premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either rich or patient is generous and vice versa.
Everyone who is creative or old is both strong and not creative and vice versa.
Everyone who is either tall or generous is humble and vice versa.
Everyone who is either funny or not funny is both not patient and not brave and vice versa.
Everyone who is both not quiet and not strong is both not wise and strong.
If someone is both not kind and creative then someone is not rich or humble and vice versa.
If someone is funny then fred is either generous or not calm and vice versa.
Everyone who is wise is old.
Everyone who is both not kind and wise is rich and vice versa.
Everyone who is not funny or not tall is either not calm or strong and vice versa.
If paul is either not wise or not funny then someone is not brave or wise and vice versa.
If someone is not tall or curious then lucy is not tall or not strong.
If someone is both calm and not humble then someone is brave or old.
If someone is either not curious or not brave then someone is both kind and not strong.
Everyone who is either creative or happy is both patient and creative and vice versa.
If susan is not calm or not kind then someone is either not happy or not old and vice versa.
Someone is not humble or not kind.
Mary is not funny or not patient.
Someone is not calm or not rich. | Fred is not rich. | contradiction | (![X]:((rich(X)<~>patient(X))<=>generous(X)))&
(![X]:((creative(X)|old(X))<=>(strong(X)&~creative(X))))&
(![X]:((tall(X)<~>generous(X))<=>humble(X)))&
(![X]:((funny(X)<~>~funny(X))<=>(~patient(X)&~brave(X))))&
(![X]:((~quiet(X)&~strong(X))=>(~wise(X)&strong(X))))&
((?[X]:((~kind(X)&creative(X))))<=>(?[X]:((~rich(X)|humble(X)))))&
((?[X]:(funny(X)))<=>((generous(fred)<~>~calm(fred))))&
(![X]:(wise(X)=>old(X)))&
(![X]:((~kind(X)&wise(X))<=>rich(X)))&
(![X]:((~funny(X)|~tall(X))<=>(~calm(X)<~>strong(X))))&
(((~wise(paul)<~>~funny(paul)))<=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((~tall(X)|curious(X))))=>((~tall(lucy)|~strong(lucy))))&
((?[X]:((calm(X)&~humble(X))))=>(?[X]:((brave(X)|old(X)))))&
((?[X]:((~curious(X)<~>~brave(X))))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((creative(X)<~>happy(X))<=>(patient(X)&creative(X))))&
(((~calm(susan)|~kind(susan)))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(?[X]:((~humble(X)|~kind(X))))&
((~funny(mary)|~patient(mary)))&
(?[X]:((~calm(X)|~rich(X)))) | ~rich(fred) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6003518489127851683807806
% SZS output start Proof for 6003518489127851683807806
2. ! [X0] : ((old(X0) | creative(X0)) <=> (~creative(X0) & strong(X0))) [input p1]
6. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X0] : (humble(X0) | ~rich(X0)) [input p5]
20. ~rich(fred) [input hypothesis]
21. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X1] : (humble(X1) | ~rich(X1)) [rectify 6]
31. ! [X0] : (((old(X0) | creative(X0)) | (creative(X0) | ~strong(X0))) & ((~creative(X0) & strong(X0)) | (~old(X0) & ~creative(X0)))) [nnf transformation 2]
32. ! [X0] : ((old(X0) | creative(X0) | creative(X0) | ~strong(X0)) & ((~creative(X0) & strong(X0)) | (~old(X0) & ~creative(X0)))) [flattening 31]
36. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & rich(X1))) & (? [X1] : (humble(X1) | ~rich(X1)) | ! [X0] : (~creative(X0) | kind(X0))) [nnf transformation 21]
37. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & rich(X1))) & (? [X2] : (humble(X2) | ~rich(X2)) | ! [X3] : (~creative(X3) | kind(X3))) [rectify 36]
38. ? [X0] : (creative(X0) & ~kind(X0)) => (creative(sK0) & ~kind(sK0)) [choice axiom]
39. ? [X2] : (humble(X2) | ~rich(X2)) => (humble(sK1) | ~rich(sK1)) [choice axiom]
40. ((creative(sK0) & ~kind(sK0)) | ! [X1] : (~humble(X1) & rich(X1))) & ((humble(sK1) | ~rich(sK1)) | ! [X3] : (~creative(X3) | kind(X3))) [skolemisation 37,39,38]
77. ~creative(X0) | ~creative(X0) [cnf transformation 32]
93. creative(sK0) | rich(X1) [cnf transformation 40]
137. ~rich(fred) [cnf transformation 20]
144. ~creative(X0) [duplicate literal removal 77]
149. rich(X1) [subsumption resolution 93,144]
212. $false [subsumption resolution 137,149]
% SZS output end Proof for 6003518489127851683807806
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not rich is both quiet and kind and vice versa. Everyone who is patient or tall is either brave or not patient and vice versa. If paul is both curious and not brave then someone is both not quiet and not rich and vice versa. If someone is not old then susan is happy or not creative and vice versa. Everyone who is both rich and not humble is both not humble and not brave and vice versa. Everyone who is not rich or kind is not strong. Everyone who is not strong or patient is not wise and vice versa. If someone is either not funny or curious then lucy is not creative or not humble. Everyone who is humble is both not brave and strong and vice versa. If someone is both not rich and generous then someone is tall or curious. Everyone who is not rich is both not patient and not old. If someone is not happy then someone is brave or not funny. Everyone who is not generous or brave is funny or generous. Everyone who is not rich is not kind or not generous. Everyone who is brave or not kind is not kind and vice versa. If fred is generous then someone is either not humble or rich. Alice is both not humble and not funny. Someone is wise. Someone is either calm or not creative. Someone is both not creative and funny. Susan is calm. Someone is either happy or not happy. Susan is not generous. Someone is funny. | Fred is generous. | neutral | (![X]:((~wise(X)<~>~rich(X))<=>(quiet(X)&kind(X))))&
(![X]:((patient(X)|tall(X))<=>(brave(X)<~>~patient(X))))&
(((curious(paul)&~brave(paul)))<=>(?[X]:((~quiet(X)&~rich(X)))))&
((?[X]:(~old(X)))<=>((happy(susan)|~creative(susan))))&
(![X]:((rich(X)&~humble(X))<=>(~humble(X)&~brave(X))))&
(![X]:((~rich(X)|kind(X))=>~strong(X)))&
(![X]:((~strong(X)|patient(X))<=>~wise(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>((~creative(lucy)|~humble(lucy))))&
(![X]:(humble(X)<=>(~brave(X)&strong(X))))&
((?[X]:((~rich(X)&generous(X))))=>(?[X]:((tall(X)|curious(X)))))&
(![X]:(~rich(X)=>(~patient(X)&~old(X))))&
((?[X]:(~happy(X)))=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((~generous(X)|brave(X))=>(funny(X)|generous(X))))&
(![X]:(~rich(X)=>(~kind(X)|~generous(X))))&
(![X]:((brave(X)|~kind(X))<=>~kind(X)))&
((generous(fred))=>(?[X]:((~humble(X)<~>rich(X)))))&
((~humble(alice)&~funny(alice)))&
(?[X]:(wise(X)))&
(?[X]:((calm(X)<~>~creative(X))))&
(?[X]:((~creative(X)&funny(X))))&
(calm(susan))&
(?[X]:((happy(X)<~>~happy(X))))&
(~generous(susan))&
(?[X]:(funny(X))) | generous(fred) | [] | null | 0 |
If lucy is wise then fred is either kind or brave and vice versa. Everyone who is either not calm or strong is both wise and not happy and vice versa. Everyone who is creative is both creative and not strong and vice versa. Everyone who is happy or curious is brave. If mary is not curious then john is both not creative and not happy. If someone is not strong or not quiet then paul is tall and vice versa. If someone is rich then alice is both not patient and not kind. Everyone who is brave or tall is not funny or not creative. Everyone who is both strong and not creative is not rich and vice versa. If paul is funny or kind then someone is old or not curious. Everyone who is not brave or not humble is either not happy or not humble. Everyone who is either not strong or wise is both not kind and generous. If someone is both funny and quiet then lucy is not rich. Everyone who is not kind is either not happy or not old. If paul is not curious or wise then fred is either not strong or not funny. Everyone who is both tall and not strong is either not rich or not strong. Lucy is not calm. Someone is either not generous or not wise. Someone is both not generous and rich. Someone is generous. Fred is not brave or rich. Someone is happy or wise. Lucy is patient. Someone is both patient and not funny. | Fred is strong. | neutral | ((wise(lucy))<=>((kind(fred)<~>brave(fred))))&
(![X]:((~calm(X)<~>strong(X))<=>(wise(X)&~happy(X))))&
(![X]:(creative(X)<=>(creative(X)&~strong(X))))&
(![X]:((happy(X)|curious(X))=>brave(X)))&
((~curious(mary))=>((~creative(john)&~happy(john))))&
((?[X]:((~strong(X)|~quiet(X))))<=>(tall(paul)))&
((?[X]:(rich(X)))=>((~patient(alice)&~kind(alice))))&
(![X]:((brave(X)|tall(X))=>(~funny(X)|~creative(X))))&
(![X]:((strong(X)&~creative(X))<=>~rich(X)))&
(((funny(paul)|kind(paul)))=>(?[X]:((old(X)|~curious(X)))))&
(![X]:((~brave(X)|~humble(X))=>(~happy(X)<~>~humble(X))))&
(![X]:((~strong(X)<~>wise(X))=>(~kind(X)&generous(X))))&
((?[X]:((funny(X)&quiet(X))))=>(~rich(lucy)))&
(![X]:(~kind(X)=>(~happy(X)<~>~old(X))))&
(((~curious(paul)|wise(paul)))=>((~strong(fred)<~>~funny(fred))))&
(![X]:((tall(X)&~strong(X))=>(~rich(X)<~>~strong(X))))&
(~calm(lucy))&
(?[X]:((~generous(X)<~>~wise(X))))&
(?[X]:((~generous(X)&rich(X))))&
(?[X]:(generous(X)))&
((~brave(fred)|rich(fred)))&
(?[X]:((happy(X)|wise(X))))&
(patient(lucy))&
(?[X]:((patient(X)&~funny(X)))) | strong(fred) | [] | null | 0 |
Everyone who is generous or kind is either old or curious. Everyone who is not happy is not wise and vice versa. Everyone who is either patient or humble is both not brave and not strong and vice versa. Everyone who is wise or kind is either not kind or not curious and vice versa. If someone is both not quiet and funny then someone is both not old and old and vice versa. Everyone who is not strong is both quiet and not generous. Everyone who is strong is humble. If susan is both not funny and patient then someone is calm and vice versa. If someone is both not humble and happy then someone is strong and vice versa. Everyone who is both not quiet and humble is not patient and vice versa. Everyone who is not quiet is both old and happy and vice versa. If mary is both not wise and brave then someone is humble and vice versa. Everyone who is tall is both patient and not generous. Everyone who is both not generous and funny is curious and vice versa. If mary is quiet then susan is either happy or not brave. Everyone who is either kind or not generous is both quiet and calm and vice versa. John is both not old and wise. Paul is tall. Paul is both not humble and not happy. Someone is not humble. Someone is either tall or not curious. Someone is not funny or calm. Alice is humble. Someone is not wise or not quiet. | Susan is funny. | contradiction | (![X]:((generous(X)|kind(X))=>(old(X)<~>curious(X))))&
(![X]:(~happy(X)<=>~wise(X)))&
(![X]:((patient(X)<~>humble(X))<=>(~brave(X)&~strong(X))))&
(![X]:((wise(X)|kind(X))<=>(~kind(X)<~>~curious(X))))&
((?[X]:((~quiet(X)&funny(X))))<=>(?[X]:((~old(X)&old(X)))))&
(![X]:(~strong(X)=>(quiet(X)&~generous(X))))&
(![X]:(strong(X)=>humble(X)))&
(((~funny(susan)&patient(susan)))<=>(?[X]:(calm(X))))&
((?[X]:((~humble(X)&happy(X))))<=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)&humble(X))<=>~patient(X)))&
(![X]:(~quiet(X)<=>(old(X)&happy(X))))&
(((~wise(mary)&brave(mary)))<=>(?[X]:(humble(X))))&
(![X]:(tall(X)=>(patient(X)&~generous(X))))&
(![X]:((~generous(X)&funny(X))<=>curious(X)))&
((quiet(mary))=>((happy(susan)<~>~brave(susan))))&
(![X]:((kind(X)<~>~generous(X))<=>(quiet(X)&calm(X))))&
((~old(john)&wise(john)))&
(tall(paul))&
((~humble(paul)&~happy(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((tall(X)<~>~curious(X))))&
(?[X]:((~funny(X)|calm(X))))&
(humble(alice))&
(?[X]:((~wise(X)|~quiet(X)))) | funny(susan) | [
"p0",
"p3",
"p7",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8890195283080630703818639
% SZS output start Proof for 8890195283080630703818639
1. ! [X0] : ((kind(X0) | generous(X0)) => (old(X0) <~> curious(X0))) [input p0]
4. ! [X0] : ((kind(X0) | wise(X0)) <=> (~kind(X0) <~> ~curious(X0))) [input p3]
8. (patient(susan) & ~funny(susan)) <=> ? [X0] : calm(X0) [input p7]
14. ! [X0] : ((funny(X0) & ~generous(X0)) <=> curious(X0)) [input p13]
16. ! [X0] : ((kind(X0) <~> ~generous(X0)) <=> (calm(X0) & quiet(X0))) [input p15]
17. wise(john) & ~old(john) [input p16]
25. funny(susan) [input hypothesis]
28. ! [X0] : ((old(X0) <~> curious(X0)) | (~kind(X0) & ~generous(X0))) [ennf transformation 1]
33. ! [X0] : (((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | (~kind(X0) & ~generous(X0))) [nnf transformation 28]
37. ! [X0] : (((kind(X0) | wise(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | (~kind(X0) & ~wise(X0)))) [nnf transformation 4]
38. ! [X0] : ((kind(X0) | wise(X0) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | (~kind(X0) & ~wise(X0)))) [flattening 37]
44. ((patient(susan) & ~funny(susan)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (~patient(susan) | funny(susan))) [nnf transformation 8]
45. ((patient(susan) & ~funny(susan)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ~patient(susan) | funny(susan)) [flattening 44]
46. ((patient(susan) & ~funny(susan)) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ~patient(susan) | funny(susan)) [rectify 45]
47. ? [X1] : calm(X1) => calm(sK2) [choice axiom]
48. ((patient(susan) & ~funny(susan)) | ! [X0] : ~calm(X0)) & (calm(sK2) | ~patient(susan) | funny(susan)) [skolemisation 46,47]
63. ! [X0] : (((funny(X0) & ~generous(X0)) | ~curious(X0)) & (curious(X0) | (~funny(X0) | generous(X0)))) [nnf transformation 14]
64. ! [X0] : (((funny(X0) & ~generous(X0)) | ~curious(X0)) & (curious(X0) | ~funny(X0) | generous(X0))) [flattening 63]
66. ! [X0] : ((((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0))))) [nnf transformation 16]
67. ! [X0] : ((((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0))))) [flattening 66]
77. ~generous(X0) | old(X0) | curious(X0) [cnf transformation 33]
78. ~kind(X0) | old(X0) | curious(X0) [cnf transformation 33]
90. ~curious(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
103. ~funny(susan) | ~calm(X0) [cnf transformation 48]
120. ~curious(X0) | ~generous(X0) [cnf transformation 64]
127. calm(X0) | kind(X0) | generous(X0) [cnf transformation 67]
130. ~old(john) [cnf transformation 17]
141. funny(susan) [cnf transformation 25]
142. ~curious(X0) | ~kind(X0) [duplicate literal removal 90]
154. 3 <=> ! [X0] : ~calm(X0) [avatar definition]
155. ~calm(X0) <- (3) [avatar component clause 154]
162. 5 <=> funny(susan) [avatar definition]
165. 3 | ~5 [avatar split clause 103,162,154]
252. 5 [avatar split clause 141,162]
299. 25 <=> curious(john) [avatar definition]
300. ~curious(john) <- (~25) [avatar component clause 299]
301. curious(john) <- (25) [avatar component clause 299]
303. 26 <=> kind(john) [avatar definition]
304. ~kind(john) <- (~26) [avatar component clause 303]
318. ~kind(john) <- (25) [resolution 301,142]
320. ~generous(john) <- (25) [resolution 301,120]
321. ~26 | ~25 [avatar split clause 318,299,303]
420. kind(X0) | generous(X0) <- (3) [resolution 127,155]
510. generous(X2) | old(X2) | curious(X2) <- (3) [resolution 420,78]
511. generous(john) <- (3, ~26) [resolution 420,304]
512. curious(X2) | old(X2) <- (3) [subsumption resolution 510,77]
513. $false <- (3, 25, ~26) [subsumption resolution 511,320]
514. ~3 | ~25 | 26 [avatar contradiction clause 513]
594. old(john) <- (3, ~25) [resolution 512,300]
597. $false <- (3, ~25) [subsumption resolution 594,130]
598. ~3 | 25 [avatar contradiction clause 597]
601. $false [avatar sat refutation 165,252,321,514,598]
% SZS output end Proof for 8890195283080630703818639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or generous is both not patient and not humble and vice versa.
Everyone who is either humble or not calm is old.
Everyone who is either not strong or brave is old.
Everyone who is not strong or not patient is both brave and generous.
Everyone who is either patient or generous is patient or creative and vice versa.
Everyone who is funny or not old is not rich and vice versa.
If mary is either rich or creative then someone is both funny and happy and vice versa.
Everyone who is calm is not patient or patient.
Everyone who is patient is not creative and vice versa.
If someone is either not strong or funny then someone is either creative or patient and vice versa.
If someone is tall or funny then someone is either curious or patient and vice versa.
If someone is not generous or not happy then someone is both rich and patient.
Everyone who is brave is patient or wise and vice versa.
If alice is both not humble and not patient then someone is calm.
If someone is wise then someone is not happy or kind.
If someone is old then someone is strong or not rich and vice versa.
Fred is not tall or rich.
Someone is strong.
Fred is curious.
Susan is creative or not quiet.
Someone is both creative and not rich.
Susan is both kind and not patient. | Mary is not wise. | contradiction | (![X]:((old(X)|generous(X))<=>(~patient(X)&~humble(X))))&
(![X]:((humble(X)<~>~calm(X))=>old(X)))&
(![X]:((~strong(X)<~>brave(X))=>old(X)))&
(![X]:((~strong(X)|~patient(X))=>(brave(X)&generous(X))))&
(![X]:((patient(X)<~>generous(X))<=>(patient(X)|creative(X))))&
(![X]:((funny(X)|~old(X))<=>~rich(X)))&
(((rich(mary)<~>creative(mary)))<=>(?[X]:((funny(X)&happy(X)))))&
(![X]:(calm(X)=>(~patient(X)|patient(X))))&
(![X]:(patient(X)<=>~creative(X)))&
((?[X]:((~strong(X)<~>funny(X))))<=>(?[X]:((creative(X)<~>patient(X)))))&
((?[X]:((tall(X)|funny(X))))<=>(?[X]:((curious(X)<~>patient(X)))))&
((?[X]:((~generous(X)|~happy(X))))=>(?[X]:((rich(X)&patient(X)))))&
(![X]:(brave(X)<=>(patient(X)|wise(X))))&
(((~humble(alice)&~patient(alice)))=>(?[X]:(calm(X))))&
((?[X]:(wise(X)))=>(?[X]:((~happy(X)|kind(X)))))&
((?[X]:(old(X)))<=>(?[X]:((strong(X)|~rich(X)))))&
((~tall(fred)|rich(fred)))&
(?[X]:(strong(X)))&
(curious(fred))&
((creative(susan)|~quiet(susan)))&
(?[X]:((creative(X)&~rich(X))))&
((kind(susan)&~patient(susan))) | ~wise(mary) | [
"p0",
"p3",
"p5",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2168288922510533616490867
% SZS output start Proof for 2168288922510533616490867
1. ! [X0] : ((generous(X0) | old(X0)) <=> (~humble(X0) & ~patient(X0))) [input p0]
4. ! [X0] : ((~patient(X0) | ~strong(X0)) => (generous(X0) & brave(X0))) [input p3]
6. ! [X0] : ((~old(X0) | funny(X0)) <=> ~rich(X0)) [input p5]
9. ! [X0] : (patient(X0) <=> ~creative(X0)) [input p8]
12. ? [X0] : (~happy(X0) | ~generous(X0)) => ? [X0] : (patient(X0) & rich(X0)) [input p11]
13. ! [X0] : (brave(X0) <=> (wise(X0) | patient(X0))) [input p12]
23. ~wise(mary) [input hypothesis]
26. ? [X0] : (~happy(X0) | ~generous(X0)) => ? [X1] : (patient(X1) & rich(X1)) [rectify 12]
34. ! [X0] : ((generous(X0) & brave(X0)) | (patient(X0) & strong(X0))) [ennf transformation 4]
37. ? [X1] : (patient(X1) & rich(X1)) | ! [X0] : (happy(X0) & generous(X0)) [ennf transformation 26]
40. ! [X0] : (((generous(X0) | old(X0)) | (humble(X0) | patient(X0))) & ((~humble(X0) & ~patient(X0)) | (~generous(X0) & ~old(X0)))) [nnf transformation 1]
41. ! [X0] : ((generous(X0) | old(X0) | humble(X0) | patient(X0)) & ((~humble(X0) & ~patient(X0)) | (~generous(X0) & ~old(X0)))) [flattening 40]
46. ! [X0] : (((~old(X0) | funny(X0)) | rich(X0)) & (~rich(X0) | (old(X0) & ~funny(X0)))) [nnf transformation 6]
47. ! [X0] : ((~old(X0) | funny(X0) | rich(X0)) & (~rich(X0) | (old(X0) & ~funny(X0)))) [flattening 46]
52. ! [X0] : ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0))) [nnf transformation 9]
63. ? [X0] : (patient(X0) & rich(X0)) | ! [X1] : (happy(X1) & generous(X1)) [rectify 37]
64. ? [X0] : (patient(X0) & rich(X0)) => (patient(sK5) & rich(sK5)) [choice axiom]
65. (patient(sK5) & rich(sK5)) | ! [X1] : (happy(X1) & generous(X1)) [skolemisation 63,64]
66. ! [X0] : ((brave(X0) | (~wise(X0) & ~patient(X0))) & ((wise(X0) | patient(X0)) | ~brave(X0))) [nnf transformation 13]
67. ! [X0] : ((brave(X0) | (~wise(X0) & ~patient(X0))) & (wise(X0) | patient(X0) | ~brave(X0))) [flattening 66]
79. ~patient(X0) | ~old(X0) [cnf transformation 41]
80. ~patient(X0) | ~generous(X0) [cnf transformation 41]
89. brave(X0) | patient(X0) [cnf transformation 34]
99. ~rich(X0) | old(X0) [cnf transformation 47]
108. ~creative(X0) | ~patient(X0) [cnf transformation 52]
109. creative(X0) | patient(X0) [cnf transformation 52]
124. rich(sK5) | generous(X1) [cnf transformation 65]
126. patient(sK5) | generous(X1) [cnf transformation 65]
128. wise(X0) | patient(X0) | ~brave(X0) [cnf transformation 67]
129. brave(X0) | ~patient(X0) [cnf transformation 67]
141. ~wise(mary) [cnf transformation 23]
154. 3 <=> creative(mary) [avatar definition]
155. creative(mary) <- (3) [avatar component clause 154]
156. ~creative(mary) <- (~3) [avatar component clause 154]
231. 19 <=> patient(sK5) [avatar definition]
233. patient(sK5) <- (19) [avatar component clause 231]
236. 20 <=> ! [X1] : generous(X1) [avatar definition]
237. generous(X1) <- (20) [avatar component clause 236]
238. 20 | 19 [avatar split clause 126,231,236]
240. 21 <=> rich(sK5) [avatar definition]
242. rich(sK5) <- (21) [avatar component clause 240]
244. 20 | 21 [avatar split clause 124,240,236]
245. brave(X0) [subsumption resolution 129,89]
246. wise(X0) | patient(X0) [subsumption resolution 128,245]
298. ~old(sK5) <- (19) [resolution 233,79]
307. old(sK5) <- (21) [resolution 99,242]
308. $false <- (19, 21) [subsumption resolution 307,298]
309. ~19 | ~21 [avatar contradiction clause 308]
319. patient(mary) <- (~3) [resolution 109,156]
323. ~generous(mary) <- (~3) [resolution 319,80]
325. $false <- (~3, 20) [subsumption resolution 323,237]
326. 3 | ~20 [avatar contradiction clause 325]
329. ~patient(mary) <- (3) [resolution 155,108]
336. patient(mary) [resolution 246,141]
338. $false <- (3) [subsumption resolution 336,329]
339. ~3 [avatar contradiction clause 338]
340. $false [avatar sat refutation 238,244,309,326,339]
% SZS output end Proof for 2168288922510533616490867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not old then paul is both funny and generous and vice versa.
Everyone who is both not quiet and quiet is not creative or generous and vice versa.
If paul is both calm and not quiet then lucy is both not curious and happy.
Everyone who is both not calm and funny is both not patient and not generous.
Everyone who is not calm is not funny or not tall.
If someone is generous or not creative then someone is rich or not creative and vice versa.
Everyone who is either not curious or funny is not patient or curious and vice versa.
Everyone who is either rich or funny is both not strong and tall.
Everyone who is both not quiet and funny is humble or happy and vice versa.
If someone is both not funny and not curious then someone is not humble and vice versa.
If alice is not tall or humble then susan is not patient or not creative.
Everyone who is either creative or not quiet is not kind or not old.
If someone is funny or not patient then fred is not patient or generous and vice versa.
Everyone who is not kind is not creative and vice versa.
Everyone who is both wise and not creative is either not humble or old.
If someone is not tall then someone is either rich or generous.
Someone is tall or funny.
John is not quiet.
Someone is funny.
Someone is either rich or not rich.
Someone is either brave or calm.
Susan is not happy.
Paul is both not happy and funny.
Fred is strong. | Fred is humble. | contradiction | ((?[X]:((humble(X)&~old(X))))<=>((funny(paul)&generous(paul))))&
(![X]:((~quiet(X)&quiet(X))<=>(~creative(X)|generous(X))))&
(((calm(paul)&~quiet(paul)))=>((~curious(lucy)&happy(lucy))))&
(![X]:((~calm(X)&funny(X))=>(~patient(X)&~generous(X))))&
(![X]:(~calm(X)=>(~funny(X)|~tall(X))))&
((?[X]:((generous(X)|~creative(X))))<=>(?[X]:((rich(X)|~creative(X)))))&
(![X]:((~curious(X)<~>funny(X))<=>(~patient(X)|curious(X))))&
(![X]:((rich(X)<~>funny(X))=>(~strong(X)&tall(X))))&
(![X]:((~quiet(X)&funny(X))<=>(humble(X)|happy(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:(~humble(X))))&
(((~tall(alice)|humble(alice)))=>((~patient(susan)|~creative(susan))))&
(![X]:((creative(X)<~>~quiet(X))=>(~kind(X)|~old(X))))&
((?[X]:((funny(X)|~patient(X))))<=>((~patient(fred)|generous(fred))))&
(![X]:(~kind(X)<=>~creative(X)))&
(![X]:((wise(X)&~creative(X))=>(~humble(X)<~>old(X))))&
((?[X]:(~tall(X)))=>(?[X]:((rich(X)<~>generous(X)))))&
(?[X]:((tall(X)|funny(X))))&
(~quiet(john))&
(?[X]:(funny(X)))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(~happy(susan))&
((~happy(paul)&funny(paul)))&
(strong(fred)) | humble(fred) | [
"p1",
"p5",
"p7",
"p8",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1101812344641292687392539
% SZS output start Proof for 1101812344641292687392539
2. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (generous(X0) | ~creative(X0))) [input p1]
6. ? [X0] : (~creative(X0) | generous(X0)) <=> ? [X0] : (~creative(X0) | rich(X0)) [input p5]
8. ! [X0] : ((rich(X0) <~> funny(X0)) => (tall(X0) & ~strong(X0))) [input p7]
9. ! [X0] : ((funny(X0) & ~quiet(X0)) <=> (happy(X0) | humble(X0))) [input p8]
24. strong(fred) [input p23]
25. humble(fred) [input hypothesis]
26. ? [X0] : (~creative(X0) | generous(X0)) <=> ? [X1] : (~creative(X1) | rich(X1)) [rectify 6]
37. ! [X0] : ((tall(X0) & ~strong(X0)) | (rich(X0) <=> funny(X0))) [ennf transformation 8]
49. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | (~quiet(X0) | quiet(X0)))) [nnf transformation 2]
50. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | ~quiet(X0) | quiet(X0))) [flattening 49]
51. (? [X0] : (~creative(X0) | generous(X0)) | ! [X1] : (creative(X1) & ~rich(X1))) & (? [X1] : (~creative(X1) | rich(X1)) | ! [X0] : (creative(X0) & ~generous(X0))) [nnf transformation 26]
52. (? [X0] : (~creative(X0) | generous(X0)) | ! [X1] : (creative(X1) & ~rich(X1))) & (? [X2] : (~creative(X2) | rich(X2)) | ! [X3] : (creative(X3) & ~generous(X3))) [rectify 51]
53. ? [X0] : (~creative(X0) | generous(X0)) => (~creative(sK1) | generous(sK1)) [choice axiom]
54. ? [X2] : (~creative(X2) | rich(X2)) => (~creative(sK2) | rich(sK2)) [choice axiom]
55. ((~creative(sK1) | generous(sK1)) | ! [X1] : (creative(X1) & ~rich(X1))) & ((~creative(sK2) | rich(sK2)) | ! [X3] : (creative(X3) & ~generous(X3))) [skolemisation 52,54,53]
58. ! [X0] : ((tall(X0) & ~strong(X0)) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0)))) [nnf transformation 37]
59. ! [X0] : (((funny(X0) & ~quiet(X0)) | (~happy(X0) & ~humble(X0))) & ((happy(X0) | humble(X0)) | (~funny(X0) | quiet(X0)))) [nnf transformation 9]
60. ! [X0] : (((funny(X0) & ~quiet(X0)) | (~happy(X0) & ~humble(X0))) & (happy(X0) | humble(X0) | ~funny(X0) | quiet(X0))) [flattening 59]
91. ~quiet(X0) | creative(X0) [cnf transformation 50]
92. ~quiet(X0) | ~generous(X0) [cnf transformation 50]
93. creative(X0) | quiet(X0) [cnf transformation 50]
94. ~generous(X0) | quiet(X0) [cnf transformation 50]
102. ~creative(sK1) | generous(sK1) | ~rich(X1) [cnf transformation 55]
111. ~strong(X0) | rich(X0) | ~funny(X0) [cnf transformation 58]
117. ~humble(X0) | funny(X0) [cnf transformation 60]
143. strong(fred) [cnf transformation 24]
144. humble(fred) [cnf transformation 25]
170. ~generous(X0) [subsumption resolution 92,94]
171. creative(X0) [subsumption resolution 91,93]
190. generous(sK1) | ~rich(X1) [subsumption resolution 102,171]
191. ~rich(X1) [subsumption resolution 190,170]
194. ~strong(X0) | ~funny(X0) [subsumption resolution 111,191]
262. funny(fred) [resolution 117,144]
267. ~funny(fred) [resolution 194,143]
268. $false [subsumption resolution 267,262]
% SZS output end Proof for 1101812344641292687392539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is humble then susan is not wise or curious and vice versa. Everyone who is either not funny or not rich is generous or not old. If susan is curious or old then susan is creative. Everyone who is both tall and not tall is not kind or creative and vice versa. If someone is kind then someone is both wise and calm and vice versa. Everyone who is not old is not brave or not old and vice versa. If alice is both not kind and patient then someone is not patient and vice versa. If someone is either happy or not generous then someone is either not old or not generous and vice versa. If someone is not happy then someone is either calm or curious. If fred is either quiet or not old then someone is both creative and brave and vice versa. Everyone who is both not patient and not strong is not generous. Everyone who is creative is not creative or not wise. If someone is quiet then someone is either not happy or not rich. If someone is both brave and not happy then mary is calm or funny. If paul is funny or calm then someone is not creative or creative. Someone is either humble or not quiet. Someone is either not tall or not rich. Someone is quiet. Someone is not tall. Paul is not patient or humble. | Susan is not curious. | entailment | ((humble(alice))<=>((~wise(susan)|curious(susan))))&
(![X]:((~funny(X)<~>~rich(X))=>(generous(X)|~old(X))))&
(((curious(susan)|old(susan)))=>(creative(susan)))&
(![X]:((tall(X)&~tall(X))<=>(~kind(X)|creative(X))))&
((?[X]:(kind(X)))<=>(?[X]:((wise(X)&calm(X)))))&
(![X]:(~old(X)<=>(~brave(X)|~old(X))))&
(((~kind(alice)&patient(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:((happy(X)<~>~generous(X))))<=>(?[X]:((~old(X)<~>~generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((calm(X)<~>curious(X)))))&
(((quiet(fred)<~>~old(fred)))<=>(?[X]:((creative(X)&brave(X)))))&
(![X]:((~patient(X)&~strong(X))=>~generous(X)))&
(![X]:(creative(X)=>(~creative(X)|~wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~happy(X)<~>~rich(X)))))&
((?[X]:((brave(X)&~happy(X))))=>((calm(mary)|funny(mary))))&
(((funny(paul)|calm(paul)))=>(?[X]:((~creative(X)|creative(X)))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:((~tall(X)<~>~rich(X))))&
(?[X]:(quiet(X)))&
(?[X]:(~tall(X)))&
((~patient(paul)|humble(paul))) | ~curious(susan) | [
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7905122336649738850484183
% SZS output start Proof for 7905122336649738850484183
3. (old(susan) | curious(susan)) => creative(susan) [input p2]
4. ! [X0] : ((~tall(X0) & tall(X0)) <=> (creative(X0) | ~kind(X0))) [input p3]
21. curious(susan) [input hypothesis]
29. creative(susan) | (~old(susan) & ~curious(susan)) [ennf transformation 3]
40. ! [X0] : (((~tall(X0) & tall(X0)) | (~creative(X0) & kind(X0))) & ((creative(X0) | ~kind(X0)) | (tall(X0) | ~tall(X0)))) [nnf transformation 4]
41. ! [X0] : (((~tall(X0) & tall(X0)) | (~creative(X0) & kind(X0))) & (creative(X0) | ~kind(X0) | tall(X0) | ~tall(X0))) [flattening 40]
88. creative(susan) | ~curious(susan) [cnf transformation 29]
92. tall(X0) | ~creative(X0) [cnf transformation 41]
94. ~tall(X0) | ~creative(X0) [cnf transformation 41]
133. curious(susan) [cnf transformation 21]
136. 1 <=> curious(susan) [avatar definition]
155. 5 <=> creative(susan) [avatar definition]
157. creative(susan) <- (5) [avatar component clause 155]
159. ~1 | 5 [avatar split clause 88,155,136]
160. ~creative(X0) [subsumption resolution 92,94]
295. 1 [avatar split clause 133,136]
298. $false <- (5) [subsumption resolution 157,160]
299. ~5 [avatar contradiction clause 298]
300. $false [avatar sat refutation 159,295,299]
% SZS output end Proof for 7905122336649738850484183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not rich is not wise and vice versa. If john is both not kind and calm then fred is both not funny and not kind and vice versa. If alice is both tall and not brave then fred is either not tall or patient. If paul is not humble or not happy then someone is happy or funny. If mary is not wise or not quiet then mary is both not humble and not rich and vice versa. If paul is not patient then fred is either brave or quiet and vice versa. If susan is either not calm or not happy then fred is not quiet and vice versa. Everyone who is either happy or humble is either not kind or not happy and vice versa. If someone is not curious or old then mary is happy or not humble and vice versa. If mary is not rich then someone is both curious and patient and vice versa. Everyone who is either not generous or curious is calm or tall. If alice is either happy or not patient then someone is both brave and not curious. Everyone who is either not kind or curious is both curious and not kind. If lucy is either funny or not happy then lucy is both not humble and not wise. If john is both happy and old then fred is both kind and not patient and vice versa. If susan is either happy or not tall then someone is both not brave and kind. Someone is either calm or not old. Fred is both tall and not curious. Someone is both not kind and not calm. Lucy is both not old and not wise. Someone is not generous. Someone is both brave and old. Someone is either not old or humble. Someone is both patient and generous. | Lucy is kind. | entailment | (![X]:((humble(X)&~rich(X))<=>~wise(X)))&
(((~kind(john)&calm(john)))<=>((~funny(fred)&~kind(fred))))&
(((tall(alice)&~brave(alice)))=>((~tall(fred)<~>patient(fred))))&
(((~humble(paul)|~happy(paul)))=>(?[X]:((happy(X)|funny(X)))))&
(((~wise(mary)|~quiet(mary)))<=>((~humble(mary)&~rich(mary))))&
((~patient(paul))<=>((brave(fred)<~>quiet(fred))))&
(((~calm(susan)<~>~happy(susan)))<=>(~quiet(fred)))&
(![X]:((happy(X)<~>humble(X))<=>(~kind(X)<~>~happy(X))))&
((?[X]:((~curious(X)|old(X))))<=>((happy(mary)|~humble(mary))))&
((~rich(mary))<=>(?[X]:((curious(X)&patient(X)))))&
(![X]:((~generous(X)<~>curious(X))=>(calm(X)|tall(X))))&
(((happy(alice)<~>~patient(alice)))=>(?[X]:((brave(X)&~curious(X)))))&
(![X]:((~kind(X)<~>curious(X))=>(curious(X)&~kind(X))))&
(((funny(lucy)<~>~happy(lucy)))=>((~humble(lucy)&~wise(lucy))))&
(((happy(john)&old(john)))<=>((kind(fred)&~patient(fred))))&
(((happy(susan)<~>~tall(susan)))=>(?[X]:((~brave(X)&kind(X)))))&
(?[X]:((calm(X)<~>~old(X))))&
((tall(fred)&~curious(fred)))&
(?[X]:((~kind(X)&~calm(X))))&
((~old(lucy)&~wise(lucy)))&
(?[X]:(~generous(X)))&
(?[X]:((brave(X)&old(X))))&
(?[X]:((~old(X)<~>humble(X))))&
(?[X]:((patient(X)&generous(X)))) | kind(lucy) | [
"p0",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2495645803724877575840323
% SZS output start Proof for 2495645803724877575840323
1. ! [X0] : ((~rich(X0) & humble(X0)) <=> ~wise(X0)) [input p0]
8. ! [X0] : ((happy(X0) <~> humble(X0)) <=> (~kind(X0) <~> ~happy(X0))) [input p7]
20. ~wise(lucy) & ~old(lucy) [input p19]
25. ~kind(lucy) [input hypothesis]
35. ! [X0] : (((~rich(X0) & humble(X0)) | wise(X0)) & (~wise(X0) | (rich(X0) | ~humble(X0)))) [nnf transformation 1]
36. ! [X0] : (((~rich(X0) & humble(X0)) | wise(X0)) & (~wise(X0) | rich(X0) | ~humble(X0))) [flattening 35]
46. ! [X0] : ((((~humble(X0) | ~happy(X0)) & (humble(X0) | happy(X0))) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0)))) & (((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0))))) [nnf transformation 8]
82. wise(X0) | humble(X0) [cnf transformation 36]
108. happy(X0) | kind(X0) | happy(X0) | ~humble(X0) [cnf transformation 46]
111. ~humble(X0) | ~happy(X0) | ~happy(X0) | kind(X0) [cnf transformation 46]
149. ~wise(lucy) [cnf transformation 20]
157. ~kind(lucy) [cnf transformation 25]
161. happy(X0) | kind(X0) | ~humble(X0) [duplicate literal removal 108]
163. ~humble(X0) | ~happy(X0) | kind(X0) [duplicate literal removal 111]
265. ~humble(X0) | kind(X0) [subsumption resolution 161,163]
332. 35 <=> wise(lucy) [avatar definition]
334. ~wise(lucy) <- (~35) [avatar component clause 332]
338. 36 <=> humble(lucy) [avatar definition]
339. humble(lucy) <- (36) [avatar component clause 338]
382. ~35 [avatar split clause 149,332]
393. humble(lucy) <- (~35) [resolution 82,334]
396. 36 | 35 [avatar split clause 393,332,338]
404. kind(lucy) <- (36) [resolution 265,339]
405. $false <- (36) [subsumption resolution 404,157]
406. ~36 [avatar contradiction clause 405]
407. $false [avatar sat refutation 382,396,406]
% SZS output end Proof for 2495645803724877575840323
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or wise is happy or not creative.
If lucy is not wise or not old then someone is not strong or funny.
Everyone who is either not happy or brave is not old or quiet and vice versa.
If someone is wise or patient then alice is funny or not old and vice versa.
Everyone who is both not humble and tall is not humble or patient.
Everyone who is either rich or not happy is humble and vice versa.
Everyone who is either kind or not curious is not strong.
If someone is both creative and not rich then fred is not old.
Everyone who is either not brave or generous is both not patient and not quiet and vice versa.
If alice is rich then someone is either old or happy.
If someone is both not happy and brave then someone is both not tall and quiet.
Everyone who is not curious or brave is not brave or humble and vice versa.
If alice is not rich then someone is old.
If alice is not funny or calm then john is generous and vice versa.
Everyone who is not happy or not calm is either generous or creative and vice versa.
Everyone who is both creative and not strong is both rich and humble.
Lucy is not curious or humble.
Alice is either not strong or rich.
John is not humble.
Someone is both tall and curious.
Susan is humble or calm.
Someone is both creative and not tall.
Someone is happy.
Mary is either brave or not wise. | John is generous. | neutral | (![X]:((tall(X)<~>wise(X))=>(happy(X)|~creative(X))))&
(((~wise(lucy)|~old(lucy)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|quiet(X))))&
((?[X]:((wise(X)|patient(X))))<=>((funny(alice)|~old(alice))))&
(![X]:((~humble(X)&tall(X))=>(~humble(X)|patient(X))))&
(![X]:((rich(X)<~>~happy(X))<=>humble(X)))&
(![X]:((kind(X)<~>~curious(X))=>~strong(X)))&
((?[X]:((creative(X)&~rich(X))))=>(~old(fred)))&
(![X]:((~brave(X)<~>generous(X))<=>(~patient(X)&~quiet(X))))&
((rich(alice))=>(?[X]:((old(X)<~>happy(X)))))&
((?[X]:((~happy(X)&brave(X))))=>(?[X]:((~tall(X)&quiet(X)))))&
(![X]:((~curious(X)|brave(X))<=>(~brave(X)|humble(X))))&
((~rich(alice))=>(?[X]:(old(X))))&
(((~funny(alice)|calm(alice)))<=>(generous(john)))&
(![X]:((~happy(X)|~calm(X))<=>(generous(X)<~>creative(X))))&
(![X]:((creative(X)&~strong(X))=>(rich(X)&humble(X))))&
((~curious(lucy)|humble(lucy)))&
((~strong(alice)<~>rich(alice)))&
(~humble(john))&
(?[X]:((tall(X)&curious(X))))&
((humble(susan)|calm(susan)))&
(?[X]:((creative(X)&~tall(X))))&
(?[X]:(happy(X)))&
((brave(mary)<~>~wise(mary))) | generous(john) | [] | null | 0 |
Everyone who is wise is either not kind or quiet. If alice is both kind and wise then someone is not rich or old and vice versa. Everyone who is not generous or tall is not wise or curious. If someone is both not kind and wise then someone is wise or not generous and vice versa. Everyone who is not kind is both not generous and strong. If fred is both funny and not brave then someone is either not happy or creative. Everyone who is both quiet and not curious is either humble or calm and vice versa. If mary is not curious then alice is old or quiet and vice versa. Everyone who is both kind and creative is kind and vice versa. If fred is either not old or not happy then someone is either not calm or kind. Everyone who is both quiet and strong is not happy or quiet and vice versa. Everyone who is either not old or not funny is either strong or humble and vice versa. If paul is both not humble and not old then lucy is patient or not tall and vice versa. Everyone who is either kind or creative is either old or not tall and vice versa. Everyone who is not creative is either not creative or creative and vice versa. If someone is rich then fred is either not curious or brave. Someone is either not generous or not calm. Mary is wise. Someone is not brave or wise. Someone is brave or not quiet. Alice is generous or patient. Someone is strong or humble. Someone is either strong or quiet. | Paul is not tall. | contradiction | (![X]:(wise(X)=>(~kind(X)<~>quiet(X))))&
(((kind(alice)&wise(alice)))<=>(?[X]:((~rich(X)|old(X)))))&
(![X]:((~generous(X)|tall(X))=>(~wise(X)|curious(X))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~generous(X)&strong(X))))&
(((funny(fred)&~brave(fred)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((quiet(X)&~curious(X))<=>(humble(X)<~>calm(X))))&
((~curious(mary))<=>((old(alice)|quiet(alice))))&
(![X]:((kind(X)&creative(X))<=>kind(X)))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))&
(((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>creative(X))))&
((?[X]:(rich(X)))=>((~curious(fred)<~>brave(fred))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(wise(mary))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((generous(alice)|patient(alice)))&
(?[X]:((strong(X)|humble(X))))&
(?[X]:((strong(X)<~>quiet(X)))) | ~tall(paul) | [
"p1",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6246702390626860870535559
% SZS output start Proof for 6246702390626860870535559
2. (wise(alice) & kind(alice)) <=> ? [X0] : (old(X0) | ~rich(X0)) [input p1]
9. ! [X0] : ((creative(X0) & kind(X0)) <=> kind(X0)) [input p8]
14. ! [X0] : ((kind(X0) <~> creative(X0)) <=> (old(X0) <~> ~tall(X0))) [input p13]
15. ! [X0] : (~creative(X0) <=> (~creative(X0) <~> creative(X0))) [input p14]
24. ~tall(paul) [input hypothesis]
35. ((wise(alice) & kind(alice)) | ! [X0] : (~old(X0) & rich(X0))) & (? [X0] : (old(X0) | ~rich(X0)) | (~wise(alice) | ~kind(alice))) [nnf transformation 2]
36. ((wise(alice) & kind(alice)) | ! [X0] : (~old(X0) & rich(X0))) & (? [X0] : (old(X0) | ~rich(X0)) | ~wise(alice) | ~kind(alice)) [flattening 35]
37. ((wise(alice) & kind(alice)) | ! [X0] : (~old(X0) & rich(X0))) & (? [X1] : (old(X1) | ~rich(X1)) | ~wise(alice) | ~kind(alice)) [rectify 36]
38. ? [X1] : (old(X1) | ~rich(X1)) => (old(sK0) | ~rich(sK0)) [choice axiom]
39. ((wise(alice) & kind(alice)) | ! [X0] : (~old(X0) & rich(X0))) & ((old(sK0) | ~rich(sK0)) | ~wise(alice) | ~kind(alice)) [skolemisation 37,38]
52. ! [X0] : (((creative(X0) & kind(X0)) | ~kind(X0)) & (kind(X0) | (~creative(X0) | ~kind(X0)))) [nnf transformation 9]
53. ! [X0] : (((creative(X0) & kind(X0)) | ~kind(X0)) & (kind(X0) | ~creative(X0) | ~kind(X0))) [flattening 52]
62. ! [X0] : ((((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0))))) [nnf transformation 14]
63. ! [X0] : ((~creative(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | creative(X0))) [nnf transformation 15]
81. kind(alice) | ~old(X0) [cnf transformation 39]
106. ~kind(X0) | creative(X0) [cnf transformation 53]
134. creative(X0) | kind(X0) | old(X0) | tall(X0) [cnf transformation 62]
136. ~creative(X0) | ~kind(X0) | old(X0) | tall(X0) [cnf transformation 62]
140. ~creative(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 63]
152. ~tall(paul) [cnf transformation 24]
156. ~creative(X0) [duplicate literal removal 140]
158. 1 <=> ! [X0] : ~old(X0) [avatar definition]
159. ~old(X0) <- (1) [avatar component clause 158]
170. 4 <=> kind(alice) [avatar definition]
172. kind(alice) <- (4) [avatar component clause 170]
173. 1 | 4 [avatar split clause 81,170,158]
288. ~kind(X0) | old(X0) | tall(X0) [subsumption resolution 136,106]
290. creative(X0) | old(X0) | tall(X0) [subsumption resolution 134,288]
351. creative(alice) <- (4) [resolution 106,172]
353. $false <- (4) [subsumption resolution 351,156]
354. ~4 [avatar contradiction clause 353]
408. old(X0) | tall(X0) [resolution 290,156]
409. tall(X0) <- (1) [subsumption resolution 408,159]
410. $false <- (1) [resolution 409,152]
415. ~1 [avatar contradiction clause 410]
416. $false [avatar sat refutation 173,354,415]
% SZS output end Proof for 6246702390626860870535559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or not creative then alice is either patient or funny.
Everyone who is generous is either kind or not funny and vice versa.
Everyone who is generous is calm and vice versa.
Everyone who is either tall or not tall is both curious and creative and vice versa.
Everyone who is calm or not funny is not funny or not generous.
If someone is either curious or not happy then fred is either not funny or brave and vice versa.
Everyone who is both not rich and generous is both not quiet and not old.
If someone is not brave then lucy is both curious and not old.
Everyone who is not kind or creative is not tall or calm and vice versa.
Everyone who is not curious is not humble or old.
Everyone who is both creative and generous is either not calm or creative and vice versa.
Everyone who is both not tall and strong is rich and vice versa.
If paul is both humble and not funny then someone is either wise or creative and vice versa.
If someone is curious then susan is not old or tall and vice versa.
If fred is humble or not rich then mary is either not rich or not brave.
If someone is not generous or calm then someone is wise or not wise.
Alice is either not curious or generous.
Someone is both not rich and generous.
Someone is both humble and not generous.
John is both not old and funny.
Someone is calm or brave.
Someone is both creative and not strong.
Fred is not humble or rich. | John is calm. | contradiction | ((?[X]:((~brave(X)|~creative(X))))=>((patient(alice)<~>funny(alice))))&
(![X]:(generous(X)<=>(kind(X)<~>~funny(X))))&
(![X]:(generous(X)<=>calm(X)))&
(![X]:((tall(X)<~>~tall(X))<=>(curious(X)&creative(X))))&
(![X]:((calm(X)|~funny(X))=>(~funny(X)|~generous(X))))&
((?[X]:((curious(X)<~>~happy(X))))<=>((~funny(fred)<~>brave(fred))))&
(![X]:((~rich(X)&generous(X))=>(~quiet(X)&~old(X))))&
((?[X]:(~brave(X)))=>((curious(lucy)&~old(lucy))))&
(![X]:((~kind(X)|creative(X))<=>(~tall(X)|calm(X))))&
(![X]:(~curious(X)=>(~humble(X)|old(X))))&
(![X]:((creative(X)&generous(X))<=>(~calm(X)<~>creative(X))))&
(![X]:((~tall(X)&strong(X))<=>rich(X)))&
(((humble(paul)&~funny(paul)))<=>(?[X]:((wise(X)<~>creative(X)))))&
((?[X]:(curious(X)))<=>((~old(susan)|tall(susan))))&
(((humble(fred)|~rich(fred)))=>((~rich(mary)<~>~brave(mary))))&
((?[X]:((~generous(X)|calm(X))))=>(?[X]:((wise(X)|~wise(X)))))&
((~curious(alice)<~>generous(alice)))&
(?[X]:((~rich(X)&generous(X))))&
(?[X]:((humble(X)&~generous(X))))&
((~old(john)&funny(john)))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:((creative(X)&~strong(X))))&
((~humble(fred)|rich(fred))) | calm(john) | [
"p2",
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 122040229205601065536724
% SZS output start Proof for 122040229205601065536724
3. ! [X0] : (generous(X0) <=> calm(X0)) [input p2]
5. ! [X0] : ((~funny(X0) | calm(X0)) => (~generous(X0) | ~funny(X0))) [input p4]
20. funny(john) & ~old(john) [input p19]
24. calm(john) [input hypothesis]
28. ! [X0] : ((~generous(X0) | ~funny(X0)) | (funny(X0) & ~calm(X0))) [ennf transformation 5]
29. ! [X0] : (~generous(X0) | ~funny(X0) | (funny(X0) & ~calm(X0))) [flattening 28]
39. ! [X0] : ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0))) [nnf transformation 3]
84. ~calm(X0) | generous(X0) [cnf transformation 39]
91. ~generous(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 29]
140. funny(john) [cnf transformation 20]
145. calm(john) [cnf transformation 24]
173. ~calm(X0) | ~funny(X0) [subsumption resolution 91,84]
284. ~funny(john) [resolution 173,145]
289. $false [subsumption resolution 284,140]
% SZS output end Proof for 122040229205601065536724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not creative or patient and vice versa. Everyone who is wise or kind is both old and not brave. Everyone who is not calm is either kind or happy and vice versa. Everyone who is both strong and not tall is strong or not strong and vice versa. Everyone who is not kind or not humble is not happy and vice versa. If someone is rich then paul is old and vice versa. Everyone who is both creative and wise is both old and not old and vice versa. Everyone who is tall or not strong is humble. If mary is not calm or patient then someone is both not strong and kind and vice versa. If alice is patient then susan is either not quiet or not strong and vice versa. If someone is old or not rich then john is either not old or not quiet and vice versa. Everyone who is both not calm and not patient is both creative and rich and vice versa. Everyone who is either patient or quiet is either funny or patient. Everyone who is either tall or not old is either not quiet or quiet. Everyone who is not generous or not wise is patient or funny and vice versa. Everyone who is not humble is either calm or not tall. Someone is either not quiet or not creative. Someone is not humble. Mary is either not kind or not calm. Someone is both funny and old. Someone is both quiet and kind. Paul is kind. Susan is both not calm and not generous. | Susan is happy. | contradiction | (![X]:(happy(X)<=>(~creative(X)|patient(X))))&
(![X]:((wise(X)|kind(X))=>(old(X)&~brave(X))))&
(![X]:(~calm(X)<=>(kind(X)<~>happy(X))))&
(![X]:((strong(X)&~tall(X))<=>(strong(X)|~strong(X))))&
(![X]:((~kind(X)|~humble(X))<=>~happy(X)))&
((?[X]:(rich(X)))<=>(old(paul)))&
(![X]:((creative(X)&wise(X))<=>(old(X)&~old(X))))&
(![X]:((tall(X)|~strong(X))=>humble(X)))&
(((~calm(mary)|patient(mary)))<=>(?[X]:((~strong(X)&kind(X)))))&
((patient(alice))<=>((~quiet(susan)<~>~strong(susan))))&
((?[X]:((old(X)|~rich(X))))<=>((~old(john)<~>~quiet(john))))&
(![X]:((~calm(X)&~patient(X))<=>(creative(X)&rich(X))))&
(![X]:((patient(X)<~>quiet(X))=>(funny(X)<~>patient(X))))&
(![X]:((tall(X)<~>~old(X))=>(~quiet(X)<~>quiet(X))))&
(![X]:((~generous(X)|~wise(X))<=>(patient(X)|funny(X))))&
(![X]:(~humble(X)=>(calm(X)<~>~tall(X))))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(?[X]:(~humble(X)))&
((~kind(mary)<~>~calm(mary)))&
(?[X]:((funny(X)&old(X))))&
(?[X]:((quiet(X)&kind(X))))&
(kind(paul))&
((~calm(susan)&~generous(susan))) | happy(susan) | [
"p2",
"p4",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7876685225467332230458441
% SZS output start Proof for 7876685225467332230458441
3. ! [X0] : (~calm(X0) <=> (kind(X0) <~> happy(X0))) [input p2]
5. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> ~happy(X0)) [input p4]
23. ~generous(susan) & ~calm(susan) [input p22]
24. happy(susan) [input hypothesis]
33. ! [X0] : ((~calm(X0) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | calm(X0))) [nnf transformation 3]
36. ! [X0] : (((~humble(X0) | ~kind(X0)) | happy(X0)) & (~happy(X0) | (humble(X0) & kind(X0)))) [nnf transformation 5]
37. ! [X0] : ((~humble(X0) | ~kind(X0) | happy(X0)) & (~happy(X0) | (humble(X0) & kind(X0)))) [flattening 36]
77. ~kind(X0) | ~happy(X0) | calm(X0) [cnf transformation 33]
85. ~happy(X0) | kind(X0) [cnf transformation 37]
139. ~calm(susan) [cnf transformation 23]
141. happy(susan) [cnf transformation 24]
244. kind(susan) [resolution 85,141]
256. ~happy(susan) | calm(susan) [resolution 77,244]
268. calm(susan) [subsumption resolution 256,141]
269. $false [subsumption resolution 268,139]
% SZS output end Proof for 7876685225467332230458441
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not old is strong or quiet. If someone is either strong or not wise then mary is creative. Everyone who is both funny and strong is curious or not rich and vice versa. If alice is wise then someone is rich or not quiet. Everyone who is either kind or not old is either curious or not wise and vice versa. Everyone who is not calm or wise is either quiet or calm and vice versa. Everyone who is both not humble and not kind is either not wise or strong and vice versa. If someone is either not curious or quiet then someone is calm or not brave. Everyone who is both not creative and not curious is happy or not old and vice versa. Everyone who is not patient or not wise is not strong. If someone is either not funny or not old then john is not old or tall. Everyone who is either not generous or generous is both not tall and not brave and vice versa. Everyone who is tall is rich or quiet and vice versa. Everyone who is both kind and tall is not humble or patient. If someone is both not quiet and not curious then paul is either tall or not brave and vice versa. Someone is either not tall or not strong. Someone is strong. Lucy is calm or quiet. Alice is generous or not wise. Someone is old or generous. | Lucy is not funny. | contradiction | (![X]:((strong(X)&~old(X))=>(strong(X)|quiet(X))))&
((?[X]:((strong(X)<~>~wise(X))))=>(creative(mary)))&
(![X]:((funny(X)&strong(X))<=>(curious(X)|~rich(X))))&
((wise(alice))=>(?[X]:((rich(X)|~quiet(X)))))&
(![X]:((kind(X)<~>~old(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((~calm(X)|wise(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~humble(X)&~kind(X))<=>(~wise(X)<~>strong(X))))&
((?[X]:((~curious(X)<~>quiet(X))))=>(?[X]:((calm(X)|~brave(X)))))&
(![X]:((~creative(X)&~curious(X))<=>(happy(X)|~old(X))))&
(![X]:((~patient(X)|~wise(X))=>~strong(X)))&
((?[X]:((~funny(X)<~>~old(X))))=>((~old(john)|tall(john))))&
(![X]:((~generous(X)<~>generous(X))<=>(~tall(X)&~brave(X))))&
(![X]:(tall(X)<=>(rich(X)|quiet(X))))&
(![X]:((kind(X)&tall(X))=>(~humble(X)|patient(X))))&
((?[X]:((~quiet(X)&~curious(X))))<=>((tall(paul)<~>~brave(paul))))&
(?[X]:((~tall(X)<~>~strong(X))))&
(?[X]:(strong(X)))&
((calm(lucy)|quiet(lucy)))&
((generous(alice)|~wise(alice)))&
(?[X]:((old(X)|generous(X)))) | ~funny(lucy) | [
"p2",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2823227073056844287736987
% SZS output start Proof for 2823227073056844287736987
3. ! [X0] : ((strong(X0) & funny(X0)) <=> (~rich(X0) | curious(X0))) [input p2]
12. ! [X0] : ((~generous(X0) <~> generous(X0)) <=> (~brave(X0) & ~tall(X0))) [input p11]
13. ! [X0] : (tall(X0) <=> (quiet(X0) | rich(X0))) [input p12]
21. ~funny(lucy) [input hypothesis]
34. ! [X0] : (((strong(X0) & funny(X0)) | (rich(X0) & ~curious(X0))) & ((~rich(X0) | curious(X0)) | (~strong(X0) | ~funny(X0)))) [nnf transformation 3]
35. ! [X0] : (((strong(X0) & funny(X0)) | (rich(X0) & ~curious(X0))) & (~rich(X0) | curious(X0) | ~strong(X0) | ~funny(X0))) [flattening 34]
50. ! [X0] : ((((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0))))) [nnf transformation 12]
51. ! [X0] : ((((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0))))) [flattening 50]
52. ! [X0] : ((tall(X0) | (~quiet(X0) & ~rich(X0))) & ((quiet(X0) | rich(X0)) | ~tall(X0))) [nnf transformation 13]
53. ! [X0] : ((tall(X0) | (~quiet(X0) & ~rich(X0))) & (quiet(X0) | rich(X0) | ~tall(X0))) [flattening 52]
70. rich(X0) | funny(X0) [cnf transformation 35]
104. ~tall(X0) | generous(X0) | generous(X0) [cnf transformation 51]
105. ~tall(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 51]
111. tall(X0) | ~rich(X0) [cnf transformation 53]
125. ~funny(lucy) [cnf transformation 21]
126. ~tall(X0) | generous(X0) [duplicate literal removal 104]
127. ~tall(X0) | ~generous(X0) [duplicate literal removal 105]
190. ~tall(X0) [subsumption resolution 126,127]
192. ~rich(X0) [subsumption resolution 111,190]
210. funny(X0) [resolution 70,192]
211. $false [resolution 210,125]
% SZS output end Proof for 2823227073056844287736987
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not calm is not patient. Everyone who is humble or quiet is both tall and calm. Everyone who is both not old and happy is both funny and humble. If lucy is not strong or not curious then fred is either not wise or not generous. If susan is either generous or not tall then someone is not humble or rich. Everyone who is old is either not generous or funny and vice versa. If someone is rich or not calm then someone is both calm and not funny and vice versa. If someone is not strong then someone is both funny and not humble. Everyone who is both rich and wise is either generous or funny and vice versa. Everyone who is either not kind or old is humble and vice versa. Everyone who is either kind or tall is both not kind and not generous. If alice is not curious then fred is both not brave and not creative and vice versa. If john is either not happy or not strong then paul is not funny or not calm. If lucy is not quiet then lucy is funny or patient and vice versa. Everyone who is either strong or generous is not strong and vice versa. Everyone who is curious is not kind and vice versa. Fred is both curious and not calm. John is patient or not funny. John is not strong. Someone is funny or creative. Mary is either happy or quiet. Someone is not wise or not creative. | Lucy is generous. | entailment | (![X]:((~creative(X)|~calm(X))=>~patient(X)))&
(![X]:((humble(X)|quiet(X))=>(tall(X)&calm(X))))&
(![X]:((~old(X)&happy(X))=>(funny(X)&humble(X))))&
(((~strong(lucy)|~curious(lucy)))=>((~wise(fred)<~>~generous(fred))))&
(((generous(susan)<~>~tall(susan)))=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:(old(X)<=>(~generous(X)<~>funny(X))))&
((?[X]:((rich(X)|~calm(X))))<=>(?[X]:((calm(X)&~funny(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((funny(X)&~humble(X)))))&
(![X]:((rich(X)&wise(X))<=>(generous(X)<~>funny(X))))&
(![X]:((~kind(X)<~>old(X))<=>humble(X)))&
(![X]:((kind(X)<~>tall(X))=>(~kind(X)&~generous(X))))&
((~curious(alice))<=>((~brave(fred)&~creative(fred))))&
(((~happy(john)<~>~strong(john)))=>((~funny(paul)|~calm(paul))))&
((~quiet(lucy))<=>((funny(lucy)|patient(lucy))))&
(![X]:((strong(X)<~>generous(X))<=>~strong(X)))&
(![X]:(curious(X)<=>~kind(X)))&
((curious(fred)&~calm(fred)))&
((patient(john)|~funny(john)))&
(~strong(john))&
(?[X]:((funny(X)|creative(X))))&
((happy(mary)<~>quiet(mary)))&
(?[X]:((~wise(X)|~creative(X)))) | generous(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1942667093873564306322283
% SZS output start Proof for 1942667093873564306322283
15. ! [X0] : ((strong(X0) <~> generous(X0)) <=> ~strong(X0)) [input p14]
23. ~generous(lucy) [input hypothesis]
58. ! [X0] : ((((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | strong(X0)) & (~strong(X0) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0))))) [nnf transformation 15]
112. ~strong(X0) | generous(X0) | ~strong(X0) [cnf transformation 58]
114. generous(X0) | strong(X0) | strong(X0) [cnf transformation 58]
126. ~generous(lucy) [cnf transformation 23]
127. ~strong(X0) | generous(X0) [duplicate literal removal 112]
128. generous(X0) | strong(X0) [duplicate literal removal 114]
259. generous(X0) [subsumption resolution 127,128]
298. $false [subsumption resolution 126,259]
% SZS output end Proof for 1942667093873564306322283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or quiet then someone is quiet and vice versa.
Everyone who is not wise or not rich is both not generous and brave and vice versa.
Everyone who is both not patient and funny is patient or not generous and vice versa.
Everyone who is not happy is not creative or not patient and vice versa.
If someone is both kind and not kind then susan is both not creative and not generous.
Everyone who is curious or kind is not kind or quiet.
Everyone who is both not tall and humble is both generous and not curious.
Everyone who is both not humble and curious is both not brave and old.
If susan is either funny or not happy then someone is not patient.
If john is patient or generous then someone is either old or not rich and vice versa.
Everyone who is brave or strong is not curious or not old.
Everyone who is either brave or kind is not rich or humble.
If someone is either curious or rich then alice is kind or humble.
If alice is quiet or not quiet then lucy is kind.
If fred is both funny and kind then someone is not creative or tall and vice versa.
If someone is both curious and not old then someone is not kind and vice versa.
Alice is not humble or tall.
Susan is funny or not patient.
Someone is wise.
Lucy is kind or not rich.
Susan is either not humble or wise.
Fred is wise or not happy.
Someone is either happy or not humble.
Susan is either not humble or not funny. | Fred is quiet. | entailment | ((?[X]:((patient(X)|quiet(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~wise(X)|~rich(X))<=>(~generous(X)&brave(X))))&
(![X]:((~patient(X)&funny(X))<=>(patient(X)|~generous(X))))&
(![X]:(~happy(X)<=>(~creative(X)|~patient(X))))&
((?[X]:((kind(X)&~kind(X))))=>((~creative(susan)&~generous(susan))))&
(![X]:((curious(X)|kind(X))=>(~kind(X)|quiet(X))))&
(![X]:((~tall(X)&humble(X))=>(generous(X)&~curious(X))))&
(![X]:((~humble(X)&curious(X))=>(~brave(X)&old(X))))&
(((funny(susan)<~>~happy(susan)))=>(?[X]:(~patient(X))))&
(((patient(john)|generous(john)))<=>(?[X]:((old(X)<~>~rich(X)))))&
(![X]:((brave(X)|strong(X))=>(~curious(X)|~old(X))))&
(![X]:((brave(X)<~>kind(X))=>(~rich(X)|humble(X))))&
((?[X]:((curious(X)<~>rich(X))))=>((kind(alice)|humble(alice))))&
(((quiet(alice)|~quiet(alice)))=>(kind(lucy)))&
(((funny(fred)&kind(fred)))<=>(?[X]:((~creative(X)|tall(X)))))&
((?[X]:((curious(X)&~old(X))))<=>(?[X]:(~kind(X))))&
((~humble(alice)|tall(alice)))&
((funny(susan)|~patient(susan)))&
(?[X]:(wise(X)))&
((kind(lucy)|~rich(lucy)))&
((~humble(susan)<~>wise(susan)))&
((wise(fred)|~happy(fred)))&
(?[X]:((happy(X)<~>~humble(X))))&
((~humble(susan)<~>~funny(susan))) | quiet(fred) | [
"p5",
"p6",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6177143481157843265769404
% SZS output start Proof for 6177143481157843265769404
6. ! [X0] : ((kind(X0) | curious(X0)) => (quiet(X0) | ~kind(X0))) [input p5]
7. ! [X0] : ((humble(X0) & ~tall(X0)) => (~curious(X0) & generous(X0))) [input p6]
8. ! [X0] : ((curious(X0) & ~humble(X0)) => (old(X0) & ~brave(X0))) [input p7]
15. (kind(fred) & funny(fred)) <=> ? [X0] : (tall(X0) | ~creative(X0)) [input p14]
16. ? [X0] : (~old(X0) & curious(X0)) <=> ? [X0] : ~kind(X0) [input p15]
25. ~quiet(fred) [input hypothesis]
27. ? [X0] : (~old(X0) & curious(X0)) <=> ? [X1] : ~kind(X1) [rectify 16]
30. ! [X0] : ((quiet(X0) | ~kind(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 6]
31. ! [X0] : (quiet(X0) | ~kind(X0) | (~kind(X0) & ~curious(X0))) [flattening 30]
32. ! [X0] : ((~curious(X0) & generous(X0)) | (~humble(X0) | tall(X0))) [ennf transformation 7]
33. ! [X0] : ((~curious(X0) & generous(X0)) | ~humble(X0) | tall(X0)) [flattening 32]
34. ! [X0] : ((old(X0) & ~brave(X0)) | (~curious(X0) | humble(X0))) [ennf transformation 8]
35. ! [X0] : ((old(X0) & ~brave(X0)) | ~curious(X0) | humble(X0)) [flattening 34]
65. ((kind(fred) & funny(fred)) | ! [X0] : (~tall(X0) & creative(X0))) & (? [X0] : (tall(X0) | ~creative(X0)) | (~kind(fred) | ~funny(fred))) [nnf transformation 15]
66. ((kind(fred) & funny(fred)) | ! [X0] : (~tall(X0) & creative(X0))) & (? [X0] : (tall(X0) | ~creative(X0)) | ~kind(fred) | ~funny(fred)) [flattening 65]
67. ((kind(fred) & funny(fred)) | ! [X0] : (~tall(X0) & creative(X0))) & (? [X1] : (tall(X1) | ~creative(X1)) | ~kind(fred) | ~funny(fred)) [rectify 66]
68. ? [X1] : (tall(X1) | ~creative(X1)) => (tall(sK4) | ~creative(sK4)) [choice axiom]
69. ((kind(fred) & funny(fred)) | ! [X0] : (~tall(X0) & creative(X0))) & ((tall(sK4) | ~creative(sK4)) | ~kind(fred) | ~funny(fred)) [skolemisation 67,68]
70. (? [X0] : (~old(X0) & curious(X0)) | ! [X1] : kind(X1)) & (? [X1] : ~kind(X1) | ! [X0] : (old(X0) | ~curious(X0))) [nnf transformation 27]
71. (? [X0] : (~old(X0) & curious(X0)) | ! [X1] : kind(X1)) & (? [X2] : ~kind(X2) | ! [X3] : (old(X3) | ~curious(X3))) [rectify 70]
72. ? [X0] : (~old(X0) & curious(X0)) => (~old(sK5) & curious(sK5)) [choice axiom]
73. ? [X2] : ~kind(X2) => ~kind(sK6) [choice axiom]
74. ((~old(sK5) & curious(sK5)) | ! [X1] : kind(X1)) & (~kind(sK6) | ! [X3] : (old(X3) | ~curious(X3))) [skolemisation 71,73,72]
101. quiet(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 31]
103. ~humble(X0) | ~curious(X0) | tall(X0) [cnf transformation 33]
105. ~curious(X0) | old(X0) | humble(X0) [cnf transformation 35]
125. kind(fred) | ~tall(X0) [cnf transformation 69]
127. curious(sK5) | kind(X1) [cnf transformation 74]
128. ~old(sK5) | kind(X1) [cnf transformation 74]
140. ~quiet(fred) [cnf transformation 25]
141. ~kind(X0) | quiet(X0) [duplicate literal removal 101]
238. 21 <=> ! [X0] : ~tall(X0) [avatar definition]
239. ~tall(X0) <- (21) [avatar component clause 238]
241. 22 <=> kind(fred) [avatar definition]
242. ~kind(fred) <- (~22) [avatar component clause 241]
243. kind(fred) <- (22) [avatar component clause 241]
244. 21 | 22 [avatar split clause 125,241,238]
265. 27 <=> ! [X1] : kind(X1) [avatar definition]
266. kind(X1) <- (27) [avatar component clause 265]
268. 28 <=> old(sK5) [avatar definition]
271. 27 | ~28 [avatar split clause 128,268,265]
273. 29 <=> curious(sK5) [avatar definition]
275. curious(sK5) <- (29) [avatar component clause 273]
276. 27 | 29 [avatar split clause 127,273,265]
332. quiet(fred) <- (22) [resolution 141,243]
337. $false <- (22) [subsumption resolution 332,140]
338. ~22 [avatar contradiction clause 337]
352. 40 <=> humble(sK5) [avatar definition]
354. humble(sK5) <- (40) [avatar component clause 352]
360. old(sK5) | humble(sK5) <- (29) [resolution 105,275]
363. 40 | 28 | ~29 [avatar split clause 360,273,268,352]
364. $false <- (~22, 27) [resolution 266,242]
366. 22 | ~27 [avatar contradiction clause 364]
377. ~curious(sK5) | tall(sK5) <- (40) [resolution 354,103]
379. tall(sK5) <- (29, 40) [subsumption resolution 377,275]
380. $false <- (21, 29, 40) [subsumption resolution 379,239]
381. ~21 | ~29 | ~40 [avatar contradiction clause 380]
383. $false [avatar sat refutation 244,271,276,338,363,366,381]
% SZS output end Proof for 6177143481157843265769404
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not calm and not humble then alice is not kind and vice versa.
Everyone who is either brave or not old is quiet and vice versa.
If john is both happy and rich then someone is not humble or funny and vice versa.
If paul is not funny or creative then alice is both not curious and not strong and vice versa.
Everyone who is both patient and not tall is rich or not patient and vice versa.
Everyone who is quiet or wise is not quiet or not funny.
If john is kind then susan is calm or not humble and vice versa.
Everyone who is either funny or strong is tall.
If someone is not wise then paul is both brave and creative and vice versa.
Everyone who is either not old or funny is either not quiet or creative and vice versa.
If john is both patient and tall then someone is brave and vice versa.
If someone is both strong and curious then someone is both curious and not patient and vice versa.
If john is old then someone is either brave or rich.
If alice is either not creative or not curious then someone is both calm and brave and vice versa.
If alice is both not curious and not funny then susan is either not calm or wise and vice versa.
Everyone who is both not old and not wise is curious and vice versa.
Susan is either not generous or not funny.
Mary is kind or not happy.
Paul is generous or not kind.
Mary is brave.
Someone is either not curious or rich.
Someone is not curious or quiet.
Mary is not happy or not kind. | Alice is wise. | entailment | (((~calm(lucy)&~humble(lucy)))<=>(~kind(alice)))&
(![X]:((brave(X)<~>~old(X))<=>quiet(X)))&
(((happy(john)&rich(john)))<=>(?[X]:((~humble(X)|funny(X)))))&
(((~funny(paul)|creative(paul)))<=>((~curious(alice)&~strong(alice))))&
(![X]:((patient(X)&~tall(X))<=>(rich(X)|~patient(X))))&
(![X]:((quiet(X)|wise(X))=>(~quiet(X)|~funny(X))))&
((kind(john))<=>((calm(susan)|~humble(susan))))&
(![X]:((funny(X)<~>strong(X))=>tall(X)))&
((?[X]:(~wise(X)))<=>((brave(paul)&creative(paul))))&
(![X]:((~old(X)<~>funny(X))<=>(~quiet(X)<~>creative(X))))&
(((patient(john)&tall(john)))<=>(?[X]:(brave(X))))&
((?[X]:((strong(X)&curious(X))))<=>(?[X]:((curious(X)&~patient(X)))))&
((old(john))=>(?[X]:((brave(X)<~>rich(X)))))&
(((~creative(alice)<~>~curious(alice)))<=>(?[X]:((calm(X)&brave(X)))))&
(((~curious(alice)&~funny(alice)))<=>((~calm(susan)<~>wise(susan))))&
(![X]:((~old(X)&~wise(X))<=>curious(X)))&
((~generous(susan)<~>~funny(susan)))&
((kind(mary)|~happy(mary)))&
((generous(paul)|~kind(paul)))&
(brave(mary))&
(?[X]:((~curious(X)<~>rich(X))))&
(?[X]:((~curious(X)|quiet(X))))&
((~happy(mary)|~kind(mary))) | wise(alice) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6238978569355125828881767
% SZS output start Proof for 6238978569355125828881767
2. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> quiet(X0)) [input p1]
3. (rich(john) & happy(john)) <=> ? [X0] : (funny(X0) | ~humble(X0)) [input p2]
5. ! [X0] : ((~tall(X0) & patient(X0)) <=> (~patient(X0) | rich(X0))) [input p4]
6. ! [X0] : ((wise(X0) | quiet(X0)) => (~funny(X0) | ~quiet(X0))) [input p5]
9. ? [X0] : ~wise(X0) <=> (creative(paul) & brave(paul)) [input p8]
10. ! [X0] : ((~old(X0) <~> funny(X0)) <=> (~quiet(X0) <~> creative(X0))) [input p9]
11. (tall(john) & patient(john)) <=> ? [X0] : brave(X0) [input p10]
24. ~wise(alice) [input hypothesis]
26. ! [X0] : ((~funny(X0) | ~quiet(X0)) | (~wise(X0) & ~quiet(X0))) [ennf transformation 6]
27. ! [X0] : (~funny(X0) | ~quiet(X0) | (~wise(X0) & ~quiet(X0))) [flattening 26]
32. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | ~quiet(X0)) & (quiet(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 2]
33. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X0] : (funny(X0) | ~humble(X0)) | (~rich(john) | ~happy(john))) [nnf transformation 3]
34. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X0] : (funny(X0) | ~humble(X0)) | ~rich(john) | ~happy(john)) [flattening 33]
35. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X1] : (funny(X1) | ~humble(X1)) | ~rich(john) | ~happy(john)) [rectify 34]
36. ? [X1] : (funny(X1) | ~humble(X1)) => (funny(sK0) | ~humble(sK0)) [choice axiom]
37. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & ((funny(sK0) | ~humble(sK0)) | ~rich(john) | ~happy(john)) [skolemisation 35,36]
40. ! [X0] : (((~tall(X0) & patient(X0)) | (patient(X0) & ~rich(X0))) & ((~patient(X0) | rich(X0)) | (tall(X0) | ~patient(X0)))) [nnf transformation 5]
41. ! [X0] : (((~tall(X0) & patient(X0)) | (patient(X0) & ~rich(X0))) & (~patient(X0) | rich(X0) | tall(X0) | ~patient(X0))) [flattening 40]
45. (? [X0] : ~wise(X0) | (~creative(paul) | ~brave(paul))) & ((creative(paul) & brave(paul)) | ! [X0] : wise(X0)) [nnf transformation 9]
46. (? [X0] : ~wise(X0) | ~creative(paul) | ~brave(paul)) & ((creative(paul) & brave(paul)) | ! [X0] : wise(X0)) [flattening 45]
47. (? [X0] : ~wise(X0) | ~creative(paul) | ~brave(paul)) & ((creative(paul) & brave(paul)) | ! [X1] : wise(X1)) [rectify 46]
48. ? [X0] : ~wise(X0) => ~wise(sK1) [choice axiom]
49. (~wise(sK1) | ~creative(paul) | ~brave(paul)) & ((creative(paul) & brave(paul)) | ! [X1] : wise(X1)) [skolemisation 47,48]
50. ! [X0] : ((((~funny(X0) | old(X0)) & (funny(X0) | ~old(X0))) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0)))) & (((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | ((~old(X0) | ~funny(X0)) & (funny(X0) | old(X0))))) [nnf transformation 10]
51. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~tall(john) | ~patient(john))) [nnf transformation 11]
52. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~tall(john) | ~patient(john)) [flattening 51]
53. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~tall(john) | ~patient(john)) [rectify 52]
54. ? [X1] : brave(X1) => brave(sK2) [choice axiom]
55. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (brave(sK2) | ~tall(john) | ~patient(john)) [skolemisation 53,54]
81. ~old(X0) | quiet(X0) | ~brave(X0) [cnf transformation 32]
84. ~quiet(X0) | ~brave(X0) | old(X0) [cnf transformation 32]
89. rich(john) | ~funny(X0) [cnf transformation 37]
98. ~tall(X0) | ~rich(X0) [cnf transformation 41]
100. ~funny(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 27]
107. brave(paul) | wise(X1) [cnf transformation 49]
108. creative(paul) | wise(X1) [cnf transformation 49]
112. ~creative(X0) | quiet(X0) | funny(X0) | old(X0) [cnf transformation 50]
115. funny(X0) | ~old(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 50]
120. tall(john) | ~brave(X0) [cnf transformation 55]
151. ~wise(alice) [cnf transformation 24]
152. ~funny(X0) | ~quiet(X0) [duplicate literal removal 100]
171. 4 <=> ! [X0] : ~funny(X0) [avatar definition]
172. ~funny(X0) <- (4) [avatar component clause 171]
174. 5 <=> rich(john) [avatar definition]
177. 4 | 5 [avatar split clause 89,174,171]
210. 13 <=> creative(paul) [avatar definition]
212. creative(paul) <- (13) [avatar component clause 210]
235. 17 <=> brave(paul) [avatar definition]
236. brave(paul) <- (17) [avatar component clause 235]
244. 19 <=> ! [X1] : wise(X1) [avatar definition]
245. wise(X1) <- (19) [avatar component clause 244]
246. 19 | 13 [avatar split clause 108,210,244]
247. 19 | 17 [avatar split clause 107,235,244]
249. ~creative(X0) | ~quiet(X0) | ~old(X0) [subsumption resolution 115,152]
253. 20 <=> ! [X0] : ~brave(X0) [avatar definition]
254. ~brave(X0) <- (20) [avatar component clause 253]
256. 21 <=> tall(john) [avatar definition]
258. tall(john) <- (21) [avatar component clause 256]
259. 20 | 21 [avatar split clause 120,256,253]
364. $false <- (17, 20) [subsumption resolution 236,254]
365. ~17 | ~20 [avatar contradiction clause 364]
370. $false <- (19) [resolution 245,151]
373. ~19 [avatar contradiction clause 370]
374. ~rich(john) <- (21) [resolution 98,258]
422. ~quiet(paul) | ~old(paul) <- (13) [resolution 249,212]
424. 48 <=> old(paul) [avatar definition]
425. old(paul) <- (48) [avatar component clause 424]
426. ~old(paul) <- (~48) [avatar component clause 424]
428. 49 <=> quiet(paul) [avatar definition]
429. quiet(paul) <- (49) [avatar component clause 428]
430. ~quiet(paul) <- (~49) [avatar component clause 428]
431. ~48 | ~49 | ~13 [avatar split clause 422,210,428,424]
445. quiet(paul) | funny(paul) | old(paul) <- (13) [resolution 112,212]
446. quiet(paul) | old(paul) <- (4, 13) [subsumption resolution 445,172]
447. quiet(paul) <- (4, 13, ~48) [subsumption resolution 446,426]
448. 49 | ~4 | ~13 | 48 [avatar split clause 447,424,210,171,428]
451. ~5 | ~21 [avatar split clause 374,256,174]
454. quiet(paul) | ~brave(paul) <- (48) [resolution 425,81]
455. ~brave(paul) <- (48, ~49) [subsumption resolution 454,430]
456. $false <- (17, 48, ~49) [subsumption resolution 455,236]
457. ~17 | ~48 | 49 [avatar contradiction clause 456]
480. ~brave(paul) | old(paul) <- (49) [resolution 429,84]
482. old(paul) <- (17, 49) [subsumption resolution 480,236]
483. $false <- (17, ~48, 49) [subsumption resolution 482,426]
484. ~17 | 48 | ~49 [avatar contradiction clause 483]
485. $false [avatar sat refutation 177,246,247,259,365,373,431,448,451,457,484]
% SZS output end Proof for 6238978569355125828881767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then someone is generous. Everyone who is not quiet is not strong. Everyone who is not strong or not brave is calm. Everyone who is creative is both not patient and not curious. If someone is creative then alice is quiet and vice versa. If someone is funny or not creative then someone is rich. Everyone who is not calm or not kind is rich or not quiet. If someone is both strong and kind then alice is both curious and not happy and vice versa. Everyone who is wise or rich is rich and vice versa. If someone is either wise or tall then someone is either strong or not old. If alice is both humble and not generous then someone is either kind or calm. Everyone who is both not generous and tall is either not humble or funny. If someone is happy or funny then mary is both strong and generous. If someone is either brave or calm then someone is both wise and not creative and vice versa. Everyone who is both tall and not funny is both not happy and generous and vice versa. If someone is either quiet or creative then someone is patient or not calm and vice versa. Someone is happy or not wise. Someone is either not rich or not brave. Someone is either not funny or not generous. Someone is both not generous and funny. Mary is both creative and not humble. Susan is both not tall and funny. Someone is wise. Someone is both patient and brave. | Alice is generous. | neutral | ((?[X]:(~calm(X)))=>(?[X]:(generous(X))))&
(![X]:(~quiet(X)=>~strong(X)))&
(![X]:((~strong(X)|~brave(X))=>calm(X)))&
(![X]:(creative(X)=>(~patient(X)&~curious(X))))&
((?[X]:(creative(X)))<=>(quiet(alice)))&
((?[X]:((funny(X)|~creative(X))))=>(?[X]:(rich(X))))&
(![X]:((~calm(X)|~kind(X))=>(rich(X)|~quiet(X))))&
((?[X]:((strong(X)&kind(X))))<=>((curious(alice)&~happy(alice))))&
(![X]:((wise(X)|rich(X))<=>rich(X)))&
((?[X]:((wise(X)<~>tall(X))))=>(?[X]:((strong(X)<~>~old(X)))))&
(((humble(alice)&~generous(alice)))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:((~generous(X)&tall(X))=>(~humble(X)<~>funny(X))))&
((?[X]:((happy(X)|funny(X))))=>((strong(mary)&generous(mary))))&
((?[X]:((brave(X)<~>calm(X))))<=>(?[X]:((wise(X)&~creative(X)))))&
(![X]:((tall(X)&~funny(X))<=>(~happy(X)&generous(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(?[X]:((patient(X)|~calm(X)))))&
(?[X]:((happy(X)|~wise(X))))&
(?[X]:((~rich(X)<~>~brave(X))))&
(?[X]:((~funny(X)<~>~generous(X))))&
(?[X]:((~generous(X)&funny(X))))&
((creative(mary)&~humble(mary)))&
((~tall(susan)&funny(susan)))&
(?[X]:(wise(X)))&
(?[X]:((patient(X)&brave(X)))) | generous(alice) | [] | null | 0 |
If someone is curious or strong then fred is brave.
If someone is not humble or happy then someone is not brave or creative and vice versa.
Everyone who is generous or not tall is either kind or not strong.
If someone is not old then lucy is either not curious or not generous and vice versa.
Everyone who is either tall or kind is either kind or not kind and vice versa.
Everyone who is either patient or not strong is not patient or old and vice versa.
Everyone who is either calm or not strong is either kind or not brave and vice versa.
Everyone who is both not patient and not funny is both old and not quiet.
Everyone who is not quiet or wise is not strong or funny and vice versa.
If someone is either curious or tall then someone is either not calm or rich.
If lucy is creative then someone is not quiet.
Everyone who is creative or not brave is not funny or patient and vice versa.
Everyone who is either not calm or curious is both not tall and wise.
Everyone who is kind or not creative is either not curious or not quiet and vice versa.
Everyone who is wise or not humble is not creative or not calm and vice versa.
Everyone who is either calm or not quiet is not quiet or kind and vice versa.
Lucy is both tall and not patient.
Fred is not happy.
Someone is both not rich and not creative.
Alice is both brave and curious.
Mary is quiet or tall.
Someone is not kind.
Lucy is either happy or patient. | Fred is strong. | entailment | ((?[X]:((curious(X)|strong(X))))=>(brave(fred)))&
((?[X]:((~humble(X)|happy(X))))<=>(?[X]:((~brave(X)|creative(X)))))&
(![X]:((generous(X)|~tall(X))=>(kind(X)<~>~strong(X))))&
((?[X]:(~old(X)))<=>((~curious(lucy)<~>~generous(lucy))))&
(![X]:((tall(X)<~>kind(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~patient(X)|old(X))))&
(![X]:((calm(X)<~>~strong(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~patient(X)&~funny(X))=>(old(X)&~quiet(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~strong(X)|funny(X))))&
((?[X]:((curious(X)<~>tall(X))))=>(?[X]:((~calm(X)<~>rich(X)))))&
((creative(lucy))=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)|~brave(X))<=>(~funny(X)|patient(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~tall(X)&wise(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)<~>~quiet(X))))&
(![X]:((wise(X)|~humble(X))<=>(~creative(X)|~calm(X))))&
(![X]:((calm(X)<~>~quiet(X))<=>(~quiet(X)|kind(X))))&
((tall(lucy)&~patient(lucy)))&
(~happy(fred))&
(?[X]:((~rich(X)&~creative(X))))&
((brave(alice)&curious(alice)))&
((quiet(mary)|tall(mary)))&
(?[X]:(~kind(X)))&
((happy(lucy)<~>patient(lucy))) | strong(fred) | [
"p0",
"p2",
"p4",
"p6",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3725216695902392789414698
% SZS output start Proof for 3725216695902392789414698
1. ? [X0] : (strong(X0) | curious(X0)) => brave(fred) [input p0]
3. ! [X0] : ((~tall(X0) | generous(X0)) => (kind(X0) <~> ~strong(X0))) [input p2]
5. ! [X0] : ((tall(X0) <~> kind(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p4]
7. ! [X0] : ((calm(X0) <~> ~strong(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p6]
16. ! [X0] : ((calm(X0) <~> ~quiet(X0)) <=> (kind(X0) | ~quiet(X0))) [input p15]
20. curious(alice) & brave(alice) [input p19]
24. ~strong(fred) [input hypothesis]
27. brave(fred) | ! [X0] : (~strong(X0) & ~curious(X0)) [ennf transformation 1]
28. ! [X0] : ((kind(X0) <~> ~strong(X0)) | (tall(X0) & ~generous(X0))) [ennf transformation 3]
39. ! [X0] : (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (tall(X0) & ~generous(X0))) [nnf transformation 28]
44. ! [X0] : ((((~kind(X0) | ~tall(X0)) & (kind(X0) | tall(X0))) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((tall(X0) | ~kind(X0)) & (kind(X0) | ~tall(X0))))) [nnf transformation 5]
47. ! [X0] : ((((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))))) [nnf transformation 7]
63. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [nnf transformation 16]
64. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [flattening 63]
70. brave(fred) | ~curious(X0) [cnf transformation 27]
79. ~kind(X0) | strong(X0) | tall(X0) [cnf transformation 39]
89. kind(X0) | tall(X0) | kind(X0) | kind(X0) [cnf transformation 44]
90. ~kind(X0) | ~tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 44]
99. ~brave(X0) | kind(X0) | calm(X0) | strong(X0) [cnf transformation 47]
135. kind(X0) | ~quiet(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 64]
139. quiet(X0) | ~calm(X0) | quiet(X0) [cnf transformation 64]
147. curious(alice) [cnf transformation 20]
152. ~strong(fred) [cnf transformation 24]
153. kind(X0) | ~quiet(X0) | ~calm(X0) [duplicate literal removal 135]
154. ~calm(X0) | quiet(X0) [duplicate literal removal 139]
162. kind(X0) | tall(X0) [duplicate literal removal 89]
163. ~kind(X0) | ~tall(X0) [duplicate literal removal 90]
169. 2 <=> brave(fred) [avatar definition]
171. brave(fred) <- (2) [avatar component clause 169]
174. 3 <=> ! [X0] : ~curious(X0) [avatar definition]
175. ~curious(X0) <- (3) [avatar component clause 174]
176. 3 | 2 [avatar split clause 70,169,174]
256. ~calm(X0) | kind(X0) [subsumption resolution 153,154]
280. strong(X0) | tall(X0) | tall(X0) [resolution 79,162]
281. tall(X0) | strong(X0) [duplicate literal removal 280]
316. $false <- (3) [resolution 175,147]
317. ~3 [avatar contradiction clause 316]
380. kind(fred) | calm(fred) | strong(fred) <- (2) [resolution 99,171]
383. kind(fred) | calm(fred) <- (2) [subsumption resolution 380,152]
384. kind(fred) <- (2) [subsumption resolution 383,256]
394. ~tall(fred) <- (2) [resolution 384,163]
532. strong(fred) <- (2) [resolution 394,281]
533. $false <- (2) [subsumption resolution 532,152]
534. ~2 [avatar contradiction clause 533]
535. $false [avatar sat refutation 176,317,534]
% SZS output end Proof for 3725216695902392789414698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and generous then someone is either old or not kind and vice versa. Everyone who is old or wise is not generous and vice versa. If paul is not tall then mary is either not creative or wise. If someone is tall or calm then someone is not patient or tall. If fred is both patient and curious then someone is both generous and not curious and vice versa. If someone is either not wise or generous then lucy is strong or not old. Everyone who is not wise is both quiet and not quiet and vice versa. Everyone who is either not funny or not calm is either quiet or creative. Everyone who is brave or creative is either humble or kind. If alice is both funny and not happy then alice is either not calm or not humble. Everyone who is not wise is both not funny and not generous and vice versa. Everyone who is both not creative and patient is rich and vice versa. If someone is either not strong or patient then someone is both generous and calm. If someone is both humble and not creative then mary is either curious or strong. Everyone who is calm or tall is both quiet and not generous. If paul is either not strong or not rich then someone is both brave and happy and vice versa. Someone is both not creative and not rich. Someone is both not brave and humble. Mary is both wise and curious. Fred is both not humble and curious. Someone is both not strong and not kind. Fred is not brave. Someone is either not generous or not quiet. | Fred is generous. | contradiction | ((?[X]:((~kind(X)&generous(X))))<=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:((old(X)|wise(X))<=>~generous(X)))&
((~tall(paul))=>((~creative(mary)<~>wise(mary))))&
((?[X]:((tall(X)|calm(X))))=>(?[X]:((~patient(X)|tall(X)))))&
(((patient(fred)&curious(fred)))<=>(?[X]:((generous(X)&~curious(X)))))&
((?[X]:((~wise(X)<~>generous(X))))=>((strong(lucy)|~old(lucy))))&
(![X]:(~wise(X)<=>(quiet(X)&~quiet(X))))&
(![X]:((~funny(X)<~>~calm(X))=>(quiet(X)<~>creative(X))))&
(![X]:((brave(X)|creative(X))=>(humble(X)<~>kind(X))))&
(((funny(alice)&~happy(alice)))=>((~calm(alice)<~>~humble(alice))))&
(![X]:(~wise(X)<=>(~funny(X)&~generous(X))))&
(![X]:((~creative(X)&patient(X))<=>rich(X)))&
((?[X]:((~strong(X)<~>patient(X))))=>(?[X]:((generous(X)&calm(X)))))&
((?[X]:((humble(X)&~creative(X))))=>((curious(mary)<~>strong(mary))))&
(![X]:((calm(X)|tall(X))=>(quiet(X)&~generous(X))))&
(((~strong(paul)<~>~rich(paul)))<=>(?[X]:((brave(X)&happy(X)))))&
(?[X]:((~creative(X)&~rich(X))))&
(?[X]:((~brave(X)&humble(X))))&
((wise(mary)&curious(mary)))&
((~humble(fred)&curious(fred)))&
(?[X]:((~strong(X)&~kind(X))))&
(~brave(fred))&
(?[X]:((~generous(X)<~>~quiet(X)))) | generous(fred) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 10296125773359125234801
% SZS output start Proof for 10296125773359125234801
2. ! [X0] : ((wise(X0) | old(X0)) <=> ~generous(X0)) [input p1]
7. ! [X0] : (~wise(X0) <=> (~quiet(X0) & quiet(X0))) [input p6]
24. generous(fred) [input hypothesis]
44. ! [X0] : (((wise(X0) | old(X0)) | generous(X0)) & (~generous(X0) | (~wise(X0) & ~old(X0)))) [nnf transformation 2]
45. ! [X0] : ((wise(X0) | old(X0) | generous(X0)) & (~generous(X0) | (~wise(X0) & ~old(X0)))) [flattening 44]
56. ! [X0] : ((~wise(X0) | (quiet(X0) | ~quiet(X0))) & ((~quiet(X0) & quiet(X0)) | wise(X0))) [nnf transformation 7]
57. ! [X0] : ((~wise(X0) | quiet(X0) | ~quiet(X0)) & ((~quiet(X0) & quiet(X0)) | wise(X0))) [flattening 56]
90. ~wise(X0) | ~generous(X0) [cnf transformation 45]
102. quiet(X0) | wise(X0) [cnf transformation 57]
103. ~quiet(X0) | wise(X0) [cnf transformation 57]
150. generous(fred) [cnf transformation 24]
247. wise(X0) [subsumption resolution 102,103]
337. ~generous(X0) [resolution 90,247]
338. $false [resolution 337,150]
% SZS output end Proof for 10296125773359125234801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not happy or rich then someone is either not happy or creative.
If paul is not strong or not generous then mary is both wise and calm.
Everyone who is brave is both not brave and not creative and vice versa.
If mary is both not quiet and wise then someone is both not curious and not rich and vice versa.
Everyone who is both not old and wise is both tall and creative and vice versa.
If fred is not calm or not funny then someone is strong.
Everyone who is generous is not funny.
If fred is not funny or kind then someone is both tall and curious.
If fred is both happy and calm then alice is either not strong or not funny.
If alice is not calm or not kind then someone is both not strong and not curious.
If fred is rich then fred is both kind and calm.
Everyone who is not strong or brave is brave.
If susan is kind then susan is both not patient and not strong and vice versa.
Everyone who is not old is both brave and curious.
If susan is both not old and not humble then someone is either patient or old and vice versa.
Everyone who is not quiet is either old or kind.
Someone is either not wise or rich.
Someone is either rich or not curious.
Lucy is either strong or kind.
John is either not quiet or generous.
Someone is not kind.
Paul is either wise or calm.
John is both humble and strong. | Fred is not old. | contradiction | (((~happy(alice)<~>rich(alice)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(((~strong(paul)|~generous(paul)))=>((wise(mary)&calm(mary))))&
(![X]:(brave(X)<=>(~brave(X)&~creative(X))))&
(((~quiet(mary)&wise(mary)))<=>(?[X]:((~curious(X)&~rich(X)))))&
(![X]:((~old(X)&wise(X))<=>(tall(X)&creative(X))))&
(((~calm(fred)|~funny(fred)))=>(?[X]:(strong(X))))&
(![X]:(generous(X)=>~funny(X)))&
(((~funny(fred)|kind(fred)))=>(?[X]:((tall(X)&curious(X)))))&
(((happy(fred)&calm(fred)))=>((~strong(alice)<~>~funny(alice))))&
(((~calm(alice)|~kind(alice)))=>(?[X]:((~strong(X)&~curious(X)))))&
((rich(fred))=>((kind(fred)&calm(fred))))&
(![X]:((~strong(X)|brave(X))=>brave(X)))&
((kind(susan))<=>((~patient(susan)&~strong(susan))))&
(![X]:(~old(X)=>(brave(X)&curious(X))))&
(((~old(susan)&~humble(susan)))<=>(?[X]:((patient(X)<~>old(X)))))&
(![X]:(~quiet(X)=>(old(X)<~>kind(X))))&
(?[X]:((~wise(X)<~>rich(X))))&
(?[X]:((rich(X)<~>~curious(X))))&
((strong(lucy)<~>kind(lucy)))&
((~quiet(john)<~>generous(john)))&
(?[X]:(~kind(X)))&
((wise(paul)<~>calm(paul)))&
((humble(john)&strong(john))) | ~old(fred) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 686602384864582994917657
% SZS output start Proof for 686602384864582994917657
3. ! [X0] : (brave(X0) <=> (~creative(X0) & ~brave(X0))) [input p2]
14. ! [X0] : (~old(X0) => (curious(X0) & brave(X0))) [input p13]
24. ~old(fred) [input hypothesis]
35. ! [X0] : ((curious(X0) & brave(X0)) | old(X0)) [ennf transformation 14]
40. ! [X0] : ((brave(X0) | (creative(X0) | brave(X0))) & ((~creative(X0) & ~brave(X0)) | ~brave(X0))) [nnf transformation 3]
41. ! [X0] : ((brave(X0) | creative(X0) | brave(X0)) & ((~creative(X0) & ~brave(X0)) | ~brave(X0))) [flattening 40]
83. ~brave(X0) | ~brave(X0) [cnf transformation 41]
114. brave(X0) | old(X0) [cnf transformation 35]
137. ~old(fred) [cnf transformation 24]
138. ~brave(X0) [duplicate literal removal 83]
271. old(X0) [subsumption resolution 114,138]
326. $false [subsumption resolution 137,271]
% SZS output end Proof for 686602384864582994917657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or kind is either old or not generous.
Everyone who is either kind or not happy is both not happy and humble and vice versa.
Everyone who is both not happy and not wise is not old and vice versa.
Everyone who is old or not strong is either patient or not creative.
If mary is humble then lucy is not curious and vice versa.
Everyone who is not calm is not wise and vice versa.
If someone is both strong and creative then john is old or tall and vice versa.
Everyone who is not old or happy is either not happy or not kind and vice versa.
Everyone who is rich or not generous is not brave.
If someone is either not curious or not funny then lucy is not calm or not old.
If fred is not humble then someone is either curious or not generous and vice versa.
Everyone who is not humble is both not quiet and not happy and vice versa.
Everyone who is rich or not curious is wise or not creative.
If john is either not old or curious then mary is not happy or not patient.
Everyone who is both happy and kind is not old.
Everyone who is both not creative and humble is patient or tall and vice versa.
Someone is both calm and not funny.
John is not happy or not brave.
Fred is either strong or rich.
Someone is not quiet or funny.
Someone is funny or humble. | John is patient. | contradiction | (![X]:((calm(X)|kind(X))=>(old(X)<~>~generous(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(~happy(X)&humble(X))))&
(![X]:((~happy(X)&~wise(X))<=>~old(X)))&
(![X]:((old(X)|~strong(X))=>(patient(X)<~>~creative(X))))&
((humble(mary))<=>(~curious(lucy)))&
(![X]:(~calm(X)<=>~wise(X)))&
((?[X]:((strong(X)&creative(X))))<=>((old(john)|tall(john))))&
(![X]:((~old(X)|happy(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((rich(X)|~generous(X))=>~brave(X)))&
((?[X]:((~curious(X)<~>~funny(X))))=>((~calm(lucy)|~old(lucy))))&
((~humble(fred))<=>(?[X]:((curious(X)<~>~generous(X)))))&
(![X]:(~humble(X)<=>(~quiet(X)&~happy(X))))&
(![X]:((rich(X)|~curious(X))=>(wise(X)|~creative(X))))&
(((~old(john)<~>curious(john)))=>((~happy(mary)|~patient(mary))))&
(![X]:((happy(X)&kind(X))=>~old(X)))&
(![X]:((~creative(X)&humble(X))<=>(patient(X)|tall(X))))&
(?[X]:((calm(X)&~funny(X))))&
((~happy(john)|~brave(john)))&
((strong(fred)<~>rich(fred)))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((funny(X)|humble(X)))) | patient(john) | [
"p1",
"p2",
"p3",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7488860038043503079292017
% SZS output start Proof for 7488860038043503079292017
2. ! [X0] : ((kind(X0) <~> ~happy(X0)) <=> (humble(X0) & ~happy(X0))) [input p1]
3. ! [X0] : ((~wise(X0) & ~happy(X0)) <=> ~old(X0)) [input p2]
4. ! [X0] : ((~strong(X0) | old(X0)) => (patient(X0) <~> ~creative(X0))) [input p3]
8. ! [X0] : ((happy(X0) | ~old(X0)) <=> (~happy(X0) <~> ~kind(X0))) [input p7]
16. ! [X0] : ((humble(X0) & ~creative(X0)) <=> (tall(X0) | patient(X0))) [input p15]
22. patient(john) [input hypothesis]
26. ! [X0] : ((patient(X0) <~> ~creative(X0)) | (strong(X0) & ~old(X0))) [ennf transformation 4]
36. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (~humble(X0) | happy(X0))) & ((humble(X0) & ~happy(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [nnf transformation 2]
37. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | ~humble(X0) | happy(X0)) & ((humble(X0) & ~happy(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [flattening 36]
38. ! [X0] : (((~wise(X0) & ~happy(X0)) | old(X0)) & (~old(X0) | (wise(X0) | happy(X0)))) [nnf transformation 3]
39. ! [X0] : (((~wise(X0) & ~happy(X0)) | old(X0)) & (~old(X0) | wise(X0) | happy(X0))) [flattening 38]
40. ! [X0] : (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | (strong(X0) & ~old(X0))) [nnf transformation 26]
48. ! [X0] : (((happy(X0) | ~old(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (~happy(X0) & old(X0)))) [nnf transformation 8]
49. ! [X0] : ((happy(X0) | ~old(X0) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (~happy(X0) & old(X0)))) [flattening 48]
58. ! [X0] : (((humble(X0) & ~creative(X0)) | (~tall(X0) & ~patient(X0))) & ((tall(X0) | patient(X0)) | (~humble(X0) | creative(X0)))) [nnf transformation 16]
59. ! [X0] : (((humble(X0) & ~creative(X0)) | (~tall(X0) & ~patient(X0))) & (tall(X0) | patient(X0) | ~humble(X0) | creative(X0))) [flattening 58]
76. happy(X0) | ~kind(X0) | ~humble(X0) | happy(X0) [cnf transformation 37]
78. ~happy(X0) | old(X0) [cnf transformation 39]
82. ~patient(X0) | creative(X0) | ~old(X0) [cnf transformation 40]
95. kind(X0) | happy(X0) | old(X0) [cnf transformation 49]
114. ~creative(X0) | ~patient(X0) [cnf transformation 59]
116. ~patient(X0) | humble(X0) [cnf transformation 59]
124. patient(john) [cnf transformation 22]
128. ~humble(X0) | ~kind(X0) | happy(X0) [duplicate literal removal 76]
149. 5 <=> old(john) [avatar definition]
150. old(john) <- (5) [avatar component clause 149]
151. ~old(john) <- (~5) [avatar component clause 149]
164. old(X0) | kind(X0) [subsumption resolution 95,78]
250. humble(john) [resolution 116,124]
253. kind(john) <- (~5) [resolution 164,151]
288. creative(john) | ~old(john) [resolution 82,124]
305. 30 <=> happy(john) [avatar definition]
307. happy(john) <- (30) [avatar component clause 305]
322. ~kind(john) | happy(john) [resolution 128,250]
326. happy(john) <- (~5) [subsumption resolution 322,253]
327. 30 | 5 [avatar split clause 326,149,305]
347. old(john) <- (30) [resolution 307,78]
352. 5 | ~30 [avatar split clause 347,305,149]
355. creative(john) <- (5) [subsumption resolution 288,150]
372. ~patient(john) <- (5) [resolution 355,114]
378. $false <- (5) [subsumption resolution 372,124]
379. ~5 [avatar contradiction clause 378]
380. $false [avatar sat refutation 327,352,379]
% SZS output end Proof for 7488860038043503079292017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either kind or patient then someone is both calm and not creative and vice versa.
Everyone who is either happy or kind is either not funny or rich and vice versa.
If someone is brave or not calm then paul is both not patient and not strong and vice versa.
If someone is patient or quiet then someone is either patient or humble.
Everyone who is both not generous and patient is both creative and kind and vice versa.
Everyone who is funny is brave or tall.
Everyone who is either old or not happy is either tall or funny and vice versa.
Everyone who is curious is not generous or rich.
If lucy is both not creative and old then someone is either curious or not tall.
If paul is either happy or not curious then someone is not tall.
Everyone who is both not curious and not kind is generous or not calm.
Everyone who is either generous or not wise is both calm and strong and vice versa.
If someone is not curious then someone is humble.
Everyone who is not kind or generous is not calm and vice versa.
Everyone who is either funny or not calm is strong or curious and vice versa.
Everyone who is not calm is both not kind and not patient and vice versa.
Someone is both not strong and creative.
Someone is creative or funny.
Paul is both not patient and creative.
Someone is both not humble and not strong.
Someone is generous.
Someone is not quiet.
Someone is not kind or brave.
Someone is curious or not creative. | Susan is quiet. | neutral | (((kind(susan)<~>patient(susan)))<=>(?[X]:((calm(X)&~creative(X)))))&
(![X]:((happy(X)<~>kind(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((brave(X)|~calm(X))))<=>((~patient(paul)&~strong(paul))))&
((?[X]:((patient(X)|quiet(X))))=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((~generous(X)&patient(X))<=>(creative(X)&kind(X))))&
(![X]:(funny(X)=>(brave(X)|tall(X))))&
(![X]:((old(X)<~>~happy(X))<=>(tall(X)<~>funny(X))))&
(![X]:(curious(X)=>(~generous(X)|rich(X))))&
(((~creative(lucy)&old(lucy)))=>(?[X]:((curious(X)<~>~tall(X)))))&
(((happy(paul)<~>~curious(paul)))=>(?[X]:(~tall(X))))&
(![X]:((~curious(X)&~kind(X))=>(generous(X)|~calm(X))))&
(![X]:((generous(X)<~>~wise(X))<=>(calm(X)&strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:(humble(X))))&
(![X]:((~kind(X)|generous(X))<=>~calm(X)))&
(![X]:((funny(X)<~>~calm(X))<=>(strong(X)|curious(X))))&
(![X]:(~calm(X)<=>(~kind(X)&~patient(X))))&
(?[X]:((~strong(X)&creative(X))))&
(?[X]:((creative(X)|funny(X))))&
((~patient(paul)&creative(paul)))&
(?[X]:((~humble(X)&~strong(X))))&
(?[X]:(generous(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((curious(X)|~creative(X)))) | quiet(susan) | [] | null | 0 |
If paul is both funny and not generous then susan is either wise or creative. Everyone who is kind is both not calm and tall and vice versa. Everyone who is not brave or creative is not happy. Everyone who is both brave and rich is quiet or not old and vice versa. Everyone who is both not quiet and funny is quiet or humble. Everyone who is not quiet or calm is creative or not patient and vice versa. If mary is not generous then someone is not old and vice versa. Everyone who is old is quiet. Everyone who is not strong or generous is not happy. If fred is either old or wise then alice is both not calm and not happy. If john is either happy or not brave then someone is not curious or not rich and vice versa. If alice is either creative or not wise then someone is curious and vice versa. Everyone who is rich is not strong or not humble. Everyone who is both strong and rich is not generous or not kind. If susan is funny then someone is not wise or happy and vice versa. Everyone who is both not curious and humble is old or not strong and vice versa. Lucy is either humble or not wise. Alice is both brave and not creative. Someone is either old or not calm. | Alice is quiet. | neutral | (((funny(paul)&~generous(paul)))=>((wise(susan)<~>creative(susan))))&
(![X]:(kind(X)<=>(~calm(X)&tall(X))))&
(![X]:((~brave(X)|creative(X))=>~happy(X)))&
(![X]:((brave(X)&rich(X))<=>(quiet(X)|~old(X))))&
(![X]:((~quiet(X)&funny(X))=>(quiet(X)|humble(X))))&
(![X]:((~quiet(X)|calm(X))<=>(creative(X)|~patient(X))))&
((~generous(mary))<=>(?[X]:(~old(X))))&
(![X]:(old(X)=>quiet(X)))&
(![X]:((~strong(X)|generous(X))=>~happy(X)))&
(((old(fred)<~>wise(fred)))=>((~calm(alice)&~happy(alice))))&
(((happy(john)<~>~brave(john)))<=>(?[X]:((~curious(X)|~rich(X)))))&
(((creative(alice)<~>~wise(alice)))<=>(?[X]:(curious(X))))&
(![X]:(rich(X)=>(~strong(X)|~humble(X))))&
(![X]:((strong(X)&rich(X))=>(~generous(X)|~kind(X))))&
((funny(susan))<=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((~curious(X)&humble(X))<=>(old(X)|~strong(X))))&
((humble(lucy)<~>~wise(lucy)))&
((brave(alice)&~creative(alice)))&
(?[X]:((old(X)<~>~calm(X)))) | quiet(alice) | [] | null | 0 |
If someone is either humble or not patient then someone is old or not kind. Everyone who is both curious and not rich is not curious and vice versa. Everyone who is not wise is humble and vice versa. Everyone who is either not creative or creative is tall. If someone is not creative or quiet then someone is both generous and not strong and vice versa. If someone is both not humble and brave then someone is either not wise or rich. If someone is either kind or old then someone is not happy or generous. If susan is both humble and patient then someone is old or not quiet. If lucy is generous or curious then someone is creative or not humble. Everyone who is either not kind or strong is either curious or old. If john is not kind or not old then someone is either curious or funny. Everyone who is either not brave or not tall is both not happy and curious and vice versa. Everyone who is wise or not curious is either rich or brave. If lucy is generous or not happy then john is not patient or old and vice versa. If someone is both wise and not funny then john is rich and vice versa. If someone is both not humble and wise then paul is either not humble or patient. Lucy is both not kind and strong. Someone is both not wise and not old. Someone is not curious or quiet. Someone is brave or tall. Susan is funny or not wise. Someone is either not brave or old. Fred is either wise or not brave. Someone is both brave and happy. | Fred is not happy. | entailment | ((?[X]:((humble(X)<~>~patient(X))))=>(?[X]:((old(X)|~kind(X)))))&
(![X]:((curious(X)&~rich(X))<=>~curious(X)))&
(![X]:(~wise(X)<=>humble(X)))&
(![X]:((~creative(X)<~>creative(X))=>tall(X)))&
((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:((generous(X)&~strong(X)))))&
((?[X]:((~humble(X)&brave(X))))=>(?[X]:((~wise(X)<~>rich(X)))))&
((?[X]:((kind(X)<~>old(X))))=>(?[X]:((~happy(X)|generous(X)))))&
(((humble(susan)&patient(susan)))=>(?[X]:((old(X)|~quiet(X)))))&
(((generous(lucy)|curious(lucy)))=>(?[X]:((creative(X)|~humble(X)))))&
(![X]:((~kind(X)<~>strong(X))=>(curious(X)<~>old(X))))&
(((~kind(john)|~old(john)))=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((~brave(X)<~>~tall(X))<=>(~happy(X)&curious(X))))&
(![X]:((wise(X)|~curious(X))=>(rich(X)<~>brave(X))))&
(((generous(lucy)|~happy(lucy)))<=>((~patient(john)|old(john))))&
((?[X]:((wise(X)&~funny(X))))<=>(rich(john)))&
((?[X]:((~humble(X)&wise(X))))=>((~humble(paul)<~>patient(paul))))&
((~kind(lucy)&strong(lucy)))&
(?[X]:((~wise(X)&~old(X))))&
(?[X]:((~curious(X)|quiet(X))))&
(?[X]:((brave(X)|tall(X))))&
((funny(susan)|~wise(susan)))&
(?[X]:((~brave(X)<~>old(X))))&
((wise(fred)<~>~brave(fred)))&
(?[X]:((brave(X)&happy(X)))) | ~happy(fred) | [
"p1",
"p3",
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 318074782671028256181825
% SZS output start Proof for 318074782671028256181825
2. ! [X0] : ((~rich(X0) & curious(X0)) <=> ~curious(X0)) [input p1]
4. ! [X0] : ((~creative(X0) <~> creative(X0)) => tall(X0)) [input p3]
12. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> (curious(X0) & ~happy(X0))) [input p11]
13. ! [X0] : ((~curious(X0) | wise(X0)) => (rich(X0) <~> brave(X0))) [input p12]
23. wise(fred) <~> ~brave(fred) [input p22]
25. happy(fred) [input hypothesis]
31. ! [X0] : (tall(X0) | (~creative(X0) <=> creative(X0))) [ennf transformation 4]
39. ! [X0] : ((rich(X0) <~> brave(X0)) | (curious(X0) & ~wise(X0))) [ennf transformation 13]
45. ! [X0] : (((~rich(X0) & curious(X0)) | curious(X0)) & (~curious(X0) | (rich(X0) | ~curious(X0)))) [nnf transformation 2]
46. ! [X0] : (((~rich(X0) & curious(X0)) | curious(X0)) & (~curious(X0) | rich(X0) | ~curious(X0))) [flattening 45]
48. ! [X0] : (tall(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) [nnf transformation 31]
70. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | (~curious(X0) | happy(X0))) & ((curious(X0) & ~happy(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 12]
71. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | ~curious(X0) | happy(X0)) & ((curious(X0) & ~happy(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [flattening 70]
72. ! [X0] : (((~brave(X0) | ~rich(X0)) & (brave(X0) | rich(X0))) | (curious(X0) & ~wise(X0))) [nnf transformation 39]
89. (brave(fred) | ~wise(fred)) & (~brave(fred) | wise(fred)) [nnf transformation 23]
94. ~curious(X0) | rich(X0) | ~curious(X0) [cnf transformation 46]
95. curious(X0) | curious(X0) [cnf transformation 46]
99. tall(X0) | creative(X0) | creative(X0) [cnf transformation 48]
100. tall(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
121. ~happy(X0) | ~tall(X0) | brave(X0) [cnf transformation 71]
129. ~brave(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 72]
149. ~brave(fred) | wise(fred) [cnf transformation 89]
150. brave(fred) | ~wise(fred) [cnf transformation 89]
153. happy(fred) [cnf transformation 25]
154. tall(X0) | creative(X0) [duplicate literal removal 99]
155. ~creative(X0) | tall(X0) [duplicate literal removal 100]
156. ~curious(X0) | rich(X0) [duplicate literal removal 94]
157. curious(X0) [duplicate literal removal 95]
174. rich(X0) [subsumption resolution 156,157]
175. tall(X0) [subsumption resolution 154,155]
283. ~happy(X0) | brave(X0) [subsumption resolution 121,175]
284. ~brave(X0) | ~wise(X0) [subsumption resolution 129,174]
337. ~wise(fred) [subsumption resolution 150,284]
338. ~brave(fred) [subsumption resolution 149,337]
357. brave(fred) [resolution 283,153]
358. $false [subsumption resolution 357,338]
% SZS output end Proof for 318074782671028256181825
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not brave is either kind or old. Everyone who is either not rich or not humble is not strong or not calm and vice versa. If fred is strong then lucy is both humble and not rich and vice versa. Everyone who is both old and not old is not humble. If someone is kind then someone is both not funny and humble and vice versa. If someone is not quiet or creative then someone is not quiet or not creative and vice versa. If john is not strong then someone is either not strong or old and vice versa. If someone is wise then someone is patient and vice versa. If fred is both not humble and not funny then someone is not wise and vice versa. Everyone who is both funny and not curious is happy or not strong and vice versa. If someone is either generous or not funny then someone is not old. Everyone who is either generous or not wise is both quiet and not tall. If someone is either not rich or patient then paul is both not wise and creative. Everyone who is generous or not brave is both not curious and calm and vice versa. If someone is both not kind and not humble then someone is not brave and vice versa. If someone is not patient then mary is both not patient and not generous. Someone is not old. Fred is both creative and happy. Someone is either not old or not curious. Mary is old. Someone is either not generous or not calm. John is not funny or not wise. Someone is both not kind and wise. | Mary is curious. | contradiction | (![X]:((~calm(X)<~>~brave(X))=>(kind(X)<~>old(X))))&
(![X]:((~rich(X)<~>~humble(X))<=>(~strong(X)|~calm(X))))&
((strong(fred))<=>((humble(lucy)&~rich(lucy))))&
(![X]:((old(X)&~old(X))=>~humble(X)))&
((?[X]:(kind(X)))<=>(?[X]:((~funny(X)&humble(X)))))&
((?[X]:((~quiet(X)|creative(X))))<=>(?[X]:((~quiet(X)|~creative(X)))))&
((~strong(john))<=>(?[X]:((~strong(X)<~>old(X)))))&
((?[X]:(wise(X)))<=>(?[X]:(patient(X))))&
(((~humble(fred)&~funny(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((funny(X)&~curious(X))<=>(happy(X)|~strong(X))))&
((?[X]:((generous(X)<~>~funny(X))))=>(?[X]:(~old(X))))&
(![X]:((generous(X)<~>~wise(X))=>(quiet(X)&~tall(X))))&
((?[X]:((~rich(X)<~>patient(X))))=>((~wise(paul)&creative(paul))))&
(![X]:((generous(X)|~brave(X))<=>(~curious(X)&calm(X))))&
((?[X]:((~kind(X)&~humble(X))))<=>(?[X]:(~brave(X))))&
((?[X]:(~patient(X)))=>((~patient(mary)&~generous(mary))))&
(?[X]:(~old(X)))&
((creative(fred)&happy(fred)))&
(?[X]:((~old(X)<~>~curious(X))))&
(old(mary))&
(?[X]:((~generous(X)<~>~calm(X))))&
((~funny(john)|~wise(john)))&
(?[X]:((~kind(X)&wise(X)))) | curious(mary) | [
"p6",
"p8",
"p9",
"p17",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 390189034640590351698069
% SZS output start Proof for 390189034640590351698069
7. ~strong(john) <=> ? [X0] : (~strong(X0) <~> old(X0)) [input p6]
9. (~funny(fred) & ~humble(fred)) <=> ? [X0] : ~wise(X0) [input p8]
10. ! [X0] : ((~curious(X0) & funny(X0)) <=> (~strong(X0) | happy(X0))) [input p9]
18. happy(fred) & creative(fred) [input p17]
20. old(mary) [input p19]
22. ~wise(john) | ~funny(john) [input p21]
24. curious(mary) [input hypothesis]
53. (~strong(john) | ! [X0] : ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (? [X0] : ((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | strong(john)) [nnf transformation 7]
54. (~strong(john) | ! [X0] : ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (? [X1] : ((~old(X1) | strong(X1)) & (old(X1) | ~strong(X1))) | strong(john)) [rectify 53]
55. ? [X1] : ((~old(X1) | strong(X1)) & (old(X1) | ~strong(X1))) => ((~old(sK4) | strong(sK4)) & (old(sK4) | ~strong(sK4))) [choice axiom]
56. (~strong(john) | ! [X0] : ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (((~old(sK4) | strong(sK4)) & (old(sK4) | ~strong(sK4))) | strong(john)) [skolemisation 54,55]
62. ((~funny(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | (funny(fred) | humble(fred))) [nnf transformation 9]
63. ((~funny(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | funny(fred) | humble(fred)) [flattening 62]
64. ((~funny(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | funny(fred) | humble(fred)) [rectify 63]
65. ? [X1] : ~wise(X1) => ~wise(sK7) [choice axiom]
66. ((~funny(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (~wise(sK7) | funny(fred) | humble(fred)) [skolemisation 64,65]
67. ! [X0] : (((~curious(X0) & funny(X0)) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | (curious(X0) | ~funny(X0)))) [nnf transformation 10]
68. ! [X0] : (((~curious(X0) & funny(X0)) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | curious(X0) | ~funny(X0))) [flattening 67]
116. ~strong(john) | ~strong(X0) | ~old(X0) [cnf transformation 56]
121. ~funny(fred) | wise(X0) [cnf transformation 66]
123. ~happy(X0) | funny(X0) [cnf transformation 68]
124. funny(X0) | strong(X0) [cnf transformation 68]
126. ~curious(X0) | strong(X0) [cnf transformation 68]
147. happy(fred) [cnf transformation 18]
150. old(mary) [cnf transformation 20]
153. ~wise(john) | ~funny(john) [cnf transformation 22]
156. curious(mary) [cnf transformation 24]
223. 16 <=> ! [X0] : (~strong(X0) | ~old(X0)) [avatar definition]
224. ~strong(X0) | ~old(X0) <- (16) [avatar component clause 223]
226. 17 <=> strong(john) [avatar definition]
229. 16 | ~17 [avatar split clause 116,226,223]
261. 25 <=> ! [X0] : wise(X0) [avatar definition]
262. wise(X0) <- (25) [avatar component clause 261]
264. 26 <=> funny(fred) [avatar definition]
267. 25 | ~26 [avatar split clause 121,264,261]
355. 46 <=> funny(john) [avatar definition]
357. ~funny(john) <- (~46) [avatar component clause 355]
359. 47 <=> wise(john) [avatar definition]
361. ~wise(john) <- (~47) [avatar component clause 359]
362. ~46 | ~47 [avatar split clause 153,359,355]
367. funny(fred) [resolution 123,147]
370. 26 [avatar split clause 367,264]
375. strong(john) <- (~46) [resolution 124,357]
378. 17 | 46 [avatar split clause 375,355,226]
380. strong(mary) [resolution 126,156]
384. ~old(mary) <- (16) [resolution 224,380]
385. $false <- (16) [subsumption resolution 384,150]
386. ~16 [avatar contradiction clause 385]
387. $false <- (25, ~47) [subsumption resolution 361,262]
388. ~25 | 47 [avatar contradiction clause 387]
389. $false [avatar sat refutation 229,267,362,370,378,386,388]
% SZS output end Proof for 390189034640590351698069
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not strong is not creative.
Everyone who is generous or wise is both creative and calm.
If someone is kind or not strong then john is either kind or not old and vice versa.
If someone is both funny and not funny then someone is patient and vice versa.
Everyone who is generous or quiet is tall or not happy.
Everyone who is not calm is either rich or not quiet and vice versa.
Everyone who is creative is either rich or creative and vice versa.
If someone is both not generous and not kind then someone is either not funny or not generous.
If mary is old then someone is strong or humble.
Everyone who is either not old or quiet is not creative.
Everyone who is either not strong or old is not wise or calm.
Everyone who is old or not strong is not happy or not funny and vice versa.
If someone is both strong and not brave then lucy is both old and not curious.
If someone is patient then someone is generous.
Everyone who is not strong is not tall and vice versa.
If alice is both not calm and funny then someone is brave or humble.
Lucy is funny.
Someone is both not generous and curious.
Someone is both not calm and not brave.
Alice is strong or not creative.
Someone is not happy or not wise.
John is generous.
Someone is quiet.
Mary is both strong and not funny. | Mary is not calm. | neutral | (![X]:((~brave(X)&~strong(X))=>~creative(X)))&
(![X]:((generous(X)|wise(X))=>(creative(X)&calm(X))))&
((?[X]:((kind(X)|~strong(X))))<=>((kind(john)<~>~old(john))))&
((?[X]:((funny(X)&~funny(X))))<=>(?[X]:(patient(X))))&
(![X]:((generous(X)|quiet(X))=>(tall(X)|~happy(X))))&
(![X]:(~calm(X)<=>(rich(X)<~>~quiet(X))))&
(![X]:(creative(X)<=>(rich(X)<~>creative(X))))&
((?[X]:((~generous(X)&~kind(X))))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((old(mary))=>(?[X]:((strong(X)|humble(X)))))&
(![X]:((~old(X)<~>quiet(X))=>~creative(X)))&
(![X]:((~strong(X)<~>old(X))=>(~wise(X)|calm(X))))&
(![X]:((old(X)|~strong(X))<=>(~happy(X)|~funny(X))))&
((?[X]:((strong(X)&~brave(X))))=>((old(lucy)&~curious(lucy))))&
((?[X]:(patient(X)))=>(?[X]:(generous(X))))&
(![X]:(~strong(X)<=>~tall(X)))&
(((~calm(alice)&funny(alice)))=>(?[X]:((brave(X)|humble(X)))))&
(funny(lucy))&
(?[X]:((~generous(X)&curious(X))))&
(?[X]:((~calm(X)&~brave(X))))&
((strong(alice)|~creative(alice)))&
(?[X]:((~happy(X)|~wise(X))))&
(generous(john))&
(?[X]:(quiet(X)))&
((strong(mary)&~funny(mary))) | ~calm(mary) | [] | null | 0 |
If alice is either not kind or not humble then someone is patient. Everyone who is rich or old is old or brave. Everyone who is either not strong or humble is old and vice versa. If mary is either kind or not quiet then susan is either rich or curious. Everyone who is either not calm or rich is quiet. If someone is either not brave or tall then someone is not wise. Everyone who is both not funny and humble is brave. Everyone who is both not quiet and quiet is funny or humble and vice versa. Everyone who is either not calm or not curious is both not wise and curious and vice versa. If someone is generous then someone is brave and vice versa. If someone is happy then someone is either not tall or strong. Everyone who is not creative is both humble and not creative and vice versa. Everyone who is not quiet is both curious and not quiet. If someone is both not creative and strong then fred is calm and vice versa. Everyone who is not brave or not creative is either generous or not strong. Everyone who is both not happy and kind is both quiet and not calm and vice versa. Paul is wise or quiet. Mary is brave or not kind. Alice is both not brave and rich. Someone is not happy or happy. Someone is not strong or kind. Paul is not happy. Susan is not strong or not happy. Fred is tall. | Fred is not funny. | entailment | (((~kind(alice)<~>~humble(alice)))=>(?[X]:(patient(X))))&
(![X]:((rich(X)|old(X))=>(old(X)|brave(X))))&
(![X]:((~strong(X)<~>humble(X))<=>old(X)))&
(((kind(mary)<~>~quiet(mary)))=>((rich(susan)<~>curious(susan))))&
(![X]:((~calm(X)<~>rich(X))=>quiet(X)))&
((?[X]:((~brave(X)<~>tall(X))))=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)&humble(X))=>brave(X)))&
(![X]:((~quiet(X)&quiet(X))<=>(funny(X)|humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(~wise(X)&curious(X))))&
((?[X]:(generous(X)))<=>(?[X]:(brave(X))))&
((?[X]:(happy(X)))=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:(~creative(X)<=>(humble(X)&~creative(X))))&
(![X]:(~quiet(X)=>(curious(X)&~quiet(X))))&
((?[X]:((~creative(X)&strong(X))))<=>(calm(fred)))&
(![X]:((~brave(X)|~creative(X))=>(generous(X)<~>~strong(X))))&
(![X]:((~happy(X)&kind(X))<=>(quiet(X)&~calm(X))))&
((wise(paul)|quiet(paul)))&
((brave(mary)|~kind(mary)))&
((~brave(alice)&rich(alice)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((~strong(X)|kind(X))))&
(~happy(paul))&
((~strong(susan)|~happy(susan)))&
(tall(fred)) | ~funny(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6441845317498090202475299
% SZS output start Proof for 6441845317498090202475299
8. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (humble(X0) | funny(X0))) [input p7]
25. funny(fred) [input hypothesis]
47. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~humble(X0) & ~funny(X0))) & ((humble(X0) | funny(X0)) | (~quiet(X0) | quiet(X0)))) [nnf transformation 8]
48. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~humble(X0) & ~funny(X0))) & (humble(X0) | funny(X0) | ~quiet(X0) | quiet(X0))) [flattening 47]
89. ~quiet(X0) | ~funny(X0) [cnf transformation 48]
91. quiet(X0) | ~funny(X0) [cnf transformation 48]
128. funny(fred) [cnf transformation 25]
164. ~funny(X0) [subsumption resolution 89,91]
238. $false [subsumption resolution 128,164]
% SZS output end Proof for 6441845317498090202475299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is not old.
Everyone who is both not patient and funny is not patient or not quiet and vice versa.
Everyone who is either not funny or not humble is not old and vice versa.
Everyone who is either generous or not strong is curious or wise.
Everyone who is not tall or not kind is either funny or strong.
If someone is old then someone is not generous or calm.
Everyone who is not humble or not funny is humble or creative and vice versa.
If someone is either not creative or tall then susan is creative or curious.
Everyone who is rich or not old is both kind and strong.
If mary is wise then someone is rich.
Everyone who is both tall and humble is old or brave.
Everyone who is either patient or funny is both generous and not curious.
If susan is calm or not creative then susan is not humble or not wise.
Everyone who is either patient or kind is wise or not generous.
If fred is not curious then paul is curious and vice versa.
If lucy is old then mary is either tall or not quiet and vice versa.
Someone is either curious or not kind.
Mary is curious.
Someone is not rich or not patient.
Alice is tall.
Alice is old.
Mary is wise or strong.
Alice is either humble or not calm.
Someone is both brave and not creative. | Alice is not calm. | entailment | (![X]:(wise(X)=>~old(X)))&
(![X]:((~patient(X)&funny(X))<=>(~patient(X)|~quiet(X))))&
(![X]:((~funny(X)<~>~humble(X))<=>~old(X)))&
(![X]:((generous(X)<~>~strong(X))=>(curious(X)|wise(X))))&
(![X]:((~tall(X)|~kind(X))=>(funny(X)<~>strong(X))))&
((?[X]:(old(X)))=>(?[X]:((~generous(X)|calm(X)))))&
(![X]:((~humble(X)|~funny(X))<=>(humble(X)|creative(X))))&
((?[X]:((~creative(X)<~>tall(X))))=>((creative(susan)|curious(susan))))&
(![X]:((rich(X)|~old(X))=>(kind(X)&strong(X))))&
((wise(mary))=>(?[X]:(rich(X))))&
(![X]:((tall(X)&humble(X))=>(old(X)|brave(X))))&
(![X]:((patient(X)<~>funny(X))=>(generous(X)&~curious(X))))&
(((calm(susan)|~creative(susan)))=>((~humble(susan)|~wise(susan))))&
(![X]:((patient(X)<~>kind(X))=>(wise(X)|~generous(X))))&
((~curious(fred))<=>(curious(paul)))&
((old(lucy))<=>((tall(mary)<~>~quiet(mary))))&
(?[X]:((curious(X)<~>~kind(X))))&
(curious(mary))&
(?[X]:((~rich(X)|~patient(X))))&
(tall(alice))&
(old(alice))&
((wise(mary)|strong(mary)))&
((humble(alice)<~>~calm(alice)))&
(?[X]:((brave(X)&~creative(X)))) | ~calm(alice) | [
"p2",
"p6",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3491162253275668039984477
% SZS output start Proof for 3491162253275668039984477
3. ! [X0] : ((~funny(X0) <~> ~humble(X0)) <=> ~old(X0)) [input p2]
7. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (creative(X0) | humble(X0))) [input p6]
21. old(alice) [input p20]
23. humble(alice) <~> ~calm(alice) [input p22]
25. calm(alice) [input hypothesis]
45. ! [X0] : ((((humble(X0) | funny(X0)) & (~humble(X0) | ~funny(X0))) | old(X0)) & (~old(X0) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0))))) [nnf transformation 3]
51. ! [X0] : (((~funny(X0) | ~humble(X0)) | (~creative(X0) & ~humble(X0))) & ((creative(X0) | humble(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 7]
52. ! [X0] : ((~funny(X0) | ~humble(X0) | (~creative(X0) & ~humble(X0))) & (creative(X0) | humble(X0) | (funny(X0) & humble(X0)))) [flattening 51]
65. (calm(alice) | ~humble(alice)) & (~calm(alice) | humble(alice)) [nnf transformation 23]
74. ~humble(X0) | ~old(X0) | funny(X0) [cnf transformation 45]
87. ~funny(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 52]
115. old(alice) [cnf transformation 21]
117. ~calm(alice) | humble(alice) [cnf transformation 65]
120. calm(alice) [cnf transformation 25]
122. ~humble(X0) | ~funny(X0) [duplicate literal removal 87]
231. 23 <=> humble(alice) [avatar definition]
232. humble(alice) <- (23) [avatar component clause 231]
235. 24 <=> calm(alice) [avatar definition]
239. 23 | ~24 [avatar split clause 117,235,231]
240. 24 [avatar split clause 120,235]
247. ~funny(alice) <- (23) [resolution 122,232]
258. ~old(alice) | funny(alice) <- (23) [resolution 74,232]
260. funny(alice) <- (23) [subsumption resolution 258,115]
261. $false <- (23) [subsumption resolution 260,247]
262. ~23 [avatar contradiction clause 261]
264. $false [avatar sat refutation 239,240,262]
% SZS output end Proof for 3491162253275668039984477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or not humble then someone is not rich or not tall.
Everyone who is both humble and tall is not humble or rich.
Everyone who is not creative is not rich and vice versa.
Everyone who is both old and wise is not patient and vice versa.
If someone is either not wise or quiet then someone is either not brave or old and vice versa.
Everyone who is not patient is either rich or not old and vice versa.
Everyone who is not rich or not old is both funny and not patient.
If fred is both patient and not kind then someone is either generous or not creative and vice versa.
Everyone who is either not patient or patient is both not brave and not kind and vice versa.
If mary is both wise and not creative then mary is patient or not calm and vice versa.
If someone is both creative and not wise then fred is patient.
If someone is both quiet and not happy then alice is not old.
If mary is humble then mary is both generous and strong and vice versa.
If someone is curious then john is both not creative and brave and vice versa.
Everyone who is either not funny or not generous is both not creative and brave.
If someone is both rich and not calm then someone is calm or not strong.
Someone is both not calm and creative.
Someone is either not strong or humble.
Someone is not happy or not humble.
Someone is either not old or not calm. | Alice is patient. | contradiction | ((?[X]:((~strong(X)|~humble(X))))=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((humble(X)&tall(X))=>(~humble(X)|rich(X))))&
(![X]:(~creative(X)<=>~rich(X)))&
(![X]:((old(X)&wise(X))<=>~patient(X)))&
((?[X]:((~wise(X)<~>quiet(X))))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:(~patient(X)<=>(rich(X)<~>~old(X))))&
(![X]:((~rich(X)|~old(X))=>(funny(X)&~patient(X))))&
(((patient(fred)&~kind(fred)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
(![X]:((~patient(X)<~>patient(X))<=>(~brave(X)&~kind(X))))&
(((wise(mary)&~creative(mary)))<=>((patient(mary)|~calm(mary))))&
((?[X]:((creative(X)&~wise(X))))=>(patient(fred)))&
((?[X]:((quiet(X)&~happy(X))))=>(~old(alice)))&
((humble(mary))<=>((generous(mary)&strong(mary))))&
((?[X]:(curious(X)))<=>((~creative(john)&brave(john))))&
(![X]:((~funny(X)<~>~generous(X))=>(~creative(X)&brave(X))))&
((?[X]:((rich(X)&~calm(X))))=>(?[X]:((calm(X)|~strong(X)))))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((~old(X)<~>~calm(X)))) | patient(alice) | [
"p3",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 187627370012011084392752
% SZS output start Proof for 187627370012011084392752
4. ! [X0] : ((wise(X0) & old(X0)) <=> ~patient(X0)) [input p3]
6. ! [X0] : (~patient(X0) <=> (rich(X0) <~> ~old(X0))) [input p5]
7. ! [X0] : ((~old(X0) | ~rich(X0)) => (~patient(X0) & funny(X0))) [input p6]
21. patient(alice) [input hypothesis]
27. ! [X0] : ((~patient(X0) & funny(X0)) | (old(X0) & rich(X0))) [ennf transformation 7]
33. ! [X0] : (((wise(X0) & old(X0)) | patient(X0)) & (~patient(X0) | (~wise(X0) | ~old(X0)))) [nnf transformation 4]
34. ! [X0] : (((wise(X0) & old(X0)) | patient(X0)) & (~patient(X0) | ~wise(X0) | ~old(X0))) [flattening 33]
40. ! [X0] : ((~patient(X0) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | patient(X0))) [nnf transformation 6]
74. patient(X0) | old(X0) [cnf transformation 34]
84. ~old(X0) | rich(X0) | patient(X0) [cnf transformation 40]
86. ~patient(X0) | ~old(X0) | ~rich(X0) [cnf transformation 40]
90. ~patient(X0) | rich(X0) [cnf transformation 27]
91. ~patient(X0) | old(X0) [cnf transformation 27]
129. patient(alice) [cnf transformation 21]
171. patient(X0) | rich(X0) [subsumption resolution 84,74]
172. old(X0) [subsumption resolution 91,74]
173. rich(X0) [subsumption resolution 90,171]
320. ~old(alice) | ~rich(alice) [resolution 86,129]
325. ~rich(alice) [subsumption resolution 320,172]
326. $false [subsumption resolution 325,173]
% SZS output end Proof for 187627370012011084392752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not tall is both generous and strong and vice versa. Everyone who is either not calm or not generous is either not kind or brave. Everyone who is either happy or not rich is both not brave and not strong. Everyone who is both not rich and not quiet is curious and vice versa. Everyone who is either happy or humble is brave. If fred is both not rich and tall then someone is quiet or not patient and vice versa. If someone is both not curious and not strong then someone is happy or not quiet. Everyone who is not funny or generous is not kind and vice versa. Everyone who is both not brave and wise is happy and vice versa. If lucy is curious then john is patient or not old. Everyone who is creative is either strong or not happy. If lucy is creative or not funny then fred is either creative or not generous and vice versa. Everyone who is not creative is rich and vice versa. Everyone who is not rich is both not strong and not patient and vice versa. If paul is quiet then someone is both not generous and quiet. Everyone who is old is either not kind or generous. Someone is not brave or not calm. Someone is either humble or old. Someone is kind. Someone is brave. Paul is either kind or humble. Someone is either happy or humble. | John is curious. | contradiction | (![X]:((~humble(X)|~tall(X))<=>(generous(X)&strong(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~kind(X)<~>brave(X))))&
(![X]:((happy(X)<~>~rich(X))=>(~brave(X)&~strong(X))))&
(![X]:((~rich(X)&~quiet(X))<=>curious(X)))&
(![X]:((happy(X)<~>humble(X))=>brave(X)))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)|~patient(X)))))&
((?[X]:((~curious(X)&~strong(X))))=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:((~funny(X)|generous(X))<=>~kind(X)))&
(![X]:((~brave(X)&wise(X))<=>happy(X)))&
((curious(lucy))=>((patient(john)|~old(john))))&
(![X]:(creative(X)=>(strong(X)<~>~happy(X))))&
(((creative(lucy)|~funny(lucy)))<=>((creative(fred)<~>~generous(fred))))&
(![X]:(~creative(X)<=>rich(X)))&
(![X]:(~rich(X)<=>(~strong(X)&~patient(X))))&
((quiet(paul))=>(?[X]:((~generous(X)&quiet(X)))))&
(![X]:(old(X)=>(~kind(X)<~>generous(X))))&
(?[X]:((~brave(X)|~calm(X))))&
(?[X]:((humble(X)<~>old(X))))&
(?[X]:(kind(X)))&
(?[X]:(brave(X)))&
((kind(paul)<~>humble(paul)))&
(?[X]:((happy(X)<~>humble(X)))) | curious(john) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5219373281473839845986066
% SZS output start Proof for 5219373281473839845986066
1. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (strong(X0) & generous(X0))) [input p0]
3. ! [X0] : ((happy(X0) <~> ~rich(X0)) => (~strong(X0) & ~brave(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) & ~rich(X0)) <=> curious(X0)) [input p3]
5. ! [X0] : ((happy(X0) <~> humble(X0)) => brave(X0)) [input p4]
6. (tall(fred) & ~rich(fred)) <=> ? [X0] : (~patient(X0) | quiet(X0)) [input p5]
11. ! [X0] : (creative(X0) => (strong(X0) <~> ~happy(X0))) [input p10]
13. ! [X0] : (~creative(X0) <=> rich(X0)) [input p12]
14. ! [X0] : (~rich(X0) <=> (~patient(X0) & ~strong(X0))) [input p13]
23. curious(john) [input hypothesis]
26. ! [X0] : ((~strong(X0) & ~brave(X0)) | (happy(X0) <=> ~rich(X0))) [ennf transformation 3]
27. ! [X0] : (brave(X0) | (happy(X0) <=> humble(X0))) [ennf transformation 5]
31. ! [X0] : ((strong(X0) <~> ~happy(X0)) | ~creative(X0)) [ennf transformation 11]
34. ! [X0] : (((~tall(X0) | ~humble(X0)) | (~strong(X0) | ~generous(X0))) & ((strong(X0) & generous(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 1]
35. ! [X0] : ((~tall(X0) | ~humble(X0) | ~strong(X0) | ~generous(X0)) & ((strong(X0) & generous(X0)) | (tall(X0) & humble(X0)))) [flattening 34]
37. ! [X0] : ((~strong(X0) & ~brave(X0)) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) [nnf transformation 26]
38. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | (quiet(X0) | rich(X0)))) [nnf transformation 4]
39. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | quiet(X0) | rich(X0))) [flattening 38]
40. ! [X0] : (brave(X0) | ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0)))) [nnf transformation 27]
41. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X0] : (~patient(X0) | quiet(X0)) | (~tall(fred) | rich(fred))) [nnf transformation 6]
42. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X0] : (~patient(X0) | quiet(X0)) | ~tall(fred) | rich(fred)) [flattening 41]
43. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X1] : (~patient(X1) | quiet(X1)) | ~tall(fred) | rich(fred)) [rectify 42]
44. ? [X1] : (~patient(X1) | quiet(X1)) => (~patient(sK0) | quiet(sK0)) [choice axiom]
45. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & ((~patient(sK0) | quiet(sK0)) | ~tall(fred) | rich(fred)) [skolemisation 43,44]
53. ! [X0] : (((happy(X0) | ~strong(X0)) & (~happy(X0) | strong(X0))) | ~creative(X0)) [nnf transformation 31]
56. ! [X0] : ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0))) [nnf transformation 13]
57. ! [X0] : ((~rich(X0) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | rich(X0))) [nnf transformation 14]
58. ! [X0] : ((~rich(X0) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | rich(X0))) [flattening 57]
77. strong(X0) | humble(X0) [cnf transformation 35]
85. ~brave(X0) | happy(X0) | rich(X0) [cnf transformation 37]
89. ~curious(X0) | ~rich(X0) [cnf transformation 39]
92. ~humble(X0) | happy(X0) | brave(X0) [cnf transformation 40]
95. ~rich(fred) | patient(X0) [cnf transformation 45]
106. ~creative(X0) | strong(X0) | ~happy(X0) [cnf transformation 53]
114. creative(X0) | rich(X0) [cnf transformation 56]
116. ~strong(X0) | rich(X0) [cnf transformation 58]
117. ~patient(X0) | rich(X0) [cnf transformation 58]
132. curious(john) [cnf transformation 23]
134. 1 <=> ! [X0] : patient(X0) [avatar definition]
135. patient(X0) <- (1) [avatar component clause 134]
146. 4 <=> rich(fred) [avatar definition]
148. ~rich(fred) <- (~4) [avatar component clause 146]
149. 1 | ~4 [avatar split clause 95,146,134]
264. ~rich(john) [resolution 89,132]
284. rich(X1) | humble(X1) [resolution 116,77]
309. humble(fred) <- (~4) [resolution 284,148]
382. strong(X0) | ~happy(X0) | rich(X0) [resolution 106,114]
384. ~happy(X0) | rich(X0) [subsumption resolution 382,116]
386. 40 <=> happy(fred) [avatar definition]
387. happy(fred) <- (40) [avatar component clause 386]
388. ~happy(fred) <- (~40) [avatar component clause 386]
492. happy(fred) | brave(fred) <- (~4) [resolution 309,92]
493. brave(fred) <- (~4, ~40) [subsumption resolution 492,388]
565. happy(fred) | rich(fred) <- (~4, ~40) [resolution 493,85]
576. rich(fred) <- (~4, ~40) [subsumption resolution 565,388]
577. $false <- (~4, ~40) [subsumption resolution 576,148]
578. 4 | 40 [avatar contradiction clause 577]
587. rich(fred) <- (40) [resolution 387,384]
599. 4 | ~40 [avatar split clause 587,386,146]
603. rich(X0) <- (1) [resolution 135,117]
622. $false <- (1) [resolution 603,264]
623. ~1 [avatar contradiction clause 622]
625. $false [avatar sat refutation 149,578,599,623]
% SZS output end Proof for 5219373281473839845986066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either happy or not calm then susan is not happy.
If mary is either humble or not old then someone is either not old or quiet.
If susan is both brave and not funny then paul is not patient or strong.
Everyone who is not old is both kind and generous.
Everyone who is not curious is either not funny or not strong.
Everyone who is kind or not old is creative or not generous and vice versa.
Everyone who is patient is not wise or creative and vice versa.
Everyone who is both happy and generous is not rich.
If susan is both calm and not tall then someone is not old and vice versa.
Everyone who is either not curious or creative is patient or not funny and vice versa.
Everyone who is both curious and happy is not old or rich and vice versa.
Everyone who is creative is not strong and vice versa.
If alice is either tall or not funny then someone is either not strong or patient and vice versa.
If someone is kind or not happy then someone is either not humble or not rich.
Everyone who is not funny or not calm is both brave and creative and vice versa.
If someone is calm then mary is both not quiet and brave and vice versa.
Someone is old or not creative.
Someone is not funny or humble.
Alice is calm.
Susan is not humble or not old.
Mary is not kind.
Someone is both not funny and old.
Susan is both kind and not quiet.
Someone is not old or not funny. | Susan is humble. | contradiction | ((?[X]:((happy(X)<~>~calm(X))))=>(~happy(susan)))&
(((humble(mary)<~>~old(mary)))=>(?[X]:((~old(X)<~>quiet(X)))))&
(((brave(susan)&~funny(susan)))=>((~patient(paul)|strong(paul))))&
(![X]:(~old(X)=>(kind(X)&generous(X))))&
(![X]:(~curious(X)=>(~funny(X)<~>~strong(X))))&
(![X]:((kind(X)|~old(X))<=>(creative(X)|~generous(X))))&
(![X]:(patient(X)<=>(~wise(X)|creative(X))))&
(![X]:((happy(X)&generous(X))=>~rich(X)))&
(((calm(susan)&~tall(susan)))<=>(?[X]:(~old(X))))&
(![X]:((~curious(X)<~>creative(X))<=>(patient(X)|~funny(X))))&
(![X]:((curious(X)&happy(X))<=>(~old(X)|rich(X))))&
(![X]:(creative(X)<=>~strong(X)))&
(((tall(alice)<~>~funny(alice)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
((?[X]:((kind(X)|~happy(X))))=>(?[X]:((~humble(X)<~>~rich(X)))))&
(![X]:((~funny(X)|~calm(X))<=>(brave(X)&creative(X))))&
((?[X]:(calm(X)))<=>((~quiet(mary)&brave(mary))))&
(?[X]:((old(X)|~creative(X))))&
(?[X]:((~funny(X)|humble(X))))&
(calm(alice))&
((~humble(susan)|~old(susan)))&
(~kind(mary))&
(?[X]:((~funny(X)&old(X))))&
((kind(susan)&~quiet(susan)))&
(?[X]:((~old(X)|~funny(X)))) | humble(susan) | [
"p0",
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3359616346055776328187810
% SZS output start Proof for 3359616346055776328187810
1. ? [X0] : (happy(X0) <~> ~calm(X0)) => ~happy(susan) [input p0]
9. (~tall(susan) & calm(susan)) <=> ? [X0] : ~old(X0) [input p8]
11. ! [X0] : ((happy(X0) & curious(X0)) <=> (rich(X0) | ~old(X0))) [input p10]
20. ~old(susan) | ~humble(susan) [input p19]
25. humble(susan) [input hypothesis]
27. ~happy(susan) | ! [X0] : (happy(X0) <=> ~calm(X0)) [ennf transformation 1]
36. ~happy(susan) | ! [X0] : ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0))) [nnf transformation 27]
45. ((~tall(susan) & calm(susan)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | (tall(susan) | ~calm(susan))) [nnf transformation 9]
46. ((~tall(susan) & calm(susan)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | tall(susan) | ~calm(susan)) [flattening 45]
47. ((~tall(susan) & calm(susan)) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | tall(susan) | ~calm(susan)) [rectify 46]
48. ? [X1] : ~old(X1) => ~old(sK1) [choice axiom]
49. ((~tall(susan) & calm(susan)) | ! [X0] : old(X0)) & (~old(sK1) | tall(susan) | ~calm(susan)) [skolemisation 47,48]
52. ! [X0] : (((happy(X0) & curious(X0)) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 11]
53. ! [X0] : (((happy(X0) & curious(X0)) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | ~happy(X0) | ~curious(X0))) [flattening 52]
78. ~happy(susan) | ~calm(X0) | ~happy(X0) [cnf transformation 36]
98. calm(susan) | old(X0) [cnf transformation 49]
109. old(X0) | happy(X0) [cnf transformation 53]
136. ~old(susan) | ~humble(susan) [cnf transformation 20]
143. humble(susan) [cnf transformation 25]
148. 2 <=> happy(susan) [avatar definition]
149. happy(susan) <- (2) [avatar component clause 148]
153. 3 <=> ! [X0] : (~calm(X0) | ~happy(X0)) [avatar definition]
154. ~calm(X0) | ~happy(X0) <- (3) [avatar component clause 153]
155. 3 | ~2 [avatar split clause 78,148,153]
197. 12 <=> ! [X0] : old(X0) [avatar definition]
198. old(X0) <- (12) [avatar component clause 197]
205. 14 <=> calm(susan) [avatar definition]
207. calm(susan) <- (14) [avatar component clause 205]
208. 12 | 14 [avatar split clause 98,205,197]
293. 32 <=> humble(susan) [avatar definition]
297. 33 <=> old(susan) [avatar definition]
299. ~old(susan) <- (~33) [avatar component clause 297]
300. ~32 | ~33 [avatar split clause 136,297,293]
310. 32 [avatar split clause 143,293]
319. happy(susan) <- (~33) [resolution 109,299]
323. 2 | 33 [avatar split clause 319,297,148]
335. ~happy(susan) <- (3, 14) [resolution 154,207]
338. $false <- (2, 3, 14) [subsumption resolution 335,149]
339. ~2 | ~3 | ~14 [avatar contradiction clause 338]
341. $false <- (12, ~33) [resolution 198,299]
342. ~12 | 33 [avatar contradiction clause 341]
344. $false [avatar sat refutation 155,208,300,310,323,339,342]
% SZS output end Proof for 3359616346055776328187810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then lucy is either not humble or calm and vice versa.
Everyone who is patient is not creative or not patient and vice versa.
Everyone who is either not happy or kind is kind and vice versa.
If someone is either happy or not old then someone is either not old or not brave and vice versa.
Everyone who is both not rich and tall is both kind and not quiet.
Everyone who is both wise and not happy is either curious or creative.
Everyone who is either rich or not happy is either not old or brave.
If someone is not wise then lucy is either kind or curious and vice versa.
If someone is both not funny and not happy then someone is not curious or quiet and vice versa.
Everyone who is not happy or not calm is not quiet and vice versa.
Everyone who is either funny or not old is both not tall and not quiet and vice versa.
If someone is either old or wise then alice is both wise and creative.
Everyone who is both strong and not brave is not strong and vice versa.
Everyone who is either not generous or calm is not generous and vice versa.
If someone is both rich and generous then lucy is not rich.
Everyone who is both not rich and not old is wise or humble.
Someone is not strong or not creative.
John is not rich.
Lucy is not generous.
Susan is both curious and not humble.
Someone is either humble or kind. | Susan is not happy. | contradiction | ((~tall(lucy))<=>((~humble(lucy)<~>calm(lucy))))&
(![X]:(patient(X)<=>(~creative(X)|~patient(X))))&
(![X]:((~happy(X)<~>kind(X))<=>kind(X)))&
((?[X]:((happy(X)<~>~old(X))))<=>(?[X]:((~old(X)<~>~brave(X)))))&
(![X]:((~rich(X)&tall(X))=>(kind(X)&~quiet(X))))&
(![X]:((wise(X)&~happy(X))=>(curious(X)<~>creative(X))))&
(![X]:((rich(X)<~>~happy(X))=>(~old(X)<~>brave(X))))&
((?[X]:(~wise(X)))<=>((kind(lucy)<~>curious(lucy))))&
((?[X]:((~funny(X)&~happy(X))))<=>(?[X]:((~curious(X)|quiet(X)))))&
(![X]:((~happy(X)|~calm(X))<=>~quiet(X)))&
(![X]:((funny(X)<~>~old(X))<=>(~tall(X)&~quiet(X))))&
((?[X]:((old(X)<~>wise(X))))=>((wise(alice)&creative(alice))))&
(![X]:((strong(X)&~brave(X))<=>~strong(X)))&
(![X]:((~generous(X)<~>calm(X))<=>~generous(X)))&
((?[X]:((rich(X)&generous(X))))=>(~rich(lucy)))&
(![X]:((~rich(X)&~old(X))=>(wise(X)|humble(X))))&
(?[X]:((~strong(X)|~creative(X))))&
(~rich(john))&
(~generous(lucy))&
((curious(susan)&~humble(susan)))&
(?[X]:((humble(X)<~>kind(X)))) | ~happy(susan) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1081821543133549165944577
% SZS output start Proof for 1081821543133549165944577
3. ! [X0] : ((~happy(X0) <~> kind(X0)) <=> kind(X0)) [input p2]
22. ~happy(susan) [input hypothesis]
37. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | ~kind(X0)) & (kind(X0) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [nnf transformation 3]
74. kind(X0) | kind(X0) | happy(X0) [cnf transformation 37]
77. ~kind(X0) | happy(X0) | ~kind(X0) [cnf transformation 37]
132. ~happy(susan) [cnf transformation 22]
137. kind(X0) | happy(X0) [duplicate literal removal 74]
138. ~kind(X0) | happy(X0) [duplicate literal removal 77]
158. happy(X0) [subsumption resolution 137,138]
237. $false [subsumption resolution 132,158]
% SZS output end Proof for 1081821543133549165944577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not calm or not humble then lucy is either not happy or curious and vice versa.
Everyone who is either patient or quiet is not rich or quiet.
If alice is either kind or not brave then someone is generous.
Everyone who is creative or patient is humble and vice versa.
If someone is not wise or curious then fred is not patient or not creative and vice versa.
If someone is kind or not curious then john is either strong or old and vice versa.
Everyone who is not rich or not patient is not calm or not funny.
Everyone who is humble or not happy is either not kind or quiet and vice versa.
Everyone who is not curious or happy is not humble.
If susan is not calm then someone is not wise or not patient and vice versa.
Everyone who is both not strong and not patient is wise.
If susan is either not wise or tall then someone is both not humble and calm.
If someone is not funny or not creative then paul is both not generous and not brave.
Everyone who is either not patient or not wise is either generous or not calm and vice versa.
If alice is both brave and not rich then mary is not kind and vice versa.
Everyone who is both not creative and not generous is not strong and vice versa.
Someone is both funny and not curious.
Someone is rich.
Someone is not kind or happy.
Someone is calm.
Lucy is not creative or not funny.
Susan is either brave or not strong.
Lucy is not funny.
Someone is happy or curious. | Lucy is not creative. | neutral | (((~calm(alice)<~>~humble(alice)))<=>((~happy(lucy)<~>curious(lucy))))&
(![X]:((patient(X)<~>quiet(X))=>(~rich(X)|quiet(X))))&
(((kind(alice)<~>~brave(alice)))=>(?[X]:(generous(X))))&
(![X]:((creative(X)|patient(X))<=>humble(X)))&
((?[X]:((~wise(X)|curious(X))))<=>((~patient(fred)|~creative(fred))))&
((?[X]:((kind(X)|~curious(X))))<=>((strong(john)<~>old(john))))&
(![X]:((~rich(X)|~patient(X))=>(~calm(X)|~funny(X))))&
(![X]:((humble(X)|~happy(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:((~curious(X)|happy(X))=>~humble(X)))&
((~calm(susan))<=>(?[X]:((~wise(X)|~patient(X)))))&
(![X]:((~strong(X)&~patient(X))=>wise(X)))&
(((~wise(susan)<~>tall(susan)))=>(?[X]:((~humble(X)&calm(X)))))&
((?[X]:((~funny(X)|~creative(X))))=>((~generous(paul)&~brave(paul))))&
(![X]:((~patient(X)<~>~wise(X))<=>(generous(X)<~>~calm(X))))&
(((brave(alice)&~rich(alice)))<=>(~kind(mary)))&
(![X]:((~creative(X)&~generous(X))<=>~strong(X)))&
(?[X]:((funny(X)&~curious(X))))&
(?[X]:(rich(X)))&
(?[X]:((~kind(X)|happy(X))))&
(?[X]:(calm(X)))&
((~creative(lucy)|~funny(lucy)))&
((brave(susan)<~>~strong(susan)))&
(~funny(lucy))&
(?[X]:((happy(X)|curious(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is either not happy or tall is tall and vice versa.
Everyone who is either not quiet or not patient is both not tall and rich.
If someone is both not brave and kind then susan is brave.
If someone is either not calm or quiet then someone is wise or not tall and vice versa.
If mary is either tall or kind then mary is patient and vice versa.
Everyone who is not patient is not kind or not tall.
If someone is both quiet and humble then someone is not humble or creative.
Everyone who is not calm is not funny or rich and vice versa.
If mary is not curious or not rich then mary is not creative.
If someone is both funny and not patient then someone is old.
Everyone who is not old is not creative or not kind.
Everyone who is brave is either not rich or not quiet.
Everyone who is happy or tall is both not funny and not quiet and vice versa.
Everyone who is not brave or not happy is strong.
Everyone who is both tall and not tall is either not funny or not creative.
Susan is both not quiet and old.
John is both brave and not wise.
Mary is either not rich or calm.
Someone is humble or not strong.
Susan is not funny.
Someone is not humble or tall.
Someone is not humble. | Mary is not funny. | entailment | (![X]:((~happy(X)<~>tall(X))<=>tall(X)))&
(![X]:((~quiet(X)<~>~patient(X))=>(~tall(X)&rich(X))))&
((?[X]:((~brave(X)&kind(X))))=>(brave(susan)))&
((?[X]:((~calm(X)<~>quiet(X))))<=>(?[X]:((wise(X)|~tall(X)))))&
(((tall(mary)<~>kind(mary)))<=>(patient(mary)))&
(![X]:(~patient(X)=>(~kind(X)|~tall(X))))&
((?[X]:((quiet(X)&humble(X))))=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:(~calm(X)<=>(~funny(X)|rich(X))))&
(((~curious(mary)|~rich(mary)))=>(~creative(mary)))&
((?[X]:((funny(X)&~patient(X))))=>(?[X]:(old(X))))&
(![X]:(~old(X)=>(~creative(X)|~kind(X))))&
(![X]:(brave(X)=>(~rich(X)<~>~quiet(X))))&
(![X]:((happy(X)|tall(X))<=>(~funny(X)&~quiet(X))))&
(![X]:((~brave(X)|~happy(X))=>strong(X)))&
(![X]:((tall(X)&~tall(X))=>(~funny(X)<~>~creative(X))))&
((~quiet(susan)&old(susan)))&
((brave(john)&~wise(john)))&
((~rich(mary)<~>calm(mary)))&
(?[X]:((humble(X)|~strong(X))))&
(~funny(susan))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:(~humble(X))) | ~funny(mary) | [
"p0",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 765889246482931349450128
% SZS output start Proof for 765889246482931349450128
1. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> tall(X0)) [input p0]
13. ! [X0] : ((tall(X0) | happy(X0)) <=> (~quiet(X0) & ~funny(X0))) [input p12]
23. funny(mary) [input hypothesis]
41. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | ~tall(X0)) & (tall(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 1]
55. ! [X0] : (((tall(X0) | happy(X0)) | (quiet(X0) | funny(X0))) & ((~quiet(X0) & ~funny(X0)) | (~tall(X0) & ~happy(X0)))) [nnf transformation 13]
56. ! [X0] : ((tall(X0) | happy(X0) | quiet(X0) | funny(X0)) & ((~quiet(X0) & ~funny(X0)) | (~tall(X0) & ~happy(X0)))) [flattening 55]
65. tall(X0) | tall(X0) | happy(X0) [cnf transformation 41]
68. ~tall(X0) | happy(X0) | ~tall(X0) [cnf transformation 41]
92. ~funny(X0) | ~happy(X0) [cnf transformation 56]
110. funny(mary) [cnf transformation 23]
111. tall(X0) | happy(X0) [duplicate literal removal 65]
112. ~tall(X0) | happy(X0) [duplicate literal removal 68]
113. happy(X0) [subsumption resolution 111,112]
194. ~funny(X0) [subsumption resolution 92,113]
216. $false [subsumption resolution 110,194]
% SZS output end Proof for 765889246482931349450128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is either not patient or brave and vice versa.
Everyone who is either old or not rich is creative or not wise.
If someone is either not kind or curious then susan is wise and vice versa.
If someone is kind then fred is either not old or rich.
Everyone who is generous or not patient is both funny and happy.
Everyone who is either not funny or not generous is either calm or generous and vice versa.
If someone is both not happy and happy then someone is not wise and vice versa.
Everyone who is either calm or creative is either not tall or strong.
If susan is both tall and old then someone is both generous and wise and vice versa.
Everyone who is either not brave or generous is either not creative or not calm and vice versa.
Everyone who is creative is both generous and strong and vice versa.
Everyone who is not brave or not quiet is generous and vice versa.
If mary is either calm or not kind then someone is not quiet.
Everyone who is either brave or calm is wise or not curious.
Everyone who is both not creative and not strong is tall.
Everyone who is either brave or not calm is not wise.
Paul is either kind or not quiet.
Mary is both not generous and humble.
Someone is curious or not creative.
Alice is both patient and not humble.
Mary is creative or not tall. | Susan is calm. | entailment | (![X]:(~tall(X)<=>(~patient(X)<~>brave(X))))&
(![X]:((old(X)<~>~rich(X))=>(creative(X)|~wise(X))))&
((?[X]:((~kind(X)<~>curious(X))))<=>(wise(susan)))&
((?[X]:(kind(X)))=>((~old(fred)<~>rich(fred))))&
(![X]:((generous(X)|~patient(X))=>(funny(X)&happy(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>(calm(X)<~>generous(X))))&
((?[X]:((~happy(X)&happy(X))))<=>(?[X]:(~wise(X))))&
(![X]:((calm(X)<~>creative(X))=>(~tall(X)<~>strong(X))))&
(((tall(susan)&old(susan)))<=>(?[X]:((generous(X)&wise(X)))))&
(![X]:((~brave(X)<~>generous(X))<=>(~creative(X)<~>~calm(X))))&
(![X]:(creative(X)<=>(generous(X)&strong(X))))&
(![X]:((~brave(X)|~quiet(X))<=>generous(X)))&
(((calm(mary)<~>~kind(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((brave(X)<~>calm(X))=>(wise(X)|~curious(X))))&
(![X]:((~creative(X)&~strong(X))=>tall(X)))&
(![X]:((brave(X)<~>~calm(X))=>~wise(X)))&
((kind(paul)<~>~quiet(paul)))&
((~generous(mary)&humble(mary)))&
(?[X]:((curious(X)|~creative(X))))&
((patient(alice)&~humble(alice)))&
((creative(mary)|~tall(mary))) | calm(susan) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2605595810716828657408519
% SZS output start Proof for 2605595810716828657408519
1. ! [X0] : (~tall(X0) <=> (~patient(X0) <~> brave(X0))) [input p0]
2. ! [X0] : ((old(X0) <~> ~rich(X0)) => (~wise(X0) | creative(X0))) [input p1]
4. ? [X0] : kind(X0) => (~old(fred) <~> rich(fred)) [input p3]
5. ! [X0] : ((~patient(X0) | generous(X0)) => (happy(X0) & funny(X0))) [input p4]
6. ! [X0] : ((~funny(X0) <~> ~generous(X0)) <=> (calm(X0) <~> generous(X0))) [input p5]
7. ? [X0] : (happy(X0) & ~happy(X0)) <=> ? [X0] : ~wise(X0) [input p6]
9. (old(susan) & tall(susan)) <=> ? [X0] : (wise(X0) & generous(X0)) [input p8]
11. ! [X0] : (creative(X0) <=> (strong(X0) & generous(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) | ~brave(X0)) <=> generous(X0)) [input p11]
17. kind(paul) <~> ~quiet(paul) [input p16]
22. ~calm(susan) [input hypothesis]
23. ? [X0] : (happy(X0) & ~happy(X0)) <=> ? [X1] : ~wise(X1) [rectify 7]
24. ! [X0] : ((~wise(X0) | creative(X0)) | (old(X0) <=> ~rich(X0))) [ennf transformation 2]
25. ! [X0] : (~wise(X0) | creative(X0) | (old(X0) <=> ~rich(X0))) [flattening 24]
26. (~old(fred) <~> rich(fred)) | ! [X0] : ~kind(X0) [ennf transformation 4]
27. ! [X0] : ((happy(X0) & funny(X0)) | (patient(X0) & ~generous(X0))) [ennf transformation 5]
35. ! [X0] : ((~tall(X0) | ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0)))) & (((~brave(X0) | patient(X0)) & (brave(X0) | ~patient(X0))) | tall(X0))) [nnf transformation 1]
36. ! [X0] : (~wise(X0) | creative(X0) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0)))) [nnf transformation 25]
41. ((~rich(fred) | old(fred)) & (rich(fred) | ~old(fred))) | ! [X0] : ~kind(X0) [nnf transformation 26]
42. ! [X0] : ((((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0))))) [nnf transformation 6]
43. (? [X0] : (happy(X0) & ~happy(X0)) | ! [X1] : wise(X1)) & (? [X1] : ~wise(X1) | ! [X0] : (~happy(X0) | happy(X0))) [nnf transformation 23]
44. (? [X0] : (happy(X0) & ~happy(X0)) | ! [X1] : wise(X1)) & (? [X2] : ~wise(X2) | ! [X3] : (~happy(X3) | happy(X3))) [rectify 43]
45. ? [X0] : (happy(X0) & ~happy(X0)) => (happy(sK1) & ~happy(sK1)) [choice axiom]
46. ? [X2] : ~wise(X2) => ~wise(sK2) [choice axiom]
47. ((happy(sK1) & ~happy(sK1)) | ! [X1] : wise(X1)) & (~wise(sK2) | ! [X3] : (~happy(X3) | happy(X3))) [skolemisation 44,46,45]
49. ((old(susan) & tall(susan)) | ! [X0] : (~wise(X0) | ~generous(X0))) & (? [X0] : (wise(X0) & generous(X0)) | (~old(susan) | ~tall(susan))) [nnf transformation 9]
50. ((old(susan) & tall(susan)) | ! [X0] : (~wise(X0) | ~generous(X0))) & (? [X0] : (wise(X0) & generous(X0)) | ~old(susan) | ~tall(susan)) [flattening 49]
51. ((old(susan) & tall(susan)) | ! [X0] : (~wise(X0) | ~generous(X0))) & (? [X1] : (wise(X1) & generous(X1)) | ~old(susan) | ~tall(susan)) [rectify 50]
52. ? [X1] : (wise(X1) & generous(X1)) => (wise(sK3) & generous(sK3)) [choice axiom]
53. ((old(susan) & tall(susan)) | ! [X0] : (~wise(X0) | ~generous(X0))) & ((wise(sK3) & generous(sK3)) | ~old(susan) | ~tall(susan)) [skolemisation 51,52]
55. ! [X0] : ((creative(X0) | (~strong(X0) | ~generous(X0))) & ((strong(X0) & generous(X0)) | ~creative(X0))) [nnf transformation 11]
56. ! [X0] : ((creative(X0) | ~strong(X0) | ~generous(X0)) & ((strong(X0) & generous(X0)) | ~creative(X0))) [flattening 55]
57. ! [X0] : (((~quiet(X0) | ~brave(X0)) | ~generous(X0)) & (generous(X0) | (quiet(X0) & brave(X0)))) [nnf transformation 12]
58. ! [X0] : ((~quiet(X0) | ~brave(X0) | ~generous(X0)) & (generous(X0) | (quiet(X0) & brave(X0)))) [flattening 57]
64. (quiet(paul) | ~kind(paul)) & (~quiet(paul) | kind(paul)) [nnf transformation 17]
70. ~brave(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 35]
71. ~wise(X0) | creative(X0) | ~rich(X0) | ~old(X0) [cnf transformation 36]
72. ~wise(X0) | creative(X0) | old(X0) | rich(X0) [cnf transformation 36]
77. rich(fred) | ~old(fred) | ~kind(X0) [cnf transformation 41]
78. ~rich(fred) | old(fred) | ~kind(X0) [cnf transformation 41]
79. ~generous(X0) | funny(X0) [cnf transformation 27]
80. funny(X0) | patient(X0) [cnf transformation 27]
84. generous(X0) | calm(X0) | ~funny(X0) | generous(X0) [cnf transformation 42]
88. ~generous(X0) | ~funny(X0) | calm(X0) | ~generous(X0) [cnf transformation 42]
92. ~happy(sK1) | wise(X1) [cnf transformation 47]
93. happy(sK1) | wise(X1) [cnf transformation 47]
100. tall(susan) | ~wise(X0) | ~generous(X0) [cnf transformation 53]
110. ~creative(X0) | generous(X0) [cnf transformation 56]
113. generous(X0) | brave(X0) [cnf transformation 58]
114. quiet(X0) | generous(X0) [cnf transformation 58]
123. ~quiet(paul) | kind(paul) [cnf transformation 64]
131. ~calm(susan) [cnf transformation 22]
132. generous(X0) | calm(X0) | ~funny(X0) [duplicate literal removal 84]
134. ~generous(X0) | ~funny(X0) | calm(X0) [duplicate literal removal 88]
159. 6 <=> ! [X0] : ~kind(X0) [avatar definition]
160. ~kind(X0) <- (6) [avatar component clause 159]
162. 7 <=> old(fred) [avatar definition]
164. old(fred) <- (7) [avatar component clause 162]
166. 8 <=> rich(fred) [avatar definition]
167. rich(fred) <- (8) [avatar component clause 166]
168. ~rich(fred) <- (~8) [avatar component clause 166]
169. 6 | 7 | ~8 [avatar split clause 78,166,162,159]
170. 6 | ~7 | 8 [avatar split clause 77,166,162,159]
172. ~generous(X0) | calm(X0) [subsumption resolution 134,79]
173. ~funny(X0) | calm(X0) [subsumption resolution 132,172]
175. 9 <=> ! [X1] : wise(X1) [avatar definition]
176. wise(X1) <- (9) [avatar component clause 175]
178. 10 <=> happy(sK1) [avatar definition]
181. 9 | 10 [avatar split clause 93,178,175]
182. 9 | ~10 [avatar split clause 92,178,175]
184. 11 <=> ! [X0] : (~wise(X0) | ~generous(X0)) [avatar definition]
185. ~generous(X0) | ~wise(X0) <- (11) [avatar component clause 184]
192. 13 <=> tall(susan) [avatar definition]
195. 11 | 13 [avatar split clause 100,192,184]
226. 19 <=> kind(paul) [avatar definition]
227. kind(paul) <- (19) [avatar component clause 226]
230. 20 <=> quiet(paul) [avatar definition]
231. ~quiet(paul) <- (~20) [avatar component clause 230]
234. 19 | ~20 [avatar split clause 123,230,226]
259. generous(paul) <- (~20) [resolution 114,231]
271. calm(X0) | brave(X0) [resolution 172,113]
274. calm(X0) | patient(X0) [resolution 173,80]
278. ~wise(paul) <- (11, ~20) [resolution 185,259]
282. $false <- (9, 11, ~20) [subsumption resolution 278,176]
283. ~9 | ~11 | 20 [avatar contradiction clause 282]
303. 27 <=> patient(susan) [avatar definition]
307. 28 <=> brave(susan) [avatar definition]
309. brave(susan) <- (28) [avatar component clause 307]
339. ~rich(X0) | creative(X0) | ~old(X0) <- (9) [resolution 71,176]
341. creative(X0) | old(X0) | rich(X0) <- (9) [resolution 72,176]
342. brave(susan) [resolution 271,131]
345. 28 [avatar split clause 342,307]
358. ~patient(susan) | ~tall(susan) <- (28) [resolution 309,70]
415. patient(susan) [resolution 274,131]
429. ~13 | ~27 | ~28 [avatar split clause 358,307,303,192]
431. 27 [avatar split clause 415,303]
432. ~generous(X0) <- (9, 11) [subsumption resolution 185,176]
466. old(X3) | rich(X3) | generous(X3) <- (9) [resolution 341,110]
478. rich(X3) | old(X3) <- (9, 11) [subsumption resolution 466,432]
500. old(fred) <- (~8, 9, 11) [resolution 478,168]
504. 7 | 8 | ~9 | ~11 [avatar split clause 500,184,175,166,162]
507. $false <- (6, 19) [resolution 160,227]
508. ~6 | ~19 [avatar contradiction clause 507]
511. creative(fred) | ~old(fred) <- (8, 9) [resolution 167,339]
512. creative(fred) <- (7, 8, 9) [subsumption resolution 511,164]
517. generous(fred) <- (7, 8, 9) [resolution 512,110]
519. $false <- (7, 8, 9, 11) [subsumption resolution 517,432]
520. ~7 | ~8 | ~9 | ~11 [avatar contradiction clause 519]
521. $false [avatar sat refutation 169,170,181,182,195,234,283,345,429,431,504,508,520]
% SZS output end Proof for 2605595810716828657408519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not quiet is both not happy and happy and vice versa. Everyone who is either kind or generous is either not wise or funny. Everyone who is either not funny or rich is humble or quiet. If alice is not creative then someone is funny and vice versa. Everyone who is humble or not wise is not quiet and vice versa. If lucy is not brave then lucy is not kind and vice versa. Everyone who is quiet is not generous. If susan is not happy then someone is generous or kind and vice versa. If john is either generous or strong then alice is not generous or not strong and vice versa. If paul is wise then alice is strong or humble. If susan is rich then someone is not tall and vice versa. If fred is both not brave and not calm then john is both not rich and generous. Everyone who is either happy or not calm is not kind or humble and vice versa. If john is not funny or generous then john is not quiet and vice versa. If susan is tall or humble then fred is tall. If paul is either funny or not creative then someone is not kind or not generous and vice versa. John is either not calm or humble. Someone is not wise or funny. Someone is not kind or not tall. Someone is not kind or not calm. John is either old or not generous. Lucy is quiet. | Paul is not old. | neutral | (![X]:((happy(X)|~quiet(X))<=>(~happy(X)&happy(X))))&
(![X]:((kind(X)<~>generous(X))=>(~wise(X)<~>funny(X))))&
(![X]:((~funny(X)<~>rich(X))=>(humble(X)|quiet(X))))&
((~creative(alice))<=>(?[X]:(funny(X))))&
(![X]:((humble(X)|~wise(X))<=>~quiet(X)))&
((~brave(lucy))<=>(~kind(lucy)))&
(![X]:(quiet(X)=>~generous(X)))&
((~happy(susan))<=>(?[X]:((generous(X)|kind(X)))))&
(((generous(john)<~>strong(john)))<=>((~generous(alice)|~strong(alice))))&
((wise(paul))=>((strong(alice)|humble(alice))))&
((rich(susan))<=>(?[X]:(~tall(X))))&
(((~brave(fred)&~calm(fred)))=>((~rich(john)&generous(john))))&
(![X]:((happy(X)<~>~calm(X))<=>(~kind(X)|humble(X))))&
(((~funny(john)|generous(john)))<=>(~quiet(john)))&
(((tall(susan)|humble(susan)))=>(tall(fred)))&
(((funny(paul)<~>~creative(paul)))<=>(?[X]:((~kind(X)|~generous(X)))))&
((~calm(john)<~>humble(john)))&
(?[X]:((~wise(X)|funny(X))))&
(?[X]:((~kind(X)|~tall(X))))&
(?[X]:((~kind(X)|~calm(X))))&
((old(john)<~>~generous(john)))&
(quiet(lucy)) | ~old(paul) | [] | null | 0 |
Everyone who is either quiet or tall is kind or strong.
Everyone who is not calm is either not humble or not wise and vice versa.
If susan is not rich then lucy is both wise and generous.
Everyone who is not humble is not quiet and vice versa.
Everyone who is either not strong or wise is either not humble or not calm.
Everyone who is quiet is not kind or humble and vice versa.
Everyone who is quiet or not rich is old or not humble.
Everyone who is not funny or kind is both quiet and not creative.
Everyone who is not kind is wise and vice versa.
Everyone who is either funny or calm is not brave or quiet.
If someone is not happy then alice is either not rich or not quiet.
Everyone who is both not humble and not generous is either not rich or not old and vice versa.
If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa.
If someone is generous or tall then alice is strong and vice versa.
Everyone who is not happy is brave or humble.
Everyone who is not happy or not funny is both creative and quiet.
Someone is either not creative or quiet.
Someone is not strong or not kind.
Someone is creative or not old.
Someone is brave or calm.
Paul is not curious or happy.
John is both not creative and curious. | Alice is happy. | entailment | (![X]:((quiet(X)<~>tall(X))=>(kind(X)|strong(X))))&
(![X]:(~calm(X)<=>(~humble(X)<~>~wise(X))))&
((~rich(susan))=>((wise(lucy)&generous(lucy))))&
(![X]:(~humble(X)<=>~quiet(X)))&
(![X]:((~strong(X)<~>wise(X))=>(~humble(X)<~>~calm(X))))&
(![X]:(quiet(X)<=>(~kind(X)|humble(X))))&
(![X]:((quiet(X)|~rich(X))=>(old(X)|~humble(X))))&
(![X]:((~funny(X)|kind(X))=>(quiet(X)&~creative(X))))&
(![X]:(~kind(X)<=>wise(X)))&
(![X]:((funny(X)<~>calm(X))=>(~brave(X)|quiet(X))))&
((?[X]:(~happy(X)))=>((~rich(alice)<~>~quiet(alice))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
(?[X]:((~creative(X)<~>quiet(X))))&
(?[X]:((~strong(X)|~kind(X))))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((brave(X)|calm(X))))&
((~curious(paul)|happy(paul)))&
((~creative(john)&curious(john))) | happy(alice) | [
"p3",
"p5",
"p6",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3876348389916040687104688
% SZS output start Proof for 3876348389916040687104688
4. ! [X0] : (~humble(X0) <=> ~quiet(X0)) [input p3]
6. ! [X0] : (quiet(X0) <=> (humble(X0) | ~kind(X0))) [input p5]
7. ! [X0] : ((~rich(X0) | quiet(X0)) => (~humble(X0) | old(X0))) [input p6]
8. ! [X0] : ((kind(X0) | ~funny(X0)) => (~creative(X0) & quiet(X0))) [input p7]
11. ? [X0] : ~happy(X0) => (~rich(alice) <~> ~quiet(alice)) [input p10]
12. ! [X0] : ((~generous(X0) & ~humble(X0)) <=> (~rich(X0) <~> ~old(X0))) [input p11]
23. ~happy(alice) [input hypothesis]
29. ! [X0] : ((~humble(X0) | old(X0)) | (rich(X0) & ~quiet(X0))) [ennf transformation 7]
30. ! [X0] : (~humble(X0) | old(X0) | (rich(X0) & ~quiet(X0))) [flattening 29]
31. ! [X0] : ((~creative(X0) & quiet(X0)) | (~kind(X0) & funny(X0))) [ennf transformation 8]
34. (~rich(alice) <~> ~quiet(alice)) | ! [X0] : happy(X0) [ennf transformation 11]
40. ! [X0] : ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))) [nnf transformation 4]
42. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ~quiet(X0))) [nnf transformation 6]
43. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ~quiet(X0))) [flattening 42]
46. ((quiet(alice) | rich(alice)) & (~quiet(alice) | ~rich(alice))) | ! [X0] : happy(X0) [nnf transformation 34]
47. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (generous(X0) | humble(X0)))) [nnf transformation 12]
48. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | generous(X0) | humble(X0))) [flattening 47]
75. ~quiet(X0) | humble(X0) [cnf transformation 40]
82. kind(X0) | quiet(X0) [cnf transformation 43]
85. ~humble(X0) | old(X0) | rich(X0) [cnf transformation 30]
87. quiet(X0) | ~kind(X0) [cnf transformation 31]
94. ~quiet(alice) | ~rich(alice) | happy(X0) [cnf transformation 46]
98. ~humble(X0) | ~old(X0) | rich(X0) [cnf transformation 48]
99. ~humble(X0) | ~rich(X0) | old(X0) [cnf transformation 48]
122. ~happy(alice) [cnf transformation 23]
140. quiet(X0) [subsumption resolution 87,82]
141. ~rich(alice) | happy(X0) [subsumption resolution 94,140]
143. 4 <=> ! [X0] : happy(X0) [avatar definition]
144. happy(X0) <- (4) [avatar component clause 143]
146. 5 <=> rich(alice) [avatar definition]
148. ~rich(alice) <- (~5) [avatar component clause 146]
149. 4 | ~5 [avatar split clause 141,146,143]
150. ~humble(X0) | old(X0) [subsumption resolution 99,85]
151. ~humble(X0) | rich(X0) [subsumption resolution 98,150]
212. humble(X0) [resolution 75,140]
232. rich(X0) [resolution 151,212]
233. $false <- (~5) [resolution 232,148]
234. 5 [avatar contradiction clause 233]
235. $false <- (4) [resolution 144,122]
236. ~4 [avatar contradiction clause 235]
237. $false [avatar sat refutation 149,234,236]
% SZS output end Proof for 3876348389916040687104688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or curious is creative or curious and vice versa.
Everyone who is strong or not kind is not curious or not kind and vice versa.
If mary is either creative or rich then someone is happy and vice versa.
If someone is both rich and not tall then susan is tall.
Everyone who is either not rich or old is both rich and old.
Everyone who is not strong or not humble is tall and vice versa.
Everyone who is not generous is not funny or old and vice versa.
Everyone who is not patient or brave is either not quiet or not strong.
If susan is strong or not old then someone is happy.
Everyone who is either curious or humble is either strong or tall.
If someone is patient then someone is not rich or not strong.
If someone is not wise or not patient then lucy is either not wise or funny and vice versa.
If mary is either calm or humble then someone is strong and vice versa.
If mary is creative then paul is not patient or tall and vice versa.
If someone is both not calm and funny then mary is funny or wise.
Everyone who is not rich or not strong is either not happy or curious.
John is not funny or patient.
Someone is both not patient and not strong.
Someone is both not wise and old.
Someone is both creative and humble.
Someone is either generous or patient.
Someone is both rich and generous. | John is not funny. | neutral | (![X]:((~creative(X)<~>curious(X))<=>(creative(X)|curious(X))))&
(![X]:((strong(X)|~kind(X))<=>(~curious(X)|~kind(X))))&
(((creative(mary)<~>rich(mary)))<=>(?[X]:(happy(X))))&
((?[X]:((rich(X)&~tall(X))))=>(tall(susan)))&
(![X]:((~rich(X)<~>old(X))=>(rich(X)&old(X))))&
(![X]:((~strong(X)|~humble(X))<=>tall(X)))&
(![X]:(~generous(X)<=>(~funny(X)|old(X))))&
(![X]:((~patient(X)|brave(X))=>(~quiet(X)<~>~strong(X))))&
(((strong(susan)|~old(susan)))=>(?[X]:(happy(X))))&
(![X]:((curious(X)<~>humble(X))=>(strong(X)<~>tall(X))))&
((?[X]:(patient(X)))=>(?[X]:((~rich(X)|~strong(X)))))&
((?[X]:((~wise(X)|~patient(X))))<=>((~wise(lucy)<~>funny(lucy))))&
(((calm(mary)<~>humble(mary)))<=>(?[X]:(strong(X))))&
((creative(mary))<=>((~patient(paul)|tall(paul))))&
((?[X]:((~calm(X)&funny(X))))=>((funny(mary)|wise(mary))))&
(![X]:((~rich(X)|~strong(X))=>(~happy(X)<~>curious(X))))&
((~funny(john)|patient(john)))&
(?[X]:((~patient(X)&~strong(X))))&
(?[X]:((~wise(X)&old(X))))&
(?[X]:((creative(X)&humble(X))))&
(?[X]:((generous(X)<~>patient(X))))&
(?[X]:((rich(X)&generous(X)))) | ~funny(john) | [] | null | 0 |
Everyone who is generous is either happy or not strong.
Everyone who is both patient and kind is both humble and patient and vice versa.
Everyone who is either not brave or not rich is both not funny and humble.
If someone is strong then someone is either happy or quiet and vice versa.
Everyone who is not curious is both brave and funny.
Everyone who is either curious or not kind is either generous or not old.
Everyone who is not humble is both quiet and generous.
Everyone who is curious or not rich is either not funny or not creative.
If paul is not strong or not humble then someone is generous or creative.
Everyone who is both not strong and not brave is not patient.
Everyone who is both tall and strong is funny.
Everyone who is either wise or not old is either not happy or not brave.
Everyone who is both kind and happy is both tall and humble and vice versa.
If someone is brave or not quiet then someone is humble.
If fred is tall then susan is not wise or not calm.
If john is tall or creative then susan is both tall and quiet.
Someone is both patient and old.
Fred is both not happy and not wise.
Lucy is not humble.
Mary is either not old or kind.
Someone is both not rich and not kind.
Someone is either not wise or not patient.
Someone is happy or not generous.
Alice is not patient. | Paul is funny. | neutral | (![X]:(generous(X)=>(happy(X)<~>~strong(X))))&
(![X]:((patient(X)&kind(X))<=>(humble(X)&patient(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(~funny(X)&humble(X))))&
((?[X]:(strong(X)))<=>(?[X]:((happy(X)<~>quiet(X)))))&
(![X]:(~curious(X)=>(brave(X)&funny(X))))&
(![X]:((curious(X)<~>~kind(X))=>(generous(X)<~>~old(X))))&
(![X]:(~humble(X)=>(quiet(X)&generous(X))))&
(![X]:((curious(X)|~rich(X))=>(~funny(X)<~>~creative(X))))&
(((~strong(paul)|~humble(paul)))=>(?[X]:((generous(X)|creative(X)))))&
(![X]:((~strong(X)&~brave(X))=>~patient(X)))&
(![X]:((tall(X)&strong(X))=>funny(X)))&
(![X]:((wise(X)<~>~old(X))=>(~happy(X)<~>~brave(X))))&
(![X]:((kind(X)&happy(X))<=>(tall(X)&humble(X))))&
((?[X]:((brave(X)|~quiet(X))))=>(?[X]:(humble(X))))&
((tall(fred))=>((~wise(susan)|~calm(susan))))&
(((tall(john)|creative(john)))=>((tall(susan)&quiet(susan))))&
(?[X]:((patient(X)&old(X))))&
((~happy(fred)&~wise(fred)))&
(~humble(lucy))&
((~old(mary)<~>kind(mary)))&
(?[X]:((~rich(X)&~kind(X))))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((happy(X)|~generous(X))))&
(~patient(alice)) | funny(paul) | [] | null | 0 |
If alice is creative or strong then alice is not generous or kind and vice versa.
Everyone who is both not creative and curious is kind and vice versa.
Everyone who is not happy or wise is both old and not patient and vice versa.
If john is not calm then someone is both not wise and not tall.
If susan is either not happy or not patient then susan is not humble and vice versa.
Everyone who is tall or rich is both rich and not strong and vice versa.
Everyone who is not strong is not curious or not brave and vice versa.
Everyone who is either not funny or old is both tall and patient.
Everyone who is generous is not funny and vice versa.
If someone is not patient then someone is old and vice versa.
Everyone who is both not brave and not kind is either creative or kind and vice versa.
If someone is patient then someone is either not quiet or quiet.
Everyone who is either kind or brave is both brave and curious.
Everyone who is either brave or not old is either not funny or not rich.
Everyone who is both humble and not funny is both not curious and brave and vice versa.
John is humble.
Someone is either not curious or not calm.
Someone is either kind or not wise.
Someone is quiet.
Lucy is both not calm and quiet.
Paul is not humble or not wise.
Someone is old or curious. | John is not strong. | entailment | (((creative(alice)|strong(alice)))<=>((~generous(alice)|kind(alice))))&
(![X]:((~creative(X)&curious(X))<=>kind(X)))&
(![X]:((~happy(X)|wise(X))<=>(old(X)&~patient(X))))&
((~calm(john))=>(?[X]:((~wise(X)&~tall(X)))))&
(((~happy(susan)<~>~patient(susan)))<=>(~humble(susan)))&
(![X]:((tall(X)|rich(X))<=>(rich(X)&~strong(X))))&
(![X]:(~strong(X)<=>(~curious(X)|~brave(X))))&
(![X]:((~funny(X)<~>old(X))=>(tall(X)&patient(X))))&
(![X]:(generous(X)<=>~funny(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(old(X))))&
(![X]:((~brave(X)&~kind(X))<=>(creative(X)<~>kind(X))))&
((?[X]:(patient(X)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((kind(X)<~>brave(X))=>(brave(X)&curious(X))))&
(![X]:((brave(X)<~>~old(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((humble(X)&~funny(X))<=>(~curious(X)&brave(X))))&
(humble(john))&
(?[X]:((~curious(X)<~>~calm(X))))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:(quiet(X)))&
((~calm(lucy)&quiet(lucy)))&
((~humble(paul)|~wise(paul)))&
(?[X]:((old(X)|curious(X)))) | ~strong(john) | [
"p1",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1451009870947829340811016
% SZS output start Proof for 1451009870947829340811016
2. ! [X0] : ((curious(X0) & ~creative(X0)) <=> kind(X0)) [input p1]
7. ! [X0] : (~strong(X0) <=> (~brave(X0) | ~curious(X0))) [input p6]
11. ! [X0] : ((~kind(X0) & ~brave(X0)) <=> (creative(X0) <~> kind(X0))) [input p10]
23. strong(john) [input hypothesis]
33. ! [X0] : (((curious(X0) & ~creative(X0)) | ~kind(X0)) & (kind(X0) | (~curious(X0) | creative(X0)))) [nnf transformation 2]
34. ! [X0] : (((curious(X0) & ~creative(X0)) | ~kind(X0)) & (kind(X0) | ~curious(X0) | creative(X0))) [flattening 33]
42. ! [X0] : ((~strong(X0) | (brave(X0) & curious(X0))) & ((~brave(X0) | ~curious(X0)) | strong(X0))) [nnf transformation 7]
43. ! [X0] : ((~strong(X0) | (brave(X0) & curious(X0))) & (~brave(X0) | ~curious(X0) | strong(X0))) [flattening 42]
51. ! [X0] : (((~kind(X0) & ~brave(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0)))) & (((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | (kind(X0) | brave(X0)))) [nnf transformation 11]
52. ! [X0] : (((~kind(X0) & ~brave(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0)))) & (((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | kind(X0) | brave(X0))) [flattening 51]
75. ~curious(X0) | kind(X0) | creative(X0) [cnf transformation 34]
76. ~kind(X0) | ~creative(X0) [cnf transformation 34]
95. ~strong(X0) | curious(X0) [cnf transformation 43]
96. ~strong(X0) | brave(X0) [cnf transformation 43]
107. ~brave(X0) | kind(X0) | ~creative(X0) [cnf transformation 52]
110. ~kind(X0) | creative(X0) | ~kind(X0) [cnf transformation 52]
135. strong(john) [cnf transformation 23]
138. ~kind(X0) | creative(X0) [duplicate literal removal 110]
206. ~kind(X0) [subsumption resolution 138,76]
207. ~brave(X0) | ~creative(X0) [subsumption resolution 107,206]
243. curious(john) [resolution 95,135]
244. brave(john) [resolution 96,135]
246. ~creative(john) [resolution 207,244]
251. kind(john) | creative(john) [resolution 75,243]
255. creative(john) [subsumption resolution 251,206]
256. $false [subsumption resolution 255,246]
% SZS output end Proof for 1451009870947829340811016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not wise is quiet or not rich.
Everyone who is either not strong or not old is either funny or calm.
If mary is either not tall or calm then alice is humble or patient.
Everyone who is funny or kind is either funny or not kind and vice versa.
Everyone who is not tall is not generous or funny.
If someone is both calm and generous then mary is both calm and not wise.
If lucy is both not rich and not calm then john is not tall and vice versa.
Everyone who is not funny is either curious or not wise.
If mary is not funny then someone is wise or not creative and vice versa.
Everyone who is not wise is generous or funny.
Everyone who is either rich or not patient is not calm or kind and vice versa.
If someone is creative or not humble then someone is humble or funny and vice versa.
Everyone who is brave or kind is happy or not kind.
Everyone who is either not kind or creative is calm or tall and vice versa.
Paul is not rich or strong.
Paul is strong.
Someone is not funny or not brave.
Lucy is curious or kind.
Lucy is both not calm and kind.
Someone is not rich or not generous.
Someone is both not quiet and strong. | Lucy is generous. | neutral | (![X]:((creative(X)&~wise(X))=>(quiet(X)|~rich(X))))&
(![X]:((~strong(X)<~>~old(X))=>(funny(X)<~>calm(X))))&
(((~tall(mary)<~>calm(mary)))=>((humble(alice)|patient(alice))))&
(![X]:((funny(X)|kind(X))<=>(funny(X)<~>~kind(X))))&
(![X]:(~tall(X)=>(~generous(X)|funny(X))))&
((?[X]:((calm(X)&generous(X))))=>((calm(mary)&~wise(mary))))&
(((~rich(lucy)&~calm(lucy)))<=>(~tall(john)))&
(![X]:(~funny(X)=>(curious(X)<~>~wise(X))))&
((~funny(mary))<=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:(~wise(X)=>(generous(X)|funny(X))))&
(![X]:((rich(X)<~>~patient(X))<=>(~calm(X)|kind(X))))&
((?[X]:((creative(X)|~humble(X))))<=>(?[X]:((humble(X)|funny(X)))))&
(![X]:((brave(X)|kind(X))=>(happy(X)|~kind(X))))&
(![X]:((~kind(X)<~>creative(X))<=>(calm(X)|tall(X))))&
((~rich(paul)|strong(paul)))&
(strong(paul))&
(?[X]:((~funny(X)|~brave(X))))&
((curious(lucy)|kind(lucy)))&
((~calm(lucy)&kind(lucy)))&
(?[X]:((~rich(X)|~generous(X))))&
(?[X]:((~quiet(X)&strong(X)))) | generous(lucy) | [] | null | 0 |
Everyone who is both happy and patient is not calm or tall.
Everyone who is brave is either humble or not wise and vice versa.
Everyone who is rich or not kind is not brave or not wise.
If someone is either quiet or not patient then john is not strong and vice versa.
Everyone who is curious is either not happy or wise and vice versa.
If fred is both wise and happy then john is not old or not brave.
Everyone who is not brave is happy or old.
Everyone who is not quiet is both creative and curious and vice versa.
If paul is strong then paul is both not calm and not curious and vice versa.
If john is not calm then someone is creative and vice versa.
Everyone who is rich or kind is both old and not kind and vice versa.
Everyone who is either not happy or rich is not kind or not calm and vice versa.
Everyone who is funny is both not kind and strong and vice versa.
If someone is both not humble and tall then someone is curious.
Everyone who is both brave and not creative is both not brave and wise and vice versa.
If someone is either not generous or generous then fred is both not old and not funny.
Fred is either not patient or funny.
Someone is curious.
Alice is either not creative or not brave.
Someone is either happy or humble.
Lucy is both strong and humble.
Paul is strong.
Someone is both happy and calm.
Someone is not creative. | Paul is kind. | contradiction | (![X]:((happy(X)&patient(X))=>(~calm(X)|tall(X))))&
(![X]:(brave(X)<=>(humble(X)<~>~wise(X))))&
(![X]:((rich(X)|~kind(X))=>(~brave(X)|~wise(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(~strong(john)))&
(![X]:(curious(X)<=>(~happy(X)<~>wise(X))))&
(((wise(fred)&happy(fred)))=>((~old(john)|~brave(john))))&
(![X]:(~brave(X)=>(happy(X)|old(X))))&
(![X]:(~quiet(X)<=>(creative(X)&curious(X))))&
((strong(paul))<=>((~calm(paul)&~curious(paul))))&
((~calm(john))<=>(?[X]:(creative(X))))&
(![X]:((rich(X)|kind(X))<=>(old(X)&~kind(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~kind(X)|~calm(X))))&
(![X]:(funny(X)<=>(~kind(X)&strong(X))))&
((?[X]:((~humble(X)&tall(X))))=>(?[X]:(curious(X))))&
(![X]:((brave(X)&~creative(X))<=>(~brave(X)&wise(X))))&
((?[X]:((~generous(X)<~>generous(X))))=>((~old(fred)&~funny(fred))))&
((~patient(fred)<~>funny(fred)))&
(?[X]:(curious(X)))&
((~creative(alice)<~>~brave(alice)))&
(?[X]:((happy(X)<~>humble(X))))&
((strong(lucy)&humble(lucy)))&
(strong(paul))&
(?[X]:((happy(X)&calm(X))))&
(?[X]:(~creative(X))) | kind(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6877408408439773840452529
% SZS output start Proof for 6877408408439773840452529
11. ! [X0] : ((kind(X0) | rich(X0)) <=> (~kind(X0) & old(X0))) [input p10]
25. kind(paul) [input hypothesis]
51. ! [X0] : (((kind(X0) | rich(X0)) | (kind(X0) | ~old(X0))) & ((~kind(X0) & old(X0)) | (~kind(X0) & ~rich(X0)))) [nnf transformation 11]
52. ! [X0] : ((kind(X0) | rich(X0) | kind(X0) | ~old(X0)) & ((~kind(X0) & old(X0)) | (~kind(X0) & ~rich(X0)))) [flattening 51]
102. ~kind(X0) | ~kind(X0) [cnf transformation 52]
135. kind(paul) [cnf transformation 25]
142. ~kind(X0) [duplicate literal removal 102]
259. $false [subsumption resolution 135,142]
% SZS output end Proof for 6877408408439773840452529
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not brave then alice is either not brave or not kind. If someone is either not strong or creative then lucy is humble or not tall and vice versa. Everyone who is both strong and not old is either strong or calm. If someone is either not quiet or not strong then someone is creative or generous. Everyone who is either not brave or happy is curious or not old. If lucy is not funny or not humble then someone is both not kind and creative. Everyone who is creative or not tall is quiet or not kind and vice versa. Everyone who is both not strong and creative is both not calm and not humble and vice versa. Everyone who is not tall or not happy is not creative or calm. Everyone who is old or not quiet is calm. Everyone who is not generous is either not strong or not rich. If alice is both not happy and not brave then alice is not happy. If alice is both not humble and curious then someone is either not quiet or funny and vice versa. If alice is both creative and not funny then lucy is creative. Everyone who is not humble or not strong is not happy. If someone is both brave and not calm then someone is generous and vice versa. Someone is both not brave and quiet. Alice is curious. Paul is both not tall and not brave. Someone is not happy or not curious. Fred is both not brave and not strong. Someone is not curious. Someone is either happy or not curious. | Alice is not humble. | neutral | (((strong(susan)|~brave(susan)))=>((~brave(alice)<~>~kind(alice))))&
((?[X]:((~strong(X)<~>creative(X))))<=>((humble(lucy)|~tall(lucy))))&
(![X]:((strong(X)&~old(X))=>(strong(X)<~>calm(X))))&
((?[X]:((~quiet(X)<~>~strong(X))))=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~brave(X)<~>happy(X))=>(curious(X)|~old(X))))&
(((~funny(lucy)|~humble(lucy)))=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((creative(X)|~tall(X))<=>(quiet(X)|~kind(X))))&
(![X]:((~strong(X)&creative(X))<=>(~calm(X)&~humble(X))))&
(![X]:((~tall(X)|~happy(X))=>(~creative(X)|calm(X))))&
(![X]:((old(X)|~quiet(X))=>calm(X)))&
(![X]:(~generous(X)=>(~strong(X)<~>~rich(X))))&
(((~happy(alice)&~brave(alice)))=>(~happy(alice)))&
(((~humble(alice)&curious(alice)))<=>(?[X]:((~quiet(X)<~>funny(X)))))&
(((creative(alice)&~funny(alice)))=>(creative(lucy)))&
(![X]:((~humble(X)|~strong(X))=>~happy(X)))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:(generous(X))))&
(?[X]:((~brave(X)&quiet(X))))&
(curious(alice))&
((~tall(paul)&~brave(paul)))&
(?[X]:((~happy(X)|~curious(X))))&
((~brave(fred)&~strong(fred)))&
(?[X]:(~curious(X)))&
(?[X]:((happy(X)<~>~curious(X)))) | ~humble(alice) | [] | null | 0 |
Everyone who is old or not curious is not curious.
Everyone who is either calm or generous is tall.
Everyone who is not brave is both kind and not strong and vice versa.
Everyone who is either quiet or not calm is not creative.
If paul is both generous and creative then someone is not funny or happy and vice versa.
Everyone who is patient or not wise is not curious.
If someone is either old or not wise then someone is both not calm and not strong and vice versa.
Everyone who is patient or strong is both kind and happy and vice versa.
Everyone who is both not calm and rich is both quiet and humble and vice versa.
If someone is kind or not old then mary is not rich.
Everyone who is both strong and patient is not rich or wise.
Everyone who is either not kind or not generous is either wise or not funny.
Everyone who is both not brave and curious is strong or brave and vice versa.
If someone is patient or not calm then mary is either happy or humble and vice versa.
If someone is both humble and not old then someone is both wise and not old and vice versa.
If someone is happy then lucy is both not wise and curious and vice versa.
Someone is creative or patient.
Someone is not wise or not calm.
Lucy is either tall or not funny.
Someone is either tall or not humble.
Someone is both not curious and quiet.
Fred is not curious or brave.
Mary is both not patient and not creative. | Mary is patient. | contradiction | (![X]:((old(X)|~curious(X))=>~curious(X)))&
(![X]:((calm(X)<~>generous(X))=>tall(X)))&
(![X]:(~brave(X)<=>(kind(X)&~strong(X))))&
(![X]:((quiet(X)<~>~calm(X))=>~creative(X)))&
(((generous(paul)&creative(paul)))<=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((patient(X)|~wise(X))=>~curious(X)))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((~calm(X)&~strong(X)))))&
(![X]:((patient(X)|strong(X))<=>(kind(X)&happy(X))))&
(![X]:((~calm(X)&rich(X))<=>(quiet(X)&humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(~rich(mary)))&
(![X]:((strong(X)&patient(X))=>(~rich(X)|wise(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)|brave(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(?[X]:((creative(X)|patient(X))))&
(?[X]:((~wise(X)|~calm(X))))&
((tall(lucy)<~>~funny(lucy)))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:((~curious(X)&quiet(X))))&
((~curious(fred)|brave(fred)))&
((~patient(mary)&~creative(mary))) | patient(mary) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5640831791526970061115279
% SZS output start Proof for 5640831791526970061115279
23. ~creative(mary) & ~patient(mary) [input p22]
24. patient(mary) [input hypothesis]
145. ~patient(mary) [cnf transformation 23]
147. patient(mary) [cnf transformation 24]
324. $false [subsumption resolution 147,145]
% SZS output end Proof for 5640831791526970061115279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either old or not kind then john is rich or funny and vice versa.
Everyone who is not brave is not strong or not curious and vice versa.
If fred is not calm or not creative then mary is both wise and not patient and vice versa.
If fred is not funny or kind then someone is both wise and generous and vice versa.
If someone is curious or not calm then someone is either brave or happy and vice versa.
If someone is not brave or not generous then fred is both not humble and kind and vice versa.
Everyone who is funny is either not old or calm.
Everyone who is either generous or not quiet is curious or calm and vice versa.
Everyone who is either not humble or old is either not calm or happy.
If susan is both brave and quiet then susan is curious and vice versa.
Everyone who is either not brave or wise is either not tall or tall.
If john is both not creative and not brave then someone is either rich or not humble.
Everyone who is either kind or not calm is either strong or not wise and vice versa.
If someone is strong or quiet then someone is either old or not humble and vice versa.
If john is not funny then fred is either quiet or humble.
Everyone who is creative or not creative is either not happy or calm and vice versa.
Someone is either not brave or not kind.
Fred is not brave.
Paul is not strong or not creative.
Someone is creative or quiet.
Paul is not brave or not humble.
Lucy is not generous or quiet.
Someone is both not old and patient. | John is not quiet. | neutral | ((?[X]:((old(X)<~>~kind(X))))<=>((rich(john)|funny(john))))&
(![X]:(~brave(X)<=>(~strong(X)|~curious(X))))&
(((~calm(fred)|~creative(fred)))<=>((wise(mary)&~patient(mary))))&
(((~funny(fred)|kind(fred)))<=>(?[X]:((wise(X)&generous(X)))))&
((?[X]:((curious(X)|~calm(X))))<=>(?[X]:((brave(X)<~>happy(X)))))&
((?[X]:((~brave(X)|~generous(X))))<=>((~humble(fred)&kind(fred))))&
(![X]:(funny(X)=>(~old(X)<~>calm(X))))&
(![X]:((generous(X)<~>~quiet(X))<=>(curious(X)|calm(X))))&
(![X]:((~humble(X)<~>old(X))=>(~calm(X)<~>happy(X))))&
(((brave(susan)&quiet(susan)))<=>(curious(susan)))&
(![X]:((~brave(X)<~>wise(X))=>(~tall(X)<~>tall(X))))&
(((~creative(john)&~brave(john)))=>(?[X]:((rich(X)<~>~humble(X)))))&
(![X]:((kind(X)<~>~calm(X))<=>(strong(X)<~>~wise(X))))&
((?[X]:((strong(X)|quiet(X))))<=>(?[X]:((old(X)<~>~humble(X)))))&
((~funny(john))=>((quiet(fred)<~>humble(fred))))&
(![X]:((creative(X)|~creative(X))<=>(~happy(X)<~>calm(X))))&
(?[X]:((~brave(X)<~>~kind(X))))&
(~brave(fred))&
((~strong(paul)|~creative(paul)))&
(?[X]:((creative(X)|quiet(X))))&
((~brave(paul)|~humble(paul)))&
((~generous(lucy)|quiet(lucy)))&
(?[X]:((~old(X)&patient(X)))) | ~quiet(john) | [] | null | 0 |
If someone is not kind or humble then someone is either not rich or not patient and vice versa. Everyone who is not quiet or brave is both not wise and rich and vice versa. If fred is either not curious or strong then paul is both patient and not patient and vice versa. Everyone who is either kind or not wise is either generous or patient and vice versa. If someone is not kind or quiet then paul is not old or strong and vice versa. If someone is not old or funny then someone is not kind and vice versa. Everyone who is both creative and not humble is either generous or quiet. If someone is not happy then someone is either humble or not brave. Everyone who is generous or not rich is both curious and humble and vice versa. If someone is old or not quiet then someone is not kind or strong and vice versa. If someone is curious then alice is either curious or not quiet and vice versa. Everyone who is old or creative is both not quiet and happy and vice versa. If john is happy then alice is either wise or not rich. Everyone who is either brave or not humble is patient or not humble and vice versa. Everyone who is quiet or not patient is not quiet and vice versa. Everyone who is either not tall or not humble is not happy or tall and vice versa. Someone is either rich or humble. Someone is old or quiet. Someone is generous or not quiet. Paul is not funny or not quiet. Someone is creative or rich. Someone is not curious. | Fred is strong. | neutral | ((?[X]:((~kind(X)|humble(X))))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
(![X]:((~quiet(X)|brave(X))<=>(~wise(X)&rich(X))))&
(((~curious(fred)<~>strong(fred)))<=>((patient(paul)&~patient(paul))))&
(![X]:((kind(X)<~>~wise(X))<=>(generous(X)<~>patient(X))))&
((?[X]:((~kind(X)|quiet(X))))<=>((~old(paul)|strong(paul))))&
((?[X]:((~old(X)|funny(X))))<=>(?[X]:(~kind(X))))&
(![X]:((creative(X)&~humble(X))=>(generous(X)<~>quiet(X))))&
((?[X]:(~happy(X)))=>(?[X]:((humble(X)<~>~brave(X)))))&
(![X]:((generous(X)|~rich(X))<=>(curious(X)&humble(X))))&
((?[X]:((old(X)|~quiet(X))))<=>(?[X]:((~kind(X)|strong(X)))))&
((?[X]:(curious(X)))<=>((curious(alice)<~>~quiet(alice))))&
(![X]:((old(X)|creative(X))<=>(~quiet(X)&happy(X))))&
((happy(john))=>((wise(alice)<~>~rich(alice))))&
(![X]:((brave(X)<~>~humble(X))<=>(patient(X)|~humble(X))))&
(![X]:((quiet(X)|~patient(X))<=>~quiet(X)))&
(![X]:((~tall(X)<~>~humble(X))<=>(~happy(X)|tall(X))))&
(?[X]:((rich(X)<~>humble(X))))&
(?[X]:((old(X)|quiet(X))))&
(?[X]:((generous(X)|~quiet(X))))&
((~funny(paul)|~quiet(paul)))&
(?[X]:((creative(X)|rich(X))))&
(?[X]:(~curious(X))) | strong(fred) | [] | null | 0 |
If someone is curious or not old then someone is not humble or kind and vice versa.
Everyone who is both humble and calm is not tall or not brave and vice versa.
Everyone who is either kind or not patient is not wise or not strong and vice versa.
Everyone who is not quiet or old is both patient and happy and vice versa.
If someone is not funny or generous then alice is quiet or not rich and vice versa.
If lucy is not curious then paul is either humble or old.
Everyone who is tall is both not curious and kind and vice versa.
If lucy is quiet or tall then susan is humble or not patient.
If john is either not calm or not strong then someone is not creative or not humble and vice versa.
If lucy is not curious then fred is both not patient and curious.
Everyone who is either happy or not curious is either not kind or humble and vice versa.
Everyone who is both not quiet and not wise is strong or quiet and vice versa.
If someone is not strong or rich then mary is not curious or not tall.
Everyone who is either not curious or strong is not kind and vice versa.
If paul is either not kind or not strong then mary is not old or brave and vice versa.
Everyone who is either not old or not humble is both rich and not funny and vice versa.
Someone is either not creative or not calm.
Someone is either quiet or not curious.
Someone is either funny or not old.
Someone is both not wise and strong.
Someone is either patient or not generous.
Someone is rich or not wise. | Lucy is wise. | entailment | ((?[X]:((curious(X)|~old(X))))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((humble(X)&calm(X))<=>(~tall(X)|~brave(X))))&
(![X]:((kind(X)<~>~patient(X))<=>(~wise(X)|~strong(X))))&
(![X]:((~quiet(X)|old(X))<=>(patient(X)&happy(X))))&
((?[X]:((~funny(X)|generous(X))))<=>((quiet(alice)|~rich(alice))))&
((~curious(lucy))=>((humble(paul)<~>old(paul))))&
(![X]:(tall(X)<=>(~curious(X)&kind(X))))&
(((quiet(lucy)|tall(lucy)))=>((humble(susan)|~patient(susan))))&
(((~calm(john)<~>~strong(john)))<=>(?[X]:((~creative(X)|~humble(X)))))&
((~curious(lucy))=>((~patient(fred)&curious(fred))))&
(![X]:((happy(X)<~>~curious(X))<=>(~kind(X)<~>humble(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(strong(X)|quiet(X))))&
((?[X]:((~strong(X)|rich(X))))=>((~curious(mary)|~tall(mary))))&
(![X]:((~curious(X)<~>strong(X))<=>~kind(X)))&
(((~kind(paul)<~>~strong(paul)))<=>((~old(mary)|brave(mary))))&
(![X]:((~old(X)<~>~humble(X))<=>(rich(X)&~funny(X))))&
(?[X]:((~creative(X)<~>~calm(X))))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((funny(X)<~>~old(X))))&
(?[X]:((~wise(X)&strong(X))))&
(?[X]:((patient(X)<~>~generous(X))))&
(?[X]:((rich(X)|~wise(X)))) | wise(lucy) | [
"p2",
"p3",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2584671909979393523238355
% SZS output start Proof for 2584671909979393523238355
3. ! [X0] : ((kind(X0) <~> ~patient(X0)) <=> (~strong(X0) | ~wise(X0))) [input p2]
4. ! [X0] : ((old(X0) | ~quiet(X0)) <=> (happy(X0) & patient(X0))) [input p3]
10. ~curious(lucy) => (curious(fred) & ~patient(fred)) [input p9]
12. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> (quiet(X0) | strong(X0))) [input p11]
14. ! [X0] : ((~curious(X0) <~> strong(X0)) <=> ~kind(X0)) [input p13]
23. ~wise(lucy) [input hypothesis]
28. (curious(fred) & ~patient(fred)) | curious(lucy) [ennf transformation 10]
38. ! [X0] : ((((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (strong(X0) & wise(X0))) & ((~strong(X0) | ~wise(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0))))) [nnf transformation 3]
39. ! [X0] : ((((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (strong(X0) & wise(X0))) & (~strong(X0) | ~wise(X0) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0))))) [flattening 38]
40. ! [X0] : (((old(X0) | ~quiet(X0)) | (~happy(X0) | ~patient(X0))) & ((happy(X0) & patient(X0)) | (~old(X0) & quiet(X0)))) [nnf transformation 4]
41. ! [X0] : ((old(X0) | ~quiet(X0) | ~happy(X0) | ~patient(X0)) & ((happy(X0) & patient(X0)) | (~old(X0) & quiet(X0)))) [flattening 40]
55. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | (wise(X0) | quiet(X0)))) [nnf transformation 12]
56. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | wise(X0) | quiet(X0))) [flattening 55]
57. ! [X0] : ((((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | kind(X0)) & (~kind(X0) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0))))) [nnf transformation 14]
89. ~patient(X0) | kind(X0) | wise(X0) [cnf transformation 39]
93. quiet(X0) | patient(X0) [cnf transformation 41]
115. ~patient(fred) | curious(lucy) [cnf transformation 28]
125. quiet(X0) | strong(X0) | wise(X0) | quiet(X0) [cnf transformation 56]
127. ~quiet(X0) | ~quiet(X0) [cnf transformation 56]
133. ~strong(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 57]
159. ~wise(lucy) [cnf transformation 23]
160. quiet(X0) | strong(X0) | wise(X0) [duplicate literal removal 125]
161. ~quiet(X0) [duplicate literal removal 127]
221. 15 <=> curious(lucy) [avatar definition]
223. curious(lucy) <- (15) [avatar component clause 221]
283. 28 <=> patient(fred) [avatar definition]
285. ~patient(fred) <- (~28) [avatar component clause 283]
286. 15 | ~28 [avatar split clause 115,283,221]
287. strong(X0) | wise(X0) [subsumption resolution 160,161]
350. patient(X0) [resolution 93,161]
366. kind(X0) | wise(X0) [resolution 89,350]
403. ~curious(X0) | ~kind(X0) | wise(X0) [resolution 133,287]
414. ~curious(X0) | wise(X0) [subsumption resolution 403,366]
460. $false <- (~28) [subsumption resolution 285,350]
461. 28 [avatar contradiction clause 460]
582. wise(lucy) <- (15) [resolution 414,223]
585. $false <- (15) [subsumption resolution 582,159]
586. ~15 [avatar contradiction clause 585]
587. $false [avatar sat refutation 286,461,586]
% SZS output end Proof for 2584671909979393523238355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and happy is either strong or not rich and vice versa.
Everyone who is not rich or humble is both curious and humble.
If paul is either humble or not funny then someone is both calm and quiet and vice versa.
Everyone who is both curious and not curious is either rich or not wise and vice versa.
Everyone who is not wise or not funny is either creative or not patient and vice versa.
Everyone who is both not calm and not brave is humble or kind and vice versa.
Everyone who is kind or calm is not calm or not creative.
Everyone who is both not funny and not rich is both calm and not old and vice versa.
Everyone who is either not generous or not brave is both humble and happy and vice versa.
Everyone who is not old or rich is curious.
If someone is either humble or not curious then lucy is both not humble and creative.
If alice is not funny or not wise then alice is strong or old and vice versa.
Everyone who is not old is either not brave or not generous and vice versa.
If someone is not rich then mary is not curious or creative.
Everyone who is not brave or brave is not humble or happy and vice versa.
Someone is either humble or not quiet.
Lucy is either old or generous.
Paul is both generous and not quiet.
Someone is not curious or brave.
Mary is either rich or not patient.
Mary is not funny. | Mary is not creative. | contradiction | (![X]:((~curious(X)&happy(X))<=>(strong(X)<~>~rich(X))))&
(![X]:((~rich(X)|humble(X))=>(curious(X)&humble(X))))&
(((humble(paul)<~>~funny(paul)))<=>(?[X]:((calm(X)&quiet(X)))))&
(![X]:((curious(X)&~curious(X))<=>(rich(X)<~>~wise(X))))&
(![X]:((~wise(X)|~funny(X))<=>(creative(X)<~>~patient(X))))&
(![X]:((~calm(X)&~brave(X))<=>(humble(X)|kind(X))))&
(![X]:((kind(X)|calm(X))=>(~calm(X)|~creative(X))))&
(![X]:((~funny(X)&~rich(X))<=>(calm(X)&~old(X))))&
(![X]:((~generous(X)<~>~brave(X))<=>(humble(X)&happy(X))))&
(![X]:((~old(X)|rich(X))=>curious(X)))&
((?[X]:((humble(X)<~>~curious(X))))=>((~humble(lucy)&creative(lucy))))&
(((~funny(alice)|~wise(alice)))<=>((strong(alice)|old(alice))))&
(![X]:(~old(X)<=>(~brave(X)<~>~generous(X))))&
((?[X]:(~rich(X)))=>((~curious(mary)|creative(mary))))&
(![X]:((~brave(X)|brave(X))<=>(~humble(X)|happy(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
((old(lucy)<~>generous(lucy)))&
((generous(paul)&~quiet(paul)))&
(?[X]:((~curious(X)|brave(X))))&
((rich(mary)<~>~patient(mary)))&
(~funny(mary)) | ~creative(mary) | [
"p1",
"p4",
"p9",
"p13",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1799901762111675948468643
% SZS output start Proof for 1799901762111675948468643
2. ! [X0] : ((humble(X0) | ~rich(X0)) => (humble(X0) & curious(X0))) [input p1]
5. ! [X0] : ((~funny(X0) | ~wise(X0)) <=> (creative(X0) <~> ~patient(X0))) [input p4]
10. ! [X0] : ((rich(X0) | ~old(X0)) => curious(X0)) [input p9]
14. ? [X0] : ~rich(X0) => (creative(mary) | ~curious(mary)) [input p13]
20. rich(mary) <~> ~patient(mary) [input p19]
21. ~funny(mary) [input p20]
22. ~creative(mary) [input hypothesis]
23. ! [X0] : ((humble(X0) & curious(X0)) | (~humble(X0) & rich(X0))) [ennf transformation 2]
26. ! [X0] : (curious(X0) | (~rich(X0) & old(X0))) [ennf transformation 10]
28. (creative(mary) | ~curious(mary)) | ! [X0] : rich(X0) [ennf transformation 14]
29. creative(mary) | ~curious(mary) | ! [X0] : rich(X0) [flattening 28]
38. ! [X0] : (((~funny(X0) | ~wise(X0)) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | (funny(X0) & wise(X0)))) [nnf transformation 5]
39. ! [X0] : ((~funny(X0) | ~wise(X0) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | (funny(X0) & wise(X0)))) [flattening 38]
58. (patient(mary) | ~rich(mary)) & (~patient(mary) | rich(mary)) [nnf transformation 20]
65. rich(X0) | curious(X0) [cnf transformation 23]
82. ~patient(X0) | creative(X0) | funny(X0) [cnf transformation 39]
105. curious(X0) | ~rich(X0) [cnf transformation 26]
118. creative(mary) | ~curious(mary) | rich(X0) [cnf transformation 29]
131. patient(mary) | ~rich(mary) [cnf transformation 58]
132. ~funny(mary) [cnf transformation 21]
133. ~creative(mary) [cnf transformation 22]
164. curious(X0) [subsumption resolution 105,65]
202. creative(mary) | rich(X0) [subsumption resolution 118,164]
204. 13 <=> ! [X0] : rich(X0) [avatar definition]
205. rich(X0) <- (13) [avatar component clause 204]
207. 14 <=> creative(mary) [avatar definition]
208. ~creative(mary) <- (~14) [avatar component clause 207]
210. 13 | 14 [avatar split clause 202,207,204]
233. 19 <=> rich(mary) [avatar definition]
235. ~rich(mary) <- (~19) [avatar component clause 233]
237. 20 <=> patient(mary) [avatar definition]
239. patient(mary) <- (20) [avatar component clause 237]
240. ~19 | 20 [avatar split clause 131,237,233]
242. ~14 [avatar split clause 133,207]
243. $false <- (13, ~19) [resolution 235,205]
244. ~13 | 19 [avatar contradiction clause 243]
266. creative(mary) | funny(mary) <- (20) [resolution 82,239]
267. funny(mary) <- (~14, 20) [subsumption resolution 266,208]
268. $false <- (~14, 20) [subsumption resolution 267,132]
269. 14 | ~20 [avatar contradiction clause 268]
270. $false [avatar sat refutation 210,240,242,244,269]
% SZS output end Proof for 1799901762111675948468643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and strong is both happy and not funny.
If someone is patient or not calm then paul is both not rich and not happy and vice versa.
If someone is both rich and not patient then someone is both not strong and happy and vice versa.
If susan is old or strong then susan is not funny or not kind.
Everyone who is both not funny and not creative is not wise and vice versa.
Everyone who is not tall or not generous is not strong or wise and vice versa.
If mary is creative then fred is both kind and not generous and vice versa.
Everyone who is not patient is not quiet or not rich and vice versa.
If alice is not kind or not patient then susan is not patient and vice versa.
If someone is either funny or wise then paul is both funny and calm and vice versa.
If someone is not brave or not wise then someone is either old or strong.
If someone is both not quiet and not wise then someone is both not quiet and tall and vice versa.
Everyone who is not strong or tall is either kind or not wise.
Everyone who is not brave or not strong is both happy and humble.
Everyone who is either not curious or not quiet is both happy and not wise and vice versa.
If someone is curious or happy then john is either tall or creative.
Paul is not wise or patient.
Lucy is not funny.
Someone is wise or calm.
Mary is calm.
Susan is rich or not kind.
Someone is both happy and creative.
Someone is not brave or humble. | Paul is kind. | contradiction | (![X]:((wise(X)&strong(X))=>(happy(X)&~funny(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((~rich(paul)&~happy(paul))))&
((?[X]:((rich(X)&~patient(X))))<=>(?[X]:((~strong(X)&happy(X)))))&
(((old(susan)|strong(susan)))=>((~funny(susan)|~kind(susan))))&
(![X]:((~funny(X)&~creative(X))<=>~wise(X)))&
(![X]:((~tall(X)|~generous(X))<=>(~strong(X)|wise(X))))&
((creative(mary))<=>((kind(fred)&~generous(fred))))&
(![X]:(~patient(X)<=>(~quiet(X)|~rich(X))))&
(((~kind(alice)|~patient(alice)))<=>(~patient(susan)))&
((?[X]:((funny(X)<~>wise(X))))<=>((funny(paul)&calm(paul))))&
((?[X]:((~brave(X)|~wise(X))))=>(?[X]:((old(X)<~>strong(X)))))&
((?[X]:((~quiet(X)&~wise(X))))<=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((~strong(X)|tall(X))=>(kind(X)<~>~wise(X))))&
(![X]:((~brave(X)|~strong(X))=>(happy(X)&humble(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(happy(X)&~wise(X))))&
((?[X]:((curious(X)|happy(X))))=>((tall(john)<~>creative(john))))&
((~wise(paul)|patient(paul)))&
(~funny(lucy))&
(?[X]:((wise(X)|calm(X))))&
(calm(mary))&
((rich(susan)|~kind(susan)))&
(?[X]:((happy(X)&creative(X))))&
(?[X]:((~brave(X)|humble(X)))) | kind(paul) | [
"p1",
"p5",
"p7",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7441203102507856535101830
% SZS output start Proof for 7441203102507856535101830
2. ? [X0] : (~calm(X0) | patient(X0)) <=> (~happy(paul) & ~rich(paul)) [input p1]
6. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (wise(X0) | ~strong(X0))) [input p5]
8. ! [X0] : (~patient(X0) <=> (~rich(X0) | ~quiet(X0))) [input p7]
13. ! [X0] : ((tall(X0) | ~strong(X0)) => (kind(X0) <~> ~wise(X0))) [input p12]
17. patient(paul) | ~wise(paul) [input p16]
24. kind(paul) [input hypothesis]
37. ! [X0] : ((kind(X0) <~> ~wise(X0)) | (~tall(X0) & strong(X0))) [ennf transformation 13]
40. (? [X0] : (~calm(X0) | patient(X0)) | (happy(paul) | rich(paul))) & ((~happy(paul) & ~rich(paul)) | ! [X0] : (calm(X0) & ~patient(X0))) [nnf transformation 2]
41. (? [X0] : (~calm(X0) | patient(X0)) | happy(paul) | rich(paul)) & ((~happy(paul) & ~rich(paul)) | ! [X0] : (calm(X0) & ~patient(X0))) [flattening 40]
42. (? [X0] : (~calm(X0) | patient(X0)) | happy(paul) | rich(paul)) & ((~happy(paul) & ~rich(paul)) | ! [X1] : (calm(X1) & ~patient(X1))) [rectify 41]
43. ? [X0] : (~calm(X0) | patient(X0)) => (~calm(sK0) | patient(sK0)) [choice axiom]
44. ((~calm(sK0) | patient(sK0)) | happy(paul) | rich(paul)) & ((~happy(paul) & ~rich(paul)) | ! [X1] : (calm(X1) & ~patient(X1))) [skolemisation 42,43]
52. ! [X0] : (((~generous(X0) | ~tall(X0)) | (~wise(X0) & strong(X0))) & ((wise(X0) | ~strong(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 6]
53. ! [X0] : ((~generous(X0) | ~tall(X0) | (~wise(X0) & strong(X0))) & (wise(X0) | ~strong(X0) | (generous(X0) & tall(X0)))) [flattening 52]
56. ! [X0] : ((~patient(X0) | (rich(X0) & quiet(X0))) & ((~rich(X0) | ~quiet(X0)) | patient(X0))) [nnf transformation 8]
57. ! [X0] : ((~patient(X0) | (rich(X0) & quiet(X0))) & (~rich(X0) | ~quiet(X0) | patient(X0))) [flattening 56]
74. ! [X0] : (((wise(X0) | ~kind(X0)) & (~wise(X0) | kind(X0))) | (~tall(X0) & strong(X0))) [nnf transformation 37]
84. ~rich(paul) | ~patient(X1) [cnf transformation 44]
98. ~strong(X0) | wise(X0) | tall(X0) [cnf transformation 53]
107. ~patient(X0) | rich(X0) [cnf transformation 57]
125. ~kind(X0) | wise(X0) | strong(X0) [cnf transformation 74]
126. ~tall(X0) | ~kind(X0) | wise(X0) [cnf transformation 74]
138. patient(paul) | ~wise(paul) [cnf transformation 17]
145. kind(paul) [cnf transformation 24]
147. 1 <=> rich(paul) [avatar definition]
168. 6 <=> ! [X1] : ~patient(X1) [avatar definition]
169. ~patient(X1) <- (6) [avatar component clause 168]
172. 6 | ~1 [avatar split clause 84,147,168]
330. 41 <=> wise(paul) [avatar definition]
332. ~wise(paul) <- (~41) [avatar component clause 330]
334. 42 <=> patient(paul) [avatar definition]
336. patient(paul) <- (42) [avatar component clause 334]
337. ~41 | 42 [avatar split clause 138,334,330]
410. rich(paul) <- (42) [resolution 336,107]
414. 1 | ~42 [avatar split clause 410,334,147]
416. $false <- (6, 42) [resolution 169,336]
417. ~6 | ~42 [avatar contradiction clause 416]
470. wise(paul) | strong(paul) [resolution 125,145]
471. strong(paul) <- (~41) [subsumption resolution 470,332]
481. wise(paul) | tall(paul) <- (~41) [resolution 471,98]
484. tall(paul) <- (~41) [subsumption resolution 481,332]
530. ~kind(paul) | wise(paul) <- (~41) [resolution 484,126]
532. wise(paul) <- (~41) [subsumption resolution 530,145]
533. $false <- (~41) [subsumption resolution 532,332]
534. 41 [avatar contradiction clause 533]
535. $false [avatar sat refutation 172,337,414,417,534]
% SZS output end Proof for 7441203102507856535101830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both humble and not rich then someone is both not rich and not funny and vice versa.
Everyone who is either quiet or not happy is either strong or not calm.
Everyone who is either quiet or curious is both not happy and not old.
If someone is not strong then mary is happy.
Everyone who is either tall or not funny is not quiet and vice versa.
Everyone who is not humble or not calm is both calm and quiet.
If john is wise then mary is both not happy and humble and vice versa.
If fred is either rich or kind then john is both not creative and happy.
If john is both not old and not strong then lucy is both not funny and happy.
Everyone who is not strong is calm or creative.
If someone is both old and calm then someone is either brave or not calm.
If lucy is strong then alice is kind.
If susan is either curious or not old then someone is not patient or not quiet.
If someone is both brave and curious then alice is both not humble and not wise.
Everyone who is strong or not brave is tall or not tall.
If fred is not curious then someone is both generous and happy and vice versa.
Someone is not humble.
Alice is rich or not calm.
Lucy is either quiet or not humble.
Lucy is not happy or not creative.
Someone is not funny or calm.
Someone is either happy or not funny.
Someone is both generous and not patient.
Someone is not creative or humble. | Susan is not calm. | contradiction | (((humble(susan)&~rich(susan)))<=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((quiet(X)<~>~happy(X))=>(strong(X)<~>~calm(X))))&
(![X]:((quiet(X)<~>curious(X))=>(~happy(X)&~old(X))))&
((?[X]:(~strong(X)))=>(happy(mary)))&
(![X]:((tall(X)<~>~funny(X))<=>~quiet(X)))&
(![X]:((~humble(X)|~calm(X))=>(calm(X)&quiet(X))))&
((wise(john))<=>((~happy(mary)&humble(mary))))&
(((rich(fred)<~>kind(fred)))=>((~creative(john)&happy(john))))&
(((~old(john)&~strong(john)))=>((~funny(lucy)&happy(lucy))))&
(![X]:(~strong(X)=>(calm(X)|creative(X))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:((brave(X)<~>~calm(X)))))&
((strong(lucy))=>(kind(alice)))&
(((curious(susan)<~>~old(susan)))=>(?[X]:((~patient(X)|~quiet(X)))))&
((?[X]:((brave(X)&curious(X))))=>((~humble(alice)&~wise(alice))))&
(![X]:((strong(X)|~brave(X))=>(tall(X)|~tall(X))))&
((~curious(fred))<=>(?[X]:((generous(X)&happy(X)))))&
(?[X]:(~humble(X)))&
((rich(alice)|~calm(alice)))&
((quiet(lucy)<~>~humble(lucy)))&
((~happy(lucy)|~creative(lucy)))&
(?[X]:((~funny(X)|calm(X))))&
(?[X]:((happy(X)<~>~funny(X))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((~creative(X)|humble(X)))) | ~calm(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6715008008302050948835610
% SZS output start Proof for 6715008008302050948835610
6. ! [X0] : ((~calm(X0) | ~humble(X0)) => (quiet(X0) & calm(X0))) [input p5]
25. ~calm(susan) [input hypothesis]
32. ! [X0] : ((quiet(X0) & calm(X0)) | (calm(X0) & humble(X0))) [ennf transformation 6]
92. calm(X0) | calm(X0) [cnf transformation 32]
125. ~calm(susan) [cnf transformation 25]
126. calm(X0) [duplicate literal removal 92]
284. $false [subsumption resolution 125,126]
% SZS output end Proof for 6715008008302050948835610
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If john is not calm then someone is either calm or not funny and vice versa.
If susan is not old or not brave then fred is either not generous or kind.
If someone is either humble or tall then someone is either not patient or not funny.
If someone is either kind or rich then someone is tall or strong.
If fred is not happy then john is either not kind or not brave.
Everyone who is both not creative and not old is either not strong or calm and vice versa.
Everyone who is both creative and not kind is creative and vice versa.
Everyone who is both funny and calm is curious or not creative and vice versa.
If john is not humble or not brave then someone is either not curious or wise and vice versa.
If alice is either tall or humble then lucy is both not brave and not funny and vice versa.
If someone is rich or strong then john is not happy.
Everyone who is not quiet or patient is both happy and rich and vice versa.
Everyone who is funny or not curious is both humble and not kind.
Everyone who is not calm is either not generous or not creative.
Everyone who is not patient or rich is either generous or old.
Everyone who is happy is not funny or creative and vice versa.
Someone is generous or brave.
John is not creative or not strong.
Someone is either calm or not wise.
Lucy is either creative or patient. | John is rich. | contradiction | ((~calm(john))<=>(?[X]:((calm(X)<~>~funny(X)))))&
(((~old(susan)|~brave(susan)))=>((~generous(fred)<~>kind(fred))))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:((~patient(X)<~>~funny(X)))))&
((?[X]:((kind(X)<~>rich(X))))=>(?[X]:((tall(X)|strong(X)))))&
((~happy(fred))=>((~kind(john)<~>~brave(john))))&
(![X]:((~creative(X)&~old(X))<=>(~strong(X)<~>calm(X))))&
(![X]:((creative(X)&~kind(X))<=>creative(X)))&
(![X]:((funny(X)&calm(X))<=>(curious(X)|~creative(X))))&
(((~humble(john)|~brave(john)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(((tall(alice)<~>humble(alice)))<=>((~brave(lucy)&~funny(lucy))))&
((?[X]:((rich(X)|strong(X))))=>(~happy(john)))&
(![X]:((~quiet(X)|patient(X))<=>(happy(X)&rich(X))))&
(![X]:((funny(X)|~curious(X))=>(humble(X)&~kind(X))))&
(![X]:(~calm(X)=>(~generous(X)<~>~creative(X))))&
(![X]:((~patient(X)|rich(X))=>(generous(X)<~>old(X))))&
(![X]:(happy(X)<=>(~funny(X)|creative(X))))&
(?[X]:((generous(X)|brave(X))))&
((~creative(john)|~strong(john)))&
(?[X]:((calm(X)<~>~wise(X))))&
((creative(lucy)<~>patient(lucy))) | rich(john) | [
"p0",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2212628636713746113478601
% SZS output start Proof for 2212628636713746113478601
1. ~calm(john) <=> ? [X0] : (calm(X0) <~> ~funny(X0)) [input p0]
8. ! [X0] : ((calm(X0) & funny(X0)) <=> (~creative(X0) | curious(X0))) [input p7]
11. ? [X0] : (strong(X0) | rich(X0)) => ~happy(john) [input p10]
16. ! [X0] : (happy(X0) <=> (creative(X0) | ~funny(X0))) [input p15]
21. rich(john) [input hypothesis]
28. ~happy(john) | ! [X0] : (~strong(X0) & ~rich(X0)) [ennf transformation 11]
32. (~calm(john) | ! [X0] : ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0)))) & (? [X0] : ((funny(X0) | ~calm(X0)) & (~funny(X0) | calm(X0))) | calm(john)) [nnf transformation 1]
33. (~calm(john) | ! [X0] : ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0)))) & (? [X1] : ((funny(X1) | ~calm(X1)) & (~funny(X1) | calm(X1))) | calm(john)) [rectify 32]
34. ? [X1] : ((funny(X1) | ~calm(X1)) & (~funny(X1) | calm(X1))) => ((funny(sK0) | ~calm(sK0)) & (~funny(sK0) | calm(sK0))) [choice axiom]
35. (~calm(john) | ! [X0] : ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0)))) & (((funny(sK0) | ~calm(sK0)) & (~funny(sK0) | calm(sK0))) | calm(john)) [skolemisation 33,34]
50. ! [X0] : (((calm(X0) & funny(X0)) | (creative(X0) & ~curious(X0))) & ((~creative(X0) | curious(X0)) | (~calm(X0) | ~funny(X0)))) [nnf transformation 8]
51. ! [X0] : (((calm(X0) & funny(X0)) | (creative(X0) & ~curious(X0))) & (~creative(X0) | curious(X0) | ~calm(X0) | ~funny(X0))) [flattening 50]
63. ! [X0] : ((happy(X0) | (~creative(X0) & funny(X0))) & ((creative(X0) | ~funny(X0)) | ~happy(X0))) [nnf transformation 16]
64. ! [X0] : ((happy(X0) | (~creative(X0) & funny(X0))) & (creative(X0) | ~funny(X0) | ~happy(X0))) [flattening 63]
73. ~calm(john) | ~funny(X0) | ~calm(X0) [cnf transformation 35]
100. creative(X0) | calm(X0) [cnf transformation 51]
113. ~happy(john) | ~rich(X0) [cnf transformation 28]
131. happy(X0) | funny(X0) [cnf transformation 64]
132. ~creative(X0) | happy(X0) [cnf transformation 64]
139. rich(john) [cnf transformation 21]
144. 2 <=> calm(john) [avatar definition]
145. calm(john) <- (2) [avatar component clause 144]
146. ~calm(john) <- (~2) [avatar component clause 144]
149. 3 <=> ! [X0] : (~funny(X0) | ~calm(X0)) [avatar definition]
150. ~funny(X0) | ~calm(X0) <- (3) [avatar component clause 149]
151. 3 | ~2 [avatar split clause 73,144,149]
280. 31 <=> happy(john) [avatar definition]
282. ~happy(john) <- (~31) [avatar component clause 280]
285. 32 <=> ! [X0] : ~rich(X0) [avatar definition]
286. ~rich(X0) <- (32) [avatar component clause 285]
287. 32 | ~31 [avatar split clause 113,280,285]
342. happy(X0) | calm(X0) [resolution 132,100]
459. calm(john) <- (~31) [resolution 342,282]
461. $false <- (~2, ~31) [subsumption resolution 459,146]
462. 2 | 31 [avatar contradiction clause 461]
467. $false <- (32) [resolution 286,139]
470. ~32 [avatar contradiction clause 467]
473. funny(john) <- (~31) [resolution 282,131]
524. ~calm(john) <- (3, ~31) [resolution 473,150]
526. $false <- (2, 3, ~31) [subsumption resolution 524,145]
527. ~2 | ~3 | 31 [avatar contradiction clause 526]
528. $false [avatar sat refutation 151,287,462,470,527]
% SZS output end Proof for 2212628636713746113478601
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not creative is tall.
Everyone who is either not humble or not generous is curious.
Everyone who is not brave is both not happy and humble and vice versa.
If someone is either not old or not generous then someone is both calm and not wise and vice versa.
Everyone who is either not generous or not kind is not curious and vice versa.
If someone is either happy or creative then mary is kind or not rich.
If paul is calm or generous then someone is rich and vice versa.
If john is either not generous or not tall then someone is both generous and funny.
Everyone who is old or tall is both not patient and not funny.
If someone is either wise or kind then someone is both not funny and generous.
If someone is either not generous or not brave then susan is tall and vice versa.
If someone is not old then someone is not curious or not patient and vice versa.
Everyone who is both wise and patient is not brave or not humble and vice versa.
If alice is both tall and curious then someone is either happy or not tall and vice versa.
Everyone who is not wise or not humble is either rich or quiet and vice versa.
Everyone who is both generous and not brave is strong.
Someone is both not creative and rich.
Someone is both not old and not patient.
Someone is both kind and not patient.
Someone is calm.
Someone is strong or patient.
Someone is either humble or not calm.
Someone is not wise or old. | Mary is not brave. | contradiction | (![X]:((~tall(X)|~creative(X))=>tall(X)))&
(![X]:((~humble(X)<~>~generous(X))=>curious(X)))&
(![X]:(~brave(X)<=>(~happy(X)&humble(X))))&
((?[X]:((~old(X)<~>~generous(X))))<=>(?[X]:((calm(X)&~wise(X)))))&
(![X]:((~generous(X)<~>~kind(X))<=>~curious(X)))&
((?[X]:((happy(X)<~>creative(X))))=>((kind(mary)|~rich(mary))))&
(((calm(paul)|generous(paul)))<=>(?[X]:(rich(X))))&
(((~generous(john)<~>~tall(john)))=>(?[X]:((generous(X)&funny(X)))))&
(![X]:((old(X)|tall(X))=>(~patient(X)&~funny(X))))&
((?[X]:((wise(X)<~>kind(X))))=>(?[X]:((~funny(X)&generous(X)))))&
((?[X]:((~generous(X)<~>~brave(X))))<=>(tall(susan)))&
((?[X]:(~old(X)))<=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:((wise(X)&patient(X))<=>(~brave(X)|~humble(X))))&
(((tall(alice)&curious(alice)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
(![X]:((~wise(X)|~humble(X))<=>(rich(X)<~>quiet(X))))&
(![X]:((generous(X)&~brave(X))=>strong(X)))&
(?[X]:((~creative(X)&rich(X))))&
(?[X]:((~old(X)&~patient(X))))&
(?[X]:((kind(X)&~patient(X))))&
(?[X]:(calm(X)))&
(?[X]:((strong(X)|patient(X))))&
(?[X]:((humble(X)<~>~calm(X))))&
(?[X]:((~wise(X)|old(X)))) | ~brave(mary) | [
"p0",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8512580092684571830848555
% SZS output start Proof for 8512580092684571830848555
1. ! [X0] : ((~creative(X0) | ~tall(X0)) => tall(X0)) [input p0]
9. ! [X0] : ((tall(X0) | old(X0)) => (~funny(X0) & ~patient(X0))) [input p8]
13. ! [X0] : ((patient(X0) & wise(X0)) <=> (~humble(X0) | ~brave(X0))) [input p12]
24. ~brave(mary) [input hypothesis]
30. ! [X0] : (tall(X0) | (creative(X0) & tall(X0))) [ennf transformation 1]
35. ! [X0] : ((~funny(X0) & ~patient(X0)) | (~tall(X0) & ~old(X0))) [ennf transformation 9]
68. ! [X0] : (((patient(X0) & wise(X0)) | (humble(X0) & brave(X0))) & ((~humble(X0) | ~brave(X0)) | (~patient(X0) | ~wise(X0)))) [nnf transformation 13]
69. ! [X0] : (((patient(X0) & wise(X0)) | (humble(X0) & brave(X0))) & (~humble(X0) | ~brave(X0) | ~patient(X0) | ~wise(X0))) [flattening 68]
90. tall(X0) | tall(X0) [cnf transformation 30]
117. ~patient(X0) | ~tall(X0) [cnf transformation 35]
134. patient(X0) | brave(X0) [cnf transformation 69]
158. ~brave(mary) [cnf transformation 24]
159. tall(X0) [duplicate literal removal 90]
242. ~patient(X0) [subsumption resolution 117,159]
269. brave(X0) [subsumption resolution 134,242]
298. $false [subsumption resolution 158,269]
% SZS output end Proof for 8512580092684571830848555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both strong and old then alice is not patient and vice versa.
Everyone who is not humble is both not wise and quiet.
Everyone who is either tall or wise is humble and vice versa.
Everyone who is patient or wise is generous or not brave.
If paul is both tall and not rich then someone is strong and vice versa.
Everyone who is not strong or generous is either not rich or not wise.
Everyone who is both quiet and not humble is either rich or not rich.
If mary is either not wise or calm then someone is both kind and old.
Everyone who is not brave is tall or not calm and vice versa.
If someone is humble or not generous then lucy is both not kind and curious.
If someone is either not patient or quiet then fred is both patient and generous.
If someone is not funny or not strong then someone is generous.
If lucy is either not generous or calm then someone is quiet and vice versa.
Everyone who is not funny or not tall is both happy and brave.
Everyone who is either funny or kind is both happy and not rich.
Everyone who is brave is brave or not brave and vice versa.
Someone is not tall or not creative.
Someone is either not creative or not humble.
Someone is not generous.
Fred is either not creative or not strong.
Fred is not kind.
Someone is both happy and not creative. | Alice is not generous. | contradiction | (((strong(susan)&old(susan)))<=>(~patient(alice)))&
(![X]:(~humble(X)=>(~wise(X)&quiet(X))))&
(![X]:((tall(X)<~>wise(X))<=>humble(X)))&
(![X]:((patient(X)|wise(X))=>(generous(X)|~brave(X))))&
(((tall(paul)&~rich(paul)))<=>(?[X]:(strong(X))))&
(![X]:((~strong(X)|generous(X))=>(~rich(X)<~>~wise(X))))&
(![X]:((quiet(X)&~humble(X))=>(rich(X)<~>~rich(X))))&
(((~wise(mary)<~>calm(mary)))=>(?[X]:((kind(X)&old(X)))))&
(![X]:(~brave(X)<=>(tall(X)|~calm(X))))&
((?[X]:((humble(X)|~generous(X))))=>((~kind(lucy)&curious(lucy))))&
((?[X]:((~patient(X)<~>quiet(X))))=>((patient(fred)&generous(fred))))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:(generous(X))))&
(((~generous(lucy)<~>calm(lucy)))<=>(?[X]:(quiet(X))))&
(![X]:((~funny(X)|~tall(X))=>(happy(X)&brave(X))))&
(![X]:((funny(X)<~>kind(X))=>(happy(X)&~rich(X))))&
(![X]:(brave(X)<=>(brave(X)|~brave(X))))&
(?[X]:((~tall(X)|~creative(X))))&
(?[X]:((~creative(X)<~>~humble(X))))&
(?[X]:(~generous(X)))&
((~creative(fred)<~>~strong(fred)))&
(~kind(fred))&
(?[X]:((happy(X)&~creative(X)))) | ~generous(alice) | [
"p0",
"p3",
"p4",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2329506709284312020697514
% SZS output start Proof for 2329506709284312020697514
1. (old(susan) & strong(susan)) <=> ~patient(alice) [input p0]
4. ! [X0] : ((wise(X0) | patient(X0)) => (~brave(X0) | generous(X0))) [input p3]
5. (~rich(paul) & tall(paul)) <=> ? [X0] : strong(X0) [input p4]
9. ! [X0] : (~brave(X0) <=> (~calm(X0) | tall(X0))) [input p8]
14. ! [X0] : ((~tall(X0) | ~funny(X0)) => (brave(X0) & happy(X0))) [input p13]
16. ! [X0] : (brave(X0) <=> (~brave(X0) | brave(X0))) [input p15]
23. ~generous(alice) [input hypothesis]
25. ! [X0] : ((~tall(X0) | ~funny(X0)) => brave(X0)) [pure predicate removal 14]
30. ! [X0] : ((~brave(X0) | generous(X0)) | (~wise(X0) & ~patient(X0))) [ennf transformation 4]
31. ! [X0] : (~brave(X0) | generous(X0) | (~wise(X0) & ~patient(X0))) [flattening 30]
39. ! [X0] : (brave(X0) | (tall(X0) & funny(X0))) [ennf transformation 25]
41. ((old(susan) & strong(susan)) | patient(alice)) & (~patient(alice) | (~old(susan) | ~strong(susan))) [nnf transformation 1]
42. ((old(susan) & strong(susan)) | patient(alice)) & (~patient(alice) | ~old(susan) | ~strong(susan)) [flattening 41]
44. ((~rich(paul) & tall(paul)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | (rich(paul) | ~tall(paul))) [nnf transformation 5]
45. ((~rich(paul) & tall(paul)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | rich(paul) | ~tall(paul)) [flattening 44]
46. ((~rich(paul) & tall(paul)) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | rich(paul) | ~tall(paul)) [rectify 45]
47. ? [X1] : strong(X1) => strong(sK0) [choice axiom]
48. ((~rich(paul) & tall(paul)) | ! [X0] : ~strong(X0)) & (strong(sK0) | rich(paul) | ~tall(paul)) [skolemisation 46,47]
54. ! [X0] : ((~brave(X0) | (calm(X0) & ~tall(X0))) & ((~calm(X0) | tall(X0)) | brave(X0))) [nnf transformation 9]
55. ! [X0] : ((~brave(X0) | (calm(X0) & ~tall(X0))) & (~calm(X0) | tall(X0) | brave(X0))) [flattening 54]
65. ! [X0] : ((brave(X0) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | ~brave(X0))) [nnf transformation 16]
66. ! [X0] : ((brave(X0) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | ~brave(X0))) [flattening 65]
78. strong(susan) | patient(alice) [cnf transformation 42]
86. ~brave(X0) | generous(X0) | ~patient(X0) [cnf transformation 31]
89. tall(paul) | ~strong(X0) [cnf transformation 48]
102. ~brave(X0) | ~tall(X0) [cnf transformation 55]
117. brave(X0) | tall(X0) [cnf transformation 39]
122. brave(X0) | brave(X0) [cnf transformation 66]
131. ~generous(alice) [cnf transformation 23]
133. brave(X0) [duplicate literal removal 122]
135. 1 <=> patient(alice) [avatar definition]
137. patient(alice) <- (1) [avatar component clause 135]
144. 3 <=> strong(susan) [avatar definition]
146. strong(susan) <- (3) [avatar component clause 144]
147. 1 | 3 [avatar split clause 78,144,135]
152. 4 <=> ! [X0] : ~strong(X0) [avatar definition]
153. ~strong(X0) <- (4) [avatar component clause 152]
160. 6 <=> tall(paul) [avatar definition]
162. tall(paul) <- (6) [avatar component clause 160]
163. 4 | 6 [avatar split clause 89,160,152]
280. $false <- (3, 4) [subsumption resolution 146,153]
281. ~3 | ~4 [avatar contradiction clause 280]
285. ~tall(X0) [resolution 102,133]
289. $false <- (6) [resolution 285,162]
290. ~6 [avatar contradiction clause 289]
301. generous(X0) | ~patient(X0) | tall(X0) [resolution 86,117]
303. ~patient(X0) | generous(X0) [subsumption resolution 301,285]
352. generous(alice) <- (1) [resolution 303,137]
353. $false <- (1) [subsumption resolution 352,131]
354. ~1 [avatar contradiction clause 353]
355. $false [avatar sat refutation 147,163,281,290,354]
% SZS output end Proof for 2329506709284312020697514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or calm is both calm and quiet.
If someone is not generous or brave then john is either kind or not quiet and vice versa.
Everyone who is funny is both rich and calm.
Everyone who is both humble and happy is not rich.
Everyone who is old is not strong or not happy.
Everyone who is not happy is either rich or happy and vice versa.
Everyone who is creative or humble is not old or not creative and vice versa.
Everyone who is both old and funny is both not strong and rich.
If lucy is either happy or not wise then someone is wise or not curious and vice versa.
Everyone who is wise is both happy and not creative.
If paul is not strong or brave then someone is humble or tall.
If susan is patient or strong then someone is not strong and vice versa.
Everyone who is either not old or not funny is either not humble or funny.
Everyone who is either not generous or brave is patient and vice versa.
Everyone who is calm is not curious or patient.
Everyone who is both happy and not old is not creative.
Someone is both calm and patient.
Someone is either tall or not calm.
Alice is happy or calm.
John is either calm or not wise.
Paul is either wise or brave.
Someone is either not curious or not kind.
Someone is both not strong and brave. | John is not funny. | entailment | (![X]:((curious(X)|calm(X))=>(calm(X)&quiet(X))))&
((?[X]:((~generous(X)|brave(X))))<=>((kind(john)<~>~quiet(john))))&
(![X]:(funny(X)=>(rich(X)&calm(X))))&
(![X]:((humble(X)&happy(X))=>~rich(X)))&
(![X]:(old(X)=>(~strong(X)|~happy(X))))&
(![X]:(~happy(X)<=>(rich(X)<~>happy(X))))&
(![X]:((creative(X)|humble(X))<=>(~old(X)|~creative(X))))&
(![X]:((old(X)&funny(X))=>(~strong(X)&rich(X))))&
(((happy(lucy)<~>~wise(lucy)))<=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:(wise(X)=>(happy(X)&~creative(X))))&
(((~strong(paul)|brave(paul)))=>(?[X]:((humble(X)|tall(X)))))&
(((patient(susan)|strong(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((~old(X)<~>~funny(X))=>(~humble(X)<~>funny(X))))&
(![X]:((~generous(X)<~>brave(X))<=>patient(X)))&
(![X]:(calm(X)=>(~curious(X)|patient(X))))&
(![X]:((happy(X)&~old(X))=>~creative(X)))&
(?[X]:((calm(X)&patient(X))))&
(?[X]:((tall(X)<~>~calm(X))))&
((happy(alice)|calm(alice)))&
((calm(john)<~>~wise(john)))&
((wise(paul)<~>brave(paul)))&
(?[X]:((~curious(X)<~>~kind(X))))&
(?[X]:((~strong(X)&brave(X)))) | ~funny(john) | [
"p2",
"p3",
"p5",
"p6",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2543794766874812876115701
% SZS output start Proof for 2543794766874812876115701
3. ! [X0] : (funny(X0) => (calm(X0) & rich(X0))) [input p2]
4. ! [X0] : ((happy(X0) & humble(X0)) => ~rich(X0)) [input p3]
6. ! [X0] : (~happy(X0) <=> (rich(X0) <~> happy(X0))) [input p5]
7. ! [X0] : ((humble(X0) | creative(X0)) <=> (~creative(X0) | ~old(X0))) [input p6]
10. ! [X0] : (wise(X0) => (~creative(X0) & happy(X0))) [input p9]
20. calm(john) <~> ~wise(john) [input p19]
24. funny(john) [input hypothesis]
26. ! [X0] : ((calm(X0) & rich(X0)) | ~funny(X0)) [ennf transformation 3]
27. ! [X0] : (~rich(X0) | (~happy(X0) | ~humble(X0))) [ennf transformation 4]
28. ! [X0] : (~rich(X0) | ~happy(X0) | ~humble(X0)) [flattening 27]
33. ! [X0] : ((~creative(X0) & happy(X0)) | ~wise(X0)) [ennf transformation 10]
44. ! [X0] : ((~happy(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | happy(X0))) [nnf transformation 6]
45. ! [X0] : (((humble(X0) | creative(X0)) | (creative(X0) & old(X0))) & ((~creative(X0) | ~old(X0)) | (~humble(X0) & ~creative(X0)))) [nnf transformation 7]
46. ! [X0] : ((humble(X0) | creative(X0) | (creative(X0) & old(X0))) & (~creative(X0) | ~old(X0) | (~humble(X0) & ~creative(X0)))) [flattening 45]
65. (wise(john) | ~calm(john)) & (~wise(john) | calm(john)) [nnf transformation 20]
83. ~funny(X0) | calm(X0) [cnf transformation 26]
84. ~happy(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 28]
86. happy(X0) | rich(X0) | happy(X0) [cnf transformation 44]
89. ~happy(X0) | rich(X0) | ~happy(X0) [cnf transformation 44]
93. humble(X0) | creative(X0) | creative(X0) [cnf transformation 46]
102. ~wise(X0) | happy(X0) [cnf transformation 33]
103. ~wise(X0) | ~creative(X0) [cnf transformation 33]
125. wise(john) | ~calm(john) [cnf transformation 65]
132. funny(john) [cnf transformation 24]
136. creative(X0) | humble(X0) [duplicate literal removal 93]
137. happy(X0) | rich(X0) [duplicate literal removal 86]
138. ~happy(X0) | rich(X0) [duplicate literal removal 89]
167. rich(X0) [subsumption resolution 137,138]
254. 25 <=> calm(john) [avatar definition]
258. 26 <=> wise(john) [avatar definition]
260. wise(john) <- (26) [avatar component clause 258]
261. ~25 | 26 [avatar split clause 125,258,254]
286. calm(john) [resolution 83,132]
289. 25 [avatar split clause 286,254]
294. happy(john) <- (26) [resolution 102,260]
295. ~creative(john) <- (26) [resolution 103,260]
296. humble(john) <- (26) [resolution 136,295]
303. ~rich(john) | ~humble(john) <- (26) [resolution 84,294]
305. ~humble(john) <- (26) [subsumption resolution 303,167]
306. $false <- (26) [subsumption resolution 305,296]
307. ~26 [avatar contradiction clause 306]
308. $false [avatar sat refutation 261,289,307]
% SZS output end Proof for 2543794766874812876115701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not curious then someone is both happy and not creative and vice versa.
Everyone who is either not humble or not calm is both happy and not quiet and vice versa.
If alice is both quiet and not curious then someone is both kind and humble.
If paul is both not brave and kind then alice is both not generous and not calm.
Everyone who is calm or not funny is either tall or not old and vice versa.
Everyone who is either rich or not rich is either generous or curious and vice versa.
Everyone who is kind or rich is rich and vice versa.
If someone is both not kind and tall then someone is both patient and not wise.
Everyone who is both strong and rich is either not happy or generous.
If someone is either not quiet or not creative then susan is creative.
If someone is patient or happy then someone is either not curious or not generous and vice versa.
If someone is rich then fred is both not generous and funny and vice versa.
If john is creative or not humble then lucy is not quiet and vice versa.
If someone is not strong then paul is both not patient and wise.
If someone is curious then mary is either happy or not happy and vice versa.
If someone is both funny and not calm then lucy is either not generous or not calm.
John is both patient and humble.
Mary is either not kind or old.
Lucy is either quiet or not kind.
Susan is either wise or not strong.
Someone is rich.
Susan is wise.
Someone is generous.
Mary is both not quiet and not creative. | Mary is not funny. | neutral | ((~curious(lucy))<=>(?[X]:((happy(X)&~creative(X)))))&
(![X]:((~humble(X)<~>~calm(X))<=>(happy(X)&~quiet(X))))&
(((quiet(alice)&~curious(alice)))=>(?[X]:((kind(X)&humble(X)))))&
(((~brave(paul)&kind(paul)))=>((~generous(alice)&~calm(alice))))&
(![X]:((calm(X)|~funny(X))<=>(tall(X)<~>~old(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(generous(X)<~>curious(X))))&
(![X]:((kind(X)|rich(X))<=>rich(X)))&
((?[X]:((~kind(X)&tall(X))))=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((strong(X)&rich(X))=>(~happy(X)<~>generous(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))=>(creative(susan)))&
((?[X]:((patient(X)|happy(X))))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
((?[X]:(rich(X)))<=>((~generous(fred)&funny(fred))))&
(((creative(john)|~humble(john)))<=>(~quiet(lucy)))&
((?[X]:(~strong(X)))=>((~patient(paul)&wise(paul))))&
((?[X]:(curious(X)))<=>((happy(mary)<~>~happy(mary))))&
((?[X]:((funny(X)&~calm(X))))=>((~generous(lucy)<~>~calm(lucy))))&
((patient(john)&humble(john)))&
((~kind(mary)<~>old(mary)))&
((quiet(lucy)<~>~kind(lucy)))&
((wise(susan)<~>~strong(susan)))&
(?[X]:(rich(X)))&
(wise(susan))&
(?[X]:(generous(X)))&
((~quiet(mary)&~creative(mary))) | ~funny(mary) | [] | null | 0 |
If susan is either not generous or not patient then someone is happy and vice versa.
Everyone who is not generous or not quiet is old.
Everyone who is either not old or humble is both happy and not funny and vice versa.
Everyone who is both funny and calm is strong and vice versa.
If mary is both tall and not quiet then someone is both wise and not calm and vice versa.
Everyone who is both patient and strong is not kind.
If someone is both not quiet and not happy then fred is both not old and patient and vice versa.
Everyone who is either patient or not tall is both patient and generous.
Everyone who is generous is kind or not patient and vice versa.
If mary is not creative then susan is either generous or rich.
Everyone who is calm is either funny or not patient and vice versa.
Everyone who is humble is both not happy and not quiet.
If mary is either not funny or funny then someone is wise or not tall.
Everyone who is creative is humble or not kind.
If mary is not brave then paul is both not curious and calm.
Everyone who is happy is curious.
Someone is either not quiet or not strong.
Someone is both not rich and curious.
Susan is either old or not calm.
Alice is either creative or not generous.
Someone is both curious and wise.
Susan is not happy or not kind.
Fred is both not quiet and not tall.
Mary is not generous. | Fred is curious. | entailment | (((~generous(susan)<~>~patient(susan)))<=>(?[X]:(happy(X))))&
(![X]:((~generous(X)|~quiet(X))=>old(X)))&
(![X]:((~old(X)<~>humble(X))<=>(happy(X)&~funny(X))))&
(![X]:((funny(X)&calm(X))<=>strong(X)))&
(((tall(mary)&~quiet(mary)))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((patient(X)&strong(X))=>~kind(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>((~old(fred)&patient(fred))))&
(![X]:((patient(X)<~>~tall(X))=>(patient(X)&generous(X))))&
(![X]:(generous(X)<=>(kind(X)|~patient(X))))&
((~creative(mary))=>((generous(susan)<~>rich(susan))))&
(![X]:(calm(X)<=>(funny(X)<~>~patient(X))))&
(![X]:(humble(X)=>(~happy(X)&~quiet(X))))&
(((~funny(mary)<~>funny(mary)))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(creative(X)=>(humble(X)|~kind(X))))&
((~brave(mary))=>((~curious(paul)&calm(paul))))&
(![X]:(happy(X)=>curious(X)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~rich(X)&curious(X))))&
((old(susan)<~>~calm(susan)))&
((creative(alice)<~>~generous(alice)))&
(?[X]:((curious(X)&wise(X))))&
((~happy(susan)|~kind(susan)))&
((~quiet(fred)&~tall(fred)))&
(~generous(mary)) | curious(fred) | [
"p1",
"p6",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2554212295504559674435306
% SZS output start Proof for 2554212295504559674435306
2. ! [X0] : ((~quiet(X0) | ~generous(X0)) => old(X0)) [input p1]
7. ? [X0] : (~happy(X0) & ~quiet(X0)) <=> (patient(fred) & ~old(fred)) [input p6]
16. ! [X0] : (happy(X0) => curious(X0)) [input p15]
23. ~tall(fred) & ~quiet(fred) [input p22]
25. ~curious(fred) [input hypothesis]
27. ! [X0] : (old(X0) | (quiet(X0) & generous(X0))) [ennf transformation 2]
36. ! [X0] : (curious(X0) | ~happy(X0)) [ennf transformation 16]
50. (? [X0] : (~happy(X0) & ~quiet(X0)) | (~patient(fred) | old(fred))) & ((patient(fred) & ~old(fred)) | ! [X0] : (happy(X0) | quiet(X0))) [nnf transformation 7]
51. (? [X0] : (~happy(X0) & ~quiet(X0)) | ~patient(fred) | old(fred)) & ((patient(fred) & ~old(fred)) | ! [X0] : (happy(X0) | quiet(X0))) [flattening 50]
52. (? [X0] : (~happy(X0) & ~quiet(X0)) | ~patient(fred) | old(fred)) & ((patient(fred) & ~old(fred)) | ! [X1] : (happy(X1) | quiet(X1))) [rectify 51]
53. ? [X0] : (~happy(X0) & ~quiet(X0)) => (~happy(sK2) & ~quiet(sK2)) [choice axiom]
54. ((~happy(sK2) & ~quiet(sK2)) | ~patient(fred) | old(fred)) & ((patient(fred) & ~old(fred)) | ! [X1] : (happy(X1) | quiet(X1))) [skolemisation 52,53]
77. old(X0) | quiet(X0) [cnf transformation 27]
92. ~old(fred) | happy(X1) | quiet(X1) [cnf transformation 54]
114. ~happy(X0) | curious(X0) [cnf transformation 36]
126. ~quiet(fred) [cnf transformation 23]
129. ~curious(fred) [cnf transformation 25]
176. 10 <=> old(fred) [avatar definition]
177. ~old(fred) <- (~10) [avatar component clause 176]
194. 14 <=> ! [X1] : (happy(X1) | quiet(X1)) [avatar definition]
195. quiet(X1) | happy(X1) <- (14) [avatar component clause 194]
197. 14 | ~10 [avatar split clause 92,176,194]
263. quiet(fred) <- (~10) [resolution 77,177]
265. $false <- (~10) [subsumption resolution 263,126]
266. 10 [avatar contradiction clause 265]
273. happy(fred) <- (14) [resolution 195,126]
282. curious(fred) <- (14) [resolution 273,114]
283. $false <- (14) [subsumption resolution 282,129]
284. ~14 [avatar contradiction clause 283]
285. $false [avatar sat refutation 197,266,284]
% SZS output end Proof for 2554212295504559674435306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either kind or not old then someone is either wise or tall. Everyone who is both funny and not patient is either tall or not happy. If someone is either wise or not happy then someone is either calm or not tall. Everyone who is quiet or not humble is not wise. If susan is either calm or patient then lucy is kind. If someone is not generous or brave then paul is either not humble or happy. Everyone who is either not quiet or not calm is either not quiet or not rich and vice versa. Everyone who is old or not generous is both generous and curious and vice versa. If someone is both not creative and patient then mary is both quiet and patient and vice versa. If someone is not quiet or not funny then someone is wise or kind and vice versa. Everyone who is both strong and rich is either not curious or calm. If someone is not humble or not quiet then someone is both curious and strong. If john is both humble and rich then lucy is not generous or generous. If paul is patient then fred is either not brave or not old and vice versa. Everyone who is tall is quiet or not old and vice versa. Everyone who is both quiet and not rich is not rich and vice versa. Paul is not strong. Fred is both not old and patient. Lucy is humble or not strong. Someone is both curious and not rich. Someone is rich or not calm. Fred is strong. John is both tall and not old. Susan is either curious or happy. | Fred is not calm. | entailment | (((kind(mary)<~>~old(mary)))=>(?[X]:((wise(X)<~>tall(X)))))&
(![X]:((funny(X)&~patient(X))=>(tall(X)<~>~happy(X))))&
((?[X]:((wise(X)<~>~happy(X))))=>(?[X]:((calm(X)<~>~tall(X)))))&
(![X]:((quiet(X)|~humble(X))=>~wise(X)))&
(((calm(susan)<~>patient(susan)))=>(kind(lucy)))&
((?[X]:((~generous(X)|brave(X))))=>((~humble(paul)<~>happy(paul))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~quiet(X)<~>~rich(X))))&
(![X]:((old(X)|~generous(X))<=>(generous(X)&curious(X))))&
((?[X]:((~creative(X)&patient(X))))<=>((quiet(mary)&patient(mary))))&
((?[X]:((~quiet(X)|~funny(X))))<=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((strong(X)&rich(X))=>(~curious(X)<~>calm(X))))&
((?[X]:((~humble(X)|~quiet(X))))=>(?[X]:((curious(X)&strong(X)))))&
(((humble(john)&rich(john)))=>((~generous(lucy)|generous(lucy))))&
((patient(paul))<=>((~brave(fred)<~>~old(fred))))&
(![X]:(tall(X)<=>(quiet(X)|~old(X))))&
(![X]:((quiet(X)&~rich(X))<=>~rich(X)))&
(~strong(paul))&
((~old(fred)&patient(fred)))&
((humble(lucy)|~strong(lucy)))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((rich(X)|~calm(X))))&
(strong(fred))&
((tall(john)&~old(john)))&
((curious(susan)<~>happy(susan))) | ~calm(fred) | [
"p6",
"p7",
"p10",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8987499709772969732830766
% SZS output start Proof for 8987499709772969732830766
7. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~quiet(X0) <~> ~rich(X0))) [input p6]
8. ! [X0] : ((~generous(X0) | old(X0)) <=> (curious(X0) & generous(X0))) [input p7]
11. ! [X0] : ((rich(X0) & strong(X0)) => (~curious(X0) <~> calm(X0))) [input p10]
18. patient(fred) & ~old(fred) [input p17]
22. strong(fred) [input p21]
25. calm(fred) [input hypothesis]
36. ! [X0] : ((~curious(X0) <~> calm(X0)) | (~rich(X0) | ~strong(X0))) [ennf transformation 11]
37. ! [X0] : ((~curious(X0) <~> calm(X0)) | ~rich(X0) | ~strong(X0)) [flattening 36]
51. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0)))) & (((rich(X0) | quiet(X0)) & (~rich(X0) | ~quiet(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 7]
52. ! [X0] : (((~generous(X0) | old(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (generous(X0) & ~old(X0)))) [nnf transformation 8]
53. ! [X0] : ((~generous(X0) | old(X0) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | (generous(X0) & ~old(X0)))) [flattening 52]
64. ! [X0] : (((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | ~rich(X0) | ~strong(X0)) [nnf transformation 37]
97. ~rich(X0) | ~quiet(X0) | ~quiet(X0) | calm(X0) [cnf transformation 51]
98. rich(X0) | quiet(X0) | ~calm(X0) | quiet(X0) [cnf transformation 51]
101. ~calm(X0) | ~quiet(X0) | ~quiet(X0) | rich(X0) [cnf transformation 51]
102. calm(X0) | quiet(X0) | ~rich(X0) | quiet(X0) [cnf transformation 51]
105. generous(X0) | generous(X0) [cnf transformation 53]
108. ~generous(X0) | old(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 53]
118. ~calm(X0) | curious(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 64]
135. ~old(fred) [cnf transformation 18]
141. strong(fred) [cnf transformation 22]
146. calm(fred) [cnf transformation 25]
147. generous(X0) [duplicate literal removal 105]
148. ~curious(X0) | old(X0) | ~generous(X0) [duplicate literal removal 108]
149. ~rich(X0) | ~quiet(X0) | calm(X0) [duplicate literal removal 97]
150. rich(X0) | quiet(X0) | ~calm(X0) [duplicate literal removal 98]
151. ~quiet(X0) | ~calm(X0) | rich(X0) [duplicate literal removal 101]
152. ~rich(X0) | quiet(X0) | calm(X0) [duplicate literal removal 102]
218. 15 <=> ! [X0] : generous(X0) [avatar definition]
219. generous(X0) <- (15) [avatar component clause 218]
223. ~calm(X0) | rich(X0) [subsumption resolution 150,151]
224. ~rich(X0) | calm(X0) [subsumption resolution 149,152]
225. 15 [avatar split clause 147,218]
281. ~strong(X0) | ~rich(X0) | curious(X0) [subsumption resolution 118,224]
298. 32 <=> old(fred) [avatar definition]
299. ~old(fred) <- (~32) [avatar component clause 298]
313. ~32 [avatar split clause 135,298]
354. rich(fred) [resolution 223,146]
384. ~rich(fred) | curious(fred) [resolution 281,141]
386. curious(fred) [subsumption resolution 384,354]
387. old(fred) | ~generous(fred) [resolution 386,148]
388. ~generous(fred) <- (~32) [subsumption resolution 387,299]
389. $false <- (15, ~32) [subsumption resolution 388,219]
390. ~15 | 32 [avatar contradiction clause 389]
391. $false [avatar sat refutation 225,313,390]
% SZS output end Proof for 8987499709772969732830766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not curious is not patient.
Everyone who is both not rich and not happy is both not brave and not rich.
If someone is both not funny and not creative then someone is not creative and vice versa.
If paul is not generous or not wise then susan is both not generous and not strong and vice versa.
If paul is not wise then someone is not rich or brave and vice versa.
If someone is not tall then fred is either funny or not generous and vice versa.
If someone is not old or kind then susan is both not curious and not creative and vice versa.
If someone is not patient then someone is both not brave and wise and vice versa.
Everyone who is both not funny and generous is both old and not generous and vice versa.
Everyone who is either not brave or creative is both not quiet and not old and vice versa.
If someone is not curious or funny then someone is either patient or humble and vice versa.
Everyone who is both wise and not wise is happy or humble and vice versa.
Everyone who is not quiet or quiet is both not humble and not curious and vice versa.
Everyone who is both kind and humble is either patient or brave and vice versa.
Someone is either happy or not brave.
Lucy is both rich and not generous.
Fred is either funny or not quiet.
Paul is either strong or kind.
John is either old or not patient.
Someone is not happy or not rich.
Someone is not brave or not humble. | Susan is strong. | contradiction | (![X]:((creative(X)&~curious(X))=>~patient(X)))&
(![X]:((~rich(X)&~happy(X))=>(~brave(X)&~rich(X))))&
((?[X]:((~funny(X)&~creative(X))))<=>(?[X]:(~creative(X))))&
(((~generous(paul)|~wise(paul)))<=>((~generous(susan)&~strong(susan))))&
((~wise(paul))<=>(?[X]:((~rich(X)|brave(X)))))&
((?[X]:(~tall(X)))<=>((funny(fred)<~>~generous(fred))))&
((?[X]:((~old(X)|kind(X))))<=>((~curious(susan)&~creative(susan))))&
((?[X]:(~patient(X)))<=>(?[X]:((~brave(X)&wise(X)))))&
(![X]:((~funny(X)&generous(X))<=>(old(X)&~generous(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)&~old(X))))&
((?[X]:((~curious(X)|funny(X))))<=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((wise(X)&~wise(X))<=>(happy(X)|humble(X))))&
(![X]:((~quiet(X)|quiet(X))<=>(~humble(X)&~curious(X))))&
(![X]:((kind(X)&humble(X))<=>(patient(X)<~>brave(X))))&
(?[X]:((happy(X)<~>~brave(X))))&
((rich(lucy)&~generous(lucy)))&
((funny(fred)<~>~quiet(fred)))&
((strong(paul)<~>kind(paul)))&
((old(john)<~>~patient(john)))&
(?[X]:((~happy(X)|~rich(X))))&
(?[X]:((~brave(X)|~humble(X)))) | strong(susan) | [
"p3",
"p4",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9022338059700895312167214
% SZS output start Proof for 9022338059700895312167214
4. (~wise(paul) | ~generous(paul)) <=> (~strong(susan) & ~generous(susan)) [input p3]
5. ~wise(paul) <=> ? [X0] : (brave(X0) | ~rich(X0)) [input p4]
11. ? [X0] : (funny(X0) | ~curious(X0)) <=> ? [X0] : (patient(X0) <~> humble(X0)) [input p10]
12. ! [X0] : ((~wise(X0) & wise(X0)) <=> (humble(X0) | happy(X0))) [input p11]
13. ! [X0] : ((quiet(X0) | ~quiet(X0)) <=> (~curious(X0) & ~humble(X0))) [input p12]
14. ! [X0] : ((humble(X0) & kind(X0)) <=> (patient(X0) <~> brave(X0))) [input p13]
22. strong(susan) [input hypothesis]
25. ? [X0] : (funny(X0) | ~curious(X0)) <=> ? [X1] : (patient(X1) <~> humble(X1)) [rectify 11]
35. ((~wise(paul) | ~generous(paul)) | (strong(susan) | generous(susan))) & ((~strong(susan) & ~generous(susan)) | (wise(paul) & generous(paul))) [nnf transformation 4]
36. (~wise(paul) | ~generous(paul) | strong(susan) | generous(susan)) & ((~strong(susan) & ~generous(susan)) | (wise(paul) & generous(paul))) [flattening 35]
37. (~wise(paul) | ! [X0] : (~brave(X0) & rich(X0))) & (? [X0] : (brave(X0) | ~rich(X0)) | wise(paul)) [nnf transformation 5]
38. (~wise(paul) | ! [X0] : (~brave(X0) & rich(X0))) & (? [X1] : (brave(X1) | ~rich(X1)) | wise(paul)) [rectify 37]
39. ? [X1] : (brave(X1) | ~rich(X1)) => (brave(sK2) | ~rich(sK2)) [choice axiom]
40. (~wise(paul) | ! [X0] : (~brave(X0) & rich(X0))) & ((brave(sK2) | ~rich(sK2)) | wise(paul)) [skolemisation 38,39]
59. (? [X0] : (funny(X0) | ~curious(X0)) | ! [X1] : ((patient(X1) | ~humble(X1)) & (humble(X1) | ~patient(X1)))) & (? [X1] : ((~humble(X1) | ~patient(X1)) & (humble(X1) | patient(X1))) | ! [X0] : (~funny(X0) & curious(X0))) [nnf transformation 25]
60. (? [X0] : (funny(X0) | ~curious(X0)) | ! [X1] : ((patient(X1) | ~humble(X1)) & (humble(X1) | ~patient(X1)))) & (? [X2] : ((~humble(X2) | ~patient(X2)) & (humble(X2) | patient(X2))) | ! [X3] : (~funny(X3) & curious(X3))) [rectify 59]
61. ? [X0] : (funny(X0) | ~curious(X0)) => (funny(sK7) | ~curious(sK7)) [choice axiom]
62. ? [X2] : ((~humble(X2) | ~patient(X2)) & (humble(X2) | patient(X2))) => ((~humble(sK8) | ~patient(sK8)) & (humble(sK8) | patient(sK8))) [choice axiom]
63. ((funny(sK7) | ~curious(sK7)) | ! [X1] : ((patient(X1) | ~humble(X1)) & (humble(X1) | ~patient(X1)))) & (((~humble(sK8) | ~patient(sK8)) & (humble(sK8) | patient(sK8))) | ! [X3] : (~funny(X3) & curious(X3))) [skolemisation 60,62,61]
64. ! [X0] : (((~wise(X0) & wise(X0)) | (~humble(X0) & ~happy(X0))) & ((humble(X0) | happy(X0)) | (wise(X0) | ~wise(X0)))) [nnf transformation 12]
65. ! [X0] : (((~wise(X0) & wise(X0)) | (~humble(X0) & ~happy(X0))) & (humble(X0) | happy(X0) | wise(X0) | ~wise(X0))) [flattening 64]
66. ! [X0] : (((quiet(X0) | ~quiet(X0)) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | (~quiet(X0) & quiet(X0)))) [nnf transformation 13]
67. ! [X0] : ((quiet(X0) | ~quiet(X0) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | (~quiet(X0) & quiet(X0)))) [flattening 66]
68. ! [X0] : (((humble(X0) & kind(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~humble(X0) | ~kind(X0)))) [nnf transformation 14]
69. ! [X0] : (((humble(X0) & kind(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | ~humble(X0) | ~kind(X0))) [flattening 68]
89. ~strong(susan) | wise(paul) [cnf transformation 36]
93. ~wise(paul) | ~brave(X0) [cnf transformation 40]
116. humble(sK8) | patient(sK8) | curious(X3) [cnf transformation 63]
124. wise(X0) | ~humble(X0) [cnf transformation 65]
126. ~humble(X0) | ~wise(X0) [cnf transformation 65]
129. ~curious(X0) | quiet(X0) [cnf transformation 67]
130. ~quiet(X0) | ~curious(X0) [cnf transformation 67]
136. humble(X0) | brave(X0) | ~patient(X0) [cnf transformation 69]
150. strong(susan) [cnf transformation 22]
179. 7 <=> strong(susan) [avatar definition]
187. 9 <=> wise(paul) [avatar definition]
191. 9 | ~7 [avatar split clause 89,179,187]
196. 10 <=> ! [X0] : ~brave(X0) [avatar definition]
197. ~brave(X0) <- (10) [avatar component clause 196]
198. 10 | ~9 [avatar split clause 93,187,196]
299. 34 <=> patient(sK8) [avatar definition]
300. patient(sK8) <- (34) [avatar component clause 299]
303. 35 <=> humble(sK8) [avatar definition]
304. humble(sK8) <- (35) [avatar component clause 303]
308. 36 <=> ! [X3] : curious(X3) [avatar definition]
309. curious(X3) <- (36) [avatar component clause 308]
312. 36 | 34 | 35 [avatar split clause 116,303,299,308]
313. ~humble(X0) [subsumption resolution 124,126]
315. ~curious(X0) [subsumption resolution 129,130]
317. ~patient(X0) | brave(X0) [subsumption resolution 136,313]
345. 7 [avatar split clause 150,179]
356. brave(sK8) <- (34) [resolution 317,300]
357. $false <- (10, 34) [subsumption resolution 356,197]
358. ~10 | ~34 [avatar contradiction clause 357]
359. $false <- (35) [subsumption resolution 304,313]
360. ~35 [avatar contradiction clause 359]
361. $false <- (36) [subsumption resolution 309,315]
362. ~36 [avatar contradiction clause 361]
363. $false [avatar sat refutation 191,198,312,345,358,360,362]
% SZS output end Proof for 9022338059700895312167214
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If susan is humble then lucy is either not happy or tall. Everyone who is both not brave and curious is either funny or creative and vice versa. If john is both not brave and happy then someone is strong and vice versa. Everyone who is both strong and not wise is rich and vice versa. If paul is both wise and not brave then fred is not happy or happy and vice versa. Everyone who is either funny or quiet is both not happy and not patient. If someone is not humble then someone is either not wise or patient and vice versa. If john is not creative or not calm then paul is rich or not happy. If mary is both not calm and strong then alice is not wise or not funny and vice versa. If susan is not strong then fred is either brave or not wise. If john is humble or calm then someone is calm or generous. Everyone who is calm is tall. Everyone who is humble is tall or strong and vice versa. If alice is both not old and not happy then lucy is not calm and vice versa. Everyone who is funny is not funny. If john is both not funny and not patient then paul is not patient and vice versa. Someone is not creative. Alice is not calm. Someone is happy or calm. Lucy is strong. Paul is patient or rich. Alice is not generous or kind. Mary is both humble and not creative. John is not wise. | Lucy is not funny. | entailment | ((humble(susan))=>((~happy(lucy)<~>tall(lucy))))&
(![X]:((~brave(X)&curious(X))<=>(funny(X)<~>creative(X))))&
(((~brave(john)&happy(john)))<=>(?[X]:(strong(X))))&
(![X]:((strong(X)&~wise(X))<=>rich(X)))&
(((wise(paul)&~brave(paul)))<=>((~happy(fred)|happy(fred))))&
(![X]:((funny(X)<~>quiet(X))=>(~happy(X)&~patient(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~wise(X)<~>patient(X)))))&
(((~creative(john)|~calm(john)))=>((rich(paul)|~happy(paul))))&
(((~calm(mary)&strong(mary)))<=>((~wise(alice)|~funny(alice))))&
((~strong(susan))=>((brave(fred)<~>~wise(fred))))&
(((humble(john)|calm(john)))=>(?[X]:((calm(X)|generous(X)))))&
(![X]:(calm(X)=>tall(X)))&
(![X]:(humble(X)<=>(tall(X)|strong(X))))&
(((~old(alice)&~happy(alice)))<=>(~calm(lucy)))&
(![X]:(funny(X)=>~funny(X)))&
(((~funny(john)&~patient(john)))<=>(~patient(paul)))&
(?[X]:(~creative(X)))&
(~calm(alice))&
(?[X]:((happy(X)|calm(X))))&
(strong(lucy))&
((patient(paul)|rich(paul)))&
((~generous(alice)|kind(alice)))&
((humble(mary)&~creative(mary)))&
(~wise(john)) | ~funny(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5004373738691567624971537
% SZS output start Proof for 5004373738691567624971537
15. ! [X0] : (funny(X0) => ~funny(X0)) [input p14]
25. funny(lucy) [input hypothesis]
37. ! [X0] : (~funny(X0) | ~funny(X0)) [ennf transformation 15]
109. ~funny(X0) | ~funny(X0) [cnf transformation 37]
121. funny(lucy) [cnf transformation 25]
122. ~funny(X0) [duplicate literal removal 109]
285. $false [subsumption resolution 121,122]
% SZS output end Proof for 5004373738691567624971537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or strong is either humble or not strong.
If mary is both not brave and not kind then alice is either creative or strong.
Everyone who is either not creative or not curious is either not rich or generous and vice versa.
Everyone who is not creative is not tall or brave and vice versa.
Everyone who is both old and not brave is not old or tall.
Everyone who is not tall or creative is not calm or patient.
If fred is not calm or not funny then someone is not brave or not generous and vice versa.
Everyone who is both calm and rich is not tall and vice versa.
If someone is tall or wise then someone is rich.
Everyone who is either not funny or not old is either tall or not wise and vice versa.
If john is either not tall or funny then fred is not tall and vice versa.
Everyone who is not wise is either not generous or happy and vice versa.
Everyone who is not generous is funny or not calm and vice versa.
Everyone who is both not tall and happy is both not humble and not happy and vice versa.
Everyone who is either not brave or humble is either tall or not curious and vice versa.
If someone is not happy then lucy is generous and vice versa.
Someone is humble.
Someone is not wise.
Fred is not wise.
John is either strong or generous.
Alice is not happy or not quiet.
Someone is not kind.
Alice is both tall and strong.
Someone is both not tall and not curious. | Mary is not brave. | neutral | (![X]:((~funny(X)|strong(X))=>(humble(X)<~>~strong(X))))&
(((~brave(mary)&~kind(mary)))=>((creative(alice)<~>strong(alice))))&
(![X]:((~creative(X)<~>~curious(X))<=>(~rich(X)<~>generous(X))))&
(![X]:(~creative(X)<=>(~tall(X)|brave(X))))&
(![X]:((old(X)&~brave(X))=>(~old(X)|tall(X))))&
(![X]:((~tall(X)|creative(X))=>(~calm(X)|patient(X))))&
(((~calm(fred)|~funny(fred)))<=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:((calm(X)&rich(X))<=>~tall(X)))&
((?[X]:((tall(X)|wise(X))))=>(?[X]:(rich(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(tall(X)<~>~wise(X))))&
(((~tall(john)<~>funny(john)))<=>(~tall(fred)))&
(![X]:(~wise(X)<=>(~generous(X)<~>happy(X))))&
(![X]:(~generous(X)<=>(funny(X)|~calm(X))))&
(![X]:((~tall(X)&happy(X))<=>(~humble(X)&~happy(X))))&
(![X]:((~brave(X)<~>humble(X))<=>(tall(X)<~>~curious(X))))&
((?[X]:(~happy(X)))<=>(generous(lucy)))&
(?[X]:(humble(X)))&
(?[X]:(~wise(X)))&
(~wise(fred))&
((strong(john)<~>generous(john)))&
((~happy(alice)|~quiet(alice)))&
(?[X]:(~kind(X)))&
((tall(alice)&strong(alice)))&
(?[X]:((~tall(X)&~curious(X)))) | ~brave(mary) | [] | null | 0 |
Everyone who is either generous or not strong is either not kind or kind and vice versa.
If someone is either happy or not patient then someone is tall or funny.
Everyone who is not wise or not curious is generous and vice versa.
Everyone who is both not humble and not creative is both tall and not brave and vice versa.
If lucy is not rich then mary is either not funny or not generous.
If someone is happy then someone is brave or not quiet.
Everyone who is either old or generous is generous or not kind and vice versa.
Everyone who is both not tall and quiet is creative.
If someone is either wise or rich then paul is both not brave and rich and vice versa.
Everyone who is both not curious and not calm is not curious or not creative.
Everyone who is calm or kind is either not funny or not curious.
Everyone who is wise or not curious is both not funny and strong.
Everyone who is humble is not strong.
If john is not brave or rich then someone is both not patient and not tall.
If someone is not kind then someone is not kind or not curious.
If someone is not strong then alice is both not creative and not calm.
Someone is either not rich or kind.
Someone is wise.
Someone is both creative and strong.
Someone is either humble or kind.
Someone is not brave. | Alice is generous. | entailment | (![X]:((generous(X)<~>~strong(X))<=>(~kind(X)<~>kind(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:((~wise(X)|~curious(X))<=>generous(X)))&
(![X]:((~humble(X)&~creative(X))<=>(tall(X)&~brave(X))))&
((~rich(lucy))=>((~funny(mary)<~>~generous(mary))))&
((?[X]:(happy(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((old(X)<~>generous(X))<=>(generous(X)|~kind(X))))&
(![X]:((~tall(X)&quiet(X))=>creative(X)))&
((?[X]:((wise(X)<~>rich(X))))<=>((~brave(paul)&rich(paul))))&
(![X]:((~curious(X)&~calm(X))=>(~curious(X)|~creative(X))))&
(![X]:((calm(X)|kind(X))=>(~funny(X)<~>~curious(X))))&
(![X]:((wise(X)|~curious(X))=>(~funny(X)&strong(X))))&
(![X]:(humble(X)=>~strong(X)))&
(((~brave(john)|rich(john)))=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((~kind(X)|~curious(X)))))&
((?[X]:(~strong(X)))=>((~creative(alice)&~calm(alice))))&
(?[X]:((~rich(X)<~>kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)&strong(X))))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:(~brave(X))) | generous(alice) | [
"p0",
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3390561602996364714834797
% SZS output start Proof for 3390561602996364714834797
1. ! [X0] : ((generous(X0) <~> ~strong(X0)) <=> (~kind(X0) <~> kind(X0))) [input p0]
3. ! [X0] : ((~curious(X0) | ~wise(X0)) <=> generous(X0)) [input p2]
12. ! [X0] : ((~curious(X0) | wise(X0)) => (strong(X0) & ~funny(X0))) [input p11]
22. ~generous(alice) [input hypothesis]
33. ! [X0] : ((strong(X0) & ~funny(X0)) | (curious(X0) & ~wise(X0))) [ennf transformation 12]
38. ! [X0] : ((((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ((generous(X0) | strong(X0)) & (~strong(X0) | ~generous(X0))))) [nnf transformation 1]
43. ! [X0] : (((~curious(X0) | ~wise(X0)) | ~generous(X0)) & (generous(X0) | (curious(X0) & wise(X0)))) [nnf transformation 3]
44. ! [X0] : ((~curious(X0) | ~wise(X0) | ~generous(X0)) & (generous(X0) | (curious(X0) & wise(X0)))) [flattening 43]
77. ~strong(X0) | generous(X0) | kind(X0) | kind(X0) [cnf transformation 38]
78. ~strong(X0) | generous(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
83. wise(X0) | generous(X0) [cnf transformation 44]
111. ~wise(X0) | strong(X0) [cnf transformation 33]
129. ~generous(alice) [cnf transformation 22]
132. ~strong(X0) | generous(X0) | kind(X0) [duplicate literal removal 77]
133. ~strong(X0) | generous(X0) | ~kind(X0) [duplicate literal removal 78]
137. ~strong(X0) | generous(X0) [subsumption resolution 132,133]
268. strong(X0) | generous(X0) [resolution 111,83]
269. generous(X0) [subsumption resolution 268,137]
272. $false [resolution 269,129]
% SZS output end Proof for 3390561602996364714834797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not wise is wise.
Everyone who is not kind or not patient is either not curious or not strong and vice versa.
If someone is not generous or not kind then paul is both not curious and calm.
If alice is old or not old then someone is not calm and vice versa.
Everyone who is both creative and not brave is not quiet.
Everyone who is not brave is not kind.
If someone is kind or rich then someone is both not calm and calm and vice versa.
If someone is not rich then someone is not curious and vice versa.
Everyone who is either generous or not wise is both not wise and not patient.
If someone is both funny and not strong then someone is both quiet and patient and vice versa.
Everyone who is both not curious and tall is not strong and vice versa.
Everyone who is quiet is both quiet and funny.
Everyone who is not creative is either happy or generous.
If someone is not wise or curious then someone is either not brave or calm and vice versa.
Everyone who is both creative and not rich is happy and vice versa.
If alice is wise or not funny then someone is both not happy and not calm and vice versa.
Paul is either not generous or funny.
Someone is not rich.
Paul is both creative and not funny.
Alice is tall or not happy.
Someone is not humble.
Someone is quiet or not kind.
John is happy.
Someone is both not patient and old. | John is not curious. | entailment | (![X]:((~kind(X)<~>~wise(X))=>wise(X)))&
(![X]:((~kind(X)|~patient(X))<=>(~curious(X)<~>~strong(X))))&
((?[X]:((~generous(X)|~kind(X))))=>((~curious(paul)&calm(paul))))&
(((old(alice)|~old(alice)))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)&~brave(X))=>~quiet(X)))&
(![X]:(~brave(X)=>~kind(X)))&
((?[X]:((kind(X)|rich(X))))<=>(?[X]:((~calm(X)&calm(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)<~>~wise(X))=>(~wise(X)&~patient(X))))&
((?[X]:((funny(X)&~strong(X))))<=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:((~curious(X)&tall(X))<=>~strong(X)))&
(![X]:(quiet(X)=>(quiet(X)&funny(X))))&
(![X]:(~creative(X)=>(happy(X)<~>generous(X))))&
((?[X]:((~wise(X)|curious(X))))<=>(?[X]:((~brave(X)<~>calm(X)))))&
(![X]:((creative(X)&~rich(X))<=>happy(X)))&
(((wise(alice)|~funny(alice)))<=>(?[X]:((~happy(X)&~calm(X)))))&
((~generous(paul)<~>funny(paul)))&
(?[X]:(~rich(X)))&
((creative(paul)&~funny(paul)))&
((tall(alice)|~happy(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((quiet(X)|~kind(X))))&
(happy(john))&
(?[X]:((~patient(X)&old(X)))) | ~curious(john) | [
"p1",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6946680377384876232873137
% SZS output start Proof for 6946680377384876232873137
2. ! [X0] : ((~patient(X0) | ~kind(X0)) <=> (~curious(X0) <~> ~strong(X0))) [input p1]
7. ? [X0] : (rich(X0) | kind(X0)) <=> ? [X0] : (calm(X0) & ~calm(X0)) [input p6]
11. ! [X0] : ((tall(X0) & ~curious(X0)) <=> ~strong(X0)) [input p10]
25. curious(john) [input hypothesis]
26. ? [X0] : (rich(X0) | kind(X0)) <=> ? [X1] : (calm(X1) & ~calm(X1)) [rectify 7]
40. ! [X0] : (((~patient(X0) | ~kind(X0)) | ((~curious(X0) | strong(X0)) & (~strong(X0) | curious(X0)))) & (((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | (patient(X0) & kind(X0)))) [nnf transformation 2]
41. ! [X0] : ((~patient(X0) | ~kind(X0) | ((~curious(X0) | strong(X0)) & (~strong(X0) | curious(X0)))) & (((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | (patient(X0) & kind(X0)))) [flattening 40]
47. (? [X0] : (rich(X0) | kind(X0)) | ! [X1] : (~calm(X1) | calm(X1))) & (? [X1] : (calm(X1) & ~calm(X1)) | ! [X0] : (~rich(X0) & ~kind(X0))) [nnf transformation 26]
48. (? [X0] : (rich(X0) | kind(X0)) | ! [X1] : (~calm(X1) | calm(X1))) & (? [X2] : (calm(X2) & ~calm(X2)) | ! [X3] : (~rich(X3) & ~kind(X3))) [rectify 47]
49. ? [X0] : (rich(X0) | kind(X0)) => (rich(sK1) | kind(sK1)) [choice axiom]
50. ? [X2] : (calm(X2) & ~calm(X2)) => (calm(sK2) & ~calm(sK2)) [choice axiom]
51. ((rich(sK1) | kind(sK1)) | ! [X1] : (~calm(X1) | calm(X1))) & ((calm(sK2) & ~calm(sK2)) | ! [X3] : (~rich(X3) & ~kind(X3))) [skolemisation 48,50,49]
63. ! [X0] : (((tall(X0) & ~curious(X0)) | strong(X0)) & (~strong(X0) | (~tall(X0) | curious(X0)))) [nnf transformation 11]
64. ! [X0] : (((tall(X0) & ~curious(X0)) | strong(X0)) & (~strong(X0) | ~tall(X0) | curious(X0))) [flattening 63]
87. ~strong(X0) | ~curious(X0) | kind(X0) [cnf transformation 41]
102. ~calm(sK2) | ~kind(X3) [cnf transformation 51]
104. calm(sK2) | ~kind(X3) [cnf transformation 51]
118. ~curious(X0) | strong(X0) [cnf transformation 64]
148. curious(john) [cnf transformation 25]
183. 8 <=> calm(sK2) [avatar definition]
188. 9 <=> ! [X3] : ~kind(X3) [avatar definition]
189. ~kind(X3) <- (9) [avatar component clause 188]
190. 9 | 8 [avatar split clause 104,183,188]
192. 9 | ~8 [avatar split clause 102,183,188]
322. strong(john) [resolution 118,148]
325. ~curious(john) | kind(john) [resolution 87,322]
326. kind(john) [subsumption resolution 325,148]
327. $false <- (9) [subsumption resolution 326,189]
328. ~9 [avatar contradiction clause 327]
329. $false [avatar sat refutation 190,192,328]
% SZS output end Proof for 6946680377384876232873137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or not patient then susan is either tall or not old.
If john is not old or kind then someone is both not humble and funny.
Everyone who is both old and not wise is either not patient or quiet and vice versa.
Everyone who is both brave and not rich is creative.
If mary is either happy or funny then someone is not creative or generous.
If alice is both not generous and not curious then someone is either brave or not funny and vice versa.
Everyone who is quiet is both not humble and not old and vice versa.
Everyone who is both patient and humble is either brave or not patient and vice versa.
If someone is either not wise or funny then someone is both brave and not generous.
If someone is both brave and tall then someone is either not wise or strong and vice versa.
If lucy is both strong and funny then someone is not patient and vice versa.
If mary is curious then someone is not curious.
Everyone who is generous or humble is not rich or old and vice versa.
If mary is either not funny or funny then someone is not brave and vice versa.
Everyone who is curious is either not patient or not rich.
Everyone who is old is tall or brave and vice versa.
Someone is either not happy or not brave.
Someone is not calm or brave.
Lucy is both not brave and not funny.
Susan is not rich or not brave.
Mary is either generous or not patient.
Fred is not creative.
John is not tall. | Lucy is quiet. | contradiction | ((?[X]:((~humble(X)|~patient(X))))=>((tall(susan)<~>~old(susan))))&
(((~old(john)|kind(john)))=>(?[X]:((~humble(X)&funny(X)))))&
(![X]:((old(X)&~wise(X))<=>(~patient(X)<~>quiet(X))))&
(![X]:((brave(X)&~rich(X))=>creative(X)))&
(((happy(mary)<~>funny(mary)))=>(?[X]:((~creative(X)|generous(X)))))&
(((~generous(alice)&~curious(alice)))<=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:(quiet(X)<=>(~humble(X)&~old(X))))&
(![X]:((patient(X)&humble(X))<=>(brave(X)<~>~patient(X))))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((brave(X)&~generous(X)))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~wise(X)<~>strong(X)))))&
(((strong(lucy)&funny(lucy)))<=>(?[X]:(~patient(X))))&
((curious(mary))=>(?[X]:(~curious(X))))&
(![X]:((generous(X)|humble(X))<=>(~rich(X)|old(X))))&
(((~funny(mary)<~>funny(mary)))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)=>(~patient(X)<~>~rich(X))))&
(![X]:(old(X)<=>(tall(X)|brave(X))))&
(?[X]:((~happy(X)<~>~brave(X))))&
(?[X]:((~calm(X)|brave(X))))&
((~brave(lucy)&~funny(lucy)))&
((~rich(susan)|~brave(susan)))&
((generous(mary)<~>~patient(mary)))&
(~creative(fred))&
(~tall(john)) | quiet(lucy) | [
"p2",
"p6",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7458862102318517943193889
% SZS output start Proof for 7458862102318517943193889
3. ! [X0] : ((~wise(X0) & old(X0)) <=> (~patient(X0) <~> quiet(X0))) [input p2]
7. ! [X0] : (quiet(X0) <=> (~old(X0) & ~humble(X0))) [input p6]
11. (funny(lucy) & strong(lucy)) <=> ? [X0] : ~patient(X0) [input p10]
19. ~funny(lucy) & ~brave(lucy) [input p18]
24. quiet(lucy) [input hypothesis]
40. ! [X0] : (((~wise(X0) & old(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0)))) & (((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (wise(X0) | ~old(X0)))) [nnf transformation 3]
41. ! [X0] : (((~wise(X0) & old(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0)))) & (((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | wise(X0) | ~old(X0))) [flattening 40]
50. ! [X0] : ((quiet(X0) | (old(X0) | humble(X0))) & ((~old(X0) & ~humble(X0)) | ~quiet(X0))) [nnf transformation 7]
51. ! [X0] : ((quiet(X0) | old(X0) | humble(X0)) & ((~old(X0) & ~humble(X0)) | ~quiet(X0))) [flattening 50]
63. ((funny(lucy) & strong(lucy)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | (~funny(lucy) | ~strong(lucy))) [nnf transformation 11]
64. ((funny(lucy) & strong(lucy)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | ~funny(lucy) | ~strong(lucy)) [flattening 63]
65. ((funny(lucy) & strong(lucy)) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | ~funny(lucy) | ~strong(lucy)) [rectify 64]
66. ? [X1] : ~patient(X1) => ~patient(sK6) [choice axiom]
67. ((funny(lucy) & strong(lucy)) | ! [X0] : patient(X0)) & (~patient(sK6) | ~funny(lucy) | ~strong(lucy)) [skolemisation 65,66]
92. ~quiet(X0) | ~patient(X0) | old(X0) [cnf transformation 41]
105. ~quiet(X0) | ~old(X0) [cnf transformation 51]
125. funny(lucy) | patient(X0) [cnf transformation 67]
143. ~funny(lucy) [cnf transformation 19]
149. quiet(lucy) [cnf transformation 24]
155. 1 <=> ! [X0] : patient(X0) [avatar definition]
156. patient(X0) <- (1) [avatar component clause 155]
283. 29 <=> funny(lucy) [avatar definition]
286. 1 | 29 [avatar split clause 125,283,155]
322. ~29 [avatar split clause 143,283]
345. ~old(lucy) [resolution 105,149]
361. ~patient(lucy) | old(lucy) [resolution 92,149]
364. old(lucy) <- (1) [subsumption resolution 361,156]
365. $false <- (1) [subsumption resolution 364,345]
366. ~1 [avatar contradiction clause 365]
367. $false [avatar sat refutation 286,322,366]
% SZS output end Proof for 7458862102318517943193889
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not strong is both tall and not kind.
If someone is both not funny and old then someone is not calm or not rich and vice versa.
Everyone who is both not calm and funny is rich or generous.
If someone is both not wise and not curious then lucy is not wise or not strong and vice versa.
If mary is patient then susan is both humble and not calm and vice versa.
If paul is not strong then someone is either kind or tall and vice versa.
Everyone who is tall is not old and vice versa.
Everyone who is both not creative and humble is tall and vice versa.
If someone is not patient then someone is either creative or tall and vice versa.
If someone is both calm and generous then someone is either generous or strong.
Everyone who is either not patient or wise is calm and vice versa.
Everyone who is not calm is not strong.
Everyone who is not happy or patient is either curious or not generous and vice versa.
Everyone who is not creative is curious or not old.
Everyone who is not generous or not brave is both not happy and not kind.
If someone is either humble or generous then someone is both kind and not wise and vice versa.
Mary is old or not quiet.
Paul is either happy or curious.
Someone is either humble or not kind.
Paul is either not generous or old.
Someone is not brave or not strong.
Mary is both not old and not patient. | Susan is wise. | contradiction | (![X]:((wise(X)|~strong(X))=>(tall(X)&~kind(X))))&
((?[X]:((~funny(X)&old(X))))<=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((~calm(X)&funny(X))=>(rich(X)|generous(X))))&
((?[X]:((~wise(X)&~curious(X))))<=>((~wise(lucy)|~strong(lucy))))&
((patient(mary))<=>((humble(susan)&~calm(susan))))&
((~strong(paul))<=>(?[X]:((kind(X)<~>tall(X)))))&
(![X]:(tall(X)<=>~old(X)))&
(![X]:((~creative(X)&humble(X))<=>tall(X)))&
((?[X]:(~patient(X)))<=>(?[X]:((creative(X)<~>tall(X)))))&
((?[X]:((calm(X)&generous(X))))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:((~patient(X)<~>wise(X))<=>calm(X)))&
(![X]:(~calm(X)=>~strong(X)))&
(![X]:((~happy(X)|patient(X))<=>(curious(X)<~>~generous(X))))&
(![X]:(~creative(X)=>(curious(X)|~old(X))))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)&~kind(X))))&
((?[X]:((humble(X)<~>generous(X))))<=>(?[X]:((kind(X)&~wise(X)))))&
((old(mary)|~quiet(mary)))&
((happy(paul)<~>curious(paul)))&
(?[X]:((humble(X)<~>~kind(X))))&
((~generous(paul)<~>old(paul)))&
(?[X]:((~brave(X)|~strong(X))))&
((~old(mary)&~patient(mary))) | wise(susan) | [
"p0",
"p5",
"p6",
"p12",
"p14",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 530395634098940187287725
% SZS output start Proof for 530395634098940187287725
1. ! [X0] : ((~strong(X0) | wise(X0)) => (~kind(X0) & tall(X0))) [input p0]
6. ~strong(paul) <=> ? [X0] : (kind(X0) <~> tall(X0)) [input p5]
7. ! [X0] : (tall(X0) <=> ~old(X0)) [input p6]
13. ! [X0] : ((patient(X0) | ~happy(X0)) <=> (curious(X0) <~> ~generous(X0))) [input p12]
15. ! [X0] : ((~brave(X0) | ~generous(X0)) => (~kind(X0) & ~happy(X0))) [input p14]
18. happy(paul) <~> curious(paul) [input p17]
20. ~generous(paul) <~> old(paul) [input p19]
23. wise(susan) [input hypothesis]
29. ! [X0] : ((~kind(X0) & tall(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 1]
36. ! [X0] : ((~kind(X0) & ~happy(X0)) | (brave(X0) & generous(X0))) [ennf transformation 15]
49. (~strong(paul) | ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0)))) & (? [X0] : ((~tall(X0) | ~kind(X0)) & (tall(X0) | kind(X0))) | strong(paul)) [nnf transformation 6]
50. (~strong(paul) | ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0)))) & (? [X1] : ((~tall(X1) | ~kind(X1)) & (tall(X1) | kind(X1))) | strong(paul)) [rectify 49]
51. ? [X1] : ((~tall(X1) | ~kind(X1)) & (tall(X1) | kind(X1))) => ((~tall(sK3) | ~kind(sK3)) & (tall(sK3) | kind(sK3))) [choice axiom]
52. (~strong(paul) | ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0)))) & (((~tall(sK3) | ~kind(sK3)) & (tall(sK3) | kind(sK3))) | strong(paul)) [skolemisation 50,51]
53. ! [X0] : ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0))) [nnf transformation 7]
66. ! [X0] : (((patient(X0) | ~happy(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~patient(X0) & happy(X0)))) [nnf transformation 13]
67. ! [X0] : ((patient(X0) | ~happy(X0) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~patient(X0) & happy(X0)))) [flattening 66]
73. (~curious(paul) | ~happy(paul)) & (curious(paul) | happy(paul)) [nnf transformation 18]
77. (~old(paul) | generous(paul)) & (old(paul) | ~generous(paul)) [nnf transformation 20]
80. ~wise(X0) | tall(X0) [cnf transformation 29]
81. tall(X0) | strong(X0) [cnf transformation 29]
82. ~kind(X0) | ~wise(X0) [cnf transformation 29]
101. ~strong(paul) | kind(X0) | ~tall(X0) [cnf transformation 52]
102. ~old(X0) | ~tall(X0) [cnf transformation 53]
120. ~curious(X0) | generous(X0) | happy(X0) [cnf transformation 67]
125. ~happy(X0) | generous(X0) [cnf transformation 36]
135. curious(paul) | happy(paul) [cnf transformation 73]
139. old(paul) | ~generous(paul) [cnf transformation 77]
144. wise(susan) [cnf transformation 23]
215. 16 <=> ! [X0] : (kind(X0) | ~tall(X0)) [avatar definition]
216. ~tall(X0) | kind(X0) <- (16) [avatar component clause 215]
218. 17 <=> strong(paul) [avatar definition]
221. 16 | ~17 [avatar split clause 101,218,215]
309. 37 <=> happy(paul) [avatar definition]
310. happy(paul) <- (37) [avatar component clause 309]
311. ~happy(paul) <- (~37) [avatar component clause 309]
313. 38 <=> curious(paul) [avatar definition]
314. curious(paul) <- (38) [avatar component clause 313]
317. 37 | 38 [avatar split clause 135,313,309]
329. 41 <=> generous(paul) [avatar definition]
330. ~generous(paul) <- (~41) [avatar component clause 329]
333. 42 <=> old(paul) [avatar definition]
334. old(paul) <- (42) [avatar component clause 333]
337. ~41 | 42 [avatar split clause 139,333,329]
356. tall(susan) [resolution 80,144]
374. generous(paul) <- (37) [resolution 125,310]
375. $false <- (37, ~41) [subsumption resolution 374,330]
376. ~37 | 41 [avatar contradiction clause 375]
507. ~tall(paul) <- (42) [resolution 334,102]
516. generous(paul) | happy(paul) <- (38) [resolution 120,314]
545. strong(paul) <- (42) [resolution 507,81]
548. 17 | ~42 [avatar split clause 545,333,218]
573. kind(susan) <- (16) [resolution 216,356]
646. ~wise(susan) <- (16) [resolution 573,82]
649. $false <- (16) [subsumption resolution 646,144]
650. ~16 [avatar contradiction clause 649]
651. generous(paul) <- (~37, 38) [subsumption resolution 516,311]
652. 41 | 37 | ~38 [avatar split clause 651,313,309,329]
653. $false [avatar sat refutation 221,317,337,376,548,650,652]
% SZS output end Proof for 530395634098940187287725
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is either rich or creative.
If someone is generous then someone is patient.
Everyone who is either tall or not rich is both patient and not wise.
If john is not humble then someone is either wise or brave and vice versa.
Everyone who is not rich or not curious is both not generous and not happy.
Everyone who is kind or not tall is happy and vice versa.
If alice is not brave or generous then paul is both quiet and humble and vice versa.
Everyone who is both funny and not quiet is both not funny and not happy and vice versa.
If someone is not old then fred is both quiet and not old and vice versa.
Everyone who is happy is either not wise or not old.
Everyone who is not kind is both generous and wise.
If someone is either not quiet or kind then fred is either not tall or not humble.
If someone is patient then lucy is both wise and not rich and vice versa.
If mary is both quiet and not funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
Mary is quiet.
Someone is strong.
Someone is kind.
Someone is both humble and rich.
John is not strong.
Someone is either creative or old.
Lucy is either rich or not happy. | Alice is not wise. | entailment | (![X]:(old(X)=>(rich(X)<~>creative(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
(![X]:((tall(X)<~>~rich(X))=>(patient(X)&~wise(X))))&
((~humble(john))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((~rich(X)|~curious(X))=>(~generous(X)&~happy(X))))&
(![X]:((kind(X)|~tall(X))<=>happy(X)))&
(((~brave(alice)|generous(alice)))<=>((quiet(paul)&humble(paul))))&
(![X]:((funny(X)&~quiet(X))<=>(~funny(X)&~happy(X))))&
((?[X]:(~old(X)))<=>((quiet(fred)&~old(fred))))&
(![X]:(happy(X)=>(~wise(X)<~>~old(X))))&
(![X]:(~kind(X)=>(generous(X)&wise(X))))&
((?[X]:((~quiet(X)<~>kind(X))))=>((~tall(fred)<~>~humble(fred))))&
((?[X]:(patient(X)))<=>((wise(lucy)&~rich(lucy))))&
(((quiet(mary)&~funny(mary)))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(quiet(mary))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&rich(X))))&
(~strong(john))&
(?[X]:((creative(X)<~>old(X))))&
((rich(lucy)<~>~happy(lucy))) | ~wise(alice) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6092774836747587986310308
% SZS output start Proof for 6092774836747587986310308
2. ? [X0] : generous(X0) => ? [X0] : patient(X0) [input p1]
3. ! [X0] : ((tall(X0) <~> ~rich(X0)) => (~wise(X0) & patient(X0))) [input p2]
5. ! [X0] : ((~curious(X0) | ~rich(X0)) => (~happy(X0) & ~generous(X0))) [input p4]
6. ! [X0] : ((~tall(X0) | kind(X0)) <=> happy(X0)) [input p5]
9. ? [X0] : ~old(X0) <=> (~old(fred) & quiet(fred)) [input p8]
10. ! [X0] : (happy(X0) => (~wise(X0) <~> ~old(X0))) [input p9]
11. ! [X0] : (~kind(X0) => (wise(X0) & generous(X0))) [input p10]
13. ? [X0] : patient(X0) <=> (~rich(lucy) & wise(lucy)) [input p12]
16. ! [X0] : ((~wise(X0) <~> ~generous(X0)) => (~quiet(X0) <~> tall(X0))) [input p15]
24. wise(alice) [input hypothesis]
25. ? [X0] : generous(X0) => ? [X1] : patient(X1) [rectify 2]
26. ! [X0] : (~rich(X0) => (~happy(X0) & ~generous(X0))) [pure predicate removal 5]
28. ? [X1] : patient(X1) | ! [X0] : ~generous(X0) [ennf transformation 25]
29. ! [X0] : ((~wise(X0) & patient(X0)) | (tall(X0) <=> ~rich(X0))) [ennf transformation 3]
30. ! [X0] : ((~happy(X0) & ~generous(X0)) | rich(X0)) [ennf transformation 26]
31. ! [X0] : ((~wise(X0) <~> ~old(X0)) | ~happy(X0)) [ennf transformation 10]
32. ! [X0] : ((wise(X0) & generous(X0)) | kind(X0)) [ennf transformation 11]
35. ! [X0] : ((~quiet(X0) <~> tall(X0)) | (~wise(X0) <=> ~generous(X0))) [ennf transformation 16]
37. ? [X0] : patient(X0) | ! [X1] : ~generous(X1) [rectify 28]
38. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
39. patient(sK0) | ! [X1] : ~generous(X1) [skolemisation 37,38]
40. ! [X0] : ((~wise(X0) & patient(X0)) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) [nnf transformation 29]
45. ! [X0] : (((~tall(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [nnf transformation 6]
46. ! [X0] : ((~tall(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [flattening 45]
51. (? [X0] : ~old(X0) | (old(fred) | ~quiet(fred))) & ((~old(fred) & quiet(fred)) | ! [X0] : old(X0)) [nnf transformation 9]
52. (? [X0] : ~old(X0) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X0] : old(X0)) [flattening 51]
53. (? [X0] : ~old(X0) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X1] : old(X1)) [rectify 52]
54. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
55. (~old(sK2) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X1] : old(X1)) [skolemisation 53,54]
56. ! [X0] : (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | ~happy(X0)) [nnf transformation 31]
58. (? [X0] : patient(X0) | (rich(lucy) | ~wise(lucy))) & ((~rich(lucy) & wise(lucy)) | ! [X0] : ~patient(X0)) [nnf transformation 13]
59. (? [X0] : patient(X0) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X0] : ~patient(X0)) [flattening 58]
60. (? [X0] : patient(X0) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X1] : ~patient(X1)) [rectify 59]
61. ? [X0] : patient(X0) => patient(sK3) [choice axiom]
62. (patient(sK3) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X1] : ~patient(X1)) [skolemisation 60,61]
68. ! [X0] : (((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) [nnf transformation 35]
81. patient(sK0) | ~generous(X1) [cnf transformation 39]
82. ~tall(X0) | ~rich(X0) | patient(X0) [cnf transformation 40]
90. ~generous(X0) | rich(X0) [cnf transformation 30]
91. ~happy(X0) | rich(X0) [cnf transformation 30]
92. ~kind(X0) | happy(X0) [cnf transformation 46]
104. quiet(fred) | old(X1) [cnf transformation 55]
105. ~old(fred) | old(X1) [cnf transformation 55]
107. ~happy(X0) | ~wise(X0) | ~old(X0) [cnf transformation 56]
108. ~happy(X0) | wise(X0) | old(X0) [cnf transformation 56]
109. kind(X0) | generous(X0) [cnf transformation 32]
110. kind(X0) | wise(X0) [cnf transformation 32]
116. ~rich(lucy) | ~patient(X1) [cnf transformation 62]
124. ~quiet(X0) | tall(X0) | ~wise(X0) | generous(X0) [cnf transformation 68]
137. wise(alice) [cnf transformation 24]
141. 1 <=> ! [X1] : ~generous(X1) [avatar definition]
142. ~generous(X1) <- (1) [avatar component clause 141]
144. 2 <=> patient(sK0) [avatar definition]
146. patient(sK0) <- (2) [avatar component clause 144]
147. 1 | 2 [avatar split clause 81,144,141]
192. 12 <=> quiet(fred) [avatar definition]
193. quiet(fred) <- (12) [avatar component clause 192]
196. 13 <=> old(fred) [avatar definition]
205. 15 <=> ! [X1] : old(X1) [avatar definition]
206. old(X1) <- (15) [avatar component clause 205]
207. 15 | ~13 [avatar split clause 105,196,205]
208. 15 | 12 [avatar split clause 104,192,205]
213. 17 <=> tall(fred) [avatar definition]
214. ~tall(fred) <- (~17) [avatar component clause 213]
215. tall(fred) <- (17) [avatar component clause 213]
232. 21 <=> rich(lucy) [avatar definition]
233. ~rich(lucy) <- (~21) [avatar component clause 232]
241. 23 <=> ! [X1] : ~patient(X1) [avatar definition]
242. ~patient(X1) <- (23) [avatar component clause 241]
243. 23 | ~21 [avatar split clause 116,232,241]
293. happy(X0) | generous(X0) [resolution 109,92]
294. happy(X0) | wise(X0) [resolution 110,92]
306. ~rich(fred) | patient(fred) <- (17) [resolution 82,215]
309. 33 <=> patient(fred) [avatar definition]
311. patient(fred) <- (33) [avatar component clause 309]
313. 34 <=> rich(fred) [avatar definition]
315. ~rich(fred) <- (~34) [avatar component clause 313]
316. 33 | ~34 | ~17 [avatar split clause 306,213,313,309]
319. generous(X0) | rich(X0) [resolution 293,91]
320. rich(X0) [subsumption resolution 319,90]
328. $false <- (~21) [resolution 320,233]
329. $false <- (~34) [resolution 320,315]
330. 34 [avatar contradiction clause 329]
331. 21 [avatar contradiction clause 328]
335. $false <- (2, 23) [resolution 242,146]
338. ~2 | ~23 [avatar contradiction clause 335]
368. ~wise(X1) | ~old(X1) | generous(X1) [resolution 107,293]
373. ~wise(X1) | ~old(X1) <- (1) [subsumption resolution 368,142]
377. wise(X0) | old(X0) | wise(X0) [resolution 108,294]
384. wise(X0) | old(X0) [duplicate literal removal 377]
404. tall(fred) | ~wise(fred) | generous(fred) <- (12) [resolution 124,193]
408. ~wise(fred) | generous(fred) <- (12, ~17) [subsumption resolution 404,214]
409. ~wise(fred) <- (1, 12, ~17) [subsumption resolution 408,142]
414. ~old(alice) <- (1) [resolution 373,137]
422. old(fred) <- (1, 12, ~17) [resolution 384,409]
427. 13 | ~1 | ~12 | 17 [avatar split clause 422,213,192,141,196]
433. $false <- (1, 15) [resolution 414,206]
434. ~1 | ~15 [avatar contradiction clause 433]
441. $false <- (23, 33) [subsumption resolution 311,242]
442. ~23 | ~33 [avatar contradiction clause 441]
443. $false [avatar sat refutation 147,207,208,243,316,330,331,338,427,434,442]
% SZS output end Proof for 6092774836747587986310308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not happy is not humble and vice versa. Everyone who is either not humble or happy is either not brave or not patient. Everyone who is not happy is calm. If someone is both not humble and kind then someone is either funny or not funny. Everyone who is either old or wise is either calm or not calm and vice versa. If someone is both kind and not funny then someone is both quiet and not rich and vice versa. If someone is both funny and humble then someone is not patient and vice versa. Everyone who is not kind is both not kind and not wise. If fred is either not humble or patient then fred is either not calm or not humble. Everyone who is not patient or not quiet is patient and vice versa. Everyone who is both strong and tall is brave or curious and vice versa. Everyone who is patient is both not strong and funny and vice versa. Everyone who is either brave or happy is either not humble or not wise and vice versa. If alice is either happy or rich then someone is both not humble and not quiet. Everyone who is rich is not curious and vice versa. Everyone who is not strong is either not generous or patient. Someone is both calm and happy. Lucy is kind or not wise. Someone is rich. John is generous or funny. Lucy is patient or old. | Fred is quiet. | contradiction | (![X]:((~curious(X)|~happy(X))<=>~humble(X)))&
(![X]:((~humble(X)<~>happy(X))=>(~brave(X)<~>~patient(X))))&
(![X]:(~happy(X)=>calm(X)))&
((?[X]:((~humble(X)&kind(X))))=>(?[X]:((funny(X)<~>~funny(X)))))&
(![X]:((old(X)<~>wise(X))<=>(calm(X)<~>~calm(X))))&
((?[X]:((kind(X)&~funny(X))))<=>(?[X]:((quiet(X)&~rich(X)))))&
((?[X]:((funny(X)&humble(X))))<=>(?[X]:(~patient(X))))&
(![X]:(~kind(X)=>(~kind(X)&~wise(X))))&
(((~humble(fred)<~>patient(fred)))=>((~calm(fred)<~>~humble(fred))))&
(![X]:((~patient(X)|~quiet(X))<=>patient(X)))&
(![X]:((strong(X)&tall(X))<=>(brave(X)|curious(X))))&
(![X]:(patient(X)<=>(~strong(X)&funny(X))))&
(![X]:((brave(X)<~>happy(X))<=>(~humble(X)<~>~wise(X))))&
(((happy(alice)<~>rich(alice)))=>(?[X]:((~humble(X)&~quiet(X)))))&
(![X]:(rich(X)<=>~curious(X)))&
(![X]:(~strong(X)=>(~generous(X)<~>patient(X))))&
(?[X]:((calm(X)&happy(X))))&
((kind(lucy)|~wise(lucy)))&
(?[X]:(rich(X)))&
((generous(john)|funny(john)))&
((patient(lucy)|old(lucy))) | quiet(fred) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6067153860796321452350309
% SZS output start Proof for 6067153860796321452350309
10. ! [X0] : ((~quiet(X0) | ~patient(X0)) <=> patient(X0)) [input p9]
22. quiet(fred) [input hypothesis]
52. ! [X0] : (((~quiet(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (quiet(X0) & patient(X0)))) [nnf transformation 10]
53. ! [X0] : ((~quiet(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (quiet(X0) & patient(X0)))) [flattening 52]
99. patient(X0) | patient(X0) [cnf transformation 53]
101. ~quiet(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 53]
132. quiet(fred) [cnf transformation 22]
133. patient(X0) [duplicate literal removal 99]
134. ~quiet(X0) | ~patient(X0) [duplicate literal removal 101]
174. 7 <=> ! [X1] : patient(X1) [avatar definition]
175. patient(X1) <- (7) [avatar component clause 174]
208. 7 [avatar split clause 133,174]
262. ~patient(fred) [resolution 134,132]
266. $false <- (7) [subsumption resolution 262,175]
267. ~7 [avatar contradiction clause 266]
270. $false [avatar sat refutation 208,267]
% SZS output end Proof for 6067153860796321452350309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or funny then someone is not old and vice versa. If someone is either quiet or not quiet then someone is kind or generous and vice versa. If paul is either curious or kind then someone is either not old or old. If someone is not old or not tall then someone is wise and vice versa. Everyone who is quiet or strong is not brave. If lucy is rich then john is either happy or not patient and vice versa. Everyone who is not brave is either not patient or not creative and vice versa. If alice is humble or not tall then fred is not patient and vice versa. Everyone who is generous or patient is humble. If john is both not brave and not tall then someone is both funny and not creative and vice versa. If someone is patient or not wise then someone is either not creative or rich and vice versa. If mary is not calm then alice is either not brave or calm. Everyone who is calm or curious is not patient or not quiet and vice versa. If paul is both not happy and curious then someone is humble and vice versa. If paul is not funny or not patient then fred is not wise and vice versa. Everyone who is quiet is both wise and brave and vice versa. Susan is either not funny or kind. Fred is either not curious or happy. Susan is either strong or not tall. Someone is old or not old. Alice is not creative or not brave. Someone is both not tall and funny. John is either not wise or not kind. | Fred is not quiet. | entailment | ((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:(~old(X))))&
((?[X]:((quiet(X)<~>~quiet(X))))<=>(?[X]:((kind(X)|generous(X)))))&
(((curious(paul)<~>kind(paul)))=>(?[X]:((~old(X)<~>old(X)))))&
((?[X]:((~old(X)|~tall(X))))<=>(?[X]:(wise(X))))&
(![X]:((quiet(X)|strong(X))=>~brave(X)))&
((rich(lucy))<=>((happy(john)<~>~patient(john))))&
(![X]:(~brave(X)<=>(~patient(X)<~>~creative(X))))&
(((humble(alice)|~tall(alice)))<=>(~patient(fred)))&
(![X]:((generous(X)|patient(X))=>humble(X)))&
(((~brave(john)&~tall(john)))<=>(?[X]:((funny(X)&~creative(X)))))&
((?[X]:((patient(X)|~wise(X))))<=>(?[X]:((~creative(X)<~>rich(X)))))&
((~calm(mary))=>((~brave(alice)<~>calm(alice))))&
(![X]:((calm(X)|curious(X))<=>(~patient(X)|~quiet(X))))&
(((~happy(paul)&curious(paul)))<=>(?[X]:(humble(X))))&
(((~funny(paul)|~patient(paul)))<=>(~wise(fred)))&
(![X]:(quiet(X)<=>(wise(X)&brave(X))))&
((~funny(susan)<~>kind(susan)))&
((~curious(fred)<~>happy(fred)))&
((strong(susan)<~>~tall(susan)))&
(?[X]:((old(X)|~old(X))))&
((~creative(alice)|~brave(alice)))&
(?[X]:((~tall(X)&funny(X))))&
((~wise(john)<~>~kind(john))) | ~quiet(fred) | [
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 420068015515241061987451
% SZS output start Proof for 420068015515241061987451
5. ! [X0] : ((strong(X0) | quiet(X0)) => ~brave(X0)) [input p4]
16. ! [X0] : (quiet(X0) <=> (brave(X0) & wise(X0))) [input p15]
24. quiet(fred) [input hypothesis]
30. ! [X0] : (~brave(X0) | (~strong(X0) & ~quiet(X0))) [ennf transformation 5]
75. ! [X0] : ((quiet(X0) | (~brave(X0) | ~wise(X0))) & ((brave(X0) & wise(X0)) | ~quiet(X0))) [nnf transformation 16]
76. ! [X0] : ((quiet(X0) | ~brave(X0) | ~wise(X0)) & ((brave(X0) & wise(X0)) | ~quiet(X0))) [flattening 75]
102. ~brave(X0) | ~quiet(X0) [cnf transformation 30]
140. brave(X0) | ~quiet(X0) [cnf transformation 76]
154. quiet(fred) [cnf transformation 24]
195. 10 <=> ! [X3] : ~quiet(X3) [avatar definition]
196. ~quiet(X3) <- (10) [avatar component clause 195]
355. ~quiet(X0) [subsumption resolution 140,102]
356. 10 [avatar split clause 355,195]
404. $false <- (10) [resolution 196,154]
405. ~10 [avatar contradiction clause 404]
406. $false [avatar sat refutation 356,405]
% SZS output end Proof for 420068015515241061987451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not funny or not brave then someone is both rich and not strong and vice versa.
Everyone who is not happy is both not wise and humble and vice versa.
If paul is not patient or brave then someone is quiet and vice versa.
Everyone who is calm or not humble is not happy or not curious and vice versa.
Everyone who is not old or not quiet is not brave and vice versa.
Everyone who is old is patient and vice versa.
Everyone who is not humble is brave and vice versa.
If someone is either not calm or happy then someone is not old or not wise.
Everyone who is not kind is not humble and vice versa.
If someone is both not brave and not old then someone is both not tall and not generous and vice versa.
Everyone who is both not curious and tall is not quiet or not patient and vice versa.
If someone is curious or not quiet then alice is both old and not calm.
Everyone who is both patient and not wise is either not old or curious and vice versa.
If john is not generous or tall then susan is not kind.
Everyone who is both tall and wise is either not quiet or not calm.
Everyone who is both calm and happy is either kind or humble and vice versa.
Someone is old or not wise.
Paul is either curious or not strong.
Someone is rich.
Alice is quiet or funny.
Mary is not strong. | Alice is not calm. | entailment | ((?[X]:((~funny(X)<~>~brave(X))))<=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:(~happy(X)<=>(~wise(X)&humble(X))))&
(((~patient(paul)|brave(paul)))<=>(?[X]:(quiet(X))))&
(![X]:((calm(X)|~humble(X))<=>(~happy(X)|~curious(X))))&
(![X]:((~old(X)|~quiet(X))<=>~brave(X)))&
(![X]:(old(X)<=>patient(X)))&
(![X]:(~humble(X)<=>brave(X)))&
((?[X]:((~calm(X)<~>happy(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:(~kind(X)<=>~humble(X)))&
((?[X]:((~brave(X)&~old(X))))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~curious(X)&tall(X))<=>(~quiet(X)|~patient(X))))&
((?[X]:((curious(X)|~quiet(X))))=>((old(alice)&~calm(alice))))&
(![X]:((patient(X)&~wise(X))<=>(~old(X)<~>curious(X))))&
(((~generous(john)|tall(john)))=>(~kind(susan)))&
(![X]:((tall(X)&wise(X))=>(~quiet(X)<~>~calm(X))))&
(![X]:((calm(X)&happy(X))<=>(kind(X)<~>humble(X))))&
(?[X]:((old(X)|~wise(X))))&
((curious(paul)<~>~strong(paul)))&
(?[X]:(rich(X)))&
((quiet(alice)|funny(alice)))&
(~strong(mary)) | ~calm(alice) | [
"p1",
"p4",
"p5",
"p6",
"p8",
"p10",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9100844497821026787218384
% SZS output start Proof for 9100844497821026787218384
2. ! [X0] : (~happy(X0) <=> (humble(X0) & ~wise(X0))) [input p1]
5. ! [X0] : ((~quiet(X0) | ~old(X0)) <=> ~brave(X0)) [input p4]
6. ! [X0] : (old(X0) <=> patient(X0)) [input p5]
7. ! [X0] : (~humble(X0) <=> brave(X0)) [input p6]
9. ! [X0] : (~kind(X0) <=> ~humble(X0)) [input p8]
11. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~patient(X0) | ~quiet(X0))) [input p10]
12. ? [X0] : (~quiet(X0) | curious(X0)) => (~calm(alice) & old(alice)) [input p11]
13. ! [X0] : ((~wise(X0) & patient(X0)) <=> (~old(X0) <~> curious(X0))) [input p12]
16. ! [X0] : ((happy(X0) & calm(X0)) <=> (kind(X0) <~> humble(X0))) [input p15]
22. calm(alice) [input hypothesis]
27. (~calm(alice) & old(alice)) | ! [X0] : (quiet(X0) & ~curious(X0)) [ennf transformation 12]
36. ! [X0] : ((~happy(X0) | (~humble(X0) | wise(X0))) & ((humble(X0) & ~wise(X0)) | happy(X0))) [nnf transformation 2]
37. ! [X0] : ((~happy(X0) | ~humble(X0) | wise(X0)) & ((humble(X0) & ~wise(X0)) | happy(X0))) [flattening 36]
45. ! [X0] : (((~quiet(X0) | ~old(X0)) | brave(X0)) & (~brave(X0) | (quiet(X0) & old(X0)))) [nnf transformation 5]
46. ! [X0] : ((~quiet(X0) | ~old(X0) | brave(X0)) & (~brave(X0) | (quiet(X0) & old(X0)))) [flattening 45]
47. ! [X0] : ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0))) [nnf transformation 6]
48. ! [X0] : ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0))) [nnf transformation 7]
53. ! [X0] : ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0))) [nnf transformation 9]
59. ! [X0] : (((tall(X0) & ~curious(X0)) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 11]
60. ! [X0] : (((tall(X0) & ~curious(X0)) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~tall(X0) | curious(X0))) [flattening 59]
61. ! [X0] : (((~wise(X0) & patient(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (wise(X0) | ~patient(X0)))) [nnf transformation 13]
62. ! [X0] : (((~wise(X0) & patient(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | wise(X0) | ~patient(X0))) [flattening 61]
64. ! [X0] : (((happy(X0) & calm(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (~happy(X0) | ~calm(X0)))) [nnf transformation 16]
65. ! [X0] : (((happy(X0) & calm(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | ~happy(X0) | ~calm(X0))) [flattening 64]
78. humble(X0) | happy(X0) [cnf transformation 37]
89. ~old(X0) | ~quiet(X0) | brave(X0) [cnf transformation 46]
90. ~old(X0) | patient(X0) [cnf transformation 47]
91. ~patient(X0) | old(X0) [cnf transformation 47]
93. ~humble(X0) | ~brave(X0) [cnf transformation 48]
96. ~humble(X0) | kind(X0) [cnf transformation 53]
97. ~kind(X0) | humble(X0) [cnf transformation 53]
104. ~curious(X0) | patient(X0) [cnf transformation 60]
110. ~calm(alice) | quiet(X0) [cnf transformation 27]
113. patient(X0) | curious(X0) | old(X0) [cnf transformation 62]
121. humble(X0) | kind(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 65]
122. ~humble(X0) | ~kind(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 65]
133. calm(alice) [cnf transformation 22]
186. 12 <=> ! [X1] : (~calm(X1) | ~happy(X1)) [avatar definition]
187. ~calm(X1) | ~happy(X1) <- (12) [avatar component clause 186]
212. 18 <=> ! [X3] : old(X3) [avatar definition]
213. old(X3) <- (18) [avatar component clause 212]
226. 21 <=> ! [X0] : quiet(X0) [avatar definition]
227. quiet(X0) <- (21) [avatar component clause 226]
229. 22 <=> calm(alice) [avatar definition]
230. calm(alice) <- (22) [avatar component clause 229]
232. 21 | ~22 [avatar split clause 110,229,226]
243. patient(X0) | curious(X0) [subsumption resolution 113,90]
244. patient(X0) [subsumption resolution 243,104]
261. ~kind(X0) | ~happy(X0) | ~calm(X0) [subsumption resolution 122,97]
262. kind(X0) | ~happy(X0) | ~calm(X0) [subsumption resolution 121,96]
263. ~happy(X0) | ~calm(X0) [subsumption resolution 262,261]
264. 12 [avatar split clause 263,186]
293. 22 [avatar split clause 133,229]
299. old(X0) [resolution 91,244]
300. 18 [avatar split clause 299,212]
305. ~brave(X1) | happy(X1) [resolution 93,78]
320. ~happy(alice) <- (12, 22) [resolution 187,230]
334. ~quiet(X0) | brave(X0) <- (18) [resolution 89,213]
335. brave(X0) <- (18, 21) [subsumption resolution 334,227]
336. happy(X0) <- (18, 21) [resolution 335,305]
342. $false <- (12, 18, 21, 22) [resolution 336,320]
343. ~12 | ~18 | ~21 | ~22 [avatar contradiction clause 342]
344. $false [avatar sat refutation 232,264,293,300,343]
% SZS output end Proof for 9100844497821026787218384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is kind then someone is not funny or not curious.
If someone is either old or rich then fred is old or brave and vice versa.
If someone is not funny then someone is either not calm or tall.
Everyone who is either generous or not strong is not wise or not funny and vice versa.
If someone is both strong and creative then fred is not calm and vice versa.
If someone is both generous and quiet then someone is not kind or not calm and vice versa.
Everyone who is funny is not funny or brave.
If fred is not rich then someone is either not tall or not humble and vice versa.
Everyone who is strong or not patient is not creative or humble and vice versa.
Everyone who is both generous and tall is rich or creative and vice versa.
Everyone who is generous or not wise is not generous.
Everyone who is both wise and not patient is wise or not brave.
Everyone who is both not creative and curious is either old or creative and vice versa.
If someone is both creative and happy then paul is both rich and brave and vice versa.
Everyone who is both not old and not creative is creative.
If paul is both not funny and rich then someone is kind or wise.
Paul is not funny or not happy.
Someone is not wise or not calm.
Paul is not old or not funny.
Someone is both funny and patient.
Mary is patient.
Someone is either not happy or not patient. | Fred is not funny. | neutral | ((kind(lucy))=>(?[X]:((~funny(X)|~curious(X)))))&
((?[X]:((old(X)<~>rich(X))))<=>((old(fred)|brave(fred))))&
((?[X]:(~funny(X)))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:((generous(X)<~>~strong(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((strong(X)&creative(X))))<=>(~calm(fred)))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:(funny(X)=>(~funny(X)|brave(X))))&
((~rich(fred))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((strong(X)|~patient(X))<=>(~creative(X)|humble(X))))&
(![X]:((generous(X)&tall(X))<=>(rich(X)|creative(X))))&
(![X]:((generous(X)|~wise(X))=>~generous(X)))&
(![X]:((wise(X)&~patient(X))=>(wise(X)|~brave(X))))&
(![X]:((~creative(X)&curious(X))<=>(old(X)<~>creative(X))))&
((?[X]:((creative(X)&happy(X))))<=>((rich(paul)&brave(paul))))&
(![X]:((~old(X)&~creative(X))=>creative(X)))&
(((~funny(paul)&rich(paul)))=>(?[X]:((kind(X)|wise(X)))))&
((~funny(paul)|~happy(paul)))&
(?[X]:((~wise(X)|~calm(X))))&
((~old(paul)|~funny(paul)))&
(?[X]:((funny(X)&patient(X))))&
(patient(mary))&
(?[X]:((~happy(X)<~>~patient(X)))) | ~funny(fred) | [] | null | 0 |
If alice is both not quiet and not humble then someone is both rich and happy and vice versa. Everyone who is happy or not patient is patient or not patient. Everyone who is curious or not funny is both creative and not funny and vice versa. Everyone who is tall is not generous. Everyone who is either creative or not kind is not old and vice versa. Everyone who is quiet or not strong is happy or kind. Everyone who is either wise or tall is either not creative or not strong. If susan is both not generous and not patient then paul is both not kind and not patient. Everyone who is not generous or generous is either not tall or humble and vice versa. Everyone who is humble or generous is happy or wise. If fred is either calm or creative then fred is either strong or creative and vice versa. Everyone who is either not calm or not happy is either funny or wise and vice versa. If someone is both kind and brave then someone is creative and vice versa. If alice is both generous and brave then someone is not rich. Everyone who is either quiet or strong is not quiet and vice versa. Everyone who is both rich and calm is happy or creative and vice versa. Fred is not rich or not patient. Mary is brave or not wise. Susan is both generous and rich. Alice is both not funny and humble. Someone is not calm or funny. Mary is funny. Paul is not old. | Susan is not happy. | entailment | (((~quiet(alice)&~humble(alice)))<=>(?[X]:((rich(X)&happy(X)))))&
(![X]:((happy(X)|~patient(X))=>(patient(X)|~patient(X))))&
(![X]:((curious(X)|~funny(X))<=>(creative(X)&~funny(X))))&
(![X]:(tall(X)=>~generous(X)))&
(![X]:((creative(X)<~>~kind(X))<=>~old(X)))&
(![X]:((quiet(X)|~strong(X))=>(happy(X)|kind(X))))&
(![X]:((wise(X)<~>tall(X))=>(~creative(X)<~>~strong(X))))&
(((~generous(susan)&~patient(susan)))=>((~kind(paul)&~patient(paul))))&
(![X]:((~generous(X)|generous(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((humble(X)|generous(X))=>(happy(X)|wise(X))))&
(((calm(fred)<~>creative(fred)))<=>((strong(fred)<~>creative(fred))))&
(![X]:((~calm(X)<~>~happy(X))<=>(funny(X)<~>wise(X))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:(creative(X))))&
(((generous(alice)&brave(alice)))=>(?[X]:(~rich(X))))&
(![X]:((quiet(X)<~>strong(X))<=>~quiet(X)))&
(![X]:((rich(X)&calm(X))<=>(happy(X)|creative(X))))&
((~rich(fred)|~patient(fred)))&
((brave(mary)|~wise(mary)))&
((generous(susan)&rich(susan)))&
((~funny(alice)&humble(alice)))&
(?[X]:((~calm(X)|funny(X))))&
(funny(mary))&
(~old(paul)) | ~happy(susan) | [
"p0",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8031972285737657674745224
% SZS output start Proof for 8031972285737657674745224
1. (~humble(alice) & ~quiet(alice)) <=> ? [X0] : (happy(X0) & rich(X0)) [input p0]
16. ! [X0] : ((calm(X0) & rich(X0)) <=> (creative(X0) | happy(X0))) [input p15]
20. humble(alice) & ~funny(alice) [input p19]
24. happy(susan) [input hypothesis]
40. ((~humble(alice) & ~quiet(alice)) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X0] : (happy(X0) & rich(X0)) | (humble(alice) | quiet(alice))) [nnf transformation 1]
41. ((~humble(alice) & ~quiet(alice)) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X0] : (happy(X0) & rich(X0)) | humble(alice) | quiet(alice)) [flattening 40]
42. ((~humble(alice) & ~quiet(alice)) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X1] : (happy(X1) & rich(X1)) | humble(alice) | quiet(alice)) [rectify 41]
43. ? [X1] : (happy(X1) & rich(X1)) => (happy(sK0) & rich(sK0)) [choice axiom]
44. ((~humble(alice) & ~quiet(alice)) | ! [X0] : (~happy(X0) | ~rich(X0))) & ((happy(sK0) & rich(sK0)) | humble(alice) | quiet(alice)) [skolemisation 42,43]
61. ! [X0] : (((calm(X0) & rich(X0)) | (~creative(X0) & ~happy(X0))) & ((creative(X0) | happy(X0)) | (~calm(X0) | ~rich(X0)))) [nnf transformation 16]
62. ! [X0] : (((calm(X0) & rich(X0)) | (~creative(X0) & ~happy(X0))) & (creative(X0) | happy(X0) | ~calm(X0) | ~rich(X0))) [flattening 61]
68. ~humble(alice) | ~happy(X0) | ~rich(X0) [cnf transformation 44]
120. rich(X0) | ~happy(X0) [cnf transformation 62]
129. humble(alice) [cnf transformation 20]
133. happy(susan) [cnf transformation 24]
142. 1 <=> ! [X0] : (~happy(X0) | ~rich(X0)) [avatar definition]
143. ~happy(X0) | ~rich(X0) <- (1) [avatar component clause 142]
145. 2 <=> humble(alice) [avatar definition]
148. 1 | ~2 [avatar split clause 68,145,142]
255. 2 [avatar split clause 129,145]
267. ~happy(X0) <- (1) [subsumption resolution 143,120]
268. $false <- (1) [resolution 267,133]
269. ~1 [avatar contradiction clause 268]
270. $false [avatar sat refutation 148,255,269]
% SZS output end Proof for 8031972285737657674745224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise then someone is either not strong or brave and vice versa.
Everyone who is both quiet and calm is either kind or not humble.
Everyone who is both creative and funny is both not quiet and patient and vice versa.
Everyone who is either not wise or generous is both not wise and not funny and vice versa.
Everyone who is both tall and not wise is not generous or tall and vice versa.
Everyone who is either patient or happy is either happy or wise.
Everyone who is either patient or humble is not funny or quiet and vice versa.
If susan is either not quiet or calm then someone is not kind and vice versa.
If someone is kind then mary is not calm and vice versa.
Everyone who is funny is curious or not curious and vice versa.
If someone is not wise or not creative then someone is either happy or old and vice versa.
If paul is not wise or humble then john is either not old or happy.
If someone is either curious or not calm then lucy is kind and vice versa.
Everyone who is creative or not old is both tall and not patient and vice versa.
Everyone who is either humble or not strong is not kind.
If someone is either not old or humble then someone is not tall or not curious.
Someone is either patient or creative.
Lucy is either generous or not quiet.
Susan is either old or brave.
Someone is either tall or old.
Lucy is rich.
Someone is either not creative or not old.
Paul is not rich or not old.
Paul is generous. | Susan is funny. | entailment | ((?[X]:(wise(X)))<=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:((quiet(X)&calm(X))=>(kind(X)<~>~humble(X))))&
(![X]:((creative(X)&funny(X))<=>(~quiet(X)&patient(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:((tall(X)&~wise(X))<=>(~generous(X)|tall(X))))&
(![X]:((patient(X)<~>happy(X))=>(happy(X)<~>wise(X))))&
(![X]:((patient(X)<~>humble(X))<=>(~funny(X)|quiet(X))))&
(((~quiet(susan)<~>calm(susan)))<=>(?[X]:(~kind(X))))&
((?[X]:(kind(X)))<=>(~calm(mary)))&
(![X]:(funny(X)<=>(curious(X)|~curious(X))))&
((?[X]:((~wise(X)|~creative(X))))<=>(?[X]:((happy(X)<~>old(X)))))&
(((~wise(paul)|humble(paul)))=>((~old(john)<~>happy(john))))&
((?[X]:((curious(X)<~>~calm(X))))<=>(kind(lucy)))&
(![X]:((creative(X)|~old(X))<=>(tall(X)&~patient(X))))&
(![X]:((humble(X)<~>~strong(X))=>~kind(X)))&
((?[X]:((~old(X)<~>humble(X))))=>(?[X]:((~tall(X)|~curious(X)))))&
(?[X]:((patient(X)<~>creative(X))))&
((generous(lucy)<~>~quiet(lucy)))&
((old(susan)<~>brave(susan)))&
(?[X]:((tall(X)<~>old(X))))&
(rich(lucy))&
(?[X]:((~creative(X)<~>~old(X))))&
((~rich(paul)|~old(paul)))&
(generous(paul)) | funny(susan) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6964503876999115667722227
% SZS output start Proof for 6964503876999115667722227
10. ! [X0] : (funny(X0) <=> (~curious(X0) | curious(X0))) [input p9]
25. ~funny(susan) [input hypothesis]
58. ! [X0] : ((funny(X0) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | ~funny(X0))) [nnf transformation 10]
59. ! [X0] : ((funny(X0) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | ~funny(X0))) [flattening 58]
126. funny(X0) | ~curious(X0) [cnf transformation 59]
127. funny(X0) | curious(X0) [cnf transformation 59]
164. ~funny(susan) [cnf transformation 25]
229. funny(X0) [subsumption resolution 126,127]
379. $false [subsumption resolution 164,229]
% SZS output end Proof for 6964503876999115667722227
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and kind is not calm.
If someone is either not patient or not curious then paul is either not humble or not funny.
Everyone who is tall is both humble and happy.
Everyone who is not quiet or not tall is curious.
If someone is either patient or not curious then someone is not happy or not rich.
Everyone who is rich is patient.
Everyone who is both curious and not tall is curious or funny and vice versa.
If someone is not tall then someone is either tall or not old.
If paul is either creative or patient then paul is creative and vice versa.
If someone is both happy and not kind then mary is not creative or not humble.
Everyone who is generous or not curious is either not humble or tall.
If susan is both not old and not strong then someone is not brave or not patient and vice versa.
If alice is both patient and not patient then someone is tall or creative and vice versa.
Everyone who is either wise or kind is both old and not old and vice versa.
If fred is both not wise and rich then alice is either wise or rich and vice versa.
Someone is both brave and not quiet.
Alice is not happy.
Lucy is not humble or not rich.
Someone is calm.
Someone is funny or not generous. | Lucy is not brave. | neutral | (![X]:((~calm(X)&kind(X))=>~calm(X)))&
((?[X]:((~patient(X)<~>~curious(X))))=>((~humble(paul)<~>~funny(paul))))&
(![X]:(tall(X)=>(humble(X)&happy(X))))&
(![X]:((~quiet(X)|~tall(X))=>curious(X)))&
((?[X]:((patient(X)<~>~curious(X))))=>(?[X]:((~happy(X)|~rich(X)))))&
(![X]:(rich(X)=>patient(X)))&
(![X]:((curious(X)&~tall(X))<=>(curious(X)|funny(X))))&
((?[X]:(~tall(X)))=>(?[X]:((tall(X)<~>~old(X)))))&
(((creative(paul)<~>patient(paul)))<=>(creative(paul)))&
((?[X]:((happy(X)&~kind(X))))=>((~creative(mary)|~humble(mary))))&
(![X]:((generous(X)|~curious(X))=>(~humble(X)<~>tall(X))))&
(((~old(susan)&~strong(susan)))<=>(?[X]:((~brave(X)|~patient(X)))))&
(((patient(alice)&~patient(alice)))<=>(?[X]:((tall(X)|creative(X)))))&
(![X]:((wise(X)<~>kind(X))<=>(old(X)&~old(X))))&
(((~wise(fred)&rich(fred)))<=>((wise(alice)<~>rich(alice))))&
(?[X]:((brave(X)&~quiet(X))))&
(~happy(alice))&
((~humble(lucy)|~rich(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((funny(X)|~generous(X)))) | ~brave(lucy) | [] | null | 0 |
Everyone who is calm or kind is strong. Everyone who is generous or calm is both not creative and kind and vice versa. Everyone who is both not curious and curious is not calm. If someone is humble then paul is either not tall or generous and vice versa. If someone is both not kind and strong then paul is both not old and rich and vice versa. Everyone who is both patient and brave is tall or funny and vice versa. Everyone who is not quiet or not rich is both kind and not rich. If someone is brave then mary is tall and vice versa. Everyone who is either not patient or not calm is either not funny or not quiet. Everyone who is not tall is either patient or not curious. Everyone who is calm or funny is old and vice versa. If mary is quiet or calm then john is curious and vice versa. Everyone who is not funny or quiet is either creative or not calm. If fred is not brave or not wise then someone is either not curious or not patient and vice versa. Everyone who is both curious and not curious is either not kind or not wise and vice versa. If someone is kind then someone is humble and vice versa. Someone is not brave or not generous. Someone is kind or not rich. Paul is not patient. Someone is either strong or not patient. Someone is rich. Someone is either wise or old. Someone is creative or calm. Lucy is both tall and funny. | John is calm. | neutral | (![X]:((calm(X)|kind(X))=>strong(X)))&
(![X]:((generous(X)|calm(X))<=>(~creative(X)&kind(X))))&
(![X]:((~curious(X)&curious(X))=>~calm(X)))&
((?[X]:(humble(X)))<=>((~tall(paul)<~>generous(paul))))&
((?[X]:((~kind(X)&strong(X))))<=>((~old(paul)&rich(paul))))&
(![X]:((patient(X)&brave(X))<=>(tall(X)|funny(X))))&
(![X]:((~quiet(X)|~rich(X))=>(kind(X)&~rich(X))))&
((?[X]:(brave(X)))<=>(tall(mary)))&
(![X]:((~patient(X)<~>~calm(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:(~tall(X)=>(patient(X)<~>~curious(X))))&
(![X]:((calm(X)|funny(X))<=>old(X)))&
(((quiet(mary)|calm(mary)))<=>(curious(john)))&
(![X]:((~funny(X)|quiet(X))=>(creative(X)<~>~calm(X))))&
(((~brave(fred)|~wise(fred)))<=>(?[X]:((~curious(X)<~>~patient(X)))))&
(![X]:((curious(X)&~curious(X))<=>(~kind(X)<~>~wise(X))))&
((?[X]:(kind(X)))<=>(?[X]:(humble(X))))&
(?[X]:((~brave(X)|~generous(X))))&
(?[X]:((kind(X)|~rich(X))))&
(~patient(paul))&
(?[X]:((strong(X)<~>~patient(X))))&
(?[X]:(rich(X)))&
(?[X]:((wise(X)<~>old(X))))&
(?[X]:((creative(X)|calm(X))))&
((tall(lucy)&funny(lucy))) | calm(john) | [] | null | 0 |
If lucy is creative or not curious then susan is both not patient and not calm.
Everyone who is either brave or not happy is both not patient and not funny and vice versa.
Everyone who is patient is both not humble and not calm.
If someone is humble then lucy is not rich or not generous.
Everyone who is both brave and wise is either kind or not curious and vice versa.
If someone is either curious or kind then john is both calm and not creative.
Everyone who is either not strong or not humble is both not calm and humble and vice versa.
If someone is happy or not quiet then someone is patient or kind and vice versa.
Everyone who is not rich is both not wise and humble.
If john is not curious or happy then someone is both humble and generous and vice versa.
Everyone who is either not kind or patient is either not kind or rich and vice versa.
If john is quiet then paul is either rich or not funny.
Everyone who is either not quiet or humble is either creative or calm.
Everyone who is not patient is either not curious or curious.
Everyone who is both old and not humble is either not quiet or generous.
Everyone who is either not funny or not calm is either strong or creative.
Paul is both old and strong.
Someone is tall.
Alice is either not happy or not humble.
Someone is happy.
Susan is either kind or humble.
Someone is not strong or not quiet.
Alice is calm.
Someone is not humble. | Paul is not strong. | contradiction | (((creative(lucy)|~curious(lucy)))=>((~patient(susan)&~calm(susan))))&
(![X]:((brave(X)<~>~happy(X))<=>(~patient(X)&~funny(X))))&
(![X]:(patient(X)=>(~humble(X)&~calm(X))))&
((?[X]:(humble(X)))=>((~rich(lucy)|~generous(lucy))))&
(![X]:((brave(X)&wise(X))<=>(kind(X)<~>~curious(X))))&
((?[X]:((curious(X)<~>kind(X))))=>((calm(john)&~creative(john))))&
(![X]:((~strong(X)<~>~humble(X))<=>(~calm(X)&humble(X))))&
((?[X]:((happy(X)|~quiet(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:(~rich(X)=>(~wise(X)&humble(X))))&
(((~curious(john)|happy(john)))<=>(?[X]:((humble(X)&generous(X)))))&
(![X]:((~kind(X)<~>patient(X))<=>(~kind(X)<~>rich(X))))&
((quiet(john))=>((rich(paul)<~>~funny(paul))))&
(![X]:((~quiet(X)<~>humble(X))=>(creative(X)<~>calm(X))))&
(![X]:(~patient(X)=>(~curious(X)<~>curious(X))))&
(![X]:((old(X)&~humble(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((~funny(X)<~>~calm(X))=>(strong(X)<~>creative(X))))&
((old(paul)&strong(paul)))&
(?[X]:(tall(X)))&
((~happy(alice)<~>~humble(alice)))&
(?[X]:(happy(X)))&
((kind(susan)<~>humble(susan)))&
(?[X]:((~strong(X)|~quiet(X))))&
(calm(alice))&
(?[X]:(~humble(X))) | ~strong(paul) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7075419820523174866646939
% SZS output start Proof for 7075419820523174866646939
17. strong(paul) & old(paul) [input p16]
25. ~strong(paul) [input hypothesis]
134. strong(paul) [cnf transformation 17]
143. ~strong(paul) [cnf transformation 25]
301. $false [subsumption resolution 143,134]
% SZS output end Proof for 7075419820523174866646939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either kind or rich then fred is happy or brave.
If paul is brave then someone is both calm and patient and vice versa.
Everyone who is not tall is not kind and vice versa.
If someone is either not curious or not strong then john is either not happy or wise.
Everyone who is not happy or kind is both not rich and happy and vice versa.
If susan is not tall or not old then someone is not creative or old.
If someone is either brave or not tall then someone is curious and vice versa.
Everyone who is creative or old is either not wise or calm.
Everyone who is both quiet and not creative is either not quiet or strong.
If fred is not funny then someone is both not creative and not calm.
Everyone who is brave or not creative is either quiet or not patient and vice versa.
Everyone who is brave or rich is funny or old and vice versa.
Everyone who is not patient or humble is not brave or not wise.
If someone is not brave or kind then someone is both rich and not old.
Everyone who is not strong is patient or not happy and vice versa.
Everyone who is generous is both kind and not generous and vice versa.
Susan is either happy or wise.
Someone is not quiet.
Paul is not generous.
Paul is either not strong or wise.
Someone is both brave and patient. | John is old. | neutral | (((kind(lucy)<~>rich(lucy)))=>((happy(fred)|brave(fred))))&
((brave(paul))<=>(?[X]:((calm(X)&patient(X)))))&
(![X]:(~tall(X)<=>~kind(X)))&
((?[X]:((~curious(X)<~>~strong(X))))=>((~happy(john)<~>wise(john))))&
(![X]:((~happy(X)|kind(X))<=>(~rich(X)&happy(X))))&
(((~tall(susan)|~old(susan)))=>(?[X]:((~creative(X)|old(X)))))&
((?[X]:((brave(X)<~>~tall(X))))<=>(?[X]:(curious(X))))&
(![X]:((creative(X)|old(X))=>(~wise(X)<~>calm(X))))&
(![X]:((quiet(X)&~creative(X))=>(~quiet(X)<~>strong(X))))&
((~funny(fred))=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((brave(X)|~creative(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:((brave(X)|rich(X))<=>(funny(X)|old(X))))&
(![X]:((~patient(X)|humble(X))=>(~brave(X)|~wise(X))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((rich(X)&~old(X)))))&
(![X]:(~strong(X)<=>(patient(X)|~happy(X))))&
(![X]:(generous(X)<=>(kind(X)&~generous(X))))&
((happy(susan)<~>wise(susan)))&
(?[X]:(~quiet(X)))&
(~generous(paul))&
((~strong(paul)<~>wise(paul)))&
(?[X]:((brave(X)&patient(X)))) | old(john) | [] | null | 0 |
Everyone who is funny or not tall is both not tall and not quiet.
Everyone who is not generous is not kind and vice versa.
If susan is not quiet then someone is both not strong and not happy.
Everyone who is either not humble or not brave is either calm or not generous.
Everyone who is either not old or generous is both calm and not strong.
If paul is both strong and not calm then alice is not rich.
Everyone who is both funny and patient is both generous and not kind.
If mary is both not kind and brave then susan is tall and vice versa.
Everyone who is both happy and not calm is either not tall or wise and vice versa.
Everyone who is not quiet or not brave is patient or wise.
If someone is not humble then someone is strong or not patient.
Everyone who is both not patient and quiet is not rich or not wise and vice versa.
Everyone who is either not rich or not funny is both calm and not funny and vice versa.
If someone is either rich or calm then fred is happy and vice versa.
Everyone who is both not generous and not rich is curious and vice versa.
If fred is either not kind or quiet then someone is both rich and old and vice versa.
Lucy is wise.
Someone is either not quiet or rich.
John is patient.
John is strong or quiet.
Someone is patient.
Someone is both creative and calm.
Someone is both rich and wise.
Paul is not funny. | Paul is funny. | contradiction | (![X]:((funny(X)|~tall(X))=>(~tall(X)&~quiet(X))))&
(![X]:(~generous(X)<=>~kind(X)))&
((~quiet(susan))=>(?[X]:((~strong(X)&~happy(X)))))&
(![X]:((~humble(X)<~>~brave(X))=>(calm(X)<~>~generous(X))))&
(![X]:((~old(X)<~>generous(X))=>(calm(X)&~strong(X))))&
(((strong(paul)&~calm(paul)))=>(~rich(alice)))&
(![X]:((funny(X)&patient(X))=>(generous(X)&~kind(X))))&
(((~kind(mary)&brave(mary)))<=>(tall(susan)))&
(![X]:((happy(X)&~calm(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~quiet(X)|~brave(X))=>(patient(X)|wise(X))))&
((?[X]:(~humble(X)))=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~patient(X)&quiet(X))<=>(~rich(X)|~wise(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(calm(X)&~funny(X))))&
((?[X]:((rich(X)<~>calm(X))))<=>(happy(fred)))&
(![X]:((~generous(X)&~rich(X))<=>curious(X)))&
(((~kind(fred)<~>quiet(fred)))<=>(?[X]:((rich(X)&old(X)))))&
(wise(lucy))&
(?[X]:((~quiet(X)<~>rich(X))))&
(patient(john))&
((strong(john)|quiet(john)))&
(?[X]:(patient(X)))&
(?[X]:((creative(X)&calm(X))))&
(?[X]:((rich(X)&wise(X))))&
(~funny(paul)) | funny(paul) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7878813963660820343853072
% SZS output start Proof for 7878813963660820343853072
24. ~funny(paul) [input p23]
25. funny(paul) [input hypothesis]
133. ~funny(paul) [cnf transformation 24]
134. funny(paul) [cnf transformation 25]
249. $false [subsumption resolution 134,133]
% SZS output end Proof for 7878813963660820343853072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not brave is not kind or quiet. If someone is not patient or not old then someone is wise or rich and vice versa. Everyone who is not funny or not humble is either calm or strong. If someone is not strong then someone is not wise and vice versa. If someone is either not old or calm then someone is either tall or not generous and vice versa. If someone is both not funny and patient then someone is humble. Everyone who is either kind or not rich is not curious and vice versa. Everyone who is both strong and not strong is not kind or quiet. If someone is not kind or patient then susan is both patient and curious and vice versa. If alice is not kind then someone is either calm or not kind and vice versa. If someone is both tall and not tall then someone is both strong and curious and vice versa. Everyone who is either not curious or not generous is curious and vice versa. If someone is not old then someone is curious and vice versa. Everyone who is both not humble and not kind is calm and vice versa. If someone is either not brave or not quiet then someone is both rich and not curious. Mary is either not kind or old. Someone is tall. John is kind or strong. Paul is both not quiet and curious. Fred is either old or calm. Someone is brave or not old. Someone is not curious. Fred is not funny. | Mary is kind. | neutral | (![X]:((~wise(X)<~>~brave(X))=>(~kind(X)|quiet(X))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((wise(X)|rich(X)))))&
(![X]:((~funny(X)|~humble(X))=>(calm(X)<~>strong(X))))&
((?[X]:(~strong(X)))<=>(?[X]:(~wise(X))))&
((?[X]:((~old(X)<~>calm(X))))<=>(?[X]:((tall(X)<~>~generous(X)))))&
((?[X]:((~funny(X)&patient(X))))=>(?[X]:(humble(X))))&
(![X]:((kind(X)<~>~rich(X))<=>~curious(X)))&
(![X]:((strong(X)&~strong(X))=>(~kind(X)|quiet(X))))&
((?[X]:((~kind(X)|patient(X))))<=>((patient(susan)&curious(susan))))&
((~kind(alice))<=>(?[X]:((calm(X)<~>~kind(X)))))&
((?[X]:((tall(X)&~tall(X))))<=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((~curious(X)<~>~generous(X))<=>curious(X)))&
((?[X]:(~old(X)))<=>(?[X]:(curious(X))))&
(![X]:((~humble(X)&~kind(X))<=>calm(X)))&
((?[X]:((~brave(X)<~>~quiet(X))))=>(?[X]:((rich(X)&~curious(X)))))&
((~kind(mary)<~>old(mary)))&
(?[X]:(tall(X)))&
((kind(john)|strong(john)))&
((~quiet(paul)&curious(paul)))&
((old(fred)<~>calm(fred)))&
(?[X]:((brave(X)|~old(X))))&
(?[X]:(~curious(X)))&
(~funny(fred)) | kind(mary) | [] | null | 0 |
Everyone who is both not patient and not creative is not rich and vice versa.
If lucy is either happy or generous then someone is patient or not curious.
Everyone who is strong or tall is old.
If lucy is either not funny or kind then fred is calm and vice versa.
Everyone who is both calm and happy is either not old or not quiet.
Everyone who is not patient or tall is either not old or not rich and vice versa.
Everyone who is not old is strong and vice versa.
If mary is either not happy or not wise then someone is not tall and vice versa.
Everyone who is either not creative or old is generous or brave.
Everyone who is funny or not creative is both generous and quiet.
If susan is both brave and generous then fred is not curious or tall and vice versa.
If john is not patient or creative then mary is both strong and curious and vice versa.
If mary is both not patient and rich then susan is either not kind or not tall.
Everyone who is either not brave or not curious is humble.
If paul is humble or not happy then alice is rich or not kind.
Everyone who is not tall is either not happy or not patient and vice versa.
Alice is funny.
Paul is both not kind and not brave.
Someone is wise or happy.
Someone is either old or not happy.
Alice is either generous or rich. | Susan is tall. | neutral | (![X]:((~patient(X)&~creative(X))<=>~rich(X)))&
(((happy(lucy)<~>generous(lucy)))=>(?[X]:((patient(X)|~curious(X)))))&
(![X]:((strong(X)|tall(X))=>old(X)))&
(((~funny(lucy)<~>kind(lucy)))<=>(calm(fred)))&
(![X]:((calm(X)&happy(X))=>(~old(X)<~>~quiet(X))))&
(![X]:((~patient(X)|tall(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(~old(X)<=>strong(X)))&
(((~happy(mary)<~>~wise(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((~creative(X)<~>old(X))=>(generous(X)|brave(X))))&
(![X]:((funny(X)|~creative(X))=>(generous(X)&quiet(X))))&
(((brave(susan)&generous(susan)))<=>((~curious(fred)|tall(fred))))&
(((~patient(john)|creative(john)))<=>((strong(mary)&curious(mary))))&
(((~patient(mary)&rich(mary)))=>((~kind(susan)<~>~tall(susan))))&
(![X]:((~brave(X)<~>~curious(X))=>humble(X)))&
(((humble(paul)|~happy(paul)))=>((rich(alice)|~kind(alice))))&
(![X]:(~tall(X)<=>(~happy(X)<~>~patient(X))))&
(funny(alice))&
((~kind(paul)&~brave(paul)))&
(?[X]:((wise(X)|happy(X))))&
(?[X]:((old(X)<~>~happy(X))))&
((generous(alice)<~>rich(alice))) | tall(susan) | [] | null | 0 |
Everyone who is both not curious and kind is happy and vice versa.
If lucy is both brave and humble then someone is patient or wise.
Everyone who is creative is generous or not calm and vice versa.
If susan is both not calm and happy then someone is both rich and not old and vice versa.
If someone is not brave or not patient then fred is old and vice versa.
If lucy is not creative then fred is not wise and vice versa.
Everyone who is brave or not tall is calm or not rich and vice versa.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Susan is not happy.
Fred is not patient.
Mary is brave or curious.
Someone is patient.
Susan is calm or not rich.
Someone is happy or strong. | Fred is curious. | entailment | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:(creative(X)<=>(generous(X)|~calm(X))))&
(((~calm(susan)&happy(susan)))<=>(?[X]:((rich(X)&~old(X)))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(~happy(susan))&
(~patient(fred))&
((brave(mary)|curious(mary)))&
(?[X]:(patient(X)))&
((calm(susan)|~rich(susan)))&
(?[X]:((happy(X)|strong(X)))) | curious(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5952154191644998489686153
% SZS output start Proof for 5952154191644998489686153
13. ! [X0] : ((generous(X0) | ~curious(X0)) <=> curious(X0)) [input p12]
22. ~curious(fred) [input hypothesis]
53. ! [X0] : (((generous(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [nnf transformation 13]
54. ! [X0] : ((generous(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [flattening 53]
93. curious(X0) | curious(X0) [cnf transformation 54]
114. ~curious(fred) [cnf transformation 22]
115. curious(X0) [duplicate literal removal 93]
221. $false [subsumption resolution 114,115]
% SZS output end Proof for 5952154191644998489686153
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and generous is patient.
Everyone who is both not old and not funny is not creative or not funny and vice versa.
Everyone who is both not patient and not creative is not tall and vice versa.
Everyone who is funny is either not strong or not brave.
Everyone who is not creative is both creative and not kind.
Everyone who is not strong is not old or not humble.
Everyone who is either strong or not humble is quiet and vice versa.
Everyone who is not rich is either calm or rich and vice versa.
Everyone who is humble or generous is both not tall and tall.
If paul is not wise then fred is both not humble and rich.
If susan is not curious then paul is either not funny or humble.
If john is not generous then alice is both not happy and kind and vice versa.
If someone is not kind or happy then fred is either funny or tall.
If alice is both generous and calm then someone is kind or tall.
Everyone who is quiet is both not funny and quiet.
Alice is either quiet or funny.
Someone is wise or not strong.
Fred is happy. | Fred is not quiet. | neutral | (![X]:((curious(X)&generous(X))=>patient(X)))&
(![X]:((~old(X)&~funny(X))<=>(~creative(X)|~funny(X))))&
(![X]:((~patient(X)&~creative(X))<=>~tall(X)))&
(![X]:(funny(X)=>(~strong(X)<~>~brave(X))))&
(![X]:(~creative(X)=>(creative(X)&~kind(X))))&
(![X]:(~strong(X)=>(~old(X)|~humble(X))))&
(![X]:((strong(X)<~>~humble(X))<=>quiet(X)))&
(![X]:(~rich(X)<=>(calm(X)<~>rich(X))))&
(![X]:((humble(X)|generous(X))=>(~tall(X)&tall(X))))&
((~wise(paul))=>((~humble(fred)&rich(fred))))&
((~curious(susan))=>((~funny(paul)<~>humble(paul))))&
((~generous(john))<=>((~happy(alice)&kind(alice))))&
((?[X]:((~kind(X)|happy(X))))=>((funny(fred)<~>tall(fred))))&
(((generous(alice)&calm(alice)))=>(?[X]:((kind(X)|tall(X)))))&
(![X]:(quiet(X)=>(~funny(X)&quiet(X))))&
((quiet(alice)<~>funny(alice)))&
(?[X]:((wise(X)|~strong(X))))&
(happy(fred)) | ~quiet(fred) | [] | null | 0 |
If lucy is strong then alice is either not old or not calm.
If john is both not old and humble then someone is either not brave or creative.
Everyone who is not generous or generous is both creative and rich.
Everyone who is both not quiet and happy is either brave or calm and vice versa.
If alice is generous or calm then someone is tall.
Everyone who is funny or not rich is either creative or not patient.
Everyone who is both quiet and funny is calm or brave and vice versa.
Everyone who is not kind is not patient and vice versa.
Everyone who is strong or curious is calm or funny and vice versa.
If someone is not curious then someone is either tall or calm.
If mary is either quiet or calm then susan is either not calm or curious.
If susan is either calm or not funny then susan is either quiet or calm and vice versa.
If alice is both not wise and calm then paul is not calm or generous and vice versa.
Everyone who is not generous or tall is either happy or not old and vice versa.
If someone is either strong or calm then someone is both not patient and strong and vice versa.
If someone is not calm or quiet then fred is both happy and not strong and vice versa.
Lucy is both funny and not curious.
Someone is either not brave or humble.
Susan is humble.
Someone is not happy.
Lucy is funny.
John is either not curious or not brave. | Mary is old. | neutral | ((strong(lucy))=>((~old(alice)<~>~calm(alice))))&
(((~old(john)&humble(john)))=>(?[X]:((~brave(X)<~>creative(X)))))&
(![X]:((~generous(X)|generous(X))=>(creative(X)&rich(X))))&
(![X]:((~quiet(X)&happy(X))<=>(brave(X)<~>calm(X))))&
(((generous(alice)|calm(alice)))=>(?[X]:(tall(X))))&
(![X]:((funny(X)|~rich(X))=>(creative(X)<~>~patient(X))))&
(![X]:((quiet(X)&funny(X))<=>(calm(X)|brave(X))))&
(![X]:(~kind(X)<=>~patient(X)))&
(![X]:((strong(X)|curious(X))<=>(calm(X)|funny(X))))&
((?[X]:(~curious(X)))=>(?[X]:((tall(X)<~>calm(X)))))&
(((quiet(mary)<~>calm(mary)))=>((~calm(susan)<~>curious(susan))))&
(((calm(susan)<~>~funny(susan)))<=>((quiet(susan)<~>calm(susan))))&
(((~wise(alice)&calm(alice)))<=>((~calm(paul)|generous(paul))))&
(![X]:((~generous(X)|tall(X))<=>(happy(X)<~>~old(X))))&
((?[X]:((strong(X)<~>calm(X))))<=>(?[X]:((~patient(X)&strong(X)))))&
((?[X]:((~calm(X)|quiet(X))))<=>((happy(fred)&~strong(fred))))&
((funny(lucy)&~curious(lucy)))&
(?[X]:((~brave(X)<~>humble(X))))&
(humble(susan))&
(?[X]:(~happy(X)))&
(funny(lucy))&
((~curious(john)<~>~brave(john))) | old(mary) | [] | null | 0 |
Everyone who is either kind or not old is either curious or not rich. If someone is not old or not curious then lucy is either strong or tall and vice versa. If john is calm then someone is either patient or not tall and vice versa. Everyone who is both not funny and not old is both not curious and rich. If someone is either not quiet or not old then someone is wise or kind and vice versa. Everyone who is both happy and not patient is quiet or not curious and vice versa. If fred is not old or not creative then someone is not quiet or funny. Everyone who is either generous or curious is patient or quiet. Everyone who is not quiet is not tall or not patient. If someone is humble then someone is either curious or brave and vice versa. Everyone who is both quiet and calm is not happy or not brave. Everyone who is both not strong and not rich is either rich or patient and vice versa. Everyone who is not humble or not happy is both not old and strong. Everyone who is not old is not brave or not curious and vice versa. Everyone who is both not kind and wise is both tall and not kind. Everyone who is not old is both not humble and funny and vice versa. Someone is not patient or quiet. Someone is generous or humble. Someone is both wise and strong. Paul is both not brave and kind. Lucy is not patient. Fred is curious or generous. Someone is either not wise or wise. Fred is either curious or happy. | Lucy is rich. | contradiction | (![X]:((kind(X)<~>~old(X))=>(curious(X)<~>~rich(X))))&
((?[X]:((~old(X)|~curious(X))))<=>((strong(lucy)<~>tall(lucy))))&
((calm(john))<=>(?[X]:((patient(X)<~>~tall(X)))))&
(![X]:((~funny(X)&~old(X))=>(~curious(X)&rich(X))))&
((?[X]:((~quiet(X)<~>~old(X))))<=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((happy(X)&~patient(X))<=>(quiet(X)|~curious(X))))&
(((~old(fred)|~creative(fred)))=>(?[X]:((~quiet(X)|funny(X)))))&
(![X]:((generous(X)<~>curious(X))=>(patient(X)|quiet(X))))&
(![X]:(~quiet(X)=>(~tall(X)|~patient(X))))&
((?[X]:(humble(X)))<=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:((quiet(X)&calm(X))=>(~happy(X)|~brave(X))))&
(![X]:((~strong(X)&~rich(X))<=>(rich(X)<~>patient(X))))&
(![X]:((~humble(X)|~happy(X))=>(~old(X)&strong(X))))&
(![X]:(~old(X)<=>(~brave(X)|~curious(X))))&
(![X]:((~kind(X)&wise(X))=>(tall(X)&~kind(X))))&
(![X]:(~old(X)<=>(~humble(X)&funny(X))))&
(?[X]:((~patient(X)|quiet(X))))&
(?[X]:((generous(X)|humble(X))))&
(?[X]:((wise(X)&strong(X))))&
((~brave(paul)&kind(paul)))&
(~patient(lucy))&
((curious(fred)|generous(fred)))&
(?[X]:((~wise(X)<~>wise(X))))&
((curious(fred)<~>happy(fred))) | rich(lucy) | [
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2503732895047041022459469
% SZS output start Proof for 2503732895047041022459469
12. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> (rich(X0) <~> patient(X0))) [input p11]
21. ~patient(lucy) [input p20]
25. rich(lucy) [input hypothesis]
66. ! [X0] : (((~rich(X0) & ~strong(X0)) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | (rich(X0) | strong(X0)))) [nnf transformation 12]
67. ! [X0] : (((~rich(X0) & ~strong(X0)) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | rich(X0) | strong(X0))) [flattening 66]
122. ~rich(X0) | patient(X0) | ~rich(X0) [cnf transformation 67]
142. ~patient(lucy) [cnf transformation 21]
148. rich(lucy) [cnf transformation 25]
150. ~rich(X0) | patient(X0) [duplicate literal removal 122]
310. patient(lucy) [resolution 150,148]
311. $false [subsumption resolution 310,142]
% SZS output end Proof for 2503732895047041022459469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or generous is not old.
Everyone who is not old is funny.
If someone is either not kind or not brave then lucy is not patient or not calm and vice versa.
Everyone who is both not wise and strong is either not creative or not humble.
Everyone who is not calm is both curious and calm.
If someone is not old then someone is both not wise and tall and vice versa.
If fred is either not wise or not happy then someone is either funny or not quiet.
Everyone who is both strong and funny is not tall or happy and vice versa.
Everyone who is either not funny or old is both not calm and brave.
Everyone who is both not happy and not kind is either patient or tall and vice versa.
Everyone who is either not rich or quiet is either curious or calm.
If fred is both brave and happy then fred is not humble.
Everyone who is funny or wise is curious.
Everyone who is both not patient and not old is not kind and vice versa.
If someone is either rich or not old then someone is wise or humble and vice versa.
Everyone who is funny or creative is patient.
Someone is patient or tall.
Someone is not kind or wise.
Someone is both not wise and not generous.
Lucy is both humble and rich.
Fred is calm.
Alice is both humble and strong. | Fred is patient. | entailment | (![X]:((~generous(X)<~>generous(X))=>~old(X)))&
(![X]:(~old(X)=>funny(X)))&
((?[X]:((~kind(X)<~>~brave(X))))<=>((~patient(lucy)|~calm(lucy))))&
(![X]:((~wise(X)&strong(X))=>(~creative(X)<~>~humble(X))))&
(![X]:(~calm(X)=>(curious(X)&calm(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~wise(X)&tall(X)))))&
(((~wise(fred)<~>~happy(fred)))=>(?[X]:((funny(X)<~>~quiet(X)))))&
(![X]:((strong(X)&funny(X))<=>(~tall(X)|happy(X))))&
(![X]:((~funny(X)<~>old(X))=>(~calm(X)&brave(X))))&
(![X]:((~happy(X)&~kind(X))<=>(patient(X)<~>tall(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(curious(X)<~>calm(X))))&
(((brave(fred)&happy(fred)))=>(~humble(fred)))&
(![X]:((funny(X)|wise(X))=>curious(X)))&
(![X]:((~patient(X)&~old(X))<=>~kind(X)))&
((?[X]:((rich(X)<~>~old(X))))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((funny(X)|creative(X))=>patient(X)))&
(?[X]:((patient(X)|tall(X))))&
(?[X]:((~kind(X)|wise(X))))&
(?[X]:((~wise(X)&~generous(X))))&
((humble(lucy)&rich(lucy)))&
(calm(fred))&
((humble(alice)&strong(alice))) | patient(fred) | [
"p0",
"p1",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5168079428320232045498446
% SZS output start Proof for 5168079428320232045498446
1. ! [X0] : ((~generous(X0) <~> generous(X0)) => ~old(X0)) [input p0]
2. ! [X0] : (~old(X0) => funny(X0)) [input p1]
16. ! [X0] : ((creative(X0) | funny(X0)) => patient(X0)) [input p15]
23. ~patient(fred) [input hypothesis]
26. ! [X0] : (~old(X0) | (~generous(X0) <=> generous(X0))) [ennf transformation 1]
27. ! [X0] : (funny(X0) | old(X0)) [ennf transformation 2]
37. ! [X0] : (patient(X0) | (~creative(X0) & ~funny(X0))) [ennf transformation 16]
38. ! [X0] : (~old(X0) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) [nnf transformation 26]
72. ~old(X0) | generous(X0) | generous(X0) [cnf transformation 38]
73. ~old(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 38]
74. funny(X0) | old(X0) [cnf transformation 27]
123. patient(X0) | ~funny(X0) [cnf transformation 37]
134. ~patient(fred) [cnf transformation 23]
136. ~old(X0) | generous(X0) [duplicate literal removal 72]
137. ~old(X0) | ~generous(X0) [duplicate literal removal 73]
138. ~old(X0) [subsumption resolution 136,137]
139. funny(X0) [subsumption resolution 74,138]
227. patient(X0) [subsumption resolution 123,139]
237. $false [subsumption resolution 134,227]
% SZS output end Proof for 5168079428320232045498446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or funny is either strong or rich.
Everyone who is quiet is curious or kind.
Everyone who is both not kind and brave is not quiet or patient and vice versa.
Everyone who is not old is not wise and vice versa.
If fred is both not patient and wise then lucy is not happy or generous.
If someone is either creative or not calm then john is rich or calm and vice versa.
Everyone who is generous is not curious or not humble and vice versa.
If lucy is both brave and not patient then someone is brave.
If susan is either not creative or curious then susan is either not tall or generous and vice versa.
If john is generous then someone is either not wise or humble and vice versa.
Everyone who is not strong is not old.
If fred is both not tall and calm then someone is both creative and not quiet.
Everyone who is not quiet is not tall.
Everyone who is quiet is brave or not quiet.
If lucy is tall then someone is either kind or not brave and vice versa.
Everyone who is either creative or not patient is either not generous or not strong and vice versa.
Fred is kind.
Someone is rich or tall.
Mary is tall.
Lucy is both not humble and not kind.
Someone is both funny and strong.
Lucy is generous or not creative.
Someone is not funny or brave. | Lucy is quiet. | entailment | (![X]:((old(X)<~>funny(X))=>(strong(X)<~>rich(X))))&
(![X]:(quiet(X)=>(curious(X)|kind(X))))&
(![X]:((~kind(X)&brave(X))<=>(~quiet(X)|patient(X))))&
(![X]:(~old(X)<=>~wise(X)))&
(((~patient(fred)&wise(fred)))=>((~happy(lucy)|generous(lucy))))&
((?[X]:((creative(X)<~>~calm(X))))<=>((rich(john)|calm(john))))&
(![X]:(generous(X)<=>(~curious(X)|~humble(X))))&
(((brave(lucy)&~patient(lucy)))=>(?[X]:(brave(X))))&
(((~creative(susan)<~>curious(susan)))<=>((~tall(susan)<~>generous(susan))))&
((generous(john))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(~strong(X)=>~old(X)))&
(((~tall(fred)&calm(fred)))=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:(~quiet(X)=>~tall(X)))&
(![X]:(quiet(X)=>(brave(X)|~quiet(X))))&
((tall(lucy))<=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>~patient(X))<=>(~generous(X)<~>~strong(X))))&
(kind(fred))&
(?[X]:((rich(X)|tall(X))))&
(tall(mary))&
((~humble(lucy)&~kind(lucy)))&
(?[X]:((funny(X)&strong(X))))&
((generous(lucy)|~creative(lucy)))&
(?[X]:((~funny(X)|brave(X)))) | quiet(lucy) | [
"p2",
"p12",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5594331548221216824169673
% SZS output start Proof for 5594331548221216824169673
3. ! [X0] : ((brave(X0) & ~kind(X0)) <=> (patient(X0) | ~quiet(X0))) [input p2]
13. ! [X0] : (~quiet(X0) => ~tall(X0)) [input p12]
14. ! [X0] : (quiet(X0) => (~quiet(X0) | brave(X0))) [input p13]
15. tall(lucy) <=> ? [X0] : (kind(X0) <~> ~brave(X0)) [input p14]
17. kind(fred) [input p16]
24. ~quiet(lucy) [input hypothesis]
34. ! [X0] : (~tall(X0) | quiet(X0)) [ennf transformation 13]
35. ! [X0] : ((~quiet(X0) | brave(X0)) | ~quiet(X0)) [ennf transformation 14]
36. ! [X0] : (~quiet(X0) | brave(X0) | ~quiet(X0)) [flattening 35]
38. ! [X0] : (((brave(X0) & ~kind(X0)) | (~patient(X0) & quiet(X0))) & ((patient(X0) | ~quiet(X0)) | (~brave(X0) | kind(X0)))) [nnf transformation 3]
39. ! [X0] : (((brave(X0) & ~kind(X0)) | (~patient(X0) & quiet(X0))) & (patient(X0) | ~quiet(X0) | ~brave(X0) | kind(X0))) [flattening 38]
57. (tall(lucy) | ! [X0] : ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (? [X0] : ((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ~tall(lucy)) [nnf transformation 15]
58. (tall(lucy) | ! [X0] : ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (? [X1] : ((brave(X1) | ~kind(X1)) & (~brave(X1) | kind(X1))) | ~tall(lucy)) [rectify 57]
59. ? [X1] : ((brave(X1) | ~kind(X1)) & (~brave(X1) | kind(X1))) => ((brave(sK4) | ~kind(sK4)) & (~brave(sK4) | kind(sK4))) [choice axiom]
60. (tall(lucy) | ! [X0] : ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(sK4) | ~kind(sK4)) & (~brave(sK4) | kind(sK4))) | ~tall(lucy)) [skolemisation 58,59]
76. brave(X0) | quiet(X0) [cnf transformation 39]
105. ~tall(X0) | quiet(X0) [cnf transformation 34]
106. ~quiet(X0) | brave(X0) | ~quiet(X0) [cnf transformation 36]
109. tall(lucy) | ~brave(X0) | ~kind(X0) [cnf transformation 60]
119. kind(fred) [cnf transformation 17]
128. ~quiet(lucy) [cnf transformation 24]
129. ~quiet(X0) | brave(X0) [duplicate literal removal 106]
237. brave(X0) [subsumption resolution 129,76]
238. tall(lucy) | ~kind(X0) [subsumption resolution 109,237]
240. 23 <=> ! [X0] : ~kind(X0) [avatar definition]
241. ~kind(X0) <- (23) [avatar component clause 240]
243. 24 <=> tall(lucy) [avatar definition]
245. tall(lucy) <- (24) [avatar component clause 243]
246. 23 | 24 [avatar split clause 238,243,240]
273. $false <- (23) [resolution 241,119]
274. ~23 [avatar contradiction clause 273]
284. quiet(lucy) <- (24) [resolution 105,245]
285. $false <- (24) [subsumption resolution 284,128]
286. ~24 [avatar contradiction clause 285]
287. $false [avatar sat refutation 246,274,286]
% SZS output end Proof for 5594331548221216824169673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or wise is either not curious or wise and vice versa.
If john is both creative and not happy then alice is either not generous or patient and vice versa.
If someone is not wise or not tall then someone is either curious or calm.
If susan is both happy and rich then someone is not happy.
Everyone who is either generous or happy is not tall and vice versa.
If someone is both generous and not generous then alice is tall or not kind.
If someone is both calm and quiet then someone is strong and vice versa.
Everyone who is old is creative and vice versa.
If someone is either humble or patient then someone is brave or curious.
Everyone who is rich or not old is wise or happy.
Everyone who is both not generous and not old is not quiet or not rich and vice versa.
Everyone who is calm is not patient or strong.
If someone is either old or not funny then someone is not funny or not happy and vice versa.
Everyone who is not curious is not tall and vice versa.
Everyone who is happy is not kind or not strong.
Everyone who is both not wise and not funny is generous and vice versa.
Someone is funny or not calm.
Someone is not humble.
Someone is both curious and brave.
Someone is both old and funny.
Lucy is both patient and old.
Someone is both kind and funny.
Alice is not kind.
Someone is both not strong and kind. | Susan is generous. | contradiction | (![X]:((~wise(X)|wise(X))<=>(~curious(X)<~>wise(X))))&
(((creative(john)&~happy(john)))<=>((~generous(alice)<~>patient(alice))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((curious(X)<~>calm(X)))))&
(((happy(susan)&rich(susan)))=>(?[X]:(~happy(X))))&
(![X]:((generous(X)<~>happy(X))<=>~tall(X)))&
((?[X]:((generous(X)&~generous(X))))=>((tall(alice)|~kind(alice))))&
((?[X]:((calm(X)&quiet(X))))<=>(?[X]:(strong(X))))&
(![X]:(old(X)<=>creative(X)))&
((?[X]:((humble(X)<~>patient(X))))=>(?[X]:((brave(X)|curious(X)))))&
(![X]:((rich(X)|~old(X))=>(wise(X)|happy(X))))&
(![X]:((~generous(X)&~old(X))<=>(~quiet(X)|~rich(X))))&
(![X]:(calm(X)=>(~patient(X)|strong(X))))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~funny(X)|~happy(X)))))&
(![X]:(~curious(X)<=>~tall(X)))&
(![X]:(happy(X)=>(~kind(X)|~strong(X))))&
(![X]:((~wise(X)&~funny(X))<=>generous(X)))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:(~humble(X)))&
(?[X]:((curious(X)&brave(X))))&
(?[X]:((old(X)&funny(X))))&
((patient(lucy)&old(lucy)))&
(?[X]:((kind(X)&funny(X))))&
(~kind(alice))&
(?[X]:((~strong(X)&kind(X)))) | generous(susan) | [
"p0",
"p4",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1003420975246360889911333
% SZS output start Proof for 1003420975246360889911333
1. ! [X0] : ((wise(X0) | ~wise(X0)) <=> (~curious(X0) <~> wise(X0))) [input p0]
5. ! [X0] : ((generous(X0) <~> happy(X0)) <=> ~tall(X0)) [input p4]
10. ! [X0] : ((~old(X0) | rich(X0)) => (happy(X0) | wise(X0))) [input p9]
11. ! [X0] : ((~old(X0) & ~generous(X0)) <=> (~rich(X0) | ~quiet(X0))) [input p10]
14. ! [X0] : (~curious(X0) <=> ~tall(X0)) [input p13]
16. ! [X0] : ((~funny(X0) & ~wise(X0)) <=> generous(X0)) [input p15]
25. generous(susan) [input hypothesis]
38. ! [X0] : ((happy(X0) | wise(X0)) | (old(X0) & ~rich(X0))) [ennf transformation 10]
39. ! [X0] : (happy(X0) | wise(X0) | (old(X0) & ~rich(X0))) [flattening 38]
44. ! [X0] : (((wise(X0) | ~wise(X0)) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0)))) & (((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | (~wise(X0) & wise(X0)))) [nnf transformation 1]
45. ! [X0] : ((wise(X0) | ~wise(X0) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0)))) & (((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | (~wise(X0) & wise(X0)))) [flattening 44]
54. ! [X0] : ((((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | tall(X0)) & (~tall(X0) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0))))) [nnf transformation 5]
61. ! [X0] : (((~old(X0) & ~generous(X0)) | (rich(X0) & quiet(X0))) & ((~rich(X0) | ~quiet(X0)) | (old(X0) | generous(X0)))) [nnf transformation 11]
62. ! [X0] : (((~old(X0) & ~generous(X0)) | (rich(X0) & quiet(X0))) & (~rich(X0) | ~quiet(X0) | old(X0) | generous(X0))) [flattening 61]
68. ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))) [nnf transformation 14]
69. ! [X0] : (((~funny(X0) & ~wise(X0)) | ~generous(X0)) & (generous(X0) | (funny(X0) | wise(X0)))) [nnf transformation 16]
70. ! [X0] : (((~funny(X0) & ~wise(X0)) | ~generous(X0)) & (generous(X0) | funny(X0) | wise(X0))) [flattening 69]
81. wise(X0) | ~curious(X0) | wise(X0) [cnf transformation 45]
101. ~generous(X0) | ~happy(X0) | tall(X0) [cnf transformation 54]
108. ~rich(X0) | wise(X0) | happy(X0) [cnf transformation 39]
112. ~generous(X0) | rich(X0) [cnf transformation 62]
122. ~tall(X0) | curious(X0) [cnf transformation 68]
126. ~generous(X0) | ~wise(X0) [cnf transformation 70]
139. generous(susan) [cnf transformation 25]
140. ~curious(X0) | wise(X0) [duplicate literal removal 81]
185. 9 <=> happy(susan) [avatar definition]
189. 10 <=> rich(susan) [avatar definition]
190. rich(susan) <- (10) [avatar component clause 189]
267. rich(susan) [resolution 112,139]
269. 10 [avatar split clause 267,189]
276. ~wise(susan) [resolution 126,139]
319. ~happy(susan) | tall(susan) [resolution 101,139]
322. 31 <=> tall(susan) [avatar definition]
324. tall(susan) <- (31) [avatar component clause 322]
325. 31 | ~9 [avatar split clause 319,185,322]
336. wise(susan) | happy(susan) <- (10) [resolution 108,190]
342. happy(susan) <- (10) [subsumption resolution 336,276]
363. 9 | ~10 [avatar split clause 342,189,185]
388. curious(susan) <- (31) [resolution 324,122]
441. wise(susan) <- (31) [resolution 388,140]
443. $false <- (31) [subsumption resolution 441,276]
444. ~31 [avatar contradiction clause 443]
445. $false [avatar sat refutation 269,325,363,444]
% SZS output end Proof for 1003420975246360889911333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is not calm and vice versa. If someone is both tall and patient then john is curious and vice versa. Everyone who is either generous or not humble is either tall or funny. Everyone who is not quiet or humble is both old and not calm and vice versa. If someone is curious then someone is funny and vice versa. Everyone who is not funny or generous is both not old and not generous. If lucy is wise or not patient then someone is patient. Everyone who is both humble and not kind is either not wise or not quiet and vice versa. If alice is both happy and not strong then someone is rich or not brave. Everyone who is quiet is both creative and not creative. Everyone who is humble or wise is rich or not quiet and vice versa. If john is either not funny or not calm then someone is old and vice versa. Everyone who is brave is either humble or rich and vice versa. If someone is not humble then mary is not old or generous. Everyone who is happy or not strong is kind. Everyone who is both not brave and not creative is not creative or wise. Someone is either patient or not creative. Susan is calm or strong. Susan is not old or not tall. Someone is not funny or not brave. Someone is tall or patient. Someone is either not funny or not quiet. | Mary is creative. | neutral | (![X]:(~tall(X)<=>~calm(X)))&
((?[X]:((tall(X)&patient(X))))<=>(curious(john)))&
(![X]:((generous(X)<~>~humble(X))=>(tall(X)<~>funny(X))))&
(![X]:((~quiet(X)|humble(X))<=>(old(X)&~calm(X))))&
((?[X]:(curious(X)))<=>(?[X]:(funny(X))))&
(![X]:((~funny(X)|generous(X))=>(~old(X)&~generous(X))))&
(((wise(lucy)|~patient(lucy)))=>(?[X]:(patient(X))))&
(![X]:((humble(X)&~kind(X))<=>(~wise(X)<~>~quiet(X))))&
(((happy(alice)&~strong(alice)))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:(quiet(X)=>(creative(X)&~creative(X))))&
(![X]:((humble(X)|wise(X))<=>(rich(X)|~quiet(X))))&
(((~funny(john)<~>~calm(john)))<=>(?[X]:(old(X))))&
(![X]:(brave(X)<=>(humble(X)<~>rich(X))))&
((?[X]:(~humble(X)))=>((~old(mary)|generous(mary))))&
(![X]:((happy(X)|~strong(X))=>kind(X)))&
(![X]:((~brave(X)&~creative(X))=>(~creative(X)|wise(X))))&
(?[X]:((patient(X)<~>~creative(X))))&
((calm(susan)|strong(susan)))&
((~old(susan)|~tall(susan)))&
(?[X]:((~funny(X)|~brave(X))))&
(?[X]:((tall(X)|patient(X))))&
(?[X]:((~funny(X)<~>~quiet(X)))) | creative(mary) | [] | null | 0 |
Everyone who is either kind or not kind is not wise. Everyone who is old or not quiet is wise. Everyone who is both not generous and not funny is either not brave or not funny and vice versa. If someone is not old then someone is either curious or not funny. Everyone who is patient is not happy or tall. Everyone who is both kind and not wise is either kind or tall. If someone is either not quiet or kind then lucy is both not patient and humble and vice versa. Everyone who is either generous or not curious is generous or not humble and vice versa. Everyone who is not humble or not strong is calm. Everyone who is not quiet is either not rich or not happy and vice versa. Everyone who is both not generous and funny is tall and vice versa. Everyone who is both quiet and creative is both not creative and not humble and vice versa. If john is both not curious and not kind then fred is not strong or creative and vice versa. If someone is either not humble or kind then john is old. If fred is calm then someone is both not happy and not kind and vice versa. John is both funny and quiet. Fred is either not happy or brave. Someone is not generous or not calm. Someone is either happy or humble. Fred is either not rich or strong. Someone is both not old and generous. Someone is rich. Susan is both quiet and not strong. | Lucy is old. | contradiction | (![X]:((kind(X)<~>~kind(X))=>~wise(X)))&
(![X]:((old(X)|~quiet(X))=>wise(X)))&
(![X]:((~generous(X)&~funny(X))<=>(~brave(X)<~>~funny(X))))&
((?[X]:(~old(X)))=>(?[X]:((curious(X)<~>~funny(X)))))&
(![X]:(patient(X)=>(~happy(X)|tall(X))))&
(![X]:((kind(X)&~wise(X))=>(kind(X)<~>tall(X))))&
((?[X]:((~quiet(X)<~>kind(X))))<=>((~patient(lucy)&humble(lucy))))&
(![X]:((generous(X)<~>~curious(X))<=>(generous(X)|~humble(X))))&
(![X]:((~humble(X)|~strong(X))=>calm(X)))&
(![X]:(~quiet(X)<=>(~rich(X)<~>~happy(X))))&
(![X]:((~generous(X)&funny(X))<=>tall(X)))&
(![X]:((quiet(X)&creative(X))<=>(~creative(X)&~humble(X))))&
(((~curious(john)&~kind(john)))<=>((~strong(fred)|creative(fred))))&
((?[X]:((~humble(X)<~>kind(X))))=>(old(john)))&
((calm(fred))<=>(?[X]:((~happy(X)&~kind(X)))))&
((funny(john)&quiet(john)))&
((~happy(fred)<~>brave(fred)))&
(?[X]:((~generous(X)|~calm(X))))&
(?[X]:((happy(X)<~>humble(X))))&
((~rich(fred)<~>strong(fred)))&
(?[X]:((~old(X)&generous(X))))&
(?[X]:(rich(X)))&
((quiet(susan)&~strong(susan))) | old(lucy) | [
"p0",
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 8456156686201328650500154
% SZS output start Proof for 8456156686201328650500154
1. ! [X0] : ((kind(X0) <~> ~kind(X0)) => ~wise(X0)) [input p0]
2. ! [X0] : ((~quiet(X0) | old(X0)) => wise(X0)) [input p1]
24. old(lucy) [input hypothesis]
26. ! [X0] : (~wise(X0) | (kind(X0) <=> ~kind(X0))) [ennf transformation 1]
27. ! [X0] : (wise(X0) | (quiet(X0) & ~old(X0))) [ennf transformation 2]
35. ! [X0] : (~wise(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 26]
73. ~wise(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 35]
74. ~wise(X0) | kind(X0) | kind(X0) [cnf transformation 35]
75. wise(X0) | ~old(X0) [cnf transformation 27]
137. old(lucy) [cnf transformation 24]
145. ~wise(X0) | ~kind(X0) [duplicate literal removal 73]
146. ~wise(X0) | kind(X0) [duplicate literal removal 74]
147. ~wise(X0) [subsumption resolution 145,146]
149. ~old(X0) [subsumption resolution 75,147]
261. $false [subsumption resolution 137,149]
% SZS output end Proof for 8456156686201328650500154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or strong is both not brave and old.
If mary is not kind or not curious then someone is not calm or calm.
Everyone who is either not curious or old is either not tall or creative.
Everyone who is not curious or not kind is both humble and creative and vice versa.
Everyone who is both curious and creative is either creative or funny.
Everyone who is wise is wise or patient.
Everyone who is not funny or creative is not creative or not old.
Everyone who is funny or strong is strong and vice versa.
If alice is tall then mary is patient.
Everyone who is both not humble and not creative is humble.
Everyone who is creative is not funny.
Everyone who is either kind or wise is either generous or not calm.
If john is either not happy or not brave then someone is wise or tall.
If someone is both quiet and kind then someone is both patient and not old.
Everyone who is not kind is not humble or humble.
Everyone who is patient is not rich or old and vice versa.
Paul is wise.
Lucy is generous.
Paul is both tall and not strong.
Someone is both curious and kind.
John is calm.
Someone is either strong or not wise.
Lucy is both curious and humble. | Paul is old. | contradiction | (![X]:((humble(X)|strong(X))=>(~brave(X)&old(X))))&
(((~kind(mary)|~curious(mary)))=>(?[X]:((~calm(X)|calm(X)))))&
(![X]:((~curious(X)<~>old(X))=>(~tall(X)<~>creative(X))))&
(![X]:((~curious(X)|~kind(X))<=>(humble(X)&creative(X))))&
(![X]:((curious(X)&creative(X))=>(creative(X)<~>funny(X))))&
(![X]:(wise(X)=>(wise(X)|patient(X))))&
(![X]:((~funny(X)|creative(X))=>(~creative(X)|~old(X))))&
(![X]:((funny(X)|strong(X))<=>strong(X)))&
((tall(alice))=>(patient(mary)))&
(![X]:((~humble(X)&~creative(X))=>humble(X)))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:((kind(X)<~>wise(X))=>(generous(X)<~>~calm(X))))&
(((~happy(john)<~>~brave(john)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((quiet(X)&kind(X))))=>(?[X]:((patient(X)&~old(X)))))&
(![X]:(~kind(X)=>(~humble(X)|humble(X))))&
(![X]:(patient(X)<=>(~rich(X)|old(X))))&
(wise(paul))&
(generous(lucy))&
((tall(paul)&~strong(paul)))&
(?[X]:((curious(X)&kind(X))))&
(calm(john))&
(?[X]:((strong(X)<~>~wise(X))))&
((curious(lucy)&humble(lucy))) | old(paul) | [
"p2",
"p3",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2423828493880804428497878
% SZS output start Proof for 2423828493880804428497878
3. ! [X0] : ((~curious(X0) <~> old(X0)) => (~tall(X0) <~> creative(X0))) [input p2]
4. ! [X0] : ((~kind(X0) | ~curious(X0)) <=> (creative(X0) & humble(X0))) [input p3]
7. ! [X0] : ((creative(X0) | ~funny(X0)) => (~old(X0) | ~creative(X0))) [input p6]
19. ~strong(paul) & tall(paul) [input p18]
24. old(paul) [input hypothesis]
34. ! [X0] : ((~tall(X0) <~> creative(X0)) | (~curious(X0) <=> old(X0))) [ennf transformation 3]
37. ! [X0] : ((~old(X0) | ~creative(X0)) | (~creative(X0) & funny(X0))) [ennf transformation 7]
38. ! [X0] : (~old(X0) | ~creative(X0) | (~creative(X0) & funny(X0))) [flattening 37]
48. ! [X0] : (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) [nnf transformation 34]
49. ! [X0] : (((~kind(X0) | ~curious(X0)) | (~creative(X0) | ~humble(X0))) & ((creative(X0) & humble(X0)) | (kind(X0) & curious(X0)))) [nnf transformation 4]
50. ! [X0] : ((~kind(X0) | ~curious(X0) | ~creative(X0) | ~humble(X0)) & ((creative(X0) & humble(X0)) | (kind(X0) & curious(X0)))) [flattening 49]
70. ~tall(X0) | creative(X0) | ~curious(X0) | ~old(X0) [cnf transformation 48]
75. creative(X0) | curious(X0) [cnf transformation 50]
81. ~old(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 38]
96. tall(paul) [cnf transformation 19]
105. old(paul) [cnf transformation 24]
107. ~creative(X0) | ~old(X0) [duplicate literal removal 81]
145. creative(paul) | ~curious(paul) | ~old(paul) [resolution 70,96]
146. creative(paul) | ~curious(paul) [subsumption resolution 145,105]
147. creative(paul) [subsumption resolution 146,75]
148. ~old(paul) [resolution 147,107]
149. $false [subsumption resolution 148,105]
% SZS output end Proof for 2423828493880804428497878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not patient then mary is both patient and rich and vice versa.
Everyone who is either calm or tall is either not kind or calm.
If someone is not happy or calm then john is tall.
Everyone who is both not old and not tall is humble.
If susan is either not kind or patient then john is either not curious or not happy and vice versa.
If someone is old or happy then alice is curious or creative and vice versa.
Everyone who is both not wise and not curious is not old or creative.
Everyone who is not quiet is not patient.
Everyone who is not wise is either not strong or old.
Everyone who is either not old or patient is either not brave or not humble.
Everyone who is either creative or calm is either calm or not old and vice versa.
If someone is either not quiet or not happy then lucy is not creative or rich.
Everyone who is either not strong or kind is kind and vice versa.
Everyone who is both kind and curious is both rich and not strong.
If fred is both humble and not curious then fred is both not funny and quiet and vice versa.
If paul is not kind then mary is either patient or not calm and vice versa.
Someone is either humble or patient.
Someone is funny.
Someone is either not wise or not curious.
Paul is not funny.
Lucy is either not funny or curious.
John is rich or not generous.
Lucy is tall. | Susan is not strong. | contradiction | ((?[X]:((~old(X)|~patient(X))))<=>((patient(mary)&rich(mary))))&
(![X]:((calm(X)<~>tall(X))=>(~kind(X)<~>calm(X))))&
((?[X]:((~happy(X)|calm(X))))=>(tall(john)))&
(![X]:((~old(X)&~tall(X))=>humble(X)))&
(((~kind(susan)<~>patient(susan)))<=>((~curious(john)<~>~happy(john))))&
((?[X]:((old(X)|happy(X))))<=>((curious(alice)|creative(alice))))&
(![X]:((~wise(X)&~curious(X))=>(~old(X)|creative(X))))&
(![X]:(~quiet(X)=>~patient(X)))&
(![X]:(~wise(X)=>(~strong(X)<~>old(X))))&
(![X]:((~old(X)<~>patient(X))=>(~brave(X)<~>~humble(X))))&
(![X]:((creative(X)<~>calm(X))<=>(calm(X)<~>~old(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))=>((~creative(lucy)|rich(lucy))))&
(![X]:((~strong(X)<~>kind(X))<=>kind(X)))&
(![X]:((kind(X)&curious(X))=>(rich(X)&~strong(X))))&
(((humble(fred)&~curious(fred)))<=>((~funny(fred)&quiet(fred))))&
((~kind(paul))<=>((patient(mary)<~>~calm(mary))))&
(?[X]:((humble(X)<~>patient(X))))&
(?[X]:(funny(X)))&
(?[X]:((~wise(X)<~>~curious(X))))&
(~funny(paul))&
((~funny(lucy)<~>curious(lucy)))&
((rich(john)|~generous(john)))&
(tall(lucy)) | ~strong(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3972330549765175682539269
% SZS output start Proof for 3972330549765175682539269
13. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> kind(X0)) [input p12]
24. ~strong(susan) [input hypothesis]
55. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | ~kind(X0)) & (kind(X0) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 13]
110. kind(X0) | kind(X0) | strong(X0) [cnf transformation 55]
113. ~kind(X0) | strong(X0) | ~kind(X0) [cnf transformation 55]
133. ~strong(susan) [cnf transformation 24]
134. kind(X0) | strong(X0) [duplicate literal removal 110]
135. ~kind(X0) | strong(X0) [duplicate literal removal 113]
249. strong(X0) [subsumption resolution 134,135]
313. $false [subsumption resolution 133,249]
% SZS output end Proof for 3972330549765175682539269
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or patient is creative or tall and vice versa.
Everyone who is either strong or not patient is not patient.
Everyone who is rich is either rich or kind and vice versa.
If fred is either creative or not patient then someone is either not kind or rich.
Everyone who is both not strong and not happy is not funny.
If lucy is quiet or not kind then someone is wise and vice versa.
If alice is not quiet then someone is either calm or not kind.
Everyone who is both brave and kind is not curious or patient.
Everyone who is either not patient or not calm is funny.
Everyone who is either funny or generous is either not generous or not brave.
If paul is not creative or tall then someone is tall.
If someone is not generous or not old then someone is both not calm and brave and vice versa.
If john is kind then someone is not tall and vice versa.
If lucy is either not patient or not kind then someone is both not quiet and not wise and vice versa.
If susan is either patient or not kind then someone is not funny.
Paul is not quiet.
Susan is either not patient or funny.
John is either generous or not curious.
Someone is either funny or kind.
Paul is either generous or brave.
Someone is both rich and not calm.
Someone is both not strong and not happy. | Fred is not happy. | neutral | (![X]:((kind(X)<~>patient(X))<=>(creative(X)|tall(X))))&
(![X]:((strong(X)<~>~patient(X))=>~patient(X)))&
(![X]:(rich(X)<=>(rich(X)<~>kind(X))))&
(((creative(fred)<~>~patient(fred)))=>(?[X]:((~kind(X)<~>rich(X)))))&
(![X]:((~strong(X)&~happy(X))=>~funny(X)))&
(((quiet(lucy)|~kind(lucy)))<=>(?[X]:(wise(X))))&
((~quiet(alice))=>(?[X]:((calm(X)<~>~kind(X)))))&
(![X]:((brave(X)&kind(X))=>(~curious(X)|patient(X))))&
(![X]:((~patient(X)<~>~calm(X))=>funny(X)))&
(![X]:((funny(X)<~>generous(X))=>(~generous(X)<~>~brave(X))))&
(((~creative(paul)|tall(paul)))=>(?[X]:(tall(X))))&
((?[X]:((~generous(X)|~old(X))))<=>(?[X]:((~calm(X)&brave(X)))))&
((kind(john))<=>(?[X]:(~tall(X))))&
(((~patient(lucy)<~>~kind(lucy)))<=>(?[X]:((~quiet(X)&~wise(X)))))&
(((patient(susan)<~>~kind(susan)))=>(?[X]:(~funny(X))))&
(~quiet(paul))&
((~patient(susan)<~>funny(susan)))&
((generous(john)<~>~curious(john)))&
(?[X]:((funny(X)<~>kind(X))))&
((generous(paul)<~>brave(paul)))&
(?[X]:((rich(X)&~calm(X))))&
(?[X]:((~strong(X)&~happy(X)))) | ~happy(fred) | [] | null | 0 |
Everyone who is patient is not funny.
Everyone who is either not wise or generous is both funny and not rich.
If susan is either not brave or generous then someone is generous or not brave and vice versa.
If someone is not strong or not calm then someone is tall or calm.
If someone is either brave or not generous then fred is both not happy and happy.
If fred is tall or funny then someone is calm or generous.
If someone is both creative and tall then someone is both quiet and not old and vice versa.
If someone is not funny then someone is both humble and generous and vice versa.
Everyone who is either not wise or not calm is not humble or not kind and vice versa.
If fred is either humble or not quiet then someone is not humble and vice versa.
If someone is either not humble or happy then someone is either not kind or old and vice versa.
If someone is not wise or wise then someone is either humble or funny and vice versa.
Everyone who is either brave or quiet is either not old or happy.
Everyone who is happy is not generous or rich.
Everyone who is creative is humble and vice versa.
If mary is both rich and not generous then someone is not quiet and vice versa.
Someone is both not kind and wise.
Someone is either patient or funny.
Someone is either humble or not generous.
Someone is either curious or humble.
Someone is humble or not tall.
John is not brave or kind.
Someone is both brave and old. | John is not funny. | contradiction | (![X]:(patient(X)=>~funny(X)))&
(![X]:((~wise(X)<~>generous(X))=>(funny(X)&~rich(X))))&
(((~brave(susan)<~>generous(susan)))<=>(?[X]:((generous(X)|~brave(X)))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:((tall(X)|calm(X)))))&
((?[X]:((brave(X)<~>~generous(X))))=>((~happy(fred)&happy(fred))))&
(((tall(fred)|funny(fred)))=>(?[X]:((calm(X)|generous(X)))))&
((?[X]:((creative(X)&tall(X))))<=>(?[X]:((quiet(X)&~old(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((humble(X)&generous(X)))))&
(![X]:((~wise(X)<~>~calm(X))<=>(~humble(X)|~kind(X))))&
(((humble(fred)<~>~quiet(fred)))<=>(?[X]:(~humble(X))))&
((?[X]:((~humble(X)<~>happy(X))))<=>(?[X]:((~kind(X)<~>old(X)))))&
((?[X]:((~wise(X)|wise(X))))<=>(?[X]:((humble(X)<~>funny(X)))))&
(![X]:((brave(X)<~>quiet(X))=>(~old(X)<~>happy(X))))&
(![X]:(happy(X)=>(~generous(X)|rich(X))))&
(![X]:(creative(X)<=>humble(X)))&
(((rich(mary)&~generous(mary)))<=>(?[X]:(~quiet(X))))&
(?[X]:((~kind(X)&wise(X))))&
(?[X]:((patient(X)<~>funny(X))))&
(?[X]:((humble(X)<~>~generous(X))))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((humble(X)|~tall(X))))&
((~brave(john)|kind(john)))&
(?[X]:((brave(X)&old(X)))) | ~funny(john) | [
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6142779997380681395123883
% SZS output start Proof for 6142779997380681395123883
3. (~brave(susan) <~> generous(susan)) <=> ? [X0] : (~brave(X0) | generous(X0)) [input p2]
5. ? [X0] : (brave(X0) <~> ~generous(X0)) => (happy(fred) & ~happy(fred)) [input p4]
8. ? [X0] : ~funny(X0) <=> ? [X0] : (generous(X0) & humble(X0)) [input p7]
24. ~funny(john) [input hypothesis]
27. ? [X0] : ~funny(X0) <=> ? [X1] : (generous(X1) & humble(X1)) [rectify 8]
34. (happy(fred) & ~happy(fred)) | ! [X0] : (brave(X0) <=> ~generous(X0)) [ennf transformation 5]
40. (((~generous(susan) | brave(susan)) & (generous(susan) | ~brave(susan))) | ! [X0] : (brave(X0) & ~generous(X0))) & (? [X0] : (~brave(X0) | generous(X0)) | ((~brave(susan) | ~generous(susan)) & (generous(susan) | brave(susan)))) [nnf transformation 3]
41. (((~generous(susan) | brave(susan)) & (generous(susan) | ~brave(susan))) | ! [X0] : (brave(X0) & ~generous(X0))) & (? [X1] : (~brave(X1) | generous(X1)) | ((~brave(susan) | ~generous(susan)) & (generous(susan) | brave(susan)))) [rectify 40]
42. ? [X1] : (~brave(X1) | generous(X1)) => (~brave(sK0) | generous(sK0)) [choice axiom]
43. (((~generous(susan) | brave(susan)) & (generous(susan) | ~brave(susan))) | ! [X0] : (brave(X0) & ~generous(X0))) & ((~brave(sK0) | generous(sK0)) | ((~brave(susan) | ~generous(susan)) & (generous(susan) | brave(susan)))) [skolemisation 41,42]
47. (happy(fred) & ~happy(fred)) | ! [X0] : ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0))) [nnf transformation 34]
55. (? [X0] : ~funny(X0) | ! [X1] : (~generous(X1) | ~humble(X1))) & (? [X1] : (generous(X1) & humble(X1)) | ! [X0] : funny(X0)) [nnf transformation 27]
56. (? [X0] : ~funny(X0) | ! [X1] : (~generous(X1) | ~humble(X1))) & (? [X2] : (generous(X2) & humble(X2)) | ! [X3] : funny(X3)) [rectify 55]
57. ? [X0] : ~funny(X0) => ~funny(sK5) [choice axiom]
58. ? [X2] : (generous(X2) & humble(X2)) => (generous(sK6) & humble(sK6)) [choice axiom]
59. (~funny(sK5) | ! [X1] : (~generous(X1) | ~humble(X1))) & ((generous(sK6) & humble(sK6)) | ! [X3] : funny(X3)) [skolemisation 56,58,57]
105. generous(susan) | ~brave(susan) | ~generous(X0) [cnf transformation 43]
107. ~generous(susan) | brave(susan) | ~generous(X0) [cnf transformation 43]
110. ~happy(fred) | ~generous(X0) | ~brave(X0) [cnf transformation 47]
111. ~happy(fred) | brave(X0) | generous(X0) [cnf transformation 47]
112. happy(fred) | ~generous(X0) | ~brave(X0) [cnf transformation 47]
113. happy(fred) | brave(X0) | generous(X0) [cnf transformation 47]
121. generous(sK6) | funny(X3) [cnf transformation 59]
169. ~funny(john) [cnf transformation 24]
174. 2 <=> brave(susan) [avatar definition]
175. ~brave(susan) <- (~2) [avatar component clause 174]
176. brave(susan) <- (2) [avatar component clause 174]
178. 3 <=> generous(susan) [avatar definition]
179. generous(susan) <- (3) [avatar component clause 178]
180. ~generous(susan) <- (~3) [avatar component clause 178]
183. 4 <=> ! [X0] : ~generous(X0) [avatar definition]
184. ~generous(X0) <- (4) [avatar component clause 183]
185. 4 | 2 | ~3 [avatar split clause 107,178,174,183]
187. 4 | ~2 | 3 [avatar split clause 105,178,174,183]
211. 10 <=> ! [X0] : (brave(X0) | generous(X0)) [avatar definition]
212. brave(X0) | generous(X0) <- (10) [avatar component clause 211]
214. 11 <=> happy(fred) [avatar definition]
217. 10 | 11 [avatar split clause 113,214,211]
219. 12 <=> ! [X0] : (~generous(X0) | ~brave(X0)) [avatar definition]
220. ~brave(X0) | ~generous(X0) <- (12) [avatar component clause 219]
221. 12 | 11 [avatar split clause 112,214,219]
222. 10 | ~11 [avatar split clause 111,214,211]
223. 12 | ~11 [avatar split clause 110,214,219]
277. 25 <=> ! [X3] : funny(X3) [avatar definition]
278. funny(X3) <- (25) [avatar component clause 277]
280. 26 <=> generous(sK6) [avatar definition]
282. generous(sK6) <- (26) [avatar component clause 280]
283. 25 | 26 [avatar split clause 121,280,277]
436. $false <- (25) [resolution 278,169]
437. ~25 [avatar contradiction clause 436]
438. $false <- (4, 26) [subsumption resolution 282,184]
439. ~4 | ~26 [avatar contradiction clause 438]
454. generous(susan) <- (~2, 10) [resolution 212,175]
457. $false <- (~2, ~3, 10) [subsumption resolution 454,180]
458. 2 | 3 | ~10 [avatar contradiction clause 457]
462. ~generous(susan) <- (2, 12) [resolution 220,176]
463. $false <- (2, 3, 12) [subsumption resolution 462,179]
464. ~2 | ~3 | ~12 [avatar contradiction clause 463]
465. $false [avatar sat refutation 185,187,217,221,222,223,283,437,439,458,464]
% SZS output end Proof for 6142779997380681395123883
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is either not kind or humble. Everyone who is not funny is both not rich and curious. Everyone who is both happy and not creative is not happy and vice versa. If someone is either not old or creative then someone is both old and not old. Everyone who is both creative and funny is curious. Everyone who is either tall or not curious is both generous and not strong and vice versa. If lucy is not curious or not strong then john is both old and not tall. If someone is not humble or not funny then alice is either old or kind. If someone is both not generous and not funny then lucy is not brave or not humble and vice versa. If fred is not patient or funny then someone is both not funny and not brave. If alice is both not creative and not rich then paul is not patient or not brave and vice versa. If fred is both kind and not curious then john is humble or calm. Everyone who is both strong and not happy is both quiet and funny and vice versa. Everyone who is not patient or quiet is quiet or happy. Everyone who is not patient is not curious. Mary is both happy and not kind. Someone is either humble or not calm. Someone is quiet or brave. Someone is either curious or strong. | Lucy is tall. | contradiction | (![X]:(quiet(X)=>(~kind(X)<~>humble(X))))&
(![X]:(~funny(X)=>(~rich(X)&curious(X))))&
(![X]:((happy(X)&~creative(X))<=>~happy(X)))&
((?[X]:((~old(X)<~>creative(X))))=>(?[X]:((old(X)&~old(X)))))&
(![X]:((creative(X)&funny(X))=>curious(X)))&
(![X]:((tall(X)<~>~curious(X))<=>(generous(X)&~strong(X))))&
(((~curious(lucy)|~strong(lucy)))=>((old(john)&~tall(john))))&
((?[X]:((~humble(X)|~funny(X))))=>((old(alice)<~>kind(alice))))&
((?[X]:((~generous(X)&~funny(X))))<=>((~brave(lucy)|~humble(lucy))))&
(((~patient(fred)|funny(fred)))=>(?[X]:((~funny(X)&~brave(X)))))&
(((~creative(alice)&~rich(alice)))<=>((~patient(paul)|~brave(paul))))&
(((kind(fred)&~curious(fred)))=>((humble(john)|calm(john))))&
(![X]:((strong(X)&~happy(X))<=>(quiet(X)&funny(X))))&
(![X]:((~patient(X)|quiet(X))=>(quiet(X)|happy(X))))&
(![X]:(~patient(X)=>~curious(X)))&
((happy(mary)&~kind(mary)))&
(?[X]:((humble(X)<~>~calm(X))))&
(?[X]:((quiet(X)|brave(X))))&
(?[X]:((curious(X)<~>strong(X)))) | tall(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 269705090799330167219098
% SZS output start Proof for 269705090799330167219098
2. ! [X0] : (~funny(X0) => (curious(X0) & ~rich(X0))) [input p1]
3. ! [X0] : ((~creative(X0) & happy(X0)) <=> ~happy(X0)) [input p2]
4. ? [X0] : (~old(X0) <~> creative(X0)) => ? [X0] : (~old(X0) & old(X0)) [input p3]
5. ! [X0] : ((funny(X0) & creative(X0)) => curious(X0)) [input p4]
6. ! [X0] : ((tall(X0) <~> ~curious(X0)) <=> (~strong(X0) & generous(X0))) [input p5]
7. (~strong(lucy) | ~curious(lucy)) => (~tall(john) & old(john)) [input p6]
20. tall(lucy) [input hypothesis]
21. ? [X0] : (~old(X0) <~> creative(X0)) => ? [X1] : (~old(X1) & old(X1)) [rectify 4]
23. ! [X0] : ((curious(X0) & ~rich(X0)) | funny(X0)) [ennf transformation 2]
24. ? [X1] : (~old(X1) & old(X1)) | ! [X0] : (~old(X0) <=> creative(X0)) [ennf transformation 21]
25. ! [X0] : (curious(X0) | (~funny(X0) | ~creative(X0))) [ennf transformation 5]
26. ! [X0] : (curious(X0) | ~funny(X0) | ~creative(X0)) [flattening 25]
27. (~tall(john) & old(john)) | (strong(lucy) & curious(lucy)) [ennf transformation 7]
36. ! [X0] : (((~creative(X0) & happy(X0)) | happy(X0)) & (~happy(X0) | (creative(X0) | ~happy(X0)))) [nnf transformation 3]
37. ! [X0] : (((~creative(X0) & happy(X0)) | happy(X0)) & (~happy(X0) | creative(X0) | ~happy(X0))) [flattening 36]
38. ? [X1] : (~old(X1) & old(X1)) | ! [X0] : ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0))) [nnf transformation 24]
39. ? [X0] : (~old(X0) & old(X0)) | ! [X1] : ((~old(X1) | ~creative(X1)) & (creative(X1) | old(X1))) [rectify 38]
40. ? [X0] : (~old(X0) & old(X0)) => (~old(sK0) & old(sK0)) [choice axiom]
41. (~old(sK0) & old(sK0)) | ! [X1] : ((~old(X1) | ~creative(X1)) & (creative(X1) | old(X1))) [skolemisation 39,40]
42. ! [X0] : ((((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (strong(X0) | ~generous(X0))) & ((~strong(X0) & generous(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))))) [nnf transformation 6]
43. ! [X0] : ((((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | strong(X0) | ~generous(X0)) & ((~strong(X0) & generous(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))))) [flattening 42]
67. curious(X0) | funny(X0) [cnf transformation 23]
68. ~happy(X0) | creative(X0) | ~happy(X0) [cnf transformation 37]
69. happy(X0) | happy(X0) [cnf transformation 37]
72. old(sK0) | ~old(X1) | ~creative(X1) [cnf transformation 41]
74. ~old(sK0) | ~old(X1) | ~creative(X1) [cnf transformation 41]
75. curious(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 26]
78. ~strong(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 43]
83. old(john) | strong(lucy) [cnf transformation 27]
119. tall(lucy) [cnf transformation 20]
120. ~happy(X0) | creative(X0) [duplicate literal removal 68]
121. happy(X0) [duplicate literal removal 69]
122. creative(X0) [subsumption resolution 120,121]
123. ~old(sK0) | ~old(X1) [subsumption resolution 74,122]
125. 1 <=> ! [X1] : ~old(X1) [avatar definition]
126. ~old(X1) <- (1) [avatar component clause 125]
128. 2 <=> old(sK0) [avatar definition]
131. 1 | ~2 [avatar split clause 123,128,125]
132. old(sK0) | ~old(X1) [subsumption resolution 72,122]
133. 1 | 2 [avatar split clause 132,128,125]
134. curious(X0) | ~funny(X0) [subsumption resolution 75,122]
135. curious(X0) [subsumption resolution 134,67]
137. ~strong(X0) | ~tall(X0) [subsumption resolution 78,135]
140. 3 <=> strong(lucy) [avatar definition]
142. strong(lucy) <- (3) [avatar component clause 140]
149. 5 <=> old(john) [avatar definition]
151. old(john) <- (5) [avatar component clause 149]
152. 3 | 5 [avatar split clause 83,149,140]
258. ~tall(lucy) <- (3) [resolution 137,142]
259. $false <- (3) [subsumption resolution 258,119]
260. ~3 [avatar contradiction clause 259]
261. $false <- (1, 5) [subsumption resolution 151,126]
262. ~1 | ~5 [avatar contradiction clause 261]
263. $false [avatar sat refutation 131,133,152,260,262]
% SZS output end Proof for 269705090799330167219098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or rich is both not old and not wise.
Everyone who is not happy is wise or not patient and vice versa.
Everyone who is not old or calm is either not kind or calm and vice versa.
Everyone who is calm is either not brave or not humble.
Everyone who is either not humble or not creative is either humble or not patient.
If someone is wise or happy then fred is either calm or not generous and vice versa.
Everyone who is rich or calm is either funny or generous and vice versa.
Everyone who is either creative or not funny is not rich or creative and vice versa.
Everyone who is funny is either not generous or not rich and vice versa.
Everyone who is brave is not curious and vice versa.
Everyone who is calm is both patient and not funny and vice versa.
If someone is either brave or not quiet then someone is both not tall and not happy and vice versa.
Everyone who is quiet is both not wise and happy.
Everyone who is both humble and not calm is tall.
If someone is not patient or calm then susan is happy or not wise.
Everyone who is humble or not patient is happy and vice versa.
Lucy is creative.
Susan is either not generous or not curious.
Lucy is curious or not humble.
Someone is patient or not creative.
Alice is quiet or generous. | Alice is not generous. | neutral | (![X]:((kind(X)|rich(X))=>(~old(X)&~wise(X))))&
(![X]:(~happy(X)<=>(wise(X)|~patient(X))))&
(![X]:((~old(X)|calm(X))<=>(~kind(X)<~>calm(X))))&
(![X]:(calm(X)=>(~brave(X)<~>~humble(X))))&
(![X]:((~humble(X)<~>~creative(X))=>(humble(X)<~>~patient(X))))&
((?[X]:((wise(X)|happy(X))))<=>((calm(fred)<~>~generous(fred))))&
(![X]:((rich(X)|calm(X))<=>(funny(X)<~>generous(X))))&
(![X]:((creative(X)<~>~funny(X))<=>(~rich(X)|creative(X))))&
(![X]:(funny(X)<=>(~generous(X)<~>~rich(X))))&
(![X]:(brave(X)<=>~curious(X)))&
(![X]:(calm(X)<=>(patient(X)&~funny(X))))&
((?[X]:((brave(X)<~>~quiet(X))))<=>(?[X]:((~tall(X)&~happy(X)))))&
(![X]:(quiet(X)=>(~wise(X)&happy(X))))&
(![X]:((humble(X)&~calm(X))=>tall(X)))&
((?[X]:((~patient(X)|calm(X))))=>((happy(susan)|~wise(susan))))&
(![X]:((humble(X)|~patient(X))<=>happy(X)))&
(creative(lucy))&
((~generous(susan)<~>~curious(susan)))&
((curious(lucy)|~humble(lucy)))&
(?[X]:((patient(X)|~creative(X))))&
((quiet(alice)|generous(alice))) | ~generous(alice) | [] | null | 0 |
If paul is not generous then lucy is not funny or creative and vice versa.
If someone is not tall or not wise then someone is not creative and vice versa.
If someone is funny or generous then fred is either happy or not tall and vice versa.
If john is not creative then lucy is both quiet and wise and vice versa.
Everyone who is brave or happy is either not tall or not generous.
If john is both happy and not tall then lucy is either not strong or not brave and vice versa.
Everyone who is both strong and tall is either creative or happy.
Everyone who is funny or brave is both calm and curious.
If mary is old or happy then john is old or brave and vice versa.
If someone is not generous then john is curious or calm.
If fred is both not calm and not quiet then someone is both not tall and not calm.
If someone is happy then fred is not calm.
If fred is not rich or not creative then someone is not funny.
Everyone who is either not curious or strong is tall or kind.
Everyone who is not kind is either humble or rich and vice versa.
Everyone who is old is strong or rich and vice versa.
Mary is either not old or not calm.
Someone is creative.
Fred is funny or not happy.
Mary is not creative.
Lucy is funny or not old.
Paul is both brave and rich.
Fred is both brave and not quiet.
Someone is humble. | Paul is brave. | entailment | ((~generous(paul))<=>((~funny(lucy)|creative(lucy))))&
((?[X]:((~tall(X)|~wise(X))))<=>(?[X]:(~creative(X))))&
((?[X]:((funny(X)|generous(X))))<=>((happy(fred)<~>~tall(fred))))&
((~creative(john))<=>((quiet(lucy)&wise(lucy))))&
(![X]:((brave(X)|happy(X))=>(~tall(X)<~>~generous(X))))&
(((happy(john)&~tall(john)))<=>((~strong(lucy)<~>~brave(lucy))))&
(![X]:((strong(X)&tall(X))=>(creative(X)<~>happy(X))))&
(![X]:((funny(X)|brave(X))=>(calm(X)&curious(X))))&
(((old(mary)|happy(mary)))<=>((old(john)|brave(john))))&
((?[X]:(~generous(X)))=>((curious(john)|calm(john))))&
(((~calm(fred)&~quiet(fred)))=>(?[X]:((~tall(X)&~calm(X)))))&
((?[X]:(happy(X)))=>(~calm(fred)))&
(((~rich(fred)|~creative(fred)))=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)<~>strong(X))=>(tall(X)|kind(X))))&
(![X]:(~kind(X)<=>(humble(X)<~>rich(X))))&
(![X]:(old(X)<=>(strong(X)|rich(X))))&
((~old(mary)<~>~calm(mary)))&
(?[X]:(creative(X)))&
((funny(fred)|~happy(fred)))&
(~creative(mary))&
((funny(lucy)|~old(lucy)))&
((brave(paul)&rich(paul)))&
((brave(fred)&~quiet(fred)))&
(?[X]:(humble(X))) | brave(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 178976445682656609896101
% SZS output start Proof for 178976445682656609896101
22. rich(paul) & brave(paul) [input p21]
25. ~brave(paul) [input hypothesis]
127. brave(paul) [cnf transformation 22]
132. ~brave(paul) [cnf transformation 25]
322. $false [subsumption resolution 132,127]
% SZS output end Proof for 178976445682656609896101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or quiet then someone is not rich.
If paul is either wise or not funny then paul is both not strong and not quiet and vice versa.
If susan is either old or not old then someone is tall or creative.
If someone is both not brave and not creative then susan is both funny and not curious.
Everyone who is not old or not brave is either not old or generous.
Everyone who is either not wise or not rich is not wise or tall and vice versa.
Everyone who is not old is both rich and not creative and vice versa.
Everyone who is generous or not funny is both not humble and not tall and vice versa.
If susan is both not kind and rich then paul is curious and vice versa.
If someone is kind or rich then someone is not wise or not kind.
If alice is both rich and funny then someone is both not funny and not happy.
Everyone who is both happy and not tall is either not patient or not curious and vice versa.
Everyone who is both not creative and not patient is strong or old.
If someone is either calm or curious then john is not funny and vice versa.
If susan is not quiet then paul is happy.
Everyone who is both not quiet and strong is wise or kind and vice versa.
Alice is either calm or not curious.
Someone is not brave or rich.
Someone is not kind.
Someone is both humble and not tall.
Alice is not rich.
Someone is not tall.
Fred is both not patient and not happy. | Alice is brave. | entailment | ((?[X]:((~happy(X)|quiet(X))))=>(?[X]:(~rich(X))))&
(((wise(paul)<~>~funny(paul)))<=>((~strong(paul)&~quiet(paul))))&
(((old(susan)<~>~old(susan)))=>(?[X]:((tall(X)|creative(X)))))&
((?[X]:((~brave(X)&~creative(X))))=>((funny(susan)&~curious(susan))))&
(![X]:((~old(X)|~brave(X))=>(~old(X)<~>generous(X))))&
(![X]:((~wise(X)<~>~rich(X))<=>(~wise(X)|tall(X))))&
(![X]:(~old(X)<=>(rich(X)&~creative(X))))&
(![X]:((generous(X)|~funny(X))<=>(~humble(X)&~tall(X))))&
(((~kind(susan)&rich(susan)))<=>(curious(paul)))&
((?[X]:((kind(X)|rich(X))))=>(?[X]:((~wise(X)|~kind(X)))))&
(((rich(alice)&funny(alice)))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:((happy(X)&~tall(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((~creative(X)&~patient(X))=>(strong(X)|old(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>(~funny(john)))&
((~quiet(susan))=>(happy(paul)))&
(![X]:((~quiet(X)&strong(X))<=>(wise(X)|kind(X))))&
((calm(alice)<~>~curious(alice)))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:((humble(X)&~tall(X))))&
(~rich(alice))&
(?[X]:(~tall(X)))&
((~patient(fred)&~happy(fred))) | brave(alice) | [
"p4",
"p5",
"p6",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2574054865499171118225971
% SZS output start Proof for 2574054865499171118225971
5. ! [X0] : ((~brave(X0) | ~old(X0)) => (~old(X0) <~> generous(X0))) [input p4]
6. ! [X0] : ((~wise(X0) <~> ~rich(X0)) <=> (tall(X0) | ~wise(X0))) [input p5]
7. ! [X0] : (~old(X0) <=> (~creative(X0) & rich(X0))) [input p6]
8. ! [X0] : ((~funny(X0) | generous(X0)) <=> (~tall(X0) & ~humble(X0))) [input p7]
21. ~rich(alice) [input p20]
24. ~brave(alice) [input hypothesis]
30. ! [X0] : ((~old(X0) <~> generous(X0)) | (brave(X0) & old(X0))) [ennf transformation 5]
45. ! [X0] : (((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | (brave(X0) & old(X0))) [nnf transformation 30]
46. ! [X0] : ((((rich(X0) | wise(X0)) & (~rich(X0) | ~wise(X0))) | (~tall(X0) & wise(X0))) & ((tall(X0) | ~wise(X0)) | ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0))))) [nnf transformation 6]
47. ! [X0] : ((((rich(X0) | wise(X0)) & (~rich(X0) | ~wise(X0))) | (~tall(X0) & wise(X0))) & (tall(X0) | ~wise(X0) | ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0))))) [flattening 46]
48. ! [X0] : ((~old(X0) | (creative(X0) | ~rich(X0))) & ((~creative(X0) & rich(X0)) | old(X0))) [nnf transformation 7]
49. ! [X0] : ((~old(X0) | creative(X0) | ~rich(X0)) & ((~creative(X0) & rich(X0)) | old(X0))) [flattening 48]
50. ! [X0] : (((~funny(X0) | generous(X0)) | (tall(X0) | humble(X0))) & ((~tall(X0) & ~humble(X0)) | (funny(X0) & ~generous(X0)))) [nnf transformation 8]
51. ! [X0] : ((~funny(X0) | generous(X0) | tall(X0) | humble(X0)) & ((~tall(X0) & ~humble(X0)) | (funny(X0) & ~generous(X0)))) [flattening 50]
89. ~old(X0) | generous(X0) | brave(X0) [cnf transformation 45]
93. tall(X0) | ~wise(X0) | ~wise(X0) | rich(X0) [cnf transformation 47]
96. rich(X0) | wise(X0) | wise(X0) [cnf transformation 47]
98. old(X0) | rich(X0) [cnf transformation 49]
103. ~generous(X0) | ~tall(X0) [cnf transformation 51]
136. ~rich(alice) [cnf transformation 21]
140. ~brave(alice) [cnf transformation 24]
141. tall(X0) | ~wise(X0) | rich(X0) [duplicate literal removal 93]
142. wise(X0) | rich(X0) [duplicate literal removal 96]
207. tall(X0) | rich(X0) [subsumption resolution 141,142]
240. 21 <=> rich(alice) [avatar definition]
242. ~rich(alice) <- (~21) [avatar component clause 240]
308. ~21 [avatar split clause 136,240]
323. generous(X0) | brave(X0) | rich(X0) [resolution 89,98]
441. brave(X2) | rich(X2) | ~tall(X2) [resolution 323,103]
443. brave(X2) | rich(X2) [subsumption resolution 441,207]
444. rich(alice) [resolution 443,140]
446. $false <- (~21) [subsumption resolution 444,242]
447. 21 [avatar contradiction clause 446]
449. $false [avatar sat refutation 308,447]
% SZS output end Proof for 2574054865499171118225971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both strong and not strong then alice is either not rich or humble and vice versa.
If alice is not generous then someone is not generous.
If susan is not kind or strong then someone is both not old and not creative and vice versa.
Everyone who is calm is patient or not happy.
Everyone who is patient is not wise or not old and vice versa.
Everyone who is either not rich or rich is not patient or strong and vice versa.
Everyone who is either creative or curious is humble or not quiet.
If someone is either humble or not kind then alice is not wise or wise and vice versa.
Everyone who is both funny and rich is either not quiet or not patient and vice versa.
Everyone who is tall or not generous is not calm or creative.
Everyone who is not strong is not quiet and vice versa.
If someone is either generous or not humble then susan is not old and vice versa.
Everyone who is either happy or funny is curious or happy and vice versa.
Everyone who is either not calm or patient is generous.
If lucy is old then lucy is both creative and not generous.
Everyone who is both humble and kind is not calm and vice versa.
Someone is not humble or not funny.
John is both not happy and old.
Fred is either quiet or kind.
Someone is brave or not old.
Mary is tall or not strong.
Someone is either not funny or calm.
Someone is not kind or not old.
Alice is funny or creative. | Alice is not humble. | neutral | (((strong(lucy)&~strong(lucy)))<=>((~rich(alice)<~>humble(alice))))&
((~generous(alice))=>(?[X]:(~generous(X))))&
(((~kind(susan)|strong(susan)))<=>(?[X]:((~old(X)&~creative(X)))))&
(![X]:(calm(X)=>(patient(X)|~happy(X))))&
(![X]:(patient(X)<=>(~wise(X)|~old(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(~patient(X)|strong(X))))&
(![X]:((creative(X)<~>curious(X))=>(humble(X)|~quiet(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>((~wise(alice)|wise(alice))))&
(![X]:((funny(X)&rich(X))<=>(~quiet(X)<~>~patient(X))))&
(![X]:((tall(X)|~generous(X))=>(~calm(X)|creative(X))))&
(![X]:(~strong(X)<=>~quiet(X)))&
((?[X]:((generous(X)<~>~humble(X))))<=>(~old(susan)))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)|happy(X))))&
(![X]:((~calm(X)<~>patient(X))=>generous(X)))&
((old(lucy))=>((creative(lucy)&~generous(lucy))))&
(![X]:((humble(X)&kind(X))<=>~calm(X)))&
(?[X]:((~humble(X)|~funny(X))))&
((~happy(john)&old(john)))&
((quiet(fred)<~>kind(fred)))&
(?[X]:((brave(X)|~old(X))))&
((tall(mary)|~strong(mary)))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:((~kind(X)|~old(X))))&
((funny(alice)|creative(alice))) | ~humble(alice) | [] | null | 0 |
Everyone who is both not happy and old is strong.
Everyone who is funny or not kind is either brave or not quiet and vice versa.
If someone is either strong or happy then lucy is tall or generous.
Everyone who is both rich and not kind is creative and vice versa.
Everyone who is not humble is rich and vice versa.
Everyone who is not generous is both not humble and old and vice versa.
If someone is both not tall and humble then someone is either not funny or not strong.
If someone is either not patient or quiet then john is either kind or calm.
Everyone who is funny is old.
If someone is either happy or not brave then someone is either generous or not quiet and vice versa.
If lucy is either not rich or old then someone is generous.
Everyone who is not brave or not calm is both not humble and curious and vice versa.
If someone is both tall and curious then fred is both strong and not happy and vice versa.
Everyone who is both calm and not patient is happy or rich and vice versa.
If mary is not humble or humble then lucy is either rich or kind.
If lucy is both patient and old then mary is tall or not rich and vice versa.
Mary is old or generous.
Someone is both not kind and not patient.
Susan is not quiet or old.
Someone is not brave.
Susan is wise.
Paul is not tall or humble.
Susan is not brave.
Mary is both not generous and not brave. | Mary is calm. | entailment | (![X]:((~happy(X)&old(X))=>strong(X)))&
(![X]:((funny(X)|~kind(X))<=>(brave(X)<~>~quiet(X))))&
((?[X]:((strong(X)<~>happy(X))))=>((tall(lucy)|generous(lucy))))&
(![X]:((rich(X)&~kind(X))<=>creative(X)))&
(![X]:(~humble(X)<=>rich(X)))&
(![X]:(~generous(X)<=>(~humble(X)&old(X))))&
((?[X]:((~tall(X)&humble(X))))=>(?[X]:((~funny(X)<~>~strong(X)))))&
((?[X]:((~patient(X)<~>quiet(X))))=>((kind(john)<~>calm(john))))&
(![X]:(funny(X)=>old(X)))&
((?[X]:((happy(X)<~>~brave(X))))<=>(?[X]:((generous(X)<~>~quiet(X)))))&
(((~rich(lucy)<~>old(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~humble(X)&curious(X))))&
((?[X]:((tall(X)&curious(X))))<=>((strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~patient(X))<=>(happy(X)|rich(X))))&
(((~humble(mary)|humble(mary)))=>((rich(lucy)<~>kind(lucy))))&
(((patient(lucy)&old(lucy)))<=>((tall(mary)|~rich(mary))))&
((old(mary)|generous(mary)))&
(?[X]:((~kind(X)&~patient(X))))&
((~quiet(susan)|old(susan)))&
(?[X]:(~brave(X)))&
(wise(susan))&
((~tall(paul)|humble(paul)))&
(~brave(susan))&
((~generous(mary)&~brave(mary))) | calm(mary) | [
"p4",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7553191289303050182283303
% SZS output start Proof for 7553191289303050182283303
5. ! [X0] : (~humble(X0) <=> rich(X0)) [input p4]
12. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> (curious(X0) & ~humble(X0))) [input p11]
14. ! [X0] : ((~patient(X0) & calm(X0)) <=> (rich(X0) | happy(X0))) [input p13]
25. ~calm(mary) [input hypothesis]
41. ! [X0] : ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0))) [nnf transformation 5]
57. ! [X0] : (((~calm(X0) | ~brave(X0)) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [nnf transformation 12]
58. ! [X0] : ((~calm(X0) | ~brave(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [flattening 57]
64. ! [X0] : (((~patient(X0) & calm(X0)) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | (patient(X0) | ~calm(X0)))) [nnf transformation 14]
65. ! [X0] : (((~patient(X0) & calm(X0)) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | patient(X0) | ~calm(X0))) [flattening 64]
82. humble(X0) | rich(X0) [cnf transformation 41]
105. ~humble(X0) | calm(X0) [cnf transformation 58]
115. calm(X0) | ~rich(X0) [cnf transformation 65]
136. ~calm(mary) [cnf transformation 25]
309. calm(X0) | rich(X0) [resolution 105,82]
310. calm(X0) [subsumption resolution 309,115]
311. $false [resolution 310,136]
% SZS output end Proof for 7553191289303050182283303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not brave.
Everyone who is either not patient or not quiet is both rich and not wise and vice versa.
Everyone who is either generous or old is not wise and vice versa.
If alice is both not tall and not patient then john is both kind and funny and vice versa.
If someone is both calm and not patient then paul is either tall or generous and vice versa.
Everyone who is curious is both not patient and humble and vice versa.
Everyone who is either wise or brave is either not humble or tall and vice versa.
Everyone who is humble is both not calm and rich and vice versa.
Everyone who is both patient and not rich is either not patient or not humble and vice versa.
Everyone who is either not patient or wise is both not patient and curious and vice versa.
If someone is not creative then someone is old or funny.
Everyone who is not creative is not generous or not quiet.
If someone is both not funny and tall then alice is either strong or not wise and vice versa.
If paul is not creative then susan is not strong and vice versa.
If john is both not kind and funny then someone is funny or generous and vice versa.
Susan is not funny or patient.
Alice is both tall and not rich.
Someone is funny or not old.
John is both happy and not rich.
Fred is either curious or not tall.
Alice is both not funny and not brave.
Someone is rich. | Susan is not humble. | neutral | (![X]:(generous(X)=>~brave(X)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(rich(X)&~wise(X))))&
(![X]:((generous(X)<~>old(X))<=>~wise(X)))&
(((~tall(alice)&~patient(alice)))<=>((kind(john)&funny(john))))&
((?[X]:((calm(X)&~patient(X))))<=>((tall(paul)<~>generous(paul))))&
(![X]:(curious(X)<=>(~patient(X)&humble(X))))&
(![X]:((wise(X)<~>brave(X))<=>(~humble(X)<~>tall(X))))&
(![X]:(humble(X)<=>(~calm(X)&rich(X))))&
(![X]:((patient(X)&~rich(X))<=>(~patient(X)<~>~humble(X))))&
(![X]:((~patient(X)<~>wise(X))<=>(~patient(X)&curious(X))))&
((?[X]:(~creative(X)))=>(?[X]:((old(X)|funny(X)))))&
(![X]:(~creative(X)=>(~generous(X)|~quiet(X))))&
((?[X]:((~funny(X)&tall(X))))<=>((strong(alice)<~>~wise(alice))))&
((~creative(paul))<=>(~strong(susan)))&
(((~kind(john)&funny(john)))<=>(?[X]:((funny(X)|generous(X)))))&
((~funny(susan)|patient(susan)))&
((tall(alice)&~rich(alice)))&
(?[X]:((funny(X)|~old(X))))&
((happy(john)&~rich(john)))&
((curious(fred)<~>~tall(fred)))&
((~funny(alice)&~brave(alice)))&
(?[X]:(rich(X))) | ~humble(susan) | [] | null | 0 |
Everyone who is not calm or generous is curious. Everyone who is either not patient or wise is both not rich and humble. If someone is not rich then someone is both curious and old. Everyone who is both not old and funny is not strong or patient. If lucy is curious or not creative then john is both not calm and not curious and vice versa. If someone is wise then someone is curious or not humble and vice versa. Everyone who is tall or calm is either not humble or funny. Everyone who is either strong or kind is both not generous and not kind. Everyone who is humble or not calm is either not curious or not strong. Everyone who is both not creative and not kind is either tall or happy and vice versa. If fred is both not wise and wise then mary is either wise or not strong and vice versa. Everyone who is wise or old is either rich or tall. Everyone who is patient or old is not patient and vice versa. If someone is both rich and not old then susan is brave and vice versa. Everyone who is not generous is both not quiet and not wise. If paul is both not creative and funny then someone is both patient and not kind and vice versa. Someone is not tall. Fred is not kind. Fred is both not curious and not kind. Someone is not calm. Someone is wise. Mary is either not happy or curious. Someone is either not generous or wise. | Susan is brave. | contradiction | (![X]:((~calm(X)|generous(X))=>curious(X)))&
(![X]:((~patient(X)<~>wise(X))=>(~rich(X)&humble(X))))&
((?[X]:(~rich(X)))=>(?[X]:((curious(X)&old(X)))))&
(![X]:((~old(X)&funny(X))=>(~strong(X)|patient(X))))&
(((curious(lucy)|~creative(lucy)))<=>((~calm(john)&~curious(john))))&
((?[X]:(wise(X)))<=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((tall(X)|calm(X))=>(~humble(X)<~>funny(X))))&
(![X]:((strong(X)<~>kind(X))=>(~generous(X)&~kind(X))))&
(![X]:((humble(X)|~calm(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((~creative(X)&~kind(X))<=>(tall(X)<~>happy(X))))&
(((~wise(fred)&wise(fred)))<=>((wise(mary)<~>~strong(mary))))&
(![X]:((wise(X)|old(X))=>(rich(X)<~>tall(X))))&
(![X]:((patient(X)|old(X))<=>~patient(X)))&
((?[X]:((rich(X)&~old(X))))<=>(brave(susan)))&
(![X]:(~generous(X)=>(~quiet(X)&~wise(X))))&
(((~creative(paul)&funny(paul)))<=>(?[X]:((patient(X)&~kind(X)))))&
(?[X]:(~tall(X)))&
(~kind(fred))&
((~curious(fred)&~kind(fred)))&
(?[X]:(~calm(X)))&
(?[X]:(wise(X)))&
((~happy(mary)<~>curious(mary)))&
(?[X]:((~generous(X)<~>wise(X)))) | brave(susan) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1066299148174910024443381
% SZS output start Proof for 1066299148174910024443381
13. ! [X0] : ((old(X0) | patient(X0)) <=> ~patient(X0)) [input p12]
14. ? [X0] : (~old(X0) & rich(X0)) <=> brave(susan) [input p13]
24. brave(susan) [input hypothesis]
57. ! [X0] : (((old(X0) | patient(X0)) | patient(X0)) & (~patient(X0) | (~old(X0) & ~patient(X0)))) [nnf transformation 13]
58. ! [X0] : ((old(X0) | patient(X0) | patient(X0)) & (~patient(X0) | (~old(X0) & ~patient(X0)))) [flattening 57]
59. (? [X0] : (~old(X0) & rich(X0)) | ~brave(susan)) & (brave(susan) | ! [X0] : (old(X0) | ~rich(X0))) [nnf transformation 14]
60. (? [X0] : (~old(X0) & rich(X0)) | ~brave(susan)) & (brave(susan) | ! [X1] : (old(X1) | ~rich(X1))) [rectify 59]
61. ? [X0] : (~old(X0) & rich(X0)) => (~old(sK3) & rich(sK3)) [choice axiom]
62. ((~old(sK3) & rich(sK3)) | ~brave(susan)) & (brave(susan) | ! [X1] : (old(X1) | ~rich(X1))) [skolemisation 60,61]
123. ~patient(X0) | ~patient(X0) [cnf transformation 58]
125. old(X0) | patient(X0) | patient(X0) [cnf transformation 58]
128. ~old(sK3) | ~brave(susan) [cnf transformation 62]
144. brave(susan) [cnf transformation 24]
145. ~patient(X0) [duplicate literal removal 123]
146. old(X0) | patient(X0) [duplicate literal removal 125]
223. 17 <=> brave(susan) [avatar definition]
227. 18 <=> old(sK3) [avatar definition]
229. ~old(sK3) <- (~18) [avatar component clause 227]
230. ~17 | ~18 [avatar split clause 128,227,223]
274. 17 [avatar split clause 144,223]
284. patient(sK3) <- (~18) [resolution 146,229]
286. $false <- (~18) [subsumption resolution 284,145]
287. 18 [avatar contradiction clause 286]
288. $false [avatar sat refutation 230,274,287]
% SZS output end Proof for 1066299148174910024443381
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is either quiet or not happy.
If fred is either wise or creative then alice is strong and vice versa.
If lucy is either not rich or brave then someone is not tall and vice versa.
Everyone who is wise or not patient is either strong or not humble.
If someone is either not creative or creative then someone is both old and not funny.
Everyone who is either not happy or not wise is not quiet or not tall and vice versa.
If someone is either not brave or happy then paul is both rich and not rich.
Everyone who is calm or generous is both rich and not brave and vice versa.
Everyone who is curious or not happy is not old or not humble and vice versa.
If paul is either not patient or not rich then someone is both not kind and not generous and vice versa.
Everyone who is not happy is rich or not generous.
If susan is strong or not old then fred is either not happy or strong and vice versa.
Everyone who is both wise and not quiet is not wise and vice versa.
Everyone who is happy is either rich or curious and vice versa.
Everyone who is happy or quiet is wise.
If someone is either not quiet or rich then someone is both not humble and calm and vice versa.
Lucy is not calm or happy.
Fred is not brave or funny.
Someone is old or generous.
Someone is both funny and curious.
Susan is both not tall and quiet.
Fred is not humble. | Alice is generous. | contradiction | (![X]:(kind(X)=>(quiet(X)<~>~happy(X))))&
(((wise(fred)<~>creative(fred)))<=>(strong(alice)))&
(((~rich(lucy)<~>brave(lucy)))<=>(?[X]:(~tall(X))))&
(![X]:((wise(X)|~patient(X))=>(strong(X)<~>~humble(X))))&
((?[X]:((~creative(X)<~>creative(X))))=>(?[X]:((old(X)&~funny(X)))))&
(![X]:((~happy(X)<~>~wise(X))<=>(~quiet(X)|~tall(X))))&
((?[X]:((~brave(X)<~>happy(X))))=>((rich(paul)&~rich(paul))))&
(![X]:((calm(X)|generous(X))<=>(rich(X)&~brave(X))))&
(![X]:((curious(X)|~happy(X))<=>(~old(X)|~humble(X))))&
(((~patient(paul)<~>~rich(paul)))<=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:(~happy(X)=>(rich(X)|~generous(X))))&
(((strong(susan)|~old(susan)))<=>((~happy(fred)<~>strong(fred))))&
(![X]:((wise(X)&~quiet(X))<=>~wise(X)))&
(![X]:(happy(X)<=>(rich(X)<~>curious(X))))&
(![X]:((happy(X)|quiet(X))=>wise(X)))&
((?[X]:((~quiet(X)<~>rich(X))))<=>(?[X]:((~humble(X)&calm(X)))))&
((~calm(lucy)|happy(lucy)))&
((~brave(fred)|funny(fred)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((funny(X)&curious(X))))&
((~tall(susan)&quiet(susan)))&
(~humble(fred)) | generous(alice) | [
"p6",
"p7",
"p8",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4545448961519133157272603
% SZS output start Proof for 4545448961519133157272603
7. ? [X0] : (~brave(X0) <~> happy(X0)) => (~rich(paul) & rich(paul)) [input p6]
8. ! [X0] : ((generous(X0) | calm(X0)) <=> (~brave(X0) & rich(X0))) [input p7]
9. ! [X0] : ((~happy(X0) | curious(X0)) <=> (~humble(X0) | ~old(X0))) [input p8]
13. ! [X0] : ((~quiet(X0) & wise(X0)) <=> ~wise(X0)) [input p12]
14. ! [X0] : (happy(X0) <=> (rich(X0) <~> curious(X0))) [input p13]
16. ? [X0] : (~quiet(X0) <~> rich(X0)) <=> ? [X0] : (calm(X0) & ~humble(X0)) [input p15]
23. generous(alice) [input hypothesis]
25. ? [X0] : (~quiet(X0) <~> rich(X0)) <=> ? [X1] : (calm(X1) & ~humble(X1)) [rectify 16]
29. (~rich(paul) & rich(paul)) | ! [X0] : (~brave(X0) <=> happy(X0)) [ennf transformation 7]
46. (~rich(paul) & rich(paul)) | ! [X0] : ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0))) [nnf transformation 29]
47. ! [X0] : (((generous(X0) | calm(X0)) | (brave(X0) | ~rich(X0))) & ((~brave(X0) & rich(X0)) | (~generous(X0) & ~calm(X0)))) [nnf transformation 8]
48. ! [X0] : ((generous(X0) | calm(X0) | brave(X0) | ~rich(X0)) & ((~brave(X0) & rich(X0)) | (~generous(X0) & ~calm(X0)))) [flattening 47]
49. ! [X0] : (((~happy(X0) | curious(X0)) | (humble(X0) & old(X0))) & ((~humble(X0) | ~old(X0)) | (happy(X0) & ~curious(X0)))) [nnf transformation 9]
50. ! [X0] : ((~happy(X0) | curious(X0) | (humble(X0) & old(X0))) & (~humble(X0) | ~old(X0) | (happy(X0) & ~curious(X0)))) [flattening 49]
57. ! [X0] : (((~quiet(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | (quiet(X0) | ~wise(X0)))) [nnf transformation 13]
58. ! [X0] : (((~quiet(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | quiet(X0) | ~wise(X0))) [flattening 57]
59. ! [X0] : ((happy(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0)))) & (((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | ~happy(X0))) [nnf transformation 14]
60. (? [X0] : ((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | ! [X1] : (~calm(X1) | humble(X1))) & (? [X1] : (calm(X1) & ~humble(X1)) | ! [X0] : ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) [nnf transformation 25]
61. (? [X0] : ((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | ! [X1] : (~calm(X1) | humble(X1))) & (? [X2] : (calm(X2) & ~humble(X2)) | ! [X3] : ((~quiet(X3) | ~rich(X3)) & (rich(X3) | quiet(X3)))) [rectify 60]
62. ? [X0] : ((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) => ((~rich(sK3) | quiet(sK3)) & (rich(sK3) | ~quiet(sK3))) [choice axiom]
63. ? [X2] : (calm(X2) & ~humble(X2)) => (calm(sK4) & ~humble(sK4)) [choice axiom]
64. (((~rich(sK3) | quiet(sK3)) & (rich(sK3) | ~quiet(sK3))) | ! [X1] : (~calm(X1) | humble(X1))) & ((calm(sK4) & ~humble(sK4)) | ! [X3] : ((~quiet(X3) | ~rich(X3)) & (rich(X3) | quiet(X3)))) [skolemisation 61,63,62]
93. rich(paul) | happy(X0) | brave(X0) [cnf transformation 46]
95. ~rich(paul) | happy(X0) | brave(X0) [cnf transformation 46]
97. ~calm(X0) | rich(X0) [cnf transformation 48]
98. ~generous(X0) | rich(X0) [cnf transformation 48]
99. ~calm(X0) | ~brave(X0) [cnf transformation 48]
105. ~happy(X0) | curious(X0) | humble(X0) [cnf transformation 50]
119. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 58]
120. wise(X0) | wise(X0) [cnf transformation 58]
123. ~curious(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 59]
129. ~humble(sK4) | ~quiet(X3) | ~rich(X3) [cnf transformation 64]
131. calm(sK4) | ~quiet(X3) | ~rich(X3) [cnf transformation 64]
142. generous(alice) [cnf transformation 23]
143. ~wise(X0) | quiet(X0) [duplicate literal removal 119]
144. wise(X0) [duplicate literal removal 120]
206. 13 <=> rich(paul) [avatar definition]
211. 14 <=> ! [X0] : (happy(X0) | brave(X0)) [avatar definition]
212. brave(X0) | happy(X0) <- (14) [avatar component clause 211]
213. 14 | ~13 [avatar split clause 95,206,211]
215. 14 | 13 [avatar split clause 93,206,211]
259. quiet(X0) [subsumption resolution 143,144]
269. calm(sK4) | ~rich(X3) [subsumption resolution 131,259]
271. 25 <=> ! [X3] : ~rich(X3) [avatar definition]
272. ~rich(X3) <- (25) [avatar component clause 271]
274. 26 <=> calm(sK4) [avatar definition]
276. calm(sK4) <- (26) [avatar component clause 274]
277. 25 | 26 [avatar split clause 269,274,271]
278. ~humble(sK4) | ~rich(X3) [subsumption resolution 129,259]
280. 27 <=> humble(sK4) [avatar definition]
282. ~humble(sK4) <- (~27) [avatar component clause 280]
283. 25 | ~27 [avatar split clause 278,280,271]
319. rich(alice) [resolution 98,142]
320. $false <- (25) [subsumption resolution 319,272]
321. ~25 [avatar contradiction clause 320]
322. rich(sK4) <- (26) [resolution 276,97]
323. ~brave(sK4) <- (26) [resolution 99,276]
330. happy(sK4) <- (14, 26) [resolution 212,323]
435. 47 <=> curious(sK4) [avatar definition]
437. curious(sK4) <- (47) [avatar component clause 435]
441. curious(sK4) | humble(sK4) <- (14, 26) [resolution 105,330]
558. ~rich(sK4) | ~happy(sK4) <- (47) [resolution 437,123]
560. ~happy(sK4) <- (26, 47) [subsumption resolution 558,322]
561. $false <- (14, 26, 47) [subsumption resolution 560,330]
562. ~14 | ~26 | ~47 [avatar contradiction clause 561]
563. curious(sK4) <- (14, 26, ~27) [subsumption resolution 441,282]
564. 47 | ~14 | ~26 | 27 [avatar split clause 563,280,274,211,435]
565. $false [avatar sat refutation 213,215,277,283,321,562,564]
% SZS output end Proof for 4545448961519133157272603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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