premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is generous or curious is not curious or quiet and vice versa.
Everyone who is either funny or tall is creative.
If mary is calm then someone is not old.
If someone is wise or not calm then someone is patient and vice versa.
Everyone who is not quiet or not creative is either not tall or quiet.
If mary is both creative and brave then susan is both not curious and brave and vice versa.
Everyone who is not old or not brave is either not tall or old.
If someone is not quiet then fred is not rich.
Everyone who is either curious or kind is not humble and vice versa.
If someone is both humble and brave then john is not creative or not kind.
If someone is quiet or not strong then someone is either not strong or happy.
Everyone who is either not creative or generous is either not patient or not old and vice versa.
Everyone who is not quiet is old or kind and vice versa.
Everyone who is both humble and tall is both creative and rich and vice versa.
If someone is either tall or old then someone is either not creative or wise and vice versa.
Everyone who is both not tall and not humble is quiet and vice versa.
Someone is both not quiet and wise.
Someone is calm.
Fred is curious.
John is not tall or curious.
Someone is not generous or not creative.
Someone is calm or not wise.
Mary is both patient and not humble. | Fred is creative. | entailment | (![X]:((generous(X)|curious(X))<=>(~curious(X)|quiet(X))))&
(![X]:((funny(X)<~>tall(X))=>creative(X)))&
((calm(mary))=>(?[X]:(~old(X))))&
((?[X]:((wise(X)|~calm(X))))<=>(?[X]:(patient(X))))&
(![X]:((~quiet(X)|~creative(X))=>(~tall(X)<~>quiet(X))))&
(((creative(mary)&brave(mary)))<=>((~curious(susan)&brave(susan))))&
(![X]:((~old(X)|~brave(X))=>(~tall(X)<~>old(X))))&
((?[X]:(~quiet(X)))=>(~rich(fred)))&
(![X]:((curious(X)<~>kind(X))<=>~humble(X)))&
((?[X]:((humble(X)&brave(X))))=>((~creative(john)|~kind(john))))&
((?[X]:((quiet(X)|~strong(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
(![X]:((~creative(X)<~>generous(X))<=>(~patient(X)<~>~old(X))))&
(![X]:(~quiet(X)<=>(old(X)|kind(X))))&
(![X]:((humble(X)&tall(X))<=>(creative(X)&rich(X))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((~creative(X)<~>wise(X)))))&
(![X]:((~tall(X)&~humble(X))<=>quiet(X)))&
(?[X]:((~quiet(X)&wise(X))))&
(?[X]:(calm(X)))&
(curious(fred))&
((~tall(john)|curious(john)))&
(?[X]:((~generous(X)|~creative(X))))&
(?[X]:((calm(X)|~wise(X))))&
((patient(mary)&~humble(mary))) | creative(fred) | [
"p0",
"p4",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1632275882603972735196702
% SZS output start Proof for 1632275882603972735196702
1. ! [X0] : ((curious(X0) | generous(X0)) <=> (quiet(X0) | ~curious(X0))) [input p0]
5. ! [X0] : ((~creative(X0) | ~quiet(X0)) => (~tall(X0) <~> quiet(X0))) [input p4]
16. ! [X0] : ((~humble(X0) & ~tall(X0)) <=> quiet(X0)) [input p15]
19. curious(fred) [input p18]
24. ~creative(fred) [input hypothesis]
30. ! [X0] : ((~tall(X0) <~> quiet(X0)) | (creative(X0) & quiet(X0))) [ennf transformation 5]
36. ! [X0] : (((curious(X0) | generous(X0)) | (~quiet(X0) & curious(X0))) & ((quiet(X0) | ~curious(X0)) | (~curious(X0) & ~generous(X0)))) [nnf transformation 1]
37. ! [X0] : ((curious(X0) | generous(X0) | (~quiet(X0) & curious(X0))) & (quiet(X0) | ~curious(X0) | (~curious(X0) & ~generous(X0)))) [flattening 36]
46. ! [X0] : (((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (creative(X0) & quiet(X0))) [nnf transformation 30]
65. ! [X0] : (((~humble(X0) & ~tall(X0)) | ~quiet(X0)) & (quiet(X0) | (humble(X0) | tall(X0)))) [nnf transformation 16]
66. ! [X0] : (((~humble(X0) & ~tall(X0)) | ~quiet(X0)) & (quiet(X0) | humble(X0) | tall(X0))) [flattening 65]
76. quiet(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 37]
85. quiet(X0) | ~tall(X0) | quiet(X0) [cnf transformation 46]
88. ~quiet(X0) | tall(X0) | creative(X0) [cnf transformation 46]
131. ~tall(X0) | ~quiet(X0) [cnf transformation 66]
136. curious(fred) [cnf transformation 19]
142. ~creative(fred) [cnf transformation 24]
144. ~tall(X0) | quiet(X0) [duplicate literal removal 85]
145. ~curious(X0) | quiet(X0) [duplicate literal removal 76]
273. ~tall(X0) [subsumption resolution 131,144]
293. quiet(fred) [resolution 145,136]
310. tall(fred) | creative(fred) [resolution 88,293]
313. creative(fred) [subsumption resolution 310,273]
314. $false [subsumption resolution 313,142]
% SZS output end Proof for 1632275882603972735196702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is happy or tall then susan is either brave or happy and vice versa.
If someone is either patient or strong then paul is both not patient and not tall.
Everyone who is funny is not patient and vice versa.
If paul is curious or not wise then paul is curious.
If someone is not old then someone is either strong or not strong.
If someone is either not patient or not happy then mary is brave and vice versa.
If someone is not creative or tall then someone is either not quiet or tall and vice versa.
Everyone who is either wise or generous is either calm or old.
Everyone who is both rich and not funny is not quiet or wise.
If mary is humble or not kind then susan is both wise and not curious.
Everyone who is both kind and creative is wise or funny and vice versa.
Everyone who is not quiet is both happy and not tall and vice versa.
If alice is both curious and not tall then someone is curious or rich.
Everyone who is not humble is both not happy and curious.
If alice is either not tall or not generous then someone is both kind and not kind and vice versa.
Everyone who is both rich and not patient is humble or not humble.
Mary is not generous or old.
Someone is either wise or happy.
Mary is either creative or not quiet.
Someone is not old or not curious.
Susan is not tall.
Someone is not brave.
Someone is quiet.
Someone is brave or not happy. | Mary is not generous. | neutral | (((happy(susan)|tall(susan)))<=>((brave(susan)<~>happy(susan))))&
((?[X]:((patient(X)<~>strong(X))))=>((~patient(paul)&~tall(paul))))&
(![X]:(funny(X)<=>~patient(X)))&
(((curious(paul)|~wise(paul)))=>(curious(paul)))&
((?[X]:(~old(X)))=>(?[X]:((strong(X)<~>~strong(X)))))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(brave(mary)))&
((?[X]:((~creative(X)|tall(X))))<=>(?[X]:((~quiet(X)<~>tall(X)))))&
(![X]:((wise(X)<~>generous(X))=>(calm(X)<~>old(X))))&
(![X]:((rich(X)&~funny(X))=>(~quiet(X)|wise(X))))&
(((humble(mary)|~kind(mary)))=>((wise(susan)&~curious(susan))))&
(![X]:((kind(X)&creative(X))<=>(wise(X)|funny(X))))&
(![X]:(~quiet(X)<=>(happy(X)&~tall(X))))&
(((curious(alice)&~tall(alice)))=>(?[X]:((curious(X)|rich(X)))))&
(![X]:(~humble(X)=>(~happy(X)&curious(X))))&
(((~tall(alice)<~>~generous(alice)))<=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((rich(X)&~patient(X))=>(humble(X)|~humble(X))))&
((~generous(mary)|old(mary)))&
(?[X]:((wise(X)<~>happy(X))))&
((creative(mary)<~>~quiet(mary)))&
(?[X]:((~old(X)|~curious(X))))&
(~tall(susan))&
(?[X]:(~brave(X)))&
(?[X]:(quiet(X)))&
(?[X]:((brave(X)|~happy(X)))) | ~generous(mary) | [] | null | 0 |
Everyone who is both patient and rich is strong or not strong and vice versa. Everyone who is humble is creative or not patient and vice versa. If paul is either humble or generous then someone is either brave or not quiet and vice versa. If someone is both old and tall then someone is either humble or not quiet. Everyone who is not tall or wise is not creative. If mary is either quiet or not humble then someone is both not humble and strong and vice versa. If susan is not tall then someone is strong or not patient and vice versa. If someone is curious or old then lucy is both not old and rich and vice versa. Everyone who is not rich or not brave is funny and vice versa. If someone is not generous then mary is both curious and not happy and vice versa. Everyone who is either not strong or strong is creative or calm. Everyone who is both not quiet and funny is not brave or generous. Everyone who is not tall or not generous is strong or not rich and vice versa. If someone is not calm then someone is rich or kind. If alice is either not humble or patient then someone is calm or not happy. Everyone who is not humble or not tall is both old and not humble and vice versa. Someone is brave or not curious. Someone is either funny or tall. Lucy is funny. Someone is happy or not tall. Susan is not strong or not old. Someone is both not happy and kind. | Paul is humble. | neutral | (![X]:((patient(X)&rich(X))<=>(strong(X)|~strong(X))))&
(![X]:(humble(X)<=>(creative(X)|~patient(X))))&
(((humble(paul)<~>generous(paul)))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
((?[X]:((old(X)&tall(X))))=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
(((quiet(mary)<~>~humble(mary)))<=>(?[X]:((~humble(X)&strong(X)))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((curious(X)|old(X))))<=>((~old(lucy)&rich(lucy))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)|calm(X))))&
(![X]:((~quiet(X)&funny(X))=>(~brave(X)|generous(X))))&
(![X]:((~tall(X)|~generous(X))<=>(strong(X)|~rich(X))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(((~humble(alice)<~>patient(alice)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((~humble(X)|~tall(X))<=>(old(X)&~humble(X))))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X))))&
(funny(lucy))&
(?[X]:((happy(X)|~tall(X))))&
((~strong(susan)|~old(susan)))&
(?[X]:((~happy(X)&kind(X)))) | humble(paul) | [] | null | 0 |
If someone is both not kind and not brave then susan is not humble.
If someone is old or not calm then paul is tall and vice versa.
Everyone who is old or funny is both not tall and not funny and vice versa.
If someone is either not happy or kind then mary is rich or curious.
If john is both not funny and not tall then fred is either quiet or wise and vice versa.
If alice is generous or not kind then someone is both kind and not creative.
If susan is not brave or rich then someone is either humble or not tall.
If someone is either not calm or humble then alice is both not strong and funny.
Everyone who is either not tall or humble is either patient or tall.
Everyone who is either curious or old is not generous or not old and vice versa.
If someone is both rich and not tall then someone is both quiet and rich.
Everyone who is calm is not brave or creative.
If someone is creative then susan is both not quiet and not tall and vice versa.
If someone is both not generous and not curious then alice is either not happy or strong.
If someone is either not old or not creative then mary is wise.
Everyone who is strong or not tall is funny.
Paul is not happy.
Someone is tall.
Someone is either not brave or calm.
Someone is either tall or patient. | Fred is not creative. | entailment | ((?[X]:((~kind(X)&~brave(X))))=>(~humble(susan)))&
((?[X]:((old(X)|~calm(X))))<=>(tall(paul)))&
(![X]:((old(X)|funny(X))<=>(~tall(X)&~funny(X))))&
((?[X]:((~happy(X)<~>kind(X))))=>((rich(mary)|curious(mary))))&
(((~funny(john)&~tall(john)))<=>((quiet(fred)<~>wise(fred))))&
(((generous(alice)|~kind(alice)))=>(?[X]:((kind(X)&~creative(X)))))&
(((~brave(susan)|rich(susan)))=>(?[X]:((humble(X)<~>~tall(X)))))&
((?[X]:((~calm(X)<~>humble(X))))=>((~strong(alice)&funny(alice))))&
(![X]:((~tall(X)<~>humble(X))=>(patient(X)<~>tall(X))))&
(![X]:((curious(X)<~>old(X))<=>(~generous(X)|~old(X))))&
((?[X]:((rich(X)&~tall(X))))=>(?[X]:((quiet(X)&rich(X)))))&
(![X]:(calm(X)=>(~brave(X)|creative(X))))&
((?[X]:(creative(X)))<=>((~quiet(susan)&~tall(susan))))&
((?[X]:((~generous(X)&~curious(X))))=>((~happy(alice)<~>strong(alice))))&
((?[X]:((~old(X)<~>~creative(X))))=>(wise(mary)))&
(![X]:((strong(X)|~tall(X))=>funny(X)))&
(~happy(paul))&
(?[X]:(tall(X)))&
(?[X]:((~brave(X)<~>calm(X))))&
(?[X]:((tall(X)<~>patient(X)))) | ~creative(fred) | [
"p2",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1345848985143572649894707
% SZS output start Proof for 1345848985143572649894707
3. ! [X0] : ((funny(X0) | old(X0)) <=> (~funny(X0) & ~tall(X0))) [input p2]
13. ? [X0] : creative(X0) <=> (~tall(susan) & ~quiet(susan)) [input p12]
16. ! [X0] : ((~tall(X0) | strong(X0)) => funny(X0)) [input p15]
21. creative(fred) [input hypothesis]
35. ! [X0] : (funny(X0) | (tall(X0) & ~strong(X0))) [ennf transformation 16]
40. ! [X0] : (((funny(X0) | old(X0)) | (funny(X0) | tall(X0))) & ((~funny(X0) & ~tall(X0)) | (~funny(X0) & ~old(X0)))) [nnf transformation 3]
41. ! [X0] : ((funny(X0) | old(X0) | funny(X0) | tall(X0)) & ((~funny(X0) & ~tall(X0)) | (~funny(X0) & ~old(X0)))) [flattening 40]
57. (? [X0] : creative(X0) | (tall(susan) | quiet(susan))) & ((~tall(susan) & ~quiet(susan)) | ! [X0] : ~creative(X0)) [nnf transformation 13]
58. (? [X0] : creative(X0) | tall(susan) | quiet(susan)) & ((~tall(susan) & ~quiet(susan)) | ! [X0] : ~creative(X0)) [flattening 57]
59. (? [X0] : creative(X0) | tall(susan) | quiet(susan)) & ((~tall(susan) & ~quiet(susan)) | ! [X1] : ~creative(X1)) [rectify 58]
60. ? [X0] : creative(X0) => creative(sK4) [choice axiom]
61. (creative(sK4) | tall(susan) | quiet(susan)) & ((~tall(susan) & ~quiet(susan)) | ! [X1] : ~creative(X1)) [skolemisation 59,60]
79. ~funny(X0) | ~funny(X0) [cnf transformation 41]
115. ~tall(susan) | ~creative(X1) [cnf transformation 61]
122. funny(X0) | tall(X0) [cnf transformation 35]
129. creative(fred) [cnf transformation 21]
134. ~funny(X0) [duplicate literal removal 79]
260. 27 <=> tall(susan) [avatar definition]
261. ~tall(susan) <- (~27) [avatar component clause 260]
269. 29 <=> ! [X1] : ~creative(X1) [avatar definition]
270. ~creative(X1) <- (29) [avatar component clause 269]
271. 29 | ~27 [avatar split clause 115,260,269]
300. tall(X0) [subsumption resolution 122,134]
313. $false <- (~27) [subsumption resolution 261,300]
314. 27 [avatar contradiction clause 313]
319. $false <- (29) [resolution 270,129]
322. ~29 [avatar contradiction clause 319]
323. $false [avatar sat refutation 271,314,322]
% SZS output end Proof for 1345848985143572649894707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both patient and not wise then someone is rich. Everyone who is both happy and not generous is either calm or not old and vice versa. If someone is happy or not tall then someone is both not old and quiet and vice versa. Everyone who is generous is either old or not rich and vice versa. Everyone who is not curious is both funny and not brave and vice versa. Everyone who is either not happy or not funny is brave. Everyone who is either not happy or calm is happy. If fred is both curious and not rich then someone is either not creative or strong and vice versa. If alice is brave or not brave then someone is wise and vice versa. Everyone who is not funny is both brave and not curious. If someone is calm then someone is either not old or funny and vice versa. Everyone who is either creative or not happy is both humble and not old. Everyone who is both not funny and happy is not kind or happy. Everyone who is creative is either not patient or not brave and vice versa. Everyone who is either not kind or not old is either kind or brave and vice versa. Lucy is not humble or not curious. Someone is either quiet or not rich. Someone is both not patient and not generous. Someone is not curious or tall. Someone is generous. Mary is either creative or patient. Someone is both rich and patient. | Fred is not happy. | contradiction | (((patient(lucy)&~wise(lucy)))=>(?[X]:(rich(X))))&
(![X]:((happy(X)&~generous(X))<=>(calm(X)<~>~old(X))))&
((?[X]:((happy(X)|~tall(X))))<=>(?[X]:((~old(X)&quiet(X)))))&
(![X]:(generous(X)<=>(old(X)<~>~rich(X))))&
(![X]:(~curious(X)<=>(funny(X)&~brave(X))))&
(![X]:((~happy(X)<~>~funny(X))=>brave(X)))&
(![X]:((~happy(X)<~>calm(X))=>happy(X)))&
(((curious(fred)&~rich(fred)))<=>(?[X]:((~creative(X)<~>strong(X)))))&
(((brave(alice)|~brave(alice)))<=>(?[X]:(wise(X))))&
(![X]:(~funny(X)=>(brave(X)&~curious(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~old(X)<~>funny(X)))))&
(![X]:((creative(X)<~>~happy(X))=>(humble(X)&~old(X))))&
(![X]:((~funny(X)&happy(X))=>(~kind(X)|happy(X))))&
(![X]:(creative(X)<=>(~patient(X)<~>~brave(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(kind(X)<~>brave(X))))&
((~humble(lucy)|~curious(lucy)))&
(?[X]:((quiet(X)<~>~rich(X))))&
(?[X]:((~patient(X)&~generous(X))))&
(?[X]:((~curious(X)|tall(X))))&
(?[X]:(generous(X)))&
((creative(mary)<~>patient(mary)))&
(?[X]:((rich(X)&patient(X)))) | ~happy(fred) | [
"p1",
"p4",
"p5",
"p6",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8572593509089148312438010
% SZS output start Proof for 8572593509089148312438010
2. ! [X0] : ((~generous(X0) & happy(X0)) <=> (calm(X0) <~> ~old(X0))) [input p1]
5. ! [X0] : (~curious(X0) <=> (~brave(X0) & funny(X0))) [input p4]
6. ! [X0] : ((~happy(X0) <~> ~funny(X0)) => brave(X0)) [input p5]
7. ! [X0] : ((~happy(X0) <~> calm(X0)) => happy(X0)) [input p6]
10. ! [X0] : (~funny(X0) => (~curious(X0) & brave(X0))) [input p9]
15. ! [X0] : ((~kind(X0) <~> ~old(X0)) <=> (kind(X0) <~> brave(X0))) [input p14]
23. ~happy(fred) [input hypothesis]
28. ! [X0] : (brave(X0) | (~happy(X0) <=> ~funny(X0))) [ennf transformation 6]
29. ! [X0] : (happy(X0) | (~happy(X0) <=> calm(X0))) [ennf transformation 7]
30. ! [X0] : ((~curious(X0) & brave(X0)) | funny(X0)) [ennf transformation 10]
36. ! [X0] : (((~generous(X0) & happy(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | (generous(X0) | ~happy(X0)))) [nnf transformation 2]
37. ! [X0] : (((~generous(X0) & happy(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | generous(X0) | ~happy(X0))) [flattening 36]
44. ! [X0] : ((~curious(X0) | (brave(X0) | ~funny(X0))) & ((~brave(X0) & funny(X0)) | curious(X0))) [nnf transformation 5]
45. ! [X0] : ((~curious(X0) | brave(X0) | ~funny(X0)) & ((~brave(X0) & funny(X0)) | curious(X0))) [flattening 44]
46. ! [X0] : (brave(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) [nnf transformation 28]
47. ! [X0] : (happy(X0) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0)))) [nnf transformation 29]
65. ! [X0] : ((((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) & (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0))))) [nnf transformation 15]
81. ~old(X0) | happy(X0) | ~calm(X0) [cnf transformation 37]
94. funny(X0) | curious(X0) [cnf transformation 45]
97. ~funny(X0) | brave(X0) | happy(X0) [cnf transformation 46]
99. happy(X0) | calm(X0) | happy(X0) [cnf transformation 47]
111. ~curious(X0) | funny(X0) [cnf transformation 30]
128. ~brave(X0) | ~kind(X0) | ~kind(X0) | old(X0) [cnf transformation 65]
132. old(X0) | kind(X0) | kind(X0) | ~brave(X0) [cnf transformation 65]
144. ~happy(fred) [cnf transformation 23]
146. ~brave(X0) | ~kind(X0) | old(X0) [duplicate literal removal 128]
148. ~brave(X0) | kind(X0) | old(X0) [duplicate literal removal 132]
149. calm(X0) | happy(X0) [duplicate literal removal 99]
231. funny(X0) [subsumption resolution 111,94]
250. ~brave(X0) | old(X0) [subsumption resolution 146,148]
382. brave(X1) | happy(X1) [resolution 97,231]
507. old(X2) | happy(X2) [resolution 382,250]
589. happy(X1) | happy(X1) | ~calm(X1) [resolution 507,81]
597. happy(X1) | ~calm(X1) [duplicate literal removal 589]
598. happy(X1) [subsumption resolution 597,149]
715. $false [resolution 598,144]
% SZS output end Proof for 8572593509089148312438010
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not curious is not strong and vice versa.
Everyone who is both humble and curious is both not patient and not humble.
Everyone who is not strong is either brave or not strong.
Everyone who is both kind and not happy is either generous or not generous and vice versa.
Everyone who is both calm and not brave is either not tall or not calm.
If someone is either old or creative then someone is either not happy or not tall and vice versa.
Everyone who is either not tall or generous is not patient.
If someone is not calm then someone is not tall.
Everyone who is calm is not wise.
If lucy is not patient or tall then someone is either not calm or not brave.
If someone is both happy and kind then someone is patient and vice versa.
If someone is happy then mary is not brave and vice versa.
If someone is either patient or not strong then someone is either humble or kind.
Everyone who is quiet or not funny is either not old or patient.
Everyone who is calm or not patient is either rich or patient.
Someone is either not old or not creative.
Someone is either creative or not happy.
Susan is either not patient or generous.
Someone is either happy or not old.
Lucy is either curious or not quiet.
Someone is both not happy and not quiet.
Paul is both curious and kind. | Lucy is not happy. | entailment | (![X]:((~tall(X)<~>~curious(X))<=>~strong(X)))&
(![X]:((humble(X)&curious(X))=>(~patient(X)&~humble(X))))&
(![X]:(~strong(X)=>(brave(X)<~>~strong(X))))&
(![X]:((kind(X)&~happy(X))<=>(generous(X)<~>~generous(X))))&
(![X]:((calm(X)&~brave(X))=>(~tall(X)<~>~calm(X))))&
((?[X]:((old(X)<~>creative(X))))<=>(?[X]:((~happy(X)<~>~tall(X)))))&
(![X]:((~tall(X)<~>generous(X))=>~patient(X)))&
((?[X]:(~calm(X)))=>(?[X]:(~tall(X))))&
(![X]:(calm(X)=>~wise(X)))&
(((~patient(lucy)|tall(lucy)))=>(?[X]:((~calm(X)<~>~brave(X)))))&
((?[X]:((happy(X)&kind(X))))<=>(?[X]:(patient(X))))&
((?[X]:(happy(X)))<=>(~brave(mary)))&
((?[X]:((patient(X)<~>~strong(X))))=>(?[X]:((humble(X)<~>kind(X)))))&
(![X]:((quiet(X)|~funny(X))=>(~old(X)<~>patient(X))))&
(![X]:((calm(X)|~patient(X))=>(rich(X)<~>patient(X))))&
(?[X]:((~old(X)<~>~creative(X))))&
(?[X]:((creative(X)<~>~happy(X))))&
((~patient(susan)<~>generous(susan)))&
(?[X]:((happy(X)<~>~old(X))))&
((curious(lucy)<~>~quiet(lucy)))&
(?[X]:((~happy(X)&~quiet(X))))&
((curious(paul)&kind(paul))) | ~happy(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1064373393350720613435310
% SZS output start Proof for 1064373393350720613435310
4. ! [X0] : ((~happy(X0) & kind(X0)) <=> (generous(X0) <~> ~generous(X0))) [input p3]
23. happy(lucy) [input hypothesis]
43. ! [X0] : (((~happy(X0) & kind(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | (happy(X0) | ~kind(X0)))) [nnf transformation 4]
44. ! [X0] : (((~happy(X0) & kind(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | happy(X0) | ~kind(X0))) [flattening 43]
98. ~happy(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 44]
99. ~happy(X0) | generous(X0) | generous(X0) [cnf transformation 44]
146. happy(lucy) [cnf transformation 23]
151. ~happy(X0) | ~generous(X0) [duplicate literal removal 98]
152. ~happy(X0) | generous(X0) [duplicate literal removal 99]
155. ~happy(X0) [subsumption resolution 151,152]
251. $false [subsumption resolution 146,155]
% SZS output end Proof for 1064373393350720613435310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not tall then someone is both not calm and not strong.
Everyone who is not generous is both not happy and tall.
Everyone who is tall or humble is either not creative or not funny.
Everyone who is both not curious and calm is either not wise or not curious.
Everyone who is either not generous or not humble is not rich or funny.
Everyone who is either brave or humble is both not quiet and calm.
If paul is both wise and curious then john is either not patient or not calm and vice versa.
If someone is both tall and not kind then mary is old.
If someone is both strong and not brave then mary is not brave.
Everyone who is patient or humble is not curious or brave and vice versa.
Everyone who is both not humble and tall is either patient or not generous.
Everyone who is creative or curious is quiet.
If someone is not wise or not humble then lucy is calm or old.
If john is either curious or not funny then someone is both not happy and curious.
Everyone who is not old or not calm is quiet.
If someone is not brave or creative then someone is kind and vice versa.
Fred is both old and not strong.
Mary is old or not brave.
Alice is not rich or not generous.
Someone is both old and not strong.
Fred is either not calm or not curious.
Alice is either not funny or not tall.
Someone is either old or tall.
Someone is brave. | John is curious. | neutral | ((~tall(paul))=>(?[X]:((~calm(X)&~strong(X)))))&
(![X]:(~generous(X)=>(~happy(X)&tall(X))))&
(![X]:((tall(X)|humble(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((~curious(X)&calm(X))=>(~wise(X)<~>~curious(X))))&
(![X]:((~generous(X)<~>~humble(X))=>(~rich(X)|funny(X))))&
(![X]:((brave(X)<~>humble(X))=>(~quiet(X)&calm(X))))&
(((wise(paul)&curious(paul)))<=>((~patient(john)<~>~calm(john))))&
((?[X]:((tall(X)&~kind(X))))=>(old(mary)))&
((?[X]:((strong(X)&~brave(X))))=>(~brave(mary)))&
(![X]:((patient(X)|humble(X))<=>(~curious(X)|brave(X))))&
(![X]:((~humble(X)&tall(X))=>(patient(X)<~>~generous(X))))&
(![X]:((creative(X)|curious(X))=>quiet(X)))&
((?[X]:((~wise(X)|~humble(X))))=>((calm(lucy)|old(lucy))))&
(((curious(john)<~>~funny(john)))=>(?[X]:((~happy(X)&curious(X)))))&
(![X]:((~old(X)|~calm(X))=>quiet(X)))&
((?[X]:((~brave(X)|creative(X))))<=>(?[X]:(kind(X))))&
((old(fred)&~strong(fred)))&
((old(mary)|~brave(mary)))&
((~rich(alice)|~generous(alice)))&
(?[X]:((old(X)&~strong(X))))&
((~calm(fred)<~>~curious(fred)))&
((~funny(alice)<~>~tall(alice)))&
(?[X]:((old(X)<~>tall(X))))&
(?[X]:(brave(X))) | curious(john) | [] | null | 0 |
If someone is either patient or strong then mary is both not curious and not kind. If mary is not strong then someone is not wise or happy. Everyone who is not happy is both generous and not creative. Everyone who is old or funny is not happy. Everyone who is not creative or not patient is both not strong and strong and vice versa. Everyone who is either not humble or not calm is generous. If someone is not wise then someone is not creative. Everyone who is either humble or not happy is both rich and brave and vice versa. If someone is both not tall and not calm then someone is wise or not strong. If someone is funny or not brave then someone is both not generous and not patient and vice versa. If alice is both not calm and rich then fred is both calm and not generous and vice versa. Everyone who is humble is quiet. If mary is not rich then lucy is not strong or not funny and vice versa. If someone is not tall then someone is strong. If someone is either calm or not brave then susan is not old or patient and vice versa. Someone is both not curious and not old. Someone is both humble and kind. Someone is not brave or not generous. Someone is brave. Alice is either not patient or not quiet. | Mary is rich. | contradiction | ((?[X]:((patient(X)<~>strong(X))))=>((~curious(mary)&~kind(mary))))&
((~strong(mary))=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:(~happy(X)=>(generous(X)&~creative(X))))&
(![X]:((old(X)|funny(X))=>~happy(X)))&
(![X]:((~creative(X)|~patient(X))<=>(~strong(X)&strong(X))))&
(![X]:((~humble(X)<~>~calm(X))=>generous(X)))&
((?[X]:(~wise(X)))=>(?[X]:(~creative(X))))&
(![X]:((humble(X)<~>~happy(X))<=>(rich(X)&brave(X))))&
((?[X]:((~tall(X)&~calm(X))))=>(?[X]:((wise(X)|~strong(X)))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~generous(X)&~patient(X)))))&
(((~calm(alice)&rich(alice)))<=>((calm(fred)&~generous(fred))))&
(![X]:(humble(X)=>quiet(X)))&
((~rich(mary))<=>((~strong(lucy)|~funny(lucy))))&
((?[X]:(~tall(X)))=>(?[X]:(strong(X))))&
((?[X]:((calm(X)<~>~brave(X))))<=>((~old(susan)|patient(susan))))&
(?[X]:((~curious(X)&~old(X))))&
(?[X]:((humble(X)&kind(X))))&
(?[X]:((~brave(X)|~generous(X))))&
(?[X]:(brave(X)))&
((~patient(alice)<~>~quiet(alice))) | rich(mary) | [
"p4",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2365401265876525267561297
% SZS output start Proof for 2365401265876525267561297
5. ! [X0] : ((~patient(X0) | ~creative(X0)) <=> (strong(X0) & ~strong(X0))) [input p4]
10. ? [X0] : (~brave(X0) | funny(X0)) <=> ? [X0] : (~patient(X0) & ~generous(X0)) [input p9]
13. ~rich(mary) <=> (~funny(lucy) | ~strong(lucy)) [input p12]
21. rich(mary) [input hypothesis]
24. ? [X0] : (~brave(X0) | funny(X0)) <=> ? [X1] : (~patient(X1) & ~generous(X1)) [rectify 10]
40. ! [X0] : (((~patient(X0) | ~creative(X0)) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | (patient(X0) & creative(X0)))) [nnf transformation 5]
41. ! [X0] : ((~patient(X0) | ~creative(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | (patient(X0) & creative(X0)))) [flattening 40]
48. (? [X0] : (~brave(X0) | funny(X0)) | ! [X1] : (patient(X1) | generous(X1))) & (? [X1] : (~patient(X1) & ~generous(X1)) | ! [X0] : (brave(X0) & ~funny(X0))) [nnf transformation 24]
49. (? [X0] : (~brave(X0) | funny(X0)) | ! [X1] : (patient(X1) | generous(X1))) & (? [X2] : (~patient(X2) & ~generous(X2)) | ! [X3] : (brave(X3) & ~funny(X3))) [rectify 48]
50. ? [X0] : (~brave(X0) | funny(X0)) => (~brave(sK2) | funny(sK2)) [choice axiom]
51. ? [X2] : (~patient(X2) & ~generous(X2)) => (~patient(sK3) & ~generous(sK3)) [choice axiom]
52. ((~brave(sK2) | funny(sK2)) | ! [X1] : (patient(X1) | generous(X1))) & ((~patient(sK3) & ~generous(sK3)) | ! [X3] : (brave(X3) & ~funny(X3))) [skolemisation 49,51,50]
55. (~rich(mary) | (funny(lucy) & strong(lucy))) & ((~funny(lucy) | ~strong(lucy)) | rich(mary)) [nnf transformation 13]
56. (~rich(mary) | (funny(lucy) & strong(lucy))) & (~funny(lucy) | ~strong(lucy) | rich(mary)) [flattening 55]
79. ~strong(X0) | patient(X0) [cnf transformation 41]
81. strong(X0) | patient(X0) [cnf transformation 41]
94. ~patient(sK3) | ~funny(X3) [cnf transformation 52]
104. ~rich(mary) | funny(lucy) [cnf transformation 56]
118. rich(mary) [cnf transformation 21]
144. patient(X0) [subsumption resolution 79,81]
148. ~funny(X3) [subsumption resolution 94,144]
169. ~rich(mary) [subsumption resolution 104,148]
174. $false [subsumption resolution 118,169]
% SZS output end Proof for 2365401265876525267561297
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or patient is either not creative or not tall and vice versa. Everyone who is not humble or not happy is old. Everyone who is both not kind and not humble is not creative and vice versa. If someone is either not patient or not rich then someone is not patient or not tall. Everyone who is not rich is both not creative and happy and vice versa. If mary is old then paul is not wise or not happy. Everyone who is not humble or old is both old and not rich and vice versa. Everyone who is curious or tall is either humble or not patient and vice versa. If fred is either calm or not funny then john is either not quiet or old and vice versa. If someone is not old or not quiet then mary is both not funny and not curious and vice versa. Everyone who is tall or wise is both humble and patient and vice versa. Everyone who is not funny or not wise is funny. Everyone who is both humble and funny is not happy or creative and vice versa. If someone is both wise and humble then susan is both quiet and not calm and vice versa. If mary is either funny or creative then someone is both not rich and not brave. If lucy is both not calm and brave then someone is both not brave and rich. Someone is curious or strong. Susan is either brave or not generous. Someone is either funny or patient. | John is happy. | entailment | (![X]:((~old(X)|patient(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((~humble(X)|~happy(X))=>old(X)))&
(![X]:((~kind(X)&~humble(X))<=>~creative(X)))&
((?[X]:((~patient(X)<~>~rich(X))))=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:(~rich(X)<=>(~creative(X)&happy(X))))&
((old(mary))=>((~wise(paul)|~happy(paul))))&
(![X]:((~humble(X)|old(X))<=>(old(X)&~rich(X))))&
(![X]:((curious(X)|tall(X))<=>(humble(X)<~>~patient(X))))&
(((calm(fred)<~>~funny(fred)))<=>((~quiet(john)<~>old(john))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~funny(mary)&~curious(mary))))&
(![X]:((tall(X)|wise(X))<=>(humble(X)&patient(X))))&
(![X]:((~funny(X)|~wise(X))=>funny(X)))&
(![X]:((humble(X)&funny(X))<=>(~happy(X)|creative(X))))&
((?[X]:((wise(X)&humble(X))))<=>((quiet(susan)&~calm(susan))))&
(((funny(mary)<~>creative(mary)))=>(?[X]:((~rich(X)&~brave(X)))))&
(((~calm(lucy)&brave(lucy)))=>(?[X]:((~brave(X)&rich(X)))))&
(?[X]:((curious(X)|strong(X))))&
((brave(susan)<~>~generous(susan)))&
(?[X]:((funny(X)<~>patient(X)))) | happy(john) | [
"p4",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4634715087389222038433869
% SZS output start Proof for 4634715087389222038433869
5. ! [X0] : (~rich(X0) <=> (happy(X0) & ~creative(X0))) [input p4]
7. ! [X0] : ((old(X0) | ~humble(X0)) <=> (~rich(X0) & old(X0))) [input p6]
10. ? [X0] : (~quiet(X0) | ~old(X0)) <=> (~curious(mary) & ~funny(mary)) [input p9]
12. ! [X0] : ((~wise(X0) | ~funny(X0)) => funny(X0)) [input p11]
20. ~happy(john) [input hypothesis]
27. ! [X0] : (funny(X0) | (wise(X0) & funny(X0))) [ennf transformation 12]
39. ! [X0] : ((~rich(X0) | (~happy(X0) | creative(X0))) & ((happy(X0) & ~creative(X0)) | rich(X0))) [nnf transformation 5]
40. ! [X0] : ((~rich(X0) | ~happy(X0) | creative(X0)) & ((happy(X0) & ~creative(X0)) | rich(X0))) [flattening 39]
41. ! [X0] : (((old(X0) | ~humble(X0)) | (rich(X0) | ~old(X0))) & ((~rich(X0) & old(X0)) | (~old(X0) & humble(X0)))) [nnf transformation 7]
42. ! [X0] : ((old(X0) | ~humble(X0) | rich(X0) | ~old(X0)) & ((~rich(X0) & old(X0)) | (~old(X0) & humble(X0)))) [flattening 41]
46. (? [X0] : (~quiet(X0) | ~old(X0)) | (curious(mary) | funny(mary))) & ((~curious(mary) & ~funny(mary)) | ! [X0] : (quiet(X0) & old(X0))) [nnf transformation 10]
47. (? [X0] : (~quiet(X0) | ~old(X0)) | curious(mary) | funny(mary)) & ((~curious(mary) & ~funny(mary)) | ! [X0] : (quiet(X0) & old(X0))) [flattening 46]
48. (? [X0] : (~quiet(X0) | ~old(X0)) | curious(mary) | funny(mary)) & ((~curious(mary) & ~funny(mary)) | ! [X1] : (quiet(X1) & old(X1))) [rectify 47]
49. ? [X0] : (~quiet(X0) | ~old(X0)) => (~quiet(sK1) | ~old(sK1)) [choice axiom]
50. ((~quiet(sK1) | ~old(sK1)) | curious(mary) | funny(mary)) & ((~curious(mary) & ~funny(mary)) | ! [X1] : (quiet(X1) & old(X1))) [skolemisation 48,49]
83. rich(X0) | happy(X0) [cnf transformation 40]
89. ~rich(X0) | ~old(X0) [cnf transformation 42]
105. ~funny(mary) | old(X1) [cnf transformation 50]
115. funny(X0) | funny(X0) [cnf transformation 27]
136. ~happy(john) [cnf transformation 20]
137. funny(X0) [duplicate literal removal 115]
192. 12 <=> funny(mary) [avatar definition]
193. ~funny(mary) <- (~12) [avatar component clause 192]
213. 17 <=> ! [X1] : old(X1) [avatar definition]
214. old(X1) <- (17) [avatar component clause 213]
217. 17 | ~12 [avatar split clause 105,192,213]
288. $false <- (~12) [subsumption resolution 193,137]
289. 12 [avatar contradiction clause 288]
305. ~old(X0) | happy(X0) [resolution 89,83]
307. happy(X0) <- (17) [subsumption resolution 305,214]
313. $false <- (17) [resolution 307,136]
314. ~17 [avatar contradiction clause 313]
315. $false [avatar sat refutation 217,289,314]
% SZS output end Proof for 4634715087389222038433869
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or funny is strong.
If someone is both not calm and not old then someone is curious and vice versa.
If alice is both funny and calm then someone is not calm.
Everyone who is not tall is either not curious or not creative and vice versa.
If john is both not funny and rich then mary is both not rich and not strong.
Everyone who is calm is both not old and not quiet and vice versa.
Everyone who is creative is both not humble and rich and vice versa.
If someone is tall then someone is quiet and vice versa.
If someone is not happy then someone is both not calm and curious and vice versa.
If susan is both not creative and not quiet then someone is brave or funny and vice versa.
Everyone who is either not generous or brave is not happy or not generous.
Everyone who is not humble or not generous is quiet and vice versa.
If someone is quiet then someone is either quiet or not curious.
Everyone who is curious or funny is either tall or not humble and vice versa.
If someone is not strong then alice is creative and vice versa.
Everyone who is both generous and creative is either strong or not brave and vice versa.
Alice is either not quiet or not rich.
Someone is not calm.
Someone is curious.
John is either creative or generous.
Someone is both not patient and kind.
Someone is either not generous or strong.
Someone is not funny.
Someone is not generous or not kind. | John is not brave. | entailment | (![X]:((quiet(X)<~>funny(X))=>strong(X)))&
((?[X]:((~calm(X)&~old(X))))<=>(?[X]:(curious(X))))&
(((funny(alice)&calm(alice)))=>(?[X]:(~calm(X))))&
(![X]:(~tall(X)<=>(~curious(X)<~>~creative(X))))&
(((~funny(john)&rich(john)))=>((~rich(mary)&~strong(mary))))&
(![X]:(calm(X)<=>(~old(X)&~quiet(X))))&
(![X]:(creative(X)<=>(~humble(X)&rich(X))))&
((?[X]:(tall(X)))<=>(?[X]:(quiet(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~calm(X)&curious(X)))))&
(((~creative(susan)&~quiet(susan)))<=>(?[X]:((brave(X)|funny(X)))))&
(![X]:((~generous(X)<~>brave(X))=>(~happy(X)|~generous(X))))&
(![X]:((~humble(X)|~generous(X))<=>quiet(X)))&
((?[X]:(quiet(X)))=>(?[X]:((quiet(X)<~>~curious(X)))))&
(![X]:((curious(X)|funny(X))<=>(tall(X)<~>~humble(X))))&
((?[X]:(~strong(X)))<=>(creative(alice)))&
(![X]:((generous(X)&creative(X))<=>(strong(X)<~>~brave(X))))&
((~quiet(alice)<~>~rich(alice)))&
(?[X]:(~calm(X)))&
(?[X]:(curious(X)))&
((creative(john)<~>generous(john)))&
(?[X]:((~patient(X)&kind(X))))&
(?[X]:((~generous(X)<~>strong(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~generous(X)|~kind(X)))) | ~brave(john) | [
"p6",
"p11",
"p14",
"p15",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3504615533910497651994796
% SZS output start Proof for 3504615533910497651994796
7. ! [X0] : (creative(X0) <=> (rich(X0) & ~humble(X0))) [input p6]
12. ! [X0] : ((~generous(X0) | ~humble(X0)) <=> quiet(X0)) [input p11]
15. ? [X0] : ~strong(X0) <=> creative(alice) [input p14]
16. ! [X0] : ((creative(X0) & generous(X0)) <=> (strong(X0) <~> ~brave(X0))) [input p15]
17. ~quiet(alice) <~> ~rich(alice) [input p16]
20. creative(john) <~> generous(john) [input p19]
25. brave(john) [input hypothesis]
50. ! [X0] : ((creative(X0) | (~rich(X0) | humble(X0))) & ((rich(X0) & ~humble(X0)) | ~creative(X0))) [nnf transformation 7]
51. ! [X0] : ((creative(X0) | ~rich(X0) | humble(X0)) & ((rich(X0) & ~humble(X0)) | ~creative(X0))) [flattening 50]
68. ! [X0] : (((~generous(X0) | ~humble(X0)) | ~quiet(X0)) & (quiet(X0) | (generous(X0) & humble(X0)))) [nnf transformation 12]
69. ! [X0] : ((~generous(X0) | ~humble(X0) | ~quiet(X0)) & (quiet(X0) | (generous(X0) & humble(X0)))) [flattening 68]
76. (? [X0] : ~strong(X0) | ~creative(alice)) & (creative(alice) | ! [X0] : strong(X0)) [nnf transformation 15]
77. (? [X0] : ~strong(X0) | ~creative(alice)) & (creative(alice) | ! [X1] : strong(X1)) [rectify 76]
78. ? [X0] : ~strong(X0) => ~strong(sK9) [choice axiom]
79. (~strong(sK9) | ~creative(alice)) & (creative(alice) | ! [X1] : strong(X1)) [skolemisation 77,78]
80. ! [X0] : (((creative(X0) & generous(X0)) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | (~creative(X0) | ~generous(X0)))) [nnf transformation 16]
81. ! [X0] : (((creative(X0) & generous(X0)) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ~creative(X0) | ~generous(X0))) [flattening 80]
82. (rich(alice) | quiet(alice)) & (~rich(alice) | ~quiet(alice)) [nnf transformation 17]
87. (~generous(john) | ~creative(john)) & (generous(john) | creative(john)) [nnf transformation 20]
112. ~humble(X0) | ~creative(X0) [cnf transformation 51]
113. ~creative(X0) | rich(X0) [cnf transformation 51]
127. humble(X0) | quiet(X0) [cnf transformation 69]
138. creative(alice) | strong(X1) [cnf transformation 79]
142. ~brave(X0) | generous(X0) | ~strong(X0) [cnf transformation 81]
144. ~brave(X0) | creative(X0) | ~strong(X0) [cnf transformation 81]
146. ~rich(alice) | ~quiet(alice) [cnf transformation 82]
151. ~generous(john) | ~creative(john) [cnf transformation 87]
157. brave(john) [cnf transformation 25]
286. 30 <=> creative(alice) [avatar definition]
287. creative(alice) <- (30) [avatar component clause 286]
295. 32 <=> ! [X1] : strong(X1) [avatar definition]
296. strong(X1) <- (32) [avatar component clause 295]
297. 32 | 30 [avatar split clause 138,286,295]
299. 33 <=> quiet(alice) [avatar definition]
300. ~quiet(alice) <- (~33) [avatar component clause 299]
303. 34 <=> rich(alice) [avatar definition]
304. ~rich(alice) <- (~34) [avatar component clause 303]
307. ~33 | ~34 [avatar split clause 146,303,299]
309. 35 <=> creative(john) [avatar definition]
313. 36 <=> generous(john) [avatar definition]
316. ~35 | ~36 [avatar split clause 151,313,309]
345. rich(alice) <- (30) [resolution 113,287]
347. $false <- (30, ~34) [subsumption resolution 345,304]
348. ~30 | 34 [avatar contradiction clause 347]
361. ~creative(X0) | quiet(X0) [resolution 127,112]
546. generous(john) | ~strong(john) [resolution 142,157]
561. creative(john) | ~strong(john) [resolution 144,157]
658. quiet(alice) <- (30) [resolution 361,287]
661. $false <- (30, ~33) [subsumption resolution 658,300]
662. ~30 | 33 [avatar contradiction clause 661]
674. creative(john) <- (32) [subsumption resolution 561,296]
675. 35 | ~32 [avatar split clause 674,295,309]
681. generous(john) <- (32) [subsumption resolution 546,296]
682. 36 | ~32 [avatar split clause 681,295,313]
683. $false [avatar sat refutation 297,307,316,348,662,675,682]
% SZS output end Proof for 3504615533910497651994796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or calm then someone is not rich or rich and vice versa.
If john is old then someone is both wise and not rich and vice versa.
Everyone who is both not tall and quiet is kind and vice versa.
Everyone who is old is either patient or not tall.
Everyone who is calm or not generous is both not curious and not brave and vice versa.
If someone is both old and strong then paul is both patient and generous and vice versa.
If someone is calm then susan is both patient and brave and vice versa.
If someone is both tall and not patient then someone is not old or creative.
If someone is not kind then someone is either generous or calm.
If someone is either not funny or not happy then john is either funny or patient and vice versa.
Everyone who is both curious and funny is either happy or not creative and vice versa.
If someone is not strong or not patient then someone is both not rich and not strong and vice versa.
Everyone who is not humble is not generous or not brave.
Everyone who is either not funny or not creative is both kind and funny.
Everyone who is humble is both not strong and tall and vice versa.
Everyone who is not wise or not humble is generous.
Someone is both brave and not calm.
Someone is not calm or happy.
Someone is not old.
Someone is not happy.
Someone is not creative.
Someone is both brave and generous.
Someone is creative or not kind.
John is not old. | Susan is humble. | neutral | ((?[X]:((~old(X)|calm(X))))<=>(?[X]:((~rich(X)|rich(X)))))&
((old(john))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~tall(X)&quiet(X))<=>kind(X)))&
(![X]:(old(X)=>(patient(X)<~>~tall(X))))&
(![X]:((calm(X)|~generous(X))<=>(~curious(X)&~brave(X))))&
((?[X]:((old(X)&strong(X))))<=>((patient(paul)&generous(paul))))&
((?[X]:(calm(X)))<=>((patient(susan)&brave(susan))))&
((?[X]:((tall(X)&~patient(X))))=>(?[X]:((~old(X)|creative(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((generous(X)<~>calm(X)))))&
((?[X]:((~funny(X)<~>~happy(X))))<=>((funny(john)<~>patient(john))))&
(![X]:((curious(X)&funny(X))<=>(happy(X)<~>~creative(X))))&
((?[X]:((~strong(X)|~patient(X))))<=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:(~humble(X)=>(~generous(X)|~brave(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(kind(X)&funny(X))))&
(![X]:(humble(X)<=>(~strong(X)&tall(X))))&
(![X]:((~wise(X)|~humble(X))=>generous(X)))&
(?[X]:((brave(X)&~calm(X))))&
(?[X]:((~calm(X)|happy(X))))&
(?[X]:(~old(X)))&
(?[X]:(~happy(X)))&
(?[X]:(~creative(X)))&
(?[X]:((brave(X)&generous(X))))&
(?[X]:((creative(X)|~kind(X))))&
(~old(john)) | humble(susan) | [] | null | 0 |
Everyone who is both not curious and not creative is either rich or not happy and vice versa.
If john is both patient and not quiet then someone is both not funny and not brave and vice versa.
Everyone who is kind or quiet is not quiet or tall.
Everyone who is quiet is both not creative and not calm and vice versa.
If alice is not kind then alice is both not kind and calm and vice versa.
Everyone who is both not happy and not patient is either not kind or not humble and vice versa.
Everyone who is generous or kind is creative and vice versa.
Everyone who is either not funny or not generous is not wise or funny.
If paul is either strong or brave then someone is both brave and quiet and vice versa.
If someone is both rich and not calm then someone is either curious or funny and vice versa.
Everyone who is either humble or patient is either not funny or curious.
If someone is both humble and not happy then susan is both humble and curious.
Everyone who is not calm is both not quiet and not generous.
If someone is quiet then someone is not calm or not rich.
Everyone who is both not curious and not wise is both not happy and not brave and vice versa.
Everyone who is not creative is both old and humble and vice versa.
Someone is both not patient and funny.
Someone is both strong and not happy.
Mary is not kind or wise.
Paul is either not creative or not curious.
Lucy is either not strong or funny.
Mary is either generous or brave.
Someone is either not rich or wise. | Lucy is not happy. | neutral | (![X]:((~curious(X)&~creative(X))<=>(rich(X)<~>~happy(X))))&
(((patient(john)&~quiet(john)))<=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((kind(X)|quiet(X))=>(~quiet(X)|tall(X))))&
(![X]:(quiet(X)<=>(~creative(X)&~calm(X))))&
((~kind(alice))<=>((~kind(alice)&calm(alice))))&
(![X]:((~happy(X)&~patient(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((generous(X)|kind(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~wise(X)|funny(X))))&
(((strong(paul)<~>brave(paul)))<=>(?[X]:((brave(X)&quiet(X)))))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~funny(X)<~>curious(X))))&
((?[X]:((humble(X)&~happy(X))))=>((humble(susan)&curious(susan))))&
(![X]:(~calm(X)=>(~quiet(X)&~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((~curious(X)&~wise(X))<=>(~happy(X)&~brave(X))))&
(![X]:(~creative(X)<=>(old(X)&humble(X))))&
(?[X]:((~patient(X)&funny(X))))&
(?[X]:((strong(X)&~happy(X))))&
((~kind(mary)|wise(mary)))&
((~creative(paul)<~>~curious(paul)))&
((~strong(lucy)<~>funny(lucy)))&
((generous(mary)<~>brave(mary)))&
(?[X]:((~rich(X)<~>wise(X)))) | ~happy(lucy) | [] | null | 0 |
Everyone who is not old is either brave or not kind and vice versa.
Everyone who is either not curious or strong is either not brave or wise and vice versa.
If mary is not patient or not quiet then susan is old.
Everyone who is not brave or old is not brave and vice versa.
Everyone who is happy is rich or not generous and vice versa.
Everyone who is not tall is not kind and vice versa.
Everyone who is not tall is not humble.
Everyone who is not humble is both happy and strong and vice versa.
Everyone who is generous or humble is tall or quiet and vice versa.
Everyone who is funny is both not quiet and not humble and vice versa.
If alice is not calm then alice is strong or not quiet and vice versa.
Everyone who is patient is both not calm and kind.
If someone is creative or not rich then fred is either rich or funny and vice versa.
If someone is not brave then lucy is not kind or humble and vice versa.
Everyone who is tall or not rich is funny and vice versa.
Everyone who is both not curious and curious is both brave and rich and vice versa.
Someone is calm or not generous.
Someone is either calm or generous.
Paul is calm or not generous.
Someone is either not brave or brave.
Someone is either not kind or not happy.
Someone is not humble.
John is humble or not curious.
Someone is not quiet or wise. | Susan is tall. | entailment | (![X]:(~old(X)<=>(brave(X)<~>~kind(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(~brave(X)<~>wise(X))))&
(((~patient(mary)|~quiet(mary)))=>(old(susan)))&
(![X]:((~brave(X)|old(X))<=>~brave(X)))&
(![X]:(happy(X)<=>(rich(X)|~generous(X))))&
(![X]:(~tall(X)<=>~kind(X)))&
(![X]:(~tall(X)=>~humble(X)))&
(![X]:(~humble(X)<=>(happy(X)&strong(X))))&
(![X]:((generous(X)|humble(X))<=>(tall(X)|quiet(X))))&
(![X]:(funny(X)<=>(~quiet(X)&~humble(X))))&
((~calm(alice))<=>((strong(alice)|~quiet(alice))))&
(![X]:(patient(X)=>(~calm(X)&kind(X))))&
((?[X]:((creative(X)|~rich(X))))<=>((rich(fred)<~>funny(fred))))&
((?[X]:(~brave(X)))<=>((~kind(lucy)|humble(lucy))))&
(![X]:((tall(X)|~rich(X))<=>funny(X)))&
(![X]:((~curious(X)&curious(X))<=>(brave(X)&rich(X))))&
(?[X]:((calm(X)|~generous(X))))&
(?[X]:((calm(X)<~>generous(X))))&
((calm(paul)|~generous(paul)))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:((~kind(X)<~>~happy(X))))&
(?[X]:(~humble(X)))&
((humble(john)|~curious(john)))&
(?[X]:((~quiet(X)|wise(X)))) | tall(susan) | [
"p0",
"p2",
"p3",
"p5",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6984264700670833536853071
% SZS output start Proof for 6984264700670833536853071
1. ! [X0] : (~old(X0) <=> (brave(X0) <~> ~kind(X0))) [input p0]
3. (~quiet(mary) | ~patient(mary)) => old(susan) [input p2]
4. ! [X0] : ((old(X0) | ~brave(X0)) <=> ~brave(X0)) [input p3]
6. ! [X0] : (~tall(X0) <=> ~kind(X0)) [input p5]
10. ! [X0] : (funny(X0) <=> (~humble(X0) & ~quiet(X0))) [input p9]
12. ! [X0] : (patient(X0) => (kind(X0) & ~calm(X0))) [input p11]
15. ! [X0] : ((~rich(X0) | tall(X0)) <=> funny(X0)) [input p14]
25. ~tall(susan) [input hypothesis]
26. old(susan) | (quiet(mary) & patient(mary)) [ennf transformation 3]
28. ! [X0] : ((kind(X0) & ~calm(X0)) | ~patient(X0)) [ennf transformation 12]
29. ! [X0] : ((~old(X0) | ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0)))) & (((kind(X0) | ~brave(X0)) & (~kind(X0) | brave(X0))) | old(X0))) [nnf transformation 1]
31. ! [X0] : (((old(X0) | ~brave(X0)) | brave(X0)) & (~brave(X0) | (~old(X0) & brave(X0)))) [nnf transformation 4]
32. ! [X0] : ((old(X0) | ~brave(X0) | brave(X0)) & (~brave(X0) | (~old(X0) & brave(X0)))) [flattening 31]
35. ! [X0] : ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))) [nnf transformation 6]
40. ! [X0] : ((funny(X0) | (humble(X0) | quiet(X0))) & ((~humble(X0) & ~quiet(X0)) | ~funny(X0))) [nnf transformation 10]
41. ! [X0] : ((funny(X0) | humble(X0) | quiet(X0)) & ((~humble(X0) & ~quiet(X0)) | ~funny(X0))) [flattening 40]
53. ! [X0] : (((~rich(X0) | tall(X0)) | ~funny(X0)) & (funny(X0) | (rich(X0) & ~tall(X0)))) [nnf transformation 15]
54. ! [X0] : ((~rich(X0) | tall(X0) | ~funny(X0)) & (funny(X0) | (rich(X0) & ~tall(X0)))) [flattening 53]
75. ~old(X0) | brave(X0) | kind(X0) [cnf transformation 29]
84. old(susan) | patient(mary) [cnf transformation 26]
85. old(susan) | quiet(mary) [cnf transformation 26]
87. ~brave(X0) | ~old(X0) [cnf transformation 32]
92. ~kind(X0) | tall(X0) [cnf transformation 35]
102. ~funny(X0) | ~quiet(X0) [cnf transformation 41]
109. ~patient(X0) | kind(X0) [cnf transformation 28]
119. ~tall(X0) | funny(X0) [cnf transformation 54]
137. ~tall(susan) [cnf transformation 25]
139. 1 <=> quiet(mary) [avatar definition]
141. quiet(mary) <- (1) [avatar component clause 139]
143. 2 <=> old(susan) [avatar definition]
145. old(susan) <- (2) [avatar component clause 143]
146. 1 | 2 [avatar split clause 85,143,139]
148. 3 <=> patient(mary) [avatar definition]
150. patient(mary) <- (3) [avatar component clause 148]
151. 3 | 2 [avatar split clause 84,143,148]
307. 31 <=> kind(susan) [avatar definition]
309. kind(susan) <- (31) [avatar component clause 307]
311. 32 <=> brave(susan) [avatar definition]
313. brave(susan) <- (32) [avatar component clause 311]
329. brave(susan) | kind(susan) <- (2) [resolution 145,75]
334. tall(susan) <- (31) [resolution 309,92]
335. $false <- (31) [subsumption resolution 334,137]
336. ~31 [avatar contradiction clause 335]
337. 31 | 32 | ~2 [avatar split clause 329,143,311,307]
342. ~old(susan) <- (32) [resolution 313,87]
345. ~2 | ~32 [avatar split clause 342,311,143]
348. kind(mary) <- (3) [resolution 150,109]
363. tall(mary) <- (3) [resolution 348,92]
410. funny(mary) <- (3) [resolution 363,119]
414. ~quiet(mary) <- (3) [resolution 410,102]
417. $false <- (1, 3) [subsumption resolution 414,141]
418. ~1 | ~3 [avatar contradiction clause 417]
419. $false [avatar sat refutation 146,151,336,337,345,418]
% SZS output end Proof for 6984264700670833536853071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or curious is either not kind or patient. If someone is not old then susan is not brave. If fred is both old and not brave then someone is not wise or not curious. If someone is either happy or not generous then someone is both not happy and kind. If someone is both generous and not wise then someone is not generous and vice versa. If mary is both not kind and quiet then lucy is both creative and not rich and vice versa. If paul is generous then someone is both wise and not wise and vice versa. If mary is both rich and not funny then someone is old and vice versa. If someone is either humble or not old then someone is not wise or humble. Everyone who is both not happy and not calm is curious or not happy. If someone is patient or not generous then susan is both not curious and funny and vice versa. If someone is both patient and old then lucy is either not brave or not quiet. Everyone who is both wise and not wise is not creative or not humble and vice versa. If mary is both not wise and funny then susan is both not quiet and not wise. Everyone who is not kind or strong is either not strong or not calm and vice versa. If someone is not strong then someone is both tall and not curious and vice versa. Someone is calm or not funny. Alice is either not generous or not calm. Susan is either rich or not rich. Alice is not calm. Susan is not creative or not wise. Someone is either brave or not brave. Someone is both not patient and curious. | Paul is humble. | entailment | (![X]:((happy(X)<~>curious(X))=>(~kind(X)<~>patient(X))))&
((?[X]:(~old(X)))=>(~brave(susan)))&
(((old(fred)&~brave(fred)))=>(?[X]:((~wise(X)|~curious(X)))))&
((?[X]:((happy(X)<~>~generous(X))))=>(?[X]:((~happy(X)&kind(X)))))&
((?[X]:((generous(X)&~wise(X))))<=>(?[X]:(~generous(X))))&
(((~kind(mary)&quiet(mary)))<=>((creative(lucy)&~rich(lucy))))&
((generous(paul))<=>(?[X]:((wise(X)&~wise(X)))))&
(((rich(mary)&~funny(mary)))<=>(?[X]:(old(X))))&
((?[X]:((humble(X)<~>~old(X))))=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:((~happy(X)&~calm(X))=>(curious(X)|~happy(X))))&
((?[X]:((patient(X)|~generous(X))))<=>((~curious(susan)&funny(susan))))&
((?[X]:((patient(X)&old(X))))=>((~brave(lucy)<~>~quiet(lucy))))&
(![X]:((wise(X)&~wise(X))<=>(~creative(X)|~humble(X))))&
(((~wise(mary)&funny(mary)))=>((~quiet(susan)&~wise(susan))))&
(![X]:((~kind(X)|strong(X))<=>(~strong(X)<~>~calm(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((tall(X)&~curious(X)))))&
(?[X]:((calm(X)|~funny(X))))&
((~generous(alice)<~>~calm(alice)))&
((rich(susan)<~>~rich(susan)))&
(~calm(alice))&
((~creative(susan)|~wise(susan)))&
(?[X]:((brave(X)<~>~brave(X))))&
(?[X]:((~patient(X)&curious(X)))) | humble(paul) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2275487697557320471901835
% SZS output start Proof for 2275487697557320471901835
13. ! [X0] : ((~wise(X0) & wise(X0)) <=> (~humble(X0) | ~creative(X0))) [input p12]
24. ~humble(paul) [input hypothesis]
73. ! [X0] : (((~wise(X0) & wise(X0)) | (humble(X0) & creative(X0))) & ((~humble(X0) | ~creative(X0)) | (wise(X0) | ~wise(X0)))) [nnf transformation 13]
74. ! [X0] : (((~wise(X0) & wise(X0)) | (humble(X0) & creative(X0))) & (~humble(X0) | ~creative(X0) | wise(X0) | ~wise(X0))) [flattening 73]
126. wise(X0) | humble(X0) [cnf transformation 74]
128. ~wise(X0) | humble(X0) [cnf transformation 74]
151. ~humble(paul) [cnf transformation 24]
319. humble(X0) [subsumption resolution 126,128]
378. $false [subsumption resolution 151,319]
% SZS output end Proof for 2275487697557320471901835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or not curious then john is either not wise or generous.
If someone is not curious or not tall then lucy is both not humble and not brave and vice versa.
If someone is wise or not curious then susan is not humble or not rich and vice versa.
If someone is both humble and not wise then someone is both tall and not wise.
Everyone who is not happy or generous is quiet and vice versa.
If someone is either quiet or funny then someone is humble or not funny and vice versa.
Everyone who is generous or creative is kind or quiet.
Everyone who is both not happy and not calm is either not rich or not humble and vice versa.
If someone is both curious and not generous then someone is not old or not calm.
If someone is both not curious and humble then someone is not funny or patient and vice versa.
If someone is humble or not humble then someone is either calm or patient and vice versa.
If someone is either not funny or strong then alice is not tall.
Everyone who is both not kind and not generous is not quiet and vice versa.
If mary is curious then someone is both not generous and not happy.
If someone is creative or patient then mary is not brave and vice versa.
If someone is funny then someone is not old or not strong and vice versa.
Fred is not quiet or not kind.
Susan is either not wise or quiet.
Fred is not brave.
Someone is not brave.
Alice is either tall or not tall.
Someone is not tall.
Someone is both not calm and not brave.
Someone is both not kind and brave. | Susan is not humble. | neutral | ((?[X]:((~humble(X)<~>~curious(X))))=>((~wise(john)<~>generous(john))))&
((?[X]:((~curious(X)|~tall(X))))<=>((~humble(lucy)&~brave(lucy))))&
((?[X]:((wise(X)|~curious(X))))<=>((~humble(susan)|~rich(susan))))&
((?[X]:((humble(X)&~wise(X))))=>(?[X]:((tall(X)&~wise(X)))))&
(![X]:((~happy(X)|generous(X))<=>quiet(X)))&
((?[X]:((quiet(X)<~>funny(X))))<=>(?[X]:((humble(X)|~funny(X)))))&
(![X]:((generous(X)|creative(X))=>(kind(X)|quiet(X))))&
(![X]:((~happy(X)&~calm(X))<=>(~rich(X)<~>~humble(X))))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:((~old(X)|~calm(X)))))&
((?[X]:((~curious(X)&humble(X))))<=>(?[X]:((~funny(X)|patient(X)))))&
((?[X]:((humble(X)|~humble(X))))<=>(?[X]:((calm(X)<~>patient(X)))))&
((?[X]:((~funny(X)<~>strong(X))))=>(~tall(alice)))&
(![X]:((~kind(X)&~generous(X))<=>~quiet(X)))&
((curious(mary))=>(?[X]:((~generous(X)&~happy(X)))))&
((?[X]:((creative(X)|patient(X))))<=>(~brave(mary)))&
((?[X]:(funny(X)))<=>(?[X]:((~old(X)|~strong(X)))))&
((~quiet(fred)|~kind(fred)))&
((~wise(susan)<~>quiet(susan)))&
(~brave(fred))&
(?[X]:(~brave(X)))&
((tall(alice)<~>~tall(alice)))&
(?[X]:(~tall(X)))&
(?[X]:((~calm(X)&~brave(X))))&
(?[X]:((~kind(X)&brave(X)))) | ~humble(susan) | [] | null | 0 |
Everyone who is both not generous and strong is not rich or not curious. Everyone who is both brave and strong is both patient and brave and vice versa. Everyone who is not brave is not quiet. Everyone who is old is both not humble and old and vice versa. If someone is quiet then alice is both creative and not old and vice versa. Everyone who is either brave or not patient is old or wise. Everyone who is patient is not strong or not brave and vice versa. Everyone who is both wise and happy is not old or kind and vice versa. Everyone who is either not old or not curious is not wise or not funny and vice versa. If someone is either not strong or not funny then alice is not kind or humble and vice versa. Everyone who is either not funny or not generous is both funny and brave. If lucy is not curious or old then someone is brave or not brave and vice versa. Everyone who is either not happy or tall is both kind and not funny and vice versa. If mary is not calm then someone is either not patient or curious and vice versa. Everyone who is rich or funny is not quiet or old and vice versa. Everyone who is either wise or quiet is both humble and rich and vice versa. Someone is not calm or happy. Someone is either rich or brave. John is creative or rich. Someone is either quiet or kind. Lucy is not calm or patient. Someone is both funny and not kind. | John is funny. | neutral | (![X]:((~generous(X)&strong(X))=>(~rich(X)|~curious(X))))&
(![X]:((brave(X)&strong(X))<=>(patient(X)&brave(X))))&
(![X]:(~brave(X)=>~quiet(X)))&
(![X]:(old(X)<=>(~humble(X)&old(X))))&
((?[X]:(quiet(X)))<=>((creative(alice)&~old(alice))))&
(![X]:((brave(X)<~>~patient(X))=>(old(X)|wise(X))))&
(![X]:(patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((wise(X)&happy(X))<=>(~old(X)|kind(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(humble(X)&rich(X))))&
(?[X]:((~calm(X)|happy(X))))&
(?[X]:((rich(X)<~>brave(X))))&
((creative(john)|rich(john)))&
(?[X]:((quiet(X)<~>kind(X))))&
((~calm(lucy)|patient(lucy)))&
(?[X]:((funny(X)&~kind(X)))) | funny(john) | [] | null | 0 |
Everyone who is either humble or old is funny or generous and vice versa. Everyone who is either not strong or humble is not tall and vice versa. Everyone who is happy or not creative is both not brave and tall. If someone is tall then mary is either calm or strong. Everyone who is curious is happy and vice versa. Everyone who is both brave and not kind is quiet and vice versa. Everyone who is kind or old is brave or not quiet and vice versa. Everyone who is not kind or calm is not brave or not funny. Everyone who is wise is not humble. Everyone who is humble or wise is both not generous and not creative. Everyone who is humble is rich or brave and vice versa. If someone is brave then lucy is not patient or not generous and vice versa. If someone is not quiet or calm then someone is not happy and vice versa. If alice is either wise or not generous then someone is both not brave and old and vice versa. Everyone who is kind is old and vice versa. If someone is both wise and not patient then someone is either wise or not wise and vice versa. Someone is not quiet or not curious. John is tall or creative. Alice is not curious. Someone is either rich or not tall. Susan is either old or not generous. Someone is both wise and patient. John is not tall or not calm. | Mary is not old. | contradiction | (![X]:((humble(X)<~>old(X))<=>(funny(X)|generous(X))))&
(![X]:((~strong(X)<~>humble(X))<=>~tall(X)))&
(![X]:((happy(X)|~creative(X))=>(~brave(X)&tall(X))))&
((?[X]:(tall(X)))=>((calm(mary)<~>strong(mary))))&
(![X]:(curious(X)<=>happy(X)))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((kind(X)|old(X))<=>(brave(X)|~quiet(X))))&
(![X]:((~kind(X)|calm(X))=>(~brave(X)|~funny(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((humble(X)|wise(X))=>(~generous(X)&~creative(X))))&
(![X]:(humble(X)<=>(rich(X)|brave(X))))&
((?[X]:(brave(X)))<=>((~patient(lucy)|~generous(lucy))))&
((?[X]:((~quiet(X)|calm(X))))<=>(?[X]:(~happy(X))))&
(((wise(alice)<~>~generous(alice)))<=>(?[X]:((~brave(X)&old(X)))))&
(![X]:(kind(X)<=>old(X)))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(?[X]:((~quiet(X)|~curious(X))))&
((tall(john)|creative(john)))&
(~curious(alice))&
(?[X]:((rich(X)<~>~tall(X))))&
((old(susan)<~>~generous(susan)))&
(?[X]:((wise(X)&patient(X))))&
((~tall(john)|~calm(john))) | ~old(mary) | [
"p2",
"p5",
"p6",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5185625987282541140512046
% SZS output start Proof for 5185625987282541140512046
3. ! [X0] : ((~creative(X0) | happy(X0)) => (tall(X0) & ~brave(X0))) [input p2]
6. ! [X0] : ((~kind(X0) & brave(X0)) <=> quiet(X0)) [input p5]
7. ! [X0] : ((old(X0) | kind(X0)) <=> (~quiet(X0) | brave(X0))) [input p6]
10. ! [X0] : ((wise(X0) | humble(X0)) => (~creative(X0) & ~generous(X0))) [input p9]
11. ! [X0] : (humble(X0) <=> (brave(X0) | rich(X0))) [input p10]
12. ? [X0] : brave(X0) <=> (~generous(lucy) | ~patient(lucy)) [input p11]
15. ! [X0] : (kind(X0) <=> old(X0)) [input p14]
24. ~old(mary) [input hypothesis]
28. ! [X0] : ((tall(X0) & ~brave(X0)) | (creative(X0) & ~happy(X0))) [ennf transformation 3]
34. ! [X0] : ((~creative(X0) & ~generous(X0)) | (~wise(X0) & ~humble(X0))) [ennf transformation 10]
39. ! [X0] : (((~kind(X0) & brave(X0)) | ~quiet(X0)) & (quiet(X0) | (kind(X0) | ~brave(X0)))) [nnf transformation 6]
40. ! [X0] : (((~kind(X0) & brave(X0)) | ~quiet(X0)) & (quiet(X0) | kind(X0) | ~brave(X0))) [flattening 39]
41. ! [X0] : (((old(X0) | kind(X0)) | (quiet(X0) & ~brave(X0))) & ((~quiet(X0) | brave(X0)) | (~old(X0) & ~kind(X0)))) [nnf transformation 7]
42. ! [X0] : ((old(X0) | kind(X0) | (quiet(X0) & ~brave(X0))) & (~quiet(X0) | brave(X0) | (~old(X0) & ~kind(X0)))) [flattening 41]
43. ! [X0] : ((humble(X0) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ~humble(X0))) [nnf transformation 11]
44. ! [X0] : ((humble(X0) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ~humble(X0))) [flattening 43]
45. (? [X0] : brave(X0) | (generous(lucy) & patient(lucy))) & ((~generous(lucy) | ~patient(lucy)) | ! [X0] : ~brave(X0)) [nnf transformation 12]
46. (? [X0] : brave(X0) | (generous(lucy) & patient(lucy))) & (~generous(lucy) | ~patient(lucy) | ! [X0] : ~brave(X0)) [flattening 45]
47. (? [X0] : brave(X0) | (generous(lucy) & patient(lucy))) & (~generous(lucy) | ~patient(lucy) | ! [X1] : ~brave(X1)) [rectify 46]
48. ? [X0] : brave(X0) => brave(sK0) [choice axiom]
49. (brave(sK0) | (generous(lucy) & patient(lucy))) & (~generous(lucy) | ~patient(lucy) | ! [X1] : ~brave(X1)) [skolemisation 47,48]
59. ! [X0] : ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))) [nnf transformation 15]
84. ~brave(X0) | creative(X0) [cnf transformation 28]
91. ~quiet(X0) | brave(X0) [cnf transformation 40]
96. quiet(X0) | kind(X0) | old(X0) [cnf transformation 42]
102. ~creative(X0) | ~humble(X0) [cnf transformation 34]
106. ~brave(X0) | humble(X0) [cnf transformation 44]
107. ~generous(lucy) | ~patient(lucy) | ~brave(X1) [cnf transformation 49]
108. brave(sK0) | patient(lucy) [cnf transformation 49]
109. brave(sK0) | generous(lucy) [cnf transformation 49]
119. ~kind(X0) | old(X0) [cnf transformation 59]
137. ~old(mary) [cnf transformation 24]
156. 4 <=> generous(lucy) [avatar definition]
160. 5 <=> brave(sK0) [avatar definition]
162. brave(sK0) <- (5) [avatar component clause 160]
163. 4 | 5 [avatar split clause 109,160,156]
165. 6 <=> patient(lucy) [avatar definition]
168. 6 | 5 [avatar split clause 108,160,165]
170. 7 <=> ! [X1] : ~brave(X1) [avatar definition]
171. ~brave(X1) <- (7) [avatar component clause 170]
172. 7 | ~6 | ~4 [avatar split clause 107,156,165,170]
285. creative(sK0) <- (5) [resolution 84,162]
291. ~humble(sK0) <- (5) [resolution 102,285]
296. humble(sK0) <- (5) [resolution 106,162]
297. $false <- (5) [subsumption resolution 296,291]
298. ~5 [avatar contradiction clause 297]
330. kind(X1) | old(X1) | brave(X1) [resolution 96,91]
332. kind(X1) | old(X1) <- (7) [subsumption resolution 330,171]
333. old(X1) <- (7) [subsumption resolution 332,119]
335. $false <- (7) [resolution 333,137]
339. ~7 [avatar contradiction clause 335]
340. $false [avatar sat refutation 163,168,172,298,339]
% SZS output end Proof for 5185625987282541140512046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or quiet is either not strong or wise and vice versa. Everyone who is either generous or patient is tall or not brave and vice versa. If paul is not rich or not tall then someone is either calm or not kind. If someone is kind or humble then fred is brave or tall and vice versa. Everyone who is not strong or not brave is both not humble and not curious and vice versa. Everyone who is both generous and not funny is both not tall and humble and vice versa. If susan is either not brave or not wise then mary is brave and vice versa. Everyone who is both not tall and not creative is both funny and patient and vice versa. Everyone who is generous is both not rich and not kind and vice versa. Everyone who is curious or creative is not patient. Everyone who is old or not strong is patient. Everyone who is not wise is both not generous and not kind and vice versa. If someone is both funny and curious then susan is wise or brave. If someone is both not curious and funny then someone is either not brave or not patient and vice versa. If someone is either not strong or tall then mary is both curious and not humble and vice versa. Everyone who is not humble or strong is both strong and brave. Mary is both wise and not quiet. Someone is both not calm and not humble. Someone is quiet. Someone is not humble. Someone is either not humble or humble. Someone is either not generous or rich. Alice is both funny and not generous. | Susan is not wise. | entailment | (![X]:((creative(X)|quiet(X))<=>(~strong(X)<~>wise(X))))&
(![X]:((generous(X)<~>patient(X))<=>(tall(X)|~brave(X))))&
(((~rich(paul)|~tall(paul)))=>(?[X]:((calm(X)<~>~kind(X)))))&
((?[X]:((kind(X)|humble(X))))<=>((brave(fred)|tall(fred))))&
(![X]:((~strong(X)|~brave(X))<=>(~humble(X)&~curious(X))))&
(![X]:((generous(X)&~funny(X))<=>(~tall(X)&humble(X))))&
(((~brave(susan)<~>~wise(susan)))<=>(brave(mary)))&
(![X]:((~tall(X)&~creative(X))<=>(funny(X)&patient(X))))&
(![X]:(generous(X)<=>(~rich(X)&~kind(X))))&
(![X]:((curious(X)|creative(X))=>~patient(X)))&
(![X]:((old(X)|~strong(X))=>patient(X)))&
(![X]:(~wise(X)<=>(~generous(X)&~kind(X))))&
((?[X]:((funny(X)&curious(X))))=>((wise(susan)|brave(susan))))&
((?[X]:((~curious(X)&funny(X))))<=>(?[X]:((~brave(X)<~>~patient(X)))))&
((?[X]:((~strong(X)<~>tall(X))))<=>((curious(mary)&~humble(mary))))&
(![X]:((~humble(X)|strong(X))=>(strong(X)&brave(X))))&
((wise(mary)&~quiet(mary)))&
(?[X]:((~calm(X)&~humble(X))))&
(?[X]:(quiet(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~humble(X)<~>humble(X))))&
(?[X]:((~generous(X)<~>rich(X))))&
((funny(alice)&~generous(alice))) | ~wise(susan) | [
"p4",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5329381787487015597263720
% SZS output start Proof for 5329381787487015597263720
5. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> (~curious(X0) & ~humble(X0))) [input p4]
7. (~brave(susan) <~> ~wise(susan)) <=> brave(mary) [input p6]
16. ! [X0] : ((strong(X0) | ~humble(X0)) => (brave(X0) & strong(X0))) [input p15]
24. wise(susan) [input hypothesis]
32. ! [X0] : ((brave(X0) & strong(X0)) | (~strong(X0) & humble(X0))) [ennf transformation 16]
45. ! [X0] : (((~brave(X0) | ~strong(X0)) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | (brave(X0) & strong(X0)))) [nnf transformation 5]
46. ! [X0] : ((~brave(X0) | ~strong(X0) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | (brave(X0) & strong(X0)))) [flattening 45]
49. (((wise(susan) | brave(susan)) & (~wise(susan) | ~brave(susan))) | ~brave(mary)) & (brave(mary) | ((~brave(susan) | wise(susan)) & (~wise(susan) | brave(susan)))) [nnf transformation 7]
99. ~humble(X0) | brave(X0) [cnf transformation 46]
109. ~wise(susan) | ~brave(susan) | ~brave(mary) [cnf transformation 49]
139. brave(X0) | humble(X0) [cnf transformation 32]
153. wise(susan) [cnf transformation 24]
201. 11 <=> brave(mary) [avatar definition]
203. ~brave(mary) <- (~11) [avatar component clause 201]
205. 12 <=> brave(susan) [avatar definition]
206. ~brave(susan) <- (~12) [avatar component clause 205]
209. 13 <=> wise(susan) [avatar definition]
213. ~11 | ~12 | ~13 [avatar split clause 109,209,205,201]
279. brave(X0) [subsumption resolution 139,99]
283. 13 [avatar split clause 153,209]
286. $false <- (~12) [subsumption resolution 206,279]
287. 12 [avatar contradiction clause 286]
288. $false <- (~11) [subsumption resolution 203,279]
289. 11 [avatar contradiction clause 288]
290. $false [avatar sat refutation 213,283,287,289]
% SZS output end Proof for 5329381787487015597263720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not brave is wise and vice versa. Everyone who is both tall and rich is either humble or not patient and vice versa. Everyone who is generous or rich is either rich or not tall. If someone is either old or patient then john is not generous or not kind. Everyone who is both not curious and curious is either not generous or calm and vice versa. Everyone who is not funny or patient is quiet or old and vice versa. If lucy is either generous or not calm then paul is both generous and kind. If someone is wise then paul is either not rich or not calm. Everyone who is either quiet or not generous is either not tall or happy and vice versa. Everyone who is either brave or not tall is not happy. If someone is both not funny and rich then someone is wise or strong and vice versa. Everyone who is not wise is not calm and vice versa. Everyone who is either not calm or not brave is both funny and happy. If fred is brave then fred is both quiet and not tall. If someone is curious then lucy is creative or not creative. Someone is not funny or happy. John is either not kind or curious. Someone is either patient or not quiet. Someone is both calm and happy. Someone is either strong or not funny. Alice is calm. Lucy is either happy or not quiet. John is generous. | Fred is brave. | contradiction | (![X]:((strong(X)&~brave(X))<=>wise(X)))&
(![X]:((tall(X)&rich(X))<=>(humble(X)<~>~patient(X))))&
(![X]:((generous(X)|rich(X))=>(rich(X)<~>~tall(X))))&
((?[X]:((old(X)<~>patient(X))))=>((~generous(john)|~kind(john))))&
(![X]:((~curious(X)&curious(X))<=>(~generous(X)<~>calm(X))))&
(![X]:((~funny(X)|patient(X))<=>(quiet(X)|old(X))))&
(((generous(lucy)<~>~calm(lucy)))=>((generous(paul)&kind(paul))))&
((?[X]:(wise(X)))=>((~rich(paul)<~>~calm(paul))))&
(![X]:((quiet(X)<~>~generous(X))<=>(~tall(X)<~>happy(X))))&
(![X]:((brave(X)<~>~tall(X))=>~happy(X)))&
((?[X]:((~funny(X)&rich(X))))<=>(?[X]:((wise(X)|strong(X)))))&
(![X]:(~wise(X)<=>~calm(X)))&
(![X]:((~calm(X)<~>~brave(X))=>(funny(X)&happy(X))))&
((brave(fred))=>((quiet(fred)&~tall(fred))))&
((?[X]:(curious(X)))=>((creative(lucy)|~creative(lucy))))&
(?[X]:((~funny(X)|happy(X))))&
((~kind(john)<~>curious(john)))&
(?[X]:((patient(X)<~>~quiet(X))))&
(?[X]:((calm(X)&happy(X))))&
(?[X]:((strong(X)<~>~funny(X))))&
(calm(alice))&
((happy(lucy)<~>~quiet(lucy)))&
(generous(john)) | brave(fred) | [
"p0",
"p4",
"p8",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1791012846691231862172115
% SZS output start Proof for 1791012846691231862172115
1. ! [X0] : ((~brave(X0) & strong(X0)) <=> wise(X0)) [input p0]
5. ! [X0] : ((curious(X0) & ~curious(X0)) <=> (~generous(X0) <~> calm(X0))) [input p4]
9. ! [X0] : ((quiet(X0) <~> ~generous(X0)) <=> (~tall(X0) <~> happy(X0))) [input p8]
12. ! [X0] : (~wise(X0) <=> ~calm(X0)) [input p11]
13. ! [X0] : ((~calm(X0) <~> ~brave(X0)) => (happy(X0) & funny(X0))) [input p12]
14. brave(fred) => (~tall(fred) & quiet(fred)) [input p13]
24. brave(fred) [input hypothesis]
32. ! [X0] : ((happy(X0) & funny(X0)) | (~calm(X0) <=> ~brave(X0))) [ennf transformation 13]
33. (~tall(fred) & quiet(fred)) | ~brave(fred) [ennf transformation 14]
36. ! [X0] : (((~brave(X0) & strong(X0)) | ~wise(X0)) & (wise(X0) | (brave(X0) | ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : (((~brave(X0) & strong(X0)) | ~wise(X0)) & (wise(X0) | brave(X0) | ~strong(X0))) [flattening 36]
42. ! [X0] : (((curious(X0) & ~curious(X0)) | ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0)))) & (((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | (~curious(X0) | curious(X0)))) [nnf transformation 5]
43. ! [X0] : (((curious(X0) & ~curious(X0)) | ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0)))) & (((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | ~curious(X0) | curious(X0))) [flattening 42]
48. ! [X0] : ((((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) & (((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0))))) [nnf transformation 9]
55. ! [X0] : ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0))) [nnf transformation 12]
56. ! [X0] : ((happy(X0) & funny(X0)) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0)))) [nnf transformation 32]
71. ~wise(X0) | ~brave(X0) [cnf transformation 37]
86. ~curious(X0) | calm(X0) | generous(X0) [cnf transformation 43]
87. ~curious(X0) | ~generous(X0) | ~calm(X0) [cnf transformation 43]
88. calm(X0) | curious(X0) | generous(X0) [cnf transformation 43]
89. ~calm(X0) | ~generous(X0) | curious(X0) [cnf transformation 43]
102. ~happy(X0) | tall(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 48]
115. ~calm(X0) | wise(X0) [cnf transformation 55]
119. ~brave(X0) | happy(X0) | calm(X0) [cnf transformation 56]
121. quiet(fred) | ~brave(fred) [cnf transformation 33]
122. ~tall(fred) | ~brave(fred) [cnf transformation 33]
137. brave(fred) [cnf transformation 24]
155. ~calm(X0) | ~generous(X0) [subsumption resolution 87,89]
156. calm(X0) | generous(X0) [subsumption resolution 86,88]
195. 13 <=> brave(fred) [avatar definition]
196. brave(fred) <- (13) [avatar component clause 195]
199. 14 <=> tall(fred) [avatar definition]
201. ~tall(fred) <- (~14) [avatar component clause 199]
202. ~13 | ~14 [avatar split clause 122,199,195]
204. 15 <=> quiet(fred) [avatar definition]
206. quiet(fred) <- (15) [avatar component clause 204]
207. ~13 | 15 [avatar split clause 121,204,195]
254. 13 [avatar split clause 137,195]
274. generous(X1) | wise(X1) [resolution 156,115]
391. happy(fred) | calm(fred) <- (13) [resolution 119,196]
401. 39 <=> generous(fred) [avatar definition]
402. generous(fred) <- (39) [avatar component clause 401]
403. ~generous(fred) <- (~39) [avatar component clause 401]
563. 55 <=> calm(fred) [avatar definition]
565. calm(fred) <- (55) [avatar component clause 563]
643. wise(fred) <- (~39) [resolution 403,274]
970. ~brave(fred) <- (~39) [resolution 643,71]
973. $false <- (13, ~39) [subsumption resolution 970,196]
974. ~13 | 39 [avatar contradiction clause 973]
976. 95 <=> happy(fred) [avatar definition]
978. happy(fred) <- (95) [avatar component clause 976]
979. 55 | 95 | ~13 [avatar split clause 391,195,976,563]
985. ~generous(fred) <- (55) [resolution 565,155]
989. $false <- (39, 55) [subsumption resolution 985,402]
990. ~39 | ~55 [avatar contradiction clause 989]
996. tall(fred) | ~generous(fred) | ~quiet(fred) <- (95) [resolution 978,102]
999. ~generous(fred) | ~quiet(fred) <- (~14, 95) [subsumption resolution 996,201]
1000. ~quiet(fred) <- (~14, 39, 95) [subsumption resolution 999,402]
1001. $false <- (~14, 15, 39, 95) [subsumption resolution 1000,206]
1002. 14 | ~15 | ~39 | ~95 [avatar contradiction clause 1001]
1003. $false [avatar sat refutation 202,207,254,974,979,990,1002]
% SZS output end Proof for 1791012846691231862172115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both kind and rich then someone is calm or not creative and vice versa. If paul is both not old and not creative then lucy is patient or humble. Everyone who is funny is not patient or wise. If someone is funny or not quiet then someone is generous and vice versa. If someone is either not wise or old then someone is not creative or not quiet and vice versa. If someone is both wise and not generous then lucy is funny or happy. If someone is both not brave and quiet then paul is happy and vice versa. Everyone who is curious or not quiet is strong or not funny and vice versa. Everyone who is not humble or generous is both tall and not generous. If fred is either funny or quiet then someone is either not strong or happy. If susan is either funny or kind then someone is both not brave and brave and vice versa. Everyone who is both not humble and rich is not happy and vice versa. If someone is not old then alice is both not kind and old and vice versa. Everyone who is wise is creative or happy. Everyone who is not patient is rich or tall and vice versa. If susan is not calm or humble then someone is both not patient and not creative. Someone is either not curious or not humble. Lucy is either strong or quiet. Someone is either creative or old. Susan is either not old or happy. Mary is either strong or not old. Someone is both calm and not rich. | Paul is not creative. | neutral | (((kind(alice)&rich(alice)))<=>(?[X]:((calm(X)|~creative(X)))))&
(((~old(paul)&~creative(paul)))=>((patient(lucy)|humble(lucy))))&
(![X]:(funny(X)=>(~patient(X)|wise(X))))&
((?[X]:((funny(X)|~quiet(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~wise(X)<~>old(X))))<=>(?[X]:((~creative(X)|~quiet(X)))))&
((?[X]:((wise(X)&~generous(X))))=>((funny(lucy)|happy(lucy))))&
((?[X]:((~brave(X)&quiet(X))))<=>(happy(paul)))&
(![X]:((curious(X)|~quiet(X))<=>(strong(X)|~funny(X))))&
(![X]:((~humble(X)|generous(X))=>(tall(X)&~generous(X))))&
(((funny(fred)<~>quiet(fred)))=>(?[X]:((~strong(X)<~>happy(X)))))&
(((funny(susan)<~>kind(susan)))<=>(?[X]:((~brave(X)&brave(X)))))&
(![X]:((~humble(X)&rich(X))<=>~happy(X)))&
((?[X]:(~old(X)))<=>((~kind(alice)&old(alice))))&
(![X]:(wise(X)=>(creative(X)|happy(X))))&
(![X]:(~patient(X)<=>(rich(X)|tall(X))))&
(((~calm(susan)|humble(susan)))=>(?[X]:((~patient(X)&~creative(X)))))&
(?[X]:((~curious(X)<~>~humble(X))))&
((strong(lucy)<~>quiet(lucy)))&
(?[X]:((creative(X)<~>old(X))))&
((~old(susan)<~>happy(susan)))&
((strong(mary)<~>~old(mary)))&
(?[X]:((calm(X)&~rich(X)))) | ~creative(paul) | [] | null | 0 |
If someone is both funny and calm then paul is tall. If lucy is creative or not rich then mary is not quiet or calm. If lucy is not tall then someone is both strong and creative and vice versa. If someone is both funny and curious then susan is either creative or generous and vice versa. If fred is strong then john is kind or wise and vice versa. If someone is happy or not brave then alice is either brave or patient and vice versa. If someone is not happy then someone is both curious and brave. Everyone who is both calm and generous is both rich and kind. If john is both not old and humble then someone is humble and vice versa. Everyone who is brave or creative is both humble and strong and vice versa. If someone is not kind then someone is not wise. Everyone who is both calm and not brave is patient or strong and vice versa. If someone is either calm or curious then lucy is either not strong or creative and vice versa. If alice is either not calm or not tall then alice is rich or humble and vice versa. If alice is kind then someone is not calm. If someone is either funny or not kind then paul is both not creative and kind. Susan is tall. Someone is both kind and curious. Someone is either not patient or not curious. Fred is both not wise and not tall. Someone is not curious or strong. Paul is quiet or not patient. Alice is funny or generous. | Alice is generous. | neutral | ((?[X]:((funny(X)&calm(X))))=>(tall(paul)))&
(((creative(lucy)|~rich(lucy)))=>((~quiet(mary)|calm(mary))))&
((~tall(lucy))<=>(?[X]:((strong(X)&creative(X)))))&
((?[X]:((funny(X)&curious(X))))<=>((creative(susan)<~>generous(susan))))&
((strong(fred))<=>((kind(john)|wise(john))))&
((?[X]:((happy(X)|~brave(X))))<=>((brave(alice)<~>patient(alice))))&
((?[X]:(~happy(X)))=>(?[X]:((curious(X)&brave(X)))))&
(![X]:((calm(X)&generous(X))=>(rich(X)&kind(X))))&
(((~old(john)&humble(john)))<=>(?[X]:(humble(X))))&
(![X]:((brave(X)|creative(X))<=>(humble(X)&strong(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~wise(X))))&
(![X]:((calm(X)&~brave(X))<=>(patient(X)|strong(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>((~strong(lucy)<~>creative(lucy))))&
(((~calm(alice)<~>~tall(alice)))<=>((rich(alice)|humble(alice))))&
((kind(alice))=>(?[X]:(~calm(X))))&
((?[X]:((funny(X)<~>~kind(X))))=>((~creative(paul)&kind(paul))))&
(tall(susan))&
(?[X]:((kind(X)&curious(X))))&
(?[X]:((~patient(X)<~>~curious(X))))&
((~wise(fred)&~tall(fred)))&
(?[X]:((~curious(X)|strong(X))))&
((quiet(paul)|~patient(paul)))&
((funny(alice)|generous(alice))) | generous(alice) | [] | null | 0 |
Everyone who is either old or brave is not strong or humble and vice versa. Everyone who is both not patient and not quiet is both creative and wise. If someone is either brave or not strong then john is either kind or patient. Everyone who is not quiet is either curious or tall and vice versa. Everyone who is either not kind or not wise is both not kind and not generous and vice versa. If someone is kind or not rich then someone is not brave and vice versa. Everyone who is old or not patient is either not generous or not rich. If someone is not rich or creative then someone is either calm or not happy and vice versa. If susan is not kind or not patient then someone is calm. If mary is rich or not patient then someone is happy or not funny and vice versa. If someone is both not creative and not rich then john is both not humble and curious. Everyone who is either not quiet or not funny is not creative. Everyone who is old is not happy and vice versa. If someone is generous then alice is not generous or not patient and vice versa. Everyone who is humble is not calm. Someone is both old and not happy. Someone is both not wise and rich. John is strong or not brave. Someone is strong. Someone is both patient and not old. Susan is either not strong or generous. Someone is curious or not generous. Susan is either not generous or quiet. | John is patient. | neutral | (![X]:((old(X)<~>brave(X))<=>(~strong(X)|humble(X))))&
(![X]:((~patient(X)&~quiet(X))=>(creative(X)&wise(X))))&
((?[X]:((brave(X)<~>~strong(X))))=>((kind(john)<~>patient(john))))&
(![X]:(~quiet(X)<=>(curious(X)<~>tall(X))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~kind(X)&~generous(X))))&
((?[X]:((kind(X)|~rich(X))))<=>(?[X]:(~brave(X))))&
(![X]:((old(X)|~patient(X))=>(~generous(X)<~>~rich(X))))&
((?[X]:((~rich(X)|creative(X))))<=>(?[X]:((calm(X)<~>~happy(X)))))&
(((~kind(susan)|~patient(susan)))=>(?[X]:(calm(X))))&
(((rich(mary)|~patient(mary)))<=>(?[X]:((happy(X)|~funny(X)))))&
((?[X]:((~creative(X)&~rich(X))))=>((~humble(john)&curious(john))))&
(![X]:((~quiet(X)<~>~funny(X))=>~creative(X)))&
(![X]:(old(X)<=>~happy(X)))&
((?[X]:(generous(X)))<=>((~generous(alice)|~patient(alice))))&
(![X]:(humble(X)=>~calm(X)))&
(?[X]:((old(X)&~happy(X))))&
(?[X]:((~wise(X)&rich(X))))&
((strong(john)|~brave(john)))&
(?[X]:(strong(X)))&
(?[X]:((patient(X)&~old(X))))&
((~strong(susan)<~>generous(susan)))&
(?[X]:((curious(X)|~generous(X))))&
((~generous(susan)<~>quiet(susan))) | patient(john) | [] | null | 0 |
If fred is both not curious and wise then susan is not curious or curious and vice versa.
Everyone who is either old or not funny is not patient and vice versa.
If someone is not old then lucy is both not old and generous.
If someone is either not creative or kind then someone is either funny or not calm.
If mary is not humble or happy then someone is both not happy and not generous and vice versa.
If someone is not funny or wise then alice is either not funny or not strong and vice versa.
Everyone who is generous is either not rich or not curious and vice versa.
If someone is either not strong or not wise then fred is both not happy and strong.
Everyone who is not wise is either not kind or not patient.
Everyone who is either not calm or not humble is both old and not happy.
If mary is calm or funny then susan is not strong and vice versa.
If paul is not kind then paul is both not creative and not old.
Everyone who is not calm is strong or rich and vice versa.
Everyone who is either creative or strong is both brave and not happy and vice versa.
Everyone who is both humble and kind is not tall.
Everyone who is either funny or not calm is either happy or not funny and vice versa.
Someone is both quiet and kind.
Lucy is not tall or not quiet.
Someone is not calm or tall.
Mary is both not humble and not wise.
Someone is either funny or strong.
Someone is both creative and not tall.
Susan is either old or not strong.
Someone is either not tall or kind. | Mary is calm. | contradiction | (((~curious(fred)&wise(fred)))<=>((~curious(susan)|curious(susan))))&
(![X]:((old(X)<~>~funny(X))<=>~patient(X)))&
((?[X]:(~old(X)))=>((~old(lucy)&generous(lucy))))&
((?[X]:((~creative(X)<~>kind(X))))=>(?[X]:((funny(X)<~>~calm(X)))))&
(((~humble(mary)|happy(mary)))<=>(?[X]:((~happy(X)&~generous(X)))))&
((?[X]:((~funny(X)|wise(X))))<=>((~funny(alice)<~>~strong(alice))))&
(![X]:(generous(X)<=>(~rich(X)<~>~curious(X))))&
((?[X]:((~strong(X)<~>~wise(X))))=>((~happy(fred)&strong(fred))))&
(![X]:(~wise(X)=>(~kind(X)<~>~patient(X))))&
(![X]:((~calm(X)<~>~humble(X))=>(old(X)&~happy(X))))&
(((calm(mary)|funny(mary)))<=>(~strong(susan)))&
((~kind(paul))=>((~creative(paul)&~old(paul))))&
(![X]:(~calm(X)<=>(strong(X)|rich(X))))&
(![X]:((creative(X)<~>strong(X))<=>(brave(X)&~happy(X))))&
(![X]:((humble(X)&kind(X))=>~tall(X)))&
(![X]:((funny(X)<~>~calm(X))<=>(happy(X)<~>~funny(X))))&
(?[X]:((quiet(X)&kind(X))))&
((~tall(lucy)|~quiet(lucy)))&
(?[X]:((~calm(X)|tall(X))))&
((~humble(mary)&~wise(mary)))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:((creative(X)&~tall(X))))&
((old(susan)<~>~strong(susan)))&
(?[X]:((~tall(X)<~>kind(X)))) | calm(mary) | [
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6549188823633554090354967
% SZS output start Proof for 6549188823633554090354967
10. ! [X0] : ((~calm(X0) <~> ~humble(X0)) => (~happy(X0) & old(X0))) [input p9]
16. ! [X0] : ((funny(X0) <~> ~calm(X0)) <=> (happy(X0) <~> ~funny(X0))) [input p15]
20. ~wise(mary) & ~humble(mary) [input p19]
25. calm(mary) [input hypothesis]
31. ! [X0] : ((~happy(X0) & old(X0)) | (~calm(X0) <=> ~humble(X0))) [ennf transformation 10]
54. ! [X0] : ((~happy(X0) & old(X0)) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) [nnf transformation 31]
61. ! [X0] : ((((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0)))) & (((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0))))) [nnf transformation 16]
114. ~happy(X0) | ~calm(X0) | humble(X0) [cnf transformation 54]
130. ~funny(X0) | happy(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 61]
135. ~calm(X0) | funny(X0) | happy(X0) | funny(X0) [cnf transformation 61]
142. ~humble(mary) [cnf transformation 20]
152. calm(mary) [cnf transformation 25]
153. ~funny(X0) | happy(X0) | ~calm(X0) [duplicate literal removal 130]
155. ~calm(X0) | funny(X0) | happy(X0) [duplicate literal removal 135]
208. 12 <=> humble(mary) [avatar definition]
210. ~humble(mary) <- (~12) [avatar component clause 208]
212. 13 <=> happy(mary) [avatar definition]
214. happy(mary) <- (13) [avatar component clause 212]
279. 27 <=> calm(mary) [avatar definition]
281. calm(mary) <- (27) [avatar component clause 279]
304. ~calm(X0) | happy(X0) [subsumption resolution 153,155]
323. ~12 [avatar split clause 142,208]
350. 27 [avatar split clause 152,279]
357. happy(mary) <- (27) [resolution 304,281]
358. 13 | ~27 [avatar split clause 357,279,212]
432. ~calm(mary) | humble(mary) <- (13) [resolution 114,214]
433. humble(mary) <- (13, 27) [subsumption resolution 432,281]
434. $false <- (~12, 13, 27) [subsumption resolution 433,210]
435. 12 | ~13 | ~27 [avatar contradiction clause 434]
436. $false [avatar sat refutation 323,350,358,435]
% SZS output end Proof for 6549188823633554090354967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not tall then susan is not quiet.
If someone is not strong then someone is either happy or calm.
Everyone who is humble or not humble is both not creative and curious.
Everyone who is patient is either not old or not creative and vice versa.
Everyone who is strong or happy is strong or not happy and vice versa.
If someone is generous then someone is both not rich and calm.
Everyone who is not strong is either funny or not creative and vice versa.
Everyone who is not quiet is both curious and not strong.
Everyone who is both not curious and not old is both rich and patient.
If fred is not wise then mary is wise or not tall and vice versa.
Everyone who is either not tall or not quiet is either generous or not humble.
Everyone who is not strong is humble.
If someone is not humble or curious then paul is either tall or patient.
If paul is happy or not tall then someone is quiet.
If john is both rich and not rich then paul is either not creative or not wise and vice versa.
If paul is both not rich and happy then someone is either calm or humble.
Paul is not funny or quiet.
Someone is funny.
Someone is not old or not patient.
Alice is either not generous or not kind.
Lucy is either not kind or not creative.
Alice is curious. | Mary is quiet. | entailment | ((?[X]:((~rich(X)|~tall(X))))=>(~quiet(susan)))&
((?[X]:(~strong(X)))=>(?[X]:((happy(X)<~>calm(X)))))&
(![X]:((humble(X)|~humble(X))=>(~creative(X)&curious(X))))&
(![X]:(patient(X)<=>(~old(X)<~>~creative(X))))&
(![X]:((strong(X)|happy(X))<=>(strong(X)|~happy(X))))&
((?[X]:(generous(X)))=>(?[X]:((~rich(X)&calm(X)))))&
(![X]:(~strong(X)<=>(funny(X)<~>~creative(X))))&
(![X]:(~quiet(X)=>(curious(X)&~strong(X))))&
(![X]:((~curious(X)&~old(X))=>(rich(X)&patient(X))))&
((~wise(fred))<=>((wise(mary)|~tall(mary))))&
(![X]:((~tall(X)<~>~quiet(X))=>(generous(X)<~>~humble(X))))&
(![X]:(~strong(X)=>humble(X)))&
((?[X]:((~humble(X)|curious(X))))=>((tall(paul)<~>patient(paul))))&
(((happy(paul)|~tall(paul)))=>(?[X]:(quiet(X))))&
(((rich(john)&~rich(john)))<=>((~creative(paul)<~>~wise(paul))))&
(((~rich(paul)&happy(paul)))=>(?[X]:((calm(X)<~>humble(X)))))&
((~funny(paul)|quiet(paul)))&
(?[X]:(funny(X)))&
(?[X]:((~old(X)|~patient(X))))&
((~generous(alice)<~>~kind(alice)))&
((~kind(lucy)<~>~creative(lucy)))&
(curious(alice)) | quiet(mary) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3893496346948204302866319
% SZS output start Proof for 3893496346948204302866319
5. ! [X0] : ((happy(X0) | strong(X0)) <=> (~happy(X0) | strong(X0))) [input p4]
8. ! [X0] : (~quiet(X0) => (~strong(X0) & curious(X0))) [input p7]
23. ~quiet(mary) [input hypothesis]
30. ! [X0] : ((~strong(X0) & curious(X0)) | quiet(X0)) [ennf transformation 8]
44. ! [X0] : (((happy(X0) | strong(X0)) | (happy(X0) & ~strong(X0))) & ((~happy(X0) | strong(X0)) | (~happy(X0) & ~strong(X0)))) [nnf transformation 5]
45. ! [X0] : ((happy(X0) | strong(X0) | (happy(X0) & ~strong(X0))) & (~happy(X0) | strong(X0) | (~happy(X0) & ~strong(X0)))) [flattening 44]
80. ~happy(X0) | strong(X0) | ~happy(X0) [cnf transformation 45]
82. happy(X0) | strong(X0) | happy(X0) [cnf transformation 45]
90. ~strong(X0) | quiet(X0) [cnf transformation 30]
123. ~quiet(mary) [cnf transformation 23]
124. ~happy(X0) | strong(X0) [duplicate literal removal 80]
125. happy(X0) | strong(X0) [duplicate literal removal 82]
139. 4 <=> ! [X1] : strong(X1) [avatar definition]
140. strong(X1) <- (4) [avatar component clause 139]
155. strong(X0) [subsumption resolution 124,125]
156. 4 [avatar split clause 155,139]
263. quiet(X0) <- (4) [resolution 90,140]
264. $false <- (4) [resolution 263,123]
267. ~4 [avatar contradiction clause 264]
268. $false [avatar sat refutation 156,267]
% SZS output end Proof for 3893496346948204302866319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then paul is either not generous or not funny and vice versa.
Everyone who is both old and not curious is not creative or calm.
If someone is not strong then lucy is both not strong and not curious.
Everyone who is not tall is not funny or generous and vice versa.
Everyone who is quiet or wise is funny or curious and vice versa.
If paul is either not quiet or quiet then susan is strong.
Everyone who is either not quiet or calm is generous.
Everyone who is both brave and not quiet is funny or wise and vice versa.
Everyone who is not wise is not quiet and vice versa.
Everyone who is either funny or tall is either generous or not kind.
If someone is both happy and not curious then paul is humble.
Everyone who is either not tall or quiet is either not funny or patient and vice versa.
Everyone who is both brave and tall is both old and not funny.
Someone is either not humble or not wise.
Susan is not rich.
Alice is happy or not rich.
John is not strong or creative.
Someone is either not funny or humble.
Alice is not tall. | John is happy. | neutral | ((?[X]:(calm(X)))<=>((~generous(paul)<~>~funny(paul))))&
(![X]:((old(X)&~curious(X))=>(~creative(X)|calm(X))))&
((?[X]:(~strong(X)))=>((~strong(lucy)&~curious(lucy))))&
(![X]:(~tall(X)<=>(~funny(X)|generous(X))))&
(![X]:((quiet(X)|wise(X))<=>(funny(X)|curious(X))))&
(((~quiet(paul)<~>quiet(paul)))=>(strong(susan)))&
(![X]:((~quiet(X)<~>calm(X))=>generous(X)))&
(![X]:((brave(X)&~quiet(X))<=>(funny(X)|wise(X))))&
(![X]:(~wise(X)<=>~quiet(X)))&
(![X]:((funny(X)<~>tall(X))=>(generous(X)<~>~kind(X))))&
((?[X]:((happy(X)&~curious(X))))=>(humble(paul)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((brave(X)&tall(X))=>(old(X)&~funny(X))))&
(?[X]:((~humble(X)<~>~wise(X))))&
(~rich(susan))&
((happy(alice)|~rich(alice)))&
((~strong(john)|creative(john)))&
(?[X]:((~funny(X)<~>humble(X))))&
(~tall(alice)) | happy(john) | [] | null | 0 |
If someone is not rich then susan is funny or not wise.
Everyone who is either not wise or not curious is not creative or not quiet.
If someone is not generous then someone is not strong and vice versa.
Everyone who is not brave is both rich and not wise and vice versa.
Everyone who is either not rich or not patient is both old and wise and vice versa.
Everyone who is not brave is either patient or rich.
Everyone who is either not tall or humble is quiet or not generous.
If someone is both creative and kind then someone is old or not creative and vice versa.
Everyone who is either not old or rich is patient.
If someone is quiet or not brave then paul is either not calm or brave.
Everyone who is either not rich or quiet is not creative.
Everyone who is not humble is wise or not kind.
If susan is not patient or kind then john is both old and generous.
Everyone who is both not curious and humble is not curious or happy and vice versa.
If paul is both creative and not tall then mary is either not happy or not old.
If lucy is both rich and not patient then susan is not wise and vice versa.
Someone is either not kind or calm.
Someone is not generous or not calm.
Mary is not strong.
Someone is either not generous or brave.
Someone is both not wise and not kind.
Someone is both quiet and curious.
Someone is both not humble and funny. | Mary is brave. | entailment | ((?[X]:(~rich(X)))=>((funny(susan)|~wise(susan))))&
(![X]:((~wise(X)<~>~curious(X))=>(~creative(X)|~quiet(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~strong(X))))&
(![X]:(~brave(X)<=>(rich(X)&~wise(X))))&
(![X]:((~rich(X)<~>~patient(X))<=>(old(X)&wise(X))))&
(![X]:(~brave(X)=>(patient(X)<~>rich(X))))&
(![X]:((~tall(X)<~>humble(X))=>(quiet(X)|~generous(X))))&
((?[X]:((creative(X)&kind(X))))<=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~old(X)<~>rich(X))=>patient(X)))&
((?[X]:((quiet(X)|~brave(X))))=>((~calm(paul)<~>brave(paul))))&
(![X]:((~rich(X)<~>quiet(X))=>~creative(X)))&
(![X]:(~humble(X)=>(wise(X)|~kind(X))))&
(((~patient(susan)|kind(susan)))=>((old(john)&generous(john))))&
(![X]:((~curious(X)&humble(X))<=>(~curious(X)|happy(X))))&
(((creative(paul)&~tall(paul)))=>((~happy(mary)<~>~old(mary))))&
(((rich(lucy)&~patient(lucy)))<=>(~wise(susan)))&
(?[X]:((~kind(X)<~>calm(X))))&
(?[X]:((~generous(X)|~calm(X))))&
(~strong(mary))&
(?[X]:((~generous(X)<~>brave(X))))&
(?[X]:((~wise(X)&~kind(X))))&
(?[X]:((quiet(X)&curious(X))))&
(?[X]:((~humble(X)&funny(X)))) | brave(mary) | [
"p3",
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4033732883935908302765115
% SZS output start Proof for 4033732883935908302765115
4. ! [X0] : (~brave(X0) <=> (~wise(X0) & rich(X0))) [input p3]
5. ! [X0] : ((~rich(X0) <~> ~patient(X0)) <=> (wise(X0) & old(X0))) [input p4]
6. ! [X0] : (~brave(X0) => (patient(X0) <~> rich(X0))) [input p5]
9. ! [X0] : ((~old(X0) <~> rich(X0)) => patient(X0)) [input p8]
24. ~brave(mary) [input hypothesis]
31. ! [X0] : ((patient(X0) <~> rich(X0)) | brave(X0)) [ennf transformation 6]
34. ! [X0] : (patient(X0) | (~old(X0) <=> rich(X0))) [ennf transformation 9]
48. ! [X0] : ((~brave(X0) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | brave(X0))) [nnf transformation 4]
49. ! [X0] : ((~brave(X0) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | brave(X0))) [flattening 48]
50. ! [X0] : ((((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | (~wise(X0) | ~old(X0))) & ((wise(X0) & old(X0)) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))))) [nnf transformation 5]
51. ! [X0] : ((((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | ~wise(X0) | ~old(X0)) & ((wise(X0) & old(X0)) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))))) [flattening 50]
52. ! [X0] : (((~rich(X0) | ~patient(X0)) & (rich(X0) | patient(X0))) | brave(X0)) [nnf transformation 31]
59. ! [X0] : (patient(X0) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0)))) [nnf transformation 34]
85. brave(X0) | rich(X0) [cnf transformation 49]
89. old(X0) | ~rich(X0) | patient(X0) [cnf transformation 51]
95. ~rich(X0) | ~patient(X0) | brave(X0) [cnf transformation 52]
104. patient(X0) | ~old(X0) | ~rich(X0) [cnf transformation 59]
137. ~brave(mary) [cnf transformation 24]
154. ~patient(X0) | brave(X0) [subsumption resolution 95,85]
185. ~rich(X0) | patient(X0) [subsumption resolution 104,89]
288. rich(mary) [resolution 85,137]
294. patient(mary) [resolution 185,288]
306. brave(mary) [resolution 294,154]
307. $false [subsumption resolution 306,137]
% SZS output end Proof for 4033732883935908302765115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or funny is not humble. Everyone who is humble or wise is humble. If someone is both not funny and rich then fred is not calm or wise and vice versa. If mary is strong or tall then fred is not creative and vice versa. Everyone who is tall or not generous is calm. Everyone who is tall is either kind or calm. Everyone who is not old or creative is rich. Everyone who is either not patient or calm is curious or not calm and vice versa. Everyone who is either wise or not rich is not humble or patient and vice versa. Everyone who is patient or tall is both not curious and creative and vice versa. Everyone who is both not happy and funny is either not calm or not strong and vice versa. Everyone who is not wise or not kind is both creative and not curious and vice versa. If john is both creative and not patient then someone is brave or not curious. If someone is both not strong and not curious then someone is either not calm or brave. Everyone who is either not kind or old is both not generous and kind. If susan is strong then someone is not happy or humble and vice versa. Paul is not generous or not rich. Paul is either humble or rich. Fred is brave or humble. Someone is wise or not funny. Susan is both not happy and brave. Someone is either rich or curious. Alice is either not humble or not creative. | Fred is calm. | entailment | (![X]:((~strong(X)|funny(X))=>~humble(X)))&
(![X]:((humble(X)|wise(X))=>humble(X)))&
((?[X]:((~funny(X)&rich(X))))<=>((~calm(fred)|wise(fred))))&
(((strong(mary)|tall(mary)))<=>(~creative(fred)))&
(![X]:((tall(X)|~generous(X))=>calm(X)))&
(![X]:(tall(X)=>(kind(X)<~>calm(X))))&
(![X]:((~old(X)|creative(X))=>rich(X)))&
(![X]:((~patient(X)<~>calm(X))<=>(curious(X)|~calm(X))))&
(![X]:((wise(X)<~>~rich(X))<=>(~humble(X)|patient(X))))&
(![X]:((patient(X)|tall(X))<=>(~curious(X)&creative(X))))&
(![X]:((~happy(X)&funny(X))<=>(~calm(X)<~>~strong(X))))&
(![X]:((~wise(X)|~kind(X))<=>(creative(X)&~curious(X))))&
(((creative(john)&~patient(john)))=>(?[X]:((brave(X)|~curious(X)))))&
((?[X]:((~strong(X)&~curious(X))))=>(?[X]:((~calm(X)<~>brave(X)))))&
(![X]:((~kind(X)<~>old(X))=>(~generous(X)&kind(X))))&
((strong(susan))<=>(?[X]:((~happy(X)|humble(X)))))&
((~generous(paul)|~rich(paul)))&
((humble(paul)<~>rich(paul)))&
((brave(fred)|humble(fred)))&
(?[X]:((wise(X)|~funny(X))))&
((~happy(susan)&brave(susan)))&
(?[X]:((rich(X)<~>curious(X))))&
((~humble(alice)<~>~creative(alice))) | calm(fred) | [
"p0",
"p1",
"p6",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4261854422397667394889561
% SZS output start Proof for 4261854422397667394889561
1. ! [X0] : ((funny(X0) | ~strong(X0)) => ~humble(X0)) [input p0]
2. ! [X0] : ((wise(X0) | humble(X0)) => humble(X0)) [input p1]
7. ! [X0] : ((creative(X0) | ~old(X0)) => rich(X0)) [input p6]
9. ! [X0] : ((wise(X0) <~> ~rich(X0)) <=> (patient(X0) | ~humble(X0))) [input p8]
11. ! [X0] : ((funny(X0) & ~happy(X0)) <=> (~calm(X0) <~> ~strong(X0))) [input p10]
12. ! [X0] : ((~kind(X0) | ~wise(X0)) <=> (~curious(X0) & creative(X0))) [input p11]
24. ~calm(fred) [input hypothesis]
26. ! [X0] : (~humble(X0) | (~funny(X0) & strong(X0))) [ennf transformation 1]
27. ! [X0] : (humble(X0) | (~wise(X0) & ~humble(X0))) [ennf transformation 2]
30. ! [X0] : (rich(X0) | (~creative(X0) & old(X0))) [ennf transformation 7]
45. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (~patient(X0) & humble(X0))) & ((patient(X0) | ~humble(X0)) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [nnf transformation 9]
46. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (~patient(X0) & humble(X0))) & (patient(X0) | ~humble(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [flattening 45]
49. ! [X0] : (((funny(X0) & ~happy(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) & (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | (~funny(X0) | happy(X0)))) [nnf transformation 11]
50. ! [X0] : (((funny(X0) & ~happy(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) & (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | ~funny(X0) | happy(X0))) [flattening 49]
51. ! [X0] : (((~kind(X0) | ~wise(X0)) | (curious(X0) | ~creative(X0))) & ((~curious(X0) & creative(X0)) | (kind(X0) & wise(X0)))) [nnf transformation 12]
52. ! [X0] : ((~kind(X0) | ~wise(X0) | curious(X0) | ~creative(X0)) & ((~curious(X0) & creative(X0)) | (kind(X0) & wise(X0)))) [flattening 51]
71. ~humble(X0) | strong(X0) [cnf transformation 26]
72. ~humble(X0) | ~funny(X0) [cnf transformation 26]
74. ~wise(X0) | humble(X0) [cnf transformation 27]
88. ~creative(X0) | rich(X0) [cnf transformation 30]
97. ~rich(X0) | wise(X0) | humble(X0) [cnf transformation 46]
110. ~strong(X0) | funny(X0) | calm(X0) [cnf transformation 50]
112. creative(X0) | wise(X0) [cnf transformation 52]
138. ~calm(fred) [cnf transformation 24]
143. 1 <=> wise(fred) [avatar definition]
144. wise(fred) <- (1) [avatar component clause 143]
152. 3 <=> calm(fred) [avatar definition]
153. ~calm(fred) <- (~3) [avatar component clause 152]
167. 6 <=> creative(fred) [avatar definition]
168. ~creative(fred) <- (~6) [avatar component clause 167]
169. creative(fred) <- (6) [avatar component clause 167]
183. ~rich(X0) | humble(X0) [subsumption resolution 97,74]
252. 23 <=> humble(fred) [avatar definition]
254. humble(fred) <- (23) [avatar component clause 252]
285. ~3 [avatar split clause 138,152]
290. rich(fred) <- (6) [resolution 88,169]
301. humble(fred) <- (6) [resolution 183,290]
302. 23 | ~6 [avatar split clause 301,167,252]
303. wise(fred) <- (~6) [resolution 168,112]
304. 1 | 6 [avatar split clause 303,167,143]
305. humble(fred) <- (1) [resolution 144,74]
306. 23 | ~1 [avatar split clause 305,143,252]
307. ~funny(fred) <- (23) [resolution 254,72]
308. strong(fred) <- (23) [resolution 254,71]
313. funny(fred) | calm(fred) <- (23) [resolution 110,308]
320. calm(fred) <- (23) [subsumption resolution 313,307]
321. $false <- (~3, 23) [subsumption resolution 320,153]
322. 3 | ~23 [avatar contradiction clause 321]
345. $false [avatar sat refutation 285,302,304,306,322]
% SZS output end Proof for 4261854422397667394889561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or wise is not calm and vice versa.
Everyone who is either funny or strong is humble or calm.
If alice is either quiet or not generous then someone is not brave and vice versa.
Everyone who is generous or not funny is either tall or not rich.
If susan is rich or strong then fred is both not strong and not happy and vice versa.
Everyone who is both calm and not rich is happy and vice versa.
If fred is both not funny and brave then susan is not humble or not old and vice versa.
Everyone who is creative or humble is kind or not patient.
Everyone who is not generous is wise or not rich and vice versa.
Everyone who is both old and not wise is not creative or not patient and vice versa.
If someone is patient or not old then alice is both wise and happy.
Everyone who is humble is either humble or not calm and vice versa.
Everyone who is either brave or not quiet is either creative or not kind and vice versa.
If fred is not calm then john is not patient or not quiet and vice versa.
If lucy is either not rich or not calm then someone is both creative and brave and vice versa.
If alice is funny or not generous then mary is calm or not humble and vice versa.
Mary is either not rich or kind.
Someone is rich or not quiet.
John is both humble and funny.
Susan is old or rich.
Someone is either not old or not tall.
Mary is not generous or not kind. | Alice is not generous. | entailment | (![X]:((~humble(X)<~>wise(X))<=>~calm(X)))&
(![X]:((funny(X)<~>strong(X))=>(humble(X)|calm(X))))&
(((quiet(alice)<~>~generous(alice)))<=>(?[X]:(~brave(X))))&
(![X]:((generous(X)|~funny(X))=>(tall(X)<~>~rich(X))))&
(((rich(susan)|strong(susan)))<=>((~strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~rich(X))<=>happy(X)))&
(((~funny(fred)&brave(fred)))<=>((~humble(susan)|~old(susan))))&
(![X]:((creative(X)|humble(X))=>(kind(X)|~patient(X))))&
(![X]:(~generous(X)<=>(wise(X)|~rich(X))))&
(![X]:((old(X)&~wise(X))<=>(~creative(X)|~patient(X))))&
((?[X]:((patient(X)|~old(X))))=>((wise(alice)&happy(alice))))&
(![X]:(humble(X)<=>(humble(X)<~>~calm(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>(creative(X)<~>~kind(X))))&
((~calm(fred))<=>((~patient(john)|~quiet(john))))&
(((~rich(lucy)<~>~calm(lucy)))<=>(?[X]:((creative(X)&brave(X)))))&
(((funny(alice)|~generous(alice)))<=>((calm(mary)|~humble(mary))))&
((~rich(mary)<~>kind(mary)))&
(?[X]:((rich(X)|~quiet(X))))&
((humble(john)&funny(john)))&
((old(susan)|rich(susan)))&
(?[X]:((~old(X)<~>~tall(X))))&
((~generous(mary)|~kind(mary))) | ~generous(alice) | [
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 57738115361135162154637
% SZS output start Proof for 57738115361135162154637
9. ! [X0] : (~generous(X0) <=> (~rich(X0) | wise(X0))) [input p8]
11. ? [X0] : (~old(X0) | patient(X0)) => (happy(alice) & wise(alice)) [input p10]
12. ! [X0] : (humble(X0) <=> (humble(X0) <~> ~calm(X0))) [input p11]
14. ~calm(fred) <=> (~quiet(john) | ~patient(john)) [input p13]
23. generous(alice) [input hypothesis]
29. (happy(alice) & wise(alice)) | ! [X0] : (old(X0) & ~patient(X0)) [ennf transformation 11]
43. ! [X0] : ((~generous(X0) | (rich(X0) & ~wise(X0))) & ((~rich(X0) | wise(X0)) | generous(X0))) [nnf transformation 9]
44. ! [X0] : ((~generous(X0) | (rich(X0) & ~wise(X0))) & (~rich(X0) | wise(X0) | generous(X0))) [flattening 43]
47. ! [X0] : ((humble(X0) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0)))) & (((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | ~humble(X0))) [nnf transformation 12]
49. (~calm(fred) | (quiet(john) & patient(john))) & ((~quiet(john) | ~patient(john)) | calm(fred)) [nnf transformation 14]
50. (~calm(fred) | (quiet(john) & patient(john))) & (~quiet(john) | ~patient(john) | calm(fred)) [flattening 49]
93. ~generous(X0) | ~wise(X0) [cnf transformation 44]
100. wise(alice) | ~patient(X0) [cnf transformation 29]
105. calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 47]
107. humble(X0) | humble(X0) | calm(X0) [cnf transformation 47]
117. ~calm(fred) | patient(john) [cnf transformation 50]
138. generous(alice) [cnf transformation 23]
139. calm(X0) | ~humble(X0) [duplicate literal removal 105]
140. humble(X0) | calm(X0) [duplicate literal removal 107]
149. 3 <=> generous(alice) [avatar definition]
151. generous(alice) <- (3) [avatar component clause 149]
211. 15 <=> ! [X0] : ~patient(X0) [avatar definition]
212. ~patient(X0) <- (15) [avatar component clause 211]
215. 16 <=> wise(alice) [avatar definition]
217. wise(alice) <- (16) [avatar component clause 215]
219. 15 | 16 [avatar split clause 100,215,211]
220. calm(X0) [subsumption resolution 139,140]
222. patient(john) [subsumption resolution 117,220]
290. 3 [avatar split clause 138,149]
291. $false <- (15) [resolution 222,212]
292. ~15 [avatar contradiction clause 291]
295. ~wise(alice) <- (3) [resolution 93,151]
296. $false <- (3, 16) [subsumption resolution 295,217]
297. ~3 | ~16 [avatar contradiction clause 296]
298. $false [avatar sat refutation 219,290,292,297]
% SZS output end Proof for 57738115361135162154637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is quiet or not old then someone is both not patient and not quiet. If paul is not curious or not old then alice is not calm or rich and vice versa. Everyone who is either not tall or not generous is happy or not old and vice versa. If fred is not quiet then susan is both tall and not strong. If someone is both not brave and funny then someone is either patient or generous and vice versa. If someone is either patient or not wise then john is not calm and vice versa. Everyone who is quiet or not humble is both not kind and not quiet and vice versa. Everyone who is both generous and not brave is either not creative or not tall and vice versa. If mary is either not calm or quiet then someone is not brave or strong and vice versa. If someone is quiet or not funny then someone is curious or not quiet. Everyone who is not curious is quiet or not old and vice versa. If someone is not rich or happy then someone is tall or creative. Everyone who is both not happy and generous is both humble and not quiet and vice versa. Everyone who is either not brave or not curious is both not generous and patient. If someone is not generous or curious then paul is rich or not brave and vice versa. Everyone who is humble is both not strong and kind and vice versa. Lucy is funny or kind. Mary is both calm and not creative. Someone is both patient and old. Someone is wise. Someone is generous or not wise. Someone is rich or patient. Someone is both not funny and wise. John is either not funny or wise. | Susan is old. | entailment | (((quiet(john)|~old(john)))=>(?[X]:((~patient(X)&~quiet(X)))))&
(((~curious(paul)|~old(paul)))<=>((~calm(alice)|rich(alice))))&
(![X]:((~tall(X)<~>~generous(X))<=>(happy(X)|~old(X))))&
((~quiet(fred))=>((tall(susan)&~strong(susan))))&
((?[X]:((~brave(X)&funny(X))))<=>(?[X]:((patient(X)<~>generous(X)))))&
((?[X]:((patient(X)<~>~wise(X))))<=>(~calm(john)))&
(![X]:((quiet(X)|~humble(X))<=>(~kind(X)&~quiet(X))))&
(![X]:((generous(X)&~brave(X))<=>(~creative(X)<~>~tall(X))))&
(((~calm(mary)<~>quiet(mary)))<=>(?[X]:((~brave(X)|strong(X)))))&
((?[X]:((quiet(X)|~funny(X))))=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:(~curious(X)<=>(quiet(X)|~old(X))))&
((?[X]:((~rich(X)|happy(X))))=>(?[X]:((tall(X)|creative(X)))))&
(![X]:((~happy(X)&generous(X))<=>(humble(X)&~quiet(X))))&
(![X]:((~brave(X)<~>~curious(X))=>(~generous(X)&patient(X))))&
((?[X]:((~generous(X)|curious(X))))<=>((rich(paul)|~brave(paul))))&
(![X]:(humble(X)<=>(~strong(X)&kind(X))))&
((funny(lucy)|kind(lucy)))&
((calm(mary)&~creative(mary)))&
(?[X]:((patient(X)&old(X))))&
(?[X]:(wise(X)))&
(?[X]:((generous(X)|~wise(X))))&
(?[X]:((rich(X)|patient(X))))&
(?[X]:((~funny(X)&wise(X))))&
((~funny(john)<~>wise(john))) | old(susan) | [
"p4",
"p6",
"p8",
"p10",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 845374185346677303776797
% SZS output start Proof for 845374185346677303776797
5. ? [X0] : (funny(X0) & ~brave(X0)) <=> ? [X0] : (patient(X0) <~> generous(X0)) [input p4]
7. ! [X0] : ((~humble(X0) | quiet(X0)) <=> (~quiet(X0) & ~kind(X0))) [input p6]
9. (~calm(mary) <~> quiet(mary)) <=> ? [X0] : (strong(X0) | ~brave(X0)) [input p8]
11. ! [X0] : (~curious(X0) <=> (~old(X0) | quiet(X0))) [input p10]
14. ! [X0] : ((~brave(X0) <~> ~curious(X0)) => (patient(X0) & ~generous(X0))) [input p13]
18. ~creative(mary) & calm(mary) [input p17]
25. ~old(susan) [input hypothesis]
26. ? [X0] : (funny(X0) & ~brave(X0)) <=> ? [X1] : (patient(X1) <~> generous(X1)) [rectify 5]
33. ! [X0] : ((patient(X0) & ~generous(X0)) | (~brave(X0) <=> ~curious(X0))) [ennf transformation 14]
40. (? [X0] : (funny(X0) & ~brave(X0)) | ! [X1] : ((patient(X1) | ~generous(X1)) & (generous(X1) | ~patient(X1)))) & (? [X1] : ((~generous(X1) | ~patient(X1)) & (generous(X1) | patient(X1))) | ! [X0] : (~funny(X0) | brave(X0))) [nnf transformation 26]
41. (? [X0] : (funny(X0) & ~brave(X0)) | ! [X1] : ((patient(X1) | ~generous(X1)) & (generous(X1) | ~patient(X1)))) & (? [X2] : ((~generous(X2) | ~patient(X2)) & (generous(X2) | patient(X2))) | ! [X3] : (~funny(X3) | brave(X3))) [rectify 40]
42. ? [X0] : (funny(X0) & ~brave(X0)) => (funny(sK1) & ~brave(sK1)) [choice axiom]
43. ? [X2] : ((~generous(X2) | ~patient(X2)) & (generous(X2) | patient(X2))) => ((~generous(sK2) | ~patient(sK2)) & (generous(sK2) | patient(sK2))) [choice axiom]
44. ((funny(sK1) & ~brave(sK1)) | ! [X1] : ((patient(X1) | ~generous(X1)) & (generous(X1) | ~patient(X1)))) & (((~generous(sK2) | ~patient(sK2)) & (generous(sK2) | patient(sK2))) | ! [X3] : (~funny(X3) | brave(X3))) [skolemisation 41,43,42]
49. ! [X0] : (((~humble(X0) | quiet(X0)) | (quiet(X0) | kind(X0))) & ((~quiet(X0) & ~kind(X0)) | (humble(X0) & ~quiet(X0)))) [nnf transformation 7]
50. ! [X0] : ((~humble(X0) | quiet(X0) | quiet(X0) | kind(X0)) & ((~quiet(X0) & ~kind(X0)) | (humble(X0) & ~quiet(X0)))) [flattening 49]
53. (((~quiet(mary) | calm(mary)) & (quiet(mary) | ~calm(mary))) | ! [X0] : (~strong(X0) & brave(X0))) & (? [X0] : (strong(X0) | ~brave(X0)) | ((~calm(mary) | ~quiet(mary)) & (quiet(mary) | calm(mary)))) [nnf transformation 9]
54. (((~quiet(mary) | calm(mary)) & (quiet(mary) | ~calm(mary))) | ! [X0] : (~strong(X0) & brave(X0))) & (? [X1] : (strong(X1) | ~brave(X1)) | ((~calm(mary) | ~quiet(mary)) & (quiet(mary) | calm(mary)))) [rectify 53]
55. ? [X1] : (strong(X1) | ~brave(X1)) => (strong(sK4) | ~brave(sK4)) [choice axiom]
56. (((~quiet(mary) | calm(mary)) & (quiet(mary) | ~calm(mary))) | ! [X0] : (~strong(X0) & brave(X0))) & ((strong(sK4) | ~brave(sK4)) | ((~calm(mary) | ~quiet(mary)) & (quiet(mary) | calm(mary)))) [skolemisation 54,55]
60. ! [X0] : ((~curious(X0) | (old(X0) & ~quiet(X0))) & ((~old(X0) | quiet(X0)) | curious(X0))) [nnf transformation 11]
61. ! [X0] : ((~curious(X0) | (old(X0) & ~quiet(X0))) & (~old(X0) | quiet(X0) | curious(X0))) [flattening 60]
67. ! [X0] : ((patient(X0) & ~generous(X0)) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) [nnf transformation 33]
104. ~brave(sK1) | generous(X1) | ~patient(X1) [cnf transformation 44]
114. ~quiet(X0) | ~quiet(X0) [cnf transformation 50]
125. quiet(mary) | ~calm(mary) | brave(X0) [cnf transformation 56]
131. ~old(X0) | quiet(X0) | curious(X0) [cnf transformation 61]
133. ~curious(X0) | old(X0) [cnf transformation 61]
141. ~brave(X0) | ~generous(X0) | curious(X0) [cnf transformation 67]
143. ~brave(X0) | patient(X0) | curious(X0) [cnf transformation 67]
152. calm(mary) [cnf transformation 18]
163. ~old(susan) [cnf transformation 25]
164. ~quiet(X0) [duplicate literal removal 114]
229. 14 <=> ! [X1] : (generous(X1) | ~patient(X1)) [avatar definition]
230. ~patient(X1) | generous(X1) <- (14) [avatar component clause 229]
233. 15 <=> brave(sK1) [avatar definition]
235. ~brave(sK1) <- (~15) [avatar component clause 233]
237. 14 | ~15 [avatar split clause 104,233,229]
278. 25 <=> calm(mary) [avatar definition]
282. ~calm(mary) | brave(X0) [subsumption resolution 125,164]
284. 26 <=> ! [X0] : brave(X0) [avatar definition]
285. brave(X0) <- (26) [avatar component clause 284]
286. 26 | ~25 [avatar split clause 282,278,284]
297. ~old(X0) | curious(X0) [subsumption resolution 131,164]
351. 25 [avatar split clause 152,278]
380. $false <- (~15, 26) [subsumption resolution 235,285]
381. 15 | ~26 [avatar contradiction clause 380]
472. ~generous(X0) | curious(X0) <- (26) [resolution 141,285]
480. curious(X0) | patient(X0) <- (26) [resolution 143,285]
523. patient(X1) | old(X1) <- (26) [resolution 480,133]
572. generous(X0) | old(X0) <- (14, 26) [resolution 523,230]
588. old(X6) | curious(X6) <- (14, 26) [resolution 572,472]
591. curious(X6) <- (14, 26) [subsumption resolution 588,297]
597. old(X1) <- (14, 26) [resolution 591,133]
610. $false <- (14, 26) [resolution 597,163]
612. ~14 | ~26 [avatar contradiction clause 610]
613. $false [avatar sat refutation 237,286,351,381,612]
% SZS output end Proof for 845374185346677303776797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is old or quiet then someone is not rich and vice versa.
If someone is patient or not old then lucy is either not wise or creative.
If john is either strong or not brave then someone is not humble.
Everyone who is humble or not funny is not humble or curious and vice versa.
Everyone who is both not rich and curious is old or not quiet and vice versa.
Everyone who is both tall and funny is both not wise and calm.
If someone is not curious or not old then susan is both not humble and generous.
If someone is not funny then someone is both creative and quiet.
If paul is calm then fred is patient and vice versa.
Everyone who is both old and humble is not strong or funny and vice versa.
Everyone who is both quiet and calm is either not generous or not old.
Everyone who is not old or not generous is not curious and vice versa.
Everyone who is tall is either not wise or patient and vice versa.
If john is both humble and generous then alice is both not old and old.
Everyone who is both old and generous is both patient and calm and vice versa.
If someone is either wise or old then someone is both humble and not rich.
Alice is rich.
Paul is not creative.
Lucy is not funny.
John is kind.
Someone is either funny or creative.
Lucy is not generous.
Lucy is not creative or not funny.
Susan is kind or happy. | Lucy is not strong. | contradiction | (((old(susan)|quiet(susan)))<=>(?[X]:(~rich(X))))&
((?[X]:((patient(X)|~old(X))))=>((~wise(lucy)<~>creative(lucy))))&
(((strong(john)<~>~brave(john)))=>(?[X]:(~humble(X))))&
(![X]:((humble(X)|~funny(X))<=>(~humble(X)|curious(X))))&
(![X]:((~rich(X)&curious(X))<=>(old(X)|~quiet(X))))&
(![X]:((tall(X)&funny(X))=>(~wise(X)&calm(X))))&
((?[X]:((~curious(X)|~old(X))))=>((~humble(susan)&generous(susan))))&
((?[X]:(~funny(X)))=>(?[X]:((creative(X)&quiet(X)))))&
((calm(paul))<=>(patient(fred)))&
(![X]:((old(X)&humble(X))<=>(~strong(X)|funny(X))))&
(![X]:((quiet(X)&calm(X))=>(~generous(X)<~>~old(X))))&
(![X]:((~old(X)|~generous(X))<=>~curious(X)))&
(![X]:(tall(X)<=>(~wise(X)<~>patient(X))))&
(((humble(john)&generous(john)))=>((~old(alice)&old(alice))))&
(![X]:((old(X)&generous(X))<=>(patient(X)&calm(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:((humble(X)&~rich(X)))))&
(rich(alice))&
(~creative(paul))&
(~funny(lucy))&
(kind(john))&
(?[X]:((funny(X)<~>creative(X))))&
(~generous(lucy))&
((~creative(lucy)|~funny(lucy)))&
((kind(susan)|happy(susan))) | ~strong(lucy) | [
"p4",
"p9",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8600171173718907713346053
% SZS output start Proof for 8600171173718907713346053
5. ! [X0] : ((curious(X0) & ~rich(X0)) <=> (~quiet(X0) | old(X0))) [input p4]
10. ! [X0] : ((humble(X0) & old(X0)) <=> (funny(X0) | ~strong(X0))) [input p9]
12. ! [X0] : ((~generous(X0) | ~old(X0)) <=> ~curious(X0)) [input p11]
22. ~generous(lucy) [input p21]
25. ~strong(lucy) [input hypothesis]
54. ! [X0] : (((curious(X0) & ~rich(X0)) | (quiet(X0) & ~old(X0))) & ((~quiet(X0) | old(X0)) | (~curious(X0) | rich(X0)))) [nnf transformation 5]
55. ! [X0] : (((curious(X0) & ~rich(X0)) | (quiet(X0) & ~old(X0))) & (~quiet(X0) | old(X0) | ~curious(X0) | rich(X0))) [flattening 54]
60. ! [X0] : (((humble(X0) & old(X0)) | (~funny(X0) & strong(X0))) & ((funny(X0) | ~strong(X0)) | (~humble(X0) | ~old(X0)))) [nnf transformation 10]
61. ! [X0] : (((humble(X0) & old(X0)) | (~funny(X0) & strong(X0))) & (funny(X0) | ~strong(X0) | ~humble(X0) | ~old(X0))) [flattening 60]
63. ! [X0] : (((~generous(X0) | ~old(X0)) | curious(X0)) & (~curious(X0) | (generous(X0) & old(X0)))) [nnf transformation 12]
64. ! [X0] : ((~generous(X0) | ~old(X0) | curious(X0)) & (~curious(X0) | (generous(X0) & old(X0)))) [flattening 63]
91. ~old(X0) | curious(X0) [cnf transformation 55]
104. strong(X0) | old(X0) [cnf transformation 61]
111. ~curious(X0) | generous(X0) [cnf transformation 64]
130. ~generous(lucy) [cnf transformation 22]
132. ~strong(lucy) [cnf transformation 25]
271. old(lucy) [resolution 104,132]
272. curious(lucy) [resolution 271,91]
281. generous(lucy) [resolution 272,111]
283. $false [subsumption resolution 281,130]
% SZS output end Proof for 8600171173718907713346053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both rich and patient then alice is both not strong and not tall.
Everyone who is rich or happy is either not quiet or strong and vice versa.
If mary is both tall and happy then someone is not calm.
If someone is not tall then mary is either not curious or not funny.
If lucy is either not humble or generous then someone is both not strong and rich.
Everyone who is not rich or curious is both not generous and creative and vice versa.
If someone is both tall and not curious then someone is either quiet or patient.
Everyone who is rich or not kind is not humble.
Everyone who is either brave or not quiet is calm.
If lucy is both generous and not generous then susan is not patient or not generous and vice versa.
Everyone who is kind or wise is both not happy and happy.
Everyone who is either not quiet or not humble is not patient and vice versa.
Everyone who is kind is curious or rich.
If someone is either not patient or happy then lucy is not calm or tall and vice versa.
If someone is either funny or not old then susan is either not old or tall and vice versa.
Everyone who is both not rich and curious is either not brave or not creative.
Mary is not happy.
Someone is kind or not generous.
John is both tall and not quiet.
Alice is either not creative or not generous.
Someone is either happy or not patient.
Lucy is both rich and funny.
Someone is not rich or calm. | John is not kind. | entailment | (((rich(mary)&patient(mary)))=>((~strong(alice)&~tall(alice))))&
(![X]:((rich(X)|happy(X))<=>(~quiet(X)<~>strong(X))))&
(((tall(mary)&happy(mary)))=>(?[X]:(~calm(X))))&
((?[X]:(~tall(X)))=>((~curious(mary)<~>~funny(mary))))&
(((~humble(lucy)<~>generous(lucy)))=>(?[X]:((~strong(X)&rich(X)))))&
(![X]:((~rich(X)|curious(X))<=>(~generous(X)&creative(X))))&
((?[X]:((tall(X)&~curious(X))))=>(?[X]:((quiet(X)<~>patient(X)))))&
(![X]:((rich(X)|~kind(X))=>~humble(X)))&
(![X]:((brave(X)<~>~quiet(X))=>calm(X)))&
(((generous(lucy)&~generous(lucy)))<=>((~patient(susan)|~generous(susan))))&
(![X]:((kind(X)|wise(X))=>(~happy(X)&happy(X))))&
(![X]:((~quiet(X)<~>~humble(X))<=>~patient(X)))&
(![X]:(kind(X)=>(curious(X)|rich(X))))&
((?[X]:((~patient(X)<~>happy(X))))<=>((~calm(lucy)|tall(lucy))))&
((?[X]:((funny(X)<~>~old(X))))<=>((~old(susan)<~>tall(susan))))&
(![X]:((~rich(X)&curious(X))=>(~brave(X)<~>~creative(X))))&
(~happy(mary))&
(?[X]:((kind(X)|~generous(X))))&
((tall(john)&~quiet(john)))&
((~creative(alice)<~>~generous(alice)))&
(?[X]:((happy(X)<~>~patient(X))))&
((rich(lucy)&funny(lucy)))&
(?[X]:((~rich(X)|calm(X)))) | ~kind(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 763955932463057724627700
% SZS output start Proof for 763955932463057724627700
11. ! [X0] : ((wise(X0) | kind(X0)) => (happy(X0) & ~happy(X0))) [input p10]
24. kind(john) [input hypothesis]
26. ! [X0] : (kind(X0) => (happy(X0) & ~happy(X0))) [pure predicate removal 11]
36. ! [X0] : ((happy(X0) & ~happy(X0)) | ~kind(X0)) [ennf transformation 26]
108. ~happy(X0) | ~kind(X0) [cnf transformation 36]
109. happy(X0) | ~kind(X0) [cnf transformation 36]
142. kind(john) [cnf transformation 24]
232. ~kind(X0) [subsumption resolution 108,109]
323. $false [subsumption resolution 142,232]
% SZS output end Proof for 763955932463057724627700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not patient or not wise then someone is both not curious and strong.
If john is both not old and old then someone is both funny and not generous and vice versa.
If someone is not funny then alice is either not patient or rich.
Everyone who is both brave and not brave is both not wise and not tall.
Everyone who is not brave is funny and vice versa.
Everyone who is both tall and not old is either not wise or not humble and vice versa.
Everyone who is either not tall or generous is not curious or not generous and vice versa.
If susan is both not humble and not old then someone is either not creative or happy and vice versa.
Everyone who is both not kind and not humble is both humble and creative and vice versa.
Everyone who is both not generous and not curious is either not generous or not rich.
If someone is not tall then lucy is not humble or creative.
Everyone who is brave is both not curious and happy.
If someone is either not tall or calm then someone is both not tall and creative and vice versa.
If someone is either not generous or humble then someone is not rich or not generous.
If john is not funny then susan is either not creative or rich.
Everyone who is both not kind and happy is not kind.
Someone is patient.
Alice is not brave.
Susan is not patient or tall.
Someone is both not happy and humble.
Fred is kind.
Fred is not calm or kind.
Someone is not quiet or tall. | Alice is not patient. | neutral | ((?[X]:((~patient(X)<~>~wise(X))))=>(?[X]:((~curious(X)&strong(X)))))&
(((~old(john)&old(john)))<=>(?[X]:((funny(X)&~generous(X)))))&
((?[X]:(~funny(X)))=>((~patient(alice)<~>rich(alice))))&
(![X]:((brave(X)&~brave(X))=>(~wise(X)&~tall(X))))&
(![X]:(~brave(X)<=>funny(X)))&
(![X]:((tall(X)&~old(X))<=>(~wise(X)<~>~humble(X))))&
(![X]:((~tall(X)<~>generous(X))<=>(~curious(X)|~generous(X))))&
(((~humble(susan)&~old(susan)))<=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:((~kind(X)&~humble(X))<=>(humble(X)&creative(X))))&
(![X]:((~generous(X)&~curious(X))=>(~generous(X)<~>~rich(X))))&
((?[X]:(~tall(X)))=>((~humble(lucy)|creative(lucy))))&
(![X]:(brave(X)=>(~curious(X)&happy(X))))&
((?[X]:((~tall(X)<~>calm(X))))<=>(?[X]:((~tall(X)&creative(X)))))&
((?[X]:((~generous(X)<~>humble(X))))=>(?[X]:((~rich(X)|~generous(X)))))&
((~funny(john))=>((~creative(susan)<~>rich(susan))))&
(![X]:((~kind(X)&happy(X))=>~kind(X)))&
(?[X]:(patient(X)))&
(~brave(alice))&
((~patient(susan)|tall(susan)))&
(?[X]:((~happy(X)&humble(X))))&
(kind(fred))&
((~calm(fred)|kind(fred)))&
(?[X]:((~quiet(X)|tall(X)))) | ~patient(alice) | [] | null | 0 |
Everyone who is not funny or not brave is either calm or not funny and vice versa.
If someone is kind then someone is both funny and patient and vice versa.
If someone is funny or happy then alice is tall or wise and vice versa.
If paul is either not tall or patient then mary is both not kind and wise and vice versa.
Everyone who is not brave is both not kind and not creative.
Everyone who is generous is both not happy and not generous.
If john is either funny or not patient then someone is humble or not rich.
If someone is both generous and humble then paul is funny and vice versa.
If someone is both not happy and not generous then paul is both not creative and not generous and vice versa.
Everyone who is both not brave and generous is both not brave and creative and vice versa.
If john is creative then someone is both not calm and not curious.
If someone is humble then alice is not humble or generous and vice versa.
If paul is either not creative or curious then alice is both not old and not brave.
Everyone who is kind is both not humble and not funny.
Everyone who is generous is strong or wise and vice versa.
Everyone who is calm or happy is either creative or not funny.
Susan is rich.
Someone is both not generous and not happy.
Someone is either generous or not brave.
John is humble or not generous.
Lucy is both not tall and humble. | Lucy is not creative. | neutral | (![X]:((~funny(X)|~brave(X))<=>(calm(X)<~>~funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((funny(X)&patient(X)))))&
((?[X]:((funny(X)|happy(X))))<=>((tall(alice)|wise(alice))))&
(((~tall(paul)<~>patient(paul)))<=>((~kind(mary)&wise(mary))))&
(![X]:(~brave(X)=>(~kind(X)&~creative(X))))&
(![X]:(generous(X)=>(~happy(X)&~generous(X))))&
(((funny(john)<~>~patient(john)))=>(?[X]:((humble(X)|~rich(X)))))&
((?[X]:((generous(X)&humble(X))))<=>(funny(paul)))&
((?[X]:((~happy(X)&~generous(X))))<=>((~creative(paul)&~generous(paul))))&
(![X]:((~brave(X)&generous(X))<=>(~brave(X)&creative(X))))&
((creative(john))=>(?[X]:((~calm(X)&~curious(X)))))&
((?[X]:(humble(X)))<=>((~humble(alice)|generous(alice))))&
(((~creative(paul)<~>curious(paul)))=>((~old(alice)&~brave(alice))))&
(![X]:(kind(X)=>(~humble(X)&~funny(X))))&
(![X]:(generous(X)<=>(strong(X)|wise(X))))&
(![X]:((calm(X)|happy(X))=>(creative(X)<~>~funny(X))))&
(rich(susan))&
(?[X]:((~generous(X)&~happy(X))))&
(?[X]:((generous(X)<~>~brave(X))))&
((humble(john)|~generous(john)))&
((~tall(lucy)&humble(lucy))) | ~creative(lucy) | [] | null | 0 |
If someone is not quiet then someone is both not generous and not humble and vice versa.
If lucy is both not patient and not quiet then fred is either humble or tall and vice versa.
Everyone who is both rich and not funny is rich or not wise and vice versa.
Everyone who is funny is happy or calm and vice versa.
If someone is either not generous or not brave then someone is not brave and vice versa.
Everyone who is either not calm or not funny is brave or not creative and vice versa.
If someone is rich or not tall then lucy is not quiet or creative.
Everyone who is not humble or strong is either not patient or not curious.
If someone is not patient then someone is either not happy or tall and vice versa.
Everyone who is not quiet is rich and vice versa.
Everyone who is either calm or happy is either not generous or happy and vice versa.
If someone is curious or not creative then fred is either not kind or not tall.
If susan is both rich and funny then someone is generous or not calm.
Everyone who is not calm or patient is wise or funny and vice versa.
If someone is both kind and not funny then mary is either not creative or not funny and vice versa.
Everyone who is quiet or not brave is either not wise or tall.
Paul is not old.
Fred is not old.
Someone is both curious and not happy.
Someone is both strong and not old.
Fred is not creative or happy.
Susan is not calm.
Someone is both not calm and not brave.
Someone is either not generous or not humble. | Susan is not generous. | contradiction | ((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)&~humble(X)))))&
(((~patient(lucy)&~quiet(lucy)))<=>((humble(fred)<~>tall(fred))))&
(![X]:((rich(X)&~funny(X))<=>(rich(X)|~wise(X))))&
(![X]:(funny(X)<=>(happy(X)|calm(X))))&
((?[X]:((~generous(X)<~>~brave(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~calm(X)<~>~funny(X))<=>(brave(X)|~creative(X))))&
((?[X]:((rich(X)|~tall(X))))=>((~quiet(lucy)|creative(lucy))))&
(![X]:((~humble(X)|strong(X))=>(~patient(X)<~>~curious(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(![X]:(~quiet(X)<=>rich(X)))&
(![X]:((calm(X)<~>happy(X))<=>(~generous(X)<~>happy(X))))&
((?[X]:((curious(X)|~creative(X))))=>((~kind(fred)<~>~tall(fred))))&
(((rich(susan)&funny(susan)))=>(?[X]:((generous(X)|~calm(X)))))&
(![X]:((~calm(X)|patient(X))<=>(wise(X)|funny(X))))&
((?[X]:((kind(X)&~funny(X))))<=>((~creative(mary)<~>~funny(mary))))&
(![X]:((quiet(X)|~brave(X))=>(~wise(X)<~>tall(X))))&
(~old(paul))&
(~old(fred))&
(?[X]:((curious(X)&~happy(X))))&
(?[X]:((strong(X)&~old(X))))&
((~creative(fred)|happy(fred)))&
(~calm(susan))&
(?[X]:((~calm(X)&~brave(X))))&
(?[X]:((~generous(X)<~>~humble(X)))) | ~generous(susan) | [
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8738854816619099310559494
% SZS output start Proof for 8738854816619099310559494
11. ! [X0] : ((calm(X0) <~> happy(X0)) <=> (~generous(X0) <~> happy(X0))) [input p10]
22. ~calm(susan) [input p21]
25. ~generous(susan) [input hypothesis]
64. ! [X0] : ((((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0)))) & (((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))))) [nnf transformation 11]
126. ~happy(X0) | generous(X0) | calm(X0) | ~happy(X0) [cnf transformation 64]
127. happy(X0) | calm(X0) | happy(X0) | generous(X0) [cnf transformation 64]
154. ~calm(susan) [cnf transformation 22]
159. ~generous(susan) [cnf transformation 25]
161. ~happy(X0) | generous(X0) | calm(X0) [duplicate literal removal 126]
162. happy(X0) | calm(X0) | generous(X0) [duplicate literal removal 127]
273. calm(X0) | generous(X0) [subsumption resolution 161,162]
351. generous(susan) [resolution 273,154]
354. $false [subsumption resolution 351,159]
% SZS output end Proof for 8738854816619099310559494
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is both not strong and creative and vice versa. Everyone who is both quiet and not calm is not happy or happy and vice versa. Everyone who is either curious or strong is not quiet or not brave and vice versa. If someone is not happy then john is rich or happy and vice versa. If someone is creative then paul is not patient and vice versa. If someone is not old then someone is both not brave and not tall. Everyone who is either humble or strong is strong or patient and vice versa. Everyone who is curious or not wise is either quiet or patient. If someone is not kind then someone is old and vice versa. If fred is old or not happy then someone is not curious. If lucy is either calm or not kind then lucy is not brave or patient and vice versa. If someone is not humble or patient then paul is both curious and not patient and vice versa. Everyone who is not funny is both brave and not curious. If someone is calm then someone is either not old or funny and vice versa. Everyone who is either creative or not happy is both humble and not old. Everyone who is both not funny and happy is not kind or happy. Someone is wise. Susan is not brave or not generous. Someone is either not tall or rich. Lucy is either calm or funny. Someone is either not old or creative. Someone is both brave and kind. Paul is wise or tall. Someone is calm or not calm. | John is quiet. | entailment | (![X]:(~patient(X)<=>(~strong(X)&creative(X))))&
(![X]:((quiet(X)&~calm(X))<=>(~happy(X)|happy(X))))&
(![X]:((curious(X)<~>strong(X))<=>(~quiet(X)|~brave(X))))&
((?[X]:(~happy(X)))<=>((rich(john)|happy(john))))&
((?[X]:(creative(X)))<=>(~patient(paul)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((humble(X)<~>strong(X))<=>(strong(X)|patient(X))))&
(![X]:((curious(X)|~wise(X))=>(quiet(X)<~>patient(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(old(X))))&
(((old(fred)|~happy(fred)))=>(?[X]:(~curious(X))))&
(((calm(lucy)<~>~kind(lucy)))<=>((~brave(lucy)|patient(lucy))))&
((?[X]:((~humble(X)|patient(X))))<=>((curious(paul)&~patient(paul))))&
(![X]:(~funny(X)=>(brave(X)&~curious(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~old(X)<~>funny(X)))))&
(![X]:((creative(X)<~>~happy(X))=>(humble(X)&~old(X))))&
(![X]:((~funny(X)&happy(X))=>(~kind(X)|happy(X))))&
(?[X]:(wise(X)))&
((~brave(susan)|~generous(susan)))&
(?[X]:((~tall(X)<~>rich(X))))&
((calm(lucy)<~>funny(lucy)))&
(?[X]:((~old(X)<~>creative(X))))&
(?[X]:((brave(X)&kind(X))))&
((wise(paul)|tall(paul)))&
(?[X]:((calm(X)|~calm(X)))) | quiet(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 7835395448953367172329584
% SZS output start Proof for 7835395448953367172329584
2. ! [X0] : ((~calm(X0) & quiet(X0)) <=> (happy(X0) | ~happy(X0))) [input p1]
25. ~quiet(john) [input hypothesis]
42. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | (calm(X0) | ~quiet(X0)))) [nnf transformation 2]
43. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | calm(X0) | ~quiet(X0))) [flattening 42]
96. quiet(X0) | happy(X0) [cnf transformation 43]
97. quiet(X0) | ~happy(X0) [cnf transformation 43]
156. ~quiet(john) [cnf transformation 25]
160. quiet(X0) [subsumption resolution 96,97]
295. $false [subsumption resolution 156,160]
% SZS output end Proof for 7835395448953367172329584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not patient or strong is not brave or patient.
Everyone who is calm or not kind is kind and vice versa.
Everyone who is both not kind and humble is old or happy and vice versa.
If someone is calm then john is curious or brave.
If someone is not quiet then alice is happy or not generous and vice versa.
If someone is old then alice is either not patient or not strong and vice versa.
If someone is not kind or not happy then someone is kind.
If someone is not humble or not happy then fred is calm or funny.
Everyone who is rich or kind is not wise or patient and vice versa.
Everyone who is not wise or not funny is either not old or rich.
If someone is not wise or humble then alice is not quiet.
Everyone who is generous is not curious or strong and vice versa.
If someone is both brave and curious then john is not patient and vice versa.
Everyone who is patient or funny is either not quiet or tall and vice versa.
Everyone who is wise or not curious is both funny and generous.
Mary is either not wise or not tall.
Someone is strong.
Someone is either curious or patient.
Someone is not old or patient.
Someone is either not brave or creative.
Fred is either funny or not generous. | John is not old. | entailment | (![X]:((~patient(X)<~>strong(X))=>(~brave(X)|patient(X))))&
(![X]:((calm(X)|~kind(X))<=>kind(X)))&
(![X]:((~kind(X)&humble(X))<=>(old(X)|happy(X))))&
((?[X]:(calm(X)))=>((curious(john)|brave(john))))&
((?[X]:(~quiet(X)))<=>((happy(alice)|~generous(alice))))&
((?[X]:(old(X)))<=>((~patient(alice)<~>~strong(alice))))&
((?[X]:((~kind(X)|~happy(X))))=>(?[X]:(kind(X))))&
((?[X]:((~humble(X)|~happy(X))))=>((calm(fred)|funny(fred))))&
(![X]:((rich(X)|kind(X))<=>(~wise(X)|patient(X))))&
(![X]:((~wise(X)|~funny(X))=>(~old(X)<~>rich(X))))&
((?[X]:((~wise(X)|humble(X))))=>(~quiet(alice)))&
(![X]:(generous(X)<=>(~curious(X)|strong(X))))&
((?[X]:((brave(X)&curious(X))))<=>(~patient(john)))&
(![X]:((patient(X)|funny(X))<=>(~quiet(X)<~>tall(X))))&
(![X]:((wise(X)|~curious(X))=>(funny(X)&generous(X))))&
((~wise(mary)<~>~tall(mary)))&
(?[X]:(strong(X)))&
(?[X]:((curious(X)<~>patient(X))))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((~brave(X)<~>creative(X))))&
((funny(fred)<~>~generous(fred))) | ~old(john) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1150121531868575303972663
% SZS output start Proof for 1150121531868575303972663
2. ! [X0] : ((~kind(X0) | calm(X0)) <=> kind(X0)) [input p1]
3. ! [X0] : ((humble(X0) & ~kind(X0)) <=> (happy(X0) | old(X0))) [input p2]
22. old(john) [input hypothesis]
35. ! [X0] : (((~kind(X0) | calm(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) & ~calm(X0)))) [nnf transformation 2]
36. ! [X0] : ((~kind(X0) | calm(X0) | ~kind(X0)) & (kind(X0) | (kind(X0) & ~calm(X0)))) [flattening 35]
37. ! [X0] : (((humble(X0) & ~kind(X0)) | (~happy(X0) & ~old(X0))) & ((happy(X0) | old(X0)) | (~humble(X0) | kind(X0)))) [nnf transformation 3]
38. ! [X0] : (((humble(X0) & ~kind(X0)) | (~happy(X0) & ~old(X0))) & (happy(X0) | old(X0) | ~humble(X0) | kind(X0))) [flattening 37]
77. kind(X0) | kind(X0) [cnf transformation 36]
80. ~kind(X0) | ~old(X0) [cnf transformation 38]
132. old(john) [cnf transformation 22]
133. kind(X0) [duplicate literal removal 77]
137. ~old(X0) [subsumption resolution 80,133]
259. $false [subsumption resolution 132,137]
% SZS output end Proof for 1150121531868575303972663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not wise is both brave and not creative and vice versa.
Everyone who is not humble is strong or generous and vice versa.
Everyone who is strong is not patient and vice versa.
Everyone who is not funny is both not quiet and tall.
Everyone who is kind is both not generous and not happy.
Everyone who is quiet or not quiet is both not rich and not kind and vice versa.
If someone is both not generous and funny then someone is both not kind and humble and vice versa.
Everyone who is both not calm and funny is patient and vice versa.
If lucy is happy then paul is not creative.
Everyone who is both not creative and not kind is both strong and humble and vice versa.
Everyone who is either quiet or not wise is both not quiet and not curious.
If mary is either not kind or humble then lucy is not calm.
If someone is either not happy or not old then lucy is either not calm or calm and vice versa.
Everyone who is happy or patient is either quiet or happy.
Everyone who is either old or wise is not generous or wise and vice versa.
Everyone who is humble or quiet is either rich or generous and vice versa.
Someone is either brave or not brave.
Susan is not strong or curious.
Someone is not calm.
Fred is not patient or not calm.
Someone is both not kind and wise.
John is happy. | Fred is brave. | neutral | (![X]:((quiet(X)&~wise(X))<=>(brave(X)&~creative(X))))&
(![X]:(~humble(X)<=>(strong(X)|generous(X))))&
(![X]:(strong(X)<=>~patient(X)))&
(![X]:(~funny(X)=>(~quiet(X)&tall(X))))&
(![X]:(kind(X)=>(~generous(X)&~happy(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~rich(X)&~kind(X))))&
((?[X]:((~generous(X)&funny(X))))<=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:((~calm(X)&funny(X))<=>patient(X)))&
((happy(lucy))=>(~creative(paul)))&
(![X]:((~creative(X)&~kind(X))<=>(strong(X)&humble(X))))&
(![X]:((quiet(X)<~>~wise(X))=>(~quiet(X)&~curious(X))))&
(((~kind(mary)<~>humble(mary)))=>(~calm(lucy)))&
((?[X]:((~happy(X)<~>~old(X))))<=>((~calm(lucy)<~>calm(lucy))))&
(![X]:((happy(X)|patient(X))=>(quiet(X)<~>happy(X))))&
(![X]:((old(X)<~>wise(X))<=>(~generous(X)|wise(X))))&
(![X]:((humble(X)|quiet(X))<=>(rich(X)<~>generous(X))))&
(?[X]:((brave(X)<~>~brave(X))))&
((~strong(susan)|curious(susan)))&
(?[X]:(~calm(X)))&
((~patient(fred)|~calm(fred)))&
(?[X]:((~kind(X)&wise(X))))&
(happy(john)) | brave(fred) | [] | null | 0 |
If someone is either brave or calm then lucy is not curious and vice versa.
Everyone who is calm or not tall is not calm or not rich and vice versa.
Everyone who is both not rich and brave is either not strong or calm.
If john is either curious or quiet then someone is not quiet or not old and vice versa.
Everyone who is either not rich or old is not calm and vice versa.
If someone is either humble or happy then susan is both funny and not calm and vice versa.
Everyone who is not curious is either not creative or old.
Everyone who is both brave and generous is both not quiet and humble and vice versa.
If paul is not calm or not kind then fred is both old and not creative.
If lucy is not humble or curious then paul is either not rich or not humble.
Everyone who is either calm or old is creative or wise.
If alice is not generous then fred is either creative or not creative.
If fred is both rich and not happy then someone is either creative or not wise.
If someone is both strong and tall then susan is humble or not calm.
Everyone who is brave or not brave is not strong or not calm.
If mary is both not calm and funny then someone is either not creative or funny and vice versa.
Mary is both not generous and not quiet.
Susan is either creative or tall.
Someone is both funny and happy.
Alice is not curious or not generous.
Paul is not humble.
Someone is not quiet.
Someone is quiet or not funny. | Fred is creative. | neutral | ((?[X]:((brave(X)<~>calm(X))))<=>(~curious(lucy)))&
(![X]:((calm(X)|~tall(X))<=>(~calm(X)|~rich(X))))&
(![X]:((~rich(X)&brave(X))=>(~strong(X)<~>calm(X))))&
(((curious(john)<~>quiet(john)))<=>(?[X]:((~quiet(X)|~old(X)))))&
(![X]:((~rich(X)<~>old(X))<=>~calm(X)))&
((?[X]:((humble(X)<~>happy(X))))<=>((funny(susan)&~calm(susan))))&
(![X]:(~curious(X)=>(~creative(X)<~>old(X))))&
(![X]:((brave(X)&generous(X))<=>(~quiet(X)&humble(X))))&
(((~calm(paul)|~kind(paul)))=>((old(fred)&~creative(fred))))&
(((~humble(lucy)|curious(lucy)))=>((~rich(paul)<~>~humble(paul))))&
(![X]:((calm(X)<~>old(X))=>(creative(X)|wise(X))))&
((~generous(alice))=>((creative(fred)<~>~creative(fred))))&
(((rich(fred)&~happy(fred)))=>(?[X]:((creative(X)<~>~wise(X)))))&
((?[X]:((strong(X)&tall(X))))=>((humble(susan)|~calm(susan))))&
(![X]:((brave(X)|~brave(X))=>(~strong(X)|~calm(X))))&
(((~calm(mary)&funny(mary)))<=>(?[X]:((~creative(X)<~>funny(X)))))&
((~generous(mary)&~quiet(mary)))&
((creative(susan)<~>tall(susan)))&
(?[X]:((funny(X)&happy(X))))&
((~curious(alice)|~generous(alice)))&
(~humble(paul))&
(?[X]:(~quiet(X)))&
(?[X]:((quiet(X)|~funny(X)))) | creative(fred) | [] | null | 0 |
Everyone who is either wise or not patient is both kind and not generous.
If someone is humble or rich then john is either old or patient and vice versa.
If someone is either not strong or happy then paul is both funny and not brave.
Everyone who is both not humble and not calm is either rich or humble.
If someone is either not calm or not wise then someone is strong or wise and vice versa.
Everyone who is not calm or happy is not humble and vice versa.
Everyone who is either not funny or calm is both funny and not rich.
Everyone who is both brave and not quiet is both generous and not calm and vice versa.
If susan is not tall then someone is either not happy or not old and vice versa.
Everyone who is not calm or not old is not happy.
If someone is humble or old then someone is both happy and not calm and vice versa.
Everyone who is either old or not funny is either quiet or calm.
Everyone who is both quiet and curious is wise or kind and vice versa.
If susan is either calm or brave then alice is both old and not kind.
If someone is either not wise or not humble then lucy is rich or not funny.
Everyone who is not funny is either calm or not rich.
Mary is not calm.
Someone is either kind or not calm.
Someone is both not strong and not patient.
Someone is tall.
Lucy is not rich or generous.
Someone is both funny and quiet.
Paul is not happy or not humble. | Lucy is rich. | entailment | (![X]:((wise(X)<~>~patient(X))=>(kind(X)&~generous(X))))&
((?[X]:((humble(X)|rich(X))))<=>((old(john)<~>patient(john))))&
((?[X]:((~strong(X)<~>happy(X))))=>((funny(paul)&~brave(paul))))&
(![X]:((~humble(X)&~calm(X))=>(rich(X)<~>humble(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((~calm(X)|happy(X))<=>~humble(X)))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:((old(X)<~>~funny(X))=>(quiet(X)<~>calm(X))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|kind(X))))&
(((calm(susan)<~>brave(susan)))=>((old(alice)&~kind(alice))))&
((?[X]:((~wise(X)<~>~humble(X))))=>((rich(lucy)|~funny(lucy))))&
(![X]:(~funny(X)=>(calm(X)<~>~rich(X))))&
(~calm(mary))&
(?[X]:((kind(X)<~>~calm(X))))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:(tall(X)))&
((~rich(lucy)|generous(lucy)))&
(?[X]:((funny(X)&quiet(X))))&
((~happy(paul)|~humble(paul))) | rich(lucy) | [
"p3",
"p4",
"p5",
"p6",
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 31105294973190059547098
% SZS output start Proof for 31105294973190059547098
4. ! [X0] : ((~calm(X0) & ~humble(X0)) => (rich(X0) <~> humble(X0))) [input p3]
5. ? [X0] : (~calm(X0) <~> ~wise(X0)) <=> ? [X0] : (wise(X0) | strong(X0)) [input p4]
6. ! [X0] : ((happy(X0) | ~calm(X0)) <=> ~humble(X0)) [input p5]
7. ! [X0] : ((~funny(X0) <~> calm(X0)) => (~rich(X0) & funny(X0))) [input p6]
10. ! [X0] : ((~old(X0) | ~calm(X0)) => ~happy(X0)) [input p9]
11. ? [X0] : (old(X0) | humble(X0)) <=> ? [X0] : (~calm(X0) & happy(X0)) [input p10]
15. ? [X0] : (~wise(X0) <~> ~humble(X0)) => (~funny(lucy) | rich(lucy)) [input p14]
16. ! [X0] : (~funny(X0) => (calm(X0) <~> ~rich(X0))) [input p15]
24. ~rich(lucy) [input hypothesis]
25. ? [X0] : (~calm(X0) <~> ~wise(X0)) <=> ? [X1] : (wise(X1) | strong(X1)) [rectify 5]
26. ? [X0] : (old(X0) | humble(X0)) <=> ? [X1] : (~calm(X1) & happy(X1)) [rectify 11]
29. ! [X0] : ((rich(X0) <~> humble(X0)) | (calm(X0) | humble(X0))) [ennf transformation 4]
30. ! [X0] : ((rich(X0) <~> humble(X0)) | calm(X0) | humble(X0)) [flattening 29]
31. ! [X0] : ((~rich(X0) & funny(X0)) | (~funny(X0) <=> calm(X0))) [ennf transformation 7]
32. ! [X0] : (~happy(X0) | (old(X0) & calm(X0))) [ennf transformation 10]
35. (~funny(lucy) | rich(lucy)) | ! [X0] : (~wise(X0) <=> ~humble(X0)) [ennf transformation 15]
36. ~funny(lucy) | rich(lucy) | ! [X0] : (~wise(X0) <=> ~humble(X0)) [flattening 35]
37. ! [X0] : ((calm(X0) <~> ~rich(X0)) | funny(X0)) [ennf transformation 16]
44. ! [X0] : (((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | calm(X0) | humble(X0)) [nnf transformation 30]
45. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | ! [X1] : (~wise(X1) & ~strong(X1))) & (? [X1] : (wise(X1) | strong(X1)) | ! [X0] : ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) [nnf transformation 25]
46. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | ! [X1] : (~wise(X1) & ~strong(X1))) & (? [X2] : (wise(X2) | strong(X2)) | ! [X3] : ((~calm(X3) | wise(X3)) & (~wise(X3) | calm(X3)))) [rectify 45]
47. ? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) => ((wise(sK1) | calm(sK1)) & (~wise(sK1) | ~calm(sK1))) [choice axiom]
48. ? [X2] : (wise(X2) | strong(X2)) => (wise(sK2) | strong(sK2)) [choice axiom]
49. (((wise(sK1) | calm(sK1)) & (~wise(sK1) | ~calm(sK1))) | ! [X1] : (~wise(X1) & ~strong(X1))) & ((wise(sK2) | strong(sK2)) | ! [X3] : ((~calm(X3) | wise(X3)) & (~wise(X3) | calm(X3)))) [skolemisation 46,48,47]
50. ! [X0] : (((happy(X0) | ~calm(X0)) | humble(X0)) & (~humble(X0) | (~happy(X0) & calm(X0)))) [nnf transformation 6]
51. ! [X0] : ((happy(X0) | ~calm(X0) | humble(X0)) & (~humble(X0) | (~happy(X0) & calm(X0)))) [flattening 50]
52. ! [X0] : ((~rich(X0) & funny(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) [nnf transformation 31]
59. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X1] : (~calm(X1) & happy(X1)) | ! [X0] : (~old(X0) & ~humble(X0))) [nnf transformation 26]
60. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X2] : (~calm(X2) & happy(X2)) | ! [X3] : (~old(X3) & ~humble(X3))) [rectify 59]
61. ? [X0] : (old(X0) | humble(X0)) => (old(sK4) | humble(sK4)) [choice axiom]
62. ? [X2] : (~calm(X2) & happy(X2)) => (~calm(sK5) & happy(sK5)) [choice axiom]
63. ((old(sK4) | humble(sK4)) | ! [X1] : (calm(X1) | ~happy(X1))) & ((~calm(sK5) & happy(sK5)) | ! [X3] : (~old(X3) & ~humble(X3))) [skolemisation 60,62,61]
68. ~funny(lucy) | rich(lucy) | ! [X0] : ((~wise(X0) | humble(X0)) & (~humble(X0) | wise(X0))) [nnf transformation 36]
69. ! [X0] : (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | funny(X0)) [nnf transformation 37]
93. humble(X0) | rich(X0) | calm(X0) | humble(X0) [cnf transformation 44]
96. wise(sK2) | strong(sK2) | ~calm(X3) | wise(X3) [cnf transformation 49]
99. wise(sK1) | calm(sK1) | ~strong(X1) [cnf transformation 49]
103. ~calm(X0) | happy(X0) | humble(X0) [cnf transformation 51]
104. funny(X0) | calm(X0) | funny(X0) [cnf transformation 52]
116. ~happy(X0) | calm(X0) [cnf transformation 32]
117. ~happy(X0) | old(X0) [cnf transformation 32]
118. happy(sK5) | ~humble(X3) [cnf transformation 63]
119. happy(sK5) | ~old(X3) [cnf transformation 63]
121. ~calm(sK5) | ~old(X3) [cnf transformation 63]
137. ~funny(lucy) | rich(lucy) | ~wise(X0) | humble(X0) [cnf transformation 68]
139. rich(X0) | ~calm(X0) | funny(X0) [cnf transformation 69]
150. ~rich(lucy) [cnf transformation 24]
151. calm(X0) | funny(X0) [duplicate literal removal 104]
152. calm(X0) | rich(X0) | humble(X0) [duplicate literal removal 93]
176. 6 <=> ! [X1] : ~humble(X1) [avatar definition]
177. ~humble(X1) <- (6) [avatar component clause 176]
200. 11 <=> ! [X1] : ~wise(X1) [avatar definition]
201. ~wise(X1) <- (11) [avatar component clause 200]
203. 12 <=> calm(sK1) [avatar definition]
205. calm(sK1) <- (12) [avatar component clause 203]
207. 13 <=> wise(sK1) [avatar definition]
209. wise(sK1) <- (13) [avatar component clause 207]
212. 14 <=> ! [X1] : ~strong(X1) [avatar definition]
213. ~strong(X1) <- (14) [avatar component clause 212]
214. 14 | 12 | 13 [avatar split clause 99,207,203,212]
218. 15 <=> ! [X3] : (~calm(X3) | wise(X3)) [avatar definition]
219. ~calm(X3) | wise(X3) <- (15) [avatar component clause 218]
221. 16 <=> strong(sK2) [avatar definition]
223. strong(sK2) <- (16) [avatar component clause 221]
225. 17 <=> wise(sK2) [avatar definition]
227. wise(sK2) <- (17) [avatar component clause 225]
228. 15 | 16 | 17 [avatar split clause 96,225,221,218]
234. 19 <=> ! [X0] : (~happy(X0) | old(X0)) [avatar definition]
235. ~happy(X0) | old(X0) <- (19) [avatar component clause 234]
255. 19 [avatar split clause 117,234]
257. 24 <=> ! [X3] : ~old(X3) [avatar definition]
258. ~old(X3) <- (24) [avatar component clause 257]
260. 25 <=> calm(sK5) [avatar definition]
263. 24 | ~25 [avatar split clause 121,260,257]
266. 26 <=> happy(sK5) [avatar definition]
268. happy(sK5) <- (26) [avatar component clause 266]
269. 24 | 26 [avatar split clause 119,266,257]
270. 6 | 26 [avatar split clause 118,266,176]
294. 31 <=> ! [X0] : (~wise(X0) | humble(X0)) [avatar definition]
295. ~wise(X0) | humble(X0) <- (31) [avatar component clause 294]
297. 32 <=> rich(lucy) [avatar definition]
298. ~rich(lucy) <- (~32) [avatar component clause 297]
301. 33 <=> funny(lucy) [avatar definition]
303. ~funny(lucy) <- (~33) [avatar component clause 301]
304. 31 | 32 | ~33 [avatar split clause 137,301,297,294]
309. funny(X0) | rich(X0) [subsumption resolution 139,151]
325. ~32 [avatar split clause 150,297]
334. calm(sK5) <- (26) [resolution 116,268]
337. 25 | ~26 [avatar split clause 334,266,260]
345. old(sK5) <- (19, 26) [resolution 235,268]
347. $false <- (19, 24, 26) [subsumption resolution 345,258]
348. ~19 | ~24 | ~26 [avatar contradiction clause 347]
353. rich(lucy) <- (~33) [resolution 309,303]
354. $false <- (~32, ~33) [subsumption resolution 353,298]
355. 32 | 33 [avatar contradiction clause 354]
356. ~wise(X0) <- (6, 31) [subsumption resolution 295,177]
357. 11 | ~6 | ~31 [avatar split clause 356,294,176,200]
368. happy(sK1) | humble(sK1) <- (12) [resolution 103,205]
371. happy(sK1) <- (6, 12) [subsumption resolution 368,177]
377. old(sK1) <- (6, 12, 19) [resolution 371,235]
381. $false <- (6, 12, 19, 24) [subsumption resolution 377,258]
382. ~6 | ~12 | ~19 | ~24 [avatar contradiction clause 381]
383. $false <- (11, 13) [subsumption resolution 209,201]
384. ~11 | ~13 [avatar contradiction clause 383]
386. $false <- (14, 16) [resolution 213,223]
387. ~14 | ~16 [avatar contradiction clause 386]
388. $false <- (11, 17) [subsumption resolution 227,201]
389. ~11 | ~17 [avatar contradiction clause 388]
390. ~calm(X3) <- (11, 15) [subsumption resolution 219,201]
400. rich(X2) | humble(X2) <- (11, 15) [resolution 152,390]
436. rich(X2) <- (6, 11, 15) [subsumption resolution 400,177]
448. $false <- (6, 11, 15, ~32) [resolution 436,298]
450. ~6 | ~11 | ~15 | 32 [avatar contradiction clause 448]
451. $false [avatar sat refutation 214,228,255,263,269,270,304,325,337,348,355,357,382,384,387,389,450]
% SZS output end Proof for 31105294973190059547098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is patient or not kind and vice versa.
Everyone who is not patient is wise or brave and vice versa.
Everyone who is wise is either strong or not happy and vice versa.
Everyone who is not humble or not strong is wise and vice versa.
If someone is either not creative or quiet then mary is generous or tall.
Everyone who is either happy or rich is generous and vice versa.
If john is strong then john is old.
If someone is both brave and not old then someone is either patient or tall.
If someone is both generous and quiet then someone is both not quiet and patient.
Everyone who is brave is either old or creative.
If fred is either humble or curious then someone is both creative and quiet.
Everyone who is not old or not funny is generous and vice versa.
Everyone who is curious is either strong or not happy and vice versa.
If someone is either not wise or not creative then alice is either quiet or not kind and vice versa.
Everyone who is wise is either wise or curious.
Everyone who is both not strong and not calm is either kind or not happy.
Someone is either generous or kind.
Fred is either rich or patient.
John is quiet.
Someone is not old or calm.
Alice is brave.
Someone is not rich or kind.
Someone is not old or kind. | Alice is happy. | contradiction | (![X]:(creative(X)<=>(patient(X)|~kind(X))))&
(![X]:(~patient(X)<=>(wise(X)|brave(X))))&
(![X]:(wise(X)<=>(strong(X)<~>~happy(X))))&
(![X]:((~humble(X)|~strong(X))<=>wise(X)))&
((?[X]:((~creative(X)<~>quiet(X))))=>((generous(mary)|tall(mary))))&
(![X]:((happy(X)<~>rich(X))<=>generous(X)))&
((strong(john))=>(old(john)))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((patient(X)<~>tall(X)))))&
((?[X]:((generous(X)&quiet(X))))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(brave(X)=>(old(X)<~>creative(X))))&
(((humble(fred)<~>curious(fred)))=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~old(X)|~funny(X))<=>generous(X)))&
(![X]:(curious(X)<=>(strong(X)<~>~happy(X))))&
((?[X]:((~wise(X)<~>~creative(X))))<=>((quiet(alice)<~>~kind(alice))))&
(![X]:(wise(X)=>(wise(X)<~>curious(X))))&
(![X]:((~strong(X)&~calm(X))=>(kind(X)<~>~happy(X))))&
(?[X]:((generous(X)<~>kind(X))))&
((rich(fred)<~>patient(fred)))&
(quiet(john))&
(?[X]:((~old(X)|calm(X))))&
(brave(alice))&
(?[X]:((~rich(X)|kind(X))))&
(?[X]:((~old(X)|kind(X)))) | happy(alice) | [
"p2",
"p3",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6767983187559586342103795
% SZS output start Proof for 6767983187559586342103795
3. ! [X0] : (wise(X0) <=> (strong(X0) <~> ~happy(X0))) [input p2]
4. ! [X0] : ((~strong(X0) | ~humble(X0)) <=> wise(X0)) [input p3]
13. ! [X0] : (curious(X0) <=> (strong(X0) <~> ~happy(X0))) [input p12]
15. ! [X0] : (wise(X0) => (wise(X0) <~> curious(X0))) [input p14]
24. happy(alice) [input hypothesis]
36. ! [X0] : ((wise(X0) <~> curious(X0)) | ~wise(X0)) [ennf transformation 15]
41. ! [X0] : ((wise(X0) | ((strong(X0) | happy(X0)) & (~happy(X0) | ~strong(X0)))) & (((happy(X0) | ~strong(X0)) & (~happy(X0) | strong(X0))) | ~wise(X0))) [nnf transformation 3]
42. ! [X0] : (((~strong(X0) | ~humble(X0)) | ~wise(X0)) & (wise(X0) | (strong(X0) & humble(X0)))) [nnf transformation 4]
43. ! [X0] : ((~strong(X0) | ~humble(X0) | ~wise(X0)) & (wise(X0) | (strong(X0) & humble(X0)))) [flattening 42]
59. ! [X0] : ((curious(X0) | ((strong(X0) | happy(X0)) & (~happy(X0) | ~strong(X0)))) & (((happy(X0) | ~strong(X0)) & (~happy(X0) | strong(X0))) | ~curious(X0))) [nnf transformation 13]
64. ! [X0] : (((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | ~wise(X0)) [nnf transformation 36]
79. ~happy(X0) | strong(X0) | ~wise(X0) [cnf transformation 41]
81. ~happy(X0) | wise(X0) | ~strong(X0) [cnf transformation 41]
84. strong(X0) | wise(X0) [cnf transformation 43]
108. ~happy(X0) | curious(X0) | ~strong(X0) [cnf transformation 59]
119. ~curious(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 64]
128. happy(alice) [cnf transformation 24]
129. ~curious(X0) | ~wise(X0) [duplicate literal removal 119]
283. strong(alice) | ~wise(alice) [resolution 79,128]
284. strong(alice) [subsumption resolution 283,84]
287. wise(alice) | ~strong(alice) [resolution 81,128]
288. wise(alice) [subsumption resolution 287,284]
365. curious(alice) | ~strong(alice) [resolution 108,128]
370. curious(alice) [subsumption resolution 365,284]
386. ~wise(alice) [resolution 370,129]
387. $false [subsumption resolution 386,288]
% SZS output end Proof for 6767983187559586342103795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and quiet is calm.
Everyone who is either not quiet or humble is either creative or not quiet and vice versa.
Everyone who is both wise and generous is either not generous or patient.
Everyone who is either rich or not wise is both brave and not tall.
Everyone who is both not rich and tall is both tall and kind and vice versa.
Everyone who is either tall or funny is either not tall or creative.
Everyone who is old is both not humble and not creative.
If fred is either humble or not creative then someone is both not rich and not calm.
If someone is not calm or not humble then mary is not tall.
Everyone who is not rich is both not humble and not funny and vice versa.
Everyone who is not strong or curious is both not strong and strong and vice versa.
Everyone who is creative is both happy and creative and vice versa.
Everyone who is both not rich and calm is either not funny or not tall.
If mary is not quiet then someone is not strong and vice versa.
If alice is both not funny and not creative then someone is tall and vice versa.
Everyone who is not wise or not strong is both not quiet and not brave and vice versa.
Someone is both not creative and not calm.
Someone is either not kind or not tall.
Paul is not rich.
Alice is patient.
Someone is both not humble and brave.
Alice is either funny or not tall.
Someone is both not kind and not calm.
Someone is both creative and funny. | Alice is quiet. | contradiction | (![X]:((~rich(X)&quiet(X))=>calm(X)))&
(![X]:((~quiet(X)<~>humble(X))<=>(creative(X)<~>~quiet(X))))&
(![X]:((wise(X)&generous(X))=>(~generous(X)<~>patient(X))))&
(![X]:((rich(X)<~>~wise(X))=>(brave(X)&~tall(X))))&
(![X]:((~rich(X)&tall(X))<=>(tall(X)&kind(X))))&
(![X]:((tall(X)<~>funny(X))=>(~tall(X)<~>creative(X))))&
(![X]:(old(X)=>(~humble(X)&~creative(X))))&
(((humble(fred)<~>~creative(fred)))=>(?[X]:((~rich(X)&~calm(X)))))&
((?[X]:((~calm(X)|~humble(X))))=>(~tall(mary)))&
(![X]:(~rich(X)<=>(~humble(X)&~funny(X))))&
(![X]:((~strong(X)|curious(X))<=>(~strong(X)&strong(X))))&
(![X]:(creative(X)<=>(happy(X)&creative(X))))&
(![X]:((~rich(X)&calm(X))=>(~funny(X)<~>~tall(X))))&
((~quiet(mary))<=>(?[X]:(~strong(X))))&
(((~funny(alice)&~creative(alice)))<=>(?[X]:(tall(X))))&
(![X]:((~wise(X)|~strong(X))<=>(~quiet(X)&~brave(X))))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:((~kind(X)<~>~tall(X))))&
(~rich(paul))&
(patient(alice))&
(?[X]:((~humble(X)&brave(X))))&
((funny(alice)<~>~tall(alice)))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((creative(X)&funny(X)))) | quiet(alice) | [
"p0",
"p1",
"p5",
"p9",
"p12",
"p14",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6880542391457199749438340
% SZS output start Proof for 6880542391457199749438340
1. ! [X0] : ((quiet(X0) & ~rich(X0)) => calm(X0)) [input p0]
2. ! [X0] : ((~quiet(X0) <~> humble(X0)) <=> (creative(X0) <~> ~quiet(X0))) [input p1]
6. ! [X0] : ((tall(X0) <~> funny(X0)) => (~tall(X0) <~> creative(X0))) [input p5]
10. ! [X0] : (~rich(X0) <=> (~funny(X0) & ~humble(X0))) [input p9]
13. ! [X0] : ((calm(X0) & ~rich(X0)) => (~funny(X0) <~> ~tall(X0))) [input p12]
15. (~creative(alice) & ~funny(alice)) <=> ? [X0] : tall(X0) [input p14]
22. funny(alice) <~> ~tall(alice) [input p21]
24. ? [X0] : (funny(X0) & creative(X0)) [input p23]
25. quiet(alice) [input hypothesis]
27. ! [X0] : (calm(X0) | (~quiet(X0) | rich(X0))) [ennf transformation 1]
28. ! [X0] : (calm(X0) | ~quiet(X0) | rich(X0)) [flattening 27]
32. ! [X0] : ((~tall(X0) <~> creative(X0)) | (tall(X0) <=> funny(X0))) [ennf transformation 6]
35. ! [X0] : ((~funny(X0) <~> ~tall(X0)) | (~calm(X0) | rich(X0))) [ennf transformation 13]
36. ! [X0] : ((~funny(X0) <~> ~tall(X0)) | ~calm(X0) | rich(X0)) [flattening 35]
37. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | ((creative(X0) | quiet(X0)) & (~quiet(X0) | ~creative(X0)))) & (((quiet(X0) | ~creative(X0)) & (~quiet(X0) | creative(X0))) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [nnf transformation 2]
42. ! [X0] : (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) [nnf transformation 32]
46. ! [X0] : ((~rich(X0) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | rich(X0))) [nnf transformation 10]
47. ! [X0] : ((~rich(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | rich(X0))) [flattening 46]
52. ! [X0] : (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | ~calm(X0) | rich(X0)) [nnf transformation 36]
57. ((~creative(alice) & ~funny(alice)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | (creative(alice) | funny(alice))) [nnf transformation 15]
58. ((~creative(alice) & ~funny(alice)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | creative(alice) | funny(alice)) [flattening 57]
59. ((~creative(alice) & ~funny(alice)) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | creative(alice) | funny(alice)) [rectify 58]
60. ? [X1] : tall(X1) => tall(sK2) [choice axiom]
61. ((~creative(alice) & ~funny(alice)) | ! [X0] : ~tall(X0)) & (tall(sK2) | creative(alice) | funny(alice)) [skolemisation 59,60]
71. (tall(alice) | ~funny(alice)) & (~tall(alice) | funny(alice)) [nnf transformation 22]
74. ? [X0] : (funny(X0) & creative(X0)) => (funny(sK7) & creative(sK7)) [choice axiom]
75. funny(sK7) & creative(sK7) [skolemisation 24,74]
76. ~quiet(X0) | calm(X0) | rich(X0) [cnf transformation 28]
78. ~quiet(X0) | creative(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 37]
84. ~humble(X0) | quiet(X0) | creative(X0) | quiet(X0) [cnf transformation 37]
98. ~creative(X0) | tall(X0) | tall(X0) | ~funny(X0) [cnf transformation 42]
106. ~funny(X0) | rich(X0) [cnf transformation 47]
107. ~rich(X0) | funny(X0) | humble(X0) [cnf transformation 47]
117. tall(X0) | funny(X0) | ~calm(X0) | rich(X0) [cnf transformation 52]
121. ~funny(alice) | ~tall(X0) [cnf transformation 61]
122. ~creative(alice) | ~tall(X0) [cnf transformation 61]
136. ~tall(alice) | funny(alice) [cnf transformation 71]
140. creative(sK7) [cnf transformation 75]
141. funny(sK7) [cnf transformation 75]
142. quiet(alice) [cnf transformation 25]
146. ~funny(X0) | tall(X0) | ~creative(X0) [duplicate literal removal 98]
148. ~quiet(X0) | creative(X0) | ~humble(X0) [duplicate literal removal 78]
151. ~humble(X0) | quiet(X0) | creative(X0) [duplicate literal removal 84]
153. ~humble(X0) | creative(X0) [subsumption resolution 148,151]
191. ~calm(X0) | tall(X0) | rich(X0) [subsumption resolution 117,106]
194. 8 <=> ! [X0] : ~tall(X0) [avatar definition]
195. ~tall(X0) <- (8) [avatar component clause 194]
197. 9 <=> creative(alice) [avatar definition]
199. ~creative(alice) <- (~9) [avatar component clause 197]
200. 8 | ~9 [avatar split clause 122,197,194]
202. 10 <=> funny(alice) [avatar definition]
204. ~funny(alice) <- (~10) [avatar component clause 202]
205. 8 | ~10 [avatar split clause 121,202,194]
223. 14 <=> tall(alice) [avatar definition]
224. ~tall(alice) <- (~14) [avatar component clause 223]
227. 10 | ~14 [avatar split clause 136,223,202]
236. calm(alice) | rich(alice) [resolution 76,142]
239. 15 <=> rich(alice) [avatar definition]
240. ~rich(alice) <- (~15) [avatar component clause 239]
241. rich(alice) <- (15) [avatar component clause 239]
243. 16 <=> calm(alice) [avatar definition]
245. calm(alice) <- (16) [avatar component clause 243]
246. 15 | 16 [avatar split clause 236,243,239]
271. funny(alice) | humble(alice) <- (15) [resolution 107,241]
287. tall(sK7) | ~creative(sK7) [resolution 146,141]
288. ~creative(sK7) <- (8) [subsumption resolution 287,195]
289. $false <- (8) [subsumption resolution 288,140]
290. ~8 [avatar contradiction clause 289]
292. humble(alice) <- (~10, 15) [subsumption resolution 271,204]
347. creative(alice) <- (~10, 15) [resolution 292,153]
349. $false <- (~9, ~10, 15) [subsumption resolution 347,199]
350. 9 | 10 | ~15 [avatar contradiction clause 349]
356. tall(alice) | rich(alice) <- (16) [resolution 245,191]
357. rich(alice) <- (~14, 16) [subsumption resolution 356,224]
358. $false <- (~14, ~15, 16) [subsumption resolution 357,240]
359. 14 | 15 | ~16 [avatar contradiction clause 358]
360. $false [avatar sat refutation 200,205,227,246,290,350,359]
% SZS output end Proof for 6880542391457199749438340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or curious is either not funny or rich and vice versa. Everyone who is brave or not brave is not funny or humble. Everyone who is either curious or kind is either not kind or not patient and vice versa. Everyone who is both not old and not kind is not strong and vice versa. Everyone who is not tall is both not old and calm and vice versa. Everyone who is not curious or not humble is rich. Everyone who is both not quiet and wise is curious and vice versa. If john is not generous then someone is either tall or curious. Everyone who is not generous is both not rich and brave. Everyone who is not patient or not brave is tall and vice versa. If susan is both brave and wise then someone is not humble or calm and vice versa. Everyone who is either generous or old is either not patient or creative and vice versa. Everyone who is not funny or not curious is either wise or not calm. Everyone who is either not humble or not funny is humble or kind. Everyone who is either not brave or not calm is not quiet or wise and vice versa. Everyone who is not brave is either old or creative. Someone is both not quiet and not curious. Fred is either not creative or brave. Mary is both brave and funny. John is both not quiet and kind. Someone is both not curious and old. | John is tall. | entailment | (![X]:((generous(X)<~>curious(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|humble(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)&~kind(X))<=>~strong(X)))&
(![X]:(~tall(X)<=>(~old(X)&calm(X))))&
(![X]:((~curious(X)|~humble(X))=>rich(X)))&
(![X]:((~quiet(X)&wise(X))<=>curious(X)))&
((~generous(john))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:(~generous(X)=>(~rich(X)&brave(X))))&
(![X]:((~patient(X)|~brave(X))<=>tall(X)))&
(((brave(susan)&wise(susan)))<=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((generous(X)<~>old(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((~funny(X)|~curious(X))=>(wise(X)<~>~calm(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(humble(X)|kind(X))))&
(![X]:((~brave(X)<~>~calm(X))<=>(~quiet(X)|wise(X))))&
(![X]:(~brave(X)=>(old(X)<~>creative(X))))&
(?[X]:((~quiet(X)&~curious(X))))&
((~creative(fred)<~>brave(fred)))&
((brave(mary)&funny(mary)))&
((~quiet(john)&kind(john)))&
(?[X]:((~curious(X)&old(X)))) | tall(john) | [
"p4",
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8937934155983705509607500
% SZS output start Proof for 8937934155983705509607500
5. ! [X0] : (~tall(X0) <=> (calm(X0) & ~old(X0))) [input p4]
7. ! [X0] : ((wise(X0) & ~quiet(X0)) <=> curious(X0)) [input p6]
10. ! [X0] : ((~brave(X0) | ~patient(X0)) <=> tall(X0)) [input p9]
13. ! [X0] : ((~curious(X0) | ~funny(X0)) => (wise(X0) <~> ~calm(X0))) [input p12]
15. ! [X0] : ((~brave(X0) <~> ~calm(X0)) <=> (wise(X0) | ~quiet(X0))) [input p14]
22. ~tall(john) [input hypothesis]
28. ! [X0] : ((wise(X0) <~> ~calm(X0)) | (curious(X0) & funny(X0))) [ennf transformation 13]
34. ! [X0] : ((~tall(X0) | (~calm(X0) | old(X0))) & ((calm(X0) & ~old(X0)) | tall(X0))) [nnf transformation 5]
35. ! [X0] : ((~tall(X0) | ~calm(X0) | old(X0)) & ((calm(X0) & ~old(X0)) | tall(X0))) [flattening 34]
36. ! [X0] : (((wise(X0) & ~quiet(X0)) | ~curious(X0)) & (curious(X0) | (~wise(X0) | quiet(X0)))) [nnf transformation 7]
37. ! [X0] : (((wise(X0) & ~quiet(X0)) | ~curious(X0)) & (curious(X0) | ~wise(X0) | quiet(X0))) [flattening 36]
41. ! [X0] : (((~brave(X0) | ~patient(X0)) | ~tall(X0)) & (tall(X0) | (brave(X0) & patient(X0)))) [nnf transformation 10]
42. ! [X0] : ((~brave(X0) | ~patient(X0) | ~tall(X0)) & (tall(X0) | (brave(X0) & patient(X0)))) [flattening 41]
49. ! [X0] : (((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | (curious(X0) & funny(X0))) [nnf transformation 28]
51. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (~wise(X0) & quiet(X0))) & ((wise(X0) | ~quiet(X0)) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [nnf transformation 15]
52. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (~wise(X0) & quiet(X0))) & (wise(X0) | ~quiet(X0) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [flattening 51]
78. calm(X0) | tall(X0) [cnf transformation 35]
84. ~curious(X0) | wise(X0) [cnf transformation 37]
90. tall(X0) | brave(X0) [cnf transformation 42]
106. ~calm(X0) | wise(X0) | curious(X0) [cnf transformation 49]
114. ~calm(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 52]
129. ~tall(john) [cnf transformation 22]
179. ~calm(X0) | wise(X0) [subsumption resolution 106,84]
180. ~calm(X0) | ~brave(X0) [subsumption resolution 114,179]
209. ~brave(X0) | tall(X0) [resolution 180,78]
210. tall(X0) [subsumption resolution 209,90]
211. $false [resolution 210,129]
% SZS output end Proof for 8937934155983705509607500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall or not quiet then paul is both not curious and not strong. Everyone who is not kind is both tall and not funny and vice versa. Everyone who is both quiet and old is both humble and not quiet. Everyone who is kind or not curious is brave or tall and vice versa. Everyone who is curious or not curious is not brave and vice versa. If someone is both not kind and strong then paul is generous or calm and vice versa. If john is either humble or creative then mary is either wise or not calm and vice versa. If someone is brave or creative then someone is either not happy or wise. Everyone who is either not generous or not kind is both patient and wise and vice versa. If someone is happy then paul is generous or not generous. If fred is tall or strong then someone is both tall and rich and vice versa. Everyone who is either not rich or not tall is both not curious and not creative. Everyone who is both generous and not humble is patient or not tall. Everyone who is both kind and not patient is both rich and not rich. Everyone who is not tall is not creative. If someone is not rich or patient then john is old. Paul is tall. Someone is both wise and calm. Someone is either not strong or not old. Fred is either old or not tall. Someone is humble. Paul is not creative or not rich. Someone is creative. Fred is both humble and strong. | Paul is curious. | contradiction | ((?[X]:((tall(X)|~quiet(X))))=>((~curious(paul)&~strong(paul))))&
(![X]:(~kind(X)<=>(tall(X)&~funny(X))))&
(![X]:((quiet(X)&old(X))=>(humble(X)&~quiet(X))))&
(![X]:((kind(X)|~curious(X))<=>(brave(X)|tall(X))))&
(![X]:((curious(X)|~curious(X))<=>~brave(X)))&
((?[X]:((~kind(X)&strong(X))))<=>((generous(paul)|calm(paul))))&
(((humble(john)<~>creative(john)))<=>((wise(mary)<~>~calm(mary))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:((~happy(X)<~>wise(X)))))&
(![X]:((~generous(X)<~>~kind(X))<=>(patient(X)&wise(X))))&
((?[X]:(happy(X)))=>((generous(paul)|~generous(paul))))&
(((tall(fred)|strong(fred)))<=>(?[X]:((tall(X)&rich(X)))))&
(![X]:((~rich(X)<~>~tall(X))=>(~curious(X)&~creative(X))))&
(![X]:((generous(X)&~humble(X))=>(patient(X)|~tall(X))))&
(![X]:((kind(X)&~patient(X))=>(rich(X)&~rich(X))))&
(![X]:(~tall(X)=>~creative(X)))&
((?[X]:((~rich(X)|patient(X))))=>(old(john)))&
(tall(paul))&
(?[X]:((wise(X)&calm(X))))&
(?[X]:((~strong(X)<~>~old(X))))&
((old(fred)<~>~tall(fred)))&
(?[X]:(humble(X)))&
((~creative(paul)|~rich(paul)))&
(?[X]:(creative(X)))&
((humble(fred)&strong(fred))) | curious(paul) | [
"p0",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1200945181871035320604645
% SZS output start Proof for 1200945181871035320604645
1. ? [X0] : (~quiet(X0) | tall(X0)) => (~strong(paul) & ~curious(paul)) [input p0]
17. tall(paul) [input p16]
25. curious(paul) [input hypothesis]
27. (~strong(paul) & ~curious(paul)) | ! [X0] : (quiet(X0) & ~tall(X0)) [ennf transformation 1]
74. ~curious(paul) | ~tall(X0) [cnf transformation 27]
129. tall(paul) [cnf transformation 17]
141. curious(paul) [cnf transformation 25]
152. 3 <=> ! [X0] : ~tall(X0) [avatar definition]
153. ~tall(X0) <- (3) [avatar component clause 152]
156. 4 <=> curious(paul) [avatar definition]
160. 3 | ~4 [avatar split clause 74,156,152]
288. 4 [avatar split clause 141,156]
289. $false <- (3) [resolution 153,129]
290. ~3 [avatar contradiction clause 289]
291. $false [avatar sat refutation 160,288,290]
% SZS output end Proof for 1200945181871035320604645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not funny then lucy is both brave and generous. Everyone who is wise is old. Everyone who is either patient or not wise is both brave and not creative. If someone is not quiet or creative then lucy is tall or wise. Everyone who is both not generous and happy is not happy and vice versa. If someone is not strong or not tall then fred is either not kind or curious. Everyone who is either not rich or funny is strong. If someone is old then fred is happy or not generous. Everyone who is tall is either not generous or not brave and vice versa. If lucy is not quiet then lucy is both not generous and not brave and vice versa. If alice is both not tall and not calm then fred is humble and vice versa. Everyone who is tall or not wise is either patient or not old and vice versa. Everyone who is either not tall or not wise is not calm or not creative and vice versa. Everyone who is not curious or humble is not funny or wise and vice versa. Everyone who is not kind or not rich is both not curious and not tall and vice versa. Everyone who is creative or not wise is both not patient and generous and vice versa. Paul is both old and generous. Someone is not funny or not tall. Susan is not patient or creative. Alice is not creative or not tall. Someone is humble or not creative. | Susan is brave. | entailment | ((?[X]:((funny(X)|~funny(X))))=>((brave(lucy)&generous(lucy))))&
(![X]:(wise(X)=>old(X)))&
(![X]:((patient(X)<~>~wise(X))=>(brave(X)&~creative(X))))&
((?[X]:((~quiet(X)|creative(X))))=>((tall(lucy)|wise(lucy))))&
(![X]:((~generous(X)&happy(X))<=>~happy(X)))&
((?[X]:((~strong(X)|~tall(X))))=>((~kind(fred)<~>curious(fred))))&
(![X]:((~rich(X)<~>funny(X))=>strong(X)))&
((?[X]:(old(X)))=>((happy(fred)|~generous(fred))))&
(![X]:(tall(X)<=>(~generous(X)<~>~brave(X))))&
((~quiet(lucy))<=>((~generous(lucy)&~brave(lucy))))&
(((~tall(alice)&~calm(alice)))<=>(humble(fred)))&
(![X]:((tall(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~calm(X)|~creative(X))))&
(![X]:((~curious(X)|humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((~kind(X)|~rich(X))<=>(~curious(X)&~tall(X))))&
(![X]:((creative(X)|~wise(X))<=>(~patient(X)&generous(X))))&
((old(paul)&generous(paul)))&
(?[X]:((~funny(X)|~tall(X))))&
((~patient(susan)|creative(susan)))&
((~creative(alice)|~tall(alice)))&
(?[X]:((humble(X)|~creative(X)))) | brave(susan) | [
"p1",
"p2",
"p4",
"p8",
"p11",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2931705176968326661801942
% SZS output start Proof for 2931705176968326661801942
2. ! [X0] : (wise(X0) => old(X0)) [input p1]
3. ! [X0] : ((patient(X0) <~> ~wise(X0)) => (~creative(X0) & brave(X0))) [input p2]
5. ! [X0] : ((happy(X0) & ~generous(X0)) <=> ~happy(X0)) [input p4]
9. ! [X0] : (tall(X0) <=> (~generous(X0) <~> ~brave(X0))) [input p8]
12. ! [X0] : ((~wise(X0) | tall(X0)) <=> (patient(X0) <~> ~old(X0))) [input p11]
16. ! [X0] : ((~wise(X0) | creative(X0)) <=> (generous(X0) & ~patient(X0))) [input p15]
19. creative(susan) | ~patient(susan) [input p18]
22. ~brave(susan) [input hypothesis]
26. ! [X0] : (old(X0) | ~wise(X0)) [ennf transformation 2]
27. ! [X0] : ((~creative(X0) & brave(X0)) | (patient(X0) <=> ~wise(X0))) [ennf transformation 3]
33. ! [X0] : ((~creative(X0) & brave(X0)) | ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0)))) [nnf transformation 27]
34. ! [X0] : (((happy(X0) & ~generous(X0)) | happy(X0)) & (~happy(X0) | (~happy(X0) | generous(X0)))) [nnf transformation 5]
35. ! [X0] : (((happy(X0) & ~generous(X0)) | happy(X0)) & (~happy(X0) | ~happy(X0) | generous(X0))) [flattening 34]
37. ! [X0] : ((tall(X0) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0)))) & (((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | ~tall(X0))) [nnf transformation 9]
42. ! [X0] : (((~wise(X0) | tall(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (wise(X0) & ~tall(X0)))) [nnf transformation 12]
43. ! [X0] : ((~wise(X0) | tall(X0) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (wise(X0) & ~tall(X0)))) [flattening 42]
50. ! [X0] : (((~wise(X0) | creative(X0)) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | (wise(X0) & ~creative(X0)))) [nnf transformation 16]
51. ! [X0] : ((~wise(X0) | creative(X0) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | (wise(X0) & ~creative(X0)))) [flattening 50]
60. ~wise(X0) | old(X0) [cnf transformation 26]
62. patient(X0) | brave(X0) | wise(X0) [cnf transformation 33]
67. ~happy(X0) | ~happy(X0) | generous(X0) [cnf transformation 35]
69. happy(X0) | happy(X0) [cnf transformation 35]
76. tall(X0) | ~generous(X0) | brave(X0) [cnf transformation 37]
83. ~tall(X0) | patient(X0) | ~old(X0) [cnf transformation 43]
86. old(X0) | ~patient(X0) | wise(X0) [cnf transformation 43]
104. ~creative(X0) | ~patient(X0) [cnf transformation 51]
112. creative(susan) | ~patient(susan) [cnf transformation 19]
115. ~brave(susan) [cnf transformation 22]
116. ~happy(X0) | generous(X0) [duplicate literal removal 67]
117. happy(X0) [duplicate literal removal 69]
152. generous(X0) [subsumption resolution 116,117]
166. tall(X0) | brave(X0) [subsumption resolution 76,152]
191. ~patient(X0) | old(X0) [subsumption resolution 86,60]
202. ~patient(susan) [subsumption resolution 112,104]
230. brave(X1) | wise(X1) | old(X1) [resolution 62,191]
235. old(X1) | brave(X1) [subsumption resolution 230,60]
238. patient(X0) | ~old(X0) | brave(X0) [resolution 83,166]
239. patient(X0) | brave(X0) [subsumption resolution 238,235]
265. brave(susan) [resolution 239,202]
270. $false [subsumption resolution 265,115]
% SZS output end Proof for 2931705176968326661801942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not humble is both rich and not strong and vice versa.
Everyone who is generous is both not generous and not quiet.
Everyone who is either calm or not rich is both not generous and not strong and vice versa.
Everyone who is both not kind and tall is either not creative or not funny and vice versa.
If someone is funny then lucy is patient or not creative.
Everyone who is patient is either not generous or calm and vice versa.
Everyone who is funny is kind or not patient.
Everyone who is either tall or not happy is old or happy and vice versa.
Everyone who is patient is not tall or not brave.
Everyone who is either not humble or brave is both kind and strong.
If someone is not patient or not humble then paul is either wise or funny.
If someone is both wise and tall then alice is kind or humble and vice versa.
If someone is not patient or patient then mary is either quiet or old.
If lucy is not patient or happy then lucy is either not strong or wise and vice versa.
If alice is both not brave and not wise then someone is not tall or strong and vice versa.
Everyone who is both old and brave is generous.
Fred is either strong or not calm.
Someone is rich.
Someone is either not strong or brave.
John is both not calm and quiet.
Someone is both not generous and kind.
Someone is not patient.
Paul is strong.
Someone is both old and humble. | John is strong. | entailment | (![X]:((~brave(X)<~>~humble(X))<=>(rich(X)&~strong(X))))&
(![X]:(generous(X)=>(~generous(X)&~quiet(X))))&
(![X]:((calm(X)<~>~rich(X))<=>(~generous(X)&~strong(X))))&
(![X]:((~kind(X)&tall(X))<=>(~creative(X)<~>~funny(X))))&
((?[X]:(funny(X)))=>((patient(lucy)|~creative(lucy))))&
(![X]:(patient(X)<=>(~generous(X)<~>calm(X))))&
(![X]:(funny(X)=>(kind(X)|~patient(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(old(X)|happy(X))))&
(![X]:(patient(X)=>(~tall(X)|~brave(X))))&
(![X]:((~humble(X)<~>brave(X))=>(kind(X)&strong(X))))&
((?[X]:((~patient(X)|~humble(X))))=>((wise(paul)<~>funny(paul))))&
((?[X]:((wise(X)&tall(X))))<=>((kind(alice)|humble(alice))))&
((?[X]:((~patient(X)|patient(X))))=>((quiet(mary)<~>old(mary))))&
(((~patient(lucy)|happy(lucy)))<=>((~strong(lucy)<~>wise(lucy))))&
(((~brave(alice)&~wise(alice)))<=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((old(X)&brave(X))=>generous(X)))&
((strong(fred)<~>~calm(fred)))&
(?[X]:(rich(X)))&
(?[X]:((~strong(X)<~>brave(X))))&
((~calm(john)&quiet(john)))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:(~patient(X)))&
(strong(paul))&
(?[X]:((old(X)&humble(X)))) | strong(john) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p8",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1421546400041696094196470
% SZS output start Proof for 1421546400041696094196470
1. ! [X0] : ((~brave(X0) <~> ~humble(X0)) <=> (~strong(X0) & rich(X0))) [input p0]
2. ! [X0] : (generous(X0) => (~quiet(X0) & ~generous(X0))) [input p1]
3. ! [X0] : ((calm(X0) <~> ~rich(X0)) <=> (~strong(X0) & ~generous(X0))) [input p2]
6. ! [X0] : (patient(X0) <=> (~generous(X0) <~> calm(X0))) [input p5]
8. ! [X0] : ((tall(X0) <~> ~happy(X0)) <=> (happy(X0) | old(X0))) [input p7]
9. ! [X0] : (patient(X0) => (~brave(X0) | ~tall(X0))) [input p8]
10. ! [X0] : ((~humble(X0) <~> brave(X0)) => (strong(X0) & kind(X0))) [input p9]
16. ! [X0] : ((brave(X0) & old(X0)) => generous(X0)) [input p15]
20. quiet(john) & ~calm(john) [input p19]
25. ~strong(john) [input hypothesis]
26. ! [X0] : ((~quiet(X0) & ~generous(X0)) | ~generous(X0)) [ennf transformation 2]
31. ! [X0] : ((~brave(X0) | ~tall(X0)) | ~patient(X0)) [ennf transformation 9]
32. ! [X0] : (~brave(X0) | ~tall(X0) | ~patient(X0)) [flattening 31]
33. ! [X0] : ((strong(X0) & kind(X0)) | (~humble(X0) <=> brave(X0))) [ennf transformation 10]
36. ! [X0] : (generous(X0) | (~brave(X0) | ~old(X0))) [ennf transformation 16]
37. ! [X0] : (generous(X0) | ~brave(X0) | ~old(X0)) [flattening 36]
38. ! [X0] : ((((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | (strong(X0) | ~rich(X0))) & ((~strong(X0) & rich(X0)) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0))))) [nnf transformation 1]
39. ! [X0] : ((((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | strong(X0) | ~rich(X0)) & ((~strong(X0) & rich(X0)) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0))))) [flattening 38]
40. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | (strong(X0) | generous(X0))) & ((~strong(X0) & ~generous(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [nnf transformation 3]
41. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | strong(X0) | generous(X0)) & ((~strong(X0) & ~generous(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [flattening 40]
44. ! [X0] : ((patient(X0) | ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0)))) & (((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | ~patient(X0))) [nnf transformation 6]
45. ! [X0] : ((((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (~happy(X0) & ~old(X0))) & ((happy(X0) | old(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))))) [nnf transformation 8]
46. ! [X0] : ((((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (~happy(X0) & ~old(X0))) & (happy(X0) | old(X0) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))))) [flattening 45]
47. ! [X0] : ((strong(X0) & kind(X0)) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0)))) [nnf transformation 33]
74. ~humble(X0) | rich(X0) | brave(X0) [cnf transformation 39]
80. ~generous(X0) | ~generous(X0) [cnf transformation 26]
86. ~rich(X0) | calm(X0) | strong(X0) | generous(X0) [cnf transformation 41]
97. patient(X0) | calm(X0) | generous(X0) [cnf transformation 44]
101. happy(X0) | old(X0) | tall(X0) | happy(X0) [cnf transformation 46]
103. ~happy(X0) | tall(X0) | ~happy(X0) [cnf transformation 46]
106. ~patient(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 32]
109. strong(X0) | brave(X0) | humble(X0) [cnf transformation 47]
135. generous(X0) | ~brave(X0) | ~old(X0) [cnf transformation 37]
141. ~calm(john) [cnf transformation 20]
149. ~strong(john) [cnf transformation 25]
150. happy(X0) | old(X0) | tall(X0) [duplicate literal removal 101]
151. ~happy(X0) | tall(X0) [duplicate literal removal 103]
152. ~generous(X0) [duplicate literal removal 80]
154. ~rich(X0) | calm(X0) | strong(X0) [subsumption resolution 86,152]
167. patient(X0) | calm(X0) [subsumption resolution 97,152]
169. old(X0) | tall(X0) [subsumption resolution 150,151]
272. ~old(X0) | ~brave(X0) [subsumption resolution 135,152]
306. ~brave(X0) | tall(X0) [resolution 272,169]
357. ~tall(X0) | ~brave(X0) | calm(X0) [resolution 106,167]
358. ~brave(X0) | calm(X0) [subsumption resolution 357,306]
367. brave(john) | humble(john) [resolution 109,149]
392. 41 <=> humble(john) [avatar definition]
394. humble(john) <- (41) [avatar component clause 392]
396. 42 <=> brave(john) [avatar definition]
398. brave(john) <- (42) [avatar component clause 396]
399. 41 | 42 [avatar split clause 367,396,392]
482. rich(john) | brave(john) <- (41) [resolution 394,74]
491. 55 <=> rich(john) [avatar definition]
493. rich(john) <- (55) [avatar component clause 491]
494. 42 | 55 | ~41 [avatar split clause 482,392,491,396]
523. calm(john) <- (42) [resolution 398,358]
526. $false <- (42) [subsumption resolution 523,141]
527. ~42 [avatar contradiction clause 526]
601. calm(john) | strong(john) <- (55) [resolution 493,154]
602. strong(john) <- (55) [subsumption resolution 601,141]
603. $false <- (55) [subsumption resolution 602,149]
604. ~55 [avatar contradiction clause 603]
605. $false [avatar sat refutation 399,494,527,604]
% SZS output end Proof for 1421546400041696094196470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If susan is curious or not curious then someone is not brave. If someone is both not rich and old then someone is not funny and vice versa. If someone is not strong or tall then fred is both not creative and not humble. If mary is not humble then someone is old or not brave and vice versa. If someone is either not rich or strong then fred is both not generous and curious. Everyone who is both not patient and tall is both not happy and curious and vice versa. Everyone who is either funny or not tall is both patient and generous and vice versa. Everyone who is either curious or not funny is both not patient and not happy. Everyone who is happy is either old or brave. If someone is both not kind and strong then john is both not generous and not creative and vice versa. Everyone who is creative is humble. If lucy is both tall and strong then someone is either not brave or not happy and vice versa. Everyone who is not old or not wise is both tall and brave and vice versa. Everyone who is not generous or not creative is both not wise and funny. Everyone who is both not generous and not curious is not calm and vice versa. If someone is either tall or curious then mary is tall. Someone is both not kind and not happy. Someone is both strong and wise. Someone is either not curious or not generous. Someone is either funny or not brave. Alice is not strong. Someone is creative or calm. Someone is not humble or not rich. | Fred is strong. | neutral | (((curious(susan)|~curious(susan)))=>(?[X]:(~brave(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((~strong(X)|tall(X))))=>((~creative(fred)&~humble(fred))))&
((~humble(mary))<=>(?[X]:((old(X)|~brave(X)))))&
((?[X]:((~rich(X)<~>strong(X))))=>((~generous(fred)&curious(fred))))&
(![X]:((~patient(X)&tall(X))<=>(~happy(X)&curious(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(patient(X)&generous(X))))&
(![X]:((curious(X)<~>~funny(X))=>(~patient(X)&~happy(X))))&
(![X]:(happy(X)=>(old(X)<~>brave(X))))&
((?[X]:((~kind(X)&strong(X))))<=>((~generous(john)&~creative(john))))&
(![X]:(creative(X)=>humble(X)))&
(((tall(lucy)&strong(lucy)))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
(![X]:((~old(X)|~wise(X))<=>(tall(X)&brave(X))))&
(![X]:((~generous(X)|~creative(X))=>(~wise(X)&funny(X))))&
(![X]:((~generous(X)&~curious(X))<=>~calm(X)))&
((?[X]:((tall(X)<~>curious(X))))=>(tall(mary)))&
(?[X]:((~kind(X)&~happy(X))))&
(?[X]:((strong(X)&wise(X))))&
(?[X]:((~curious(X)<~>~generous(X))))&
(?[X]:((funny(X)<~>~brave(X))))&
(~strong(alice))&
(?[X]:((creative(X)|calm(X))))&
(?[X]:((~humble(X)|~rich(X)))) | strong(fred) | [] | null | 0 |
Everyone who is both humble and not strong is both rich and tall. If paul is not funny then someone is rich or wise. If alice is not old or calm then mary is quiet. If lucy is not quiet then susan is either not kind or not happy and vice versa. If someone is happy or not old then someone is both not strong and patient. Everyone who is not creative or happy is either tall or not quiet and vice versa. If someone is both not funny and old then someone is not brave or not kind. Everyone who is both not strong and old is not humble or not wise and vice versa. If mary is both not creative and old then someone is not kind or creative and vice versa. Everyone who is not strong or calm is both old and funny and vice versa. Everyone who is either creative or not humble is both strong and not creative. Everyone who is both not kind and strong is calm or not kind. Everyone who is not humble is either not quiet or not wise. Everyone who is not old or calm is not humble or patient and vice versa. Everyone who is either not happy or patient is either curious or not brave. Everyone who is both quiet and not tall is generous and vice versa. Mary is either not quiet or creative. Fred is either curious or not quiet. Someone is not rich. Someone is either not strong or not old. Alice is not generous. Susan is not happy or not rich. Alice is either not humble or not brave. | Alice is not patient. | entailment | (![X]:((humble(X)&~strong(X))=>(rich(X)&tall(X))))&
((~funny(paul))=>(?[X]:((rich(X)|wise(X)))))&
(((~old(alice)|calm(alice)))=>(quiet(mary)))&
((~quiet(lucy))<=>((~kind(susan)<~>~happy(susan))))&
((?[X]:((happy(X)|~old(X))))=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~creative(X)|happy(X))<=>(tall(X)<~>~quiet(X))))&
((?[X]:((~funny(X)&old(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~strong(X)&old(X))<=>(~humble(X)|~wise(X))))&
(((~creative(mary)&old(mary)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~strong(X)|calm(X))<=>(old(X)&funny(X))))&
(![X]:((creative(X)<~>~humble(X))=>(strong(X)&~creative(X))))&
(![X]:((~kind(X)&strong(X))=>(calm(X)|~kind(X))))&
(![X]:(~humble(X)=>(~quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|calm(X))<=>(~humble(X)|patient(X))))&
(![X]:((~happy(X)<~>patient(X))=>(curious(X)<~>~brave(X))))&
(![X]:((quiet(X)&~tall(X))<=>generous(X)))&
((~quiet(mary)<~>creative(mary)))&
((curious(fred)<~>~quiet(fred)))&
(?[X]:(~rich(X)))&
(?[X]:((~strong(X)<~>~old(X))))&
(~generous(alice))&
((~happy(susan)|~rich(susan)))&
((~humble(alice)<~>~brave(alice))) | ~patient(alice) | [
"p2",
"p7",
"p8",
"p10",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6681334506774131746181028
% SZS output start Proof for 6681334506774131746181028
3. (calm(alice) | ~old(alice)) => quiet(mary) [input p2]
8. ! [X0] : ((old(X0) & ~strong(X0)) <=> (~wise(X0) | ~humble(X0))) [input p7]
9. (old(mary) & ~creative(mary)) <=> ? [X0] : (creative(X0) | ~kind(X0)) [input p8]
11. ! [X0] : ((creative(X0) <~> ~humble(X0)) => (~creative(X0) & strong(X0))) [input p10]
14. ! [X0] : ((calm(X0) | ~old(X0)) <=> (patient(X0) | ~humble(X0))) [input p13]
17. ~quiet(mary) <~> creative(mary) [input p16]
24. patient(alice) [input hypothesis]
31. quiet(mary) | (~calm(alice) & old(alice)) [ennf transformation 3]
34. ! [X0] : ((~creative(X0) & strong(X0)) | (creative(X0) <=> ~humble(X0))) [ennf transformation 11]
52. ! [X0] : (((old(X0) & ~strong(X0)) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | (~old(X0) | strong(X0)))) [nnf transformation 8]
53. ! [X0] : (((old(X0) & ~strong(X0)) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | ~old(X0) | strong(X0))) [flattening 52]
54. ((old(mary) & ~creative(mary)) | ! [X0] : (~creative(X0) & kind(X0))) & (? [X0] : (creative(X0) | ~kind(X0)) | (~old(mary) | creative(mary))) [nnf transformation 9]
55. ((old(mary) & ~creative(mary)) | ! [X0] : (~creative(X0) & kind(X0))) & (? [X0] : (creative(X0) | ~kind(X0)) | ~old(mary) | creative(mary)) [flattening 54]
56. ((old(mary) & ~creative(mary)) | ! [X0] : (~creative(X0) & kind(X0))) & (? [X1] : (creative(X1) | ~kind(X1)) | ~old(mary) | creative(mary)) [rectify 55]
57. ? [X1] : (creative(X1) | ~kind(X1)) => (creative(sK3) | ~kind(sK3)) [choice axiom]
58. ((old(mary) & ~creative(mary)) | ! [X0] : (~creative(X0) & kind(X0))) & ((creative(sK3) | ~kind(sK3)) | ~old(mary) | creative(mary)) [skolemisation 56,57]
61. ! [X0] : ((~creative(X0) & strong(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) [nnf transformation 34]
63. ! [X0] : (((calm(X0) | ~old(X0)) | (~patient(X0) & humble(X0))) & ((patient(X0) | ~humble(X0)) | (~calm(X0) & old(X0)))) [nnf transformation 14]
64. ! [X0] : ((calm(X0) | ~old(X0) | (~patient(X0) & humble(X0))) & (patient(X0) | ~humble(X0) | (~calm(X0) & old(X0)))) [flattening 63]
66. (~creative(mary) | quiet(mary)) & (creative(mary) | ~quiet(mary)) [nnf transformation 17]
77. quiet(mary) | old(alice) [cnf transformation 31]
78. quiet(mary) | ~calm(alice) [cnf transformation 31]
95. ~strong(X0) | humble(X0) [cnf transformation 53]
101. ~creative(mary) | ~creative(X0) [cnf transformation 58]
110. strong(X0) | creative(X0) | humble(X0) [cnf transformation 61]
111. ~creative(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 61]
119. ~patient(X0) | ~old(X0) | calm(X0) [cnf transformation 64]
125. creative(mary) | ~quiet(mary) [cnf transformation 66]
136. patient(alice) [cnf transformation 24]
137. ~creative(X0) | ~humble(X0) [duplicate literal removal 111]
152. 4 <=> calm(alice) [avatar definition]
154. ~calm(alice) <- (~4) [avatar component clause 152]
156. 5 <=> quiet(mary) [avatar definition]
159. ~4 | 5 [avatar split clause 78,156,152]
161. 6 <=> old(alice) [avatar definition]
163. old(alice) <- (6) [avatar component clause 161]
164. 6 | 5 [avatar split clause 77,156,161]
212. 17 <=> ! [X0] : ~creative(X0) [avatar definition]
213. ~creative(X0) <- (17) [avatar component clause 212]
224. 20 <=> creative(mary) [avatar definition]
225. creative(mary) <- (20) [avatar component clause 224]
227. 17 | ~20 [avatar split clause 101,224,212]
238. creative(X0) | humble(X0) [subsumption resolution 110,95]
242. ~5 | 20 [avatar split clause 125,224,156]
305. humble(X0) <- (17) [resolution 213,238]
313. ~humble(mary) <- (20) [resolution 225,137]
315. $false <- (17, 20) [subsumption resolution 313,305]
316. ~17 | ~20 [avatar contradiction clause 315]
351. ~old(alice) | calm(alice) [resolution 119,136]
354. calm(alice) <- (6) [subsumption resolution 351,163]
355. $false <- (~4, 6) [subsumption resolution 354,154]
356. 4 | ~6 [avatar contradiction clause 355]
366. $false [avatar sat refutation 159,164,227,242,316,356]
% SZS output end Proof for 6681334506774131746181028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not humble is either not wise or not humble and vice versa.
If mary is either not happy or wise then lucy is not rich or tall.
Everyone who is either old or not calm is not funny or creative and vice versa.
Everyone who is both calm and happy is both strong and not tall and vice versa.
Everyone who is rich is both wise and kind and vice versa.
Everyone who is not creative or not humble is funny and vice versa.
Everyone who is either curious or kind is brave and vice versa.
Everyone who is wise or curious is humble or not calm.
If lucy is quiet or brave then someone is funny.
If someone is both not funny and not curious then alice is funny and vice versa.
Everyone who is not wise or quiet is both curious and not humble and vice versa.
If john is both calm and not tall then paul is both calm and happy.
If mary is both not strong and old then fred is both funny and not brave and vice versa.
If someone is patient or not humble then paul is happy or wise.
Everyone who is either humble or funny is not kind or not strong.
If susan is not kind then susan is both generous and not old and vice versa.
Someone is humble or tall.
Susan is both wise and humble.
Mary is both old and not tall.
Someone is not calm.
Someone is both not rich and funny.
Someone is both not quiet and funny.
John is both not brave and not quiet.
Someone is either patient or curious. | Mary is strong. | contradiction | (![X]:((~tall(X)<~>~humble(X))<=>(~wise(X)<~>~humble(X))))&
(((~happy(mary)<~>wise(mary)))=>((~rich(lucy)|tall(lucy))))&
(![X]:((old(X)<~>~calm(X))<=>(~funny(X)|creative(X))))&
(![X]:((calm(X)&happy(X))<=>(strong(X)&~tall(X))))&
(![X]:(rich(X)<=>(wise(X)&kind(X))))&
(![X]:((~creative(X)|~humble(X))<=>funny(X)))&
(![X]:((curious(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|curious(X))=>(humble(X)|~calm(X))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:(funny(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(funny(alice)))&
(![X]:((~wise(X)|quiet(X))<=>(curious(X)&~humble(X))))&
(((calm(john)&~tall(john)))=>((calm(paul)&happy(paul))))&
(((~strong(mary)&old(mary)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((patient(X)|~humble(X))))=>((happy(paul)|wise(paul))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)|~strong(X))))&
((~kind(susan))<=>((generous(susan)&~old(susan))))&
(?[X]:((humble(X)|tall(X))))&
((wise(susan)&humble(susan)))&
((old(mary)&~tall(mary)))&
(?[X]:(~calm(X)))&
(?[X]:((~rich(X)&funny(X))))&
(?[X]:((~quiet(X)&funny(X))))&
((~brave(john)&~quiet(john)))&
(?[X]:((patient(X)<~>curious(X)))) | strong(mary) | [
"p0",
"p3",
"p7",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2587409459855983919341709
% SZS output start Proof for 2587409459855983919341709
1. ! [X0] : ((~tall(X0) <~> ~humble(X0)) <=> (~wise(X0) <~> ~humble(X0))) [input p0]
4. ! [X0] : ((happy(X0) & calm(X0)) <=> (~tall(X0) & strong(X0))) [input p3]
8. ! [X0] : ((curious(X0) | wise(X0)) => (~calm(X0) | humble(X0))) [input p7]
11. ! [X0] : ((quiet(X0) | ~wise(X0)) <=> (~humble(X0) & curious(X0))) [input p10]
19. ~tall(mary) & old(mary) [input p18]
25. strong(mary) [input hypothesis]
31. ! [X0] : ((~calm(X0) | humble(X0)) | (~curious(X0) & ~wise(X0))) [ennf transformation 8]
32. ! [X0] : (~calm(X0) | humble(X0) | (~curious(X0) & ~wise(X0))) [flattening 31]
40. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ((~wise(X0) | humble(X0)) & (~humble(X0) | wise(X0)))) & (((humble(X0) | wise(X0)) & (~humble(X0) | ~wise(X0))) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [nnf transformation 1]
44. ! [X0] : (((happy(X0) & calm(X0)) | (tall(X0) | ~strong(X0))) & ((~tall(X0) & strong(X0)) | (~happy(X0) | ~calm(X0)))) [nnf transformation 4]
45. ! [X0] : (((happy(X0) & calm(X0)) | tall(X0) | ~strong(X0)) & ((~tall(X0) & strong(X0)) | ~happy(X0) | ~calm(X0))) [flattening 44]
55. ! [X0] : (((quiet(X0) | ~wise(X0)) | (humble(X0) | ~curious(X0))) & ((~humble(X0) & curious(X0)) | (~quiet(X0) & wise(X0)))) [nnf transformation 11]
56. ! [X0] : ((quiet(X0) | ~wise(X0) | humble(X0) | ~curious(X0)) & ((~humble(X0) & curious(X0)) | (~quiet(X0) & wise(X0)))) [flattening 55]
73. ~humble(X0) | ~wise(X0) | ~humble(X0) | tall(X0) [cnf transformation 40]
80. humble(X0) | tall(X0) | ~wise(X0) | humble(X0) [cnf transformation 40]
91. ~strong(X0) | tall(X0) | calm(X0) [cnf transformation 45]
102. ~curious(X0) | humble(X0) | ~calm(X0) [cnf transformation 32]
108. curious(X0) | wise(X0) [cnf transformation 56]
110. ~humble(X0) | wise(X0) [cnf transformation 56]
130. ~tall(mary) [cnf transformation 19]
140. strong(mary) [cnf transformation 25]
141. ~humble(X0) | ~wise(X0) | tall(X0) [duplicate literal removal 73]
144. humble(X0) | tall(X0) | ~wise(X0) [duplicate literal removal 80]
146. ~wise(X0) | tall(X0) [subsumption resolution 141,144]
148. 1 <=> wise(mary) [avatar definition]
149. wise(mary) <- (1) [avatar component clause 148]
229. 19 <=> strong(mary) [avatar definition]
230. strong(mary) <- (19) [avatar component clause 229]
284. 19 [avatar split clause 140,229]
308. 31 <=> calm(mary) [avatar definition]
310. calm(mary) <- (31) [avatar component clause 308]
316. tall(mary) | calm(mary) <- (19) [resolution 91,230]
317. calm(mary) <- (19) [subsumption resolution 316,130]
318. 31 | ~19 [avatar split clause 317,229,308]
333. humble(X0) | ~calm(X0) | wise(X0) [resolution 102,108]
334. ~calm(X0) | wise(X0) [subsumption resolution 333,110]
335. wise(mary) <- (31) [resolution 334,310]
338. 1 | ~31 [avatar split clause 335,308,148]
339. tall(mary) <- (1) [resolution 149,146]
340. $false <- (1) [subsumption resolution 339,130]
341. ~1 [avatar contradiction clause 340]
342. $false [avatar sat refutation 284,318,338,341]
% SZS output end Proof for 2587409459855983919341709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or curious then fred is not quiet and vice versa.
Everyone who is not curious is either not patient or quiet and vice versa.
Everyone who is both brave and not wise is both not curious and not happy.
Everyone who is either not calm or not creative is not patient.
Everyone who is either humble or not old is wise.
Everyone who is both humble and happy is both not brave and not patient and vice versa.
If mary is not strong or not tall then lucy is creative or strong and vice versa.
Everyone who is not creative or not happy is not creative and vice versa.
Everyone who is funny is either calm or not humble.
If someone is not calm or quiet then someone is either kind or not calm.
Everyone who is either not brave or not happy is old or not curious and vice versa.
If lucy is either generous or not funny then alice is not old.
Everyone who is creative or not patient is either not humble or not generous and vice versa.
If fred is calm or patient then john is both not funny and not wise.
Everyone who is both not happy and tall is both patient and creative and vice versa.
Everyone who is either not generous or tall is either old or not patient and vice versa.
Susan is not creative or curious.
Someone is patient or not kind.
Someone is not quiet or rich.
Lucy is both funny and not calm.
Someone is either wise or not rich.
Someone is both not humble and creative.
Someone is both not brave and not funny.
Someone is either tall or old. | John is not generous. | neutral | ((?[X]:((funny(X)|curious(X))))<=>(~quiet(fred)))&
(![X]:(~curious(X)<=>(~patient(X)<~>quiet(X))))&
(![X]:((brave(X)&~wise(X))=>(~curious(X)&~happy(X))))&
(![X]:((~calm(X)<~>~creative(X))=>~patient(X)))&
(![X]:((humble(X)<~>~old(X))=>wise(X)))&
(![X]:((humble(X)&happy(X))<=>(~brave(X)&~patient(X))))&
(((~strong(mary)|~tall(mary)))<=>((creative(lucy)|strong(lucy))))&
(![X]:((~creative(X)|~happy(X))<=>~creative(X)))&
(![X]:(funny(X)=>(calm(X)<~>~humble(X))))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:((~brave(X)<~>~happy(X))<=>(old(X)|~curious(X))))&
(((generous(lucy)<~>~funny(lucy)))=>(~old(alice)))&
(![X]:((creative(X)|~patient(X))<=>(~humble(X)<~>~generous(X))))&
(((calm(fred)|patient(fred)))=>((~funny(john)&~wise(john))))&
(![X]:((~happy(X)&tall(X))<=>(patient(X)&creative(X))))&
(![X]:((~generous(X)<~>tall(X))<=>(old(X)<~>~patient(X))))&
((~creative(susan)|curious(susan)))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:((~quiet(X)|rich(X))))&
((funny(lucy)&~calm(lucy)))&
(?[X]:((wise(X)<~>~rich(X))))&
(?[X]:((~humble(X)&creative(X))))&
(?[X]:((~brave(X)&~funny(X))))&
(?[X]:((tall(X)<~>old(X)))) | ~generous(john) | [] | null | 0 |
If someone is not brave or not creative then alice is either patient or funny.
Everyone who is generous is either kind or not funny and vice versa.
Everyone who is generous is calm and vice versa.
Everyone who is either tall or not tall is both curious and creative and vice versa.
Everyone who is calm or not funny is not funny or not generous.
If someone is either curious or not happy then fred is either not funny or brave and vice versa.
Everyone who is both not rich and generous is both not quiet and not old.
If someone is not brave then lucy is both curious and not old.
Everyone who is not kind or creative is not tall or calm and vice versa.
Everyone who is not curious is not humble or old.
Everyone who is both creative and generous is either not calm or creative and vice versa.
Everyone who is both not tall and strong is rich and vice versa.
If paul is both humble and not funny then someone is either wise or creative and vice versa.
If someone is curious then susan is not old or tall and vice versa.
If fred is humble or not rich then mary is either not rich or not brave.
If someone is not generous or calm then someone is wise or not wise.
Alice is either not curious or generous.
Someone is both not rich and generous.
Someone is both humble and not generous.
John is both not old and funny.
Someone is calm or brave.
Someone is both creative and not strong.
Fred is not humble or rich. | Paul is curious. | entailment | ((?[X]:((~brave(X)|~creative(X))))=>((patient(alice)<~>funny(alice))))&
(![X]:(generous(X)<=>(kind(X)<~>~funny(X))))&
(![X]:(generous(X)<=>calm(X)))&
(![X]:((tall(X)<~>~tall(X))<=>(curious(X)&creative(X))))&
(![X]:((calm(X)|~funny(X))=>(~funny(X)|~generous(X))))&
((?[X]:((curious(X)<~>~happy(X))))<=>((~funny(fred)<~>brave(fred))))&
(![X]:((~rich(X)&generous(X))=>(~quiet(X)&~old(X))))&
((?[X]:(~brave(X)))=>((curious(lucy)&~old(lucy))))&
(![X]:((~kind(X)|creative(X))<=>(~tall(X)|calm(X))))&
(![X]:(~curious(X)=>(~humble(X)|old(X))))&
(![X]:((creative(X)&generous(X))<=>(~calm(X)<~>creative(X))))&
(![X]:((~tall(X)&strong(X))<=>rich(X)))&
(((humble(paul)&~funny(paul)))<=>(?[X]:((wise(X)<~>creative(X)))))&
((?[X]:(curious(X)))<=>((~old(susan)|tall(susan))))&
(((humble(fred)|~rich(fred)))=>((~rich(mary)<~>~brave(mary))))&
((?[X]:((~generous(X)|calm(X))))=>(?[X]:((wise(X)|~wise(X)))))&
((~curious(alice)<~>generous(alice)))&
(?[X]:((~rich(X)&generous(X))))&
(?[X]:((humble(X)&~generous(X))))&
((~old(john)&funny(john)))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:((creative(X)&~strong(X))))&
((~humble(fred)|rich(fred))) | curious(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 9191947391282165967482243
% SZS output start Proof for 9191947391282165967482243
4. ! [X0] : ((tall(X0) <~> ~tall(X0)) <=> (creative(X0) & curious(X0))) [input p3]
24. ~curious(paul) [input hypothesis]
40. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | (~creative(X0) | ~curious(X0))) & ((creative(X0) & curious(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [nnf transformation 4]
41. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ~creative(X0) | ~curious(X0)) & ((creative(X0) & curious(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [flattening 40]
85. curious(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 41]
86. curious(X0) | tall(X0) | tall(X0) [cnf transformation 41]
145. ~curious(paul) [cnf transformation 24]
148. curious(X0) | ~tall(X0) [duplicate literal removal 85]
149. curious(X0) | tall(X0) [duplicate literal removal 86]
172. curious(X0) [subsumption resolution 148,149]
272. $false [subsumption resolution 145,172]
% SZS output end Proof for 9191947391282165967482243
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If john is either kind or not wise then someone is both quiet and happy. If someone is not wise or not brave then someone is not creative or not funny and vice versa. If someone is tall then fred is creative or tall and vice versa. Everyone who is not rich is rich or not creative and vice versa. Everyone who is not patient is old and vice versa. Everyone who is both not strong and not quiet is not happy or creative. Everyone who is not brave is calm. If fred is not old then fred is either funny or creative. If someone is humble or not generous then lucy is strong and vice versa. Everyone who is curious is not happy. If someone is curious then lucy is either not brave or generous. If susan is both happy and quiet then mary is funny or not happy. If lucy is funny then john is either not calm or not tall and vice versa. If alice is not patient then mary is old or creative and vice versa. Everyone who is not creative is both old and tall. Everyone who is funny or not calm is kind or not generous. Alice is either quiet or humble. Someone is not old or wise. Someone is either creative or strong. Susan is not brave or brave. Someone is calm or not creative. Someone is brave. | Lucy is patient. | contradiction | (((kind(john)<~>~wise(john)))=>(?[X]:((quiet(X)&happy(X)))))&
((?[X]:((~wise(X)|~brave(X))))<=>(?[X]:((~creative(X)|~funny(X)))))&
((?[X]:(tall(X)))<=>((creative(fred)|tall(fred))))&
(![X]:(~rich(X)<=>(rich(X)|~creative(X))))&
(![X]:(~patient(X)<=>old(X)))&
(![X]:((~strong(X)&~quiet(X))=>(~happy(X)|creative(X))))&
(![X]:(~brave(X)=>calm(X)))&
((~old(fred))=>((funny(fred)<~>creative(fred))))&
((?[X]:((humble(X)|~generous(X))))<=>(strong(lucy)))&
(![X]:(curious(X)=>~happy(X)))&
((?[X]:(curious(X)))=>((~brave(lucy)<~>generous(lucy))))&
(((happy(susan)&quiet(susan)))=>((funny(mary)|~happy(mary))))&
((funny(lucy))<=>((~calm(john)<~>~tall(john))))&
((~patient(alice))<=>((old(mary)|creative(mary))))&
(![X]:(~creative(X)=>(old(X)&tall(X))))&
(![X]:((funny(X)|~calm(X))=>(kind(X)|~generous(X))))&
((quiet(alice)<~>humble(alice)))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:((creative(X)<~>strong(X))))&
((~brave(susan)|brave(susan)))&
(?[X]:((calm(X)|~creative(X))))&
(?[X]:(brave(X))) | patient(lucy) | [
"p3",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6746751209624339947331771
% SZS output start Proof for 6746751209624339947331771
4. ! [X0] : (~rich(X0) <=> (~creative(X0) | rich(X0))) [input p3]
5. ! [X0] : (~patient(X0) <=> old(X0)) [input p4]
15. ! [X0] : (~creative(X0) => (tall(X0) & old(X0))) [input p14]
23. patient(lucy) [input hypothesis]
34. ! [X0] : ((tall(X0) & old(X0)) | creative(X0)) [ennf transformation 15]
50. ! [X0] : ((~rich(X0) | (creative(X0) & ~rich(X0))) & ((~creative(X0) | rich(X0)) | rich(X0))) [nnf transformation 4]
51. ! [X0] : ((~rich(X0) | (creative(X0) & ~rich(X0))) & (~creative(X0) | rich(X0) | rich(X0))) [flattening 50]
52. ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0))) [nnf transformation 5]
82. ~creative(X0) | rich(X0) | rich(X0) [cnf transformation 51]
83. ~rich(X0) | ~rich(X0) [cnf transformation 51]
86. ~old(X0) | ~patient(X0) [cnf transformation 52]
102. old(X0) | creative(X0) [cnf transformation 34]
114. patient(lucy) [cnf transformation 23]
115. ~creative(X0) | rich(X0) [duplicate literal removal 82]
116. ~rich(X0) [duplicate literal removal 83]
187. ~creative(X0) [subsumption resolution 115,116]
265. old(X0) [subsumption resolution 102,187]
281. ~patient(X1) [resolution 86,265]
282. $false [resolution 281,114]
% SZS output end Proof for 6746751209624339947331771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is either quiet or not creative.
Everyone who is brave is either not curious or creative and vice versa.
Everyone who is not patient is rich or not creative and vice versa.
If fred is either quiet or not brave then someone is either not strong or not brave.
Everyone who is quiet or old is either curious or not old.
Everyone who is both not funny and humble is not brave or not happy.
Everyone who is strong or patient is generous.
Everyone who is not strong is both not humble and not generous.
If someone is either generous or tall then mary is either not generous or patient.
Everyone who is both creative and calm is not generous or happy and vice versa.
If someone is patient then lucy is tall.
If john is either not funny or not curious then someone is brave or patient.
Everyone who is either tall or not brave is curious or not happy and vice versa.
If mary is not wise or not humble then someone is both strong and brave and vice versa.
If someone is not kind then fred is both rich and not funny.
Everyone who is rich or not old is both patient and not creative.
Alice is both generous and not wise.
Someone is either calm or strong.
Someone is either not generous or happy.
Susan is generous.
Alice is both generous and funny.
Alice is not tall. | Mary is not funny. | neutral | (![X]:(~wise(X)=>(quiet(X)<~>~creative(X))))&
(![X]:(brave(X)<=>(~curious(X)<~>creative(X))))&
(![X]:(~patient(X)<=>(rich(X)|~creative(X))))&
(((quiet(fred)<~>~brave(fred)))=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:((quiet(X)|old(X))=>(curious(X)<~>~old(X))))&
(![X]:((~funny(X)&humble(X))=>(~brave(X)|~happy(X))))&
(![X]:((strong(X)|patient(X))=>generous(X)))&
(![X]:(~strong(X)=>(~humble(X)&~generous(X))))&
((?[X]:((generous(X)<~>tall(X))))=>((~generous(mary)<~>patient(mary))))&
(![X]:((creative(X)&calm(X))<=>(~generous(X)|happy(X))))&
((?[X]:(patient(X)))=>(tall(lucy)))&
(((~funny(john)<~>~curious(john)))=>(?[X]:((brave(X)|patient(X)))))&
(![X]:((tall(X)<~>~brave(X))<=>(curious(X)|~happy(X))))&
(((~wise(mary)|~humble(mary)))<=>(?[X]:((strong(X)&brave(X)))))&
((?[X]:(~kind(X)))=>((rich(fred)&~funny(fred))))&
(![X]:((rich(X)|~old(X))=>(patient(X)&~creative(X))))&
((generous(alice)&~wise(alice)))&
(?[X]:((calm(X)<~>strong(X))))&
(?[X]:((~generous(X)<~>happy(X))))&
(generous(susan))&
((generous(alice)&funny(alice)))&
(~tall(alice)) | ~funny(mary) | [] | null | 0 |
If someone is both curious and wise then susan is both not funny and strong and vice versa.
Everyone who is either wise or not calm is either brave or not rich and vice versa.
Everyone who is not old is brave or strong and vice versa.
Everyone who is either tall or not kind is both not old and old and vice versa.
If someone is patient then alice is both not wise and not old.
Everyone who is not patient is not kind or not old.
Everyone who is not old or not funny is either not humble or not quiet and vice versa.
If someone is not generous then lucy is tall and vice versa.
If paul is either not funny or not wise then someone is humble and vice versa.
If john is both strong and rich then paul is funny and vice versa.
Everyone who is not strong is not funny or curious.
If someone is both not brave and strong then someone is quiet or tall.
Everyone who is wise or not calm is both happy and not generous.
If someone is both not tall and generous then alice is either rich or not generous.
If someone is curious then someone is calm and vice versa.
Everyone who is either rich or not old is both kind and not strong and vice versa.
Someone is not brave.
Lucy is rich or not strong.
Lucy is not creative.
Someone is both not happy and tall.
Mary is either generous or humble.
Fred is brave or old.
Susan is either calm or patient. | Lucy is generous. | neutral | ((?[X]:((curious(X)&wise(X))))<=>((~funny(susan)&strong(susan))))&
(![X]:((wise(X)<~>~calm(X))<=>(brave(X)<~>~rich(X))))&
(![X]:(~old(X)<=>(brave(X)|strong(X))))&
(![X]:((tall(X)<~>~kind(X))<=>(~old(X)&old(X))))&
((?[X]:(patient(X)))=>((~wise(alice)&~old(alice))))&
(![X]:(~patient(X)=>(~kind(X)|~old(X))))&
(![X]:((~old(X)|~funny(X))<=>(~humble(X)<~>~quiet(X))))&
((?[X]:(~generous(X)))<=>(tall(lucy)))&
(((~funny(paul)<~>~wise(paul)))<=>(?[X]:(humble(X))))&
(((strong(john)&rich(john)))<=>(funny(paul)))&
(![X]:(~strong(X)=>(~funny(X)|curious(X))))&
((?[X]:((~brave(X)&strong(X))))=>(?[X]:((quiet(X)|tall(X)))))&
(![X]:((wise(X)|~calm(X))=>(happy(X)&~generous(X))))&
((?[X]:((~tall(X)&generous(X))))=>((rich(alice)<~>~generous(alice))))&
((?[X]:(curious(X)))<=>(?[X]:(calm(X))))&
(![X]:((rich(X)<~>~old(X))<=>(kind(X)&~strong(X))))&
(?[X]:(~brave(X)))&
((rich(lucy)|~strong(lucy)))&
(~creative(lucy))&
(?[X]:((~happy(X)&tall(X))))&
((generous(mary)<~>humble(mary)))&
((brave(fred)|old(fred)))&
((calm(susan)<~>patient(susan))) | generous(lucy) | [] | null | 0 |
If someone is not happy or not brave then susan is both calm and not rich.
If someone is either not funny or funny then paul is either not calm or not tall and vice versa.
If someone is both generous and not generous then someone is kind and vice versa.
Everyone who is not funny is not calm or not generous and vice versa.
If alice is both patient and not generous then someone is wise.
If susan is tall then someone is not brave or not happy and vice versa.
If someone is either not calm or not brave then someone is both generous and not curious.
Everyone who is both rich and funny is not happy and vice versa.
Everyone who is both kind and creative is quiet and vice versa.
Everyone who is happy or old is both not funny and humble.
If lucy is either not generous or generous then someone is not funny or generous and vice versa.
Everyone who is tall or creative is either kind or not humble and vice versa.
Everyone who is not quiet is either not strong or funny and vice versa.
If someone is not brave or humble then someone is either not brave or not generous.
Everyone who is not strong or wise is either old or not rich.
If someone is both not old and not wise then someone is both not strong and curious.
Someone is not strong.
Someone is either patient or brave.
Someone is both not generous and humble.
John is both not quiet and not funny. | Susan is not humble. | contradiction | ((?[X]:((~happy(X)|~brave(X))))=>((calm(susan)&~rich(susan))))&
((?[X]:((~funny(X)<~>funny(X))))<=>((~calm(paul)<~>~tall(paul))))&
((?[X]:((generous(X)&~generous(X))))<=>(?[X]:(kind(X))))&
(![X]:(~funny(X)<=>(~calm(X)|~generous(X))))&
(((patient(alice)&~generous(alice)))=>(?[X]:(wise(X))))&
((tall(susan))<=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:((~calm(X)<~>~brave(X))))=>(?[X]:((generous(X)&~curious(X)))))&
(![X]:((rich(X)&funny(X))<=>~happy(X)))&
(![X]:((kind(X)&creative(X))<=>quiet(X)))&
(![X]:((happy(X)|old(X))=>(~funny(X)&humble(X))))&
(((~generous(lucy)<~>generous(lucy)))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((tall(X)|creative(X))<=>(kind(X)<~>~humble(X))))&
(![X]:(~quiet(X)<=>(~strong(X)<~>funny(X))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:((~brave(X)<~>~generous(X)))))&
(![X]:((~strong(X)|wise(X))=>(old(X)<~>~rich(X))))&
((?[X]:((~old(X)&~wise(X))))=>(?[X]:((~strong(X)&curious(X)))))&
(?[X]:(~strong(X)))&
(?[X]:((patient(X)<~>brave(X))))&
(?[X]:((~generous(X)&humble(X))))&
((~quiet(john)&~funny(john))) | ~humble(susan) | [
"p0",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8643502658954021484544661
% SZS output start Proof for 8643502658954021484544661
1. ? [X0] : (~brave(X0) | ~happy(X0)) => (~rich(susan) & calm(susan)) [input p0]
8. ! [X0] : ((funny(X0) & rich(X0)) <=> ~happy(X0)) [input p7]
10. ! [X0] : ((old(X0) | happy(X0)) => (humble(X0) & ~funny(X0))) [input p9]
21. ~humble(susan) [input hypothesis]
26. (~rich(susan) & calm(susan)) | ! [X0] : (brave(X0) & happy(X0)) [ennf transformation 1]
30. ! [X0] : ((humble(X0) & ~funny(X0)) | (~old(X0) & ~happy(X0))) [ennf transformation 10]
55. ! [X0] : (((funny(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | (~funny(X0) | ~rich(X0)))) [nnf transformation 8]
56. ! [X0] : (((funny(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | ~funny(X0) | ~rich(X0))) [flattening 55]
83. ~rich(susan) | happy(X0) [cnf transformation 26]
108. rich(X0) | happy(X0) [cnf transformation 56]
115. ~happy(X0) | humble(X0) [cnf transformation 30]
150. ~humble(susan) [cnf transformation 21]
161. 2 <=> rich(susan) [avatar definition]
163. ~rich(susan) <- (~2) [avatar component clause 161]
166. 3 <=> ! [X0] : happy(X0) [avatar definition]
167. happy(X0) <- (3) [avatar component clause 166]
168. 3 | ~2 [avatar split clause 83,161,166]
286. happy(susan) <- (~2) [resolution 108,163]
291. humble(susan) <- (~2) [resolution 115,286]
293. $false <- (~2) [subsumption resolution 291,150]
294. 2 [avatar contradiction clause 293]
301. humble(X0) <- (3) [resolution 167,115]
302. $false <- (3) [resolution 301,150]
303. ~3 [avatar contradiction clause 302]
304. $false [avatar sat refutation 168,294,303]
% SZS output end Proof for 8643502658954021484544661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either quiet or not happy is happy or not creative and vice versa.
Everyone who is not funny is not brave and vice versa.
If alice is either not calm or calm then someone is quiet or not humble.
Everyone who is not brave or old is either quiet or rich.
Everyone who is both not tall and curious is curious or not calm.
If paul is both happy and not rich then someone is brave.
Everyone who is not wise or not quiet is tall.
If paul is wise then fred is not curious.
If someone is either not funny or rich then john is humble or not brave and vice versa.
Everyone who is either quiet or wise is both not humble and not old and vice versa.
If mary is patient or quiet then lucy is not patient or strong.
If someone is rich or kind then fred is not old or not creative and vice versa.
If someone is not patient or old then mary is generous or not happy.
If someone is not curious then someone is curious and vice versa.
Everyone who is both not old and not brave is strong and vice versa.
Everyone who is kind or not kind is not wise and vice versa.
Alice is either not old or not creative.
Mary is either funny or not generous.
Mary is happy.
John is not curious.
Someone is patient.
Susan is either not wise or kind.
Mary is not patient or not happy.
John is quiet. | Paul is not patient. | neutral | (![X]:((quiet(X)<~>~happy(X))<=>(happy(X)|~creative(X))))&
(![X]:(~funny(X)<=>~brave(X)))&
(((~calm(alice)<~>calm(alice)))=>(?[X]:((quiet(X)|~humble(X)))))&
(![X]:((~brave(X)|old(X))=>(quiet(X)<~>rich(X))))&
(![X]:((~tall(X)&curious(X))=>(curious(X)|~calm(X))))&
(((happy(paul)&~rich(paul)))=>(?[X]:(brave(X))))&
(![X]:((~wise(X)|~quiet(X))=>tall(X)))&
((wise(paul))=>(~curious(fred)))&
((?[X]:((~funny(X)<~>rich(X))))<=>((humble(john)|~brave(john))))&
(![X]:((quiet(X)<~>wise(X))<=>(~humble(X)&~old(X))))&
(((patient(mary)|quiet(mary)))=>((~patient(lucy)|strong(lucy))))&
((?[X]:((rich(X)|kind(X))))<=>((~old(fred)|~creative(fred))))&
((?[X]:((~patient(X)|old(X))))=>((generous(mary)|~happy(mary))))&
((?[X]:(~curious(X)))<=>(?[X]:(curious(X))))&
(![X]:((~old(X)&~brave(X))<=>strong(X)))&
(![X]:((kind(X)|~kind(X))<=>~wise(X)))&
((~old(alice)<~>~creative(alice)))&
((funny(mary)<~>~generous(mary)))&
(happy(mary))&
(~curious(john))&
(?[X]:(patient(X)))&
((~wise(susan)<~>kind(susan)))&
((~patient(mary)|~happy(mary)))&
(quiet(john)) | ~patient(paul) | [] | null | 0 |
Everyone who is either not brave or brave is not strong. Everyone who is both not funny and quiet is either generous or not humble. If someone is both generous and not strong then someone is generous or humble and vice versa. If alice is happy then someone is either patient or not old. Everyone who is not tall is both not humble and tall. Everyone who is not happy or brave is not humble and vice versa. Everyone who is either quiet or not patient is strong and vice versa. If someone is quiet then someone is kind. Everyone who is both not creative and quiet is not humble or not strong and vice versa. If paul is both happy and rich then someone is both not calm and curious and vice versa. If lucy is both patient and not strong then susan is not quiet and vice versa. If someone is either humble or not brave then mary is not quiet or quiet and vice versa. Everyone who is happy or not humble is either not tall or quiet. Everyone who is creative is either not happy or funny. If lucy is both not calm and not generous then lucy is not rich. Paul is quiet. Fred is both old and not humble. John is either wise or not funny. Alice is humble or rich. Someone is humble. Susan is both curious and humble. Paul is calm or humble. | Mary is not creative. | entailment | (![X]:((~brave(X)<~>brave(X))=>~strong(X)))&
(![X]:((~funny(X)&quiet(X))=>(generous(X)<~>~humble(X))))&
((?[X]:((generous(X)&~strong(X))))<=>(?[X]:((generous(X)|humble(X)))))&
((happy(alice))=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:(~tall(X)=>(~humble(X)&tall(X))))&
(![X]:((~happy(X)|brave(X))<=>~humble(X)))&
(![X]:((quiet(X)<~>~patient(X))<=>strong(X)))&
((?[X]:(quiet(X)))=>(?[X]:(kind(X))))&
(![X]:((~creative(X)&quiet(X))<=>(~humble(X)|~strong(X))))&
(((happy(paul)&rich(paul)))<=>(?[X]:((~calm(X)&curious(X)))))&
(((patient(lucy)&~strong(lucy)))<=>(~quiet(susan)))&
((?[X]:((humble(X)<~>~brave(X))))<=>((~quiet(mary)|quiet(mary))))&
(![X]:((happy(X)|~humble(X))=>(~tall(X)<~>quiet(X))))&
(![X]:(creative(X)=>(~happy(X)<~>funny(X))))&
(((~calm(lucy)&~generous(lucy)))=>(~rich(lucy)))&
(quiet(paul))&
((old(fred)&~humble(fred)))&
((wise(john)<~>~funny(john)))&
((humble(alice)|rich(alice)))&
(?[X]:(humble(X)))&
((curious(susan)&humble(susan)))&
((calm(paul)|humble(paul))) | ~creative(mary) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 9133068703841005478518094
% SZS output start Proof for 9133068703841005478518094
1. ! [X0] : ((~brave(X0) <~> brave(X0)) => ~strong(X0)) [input p0]
9. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> (~strong(X0) | ~humble(X0))) [input p8]
23. creative(mary) [input hypothesis]
27. ! [X0] : (~strong(X0) | (~brave(X0) <=> brave(X0))) [ennf transformation 1]
36. ! [X0] : (~strong(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) [nnf transformation 27]
49. ! [X0] : (((quiet(X0) & ~creative(X0)) | (strong(X0) & humble(X0))) & ((~strong(X0) | ~humble(X0)) | (~quiet(X0) | creative(X0)))) [nnf transformation 9]
50. ! [X0] : (((quiet(X0) & ~creative(X0)) | (strong(X0) & humble(X0))) & (~strong(X0) | ~humble(X0) | ~quiet(X0) | creative(X0))) [flattening 49]
68. ~strong(X0) | brave(X0) | brave(X0) [cnf transformation 36]
69. ~strong(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 36]
90. ~creative(X0) | strong(X0) [cnf transformation 50]
123. creative(mary) [cnf transformation 23]
125. ~strong(X0) | brave(X0) [duplicate literal removal 68]
126. ~strong(X0) | ~brave(X0) [duplicate literal removal 69]
127. ~strong(X0) [subsumption resolution 125,126]
167. ~creative(X0) [subsumption resolution 90,127]
238. $false [subsumption resolution 123,167]
% SZS output end Proof for 9133068703841005478518094
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or old then john is either not creative or not funny and vice versa.
If john is either not tall or generous then someone is either tall or happy and vice versa.
Everyone who is either not brave or curious is creative or not creative.
Everyone who is both humble and not happy is not creative and vice versa.
If someone is curious then john is either strong or not brave and vice versa.
If someone is not creative or brave then someone is wise or generous.
If someone is not funny then susan is tall or not wise and vice versa.
Everyone who is either strong or not curious is both not brave and patient and vice versa.
If someone is calm or kind then susan is quiet or calm and vice versa.
Everyone who is both patient and not creative is curious or old and vice versa.
Everyone who is wise is either not tall or strong and vice versa.
If lucy is brave then someone is creative or not strong.
Everyone who is not happy or not rich is either not old or tall.
If alice is not patient then someone is not old or happy and vice versa.
Everyone who is either not quiet or not generous is not generous or patient and vice versa.
If john is funny then someone is patient or calm.
Alice is either not creative or not happy.
Fred is not humble or funny.
Someone is either wise or rich.
Alice is not generous.
Mary is tall.
Someone is either old or not wise.
Someone is either curious or not wise.
Lucy is creative or quiet. | Mary is not old. | neutral | ((?[X]:((~calm(X)|old(X))))<=>((~creative(john)<~>~funny(john))))&
(((~tall(john)<~>generous(john)))<=>(?[X]:((tall(X)<~>happy(X)))))&
(![X]:((~brave(X)<~>curious(X))=>(creative(X)|~creative(X))))&
(![X]:((humble(X)&~happy(X))<=>~creative(X)))&
((?[X]:(curious(X)))<=>((strong(john)<~>~brave(john))))&
((?[X]:((~creative(X)|brave(X))))=>(?[X]:((wise(X)|generous(X)))))&
((?[X]:(~funny(X)))<=>((tall(susan)|~wise(susan))))&
(![X]:((strong(X)<~>~curious(X))<=>(~brave(X)&patient(X))))&
((?[X]:((calm(X)|kind(X))))<=>((quiet(susan)|calm(susan))))&
(![X]:((patient(X)&~creative(X))<=>(curious(X)|old(X))))&
(![X]:(wise(X)<=>(~tall(X)<~>strong(X))))&
((brave(lucy))=>(?[X]:((creative(X)|~strong(X)))))&
(![X]:((~happy(X)|~rich(X))=>(~old(X)<~>tall(X))))&
((~patient(alice))<=>(?[X]:((~old(X)|happy(X)))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~generous(X)|patient(X))))&
((funny(john))=>(?[X]:((patient(X)|calm(X)))))&
((~creative(alice)<~>~happy(alice)))&
((~humble(fred)|funny(fred)))&
(?[X]:((wise(X)<~>rich(X))))&
(~generous(alice))&
(tall(mary))&
(?[X]:((old(X)<~>~wise(X))))&
(?[X]:((curious(X)<~>~wise(X))))&
((creative(lucy)|quiet(lucy))) | ~old(mary) | [] | null | 0 |
Everyone who is either curious or brave is tall or humble.
If john is both not generous and not patient then alice is not rich.
Everyone who is both not happy and not tall is both humble and old.
Everyone who is both not generous and calm is either not kind or old and vice versa.
Everyone who is not generous is both kind and not quiet and vice versa.
Everyone who is humble or generous is not wise or not happy and vice versa.
If alice is not creative or not kind then someone is not funny or old and vice versa.
If paul is not calm or not generous then lucy is not old or not tall and vice versa.
If someone is not calm then fred is not curious or strong and vice versa.
If john is both old and rich then someone is both not wise and not kind.
Everyone who is not brave is both funny and not wise and vice versa.
Everyone who is happy or not quiet is quiet and vice versa.
Everyone who is kind or not rich is brave or not wise.
Everyone who is quiet or not happy is both kind and not tall.
Everyone who is brave or not wise is rich or brave.
Everyone who is both not quiet and curious is either curious or funny.
Someone is both generous and not creative.
Alice is rich or creative.
Fred is either old or funny.
Susan is not funny.
Alice is not wise. | Susan is not strong. | neutral | (![X]:((curious(X)<~>brave(X))=>(tall(X)|humble(X))))&
(((~generous(john)&~patient(john)))=>(~rich(alice)))&
(![X]:((~happy(X)&~tall(X))=>(humble(X)&old(X))))&
(![X]:((~generous(X)&calm(X))<=>(~kind(X)<~>old(X))))&
(![X]:(~generous(X)<=>(kind(X)&~quiet(X))))&
(![X]:((humble(X)|generous(X))<=>(~wise(X)|~happy(X))))&
(((~creative(alice)|~kind(alice)))<=>(?[X]:((~funny(X)|old(X)))))&
(((~calm(paul)|~generous(paul)))<=>((~old(lucy)|~tall(lucy))))&
((?[X]:(~calm(X)))<=>((~curious(fred)|strong(fred))))&
(((old(john)&rich(john)))=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(~brave(X)<=>(funny(X)&~wise(X))))&
(![X]:((happy(X)|~quiet(X))<=>quiet(X)))&
(![X]:((kind(X)|~rich(X))=>(brave(X)|~wise(X))))&
(![X]:((quiet(X)|~happy(X))=>(kind(X)&~tall(X))))&
(![X]:((brave(X)|~wise(X))=>(rich(X)|brave(X))))&
(![X]:((~quiet(X)&curious(X))=>(curious(X)<~>funny(X))))&
(?[X]:((generous(X)&~creative(X))))&
((rich(alice)|creative(alice)))&
((old(fred)<~>funny(fred)))&
(~funny(susan))&
(~wise(alice)) | ~strong(susan) | [] | null | 0 |
Everyone who is either not wise or not curious is both not curious and not generous and vice versa.
Everyone who is both not wise and kind is patient or not calm and vice versa.
If someone is not creative then someone is not generous.
If susan is not rich or not strong then someone is either not calm or generous.
Everyone who is not curious or creative is curious and vice versa.
If alice is not creative or creative then alice is either wise or not rich.
Everyone who is either funny or not rich is not strong and vice versa.
If john is both patient and not old then someone is creative or not happy.
Everyone who is either not generous or generous is either not creative or old and vice versa.
If fred is both not rich and not wise then someone is not kind or not creative.
Everyone who is either curious or not creative is funny and vice versa.
If fred is patient then someone is not tall.
Everyone who is strong or curious is funny or not calm.
Everyone who is both calm and strong is either rich or wise and vice versa.
Someone is wise or not funny.
Lucy is either strong or rich.
Someone is curious.
Someone is old.
Someone is not funny or not tall.
Someone is either old or rich.
Alice is not kind. | Alice is not funny. | contradiction | (![X]:((~wise(X)<~>~curious(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~wise(X)&kind(X))<=>(patient(X)|~calm(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~generous(X))))&
(((~rich(susan)|~strong(susan)))=>(?[X]:((~calm(X)<~>generous(X)))))&
(![X]:((~curious(X)|creative(X))<=>curious(X)))&
(((~creative(alice)|creative(alice)))=>((wise(alice)<~>~rich(alice))))&
(![X]:((funny(X)<~>~rich(X))<=>~strong(X)))&
(((patient(john)&~old(john)))=>(?[X]:((creative(X)|~happy(X)))))&
(![X]:((~generous(X)<~>generous(X))<=>(~creative(X)<~>old(X))))&
(((~rich(fred)&~wise(fred)))=>(?[X]:((~kind(X)|~creative(X)))))&
(![X]:((curious(X)<~>~creative(X))<=>funny(X)))&
((patient(fred))=>(?[X]:(~tall(X))))&
(![X]:((strong(X)|curious(X))=>(funny(X)|~calm(X))))&
(![X]:((calm(X)&strong(X))<=>(rich(X)<~>wise(X))))&
(?[X]:((wise(X)|~funny(X))))&
((strong(lucy)<~>rich(lucy)))&
(?[X]:(curious(X)))&
(?[X]:(old(X)))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((old(X)<~>rich(X))))&
(~kind(alice)) | ~funny(alice) | [
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8513550745425089994536517
% SZS output start Proof for 8513550745425089994536517
5. ! [X0] : ((creative(X0) | ~curious(X0)) <=> curious(X0)) [input p4]
11. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> funny(X0)) [input p10]
22. ~funny(alice) [input hypothesis]
44. ! [X0] : (((creative(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~creative(X0) & curious(X0)))) [nnf transformation 5]
45. ! [X0] : ((creative(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~creative(X0) & curious(X0)))) [flattening 44]
51. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | ~funny(X0)) & (funny(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 11]
80. curious(X0) | curious(X0) [cnf transformation 45]
82. creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 45]
100. funny(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 51]
120. ~funny(alice) [cnf transformation 22]
125. curious(X0) [duplicate literal removal 80]
126. ~curious(X0) | creative(X0) [duplicate literal removal 82]
130. 1 <=> ! [X1] : creative(X1) [avatar definition]
131. creative(X1) <- (1) [avatar component clause 130]
192. ~creative(X0) | funny(X0) [subsumption resolution 100,125]
226. creative(X0) [resolution 126,125]
227. 1 [avatar split clause 226,130]
243. funny(X0) <- (1) [resolution 192,131]
244. $false <- (1) [resolution 243,120]
247. ~1 [avatar contradiction clause 244]
248. $false [avatar sat refutation 227,247]
% SZS output end Proof for 8513550745425089994536517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and quiet is both not tall and not patient and vice versa.
If fred is either funny or not kind then someone is not tall or not brave.
If someone is both not wise and not calm then someone is old and vice versa.
Everyone who is both not patient and not brave is both brave and not humble.
Everyone who is not quiet is patient or generous and vice versa.
If lucy is either not tall or funny then someone is generous or not curious and vice versa.
Everyone who is either strong or patient is either brave or not strong and vice versa.
Everyone who is generous or not generous is both not tall and quiet and vice versa.
If susan is creative then someone is wise.
Everyone who is humble or happy is either brave or calm and vice versa.
If someone is both not quiet and old then someone is both brave and not old and vice versa.
Everyone who is brave or calm is either not patient or not kind.
Everyone who is both not funny and generous is both not happy and brave.
If mary is either creative or not old then mary is not curious or brave.
If someone is both humble and strong then alice is curious or not humble and vice versa.
Someone is either funny or calm.
Alice is either happy or curious.
Mary is both curious and brave.
Alice is not strong or not wise.
Someone is not happy or wise.
Someone is both not calm and not happy. | Alice is patient. | contradiction | (![X]:((~calm(X)&quiet(X))<=>(~tall(X)&~patient(X))))&
(((funny(fred)<~>~kind(fred)))=>(?[X]:((~tall(X)|~brave(X)))))&
((?[X]:((~wise(X)&~calm(X))))<=>(?[X]:(old(X))))&
(![X]:((~patient(X)&~brave(X))=>(brave(X)&~humble(X))))&
(![X]:(~quiet(X)<=>(patient(X)|generous(X))))&
(((~tall(lucy)<~>funny(lucy)))<=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((strong(X)<~>patient(X))<=>(brave(X)<~>~strong(X))))&
(![X]:((generous(X)|~generous(X))<=>(~tall(X)&quiet(X))))&
((creative(susan))=>(?[X]:(wise(X))))&
(![X]:((humble(X)|happy(X))<=>(brave(X)<~>calm(X))))&
((?[X]:((~quiet(X)&old(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((brave(X)|calm(X))=>(~patient(X)<~>~kind(X))))&
(![X]:((~funny(X)&generous(X))=>(~happy(X)&brave(X))))&
(((creative(mary)<~>~old(mary)))=>((~curious(mary)|brave(mary))))&
((?[X]:((humble(X)&strong(X))))<=>((curious(alice)|~humble(alice))))&
(?[X]:((funny(X)<~>calm(X))))&
((happy(alice)<~>curious(alice)))&
((curious(mary)&brave(mary)))&
((~strong(alice)|~wise(alice)))&
(?[X]:((~happy(X)|wise(X))))&
(?[X]:((~calm(X)&~happy(X)))) | patient(alice) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2379580909155187385572437
% SZS output start Proof for 2379580909155187385572437
5. ! [X0] : (~quiet(X0) <=> (generous(X0) | patient(X0))) [input p4]
8. ! [X0] : ((~generous(X0) | generous(X0)) <=> (quiet(X0) & ~tall(X0))) [input p7]
22. patient(alice) [input hypothesis]
44. ! [X0] : ((~quiet(X0) | (~generous(X0) & ~patient(X0))) & ((generous(X0) | patient(X0)) | quiet(X0))) [nnf transformation 5]
45. ! [X0] : ((~quiet(X0) | (~generous(X0) & ~patient(X0))) & (generous(X0) | patient(X0) | quiet(X0))) [flattening 44]
51. ! [X0] : (((~generous(X0) | generous(X0)) | (~quiet(X0) | tall(X0))) & ((quiet(X0) & ~tall(X0)) | (generous(X0) & ~generous(X0)))) [nnf transformation 8]
52. ! [X0] : ((~generous(X0) | generous(X0) | ~quiet(X0) | tall(X0)) & ((quiet(X0) & ~tall(X0)) | (generous(X0) & ~generous(X0)))) [flattening 51]
89. ~patient(X0) | ~quiet(X0) [cnf transformation 45]
90. ~generous(X0) | ~quiet(X0) [cnf transformation 45]
107. quiet(X0) | ~generous(X0) [cnf transformation 52]
108. generous(X0) | quiet(X0) [cnf transformation 52]
144. patient(alice) [cnf transformation 22]
202. 13 <=> ! [X0] : ~generous(X0) [avatar definition]
203. ~generous(X0) <- (13) [avatar component clause 202]
218. ~generous(X0) [subsumption resolution 107,90]
219. 13 [avatar split clause 218,202]
335. ~quiet(alice) [resolution 89,144]
337. quiet(X1) <- (13) [resolution 108,203]
338. $false <- (13) [resolution 337,335]
339. ~13 [avatar contradiction clause 338]
340. $false [avatar sat refutation 219,339]
% SZS output end Proof for 2379580909155187385572437
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is both not kind and strong.
Everyone who is either funny or not creative is either wise or brave.
If someone is kind then someone is either not quiet or humble.
Everyone who is not kind is generous or not quiet.
Everyone who is both not kind and curious is calm.
Everyone who is not curious or strong is old and vice versa.
If susan is not old then someone is both creative and not funny and vice versa.
Everyone who is either not funny or curious is generous or not brave.
If someone is either not humble or tall then someone is either rich or not patient and vice versa.
Everyone who is brave is not old.
Everyone who is both patient and not kind is both old and not wise and vice versa.
Everyone who is rich is not humble or generous and vice versa.
Everyone who is either not funny or not brave is either happy or quiet and vice versa.
Everyone who is both curious and not wise is quiet or not funny.
If someone is both not calm and calm then someone is either not funny or brave.
Everyone who is curious is calm or not strong.
Someone is both generous and creative.
Someone is both not generous and humble.
John is either not tall or kind.
Someone is either not generous or humble.
Fred is either not strong or not humble.
Someone is not patient or calm.
Mary is not creative.
Someone is not quiet. | Fred is not rich. | contradiction | (![X]:(~generous(X)=>(~kind(X)&strong(X))))&
(![X]:((funny(X)<~>~creative(X))=>(wise(X)<~>brave(X))))&
((?[X]:(kind(X)))=>(?[X]:((~quiet(X)<~>humble(X)))))&
(![X]:(~kind(X)=>(generous(X)|~quiet(X))))&
(![X]:((~kind(X)&curious(X))=>calm(X)))&
(![X]:((~curious(X)|strong(X))<=>old(X)))&
((~old(susan))<=>(?[X]:((creative(X)&~funny(X)))))&
(![X]:((~funny(X)<~>curious(X))=>(generous(X)|~brave(X))))&
((?[X]:((~humble(X)<~>tall(X))))<=>(?[X]:((rich(X)<~>~patient(X)))))&
(![X]:(brave(X)=>~old(X)))&
(![X]:((patient(X)&~kind(X))<=>(old(X)&~wise(X))))&
(![X]:(rich(X)<=>(~humble(X)|generous(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(happy(X)<~>quiet(X))))&
(![X]:((curious(X)&~wise(X))=>(quiet(X)|~funny(X))))&
((?[X]:((~calm(X)&calm(X))))=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:(curious(X)=>(calm(X)|~strong(X))))&
(?[X]:((generous(X)&creative(X))))&
(?[X]:((~generous(X)&humble(X))))&
((~tall(john)<~>kind(john)))&
(?[X]:((~generous(X)<~>humble(X))))&
((~strong(fred)<~>~humble(fred)))&
(?[X]:((~patient(X)|calm(X))))&
(~creative(mary))&
(?[X]:(~quiet(X))) | ~rich(fred) | [
"p0",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2348901978331741323211613
% SZS output start Proof for 2348901978331741323211613
1. ! [X0] : (~generous(X0) => (strong(X0) & ~kind(X0))) [input p0]
12. ! [X0] : (rich(X0) <=> (generous(X0) | ~humble(X0))) [input p11]
21. ~strong(fred) <~> ~humble(fred) [input p20]
25. ~rich(fred) [input hypothesis]
29. ! [X0] : ((strong(X0) & ~kind(X0)) | generous(X0)) [ennf transformation 1]
63. ! [X0] : ((rich(X0) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | ~rich(X0))) [nnf transformation 12]
64. ! [X0] : ((rich(X0) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | ~rich(X0))) [flattening 63]
78. (humble(fred) | strong(fred)) & (~humble(fred) | ~strong(fred)) [nnf transformation 21]
84. strong(X0) | generous(X0) [cnf transformation 29]
115. rich(X0) | humble(X0) [cnf transformation 64]
116. ~generous(X0) | rich(X0) [cnf transformation 64]
137. ~humble(fred) | ~strong(fred) [cnf transformation 78]
142. ~rich(fred) [cnf transformation 25]
232. 20 <=> strong(fred) [avatar definition]
233. ~strong(fred) <- (~20) [avatar component clause 232]
236. 21 <=> humble(fred) [avatar definition]
240. ~20 | ~21 [avatar split clause 137,236,232]
255. humble(fred) [resolution 115,142]
259. 21 [avatar split clause 255,236]
260. generous(fred) <- (~20) [resolution 233,84]
262. rich(fred) <- (~20) [resolution 260,116]
263. $false <- (~20) [subsumption resolution 262,142]
264. 20 [avatar contradiction clause 263]
265. $false [avatar sat refutation 240,259,264]
% SZS output end Proof for 2348901978331741323211613
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or not funny then someone is both wise and not happy and vice versa.
If someone is not curious or generous then lucy is rich or not old.
Everyone who is funny or not tall is either not creative or not generous.
If fred is both not humble and generous then john is wise.
If alice is either not patient or brave then someone is not curious.
Everyone who is not humble is both rich and not funny and vice versa.
Everyone who is both creative and not quiet is generous or not calm and vice versa.
Everyone who is both creative and not rich is humble.
If susan is either curious or rich then someone is curious or rich.
If paul is either not tall or calm then paul is either not kind or calm and vice versa.
Everyone who is both not tall and brave is generous or not strong and vice versa.
Everyone who is rich is either not calm or humble and vice versa.
If someone is not wise or not old then someone is either tall or not wise.
If someone is both not rich and not happy then someone is not patient or brave.
Someone is either kind or not kind.
Someone is either not quiet or not brave.
Someone is either old or quiet.
Paul is patient or not quiet.
Alice is not tall or funny. | John is not tall. | neutral | ((?[X]:((creative(X)|~funny(X))))<=>(?[X]:((wise(X)&~happy(X)))))&
((?[X]:((~curious(X)|generous(X))))=>((rich(lucy)|~old(lucy))))&
(![X]:((funny(X)|~tall(X))=>(~creative(X)<~>~generous(X))))&
(((~humble(fred)&generous(fred)))=>(wise(john)))&
(((~patient(alice)<~>brave(alice)))=>(?[X]:(~curious(X))))&
(![X]:(~humble(X)<=>(rich(X)&~funny(X))))&
(![X]:((creative(X)&~quiet(X))<=>(generous(X)|~calm(X))))&
(![X]:((creative(X)&~rich(X))=>humble(X)))&
(((curious(susan)<~>rich(susan)))=>(?[X]:((curious(X)|rich(X)))))&
(((~tall(paul)<~>calm(paul)))<=>((~kind(paul)<~>calm(paul))))&
(![X]:((~tall(X)&brave(X))<=>(generous(X)|~strong(X))))&
(![X]:(rich(X)<=>(~calm(X)<~>humble(X))))&
((?[X]:((~wise(X)|~old(X))))=>(?[X]:((tall(X)<~>~wise(X)))))&
((?[X]:((~rich(X)&~happy(X))))=>(?[X]:((~patient(X)|brave(X)))))&
(?[X]:((kind(X)<~>~kind(X))))&
(?[X]:((~quiet(X)<~>~brave(X))))&
(?[X]:((old(X)<~>quiet(X))))&
((patient(paul)|~quiet(paul)))&
((~tall(alice)|funny(alice))) | ~tall(john) | [] | null | 0 |
If mary is both patient and creative then someone is old or curious.
Everyone who is not funny is both creative and not creative.
If someone is kind then someone is not kind or curious.
Everyone who is both not wise and quiet is both not quiet and not rich.
Everyone who is not rich or not happy is not happy or tall.
Everyone who is generous or kind is both not kind and creative.
If someone is both not calm and not funny then someone is humble or not funny.
If someone is wise or not tall then lucy is humble.
If someone is both not rich and not patient then lucy is both rich and funny.
Everyone who is either not quiet or not old is either not wise or generous.
Everyone who is both not creative and not quiet is both generous and tall.
If mary is both not tall and not generous then someone is humble or creative and vice versa.
Everyone who is either kind or not generous is not wise or not calm.
Everyone who is either not rich or wise is creative.
Fred is either not curious or curious.
Someone is either not humble or calm.
Someone is not generous or not tall.
Someone is either not curious or calm. | Lucy is not creative. | neutral | (((patient(mary)&creative(mary)))=>(?[X]:((old(X)|curious(X)))))&
(![X]:(~funny(X)=>(creative(X)&~creative(X))))&
((?[X]:(kind(X)))=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~wise(X)&quiet(X))=>(~quiet(X)&~rich(X))))&
(![X]:((~rich(X)|~happy(X))=>(~happy(X)|tall(X))))&
(![X]:((generous(X)|kind(X))=>(~kind(X)&creative(X))))&
((?[X]:((~calm(X)&~funny(X))))=>(?[X]:((humble(X)|~funny(X)))))&
((?[X]:((wise(X)|~tall(X))))=>(humble(lucy)))&
((?[X]:((~rich(X)&~patient(X))))=>((rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)<~>~old(X))=>(~wise(X)<~>generous(X))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)&tall(X))))&
(((~tall(mary)&~generous(mary)))<=>(?[X]:((humble(X)|creative(X)))))&
(![X]:((kind(X)<~>~generous(X))=>(~wise(X)|~calm(X))))&
(![X]:((~rich(X)<~>wise(X))=>creative(X)))&
((~curious(fred)<~>curious(fred)))&
(?[X]:((~humble(X)<~>calm(X))))&
(?[X]:((~generous(X)|~tall(X))))&
(?[X]:((~curious(X)<~>calm(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is humble is brave or not humble. If someone is both not strong and calm then someone is both wise and not old. Everyone who is either kind or tall is either calm or rich. If lucy is not strong then john is both not kind and tall and vice versa. Everyone who is either not generous or strong is either not humble or not wise and vice versa. Everyone who is not kind or wise is either not funny or happy and vice versa. Everyone who is both not tall and not quiet is either not creative or not kind and vice versa. Everyone who is not quiet is either not creative or kind. Everyone who is both rich and not wise is either not patient or strong and vice versa. If john is both not wise and not generous then someone is both not patient and not quiet. Everyone who is not kind or rich is either not tall or tall and vice versa. If alice is wise then someone is both funny and not wise and vice versa. If someone is rich then someone is both generous and not rich and vice versa. Everyone who is not funny or quiet is both not brave and kind. Everyone who is either calm or funny is not curious and vice versa. If paul is both not happy and not calm then someone is both not funny and happy. Alice is curious or happy. John is both calm and not brave. Mary is either creative or patient. Susan is both wise and quiet. Someone is both not curious and calm. Someone is both not funny and calm. Someone is both tall and not old. Mary is kind. | Susan is strong. | neutral | (![X]:(humble(X)=>(brave(X)|~humble(X))))&
((?[X]:((~strong(X)&calm(X))))=>(?[X]:((wise(X)&~old(X)))))&
(![X]:((kind(X)<~>tall(X))=>(calm(X)<~>rich(X))))&
((~strong(lucy))<=>((~kind(john)&tall(john))))&
(![X]:((~generous(X)<~>strong(X))<=>(~humble(X)<~>~wise(X))))&
(![X]:((~kind(X)|wise(X))<=>(~funny(X)<~>happy(X))))&
(![X]:((~tall(X)&~quiet(X))<=>(~creative(X)<~>~kind(X))))&
(![X]:(~quiet(X)=>(~creative(X)<~>kind(X))))&
(![X]:((rich(X)&~wise(X))<=>(~patient(X)<~>strong(X))))&
(((~wise(john)&~generous(john)))=>(?[X]:((~patient(X)&~quiet(X)))))&
(![X]:((~kind(X)|rich(X))<=>(~tall(X)<~>tall(X))))&
((wise(alice))<=>(?[X]:((funny(X)&~wise(X)))))&
((?[X]:(rich(X)))<=>(?[X]:((generous(X)&~rich(X)))))&
(![X]:((~funny(X)|quiet(X))=>(~brave(X)&kind(X))))&
(![X]:((calm(X)<~>funny(X))<=>~curious(X)))&
(((~happy(paul)&~calm(paul)))=>(?[X]:((~funny(X)&happy(X)))))&
((curious(alice)|happy(alice)))&
((calm(john)&~brave(john)))&
((creative(mary)<~>patient(mary)))&
((wise(susan)&quiet(susan)))&
(?[X]:((~curious(X)&calm(X))))&
(?[X]:((~funny(X)&calm(X))))&
(?[X]:((tall(X)&~old(X))))&
(kind(mary)) | strong(susan) | [] | null | 0 |
Everyone who is either not generous or kind is funny or brave.
Everyone who is both funny and brave is either patient or not strong and vice versa.
If someone is brave then someone is either wise or not funny and vice versa.
If lucy is both creative and not humble then fred is funny.
Everyone who is curious or not happy is either humble or not creative and vice versa.
Everyone who is not funny or not humble is both not calm and rich.
Everyone who is not rich is not curious.
If someone is not strong then alice is not calm or not happy and vice versa.
If someone is both patient and not generous then someone is not tall and vice versa.
Everyone who is either quiet or not happy is brave.
If someone is strong or tall then someone is either kind or funny and vice versa.
If alice is either quiet or not old then someone is both not strong and not kind and vice versa.
Everyone who is tall or brave is either not brave or not funny.
If john is not tall or quiet then john is both rich and not strong and vice versa.
Everyone who is either generous or wise is not rich and vice versa.
If someone is not patient then someone is both old and not calm.
Lucy is not rich or quiet.
Alice is both not humble and not wise.
Someone is not humble or not strong.
Someone is both not rich and not calm.
Someone is either brave or not rich.
Lucy is both calm and happy.
Alice is curious.
Someone is both not quiet and not old. | Lucy is humble. | entailment | (![X]:((~generous(X)<~>kind(X))=>(funny(X)|brave(X))))&
(![X]:((funny(X)&brave(X))<=>(patient(X)<~>~strong(X))))&
((?[X]:(brave(X)))<=>(?[X]:((wise(X)<~>~funny(X)))))&
(((creative(lucy)&~humble(lucy)))=>(funny(fred)))&
(![X]:((curious(X)|~happy(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((~funny(X)|~humble(X))=>(~calm(X)&rich(X))))&
(![X]:(~rich(X)=>~curious(X)))&
((?[X]:(~strong(X)))<=>((~calm(alice)|~happy(alice))))&
((?[X]:((patient(X)&~generous(X))))<=>(?[X]:(~tall(X))))&
(![X]:((quiet(X)<~>~happy(X))=>brave(X)))&
((?[X]:((strong(X)|tall(X))))<=>(?[X]:((kind(X)<~>funny(X)))))&
(((quiet(alice)<~>~old(alice)))<=>(?[X]:((~strong(X)&~kind(X)))))&
(![X]:((tall(X)|brave(X))=>(~brave(X)<~>~funny(X))))&
(((~tall(john)|quiet(john)))<=>((rich(john)&~strong(john))))&
(![X]:((generous(X)<~>wise(X))<=>~rich(X)))&
((?[X]:(~patient(X)))=>(?[X]:((old(X)&~calm(X)))))&
((~rich(lucy)|quiet(lucy)))&
((~humble(alice)&~wise(alice)))&
(?[X]:((~humble(X)|~strong(X))))&
(?[X]:((~rich(X)&~calm(X))))&
(?[X]:((brave(X)<~>~rich(X))))&
((calm(lucy)&happy(lucy)))&
(curious(alice))&
(?[X]:((~quiet(X)&~old(X)))) | humble(lucy) | [
"p5",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8454787591632867162475143
% SZS output start Proof for 8454787591632867162475143
6. ! [X0] : ((~humble(X0) | ~funny(X0)) => (rich(X0) & ~calm(X0))) [input p5]
22. happy(lucy) & calm(lucy) [input p21]
25. ~humble(lucy) [input hypothesis]
34. ! [X0] : ((rich(X0) & ~calm(X0)) | (humble(X0) & funny(X0))) [ennf transformation 6]
105. ~calm(X0) | humble(X0) [cnf transformation 34]
152. calm(lucy) [cnf transformation 22]
157. ~humble(lucy) [cnf transformation 25]
189. 8 <=> humble(lucy) [avatar definition]
190. ~humble(lucy) <- (~8) [avatar component clause 189]
357. ~8 [avatar split clause 157,189]
361. humble(lucy) [resolution 105,152]
362. $false <- (~8) [subsumption resolution 361,190]
363. 8 [avatar contradiction clause 362]
364. $false [avatar sat refutation 357,363]
% SZS output end Proof for 8454787591632867162475143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and calm then susan is either not happy or not kind and vice versa.
Everyone who is either not old or not creative is not quiet and vice versa.
Everyone who is not wise or not patient is both tall and not kind and vice versa.
Everyone who is kind is not kind or humble and vice versa.
Everyone who is either old or brave is both tall and brave and vice versa.
Everyone who is either not wise or not rich is generous and vice versa.
Everyone who is quiet is both not patient and calm.
Everyone who is either brave or funny is quiet.
If someone is not calm or old then someone is both not kind and generous.
Everyone who is either not brave or wise is either not creative or not generous.
Everyone who is both not kind and old is quiet and vice versa.
If susan is both not quiet and not strong then someone is patient and vice versa.
If fred is creative then susan is not quiet or patient and vice versa.
Everyone who is not creative is not humble or tall and vice versa.
Everyone who is either rich or not curious is both not old and curious.
Someone is happy or old.
Mary is kind.
Someone is not brave or patient.
Someone is both not strong and calm.
Paul is humble or quiet. | Susan is brave. | contradiction | ((?[X]:((~rich(X)&calm(X))))<=>((~happy(susan)<~>~kind(susan))))&
(![X]:((~old(X)<~>~creative(X))<=>~quiet(X)))&
(![X]:((~wise(X)|~patient(X))<=>(tall(X)&~kind(X))))&
(![X]:(kind(X)<=>(~kind(X)|humble(X))))&
(![X]:((old(X)<~>brave(X))<=>(tall(X)&brave(X))))&
(![X]:((~wise(X)<~>~rich(X))<=>generous(X)))&
(![X]:(quiet(X)=>(~patient(X)&calm(X))))&
(![X]:((brave(X)<~>funny(X))=>quiet(X)))&
((?[X]:((~calm(X)|old(X))))=>(?[X]:((~kind(X)&generous(X)))))&
(![X]:((~brave(X)<~>wise(X))=>(~creative(X)<~>~generous(X))))&
(![X]:((~kind(X)&old(X))<=>quiet(X)))&
(((~quiet(susan)&~strong(susan)))<=>(?[X]:(patient(X))))&
((creative(fred))<=>((~quiet(susan)|patient(susan))))&
(![X]:(~creative(X)<=>(~humble(X)|tall(X))))&
(![X]:((rich(X)<~>~curious(X))=>(~old(X)&curious(X))))&
(?[X]:((happy(X)|old(X))))&
(kind(mary))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((~strong(X)&calm(X))))&
((humble(paul)|quiet(paul))) | brave(susan) | [
"p1",
"p3",
"p4",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 117206804434122718823969
% SZS output start Proof for 117206804434122718823969
2. ! [X0] : ((~old(X0) <~> ~creative(X0)) <=> ~quiet(X0)) [input p1]
4. ! [X0] : (kind(X0) <=> (humble(X0) | ~kind(X0))) [input p3]
5. ! [X0] : ((old(X0) <~> brave(X0)) <=> (brave(X0) & tall(X0))) [input p4]
9. ? [X0] : (old(X0) | ~calm(X0)) => ? [X0] : (generous(X0) & ~kind(X0)) [input p8]
11. ! [X0] : ((old(X0) & ~kind(X0)) <=> quiet(X0)) [input p10]
14. ! [X0] : (~creative(X0) <=> (tall(X0) | ~humble(X0))) [input p13]
21. brave(susan) [input hypothesis]
22. ? [X0] : (old(X0) | ~calm(X0)) => ? [X1] : (generous(X1) & ~kind(X1)) [rectify 9]
25. ? [X1] : (generous(X1) & ~kind(X1)) | ! [X0] : (~old(X0) & calm(X0)) [ennf transformation 22]
32. ! [X0] : ((((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | quiet(X0)) & (~quiet(X0) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))))) [nnf transformation 2]
35. ! [X0] : ((kind(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ~kind(X0))) [nnf transformation 4]
36. ! [X0] : ((kind(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ~kind(X0))) [flattening 35]
37. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (~brave(X0) | ~tall(X0))) & ((brave(X0) & tall(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [nnf transformation 5]
38. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | ~brave(X0) | ~tall(X0)) & ((brave(X0) & tall(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [flattening 37]
41. ? [X0] : (generous(X0) & ~kind(X0)) | ! [X1] : (~old(X1) & calm(X1)) [rectify 25]
42. ? [X0] : (generous(X0) & ~kind(X0)) => (generous(sK1) & ~kind(sK1)) [choice axiom]
43. (generous(sK1) & ~kind(sK1)) | ! [X1] : (~old(X1) & calm(X1)) [skolemisation 41,42]
45. ! [X0] : (((old(X0) & ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | (~old(X0) | kind(X0)))) [nnf transformation 11]
46. ! [X0] : (((old(X0) & ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | ~old(X0) | kind(X0))) [flattening 45]
54. ! [X0] : ((~creative(X0) | (~tall(X0) & humble(X0))) & ((tall(X0) | ~humble(X0)) | creative(X0))) [nnf transformation 14]
55. ! [X0] : ((~creative(X0) | (~tall(X0) & humble(X0))) & (tall(X0) | ~humble(X0) | creative(X0))) [flattening 54]
72. quiet(X0) | old(X0) | creative(X0) [cnf transformation 32]
79. kind(X0) | kind(X0) [cnf transformation 36]
82. ~brave(X0) | old(X0) | tall(X0) [cnf transformation 38]
96. ~kind(sK1) | ~old(X1) [cnf transformation 43]
105. ~quiet(X0) | old(X0) [cnf transformation 46]
114. ~tall(X0) | ~creative(X0) [cnf transformation 55]
125. brave(susan) [cnf transformation 21]
130. kind(X0) [duplicate literal removal 79]
158. 6 <=> ! [X1] : ~old(X1) [avatar definition]
159. ~old(X1) <- (6) [avatar component clause 158]
169. ~old(X1) [subsumption resolution 96,130]
170. 6 [avatar split clause 169,158]
232. old(X2) | creative(X2) | old(X2) [resolution 72,105]
235. old(X2) | creative(X2) [duplicate literal removal 232]
238. creative(X2) <- (6) [subsumption resolution 235,159]
240. old(susan) | tall(susan) [resolution 82,125]
241. tall(susan) <- (6) [subsumption resolution 240,159]
242. ~creative(susan) <- (6) [resolution 241,114]
243. $false <- (6) [subsumption resolution 242,238]
244. ~6 [avatar contradiction clause 243]
245. $false [avatar sat refutation 170,244]
% SZS output end Proof for 117206804434122718823969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both creative and not calm. Everyone who is not kind is either funny or not patient. If someone is either not brave or not rich then someone is either funny or not happy and vice versa. Everyone who is brave or not rich is either not kind or quiet. Everyone who is not tall is both tall and not patient. If alice is not patient then susan is wise or not kind and vice versa. Everyone who is both not creative and not brave is wise or happy and vice versa. Everyone who is both curious and not brave is both not kind and not humble and vice versa. Everyone who is either generous or old is not generous. If someone is either happy or curious then paul is quiet or not humble and vice versa. Everyone who is both generous and strong is either patient or not old. If alice is both not quiet and happy then alice is not old. If fred is brave or wise then someone is both calm and funny and vice versa. Everyone who is not calm is both not creative and not curious. If lucy is not happy or old then someone is humble. If someone is not old then someone is either not funny or not brave and vice versa. Someone is either not strong or not curious. John is either tall or old. Alice is curious or not creative. Fred is either not patient or not wise. Someone is not kind or not patient. Mary is patient or not strong. Fred is not kind or kind. Someone is not patient. | John is not generous. | entailment | (![X]:(brave(X)=>(creative(X)&~calm(X))))&
(![X]:(~kind(X)=>(funny(X)<~>~patient(X))))&
((?[X]:((~brave(X)<~>~rich(X))))<=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:((brave(X)|~rich(X))=>(~kind(X)<~>quiet(X))))&
(![X]:(~tall(X)=>(tall(X)&~patient(X))))&
((~patient(alice))<=>((wise(susan)|~kind(susan))))&
(![X]:((~creative(X)&~brave(X))<=>(wise(X)|happy(X))))&
(![X]:((curious(X)&~brave(X))<=>(~kind(X)&~humble(X))))&
(![X]:((generous(X)<~>old(X))=>~generous(X)))&
((?[X]:((happy(X)<~>curious(X))))<=>((quiet(paul)|~humble(paul))))&
(![X]:((generous(X)&strong(X))=>(patient(X)<~>~old(X))))&
(((~quiet(alice)&happy(alice)))=>(~old(alice)))&
(((brave(fred)|wise(fred)))<=>(?[X]:((calm(X)&funny(X)))))&
(![X]:(~calm(X)=>(~creative(X)&~curious(X))))&
(((~happy(lucy)|old(lucy)))=>(?[X]:(humble(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~funny(X)<~>~brave(X)))))&
(?[X]:((~strong(X)<~>~curious(X))))&
((tall(john)<~>old(john)))&
((curious(alice)|~creative(alice)))&
((~patient(fred)<~>~wise(fred)))&
(?[X]:((~kind(X)|~patient(X))))&
((patient(mary)|~strong(mary)))&
((~kind(fred)|kind(fred)))&
(?[X]:(~patient(X))) | ~generous(john) | [
"p4",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7637166845112755941922586
% SZS output start Proof for 7637166845112755941922586
5. ! [X0] : (~tall(X0) => (~patient(X0) & tall(X0))) [input p4]
9. ! [X0] : ((generous(X0) <~> old(X0)) => ~generous(X0)) [input p8]
18. tall(john) <~> old(john) [input p17]
25. generous(john) [input hypothesis]
31. ! [X0] : ((~patient(X0) & tall(X0)) | tall(X0)) [ennf transformation 5]
32. ! [X0] : (~generous(X0) | (generous(X0) <=> old(X0))) [ennf transformation 9]
52. ! [X0] : (~generous(X0) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0)))) [nnf transformation 32]
74. (~old(john) | ~tall(john)) & (old(john) | tall(john)) [nnf transformation 18]
96. tall(X0) | tall(X0) [cnf transformation 31]
110. ~generous(X0) | old(X0) | ~generous(X0) [cnf transformation 52]
137. ~old(john) | ~tall(john) [cnf transformation 74]
145. generous(john) [cnf transformation 25]
146. ~generous(X0) | old(X0) [duplicate literal removal 110]
147. tall(X0) [duplicate literal removal 96]
315. ~old(john) [subsumption resolution 137,147]
366. old(john) [resolution 146,145]
367. $false [subsumption resolution 366,315]
% SZS output end Proof for 7637166845112755941922586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or rich is both not old and not wise.
Everyone who is not happy is wise or not patient and vice versa.
Everyone who is not old or calm is either not kind or calm and vice versa.
Everyone who is calm is either not brave or not humble.
Everyone who is either not humble or not creative is either humble or not patient.
If someone is wise or happy then fred is either calm or not generous and vice versa.
Everyone who is rich or calm is either funny or generous and vice versa.
Everyone who is either creative or not funny is not rich or creative and vice versa.
Everyone who is funny is either not generous or not rich and vice versa.
Everyone who is brave is not curious and vice versa.
Everyone who is calm is both patient and not funny and vice versa.
If someone is either brave or not quiet then someone is both not tall and not happy and vice versa.
Everyone who is quiet is both not wise and happy.
Everyone who is both humble and not calm is tall.
If someone is not patient or calm then susan is happy or not wise.
Everyone who is humble or not patient is happy and vice versa.
Lucy is creative.
Susan is either not generous or not curious.
Lucy is curious or not humble.
Someone is patient or not creative.
Alice is quiet or generous. | Lucy is not quiet. | contradiction | (![X]:((kind(X)|rich(X))=>(~old(X)&~wise(X))))&
(![X]:(~happy(X)<=>(wise(X)|~patient(X))))&
(![X]:((~old(X)|calm(X))<=>(~kind(X)<~>calm(X))))&
(![X]:(calm(X)=>(~brave(X)<~>~humble(X))))&
(![X]:((~humble(X)<~>~creative(X))=>(humble(X)<~>~patient(X))))&
((?[X]:((wise(X)|happy(X))))<=>((calm(fred)<~>~generous(fred))))&
(![X]:((rich(X)|calm(X))<=>(funny(X)<~>generous(X))))&
(![X]:((creative(X)<~>~funny(X))<=>(~rich(X)|creative(X))))&
(![X]:(funny(X)<=>(~generous(X)<~>~rich(X))))&
(![X]:(brave(X)<=>~curious(X)))&
(![X]:(calm(X)<=>(patient(X)&~funny(X))))&
((?[X]:((brave(X)<~>~quiet(X))))<=>(?[X]:((~tall(X)&~happy(X)))))&
(![X]:(quiet(X)=>(~wise(X)&happy(X))))&
(![X]:((humble(X)&~calm(X))=>tall(X)))&
((?[X]:((~patient(X)|calm(X))))=>((happy(susan)|~wise(susan))))&
(![X]:((humble(X)|~patient(X))<=>happy(X)))&
(creative(lucy))&
((~generous(susan)<~>~curious(susan)))&
((curious(lucy)|~humble(lucy)))&
(?[X]:((patient(X)|~creative(X))))&
((quiet(alice)|generous(alice))) | ~quiet(lucy) | [
"p0",
"p1",
"p2",
"p4",
"p7",
"p9",
"p10",
"p11",
"p13",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6115721667113790433226693
% SZS output start Proof for 6115721667113790433226693
1. ! [X0] : ((rich(X0) | kind(X0)) => (~wise(X0) & ~old(X0))) [input p0]
2. ! [X0] : (~happy(X0) <=> (~patient(X0) | wise(X0))) [input p1]
3. ! [X0] : ((calm(X0) | ~old(X0)) <=> (~kind(X0) <~> calm(X0))) [input p2]
5. ! [X0] : ((~humble(X0) <~> ~creative(X0)) => (humble(X0) <~> ~patient(X0))) [input p4]
8. ! [X0] : ((creative(X0) <~> ~funny(X0)) <=> (creative(X0) | ~rich(X0))) [input p7]
10. ! [X0] : (brave(X0) <=> ~curious(X0)) [input p9]
11. ! [X0] : (calm(X0) <=> (~funny(X0) & patient(X0))) [input p10]
12. ? [X0] : (brave(X0) <~> ~quiet(X0)) <=> ? [X0] : (~happy(X0) & ~tall(X0)) [input p11]
14. ! [X0] : ((~calm(X0) & humble(X0)) => tall(X0)) [input p13]
16. ! [X0] : ((~patient(X0) | humble(X0)) <=> happy(X0)) [input p15]
17. creative(lucy) [input p16]
19. ~humble(lucy) | curious(lucy) [input p18]
22. ~quiet(lucy) [input hypothesis]
23. ? [X0] : (brave(X0) <~> ~quiet(X0)) <=> ? [X1] : (~happy(X1) & ~tall(X1)) [rectify 12]
24. ! [X0] : ((~wise(X0) & ~old(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 1]
26. ! [X0] : ((humble(X0) <~> ~patient(X0)) | (~humble(X0) <=> ~creative(X0))) [ennf transformation 5]
28. ! [X0] : (tall(X0) | (calm(X0) | ~humble(X0))) [ennf transformation 14]
29. ! [X0] : (tall(X0) | calm(X0) | ~humble(X0)) [flattening 28]
32. ! [X0] : ((~happy(X0) | (patient(X0) & ~wise(X0))) & ((~patient(X0) | wise(X0)) | happy(X0))) [nnf transformation 2]
33. ! [X0] : ((~happy(X0) | (patient(X0) & ~wise(X0))) & (~patient(X0) | wise(X0) | happy(X0))) [flattening 32]
34. ! [X0] : (((calm(X0) | ~old(X0)) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0)))) & (((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (~calm(X0) & old(X0)))) [nnf transformation 3]
35. ! [X0] : ((calm(X0) | ~old(X0) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0)))) & (((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (~calm(X0) & old(X0)))) [flattening 34]
37. ! [X0] : (((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0)))) [nnf transformation 26]
44. ! [X0] : ((((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | (~creative(X0) & rich(X0))) & ((creative(X0) | ~rich(X0)) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))))) [nnf transformation 8]
45. ! [X0] : ((((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | (~creative(X0) & rich(X0))) & (creative(X0) | ~rich(X0) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))))) [flattening 44]
47. ! [X0] : ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0))) [nnf transformation 10]
48. ! [X0] : ((calm(X0) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | ~calm(X0))) [nnf transformation 11]
49. ! [X0] : ((calm(X0) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | ~calm(X0))) [flattening 48]
50. (? [X0] : ((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | ! [X1] : (happy(X1) | tall(X1))) & (? [X1] : (~happy(X1) & ~tall(X1)) | ! [X0] : ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0)))) [nnf transformation 23]
51. (? [X0] : ((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | ! [X1] : (happy(X1) | tall(X1))) & (? [X2] : (~happy(X2) & ~tall(X2)) | ! [X3] : ((brave(X3) | quiet(X3)) & (~quiet(X3) | ~brave(X3)))) [rectify 50]
52. ? [X0] : ((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) => ((quiet(sK1) | ~brave(sK1)) & (~quiet(sK1) | brave(sK1))) [choice axiom]
53. ? [X2] : (~happy(X2) & ~tall(X2)) => (~happy(sK2) & ~tall(sK2)) [choice axiom]
54. (((quiet(sK1) | ~brave(sK1)) & (~quiet(sK1) | brave(sK1))) | ! [X1] : (happy(X1) | tall(X1))) & ((~happy(sK2) & ~tall(sK2)) | ! [X3] : ((brave(X3) | quiet(X3)) & (~quiet(X3) | ~brave(X3)))) [skolemisation 51,53,52]
55. ! [X0] : (((~patient(X0) | humble(X0)) | ~happy(X0)) & (happy(X0) | (patient(X0) & ~humble(X0)))) [nnf transformation 16]
56. ! [X0] : ((~patient(X0) | humble(X0) | ~happy(X0)) & (happy(X0) | (patient(X0) & ~humble(X0)))) [flattening 55]
62. ~wise(X0) | ~kind(X0) [cnf transformation 24]
63. ~wise(X0) | ~rich(X0) [cnf transformation 24]
64. ~patient(X0) | wise(X0) | happy(X0) [cnf transformation 33]
66. ~happy(X0) | patient(X0) [cnf transformation 33]
70. ~calm(X0) | kind(X0) | ~calm(X0) [cnf transformation 35]
75. ~patient(X0) | humble(X0) | ~creative(X0) | humble(X0) [cnf transformation 37]
93. ~funny(X0) | creative(X0) | rich(X0) [cnf transformation 45]
101. ~curious(X0) | ~brave(X0) [cnf transformation 47]
105. ~patient(X0) | funny(X0) | calm(X0) [cnf transformation 49]
107. ~tall(sK2) | brave(X3) | quiet(X3) [cnf transformation 54]
109. ~happy(sK2) | brave(X3) | quiet(X3) [cnf transformation 54]
114. ~humble(X0) | calm(X0) | tall(X0) [cnf transformation 29]
118. happy(X0) | patient(X0) [cnf transformation 56]
120. creative(lucy) [cnf transformation 17]
123. ~humble(lucy) | curious(lucy) [cnf transformation 19]
126. ~quiet(lucy) [cnf transformation 22]
129. ~creative(X0) | humble(X0) | ~patient(X0) [duplicate literal removal 75]
131. ~calm(X0) | kind(X0) [duplicate literal removal 70]
179. 10 <=> ! [X3] : (brave(X3) | quiet(X3)) [avatar definition]
180. quiet(X3) | brave(X3) <- (10) [avatar component clause 179]
182. 11 <=> happy(sK2) [avatar definition]
184. ~happy(sK2) <- (~11) [avatar component clause 182]
185. 10 | ~11 [avatar split clause 109,182,179]
191. 13 <=> tall(sK2) [avatar definition]
193. ~tall(sK2) <- (~13) [avatar component clause 191]
194. 10 | ~13 [avatar split clause 107,191,179]
207. 16 <=> ! [X0] : patient(X0) [avatar definition]
208. patient(X0) <- (16) [avatar component clause 207]
211. patient(X0) [subsumption resolution 118,66]
212. 16 [avatar split clause 211,207]
224. 19 <=> curious(lucy) [avatar definition]
226. curious(lucy) <- (19) [avatar component clause 224]
228. 20 <=> humble(lucy) [avatar definition]
231. 19 | ~20 [avatar split clause 123,228,224]
263. happy(X0) | wise(X0) <- (16) [resolution 64,208]
275. wise(sK2) <- (~11, 16) [resolution 263,184]
279. ~rich(sK2) <- (~11, 16) [resolution 275,63]
280. ~kind(sK2) <- (~11, 16) [resolution 275,62]
306. funny(X0) | calm(X0) <- (16) [resolution 105,208]
309. humble(lucy) | ~patient(lucy) [resolution 129,120]
315. humble(lucy) <- (16) [subsumption resolution 309,208]
316. 20 | ~16 [avatar split clause 315,207,228]
317. ~brave(lucy) <- (19) [resolution 226,101]
332. creative(X2) | calm(X2) | rich(X2) <- (16) [resolution 306,93]
347. calm(X0) | rich(X0) | humble(X0) | ~patient(X0) <- (16) [resolution 332,129]
358. humble(X0) | rich(X0) | calm(X0) <- (16) [subsumption resolution 347,208]
411. rich(X1) | calm(X1) | calm(X1) | tall(X1) <- (16) [resolution 358,114]
414. tall(X1) | calm(X1) | rich(X1) <- (16) [duplicate literal removal 411]
427. calm(sK2) | rich(sK2) <- (~13, 16) [resolution 414,193]
428. calm(sK2) <- (~11, ~13, 16) [subsumption resolution 427,279]
431. kind(sK2) <- (~11, ~13, 16) [resolution 428,131]
443. $false <- (~11, ~13, 16) [subsumption resolution 431,280]
444. 11 | 13 | ~16 [avatar contradiction clause 443]
445. brave(lucy) <- (10) [resolution 180,126]
449. $false <- (10, 19) [subsumption resolution 445,317]
450. ~10 | ~19 [avatar contradiction clause 449]
453. $false [avatar sat refutation 185,194,212,231,316,444,450]
% SZS output end Proof for 6115721667113790433226693
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not funny is either brave or calm and vice versa.
Everyone who is not calm is both not quiet and happy and vice versa.
Everyone who is either happy or not kind is either not quiet or rich and vice versa.
Everyone who is either brave or not happy is both curious and tall.
If paul is either not humble or not rich then susan is curious.
If paul is either humble or not creative then someone is either not creative or old and vice versa.
If someone is wise then fred is both curious and not generous and vice versa.
Everyone who is not creative is either not brave or rich and vice versa.
Everyone who is either patient or creative is not generous.
If mary is generous or not humble then mary is both not old and wise.
Everyone who is either happy or rich is either strong or generous and vice versa.
Everyone who is not rich is both calm and not funny.
Everyone who is either not calm or not humble is old or wise.
Everyone who is not patient is not tall or quiet.
If someone is not tall then lucy is not generous and vice versa.
If mary is both tall and not old then john is both happy and tall and vice versa.
Fred is patient or not curious.
Lucy is tall or creative.
Someone is either old or not rich.
Alice is both generous and quiet.
Someone is not old.
Lucy is either not happy or funny.
Someone is either not tall or not generous. | Alice is tall. | neutral | (![X]:((~curious(X)<~>~funny(X))<=>(brave(X)<~>calm(X))))&
(![X]:(~calm(X)<=>(~quiet(X)&happy(X))))&
(![X]:((happy(X)<~>~kind(X))<=>(~quiet(X)<~>rich(X))))&
(![X]:((brave(X)<~>~happy(X))=>(curious(X)&tall(X))))&
(((~humble(paul)<~>~rich(paul)))=>(curious(susan)))&
(((humble(paul)<~>~creative(paul)))<=>(?[X]:((~creative(X)<~>old(X)))))&
((?[X]:(wise(X)))<=>((curious(fred)&~generous(fred))))&
(![X]:(~creative(X)<=>(~brave(X)<~>rich(X))))&
(![X]:((patient(X)<~>creative(X))=>~generous(X)))&
(((generous(mary)|~humble(mary)))=>((~old(mary)&wise(mary))))&
(![X]:((happy(X)<~>rich(X))<=>(strong(X)<~>generous(X))))&
(![X]:(~rich(X)=>(calm(X)&~funny(X))))&
(![X]:((~calm(X)<~>~humble(X))=>(old(X)|wise(X))))&
(![X]:(~patient(X)=>(~tall(X)|quiet(X))))&
((?[X]:(~tall(X)))<=>(~generous(lucy)))&
(((tall(mary)&~old(mary)))<=>((happy(john)&tall(john))))&
((patient(fred)|~curious(fred)))&
((tall(lucy)|creative(lucy)))&
(?[X]:((old(X)<~>~rich(X))))&
((generous(alice)&quiet(alice)))&
(?[X]:(~old(X)))&
((~happy(lucy)<~>funny(lucy)))&
(?[X]:((~tall(X)<~>~generous(X)))) | tall(alice) | [] | null | 0 |
Everyone who is quiet is both tall and generous and vice versa. If lucy is both old and wise then someone is both not brave and creative. Everyone who is old or not humble is both not strong and not tall and vice versa. If fred is generous then alice is both not kind and creative. Everyone who is both brave and not rich is not calm or not kind. Everyone who is humble or not strong is either calm or funny and vice versa. Everyone who is rich or brave is either not curious or not creative and vice versa. If someone is humble or tall then someone is both not funny and generous. If someone is either tall or patient then paul is not wise. If lucy is not humble or kind then lucy is either creative or not funny and vice versa. Everyone who is strong is not wise and vice versa. Everyone who is kind or not strong is funny or not creative and vice versa. If someone is creative or happy then someone is quiet or not creative. Everyone who is quiet is old or not happy and vice versa. Everyone who is either old or not kind is both wise and not old. If someone is not rich then paul is quiet and vice versa. Susan is either quiet or curious. Mary is both not quiet and brave. Someone is not curious. Mary is either not quiet or rich. Someone is brave. Someone is both brave and not creative. Someone is either not wise or not brave. Someone is both not tall and not brave. | Paul is quiet. | entailment | (![X]:(quiet(X)<=>(tall(X)&generous(X))))&
(((old(lucy)&wise(lucy)))=>(?[X]:((~brave(X)&creative(X)))))&
(![X]:((old(X)|~humble(X))<=>(~strong(X)&~tall(X))))&
((generous(fred))=>((~kind(alice)&creative(alice))))&
(![X]:((brave(X)&~rich(X))=>(~calm(X)|~kind(X))))&
(![X]:((humble(X)|~strong(X))<=>(calm(X)<~>funny(X))))&
(![X]:((rich(X)|brave(X))<=>(~curious(X)<~>~creative(X))))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:((~funny(X)&generous(X)))))&
((?[X]:((tall(X)<~>patient(X))))=>(~wise(paul)))&
(((~humble(lucy)|kind(lucy)))<=>((creative(lucy)<~>~funny(lucy))))&
(![X]:(strong(X)<=>~wise(X)))&
(![X]:((kind(X)|~strong(X))<=>(funny(X)|~creative(X))))&
((?[X]:((creative(X)|happy(X))))=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:(quiet(X)<=>(old(X)|~happy(X))))&
(![X]:((old(X)<~>~kind(X))=>(wise(X)&~old(X))))&
((?[X]:(~rich(X)))<=>(quiet(paul)))&
((quiet(susan)<~>curious(susan)))&
((~quiet(mary)&brave(mary)))&
(?[X]:(~curious(X)))&
((~quiet(mary)<~>rich(mary)))&
(?[X]:(brave(X)))&
(?[X]:((brave(X)&~creative(X))))&
(?[X]:((~wise(X)<~>~brave(X))))&
(?[X]:((~tall(X)&~brave(X)))) | quiet(paul) | [
"p15",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7881229522926535501226561
% SZS output start Proof for 7881229522926535501226561
16. ? [X0] : ~rich(X0) <=> quiet(paul) [input p15]
18. brave(mary) & ~quiet(mary) [input p17]
20. ~quiet(mary) <~> rich(mary) [input p19]
25. ~quiet(paul) [input hypothesis]
62. (? [X0] : ~rich(X0) | ~quiet(paul)) & (quiet(paul) | ! [X0] : rich(X0)) [nnf transformation 16]
63. (? [X0] : ~rich(X0) | ~quiet(paul)) & (quiet(paul) | ! [X1] : rich(X1)) [rectify 62]
64. ? [X0] : ~rich(X0) => ~rich(sK3) [choice axiom]
65. (~rich(sK3) | ~quiet(paul)) & (quiet(paul) | ! [X1] : rich(X1)) [skolemisation 63,64]
69. (~rich(mary) | quiet(mary)) & (rich(mary) | ~quiet(mary)) [nnf transformation 20]
131. quiet(paul) | rich(X1) [cnf transformation 65]
135. ~quiet(mary) [cnf transformation 18]
139. ~rich(mary) | quiet(mary) [cnf transformation 69]
147. ~quiet(paul) [cnf transformation 25]
250. 23 <=> quiet(paul) [avatar definition]
259. 25 <=> ! [X1] : rich(X1) [avatar definition]
260. rich(X1) <- (25) [avatar component clause 259]
261. 25 | 23 [avatar split clause 131,250,259]
272. ~rich(mary) [subsumption resolution 139,135]
283. ~23 [avatar split clause 147,250]
284. $false <- (25) [resolution 272,260]
285. ~25 [avatar contradiction clause 284]
286. $false [avatar sat refutation 261,283,285]
% SZS output end Proof for 7881229522926535501226561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is calm or not funny is both rich and not tall. Everyone who is curious is both not funny and not happy. Everyone who is both quiet and not generous is either funny or wise. Everyone who is either brave or not funny is both kind and not happy and vice versa. If paul is both not calm and humble then paul is both humble and not tall. Everyone who is funny or not generous is either not funny or brave and vice versa. If someone is both not calm and funny then someone is not rich or strong. Everyone who is strong is creative or not brave. Everyone who is brave or not old is not kind and vice versa. Everyone who is both rich and funny is both strong and calm and vice versa. Everyone who is not creative is not happy. Everyone who is strong or humble is either quiet or creative. If alice is not funny then lucy is not old. If mary is not wise or not tall then paul is both quiet and not brave and vice versa. Everyone who is brave or not generous is not funny. Lucy is strong or brave. Lucy is not old. Lucy is either not happy or old. Someone is kind or quiet. Someone is either not quiet or wise. Someone is strong or not humble. Lucy is either kind or brave. | Paul is brave. | contradiction | (![X]:((calm(X)|~funny(X))=>(rich(X)&~tall(X))))&
(![X]:(curious(X)=>(~funny(X)&~happy(X))))&
(![X]:((quiet(X)&~generous(X))=>(funny(X)<~>wise(X))))&
(![X]:((brave(X)<~>~funny(X))<=>(kind(X)&~happy(X))))&
(((~calm(paul)&humble(paul)))=>((humble(paul)&~tall(paul))))&
(![X]:((funny(X)|~generous(X))<=>(~funny(X)<~>brave(X))))&
((?[X]:((~calm(X)&funny(X))))=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:(strong(X)=>(creative(X)|~brave(X))))&
(![X]:((brave(X)|~old(X))<=>~kind(X)))&
(![X]:((rich(X)&funny(X))<=>(strong(X)&calm(X))))&
(![X]:(~creative(X)=>~happy(X)))&
(![X]:((strong(X)|humble(X))=>(quiet(X)<~>creative(X))))&
((~funny(alice))=>(~old(lucy)))&
(((~wise(mary)|~tall(mary)))<=>((quiet(paul)&~brave(paul))))&
(![X]:((brave(X)|~generous(X))=>~funny(X)))&
((strong(lucy)|brave(lucy)))&
(~old(lucy))&
((~happy(lucy)<~>old(lucy)))&
(?[X]:((kind(X)|quiet(X))))&
(?[X]:((~quiet(X)<~>wise(X))))&
(?[X]:((strong(X)|~humble(X))))&
((kind(lucy)<~>brave(lucy))) | brave(paul) | [
"p0",
"p5",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5482840102226865751566119
% SZS output start Proof for 5482840102226865751566119
1. ! [X0] : ((~funny(X0) | calm(X0)) => (~tall(X0) & rich(X0))) [input p0]
6. ! [X0] : ((~generous(X0) | funny(X0)) <=> (~funny(X0) <~> brave(X0))) [input p5]
14. (~tall(mary) | ~wise(mary)) <=> (~brave(paul) & quiet(paul)) [input p13]
15. ! [X0] : ((~generous(X0) | brave(X0)) => ~funny(X0)) [input p14]
23. brave(paul) [input hypothesis]
26. ! [X0] : ((~tall(X0) & rich(X0)) | (funny(X0) & ~calm(X0))) [ennf transformation 1]
37. ! [X0] : (~funny(X0) | (generous(X0) & ~brave(X0))) [ennf transformation 15]
41. ! [X0] : (((~generous(X0) | funny(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) & (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (generous(X0) & ~funny(X0)))) [nnf transformation 6]
42. ! [X0] : ((~generous(X0) | funny(X0) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) & (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (generous(X0) & ~funny(X0)))) [flattening 41]
51. ((~tall(mary) | ~wise(mary)) | (brave(paul) | ~quiet(paul))) & ((~brave(paul) & quiet(paul)) | (tall(mary) & wise(mary))) [nnf transformation 14]
52. (~tall(mary) | ~wise(mary) | brave(paul) | ~quiet(paul)) & ((~brave(paul) & quiet(paul)) | (tall(mary) & wise(mary))) [flattening 51]
65. ~tall(X0) | funny(X0) [cnf transformation 26]
76. brave(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 42]
100. ~brave(paul) | tall(mary) [cnf transformation 52]
102. ~funny(X0) | ~brave(X0) [cnf transformation 37]
114. brave(paul) [cnf transformation 23]
115. brave(X0) | ~funny(X0) [duplicate literal removal 76]
153. 9 <=> brave(paul) [avatar definition]
161. 11 <=> tall(mary) [avatar definition]
162. tall(mary) <- (11) [avatar component clause 161]
165. 11 | ~9 [avatar split clause 100,153,161]
169. ~funny(X0) [subsumption resolution 102,115]
219. 9 [avatar split clause 114,153]
224. funny(mary) <- (11) [resolution 65,162]
225. $false <- (11) [subsumption resolution 224,169]
226. ~11 [avatar contradiction clause 225]
227. $false [avatar sat refutation 165,219,226]
% SZS output end Proof for 5482840102226865751566119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not wise and not quiet then someone is both not funny and tall and vice versa. If john is either not rich or not calm then john is both not wise and not kind. Everyone who is both not strong and not generous is funny or curious and vice versa. Everyone who is both generous and not patient is not humble. If alice is both not old and old then paul is strong or wise and vice versa. If someone is either curious or generous then someone is either calm or happy. Everyone who is rich or not creative is both kind and not generous. If someone is funny then someone is not curious and vice versa. If someone is not rich or not creative then someone is funny or not quiet and vice versa. Everyone who is not rich is either not old or creative and vice versa. Everyone who is calm is generous. If someone is calm or rich then susan is either not quiet or creative and vice versa. Everyone who is brave or not brave is not brave and vice versa. If someone is both not quiet and not happy then john is not rich and vice versa. Everyone who is both not strong and not brave is both not funny and not brave. Everyone who is not funny or not humble is wise or not creative. Mary is either wise or kind. Someone is not humble. Alice is either curious or brave. Fred is either happy or not quiet. Someone is either kind or generous. | Fred is funny. | contradiction | (((~wise(fred)&~quiet(fred)))<=>(?[X]:((~funny(X)&tall(X)))))&
(((~rich(john)<~>~calm(john)))=>((~wise(john)&~kind(john))))&
(![X]:((~strong(X)&~generous(X))<=>(funny(X)|curious(X))))&
(![X]:((generous(X)&~patient(X))=>~humble(X)))&
(((~old(alice)&old(alice)))<=>((strong(paul)|wise(paul))))&
((?[X]:((curious(X)<~>generous(X))))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((rich(X)|~creative(X))=>(kind(X)&~generous(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((~rich(X)|~creative(X))))<=>(?[X]:((funny(X)|~quiet(X)))))&
(![X]:(~rich(X)<=>(~old(X)<~>creative(X))))&
(![X]:(calm(X)=>generous(X)))&
((?[X]:((calm(X)|rich(X))))<=>((~quiet(susan)<~>creative(susan))))&
(![X]:((brave(X)|~brave(X))<=>~brave(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>(~rich(john)))&
(![X]:((~strong(X)&~brave(X))=>(~funny(X)&~brave(X))))&
(![X]:((~funny(X)|~humble(X))=>(wise(X)|~creative(X))))&
((wise(mary)<~>kind(mary)))&
(?[X]:(~humble(X)))&
((curious(alice)<~>brave(alice)))&
((happy(fred)<~>~quiet(fred)))&
(?[X]:((kind(X)<~>generous(X)))) | funny(fred) | [
"p2",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2899663857808329401768380
% SZS output start Proof for 2899663857808329401768380
3. ! [X0] : ((~generous(X0) & ~strong(X0)) <=> (curious(X0) | funny(X0))) [input p2]
13. ! [X0] : ((~brave(X0) | brave(X0)) <=> ~brave(X0)) [input p12]
15. ! [X0] : ((~brave(X0) & ~strong(X0)) => (~brave(X0) & ~funny(X0))) [input p14]
22. funny(fred) [input hypothesis]
31. ! [X0] : ((~brave(X0) & ~funny(X0)) | (brave(X0) | strong(X0))) [ennf transformation 15]
32. ! [X0] : ((~brave(X0) & ~funny(X0)) | brave(X0) | strong(X0)) [flattening 31]
41. ! [X0] : (((~generous(X0) & ~strong(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (generous(X0) | strong(X0)))) [nnf transformation 3]
42. ! [X0] : (((~generous(X0) & ~strong(X0)) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | generous(X0) | strong(X0))) [flattening 41]
64. ! [X0] : (((~brave(X0) | brave(X0)) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [nnf transformation 13]
65. ! [X0] : ((~brave(X0) | brave(X0) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [flattening 64]
87. ~strong(X0) | ~funny(X0) [cnf transformation 42]
121. ~brave(X0) | ~brave(X0) [cnf transformation 65]
127. ~funny(X0) | brave(X0) | strong(X0) [cnf transformation 32]
140. funny(fred) [cnf transformation 22]
141. ~brave(X0) [duplicate literal removal 121]
233. 19 <=> ! [X3] : ~funny(X3) [avatar definition]
234. ~funny(X3) <- (19) [avatar component clause 233]
311. ~funny(X0) | strong(X0) [subsumption resolution 127,141]
312. ~funny(X0) [subsumption resolution 311,87]
313. 19 [avatar split clause 312,233]
341. $false <- (19) [resolution 234,140]
342. ~19 [avatar contradiction clause 341]
343. $false [avatar sat refutation 313,342]
% SZS output end Proof for 2899663857808329401768380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or humble then fred is both not funny and not rich.
Everyone who is either rich or not rich is both old and quiet and vice versa.
Everyone who is tall is not funny or not quiet and vice versa.
If someone is brave or quiet then someone is either calm or wise.
Everyone who is curious is either patient or not humble and vice versa.
If lucy is generous or not tall then someone is either not creative or not generous.
If paul is not generous then susan is calm.
If someone is both not brave and old then someone is happy or old and vice versa.
Everyone who is both not curious and not kind is either generous or not funny and vice versa.
If mary is old then someone is either not rich or creative and vice versa.
Everyone who is tall is not curious and vice versa.
Everyone who is both not rich and not patient is either rich or brave and vice versa.
If paul is not patient or strong then someone is not rich and vice versa.
Everyone who is either generous or curious is both not calm and calm.
Everyone who is both tall and brave is both wise and not tall and vice versa.
Everyone who is creative is not calm or wise and vice versa.
Someone is not funny.
Someone is either creative or not quiet.
Someone is not brave. | Lucy is not patient. | contradiction | ((?[X]:((kind(X)|humble(X))))=>((~funny(fred)&~rich(fred))))&
(![X]:((rich(X)<~>~rich(X))<=>(old(X)&quiet(X))))&
(![X]:(tall(X)<=>(~funny(X)|~quiet(X))))&
((?[X]:((brave(X)|quiet(X))))=>(?[X]:((calm(X)<~>wise(X)))))&
(![X]:(curious(X)<=>(patient(X)<~>~humble(X))))&
(((generous(lucy)|~tall(lucy)))=>(?[X]:((~creative(X)<~>~generous(X)))))&
((~generous(paul))=>(calm(susan)))&
((?[X]:((~brave(X)&old(X))))<=>(?[X]:((happy(X)|old(X)))))&
(![X]:((~curious(X)&~kind(X))<=>(generous(X)<~>~funny(X))))&
((old(mary))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:(tall(X)<=>~curious(X)))&
(![X]:((~rich(X)&~patient(X))<=>(rich(X)<~>brave(X))))&
(((~patient(paul)|strong(paul)))<=>(?[X]:(~rich(X))))&
(![X]:((generous(X)<~>curious(X))=>(~calm(X)&calm(X))))&
(![X]:((tall(X)&brave(X))<=>(wise(X)&~tall(X))))&
(![X]:(creative(X)<=>(~calm(X)|wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)<~>~quiet(X))))&
(?[X]:(~brave(X))) | ~patient(lucy) | [
"p2",
"p8",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4212809785828810821323418
% SZS output start Proof for 4212809785828810821323418
3. ! [X0] : (tall(X0) <=> (~quiet(X0) | ~funny(X0))) [input p2]
9. ! [X0] : ((~kind(X0) & ~curious(X0)) <=> (generous(X0) <~> ~funny(X0))) [input p8]
11. ! [X0] : (tall(X0) <=> ~curious(X0)) [input p10]
12. ! [X0] : ((~patient(X0) & ~rich(X0)) <=> (rich(X0) <~> brave(X0))) [input p11]
14. ! [X0] : ((generous(X0) <~> curious(X0)) => (calm(X0) & ~calm(X0))) [input p13]
15. ! [X0] : ((brave(X0) & tall(X0)) <=> (~tall(X0) & wise(X0))) [input p14]
20. ~patient(lucy) [input hypothesis]
27. ! [X0] : ((calm(X0) & ~calm(X0)) | (generous(X0) <=> curious(X0))) [ennf transformation 14]
30. ! [X0] : ((tall(X0) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | ~tall(X0))) [nnf transformation 3]
31. ! [X0] : ((tall(X0) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~tall(X0))) [flattening 30]
45. ! [X0] : (((~kind(X0) & ~curious(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (kind(X0) | curious(X0)))) [nnf transformation 9]
46. ! [X0] : (((~kind(X0) & ~curious(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | kind(X0) | curious(X0))) [flattening 45]
51. ! [X0] : ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))) [nnf transformation 11]
52. ! [X0] : (((~patient(X0) & ~rich(X0)) | ((rich(X0) | ~brave(X0)) & (brave(X0) | ~rich(X0)))) & (((~brave(X0) | ~rich(X0)) & (brave(X0) | rich(X0))) | (patient(X0) | rich(X0)))) [nnf transformation 12]
53. ! [X0] : (((~patient(X0) & ~rich(X0)) | ((rich(X0) | ~brave(X0)) & (brave(X0) | ~rich(X0)))) & (((~brave(X0) | ~rich(X0)) & (brave(X0) | rich(X0))) | patient(X0) | rich(X0))) [flattening 52]
59. ! [X0] : ((calm(X0) & ~calm(X0)) | ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) [nnf transformation 27]
60. ! [X0] : (((brave(X0) & tall(X0)) | (tall(X0) | ~wise(X0))) & ((~tall(X0) & wise(X0)) | (~brave(X0) | ~tall(X0)))) [nnf transformation 15]
61. ! [X0] : (((brave(X0) & tall(X0)) | tall(X0) | ~wise(X0)) & ((~tall(X0) & wise(X0)) | ~brave(X0) | ~tall(X0))) [flattening 60]
82. tall(X0) | funny(X0) [cnf transformation 31]
104. ~generous(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 46]
112. ~curious(X0) | ~tall(X0) [cnf transformation 51]
113. curious(X0) | tall(X0) [cnf transformation 51]
114. brave(X0) | rich(X0) | patient(X0) | rich(X0) [cnf transformation 53]
116. ~rich(X0) | brave(X0) | ~rich(X0) [cnf transformation 53]
123. ~calm(X0) | curious(X0) | ~generous(X0) [cnf transformation 59]
124. ~calm(X0) | generous(X0) | ~curious(X0) [cnf transformation 59]
125. ~generous(X0) | curious(X0) | calm(X0) [cnf transformation 59]
126. ~curious(X0) | generous(X0) | calm(X0) [cnf transformation 59]
128. ~tall(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 61]
138. ~patient(lucy) [cnf transformation 20]
139. ~brave(X0) | ~tall(X0) [duplicate literal removal 128]
141. brave(X0) | rich(X0) | patient(X0) [duplicate literal removal 114]
142. ~rich(X0) | brave(X0) [duplicate literal removal 116]
186. 8 <=> tall(lucy) [avatar definition]
187. ~tall(lucy) <- (~8) [avatar component clause 186]
199. 11 <=> generous(lucy) [avatar definition]
200. generous(lucy) <- (11) [avatar component clause 199]
201. ~generous(lucy) <- (~11) [avatar component clause 199]
227. patient(X0) | brave(X0) [subsumption resolution 141,142]
246. ~curious(X0) | generous(X0) [subsumption resolution 124,126]
247. ~generous(X0) | curious(X0) [subsumption resolution 123,125]
253. brave(lucy) [resolution 227,138]
255. ~tall(lucy) [resolution 253,139]
258. ~8 [avatar split clause 255,186]
259. funny(lucy) <- (~8) [resolution 187,82]
261. generous(X0) | tall(X0) [resolution 246,113]
282. 21 <=> curious(lucy) [avatar definition]
284. curious(lucy) <- (21) [avatar component clause 282]
331. tall(X2) | ~funny(X2) | ~curious(X2) [resolution 261,104]
333. tall(lucy) <- (~11) [resolution 261,201]
337. ~curious(X2) | ~funny(X2) [subsumption resolution 331,112]
338. $false <- (~8, ~11) [subsumption resolution 333,187]
339. 8 | 11 [avatar contradiction clause 338]
343. curious(lucy) <- (11) [resolution 200,247]
349. 21 | ~11 [avatar split clause 343,199,282]
389. ~funny(lucy) <- (21) [resolution 337,284]
391. $false <- (~8, 21) [subsumption resolution 389,259]
392. 8 | ~21 [avatar contradiction clause 391]
393. $false [avatar sat refutation 258,339,349,392]
% SZS output end Proof for 4212809785828810821323418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative or curious then someone is funny or calm.
Everyone who is both not old and strong is generous or not patient and vice versa.
Everyone who is both strong and brave is not creative.
Everyone who is both not generous and not curious is funny.
Everyone who is not strong is both not strong and patient and vice versa.
Everyone who is both not happy and tall is both not tall and not creative.
Everyone who is either not creative or happy is not rich or not tall.
If someone is both quiet and not tall then fred is wise or creative.
If alice is either not funny or not happy then paul is not funny or strong.
If susan is creative or generous then someone is both not wise and brave and vice versa.
Everyone who is either tall or not tall is either tall or generous and vice versa.
Everyone who is not tall is either not old or humble and vice versa.
Everyone who is both kind and happy is not quiet or brave.
Everyone who is funny or not strong is humble or happy and vice versa.
If mary is not patient then mary is old or not tall and vice versa.
Everyone who is not rich or not humble is not quiet or patient.
Susan is not creative.
Someone is not humble or not funny.
Mary is not rich.
Paul is either not generous or not funny.
Fred is both tall and not calm.
John is not generous or humble.
Someone is both creative and not tall.
Fred is either not kind or quiet. | John is generous. | contradiction | ((?[X]:((~creative(X)|curious(X))))=>(?[X]:((funny(X)|calm(X)))))&
(![X]:((~old(X)&strong(X))<=>(generous(X)|~patient(X))))&
(![X]:((strong(X)&brave(X))=>~creative(X)))&
(![X]:((~generous(X)&~curious(X))=>funny(X)))&
(![X]:(~strong(X)<=>(~strong(X)&patient(X))))&
(![X]:((~happy(X)&tall(X))=>(~tall(X)&~creative(X))))&
(![X]:((~creative(X)<~>happy(X))=>(~rich(X)|~tall(X))))&
((?[X]:((quiet(X)&~tall(X))))=>((wise(fred)|creative(fred))))&
(((~funny(alice)<~>~happy(alice)))=>((~funny(paul)|strong(paul))))&
(((creative(susan)|generous(susan)))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((tall(X)<~>~tall(X))<=>(tall(X)<~>generous(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>humble(X))))&
(![X]:((kind(X)&happy(X))=>(~quiet(X)|brave(X))))&
(![X]:((funny(X)|~strong(X))<=>(humble(X)|happy(X))))&
((~patient(mary))<=>((old(mary)|~tall(mary))))&
(![X]:((~rich(X)|~humble(X))=>(~quiet(X)|patient(X))))&
(~creative(susan))&
(?[X]:((~humble(X)|~funny(X))))&
(~rich(mary))&
((~generous(paul)<~>~funny(paul)))&
((tall(fred)&~calm(fred)))&
((~generous(john)|humble(john)))&
(?[X]:((creative(X)&~tall(X))))&
((~kind(fred)<~>quiet(fred))) | generous(john) | [
"p1",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5641027633305520776458507
% SZS output start Proof for 5641027633305520776458507
2. ! [X0] : ((strong(X0) & ~old(X0)) <=> (~patient(X0) | generous(X0))) [input p1]
11. ! [X0] : ((tall(X0) <~> ~tall(X0)) <=> (tall(X0) <~> generous(X0))) [input p10]
12. ! [X0] : (~tall(X0) <=> (~old(X0) <~> humble(X0))) [input p11]
22. humble(john) | ~generous(john) [input p21]
25. generous(john) [input hypothesis]
47. ! [X0] : (((strong(X0) & ~old(X0)) | (patient(X0) & ~generous(X0))) & ((~patient(X0) | generous(X0)) | (~strong(X0) | old(X0)))) [nnf transformation 2]
48. ! [X0] : (((strong(X0) & ~old(X0)) | (patient(X0) & ~generous(X0))) & (~patient(X0) | generous(X0) | ~strong(X0) | old(X0))) [flattening 47]
58. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0)))) & (((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [nnf transformation 11]
59. ! [X0] : ((~tall(X0) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) & (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | tall(X0))) [nnf transformation 12]
73. ~generous(X0) | ~old(X0) [cnf transformation 48]
96. ~generous(X0) | ~tall(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 58]
103. ~humble(X0) | old(X0) | tall(X0) [cnf transformation 59]
123. humble(john) | ~generous(john) [cnf transformation 22]
128. generous(john) [cnf transformation 25]
131. ~tall(X0) | ~generous(X0) [duplicate literal removal 96]
238. 22 <=> generous(john) [avatar definition]
239. generous(john) <- (22) [avatar component clause 238]
242. 23 <=> humble(john) [avatar definition]
244. humble(john) <- (23) [avatar component clause 242]
245. ~22 | 23 [avatar split clause 123,242,238]
256. 22 [avatar split clause 128,238]
257. ~old(john) <- (22) [resolution 73,239]
310. old(john) | tall(john) <- (23) [resolution 103,244]
311. tall(john) <- (22, 23) [subsumption resolution 310,257]
326. ~generous(john) <- (22, 23) [resolution 311,131]
337. $false <- (22, 23) [subsumption resolution 326,239]
338. ~22 | ~23 [avatar contradiction clause 337]
339. $false [avatar sat refutation 245,256,338]
% SZS output end Proof for 5641027633305520776458507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or generous is not creative.
Everyone who is both tall and not creative is both not calm and not creative.
Everyone who is not curious is strong and vice versa.
If someone is both not brave and not calm then lucy is not humble or not tall and vice versa.
Everyone who is either not quiet or calm is quiet.
If someone is not generous or not quiet then someone is curious and vice versa.
Everyone who is either strong or creative is wise or not strong.
Everyone who is not humble or not generous is either not old or brave and vice versa.
Everyone who is both curious and not happy is either not calm or creative and vice versa.
Everyone who is calm is rich or quiet and vice versa.
If someone is kind or brave then someone is either old or not funny.
Everyone who is either not kind or not tall is both not wise and not humble and vice versa.
If someone is curious then susan is tall.
If someone is both curious and not generous then mary is kind or calm and vice versa.
If susan is happy or funny then someone is either generous or curious and vice versa.
If mary is either quiet or not happy then lucy is either wise or creative.
Someone is not wise.
Mary is not happy.
John is both generous and not wise.
John is creative or not wise.
Someone is both not generous and not strong.
Someone is either generous or kind.
Mary is either not wise or calm.
Someone is both not kind and not quiet. | Mary is quiet. | neutral | (![X]:((~old(X)|generous(X))=>~creative(X)))&
(![X]:((tall(X)&~creative(X))=>(~calm(X)&~creative(X))))&
(![X]:(~curious(X)<=>strong(X)))&
((?[X]:((~brave(X)&~calm(X))))<=>((~humble(lucy)|~tall(lucy))))&
(![X]:((~quiet(X)<~>calm(X))=>quiet(X)))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:(curious(X))))&
(![X]:((strong(X)<~>creative(X))=>(wise(X)|~strong(X))))&
(![X]:((~humble(X)|~generous(X))<=>(~old(X)<~>brave(X))))&
(![X]:((curious(X)&~happy(X))<=>(~calm(X)<~>creative(X))))&
(![X]:(calm(X)<=>(rich(X)|quiet(X))))&
((?[X]:((kind(X)|brave(X))))=>(?[X]:((old(X)<~>~funny(X)))))&
(![X]:((~kind(X)<~>~tall(X))<=>(~wise(X)&~humble(X))))&
((?[X]:(curious(X)))=>(tall(susan)))&
((?[X]:((curious(X)&~generous(X))))<=>((kind(mary)|calm(mary))))&
(((happy(susan)|funny(susan)))<=>(?[X]:((generous(X)<~>curious(X)))))&
(((quiet(mary)<~>~happy(mary)))=>((wise(lucy)<~>creative(lucy))))&
(?[X]:(~wise(X)))&
(~happy(mary))&
((generous(john)&~wise(john)))&
((creative(john)|~wise(john)))&
(?[X]:((~generous(X)&~strong(X))))&
(?[X]:((generous(X)<~>kind(X))))&
((~wise(mary)<~>calm(mary)))&
(?[X]:((~kind(X)&~quiet(X)))) | quiet(mary) | [] | null | 0 |
Everyone who is not calm or rich is not funny or not curious and vice versa.
Everyone who is both not happy and wise is either not quiet or not funny and vice versa.
Everyone who is either tall or strong is not kind and vice versa.
If mary is not funny then someone is not calm.
If someone is both not creative and happy then someone is both generous and not creative and vice versa.
Everyone who is not generous or generous is happy.
Everyone who is not patient or funny is either curious or calm.
Everyone who is not curious is rich and vice versa.
Everyone who is both not brave and tall is not kind.
Everyone who is quiet is not patient.
If someone is old or strong then john is both not happy and not calm.
Everyone who is not funny or not rich is not curious or generous and vice versa.
If someone is quiet or humble then john is either generous or not creative and vice versa.
Everyone who is either not curious or not generous is either not calm or not kind and vice versa.
If someone is either humble or old then someone is both not wise and tall.
Everyone who is not generous or not curious is either not funny or not quiet and vice versa.
Alice is both not rich and not quiet.
Someone is humble.
Fred is not calm or wise. | Alice is happy. | entailment | (![X]:((~calm(X)|rich(X))<=>(~funny(X)|~curious(X))))&
(![X]:((~happy(X)&wise(X))<=>(~quiet(X)<~>~funny(X))))&
(![X]:((tall(X)<~>strong(X))<=>~kind(X)))&
((~funny(mary))=>(?[X]:(~calm(X))))&
((?[X]:((~creative(X)&happy(X))))<=>(?[X]:((generous(X)&~creative(X)))))&
(![X]:((~generous(X)|generous(X))=>happy(X)))&
(![X]:((~patient(X)|funny(X))=>(curious(X)<~>calm(X))))&
(![X]:(~curious(X)<=>rich(X)))&
(![X]:((~brave(X)&tall(X))=>~kind(X)))&
(![X]:(quiet(X)=>~patient(X)))&
((?[X]:((old(X)|strong(X))))=>((~happy(john)&~calm(john))))&
(![X]:((~funny(X)|~rich(X))<=>(~curious(X)|generous(X))))&
((?[X]:((quiet(X)|humble(X))))<=>((generous(john)<~>~creative(john))))&
(![X]:((~curious(X)<~>~generous(X))<=>(~calm(X)<~>~kind(X))))&
((?[X]:((humble(X)<~>old(X))))=>(?[X]:((~wise(X)&tall(X)))))&
(![X]:((~generous(X)|~curious(X))<=>(~funny(X)<~>~quiet(X))))&
((~rich(alice)&~quiet(alice)))&
(?[X]:(humble(X)))&
((~calm(fred)|wise(fred))) | happy(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3334222702753094625265061
% SZS output start Proof for 3334222702753094625265061
6. ! [X0] : ((generous(X0) | ~generous(X0)) => happy(X0)) [input p5]
20. ~happy(alice) [input hypothesis]
25. ! [X0] : (happy(X0) | (~generous(X0) & generous(X0))) [ennf transformation 6]
78. happy(X0) | generous(X0) [cnf transformation 25]
79. happy(X0) | ~generous(X0) [cnf transformation 25]
123. ~happy(alice) [cnf transformation 20]
159. happy(X0) [subsumption resolution 78,79]
245. $false [subsumption resolution 123,159]
% SZS output end Proof for 3334222702753094625265061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or wise is patient and vice versa. Everyone who is creative or not old is funny. If alice is either tall or not generous then someone is not strong or generous and vice versa. Everyone who is not quiet is both not curious and brave and vice versa. If alice is strong then fred is not calm or not kind and vice versa. If fred is both not wise and curious then susan is both not brave and not happy and vice versa. If john is not calm then someone is either curious or rich. Everyone who is wise or not quiet is both not rich and creative. If someone is both calm and patient then alice is not happy or quiet. If susan is not brave or humble then alice is not happy or not generous and vice versa. Everyone who is either humble or quiet is either not patient or curious and vice versa. Everyone who is both not patient and not brave is not curious or not tall and vice versa. Everyone who is either not happy or humble is not rich and vice versa. Everyone who is strong is not curious and vice versa. Everyone who is either old or strong is either not funny or patient and vice versa. Everyone who is both rich and kind is both not quiet and brave. Someone is not old or creative. Someone is both strong and not happy. Someone is either not strong or humble. Someone is either not kind or brave. John is creative. Susan is humble or not wise. Mary is either not curious or brave. John is both creative and patient. | Alice is not funny. | contradiction | (![X]:((~strong(X)<~>wise(X))<=>patient(X)))&
(![X]:((creative(X)|~old(X))=>funny(X)))&
(((tall(alice)<~>~generous(alice)))<=>(?[X]:((~strong(X)|generous(X)))))&
(![X]:(~quiet(X)<=>(~curious(X)&brave(X))))&
((strong(alice))<=>((~calm(fred)|~kind(fred))))&
(((~wise(fred)&curious(fred)))<=>((~brave(susan)&~happy(susan))))&
((~calm(john))=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:((wise(X)|~quiet(X))=>(~rich(X)&creative(X))))&
((?[X]:((calm(X)&patient(X))))=>((~happy(alice)|quiet(alice))))&
(((~brave(susan)|humble(susan)))<=>((~happy(alice)|~generous(alice))))&
(![X]:((humble(X)<~>quiet(X))<=>(~patient(X)<~>curious(X))))&
(![X]:((~patient(X)&~brave(X))<=>(~curious(X)|~tall(X))))&
(![X]:((~happy(X)<~>humble(X))<=>~rich(X)))&
(![X]:(strong(X)<=>~curious(X)))&
(![X]:((old(X)<~>strong(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((rich(X)&kind(X))=>(~quiet(X)&brave(X))))&
(?[X]:((~old(X)|creative(X))))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:((~kind(X)<~>brave(X))))&
(creative(john))&
((humble(susan)|~wise(susan)))&
((~curious(mary)<~>brave(mary)))&
((creative(john)&patient(john))) | ~funny(alice) | [
"p0",
"p1",
"p7",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3436789672218006690310293
% SZS output start Proof for 3436789672218006690310293
1. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> patient(X0)) [input p0]
2. ! [X0] : ((~old(X0) | creative(X0)) => funny(X0)) [input p1]
8. ! [X0] : ((~quiet(X0) | wise(X0)) => (creative(X0) & ~rich(X0))) [input p7]
12. ! [X0] : ((~brave(X0) & ~patient(X0)) <=> (~tall(X0) | ~curious(X0))) [input p11]
14. ! [X0] : (strong(X0) <=> ~curious(X0)) [input p13]
15. ! [X0] : ((old(X0) <~> strong(X0)) <=> (~funny(X0) <~> patient(X0))) [input p14]
25. ~funny(alice) [input hypothesis]
26. ! [X0] : (funny(X0) | (old(X0) & ~creative(X0))) [ennf transformation 2]
28. ! [X0] : ((creative(X0) & ~rich(X0)) | (quiet(X0) & ~wise(X0))) [ennf transformation 8]
33. ! [X0] : ((((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~patient(X0)) & (patient(X0) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))))) [nnf transformation 1]
50. ! [X0] : (((~brave(X0) & ~patient(X0)) | (tall(X0) & curious(X0))) & ((~tall(X0) | ~curious(X0)) | (brave(X0) | patient(X0)))) [nnf transformation 12]
51. ! [X0] : (((~brave(X0) & ~patient(X0)) | (tall(X0) & curious(X0))) & (~tall(X0) | ~curious(X0) | brave(X0) | patient(X0))) [flattening 50]
53. ! [X0] : ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))) [nnf transformation 14]
54. ! [X0] : ((((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))))) [nnf transformation 15]
66. patient(X0) | wise(X0) | strong(X0) [cnf transformation 33]
70. ~creative(X0) | funny(X0) [cnf transformation 26]
71. funny(X0) | old(X0) [cnf transformation 26]
92. ~wise(X0) | creative(X0) [cnf transformation 28]
108. ~patient(X0) | curious(X0) [cnf transformation 51]
116. ~curious(X0) | ~strong(X0) [cnf transformation 53]
120. ~patient(X0) | funny(X0) | strong(X0) | ~old(X0) [cnf transformation 54]
124. ~strong(X0) | ~old(X0) | patient(X0) | funny(X0) [cnf transformation 54]
141. ~funny(alice) [cnf transformation 25]
175. 8 <=> strong(alice) [avatar definition]
176. ~strong(alice) <- (~8) [avatar component clause 175]
177. strong(alice) <- (8) [avatar component clause 175]
243. ~strong(X0) | patient(X0) | funny(X0) [subsumption resolution 124,71]
245. ~patient(X0) | funny(X0) | strong(X0) [subsumption resolution 120,71]
394. funny(X0) | strong(X0) | wise(X0) | strong(X0) [resolution 245,66]
395. funny(X0) | strong(X0) | wise(X0) [duplicate literal removal 394]
491. strong(alice) | wise(alice) [resolution 395,141]
558. wise(alice) <- (~8) [subsumption resolution 491,176]
564. 44 <=> patient(alice) [avatar definition]
566. patient(alice) <- (44) [avatar component clause 564]
573. creative(alice) <- (~8) [resolution 558,92]
616. funny(alice) <- (~8) [resolution 573,70]
617. $false <- (~8) [subsumption resolution 616,141]
618. 8 [avatar contradiction clause 617]
626. patient(alice) | funny(alice) <- (8) [resolution 177,243]
630. patient(alice) <- (8) [subsumption resolution 626,141]
631. 44 | ~8 [avatar split clause 630,175,564]
637. curious(alice) <- (44) [resolution 566,108]
651. ~strong(alice) <- (44) [resolution 637,116]
653. $false <- (8, 44) [subsumption resolution 651,177]
654. ~8 | ~44 [avatar contradiction clause 653]
655. $false [avatar sat refutation 618,631,654]
% SZS output end Proof for 3436789672218006690310293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not wise and brave then someone is both not kind and not rich and vice versa. Everyone who is both generous and funny is calm or not funny. Everyone who is not funny or funny is calm. Everyone who is both creative and not humble is both generous and not creative and vice versa. If someone is generous or not curious then alice is both humble and quiet. Everyone who is funny is patient. Everyone who is not quiet is brave or not kind and vice versa. Everyone who is both patient and brave is both calm and not tall. Everyone who is both not strong and quiet is not kind. If john is both not happy and not wise then someone is either calm or not curious and vice versa. Everyone who is both old and generous is either not patient or not funny and vice versa. If someone is either not kind or not creative then someone is both not quiet and generous. Everyone who is either not happy or rich is both tall and not brave and vice versa. If susan is not rich or brave then someone is not brave or curious and vice versa. Everyone who is either quiet or not brave is either not funny or tall and vice versa. If paul is rich or not strong then mary is either strong or not funny and vice versa. Mary is either calm or humble. Fred is both rich and curious. Someone is not humble or wise. Someone is not creative or not patient. Susan is both creative and not strong. John is not creative. John is either strong or not quiet. Paul is not creative or generous. | Susan is not creative. | contradiction | (((~wise(lucy)&brave(lucy)))<=>(?[X]:((~kind(X)&~rich(X)))))&
(![X]:((generous(X)&funny(X))=>(calm(X)|~funny(X))))&
(![X]:((~funny(X)|funny(X))=>calm(X)))&
(![X]:((creative(X)&~humble(X))<=>(generous(X)&~creative(X))))&
((?[X]:((generous(X)|~curious(X))))=>((humble(alice)&quiet(alice))))&
(![X]:(funny(X)=>patient(X)))&
(![X]:(~quiet(X)<=>(brave(X)|~kind(X))))&
(![X]:((patient(X)&brave(X))=>(calm(X)&~tall(X))))&
(![X]:((~strong(X)&quiet(X))=>~kind(X)))&
(((~happy(john)&~wise(john)))<=>(?[X]:((calm(X)<~>~curious(X)))))&
(![X]:((old(X)&generous(X))<=>(~patient(X)<~>~funny(X))))&
((?[X]:((~kind(X)<~>~creative(X))))=>(?[X]:((~quiet(X)&generous(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(tall(X)&~brave(X))))&
(((~rich(susan)|brave(susan)))<=>(?[X]:((~brave(X)|curious(X)))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~funny(X)<~>tall(X))))&
(((rich(paul)|~strong(paul)))<=>((strong(mary)<~>~funny(mary))))&
((calm(mary)<~>humble(mary)))&
((rich(fred)&curious(fred)))&
(?[X]:((~humble(X)|wise(X))))&
(?[X]:((~creative(X)|~patient(X))))&
((creative(susan)&~strong(susan)))&
(~creative(john))&
((strong(john)<~>~quiet(john)))&
((~creative(paul)|generous(paul))) | ~creative(susan) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7850341380643033469486092
% SZS output start Proof for 7850341380643033469486092
21. ~strong(susan) & creative(susan) [input p20]
25. ~creative(susan) [input hypothesis]
141. creative(susan) [cnf transformation 21]
147. ~creative(susan) [cnf transformation 25]
321. $false [subsumption resolution 147,141]
% SZS output end Proof for 7850341380643033469486092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or not old is calm.
Everyone who is either old or curious is both happy and calm.
Everyone who is both not creative and brave is kind.
If someone is generous or tall then someone is patient or not humble and vice versa.
If susan is not old or not quiet then someone is generous and vice versa.
Everyone who is both not generous and quiet is both not quiet and not tall.
Everyone who is both curious and not generous is quiet and vice versa.
Everyone who is either generous or patient is not rich or not brave.
Everyone who is happy or curious is both not tall and not calm.
If someone is both not patient and patient then someone is both not curious and not kind and vice versa.
Everyone who is either old or brave is not curious or happy and vice versa.
If fred is not kind or not quiet then someone is either rich or tall and vice versa.
Everyone who is both strong and not kind is generous or not patient.
Everyone who is not old or not generous is either not curious or strong and vice versa.
If susan is not patient then someone is not brave or generous.
Everyone who is quiet is either curious or not old.
Alice is not patient.
Someone is either rich or not wise.
Someone is both calm and not happy.
Someone is either not happy or not funny.
Someone is not strong or not kind.
Alice is calm.
Someone is either tall or quiet.
Mary is not funny or not humble. | Alice is strong. | contradiction | (![X]:((~happy(X)<~>~old(X))=>calm(X)))&
(![X]:((old(X)<~>curious(X))=>(happy(X)&calm(X))))&
(![X]:((~creative(X)&brave(X))=>kind(X)))&
((?[X]:((generous(X)|tall(X))))<=>(?[X]:((patient(X)|~humble(X)))))&
(((~old(susan)|~quiet(susan)))<=>(?[X]:(generous(X))))&
(![X]:((~generous(X)&quiet(X))=>(~quiet(X)&~tall(X))))&
(![X]:((curious(X)&~generous(X))<=>quiet(X)))&
(![X]:((generous(X)<~>patient(X))=>(~rich(X)|~brave(X))))&
(![X]:((happy(X)|curious(X))=>(~tall(X)&~calm(X))))&
((?[X]:((~patient(X)&patient(X))))<=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:((old(X)<~>brave(X))<=>(~curious(X)|happy(X))))&
(((~kind(fred)|~quiet(fred)))<=>(?[X]:((rich(X)<~>tall(X)))))&
(![X]:((strong(X)&~kind(X))=>(generous(X)|~patient(X))))&
(![X]:((~old(X)|~generous(X))<=>(~curious(X)<~>strong(X))))&
((~patient(susan))=>(?[X]:((~brave(X)|generous(X)))))&
(![X]:(quiet(X)=>(curious(X)<~>~old(X))))&
(~patient(alice))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:((calm(X)&~happy(X))))&
(?[X]:((~happy(X)<~>~funny(X))))&
(?[X]:((~strong(X)|~kind(X))))&
(calm(alice))&
(?[X]:((tall(X)<~>quiet(X))))&
((~funny(mary)|~humble(mary))) | strong(alice) | [
"p1",
"p8",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 742833678625680727578952
% SZS output start Proof for 742833678625680727578952
2. ! [X0] : ((old(X0) <~> curious(X0)) => (calm(X0) & happy(X0))) [input p1]
9. ! [X0] : ((curious(X0) | happy(X0)) => (~calm(X0) & ~tall(X0))) [input p8]
14. ! [X0] : ((~generous(X0) | ~old(X0)) <=> (~curious(X0) <~> strong(X0))) [input p13]
22. calm(alice) [input p21]
25. strong(alice) [input hypothesis]
30. ! [X0] : ((calm(X0) & happy(X0)) | (old(X0) <=> curious(X0))) [ennf transformation 2]
35. ! [X0] : ((~calm(X0) & ~tall(X0)) | (~curious(X0) & ~happy(X0))) [ennf transformation 9]
41. ! [X0] : ((calm(X0) & happy(X0)) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0)))) [nnf transformation 30]
67. ! [X0] : (((~generous(X0) | ~old(X0)) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0)))) & (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | (generous(X0) & old(X0)))) [nnf transformation 14]
68. ! [X0] : ((~generous(X0) | ~old(X0) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0)))) & (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | (generous(X0) & old(X0)))) [flattening 67]
87. ~old(X0) | curious(X0) | happy(X0) [cnf transformation 41]
107. ~calm(X0) | ~happy(X0) [cnf transformation 35]
108. ~curious(X0) | ~calm(X0) [cnf transformation 35]
128. ~strong(X0) | curious(X0) | old(X0) [cnf transformation 68]
143. calm(alice) [cnf transformation 22]
147. strong(alice) [cnf transformation 25]
287. ~happy(alice) [resolution 107,143]
338. curious(alice) | old(alice) [resolution 128,147]
340. 36 <=> old(alice) [avatar definition]
342. old(alice) <- (36) [avatar component clause 340]
344. 37 <=> curious(alice) [avatar definition]
346. curious(alice) <- (37) [avatar component clause 344]
347. 36 | 37 [avatar split clause 338,344,340]
349. curious(alice) | happy(alice) <- (36) [resolution 342,87]
351. curious(alice) <- (36) [subsumption resolution 349,287]
352. 37 | ~36 [avatar split clause 351,340,344]
358. ~calm(alice) <- (37) [resolution 346,108]
360. $false <- (37) [subsumption resolution 358,143]
361. ~37 [avatar contradiction clause 360]
362. $false [avatar sat refutation 347,352,361]
% SZS output end Proof for 742833678625680727578952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or funny is both patient and not old.
If john is either not patient or not kind then someone is both not tall and happy.
Everyone who is either brave or kind is not happy.
If someone is either generous or funny then alice is not generous and vice versa.
If paul is not creative then mary is not curious or generous.
Everyone who is not generous or calm is both not quiet and creative.
If someone is either not calm or not humble then mary is not patient and vice versa.
Everyone who is calm is both happy and tall and vice versa.
Everyone who is either old or not quiet is either rich or not quiet and vice versa.
If john is not old then susan is not brave or not kind and vice versa.
If susan is not wise or curious then lucy is not quiet.
If lucy is both calm and not quiet then susan is either tall or not strong.
Everyone who is funny is humble or not wise and vice versa.
Everyone who is not creative or quiet is not creative.
Everyone who is both wise and curious is either not humble or generous and vice versa.
Everyone who is either not kind or strong is both not happy and not wise and vice versa.
Lucy is either not creative or not curious.
John is both humble and not creative.
Someone is either not kind or not rich.
Someone is brave.
Fred is both quiet and not strong.
Someone is humble or funny.
Alice is not tall.
Someone is not strong. | John is rich. | contradiction | (![X]:((~rich(X)<~>funny(X))=>(patient(X)&~old(X))))&
(((~patient(john)<~>~kind(john)))=>(?[X]:((~tall(X)&happy(X)))))&
(![X]:((brave(X)<~>kind(X))=>~happy(X)))&
((?[X]:((generous(X)<~>funny(X))))<=>(~generous(alice)))&
((~creative(paul))=>((~curious(mary)|generous(mary))))&
(![X]:((~generous(X)|calm(X))=>(~quiet(X)&creative(X))))&
((?[X]:((~calm(X)<~>~humble(X))))<=>(~patient(mary)))&
(![X]:(calm(X)<=>(happy(X)&tall(X))))&
(![X]:((old(X)<~>~quiet(X))<=>(rich(X)<~>~quiet(X))))&
((~old(john))<=>((~brave(susan)|~kind(susan))))&
(((~wise(susan)|curious(susan)))=>(~quiet(lucy)))&
(((calm(lucy)&~quiet(lucy)))=>((tall(susan)<~>~strong(susan))))&
(![X]:(funny(X)<=>(humble(X)|~wise(X))))&
(![X]:((~creative(X)|quiet(X))=>~creative(X)))&
(![X]:((wise(X)&curious(X))<=>(~humble(X)<~>generous(X))))&
(![X]:((~kind(X)<~>strong(X))<=>(~happy(X)&~wise(X))))&
((~creative(lucy)<~>~curious(lucy)))&
((humble(john)&~creative(john)))&
(?[X]:((~kind(X)<~>~rich(X))))&
(?[X]:(brave(X)))&
((quiet(fred)&~strong(fred)))&
(?[X]:((humble(X)|funny(X))))&
(~tall(alice))&
(?[X]:(~strong(X))) | rich(john) | [
"p0",
"p8",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4673660467729360611757057
% SZS output start Proof for 4673660467729360611757057
1. ! [X0] : ((~rich(X0) <~> funny(X0)) => (~old(X0) & patient(X0))) [input p0]
9. ! [X0] : ((old(X0) <~> ~quiet(X0)) <=> (rich(X0) <~> ~quiet(X0))) [input p8]
13. ! [X0] : (funny(X0) <=> (~wise(X0) | humble(X0))) [input p12]
18. ~creative(john) & humble(john) [input p17]
25. rich(john) [input hypothesis]
26. ! [X0] : ((~old(X0) & patient(X0)) | (~rich(X0) <=> funny(X0))) [ennf transformation 1]
36. ! [X0] : ((~old(X0) & patient(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) [nnf transformation 26]
51. ! [X0] : ((((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0)))) & (((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0))))) [nnf transformation 9]
55. ! [X0] : ((funny(X0) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | ~funny(X0))) [nnf transformation 13]
56. ! [X0] : ((funny(X0) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | ~funny(X0))) [flattening 55]
74. ~old(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 36]
100. quiet(X0) | ~rich(X0) | old(X0) | quiet(X0) [cnf transformation 51]
101. ~quiet(X0) | old(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 51]
113. ~humble(X0) | funny(X0) [cnf transformation 56]
131. humble(john) [cnf transformation 18]
141. rich(john) [cnf transformation 25]
143. quiet(X0) | ~rich(X0) | old(X0) [duplicate literal removal 100]
144. ~quiet(X0) | old(X0) | ~rich(X0) [duplicate literal removal 101]
223. ~rich(X0) | old(X0) [subsumption resolution 143,144]
230. 19 <=> old(john) [avatar definition]
231. old(john) <- (19) [avatar component clause 230]
297. funny(john) [resolution 113,131]
300. old(john) [resolution 223,141]
303. 19 [avatar split clause 300,230]
344. ~rich(john) | ~funny(john) <- (19) [resolution 74,231]
345. ~funny(john) <- (19) [subsumption resolution 344,141]
346. $false <- (19) [subsumption resolution 345,297]
347. ~19 [avatar contradiction clause 346]
348. $false [avatar sat refutation 303,347]
% SZS output end Proof for 4673660467729360611757057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or wise then someone is both not quiet and tall and vice versa.
Everyone who is not quiet is both tall and old.
If someone is either funny or not tall then someone is not creative or not rich and vice versa.
Everyone who is either quiet or not calm is both not strong and not quiet and vice versa.
Everyone who is wise or calm is not funny and vice versa.
If someone is both humble and not patient then john is both quiet and creative and vice versa.
If someone is not brave or not patient then alice is rich or humble.
If mary is both humble and not patient then lucy is old or not tall and vice versa.
If lucy is both not quiet and not creative then paul is either calm or brave and vice versa.
Everyone who is both curious and not strong is either not wise or curious.
Everyone who is either not calm or not generous is not brave or not rich and vice versa.
If lucy is not old then someone is not kind and vice versa.
Everyone who is either happy or not humble is not happy and vice versa.
Everyone who is humble or rich is either calm or brave and vice versa.
Everyone who is not humble or tall is either not brave or quiet.
If someone is both tall and patient then someone is not happy.
Someone is not old.
Fred is either generous or patient.
Alice is not funny or not humble.
Susan is curious.
Someone is both rich and quiet.
Susan is not quiet. | Susan is funny. | contradiction | (((~old(alice)<~>wise(alice)))<=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:(~quiet(X)=>(tall(X)&old(X))))&
((?[X]:((funny(X)<~>~tall(X))))<=>(?[X]:((~creative(X)|~rich(X)))))&
(![X]:((quiet(X)<~>~calm(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((wise(X)|calm(X))<=>~funny(X)))&
((?[X]:((humble(X)&~patient(X))))<=>((quiet(john)&creative(john))))&
((?[X]:((~brave(X)|~patient(X))))=>((rich(alice)|humble(alice))))&
(((humble(mary)&~patient(mary)))<=>((old(lucy)|~tall(lucy))))&
(((~quiet(lucy)&~creative(lucy)))<=>((calm(paul)<~>brave(paul))))&
(![X]:((curious(X)&~strong(X))=>(~wise(X)<~>curious(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~brave(X)|~rich(X))))&
((~old(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((happy(X)<~>~humble(X))<=>~happy(X)))&
(![X]:((humble(X)|rich(X))<=>(calm(X)<~>brave(X))))&
(![X]:((~humble(X)|tall(X))=>(~brave(X)<~>quiet(X))))&
((?[X]:((tall(X)&patient(X))))=>(?[X]:(~happy(X))))&
(?[X]:(~old(X)))&
((generous(fred)<~>patient(fred)))&
((~funny(alice)|~humble(alice)))&
(curious(susan))&
(?[X]:((rich(X)&quiet(X))))&
(~quiet(susan)) | funny(susan) | [
"p3",
"p4",
"p9",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5092273708528206406686223
% SZS output start Proof for 5092273708528206406686223
4. ! [X0] : ((quiet(X0) <~> ~calm(X0)) <=> (~quiet(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((calm(X0) | wise(X0)) <=> ~funny(X0)) [input p4]
10. ! [X0] : ((~strong(X0) & curious(X0)) => (~wise(X0) <~> curious(X0))) [input p9]
20. curious(susan) [input p19]
22. ~quiet(susan) [input p21]
23. funny(susan) [input hypothesis]
29. ! [X0] : ((~wise(X0) <~> curious(X0)) | (strong(X0) | ~curious(X0))) [ennf transformation 10]
30. ! [X0] : ((~wise(X0) <~> curious(X0)) | strong(X0) | ~curious(X0)) [flattening 29]
42. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | (quiet(X0) | strong(X0))) & ((~quiet(X0) & ~strong(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [nnf transformation 4]
43. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | quiet(X0) | strong(X0)) & ((~quiet(X0) & ~strong(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [flattening 42]
44. ! [X0] : (((calm(X0) | wise(X0)) | funny(X0)) & (~funny(X0) | (~calm(X0) & ~wise(X0)))) [nnf transformation 5]
45. ! [X0] : ((calm(X0) | wise(X0) | funny(X0)) & (~funny(X0) | (~calm(X0) & ~wise(X0)))) [flattening 44]
55. ! [X0] : (((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | strong(X0) | ~curious(X0)) [nnf transformation 30]
89. ~strong(X0) | quiet(X0) | calm(X0) [cnf transformation 43]
94. ~funny(X0) | ~wise(X0) [cnf transformation 45]
95. ~calm(X0) | ~funny(X0) [cnf transformation 45]
115. ~curious(X0) | wise(X0) | strong(X0) | ~curious(X0) [cnf transformation 55]
143. curious(susan) [cnf transformation 20]
146. ~quiet(susan) [cnf transformation 22]
147. funny(susan) [cnf transformation 23]
150. ~curious(X0) | wise(X0) | strong(X0) [duplicate literal removal 115]
334. ~wise(susan) [resolution 94,147]
434. wise(susan) | strong(susan) [resolution 150,143]
435. strong(susan) [subsumption resolution 434,334]
454. quiet(susan) | calm(susan) [resolution 435,89]
455. calm(susan) [subsumption resolution 454,146]
574. ~funny(susan) [resolution 455,95]
584. $false [subsumption resolution 574,147]
% SZS output end Proof for 5092273708528206406686223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either not quiet or calm and vice versa. If someone is both not tall and not strong then someone is both creative and not tall and vice versa. If someone is both brave and not generous then someone is not brave or not patient. If someone is either funny or not creative then susan is both kind and not rich and vice versa. If someone is not brave then alice is quiet or not calm and vice versa. If someone is both tall and patient then fred is not creative. If paul is not kind or not funny then alice is not strong or brave. If someone is both not funny and not curious then someone is not curious. Everyone who is both not calm and not curious is curious or not old and vice versa. If fred is either curious or generous then someone is either not wise or not quiet. Everyone who is both not happy and happy is not happy or not humble and vice versa. If someone is not old or not wise then someone is not calm or wise and vice versa. Everyone who is curious or kind is both not generous and not calm. If someone is both not creative and calm then someone is both happy and patient and vice versa. If someone is either not calm or funny then someone is rich and vice versa. If paul is either not wise or tall then lucy is not strong or not happy and vice versa. Someone is brave. Alice is not calm. Someone is either brave or strong. Lucy is either not generous or not patient. Mary is quiet. | Lucy is old. | contradiction | (![X]:(~quiet(X)<=>(~quiet(X)<~>calm(X))))&
((?[X]:((~tall(X)&~strong(X))))<=>(?[X]:((creative(X)&~tall(X)))))&
((?[X]:((brave(X)&~generous(X))))=>(?[X]:((~brave(X)|~patient(X)))))&
((?[X]:((funny(X)<~>~creative(X))))<=>((kind(susan)&~rich(susan))))&
((?[X]:(~brave(X)))<=>((quiet(alice)|~calm(alice))))&
((?[X]:((tall(X)&patient(X))))=>(~creative(fred)))&
(((~kind(paul)|~funny(paul)))=>((~strong(alice)|brave(alice))))&
((?[X]:((~funny(X)&~curious(X))))=>(?[X]:(~curious(X))))&
(![X]:((~calm(X)&~curious(X))<=>(curious(X)|~old(X))))&
(((curious(fred)<~>generous(fred)))=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:((~happy(X)&happy(X))<=>(~happy(X)|~humble(X))))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:((~calm(X)|wise(X)))))&
(![X]:((curious(X)|kind(X))=>(~generous(X)&~calm(X))))&
((?[X]:((~creative(X)&calm(X))))<=>(?[X]:((happy(X)&patient(X)))))&
((?[X]:((~calm(X)<~>funny(X))))<=>(?[X]:(rich(X))))&
(((~wise(paul)<~>tall(paul)))<=>((~strong(lucy)|~happy(lucy))))&
(?[X]:(brave(X)))&
(~calm(alice))&
(?[X]:((brave(X)<~>strong(X))))&
((~generous(lucy)<~>~patient(lucy)))&
(quiet(mary)) | old(lucy) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3956580593509190529379764
% SZS output start Proof for 3956580593509190529379764
1. ! [X0] : (~quiet(X0) <=> (~quiet(X0) <~> calm(X0))) [input p0]
9. ! [X0] : ((~curious(X0) & ~calm(X0)) <=> (~old(X0) | curious(X0))) [input p8]
22. old(lucy) [input hypothesis]
36. ! [X0] : ((~quiet(X0) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0)))) & (((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | quiet(X0))) [nnf transformation 1]
58. ! [X0] : (((~curious(X0) & ~calm(X0)) | (old(X0) & ~curious(X0))) & ((~old(X0) | curious(X0)) | (curious(X0) | calm(X0)))) [nnf transformation 9]
59. ! [X0] : (((~curious(X0) & ~calm(X0)) | (old(X0) & ~curious(X0))) & (~old(X0) | curious(X0) | curious(X0) | calm(X0))) [flattening 58]
89. ~calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 36]
91. ~quiet(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 36]
110. ~old(X0) | curious(X0) | curious(X0) | calm(X0) [cnf transformation 59]
113. ~curious(X0) | ~curious(X0) [cnf transformation 59]
153. old(lucy) [cnf transformation 22]
156. ~old(X0) | curious(X0) | calm(X0) [duplicate literal removal 110]
157. ~curious(X0) [duplicate literal removal 113]
158. ~calm(X0) | quiet(X0) [duplicate literal removal 89]
159. ~quiet(X0) | ~calm(X0) [duplicate literal removal 91]
160. ~calm(X0) [subsumption resolution 158,159]
262. ~old(X0) | calm(X0) [subsumption resolution 156,157]
263. ~old(X0) [subsumption resolution 262,160]
330. $false [subsumption resolution 153,263]
% SZS output end Proof for 3956580593509190529379764
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and brave then susan is not wise. If lucy is quiet or not creative then someone is happy or not patient and vice versa. Everyone who is either rich or curious is old. If someone is both calm and rich then someone is not brave. If fred is either not old or humble then someone is not strong. Everyone who is funny is both calm and not rich. If paul is rich or happy then lucy is not curious or tall. Everyone who is wise is strong and vice versa. Everyone who is either creative or rich is either not kind or quiet. Everyone who is brave or humble is not generous and vice versa. If susan is either old or funny then someone is kind. If fred is old then someone is either generous or humble and vice versa. If mary is not creative then mary is either calm or brave and vice versa. Everyone who is old is funny and vice versa. If someone is not old then fred is either not humble or not tall and vice versa. Everyone who is either strong or not wise is brave and vice versa. Lucy is rich. Someone is happy or not rich. Mary is both not calm and not wise. Fred is either not kind or not strong. Alice is wise. Someone is not patient. Someone is both old and brave. Someone is either not tall or rich. | Fred is not brave. | contradiction | ((?[X]:((tall(X)&brave(X))))=>(~wise(susan)))&
(((quiet(lucy)|~creative(lucy)))<=>(?[X]:((happy(X)|~patient(X)))))&
(![X]:((rich(X)<~>curious(X))=>old(X)))&
((?[X]:((calm(X)&rich(X))))=>(?[X]:(~brave(X))))&
(((~old(fred)<~>humble(fred)))=>(?[X]:(~strong(X))))&
(![X]:(funny(X)=>(calm(X)&~rich(X))))&
(((rich(paul)|happy(paul)))=>((~curious(lucy)|tall(lucy))))&
(![X]:(wise(X)<=>strong(X)))&
(![X]:((creative(X)<~>rich(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((brave(X)|humble(X))<=>~generous(X)))&
(((old(susan)<~>funny(susan)))=>(?[X]:(kind(X))))&
((old(fred))<=>(?[X]:((generous(X)<~>humble(X)))))&
((~creative(mary))<=>((calm(mary)<~>brave(mary))))&
(![X]:(old(X)<=>funny(X)))&
((?[X]:(~old(X)))<=>((~humble(fred)<~>~tall(fred))))&
(![X]:((strong(X)<~>~wise(X))<=>brave(X)))&
(rich(lucy))&
(?[X]:((happy(X)|~rich(X))))&
((~calm(mary)&~wise(mary)))&
((~kind(fred)<~>~strong(fred)))&
(wise(alice))&
(?[X]:(~patient(X)))&
(?[X]:((old(X)&brave(X))))&
(?[X]:((~tall(X)<~>rich(X)))) | ~brave(fred) | [
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 586043454154736588122634
% SZS output start Proof for 586043454154736588122634
8. ! [X0] : (wise(X0) <=> strong(X0)) [input p7]
16. ! [X0] : ((strong(X0) <~> ~wise(X0)) <=> brave(X0)) [input p15]
25. ~brave(fred) [input hypothesis]
48. ! [X0] : ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0))) [nnf transformation 8]
65. ! [X0] : ((((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | ~brave(X0)) & (brave(X0) | ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0))))) [nnf transformation 16]
90. strong(X0) | ~wise(X0) [cnf transformation 48]
91. wise(X0) | ~strong(X0) [cnf transformation 48]
115. brave(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 65]
116. brave(X0) | strong(X0) | wise(X0) [cnf transformation 65]
131. ~brave(fred) [cnf transformation 25]
270. brave(X0) | wise(X0) [subsumption resolution 116,91]
271. brave(X0) | ~wise(X0) [subsumption resolution 115,90]
272. brave(X0) [subsumption resolution 271,270]
303. $false [subsumption resolution 131,272]
% SZS output end Proof for 586043454154736588122634
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not funny then lucy is patient and vice versa.
Everyone who is not strong or old is both tall and patient and vice versa.
Everyone who is funny or curious is not rich.
Everyone who is not happy or not patient is either rich or funny and vice versa.
If someone is kind then someone is wise or rich and vice versa.
If someone is either not curious or rich then someone is both kind and creative.
Everyone who is not wise is both quiet and patient.
Everyone who is either brave or not humble is both not humble and strong and vice versa.
Everyone who is either generous or tall is patient or calm and vice versa.
If lucy is either rich or not creative then someone is not strong or not old and vice versa.
If paul is humble or calm then someone is both kind and not patient.
Everyone who is rich or not curious is not funny and vice versa.
Everyone who is not brave or not strong is either rich or not curious.
If someone is generous or not happy then someone is rich or not tall.
Everyone who is quiet is both calm and brave.
Everyone who is either not kind or not old is both rich and not wise and vice versa.
Lucy is happy.
Susan is humble or brave.
Susan is both humble and not old.
Fred is patient.
Someone is kind.
Paul is humble or not brave. | Susan is happy. | entailment | (((creative(fred)|~funny(fred)))<=>(patient(lucy)))&
(![X]:((~strong(X)|old(X))<=>(tall(X)&patient(X))))&
(![X]:((funny(X)|curious(X))=>~rich(X)))&
(![X]:((~happy(X)|~patient(X))<=>(rich(X)<~>funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((wise(X)|rich(X)))))&
((?[X]:((~curious(X)<~>rich(X))))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:(~wise(X)=>(quiet(X)&patient(X))))&
(![X]:((brave(X)<~>~humble(X))<=>(~humble(X)&strong(X))))&
(![X]:((generous(X)<~>tall(X))<=>(patient(X)|calm(X))))&
(((rich(lucy)<~>~creative(lucy)))<=>(?[X]:((~strong(X)|~old(X)))))&
(((humble(paul)|calm(paul)))=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:((rich(X)|~curious(X))<=>~funny(X)))&
(![X]:((~brave(X)|~strong(X))=>(rich(X)<~>~curious(X))))&
((?[X]:((generous(X)|~happy(X))))=>(?[X]:((rich(X)|~tall(X)))))&
(![X]:(quiet(X)=>(calm(X)&brave(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(rich(X)&~wise(X))))&
(happy(lucy))&
((humble(susan)|brave(susan)))&
((humble(susan)&~old(susan)))&
(patient(fred))&
(?[X]:(kind(X)))&
((humble(paul)|~brave(paul))) | happy(susan) | [
"p2",
"p3",
"p7",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8683971818313857692695079
% SZS output start Proof for 8683971818313857692695079
3. ! [X0] : ((curious(X0) | funny(X0)) => ~rich(X0)) [input p2]
4. ! [X0] : ((~patient(X0) | ~happy(X0)) <=> (rich(X0) <~> funny(X0))) [input p3]
8. ! [X0] : ((brave(X0) <~> ~humble(X0)) <=> (strong(X0) & ~humble(X0))) [input p7]
12. ! [X0] : ((~curious(X0) | rich(X0)) <=> ~funny(X0)) [input p11]
13. ! [X0] : ((~strong(X0) | ~brave(X0)) => (rich(X0) <~> ~curious(X0))) [input p12]
19. ~old(susan) & humble(susan) [input p18]
23. ~happy(susan) [input hypothesis]
27. ! [X0] : (~rich(X0) | (~curious(X0) & ~funny(X0))) [ennf transformation 3]
31. ! [X0] : ((rich(X0) <~> ~curious(X0)) | (strong(X0) & brave(X0))) [ennf transformation 13]
38. ! [X0] : (((~patient(X0) | ~happy(X0)) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0)))) & (((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | (patient(X0) & happy(X0)))) [nnf transformation 4]
39. ! [X0] : ((~patient(X0) | ~happy(X0) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0)))) & (((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | (patient(X0) & happy(X0)))) [flattening 38]
49. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (~strong(X0) | humble(X0))) & ((strong(X0) & ~humble(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [nnf transformation 8]
50. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | ~strong(X0) | humble(X0)) & ((strong(X0) & ~humble(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [flattening 49]
59. ! [X0] : (((~curious(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (curious(X0) & ~rich(X0)))) [nnf transformation 12]
60. ! [X0] : ((~curious(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (curious(X0) & ~rich(X0)))) [flattening 59]
61. ! [X0] : (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (strong(X0) & brave(X0))) [nnf transformation 31]
78. ~rich(X0) | ~curious(X0) [cnf transformation 27]
79. happy(X0) | rich(X0) | funny(X0) [cnf transformation 39]
94. ~humble(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 50]
117. ~funny(X0) | curious(X0) [cnf transformation 60]
119. ~curious(X0) | rich(X0) | brave(X0) [cnf transformation 61]
121. curious(X0) | ~rich(X0) | brave(X0) [cnf transformation 61]
135. humble(susan) [cnf transformation 19]
140. ~happy(susan) [cnf transformation 23]
141. ~humble(X0) | ~brave(X0) [duplicate literal removal 94]
247. ~rich(X0) | brave(X0) [subsumption resolution 121,78]
249. ~curious(X0) | brave(X0) [subsumption resolution 119,247]
267. 27 <=> humble(susan) [avatar definition]
269. humble(susan) <- (27) [avatar component clause 267]
271. 28 <=> brave(susan) [avatar definition]
272. ~brave(susan) <- (~28) [avatar component clause 271]
275. 27 [avatar split clause 135,267]
283. ~brave(susan) <- (27) [resolution 141,269]
284. ~28 | ~27 [avatar split clause 283,267,271]
296. rich(susan) | funny(susan) [resolution 79,140]
298. 29 <=> funny(susan) [avatar definition]
300. funny(susan) <- (29) [avatar component clause 298]
302. 30 <=> rich(susan) [avatar definition]
304. rich(susan) <- (30) [avatar component clause 302]
305. 29 | 30 [avatar split clause 296,302,298]
306. curious(susan) <- (29) [resolution 300,117]
315. brave(susan) <- (29) [resolution 306,249]
318. $false <- (~28, 29) [subsumption resolution 315,272]
319. 28 | ~29 [avatar contradiction clause 318]
335. brave(susan) <- (30) [resolution 304,247]
339. $false <- (~28, 30) [subsumption resolution 335,272]
340. 28 | ~30 [avatar contradiction clause 339]
341. $false [avatar sat refutation 275,284,305,319,340]
% SZS output end Proof for 8683971818313857692695079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then someone is either not generous or creative and vice versa.
Everyone who is both not wise and wise is both happy and not rich.
Everyone who is both rich and not curious is both creative and not kind and vice versa.
If someone is quiet then someone is not calm and vice versa.
If someone is not curious or rich then someone is both not wise and not humble.
Everyone who is not wise is both curious and brave and vice versa.
If someone is kind or not generous then someone is curious or not rich.
Everyone who is both happy and not tall is not wise or quiet and vice versa.
If mary is not calm then john is both not tall and old.
If alice is either patient or not rich then someone is both not wise and creative.
Everyone who is both not wise and quiet is either calm or not funny and vice versa.
If mary is not humble then someone is either strong or not rich and vice versa.
Everyone who is either not happy or humble is not rich or generous.
Everyone who is not generous is either curious or not tall.
If john is either not funny or brave then someone is not kind or wise and vice versa.
If lucy is funny then someone is either kind or patient and vice versa.
Someone is both not patient and not happy.
Fred is either not funny or rich.
Susan is either creative or not funny.
Someone is either not strong or old.
Someone is either not quiet or rich.
Someone is both not happy and not rich.
Someone is both not generous and not curious. | Susan is not funny. | neutral | ((?[X]:(~kind(X)))<=>(?[X]:((~generous(X)<~>creative(X)))))&
(![X]:((~wise(X)&wise(X))=>(happy(X)&~rich(X))))&
(![X]:((rich(X)&~curious(X))<=>(creative(X)&~kind(X))))&
((?[X]:(quiet(X)))<=>(?[X]:(~calm(X))))&
((?[X]:((~curious(X)|rich(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(curious(X)&brave(X))))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:((curious(X)|~rich(X)))))&
(![X]:((happy(X)&~tall(X))<=>(~wise(X)|quiet(X))))&
((~calm(mary))=>((~tall(john)&old(john))))&
(((patient(alice)<~>~rich(alice)))=>(?[X]:((~wise(X)&creative(X)))))&
(![X]:((~wise(X)&quiet(X))<=>(calm(X)<~>~funny(X))))&
((~humble(mary))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(![X]:((~happy(X)<~>humble(X))=>(~rich(X)|generous(X))))&
(![X]:(~generous(X)=>(curious(X)<~>~tall(X))))&
(((~funny(john)<~>brave(john)))<=>(?[X]:((~kind(X)|wise(X)))))&
((funny(lucy))<=>(?[X]:((kind(X)<~>patient(X)))))&
(?[X]:((~patient(X)&~happy(X))))&
((~funny(fred)<~>rich(fred)))&
((creative(susan)<~>~funny(susan)))&
(?[X]:((~strong(X)<~>old(X))))&
(?[X]:((~quiet(X)<~>rich(X))))&
(?[X]:((~happy(X)&~rich(X))))&
(?[X]:((~generous(X)&~curious(X)))) | ~funny(susan) | [] | null | 0 |
If someone is not old then alice is wise and vice versa. Everyone who is both not generous and generous is not tall or not creative. Everyone who is rich or not happy is not quiet or strong and vice versa. Everyone who is funny is both not humble and not tall. Everyone who is either kind or wise is both humble and not calm. Everyone who is either funny or strong is either rich or brave. Everyone who is both not happy and not funny is either not rich or generous. Everyone who is both not brave and humble is not happy or not kind. Everyone who is brave is both strong and quiet and vice versa. If john is old or not old then someone is quiet or not quiet. If someone is not creative then john is both humble and calm and vice versa. If lucy is not kind or not tall then susan is both calm and wise and vice versa. Everyone who is both not humble and not kind is both brave and old. Everyone who is creative or not calm is both not funny and strong. Everyone who is brave or humble is both strong and wise and vice versa. Lucy is brave. Someone is either humble or patient. Someone is either patient or generous. Susan is either not generous or humble. Paul is creative or not tall. Fred is patient or not humble. Someone is both not patient and not happy. Someone is not patient or not curious. | Paul is not tall. | neutral | ((?[X]:(~old(X)))<=>(wise(alice)))&
(![X]:((~generous(X)&generous(X))=>(~tall(X)|~creative(X))))&
(![X]:((rich(X)|~happy(X))<=>(~quiet(X)|strong(X))))&
(![X]:(funny(X)=>(~humble(X)&~tall(X))))&
(![X]:((kind(X)<~>wise(X))=>(humble(X)&~calm(X))))&
(![X]:((funny(X)<~>strong(X))=>(rich(X)<~>brave(X))))&
(![X]:((~happy(X)&~funny(X))=>(~rich(X)<~>generous(X))))&
(![X]:((~brave(X)&humble(X))=>(~happy(X)|~kind(X))))&
(![X]:(brave(X)<=>(strong(X)&quiet(X))))&
(((old(john)|~old(john)))=>(?[X]:((quiet(X)|~quiet(X)))))&
((?[X]:(~creative(X)))<=>((humble(john)&calm(john))))&
(((~kind(lucy)|~tall(lucy)))<=>((calm(susan)&wise(susan))))&
(![X]:((~humble(X)&~kind(X))=>(brave(X)&old(X))))&
(![X]:((creative(X)|~calm(X))=>(~funny(X)&strong(X))))&
(![X]:((brave(X)|humble(X))<=>(strong(X)&wise(X))))&
(brave(lucy))&
(?[X]:((humble(X)<~>patient(X))))&
(?[X]:((patient(X)<~>generous(X))))&
((~generous(susan)<~>humble(susan)))&
((creative(paul)|~tall(paul)))&
((patient(fred)|~humble(fred)))&
(?[X]:((~patient(X)&~happy(X))))&
(?[X]:((~patient(X)|~curious(X)))) | ~tall(paul) | [] | null | 0 |
If someone is either not tall or not rich then susan is kind and vice versa.
If someone is not humble then someone is not tall or curious and vice versa.
Everyone who is both not generous and brave is either not happy or quiet.
Everyone who is both not rich and strong is tall and vice versa.
If john is either funny or not curious then paul is not kind or not calm.
If paul is strong then someone is old.
Everyone who is happy or not old is patient or not strong and vice versa.
Everyone who is both tall and not tall is rich or not strong and vice versa.
If paul is both not calm and not humble then mary is either brave or creative.
Everyone who is tall or rich is either not wise or brave.
Everyone who is both not humble and funny is either not quiet or not generous and vice versa.
Everyone who is not generous is funny or creative and vice versa.
If alice is either not wise or patient then mary is not quiet or happy and vice versa.
Everyone who is both curious and happy is curious or old and vice versa.
If someone is either not old or not strong then someone is either funny or not happy.
Everyone who is not wise or not rich is both strong and not creative.
Someone is brave or not tall.
Someone is not old or not brave.
Someone is either not generous or not wise.
Fred is quiet or not curious.
Someone is either brave or not quiet.
Fred is not wise. | Fred is not generous. | neutral | ((?[X]:((~tall(X)<~>~rich(X))))<=>(kind(susan)))&
((?[X]:(~humble(X)))<=>(?[X]:((~tall(X)|curious(X)))))&
(![X]:((~generous(X)&brave(X))=>(~happy(X)<~>quiet(X))))&
(![X]:((~rich(X)&strong(X))<=>tall(X)))&
(((funny(john)<~>~curious(john)))=>((~kind(paul)|~calm(paul))))&
((strong(paul))=>(?[X]:(old(X))))&
(![X]:((happy(X)|~old(X))<=>(patient(X)|~strong(X))))&
(![X]:((tall(X)&~tall(X))<=>(rich(X)|~strong(X))))&
(((~calm(paul)&~humble(paul)))=>((brave(mary)<~>creative(mary))))&
(![X]:((tall(X)|rich(X))=>(~wise(X)<~>brave(X))))&
(![X]:((~humble(X)&funny(X))<=>(~quiet(X)<~>~generous(X))))&
(![X]:(~generous(X)<=>(funny(X)|creative(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~quiet(mary)|happy(mary))))&
(![X]:((curious(X)&happy(X))<=>(curious(X)|old(X))))&
((?[X]:((~old(X)<~>~strong(X))))=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:((~wise(X)|~rich(X))=>(strong(X)&~creative(X))))&
(?[X]:((brave(X)|~tall(X))))&
(?[X]:((~old(X)|~brave(X))))&
(?[X]:((~generous(X)<~>~wise(X))))&
((quiet(fred)|~curious(fred)))&
(?[X]:((brave(X)<~>~quiet(X))))&
(~wise(fred)) | ~generous(fred) | [] | null | 0 |
Everyone who is not humble or happy is not humble and vice versa.
Everyone who is wise or not kind is tall and vice versa.
Everyone who is kind or not old is both calm and old and vice versa.
Everyone who is both funny and strong is not kind or happy.
Everyone who is not rich is not calm or not curious.
Everyone who is either calm or not old is both not quiet and not patient and vice versa.
If john is either quiet or humble then someone is calm or generous and vice versa.
Everyone who is both not calm and happy is not brave.
Everyone who is not calm is not strong.
If someone is wise or tall then someone is both old and creative.
Everyone who is both rich and calm is not generous or old and vice versa.
Everyone who is both creative and quiet is either not patient or patient.
If someone is either old or generous then susan is both not rich and not quiet and vice versa.
Everyone who is both not patient and brave is both not quiet and old.
Everyone who is either not wise or not generous is either kind or not rich.
John is generous.
Someone is not calm or not tall.
Alice is either strong or happy.
Someone is tall or calm. | Susan is calm. | entailment | (![X]:((~humble(X)|happy(X))<=>~humble(X)))&
(![X]:((wise(X)|~kind(X))<=>tall(X)))&
(![X]:((kind(X)|~old(X))<=>(calm(X)&old(X))))&
(![X]:((funny(X)&strong(X))=>(~kind(X)|happy(X))))&
(![X]:(~rich(X)=>(~calm(X)|~curious(X))))&
(![X]:((calm(X)<~>~old(X))<=>(~quiet(X)&~patient(X))))&
(((quiet(john)<~>humble(john)))<=>(?[X]:((calm(X)|generous(X)))))&
(![X]:((~calm(X)&happy(X))=>~brave(X)))&
(![X]:(~calm(X)=>~strong(X)))&
((?[X]:((wise(X)|tall(X))))=>(?[X]:((old(X)&creative(X)))))&
(![X]:((rich(X)&calm(X))<=>(~generous(X)|old(X))))&
(![X]:((creative(X)&quiet(X))=>(~patient(X)<~>patient(X))))&
((?[X]:((old(X)<~>generous(X))))<=>((~rich(susan)&~quiet(susan))))&
(![X]:((~patient(X)&brave(X))=>(~quiet(X)&old(X))))&
(![X]:((~wise(X)<~>~generous(X))=>(kind(X)<~>~rich(X))))&
(generous(john))&
(?[X]:((~calm(X)|~tall(X))))&
((strong(alice)<~>happy(alice)))&
(?[X]:((tall(X)|calm(X)))) | calm(susan) | [
"p2",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5891580476405714229373122
% SZS output start Proof for 5891580476405714229373122
3. ! [X0] : ((~old(X0) | kind(X0)) <=> (old(X0) & calm(X0))) [input p2]
11. ! [X0] : ((calm(X0) & rich(X0)) <=> (old(X0) | ~generous(X0))) [input p10]
20. ~calm(susan) [input hypothesis]
35. ! [X0] : (((~old(X0) | kind(X0)) | (~old(X0) | ~calm(X0))) & ((old(X0) & calm(X0)) | (old(X0) & ~kind(X0)))) [nnf transformation 3]
36. ! [X0] : ((~old(X0) | kind(X0) | ~old(X0) | ~calm(X0)) & ((old(X0) & calm(X0)) | (old(X0) & ~kind(X0)))) [flattening 35]
46. ! [X0] : (((calm(X0) & rich(X0)) | (~old(X0) & generous(X0))) & ((old(X0) | ~generous(X0)) | (~calm(X0) | ~rich(X0)))) [nnf transformation 11]
47. ! [X0] : (((calm(X0) & rich(X0)) | (~old(X0) & generous(X0))) & (old(X0) | ~generous(X0) | ~calm(X0) | ~rich(X0))) [flattening 46]
69. old(X0) | old(X0) [cnf transformation 36]
92. calm(X0) | ~old(X0) [cnf transformation 47]
110. ~calm(susan) [cnf transformation 20]
111. old(X0) [duplicate literal removal 69]
156. calm(X0) [subsumption resolution 92,111]
183. $false [subsumption resolution 110,156]
% SZS output end Proof for 5891580476405714229373122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then fred is not tall or not generous and vice versa. If fred is not happy then someone is not calm or not creative and vice versa. If fred is brave or not quiet then someone is either brave or not kind and vice versa. Everyone who is either not funny or old is kind. Everyone who is tall or kind is either curious or tall and vice versa. Everyone who is both strong and funny is old. Everyone who is wise or curious is both not funny and generous. Everyone who is both not calm and not humble is both not old and calm and vice versa. If someone is not wise or not tall then someone is brave or not quiet and vice versa. Everyone who is happy or not old is both generous and rich and vice versa. Everyone who is rich or funny is generous and vice versa. If mary is not kind or generous then john is not patient and vice versa. Everyone who is generous or not kind is either strong or not kind. If someone is either quiet or old then someone is patient or tall and vice versa. Everyone who is brave is either not brave or not funny. If susan is either not calm or generous then fred is not tall and vice versa. John is happy or not funny. Susan is not brave. Someone is not humble. Someone is tall. Someone is both tall and wise. Paul is both tall and wise. Someone is either rich or not curious. | Fred is happy. | neutral | ((?[X]:(old(X)))<=>((~tall(fred)|~generous(fred))))&
((~happy(fred))<=>(?[X]:((~calm(X)|~creative(X)))))&
(((brave(fred)|~quiet(fred)))<=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:((~funny(X)<~>old(X))=>kind(X)))&
(![X]:((tall(X)|kind(X))<=>(curious(X)<~>tall(X))))&
(![X]:((strong(X)&funny(X))=>old(X)))&
(![X]:((wise(X)|curious(X))=>(~funny(X)&generous(X))))&
(![X]:((~calm(X)&~humble(X))<=>(~old(X)&calm(X))))&
((?[X]:((~wise(X)|~tall(X))))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((happy(X)|~old(X))<=>(generous(X)&rich(X))))&
(![X]:((rich(X)|funny(X))<=>generous(X)))&
(((~kind(mary)|generous(mary)))<=>(~patient(john)))&
(![X]:((generous(X)|~kind(X))=>(strong(X)<~>~kind(X))))&
((?[X]:((quiet(X)<~>old(X))))<=>(?[X]:((patient(X)|tall(X)))))&
(![X]:(brave(X)=>(~brave(X)<~>~funny(X))))&
(((~calm(susan)<~>generous(susan)))<=>(~tall(fred)))&
((happy(john)|~funny(john)))&
(~brave(susan))&
(?[X]:(~humble(X)))&
(?[X]:(tall(X)))&
(?[X]:((tall(X)&wise(X))))&
((tall(paul)&wise(paul)))&
(?[X]:((rich(X)<~>~curious(X)))) | happy(fred) | [] | null | 0 |
Everyone who is not calm or patient is old.
Everyone who is old or not kind is both calm and generous and vice versa.
Everyone who is either not rich or wise is both not humble and curious and vice versa.
If someone is not creative or not calm then susan is either not old or not strong and vice versa.
Everyone who is old is either quiet or not strong.
Everyone who is not strong is either kind or not calm.
If someone is not curious then someone is either not brave or quiet and vice versa.
Everyone who is either curious or funny is both brave and curious.
Everyone who is both not rich and brave is not generous.
If john is both not happy and kind then someone is either not funny or brave.
Everyone who is both funny and not brave is wise or not calm.
If fred is humble then lucy is both wise and not patient.
Everyone who is either not old or calm is both not curious and patient and vice versa.
Everyone who is wise is either not kind or happy.
If lucy is not patient or old then alice is brave and vice versa.
If someone is not humble then someone is not curious or not old.
Someone is wise.
Someone is both calm and wise.
Mary is not strong or not kind.
Someone is either not humble or kind.
Someone is creative.
John is both old and wise.
Someone is not curious.
Paul is either not strong or not funny. | John is brave. | contradiction | (![X]:((~calm(X)|patient(X))=>old(X)))&
(![X]:((old(X)|~kind(X))<=>(calm(X)&generous(X))))&
(![X]:((~rich(X)<~>wise(X))<=>(~humble(X)&curious(X))))&
((?[X]:((~creative(X)|~calm(X))))<=>((~old(susan)<~>~strong(susan))))&
(![X]:(old(X)=>(quiet(X)<~>~strong(X))))&
(![X]:(~strong(X)=>(kind(X)<~>~calm(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:((curious(X)<~>funny(X))=>(brave(X)&curious(X))))&
(![X]:((~rich(X)&brave(X))=>~generous(X)))&
(((~happy(john)&kind(john)))=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:((funny(X)&~brave(X))=>(wise(X)|~calm(X))))&
((humble(fred))=>((wise(lucy)&~patient(lucy))))&
(![X]:((~old(X)<~>calm(X))<=>(~curious(X)&patient(X))))&
(![X]:(wise(X)=>(~kind(X)<~>happy(X))))&
(((~patient(lucy)|old(lucy)))<=>(brave(alice)))&
((?[X]:(~humble(X)))=>(?[X]:((~curious(X)|~old(X)))))&
(?[X]:(wise(X)))&
(?[X]:((calm(X)&wise(X))))&
((~strong(mary)|~kind(mary)))&
(?[X]:((~humble(X)<~>kind(X))))&
(?[X]:(creative(X)))&
((old(john)&wise(john)))&
(?[X]:(~curious(X)))&
((~strong(paul)<~>~funny(paul))) | brave(john) | [
"p0",
"p1",
"p2",
"p8",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3681238110492811770218935
% SZS output start Proof for 3681238110492811770218935
1. ! [X0] : ((patient(X0) | ~calm(X0)) => old(X0)) [input p0]
2. ! [X0] : ((~kind(X0) | old(X0)) <=> (generous(X0) & calm(X0))) [input p1]
3. ! [X0] : ((~rich(X0) <~> wise(X0)) <=> (curious(X0) & ~humble(X0))) [input p2]
9. ! [X0] : ((brave(X0) & ~rich(X0)) => ~generous(X0)) [input p8]
13. ! [X0] : ((~old(X0) <~> calm(X0)) <=> (patient(X0) & ~curious(X0))) [input p12]
22. wise(john) & old(john) [input p21]
25. brave(john) [input hypothesis]
28. ! [X0] : (old(X0) | (~patient(X0) & calm(X0))) [ennf transformation 1]
32. ! [X0] : (~generous(X0) | (~brave(X0) | rich(X0))) [ennf transformation 9]
33. ! [X0] : (~generous(X0) | ~brave(X0) | rich(X0)) [flattening 32]
41. ! [X0] : (((~kind(X0) | old(X0)) | (~generous(X0) | ~calm(X0))) & ((generous(X0) & calm(X0)) | (kind(X0) & ~old(X0)))) [nnf transformation 2]
42. ! [X0] : ((~kind(X0) | old(X0) | ~generous(X0) | ~calm(X0)) & ((generous(X0) & calm(X0)) | (kind(X0) & ~old(X0)))) [flattening 41]
43. ! [X0] : ((((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0))))) [nnf transformation 3]
44. ! [X0] : ((((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0))))) [flattening 43]
60. ! [X0] : ((((~calm(X0) | old(X0)) & (calm(X0) | ~old(X0))) | (~patient(X0) | curious(X0))) & ((patient(X0) & ~curious(X0)) | ((~old(X0) | ~calm(X0)) & (calm(X0) | old(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~calm(X0) | old(X0)) & (calm(X0) | ~old(X0))) | ~patient(X0) | curious(X0)) & ((patient(X0) & ~curious(X0)) | ((~old(X0) | ~calm(X0)) & (calm(X0) | old(X0))))) [flattening 60]
80. old(X0) | calm(X0) [cnf transformation 28]
82. calm(X0) | ~old(X0) [cnf transformation 42]
84. ~old(X0) | generous(X0) [cnf transformation 42]
90. ~wise(X0) | ~rich(X0) | curious(X0) [cnf transformation 44]
111. ~brave(X0) | ~generous(X0) | rich(X0) [cnf transformation 33]
118. ~curious(X0) | ~old(X0) | ~calm(X0) [cnf transformation 61]
136. old(john) [cnf transformation 22]
137. wise(john) [cnf transformation 22]
141. brave(john) [cnf transformation 25]
144. calm(X0) [subsumption resolution 82,80]
226. ~curious(X0) | ~old(X0) [subsumption resolution 118,144]
276. generous(john) [resolution 84,136]
308. ~rich(john) | curious(john) [resolution 90,137]
328. 34 <=> curious(john) [avatar definition]
330. curious(john) <- (34) [avatar component clause 328]
332. 35 <=> rich(john) [avatar definition]
335. 34 | ~35 [avatar split clause 308,332,328]
352. ~generous(john) | rich(john) [resolution 111,141]
354. rich(john) [subsumption resolution 352,276]
366. 35 [avatar split clause 354,332]
399. ~old(john) <- (34) [resolution 330,226]
400. $false <- (34) [subsumption resolution 399,136]
401. ~34 [avatar contradiction clause 400]
402. $false [avatar sat refutation 335,366,401]
% SZS output end Proof for 3681238110492811770218935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not curious is either old or tall. Everyone who is not patient is happy and vice versa. If lucy is both wise and not wise then someone is not curious or rich. If someone is either not old or not curious then paul is either not happy or kind and vice versa. Everyone who is patient or strong is not curious or not humble. Everyone who is calm or not old is not creative and vice versa. If alice is not strong then someone is not kind. Everyone who is not brave or not humble is brave and vice versa. Everyone who is not rich is both not funny and quiet. If mary is either happy or calm then paul is both calm and not brave and vice versa. Everyone who is either wise or not quiet is either not brave or not quiet and vice versa. If john is funny then paul is not tall. Everyone who is calm is not old or calm. Everyone who is either creative or rich is both not quiet and curious. Everyone who is humble or not happy is creative or not calm. Everyone who is not rich is generous or not humble and vice versa. Mary is curious or strong. Alice is tall or not calm. Someone is not kind or brave. Mary is either not quiet or not rich. Someone is either strong or patient. Someone is both not calm and generous. Someone is not patient. | Mary is curious. | neutral | (![X]:((funny(X)<~>~curious(X))=>(old(X)<~>tall(X))))&
(![X]:(~patient(X)<=>happy(X)))&
(((wise(lucy)&~wise(lucy)))=>(?[X]:((~curious(X)|rich(X)))))&
((?[X]:((~old(X)<~>~curious(X))))<=>((~happy(paul)<~>kind(paul))))&
(![X]:((patient(X)|strong(X))=>(~curious(X)|~humble(X))))&
(![X]:((calm(X)|~old(X))<=>~creative(X)))&
((~strong(alice))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)|~humble(X))<=>brave(X)))&
(![X]:(~rich(X)=>(~funny(X)&quiet(X))))&
(((happy(mary)<~>calm(mary)))<=>((calm(paul)&~brave(paul))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~brave(X)<~>~quiet(X))))&
((funny(john))=>(~tall(paul)))&
(![X]:(calm(X)=>(~old(X)|calm(X))))&
(![X]:((creative(X)<~>rich(X))=>(~quiet(X)&curious(X))))&
(![X]:((humble(X)|~happy(X))=>(creative(X)|~calm(X))))&
(![X]:(~rich(X)<=>(generous(X)|~humble(X))))&
((curious(mary)|strong(mary)))&
((tall(alice)|~calm(alice)))&
(?[X]:((~kind(X)|brave(X))))&
((~quiet(mary)<~>~rich(mary)))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((~calm(X)&generous(X))))&
(?[X]:(~patient(X))) | curious(mary) | [] | null | 0 |
Everyone who is either not funny or quiet is either quiet or not funny.
If fred is not strong then mary is not old or not curious and vice versa.
If susan is humble then alice is funny and vice versa.
Everyone who is both strong and quiet is both not calm and not kind and vice versa.
Everyone who is either not creative or kind is not curious or creative and vice versa.
Everyone who is patient is both wise and not wise and vice versa.
Everyone who is not humble is either not strong or not calm and vice versa.
Everyone who is both not quiet and not humble is both not generous and not happy.
If john is both calm and not strong then susan is either generous or happy and vice versa.
If someone is not patient or not kind then john is quiet or not wise.
If someone is curious or not funny then alice is not strong and vice versa.
Everyone who is patient is both strong and kind.
If mary is both generous and kind then someone is not funny or generous and vice versa.
Everyone who is both not wise and not creative is either not brave or happy and vice versa.
If someone is generous then mary is not funny.
If someone is either happy or not generous then someone is not funny or curious and vice versa.
Someone is strong.
Lucy is not calm.
Someone is either patient or strong.
Fred is not quiet or kind.
Someone is both creative and old.
Susan is curious or strong.
Susan is not tall. | Lucy is patient. | contradiction | (![X]:((~funny(X)<~>quiet(X))=>(quiet(X)<~>~funny(X))))&
((~strong(fred))<=>((~old(mary)|~curious(mary))))&
((humble(susan))<=>(funny(alice)))&
(![X]:((strong(X)&quiet(X))<=>(~calm(X)&~kind(X))))&
(![X]:((~creative(X)<~>kind(X))<=>(~curious(X)|creative(X))))&
(![X]:(patient(X)<=>(wise(X)&~wise(X))))&
(![X]:(~humble(X)<=>(~strong(X)<~>~calm(X))))&
(![X]:((~quiet(X)&~humble(X))=>(~generous(X)&~happy(X))))&
(((calm(john)&~strong(john)))<=>((generous(susan)<~>happy(susan))))&
((?[X]:((~patient(X)|~kind(X))))=>((quiet(john)|~wise(john))))&
((?[X]:((curious(X)|~funny(X))))<=>(~strong(alice)))&
(![X]:(patient(X)=>(strong(X)&kind(X))))&
(((generous(mary)&kind(mary)))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((~wise(X)&~creative(X))<=>(~brave(X)<~>happy(X))))&
((?[X]:(generous(X)))=>(~funny(mary)))&
((?[X]:((happy(X)<~>~generous(X))))<=>(?[X]:((~funny(X)|curious(X)))))&
(?[X]:(strong(X)))&
(~calm(lucy))&
(?[X]:((patient(X)<~>strong(X))))&
((~quiet(fred)|kind(fred)))&
(?[X]:((creative(X)&old(X))))&
((curious(susan)|strong(susan)))&
(~tall(susan)) | patient(lucy) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2625715174947377718509
% SZS output start Proof for 2625715174947377718509
6. ! [X0] : (patient(X0) <=> (~wise(X0) & wise(X0))) [input p5]
24. patient(lucy) [input hypothesis]
42. ! [X0] : ((patient(X0) | (wise(X0) | ~wise(X0))) & ((~wise(X0) & wise(X0)) | ~patient(X0))) [nnf transformation 6]
43. ! [X0] : ((patient(X0) | wise(X0) | ~wise(X0)) & ((~wise(X0) & wise(X0)) | ~patient(X0))) [flattening 42]
89. wise(X0) | ~patient(X0) [cnf transformation 43]
90. ~wise(X0) | ~patient(X0) [cnf transformation 43]
137. patient(lucy) [cnf transformation 24]
170. ~patient(X0) [subsumption resolution 89,90]
304. $false [subsumption resolution 137,170]
% SZS output end Proof for 2625715174947377718509
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both happy and not tall then someone is either not funny or quiet and vice versa. If lucy is not wise then someone is either funny or not quiet and vice versa. If mary is brave or not patient then mary is both not patient and old and vice versa. Everyone who is not patient or curious is both not calm and quiet and vice versa. Everyone who is calm or not kind is both not calm and kind. If paul is not old then lucy is both happy and not funny. Everyone who is either brave or not rich is both humble and funny. Everyone who is both not funny and generous is funny or happy and vice versa. If someone is not quiet then fred is both funny and calm. If alice is both tall and not generous then someone is both not wise and strong and vice versa. If susan is humble then lucy is brave and vice versa. Everyone who is either humble or not happy is calm and vice versa. Everyone who is creative or not creative is either not calm or not wise. If someone is strong then fred is not curious and vice versa. Everyone who is either not wise or patient is either funny or not humble. Everyone who is creative is either quiet or not tall and vice versa. Lucy is rich. Someone is both tall and rich. Someone is generous or not kind. Someone is not generous or quiet. Mary is rich or not humble. John is both rich and not happy. | Fred is not brave. | neutral | (((happy(fred)&~tall(fred)))<=>(?[X]:((~funny(X)<~>quiet(X)))))&
((~wise(lucy))<=>(?[X]:((funny(X)<~>~quiet(X)))))&
(((brave(mary)|~patient(mary)))<=>((~patient(mary)&old(mary))))&
(![X]:((~patient(X)|curious(X))<=>(~calm(X)&quiet(X))))&
(![X]:((calm(X)|~kind(X))=>(~calm(X)&kind(X))))&
((~old(paul))=>((happy(lucy)&~funny(lucy))))&
(![X]:((brave(X)<~>~rich(X))=>(humble(X)&funny(X))))&
(![X]:((~funny(X)&generous(X))<=>(funny(X)|happy(X))))&
((?[X]:(~quiet(X)))=>((funny(fred)&calm(fred))))&
(((tall(alice)&~generous(alice)))<=>(?[X]:((~wise(X)&strong(X)))))&
((humble(susan))<=>(brave(lucy)))&
(![X]:((humble(X)<~>~happy(X))<=>calm(X)))&
(![X]:((creative(X)|~creative(X))=>(~calm(X)<~>~wise(X))))&
((?[X]:(strong(X)))<=>(~curious(fred)))&
(![X]:((~wise(X)<~>patient(X))=>(funny(X)<~>~humble(X))))&
(![X]:(creative(X)<=>(quiet(X)<~>~tall(X))))&
(rich(lucy))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:((~generous(X)|quiet(X))))&
((rich(mary)|~humble(mary)))&
((rich(john)&~happy(john))) | ~brave(fred) | [] | null | 0 |
Everyone who is not calm or not quiet is both not patient and patient.
Everyone who is both rich and not quiet is generous or not old.
Everyone who is generous or creative is not rich or funny.
Everyone who is not rich is not calm or strong and vice versa.
If someone is not old or strong then someone is either kind or not quiet.
Everyone who is creative is not tall.
Everyone who is both not calm and not kind is creative and vice versa.
Everyone who is either creative or calm is either kind or not humble and vice versa.
If someone is either humble or not generous then someone is not old.
Everyone who is creative is creative or not generous and vice versa.
If someone is both funny and wise then someone is not kind.
Everyone who is either not strong or tall is both not curious and not rich and vice versa.
If paul is either not generous or not happy then someone is either generous or calm and vice versa.
If john is not kind then alice is both creative and generous and vice versa.
If someone is either not tall or happy then someone is not brave.
Everyone who is either old or strong is happy or not humble and vice versa.
Someone is either not funny or generous.
Fred is patient.
Paul is not creative or strong.
Mary is both not funny and not wise.
Paul is both not patient and not humble.
Alice is either patient or funny.
Someone is either not quiet or not funny. | Mary is funny. | contradiction | (![X]:((~calm(X)|~quiet(X))=>(~patient(X)&patient(X))))&
(![X]:((rich(X)&~quiet(X))=>(generous(X)|~old(X))))&
(![X]:((generous(X)|creative(X))=>(~rich(X)|funny(X))))&
(![X]:(~rich(X)<=>(~calm(X)|strong(X))))&
((?[X]:((~old(X)|strong(X))))=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:(creative(X)=>~tall(X)))&
(![X]:((~calm(X)&~kind(X))<=>creative(X)))&
(![X]:((creative(X)<~>calm(X))<=>(kind(X)<~>~humble(X))))&
((?[X]:((humble(X)<~>~generous(X))))=>(?[X]:(~old(X))))&
(![X]:(creative(X)<=>(creative(X)|~generous(X))))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(~curious(X)&~rich(X))))&
(((~generous(paul)<~>~happy(paul)))<=>(?[X]:((generous(X)<~>calm(X)))))&
((~kind(john))<=>((creative(alice)&generous(alice))))&
((?[X]:((~tall(X)<~>happy(X))))=>(?[X]:(~brave(X))))&
(![X]:((old(X)<~>strong(X))<=>(happy(X)|~humble(X))))&
(?[X]:((~funny(X)<~>generous(X))))&
(patient(fred))&
((~creative(paul)|strong(paul)))&
((~funny(mary)&~wise(mary)))&
((~patient(paul)&~humble(paul)))&
((patient(alice)<~>funny(alice)))&
(?[X]:((~quiet(X)<~>~funny(X)))) | funny(mary) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1517706435499221921429629
% SZS output start Proof for 1517706435499221921429629
20. ~wise(mary) & ~funny(mary) [input p19]
24. funny(mary) [input hypothesis]
31. ~funny(mary) [pure predicate removal 20]
130. ~funny(mary) [cnf transformation 31]
137. funny(mary) [cnf transformation 24]
191. $false [subsumption resolution 137,130]
% SZS output end Proof for 1517706435499221921429629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not calm is quiet or tall. Everyone who is wise or not kind is either not strong or not quiet. Everyone who is quiet is funny or not happy and vice versa. Everyone who is either curious or not creative is either creative or old. Everyone who is not patient or not curious is strong. If someone is rich then john is not funny and vice versa. If someone is rich then alice is both wise and not generous and vice versa. If fred is either not tall or old then alice is curious or not rich. Everyone who is both not brave and rich is not patient and vice versa. Everyone who is quiet or funny is both not brave and rich and vice versa. Everyone who is rich or not humble is either not rich or strong and vice versa. Everyone who is both brave and not funny is either not wise or not humble. If someone is not quiet or brave then someone is either not calm or funny. If someone is either calm or old then someone is not happy or quiet and vice versa. If someone is humble then someone is both not rich and kind and vice versa. Everyone who is either not strong or not funny is patient and vice versa. Alice is both not kind and curious. Paul is both not curious and rich. Someone is either not funny or strong. Someone is both not brave and quiet. Someone is both strong and old. Someone is not curious or not tall. Lucy is either creative or not creative. Paul is either strong or not calm. | John is not strong. | contradiction | (![X]:((~brave(X)|~calm(X))=>(quiet(X)|tall(X))))&
(![X]:((wise(X)|~kind(X))=>(~strong(X)<~>~quiet(X))))&
(![X]:(quiet(X)<=>(funny(X)|~happy(X))))&
(![X]:((curious(X)<~>~creative(X))=>(creative(X)<~>old(X))))&
(![X]:((~patient(X)|~curious(X))=>strong(X)))&
((?[X]:(rich(X)))<=>(~funny(john)))&
((?[X]:(rich(X)))<=>((wise(alice)&~generous(alice))))&
(((~tall(fred)<~>old(fred)))=>((curious(alice)|~rich(alice))))&
(![X]:((~brave(X)&rich(X))<=>~patient(X)))&
(![X]:((quiet(X)|funny(X))<=>(~brave(X)&rich(X))))&
(![X]:((rich(X)|~humble(X))<=>(~rich(X)<~>strong(X))))&
(![X]:((brave(X)&~funny(X))=>(~wise(X)<~>~humble(X))))&
((?[X]:((~quiet(X)|brave(X))))=>(?[X]:((~calm(X)<~>funny(X)))))&
((?[X]:((calm(X)<~>old(X))))<=>(?[X]:((~happy(X)|quiet(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~rich(X)&kind(X)))))&
(![X]:((~strong(X)<~>~funny(X))<=>patient(X)))&
((~kind(alice)&curious(alice)))&
((~curious(paul)&rich(paul)))&
(?[X]:((~funny(X)<~>strong(X))))&
(?[X]:((~brave(X)&quiet(X))))&
(?[X]:((strong(X)&old(X))))&
(?[X]:((~curious(X)|~tall(X))))&
((creative(lucy)<~>~creative(lucy)))&
((strong(paul)<~>~calm(paul))) | ~strong(john) | [
"p4",
"p5",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8732132408624528749124240
% SZS output start Proof for 8732132408624528749124240
5. ! [X0] : ((~curious(X0) | ~patient(X0)) => strong(X0)) [input p4]
6. ? [X0] : rich(X0) <=> ~funny(john) [input p5]
16. ! [X0] : ((~strong(X0) <~> ~funny(X0)) <=> patient(X0)) [input p15]
18. rich(paul) & ~curious(paul) [input p17]
25. ~strong(john) [input hypothesis]
33. ! [X0] : (strong(X0) | (curious(X0) & patient(X0))) [ennf transformation 5]
43. (? [X0] : rich(X0) | funny(john)) & (~funny(john) | ! [X0] : ~rich(X0)) [nnf transformation 6]
44. (? [X0] : rich(X0) | funny(john)) & (~funny(john) | ! [X1] : ~rich(X1)) [rectify 43]
45. ? [X0] : rich(X0) => rich(sK0) [choice axiom]
46. (rich(sK0) | funny(john)) & (~funny(john) | ! [X1] : ~rich(X1)) [skolemisation 44,45]
74. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ~patient(X0)) & (patient(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [nnf transformation 16]
99. patient(X0) | strong(X0) [cnf transformation 33]
101. ~funny(john) | ~rich(X1) [cnf transformation 46]
140. funny(X0) | strong(X0) | ~patient(X0) [cnf transformation 74]
144. rich(paul) [cnf transformation 18]
156. ~strong(john) [cnf transformation 25]
162. 1 <=> funny(john) [avatar definition]
163. ~funny(john) <- (~1) [avatar component clause 162]
171. 3 <=> ! [X1] : ~rich(X1) [avatar definition]
172. ~rich(X1) <- (3) [avatar component clause 171]
173. 3 | ~1 [avatar split clause 101,162,171]
281. funny(X0) | strong(X0) [subsumption resolution 140,99]
307. $false <- (3) [resolution 172,144]
308. ~3 [avatar contradiction clause 307]
328. strong(john) <- (~1) [resolution 281,163]
333. $false <- (~1) [subsumption resolution 328,156]
334. 1 [avatar contradiction clause 333]
336. $false [avatar sat refutation 173,308,334]
% SZS output end Proof for 8732132408624528749124240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is quiet is both strong and not quiet.
Everyone who is both not old and generous is generous and vice versa.
If susan is either strong or calm then someone is old.
If fred is both not quiet and not kind then paul is both humble and not tall.
If john is not humble then someone is not quiet or calm and vice versa.
Everyone who is either not old or not calm is both funny and not generous and vice versa.
If mary is both not patient and not quiet then someone is either not rich or not old and vice versa.
If fred is quiet or old then lucy is not brave or humble and vice versa.
If lucy is both not brave and patient then someone is strong and vice versa.
If someone is curious or not curious then susan is either old or humble.
Everyone who is either creative or wise is both funny and not quiet and vice versa.
Everyone who is not kind is humble and vice versa.
If alice is both not curious and brave then someone is both old and kind and vice versa.
If someone is either not humble or happy then someone is curious and vice versa.
Everyone who is patient or kind is not brave and vice versa.
If someone is both happy and quiet then someone is brave.
Mary is both not happy and patient.
John is both not wise and not creative.
Someone is creative.
Someone is both not quiet and not calm.
Someone is either brave or patient.
John is calm.
Alice is not happy or not kind. | Fred is not rich. | contradiction | (![X]:(quiet(X)=>(strong(X)&~quiet(X))))&
(![X]:((~old(X)&generous(X))<=>generous(X)))&
(((strong(susan)<~>calm(susan)))=>(?[X]:(old(X))))&
(((~quiet(fred)&~kind(fred)))=>((humble(paul)&~tall(paul))))&
((~humble(john))<=>(?[X]:((~quiet(X)|calm(X)))))&
(![X]:((~old(X)<~>~calm(X))<=>(funny(X)&~generous(X))))&
(((~patient(mary)&~quiet(mary)))<=>(?[X]:((~rich(X)<~>~old(X)))))&
(((quiet(fred)|old(fred)))<=>((~brave(lucy)|humble(lucy))))&
(((~brave(lucy)&patient(lucy)))<=>(?[X]:(strong(X))))&
((?[X]:((curious(X)|~curious(X))))=>((old(susan)<~>humble(susan))))&
(![X]:((creative(X)<~>wise(X))<=>(funny(X)&~quiet(X))))&
(![X]:(~kind(X)<=>humble(X)))&
(((~curious(alice)&brave(alice)))<=>(?[X]:((old(X)&kind(X)))))&
((?[X]:((~humble(X)<~>happy(X))))<=>(?[X]:(curious(X))))&
(![X]:((patient(X)|kind(X))<=>~brave(X)))&
((?[X]:((happy(X)&quiet(X))))=>(?[X]:(brave(X))))&
((~happy(mary)&patient(mary)))&
((~wise(john)&~creative(john)))&
(?[X]:(creative(X)))&
(?[X]:((~quiet(X)&~calm(X))))&
(?[X]:((brave(X)<~>patient(X))))&
(calm(john))&
((~happy(alice)|~kind(alice))) | ~rich(fred) | [
"p0",
"p6",
"p7",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 513630533083809031340851
% SZS output start Proof for 513630533083809031340851
1. ! [X0] : (quiet(X0) => (~quiet(X0) & strong(X0))) [input p0]
7. (~quiet(mary) & ~patient(mary)) <=> ? [X0] : (~rich(X0) <~> ~old(X0)) [input p6]
8. (old(fred) | quiet(fred)) <=> (humble(lucy) | ~brave(lucy)) [input p7]
12. ! [X0] : (~kind(X0) <=> humble(X0)) [input p11]
15. ! [X0] : ((kind(X0) | patient(X0)) <=> ~brave(X0)) [input p14]
17. patient(mary) & ~happy(mary) [input p16]
24. ~rich(fred) [input hypothesis]
28. ! [X0] : ((~quiet(X0) & strong(X0)) | ~quiet(X0)) [ennf transformation 1]
45. ((~quiet(mary) & ~patient(mary)) | ! [X0] : ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (? [X0] : ((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (quiet(mary) | patient(mary))) [nnf transformation 7]
46. ((~quiet(mary) & ~patient(mary)) | ! [X0] : ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (? [X0] : ((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | quiet(mary) | patient(mary)) [flattening 45]
47. ((~quiet(mary) & ~patient(mary)) | ! [X0] : ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (? [X1] : ((old(X1) | rich(X1)) & (~old(X1) | ~rich(X1))) | quiet(mary) | patient(mary)) [rectify 46]
48. ? [X1] : ((old(X1) | rich(X1)) & (~old(X1) | ~rich(X1))) => ((old(sK2) | rich(sK2)) & (~old(sK2) | ~rich(sK2))) [choice axiom]
49. ((~quiet(mary) & ~patient(mary)) | ! [X0] : ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(sK2) | rich(sK2)) & (~old(sK2) | ~rich(sK2))) | quiet(mary) | patient(mary)) [skolemisation 47,48]
50. ((old(fred) | quiet(fred)) | (~humble(lucy) & brave(lucy))) & ((humble(lucy) | ~brave(lucy)) | (~old(fred) & ~quiet(fred))) [nnf transformation 8]
51. (old(fred) | quiet(fred) | (~humble(lucy) & brave(lucy))) & (humble(lucy) | ~brave(lucy) | (~old(fred) & ~quiet(fred))) [flattening 50]
60. ! [X0] : ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0))) [nnf transformation 12]
71. ! [X0] : (((kind(X0) | patient(X0)) | brave(X0)) & (~brave(X0) | (~kind(X0) & ~patient(X0)))) [nnf transformation 15]
72. ! [X0] : ((kind(X0) | patient(X0) | brave(X0)) & (~brave(X0) | (~kind(X0) & ~patient(X0)))) [flattening 71]
84. ~quiet(X0) | ~quiet(X0) [cnf transformation 28]
102. ~patient(mary) | ~old(X0) | rich(X0) [cnf transformation 49]
108. old(fred) | quiet(fred) | brave(lucy) [cnf transformation 51]
109. old(fred) | quiet(fred) | ~humble(lucy) [cnf transformation 51]
123. humble(X0) | kind(X0) [cnf transformation 60]
134. ~brave(X0) | ~kind(X0) [cnf transformation 72]
138. patient(mary) [cnf transformation 17]
148. ~rich(fred) [cnf transformation 24]
149. ~quiet(X0) [duplicate literal removal 84]
190. 9 <=> patient(mary) [avatar definition]
195. 10 <=> ! [X0] : (~old(X0) | rich(X0)) [avatar definition]
196. ~old(X0) | rich(X0) <- (10) [avatar component clause 195]
197. 10 | ~9 [avatar split clause 102,190,195]
210. old(fred) | ~humble(lucy) [subsumption resolution 109,149]
212. 13 <=> humble(lucy) [avatar definition]
214. ~humble(lucy) <- (~13) [avatar component clause 212]
216. 14 <=> old(fred) [avatar definition]
218. old(fred) <- (14) [avatar component clause 216]
219. ~13 | 14 [avatar split clause 210,216,212]
220. old(fred) | brave(lucy) [subsumption resolution 108,149]
222. 15 <=> brave(lucy) [avatar definition]
224. brave(lucy) <- (15) [avatar component clause 222]
225. 15 | 14 [avatar split clause 220,216,222]
306. 9 [avatar split clause 138,190]
333. rich(fred) <- (10, 14) [resolution 196,218]
335. $false <- (10, 14) [subsumption resolution 333,148]
336. ~10 | ~14 [avatar contradiction clause 335]
337. kind(lucy) <- (~13) [resolution 214,123]
338. ~kind(lucy) <- (15) [resolution 224,134]
340. $false <- (~13, 15) [subsumption resolution 338,337]
341. 13 | ~15 [avatar contradiction clause 340]
342. $false [avatar sat refutation 197,219,225,306,336,341]
% SZS output end Proof for 513630533083809031340851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both calm and not wise is both brave and not humble and vice versa.
If paul is either funny or not kind then someone is patient or not happy.
Everyone who is both not wise and creative is either strong or not quiet.
If mary is either old or calm then susan is not curious.
If fred is curious then someone is not wise.
If alice is old then someone is both not brave and strong and vice versa.
If john is not tall then fred is not creative or old.
If someone is not rich or not calm then someone is both wise and not strong and vice versa.
Everyone who is not tall is both calm and tall and vice versa.
Everyone who is not rich is either patient or not kind.
If john is humble or funny then mary is either not patient or humble.
Everyone who is either wise or not rich is either tall or patient and vice versa.
If someone is either funny or not old then someone is wise and vice versa.
If john is both quiet and brave then someone is not happy or not patient and vice versa.
Everyone who is calm or generous is old.
If fred is brave or strong then someone is both not rich and funny and vice versa.
Mary is either patient or not strong.
Paul is either happy or kind.
Mary is creative or happy.
Fred is both old and not rich.
Lucy is either calm or kind.
Mary is not wise.
Someone is both not humble and creative.
Alice is both not funny and strong. | Fred is calm. | contradiction | (![X]:((calm(X)&~wise(X))<=>(brave(X)&~humble(X))))&
(((funny(paul)<~>~kind(paul)))=>(?[X]:((patient(X)|~happy(X)))))&
(![X]:((~wise(X)&creative(X))=>(strong(X)<~>~quiet(X))))&
(((old(mary)<~>calm(mary)))=>(~curious(susan)))&
((curious(fred))=>(?[X]:(~wise(X))))&
((old(alice))<=>(?[X]:((~brave(X)&strong(X)))))&
((~tall(john))=>((~creative(fred)|old(fred))))&
((?[X]:((~rich(X)|~calm(X))))<=>(?[X]:((wise(X)&~strong(X)))))&
(![X]:(~tall(X)<=>(calm(X)&tall(X))))&
(![X]:(~rich(X)=>(patient(X)<~>~kind(X))))&
(((humble(john)|funny(john)))=>((~patient(mary)<~>humble(mary))))&
(![X]:((wise(X)<~>~rich(X))<=>(tall(X)<~>patient(X))))&
((?[X]:((funny(X)<~>~old(X))))<=>(?[X]:(wise(X))))&
(((quiet(john)&brave(john)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((calm(X)|generous(X))=>old(X)))&
(((brave(fred)|strong(fred)))<=>(?[X]:((~rich(X)&funny(X)))))&
((patient(mary)<~>~strong(mary)))&
((happy(paul)<~>kind(paul)))&
((creative(mary)|happy(mary)))&
((old(fred)&~rich(fred)))&
((calm(lucy)<~>kind(lucy)))&
(~wise(mary))&
(?[X]:((~humble(X)&creative(X))))&
((~funny(alice)&strong(alice))) | calm(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5774604414422396015222609
% SZS output start Proof for 5774604414422396015222609
9. ! [X0] : (~tall(X0) <=> (tall(X0) & calm(X0))) [input p8]
25. calm(fred) [input hypothesis]
54. ! [X0] : ((~tall(X0) | (~tall(X0) | ~calm(X0))) & ((tall(X0) & calm(X0)) | tall(X0))) [nnf transformation 9]
55. ! [X0] : ((~tall(X0) | ~tall(X0) | ~calm(X0)) & ((tall(X0) & calm(X0)) | tall(X0))) [flattening 54]
97. tall(X0) | tall(X0) [cnf transformation 55]
98. ~tall(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 55]
142. calm(fred) [cnf transformation 25]
143. tall(X0) [duplicate literal removal 97]
144. ~tall(X0) | ~calm(X0) [duplicate literal removal 98]
371. ~calm(X0) [resolution 144,143]
377. $false [resolution 371,142]
% SZS output end Proof for 5774604414422396015222609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not humble is either rich or tall. Everyone who is quiet is not patient and vice versa. Everyone who is both calm and not curious is either not calm or old and vice versa. Everyone who is either tall or not wise is brave. If paul is both not strong and creative then someone is both wise and not brave. Everyone who is not happy or strong is not humble or not rich and vice versa. Everyone who is either not creative or patient is both creative and rich. Everyone who is not creative is tall or wise. If fred is kind or not quiet then alice is old or rich and vice versa. Everyone who is not old or kind is not curious and vice versa. Everyone who is both calm and not strong is calm and vice versa. Everyone who is patient or not strong is calm or generous. Everyone who is not funny is quiet and vice versa. If someone is patient or not generous then someone is both not brave and not old. Everyone who is either quiet or rich is both creative and not rich and vice versa. Someone is not patient. Alice is happy. Someone is quiet or humble. | Paul is not funny. | entailment | (![X]:((~rich(X)|~humble(X))=>(rich(X)<~>tall(X))))&
(![X]:(quiet(X)<=>~patient(X)))&
(![X]:((calm(X)&~curious(X))<=>(~calm(X)<~>old(X))))&
(![X]:((tall(X)<~>~wise(X))=>brave(X)))&
(((~strong(paul)&creative(paul)))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((~happy(X)|strong(X))<=>(~humble(X)|~rich(X))))&
(![X]:((~creative(X)<~>patient(X))=>(creative(X)&rich(X))))&
(![X]:(~creative(X)=>(tall(X)|wise(X))))&
(((kind(fred)|~quiet(fred)))<=>((old(alice)|rich(alice))))&
(![X]:((~old(X)|kind(X))<=>~curious(X)))&
(![X]:((calm(X)&~strong(X))<=>calm(X)))&
(![X]:((patient(X)|~strong(X))=>(calm(X)|generous(X))))&
(![X]:(~funny(X)<=>quiet(X)))&
((?[X]:((patient(X)|~generous(X))))=>(?[X]:((~brave(X)&~old(X)))))&
(![X]:((quiet(X)<~>rich(X))<=>(creative(X)&~rich(X))))&
(?[X]:(~patient(X)))&
(happy(alice))&
(?[X]:((quiet(X)|humble(X)))) | ~funny(paul) | [
"p1",
"p2",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4966377599515390465181837
% SZS output start Proof for 4966377599515390465181837
2. ! [X0] : (quiet(X0) <=> ~patient(X0)) [input p1]
3. ! [X0] : ((~curious(X0) & calm(X0)) <=> (~calm(X0) <~> old(X0))) [input p2]
10. ! [X0] : ((kind(X0) | ~old(X0)) <=> ~curious(X0)) [input p9]
13. ! [X0] : (~funny(X0) <=> quiet(X0)) [input p12]
14. ? [X0] : (~generous(X0) | patient(X0)) => ? [X0] : (~old(X0) & ~brave(X0)) [input p13]
19. funny(paul) [input hypothesis]
20. ? [X0] : (~generous(X0) | patient(X0)) => ? [X1] : (~old(X1) & ~brave(X1)) [rectify 14]
21. ! [X0] : (quiet(X0) => ~funny(X0)) [unused predicate definition removal 13]
23. ? [X0] : patient(X0) => ? [X1] : (~old(X1) & ~brave(X1)) [pure predicate removal 20]
31. ! [X0] : (~funny(X0) | ~quiet(X0)) [ennf transformation 21]
32. ? [X1] : (~old(X1) & ~brave(X1)) | ! [X0] : ~patient(X0) [ennf transformation 23]
34. ! [X0] : ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))) [nnf transformation 2]
35. ! [X0] : (((~curious(X0) & calm(X0)) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | (curious(X0) | ~calm(X0)))) [nnf transformation 3]
36. ! [X0] : (((~curious(X0) & calm(X0)) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | curious(X0) | ~calm(X0))) [flattening 35]
45. ! [X0] : (((kind(X0) | ~old(X0)) | curious(X0)) & (~curious(X0) | (~kind(X0) & old(X0)))) [nnf transformation 10]
46. ! [X0] : ((kind(X0) | ~old(X0) | curious(X0)) & (~curious(X0) | (~kind(X0) & old(X0)))) [flattening 45]
49. ? [X0] : (~old(X0) & ~brave(X0)) | ! [X1] : ~patient(X1) [rectify 32]
50. ? [X0] : (~old(X0) & ~brave(X0)) => (~old(sK1) & ~brave(sK1)) [choice axiom]
51. (~old(sK1) & ~brave(sK1)) | ! [X1] : ~patient(X1) [skolemisation 49,50]
63. patient(X0) | quiet(X0) [cnf transformation 34]
64. old(X0) | ~calm(X0) | curious(X0) | ~calm(X0) [cnf transformation 36]
66. calm(X0) | old(X0) | calm(X0) [cnf transformation 36]
87. ~curious(X0) | old(X0) [cnf transformation 46]
93. ~funny(X0) | ~quiet(X0) [cnf transformation 31]
95. ~old(sK1) | ~patient(X1) [cnf transformation 51]
105. funny(paul) [cnf transformation 19]
109. old(X0) | ~calm(X0) | curious(X0) [duplicate literal removal 64]
110. calm(X0) | old(X0) [duplicate literal removal 66]
112. old(X0) | curious(X0) [subsumption resolution 109,110]
152. old(X0) [subsumption resolution 87,112]
153. ~patient(X1) [subsumption resolution 95,152]
164. quiet(X1) [resolution 63,153]
168. ~quiet(paul) [resolution 93,105]
169. $false [subsumption resolution 168,164]
% SZS output end Proof for 4966377599515390465181837
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
Everyone who is generous is generous or not kind and vice versa.
If someone is both kind and quiet then someone is strong or not old.
Everyone who is both old and not calm is not rich or not funny and vice versa.
Everyone who is both rich and not wise is both curious and quiet.
If john is both curious and old then susan is rich and vice versa.
Everyone who is either patient or happy is funny or not curious and vice versa.
If someone is rich or calm then alice is rich or not old and vice versa.
Someone is humble or not funny.
Someone is either not curious or not creative.
Someone is both strong and humble.
Someone is either not happy or not funny.
Someone is either not rich or not tall.
Lucy is both not funny and humble.
Fred is rich or tall.
Alice is either kind or not happy. | Alice is calm. | contradiction | (![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)&~calm(X))<=>(~rich(X)|~funny(X))))&
(![X]:((rich(X)&~wise(X))=>(curious(X)&quiet(X))))&
(((curious(john)&old(john)))<=>(rich(susan)))&
(![X]:((patient(X)<~>happy(X))<=>(funny(X)|~curious(X))))&
((?[X]:((rich(X)|calm(X))))<=>((rich(alice)|~old(alice))))&
(?[X]:((humble(X)|~funny(X))))&
(?[X]:((~curious(X)<~>~creative(X))))&
(?[X]:((strong(X)&humble(X))))&
(?[X]:((~happy(X)<~>~funny(X))))&
(?[X]:((~rich(X)<~>~tall(X))))&
((~funny(lucy)&humble(lucy)))&
((rich(fred)|tall(fred)))&
((kind(alice)<~>~happy(alice))) | calm(alice) | [
"p0",
"p1",
"p5",
"p6",
"p11",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6976979087525171003282055
% SZS output start Proof for 6976979087525171003282055
1. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p0]
2. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p1]
6. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (funny(X0) | curious(X0))) [input p5]
7. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p6]
12. ! [X0] : ((~calm(X0) & old(X0)) <=> (~funny(X0) | ~rich(X0))) [input p11]
15. ! [X0] : ((patient(X0) <~> happy(X0)) <=> (~curious(X0) | funny(X0))) [input p14]
24. kind(alice) <~> ~happy(alice) [input p23]
25. calm(alice) [input hypothesis]
32. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 1]
33. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 32]
34. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 2]
35. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 34]
43. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 6]
44. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 43]
45. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 7]
46. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 45]
59. ! [X0] : (((~calm(X0) & old(X0)) | (funny(X0) & rich(X0))) & ((~funny(X0) | ~rich(X0)) | (calm(X0) | ~old(X0)))) [nnf transformation 12]
60. ! [X0] : (((~calm(X0) & old(X0)) | (funny(X0) & rich(X0))) & (~funny(X0) | ~rich(X0) | calm(X0) | ~old(X0))) [flattening 59]
63. ! [X0] : ((((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | (curious(X0) & ~funny(X0))) & ((~curious(X0) | funny(X0)) | ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0))))) [nnf transformation 15]
64. ! [X0] : ((((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | (curious(X0) & ~funny(X0))) & (~curious(X0) | funny(X0) | ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0))))) [flattening 63]
83. (happy(alice) | ~kind(alice)) & (~happy(alice) | kind(alice)) [nnf transformation 24]
84. ~calm(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 33]
87. brave(X0) | patient(X0) | strong(X0) [cnf transformation 33]
90. ~calm(X0) | kind(X0) | strong(X0) [cnf transformation 35]
91. ~kind(X0) | ~strong(X0) [cnf transformation 35]
104. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 44]
108. ~calm(X0) | curious(X0) [cnf transformation 46]
130. ~calm(X0) | funny(X0) [cnf transformation 60]
136. ~funny(X0) | patient(X0) | happy(X0) [cnf transformation 64]
138. ~funny(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 64]
156. ~happy(alice) | kind(alice) [cnf transformation 83]
157. happy(alice) | ~kind(alice) [cnf transformation 83]
158. calm(alice) [cnf transformation 25]
160. ~curious(X0) | ~brave(X0) [duplicate literal removal 104]
323. 34 <=> kind(alice) [avatar definition]
324. kind(alice) <- (34) [avatar component clause 323]
327. 35 <=> happy(alice) [avatar definition]
328. ~happy(alice) <- (~35) [avatar component clause 327]
329. happy(alice) <- (35) [avatar component clause 327]
330. ~34 | 35 [avatar split clause 157,327,323]
331. 34 | ~35 [avatar split clause 156,327,323]
335. curious(alice) [resolution 108,158]
344. funny(alice) [resolution 130,158]
347. ~brave(alice) [resolution 160,335]
349. ~strong(alice) | ~patient(alice) [resolution 84,158]
352. 36 <=> patient(alice) [avatar definition]
356. 37 <=> strong(alice) [avatar definition]
358. ~strong(alice) <- (~37) [avatar component clause 356]
359. ~36 | ~37 [avatar split clause 349,356,352]
380. kind(alice) | strong(alice) [resolution 90,158]
382. patient(alice) | strong(alice) [resolution 347,87]
423. patient(alice) | happy(alice) [resolution 136,344]
429. patient(alice) <- (~35) [subsumption resolution 423,328]
430. 36 | 35 [avatar split clause 429,327,352]
432. 37 | 36 [avatar split clause 382,352,356]
435. kind(alice) <- (~37) [subsumption resolution 380,358]
436. 34 | 37 [avatar split clause 435,356,323]
437. ~strong(alice) <- (34) [resolution 324,91]
462. ~patient(alice) | ~happy(alice) [resolution 138,344]
467. ~patient(alice) <- (35) [subsumption resolution 462,329]
468. ~36 | ~35 [avatar split clause 467,327,352]
469. ~37 | ~34 [avatar split clause 437,323,356]
470. $false [avatar sat refutation 330,331,359,430,432,436,468,469]
% SZS output end Proof for 6976979087525171003282055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not wise then lucy is humble or not strong and vice versa. Everyone who is rich is not humble or wise and vice versa. Everyone who is wise is either not kind or not patient and vice versa. Everyone who is either not strong or not tall is either not strong or not calm and vice versa. Everyone who is not patient or not calm is rich or tall. Everyone who is kind is not generous or not quiet and vice versa. If someone is either not generous or rich then someone is wise or generous and vice versa. Everyone who is wise or not rich is both wise and not creative. If someone is not strong or wise then someone is either not patient or not humble. If john is not funny then mary is not funny and vice versa. If lucy is both curious and old then john is not brave. If someone is either not wise or not tall then someone is not generous or tall and vice versa. Everyone who is both creative and not happy is either not strong or brave. Everyone who is tall or kind is either not calm or not happy. If alice is both tall and not quiet then someone is rich or old and vice versa. If susan is either humble or not creative then someone is not happy or not creative. Someone is brave. John is both calm and not creative. Paul is rich or generous. Someone is either not happy or curious. Alice is either not happy or not humble. Someone is not happy or rich. Someone is either not old or funny. Someone is happy. | Alice is wise. | entailment | ((~wise(alice))<=>((humble(lucy)|~strong(lucy))))&
(![X]:(rich(X)<=>(~humble(X)|wise(X))))&
(![X]:(wise(X)<=>(~kind(X)<~>~patient(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:((~patient(X)|~calm(X))=>(rich(X)|tall(X))))&
(![X]:(kind(X)<=>(~generous(X)|~quiet(X))))&
((?[X]:((~generous(X)<~>rich(X))))<=>(?[X]:((wise(X)|generous(X)))))&
(![X]:((wise(X)|~rich(X))=>(wise(X)&~creative(X))))&
((?[X]:((~strong(X)|wise(X))))=>(?[X]:((~patient(X)<~>~humble(X)))))&
((~funny(john))<=>(~funny(mary)))&
(((curious(lucy)&old(lucy)))=>(~brave(john)))&
((?[X]:((~wise(X)<~>~tall(X))))<=>(?[X]:((~generous(X)|tall(X)))))&
(![X]:((creative(X)&~happy(X))=>(~strong(X)<~>brave(X))))&
(![X]:((tall(X)|kind(X))=>(~calm(X)<~>~happy(X))))&
(((tall(alice)&~quiet(alice)))<=>(?[X]:((rich(X)|old(X)))))&
(((humble(susan)<~>~creative(susan)))=>(?[X]:((~happy(X)|~creative(X)))))&
(?[X]:(brave(X)))&
((calm(john)&~creative(john)))&
((rich(paul)|generous(paul)))&
(?[X]:((~happy(X)<~>curious(X))))&
((~happy(alice)<~>~humble(alice)))&
(?[X]:((~happy(X)|rich(X))))&
(?[X]:((~old(X)<~>funny(X))))&
(?[X]:(happy(X))) | wise(alice) | [
"p1",
"p3",
"p7",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5539848936969005706891065
% SZS output start Proof for 5539848936969005706891065
2. ! [X0] : (rich(X0) <=> (wise(X0) | ~humble(X0))) [input p1]
4. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> (~strong(X0) <~> ~calm(X0))) [input p3]
8. ! [X0] : ((~rich(X0) | wise(X0)) => (~creative(X0) & wise(X0))) [input p7]
14. ! [X0] : ((kind(X0) | tall(X0)) => (~calm(X0) <~> ~happy(X0))) [input p13]
15. (~quiet(alice) & tall(alice)) <=> ? [X0] : (old(X0) | rich(X0)) [input p14]
21. ~happy(alice) <~> ~humble(alice) [input p20]
25. ~wise(alice) [input hypothesis]
31. ! [X0] : ((~creative(X0) & wise(X0)) | (rich(X0) & ~wise(X0))) [ennf transformation 8]
37. ! [X0] : ((~calm(X0) <~> ~happy(X0)) | (~kind(X0) & ~tall(X0))) [ennf transformation 14]
41. ! [X0] : ((rich(X0) | (~wise(X0) & humble(X0))) & ((wise(X0) | ~humble(X0)) | ~rich(X0))) [nnf transformation 2]
42. ! [X0] : ((rich(X0) | (~wise(X0) & humble(X0))) & (wise(X0) | ~humble(X0) | ~rich(X0))) [flattening 41]
44. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 4]
63. ! [X0] : (((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | (~kind(X0) & ~tall(X0))) [nnf transformation 37]
64. ((~quiet(alice) & tall(alice)) | ! [X0] : (~old(X0) & ~rich(X0))) & (? [X0] : (old(X0) | rich(X0)) | (quiet(alice) | ~tall(alice))) [nnf transformation 15]
65. ((~quiet(alice) & tall(alice)) | ! [X0] : (~old(X0) & ~rich(X0))) & (? [X0] : (old(X0) | rich(X0)) | quiet(alice) | ~tall(alice)) [flattening 64]
66. ((~quiet(alice) & tall(alice)) | ! [X0] : (~old(X0) & ~rich(X0))) & (? [X1] : (old(X1) | rich(X1)) | quiet(alice) | ~tall(alice)) [rectify 65]
67. ? [X1] : (old(X1) | rich(X1)) => (old(sK5) | rich(sK5)) [choice axiom]
68. ((~quiet(alice) & tall(alice)) | ! [X0] : (~old(X0) & ~rich(X0))) & ((old(sK5) | rich(sK5)) | quiet(alice) | ~tall(alice)) [skolemisation 66,67]
77. (humble(alice) | happy(alice)) & (~humble(alice) | ~happy(alice)) [nnf transformation 21]
88. ~rich(X0) | ~humble(X0) | wise(X0) [cnf transformation 42]
90. ~wise(X0) | rich(X0) [cnf transformation 42]
96. ~calm(X0) | ~strong(X0) | ~strong(X0) | tall(X0) [cnf transformation 44]
97. calm(X0) | strong(X0) | ~tall(X0) | strong(X0) [cnf transformation 44]
100. ~tall(X0) | ~strong(X0) | ~strong(X0) | calm(X0) [cnf transformation 44]
101. tall(X0) | strong(X0) | ~calm(X0) | strong(X0) [cnf transformation 44]
115. wise(X0) | rich(X0) [cnf transformation 31]
133. ~happy(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 63]
138. tall(alice) | ~rich(X0) [cnf transformation 68]
151. humble(alice) | happy(alice) [cnf transformation 77]
156. ~wise(alice) [cnf transformation 25]
157. ~calm(X0) | ~strong(X0) | tall(X0) [duplicate literal removal 96]
158. calm(X0) | strong(X0) | ~tall(X0) [duplicate literal removal 97]
159. ~tall(X0) | ~strong(X0) | calm(X0) [duplicate literal removal 100]
160. tall(X0) | strong(X0) | ~calm(X0) [duplicate literal removal 101]
166. 2 <=> wise(alice) [avatar definition]
168. ~wise(alice) <- (~2) [avatar component clause 166]
176. ~tall(X0) | calm(X0) [subsumption resolution 158,159]
177. ~calm(X0) | tall(X0) [subsumption resolution 157,160]
213. rich(X0) [subsumption resolution 115,90]
286. ~happy(X0) | ~calm(X0) [subsumption resolution 133,177]
298. 30 <=> tall(alice) [avatar definition]
300. tall(alice) <- (30) [avatar component clause 298]
302. tall(alice) [subsumption resolution 138,213]
303. 30 [avatar split clause 302,298]
333. 37 <=> happy(alice) [avatar definition]
335. happy(alice) <- (37) [avatar component clause 333]
337. 38 <=> humble(alice) [avatar definition]
339. humble(alice) <- (38) [avatar component clause 337]
340. 37 | 38 [avatar split clause 151,337,333]
352. ~2 [avatar split clause 156,166]
359. calm(alice) <- (30) [resolution 176,300]
365. ~calm(alice) <- (37) [resolution 286,335]
366. $false <- (30, 37) [subsumption resolution 365,359]
367. ~30 | ~37 [avatar contradiction clause 366]
370. ~humble(X1) | wise(X1) [resolution 88,213]
371. wise(alice) <- (38) [resolution 370,339]
372. $false <- (~2, 38) [subsumption resolution 371,168]
373. 2 | ~38 [avatar contradiction clause 372]
374. $false [avatar sat refutation 303,340,352,367,373]
% SZS output end Proof for 5539848936969005706891065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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