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
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is funny or not curious is either curious or not quiet and vice versa. Everyone who is both generous and happy is not brave. Everyone who is funny or happy is both calm and not rich and vice versa. Everyone who is both not curious and brave is either quiet or curious and vice versa. If someone is both not rich and not brave then someone is either curious or not quiet and vice versa. If alice is either creative or wise then susan is creative and vice versa. If someone is both humble and creative then alice is not wise or not tall and vice versa. If susan is not happy then susan is either brave or wise. Everyone who is either curious or patient is either not generous or quiet. If someone is both not happy and generous then someone is creative or not curious and vice versa. If someone is not brave or not kind then someone is not old. Everyone who is not rich is both tall and not funny and vice versa. If mary is either not rich or rich then alice is either curious or not patient and vice versa. If someone is both patient and wise then john is not brave and vice versa. If someone is both kind and not patient then lucy is both not tall and tall and vice versa. If someone is not old then someone is not kind or not humble. Susan is patient or generous. Someone is either not happy or not wise. Someone is both calm and tall. Someone is either old or not brave. Alice is both humble and not brave. Someone is both not kind and not wise. | Susan is not tall. | neutral | (![X]:((funny(X)|~curious(X))<=>(curious(X)<~>~quiet(X))))&
(![X]:((generous(X)&happy(X))=>~brave(X)))&
(![X]:((funny(X)|happy(X))<=>(calm(X)&~rich(X))))&
(![X]:((~curious(X)&brave(X))<=>(quiet(X)<~>curious(X))))&
((?[X]:((~rich(X)&~brave(X))))<=>(?[X]:((curious(X)<~>~quiet(X)))))&
(((creative(alice)<~>wise(alice)))<=>(creative(susan)))&
((?[X]:((humble(X)&creative(X))))<=>((~wise(alice)|~tall(alice))))&
((~happy(susan))=>((brave(susan)<~>wise(susan))))&
(![X]:((curious(X)<~>patient(X))=>(~generous(X)<~>quiet(X))))&
((?[X]:((~happy(X)&generous(X))))<=>(?[X]:((creative(X)|~curious(X)))))&
((?[X]:((~brave(X)|~kind(X))))=>(?[X]:(~old(X))))&
(![X]:(~rich(X)<=>(tall(X)&~funny(X))))&
(((~rich(mary)<~>rich(mary)))<=>((curious(alice)<~>~patient(alice))))&
((?[X]:((patient(X)&wise(X))))<=>(~brave(john)))&
((?[X]:((kind(X)&~patient(X))))<=>((~tall(lucy)&tall(lucy))))&
((?[X]:(~old(X)))=>(?[X]:((~kind(X)|~humble(X)))))&
((patient(susan)|generous(susan)))&
(?[X]:((~happy(X)<~>~wise(X))))&
(?[X]:((calm(X)&tall(X))))&
(?[X]:((old(X)<~>~brave(X))))&
((humble(alice)&~brave(alice)))&
(?[X]:((~kind(X)&~wise(X)))) | ~tall(susan) | [] | null | 0 |
Everyone who is generous is both quiet and not funny. Everyone who is both patient and not humble is either patient or not generous and vice versa. Everyone who is tall or not happy is not patient or quiet. Everyone who is not patient is both wise and calm. If mary is kind or not calm then someone is not kind. If someone is either not brave or old then lucy is funny or not rich and vice versa. If fred is either strong or not strong then someone is both not old and brave. Everyone who is either humble or not funny is wise. If someone is not funny or brave then john is both old and generous and vice versa. Everyone who is either not curious or not rich is either not old or generous. If someone is both not quiet and not calm then someone is either not wise or old. If someone is not funny then someone is either old or brave. Everyone who is not rich is either happy or not rich and vice versa. If someone is strong then someone is funny or rich. If someone is either old or not strong then john is either not generous or not funny. If someone is both not funny and not kind then someone is both strong and not patient. Susan is quiet or curious. Susan is creative or old. Someone is not generous or curious. Fred is either rich or calm. Alice is either not strong or not funny. Someone is either not generous or not tall. Someone is not happy. | John is funny. | contradiction | (![X]:(generous(X)=>(quiet(X)&~funny(X))))&
(![X]:((patient(X)&~humble(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((tall(X)|~happy(X))=>(~patient(X)|quiet(X))))&
(![X]:(~patient(X)=>(wise(X)&calm(X))))&
(((kind(mary)|~calm(mary)))=>(?[X]:(~kind(X))))&
((?[X]:((~brave(X)<~>old(X))))<=>((funny(lucy)|~rich(lucy))))&
(((strong(fred)<~>~strong(fred)))=>(?[X]:((~old(X)&brave(X)))))&
(![X]:((humble(X)<~>~funny(X))=>wise(X)))&
((?[X]:((~funny(X)|brave(X))))<=>((old(john)&generous(john))))&
(![X]:((~curious(X)<~>~rich(X))=>(~old(X)<~>generous(X))))&
((?[X]:((~quiet(X)&~calm(X))))=>(?[X]:((~wise(X)<~>old(X)))))&
((?[X]:(~funny(X)))=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:(~rich(X)<=>(happy(X)<~>~rich(X))))&
((?[X]:(strong(X)))=>(?[X]:((funny(X)|rich(X)))))&
((?[X]:((old(X)<~>~strong(X))))=>((~generous(john)<~>~funny(john))))&
((?[X]:((~funny(X)&~kind(X))))=>(?[X]:((strong(X)&~patient(X)))))&
((quiet(susan)|curious(susan)))&
((creative(susan)|old(susan)))&
(?[X]:((~generous(X)|curious(X))))&
((rich(fred)<~>calm(fred)))&
((~strong(alice)<~>~funny(alice)))&
(?[X]:((~generous(X)<~>~tall(X))))&
(?[X]:(~happy(X))) | funny(john) | [
"p0",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8367517308290922341503934
% SZS output start Proof for 8367517308290922341503934
1. ! [X0] : (generous(X0) => (~funny(X0) & quiet(X0))) [input p0]
7. (strong(fred) <~> ~strong(fred)) => ? [X0] : (brave(X0) & ~old(X0)) [input p6]
9. ? [X0] : (brave(X0) | ~funny(X0)) <=> (generous(john) & old(john)) [input p8]
24. funny(john) [input hypothesis]
31. ! [X0] : (generous(X0) => ~funny(X0)) [pure predicate removal 1]
36. ! [X0] : (~funny(X0) | ~generous(X0)) [ennf transformation 31]
39. ? [X0] : (brave(X0) & ~old(X0)) | (strong(fred) <=> ~strong(fred)) [ennf transformation 7]
54. ? [X0] : (brave(X0) & ~old(X0)) | ((strong(fred) | strong(fred)) & (~strong(fred) | ~strong(fred))) [nnf transformation 39]
55. ? [X0] : (brave(X0) & ~old(X0)) => (brave(sK2) & ~old(sK2)) [choice axiom]
56. (brave(sK2) & ~old(sK2)) | ((strong(fred) | strong(fred)) & (~strong(fred) | ~strong(fred))) [skolemisation 54,55]
57. (? [X0] : (brave(X0) | ~funny(X0)) | (~generous(john) | ~old(john))) & ((generous(john) & old(john)) | ! [X0] : (~brave(X0) & funny(X0))) [nnf transformation 9]
58. (? [X0] : (brave(X0) | ~funny(X0)) | ~generous(john) | ~old(john)) & ((generous(john) & old(john)) | ! [X0] : (~brave(X0) & funny(X0))) [flattening 57]
59. (? [X0] : (brave(X0) | ~funny(X0)) | ~generous(john) | ~old(john)) & ((generous(john) & old(john)) | ! [X1] : (~brave(X1) & funny(X1))) [rectify 58]
60. ? [X0] : (brave(X0) | ~funny(X0)) => (brave(sK3) | ~funny(sK3)) [choice axiom]
61. ((brave(sK3) | ~funny(sK3)) | ~generous(john) | ~old(john)) & ((generous(john) & old(john)) | ! [X1] : (~brave(X1) & funny(X1))) [skolemisation 59,60]
84. ~funny(X0) | ~generous(X0) [cnf transformation 36]
102. brave(sK2) | ~strong(fred) | ~strong(fred) [cnf transformation 56]
103. brave(sK2) | strong(fred) | strong(fred) [cnf transformation 56]
107. generous(john) | ~brave(X1) [cnf transformation 61]
134. funny(john) [cnf transformation 24]
139. brave(sK2) | ~strong(fred) [duplicate literal removal 102]
140. brave(sK2) | strong(fred) [duplicate literal removal 103]
187. 10 <=> strong(fred) [avatar definition]
191. 11 <=> brave(sK2) [avatar definition]
193. brave(sK2) <- (11) [avatar component clause 191]
194. 10 | 11 [avatar split clause 140,191,187]
195. ~10 | 11 [avatar split clause 139,191,187]
207. 14 <=> generous(john) [avatar definition]
220. 17 <=> ! [X1] : ~brave(X1) [avatar definition]
221. ~brave(X1) <- (17) [avatar component clause 220]
222. 17 | 14 [avatar split clause 107,207,220]
256. 25 <=> funny(john) [avatar definition]
258. funny(john) <- (25) [avatar component clause 256]
316. 25 [avatar split clause 134,256]
323. ~generous(john) <- (25) [resolution 84,258]
328. ~14 | ~25 [avatar split clause 323,256,207]
329. $false <- (11, 17) [resolution 221,193]
332. ~11 | ~17 [avatar contradiction clause 329]
333. $false [avatar sat refutation 194,195,222,316,328,332]
% SZS output end Proof for 8367517308290922341503934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is tall.
If someone is either not happy or patient then someone is rich and vice versa.
If paul is creative or calm then someone is both not old and tall and vice versa.
Everyone who is both not wise and not brave is kind or not patient.
Everyone who is both tall and not old is both not generous and not patient.
If someone is not patient then paul is either not humble or brave and vice versa.
Everyone who is both generous and tall is patient and vice versa.
If someone is either not humble or patient then fred is either strong or tall.
If paul is generous or not happy then someone is generous.
Everyone who is either strong or not old is tall and vice versa.
Everyone who is not tall or not brave is brave or humble.
If susan is happy or not calm then someone is both not kind and not curious and vice versa.
If mary is both patient and not tall then someone is either strong or wise and vice versa.
Everyone who is calm is not calm or funny and vice versa.
If susan is both not quiet and not wise then mary is both old and not creative.
Everyone who is generous or creative is either wise or curious and vice versa.
Someone is either creative or happy.
John is both rich and quiet.
Paul is strong or not generous.
Lucy is calm.
Mary is generous.
John is either funny or not curious.
John is brave or not old.
Fred is both not humble and curious. | Susan is not quiet. | neutral | (![X]:(strong(X)=>tall(X)))&
((?[X]:((~happy(X)<~>patient(X))))<=>(?[X]:(rich(X))))&
(((creative(paul)|calm(paul)))<=>(?[X]:((~old(X)&tall(X)))))&
(![X]:((~wise(X)&~brave(X))=>(kind(X)|~patient(X))))&
(![X]:((tall(X)&~old(X))=>(~generous(X)&~patient(X))))&
((?[X]:(~patient(X)))<=>((~humble(paul)<~>brave(paul))))&
(![X]:((generous(X)&tall(X))<=>patient(X)))&
((?[X]:((~humble(X)<~>patient(X))))=>((strong(fred)<~>tall(fred))))&
(((generous(paul)|~happy(paul)))=>(?[X]:(generous(X))))&
(![X]:((strong(X)<~>~old(X))<=>tall(X)))&
(![X]:((~tall(X)|~brave(X))=>(brave(X)|humble(X))))&
(((happy(susan)|~calm(susan)))<=>(?[X]:((~kind(X)&~curious(X)))))&
(((patient(mary)&~tall(mary)))<=>(?[X]:((strong(X)<~>wise(X)))))&
(![X]:(calm(X)<=>(~calm(X)|funny(X))))&
(((~quiet(susan)&~wise(susan)))=>((old(mary)&~creative(mary))))&
(![X]:((generous(X)|creative(X))<=>(wise(X)<~>curious(X))))&
(?[X]:((creative(X)<~>happy(X))))&
((rich(john)&quiet(john)))&
((strong(paul)|~generous(paul)))&
(calm(lucy))&
(generous(mary))&
((funny(john)<~>~curious(john)))&
((brave(john)|~old(john)))&
((~humble(fred)&curious(fred))) | ~quiet(susan) | [] | null | 0 |
If susan is either not humble or creative then paul is both not wise and not strong and vice versa.
Everyone who is both not calm and calm is not quiet and vice versa.
If someone is not wise or not curious then mary is not curious and vice versa.
Everyone who is not wise is either not tall or not kind.
Everyone who is not funny or funny is either not brave or old.
Everyone who is not generous is old and vice versa.
Everyone who is funny is not generous.
Everyone who is either not calm or curious is both generous and not kind and vice versa.
Everyone who is not wise is both not happy and generous and vice versa.
Everyone who is either happy or humble is both not kind and strong and vice versa.
If someone is either not creative or patient then someone is not quiet.
Everyone who is either not creative or not strong is either not old or not funny and vice versa.
If paul is either brave or quiet then someone is both not old and old.
Everyone who is not old or not rich is funny or old and vice versa.
If someone is not quiet then someone is generous or rich.
Everyone who is both not wise and tall is either not tall or patient.
Someone is both old and curious.
Fred is not patient or happy.
John is not quiet or brave.
Fred is strong.
John is either kind or happy.
Mary is wise or not rich.
Mary is calm or humble. | Mary is brave. | entailment | (((~humble(susan)<~>creative(susan)))<=>((~wise(paul)&~strong(paul))))&
(![X]:((~calm(X)&calm(X))<=>~quiet(X)))&
((?[X]:((~wise(X)|~curious(X))))<=>(~curious(mary)))&
(![X]:(~wise(X)=>(~tall(X)<~>~kind(X))))&
(![X]:((~funny(X)|funny(X))=>(~brave(X)<~>old(X))))&
(![X]:(~generous(X)<=>old(X)))&
(![X]:(funny(X)=>~generous(X)))&
(![X]:((~calm(X)<~>curious(X))<=>(generous(X)&~kind(X))))&
(![X]:(~wise(X)<=>(~happy(X)&generous(X))))&
(![X]:((happy(X)<~>humble(X))<=>(~kind(X)&strong(X))))&
((?[X]:((~creative(X)<~>patient(X))))=>(?[X]:(~quiet(X))))&
(![X]:((~creative(X)<~>~strong(X))<=>(~old(X)<~>~funny(X))))&
(((brave(paul)<~>quiet(paul)))=>(?[X]:((~old(X)&old(X)))))&
(![X]:((~old(X)|~rich(X))<=>(funny(X)|old(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((generous(X)|rich(X)))))&
(![X]:((~wise(X)&tall(X))=>(~tall(X)<~>patient(X))))&
(?[X]:((old(X)&curious(X))))&
((~patient(fred)|happy(fred)))&
((~quiet(john)|brave(john)))&
(strong(fred))&
((kind(john)<~>happy(john)))&
((wise(mary)|~rich(mary)))&
((calm(mary)|humble(mary))) | brave(mary) | [
"p4",
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5816938306340289772407376
% SZS output start Proof for 5816938306340289772407376
5. ! [X0] : ((funny(X0) | ~funny(X0)) => (~brave(X0) <~> old(X0))) [input p4]
6. ! [X0] : (~generous(X0) <=> old(X0)) [input p5]
7. ! [X0] : (funny(X0) => ~generous(X0)) [input p6]
14. ! [X0] : ((~rich(X0) | ~old(X0)) <=> (old(X0) | funny(X0))) [input p13]
24. ~brave(mary) [input hypothesis]
28. ! [X0] : ((~brave(X0) <~> old(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 5]
29. ! [X0] : (~generous(X0) | ~funny(X0)) [ennf transformation 7]
44. ! [X0] : (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | (~funny(X0) & funny(X0))) [nnf transformation 28]
45. ! [X0] : ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0))) [nnf transformation 6]
60. ! [X0] : (((~rich(X0) | ~old(X0)) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | (rich(X0) & old(X0)))) [nnf transformation 14]
61. ! [X0] : ((~rich(X0) | ~old(X0) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | (rich(X0) & old(X0)))) [flattening 60]
85. ~old(X0) | brave(X0) | funny(X0) [cnf transformation 44]
86. ~old(X0) | brave(X0) | ~funny(X0) [cnf transformation 44]
87. generous(X0) | old(X0) [cnf transformation 45]
89. ~generous(X0) | ~funny(X0) [cnf transformation 29]
119. old(X0) | funny(X0) | old(X0) [cnf transformation 61]
135. ~brave(mary) [cnf transformation 24]
137. old(X0) | funny(X0) [duplicate literal removal 119]
183. ~old(X0) | brave(X0) [subsumption resolution 85,86]
238. ~funny(X0) | old(X0) [resolution 89,87]
239. old(X0) [subsumption resolution 238,137]
248. brave(X1) [resolution 183,239]
252. $false [resolution 248,135]
% SZS output end Proof for 5816938306340289772407376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not old is both not funny and wise.
If someone is brave then susan is quiet.
Everyone who is either curious or strong is not quiet and vice versa.
If someone is either old or not strong then alice is either humble or calm and vice versa.
If lucy is tall or not tall then someone is not strong or happy.
Everyone who is either wise or patient is either humble or calm and vice versa.
Everyone who is generous is either not strong or not tall.
Everyone who is either kind or not old is not patient or wise and vice versa.
If john is either not curious or not tall then someone is both funny and not strong.
Everyone who is funny or calm is not brave and vice versa.
If someone is either happy or not happy then susan is brave and vice versa.
Everyone who is both patient and happy is both rich and curious and vice versa.
Everyone who is not happy is not happy or humble.
Everyone who is old or tall is either not kind or not patient and vice versa.
Everyone who is both not brave and quiet is both not quiet and curious and vice versa.
Everyone who is not old is both kind and not wise.
Alice is both kind and tall.
Someone is both not calm and rich.
Someone is generous.
Someone is both not calm and patient.
John is tall or not happy.
Mary is generous.
Lucy is either humble or rich. | John is not curious. | neutral | (![X]:((brave(X)|~old(X))=>(~funny(X)&wise(X))))&
((?[X]:(brave(X)))=>(quiet(susan)))&
(![X]:((curious(X)<~>strong(X))<=>~quiet(X)))&
((?[X]:((old(X)<~>~strong(X))))<=>((humble(alice)<~>calm(alice))))&
(((tall(lucy)|~tall(lucy)))=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:((wise(X)<~>patient(X))<=>(humble(X)<~>calm(X))))&
(![X]:(generous(X)=>(~strong(X)<~>~tall(X))))&
(![X]:((kind(X)<~>~old(X))<=>(~patient(X)|wise(X))))&
(((~curious(john)<~>~tall(john)))=>(?[X]:((funny(X)&~strong(X)))))&
(![X]:((funny(X)|calm(X))<=>~brave(X)))&
((?[X]:((happy(X)<~>~happy(X))))<=>(brave(susan)))&
(![X]:((patient(X)&happy(X))<=>(rich(X)&curious(X))))&
(![X]:(~happy(X)=>(~happy(X)|humble(X))))&
(![X]:((old(X)|tall(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~brave(X)&quiet(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~old(X)=>(kind(X)&~wise(X))))&
((kind(alice)&tall(alice)))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)&patient(X))))&
((tall(john)|~happy(john)))&
(generous(mary))&
((humble(lucy)<~>rich(lucy))) | ~curious(john) | [] | null | 0 |
Everyone who is calm or not generous is both not rich and kind. Everyone who is not wise or kind is strong and vice versa. Everyone who is either strong or quiet is kind or old. If susan is either quiet or not kind then someone is both not wise and not patient. If someone is not strong then alice is both kind and not rich and vice versa. If paul is calm then someone is both not curious and kind and vice versa. Everyone who is calm or strong is both not tall and not humble and vice versa. If paul is rich then lucy is either not old or not rich. Everyone who is both old and wise is both wise and not tall and vice versa. Everyone who is not patient is either not humble or kind. Everyone who is brave or not kind is not brave or not calm and vice versa. Everyone who is either calm or not generous is either kind or rich and vice versa. If someone is either curious or not happy then someone is either not generous or not calm. Everyone who is either strong or calm is not kind or wise and vice versa. If mary is brave or happy then alice is both generous and curious and vice versa. Everyone who is either not funny or not wise is either curious or happy. Fred is wise. Mary is both not quiet and wise. John is either not kind or happy. John is either old or not wise. Someone is patient or quiet. Susan is either curious or not creative. | Mary is not curious. | contradiction | (![X]:((calm(X)|~generous(X))=>(~rich(X)&kind(X))))&
(![X]:((~wise(X)|kind(X))<=>strong(X)))&
(![X]:((strong(X)<~>quiet(X))=>(kind(X)|old(X))))&
(((quiet(susan)<~>~kind(susan)))=>(?[X]:((~wise(X)&~patient(X)))))&
((?[X]:(~strong(X)))<=>((kind(alice)&~rich(alice))))&
((calm(paul))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((calm(X)|strong(X))<=>(~tall(X)&~humble(X))))&
((rich(paul))=>((~old(lucy)<~>~rich(lucy))))&
(![X]:((old(X)&wise(X))<=>(wise(X)&~tall(X))))&
(![X]:(~patient(X)=>(~humble(X)<~>kind(X))))&
(![X]:((brave(X)|~kind(X))<=>(~brave(X)|~calm(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(kind(X)<~>rich(X))))&
((?[X]:((curious(X)<~>~happy(X))))=>(?[X]:((~generous(X)<~>~calm(X)))))&
(![X]:((strong(X)<~>calm(X))<=>(~kind(X)|wise(X))))&
(((brave(mary)|happy(mary)))<=>((generous(alice)&curious(alice))))&
(![X]:((~funny(X)<~>~wise(X))=>(curious(X)<~>happy(X))))&
(wise(fred))&
((~quiet(mary)&wise(mary)))&
((~kind(john)<~>happy(john)))&
((old(john)<~>~wise(john)))&
(?[X]:((patient(X)|quiet(X))))&
((curious(susan)<~>~creative(susan))) | ~curious(mary) | [
"p0",
"p1",
"p5",
"p10",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3375327835162821683241208
% SZS output start Proof for 3375327835162821683241208
1. ! [X0] : ((~generous(X0) | calm(X0)) => (kind(X0) & ~rich(X0))) [input p0]
2. ! [X0] : ((kind(X0) | ~wise(X0)) <=> strong(X0)) [input p1]
6. calm(paul) <=> ? [X0] : (kind(X0) & ~curious(X0)) [input p5]
11. ! [X0] : ((~kind(X0) | brave(X0)) <=> (~calm(X0) | ~brave(X0))) [input p10]
14. ! [X0] : ((strong(X0) <~> calm(X0)) <=> (wise(X0) | ~kind(X0))) [input p13]
18. wise(mary) & ~quiet(mary) [input p17]
23. ~curious(mary) [input hypothesis]
25. ! [X0] : ((kind(X0) & ~rich(X0)) | (generous(X0) & ~calm(X0))) [ennf transformation 1]
33. ! [X0] : (((kind(X0) | ~wise(X0)) | ~strong(X0)) & (strong(X0) | (~kind(X0) & wise(X0)))) [nnf transformation 2]
34. ! [X0] : ((kind(X0) | ~wise(X0) | ~strong(X0)) & (strong(X0) | (~kind(X0) & wise(X0)))) [flattening 33]
44. (calm(paul) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X0] : (kind(X0) & ~curious(X0)) | ~calm(paul)) [nnf transformation 6]
45. (calm(paul) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X1] : (kind(X1) & ~curious(X1)) | ~calm(paul)) [rectify 44]
46. ? [X1] : (kind(X1) & ~curious(X1)) => (kind(sK2) & ~curious(sK2)) [choice axiom]
47. (calm(paul) | ! [X0] : (~kind(X0) | curious(X0))) & ((kind(sK2) & ~curious(sK2)) | ~calm(paul)) [skolemisation 45,46]
54. ! [X0] : (((~kind(X0) | brave(X0)) | (calm(X0) & brave(X0))) & ((~calm(X0) | ~brave(X0)) | (kind(X0) & ~brave(X0)))) [nnf transformation 11]
55. ! [X0] : ((~kind(X0) | brave(X0) | (calm(X0) & brave(X0))) & (~calm(X0) | ~brave(X0) | (kind(X0) & ~brave(X0)))) [flattening 54]
61. ! [X0] : ((((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | (~wise(X0) & kind(X0))) & ((wise(X0) | ~kind(X0)) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | (~wise(X0) & kind(X0))) & (wise(X0) | ~kind(X0) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0))))) [flattening 61]
73. ~calm(X0) | kind(X0) [cnf transformation 25]
75. strong(X0) | wise(X0) [cnf transformation 34]
77. ~strong(X0) | ~wise(X0) | kind(X0) [cnf transformation 34]
89. calm(paul) | ~kind(X0) | curious(X0) [cnf transformation 47]
103. ~calm(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 55]
105. ~kind(X0) | brave(X0) | brave(X0) [cnf transformation 55]
122. calm(X0) | strong(X0) | ~wise(X0) [cnf transformation 62]
136. wise(mary) [cnf transformation 18]
144. ~curious(mary) [cnf transformation 23]
145. ~brave(X0) | ~calm(X0) [duplicate literal removal 103]
146. ~kind(X0) | brave(X0) [duplicate literal removal 105]
187. 9 <=> ! [X0] : (~kind(X0) | curious(X0)) [avatar definition]
188. ~kind(X0) | curious(X0) <- (9) [avatar component clause 187]
190. 10 <=> calm(paul) [avatar definition]
192. calm(paul) <- (10) [avatar component clause 190]
193. 9 | 10 [avatar split clause 89,190,187]
244. strong(X0) | calm(X0) [subsumption resolution 122,75]
333. ~wise(X0) | kind(X0) | calm(X0) [resolution 77,244]
336. ~wise(X0) | kind(X0) [subsumption resolution 333,73]
402. kind(mary) [resolution 336,136]
436. curious(mary) <- (9) [resolution 402,188]
441. $false <- (9) [subsumption resolution 436,144]
442. ~9 [avatar contradiction clause 441]
461. kind(paul) <- (10) [resolution 192,73]
531. brave(paul) <- (10) [resolution 461,146]
584. ~calm(paul) <- (10) [resolution 531,145]
585. $false <- (10) [subsumption resolution 584,192]
586. ~10 [avatar contradiction clause 585]
587. $false [avatar sat refutation 193,442,586]
% SZS output end Proof for 3375327835162821683241208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not patient then someone is either not generous or calm and vice versa.
Everyone who is not rich is curious or not humble and vice versa.
If someone is both not patient and not kind then someone is either not tall or not curious and vice versa.
If someone is both wise and calm then john is either not old or not calm and vice versa.
If paul is not funny then someone is either brave or strong.
Everyone who is generous is both not quiet and calm and vice versa.
If fred is either not happy or not quiet then mary is not patient and vice versa.
Everyone who is both tall and generous is quiet or rich.
Everyone who is both not generous and humble is patient.
Everyone who is either strong or funny is either not brave or creative and vice versa.
If someone is not strong then john is tall.
Everyone who is both strong and generous is both generous and not calm.
Everyone who is both not humble and not generous is either not curious or not strong and vice versa.
Everyone who is not funny or not brave is either funny or not creative and vice versa.
Everyone who is both strong and kind is both not rich and patient.
Everyone who is not generous is either not generous or not tall and vice versa.
Susan is not patient or old.
Alice is either not curious or rich.
Someone is rich or quiet.
Someone is not kind.
Fred is either funny or wise.
Someone is not patient or calm.
John is not wise. | Susan is not tall. | contradiction | ((~patient(mary))<=>(?[X]:((~generous(X)<~>calm(X)))))&
(![X]:(~rich(X)<=>(curious(X)|~humble(X))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:((~tall(X)<~>~curious(X)))))&
((?[X]:((wise(X)&calm(X))))<=>((~old(john)<~>~calm(john))))&
((~funny(paul))=>(?[X]:((brave(X)<~>strong(X)))))&
(![X]:(generous(X)<=>(~quiet(X)&calm(X))))&
(((~happy(fred)<~>~quiet(fred)))<=>(~patient(mary)))&
(![X]:((tall(X)&generous(X))=>(quiet(X)|rich(X))))&
(![X]:((~generous(X)&humble(X))=>patient(X)))&
(![X]:((strong(X)<~>funny(X))<=>(~brave(X)<~>creative(X))))&
((?[X]:(~strong(X)))=>(tall(john)))&
(![X]:((strong(X)&generous(X))=>(generous(X)&~calm(X))))&
(![X]:((~humble(X)&~generous(X))<=>(~curious(X)<~>~strong(X))))&
(![X]:((~funny(X)|~brave(X))<=>(funny(X)<~>~creative(X))))&
(![X]:((strong(X)&kind(X))=>(~rich(X)&patient(X))))&
(![X]:(~generous(X)<=>(~generous(X)<~>~tall(X))))&
((~patient(susan)|old(susan)))&
((~curious(alice)<~>rich(alice)))&
(?[X]:((rich(X)|quiet(X))))&
(?[X]:(~kind(X)))&
((funny(fred)<~>wise(fred)))&
(?[X]:((~patient(X)|calm(X))))&
(~wise(john)) | ~tall(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 125995989470276247659688
% SZS output start Proof for 125995989470276247659688
16. ! [X0] : (~generous(X0) <=> (~generous(X0) <~> ~tall(X0))) [input p15]
24. ~tall(susan) [input hypothesis]
62. ! [X0] : ((~generous(X0) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0)))) & (((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | generous(X0))) [nnf transformation 16]
127. tall(X0) | generous(X0) | generous(X0) [cnf transformation 62]
129. ~generous(X0) | ~generous(X0) | tall(X0) [cnf transformation 62]
139. ~tall(susan) [cnf transformation 24]
140. tall(X0) | generous(X0) [duplicate literal removal 127]
141. ~generous(X0) | tall(X0) [duplicate literal removal 129]
260. tall(X0) [subsumption resolution 140,141]
300. $false [subsumption resolution 139,260]
% SZS output end Proof for 125995989470276247659688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is both old and kind and vice versa.
If someone is funny or not kind then john is both not creative and brave and vice versa.
If someone is not curious or rich then fred is both patient and not patient and vice versa.
Everyone who is not happy is both not quiet and not strong and vice versa.
Everyone who is either kind or not brave is both not patient and kind and vice versa.
Everyone who is not funny is either not patient or brave and vice versa.
Everyone who is either patient or not humble is not funny.
If john is wise then someone is tall and vice versa.
Everyone who is either curious or not generous is both brave and strong.
Everyone who is creative is both creative and curious and vice versa.
If someone is both not funny and strong then someone is either not kind or not calm and vice versa.
If someone is not funny then someone is both wise and generous and vice versa.
Everyone who is either wise or rich is not creative.
Everyone who is creative is not happy and vice versa.
Everyone who is happy is strong and vice versa.
Alice is either wise or not curious.
Lucy is both tall and happy.
Someone is generous or creative.
Someone is not creative. | John is quiet. | neutral | (![X]:(~brave(X)<=>(old(X)&kind(X))))&
((?[X]:((funny(X)|~kind(X))))<=>((~creative(john)&brave(john))))&
((?[X]:((~curious(X)|rich(X))))<=>((patient(fred)&~patient(fred))))&
(![X]:(~happy(X)<=>(~quiet(X)&~strong(X))))&
(![X]:((kind(X)<~>~brave(X))<=>(~patient(X)&kind(X))))&
(![X]:(~funny(X)<=>(~patient(X)<~>brave(X))))&
(![X]:((patient(X)<~>~humble(X))=>~funny(X)))&
((wise(john))<=>(?[X]:(tall(X))))&
(![X]:((curious(X)<~>~generous(X))=>(brave(X)&strong(X))))&
(![X]:(creative(X)<=>(creative(X)&curious(X))))&
((?[X]:((~funny(X)&strong(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((wise(X)&generous(X)))))&
(![X]:((wise(X)<~>rich(X))=>~creative(X)))&
(![X]:(creative(X)<=>~happy(X)))&
(![X]:(happy(X)<=>strong(X)))&
((wise(alice)<~>~curious(alice)))&
((tall(lucy)&happy(lucy)))&
(?[X]:((generous(X)|creative(X))))&
(?[X]:(~creative(X))) | quiet(john) | [] | null | 0 |
Everyone who is either not wise or not patient is both not kind and not generous.
If someone is funny then fred is either wise or not strong.
Everyone who is brave is either old or not funny and vice versa.
Everyone who is not humble or generous is both quiet and not curious.
If mary is strong then fred is patient or brave.
If someone is not wise or rich then someone is both strong and generous and vice versa.
If mary is both rich and brave then mary is both creative and patient.
Everyone who is either not wise or not curious is not funny.
If someone is either not creative or kind then alice is either not generous or wise and vice versa.
If someone is not brave then susan is calm and vice versa.
If someone is both not wise and wise then someone is rich and vice versa.
If susan is both not funny and calm then someone is both quiet and funny and vice versa.
If fred is not funny or kind then someone is either not strong or brave.
If someone is wise or not brave then someone is rich.
Everyone who is kind or not quiet is generous or brave and vice versa.
If paul is both patient and not tall then paul is not generous and vice versa.
Susan is both not old and not quiet.
Someone is either funny or not old.
Lucy is not kind.
Mary is wise or not calm.
Mary is not wise or humble.
Someone is patient or not creative. | Mary is calm. | contradiction | (![X]:((~wise(X)<~>~patient(X))=>(~kind(X)&~generous(X))))&
((?[X]:(funny(X)))=>((wise(fred)<~>~strong(fred))))&
(![X]:(brave(X)<=>(old(X)<~>~funny(X))))&
(![X]:((~humble(X)|generous(X))=>(quiet(X)&~curious(X))))&
((strong(mary))=>((patient(fred)|brave(fred))))&
((?[X]:((~wise(X)|rich(X))))<=>(?[X]:((strong(X)&generous(X)))))&
(((rich(mary)&brave(mary)))=>((creative(mary)&patient(mary))))&
(![X]:((~wise(X)<~>~curious(X))=>~funny(X)))&
((?[X]:((~creative(X)<~>kind(X))))<=>((~generous(alice)<~>wise(alice))))&
((?[X]:(~brave(X)))<=>(calm(susan)))&
((?[X]:((~wise(X)&wise(X))))<=>(?[X]:(rich(X))))&
(((~funny(susan)&calm(susan)))<=>(?[X]:((quiet(X)&funny(X)))))&
(((~funny(fred)|kind(fred)))=>(?[X]:((~strong(X)<~>brave(X)))))&
((?[X]:((wise(X)|~brave(X))))=>(?[X]:(rich(X))))&
(![X]:((kind(X)|~quiet(X))<=>(generous(X)|brave(X))))&
(((patient(paul)&~tall(paul)))<=>(~generous(paul)))&
((~old(susan)&~quiet(susan)))&
(?[X]:((funny(X)<~>~old(X))))&
(~kind(lucy))&
((wise(mary)|~calm(mary)))&
((~wise(mary)|humble(mary)))&
(?[X]:((patient(X)|~creative(X)))) | calm(mary) | [
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5325915850616400817567642
% SZS output start Proof for 5325915850616400817567642
11. ? [X0] : (wise(X0) & ~wise(X0)) <=> ? [X0] : rich(X0) [input p10]
14. ? [X0] : (~brave(X0) | wise(X0)) => ? [X0] : rich(X0) [input p13]
20. ~calm(mary) | wise(mary) [input p19]
23. calm(mary) [input hypothesis]
25. ? [X0] : (wise(X0) & ~wise(X0)) <=> ? [X1] : rich(X1) [rectify 11]
26. ? [X0] : (~brave(X0) | wise(X0)) => ? [X1] : rich(X1) [rectify 14]
38. ? [X1] : rich(X1) | ! [X0] : (brave(X0) & ~wise(X0)) [ennf transformation 26]
56. (? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (~wise(X0) | wise(X0))) [nnf transformation 25]
57. (? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (~wise(X3) | wise(X3))) [rectify 56]
58. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK4) & ~wise(sK4)) [choice axiom]
59. ? [X2] : rich(X2) => rich(sK5) [choice axiom]
60. ((wise(sK4) & ~wise(sK4)) | ! [X1] : ~rich(X1)) & (rich(sK5) | ! [X3] : (~wise(X3) | wise(X3))) [skolemisation 57,59,58]
69. ? [X0] : rich(X0) | ! [X1] : (brave(X1) & ~wise(X1)) [rectify 38]
70. ? [X0] : rich(X0) => rich(sK8) [choice axiom]
71. rich(sK8) | ! [X1] : (brave(X1) & ~wise(X1)) [skolemisation 69,70]
114. ~wise(sK4) | ~rich(X1) [cnf transformation 60]
115. wise(sK4) | ~rich(X1) [cnf transformation 60]
124. rich(sK8) | ~wise(X1) [cnf transformation 71]
138. ~calm(mary) | wise(mary) [cnf transformation 20]
140. calm(mary) [cnf transformation 23]
180. 10 <=> ! [X3] : ~rich(X3) [avatar definition]
181. ~rich(X3) <- (10) [avatar component clause 180]
259. 27 <=> wise(sK4) [avatar definition]
262. 10 | 27 [avatar split clause 115,259,180]
263. 10 | ~27 [avatar split clause 114,259,180]
304. 36 <=> rich(sK8) [avatar definition]
306. rich(sK8) <- (36) [avatar component clause 304]
309. 37 <=> ! [X1] : ~wise(X1) [avatar definition]
310. ~wise(X1) <- (37) [avatar component clause 309]
311. 37 | 36 [avatar split clause 124,304,309]
340. 43 <=> wise(mary) [avatar definition]
342. wise(mary) <- (43) [avatar component clause 340]
344. 44 <=> calm(mary) [avatar definition]
347. 43 | ~44 [avatar split clause 138,344,340]
357. 44 [avatar split clause 140,344]
366. $false <- (10, 36) [resolution 306,181]
367. ~10 | ~36 [avatar contradiction clause 366]
370. $false <- (37, 43) [resolution 342,310]
371. ~37 | ~43 [avatar contradiction clause 370]
372. $false [avatar sat refutation 262,263,311,347,357,367,371]
% SZS output end Proof for 5325915850616400817567642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is not humble or not calm and vice versa.
Everyone who is either not calm or not strong is not funny.
If fred is not brave or not curious then someone is both curious and not generous and vice versa.
Everyone who is both not happy and not curious is old or not wise.
Everyone who is curious or tall is not rich and vice versa.
If someone is quiet or not generous then fred is both not generous and strong.
Everyone who is either happy or not rich is not rich and vice versa.
If someone is creative then john is strong and vice versa.
If someone is creative then someone is curious.
Everyone who is not humble is both creative and rich and vice versa.
Everyone who is either not tall or tall is not strong.
Everyone who is funny is both happy and patient.
Everyone who is patient is tall or wise and vice versa.
If someone is both not humble and not calm then lucy is wise and vice versa.
If susan is both not brave and not creative then john is not creative.
Everyone who is quiet is not kind or creative.
Lucy is not creative.
Someone is either not tall or not patient.
Lucy is not quiet or patient.
Someone is either not funny or quiet.
Susan is not wise. | Fred is not generous. | contradiction | (![X]:(~generous(X)<=>(~humble(X)|~calm(X))))&
(![X]:((~calm(X)<~>~strong(X))=>~funny(X)))&
(((~brave(fred)|~curious(fred)))<=>(?[X]:((curious(X)&~generous(X)))))&
(![X]:((~happy(X)&~curious(X))=>(old(X)|~wise(X))))&
(![X]:((curious(X)|tall(X))<=>~rich(X)))&
((?[X]:((quiet(X)|~generous(X))))=>((~generous(fred)&strong(fred))))&
(![X]:((happy(X)<~>~rich(X))<=>~rich(X)))&
((?[X]:(creative(X)))<=>(strong(john)))&
((?[X]:(creative(X)))=>(?[X]:(curious(X))))&
(![X]:(~humble(X)<=>(creative(X)&rich(X))))&
(![X]:((~tall(X)<~>tall(X))=>~strong(X)))&
(![X]:(funny(X)=>(happy(X)&patient(X))))&
(![X]:(patient(X)<=>(tall(X)|wise(X))))&
((?[X]:((~humble(X)&~calm(X))))<=>(wise(lucy)))&
(((~brave(susan)&~creative(susan)))=>(~creative(john)))&
(![X]:(quiet(X)=>(~kind(X)|creative(X))))&
(~creative(lucy))&
(?[X]:((~tall(X)<~>~patient(X))))&
((~quiet(lucy)|patient(lucy)))&
(?[X]:((~funny(X)<~>quiet(X))))&
(~wise(susan)) | ~generous(fred) | [
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7746565665801535156718576
% SZS output start Proof for 7746565665801535156718576
6. ? [X0] : (~generous(X0) | quiet(X0)) => (strong(fred) & ~generous(fred)) [input p5]
11. ! [X0] : ((~tall(X0) <~> tall(X0)) => ~strong(X0)) [input p10]
22. ~generous(fred) [input hypothesis]
27. (strong(fred) & ~generous(fred)) | ! [X0] : (generous(X0) & ~quiet(X0)) [ennf transformation 6]
29. ! [X0] : (~strong(X0) | (~tall(X0) <=> tall(X0))) [ennf transformation 11]
53. ! [X0] : (~strong(X0) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) [nnf transformation 29]
82. strong(fred) | generous(X0) [cnf transformation 27]
93. ~strong(X0) | tall(X0) | tall(X0) [cnf transformation 53]
94. ~strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 53]
111. ~generous(fred) [cnf transformation 22]
112. ~strong(X0) | tall(X0) [duplicate literal removal 93]
113. ~strong(X0) | ~tall(X0) [duplicate literal removal 94]
141. 6 <=> ! [X0] : generous(X0) [avatar definition]
142. generous(X0) <- (6) [avatar component clause 141]
144. 7 <=> strong(fred) [avatar definition]
146. strong(fred) <- (7) [avatar component clause 144]
147. 6 | 7 [avatar split clause 82,144,141]
153. 9 <=> generous(fred) [avatar definition]
155. ~generous(fred) <- (~9) [avatar component clause 153]
177. ~strong(X0) [subsumption resolution 112,113]
222. ~9 [avatar split clause 111,153]
223. $false <- (7) [subsumption resolution 146,177]
224. ~7 [avatar contradiction clause 223]
227. $false <- (6, ~9) [resolution 155,142]
228. ~6 | 9 [avatar contradiction clause 227]
229. $false [avatar sat refutation 147,222,224,228]
% SZS output end Proof for 7746565665801535156718576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not rich is both quiet and not tall. If someone is humble or not funny then alice is not humble or patient and vice versa. Everyone who is both not funny and not curious is not tall and vice versa. Everyone who is not curious is both generous and not kind and vice versa. Everyone who is not brave is both quiet and humble. Everyone who is both not quiet and quiet is not humble or kind and vice versa. If someone is not quiet or funny then someone is not creative or old and vice versa. If susan is both humble and calm then someone is not curious or not strong. Everyone who is either creative or quiet is both not patient and not generous. Everyone who is either rich or not humble is old and vice versa. Everyone who is either not happy or patient is both funny and not creative and vice versa. Everyone who is either old or creative is either not calm or not tall. Everyone who is rich is tall or old and vice versa. If someone is tall or not rich then someone is either quiet or creative and vice versa. Everyone who is kind or not generous is either strong or not quiet and vice versa. If someone is either calm or not wise then someone is not tall. Susan is tall or not strong. Lucy is not calm or not humble. Someone is generous or patient. Alice is both generous and not rich. Susan is not curious. Lucy is humble or quiet. Mary is either quiet or not creative. Someone is not patient. | Lucy is rich. | neutral | (![X]:((generous(X)<~>~rich(X))=>(quiet(X)&~tall(X))))&
((?[X]:((humble(X)|~funny(X))))<=>((~humble(alice)|patient(alice))))&
(![X]:((~funny(X)&~curious(X))<=>~tall(X)))&
(![X]:(~curious(X)<=>(generous(X)&~kind(X))))&
(![X]:(~brave(X)=>(quiet(X)&humble(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~quiet(X)|funny(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(((humble(susan)&calm(susan)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((creative(X)<~>quiet(X))=>(~patient(X)&~generous(X))))&
(![X]:((rich(X)<~>~humble(X))<=>old(X)))&
(![X]:((~happy(X)<~>patient(X))<=>(funny(X)&~creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((kind(X)|~generous(X))<=>(strong(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>(?[X]:(~tall(X))))&
((tall(susan)|~strong(susan)))&
((~calm(lucy)|~humble(lucy)))&
(?[X]:((generous(X)|patient(X))))&
((generous(alice)&~rich(alice)))&
(~curious(susan))&
((humble(lucy)|quiet(lucy)))&
((quiet(mary)<~>~creative(mary)))&
(?[X]:(~patient(X))) | rich(lucy) | [] | null | 0 |
If someone is humble or rich then someone is both old and not wise. If susan is either not quiet or not calm then john is brave. Everyone who is both not curious and quiet is both not generous and happy and vice versa. Everyone who is not old or not wise is not old and vice versa. Everyone who is both not patient and not humble is both not creative and not happy and vice versa. If fred is either kind or patient then alice is creative and vice versa. If paul is either not calm or calm then mary is either not old or generous. Everyone who is both not rich and old is either not tall or calm and vice versa. If someone is not generous then alice is happy or curious. If fred is either not funny or funny then someone is old or funny and vice versa. If fred is patient then someone is either not rich or not calm and vice versa. If alice is not kind or not happy then susan is quiet. Everyone who is both happy and humble is creative or not old. Everyone who is kind or patient is rich. Everyone who is not curious is either funny or not patient and vice versa. Everyone who is either not generous or not creative is quiet and vice versa. Lucy is either creative or generous. Someone is either not happy or not curious. Someone is both not generous and not brave. Fred is either not tall or humble. Someone is not strong. | Susan is not old. | neutral | ((?[X]:((humble(X)|rich(X))))=>(?[X]:((old(X)&~wise(X)))))&
(((~quiet(susan)<~>~calm(susan)))=>(brave(john)))&
(![X]:((~curious(X)&quiet(X))<=>(~generous(X)&happy(X))))&
(![X]:((~old(X)|~wise(X))<=>~old(X)))&
(![X]:((~patient(X)&~humble(X))<=>(~creative(X)&~happy(X))))&
(((kind(fred)<~>patient(fred)))<=>(creative(alice)))&
(((~calm(paul)<~>calm(paul)))=>((~old(mary)<~>generous(mary))))&
(![X]:((~rich(X)&old(X))<=>(~tall(X)<~>calm(X))))&
((?[X]:(~generous(X)))=>((happy(alice)|curious(alice))))&
(((~funny(fred)<~>funny(fred)))<=>(?[X]:((old(X)|funny(X)))))&
((patient(fred))<=>(?[X]:((~rich(X)<~>~calm(X)))))&
(((~kind(alice)|~happy(alice)))=>(quiet(susan)))&
(![X]:((happy(X)&humble(X))=>(creative(X)|~old(X))))&
(![X]:((kind(X)|patient(X))=>rich(X)))&
(![X]:(~curious(X)<=>(funny(X)<~>~patient(X))))&
(![X]:((~generous(X)<~>~creative(X))<=>quiet(X)))&
((creative(lucy)<~>generous(lucy)))&
(?[X]:((~happy(X)<~>~curious(X))))&
(?[X]:((~generous(X)&~brave(X))))&
((~tall(fred)<~>humble(fred)))&
(?[X]:(~strong(X))) | ~old(susan) | [] | null | 0 |
Everyone who is either not calm or brave is either not patient or rich and vice versa.
Everyone who is not funny is wise and vice versa.
Everyone who is not curious is both not kind and not wise.
If someone is calm then john is tall.
Everyone who is either wise or not quiet is either not humble or not strong and vice versa.
If someone is not calm or curious then alice is curious and vice versa.
Everyone who is both not calm and not tall is both curious and old and vice versa.
Everyone who is not kind is either strong or not calm and vice versa.
If paul is not brave or calm then someone is curious and vice versa.
Everyone who is either quiet or not calm is rich and vice versa.
If john is not calm then paul is not wise or rich and vice versa.
If lucy is calm then mary is either not old or not generous and vice versa.
Everyone who is happy or strong is curious.
If someone is either not wise or rich then fred is not patient or calm and vice versa.
Everyone who is not funny or curious is humble and vice versa.
Everyone who is curious or brave is either happy or not patient and vice versa.
Mary is happy or not happy.
Someone is not happy.
Alice is not generous.
Alice is not creative or not old.
Someone is not tall or kind.
Susan is not kind. | Paul is not generous. | neutral | (![X]:((~calm(X)<~>brave(X))<=>(~patient(X)<~>rich(X))))&
(![X]:(~funny(X)<=>wise(X)))&
(![X]:(~curious(X)=>(~kind(X)&~wise(X))))&
((?[X]:(calm(X)))=>(tall(john)))&
(![X]:((wise(X)<~>~quiet(X))<=>(~humble(X)<~>~strong(X))))&
((?[X]:((~calm(X)|curious(X))))<=>(curious(alice)))&
(![X]:((~calm(X)&~tall(X))<=>(curious(X)&old(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>~calm(X))))&
(((~brave(paul)|calm(paul)))<=>(?[X]:(curious(X))))&
(![X]:((quiet(X)<~>~calm(X))<=>rich(X)))&
((~calm(john))<=>((~wise(paul)|rich(paul))))&
((calm(lucy))<=>((~old(mary)<~>~generous(mary))))&
(![X]:((happy(X)|strong(X))=>curious(X)))&
((?[X]:((~wise(X)<~>rich(X))))<=>((~patient(fred)|calm(fred))))&
(![X]:((~funny(X)|curious(X))<=>humble(X)))&
(![X]:((curious(X)|brave(X))<=>(happy(X)<~>~patient(X))))&
((happy(mary)|~happy(mary)))&
(?[X]:(~happy(X)))&
(~generous(alice))&
((~creative(alice)|~old(alice)))&
(?[X]:((~tall(X)|kind(X))))&
(~kind(susan)) | ~generous(paul) | [] | null | 0 |
If someone is not curious then john is both happy and not strong.
Everyone who is either humble or rich is tall or not patient and vice versa.
Everyone who is both generous and strong is brave or happy and vice versa.
Everyone who is not old or not kind is not funny.
If john is either wise or not funny then someone is either curious or rich and vice versa.
Everyone who is both rich and not brave is patient and vice versa.
If someone is both not patient and not creative then john is not brave.
Everyone who is not funny is either not old or tall and vice versa.
Everyone who is not patient or generous is not calm.
Everyone who is tall is not wise and vice versa.
Everyone who is both generous and calm is both not generous and not old and vice versa.
Everyone who is quiet is not rich and vice versa.
Everyone who is not old is curious and vice versa.
If someone is funny then someone is not wise or not curious.
If susan is both not creative and kind then someone is either not creative or kind.
Everyone who is not funny is not calm or rich.
Someone is creative.
Fred is rich.
Someone is either not generous or happy.
Someone is happy.
Someone is not kind or not patient.
Someone is rich. | Susan is not quiet. | entailment | ((?[X]:(~curious(X)))=>((happy(john)&~strong(john))))&
(![X]:((humble(X)<~>rich(X))<=>(tall(X)|~patient(X))))&
(![X]:((generous(X)&strong(X))<=>(brave(X)|happy(X))))&
(![X]:((~old(X)|~kind(X))=>~funny(X)))&
(((wise(john)<~>~funny(john)))<=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:((rich(X)&~brave(X))<=>patient(X)))&
((?[X]:((~patient(X)&~creative(X))))=>(~brave(john)))&
(![X]:(~funny(X)<=>(~old(X)<~>tall(X))))&
(![X]:((~patient(X)|generous(X))=>~calm(X)))&
(![X]:(tall(X)<=>~wise(X)))&
(![X]:((generous(X)&calm(X))<=>(~generous(X)&~old(X))))&
(![X]:(quiet(X)<=>~rich(X)))&
(![X]:(~old(X)<=>curious(X)))&
((?[X]:(funny(X)))=>(?[X]:((~wise(X)|~curious(X)))))&
(((~creative(susan)&kind(susan)))=>(?[X]:((~creative(X)<~>kind(X)))))&
(![X]:(~funny(X)=>(~calm(X)|rich(X))))&
(?[X]:(creative(X)))&
(rich(fred))&
(?[X]:((~generous(X)<~>happy(X))))&
(?[X]:(happy(X)))&
(?[X]:((~kind(X)|~patient(X))))&
(?[X]:(rich(X))) | ~quiet(susan) | [
"p0",
"p2",
"p3",
"p4",
"p7",
"p9",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2467973345217521893580849
% SZS output start Proof for 2467973345217521893580849
1. ? [X0] : ~curious(X0) => (~strong(john) & happy(john)) [input p0]
3. ! [X0] : ((strong(X0) & generous(X0)) <=> (happy(X0) | brave(X0))) [input p2]
4. ! [X0] : ((~kind(X0) | ~old(X0)) => ~funny(X0)) [input p3]
5. (wise(john) <~> ~funny(john)) <=> ? [X0] : (curious(X0) <~> rich(X0)) [input p4]
8. ! [X0] : (~funny(X0) <=> (~old(X0) <~> tall(X0))) [input p7]
10. ! [X0] : (tall(X0) <=> ~wise(X0)) [input p9]
12. ! [X0] : (quiet(X0) <=> ~rich(X0)) [input p11]
13. ! [X0] : (~old(X0) <=> curious(X0)) [input p12]
14. ? [X0] : funny(X0) => ? [X0] : (~curious(X0) | ~wise(X0)) [input p13]
23. quiet(susan) [input hypothesis]
24. ? [X0] : funny(X0) => ? [X1] : (~curious(X1) | ~wise(X1)) [rectify 14]
25. ! [X0] : (quiet(X0) => ~rich(X0)) [unused predicate definition removal 12]
26. (~strong(john) & happy(john)) | ! [X0] : curious(X0) [ennf transformation 1]
27. ! [X0] : (~funny(X0) | (kind(X0) & old(X0))) [ennf transformation 4]
30. ! [X0] : (~rich(X0) | ~quiet(X0)) [ennf transformation 25]
31. ? [X1] : (~curious(X1) | ~wise(X1)) | ! [X0] : ~funny(X0) [ennf transformation 24]
38. ! [X0] : (((strong(X0) & generous(X0)) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | (~strong(X0) | ~generous(X0)))) [nnf transformation 3]
39. ! [X0] : (((strong(X0) & generous(X0)) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ~strong(X0) | ~generous(X0))) [flattening 38]
40. (((funny(john) | ~wise(john)) & (~funny(john) | wise(john))) | ! [X0] : ((curious(X0) | ~rich(X0)) & (rich(X0) | ~curious(X0)))) & (? [X0] : ((~rich(X0) | ~curious(X0)) & (rich(X0) | curious(X0))) | ((wise(john) | funny(john)) & (~funny(john) | ~wise(john)))) [nnf transformation 5]
41. (((funny(john) | ~wise(john)) & (~funny(john) | wise(john))) | ! [X0] : ((curious(X0) | ~rich(X0)) & (rich(X0) | ~curious(X0)))) & (? [X1] : ((~rich(X1) | ~curious(X1)) & (rich(X1) | curious(X1))) | ((wise(john) | funny(john)) & (~funny(john) | ~wise(john)))) [rectify 40]
42. ? [X1] : ((~rich(X1) | ~curious(X1)) & (rich(X1) | curious(X1))) => ((~rich(sK0) | ~curious(sK0)) & (rich(sK0) | curious(sK0))) [choice axiom]
43. (((funny(john) | ~wise(john)) & (~funny(john) | wise(john))) | ! [X0] : ((curious(X0) | ~rich(X0)) & (rich(X0) | ~curious(X0)))) & (((~rich(sK0) | ~curious(sK0)) & (rich(sK0) | curious(sK0))) | ((wise(john) | funny(john)) & (~funny(john) | ~wise(john)))) [skolemisation 41,42]
46. ! [X0] : ((~funny(X0) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0)))) & (((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | funny(X0))) [nnf transformation 8]
47. ! [X0] : ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0))) [nnf transformation 10]
50. ! [X0] : ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0))) [nnf transformation 13]
51. ? [X0] : (~curious(X0) | ~wise(X0)) | ! [X1] : ~funny(X1) [rectify 31]
52. ? [X0] : (~curious(X0) | ~wise(X0)) => (~curious(sK1) | ~wise(sK1)) [choice axiom]
53. (~curious(sK1) | ~wise(sK1)) | ! [X1] : ~funny(X1) [skolemisation 51,52]
68. happy(john) | curious(X0) [cnf transformation 26]
69. ~strong(john) | curious(X0) [cnf transformation 26]
80. ~happy(X0) | strong(X0) [cnf transformation 39]
81. ~funny(X0) | old(X0) [cnf transformation 27]
89. funny(john) | ~wise(john) | rich(X0) | ~curious(X0) [cnf transformation 43]
96. ~tall(X0) | old(X0) | funny(X0) [cnf transformation 46]
98. ~funny(X0) | ~old(X0) | ~tall(X0) [cnf transformation 46]
102. wise(X0) | tall(X0) [cnf transformation 47]
107. ~quiet(X0) | ~rich(X0) [cnf transformation 30]
109. ~old(X0) | ~curious(X0) [cnf transformation 50]
110. ~curious(sK1) | ~wise(sK1) | ~funny(X1) [cnf transformation 53]
121. quiet(susan) [cnf transformation 23]
125. 1 <=> ! [X0] : curious(X0) [avatar definition]
126. curious(X0) <- (1) [avatar component clause 125]
128. 2 <=> strong(john) [avatar definition]
131. 1 | ~2 [avatar split clause 69,128,125]
133. 3 <=> happy(john) [avatar definition]
135. happy(john) <- (3) [avatar component clause 133]
136. 1 | 3 [avatar split clause 68,133,125]
141. 5 <=> wise(john) [avatar definition]
143. ~wise(john) <- (~5) [avatar component clause 141]
145. 6 <=> funny(john) [avatar definition]
147. funny(john) <- (6) [avatar component clause 145]
150. 7 <=> ! [X0] : (rich(X0) | ~curious(X0)) [avatar definition]
151. ~curious(X0) | rich(X0) <- (7) [avatar component clause 150]
152. 7 | ~5 | 6 [avatar split clause 89,145,141,150]
175. ~funny(X0) | ~tall(X0) [subsumption resolution 98,81]
176. ~tall(X0) | old(X0) [subsumption resolution 96,175]
178. 12 <=> ! [X1] : ~funny(X1) [avatar definition]
179. ~funny(X1) <- (12) [avatar component clause 178]
181. 13 <=> wise(sK1) [avatar definition]
183. ~wise(sK1) <- (~13) [avatar component clause 181]
185. 14 <=> curious(sK1) [avatar definition]
187. ~curious(sK1) <- (~14) [avatar component clause 185]
188. 12 | ~13 | ~14 [avatar split clause 110,185,181,178]
228. strong(john) <- (3) [resolution 80,135]
231. 2 | ~3 [avatar split clause 228,133,128]
232. $false <- (1, ~14) [resolution 126,187]
233. ~1 | 14 [avatar contradiction clause 232]
235. tall(sK1) <- (~13) [resolution 102,183]
237. ~rich(susan) [resolution 107,121]
247. rich(X0) <- (1, 7) [resolution 151,126]
248. $false <- (1, 7) [resolution 247,237]
250. ~1 | ~7 [avatar contradiction clause 248]
253. tall(john) <- (~5) [resolution 143,102]
254. old(sK1) <- (~13) [resolution 176,235]
255. old(john) <- (~5) [resolution 253,176]
276. ~curious(sK1) <- (~13) [resolution 254,109]
277. $false <- (1, ~13) [subsumption resolution 276,126]
278. ~1 | 13 [avatar contradiction clause 277]
345. ~curious(john) <- (~5) [resolution 255,109]
346. $false <- (1, ~5) [subsumption resolution 345,126]
347. ~1 | 5 [avatar contradiction clause 346]
348. $false <- (6, 12) [subsumption resolution 147,179]
349. ~6 | ~12 [avatar contradiction clause 348]
350. $false [avatar sat refutation 131,136,152,188,231,233,250,278,347,349]
% SZS output end Proof for 2467973345217521893580849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If john is curious then someone is patient or not calm and vice versa. If mary is curious then someone is both funny and generous. Everyone who is old is either wise or not patient and vice versa. If fred is strong or not calm then paul is not humble and vice versa. If john is either not kind or not generous then alice is either not quiet or creative. If someone is funny then someone is not quiet and vice versa. Everyone who is either quiet or not creative is not rich and vice versa. Everyone who is not tall is funny and vice versa. Everyone who is not humble or humble is both not patient and not rich. If someone is either not humble or funny then fred is old and vice versa. If someone is not strong or patient then someone is creative or not old and vice versa. Everyone who is either patient or curious is calm or brave. Everyone who is not curious or curious is either rich or brave and vice versa. If susan is old or not kind then lucy is not old or creative. Everyone who is humble is kind or not funny and vice versa. If someone is funny or not kind then someone is both not patient and old and vice versa. Someone is not curious or not old. Someone is humble or not curious. Someone is either not generous or not tall. Lucy is both not quiet and funny. Fred is not patient or not creative. John is creative or not generous. Someone is either old or not kind. | Lucy is not generous. | neutral | ((curious(john))<=>(?[X]:((patient(X)|~calm(X)))))&
((curious(mary))=>(?[X]:((funny(X)&generous(X)))))&
(![X]:(old(X)<=>(wise(X)<~>~patient(X))))&
(((strong(fred)|~calm(fred)))<=>(~humble(paul)))&
(((~kind(john)<~>~generous(john)))=>((~quiet(alice)<~>creative(alice))))&
((?[X]:(funny(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>~rich(X)))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~humble(X)|humble(X))=>(~patient(X)&~rich(X))))&
((?[X]:((~humble(X)<~>funny(X))))<=>(old(fred)))&
((?[X]:((~strong(X)|patient(X))))<=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((patient(X)<~>curious(X))=>(calm(X)|brave(X))))&
(![X]:((~curious(X)|curious(X))<=>(rich(X)<~>brave(X))))&
(((old(susan)|~kind(susan)))=>((~old(lucy)|creative(lucy))))&
(![X]:(humble(X)<=>(kind(X)|~funny(X))))&
((?[X]:((funny(X)|~kind(X))))<=>(?[X]:((~patient(X)&old(X)))))&
(?[X]:((~curious(X)|~old(X))))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:((~generous(X)<~>~tall(X))))&
((~quiet(lucy)&funny(lucy)))&
((~patient(fred)|~creative(fred)))&
((creative(john)|~generous(john)))&
(?[X]:((old(X)<~>~kind(X)))) | ~generous(lucy) | [] | null | 0 |
Everyone who is humble or not calm is not quiet or not tall.
Everyone who is not creative or creative is tall or quiet and vice versa.
Everyone who is both not curious and wise is either not humble or not brave.
Everyone who is both funny and not old is both not creative and not quiet and vice versa.
If someone is not rich or not calm then susan is both not old and old and vice versa.
If fred is both not rich and happy then someone is either not strong or not happy and vice versa.
If susan is wise or old then fred is both not funny and wise.
Everyone who is either not happy or not quiet is not tall and vice versa.
If someone is both wise and not curious then someone is both not calm and not kind and vice versa.
If someone is not tall then paul is both generous and old and vice versa.
Everyone who is not humble or not generous is both not curious and not old.
If lucy is not curious or kind then someone is not wise or not calm.
If someone is quiet or funny then someone is both wise and kind.
If susan is either wise or not strong then someone is both not calm and creative.
Everyone who is either humble or rich is wise or not rich.
Someone is either not generous or humble.
Someone is both not kind and not wise.
Someone is either not patient or curious.
John is not quiet.
Someone is strong or not curious.
Mary is either not old or not creative. | Paul is not strong. | entailment | (![X]:((humble(X)|~calm(X))=>(~quiet(X)|~tall(X))))&
(![X]:((~creative(X)|creative(X))<=>(tall(X)|quiet(X))))&
(![X]:((~curious(X)&wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((funny(X)&~old(X))<=>(~creative(X)&~quiet(X))))&
((?[X]:((~rich(X)|~calm(X))))<=>((~old(susan)&old(susan))))&
(((~rich(fred)&happy(fred)))<=>(?[X]:((~strong(X)<~>~happy(X)))))&
(((wise(susan)|old(susan)))=>((~funny(fred)&wise(fred))))&
(![X]:((~happy(X)<~>~quiet(X))<=>~tall(X)))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((~calm(X)&~kind(X)))))&
((?[X]:(~tall(X)))<=>((generous(paul)&old(paul))))&
(![X]:((~humble(X)|~generous(X))=>(~curious(X)&~old(X))))&
(((~curious(lucy)|kind(lucy)))=>(?[X]:((~wise(X)|~calm(X)))))&
((?[X]:((quiet(X)|funny(X))))=>(?[X]:((wise(X)&kind(X)))))&
(((wise(susan)<~>~strong(susan)))=>(?[X]:((~calm(X)&creative(X)))))&
(![X]:((humble(X)<~>rich(X))=>(wise(X)|~rich(X))))&
(?[X]:((~generous(X)<~>humble(X))))&
(?[X]:((~kind(X)&~wise(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(~quiet(john))&
(?[X]:((strong(X)|~curious(X))))&
((~old(mary)<~>~creative(mary))) | ~strong(paul) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 476013040864690556616372
% SZS output start Proof for 476013040864690556616372
1. ! [X0] : ((~calm(X0) | humble(X0)) => (~tall(X0) | ~quiet(X0))) [input p0]
2. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (quiet(X0) | tall(X0))) [input p1]
5. ? [X0] : (~calm(X0) | ~rich(X0)) <=> (old(susan) & ~old(susan)) [input p4]
6. (happy(fred) & ~rich(fred)) <=> ? [X0] : (~strong(X0) <~> ~happy(X0)) [input p5]
8. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) <=> ~tall(X0)) [input p7]
9. ? [X0] : (~curious(X0) & wise(X0)) <=> ? [X0] : (~kind(X0) & ~calm(X0)) [input p8]
11. ! [X0] : ((~generous(X0) | ~humble(X0)) => (~old(X0) & ~curious(X0))) [input p10]
15. ! [X0] : ((humble(X0) <~> rich(X0)) => (~rich(X0) | wise(X0))) [input p14]
22. strong(paul) [input hypothesis]
23. ? [X0] : (~curious(X0) & wise(X0)) <=> ? [X1] : (~kind(X1) & ~calm(X1)) [rectify 9]
25. ! [X0] : ((~tall(X0) | ~quiet(X0)) | (calm(X0) & ~humble(X0))) [ennf transformation 1]
26. ! [X0] : (~tall(X0) | ~quiet(X0) | (calm(X0) & ~humble(X0))) [flattening 25]
30. ! [X0] : ((~old(X0) & ~curious(X0)) | (generous(X0) & humble(X0))) [ennf transformation 11]
34. ! [X0] : ((~rich(X0) | wise(X0)) | (humble(X0) <=> rich(X0))) [ennf transformation 15]
35. ! [X0] : (~rich(X0) | wise(X0) | (humble(X0) <=> rich(X0))) [flattening 34]
36. ! [X0] : (((creative(X0) | ~creative(X0)) | (~quiet(X0) & ~tall(X0))) & ((quiet(X0) | tall(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 2]
37. ! [X0] : ((creative(X0) | ~creative(X0) | (~quiet(X0) & ~tall(X0))) & (quiet(X0) | tall(X0) | (~creative(X0) & creative(X0)))) [flattening 36]
41. (? [X0] : (~calm(X0) | ~rich(X0)) | (~old(susan) | old(susan))) & ((old(susan) & ~old(susan)) | ! [X0] : (calm(X0) & rich(X0))) [nnf transformation 5]
42. (? [X0] : (~calm(X0) | ~rich(X0)) | ~old(susan) | old(susan)) & ((old(susan) & ~old(susan)) | ! [X0] : (calm(X0) & rich(X0))) [flattening 41]
43. (? [X0] : (~calm(X0) | ~rich(X0)) | ~old(susan) | old(susan)) & ((old(susan) & ~old(susan)) | ! [X1] : (calm(X1) & rich(X1))) [rectify 42]
44. ? [X0] : (~calm(X0) | ~rich(X0)) => (~calm(sK0) | ~rich(sK0)) [choice axiom]
45. ((~calm(sK0) | ~rich(sK0)) | ~old(susan) | old(susan)) & ((old(susan) & ~old(susan)) | ! [X1] : (calm(X1) & rich(X1))) [skolemisation 43,44]
46. ((happy(fred) & ~rich(fred)) | ! [X0] : ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (? [X0] : ((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | (~happy(fred) | rich(fred))) [nnf transformation 6]
47. ((happy(fred) & ~rich(fred)) | ! [X0] : ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (? [X0] : ((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | ~happy(fred) | rich(fred)) [flattening 46]
48. ((happy(fred) & ~rich(fred)) | ! [X0] : ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (? [X1] : ((happy(X1) | strong(X1)) & (~happy(X1) | ~strong(X1))) | ~happy(fred) | rich(fred)) [rectify 47]
49. ? [X1] : ((happy(X1) | strong(X1)) & (~happy(X1) | ~strong(X1))) => ((happy(sK1) | strong(sK1)) & (~happy(sK1) | ~strong(sK1))) [choice axiom]
50. ((happy(fred) & ~rich(fred)) | ! [X0] : ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (((happy(sK1) | strong(sK1)) & (~happy(sK1) | ~strong(sK1))) | ~happy(fred) | rich(fred)) [skolemisation 48,49]
51. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | tall(X0)) & (~tall(X0) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [nnf transformation 8]
52. (? [X0] : (~curious(X0) & wise(X0)) | ! [X1] : (kind(X1) | calm(X1))) & (? [X1] : (~kind(X1) & ~calm(X1)) | ! [X0] : (curious(X0) | ~wise(X0))) [nnf transformation 23]
53. (? [X0] : (~curious(X0) & wise(X0)) | ! [X1] : (kind(X1) | calm(X1))) & (? [X2] : (~kind(X2) & ~calm(X2)) | ! [X3] : (curious(X3) | ~wise(X3))) [rectify 52]
54. ? [X0] : (~curious(X0) & wise(X0)) => (~curious(sK2) & wise(sK2)) [choice axiom]
55. ? [X2] : (~kind(X2) & ~calm(X2)) => (~kind(sK3) & ~calm(sK3)) [choice axiom]
56. ((~curious(sK2) & wise(sK2)) | ! [X1] : (kind(X1) | calm(X1))) & ((~kind(sK3) & ~calm(sK3)) | ! [X3] : (curious(X3) | ~wise(X3))) [skolemisation 53,55,54]
70. ! [X0] : (~rich(X0) | wise(X0) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) [nnf transformation 35]
82. ~tall(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 26]
84. quiet(X0) | tall(X0) | creative(X0) [cnf transformation 37]
85. ~creative(X0) | tall(X0) | quiet(X0) [cnf transformation 37]
94. ~old(susan) | rich(X1) [cnf transformation 45]
95. ~old(susan) | calm(X1) [cnf transformation 45]
96. old(susan) | rich(X1) [cnf transformation 45]
97. old(susan) | calm(X1) [cnf transformation 45]
102. ~rich(fred) | ~strong(X0) | happy(X0) [cnf transformation 50]
110. ~tall(X0) | ~happy(X0) | quiet(X0) [cnf transformation 51]
111. ~quiet(X0) | ~happy(X0) | tall(X0) [cnf transformation 51]
113. ~calm(sK3) | curious(X3) | ~wise(X3) [cnf transformation 56]
120. ~curious(X0) | humble(X0) [cnf transformation 30]
135. ~rich(X0) | wise(X0) | humble(X0) | ~rich(X0) [cnf transformation 70]
146. strong(paul) [cnf transformation 22]
147. ~rich(X0) | wise(X0) | humble(X0) [duplicate literal removal 135]
148. tall(X0) | quiet(X0) [subsumption resolution 84,85]
150. 1 <=> ! [X1] : calm(X1) [avatar definition]
151. calm(X1) <- (1) [avatar component clause 150]
153. 2 <=> old(susan) [avatar definition]
156. 1 | 2 [avatar split clause 97,153,150]
158. 3 <=> ! [X1] : rich(X1) [avatar definition]
159. rich(X1) <- (3) [avatar component clause 158]
160. 3 | 2 [avatar split clause 96,153,158]
161. 1 | ~2 [avatar split clause 95,153,150]
162. 3 | ~2 [avatar split clause 94,153,158]
164. 4 <=> ! [X0] : (~strong(X0) | happy(X0)) [avatar definition]
165. ~strong(X0) | happy(X0) <- (4) [avatar component clause 164]
176. 7 <=> rich(fred) [avatar definition]
178. ~rich(fred) <- (~7) [avatar component clause 176]
179. 4 | ~7 [avatar split clause 102,176,164]
207. ~happy(X0) | tall(X0) [subsumption resolution 111,148]
208. ~happy(X0) | quiet(X0) [subsumption resolution 110,207]
223. 16 <=> ! [X3] : (curious(X3) | ~wise(X3)) [avatar definition]
224. ~wise(X3) | curious(X3) <- (16) [avatar component clause 223]
231. 18 <=> calm(sK3) [avatar definition]
233. ~calm(sK3) <- (~18) [avatar component clause 231]
234. 16 | ~18 [avatar split clause 113,231,223]
344. $false <- (1, ~18) [resolution 233,151]
345. ~1 | 18 [avatar contradiction clause 344]
357. $false <- (3, ~7) [subsumption resolution 178,159]
358. ~3 | 7 [avatar contradiction clause 357]
362. happy(paul) <- (4) [resolution 165,146]
378. quiet(paul) <- (4) [resolution 362,208]
379. tall(paul) <- (4) [resolution 362,207]
395. wise(X0) | humble(X0) <- (3) [resolution 147,159]
411. humble(X1) | curious(X1) <- (3, 16) [resolution 395,224]
414. humble(X1) <- (3, 16) [subsumption resolution 411,120]
427. ~quiet(paul) | ~humble(paul) <- (4) [resolution 379,82]
428. ~humble(paul) <- (4) [subsumption resolution 427,378]
429. $false <- (3, 4, 16) [subsumption resolution 428,414]
430. ~3 | ~4 | ~16 [avatar contradiction clause 429]
431. $false [avatar sat refutation 156,160,161,162,179,234,345,358,430]
% SZS output end Proof for 476013040864690556616372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or brave is patient and vice versa. If someone is both brave and old then lucy is both humble and generous and vice versa. Everyone who is not quiet or not rich is not wise or curious. Everyone who is either not old or wise is not strong or humble and vice versa. Everyone who is not patient is both strong and not curious. If someone is not creative then lucy is both strong and not rich and vice versa. Everyone who is either strong or not creative is calm. Everyone who is both quiet and funny is calm or strong and vice versa. If someone is either brave or calm then john is creative. If someone is happy or wise then fred is both not brave and rich. If someone is both funny and creative then someone is both not quiet and rich and vice versa. If someone is both not funny and not generous then someone is patient or humble and vice versa. Everyone who is not creative or not rich is both quiet and not strong and vice versa. If susan is not tall or kind then someone is not curious or tall. If fred is either patient or not humble then someone is either not creative or not tall. If someone is creative then susan is funny and vice versa. Alice is not happy. John is both calm and not wise. Someone is either funny or quiet. Someone is both not brave and old. Someone is both creative and not generous. Alice is not wise. Paul is tall. Lucy is wise. | Fred is not creative. | contradiction | (![X]:((wise(X)<~>brave(X))<=>patient(X)))&
((?[X]:((brave(X)&old(X))))<=>((humble(lucy)&generous(lucy))))&
(![X]:((~quiet(X)|~rich(X))=>(~wise(X)|curious(X))))&
(![X]:((~old(X)<~>wise(X))<=>(~strong(X)|humble(X))))&
(![X]:(~patient(X)=>(strong(X)&~curious(X))))&
((?[X]:(~creative(X)))<=>((strong(lucy)&~rich(lucy))))&
(![X]:((strong(X)<~>~creative(X))=>calm(X)))&
(![X]:((quiet(X)&funny(X))<=>(calm(X)|strong(X))))&
((?[X]:((brave(X)<~>calm(X))))=>(creative(john)))&
((?[X]:((happy(X)|wise(X))))=>((~brave(fred)&rich(fred))))&
((?[X]:((funny(X)&creative(X))))<=>(?[X]:((~quiet(X)&rich(X)))))&
((?[X]:((~funny(X)&~generous(X))))<=>(?[X]:((patient(X)|humble(X)))))&
(![X]:((~creative(X)|~rich(X))<=>(quiet(X)&~strong(X))))&
(((~tall(susan)|kind(susan)))=>(?[X]:((~curious(X)|tall(X)))))&
(((patient(fred)<~>~humble(fred)))=>(?[X]:((~creative(X)<~>~tall(X)))))&
((?[X]:(creative(X)))<=>(funny(susan)))&
(~happy(alice))&
((calm(john)&~wise(john)))&
(?[X]:((funny(X)<~>quiet(X))))&
(?[X]:((~brave(X)&old(X))))&
(?[X]:((creative(X)&~generous(X))))&
(~wise(alice))&
(tall(paul))&
(wise(lucy)) | ~creative(fred) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 54548917788772781632637
% SZS output start Proof for 54548917788772781632637
6. ? [X0] : ~creative(X0) <=> (~rich(lucy) & strong(lucy)) [input p5]
13. ! [X0] : ((~rich(X0) | ~creative(X0)) <=> (~strong(X0) & quiet(X0))) [input p12]
25. ~creative(fred) [input hypothesis]
47. (? [X0] : ~creative(X0) | (rich(lucy) | ~strong(lucy))) & ((~rich(lucy) & strong(lucy)) | ! [X0] : creative(X0)) [nnf transformation 6]
48. (? [X0] : ~creative(X0) | rich(lucy) | ~strong(lucy)) & ((~rich(lucy) & strong(lucy)) | ! [X0] : creative(X0)) [flattening 47]
49. (? [X0] : ~creative(X0) | rich(lucy) | ~strong(lucy)) & ((~rich(lucy) & strong(lucy)) | ! [X1] : creative(X1)) [rectify 48]
50. ? [X0] : ~creative(X0) => ~creative(sK1) [choice axiom]
51. (~creative(sK1) | rich(lucy) | ~strong(lucy)) & ((~rich(lucy) & strong(lucy)) | ! [X1] : creative(X1)) [skolemisation 49,50]
66. ! [X0] : (((~rich(X0) | ~creative(X0)) | (strong(X0) | ~quiet(X0))) & ((~strong(X0) & quiet(X0)) | (rich(X0) & creative(X0)))) [nnf transformation 13]
67. ! [X0] : ((~rich(X0) | ~creative(X0) | strong(X0) | ~quiet(X0)) & ((~strong(X0) & quiet(X0)) | (rich(X0) & creative(X0)))) [flattening 66]
102. strong(lucy) | creative(X1) [cnf transformation 51]
103. ~rich(lucy) | creative(X1) [cnf transformation 51]
128. ~strong(X0) | rich(X0) [cnf transformation 67]
148. ~creative(fred) [cnf transformation 25]
173. 6 <=> strong(lucy) [avatar definition]
174. strong(lucy) <- (6) [avatar component clause 173]
177. 7 <=> rich(lucy) [avatar definition]
186. 9 <=> ! [X1] : creative(X1) [avatar definition]
187. creative(X1) <- (9) [avatar component clause 186]
188. 9 | ~7 [avatar split clause 103,177,186]
189. 9 | 6 [avatar split clause 102,173,186]
343. rich(lucy) <- (6) [resolution 128,174]
347. 7 | ~6 [avatar split clause 343,173,177]
348. $false <- (9) [resolution 187,148]
351. ~9 [avatar contradiction clause 348]
352. $false [avatar sat refutation 188,189,347,351]
% SZS output end Proof for 54548917788772781632637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is kind then john is not funny. Everyone who is either tall or not rich is both not happy and patient and vice versa. Everyone who is both happy and old is happy or curious and vice versa. If paul is either rich or not kind then someone is both not happy and not kind. Everyone who is either curious or not curious is both not brave and not old and vice versa. If lucy is not strong then paul is both strong and not quiet. Everyone who is both kind and not funny is curious or quiet and vice versa. Everyone who is funny or not creative is not patient or not funny and vice versa. If someone is not curious then mary is patient. Everyone who is both quiet and kind is either not creative or not wise. Everyone who is either not patient or not wise is kind or rich. If lucy is not curious then mary is either old or strong. Everyone who is both strong and not quiet is either not brave or patient. If lucy is both not happy and rich then mary is calm or not creative and vice versa. If susan is creative or not strong then someone is either calm or strong. Alice is either brave or strong. Lucy is not old. Someone is not rich or kind. Fred is not old or brave. Mary is not brave or not rich. Lucy is either creative or not strong. Someone is humble or wise. | Fred is not happy. | entailment | ((kind(mary))=>(~funny(john)))&
(![X]:((tall(X)<~>~rich(X))<=>(~happy(X)&patient(X))))&
(![X]:((happy(X)&old(X))<=>(happy(X)|curious(X))))&
(((rich(paul)<~>~kind(paul)))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~brave(X)&~old(X))))&
((~strong(lucy))=>((strong(paul)&~quiet(paul))))&
(![X]:((kind(X)&~funny(X))<=>(curious(X)|quiet(X))))&
(![X]:((funny(X)|~creative(X))<=>(~patient(X)|~funny(X))))&
((?[X]:(~curious(X)))=>(patient(mary)))&
(![X]:((quiet(X)&kind(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((~patient(X)<~>~wise(X))=>(kind(X)|rich(X))))&
((~curious(lucy))=>((old(mary)<~>strong(mary))))&
(![X]:((strong(X)&~quiet(X))=>(~brave(X)<~>patient(X))))&
(((~happy(lucy)&rich(lucy)))<=>((calm(mary)|~creative(mary))))&
(((creative(susan)|~strong(susan)))=>(?[X]:((calm(X)<~>strong(X)))))&
((brave(alice)<~>strong(alice)))&
(~old(lucy))&
(?[X]:((~rich(X)|kind(X))))&
((~old(fred)|brave(fred)))&
((~brave(mary)|~rich(mary)))&
((creative(lucy)<~>~strong(lucy)))&
(?[X]:((humble(X)|wise(X)))) | ~happy(fred) | [
"p2",
"p4",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5670452193348447901777081
% SZS output start Proof for 5670452193348447901777081
3. ! [X0] : ((old(X0) & happy(X0)) <=> (curious(X0) | happy(X0))) [input p2]
5. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (~old(X0) & ~brave(X0))) [input p4]
19. brave(fred) | ~old(fred) [input p18]
23. happy(fred) [input hypothesis]
39. ! [X0] : (((old(X0) & happy(X0)) | (~curious(X0) & ~happy(X0))) & ((curious(X0) | happy(X0)) | (~old(X0) | ~happy(X0)))) [nnf transformation 3]
40. ! [X0] : (((old(X0) & happy(X0)) | (~curious(X0) & ~happy(X0))) & (curious(X0) | happy(X0) | ~old(X0) | ~happy(X0))) [flattening 39]
44. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (old(X0) | brave(X0))) & ((~old(X0) & ~brave(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 5]
45. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | old(X0) | brave(X0)) & ((~old(X0) & ~brave(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 44]
73. ~happy(X0) | old(X0) [cnf transformation 40]
74. old(X0) | ~curious(X0) [cnf transformation 40]
80. ~brave(X0) | curious(X0) | curious(X0) [cnf transformation 45]
81. ~old(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 45]
118. brave(fred) | ~old(fred) [cnf transformation 19]
122. happy(fred) [cnf transformation 23]
126. ~brave(X0) | curious(X0) [duplicate literal removal 80]
127. ~old(X0) | ~curious(X0) [duplicate literal removal 81]
158. ~curious(X0) [subsumption resolution 127,74]
159. ~brave(X0) [subsumption resolution 126,158]
242. ~old(fred) [subsumption resolution 118,159]
249. old(fred) [resolution 73,122]
250. $false [subsumption resolution 249,242]
% SZS output end Proof for 5670452193348447901777081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and creative is both generous and tall and vice versa. Everyone who is humble is both not rich and not humble and vice versa. Everyone who is not old is strong. If paul is not rich then paul is either creative or not generous and vice versa. Everyone who is not brave is not tall or old and vice versa. If someone is not calm then someone is not brave and vice versa. If someone is both wise and not wise then mary is both not humble and patient and vice versa. If paul is both not creative and not kind then mary is either not quiet or not patient. If susan is not kind then someone is curious and vice versa. Everyone who is not generous is not kind or strong and vice versa. If john is old or not rich then someone is not happy and vice versa. Everyone who is not quiet is not quiet or funny and vice versa. Everyone who is either rich or funny is both not brave and not rich and vice versa. Everyone who is not strong is not quiet or curious and vice versa. If someone is either not humble or not tall then alice is both wise and brave and vice versa. Everyone who is strong or humble is not rich or brave. Someone is both not tall and happy. John is not calm or curious. John is either not old or wise. Someone is either generous or rich. Someone is either not generous or not calm. | Paul is creative. | neutral | (![X]:((~calm(X)&creative(X))<=>(generous(X)&tall(X))))&
(![X]:(humble(X)<=>(~rich(X)&~humble(X))))&
(![X]:(~old(X)=>strong(X)))&
((~rich(paul))<=>((creative(paul)<~>~generous(paul))))&
(![X]:(~brave(X)<=>(~tall(X)|old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~brave(X))))&
((?[X]:((wise(X)&~wise(X))))<=>((~humble(mary)&patient(mary))))&
(((~creative(paul)&~kind(paul)))=>((~quiet(mary)<~>~patient(mary))))&
((~kind(susan))<=>(?[X]:(curious(X))))&
(![X]:(~generous(X)<=>(~kind(X)|strong(X))))&
(((old(john)|~rich(john)))<=>(?[X]:(~happy(X))))&
(![X]:(~quiet(X)<=>(~quiet(X)|funny(X))))&
(![X]:((rich(X)<~>funny(X))<=>(~brave(X)&~rich(X))))&
(![X]:(~strong(X)<=>(~quiet(X)|curious(X))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>((wise(alice)&brave(alice))))&
(![X]:((strong(X)|humble(X))=>(~rich(X)|brave(X))))&
(?[X]:((~tall(X)&happy(X))))&
((~calm(john)|curious(john)))&
((~old(john)<~>wise(john)))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:((~generous(X)<~>~calm(X)))) | creative(paul) | [] | null | 0 |
If paul is both brave and not funny then someone is both funny and not tall and vice versa. If fred is both not old and not strong then susan is curious and vice versa. If mary is happy then mary is either not patient or creative and vice versa. If susan is either not curious or not funny then someone is not quiet and vice versa. Everyone who is both not calm and not wise is both quiet and not calm. Everyone who is kind or tall is both old and funny and vice versa. Everyone who is both tall and quiet is either wise or brave and vice versa. Everyone who is either not generous or not calm is funny or old. If mary is not patient then fred is both not creative and not happy and vice versa. Everyone who is not quiet is both creative and not kind and vice versa. Everyone who is either not humble or not brave is both curious and kind. If john is either not patient or old then john is either brave or not curious. If someone is kind or not curious then susan is strong or not strong and vice versa. Everyone who is either not strong or happy is either strong or funny and vice versa. If alice is not kind then someone is both humble and curious. Everyone who is funny is both not generous and creative. Alice is either not creative or kind. Mary is not creative or not brave. Someone is either wise or not calm. John is calm or not creative. Paul is creative. Someone is rich. Someone is either curious or not rich. | Alice is creative. | neutral | (((brave(paul)&~funny(paul)))<=>(?[X]:((funny(X)&~tall(X)))))&
(((~old(fred)&~strong(fred)))<=>(curious(susan)))&
((happy(mary))<=>((~patient(mary)<~>creative(mary))))&
(((~curious(susan)<~>~funny(susan)))<=>(?[X]:(~quiet(X))))&
(![X]:((~calm(X)&~wise(X))=>(quiet(X)&~calm(X))))&
(![X]:((kind(X)|tall(X))<=>(old(X)&funny(X))))&
(![X]:((tall(X)&quiet(X))<=>(wise(X)<~>brave(X))))&
(![X]:((~generous(X)<~>~calm(X))=>(funny(X)|old(X))))&
((~patient(mary))<=>((~creative(fred)&~happy(fred))))&
(![X]:(~quiet(X)<=>(creative(X)&~kind(X))))&
(![X]:((~humble(X)<~>~brave(X))=>(curious(X)&kind(X))))&
(((~patient(john)<~>old(john)))=>((brave(john)<~>~curious(john))))&
((?[X]:((kind(X)|~curious(X))))<=>((strong(susan)|~strong(susan))))&
(![X]:((~strong(X)<~>happy(X))<=>(strong(X)<~>funny(X))))&
((~kind(alice))=>(?[X]:((humble(X)&curious(X)))))&
(![X]:(funny(X)=>(~generous(X)&creative(X))))&
((~creative(alice)<~>kind(alice)))&
((~creative(mary)|~brave(mary)))&
(?[X]:((wise(X)<~>~calm(X))))&
((calm(john)|~creative(john)))&
(creative(paul))&
(?[X]:(rich(X)))&
(?[X]:((curious(X)<~>~rich(X)))) | creative(alice) | [] | null | 0 |
If someone is wise or not brave then someone is not wise or not kind. If someone is either happy or quiet then someone is either quiet or wise. If someone is not happy or patient then mary is not happy. If someone is either not calm or not happy then someone is both strong and not patient. If someone is either not quiet or quiet then fred is either not strong or not calm and vice versa. If someone is not patient or not generous then lucy is both not creative and tall and vice versa. Everyone who is wise or not calm is not tall or old and vice versa. Everyone who is strong or calm is funny and vice versa. Everyone who is rich is both not strong and calm and vice versa. Everyone who is generous or rich is both old and not funny and vice versa. If someone is not brave then alice is strong or humble. Everyone who is not happy is old or happy. If someone is not funny then susan is wise or not quiet. If someone is tall then someone is both not old and not strong. Everyone who is not wise is old or brave and vice versa. Everyone who is either quiet or not quiet is both not quiet and not curious. Someone is both not creative and not kind. Someone is both old and generous. Someone is either not funny or happy. Lucy is either generous or not curious. Someone is calm. Alice is not creative. Someone is tall or not strong. Susan is either wise or rich. | Susan is happy. | entailment | ((?[X]:((wise(X)|~brave(X))))=>(?[X]:((~wise(X)|~kind(X)))))&
((?[X]:((happy(X)<~>quiet(X))))=>(?[X]:((quiet(X)<~>wise(X)))))&
((?[X]:((~happy(X)|patient(X))))=>(~happy(mary)))&
((?[X]:((~calm(X)<~>~happy(X))))=>(?[X]:((strong(X)&~patient(X)))))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>((~strong(fred)<~>~calm(fred))))&
((?[X]:((~patient(X)|~generous(X))))<=>((~creative(lucy)&tall(lucy))))&
(![X]:((wise(X)|~calm(X))<=>(~tall(X)|old(X))))&
(![X]:((strong(X)|calm(X))<=>funny(X)))&
(![X]:(rich(X)<=>(~strong(X)&calm(X))))&
(![X]:((generous(X)|rich(X))<=>(old(X)&~funny(X))))&
((?[X]:(~brave(X)))=>((strong(alice)|humble(alice))))&
(![X]:(~happy(X)=>(old(X)|happy(X))))&
((?[X]:(~funny(X)))=>((wise(susan)|~quiet(susan))))&
((?[X]:(tall(X)))=>(?[X]:((~old(X)&~strong(X)))))&
(![X]:(~wise(X)<=>(old(X)|brave(X))))&
(![X]:((quiet(X)<~>~quiet(X))=>(~quiet(X)&~curious(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(?[X]:((old(X)&generous(X))))&
(?[X]:((~funny(X)<~>happy(X))))&
((generous(lucy)<~>~curious(lucy)))&
(?[X]:(calm(X)))&
(~creative(alice))&
(?[X]:((tall(X)|~strong(X))))&
((wise(susan)<~>rich(susan))) | happy(susan) | [
"p6",
"p8",
"p9",
"p11",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8001804095813769336126916
% SZS output start Proof for 8001804095813769336126916
7. ! [X0] : ((~calm(X0) | wise(X0)) <=> (old(X0) | ~tall(X0))) [input p6]
9. ! [X0] : (rich(X0) <=> (calm(X0) & ~strong(X0))) [input p8]
10. ! [X0] : ((rich(X0) | generous(X0)) <=> (~funny(X0) & old(X0))) [input p9]
12. ! [X0] : (~happy(X0) => (happy(X0) | old(X0))) [input p11]
15. ! [X0] : (~wise(X0) <=> (brave(X0) | old(X0))) [input p14]
24. wise(susan) <~> rich(susan) [input p23]
25. ~happy(susan) [input hypothesis]
36. ! [X0] : ((happy(X0) | old(X0)) | happy(X0)) [ennf transformation 12]
37. ! [X0] : (happy(X0) | old(X0) | happy(X0)) [flattening 36]
59. ! [X0] : (((~calm(X0) | wise(X0)) | (~old(X0) & tall(X0))) & ((old(X0) | ~tall(X0)) | (calm(X0) & ~wise(X0)))) [nnf transformation 7]
60. ! [X0] : ((~calm(X0) | wise(X0) | (~old(X0) & tall(X0))) & (old(X0) | ~tall(X0) | (calm(X0) & ~wise(X0)))) [flattening 59]
63. ! [X0] : ((rich(X0) | (~calm(X0) | strong(X0))) & ((calm(X0) & ~strong(X0)) | ~rich(X0))) [nnf transformation 9]
64. ! [X0] : ((rich(X0) | ~calm(X0) | strong(X0)) & ((calm(X0) & ~strong(X0)) | ~rich(X0))) [flattening 63]
65. ! [X0] : (((rich(X0) | generous(X0)) | (funny(X0) | ~old(X0))) & ((~funny(X0) & old(X0)) | (~rich(X0) & ~generous(X0)))) [nnf transformation 10]
66. ! [X0] : ((rich(X0) | generous(X0) | funny(X0) | ~old(X0)) & ((~funny(X0) & old(X0)) | (~rich(X0) & ~generous(X0)))) [flattening 65]
70. ! [X0] : ((~wise(X0) | (~brave(X0) & ~old(X0))) & ((brave(X0) | old(X0)) | wise(X0))) [nnf transformation 15]
71. ! [X0] : ((~wise(X0) | (~brave(X0) & ~old(X0))) & (brave(X0) | old(X0) | wise(X0))) [flattening 70]
85. (~rich(susan) | ~wise(susan)) & (rich(susan) | wise(susan)) [nnf transformation 24]
112. ~old(X0) | wise(X0) | ~calm(X0) [cnf transformation 60]
117. ~rich(X0) | calm(X0) [cnf transformation 64]
120. ~rich(X0) | old(X0) [cnf transformation 66]
124. happy(X0) | old(X0) | happy(X0) [cnf transformation 37]
129. ~old(X0) | ~wise(X0) [cnf transformation 71]
145. rich(susan) | wise(susan) [cnf transformation 85]
147. ~happy(susan) [cnf transformation 25]
152. old(X0) | happy(X0) [duplicate literal removal 124]
254. 23 <=> wise(susan) [avatar definition]
255. ~wise(susan) <- (~23) [avatar component clause 254]
256. wise(susan) <- (23) [avatar component clause 254]
298. 32 <=> rich(susan) [avatar definition]
299. rich(susan) <- (32) [avatar component clause 298]
302. 23 | 32 [avatar split clause 145,298,254]
312. ~wise(X0) | happy(X0) [resolution 152,129]
435. happy(susan) <- (23) [resolution 312,256]
436. $false <- (23) [subsumption resolution 435,147]
437. ~23 [avatar contradiction clause 436]
439. old(susan) <- (32) [resolution 299,120]
440. calm(susan) <- (32) [resolution 299,117]
443. wise(susan) | ~calm(susan) <- (32) [resolution 439,112]
445. ~calm(susan) <- (~23, 32) [subsumption resolution 443,255]
446. $false <- (~23, 32) [subsumption resolution 445,440]
447. 23 | ~32 [avatar contradiction clause 446]
448. $false [avatar sat refutation 302,437,447]
% SZS output end Proof for 8001804095813769336126916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and strong then alice is both not patient and brave and vice versa. Everyone who is old is funny and vice versa. If john is funny then lucy is not generous or not humble and vice versa. Everyone who is both not generous and not curious is both happy and not patient and vice versa. Everyone who is brave or not happy is both kind and not calm. Everyone who is rich is wise or not tall. Everyone who is either not curious or not calm is curious and vice versa. Everyone who is both tall and not generous is either wise or not happy. Everyone who is not rich is both not calm and calm and vice versa. If someone is humble or brave then someone is not rich. If someone is not funny then lucy is brave. Everyone who is either not curious or humble is both not patient and tall. Everyone who is old is not kind. If someone is not creative or humble then john is both quiet and not strong and vice versa. If john is both creative and not happy then paul is not strong. If mary is brave or not strong then someone is either strong or not patient and vice versa. Fred is either patient or calm. Lucy is not quiet. Lucy is not quiet or not strong. Someone is not curious or happy. Paul is either creative or patient. | Mary is not tall. | neutral | ((?[X]:((~happy(X)&strong(X))))<=>((~patient(alice)&brave(alice))))&
(![X]:(old(X)<=>funny(X)))&
((funny(john))<=>((~generous(lucy)|~humble(lucy))))&
(![X]:((~generous(X)&~curious(X))<=>(happy(X)&~patient(X))))&
(![X]:((brave(X)|~happy(X))=>(kind(X)&~calm(X))))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
((?[X]:(~funny(X)))=>(brave(lucy)))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
((patient(fred)<~>calm(fred)))&
(~quiet(lucy))&
((~quiet(lucy)|~strong(lucy)))&
(?[X]:((~curious(X)|happy(X))))&
((creative(paul)<~>patient(paul))) | ~tall(mary) | [] | null | 0 |
Everyone who is both kind and tall is both generous and curious. Everyone who is happy is both not kind and not generous. Everyone who is either brave or patient is both humble and not creative. If alice is not patient or not rich then lucy is generous or not strong and vice versa. If alice is brave then someone is tall or strong and vice versa. If someone is both not brave and funny then susan is both not brave and not creative. Everyone who is either calm or not tall is both not creative and strong and vice versa. Everyone who is both not tall and curious is not tall and vice versa. If someone is both generous and old then someone is not humble and vice versa. If mary is not rich or not funny then susan is funny or not humble and vice versa. If lucy is both not generous and strong then john is both patient and old. If someone is either strong or not creative then mary is either creative or not happy. If someone is both old and not brave then someone is rich or old. Everyone who is both not strong and not old is either funny or patient and vice versa. If someone is not creative or old then fred is patient. Everyone who is both brave and not happy is both not creative and happy. Alice is not creative or not old. Fred is creative or not brave. Lucy is both not funny and happy. Alice is not happy. Susan is either old or kind. Someone is not old or not happy. Alice is either creative or not calm. | Lucy is not tall. | entailment | (![X]:((kind(X)&tall(X))=>(generous(X)&curious(X))))&
(![X]:(happy(X)=>(~kind(X)&~generous(X))))&
(![X]:((brave(X)<~>patient(X))=>(humble(X)&~creative(X))))&
(((~patient(alice)|~rich(alice)))<=>((generous(lucy)|~strong(lucy))))&
((brave(alice))<=>(?[X]:((tall(X)|strong(X)))))&
((?[X]:((~brave(X)&funny(X))))=>((~brave(susan)&~creative(susan))))&
(![X]:((calm(X)<~>~tall(X))<=>(~creative(X)&strong(X))))&
(![X]:((~tall(X)&curious(X))<=>~tall(X)))&
((?[X]:((generous(X)&old(X))))<=>(?[X]:(~humble(X))))&
(((~rich(mary)|~funny(mary)))<=>((funny(susan)|~humble(susan))))&
(((~generous(lucy)&strong(lucy)))=>((patient(john)&old(john))))&
((?[X]:((strong(X)<~>~creative(X))))=>((creative(mary)<~>~happy(mary))))&
((?[X]:((old(X)&~brave(X))))=>(?[X]:((rich(X)|old(X)))))&
(![X]:((~strong(X)&~old(X))<=>(funny(X)<~>patient(X))))&
((?[X]:((~creative(X)|old(X))))=>(patient(fred)))&
(![X]:((brave(X)&~happy(X))=>(~creative(X)&happy(X))))&
((~creative(alice)|~old(alice)))&
((creative(fred)|~brave(fred)))&
((~funny(lucy)&happy(lucy)))&
(~happy(alice))&
((old(susan)<~>kind(susan)))&
(?[X]:((~old(X)|~happy(X))))&
((creative(alice)<~>~calm(alice))) | ~tall(lucy) | [
"p4",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5115627092153919645841060
% SZS output start Proof for 5115627092153919645841060
5. brave(alice) <=> ? [X0] : (strong(X0) | tall(X0)) [input p4]
16. ! [X0] : ((~happy(X0) & brave(X0)) => (happy(X0) & ~creative(X0))) [input p15]
20. ~happy(alice) [input p19]
24. tall(lucy) [input hypothesis]
37. ! [X0] : ((happy(X0) & ~creative(X0)) | (happy(X0) | ~brave(X0))) [ennf transformation 16]
38. ! [X0] : ((happy(X0) & ~creative(X0)) | happy(X0) | ~brave(X0)) [flattening 37]
42. (brave(alice) | ! [X0] : (~strong(X0) & ~tall(X0))) & (? [X0] : (strong(X0) | tall(X0)) | ~brave(alice)) [nnf transformation 5]
43. (brave(alice) | ! [X0] : (~strong(X0) & ~tall(X0))) & (? [X1] : (strong(X1) | tall(X1)) | ~brave(alice)) [rectify 42]
44. ? [X1] : (strong(X1) | tall(X1)) => (strong(sK0) | tall(sK0)) [choice axiom]
45. (brave(alice) | ! [X0] : (~strong(X0) & ~tall(X0))) & ((strong(sK0) | tall(sK0)) | ~brave(alice)) [skolemisation 43,44]
80. brave(alice) | ~tall(X0) [cnf transformation 45]
116. happy(X0) | happy(X0) | ~brave(X0) [cnf transformation 38]
121. ~happy(alice) [cnf transformation 20]
127. tall(lucy) [cnf transformation 24]
128. ~brave(X0) | happy(X0) [duplicate literal removal 116]
153. 6 <=> brave(alice) [avatar definition]
155. brave(alice) <- (6) [avatar component clause 153]
158. 7 <=> ! [X0] : ~tall(X0) [avatar definition]
159. ~tall(X0) <- (7) [avatar component clause 158]
160. 7 | 6 [avatar split clause 80,153,158]
319. $false <- (7) [resolution 159,127]
320. ~7 [avatar contradiction clause 319]
326. happy(alice) <- (6) [resolution 128,155]
327. $false <- (6) [subsumption resolution 326,121]
328. ~6 [avatar contradiction clause 327]
329. $false [avatar sat refutation 160,320,328]
% SZS output end Proof for 5115627092153919645841060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not tall or tall then alice is not kind and vice versa. Everyone who is happy is humble and vice versa. Everyone who is either not old or not quiet is curious or not creative and vice versa. Everyone who is strong or brave is not patient. Everyone who is either not generous or not funny is both not creative and not patient and vice versa. Everyone who is humble or not strong is both patient and not brave and vice versa. Everyone who is not quiet or not generous is humble or kind and vice versa. If someone is curious then someone is both generous and not rich. If alice is both old and not happy then john is not strong and vice versa. Everyone who is not happy is both brave and not kind and vice versa. If someone is not creative then mary is both not patient and quiet and vice versa. Everyone who is not curious is both not humble and tall. If someone is generous then someone is wise. Everyone who is either patient or creative is both not old and not quiet. If paul is happy then someone is not patient or generous. If someone is not quiet then someone is curious or strong. Someone is wise or patient. Someone is not quiet. Susan is both calm and not patient. Paul is not humble. Fred is either happy or not humble. Mary is kind or not calm. Susan is strong. | Paul is not strong. | contradiction | (((~tall(lucy)<~>tall(lucy)))<=>(~kind(alice)))&
(![X]:(happy(X)<=>humble(X)))&
(![X]:((~old(X)<~>~quiet(X))<=>(curious(X)|~creative(X))))&
(![X]:((strong(X)|brave(X))=>~patient(X)))&
(![X]:((~generous(X)<~>~funny(X))<=>(~creative(X)&~patient(X))))&
(![X]:((humble(X)|~strong(X))<=>(patient(X)&~brave(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(humble(X)|kind(X))))&
((?[X]:(curious(X)))=>(?[X]:((generous(X)&~rich(X)))))&
(((old(alice)&~happy(alice)))<=>(~strong(john)))&
(![X]:(~happy(X)<=>(brave(X)&~kind(X))))&
((?[X]:(~creative(X)))<=>((~patient(mary)&quiet(mary))))&
(![X]:(~curious(X)=>(~humble(X)&tall(X))))&
((?[X]:(generous(X)))=>(?[X]:(wise(X))))&
(![X]:((patient(X)<~>creative(X))=>(~old(X)&~quiet(X))))&
((happy(paul))=>(?[X]:((~patient(X)|generous(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((curious(X)|strong(X)))))&
(?[X]:((wise(X)|patient(X))))&
(?[X]:(~quiet(X)))&
((calm(susan)&~patient(susan)))&
(~humble(paul))&
((happy(fred)<~>~humble(fred)))&
((kind(mary)|~calm(mary)))&
(strong(susan)) | ~strong(paul) | [
"p1",
"p5",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 911005287816407698359238
% SZS output start Proof for 911005287816407698359238
2. ! [X0] : (happy(X0) <=> humble(X0)) [input p1]
6. ! [X0] : ((~strong(X0) | humble(X0)) <=> (~brave(X0) & patient(X0))) [input p5]
10. ! [X0] : (~happy(X0) <=> (~kind(X0) & brave(X0))) [input p9]
20. ~humble(paul) [input p19]
24. ~strong(paul) [input hypothesis]
38. ! [X0] : ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0))) [nnf transformation 2]
43. ! [X0] : (((~strong(X0) | humble(X0)) | (brave(X0) | ~patient(X0))) & ((~brave(X0) & patient(X0)) | (strong(X0) & ~humble(X0)))) [nnf transformation 6]
44. ! [X0] : ((~strong(X0) | humble(X0) | brave(X0) | ~patient(X0)) & ((~brave(X0) & patient(X0)) | (strong(X0) & ~humble(X0)))) [flattening 43]
52. ! [X0] : ((~happy(X0) | (kind(X0) | ~brave(X0))) & ((~kind(X0) & brave(X0)) | happy(X0))) [nnf transformation 10]
53. ! [X0] : ((~happy(X0) | kind(X0) | ~brave(X0)) & ((~kind(X0) & brave(X0)) | happy(X0))) [flattening 52]
72. ~happy(X0) | humble(X0) [cnf transformation 38]
91. ~brave(X0) | strong(X0) [cnf transformation 44]
101. brave(X0) | happy(X0) [cnf transformation 53]
118. ~humble(paul) [cnf transformation 20]
123. ~strong(paul) [cnf transformation 24]
178. 12 <=> happy(paul) [avatar definition]
179. happy(paul) <- (12) [avatar component clause 178]
220. strong(X0) | happy(X0) [resolution 101,91]
222. happy(paul) [resolution 220,123]
223. 12 [avatar split clause 222,178]
224. humble(paul) <- (12) [resolution 179,72]
225. $false <- (12) [subsumption resolution 224,118]
226. ~12 [avatar contradiction clause 225]
227. $false [avatar sat refutation 223,226]
% SZS output end Proof for 911005287816407698359238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or quiet is both quiet and calm. If mary is either not curious or tall then someone is quiet and vice versa. If someone is both generous and not generous then someone is both not curious and humble and vice versa. If lucy is quiet then susan is not wise or not humble. Everyone who is either not wise or creative is not creative or not tall and vice versa. If someone is both not rich and happy then fred is both not calm and calm. Everyone who is not calm is either old or not brave and vice versa. Everyone who is not old or not patient is not generous or rich and vice versa. If paul is both quiet and calm then someone is both not wise and not kind and vice versa. If someone is both patient and wise then paul is not creative and vice versa. Everyone who is either tall or not strong is either not old or not curious and vice versa. Everyone who is not strong or kind is not rich or not tall and vice versa. If someone is not funny or not generous then someone is not brave or strong. Everyone who is either kind or curious is not wise and vice versa. Everyone who is either not happy or not kind is both humble and patient. Everyone who is both not funny and not strong is not generous. John is generous. Susan is kind. Someone is either not old or generous. Someone is not strong or not calm. Fred is either generous or humble. Susan is both funny and quiet. Someone is either not old or not quiet. Mary is patient or strong. | Susan is tall. | contradiction | (![X]:((~brave(X)<~>quiet(X))=>(quiet(X)&calm(X))))&
(((~curious(mary)<~>tall(mary)))<=>(?[X]:(quiet(X))))&
((?[X]:((generous(X)&~generous(X))))<=>(?[X]:((~curious(X)&humble(X)))))&
((quiet(lucy))=>((~wise(susan)|~humble(susan))))&
(![X]:((~wise(X)<~>creative(X))<=>(~creative(X)|~tall(X))))&
((?[X]:((~rich(X)&happy(X))))=>((~calm(fred)&calm(fred))))&
(![X]:(~calm(X)<=>(old(X)<~>~brave(X))))&
(![X]:((~old(X)|~patient(X))<=>(~generous(X)|rich(X))))&
(((quiet(paul)&calm(paul)))<=>(?[X]:((~wise(X)&~kind(X)))))&
((?[X]:((patient(X)&wise(X))))<=>(~creative(paul)))&
(![X]:((tall(X)<~>~strong(X))<=>(~old(X)<~>~curious(X))))&
(![X]:((~strong(X)|kind(X))<=>(~rich(X)|~tall(X))))&
((?[X]:((~funny(X)|~generous(X))))=>(?[X]:((~brave(X)|strong(X)))))&
(![X]:((kind(X)<~>curious(X))<=>~wise(X)))&
(![X]:((~happy(X)<~>~kind(X))=>(humble(X)&patient(X))))&
(![X]:((~funny(X)&~strong(X))=>~generous(X)))&
(generous(john))&
(kind(susan))&
(?[X]:((~old(X)<~>generous(X))))&
(?[X]:((~strong(X)|~calm(X))))&
((generous(fred)<~>humble(fred)))&
((funny(susan)&quiet(susan)))&
(?[X]:((~old(X)<~>~quiet(X))))&
((patient(mary)|strong(mary))) | tall(susan) | [
"p2",
"p4",
"p5",
"p11",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8682274137827908920302424
% SZS output start Proof for 8682274137827908920302424
3. ? [X0] : (~generous(X0) & generous(X0)) <=> ? [X0] : (humble(X0) & ~curious(X0)) [input p2]
5. ! [X0] : ((~wise(X0) <~> creative(X0)) <=> (~tall(X0) | ~creative(X0))) [input p4]
6. ? [X0] : (happy(X0) & ~rich(X0)) => (calm(fred) & ~calm(fred)) [input p5]
12. ! [X0] : ((kind(X0) | ~strong(X0)) <=> (~tall(X0) | ~rich(X0))) [input p11]
14. ! [X0] : ((kind(X0) <~> curious(X0)) <=> ~wise(X0)) [input p13]
15. ! [X0] : ((~happy(X0) <~> ~kind(X0)) => (patient(X0) & humble(X0))) [input p14]
18. kind(susan) [input p17]
25. tall(susan) [input hypothesis]
26. ? [X0] : (~generous(X0) & generous(X0)) <=> ? [X1] : (humble(X1) & ~curious(X1)) [rectify 3]
34. (calm(fred) & ~calm(fred)) | ! [X0] : (~happy(X0) | rich(X0)) [ennf transformation 6]
36. ! [X0] : ((patient(X0) & humble(X0)) | (~happy(X0) <=> ~kind(X0))) [ennf transformation 15]
42. (? [X0] : (~generous(X0) & generous(X0)) | ! [X1] : (~humble(X1) | curious(X1))) & (? [X1] : (humble(X1) & ~curious(X1)) | ! [X0] : (generous(X0) | ~generous(X0))) [nnf transformation 26]
43. (? [X0] : (~generous(X0) & generous(X0)) | ! [X1] : (~humble(X1) | curious(X1))) & (? [X2] : (humble(X2) & ~curious(X2)) | ! [X3] : (generous(X3) | ~generous(X3))) [rectify 42]
44. ? [X0] : (~generous(X0) & generous(X0)) => (~generous(sK1) & generous(sK1)) [choice axiom]
45. ? [X2] : (humble(X2) & ~curious(X2)) => (humble(sK2) & ~curious(sK2)) [choice axiom]
46. ((~generous(sK1) & generous(sK1)) | ! [X1] : (~humble(X1) | curious(X1))) & ((humble(sK2) & ~curious(sK2)) | ! [X3] : (generous(X3) | ~generous(X3))) [skolemisation 43,45,44]
47. ! [X0] : ((((~creative(X0) | wise(X0)) & (creative(X0) | ~wise(X0))) | (tall(X0) & creative(X0))) & ((~tall(X0) | ~creative(X0)) | ((~wise(X0) | ~creative(X0)) & (creative(X0) | wise(X0))))) [nnf transformation 5]
48. ! [X0] : ((((~creative(X0) | wise(X0)) & (creative(X0) | ~wise(X0))) | (tall(X0) & creative(X0))) & (~tall(X0) | ~creative(X0) | ((~wise(X0) | ~creative(X0)) & (creative(X0) | wise(X0))))) [flattening 47]
62. ! [X0] : (((kind(X0) | ~strong(X0)) | (tall(X0) & rich(X0))) & ((~tall(X0) | ~rich(X0)) | (~kind(X0) & strong(X0)))) [nnf transformation 12]
63. ! [X0] : ((kind(X0) | ~strong(X0) | (tall(X0) & rich(X0))) & (~tall(X0) | ~rich(X0) | (~kind(X0) & strong(X0)))) [flattening 62]
67. ! [X0] : ((((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | wise(X0)) & (~wise(X0) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))))) [nnf transformation 14]
68. ! [X0] : ((patient(X0) & humble(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) [nnf transformation 36]
88. generous(sK1) | ~humble(X1) | curious(X1) [cnf transformation 46]
89. ~generous(sK1) | ~humble(X1) | curious(X1) [cnf transformation 46]
92. ~tall(X0) | ~creative(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 48]
93. creative(X0) | ~wise(X0) | creative(X0) [cnf transformation 48]
97. ~calm(fred) | ~happy(X0) | rich(X0) [cnf transformation 34]
98. calm(fred) | ~happy(X0) | rich(X0) [cnf transformation 34]
123. ~kind(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 63]
130. ~kind(X0) | ~curious(X0) | wise(X0) [cnf transformation 67]
131. ~kind(X0) | humble(X0) | happy(X0) [cnf transformation 68]
136. kind(susan) [cnf transformation 18]
146. tall(susan) [cnf transformation 25]
147. ~tall(X0) | ~creative(X0) | ~wise(X0) [duplicate literal removal 92]
148. ~wise(X0) | creative(X0) [duplicate literal removal 93]
170. 5 <=> ! [X1] : (~humble(X1) | curious(X1)) [avatar definition]
171. ~humble(X1) | curious(X1) <- (5) [avatar component clause 170]
173. 6 <=> generous(sK1) [avatar definition]
176. 5 | ~6 [avatar split clause 89,173,170]
177. 5 | 6 [avatar split clause 88,173,170]
183. 8 <=> wise(susan) [avatar definition]
184. wise(susan) <- (8) [avatar component clause 183]
185. ~wise(susan) <- (~8) [avatar component clause 183]
187. 9 <=> humble(susan) [avatar definition]
188. humble(susan) <- (9) [avatar component clause 187]
189. ~humble(susan) <- (~9) [avatar component clause 187]
191. ~wise(X0) | ~tall(X0) [subsumption resolution 147,148]
193. 10 <=> ! [X0] : (~happy(X0) | rich(X0)) [avatar definition]
194. ~happy(X0) | rich(X0) <- (10) [avatar component clause 193]
196. 11 <=> calm(fred) [avatar definition]
199. 10 | 11 [avatar split clause 98,196,193]
200. 10 | ~11 [avatar split clause 97,196,193]
416. ~rich(susan) | ~tall(susan) [resolution 123,136]
418. ~rich(susan) [subsumption resolution 416,146]
423. 52 <=> curious(susan) [avatar definition]
442. ~curious(susan) | wise(susan) [resolution 130,136]
447. ~curious(susan) <- (~8) [subsumption resolution 442,185]
448. ~52 | 8 [avatar split clause 447,183,423]
449. humble(susan) | happy(susan) [resolution 131,136]
452. happy(susan) <- (~9) [subsumption resolution 449,189]
454. rich(susan) <- (~9, 10) [resolution 452,194]
455. $false <- (~9, 10) [subsumption resolution 454,418]
456. 9 | ~10 [avatar contradiction clause 455]
463. curious(susan) <- (5, 9) [resolution 188,171]
466. 52 | ~5 | ~9 [avatar split clause 463,187,170,423]
470. ~tall(susan) <- (8) [resolution 184,191]
472. $false <- (8) [subsumption resolution 470,146]
473. ~8 [avatar contradiction clause 472]
474. $false [avatar sat refutation 176,177,199,200,448,456,466,473]
% SZS output end Proof for 8682274137827908920302424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble or not happy then someone is both not quiet and kind and vice versa.
Everyone who is either creative or not brave is not brave and vice versa.
If someone is both not strong and calm then someone is either kind or humble.
If someone is strong then lucy is both funny and happy.
Everyone who is either not tall or not rich is not brave.
If someone is either wise or curious then someone is either not calm or not patient and vice versa.
Everyone who is old or not generous is old and vice versa.
If susan is both not happy and not quiet then susan is both brave and calm.
Everyone who is either not patient or not rich is either not brave or not happy.
Everyone who is wise is either curious or rich and vice versa.
Everyone who is not old is old or not wise and vice versa.
Everyone who is both funny and calm is both patient and not old and vice versa.
Everyone who is either funny or humble is either old or quiet.
If susan is either happy or not rich then john is patient or humble.
Everyone who is not generous or calm is both not creative and not happy.
Everyone who is either humble or creative is either not strong or not humble and vice versa.
Someone is either not patient or strong.
Someone is either kind or old.
Someone is both not kind and not wise.
Lucy is both not kind and not tall.
Someone is brave or curious. | John is not curious. | neutral | ((?[X]:((humble(X)|~happy(X))))<=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((creative(X)<~>~brave(X))<=>~brave(X)))&
((?[X]:((~strong(X)&calm(X))))=>(?[X]:((kind(X)<~>humble(X)))))&
((?[X]:(strong(X)))=>((funny(lucy)&happy(lucy))))&
(![X]:((~tall(X)<~>~rich(X))=>~brave(X)))&
((?[X]:((wise(X)<~>curious(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((old(X)|~generous(X))<=>old(X)))&
(((~happy(susan)&~quiet(susan)))=>((brave(susan)&calm(susan))))&
(![X]:((~patient(X)<~>~rich(X))=>(~brave(X)<~>~happy(X))))&
(![X]:(wise(X)<=>(curious(X)<~>rich(X))))&
(![X]:(~old(X)<=>(old(X)|~wise(X))))&
(![X]:((funny(X)&calm(X))<=>(patient(X)&~old(X))))&
(![X]:((funny(X)<~>humble(X))=>(old(X)<~>quiet(X))))&
(((happy(susan)<~>~rich(susan)))=>((patient(john)|humble(john))))&
(![X]:((~generous(X)|calm(X))=>(~creative(X)&~happy(X))))&
(![X]:((humble(X)<~>creative(X))<=>(~strong(X)<~>~humble(X))))&
(?[X]:((~patient(X)<~>strong(X))))&
(?[X]:((kind(X)<~>old(X))))&
(?[X]:((~kind(X)&~wise(X))))&
((~kind(lucy)&~tall(lucy)))&
(?[X]:((brave(X)|curious(X)))) | ~curious(john) | [] | null | 0 |
Everyone who is not rich is both happy and kind.
If fred is either not patient or not calm then lucy is not tall or tall.
If someone is either not kind or not generous then someone is either calm or not humble and vice versa.
Everyone who is not strong is either tall or happy.
Everyone who is brave or old is either not calm or not generous and vice versa.
If someone is either not tall or not patient then john is funny and vice versa.
Everyone who is both not funny and quiet is both quiet and not brave.
Everyone who is tall or strong is not strong.
Everyone who is calm or not tall is not patient or not generous and vice versa.
Everyone who is tall is not kind or humble.
If someone is both patient and kind then paul is either not happy or not rich.
Everyone who is not brave or calm is generous or not calm.
If mary is both not funny and generous then john is both tall and not quiet.
Everyone who is either not patient or not tall is either not rich or not generous and vice versa.
If susan is either calm or not quiet then someone is not generous and vice versa.
If fred is both not creative and patient then someone is not rich or generous.
Lucy is either not calm or not rich.
Someone is not creative.
Someone is generous.
Paul is both generous and calm.
John is both creative and rich.
Someone is kind.
Alice is either creative or not strong.
Fred is tall. | Fred is not calm. | entailment | (![X]:(~rich(X)=>(happy(X)&kind(X))))&
(((~patient(fred)<~>~calm(fred)))=>((~tall(lucy)|tall(lucy))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((calm(X)<~>~humble(X)))))&
(![X]:(~strong(X)=>(tall(X)<~>happy(X))))&
(![X]:((brave(X)|old(X))<=>(~calm(X)<~>~generous(X))))&
((?[X]:((~tall(X)<~>~patient(X))))<=>(funny(john)))&
(![X]:((~funny(X)&quiet(X))=>(quiet(X)&~brave(X))))&
(![X]:((tall(X)|strong(X))=>~strong(X)))&
(![X]:((calm(X)|~tall(X))<=>(~patient(X)|~generous(X))))&
(![X]:(tall(X)=>(~kind(X)|humble(X))))&
((?[X]:((patient(X)&kind(X))))=>((~happy(paul)<~>~rich(paul))))&
(![X]:((~brave(X)|calm(X))=>(generous(X)|~calm(X))))&
(((~funny(mary)&generous(mary)))=>((tall(john)&~quiet(john))))&
(![X]:((~patient(X)<~>~tall(X))<=>(~rich(X)<~>~generous(X))))&
(((calm(susan)<~>~quiet(susan)))<=>(?[X]:(~generous(X))))&
(((~creative(fred)&patient(fred)))=>(?[X]:((~rich(X)|generous(X)))))&
((~calm(lucy)<~>~rich(lucy)))&
(?[X]:(~creative(X)))&
(?[X]:(generous(X)))&
((generous(paul)&calm(paul)))&
((creative(john)&rich(john)))&
(?[X]:(kind(X)))&
((creative(alice)<~>~strong(alice)))&
(tall(fred)) | ~calm(fred) | [
"p0",
"p3",
"p7",
"p8",
"p11",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 24080424910735839987528
% SZS output start Proof for 24080424910735839987528
1. ! [X0] : (~rich(X0) => (kind(X0) & happy(X0))) [input p0]
4. ! [X0] : (~strong(X0) => (tall(X0) <~> happy(X0))) [input p3]
8. ! [X0] : ((strong(X0) | tall(X0)) => ~strong(X0)) [input p7]
9. ! [X0] : ((~tall(X0) | calm(X0)) <=> (~generous(X0) | ~patient(X0))) [input p8]
12. ! [X0] : ((calm(X0) | ~brave(X0)) => (~calm(X0) | generous(X0))) [input p11]
14. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> (~rich(X0) <~> ~generous(X0))) [input p13]
24. tall(fred) [input p23]
25. calm(fred) [input hypothesis]
27. ! [X0] : ((kind(X0) & happy(X0)) | rich(X0)) [ennf transformation 1]
30. ! [X0] : ((tall(X0) <~> happy(X0)) | strong(X0)) [ennf transformation 4]
33. ! [X0] : (~strong(X0) | (~strong(X0) & ~tall(X0))) [ennf transformation 8]
37. ! [X0] : ((~calm(X0) | generous(X0)) | (~calm(X0) & brave(X0))) [ennf transformation 12]
38. ! [X0] : (~calm(X0) | generous(X0) | (~calm(X0) & brave(X0))) [flattening 37]
49. ! [X0] : (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | strong(X0)) [nnf transformation 30]
56. ! [X0] : (((~tall(X0) | calm(X0)) | (generous(X0) & patient(X0))) & ((~generous(X0) | ~patient(X0)) | (tall(X0) & ~calm(X0)))) [nnf transformation 9]
57. ! [X0] : ((~tall(X0) | calm(X0) | (generous(X0) & patient(X0))) & (~generous(X0) | ~patient(X0) | (tall(X0) & ~calm(X0)))) [flattening 56]
59. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0)))) & (((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 14]
74. happy(X0) | rich(X0) [cnf transformation 27]
87. ~tall(X0) | ~happy(X0) | strong(X0) [cnf transformation 49]
101. ~strong(X0) | ~strong(X0) [cnf transformation 33]
102. ~generous(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 57]
110. ~calm(X0) | generous(X0) | ~calm(X0) [cnf transformation 38]
113. ~generous(X0) | ~rich(X0) | ~tall(X0) | patient(X0) [cnf transformation 59]
137. tall(fred) [cnf transformation 24]
138. calm(fred) [cnf transformation 25]
139. ~calm(X0) | generous(X0) [duplicate literal removal 110]
140. ~strong(X0) [duplicate literal removal 101]
256. 26 <=> patient(fred) [avatar definition]
280. generous(fred) [resolution 139,138]
283. ~happy(fred) | strong(fred) [resolution 87,137]
285. ~happy(fred) [subsumption resolution 283,140]
287. rich(fred) [resolution 285,74]
290. ~patient(fred) | ~calm(fred) [resolution 102,280]
414. ~rich(fred) | ~tall(fred) | patient(fred) [resolution 113,280]
418. ~tall(fred) | patient(fred) [subsumption resolution 414,287]
419. patient(fred) [subsumption resolution 418,137]
428. 26 [avatar split clause 419,256]
429. ~patient(fred) [subsumption resolution 290,138]
430. ~26 [avatar split clause 429,256]
431. $false [avatar sat refutation 428,430]
% SZS output end Proof for 24080424910735839987528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and creative is rich.
If someone is either not creative or quiet then someone is both kind and not humble and vice versa.
Everyone who is funny is humble.
If john is either not old or not quiet then someone is not wise and vice versa.
Everyone who is either not happy or not creative is either old or not rich and vice versa.
If someone is old or not kind then alice is not funny or not generous and vice versa.
If someone is not patient then someone is not patient or calm and vice versa.
Everyone who is either brave or not wise is not wise or not creative.
Everyone who is brave or not brave is either not strong or strong and vice versa.
Everyone who is either tall or strong is either not curious or not humble and vice versa.
Everyone who is creative or not humble is creative or not old and vice versa.
If fred is both funny and curious then someone is not creative or rich and vice versa.
Everyone who is not happy or not strong is old and vice versa.
Everyone who is both not curious and quiet is not patient or wise.
Everyone who is not generous is both brave and not wise.
If paul is not funny or not generous then lucy is both not kind and not creative and vice versa.
John is tall.
Mary is either wise or patient.
Someone is not creative.
Lucy is both creative and not generous.
Mary is both curious and quiet.
Alice is either not quiet or tall.
Someone is either not strong or humble.
Someone is calm or brave. | Lucy is not brave. | contradiction | (![X]:((~kind(X)&creative(X))=>rich(X)))&
((?[X]:((~creative(X)<~>quiet(X))))<=>(?[X]:((kind(X)&~humble(X)))))&
(![X]:(funny(X)=>humble(X)))&
(((~old(john)<~>~quiet(john)))<=>(?[X]:(~wise(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(old(X)<~>~rich(X))))&
((?[X]:((old(X)|~kind(X))))<=>((~funny(alice)|~generous(alice))))&
((?[X]:(~patient(X)))<=>(?[X]:((~patient(X)|calm(X)))))&
(![X]:((brave(X)<~>~wise(X))=>(~wise(X)|~creative(X))))&
(![X]:((brave(X)|~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((tall(X)<~>strong(X))<=>(~curious(X)<~>~humble(X))))&
(![X]:((creative(X)|~humble(X))<=>(creative(X)|~old(X))))&
(((funny(fred)&curious(fred)))<=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((~happy(X)|~strong(X))<=>old(X)))&
(![X]:((~curious(X)&quiet(X))=>(~patient(X)|wise(X))))&
(![X]:(~generous(X)=>(brave(X)&~wise(X))))&
(((~funny(paul)|~generous(paul)))<=>((~kind(lucy)&~creative(lucy))))&
(tall(john))&
((wise(mary)<~>patient(mary)))&
(?[X]:(~creative(X)))&
((creative(lucy)&~generous(lucy)))&
((curious(mary)&quiet(mary)))&
((~quiet(alice)<~>tall(alice)))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:((calm(X)|brave(X)))) | ~brave(lucy) | [
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8127000019738864071770182
% SZS output start Proof for 8127000019738864071770182
15. ! [X0] : (~generous(X0) => (~wise(X0) & brave(X0))) [input p14]
20. ~generous(lucy) & creative(lucy) [input p19]
25. ~brave(lucy) [input hypothesis]
35. ! [X0] : ((~wise(X0) & brave(X0)) | generous(X0)) [ennf transformation 15]
136. brave(X0) | generous(X0) [cnf transformation 35]
148. ~generous(lucy) [cnf transformation 20]
156. ~brave(lucy) [cnf transformation 25]
351. generous(lucy) [resolution 136,156]
352. $false [subsumption resolution 351,148]
% SZS output end Proof for 8127000019738864071770182
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either kind or not patient then someone is not calm or not patient.
Everyone who is either not old or rich is strong.
If someone is both not strong and wise then someone is not quiet.
If someone is either not quiet or not generous then alice is either happy or not happy.
If someone is happy or not funny then someone is brave or tall and vice versa.
Everyone who is either kind or happy is both calm and humble.
If someone is quiet then someone is both not calm and not creative and vice versa.
Everyone who is both wise and not kind is old and vice versa.
Everyone who is both not funny and rich is generous and vice versa.
Everyone who is not creative or tall is creative and vice versa.
Everyone who is either funny or not brave is brave and vice versa.
Everyone who is humble or calm is either not rich or wise.
Everyone who is not old or not tall is creative and vice versa.
If john is both tall and not curious then someone is not happy.
If john is both not patient and quiet then someone is not wise or brave.
Everyone who is not generous is happy and vice versa.
Someone is both humble and not calm.
John is not calm or wise.
Someone is either not brave or not creative.
John is happy or not humble.
Someone is not generous.
Fred is kind or not happy.
Paul is both rich and not brave. | Paul is not calm. | neutral | (((kind(alice)<~>~patient(alice)))=>(?[X]:((~calm(X)|~patient(X)))))&
(![X]:((~old(X)<~>rich(X))=>strong(X)))&
((?[X]:((~strong(X)&wise(X))))=>(?[X]:(~quiet(X))))&
((?[X]:((~quiet(X)<~>~generous(X))))=>((happy(alice)<~>~happy(alice))))&
((?[X]:((happy(X)|~funny(X))))<=>(?[X]:((brave(X)|tall(X)))))&
(![X]:((kind(X)<~>happy(X))=>(calm(X)&humble(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((~calm(X)&~creative(X)))))&
(![X]:((wise(X)&~kind(X))<=>old(X)))&
(![X]:((~funny(X)&rich(X))<=>generous(X)))&
(![X]:((~creative(X)|tall(X))<=>creative(X)))&
(![X]:((funny(X)<~>~brave(X))<=>brave(X)))&
(![X]:((humble(X)|calm(X))=>(~rich(X)<~>wise(X))))&
(![X]:((~old(X)|~tall(X))<=>creative(X)))&
(((tall(john)&~curious(john)))=>(?[X]:(~happy(X))))&
(((~patient(john)&quiet(john)))=>(?[X]:((~wise(X)|brave(X)))))&
(![X]:(~generous(X)<=>happy(X)))&
(?[X]:((humble(X)&~calm(X))))&
((~calm(john)|wise(john)))&
(?[X]:((~brave(X)<~>~creative(X))))&
((happy(john)|~humble(john)))&
(?[X]:(~generous(X)))&
((kind(fred)|~happy(fred)))&
((rich(paul)&~brave(paul))) | ~calm(paul) | [] | null | 0 |
Everyone who is both not kind and quiet is patient and vice versa. Everyone who is either strong or not wise is either not strong or generous and vice versa. Everyone who is calm is either creative or not patient and vice versa. If fred is both creative and rich then susan is patient or not patient. Everyone who is either generous or not humble is wise or kind and vice versa. If mary is humble then paul is not humble or not brave and vice versa. Everyone who is funny or not humble is not rich and vice versa. Everyone who is either not generous or not creative is both happy and patient and vice versa. Everyone who is brave or not brave is creative. If lucy is both not calm and generous then someone is old and vice versa. Everyone who is not patient is both funny and not brave and vice versa. If someone is patient then someone is either not quiet or kind and vice versa. If someone is either not curious or brave then john is both strong and not funny. If someone is either not strong or not funny then lucy is both brave and calm. Everyone who is either not calm or not patient is not generous and vice versa. If mary is both not funny and not curious then mary is both not humble and not tall and vice versa. Alice is not strong. Someone is either creative or not calm. Someone is kind. Someone is quiet. Paul is wise. Lucy is both strong and not kind. | Mary is not creative. | contradiction | (![X]:((~kind(X)&quiet(X))<=>patient(X)))&
(![X]:((strong(X)<~>~wise(X))<=>(~strong(X)<~>generous(X))))&
(![X]:(calm(X)<=>(creative(X)<~>~patient(X))))&
(((creative(fred)&rich(fred)))=>((patient(susan)|~patient(susan))))&
(![X]:((generous(X)<~>~humble(X))<=>(wise(X)|kind(X))))&
((humble(mary))<=>((~humble(paul)|~brave(paul))))&
(![X]:((funny(X)|~humble(X))<=>~rich(X)))&
(![X]:((~generous(X)<~>~creative(X))<=>(happy(X)&patient(X))))&
(![X]:((brave(X)|~brave(X))=>creative(X)))&
(((~calm(lucy)&generous(lucy)))<=>(?[X]:(old(X))))&
(![X]:(~patient(X)<=>(funny(X)&~brave(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~quiet(X)<~>kind(X)))))&
((?[X]:((~curious(X)<~>brave(X))))=>((strong(john)&~funny(john))))&
((?[X]:((~strong(X)<~>~funny(X))))=>((brave(lucy)&calm(lucy))))&
(![X]:((~calm(X)<~>~patient(X))<=>~generous(X)))&
(((~funny(mary)&~curious(mary)))<=>((~humble(mary)&~tall(mary))))&
(~strong(alice))&
(?[X]:((creative(X)<~>~calm(X))))&
(?[X]:(kind(X)))&
(?[X]:(quiet(X)))&
(wise(paul))&
((strong(lucy)&~kind(lucy))) | ~creative(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 764543139076325255710563
% SZS output start Proof for 764543139076325255710563
9. ! [X0] : ((~brave(X0) | brave(X0)) => creative(X0)) [input p8]
23. ~creative(mary) [input hypothesis]
30. ! [X0] : (creative(X0) | (brave(X0) & ~brave(X0))) [ennf transformation 9]
99. creative(X0) | ~brave(X0) [cnf transformation 30]
100. creative(X0) | brave(X0) [cnf transformation 30]
135. ~creative(mary) [cnf transformation 23]
160. creative(X0) [subsumption resolution 99,100]
253. $false [subsumption resolution 135,160]
% SZS output end Proof for 764543139076325255710563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not strong is generous or not old and vice versa. Everyone who is either not kind or not humble is not kind. If mary is both rich and funny then someone is not quiet or funny. If someone is kind then someone is both not wise and happy. If someone is either wise or happy then john is both quiet and not humble. Everyone who is both not humble and strong is not curious. Everyone who is not tall is both rich and quiet and vice versa. Everyone who is kind is either quiet or not rich and vice versa. If someone is both not generous and not wise then someone is either not kind or not quiet and vice versa. If someone is both not patient and not tall then alice is both quiet and not brave and vice versa. Everyone who is either not kind or happy is not quiet and vice versa. If lucy is either not humble or not funny then someone is strong and vice versa. If john is both not tall and not generous then someone is strong or not rich. 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. Mary is both wise and strong. | Lucy is not kind. | entailment | (![X]:((~curious(X)&~strong(X))<=>(generous(X)|~old(X))))&
(![X]:((~kind(X)<~>~humble(X))=>~kind(X)))&
(((rich(mary)&funny(mary)))=>(?[X]:((~quiet(X)|funny(X)))))&
((?[X]:(kind(X)))=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:((wise(X)<~>happy(X))))=>((quiet(john)&~humble(john))))&
(![X]:((~humble(X)&strong(X))=>~curious(X)))&
(![X]:(~tall(X)<=>(rich(X)&quiet(X))))&
(![X]:(kind(X)<=>(quiet(X)<~>~rich(X))))&
((?[X]:((~generous(X)&~wise(X))))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((?[X]:((~patient(X)&~tall(X))))<=>((quiet(alice)&~brave(alice))))&
(![X]:((~kind(X)<~>happy(X))<=>~quiet(X)))&
(((~humble(lucy)<~>~funny(lucy)))<=>(?[X]:(strong(X))))&
(((~tall(john)&~generous(john)))=>(?[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)))&
((wise(mary)&strong(mary))) | ~kind(lucy) | [
"p1",
"p11",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5114730494570766126517206
% SZS output start Proof for 5114730494570766126517206
2. ! [X0] : ((~kind(X0) <~> ~humble(X0)) => ~kind(X0)) [input p1]
12. (~humble(lucy) <~> ~funny(lucy)) <=> ? [X0] : strong(X0) [input p11]
19. funny(lucy) [input p18]
22. strong(mary) & wise(mary) [input p21]
23. kind(lucy) [input hypothesis]
29. ! [X0] : (~kind(X0) | (~kind(X0) <=> ~humble(X0))) [ennf transformation 2]
40. ! [X0] : (~kind(X0) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) [nnf transformation 29]
61. (((funny(lucy) | humble(lucy)) & (~funny(lucy) | ~humble(lucy))) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | ((~humble(lucy) | funny(lucy)) & (~funny(lucy) | humble(lucy)))) [nnf transformation 12]
62. (((funny(lucy) | humble(lucy)) & (~funny(lucy) | ~humble(lucy))) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | ((~humble(lucy) | funny(lucy)) & (~funny(lucy) | humble(lucy)))) [rectify 61]
63. ? [X1] : strong(X1) => strong(sK5) [choice axiom]
64. (((funny(lucy) | humble(lucy)) & (~funny(lucy) | ~humble(lucy))) | ! [X0] : ~strong(X0)) & (strong(sK5) | ((~humble(lucy) | funny(lucy)) & (~funny(lucy) | humble(lucy)))) [skolemisation 62,63]
82. ~kind(X0) | ~kind(X0) | humble(X0) [cnf transformation 40]
114. ~funny(lucy) | ~humble(lucy) | ~strong(X0) [cnf transformation 64]
125. funny(lucy) [cnf transformation 19]
129. strong(mary) [cnf transformation 22]
130. kind(lucy) [cnf transformation 23]
131. ~kind(X0) | humble(X0) [duplicate literal removal 82]
235. 24 <=> ! [X0] : ~strong(X0) [avatar definition]
236. ~strong(X0) <- (24) [avatar component clause 235]
238. 25 <=> humble(lucy) [avatar definition]
239. ~humble(lucy) <- (~25) [avatar component clause 238]
242. 26 <=> funny(lucy) [avatar definition]
246. 24 | ~25 | ~26 [avatar split clause 114,242,238,235]
289. 26 [avatar split clause 125,242]
302. $false <- (24) [resolution 236,129]
303. ~24 [avatar contradiction clause 302]
317. humble(lucy) [resolution 131,130]
318. $false <- (~25) [subsumption resolution 317,239]
319. 25 [avatar contradiction clause 318]
320. $false [avatar sat refutation 246,289,303,319]
% SZS output end Proof for 5114730494570766126517206
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not curious then someone is either tall or not generous and vice versa. If john is brave then someone is either brave or not tall and vice versa. If someone is either patient or not humble then someone is humble or brave. If someone is either old or curious then someone is calm. Everyone who is happy is generous and vice versa. Everyone who is either not curious or patient is not old or rich and vice versa. If someone is generous then someone is both old and not strong. If someone is not quiet then lucy is either not old or not brave and vice versa. Everyone who is curious is not strong and vice versa. If mary is both curious and not calm then someone is not tall and vice versa. Everyone who is both rich and not funny is either tall or not brave and vice versa. Everyone who is not old or not tall is both generous and rich and vice versa. Everyone who is curious or not old is either not kind or not patient and vice versa. If someone is not generous or kind then susan is both curious and strong. If someone is both not old and wise then john is not calm or not curious and vice versa. If mary is both generous and not creative then someone is either not rich or not patient. Someone is either humble or not strong. Someone is curious or not quiet. Someone is both not tall and not quiet. Someone is both not calm and patient. Someone is not wise or creative. John is not brave. | Lucy is brave. | entailment | ((?[X]:((curious(X)|~curious(X))))<=>(?[X]:((tall(X)<~>~generous(X)))))&
((brave(john))<=>(?[X]:((brave(X)<~>~tall(X)))))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((humble(X)|brave(X)))))&
((?[X]:((old(X)<~>curious(X))))=>(?[X]:(calm(X))))&
(![X]:(happy(X)<=>generous(X)))&
(![X]:((~curious(X)<~>patient(X))<=>(~old(X)|rich(X))))&
((?[X]:(generous(X)))=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:(~quiet(X)))<=>((~old(lucy)<~>~brave(lucy))))&
(![X]:(curious(X)<=>~strong(X)))&
(((curious(mary)&~calm(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((rich(X)&~funny(X))<=>(tall(X)<~>~brave(X))))&
(![X]:((~old(X)|~tall(X))<=>(generous(X)&rich(X))))&
(![X]:((curious(X)|~old(X))<=>(~kind(X)<~>~patient(X))))&
((?[X]:((~generous(X)|kind(X))))=>((curious(susan)&strong(susan))))&
((?[X]:((~old(X)&wise(X))))<=>((~calm(john)|~curious(john))))&
(((generous(mary)&~creative(mary)))=>(?[X]:((~rich(X)<~>~patient(X)))))&
(?[X]:((humble(X)<~>~strong(X))))&
(?[X]:((curious(X)|~quiet(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
(?[X]:((~calm(X)&patient(X))))&
(?[X]:((~wise(X)|creative(X))))&
(~brave(john)) | brave(lucy) | [
"p1",
"p5",
"p7",
"p8",
"p11",
"p12",
"p13",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6161533309775369798450764
% SZS output start Proof for 6161533309775369798450764
2. brave(john) <=> ? [X0] : (brave(X0) <~> ~tall(X0)) [input p1]
6. ! [X0] : ((~curious(X0) <~> patient(X0)) <=> (rich(X0) | ~old(X0))) [input p5]
8. ? [X0] : ~quiet(X0) <=> (~old(lucy) <~> ~brave(lucy)) [input p7]
9. ! [X0] : (curious(X0) <=> ~strong(X0)) [input p8]
12. ! [X0] : ((~tall(X0) | ~old(X0)) <=> (rich(X0) & generous(X0))) [input p11]
13. ! [X0] : ((~old(X0) | curious(X0)) <=> (~kind(X0) <~> ~patient(X0))) [input p12]
14. ? [X0] : (kind(X0) | ~generous(X0)) => (strong(susan) & curious(susan)) [input p13]
19. ? [X0] : (~quiet(X0) & ~tall(X0)) [input p18]
22. ~brave(john) [input p21]
23. ~brave(lucy) [input hypothesis]
33. (strong(susan) & curious(susan)) | ! [X0] : (~kind(X0) & generous(X0)) [ennf transformation 14]
39. (brave(john) | ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (? [X0] : ((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | ~brave(john)) [nnf transformation 2]
40. (brave(john) | ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (? [X1] : ((tall(X1) | ~brave(X1)) & (~tall(X1) | brave(X1))) | ~brave(john)) [rectify 39]
41. ? [X1] : ((tall(X1) | ~brave(X1)) & (~tall(X1) | brave(X1))) => ((tall(sK2) | ~brave(sK2)) & (~tall(sK2) | brave(sK2))) [choice axiom]
42. (brave(john) | ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (((tall(sK2) | ~brave(sK2)) & (~tall(sK2) | brave(sK2))) | ~brave(john)) [skolemisation 40,41]
51. ! [X0] : ((((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))))) [nnf transformation 6]
52. ! [X0] : ((((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))))) [flattening 51]
56. (? [X0] : ~quiet(X0) | ((~old(lucy) | brave(lucy)) & (~brave(lucy) | old(lucy)))) & (((brave(lucy) | old(lucy)) & (~brave(lucy) | ~old(lucy))) | ! [X0] : quiet(X0)) [nnf transformation 8]
57. (? [X0] : ~quiet(X0) | ((~old(lucy) | brave(lucy)) & (~brave(lucy) | old(lucy)))) & (((brave(lucy) | old(lucy)) & (~brave(lucy) | ~old(lucy))) | ! [X1] : quiet(X1)) [rectify 56]
58. ? [X0] : ~quiet(X0) => ~quiet(sK6) [choice axiom]
59. (~quiet(sK6) | ((~old(lucy) | brave(lucy)) & (~brave(lucy) | old(lucy)))) & (((brave(lucy) | old(lucy)) & (~brave(lucy) | ~old(lucy))) | ! [X1] : quiet(X1)) [skolemisation 57,58]
60. ! [X0] : ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0))) [nnf transformation 9]
68. ! [X0] : (((~tall(X0) | ~old(X0)) | (~rich(X0) | ~generous(X0))) & ((rich(X0) & generous(X0)) | (tall(X0) & old(X0)))) [nnf transformation 12]
69. ! [X0] : ((~tall(X0) | ~old(X0) | ~rich(X0) | ~generous(X0)) & ((rich(X0) & generous(X0)) | (tall(X0) & old(X0)))) [flattening 68]
70. ! [X0] : (((~old(X0) | curious(X0)) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (old(X0) & ~curious(X0)))) [nnf transformation 13]
71. ! [X0] : ((~old(X0) | curious(X0) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (old(X0) & ~curious(X0)))) [flattening 70]
82. ? [X0] : (~quiet(X0) & ~tall(X0)) => (~quiet(sK11) & ~tall(sK11)) [choice axiom]
83. ~quiet(sK11) & ~tall(sK11) [skolemisation 19,82]
95. brave(john) | brave(X0) | tall(X0) [cnf transformation 42]
100. ~old(X0) | rich(X0) | patient(X0) | curious(X0) [cnf transformation 52]
101. ~old(X0) | rich(X0) | ~curious(X0) | ~patient(X0) [cnf transformation 52]
104. ~patient(X0) | curious(X0) | old(X0) [cnf transformation 52]
109. brave(lucy) | old(lucy) | quiet(X1) [cnf transformation 59]
112. ~strong(X0) | ~curious(X0) [cnf transformation 60]
127. ~rich(X0) | ~old(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 69]
130. ~curious(X0) | kind(X0) | patient(X0) [cnf transformation 71]
132. ~old(X0) | curious(X0) | ~patient(X0) | kind(X0) [cnf transformation 71]
134. curious(susan) | generous(X0) [cnf transformation 33]
135. curious(susan) | ~kind(X0) [cnf transformation 33]
136. strong(susan) | generous(X0) [cnf transformation 33]
137. strong(susan) | ~kind(X0) [cnf transformation 33]
147. ~quiet(sK11) [cnf transformation 83]
150. ~brave(john) [cnf transformation 22]
151. ~brave(lucy) [cnf transformation 23]
171. 5 <=> ! [X0] : (brave(X0) | tall(X0)) [avatar definition]
172. brave(X0) | tall(X0) <- (5) [avatar component clause 171]
174. 6 <=> brave(john) [avatar definition]
177. 5 | 6 [avatar split clause 95,174,171]
234. 20 <=> brave(lucy) [avatar definition]
235. ~brave(lucy) <- (~20) [avatar component clause 234]
238. 21 <=> old(lucy) [avatar definition]
239. old(lucy) <- (21) [avatar component clause 238]
248. 23 <=> ! [X1] : quiet(X1) [avatar definition]
249. quiet(X1) <- (23) [avatar component clause 248]
250. 23 | 21 | 20 [avatar split clause 109,234,238,248]
270. ~patient(X0) | curious(X0) | kind(X0) [subsumption resolution 132,104]
272. 28 <=> ! [X0] : ~kind(X0) [avatar definition]
273. ~kind(X0) <- (28) [avatar component clause 272]
275. 29 <=> strong(susan) [avatar definition]
277. strong(susan) <- (29) [avatar component clause 275]
278. 28 | 29 [avatar split clause 137,275,272]
280. 30 <=> ! [X0] : generous(X0) [avatar definition]
281. generous(X0) <- (30) [avatar component clause 280]
282. 30 | 29 [avatar split clause 136,275,280]
284. 31 <=> curious(susan) [avatar definition]
287. 28 | 31 [avatar split clause 135,284,272]
288. 30 | 31 [avatar split clause 134,284,280]
332. ~6 [avatar split clause 150,174]
333. ~20 [avatar split clause 151,234]
341. ~curious(susan) <- (29) [resolution 112,277]
344. ~31 | ~29 [avatar split clause 341,275,284]
355. tall(lucy) <- (5, ~20) [resolution 172,235]
454. $false <- (23) [resolution 249,147]
459. ~23 [avatar contradiction clause 454]
483. rich(lucy) | ~curious(lucy) | ~patient(lucy) <- (21) [resolution 239,101]
484. rich(lucy) | patient(lucy) | curious(lucy) <- (21) [resolution 239,100]
486. 47 <=> patient(lucy) [avatar definition]
487. patient(lucy) <- (47) [avatar component clause 486]
490. 48 <=> curious(lucy) [avatar definition]
491. curious(lucy) <- (48) [avatar component clause 490]
494. 49 <=> rich(lucy) [avatar definition]
496. rich(lucy) <- (49) [avatar component clause 494]
497. ~47 | ~48 | 49 | ~21 [avatar split clause 483,238,494,490,486]
498. 48 | 47 | 49 | ~21 [avatar split clause 484,238,494,486,490]
528. kind(lucy) | patient(lucy) <- (48) [resolution 491,130]
530. patient(lucy) <- (28, 48) [subsumption resolution 528,273]
533. 47 | ~28 | ~48 [avatar split clause 530,490,272,486]
534. curious(lucy) | kind(lucy) <- (47) [resolution 487,270]
536. ~old(lucy) | ~tall(lucy) | ~generous(lucy) <- (49) [resolution 496,127]
541. ~tall(lucy) | ~generous(lucy) <- (21, 49) [subsumption resolution 536,239]
542. ~generous(lucy) <- (5, ~20, 21, 49) [subsumption resolution 541,355]
543. $false <- (5, ~20, 21, 30, 49) [subsumption resolution 542,281]
544. ~5 | 20 | ~21 | ~30 | ~49 [avatar contradiction clause 543]
547. curious(lucy) <- (28, 47) [subsumption resolution 534,273]
548. 48 | ~28 | ~47 [avatar split clause 547,486,272,490]
549. $false [avatar sat refutation 177,250,278,282,287,288,332,333,344,459,497,498,533,544,548]
% SZS output end Proof for 6161533309775369798450764
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is wise or quiet.
Everyone who is either not curious or rich is rich.
If john is both not curious and not humble then lucy is either not wise or old.
If susan is either not kind or not generous then susan is both tall and not kind.
Everyone who is either not rich or not curious is both strong and not calm.
Everyone who is patient or not old is generous or curious.
Everyone who is either wise or not generous is strong.
Everyone who is either wise or not curious is not patient.
Everyone who is not happy or not rich is not creative.
If lucy is not generous or calm then paul is not old or not calm and vice versa.
Everyone who is both curious and not quiet is both not calm and happy.
If john is both not tall and not strong then fred is both not humble and not old and vice versa.
If mary is either old or not calm then susan is not creative or brave and vice versa.
If lucy is either not quiet or funny then susan is either not kind or creative.
Everyone who is creative or calm is not old and vice versa.
If someone is not rich or patient then someone is funny.
Fred is both rich and strong.
Susan is both funny and not rich.
Someone is either not kind or quiet.
Someone is either generous or not rich.
Fred is patient.
Fred is quiet or not kind. | Mary is old. | contradiction | (![X]:(tall(X)=>(wise(X)|quiet(X))))&
(![X]:((~curious(X)<~>rich(X))=>rich(X)))&
(((~curious(john)&~humble(john)))=>((~wise(lucy)<~>old(lucy))))&
(((~kind(susan)<~>~generous(susan)))=>((tall(susan)&~kind(susan))))&
(![X]:((~rich(X)<~>~curious(X))=>(strong(X)&~calm(X))))&
(![X]:((patient(X)|~old(X))=>(generous(X)|curious(X))))&
(![X]:((wise(X)<~>~generous(X))=>strong(X)))&
(![X]:((wise(X)<~>~curious(X))=>~patient(X)))&
(![X]:((~happy(X)|~rich(X))=>~creative(X)))&
(((~generous(lucy)|calm(lucy)))<=>((~old(paul)|~calm(paul))))&
(![X]:((curious(X)&~quiet(X))=>(~calm(X)&happy(X))))&
(((~tall(john)&~strong(john)))<=>((~humble(fred)&~old(fred))))&
(((old(mary)<~>~calm(mary)))<=>((~creative(susan)|brave(susan))))&
(((~quiet(lucy)<~>funny(lucy)))=>((~kind(susan)<~>creative(susan))))&
(![X]:((creative(X)|calm(X))<=>~old(X)))&
((?[X]:((~rich(X)|patient(X))))=>(?[X]:(funny(X))))&
((rich(fred)&strong(fred)))&
((funny(susan)&~rich(susan)))&
(?[X]:((~kind(X)<~>quiet(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
(patient(fred))&
((quiet(fred)|~kind(fred))) | old(mary) | [
"p8",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 853104503267766711957182
% SZS output start Proof for 853104503267766711957182
9. ! [X0] : ((~rich(X0) | ~happy(X0)) => ~creative(X0)) [input p8]
13. (old(mary) <~> ~calm(mary)) <=> (brave(susan) | ~creative(susan)) [input p12]
15. ! [X0] : ((calm(X0) | creative(X0)) <=> ~old(X0)) [input p14]
18. ~rich(susan) & funny(susan) [input p17]
23. old(mary) [input hypothesis]
26. ! [X0] : (~rich(X0) => ~creative(X0)) [pure predicate removal 9]
38. ! [X0] : (~creative(X0) | rich(X0)) [ennf transformation 26]
53. (((calm(mary) | ~old(mary)) & (~calm(mary) | old(mary))) | (~brave(susan) & creative(susan))) & ((brave(susan) | ~creative(susan)) | ((old(mary) | calm(mary)) & (~calm(mary) | ~old(mary)))) [nnf transformation 13]
54. (((calm(mary) | ~old(mary)) & (~calm(mary) | old(mary))) | (~brave(susan) & creative(susan))) & (brave(susan) | ~creative(susan) | ((old(mary) | calm(mary)) & (~calm(mary) | ~old(mary)))) [flattening 53]
56. ! [X0] : (((calm(X0) | creative(X0)) | old(X0)) & (~old(X0) | (~calm(X0) & ~creative(X0)))) [nnf transformation 15]
57. ! [X0] : ((calm(X0) | creative(X0) | old(X0)) & (~old(X0) | (~calm(X0) & ~creative(X0)))) [flattening 56]
86. ~creative(X0) | rich(X0) [cnf transformation 38]
100. calm(mary) | ~old(mary) | creative(susan) [cnf transformation 54]
107. ~calm(X0) | ~old(X0) [cnf transformation 57]
114. ~rich(susan) [cnf transformation 18]
121. old(mary) [cnf transformation 23]
207. 17 <=> old(mary) [avatar definition]
208. old(mary) <- (17) [avatar component clause 207]
211. 18 <=> calm(mary) [avatar definition]
213. calm(mary) <- (18) [avatar component clause 211]
216. 19 <=> creative(susan) [avatar definition]
218. creative(susan) <- (19) [avatar component clause 216]
219. 19 | ~17 | 18 [avatar split clause 100,211,207,216]
277. 17 [avatar split clause 121,207]
278. ~old(mary) <- (18) [resolution 107,213]
279. $false <- (17, 18) [subsumption resolution 278,208]
280. ~17 | ~18 [avatar contradiction clause 279]
282. rich(susan) <- (19) [resolution 218,86]
283. $false <- (19) [subsumption resolution 282,114]
284. ~19 [avatar contradiction clause 283]
285. $false [avatar sat refutation 219,277,280,284]
% SZS output end Proof for 853104503267766711957182
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is either patient or not curious and vice versa.
If someone is both not wise and not strong then someone is quiet and vice versa.
Everyone who is either calm or strong is both rich and not kind.
If paul is both not patient and not old then someone is not tall.
Everyone who is both not strong and not curious is both generous and quiet.
Everyone who is not strong is both old and not quiet.
If susan is wise then someone is both kind and not creative and vice versa.
Everyone who is calm is happy or not quiet and vice versa.
Everyone who is both humble and not wise is either not generous or humble.
Everyone who is not rich or patient is not wise.
If john is not generous then alice is both not happy and creative.
Everyone who is not kind is either strong or not happy and vice versa.
If someone is either old or not quiet then lucy is not wise or strong and vice versa.
Everyone who is patient or happy is either happy or rich and vice versa.
If someone is kind then susan is quiet or calm.
Everyone who is both patient and not creative is curious or old and vice versa.
Alice is tall.
Susan is not quiet or wise.
Someone is not kind.
Someone is both funny and not quiet.
Lucy is either calm or kind.
Someone is not old or generous.
Fred is both not old and kind.
Susan is not rich or not strong. | Fred is not calm. | contradiction | (![X]:(~funny(X)<=>(patient(X)<~>~curious(X))))&
((?[X]:((~wise(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
(![X]:((calm(X)<~>strong(X))=>(rich(X)&~kind(X))))&
(((~patient(paul)&~old(paul)))=>(?[X]:(~tall(X))))&
(![X]:((~strong(X)&~curious(X))=>(generous(X)&quiet(X))))&
(![X]:(~strong(X)=>(old(X)&~quiet(X))))&
((wise(susan))<=>(?[X]:((kind(X)&~creative(X)))))&
(![X]:(calm(X)<=>(happy(X)|~quiet(X))))&
(![X]:((humble(X)&~wise(X))=>(~generous(X)<~>humble(X))))&
(![X]:((~rich(X)|patient(X))=>~wise(X)))&
((~generous(john))=>((~happy(alice)&creative(alice))))&
(![X]:(~kind(X)<=>(strong(X)<~>~happy(X))))&
((?[X]:((old(X)<~>~quiet(X))))<=>((~wise(lucy)|strong(lucy))))&
(![X]:((patient(X)|happy(X))<=>(happy(X)<~>rich(X))))&
((?[X]:(kind(X)))=>((quiet(susan)|calm(susan))))&
(![X]:((patient(X)&~creative(X))<=>(curious(X)|old(X))))&
(tall(alice))&
((~quiet(susan)|wise(susan)))&
(?[X]:(~kind(X)))&
(?[X]:((funny(X)&~quiet(X))))&
((calm(lucy)<~>kind(lucy)))&
(?[X]:((~old(X)|generous(X))))&
((~old(fred)&kind(fred)))&
((~rich(susan)|~strong(susan))) | ~calm(fred) | [
"p2",
"p5",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 777797176399350781013592
% SZS output start Proof for 777797176399350781013592
3. ! [X0] : ((calm(X0) <~> strong(X0)) => (~kind(X0) & rich(X0))) [input p2]
6. ! [X0] : (~strong(X0) => (~quiet(X0) & old(X0))) [input p5]
23. kind(fred) & ~old(fred) [input p22]
25. ~calm(fred) [input hypothesis]
29. ! [X0] : ((~kind(X0) & rich(X0)) | (calm(X0) <=> strong(X0))) [ennf transformation 3]
34. ! [X0] : ((~quiet(X0) & old(X0)) | strong(X0)) [ennf transformation 6]
47. ! [X0] : ((~kind(X0) & rich(X0)) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) [nnf transformation 29]
82. ~kind(X0) | calm(X0) | ~strong(X0) [cnf transformation 47]
86. old(X0) | strong(X0) [cnf transformation 34]
130. ~old(fred) [cnf transformation 23]
131. kind(fred) [cnf transformation 23]
133. ~calm(fred) [cnf transformation 25]
264. strong(fred) [resolution 86,130]
334. calm(fred) | ~strong(fred) [resolution 82,131]
335. ~strong(fred) [subsumption resolution 334,133]
336. $false [subsumption resolution 335,264]
% SZS output end Proof for 777797176399350781013592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both not tall and not old then paul is not tall and vice versa. Everyone who is either not creative or wise is not old. Everyone who is either not brave or not creative is happy and vice versa. If someone is either not calm or tall then someone is either kind or not tall. Everyone who is funny is not rich or rich and vice versa. Everyone who is either curious or patient is not creative and vice versa. Everyone who is not kind is either humble or not humble. Everyone who is brave or calm is either not generous or brave. If susan is quiet or strong then paul is rich and vice versa. Everyone who is both not wise and not old is generous and vice versa. If fred is both patient and not brave then john is happy or kind and vice versa. Everyone who is either not generous or not kind is either not quiet or curious and vice versa. Everyone who is either not happy or old is happy. Everyone who is not happy is both kind and not tall. Everyone who is either not tall or patient is either not curious or not patient. Everyone who is not generous or curious is funny and vice versa. Lucy is not strong or not curious. Paul is not curious or not strong. Someone is humble or kind. Someone is not kind. Lucy is either not rich or funny. Someone is not tall or humble. John is not rich or not funny. | Susan is calm. | neutral | ((?[X]:((~tall(X)&~old(X))))<=>(~tall(paul)))&
(![X]:((~creative(X)<~>wise(X))=>~old(X)))&
(![X]:((~brave(X)<~>~creative(X))<=>happy(X)))&
((?[X]:((~calm(X)<~>tall(X))))=>(?[X]:((kind(X)<~>~tall(X)))))&
(![X]:(funny(X)<=>(~rich(X)|rich(X))))&
(![X]:((curious(X)<~>patient(X))<=>~creative(X)))&
(![X]:(~kind(X)=>(humble(X)<~>~humble(X))))&
(![X]:((brave(X)|calm(X))=>(~generous(X)<~>brave(X))))&
(((quiet(susan)|strong(susan)))<=>(rich(paul)))&
(![X]:((~wise(X)&~old(X))<=>generous(X)))&
(((patient(fred)&~brave(fred)))<=>((happy(john)|kind(john))))&
(![X]:((~generous(X)<~>~kind(X))<=>(~quiet(X)<~>curious(X))))&
(![X]:((~happy(X)<~>old(X))=>happy(X)))&
(![X]:(~happy(X)=>(kind(X)&~tall(X))))&
(![X]:((~tall(X)<~>patient(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((~generous(X)|curious(X))<=>funny(X)))&
((~strong(lucy)|~curious(lucy)))&
((~curious(paul)|~strong(paul)))&
(?[X]:((humble(X)|kind(X))))&
(?[X]:(~kind(X)))&
((~rich(lucy)<~>funny(lucy)))&
(?[X]:((~tall(X)|humble(X))))&
((~rich(john)|~funny(john))) | calm(susan) | [] | null | 0 |
Everyone who is brave is both old and tall and vice versa.
If susan is kind then alice is either kind or not generous and vice versa.
If susan is both humble and not patient then paul is not wise or calm.
If fred is not strong or not quiet then someone is both not old and not funny and vice versa.
If someone is either strong or humble then alice is not strong.
Everyone who is either kind or creative is both tall and funny and vice versa.
Everyone who is either curious or not calm is not brave.
If fred is kind or not creative then someone is kind or brave.
Everyone who is old is brave and vice versa.
Everyone who is not old or not curious is either not creative or not brave.
If someone is both not patient and not humble then mary is both happy and not quiet.
If someone is not humble then paul is both not patient and not creative and vice versa.
If someone is either not tall or generous then mary is both not brave and not happy and vice versa.
If someone is creative or not quiet then someone is both strong and not strong.
If mary is calm or not happy then paul is both not tall and old.
If mary is either not strong or kind then someone is either not quiet or not happy and vice versa.
Mary is brave.
Someone is either not curious or generous.
Someone is not brave or brave.
Alice is calm.
Susan is both not curious and strong.
Someone is either not calm or strong.
Fred is old.
Someone is not creative. | Alice is not quiet. | contradiction | (![X]:(brave(X)<=>(old(X)&tall(X))))&
((kind(susan))<=>((kind(alice)<~>~generous(alice))))&
(((humble(susan)&~patient(susan)))=>((~wise(paul)|calm(paul))))&
(((~strong(fred)|~quiet(fred)))<=>(?[X]:((~old(X)&~funny(X)))))&
((?[X]:((strong(X)<~>humble(X))))=>(~strong(alice)))&
(![X]:((kind(X)<~>creative(X))<=>(tall(X)&funny(X))))&
(![X]:((curious(X)<~>~calm(X))=>~brave(X)))&
(((kind(fred)|~creative(fred)))=>(?[X]:((kind(X)|brave(X)))))&
(![X]:(old(X)<=>brave(X)))&
(![X]:((~old(X)|~curious(X))=>(~creative(X)<~>~brave(X))))&
((?[X]:((~patient(X)&~humble(X))))=>((happy(mary)&~quiet(mary))))&
((?[X]:(~humble(X)))<=>((~patient(paul)&~creative(paul))))&
((?[X]:((~tall(X)<~>generous(X))))<=>((~brave(mary)&~happy(mary))))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(((calm(mary)|~happy(mary)))=>((~tall(paul)&old(paul))))&
(((~strong(mary)<~>kind(mary)))<=>(?[X]:((~quiet(X)<~>~happy(X)))))&
(brave(mary))&
(?[X]:((~curious(X)<~>generous(X))))&
(?[X]:((~brave(X)|brave(X))))&
(calm(alice))&
((~curious(susan)&strong(susan)))&
(?[X]:((~calm(X)<~>strong(X))))&
(old(fred))&
(?[X]:(~creative(X))) | ~quiet(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4547133934824701726964717
% SZS output start Proof for 4547133934824701726964717
14. ? [X0] : (~quiet(X0) | creative(X0)) => ? [X0] : (~strong(X0) & strong(X0)) [input p13]
25. ~quiet(alice) [input hypothesis]
26. ? [X0] : (~quiet(X0) | creative(X0)) => ? [X1] : (~strong(X1) & strong(X1)) [rectify 14]
33. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : (quiet(X0) & ~creative(X0)) [ennf transformation 26]
61. ? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : (quiet(X1) & ~creative(X1)) [rectify 33]
62. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK4) & strong(sK4)) [choice axiom]
63. (~strong(sK4) & strong(sK4)) | ! [X1] : (quiet(X1) & ~creative(X1)) [skolemisation 61,62]
120. strong(sK4) | quiet(X1) [cnf transformation 63]
122. ~strong(sK4) | quiet(X1) [cnf transformation 63]
146. ~quiet(alice) [cnf transformation 25]
274. 28 <=> ! [X1] : quiet(X1) [avatar definition]
275. quiet(X1) <- (28) [avatar component clause 274]
277. 29 <=> strong(sK4) [avatar definition]
280. 28 | ~29 [avatar split clause 122,277,274]
285. 28 | 29 [avatar split clause 120,277,274]
358. $false <- (28) [resolution 275,146]
359. ~28 [avatar contradiction clause 358]
360. $false [avatar sat refutation 280,285,359]
% SZS output end Proof for 4547133934824701726964717
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not curious then someone is strong.
Everyone who is either curious or not patient is both not old and not strong and vice versa.
If lucy is not happy then someone is wise.
If someone is calm or not quiet then someone is both strong and quiet.
If someone is either patient or kind then john is either not funny or happy and vice versa.
Everyone who is old is both not quiet and kind and vice versa.
If someone is not brave or patient then mary is kind or not humble.
If mary is curious or patient then someone is either humble or not humble.
Everyone who is not curious or quiet is not curious or funny and vice versa.
Everyone who is brave is not wise or not quiet.
Everyone who is happy or not calm is generous or not brave.
Everyone who is not creative or not kind is not humble and vice versa.
If someone is either generous or calm then someone is either not old or not wise.
If someone is both patient and not tall then someone is not humble and vice versa.
Everyone who is both curious and quiet is not kind.
If someone is not tall then susan is curious.
John is tall or not calm.
Someone is not wise.
Someone is creative or not calm.
Someone is either not brave or not patient.
Someone is both not creative and not wise.
Susan is either not humble or generous.
Someone is not generous or not curious.
Someone is either old or not old. | Mary is humble. | neutral | ((?[X]:((humble(X)&~curious(X))))=>(?[X]:(strong(X))))&
(![X]:((curious(X)<~>~patient(X))<=>(~old(X)&~strong(X))))&
((~happy(lucy))=>(?[X]:(wise(X))))&
((?[X]:((calm(X)|~quiet(X))))=>(?[X]:((strong(X)&quiet(X)))))&
((?[X]:((patient(X)<~>kind(X))))<=>((~funny(john)<~>happy(john))))&
(![X]:(old(X)<=>(~quiet(X)&kind(X))))&
((?[X]:((~brave(X)|patient(X))))=>((kind(mary)|~humble(mary))))&
(((curious(mary)|patient(mary)))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~curious(X)|quiet(X))<=>(~curious(X)|funny(X))))&
(![X]:(brave(X)=>(~wise(X)|~quiet(X))))&
(![X]:((happy(X)|~calm(X))=>(generous(X)|~brave(X))))&
(![X]:((~creative(X)|~kind(X))<=>~humble(X)))&
((?[X]:((generous(X)<~>calm(X))))=>(?[X]:((~old(X)<~>~wise(X)))))&
((?[X]:((patient(X)&~tall(X))))<=>(?[X]:(~humble(X))))&
(![X]:((curious(X)&quiet(X))=>~kind(X)))&
((?[X]:(~tall(X)))=>(curious(susan)))&
((tall(john)|~calm(john)))&
(?[X]:(~wise(X)))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((~brave(X)<~>~patient(X))))&
(?[X]:((~creative(X)&~wise(X))))&
((~humble(susan)<~>generous(susan)))&
(?[X]:((~generous(X)|~curious(X))))&
(?[X]:((old(X)<~>~old(X)))) | humble(mary) | [] | null | 0 |
Everyone who is either not rich or old is not tall or funny and vice versa. If alice is both wise and patient then someone is both not creative and not calm. If mary is brave or not tall then susan is calm or not patient. If paul is both wise and funny then alice is not creative or not rich. Everyone who is strong is both not humble and not strong and vice versa. If alice is kind or curious then alice is not old and vice versa. If susan is either not brave or creative then someone is either wise or generous and vice versa. Everyone who is both kind and quiet is happy or not tall and vice versa. Everyone who is quiet is not brave. Everyone who is either not calm or not rich is either not tall or not quiet and vice versa. If mary is not kind then someone is funny or not humble. If someone is either old or not curious then susan is either not patient or not brave. Everyone who is old or not calm is both strong and old and vice versa. If john is kind then someone is both old and quiet and vice versa. If someone is not strong then someone is both not patient and not curious. If someone is not brave then paul is either tall or not brave and vice versa. Paul is either not funny or not old. Someone is either not generous or not calm. John is strong or not funny. Lucy is not quiet or not creative. Mary is both not curious and patient. Alice is patient or tall. | Lucy is humble. | entailment | (![X]:((~rich(X)<~>old(X))<=>(~tall(X)|funny(X))))&
(((wise(alice)&patient(alice)))=>(?[X]:((~creative(X)&~calm(X)))))&
(((brave(mary)|~tall(mary)))=>((calm(susan)|~patient(susan))))&
(((wise(paul)&funny(paul)))=>((~creative(alice)|~rich(alice))))&
(![X]:(strong(X)<=>(~humble(X)&~strong(X))))&
(((kind(alice)|curious(alice)))<=>(~old(alice)))&
(((~brave(susan)<~>creative(susan)))<=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((kind(X)&quiet(X))<=>(happy(X)|~tall(X))))&
(![X]:(quiet(X)=>~brave(X)))&
(![X]:((~calm(X)<~>~rich(X))<=>(~tall(X)<~>~quiet(X))))&
((~kind(mary))=>(?[X]:((funny(X)|~humble(X)))))&
((?[X]:((old(X)<~>~curious(X))))=>((~patient(susan)<~>~brave(susan))))&
(![X]:((old(X)|~calm(X))<=>(strong(X)&old(X))))&
((kind(john))<=>(?[X]:((old(X)&quiet(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((~patient(X)&~curious(X)))))&
((?[X]:(~brave(X)))<=>((tall(paul)<~>~brave(paul))))&
((~funny(paul)<~>~old(paul)))&
(?[X]:((~generous(X)<~>~calm(X))))&
((strong(john)|~funny(john)))&
((~quiet(lucy)|~creative(lucy)))&
((~curious(mary)&patient(mary)))&
((patient(alice)|tall(alice))) | humble(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1289651475978398894858668
% SZS output start Proof for 1289651475978398894858668
5. ! [X0] : (strong(X0) <=> (~strong(X0) & ~humble(X0))) [input p4]
23. ~humble(lucy) [input hypothesis]
39. ! [X0] : ((strong(X0) | (strong(X0) | humble(X0))) & ((~strong(X0) & ~humble(X0)) | ~strong(X0))) [nnf transformation 5]
40. ! [X0] : ((strong(X0) | strong(X0) | humble(X0)) & ((~strong(X0) & ~humble(X0)) | ~strong(X0))) [flattening 39]
82. ~strong(X0) | ~strong(X0) [cnf transformation 40]
83. strong(X0) | strong(X0) | humble(X0) [cnf transformation 40]
137. ~humble(lucy) [cnf transformation 23]
138. ~strong(X0) [duplicate literal removal 82]
139. humble(X0) | strong(X0) [duplicate literal removal 83]
321. strong(lucy) [resolution 139,137]
323. $false [subsumption resolution 321,138]
% SZS output end Proof for 1289651475978398894858668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or kind is curious or rich and vice versa.
Everyone who is wise is either not brave or kind.
If susan is patient then someone is either not brave or not quiet.
Everyone who is rich or curious is not wise.
Everyone who is not tall or not funny is either happy or not humble and vice versa.
Everyone who is both kind and strong is rich.
If john is not rich or quiet then someone is tall or generous and vice versa.
Everyone who is not kind is both quiet and generous and vice versa.
If someone is not strong then someone is quiet or patient.
Everyone who is either not tall or not happy is tall or not rich and vice versa.
Everyone who is both happy and not happy is not wise or creative.
Everyone who is either strong or humble is not kind or wise.
If lucy is both old and not patient then someone is both not old and not generous.
Everyone who is both humble and tall is not quiet.
If someone is not calm or not strong then someone is not old and vice versa.
If john is both not curious and funny then susan is patient and vice versa.
Someone is both not happy and old.
Lucy is both not strong and funny.
Paul is generous.
Mary is not old or old.
Someone is not patient or not humble.
John is funny or not strong.
Someone is both brave and patient.
John is rich or humble. | John is quiet. | entailment | (![X]:((creative(X)|kind(X))<=>(curious(X)|rich(X))))&
(![X]:(wise(X)=>(~brave(X)<~>kind(X))))&
((patient(susan))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((rich(X)|curious(X))=>~wise(X)))&
(![X]:((~tall(X)|~funny(X))<=>(happy(X)<~>~humble(X))))&
(![X]:((kind(X)&strong(X))=>rich(X)))&
(((~rich(john)|quiet(john)))<=>(?[X]:((tall(X)|generous(X)))))&
(![X]:(~kind(X)<=>(quiet(X)&generous(X))))&
((?[X]:(~strong(X)))=>(?[X]:((quiet(X)|patient(X)))))&
(![X]:((~tall(X)<~>~happy(X))<=>(tall(X)|~rich(X))))&
(![X]:((happy(X)&~happy(X))=>(~wise(X)|creative(X))))&
(![X]:((strong(X)<~>humble(X))=>(~kind(X)|wise(X))))&
(((old(lucy)&~patient(lucy)))=>(?[X]:((~old(X)&~generous(X)))))&
(![X]:((humble(X)&tall(X))=>~quiet(X)))&
((?[X]:((~calm(X)|~strong(X))))<=>(?[X]:(~old(X))))&
(((~curious(john)&funny(john)))<=>(patient(susan)))&
(?[X]:((~happy(X)&old(X))))&
((~strong(lucy)&funny(lucy)))&
(generous(paul))&
((~old(mary)|old(mary)))&
(?[X]:((~patient(X)|~humble(X))))&
((funny(john)|~strong(john)))&
(?[X]:((brave(X)&patient(X))))&
((rich(john)|humble(john))) | quiet(john) | [
"p0",
"p3",
"p5",
"p6",
"p7",
"p11",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8658237847389008597427526
% SZS output start Proof for 8658237847389008597427526
1. ! [X0] : ((kind(X0) | creative(X0)) <=> (rich(X0) | curious(X0))) [input p0]
4. ! [X0] : ((curious(X0) | rich(X0)) => ~wise(X0)) [input p3]
6. ! [X0] : ((strong(X0) & kind(X0)) => rich(X0)) [input p5]
7. (quiet(john) | ~rich(john)) <=> ? [X0] : (generous(X0) | tall(X0)) [input p6]
8. ! [X0] : (~kind(X0) <=> (generous(X0) & quiet(X0))) [input p7]
12. ! [X0] : ((strong(X0) <~> humble(X0)) => (wise(X0) | ~kind(X0))) [input p11]
19. generous(paul) [input p18]
24. humble(john) | rich(john) [input p23]
25. ~quiet(john) [input hypothesis]
30. ! [X0] : (~wise(X0) | (~curious(X0) & ~rich(X0))) [ennf transformation 4]
31. ! [X0] : (rich(X0) | (~strong(X0) | ~kind(X0))) [ennf transformation 6]
32. ! [X0] : (rich(X0) | ~strong(X0) | ~kind(X0)) [flattening 31]
36. ! [X0] : ((wise(X0) | ~kind(X0)) | (strong(X0) <=> humble(X0))) [ennf transformation 12]
37. ! [X0] : (wise(X0) | ~kind(X0) | (strong(X0) <=> humble(X0))) [flattening 36]
42. ! [X0] : (((kind(X0) | creative(X0)) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | (~kind(X0) & ~creative(X0)))) [nnf transformation 1]
43. ! [X0] : ((kind(X0) | creative(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | (~kind(X0) & ~creative(X0)))) [flattening 42]
50. ((quiet(john) | ~rich(john)) | ! [X0] : (~generous(X0) & ~tall(X0))) & (? [X0] : (generous(X0) | tall(X0)) | (~quiet(john) & rich(john))) [nnf transformation 7]
51. (quiet(john) | ~rich(john) | ! [X0] : (~generous(X0) & ~tall(X0))) & (? [X0] : (generous(X0) | tall(X0)) | (~quiet(john) & rich(john))) [flattening 50]
52. (quiet(john) | ~rich(john) | ! [X0] : (~generous(X0) & ~tall(X0))) & (? [X1] : (generous(X1) | tall(X1)) | (~quiet(john) & rich(john))) [rectify 51]
53. ? [X1] : (generous(X1) | tall(X1)) => (generous(sK1) | tall(sK1)) [choice axiom]
54. (quiet(john) | ~rich(john) | ! [X0] : (~generous(X0) & ~tall(X0))) & ((generous(sK1) | tall(sK1)) | (~quiet(john) & rich(john))) [skolemisation 52,53]
55. ! [X0] : ((~kind(X0) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | kind(X0))) [nnf transformation 8]
56. ! [X0] : ((~kind(X0) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | kind(X0))) [flattening 55]
62. ! [X0] : (wise(X0) | ~kind(X0) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) [nnf transformation 37]
79. ~kind(X0) | curious(X0) | rich(X0) [cnf transformation 43]
87. ~wise(X0) | ~curious(X0) [cnf transformation 30]
94. ~strong(X0) | rich(X0) | ~kind(X0) [cnf transformation 32]
98. quiet(john) | ~rich(john) | ~generous(X0) [cnf transformation 54]
99. quiet(X0) | kind(X0) [cnf transformation 56]
111. ~humble(X0) | ~kind(X0) | strong(X0) | wise(X0) [cnf transformation 62]
125. generous(paul) [cnf transformation 19]
131. humble(john) | rich(john) [cnf transformation 24]
132. ~quiet(john) [cnf transformation 25]
150. 4 <=> ! [X0] : ~generous(X0) [avatar definition]
151. ~generous(X0) <- (4) [avatar component clause 150]
153. 5 <=> rich(john) [avatar definition]
155. ~rich(john) <- (~5) [avatar component clause 153]
157. 6 <=> quiet(john) [avatar definition]
158. ~quiet(john) <- (~6) [avatar component clause 157]
160. 4 | ~5 | 6 [avatar split clause 98,157,153,150]
233. 23 <=> curious(john) [avatar definition]
234. curious(john) <- (23) [avatar component clause 233]
248. 26 <=> strong(john) [avatar definition]
249. strong(john) <- (26) [avatar component clause 248]
250. ~strong(john) <- (~26) [avatar component clause 248]
253. 27 <=> humble(john) [avatar definition]
255. humble(john) <- (27) [avatar component clause 253]
256. 5 | 27 [avatar split clause 131,253,153]
257. ~6 [avatar split clause 132,157]
258. $false <- (4) [resolution 151,125]
259. ~4 [avatar contradiction clause 258]
264. kind(john) <- (~6) [resolution 99,158]
265. curious(john) | rich(john) <- (~6) [resolution 79,264]
266. curious(john) <- (~5, ~6) [subsumption resolution 265,155]
267. 23 | 5 | 6 [avatar split clause 266,157,153,233]
347. ~kind(john) | strong(john) | wise(john) <- (27) [resolution 111,255]
348. strong(john) | wise(john) <- (~6, 27) [subsumption resolution 347,264]
349. wise(john) <- (~6, ~26, 27) [subsumption resolution 348,250]
351. ~curious(john) <- (~6, ~26, 27) [resolution 349,87]
354. $false <- (~6, 23, ~26, 27) [subsumption resolution 351,234]
355. 6 | ~23 | 26 | ~27 [avatar contradiction clause 354]
362. rich(john) | ~kind(john) <- (26) [resolution 249,94]
363. ~kind(john) <- (~5, 26) [subsumption resolution 362,155]
364. $false <- (~5, ~6, 26) [subsumption resolution 363,264]
365. 5 | 6 | ~26 [avatar contradiction clause 364]
366. $false [avatar sat refutation 160,256,257,259,267,355,365]
% SZS output end Proof for 8658237847389008597427526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not patient is calm or tall.
Everyone who is not quiet or not old is calm and vice versa.
If john is not wise or curious then someone is not patient.
If paul is strong or old then paul is not tall and vice versa.
If someone is wise or kind then someone is both quiet and calm and vice versa.
If lucy is both happy and wise then susan is quiet and vice versa.
If alice is curious or brave then someone is tall or not humble.
Everyone who is not old or not humble is funny and vice versa.
If someone is either funny or not humble then someone is either brave or not calm and vice versa.
Everyone who is funny or not old is both wise and not strong and vice versa.
Everyone who is either strong or not funny is either not tall or tall and vice versa.
If fred is not tall or tall then someone is not curious and vice versa.
If someone is both not curious and happy then someone is both not humble and not wise.
If mary is not quiet or not strong then alice is kind or not tall.
If fred is either calm or not curious then lucy is not rich or brave.
If someone is wise then someone is kind.
Someone is wise or not wise.
Someone is not funny.
Someone is both creative and happy.
Lucy is not old or not happy.
Lucy is wise or creative. | Mary is funny. | contradiction | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~quiet(X)|~old(X))<=>calm(X)))&
(((~wise(john)|curious(john)))=>(?[X]:(~patient(X))))&
(((strong(paul)|old(paul)))<=>(~tall(paul)))&
((?[X]:((wise(X)|kind(X))))<=>(?[X]:((quiet(X)&calm(X)))))&
(((happy(lucy)&wise(lucy)))<=>(quiet(susan)))&
(((curious(alice)|brave(alice)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~old(X)|~humble(X))<=>funny(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((funny(X)|~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~tall(X)<~>tall(X))))&
(((~tall(fred)|tall(fred)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~humble(X)&~wise(X)))))&
(((~quiet(mary)|~strong(mary)))=>((kind(alice)|~tall(alice))))&
(((calm(fred)<~>~curious(fred)))=>((~rich(lucy)|brave(lucy))))&
((?[X]:(wise(X)))=>(?[X]:(kind(X))))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)&happy(X))))&
((~old(lucy)|~happy(lucy)))&
((wise(lucy)|creative(lucy))) | funny(mary) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6268036344303512845139331
% SZS output start Proof for 6268036344303512845139331
10. ! [X0] : ((~old(X0) | funny(X0)) <=> (~strong(X0) & wise(X0))) [input p9]
11. ! [X0] : ((strong(X0) <~> ~funny(X0)) <=> (~tall(X0) <~> tall(X0))) [input p10]
22. funny(mary) [input hypothesis]
60. ! [X0] : (((~old(X0) | funny(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (old(X0) & ~funny(X0)))) [nnf transformation 10]
61. ! [X0] : ((~old(X0) | funny(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (old(X0) & ~funny(X0)))) [flattening 60]
62. ! [X0] : ((((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0))))) [nnf transformation 11]
113. ~strong(X0) | ~funny(X0) [cnf transformation 61]
120. ~funny(X0) | strong(X0) | tall(X0) | tall(X0) [cnf transformation 62]
121. ~funny(X0) | strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 62]
122. funny(X0) | ~strong(X0) | tall(X0) | tall(X0) [cnf transformation 62]
123. funny(X0) | ~strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 62]
136. funny(mary) [cnf transformation 22]
137. ~funny(X0) | strong(X0) | tall(X0) [duplicate literal removal 120]
138. ~funny(X0) | strong(X0) | ~tall(X0) [duplicate literal removal 121]
139. funny(X0) | ~strong(X0) | tall(X0) [duplicate literal removal 122]
140. funny(X0) | ~strong(X0) | ~tall(X0) [duplicate literal removal 123]
270. ~strong(X0) | ~tall(X0) [subsumption resolution 140,113]
271. ~strong(X0) | tall(X0) [subsumption resolution 139,113]
272. ~strong(X0) [subsumption resolution 271,270]
273. ~funny(X0) | ~tall(X0) [subsumption resolution 138,272]
274. ~funny(X0) | tall(X0) [subsumption resolution 137,272]
275. ~funny(X0) [subsumption resolution 274,273]
324. $false [subsumption resolution 136,275]
% SZS output end Proof for 6268036344303512845139331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then lucy is either not strong or not rich.
If someone is either not patient or not quiet then someone is curious.
Everyone who is patient is both not tall and happy.
Everyone who is not rich is not brave or not creative and vice versa.
If someone is either tall or patient then someone is either happy or curious and vice versa.
Everyone who is creative or not creative is kind or not quiet and vice versa.
If paul is not calm or creative then someone is both wise and rich and vice versa.
If alice is not funny then john is humble and vice versa.
If someone is not strong then someone is either not kind or not old.
If fred is curious then someone is both not strong and not brave and vice versa.
Everyone who is kind or not calm is not old.
Everyone who is not old is both not creative and not strong and vice versa.
Everyone who is brave is either humble or not funny and vice versa.
Everyone who is rich is creative and vice versa.
If mary is happy or creative then someone is not funny and vice versa.
Everyone who is either not old or not kind is kind.
Someone is either generous or kind.
Mary is rich or calm.
Lucy is not calm or brave.
Someone is both not wise and curious.
Someone is not quiet.
Someone is either not generous or not patient.
Susan is not patient. | Fred is not creative. | entailment | ((?[X]:(quiet(X)))=>((~strong(lucy)<~>~rich(lucy))))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:(curious(X))))&
(![X]:(patient(X)=>(~tall(X)&happy(X))))&
(![X]:(~rich(X)<=>(~brave(X)|~creative(X))))&
((?[X]:((tall(X)<~>patient(X))))<=>(?[X]:((happy(X)<~>curious(X)))))&
(![X]:((creative(X)|~creative(X))<=>(kind(X)|~quiet(X))))&
(((~calm(paul)|creative(paul)))<=>(?[X]:((wise(X)&rich(X)))))&
((~funny(alice))<=>(humble(john)))&
((?[X]:(~strong(X)))=>(?[X]:((~kind(X)<~>~old(X)))))&
((curious(fred))<=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((kind(X)|~calm(X))=>~old(X)))&
(![X]:(~old(X)<=>(~creative(X)&~strong(X))))&
(![X]:(brave(X)<=>(humble(X)<~>~funny(X))))&
(![X]:(rich(X)<=>creative(X)))&
(((happy(mary)|creative(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)<~>~kind(X))=>kind(X)))&
(?[X]:((generous(X)<~>kind(X))))&
((rich(mary)|calm(mary)))&
((~calm(lucy)|brave(lucy)))&
(?[X]:((~wise(X)&curious(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)<~>~patient(X))))&
(~patient(susan)) | ~creative(fred) | [
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6415491393215643138618482
% SZS output start Proof for 6415491393215643138618482
11. ! [X0] : ((~calm(X0) | kind(X0)) => ~old(X0)) [input p10]
12. ! [X0] : (~old(X0) <=> (~strong(X0) & ~creative(X0))) [input p11]
16. ! [X0] : ((~old(X0) <~> ~kind(X0)) => kind(X0)) [input p15]
24. creative(fred) [input hypothesis]
32. ! [X0] : (~old(X0) | (calm(X0) & ~kind(X0))) [ennf transformation 11]
33. ! [X0] : (kind(X0) | (~old(X0) <=> ~kind(X0))) [ennf transformation 16]
62. ! [X0] : ((~old(X0) | (strong(X0) | creative(X0))) & ((~strong(X0) & ~creative(X0)) | old(X0))) [nnf transformation 12]
63. ! [X0] : ((~old(X0) | strong(X0) | creative(X0)) & ((~strong(X0) & ~creative(X0)) | old(X0))) [flattening 62]
71. ! [X0] : (kind(X0) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 33]
115. ~old(X0) | ~kind(X0) [cnf transformation 32]
117. ~creative(X0) | old(X0) [cnf transformation 63]
130. kind(X0) | ~old(X0) | kind(X0) [cnf transformation 71]
141. creative(fred) [cnf transformation 24]
142. kind(X0) | ~old(X0) [duplicate literal removal 130]
290. ~old(X0) [subsumption resolution 142,115]
338. old(fred) [resolution 117,141]
340. $false [subsumption resolution 338,290]
% SZS output end Proof for 6415491393215643138618482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or not brave then alice is not generous.
If fred is not rich or generous then fred is both tall and brave and vice versa.
Everyone who is both funny and kind is both curious and not funny and vice versa.
Everyone who is rich or brave is either not old or not tall.
If someone is not old or creative then paul is either not kind or not strong.
Everyone who is not patient or not kind is not patient.
Everyone who is not creative is not wise.
If mary is either not quiet or brave then someone is either generous or not creative and vice versa.
Everyone who is both not brave and calm is both generous and kind and vice versa.
If fred is humble or tall then lucy is not calm or wise.
Everyone who is both tall and kind is tall or not generous.
Everyone who is either happy or not rich is either curious or not curious.
If susan is not old or tall then someone is strong and vice versa.
If someone is not happy then someone is both happy and not funny.
Everyone who is rich is curious and vice versa.
Everyone who is not rich or not curious is both creative and not creative and vice versa.
Someone is not brave.
Someone is not quiet.
Someone is curious or old.
John is either not generous or quiet.
Fred is both not generous and not humble. | Mary is not calm. | neutral | (((~happy(susan)|~brave(susan)))=>(~generous(alice)))&
(((~rich(fred)|generous(fred)))<=>((tall(fred)&brave(fred))))&
(![X]:((funny(X)&kind(X))<=>(curious(X)&~funny(X))))&
(![X]:((rich(X)|brave(X))=>(~old(X)<~>~tall(X))))&
((?[X]:((~old(X)|creative(X))))=>((~kind(paul)<~>~strong(paul))))&
(![X]:((~patient(X)|~kind(X))=>~patient(X)))&
(![X]:(~creative(X)=>~wise(X)))&
(((~quiet(mary)<~>brave(mary)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
(![X]:((~brave(X)&calm(X))<=>(generous(X)&kind(X))))&
(((humble(fred)|tall(fred)))=>((~calm(lucy)|wise(lucy))))&
(![X]:((tall(X)&kind(X))=>(tall(X)|~generous(X))))&
(![X]:((happy(X)<~>~rich(X))=>(curious(X)<~>~curious(X))))&
(((~old(susan)|tall(susan)))<=>(?[X]:(strong(X))))&
((?[X]:(~happy(X)))=>(?[X]:((happy(X)&~funny(X)))))&
(![X]:(rich(X)<=>curious(X)))&
(![X]:((~rich(X)|~curious(X))<=>(creative(X)&~creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((curious(X)|old(X))))&
((~generous(john)<~>quiet(john)))&
((~generous(fred)&~humble(fred))) | ~calm(mary) | [] | null | 0 |
If paul is wise or not old then fred is both quiet and not quiet and vice versa. Everyone who is either kind or generous is both not curious and not funny and vice versa. Everyone who is both not old and not quiet is either not old or not quiet and vice versa. Everyone who is generous is curious or old and vice versa. Everyone who is strong or not curious is either not kind or patient and vice versa. Everyone who is both funny and not patient is both old and not patient and vice versa. Everyone who is both quiet and not quiet is strong or calm and vice versa. If alice is happy then someone is both old and not quiet and vice versa. Everyone who is either rich or not curious is either not wise or not old and vice versa. Everyone who is either not patient or calm is either not tall or generous. Everyone who is both tall and not humble is both not patient and funny and vice versa. Everyone who is funny is not wise and vice versa. If fred is curious or brave then someone is either creative or not strong and vice versa. If mary is not wise or curious then fred is humble or not patient and vice versa. Everyone who is either funny or not brave is calm and vice versa. Fred is not kind or not curious. Someone is both generous and patient. Paul is humble. Someone is generous or not old. Mary is not brave. | Fred is not calm. | entailment | (((wise(paul)|~old(paul)))<=>((quiet(fred)&~quiet(fred))))&
(![X]:((kind(X)<~>generous(X))<=>(~curious(X)&~funny(X))))&
(![X]:((~old(X)&~quiet(X))<=>(~old(X)<~>~quiet(X))))&
(![X]:(generous(X)<=>(curious(X)|old(X))))&
(![X]:((strong(X)|~curious(X))<=>(~kind(X)<~>patient(X))))&
(![X]:((funny(X)&~patient(X))<=>(old(X)&~patient(X))))&
(![X]:((quiet(X)&~quiet(X))<=>(strong(X)|calm(X))))&
((happy(alice))<=>(?[X]:((old(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~curious(X))<=>(~wise(X)<~>~old(X))))&
(![X]:((~patient(X)<~>calm(X))=>(~tall(X)<~>generous(X))))&
(![X]:((tall(X)&~humble(X))<=>(~patient(X)&funny(X))))&
(![X]:(funny(X)<=>~wise(X)))&
(((curious(fred)|brave(fred)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(((~wise(mary)|curious(mary)))<=>((humble(fred)|~patient(fred))))&
(![X]:((funny(X)<~>~brave(X))<=>calm(X)))&
((~kind(fred)|~curious(fred)))&
(?[X]:((generous(X)&patient(X))))&
(humble(paul))&
(?[X]:((generous(X)|~old(X))))&
(~brave(mary)) | ~calm(fred) | [
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3742020152726688611748044
% SZS output start Proof for 3742020152726688611748044
3. ! [X0] : ((~quiet(X0) & ~old(X0)) <=> (~old(X0) <~> ~quiet(X0))) [input p2]
7. ! [X0] : ((~quiet(X0) & quiet(X0)) <=> (calm(X0) | strong(X0))) [input p6]
21. calm(fred) [input hypothesis]
27. ! [X0] : (((~quiet(X0) & ~old(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0)))) & (((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | (quiet(X0) | old(X0)))) [nnf transformation 3]
28. ! [X0] : (((~quiet(X0) & ~old(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0)))) & (((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | quiet(X0) | old(X0))) [flattening 27]
35. ! [X0] : (((~quiet(X0) & quiet(X0)) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | (quiet(X0) | ~quiet(X0)))) [nnf transformation 7]
36. ! [X0] : (((~quiet(X0) & quiet(X0)) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | quiet(X0) | ~quiet(X0))) [flattening 35]
70. quiet(X0) | old(X0) | quiet(X0) | old(X0) [cnf transformation 28]
72. ~old(X0) | ~old(X0) | quiet(X0) [cnf transformation 28]
92. ~quiet(X0) | ~calm(X0) [cnf transformation 36]
134. calm(fred) [cnf transformation 21]
135. quiet(X0) | old(X0) [duplicate literal removal 70]
136. ~old(X0) | quiet(X0) [duplicate literal removal 72]
154. quiet(X0) [subsumption resolution 135,136]
155. ~calm(X0) [subsumption resolution 92,154]
208. $false [subsumption resolution 134,155]
% SZS output end Proof for 3742020152726688611748044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not kind is not old and vice versa.
If someone is either not tall or not brave then lucy is kind.
If fred is either strong or tall then someone is not calm and vice versa.
Everyone who is either not brave or not wise is not strong or not curious and vice versa.
If someone is both funny and not creative then someone is both not creative and not kind and vice versa.
Everyone who is both not patient and not quiet is old or not kind and vice versa.
If paul is tall or not brave then someone is both strong and not curious and vice versa.
Everyone who is not patient is not patient or old.
If susan is either not generous or not quiet then someone is either generous or not strong.
Everyone who is wise or not old is not strong or calm and vice versa.
Everyone who is either not wise or not quiet is not calm and vice versa.
If someone is either not calm or not curious then someone is either not tall or old.
If fred is both brave and not curious then someone is either generous or not kind and vice versa.
Everyone who is both not kind and happy is not generous and vice versa.
Everyone who is either kind or curious is not brave and vice versa.
Someone is either happy or not kind.
Mary is both curious and humble.
Someone is either rich or strong.
Someone is both humble and not brave.
John is brave or humble.
Someone is both funny and curious.
Lucy is either humble or curious.
Someone is calm or kind. | Mary is not kind. | entailment | (![X]:((~curious(X)|~kind(X))<=>~old(X)))&
((?[X]:((~tall(X)<~>~brave(X))))=>(kind(lucy)))&
(((strong(fred)<~>tall(fred)))<=>(?[X]:(~calm(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(~strong(X)|~curious(X))))&
((?[X]:((funny(X)&~creative(X))))<=>(?[X]:((~creative(X)&~kind(X)))))&
(![X]:((~patient(X)&~quiet(X))<=>(old(X)|~kind(X))))&
(((tall(paul)|~brave(paul)))<=>(?[X]:((strong(X)&~curious(X)))))&
(![X]:(~patient(X)=>(~patient(X)|old(X))))&
(((~generous(susan)<~>~quiet(susan)))=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((wise(X)|~old(X))<=>(~strong(X)|calm(X))))&
(![X]:((~wise(X)<~>~quiet(X))<=>~calm(X)))&
((?[X]:((~calm(X)<~>~curious(X))))=>(?[X]:((~tall(X)<~>old(X)))))&
(((brave(fred)&~curious(fred)))<=>(?[X]:((generous(X)<~>~kind(X)))))&
(![X]:((~kind(X)&happy(X))<=>~generous(X)))&
(![X]:((kind(X)<~>curious(X))<=>~brave(X)))&
(?[X]:((happy(X)<~>~kind(X))))&
((curious(mary)&humble(mary)))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((humble(X)&~brave(X))))&
((brave(john)|humble(john)))&
(?[X]:((funny(X)&curious(X))))&
((humble(lucy)<~>curious(lucy)))&
(?[X]:((calm(X)|kind(X)))) | ~kind(mary) | [
"p0",
"p3",
"p5",
"p9",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 351773348905967536426857
% SZS output start Proof for 351773348905967536426857
1. ! [X0] : ((~kind(X0) | ~curious(X0)) <=> ~old(X0)) [input p0]
4. ! [X0] : ((~brave(X0) <~> ~wise(X0)) <=> (~curious(X0) | ~strong(X0))) [input p3]
6. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> (~kind(X0) | old(X0))) [input p5]
10. ! [X0] : ((~old(X0) | wise(X0)) <=> (calm(X0) | ~strong(X0))) [input p9]
11. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) <=> ~calm(X0)) [input p10]
15. ! [X0] : ((kind(X0) <~> curious(X0)) <=> ~brave(X0)) [input p14]
17. humble(mary) & curious(mary) [input p16]
24. kind(mary) [input hypothesis]
32. ! [X0] : (((~kind(X0) | ~curious(X0)) | old(X0)) & (~old(X0) | (kind(X0) & curious(X0)))) [nnf transformation 1]
33. ! [X0] : ((~kind(X0) | ~curious(X0) | old(X0)) & (~old(X0) | (kind(X0) & curious(X0)))) [flattening 32]
39. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (curious(X0) & strong(X0))) & ((~curious(X0) | ~strong(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [nnf transformation 4]
40. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (curious(X0) & strong(X0))) & (~curious(X0) | ~strong(X0) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [flattening 39]
46. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (kind(X0) & ~old(X0))) & ((~kind(X0) | old(X0)) | (quiet(X0) | patient(X0)))) [nnf transformation 6]
47. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (kind(X0) & ~old(X0))) & (~kind(X0) | old(X0) | quiet(X0) | patient(X0))) [flattening 46]
56. ! [X0] : (((~old(X0) | wise(X0)) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | (old(X0) & ~wise(X0)))) [nnf transformation 10]
57. ! [X0] : ((~old(X0) | wise(X0) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | (old(X0) & ~wise(X0)))) [flattening 56]
58. ! [X0] : ((((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | calm(X0)) & (~calm(X0) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))))) [nnf transformation 11]
70. ! [X0] : ((((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | brave(X0)) & (~brave(X0) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))))) [nnf transformation 15]
86. ~kind(X0) | ~curious(X0) | old(X0) [cnf transformation 33]
95. ~wise(X0) | ~brave(X0) | strong(X0) [cnf transformation 40]
106. ~quiet(X0) | ~old(X0) [cnf transformation 47]
118. ~wise(X0) | ~strong(X0) | calm(X0) [cnf transformation 57]
121. ~calm(X0) | wise(X0) | ~old(X0) [cnf transformation 57]
123. ~wise(X0) | ~calm(X0) | quiet(X0) [cnf transformation 58]
125. quiet(X0) | wise(X0) | calm(X0) [cnf transformation 58]
142. ~kind(X0) | ~curious(X0) | brave(X0) [cnf transformation 70]
145. curious(mary) [cnf transformation 17]
157. kind(mary) [cnf transformation 24]
371. ~curious(mary) | old(mary) [resolution 86,157]
373. old(mary) [subsumption resolution 371,145]
386. 43 <=> strong(mary) [avatar definition]
390. 44 <=> wise(mary) [avatar definition]
392. wise(mary) <- (44) [avatar component clause 390]
414. wise(X3) | calm(X3) | ~old(X3) [resolution 125,106]
417. ~old(X3) | wise(X3) [subsumption resolution 414,121]
418. wise(mary) [resolution 417,373]
419. 44 [avatar split clause 418,390]
421. ~calm(mary) | quiet(mary) <- (44) [resolution 392,123]
422. ~strong(mary) | calm(mary) <- (44) [resolution 392,118]
424. ~brave(mary) | strong(mary) <- (44) [resolution 392,95]
426. 47 <=> quiet(mary) [avatar definition]
428. quiet(mary) <- (47) [avatar component clause 426]
430. 48 <=> calm(mary) [avatar definition]
433. 47 | ~48 | ~44 [avatar split clause 421,390,430,426]
437. 49 <=> brave(mary) [avatar definition]
440. 43 | ~49 | ~44 [avatar split clause 424,390,437,386]
441. 48 | ~43 | ~44 [avatar split clause 422,390,386,430]
485. ~curious(mary) | brave(mary) [resolution 142,157]
487. brave(mary) [subsumption resolution 485,145]
490. 49 [avatar split clause 487,437]
663. ~old(mary) <- (47) [resolution 428,106]
664. $false <- (47) [subsumption resolution 663,373]
665. ~47 [avatar contradiction clause 664]
666. $false [avatar sat refutation 419,433,440,441,490,665]
% SZS output end Proof for 351773348905967536426857
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is both not rich and not curious.
Everyone who is funny is both rich and patient and vice versa.
Everyone who is not strong is funny and vice versa.
If someone is rich or not old then susan is both rich and happy and vice versa.
If fred is tall or funny then paul is either kind or not strong.
Everyone who is both not happy and not tall is either funny or brave.
Everyone who is both not creative and calm is not rich or not wise.
Everyone who is both generous and not creative is either happy or quiet and vice versa.
Everyone who is generous or not curious is creative or curious.
Everyone who is not humble is either not humble or not kind.
If susan is not rich or brave then john is strong and vice versa.
Everyone who is both rich and creative is not quiet or not brave and vice versa.
If alice is kind or not funny then someone is funny and vice versa.
Everyone who is tall is happy.
Everyone who is both tall and not strong is rich or kind.
If alice is both quiet and wise then someone is not strong and vice versa.
Someone is not curious or not quiet.
Susan is both creative and not brave.
Someone is either not tall or calm.
Someone is not quiet.
Alice is both happy and kind.
Fred is either not quiet or creative.
John is either quiet or brave.
Someone is either strong or humble. | Alice is not quiet. | contradiction | (![X]:(~creative(X)=>(~rich(X)&~curious(X))))&
(![X]:(funny(X)<=>(rich(X)&patient(X))))&
(![X]:(~strong(X)<=>funny(X)))&
((?[X]:((rich(X)|~old(X))))<=>((rich(susan)&happy(susan))))&
(((tall(fred)|funny(fred)))=>((kind(paul)<~>~strong(paul))))&
(![X]:((~happy(X)&~tall(X))=>(funny(X)<~>brave(X))))&
(![X]:((~creative(X)&calm(X))=>(~rich(X)|~wise(X))))&
(![X]:((generous(X)&~creative(X))<=>(happy(X)<~>quiet(X))))&
(![X]:((generous(X)|~curious(X))=>(creative(X)|curious(X))))&
(![X]:(~humble(X)=>(~humble(X)<~>~kind(X))))&
(((~rich(susan)|brave(susan)))<=>(strong(john)))&
(![X]:((rich(X)&creative(X))<=>(~quiet(X)|~brave(X))))&
(((kind(alice)|~funny(alice)))<=>(?[X]:(funny(X))))&
(![X]:(tall(X)=>happy(X)))&
(![X]:((tall(X)&~strong(X))=>(rich(X)|kind(X))))&
(((quiet(alice)&wise(alice)))<=>(?[X]:(~strong(X))))&
(?[X]:((~curious(X)|~quiet(X))))&
((creative(susan)&~brave(susan)))&
(?[X]:((~tall(X)<~>calm(X))))&
(?[X]:(~quiet(X)))&
((happy(alice)&kind(alice)))&
((~quiet(fred)<~>creative(fred)))&
((quiet(john)<~>brave(john)))&
(?[X]:((strong(X)<~>humble(X)))) | ~quiet(alice) | [
"p1",
"p3",
"p10",
"p12",
"p15",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8958394156807624216274761
% SZS output start Proof for 8958394156807624216274761
2. ! [X0] : (funny(X0) <=> (patient(X0) & rich(X0))) [input p1]
4. ? [X0] : (~old(X0) | rich(X0)) <=> (happy(susan) & rich(susan)) [input p3]
11. (brave(susan) | ~rich(susan)) <=> strong(john) [input p10]
13. (~funny(alice) | kind(alice)) <=> ? [X0] : funny(X0) [input p12]
16. (wise(alice) & quiet(alice)) <=> ? [X0] : ~strong(X0) [input p15]
18. ~brave(susan) & creative(susan) [input p17]
21. kind(alice) & happy(alice) [input p20]
25. ~quiet(alice) [input hypothesis]
38. ! [X0] : ((funny(X0) | (~patient(X0) | ~rich(X0))) & ((patient(X0) & rich(X0)) | ~funny(X0))) [nnf transformation 2]
39. ! [X0] : ((funny(X0) | ~patient(X0) | ~rich(X0)) & ((patient(X0) & rich(X0)) | ~funny(X0))) [flattening 38]
41. (? [X0] : (~old(X0) | rich(X0)) | (~happy(susan) | ~rich(susan))) & ((happy(susan) & rich(susan)) | ! [X0] : (old(X0) & ~rich(X0))) [nnf transformation 4]
42. (? [X0] : (~old(X0) | rich(X0)) | ~happy(susan) | ~rich(susan)) & ((happy(susan) & rich(susan)) | ! [X0] : (old(X0) & ~rich(X0))) [flattening 41]
43. (? [X0] : (~old(X0) | rich(X0)) | ~happy(susan) | ~rich(susan)) & ((happy(susan) & rich(susan)) | ! [X1] : (old(X1) & ~rich(X1))) [rectify 42]
44. ? [X0] : (~old(X0) | rich(X0)) => (~old(sK0) | rich(sK0)) [choice axiom]
45. ((~old(sK0) | rich(sK0)) | ~happy(susan) | ~rich(susan)) & ((happy(susan) & rich(susan)) | ! [X1] : (old(X1) & ~rich(X1))) [skolemisation 43,44]
51. ((brave(susan) | ~rich(susan)) | ~strong(john)) & (strong(john) | (~brave(susan) & rich(susan))) [nnf transformation 11]
52. (brave(susan) | ~rich(susan) | ~strong(john)) & (strong(john) | (~brave(susan) & rich(susan))) [flattening 51]
55. ((~funny(alice) | kind(alice)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | (funny(alice) & ~kind(alice))) [nnf transformation 13]
56. (~funny(alice) | kind(alice) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | (funny(alice) & ~kind(alice))) [flattening 55]
57. (~funny(alice) | kind(alice) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | (funny(alice) & ~kind(alice))) [rectify 56]
58. ? [X1] : funny(X1) => funny(sK1) [choice axiom]
59. (~funny(alice) | kind(alice) | ! [X0] : ~funny(X0)) & (funny(sK1) | (funny(alice) & ~kind(alice))) [skolemisation 57,58]
60. ((wise(alice) & quiet(alice)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | (~wise(alice) | ~quiet(alice))) [nnf transformation 16]
61. ((wise(alice) & quiet(alice)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | ~wise(alice) | ~quiet(alice)) [flattening 60]
62. ((wise(alice) & quiet(alice)) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | ~wise(alice) | ~quiet(alice)) [rectify 61]
63. ? [X1] : ~strong(X1) => ~strong(sK2) [choice axiom]
64. ((wise(alice) & quiet(alice)) | ! [X0] : strong(X0)) & (~strong(sK2) | ~wise(alice) | ~quiet(alice)) [skolemisation 62,63]
79. ~funny(X0) | rich(X0) [cnf transformation 39]
84. rich(susan) | ~rich(X1) [cnf transformation 45]
108. brave(susan) | ~rich(susan) | ~strong(john) [cnf transformation 52]
114. funny(sK1) | ~kind(alice) [cnf transformation 59]
120. quiet(alice) | strong(X0) [cnf transformation 64]
124. ~brave(susan) [cnf transformation 18]
129. kind(alice) [cnf transformation 21]
136. ~quiet(alice) [cnf transformation 25]
140. 1 <=> rich(susan) [avatar definition]
161. 6 <=> ! [X1] : ~rich(X1) [avatar definition]
162. ~rich(X1) <- (6) [avatar component clause 161]
165. 6 | 1 [avatar split clause 84,140,161]
188. 11 <=> strong(john) [avatar definition]
190. ~strong(john) <- (~11) [avatar component clause 188]
192. 12 <=> brave(susan) [avatar definition]
195. ~11 | ~1 | 12 [avatar split clause 108,192,140,188]
203. 14 <=> kind(alice) [avatar definition]
212. 16 <=> funny(sK1) [avatar definition]
214. funny(sK1) <- (16) [avatar component clause 212]
216. ~14 | 16 [avatar split clause 114,212,203]
218. 17 <=> ! [X0] : strong(X0) [avatar definition]
219. strong(X0) <- (17) [avatar component clause 218]
226. 19 <=> quiet(alice) [avatar definition]
229. 17 | 19 [avatar split clause 120,226,218]
244. ~12 [avatar split clause 124,192]
255. 14 [avatar split clause 129,203]
277. ~19 [avatar split clause 136,226]
280. rich(sK1) <- (16) [resolution 79,214]
281. $false <- (6, 16) [subsumption resolution 280,162]
282. ~6 | ~16 [avatar contradiction clause 281]
283. $false <- (~11, 17) [subsumption resolution 190,219]
284. 11 | ~17 [avatar contradiction clause 283]
287. $false [avatar sat refutation 165,195,216,229,244,255,277,282,284]
% SZS output end Proof for 8958394156807624216274761
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or strong is not creative and vice versa.
Everyone who is either calm or not humble is patient or not humble and vice versa.
If someone is not quiet or strong then someone is either happy or humble and vice versa.
Everyone who is either not calm or old is either creative or kind and vice versa.
If susan is rich or not wise then alice is both strong and not wise and vice versa.
Everyone who is not humble or not brave is not patient and vice versa.
If mary is either old or not happy then someone is happy.
Everyone who is both not brave and not rich is both brave and not generous and vice versa.
If someone is not curious then susan is both not brave and not tall.
If john is not generous then someone is both strong and not quiet and vice versa.
If someone is both rich and not generous then someone is both not tall and not generous and vice versa.
Everyone who is both wise and not rich is either strong or curious and vice versa.
If someone is either curious or wise then someone is either not humble or generous and vice versa.
If someone is not strong or not patient then someone is both not humble and not brave.
Everyone who is either not rich or not humble is both generous and brave.
Fred is either not quiet or not old.
Mary is both not funny and strong.
Susan is not creative or kind.
Paul is happy.
Lucy is either happy or not curious.
Paul is brave. | Fred is humble. | entailment | (![X]:((~old(X)<~>strong(X))<=>~creative(X)))&
(![X]:((calm(X)<~>~humble(X))<=>(patient(X)|~humble(X))))&
((?[X]:((~quiet(X)|strong(X))))<=>(?[X]:((happy(X)<~>humble(X)))))&
(![X]:((~calm(X)<~>old(X))<=>(creative(X)<~>kind(X))))&
(((rich(susan)|~wise(susan)))<=>((strong(alice)&~wise(alice))))&
(![X]:((~humble(X)|~brave(X))<=>~patient(X)))&
(((old(mary)<~>~happy(mary)))=>(?[X]:(happy(X))))&
(![X]:((~brave(X)&~rich(X))<=>(brave(X)&~generous(X))))&
((?[X]:(~curious(X)))=>((~brave(susan)&~tall(susan))))&
((~generous(john))<=>(?[X]:((strong(X)&~quiet(X)))))&
((?[X]:((rich(X)&~generous(X))))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((wise(X)&~rich(X))<=>(strong(X)<~>curious(X))))&
((?[X]:((curious(X)<~>wise(X))))<=>(?[X]:((~humble(X)<~>generous(X)))))&
((?[X]:((~strong(X)|~patient(X))))=>(?[X]:((~humble(X)&~brave(X)))))&
(![X]:((~rich(X)<~>~humble(X))=>(generous(X)&brave(X))))&
((~quiet(fred)<~>~old(fred)))&
((~funny(mary)&strong(mary)))&
((~creative(susan)|kind(susan)))&
(happy(paul))&
((happy(lucy)<~>~curious(lucy)))&
(brave(paul)) | humble(fred) | [
"p5",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3461150433102200145515189
% SZS output start Proof for 3461150433102200145515189
6. ! [X0] : ((~brave(X0) | ~humble(X0)) <=> ~patient(X0)) [input p5]
8. ! [X0] : ((~rich(X0) & ~brave(X0)) <=> (~generous(X0) & brave(X0))) [input p7]
14. ? [X0] : (~patient(X0) | ~strong(X0)) => ? [X0] : (~brave(X0) & ~humble(X0)) [input p13]
15. ! [X0] : ((~rich(X0) <~> ~humble(X0)) => (brave(X0) & generous(X0))) [input p14]
22. ~humble(fred) [input hypothesis]
26. ? [X0] : (~patient(X0) | ~strong(X0)) => ? [X1] : (~brave(X1) & ~humble(X1)) [rectify 14]
30. ? [X1] : (~brave(X1) & ~humble(X1)) | ! [X0] : (patient(X0) & strong(X0)) [ennf transformation 26]
31. ! [X0] : ((brave(X0) & generous(X0)) | (~rich(X0) <=> ~humble(X0))) [ennf transformation 15]
43. ! [X0] : (((~brave(X0) | ~humble(X0)) | patient(X0)) & (~patient(X0) | (brave(X0) & humble(X0)))) [nnf transformation 6]
44. ! [X0] : ((~brave(X0) | ~humble(X0) | patient(X0)) & (~patient(X0) | (brave(X0) & humble(X0)))) [flattening 43]
48. ! [X0] : (((~rich(X0) & ~brave(X0)) | (generous(X0) | ~brave(X0))) & ((~generous(X0) & brave(X0)) | (rich(X0) | brave(X0)))) [nnf transformation 8]
49. ! [X0] : (((~rich(X0) & ~brave(X0)) | generous(X0) | ~brave(X0)) & ((~generous(X0) & brave(X0)) | rich(X0) | brave(X0))) [flattening 48]
66. ? [X0] : (~brave(X0) & ~humble(X0)) | ! [X1] : (patient(X1) & strong(X1)) [rectify 30]
67. ? [X0] : (~brave(X0) & ~humble(X0)) => (~brave(sK8) & ~humble(sK8)) [choice axiom]
68. (~brave(sK8) & ~humble(sK8)) | ! [X1] : (patient(X1) & strong(X1)) [skolemisation 66,67]
69. ! [X0] : ((brave(X0) & generous(X0)) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0)))) [nnf transformation 31]
101. ~patient(X0) | humble(X0) [cnf transformation 44]
106. brave(X0) | rich(X0) | brave(X0) [cnf transformation 49]
134. ~humble(sK8) | patient(X1) [cnf transformation 68]
136. ~brave(sK8) | patient(X1) [cnf transformation 68]
140. brave(X0) | ~rich(X0) | humble(X0) [cnf transformation 69]
149. ~humble(fred) [cnf transformation 22]
150. brave(X0) | rich(X0) [duplicate literal removal 106]
318. 37 <=> ! [X1] : patient(X1) [avatar definition]
319. patient(X1) <- (37) [avatar component clause 318]
321. 38 <=> brave(sK8) [avatar definition]
323. ~brave(sK8) <- (~38) [avatar component clause 321]
324. 37 | ~38 [avatar split clause 136,321,318]
330. 40 <=> humble(sK8) [avatar definition]
332. ~humble(sK8) <- (~40) [avatar component clause 330]
333. 37 | ~40 [avatar split clause 134,330,318]
335. brave(X0) | humble(X0) [subsumption resolution 140,150]
377. humble(sK8) <- (~38) [resolution 335,323]
379. $false <- (~38, ~40) [subsumption resolution 377,332]
380. 38 | 40 [avatar contradiction clause 379]
383. humble(X1) <- (37) [resolution 319,101]
398. $false <- (37) [resolution 383,149]
403. ~37 [avatar contradiction clause 398]
404. $false [avatar sat refutation 324,333,380,403]
% SZS output end Proof for 3461150433102200145515189
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative or not brave then someone is both kind and not kind and vice versa.
Everyone who is either old or brave is rich or not brave and vice versa.
Everyone who is strong or not tall is both creative and not brave.
Everyone who is calm or quiet is either generous or not curious and vice versa.
If lucy is not strong or generous then alice is not wise and vice versa.
Everyone who is wise or patient is either not generous or brave and vice versa.
Everyone who is not creative is either brave or not curious.
If paul is both brave and not happy then someone is not wise or wise and vice versa.
Everyone who is not tall or not strong is humble and vice versa.
Everyone who is either not funny or not strong is not generous and vice versa.
Everyone who is either humble or not brave is creative or not curious.
If paul is rich or not generous then someone is both not quiet and not calm.
Everyone who is not humble or not kind is either not patient or quiet.
If alice is either not quiet or not creative then someone is both not tall and funny.
If someone is curious or not wise then someone is either not strong or curious.
If lucy is either happy or kind then someone is not humble.
Lucy is both not patient and not strong.
Alice is not tall or not calm.
Paul is both curious and not kind.
Someone is both generous and calm.
Someone is humble.
Lucy is not rich.
Mary is either not humble or not old. | Alice is not rich. | neutral | ((?[X]:((~creative(X)|~brave(X))))<=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((old(X)<~>brave(X))<=>(rich(X)|~brave(X))))&
(![X]:((strong(X)|~tall(X))=>(creative(X)&~brave(X))))&
(![X]:((calm(X)|quiet(X))<=>(generous(X)<~>~curious(X))))&
(((~strong(lucy)|generous(lucy)))<=>(~wise(alice)))&
(![X]:((wise(X)|patient(X))<=>(~generous(X)<~>brave(X))))&
(![X]:(~creative(X)=>(brave(X)<~>~curious(X))))&
(((brave(paul)&~happy(paul)))<=>(?[X]:((~wise(X)|wise(X)))))&
(![X]:((~tall(X)|~strong(X))<=>humble(X)))&
(![X]:((~funny(X)<~>~strong(X))<=>~generous(X)))&
(![X]:((humble(X)<~>~brave(X))=>(creative(X)|~curious(X))))&
(((rich(paul)|~generous(paul)))=>(?[X]:((~quiet(X)&~calm(X)))))&
(![X]:((~humble(X)|~kind(X))=>(~patient(X)<~>quiet(X))))&
(((~quiet(alice)<~>~creative(alice)))=>(?[X]:((~tall(X)&funny(X)))))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:((~strong(X)<~>curious(X)))))&
(((happy(lucy)<~>kind(lucy)))=>(?[X]:(~humble(X))))&
((~patient(lucy)&~strong(lucy)))&
((~tall(alice)|~calm(alice)))&
((curious(paul)&~kind(paul)))&
(?[X]:((generous(X)&calm(X))))&
(?[X]:(humble(X)))&
(~rich(lucy))&
((~humble(mary)<~>~old(mary))) | ~rich(alice) | [] | null | 0 |
Everyone who is either funny or not curious is either not tall or generous and vice versa.
If someone is kind then lucy is tall and vice versa.
Everyone who is both not rich and not generous is wise or not old.
If lucy is both calm and old then someone is either not brave or not old and vice versa.
If someone is either not tall or old then someone is both tall and not rich.
Everyone who is either quiet or rich is not brave or tall.
Everyone who is both not brave and not quiet is both humble and old.
If alice is not humble or calm then someone is tall and vice versa.
Everyone who is either not funny or happy is rich and vice versa.
If someone is both not patient and humble then alice is not rich or not calm.
Everyone who is curious is curious or not wise.
Everyone who is either not humble or curious is both generous and happy and vice versa.
If alice is not quiet or kind then john is either tall or happy and vice versa.
Everyone who is both not brave and tall is either not funny or not strong and vice versa.
If someone is brave then mary is either not funny or not humble and vice versa.
Everyone who is not quiet or quiet is generous or rich and vice versa.
Someone is either tall or strong.
Fred is both wise and rich.
Susan is not happy or calm.
Mary is either not strong or wise.
Mary is both not tall and not generous.
Someone is not curious or calm.
Paul is both funny and calm. | Lucy is tall. | neutral | (![X]:((funny(X)<~>~curious(X))<=>(~tall(X)<~>generous(X))))&
((?[X]:(kind(X)))<=>(tall(lucy)))&
(![X]:((~rich(X)&~generous(X))=>(wise(X)|~old(X))))&
(((calm(lucy)&old(lucy)))<=>(?[X]:((~brave(X)<~>~old(X)))))&
((?[X]:((~tall(X)<~>old(X))))=>(?[X]:((tall(X)&~rich(X)))))&
(![X]:((quiet(X)<~>rich(X))=>(~brave(X)|tall(X))))&
(![X]:((~brave(X)&~quiet(X))=>(humble(X)&old(X))))&
(((~humble(alice)|calm(alice)))<=>(?[X]:(tall(X))))&
(![X]:((~funny(X)<~>happy(X))<=>rich(X)))&
((?[X]:((~patient(X)&humble(X))))=>((~rich(alice)|~calm(alice))))&
(![X]:(curious(X)=>(curious(X)|~wise(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(generous(X)&happy(X))))&
(((~quiet(alice)|kind(alice)))<=>((tall(john)<~>happy(john))))&
(![X]:((~brave(X)&tall(X))<=>(~funny(X)<~>~strong(X))))&
((?[X]:(brave(X)))<=>((~funny(mary)<~>~humble(mary))))&
(![X]:((~quiet(X)|quiet(X))<=>(generous(X)|rich(X))))&
(?[X]:((tall(X)<~>strong(X))))&
((wise(fred)&rich(fred)))&
((~happy(susan)|calm(susan)))&
((~strong(mary)<~>wise(mary)))&
((~tall(mary)&~generous(mary)))&
(?[X]:((~curious(X)|calm(X))))&
((funny(paul)&calm(paul))) | tall(lucy) | [] | null | 0 |
If someone is either creative or old then someone is either not calm or not brave.
Everyone who is both not creative and creative is both wise and not tall and vice versa.
Everyone who is quiet is either happy or not tall.
If someone is both generous and brave then someone is either tall or generous and vice versa.
Everyone who is either tall or not curious is both not tall and patient.
Everyone who is patient is both not rich and curious and vice versa.
Everyone who is not quiet or not kind is either not rich or tall.
If someone is not patient then someone is both funny and not funny.
If lucy is both not old and not quiet then alice is funny or kind.
If john is both not strong and old then susan is either humble or rich.
Everyone who is not kind or kind is both strong and patient and vice versa.
Everyone who is both not brave and patient is either not calm or not patient.
If someone is either old or kind then someone is creative or not generous and vice versa.
Everyone who is either rich or not brave is both quiet and brave and vice versa.
If someone is both not curious and tall then mary is both not old and old and vice versa.
Everyone who is both not calm and not quiet is tall or wise and vice versa.
Someone is not wise.
Someone is either not quiet or not strong.
Someone is not calm or creative.
Mary is both not rich and not happy.
Someone is either not kind or not brave. | Lucy is not quiet. | entailment | ((?[X]:((creative(X)<~>old(X))))=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:((~creative(X)&creative(X))<=>(wise(X)&~tall(X))))&
(![X]:(quiet(X)=>(happy(X)<~>~tall(X))))&
((?[X]:((generous(X)&brave(X))))<=>(?[X]:((tall(X)<~>generous(X)))))&
(![X]:((tall(X)<~>~curious(X))=>(~tall(X)&patient(X))))&
(![X]:(patient(X)<=>(~rich(X)&curious(X))))&
(![X]:((~quiet(X)|~kind(X))=>(~rich(X)<~>tall(X))))&
((?[X]:(~patient(X)))=>(?[X]:((funny(X)&~funny(X)))))&
(((~old(lucy)&~quiet(lucy)))=>((funny(alice)|kind(alice))))&
(((~strong(john)&old(john)))=>((humble(susan)<~>rich(susan))))&
(![X]:((~kind(X)|kind(X))<=>(strong(X)&patient(X))))&
(![X]:((~brave(X)&patient(X))=>(~calm(X)<~>~patient(X))))&
((?[X]:((old(X)<~>kind(X))))<=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:((rich(X)<~>~brave(X))<=>(quiet(X)&brave(X))))&
((?[X]:((~curious(X)&tall(X))))<=>((~old(mary)&old(mary))))&
(![X]:((~calm(X)&~quiet(X))<=>(tall(X)|wise(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~calm(X)|creative(X))))&
((~rich(mary)&~happy(mary)))&
(?[X]:((~kind(X)<~>~brave(X)))) | ~quiet(lucy) | [
"p5",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7084374110789053741357413
% SZS output start Proof for 7084374110789053741357413
6. ! [X0] : (patient(X0) <=> (curious(X0) & ~rich(X0))) [input p5]
11. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (patient(X0) & strong(X0))) [input p10]
14. ! [X0] : ((rich(X0) <~> ~brave(X0)) <=> (brave(X0) & quiet(X0))) [input p13]
22. quiet(lucy) [input hypothesis]
51. ! [X0] : ((patient(X0) | (~curious(X0) | rich(X0))) & ((curious(X0) & ~rich(X0)) | ~patient(X0))) [nnf transformation 6]
52. ! [X0] : ((patient(X0) | ~curious(X0) | rich(X0)) & ((curious(X0) & ~rich(X0)) | ~patient(X0))) [flattening 51]
58. ! [X0] : (((kind(X0) | ~kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 11]
59. ! [X0] : ((kind(X0) | ~kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~kind(X0) & kind(X0)))) [flattening 58]
66. ! [X0] : ((((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | (~brave(X0) | ~quiet(X0))) & ((brave(X0) & quiet(X0)) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0))))) [nnf transformation 14]
67. ! [X0] : ((((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | ~brave(X0) | ~quiet(X0)) & ((brave(X0) & quiet(X0)) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0))))) [flattening 66]
105. ~rich(X0) | ~patient(X0) [cnf transformation 52]
119. patient(X0) | kind(X0) [cnf transformation 59]
120. ~kind(X0) | patient(X0) [cnf transformation 59]
133. brave(X0) | rich(X0) | brave(X0) [cnf transformation 67]
134. ~brave(X0) | rich(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 67]
153. quiet(lucy) [cnf transformation 22]
154. rich(X0) | brave(X0) [duplicate literal removal 133]
155. ~quiet(X0) | rich(X0) | ~brave(X0) [duplicate literal removal 134]
209. 12 <=> ! [X1] : patient(X1) [avatar definition]
210. patient(X1) <- (12) [avatar component clause 209]
222. 15 <=> quiet(lucy) [avatar definition]
224. quiet(lucy) <- (15) [avatar component clause 222]
252. patient(X0) [subsumption resolution 119,120]
253. 12 [avatar split clause 252,209]
321. 15 [avatar split clause 153,222]
329. brave(X0) | ~patient(X0) [resolution 154,105]
330. brave(X0) <- (12) [subsumption resolution 329,210]
346. rich(lucy) | ~brave(lucy) <- (15) [resolution 155,224]
347. rich(lucy) <- (12, 15) [subsumption resolution 346,330]
351. ~patient(lucy) <- (12, 15) [resolution 347,105]
353. $false <- (12, 15) [subsumption resolution 351,210]
354. ~12 | ~15 [avatar contradiction clause 353]
355. $false [avatar sat refutation 253,321,354]
% SZS output end Proof for 7084374110789053741357413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not curious or not funny then mary is funny and vice versa.
Everyone who is either curious or generous is calm.
Everyone who is not wise is both not happy and not patient and vice versa.
If fred is not old or creative then someone is both not patient and not funny and vice versa.
Everyone who is both tall and kind is not patient.
If someone is either not brave or humble then someone is either not brave or kind.
Everyone who is quiet is both not patient and not wise and vice versa.
If paul is both not happy and not rich then someone is strong or not patient and vice versa.
If someone is not creative or old then someone is either old or not strong and vice versa.
If mary is humble then someone is either strong or creative and vice versa.
If alice is both creative and not patient then alice is not humble or not strong.
If someone is creative or not funny then paul is not funny or not creative and vice versa.
Everyone who is either funny or not brave is not rich and vice versa.
Everyone who is not creative or tall is not quiet and vice versa.
Everyone who is not funny or curious is not generous or not patient and vice versa.
Everyone who is both not calm and not tall is both kind and not quiet.
Alice is not happy.
Mary is both not wise and not funny.
Someone is tall or not old.
Fred is not kind or not humble.
Alice is not funny or wise.
Someone is brave or not generous.
Someone is happy or not calm. | Alice is not wise. | neutral | (((~curious(paul)|~funny(paul)))<=>(funny(mary)))&
(![X]:((curious(X)<~>generous(X))=>calm(X)))&
(![X]:(~wise(X)<=>(~happy(X)&~patient(X))))&
(((~old(fred)|creative(fred)))<=>(?[X]:((~patient(X)&~funny(X)))))&
(![X]:((tall(X)&kind(X))=>~patient(X)))&
((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:((~brave(X)<~>kind(X)))))&
(![X]:(quiet(X)<=>(~patient(X)&~wise(X))))&
(((~happy(paul)&~rich(paul)))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((~creative(X)|old(X))))<=>(?[X]:((old(X)<~>~strong(X)))))&
((humble(mary))<=>(?[X]:((strong(X)<~>creative(X)))))&
(((creative(alice)&~patient(alice)))=>((~humble(alice)|~strong(alice))))&
((?[X]:((creative(X)|~funny(X))))<=>((~funny(paul)|~creative(paul))))&
(![X]:((funny(X)<~>~brave(X))<=>~rich(X)))&
(![X]:((~creative(X)|tall(X))<=>~quiet(X)))&
(![X]:((~funny(X)|curious(X))<=>(~generous(X)|~patient(X))))&
(![X]:((~calm(X)&~tall(X))=>(kind(X)&~quiet(X))))&
(~happy(alice))&
((~wise(mary)&~funny(mary)))&
(?[X]:((tall(X)|~old(X))))&
((~kind(fred)|~humble(fred)))&
((~funny(alice)|wise(alice)))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:((happy(X)|~calm(X)))) | ~wise(alice) | [] | null | 0 |
If someone is not happy then someone is funny and vice versa.
Everyone who is not brave or not kind is not generous.
If someone is both wise and not funny then john is not happy or calm and vice versa.
Everyone who is either generous or not curious is not curious or happy.
Everyone who is either not wise or patient is not patient or not humble and vice versa.
If someone is not funny or not humble then paul is not generous and vice versa.
If someone is not wise then someone is not humble and vice versa.
If paul is either curious or happy then someone is wise or not old.
Everyone who is both patient and funny is both not patient and not quiet and vice versa.
If someone is kind then someone is not kind and vice versa.
If someone is not wise then susan is either kind or rich.
If lucy is both not creative and strong then someone is both not creative and not calm and vice versa.
Everyone who is strong or not curious is both not strong and not rich.
Everyone who is not kind or not quiet is tall and vice versa.
If paul is both not brave and rich then someone is either not rich or curious and vice versa.
Everyone who is creative is either not old or funny and vice versa.
Someone is either not calm or not quiet.
John is either curious or not humble.
Someone is either not rich or generous.
Alice is generous.
Mary is not kind.
Someone is either not patient or not kind.
Lucy is wise.
Fred is either creative or old. | Paul is generous. | contradiction | ((?[X]:(~happy(X)))<=>(?[X]:(funny(X))))&
(![X]:((~brave(X)|~kind(X))=>~generous(X)))&
((?[X]:((wise(X)&~funny(X))))<=>((~happy(john)|calm(john))))&
(![X]:((generous(X)<~>~curious(X))=>(~curious(X)|happy(X))))&
(![X]:((~wise(X)<~>patient(X))<=>(~patient(X)|~humble(X))))&
((?[X]:((~funny(X)|~humble(X))))<=>(~generous(paul)))&
((?[X]:(~wise(X)))<=>(?[X]:(~humble(X))))&
(((curious(paul)<~>happy(paul)))=>(?[X]:((wise(X)|~old(X)))))&
(![X]:((patient(X)&funny(X))<=>(~patient(X)&~quiet(X))))&
((?[X]:(kind(X)))<=>(?[X]:(~kind(X))))&
((?[X]:(~wise(X)))=>((kind(susan)<~>rich(susan))))&
(((~creative(lucy)&strong(lucy)))<=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((strong(X)|~curious(X))=>(~strong(X)&~rich(X))))&
(![X]:((~kind(X)|~quiet(X))<=>tall(X)))&
(((~brave(paul)&rich(paul)))<=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:(creative(X)<=>(~old(X)<~>funny(X))))&
(?[X]:((~calm(X)<~>~quiet(X))))&
((curious(john)<~>~humble(john)))&
(?[X]:((~rich(X)<~>generous(X))))&
(generous(alice))&
(~kind(mary))&
(?[X]:((~patient(X)<~>~kind(X))))&
(wise(lucy))&
((creative(fred)<~>old(fred))) | generous(paul) | [
"p4",
"p5",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5731846459106636347586930
% SZS output start Proof for 5731846459106636347586930
5. ! [X0] : ((~wise(X0) <~> patient(X0)) <=> (~humble(X0) | ~patient(X0))) [input p4]
6. ? [X0] : (~humble(X0) | ~funny(X0)) <=> ~generous(paul) [input p5]
9. ! [X0] : ((funny(X0) & patient(X0)) <=> (~quiet(X0) & ~patient(X0))) [input p8]
23. wise(lucy) [input p22]
25. generous(paul) [input hypothesis]
46. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | (humble(X0) & patient(X0))) & ((~humble(X0) | ~patient(X0)) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [nnf transformation 5]
47. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | (humble(X0) & patient(X0))) & (~humble(X0) | ~patient(X0) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [flattening 46]
48. (? [X0] : (~humble(X0) | ~funny(X0)) | generous(paul)) & (~generous(paul) | ! [X0] : (humble(X0) & funny(X0))) [nnf transformation 6]
49. (? [X0] : (~humble(X0) | ~funny(X0)) | generous(paul)) & (~generous(paul) | ! [X1] : (humble(X1) & funny(X1))) [rectify 48]
50. ? [X0] : (~humble(X0) | ~funny(X0)) => (~humble(sK3) | ~funny(sK3)) [choice axiom]
51. ((~humble(sK3) | ~funny(sK3)) | generous(paul)) & (~generous(paul) | ! [X1] : (humble(X1) & funny(X1))) [skolemisation 49,50]
60. ! [X0] : (((funny(X0) & patient(X0)) | (quiet(X0) | patient(X0))) & ((~quiet(X0) & ~patient(X0)) | (~funny(X0) | ~patient(X0)))) [nnf transformation 9]
61. ! [X0] : (((funny(X0) & patient(X0)) | quiet(X0) | patient(X0)) & ((~quiet(X0) & ~patient(X0)) | ~funny(X0) | ~patient(X0))) [flattening 60]
103. patient(X0) | ~wise(X0) | patient(X0) [cnf transformation 47]
107. ~generous(paul) | funny(X1) [cnf transformation 51]
114. ~patient(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 61]
150. wise(lucy) [cnf transformation 23]
153. generous(paul) [cnf transformation 25]
155. ~patient(X0) | ~funny(X0) [duplicate literal removal 114]
158. ~wise(X0) | patient(X0) [duplicate literal removal 103]
202. 10 <=> generous(paul) [avatar definition]
219. 14 <=> ! [X1] : funny(X1) [avatar definition]
220. funny(X1) <- (14) [avatar component clause 219]
221. 14 | ~10 [avatar split clause 107,202,219]
383. 10 [avatar split clause 153,202]
410. patient(lucy) [resolution 158,150]
412. ~funny(lucy) [resolution 410,155]
413. $false <- (14) [subsumption resolution 412,220]
414. ~14 [avatar contradiction clause 413]
415. $false [avatar sat refutation 221,383,414]
% SZS output end Proof for 5731846459106636347586930
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then someone is either not funny or not tall. Everyone who is rich is curious or calm and vice versa. Everyone who is either funny or not kind is creative or strong and vice versa. Everyone who is funny is humble. Everyone who is either curious or patient is both not old and rich and vice versa. Everyone who is strong is calm and vice versa. Everyone who is patient is quiet or humble and vice versa. If paul is tall or not generous then someone is generous or not kind. Everyone who is not funny is both not tall and quiet and vice versa. Everyone who is both not rich and quiet is either strong or old. Everyone who is not quiet or kind is both rich and brave. If susan is generous or not creative then paul is either strong or not humble. If alice is either not curious or kind then someone is not calm or brave and vice versa. If john is quiet or tall then someone is both strong and not patient and vice versa. Everyone who is either rich or creative is not humble. Everyone who is not rich or brave is either not quiet or not generous. Someone is not humble or happy. Someone is both humble and not tall. Someone is not quiet or kind. Susan is curious or calm. Someone is either not curious or wise. Lucy is not wise. Someone is both not old and not curious. Mary is generous. | Alice is not rich. | contradiction | ((?[X]:(happy(X)))=>(?[X]:((~funny(X)<~>~tall(X)))))&
(![X]:(rich(X)<=>(curious(X)|calm(X))))&
(![X]:((funny(X)<~>~kind(X))<=>(creative(X)|strong(X))))&
(![X]:(funny(X)=>humble(X)))&
(![X]:((curious(X)<~>patient(X))<=>(~old(X)&rich(X))))&
(![X]:(strong(X)<=>calm(X)))&
(![X]:(patient(X)<=>(quiet(X)|humble(X))))&
(((tall(paul)|~generous(paul)))=>(?[X]:((generous(X)|~kind(X)))))&
(![X]:(~funny(X)<=>(~tall(X)&quiet(X))))&
(![X]:((~rich(X)&quiet(X))=>(strong(X)<~>old(X))))&
(![X]:((~quiet(X)|kind(X))=>(rich(X)&brave(X))))&
(((generous(susan)|~creative(susan)))=>((strong(paul)<~>~humble(paul))))&
(((~curious(alice)<~>kind(alice)))<=>(?[X]:((~calm(X)|brave(X)))))&
(((quiet(john)|tall(john)))<=>(?[X]:((strong(X)&~patient(X)))))&
(![X]:((rich(X)<~>creative(X))=>~humble(X)))&
(![X]:((~rich(X)|brave(X))=>(~quiet(X)<~>~generous(X))))&
(?[X]:((~humble(X)|happy(X))))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:((~quiet(X)|kind(X))))&
((curious(susan)|calm(susan)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~wise(lucy))&
(?[X]:((~old(X)&~curious(X))))&
(generous(mary)) | ~rich(alice) | [
"p1",
"p4",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6602111357338138469820606
% SZS output start Proof for 6602111357338138469820606
2. ! [X0] : (rich(X0) <=> (calm(X0) | curious(X0))) [input p1]
5. ! [X0] : ((curious(X0) <~> patient(X0)) <=> (rich(X0) & ~old(X0))) [input p4]
7. ! [X0] : (patient(X0) <=> (humble(X0) | quiet(X0))) [input p6]
11. ! [X0] : ((kind(X0) | ~quiet(X0)) => (brave(X0) & rich(X0))) [input p10]
25. ~rich(alice) [input hypothesis]
32. ! [X0] : ((brave(X0) & rich(X0)) | (~kind(X0) & quiet(X0))) [ennf transformation 11]
40. ! [X0] : ((rich(X0) | (~calm(X0) & ~curious(X0))) & ((calm(X0) | curious(X0)) | ~rich(X0))) [nnf transformation 2]
41. ! [X0] : ((rich(X0) | (~calm(X0) & ~curious(X0))) & (calm(X0) | curious(X0) | ~rich(X0))) [flattening 40]
44. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (~rich(X0) | old(X0))) & ((rich(X0) & ~old(X0)) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 5]
45. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | ~rich(X0) | old(X0)) & ((rich(X0) & ~old(X0)) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [flattening 44]
47. ! [X0] : ((patient(X0) | (~humble(X0) & ~quiet(X0))) & ((humble(X0) | quiet(X0)) | ~patient(X0))) [nnf transformation 7]
48. ! [X0] : ((patient(X0) | (~humble(X0) & ~quiet(X0))) & (humble(X0) | quiet(X0) | ~patient(X0))) [flattening 47]
80. ~curious(X0) | rich(X0) [cnf transformation 41]
92. rich(X0) | curious(X0) | ~patient(X0) [cnf transformation 45]
98. ~quiet(X0) | patient(X0) [cnf transformation 48]
107. quiet(X0) | rich(X0) [cnf transformation 32]
143. ~rich(alice) [cnf transformation 25]
158. rich(X0) | ~patient(X0) [subsumption resolution 92,80]
298. rich(X0) | patient(X0) [resolution 107,98]
299. rich(X0) [subsumption resolution 298,158]
301. $false [resolution 299,143]
% SZS output end Proof for 6602111357338138469820606
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not generous then lucy is not happy or rich.
Everyone who is not quiet or rich is patient.
Everyone who is both not old and happy is both not wise and patient and vice versa.
If john is either not happy or creative then someone is not brave or not tall.
Everyone who is either not funny or not creative is either not brave or wise and vice versa.
If someone is rich or wise then someone is either not brave or not wise and vice versa.
If john is not curious then someone is wise.
If mary is both humble and kind then someone is quiet and vice versa.
Everyone who is both not quiet and not old is either old or not wise and vice versa.
Everyone who is strong or rich is kind.
Everyone who is rich or not curious is both not wise and calm.
Everyone who is both curious and kind is either not rich or brave and vice versa.
Everyone who is patient is not brave and vice versa.
If mary is kind or humble then someone is either happy or wise.
If lucy is not generous or strong then someone is both creative and curious.
If alice is both not funny and not curious then susan is generous or not quiet.
Someone is not rich.
Someone is strong.
Mary is not humble.
John is either not happy or calm.
Someone is funny.
Lucy is brave or tall.
Paul is either humble or not strong. | Susan is not curious. | contradiction | ((~generous(paul))=>((~happy(lucy)|rich(lucy))))&
(![X]:((~quiet(X)|rich(X))=>patient(X)))&
(![X]:((~old(X)&happy(X))<=>(~wise(X)&patient(X))))&
(((~happy(john)<~>creative(john)))=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~funny(X)<~>~creative(X))<=>(~brave(X)<~>wise(X))))&
((?[X]:((rich(X)|wise(X))))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((~curious(john))=>(?[X]:(wise(X))))&
(((humble(mary)&kind(mary)))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&~old(X))<=>(old(X)<~>~wise(X))))&
(![X]:((strong(X)|rich(X))=>kind(X)))&
(![X]:((rich(X)|~curious(X))=>(~wise(X)&calm(X))))&
(![X]:((curious(X)&kind(X))<=>(~rich(X)<~>brave(X))))&
(![X]:(patient(X)<=>~brave(X)))&
(((kind(mary)|humble(mary)))=>(?[X]:((happy(X)<~>wise(X)))))&
(((~generous(lucy)|strong(lucy)))=>(?[X]:((creative(X)&curious(X)))))&
(((~funny(alice)&~curious(alice)))=>((generous(susan)|~quiet(susan))))&
(?[X]:(~rich(X)))&
(?[X]:(strong(X)))&
(~humble(mary))&
((~happy(john)<~>calm(john)))&
(?[X]:(funny(X)))&
((brave(lucy)|tall(lucy)))&
((humble(paul)<~>~strong(paul))) | ~curious(susan) | [
"p1",
"p5",
"p7",
"p8",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 929106447421028745569053
% SZS output start Proof for 929106447421028745569053
2. ! [X0] : ((rich(X0) | ~quiet(X0)) => patient(X0)) [input p1]
6. ? [X0] : (wise(X0) | rich(X0)) <=> ? [X0] : (~brave(X0) <~> ~wise(X0)) [input p5]
8. (kind(mary) & humble(mary)) <=> ? [X0] : quiet(X0) [input p7]
9. ! [X0] : ((~old(X0) & ~quiet(X0)) <=> (old(X0) <~> ~wise(X0))) [input p8]
12. ! [X0] : ((kind(X0) & curious(X0)) <=> (~rich(X0) <~> brave(X0))) [input p11]
13. ! [X0] : (patient(X0) <=> ~brave(X0)) [input p12]
19. ~humble(mary) [input p18]
24. ~curious(susan) [input hypothesis]
25. ? [X0] : (wise(X0) | rich(X0)) <=> ? [X1] : (~brave(X1) <~> ~wise(X1)) [rectify 6]
29. ! [X0] : (patient(X0) | (~rich(X0) & quiet(X0))) [ennf transformation 2]
42. (? [X0] : (wise(X0) | rich(X0)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (? [X1] : ((wise(X1) | brave(X1)) & (~wise(X1) | ~brave(X1))) | ! [X0] : (~wise(X0) & ~rich(X0))) [nnf transformation 25]
43. (? [X0] : (wise(X0) | rich(X0)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (? [X2] : ((wise(X2) | brave(X2)) & (~wise(X2) | ~brave(X2))) | ! [X3] : (~wise(X3) & ~rich(X3))) [rectify 42]
44. ? [X0] : (wise(X0) | rich(X0)) => (wise(sK1) | rich(sK1)) [choice axiom]
45. ? [X2] : ((wise(X2) | brave(X2)) & (~wise(X2) | ~brave(X2))) => ((wise(sK2) | brave(sK2)) & (~wise(sK2) | ~brave(sK2))) [choice axiom]
46. ((wise(sK1) | rich(sK1)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (((wise(sK2) | brave(sK2)) & (~wise(sK2) | ~brave(sK2))) | ! [X3] : (~wise(X3) & ~rich(X3))) [skolemisation 43,45,44]
49. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | (~kind(mary) | ~humble(mary))) [nnf transformation 8]
50. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | ~kind(mary) | ~humble(mary)) [flattening 49]
51. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | ~kind(mary) | ~humble(mary)) [rectify 50]
52. ? [X1] : quiet(X1) => quiet(sK4) [choice axiom]
53. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (quiet(sK4) | ~kind(mary) | ~humble(mary)) [skolemisation 51,52]
54. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | (old(X0) | quiet(X0)))) [nnf transformation 9]
55. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | old(X0) | quiet(X0))) [flattening 54]
56. ! [X0] : (((kind(X0) & curious(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~kind(X0) | ~curious(X0)))) [nnf transformation 12]
57. ! [X0] : (((kind(X0) & curious(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~kind(X0) | ~curious(X0))) [flattening 56]
58. ! [X0] : ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))) [nnf transformation 13]
72. patient(X0) | quiet(X0) [cnf transformation 29]
90. wise(sK2) | brave(sK2) | ~rich(X3) [cnf transformation 46]
91. wise(sK2) | brave(sK2) | ~wise(X3) [cnf transformation 46]
93. wise(sK1) | rich(sK1) | ~brave(X1) | wise(X1) [cnf transformation 46]
96. humble(mary) | ~quiet(X0) [cnf transformation 53]
98. ~wise(X0) | old(X0) | old(X0) | quiet(X0) [cnf transformation 55]
102. ~old(X0) | ~wise(X0) | ~old(X0) [cnf transformation 55]
112. curious(X0) | brave(X0) | rich(X0) [cnf transformation 57]
116. ~brave(X0) | ~patient(X0) [cnf transformation 58]
126. ~humble(mary) [cnf transformation 19]
133. ~curious(susan) [cnf transformation 24]
134. ~wise(X0) | old(X0) | quiet(X0) [duplicate literal removal 98]
135. ~wise(X0) | ~old(X0) [duplicate literal removal 102]
155. 5 <=> ! [X1] : (~brave(X1) | wise(X1)) [avatar definition]
156. ~brave(X1) | wise(X1) <- (5) [avatar component clause 155]
158. 6 <=> rich(sK1) [avatar definition]
160. rich(sK1) <- (6) [avatar component clause 158]
162. 7 <=> wise(sK1) [avatar definition]
164. wise(sK1) <- (7) [avatar component clause 162]
165. 5 | 6 | 7 [avatar split clause 93,162,158,155]
171. 9 <=> ! [X3] : ~wise(X3) [avatar definition]
172. ~wise(X3) <- (9) [avatar component clause 171]
174. 10 <=> brave(sK2) [avatar definition]
176. brave(sK2) <- (10) [avatar component clause 174]
178. 11 <=> wise(sK2) [avatar definition]
180. wise(sK2) <- (11) [avatar component clause 178]
181. 9 | 10 | 11 [avatar split clause 91,178,174,171]
183. 12 <=> ! [X3] : ~rich(X3) [avatar definition]
184. ~rich(X3) <- (12) [avatar component clause 183]
185. 12 | 10 | 11 [avatar split clause 90,178,174,183]
198. 15 <=> ! [X0] : ~quiet(X0) [avatar definition]
199. ~quiet(X0) <- (15) [avatar component clause 198]
206. 17 <=> humble(mary) [avatar definition]
209. 15 | 17 [avatar split clause 96,206,198]
215. ~wise(X0) | quiet(X0) [subsumption resolution 134,135]
244. ~17 [avatar split clause 126,206]
275. ~patient(sK2) <- (10) [resolution 116,176]
278. quiet(sK2) <- (10) [resolution 275,72]
279. $false <- (10, 15) [subsumption resolution 278,199]
280. ~10 | ~15 [avatar contradiction clause 279]
289. quiet(sK2) <- (11) [resolution 215,180]
290. $false <- (11, 15) [subsumption resolution 289,199]
291. ~11 | ~15 [avatar contradiction clause 290]
292. $false <- (6, 12) [resolution 184,160]
293. ~6 | ~12 [avatar contradiction clause 292]
294. $false <- (7, 9) [subsumption resolution 164,172]
295. ~7 | ~9 [avatar contradiction clause 294]
296. ~brave(X1) <- (5, 9) [subsumption resolution 156,172]
310. brave(susan) | rich(susan) [resolution 112,133]
311. rich(susan) <- (5, 9) [subsumption resolution 310,296]
312. $false <- (5, 9, 12) [subsumption resolution 311,184]
313. ~5 | ~9 | ~12 [avatar contradiction clause 312]
314. $false [avatar sat refutation 165,181,185,209,244,280,291,293,295,313]
% SZS output end Proof for 929106447421028745569053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not old then paul is either calm or not tall. Everyone who is not creative or not old is either funny or not old and vice versa. Everyone who is both not curious and not funny is both creative and not quiet. If john is either not tall or rich then alice is not rich and vice versa. Everyone who is old is not tall. Everyone who is wise or quiet is not rich. Everyone who is either kind or generous is both tall and curious. If someone is either creative or quiet then someone is both old and tall and vice versa. If someone is not humble or wise then someone is both calm and quiet and vice versa. If susan is funny then alice is humble. If someone is both not quiet and not patient then someone is not wise. If someone is kind or not old then susan is both patient and not quiet. Everyone who is kind or not funny is both funny and tall. Everyone who is not strong or happy is both not calm and not rich and vice versa. Everyone who is either not wise or not brave is not curious. Someone is either not humble or strong. Someone is not wise. Someone is brave or not brave. Mary is not curious or tall. Someone is not quiet or not curious. Someone is not happy. Someone is not strong or brave. | Susan is wise. | contradiction | ((~old(fred))=>((calm(paul)<~>~tall(paul))))&
(![X]:((~creative(X)|~old(X))<=>(funny(X)<~>~old(X))))&
(![X]:((~curious(X)&~funny(X))=>(creative(X)&~quiet(X))))&
(((~tall(john)<~>rich(john)))<=>(~rich(alice)))&
(![X]:(old(X)=>~tall(X)))&
(![X]:((wise(X)|quiet(X))=>~rich(X)))&
(![X]:((kind(X)<~>generous(X))=>(tall(X)&curious(X))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:((calm(X)&quiet(X)))))&
((funny(susan))=>(humble(alice)))&
((?[X]:((~quiet(X)&~patient(X))))=>(?[X]:(~wise(X))))&
((?[X]:((kind(X)|~old(X))))=>((patient(susan)&~quiet(susan))))&
(![X]:((kind(X)|~funny(X))=>(funny(X)&tall(X))))&
(![X]:((~strong(X)|happy(X))<=>(~calm(X)&~rich(X))))&
(![X]:((~wise(X)<~>~brave(X))=>~curious(X)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)|~brave(X))))&
((~curious(mary)|tall(mary)))&
(?[X]:((~quiet(X)|~curious(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~strong(X)|brave(X)))) | wise(susan) | [
"p1",
"p4",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3632476880582571939308518
% SZS output start Proof for 3632476880582571939308518
2. ! [X0] : ((~old(X0) | ~creative(X0)) <=> (funny(X0) <~> ~old(X0))) [input p1]
5. ! [X0] : (old(X0) => ~tall(X0)) [input p4]
8. ? [X0] : (creative(X0) <~> quiet(X0)) <=> ? [X0] : (tall(X0) & old(X0)) [input p7]
9. ? [X0] : (wise(X0) | ~humble(X0)) <=> ? [X0] : (quiet(X0) & calm(X0)) [input p8]
13. ! [X0] : ((~funny(X0) | kind(X0)) => (tall(X0) & funny(X0))) [input p12]
23. wise(susan) [input hypothesis]
24. ? [X0] : (creative(X0) <~> quiet(X0)) <=> ? [X1] : (tall(X1) & old(X1)) [rectify 8]
25. ? [X0] : (wise(X0) | ~humble(X0)) <=> ? [X1] : (quiet(X1) & calm(X1)) [rectify 9]
32. ! [X0] : (~tall(X0) | ~old(X0)) [ennf transformation 5]
37. ! [X0] : ((tall(X0) & funny(X0)) | (funny(X0) & ~kind(X0))) [ennf transformation 13]
40. ! [X0] : (((~old(X0) | ~creative(X0)) | ((funny(X0) | old(X0)) & (~old(X0) | ~funny(X0)))) & (((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) | (old(X0) & creative(X0)))) [nnf transformation 2]
41. ! [X0] : ((~old(X0) | ~creative(X0) | ((funny(X0) | old(X0)) & (~old(X0) | ~funny(X0)))) & (((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) | (old(X0) & creative(X0)))) [flattening 40]
44. (? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ! [X1] : (~tall(X1) | ~old(X1))) & (? [X1] : (tall(X1) & old(X1)) | ! [X0] : ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0)))) [nnf transformation 24]
45. (? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ! [X1] : (~tall(X1) | ~old(X1))) & (? [X2] : (tall(X2) & old(X2)) | ! [X3] : ((creative(X3) | ~quiet(X3)) & (quiet(X3) | ~creative(X3)))) [rectify 44]
46. ? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) => ((~quiet(sK0) | ~creative(sK0)) & (quiet(sK0) | creative(sK0))) [choice axiom]
47. ? [X2] : (tall(X2) & old(X2)) => (tall(sK1) & old(sK1)) [choice axiom]
48. (((~quiet(sK0) | ~creative(sK0)) & (quiet(sK0) | creative(sK0))) | ! [X1] : (~tall(X1) | ~old(X1))) & ((tall(sK1) & old(sK1)) | ! [X3] : ((creative(X3) | ~quiet(X3)) & (quiet(X3) | ~creative(X3)))) [skolemisation 45,47,46]
49. (? [X0] : (wise(X0) | ~humble(X0)) | ! [X1] : (~quiet(X1) | ~calm(X1))) & (? [X1] : (quiet(X1) & calm(X1)) | ! [X0] : (~wise(X0) & humble(X0))) [nnf transformation 25]
50. (? [X0] : (wise(X0) | ~humble(X0)) | ! [X1] : (~quiet(X1) | ~calm(X1))) & (? [X2] : (quiet(X2) & calm(X2)) | ! [X3] : (~wise(X3) & humble(X3))) [rectify 49]
51. ? [X0] : (wise(X0) | ~humble(X0)) => (wise(sK2) | ~humble(sK2)) [choice axiom]
52. ? [X2] : (quiet(X2) & calm(X2)) => (quiet(sK3) & calm(sK3)) [choice axiom]
53. ((wise(sK2) | ~humble(sK2)) | ! [X1] : (~quiet(X1) | ~calm(X1))) & ((quiet(sK3) & calm(sK3)) | ! [X3] : (~wise(X3) & humble(X3))) [skolemisation 50,52,51]
75. old(X0) | ~funny(X0) | old(X0) [cnf transformation 41]
76. ~old(X0) | ~creative(X0) | ~old(X0) | ~funny(X0) [cnf transformation 41]
84. ~tall(X0) | ~old(X0) [cnf transformation 32]
94. tall(sK1) | creative(X3) | ~quiet(X3) [cnf transformation 48]
100. quiet(sK3) | ~wise(X3) [cnf transformation 53]
106. funny(X0) | funny(X0) [cnf transformation 37]
124. wise(susan) [cnf transformation 23]
125. funny(X0) [duplicate literal removal 106]
126. ~funny(X0) | old(X0) [duplicate literal removal 75]
127. ~funny(X0) | ~creative(X0) | ~old(X0) [duplicate literal removal 76]
159. 7 <=> ! [X3] : (creative(X3) | ~quiet(X3)) [avatar definition]
160. ~quiet(X3) | creative(X3) <- (7) [avatar component clause 159]
162. 8 <=> tall(sK1) [avatar definition]
164. tall(sK1) <- (8) [avatar component clause 162]
165. 7 | 8 [avatar split clause 94,162,159]
189. 14 <=> ! [X3] : ~wise(X3) [avatar definition]
190. ~wise(X3) <- (14) [avatar component clause 189]
192. 15 <=> quiet(sK3) [avatar definition]
194. quiet(sK3) <- (15) [avatar component clause 192]
195. 14 | 15 [avatar split clause 100,192,189]
216. 20 <=> ! [X0] : old(X0) [avatar definition]
217. old(X0) <- (20) [avatar component clause 216]
268. $false <- (14) [resolution 190,124]
269. ~14 [avatar contradiction clause 268]
275. old(X1) [resolution 126,125]
276. 20 [avatar split clause 275,216]
277. creative(sK3) <- (7, 15) [resolution 160,194]
299. ~creative(X1) | ~old(X1) [resolution 127,125]
301. ~creative(X1) <- (20) [subsumption resolution 299,217]
304. $false <- (7, 15, 20) [resolution 301,277]
305. ~7 | ~15 | ~20 [avatar contradiction clause 304]
306. ~old(sK1) <- (8) [resolution 164,84]
307. $false <- (8, 20) [subsumption resolution 306,217]
308. ~8 | ~20 [avatar contradiction clause 307]
309. $false [avatar sat refutation 165,195,269,276,305,308]
% SZS output end Proof for 3632476880582571939308518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not funny or not calm then mary is either not rich or curious and vice versa.
Everyone who is either creative or funny is not funny or patient and vice versa.
Everyone who is tall is brave and vice versa.
Everyone who is not brave or not wise is either not calm or tall and vice versa.
If john is not kind then mary is not funny or humble.
If someone is both not patient and curious then john is not calm.
Everyone who is rich is both not humble and calm and vice versa.
Everyone who is not kind is either not curious or funny and vice versa.
Everyone who is not brave or not creative is not old or not quiet.
Everyone who is not strong is not curious.
Everyone who is both not strong and not rich is not happy and vice versa.
Everyone who is not calm is both not kind and curious.
If someone is both curious and not humble then paul is generous or calm.
Everyone who is either creative or not generous is not quiet and vice versa.
If someone is not funny then someone is not strong or curious.
If mary is curious or not generous then alice is generous.
Someone is not creative or old.
Paul is not curious.
Someone is both creative and not happy.
Lucy is not calm.
Susan is not calm.
Mary is either not quiet or not strong.
Someone is either creative or not old.
Someone is either calm or not curious. | Paul is not tall. | contradiction | (((~funny(paul)|~calm(paul)))<=>((~rich(mary)<~>curious(mary))))&
(![X]:((creative(X)<~>funny(X))<=>(~funny(X)|patient(X))))&
(![X]:(tall(X)<=>brave(X)))&
(![X]:((~brave(X)|~wise(X))<=>(~calm(X)<~>tall(X))))&
((~kind(john))=>((~funny(mary)|humble(mary))))&
((?[X]:((~patient(X)&curious(X))))=>(~calm(john)))&
(![X]:(rich(X)<=>(~humble(X)&calm(X))))&
(![X]:(~kind(X)<=>(~curious(X)<~>funny(X))))&
(![X]:((~brave(X)|~creative(X))=>(~old(X)|~quiet(X))))&
(![X]:(~strong(X)=>~curious(X)))&
(![X]:((~strong(X)&~rich(X))<=>~happy(X)))&
(![X]:(~calm(X)=>(~kind(X)&curious(X))))&
((?[X]:((curious(X)&~humble(X))))=>((generous(paul)|calm(paul))))&
(![X]:((creative(X)<~>~generous(X))<=>~quiet(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~strong(X)|curious(X)))))&
(((curious(mary)|~generous(mary)))=>(generous(alice)))&
(?[X]:((~creative(X)|old(X))))&
(~curious(paul))&
(?[X]:((creative(X)&~happy(X))))&
(~calm(lucy))&
(~calm(susan))&
((~quiet(mary)<~>~strong(mary)))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:((calm(X)<~>~curious(X)))) | ~tall(paul) | [
"p2",
"p3",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1911016721082561504133165
% SZS output start Proof for 1911016721082561504133165
3. ! [X0] : (tall(X0) <=> brave(X0)) [input p2]
4. ! [X0] : ((~wise(X0) | ~brave(X0)) <=> (~calm(X0) <~> tall(X0))) [input p3]
12. ! [X0] : (~calm(X0) => (curious(X0) & ~kind(X0))) [input p11]
18. ~curious(paul) [input p17]
25. ~tall(paul) [input hypothesis]
35. ! [X0] : ((curious(X0) & ~kind(X0)) | calm(X0)) [ennf transformation 12]
44. ! [X0] : ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))) [nnf transformation 3]
45. ! [X0] : (((~wise(X0) | ~brave(X0)) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0)))) & (((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | (wise(X0) & brave(X0)))) [nnf transformation 4]
46. ! [X0] : ((~wise(X0) | ~brave(X0) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0)))) & (((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | (wise(X0) & brave(X0)))) [flattening 45]
77. ~tall(X0) | brave(X0) [cnf transformation 44]
78. ~brave(X0) | tall(X0) [cnf transformation 44]
79. tall(X0) | ~calm(X0) | brave(X0) [cnf transformation 46]
100. curious(X0) | calm(X0) [cnf transformation 35]
110. ~curious(paul) [cnf transformation 18]
121. ~tall(paul) [cnf transformation 25]
137. 4 <=> calm(paul) [avatar definition]
138. calm(paul) <- (4) [avatar component clause 137]
148. ~calm(X0) | brave(X0) [subsumption resolution 79,77]
233. calm(paul) [resolution 100,110]
238. brave(paul) <- (4) [resolution 148,138]
241. tall(paul) <- (4) [resolution 238,78]
242. $false <- (4) [subsumption resolution 241,121]
243. ~4 [avatar contradiction clause 242]
244. 4 [avatar split clause 233,137]
245. $false [avatar sat refutation 243,244]
% SZS output end Proof for 1911016721082561504133165
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or brave is both not curious and not rich and vice versa.
Everyone who is either not old or funny is not brave and vice versa.
Everyone who is not funny or old is both generous and creative.
If john is either calm or not strong then alice is funny.
Everyone who is not old is both not quiet and not generous and vice versa.
Everyone who is either wise or curious is not brave or not strong and vice versa.
Everyone who is generous is either kind or patient.
Everyone who is both not generous and not tall is wise or not old and vice versa.
Everyone who is curious is both humble and not rich.
If mary is old or not funny then susan is either not wise or happy and vice versa.
Everyone who is not kind or not strong is rich and vice versa.
If alice is not wise or calm then mary is both not calm and not funny and vice versa.
Everyone who is either not generous or wise is kind and vice versa.
If susan is both not humble and creative then fred is not humble or generous.
If paul is both quiet and rich then lucy is generous or rich.
Someone is quiet or funny.
Someone is strong or wise.
Lucy is both not strong and not humble.
Someone is humble. | Fred is rich. | neutral | (![X]:((~creative(X)<~>brave(X))<=>(~curious(X)&~rich(X))))&
(![X]:((~old(X)<~>funny(X))<=>~brave(X)))&
(![X]:((~funny(X)|old(X))=>(generous(X)&creative(X))))&
(((calm(john)<~>~strong(john)))=>(funny(alice)))&
(![X]:(~old(X)<=>(~quiet(X)&~generous(X))))&
(![X]:((wise(X)<~>curious(X))<=>(~brave(X)|~strong(X))))&
(![X]:(generous(X)=>(kind(X)<~>patient(X))))&
(![X]:((~generous(X)&~tall(X))<=>(wise(X)|~old(X))))&
(![X]:(curious(X)=>(humble(X)&~rich(X))))&
(((old(mary)|~funny(mary)))<=>((~wise(susan)<~>happy(susan))))&
(![X]:((~kind(X)|~strong(X))<=>rich(X)))&
(((~wise(alice)|calm(alice)))<=>((~calm(mary)&~funny(mary))))&
(![X]:((~generous(X)<~>wise(X))<=>kind(X)))&
(((~humble(susan)&creative(susan)))=>((~humble(fred)|generous(fred))))&
(((quiet(paul)&rich(paul)))=>((generous(lucy)|rich(lucy))))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:((strong(X)|wise(X))))&
((~strong(lucy)&~humble(lucy)))&
(?[X]:(humble(X))) | rich(fred) | [] | null | 0 |
If someone is not humble then someone is old.
Everyone who is not wise or not generous is happy.
If susan is either funny or happy then susan is not quiet and vice versa.
Everyone who is either curious or not tall is both humble and not kind and vice versa.
Everyone who is either humble or old is not quiet and vice versa.
Everyone who is either not old or tall is not tall and vice versa.
Everyone who is both happy and not happy is patient or happy and vice versa.
If susan is not happy then fred is curious or calm.
Everyone who is not quiet is both curious and not brave and vice versa.
If alice is either old or not creative then someone is either strong or not curious.
Everyone who is either wise or creative is both creative and not quiet.
If someone is either calm or not strong then john is happy.
If susan is not creative or not brave then someone is calm or not creative and vice versa.
Everyone who is either strong or calm is either quiet or not happy.
Everyone who is not creative is not curious and vice versa.
Someone is kind.
Mary is either not brave or tall.
Fred is either quiet or not tall.
Someone is either not brave or brave.
Someone is both not brave and humble.
Fred is calm or strong.
Someone is strong. | Mary is not curious. | contradiction | ((?[X]:(~humble(X)))=>(?[X]:(old(X))))&
(![X]:((~wise(X)|~generous(X))=>happy(X)))&
(((funny(susan)<~>happy(susan)))<=>(~quiet(susan)))&
(![X]:((curious(X)<~>~tall(X))<=>(humble(X)&~kind(X))))&
(![X]:((humble(X)<~>old(X))<=>~quiet(X)))&
(![X]:((~old(X)<~>tall(X))<=>~tall(X)))&
(![X]:((happy(X)&~happy(X))<=>(patient(X)|happy(X))))&
((~happy(susan))=>((curious(fred)|calm(fred))))&
(![X]:(~quiet(X)<=>(curious(X)&~brave(X))))&
(((old(alice)<~>~creative(alice)))=>(?[X]:((strong(X)<~>~curious(X)))))&
(![X]:((wise(X)<~>creative(X))=>(creative(X)&~quiet(X))))&
((?[X]:((calm(X)<~>~strong(X))))=>(happy(john)))&
(((~creative(susan)|~brave(susan)))<=>(?[X]:((calm(X)|~creative(X)))))&
(![X]:((strong(X)<~>calm(X))=>(quiet(X)<~>~happy(X))))&
(![X]:(~creative(X)<=>~curious(X)))&
(?[X]:(kind(X)))&
((~brave(mary)<~>tall(mary)))&
((quiet(fred)<~>~tall(fred)))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:((~brave(X)&humble(X))))&
((calm(fred)|strong(fred)))&
(?[X]:(strong(X))) | ~curious(mary) | [
"p6",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9034154091127848918790143
% SZS output start Proof for 9034154091127848918790143
7. ! [X0] : ((~happy(X0) & happy(X0)) <=> (happy(X0) | patient(X0))) [input p6]
9. ! [X0] : (~quiet(X0) <=> (~brave(X0) & curious(X0))) [input p8]
12. ? [X0] : (calm(X0) <~> ~strong(X0)) => happy(john) [input p11]
14. ! [X0] : ((strong(X0) <~> calm(X0)) => (quiet(X0) <~> ~happy(X0))) [input p13]
23. ~curious(mary) [input hypothesis]
32. happy(john) | ! [X0] : (calm(X0) <=> ~strong(X0)) [ennf transformation 12]
33. ! [X0] : ((quiet(X0) <~> ~happy(X0)) | (strong(X0) <=> calm(X0))) [ennf transformation 14]
42. ! [X0] : (((~happy(X0) & happy(X0)) | (~happy(X0) & ~patient(X0))) & ((happy(X0) | patient(X0)) | (happy(X0) | ~happy(X0)))) [nnf transformation 7]
43. ! [X0] : (((~happy(X0) & happy(X0)) | (~happy(X0) & ~patient(X0))) & (happy(X0) | patient(X0) | happy(X0) | ~happy(X0))) [flattening 42]
44. ! [X0] : ((~quiet(X0) | (brave(X0) | ~curious(X0))) & ((~brave(X0) & curious(X0)) | quiet(X0))) [nnf transformation 9]
45. ! [X0] : ((~quiet(X0) | brave(X0) | ~curious(X0)) & ((~brave(X0) & curious(X0)) | quiet(X0))) [flattening 44]
50. happy(john) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))) [nnf transformation 32]
56. ! [X0] : (((happy(X0) | ~quiet(X0)) & (~happy(X0) | quiet(X0))) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) [nnf transformation 33]
93. ~happy(X0) | ~happy(X0) [cnf transformation 43]
95. curious(X0) | quiet(X0) [cnf transformation 45]
106. happy(john) | ~strong(X0) | ~calm(X0) [cnf transformation 50]
107. happy(john) | calm(X0) | strong(X0) [cnf transformation 50]
114. happy(X0) | ~quiet(X0) | calm(X0) | ~strong(X0) [cnf transformation 56]
115. happy(X0) | ~quiet(X0) | strong(X0) | ~calm(X0) [cnf transformation 56]
129. ~curious(mary) [cnf transformation 23]
132. ~happy(X0) [duplicate literal removal 93]
187. calm(X0) | strong(X0) [subsumption resolution 107,132]
188. ~strong(X0) | ~calm(X0) [subsumption resolution 106,132]
215. ~quiet(X0) | strong(X0) | ~calm(X0) [subsumption resolution 115,132]
216. ~quiet(X0) | ~calm(X0) [subsumption resolution 215,188]
217. ~quiet(X0) | calm(X0) | ~strong(X0) [subsumption resolution 114,132]
218. ~quiet(X0) | calm(X0) [subsumption resolution 217,187]
219. ~quiet(X0) [subsumption resolution 218,216]
236. quiet(mary) [resolution 95,129]
238. $false [subsumption resolution 236,219]
% SZS output end Proof for 9034154091127848918790143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or patient is either not wise or quiet and vice versa. Everyone who is either not funny or creative is rich. If susan is strong then fred is strong or not calm. If alice is either not patient or funny then someone is wise or tall. Everyone who is not humble or not patient is either wise or not patient. If someone is either not strong or rich then susan is not rich or not curious and vice versa. Everyone who is not generous is old or quiet and vice versa. Everyone who is both curious and not kind is both not generous and old. If someone is either patient or not brave then lucy is kind or brave and vice versa. Everyone who is both not kind and not generous is both creative and not generous. If someone is happy then someone is wise and vice versa. Everyone who is not funny or not patient is not happy or wise and vice versa. Everyone who is either patient or generous is not quiet and vice versa. If someone is not quiet then lucy is either not tall or brave. If someone is not kind or not tall then lucy is wise and vice versa. If someone is not brave then someone is either not calm or kind and vice versa. Paul is both generous and not humble. Someone is either not humble or curious. Someone is either not humble or humble. Someone is either not old or not kind. Lucy is not generous or tall. | Alice is not quiet. | entailment | (![X]:((~happy(X)|patient(X))<=>(~wise(X)<~>quiet(X))))&
(![X]:((~funny(X)<~>creative(X))=>rich(X)))&
((strong(susan))=>((strong(fred)|~calm(fred))))&
(((~patient(alice)<~>funny(alice)))=>(?[X]:((wise(X)|tall(X)))))&
(![X]:((~humble(X)|~patient(X))=>(wise(X)<~>~patient(X))))&
((?[X]:((~strong(X)<~>rich(X))))<=>((~rich(susan)|~curious(susan))))&
(![X]:(~generous(X)<=>(old(X)|quiet(X))))&
(![X]:((curious(X)&~kind(X))=>(~generous(X)&old(X))))&
((?[X]:((patient(X)<~>~brave(X))))<=>((kind(lucy)|brave(lucy))))&
(![X]:((~kind(X)&~generous(X))=>(creative(X)&~generous(X))))&
((?[X]:(happy(X)))<=>(?[X]:(wise(X))))&
(![X]:((~funny(X)|~patient(X))<=>(~happy(X)|wise(X))))&
(![X]:((patient(X)<~>generous(X))<=>~quiet(X)))&
((?[X]:(~quiet(X)))=>((~tall(lucy)<~>brave(lucy))))&
((?[X]:((~kind(X)|~tall(X))))<=>(wise(lucy)))&
((?[X]:(~brave(X)))<=>(?[X]:((~calm(X)<~>kind(X)))))&
((generous(paul)&~humble(paul)))&
(?[X]:((~humble(X)<~>curious(X))))&
(?[X]:((~humble(X)<~>humble(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
((~generous(lucy)|tall(lucy))) | ~quiet(alice) | [
"p0",
"p4",
"p6",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 144755610155954139691312
% SZS output start Proof for 144755610155954139691312
1. ! [X0] : ((patient(X0) | ~happy(X0)) <=> (~wise(X0) <~> quiet(X0))) [input p0]
5. ! [X0] : ((~patient(X0) | ~humble(X0)) => (wise(X0) <~> ~patient(X0))) [input p4]
7. ! [X0] : (~generous(X0) <=> (quiet(X0) | old(X0))) [input p6]
11. ? [X0] : happy(X0) <=> ? [X0] : wise(X0) [input p10]
13. ! [X0] : ((patient(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p12]
22. quiet(alice) [input hypothesis]
23. ? [X0] : happy(X0) <=> ? [X1] : wise(X1) [rectify 11]
29. ! [X0] : ((wise(X0) <~> ~patient(X0)) | (patient(X0) & humble(X0))) [ennf transformation 5]
35. ! [X0] : (((patient(X0) | ~happy(X0)) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | (~patient(X0) & happy(X0)))) [nnf transformation 1]
36. ! [X0] : ((patient(X0) | ~happy(X0) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | (~patient(X0) & happy(X0)))) [flattening 35]
41. ! [X0] : (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (patient(X0) & humble(X0))) [nnf transformation 29]
47. ! [X0] : ((~generous(X0) | (~quiet(X0) & ~old(X0))) & ((quiet(X0) | old(X0)) | generous(X0))) [nnf transformation 7]
48. ! [X0] : ((~generous(X0) | (~quiet(X0) & ~old(X0))) & (quiet(X0) | old(X0) | generous(X0))) [flattening 47]
54. (? [X0] : happy(X0) | ! [X1] : ~wise(X1)) & (? [X1] : wise(X1) | ! [X0] : ~happy(X0)) [nnf transformation 23]
55. (? [X0] : happy(X0) | ! [X1] : ~wise(X1)) & (? [X2] : wise(X2) | ! [X3] : ~happy(X3)) [rectify 54]
56. ? [X0] : happy(X0) => happy(sK3) [choice axiom]
57. ? [X2] : wise(X2) => wise(sK4) [choice axiom]
58. (happy(sK3) | ! [X1] : ~wise(X1)) & (wise(sK4) | ! [X3] : ~happy(X3)) [skolemisation 55,57,56]
61. ! [X0] : ((((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | quiet(X0)) & (~quiet(X0) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0))))) [nnf transformation 13]
82. ~wise(X0) | quiet(X0) | ~patient(X0) [cnf transformation 36]
83. ~quiet(X0) | wise(X0) | happy(X0) [cnf transformation 36]
95. patient(X0) | ~wise(X0) | patient(X0) [cnf transformation 41]
104. ~generous(X0) | ~quiet(X0) [cnf transformation 48]
115. wise(sK4) | ~happy(X3) [cnf transformation 58]
116. happy(sK3) | ~wise(X1) [cnf transformation 58]
121. ~quiet(X0) | generous(X0) | ~patient(X0) [cnf transformation 61]
143. quiet(alice) [cnf transformation 22]
144. ~wise(X0) | patient(X0) [duplicate literal removal 95]
233. 20 <=> ! [X1] : ~wise(X1) [avatar definition]
234. ~wise(X1) <- (20) [avatar component clause 233]
236. 21 <=> happy(sK3) [avatar definition]
238. happy(sK3) <- (21) [avatar component clause 236]
239. 20 | 21 [avatar split clause 116,236,233]
241. 22 <=> ! [X3] : ~happy(X3) [avatar definition]
242. ~happy(X3) <- (22) [avatar component clause 241]
244. 23 <=> wise(sK4) [avatar definition]
246. wise(sK4) <- (23) [avatar component clause 244]
247. 22 | 23 [avatar split clause 115,244,241]
251. ~quiet(X0) | ~patient(X0) [subsumption resolution 121,104]
334. $false <- (21, 22) [subsumption resolution 238,242]
335. ~21 | ~22 [avatar contradiction clause 334]
377. wise(alice) | happy(alice) [resolution 83,143]
384. quiet(sK4) | ~patient(sK4) <- (23) [resolution 246,82]
386. patient(sK4) <- (23) [resolution 246,144]
387. ~patient(sK4) <- (23) [subsumption resolution 384,251]
388. $false <- (23) [subsumption resolution 386,387]
389. ~23 [avatar contradiction clause 388]
391. 46 <=> happy(alice) [avatar definition]
393. happy(alice) <- (46) [avatar component clause 391]
395. 47 <=> wise(alice) [avatar definition]
397. wise(alice) <- (47) [avatar component clause 395]
398. 46 | 47 [avatar split clause 377,395,391]
400. $false <- (22, 46) [subsumption resolution 393,242]
401. ~22 | ~46 [avatar contradiction clause 400]
404. $false <- (20, 47) [subsumption resolution 397,234]
405. ~20 | ~47 [avatar contradiction clause 404]
406. $false [avatar sat refutation 239,247,335,389,398,401,405]
% SZS output end Proof for 144755610155954139691312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If john is funny or not brave then someone is not generous or not funny. Everyone who is not brave or not wise is brave or calm and vice versa. Everyone who is brave or not wise is either not creative or not humble and vice versa. If someone is either tall or generous then someone is both tall and not generous and vice versa. If lucy is either brave or wise then someone is either not patient or humble and vice versa. If lucy is creative then lucy is not old or not patient. If susan is both not creative and not tall then fred is creative and vice versa. Everyone who is either not quiet or creative is both strong and funny. Everyone who is not old or not happy is both not rich and not calm. Everyone who is both brave and not strong is not tall and vice versa. If someone is both wise and not curious then someone is both generous and tall and vice versa. If alice is both not generous and kind then fred is curious or not patient and vice versa. Everyone who is not humble is strong. Everyone who is either kind or not curious is either not quiet or not wise and vice versa. If someone is either not old or old then someone is not curious or not kind and vice versa. Everyone who is not strong is not old or not quiet. Someone is both not humble and not calm. Mary is not wise. Someone is both quiet and not creative. Alice is not wise. Mary is happy. Someone is both strong and happy. Lucy is either brave or not calm. Fred is both creative and generous. | Mary is wise. | contradiction | (((funny(john)|~brave(john)))=>(?[X]:((~generous(X)|~funny(X)))))&
(![X]:((~brave(X)|~wise(X))<=>(brave(X)|calm(X))))&
(![X]:((brave(X)|~wise(X))<=>(~creative(X)<~>~humble(X))))&
((?[X]:((tall(X)<~>generous(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
(((brave(lucy)<~>wise(lucy)))<=>(?[X]:((~patient(X)<~>humble(X)))))&
((creative(lucy))=>((~old(lucy)|~patient(lucy))))&
(((~creative(susan)&~tall(susan)))<=>(creative(fred)))&
(![X]:((~quiet(X)<~>creative(X))=>(strong(X)&funny(X))))&
(![X]:((~old(X)|~happy(X))=>(~rich(X)&~calm(X))))&
(![X]:((brave(X)&~strong(X))<=>~tall(X)))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((generous(X)&tall(X)))))&
(((~generous(alice)&kind(alice)))<=>((curious(fred)|~patient(fred))))&
(![X]:(~humble(X)=>strong(X)))&
(![X]:((kind(X)<~>~curious(X))<=>(~quiet(X)<~>~wise(X))))&
((?[X]:((~old(X)<~>old(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:(~strong(X)=>(~old(X)|~quiet(X))))&
(?[X]:((~humble(X)&~calm(X))))&
(~wise(mary))&
(?[X]:((quiet(X)&~creative(X))))&
(~wise(alice))&
(happy(mary))&
(?[X]:((strong(X)&happy(X))))&
((brave(lucy)<~>~calm(lucy)))&
((creative(fred)&generous(fred))) | wise(mary) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1177826648395041074303625
% SZS output start Proof for 1177826648395041074303625
18. ~wise(mary) [input p17]
25. wise(mary) [input hypothesis]
146. ~wise(mary) [cnf transformation 18]
155. wise(mary) [cnf transformation 25]
335. $false [subsumption resolution 155,146]
% SZS output end Proof for 1177826648395041074303625
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not wise and funny then someone is not tall or not curious and vice versa. Everyone who is both happy and not humble is both not kind and humble and vice versa. If someone is either generous or creative then alice is brave or rich. Everyone who is old is creative or kind and vice versa. If someone is not curious or wise then someone is old. Everyone who is not brave is not curious or strong. If someone is calm then someone is both humble and not old and vice versa. Everyone who is humble is both happy and not brave and vice versa. If someone is tall then alice is humble. If fred is not humble or creative then paul is not humble or not happy and vice versa. Everyone who is calm or rich is quiet or not brave. Everyone who is either calm or humble is happy or not happy and vice versa. Everyone who is either patient or not kind is not kind. If john is not old then someone is either brave or tall. Everyone who is either not generous or not humble is either strong or not generous and vice versa. Everyone who is both kind and rich is either humble or not tall and vice versa. Alice is both humble and quiet. Someone is either calm or happy. Paul is either not happy or not patient. Someone is wise. Susan is humble. Fred is funny. Mary is old or happy. Someone is old. | Susan is not kind. | contradiction | (((~wise(susan)&funny(susan)))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((happy(X)&~humble(X))<=>(~kind(X)&humble(X))))&
((?[X]:((generous(X)<~>creative(X))))=>((brave(alice)|rich(alice))))&
(![X]:(old(X)<=>(creative(X)|kind(X))))&
((?[X]:((~curious(X)|wise(X))))=>(?[X]:(old(X))))&
(![X]:(~brave(X)=>(~curious(X)|strong(X))))&
((?[X]:(calm(X)))<=>(?[X]:((humble(X)&~old(X)))))&
(![X]:(humble(X)<=>(happy(X)&~brave(X))))&
((?[X]:(tall(X)))=>(humble(alice)))&
(((~humble(fred)|creative(fred)))<=>((~humble(paul)|~happy(paul))))&
(![X]:((calm(X)|rich(X))=>(quiet(X)|~brave(X))))&
(![X]:((calm(X)<~>humble(X))<=>(happy(X)|~happy(X))))&
(![X]:((patient(X)<~>~kind(X))=>~kind(X)))&
((~old(john))=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((~generous(X)<~>~humble(X))<=>(strong(X)<~>~generous(X))))&
(![X]:((kind(X)&rich(X))<=>(humble(X)<~>~tall(X))))&
((humble(alice)&quiet(alice)))&
(?[X]:((calm(X)<~>happy(X))))&
((~happy(paul)<~>~patient(paul)))&
(?[X]:(wise(X)))&
(humble(susan))&
(funny(fred))&
((old(mary)|happy(mary)))&
(?[X]:(old(X))) | ~kind(susan) | [
"p1",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 13455343918308615889881
% SZS output start Proof for 13455343918308615889881
2. ! [X0] : ((~humble(X0) & happy(X0)) <=> (humble(X0) & ~kind(X0))) [input p1]
21. humble(susan) [input p20]
25. ~kind(susan) [input hypothesis]
43. ! [X0] : (((~humble(X0) & happy(X0)) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | (humble(X0) | ~happy(X0)))) [nnf transformation 2]
44. ! [X0] : (((~humble(X0) & happy(X0)) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | humble(X0) | ~happy(X0))) [flattening 43]
85. ~humble(X0) | ~humble(X0) | kind(X0) [cnf transformation 44]
135. humble(susan) [cnf transformation 21]
139. ~kind(susan) [cnf transformation 25]
146. ~humble(X0) | kind(X0) [duplicate literal removal 85]
299. kind(susan) [resolution 146,135]
303. $false [subsumption resolution 299,139]
% SZS output end Proof for 13455343918308615889881
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either curious or funny is both not funny and not happy.
Everyone who is both not creative and calm is both not rich and kind and vice versa.
Everyone who is either creative or not brave is either not happy or not rich and vice versa.
If john is not tall or not quiet then alice is creative or tall.
Everyone who is either curious or not rich is either not creative or not humble.
Everyone who is patient or not humble is both kind and funny.
Everyone who is either quiet or not happy is tall.
If someone is kind or not creative then mary is both funny and happy and vice versa.
If someone is tall or creative then lucy is creative and vice versa.
If someone is either humble or not strong then someone is patient and vice versa.
Everyone who is wise or humble is creative and vice versa.
Everyone who is not creative or kind is both not curious and happy.
If alice is either not brave or not calm then john is strong and vice versa.
If susan is both not calm and not creative then alice is both happy and wise and vice versa.
Everyone who is not strong or not kind is both not happy and tall.
If someone is not patient or not calm then someone is not quiet and vice versa.
Fred is not brave or calm.
Someone is not happy.
Someone is either not curious or not humble.
Susan is not old.
Someone is both brave and not calm.
Someone is generous.
Lucy is not quiet or not rich. | Alice is not strong. | entailment | (![X]:((curious(X)<~>funny(X))=>(~funny(X)&~happy(X))))&
(![X]:((~creative(X)&calm(X))<=>(~rich(X)&kind(X))))&
(![X]:((creative(X)<~>~brave(X))<=>(~happy(X)<~>~rich(X))))&
(((~tall(john)|~quiet(john)))=>((creative(alice)|tall(alice))))&
(![X]:((curious(X)<~>~rich(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((patient(X)|~humble(X))=>(kind(X)&funny(X))))&
(![X]:((quiet(X)<~>~happy(X))=>tall(X)))&
((?[X]:((kind(X)|~creative(X))))<=>((funny(mary)&happy(mary))))&
((?[X]:((tall(X)|creative(X))))<=>(creative(lucy)))&
((?[X]:((humble(X)<~>~strong(X))))<=>(?[X]:(patient(X))))&
(![X]:((wise(X)|humble(X))<=>creative(X)))&
(![X]:((~creative(X)|kind(X))=>(~curious(X)&happy(X))))&
(((~brave(alice)<~>~calm(alice)))<=>(strong(john)))&
(((~calm(susan)&~creative(susan)))<=>((happy(alice)&wise(alice))))&
(![X]:((~strong(X)|~kind(X))=>(~happy(X)&tall(X))))&
((?[X]:((~patient(X)|~calm(X))))<=>(?[X]:(~quiet(X))))&
((~brave(fred)|calm(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((~curious(X)<~>~humble(X))))&
(~old(susan))&
(?[X]:((brave(X)&~calm(X))))&
(?[X]:(generous(X)))&
((~quiet(lucy)|~rich(lucy))) | ~strong(alice) | [
"p0",
"p5",
"p7",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 639911073683091241643378
% SZS output start Proof for 639911073683091241643378
1. ! [X0] : ((curious(X0) <~> funny(X0)) => (~happy(X0) & ~funny(X0))) [input p0]
6. ! [X0] : ((~humble(X0) | patient(X0)) => (funny(X0) & kind(X0))) [input p5]
8. ? [X0] : (~creative(X0) | kind(X0)) <=> (happy(mary) & funny(mary)) [input p7]
10. ? [X0] : (humble(X0) <~> ~strong(X0)) <=> ? [X0] : patient(X0) [input p9]
12. ! [X0] : ((kind(X0) | ~creative(X0)) => (happy(X0) & ~curious(X0))) [input p11]
15. ! [X0] : ((~kind(X0) | ~strong(X0)) => (tall(X0) & ~happy(X0))) [input p14]
24. strong(alice) [input hypothesis]
25. ? [X0] : (humble(X0) <~> ~strong(X0)) <=> ? [X1] : patient(X1) [rectify 10]
29. ! [X0] : ((~happy(X0) & ~funny(X0)) | (curious(X0) <=> funny(X0))) [ennf transformation 1]
33. ! [X0] : ((funny(X0) & kind(X0)) | (humble(X0) & ~patient(X0))) [ennf transformation 6]
35. ! [X0] : ((happy(X0) & ~curious(X0)) | (~kind(X0) & creative(X0))) [ennf transformation 12]
36. ! [X0] : ((tall(X0) & ~happy(X0)) | (kind(X0) & strong(X0))) [ennf transformation 15]
37. ! [X0] : ((~happy(X0) & ~funny(X0)) | ((curious(X0) | ~funny(X0)) & (funny(X0) | ~curious(X0)))) [nnf transformation 29]
43. (? [X0] : (~creative(X0) | kind(X0)) | (~happy(mary) | ~funny(mary))) & ((happy(mary) & funny(mary)) | ! [X0] : (creative(X0) & ~kind(X0))) [nnf transformation 8]
44. (? [X0] : (~creative(X0) | kind(X0)) | ~happy(mary) | ~funny(mary)) & ((happy(mary) & funny(mary)) | ! [X0] : (creative(X0) & ~kind(X0))) [flattening 43]
45. (? [X0] : (~creative(X0) | kind(X0)) | ~happy(mary) | ~funny(mary)) & ((happy(mary) & funny(mary)) | ! [X1] : (creative(X1) & ~kind(X1))) [rectify 44]
46. ? [X0] : (~creative(X0) | kind(X0)) => (~creative(sK0) | kind(sK0)) [choice axiom]
47. ((~creative(sK0) | kind(sK0)) | ~happy(mary) | ~funny(mary)) & ((happy(mary) & funny(mary)) | ! [X1] : (creative(X1) & ~kind(X1))) [skolemisation 45,46]
52. (? [X0] : ((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | ! [X1] : ~patient(X1)) & (? [X1] : patient(X1) | ! [X0] : ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0)))) [nnf transformation 25]
53. (? [X0] : ((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | ! [X1] : ~patient(X1)) & (? [X2] : patient(X2) | ! [X3] : ((humble(X3) | strong(X3)) & (~strong(X3) | ~humble(X3)))) [rectify 52]
54. ? [X0] : ((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) => ((strong(sK2) | ~humble(sK2)) & (~strong(sK2) | humble(sK2))) [choice axiom]
55. ? [X2] : patient(X2) => patient(sK3) [choice axiom]
56. (((strong(sK2) | ~humble(sK2)) & (~strong(sK2) | humble(sK2))) | ! [X1] : ~patient(X1)) & (patient(sK3) | ! [X3] : ((humble(X3) | strong(X3)) & (~strong(X3) | ~humble(X3)))) [skolemisation 53,55,54]
75. ~funny(X0) | curious(X0) | ~funny(X0) [cnf transformation 37]
96. ~patient(X0) | kind(X0) [cnf transformation 33]
97. humble(X0) | kind(X0) [cnf transformation 33]
98. ~patient(X0) | funny(X0) [cnf transformation 33]
102. funny(mary) | ~kind(X1) [cnf transformation 47]
104. happy(mary) | ~kind(X1) [cnf transformation 47]
110. patient(sK3) | ~strong(X3) | ~humble(X3) [cnf transformation 56]
118. ~kind(X0) | ~curious(X0) [cnf transformation 35]
130. ~happy(X0) | kind(X0) [cnf transformation 36]
143. strong(alice) [cnf transformation 24]
144. ~funny(X0) | curious(X0) [duplicate literal removal 75]
164. 5 <=> funny(mary) [avatar definition]
165. funny(mary) <- (5) [avatar component clause 164]
168. 6 <=> happy(mary) [avatar definition]
169. happy(mary) <- (6) [avatar component clause 168]
185. 10 <=> ! [X1] : ~kind(X1) [avatar definition]
186. ~kind(X1) <- (10) [avatar component clause 185]
187. 10 | 6 [avatar split clause 104,168,185]
189. 10 | 5 [avatar split clause 102,164,185]
228. 20 <=> patient(sK3) [avatar definition]
230. patient(sK3) <- (20) [avatar component clause 228]
233. 21 <=> ! [X3] : (~strong(X3) | ~humble(X3)) [avatar definition]
234. ~strong(X3) | ~humble(X3) <- (21) [avatar component clause 233]
235. 21 | 20 [avatar split clause 110,228,233]
324. kind(sK3) <- (20) [resolution 96,230]
327. funny(sK3) <- (20) [resolution 98,230]
334. ~curious(sK3) <- (20) [resolution 118,324]
349. kind(mary) <- (6) [resolution 130,169]
360. curious(mary) <- (5) [resolution 144,165]
362. curious(sK3) <- (20) [resolution 144,327]
365. $false <- (20) [subsumption resolution 362,334]
366. ~20 [avatar contradiction clause 365]
371. ~curious(mary) <- (6) [resolution 349,118]
372. $false <- (5, 6) [subsumption resolution 371,360]
373. ~5 | ~6 [avatar contradiction clause 372]
380. ~humble(alice) <- (21) [resolution 234,143]
386. kind(alice) <- (21) [resolution 380,97]
387. $false <- (10, 21) [subsumption resolution 386,186]
388. ~10 | ~21 [avatar contradiction clause 387]
389. $false [avatar sat refutation 187,189,235,366,373,388]
% SZS output end Proof for 639911073683091241643378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is not brave or old. Everyone who is either strong or not brave is both not patient and kind. If someone is both creative and wise then paul is either not humble or generous. Everyone who is either brave or humble is creative. If alice is both creative and calm then fred is old. If susan is either not funny or not generous then fred is kind and vice versa. If someone is either not curious or creative then someone is quiet and vice versa. Everyone who is not brave or not calm is both brave and not brave. If someone is not old then someone is either not wise or happy. If someone is both humble and not funny then alice is both not humble and tall and vice versa. If someone is either not brave or not patient then fred is either not brave or quiet and vice versa. Everyone who is either not curious or not kind is either not rich or creative. Everyone who is both not generous and kind is funny or creative and vice versa. If someone is either not funny or funny then someone is either quiet or not brave and vice versa. Everyone who is not generous or funny is not creative. Everyone who is both strong and not old is not happy or wise. Someone is either not kind or patient. Paul is not happy. Someone is either creative or not rich. Susan is either kind or old. Someone is humble. | Susan is kind. | entailment | (![X]:(~curious(X)=>(~brave(X)|old(X))))&
(![X]:((strong(X)<~>~brave(X))=>(~patient(X)&kind(X))))&
((?[X]:((creative(X)&wise(X))))=>((~humble(paul)<~>generous(paul))))&
(![X]:((brave(X)<~>humble(X))=>creative(X)))&
(((creative(alice)&calm(alice)))=>(old(fred)))&
(((~funny(susan)<~>~generous(susan)))<=>(kind(fred)))&
((?[X]:((~curious(X)<~>creative(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~brave(X)|~calm(X))=>(brave(X)&~brave(X))))&
((?[X]:(~old(X)))=>(?[X]:((~wise(X)<~>happy(X)))))&
((?[X]:((humble(X)&~funny(X))))<=>((~humble(alice)&tall(alice))))&
((?[X]:((~brave(X)<~>~patient(X))))<=>((~brave(fred)<~>quiet(fred))))&
(![X]:((~curious(X)<~>~kind(X))=>(~rich(X)<~>creative(X))))&
(![X]:((~generous(X)&kind(X))<=>(funny(X)|creative(X))))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:((quiet(X)<~>~brave(X)))))&
(![X]:((~generous(X)|funny(X))=>~creative(X)))&
(![X]:((strong(X)&~old(X))=>(~happy(X)|wise(X))))&
(?[X]:((~kind(X)<~>patient(X))))&
(~happy(paul))&
(?[X]:((creative(X)<~>~rich(X))))&
((kind(susan)<~>old(susan)))&
(?[X]:(humble(X))) | kind(susan) | [
"p3",
"p7",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 178561489207781620646644
% SZS output start Proof for 178561489207781620646644
4. ! [X0] : ((brave(X0) <~> humble(X0)) => creative(X0)) [input p3]
8. ! [X0] : ((~calm(X0) | ~brave(X0)) => (~brave(X0) & brave(X0))) [input p7]
10. ? [X0] : (~funny(X0) & humble(X0)) <=> (tall(alice) & ~humble(alice)) [input p9]
13. ! [X0] : ((kind(X0) & ~generous(X0)) <=> (creative(X0) | funny(X0))) [input p12]
15. ! [X0] : ((funny(X0) | ~generous(X0)) => ~creative(X0)) [input p14]
22. ~kind(susan) [input hypothesis]
30. ! [X0] : (creative(X0) | (brave(X0) <=> humble(X0))) [ennf transformation 4]
33. ! [X0] : ((~brave(X0) & brave(X0)) | (calm(X0) & brave(X0))) [ennf transformation 8]
36. ! [X0] : (~creative(X0) | (~funny(X0) & generous(X0))) [ennf transformation 15]
41. ! [X0] : (creative(X0) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0)))) [nnf transformation 30]
52. (? [X0] : (~funny(X0) & humble(X0)) | (~tall(alice) | humble(alice))) & ((tall(alice) & ~humble(alice)) | ! [X0] : (funny(X0) | ~humble(X0))) [nnf transformation 10]
53. (? [X0] : (~funny(X0) & humble(X0)) | ~tall(alice) | humble(alice)) & ((tall(alice) & ~humble(alice)) | ! [X0] : (funny(X0) | ~humble(X0))) [flattening 52]
54. (? [X0] : (~funny(X0) & humble(X0)) | ~tall(alice) | humble(alice)) & ((tall(alice) & ~humble(alice)) | ! [X1] : (funny(X1) | ~humble(X1))) [rectify 53]
55. ? [X0] : (~funny(X0) & humble(X0)) => (~funny(sK3) & humble(sK3)) [choice axiom]
56. ((~funny(sK3) & humble(sK3)) | ~tall(alice) | humble(alice)) & ((tall(alice) & ~humble(alice)) | ! [X1] : (funny(X1) | ~humble(X1))) [skolemisation 54,55]
62. ! [X0] : (((kind(X0) & ~generous(X0)) | (~creative(X0) & ~funny(X0))) & ((creative(X0) | funny(X0)) | (~kind(X0) | generous(X0)))) [nnf transformation 13]
63. ! [X0] : (((kind(X0) & ~generous(X0)) | (~creative(X0) & ~funny(X0))) & (creative(X0) | funny(X0) | ~kind(X0) | generous(X0))) [flattening 62]
85. ~brave(X0) | humble(X0) | creative(X0) [cnf transformation 41]
96. brave(X0) | brave(X0) [cnf transformation 33]
102. ~humble(alice) | funny(X1) | ~humble(X1) [cnf transformation 56]
120. ~generous(X0) | ~creative(X0) [cnf transformation 63]
121. ~funny(X0) | kind(X0) [cnf transformation 63]
131. ~creative(X0) | generous(X0) [cnf transformation 36]
142. ~kind(susan) [cnf transformation 22]
147. brave(X0) [duplicate literal removal 96]
230. 19 <=> humble(alice) [avatar definition]
231. ~humble(alice) <- (~19) [avatar component clause 230]
248. 23 <=> ! [X1] : (funny(X1) | ~humble(X1)) [avatar definition]
249. funny(X1) | ~humble(X1) <- (23) [avatar component clause 248]
251. 23 | ~19 [avatar split clause 102,230,248]
280. 29 <=> ! [X3] : funny(X3) [avatar definition]
281. funny(X3) <- (29) [avatar component clause 280]
283. ~creative(X0) [subsumption resolution 131,120]
296. 32 <=> kind(susan) [avatar definition]
298. ~kind(susan) <- (~32) [avatar component clause 296]
305. ~32 [avatar split clause 142,296]
313. humble(X0) | creative(X0) [resolution 85,147]
314. humble(X0) [subsumption resolution 313,283]
318. $false <- (~19) [resolution 314,231]
320. 19 [avatar contradiction clause 318]
322. funny(X1) <- (23) [subsumption resolution 249,314]
323. 29 | ~23 [avatar split clause 322,248,280]
328. kind(X1) <- (29) [resolution 281,121]
332. $false <- (29, ~32) [resolution 328,298]
335. ~29 | 32 [avatar contradiction clause 332]
336. $false [avatar sat refutation 251,305,320,323,335]
% SZS output end Proof for 178561489207781620646644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is not rich.
Everyone who is patient or kind is humble or not tall.
Everyone who is either not humble or not wise is both calm and curious and vice versa.
Everyone who is both not tall and creative is creative or wise and vice versa.
Everyone who is calm or creative is not brave and vice versa.
Everyone who is not patient is funny.
Everyone who is either not patient or not generous is not funny or funny.
If someone is not funny then someone is both funny and brave.
Everyone who is old is wise.
If someone is either brave or kind then someone is not kind or patient.
If mary is either not quiet or humble then fred is wise.
Everyone who is not happy or happy is both brave and rich.
Everyone who is both not brave and patient is not tall and vice versa.
Everyone who is either brave or not humble is quiet or calm.
If someone is either not curious or generous then susan is either not strong or not generous and vice versa.
If someone is quiet or not happy then someone is not generous and vice versa.
Lucy is both not creative and not kind.
John is kind or not old.
Mary is not happy or happy.
Someone is not humble.
Susan is either not humble or not curious. | Susan is humble. | contradiction | (![X]:(~strong(X)=>~rich(X)))&
(![X]:((patient(X)|kind(X))=>(humble(X)|~tall(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>(calm(X)&curious(X))))&
(![X]:((~tall(X)&creative(X))<=>(creative(X)|wise(X))))&
(![X]:((calm(X)|creative(X))<=>~brave(X)))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:((~patient(X)<~>~generous(X))=>(~funny(X)|funny(X))))&
((?[X]:(~funny(X)))=>(?[X]:((funny(X)&brave(X)))))&
(![X]:(old(X)=>wise(X)))&
((?[X]:((brave(X)<~>kind(X))))=>(?[X]:((~kind(X)|patient(X)))))&
(((~quiet(mary)<~>humble(mary)))=>(wise(fred)))&
(![X]:((~happy(X)|happy(X))=>(brave(X)&rich(X))))&
(![X]:((~brave(X)&patient(X))<=>~tall(X)))&
(![X]:((brave(X)<~>~humble(X))=>(quiet(X)|calm(X))))&
((?[X]:((~curious(X)<~>generous(X))))<=>((~strong(susan)<~>~generous(susan))))&
((?[X]:((quiet(X)|~happy(X))))<=>(?[X]:(~generous(X))))&
((~creative(lucy)&~kind(lucy)))&
((kind(john)|~old(john)))&
((~happy(mary)|happy(mary)))&
(?[X]:(~humble(X)))&
((~humble(susan)<~>~curious(susan))) | humble(susan) | [
"p2",
"p3",
"p4",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7159999033247476263712534
% SZS output start Proof for 7159999033247476263712534
3. ! [X0] : ((~humble(X0) <~> ~wise(X0)) <=> (curious(X0) & calm(X0))) [input p2]
4. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (wise(X0) | creative(X0))) [input p3]
5. ! [X0] : ((creative(X0) | calm(X0)) <=> ~brave(X0)) [input p4]
12. ! [X0] : ((happy(X0) | ~happy(X0)) => (rich(X0) & brave(X0))) [input p11]
13. ! [X0] : ((patient(X0) & ~brave(X0)) <=> ~tall(X0)) [input p12]
22. humble(susan) [input hypothesis]
37. ! [X0] : ((rich(X0) & brave(X0)) | (~happy(X0) & happy(X0))) [ennf transformation 12]
40. ! [X0] : ((((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) | (~curious(X0) | ~calm(X0))) & ((curious(X0) & calm(X0)) | ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0))))) [nnf transformation 3]
41. ! [X0] : ((((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) | ~curious(X0) | ~calm(X0)) & ((curious(X0) & calm(X0)) | ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0))))) [flattening 40]
42. ! [X0] : (((creative(X0) & ~tall(X0)) | (~wise(X0) & ~creative(X0))) & ((wise(X0) | creative(X0)) | (~creative(X0) | tall(X0)))) [nnf transformation 4]
43. ! [X0] : (((creative(X0) & ~tall(X0)) | (~wise(X0) & ~creative(X0))) & (wise(X0) | creative(X0) | ~creative(X0) | tall(X0))) [flattening 42]
44. ! [X0] : (((creative(X0) | calm(X0)) | brave(X0)) & (~brave(X0) | (~creative(X0) & ~calm(X0)))) [nnf transformation 5]
45. ! [X0] : ((creative(X0) | calm(X0) | brave(X0)) & (~brave(X0) | (~creative(X0) & ~calm(X0)))) [flattening 44]
55. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) | brave(X0)))) [nnf transformation 13]
56. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | ~patient(X0) | brave(X0))) [flattening 55]
74. ~humble(X0) | calm(X0) | wise(X0) [cnf transformation 41]
81. ~wise(X0) | ~tall(X0) [cnf transformation 43]
84. ~brave(X0) | ~calm(X0) [cnf transformation 45]
96. brave(X0) | happy(X0) [cnf transformation 37]
97. ~happy(X0) | brave(X0) [cnf transformation 37]
101. ~brave(X0) | tall(X0) [cnf transformation 56]
122. humble(susan) [cnf transformation 22]
167. brave(X0) [subsumption resolution 96,97]
168. tall(X0) [subsumption resolution 101,167]
225. 23 <=> humble(susan) [avatar definition]
227. humble(susan) <- (23) [avatar component clause 225]
234. 23 [avatar split clause 122,225]
238. ~calm(X0) [resolution 84,167]
246. calm(susan) | wise(susan) <- (23) [resolution 74,227]
248. wise(susan) <- (23) [subsumption resolution 246,238]
259. ~tall(susan) <- (23) [resolution 248,81]
262. $false <- (23) [subsumption resolution 259,168]
263. ~23 [avatar contradiction clause 262]
264. $false [avatar sat refutation 234,263]
% SZS output end Proof for 7159999033247476263712534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not kind is creative and vice versa.
Everyone who is both kind and not brave is not creative or brave and vice versa.
If fred is either generous or not calm then john is both kind and generous.
Everyone who is both happy and not generous is not rich.
Everyone who is humble is not wise or patient.
Everyone who is not calm is both quiet and not old and vice versa.
If alice is not calm then someone is both generous and not generous.
If paul is not funny then susan is both funny and strong.
If someone is not patient or humble then mary is both not kind and not curious and vice versa.
Everyone who is either curious or rich is both patient and old and vice versa.
If mary is wise or tall then someone is not kind.
Everyone who is both old and brave is both funny and not calm and vice versa.
Everyone who is either not tall or not happy is both not brave and not creative.
If someone is strong or not creative then fred is both not curious and rich and vice versa.
If susan is funny then john is patient or kind.
If john is not calm or tall then mary is brave.
Someone is strong or generous.
Someone is calm or not humble.
Alice is not quiet or not humble.
Paul is either calm or generous.
Someone is either not strong or curious.
John is either generous or not quiet.
Someone is old or not old.
Someone is either not generous or not funny. | Mary is curious. | neutral | (![X]:((old(X)&~kind(X))<=>creative(X)))&
(![X]:((kind(X)&~brave(X))<=>(~creative(X)|brave(X))))&
(((generous(fred)<~>~calm(fred)))=>((kind(john)&generous(john))))&
(![X]:((happy(X)&~generous(X))=>~rich(X)))&
(![X]:(humble(X)=>(~wise(X)|patient(X))))&
(![X]:(~calm(X)<=>(quiet(X)&~old(X))))&
((~calm(alice))=>(?[X]:((generous(X)&~generous(X)))))&
((~funny(paul))=>((funny(susan)&strong(susan))))&
((?[X]:((~patient(X)|humble(X))))<=>((~kind(mary)&~curious(mary))))&
(![X]:((curious(X)<~>rich(X))<=>(patient(X)&old(X))))&
(((wise(mary)|tall(mary)))=>(?[X]:(~kind(X))))&
(![X]:((old(X)&brave(X))<=>(funny(X)&~calm(X))))&
(![X]:((~tall(X)<~>~happy(X))=>(~brave(X)&~creative(X))))&
((?[X]:((strong(X)|~creative(X))))<=>((~curious(fred)&rich(fred))))&
((funny(susan))=>((patient(john)|kind(john))))&
(((~calm(john)|tall(john)))=>(brave(mary)))&
(?[X]:((strong(X)|generous(X))))&
(?[X]:((calm(X)|~humble(X))))&
((~quiet(alice)|~humble(alice)))&
((calm(paul)<~>generous(paul)))&
(?[X]:((~strong(X)<~>curious(X))))&
((generous(john)<~>~quiet(john)))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~generous(X)<~>~funny(X)))) | curious(mary) | [] | null | 0 |
If mary is not funny then susan is generous or not funny. If lucy is both not rich and humble then susan is either funny or not strong and vice versa. Everyone who is both not curious and curious is both patient and not brave. Everyone who is not brave or not humble is happy or curious and vice versa. If mary is both tall and not quiet then someone is either not old or not brave and vice versa. Everyone who is not happy is both wise and not generous. Everyone who is not funny is both wise and humble. Everyone who is quiet or creative is both funny and humble. If susan is not humble or old then someone is not quiet and vice versa. If someone is both not humble and generous then susan is generous and vice versa. If someone is rich or not old then someone is either not humble or not funny. If someone is either funny or not patient then someone is either wise or funny and vice versa. Everyone who is both rich and not kind is not calm and vice versa. Everyone who is either not wise or not curious is either brave or not wise and vice versa. If someone is not happy or not rich then lucy is old and vice versa. Everyone who is both brave and not quiet is tall or calm and vice versa. Someone is not tall. Someone is either not funny or rich. Someone is not rich. Someone is old. Someone is quiet or wise. Alice is either happy or not patient. Someone is tall or not quiet. Mary is not curious. | Susan is not funny. | neutral | ((~funny(mary))=>((generous(susan)|~funny(susan))))&
(((~rich(lucy)&humble(lucy)))<=>((funny(susan)<~>~strong(susan))))&
(![X]:((~curious(X)&curious(X))=>(patient(X)&~brave(X))))&
(![X]:((~brave(X)|~humble(X))<=>(happy(X)|curious(X))))&
(((tall(mary)&~quiet(mary)))<=>(?[X]:((~old(X)<~>~brave(X)))))&
(![X]:(~happy(X)=>(wise(X)&~generous(X))))&
(![X]:(~funny(X)=>(wise(X)&humble(X))))&
(![X]:((quiet(X)|creative(X))=>(funny(X)&humble(X))))&
(((~humble(susan)|old(susan)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~humble(X)&generous(X))))<=>(generous(susan)))&
((?[X]:((rich(X)|~old(X))))=>(?[X]:((~humble(X)<~>~funny(X)))))&
((?[X]:((funny(X)<~>~patient(X))))<=>(?[X]:((wise(X)<~>funny(X)))))&
(![X]:((rich(X)&~kind(X))<=>~calm(X)))&
(![X]:((~wise(X)<~>~curious(X))<=>(brave(X)<~>~wise(X))))&
((?[X]:((~happy(X)|~rich(X))))<=>(old(lucy)))&
(![X]:((brave(X)&~quiet(X))<=>(tall(X)|calm(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~funny(X)<~>rich(X))))&
(?[X]:(~rich(X)))&
(?[X]:(old(X)))&
(?[X]:((quiet(X)|wise(X))))&
((happy(alice)<~>~patient(alice)))&
(?[X]:((tall(X)|~quiet(X))))&
(~curious(mary)) | ~funny(susan) | [] | null | 0 |
Everyone who is both calm and curious is wise or happy. If someone is both not calm and quiet then someone is not brave or not tall and vice versa. Everyone who is both not generous and kind is either not kind or not funny and vice versa. Everyone who is wise or quiet is both not curious and brave and vice versa. If someone is either creative or old then someone is both calm and kind. Everyone who is both not curious and not old is brave or rich. Everyone who is either not creative or funny is either not curious or not rich. Everyone who is either not generous or generous is either not wise or happy. Everyone who is both brave and calm is not quiet and vice versa. If someone is either generous or not old then someone is both not curious and happy and vice versa. Everyone who is humble is either not quiet or not calm. Everyone who is not kind or not old is not patient. Everyone who is tall or not calm is both not humble and old and vice versa. If john is humble then someone is either not humble or not calm and vice versa. If someone is not generous then someone is either not old or not calm and vice versa. If someone is funny or not patient then john is either wise or happy and vice versa. Alice is either tall or rich. Fred is either old or not creative. Someone is rich. Mary is not humble. John is funny or tall. | John is calm. | contradiction | (![X]:((calm(X)&curious(X))=>(wise(X)|happy(X))))&
((?[X]:((~calm(X)&quiet(X))))<=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~generous(X)&kind(X))<=>(~kind(X)<~>~funny(X))))&
(![X]:((wise(X)|quiet(X))<=>(~curious(X)&brave(X))))&
((?[X]:((creative(X)<~>old(X))))=>(?[X]:((calm(X)&kind(X)))))&
(![X]:((~curious(X)&~old(X))=>(brave(X)|rich(X))))&
(![X]:((~creative(X)<~>funny(X))=>(~curious(X)<~>~rich(X))))&
(![X]:((~generous(X)<~>generous(X))=>(~wise(X)<~>happy(X))))&
(![X]:((brave(X)&calm(X))<=>~quiet(X)))&
((?[X]:((generous(X)<~>~old(X))))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(humble(X)=>(~quiet(X)<~>~calm(X))))&
(![X]:((~kind(X)|~old(X))=>~patient(X)))&
(![X]:((tall(X)|~calm(X))<=>(~humble(X)&old(X))))&
((humble(john))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
((?[X]:((funny(X)|~patient(X))))<=>((wise(john)<~>happy(john))))&
((tall(alice)<~>rich(alice)))&
((old(fred)<~>~creative(fred)))&
(?[X]:(rich(X)))&
(~humble(mary))&
((funny(john)|tall(john))) | calm(john) | [
"p7",
"p12",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5243129044311888200781435
% SZS output start Proof for 5243129044311888200781435
8. ! [X0] : ((~generous(X0) <~> generous(X0)) => (~wise(X0) <~> happy(X0))) [input p7]
13. ! [X0] : ((~calm(X0) | tall(X0)) <=> (old(X0) & ~humble(X0))) [input p12]
14. humble(john) <=> ? [X0] : (~humble(X0) <~> ~calm(X0)) [input p13]
16. ? [X0] : (~patient(X0) | funny(X0)) <=> (wise(john) <~> happy(john)) [input p15]
21. tall(john) | funny(john) [input p20]
22. calm(john) [input hypothesis]
33. ! [X0] : ((~wise(X0) <~> happy(X0)) | (~generous(X0) <=> generous(X0))) [ennf transformation 8]
50. ! [X0] : (((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) [nnf transformation 33]
59. ! [X0] : (((~calm(X0) | tall(X0)) | (~old(X0) | humble(X0))) & ((old(X0) & ~humble(X0)) | (calm(X0) & ~tall(X0)))) [nnf transformation 13]
60. ! [X0] : ((~calm(X0) | tall(X0) | ~old(X0) | humble(X0)) & ((old(X0) & ~humble(X0)) | (calm(X0) & ~tall(X0)))) [flattening 59]
61. (humble(john) | ! [X0] : ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) & (? [X0] : ((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | ~humble(john)) [nnf transformation 14]
62. (humble(john) | ! [X0] : ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) & (? [X1] : ((calm(X1) | humble(X1)) & (~calm(X1) | ~humble(X1))) | ~humble(john)) [rectify 61]
63. ? [X1] : ((calm(X1) | humble(X1)) & (~calm(X1) | ~humble(X1))) => ((calm(sK5) | humble(sK5)) & (~calm(sK5) | ~humble(sK5))) [choice axiom]
64. (humble(john) | ! [X0] : ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) & (((calm(sK5) | humble(sK5)) & (~calm(sK5) | ~humble(sK5))) | ~humble(john)) [skolemisation 62,63]
70. (? [X0] : (~patient(X0) | funny(X0)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X0] : (patient(X0) & ~funny(X0))) [nnf transformation 16]
71. (? [X0] : (~patient(X0) | funny(X0)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X1] : (patient(X1) & ~funny(X1))) [rectify 70]
72. ? [X0] : (~patient(X0) | funny(X0)) => (~patient(sK8) | funny(sK8)) [choice axiom]
73. ((~patient(sK8) | funny(sK8)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X1] : (patient(X1) & ~funny(X1))) [skolemisation 71,72]
104. happy(X0) | ~wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
105. happy(X0) | ~wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
106. ~happy(X0) | wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
107. ~happy(X0) | wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
121. ~humble(X0) | ~tall(X0) [cnf transformation 60]
128. humble(john) | ~calm(X0) | humble(X0) [cnf transformation 64]
134. happy(john) | wise(john) | ~funny(X1) [cnf transformation 73]
136. ~happy(john) | ~wise(john) | ~funny(X1) [cnf transformation 73]
146. tall(john) | funny(john) [cnf transformation 21]
147. calm(john) [cnf transformation 22]
148. happy(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 104]
149. happy(X0) | ~wise(X0) | ~generous(X0) [duplicate literal removal 105]
150. ~happy(X0) | wise(X0) | generous(X0) [duplicate literal removal 106]
151. ~happy(X0) | wise(X0) | ~generous(X0) [duplicate literal removal 107]
203. ~happy(X0) | wise(X0) [subsumption resolution 150,151]
204. ~wise(X0) | happy(X0) [subsumption resolution 148,149]
240. 19 <=> ! [X0] : (~calm(X0) | humble(X0)) [avatar definition]
241. ~calm(X0) | humble(X0) <- (19) [avatar component clause 240]
243. 20 <=> humble(john) [avatar definition]
245. humble(john) <- (20) [avatar component clause 243]
246. 19 | 20 [avatar split clause 128,243,240]
290. 30 <=> wise(john) [avatar definition]
294. ~wise(john) | ~funny(X1) [subsumption resolution 136,204]
296. 31 <=> ! [X1] : ~funny(X1) [avatar definition]
297. ~funny(X1) <- (31) [avatar component clause 296]
298. 31 | ~30 [avatar split clause 294,290,296]
301. wise(john) | ~funny(X1) [subsumption resolution 134,203]
302. 31 | 30 [avatar split clause 301,290,296]
324. 36 <=> funny(john) [avatar definition]
326. funny(john) <- (36) [avatar component clause 324]
328. 37 <=> tall(john) [avatar definition]
330. tall(john) <- (37) [avatar component clause 328]
331. 36 | 37 [avatar split clause 146,328,324]
332. $false <- (31, 36) [resolution 326,297]
333. ~31 | ~36 [avatar contradiction clause 332]
353. humble(john) <- (19) [resolution 241,147]
357. 20 | ~19 [avatar split clause 353,240,243]
359. ~tall(john) <- (20) [resolution 245,121]
360. $false <- (20, 37) [subsumption resolution 359,330]
361. ~20 | ~37 [avatar contradiction clause 360]
362. $false [avatar sat refutation 246,298,302,331,333,357,361]
% SZS output end Proof for 5243129044311888200781435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or curious is both brave and not generous and vice versa.
If someone is either tall or strong then mary is both not wise and not quiet.
Everyone who is not tall is not rich or old and vice versa.
Everyone who is either old or not happy is both not kind and wise and vice versa.
If someone is either brave or not tall then someone is both not wise and not funny.
Everyone who is either not brave or not kind is tall or brave and vice versa.
If mary is either not kind or not creative then someone is not curious.
Everyone who is both not tall and not creative is either not funny or not brave.
Everyone who is not kind is both strong and not quiet and vice versa.
If alice is not strong then mary is either not calm or wise.
If fred is either not quiet or not curious then someone is strong.
If fred is not brave or not curious then john is not tall.
Everyone who is calm is creative and vice versa.
If someone is not wise then fred is not kind or wise and vice versa.
If someone is both tall and old then alice is brave or tall.
If susan is generous then paul is old or not quiet.
Someone is either wise or humble.
Fred is both patient and not wise.
Susan is old or kind.
Fred is old or not quiet.
Alice is not rich.
Someone is either curious or calm.
Someone is either funny or happy.
Someone is kind or not humble. | Mary is wise. | contradiction | (![X]:((~strong(X)<~>curious(X))<=>(brave(X)&~generous(X))))&
((?[X]:((tall(X)<~>strong(X))))=>((~wise(mary)&~quiet(mary))))&
(![X]:(~tall(X)<=>(~rich(X)|old(X))))&
(![X]:((old(X)<~>~happy(X))<=>(~kind(X)&wise(X))))&
((?[X]:((brave(X)<~>~tall(X))))=>(?[X]:((~wise(X)&~funny(X)))))&
(![X]:((~brave(X)<~>~kind(X))<=>(tall(X)|brave(X))))&
(((~kind(mary)<~>~creative(mary)))=>(?[X]:(~curious(X))))&
(![X]:((~tall(X)&~creative(X))=>(~funny(X)<~>~brave(X))))&
(![X]:(~kind(X)<=>(strong(X)&~quiet(X))))&
((~strong(alice))=>((~calm(mary)<~>wise(mary))))&
(((~quiet(fred)<~>~curious(fred)))=>(?[X]:(strong(X))))&
(((~brave(fred)|~curious(fred)))=>(~tall(john)))&
(![X]:(calm(X)<=>creative(X)))&
((?[X]:(~wise(X)))<=>((~kind(fred)|wise(fred))))&
((?[X]:((tall(X)&old(X))))=>((brave(alice)|tall(alice))))&
((generous(susan))=>((old(paul)|~quiet(paul))))&
(?[X]:((wise(X)<~>humble(X))))&
((patient(fred)&~wise(fred)))&
((old(susan)|kind(susan)))&
((old(fred)|~quiet(fred)))&
(~rich(alice))&
(?[X]:((curious(X)<~>calm(X))))&
(?[X]:((funny(X)<~>happy(X))))&
(?[X]:((kind(X)|~humble(X)))) | wise(mary) | [
"p1",
"p2",
"p5",
"p8",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8580576006460234908676481
% SZS output start Proof for 8580576006460234908676481
2. ? [X0] : (tall(X0) <~> strong(X0)) => (~quiet(mary) & ~wise(mary)) [input p1]
3. ! [X0] : (~tall(X0) <=> (old(X0) | ~rich(X0))) [input p2]
6. ! [X0] : ((~brave(X0) <~> ~kind(X0)) <=> (brave(X0) | tall(X0))) [input p5]
9. ! [X0] : (~kind(X0) <=> (~quiet(X0) & strong(X0))) [input p8]
21. ~rich(alice) [input p20]
25. wise(mary) [input hypothesis]
28. (~quiet(mary) & ~wise(mary)) | ! [X0] : (tall(X0) <=> strong(X0)) [ennf transformation 2]
42. (~quiet(mary) & ~wise(mary)) | ! [X0] : ((tall(X0) | ~strong(X0)) & (strong(X0) | ~tall(X0))) [nnf transformation 28]
43. ! [X0] : ((~tall(X0) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | tall(X0))) [nnf transformation 3]
44. ! [X0] : ((~tall(X0) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | tall(X0))) [flattening 43]
51. ! [X0] : ((((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0))))) [nnf transformation 6]
52. ! [X0] : ((((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0))))) [flattening 51]
57. ! [X0] : ((~kind(X0) | (quiet(X0) | ~strong(X0))) & ((~quiet(X0) & strong(X0)) | kind(X0))) [nnf transformation 9]
58. ! [X0] : ((~kind(X0) | quiet(X0) | ~strong(X0)) & ((~quiet(X0) & strong(X0)) | kind(X0))) [flattening 57]
86. ~wise(mary) | strong(X0) | ~tall(X0) [cnf transformation 42]
87. ~wise(mary) | tall(X0) | ~strong(X0) [cnf transformation 42]
91. ~tall(X0) | rich(X0) [cnf transformation 44]
103. brave(X0) | tall(X0) | ~kind(X0) | brave(X0) [cnf transformation 52]
106. ~kind(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 52]
113. kind(X0) | strong(X0) [cnf transformation 58]
134. ~rich(alice) [cnf transformation 21]
140. wise(mary) [cnf transformation 25]
141. brave(X0) | tall(X0) | ~kind(X0) [duplicate literal removal 103]
142. ~kind(X0) | ~brave(X0) [duplicate literal removal 106]
144. 1 <=> ! [X0] : (tall(X0) | ~strong(X0)) [avatar definition]
145. ~strong(X0) | tall(X0) <- (1) [avatar component clause 144]
152. 3 <=> ! [X0] : (strong(X0) | ~tall(X0)) [avatar definition]
153. ~tall(X0) | strong(X0) <- (3) [avatar component clause 152]
156. 4 <=> wise(mary) [avatar definition]
159. 1 | ~4 [avatar split clause 87,156,144]
160. 3 | ~4 [avatar split clause 86,156,152]
179. ~kind(X0) | tall(X0) [subsumption resolution 141,142]
195. 12 <=> strong(alice) [avatar definition]
196. ~strong(alice) <- (~12) [avatar component clause 195]
197. strong(alice) <- (12) [avatar component clause 195]
313. 4 [avatar split clause 140,156]
317. tall(alice) <- (1, 12) [resolution 145,197]
320. rich(alice) <- (1, 12) [resolution 317,91]
321. $false <- (1, 12) [subsumption resolution 320,134]
322. ~1 | ~12 [avatar contradiction clause 321]
328. tall(X0) | strong(X0) [resolution 179,113]
329. tall(X0) <- (1) [subsumption resolution 328,145]
331. strong(X0) <- (1, 3) [resolution 329,153]
343. $false <- (1, 3, ~12) [resolution 331,196]
344. ~1 | ~3 | 12 [avatar contradiction clause 343]
345. $false [avatar sat refutation 159,160,313,322,344]
% SZS output end Proof for 8580576006460234908676481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not rich is either rich or not generous and vice versa.
If someone is either curious or not calm then lucy is both not generous and calm and vice versa.
If someone is curious or not wise then someone is both not quiet and old.
Everyone who is both happy and not wise is generous or funny.
If someone is both happy and not quiet then someone is not happy or not tall.
Everyone who is either not patient or not kind is patient and vice versa.
If paul is not strong then someone is either wise or not happy.
Everyone who is both tall and not happy is generous or kind and vice versa.
Everyone who is either rich or not rich is both not happy and not old.
If someone is quiet then someone is old or not calm and vice versa.
If someone is both funny and not patient then someone is quiet.
If alice is both happy and tall then paul is both curious and not calm and vice versa.
If someone is not happy then fred is brave or not kind and vice versa.
Everyone who is brave or wise is rich or strong.
If susan is creative then someone is strong and vice versa.
If someone is strong then someone is not funny.
Someone is not quiet.
Someone is either happy or strong.
Alice is both funny and not quiet.
Someone is patient or quiet.
Someone is either not patient or not creative. | Susan is not happy. | entailment | (![X]:((patient(X)|~rich(X))<=>(rich(X)<~>~generous(X))))&
((?[X]:((curious(X)<~>~calm(X))))<=>((~generous(lucy)&calm(lucy))))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:((~quiet(X)&old(X)))))&
(![X]:((happy(X)&~wise(X))=>(generous(X)|funny(X))))&
((?[X]:((happy(X)&~quiet(X))))=>(?[X]:((~happy(X)|~tall(X)))))&
(![X]:((~patient(X)<~>~kind(X))<=>patient(X)))&
((~strong(paul))=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:((tall(X)&~happy(X))<=>(generous(X)|kind(X))))&
(![X]:((rich(X)<~>~rich(X))=>(~happy(X)&~old(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((old(X)|~calm(X)))))&
((?[X]:((funny(X)&~patient(X))))=>(?[X]:(quiet(X))))&
(((happy(alice)&tall(alice)))<=>((curious(paul)&~calm(paul))))&
((?[X]:(~happy(X)))<=>((brave(fred)|~kind(fred))))&
(![X]:((brave(X)|wise(X))=>(rich(X)|strong(X))))&
((creative(susan))<=>(?[X]:(strong(X))))&
((?[X]:(strong(X)))=>(?[X]:(~funny(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((happy(X)<~>strong(X))))&
((funny(alice)&~quiet(alice)))&
(?[X]:((patient(X)|quiet(X))))&
(?[X]:((~patient(X)<~>~creative(X)))) | ~happy(susan) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3389685406894812739969939
% SZS output start Proof for 3389685406894812739969939
9. ! [X0] : ((rich(X0) <~> ~rich(X0)) => (~old(X0) & ~happy(X0))) [input p8]
22. happy(susan) [input hypothesis]
33. ! [X0] : ((~old(X0) & ~happy(X0)) | (rich(X0) <=> ~rich(X0))) [ennf transformation 9]
57. ! [X0] : ((~old(X0) & ~happy(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) [nnf transformation 33]
119. ~happy(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 57]
120. ~happy(X0) | rich(X0) | rich(X0) [cnf transformation 57]
147. happy(susan) [cnf transformation 22]
148. ~happy(X0) | ~rich(X0) [duplicate literal removal 119]
149. ~happy(X0) | rich(X0) [duplicate literal removal 120]
231. ~happy(X0) [subsumption resolution 148,149]
310. $false [subsumption resolution 147,231]
% SZS output end Proof for 3389685406894812739969939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then fred is either rich or kind and vice versa.
If mary is not happy or humble then someone is not happy or not generous and vice versa.
If susan is calm or not creative then someone is not happy and vice versa.
If alice is not strong or not funny then someone is tall.
If someone is both funny and not strong then someone is rich and vice versa.
If someone is both strong and calm then fred is either strong or not tall and vice versa.
If someone is not patient then susan is either rich or not rich.
Everyone who is both not happy and not strong is happy and vice versa.
If john is either rich or tall then lucy is either tall or humble.
Everyone who is not happy or creative is both not creative and calm.
If alice is either not creative or not generous then john is rich.
Everyone who is not calm is both quiet and creative and vice versa.
Everyone who is both not generous and wise is humble.
If lucy is funny or curious then susan is both humble and funny and vice versa.
If lucy is both not brave and kind then paul is both not old and not generous.
If fred is either curious or brave then alice is not tall.
Someone is either not rich or wise.
Lucy is not kind or kind.
Mary is both not brave and calm.
Someone is not curious.
Someone is strong or not old.
Someone is both not patient and not kind. | Alice is not generous. | entailment | ((?[X]:(~generous(X)))<=>((rich(fred)<~>kind(fred))))&
(((~happy(mary)|humble(mary)))<=>(?[X]:((~happy(X)|~generous(X)))))&
(((calm(susan)|~creative(susan)))<=>(?[X]:(~happy(X))))&
(((~strong(alice)|~funny(alice)))=>(?[X]:(tall(X))))&
((?[X]:((funny(X)&~strong(X))))<=>(?[X]:(rich(X))))&
((?[X]:((strong(X)&calm(X))))<=>((strong(fred)<~>~tall(fred))))&
((?[X]:(~patient(X)))=>((rich(susan)<~>~rich(susan))))&
(![X]:((~happy(X)&~strong(X))<=>happy(X)))&
(((rich(john)<~>tall(john)))=>((tall(lucy)<~>humble(lucy))))&
(![X]:((~happy(X)|creative(X))=>(~creative(X)&calm(X))))&
(((~creative(alice)<~>~generous(alice)))=>(rich(john)))&
(![X]:(~calm(X)<=>(quiet(X)&creative(X))))&
(![X]:((~generous(X)&wise(X))=>humble(X)))&
(((funny(lucy)|curious(lucy)))<=>((humble(susan)&funny(susan))))&
(((~brave(lucy)&kind(lucy)))=>((~old(paul)&~generous(paul))))&
(((curious(fred)<~>brave(fred)))=>(~tall(alice)))&
(?[X]:((~rich(X)<~>wise(X))))&
((~kind(lucy)|kind(lucy)))&
((~brave(mary)&calm(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((strong(X)|~old(X))))&
(?[X]:((~patient(X)&~kind(X)))) | ~generous(alice) | [
"p4",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8712863755083942114194644
% SZS output start Proof for 8712863755083942114194644
5. ? [X0] : (~strong(X0) & funny(X0)) <=> ? [X0] : rich(X0) [input p4]
8. ! [X0] : ((~strong(X0) & ~happy(X0)) <=> happy(X0)) [input p7]
10. ! [X0] : ((creative(X0) | ~happy(X0)) => (calm(X0) & ~creative(X0))) [input p9]
11. (~creative(alice) <~> ~generous(alice)) => rich(john) [input p10]
23. generous(alice) [input hypothesis]
24. ? [X0] : (~strong(X0) & funny(X0)) <=> ? [X1] : rich(X1) [rectify 5]
30. ! [X0] : ((calm(X0) & ~creative(X0)) | (~creative(X0) & happy(X0))) [ennf transformation 10]
31. rich(john) | (~creative(alice) <=> ~generous(alice)) [ennf transformation 11]
53. (? [X0] : (~strong(X0) & funny(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (strong(X0) | ~funny(X0))) [nnf transformation 24]
54. (? [X0] : (~strong(X0) & funny(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (strong(X3) | ~funny(X3))) [rectify 53]
55. ? [X0] : (~strong(X0) & funny(X0)) => (~strong(sK4) & funny(sK4)) [choice axiom]
56. ? [X2] : rich(X2) => rich(sK5) [choice axiom]
57. ((~strong(sK4) & funny(sK4)) | ! [X1] : ~rich(X1)) & (rich(sK5) | ! [X3] : (strong(X3) | ~funny(X3))) [skolemisation 54,56,55]
63. ! [X0] : (((~strong(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | (strong(X0) | happy(X0)))) [nnf transformation 8]
64. ! [X0] : (((~strong(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | strong(X0) | happy(X0))) [flattening 63]
66. rich(john) | ((~creative(alice) | generous(alice)) & (~generous(alice) | creative(alice))) [nnf transformation 31]
94. ~strong(sK4) | ~rich(X1) [cnf transformation 57]
103. happy(X0) | strong(X0) | happy(X0) [cnf transformation 64]
104. ~happy(X0) | ~happy(X0) [cnf transformation 64]
111. ~creative(X0) | ~creative(X0) [cnf transformation 30]
114. rich(john) | ~generous(alice) | creative(alice) [cnf transformation 66]
136. generous(alice) [cnf transformation 23]
137. ~creative(X0) [duplicate literal removal 111]
138. happy(X0) | strong(X0) [duplicate literal removal 103]
139. ~happy(X0) [duplicate literal removal 104]
212. 16 <=> ! [X1] : ~rich(X1) [avatar definition]
213. ~rich(X1) <- (16) [avatar component clause 212]
215. 17 <=> strong(sK4) [avatar definition]
217. ~strong(sK4) <- (~17) [avatar component clause 215]
218. 16 | ~17 [avatar split clause 94,215,212]
257. strong(X0) [subsumption resolution 138,139]
263. 27 <=> rich(john) [avatar definition]
265. rich(john) <- (27) [avatar component clause 263]
279. rich(john) | ~generous(alice) [subsumption resolution 114,137]
281. 30 <=> generous(alice) [avatar definition]
284. ~30 | 27 [avatar split clause 279,263,281]
343. 30 [avatar split clause 136,281]
351. $false <- (16, 27) [resolution 265,213]
352. ~16 | ~27 [avatar contradiction clause 351]
353. $false <- (~17) [subsumption resolution 217,257]
354. 17 [avatar contradiction clause 353]
355. $false [avatar sat refutation 218,284,343,352,354]
% SZS output end Proof for 8712863755083942114194644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not curious is either not happy or not kind and vice versa. If someone is both funny and humble then someone is either not calm or not curious. If someone is not strong or not kind then susan is both funny and not humble and vice versa. Everyone who is not humble is not funny and vice versa. If mary is not wise then lucy is tall. Everyone who is both creative and not quiet is either rich or not strong and vice versa. If someone is happy then paul is kind or not humble and vice versa. If alice is not brave or strong then susan is both not wise and not humble. Everyone who is both tall and not rich is not happy or not humble and vice versa. Everyone who is both strong and creative is brave. If someone is patient then someone is either patient or curious and vice versa. If paul is either curious or happy then someone is funny or not happy and vice versa. Everyone who is both not quiet and humble is not tall or humble. Everyone who is not brave or creative is either not rich or not curious. If paul is brave then alice is both not quiet and rich. Alice is not generous. Someone is either not tall or old. Someone is tall. John is strong. Someone is strong. | Mary is tall. | entailment | (![X]:((~generous(X)&~curious(X))<=>(~happy(X)<~>~kind(X))))&
((?[X]:((funny(X)&humble(X))))=>(?[X]:((~calm(X)<~>~curious(X)))))&
((?[X]:((~strong(X)|~kind(X))))<=>((funny(susan)&~humble(susan))))&
(![X]:(~humble(X)<=>~funny(X)))&
((~wise(mary))=>(tall(lucy)))&
(![X]:((creative(X)&~quiet(X))<=>(rich(X)<~>~strong(X))))&
((?[X]:(happy(X)))<=>((kind(paul)|~humble(paul))))&
(((~brave(alice)|strong(alice)))=>((~wise(susan)&~humble(susan))))&
(![X]:((tall(X)&~rich(X))<=>(~happy(X)|~humble(X))))&
(![X]:((strong(X)&creative(X))=>brave(X)))&
((?[X]:(patient(X)))<=>(?[X]:((patient(X)<~>curious(X)))))&
(((curious(paul)<~>happy(paul)))<=>(?[X]:((funny(X)|~happy(X)))))&
(![X]:((~quiet(X)&humble(X))=>(~tall(X)|humble(X))))&
(![X]:((~brave(X)|creative(X))=>(~rich(X)<~>~curious(X))))&
((brave(paul))=>((~quiet(alice)&rich(alice))))&
(~generous(alice))&
(?[X]:((~tall(X)<~>old(X))))&
(?[X]:(tall(X)))&
(strong(john))&
(?[X]:(strong(X))) | tall(mary) | [
"p0",
"p2",
"p3",
"p5",
"p7",
"p8",
"p9",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7585327527807073172347872
% SZS output start Proof for 7585327527807073172347872
1. ! [X0] : ((~curious(X0) & ~generous(X0)) <=> (~happy(X0) <~> ~kind(X0))) [input p0]
3. ? [X0] : (~kind(X0) | ~strong(X0)) <=> (~humble(susan) & funny(susan)) [input p2]
4. ! [X0] : (~humble(X0) <=> ~funny(X0)) [input p3]
6. ! [X0] : ((~quiet(X0) & creative(X0)) <=> (rich(X0) <~> ~strong(X0))) [input p5]
8. (strong(alice) | ~brave(alice)) => (~humble(susan) & ~wise(susan)) [input p7]
9. ! [X0] : ((~rich(X0) & tall(X0)) <=> (~humble(X0) | ~happy(X0))) [input p8]
10. ! [X0] : ((creative(X0) & strong(X0)) => brave(X0)) [input p9]
12. (curious(paul) <~> happy(paul)) <=> ? [X0] : (~happy(X0) | funny(X0)) [input p11]
14. ! [X0] : ((creative(X0) | ~brave(X0)) => (~rich(X0) <~> ~curious(X0))) [input p13]
15. brave(paul) => (rich(alice) & ~quiet(alice)) [input p14]
16. ~generous(alice) [input p15]
21. ~tall(mary) [input hypothesis]
26. (~humble(susan) & ~wise(susan)) | (~strong(alice) & brave(alice)) [ennf transformation 8]
27. ! [X0] : (brave(X0) | (~creative(X0) | ~strong(X0))) [ennf transformation 10]
28. ! [X0] : (brave(X0) | ~creative(X0) | ~strong(X0)) [flattening 27]
31. ! [X0] : ((~rich(X0) <~> ~curious(X0)) | (~creative(X0) & brave(X0))) [ennf transformation 14]
32. (rich(alice) & ~quiet(alice)) | ~brave(paul) [ennf transformation 15]
33. ! [X0] : (((~curious(X0) & ~generous(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (curious(X0) | generous(X0)))) [nnf transformation 1]
34. ! [X0] : (((~curious(X0) & ~generous(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | curious(X0) | generous(X0))) [flattening 33]
39. (? [X0] : (~kind(X0) | ~strong(X0)) | (humble(susan) | ~funny(susan))) & ((~humble(susan) & funny(susan)) | ! [X0] : (kind(X0) & strong(X0))) [nnf transformation 3]
40. (? [X0] : (~kind(X0) | ~strong(X0)) | humble(susan) | ~funny(susan)) & ((~humble(susan) & funny(susan)) | ! [X0] : (kind(X0) & strong(X0))) [flattening 39]
41. (? [X0] : (~kind(X0) | ~strong(X0)) | humble(susan) | ~funny(susan)) & ((~humble(susan) & funny(susan)) | ! [X1] : (kind(X1) & strong(X1))) [rectify 40]
42. ? [X0] : (~kind(X0) | ~strong(X0)) => (~kind(sK1) | ~strong(sK1)) [choice axiom]
43. ((~kind(sK1) | ~strong(sK1)) | humble(susan) | ~funny(susan)) & ((~humble(susan) & funny(susan)) | ! [X1] : (kind(X1) & strong(X1))) [skolemisation 41,42]
44. ! [X0] : ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))) [nnf transformation 4]
45. ! [X0] : (((~quiet(X0) & creative(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (quiet(X0) | ~creative(X0)))) [nnf transformation 6]
46. ! [X0] : (((~quiet(X0) & creative(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | quiet(X0) | ~creative(X0))) [flattening 45]
52. ! [X0] : (((~rich(X0) & tall(X0)) | (humble(X0) & happy(X0))) & ((~humble(X0) | ~happy(X0)) | (rich(X0) | ~tall(X0)))) [nnf transformation 9]
53. ! [X0] : (((~rich(X0) & tall(X0)) | (humble(X0) & happy(X0))) & (~humble(X0) | ~happy(X0) | rich(X0) | ~tall(X0))) [flattening 52]
59. (((~happy(paul) | ~curious(paul)) & (happy(paul) | curious(paul))) | ! [X0] : (happy(X0) & ~funny(X0))) & (? [X0] : (~happy(X0) | funny(X0)) | ((curious(paul) | ~happy(paul)) & (happy(paul) | ~curious(paul)))) [nnf transformation 12]
60. (((~happy(paul) | ~curious(paul)) & (happy(paul) | curious(paul))) | ! [X0] : (happy(X0) & ~funny(X0))) & (? [X1] : (~happy(X1) | funny(X1)) | ((curious(paul) | ~happy(paul)) & (happy(paul) | ~curious(paul)))) [rectify 59]
61. ? [X1] : (~happy(X1) | funny(X1)) => (~happy(sK5) | funny(sK5)) [choice axiom]
62. (((~happy(paul) | ~curious(paul)) & (happy(paul) | curious(paul))) | ! [X0] : (happy(X0) & ~funny(X0))) & ((~happy(sK5) | funny(sK5)) | ((curious(paul) | ~happy(paul)) & (happy(paul) | ~curious(paul)))) [skolemisation 60,61]
63. ! [X0] : (((curious(X0) | rich(X0)) & (~curious(X0) | ~rich(X0))) | (~creative(X0) & brave(X0))) [nnf transformation 31]
71. ~kind(X0) | ~happy(X0) | curious(X0) | generous(X0) [cnf transformation 34]
75. ~kind(X0) | ~curious(X0) | happy(X0) [cnf transformation 34]
79. funny(susan) | strong(X1) [cnf transformation 43]
80. funny(susan) | kind(X1) [cnf transformation 43]
81. ~humble(susan) | strong(X1) [cnf transformation 43]
84. ~funny(X0) | humble(X0) [cnf transformation 44]
85. ~humble(X0) | funny(X0) [cnf transformation 44]
89. ~rich(X0) | ~strong(X0) | creative(X0) [cnf transformation 46]
99. ~humble(susan) | ~strong(alice) [cnf transformation 26]
102. tall(X0) | humble(X0) [cnf transformation 53]
103. ~rich(X0) | happy(X0) [cnf transformation 53]
105. ~creative(X0) | brave(X0) | ~strong(X0) [cnf transformation 28]
114. ~happy(paul) | ~curious(paul) | ~funny(X0) [cnf transformation 62]
118. ~rich(X0) | ~curious(X0) | ~creative(X0) [cnf transformation 63]
119. brave(X0) | rich(X0) | curious(X0) [cnf transformation 63]
122. rich(alice) | ~brave(paul) [cnf transformation 32]
123. ~generous(alice) [cnf transformation 16]
129. ~tall(mary) [cnf transformation 21]
144. 4 <=> funny(susan) [avatar definition]
145. funny(susan) <- (4) [avatar component clause 144]
148. 5 <=> humble(susan) [avatar definition]
149. ~humble(susan) <- (~5) [avatar component clause 148]
161. 8 <=> ! [X1] : kind(X1) [avatar definition]
162. kind(X1) <- (8) [avatar component clause 161]
165. 9 <=> ! [X1] : strong(X1) [avatar definition]
166. strong(X1) <- (9) [avatar component clause 165]
167. 9 | ~5 [avatar split clause 81,148,165]
168. 8 | 4 [avatar split clause 80,144,161]
169. 9 | 4 [avatar split clause 79,144,165]
198. 16 <=> strong(alice) [avatar definition]
200. ~strong(alice) <- (~16) [avatar component clause 198]
201. ~16 | ~5 [avatar split clause 99,148,198]
242. 26 <=> curious(paul) [avatar definition]
243. curious(paul) <- (26) [avatar component clause 242]
244. ~curious(paul) <- (~26) [avatar component clause 242]
246. 27 <=> happy(paul) [avatar definition]
251. 28 <=> ! [X0] : ~funny(X0) [avatar definition]
252. ~funny(X0) <- (28) [avatar component clause 251]
253. 28 | ~26 | ~27 [avatar split clause 114,246,242,251]
267. 31 <=> brave(paul) [avatar definition]
269. ~brave(paul) <- (~31) [avatar component clause 267]
271. 32 <=> rich(alice) [avatar definition]
273. rich(alice) <- (32) [avatar component clause 271]
274. ~31 | 32 [avatar split clause 122,271,267]
295. humble(susan) <- (4) [resolution 84,145]
296. $false <- (4, ~5) [subsumption resolution 295,149]
297. ~4 | 5 [avatar contradiction clause 296]
302. humble(mary) [resolution 102,129]
304. funny(mary) [resolution 302,85]
312. ~curious(X0) | happy(X0) <- (8) [resolution 75,162]
317. happy(paul) <- (8, 26) [resolution 312,243]
322. 27 | ~8 | ~26 [avatar split clause 317,242,161,246]
323. $false <- (9, ~16) [subsumption resolution 200,166]
324. ~9 | 16 [avatar contradiction clause 323]
331. $false <- (28) [resolution 252,304]
334. ~28 [avatar contradiction clause 331]
348. rich(paul) | curious(paul) <- (~31) [resolution 119,269]
349. rich(paul) <- (~26, ~31) [subsumption resolution 348,244]
353. ~strong(paul) | creative(paul) <- (~26, ~31) [resolution 349,89]
357. creative(paul) <- (9, ~26, ~31) [subsumption resolution 353,166]
363. ~happy(X0) | curious(X0) | generous(X0) <- (8) [resolution 71,162]
372. brave(paul) | ~strong(paul) <- (9, ~26, ~31) [resolution 357,105]
373. ~strong(paul) <- (9, ~26, ~31) [subsumption resolution 372,269]
374. $false <- (9, ~26, ~31) [subsumption resolution 373,166]
375. ~9 | 26 | 31 [avatar contradiction clause 374]
376. ~curious(alice) | ~creative(alice) <- (32) [resolution 273,118]
379. ~strong(alice) | creative(alice) <- (32) [resolution 273,89]
381. happy(alice) <- (32) [resolution 273,103]
383. 36 <=> creative(alice) [avatar definition]
387. 37 <=> curious(alice) [avatar definition]
389. ~curious(alice) <- (~37) [avatar component clause 387]
390. ~36 | ~37 | ~32 [avatar split clause 376,271,387,383]
391. creative(alice) <- (9, 32) [subsumption resolution 379,166]
392. 36 | ~9 | ~32 [avatar split clause 391,271,165,383]
426. curious(alice) | generous(alice) <- (8, 32) [resolution 363,381]
442. generous(alice) <- (8, 32, ~37) [subsumption resolution 426,389]
443. $false <- (8, 32, ~37) [subsumption resolution 442,123]
444. ~8 | ~32 | 37 [avatar contradiction clause 443]
472. $false [avatar sat refutation 167,168,169,201,253,274,297,322,324,334,375,390,392,444]
% SZS output end Proof for 7585327527807073172347872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not wise and not calm then someone is both not funny and not patient. Everyone who is rich is either strong or creative and vice versa. Everyone who is either humble or patient is either quiet or not curious and vice versa. If someone is either not humble or tall then john is quiet and vice versa. Everyone who is not funny is not humble or not rich and vice versa. Everyone who is kind or not generous is both creative and not funny and vice versa. Everyone who is not happy or calm is both humble and not quiet. Everyone who is either happy or old is not generous or not funny and vice versa. Everyone who is not patient or not creative is either generous or not humble. Everyone who is wise is tall and vice versa. Everyone who is not funny is old and vice versa. Everyone who is not patient or patient is not old and vice versa. If someone is not patient then someone is both not brave and strong. If someone is brave then susan is funny and vice versa. Paul is not wise. Someone is both strong and not happy. Lucy is either creative or not tall. Someone is strong or not quiet. | Lucy is not quiet. | entailment | (((~wise(lucy)&~calm(lucy)))=>(?[X]:((~funny(X)&~patient(X)))))&
(![X]:(rich(X)<=>(strong(X)<~>creative(X))))&
(![X]:((humble(X)<~>patient(X))<=>(quiet(X)<~>~curious(X))))&
((?[X]:((~humble(X)<~>tall(X))))<=>(quiet(john)))&
(![X]:(~funny(X)<=>(~humble(X)|~rich(X))))&
(![X]:((kind(X)|~generous(X))<=>(creative(X)&~funny(X))))&
(![X]:((~happy(X)|calm(X))=>(humble(X)&~quiet(X))))&
(![X]:((happy(X)<~>old(X))<=>(~generous(X)|~funny(X))))&
(![X]:((~patient(X)|~creative(X))=>(generous(X)<~>~humble(X))))&
(![X]:(wise(X)<=>tall(X)))&
(![X]:(~funny(X)<=>old(X)))&
(![X]:((~patient(X)|patient(X))<=>~old(X)))&
((?[X]:(~patient(X)))=>(?[X]:((~brave(X)&strong(X)))))&
((?[X]:(brave(X)))<=>(funny(susan)))&
(~wise(paul))&
(?[X]:((strong(X)&~happy(X))))&
((creative(lucy)<~>~tall(lucy)))&
(?[X]:((strong(X)|~quiet(X)))) | ~quiet(lucy) | [
"p5",
"p6",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6012963620847523362364594
% SZS output start Proof for 6012963620847523362364594
6. ! [X0] : ((~generous(X0) | kind(X0)) <=> (~funny(X0) & creative(X0))) [input p5]
7. ! [X0] : ((calm(X0) | ~happy(X0)) => (~quiet(X0) & humble(X0))) [input p6]
8. ! [X0] : ((happy(X0) <~> old(X0)) <=> (~funny(X0) | ~generous(X0))) [input p7]
11. ! [X0] : (~funny(X0) <=> old(X0)) [input p10]
12. ! [X0] : ((patient(X0) | ~patient(X0)) <=> ~old(X0)) [input p11]
19. quiet(lucy) [input hypothesis]
23. ! [X0] : ((~quiet(X0) & humble(X0)) | (~calm(X0) & happy(X0))) [ennf transformation 7]
36. ! [X0] : (((~generous(X0) | kind(X0)) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | (generous(X0) & ~kind(X0)))) [nnf transformation 6]
37. ! [X0] : ((~generous(X0) | kind(X0) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | (generous(X0) & ~kind(X0)))) [flattening 36]
38. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (funny(X0) & generous(X0))) & ((~funny(X0) | ~generous(X0)) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [nnf transformation 8]
39. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (funny(X0) & generous(X0))) & (~funny(X0) | ~generous(X0) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [flattening 38]
42. ! [X0] : ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0))) [nnf transformation 11]
43. ! [X0] : (((patient(X0) | ~patient(X0)) | old(X0)) & (~old(X0) | (~patient(X0) & patient(X0)))) [nnf transformation 12]
44. ! [X0] : ((patient(X0) | ~patient(X0) | old(X0)) & (~old(X0) | (~patient(X0) & patient(X0)))) [flattening 43]
81. ~funny(X0) | generous(X0) [cnf transformation 37]
85. ~quiet(X0) | happy(X0) [cnf transformation 23]
87. ~funny(X0) | ~generous(X0) | old(X0) | ~happy(X0) [cnf transformation 39]
99. old(X0) | funny(X0) [cnf transformation 42]
101. ~old(X0) | patient(X0) [cnf transformation 44]
102. ~old(X0) | ~patient(X0) [cnf transformation 44]
114. quiet(lucy) [cnf transformation 19]
156. ~happy(X0) | old(X0) | ~funny(X0) [subsumption resolution 87,81]
158. ~old(X0) [subsumption resolution 101,102]
210. happy(lucy) [resolution 85,114]
215. funny(X0) [resolution 99,158]
288. old(lucy) | ~funny(lucy) [resolution 156,210]
290. ~funny(lucy) [subsumption resolution 288,158]
291. $false [subsumption resolution 290,215]
% SZS output end Proof for 6012963620847523362364594
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is not generous and vice versa. If someone is both wise and generous then mary is both humble and not calm and vice versa. If someone is either patient or tall then mary is creative or happy and vice versa. Everyone who is either not creative or not humble is both humble and not curious and vice versa. If someone is not curious then paul is both not curious and brave. Everyone who is curious is both not rich and generous. Everyone who is either patient or brave is brave or not wise. Everyone who is either not quiet or not brave is quiet and vice versa. If lucy is both kind and old then lucy is either kind or not patient and vice versa. Everyone who is not humble or not happy is either not kind or tall. If someone is quiet then someone is not patient or tall. Everyone who is quiet is not old or happy. If paul is both rich and not old then fred is not humble. If someone is both not happy and not rich then someone is not wise or not creative. Everyone who is both humble and curious is old or not happy. Someone is either funny or strong. Someone is not rich or patient. Susan is either not creative or not wise. Susan is not brave. Someone is not quiet or not humble. Paul is both not calm and not happy. Someone is either generous or not curious. Fred is both funny and creative. | Mary is not brave. | entailment | (![X]:(kind(X)<=>~generous(X)))&
((?[X]:((wise(X)&generous(X))))<=>((humble(mary)&~calm(mary))))&
((?[X]:((patient(X)<~>tall(X))))<=>((creative(mary)|happy(mary))))&
(![X]:((~creative(X)<~>~humble(X))<=>(humble(X)&~curious(X))))&
((?[X]:(~curious(X)))=>((~curious(paul)&brave(paul))))&
(![X]:(curious(X)=>(~rich(X)&generous(X))))&
(![X]:((patient(X)<~>brave(X))=>(brave(X)|~wise(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>quiet(X)))&
(((kind(lucy)&old(lucy)))<=>((kind(lucy)<~>~patient(lucy))))&
(![X]:((~humble(X)|~happy(X))=>(~kind(X)<~>tall(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~patient(X)|tall(X)))))&
(![X]:(quiet(X)=>(~old(X)|happy(X))))&
(((rich(paul)&~old(paul)))=>(~humble(fred)))&
((?[X]:((~happy(X)&~rich(X))))=>(?[X]:((~wise(X)|~creative(X)))))&
(![X]:((humble(X)&curious(X))=>(old(X)|~happy(X))))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:((~rich(X)|patient(X))))&
((~creative(susan)<~>~wise(susan)))&
(~brave(susan))&
(?[X]:((~quiet(X)|~humble(X))))&
((~calm(paul)&~happy(paul)))&
(?[X]:((generous(X)<~>~curious(X))))&
((funny(fred)&creative(fred))) | ~brave(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6766636266015220354617146
% SZS output start Proof for 6766636266015220354617146
8. ! [X0] : ((~quiet(X0) <~> ~brave(X0)) <=> quiet(X0)) [input p7]
24. brave(mary) [input hypothesis]
54. ! [X0] : ((((brave(X0) | quiet(X0)) & (~brave(X0) | ~quiet(X0))) | ~quiet(X0)) & (quiet(X0) | ((~quiet(X0) | brave(X0)) & (~brave(X0) | quiet(X0))))) [nnf transformation 8]
99. quiet(X0) | ~brave(X0) | quiet(X0) [cnf transformation 54]
101. ~brave(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
131. brave(mary) [cnf transformation 24]
134. quiet(X0) | ~brave(X0) [duplicate literal removal 99]
135. ~brave(X0) | ~quiet(X0) [duplicate literal removal 101]
203. ~brave(X0) [subsumption resolution 134,135]
304. $false [subsumption resolution 131,203]
% SZS output end Proof for 6766636266015220354617146
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then someone is either not old or not generous and vice versa.
Everyone who is either strong or old is both not creative and tall and vice versa.
If someone is both calm and not old then alice is either not curious or not rich and vice versa.
Everyone who is both old and generous is strong or rich and vice versa.
Everyone who is not creative is both not patient and not funny.
If someone is not generous or not quiet then someone is both not creative and not old.
Everyone who is curious or kind is either not happy or not old.
Everyone who is either happy or not strong is rich.
If paul is both funny and creative then mary is rich and vice versa.
Everyone who is both humble and patient is tall or not patient and vice versa.
Everyone who is either not funny or not kind is both not funny and old.
If susan is both curious and rich then someone is not rich or not quiet.
Everyone who is brave or creative is either curious or calm.
If someone is either not strong or tall then lucy is old or not calm.
Everyone who is either not brave or not happy is not wise.
Everyone who is not curious or not calm is not wise or rich and vice versa.
Alice is either not old or old.
Someone is creative or not strong.
Susan is brave.
Paul is either funny or humble.
Paul is both old and creative.
Susan is either humble or not quiet. | Lucy is not humble. | neutral | ((?[X]:(~humble(X)))<=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((strong(X)<~>old(X))<=>(~creative(X)&tall(X))))&
((?[X]:((calm(X)&~old(X))))<=>((~curious(alice)<~>~rich(alice))))&
(![X]:((old(X)&generous(X))<=>(strong(X)|rich(X))))&
(![X]:(~creative(X)=>(~patient(X)&~funny(X))))&
((?[X]:((~generous(X)|~quiet(X))))=>(?[X]:((~creative(X)&~old(X)))))&
(![X]:((curious(X)|kind(X))=>(~happy(X)<~>~old(X))))&
(![X]:((happy(X)<~>~strong(X))=>rich(X)))&
(((funny(paul)&creative(paul)))<=>(rich(mary)))&
(![X]:((humble(X)&patient(X))<=>(tall(X)|~patient(X))))&
(![X]:((~funny(X)<~>~kind(X))=>(~funny(X)&old(X))))&
(((curious(susan)&rich(susan)))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((brave(X)|creative(X))=>(curious(X)<~>calm(X))))&
((?[X]:((~strong(X)<~>tall(X))))=>((old(lucy)|~calm(lucy))))&
(![X]:((~brave(X)<~>~happy(X))=>~wise(X)))&
(![X]:((~curious(X)|~calm(X))<=>(~wise(X)|rich(X))))&
((~old(alice)<~>old(alice)))&
(?[X]:((creative(X)|~strong(X))))&
(brave(susan))&
((funny(paul)<~>humble(paul)))&
((old(paul)&creative(paul)))&
((humble(susan)<~>~quiet(susan))) | ~humble(lucy) | [] | null | 0 |
Everyone who is either not patient or not calm is both creative and generous and vice versa.
Everyone who is either funny or tall is both creative and not brave and vice versa.
If someone is not kind then someone is both not wise and not tall.
Everyone who is either generous or rich is either not tall or tall and vice versa.
If lucy is both not curious and strong then fred is quiet and vice versa.
Everyone who is tall is both not patient and not humble.
If someone is not calm then someone is not old or not brave and vice versa.
If lucy is not quiet or calm then someone is not rich or not funny.
If susan is both happy and not kind then someone is not funny and vice versa.
Everyone who is not strong or brave is not kind.
If someone is either not humble or tall then someone is both not rich and wise and vice versa.
If someone is not humble or tall then susan is funny or generous.
Everyone who is both not rich and tall is quiet and vice versa.
If fred is both brave and not brave then someone is both not quiet and generous and vice versa.
Everyone who is both happy and patient is either funny or generous and vice versa.
Everyone who is both quiet and not funny is both tall and quiet and vice versa.
Fred is both wise and not tall.
Someone is wise or not humble.
Someone is both humble and not patient.
Someone is happy.
John is not humble or not creative. | John is not generous. | entailment | (![X]:((~patient(X)<~>~calm(X))<=>(creative(X)&generous(X))))&
(![X]:((funny(X)<~>tall(X))<=>(creative(X)&~brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:((generous(X)<~>rich(X))<=>(~tall(X)<~>tall(X))))&
(((~curious(lucy)&strong(lucy)))<=>(quiet(fred)))&
(![X]:(tall(X)=>(~patient(X)&~humble(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~old(X)|~brave(X)))))&
(((~quiet(lucy)|calm(lucy)))=>(?[X]:((~rich(X)|~funny(X)))))&
(((happy(susan)&~kind(susan)))<=>(?[X]:(~funny(X))))&
(![X]:((~strong(X)|brave(X))=>~kind(X)))&
((?[X]:((~humble(X)<~>tall(X))))<=>(?[X]:((~rich(X)&wise(X)))))&
((?[X]:((~humble(X)|tall(X))))=>((funny(susan)|generous(susan))))&
(![X]:((~rich(X)&tall(X))<=>quiet(X)))&
(((brave(fred)&~brave(fred)))<=>(?[X]:((~quiet(X)&generous(X)))))&
(![X]:((happy(X)&patient(X))<=>(funny(X)<~>generous(X))))&
(![X]:((quiet(X)&~funny(X))<=>(tall(X)&quiet(X))))&
((wise(fred)&~tall(fred)))&
(?[X]:((wise(X)|~humble(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:(happy(X)))&
((~humble(john)|~creative(john))) | ~generous(john) | [
"p5",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3681437123282682253674782
% SZS output start Proof for 3681437123282682253674782
6. ! [X0] : (tall(X0) => (~humble(X0) & ~patient(X0))) [input p5]
13. ! [X0] : ((tall(X0) & ~rich(X0)) <=> quiet(X0)) [input p12]
14. (~brave(fred) & brave(fred)) <=> ? [X0] : (generous(X0) & ~quiet(X0)) [input p13]
15. ! [X0] : ((patient(X0) & happy(X0)) <=> (funny(X0) <~> generous(X0))) [input p14]
16. ! [X0] : ((~funny(X0) & quiet(X0)) <=> (quiet(X0) & tall(X0))) [input p15]
22. generous(john) [input hypothesis]
27. ! [X0] : ((~humble(X0) & ~patient(X0)) | ~tall(X0)) [ennf transformation 6]
59. ! [X0] : (((tall(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (~tall(X0) | rich(X0)))) [nnf transformation 13]
60. ! [X0] : (((tall(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | ~tall(X0) | rich(X0))) [flattening 59]
61. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X0] : (generous(X0) & ~quiet(X0)) | (brave(fred) | ~brave(fred))) [nnf transformation 14]
62. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X0] : (generous(X0) & ~quiet(X0)) | brave(fred) | ~brave(fred)) [flattening 61]
63. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X1] : (generous(X1) & ~quiet(X1)) | brave(fred) | ~brave(fred)) [rectify 62]
64. ? [X1] : (generous(X1) & ~quiet(X1)) => (generous(sK7) & ~quiet(sK7)) [choice axiom]
65. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & ((generous(sK7) & ~quiet(sK7)) | brave(fred) | ~brave(fred)) [skolemisation 63,64]
66. ! [X0] : (((patient(X0) & happy(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~patient(X0) | ~happy(X0)))) [nnf transformation 15]
67. ! [X0] : (((patient(X0) & happy(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | ~patient(X0) | ~happy(X0))) [flattening 66]
68. ! [X0] : (((~funny(X0) & quiet(X0)) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | (funny(X0) | ~quiet(X0)))) [nnf transformation 16]
69. ! [X0] : (((~funny(X0) & quiet(X0)) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | funny(X0) | ~quiet(X0))) [flattening 68]
101. ~tall(X0) | ~patient(X0) [cnf transformation 27]
123. ~quiet(X0) | tall(X0) [cnf transformation 60]
126. brave(fred) | ~generous(X0) | quiet(X0) [cnf transformation 65]
127. ~brave(fred) | ~generous(X0) | quiet(X0) [cnf transformation 65]
133. ~generous(X0) | funny(X0) | patient(X0) [cnf transformation 67]
137. ~funny(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 69]
145. generous(john) [cnf transformation 22]
285. 31 <=> ! [X0] : (~generous(X0) | quiet(X0)) [avatar definition]
286. ~generous(X0) | quiet(X0) <- (31) [avatar component clause 285]
288. 32 <=> brave(fred) [avatar definition]
291. 31 | ~32 [avatar split clause 127,288,285]
292. 31 | 32 [avatar split clause 126,288,285]
293. ~quiet(X0) | ~funny(X0) [subsumption resolution 137,123]
325. quiet(john) <- (31) [resolution 286,145]
329. ~funny(john) <- (31) [resolution 325,293]
330. tall(john) <- (31) [resolution 325,123]
371. ~patient(john) <- (31) [resolution 330,101]
405. funny(john) | patient(john) [resolution 133,145]
407. patient(john) <- (31) [subsumption resolution 405,329]
408. $false <- (31) [subsumption resolution 407,371]
409. ~31 [avatar contradiction clause 408]
411. $false [avatar sat refutation 291,292,409]
% SZS output end Proof for 3681437123282682253674782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then alice is both not calm and kind.
Everyone who is old is either curious or not funny.
If paul is either wise or old then lucy is generous or creative.
If john is both not curious and not brave then mary is either wise or not tall and vice versa.
Everyone who is either tall or not strong is rich.
Everyone who is quiet or not funny is either old or tall.
Everyone who is kind is brave or not curious.
If someone is both curious and creative then someone is not humble or not happy and vice versa.
If someone is not calm or patient then mary is not old or not calm.
Everyone who is funny is not tall or not humble.
If someone is both happy and not quiet then fred is not quiet.
Everyone who is curious is either patient or happy.
Everyone who is happy is not wise or patient.
Everyone who is not patient is either strong or not creative.
Everyone who is not humble or quiet is not strong or old and vice versa.
Everyone who is either patient or not calm is both kind and not curious.
Someone is both wise and not old.
Mary is both creative and not funny.
Alice is not humble.
Someone is either not wise or wise.
Susan is not happy or not humble.
Mary is both not patient and generous.
Fred is either brave or humble. | Susan is happy. | neutral | ((?[X]:(kind(X)))=>((~calm(alice)&kind(alice))))&
(![X]:(old(X)=>(curious(X)<~>~funny(X))))&
(((wise(paul)<~>old(paul)))=>((generous(lucy)|creative(lucy))))&
(((~curious(john)&~brave(john)))<=>((wise(mary)<~>~tall(mary))))&
(![X]:((tall(X)<~>~strong(X))=>rich(X)))&
(![X]:((quiet(X)|~funny(X))=>(old(X)<~>tall(X))))&
(![X]:(kind(X)=>(brave(X)|~curious(X))))&
((?[X]:((curious(X)&creative(X))))<=>(?[X]:((~humble(X)|~happy(X)))))&
((?[X]:((~calm(X)|patient(X))))=>((~old(mary)|~calm(mary))))&
(![X]:(funny(X)=>(~tall(X)|~humble(X))))&
((?[X]:((happy(X)&~quiet(X))))=>(~quiet(fred)))&
(![X]:(curious(X)=>(patient(X)<~>happy(X))))&
(![X]:(happy(X)=>(~wise(X)|patient(X))))&
(![X]:(~patient(X)=>(strong(X)<~>~creative(X))))&
(![X]:((~humble(X)|quiet(X))<=>(~strong(X)|old(X))))&
(![X]:((patient(X)<~>~calm(X))=>(kind(X)&~curious(X))))&
(?[X]:((wise(X)&~old(X))))&
((creative(mary)&~funny(mary)))&
(~humble(alice))&
(?[X]:((~wise(X)<~>wise(X))))&
((~happy(susan)|~humble(susan)))&
((~patient(mary)&generous(mary)))&
((brave(fred)<~>humble(fred))) | happy(susan) | [] | null | 0 |
If mary is old then someone is happy or not strong.
Everyone who is both not happy and not kind is humble or not wise and vice versa.
If someone is either not wise or patient then john is not quiet or not tall and vice versa.
If mary is not rich or humble then alice is brave.
Everyone who is not kind or not happy is both not calm and wise and vice versa.
If someone is either generous or not calm then lucy is quiet or wise and vice versa.
Everyone who is not creative is quiet or not rich.
Everyone who is either not funny or not patient is both not tall and not happy.
Everyone who is both not happy and patient is not humble and vice versa.
If susan is creative or generous then alice is not strong.
If alice is both not calm and not old then mary is funny.
Everyone who is both tall and strong is not humble or calm.
If someone is not old then john is either kind or quiet and vice versa.
Everyone who is either brave or strong is not old.
If someone is either generous or rich then someone is old.
Everyone who is either calm or not old is both not patient and not rich and vice versa.
Lucy is funny or curious.
Someone is not tall or happy.
Susan is not kind.
Someone is either not funny or patient.
Lucy is not humble.
Paul is both not quiet and curious.
Paul is both old and not strong.
Susan is both creative and rich. | Alice is calm. | contradiction | ((old(mary))=>(?[X]:((happy(X)|~strong(X)))))&
(![X]:((~happy(X)&~kind(X))<=>(humble(X)|~wise(X))))&
((?[X]:((~wise(X)<~>patient(X))))<=>((~quiet(john)|~tall(john))))&
(((~rich(mary)|humble(mary)))=>(brave(alice)))&
(![X]:((~kind(X)|~happy(X))<=>(~calm(X)&wise(X))))&
((?[X]:((generous(X)<~>~calm(X))))<=>((quiet(lucy)|wise(lucy))))&
(![X]:(~creative(X)=>(quiet(X)|~rich(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(~tall(X)&~happy(X))))&
(![X]:((~happy(X)&patient(X))<=>~humble(X)))&
(((creative(susan)|generous(susan)))=>(~strong(alice)))&
(((~calm(alice)&~old(alice)))=>(funny(mary)))&
(![X]:((tall(X)&strong(X))=>(~humble(X)|calm(X))))&
((?[X]:(~old(X)))<=>((kind(john)<~>quiet(john))))&
(![X]:((brave(X)<~>strong(X))=>~old(X)))&
((?[X]:((generous(X)<~>rich(X))))=>(?[X]:(old(X))))&
(![X]:((calm(X)<~>~old(X))<=>(~patient(X)&~rich(X))))&
((funny(lucy)|curious(lucy)))&
(?[X]:((~tall(X)|happy(X))))&
(~kind(susan))&
(?[X]:((~funny(X)<~>patient(X))))&
(~humble(lucy))&
((~quiet(paul)&curious(paul)))&
((old(paul)&~strong(paul)))&
((creative(susan)&rich(susan))) | calm(alice) | [
"p1",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 301498317137725780990698
% SZS output start Proof for 301498317137725780990698
2. ! [X0] : ((~kind(X0) & ~happy(X0)) <=> (~wise(X0) | humble(X0))) [input p1]
5. ! [X0] : ((~happy(X0) | ~kind(X0)) <=> (wise(X0) & ~calm(X0))) [input p4]
9. ! [X0] : ((patient(X0) & ~happy(X0)) <=> ~humble(X0)) [input p8]
25. calm(alice) [input hypothesis]
43. ! [X0] : (((~kind(X0) & ~happy(X0)) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | (kind(X0) | happy(X0)))) [nnf transformation 2]
44. ! [X0] : (((~kind(X0) & ~happy(X0)) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | kind(X0) | happy(X0))) [flattening 43]
50. ! [X0] : (((~happy(X0) | ~kind(X0)) | (~wise(X0) | calm(X0))) & ((wise(X0) & ~calm(X0)) | (happy(X0) & kind(X0)))) [nnf transformation 5]
51. ! [X0] : ((~happy(X0) | ~kind(X0) | ~wise(X0) | calm(X0)) & ((wise(X0) & ~calm(X0)) | (happy(X0) & kind(X0)))) [flattening 50]
58. ! [X0] : (((patient(X0) & ~happy(X0)) | humble(X0)) & (~humble(X0) | (~patient(X0) | happy(X0)))) [nnf transformation 9]
59. ! [X0] : (((patient(X0) & ~happy(X0)) | humble(X0)) & (~humble(X0) | ~patient(X0) | happy(X0))) [flattening 58]
78. ~humble(X0) | ~happy(X0) [cnf transformation 44]
91. ~calm(X0) | happy(X0) [cnf transformation 51]
107. ~happy(X0) | humble(X0) [cnf transformation 59]
137. calm(alice) [cnf transformation 25]
213. ~happy(X0) [subsumption resolution 107,78]
230. 19 <=> calm(alice) [avatar definition]
232. calm(alice) <- (19) [avatar component clause 230]
281. 19 [avatar split clause 137,230]
285. happy(alice) <- (19) [resolution 91,232]
286. $false <- (19) [subsumption resolution 285,213]
287. ~19 [avatar contradiction clause 286]
288. $false [avatar sat refutation 281,287]
% SZS output end Proof for 301498317137725780990698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or happy is not rich. If john is strong then alice is quiet. If someone is not calm then someone is not creative. If someone is either not patient or tall then lucy is either not generous or kind. Everyone who is not humble or not happy is both curious and not tall. Everyone who is both quiet and curious is both creative and not strong. If someone is humble then someone is not old. If someone is both not rich and quiet then john is not curious or curious. If fred is not old then someone is both not patient and not strong and vice versa. If fred is tall then someone is happy and vice versa. Everyone who is either not tall or patient is generous and vice versa. If someone is not happy or quiet then fred is not happy and vice versa. Everyone who is not rich is both not quiet and wise. If someone is either calm or curious then someone is either kind or happy and vice versa. If alice is either not strong or funny then someone is both not wise and tall and vice versa. Everyone who is humble or generous is both not strong and tall. Lucy is happy or quiet. Someone is not old. Alice is brave or humble. Fred is funny or not funny. John is humble or rich. Mary is both happy and humble. Alice is humble or not curious. Someone is either not strong or calm. | Fred is quiet. | contradiction | (![X]:((~tall(X)|happy(X))=>~rich(X)))&
((strong(john))=>(quiet(alice)))&
((?[X]:(~calm(X)))=>(?[X]:(~creative(X))))&
((?[X]:((~patient(X)<~>tall(X))))=>((~generous(lucy)<~>kind(lucy))))&
(![X]:((~humble(X)|~happy(X))=>(curious(X)&~tall(X))))&
(![X]:((quiet(X)&curious(X))=>(creative(X)&~strong(X))))&
((?[X]:(humble(X)))=>(?[X]:(~old(X))))&
((?[X]:((~rich(X)&quiet(X))))=>((~curious(john)|curious(john))))&
((~old(fred))<=>(?[X]:((~patient(X)&~strong(X)))))&
((tall(fred))<=>(?[X]:(happy(X))))&
(![X]:((~tall(X)<~>patient(X))<=>generous(X)))&
((?[X]:((~happy(X)|quiet(X))))<=>(~happy(fred)))&
(![X]:(~rich(X)=>(~quiet(X)&wise(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((kind(X)<~>happy(X)))))&
(((~strong(alice)<~>funny(alice)))<=>(?[X]:((~wise(X)&tall(X)))))&
(![X]:((humble(X)|generous(X))=>(~strong(X)&tall(X))))&
((happy(lucy)|quiet(lucy)))&
(?[X]:(~old(X)))&
((brave(alice)|humble(alice)))&
((funny(fred)|~funny(fred)))&
((humble(john)|rich(john)))&
((happy(mary)&humble(mary)))&
((humble(alice)|~curious(alice)))&
(?[X]:((~strong(X)<~>calm(X)))) | quiet(fred) | [
"p4",
"p9",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7783984096496655006903788
% SZS output start Proof for 7783984096496655006903788
5. ! [X0] : ((~happy(X0) | ~humble(X0)) => (~tall(X0) & curious(X0))) [input p4]
10. tall(fred) <=> ? [X0] : happy(X0) [input p9]
12. ? [X0] : (quiet(X0) | ~happy(X0)) <=> ~happy(fred) [input p11]
22. humble(mary) & happy(mary) [input p21]
25. quiet(fred) [input hypothesis]
34. ! [X0] : ((~tall(X0) & curious(X0)) | (happy(X0) & humble(X0))) [ennf transformation 5]
53. (tall(fred) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | ~tall(fred)) [nnf transformation 10]
54. (tall(fred) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | ~tall(fred)) [rectify 53]
55. ? [X1] : happy(X1) => happy(sK3) [choice axiom]
56. (tall(fred) | ! [X0] : ~happy(X0)) & (happy(sK3) | ~tall(fred)) [skolemisation 54,55]
58. (? [X0] : (quiet(X0) | ~happy(X0)) | happy(fred)) & (~happy(fred) | ! [X0] : (~quiet(X0) & happy(X0))) [nnf transformation 12]
59. (? [X0] : (quiet(X0) | ~happy(X0)) | happy(fred)) & (~happy(fred) | ! [X1] : (~quiet(X1) & happy(X1))) [rectify 58]
60. ? [X0] : (quiet(X0) | ~happy(X0)) => (quiet(sK4) | ~happy(sK4)) [choice axiom]
61. ((quiet(sK4) | ~happy(sK4)) | happy(fred)) & (~happy(fred) | ! [X1] : (~quiet(X1) & happy(X1))) [skolemisation 59,60]
87. ~tall(X0) | happy(X0) [cnf transformation 34]
96. tall(fred) | ~happy(X0) [cnf transformation 56]
102. ~happy(fred) | ~quiet(X1) [cnf transformation 61]
128. happy(mary) [cnf transformation 22]
133. quiet(fred) [cnf transformation 25]
196. 15 <=> ! [X0] : ~happy(X0) [avatar definition]
197. ~happy(X0) <- (15) [avatar component clause 196]
199. 16 <=> tall(fred) [avatar definition]
201. tall(fred) <- (16) [avatar component clause 199]
202. 15 | 16 [avatar split clause 96,199,196]
209. 18 <=> happy(fred) [avatar definition]
222. 21 <=> ! [X1] : ~quiet(X1) [avatar definition]
223. ~quiet(X1) <- (21) [avatar component clause 222]
224. 21 | ~18 [avatar split clause 102,209,222]
319. $false <- (15) [resolution 197,128]
320. ~15 [avatar contradiction clause 319]
324. happy(fred) <- (16) [resolution 87,201]
327. 18 | ~16 [avatar split clause 324,199,209]
328. $false <- (21) [resolution 223,133]
329. ~21 [avatar contradiction clause 328]
330. $false [avatar sat refutation 202,224,320,327,329]
% SZS output end Proof for 7783984096496655006903788
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not creative is either humble or not wise and vice versa.
If mary is both rich and patient then john is creative or old and vice versa.
Everyone who is not tall or not patient is rich and vice versa.
Everyone who is funny or creative is old or not humble.
If lucy is rich then fred is curious or tall.
If someone is not kind or happy then mary is not rich and vice versa.
If fred is either happy or quiet then someone is both not patient and not tall.
Everyone who is either not generous or not tall is either not funny or not brave.
If paul is either calm or not generous then lucy is not curious and vice versa.
If alice is either curious or not strong then someone is either not patient or not creative.
Everyone who is either humble or not brave is both not funny and not kind and vice versa.
Everyone who is either wise or curious is rich.
If someone is either kind or wise then mary is not calm or not happy and vice versa.
If susan is both not quiet and not creative then alice is old or funny and vice versa.
Everyone who is either not strong or not calm is both happy and tall and vice versa.
Everyone who is not calm is not strong or not brave.
Someone is not creative or strong.
Someone is happy.
Someone is not strong or generous.
John is either not generous or creative.
Someone is either quiet or not tall.
Someone is either quiet or funny.
Someone is either not curious or funny.
Lucy is both patient and kind. | John is generous. | contradiction | (![X]:((rich(X)<~>~creative(X))<=>(humble(X)<~>~wise(X))))&
(((rich(mary)&patient(mary)))<=>((creative(john)|old(john))))&
(![X]:((~tall(X)|~patient(X))<=>rich(X)))&
(![X]:((funny(X)|creative(X))=>(old(X)|~humble(X))))&
((rich(lucy))=>((curious(fred)|tall(fred))))&
((?[X]:((~kind(X)|happy(X))))<=>(~rich(mary)))&
(((happy(fred)<~>quiet(fred)))=>(?[X]:((~patient(X)&~tall(X)))))&
(![X]:((~generous(X)<~>~tall(X))=>(~funny(X)<~>~brave(X))))&
(((calm(paul)<~>~generous(paul)))<=>(~curious(lucy)))&
(((curious(alice)<~>~strong(alice)))=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:((humble(X)<~>~brave(X))<=>(~funny(X)&~kind(X))))&
(![X]:((wise(X)<~>curious(X))=>rich(X)))&
((?[X]:((kind(X)<~>wise(X))))<=>((~calm(mary)|~happy(mary))))&
(((~quiet(susan)&~creative(susan)))<=>((old(alice)|funny(alice))))&
(![X]:((~strong(X)<~>~calm(X))<=>(happy(X)&tall(X))))&
(![X]:(~calm(X)=>(~strong(X)|~brave(X))))&
(?[X]:((~creative(X)|strong(X))))&
(?[X]:(happy(X)))&
(?[X]:((~strong(X)|generous(X))))&
((~generous(john)<~>creative(john)))&
(?[X]:((quiet(X)<~>~tall(X))))&
(?[X]:((quiet(X)<~>funny(X))))&
(?[X]:((~curious(X)<~>funny(X))))&
((patient(lucy)&kind(lucy))) | generous(john) | [
"p1",
"p5",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6949034532715199856392483
% SZS output start Proof for 6949034532715199856392483
2. (patient(mary) & rich(mary)) <=> (old(john) | creative(john)) [input p1]
6. ? [X0] : (happy(X0) | ~kind(X0)) <=> ~rich(mary) [input p5]
18. ? [X0] : happy(X0) [input p17]
20. ~generous(john) <~> creative(john) [input p19]
25. generous(john) [input hypothesis]
37. ((patient(mary) & rich(mary)) | (~old(john) & ~creative(john))) & ((old(john) | creative(john)) | (~patient(mary) | ~rich(mary))) [nnf transformation 2]
38. ((patient(mary) & rich(mary)) | (~old(john) & ~creative(john))) & (old(john) | creative(john) | ~patient(mary) | ~rich(mary)) [flattening 37]
41. (? [X0] : (happy(X0) | ~kind(X0)) | rich(mary)) & (~rich(mary) | ! [X0] : (~happy(X0) & kind(X0))) [nnf transformation 6]
42. (? [X0] : (happy(X0) | ~kind(X0)) | rich(mary)) & (~rich(mary) | ! [X1] : (~happy(X1) & kind(X1))) [rectify 41]
43. ? [X0] : (happy(X0) | ~kind(X0)) => (happy(sK0) | ~kind(sK0)) [choice axiom]
44. ((happy(sK0) | ~kind(sK0)) | rich(mary)) & (~rich(mary) | ! [X1] : (~happy(X1) & kind(X1))) [skolemisation 42,43]
67. ? [X0] : happy(X0) => happy(sK5) [choice axiom]
68. happy(sK5) [skolemisation 18,67]
71. (~creative(john) | generous(john)) & (creative(john) | ~generous(john)) [nnf transformation 20]
90. rich(mary) | ~creative(john) [cnf transformation 38]
101. ~rich(mary) | ~happy(X1) [cnf transformation 44]
146. happy(sK5) [cnf transformation 68]
148. creative(john) | ~generous(john) [cnf transformation 71]
158. generous(john) [cnf transformation 25]
169. 3 <=> creative(john) [avatar definition]
174. 4 <=> rich(mary) [avatar definition]
178. ~3 | 4 [avatar split clause 90,174,169]
203. 10 <=> ! [X1] : ~happy(X1) [avatar definition]
204. ~happy(X1) <- (10) [avatar component clause 203]
205. 10 | ~4 [avatar split clause 101,174,203]
334. 37 <=> generous(john) [avatar definition]
338. ~37 | 3 [avatar split clause 148,169,334]
369. 37 [avatar split clause 158,334]
370. $false <- (10) [resolution 204,146]
371. ~10 [avatar contradiction clause 370]
372. $false [avatar sat refutation 178,205,338,369,371]
% SZS output end Proof for 6949034532715199856392483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is rich or not strong then paul is both not kind and not funny. If fred is humble or tall then mary is either creative or rich. Everyone who is both not funny and not quiet is quiet or tall and vice versa. If susan is not old then someone is either brave or generous and vice versa. Everyone who is not humble or brave is not generous. If someone is both patient and creative then someone is either not funny or patient and vice versa. Everyone who is both not humble and not brave is rich or wise and vice versa. Everyone who is not kind is either not generous or wise. Everyone who is patient is either not wise or strong. Everyone who is rich or patient is both wise and not patient and vice versa. Everyone who is both humble and happy is wise or happy and vice versa. Everyone who is not strong or not generous is either tall or not curious and vice versa. If someone is either not quiet or not curious then someone is both not old and funny. Everyone who is patient or not kind is not strong or happy and vice versa. Everyone who is not old or not happy is curious and vice versa. Everyone who is either creative or not patient is either not quiet or not tall and vice versa. Susan is creative or old. Someone is either not quiet or not kind. Lucy is patient or creative. John is not rich. Someone is either not wise or not generous. Lucy is not happy. Someone is either not humble or kind. | Mary is wise. | contradiction | (((rich(lucy)|~strong(lucy)))=>((~kind(paul)&~funny(paul))))&
(((humble(fred)|tall(fred)))=>((creative(mary)<~>rich(mary))))&
(![X]:((~funny(X)&~quiet(X))<=>(quiet(X)|tall(X))))&
((~old(susan))<=>(?[X]:((brave(X)<~>generous(X)))))&
(![X]:((~humble(X)|brave(X))=>~generous(X)))&
((?[X]:((patient(X)&creative(X))))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((~humble(X)&~brave(X))<=>(rich(X)|wise(X))))&
(![X]:(~kind(X)=>(~generous(X)<~>wise(X))))&
(![X]:(patient(X)=>(~wise(X)<~>strong(X))))&
(![X]:((rich(X)|patient(X))<=>(wise(X)&~patient(X))))&
(![X]:((humble(X)&happy(X))<=>(wise(X)|happy(X))))&
(![X]:((~strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((patient(X)|~kind(X))<=>(~strong(X)|happy(X))))&
(![X]:((~old(X)|~happy(X))<=>curious(X)))&
(![X]:((creative(X)<~>~patient(X))<=>(~quiet(X)<~>~tall(X))))&
((creative(susan)|old(susan)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
((patient(lucy)|creative(lucy)))&
(~rich(john))&
(?[X]:((~wise(X)<~>~generous(X))))&
(~happy(lucy))&
(?[X]:((~humble(X)<~>kind(X)))) | wise(mary) | [
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5871866327559390519812093
% SZS output start Proof for 5871866327559390519812093
7. ! [X0] : ((~brave(X0) & ~humble(X0)) <=> (wise(X0) | rich(X0))) [input p6]
11. ! [X0] : ((happy(X0) & humble(X0)) <=> (happy(X0) | wise(X0))) [input p10]
24. wise(mary) [input hypothesis]
45. ! [X0] : (((~brave(X0) & ~humble(X0)) | (~wise(X0) & ~rich(X0))) & ((wise(X0) | rich(X0)) | (brave(X0) | humble(X0)))) [nnf transformation 7]
46. ! [X0] : (((~brave(X0) & ~humble(X0)) | (~wise(X0) & ~rich(X0))) & (wise(X0) | rich(X0) | brave(X0) | humble(X0))) [flattening 45]
51. ! [X0] : (((happy(X0) & humble(X0)) | (~happy(X0) & ~wise(X0))) & ((happy(X0) | wise(X0)) | (~happy(X0) | ~humble(X0)))) [nnf transformation 11]
52. ! [X0] : (((happy(X0) & humble(X0)) | (~happy(X0) & ~wise(X0))) & (happy(X0) | wise(X0) | ~happy(X0) | ~humble(X0))) [flattening 51]
100. ~humble(X0) | ~wise(X0) [cnf transformation 46]
113. humble(X0) | ~wise(X0) [cnf transformation 52]
152. wise(mary) [cnf transformation 24]
251. ~wise(X0) [subsumption resolution 113,100]
291. $false [subsumption resolution 152,251]
% SZS output end Proof for 5871866327559390519812093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or generous is humble or not generous.
If john is either tall or not brave then someone is not calm or quiet and vice versa.
Everyone who is either calm or not creative is funny or not happy.
Everyone who is both not patient and not calm is either calm or funny and vice versa.
Everyone who is humble is either not humble or brave.
Everyone who is either not creative or creative is either not funny or kind and vice versa.
Everyone who is rich or creative is not creative and vice versa.
Everyone who is quiet is rich or quiet and vice versa.
Everyone who is generous or not happy is not strong and vice versa.
If someone is both not quiet and calm then fred is happy or not generous and vice versa.
Everyone who is either not rich or not humble is both not quiet and not wise and vice versa.
If fred is not kind or not strong then fred is not tall or quiet and vice versa.
Everyone who is happy is patient.
Everyone who is both tall and not strong is both wise and not humble and vice versa.
Everyone who is either brave or not wise is rich.
If someone is either tall or not old then lucy is not humble.
Fred is both old and not calm.
Fred is not kind.
Someone is strong or not funny.
Lucy is either creative or humble.
Lucy is either not happy or humble.
Alice is not old. | Lucy is not happy. | contradiction | (![X]:((rich(X)|generous(X))=>(humble(X)|~generous(X))))&
(((tall(john)<~>~brave(john)))<=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:((calm(X)<~>~creative(X))=>(funny(X)|~happy(X))))&
(![X]:((~patient(X)&~calm(X))<=>(calm(X)<~>funny(X))))&
(![X]:(humble(X)=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((rich(X)|creative(X))<=>~creative(X)))&
(![X]:(quiet(X)<=>(rich(X)|quiet(X))))&
(![X]:((generous(X)|~happy(X))<=>~strong(X)))&
((?[X]:((~quiet(X)&calm(X))))<=>((happy(fred)|~generous(fred))))&
(![X]:((~rich(X)<~>~humble(X))<=>(~quiet(X)&~wise(X))))&
(((~kind(fred)|~strong(fred)))<=>((~tall(fred)|quiet(fred))))&
(![X]:(happy(X)=>patient(X)))&
(![X]:((tall(X)&~strong(X))<=>(wise(X)&~humble(X))))&
(![X]:((brave(X)<~>~wise(X))=>rich(X)))&
((?[X]:((tall(X)<~>~old(X))))=>(~humble(lucy)))&
((old(fred)&~calm(fred)))&
(~kind(fred))&
(?[X]:((strong(X)|~funny(X))))&
((creative(lucy)<~>humble(lucy)))&
((~happy(lucy)<~>humble(lucy)))&
(~old(alice)) | ~happy(lucy) | [
"p6",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6989739985647019284182756
% SZS output start Proof for 6989739985647019284182756
7. ! [X0] : ((creative(X0) | rich(X0)) <=> ~creative(X0)) [input p6]
20. creative(lucy) <~> humble(lucy) [input p19]
21. ~happy(lucy) <~> humble(lucy) [input p20]
23. ~happy(lucy) [input hypothesis]
41. ! [X0] : (((creative(X0) | rich(X0)) | creative(X0)) & (~creative(X0) | (~creative(X0) & ~rich(X0)))) [nnf transformation 7]
42. ! [X0] : ((creative(X0) | rich(X0) | creative(X0)) & (~creative(X0) | (~creative(X0) & ~rich(X0)))) [flattening 41]
62. (~humble(lucy) | ~creative(lucy)) & (humble(lucy) | creative(lucy)) [nnf transformation 20]
63. (~humble(lucy) | happy(lucy)) & (humble(lucy) | ~happy(lucy)) [nnf transformation 21]
91. ~creative(X0) | ~creative(X0) [cnf transformation 42]
127. humble(lucy) | creative(lucy) [cnf transformation 62]
130. ~humble(lucy) | happy(lucy) [cnf transformation 63]
132. ~happy(lucy) [cnf transformation 23]
133. ~creative(X0) [duplicate literal removal 91]
224. 17 <=> humble(lucy) [avatar definition]
242. humble(lucy) [subsumption resolution 127,133]
243. 17 [avatar split clause 242,224]
245. 21 <=> happy(lucy) [avatar definition]
248. 21 | ~17 [avatar split clause 130,224,245]
250. ~21 [avatar split clause 132,245]
251. $false [avatar sat refutation 243,248,250]
% SZS output end Proof for 6989739985647019284182756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not happy is either not kind or not old.
If someone is not curious or rich then fred is either humble or not creative.
If someone is humble then someone is not generous and vice versa.
If mary is both not tall and curious then someone is both wise and tall and vice versa.
Everyone who is not happy or curious is either not creative or not funny and vice versa.
Everyone who is both not quiet and not old is both not quiet and not wise and vice versa.
Everyone who is strong is not humble or wise and vice versa.
Everyone who is not brave is both quiet and wise.
If someone is either creative or rich then someone is not brave or generous.
Everyone who is both quiet and humble is either not wise or not strong and vice versa.
If someone is both not brave and not wise then someone is strong or creative.
Everyone who is either not creative or not curious is funny and vice versa.
Everyone who is not happy is brave.
If someone is curious then someone is either not brave or old and vice versa.
Everyone who is both not wise and tall is either curious or not humble.
If someone is not tall then someone is both not happy and not calm and vice versa.
Mary is strong or not rich.
Alice is not calm.
Paul is not wise or rich.
Someone is both rich and generous.
Susan is rich or not rich.
Alice is both creative and tall.
Someone is brave or not curious.
Someone is not quiet. | Alice is brave. | neutral | (![X]:((kind(X)|~happy(X))=>(~kind(X)<~>~old(X))))&
((?[X]:((~curious(X)|rich(X))))=>((humble(fred)<~>~creative(fred))))&
((?[X]:(humble(X)))<=>(?[X]:(~generous(X))))&
(((~tall(mary)&curious(mary)))<=>(?[X]:((wise(X)&tall(X)))))&
(![X]:((~happy(X)|curious(X))<=>(~creative(X)<~>~funny(X))))&
(![X]:((~quiet(X)&~old(X))<=>(~quiet(X)&~wise(X))))&
(![X]:(strong(X)<=>(~humble(X)|wise(X))))&
(![X]:(~brave(X)=>(quiet(X)&wise(X))))&
((?[X]:((creative(X)<~>rich(X))))=>(?[X]:((~brave(X)|generous(X)))))&
(![X]:((quiet(X)&humble(X))<=>(~wise(X)<~>~strong(X))))&
((?[X]:((~brave(X)&~wise(X))))=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((~creative(X)<~>~curious(X))<=>funny(X)))&
(![X]:(~happy(X)=>brave(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:((~wise(X)&tall(X))=>(curious(X)<~>~humble(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~happy(X)&~calm(X)))))&
((strong(mary)|~rich(mary)))&
(~calm(alice))&
((~wise(paul)|rich(paul)))&
(?[X]:((rich(X)&generous(X))))&
((rich(susan)|~rich(susan)))&
((creative(alice)&tall(alice)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:(~quiet(X))) | brave(alice) | [] | null | 0 |
Everyone who is wise or tall is either not kind or calm.
If someone is creative or strong then alice is both old and not curious and vice versa.
Everyone who is both not brave and kind is either not brave or not quiet.
If fred is either rich or kind then someone is calm.
If someone is not curious or not creative then someone is quiet and vice versa.
Everyone who is both generous and not rich is both curious and not rich and vice versa.
If fred is either tall or not happy then paul is not funny and vice versa.
If john is brave then someone is both not strong and creative.
If someone is both not strong and not old then paul is not tall.
Everyone who is either brave or not creative is not tall or wise and vice versa.
Everyone who is both not tall and kind is generous or not curious and vice versa.
If someone is not rich or wise then alice is old or happy.
Everyone who is generous or old is curious and vice versa.
Everyone who is both happy and calm is not quiet and vice versa.
Everyone who is either not tall or brave is both not tall and rich.
Someone is kind.
Someone is not humble or quiet.
Someone is not calm.
Someone is not funny.
Mary is either not patient or curious.
John is not quiet or not old.
Someone is humble or generous.
Mary is strong or not strong. | Mary is not strong. | entailment | (![X]:((wise(X)|tall(X))=>(~kind(X)<~>calm(X))))&
((?[X]:((creative(X)|strong(X))))<=>((old(alice)&~curious(alice))))&
(![X]:((~brave(X)&kind(X))=>(~brave(X)<~>~quiet(X))))&
(((rich(fred)<~>kind(fred)))=>(?[X]:(calm(X))))&
((?[X]:((~curious(X)|~creative(X))))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)&~rich(X))<=>(curious(X)&~rich(X))))&
(((tall(fred)<~>~happy(fred)))<=>(~funny(paul)))&
((brave(john))=>(?[X]:((~strong(X)&creative(X)))))&
((?[X]:((~strong(X)&~old(X))))=>(~tall(paul)))&
(![X]:((brave(X)<~>~creative(X))<=>(~tall(X)|wise(X))))&
(![X]:((~tall(X)&kind(X))<=>(generous(X)|~curious(X))))&
((?[X]:((~rich(X)|wise(X))))=>((old(alice)|happy(alice))))&
(![X]:((generous(X)|old(X))<=>curious(X)))&
(![X]:((happy(X)&calm(X))<=>~quiet(X)))&
(![X]:((~tall(X)<~>brave(X))=>(~tall(X)&rich(X))))&
(?[X]:(kind(X)))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:(~calm(X)))&
(?[X]:(~funny(X)))&
((~patient(mary)<~>curious(mary)))&
((~quiet(john)|~old(john)))&
(?[X]:((humble(X)|generous(X))))&
((strong(mary)|~strong(mary))) | ~strong(mary) | [
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7652299058854502773963794
% SZS output start Proof for 7652299058854502773963794
2. ? [X0] : (strong(X0) | creative(X0)) <=> (~curious(alice) & old(alice)) [input p1]
13. ! [X0] : ((old(X0) | generous(X0)) <=> curious(X0)) [input p12]
24. strong(mary) [input hypothesis]
36. (? [X0] : (strong(X0) | creative(X0)) | (curious(alice) | ~old(alice))) & ((~curious(alice) & old(alice)) | ! [X0] : (~strong(X0) & ~creative(X0))) [nnf transformation 2]
37. (? [X0] : (strong(X0) | creative(X0)) | curious(alice) | ~old(alice)) & ((~curious(alice) & old(alice)) | ! [X0] : (~strong(X0) & ~creative(X0))) [flattening 36]
38. (? [X0] : (strong(X0) | creative(X0)) | curious(alice) | ~old(alice)) & ((~curious(alice) & old(alice)) | ! [X1] : (~strong(X1) & ~creative(X1))) [rectify 37]
39. ? [X0] : (strong(X0) | creative(X0)) => (strong(sK0) | creative(sK0)) [choice axiom]
40. ((strong(sK0) | creative(sK0)) | curious(alice) | ~old(alice)) & ((~curious(alice) & old(alice)) | ! [X1] : (~strong(X1) & ~creative(X1))) [skolemisation 38,39]
59. ! [X0] : (((old(X0) | generous(X0)) | ~curious(X0)) & (curious(X0) | (~old(X0) & ~generous(X0)))) [nnf transformation 13]
60. ! [X0] : ((old(X0) | generous(X0) | ~curious(X0)) & (curious(X0) | (~old(X0) & ~generous(X0)))) [flattening 59]
80. old(alice) | ~strong(X1) [cnf transformation 40]
82. ~curious(alice) | ~strong(X1) [cnf transformation 40]
116. ~old(X0) | curious(X0) [cnf transformation 60]
134. strong(mary) [cnf transformation 24]
138. 1 <=> old(alice) [avatar definition]
139. old(alice) <- (1) [avatar component clause 138]
142. 2 <=> curious(alice) [avatar definition]
143. ~curious(alice) <- (~2) [avatar component clause 142]
155. 5 <=> ! [X1] : ~strong(X1) [avatar definition]
156. ~strong(X1) <- (5) [avatar component clause 155]
157. 5 | ~2 [avatar split clause 82,142,155]
162. 5 | 1 [avatar split clause 80,138,155]
289. $false <- (5) [resolution 156,134]
290. ~5 [avatar contradiction clause 289]
295. curious(alice) <- (1) [resolution 116,139]
296. $false <- (1, ~2) [subsumption resolution 295,143]
297. ~1 | 2 [avatar contradiction clause 296]
298. $false [avatar sat refutation 157,162,290,297]
% SZS output end Proof for 7652299058854502773963794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not happy or not brave then alice is not generous.
If fred is not rich or generous then fred is both tall and brave and vice versa.
Everyone who is both funny and kind is both curious and not funny and vice versa.
Everyone who is rich or brave is either not old or not tall.
If someone is not old or creative then paul is either not kind or not strong.
Everyone who is not patient or not kind is not patient.
Everyone who is not creative is not wise.
If mary is either not quiet or brave then someone is either generous or not creative and vice versa.
Everyone who is both not brave and calm is both generous and kind and vice versa.
If fred is humble or tall then lucy is not calm or wise.
Everyone who is both tall and kind is tall or not generous.
Everyone who is either happy or not rich is either curious or not curious.
If susan is not old or tall then someone is strong and vice versa.
If someone is not happy then someone is both happy and not funny.
Everyone who is rich is curious and vice versa.
Everyone who is not rich or not curious is both creative and not creative and vice versa.
Someone is not brave.
Someone is not quiet.
Someone is curious or old.
John is either not generous or quiet.
Fred is both not generous and not humble. | Susan is not kind. | entailment | (((~happy(susan)|~brave(susan)))=>(~generous(alice)))&
(((~rich(fred)|generous(fred)))<=>((tall(fred)&brave(fred))))&
(![X]:((funny(X)&kind(X))<=>(curious(X)&~funny(X))))&
(![X]:((rich(X)|brave(X))=>(~old(X)<~>~tall(X))))&
((?[X]:((~old(X)|creative(X))))=>((~kind(paul)<~>~strong(paul))))&
(![X]:((~patient(X)|~kind(X))=>~patient(X)))&
(![X]:(~creative(X)=>~wise(X)))&
(((~quiet(mary)<~>brave(mary)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
(![X]:((~brave(X)&calm(X))<=>(generous(X)&kind(X))))&
(((humble(fred)|tall(fred)))=>((~calm(lucy)|wise(lucy))))&
(![X]:((tall(X)&kind(X))=>(tall(X)|~generous(X))))&
(![X]:((happy(X)<~>~rich(X))=>(curious(X)<~>~curious(X))))&
(((~old(susan)|tall(susan)))<=>(?[X]:(strong(X))))&
((?[X]:(~happy(X)))=>(?[X]:((happy(X)&~funny(X)))))&
(![X]:(rich(X)<=>curious(X)))&
(![X]:((~rich(X)|~curious(X))<=>(creative(X)&~creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((curious(X)|old(X))))&
((~generous(john)<~>quiet(john)))&
((~generous(fred)&~humble(fred))) | ~kind(susan) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7557332079420234705868838
% SZS output start Proof for 7557332079420234705868838
3. ! [X0] : ((kind(X0) & funny(X0)) <=> (~funny(X0) & curious(X0))) [input p2]
16. ! [X0] : ((~curious(X0) | ~rich(X0)) <=> (~creative(X0) & creative(X0))) [input p15]
22. kind(susan) [input hypothesis]
39. ! [X0] : (((kind(X0) & funny(X0)) | (funny(X0) | ~curious(X0))) & ((~funny(X0) & curious(X0)) | (~kind(X0) | ~funny(X0)))) [nnf transformation 3]
40. ! [X0] : (((kind(X0) & funny(X0)) | funny(X0) | ~curious(X0)) & ((~funny(X0) & curious(X0)) | ~kind(X0) | ~funny(X0))) [flattening 39]
59. ! [X0] : (((~curious(X0) | ~rich(X0)) | (creative(X0) | ~creative(X0))) & ((~creative(X0) & creative(X0)) | (curious(X0) & rich(X0)))) [nnf transformation 16]
60. ! [X0] : ((~curious(X0) | ~rich(X0) | creative(X0) | ~creative(X0)) & ((~creative(X0) & creative(X0)) | (curious(X0) & rich(X0)))) [flattening 59]
76. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 40]
77. funny(X0) | funny(X0) | ~curious(X0) [cnf transformation 40]
116. creative(X0) | curious(X0) [cnf transformation 60]
118. ~creative(X0) | curious(X0) [cnf transformation 60]
126. kind(susan) [cnf transformation 22]
127. ~kind(X0) | ~funny(X0) [duplicate literal removal 76]
128. ~curious(X0) | funny(X0) [duplicate literal removal 77]
252. curious(X0) [subsumption resolution 116,118]
269. ~funny(susan) [resolution 127,126]
271. funny(X0) [resolution 128,252]
273. $false [resolution 271,269]
% SZS output end Proof for 7557332079420234705868838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or brave is not wise and vice versa.
Everyone who is not humble is patient or happy.
If someone is either curious or not kind then someone is not creative.
Everyone who is not calm is creative.
Everyone who is both not humble and not kind is funny.
Everyone who is not generous or not brave is either not happy or not curious.
Everyone who is curious or generous is not brave and vice versa.
Everyone who is both not generous and humble is both rich and humble and vice versa.
If susan is either not quiet or not strong then someone is not creative and vice versa.
If lucy is either not brave or happy then susan is both funny and calm and vice versa.
If mary is not funny then someone is either calm or not generous.
If someone is either not patient or not curious then someone is either funny or not strong and vice versa.
Everyone who is both not funny and not calm is either brave or not brave and vice versa.
If mary is both tall and rich then someone is not generous.
If susan is not rich then someone is either brave or not tall and vice versa.
Everyone who is old or wise is both patient and not funny.
Someone is not happy or not calm.
Someone is not patient or funny.
Someone is either not curious or generous.
Someone is generous or calm.
Someone is both not humble and rich.
Lucy is not rich.
Fred is tall. | Lucy is not kind. | contradiction | (![X]:((quiet(X)|brave(X))<=>~wise(X)))&
(![X]:(~humble(X)=>(patient(X)|happy(X))))&
((?[X]:((curious(X)<~>~kind(X))))=>(?[X]:(~creative(X))))&
(![X]:(~calm(X)=>creative(X)))&
(![X]:((~humble(X)&~kind(X))=>funny(X)))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)<~>~curious(X))))&
(![X]:((curious(X)|generous(X))<=>~brave(X)))&
(![X]:((~generous(X)&humble(X))<=>(rich(X)&humble(X))))&
(((~quiet(susan)<~>~strong(susan)))<=>(?[X]:(~creative(X))))&
(((~brave(lucy)<~>happy(lucy)))<=>((funny(susan)&calm(susan))))&
((~funny(mary))=>(?[X]:((calm(X)<~>~generous(X)))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:((funny(X)<~>~strong(X)))))&
(![X]:((~funny(X)&~calm(X))<=>(brave(X)<~>~brave(X))))&
(((tall(mary)&rich(mary)))=>(?[X]:(~generous(X))))&
((~rich(susan))<=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:((old(X)|wise(X))=>(patient(X)&~funny(X))))&
(?[X]:((~happy(X)|~calm(X))))&
(?[X]:((~patient(X)|funny(X))))&
(?[X]:((~curious(X)<~>generous(X))))&
(?[X]:((generous(X)|calm(X))))&
(?[X]:((~humble(X)&rich(X))))&
(~rich(lucy))&
(tall(fred)) | ~kind(lucy) | [
"p2",
"p3",
"p5",
"p6",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 252667518338101777104977
% SZS output start Proof for 252667518338101777104977
3. ? [X0] : (curious(X0) <~> ~kind(X0)) => ? [X0] : ~creative(X0) [input p2]
4. ! [X0] : (~calm(X0) => creative(X0)) [input p3]
6. ! [X0] : ((~brave(X0) | ~generous(X0)) => (~happy(X0) <~> ~curious(X0))) [input p5]
7. ! [X0] : ((generous(X0) | curious(X0)) <=> ~brave(X0)) [input p6]
10. (~brave(lucy) <~> happy(lucy)) <=> (calm(susan) & funny(susan)) [input p9]
13. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> (brave(X0) <~> ~brave(X0))) [input p12]
24. ~kind(lucy) [input hypothesis]
25. ? [X0] : (curious(X0) <~> ~kind(X0)) => ? [X1] : ~creative(X1) [rectify 3]
33. ? [X1] : ~creative(X1) | ! [X0] : (curious(X0) <=> ~kind(X0)) [ennf transformation 25]
34. ! [X0] : (creative(X0) | calm(X0)) [ennf transformation 4]
37. ! [X0] : ((~happy(X0) <~> ~curious(X0)) | (brave(X0) & generous(X0))) [ennf transformation 6]
42. ? [X1] : ~creative(X1) | ! [X0] : ((curious(X0) | kind(X0)) & (~kind(X0) | ~curious(X0))) [nnf transformation 33]
43. ? [X0] : ~creative(X0) | ! [X1] : ((curious(X1) | kind(X1)) & (~kind(X1) | ~curious(X1))) [rectify 42]
44. ? [X0] : ~creative(X0) => ~creative(sK0) [choice axiom]
45. ~creative(sK0) | ! [X1] : ((curious(X1) | kind(X1)) & (~kind(X1) | ~curious(X1))) [skolemisation 43,44]
46. ! [X0] : (((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | (brave(X0) & generous(X0))) [nnf transformation 37]
47. ! [X0] : (((generous(X0) | curious(X0)) | brave(X0)) & (~brave(X0) | (~generous(X0) & ~curious(X0)))) [nnf transformation 7]
48. ! [X0] : ((generous(X0) | curious(X0) | brave(X0)) & (~brave(X0) | (~generous(X0) & ~curious(X0)))) [flattening 47]
55. (((~happy(lucy) | brave(lucy)) & (happy(lucy) | ~brave(lucy))) | (~calm(susan) | ~funny(susan))) & ((calm(susan) & funny(susan)) | ((~brave(lucy) | ~happy(lucy)) & (happy(lucy) | brave(lucy)))) [nnf transformation 10]
56. (((~happy(lucy) | brave(lucy)) & (happy(lucy) | ~brave(lucy))) | ~calm(susan) | ~funny(susan)) & ((calm(susan) & funny(susan)) | ((~brave(lucy) | ~happy(lucy)) & (happy(lucy) | brave(lucy)))) [flattening 55]
65. ! [X0] : (((~calm(X0) & ~funny(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (calm(X0) | funny(X0)))) [nnf transformation 13]
66. ! [X0] : (((~calm(X0) & ~funny(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | calm(X0) | funny(X0))) [flattening 65]
87. ~creative(sK0) | curious(X1) | kind(X1) [cnf transformation 45]
88. calm(X0) | creative(X0) [cnf transformation 34]
91. ~curious(X0) | ~happy(X0) | brave(X0) [cnf transformation 46]
94. ~curious(X0) | ~brave(X0) [cnf transformation 48]
105. funny(susan) | happy(lucy) | brave(lucy) [cnf transformation 56]
123. ~funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 66]
124. ~funny(X0) | brave(X0) | brave(X0) [cnf transformation 66]
125. ~calm(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 66]
126. ~calm(X0) | brave(X0) | brave(X0) [cnf transformation 66]
143. ~kind(lucy) [cnf transformation 24]
144. ~funny(X0) | ~brave(X0) [duplicate literal removal 123]
145. ~funny(X0) | brave(X0) [duplicate literal removal 124]
146. ~calm(X0) | ~brave(X0) [duplicate literal removal 125]
147. ~calm(X0) | brave(X0) [duplicate literal removal 126]
149. 1 <=> ! [X1] : (curious(X1) | kind(X1)) [avatar definition]
150. kind(X1) | curious(X1) <- (1) [avatar component clause 149]
152. 2 <=> creative(sK0) [avatar definition]
154. ~creative(sK0) <- (~2) [avatar component clause 152]
155. 1 | ~2 [avatar split clause 87,152,149]
161. 4 <=> ! [X0] : creative(X0) [avatar definition]
162. creative(X0) <- (4) [avatar component clause 161]
180. 8 <=> funny(susan) [avatar definition]
181. funny(susan) <- (8) [avatar component clause 180]
188. 10 <=> brave(lucy) [avatar definition]
189. ~brave(lucy) <- (~10) [avatar component clause 188]
192. 11 <=> happy(lucy) [avatar definition]
193. happy(lucy) <- (11) [avatar component clause 192]
200. 10 | 11 | 8 [avatar split clause 105,180,192,188]
251. ~calm(X0) [subsumption resolution 146,147]
252. ~funny(X0) [subsumption resolution 144,145]
302. $false <- (8) [subsumption resolution 181,252]
303. ~8 [avatar contradiction clause 302]
304. $false <- (~2, 4) [subsumption resolution 154,162]
305. 2 | ~4 [avatar contradiction clause 304]
306. creative(X0) [resolution 88,251]
307. 4 [avatar split clause 306,161]
312. curious(lucy) <- (1) [resolution 150,143]
314. ~brave(lucy) <- (1) [resolution 312,94]
317. ~10 | ~1 [avatar split clause 314,149,188]
325. ~happy(lucy) | brave(lucy) <- (1) [resolution 91,312]
326. brave(lucy) <- (1, 11) [subsumption resolution 325,193]
327. $false <- (1, ~10, 11) [subsumption resolution 326,189]
328. ~1 | 10 | ~11 [avatar contradiction clause 327]
329. $false [avatar sat refutation 155,200,303,305,307,317,328]
% SZS output end Proof for 252667518338101777104977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and patient is both brave and quiet.
If someone is both not kind and strong then mary is not patient and vice versa.
If paul is not kind or generous then someone is not quiet or not humble and vice versa.
If john is not wise or not rich then lucy is not quiet and vice versa.
Everyone who is both happy and brave is both strong and quiet.
If someone is old then someone is both not funny and humble and vice versa.
Everyone who is either not tall or quiet is both not tall and not patient and vice versa.
Everyone who is both not tall and creative is funny or curious and vice versa.
Everyone who is strong is humble.
If someone is not old or not patient then paul is both creative and strong.
Everyone who is either humble or brave is both happy and quiet.
If fred is either not brave or not humble then someone is both rich and not rich and vice versa.
If someone is either not rich or not patient then someone is both not wise and not generous and vice versa.
Everyone who is old or brave is both rich and not strong.
Everyone who is not kind is both not creative and wise and vice versa.
If mary is funny then someone is rich and vice versa.
Someone is either patient or not rich.
Someone is both not happy and humble.
Someone is not quiet or old.
Someone is both not patient and creative.
Mary is both creative and old.
Fred is old.
Lucy is either tall or calm. | Mary is tall. | contradiction | (![X]:((calm(X)&patient(X))=>(brave(X)&quiet(X))))&
((?[X]:((~kind(X)&strong(X))))<=>(~patient(mary)))&
(((~kind(paul)|generous(paul)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(((~wise(john)|~rich(john)))<=>(~quiet(lucy)))&
(![X]:((happy(X)&brave(X))=>(strong(X)&quiet(X))))&
((?[X]:(old(X)))<=>(?[X]:((~funny(X)&humble(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)&~patient(X))))&
(![X]:((~tall(X)&creative(X))<=>(funny(X)|curious(X))))&
(![X]:(strong(X)=>humble(X)))&
((?[X]:((~old(X)|~patient(X))))=>((creative(paul)&strong(paul))))&
(![X]:((humble(X)<~>brave(X))=>(happy(X)&quiet(X))))&
(((~brave(fred)<~>~humble(fred)))<=>(?[X]:((rich(X)&~rich(X)))))&
((?[X]:((~rich(X)<~>~patient(X))))<=>(?[X]:((~wise(X)&~generous(X)))))&
(![X]:((old(X)|brave(X))=>(rich(X)&~strong(X))))&
(![X]:(~kind(X)<=>(~creative(X)&wise(X))))&
((funny(mary))<=>(?[X]:(rich(X))))&
(?[X]:((patient(X)<~>~rich(X))))&
(?[X]:((~happy(X)&humble(X))))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:((~patient(X)&creative(X))))&
((creative(mary)&old(mary)))&
(old(fred))&
((tall(lucy)<~>calm(lucy))) | tall(mary) | [
"p7",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5360287713292840291880164
% SZS output start Proof for 5360287713292840291880164
8. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (curious(X0) | funny(X0))) [input p7]
14. ! [X0] : ((brave(X0) | old(X0)) => (~strong(X0) & rich(X0))) [input p13]
16. funny(mary) <=> ? [X0] : rich(X0) [input p15]
22. old(fred) [input p21]
24. tall(mary) [input hypothesis]
34. ! [X0] : ((~strong(X0) & rich(X0)) | (~brave(X0) & ~old(X0))) [ennf transformation 14]
53. ! [X0] : (((creative(X0) & ~tall(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (~creative(X0) | tall(X0)))) [nnf transformation 8]
54. ! [X0] : (((creative(X0) & ~tall(X0)) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | ~creative(X0) | tall(X0))) [flattening 53]
67. (funny(mary) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | ~funny(mary)) [nnf transformation 16]
68. (funny(mary) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | ~funny(mary)) [rectify 67]
69. ? [X1] : rich(X1) => rich(sK7) [choice axiom]
70. (funny(mary) | ! [X0] : ~rich(X0)) & (rich(sK7) | ~funny(mary)) [skolemisation 68,69]
105. ~tall(X0) | ~funny(X0) [cnf transformation 54]
130. ~old(X0) | rich(X0) [cnf transformation 34]
138. funny(mary) | ~rich(X0) [cnf transformation 70]
148. old(fred) [cnf transformation 22]
151. tall(mary) [cnf transformation 24]
300. 33 <=> ! [X0] : ~rich(X0) [avatar definition]
301. ~rich(X0) <- (33) [avatar component clause 300]
303. 34 <=> funny(mary) [avatar definition]
306. 33 | 34 [avatar split clause 138,303,300]
345. ~funny(mary) [resolution 105,151]
350. rich(fred) [resolution 130,148]
354. $false <- (33) [subsumption resolution 350,301]
355. ~33 [avatar contradiction clause 354]
358. ~34 [avatar split clause 345,303]
359. $false [avatar sat refutation 306,355,358]
% SZS output end Proof for 5360287713292840291880164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not humble and not happy then paul is either humble or quiet and vice versa.
Everyone who is not rich is not happy or not generous.
Everyone who is either not strong or not calm is not patient.
If paul is not calm or curious then someone is either not quiet or humble and vice versa.
Everyone who is either not calm or calm is either not happy or brave and vice versa.
Everyone who is not old or not brave is not strong and vice versa.
Everyone who is both brave and not patient is either rich or old and vice versa.
Everyone who is not funny is both happy and not kind and vice versa.
Everyone who is not strong or not creative is not patient and vice versa.
Everyone who is both not old and quiet is not wise or not quiet and vice versa.
If john is either not quiet or brave then someone is generous.
Everyone who is not wise is happy.
If someone is both quiet and not generous then someone is both creative and not brave.
If someone is either generous or humble then someone is strong and vice versa.
If alice is not creative then susan is not creative.
If someone is humble or brave then someone is not quiet.
Someone is not happy or not old.
Paul is old.
Someone is both rich and tall.
Someone is not kind or wise.
Alice is either old or tall.
Someone is curious or kind. | John is not funny. | contradiction | ((?[X]:((~humble(X)&~happy(X))))<=>((humble(paul)<~>quiet(paul))))&
(![X]:(~rich(X)=>(~happy(X)|~generous(X))))&
(![X]:((~strong(X)<~>~calm(X))=>~patient(X)))&
(((~calm(paul)|curious(paul)))<=>(?[X]:((~quiet(X)<~>humble(X)))))&
(![X]:((~calm(X)<~>calm(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~old(X)|~brave(X))<=>~strong(X)))&
(![X]:((brave(X)&~patient(X))<=>(rich(X)<~>old(X))))&
(![X]:(~funny(X)<=>(happy(X)&~kind(X))))&
(![X]:((~strong(X)|~creative(X))<=>~patient(X)))&
(![X]:((~old(X)&quiet(X))<=>(~wise(X)|~quiet(X))))&
(((~quiet(john)<~>brave(john)))=>(?[X]:(generous(X))))&
(![X]:(~wise(X)=>happy(X)))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:((creative(X)&~brave(X)))))&
((?[X]:((generous(X)<~>humble(X))))<=>(?[X]:(strong(X))))&
((~creative(alice))=>(~creative(susan)))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~quiet(X))))&
(?[X]:((~happy(X)|~old(X))))&
(old(paul))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((~kind(X)|wise(X))))&
((old(alice)<~>tall(alice)))&
(?[X]:((curious(X)|kind(X)))) | ~funny(john) | [
"p4",
"p7",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4866207984851388964562319
% SZS output start Proof for 4866207984851388964562319
5. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> (~happy(X0) <~> brave(X0))) [input p4]
8. ! [X0] : (~funny(X0) <=> (~kind(X0) & happy(X0))) [input p7]
10. ! [X0] : ((quiet(X0) & ~old(X0)) <=> (~quiet(X0) | ~wise(X0))) [input p9]
16. ? [X0] : (brave(X0) | humble(X0)) => ? [X0] : ~quiet(X0) [input p15]
23. ~funny(john) [input hypothesis]
26. ? [X0] : (brave(X0) | humble(X0)) => ? [X1] : ~quiet(X1) [rectify 16]
27. ! [X0] : (~funny(X0) => (~kind(X0) & happy(X0))) [unused predicate definition removal 8]
31. ! [X0] : ((~kind(X0) & happy(X0)) | funny(X0)) [ennf transformation 27]
36. ? [X1] : ~quiet(X1) | ! [X0] : (~brave(X0) & ~humble(X0)) [ennf transformation 26]
47. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 5]
54. ! [X0] : (((quiet(X0) & ~old(X0)) | (quiet(X0) & wise(X0))) & ((~quiet(X0) | ~wise(X0)) | (~quiet(X0) | old(X0)))) [nnf transformation 10]
55. ! [X0] : (((quiet(X0) & ~old(X0)) | (quiet(X0) & wise(X0))) & (~quiet(X0) | ~wise(X0) | ~quiet(X0) | old(X0))) [flattening 54]
67. ? [X0] : ~quiet(X0) | ! [X1] : (~brave(X1) & ~humble(X1)) [rectify 36]
68. ? [X0] : ~quiet(X0) => ~quiet(sK6) [choice axiom]
69. ~quiet(sK6) | ! [X1] : (~brave(X1) & ~humble(X1)) [skolemisation 67,68]
94. brave(X0) | ~happy(X0) | calm(X0) | calm(X0) [cnf transformation 47]
95. brave(X0) | ~happy(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 47]
111. funny(X0) | happy(X0) [cnf transformation 31]
120. quiet(X0) | quiet(X0) [cnf transformation 55]
132. ~quiet(sK6) | ~brave(X1) [cnf transformation 69]
141. ~funny(john) [cnf transformation 23]
143. quiet(X0) [duplicate literal removal 120]
144. brave(X0) | ~happy(X0) | calm(X0) [duplicate literal removal 94]
145. brave(X0) | ~happy(X0) | ~calm(X0) [duplicate literal removal 95]
202. ~happy(X0) | brave(X0) [subsumption resolution 144,145]
263. ~brave(X1) [subsumption resolution 132,143]
319. happy(john) [resolution 111,141]
322. brave(john) [resolution 202,319]
323. $false [subsumption resolution 322,263]
% SZS output end Proof for 4866207984851388964562319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not happy. If someone is either tall or not humble then susan is not kind or not brave and vice versa. If someone is either not funny or brave then someone is either curious or not curious. If fred is old or not strong then susan is funny or creative and vice versa. Everyone who is strong or humble is kind. Everyone who is not funny is humble or creative and vice versa. Everyone who is not tall or curious is both humble and curious and vice versa. If mary is not tall or not happy then someone is not rich and vice versa. If someone is not tall then someone is brave or not tall and vice versa. If alice is either not wise or not rich then mary is both patient and not humble and vice versa. Everyone who is either curious or wise is either not rich or not old and vice versa. If someone is either not strong or humble then someone is either quiet or not patient and vice versa. If john is not wise or not brave then fred is both patient and not happy. If someone is not generous or not patient then someone is either not quiet or wise and vice versa. If susan is either humble or not creative then alice is funny or rich. If lucy is both happy and not tall then alice is generous. Paul is not calm. Alice is not wise or creative. Someone is curious. Susan is both not wise and generous. Someone is strong. Alice is either not calm or not brave. Alice is both not tall and generous. Someone is not creative. | Alice is funny. | contradiction | (![X]:(generous(X)=>~happy(X)))&
((?[X]:((tall(X)<~>~humble(X))))<=>((~kind(susan)|~brave(susan))))&
((?[X]:((~funny(X)<~>brave(X))))=>(?[X]:((curious(X)<~>~curious(X)))))&
(((old(fred)|~strong(fred)))<=>((funny(susan)|creative(susan))))&
(![X]:((strong(X)|humble(X))=>kind(X)))&
(![X]:(~funny(X)<=>(humble(X)|creative(X))))&
(![X]:((~tall(X)|curious(X))<=>(humble(X)&curious(X))))&
(((~tall(mary)|~happy(mary)))<=>(?[X]:(~rich(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((brave(X)|~tall(X)))))&
(((~wise(alice)<~>~rich(alice)))<=>((patient(mary)&~humble(mary))))&
(![X]:((curious(X)<~>wise(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~strong(X)<~>humble(X))))<=>(?[X]:((quiet(X)<~>~patient(X)))))&
(((~wise(john)|~brave(john)))=>((patient(fred)&~happy(fred))))&
((?[X]:((~generous(X)|~patient(X))))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
(((humble(susan)<~>~creative(susan)))=>((funny(alice)|rich(alice))))&
(((happy(lucy)&~tall(lucy)))=>(generous(alice)))&
(~calm(paul))&
((~wise(alice)|creative(alice)))&
(?[X]:(curious(X)))&
((~wise(susan)&generous(susan)))&
(?[X]:(strong(X)))&
((~calm(alice)<~>~brave(alice)))&
((~tall(alice)&generous(alice)))&
(?[X]:(~creative(X))) | funny(alice) | [
"p5",
"p6",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7241669050375914621758370
% SZS output start Proof for 7241669050375914621758370
6. ! [X0] : (~funny(X0) <=> (creative(X0) | humble(X0))) [input p5]
7. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (curious(X0) & humble(X0))) [input p6]
23. generous(alice) & ~tall(alice) [input p22]
25. funny(alice) [input hypothesis]
49. ! [X0] : ((~funny(X0) | (~creative(X0) & ~humble(X0))) & ((creative(X0) | humble(X0)) | funny(X0))) [nnf transformation 6]
50. ! [X0] : ((~funny(X0) | (~creative(X0) & ~humble(X0))) & (creative(X0) | humble(X0) | funny(X0))) [flattening 49]
51. ! [X0] : (((curious(X0) | ~tall(X0)) | (~curious(X0) | ~humble(X0))) & ((curious(X0) & humble(X0)) | (~curious(X0) & tall(X0)))) [nnf transformation 7]
52. ! [X0] : ((curious(X0) | ~tall(X0) | ~curious(X0) | ~humble(X0)) & ((curious(X0) & humble(X0)) | (~curious(X0) & tall(X0)))) [flattening 51]
102. ~funny(X0) | ~humble(X0) [cnf transformation 50]
104. humble(X0) | tall(X0) [cnf transformation 52]
158. ~tall(alice) [cnf transformation 23]
161. funny(alice) [cnf transformation 25]
183. 5 <=> ! [X1] : (tall(X1) | humble(X1)) [avatar definition]
184. humble(X1) | tall(X1) <- (5) [avatar component clause 183]
210. 5 [avatar split clause 104,183]
367. 45 <=> funny(alice) [avatar definition]
369. funny(alice) <- (45) [avatar component clause 367]
401. 45 [avatar split clause 161,367]
403. ~humble(alice) <- (45) [resolution 102,369]
410. tall(alice) <- (5, 45) [resolution 184,403]
413. $false <- (5, 45) [subsumption resolution 410,158]
414. ~5 | ~45 [avatar contradiction clause 413]
417. $false [avatar sat refutation 210,401,414]
% SZS output end Proof for 7241669050375914621758370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not calm is either not funny or happy and vice versa.
Everyone who is funny is either generous or tall and vice versa.
If someone is not generous or old then someone is not old.
If someone is happy or not kind then someone is either creative or old and vice versa.
If alice is curious then someone is not kind.
If lucy is both wise and not humble then someone is either not old or calm and vice versa.
Everyone who is either not tall or not old is not creative and vice versa.
If mary is tall then fred is either not creative or wise.
If susan is both happy and curious then someone is tall or not curious and vice versa.
Everyone who is both not humble and not tall is brave.
Everyone who is not funny is both brave and kind and vice versa.
Everyone who is not creative is not strong and vice versa.
Everyone who is kind is both strong and not curious and vice versa.
Everyone who is not creative is both not brave and wise and vice versa.
Everyone who is both tall and not tall is either brave or creative and vice versa.
If susan is either not patient or happy then someone is happy.
Someone is both calm and not strong.
John is rich or not wise.
Fred is brave.
Alice is both not creative and not old.
John is not funny.
Susan is either brave or not generous.
Someone is either funny or calm. | Fred is tall. | neutral | (![X]:((~humble(X)<~>~calm(X))<=>(~funny(X)<~>happy(X))))&
(![X]:(funny(X)<=>(generous(X)<~>tall(X))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:(~old(X))))&
((?[X]:((happy(X)|~kind(X))))<=>(?[X]:((creative(X)<~>old(X)))))&
((curious(alice))=>(?[X]:(~kind(X))))&
(((wise(lucy)&~humble(lucy)))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((~tall(X)<~>~old(X))<=>~creative(X)))&
((tall(mary))=>((~creative(fred)<~>wise(fred))))&
(((happy(susan)&curious(susan)))<=>(?[X]:((tall(X)|~curious(X)))))&
(![X]:((~humble(X)&~tall(X))=>brave(X)))&
(![X]:(~funny(X)<=>(brave(X)&kind(X))))&
(![X]:(~creative(X)<=>~strong(X)))&
(![X]:(kind(X)<=>(strong(X)&~curious(X))))&
(![X]:(~creative(X)<=>(~brave(X)&wise(X))))&
(![X]:((tall(X)&~tall(X))<=>(brave(X)<~>creative(X))))&
(((~patient(susan)<~>happy(susan)))=>(?[X]:(happy(X))))&
(?[X]:((calm(X)&~strong(X))))&
((rich(john)|~wise(john)))&
(brave(fred))&
((~creative(alice)&~old(alice)))&
(~funny(john))&
((brave(susan)<~>~generous(susan)))&
(?[X]:((funny(X)<~>calm(X)))) | tall(fred) | [] | null | 0 |
If john is both creative and not happy then someone is both humble and not quiet and vice versa.
If susan is not brave then someone is both not wise and not tall and vice versa.
If lucy is either not generous or not old then someone is patient or not rich and vice versa.
Everyone who is not tall or quiet is not generous.
Everyone who is either humble or curious is both calm and patient and vice versa.
Everyone who is both not quiet and wise is brave.
Everyone who is not curious or not old is either not calm or not humble and vice versa.
Everyone who is strong or not calm is either not strong or quiet.
Everyone who is not curious is either not brave or not old.
If paul is generous or not happy then paul is not quiet or not curious.
Everyone who is either humble or not kind is not brave and vice versa.
If someone is either not creative or not tall then someone is both tall and kind and vice versa.
Everyone who is not kind is not kind or not humble.
If paul is not curious or not wise then someone is both not old and calm.
Everyone who is not kind is both kind and not curious.
Everyone who is either not calm or strong is not generous and vice versa.
John is both not rich and not wise.
Mary is happy or not tall.
Someone is either quiet or not happy.
Someone is both brave and patient.
Someone is either calm or strong.
Paul is either quiet or not quiet.
Someone is not old or strong.
Lucy is old. | Lucy is not quiet. | contradiction | (((creative(john)&~happy(john)))<=>(?[X]:((humble(X)&~quiet(X)))))&
((~brave(susan))<=>(?[X]:((~wise(X)&~tall(X)))))&
(((~generous(lucy)<~>~old(lucy)))<=>(?[X]:((patient(X)|~rich(X)))))&
(![X]:((~tall(X)|quiet(X))=>~generous(X)))&
(![X]:((humble(X)<~>curious(X))<=>(calm(X)&patient(X))))&
(![X]:((~quiet(X)&wise(X))=>brave(X)))&
(![X]:((~curious(X)|~old(X))<=>(~calm(X)<~>~humble(X))))&
(![X]:((strong(X)|~calm(X))=>(~strong(X)<~>quiet(X))))&
(![X]:(~curious(X)=>(~brave(X)<~>~old(X))))&
(((generous(paul)|~happy(paul)))=>((~quiet(paul)|~curious(paul))))&
(![X]:((humble(X)<~>~kind(X))<=>~brave(X)))&
((?[X]:((~creative(X)<~>~tall(X))))<=>(?[X]:((tall(X)&kind(X)))))&
(![X]:(~kind(X)=>(~kind(X)|~humble(X))))&
(((~curious(paul)|~wise(paul)))=>(?[X]:((~old(X)&calm(X)))))&
(![X]:(~kind(X)=>(kind(X)&~curious(X))))&
(![X]:((~calm(X)<~>strong(X))<=>~generous(X)))&
((~rich(john)&~wise(john)))&
((happy(mary)|~tall(mary)))&
(?[X]:((quiet(X)<~>~happy(X))))&
(?[X]:((brave(X)&patient(X))))&
(?[X]:((calm(X)<~>strong(X))))&
((quiet(paul)<~>~quiet(paul)))&
(?[X]:((~old(X)|strong(X))))&
(old(lucy)) | ~quiet(lucy) | [
"p2",
"p4",
"p6",
"p7",
"p8",
"p10",
"p14",
"p15",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2665534985683638542360971
% SZS output start Proof for 2665534985683638542360971
3. (~generous(lucy) <~> ~old(lucy)) <=> ? [X0] : (~rich(X0) | patient(X0)) [input p2]
5. ! [X0] : ((humble(X0) <~> curious(X0)) <=> (patient(X0) & calm(X0))) [input p4]
7. ! [X0] : ((~old(X0) | ~curious(X0)) <=> (~calm(X0) <~> ~humble(X0))) [input p6]
8. ! [X0] : ((~calm(X0) | strong(X0)) => (~strong(X0) <~> quiet(X0))) [input p7]
9. ! [X0] : (~curious(X0) => (~brave(X0) <~> ~old(X0))) [input p8]
11. ! [X0] : ((humble(X0) <~> ~kind(X0)) <=> ~brave(X0)) [input p10]
15. ! [X0] : (~kind(X0) => (~curious(X0) & kind(X0))) [input p14]
16. ! [X0] : ((~calm(X0) <~> strong(X0)) <=> ~generous(X0)) [input p15]
20. ? [X0] : (patient(X0) & brave(X0)) [input p19]
24. old(lucy) [input p23]
25. ~quiet(lucy) [input hypothesis]
30. ! [X0] : ((~strong(X0) <~> quiet(X0)) | (calm(X0) & ~strong(X0))) [ennf transformation 8]
31. ! [X0] : ((~brave(X0) <~> ~old(X0)) | curious(X0)) [ennf transformation 9]
37. ! [X0] : ((~curious(X0) & kind(X0)) | kind(X0)) [ennf transformation 15]
47. (((old(lucy) | generous(lucy)) & (~old(lucy) | ~generous(lucy))) | ! [X0] : (rich(X0) & ~patient(X0))) & (? [X0] : (~rich(X0) | patient(X0)) | ((~generous(lucy) | old(lucy)) & (~old(lucy) | generous(lucy)))) [nnf transformation 3]
48. (((old(lucy) | generous(lucy)) & (~old(lucy) | ~generous(lucy))) | ! [X0] : (rich(X0) & ~patient(X0))) & (? [X1] : (~rich(X1) | patient(X1)) | ((~generous(lucy) | old(lucy)) & (~old(lucy) | generous(lucy)))) [rectify 47]
49. ? [X1] : (~rich(X1) | patient(X1)) => (~rich(sK2) | patient(sK2)) [choice axiom]
50. (((old(lucy) | generous(lucy)) & (~old(lucy) | ~generous(lucy))) | ! [X0] : (rich(X0) & ~patient(X0))) & ((~rich(sK2) | patient(sK2)) | ((~generous(lucy) | old(lucy)) & (~old(lucy) | generous(lucy)))) [skolemisation 48,49]
51. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | (~patient(X0) | ~calm(X0))) & ((patient(X0) & calm(X0)) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [nnf transformation 5]
52. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | ~patient(X0) | ~calm(X0)) & ((patient(X0) & calm(X0)) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [flattening 51]
53. ! [X0] : (((~old(X0) | ~curious(X0)) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) & (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (old(X0) & curious(X0)))) [nnf transformation 7]
54. ! [X0] : ((~old(X0) | ~curious(X0) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) & (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (old(X0) & curious(X0)))) [flattening 53]
55. ! [X0] : (((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | (calm(X0) & ~strong(X0))) [nnf transformation 30]
56. ! [X0] : (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | curious(X0)) [nnf transformation 31]
57. ! [X0] : ((((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | brave(X0)) & (~brave(X0) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0))))) [nnf transformation 11]
65. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | generous(X0)) & (~generous(X0) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [nnf transformation 16]
69. ? [X0] : (patient(X0) & brave(X0)) => (patient(sK7) & brave(sK7)) [choice axiom]
70. patient(sK7) & brave(sK7) [skolemisation 20,69]
86. ~old(lucy) | ~generous(lucy) | ~patient(X0) [cnf transformation 50]
92. ~humble(X0) | curious(X0) | calm(X0) [cnf transformation 52]
93. ~curious(X0) | humble(X0) | calm(X0) [cnf transformation 52]
103. ~old(X0) | ~curious(X0) | ~humble(X0) | calm(X0) [cnf transformation 54]
104. ~old(X0) | ~curious(X0) | ~calm(X0) | humble(X0) [cnf transformation 54]
105. quiet(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 55]
109. ~old(X0) | ~brave(X0) | curious(X0) [cnf transformation 56]
113. ~kind(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 57]
115. ~kind(X0) | humble(X0) | brave(X0) [cnf transformation 57]
128. kind(X0) | kind(X0) [cnf transformation 37]
132. ~calm(X0) | strong(X0) | generous(X0) [cnf transformation 65]
140. patient(sK7) [cnf transformation 70]
146. old(lucy) [cnf transformation 24]
147. ~quiet(lucy) [cnf transformation 25]
148. kind(X0) [duplicate literal removal 128]
149. ~strong(X0) | quiet(X0) [duplicate literal removal 105]
195. 11 <=> generous(lucy) [avatar definition]
196. ~generous(lucy) <- (~11) [avatar component clause 195]
199. 12 <=> old(lucy) [avatar definition]
201. old(lucy) <- (12) [avatar component clause 199]
204. 13 <=> ! [X0] : ~patient(X0) [avatar definition]
205. ~patient(X0) <- (13) [avatar component clause 204]
208. 13 | ~11 | ~12 [avatar split clause 86,199,195,204]
219. ~curious(X0) | ~old(X0) | humble(X0) [subsumption resolution 104,93]
220. ~old(X0) | ~humble(X0) | calm(X0) [subsumption resolution 103,92]
321. 12 [avatar split clause 146,199]
376. ~brave(lucy) | curious(lucy) <- (12) [resolution 109,201]
378. 43 <=> curious(lucy) [avatar definition]
380. curious(lucy) <- (43) [avatar component clause 378]
382. 44 <=> brave(lucy) [avatar definition]
383. brave(lucy) <- (44) [avatar component clause 382]
384. ~brave(lucy) <- (~44) [avatar component clause 382]
385. 43 | ~44 | ~12 [avatar split clause 376,199,382,378]
389. ~brave(X0) | ~humble(X0) [resolution 113,148]
394. brave(X0) | humble(X0) [resolution 115,148]
396. humble(lucy) <- (~44) [resolution 394,384]
449. ~old(lucy) | humble(lucy) <- (43) [resolution 219,380]
454. ~humble(lucy) | calm(lucy) <- (12) [resolution 220,201]
455. calm(lucy) <- (12, ~44) [subsumption resolution 454,396]
456. strong(lucy) | generous(lucy) <- (12, ~44) [resolution 455,132]
458. strong(lucy) <- (~11, 12, ~44) [subsumption resolution 456,196]
481. quiet(lucy) <- (~11, 12, ~44) [resolution 458,149]
482. $false <- (~11, 12, ~44) [subsumption resolution 481,147]
483. 11 | ~12 | 44 [avatar contradiction clause 482]
498. 52 <=> humble(lucy) [avatar definition]
499. humble(lucy) <- (52) [avatar component clause 498]
502. humble(lucy) <- (12, 43) [subsumption resolution 449,201]
503. 52 | ~12 | ~43 [avatar split clause 502,378,199,498]
507. $false <- (13) [resolution 205,140]
510. ~13 [avatar contradiction clause 507]
512. ~humble(lucy) <- (44) [resolution 383,389]
513. $false <- (44, 52) [subsumption resolution 512,499]
514. ~44 | ~52 [avatar contradiction clause 513]
515. $false [avatar sat refutation 208,321,385,483,503,510,514]
% SZS output end Proof for 2665534985683638542360971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either funny or not tall then fred is wise or not kind and vice versa.
Everyone who is both patient and not patient is both not creative and quiet.
Everyone who is generous is brave and vice versa.
If someone is both not kind and creative then someone is either rich or strong and vice versa.
If someone is happy then fred is either happy or not funny and vice versa.
Everyone who is both tall and quiet is calm.
Everyone who is both quiet and not rich is not tall or tall and vice versa.
Everyone who is both not generous and not quiet is humble.
Everyone who is old or rich is not calm or not kind and vice versa.
If someone is both not curious and not kind then john is creative.
If paul is tall or not happy then fred is both not patient and not kind and vice versa.
Everyone who is either not wise or not kind is either not creative or old.
If someone is either calm or not calm then mary is curious.
If fred is either not strong or creative then paul is both curious and rich and vice versa.
If someone is old then someone is not brave or not funny.
If susan is not humble or not quiet then john is both funny and old.
Susan is not generous.
Someone is not humble or not happy.
John is both kind and quiet.
Someone is either not humble or not generous.
Someone is old.
Someone is both brave and calm.
Someone is both not generous and creative. | Susan is brave. | contradiction | (((funny(alice)<~>~tall(alice)))<=>((wise(fred)|~kind(fred))))&
(![X]:((patient(X)&~patient(X))=>(~creative(X)&quiet(X))))&
(![X]:(generous(X)<=>brave(X)))&
((?[X]:((~kind(X)&creative(X))))<=>(?[X]:((rich(X)<~>strong(X)))))&
((?[X]:(happy(X)))<=>((happy(fred)<~>~funny(fred))))&
(![X]:((tall(X)&quiet(X))=>calm(X)))&
(![X]:((quiet(X)&~rich(X))<=>(~tall(X)|tall(X))))&
(![X]:((~generous(X)&~quiet(X))=>humble(X)))&
(![X]:((old(X)|rich(X))<=>(~calm(X)|~kind(X))))&
((?[X]:((~curious(X)&~kind(X))))=>(creative(john)))&
(((tall(paul)|~happy(paul)))<=>((~patient(fred)&~kind(fred))))&
(![X]:((~wise(X)<~>~kind(X))=>(~creative(X)<~>old(X))))&
((?[X]:((calm(X)<~>~calm(X))))=>(curious(mary)))&
(((~strong(fred)<~>creative(fred)))<=>((curious(paul)&rich(paul))))&
((?[X]:(old(X)))=>(?[X]:((~brave(X)|~funny(X)))))&
(((~humble(susan)|~quiet(susan)))=>((funny(john)&old(john))))&
(~generous(susan))&
(?[X]:((~humble(X)|~happy(X))))&
((kind(john)&quiet(john)))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:(old(X)))&
(?[X]:((brave(X)&calm(X))))&
(?[X]:((~generous(X)&creative(X)))) | brave(susan) | [
"p2",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2157441681606906679961603
% SZS output start Proof for 2157441681606906679961603
3. ! [X0] : (generous(X0) <=> brave(X0)) [input p2]
17. ~generous(susan) [input p16]
24. brave(susan) [input hypothesis]
40. ! [X0] : ((generous(X0) | ~brave(X0)) & (brave(X0) | ~generous(X0))) [nnf transformation 3]
83. ~brave(X0) | generous(X0) [cnf transformation 40]
128. ~generous(susan) [cnf transformation 17]
139. brave(susan) [cnf transformation 24]
321. generous(susan) [resolution 83,139]
322. $false [subsumption resolution 321,128]
% SZS output end Proof for 2157441681606906679961603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and happy then susan is not generous.
Everyone who is not brave or humble is humble.
If paul is funny then fred is both brave and not patient and vice versa.
Everyone who is either not old or not humble is both not curious and rich and vice versa.
Everyone who is both not tall and generous is not patient or not humble.
If paul is not old or not curious then mary is not happy and vice versa.
Everyone who is both not humble and quiet is both not strong and not kind and vice versa.
Everyone who is happy is either not quiet or not patient and vice versa.
Everyone who is not rich or creative is creative or rich.
Everyone who is curious or rich is not rich or not calm and vice versa.
Everyone who is both happy and not curious is wise or kind and vice versa.
If susan is not brave then fred is either curious or not humble.
Everyone who is either not kind or curious is either calm or not creative and vice versa.
If john is either not funny or not rich then lucy is not wise or patient and vice versa.
Everyone who is not happy or kind is old or not patient and vice versa.
If alice is calm then someone is either creative or not humble and vice versa.
Someone is either not happy or not kind.
Someone is both not calm and old.
Alice is either not creative or not patient.
John is strong or curious. | Paul is not tall. | neutral | ((?[X]:((creative(X)&happy(X))))=>(~generous(susan)))&
(![X]:((~brave(X)|humble(X))=>humble(X)))&
((funny(paul))<=>((brave(fred)&~patient(fred))))&
(![X]:((~old(X)<~>~humble(X))<=>(~curious(X)&rich(X))))&
(![X]:((~tall(X)&generous(X))=>(~patient(X)|~humble(X))))&
(((~old(paul)|~curious(paul)))<=>(~happy(mary)))&
(![X]:((~humble(X)&quiet(X))<=>(~strong(X)&~kind(X))))&
(![X]:(happy(X)<=>(~quiet(X)<~>~patient(X))))&
(![X]:((~rich(X)|creative(X))=>(creative(X)|rich(X))))&
(![X]:((curious(X)|rich(X))<=>(~rich(X)|~calm(X))))&
(![X]:((happy(X)&~curious(X))<=>(wise(X)|kind(X))))&
((~brave(susan))=>((curious(fred)<~>~humble(fred))))&
(![X]:((~kind(X)<~>curious(X))<=>(calm(X)<~>~creative(X))))&
(((~funny(john)<~>~rich(john)))<=>((~wise(lucy)|patient(lucy))))&
(![X]:((~happy(X)|kind(X))<=>(old(X)|~patient(X))))&
((calm(alice))<=>(?[X]:((creative(X)<~>~humble(X)))))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((~calm(X)&old(X))))&
((~creative(alice)<~>~patient(alice)))&
((strong(john)|curious(john))) | ~tall(paul) | [] | null | 0 |
If alice is rich or not creative then someone is not kind and vice versa. If paul is not kind then fred is both tall and not calm. If susan is not kind or not quiet then lucy is old. If someone is both not patient and funny then lucy is not rich or not brave. Everyone who is calm or not brave is not kind or not rich and vice versa. Everyone who is old is either not creative or kind. Everyone who is either not patient or not calm is creative or patient. Everyone who is either not calm or not generous is both patient and tall and vice versa. If someone is calm then someone is both old and happy. If susan is both rich and generous then someone is both quiet and happy and vice versa. Everyone who is not quiet or not tall is both kind and not funny. If someone is curious or tall then someone is both kind and not kind and vice versa. Everyone who is either rich or not kind is either tall or calm and vice versa. If someone is strong then someone is either not tall or not brave. If susan is not humble then john is tall. Someone is humble or not funny. Someone is either old or funny. Someone is strong or patient. Someone is not brave or happy. Susan is both not generous and not creative. John is both not happy and not old. Paul is not generous. | John is strong. | contradiction | (((rich(alice)|~creative(alice)))<=>(?[X]:(~kind(X))))&
((~kind(paul))=>((tall(fred)&~calm(fred))))&
(((~kind(susan)|~quiet(susan)))=>(old(lucy)))&
((?[X]:((~patient(X)&funny(X))))=>((~rich(lucy)|~brave(lucy))))&
(![X]:((calm(X)|~brave(X))<=>(~kind(X)|~rich(X))))&
(![X]:(old(X)=>(~creative(X)<~>kind(X))))&
(![X]:((~patient(X)<~>~calm(X))=>(creative(X)|patient(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(patient(X)&tall(X))))&
((?[X]:(calm(X)))=>(?[X]:((old(X)&happy(X)))))&
(((rich(susan)&generous(susan)))<=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((~quiet(X)|~tall(X))=>(kind(X)&~funny(X))))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((rich(X)<~>~kind(X))<=>(tall(X)<~>calm(X))))&
((?[X]:(strong(X)))=>(?[X]:((~tall(X)<~>~brave(X)))))&
((~humble(susan))=>(tall(john)))&
(?[X]:((humble(X)|~funny(X))))&
(?[X]:((old(X)<~>funny(X))))&
(?[X]:((strong(X)|patient(X))))&
(?[X]:((~brave(X)|happy(X))))&
((~generous(susan)&~creative(susan)))&
((~happy(john)&~old(john)))&
(~generous(paul)) | strong(john) | [
"p4",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8297558627846522505334857
% SZS output start Proof for 8297558627846522505334857
5. ! [X0] : ((~brave(X0) | calm(X0)) <=> (~rich(X0) | ~kind(X0))) [input p4]
11. ! [X0] : ((~tall(X0) | ~quiet(X0)) => (~funny(X0) & kind(X0))) [input p10]
12. ? [X0] : (tall(X0) | curious(X0)) <=> ? [X0] : (~kind(X0) & kind(X0)) [input p11]
13. ! [X0] : ((rich(X0) <~> ~kind(X0)) <=> (tall(X0) <~> calm(X0))) [input p12]
14. ? [X0] : strong(X0) => ? [X0] : (~tall(X0) <~> ~brave(X0)) [input p13]
23. strong(john) [input hypothesis]
25. ? [X0] : (tall(X0) | curious(X0)) <=> ? [X1] : (~kind(X1) & kind(X1)) [rectify 12]
26. ? [X0] : strong(X0) => ? [X1] : (~tall(X1) <~> ~brave(X1)) [rectify 14]
37. ! [X0] : ((~funny(X0) & kind(X0)) | (tall(X0) & quiet(X0))) [ennf transformation 11]
38. ? [X1] : (~tall(X1) <~> ~brave(X1)) | ! [X0] : ~strong(X0) [ennf transformation 26]
44. ! [X0] : (((~brave(X0) | calm(X0)) | (rich(X0) & kind(X0))) & ((~rich(X0) | ~kind(X0)) | (brave(X0) & ~calm(X0)))) [nnf transformation 5]
45. ! [X0] : ((~brave(X0) | calm(X0) | (rich(X0) & kind(X0))) & (~rich(X0) | ~kind(X0) | (brave(X0) & ~calm(X0)))) [flattening 44]
58. (? [X0] : (tall(X0) | curious(X0)) | ! [X1] : (kind(X1) | ~kind(X1))) & (? [X1] : (~kind(X1) & kind(X1)) | ! [X0] : (~tall(X0) & ~curious(X0))) [nnf transformation 25]
59. (? [X0] : (tall(X0) | curious(X0)) | ! [X1] : (kind(X1) | ~kind(X1))) & (? [X2] : (~kind(X2) & kind(X2)) | ! [X3] : (~tall(X3) & ~curious(X3))) [rectify 58]
60. ? [X0] : (tall(X0) | curious(X0)) => (tall(sK3) | curious(sK3)) [choice axiom]
61. ? [X2] : (~kind(X2) & kind(X2)) => (~kind(sK4) & kind(sK4)) [choice axiom]
62. ((tall(sK3) | curious(sK3)) | ! [X1] : (kind(X1) | ~kind(X1))) & ((~kind(sK4) & kind(sK4)) | ! [X3] : (~tall(X3) & ~curious(X3))) [skolemisation 59,61,60]
63. ! [X0] : ((((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0)))) & (((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))))) [nnf transformation 13]
64. ? [X1] : ((brave(X1) | tall(X1)) & (~brave(X1) | ~tall(X1))) | ! [X0] : ~strong(X0) [nnf transformation 38]
65. ? [X0] : ((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) | ! [X1] : ~strong(X1) [rectify 64]
66. ? [X0] : ((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) => ((brave(sK5) | tall(sK5)) & (~brave(sK5) | ~tall(sK5))) [choice axiom]
67. ((brave(sK5) | tall(sK5)) & (~brave(sK5) | ~tall(sK5))) | ! [X1] : ~strong(X1) [skolemisation 65,66]
83. ~calm(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 45]
86. ~brave(X0) | calm(X0) | rich(X0) [cnf transformation 45]
104. tall(X0) | kind(X0) [cnf transformation 37]
108. kind(sK4) | ~tall(X3) [cnf transformation 62]
110. ~kind(sK4) | ~tall(X3) [cnf transformation 62]
112. calm(X0) | tall(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 63]
117. ~kind(X0) | rich(X0) | tall(X0) | ~calm(X0) [cnf transformation 63]
118. kind(X0) | ~rich(X0) | calm(X0) | ~tall(X0) [cnf transformation 63]
121. brave(sK5) | tall(sK5) | ~strong(X1) [cnf transformation 67]
131. strong(john) [cnf transformation 23]
228. 22 <=> ! [X3] : ~tall(X3) [avatar definition]
229. ~tall(X3) <- (22) [avatar component clause 228]
231. 23 <=> kind(sK4) [avatar definition]
234. 22 | ~23 [avatar split clause 110,231,228]
239. 22 | 23 [avatar split clause 108,231,228]
241. kind(X0) | ~rich(X0) | calm(X0) [subsumption resolution 118,104]
242. ~kind(X0) | tall(X0) | ~calm(X0) [subsumption resolution 117,83]
243. ~calm(X0) | tall(X0) [subsumption resolution 242,104]
245. calm(X0) | tall(X0) | ~rich(X0) [subsumption resolution 112,241]
246. ~rich(X0) | tall(X0) [subsumption resolution 245,243]
248. 25 <=> ! [X1] : ~strong(X1) [avatar definition]
249. ~strong(X1) <- (25) [avatar component clause 248]
251. 26 <=> tall(sK5) [avatar definition]
253. tall(sK5) <- (26) [avatar component clause 251]
255. 27 <=> brave(sK5) [avatar definition]
257. brave(sK5) <- (27) [avatar component clause 255]
258. 25 | 26 | 27 [avatar split clause 121,255,251,248]
291. $false <- (25) [resolution 249,131]
292. ~25 [avatar contradiction clause 291]
293. $false <- (22, 26) [subsumption resolution 253,229]
294. ~22 | ~26 [avatar contradiction clause 293]
311. calm(sK5) | rich(sK5) <- (27) [resolution 86,257]
318. 36 <=> rich(sK5) [avatar definition]
320. rich(sK5) <- (36) [avatar component clause 318]
322. 37 <=> calm(sK5) [avatar definition]
324. calm(sK5) <- (37) [avatar component clause 322]
325. 36 | 37 | ~27 [avatar split clause 311,255,322,318]
328. tall(sK5) <- (36) [resolution 320,246]
329. $false <- (22, 36) [subsumption resolution 328,229]
330. ~22 | ~36 [avatar contradiction clause 329]
341. tall(sK5) <- (37) [resolution 324,243]
342. $false <- (22, 37) [subsumption resolution 341,229]
343. ~22 | ~37 [avatar contradiction clause 342]
344. $false [avatar sat refutation 234,239,258,292,294,325,330,343]
% SZS output end Proof for 8297558627846522505334857
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and creative is both calm and not tall and vice versa. If susan is either not curious or not old then someone is brave and vice versa. Everyone who is humble or curious is both not calm and strong and vice versa. If someone is either patient or not funny then susan is either rich or creative and vice versa. If fred is either creative or not calm then paul is both not wise and generous and vice versa. Everyone who is either not quiet or wise is either not strong or kind. Everyone who is not funny or brave is either generous or happy. Everyone who is not happy is either not wise or not generous. If someone is not generous or patient then susan is both not creative and not rich. Everyone who is funny is not happy or rich. Everyone who is strong or humble is not humble or not rich. If john is both rich and not quiet then someone is creative or not curious. Everyone who is either not patient or calm is not generous. Everyone who is both wise and funny is both not wise and not humble and vice versa. If fred is both kind and not humble then susan is funny and vice versa. If mary is both calm and rich then someone is not calm. Someone is either not old or strong. Someone is not tall. Someone is either not wise or not rich. Alice is not happy. Alice is humble or kind. Someone is both not funny and not curious. Susan is both not rich and brave. Mary is kind. | Susan is not funny. | entailment | (![X]:((~funny(X)&creative(X))<=>(calm(X)&~tall(X))))&
(((~curious(susan)<~>~old(susan)))<=>(?[X]:(brave(X))))&
(![X]:((humble(X)|curious(X))<=>(~calm(X)&strong(X))))&
((?[X]:((patient(X)<~>~funny(X))))<=>((rich(susan)<~>creative(susan))))&
(((creative(fred)<~>~calm(fred)))<=>((~wise(paul)&generous(paul))))&
(![X]:((~quiet(X)<~>wise(X))=>(~strong(X)<~>kind(X))))&
(![X]:((~funny(X)|brave(X))=>(generous(X)<~>happy(X))))&
(![X]:(~happy(X)=>(~wise(X)<~>~generous(X))))&
((?[X]:((~generous(X)|patient(X))))=>((~creative(susan)&~rich(susan))))&
(![X]:(funny(X)=>(~happy(X)|rich(X))))&
(![X]:((strong(X)|humble(X))=>(~humble(X)|~rich(X))))&
(((rich(john)&~quiet(john)))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>~generous(X)))&
(![X]:((wise(X)&funny(X))<=>(~wise(X)&~humble(X))))&
(((kind(fred)&~humble(fred)))<=>(funny(susan)))&
(((calm(mary)&rich(mary)))=>(?[X]:(~calm(X))))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(~happy(alice))&
((humble(alice)|kind(alice)))&
(?[X]:((~funny(X)&~curious(X))))&
((~rich(susan)&brave(susan)))&
(kind(mary)) | ~funny(susan) | [
"p2",
"p3",
"p6",
"p8",
"p9",
"p12",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5729281520844599789125177
% SZS output start Proof for 5729281520844599789125177
3. ! [X0] : ((curious(X0) | humble(X0)) <=> (strong(X0) & ~calm(X0))) [input p2]
4. ? [X0] : (patient(X0) <~> ~funny(X0)) <=> (rich(susan) <~> creative(susan)) [input p3]
7. ! [X0] : ((brave(X0) | ~funny(X0)) => (generous(X0) <~> happy(X0))) [input p6]
9. ? [X0] : (patient(X0) | ~generous(X0)) => (~rich(susan) & ~creative(susan)) [input p8]
10. ! [X0] : (funny(X0) => (rich(X0) | ~happy(X0))) [input p9]
13. ! [X0] : ((~patient(X0) <~> calm(X0)) => ~generous(X0)) [input p12]
14. ! [X0] : ((funny(X0) & wise(X0)) <=> (~humble(X0) & ~wise(X0))) [input p13]
23. brave(susan) & ~rich(susan) [input p22]
25. funny(susan) [input hypothesis]
27. ! [X0] : ((generous(X0) <~> happy(X0)) | (~brave(X0) & funny(X0))) [ennf transformation 7]
29. (~rich(susan) & ~creative(susan)) | ! [X0] : (~patient(X0) & generous(X0)) [ennf transformation 9]
30. ! [X0] : ((rich(X0) | ~happy(X0)) | ~funny(X0)) [ennf transformation 10]
31. ! [X0] : (rich(X0) | ~happy(X0) | ~funny(X0)) [flattening 30]
36. ! [X0] : (~generous(X0) | (~patient(X0) <=> calm(X0))) [ennf transformation 13]
45. ! [X0] : (((curious(X0) | humble(X0)) | (~strong(X0) | calm(X0))) & ((strong(X0) & ~calm(X0)) | (~curious(X0) & ~humble(X0)))) [nnf transformation 3]
46. ! [X0] : ((curious(X0) | humble(X0) | ~strong(X0) | calm(X0)) & ((strong(X0) & ~calm(X0)) | (~curious(X0) & ~humble(X0)))) [flattening 45]
47. (? [X0] : ((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ((rich(susan) | ~creative(susan)) & (creative(susan) | ~rich(susan)))) & (((~creative(susan) | ~rich(susan)) & (creative(susan) | rich(susan))) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) [nnf transformation 4]
48. (? [X0] : ((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ((rich(susan) | ~creative(susan)) & (creative(susan) | ~rich(susan)))) & (((~creative(susan) | ~rich(susan)) & (creative(susan) | rich(susan))) | ! [X1] : ((patient(X1) | funny(X1)) & (~funny(X1) | ~patient(X1)))) [rectify 47]
49. ? [X0] : ((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) => ((funny(sK1) | ~patient(sK1)) & (~funny(sK1) | patient(sK1))) [choice axiom]
50. (((funny(sK1) | ~patient(sK1)) & (~funny(sK1) | patient(sK1))) | ((rich(susan) | ~creative(susan)) & (creative(susan) | ~rich(susan)))) & (((~creative(susan) | ~rich(susan)) & (creative(susan) | rich(susan))) | ! [X1] : ((patient(X1) | funny(X1)) & (~funny(X1) | ~patient(X1)))) [skolemisation 48,49]
54. ! [X0] : (((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | (~brave(X0) & funny(X0))) [nnf transformation 27]
58. ! [X0] : (~generous(X0) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) [nnf transformation 36]
59. ! [X0] : (((funny(X0) & wise(X0)) | (humble(X0) | wise(X0))) & ((~humble(X0) & ~wise(X0)) | (~funny(X0) | ~wise(X0)))) [nnf transformation 14]
60. ! [X0] : (((funny(X0) & wise(X0)) | humble(X0) | wise(X0)) & ((~humble(X0) & ~wise(X0)) | ~funny(X0) | ~wise(X0))) [flattening 59]
83. ~humble(X0) | ~calm(X0) [cnf transformation 46]
88. creative(susan) | rich(susan) | ~funny(X1) | ~patient(X1) [cnf transformation 50]
107. ~brave(X0) | generous(X0) | happy(X0) [cnf transformation 54]
113. ~creative(susan) | ~patient(X0) [cnf transformation 29]
116. ~happy(X0) | rich(X0) | ~funny(X0) [cnf transformation 31]
120. ~generous(X0) | calm(X0) | patient(X0) [cnf transformation 58]
122. ~wise(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 60]
124. wise(X0) | humble(X0) | wise(X0) [cnf transformation 60]
139. ~rich(susan) [cnf transformation 23]
140. brave(susan) [cnf transformation 23]
142. funny(susan) [cnf transformation 25]
143. ~wise(X0) | ~funny(X0) [duplicate literal removal 122]
144. wise(X0) | humble(X0) [duplicate literal removal 124]
166. 5 <=> creative(susan) [avatar definition]
170. 6 <=> rich(susan) [avatar definition]
171. ~rich(susan) <- (~6) [avatar component clause 170]
190. 10 <=> ! [X1] : (~funny(X1) | ~patient(X1)) [avatar definition]
191. ~patient(X1) | ~funny(X1) <- (10) [avatar component clause 190]
194. 10 | 6 | 5 [avatar split clause 88,166,170,190]
218. 15 <=> ! [X0] : ~patient(X0) [avatar definition]
219. ~patient(X0) <- (15) [avatar component clause 218]
225. 15 | ~5 [avatar split clause 113,166,218]
245. 21 <=> funny(susan) [avatar definition]
246. funny(susan) <- (21) [avatar component clause 245]
301. ~6 [avatar split clause 139,170]
302. 21 [avatar split clause 142,245]
309. ~funny(X0) | humble(X0) [resolution 144,143]
313. humble(susan) <- (21) [resolution 309,246]
315. ~calm(susan) <- (21) [resolution 313,83]
326. generous(susan) | happy(susan) [resolution 107,140]
329. 35 <=> happy(susan) [avatar definition]
331. happy(susan) <- (35) [avatar component clause 329]
333. 36 <=> generous(susan) [avatar definition]
335. generous(susan) <- (36) [avatar component clause 333]
336. 35 | 36 [avatar split clause 326,333,329]
470. rich(susan) | ~funny(susan) <- (35) [resolution 331,116]
473. ~funny(susan) <- (~6, 35) [subsumption resolution 470,171]
474. $false <- (~6, 21, 35) [subsumption resolution 473,246]
475. 6 | ~21 | ~35 [avatar contradiction clause 474]
508. calm(susan) | patient(susan) <- (36) [resolution 335,120]
550. patient(susan) <- (21, 36) [subsumption resolution 508,315]
551. $false <- (15, 21, 36) [subsumption resolution 550,219]
552. ~15 | ~21 | ~36 [avatar contradiction clause 551]
667. ~funny(susan) <- (10, 21, 36) [resolution 550,191]
668. $false <- (10, 21, 36) [subsumption resolution 667,246]
669. ~10 | ~21 | ~36 [avatar contradiction clause 668]
670. $false [avatar sat refutation 194,225,301,302,336,475,552,669]
% SZS output end Proof for 5729281520844599789125177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble or rich then someone is both old and not generous.
If fred is not wise then mary is tall or humble and vice versa.
If someone is both tall and generous then susan is not rich or not funny and vice versa.
Everyone who is either not happy or patient is both creative and humble and vice versa.
If someone is both not strong and not brave then someone is either tall or not quiet and vice versa.
If someone is not strong then someone is kind or wise.
If mary is both not generous and brave then someone is brave or not calm and vice versa.
Everyone who is either generous or not generous is both not happy and not quiet and vice versa.
Everyone who is either curious or not quiet is happy.
Everyone who is both not funny and not patient is not funny.
If paul is not quiet then someone is humble or quiet.
If fred is both happy and not generous then someone is both strong and calm.
Everyone who is not strong is happy and vice versa.
Everyone who is not funny is humble.
Everyone who is either not funny or tall is either rich or calm and vice versa.
Someone is both old and not kind.
Lucy is both not creative and not rich.
Someone is either curious or humble.
Someone is strong or quiet.
Lucy is not funny or not wise.
Someone is either not old or generous. | Susan is not curious. | contradiction | ((?[X]:((humble(X)|rich(X))))=>(?[X]:((old(X)&~generous(X)))))&
((~wise(fred))<=>((tall(mary)|humble(mary))))&
((?[X]:((tall(X)&generous(X))))<=>((~rich(susan)|~funny(susan))))&
(![X]:((~happy(X)<~>patient(X))<=>(creative(X)&humble(X))))&
((?[X]:((~strong(X)&~brave(X))))<=>(?[X]:((tall(X)<~>~quiet(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((kind(X)|wise(X)))))&
(((~generous(mary)&brave(mary)))<=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:((generous(X)<~>~generous(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((curious(X)<~>~quiet(X))=>happy(X)))&
(![X]:((~funny(X)&~patient(X))=>~funny(X)))&
((~quiet(paul))=>(?[X]:((humble(X)|quiet(X)))))&
(((happy(fred)&~generous(fred)))=>(?[X]:((strong(X)&calm(X)))))&
(![X]:(~strong(X)<=>happy(X)))&
(![X]:(~funny(X)=>humble(X)))&
(![X]:((~funny(X)<~>tall(X))<=>(rich(X)<~>calm(X))))&
(?[X]:((old(X)&~kind(X))))&
((~creative(lucy)&~rich(lucy)))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((strong(X)|quiet(X))))&
((~funny(lucy)|~wise(lucy)))&
(?[X]:((~old(X)<~>generous(X)))) | ~curious(susan) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8980271365166988846108774
% SZS output start Proof for 8980271365166988846108774
8. ! [X0] : ((generous(X0) <~> ~generous(X0)) <=> (~quiet(X0) & ~happy(X0))) [input p7]
9. ! [X0] : ((curious(X0) <~> ~quiet(X0)) => happy(X0)) [input p8]
22. ~curious(susan) [input hypothesis]
28. ! [X0] : (happy(X0) | (curious(X0) <=> ~quiet(X0))) [ennf transformation 9]
60. ! [X0] : ((((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | (quiet(X0) | happy(X0))) & ((~quiet(X0) & ~happy(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0))))) [nnf transformation 8]
61. ! [X0] : ((((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | quiet(X0) | happy(X0)) & ((~quiet(X0) & ~happy(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0))))) [flattening 60]
62. ! [X0] : (happy(X0) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) [nnf transformation 28]
109. ~happy(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 61]
110. ~happy(X0) | generous(X0) | generous(X0) [cnf transformation 61]
111. ~quiet(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 61]
112. ~quiet(X0) | generous(X0) | generous(X0) [cnf transformation 61]
116. happy(X0) | curious(X0) | quiet(X0) [cnf transformation 62]
142. ~curious(susan) [cnf transformation 22]
143. ~happy(X0) | ~generous(X0) [duplicate literal removal 109]
144. ~happy(X0) | generous(X0) [duplicate literal removal 110]
145. ~quiet(X0) | ~generous(X0) [duplicate literal removal 111]
146. ~quiet(X0) | generous(X0) [duplicate literal removal 112]
274. ~quiet(X0) [subsumption resolution 145,146]
275. ~happy(X0) [subsumption resolution 143,144]
276. curious(X0) | quiet(X0) [subsumption resolution 116,275]
277. curious(X0) [subsumption resolution 276,274]
303. $false [subsumption resolution 142,277]
% SZS output end Proof for 8980271365166988846108774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or happy is not curious or brave and vice versa.
If fred is not wise or happy then lucy is both strong and wise and vice versa.
If someone is tall then susan is not patient and vice versa.
If mary is humble or kind then paul is not rich or strong.
Everyone who is either humble or not kind is not strong or creative and vice versa.
Everyone who is both not rich and happy is not tall.
Everyone who is both not humble and not old is old and vice versa.
Everyone who is not old or brave is either generous or not creative and vice versa.
Everyone who is both generous and not brave is either funny or kind and vice versa.
Everyone who is either curious or rich is strong.
Everyone who is not funny or funny is curious or not humble.
Everyone who is kind is both not humble and funny.
If someone is both quiet and curious then someone is either happy or brave and vice versa.
Everyone who is rich or not strong is strong or not humble.
If someone is brave or curious then paul is either not curious or not generous.
Everyone who is either humble or not funny is not wise.
Alice is calm.
Someone is happy.
Fred is not quiet.
Mary is either funny or curious.
Someone is both wise and rich.
Someone is humble.
Lucy is both not patient and happy.
Someone is tall. | Lucy is brave. | contradiction | (![X]:((~patient(X)<~>happy(X))<=>(~curious(X)|brave(X))))&
(((~wise(fred)|happy(fred)))<=>((strong(lucy)&wise(lucy))))&
((?[X]:(tall(X)))<=>(~patient(susan)))&
(((humble(mary)|kind(mary)))=>((~rich(paul)|strong(paul))))&
(![X]:((humble(X)<~>~kind(X))<=>(~strong(X)|creative(X))))&
(![X]:((~rich(X)&happy(X))=>~tall(X)))&
(![X]:((~humble(X)&~old(X))<=>old(X)))&
(![X]:((~old(X)|brave(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((generous(X)&~brave(X))<=>(funny(X)<~>kind(X))))&
(![X]:((curious(X)<~>rich(X))=>strong(X)))&
(![X]:((~funny(X)|funny(X))=>(curious(X)|~humble(X))))&
(![X]:(kind(X)=>(~humble(X)&funny(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((rich(X)|~strong(X))=>(strong(X)|~humble(X))))&
((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((humble(X)<~>~funny(X))=>~wise(X)))&
(calm(alice))&
(?[X]:(happy(X)))&
(~quiet(fred))&
((funny(mary)<~>curious(mary)))&
(?[X]:((wise(X)&rich(X))))&
(?[X]:(humble(X)))&
((~patient(lucy)&happy(lucy)))&
(?[X]:(tall(X))) | brave(lucy) | [
"p0",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2922748888991896800310824
% SZS output start Proof for 2922748888991896800310824
1. ! [X0] : ((~patient(X0) <~> happy(X0)) <=> (brave(X0) | ~curious(X0))) [input p0]
23. happy(lucy) & ~patient(lucy) [input p22]
25. brave(lucy) [input hypothesis]
40. ! [X0] : ((((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | (~brave(X0) & curious(X0))) & ((brave(X0) | ~curious(X0)) | ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0))))) [nnf transformation 1]
41. ! [X0] : ((((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | (~brave(X0) & curious(X0))) & (brave(X0) | ~curious(X0) | ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0))))) [flattening 40]
78. ~brave(X0) | patient(X0) | ~happy(X0) [cnf transformation 41]
137. ~patient(lucy) [cnf transformation 23]
138. happy(lucy) [cnf transformation 23]
140. brave(lucy) [cnf transformation 25]
247. patient(lucy) | ~happy(lucy) [resolution 78,140]
249. ~happy(lucy) [subsumption resolution 247,137]
250. $false [subsumption resolution 249,138]
% SZS output end Proof for 2922748888991896800310824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not calm then someone is both not strong and wise and vice versa. If someone is tall or not curious then someone is not curious or kind and vice versa. Everyone who is not creative or brave is not curious or rich. Everyone who is either happy or not quiet is strong or not quiet and vice versa. Everyone who is either happy or not old is either not calm or creative and vice versa. Everyone who is either quiet or strong is not brave or wise. Everyone who is not happy is both happy and curious and vice versa. Everyone who is both not funny and patient is not generous or not creative. If john is brave or rich then someone is not kind. Everyone who is strong or old is either not patient or not quiet and vice versa. Everyone who is patient is quiet or not calm. Everyone who is both not quiet and not brave is kind or generous and vice versa. If someone is curious then someone is not old. Everyone who is either not brave or patient is not strong. Everyone who is both patient and not patient is humble and vice versa. Someone is either not generous or funny. Someone is either wise or not calm. Alice is not funny. Someone is funny or patient. Someone is brave. Someone is quiet or creative. | Alice is not strong. | contradiction | ((~calm(lucy))<=>(?[X]:((~strong(X)&wise(X)))))&
((?[X]:((tall(X)|~curious(X))))<=>(?[X]:((~curious(X)|kind(X)))))&
(![X]:((~creative(X)|brave(X))=>(~curious(X)|rich(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(strong(X)|~quiet(X))))&
(![X]:((happy(X)<~>~old(X))<=>(~calm(X)<~>creative(X))))&
(![X]:((quiet(X)<~>strong(X))=>(~brave(X)|wise(X))))&
(![X]:(~happy(X)<=>(happy(X)&curious(X))))&
(![X]:((~funny(X)&patient(X))=>(~generous(X)|~creative(X))))&
(((brave(john)|rich(john)))=>(?[X]:(~kind(X))))&
(![X]:((strong(X)|old(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:(patient(X)=>(quiet(X)|~calm(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(kind(X)|generous(X))))&
((?[X]:(curious(X)))=>(?[X]:(~old(X))))&
(![X]:((~brave(X)<~>patient(X))=>~strong(X)))&
(![X]:((patient(X)&~patient(X))<=>humble(X)))&
(?[X]:((~generous(X)<~>funny(X))))&
(?[X]:((wise(X)<~>~calm(X))))&
(~funny(alice))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:(brave(X)))&
(?[X]:((quiet(X)|creative(X)))) | ~strong(alice) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8100678290150477815169848
% SZS output start Proof for 8100678290150477815169848
4. ! [X0] : ((happy(X0) <~> ~quiet(X0)) <=> (~quiet(X0) | strong(X0))) [input p3]
7. ! [X0] : (~happy(X0) <=> (curious(X0) & happy(X0))) [input p6]
22. ~strong(alice) [input hypothesis]
45. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [nnf transformation 4]
46. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [flattening 45]
49. ! [X0] : ((~happy(X0) | (~curious(X0) | ~happy(X0))) & ((curious(X0) & happy(X0)) | happy(X0))) [nnf transformation 7]
50. ! [X0] : ((~happy(X0) | ~curious(X0) | ~happy(X0)) & ((curious(X0) & happy(X0)) | happy(X0))) [flattening 49]
82. ~quiet(X0) | strong(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 46]
87. quiet(X0) | ~happy(X0) | quiet(X0) [cnf transformation 46]
98. happy(X0) | happy(X0) [cnf transformation 50]
99. happy(X0) | curious(X0) [cnf transformation 50]
100. ~happy(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 50]
127. ~strong(alice) [cnf transformation 22]
128. happy(X0) [duplicate literal removal 98]
129. ~happy(X0) | ~curious(X0) [duplicate literal removal 100]
130. ~quiet(X0) | strong(X0) | ~happy(X0) [duplicate literal removal 82]
131. ~happy(X0) | quiet(X0) [duplicate literal removal 87]
179. ~happy(X0) | strong(X0) [subsumption resolution 130,131]
195. 15 <=> ! [X1] : ~curious(X1) [avatar definition]
196. ~curious(X1) <- (15) [avatar component clause 195]
243. ~curious(X1) [resolution 129,128]
244. 15 [avatar split clause 243,195]
248. strong(X0) | curious(X0) [resolution 179,99]
250. strong(X0) <- (15) [subsumption resolution 248,196]
253. $false <- (15) [resolution 250,127]
256. ~15 [avatar contradiction clause 253]
257. $false [avatar sat refutation 244,256]
% SZS output end Proof for 8100678290150477815169848
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not rich is patient or curious and vice versa.
If susan is brave or rich then paul is either not quiet or curious.
If john is both patient and not happy then john is both not happy and not creative and vice versa.
Everyone who is both generous and quiet is both not wise and kind.
Everyone who is not generous or not curious is not humble.
Everyone who is calm is both rich and not brave and vice versa.
Everyone who is both not happy and not brave is not funny or tall and vice versa.
Everyone who is either not patient or not strong is either tall or not kind.
If someone is either not funny or tall then lucy is calm or brave and vice versa.
Everyone who is either not humble or tall is kind or not wise and vice versa.
If someone is not patient or happy then mary is either patient or not brave.
Everyone who is not patient or old is not calm or not tall.
Everyone who is both not curious and not brave is either wise or not wise.
Everyone who is strong or patient is patient and vice versa.
If someone is either old or not strong then fred is either not patient or not strong.
Everyone who is creative is both not happy and not creative and vice versa.
Paul is either generous or not patient.
Alice is not tall.
Susan is not quiet.
Susan is both not tall and patient.
Lucy is tall or happy.
John is either not happy or patient. | Mary is not kind. | neutral | (![X]:((~humble(X)|~rich(X))<=>(patient(X)|curious(X))))&
(((brave(susan)|rich(susan)))=>((~quiet(paul)<~>curious(paul))))&
(((patient(john)&~happy(john)))<=>((~happy(john)&~creative(john))))&
(![X]:((generous(X)&quiet(X))=>(~wise(X)&kind(X))))&
(![X]:((~generous(X)|~curious(X))=>~humble(X)))&
(![X]:(calm(X)<=>(rich(X)&~brave(X))))&
(![X]:((~happy(X)&~brave(X))<=>(~funny(X)|tall(X))))&
(![X]:((~patient(X)<~>~strong(X))=>(tall(X)<~>~kind(X))))&
((?[X]:((~funny(X)<~>tall(X))))<=>((calm(lucy)|brave(lucy))))&
(![X]:((~humble(X)<~>tall(X))<=>(kind(X)|~wise(X))))&
((?[X]:((~patient(X)|happy(X))))=>((patient(mary)<~>~brave(mary))))&
(![X]:((~patient(X)|old(X))=>(~calm(X)|~tall(X))))&
(![X]:((~curious(X)&~brave(X))=>(wise(X)<~>~wise(X))))&
(![X]:((strong(X)|patient(X))<=>patient(X)))&
((?[X]:((old(X)<~>~strong(X))))=>((~patient(fred)<~>~strong(fred))))&
(![X]:(creative(X)<=>(~happy(X)&~creative(X))))&
((generous(paul)<~>~patient(paul)))&
(~tall(alice))&
(~quiet(susan))&
((~tall(susan)&patient(susan)))&
((tall(lucy)|happy(lucy)))&
((~happy(john)<~>patient(john))) | ~kind(mary) | [] | null | 0 |
If someone is not strong or old then someone is both calm and not quiet. If someone is either not patient or not rich then mary is either strong or not calm. Everyone who is both not old and not quiet is not creative or not calm and vice versa. Everyone who is both not generous and not curious is both not humble and creative and vice versa. If mary is brave or not quiet then mary is not wise and vice versa. Everyone who is both curious and quiet is both brave and tall. Everyone who is creative is either not quiet or not calm. Everyone who is not happy is either old or not kind and vice versa. If someone is not humble then someone is kind. Everyone who is both not kind and not humble is brave or not wise and vice versa. If paul is both humble and patient then someone is both not happy and old. If someone is both rich and not funny then paul is wise or not curious and vice versa. If fred is both quiet and rich then paul is quiet and vice versa. If someone is tall then someone is both not strong and tall. If someone is quiet then someone is old or not strong and vice versa. Everyone who is not creative or quiet is either not curious or not old and vice versa. Someone is either not old or kind. Paul is both not tall and happy. Someone is either not curious or not generous. Someone is both patient and not old. Alice is either not creative or generous. Someone is not patient. | Paul is not kind. | contradiction | ((?[X]:((~strong(X)|old(X))))=>(?[X]:((calm(X)&~quiet(X)))))&
((?[X]:((~patient(X)<~>~rich(X))))=>((strong(mary)<~>~calm(mary))))&
(![X]:((~old(X)&~quiet(X))<=>(~creative(X)|~calm(X))))&
(![X]:((~generous(X)&~curious(X))<=>(~humble(X)&creative(X))))&
(((brave(mary)|~quiet(mary)))<=>(~wise(mary)))&
(![X]:((curious(X)&quiet(X))=>(brave(X)&tall(X))))&
(![X]:(creative(X)=>(~quiet(X)<~>~calm(X))))&
(![X]:(~happy(X)<=>(old(X)<~>~kind(X))))&
((?[X]:(~humble(X)))=>(?[X]:(kind(X))))&
(![X]:((~kind(X)&~humble(X))<=>(brave(X)|~wise(X))))&
(((humble(paul)&patient(paul)))=>(?[X]:((~happy(X)&old(X)))))&
((?[X]:((rich(X)&~funny(X))))<=>((wise(paul)|~curious(paul))))&
(((quiet(fred)&rich(fred)))<=>(quiet(paul)))&
((?[X]:(tall(X)))=>(?[X]:((~strong(X)&tall(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~creative(X)|quiet(X))<=>(~curious(X)<~>~old(X))))&
(?[X]:((~old(X)<~>kind(X))))&
((~tall(paul)&happy(paul)))&
(?[X]:((~curious(X)<~>~generous(X))))&
(?[X]:((patient(X)&~old(X))))&
((~creative(alice)<~>generous(alice)))&
(?[X]:(~patient(X))) | ~kind(paul) | [
"p2",
"p6",
"p7",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4188033860379151911504673
% SZS output start Proof for 4188033860379151911504673
3. ! [X0] : ((~quiet(X0) & ~old(X0)) <=> (~calm(X0) | ~creative(X0))) [input p2]
7. ! [X0] : (creative(X0) => (~quiet(X0) <~> ~calm(X0))) [input p6]
8. ! [X0] : (~happy(X0) <=> (old(X0) <~> ~kind(X0))) [input p7]
15. ? [X0] : quiet(X0) <=> ? [X0] : (~strong(X0) | old(X0)) [input p14]
18. happy(paul) & ~tall(paul) [input p17]
23. ~kind(paul) [input hypothesis]
27. ? [X0] : quiet(X0) <=> ? [X1] : (~strong(X1) | old(X1)) [rectify 15]
32. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) | ~creative(X0)) [ennf transformation 7]
41. ! [X0] : (((~quiet(X0) & ~old(X0)) | (calm(X0) & creative(X0))) & ((~calm(X0) | ~creative(X0)) | (quiet(X0) | old(X0)))) [nnf transformation 3]
42. ! [X0] : (((~quiet(X0) & ~old(X0)) | (calm(X0) & creative(X0))) & (~calm(X0) | ~creative(X0) | quiet(X0) | old(X0))) [flattening 41]
47. ! [X0] : (((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ~creative(X0)) [nnf transformation 32]
48. ! [X0] : ((~happy(X0) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | happy(X0))) [nnf transformation 8]
66. (? [X0] : quiet(X0) | ! [X1] : (strong(X1) & ~old(X1))) & (? [X1] : (~strong(X1) | old(X1)) | ! [X0] : ~quiet(X0)) [nnf transformation 27]
67. (? [X0] : quiet(X0) | ! [X1] : (strong(X1) & ~old(X1))) & (? [X2] : (~strong(X2) | old(X2)) | ! [X3] : ~quiet(X3)) [rectify 66]
68. ? [X0] : quiet(X0) => quiet(sK5) [choice axiom]
69. ? [X2] : (~strong(X2) | old(X2)) => (~strong(sK6) | old(sK6)) [choice axiom]
70. (quiet(sK5) | ! [X1] : (strong(X1) & ~old(X1))) & ((~strong(sK6) | old(sK6)) | ! [X3] : ~quiet(X3)) [skolemisation 67,69,68]
95. ~quiet(X0) | creative(X0) [cnf transformation 42]
96. ~quiet(X0) | calm(X0) [cnf transformation 42]
106. ~calm(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 47]
107. calm(X0) | quiet(X0) | ~creative(X0) [cnf transformation 47]
111. ~happy(X0) | old(X0) | kind(X0) [cnf transformation 48]
131. quiet(sK5) | ~old(X1) [cnf transformation 70]
142. happy(paul) [cnf transformation 18]
150. ~kind(paul) [cnf transformation 23]
152. 1 <=> ! [X1] : ~old(X1) [avatar definition]
153. ~old(X1) <- (1) [avatar component clause 152]
202. ~creative(X0) | calm(X0) [subsumption resolution 107,96]
203. ~quiet(X0) | ~creative(X0) [subsumption resolution 106,202]
204. ~quiet(X0) [subsumption resolution 203,95]
270. ~old(X1) [subsumption resolution 131,204]
271. 1 [avatar split clause 270,152]
339. old(paul) | kind(paul) [resolution 111,142]
341. kind(paul) <- (1) [subsumption resolution 339,153]
342. $false <- (1) [subsumption resolution 341,150]
343. ~1 [avatar contradiction clause 342]
344. $false [avatar sat refutation 271,343]
% SZS output end Proof for 4188033860379151911504673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not brave then lucy is both not calm and not happy and vice versa. Everyone who is either not curious or not old is not creative or not curious and vice versa. Everyone who is both not old and not humble is both creative and patient. If john is not wise then mary is either not quiet or calm. Everyone who is not wise is not rich and vice versa. Everyone who is not creative is kind or quiet and vice versa. Everyone who is both not happy and funny is either tall or brave and vice versa. Everyone who is either old or not kind is creative. Everyone who is both not quiet and not brave is both not quiet and curious and vice versa. If paul is tall then fred is either old or creative. Everyone who is not brave or curious is both strong and not kind. Everyone who is humble or not generous is both not curious and happy. If someone is not rich or patient then mary is brave. Everyone who is either quiet or wise is not quiet and vice versa. If fred is both not curious and not calm then someone is either not humble or not tall. Everyone who is happy is either not generous or not rich. Someone is wise. Someone is either creative or humble. Someone is both generous and not funny. Mary is not brave or tall. Someone is rich or not happy. John is either not kind or patient. | Mary is funny. | neutral | ((?[X]:((~creative(X)<~>~brave(X))))<=>((~calm(lucy)&~happy(lucy))))&
(![X]:((~curious(X)<~>~old(X))<=>(~creative(X)|~curious(X))))&
(![X]:((~old(X)&~humble(X))=>(creative(X)&patient(X))))&
((~wise(john))=>((~quiet(mary)<~>calm(mary))))&
(![X]:(~wise(X)<=>~rich(X)))&
(![X]:(~creative(X)<=>(kind(X)|quiet(X))))&
(![X]:((~happy(X)&funny(X))<=>(tall(X)<~>brave(X))))&
(![X]:((old(X)<~>~kind(X))=>creative(X)))&
(![X]:((~quiet(X)&~brave(X))<=>(~quiet(X)&curious(X))))&
((tall(paul))=>((old(fred)<~>creative(fred))))&
(![X]:((~brave(X)|curious(X))=>(strong(X)&~kind(X))))&
(![X]:((humble(X)|~generous(X))=>(~curious(X)&happy(X))))&
((?[X]:((~rich(X)|patient(X))))=>(brave(mary)))&
(![X]:((quiet(X)<~>wise(X))<=>~quiet(X)))&
(((~curious(fred)&~calm(fred)))=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(happy(X)=>(~generous(X)<~>~rich(X))))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)<~>humble(X))))&
(?[X]:((generous(X)&~funny(X))))&
((~brave(mary)|tall(mary)))&
(?[X]:((rich(X)|~happy(X))))&
((~kind(john)<~>patient(john))) | funny(mary) | [] | null | 0 |
If someone is both not humble and old then alice is not generous and vice versa. Everyone who is both not generous and generous is either not tall or not strong and vice versa. If mary is either humble or creative then susan is not generous or creative and vice versa. If lucy is not wise then susan is wise and vice versa. Everyone who is both old and not wise is rich or not kind and vice versa. If someone is calm or not creative then someone is both brave and patient and vice versa. If paul is not kind then someone is both not old and kind and vice versa. Everyone who is both creative and old is both not wise and humble. Everyone who is not curious is both old and not old and vice versa. Everyone who is patient is either not brave or strong and vice versa. If someone is not tall or not humble then lucy is both funny and not wise. If fred is wise then someone is wise or generous. If alice is either not brave or not quiet then someone is both patient and not happy and vice versa. Everyone who is not rich or not patient is not calm. Everyone who is either not quiet or happy is both curious and strong and vice versa. Everyone who is both not calm and not generous is calm. Someone is not strong or strong. Lucy is strong. Mary is not patient or strong. Someone is old. John is both generous and not calm. Someone is both happy and brave. Someone is both not brave and not wise. Someone is not patient. | Alice is creative. | neutral | ((?[X]:((~humble(X)&old(X))))<=>(~generous(alice)))&
(![X]:((~generous(X)&generous(X))<=>(~tall(X)<~>~strong(X))))&
(((humble(mary)<~>creative(mary)))<=>((~generous(susan)|creative(susan))))&
((~wise(lucy))<=>(wise(susan)))&
(![X]:((old(X)&~wise(X))<=>(rich(X)|~kind(X))))&
((?[X]:((calm(X)|~creative(X))))<=>(?[X]:((brave(X)&patient(X)))))&
((~kind(paul))<=>(?[X]:((~old(X)&kind(X)))))&
(![X]:((creative(X)&old(X))=>(~wise(X)&humble(X))))&
(![X]:(~curious(X)<=>(old(X)&~old(X))))&
(![X]:(patient(X)<=>(~brave(X)<~>strong(X))))&
((?[X]:((~tall(X)|~humble(X))))=>((funny(lucy)&~wise(lucy))))&
((wise(fred))=>(?[X]:((wise(X)|generous(X)))))&
(((~brave(alice)<~>~quiet(alice)))<=>(?[X]:((patient(X)&~happy(X)))))&
(![X]:((~rich(X)|~patient(X))=>~calm(X)))&
(![X]:((~quiet(X)<~>happy(X))<=>(curious(X)&strong(X))))&
(![X]:((~calm(X)&~generous(X))=>calm(X)))&
(?[X]:((~strong(X)|strong(X))))&
(strong(lucy))&
((~patient(mary)|strong(mary)))&
(?[X]:(old(X)))&
((generous(john)&~calm(john)))&
(?[X]:((happy(X)&brave(X))))&
(?[X]:((~brave(X)&~wise(X))))&
(?[X]:(~patient(X))) | creative(alice) | [] | null | 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.