. 22 <=> strong(lucy) [avatar definition]
258. strong(lucy) <- (22) [avatar component clause 256]
259. 21 | 22 [avatar split clause 115,256,253]
265. 24 <=> quiet(lucy) [avatar definition]
267. quiet(lucy) <- (24) [avatar component clause 265]
268. 21 | 24 [avatar split clause 113,265,253]
291. ~rich(X0) | funny(X0) [subsumption resolution 155,156]
382. 49 <=> tall(lucy) [avatar definition]
384. tall(lucy) <- (49) [avatar component clause 382]
385. 49 | ~24 [avatar split clause 151,265,382]
391. $false <- (21) [resolution 254,153]
392. ~21 [avatar contradiction clause 391]
398. curious(lucy) <- (10, 24) [resolution 198,267]
405. funny(fred) [resolution 291,154]
457. ~creative(lucy) | ~generous(lucy) <- (22) [resolution 111,258]
460. 56 <=> generous(lucy) [avatar definition]
461. generous(lucy) <- (56) [avatar component clause 460]
462. ~generous(lucy) <- (~56) [avatar component clause 460]
464. 57 <=> creative(lucy) [avatar definition]
466. ~creative(lucy) <- (~57) [avatar component clause 464]
467. ~56 | ~57 | ~22 [avatar split clause 457,256,464,460]
512. ~creative(lucy) | ~tall(lucy) | generous(lucy) <- (10, 24) [resolution 81,398]
516. ~creative(lucy) | generous(lucy) <- (10, 24, 49) [subsumption resolution 512,384]
517. ~creative(lucy) <- (10, 24, 49, ~56) [subsumption resolution 516,462]
518. ~57 | ~10 | ~24 | ~49 | 56 [avatar split clause 517,460,382,265,197,464]
530. generous(lucy) <- (~57) [resolution 466,110]
533. 56 | 57 [avatar split clause 530,464,460]
545. ~tall(lucy) | creative(lucy) <- (56) [resolution 461,83]
546. creative(lucy) <- (49, 56) [subsumption resolution 545,384]
547. $false <- (49, 56, ~57) [subsumption resolution 546,466]
548. ~49 | ~56 | 57 [avatar contradiction clause 547]
556. 11 [avatar split clause 405,203]
557. $false [avatar sat refutation 223,259,268,385,392,467,518,533,548,556]
% SZS output end Proof for 4793831165541214550379228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and calm is generous or not patient and vice versa.
Everyone who is not curious is calm and vice versa.
If someone is curious or quiet then someone is not rich.
Everyone who is either curious or funny is calm.
If someone is either curious or not funny then john is calm.
If alice is not strong then alice is not creative or creative and vice versa.
Everyone who is both not tall and rich is either not happy or brave and vice versa.
If john is not funny then fred is either not humble or wise and vice versa.
If john is either not calm or not wise then lucy is calm and vice versa.
Everyone who is both humble and not creative is curious or happy.
Everyone who is funny or not humble is either not generous or not rich and vice versa.
Everyone who is not calm or old is not wise or patient.
Everyone who is not funny is either not patient or not quiet and vice versa.
If alice is curious then mary is strong and vice versa.
If someone is both not happy and not humble then someone is not creative or kind.
Everyone who is either humble or happy is kind and vice versa.
Someone is curious or not happy.
Mary is both brave and not wise.
Susan is happy.
Someone is not creative or not happy.
Alice is not patient.
Paul is either not funny or not patient.
Someone is not old. | Fred is quiet. | neutral | (![X]:((creative(X)&calm(X))<=>(generous(X)|~patient(X))))&
(![X]:(~curious(X)<=>calm(X)))&
((?[X]:((curious(X)|quiet(X))))=>(?[X]:(~rich(X))))&
(![X]:((curious(X)<~>funny(X))=>calm(X)))&
((?[X]:((curious(X)<~>~funny(X))))=>(calm(john)))&
((~strong(alice))<=>((~creative(alice)|creative(alice))))&
(![X]:((~tall(X)&rich(X))<=>(~happy(X)<~>brave(X))))&
((~funny(john))<=>((~humble(fred)<~>wise(fred))))&
(((~calm(john)<~>~wise(john)))<=>(calm(lucy)))&
(![X]:((humble(X)&~creative(X))=>(curious(X)|happy(X))))&
(![X]:((funny(X)|~humble(X))<=>(~generous(X)<~>~rich(X))))&
(![X]:((~calm(X)|old(X))=>(~wise(X)|patient(X))))&
(![X]:(~funny(X)<=>(~patient(X)<~>~quiet(X))))&
((curious(alice))<=>(strong(mary)))&
((?[X]:((~happy(X)&~humble(X))))=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((humble(X)<~>happy(X))<=>kind(X)))&
(?[X]:((curious(X)|~happy(X))))&
((brave(mary)&~wise(mary)))&
(happy(susan))&
(?[X]:((~creative(X)|~happy(X))))&
(~patient(alice))&
((~funny(paul)<~>~patient(paul)))&
(?[X]:(~old(X))) | quiet(fred) | [] | null | 0 |
Everyone who is both not rich and not funny is both rich and not curious and vice versa.
Everyone who is either not wise or not patient is not calm or kind and vice versa.
Everyone who is either not calm or calm is both not rich and quiet and vice versa.
Everyone who is not wise is both not patient and not wise and vice versa.
If paul is both not creative and not quiet then someone is rich or not happy and vice versa.
Everyone who is not funny is kind or not kind.
Everyone who is quiet is not tall or wise and vice versa.
Everyone who is either funny or strong is not generous or humble.
If someone is either wise or not patient then mary is either kind or not tall and vice versa.
Everyone who is both not old and not generous is happy or patient.
If someone is both not wise and not generous then paul is curious.
Everyone who is not quiet or tall is generous and vice versa.
Everyone who is humble is both old and not happy.
Everyone who is either not wise or kind is either not wise or generous and vice versa.
Everyone who is either not tall or not humble is both calm and not quiet and vice versa.
If someone is not wise or not curious then mary is not curious and vice versa.
Susan is not curious.
Someone is both brave and not humble.
Alice is either not patient or not humble.
Lucy is either tall or not humble.
Someone is either not wise or not generous. | Alice is generous. | contradiction | (![X]:((~rich(X)&~funny(X))<=>(rich(X)&~curious(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~calm(X)|kind(X))))&
(![X]:((~calm(X)<~>calm(X))<=>(~rich(X)&quiet(X))))&
(![X]:(~wise(X)<=>(~patient(X)&~wise(X))))&
(((~creative(paul)&~quiet(paul)))<=>(?[X]:((rich(X)|~happy(X)))))&
(![X]:(~funny(X)=>(kind(X)|~kind(X))))&
(![X]:(quiet(X)<=>(~tall(X)|wise(X))))&
(![X]:((funny(X)<~>strong(X))=>(~generous(X)|humble(X))))&
((?[X]:((wise(X)<~>~patient(X))))<=>((kind(mary)<~>~tall(mary))))&
(![X]:((~old(X)&~generous(X))=>(happy(X)|patient(X))))&
((?[X]:((~wise(X)&~generous(X))))=>(curious(paul)))&
(![X]:((~quiet(X)|tall(X))<=>generous(X)))&
(![X]:(humble(X)=>(old(X)&~happy(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(~wise(X)<~>generous(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(calm(X)&~quiet(X))))&
((?[X]:((~wise(X)|~curious(X))))<=>(~curious(mary)))&
(~curious(susan))&
(?[X]:((brave(X)&~humble(X))))&
((~patient(alice)<~>~humble(alice)))&
((tall(lucy)<~>~humble(lucy)))&
(?[X]:((~wise(X)<~>~generous(X)))) | generous(alice) | [
"p2",
"p4",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7139697500356689666872626
% SZS output start Proof for 7139697500356689666872626
3. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> (quiet(X0) & ~rich(X0))) [input p2]
5. (~quiet(paul) & ~creative(paul)) <=> ? [X0] : (~happy(X0) | rich(X0)) [input p4]
12. ! [X0] : ((tall(X0) | ~quiet(X0)) <=> generous(X0)) [input p11]
13. ! [X0] : (humble(X0) => (~happy(X0) & old(X0))) [input p12]
15. ! [X0] : ((~tall(X0) <~> ~humble(X0)) <=> (~quiet(X0) & calm(X0))) [input p14]
22. generous(alice) [input hypothesis]
25. ! [X0] : (humble(X0) => ~happy(X0)) [pure predicate removal 13]
31. ! [X0] : (~happy(X0) | ~humble(X0)) [ennf transformation 25]
36. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~quiet(X0) | rich(X0))) & ((quiet(X0) & ~rich(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 3]
37. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~quiet(X0) | rich(X0)) & ((quiet(X0) & ~rich(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [flattening 36]
40. ((~quiet(paul) & ~creative(paul)) | ! [X0] : (happy(X0) & ~rich(X0))) & (? [X0] : (~happy(X0) | rich(X0)) | (quiet(paul) | creative(paul))) [nnf transformation 5]
41. ((~quiet(paul) & ~creative(paul)) | ! [X0] : (happy(X0) & ~rich(X0))) & (? [X0] : (~happy(X0) | rich(X0)) | quiet(paul) | creative(paul)) [flattening 40]
42. ((~quiet(paul) & ~creative(paul)) | ! [X0] : (happy(X0) & ~rich(X0))) & (? [X1] : (~happy(X1) | rich(X1)) | quiet(paul) | creative(paul)) [rectify 41]
43. ? [X1] : (~happy(X1) | rich(X1)) => (~happy(sK0) | rich(sK0)) [choice axiom]
44. ((~quiet(paul) & ~creative(paul)) | ! [X0] : (happy(X0) & ~rich(X0))) & ((~happy(sK0) | rich(sK0)) | quiet(paul) | creative(paul)) [skolemisation 42,43]
52. ! [X0] : (((tall(X0) | ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (~tall(X0) & quiet(X0)))) [nnf transformation 12]
53. ! [X0] : ((tall(X0) | ~quiet(X0) | ~generous(X0)) & (generous(X0) | (~tall(X0) & quiet(X0)))) [flattening 52]
55. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (quiet(X0) | ~calm(X0))) & ((~quiet(X0) & calm(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [nnf transformation 15]
56. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | quiet(X0) | ~calm(X0)) & ((~quiet(X0) & calm(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [flattening 55]
80. quiet(X0) | calm(X0) | calm(X0) [cnf transformation 37]
81. quiet(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 37]
91. ~quiet(paul) | happy(X0) [cnf transformation 44]
109. tall(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 53]
110. ~happy(X0) | ~humble(X0) [cnf transformation 31]
122. ~quiet(X0) | ~tall(X0) | humble(X0) [cnf transformation 56]
136. generous(alice) [cnf transformation 22]
143. quiet(X0) | calm(X0) [duplicate literal removal 80]
144. ~calm(X0) | quiet(X0) [duplicate literal removal 81]
147. quiet(X0) [subsumption resolution 143,144]
149. happy(X0) [subsumption resolution 91,147]
191. ~generous(X0) | tall(X0) [subsumption resolution 109,147]
192. ~humble(X0) [subsumption resolution 110,149]
195. ~tall(X0) | humble(X0) [subsumption resolution 122,147]
196. ~tall(X0) [subsumption resolution 195,192]
228. tall(alice) [resolution 191,136]
230. $false [subsumption resolution 228,196]
% SZS output end Proof for 7139697500356689666872626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is not old or wise.
If someone is either not humble or wise then someone is both funny and happy.
Everyone who is rich is not brave or not patient.
Everyone who is both tall and strong is both not generous and not wise and vice versa.
If mary is both not rich and rich then someone is kind or not rich and vice versa.
If someone is both old and curious then mary is both creative and not patient.
If someone is tall or not humble then alice is not quiet and vice versa.
Everyone who is either strong or creative is both not rich and humble.
If someone is either not quiet or happy then susan is not brave.
Everyone who is either not patient or not quiet is either old or strong and vice versa.
Everyone who is not brave or not happy is either not brave or generous and vice versa.
If someone is not tall then someone is both creative and not calm.
Everyone who is either calm or not rich is happy and vice versa.
If someone is both not humble and not wise then alice is either not strong or curious and vice versa.
If someone is both brave and not wise then paul is both not humble and funny.
Someone is not creative or generous.
Mary is rich or strong.
Someone is not creative.
Someone is both not generous and patient.
Lucy is brave.
Alice is not generous.
Lucy is both old and tall.
Someone is either old or brave. | Lucy is not patient. | entailment | ((?[X]:(~old(X)))=>(?[X]:((~old(X)|wise(X)))))&
((?[X]:((~humble(X)<~>wise(X))))=>(?[X]:((funny(X)&happy(X)))))&
(![X]:(rich(X)=>(~brave(X)|~patient(X))))&
(![X]:((tall(X)&strong(X))<=>(~generous(X)&~wise(X))))&
(((~rich(mary)&rich(mary)))<=>(?[X]:((kind(X)|~rich(X)))))&
((?[X]:((old(X)&curious(X))))=>((creative(mary)&~patient(mary))))&
((?[X]:((tall(X)|~humble(X))))<=>(~quiet(alice)))&
(![X]:((strong(X)<~>creative(X))=>(~rich(X)&humble(X))))&
((?[X]:((~quiet(X)<~>happy(X))))=>(~brave(susan)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(old(X)<~>strong(X))))&
(![X]:((~brave(X)|~happy(X))<=>(~brave(X)<~>generous(X))))&
((?[X]:(~tall(X)))=>(?[X]:((creative(X)&~calm(X)))))&
(![X]:((calm(X)<~>~rich(X))<=>happy(X)))&
((?[X]:((~humble(X)&~wise(X))))<=>((~strong(alice)<~>curious(alice))))&
((?[X]:((brave(X)&~wise(X))))=>((~humble(paul)&funny(paul))))&
(?[X]:((~creative(X)|generous(X))))&
((rich(mary)|strong(mary)))&
(?[X]:(~creative(X)))&
(?[X]:((~generous(X)&patient(X))))&
(brave(lucy))&
(~generous(alice))&
((old(lucy)&tall(lucy)))&
(?[X]:((old(X)<~>brave(X)))) | ~patient(lucy) | [
"p2",
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6013471532051437059263509
% SZS output start Proof for 6013471532051437059263509
3. ! [X0] : (rich(X0) => (~patient(X0) | ~brave(X0))) [input p2]
5. (rich(mary) & ~rich(mary)) <=> ? [X0] : (~rich(X0) | kind(X0)) [input p4]
20. brave(lucy) [input p19]
24. patient(lucy) [input hypothesis]
32. ! [X0] : ((~patient(X0) | ~brave(X0)) | ~rich(X0)) [ennf transformation 3]
33. ! [X0] : (~patient(X0) | ~brave(X0) | ~rich(X0)) [flattening 32]
48. ((rich(mary) & ~rich(mary)) | ! [X0] : (rich(X0) & ~kind(X0))) & (? [X0] : (~rich(X0) | kind(X0)) | (~rich(mary) | rich(mary))) [nnf transformation 5]
49. ((rich(mary) & ~rich(mary)) | ! [X0] : (rich(X0) & ~kind(X0))) & (? [X0] : (~rich(X0) | kind(X0)) | ~rich(mary) | rich(mary)) [flattening 48]
50. ((rich(mary) & ~rich(mary)) | ! [X0] : (rich(X0) & ~kind(X0))) & (? [X1] : (~rich(X1) | kind(X1)) | ~rich(mary) | rich(mary)) [rectify 49]
51. ? [X1] : (~rich(X1) | kind(X1)) => (~rich(sK2) | kind(sK2)) [choice axiom]
52. ((rich(mary) & ~rich(mary)) | ! [X0] : (rich(X0) & ~kind(X0))) & ((~rich(sK2) | kind(sK2)) | ~rich(mary) | rich(mary)) [skolemisation 50,51]
82. ~patient(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 33]
89. ~rich(mary) | rich(X0) [cnf transformation 52]
91. rich(mary) | rich(X0) [cnf transformation 52]
135. brave(lucy) [cnf transformation 20]
141. patient(lucy) [cnf transformation 24]
169. 7 <=> ! [X0] : rich(X0) [avatar definition]
170. rich(X0) <- (7) [avatar component clause 169]
172. 8 <=> rich(mary) [avatar definition]
175. 7 | 8 [avatar split clause 91,172,169]
180. 7 | ~8 [avatar split clause 89,172,169]
296. ~brave(lucy) | ~rich(lucy) [resolution 82,141]
298. ~rich(lucy) [subsumption resolution 296,135]
299. $false <- (7) [subsumption resolution 298,170]
300. ~7 [avatar contradiction clause 299]
301. $false [avatar sat refutation 175,180,300]
% SZS output end Proof for 6013471532051437059263509
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is not old and vice versa.
If someone is both not creative and calm then paul is generous.
Everyone who is both brave and not happy is either not curious or strong.
If paul is not kind or not tall then someone is rich.
Everyone who is generous or wise is both not quiet and not wise and vice versa.
Everyone who is not generous is either strong or not funny.
If fred is not creative then someone is either old or not brave.
Everyone who is not rich or not patient is not funny or calm.
If someone is both tall and brave then susan is either not brave or patient and vice versa.
If john is either humble or wise then someone is rich or kind and vice versa.
Everyone who is either calm or not quiet is not patient and vice versa.
Everyone who is both not curious and calm is curious or rich and vice versa.
If someone is curious or old then someone is either rich or quiet.
If someone is quiet or not creative then someone is either strong or rich.
If paul is either not tall or kind then someone is either calm or funny.
If someone is humble or not generous then someone is either creative or humble.
Someone is either humble or not generous.
Susan is rich or kind.
Paul is tall or not curious.
Lucy is wise or not generous.
Someone is quiet or not generous.
Someone is either happy or creative.
Someone is funny. | Paul is not curious. | entailment | ((?[X]:(~creative(X)))<=>(?[X]:(~old(X))))&
((?[X]:((~creative(X)&calm(X))))=>(generous(paul)))&
(![X]:((brave(X)&~happy(X))=>(~curious(X)<~>strong(X))))&
(((~kind(paul)|~tall(paul)))=>(?[X]:(rich(X))))&
(![X]:((generous(X)|wise(X))<=>(~quiet(X)&~wise(X))))&
(![X]:(~generous(X)=>(strong(X)<~>~funny(X))))&
((~creative(fred))=>(?[X]:((old(X)<~>~brave(X)))))&
(![X]:((~rich(X)|~patient(X))=>(~funny(X)|calm(X))))&
((?[X]:((tall(X)&brave(X))))<=>((~brave(susan)<~>patient(susan))))&
(((humble(john)<~>wise(john)))<=>(?[X]:((rich(X)|kind(X)))))&
(![X]:((calm(X)<~>~quiet(X))<=>~patient(X)))&
(![X]:((~curious(X)&calm(X))<=>(curious(X)|rich(X))))&
((?[X]:((curious(X)|old(X))))=>(?[X]:((rich(X)<~>quiet(X)))))&
((?[X]:((quiet(X)|~creative(X))))=>(?[X]:((strong(X)<~>rich(X)))))&
(((~tall(paul)<~>kind(paul)))=>(?[X]:((calm(X)<~>funny(X)))))&
((?[X]:((humble(X)|~generous(X))))=>(?[X]:((creative(X)<~>humble(X)))))&
(?[X]:((humble(X)<~>~generous(X))))&
((rich(susan)|kind(susan)))&
((tall(paul)|~curious(paul)))&
((wise(lucy)|~generous(lucy)))&
(?[X]:((quiet(X)|~generous(X))))&
(?[X]:((happy(X)<~>creative(X))))&
(?[X]:(funny(X))) | ~curious(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6120908536193291503367470
% SZS output start Proof for 6120908536193291503367470
12. ! [X0] : ((calm(X0) & ~curious(X0)) <=> (rich(X0) | curious(X0))) [input p11]
24. curious(paul) [input hypothesis]
64. ! [X0] : (((calm(X0) & ~curious(X0)) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | (~calm(X0) | curious(X0)))) [nnf transformation 12]
65. ! [X0] : (((calm(X0) & ~curious(X0)) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~calm(X0) | curious(X0))) [flattening 64]
126. ~curious(X0) | ~curious(X0) [cnf transformation 65]
155. curious(paul) [cnf transformation 24]
157. ~curious(X0) [duplicate literal removal 126]
351. $false [subsumption resolution 155,157]
% SZS output end Proof for 6120908536193291503367470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not rich is either tall or kind.
If fred is brave or not humble then someone is not funny and vice versa.
If alice is rich then someone is either not old or humble and vice versa.
If susan is not humble then someone is not tall or funny.
If someone is not strong or funny then someone is both kind and rich.
If someone is both calm and not generous then someone is not funny or not quiet and vice versa.
If alice is brave then fred is creative or old.
Everyone who is not strong is both wise and strong and vice versa.
Everyone who is both wise and not kind is either not quiet or patient and vice versa.
Everyone who is old is either brave or quiet and vice versa.
Everyone who is both quiet and brave is either old or not happy and vice versa.
Everyone who is not creative or happy is either not patient or quiet.
If someone is both patient and generous then someone is either not funny or not calm and vice versa.
Everyone who is not old is not rich.
Everyone who is both patient and calm is not curious or rich and vice versa.
Everyone who is not happy is both curious and humble and vice versa.
John is either calm or brave.
Someone is quiet.
Fred is both not calm and patient.
Paul is not happy or not patient.
Mary is either patient or old.
Someone is both not brave and not calm.
John is both not old and curious.
Someone is brave. | Mary is not strong. | contradiction | (![X]:((~kind(X)&~rich(X))=>(tall(X)<~>kind(X))))&
(((brave(fred)|~humble(fred)))<=>(?[X]:(~funny(X))))&
((rich(alice))<=>(?[X]:((~old(X)<~>humble(X)))))&
((~humble(susan))=>(?[X]:((~tall(X)|funny(X)))))&
((?[X]:((~strong(X)|funny(X))))=>(?[X]:((kind(X)&rich(X)))))&
((?[X]:((calm(X)&~generous(X))))<=>(?[X]:((~funny(X)|~quiet(X)))))&
((brave(alice))=>((creative(fred)|old(fred))))&
(![X]:(~strong(X)<=>(wise(X)&strong(X))))&
(![X]:((wise(X)&~kind(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:(old(X)<=>(brave(X)<~>quiet(X))))&
(![X]:((quiet(X)&brave(X))<=>(old(X)<~>~happy(X))))&
(![X]:((~creative(X)|happy(X))=>(~patient(X)<~>quiet(X))))&
((?[X]:((patient(X)&generous(X))))<=>(?[X]:((~funny(X)<~>~calm(X)))))&
(![X]:(~old(X)=>~rich(X)))&
(![X]:((patient(X)&calm(X))<=>(~curious(X)|rich(X))))&
(![X]:(~happy(X)<=>(curious(X)&humble(X))))&
((calm(john)<~>brave(john)))&
(?[X]:(quiet(X)))&
((~calm(fred)&patient(fred)))&
((~happy(paul)|~patient(paul)))&
((patient(mary)<~>old(mary)))&
(?[X]:((~brave(X)&~calm(X))))&
((~old(john)&curious(john)))&
(?[X]:(brave(X))) | ~strong(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5919275843387224498814259
% SZS output start Proof for 5919275843387224498814259
8. ! [X0] : (~strong(X0) <=> (strong(X0) & wise(X0))) [input p7]
25. ~strong(mary) [input hypothesis]
57. ! [X0] : ((~strong(X0) | (~strong(X0) | ~wise(X0))) & ((strong(X0) & wise(X0)) | strong(X0))) [nnf transformation 8]
58. ! [X0] : ((~strong(X0) | ~strong(X0) | ~wise(X0)) & ((strong(X0) & wise(X0)) | strong(X0))) [flattening 57]
102. strong(X0) | strong(X0) [cnf transformation 58]
150. ~strong(mary) [cnf transformation 25]
151. strong(X0) [duplicate literal removal 102]
216. 15 <=> ! [X1] : strong(X1) [avatar definition]
217. strong(X1) <- (15) [avatar component clause 216]
252. 15 [avatar split clause 151,216]
314. $false <- (15) [resolution 217,150]
315. ~15 [avatar contradiction clause 314]
316. $false [avatar sat refutation 252,315]
% SZS output end Proof for 5919275843387224498814259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or not brave is both not strong and not kind and vice versa.
Everyone who is both generous and quiet is not wise or not patient.
If susan is patient or not wise then lucy is both not brave and not kind and vice versa.
Everyone who is both tall and not humble is not happy or strong and vice versa.
If susan is both not happy and quiet then lucy is either not funny or creative and vice versa.
Everyone who is not quiet or not curious is either funny or rich and vice versa.
Everyone who is both wise and not rich is brave or humble and vice versa.
Everyone who is not tall is calm and vice versa.
If someone is either not kind or happy then someone is both not patient and not creative and vice versa.
Everyone who is not tall or not humble is not curious or patient.
If someone is calm or tall then susan is either not humble or not patient.
Everyone who is humble or patient is calm or generous and vice versa.
If someone is both not kind and not quiet then someone is humble or funny.
Everyone who is not strong is both not brave and patient and vice versa.
If susan is calm then mary is wise or rich.
Everyone who is either quiet or not calm is wise and vice versa.
Lucy is brave or not tall.
Susan is calm or creative.
Someone is either not old or not creative.
Fred is either rich or not strong.
Someone is both wise and not quiet.
Alice is both creative and not happy.
Someone is either not patient or tall.
Someone is either happy or calm. | Fred is strong. | contradiction | (![X]:((quiet(X)|~brave(X))<=>(~strong(X)&~kind(X))))&
(![X]:((generous(X)&quiet(X))=>(~wise(X)|~patient(X))))&
(((patient(susan)|~wise(susan)))<=>((~brave(lucy)&~kind(lucy))))&
(![X]:((tall(X)&~humble(X))<=>(~happy(X)|strong(X))))&
(((~happy(susan)&quiet(susan)))<=>((~funny(lucy)<~>creative(lucy))))&
(![X]:((~quiet(X)|~curious(X))<=>(funny(X)<~>rich(X))))&
(![X]:((wise(X)&~rich(X))<=>(brave(X)|humble(X))))&
(![X]:(~tall(X)<=>calm(X)))&
((?[X]:((~kind(X)<~>happy(X))))<=>(?[X]:((~patient(X)&~creative(X)))))&
(![X]:((~tall(X)|~humble(X))=>(~curious(X)|patient(X))))&
((?[X]:((calm(X)|tall(X))))=>((~humble(susan)<~>~patient(susan))))&
(![X]:((humble(X)|patient(X))<=>(calm(X)|generous(X))))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:((humble(X)|funny(X)))))&
(![X]:(~strong(X)<=>(~brave(X)&patient(X))))&
((calm(susan))=>((wise(mary)|rich(mary))))&
(![X]:((quiet(X)<~>~calm(X))<=>wise(X)))&
((brave(lucy)|~tall(lucy)))&
((calm(susan)|creative(susan)))&
(?[X]:((~old(X)<~>~creative(X))))&
((rich(fred)<~>~strong(fred)))&
(?[X]:((wise(X)&~quiet(X))))&
((creative(alice)&~happy(alice)))&
(?[X]:((~patient(X)<~>tall(X))))&
(?[X]:((happy(X)<~>calm(X)))) | strong(fred) | [
"p0",
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6470966268609486990297630
% SZS output start Proof for 6470966268609486990297630
1. ! [X0] : ((~brave(X0) | quiet(X0)) <=> (~kind(X0) & ~strong(X0))) [input p0]
7. ! [X0] : ((~rich(X0) & wise(X0)) <=> (humble(X0) | brave(X0))) [input p6]
20. rich(fred) <~> ~strong(fred) [input p19]
25. strong(fred) [input hypothesis]
36. ! [X0] : (((~brave(X0) | quiet(X0)) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | (brave(X0) & ~quiet(X0)))) [nnf transformation 1]
37. ! [X0] : ((~brave(X0) | quiet(X0) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | (brave(X0) & ~quiet(X0)))) [flattening 36]
46. ! [X0] : (((~rich(X0) & wise(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (rich(X0) | ~wise(X0)))) [nnf transformation 7]
47. ! [X0] : (((~rich(X0) & wise(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | rich(X0) | ~wise(X0))) [flattening 46]
66. (strong(fred) | ~rich(fred)) & (~strong(fred) | rich(fred)) [nnf transformation 20]
76. ~strong(X0) | brave(X0) [cnf transformation 37]
106. ~rich(X0) | ~brave(X0) [cnf transformation 47]
139. ~strong(fred) | rich(fred) [cnf transformation 66]
149. strong(fred) [cnf transformation 25]
285. 29 <=> rich(fred) [avatar definition]
286. rich(fred) <- (29) [avatar component clause 285]
289. 30 <=> strong(fred) [avatar definition]
291. strong(fred) <- (30) [avatar component clause 289]
293. 29 | ~30 [avatar split clause 139,289,285]
314. 30 [avatar split clause 149,289]
316. brave(fred) <- (30) [resolution 76,291]
321. ~brave(fred) <- (29) [resolution 106,286]
322. $false <- (29, 30) [subsumption resolution 321,316]
323. ~29 | ~30 [avatar contradiction clause 322]
324. $false [avatar sat refutation 293,314,323]
% SZS output end Proof for 6470966268609486990297630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If john is both old and not wise then mary is both rich and not calm and vice versa.
Everyone who is either not old or not happy is not brave and vice versa.
Everyone who is calm or strong is both quiet and curious and vice versa.
Everyone who is both not strong and not kind is not happy or quiet.
Everyone who is both quiet and not tall is generous or calm.
Everyone who is calm is either not funny or not old and vice versa.
Everyone who is patient or humble is either funny or humble.
Everyone who is both calm and not quiet is both not brave and not strong and vice versa.
Everyone who is old is not quiet and vice versa.
Everyone who is old is not curious or not calm and vice versa.
Everyone who is not wise is either happy or not curious and vice versa.
Everyone who is calm or not humble is happy or not curious.
Everyone who is both creative and not brave is both not brave and not patient.
Everyone who is either not rich or not old is humble.
Everyone who is brave or not wise is both quiet and strong.
If someone is both not generous and creative then lucy is rich or not old and vice versa.
Someone is not calm or not kind.
John is tall or creative.
Someone is calm.
Susan is happy or not creative.
Mary is either not curious or curious.
Someone is kind.
Paul is calm or kind.
Alice is tall. | Alice is not brave. | entailment | (((old(john)&~wise(john)))<=>((rich(mary)&~calm(mary))))&
(![X]:((~old(X)<~>~happy(X))<=>~brave(X)))&
(![X]:((calm(X)|strong(X))<=>(quiet(X)&curious(X))))&
(![X]:((~strong(X)&~kind(X))=>(~happy(X)|quiet(X))))&
(![X]:((quiet(X)&~tall(X))=>(generous(X)|calm(X))))&
(![X]:(calm(X)<=>(~funny(X)<~>~old(X))))&
(![X]:((patient(X)|humble(X))=>(funny(X)<~>humble(X))))&
(![X]:((calm(X)&~quiet(X))<=>(~brave(X)&~strong(X))))&
(![X]:(old(X)<=>~quiet(X)))&
(![X]:(old(X)<=>(~curious(X)|~calm(X))))&
(![X]:(~wise(X)<=>(happy(X)<~>~curious(X))))&
(![X]:((calm(X)|~humble(X))=>(happy(X)|~curious(X))))&
(![X]:((creative(X)&~brave(X))=>(~brave(X)&~patient(X))))&
(![X]:((~rich(X)<~>~old(X))=>humble(X)))&
(![X]:((brave(X)|~wise(X))=>(quiet(X)&strong(X))))&
((?[X]:((~generous(X)&creative(X))))<=>((rich(lucy)|~old(lucy))))&
(?[X]:((~calm(X)|~kind(X))))&
((tall(john)|creative(john)))&
(?[X]:(calm(X)))&
((happy(susan)|~creative(susan)))&
((~curious(mary)<~>curious(mary)))&
(?[X]:(kind(X)))&
((calm(paul)|kind(paul)))&
(tall(alice)) | ~brave(alice) | [
"p1",
"p2",
"p8",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6076121648229410278720280
% SZS output start Proof for 6076121648229410278720280
2. ! [X0] : ((~old(X0) <~> ~happy(X0)) <=> ~brave(X0)) [input p1]
3. ! [X0] : ((strong(X0) | calm(X0)) <=> (curious(X0) & quiet(X0))) [input p2]
9. ! [X0] : (old(X0) <=> ~quiet(X0)) [input p8]
10. ! [X0] : (old(X0) <=> (~calm(X0) | ~curious(X0))) [input p9]
12. ! [X0] : ((~humble(X0) | calm(X0)) => (~curious(X0) | happy(X0))) [input p11]
15. ! [X0] : ((~wise(X0) | brave(X0)) => (strong(X0) & quiet(X0))) [input p14]
25. brave(alice) [input hypothesis]
34. ! [X0] : ((~curious(X0) | happy(X0)) | (humble(X0) & ~calm(X0))) [ennf transformation 12]
35. ! [X0] : (~curious(X0) | happy(X0) | (humble(X0) & ~calm(X0))) [flattening 34]
39. ! [X0] : ((strong(X0) & quiet(X0)) | (wise(X0) & ~brave(X0))) [ennf transformation 15]
42. ! [X0] : ((((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | brave(X0)) & (~brave(X0) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))))) [nnf transformation 2]
43. ! [X0] : (((strong(X0) | calm(X0)) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | (~strong(X0) & ~calm(X0)))) [nnf transformation 3]
44. ! [X0] : ((strong(X0) | calm(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | (~strong(X0) & ~calm(X0)))) [flattening 43]
49. ! [X0] : ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0))) [nnf transformation 9]
50. ! [X0] : ((old(X0) | (calm(X0) & curious(X0))) & ((~calm(X0) | ~curious(X0)) | ~old(X0))) [nnf transformation 10]
51. ! [X0] : ((old(X0) | (calm(X0) & curious(X0))) & (~calm(X0) | ~curious(X0) | ~old(X0))) [flattening 50]
70. ~brave(X0) | ~happy(X0) | old(X0) [cnf transformation 42]
76. ~calm(X0) | curious(X0) [cnf transformation 44]
90. ~quiet(X0) | ~old(X0) [cnf transformation 49]
94. calm(X0) | old(X0) [cnf transformation 51]
99. ~curious(X0) | happy(X0) | ~calm(X0) [cnf transformation 35]
104. ~brave(X0) | quiet(X0) [cnf transformation 39]
120. brave(alice) [cnf transformation 25]
144. ~calm(X0) | happy(X0) [subsumption resolution 99,76]
206. quiet(alice) [resolution 104,120]
208. ~old(alice) [resolution 206,90]
219. happy(X0) | old(X0) [resolution 144,94]
220. ~happy(alice) | old(alice) [resolution 70,120]
221. ~happy(alice) [subsumption resolution 220,208]
312. old(alice) [resolution 219,221]
313. $false [subsumption resolution 312,208]
% SZS output end Proof for 6076121648229410278720280
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not calm is not wise and vice versa.
If someone is strong then someone is either old or quiet.
If someone is both not generous and not patient then someone is both not tall and not rich.
If someone is not old or not curious then mary is wise.
Everyone who is both generous and not generous is either not kind or brave.
If someone is wise or not happy then someone is both rich and old and vice versa.
Everyone who is not quiet is patient.
Everyone who is both not funny and not rich is either not strong or not funny and vice versa.
Everyone who is not old or creative is either kind or not wise.
Everyone who is either funny or wise is strong.
If someone is not rich or not brave then someone is both curious and not kind.
Everyone who is either not creative or not curious is both calm and brave.
If someone is curious or calm then someone is not kind or not calm.
If john is not generous or not strong then someone is not wise and vice versa.
Everyone who is both brave and not calm is patient or not tall.
Everyone who is both not creative and not strong is both creative and tall.
Fred is not happy or not tall.
Someone is not quiet.
Paul is both patient and not funny.
Someone is either quiet or not quiet.
Alice is brave.
John is not strong or not kind.
Someone is either not strong or not happy.
Someone is not strong. | Fred is not tall. | neutral | (![X]:((~generous(X)<~>~calm(X))<=>~wise(X)))&
((?[X]:(strong(X)))=>(?[X]:((old(X)<~>quiet(X)))))&
((?[X]:((~generous(X)&~patient(X))))=>(?[X]:((~tall(X)&~rich(X)))))&
((?[X]:((~old(X)|~curious(X))))=>(wise(mary)))&
(![X]:((generous(X)&~generous(X))=>(~kind(X)<~>brave(X))))&
((?[X]:((wise(X)|~happy(X))))<=>(?[X]:((rich(X)&old(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
(![X]:((~funny(X)&~rich(X))<=>(~strong(X)<~>~funny(X))))&
(![X]:((~old(X)|creative(X))=>(kind(X)<~>~wise(X))))&
(![X]:((funny(X)<~>wise(X))=>strong(X)))&
((?[X]:((~rich(X)|~brave(X))))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((~creative(X)<~>~curious(X))=>(calm(X)&brave(X))))&
((?[X]:((curious(X)|calm(X))))=>(?[X]:((~kind(X)|~calm(X)))))&
(((~generous(john)|~strong(john)))<=>(?[X]:(~wise(X))))&
(![X]:((brave(X)&~calm(X))=>(patient(X)|~tall(X))))&
(![X]:((~creative(X)&~strong(X))=>(creative(X)&tall(X))))&
((~happy(fred)|~tall(fred)))&
(?[X]:(~quiet(X)))&
((patient(paul)&~funny(paul)))&
(?[X]:((quiet(X)<~>~quiet(X))))&
(brave(alice))&
((~strong(john)|~kind(john)))&
(?[X]:((~strong(X)<~>~happy(X))))&
(?[X]:(~strong(X))) | ~tall(fred) | [] | null | 0 |
If susan is not brave or not humble then someone is either not tall or wise and vice versa.
Everyone who is not generous is generous or not funny.
Everyone who is patient is either not kind or funny.
Everyone who is both curious and not wise is not funny.
Everyone who is both not patient and not humble is either funny or not old and vice versa.
Everyone who is either tall or funny is calm and vice versa.
If someone is both wise and rich then someone is not creative or curious and vice versa.
Everyone who is not calm or rich is both old and wise.
Everyone who is quiet is both funny and not tall and vice versa.
If someone is both happy and rich then someone is either old or quiet.
If someone is either generous or not creative then someone is not humble or kind.
Everyone who is not rich or not humble is both not wise and brave and vice versa.
If mary is both not funny and generous then someone is not happy or strong and vice versa.
If fred is both not funny and not tall then alice is either not calm or creative and vice versa.
Everyone who is not wise or kind is calm.
If alice is calm then someone is both not creative and old and vice versa.
Alice is tall.
Someone is not kind or not rich.
John is kind.
Someone is not patient.
Alice is either not curious or generous.
Someone is not creative.
Someone is calm.
Mary is either curious or not kind. | Alice is not curious. | neutral | (((~brave(susan)|~humble(susan)))<=>(?[X]:((~tall(X)<~>wise(X)))))&
(![X]:(~generous(X)=>(generous(X)|~funny(X))))&
(![X]:(patient(X)=>(~kind(X)<~>funny(X))))&
(![X]:((curious(X)&~wise(X))=>~funny(X)))&
(![X]:((~patient(X)&~humble(X))<=>(funny(X)<~>~old(X))))&
(![X]:((tall(X)<~>funny(X))<=>calm(X)))&
((?[X]:((wise(X)&rich(X))))<=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:((~calm(X)|rich(X))=>(old(X)&wise(X))))&
(![X]:(quiet(X)<=>(funny(X)&~tall(X))))&
((?[X]:((happy(X)&rich(X))))=>(?[X]:((old(X)<~>quiet(X)))))&
((?[X]:((generous(X)<~>~creative(X))))=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((~rich(X)|~humble(X))<=>(~wise(X)&brave(X))))&
(((~funny(mary)&generous(mary)))<=>(?[X]:((~happy(X)|strong(X)))))&
(((~funny(fred)&~tall(fred)))<=>((~calm(alice)<~>creative(alice))))&
(![X]:((~wise(X)|kind(X))=>calm(X)))&
((calm(alice))<=>(?[X]:((~creative(X)&old(X)))))&
(tall(alice))&
(?[X]:((~kind(X)|~rich(X))))&
(kind(john))&
(?[X]:(~patient(X)))&
((~curious(alice)<~>generous(alice)))&
(?[X]:(~creative(X)))&
(?[X]:(calm(X)))&
((curious(mary)<~>~kind(mary))) | ~curious(alice) | [] | null | 0 |
If someone is not humble or not curious then someone is funny or not old and vice versa.
If someone is strong then alice is not rich.
Everyone who is either creative or strong is both not humble and not curious and vice versa.
If fred is strong then someone is either tall or not curious.
If john is not patient then alice is happy and vice versa.
If mary is both strong and humble then someone is either not wise or strong and vice versa.
Everyone who is either not kind or humble is not wise.
Everyone who is not generous or not calm is not kind.
Everyone who is either not generous or humble is both old and patient.
Everyone who is kind is either creative or not creative and vice versa.
Everyone who is not tall is not funny.
Everyone who is not tall is both not wise and rich.
If someone is either not humble or brave then someone is both old and not calm and vice versa.
Everyone who is either not patient or not kind is brave.
If someone is brave or happy then someone is either happy or not brave and vice versa.
Lucy is either brave or not old.
Lucy is creative.
Someone is not happy or kind.
Someone is both not strong and funny.
Fred is humble.
Someone is either not kind or creative.
Someone is either strong or not calm.
Someone is both quiet and not creative. | Alice is rich. | contradiction | ((?[X]:((~humble(X)|~curious(X))))<=>(?[X]:((funny(X)|~old(X)))))&
((?[X]:(strong(X)))=>(~rich(alice)))&
(![X]:((creative(X)<~>strong(X))<=>(~humble(X)&~curious(X))))&
((strong(fred))=>(?[X]:((tall(X)<~>~curious(X)))))&
((~patient(john))<=>(happy(alice)))&
(((strong(mary)&humble(mary)))<=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:((~kind(X)<~>humble(X))=>~wise(X)))&
(![X]:((~generous(X)|~calm(X))=>~kind(X)))&
(![X]:((~generous(X)<~>humble(X))=>(old(X)&patient(X))))&
(![X]:(kind(X)<=>(creative(X)<~>~creative(X))))&
(![X]:(~tall(X)=>~funny(X)))&
(![X]:(~tall(X)=>(~wise(X)&rich(X))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((old(X)&~calm(X)))))&
(![X]:((~patient(X)<~>~kind(X))=>brave(X)))&
((?[X]:((brave(X)|happy(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
((brave(lucy)<~>~old(lucy)))&
(creative(lucy))&
(?[X]:((~happy(X)|kind(X))))&
(?[X]:((~strong(X)&funny(X))))&
(humble(fred))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((strong(X)<~>~calm(X))))&
(?[X]:((quiet(X)&~creative(X)))) | rich(alice) | [
"p1",
"p7",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1916215981418059096774220
% SZS output start Proof for 1916215981418059096774220
2. ? [X0] : strong(X0) => ~rich(alice) [input p1]
8. ! [X0] : ((~calm(X0) | ~generous(X0)) => ~kind(X0)) [input p7]
10. ! [X0] : (kind(X0) <=> (creative(X0) <~> ~creative(X0))) [input p9]
22. ? [X0] : (strong(X0) <~> ~calm(X0)) [input p21]
24. rich(alice) [input hypothesis]
29. ~rich(alice) | ! [X0] : ~strong(X0) [ennf transformation 2]
32. ! [X0] : (~kind(X0) | (calm(X0) & generous(X0))) [ennf transformation 8]
55. ! [X0] : ((kind(X0) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~kind(X0))) [nnf transformation 10]
75. ? [X0] : ((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) [nnf transformation 22]
76. ? [X0] : ((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) => ((calm(sK11) | ~strong(sK11)) & (~calm(sK11) | strong(sK11))) [choice axiom]
77. (calm(sK11) | ~strong(sK11)) & (~calm(sK11) | strong(sK11)) [skolemisation 75,76]
84. ~rich(alice) | ~strong(X0) [cnf transformation 29]
104. ~kind(X0) | calm(X0) [cnf transformation 32]
111. kind(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 55]
112. kind(X0) | creative(X0) | creative(X0) [cnf transformation 55]
139. ~calm(sK11) | strong(sK11) [cnf transformation 77]
142. rich(alice) [cnf transformation 24]
143. kind(X0) | ~creative(X0) [duplicate literal removal 111]
144. kind(X0) | creative(X0) [duplicate literal removal 112]
178. 9 <=> ! [X0] : ~strong(X0) [avatar definition]
179. ~strong(X0) <- (9) [avatar component clause 178]
181. 10 <=> rich(alice) [avatar definition]
184. 9 | ~10 [avatar split clause 84,181,178]
237. kind(X0) [subsumption resolution 143,144]
316. 39 <=> strong(sK11) [avatar definition]
317. strong(sK11) <- (39) [avatar component clause 316]
320. 40 <=> calm(sK11) [avatar definition]
321. ~calm(sK11) <- (~40) [avatar component clause 320]
324. 39 | ~40 [avatar split clause 139,320,316]
325. 10 [avatar split clause 142,181]
327. calm(X0) [resolution 104,237]
329. $false <- (~40) [resolution 327,321]
330. 40 [avatar contradiction clause 329]
331. $false <- (9, 39) [subsumption resolution 317,179]
332. ~9 | ~39 [avatar contradiction clause 331]
333. $false [avatar sat refutation 184,324,325,330,332]
% SZS output end Proof for 1916215981418059096774220
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and not quiet then someone is tall or old and vice versa.
Everyone who is both happy and not funny is tall or not strong and vice versa.
Everyone who is either not tall or not wise is either kind or not creative and vice versa.
If fred is both not funny and tall then lucy is either wise or not strong.
If fred is curious then someone is quiet.
Everyone who is either not calm or brave is happy or not generous and vice versa.
If john is both generous and not calm then alice is either not creative or not rich.
Everyone who is both generous and tall is either old or generous.
If mary is not old or wise then someone is either old or not happy.
Everyone who is both not brave and generous is not funny or not wise and vice versa.
Everyone who is not brave is either not wise or generous and vice versa.
If someone is tall then paul is both not kind and not quiet and vice versa.
Everyone who is patient is not happy or not humble and vice versa.
Everyone who is both rich and not brave is brave or strong.
If someone is strong or not funny then someone is both not creative and not kind and vice versa.
If susan is both funny and patient then fred is not calm.
Paul is both rich and not old.
Mary is either generous or wise.
Paul is strong or curious.
Alice is generous or not brave.
Someone is either not old or not tall.
Someone is either not strong or happy.
John is either not creative or old.
Paul is both not kind and not calm. | Susan is wise. | entailment | ((?[X]:((tall(X)&~quiet(X))))<=>(?[X]:((tall(X)|old(X)))))&
(![X]:((happy(X)&~funny(X))<=>(tall(X)|~strong(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(kind(X)<~>~creative(X))))&
(((~funny(fred)&tall(fred)))=>((wise(lucy)<~>~strong(lucy))))&
((curious(fred))=>(?[X]:(quiet(X))))&
(![X]:((~calm(X)<~>brave(X))<=>(happy(X)|~generous(X))))&
(((generous(john)&~calm(john)))=>((~creative(alice)<~>~rich(alice))))&
(![X]:((generous(X)&tall(X))=>(old(X)<~>generous(X))))&
(((~old(mary)|wise(mary)))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:((~brave(X)&generous(X))<=>(~funny(X)|~wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)<~>generous(X))))&
((?[X]:(tall(X)))<=>((~kind(paul)&~quiet(paul))))&
(![X]:(patient(X)<=>(~happy(X)|~humble(X))))&
(![X]:((rich(X)&~brave(X))=>(brave(X)|strong(X))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:((~creative(X)&~kind(X)))))&
(((funny(susan)&patient(susan)))=>(~calm(fred)))&
((rich(paul)&~old(paul)))&
((generous(mary)<~>wise(mary)))&
((strong(paul)|curious(paul)))&
((generous(alice)|~brave(alice)))&
(?[X]:((~old(X)<~>~tall(X))))&
(?[X]:((~strong(X)<~>happy(X))))&
((~creative(john)<~>old(john)))&
((~kind(paul)&~calm(paul))) | wise(susan) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 844473065748024007463817
% SZS output start Proof for 844473065748024007463817
10. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (~wise(X0) | ~funny(X0))) [input p9]
11. ! [X0] : (~brave(X0) <=> (~wise(X0) <~> generous(X0))) [input p10]
25. ~wise(susan) [input hypothesis]
61. ! [X0] : (((generous(X0) & ~brave(X0)) | (wise(X0) & funny(X0))) & ((~wise(X0) | ~funny(X0)) | (~generous(X0) | brave(X0)))) [nnf transformation 10]
62. ! [X0] : (((generous(X0) & ~brave(X0)) | (wise(X0) & funny(X0))) & (~wise(X0) | ~funny(X0) | ~generous(X0) | brave(X0))) [flattening 61]
63. ! [X0] : ((~brave(X0) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | brave(X0))) [nnf transformation 11]
119. ~brave(X0) | wise(X0) [cnf transformation 62]
121. generous(X0) | wise(X0) [cnf transformation 62]
123. ~generous(X0) | wise(X0) | brave(X0) [cnf transformation 63]
151. ~wise(susan) [cnf transformation 25]
248. wise(X0) | brave(X0) [subsumption resolution 123,121]
249. wise(X0) [subsumption resolution 248,119]
331. $false [subsumption resolution 151,249]
% SZS output end Proof for 844473065748024007463817
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not humble is either quiet or wise. If susan is either tall or not rich then someone is either not happy or creative. If alice is both not funny and not kind then someone is not old and vice versa. Everyone who is brave is not kind and vice versa. Everyone who is both curious and not funny is curious or happy. Everyone who is brave or calm is both not brave and not quiet and vice versa. If someone is either not calm or not curious then susan is not creative or not old and vice versa. Everyone who is both kind and not calm is rich or kind. Everyone who is rich or not wise is generous. Everyone who is not strong is not tall or patient. Everyone who is both not creative and not generous is not calm and vice versa. If mary is both kind and happy then susan is either not kind or quiet and vice versa. Everyone who is not tall or not quiet is funny or rich and vice versa. Everyone who is not creative is old or tall and vice versa. If mary is either wise or not patient then john is either old or not old and vice versa. Everyone who is not funny or not wise is curious or not wise and vice versa. Someone is either not rich or tall. Someone is quiet. Someone is either not creative or not wise. Lucy is not generous. Someone is both happy and not patient. Someone is both happy and funny. Someone is either not wise or not calm. | Lucy is not calm. | entailment | (![X]:((~tall(X)<~>~humble(X))=>(quiet(X)<~>wise(X))))&
(((tall(susan)<~>~rich(susan)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(((~funny(alice)&~kind(alice)))<=>(?[X]:(~old(X))))&
(![X]:(brave(X)<=>~kind(X)))&
(![X]:((curious(X)&~funny(X))=>(curious(X)|happy(X))))&
(![X]:((brave(X)|calm(X))<=>(~brave(X)&~quiet(X))))&
((?[X]:((~calm(X)<~>~curious(X))))<=>((~creative(susan)|~old(susan))))&
(![X]:((kind(X)&~calm(X))=>(rich(X)|kind(X))))&
(![X]:((rich(X)|~wise(X))=>generous(X)))&
(![X]:(~strong(X)=>(~tall(X)|patient(X))))&
(![X]:((~creative(X)&~generous(X))<=>~calm(X)))&
(((kind(mary)&happy(mary)))<=>((~kind(susan)<~>quiet(susan))))&
(![X]:((~tall(X)|~quiet(X))<=>(funny(X)|rich(X))))&
(![X]:(~creative(X)<=>(old(X)|tall(X))))&
(((wise(mary)<~>~patient(mary)))<=>((old(john)<~>~old(john))))&
(![X]:((~funny(X)|~wise(X))<=>(curious(X)|~wise(X))))&
(?[X]:((~rich(X)<~>tall(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~creative(X)<~>~wise(X))))&
(~generous(lucy))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((happy(X)&funny(X))))&
(?[X]:((~wise(X)<~>~calm(X)))) | ~calm(lucy) | [
"p2",
"p3",
"p5",
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6686790767094901218639880
% SZS output start Proof for 6686790767094901218639880
3. (~kind(alice) & ~funny(alice)) <=> ? [X0] : ~old(X0) [input p2]
4. ! [X0] : (brave(X0) <=> ~kind(X0)) [input p3]
6. ! [X0] : ((calm(X0) | brave(X0)) <=> (~quiet(X0) & ~brave(X0))) [input p5]
11. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> ~calm(X0)) [input p10]
14. ! [X0] : (~creative(X0) <=> (tall(X0) | old(X0))) [input p13]
20. ~generous(lucy) [input p19]
24. calm(lucy) [input hypothesis]
37. ((~kind(alice) & ~funny(alice)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | (kind(alice) | funny(alice))) [nnf transformation 3]
38. ((~kind(alice) & ~funny(alice)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | kind(alice) | funny(alice)) [flattening 37]
39. ((~kind(alice) & ~funny(alice)) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | kind(alice) | funny(alice)) [rectify 38]
40. ? [X1] : ~old(X1) => ~old(sK1) [choice axiom]
41. ((~kind(alice) & ~funny(alice)) | ! [X0] : old(X0)) & (~old(sK1) | kind(alice) | funny(alice)) [skolemisation 39,40]
42. ! [X0] : ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0))) [nnf transformation 4]
43. ! [X0] : (((calm(X0) | brave(X0)) | (quiet(X0) | brave(X0))) & ((~quiet(X0) & ~brave(X0)) | (~calm(X0) & ~brave(X0)))) [nnf transformation 6]
44. ! [X0] : ((calm(X0) | brave(X0) | quiet(X0) | brave(X0)) & ((~quiet(X0) & ~brave(X0)) | (~calm(X0) & ~brave(X0)))) [flattening 43]
50. ! [X0] : (((~generous(X0) & ~creative(X0)) | calm(X0)) & (~calm(X0) | (generous(X0) | creative(X0)))) [nnf transformation 11]
51. ! [X0] : (((~generous(X0) & ~creative(X0)) | calm(X0)) & (~calm(X0) | generous(X0) | creative(X0))) [flattening 50]
56. ! [X0] : ((~creative(X0) | (~tall(X0) & ~old(X0))) & ((tall(X0) | old(X0)) | creative(X0))) [nnf transformation 14]
57. ! [X0] : ((~creative(X0) | (~tall(X0) & ~old(X0))) & (tall(X0) | old(X0) | creative(X0))) [flattening 56]
86. ~kind(alice) | old(X0) [cnf transformation 41]
88. brave(X0) | kind(X0) [cnf transformation 42]
90. ~brave(X0) | ~brave(X0) [cnf transformation 44]
104. ~calm(X0) | generous(X0) | creative(X0) [cnf transformation 51]
118. ~old(X0) | ~creative(X0) [cnf transformation 57]
137. ~generous(lucy) [cnf transformation 20]
144. calm(lucy) [cnf transformation 24]
149. ~brave(X0) [duplicate literal removal 90]
172. 5 <=> ! [X0] : old(X0) [avatar definition]
173. old(X0) <- (5) [avatar component clause 172]
175. 6 <=> kind(alice) [avatar definition]
177. ~kind(alice) <- (~6) [avatar component clause 175]
178. 5 | ~6 [avatar split clause 86,175,172]
286. kind(X1) [resolution 88,149]
289. $false <- (~6) [resolution 286,177]
294. 6 [avatar contradiction clause 289]
309. ~creative(X0) <- (5) [resolution 118,173]
312. generous(lucy) | creative(lucy) [resolution 104,144]
314. creative(lucy) [subsumption resolution 312,137]
315. $false <- (5) [subsumption resolution 314,309]
316. ~5 [avatar contradiction clause 315]
318. $false [avatar sat refutation 178,294,316]
% SZS output end Proof for 6686790767094901218639880
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or calm is both tall and not happy. Everyone who is not kind or not brave is either brave or calm and vice versa. Everyone who is generous or happy is tall or quiet and vice versa. If susan is patient then someone is not funny. Everyone who is not tall or not old is not funny or funny and vice versa. If mary is both not calm and not humble then fred is wise and vice versa. Everyone who is either strong or tall is not rich and vice versa. If mary is either not kind or funny then someone is both not rich and not funny and vice versa. Everyone who is both not happy and not wise is not generous or curious. Everyone who is not old is either not strong or patient. Everyone who is not humble or not patient is either not funny or not tall and vice versa. If someone is not quiet then someone is calm and vice versa. Everyone who is brave or not tall is brave. Everyone who is humble or old is funny. Everyone who is either happy or old is old or calm. Everyone who is kind or funny is not humble or old and vice versa. Fred is patient. Someone is strong. Lucy is strong. Mary is both not patient and quiet. Someone is both not patient and wise. Someone is not wise or old. Someone is not generous or brave. | Mary is not rich. | neutral | (![X]:((funny(X)<~>calm(X))=>(tall(X)&~happy(X))))&
(![X]:((~kind(X)|~brave(X))<=>(brave(X)<~>calm(X))))&
(![X]:((generous(X)|happy(X))<=>(tall(X)|quiet(X))))&
((patient(susan))=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)|~old(X))<=>(~funny(X)|funny(X))))&
(((~calm(mary)&~humble(mary)))<=>(wise(fred)))&
(![X]:((strong(X)<~>tall(X))<=>~rich(X)))&
(((~kind(mary)<~>funny(mary)))<=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((~happy(X)&~wise(X))=>(~generous(X)|curious(X))))&
(![X]:(~old(X)=>(~strong(X)<~>patient(X))))&
(![X]:((~humble(X)|~patient(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(calm(X))))&
(![X]:((brave(X)|~tall(X))=>brave(X)))&
(![X]:((humble(X)|old(X))=>funny(X)))&
(![X]:((happy(X)<~>old(X))=>(old(X)|calm(X))))&
(![X]:((kind(X)|funny(X))<=>(~humble(X)|old(X))))&
(patient(fred))&
(?[X]:(strong(X)))&
(strong(lucy))&
((~patient(mary)&quiet(mary)))&
(?[X]:((~patient(X)&wise(X))))&
(?[X]:((~wise(X)|old(X))))&
(?[X]:((~generous(X)|brave(X)))) | ~rich(mary) | [] | null | 0 |
If lucy is happy or not quiet then john is either not happy or not rich and vice versa.
If someone is both not funny and not old then someone is patient and vice versa.
Everyone who is both patient and not calm is quiet or not kind and vice versa.
Everyone who is either strong or not strong is curious and vice versa.
If someone is not tall or humble then lucy is humble.
Everyone who is either brave or not humble is both kind and not old.
Everyone who is happy is both not funny and not brave and vice versa.
If alice is both not curious and not funny then someone is either brave or not old.
Everyone who is either not tall or rich is not strong.
If someone is tall then someone is humble or tall.
Everyone who is funny is either creative or not calm and vice versa.
Everyone who is both not rich and quiet is not funny or tall and vice versa.
If someone is both happy and not happy then fred is generous or happy.
If paul is both not patient and not funny then someone is both rich and patient.
Everyone who is not rich or quiet is calm and vice versa.
If someone is both not tall and not strong then lucy is both generous and wise.
Paul is rich.
Susan is either rich or not curious.
Lucy is not brave or not humble.
Mary is either generous or not tall.
Someone is not brave or not strong.
Someone is generous.
Someone is not creative.
Someone is either strong or not old. | Alice is tall. | contradiction | (((happy(lucy)|~quiet(lucy)))<=>((~happy(john)<~>~rich(john))))&
((?[X]:((~funny(X)&~old(X))))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~calm(X))<=>(quiet(X)|~kind(X))))&
(![X]:((strong(X)<~>~strong(X))<=>curious(X)))&
((?[X]:((~tall(X)|humble(X))))=>(humble(lucy)))&
(![X]:((brave(X)<~>~humble(X))=>(kind(X)&~old(X))))&
(![X]:(happy(X)<=>(~funny(X)&~brave(X))))&
(((~curious(alice)&~funny(alice)))=>(?[X]:((brave(X)<~>~old(X)))))&
(![X]:((~tall(X)<~>rich(X))=>~strong(X)))&
((?[X]:(tall(X)))=>(?[X]:((humble(X)|tall(X)))))&
(![X]:(funny(X)<=>(creative(X)<~>~calm(X))))&
(![X]:((~rich(X)&quiet(X))<=>(~funny(X)|tall(X))))&
((?[X]:((happy(X)&~happy(X))))=>((generous(fred)|happy(fred))))&
(((~patient(paul)&~funny(paul)))=>(?[X]:((rich(X)&patient(X)))))&
(![X]:((~rich(X)|quiet(X))<=>calm(X)))&
((?[X]:((~tall(X)&~strong(X))))=>((generous(lucy)&wise(lucy))))&
(rich(paul))&
((rich(susan)<~>~curious(susan)))&
((~brave(lucy)|~humble(lucy)))&
((generous(mary)<~>~tall(mary)))&
(?[X]:((~brave(X)|~strong(X))))&
(?[X]:(generous(X)))&
(?[X]:(~creative(X)))&
(?[X]:((strong(X)<~>~old(X)))) | tall(alice) | [
"p2",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 63817924515586639922519
% SZS output start Proof for 63817924515586639922519
3. ! [X0] : ((~calm(X0) & patient(X0)) <=> (~kind(X0) | quiet(X0))) [input p2]
12. ! [X0] : ((quiet(X0) & ~rich(X0)) <=> (tall(X0) | ~funny(X0))) [input p11]
15. ! [X0] : ((quiet(X0) | ~rich(X0)) <=> calm(X0)) [input p14]
25. tall(alice) [input hypothesis]
47. ! [X0] : (((~calm(X0) & patient(X0)) | (kind(X0) & ~quiet(X0))) & ((~kind(X0) | quiet(X0)) | (calm(X0) | ~patient(X0)))) [nnf transformation 3]
48. ! [X0] : (((~calm(X0) & patient(X0)) | (kind(X0) & ~quiet(X0))) & (~kind(X0) | quiet(X0) | calm(X0) | ~patient(X0))) [flattening 47]
61. ! [X0] : (((quiet(X0) & ~rich(X0)) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | (~quiet(X0) | rich(X0)))) [nnf transformation 12]
62. ! [X0] : (((quiet(X0) & ~rich(X0)) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~quiet(X0) | rich(X0))) [flattening 61]
65. ! [X0] : (((quiet(X0) | ~rich(X0)) | ~calm(X0)) & (calm(X0) | (~quiet(X0) & rich(X0)))) [nnf transformation 15]
66. ! [X0] : ((quiet(X0) | ~rich(X0) | ~calm(X0)) & (calm(X0) | (~quiet(X0) & rich(X0)))) [flattening 65]
90. ~calm(X0) | ~quiet(X0) [cnf transformation 48]
118. ~tall(X0) | quiet(X0) [cnf transformation 62]
123. calm(X0) | ~quiet(X0) [cnf transformation 66]
137. tall(alice) [cnf transformation 25]
227. ~quiet(X0) [subsumption resolution 123,90]
287. quiet(alice) [resolution 118,137]
288. $false [subsumption resolution 287,227]
% SZS output end Proof for 63817924515586639922519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not kind or not calm is quiet and vice versa.
Everyone who is not humble or not funny is creative or kind and vice versa.
If john is tall then fred is not wise or not humble.
If someone is either not patient or not brave then someone is strong.
Everyone who is either wise or not wise is curious or strong and vice versa.
Everyone who is not generous is either rich or not tall and vice versa.
Everyone who is both not happy and not tall is both creative and brave and vice versa.
Everyone who is both brave and wise is both quiet and not humble and vice versa.
Everyone who is not humble or calm is not calm and vice versa.
If john is both funny and not wise then someone is not patient.
If alice is both not patient and not brave then someone is not tall or happy and vice versa.
If someone is not quiet then someone is both calm and kind.
Everyone who is both not creative and curious is kind and vice versa.
Everyone who is not happy or wise is both old and not patient and vice versa.
Someone is not calm or rich.
Someone is rich.
Someone is old or not old.
Mary is either not funny or old.
Someone is old.
Someone is either not humble or creative. | Fred is not wise. | contradiction | (![X]:((~kind(X)|~calm(X))<=>quiet(X)))&
(![X]:((~humble(X)|~funny(X))<=>(creative(X)|kind(X))))&
((tall(john))=>((~wise(fred)|~humble(fred))))&
((?[X]:((~patient(X)<~>~brave(X))))=>(?[X]:(strong(X))))&
(![X]:((wise(X)<~>~wise(X))<=>(curious(X)|strong(X))))&
(![X]:(~generous(X)<=>(rich(X)<~>~tall(X))))&
(![X]:((~happy(X)&~tall(X))<=>(creative(X)&brave(X))))&
(![X]:((brave(X)&wise(X))<=>(quiet(X)&~humble(X))))&
(![X]:((~humble(X)|calm(X))<=>~calm(X)))&
(((funny(john)&~wise(john)))=>(?[X]:(~patient(X))))&
(((~patient(alice)&~brave(alice)))<=>(?[X]:((~tall(X)|happy(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((calm(X)&kind(X)))))&
(![X]:((~creative(X)&curious(X))<=>kind(X)))&
(![X]:((~happy(X)|wise(X))<=>(old(X)&~patient(X))))&
(?[X]:((~calm(X)|rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((old(X)|~old(X))))&
((~funny(mary)<~>old(mary)))&
(?[X]:(old(X)))&
(?[X]:((~humble(X)<~>creative(X)))) | ~wise(fred) | [
"p0",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8630252534245910366760601
% SZS output start Proof for 8630252534245910366760601
1. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> quiet(X0)) [input p0]
8. ! [X0] : ((wise(X0) & brave(X0)) <=> (~humble(X0) & quiet(X0))) [input p7]
9. ! [X0] : ((calm(X0) | ~humble(X0)) <=> ~calm(X0)) [input p8]
21. ~wise(fred) [input hypothesis]
32. ! [X0] : (((~calm(X0) | ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | (calm(X0) & kind(X0)))) [nnf transformation 1]
33. ! [X0] : ((~calm(X0) | ~kind(X0) | ~quiet(X0)) & (quiet(X0) | (calm(X0) & kind(X0)))) [flattening 32]
44. ! [X0] : (((wise(X0) & brave(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (~wise(X0) | ~brave(X0)))) [nnf transformation 8]
45. ! [X0] : (((wise(X0) & brave(X0)) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | ~wise(X0) | ~brave(X0))) [flattening 44]
46. ! [X0] : (((calm(X0) | ~humble(X0)) | calm(X0)) & (~calm(X0) | (~calm(X0) & humble(X0)))) [nnf transformation 9]
47. ! [X0] : ((calm(X0) | ~humble(X0) | calm(X0)) & (~calm(X0) | (~calm(X0) & humble(X0)))) [flattening 46]
71. quiet(X0) | calm(X0) [cnf transformation 33]
93. ~quiet(X0) | humble(X0) | wise(X0) [cnf transformation 45]
95. ~calm(X0) | ~calm(X0) [cnf transformation 47]
96. calm(X0) | ~humble(X0) | calm(X0) [cnf transformation 47]
119. ~wise(fred) [cnf transformation 21]
120. ~calm(X0) [duplicate literal removal 95]
121. ~humble(X0) | calm(X0) [duplicate literal removal 96]
129. 2 <=> wise(fred) [avatar definition]
131. ~wise(fred) <- (~2) [avatar component clause 129]
133. 3 <=> humble(fred) [avatar definition]
134. humble(fred) <- (3) [avatar component clause 133]
220. ~2 [avatar split clause 119,129]
253. humble(X0) | wise(X0) | calm(X0) [resolution 93,71]
256. wise(X0) | humble(X0) [subsumption resolution 253,120]
319. humble(fred) <- (~2) [resolution 256,131]
322. 3 | 2 [avatar split clause 319,129,133]
325. calm(fred) <- (3) [resolution 134,121]
326. $false <- (3) [subsumption resolution 325,120]
327. ~3 [avatar contradiction clause 326]
328. $false [avatar sat refutation 220,322,327]
% SZS output end Proof for 8630252534245910366760601
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or happy then paul is either not curious or not happy. Everyone who is either not strong or not kind is both not creative and not quiet and vice versa. Everyone who is both generous and not tall is both not quiet and not kind and vice versa. If lucy is funny or patient then someone is both not patient and not old. If john is both not wise and not old then paul is either creative or patient and vice versa. If someone is either creative or not patient then someone is either rich or tall. If someone is not humble then paul is not curious. Everyone who is both wise and calm is either not old or not kind. Everyone who is both not funny and kind is both not calm and not happy. If someone is both not patient and happy then someone is both not generous and not funny and vice versa. Everyone who is either kind or not happy is not brave or kind and vice versa. If someone is either funny or not brave then john is both calm and kind. If john is both brave and not calm then someone is not wise or old and vice versa. Everyone who is quiet is both quiet and old. If someone is either quiet or not rich then susan is not happy. If paul is both not curious and generous then john is not patient and vice versa. Lucy is kind or not wise. Alice is generous or not strong. Fred is either not old or creative. Someone is brave. Fred is both not strong and tall. Mary is not funny. John is not patient or not happy. Someone is both not kind and not brave. | Mary is happy. | entailment | (((strong(john)|happy(john)))=>((~curious(paul)<~>~happy(paul))))&
(![X]:((~strong(X)<~>~kind(X))<=>(~creative(X)&~quiet(X))))&
(![X]:((generous(X)&~tall(X))<=>(~quiet(X)&~kind(X))))&
(((funny(lucy)|patient(lucy)))=>(?[X]:((~patient(X)&~old(X)))))&
(((~wise(john)&~old(john)))<=>((creative(paul)<~>patient(paul))))&
((?[X]:((creative(X)<~>~patient(X))))=>(?[X]:((rich(X)<~>tall(X)))))&
((?[X]:(~humble(X)))=>(~curious(paul)))&
(![X]:((wise(X)&calm(X))=>(~old(X)<~>~kind(X))))&
(![X]:((~funny(X)&kind(X))=>(~calm(X)&~happy(X))))&
((?[X]:((~patient(X)&happy(X))))<=>(?[X]:((~generous(X)&~funny(X)))))&
(![X]:((kind(X)<~>~happy(X))<=>(~brave(X)|kind(X))))&
((?[X]:((funny(X)<~>~brave(X))))=>((calm(john)&kind(john))))&
(((brave(john)&~calm(john)))<=>(?[X]:((~wise(X)|old(X)))))&
(![X]:(quiet(X)=>(quiet(X)&old(X))))&
((?[X]:((quiet(X)<~>~rich(X))))=>(~happy(susan)))&
(((~curious(paul)&generous(paul)))<=>(~patient(john)))&
((kind(lucy)|~wise(lucy)))&
((generous(alice)|~strong(alice)))&
((~old(fred)<~>creative(fred)))&
(?[X]:(brave(X)))&
((~strong(fred)&tall(fred)))&
(~funny(mary))&
((~patient(john)|~happy(john)))&
(?[X]:((~kind(X)&~brave(X)))) | happy(mary) | [
"p2",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6204382128458942083557576
% SZS output start Proof for 6204382128458942083557576
3. ! [X0] : ((~tall(X0) & generous(X0)) <=> (~kind(X0) & ~quiet(X0))) [input p2]
9. ! [X0] : ((kind(X0) & ~funny(X0)) => (~happy(X0) & ~calm(X0))) [input p8]
10. ? [X0] : (happy(X0) & ~patient(X0)) <=> ? [X0] : (~funny(X0) & ~generous(X0)) [input p9]
11. ! [X0] : ((kind(X0) <~> ~happy(X0)) <=> (kind(X0) | ~brave(X0))) [input p10]
12. ? [X0] : (funny(X0) <~> ~brave(X0)) => (kind(john) & calm(john)) [input p11]
13. (~calm(john) & brave(john)) <=> ? [X0] : (old(X0) | ~wise(X0)) [input p12]
14. ! [X0] : (quiet(X0) => (old(X0) & quiet(X0))) [input p13]
22. ~funny(mary) [input p21]
23. ~happy(john) | ~patient(john) [input p22]
25. ~happy(mary) [input hypothesis]
27. ? [X0] : (happy(X0) & ~patient(X0)) <=> ? [X1] : (~funny(X1) & ~generous(X1)) [rectify 10]
34. ! [X0] : ((~happy(X0) & ~calm(X0)) | (~kind(X0) | funny(X0))) [ennf transformation 9]
35. ! [X0] : ((~happy(X0) & ~calm(X0)) | ~kind(X0) | funny(X0)) [flattening 34]
36. (kind(john) & calm(john)) | ! [X0] : (funny(X0) <=> ~brave(X0)) [ennf transformation 12]
37. ! [X0] : ((old(X0) & quiet(X0)) | ~quiet(X0)) [ennf transformation 14]
42. ! [X0] : (((~tall(X0) & generous(X0)) | (kind(X0) | quiet(X0))) & ((~kind(X0) & ~quiet(X0)) | (tall(X0) | ~generous(X0)))) [nnf transformation 3]
43. ! [X0] : (((~tall(X0) & generous(X0)) | kind(X0) | quiet(X0)) & ((~kind(X0) & ~quiet(X0)) | tall(X0) | ~generous(X0))) [flattening 42]
53. (? [X0] : (happy(X0) & ~patient(X0)) | ! [X1] : (funny(X1) | generous(X1))) & (? [X1] : (~funny(X1) & ~generous(X1)) | ! [X0] : (~happy(X0) | patient(X0))) [nnf transformation 27]
54. (? [X0] : (happy(X0) & ~patient(X0)) | ! [X1] : (funny(X1) | generous(X1))) & (? [X2] : (~funny(X2) & ~generous(X2)) | ! [X3] : (~happy(X3) | patient(X3))) [rectify 53]
55. ? [X0] : (happy(X0) & ~patient(X0)) => (happy(sK2) & ~patient(sK2)) [choice axiom]
56. ? [X2] : (~funny(X2) & ~generous(X2)) => (~funny(sK3) & ~generous(sK3)) [choice axiom]
57. ((happy(sK2) & ~patient(sK2)) | ! [X1] : (funny(X1) | generous(X1))) & ((~funny(sK3) & ~generous(sK3)) | ! [X3] : (~happy(X3) | patient(X3))) [skolemisation 54,56,55]
58. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (~kind(X0) & brave(X0))) & ((kind(X0) | ~brave(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [nnf transformation 11]
59. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (~kind(X0) & brave(X0))) & (kind(X0) | ~brave(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [flattening 58]
60. (kind(john) & calm(john)) | ! [X0] : ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))) [nnf transformation 36]
61. ((~calm(john) & brave(john)) | ! [X0] : (~old(X0) & wise(X0))) & (? [X0] : (old(X0) | ~wise(X0)) | (calm(john) | ~brave(john))) [nnf transformation 13]
62. ((~calm(john) & brave(john)) | ! [X0] : (~old(X0) & wise(X0))) & (? [X0] : (old(X0) | ~wise(X0)) | calm(john) | ~brave(john)) [flattening 61]
63. ((~calm(john) & brave(john)) | ! [X0] : (~old(X0) & wise(X0))) & (? [X1] : (old(X1) | ~wise(X1)) | calm(john) | ~brave(john)) [rectify 62]
64. ? [X1] : (old(X1) | ~wise(X1)) => (old(sK4) | ~wise(sK4)) [choice axiom]
65. ((~calm(john) & brave(john)) | ! [X0] : (~old(X0) & wise(X0))) & ((old(sK4) | ~wise(sK4)) | calm(john) | ~brave(john)) [skolemisation 63,64]
86. generous(X0) | kind(X0) | quiet(X0) [cnf transformation 43]
105. ~kind(X0) | ~happy(X0) | funny(X0) [cnf transformation 35]
106. ~generous(sK3) | ~happy(X3) | patient(X3) [cnf transformation 57]
107. ~funny(sK3) | ~happy(X3) | patient(X3) [cnf transformation 57]
111. kind(X0) | ~brave(X0) | kind(X0) | happy(X0) [cnf transformation 59]
115. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 59]
117. calm(john) | funny(X0) | brave(X0) [cnf transformation 60]
119. kind(john) | funny(X0) | brave(X0) [cnf transformation 60]
124. ~calm(john) | ~old(X0) [cnf transformation 65]
126. ~quiet(X0) | old(X0) [cnf transformation 37]
139. ~funny(mary) [cnf transformation 22]
140. ~happy(john) | ~patient(john) [cnf transformation 23]
143. ~happy(mary) [cnf transformation 25]
144. kind(X0) | ~brave(X0) | happy(X0) [duplicate literal removal 111]
145. ~kind(X0) | happy(X0) [duplicate literal removal 115]
147. 1 <=> happy(john) [avatar definition]
148. happy(john) <- (1) [avatar component clause 147]
240. 20 <=> ! [X3] : (~happy(X3) | patient(X3)) [avatar definition]
241. ~happy(X3) | patient(X3) <- (20) [avatar component clause 240]
243. 21 <=> funny(sK3) [avatar definition]
245. ~funny(sK3) <- (~21) [avatar component clause 243]
246. 20 | ~21 [avatar split clause 107,243,240]
248. 22 <=> generous(sK3) [avatar definition]
250. ~generous(sK3) <- (~22) [avatar component clause 248]
251. 20 | ~22 [avatar split clause 106,248,240]
252. ~brave(X0) | happy(X0) [subsumption resolution 144,145]
254. 23 <=> ! [X0] : (funny(X0) | brave(X0)) [avatar definition]
255. brave(X0) | funny(X0) <- (23) [avatar component clause 254]
257. 24 <=> kind(john) [avatar definition]
259. kind(john) <- (24) [avatar component clause 257]
260. 23 | 24 [avatar split clause 119,257,254]
266. 26 <=> calm(john) [avatar definition]
269. 23 | 26 [avatar split clause 117,266,254]
272. 27 <=> ! [X0] : ~old(X0) [avatar definition]
273. ~old(X0) <- (27) [avatar component clause 272]
274. 27 | ~26 [avatar split clause 124,266,272]
307. 35 <=> patient(john) [avatar definition]
308. ~patient(john) <- (~35) [avatar component clause 307]
345. ~35 | ~1 [avatar split clause 140,147,307]
362. funny(X0) | happy(X0) <- (23) [resolution 255,252]
366. happy(mary) <- (23) [resolution 362,139]
369. $false <- (23) [subsumption resolution 366,143]
370. ~23 [avatar contradiction clause 369]
371. happy(john) <- (24) [resolution 259,145]
374. 1 | ~24 [avatar split clause 371,257,147]
395. 46 <=> quiet(sK3) [avatar definition]
397. quiet(sK3) <- (46) [avatar component clause 395]
399. 47 <=> kind(sK3) [avatar definition]
401. kind(sK3) <- (47) [avatar component clause 399]
411. patient(john) <- (1, 20) [resolution 241,148]
416. $false <- (1, 20, ~35) [subsumption resolution 411,308]
417. ~1 | ~20 | 35 [avatar contradiction clause 416]
423. kind(sK3) | quiet(sK3) <- (~22) [resolution 250,86]
438. old(sK3) <- (46) [resolution 397,126]
440. $false <- (27, 46) [subsumption resolution 438,273]
441. ~27 | ~46 [avatar contradiction clause 440]
442. 46 | 47 | 22 [avatar split clause 423,248,399,395]
478. ~happy(sK3) | funny(sK3) <- (47) [resolution 401,105]
479. happy(sK3) <- (47) [resolution 401,145]
490. ~happy(sK3) <- (~21, 47) [subsumption resolution 478,245]
491. $false <- (~21, 47) [subsumption resolution 479,490]
492. 21 | ~47 [avatar contradiction clause 491]
493. $false [avatar sat refutation 246,251,260,269,274,345,370,374,417,441,442,492]
% SZS output end Proof for 6204382128458942083557576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not curious or not rich then someone is funny or quiet.
Everyone who is either not happy or not tall is either calm or not patient and vice versa.
Everyone who is both not creative and not quiet is tall or not strong and vice versa.
Everyone who is both wise and not creative is rich or patient.
If someone is either not happy or curious then someone is tall and vice versa.
If someone is both quiet and generous then someone is either kind or generous.
If someone is patient or not quiet then someone is wise and vice versa.
Everyone who is kind or not strong is either generous or not kind.
Everyone who is not quiet or not rich is both not happy and not patient.
Everyone who is not old or not wise is either rich or not tall and vice versa.
If someone is both brave and tall then someone is both not wise and not creative and vice versa.
Everyone who is curious is not happy and vice versa.
Everyone who is both not generous and quiet is not generous or not kind.
Everyone who is either not kind or happy is both not curious and creative.
Everyone who is not generous is not kind or not tall and vice versa.
Someone is either not curious or curious.
Paul is not kind or happy.
Someone is not funny. | Paul is creative. | neutral | (((~curious(alice)|~rich(alice)))=>(?[X]:((funny(X)|quiet(X)))))&
(![X]:((~happy(X)<~>~tall(X))<=>(calm(X)<~>~patient(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(tall(X)|~strong(X))))&
(![X]:((wise(X)&~creative(X))=>(rich(X)|patient(X))))&
((?[X]:((~happy(X)<~>curious(X))))<=>(?[X]:(tall(X))))&
((?[X]:((quiet(X)&generous(X))))=>(?[X]:((kind(X)<~>generous(X)))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~strong(X))=>(generous(X)<~>~kind(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~happy(X)&~patient(X))))&
(![X]:((~old(X)|~wise(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:(curious(X)<=>~happy(X)))&
(![X]:((~generous(X)&quiet(X))=>(~generous(X)|~kind(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~curious(X)&creative(X))))&
(![X]:(~generous(X)<=>(~kind(X)|~tall(X))))&
(?[X]:((~curious(X)<~>curious(X))))&
((~kind(paul)|happy(paul)))&
(?[X]:(~funny(X))) | creative(paul) | [] | null | 0 |
If lucy is both kind and not happy then someone is calm or not brave.
If someone is both kind and not curious then mary is not generous and vice versa.
Everyone who is both not generous and not quiet is not funny and vice versa.
If someone is either wise or quiet then mary is not humble and vice versa.
Everyone who is both not funny and not strong is not kind and vice versa.
Everyone who is both not old and not kind is generous or not wise and vice versa.
If someone is not calm or not kind then paul is both humble and generous.
If someone is either funny or not tall then paul is strong.
If someone is old then alice is either not funny or wise and vice versa.
Everyone who is both not curious and not brave is calm or not quiet.
If someone is calm then susan is happy or tall and vice versa.
Everyone who is curious is both not strong and tall.
Everyone who is rich is both wise and strong and vice versa.
Everyone who is creative is both not wise and strong and vice versa.
If someone is wise or quiet then fred is not humble or not generous and vice versa.
Everyone who is not quiet or not tall is both not brave and not old.
Someone is either not kind or not funny.
Someone is not brave or patient.
Lucy is both not tall and not happy.
Fred is either not old or generous.
Someone is either not curious or not creative.
John is strong or not curious.
Paul is brave. | Paul is not wise. | contradiction | (((kind(lucy)&~happy(lucy)))=>(?[X]:((calm(X)|~brave(X)))))&
((?[X]:((kind(X)&~curious(X))))<=>(~generous(mary)))&
(![X]:((~generous(X)&~quiet(X))<=>~funny(X)))&
((?[X]:((wise(X)<~>quiet(X))))<=>(~humble(mary)))&
(![X]:((~funny(X)&~strong(X))<=>~kind(X)))&
(![X]:((~old(X)&~kind(X))<=>(generous(X)|~wise(X))))&
((?[X]:((~calm(X)|~kind(X))))=>((humble(paul)&generous(paul))))&
((?[X]:((funny(X)<~>~tall(X))))=>(strong(paul)))&
((?[X]:(old(X)))<=>((~funny(alice)<~>wise(alice))))&
(![X]:((~curious(X)&~brave(X))=>(calm(X)|~quiet(X))))&
((?[X]:(calm(X)))<=>((happy(susan)|tall(susan))))&
(![X]:(curious(X)=>(~strong(X)&tall(X))))&
(![X]:(rich(X)<=>(wise(X)&strong(X))))&
(![X]:(creative(X)<=>(~wise(X)&strong(X))))&
((?[X]:((wise(X)|quiet(X))))<=>((~humble(fred)|~generous(fred))))&
(![X]:((~quiet(X)|~tall(X))=>(~brave(X)&~old(X))))&
(?[X]:((~kind(X)<~>~funny(X))))&
(?[X]:((~brave(X)|patient(X))))&
((~tall(lucy)&~happy(lucy)))&
((~old(fred)<~>generous(fred)))&
(?[X]:((~curious(X)<~>~creative(X))))&
((strong(john)|~curious(john)))&
(brave(paul)) | ~wise(paul) | [
"p2",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3510547066630564429607360
% SZS output start Proof for 3510547066630564429607360
3. ! [X0] : ((~quiet(X0) & ~generous(X0)) <=> ~funny(X0)) [input p2]
5. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> ~kind(X0)) [input p4]
6. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~wise(X0) | generous(X0))) [input p5]
7. ? [X0] : (~kind(X0) | ~calm(X0)) => (generous(paul) & humble(paul)) [input p6]
24. ~wise(paul) [input hypothesis]
28. (generous(paul) & humble(paul)) | ! [X0] : (kind(X0) & calm(X0)) [ennf transformation 7]
40. ! [X0] : (((~quiet(X0) & ~generous(X0)) | funny(X0)) & (~funny(X0) | (quiet(X0) | generous(X0)))) [nnf transformation 3]
41. ! [X0] : (((~quiet(X0) & ~generous(X0)) | funny(X0)) & (~funny(X0) | quiet(X0) | generous(X0))) [flattening 40]
46. ! [X0] : (((~strong(X0) & ~funny(X0)) | kind(X0)) & (~kind(X0) | (strong(X0) | funny(X0)))) [nnf transformation 5]
47. ! [X0] : (((~strong(X0) & ~funny(X0)) | kind(X0)) & (~kind(X0) | strong(X0) | funny(X0))) [flattening 46]
48. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (kind(X0) | old(X0)))) [nnf transformation 6]
49. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | kind(X0) | old(X0))) [flattening 48]
79. ~generous(X0) | funny(X0) [cnf transformation 41]
86. ~funny(X0) | kind(X0) [cnf transformation 47]
91. ~generous(X0) | ~kind(X0) [cnf transformation 49]
92. ~kind(X0) | wise(X0) [cnf transformation 49]
96. generous(paul) | kind(X0) [cnf transformation 28]
130. ~wise(paul) [cnf transformation 24]
189. 14 <=> ! [X0] : kind(X0) [avatar definition]
190. kind(X0) <- (14) [avatar component clause 189]
192. 15 <=> generous(paul) [avatar definition]
194. generous(paul) <- (15) [avatar component clause 192]
195. 14 | 15 [avatar split clause 96,192,189]
305. wise(X0) <- (14) [resolution 92,190]
308. $false <- (14) [resolution 305,130]
313. ~14 [avatar contradiction clause 308]
316. ~kind(paul) <- (15) [resolution 194,91]
317. funny(paul) <- (15) [resolution 194,79]
322. kind(paul) <- (15) [resolution 317,86]
323. $false <- (15) [subsumption resolution 322,316]
324. ~15 [avatar contradiction clause 323]
325. $false [avatar sat refutation 195,313,324]
% SZS output end Proof for 3510547066630564429607360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not creative or curious then someone is strong or brave and vice versa. If someone is either quiet or not patient then mary is not happy and vice versa. If someone is not generous then someone is both not rich and old. If paul is not calm or not happy then someone is patient or not wise and vice versa. If someone is not wise then mary is quiet. Everyone who is curious or not old is not brave or generous. Everyone who is either not funny or not creative is both quiet and not rich. Everyone who is either not kind or not rich is both humble and strong. If someone is both brave and patient then someone is either tall or not funny and vice versa. If john is not creative or not patient then someone is not patient and vice versa. Everyone who is not rich or happy is both quiet and happy. Everyone who is either funny or curious is both humble and not rich. If paul is either not wise or not patient then someone is not creative or not tall. If someone is not rich then alice is not wise or not curious. If someone is not quiet then alice is curious or not old and vice versa. If someone is rich then mary is either creative or not patient and vice versa. Someone is old. Someone is not wise or not kind. Someone is not tall or not happy. Susan is both not old and not humble. John is quiet or funny. Mary is not happy or wise. Alice is curious or not rich. Mary is not rich. | John is patient. | contradiction | (((~creative(alice)|curious(alice)))<=>(?[X]:((strong(X)|brave(X)))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(~happy(mary)))&
((?[X]:(~generous(X)))=>(?[X]:((~rich(X)&old(X)))))&
(((~calm(paul)|~happy(paul)))<=>(?[X]:((patient(X)|~wise(X)))))&
((?[X]:(~wise(X)))=>(quiet(mary)))&
(![X]:((curious(X)|~old(X))=>(~brave(X)|generous(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(quiet(X)&~rich(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(humble(X)&strong(X))))&
((?[X]:((brave(X)&patient(X))))<=>(?[X]:((tall(X)<~>~funny(X)))))&
(((~creative(john)|~patient(john)))<=>(?[X]:(~patient(X))))&
(![X]:((~rich(X)|happy(X))=>(quiet(X)&happy(X))))&
(![X]:((funny(X)<~>curious(X))=>(humble(X)&~rich(X))))&
(((~wise(paul)<~>~patient(paul)))=>(?[X]:((~creative(X)|~tall(X)))))&
((?[X]:(~rich(X)))=>((~wise(alice)|~curious(alice))))&
((?[X]:(~quiet(X)))<=>((curious(alice)|~old(alice))))&
((?[X]:(rich(X)))<=>((creative(mary)<~>~patient(mary))))&
(?[X]:(old(X)))&
(?[X]:((~wise(X)|~kind(X))))&
(?[X]:((~tall(X)|~happy(X))))&
((~old(susan)&~humble(susan)))&
((quiet(john)|funny(john)))&
((~happy(mary)|wise(mary)))&
((curious(alice)|~rich(alice)))&
(~rich(mary)) | patient(john) | [
"p1",
"p6",
"p9",
"p10",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8836086904803395162774885
% SZS output start Proof for 8836086904803395162774885
2. ? [X0] : (quiet(X0) <~> ~patient(X0)) <=> ~happy(mary) [input p1]
7. ! [X0] : ((~funny(X0) <~> ~creative(X0)) => (~rich(X0) & quiet(X0))) [input p6]
10. (~patient(john) | ~creative(john)) <=> ? [X0] : ~patient(X0) [input p9]
11. ! [X0] : ((happy(X0) | ~rich(X0)) => (happy(X0) & quiet(X0))) [input p10]
21. funny(john) | quiet(john) [input p20]
24. ~rich(mary) [input p23]
25. patient(john) [input hypothesis]
31. ! [X0] : ((~rich(X0) & quiet(X0)) | (~funny(X0) <=> ~creative(X0))) [ennf transformation 7]
33. ! [X0] : ((happy(X0) & quiet(X0)) | (~happy(X0) & rich(X0))) [ennf transformation 11]
43. (? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | happy(mary)) & (~happy(mary) | ! [X0] : ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) [nnf transformation 2]
44. (? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | happy(mary)) & (~happy(mary) | ! [X1] : ((quiet(X1) | patient(X1)) & (~patient(X1) | ~quiet(X1)))) [rectify 43]
45. ? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) => ((patient(sK1) | ~quiet(sK1)) & (~patient(sK1) | quiet(sK1))) [choice axiom]
46. (((patient(sK1) | ~quiet(sK1)) & (~patient(sK1) | quiet(sK1))) | happy(mary)) & (~happy(mary) | ! [X1] : ((quiet(X1) | patient(X1)) & (~patient(X1) | ~quiet(X1)))) [skolemisation 44,45]
52. ! [X0] : ((~rich(X0) & quiet(X0)) | ((~funny(X0) | creative(X0)) & (~creative(X0) | funny(X0)))) [nnf transformation 31]
59. ((~patient(john) | ~creative(john)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | (patient(john) & creative(john))) [nnf transformation 10]
60. (~patient(john) | ~creative(john) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | (patient(john) & creative(john))) [flattening 59]
61. (~patient(john) | ~creative(john) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | (patient(john) & creative(john))) [rectify 60]
62. ? [X1] : ~patient(X1) => ~patient(sK5) [choice axiom]
63. (~patient(john) | ~creative(john) | ! [X0] : patient(X0)) & (~patient(sK5) | (patient(john) & creative(john))) [skolemisation 61,62]
87. ~happy(mary) | ~patient(X1) | ~quiet(X1) [cnf transformation 46]
97. ~funny(X0) | quiet(X0) | creative(X0) [cnf transformation 52]
112. ~patient(john) | ~creative(john) | patient(X0) [cnf transformation 63]
113. rich(X0) | quiet(X0) [cnf transformation 33]
115. rich(X0) | happy(X0) [cnf transformation 33]
136. funny(john) | quiet(john) [cnf transformation 21]
139. ~rich(mary) [cnf transformation 24]
140. patient(john) [cnf transformation 25]
168. 7 <=> happy(mary) [avatar definition]
186. 11 <=> ! [X1] : (~patient(X1) | ~quiet(X1)) [avatar definition]
187. ~patient(X1) | ~quiet(X1) <- (11) [avatar component clause 186]
188. 11 | ~7 [avatar split clause 87,168,186]
252. 26 <=> ! [X0] : patient(X0) [avatar definition]
253. patient(X0) <- (26) [avatar component clause 252]
255. 27 <=> creative(john) [avatar definition]
259. 28 <=> patient(john) [avatar definition]
260. patient(john) <- (28) [avatar component clause 259]
262. 26 | ~27 | ~28 [avatar split clause 112,259,255,252]
347. 47 <=> quiet(john) [avatar definition]
348. ~quiet(john) <- (~47) [avatar component clause 347]
351. 48 <=> funny(john) [avatar definition]
353. funny(john) <- (48) [avatar component clause 351]
354. 47 | 48 [avatar split clause 136,351,347]
365. 28 [avatar split clause 140,259]
370. quiet(mary) [resolution 113,139]
372. happy(mary) [resolution 115,139]
376. 7 [avatar split clause 372,168]
384. ~quiet(john) <- (11, 28) [resolution 187,260]
389. ~47 | ~11 | ~28 [avatar split clause 384,259,186,347]
401. quiet(john) | creative(john) <- (48) [resolution 97,353]
403. creative(john) <- (~47, 48) [subsumption resolution 401,348]
415. 27 | 47 | ~48 [avatar split clause 403,351,347,255]
419. ~quiet(X1) <- (11, 26) [resolution 253,187]
441. $false <- (11, 26) [subsumption resolution 370,419]
442. ~11 | ~26 [avatar contradiction clause 441]
443. $false [avatar sat refutation 188,262,354,365,376,389,415,442]
% SZS output end Proof for 8836086904803395162774885
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not funny or not brave then someone is both rich and not strong and vice versa.
Everyone who is not happy is both not wise and humble and vice versa.
If paul is not patient or brave then someone is quiet and vice versa.
Everyone who is calm or not humble is not happy or not curious and vice versa.
Everyone who is not old or not quiet is not brave and vice versa.
Everyone who is old is patient and vice versa.
Everyone who is not humble is brave and vice versa.
If someone is either not calm or happy then someone is not old or not wise.
Everyone who is not kind is not humble and vice versa.
If someone is both not brave and not old then someone is both not tall and not generous and vice versa.
Everyone who is both not curious and tall is not quiet or not patient and vice versa.
If someone is curious or not quiet then alice is both old and not calm.
Everyone who is both patient and not wise is either not old or curious and vice versa.
If john is not generous or tall then susan is not kind.
Everyone who is both tall and wise is either not quiet or not calm.
Everyone who is both calm and happy is either kind or humble and vice versa.
Someone is old or not wise.
Paul is either curious or not strong.
Someone is rich.
Alice is quiet or funny.
Mary is not strong. | Mary is not kind. | entailment | ((?[X]:((~funny(X)<~>~brave(X))))<=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:(~happy(X)<=>(~wise(X)&humble(X))))&
(((~patient(paul)|brave(paul)))<=>(?[X]:(quiet(X))))&
(![X]:((calm(X)|~humble(X))<=>(~happy(X)|~curious(X))))&
(![X]:((~old(X)|~quiet(X))<=>~brave(X)))&
(![X]:(old(X)<=>patient(X)))&
(![X]:(~humble(X)<=>brave(X)))&
((?[X]:((~calm(X)<~>happy(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:(~kind(X)<=>~humble(X)))&
((?[X]:((~brave(X)&~old(X))))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~curious(X)&tall(X))<=>(~quiet(X)|~patient(X))))&
((?[X]:((curious(X)|~quiet(X))))=>((old(alice)&~calm(alice))))&
(![X]:((patient(X)&~wise(X))<=>(~old(X)<~>curious(X))))&
(((~generous(john)|tall(john)))=>(~kind(susan)))&
(![X]:((tall(X)&wise(X))=>(~quiet(X)<~>~calm(X))))&
(![X]:((calm(X)&happy(X))<=>(kind(X)<~>humble(X))))&
(?[X]:((old(X)|~wise(X))))&
((curious(paul)<~>~strong(paul)))&
(?[X]:(rich(X)))&
((quiet(alice)|funny(alice)))&
(~strong(mary)) | ~kind(mary) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2701130164355224602822929
% SZS output start Proof for 2701130164355224602822929
2. ! [X0] : (~happy(X0) <=> (humble(X0) & ~wise(X0))) [input p1]
4. ! [X0] : ((~humble(X0) | calm(X0)) <=> (~curious(X0) | ~happy(X0))) [input p3]
5. ! [X0] : ((~quiet(X0) | ~old(X0)) <=> ~brave(X0)) [input p4]
6. ! [X0] : (old(X0) <=> patient(X0)) [input p5]
7. ! [X0] : (~humble(X0) <=> brave(X0)) [input p6]
9. ! [X0] : (~kind(X0) <=> ~humble(X0)) [input p8]
11. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~patient(X0) | ~quiet(X0))) [input p10]
13. ! [X0] : ((~wise(X0) & patient(X0)) <=> (~old(X0) <~> curious(X0))) [input p12]
16. ! [X0] : ((happy(X0) & calm(X0)) <=> (kind(X0) <~> humble(X0))) [input p15]
22. kind(mary) [input hypothesis]
36. ! [X0] : ((~happy(X0) | (~humble(X0) | wise(X0))) & ((humble(X0) & ~wise(X0)) | happy(X0))) [nnf transformation 2]
37. ! [X0] : ((~happy(X0) | ~humble(X0) | wise(X0)) & ((humble(X0) & ~wise(X0)) | happy(X0))) [flattening 36]
43. ! [X0] : (((~humble(X0) | calm(X0)) | (curious(X0) & happy(X0))) & ((~curious(X0) | ~happy(X0)) | (humble(X0) & ~calm(X0)))) [nnf transformation 4]
44. ! [X0] : ((~humble(X0) | calm(X0) | (curious(X0) & happy(X0))) & (~curious(X0) | ~happy(X0) | (humble(X0) & ~calm(X0)))) [flattening 43]
45. ! [X0] : (((~quiet(X0) | ~old(X0)) | brave(X0)) & (~brave(X0) | (quiet(X0) & old(X0)))) [nnf transformation 5]
46. ! [X0] : ((~quiet(X0) | ~old(X0) | brave(X0)) & (~brave(X0) | (quiet(X0) & old(X0)))) [flattening 45]
47. ! [X0] : ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0))) [nnf transformation 6]
48. ! [X0] : ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0))) [nnf transformation 7]
53. ! [X0] : ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0))) [nnf transformation 9]
59. ! [X0] : (((tall(X0) & ~curious(X0)) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 11]
60. ! [X0] : (((tall(X0) & ~curious(X0)) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~tall(X0) | curious(X0))) [flattening 59]
61. ! [X0] : (((~wise(X0) & patient(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (wise(X0) | ~patient(X0)))) [nnf transformation 13]
62. ! [X0] : (((~wise(X0) & patient(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | wise(X0) | ~patient(X0))) [flattening 61]
64. ! [X0] : (((happy(X0) & calm(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (~happy(X0) | ~calm(X0)))) [nnf transformation 16]
65. ! [X0] : (((happy(X0) & calm(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | ~happy(X0) | ~calm(X0))) [flattening 64]
77. ~wise(X0) | happy(X0) [cnf transformation 37]
78. humble(X0) | happy(X0) [cnf transformation 37]
84. ~curious(X0) | ~happy(X0) | humble(X0) [cnf transformation 44]
86. ~humble(X0) | calm(X0) | curious(X0) [cnf transformation 44]
89. ~old(X0) | ~quiet(X0) | brave(X0) [cnf transformation 46]
90. ~old(X0) | patient(X0) [cnf transformation 47]
91. ~patient(X0) | old(X0) [cnf transformation 47]
93. ~humble(X0) | ~brave(X0) [cnf transformation 48]
96. ~humble(X0) | kind(X0) [cnf transformation 53]
97. ~kind(X0) | humble(X0) [cnf transformation 53]
103. ~curious(X0) | quiet(X0) [cnf transformation 60]
104. ~curious(X0) | patient(X0) [cnf transformation 60]
111. curious(X0) | ~old(X0) | wise(X0) | ~patient(X0) [cnf transformation 62]
113. patient(X0) | curious(X0) | old(X0) [cnf transformation 62]
116. ~old(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 62]
121. humble(X0) | kind(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 65]
122. ~humble(X0) | ~kind(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 65]
133. kind(mary) [cnf transformation 22]
184. ~curious(X0) | humble(X0) [subsumption resolution 84,78]
186. 12 <=> ! [X1] : (~calm(X1) | ~happy(X1)) [avatar definition]
187. ~calm(X1) | ~happy(X1) <- (12) [avatar component clause 186]
212. 18 <=> ! [X3] : old(X3) [avatar definition]
213. old(X3) <- (18) [avatar component clause 212]
243. patient(X0) | curious(X0) [subsumption resolution 113,90]
244. patient(X0) [subsumption resolution 243,104]
245. ~old(X0) | curious(X0) | wise(X0) [subsumption resolution 111,244]
261. ~kind(X0) | ~happy(X0) | ~calm(X0) [subsumption resolution 122,97]
262. kind(X0) | ~happy(X0) | ~calm(X0) [subsumption resolution 121,96]
263. ~happy(X0) | ~calm(X0) [subsumption resolution 262,261]
264. 12 [avatar split clause 263,186]
298. old(X0) [resolution 91,244]
299. 18 [avatar split clause 298,212]
307. humble(mary) [resolution 97,133]
343. calm(mary) | curious(mary) [resolution 86,307]
347. ~quiet(X0) | brave(X0) <- (18) [resolution 89,213]
359. ~curious(X0) | ~wise(X0) <- (18) [resolution 116,213]
361. curious(X0) | wise(X0) <- (18) [resolution 245,213]
370. 36 <=> curious(mary) [avatar definition]
372. curious(mary) <- (36) [avatar component clause 370]
374. 37 <=> calm(mary) [avatar definition]
376. calm(mary) <- (37) [avatar component clause 374]
377. 36 | 37 [avatar split clause 343,374,370]
398. ~happy(mary) <- (12, 37) [resolution 376,187]
426. humble(X2) | wise(X2) <- (18) [resolution 361,184]
428. quiet(X4) | wise(X4) <- (18) [resolution 361,103]
447. ~brave(X3) | wise(X3) <- (18) [resolution 426,93]
450. wise(X0) | brave(X0) <- (18) [resolution 428,347]
451. wise(X0) <- (18) [subsumption resolution 450,447]
472. happy(X3) <- (18) [resolution 451,77]
525. $false <- (12, 18, 37) [subsumption resolution 398,472]
526. ~12 | ~18 | ~37 [avatar contradiction clause 525]
527. ~wise(mary) <- (18, 36) [resolution 372,359]
532. $false <- (18, 36) [subsumption resolution 527,451]
533. ~18 | ~36 [avatar contradiction clause 532]
534. $false [avatar sat refutation 264,299,377,526,533]
% SZS output end Proof for 2701130164355224602822929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or wise then mary is either not creative or strong.
If alice is creative then someone is not kind or old and vice versa.
Everyone who is either strong or not happy is not funny and vice versa.
Everyone who is generous is not curious and vice versa.
Everyone who is either not humble or not strong is not tall and vice versa.
Everyone who is not strong is both not kind and tall.
If susan is either not happy or wise then lucy is either not generous or creative.
If john is humble or patient then lucy is not humble.
Everyone who is humble or not kind is both brave and not happy.
Everyone who is both not patient and not kind is both humble and creative.
If someone is old then someone is either rich or not rich.
If someone is both kind and not generous then john is either strong or humble and vice versa.
If mary is generous then alice is not patient and vice versa.
Everyone who is calm or old is not patient or wise and vice versa.
If someone is rich then someone is either not old or not generous and vice versa.
Everyone who is both not happy and not generous is not tall.
Mary is not funny or tall.
Susan is either not humble or not curious.
Someone is either wise or not calm.
Someone is both wise and not curious.
Alice is patient.
Paul is either brave or quiet.
Susan is either not quiet or quiet.
Someone is not happy. | Mary is generous. | contradiction | ((?[X]:((strong(X)<~>wise(X))))=>((~creative(mary)<~>strong(mary))))&
((creative(alice))<=>(?[X]:((~kind(X)|old(X)))))&
(![X]:((strong(X)<~>~happy(X))<=>~funny(X)))&
(![X]:(generous(X)<=>~curious(X)))&
(![X]:((~humble(X)<~>~strong(X))<=>~tall(X)))&
(![X]:(~strong(X)=>(~kind(X)&tall(X))))&
(((~happy(susan)<~>wise(susan)))=>((~generous(lucy)<~>creative(lucy))))&
(((humble(john)|patient(john)))=>(~humble(lucy)))&
(![X]:((humble(X)|~kind(X))=>(brave(X)&~happy(X))))&
(![X]:((~patient(X)&~kind(X))=>(humble(X)&creative(X))))&
((?[X]:(old(X)))=>(?[X]:((rich(X)<~>~rich(X)))))&
((?[X]:((kind(X)&~generous(X))))<=>((strong(john)<~>humble(john))))&
((generous(mary))<=>(~patient(alice)))&
(![X]:((calm(X)|old(X))<=>(~patient(X)|wise(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((~happy(X)&~generous(X))=>~tall(X)))&
((~funny(mary)|tall(mary)))&
((~humble(susan)<~>~curious(susan)))&
(?[X]:((wise(X)<~>~calm(X))))&
(?[X]:((wise(X)&~curious(X))))&
(patient(alice))&
((brave(paul)<~>quiet(paul)))&
((~quiet(susan)<~>quiet(susan)))&
(?[X]:(~happy(X))) | generous(mary) | [
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6040682771643673592384683
% SZS output start Proof for 6040682771643673592384683
13. generous(mary) <=> ~patient(alice) [input p12]
21. patient(alice) [input p20]
25. generous(mary) [input hypothesis]
57. (generous(mary) | patient(alice)) & (~patient(alice) | ~generous(mary)) [nnf transformation 13]
112. ~patient(alice) | ~generous(mary) [cnf transformation 57]
130. patient(alice) [cnf transformation 21]
136. generous(mary) [cnf transformation 25]
232. 21 <=> patient(alice) [avatar definition]
236. 22 <=> generous(mary) [avatar definition]
240. ~22 | ~21 [avatar split clause 112,232,236]
295. 21 [avatar split clause 130,232]
306. 22 [avatar split clause 136,236]
307. $false [avatar sat refutation 240,295,306]
% SZS output end Proof for 6040682771643673592384683
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not wise is either not calm or not generous and vice versa. If mary is old or not calm then lucy is not funny. Everyone who is either funny or tall is either not wise or not kind and vice versa. Everyone who is either not kind or not brave is either creative or not old. Everyone who is both calm and not funny is both not quiet and not generous. If someone is not wise then john is not patient and vice versa. Everyone who is not wise is either patient or not rich and vice versa. Everyone who is quiet or happy is creative or not brave. If alice is quiet or old then someone is either curious or not generous. Everyone who is not tall is both creative and not tall and vice versa. Everyone who is generous or not curious is creative or not quiet and vice versa. Everyone who is either not funny or not humble is either not funny or calm and vice versa. If someone is not kind or not humble then paul is rich or not strong and vice versa. Everyone who is either not creative or not calm is not brave or not wise and vice versa. Everyone who is either not generous or strong is creative. If someone is either not patient or not old then mary is not brave or not wise. Someone is both not calm and not quiet. Someone is strong. Someone is not calm. Lucy is kind or not strong. Someone is either generous or tall. Someone is brave or not rich. Mary is kind or not happy. | Alice is kind. | neutral | (![X]:((~creative(X)<~>~wise(X))<=>(~calm(X)<~>~generous(X))))&
(((old(mary)|~calm(mary)))=>(~funny(lucy)))&
(![X]:((funny(X)<~>tall(X))<=>(~wise(X)<~>~kind(X))))&
(![X]:((~kind(X)<~>~brave(X))=>(creative(X)<~>~old(X))))&
(![X]:((calm(X)&~funny(X))=>(~quiet(X)&~generous(X))))&
((?[X]:(~wise(X)))<=>(~patient(john)))&
(![X]:(~wise(X)<=>(patient(X)<~>~rich(X))))&
(![X]:((quiet(X)|happy(X))=>(creative(X)|~brave(X))))&
(((quiet(alice)|old(alice)))=>(?[X]:((curious(X)<~>~generous(X)))))&
(![X]:(~tall(X)<=>(creative(X)&~tall(X))))&
(![X]:((generous(X)|~curious(X))<=>(creative(X)|~quiet(X))))&
(![X]:((~funny(X)<~>~humble(X))<=>(~funny(X)<~>calm(X))))&
((?[X]:((~kind(X)|~humble(X))))<=>((rich(paul)|~strong(paul))))&
(![X]:((~creative(X)<~>~calm(X))<=>(~brave(X)|~wise(X))))&
(![X]:((~generous(X)<~>strong(X))=>creative(X)))&
((?[X]:((~patient(X)<~>~old(X))))=>((~brave(mary)|~wise(mary))))&
(?[X]:((~calm(X)&~quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:(~calm(X)))&
((kind(lucy)|~strong(lucy)))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((brave(X)|~rich(X))))&
((kind(mary)|~happy(mary))) | kind(alice) | [] | null | 0 |
If someone is either humble or not creative then susan is both not kind and curious and vice versa.
If someone is not rich then someone is either not strong or not quiet and vice versa.
Everyone who is not generous is not old.
Everyone who is either happy or quiet is not creative or not kind and vice versa.
Everyone who is either happy or old is both funny and not old and vice versa.
Everyone who is both not creative and quiet is not strong or not happy and vice versa.
If fred is either rich or kind then someone is not patient or not funny and vice versa.
If someone is both not rich and not happy then lucy is not tall or not humble.
Everyone who is not brave is either not calm or brave.
If susan is creative then paul is not tall or patient and vice versa.
If someone is rich then someone is wise and vice versa.
Everyone who is quiet or not creative is not calm or tall and vice versa.
If fred is not kind or kind then someone is both not curious and not kind and vice versa.
Everyone who is not calm or patient is not generous.
If susan is old or not curious then mary is either not calm or happy and vice versa.
If fred is either not humble or patient then paul is kind.
Fred is both not happy and patient.
Susan is either patient or quiet.
Someone is both happy and not old.
Lucy is either not quiet or quiet.
Susan is generous or not rich.
Someone is either not wise or brave.
Someone is either rich or brave.
Alice is old or not rich. | Fred is old. | contradiction | ((?[X]:((humble(X)<~>~creative(X))))<=>((~kind(susan)&curious(susan))))&
((?[X]:(~rich(X)))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:(~generous(X)=>~old(X)))&
(![X]:((happy(X)<~>quiet(X))<=>(~creative(X)|~kind(X))))&
(![X]:((happy(X)<~>old(X))<=>(funny(X)&~old(X))))&
(![X]:((~creative(X)&quiet(X))<=>(~strong(X)|~happy(X))))&
(((rich(fred)<~>kind(fred)))<=>(?[X]:((~patient(X)|~funny(X)))))&
((?[X]:((~rich(X)&~happy(X))))=>((~tall(lucy)|~humble(lucy))))&
(![X]:(~brave(X)=>(~calm(X)<~>brave(X))))&
((creative(susan))<=>((~tall(paul)|patient(paul))))&
((?[X]:(rich(X)))<=>(?[X]:(wise(X))))&
(![X]:((quiet(X)|~creative(X))<=>(~calm(X)|tall(X))))&
(((~kind(fred)|kind(fred)))<=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:((~calm(X)|patient(X))=>~generous(X)))&
(((old(susan)|~curious(susan)))<=>((~calm(mary)<~>happy(mary))))&
(((~humble(fred)<~>patient(fred)))=>(kind(paul)))&
((~happy(fred)&patient(fred)))&
((patient(susan)<~>quiet(susan)))&
(?[X]:((happy(X)&~old(X))))&
((~quiet(lucy)<~>quiet(lucy)))&
((generous(susan)|~rich(susan)))&
(?[X]:((~wise(X)<~>brave(X))))&
(?[X]:((rich(X)<~>brave(X))))&
((old(alice)|~rich(alice))) | old(fred) | [
"p2",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9030761853996206800347744
% SZS output start Proof for 9030761853996206800347744
3. ! [X0] : (~generous(X0) => ~old(X0)) [input p2]
14. ! [X0] : ((patient(X0) | ~calm(X0)) => ~generous(X0)) [input p13]
17. patient(fred) & ~happy(fred) [input p16]
25. old(fred) [input hypothesis]
28. ! [X0] : (~old(X0) | generous(X0)) [ennf transformation 3]
32. ! [X0] : (~generous(X0) | (~patient(X0) & calm(X0))) [ennf transformation 14]
92. ~old(X0) | generous(X0) [cnf transformation 28]
134. ~patient(X0) | ~generous(X0) [cnf transformation 32]
144. patient(fred) [cnf transformation 17]
157. old(fred) [cnf transformation 25]
316. 34 <=> patient(fred) [avatar definition]
317. patient(fred) <- (34) [avatar component clause 316]
329. 34 [avatar split clause 144,316]
386. generous(fred) [resolution 92,157]
394. ~generous(fred) <- (34) [resolution 134,317]
396. $false <- (34) [subsumption resolution 394,386]
397. ~34 [avatar contradiction clause 396]
399. $false [avatar sat refutation 329,397]
% SZS output end Proof for 9030761853996206800347744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not happy is either not generous or brave. If someone is curious then someone is both brave and generous and vice versa. If paul is funny then someone is either not humble or calm. If someone is both rich and wise then john is old and vice versa. Everyone who is not old is not wise or not funny and vice versa. Everyone who is not wise or strong is brave. If someone is both not wise and rich then john is brave or not brave. If paul is quiet then someone is either curious or not rich and vice versa. If someone is either not generous or kind then paul is both rich and kind. Everyone who is rich or kind is not wise or rich. If someone is wise then someone is not happy or not humble. If paul is strong or not brave then someone is either not funny or wise and vice versa. If someone is not funny then lucy is old and vice versa. Everyone who is quiet or rich is both not rich and funny and vice versa. If someone is strong or curious then mary is not kind. Everyone who is not generous or patient is not quiet or rich and vice versa. John is both not old and quiet. Susan is both funny and not brave. Fred is either not funny or not old. Someone is either humble or brave. Someone is not strong. Mary is either wise or generous. Someone is both not strong and happy. | Mary is generous. | entailment | (![X]:((patient(X)&~happy(X))=>(~generous(X)<~>brave(X))))&
((?[X]:(curious(X)))<=>(?[X]:((brave(X)&generous(X)))))&
((funny(paul))=>(?[X]:((~humble(X)<~>calm(X)))))&
((?[X]:((rich(X)&wise(X))))<=>(old(john)))&
(![X]:(~old(X)<=>(~wise(X)|~funny(X))))&
(![X]:((~wise(X)|strong(X))=>brave(X)))&
((?[X]:((~wise(X)&rich(X))))=>((brave(john)|~brave(john))))&
((quiet(paul))<=>(?[X]:((curious(X)<~>~rich(X)))))&
((?[X]:((~generous(X)<~>kind(X))))=>((rich(paul)&kind(paul))))&
(![X]:((rich(X)|kind(X))=>(~wise(X)|rich(X))))&
((?[X]:(wise(X)))=>(?[X]:((~happy(X)|~humble(X)))))&
(((strong(paul)|~brave(paul)))<=>(?[X]:((~funny(X)<~>wise(X)))))&
((?[X]:(~funny(X)))<=>(old(lucy)))&
(![X]:((quiet(X)|rich(X))<=>(~rich(X)&funny(X))))&
((?[X]:((strong(X)|curious(X))))=>(~kind(mary)))&
(![X]:((~generous(X)|patient(X))<=>(~quiet(X)|rich(X))))&
((~old(john)&quiet(john)))&
((funny(susan)&~brave(susan)))&
((~funny(fred)<~>~old(fred)))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:(~strong(X)))&
((wise(mary)<~>generous(mary)))&
(?[X]:((~strong(X)&happy(X)))) | generous(mary) | [
"p8",
"p9",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4627895350148989088799326
% SZS output start Proof for 4627895350148989088799326
9. ? [X0] : (~generous(X0) <~> kind(X0)) => (kind(paul) & rich(paul)) [input p8]
10. ! [X0] : ((kind(X0) | rich(X0)) => (rich(X0) | ~wise(X0))) [input p9]
14. ! [X0] : ((rich(X0) | quiet(X0)) <=> (funny(X0) & ~rich(X0))) [input p13]
22. wise(mary) <~> generous(mary) [input p21]
24. ~generous(mary) [input hypothesis]
33. (kind(paul) & rich(paul)) | ! [X0] : (~generous(X0) <=> kind(X0)) [ennf transformation 9]
34. ! [X0] : ((rich(X0) | ~wise(X0)) | (~kind(X0) & ~rich(X0))) [ennf transformation 10]
35. ! [X0] : (rich(X0) | ~wise(X0) | (~kind(X0) & ~rich(X0))) [flattening 34]
57. (kind(paul) & rich(paul)) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))) [nnf transformation 33]
70. ! [X0] : (((rich(X0) | quiet(X0)) | (~funny(X0) | rich(X0))) & ((funny(X0) & ~rich(X0)) | (~rich(X0) & ~quiet(X0)))) [nnf transformation 14]
71. ! [X0] : ((rich(X0) | quiet(X0) | ~funny(X0) | rich(X0)) & ((funny(X0) & ~rich(X0)) | (~rich(X0) & ~quiet(X0)))) [flattening 70]
80. (~generous(mary) | ~wise(mary)) & (generous(mary) | wise(mary)) [nnf transformation 22]
103. rich(paul) | kind(X0) | generous(X0) [cnf transformation 57]
108. ~kind(X0) | ~wise(X0) | rich(X0) [cnf transformation 35]
119. ~rich(X0) | ~rich(X0) [cnf transformation 71]
138. generous(mary) | wise(mary) [cnf transformation 80]
142. ~generous(mary) [cnf transformation 24]
143. ~rich(X0) [duplicate literal removal 119]
229. 20 <=> ! [X0] : (kind(X0) | generous(X0)) [avatar definition]
230. kind(X0) | generous(X0) <- (20) [avatar component clause 229]
233. 21 <=> rich(paul) [avatar definition]
235. rich(paul) <- (21) [avatar component clause 233]
237. 20 | 21 [avatar split clause 103,233,229]
292. 34 <=> kind(mary) [avatar definition]
293. kind(mary) <- (34) [avatar component clause 292]
294. ~kind(mary) <- (~34) [avatar component clause 292]
316. 38 <=> wise(mary) [avatar definition]
317. wise(mary) <- (38) [avatar component clause 316]
320. 39 <=> generous(mary) [avatar definition]
322. ~generous(mary) <- (~39) [avatar component clause 320]
324. 38 | 39 [avatar split clause 138,320,316]
325. ~39 [avatar split clause 142,320]
337. generous(mary) <- (20, ~34) [resolution 230,294]
339. $false <- (20, ~34, ~39) [subsumption resolution 337,322]
340. ~20 | 34 | 39 [avatar contradiction clause 339]
341. $false <- (21) [subsumption resolution 235,143]
342. ~21 [avatar contradiction clause 341]
372. ~wise(mary) | rich(mary) <- (34) [resolution 108,293]
374. rich(mary) <- (34, 38) [subsumption resolution 372,317]
375. $false <- (34, 38) [subsumption resolution 374,143]
376. ~34 | ~38 [avatar contradiction clause 375]
377. $false [avatar sat refutation 237,324,325,340,342,376]
% SZS output end Proof for 4627895350148989088799326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not wise is either curious or not generous and vice versa.
Everyone who is either patient or not generous is not wise or old.
If someone is old then fred is not funny and vice versa.
If mary is either not wise or not kind then susan is not quiet or not calm and vice versa.
Everyone who is not generous or quiet is both patient and not tall and vice versa.
Everyone who is either not curious or not funny is kind and vice versa.
If someone is both not calm and patient then someone is not calm and vice versa.
If someone is not quiet then someone is either not generous or rich and vice versa.
If john is both brave and kind then paul is patient or not curious.
If someone is not tall or not strong then john is humble and vice versa.
Everyone who is either patient or creative is not calm or not generous and vice versa.
If someone is either not calm or not creative then someone is either not quiet or brave and vice versa.
If someone is quiet or not old then john is both not creative and not humble.
If alice is not patient then alice is tall or not wise and vice versa.
If someone is humble then john is not humble.
Everyone who is strong is both calm and not funny and vice versa.
Someone is both creative and old.
Lucy is wise.
Fred is strong or not quiet.
Someone is not humble. | John is quiet. | contradiction | (![X]:((tall(X)&~wise(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((patient(X)<~>~generous(X))=>(~wise(X)|old(X))))&
((?[X]:(old(X)))<=>(~funny(fred)))&
(((~wise(mary)<~>~kind(mary)))<=>((~quiet(susan)|~calm(susan))))&
(![X]:((~generous(X)|quiet(X))<=>(patient(X)&~tall(X))))&
(![X]:((~curious(X)<~>~funny(X))<=>kind(X)))&
((?[X]:((~calm(X)&patient(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(((brave(john)&kind(john)))=>((patient(paul)|~curious(paul))))&
((?[X]:((~tall(X)|~strong(X))))<=>(humble(john)))&
(![X]:((patient(X)<~>creative(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((quiet(X)|~old(X))))=>((~creative(john)&~humble(john))))&
((~patient(alice))<=>((tall(alice)|~wise(alice))))&
((?[X]:(humble(X)))=>(~humble(john)))&
(![X]:(strong(X)<=>(calm(X)&~funny(X))))&
(?[X]:((creative(X)&old(X))))&
(wise(lucy))&
((strong(fred)|~quiet(fred)))&
(?[X]:(~humble(X))) | quiet(john) | [
"p4",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5397322431898967481251296
% SZS output start Proof for 5397322431898967481251296
5. ! [X0] : ((quiet(X0) | ~generous(X0)) <=> (~tall(X0) & patient(X0))) [input p4]
10. ? [X0] : (~strong(X0) | ~tall(X0)) <=> humble(john) [input p9]
15. ? [X0] : humble(X0) => ~humble(john) [input p14]
21. quiet(john) [input hypothesis]
30. ~humble(john) | ! [X0] : ~humble(X0) [ennf transformation 15]
40. ! [X0] : (((quiet(X0) | ~generous(X0)) | (tall(X0) | ~patient(X0))) & ((~tall(X0) & patient(X0)) | (~quiet(X0) & generous(X0)))) [nnf transformation 5]
41. ! [X0] : ((quiet(X0) | ~generous(X0) | tall(X0) | ~patient(X0)) & ((~tall(X0) & patient(X0)) | (~quiet(X0) & generous(X0)))) [flattening 40]
53. (? [X0] : (~strong(X0) | ~tall(X0)) | ~humble(john)) & (humble(john) | ! [X0] : (strong(X0) & tall(X0))) [nnf transformation 10]
54. (? [X0] : (~strong(X0) | ~tall(X0)) | ~humble(john)) & (humble(john) | ! [X1] : (strong(X1) & tall(X1))) [rectify 53]
55. ? [X0] : (~strong(X0) | ~tall(X0)) => (~strong(sK5) | ~tall(sK5)) [choice axiom]
56. ((~strong(sK5) | ~tall(sK5)) | ~humble(john)) & (humble(john) | ! [X1] : (strong(X1) & tall(X1))) [skolemisation 54,55]
91. ~quiet(X0) | ~tall(X0) [cnf transformation 41]
105. humble(john) | tall(X1) [cnf transformation 56]
129. ~humble(john) | ~humble(X0) [cnf transformation 30]
138. quiet(john) [cnf transformation 21]
238. 23 <=> humble(john) [avatar definition]
239. humble(john) <- (23) [avatar component clause 238]
255. 27 <=> ! [X1] : tall(X1) [avatar definition]
256. tall(X1) <- (27) [avatar component clause 255]
257. 27 | 23 [avatar split clause 105,238,255]
326. 42 <=> ! [X0] : ~humble(X0) [avatar definition]
327. ~humble(X0) <- (42) [avatar component clause 326]
328. 42 | ~23 [avatar split clause 129,238,326]
354. ~tall(john) [resolution 91,138]
355. $false <- (27) [subsumption resolution 354,256]
356. ~27 [avatar contradiction clause 355]
357. $false <- (23, 42) [subsumption resolution 239,327]
358. ~23 | ~42 [avatar contradiction clause 357]
359. $false [avatar sat refutation 257,328,356,358]
% SZS output end Proof for 5397322431898967481251296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or brave is curious and vice versa.
If mary is not creative or not funny then someone is either not wise or not humble and vice versa.
Everyone who is rich or generous is either patient or not tall and vice versa.
Everyone who is both wise and patient is either happy or not calm and vice versa.
Everyone who is both not quiet and strong is either not tall or brave.
If someone is not curious or not patient then someone is brave.
If mary is not creative or brave then someone is not brave or not patient and vice versa.
If mary is not happy then susan is both not wise and quiet and vice versa.
Everyone who is not generous or not happy is patient or not patient and vice versa.
If someone is either not kind or not rich then someone is not funny and vice versa.
Everyone who is not patient is brave or wise and vice versa.
If someone is curious or brave then susan is either wise or funny and vice versa.
If someone is not brave or not tall then someone is both not brave and not creative and vice versa.
If someone is humble then john is both not generous and brave.
Everyone who is either funny or not funny is not calm.
Everyone who is old or kind is either calm or happy and vice versa.
Someone is wise or strong.
Lucy is quiet or curious.
Lucy is either old or not rich.
Someone is both not humble and creative.
Alice is either not strong or creative. | Lucy is not wise. | neutral | (![X]:((patient(X)<~>brave(X))<=>curious(X)))&
(((~creative(mary)|~funny(mary)))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((rich(X)|generous(X))<=>(patient(X)<~>~tall(X))))&
(![X]:((wise(X)&patient(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((~quiet(X)&strong(X))=>(~tall(X)<~>brave(X))))&
((?[X]:((~curious(X)|~patient(X))))=>(?[X]:(brave(X))))&
(((~creative(mary)|brave(mary)))<=>(?[X]:((~brave(X)|~patient(X)))))&
((~happy(mary))<=>((~wise(susan)&quiet(susan))))&
(![X]:((~generous(X)|~happy(X))<=>(patient(X)|~patient(X))))&
((?[X]:((~kind(X)<~>~rich(X))))<=>(?[X]:(~funny(X))))&
(![X]:(~patient(X)<=>(brave(X)|wise(X))))&
((?[X]:((curious(X)|brave(X))))<=>((wise(susan)<~>funny(susan))))&
((?[X]:((~brave(X)|~tall(X))))<=>(?[X]:((~brave(X)&~creative(X)))))&
((?[X]:(humble(X)))=>((~generous(john)&brave(john))))&
(![X]:((funny(X)<~>~funny(X))=>~calm(X)))&
(![X]:((old(X)|kind(X))<=>(calm(X)<~>happy(X))))&
(?[X]:((wise(X)|strong(X))))&
((quiet(lucy)|curious(lucy)))&
((old(lucy)<~>~rich(lucy)))&
(?[X]:((~humble(X)&creative(X))))&
((~strong(alice)<~>creative(alice))) | ~wise(lucy) | [] | null | 0 |
Everyone who is either not kind or not calm is creative or not kind and vice versa.
Everyone who is both funny and not calm is generous.
If someone is not strong then john is both not wise and not brave and vice versa.
Everyone who is quiet is both not strong and not brave.
Everyone who is kind or wise is both not brave and not calm.
If someone is not brave then someone is tall and vice versa.
Everyone who is both tall and patient is either not creative or not calm and vice versa.
If susan is both not happy and not calm then susan is both curious and not quiet.
Everyone who is both not patient and not kind is not creative and vice versa.
Everyone who is calm or not calm is either not creative or brave and vice versa.
Everyone who is both tall and not calm is not brave.
Everyone who is not quiet is both creative and strong.
If someone is both not funny and strong then mary is not quiet and vice versa.
Everyone who is both creative and not kind is either not rich or patient.
If someone is quiet or rich then susan is either calm or quiet and vice versa.
John is not quiet.
Someone is either humble or funny.
Susan is not old.
Lucy is not kind or kind.
Mary is both not kind and curious.
Fred is not rich or funny.
Someone is not quiet or calm. | John is not calm. | contradiction | (![X]:((~kind(X)<~>~calm(X))<=>(creative(X)|~kind(X))))&
(![X]:((funny(X)&~calm(X))=>generous(X)))&
((?[X]:(~strong(X)))<=>((~wise(john)&~brave(john))))&
(![X]:(quiet(X)=>(~strong(X)&~brave(X))))&
(![X]:((kind(X)|wise(X))=>(~brave(X)&~calm(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(tall(X))))&
(![X]:((tall(X)&patient(X))<=>(~creative(X)<~>~calm(X))))&
(((~happy(susan)&~calm(susan)))=>((curious(susan)&~quiet(susan))))&
(![X]:((~patient(X)&~kind(X))<=>~creative(X)))&
(![X]:((calm(X)|~calm(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((tall(X)&~calm(X))=>~brave(X)))&
(![X]:(~quiet(X)=>(creative(X)&strong(X))))&
((?[X]:((~funny(X)&strong(X))))<=>(~quiet(mary)))&
(![X]:((creative(X)&~kind(X))=>(~rich(X)<~>patient(X))))&
((?[X]:((quiet(X)|rich(X))))<=>((calm(susan)<~>quiet(susan))))&
(~quiet(john))&
(?[X]:((humble(X)<~>funny(X))))&
(~old(susan))&
((~kind(lucy)|kind(lucy)))&
((~kind(mary)&curious(mary)))&
((~rich(fred)|funny(fred)))&
(?[X]:((~quiet(X)|calm(X)))) | ~calm(john) | [
"p0",
"p6",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6446926811150666833645626
% SZS output start Proof for 6446926811150666833645626
1. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> (~kind(X0) | creative(X0))) [input p0]
7. ! [X0] : ((patient(X0) & tall(X0)) <=> (~creative(X0) <~> ~calm(X0))) [input p6]
9. ! [X0] : ((~kind(X0) & ~patient(X0)) <=> ~creative(X0)) [input p8]
10. ! [X0] : ((~calm(X0) | calm(X0)) <=> (~creative(X0) <~> brave(X0))) [input p9]
11. ! [X0] : ((~calm(X0) & tall(X0)) => ~brave(X0)) [input p10]
23. ~calm(john) [input hypothesis]
32. ! [X0] : (~brave(X0) | (calm(X0) | ~tall(X0))) [ennf transformation 11]
33. ! [X0] : (~brave(X0) | calm(X0) | ~tall(X0)) [flattening 32]
37. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | (kind(X0) & ~creative(X0))) & ((~kind(X0) | creative(X0)) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 1]
38. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | (kind(X0) & ~creative(X0))) & (~kind(X0) | creative(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [flattening 37]
49. ! [X0] : (((patient(X0) & tall(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (~patient(X0) | ~tall(X0)))) [nnf transformation 7]
50. ! [X0] : (((patient(X0) & tall(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ~patient(X0) | ~tall(X0))) [flattening 49]
51. ! [X0] : (((~kind(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | (kind(X0) | patient(X0)))) [nnf transformation 9]
52. ! [X0] : (((~kind(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | kind(X0) | patient(X0))) [flattening 51]
53. ! [X0] : (((~calm(X0) | calm(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (calm(X0) & ~calm(X0)))) [nnf transformation 10]
54. ! [X0] : ((~calm(X0) | calm(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (calm(X0) & ~calm(X0)))) [flattening 53]
70. ~kind(X0) | creative(X0) | ~kind(X0) | calm(X0) [cnf transformation 38]
74. calm(X0) | kind(X0) | kind(X0) [cnf transformation 38]
89. tall(X0) | ~creative(X0) | calm(X0) [cnf transformation 50]
90. patient(X0) | ~calm(X0) | creative(X0) [cnf transformation 50]
93. ~patient(X0) | creative(X0) [cnf transformation 52]
96. brave(X0) | ~creative(X0) | calm(X0) [cnf transformation 54]
101. ~brave(X0) | calm(X0) | ~tall(X0) [cnf transformation 33]
122. ~calm(john) [cnf transformation 23]
123. ~kind(X0) | creative(X0) | calm(X0) [duplicate literal removal 70]
124. calm(X0) | kind(X0) [duplicate literal removal 74]
125. creative(X0) | calm(X0) [subsumption resolution 123,124]
161. patient(X0) | creative(X0) [subsumption resolution 90,125]
162. tall(X0) | calm(X0) [subsumption resolution 89,125]
164. creative(X0) [subsumption resolution 93,161]
166. brave(X0) | calm(X0) [subsumption resolution 96,164]
170. calm(X0) | ~tall(X0) [subsumption resolution 101,166]
171. calm(X0) [subsumption resolution 170,162]
235. $false [subsumption resolution 122,171]
% SZS output end Proof for 6446926811150666833645626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and calm is both humble and patient and vice versa. If someone is not rich or brave then lucy is both old and wise. Everyone who is not humble is generous or tall. Everyone who is curious is both humble and rich and vice versa. If someone is both not patient and strong then john is strong and vice versa. If susan is calm or not kind then fred is both creative and not happy and vice versa. If fred is both not quiet and kind then someone is both wise and funny and vice versa. If someone is either not brave or not curious then someone is both rich and calm and vice versa. Everyone who is wise is both not humble and old and vice versa. If someone is generous then paul is not quiet or strong. If someone is kind or patient then lucy is either brave or not old. If someone is both not quiet and quiet then mary is creative and vice versa. If fred is not humble then fred is either creative or not strong. Everyone who is happy is either funny or kind. If someone is quiet then john is not brave and vice versa. Everyone who is not kind or strong is either kind or calm and vice versa. Someone is calm or not rich. Alice is calm or quiet. Lucy is happy. Fred is both patient and brave. Paul is not strong. Paul is brave or generous. Susan is not old or quiet. Mary is both not wise and not happy. | Mary is not tall. | neutral | (![X]:((~curious(X)&calm(X))<=>(humble(X)&patient(X))))&
((?[X]:((~rich(X)|brave(X))))=>((old(lucy)&wise(lucy))))&
(![X]:(~humble(X)=>(generous(X)|tall(X))))&
(![X]:(curious(X)<=>(humble(X)&rich(X))))&
((?[X]:((~patient(X)&strong(X))))<=>(strong(john)))&
(((calm(susan)|~kind(susan)))<=>((creative(fred)&~happy(fred))))&
(((~quiet(fred)&kind(fred)))<=>(?[X]:((wise(X)&funny(X)))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>(?[X]:((rich(X)&calm(X)))))&
(![X]:(wise(X)<=>(~humble(X)&old(X))))&
((?[X]:(generous(X)))=>((~quiet(paul)|strong(paul))))&
((?[X]:((kind(X)|patient(X))))=>((brave(lucy)<~>~old(lucy))))&
((?[X]:((~quiet(X)&quiet(X))))<=>(creative(mary)))&
((~humble(fred))=>((creative(fred)<~>~strong(fred))))&
(![X]:(happy(X)=>(funny(X)<~>kind(X))))&
((?[X]:(quiet(X)))<=>(~brave(john)))&
(![X]:((~kind(X)|strong(X))<=>(kind(X)<~>calm(X))))&
(?[X]:((calm(X)|~rich(X))))&
((calm(alice)|quiet(alice)))&
(happy(lucy))&
((patient(fred)&brave(fred)))&
(~strong(paul))&
((brave(paul)|generous(paul)))&
((~old(susan)|quiet(susan)))&
((~wise(mary)&~happy(mary))) | ~tall(mary) | [] | null | 0 |
Everyone who is both generous and strong is rich or old. Everyone who is both not brave and not funny is either quiet or curious. If someone is both humble and generous then someone is either strong or happy and vice versa. Everyone who is both not strong and not creative is wise and vice versa. If someone is not tall then someone is kind and vice versa. If someone is both not patient and not curious then someone is not wise. If mary is wise then alice is both not creative and not happy. Everyone who is both old and not old is wise and vice versa. Everyone who is happy is wise and vice versa. If someone is not happy or tall then fred is either not generous or funny and vice versa. Everyone who is creative or patient is either not old or curious and vice versa. If someone is old then lucy is not humble. Everyone who is not patient is not curious or not humble. If fred is not curious or creative then paul is both old and kind. If mary is either curious or not humble then john is happy or patient and vice versa. Everyone who is tall is both curious and not creative and vice versa. Someone is not rich. Someone is both not curious and not wise. John is either not strong or not quiet. John is either not humble or creative. John is either curious or not funny. Alice is not quiet or not brave. John is not quiet or wise. Someone is curious. | Paul is wise. | contradiction | (![X]:((generous(X)&strong(X))=>(rich(X)|old(X))))&
(![X]:((~brave(X)&~funny(X))=>(quiet(X)<~>curious(X))))&
((?[X]:((humble(X)&generous(X))))<=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:((~strong(X)&~creative(X))<=>wise(X)))&
((?[X]:(~tall(X)))<=>(?[X]:(kind(X))))&
((?[X]:((~patient(X)&~curious(X))))=>(?[X]:(~wise(X))))&
((wise(mary))=>((~creative(alice)&~happy(alice))))&
(![X]:((old(X)&~old(X))<=>wise(X)))&
(![X]:(happy(X)<=>wise(X)))&
((?[X]:((~happy(X)|tall(X))))<=>((~generous(fred)<~>funny(fred))))&
(![X]:((creative(X)|patient(X))<=>(~old(X)<~>curious(X))))&
((?[X]:(old(X)))=>(~humble(lucy)))&
(![X]:(~patient(X)=>(~curious(X)|~humble(X))))&
(((~curious(fred)|creative(fred)))=>((old(paul)&kind(paul))))&
(((curious(mary)<~>~humble(mary)))<=>((happy(john)|patient(john))))&
(![X]:(tall(X)<=>(curious(X)&~creative(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~curious(X)&~wise(X))))&
((~strong(john)<~>~quiet(john)))&
((~humble(john)<~>creative(john)))&
((curious(john)<~>~funny(john)))&
((~quiet(alice)|~brave(alice)))&
((~quiet(john)|wise(john)))&
(?[X]:(curious(X))) | wise(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6795288991226954898566483
% SZS output start Proof for 6795288991226954898566483
8. ! [X0] : ((~old(X0) & old(X0)) <=> wise(X0)) [input p7]
25. wise(paul) [input hypothesis]
55. ! [X0] : (((~old(X0) & old(X0)) | ~wise(X0)) & (wise(X0) | (old(X0) | ~old(X0)))) [nnf transformation 8]
56. ! [X0] : (((~old(X0) & old(X0)) | ~wise(X0)) & (wise(X0) | old(X0) | ~old(X0))) [flattening 55]
95. old(X0) | ~wise(X0) [cnf transformation 56]
96. ~old(X0) | ~wise(X0) [cnf transformation 56]
138. wise(paul) [cnf transformation 25]
208. ~wise(X0) [subsumption resolution 95,96]
314. $false [subsumption resolution 138,208]
% SZS output end Proof for 6795288991226954898566483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or calm is both not tall and not rich and vice versa.
Everyone who is either not old or not rich is calm or funny and vice versa.
Everyone who is either brave or humble is either patient or old and vice versa.
Everyone who is both creative and not tall is both not old and patient.
If someone is not generous then someone is both not generous and not rich and vice versa.
If someone is humble then alice is curious and vice versa.
If mary is not old then someone is humble and vice versa.
If someone is both funny and not generous then alice is either rich or funny.
Everyone who is not rich or curious is tall or not rich and vice versa.
Everyone who is either rich or old is not humble.
Everyone who is tall or not creative is quiet.
Everyone who is both generous and not patient is not calm or funny.
Everyone who is either humble or strong is both creative and funny.
Everyone who is not humble or not funny is both strong and not funny and vice versa.
Everyone who is old is not strong or tall and vice versa.
If someone is either old or curious then someone is kind or not rich and vice versa.
Someone is not wise.
Lucy is not tall or not strong.
Someone is either not kind or not generous.
Fred is both not rich and not brave.
Someone is both patient and not rich.
Someone is either generous or not funny. | Fred is not strong. | contradiction | (![X]:((strong(X)|calm(X))<=>(~tall(X)&~rich(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(calm(X)|funny(X))))&
(![X]:((brave(X)<~>humble(X))<=>(patient(X)<~>old(X))))&
(![X]:((creative(X)&~tall(X))=>(~old(X)&patient(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)&~rich(X)))))&
((?[X]:(humble(X)))<=>(curious(alice)))&
((~old(mary))<=>(?[X]:(humble(X))))&
((?[X]:((funny(X)&~generous(X))))=>((rich(alice)<~>funny(alice))))&
(![X]:((~rich(X)|curious(X))<=>(tall(X)|~rich(X))))&
(![X]:((rich(X)<~>old(X))=>~humble(X)))&
(![X]:((tall(X)|~creative(X))=>quiet(X)))&
(![X]:((generous(X)&~patient(X))=>(~calm(X)|funny(X))))&
(![X]:((humble(X)<~>strong(X))=>(creative(X)&funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(strong(X)&~funny(X))))&
(![X]:(old(X)<=>(~strong(X)|tall(X))))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:((kind(X)|~rich(X)))))&
(?[X]:(~wise(X)))&
((~tall(lucy)|~strong(lucy)))&
(?[X]:((~kind(X)<~>~generous(X))))&
((~rich(fred)&~brave(fred)))&
(?[X]:((patient(X)&~rich(X))))&
(?[X]:((generous(X)<~>~funny(X)))) | ~strong(fred) | [
"p0",
"p1",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9146532319258096960476376
% SZS output start Proof for 9146532319258096960476376
1. ! [X0] : ((calm(X0) | strong(X0)) <=> (~rich(X0) & ~tall(X0))) [input p0]
2. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (funny(X0) | calm(X0))) [input p1]
10. ! [X0] : ((rich(X0) <~> old(X0)) => ~humble(X0)) [input p9]
14. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (~funny(X0) & strong(X0))) [input p13]
15. ! [X0] : (old(X0) <=> (tall(X0) | ~strong(X0))) [input p14]
23. ~strong(fred) [input hypothesis]
31. ! [X0] : (~humble(X0) | (rich(X0) <=> old(X0))) [ennf transformation 10]
35. ! [X0] : (((calm(X0) | strong(X0)) | (rich(X0) | tall(X0))) & ((~rich(X0) & ~tall(X0)) | (~calm(X0) & ~strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((calm(X0) | strong(X0) | rich(X0) | tall(X0)) & ((~rich(X0) & ~tall(X0)) | (~calm(X0) & ~strong(X0)))) [flattening 35]
37. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 2]
38. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 37]
56. ! [X0] : (~humble(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) [nnf transformation 31]
58. ! [X0] : (((~funny(X0) | ~humble(X0)) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 14]
59. ! [X0] : ((~funny(X0) | ~humble(X0) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [flattening 58]
60. ! [X0] : ((old(X0) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ~old(X0))) [nnf transformation 15]
61. ! [X0] : ((old(X0) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ~old(X0))) [flattening 60]
77. ~rich(X0) | ~strong(X0) [cnf transformation 36]
83. ~funny(X0) | ~old(X0) | ~rich(X0) [cnf transformation 38]
110. ~humble(X0) | rich(X0) | ~old(X0) [cnf transformation 56]
116. humble(X0) | strong(X0) [cnf transformation 59]
117. funny(X0) | strong(X0) [cnf transformation 59]
122. old(X0) | strong(X0) [cnf transformation 61]
139. ~strong(fred) [cnf transformation 23]
263. ~old(X0) | ~rich(X0) | strong(X0) [resolution 83,117]
264. ~rich(X0) | strong(X0) [subsumption resolution 263,122]
265. ~rich(X0) [subsumption resolution 264,77]
275. rich(X0) | ~old(X0) | strong(X0) [resolution 110,116]
278. ~old(X0) | strong(X0) [subsumption resolution 275,265]
279. strong(X0) [subsumption resolution 278,122]
286. $false [resolution 279,139]
% SZS output end Proof for 9146532319258096960476376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not humble is not old or not humble.
If susan is both curious and not strong then someone is humble.
Everyone who is both wise and happy is not rich or not quiet and vice versa.
If someone is old then someone is both not tall and humble.
If lucy is either old or not brave then someone is either not strong or not calm and vice versa.
Everyone who is humble is funny and vice versa.
If someone is curious then someone is either not happy or humble.
Everyone who is not wise or not tall is both not wise and humble and vice versa.
Everyone who is both tall and not strong is both calm and not creative.
Everyone who is both brave and not tall is both funny and not rich and vice versa.
Everyone who is both not wise and calm is kind or tall.
If mary is either creative or not humble then someone is kind or calm and vice versa.
Everyone who is both not creative and tall is either not rich or not creative.
Everyone who is creative or not rich is not old or creative and vice versa.
If someone is not calm or not quiet then john is not calm or not happy and vice versa.
Everyone who is quiet is not happy.
Alice is both not brave and not funny.
Mary is not rich.
Someone is not creative.
Susan is either not old or wise.
Someone is not humble or rich.
Fred is quiet.
Someone is either not funny or happy.
Lucy is both not curious and not strong. | John is kind. | contradiction | (![X]:((~funny(X)<~>~humble(X))=>(~old(X)|~humble(X))))&
(((curious(susan)&~strong(susan)))=>(?[X]:(humble(X))))&
(![X]:((wise(X)&happy(X))<=>(~rich(X)|~quiet(X))))&
((?[X]:(old(X)))=>(?[X]:((~tall(X)&humble(X)))))&
(((old(lucy)<~>~brave(lucy)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:(humble(X)<=>funny(X)))&
((?[X]:(curious(X)))=>(?[X]:((~happy(X)<~>humble(X)))))&
(![X]:((~wise(X)|~tall(X))<=>(~wise(X)&humble(X))))&
(![X]:((tall(X)&~strong(X))=>(calm(X)&~creative(X))))&
(![X]:((brave(X)&~tall(X))<=>(funny(X)&~rich(X))))&
(![X]:((~wise(X)&calm(X))=>(kind(X)|tall(X))))&
(((creative(mary)<~>~humble(mary)))<=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((~creative(X)&tall(X))=>(~rich(X)<~>~creative(X))))&
(![X]:((creative(X)|~rich(X))<=>(~old(X)|creative(X))))&
((?[X]:((~calm(X)|~quiet(X))))<=>((~calm(john)|~happy(john))))&
(![X]:(quiet(X)=>~happy(X)))&
((~brave(alice)&~funny(alice)))&
(~rich(mary))&
(?[X]:(~creative(X)))&
((~old(susan)<~>wise(susan)))&
(?[X]:((~humble(X)|rich(X))))&
(quiet(fred))&
(?[X]:((~funny(X)<~>happy(X))))&
((~curious(lucy)&~strong(lucy))) | kind(john) | [
"p2",
"p5",
"p7",
"p9",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4242859504742209944400226
% SZS output start Proof for 4242859504742209944400226
3. ! [X0] : ((happy(X0) & wise(X0)) <=> (~quiet(X0) | ~rich(X0))) [input p2]
6. ! [X0] : (humble(X0) <=> funny(X0)) [input p5]
8. ! [X0] : ((~tall(X0) | ~wise(X0)) <=> (humble(X0) & ~wise(X0))) [input p7]
10. ! [X0] : ((~tall(X0) & brave(X0)) <=> (~rich(X0) & funny(X0))) [input p9]
12. (creative(mary) <~> ~humble(mary)) <=> ? [X0] : (calm(X0) | kind(X0)) [input p11]
13. ! [X0] : ((tall(X0) & ~creative(X0)) => (~rich(X0) <~> ~creative(X0))) [input p12]
18. ~rich(mary) [input p17]
25. kind(john) [input hypothesis]
38. ! [X0] : ((~rich(X0) <~> ~creative(X0)) | (~tall(X0) | creative(X0))) [ennf transformation 13]
39. ! [X0] : ((~rich(X0) <~> ~creative(X0)) | ~tall(X0) | creative(X0)) [flattening 38]
42. ! [X0] : (((happy(X0) & wise(X0)) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | (~happy(X0) | ~wise(X0)))) [nnf transformation 3]
43. ! [X0] : (((happy(X0) & wise(X0)) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | ~happy(X0) | ~wise(X0))) [flattening 42]
51. ! [X0] : ((humble(X0) | ~funny(X0)) & (funny(X0) | ~humble(X0))) [nnf transformation 6]
52. ! [X0] : (((~tall(X0) | ~wise(X0)) | (~humble(X0) | wise(X0))) & ((humble(X0) & ~wise(X0)) | (tall(X0) & wise(X0)))) [nnf transformation 8]
53. ! [X0] : ((~tall(X0) | ~wise(X0) | ~humble(X0) | wise(X0)) & ((humble(X0) & ~wise(X0)) | (tall(X0) & wise(X0)))) [flattening 52]
54. ! [X0] : (((~tall(X0) & brave(X0)) | (rich(X0) | ~funny(X0))) & ((~rich(X0) & funny(X0)) | (tall(X0) | ~brave(X0)))) [nnf transformation 10]
55. ! [X0] : (((~tall(X0) & brave(X0)) | rich(X0) | ~funny(X0)) & ((~rich(X0) & funny(X0)) | tall(X0) | ~brave(X0))) [flattening 54]
56. (((humble(mary) | ~creative(mary)) & (~humble(mary) | creative(mary))) | ! [X0] : (~calm(X0) & ~kind(X0))) & (? [X0] : (calm(X0) | kind(X0)) | ((creative(mary) | humble(mary)) & (~humble(mary) | ~creative(mary)))) [nnf transformation 12]
57. (((humble(mary) | ~creative(mary)) & (~humble(mary) | creative(mary))) | ! [X0] : (~calm(X0) & ~kind(X0))) & (? [X1] : (calm(X1) | kind(X1)) | ((creative(mary) | humble(mary)) & (~humble(mary) | ~creative(mary)))) [rectify 56]
58. ? [X1] : (calm(X1) | kind(X1)) => (calm(sK2) | kind(sK2)) [choice axiom]
59. (((humble(mary) | ~creative(mary)) & (~humble(mary) | creative(mary))) | ! [X0] : (~calm(X0) & ~kind(X0))) & ((calm(sK2) | kind(sK2)) | ((creative(mary) | humble(mary)) & (~humble(mary) | ~creative(mary)))) [skolemisation 57,58]
60. ! [X0] : (((creative(X0) | rich(X0)) & (~creative(X0) | ~rich(X0))) | ~tall(X0) | creative(X0)) [nnf transformation 39]
79. rich(X0) | wise(X0) [cnf transformation 43]
93. ~humble(X0) | funny(X0) [cnf transformation 51]
96. ~wise(X0) | tall(X0) [cnf transformation 53]
105. ~tall(X0) | rich(X0) | ~funny(X0) [cnf transformation 55]
111. humble(mary) | ~creative(mary) | ~kind(X0) [cnf transformation 59]
114. creative(X0) | rich(X0) | ~tall(X0) | creative(X0) [cnf transformation 60]
126. ~rich(mary) [cnf transformation 18]
135. kind(john) [cnf transformation 25]
136. ~tall(X0) | rich(X0) | creative(X0) [duplicate literal removal 114]
186. 11 <=> creative(mary) [avatar definition]
190. 12 <=> humble(mary) [avatar definition]
192. humble(mary) <- (12) [avatar component clause 190]
195. 13 <=> ! [X0] : ~kind(X0) [avatar definition]
196. ~kind(X0) <- (13) [avatar component clause 195]
197. 13 | ~11 | 12 [avatar split clause 111,190,186,195]
266. $false <- (13) [resolution 196,135]
267. ~13 [avatar contradiction clause 266]
270. wise(mary) [resolution 79,126]
274. tall(mary) [resolution 96,270]
333. rich(mary) | ~funny(mary) [resolution 105,274]
335. ~funny(mary) [subsumption resolution 333,126]
345. rich(mary) | creative(mary) [resolution 136,274]
347. creative(mary) [subsumption resolution 345,126]
350. 11 [avatar split clause 347,186]
352. funny(mary) <- (12) [resolution 192,93]
353. $false <- (12) [subsumption resolution 352,335]
354. ~12 [avatar contradiction clause 353]
355. $false [avatar sat refutation 197,267,350,354]
% SZS output end Proof for 4242859504742209944400226
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or curious is kind.
Everyone who is not humble or curious is generous.
Everyone who is not quiet is not strong and vice versa.
Everyone who is not happy is both not kind and not calm and vice versa.
If john is not curious or not humble then someone is both calm and not quiet.
Everyone who is not calm or funny is not funny and vice versa.
If paul is not creative or funny then someone is not calm or not happy.
Everyone who is not calm or old is either not patient or tall.
Everyone who is patient or not tall is patient or funny.
If someone is either curious or not funny then susan is either not quiet or not old and vice versa.
If someone is strong then someone is not funny and vice versa.
If someone is either not happy or creative then susan is not wise or generous and vice versa.
If someone is both tall and not curious then someone is not tall and vice versa.
Everyone who is either creative or not tall is humble or not creative.
If paul is not generous then someone is not old.
Everyone who is both creative and not quiet is either not old or creative and vice versa.
Paul is strong.
Mary is either strong or not quiet.
Susan is calm or not brave.
Mary is either calm or not quiet.
Lucy is either wise or creative. | Susan is generous. | entailment | (![X]:((~wise(X)|curious(X))=>kind(X)))&
(![X]:((~humble(X)|curious(X))=>generous(X)))&
(![X]:(~quiet(X)<=>~strong(X)))&
(![X]:(~happy(X)<=>(~kind(X)&~calm(X))))&
(((~curious(john)|~humble(john)))=>(?[X]:((calm(X)&~quiet(X)))))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(((~creative(paul)|funny(paul)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~calm(X)|old(X))=>(~patient(X)<~>tall(X))))&
(![X]:((patient(X)|~tall(X))=>(patient(X)|funny(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>((~quiet(susan)<~>~old(susan))))&
((?[X]:(strong(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~happy(X)<~>creative(X))))<=>((~wise(susan)|generous(susan))))&
((?[X]:((tall(X)&~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>~tall(X))=>(humble(X)|~creative(X))))&
((~generous(paul))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)<~>creative(X))))&
(strong(paul))&
((strong(mary)<~>~quiet(mary)))&
((calm(susan)|~brave(susan)))&
((calm(mary)<~>~quiet(mary)))&
((wise(lucy)<~>creative(lucy))) | generous(susan) | [
"p1",
"p5",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4291675761470321854512254
% SZS output start Proof for 4291675761470321854512254
2. ! [X0] : ((curious(X0) | ~humble(X0)) => generous(X0)) [input p1]
6. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p5]
8. ! [X0] : ((old(X0) | ~calm(X0)) => (~patient(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((~tall(X0) | patient(X0)) => (funny(X0) | patient(X0))) [input p8]
13. ? [X0] : (~curious(X0) & tall(X0)) <=> ? [X0] : ~tall(X0) [input p12]
22. ~generous(susan) [input hypothesis]
24. ? [X0] : (~curious(X0) & tall(X0)) <=> ? [X1] : ~tall(X1) [rectify 13]
26. ! [X0] : (curious(X0) => generous(X0)) [pure predicate removal 2]
30. ! [X0] : (generous(X0) | ~curious(X0)) [ennf transformation 26]
33. ! [X0] : ((~patient(X0) <~> tall(X0)) | (~old(X0) & calm(X0))) [ennf transformation 8]
34. ! [X0] : ((funny(X0) | patient(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 9]
35. ! [X0] : (funny(X0) | patient(X0) | (tall(X0) & ~patient(X0))) [flattening 34]
42. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 6]
43. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 42]
46. ! [X0] : (((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | (~old(X0) & calm(X0))) [nnf transformation 33]
61. (? [X0] : (~curious(X0) & tall(X0)) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : (curious(X0) | ~tall(X0))) [nnf transformation 24]
62. (? [X0] : (~curious(X0) & tall(X0)) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : (curious(X3) | ~tall(X3))) [rectify 61]
63. ? [X0] : (~curious(X0) & tall(X0)) => (~curious(sK6) & tall(sK6)) [choice axiom]
64. ? [X2] : ~tall(X2) => ~tall(sK7) [choice axiom]
65. ((~curious(sK6) & tall(sK6)) | ! [X1] : tall(X1)) & (~tall(sK7) | ! [X3] : (curious(X3) | ~tall(X3))) [skolemisation 62,64,63]
75. ~curious(X0) | generous(X0) [cnf transformation 30]
84. ~funny(X0) | ~funny(X0) [cnf transformation 43]
85. funny(X0) | ~calm(X0) | funny(X0) [cnf transformation 43]
88. ~patient(X0) | tall(X0) | calm(X0) [cnf transformation 46]
93. funny(X0) | patient(X0) | tall(X0) [cnf transformation 35]
110. ~tall(sK7) | curious(X3) | ~tall(X3) [cnf transformation 65]
111. tall(sK6) | tall(X1) [cnf transformation 65]
112. ~curious(sK6) | tall(X1) [cnf transformation 65]
127. ~generous(susan) [cnf transformation 22]
130. ~funny(X0) [duplicate literal removal 84]
131. ~calm(X0) | funny(X0) [duplicate literal removal 85]
156. tall(X0) | patient(X0) [subsumption resolution 93,130]
175. 9 <=> ! [X1] : curious(X1) [avatar definition]
176. curious(X1) <- (9) [avatar component clause 175]
182. 10 <=> generous(susan) [avatar definition]
184. ~generous(susan) <- (~10) [avatar component clause 182]
210. 16 <=> ! [X1] : tall(X1) [avatar definition]
211. tall(X1) <- (16) [avatar component clause 210]
213. 17 <=> curious(sK6) [avatar definition]
216. 16 | ~17 [avatar split clause 112,213,210]
218. 18 <=> tall(sK6) [avatar definition]
220. tall(sK6) <- (18) [avatar component clause 218]
221. 16 | 18 [avatar split clause 111,218,210]
223. 19 <=> ! [X3] : (curious(X3) | ~tall(X3)) [avatar definition]
224. ~tall(X3) | curious(X3) <- (19) [avatar component clause 223]
226. 20 <=> tall(sK7) [avatar definition]
228. ~tall(sK7) <- (~20) [avatar component clause 226]
229. 19 | ~20 [avatar split clause 110,226,223]
260. ~10 [avatar split clause 127,182]
302. curious(X0) <- (16, 19) [resolution 224,211]
305. 9 | ~16 | ~19 [avatar split clause 302,223,210,175]
313. patient(sK7) <- (~20) [resolution 228,156]
330. tall(sK7) | calm(sK7) <- (~20) [resolution 313,88]
332. calm(sK7) <- (~20) [subsumption resolution 330,228]
341. funny(sK7) <- (~20) [resolution 332,131]
343. $false <- (~20) [subsumption resolution 341,130]
344. 20 [avatar contradiction clause 343]
348. curious(sK6) <- (18, 19) [resolution 224,220]
352. 17 | ~18 | ~19 [avatar split clause 348,223,218,213]
361. generous(X0) <- (9) [resolution 176,75]
371. $false <- (9, ~10) [resolution 361,184]
372. ~9 | 10 [avatar contradiction clause 371]
373. $false [avatar sat refutation 216,221,229,260,305,344,352,372]
% SZS output end Proof for 4291675761470321854512254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is happy or not wise and vice versa.
Everyone who is not old is both not quiet and creative and vice versa.
If someone is either kind or not happy then lucy is both not rich and old and vice versa.
Everyone who is rich or not kind is both not happy and not creative and vice versa.
If someone is curious or generous then susan is either patient or old.
Everyone who is humble or not old is not humble or happy.
If paul is not rich then paul is either not patient or not kind.
Everyone who is calm or not happy is humble or wise.
If someone is strong or wise then someone is either not calm or calm and vice versa.
Everyone who is not old or rich is patient.
Everyone who is either patient or not patient is both not brave and not wise and vice versa.
Everyone who is kind or not creative is both happy and not calm.
If lucy is both not quiet and wise then someone is not wise.
If lucy is either not calm or not humble then paul is both generous and not wise.
Alice is either calm or patient.
Paul is both not calm and old.
Someone is either funny or not generous.
Someone is not quiet.
Mary is not patient or rich. | Paul is wise. | contradiction | (![X]:(generous(X)<=>(happy(X)|~wise(X))))&
(![X]:(~old(X)<=>(~quiet(X)&creative(X))))&
((?[X]:((kind(X)<~>~happy(X))))<=>((~rich(lucy)&old(lucy))))&
(![X]:((rich(X)|~kind(X))<=>(~happy(X)&~creative(X))))&
((?[X]:((curious(X)|generous(X))))=>((patient(susan)<~>old(susan))))&
(![X]:((humble(X)|~old(X))=>(~humble(X)|happy(X))))&
((~rich(paul))=>((~patient(paul)<~>~kind(paul))))&
(![X]:((calm(X)|~happy(X))=>(humble(X)|wise(X))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((~old(X)|rich(X))=>patient(X)))&
(![X]:((patient(X)<~>~patient(X))<=>(~brave(X)&~wise(X))))&
(![X]:((kind(X)|~creative(X))=>(happy(X)&~calm(X))))&
(((~quiet(lucy)&wise(lucy)))=>(?[X]:(~wise(X))))&
(((~calm(lucy)<~>~humble(lucy)))=>((generous(paul)&~wise(paul))))&
((calm(alice)<~>patient(alice)))&
((~calm(paul)&old(paul)))&
(?[X]:((funny(X)<~>~generous(X))))&
(?[X]:(~quiet(X)))&
((~patient(mary)|rich(mary))) | wise(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5975308437387409005705019
% SZS output start Proof for 5975308437387409005705019
11. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> (~wise(X0) & ~brave(X0))) [input p10]
20. wise(paul) [input hypothesis]
52. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (wise(X0) | brave(X0))) & ((~wise(X0) & ~brave(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 11]
53. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | wise(X0) | brave(X0)) & ((~wise(X0) & ~brave(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [flattening 52]
98. ~wise(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 53]
99. ~wise(X0) | patient(X0) | patient(X0) [cnf transformation 53]
119. wise(paul) [cnf transformation 20]
122. ~wise(X0) | ~patient(X0) [duplicate literal removal 98]
123. ~wise(X0) | patient(X0) [duplicate literal removal 99]
199. ~wise(X0) [subsumption resolution 122,123]
244. $false [subsumption resolution 119,199]
% SZS output end Proof for 5975308437387409005705019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not kind and quiet then someone is quiet or not tall.
Everyone who is not kind or happy is both creative and rich.
Everyone who is both not humble and not curious is not rich and vice versa.
If someone is both not funny and not rich then someone is either not generous or not old.
If someone is not generous or happy then someone is not creative and vice versa.
Everyone who is rich is both old and happy.
Everyone who is both not kind and kind is either old or tall and vice versa.
Everyone who is both not old and not generous is either generous or old.
Everyone who is either patient or old is either happy or not curious and vice versa.
Everyone who is not kind is both not strong and calm.
Everyone who is not old or generous is not wise or not old and vice versa.
Everyone who is either not happy or brave is either not calm or rich and vice versa.
Everyone who is generous or rich is either old or rich.
If someone is either funny or humble then someone is creative.
If someone is either not quiet or not kind then someone is either humble or not humble.
If someone is not curious or funny then someone is calm.
Someone is either tall or calm.
John is either kind or generous.
Lucy is not strong or not happy.
Someone is not creative or not brave.
Someone is either not creative or not curious.
Mary is not funny or strong.
Someone is either not patient or brave. | Mary is not curious. | entailment | (((~kind(mary)&quiet(mary)))=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((~kind(X)|happy(X))=>(creative(X)&rich(X))))&
(![X]:((~humble(X)&~curious(X))<=>~rich(X)))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((~generous(X)<~>~old(X)))))&
((?[X]:((~generous(X)|happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:(rich(X)=>(old(X)&happy(X))))&
(![X]:((~kind(X)&kind(X))<=>(old(X)<~>tall(X))))&
(![X]:((~old(X)&~generous(X))=>(generous(X)<~>old(X))))&
(![X]:((patient(X)<~>old(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(~kind(X)=>(~strong(X)&calm(X))))&
(![X]:((~old(X)|generous(X))<=>(~wise(X)|~old(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((generous(X)|rich(X))=>(old(X)<~>rich(X))))&
((?[X]:((funny(X)<~>humble(X))))=>(?[X]:(creative(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
((?[X]:((~curious(X)|funny(X))))=>(?[X]:(calm(X))))&
(?[X]:((tall(X)<~>calm(X))))&
((kind(john)<~>generous(john)))&
((~strong(lucy)|~happy(lucy)))&
(?[X]:((~creative(X)|~brave(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
((~funny(mary)|strong(mary)))&
(?[X]:((~patient(X)<~>brave(X)))) | ~curious(mary) | [
"p2",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2112301359269453156609860
% SZS output start Proof for 2112301359269453156609860
3. ! [X0] : ((~curious(X0) & ~humble(X0)) <=> ~rich(X0)) [input p2]
6. ! [X0] : (rich(X0) => (happy(X0) & old(X0))) [input p5]
13. ! [X0] : ((rich(X0) | generous(X0)) => (old(X0) <~> rich(X0))) [input p12]
24. curious(mary) [input hypothesis]
34. ! [X0] : ((happy(X0) & old(X0)) | ~rich(X0)) [ennf transformation 6]
38. ! [X0] : ((old(X0) <~> rich(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 13]
44. ! [X0] : (((~curious(X0) & ~humble(X0)) | rich(X0)) & (~rich(X0) | (curious(X0) | humble(X0)))) [nnf transformation 3]
45. ! [X0] : (((~curious(X0) & ~humble(X0)) | rich(X0)) & (~rich(X0) | curious(X0) | humble(X0))) [flattening 44]
62. ! [X0] : (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (~rich(X0) & ~generous(X0))) [nnf transformation 38]
93. ~curious(X0) | rich(X0) [cnf transformation 45]
99. old(X0) | ~rich(X0) [cnf transformation 34]
134. ~rich(X0) | ~old(X0) | ~rich(X0) [cnf transformation 62]
154. curious(mary) [cnf transformation 24]
155. ~rich(X0) | ~old(X0) [duplicate literal removal 134]
218. ~rich(X0) [subsumption resolution 155,99]
319. rich(mary) [resolution 93,154]
320. $false [subsumption resolution 319,218]
% SZS output end Proof for 2112301359269453156609860
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not funny or quiet then someone is not quiet.
If someone is not old then mary is either generous or brave.
Everyone who is not curious is not generous or not kind.
If susan is not generous then alice is strong or rich and vice versa.
Everyone who is patient is creative and vice versa.
If susan is either not creative or creative then someone is not strong.
Everyone who is either not strong or not creative is not brave and vice versa.
Everyone who is wise or not calm is both not kind and patient and vice versa.
If paul is not happy then susan is either not brave or old.
Everyone who is creative or generous is both not old and not calm and vice versa.
If john is both not quiet and creative then john is calm and vice versa.
Everyone who is both not creative and not curious is both rich and patient and vice versa.
If someone is not wise or tall then someone is both not wise and not patient.
If john is either happy or quiet then someone is both calm and not calm.
If someone is both not strong and not happy then someone is both patient and creative and vice versa.
Everyone who is both funny and not old is both not brave and wise.
Paul is not generous or not quiet.
John is wise or not happy.
Susan is both creative and patient.
Lucy is either creative or not humble.
Lucy is not strong.
Someone is kind.
Someone is not rich or not kind.
Someone is both not curious and strong. | John is not rich. | entailment | ((?[X]:((~funny(X)|quiet(X))))=>(?[X]:(~quiet(X))))&
((?[X]:(~old(X)))=>((generous(mary)<~>brave(mary))))&
(![X]:(~curious(X)=>(~generous(X)|~kind(X))))&
((~generous(susan))<=>((strong(alice)|rich(alice))))&
(![X]:(patient(X)<=>creative(X)))&
(((~creative(susan)<~>creative(susan)))=>(?[X]:(~strong(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>~brave(X)))&
(![X]:((wise(X)|~calm(X))<=>(~kind(X)&patient(X))))&
((~happy(paul))=>((~brave(susan)<~>old(susan))))&
(![X]:((creative(X)|generous(X))<=>(~old(X)&~calm(X))))&
(((~quiet(john)&creative(john)))<=>(calm(john)))&
(![X]:((~creative(X)&~curious(X))<=>(rich(X)&patient(X))))&
((?[X]:((~wise(X)|tall(X))))=>(?[X]:((~wise(X)&~patient(X)))))&
(((happy(john)<~>quiet(john)))=>(?[X]:((calm(X)&~calm(X)))))&
((?[X]:((~strong(X)&~happy(X))))<=>(?[X]:((patient(X)&creative(X)))))&
(![X]:((funny(X)&~old(X))=>(~brave(X)&wise(X))))&
((~generous(paul)|~quiet(paul)))&
((wise(john)|~happy(john)))&
((creative(susan)&patient(susan)))&
((creative(lucy)<~>~humble(lucy)))&
(~strong(lucy))&
(?[X]:(kind(X)))&
(?[X]:((~rich(X)|~kind(X))))&
(?[X]:((~curious(X)&strong(X)))) | ~rich(john) | [
"p4",
"p7",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 580543678814672622757737
% SZS output start Proof for 580543678814672622757737
5. ! [X0] : (patient(X0) <=> creative(X0)) [input p4]
8. ! [X0] : ((~calm(X0) | wise(X0)) <=> (patient(X0) & ~kind(X0))) [input p7]
10. ! [X0] : ((generous(X0) | creative(X0)) <=> (~calm(X0) & ~old(X0))) [input p9]
11. (creative(john) & ~quiet(john)) <=> calm(john) [input p10]
12. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (patient(X0) & rich(X0))) [input p11]
25. rich(john) [input hypothesis]
46. ! [X0] : ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))) [nnf transformation 5]
51. ! [X0] : (((~calm(X0) | wise(X0)) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | (calm(X0) & ~wise(X0)))) [nnf transformation 8]
52. ! [X0] : ((~calm(X0) | wise(X0) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | (calm(X0) & ~wise(X0)))) [flattening 51]
54. ! [X0] : (((generous(X0) | creative(X0)) | (calm(X0) | old(X0))) & ((~calm(X0) & ~old(X0)) | (~generous(X0) & ~creative(X0)))) [nnf transformation 10]
55. ! [X0] : ((generous(X0) | creative(X0) | calm(X0) | old(X0)) & ((~calm(X0) & ~old(X0)) | (~generous(X0) & ~creative(X0)))) [flattening 54]
56. ((creative(john) & ~quiet(john)) | ~calm(john)) & (calm(john) | (~creative(john) | quiet(john))) [nnf transformation 11]
57. ((creative(john) & ~quiet(john)) | ~calm(john)) & (calm(john) | ~creative(john) | quiet(john)) [flattening 56]
58. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~patient(X0) | ~rich(X0))) & ((patient(X0) & rich(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 12]
59. ! [X0] : (((~curious(X0) & ~creative(X0)) | ~patient(X0) | ~rich(X0)) & ((patient(X0) & rich(X0)) | curious(X0) | creative(X0))) [flattening 58]
86. ~patient(X0) | creative(X0) [cnf transformation 46]
97. calm(X0) | patient(X0) [cnf transformation 52]
103. ~calm(X0) | ~creative(X0) [cnf transformation 55]
108. creative(john) | ~calm(john) [cnf transformation 57]
111. ~creative(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 59]
136. rich(john) [cnf transformation 25]
203. ~calm(john) [subsumption resolution 108,103]
214. ~patient(X0) | ~rich(X0) [subsumption resolution 111,86]
308. patient(john) [resolution 97,203]
324. ~rich(john) [resolution 214,308]
325. $false [subsumption resolution 324,136]
% SZS output end Proof for 580543678814672622757737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either funny or brave then lucy is both not strong and strong. Everyone who is both creative and rich is either quiet or calm and vice versa. Everyone who is either brave or not humble is not rich. Everyone who is both not rich and happy is either old or not quiet and vice versa. Everyone who is either not generous or not calm is not quiet and vice versa. Everyone who is either not old or wise is both humble and tall. Everyone who is not brave or brave is both old and wise. Everyone who is either not old or not funny is curious and vice versa. If someone is both not old and not strong then someone is both funny and kind and vice versa. Everyone who is not rich is not creative or patient and vice versa. If alice is not generous or not humble then someone is not brave. Everyone who is brave or not quiet is both generous and curious and vice versa. If someone is not wise or not happy then someone is not creative and vice versa. Everyone who is not happy or old is either curious or not kind and vice versa. If someone is either not wise or calm then someone is curious or calm. Mary is either tall or strong. Someone is patient. Someone is both wise and not kind. Someone is either calm or not wise. Someone is not strong or not generous. Someone is curious. | Mary is not curious. | neutral | (((funny(fred)<~>brave(fred)))=>((~strong(lucy)&strong(lucy))))&
(![X]:((creative(X)&rich(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((brave(X)<~>~humble(X))=>~rich(X)))&
(![X]:((~rich(X)&happy(X))<=>(old(X)<~>~quiet(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((~old(X)<~>wise(X))=>(humble(X)&tall(X))))&
(![X]:((~brave(X)|brave(X))=>(old(X)&wise(X))))&
(![X]:((~old(X)<~>~funny(X))<=>curious(X)))&
((?[X]:((~old(X)&~strong(X))))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:(~rich(X)<=>(~creative(X)|patient(X))))&
(((~generous(alice)|~humble(alice)))=>(?[X]:(~brave(X))))&
(![X]:((brave(X)|~quiet(X))<=>(generous(X)&curious(X))))&
((?[X]:((~wise(X)|~happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~happy(X)|old(X))<=>(curious(X)<~>~kind(X))))&
((?[X]:((~wise(X)<~>calm(X))))=>(?[X]:((curious(X)|calm(X)))))&
((tall(mary)<~>strong(mary)))&
(?[X]:(patient(X)))&
(?[X]:((wise(X)&~kind(X))))&
(?[X]:((calm(X)<~>~wise(X))))&
(?[X]:((~strong(X)|~generous(X))))&
(?[X]:(curious(X))) | ~curious(mary) | [] | null | 0 |
Everyone who is both strong and not quiet is either not old or patient and vice versa. If paul is not calm or not generous then susan is quiet and vice versa. Everyone who is both curious and calm is happy or not tall and vice versa. If someone is kind or not quiet then someone is tall and vice versa. If someone is both not patient and strong then someone is creative. Everyone who is either quiet or not old is brave and vice versa. If susan is both not curious and not quiet then mary is happy and vice versa. Everyone who is tall is not funny and vice versa. If someone is not old or not funny then mary is both kind and rich and vice versa. Everyone who is either not brave or old is not wise or quiet and vice versa. Everyone who is either generous or kind is both not rich and not brave. Everyone who is both not calm and creative is not funny. If someone is humble or tall then someone is creative. Everyone who is not patient is either not quiet or creative and vice versa. If alice is tall or wise then susan is creative or not strong. Everyone who is both tall and not strong is strong and vice versa. Someone is either not patient or generous. Someone is either tall or not generous. Susan is either patient or rich. Susan is both not kind and not patient. | Mary is patient. | contradiction | (![X]:((strong(X)&~quiet(X))<=>(~old(X)<~>patient(X))))&
(((~calm(paul)|~generous(paul)))<=>(quiet(susan)))&
(![X]:((curious(X)&calm(X))<=>(happy(X)|~tall(X))))&
((?[X]:((kind(X)|~quiet(X))))<=>(?[X]:(tall(X))))&
((?[X]:((~patient(X)&strong(X))))=>(?[X]:(creative(X))))&
(![X]:((quiet(X)<~>~old(X))<=>brave(X)))&
(((~curious(susan)&~quiet(susan)))<=>(happy(mary)))&
(![X]:(tall(X)<=>~funny(X)))&
((?[X]:((~old(X)|~funny(X))))<=>((kind(mary)&rich(mary))))&
(![X]:((~brave(X)<~>old(X))<=>(~wise(X)|quiet(X))))&
(![X]:((generous(X)<~>kind(X))=>(~rich(X)&~brave(X))))&
(![X]:((~calm(X)&creative(X))=>~funny(X)))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:(creative(X))))&
(![X]:(~patient(X)<=>(~quiet(X)<~>creative(X))))&
(((tall(alice)|wise(alice)))=>((creative(susan)|~strong(susan))))&
(![X]:((tall(X)&~strong(X))<=>strong(X)))&
(?[X]:((~patient(X)<~>generous(X))))&
(?[X]:((tall(X)<~>~generous(X))))&
((patient(susan)<~>rich(susan)))&
((~kind(susan)&~patient(susan))) | patient(mary) | [
"p0",
"p3",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 549165424066544925612205
% SZS output start Proof for 549165424066544925612205
1. ! [X0] : ((~quiet(X0) & strong(X0)) <=> (~old(X0) <~> patient(X0))) [input p0]
4. ? [X0] : (~quiet(X0) | kind(X0)) <=> ? [X0] : tall(X0) [input p3]
9. ? [X0] : (~funny(X0) | ~old(X0)) <=> (rich(mary) & kind(mary)) [input p8]
16. ! [X0] : ((~strong(X0) & tall(X0)) <=> strong(X0)) [input p15]
21. patient(mary) [input hypothesis]
22. ? [X0] : (~quiet(X0) | kind(X0)) <=> ? [X1] : tall(X1) [rectify 4]
33. ! [X0] : (((~quiet(X0) & strong(X0)) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) & (((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | (quiet(X0) | ~strong(X0)))) [nnf transformation 1]
34. ! [X0] : (((~quiet(X0) & strong(X0)) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) & (((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | quiet(X0) | ~strong(X0))) [flattening 33]
39. (? [X0] : (~quiet(X0) | kind(X0)) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : (quiet(X0) & ~kind(X0))) [nnf transformation 22]
40. (? [X0] : (~quiet(X0) | kind(X0)) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : (quiet(X3) & ~kind(X3))) [rectify 39]
41. ? [X0] : (~quiet(X0) | kind(X0)) => (~quiet(sK0) | kind(sK0)) [choice axiom]
42. ? [X2] : tall(X2) => tall(sK1) [choice axiom]
43. ((~quiet(sK0) | kind(sK0)) | ! [X1] : ~tall(X1)) & (tall(sK1) | ! [X3] : (quiet(X3) & ~kind(X3))) [skolemisation 40,42,41]
51. (? [X0] : (~funny(X0) | ~old(X0)) | (~rich(mary) | ~kind(mary))) & ((rich(mary) & kind(mary)) | ! [X0] : (funny(X0) & old(X0))) [nnf transformation 9]
52. (? [X0] : (~funny(X0) | ~old(X0)) | ~rich(mary) | ~kind(mary)) & ((rich(mary) & kind(mary)) | ! [X0] : (funny(X0) & old(X0))) [flattening 51]
53. (? [X0] : (~funny(X0) | ~old(X0)) | ~rich(mary) | ~kind(mary)) & ((rich(mary) & kind(mary)) | ! [X1] : (funny(X1) & old(X1))) [rectify 52]
54. ? [X0] : (~funny(X0) | ~old(X0)) => (~funny(sK3) | ~old(sK3)) [choice axiom]
55. ((~funny(sK3) | ~old(sK3)) | ~rich(mary) | ~kind(mary)) & ((rich(mary) & kind(mary)) | ! [X1] : (funny(X1) & old(X1))) [skolemisation 53,54]
63. ! [X0] : (((~strong(X0) & tall(X0)) | ~strong(X0)) & (strong(X0) | (strong(X0) | ~tall(X0)))) [nnf transformation 16]
64. ! [X0] : (((~strong(X0) & tall(X0)) | ~strong(X0)) & (strong(X0) | strong(X0) | ~tall(X0))) [flattening 63]
75. ~patient(X0) | ~old(X0) | strong(X0) [cnf transformation 34]
86. tall(sK1) | ~kind(X3) [cnf transformation 43]
99. kind(mary) | old(X1) [cnf transformation 55]
122. strong(X0) | strong(X0) | ~tall(X0) [cnf transformation 64]
124. ~strong(X0) | ~strong(X0) [cnf transformation 64]
133. patient(mary) [cnf transformation 21]
134. strong(X0) | ~tall(X0) [duplicate literal removal 122]
135. ~strong(X0) [duplicate literal removal 124]
152. 4 <=> ! [X1] : ~tall(X1) [avatar definition]
153. ~tall(X1) <- (4) [avatar component clause 152]
167. 8 <=> tall(sK1) [avatar definition]
169. tall(sK1) <- (8) [avatar component clause 167]
172. 9 <=> ! [X3] : ~kind(X3) [avatar definition]
173. ~kind(X3) <- (9) [avatar component clause 172]
174. 9 | 8 [avatar split clause 86,167,172]
195. 14 <=> kind(mary) [avatar definition]
196. kind(mary) <- (14) [avatar component clause 195]
216. 19 <=> ! [X1] : old(X1) [avatar definition]
217. old(X1) <- (19) [avatar component clause 216]
220. 19 | 14 [avatar split clause 99,195,216]
244. ~tall(X0) [subsumption resolution 134,135]
245. 4 [avatar split clause 244,152]
277. $false <- (4, 8) [resolution 169,153]
278. ~4 | ~8 [avatar contradiction clause 277]
281. $false <- (9, 14) [resolution 196,173]
282. ~9 | ~14 [avatar contradiction clause 281]
295. ~old(mary) | strong(mary) [resolution 75,133]
298. strong(mary) <- (19) [subsumption resolution 295,217]
299. $false <- (19) [subsumption resolution 298,135]
300. ~19 [avatar contradiction clause 299]
301. $false [avatar sat refutation 174,220,245,278,282,300]
% SZS output end Proof for 549165424066544925612205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then someone is both not curious and tall and vice versa.
Everyone who is both brave and not kind is not creative and vice versa.
If alice is curious or not creative then someone is kind.
Everyone who is both curious and not humble is quiet and vice versa.
Everyone who is both wise and creative is not quiet.
If paul is both not quiet and not humble then someone is either strong or brave and vice versa.
Everyone who is both happy and curious is wise.
Everyone who is both rich and not wise is not curious and vice versa.
If someone is either happy or strong then someone is old.
If someone is not rich or not tall then mary is not old.
If someone is both generous and not old then lucy is either not curious or not generous.
Everyone who is either tall or kind is either kind or not kind and vice versa.
Everyone who is either patient or not strong is not patient or old and vice versa.
Everyone who is either calm or not strong is either kind or not brave and vice versa.
Everyone who is both not patient and not funny is both old and not quiet.
Everyone who is not quiet or wise is not strong or funny and vice versa.
Someone is either curious or creative.
Someone is either not old or rich.
Fred is both curious and brave.
Someone is either not curious or creative.
Someone is creative.
Someone is either creative or humble.
John is not patient or calm. | Lucy is wise. | neutral | ((?[X]:(~quiet(X)))<=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:((brave(X)&~kind(X))<=>~creative(X)))&
(((curious(alice)|~creative(alice)))=>(?[X]:(kind(X))))&
(![X]:((curious(X)&~humble(X))<=>quiet(X)))&
(![X]:((wise(X)&creative(X))=>~quiet(X)))&
(((~quiet(paul)&~humble(paul)))<=>(?[X]:((strong(X)<~>brave(X)))))&
(![X]:((happy(X)&curious(X))=>wise(X)))&
(![X]:((rich(X)&~wise(X))<=>~curious(X)))&
((?[X]:((happy(X)<~>strong(X))))=>(?[X]:(old(X))))&
((?[X]:((~rich(X)|~tall(X))))=>(~old(mary)))&
((?[X]:((generous(X)&~old(X))))=>((~curious(lucy)<~>~generous(lucy))))&
(![X]:((tall(X)<~>kind(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~patient(X)|old(X))))&
(![X]:((calm(X)<~>~strong(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~patient(X)&~funny(X))=>(old(X)&~quiet(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~strong(X)|funny(X))))&
(?[X]:((curious(X)<~>creative(X))))&
(?[X]:((~old(X)<~>rich(X))))&
((curious(fred)&brave(fred)))&
(?[X]:((~curious(X)<~>creative(X))))&
(?[X]:(creative(X)))&
(?[X]:((creative(X)<~>humble(X))))&
((~patient(john)|calm(john))) | wise(lucy) | [] | null | 0 |
Everyone who is either curious or kind is not curious.
Everyone who is creative or old is not calm and vice versa.
Everyone who is not creative is not tall or funny and vice versa.
Everyone who is either not humble or not kind is not patient.
If someone is not happy then mary is not happy or not wise.
If someone is both curious and not rich then susan is either funny or not kind.
If someone is not curious or not creative then someone is both not wise and calm and vice versa.
Everyone who is either curious or not wise is both not calm and rich.
Everyone who is brave is not creative and vice versa.
If someone is either not curious or generous then mary is either kind or creative and vice versa.
Everyone who is not creative or not calm is not generous or not rich and vice versa.
Everyone who is happy is both curious and funny.
Everyone who is both not creative and not old is both calm and humble and vice versa.
Everyone who is brave or happy is humble or not wise.
If fred is not rich or not humble then someone is either quiet or rich and vice versa.
Lucy is either tall or curious.
Someone is not tall.
Susan is strong or funny.
Lucy is either not quiet or not tall.
Paul is rich.
Someone is either not old or rich. | Fred is wise. | neutral | (![X]:((curious(X)<~>kind(X))=>~curious(X)))&
(![X]:((creative(X)|old(X))<=>~calm(X)))&
(![X]:(~creative(X)<=>(~tall(X)|funny(X))))&
(![X]:((~humble(X)<~>~kind(X))=>~patient(X)))&
((?[X]:(~happy(X)))=>((~happy(mary)|~wise(mary))))&
((?[X]:((curious(X)&~rich(X))))=>((funny(susan)<~>~kind(susan))))&
((?[X]:((~curious(X)|~creative(X))))<=>(?[X]:((~wise(X)&calm(X)))))&
(![X]:((curious(X)<~>~wise(X))=>(~calm(X)&rich(X))))&
(![X]:(brave(X)<=>~creative(X)))&
((?[X]:((~curious(X)<~>generous(X))))<=>((kind(mary)<~>creative(mary))))&
(![X]:((~creative(X)|~calm(X))<=>(~generous(X)|~rich(X))))&
(![X]:(happy(X)=>(curious(X)&funny(X))))&
(![X]:((~creative(X)&~old(X))<=>(calm(X)&humble(X))))&
(![X]:((brave(X)|happy(X))=>(humble(X)|~wise(X))))&
(((~rich(fred)|~humble(fred)))<=>(?[X]:((quiet(X)<~>rich(X)))))&
((tall(lucy)<~>curious(lucy)))&
(?[X]:(~tall(X)))&
((strong(susan)|funny(susan)))&
((~quiet(lucy)<~>~tall(lucy)))&
(rich(paul))&
(?[X]:((~old(X)<~>rich(X)))) | wise(fred) | [] | null | 0 |
Everyone who is either not happy or not old is either brave or not happy and vice versa.
Everyone who is either quiet or tall is not happy or not humble and vice versa.
Everyone who is not generous or not kind is both generous and creative and vice versa.
Everyone who is both old and not strong is both humble and old and vice versa.
Everyone who is not kind is either not rich or humble.
Everyone who is not patient is funny.
Everyone who is funny is either old or not happy and vice versa.
If john is funny then fred is either wise or creative.
Everyone who is either quiet or happy is both not old and not tall and vice versa.
If lucy is either patient or not calm then alice is both wise and not tall and vice versa.
If paul is both not calm and tall then someone is both curious and kind.
If someone is both not curious and kind then susan is both not wise and not curious.
Everyone who is both rich and not calm is either not brave or not rich and vice versa.
Everyone who is both not happy and not rich is both generous and not old.
If someone is not calm then someone is both not wise and not quiet and vice versa.
Everyone who is not happy or not brave is not quiet.
Lucy is either quiet or not generous.
Someone is both curious and not old.
Paul is calm.
Someone is not kind or tall.
Mary is not curious or not old.
Susan is not kind or not old.
Someone is either rich or not brave.
Someone is happy or not creative. | Paul is not curious. | neutral | (![X]:((~happy(X)<~>~old(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~happy(X)|~humble(X))))&
(![X]:((~generous(X)|~kind(X))<=>(generous(X)&creative(X))))&
(![X]:((old(X)&~strong(X))<=>(humble(X)&old(X))))&
(![X]:(~kind(X)=>(~rich(X)<~>humble(X))))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:(funny(X)<=>(old(X)<~>~happy(X))))&
((funny(john))=>((wise(fred)<~>creative(fred))))&
(![X]:((quiet(X)<~>happy(X))<=>(~old(X)&~tall(X))))&
(((patient(lucy)<~>~calm(lucy)))<=>((wise(alice)&~tall(alice))))&
(((~calm(paul)&tall(paul)))=>(?[X]:((curious(X)&kind(X)))))&
((?[X]:((~curious(X)&kind(X))))=>((~wise(susan)&~curious(susan))))&
(![X]:((rich(X)&~calm(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:((~happy(X)&~rich(X))=>(generous(X)&~old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:((~happy(X)|~brave(X))=>~quiet(X)))&
((quiet(lucy)<~>~generous(lucy)))&
(?[X]:((curious(X)&~old(X))))&
(calm(paul))&
(?[X]:((~kind(X)|tall(X))))&
((~curious(mary)|~old(mary)))&
((~kind(susan)|~old(susan)))&
(?[X]:((rich(X)<~>~brave(X))))&
(?[X]:((happy(X)|~creative(X)))) | ~curious(paul) | [] | null | 0 |
If john is either not brave or not kind then someone is both tall and rich. Everyone who is not humble is either calm or kind and vice versa. Everyone who is not brave or funny is not quiet and vice versa. If someone is not rich or not calm then susan is strong. Everyone who is not old is kind or not calm. Everyone who is not curious or not patient is happy and vice versa. If susan is both curious and not tall then alice is either happy or strong and vice versa. If someone is both not quiet and not humble then susan is not patient and vice versa. Everyone who is not old is not strong or not generous and vice versa. Everyone who is either kind or happy is patient or not old. Everyone who is either curious or wise is not curious and vice versa. Everyone who is patient or curious is funny or not patient and vice versa. Everyone who is not kind or not strong is both not old and calm and vice versa. Everyone who is quiet is happy or not funny. If someone is not strong then susan is both patient and old. Everyone who is not kind or not strong is either not quiet or humble. Someone is not calm or curious. Someone is either kind or not quiet. Someone is quiet or rich. Someone is either happy or old. Lucy is both not quiet and not creative. Someone is not happy or happy. Someone is both curious and not strong. | Susan is not patient. | contradiction | (((~brave(john)<~>~kind(john)))=>(?[X]:((tall(X)&rich(X)))))&
(![X]:(~humble(X)<=>(calm(X)<~>kind(X))))&
(![X]:((~brave(X)|funny(X))<=>~quiet(X)))&
((?[X]:((~rich(X)|~calm(X))))=>(strong(susan)))&
(![X]:(~old(X)=>(kind(X)|~calm(X))))&
(![X]:((~curious(X)|~patient(X))<=>happy(X)))&
(((curious(susan)&~tall(susan)))<=>((happy(alice)<~>strong(alice))))&
((?[X]:((~quiet(X)&~humble(X))))<=>(~patient(susan)))&
(![X]:(~old(X)<=>(~strong(X)|~generous(X))))&
(![X]:((kind(X)<~>happy(X))=>(patient(X)|~old(X))))&
(![X]:((curious(X)<~>wise(X))<=>~curious(X)))&
(![X]:((patient(X)|curious(X))<=>(funny(X)|~patient(X))))&
(![X]:((~kind(X)|~strong(X))<=>(~old(X)&calm(X))))&
(![X]:(quiet(X)=>(happy(X)|~funny(X))))&
((?[X]:(~strong(X)))=>((patient(susan)&old(susan))))&
(![X]:((~kind(X)|~strong(X))=>(~quiet(X)<~>humble(X))))&
(?[X]:((~calm(X)|curious(X))))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:((quiet(X)|rich(X))))&
(?[X]:((happy(X)<~>old(X))))&
((~quiet(lucy)&~creative(lucy)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((curious(X)&~strong(X)))) | ~patient(susan) | [
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5623676852977387728794183
% SZS output start Proof for 5623676852977387728794183
15. ? [X0] : ~strong(X0) => (old(susan) & patient(susan)) [input p14]
23. ? [X0] : (~strong(X0) & curious(X0)) [input p22]
24. ~patient(susan) [input hypothesis]
37. (old(susan) & patient(susan)) | ! [X0] : strong(X0) [ennf transformation 15]
72. ? [X0] : (~strong(X0) & curious(X0)) => (~strong(sK6) & curious(sK6)) [choice axiom]
73. ~strong(sK6) & curious(sK6) [skolemisation 23,72]
116. patient(susan) | strong(X0) [cnf transformation 37]
130. ~strong(sK6) [cnf transformation 73]
131. ~patient(susan) [cnf transformation 24]
181. 10 <=> patient(susan) [avatar definition]
202. 14 <=> ! [X0] : strong(X0) [avatar definition]
203. strong(X0) <- (14) [avatar component clause 202]
209. 14 | 10 [avatar split clause 116,181,202]
239. ~10 [avatar split clause 131,181]
242. $false <- (14) [resolution 203,130]
243. ~14 [avatar contradiction clause 242]
244. $false [avatar sat refutation 209,239,243]
% SZS output end Proof for 5623676852977387728794183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not brave is curious.
Everyone who is both old and not kind is quiet or creative.
Everyone who is happy or old is not calm or not funny.
If someone is either not funny or happy then mary is not calm and vice versa.
Everyone who is either quiet or curious is both brave and not generous and vice versa.
If fred is both rich and not funny then someone is either humble or quiet and vice versa.
If lucy is not happy or creative then fred is both not brave and not funny and vice versa.
If someone is not patient then alice is not generous and vice versa.
Everyone who is either not quiet or not tall is patient or quiet and vice versa.
If someone is either humble or not curious then someone is either not creative or not happy.
If alice is not creative or not kind then someone is both not strong and not funny and vice versa.
If someone is either happy or not humble then fred is not kind and vice versa.
Everyone who is generous or not calm is quiet or rich and vice versa.
Everyone who is both not happy and creative is calm.
Everyone who is both not quiet and humble is either not tall or creative and vice versa.
Everyone who is not strong is both patient and not brave and vice versa.
Fred is either rich or not funny.
Alice is not old.
Mary is not curious or brave.
Susan is not wise or not creative.
Alice is either patient or not creative.
Someone is brave or happy.
Lucy is not brave or not kind.
Someone is either not brave or not curious. | Alice is not creative. | contradiction | (![X]:((~kind(X)|~brave(X))=>curious(X)))&
(![X]:((old(X)&~kind(X))=>(quiet(X)|creative(X))))&
(![X]:((happy(X)|old(X))=>(~calm(X)|~funny(X))))&
((?[X]:((~funny(X)<~>happy(X))))<=>(~calm(mary)))&
(![X]:((quiet(X)<~>curious(X))<=>(brave(X)&~generous(X))))&
(((rich(fred)&~funny(fred)))<=>(?[X]:((humble(X)<~>quiet(X)))))&
(((~happy(lucy)|creative(lucy)))<=>((~brave(fred)&~funny(fred))))&
((?[X]:(~patient(X)))<=>(~generous(alice)))&
(![X]:((~quiet(X)<~>~tall(X))<=>(patient(X)|quiet(X))))&
((?[X]:((humble(X)<~>~curious(X))))=>(?[X]:((~creative(X)<~>~happy(X)))))&
(((~creative(alice)|~kind(alice)))<=>(?[X]:((~strong(X)&~funny(X)))))&
((?[X]:((happy(X)<~>~humble(X))))<=>(~kind(fred)))&
(![X]:((generous(X)|~calm(X))<=>(quiet(X)|rich(X))))&
(![X]:((~happy(X)&creative(X))=>calm(X)))&
(![X]:((~quiet(X)&humble(X))<=>(~tall(X)<~>creative(X))))&
(![X]:(~strong(X)<=>(patient(X)&~brave(X))))&
((rich(fred)<~>~funny(fred)))&
(~old(alice))&
((~curious(mary)|brave(mary)))&
((~wise(susan)|~creative(susan)))&
((patient(alice)<~>~creative(alice)))&
(?[X]:((brave(X)|happy(X))))&
((~brave(lucy)|~kind(lucy)))&
(?[X]:((~brave(X)<~>~curious(X)))) | ~creative(alice) | [
"p5",
"p8",
"p14",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8337744786784642279985871
% SZS output start Proof for 8337744786784642279985871
6. (~funny(fred) & rich(fred)) <=> ? [X0] : (humble(X0) <~> quiet(X0)) [input p5]
9. ! [X0] : ((~quiet(X0) <~> ~tall(X0)) <=> (quiet(X0) | patient(X0))) [input p8]
15. ! [X0] : ((humble(X0) & ~quiet(X0)) <=> (~tall(X0) <~> creative(X0))) [input p14]
17. rich(fred) <~> ~funny(fred) [input p16]
21. patient(alice) <~> ~creative(alice) [input p20]
25. ~creative(alice) [input hypothesis]
43. ((~funny(fred) & rich(fred)) | ! [X0] : ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (? [X0] : ((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | (funny(fred) | ~rich(fred))) [nnf transformation 6]
44. ((~funny(fred) & rich(fred)) | ! [X0] : ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (? [X0] : ((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | funny(fred) | ~rich(fred)) [flattening 43]
45. ((~funny(fred) & rich(fred)) | ! [X0] : ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (? [X1] : ((~quiet(X1) | ~humble(X1)) & (quiet(X1) | humble(X1))) | funny(fred) | ~rich(fred)) [rectify 44]
46. ? [X1] : ((~quiet(X1) | ~humble(X1)) & (quiet(X1) | humble(X1))) => ((~quiet(sK1) | ~humble(sK1)) & (quiet(sK1) | humble(sK1))) [choice axiom]
47. ((~funny(fred) & rich(fred)) | ! [X0] : ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (((~quiet(sK1) | ~humble(sK1)) & (quiet(sK1) | humble(sK1))) | funny(fred) | ~rich(fred)) [skolemisation 45,46]
54. ! [X0] : ((((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))))) [nnf transformation 9]
55. ! [X0] : ((((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))))) [flattening 54]
71. ! [X0] : (((humble(X0) & ~quiet(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | (~humble(X0) | quiet(X0)))) [nnf transformation 15]
72. ! [X0] : (((humble(X0) & ~quiet(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | ~humble(X0) | quiet(X0))) [flattening 71]
75. (funny(fred) | ~rich(fred)) & (~funny(fred) | rich(fred)) [nnf transformation 17]
76. (creative(alice) | ~patient(alice)) & (~creative(alice) | patient(alice)) [nnf transformation 21]
97. rich(fred) | quiet(X0) | ~humble(X0) [cnf transformation 47]
99. ~funny(fred) | quiet(X0) | ~humble(X0) [cnf transformation 47]
108. quiet(X0) | patient(X0) | ~tall(X0) | quiet(X0) [cnf transformation 55]
111. ~tall(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 55]
134. ~quiet(X0) | creative(X0) | tall(X0) [cnf transformation 72]
136. tall(X0) | creative(X0) | humble(X0) [cnf transformation 72]
142. funny(fred) | ~rich(fred) [cnf transformation 75]
145. creative(alice) | ~patient(alice) [cnf transformation 76]
150. ~creative(alice) [cnf transformation 25]
151. quiet(X0) | patient(X0) | ~tall(X0) [duplicate literal removal 108]
152. ~tall(X0) | ~quiet(X0) [duplicate literal removal 111]
181. 7 <=> funny(fred) [avatar definition]
186. 8 <=> ! [X0] : (quiet(X0) | ~humble(X0)) [avatar definition]
187. ~humble(X0) | quiet(X0) <- (8) [avatar component clause 186]
188. 8 | ~7 [avatar split clause 99,181,186]
190. 9 <=> rich(fred) [avatar definition]
194. 8 | 9 [avatar split clause 97,190,186]
235. ~tall(X0) | patient(X0) [subsumption resolution 151,152]
258. 23 <=> creative(alice) [avatar definition]
260. ~creative(alice) <- (~23) [avatar component clause 258]
300. ~quiet(X0) | creative(X0) [subsumption resolution 134,152]
302. ~9 | 7 [avatar split clause 142,181,190]
306. 32 <=> patient(alice) [avatar definition]
308. ~patient(alice) <- (~32) [avatar component clause 306]
309. ~32 | 23 [avatar split clause 145,258,306]
338. ~23 [avatar split clause 150,258]
394. patient(X0) | humble(X0) | creative(X0) [resolution 136,235]
429. 49 <=> quiet(alice) [avatar definition]
431. quiet(alice) <- (49) [avatar component clause 429]
487. humble(alice) | creative(alice) <- (~32) [resolution 394,308]
498. humble(alice) <- (~23, ~32) [subsumption resolution 487,260]
514. quiet(alice) <- (8, ~23, ~32) [resolution 498,187]
515. 49 | ~8 | 23 | 32 [avatar split clause 514,306,258,186,429]
517. creative(alice) <- (49) [resolution 431,300]
523. $false <- (~23, 49) [subsumption resolution 517,260]
524. 23 | ~49 [avatar contradiction clause 523]
525. $false [avatar sat refutation 188,194,302,309,338,515,524]
% SZS output end Proof for 8337744786784642279985871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not calm then someone is not humble or humble and vice versa. Everyone who is either not quiet or generous is both quiet and not old and vice versa. Everyone who is not wise or not rich is both not generous and brave and vice versa. Everyone who is both not patient and funny is patient or not generous and vice versa. Everyone who is not happy is not creative or not patient and vice versa. If someone is both kind and not kind then susan is both not creative and not generous. Everyone who is curious or kind is not kind or quiet. Everyone who is both not tall and humble is both generous and not curious. Everyone who is both not humble and curious is both not brave and old. If susan is either funny or not happy then someone is not patient. If john is patient or generous then someone is either old or not rich and vice versa. Everyone who is brave or strong is not curious or not old. Everyone who is either brave or kind is not rich or humble. If someone is either curious or rich then alice is kind or humble. If alice is quiet or not quiet then lucy is kind. If fred is both funny and kind then someone is not creative or tall and vice versa. Mary is either not wise or funny. Fred is not tall. Paul is not rich. Someone is not generous or not humble. Someone is both not quiet and curious. Someone is either not tall or not funny. Someone is not brave. Mary is either wise or creative. | Fred is not brave. | contradiction | ((?[X]:((tall(X)|~calm(X))))<=>(?[X]:((~humble(X)|humble(X)))))&
(![X]:((~quiet(X)<~>generous(X))<=>(quiet(X)&~old(X))))&
(![X]:((~wise(X)|~rich(X))<=>(~generous(X)&brave(X))))&
(![X]:((~patient(X)&funny(X))<=>(patient(X)|~generous(X))))&
(![X]:(~happy(X)<=>(~creative(X)|~patient(X))))&
((?[X]:((kind(X)&~kind(X))))=>((~creative(susan)&~generous(susan))))&
(![X]:((curious(X)|kind(X))=>(~kind(X)|quiet(X))))&
(![X]:((~tall(X)&humble(X))=>(generous(X)&~curious(X))))&
(![X]:((~humble(X)&curious(X))=>(~brave(X)&old(X))))&
(((funny(susan)<~>~happy(susan)))=>(?[X]:(~patient(X))))&
(((patient(john)|generous(john)))<=>(?[X]:((old(X)<~>~rich(X)))))&
(![X]:((brave(X)|strong(X))=>(~curious(X)|~old(X))))&
(![X]:((brave(X)<~>kind(X))=>(~rich(X)|humble(X))))&
((?[X]:((curious(X)<~>rich(X))))=>((kind(alice)|humble(alice))))&
(((quiet(alice)|~quiet(alice)))=>(kind(lucy)))&
(((funny(fred)&kind(fred)))<=>(?[X]:((~creative(X)|tall(X)))))&
((~wise(mary)<~>funny(mary)))&
(~tall(fred))&
(~rich(paul))&
(?[X]:((~generous(X)|~humble(X))))&
(?[X]:((~quiet(X)&curious(X))))&
(?[X]:((~tall(X)<~>~funny(X))))&
(?[X]:(~brave(X)))&
((wise(mary)<~>creative(mary))) | ~brave(fred) | [
"p2",
"p3",
"p7",
"p12",
"p15",
"p16",
"p17",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 864778359676246690034878
% SZS output start Proof for 864778359676246690034878
3. ! [X0] : ((~rich(X0) | ~wise(X0)) <=> (brave(X0) & ~generous(X0))) [input p2]
4. ! [X0] : ((funny(X0) & ~patient(X0)) <=> (~generous(X0) | patient(X0))) [input p3]
8. ! [X0] : ((humble(X0) & ~tall(X0)) => (~curious(X0) & generous(X0))) [input p7]
13. ! [X0] : ((brave(X0) <~> kind(X0)) => (humble(X0) | ~rich(X0))) [input p12]
16. (kind(fred) & funny(fred)) <=> ? [X0] : (tall(X0) | ~creative(X0)) [input p15]
17. ~wise(mary) <~> funny(mary) [input p16]
18. ~tall(fred) [input p17]
24. wise(mary) <~> creative(mary) [input p23]
25. ~brave(fred) [input hypothesis]
31. ! [X0] : ((~curious(X0) & generous(X0)) | (~humble(X0) | tall(X0))) [ennf transformation 8]
32. ! [X0] : ((~curious(X0) & generous(X0)) | ~humble(X0) | tall(X0)) [flattening 31]
38. ! [X0] : ((humble(X0) | ~rich(X0)) | (brave(X0) <=> kind(X0))) [ennf transformation 13]
39. ! [X0] : (humble(X0) | ~rich(X0) | (brave(X0) <=> kind(X0))) [flattening 38]
50. ! [X0] : (((~rich(X0) | ~wise(X0)) | (~brave(X0) | generous(X0))) & ((brave(X0) & ~generous(X0)) | (rich(X0) & wise(X0)))) [nnf transformation 3]
51. ! [X0] : ((~rich(X0) | ~wise(X0) | ~brave(X0) | generous(X0)) & ((brave(X0) & ~generous(X0)) | (rich(X0) & wise(X0)))) [flattening 50]
52. ! [X0] : (((funny(X0) & ~patient(X0)) | (generous(X0) & ~patient(X0))) & ((~generous(X0) | patient(X0)) | (~funny(X0) | patient(X0)))) [nnf transformation 4]
53. ! [X0] : (((funny(X0) & ~patient(X0)) | (generous(X0) & ~patient(X0))) & (~generous(X0) | patient(X0) | ~funny(X0) | patient(X0))) [flattening 52]
64. ! [X0] : (humble(X0) | ~rich(X0) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) [nnf transformation 39]
66. ((kind(fred) & funny(fred)) | ! [X0] : (~tall(X0) & creative(X0))) & (? [X0] : (tall(X0) | ~creative(X0)) | (~kind(fred) | ~funny(fred))) [nnf transformation 16]
67. ((kind(fred) & funny(fred)) | ! [X0] : (~tall(X0) & creative(X0))) & (? [X0] : (tall(X0) | ~creative(X0)) | ~kind(fred) | ~funny(fred)) [flattening 66]
68. ((kind(fred) & funny(fred)) | ! [X0] : (~tall(X0) & creative(X0))) & (? [X1] : (tall(X1) | ~creative(X1)) | ~kind(fred) | ~funny(fred)) [rectify 67]
69. ? [X1] : (tall(X1) | ~creative(X1)) => (tall(sK4) | ~creative(sK4)) [choice axiom]
70. ((kind(fred) & funny(fred)) | ! [X0] : (~tall(X0) & creative(X0))) & ((tall(sK4) | ~creative(sK4)) | ~kind(fred) | ~funny(fred)) [skolemisation 68,69]
71. (~funny(mary) | wise(mary)) & (funny(mary) | ~wise(mary)) [nnf transformation 17]
81. (~creative(mary) | ~wise(mary)) & (creative(mary) | wise(mary)) [nnf transformation 24]
92. ~generous(X0) | wise(X0) [cnf transformation 51]
95. brave(X0) | rich(X0) [cnf transformation 51]
97. ~generous(X0) | patient(X0) | ~funny(X0) | patient(X0) [cnf transformation 53]
98. ~patient(X0) | ~patient(X0) [cnf transformation 53]
101. funny(X0) | generous(X0) [cnf transformation 53]
109. ~humble(X0) | generous(X0) | tall(X0) [cnf transformation 32]
123. humble(X0) | ~rich(X0) | brave(X0) | ~kind(X0) [cnf transformation 64]
129. funny(fred) | creative(X0) [cnf transformation 70]
131. kind(fred) | creative(X0) [cnf transformation 70]
134. ~funny(mary) | wise(mary) [cnf transformation 71]
135. ~tall(fred) [cnf transformation 18]
144. ~creative(mary) | ~wise(mary) [cnf transformation 81]
145. ~brave(fred) [cnf transformation 25]
147. ~generous(X0) | patient(X0) | ~funny(X0) [duplicate literal removal 97]
148. ~patient(X0) [duplicate literal removal 98]
167. ~funny(X0) | ~generous(X0) [subsumption resolution 147,148]
193. ~kind(X0) | brave(X0) | humble(X0) [subsumption resolution 123,95]
224. 17 <=> kind(fred) [avatar definition]
226. kind(fred) <- (17) [avatar component clause 224]
229. 18 <=> ! [X0] : creative(X0) [avatar definition]
230. creative(X0) <- (18) [avatar component clause 229]
231. 18 | 17 [avatar split clause 131,224,229]
233. 19 <=> funny(fred) [avatar definition]
235. funny(fred) <- (19) [avatar component clause 233]
237. 18 | 19 [avatar split clause 129,233,229]
248. 22 <=> wise(mary) [avatar definition]
249. ~wise(mary) <- (~22) [avatar component clause 248]
252. 23 <=> funny(mary) [avatar definition]
254. ~funny(mary) <- (~23) [avatar component clause 252]
255. 22 | ~23 [avatar split clause 134,252,248]
277. 28 <=> creative(mary) [avatar definition]
279. ~creative(mary) <- (~28) [avatar component clause 277]
280. ~22 | ~28 [avatar split clause 144,277,248]
301. ~generous(fred) <- (19) [resolution 167,235]
353. brave(fred) | humble(fred) <- (17) [resolution 193,226]
368. humble(fred) <- (17) [subsumption resolution 353,145]
393. generous(fred) | tall(fred) <- (17) [resolution 368,109]
394. tall(fred) <- (17, 19) [subsumption resolution 393,301]
395. $false <- (17, 19) [subsumption resolution 394,135]
396. ~17 | ~19 [avatar contradiction clause 395]
398. $false <- (18, ~28) [resolution 230,279]
399. ~18 | 28 [avatar contradiction clause 398]
401. generous(mary) <- (~23) [resolution 254,101]
410. wise(mary) <- (~23) [resolution 401,92]
411. $false <- (~22, ~23) [subsumption resolution 410,249]
412. 22 | 23 [avatar contradiction clause 411]
413. $false [avatar sat refutation 231,237,255,280,396,399,412]
% SZS output end Proof for 864778359676246690034878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not strong is both rich and not calm and vice versa.
If mary is either not rich or not brave then someone is either curious or humble.
Everyone who is both creative and quiet is both not brave and not funny and vice versa.
If alice is not patient or not humble then john is generous or happy and vice versa.
If john is kind then someone is both not funny and curious and vice versa.
Everyone who is not humble is either kind or old and vice versa.
Everyone who is both not quiet and not curious is not funny or not old.
If someone is old or patient then someone is either kind or old and vice versa.
If someone is both old and not tall then someone is brave.
Everyone who is both generous and old is either not brave or humble and vice versa.
If john is both kind and curious then john is either not tall or strong and vice versa.
If mary is either not rich or not curious then paul is curious and vice versa.
Everyone who is kind is not happy or brave.
Everyone who is old is either brave or calm and vice versa.
If mary is kind or wise then someone is both happy and not tall.
If lucy is both not calm and kind then someone is both strong and not wise and vice versa.
Someone is not kind.
Fred is happy.
Someone is both not strong and wise.
Mary is both not old and not happy.
Lucy is creative or not strong.
Alice is patient.
Someone is wise or not happy.
Paul is either not rich or patient. | Fred is rich. | neutral | (![X]:((~rich(X)&~strong(X))<=>(rich(X)&~calm(X))))&
(((~rich(mary)<~>~brave(mary)))=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((creative(X)&quiet(X))<=>(~brave(X)&~funny(X))))&
(((~patient(alice)|~humble(alice)))<=>((generous(john)|happy(john))))&
((kind(john))<=>(?[X]:((~funny(X)&curious(X)))))&
(![X]:(~humble(X)<=>(kind(X)<~>old(X))))&
(![X]:((~quiet(X)&~curious(X))=>(~funny(X)|~old(X))))&
((?[X]:((old(X)|patient(X))))<=>(?[X]:((kind(X)<~>old(X)))))&
((?[X]:((old(X)&~tall(X))))=>(?[X]:(brave(X))))&
(![X]:((generous(X)&old(X))<=>(~brave(X)<~>humble(X))))&
(((kind(john)&curious(john)))<=>((~tall(john)<~>strong(john))))&
(((~rich(mary)<~>~curious(mary)))<=>(curious(paul)))&
(![X]:(kind(X)=>(~happy(X)|brave(X))))&
(![X]:(old(X)<=>(brave(X)<~>calm(X))))&
(((kind(mary)|wise(mary)))=>(?[X]:((happy(X)&~tall(X)))))&
(((~calm(lucy)&kind(lucy)))<=>(?[X]:((strong(X)&~wise(X)))))&
(?[X]:(~kind(X)))&
(happy(fred))&
(?[X]:((~strong(X)&wise(X))))&
((~old(mary)&~happy(mary)))&
((creative(lucy)|~strong(lucy)))&
(patient(alice))&
(?[X]:((wise(X)|~happy(X))))&
((~rich(paul)<~>patient(paul))) | rich(fred) | [] | null | 0 |
Everyone who is funny is either rich or not creative and vice versa.
If fred is not curious or not quiet then mary is not patient and vice versa.
Everyone who is not strong is either not rich or wise.
Everyone who is creative is tall or funny and vice versa.
Everyone who is both not kind and not happy is not wise or calm.
Everyone who is either not funny or not patient is both not funny and not quiet and vice versa.
If mary is either wise or not tall then john is not humble.
Everyone who is either curious or calm is either creative or funny.
Everyone who is both rich and quiet is either calm or not quiet.
If someone is not funny then alice is both creative and curious and vice versa.
If fred is not quiet or not creative then mary is both happy and humble.
Everyone who is tall is both not calm and not tall and vice versa.
If someone is both not happy and strong then someone is not happy or not calm and vice versa.
If fred is not curious or patient then john is either not kind or not happy and vice versa.
If someone is not rich or not tall then someone is calm or patient and vice versa.
Someone is patient.
Someone is either rich or not funny.
Mary is both happy and rich.
John is not generous.
Someone is curious or calm.
Someone is quiet.
Someone is either not kind or generous. | John is not rich. | contradiction | (![X]:(funny(X)<=>(rich(X)<~>~creative(X))))&
(((~curious(fred)|~quiet(fred)))<=>(~patient(mary)))&
(![X]:(~strong(X)=>(~rich(X)<~>wise(X))))&
(![X]:(creative(X)<=>(tall(X)|funny(X))))&
(![X]:((~kind(X)&~happy(X))=>(~wise(X)|calm(X))))&
(![X]:((~funny(X)<~>~patient(X))<=>(~funny(X)&~quiet(X))))&
(((wise(mary)<~>~tall(mary)))=>(~humble(john)))&
(![X]:((curious(X)<~>calm(X))=>(creative(X)<~>funny(X))))&
(![X]:((rich(X)&quiet(X))=>(calm(X)<~>~quiet(X))))&
((?[X]:(~funny(X)))<=>((creative(alice)&curious(alice))))&
(((~quiet(fred)|~creative(fred)))=>((happy(mary)&humble(mary))))&
(![X]:(tall(X)<=>(~calm(X)&~tall(X))))&
((?[X]:((~happy(X)&strong(X))))<=>(?[X]:((~happy(X)|~calm(X)))))&
(((~curious(fred)|patient(fred)))<=>((~kind(john)<~>~happy(john))))&
((?[X]:((~rich(X)|~tall(X))))<=>(?[X]:((calm(X)|patient(X)))))&
(?[X]:(patient(X)))&
(?[X]:((rich(X)<~>~funny(X))))&
((happy(mary)&rich(mary)))&
(~generous(john))&
(?[X]:((curious(X)|calm(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~kind(X)<~>generous(X)))) | ~rich(john) | [
"p0",
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6691771513321666592316203
% SZS output start Proof for 6691771513321666592316203
1. ! [X0] : (funny(X0) <=> (rich(X0) <~> ~creative(X0))) [input p0]
4. ! [X0] : (creative(X0) <=> (funny(X0) | tall(X0))) [input p3]
12. ! [X0] : (tall(X0) <=> (~tall(X0) & ~calm(X0))) [input p11]
23. ~rich(john) [input hypothesis]
34. ! [X0] : ((funny(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | ~funny(X0))) [nnf transformation 1]
38. ! [X0] : ((creative(X0) | (~funny(X0) & ~tall(X0))) & ((funny(X0) | tall(X0)) | ~creative(X0))) [nnf transformation 4]
39. ! [X0] : ((creative(X0) | (~funny(X0) & ~tall(X0))) & (funny(X0) | tall(X0) | ~creative(X0))) [flattening 38]
50. ! [X0] : ((tall(X0) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | ~tall(X0))) [nnf transformation 12]
51. ! [X0] : ((tall(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | ~tall(X0))) [flattening 50]
76. ~creative(X0) | rich(X0) | ~funny(X0) [cnf transformation 34]
79. creative(X0) | rich(X0) | funny(X0) [cnf transformation 34]
85. ~creative(X0) | tall(X0) | funny(X0) [cnf transformation 39]
87. ~funny(X0) | creative(X0) [cnf transformation 39]
111. ~tall(X0) | ~tall(X0) [cnf transformation 51]
138. ~rich(john) [cnf transformation 23]
139. ~tall(X0) [duplicate literal removal 111]
332. tall(X0) | funny(X0) | rich(X0) | funny(X0) [resolution 85,79]
333. tall(X0) | funny(X0) | rich(X0) [duplicate literal removal 332]
337. rich(X0) | funny(X0) [subsumption resolution 333,139]
525. funny(john) [resolution 337,138]
563. creative(john) [resolution 525,87]
582. rich(john) | ~funny(john) [resolution 563,76]
583. ~funny(john) [subsumption resolution 582,138]
584. $false [subsumption resolution 583,525]
% SZS output end Proof for 6691771513321666592316203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either humble or not happy is either not quiet or calm.
Everyone who is either curious or not wise is either not brave or not rich and vice versa.
Everyone who is either not creative or not strong is either not tall or patient.
If someone is both not kind and not rich then mary is either not kind or quiet and vice versa.
If john is both calm and curious then someone is both old and generous and vice versa.
Everyone who is either humble or generous is both rich and not patient and vice versa.
Everyone who is either not generous or not tall is funny and vice versa.
Everyone who is not creative or humble is not generous or not calm.
Everyone who is happy is funny and vice versa.
If fred is curious then someone is not wise and vice versa.
Everyone who is not patient is tall.
Everyone who is either strong or not humble is either funny or not old and vice versa.
Everyone who is not tall is both humble and creative.
Everyone who is both not tall and tall is not humble or not quiet.
If someone is both humble and not wise then someone is rich and vice versa.
Everyone who is not tall is either not kind or not calm and vice versa.
Mary is wise.
Paul is either funny or calm.
Fred is funny.
Alice is funny or not kind.
Alice is both old and curious.
Susan is both quiet and not patient.
Someone is either not curious or not rich.
Fred is both wise and rich. | John is quiet. | neutral | (![X]:((humble(X)<~>~happy(X))=>(~quiet(X)<~>calm(X))))&
(![X]:((curious(X)<~>~wise(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:((~creative(X)<~>~strong(X))=>(~tall(X)<~>patient(X))))&
((?[X]:((~kind(X)&~rich(X))))<=>((~kind(mary)<~>quiet(mary))))&
(((calm(john)&curious(john)))<=>(?[X]:((old(X)&generous(X)))))&
(![X]:((humble(X)<~>generous(X))<=>(rich(X)&~patient(X))))&
(![X]:((~generous(X)<~>~tall(X))<=>funny(X)))&
(![X]:((~creative(X)|humble(X))=>(~generous(X)|~calm(X))))&
(![X]:(happy(X)<=>funny(X)))&
((curious(fred))<=>(?[X]:(~wise(X))))&
(![X]:(~patient(X)=>tall(X)))&
(![X]:((strong(X)<~>~humble(X))<=>(funny(X)<~>~old(X))))&
(![X]:(~tall(X)=>(humble(X)&creative(X))))&
(![X]:((~tall(X)&tall(X))=>(~humble(X)|~quiet(X))))&
((?[X]:((humble(X)&~wise(X))))<=>(?[X]:(rich(X))))&
(![X]:(~tall(X)<=>(~kind(X)<~>~calm(X))))&
(wise(mary))&
((funny(paul)<~>calm(paul)))&
(funny(fred))&
((funny(alice)|~kind(alice)))&
((old(alice)&curious(alice)))&
((quiet(susan)&~patient(susan)))&
(?[X]:((~curious(X)<~>~rich(X))))&
((wise(fred)&rich(fred))) | quiet(john) | [] | null | 0 |
Everyone who is not patient is both humble and funny and vice versa. Everyone who is wise is either not tall or happy and vice versa. If someone is not strong or not calm then fred is either not quiet or funny and vice versa. Everyone who is both not quiet and patient is either not rich or humble and vice versa. Everyone who is both kind and funny is either not calm or kind. If someone is calm or kind then susan is either funny or generous and vice versa. Everyone who is either not funny or quiet is not quiet and vice versa. Everyone who is not tall is either not patient or not rich. Everyone who is not humble or funny is both not tall and not happy and vice versa. Everyone who is happy or wise is both generous and not tall and vice versa. If someone is either not curious or calm then someone is both not strong and funny and vice versa. If someone is both not generous and not happy then lucy is not tall. Everyone who is either quiet or strong is old. Everyone who is either not rich or not calm is both not old and kind and vice versa. Everyone who is wise or humble is either calm or not creative and vice versa. If alice is both curious and not humble then someone is not patient and vice versa. Alice is both generous and not rich. Someone is old. Someone is either patient or not calm. Fred is either funny or quiet. Someone is either not funny or happy. Someone is not brave or old. John is strong. | Fred is quiet. | entailment | (![X]:(~patient(X)<=>(humble(X)&funny(X))))&
(![X]:(wise(X)<=>(~tall(X)<~>happy(X))))&
((?[X]:((~strong(X)|~calm(X))))<=>((~quiet(fred)<~>funny(fred))))&
(![X]:((~quiet(X)&patient(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((kind(X)&funny(X))=>(~calm(X)<~>kind(X))))&
((?[X]:((calm(X)|kind(X))))<=>((funny(susan)<~>generous(susan))))&
(![X]:((~funny(X)<~>quiet(X))<=>~quiet(X)))&
(![X]:(~tall(X)=>(~patient(X)<~>~rich(X))))&
(![X]:((~humble(X)|funny(X))<=>(~tall(X)&~happy(X))))&
(![X]:((happy(X)|wise(X))<=>(generous(X)&~tall(X))))&
((?[X]:((~curious(X)<~>calm(X))))<=>(?[X]:((~strong(X)&funny(X)))))&
((?[X]:((~generous(X)&~happy(X))))=>(~tall(lucy)))&
(![X]:((quiet(X)<~>strong(X))=>old(X)))&
(![X]:((~rich(X)<~>~calm(X))<=>(~old(X)&kind(X))))&
(![X]:((wise(X)|humble(X))<=>(calm(X)<~>~creative(X))))&
(((curious(alice)&~humble(alice)))<=>(?[X]:(~patient(X))))&
((generous(alice)&~rich(alice)))&
(?[X]:(old(X)))&
(?[X]:((patient(X)<~>~calm(X))))&
((funny(fred)<~>quiet(fred)))&
(?[X]:((~funny(X)<~>happy(X))))&
(?[X]:((~brave(X)|old(X))))&
(strong(john)) | quiet(fred) | [
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2711284288318427770384677
% SZS output start Proof for 2711284288318427770384677
7. ! [X0] : ((~funny(X0) <~> quiet(X0)) <=> ~quiet(X0)) [input p6]
20. funny(fred) <~> quiet(fred) [input p19]
24. ~quiet(fred) [input hypothesis]
46. ! [X0] : ((((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | quiet(X0)) & (~quiet(X0) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0))))) [nnf transformation 7]
72. (~quiet(fred) | ~funny(fred)) & (quiet(fred) | funny(fred)) [nnf transformation 20]
104. ~quiet(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 46]
105. quiet(X0) | ~funny(X0) | quiet(X0) [cnf transformation 46]
148. quiet(fred) | funny(fred) [cnf transformation 72]
153. ~quiet(fred) [cnf transformation 24]
154. ~quiet(X0) | ~funny(X0) [duplicate literal removal 104]
155. quiet(X0) | ~funny(X0) [duplicate literal removal 105]
162. 2 <=> quiet(fred) [avatar definition]
215. ~funny(X0) [subsumption resolution 154,155]
258. quiet(fred) [subsumption resolution 148,215]
259. 2 [avatar split clause 258,162]
261. ~2 [avatar split clause 153,162]
262. $false [avatar sat refutation 259,261]
% SZS output end Proof for 2711284288318427770384677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is funny and vice versa.
Everyone who is not funny is either tall or kind and vice versa.
If someone is not humble then someone is brave and vice versa.
Everyone who is calm is both creative and not calm.
Everyone who is either not tall or calm is both tall and wise.
Everyone who is either strong or not patient is both creative and not brave and vice versa.
If paul is either curious or old then susan is happy and vice versa.
Everyone who is both tall and not happy is not old or not rich.
Everyone who is not funny or not generous is happy or not wise.
If lucy is not humble or wise then paul is either not rich or not generous and vice versa.
If someone is happy or humble then paul is both not wise and wise.
Everyone who is not creative is rich.
If someone is either creative or not generous then paul is not happy or wise and vice versa.
Everyone who is funny is both quiet and generous.
If paul is kind then someone is either not patient or not wise.
Everyone who is calm is either patient or humble.
Someone is either happy or not brave.
Susan is both quiet and not wise.
John is creative.
Mary is both not humble and not strong.
Someone is brave.
Paul is either not curious or not creative.
Someone is not kind or humble. | Paul is old. | contradiction | (![X]:(humble(X)<=>funny(X)))&
(![X]:(~funny(X)<=>(tall(X)<~>kind(X))))&
((?[X]:(~humble(X)))<=>(?[X]:(brave(X))))&
(![X]:(calm(X)=>(creative(X)&~calm(X))))&
(![X]:((~tall(X)<~>calm(X))=>(tall(X)&wise(X))))&
(![X]:((strong(X)<~>~patient(X))<=>(creative(X)&~brave(X))))&
(((curious(paul)<~>old(paul)))<=>(happy(susan)))&
(![X]:((tall(X)&~happy(X))=>(~old(X)|~rich(X))))&
(![X]:((~funny(X)|~generous(X))=>(happy(X)|~wise(X))))&
(((~humble(lucy)|wise(lucy)))<=>((~rich(paul)<~>~generous(paul))))&
((?[X]:((happy(X)|humble(X))))=>((~wise(paul)&wise(paul))))&
(![X]:(~creative(X)=>rich(X)))&
((?[X]:((creative(X)<~>~generous(X))))<=>((~happy(paul)|wise(paul))))&
(![X]:(funny(X)=>(quiet(X)&generous(X))))&
((kind(paul))=>(?[X]:((~patient(X)<~>~wise(X)))))&
(![X]:(calm(X)=>(patient(X)<~>humble(X))))&
(?[X]:((happy(X)<~>~brave(X))))&
((quiet(susan)&~wise(susan)))&
(creative(john))&
((~humble(mary)&~strong(mary)))&
(?[X]:(brave(X)))&
((~curious(paul)<~>~creative(paul)))&
(?[X]:((~kind(X)|humble(X)))) | old(paul) | [
"p3",
"p4",
"p6",
"p7",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3644825942522577278803689
% SZS output start Proof for 3644825942522577278803689
4. ! [X0] : (calm(X0) => (~calm(X0) & creative(X0))) [input p3]
5. ! [X0] : ((~tall(X0) <~> calm(X0)) => (wise(X0) & tall(X0))) [input p4]
7. (curious(paul) <~> old(paul)) <=> happy(susan) [input p6]
8. ! [X0] : ((~happy(X0) & tall(X0)) => (~rich(X0) | ~old(X0))) [input p7]
11. ? [X0] : (humble(X0) | happy(X0)) => (wise(paul) & ~wise(paul)) [input p10]
12. ! [X0] : (~creative(X0) => rich(X0)) [input p11]
22. ~curious(paul) <~> ~creative(paul) [input p21]
24. old(paul) [input hypothesis]
28. ! [X0] : ((~calm(X0) & creative(X0)) | ~calm(X0)) [ennf transformation 4]
29. ! [X0] : ((wise(X0) & tall(X0)) | (~tall(X0) <=> calm(X0))) [ennf transformation 5]
30. ! [X0] : ((~rich(X0) | ~old(X0)) | (happy(X0) | ~tall(X0))) [ennf transformation 8]
31. ! [X0] : (~rich(X0) | ~old(X0) | happy(X0) | ~tall(X0)) [flattening 30]
34. (wise(paul) & ~wise(paul)) | ! [X0] : (~humble(X0) & ~happy(X0)) [ennf transformation 11]
35. ! [X0] : (rich(X0) | creative(X0)) [ennf transformation 12]
46. ! [X0] : ((wise(X0) & tall(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0)))) [nnf transformation 29]
49. (((~old(paul) | ~curious(paul)) & (old(paul) | curious(paul))) | ~happy(susan)) & (happy(susan) | ((curious(paul) | ~old(paul)) & (old(paul) | ~curious(paul)))) [nnf transformation 7]
66. (creative(paul) | curious(paul)) & (~creative(paul) | ~curious(paul)) [nnf transformation 22]
78. ~calm(X0) | ~calm(X0) [cnf transformation 28]
79. tall(X0) | calm(X0) | tall(X0) [cnf transformation 46]
90. happy(susan) | curious(paul) | ~old(paul) [cnf transformation 49]
93. ~rich(X0) | ~old(X0) | happy(X0) | ~tall(X0) [cnf transformation 31]
102. ~wise(paul) | ~happy(X0) [cnf transformation 34]
104. wise(paul) | ~happy(X0) [cnf transformation 34]
106. rich(X0) | creative(X0) [cnf transformation 35]
125. ~creative(paul) | ~curious(paul) [cnf transformation 66]
128. old(paul) [cnf transformation 24]
129. tall(X0) | calm(X0) [duplicate literal removal 79]
130. ~calm(X0) [duplicate literal removal 78]
148. tall(X0) [subsumption resolution 129,130]
150. 5 <=> happy(susan) [avatar definition]
151. happy(susan) <- (5) [avatar component clause 150]
154. 6 <=> curious(paul) [avatar definition]
158. 7 <=> old(paul) [avatar definition]
159. old(paul) <- (7) [avatar component clause 158]
163. ~7 | 6 | 5 [avatar split clause 90,150,154,158]
165. ~rich(X0) | ~old(X0) | happy(X0) [subsumption resolution 93,148]
171. 9 <=> rich(paul) [avatar definition]
172. rich(paul) <- (9) [avatar component clause 171]
173. ~rich(paul) <- (~9) [avatar component clause 171]
192. 13 <=> wise(paul) [avatar definition]
197. 14 <=> ! [X0] : ~happy(X0) [avatar definition]
198. ~happy(X0) <- (14) [avatar component clause 197]
199. 14 | 13 [avatar split clause 104,192,197]
201. 14 | ~13 [avatar split clause 102,192,197]
251. 25 <=> creative(paul) [avatar definition]
252. ~creative(paul) <- (~25) [avatar component clause 251]
255. ~6 | ~25 [avatar split clause 125,251,154]
265. 7 [avatar split clause 128,158]
266. creative(paul) <- (~9) [resolution 106,173]
267. $false <- (~9, ~25) [subsumption resolution 266,252]
268. 9 | 25 [avatar contradiction clause 267]
323. $false <- (5, 14) [subsumption resolution 151,198]
324. ~5 | ~14 [avatar contradiction clause 323]
328. ~old(paul) | happy(paul) <- (9) [resolution 165,172]
330. happy(paul) <- (7, 9) [subsumption resolution 328,159]
331. $false <- (7, 9, 14) [subsumption resolution 330,198]
332. ~7 | ~9 | ~14 [avatar contradiction clause 331]
333. $false [avatar sat refutation 163,199,201,255,265,268,324,332]
% SZS output end Proof for 3644825942522577278803689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or kind is not old. If someone is not kind then someone is not brave or creative. If someone is either not funny or wise then lucy is both not patient and wise and vice versa. Everyone who is either brave or not curious is calm or not wise. Everyone who is creative is calm or not strong and vice versa. Everyone who is not creative or not funny is brave and vice versa. If fred is brave then someone is funny and vice versa. Everyone who is both not calm and patient is either not curious or not calm and vice versa. Everyone who is both old and not curious is rich. If susan is both rich and not quiet then alice is either not patient or not happy and vice versa. If fred is not funny then someone is creative or not old and vice versa. Everyone who is both tall and not humble is either brave or curious and vice versa. If john is either rich or not tall then mary is either generous or creative. If paul is rich then someone is both not tall and wise and vice versa. Everyone who is either not curious or generous is either funny or not curious. Everyone who is either old or not generous is old or kind and vice versa. Mary is old or not patient. Someone is not tall. John is either not old or curious. Fred is generous. Someone is strong. Someone is not strong. | Paul is not generous. | neutral | (![X]:((generous(X)|kind(X))=>~old(X)))&
((?[X]:(~kind(X)))=>(?[X]:((~brave(X)|creative(X)))))&
((?[X]:((~funny(X)<~>wise(X))))<=>((~patient(lucy)&wise(lucy))))&
(![X]:((brave(X)<~>~curious(X))=>(calm(X)|~wise(X))))&
(![X]:(creative(X)<=>(calm(X)|~strong(X))))&
(![X]:((~creative(X)|~funny(X))<=>brave(X)))&
((brave(fred))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)&patient(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((old(X)&~curious(X))=>rich(X)))&
(((rich(susan)&~quiet(susan)))<=>((~patient(alice)<~>~happy(alice))))&
((~funny(fred))<=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((tall(X)&~humble(X))<=>(brave(X)<~>curious(X))))&
(((rich(john)<~>~tall(john)))=>((generous(mary)<~>creative(mary))))&
((rich(paul))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((~curious(X)<~>generous(X))=>(funny(X)<~>~curious(X))))&
(![X]:((old(X)<~>~generous(X))<=>(old(X)|kind(X))))&
((old(mary)|~patient(mary)))&
(?[X]:(~tall(X)))&
((~old(john)<~>curious(john)))&
(generous(fred))&
(?[X]:(strong(X)))&
(?[X]:(~strong(X))) | ~generous(paul) | [] | null | 0 |
Everyone who is not creative is curious or not kind and vice versa.
If someone is quiet or not strong then susan is patient or not quiet and vice versa.
Everyone who is both not patient and not quiet is both not old and patient and vice versa.
Everyone who is both creative and strong is humble and vice versa.
If someone is either tall or not strong then alice is patient or not creative and vice versa.
Everyone who is not rich or brave is strong and vice versa.
If john is either not strong or not happy then lucy is not humble or not strong and vice versa.
Everyone who is not tall or generous is patient and vice versa.
If paul is either creative or not wise then mary is calm.
Everyone who is quiet or strong is both not happy and old.
Everyone who is rich or old is not funny.
If someone is either patient or not happy then someone is both strong and not creative.
If someone is either not old or old then paul is not creative or kind.
Everyone who is quiet or creative is humble or curious.
Everyone who is not humble is either rich or strong.
If someone is not patient then someone is not kind or not strong and vice versa.
Mary is both calm and not quiet.
Paul is either kind or not brave.
Alice is kind.
Mary is funny or not generous.
Someone is either not rich or not calm.
John is both happy and not curious.
Someone is not strong or happy. | Paul is wise. | neutral | (![X]:(~creative(X)<=>(curious(X)|~kind(X))))&
((?[X]:((quiet(X)|~strong(X))))<=>((patient(susan)|~quiet(susan))))&
(![X]:((~patient(X)&~quiet(X))<=>(~old(X)&patient(X))))&
(![X]:((creative(X)&strong(X))<=>humble(X)))&
((?[X]:((tall(X)<~>~strong(X))))<=>((patient(alice)|~creative(alice))))&
(![X]:((~rich(X)|brave(X))<=>strong(X)))&
(((~strong(john)<~>~happy(john)))<=>((~humble(lucy)|~strong(lucy))))&
(![X]:((~tall(X)|generous(X))<=>patient(X)))&
(((creative(paul)<~>~wise(paul)))=>(calm(mary)))&
(![X]:((quiet(X)|strong(X))=>(~happy(X)&old(X))))&
(![X]:((rich(X)|old(X))=>~funny(X)))&
((?[X]:((patient(X)<~>~happy(X))))=>(?[X]:((strong(X)&~creative(X)))))&
((?[X]:((~old(X)<~>old(X))))=>((~creative(paul)|kind(paul))))&
(![X]:((quiet(X)|creative(X))=>(humble(X)|curious(X))))&
(![X]:(~humble(X)=>(rich(X)<~>strong(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~kind(X)|~strong(X)))))&
((calm(mary)&~quiet(mary)))&
((kind(paul)<~>~brave(paul)))&
(kind(alice))&
((funny(mary)|~generous(mary)))&
(?[X]:((~rich(X)<~>~calm(X))))&
((happy(john)&~curious(john)))&
(?[X]:((~strong(X)|happy(X)))) | wise(paul) | [] | null | 0 |
If someone is not kind then someone is not calm or funny and vice versa.
Everyone who is not funny or not rich is not patient or not quiet and vice versa.
If someone is not old then someone is not creative.
Everyone who is either not kind or not calm is both old and not calm and vice versa.
Everyone who is not funny is not happy or not quiet.
If lucy is both tall and wise then someone is not tall or not calm.
If john is tall then someone is either not patient or not funny and vice versa.
If someone is not kind then lucy is curious and vice versa.
Everyone who is both happy and not brave is strong and vice versa.
Everyone who is not creative is both creative and not brave.
If someone is not happy then someone is brave and vice versa.
Everyone who is both curious and not strong is patient or not patient.
If someone is not curious or not quiet then someone is either not generous or not brave and vice versa.
If someone is humble or creative then someone is either calm or rich and vice versa.
If john is both not quiet and quiet then someone is either brave or tall.
If someone is curious or patient then alice is either rich or not creative and vice versa.
Susan is both not humble and brave.
Alice is not creative or not strong.
Someone is brave or tall.
Alice is not rich or patient.
John is either not rich or not happy.
Someone is both happy and generous. | Susan is rich. | neutral | ((?[X]:(~kind(X)))<=>(?[X]:((~calm(X)|funny(X)))))&
(![X]:((~funny(X)|~rich(X))<=>(~patient(X)|~quiet(X))))&
((?[X]:(~old(X)))=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)<~>~calm(X))<=>(old(X)&~calm(X))))&
(![X]:(~funny(X)=>(~happy(X)|~quiet(X))))&
(((tall(lucy)&wise(lucy)))=>(?[X]:((~tall(X)|~calm(X)))))&
((tall(john))<=>(?[X]:((~patient(X)<~>~funny(X)))))&
((?[X]:(~kind(X)))<=>(curious(lucy)))&
(![X]:((happy(X)&~brave(X))<=>strong(X)))&
(![X]:(~creative(X)=>(creative(X)&~brave(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(brave(X))))&
(![X]:((curious(X)&~strong(X))=>(patient(X)|~patient(X))))&
((?[X]:((~curious(X)|~quiet(X))))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
((?[X]:((humble(X)|creative(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(((~quiet(john)&quiet(john)))=>(?[X]:((brave(X)<~>tall(X)))))&
((?[X]:((curious(X)|patient(X))))<=>((rich(alice)<~>~creative(alice))))&
((~humble(susan)&brave(susan)))&
((~creative(alice)|~strong(alice)))&
(?[X]:((brave(X)|tall(X))))&
((~rich(alice)|patient(alice)))&
((~rich(john)<~>~happy(john)))&
(?[X]:((happy(X)&generous(X)))) | rich(susan) | [] | null | 0 |
If someone is either not tall or not happy then susan is either funny or not calm and vice versa. Everyone who is both not tall and rich is not brave or funny and vice versa. Everyone who is either not old or not brave is both not curious and patient. If someone is not kind or patient then someone is patient or tall. Everyone who is both strong and not brave is either kind or old. If paul is not humble then susan is not humble or not quiet. Everyone who is strong or not tall is either not tall or not calm. Everyone who is both not calm and not generous is either not rich or tall. Everyone who is either not tall or tall is not wise or old and vice versa. If someone is not happy then john is both not strong and kind and vice versa. If lucy is both not brave and not funny then someone is not rich or generous. Everyone who is patient is not brave. Everyone who is not kind is both not rich and curious. If paul is both not kind and not quiet then someone is either happy or creative and vice versa. If someone is wise then someone is not funny or not tall. If mary is both funny and not creative then lucy is creative. Paul is funny or not old. Someone is both happy and kind. Someone is either old or kind. Someone is wise. Paul is not patient. John is both not wise and curious. Mary is not happy or not strong. John is not rich or not curious. | John is not old. | contradiction | ((?[X]:((~tall(X)<~>~happy(X))))<=>((funny(susan)<~>~calm(susan))))&
(![X]:((~tall(X)&rich(X))<=>(~brave(X)|funny(X))))&
(![X]:((~old(X)<~>~brave(X))=>(~curious(X)&patient(X))))&
((?[X]:((~kind(X)|patient(X))))=>(?[X]:((patient(X)|tall(X)))))&
(![X]:((strong(X)&~brave(X))=>(kind(X)<~>old(X))))&
((~humble(paul))=>((~humble(susan)|~quiet(susan))))&
(![X]:((strong(X)|~tall(X))=>(~tall(X)<~>~calm(X))))&
(![X]:((~calm(X)&~generous(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~tall(X)<~>tall(X))<=>(~wise(X)|old(X))))&
((?[X]:(~happy(X)))<=>((~strong(john)&kind(john))))&
(((~brave(lucy)&~funny(lucy)))=>(?[X]:((~rich(X)|generous(X)))))&
(![X]:(patient(X)=>~brave(X)))&
(![X]:(~kind(X)=>(~rich(X)&curious(X))))&
(((~kind(paul)&~quiet(paul)))<=>(?[X]:((happy(X)<~>creative(X)))))&
((?[X]:(wise(X)))=>(?[X]:((~funny(X)|~tall(X)))))&
(((funny(mary)&~creative(mary)))=>(creative(lucy)))&
((funny(paul)|~old(paul)))&
(?[X]:((happy(X)&kind(X))))&
(?[X]:((old(X)<~>kind(X))))&
(?[X]:(wise(X)))&
(~patient(paul))&
((~wise(john)&curious(john)))&
((~happy(mary)|~strong(mary)))&
((~rich(john)|~curious(john))) | ~old(john) | [
"p1",
"p2",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5328195467328024941918025
% SZS output start Proof for 5328195467328024941918025
2. ! [X0] : ((rich(X0) & ~tall(X0)) <=> (funny(X0) | ~brave(X0))) [input p1]
3. ! [X0] : ((~old(X0) <~> ~brave(X0)) => (patient(X0) & ~curious(X0))) [input p2]
22. curious(john) & ~wise(john) [input p21]
24. ~curious(john) | ~rich(john) [input p23]
25. ~old(john) [input hypothesis]
30. ! [X0] : ((patient(X0) & ~curious(X0)) | (~old(X0) <=> ~brave(X0))) [ennf transformation 3]
46. ! [X0] : (((rich(X0) & ~tall(X0)) | (~funny(X0) & brave(X0))) & ((funny(X0) | ~brave(X0)) | (~rich(X0) | tall(X0)))) [nnf transformation 2]
47. ! [X0] : (((rich(X0) & ~tall(X0)) | (~funny(X0) & brave(X0))) & (funny(X0) | ~brave(X0) | ~rich(X0) | tall(X0))) [flattening 46]
48. ! [X0] : ((patient(X0) & ~curious(X0)) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) [nnf transformation 30]
87. brave(X0) | rich(X0) [cnf transformation 47]
89. ~curious(X0) | ~brave(X0) | old(X0) [cnf transformation 48]
130. curious(john) [cnf transformation 22]
132. ~curious(john) | ~rich(john) [cnf transformation 24]
133. ~old(john) [cnf transformation 25]
284. ~rich(john) [subsumption resolution 132,130]
295. ~brave(john) | old(john) [resolution 89,130]
297. ~brave(john) [subsumption resolution 295,133]
298. rich(john) [resolution 297,87]
299. $false [subsumption resolution 298,284]
% SZS output end Proof for 5328195467328024941918025
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and vice versa.
If someone is both wise and not patient then someone is not quiet or not brave and vice versa.
If john is tall or not funny then alice is wise or not creative and vice versa.
If someone is both funny and wise then alice is either not patient or not wise.
Everyone who is not brave or not old is not calm and vice versa.
Everyone who is either not tall or curious is both strong and not creative and vice versa.
If fred is not funny then paul is not old.
If fred is either rich or humble then someone is strong or rich.
Everyone who is either quiet or calm is kind and vice versa.
Everyone who is both curious and not patient is tall.
Everyone who is both not generous and not rich is both calm and not creative and vice versa.
Everyone who is either wise or humble is both not curious and not wise and vice versa.
If paul is either not happy or not quiet then someone is patient and vice versa.
Everyone who is not calm is either not happy or not wise and vice versa.
Everyone who is not tall or not humble is both strong and generous and vice versa.
If mary is either quiet or not brave then paul is rich.
Someone is not kind or not curious.
Mary is not tall.
Lucy is either not funny or quiet.
Someone is not creative or not funny.
Someone is old or brave.
Susan is not strong or not kind.
Someone is not old or generous. | Mary is not calm. | entailment | (![X]:(~strong(X)<=>creative(X)))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((~quiet(X)|~brave(X)))))&
(((tall(john)|~funny(john)))<=>((wise(alice)|~creative(alice))))&
((?[X]:((funny(X)&wise(X))))=>((~patient(alice)<~>~wise(alice))))&
(![X]:((~brave(X)|~old(X))<=>~calm(X)))&
(![X]:((~tall(X)<~>curious(X))<=>(strong(X)&~creative(X))))&
((~funny(fred))=>(~old(paul)))&
(((rich(fred)<~>humble(fred)))=>(?[X]:((strong(X)|rich(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>kind(X)))&
(![X]:((curious(X)&~patient(X))=>tall(X)))&
(![X]:((~generous(X)&~rich(X))<=>(calm(X)&~creative(X))))&
(![X]:((wise(X)<~>humble(X))<=>(~curious(X)&~wise(X))))&
(((~happy(paul)<~>~quiet(paul)))<=>(?[X]:(patient(X))))&
(![X]:(~calm(X)<=>(~happy(X)<~>~wise(X))))&
(![X]:((~tall(X)|~humble(X))<=>(strong(X)&generous(X))))&
(((quiet(mary)<~>~brave(mary)))=>(rich(paul)))&
(?[X]:((~kind(X)|~curious(X))))&
(~tall(mary))&
((~funny(lucy)<~>quiet(lucy)))&
(?[X]:((~creative(X)|~funny(X))))&
(?[X]:((old(X)|brave(X))))&
((~strong(susan)|~kind(susan)))&
(?[X]:((~old(X)|generous(X)))) | ~calm(mary) | [
"p0",
"p10",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 486841928807937540104446
% SZS output start Proof for 486841928807937540104446
1. ! [X0] : (~strong(X0) <=> creative(X0)) [input p0]
11. ! [X0] : ((~rich(X0) & ~generous(X0)) <=> (~creative(X0) & calm(X0))) [input p10]
15. ! [X0] : ((~humble(X0) | ~tall(X0)) <=> (generous(X0) & strong(X0))) [input p14]
18. ~tall(mary) [input p17]
24. calm(mary) [input hypothesis]
34. ! [X0] : ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0))) [nnf transformation 1]
51. ! [X0] : (((~rich(X0) & ~generous(X0)) | (creative(X0) | ~calm(X0))) & ((~creative(X0) & calm(X0)) | (rich(X0) | generous(X0)))) [nnf transformation 11]
52. ! [X0] : (((~rich(X0) & ~generous(X0)) | creative(X0) | ~calm(X0)) & ((~creative(X0) & calm(X0)) | rich(X0) | generous(X0))) [flattening 51]
60. ! [X0] : (((~humble(X0) | ~tall(X0)) | (~generous(X0) | ~strong(X0))) & ((generous(X0) & strong(X0)) | (humble(X0) & tall(X0)))) [nnf transformation 15]
61. ! [X0] : ((~humble(X0) | ~tall(X0) | ~generous(X0) | ~strong(X0)) & ((generous(X0) & strong(X0)) | (humble(X0) & tall(X0)))) [flattening 60]
73. ~creative(X0) | ~strong(X0) [cnf transformation 34]
102. ~generous(X0) | creative(X0) | ~calm(X0) [cnf transformation 52]
118. tall(X0) | strong(X0) [cnf transformation 61]
120. generous(X0) | tall(X0) [cnf transformation 61]
126. ~tall(mary) [cnf transformation 18]
133. calm(mary) [cnf transformation 24]
315. strong(mary) [resolution 118,126]
338. ~calm(X2) | creative(X2) | tall(X2) [resolution 102,120]
418. 50 <=> creative(mary) [avatar definition]
420. creative(mary) <- (50) [avatar component clause 418]
422. creative(mary) | tall(mary) [resolution 338,133]
423. creative(mary) [subsumption resolution 422,126]
424. 50 [avatar split clause 423,418]
431. ~strong(mary) <- (50) [resolution 420,73]
444. $false <- (50) [subsumption resolution 431,315]
445. ~50 [avatar contradiction clause 444]
446. $false [avatar sat refutation 424,445]
% SZS output end Proof for 486841928807937540104446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or old is either not quiet or happy and vice versa. If alice is either not humble or strong then fred is not creative or strong and vice versa. Everyone who is not old is either not quiet or rich and vice versa. Everyone who is not curious or not kind is not brave. Everyone who is either not generous or not funny is either wise or not humble. Everyone who is not tall or old is either calm or humble and vice versa. Everyone who is both not rich and not kind is brave and vice versa. If alice is either not tall or funny then someone is not tall and vice versa. Everyone who is either wise or calm is either wise or tall. Everyone who is not curious or not creative is both tall and calm and vice versa. If someone is not generous or not quiet then susan is not generous or not kind. Everyone who is tall or not old is strong or humble. Everyone who is either not calm or rich is not rich or not strong and vice versa. Everyone who is not calm is generous or patient. Everyone who is either wise or not calm is both happy and not patient and vice versa. If someone is not strong then john is not rich or wise and vice versa. Someone is not funny or not quiet. Someone is either wise or humble. Someone is quiet. Lucy is not quiet or patient. Someone is either humble or not kind. Susan is both kind and wise. Lucy is not strong. Susan is not strong or not wise. | Susan is humble. | entailment | (![X]:((happy(X)|old(X))<=>(~quiet(X)<~>happy(X))))&
(((~humble(alice)<~>strong(alice)))<=>((~creative(fred)|strong(fred))))&
(![X]:(~old(X)<=>(~quiet(X)<~>rich(X))))&
(![X]:((~curious(X)|~kind(X))=>~brave(X)))&
(![X]:((~generous(X)<~>~funny(X))=>(wise(X)<~>~humble(X))))&
(![X]:((~tall(X)|old(X))<=>(calm(X)<~>humble(X))))&
(![X]:((~rich(X)&~kind(X))<=>brave(X)))&
(((~tall(alice)<~>funny(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((wise(X)<~>calm(X))=>(wise(X)<~>tall(X))))&
(![X]:((~curious(X)|~creative(X))<=>(tall(X)&calm(X))))&
((?[X]:((~generous(X)|~quiet(X))))=>((~generous(susan)|~kind(susan))))&
(![X]:((tall(X)|~old(X))=>(strong(X)|humble(X))))&
(![X]:((~calm(X)<~>rich(X))<=>(~rich(X)|~strong(X))))&
(![X]:(~calm(X)=>(generous(X)|patient(X))))&
(![X]:((wise(X)<~>~calm(X))<=>(happy(X)&~patient(X))))&
((?[X]:(~strong(X)))<=>((~rich(john)|wise(john))))&
(?[X]:((~funny(X)|~quiet(X))))&
(?[X]:((wise(X)<~>humble(X))))&
(?[X]:(quiet(X)))&
((~quiet(lucy)|patient(lucy)))&
(?[X]:((humble(X)<~>~kind(X))))&
((kind(susan)&wise(susan)))&
(~strong(lucy))&
((~strong(susan)|~wise(susan))) | humble(susan) | [
"p0",
"p2",
"p5",
"p11",
"p12",
"p14",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5003768816170737267362940
% SZS output start Proof for 5003768816170737267362940
1. ! [X0] : ((old(X0) | happy(X0)) <=> (~quiet(X0) <~> happy(X0))) [input p0]
3. ! [X0] : (~old(X0) <=> (~quiet(X0) <~> rich(X0))) [input p2]
6. ! [X0] : ((old(X0) | ~tall(X0)) <=> (calm(X0) <~> humble(X0))) [input p5]
12. ! [X0] : ((~old(X0) | tall(X0)) => (humble(X0) | strong(X0))) [input p11]
13. ! [X0] : ((~calm(X0) <~> rich(X0)) <=> (~strong(X0) | ~rich(X0))) [input p12]
15. ! [X0] : ((wise(X0) <~> ~calm(X0)) <=> (~patient(X0) & happy(X0))) [input p14]
22. wise(susan) & kind(susan) [input p21]
24. ~wise(susan) | ~strong(susan) [input p23]
25. ~humble(susan) [input hypothesis]
34. ! [X0] : ((humble(X0) | strong(X0)) | (old(X0) & ~tall(X0))) [ennf transformation 12]
35. ! [X0] : (humble(X0) | strong(X0) | (old(X0) & ~tall(X0))) [flattening 34]
38. ! [X0] : (((old(X0) | happy(X0)) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) & (((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (~old(X0) & ~happy(X0)))) [nnf transformation 1]
39. ! [X0] : ((old(X0) | happy(X0) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) & (((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (~old(X0) & ~happy(X0)))) [flattening 38]
42. ! [X0] : ((~old(X0) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | old(X0))) [nnf transformation 3]
44. ! [X0] : (((old(X0) | ~tall(X0)) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) & (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (~old(X0) & tall(X0)))) [nnf transformation 6]
45. ! [X0] : ((old(X0) | ~tall(X0) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) & (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (~old(X0) & tall(X0)))) [flattening 44]
53. ! [X0] : ((((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (strong(X0) & rich(X0))) & ((~strong(X0) | ~rich(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0))))) [nnf transformation 13]
54. ! [X0] : ((((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (strong(X0) & rich(X0))) & (~strong(X0) | ~rich(X0) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0))))) [flattening 53]
55. ! [X0] : ((((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | (patient(X0) | ~happy(X0))) & ((~patient(X0) & happy(X0)) | ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0))))) [nnf transformation 15]
56. ! [X0] : ((((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | patient(X0) | ~happy(X0)) & ((~patient(X0) & happy(X0)) | ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0))))) [flattening 55]
74. ~happy(X0) | quiet(X0) | ~happy(X0) [cnf transformation 39]
87. ~rich(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 42]
95. ~old(X0) | calm(X0) | humble(X0) [cnf transformation 45]
117. strong(X0) | humble(X0) | old(X0) [cnf transformation 35]
121. ~calm(X0) | rich(X0) | strong(X0) [cnf transformation 54]
125. ~calm(X0) | happy(X0) | ~wise(X0) [cnf transformation 56]
142. wise(susan) [cnf transformation 22]
144. ~wise(susan) | ~strong(susan) [cnf transformation 24]
145. ~humble(susan) [cnf transformation 25]
150. ~happy(X0) | quiet(X0) [duplicate literal removal 74]
268. ~strong(susan) [subsumption resolution 144,142]
322. humble(susan) | old(susan) [resolution 117,268]
326. old(susan) [subsumption resolution 322,145]
393. calm(susan) | humble(susan) [resolution 326,95]
396. calm(susan) [subsumption resolution 393,145]
398. 40 <=> quiet(susan) [avatar definition]
402. 41 <=> rich(susan) [avatar definition]
404. rich(susan) <- (41) [avatar component clause 402]
456. happy(susan) | ~wise(susan) [resolution 396,125]
457. rich(susan) | strong(susan) [resolution 396,121]
462. happy(susan) [subsumption resolution 456,142]
465. ~quiet(susan) | ~old(susan) <- (41) [resolution 404,87]
467. ~quiet(susan) <- (41) [subsumption resolution 465,326]
468. ~40 | ~41 [avatar split clause 467,402,398]
1113. quiet(susan) [resolution 462,150]
1116. 40 [avatar split clause 1113,398]
1118. rich(susan) [subsumption resolution 457,268]
1119. 41 [avatar split clause 1118,402]
1120. $false [avatar sat refutation 468,1116,1119]
% SZS output end Proof for 5003768816170737267362940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not strong is not calm or curious.
Everyone who is both generous and quiet is both wise and calm.
If someone is both not old and not patient then someone is both not old and not calm and vice versa.
Everyone who is humble or not brave is both not patient and not generous.
If someone is not patient then susan is either not funny or funny.
Everyone who is either not generous or old is either not old or tall.
If mary is rich then someone is rich and vice versa.
If alice is creative then someone is either not funny or not happy.
Everyone who is not rich or not calm is either not creative or wise and vice versa.
If someone is happy then someone is not creative and vice versa.
If someone is either not funny or creative then fred is not quiet or not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
If john is kind or not patient then someone is not creative or not strong and vice versa.
Someone is both not strong and tall.
Mary is either not patient or tall.
Paul is not creative or not wise.
John is not wise.
Someone is kind or not generous.
Someone is curious or not wise.
Alice is brave.
Alice is both happy and funny. | Susan is funny. | neutral | (![X]:((tall(X)|~strong(X))=>(~calm(X)|curious(X))))&
(![X]:((generous(X)&quiet(X))=>(wise(X)&calm(X))))&
((?[X]:((~old(X)&~patient(X))))<=>(?[X]:((~old(X)&~calm(X)))))&
(![X]:((humble(X)|~brave(X))=>(~patient(X)&~generous(X))))&
((?[X]:(~patient(X)))=>((~funny(susan)<~>funny(susan))))&
(![X]:((~generous(X)<~>old(X))=>(~old(X)<~>tall(X))))&
((rich(mary))<=>(?[X]:(rich(X))))&
((creative(alice))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~quiet(fred)|~patient(fred))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
(((kind(john)|~patient(john)))<=>(?[X]:((~creative(X)|~strong(X)))))&
(?[X]:((~strong(X)&tall(X))))&
((~patient(mary)<~>tall(mary)))&
((~creative(paul)|~wise(paul)))&
(~wise(john))&
(?[X]:((kind(X)|~generous(X))))&
(?[X]:((curious(X)|~wise(X))))&
(brave(alice))&
((happy(alice)&funny(alice))) | funny(susan) | [] | null | 0 |
If fred is quiet then alice is calm.
If susan is both not patient and not brave then someone is both not kind and curious.
If someone is both funny and not brave then someone is humble and vice versa.
Everyone who is either tall or not curious is brave or creative and vice versa.
If someone is not happy or not generous then lucy is not curious.
Everyone who is both not brave and not curious is not tall or not patient and vice versa.
Everyone who is not funny is both not quiet and not humble.
If lucy is rich then alice is brave or not humble.
Everyone who is both generous and quiet is either creative or strong and vice versa.
Everyone who is either brave or not funny is either not humble or not curious.
If mary is not curious then someone is either not kind or rich and vice versa.
If fred is not calm or rich then someone is not happy or quiet.
Everyone who is not calm is both creative and not humble.
If fred is not creative then someone is both calm and happy.
Everyone who is brave or not rich is either not rich or not strong and vice versa.
If someone is either rich or patient then someone is either happy or calm.
Someone is wise.
Someone is brave or tall.
Someone is either happy or not generous.
Someone is either quiet or generous.
Fred is not funny or curious.
Someone is curious.
Someone is humble or not calm. | Fred is tall. | entailment | ((quiet(fred))=>(calm(alice)))&
(((~patient(susan)&~brave(susan)))=>(?[X]:((~kind(X)&curious(X)))))&
((?[X]:((funny(X)&~brave(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)<~>~curious(X))<=>(brave(X)|creative(X))))&
((?[X]:((~happy(X)|~generous(X))))=>(~curious(lucy)))&
(![X]:((~brave(X)&~curious(X))<=>(~tall(X)|~patient(X))))&
(![X]:(~funny(X)=>(~quiet(X)&~humble(X))))&
((rich(lucy))=>((brave(alice)|~humble(alice))))&
(![X]:((generous(X)&quiet(X))<=>(creative(X)<~>strong(X))))&
(![X]:((brave(X)<~>~funny(X))=>(~humble(X)<~>~curious(X))))&
((~curious(mary))<=>(?[X]:((~kind(X)<~>rich(X)))))&
(((~calm(fred)|rich(fred)))=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:(~calm(X)=>(creative(X)&~humble(X))))&
((~creative(fred))=>(?[X]:((calm(X)&happy(X)))))&
(![X]:((brave(X)|~rich(X))<=>(~rich(X)<~>~strong(X))))&
((?[X]:((rich(X)<~>patient(X))))=>(?[X]:((happy(X)<~>calm(X)))))&
(?[X]:(wise(X)))&
(?[X]:((brave(X)|tall(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
(?[X]:((quiet(X)<~>generous(X))))&
((~funny(fred)|curious(fred)))&
(?[X]:(curious(X)))&
(?[X]:((humble(X)|~calm(X)))) | tall(fred) | [
"p5",
"p6",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3916288206076683458418952
% SZS output start Proof for 3916288206076683458418952
6. ! [X0] : ((~curious(X0) & ~brave(X0)) <=> (~patient(X0) | ~tall(X0))) [input p5]
7. ! [X0] : (~funny(X0) => (~humble(X0) & ~quiet(X0))) [input p6]
10. ! [X0] : ((brave(X0) <~> ~funny(X0)) => (~humble(X0) <~> ~curious(X0))) [input p9]
21. curious(fred) | ~funny(fred) [input p20]
24. ~tall(fred) [input hypothesis]
32. ! [X0] : ((~humble(X0) & ~quiet(X0)) | funny(X0)) [ennf transformation 7]
35. ! [X0] : ((~humble(X0) <~> ~curious(X0)) | (brave(X0) <=> ~funny(X0))) [ennf transformation 10]
49. ! [X0] : (((~curious(X0) & ~brave(X0)) | (patient(X0) & tall(X0))) & ((~patient(X0) | ~tall(X0)) | (curious(X0) | brave(X0)))) [nnf transformation 6]
50. ! [X0] : (((~curious(X0) & ~brave(X0)) | (patient(X0) & tall(X0))) & (~patient(X0) | ~tall(X0) | curious(X0) | brave(X0))) [flattening 49]
53. ! [X0] : (((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0)))) [nnf transformation 35]
95. ~brave(X0) | tall(X0) [cnf transformation 50]
97. ~curious(X0) | tall(X0) [cnf transformation 50]
100. ~humble(X0) | funny(X0) [cnf transformation 32]
111. curious(X0) | humble(X0) | brave(X0) | funny(X0) [cnf transformation 53]
137. curious(fred) | ~funny(fred) [cnf transformation 21]
140. ~tall(fred) [cnf transformation 24]
217. funny(X0) | brave(X0) | curious(X0) [subsumption resolution 111,100]
313. 38 <=> funny(fred) [avatar definition]
315. ~funny(fred) <- (~38) [avatar component clause 313]
317. 39 <=> curious(fred) [avatar definition]
319. curious(fred) <- (39) [avatar component clause 317]
320. ~38 | 39 [avatar split clause 137,317,313]
382. brave(fred) | curious(fred) <- (~38) [resolution 217,315]
386. 47 <=> brave(fred) [avatar definition]
388. brave(fred) <- (47) [avatar component clause 386]
389. 39 | 47 | 38 [avatar split clause 382,313,386,317]
392. tall(fred) <- (39) [resolution 319,97]
393. $false <- (39) [subsumption resolution 392,140]
394. ~39 [avatar contradiction clause 393]
396. tall(fred) <- (47) [resolution 388,95]
397. $false <- (47) [subsumption resolution 396,140]
398. ~47 [avatar contradiction clause 397]
399. $false [avatar sat refutation 320,389,394,398]
% SZS output end Proof for 3916288206076683458418952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or curious is curious and vice versa.
Everyone who is either not brave or rich is either not patient or not calm and vice versa.
Everyone who is quiet is both not tall and rich and vice versa.
Everyone who is either not strong or not old is either happy or curious and vice versa.
If lucy is either kind or old then fred is both kind and creative and vice versa.
Everyone who is generous or not generous is both wise and rich.
Everyone who is calm or not wise is both not wise and creative and vice versa.
Everyone who is not patient is both not happy and brave and vice versa.
Everyone who is both curious and brave is both curious and not old.
Everyone who is funny or humble is either not strong or not brave and vice versa.
If john is both not curious and humble then susan is patient.
Everyone who is calm or funny is brave.
If john is either not funny or brave then someone is not wise.
If someone is creative or not calm then fred is not calm and vice versa.
Everyone who is both strong and tall is strong and vice versa.
Everyone who is both rich and not brave is patient or humble.
Fred is both not calm and not tall.
Someone is both not kind and generous.
Alice is humble or brave.
John is both not tall and not kind.
Someone is either patient or creative.
Someone is either not kind or not old.
Mary is not tall or not generous. | Mary is brave. | entailment | (![X]:((~curious(X)<~>curious(X))<=>curious(X)))&
(![X]:((~brave(X)<~>rich(X))<=>(~patient(X)<~>~calm(X))))&
(![X]:(quiet(X)<=>(~tall(X)&rich(X))))&
(![X]:((~strong(X)<~>~old(X))<=>(happy(X)<~>curious(X))))&
(((kind(lucy)<~>old(lucy)))<=>((kind(fred)&creative(fred))))&
(![X]:((generous(X)|~generous(X))=>(wise(X)&rich(X))))&
(![X]:((calm(X)|~wise(X))<=>(~wise(X)&creative(X))))&
(![X]:(~patient(X)<=>(~happy(X)&brave(X))))&
(![X]:((curious(X)&brave(X))=>(curious(X)&~old(X))))&
(![X]:((funny(X)|humble(X))<=>(~strong(X)<~>~brave(X))))&
(((~curious(john)&humble(john)))=>(patient(susan)))&
(![X]:((calm(X)|funny(X))=>brave(X)))&
(((~funny(john)<~>brave(john)))=>(?[X]:(~wise(X))))&
((?[X]:((creative(X)|~calm(X))))<=>(~calm(fred)))&
(![X]:((strong(X)&tall(X))<=>strong(X)))&
(![X]:((rich(X)&~brave(X))=>(patient(X)|humble(X))))&
((~calm(fred)&~tall(fred)))&
(?[X]:((~kind(X)&generous(X))))&
((humble(alice)|brave(alice)))&
((~tall(john)&~kind(john)))&
(?[X]:((patient(X)<~>creative(X))))&
(?[X]:((~kind(X)<~>~old(X))))&
((~tall(mary)|~generous(mary))) | brave(mary) | [
"p1",
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3968613909715179738580058
% SZS output start Proof for 3968613909715179738580058
2. ! [X0] : ((~brave(X0) <~> rich(X0)) <=> (~patient(X0) <~> ~calm(X0))) [input p1]
6. ! [X0] : ((~generous(X0) | generous(X0)) => (rich(X0) & wise(X0))) [input p5]
7. ! [X0] : ((~wise(X0) | calm(X0)) <=> (creative(X0) & ~wise(X0))) [input p6]
8. ! [X0] : (~patient(X0) <=> (brave(X0) & ~happy(X0))) [input p7]
24. ~brave(mary) [input hypothesis]
25. ! [X0] : ((rich(X0) & wise(X0)) | (generous(X0) & ~generous(X0))) [ennf transformation 6]
35. ! [X0] : ((((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0))))) [nnf transformation 2]
39. ! [X0] : (((~wise(X0) | calm(X0)) | (~creative(X0) | wise(X0))) & ((creative(X0) & ~wise(X0)) | (wise(X0) & ~calm(X0)))) [nnf transformation 7]
40. ! [X0] : ((~wise(X0) | calm(X0) | ~creative(X0) | wise(X0)) & ((creative(X0) & ~wise(X0)) | (wise(X0) & ~calm(X0)))) [flattening 39]
41. ! [X0] : ((~patient(X0) | (~brave(X0) | happy(X0))) & ((brave(X0) & ~happy(X0)) | patient(X0))) [nnf transformation 8]
42. ! [X0] : ((~patient(X0) | ~brave(X0) | happy(X0)) & ((brave(X0) & ~happy(X0)) | patient(X0))) [flattening 41]
69. ~rich(X0) | patient(X0) | ~brave(X0) | calm(X0) [cnf transformation 35]
73. ~patient(X0) | brave(X0) | ~rich(X0) | calm(X0) [cnf transformation 35]
88. wise(X0) | ~generous(X0) [cnf transformation 25]
89. wise(X0) | generous(X0) [cnf transformation 25]
90. rich(X0) | ~generous(X0) [cnf transformation 25]
91. generous(X0) | rich(X0) [cnf transformation 25]
92. ~wise(X0) | ~calm(X0) [cnf transformation 40]
98. patient(X0) | brave(X0) [cnf transformation 42]
132. ~brave(mary) [cnf transformation 24]
163. rich(X0) [subsumption resolution 90,91]
164. wise(X0) [subsumption resolution 88,89]
165. ~calm(X0) [subsumption resolution 92,164]
280. patient(X0) | ~brave(X0) | calm(X0) [resolution 69,163]
281. patient(X0) | ~brave(X0) [subsumption resolution 280,165]
282. patient(X0) [subsumption resolution 281,98]
311. brave(X0) | ~rich(X0) | calm(X0) [resolution 73,282]
319. brave(X0) | calm(X0) [subsumption resolution 311,163]
320. brave(X0) [subsumption resolution 319,165]
346. $false [resolution 320,132]
% SZS output end Proof for 3968613909715179738580058
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not brave is both not tall and not quiet and vice versa.
Everyone who is patient is either not tall or not rich and vice versa.
If lucy is both curious and not humble then fred is either wise or not old and vice versa.
Everyone who is both not kind and not patient is happy.
If someone is either not creative or not calm then someone is not quiet or not happy.
If mary is rich or humble then someone is both quiet and not happy and vice versa.
If someone is both not kind and strong then someone is not happy and vice versa.
Everyone who is both strong and not patient is both not calm and not strong and vice versa.
Everyone who is brave or creative is either not rich or creative and vice versa.
If someone is both tall and strong then someone is either not tall or not happy.
If someone is tall then fred is not rich or tall and vice versa.
Everyone who is not happy or not tall is not rich and vice versa.
Everyone who is either generous or not brave is both not old and not generous and vice versa.
Everyone who is either not curious or not creative is strong or happy and vice versa.
Everyone who is either wise or not generous is both not funny and not patient and vice versa.
If lucy is not curious or creative then john is both calm and creative.
Someone is either not quiet or wise.
Fred is both quiet and not brave.
Susan is creative.
Someone is not old.
Alice is both kind and not creative.
Fred is not kind or tall.
Someone is either not humble or not funny. | Susan is not tall. | contradiction | (![X]:((~funny(X)&~brave(X))<=>(~tall(X)&~quiet(X))))&
(![X]:(patient(X)<=>(~tall(X)<~>~rich(X))))&
(((curious(lucy)&~humble(lucy)))<=>((wise(fred)<~>~old(fred))))&
(![X]:((~kind(X)&~patient(X))=>happy(X)))&
((?[X]:((~creative(X)<~>~calm(X))))=>(?[X]:((~quiet(X)|~happy(X)))))&
(((rich(mary)|humble(mary)))<=>(?[X]:((quiet(X)&~happy(X)))))&
((?[X]:((~kind(X)&strong(X))))<=>(?[X]:(~happy(X))))&
(![X]:((strong(X)&~patient(X))<=>(~calm(X)&~strong(X))))&
(![X]:((brave(X)|creative(X))<=>(~rich(X)<~>creative(X))))&
((?[X]:((tall(X)&strong(X))))=>(?[X]:((~tall(X)<~>~happy(X)))))&
((?[X]:(tall(X)))<=>((~rich(fred)|tall(fred))))&
(![X]:((~happy(X)|~tall(X))<=>~rich(X)))&
(![X]:((generous(X)<~>~brave(X))<=>(~old(X)&~generous(X))))&
(![X]:((~curious(X)<~>~creative(X))<=>(strong(X)|happy(X))))&
(![X]:((wise(X)<~>~generous(X))<=>(~funny(X)&~patient(X))))&
(((~curious(lucy)|creative(lucy)))=>((calm(john)&creative(john))))&
(?[X]:((~quiet(X)<~>wise(X))))&
((quiet(fred)&~brave(fred)))&
(creative(susan))&
(?[X]:(~old(X)))&
((kind(alice)&~creative(alice)))&
((~kind(fred)|tall(fred)))&
(?[X]:((~humble(X)<~>~funny(X)))) | ~tall(susan) | [
"p8",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6897122753686983151561834
% SZS output start Proof for 6897122753686983151561834
9. ! [X0] : ((creative(X0) | brave(X0)) <=> (~rich(X0) <~> creative(X0))) [input p8]
12. ! [X0] : ((~tall(X0) | ~happy(X0)) <=> ~rich(X0)) [input p11]
19. creative(susan) [input p18]
24. ~tall(susan) [input hypothesis]
54. ! [X0] : (((creative(X0) | brave(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) & (((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~creative(X0) & ~brave(X0)))) [nnf transformation 9]
55. ! [X0] : ((creative(X0) | brave(X0) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) & (((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~creative(X0) & ~brave(X0)))) [flattening 54]
65. ! [X0] : (((~tall(X0) | ~happy(X0)) | rich(X0)) & (~rich(X0) | (tall(X0) & happy(X0)))) [nnf transformation 12]
66. ! [X0] : ((~tall(X0) | ~happy(X0) | rich(X0)) & (~rich(X0) | (tall(X0) & happy(X0)))) [flattening 65]
113. ~creative(X0) | rich(X0) | ~creative(X0) [cnf transformation 55]
122. ~rich(X0) | tall(X0) [cnf transformation 66]
150. creative(susan) [cnf transformation 19]
157. ~tall(susan) [cnf transformation 24]
160. ~creative(X0) | rich(X0) [duplicate literal removal 113]
321. rich(susan) [resolution 160,150]
322. tall(susan) [resolution 321,122]
324. $false [subsumption resolution 322,157]
% SZS output end Proof for 6897122753686983151561834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious then paul is both strong and wise and vice versa. Everyone who is both not calm and not funny is not kind or calm. If someone is creative or not wise then john is patient. If fred is kind or not happy then someone is not strong. If someone is not curious then someone is funny or not patient. If someone is not generous or strong then someone is creative. Everyone who is not generous is not calm or not strong and vice versa. If someone is generous then someone is not funny or not happy and vice versa. If paul is old or not brave then susan is calm and vice versa. If lucy is quiet or not humble then paul is either not wise or not quiet. If mary is funny or tall then someone is not funny and vice versa. Everyone who is either not wise or wise is not calm or rich and vice versa. Everyone who is both patient and generous is generous or humble. Everyone who is either not calm or wise is wise and vice versa. If fred is both not patient and patient then alice is either creative or not wise and vice versa. Everyone who is not happy is either brave or not brave. Fred is not creative or generous. Someone is not curious. Someone is either not strong or kind. Someone is either not kind or creative. Alice is both creative and brave. | Alice is not humble. | neutral | ((?[X]:(curious(X)))<=>((strong(paul)&wise(paul))))&
(![X]:((~calm(X)&~funny(X))=>(~kind(X)|calm(X))))&
((?[X]:((creative(X)|~wise(X))))=>(patient(john)))&
(((kind(fred)|~happy(fred)))=>(?[X]:(~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((funny(X)|~patient(X)))))&
((?[X]:((~generous(X)|strong(X))))=>(?[X]:(creative(X))))&
(![X]:(~generous(X)<=>(~calm(X)|~strong(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~funny(X)|~happy(X)))))&
(((old(paul)|~brave(paul)))<=>(calm(susan)))&
(((quiet(lucy)|~humble(lucy)))=>((~wise(paul)<~>~quiet(paul))))&
(((funny(mary)|tall(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((~wise(X)<~>wise(X))<=>(~calm(X)|rich(X))))&
(![X]:((patient(X)&generous(X))=>(generous(X)|humble(X))))&
(![X]:((~calm(X)<~>wise(X))<=>wise(X)))&
(((~patient(fred)&patient(fred)))<=>((creative(alice)<~>~wise(alice))))&
(![X]:(~happy(X)=>(brave(X)<~>~brave(X))))&
((~creative(fred)|generous(fred)))&
(?[X]:(~curious(X)))&
(?[X]:((~strong(X)<~>kind(X))))&
(?[X]:((~kind(X)<~>creative(X))))&
((creative(alice)&brave(alice))) | ~humble(alice) | [] | null | 0 |
If susan is both not curious and humble then someone is funny and vice versa.
Everyone who is either funny or patient is patient.
Everyone who is either not calm or not generous is both quiet and not curious.
Everyone who is either not tall or patient is not strong or patient and vice versa.
If john is both creative and strong then someone is both not tall and not curious.
Everyone who is either not patient or calm is generous or not funny.
If someone is either quiet or not calm then someone is kind or rich.
Everyone who is not funny or not wise is both old and kind.
Everyone who is both strong and tall is not happy and vice versa.
If alice is both funny and not calm then lucy is both not humble and wise.
If someone is either brave or calm then susan is both not quiet and not wise.
If someone is either quiet or not generous then someone is not tall or quiet.
If someone is not creative then someone is both not funny and brave and vice versa.
Everyone who is not funny is both tall and not calm.
If mary is not generous then susan is not curious.
Everyone who is rich or generous is quiet.
Someone is funny.
Someone is curious or quiet.
Someone is kind.
Someone is both not strong and patient.
Susan is kind or not calm.
Mary is both quiet and not funny.
Susan is calm or not humble.
John is both happy and not quiet. | John is brave. | contradiction | (((~curious(susan)&humble(susan)))<=>(?[X]:(funny(X))))&
(![X]:((funny(X)<~>patient(X))=>patient(X)))&
(![X]:((~calm(X)<~>~generous(X))=>(quiet(X)&~curious(X))))&
(![X]:((~tall(X)<~>patient(X))<=>(~strong(X)|patient(X))))&
(((creative(john)&strong(john)))=>(?[X]:((~tall(X)&~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>(generous(X)|~funny(X))))&
((?[X]:((quiet(X)<~>~calm(X))))=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((~funny(X)|~wise(X))=>(old(X)&kind(X))))&
(![X]:((strong(X)&tall(X))<=>~happy(X)))&
(((funny(alice)&~calm(alice)))=>((~humble(lucy)&wise(lucy))))&
((?[X]:((brave(X)<~>calm(X))))=>((~quiet(susan)&~wise(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:(~funny(X)=>(tall(X)&~calm(X))))&
((~generous(mary))=>(~curious(susan)))&
(![X]:((rich(X)|generous(X))=>quiet(X)))&
(?[X]:(funny(X)))&
(?[X]:((curious(X)|quiet(X))))&
(?[X]:(kind(X)))&
(?[X]:((~strong(X)&patient(X))))&
((kind(susan)|~calm(susan)))&
((quiet(mary)&~funny(mary)))&
((calm(susan)|~humble(susan)))&
((happy(john)&~quiet(john))) | brave(john) | [
"p0",
"p2",
"p10",
"p15",
"p16",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4661123276031694972572527
% SZS output start Proof for 4661123276031694972572527
1. (humble(susan) & ~curious(susan)) <=> ? [X0] : funny(X0) [input p0]
3. ! [X0] : ((~calm(X0) <~> ~generous(X0)) => (~curious(X0) & quiet(X0))) [input p2]
11. ? [X0] : (brave(X0) <~> calm(X0)) => (~wise(susan) & ~quiet(susan)) [input p10]
16. ! [X0] : ((generous(X0) | rich(X0)) => quiet(X0)) [input p15]
17. ? [X0] : funny(X0) [input p16]
23. ~humble(susan) | calm(susan) [input p22]
24. ~quiet(john) & happy(john) [input p23]
25. brave(john) [input hypothesis]
35. ! [X0] : (generous(X0) => quiet(X0)) [pure predicate removal 16]
37. ! [X0] : ((~curious(X0) & quiet(X0)) | (~calm(X0) <=> ~generous(X0))) [ennf transformation 3]
46. (~wise(susan) & ~quiet(susan)) | ! [X0] : (brave(X0) <=> calm(X0)) [ennf transformation 11]
50. ! [X0] : (quiet(X0) | ~generous(X0)) [ennf transformation 35]
51. ((humble(susan) & ~curious(susan)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | (~humble(susan) | curious(susan))) [nnf transformation 1]
52. ((humble(susan) & ~curious(susan)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | ~humble(susan) | curious(susan)) [flattening 51]
53. ((humble(susan) & ~curious(susan)) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | ~humble(susan) | curious(susan)) [rectify 52]
54. ? [X1] : funny(X1) => funny(sK0) [choice axiom]
55. ((humble(susan) & ~curious(susan)) | ! [X0] : ~funny(X0)) & (funny(sK0) | ~humble(susan) | curious(susan)) [skolemisation 53,54]
57. ! [X0] : ((~curious(X0) & quiet(X0)) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0)))) [nnf transformation 37]
63. (~wise(susan) & ~quiet(susan)) | ! [X0] : ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))) [nnf transformation 46]
73. ? [X0] : funny(X0) => funny(sK5) [choice axiom]
74. funny(sK5) [skolemisation 17,73]
81. humble(susan) | ~funny(X0) [cnf transformation 55]
85. ~calm(X0) | quiet(X0) | generous(X0) [cnf transformation 57]
101. ~quiet(susan) | calm(X0) | ~brave(X0) [cnf transformation 63]
113. ~generous(X0) | quiet(X0) [cnf transformation 50]
114. funny(sK5) [cnf transformation 74]
120. ~humble(susan) | calm(susan) [cnf transformation 23]
122. ~quiet(john) [cnf transformation 24]
123. brave(john) [cnf transformation 25]
128. 1 <=> ! [X0] : ~funny(X0) [avatar definition]
129. ~funny(X0) <- (1) [avatar component clause 128]
131. 2 <=> humble(susan) [avatar definition]
134. 1 | 2 [avatar split clause 81,131,128]
193. 15 <=> ! [X0] : (calm(X0) | ~brave(X0)) [avatar definition]
194. ~brave(X0) | calm(X0) <- (15) [avatar component clause 193]
197. 16 <=> quiet(susan) [avatar definition]
201. 15 | ~16 [avatar split clause 101,197,193]
254. 29 <=> calm(susan) [avatar definition]
256. calm(susan) <- (29) [avatar component clause 254]
257. 29 | ~2 [avatar split clause 120,131,254]
273. quiet(susan) | generous(susan) <- (29) [resolution 85,256]
279. quiet(susan) <- (29) [subsumption resolution 273,113]
280. 16 | ~29 [avatar split clause 279,254,197]
298. $false <- (1) [resolution 129,114]
299. ~1 [avatar contradiction clause 298]
305. calm(john) <- (15) [resolution 194,123]
313. quiet(john) | generous(john) <- (15) [resolution 305,85]
316. 30 <=> generous(john) [avatar definition]
318. generous(john) <- (30) [avatar component clause 316]
324. generous(john) <- (15) [subsumption resolution 313,122]
325. 30 | ~15 [avatar split clause 324,193,316]
346. quiet(john) <- (30) [resolution 318,113]
347. $false <- (30) [subsumption resolution 346,122]
348. ~30 [avatar contradiction clause 347]
349. $false [avatar sat refutation 134,201,257,280,299,325,348]
% SZS output end Proof for 4661123276031694972572527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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 |
If alice is humble then someone is either generous or kind.
Everyone who is both happy and strong is either not wise or not calm.
If someone is not curious or not patient then paul is tall.
Everyone who is either not brave or not generous is both generous and not tall and vice versa.
Everyone who is not wise is either strong or happy and vice versa.
Everyone who is either strong or generous is both tall and humble.
Everyone who is either funny or curious is either not generous or not curious and vice versa.
If someone is both strong and not calm then fred is funny or happy.
Everyone who is not funny or not creative is either not rich or generous.
If someone is both not quiet and not brave then someone is either calm or not humble and vice versa.
If susan is both not calm and patient then mary is either not generous or patient.
Everyone who is not old is not old or not brave and vice versa.
Everyone who is not rich or brave is not old or quiet and vice versa.
Everyone who is either not curious or curious is not rich and vice versa.
Everyone who is not quiet or calm is humble.
If lucy is either old or not rich then someone is either kind or creative and vice versa.
Someone is not generous.
Someone is either not kind or not patient.
Someone is not creative.
Mary is either humble or not calm.
Someone is either creative or quiet.
Someone is not kind.
Fred is not quiet or not funny. | Alice is rich. | contradiction | ((humble(alice))=>(?[X]:((generous(X)<~>kind(X)))))&
(![X]:((happy(X)&strong(X))=>(~wise(X)<~>~calm(X))))&
((?[X]:((~curious(X)|~patient(X))))=>(tall(paul)))&
(![X]:((~brave(X)<~>~generous(X))<=>(generous(X)&~tall(X))))&
(![X]:(~wise(X)<=>(strong(X)<~>happy(X))))&
(![X]:((strong(X)<~>generous(X))=>(tall(X)&humble(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:((strong(X)&~calm(X))))=>((funny(fred)|happy(fred))))&
(![X]:((~funny(X)|~creative(X))=>(~rich(X)<~>generous(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((calm(X)<~>~humble(X)))))&
(((~calm(susan)&patient(susan)))=>((~generous(mary)<~>patient(mary))))&
(![X]:(~old(X)<=>(~old(X)|~brave(X))))&
(![X]:((~rich(X)|brave(X))<=>(~old(X)|quiet(X))))&
(![X]:((~curious(X)<~>curious(X))<=>~rich(X)))&
(![X]:((~quiet(X)|calm(X))=>humble(X)))&
(((old(lucy)<~>~rich(lucy)))<=>(?[X]:((kind(X)<~>creative(X)))))&
(?[X]:(~generous(X)))&
(?[X]:((~kind(X)<~>~patient(X))))&
(?[X]:(~creative(X)))&
((humble(mary)<~>~calm(mary)))&
(?[X]:((creative(X)<~>quiet(X))))&
(?[X]:(~kind(X)))&
((~quiet(fred)|~funny(fred))) | rich(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5617600415436543562219300
% SZS output start Proof for 5617600415436543562219300
14. ! [X0] : ((~curious(X0) <~> curious(X0)) <=> ~rich(X0)) [input p13]
24. rich(alice) [input hypothesis]
57. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | rich(X0)) & (~rich(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [nnf transformation 14]
123. ~rich(X0) | curious(X0) | curious(X0) [cnf transformation 57]
124. ~rich(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 57]
147. rich(alice) [cnf transformation 24]
148. ~rich(X0) | curious(X0) [duplicate literal removal 123]
149. ~rich(X0) | ~curious(X0) [duplicate literal removal 124]
248. ~rich(X0) [subsumption resolution 148,149]
309. $false [subsumption resolution 147,248]
% SZS output end Proof for 5617600415436543562219300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or creative is both not old and not curious.
If someone is old then mary is not creative or kind and vice versa.
Everyone who is not curious is not calm and vice versa.
If someone is happy or not kind then someone is not patient or not strong.
Everyone who is not funny or not old is both not quiet and generous and vice versa.
If paul is wise or not tall then john is curious or not tall and vice versa.
If alice is not brave then someone is not wise or not patient.
If paul is either not patient or not kind then susan is either old or not humble and vice versa.
Everyone who is either patient or not quiet is calm and vice versa.
Everyone who is both not humble and not wise is not calm or not rich and vice versa.
Everyone who is not brave is rich and vice versa.
If someone is not curious or not strong then someone is not creative or quiet and vice versa.
If someone is not happy or old then someone is not quiet or kind and vice versa.
If lucy is generous then someone is either not humble or funny.
Everyone who is not calm or calm is both old and funny.
If someone is not creative then paul is rich or not old.
Someone is funny or patient.
Someone is both not creative and not kind.
Paul is not wise.
Someone is both not happy and quiet.
Someone is generous or not happy.
Paul is both not calm and not humble. | Paul is not tall. | neutral | (![X]:((calm(X)|creative(X))=>(~old(X)&~curious(X))))&
((?[X]:(old(X)))<=>((~creative(mary)|kind(mary))))&
(![X]:(~curious(X)<=>~calm(X)))&
((?[X]:((happy(X)|~kind(X))))=>(?[X]:((~patient(X)|~strong(X)))))&
(![X]:((~funny(X)|~old(X))<=>(~quiet(X)&generous(X))))&
(((wise(paul)|~tall(paul)))<=>((curious(john)|~tall(john))))&
((~brave(alice))=>(?[X]:((~wise(X)|~patient(X)))))&
(((~patient(paul)<~>~kind(paul)))<=>((old(susan)<~>~humble(susan))))&
(![X]:((patient(X)<~>~quiet(X))<=>calm(X)))&
(![X]:((~humble(X)&~wise(X))<=>(~calm(X)|~rich(X))))&
(![X]:(~brave(X)<=>rich(X)))&
((?[X]:((~curious(X)|~strong(X))))<=>(?[X]:((~creative(X)|quiet(X)))))&
((?[X]:((~happy(X)|old(X))))<=>(?[X]:((~quiet(X)|kind(X)))))&
((generous(lucy))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~calm(X)|calm(X))=>(old(X)&funny(X))))&
((?[X]:(~creative(X)))=>((rich(paul)|~old(paul))))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(~wise(paul))&
(?[X]:((~happy(X)&quiet(X))))&
(?[X]:((generous(X)|~happy(X))))&
((~calm(paul)&~humble(paul))) | ~tall(paul) | [] | null | 0 |
If fred is not brave or not tall then mary is wise and vice versa.
If someone is happy or tall then someone is tall.
Everyone who is not curious is both not wise and wise.
If susan is creative or happy then mary is not creative and vice versa.
Everyone who is either patient or tall is both wise and not brave.
If alice is both funny and rich then alice is both not funny and kind.
Everyone who is not calm or humble is both strong and quiet.
If fred is not tall then susan is both not creative and brave and vice versa.
If john is either old or not humble then someone is either patient or not wise.
Everyone who is not quiet is both funny and calm and vice versa.
If fred is not creative or not happy then someone is not strong or tall and vice versa.
If alice is not happy then john is rich and vice versa.
If john is brave then someone is both happy and strong and vice versa.
Everyone who is old or not strong is not curious and vice versa.
Everyone who is either not creative or wise is either not quiet or patient and vice versa.
If someone is humble or not brave then lucy is not funny and vice versa.
Susan is both calm and not creative.
Someone is not creative.
Someone is either brave or patient.
Paul is not calm or wise.
Susan is either not brave or strong.
Someone is not old.
Someone is wise.
Someone is not quiet. | Susan is not brave. | contradiction | (((~brave(fred)|~tall(fred)))<=>(wise(mary)))&
((?[X]:((happy(X)|tall(X))))=>(?[X]:(tall(X))))&
(![X]:(~curious(X)=>(~wise(X)&wise(X))))&
(((creative(susan)|happy(susan)))<=>(~creative(mary)))&
(![X]:((patient(X)<~>tall(X))=>(wise(X)&~brave(X))))&
(((funny(alice)&rich(alice)))=>((~funny(alice)&kind(alice))))&
(![X]:((~calm(X)|humble(X))=>(strong(X)&quiet(X))))&
((~tall(fred))<=>((~creative(susan)&brave(susan))))&
(((old(john)<~>~humble(john)))=>(?[X]:((patient(X)<~>~wise(X)))))&
(![X]:(~quiet(X)<=>(funny(X)&calm(X))))&
(((~creative(fred)|~happy(fred)))<=>(?[X]:((~strong(X)|tall(X)))))&
((~happy(alice))<=>(rich(john)))&
((brave(john))<=>(?[X]:((happy(X)&strong(X)))))&
(![X]:((old(X)|~strong(X))<=>~curious(X)))&
(![X]:((~creative(X)<~>wise(X))<=>(~quiet(X)<~>patient(X))))&
((?[X]:((humble(X)|~brave(X))))<=>(~funny(lucy)))&
((calm(susan)&~creative(susan)))&
(?[X]:(~creative(X)))&
(?[X]:((brave(X)<~>patient(X))))&
((~calm(paul)|wise(paul)))&
((~brave(susan)<~>strong(susan)))&
(?[X]:(~old(X)))&
(?[X]:(wise(X)))&
(?[X]:(~quiet(X))) | ~brave(susan) | [
"p2",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7105892124749619341553129
% SZS output start Proof for 7105892124749619341553129
3. ! [X0] : (~curious(X0) => (wise(X0) & ~wise(X0))) [input p2]
14. ! [X0] : ((~strong(X0) | old(X0)) <=> ~curious(X0)) [input p13]
21. ~brave(susan) <~> strong(susan) [input p20]
25. ~brave(susan) [input hypothesis]
27. ! [X0] : ((~strong(X0) | old(X0)) => ~curious(X0)) [unused predicate definition removal 14]
30. ! [X0] : ((wise(X0) & ~wise(X0)) | curious(X0)) [ennf transformation 3]
36. ! [X0] : (~curious(X0) | (strong(X0) & ~old(X0))) [ennf transformation 27]
72. (~strong(susan) | brave(susan)) & (strong(susan) | ~brave(susan)) [nnf transformation 21]
84. ~wise(X0) | curious(X0) [cnf transformation 30]
85. wise(X0) | curious(X0) [cnf transformation 30]
118. ~curious(X0) | strong(X0) [cnf transformation 36]
137. ~strong(susan) | brave(susan) [cnf transformation 72]
141. ~brave(susan) [cnf transformation 25]
170. curious(X0) [subsumption resolution 84,85]
196. 12 <=> brave(susan) [avatar definition]
232. 19 <=> ! [X0] : strong(X0) [avatar definition]
233. strong(X0) <- (19) [avatar component clause 232]
273. strong(X0) [subsumption resolution 118,170]
274. 19 [avatar split clause 273,232]
318. 37 <=> strong(susan) [avatar definition]
320. ~strong(susan) <- (~37) [avatar component clause 318]
321. 12 | ~37 [avatar split clause 137,318,196]
323. ~12 [avatar split clause 141,196]
326. $false <- (19, ~37) [resolution 320,233]
327. ~19 | 37 [avatar contradiction clause 326]
328. $false [avatar sat refutation 274,321,323,327]
% SZS output end Proof for 7105892124749619341553129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or tall then someone is either not calm or not tall and vice versa.
Everyone who is funny or curious is either tall or happy.
Everyone who is both calm and not generous is not wise and vice versa.
Everyone who is both not rich and not generous is rich or calm and vice versa.
Everyone who is either tall or not generous is not creative or not kind and vice versa.
If paul is either not funny or not creative then someone is either generous or brave.
If fred is not funny then someone is either funny or not strong and vice versa.
If someone is both kind and rich then someone is both brave and not strong and vice versa.
If susan is not rich or not brave then someone is either humble or not happy and vice versa.
Everyone who is quiet or not curious is both not creative and happy and vice versa.
Everyone who is tall or not strong is both not tall and kind.
If someone is not brave then someone is kind and vice versa.
Everyone who is not calm or strong is both not curious and strong.
Everyone who is both not funny and kind is both not calm and not humble.
Everyone who is either not brave or kind is not strong or wise and vice versa.
If john is not curious then fred is not quiet.
Fred is strong.
Someone is not creative.
Someone is old.
Someone is not humble.
Mary is happy or creative. | Mary is generous. | contradiction | (((~kind(alice)|tall(alice)))<=>(?[X]:((~calm(X)<~>~tall(X)))))&
(![X]:((funny(X)|curious(X))=>(tall(X)<~>happy(X))))&
(![X]:((calm(X)&~generous(X))<=>~wise(X)))&
(![X]:((~rich(X)&~generous(X))<=>(rich(X)|calm(X))))&
(![X]:((tall(X)<~>~generous(X))<=>(~creative(X)|~kind(X))))&
(((~funny(paul)<~>~creative(paul)))=>(?[X]:((generous(X)<~>brave(X)))))&
((~funny(fred))<=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:((kind(X)&rich(X))))<=>(?[X]:((brave(X)&~strong(X)))))&
(((~rich(susan)|~brave(susan)))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((quiet(X)|~curious(X))<=>(~creative(X)&happy(X))))&
(![X]:((tall(X)|~strong(X))=>(~tall(X)&kind(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(kind(X))))&
(![X]:((~calm(X)|strong(X))=>(~curious(X)&strong(X))))&
(![X]:((~funny(X)&kind(X))=>(~calm(X)&~humble(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(~strong(X)|wise(X))))&
((~curious(john))=>(~quiet(fred)))&
(strong(fred))&
(?[X]:(~creative(X)))&
(?[X]:(old(X)))&
(?[X]:(~humble(X)))&
((happy(mary)|creative(mary))) | generous(mary) | [
"p3",
"p4",
"p7",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3817227753108899257974
% SZS output start Proof for 3817227753108899257974
4. ! [X0] : ((~generous(X0) & ~rich(X0)) <=> (calm(X0) | rich(X0))) [input p3]
5. ! [X0] : ((tall(X0) <~> ~generous(X0)) <=> (~kind(X0) | ~creative(X0))) [input p4]
8. ? [X0] : (rich(X0) & kind(X0)) <=> ? [X0] : (~strong(X0) & brave(X0)) [input p7]
10. ! [X0] : ((~curious(X0) | quiet(X0)) <=> (happy(X0) & ~creative(X0))) [input p9]
11. ! [X0] : ((~strong(X0) | tall(X0)) => (kind(X0) & ~tall(X0))) [input p10]
13. ! [X0] : ((strong(X0) | ~calm(X0)) => (strong(X0) & ~curious(X0))) [input p12]
15. ! [X0] : ((~brave(X0) <~> kind(X0)) <=> (wise(X0) | ~strong(X0))) [input p14]
22. generous(mary) [input hypothesis]
23. ? [X0] : (rich(X0) & kind(X0)) <=> ? [X1] : (~strong(X1) & brave(X1)) [rectify 8]
28. ! [X0] : ((kind(X0) & ~tall(X0)) | (strong(X0) & ~tall(X0))) [ennf transformation 11]
29. ! [X0] : ((strong(X0) & ~curious(X0)) | (~strong(X0) & calm(X0))) [ennf transformation 13]
41. ! [X0] : (((~generous(X0) & ~rich(X0)) | (~calm(X0) & ~rich(X0))) & ((calm(X0) | rich(X0)) | (generous(X0) | rich(X0)))) [nnf transformation 4]
42. ! [X0] : (((~generous(X0) & ~rich(X0)) | (~calm(X0) & ~rich(X0))) & (calm(X0) | rich(X0) | generous(X0) | rich(X0))) [flattening 41]
43. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [nnf transformation 5]
44. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [flattening 43]
52. (? [X0] : (rich(X0) & kind(X0)) | ! [X1] : (strong(X1) | ~brave(X1))) & (? [X1] : (~strong(X1) & brave(X1)) | ! [X0] : (~rich(X0) | ~kind(X0))) [nnf transformation 23]
53. (? [X0] : (rich(X0) & kind(X0)) | ! [X1] : (strong(X1) | ~brave(X1))) & (? [X2] : (~strong(X2) & brave(X2)) | ! [X3] : (~rich(X3) | ~kind(X3))) [rectify 52]
54. ? [X0] : (rich(X0) & kind(X0)) => (rich(sK3) & kind(sK3)) [choice axiom]
55. ? [X2] : (~strong(X2) & brave(X2)) => (~strong(sK4) & brave(sK4)) [choice axiom]
56. ((rich(sK3) & kind(sK3)) | ! [X1] : (strong(X1) | ~brave(X1))) & ((~strong(sK4) & brave(sK4)) | ! [X3] : (~rich(X3) | ~kind(X3))) [skolemisation 53,55,54]
62. ! [X0] : (((~curious(X0) | quiet(X0)) | (~happy(X0) | creative(X0))) & ((happy(X0) & ~creative(X0)) | (curious(X0) & ~quiet(X0)))) [nnf transformation 10]
63. ! [X0] : ((~curious(X0) | quiet(X0) | ~happy(X0) | creative(X0)) & ((happy(X0) & ~creative(X0)) | (curious(X0) & ~quiet(X0)))) [flattening 62]
69. ! [X0] : ((((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | (~wise(X0) & strong(X0))) & ((wise(X0) | ~strong(X0)) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))))) [nnf transformation 15]
70. ! [X0] : ((((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | (~wise(X0) & strong(X0))) & (wise(X0) | ~strong(X0) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))))) [flattening 69]
89. ~rich(X0) | ~rich(X0) [cnf transformation 42]
95. ~generous(X0) | tall(X0) | creative(X0) [cnf transformation 44]
110. rich(sK3) | strong(X1) | ~brave(X1) [cnf transformation 56]
118. ~creative(X0) | curious(X0) [cnf transformation 63]
122. ~tall(X0) | ~tall(X0) [cnf transformation 28]
125. strong(X0) | kind(X0) [cnf transformation 28]
129. ~strong(X0) | ~curious(X0) [cnf transformation 29]
138. ~kind(X0) | brave(X0) | strong(X0) [cnf transformation 70]
145. generous(mary) [cnf transformation 22]
146. ~tall(X0) [duplicate literal removal 122]
148. ~rich(X0) [duplicate literal removal 89]
220. ~brave(X1) | strong(X1) [subsumption resolution 110,148]
255. brave(X0) | strong(X0) [subsumption resolution 138,125]
256. strong(X0) [subsumption resolution 255,220]
273. 26 <=> creative(mary) [avatar definition]
275. creative(mary) <- (26) [avatar component clause 273]
297. ~curious(X1) [resolution 129,256]
314. tall(mary) | creative(mary) [resolution 95,145]
316. creative(mary) [subsumption resolution 314,146]
317. 26 [avatar split clause 316,273]
334. curious(mary) <- (26) [resolution 275,118]
335. $false <- (26) [subsumption resolution 334,297]
336. ~26 [avatar contradiction clause 335]
337. $false [avatar sat refutation 317,336]
% SZS output end Proof for 3817227753108899257974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or not funny then someone is both patient and not quiet and vice versa.
Everyone who is either rich or calm is either not happy or patient and vice versa.
If someone is both not patient and not strong then someone is both funny and not wise.
Everyone who is either wise or quiet is curious.
Everyone who is both not old and strong is wise or not brave.
Everyone who is both not kind and not calm is humble and vice versa.
If john is either not patient or curious then someone is both not happy and not kind.
Everyone who is humble is not quiet or not funny and vice versa.
Everyone who is not kind is both brave and funny.
Everyone who is both not brave and not quiet is not kind or tall.
Everyone who is not humble or not happy is both tall and quiet and vice versa.
If lucy is both humble and not generous then someone is both not tall and not wise and vice versa.
If fred is both patient and kind then someone is old or humble and vice versa.
Everyone who is happy is both curious and happy and vice versa.
If lucy is either brave or tall then someone is both curious and not generous.
Everyone who is rich is both creative and not humble and vice versa.
Someone is not tall.
Susan is both not tall and curious.
Someone is generous.
Susan is both humble and not tall.
Someone is funny or kind.
Lucy is either not kind or creative.
Someone is generous or kind.
Someone is either not quiet or not brave. | Fred is not humble. | entailment | ((?[X]:((~happy(X)<~>~funny(X))))<=>(?[X]:((patient(X)&~quiet(X)))))&
(![X]:((rich(X)<~>calm(X))<=>(~happy(X)<~>patient(X))))&
((?[X]:((~patient(X)&~strong(X))))=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((wise(X)<~>quiet(X))=>curious(X)))&
(![X]:((~old(X)&strong(X))=>(wise(X)|~brave(X))))&
(![X]:((~kind(X)&~calm(X))<=>humble(X)))&
(((~patient(john)<~>curious(john)))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:(humble(X)<=>(~quiet(X)|~funny(X))))&
(![X]:(~kind(X)=>(brave(X)&funny(X))))&
(![X]:((~brave(X)&~quiet(X))=>(~kind(X)|tall(X))))&
(![X]:((~humble(X)|~happy(X))<=>(tall(X)&quiet(X))))&
(((humble(lucy)&~generous(lucy)))<=>(?[X]:((~tall(X)&~wise(X)))))&
(((patient(fred)&kind(fred)))<=>(?[X]:((old(X)|humble(X)))))&
(![X]:(happy(X)<=>(curious(X)&happy(X))))&
(((brave(lucy)<~>tall(lucy)))=>(?[X]:((curious(X)&~generous(X)))))&
(![X]:(rich(X)<=>(creative(X)&~humble(X))))&
(?[X]:(~tall(X)))&
((~tall(susan)&curious(susan)))&
(?[X]:(generous(X)))&
((humble(susan)&~tall(susan)))&
(?[X]:((funny(X)|kind(X))))&
((~kind(lucy)<~>creative(lucy)))&
(?[X]:((generous(X)|kind(X))))&
(?[X]:((~quiet(X)<~>~brave(X)))) | ~humble(fred) | [
"p5",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 393393537267530126400195
% SZS output start Proof for 393393537267530126400195
6. ! [X0] : ((~calm(X0) & ~kind(X0)) <=> humble(X0)) [input p5]
13. (kind(fred) & patient(fred)) <=> ? [X0] : (humble(X0) | old(X0)) [input p12]
20. ~tall(susan) & humble(susan) [input p19]
25. humble(fred) [input hypothesis]
47. ! [X0] : (((~calm(X0) & ~kind(X0)) | ~humble(X0)) & (humble(X0) | (calm(X0) | kind(X0)))) [nnf transformation 6]
48. ! [X0] : (((~calm(X0) & ~kind(X0)) | ~humble(X0)) & (humble(X0) | calm(X0) | kind(X0))) [flattening 47]
61. ((kind(fred) & patient(fred)) | ! [X0] : (~humble(X0) & ~old(X0))) & (? [X0] : (humble(X0) | old(X0)) | (~kind(fred) | ~patient(fred))) [nnf transformation 13]
62. ((kind(fred) & patient(fred)) | ! [X0] : (~humble(X0) & ~old(X0))) & (? [X0] : (humble(X0) | old(X0)) | ~kind(fred) | ~patient(fred)) [flattening 61]
63. ((kind(fred) & patient(fred)) | ! [X0] : (~humble(X0) & ~old(X0))) & (? [X1] : (humble(X1) | old(X1)) | ~kind(fred) | ~patient(fred)) [rectify 62]
64. ? [X1] : (humble(X1) | old(X1)) => (humble(sK5) | old(sK5)) [choice axiom]
65. ((kind(fred) & patient(fred)) | ! [X0] : (~humble(X0) & ~old(X0))) & ((humble(sK5) | old(sK5)) | ~kind(fred) | ~patient(fred)) [skolemisation 63,64]
105. ~humble(X0) | ~kind(X0) [cnf transformation 48]
130. kind(fred) | ~humble(X0) [cnf transformation 65]
145. humble(susan) [cnf transformation 20]
153. humble(fred) [cnf transformation 25]
243. 20 <=> ! [X0] : ~humble(X0) [avatar definition]
244. ~humble(X0) <- (20) [avatar component clause 243]
246. 21 <=> kind(fred) [avatar definition]
248. kind(fred) <- (21) [avatar component clause 246]
249. 20 | 21 [avatar split clause 130,246,243]
318. $false <- (20) [resolution 244,145]
321. ~20 [avatar contradiction clause 318]
325. ~kind(fred) [resolution 105,153]
326. $false <- (21) [subsumption resolution 325,248]
327. ~21 [avatar contradiction clause 326]
328. $false [avatar sat refutation 249,321,327]
% SZS output end Proof for 393393537267530126400195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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