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 humble or not calm is generous and vice versa. If lucy is either funny or not kind then someone is either not old or not creative and vice versa. If someone is not creative or not generous then fred is either old or not tall and vice versa. If someone is either strong or generous then mary is generous or strong and vice versa. Everyone who is funny is not old. If someone is creative or quiet then susan is not humble. Everyone who is either funny or not quiet is both funny and wise. Everyone who is both not creative and creative is either not strong or wise and vice versa. If someone is not calm or not tall then someone is both curious and not tall and vice versa. Everyone who is curious or not generous is not quiet and vice versa. If someone is funny then someone is either not old or not happy. Everyone who is either calm or not patient is both kind and not rich. Everyone who is either quiet or not kind is either not generous or not strong and vice versa. If someone is funny then susan is rich. If someone is both rich and not strong then mary is both not patient and not generous. If someone is either not humble or not creative then someone is not brave. Someone is not brave or creative. Mary is humble. Someone is both not calm and wise. Lucy is both happy and wise. Susan is either quiet or not old. Fred is either not quiet or funny. Someone is tall or not strong. Someone is either not kind or generous. | Fred is not wise. | contradiction | (![X]:((humble(X)<~>~calm(X))<=>generous(X)))&
(((funny(lucy)<~>~kind(lucy)))<=>(?[X]:((~old(X)<~>~creative(X)))))&
((?[X]:((~creative(X)|~generous(X))))<=>((old(fred)<~>~tall(fred))))&
((?[X]:((strong(X)<~>generous(X))))<=>((generous(mary)|strong(mary))))&
(![X]:(funny(X)=>~old(X)))&
((?[X]:((creative(X)|quiet(X))))=>(~humble(susan)))&
(![X]:((funny(X)<~>~quiet(X))=>(funny(X)&wise(X))))&
(![X]:((~creative(X)&creative(X))<=>(~strong(X)<~>wise(X))))&
((?[X]:((~calm(X)|~tall(X))))<=>(?[X]:((curious(X)&~tall(X)))))&
(![X]:((curious(X)|~generous(X))<=>~quiet(X)))&
((?[X]:(funny(X)))=>(?[X]:((~old(X)<~>~happy(X)))))&
(![X]:((calm(X)<~>~patient(X))=>(kind(X)&~rich(X))))&
(![X]:((quiet(X)<~>~kind(X))<=>(~generous(X)<~>~strong(X))))&
((?[X]:(funny(X)))=>(rich(susan)))&
((?[X]:((rich(X)&~strong(X))))=>((~patient(mary)&~generous(mary))))&
((?[X]:((~humble(X)<~>~creative(X))))=>(?[X]:(~brave(X))))&
(?[X]:((~brave(X)|creative(X))))&
(humble(mary))&
(?[X]:((~calm(X)&wise(X))))&
((happy(lucy)&wise(lucy)))&
((quiet(susan)<~>~old(susan)))&
((~quiet(fred)<~>funny(fred)))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:((~kind(X)<~>generous(X)))) | ~wise(fred) | [
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3214691763590860062629475
% SZS output start Proof for 3214691763590860062629475
7. ! [X0] : ((funny(X0) <~> ~quiet(X0)) => (wise(X0) & funny(X0))) [input p6]
22. ~quiet(fred) <~> funny(fred) [input p21]
25. ~wise(fred) [input hypothesis]
33. ! [X0] : ((wise(X0) & funny(X0)) | (funny(X0) <=> ~quiet(X0))) [ennf transformation 7]
52. ! [X0] : ((wise(X0) & funny(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0)))) [nnf transformation 33]
71. (~funny(fred) | quiet(fred)) & (funny(fred) | ~quiet(fred)) [nnf transformation 22]
105. funny(X0) | funny(X0) | quiet(X0) [cnf transformation 52]
106. ~quiet(X0) | wise(X0) | ~funny(X0) [cnf transformation 52]
146. funny(fred) | ~quiet(fred) [cnf transformation 71]
147. ~funny(fred) | quiet(fred) [cnf transformation 71]
151. ~wise(fred) [cnf transformation 25]
152. quiet(X0) | funny(X0) [duplicate literal removal 105]
324. quiet(fred) [subsumption resolution 147,152]
325. funny(fred) [subsumption resolution 146,324]
442. wise(fred) | ~funny(fred) [resolution 106,324]
444. ~funny(fred) [subsumption resolution 442,151]
445. $false [subsumption resolution 444,325]
% SZS output end Proof for 3214691763590860062629475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either old or not curious is not funny.
If alice is not quiet or not happy then someone is not funny.
Everyone who is both not tall and not kind is generous and vice versa.
If someone is calm or not patient then lucy is both rich and strong.
Everyone who is not patient is humble.
If someone is both kind and funny then someone is creative and vice versa.
If mary is either not creative or not funny then fred is both old and not wise and vice versa.
Everyone who is not wise is both not humble and brave.
Everyone who is not tall or not wise is tall.
If lucy is both quiet and not old then someone is both calm and brave and vice versa.
If lucy is both not strong and not patient then someone is both old and not old and vice versa.
If someone is both calm and not old then paul is strong and vice versa.
If john is both not creative and not wise then someone is either tall or not rich.
Everyone who is both not curious and not humble is either strong or calm.
If someone is either not strong or curious then john is kind or not patient and vice versa.
Everyone who is both not strong and not brave is not humble and vice versa.
Lucy is old.
Someone is both not old and happy.
Someone is either not tall or not old.
Paul is wise.
Lucy is not strong.
Mary is not happy.
Someone is not wise or brave. | Mary is not calm. | entailment | (![X]:((old(X)<~>~curious(X))=>~funny(X)))&
(((~quiet(alice)|~happy(alice)))=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)&~kind(X))<=>generous(X)))&
((?[X]:((calm(X)|~patient(X))))=>((rich(lucy)&strong(lucy))))&
(![X]:(~patient(X)=>humble(X)))&
((?[X]:((kind(X)&funny(X))))<=>(?[X]:(creative(X))))&
(((~creative(mary)<~>~funny(mary)))<=>((old(fred)&~wise(fred))))&
(![X]:(~wise(X)=>(~humble(X)&brave(X))))&
(![X]:((~tall(X)|~wise(X))=>tall(X)))&
(((quiet(lucy)&~old(lucy)))<=>(?[X]:((calm(X)&brave(X)))))&
(((~strong(lucy)&~patient(lucy)))<=>(?[X]:((old(X)&~old(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(strong(paul)))&
(((~creative(john)&~wise(john)))=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((~curious(X)&~humble(X))=>(strong(X)<~>calm(X))))&
((?[X]:((~strong(X)<~>curious(X))))<=>((kind(john)|~patient(john))))&
(![X]:((~strong(X)&~brave(X))<=>~humble(X)))&
(old(lucy))&
(?[X]:((~old(X)&happy(X))))&
(?[X]:((~tall(X)<~>~old(X))))&
(wise(paul))&
(~strong(lucy))&
(~happy(mary))&
(?[X]:((~wise(X)|brave(X)))) | ~calm(mary) | [
"p3",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6225736633301534208795891
% SZS output start Proof for 6225736633301534208795891
4. ? [X0] : (~patient(X0) | calm(X0)) => (strong(lucy) & rich(lucy)) [input p3]
21. ~strong(lucy) [input p20]
24. calm(mary) [input hypothesis]
28. (strong(lucy) & rich(lucy)) | ! [X0] : (patient(X0) & ~calm(X0)) [ennf transformation 4]
84. strong(lucy) | ~calm(X0) [cnf transformation 28]
130. ~strong(lucy) [cnf transformation 21]
133. calm(mary) [cnf transformation 24]
153. 5 <=> strong(lucy) [avatar definition]
158. 6 <=> ! [X0] : ~calm(X0) [avatar definition]
159. ~calm(X0) <- (6) [avatar component clause 158]
160. 6 | 5 [avatar split clause 84,153,158]
305. ~5 [avatar split clause 130,153]
307. $false <- (6) [resolution 159,133]
308. ~6 [avatar contradiction clause 307]
309. $false [avatar sat refutation 160,305,308]
% SZS output end Proof for 6225736633301534208795891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not brave is either brave or strong and vice versa. Everyone who is tall is either tall or not funny. If someone is not generous or generous then someone is either not happy or not rich and vice versa. If fred is both not wise and strong then someone is both not curious and not kind. Everyone who is calm is funny or not humble and vice versa. Everyone who is not calm is not patient and vice versa. Everyone who is either old or funny is curious or not wise and vice versa. Everyone who is both old and curious is either not generous or humble and vice versa. If susan is both curious and not curious then fred is old or patient. Everyone who is creative or not generous is both not kind and not patient. Everyone who is not tall or funny is either not strong or kind. If someone is either not patient or not generous then someone is old or not old and vice versa. If someone is either old or not funny then someone is both not kind and not calm and vice versa. Everyone who is not happy or kind is kind. If someone is both happy and patient then paul is either tall or wise and vice versa. If fred is either funny or calm then someone is either calm or not curious. Someone is either creative or brave. Susan is either old or not calm. Fred is happy. Someone is not kind. Lucy is not rich. Someone is either tall or quiet. Susan is either not wise or quiet. | Susan is not calm. | neutral | (![X]:((old(X)&~brave(X))<=>(brave(X)<~>strong(X))))&
(![X]:(tall(X)=>(tall(X)<~>~funny(X))))&
((?[X]:((~generous(X)|generous(X))))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
(((~wise(fred)&strong(fred)))=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:(calm(X)<=>(funny(X)|~humble(X))))&
(![X]:(~calm(X)<=>~patient(X)))&
(![X]:((old(X)<~>funny(X))<=>(curious(X)|~wise(X))))&
(![X]:((old(X)&curious(X))<=>(~generous(X)<~>humble(X))))&
(((curious(susan)&~curious(susan)))=>((old(fred)|patient(fred))))&
(![X]:((creative(X)|~generous(X))=>(~kind(X)&~patient(X))))&
(![X]:((~tall(X)|funny(X))=>(~strong(X)<~>kind(X))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>(?[X]:((old(X)|~old(X)))))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~kind(X)&~calm(X)))))&
(![X]:((~happy(X)|kind(X))=>kind(X)))&
((?[X]:((happy(X)&patient(X))))<=>((tall(paul)<~>wise(paul))))&
(((funny(fred)<~>calm(fred)))=>(?[X]:((calm(X)<~>~curious(X)))))&
(?[X]:((creative(X)<~>brave(X))))&
((old(susan)<~>~calm(susan)))&
(happy(fred))&
(?[X]:(~kind(X)))&
(~rich(lucy))&
(?[X]:((tall(X)<~>quiet(X))))&
((~wise(susan)<~>quiet(susan))) | ~calm(susan) | [] | null | 0 |
If lucy is not wise then someone is not quiet and vice versa.
Everyone who is not generous or wise is either curious or happy.
Everyone who is not rich or not funny is wise.
Everyone who is both not curious and patient is not calm and vice versa.
If paul is either not humble or old then someone is either tall or not humble and vice versa.
If alice is either not quiet or not creative then lucy is both not funny and not calm and vice versa.
If someone is either not creative or not happy then someone is brave or kind.
If lucy is not calm then someone is not brave and vice versa.
Everyone who is old is either generous or wise and vice versa.
If lucy is strong then someone is either not kind or not rich and vice versa.
Everyone who is either not curious or rich is not creative or not brave and vice versa.
Everyone who is not kind or not patient is both rich and funny.
Everyone who is brave or not patient is both not funny and old.
If someone is both tall and not kind then alice is not creative and vice versa.
Everyone who is either not funny or not happy is either rich or not generous and vice versa.
Everyone who is both not wise and not old is both happy and kind.
Someone is not funny or wise.
Someone is not humble or happy.
Paul is either kind or not rich.
Fred is not brave.
Paul is not happy.
John is both tall and not wise.
Someone is either strong or happy. | Fred is not curious. | neutral | ((~wise(lucy))<=>(?[X]:(~quiet(X))))&
(![X]:((~generous(X)|wise(X))=>(curious(X)<~>happy(X))))&
(![X]:((~rich(X)|~funny(X))=>wise(X)))&
(![X]:((~curious(X)&patient(X))<=>~calm(X)))&
(((~humble(paul)<~>old(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(((~quiet(alice)<~>~creative(alice)))<=>((~funny(lucy)&~calm(lucy))))&
((?[X]:((~creative(X)<~>~happy(X))))=>(?[X]:((brave(X)|kind(X)))))&
((~calm(lucy))<=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>(generous(X)<~>wise(X))))&
((strong(lucy))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((~curious(X)<~>rich(X))<=>(~creative(X)|~brave(X))))&
(![X]:((~kind(X)|~patient(X))=>(rich(X)&funny(X))))&
(![X]:((brave(X)|~patient(X))=>(~funny(X)&old(X))))&
((?[X]:((tall(X)&~kind(X))))<=>(~creative(alice)))&
(![X]:((~funny(X)<~>~happy(X))<=>(rich(X)<~>~generous(X))))&
(![X]:((~wise(X)&~old(X))=>(happy(X)&kind(X))))&
(?[X]:((~funny(X)|wise(X))))&
(?[X]:((~humble(X)|happy(X))))&
((kind(paul)<~>~rich(paul)))&
(~brave(fred))&
(~happy(paul))&
((tall(john)&~wise(john)))&
(?[X]:((strong(X)<~>happy(X)))) | ~curious(fred) | [] | null | 0 |
Everyone who is either quiet or old is rich and vice versa. Everyone who is both calm and not brave is not generous or not old. If someone is not humble or happy then someone is either happy or not patient. If john is both not old and tall then paul is old and vice versa. Everyone who is both not old and not generous is not calm or calm and vice versa. Everyone who is either creative or not old is not humble or strong and vice versa. Everyone who is not tall or not rich is not creative and vice versa. Everyone who is rich is either rich or happy and vice versa. Everyone who is not humble or happy is calm and vice versa. If alice is either funny or not wise then alice is either generous or not tall. If fred is curious or kind then someone is both quiet and not quiet. If fred is humble or calm then someone is old or creative and vice versa. Everyone who is both happy and not quiet is funny or not patient and vice versa. If john is either strong or not tall then susan is both not wise and funny and vice versa. Everyone who is not wise is either not humble or curious and vice versa. If paul is happy or kind then someone is both not creative and not brave. Someone is either not curious or not quiet. Alice is quiet or not rich. Mary is not wise. Alice is not quiet. Someone is not curious or old. Someone is not old. | Mary is not generous. | entailment | (![X]:((quiet(X)<~>old(X))<=>rich(X)))&
(![X]:((calm(X)&~brave(X))=>(~generous(X)|~old(X))))&
((?[X]:((~humble(X)|happy(X))))=>(?[X]:((happy(X)<~>~patient(X)))))&
(((~old(john)&tall(john)))<=>(old(paul)))&
(![X]:((~old(X)&~generous(X))<=>(~calm(X)|calm(X))))&
(![X]:((creative(X)<~>~old(X))<=>(~humble(X)|strong(X))))&
(![X]:((~tall(X)|~rich(X))<=>~creative(X)))&
(![X]:(rich(X)<=>(rich(X)<~>happy(X))))&
(![X]:((~humble(X)|happy(X))<=>calm(X)))&
(((funny(alice)<~>~wise(alice)))=>((generous(alice)<~>~tall(alice))))&
(((curious(fred)|kind(fred)))=>(?[X]:((quiet(X)&~quiet(X)))))&
(((humble(fred)|calm(fred)))<=>(?[X]:((old(X)|creative(X)))))&
(![X]:((happy(X)&~quiet(X))<=>(funny(X)|~patient(X))))&
(((strong(john)<~>~tall(john)))<=>((~wise(susan)&funny(susan))))&
(![X]:(~wise(X)<=>(~humble(X)<~>curious(X))))&
(((happy(paul)|kind(paul)))=>(?[X]:((~creative(X)&~brave(X)))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
((quiet(alice)|~rich(alice)))&
(~wise(mary))&
(~quiet(alice))&
(?[X]:((~curious(X)|old(X))))&
(?[X]:(~old(X))) | ~generous(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6010488016663428794182328
% SZS output start Proof for 6010488016663428794182328
5. ! [X0] : ((~generous(X0) & ~old(X0)) <=> (calm(X0) | ~calm(X0))) [input p4]
23. generous(mary) [input hypothesis]
40. ! [X0] : (((~generous(X0) & ~old(X0)) | (~calm(X0) & calm(X0))) & ((calm(X0) | ~calm(X0)) | (generous(X0) | old(X0)))) [nnf transformation 5]
41. ! [X0] : (((~generous(X0) & ~old(X0)) | (~calm(X0) & calm(X0))) & (calm(X0) | ~calm(X0) | generous(X0) | old(X0))) [flattening 40]
86. ~generous(X0) | calm(X0) [cnf transformation 41]
87. ~generous(X0) | ~calm(X0) [cnf transformation 41]
138. generous(mary) [cnf transformation 23]
174. ~generous(X0) [subsumption resolution 86,87]
276. $false [subsumption resolution 138,174]
% SZS output end Proof for 6010488016663428794182328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and tall then someone is funny or creative and vice versa.
If someone is creative then someone is either happy or kind and vice versa.
If susan is either strong or not humble then mary is not funny or not generous.
Everyone who is both generous and not funny is both creative and not happy.
Everyone who is funny or rich is either not old or generous.
Everyone who is happy or not brave is not happy or not kind.
Everyone who is either humble or brave is either calm or not wise and vice versa.
If mary is not funny then someone is not rich or not strong and vice versa.
Everyone who is quiet or generous is both not wise and generous.
Everyone who is funny or not quiet is either wise or not old and vice versa.
If someone is generous or not tall then lucy is not quiet.
Everyone who is not brave is both not funny and not generous and vice versa.
Everyone who is creative is both not curious and curious and vice versa.
If someone is tall then fred is both old and not happy.
If someone is generous or funny then someone is either funny or not funny and vice versa.
If someone is either rich or curious then someone is not curious and vice versa.
Someone is either not curious or not humble.
Someone is not wise.
Susan is both not curious and not brave.
Someone is not strong.
Fred is not patient.
Someone is funny or curious.
Someone is not quiet or old. | Fred is not old. | contradiction | ((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((funny(X)|creative(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((happy(X)<~>kind(X)))))&
(((strong(susan)<~>~humble(susan)))=>((~funny(mary)|~generous(mary))))&
(![X]:((generous(X)&~funny(X))=>(creative(X)&~happy(X))))&
(![X]:((funny(X)|rich(X))=>(~old(X)<~>generous(X))))&
(![X]:((happy(X)|~brave(X))=>(~happy(X)|~kind(X))))&
(![X]:((humble(X)<~>brave(X))<=>(calm(X)<~>~wise(X))))&
((~funny(mary))<=>(?[X]:((~rich(X)|~strong(X)))))&
(![X]:((quiet(X)|generous(X))=>(~wise(X)&generous(X))))&
(![X]:((funny(X)|~quiet(X))<=>(wise(X)<~>~old(X))))&
((?[X]:((generous(X)|~tall(X))))=>(~quiet(lucy)))&
(![X]:(~brave(X)<=>(~funny(X)&~generous(X))))&
(![X]:(creative(X)<=>(~curious(X)&curious(X))))&
((?[X]:(tall(X)))=>((old(fred)&~happy(fred))))&
((?[X]:((generous(X)|funny(X))))<=>(?[X]:((funny(X)<~>~funny(X)))))&
((?[X]:((rich(X)<~>curious(X))))<=>(?[X]:(~curious(X))))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:(~wise(X)))&
((~curious(susan)&~brave(susan)))&
(?[X]:(~strong(X)))&
(~patient(fred))&
(?[X]:((funny(X)|curious(X))))&
(?[X]:((~quiet(X)|old(X)))) | ~old(fred) | [
"p0",
"p3",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2165692150327628853566197
% SZS output start Proof for 2165692150327628853566197
1. ? [X0] : (tall(X0) & ~rich(X0)) <=> ? [X0] : (creative(X0) | funny(X0)) [input p0]
4. ! [X0] : ((~funny(X0) & generous(X0)) => (~happy(X0) & creative(X0))) [input p3]
13. ! [X0] : (creative(X0) <=> (curious(X0) & ~curious(X0))) [input p12]
14. ? [X0] : tall(X0) => (~happy(fred) & old(fred)) [input p13]
15. ? [X0] : (funny(X0) | generous(X0)) <=> ? [X0] : (funny(X0) <~> ~funny(X0)) [input p14]
24. ~old(fred) [input hypothesis]
25. ? [X0] : (tall(X0) & ~rich(X0)) <=> ? [X1] : (creative(X1) | funny(X1)) [rectify 1]
27. ? [X0] : (funny(X0) | generous(X0)) <=> ? [X1] : (funny(X1) <~> ~funny(X1)) [rectify 15]
32. ! [X0] : ((~happy(X0) & creative(X0)) | (funny(X0) | ~generous(X0))) [ennf transformation 4]
33. ! [X0] : ((~happy(X0) & creative(X0)) | funny(X0) | ~generous(X0)) [flattening 32]
39. (~happy(fred) & old(fred)) | ! [X0] : ~tall(X0) [ennf transformation 14]
40. (? [X0] : (tall(X0) & ~rich(X0)) | ! [X1] : (~creative(X1) & ~funny(X1))) & (? [X1] : (creative(X1) | funny(X1)) | ! [X0] : (~tall(X0) | rich(X0))) [nnf transformation 25]
41. (? [X0] : (tall(X0) & ~rich(X0)) | ! [X1] : (~creative(X1) & ~funny(X1))) & (? [X2] : (creative(X2) | funny(X2)) | ! [X3] : (~tall(X3) | rich(X3))) [rectify 40]
42. ? [X0] : (tall(X0) & ~rich(X0)) => (tall(sK0) & ~rich(sK0)) [choice axiom]
43. ? [X2] : (creative(X2) | funny(X2)) => (creative(sK1) | funny(sK1)) [choice axiom]
44. ((tall(sK0) & ~rich(sK0)) | ! [X1] : (~creative(X1) & ~funny(X1))) & ((creative(sK1) | funny(sK1)) | ! [X3] : (~tall(X3) | rich(X3))) [skolemisation 41,43,42]
61. ! [X0] : ((creative(X0) | (~curious(X0) | curious(X0))) & ((curious(X0) & ~curious(X0)) | ~creative(X0))) [nnf transformation 13]
62. ! [X0] : ((creative(X0) | ~curious(X0) | curious(X0)) & ((curious(X0) & ~curious(X0)) | ~creative(X0))) [flattening 61]
63. (? [X0] : (funny(X0) | generous(X0)) | ! [X1] : ((funny(X1) | funny(X1)) & (~funny(X1) | ~funny(X1)))) & (? [X1] : ((funny(X1) | ~funny(X1)) & (~funny(X1) | funny(X1))) | ! [X0] : (~funny(X0) & ~generous(X0))) [nnf transformation 27]
64. (? [X0] : (funny(X0) | generous(X0)) | ! [X1] : ((funny(X1) | funny(X1)) & (~funny(X1) | ~funny(X1)))) & (? [X2] : ((funny(X2) | ~funny(X2)) & (~funny(X2) | funny(X2))) | ! [X3] : (~funny(X3) & ~generous(X3))) [rectify 63]
65. ? [X0] : (funny(X0) | generous(X0)) => (funny(sK5) | generous(sK5)) [choice axiom]
66. ? [X2] : ((funny(X2) | ~funny(X2)) & (~funny(X2) | funny(X2))) => ((funny(sK6) | ~funny(sK6)) & (~funny(sK6) | funny(sK6))) [choice axiom]
67. ((funny(sK5) | generous(sK5)) | ! [X1] : ((funny(X1) | funny(X1)) & (~funny(X1) | ~funny(X1)))) & (((funny(sK6) | ~funny(sK6)) & (~funny(sK6) | funny(sK6))) | ! [X3] : (~funny(X3) & ~generous(X3))) [skolemisation 64,66,65]
87. tall(sK0) | ~funny(X1) [cnf transformation 44]
95. ~generous(X0) | funny(X0) | creative(X0) [cnf transformation 33]
129. ~curious(X0) | ~creative(X0) [cnf transformation 62]
130. ~creative(X0) | curious(X0) [cnf transformation 62]
132. old(fred) | ~tall(X0) [cnf transformation 39]
139. funny(sK5) | generous(sK5) | funny(X1) | funny(X1) [cnf transformation 67]
152. ~old(fred) [cnf transformation 24]
154. funny(sK5) | generous(sK5) | funny(X1) [duplicate literal removal 139]
157. 1 <=> ! [X1] : ~creative(X1) [avatar definition]
158. ~creative(X1) <- (1) [avatar component clause 157]
160. 2 <=> tall(sK0) [avatar definition]
162. tall(sK0) <- (2) [avatar component clause 160]
165. 3 <=> ! [X1] : ~funny(X1) [avatar definition]
166. ~funny(X1) <- (3) [avatar component clause 165]
167. 3 | 2 [avatar split clause 87,160,165]
257. ~creative(X0) [subsumption resolution 129,130]
258. 1 [avatar split clause 257,157]
260. 24 <=> ! [X0] : ~tall(X0) [avatar definition]
261. ~tall(X0) <- (24) [avatar component clause 260]
268. 26 <=> old(fred) [avatar definition]
271. 24 | 26 [avatar split clause 132,268,260]
273. 27 <=> ! [X1] : funny(X1) [avatar definition]
274. funny(X1) <- (27) [avatar component clause 273]
276. 28 <=> generous(sK5) [avatar definition]
278. generous(sK5) <- (28) [avatar component clause 276]
280. 29 <=> funny(sK5) [avatar definition]
282. funny(sK5) <- (29) [avatar component clause 280]
283. 27 | 28 | 29 [avatar split clause 154,280,276,273]
338. ~26 [avatar split clause 152,268]
341. $false <- (3, 27) [subsumption resolution 166,274]
342. ~3 | ~27 [avatar contradiction clause 341]
352. funny(sK5) | creative(sK5) <- (28) [resolution 95,278]
353. creative(sK5) <- (3, 28) [subsumption resolution 352,166]
354. $false <- (1, 3, 28) [subsumption resolution 353,158]
355. ~1 | ~3 | ~28 [avatar contradiction clause 354]
356. $false <- (3, 29) [subsumption resolution 282,166]
357. ~3 | ~29 [avatar contradiction clause 356]
358. $false <- (2, 24) [subsumption resolution 162,261]
359. ~2 | ~24 [avatar contradiction clause 358]
360. $false [avatar sat refutation 167,258,271,283,338,342,355,357,359]
% SZS output end Proof for 2165692150327628853566197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or patient is not happy and vice versa.
Everyone who is both not strong and not old is both curious and strong.
Everyone who is both generous and rich is both not strong and rich.
Everyone who is both not kind and not generous is not patient and vice versa.
Everyone who is wise or not quiet is patient or wise and vice versa.
Everyone who is brave or happy is both not generous and happy and vice versa.
If fred is humble or not curious then someone is both not generous and tall and vice versa.
If susan is curious or happy then john is either not generous or funny.
If fred is either not quiet or kind then someone is not patient or not generous.
Everyone who is not humble is both not humble and not old and vice versa.
If fred is not funny or not creative then alice is both not curious and not tall.
Everyone who is either not strong or generous is either not happy or not brave and vice versa.
If someone is both not rich and not old then someone is wise or patient.
If someone is patient or not kind then someone is generous or rich.
If john is curious or not kind then fred is both not creative and humble and vice versa.
Everyone who is rich is wise or not funny.
Fred is both not calm and not humble.
Fred is not humble.
Someone is both quiet and not brave.
Mary is either not creative or not rich.
Someone is either not happy or calm.
John is not generous or curious. | Mary is not calm. | neutral | (![X]:((~curious(X)<~>patient(X))<=>~happy(X)))&
(![X]:((~strong(X)&~old(X))=>(curious(X)&strong(X))))&
(![X]:((generous(X)&rich(X))=>(~strong(X)&rich(X))))&
(![X]:((~kind(X)&~generous(X))<=>~patient(X)))&
(![X]:((wise(X)|~quiet(X))<=>(patient(X)|wise(X))))&
(![X]:((brave(X)|happy(X))<=>(~generous(X)&happy(X))))&
(((humble(fred)|~curious(fred)))<=>(?[X]:((~generous(X)&tall(X)))))&
(((curious(susan)|happy(susan)))=>((~generous(john)<~>funny(john))))&
(((~quiet(fred)<~>kind(fred)))=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:(~humble(X)<=>(~humble(X)&~old(X))))&
(((~funny(fred)|~creative(fred)))=>((~curious(alice)&~tall(alice))))&
(![X]:((~strong(X)<~>generous(X))<=>(~happy(X)<~>~brave(X))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:((wise(X)|patient(X)))))&
((?[X]:((patient(X)|~kind(X))))=>(?[X]:((generous(X)|rich(X)))))&
(((curious(john)|~kind(john)))<=>((~creative(fred)&humble(fred))))&
(![X]:(rich(X)=>(wise(X)|~funny(X))))&
((~calm(fred)&~humble(fred)))&
(~humble(fred))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(mary)<~>~rich(mary)))&
(?[X]:((~happy(X)<~>calm(X))))&
((~generous(john)|curious(john))) | ~calm(mary) | [] | null | 0 |
If someone is either humble or not kind then someone is creative or not brave and vice versa. Everyone who is either generous or not old is brave or not patient and vice versa. If someone is brave or tall then someone is not old and vice versa. If someone is both not tall and not funny then someone is either not wise or creative and vice versa. Everyone who is both humble and tall is either creative or funny and vice versa. If fred is tall or not kind then lucy is both not quiet and funny and vice versa. Everyone who is either strong or funny is patient or not quiet. If someone is either tall or not generous then alice is wise. If lucy is either not strong or generous then someone is not quiet or not creative. If someone is either not patient or not humble then someone is either not tall or patient and vice versa. Everyone who is not generous or generous is either creative or humble and vice versa. Everyone who is funny or not happy is not strong or not rich and vice versa. If susan is not generous or not funny then alice is calm and vice versa. Everyone who is both not funny and happy is not old and vice versa. If someone is both not wise and quiet then susan is either not old or not creative and vice versa. Everyone who is not old or generous is both not brave and strong and vice versa. Alice is both not creative and not kind. Susan is both quiet and not funny. Susan is not wise. Someone is funny. Alice is either not rich or curious. Paul is either not curious or not rich. John is not quiet. | Susan is old. | entailment | ((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((creative(X)|~brave(X)))))&
(![X]:((generous(X)<~>~old(X))<=>(brave(X)|~patient(X))))&
((?[X]:((brave(X)|tall(X))))<=>(?[X]:(~old(X))))&
((?[X]:((~tall(X)&~funny(X))))<=>(?[X]:((~wise(X)<~>creative(X)))))&
(![X]:((humble(X)&tall(X))<=>(creative(X)<~>funny(X))))&
(((tall(fred)|~kind(fred)))<=>((~quiet(lucy)&funny(lucy))))&
(![X]:((strong(X)<~>funny(X))=>(patient(X)|~quiet(X))))&
((?[X]:((tall(X)<~>~generous(X))))=>(wise(alice)))&
(((~strong(lucy)<~>generous(lucy)))=>(?[X]:((~quiet(X)|~creative(X)))))&
((?[X]:((~patient(X)<~>~humble(X))))<=>(?[X]:((~tall(X)<~>patient(X)))))&
(![X]:((~generous(X)|generous(X))<=>(creative(X)<~>humble(X))))&
(![X]:((funny(X)|~happy(X))<=>(~strong(X)|~rich(X))))&
(((~generous(susan)|~funny(susan)))<=>(calm(alice)))&
(![X]:((~funny(X)&happy(X))<=>~old(X)))&
((?[X]:((~wise(X)&quiet(X))))<=>((~old(susan)<~>~creative(susan))))&
(![X]:((~old(X)|generous(X))<=>(~brave(X)&strong(X))))&
((~creative(alice)&~kind(alice)))&
((quiet(susan)&~funny(susan)))&
(~wise(susan))&
(?[X]:(funny(X)))&
((~rich(alice)<~>curious(alice)))&
((~curious(paul)<~>~rich(paul)))&
(~quiet(john)) | old(susan) | [
"p4",
"p10",
"p14",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5869058912154277866613839
% SZS output start Proof for 5869058912154277866613839
5. ! [X0] : ((tall(X0) & humble(X0)) <=> (creative(X0) <~> funny(X0))) [input p4]
11. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (creative(X0) <~> humble(X0))) [input p10]
15. ? [X0] : (quiet(X0) & ~wise(X0)) <=> (~old(susan) <~> ~creative(susan)) [input p14]
18. ~funny(susan) & quiet(susan) [input p17]
19. ~wise(susan) [input p18]
24. ~old(susan) [input hypothesis]
50. ! [X0] : (((tall(X0) & humble(X0)) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0)))) & (((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | (~tall(X0) | ~humble(X0)))) [nnf transformation 5]
51. ! [X0] : (((tall(X0) & humble(X0)) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0)))) & (((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | ~tall(X0) | ~humble(X0))) [flattening 50]
64. ! [X0] : (((generous(X0) | ~generous(X0)) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0)))) & (((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | (~generous(X0) & generous(X0)))) [nnf transformation 11]
65. ! [X0] : ((generous(X0) | ~generous(X0) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0)))) & (((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | (~generous(X0) & generous(X0)))) [flattening 64]
72. (? [X0] : (quiet(X0) & ~wise(X0)) | ((~old(susan) | creative(susan)) & (~creative(susan) | old(susan)))) & (((creative(susan) | old(susan)) & (~creative(susan) | ~old(susan))) | ! [X0] : (~quiet(X0) | wise(X0))) [nnf transformation 15]
73. (? [X0] : (quiet(X0) & ~wise(X0)) | ((~old(susan) | creative(susan)) & (~creative(susan) | old(susan)))) & (((creative(susan) | old(susan)) & (~creative(susan) | ~old(susan))) | ! [X1] : (~quiet(X1) | wise(X1))) [rectify 72]
74. ? [X0] : (quiet(X0) & ~wise(X0)) => (quiet(sK9) & ~wise(sK9)) [choice axiom]
75. ((quiet(sK9) & ~wise(sK9)) | ((~old(susan) | creative(susan)) & (~creative(susan) | old(susan)))) & (((creative(susan) | old(susan)) & (~creative(susan) | ~old(susan))) | ! [X1] : (~quiet(X1) | wise(X1))) [skolemisation 73,74]
105. ~creative(X0) | funny(X0) | humble(X0) [cnf transformation 51]
130. ~humble(X0) | ~creative(X0) | generous(X0) [cnf transformation 65]
131. ~humble(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 65]
145. creative(susan) | old(susan) | ~quiet(X1) | wise(X1) [cnf transformation 75]
157. quiet(susan) [cnf transformation 18]
158. ~funny(susan) [cnf transformation 18]
159. ~wise(susan) [cnf transformation 19]
166. ~old(susan) [cnf transformation 24]
343. ~creative(X0) | ~humble(X0) [subsumption resolution 130,131]
354. 43 <=> funny(susan) [avatar definition]
356. ~funny(susan) <- (~43) [avatar component clause 354]
361. 44 <=> creative(susan) [avatar definition]
363. creative(susan) <- (44) [avatar component clause 361]
365. 45 <=> old(susan) [avatar definition]
381. 48 <=> ! [X1] : (~quiet(X1) | wise(X1)) [avatar definition]
382. ~quiet(X1) | wise(X1) <- (48) [avatar component clause 381]
383. 48 | 45 | 44 [avatar split clause 145,361,365,381]
386. ~43 [avatar split clause 158,354]
407. ~45 [avatar split clause 166,365]
413. ~humble(susan) <- (44) [resolution 343,363]
440. funny(susan) | humble(susan) <- (44) [resolution 105,363]
443. humble(susan) <- (~43, 44) [subsumption resolution 440,356]
444. $false <- (~43, 44) [subsumption resolution 443,413]
445. 43 | ~44 [avatar contradiction clause 444]
447. wise(susan) <- (48) [resolution 382,157]
449. $false <- (48) [subsumption resolution 447,159]
450. ~48 [avatar contradiction clause 449]
453. $false [avatar sat refutation 383,386,407,445,450]
% SZS output end Proof for 5869058912154277866613839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not creative is rich and vice versa.
Everyone who is generous is patient or humble and vice versa.
Everyone who is not strong or not humble is creative or kind and vice versa.
Everyone who is creative or not funny is not humble or old and vice versa.
Everyone who is both curious and not humble is either not quiet or not strong and vice versa.
If lucy is not calm or not wise then someone is not brave or funny.
Everyone who is either generous or not generous is curious or not generous.
Everyone who is funny or curious is calm.
If someone is not brave or not patient then someone is either not curious or creative and vice versa.
If alice is either happy or not rich then john is either old or not funny.
If susan is rich then someone is either happy or not tall.
If paul is rich then someone is both humble and happy.
Everyone who is brave or not quiet is both not curious and calm and vice versa.
Everyone who is either not funny or curious is either not funny or creative and vice versa.
Everyone who is both wise and not brave is old or not rich and vice versa.
If mary is generous or strong then alice is both calm and kind and vice versa.
Susan is generous or not creative.
Someone is both not calm and kind.
Someone is either wise or not happy.
Susan is both generous and not rich.
Fred is either brave or creative.
Paul is curious.
Lucy is either patient or brave.
Someone is rich or strong. | Susan is not brave. | entailment | (![X]:((strong(X)&~creative(X))<=>rich(X)))&
(![X]:(generous(X)<=>(patient(X)|humble(X))))&
(![X]:((~strong(X)|~humble(X))<=>(creative(X)|kind(X))))&
(![X]:((creative(X)|~funny(X))<=>(~humble(X)|old(X))))&
(![X]:((curious(X)&~humble(X))<=>(~quiet(X)<~>~strong(X))))&
(((~calm(lucy)|~wise(lucy)))=>(?[X]:((~brave(X)|funny(X)))))&
(![X]:((generous(X)<~>~generous(X))=>(curious(X)|~generous(X))))&
(![X]:((funny(X)|curious(X))=>calm(X)))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((~curious(X)<~>creative(X)))))&
(((happy(alice)<~>~rich(alice)))=>((old(john)<~>~funny(john))))&
((rich(susan))=>(?[X]:((happy(X)<~>~tall(X)))))&
((rich(paul))=>(?[X]:((humble(X)&happy(X)))))&
(![X]:((brave(X)|~quiet(X))<=>(~curious(X)&calm(X))))&
(![X]:((~funny(X)<~>curious(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((wise(X)&~brave(X))<=>(old(X)|~rich(X))))&
(((generous(mary)|strong(mary)))<=>((calm(alice)&kind(alice))))&
((generous(susan)|~creative(susan)))&
(?[X]:((~calm(X)&kind(X))))&
(?[X]:((wise(X)<~>~happy(X))))&
((generous(susan)&~rich(susan)))&
((brave(fred)<~>creative(fred)))&
(curious(paul))&
((patient(lucy)<~>brave(lucy)))&
(?[X]:((rich(X)|strong(X)))) | ~brave(susan) | [
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7305906874777567252749029
% SZS output start Proof for 7305906874777567252749029
15. ! [X0] : ((~brave(X0) & wise(X0)) <=> (~rich(X0) | old(X0))) [input p14]
20. ~rich(susan) & generous(susan) [input p19]
25. brave(susan) [input hypothesis]
61. ! [X0] : (((~brave(X0) & wise(X0)) | (rich(X0) & ~old(X0))) & ((~rich(X0) | old(X0)) | (brave(X0) | ~wise(X0)))) [nnf transformation 15]
62. ! [X0] : (((~brave(X0) & wise(X0)) | (rich(X0) & ~old(X0))) & (~rich(X0) | old(X0) | brave(X0) | ~wise(X0))) [flattening 61]
131. ~brave(X0) | rich(X0) [cnf transformation 62]
143. ~rich(susan) [cnf transformation 20]
150. brave(susan) [cnf transformation 25]
230. 17 <=> rich(susan) [avatar definition]
232. ~rich(susan) <- (~17) [avatar component clause 230]
299. ~17 [avatar split clause 143,230]
334. rich(susan) [resolution 131,150]
336. $false <- (~17) [subsumption resolution 334,232]
337. 17 [avatar contradiction clause 336]
338. $false [avatar sat refutation 299,337]
% SZS output end Proof for 7305906874777567252749029
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then someone is not tall. Everyone who is quiet or patient is either not kind or not patient. Everyone who is either not wise or not generous is not rich or calm. Everyone who is both funny and kind is either wise or not rich and vice versa. If someone is both not curious and patient then fred is creative. Everyone who is brave is either humble or not patient. Everyone who is either old or not funny is not curious. Everyone who is both not rich and not wise is not kind and vice versa. If john is not calm then fred is either happy or not generous and vice versa. Everyone who is not funny is not calm or not kind and vice versa. Everyone who is rich is not creative. If someone is patient then someone is tall and vice versa. If john is both calm and not happy then paul is not creative or not strong. Everyone who is not generous or not old is both quiet and not quiet. If someone is not curious then someone is kind or not rich. If john is tall or brave then someone is both not quiet and not tall and vice versa. Alice is both curious and creative. Someone is either not humble or curious. Someone is not generous or quiet. Paul is either funny or not wise. Someone is not tall or humble. Fred is not curious or not calm. | Fred is humble. | neutral | ((?[X]:(~wise(X)))=>(?[X]:(~tall(X))))&
(![X]:((quiet(X)|patient(X))=>(~kind(X)<~>~patient(X))))&
(![X]:((~wise(X)<~>~generous(X))=>(~rich(X)|calm(X))))&
(![X]:((funny(X)&kind(X))<=>(wise(X)<~>~rich(X))))&
((?[X]:((~curious(X)&patient(X))))=>(creative(fred)))&
(![X]:(brave(X)=>(humble(X)<~>~patient(X))))&
(![X]:((old(X)<~>~funny(X))=>~curious(X)))&
(![X]:((~rich(X)&~wise(X))<=>~kind(X)))&
((~calm(john))<=>((happy(fred)<~>~generous(fred))))&
(![X]:(~funny(X)<=>(~calm(X)|~kind(X))))&
(![X]:(rich(X)=>~creative(X)))&
((?[X]:(patient(X)))<=>(?[X]:(tall(X))))&
(((calm(john)&~happy(john)))=>((~creative(paul)|~strong(paul))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&~quiet(X))))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~rich(X)))))&
(((tall(john)|brave(john)))<=>(?[X]:((~quiet(X)&~tall(X)))))&
((curious(alice)&creative(alice)))&
(?[X]:((~humble(X)<~>curious(X))))&
(?[X]:((~generous(X)|quiet(X))))&
((funny(paul)<~>~wise(paul)))&
(?[X]:((~tall(X)|humble(X))))&
((~curious(fred)|~calm(fred))) | humble(fred) | [] | null | 0 |
If someone is both brave and happy then susan is curious or calm.
Everyone who is generous is both not brave and not creative.
If someone is both not generous and not wise then fred is both rich and creative.
Everyone who is either not curious or wise is not quiet and vice versa.
Everyone who is both kind and not kind is not patient or old and vice versa.
If lucy is either not funny or not humble then someone is not brave or humble and vice versa.
Everyone who is brave or strong is not brave and vice versa.
Everyone who is both rich and not tall is either tall or not tall.
If someone is not funny or not strong then someone is humble or not quiet.
Everyone who is either not strong or strong is either creative or not humble.
If someone is funny then alice is either not rich or not happy and vice versa.
If alice is rich then mary is curious and vice versa.
Everyone who is both quiet and curious is not calm or calm.
Everyone who is not generous or funny is not creative.
If john is either tall or quiet then john is generous and vice versa.
Everyone who is not calm or calm is either not kind or humble.
Someone is not happy.
Lucy is both wise and not brave.
Someone is either rich or not rich.
Someone is funny.
Alice is funny.
Someone is either curious or creative. | Mary is not brave. | entailment | ((?[X]:((brave(X)&happy(X))))=>((curious(susan)|calm(susan))))&
(![X]:(generous(X)=>(~brave(X)&~creative(X))))&
((?[X]:((~generous(X)&~wise(X))))=>((rich(fred)&creative(fred))))&
(![X]:((~curious(X)<~>wise(X))<=>~quiet(X)))&
(![X]:((kind(X)&~kind(X))<=>(~patient(X)|old(X))))&
(((~funny(lucy)<~>~humble(lucy)))<=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((brave(X)|strong(X))<=>~brave(X)))&
(![X]:((rich(X)&~tall(X))=>(tall(X)<~>~tall(X))))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)<~>~humble(X))))&
((?[X]:(funny(X)))<=>((~rich(alice)<~>~happy(alice))))&
((rich(alice))<=>(curious(mary)))&
(![X]:((quiet(X)&curious(X))=>(~calm(X)|calm(X))))&
(![X]:((~generous(X)|funny(X))=>~creative(X)))&
(((tall(john)<~>quiet(john)))<=>(generous(john)))&
(![X]:((~calm(X)|calm(X))=>(~kind(X)<~>humble(X))))&
(?[X]:(~happy(X)))&
((wise(lucy)&~brave(lucy)))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:(funny(X)))&
(funny(alice))&
(?[X]:((curious(X)<~>creative(X)))) | ~brave(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3493309431005237535533827
% SZS output start Proof for 3493309431005237535533827
7. ! [X0] : ((strong(X0) | brave(X0)) <=> ~brave(X0)) [input p6]
23. brave(mary) [input hypothesis]
44. ! [X0] : (((strong(X0) | brave(X0)) | brave(X0)) & (~brave(X0) | (~strong(X0) & ~brave(X0)))) [nnf transformation 7]
45. ! [X0] : ((strong(X0) | brave(X0) | brave(X0)) & (~brave(X0) | (~strong(X0) & ~brave(X0)))) [flattening 44]
88. ~brave(X0) | ~brave(X0) [cnf transformation 45]
125. brave(mary) [cnf transformation 23]
132. ~brave(X0) [duplicate literal removal 88]
252. $false [subsumption resolution 125,132]
% SZS output end Proof for 3493309431005237535533827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not old then someone is either brave or generous and vice versa.
Everyone who is not humble or brave is not generous.
If someone is both patient and creative then someone is either not funny or patient and vice versa.
Everyone who is both not humble and not brave is rich or wise and vice versa.
Everyone who is not kind is either not generous or wise.
Everyone who is patient is either not wise or strong.
Everyone who is rich or patient is both wise and not patient and vice versa.
Everyone who is both humble and happy is wise or happy and vice versa.
Everyone who is not strong or not generous is either tall or not curious and vice versa.
If someone is either not quiet or not curious then someone is both not old and funny.
Everyone who is patient or not kind is not strong or happy and vice versa.
Everyone who is not old or not happy is curious and vice versa.
Everyone who is either creative or not patient is either not quiet or not tall and vice versa.
Everyone who is either not calm or old is either not quiet or not kind.
Everyone who is not strong is either strong or generous.
If paul is either curious or quiet then alice is rich or wise.
Paul is kind or curious.
Paul is not strong or tall.
Someone is not rich.
Someone is either tall or not tall.
Mary is not humble or not funny.
Someone is either not quiet or not happy.
Alice is either not old or old. | Mary is strong. | entailment | ((~old(susan))<=>(?[X]:((brave(X)<~>generous(X)))))&
(![X]:((~humble(X)|brave(X))=>~generous(X)))&
((?[X]:((patient(X)&creative(X))))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((~humble(X)&~brave(X))<=>(rich(X)|wise(X))))&
(![X]:(~kind(X)=>(~generous(X)<~>wise(X))))&
(![X]:(patient(X)=>(~wise(X)<~>strong(X))))&
(![X]:((rich(X)|patient(X))<=>(wise(X)&~patient(X))))&
(![X]:((humble(X)&happy(X))<=>(wise(X)|happy(X))))&
(![X]:((~strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((patient(X)|~kind(X))<=>(~strong(X)|happy(X))))&
(![X]:((~old(X)|~happy(X))<=>curious(X)))&
(![X]:((creative(X)<~>~patient(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((~calm(X)<~>old(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:(~strong(X)=>(strong(X)<~>generous(X))))&
(((curious(paul)<~>quiet(paul)))=>((rich(alice)|wise(alice))))&
((kind(paul)|curious(paul)))&
((~strong(paul)|tall(paul)))&
(?[X]:(~rich(X)))&
(?[X]:((tall(X)<~>~tall(X))))&
((~humble(mary)|~funny(mary)))&
(?[X]:((~quiet(X)<~>~happy(X))))&
((~old(alice)<~>old(alice))) | strong(mary) | [
"p1",
"p2",
"p6",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8600061158241168541328400
% SZS output start Proof for 8600061158241168541328400
2. ! [X0] : ((brave(X0) | ~humble(X0)) => ~generous(X0)) [input p1]
3. ? [X0] : (creative(X0) & patient(X0)) <=> ? [X0] : (~funny(X0) <~> patient(X0)) [input p2]
7. ! [X0] : ((patient(X0) | rich(X0)) <=> (~patient(X0) & wise(X0))) [input p6]
15. ! [X0] : (~strong(X0) => (strong(X0) <~> generous(X0))) [input p14]
21. ~funny(mary) | ~humble(mary) [input p20]
24. ~strong(mary) [input hypothesis]
25. ? [X0] : (creative(X0) & patient(X0)) <=> ? [X1] : (~funny(X1) <~> patient(X1)) [rectify 3]
27. ! [X0] : (~generous(X0) | (~brave(X0) & humble(X0))) [ennf transformation 2]
32. ! [X0] : ((strong(X0) <~> generous(X0)) | strong(X0)) [ennf transformation 15]
39. (? [X0] : (creative(X0) & patient(X0)) | ! [X1] : ((~funny(X1) | ~patient(X1)) & (patient(X1) | funny(X1)))) & (? [X1] : ((~patient(X1) | funny(X1)) & (patient(X1) | ~funny(X1))) | ! [X0] : (~creative(X0) | ~patient(X0))) [nnf transformation 25]
40. (? [X0] : (creative(X0) & patient(X0)) | ! [X1] : ((~funny(X1) | ~patient(X1)) & (patient(X1) | funny(X1)))) & (? [X2] : ((~patient(X2) | funny(X2)) & (patient(X2) | ~funny(X2))) | ! [X3] : (~creative(X3) | ~patient(X3))) [rectify 39]
41. ? [X0] : (creative(X0) & patient(X0)) => (creative(sK1) & patient(sK1)) [choice axiom]
42. ? [X2] : ((~patient(X2) | funny(X2)) & (patient(X2) | ~funny(X2))) => ((~patient(sK2) | funny(sK2)) & (patient(sK2) | ~funny(sK2))) [choice axiom]
43. ((creative(sK1) & patient(sK1)) | ! [X1] : ((~funny(X1) | ~patient(X1)) & (patient(X1) | funny(X1)))) & (((~patient(sK2) | funny(sK2)) & (patient(sK2) | ~funny(sK2))) | ! [X3] : (~creative(X3) | ~patient(X3))) [skolemisation 40,42,41]
48. ! [X0] : (((patient(X0) | rich(X0)) | (patient(X0) | ~wise(X0))) & ((~patient(X0) & wise(X0)) | (~patient(X0) & ~rich(X0)))) [nnf transformation 7]
49. ! [X0] : ((patient(X0) | rich(X0) | patient(X0) | ~wise(X0)) & ((~patient(X0) & wise(X0)) | (~patient(X0) & ~rich(X0)))) [flattening 48]
64. ! [X0] : (((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | strong(X0)) [nnf transformation 32]
79. ~generous(X0) | humble(X0) [cnf transformation 27]
83. patient(sK1) | patient(X1) | funny(X1) [cnf transformation 43]
99. ~patient(X0) | ~patient(X0) [cnf transformation 49]
135. generous(X0) | strong(X0) | strong(X0) [cnf transformation 64]
144. ~funny(mary) | ~humble(mary) [cnf transformation 21]
149. ~strong(mary) [cnf transformation 24]
150. strong(X0) | generous(X0) [duplicate literal removal 135]
151. ~patient(X0) [duplicate literal removal 99]
184. 8 <=> ! [X1] : (patient(X1) | funny(X1)) [avatar definition]
185. patient(X1) | funny(X1) <- (8) [avatar component clause 184]
188. 9 <=> patient(sK1) [avatar definition]
190. patient(sK1) <- (9) [avatar component clause 188]
192. 8 | 9 [avatar split clause 83,188,184]
262. 23 <=> humble(mary) [avatar definition]
264. ~humble(mary) <- (~23) [avatar component clause 262]
266. 24 <=> funny(mary) [avatar definition]
268. ~funny(mary) <- (~24) [avatar component clause 266]
269. ~23 | ~24 [avatar split clause 144,266,262]
280. funny(X1) <- (8) [subsumption resolution 185,151]
282. $false <- (8, ~24) [resolution 280,268]
283. ~8 | 24 [avatar contradiction clause 282]
285. $false <- (9) [subsumption resolution 190,151]
286. ~9 [avatar contradiction clause 285]
288. generous(mary) [resolution 150,149]
291. humble(mary) [resolution 288,79]
292. $false <- (~23) [subsumption resolution 291,264]
293. 23 [avatar contradiction clause 292]
294. $false [avatar sat refutation 192,269,283,286,293]
% SZS output end Proof for 8600061158241168541328400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not tall or not funny then someone is either not tall or funny and vice versa.
Everyone who is not kind is humble or not generous.
If someone is not wise or not old then someone is not kind.
If someone is curious or not quiet then someone is creative or happy.
Everyone who is not wise or not brave is either funny or not humble.
Everyone who is either not kind or strong is quiet or not creative and vice versa.
Everyone who is rich or not patient is not humble.
Everyone who is not tall or not wise is strong or calm.
If someone is not rich then paul is brave or happy.
Everyone who is both tall and not humble is brave or creative.
Everyone who is both not kind and not creative is not quiet or not funny and vice versa.
Everyone who is both creative and not wise is both creative and not old.
Everyone who is not brave is both not curious and kind and vice versa.
If john is either not quiet or not wise then susan is not calm or not patient.
Everyone who is old or not generous is either happy or not rich.
If someone is not patient then someone is not generous.
Lucy is kind.
Someone is strong or not patient.
Lucy is not curious.
Lucy is both not curious and tall.
Susan is both rich and not humble.
Alice is not rich or generous.
Lucy is either rich or not wise.
Someone is not strong or not rich. | Lucy is not wise. | entailment | (((~tall(paul)<~>~funny(paul)))<=>(?[X]:((~tall(X)<~>funny(X)))))&
(![X]:(~kind(X)=>(humble(X)|~generous(X))))&
((?[X]:((~wise(X)|~old(X))))=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)|~quiet(X))))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:((~wise(X)|~brave(X))=>(funny(X)<~>~humble(X))))&
(![X]:((~kind(X)<~>strong(X))<=>(quiet(X)|~creative(X))))&
(![X]:((rich(X)|~patient(X))=>~humble(X)))&
(![X]:((~tall(X)|~wise(X))=>(strong(X)|calm(X))))&
((?[X]:(~rich(X)))=>((brave(paul)|happy(paul))))&
(![X]:((tall(X)&~humble(X))=>(brave(X)|creative(X))))&
(![X]:((~kind(X)&~creative(X))<=>(~quiet(X)|~funny(X))))&
(![X]:((creative(X)&~wise(X))=>(creative(X)&~old(X))))&
(![X]:(~brave(X)<=>(~curious(X)&kind(X))))&
(((~quiet(john)<~>~wise(john)))=>((~calm(susan)|~patient(susan))))&
(![X]:((old(X)|~generous(X))=>(happy(X)<~>~rich(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~generous(X))))&
(kind(lucy))&
(?[X]:((strong(X)|~patient(X))))&
(~curious(lucy))&
((~curious(lucy)&tall(lucy)))&
((rich(susan)&~humble(susan)))&
((~rich(alice)|generous(alice)))&
((rich(lucy)<~>~wise(lucy)))&
(?[X]:((~strong(X)|~rich(X)))) | ~wise(lucy) | [
"p4",
"p6",
"p10",
"p12",
"p16",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 948203885115822173108695
% SZS output start Proof for 948203885115822173108695
5. ! [X0] : ((~brave(X0) | ~wise(X0)) => (funny(X0) <~> ~humble(X0))) [input p4]
7. ! [X0] : ((~patient(X0) | rich(X0)) => ~humble(X0)) [input p6]
11. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (~funny(X0) | ~quiet(X0))) [input p10]
13. ! [X0] : (~brave(X0) <=> (kind(X0) & ~curious(X0))) [input p12]
17. kind(lucy) [input p16]
19. ~curious(lucy) [input p18]
23. rich(lucy) <~> ~wise(lucy) [input p22]
25. wise(lucy) [input hypothesis]
29. ! [X0] : ((kind(X0) & ~curious(X0)) => ~brave(X0)) [unused predicate definition removal 13]
34. ! [X0] : ((funny(X0) <~> ~humble(X0)) | (brave(X0) & wise(X0))) [ennf transformation 5]
35. ! [X0] : (~humble(X0) | (patient(X0) & ~rich(X0))) [ennf transformation 7]
44. ! [X0] : (~brave(X0) | (~kind(X0) | curious(X0))) [ennf transformation 29]
45. ! [X0] : (~brave(X0) | ~kind(X0) | curious(X0)) [flattening 44]
60. ! [X0] : (((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (brave(X0) & wise(X0))) [nnf transformation 34]
63. ! [X0] : (((~creative(X0) & ~kind(X0)) | (funny(X0) & quiet(X0))) & ((~funny(X0) | ~quiet(X0)) | (creative(X0) | kind(X0)))) [nnf transformation 11]
64. ! [X0] : (((~creative(X0) & ~kind(X0)) | (funny(X0) & quiet(X0))) & (~funny(X0) | ~quiet(X0) | creative(X0) | kind(X0))) [flattening 63]
72. (wise(lucy) | ~rich(lucy)) & (~wise(lucy) | rich(lucy)) [nnf transformation 23]
91. ~funny(X0) | humble(X0) | brave(X0) [cnf transformation 60]
98. ~rich(X0) | ~humble(X0) [cnf transformation 35]
106. ~kind(X0) | funny(X0) [cnf transformation 64]
111. ~brave(X0) | ~kind(X0) | curious(X0) [cnf transformation 45]
119. kind(lucy) [cnf transformation 17]
121. ~curious(lucy) [cnf transformation 19]
127. ~wise(lucy) | rich(lucy) [cnf transformation 72]
130. wise(lucy) [cnf transformation 25]
246. 27 <=> rich(lucy) [avatar definition]
247. rich(lucy) <- (27) [avatar component clause 246]
250. 28 <=> wise(lucy) [avatar definition]
254. 27 | ~28 [avatar split clause 127,250,246]
264. 28 [avatar split clause 130,250]
268. ~humble(lucy) <- (27) [resolution 98,247]
270. funny(lucy) [resolution 106,119]
284. humble(lucy) | brave(lucy) [resolution 91,270]
285. brave(lucy) <- (27) [subsumption resolution 284,268]
302. ~kind(lucy) | curious(lucy) <- (27) [resolution 111,285]
312. curious(lucy) <- (27) [subsumption resolution 302,119]
313. $false <- (27) [subsumption resolution 312,121]
314. ~27 [avatar contradiction clause 313]
315. $false [avatar sat refutation 254,264,314]
% SZS output end Proof for 948203885115822173108695
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative is humble or generous and vice versa.
If someone is both not humble and not curious then paul is both not quiet and not brave.
Everyone who is either not wise or not old is strong and vice versa.
Everyone who is not curious or not old is wise and vice versa.
Everyone who is quiet is strong or not humble and vice versa.
If susan is either not brave or not tall then mary is not creative.
If someone is not happy or not funny then alice is not humble and vice versa.
If mary is both wise and curious then someone is brave.
If someone is brave then someone is not calm.
Everyone who is both not curious and not funny is not rich and vice versa.
Everyone who is either calm or humble is either not quiet or not brave.
Everyone who is both wise and humble is either wise or not brave and vice versa.
Everyone who is generous or strong is brave and vice versa.
Everyone who is old or rich is not generous or not curious and vice versa.
Everyone who is either kind or curious is both not old and not rich and vice versa.
Everyone who is patient is both creative and humble and vice versa.
Someone is both not funny and not creative.
Someone is both old and strong.
Mary is kind or not old.
Alice is wise or not calm.
Someone is both not kind and not calm.
Fred is not funny. | Mary is not old. | neutral | (![X]:((wise(X)&~creative(X))<=>(humble(X)|generous(X))))&
((?[X]:((~humble(X)&~curious(X))))=>((~quiet(paul)&~brave(paul))))&
(![X]:((~wise(X)<~>~old(X))<=>strong(X)))&
(![X]:((~curious(X)|~old(X))<=>wise(X)))&
(![X]:(quiet(X)<=>(strong(X)|~humble(X))))&
(((~brave(susan)<~>~tall(susan)))=>(~creative(mary)))&
((?[X]:((~happy(X)|~funny(X))))<=>(~humble(alice)))&
(((wise(mary)&curious(mary)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:(~calm(X))))&
(![X]:((~curious(X)&~funny(X))<=>~rich(X)))&
(![X]:((calm(X)<~>humble(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((wise(X)&humble(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((generous(X)|strong(X))<=>brave(X)))&
(![X]:((old(X)|rich(X))<=>(~generous(X)|~curious(X))))&
(![X]:((kind(X)<~>curious(X))<=>(~old(X)&~rich(X))))&
(![X]:(patient(X)<=>(creative(X)&humble(X))))&
(?[X]:((~funny(X)&~creative(X))))&
(?[X]:((old(X)&strong(X))))&
((kind(mary)|~old(mary)))&
((wise(alice)|~calm(alice)))&
(?[X]:((~kind(X)&~calm(X))))&
(~funny(fred)) | ~old(mary) | [] | null | 0 |
Everyone who is both not rich and patient is either not strong or quiet and vice versa.
If john is strong or wise then someone is old or not patient and vice versa.
If mary is not wise then mary is not humble and vice versa.
Everyone who is not wise is either not tall or not humble.
Everyone who is both not old and not brave is creative or not tall and vice versa.
Everyone who is strong or creative is both not quiet and funny.
Everyone who is both not patient and not creative is not wise.
If someone is humble or not generous then susan is wise or not calm.
Everyone who is creative is both generous and not patient.
Everyone who is either funny or curious is not creative or not kind and vice versa.
If someone is rich or not strong then john is both strong and not funny and vice versa.
If lucy is old or rich then fred is both tall and brave and vice versa.
If lucy is calm or tall then someone is both strong and brave and vice versa.
Everyone who is not kind or not curious is both kind and not happy and vice versa.
Everyone who is either wise or not calm is both not wise and not humble.
Everyone who is either not old or old is not tall.
Someone is both not humble and not quiet.
Susan is generous.
Someone is both not quiet and funny.
Someone is either humble or not rich.
Someone is not tall.
Lucy is quiet or not rich.
Someone is either tall or curious. | John is strong. | entailment | (![X]:((~rich(X)&patient(X))<=>(~strong(X)<~>quiet(X))))&
(((strong(john)|wise(john)))<=>(?[X]:((old(X)|~patient(X)))))&
((~wise(mary))<=>(~humble(mary)))&
(![X]:(~wise(X)=>(~tall(X)<~>~humble(X))))&
(![X]:((~old(X)&~brave(X))<=>(creative(X)|~tall(X))))&
(![X]:((strong(X)|creative(X))=>(~quiet(X)&funny(X))))&
(![X]:((~patient(X)&~creative(X))=>~wise(X)))&
((?[X]:((humble(X)|~generous(X))))=>((wise(susan)|~calm(susan))))&
(![X]:(creative(X)=>(generous(X)&~patient(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((rich(X)|~strong(X))))<=>((strong(john)&~funny(john))))&
(((old(lucy)|rich(lucy)))<=>((tall(fred)&brave(fred))))&
(((calm(lucy)|tall(lucy)))<=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(kind(X)&~happy(X))))&
(![X]:((wise(X)<~>~calm(X))=>(~wise(X)&~humble(X))))&
(![X]:((~old(X)<~>old(X))=>~tall(X)))&
(?[X]:((~humble(X)&~quiet(X))))&
(generous(susan))&
(?[X]:((~quiet(X)&funny(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:(~tall(X)))&
((quiet(lucy)|~rich(lucy)))&
(?[X]:((tall(X)<~>curious(X)))) | strong(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2912418990290686870188298
% SZS output start Proof for 2912418990290686870188298
11. ? [X0] : (~strong(X0) | rich(X0)) <=> (~funny(john) & strong(john)) [input p10]
24. ~strong(john) [input hypothesis]
50. (? [X0] : (~strong(X0) | rich(X0)) | (funny(john) | ~strong(john))) & ((~funny(john) & strong(john)) | ! [X0] : (strong(X0) & ~rich(X0))) [nnf transformation 11]
51. (? [X0] : (~strong(X0) | rich(X0)) | funny(john) | ~strong(john)) & ((~funny(john) & strong(john)) | ! [X0] : (strong(X0) & ~rich(X0))) [flattening 50]
52. (? [X0] : (~strong(X0) | rich(X0)) | funny(john) | ~strong(john)) & ((~funny(john) & strong(john)) | ! [X1] : (strong(X1) & ~rich(X1))) [rectify 51]
53. ? [X0] : (~strong(X0) | rich(X0)) => (~strong(sK1) | rich(sK1)) [choice axiom]
54. ((~strong(sK1) | rich(sK1)) | funny(john) | ~strong(john)) & ((~funny(john) & strong(john)) | ! [X1] : (strong(X1) & ~rich(X1))) [skolemisation 52,53]
111. strong(john) | strong(X1) [cnf transformation 54]
146. ~strong(john) [cnf transformation 24]
156. 2 <=> strong(john) [avatar definition]
157. ~strong(john) <- (~2) [avatar component clause 156]
203. 12 <=> ! [X1] : strong(X1) [avatar definition]
204. strong(X1) <- (12) [avatar component clause 203]
214. 12 | 2 [avatar split clause 111,156,203]
289. ~2 [avatar split clause 146,156]
290. $false <- (~2, 12) [subsumption resolution 157,204]
291. 2 | ~12 [avatar contradiction clause 290]
292. $false [avatar sat refutation 214,289,291]
% SZS output end Proof for 2912418990290686870188298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or brave then alice is funny or not tall.
Everyone who is either not rich or not creative is both not humble and not calm and vice versa.
Everyone who is both not tall and brave is generous or not tall and vice versa.
Everyone who is both not creative and not humble is either patient or brave and vice versa.
If john is generous then someone is either patient or rich and vice versa.
Everyone who is not strong or not tall is either not brave or not tall and vice versa.
Everyone who is both rich and not kind is generous or not generous and vice versa.
Everyone who is generous or strong is not old and vice versa.
Everyone who is either rich or not wise is humble and vice versa.
If paul is both not tall and not curious then susan is calm or not patient and vice versa.
If someone is either rich or old then someone is both not rich and wise.
If paul is both kind and old then john is both old and not generous.
Everyone who is generous or not funny is curious and vice versa.
If mary is either rich or not humble then mary is not funny and vice versa.
Everyone who is either funny or quiet is old and vice versa.
Someone is both funny and brave.
Lucy is both not humble and not quiet.
John is either quiet or not humble.
Someone is funny or patient.
Someone is old or curious.
Someone is not wise or not generous. | Susan is quiet. | neutral | ((?[X]:((patient(X)<~>brave(X))))=>((funny(alice)|~tall(alice))))&
(![X]:((~rich(X)<~>~creative(X))<=>(~humble(X)&~calm(X))))&
(![X]:((~tall(X)&brave(X))<=>(generous(X)|~tall(X))))&
(![X]:((~creative(X)&~humble(X))<=>(patient(X)<~>brave(X))))&
((generous(john))<=>(?[X]:((patient(X)<~>rich(X)))))&
(![X]:((~strong(X)|~tall(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:((rich(X)&~kind(X))<=>(generous(X)|~generous(X))))&
(![X]:((generous(X)|strong(X))<=>~old(X)))&
(![X]:((rich(X)<~>~wise(X))<=>humble(X)))&
(((~tall(paul)&~curious(paul)))<=>((calm(susan)|~patient(susan))))&
((?[X]:((rich(X)<~>old(X))))=>(?[X]:((~rich(X)&wise(X)))))&
(((kind(paul)&old(paul)))=>((old(john)&~generous(john))))&
(![X]:((generous(X)|~funny(X))<=>curious(X)))&
(((rich(mary)<~>~humble(mary)))<=>(~funny(mary)))&
(![X]:((funny(X)<~>quiet(X))<=>old(X)))&
(?[X]:((funny(X)&brave(X))))&
((~humble(lucy)&~quiet(lucy)))&
((quiet(john)<~>~humble(john)))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:((old(X)|curious(X))))&
(?[X]:((~wise(X)|~generous(X)))) | quiet(susan) | [] | null | 0 |
If someone is tall then alice is both not funny and not strong and vice versa. Everyone who is not rich or calm is both not calm and not creative. If susan is not happy then someone is either patient or not creative. If alice is both not creative and not kind then paul is happy. Everyone who is not patient is both wise and not brave. If mary is not quiet then john is both not quiet and not kind and vice versa. Everyone who is kind is brave and vice versa. If someone is both not humble and not kind then john is both brave and not happy. Everyone who is tall or not creative is either tall or not kind and vice versa. If someone is not curious or wise then lucy is both not creative and not kind. Everyone who is brave or not patient is brave or not happy. Everyone who is not quiet is not tall or not wise. Everyone who is generous or brave is both kind and not old and vice versa. Everyone who is either not humble or happy is strong. If susan is humble then fred is not generous. Everyone who is kind or not humble is both not calm and not patient. Fred is both not generous and not creative. Paul is not rich or strong. Someone is humble. John is humble or patient. Someone is not happy or kind. Mary is either happy or not generous. | Fred is not kind. | entailment | ((?[X]:(tall(X)))<=>((~funny(alice)&~strong(alice))))&
(![X]:((~rich(X)|calm(X))=>(~calm(X)&~creative(X))))&
((~happy(susan))=>(?[X]:((patient(X)<~>~creative(X)))))&
(((~creative(alice)&~kind(alice)))=>(happy(paul)))&
(![X]:(~patient(X)=>(wise(X)&~brave(X))))&
((~quiet(mary))<=>((~quiet(john)&~kind(john))))&
(![X]:(kind(X)<=>brave(X)))&
((?[X]:((~humble(X)&~kind(X))))=>((brave(john)&~happy(john))))&
(![X]:((tall(X)|~creative(X))<=>(tall(X)<~>~kind(X))))&
((?[X]:((~curious(X)|wise(X))))=>((~creative(lucy)&~kind(lucy))))&
(![X]:((brave(X)|~patient(X))=>(brave(X)|~happy(X))))&
(![X]:(~quiet(X)=>(~tall(X)|~wise(X))))&
(![X]:((generous(X)|brave(X))<=>(kind(X)&~old(X))))&
(![X]:((~humble(X)<~>happy(X))=>strong(X)))&
((humble(susan))=>(~generous(fred)))&
(![X]:((kind(X)|~humble(X))=>(~calm(X)&~patient(X))))&
((~generous(fred)&~creative(fred)))&
((~rich(paul)|strong(paul)))&
(?[X]:(humble(X)))&
((humble(john)|patient(john)))&
(?[X]:((~happy(X)|kind(X))))&
((happy(mary)<~>~generous(mary))) | ~kind(fred) | [
"p4",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 102909014927404495668856
% SZS output start Proof for 102909014927404495668856
5. ! [X0] : (~patient(X0) => (~brave(X0) & wise(X0))) [input p4]
7. ! [X0] : (kind(X0) <=> brave(X0)) [input p6]
16. ! [X0] : ((~humble(X0) | kind(X0)) => (~patient(X0) & ~calm(X0))) [input p15]
23. kind(fred) [input hypothesis]
26. ! [X0] : ((~humble(X0) | kind(X0)) => ~patient(X0)) [pure predicate removal 16]
31. ! [X0] : ((~brave(X0) & wise(X0)) | patient(X0)) [ennf transformation 5]
40. ! [X0] : (~patient(X0) | (humble(X0) & ~kind(X0))) [ennf transformation 26]
51. ! [X0] : ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0))) [nnf transformation 7]
70. ~brave(X0) | patient(X0) [cnf transformation 31]
74. ~kind(X0) | brave(X0) [cnf transformation 51]
97. ~kind(X0) | ~patient(X0) [cnf transformation 40]
107. kind(fred) [cnf transformation 23]
237. brave(fred) [resolution 74,107]
239. patient(fred) [resolution 237,70]
240. ~patient(fred) [resolution 97,107]
241. $false [subsumption resolution 240,239]
% SZS output end Proof for 102909014927404495668856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not strong is either not generous or creative.
If susan is not wise or curious then someone is both kind and not calm and vice versa.
If john is both generous and not creative then mary is not brave and vice versa.
Everyone who is generous or not patient is both old and not kind and vice versa.
If fred is either humble or kind then susan is old or humble and vice versa.
If someone is not happy or old then someone is not rich or not patient.
If mary is not generous or brave then someone is both generous and not funny.
If someone is either kind or not calm then susan is generous and vice versa.
Everyone who is not strong is not funny or not tall and vice versa.
If john is old or creative then lucy is not humble.
If susan is either not strong or not patient then someone is not humble and vice versa.
Everyone who is not funny or generous is curious or wise and vice versa.
Everyone who is both not calm and kind is both old and wise.
Everyone who is not happy or not kind is rich and vice versa.
If fred is not wise then someone is either strong or not patient and vice versa.
Someone is either humble or brave.
Someone is either not curious or patient.
Someone is both tall and calm.
Susan is either not curious or creative. | John is not strong. | neutral | (![X]:((strong(X)|~strong(X))=>(~generous(X)<~>creative(X))))&
(((~wise(susan)|curious(susan)))<=>(?[X]:((kind(X)&~calm(X)))))&
(((generous(john)&~creative(john)))<=>(~brave(mary)))&
(![X]:((generous(X)|~patient(X))<=>(old(X)&~kind(X))))&
(((humble(fred)<~>kind(fred)))<=>((old(susan)|humble(susan))))&
((?[X]:((~happy(X)|old(X))))=>(?[X]:((~rich(X)|~patient(X)))))&
(((~generous(mary)|brave(mary)))=>(?[X]:((generous(X)&~funny(X)))))&
((?[X]:((kind(X)<~>~calm(X))))<=>(generous(susan)))&
(![X]:(~strong(X)<=>(~funny(X)|~tall(X))))&
(((old(john)|creative(john)))=>(~humble(lucy)))&
(((~strong(susan)<~>~patient(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((~funny(X)|generous(X))<=>(curious(X)|wise(X))))&
(![X]:((~calm(X)&kind(X))=>(old(X)&wise(X))))&
(![X]:((~happy(X)|~kind(X))<=>rich(X)))&
((~wise(fred))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:((~curious(X)<~>patient(X))))&
(?[X]:((tall(X)&calm(X))))&
((~curious(susan)<~>creative(susan))) | ~strong(john) | [] | null | 0 |
If someone is not calm or not happy then someone is both not funny and creative.
If lucy is humble then susan is happy and vice versa.
Everyone who is not rich or humble is either creative or not rich.
If someone is either strong or not calm then someone is either rich or humble and vice versa.
If alice is quiet then alice is creative or quiet and vice versa.
Everyone who is either not curious or curious is both happy and wise.
If someone is both not funny and wise then john is not rich and vice versa.
If someone is either not patient or not tall then someone is both not tall and brave.
Everyone who is not quiet is not creative and vice versa.
If someone is either humble or not generous then mary is strong and vice versa.
Everyone who is creative is either funny or quiet and vice versa.
Everyone who is both not brave and generous is not patient or tall and vice versa.
Everyone who is either generous or not humble is old.
Everyone who is both generous and wise is both not old and patient and vice versa.
If john is both tall and not happy then mary is either kind or not generous and vice versa.
If fred is creative then someone is not curious.
John is brave.
Someone is either not quiet or not kind.
Someone is quiet.
Someone is humble or wise.
Fred is either not wise or not rich.
Fred is not kind or happy. | Mary is patient. | entailment | ((?[X]:((~calm(X)|~happy(X))))=>(?[X]:((~funny(X)&creative(X)))))&
((humble(lucy))<=>(happy(susan)))&
(![X]:((~rich(X)|humble(X))=>(creative(X)<~>~rich(X))))&
((?[X]:((strong(X)<~>~calm(X))))<=>(?[X]:((rich(X)<~>humble(X)))))&
((quiet(alice))<=>((creative(alice)|quiet(alice))))&
(![X]:((~curious(X)<~>curious(X))=>(happy(X)&wise(X))))&
((?[X]:((~funny(X)&wise(X))))<=>(~rich(john)))&
((?[X]:((~patient(X)<~>~tall(X))))=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:(~quiet(X)<=>~creative(X)))&
((?[X]:((humble(X)<~>~generous(X))))<=>(strong(mary)))&
(![X]:(creative(X)<=>(funny(X)<~>quiet(X))))&
(![X]:((~brave(X)&generous(X))<=>(~patient(X)|tall(X))))&
(![X]:((generous(X)<~>~humble(X))=>old(X)))&
(![X]:((generous(X)&wise(X))<=>(~old(X)&patient(X))))&
(((tall(john)&~happy(john)))<=>((kind(mary)<~>~generous(mary))))&
((creative(fred))=>(?[X]:(~curious(X))))&
(brave(john))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:(quiet(X)))&
(?[X]:((humble(X)|wise(X))))&
((~wise(fred)<~>~rich(fred)))&
((~kind(fred)|happy(fred))) | patient(mary) | [
"p5",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4225116726174760296653518
% SZS output start Proof for 4225116726174760296653518
6. ! [X0] : ((~curious(X0) <~> curious(X0)) => (wise(X0) & happy(X0))) [input p5]
12. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (tall(X0) | ~patient(X0))) [input p11]
14. ! [X0] : ((wise(X0) & generous(X0)) <=> (patient(X0) & ~old(X0))) [input p13]
23. ~patient(mary) [input hypothesis]
29. ! [X0] : ((wise(X0) & happy(X0)) | (~curious(X0) <=> curious(X0))) [ennf transformation 6]
45. ! [X0] : ((wise(X0) & happy(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) [nnf transformation 29]
60. ! [X0] : (((generous(X0) & ~brave(X0)) | (~tall(X0) & patient(X0))) & ((tall(X0) | ~patient(X0)) | (~generous(X0) | brave(X0)))) [nnf transformation 12]
61. ! [X0] : (((generous(X0) & ~brave(X0)) | (~tall(X0) & patient(X0))) & (tall(X0) | ~patient(X0) | ~generous(X0) | brave(X0))) [flattening 60]
63. ! [X0] : (((wise(X0) & generous(X0)) | (~patient(X0) | old(X0))) & ((patient(X0) & ~old(X0)) | (~wise(X0) | ~generous(X0)))) [nnf transformation 14]
64. ! [X0] : (((wise(X0) & generous(X0)) | ~patient(X0) | old(X0)) & ((patient(X0) & ~old(X0)) | ~wise(X0) | ~generous(X0))) [flattening 63]
100. wise(X0) | curious(X0) | curious(X0) [cnf transformation 45]
101. wise(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 45]
122. generous(X0) | patient(X0) [cnf transformation 61]
127. patient(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 64]
145. ~patient(mary) [cnf transformation 23]
148. wise(X0) | curious(X0) [duplicate literal removal 100]
149. wise(X0) | ~curious(X0) [duplicate literal removal 101]
224. wise(X0) [subsumption resolution 148,149]
284. patient(X0) | ~generous(X0) [subsumption resolution 127,224]
285. patient(X0) [subsumption resolution 284,122]
338. $false [subsumption resolution 145,285]
% SZS output end Proof for 4225116726174760296653518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not happy and creative then someone is both not brave and not patient. If susan is both not rich and not funny then john is both curious and strong. Everyone who is not wise is both rich and wise and vice versa. Everyone who is generous or funny is either curious or happy. Everyone who is generous is both not patient and funny and vice versa. If someone is quiet then someone is both not strong and not curious and vice versa. Everyone who is either not happy or tall is both not quiet and not brave. Everyone who is both not tall and rich is either patient or not calm and vice versa. If someone is not brave then alice is not strong or brave. If paul is wise or not tall then mary is both not strong and generous and vice versa. If someone is not kind then someone is either brave or not creative and vice versa. Everyone who is either not brave or curious is both not funny and curious and vice versa. If lucy is creative or not patient then john is quiet and vice versa. If john is not creative or not strong then susan is both not rich and tall. Everyone who is either happy or rich is both not old and not humble and vice versa. Everyone who is both not humble and not wise is either not patient or not old and vice versa. Someone is not brave. Someone is either not humble or tall. Someone is either not creative or not quiet. John is happy. Someone is creative. Someone is not rich or not quiet. Someone is either not quiet or tall. | Paul is not kind. | neutral | (((~happy(susan)&creative(susan)))=>(?[X]:((~brave(X)&~patient(X)))))&
(((~rich(susan)&~funny(susan)))=>((curious(john)&strong(john))))&
(![X]:(~wise(X)<=>(rich(X)&wise(X))))&
(![X]:((generous(X)|funny(X))=>(curious(X)<~>happy(X))))&
(![X]:(generous(X)<=>(~patient(X)&funny(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((~happy(X)<~>tall(X))=>(~quiet(X)&~brave(X))))&
(![X]:((~tall(X)&rich(X))<=>(patient(X)<~>~calm(X))))&
((?[X]:(~brave(X)))=>((~strong(alice)|brave(alice))))&
(((wise(paul)|~tall(paul)))<=>((~strong(mary)&generous(mary))))&
((?[X]:(~kind(X)))<=>(?[X]:((brave(X)<~>~creative(X)))))&
(![X]:((~brave(X)<~>curious(X))<=>(~funny(X)&curious(X))))&
(((creative(lucy)|~patient(lucy)))<=>(quiet(john)))&
(((~creative(john)|~strong(john)))=>((~rich(susan)&tall(susan))))&
(![X]:((happy(X)<~>rich(X))<=>(~old(X)&~humble(X))))&
(![X]:((~humble(X)&~wise(X))<=>(~patient(X)<~>~old(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~humble(X)<~>tall(X))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(happy(john))&
(?[X]:(creative(X)))&
(?[X]:((~rich(X)|~quiet(X))))&
(?[X]:((~quiet(X)<~>tall(X)))) | ~kind(paul) | [] | null | 0 |
If someone is both brave and not humble then alice is both not patient and quiet and vice versa. If susan is either kind or not creative then john is either funny or curious. Everyone who is tall or not wise is either funny or strong. Everyone who is curious is either old or not happy. Everyone who is both not rich and rich is not patient and vice versa. Everyone who is either not calm or not brave is both strong and not funny. If fred is calm or not creative then someone is brave or not creative and vice versa. If john is either quiet or not happy then lucy is not brave or not rich. If paul is both wise and not generous then susan is not calm. If mary is either not generous or not funny then alice is not happy. Everyone who is generous or strong is both not generous and not calm and vice versa. If someone is either not rich or strong then someone is old and vice versa. Everyone who is kind or not wise is wise or funny and vice versa. If mary is both not curious and not wise then john is either not rich or generous. Everyone who is both not curious and not creative is either patient or old. Everyone who is not wise or quiet is not curious or not wise. John is brave or not humble. Someone is not calm. Fred is not generous. Susan is curious. Someone is both curious and not happy. Someone is tall. | John is patient. | entailment | ((?[X]:((brave(X)&~humble(X))))<=>((~patient(alice)&quiet(alice))))&
(((kind(susan)<~>~creative(susan)))=>((funny(john)<~>curious(john))))&
(![X]:((tall(X)|~wise(X))=>(funny(X)<~>strong(X))))&
(![X]:(curious(X)=>(old(X)<~>~happy(X))))&
(![X]:((~rich(X)&rich(X))<=>~patient(X)))&
(![X]:((~calm(X)<~>~brave(X))=>(strong(X)&~funny(X))))&
(((calm(fred)|~creative(fred)))<=>(?[X]:((brave(X)|~creative(X)))))&
(((quiet(john)<~>~happy(john)))=>((~brave(lucy)|~rich(lucy))))&
(((wise(paul)&~generous(paul)))=>(~calm(susan)))&
(((~generous(mary)<~>~funny(mary)))=>(~happy(alice)))&
(![X]:((generous(X)|strong(X))<=>(~generous(X)&~calm(X))))&
((?[X]:((~rich(X)<~>strong(X))))<=>(?[X]:(old(X))))&
(![X]:((kind(X)|~wise(X))<=>(wise(X)|funny(X))))&
(((~curious(mary)&~wise(mary)))=>((~rich(john)<~>generous(john))))&
(![X]:((~curious(X)&~creative(X))=>(patient(X)<~>old(X))))&
(![X]:((~wise(X)|quiet(X))=>(~curious(X)|~wise(X))))&
((brave(john)|~humble(john)))&
(?[X]:(~calm(X)))&
(~generous(fred))&
(curious(susan))&
(?[X]:((curious(X)&~happy(X))))&
(?[X]:(tall(X))) | patient(john) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 2798966828546909174873431
% SZS output start Proof for 2798966828546909174873431
5. ! [X0] : ((rich(X0) & ~rich(X0)) <=> ~patient(X0)) [input p4]
23. ~patient(john) [input hypothesis]
48. ! [X0] : (((rich(X0) & ~rich(X0)) | patient(X0)) & (~patient(X0) | (~rich(X0) | rich(X0)))) [nnf transformation 5]
49. ! [X0] : (((rich(X0) & ~rich(X0)) | patient(X0)) & (~patient(X0) | ~rich(X0) | rich(X0))) [flattening 48]
90. ~rich(X0) | patient(X0) [cnf transformation 49]
91. rich(X0) | patient(X0) [cnf transformation 49]
131. ~patient(john) [cnf transformation 23]
179. patient(X0) [subsumption resolution 90,91]
300. $false [subsumption resolution 131,179]
% SZS output end Proof for 2798966828546909174873431
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or patient is either not patient or not curious.
If someone is either not brave or kind then someone is both not generous and humble.
If someone is either not strong or not rich then mary is both generous and not happy.
Everyone who is both brave and generous is not happy and vice versa.
Everyone who is either not creative or quiet is either not wise or humble and vice versa.
Everyone who is not quiet or not generous is either curious or not old and vice versa.
Everyone who is either not quiet or not patient is both not curious and quiet.
Everyone who is either not old or not rich is both not quiet and calm and vice versa.
If someone is either not wise or not brave then someone is not wise.
If alice is tall or not rich then someone is both calm and not happy and vice versa.
Everyone who is both not brave and not kind is not strong or quiet.
If someone is not humble then john is either brave or rich and vice versa.
If paul is not humble or old then someone is either not creative or not strong.
If alice is both creative and tall then someone is funny and vice versa.
If someone is both not curious and not tall then someone is either curious or not old and vice versa.
Everyone who is not tall or not brave is both kind and curious.
Susan is either tall or not wise.
Someone is both old and humble.
Mary is either not creative or brave.
Paul is both creative and not happy.
Someone is either not curious or generous.
Someone is both funny and patient.
Fred is quiet. | Mary is creative. | entailment | (![X]:((~kind(X)<~>patient(X))=>(~patient(X)<~>~curious(X))))&
((?[X]:((~brave(X)<~>kind(X))))=>(?[X]:((~generous(X)&humble(X)))))&
((?[X]:((~strong(X)<~>~rich(X))))=>((generous(mary)&~happy(mary))))&
(![X]:((brave(X)&generous(X))<=>~happy(X)))&
(![X]:((~creative(X)<~>quiet(X))<=>(~wise(X)<~>humble(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(curious(X)<~>~old(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(~curious(X)&quiet(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(~quiet(X)&calm(X))))&
((?[X]:((~wise(X)<~>~brave(X))))=>(?[X]:(~wise(X))))&
(((tall(alice)|~rich(alice)))<=>(?[X]:((calm(X)&~happy(X)))))&
(![X]:((~brave(X)&~kind(X))=>(~strong(X)|quiet(X))))&
((?[X]:(~humble(X)))<=>((brave(john)<~>rich(john))))&
(((~humble(paul)|old(paul)))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(((creative(alice)&tall(alice)))<=>(?[X]:(funny(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((~tall(X)|~brave(X))=>(kind(X)&curious(X))))&
((tall(susan)<~>~wise(susan)))&
(?[X]:((old(X)&humble(X))))&
((~creative(mary)<~>brave(mary)))&
((creative(paul)&~happy(paul)))&
(?[X]:((~curious(X)<~>generous(X))))&
(?[X]:((funny(X)&patient(X))))&
(quiet(fred)) | creative(mary) | [
"p0",
"p5",
"p6",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5745671477887368554757324
% SZS output start Proof for 5745671477887368554757324
1. ! [X0] : ((~kind(X0) <~> patient(X0)) => (~patient(X0) <~> ~curious(X0))) [input p0]
6. ! [X0] : ((~generous(X0) | ~quiet(X0)) <=> (curious(X0) <~> ~old(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) <~> ~patient(X0)) => (quiet(X0) & ~curious(X0))) [input p6]
15. ? [X0] : (~tall(X0) & ~curious(X0)) <=> ? [X0] : (curious(X0) <~> ~old(X0)) [input p14]
16. ! [X0] : ((~brave(X0) | ~tall(X0)) => (curious(X0) & kind(X0))) [input p15]
19. ~creative(mary) <~> brave(mary) [input p18]
24. ~creative(mary) [input hypothesis]
27. ? [X0] : (~tall(X0) & ~curious(X0)) <=> ? [X1] : (curious(X1) <~> ~old(X1)) [rectify 15]
28. ! [X0] : ((~patient(X0) <~> ~curious(X0)) | (~kind(X0) <=> patient(X0))) [ennf transformation 1]
31. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~quiet(X0) <=> ~patient(X0))) [ennf transformation 7]
36. ! [X0] : ((curious(X0) & kind(X0)) | (brave(X0) & tall(X0))) [ennf transformation 16]
37. ! [X0] : (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) [nnf transformation 28]
46. ! [X0] : (((~generous(X0) | ~quiet(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (generous(X0) & quiet(X0)))) [nnf transformation 6]
47. ! [X0] : ((~generous(X0) | ~quiet(X0) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (generous(X0) & quiet(X0)))) [flattening 46]
48. ! [X0] : ((quiet(X0) & ~curious(X0)) | ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0)))) [nnf transformation 31]
72. (? [X0] : (~tall(X0) & ~curious(X0)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (? [X1] : ((old(X1) | ~curious(X1)) & (~old(X1) | curious(X1))) | ! [X0] : (tall(X0) | curious(X0))) [nnf transformation 27]
73. (? [X0] : (~tall(X0) & ~curious(X0)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (? [X2] : ((old(X2) | ~curious(X2)) & (~old(X2) | curious(X2))) | ! [X3] : (tall(X3) | curious(X3))) [rectify 72]
74. ? [X0] : (~tall(X0) & ~curious(X0)) => (~tall(sK6) & ~curious(sK6)) [choice axiom]
75. ? [X2] : ((old(X2) | ~curious(X2)) & (~old(X2) | curious(X2))) => ((old(sK7) | ~curious(sK7)) & (~old(sK7) | curious(sK7))) [choice axiom]
76. ((~tall(sK6) & ~curious(sK6)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (((old(sK7) | ~curious(sK7)) & (~old(sK7) | curious(sK7))) | ! [X3] : (tall(X3) | curious(X3))) [skolemisation 73,75,74]
80. (~brave(mary) | creative(mary)) & (brave(mary) | ~creative(mary)) [nnf transformation 19]
87. ~curious(X0) | ~patient(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 37]
111. ~curious(X0) | old(X0) | quiet(X0) [cnf transformation 47]
116. ~quiet(X0) | ~curious(X0) | patient(X0) [cnf transformation 48]
146. ~curious(sK6) | ~old(X1) | ~curious(X1) [cnf transformation 76]
148. ~tall(sK6) | ~old(X1) | ~curious(X1) [cnf transformation 76]
151. kind(X0) | brave(X0) [cnf transformation 36]
152. curious(X0) | tall(X0) [cnf transformation 36]
153. brave(X0) | curious(X0) [cnf transformation 36]
159. ~brave(mary) | creative(mary) [cnf transformation 80]
167. ~creative(mary) [cnf transformation 24]
169. ~curious(X0) | ~patient(X0) | ~kind(X0) [duplicate literal removal 87]
180. 3 <=> ! [X1] : (kind(X1) | brave(X1)) [avatar definition]
181. brave(X1) | kind(X1) <- (3) [avatar component clause 180]
300. 29 <=> tall(sK6) [avatar definition]
302. ~tall(sK6) <- (~29) [avatar component clause 300]
305. 30 <=> ! [X1] : (~old(X1) | ~curious(X1)) [avatar definition]
306. ~old(X1) | ~curious(X1) <- (30) [avatar component clause 305]
307. 30 | ~29 [avatar split clause 148,300,305]
309. 31 <=> curious(sK6) [avatar definition]
311. ~curious(sK6) <- (~31) [avatar component clause 309]
313. 30 | ~31 [avatar split clause 146,309,305]
315. 32 <=> ! [X3] : (tall(X3) | curious(X3)) [avatar definition]
316. tall(X3) | curious(X3) <- (32) [avatar component clause 315]
327. 32 [avatar split clause 152,315]
328. 3 [avatar split clause 151,180]
340. 37 <=> creative(mary) [avatar definition]
344. 38 <=> brave(mary) [avatar definition]
346. ~brave(mary) <- (~38) [avatar component clause 344]
347. 37 | ~38 [avatar split clause 159,344,340]
359. ~37 [avatar split clause 167,340]
372. curious(mary) <- (~38) [resolution 153,346]
375. kind(mary) <- (3, ~38) [resolution 181,346]
381. curious(sK6) <- (~29, 32) [resolution 316,302]
383. $false <- (~29, ~31, 32) [subsumption resolution 381,311]
384. 29 | 31 | ~32 [avatar contradiction clause 383]
401. old(mary) | quiet(mary) <- (~38) [resolution 111,372]
413. 43 <=> quiet(mary) [avatar definition]
415. quiet(mary) <- (43) [avatar component clause 413]
417. 44 <=> old(mary) [avatar definition]
419. old(mary) <- (44) [avatar component clause 417]
420. 43 | 44 | 38 [avatar split clause 401,344,417,413]
483. ~patient(mary) | ~kind(mary) <- (~38) [resolution 169,372]
484. ~patient(mary) <- (3, ~38) [subsumption resolution 483,375]
486. ~curious(mary) | patient(mary) <- (43) [resolution 415,116]
487. patient(mary) <- (~38, 43) [subsumption resolution 486,372]
488. $false <- (3, ~38, 43) [subsumption resolution 487,484]
489. ~3 | 38 | ~43 [avatar contradiction clause 488]
888. ~curious(mary) <- (30, 44) [resolution 419,306]
898. $false <- (30, ~38, 44) [subsumption resolution 888,372]
899. ~30 | 38 | ~44 [avatar contradiction clause 898]
900. $false [avatar sat refutation 307,313,327,328,347,359,384,420,489,899]
% SZS output end Proof for 5745671477887368554757324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not quiet is either not funny or brave and vice versa. If someone is either quiet or calm then mary is both happy and humble. If lucy is humble or rich then mary is happy or not strong. If lucy is either curious or not humble then someone is not old or rich. If mary is not funny then paul is both not kind and not strong. If john is rich or not calm then susan is not quiet and vice versa. Everyone who is either kind or brave is curious or not generous and vice versa. Everyone who is either wise or not creative is patient or old. If lucy is not patient or wise then alice is both not curious and old. Everyone who is quiet is both not calm and not kind and vice versa. If someone is either curious or old then someone is not brave or kind. If someone is not tall then someone is either not strong or not generous. Everyone who is patient is both strong and not rich and vice versa. Everyone who is quiet or kind is either calm or humble. If someone is kind or not patient then someone is wise or kind. Everyone who is creative is both calm and not generous. Mary is calm. Susan is either not brave or wise. Paul is funny or happy. Fred is creative or brave. Alice is both not creative and not humble. Fred is either not wise or generous. Lucy is strong or not calm. Someone is not curious. | Alice is quiet. | contradiction | (![X]:((~brave(X)&~quiet(X))<=>(~funny(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>calm(X))))=>((happy(mary)&humble(mary))))&
(((humble(lucy)|rich(lucy)))=>((happy(mary)|~strong(mary))))&
(((curious(lucy)<~>~humble(lucy)))=>(?[X]:((~old(X)|rich(X)))))&
((~funny(mary))=>((~kind(paul)&~strong(paul))))&
(((rich(john)|~calm(john)))<=>(~quiet(susan)))&
(![X]:((kind(X)<~>brave(X))<=>(curious(X)|~generous(X))))&
(![X]:((wise(X)<~>~creative(X))=>(patient(X)|old(X))))&
(((~patient(lucy)|wise(lucy)))=>((~curious(alice)&old(alice))))&
(![X]:(quiet(X)<=>(~calm(X)&~kind(X))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~brave(X)|kind(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:(patient(X)<=>(strong(X)&~rich(X))))&
(![X]:((quiet(X)|kind(X))=>(calm(X)<~>humble(X))))&
((?[X]:((kind(X)|~patient(X))))=>(?[X]:((wise(X)|kind(X)))))&
(![X]:(creative(X)=>(calm(X)&~generous(X))))&
(calm(mary))&
((~brave(susan)<~>wise(susan)))&
((funny(paul)|happy(paul)))&
((creative(fred)|brave(fred)))&
((~creative(alice)&~humble(alice)))&
((~wise(fred)<~>generous(fred)))&
((strong(lucy)|~calm(lucy)))&
(?[X]:(~curious(X))) | quiet(alice) | [
"p9",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5240672831739081581898337
% SZS output start Proof for 5240672831739081581898337
10. ! [X0] : (quiet(X0) <=> (~kind(X0) & ~calm(X0))) [input p9]
14. ! [X0] : ((kind(X0) | quiet(X0)) => (calm(X0) <~> humble(X0))) [input p13]
21. ~humble(alice) & ~creative(alice) [input p20]
25. quiet(alice) [input hypothesis]
42. ! [X0] : ((calm(X0) <~> humble(X0)) | (~kind(X0) & ~quiet(X0))) [ennf transformation 14]
56. ! [X0] : ((quiet(X0) | (kind(X0) | calm(X0))) & ((~kind(X0) & ~calm(X0)) | ~quiet(X0))) [nnf transformation 10]
57. ! [X0] : ((quiet(X0) | kind(X0) | calm(X0)) & ((~kind(X0) & ~calm(X0)) | ~quiet(X0))) [flattening 56]
62. ! [X0] : (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (~kind(X0) & ~quiet(X0))) [nnf transformation 42]
97. ~calm(X0) | ~quiet(X0) [cnf transformation 57]
104. humble(X0) | calm(X0) | ~quiet(X0) [cnf transformation 62]
117. ~humble(alice) [cnf transformation 21]
122. quiet(alice) [cnf transformation 25]
221. ~quiet(X0) | humble(X0) [subsumption resolution 104,97]
280. humble(alice) [resolution 221,122]
281. $false [subsumption resolution 280,117]
% SZS output end Proof for 5240672831739081581898337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either humble or tall then someone is calm.
Everyone who is creative or calm is kind and vice versa.
Everyone who is either not funny or kind is quiet.
Everyone who is either not generous or not wise is both humble and strong.
Everyone who is happy is not kind.
Everyone who is quiet or happy is both not happy and happy and vice versa.
If someone is not tall or not humble then someone is either not calm or brave and vice versa.
Everyone who is generous or not brave is both not wise and not brave and vice versa.
If someone is both creative and quiet then someone is either humble or rich and vice versa.
If alice is both not happy and not funny then someone is happy and vice versa.
If someone is calm or not patient then lucy is either not brave or not strong and vice versa.
If mary is both calm and wise then alice is both not quiet and brave.
If someone is either humble or not generous then someone is not calm or happy.
If someone is not happy or wise then someone is either humble or generous.
Everyone who is patient or strong is not happy and vice versa.
If someone is kind or creative then fred is not old and vice versa.
Someone is quiet or not tall.
Someone is not happy or not quiet.
Someone is both patient and not happy.
Fred is either kind or not calm.
Someone is not old.
Someone is wise. | Mary is not brave. | neutral | (((humble(john)<~>tall(john)))=>(?[X]:(calm(X))))&
(![X]:((creative(X)|calm(X))<=>kind(X)))&
(![X]:((~funny(X)<~>kind(X))=>quiet(X)))&
(![X]:((~generous(X)<~>~wise(X))=>(humble(X)&strong(X))))&
(![X]:(happy(X)=>~kind(X)))&
(![X]:((quiet(X)|happy(X))<=>(~happy(X)&happy(X))))&
((?[X]:((~tall(X)|~humble(X))))<=>(?[X]:((~calm(X)<~>brave(X)))))&
(![X]:((generous(X)|~brave(X))<=>(~wise(X)&~brave(X))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:((humble(X)<~>rich(X)))))&
(((~happy(alice)&~funny(alice)))<=>(?[X]:(happy(X))))&
((?[X]:((calm(X)|~patient(X))))<=>((~brave(lucy)<~>~strong(lucy))))&
(((calm(mary)&wise(mary)))=>((~quiet(alice)&brave(alice))))&
((?[X]:((humble(X)<~>~generous(X))))=>(?[X]:((~calm(X)|happy(X)))))&
((?[X]:((~happy(X)|wise(X))))=>(?[X]:((humble(X)<~>generous(X)))))&
(![X]:((patient(X)|strong(X))<=>~happy(X)))&
((?[X]:((kind(X)|creative(X))))<=>(~old(fred)))&
(?[X]:((quiet(X)|~tall(X))))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>~calm(fred)))&
(?[X]:(~old(X)))&
(?[X]:(wise(X))) | ~brave(mary) | [] | null | 0 |
If someone is not curious or tall then fred is both not happy and not generous and vice versa.
Everyone who is both not patient and not happy is kind or patient and vice versa.
If someone is not quiet or not kind then fred is either not rich or funny and vice versa.
If lucy is either not kind or not funny then someone is not wise or funny.
Everyone who is not creative or not quiet is happy or kind and vice versa.
Everyone who is both curious and brave is both rich and humble.
If someone is either patient or tall then someone is both not kind and not calm and vice versa.
Everyone who is not rich or not funny is not funny or not tall.
Everyone who is wise or not kind is both not quiet and humble.
If mary is both not strong and kind then john is either funny or tall.
Everyone who is not happy is wise and vice versa.
If susan is not tall or not quiet then mary is funny or not funny.
If paul is either rich or not brave then john is happy or strong and vice versa.
If someone is either not generous or generous then mary is curious.
Everyone who is not patient or strong is creative or not tall.
Everyone who is not humble is both calm and not happy.
Mary is either happy or calm.
Lucy is not happy.
Susan is humble.
Mary is not kind or rich.
Someone is not quiet. | John is not quiet. | entailment | ((?[X]:((~curious(X)|tall(X))))<=>((~happy(fred)&~generous(fred))))&
(![X]:((~patient(X)&~happy(X))<=>(kind(X)|patient(X))))&
((?[X]:((~quiet(X)|~kind(X))))<=>((~rich(fred)<~>funny(fred))))&
(((~kind(lucy)<~>~funny(lucy)))=>(?[X]:((~wise(X)|funny(X)))))&
(![X]:((~creative(X)|~quiet(X))<=>(happy(X)|kind(X))))&
(![X]:((curious(X)&brave(X))=>(rich(X)&humble(X))))&
((?[X]:((patient(X)<~>tall(X))))<=>(?[X]:((~kind(X)&~calm(X)))))&
(![X]:((~rich(X)|~funny(X))=>(~funny(X)|~tall(X))))&
(![X]:((wise(X)|~kind(X))=>(~quiet(X)&humble(X))))&
(((~strong(mary)&kind(mary)))=>((funny(john)<~>tall(john))))&
(![X]:(~happy(X)<=>wise(X)))&
(((~tall(susan)|~quiet(susan)))=>((funny(mary)|~funny(mary))))&
(((rich(paul)<~>~brave(paul)))<=>((happy(john)|strong(john))))&
((?[X]:((~generous(X)<~>generous(X))))=>(curious(mary)))&
(![X]:((~patient(X)|strong(X))=>(creative(X)|~tall(X))))&
(![X]:(~humble(X)=>(calm(X)&~happy(X))))&
((happy(mary)<~>calm(mary)))&
(~happy(lucy))&
(humble(susan))&
((~kind(mary)|rich(mary)))&
(?[X]:(~quiet(X))) | ~quiet(john) | [
"p1",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 56694599556349344338671
% SZS output start Proof for 56694599556349344338671
2. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (patient(X0) | kind(X0))) [input p1]
9. ! [X0] : ((~kind(X0) | wise(X0)) => (humble(X0) & ~quiet(X0))) [input p8]
11. ! [X0] : (~happy(X0) <=> wise(X0)) [input p10]
22. quiet(john) [input hypothesis]
25. ! [X0] : ((~kind(X0) | wise(X0)) => ~quiet(X0)) [pure predicate removal 9]
33. ! [X0] : (~quiet(X0) | (kind(X0) & ~wise(X0))) [ennf transformation 25]
46. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 2]
47. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | happy(X0) | patient(X0))) [flattening 46]
63. ! [X0] : ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))) [nnf transformation 11]
78. ~kind(X0) | ~happy(X0) [cnf transformation 47]
101. ~wise(X0) | ~quiet(X0) [cnf transformation 33]
102. ~quiet(X0) | kind(X0) [cnf transformation 33]
105. wise(X0) | happy(X0) [cnf transformation 63]
124. quiet(john) [cnf transformation 22]
256. 28 <=> happy(john) [avatar definition]
258. ~happy(john) <- (~28) [avatar component clause 256]
292. kind(john) [resolution 102,124]
293. ~happy(john) [resolution 292,78]
294. ~28 [avatar split clause 293,256]
296. ~quiet(X0) | happy(X0) [resolution 105,101]
311. happy(john) [resolution 296,124]
312. $false <- (~28) [subsumption resolution 311,258]
313. 28 [avatar contradiction clause 312]
314. $false [avatar sat refutation 294,313]
% SZS output end Proof for 56694599556349344338671
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not kind is not rich or not old.
Everyone who is not generous or happy is not generous or not happy.
Everyone who is quiet or not creative is either not quiet or funny.
Everyone who is generous is both funny and not curious and vice versa.
Everyone who is either not generous or not creative is both old and not rich.
Everyone who is not creative is curious.
Everyone who is either not funny or tall is both kind and rich and vice versa.
If john is rich or happy then susan is not kind.
If mary is either not curious or tall then someone is humble or not wise and vice versa.
If someone is not patient or kind then fred is either humble or not brave and vice versa.
Everyone who is either not creative or kind is old and vice versa.
If someone is tall then someone is not tall or quiet and vice versa.
If someone is creative then alice is wise and vice versa.
If fred is old or happy then lucy is either kind or quiet.
Everyone who is both brave and kind is not happy and vice versa.
If someone is wise then someone is both not wise and not kind and vice versa.
Someone is both brave and creative.
John is not happy.
Mary is both not wise and not kind.
Someone is either brave or not kind.
Alice is creative.
Lucy is not humble.
Susan is either tall or not rich.
John is rich. | Mary is not creative. | entailment | (![X]:((patient(X)<~>~kind(X))=>(~rich(X)|~old(X))))&
(![X]:((~generous(X)|happy(X))=>(~generous(X)|~happy(X))))&
(![X]:((quiet(X)|~creative(X))=>(~quiet(X)<~>funny(X))))&
(![X]:(generous(X)<=>(funny(X)&~curious(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(old(X)&~rich(X))))&
(![X]:(~creative(X)=>curious(X)))&
(![X]:((~funny(X)<~>tall(X))<=>(kind(X)&rich(X))))&
(((rich(john)|happy(john)))=>(~kind(susan)))&
(((~curious(mary)<~>tall(mary)))<=>(?[X]:((humble(X)|~wise(X)))))&
((?[X]:((~patient(X)|kind(X))))<=>((humble(fred)<~>~brave(fred))))&
(![X]:((~creative(X)<~>kind(X))<=>old(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:(creative(X)))<=>(wise(alice)))&
(((old(fred)|happy(fred)))=>((kind(lucy)<~>quiet(lucy))))&
(![X]:((brave(X)&kind(X))<=>~happy(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~wise(X)&~kind(X)))))&
(?[X]:((brave(X)&creative(X))))&
(~happy(john))&
((~wise(mary)&~kind(mary)))&
(?[X]:((brave(X)<~>~kind(X))))&
(creative(alice))&
(~humble(lucy))&
((tall(susan)<~>~rich(susan)))&
(rich(john)) | ~creative(mary) | [
"p1",
"p4",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3968392897149743612320295
% SZS output start Proof for 3968392897149743612320295
2. ! [X0] : ((happy(X0) | ~generous(X0)) => (~happy(X0) | ~generous(X0))) [input p1]
5. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => (~rich(X0) & old(X0))) [input p4]
11. ! [X0] : ((~creative(X0) <~> kind(X0)) <=> old(X0)) [input p10]
15. ! [X0] : ((kind(X0) & brave(X0)) <=> ~happy(X0)) [input p14]
19. ~kind(mary) & ~wise(mary) [input p18]
25. creative(mary) [input hypothesis]
28. ! [X0] : (~happy(X0) => (kind(X0) & brave(X0))) [unused predicate definition removal 15]
31. ! [X0] : ((~happy(X0) | ~generous(X0)) | (~happy(X0) & generous(X0))) [ennf transformation 2]
32. ! [X0] : (~happy(X0) | ~generous(X0) | (~happy(X0) & generous(X0))) [flattening 31]
34. ! [X0] : ((~rich(X0) & old(X0)) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 5]
38. ! [X0] : ((kind(X0) & brave(X0)) | happy(X0)) [ennf transformation 28]
43. ! [X0] : ((~rich(X0) & old(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 34]
54. ! [X0] : ((((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | ~old(X0)) & (old(X0) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))))) [nnf transformation 11]
79. ~happy(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 32]
87. ~creative(X0) | old(X0) | generous(X0) [cnf transformation 43]
114. ~creative(X0) | kind(X0) | ~old(X0) [cnf transformation 54]
126. happy(X0) | kind(X0) [cnf transformation 38]
134. ~kind(mary) [cnf transformation 19]
142. creative(mary) [cnf transformation 25]
144. ~happy(X0) | ~generous(X0) [duplicate literal removal 79]
324. ~generous(X0) | kind(X0) [resolution 144,126]
332. old(mary) | generous(mary) [resolution 87,142]
337. 38 <=> generous(mary) [avatar definition]
339. generous(mary) <- (38) [avatar component clause 337]
341. 39 <=> old(mary) [avatar definition]
343. old(mary) <- (39) [avatar component clause 341]
344. 38 | 39 [avatar split clause 332,341,337]
380. kind(mary) <- (38) [resolution 339,324]
383. $false <- (38) [subsumption resolution 380,134]
384. ~38 [avatar contradiction clause 383]
467. kind(mary) | ~old(mary) [resolution 114,142]
472. ~old(mary) [subsumption resolution 467,134]
473. $false <- (39) [subsumption resolution 472,343]
474. ~39 [avatar contradiction clause 473]
475. $false [avatar sat refutation 344,384,474]
% SZS output end Proof for 3968392897149743612320295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not curious is curious. If paul is not old or patient then paul is both not generous and patient. If someone is both not rich and not brave then lucy is not patient or not creative and vice versa. If susan is both curious and rich then paul is not tall and vice versa. Everyone who is both not wise and happy is both quiet and not old. If john is either happy or wise then fred is wise and vice versa. Everyone who is both not happy and not curious is wise and vice versa. If lucy is not funny or kind then fred is either not wise or not quiet and vice versa. If mary is both kind and not brave then someone is either humble or not rich and vice versa. If someone is both wise and not quiet then fred is either not wise or generous and vice versa. Everyone who is not funny is strong or happy. If someone is not strong then someone is strong and vice versa. If someone is either not brave or not creative then lucy is not curious or quiet. Everyone who is either generous or not happy is not curious or not rich. If mary is both not brave and patient then susan is not wise or strong and vice versa. If someone is wise or funny then someone is either curious or funny. Susan is not humble. Paul is patient or not rich. Mary is happy. Someone is either not brave or not rich. Alice is either not quiet or not curious. Someone is both rich and not old. Paul is either not humble or generous. | Alice is not kind. | neutral | (![X]:((kind(X)&~curious(X))=>curious(X)))&
(((~old(paul)|patient(paul)))=>((~generous(paul)&patient(paul))))&
((?[X]:((~rich(X)&~brave(X))))<=>((~patient(lucy)|~creative(lucy))))&
(((curious(susan)&rich(susan)))<=>(~tall(paul)))&
(![X]:((~wise(X)&happy(X))=>(quiet(X)&~old(X))))&
(((happy(john)<~>wise(john)))<=>(wise(fred)))&
(![X]:((~happy(X)&~curious(X))<=>wise(X)))&
(((~funny(lucy)|kind(lucy)))<=>((~wise(fred)<~>~quiet(fred))))&
(((kind(mary)&~brave(mary)))<=>(?[X]:((humble(X)<~>~rich(X)))))&
((?[X]:((wise(X)&~quiet(X))))<=>((~wise(fred)<~>generous(fred))))&
(![X]:(~funny(X)=>(strong(X)|happy(X))))&
((?[X]:(~strong(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>~creative(X))))=>((~curious(lucy)|quiet(lucy))))&
(![X]:((generous(X)<~>~happy(X))=>(~curious(X)|~rich(X))))&
(((~brave(mary)&patient(mary)))<=>((~wise(susan)|strong(susan))))&
((?[X]:((wise(X)|funny(X))))=>(?[X]:((curious(X)<~>funny(X)))))&
(~humble(susan))&
((patient(paul)|~rich(paul)))&
(happy(mary))&
(?[X]:((~brave(X)<~>~rich(X))))&
((~quiet(alice)<~>~curious(alice)))&
(?[X]:((rich(X)&~old(X))))&
((~humble(paul)<~>generous(paul))) | ~kind(alice) | [] | null | 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 not kind is wise and vice versa. If susan is both funny and not patient then fred is either not brave or not calm and vice versa. If someone is either wise or funny then john is wise or not patient and vice versa. If someone is not old then someone is not happy or not creative. If alice is not calm then someone is humble and vice versa. Everyone who is not generous is not patient or not calm. If paul is both not calm and not wise then someone is happy or generous and vice versa. Everyone who is not tall or patient is not creative or happy. Everyone who is calm or not strong is not patient or funny and vice versa. Everyone who is generous or not creative is both not humble and generous and vice versa. If someone is patient or not quiet then someone is both creative and generous and vice versa. Everyone who is both rich and quiet is not humble or not calm and vice versa. Everyone who is either rich or not calm is calm or not strong. Someone is both not calm and creative. Someone is either not strong or humble. Someone is not old. Someone is not happy or not humble. Someone is either not old or kind. Someone is both funny and old. Someone is either not old or not calm. Susan is either rich or old. | Susan is not old. | entailment | ((?[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)&~kind(X))<=>wise(X)))&
(((funny(susan)&~patient(susan)))<=>((~brave(fred)<~>~calm(fred))))&
((?[X]:((wise(X)<~>funny(X))))<=>((wise(john)|~patient(john))))&
((?[X]:(~old(X)))=>(?[X]:((~happy(X)|~creative(X)))))&
((~calm(alice))<=>(?[X]:(humble(X))))&
(![X]:(~generous(X)=>(~patient(X)|~calm(X))))&
(((~calm(paul)&~wise(paul)))<=>(?[X]:((happy(X)|generous(X)))))&
(![X]:((~tall(X)|patient(X))=>(~creative(X)|happy(X))))&
(![X]:((calm(X)|~strong(X))<=>(~patient(X)|funny(X))))&
(![X]:((generous(X)|~creative(X))<=>(~humble(X)&generous(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:((creative(X)&generous(X)))))&
(![X]:((rich(X)&quiet(X))<=>(~humble(X)|~calm(X))))&
(![X]:((rich(X)<~>~calm(X))=>(calm(X)|~strong(X))))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:(~old(X)))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:((funny(X)&old(X))))&
(?[X]:((~old(X)<~>~calm(X))))&
((rich(susan)<~>old(susan))) | ~old(susan) | [
"p2",
"p12",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6586058327095428219250025
% SZS output start Proof for 6586058327095428219250025
3. ! [X0] : (~creative(X0) <=> ~rich(X0)) [input p2]
13. ! [X0] : ((~creative(X0) | generous(X0)) <=> (generous(X0) & ~humble(X0))) [input p12]
15. ! [X0] : ((quiet(X0) & rich(X0)) <=> (~calm(X0) | ~humble(X0))) [input p14]
24. rich(susan) <~> old(susan) [input p23]
25. old(susan) [input hypothesis]
42. ! [X0] : ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0))) [nnf transformation 3]
66. ! [X0] : (((~creative(X0) | generous(X0)) | (~generous(X0) | humble(X0))) & ((generous(X0) & ~humble(X0)) | (creative(X0) & ~generous(X0)))) [nnf transformation 13]
67. ! [X0] : ((~creative(X0) | generous(X0) | ~generous(X0) | humble(X0)) & ((generous(X0) & ~humble(X0)) | (creative(X0) & ~generous(X0)))) [flattening 66]
73. ! [X0] : (((quiet(X0) & rich(X0)) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | (~quiet(X0) | ~rich(X0)))) [nnf transformation 15]
74. ! [X0] : (((quiet(X0) & rich(X0)) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | ~quiet(X0) | ~rich(X0))) [flattening 73]
93. (~old(susan) | ~rich(susan)) & (old(susan) | rich(susan)) [nnf transformation 24]
97. ~rich(X0) | creative(X0) [cnf transformation 42]
98. ~creative(X0) | rich(X0) [cnf transformation 42]
130. ~humble(X0) | creative(X0) [cnf transformation 67]
140. rich(X0) | humble(X0) [cnf transformation 74]
159. ~old(susan) | ~rich(susan) [cnf transformation 93]
160. old(susan) [cnf transformation 25]
351. 42 <=> rich(susan) [avatar definition]
353. ~rich(susan) <- (~42) [avatar component clause 351]
355. 43 <=> old(susan) [avatar definition]
358. ~42 | ~43 [avatar split clause 159,355,351]
360. 43 [avatar split clause 160,355]
373. humble(X0) | creative(X0) [resolution 140,97]
391. creative(X0) [subsumption resolution 373,130]
460. rich(X1) [resolution 391,98]
490. $false <- (~42) [resolution 460,353]
492. 42 [avatar contradiction clause 490]
494. $false [avatar sat refutation 358,360,492]
% SZS output end Proof for 6586058327095428219250025
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not humble and generous then someone is strong or not old.
Everyone who is not calm is either curious or not patient.
If john is both not calm and brave then someone is not kind.
Everyone who is either curious or generous is not strong.
Everyone who is either strong or not curious is both happy and old and vice versa.
If someone is both funny and not calm then someone is generous.
Everyone who is calm or not quiet is strong or not curious and vice versa.
Everyone who is not generous is both not rich and not strong and vice versa.
If mary is generous then someone is calm and vice versa.
Everyone who is either not quiet or tall is both not funny and wise and vice versa.
If someone is patient then fred is not calm or creative and vice versa.
Everyone who is both not calm and old is either not old or calm.
Everyone who is either rich or not rich is either not happy or curious.
If mary is both not creative and not old then someone is both quiet and not happy and vice versa.
If someone is not curious or rich then john is either not kind or wise and vice versa.
If fred is both not wise and wise then someone is both not humble and patient.
Someone is tall.
Someone is not quiet.
Someone is strong or tall.
Mary is both kind and not strong.
Someone is humble.
Paul is strong.
John is both wise and rich.
Someone is wise. | Mary is not patient. | contradiction | (((~humble(mary)&generous(mary)))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:(~calm(X)=>(curious(X)<~>~patient(X))))&
(((~calm(john)&brave(john)))=>(?[X]:(~kind(X))))&
(![X]:((curious(X)<~>generous(X))=>~strong(X)))&
(![X]:((strong(X)<~>~curious(X))<=>(happy(X)&old(X))))&
((?[X]:((funny(X)&~calm(X))))=>(?[X]:(generous(X))))&
(![X]:((calm(X)|~quiet(X))<=>(strong(X)|~curious(X))))&
(![X]:(~generous(X)<=>(~rich(X)&~strong(X))))&
((generous(mary))<=>(?[X]:(calm(X))))&
(![X]:((~quiet(X)<~>tall(X))<=>(~funny(X)&wise(X))))&
((?[X]:(patient(X)))<=>((~calm(fred)|creative(fred))))&
(![X]:((~calm(X)&old(X))=>(~old(X)<~>calm(X))))&
(![X]:((rich(X)<~>~rich(X))=>(~happy(X)<~>curious(X))))&
(((~creative(mary)&~old(mary)))<=>(?[X]:((quiet(X)&~happy(X)))))&
((?[X]:((~curious(X)|rich(X))))<=>((~kind(john)<~>wise(john))))&
(((~wise(fred)&wise(fred)))=>(?[X]:((~humble(X)&patient(X)))))&
(?[X]:(tall(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((strong(X)|tall(X))))&
((kind(mary)&~strong(mary)))&
(?[X]:(humble(X)))&
(strong(paul))&
((wise(john)&rich(john)))&
(?[X]:(wise(X))) | ~patient(mary) | [
"p1",
"p4",
"p6",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7141491177446997328576951
% SZS output start Proof for 7141491177446997328576951
2. ! [X0] : (~calm(X0) => (curious(X0) <~> ~patient(X0))) [input p1]
5. ! [X0] : ((strong(X0) <~> ~curious(X0)) <=> (old(X0) & happy(X0))) [input p4]
7. ! [X0] : ((~quiet(X0) | calm(X0)) <=> (~curious(X0) | strong(X0))) [input p6]
13. ! [X0] : ((rich(X0) <~> ~rich(X0)) => (~happy(X0) <~> curious(X0))) [input p12]
20. ~strong(mary) & kind(mary) [input p19]
25. ~patient(mary) [input hypothesis]
30. ! [X0] : ((curious(X0) <~> ~patient(X0)) | calm(X0)) [ennf transformation 2]
35. ! [X0] : ((~happy(X0) <~> curious(X0)) | (rich(X0) <=> ~rich(X0))) [ennf transformation 13]
40. ! [X0] : (((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | calm(X0)) [nnf transformation 30]
42. ! [X0] : ((((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | (~old(X0) | ~happy(X0))) & ((old(X0) & happy(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))))) [nnf transformation 5]
43. ! [X0] : ((((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | ~old(X0) | ~happy(X0)) & ((old(X0) & happy(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))))) [flattening 42]
47. ! [X0] : (((~quiet(X0) | calm(X0)) | (curious(X0) & ~strong(X0))) & ((~curious(X0) | strong(X0)) | (quiet(X0) & ~calm(X0)))) [nnf transformation 7]
48. ! [X0] : ((~quiet(X0) | calm(X0) | (curious(X0) & ~strong(X0))) & (~curious(X0) | strong(X0) | (quiet(X0) & ~calm(X0)))) [flattening 47]
63. ! [X0] : (((~curious(X0) | happy(X0)) & (curious(X0) | ~happy(X0))) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) [nnf transformation 35]
87. ~curious(X0) | patient(X0) | calm(X0) [cnf transformation 40]
91. happy(X0) | strong(X0) | curious(X0) [cnf transformation 43]
97. ~curious(X0) | strong(X0) | ~calm(X0) [cnf transformation 48]
117. curious(X0) | ~happy(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
118. curious(X0) | ~happy(X0) | rich(X0) | rich(X0) [cnf transformation 63]
137. ~strong(mary) [cnf transformation 20]
143. ~patient(mary) [cnf transformation 25]
144. curious(X0) | ~happy(X0) | ~rich(X0) [duplicate literal removal 117]
145. ~happy(X0) | curious(X0) | rich(X0) [duplicate literal removal 118]
202. ~happy(X0) | curious(X0) [subsumption resolution 144,145]
296. strong(X0) | curious(X0) | curious(X0) [resolution 91,202]
297. curious(X0) | strong(X0) [duplicate literal removal 296]
379. strong(X0) | patient(X0) | calm(X0) [resolution 297,87]
383. strong(X4) | strong(X4) | ~calm(X4) [resolution 297,97]
389. ~calm(X4) | strong(X4) [duplicate literal removal 383]
400. patient(X0) | strong(X0) [subsumption resolution 379,389]
514. strong(mary) [resolution 400,143]
516. $false [subsumption resolution 514,137]
% SZS output end Proof for 7141491177446997328576951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then lucy is either old or not patient and vice versa.
Everyone who is happy or not old is both patient and rich.
If lucy is both strong and creative then susan is happy and vice versa.
If lucy is not generous or not old then someone is either not funny or not kind and vice versa.
If alice is kind then someone is not kind and vice versa.
Everyone who is not generous is creative or not tall.
Everyone who is both not humble and happy is not brave and vice versa.
If lucy is tall then someone is not funny or not patient and vice versa.
If paul is humble then someone is not patient or patient and vice versa.
If someone is both not curious and humble then mary is either curious or patient and vice versa.
If someone is both curious and not humble then susan is not rich or old and vice versa.
If someone is rich or not generous then alice is not tall.
Everyone who is both not quiet and curious is not tall or not kind.
If someone is either wise or kind then someone is both not brave and not calm and vice versa.
If paul is both not quiet and not patient then someone is either quiet or humble and vice versa.
Everyone who is strong or wise is not funny or not old.
Someone is both not humble and wise.
Someone is kind.
Paul is either old or not happy.
Paul is both humble and not funny.
Someone is either not kind or creative.
Someone is either calm or not rich.
Alice is both strong and not humble.
Lucy is not kind. | Lucy is not old. | contradiction | ((?[X]:(~funny(X)))<=>((old(lucy)<~>~patient(lucy))))&
(![X]:((happy(X)|~old(X))=>(patient(X)&rich(X))))&
(((strong(lucy)&creative(lucy)))<=>(happy(susan)))&
(((~generous(lucy)|~old(lucy)))<=>(?[X]:((~funny(X)<~>~kind(X)))))&
((kind(alice))<=>(?[X]:(~kind(X))))&
(![X]:(~generous(X)=>(creative(X)|~tall(X))))&
(![X]:((~humble(X)&happy(X))<=>~brave(X)))&
((tall(lucy))<=>(?[X]:((~funny(X)|~patient(X)))))&
((humble(paul))<=>(?[X]:((~patient(X)|patient(X)))))&
((?[X]:((~curious(X)&humble(X))))<=>((curious(mary)<~>patient(mary))))&
((?[X]:((curious(X)&~humble(X))))<=>((~rich(susan)|old(susan))))&
((?[X]:((rich(X)|~generous(X))))=>(~tall(alice)))&
(![X]:((~quiet(X)&curious(X))=>(~tall(X)|~kind(X))))&
((?[X]:((wise(X)<~>kind(X))))<=>(?[X]:((~brave(X)&~calm(X)))))&
(((~quiet(paul)&~patient(paul)))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:((strong(X)|wise(X))=>(~funny(X)|~old(X))))&
(?[X]:((~humble(X)&wise(X))))&
(?[X]:(kind(X)))&
((old(paul)<~>~happy(paul)))&
((humble(paul)&~funny(paul)))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((calm(X)<~>~rich(X))))&
((strong(alice)&~humble(alice)))&
(~kind(lucy)) | ~old(lucy) | [
"p0",
"p1",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5910144239267151928590417
% SZS output start Proof for 5910144239267151928590417
1. ? [X0] : ~funny(X0) <=> (old(lucy) <~> ~patient(lucy)) [input p0]
2. ! [X0] : ((~old(X0) | happy(X0)) => (rich(X0) & patient(X0))) [input p1]
20. ~funny(paul) & humble(paul) [input p19]
25. ~old(lucy) [input hypothesis]
27. ! [X0] : ((rich(X0) & patient(X0)) | (old(X0) & ~happy(X0))) [ennf transformation 2]
35. (? [X0] : ~funny(X0) | ((old(lucy) | patient(lucy)) & (~patient(lucy) | ~old(lucy)))) & (((patient(lucy) | ~old(lucy)) & (~patient(lucy) | old(lucy))) | ! [X0] : funny(X0)) [nnf transformation 1]
36. (? [X0] : ~funny(X0) | ((old(lucy) | patient(lucy)) & (~patient(lucy) | ~old(lucy)))) & (((patient(lucy) | ~old(lucy)) & (~patient(lucy) | old(lucy))) | ! [X1] : funny(X1)) [rectify 35]
37. ? [X0] : ~funny(X0) => ~funny(sK0) [choice axiom]
38. (~funny(sK0) | ((old(lucy) | patient(lucy)) & (~patient(lucy) | ~old(lucy)))) & (((patient(lucy) | ~old(lucy)) & (~patient(lucy) | old(lucy))) | ! [X1] : funny(X1)) [skolemisation 36,37]
90. ~patient(lucy) | old(lucy) | funny(X1) [cnf transformation 38]
95. patient(X0) | old(X0) [cnf transformation 27]
153. ~funny(paul) [cnf transformation 20]
161. ~old(lucy) [cnf transformation 25]
163. 1 <=> patient(lucy) [avatar definition]
164. ~patient(lucy) <- (~1) [avatar component clause 163]
167. 2 <=> old(lucy) [avatar definition]
168. ~old(lucy) <- (~2) [avatar component clause 167]
177. 4 <=> ! [X1] : funny(X1) [avatar definition]
178. funny(X1) <- (4) [avatar component clause 177]
180. 4 | 2 | ~1 [avatar split clause 90,163,167,177]
412. ~2 [avatar split clause 161,167]
415. $false <- (4) [resolution 178,153]
416. ~4 [avatar contradiction clause 415]
421. old(lucy) <- (~1) [resolution 95,164]
422. $false <- (~1, ~2) [subsumption resolution 421,168]
423. 1 | 2 [avatar contradiction clause 422]
424. $false [avatar sat refutation 180,412,416,423]
% SZS output end Proof for 5910144239267151928590417
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or old is not quiet or kind.
Everyone who is both not generous and not wise is either not old or not curious and vice versa.
Everyone who is not happy is kind or humble and vice versa.
Everyone who is happy or wise is brave or curious.
If paul is not brave then lucy is both not old and not funny and vice versa.
Everyone who is either not happy or not rich is not patient.
If someone is tall then someone is either happy or rich and vice versa.
Everyone who is not strong or not kind is both not quiet and rich and vice versa.
Everyone who is both curious and not patient is not rich.
Everyone who is not patient or not funny is both old and not patient.
Everyone who is both patient and not generous is either not kind or not funny.
Everyone who is curious or tall is not rich and vice versa.
Everyone who is both curious and strong is both patient and not funny.
Everyone who is both wise and not humble is both generous and not brave and vice versa.
Everyone who is not old is both not quiet and not brave.
Everyone who is both not calm and not generous is either not calm or not brave.
Someone is both happy and not wise.
Someone is both humble and not generous.
Alice is patient.
Someone is either not happy or not kind.
Fred is creative.
Lucy is either old or creative.
John is either not kind or not humble.
Someone is either not strong or not old. | Alice is generous. | contradiction | (![X]:((~curious(X)<~>old(X))=>(~quiet(X)|kind(X))))&
(![X]:((~generous(X)&~wise(X))<=>(~old(X)<~>~curious(X))))&
(![X]:(~happy(X)<=>(kind(X)|humble(X))))&
(![X]:((happy(X)|wise(X))=>(brave(X)|curious(X))))&
((~brave(paul))<=>((~old(lucy)&~funny(lucy))))&
(![X]:((~happy(X)<~>~rich(X))=>~patient(X)))&
((?[X]:(tall(X)))<=>(?[X]:((happy(X)<~>rich(X)))))&
(![X]:((~strong(X)|~kind(X))<=>(~quiet(X)&rich(X))))&
(![X]:((curious(X)&~patient(X))=>~rich(X)))&
(![X]:((~patient(X)|~funny(X))=>(old(X)&~patient(X))))&
(![X]:((patient(X)&~generous(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((curious(X)|tall(X))<=>~rich(X)))&
(![X]:((curious(X)&strong(X))=>(patient(X)&~funny(X))))&
(![X]:((wise(X)&~humble(X))<=>(generous(X)&~brave(X))))&
(![X]:(~old(X)=>(~quiet(X)&~brave(X))))&
(![X]:((~calm(X)&~generous(X))=>(~calm(X)<~>~brave(X))))&
(?[X]:((happy(X)&~wise(X))))&
(?[X]:((humble(X)&~generous(X))))&
(patient(alice))&
(?[X]:((~happy(X)<~>~kind(X))))&
(creative(fred))&
((old(lucy)<~>creative(lucy)))&
((~kind(john)<~>~humble(john)))&
(?[X]:((~strong(X)<~>~old(X)))) | generous(alice) | [
"p1",
"p3",
"p7",
"p9",
"p11",
"p12",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7407526885632722546930176
% SZS output start Proof for 7407526885632722546930176
2. ! [X0] : ((~wise(X0) & ~generous(X0)) <=> (~old(X0) <~> ~curious(X0))) [input p1]
4. ! [X0] : ((wise(X0) | happy(X0)) => (curious(X0) | brave(X0))) [input p3]
8. ! [X0] : ((~kind(X0) | ~strong(X0)) <=> (rich(X0) & ~quiet(X0))) [input p7]
10. ! [X0] : ((~funny(X0) | ~patient(X0)) => (~patient(X0) & old(X0))) [input p9]
12. ! [X0] : ((tall(X0) | curious(X0)) <=> ~rich(X0)) [input p11]
13. ! [X0] : ((strong(X0) & curious(X0)) => (~funny(X0) & patient(X0))) [input p12]
14. ! [X0] : ((~humble(X0) & wise(X0)) <=> (~brave(X0) & generous(X0))) [input p13]
15. ! [X0] : (~old(X0) => (~brave(X0) & ~quiet(X0))) [input p14]
19. patient(alice) [input p18]
25. generous(alice) [input hypothesis]
29. ! [X0] : ((curious(X0) | brave(X0)) | (~wise(X0) & ~happy(X0))) [ennf transformation 4]
30. ! [X0] : (curious(X0) | brave(X0) | (~wise(X0) & ~happy(X0))) [flattening 29]
34. ! [X0] : ((~patient(X0) & old(X0)) | (funny(X0) & patient(X0))) [ennf transformation 10]
37. ! [X0] : ((~funny(X0) & patient(X0)) | (~strong(X0) | ~curious(X0))) [ennf transformation 13]
38. ! [X0] : ((~funny(X0) & patient(X0)) | ~strong(X0) | ~curious(X0)) [flattening 37]
39. ! [X0] : ((~brave(X0) & ~quiet(X0)) | old(X0)) [ennf transformation 15]
43. ! [X0] : (((~wise(X0) & ~generous(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (wise(X0) | generous(X0)))) [nnf transformation 2]
44. ! [X0] : (((~wise(X0) & ~generous(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | wise(X0) | generous(X0))) [flattening 43]
55. ! [X0] : (((~kind(X0) | ~strong(X0)) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | (kind(X0) & strong(X0)))) [nnf transformation 8]
56. ! [X0] : ((~kind(X0) | ~strong(X0) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | (kind(X0) & strong(X0)))) [flattening 55]
58. ! [X0] : (((tall(X0) | curious(X0)) | rich(X0)) & (~rich(X0) | (~tall(X0) & ~curious(X0)))) [nnf transformation 12]
59. ! [X0] : ((tall(X0) | curious(X0) | rich(X0)) & (~rich(X0) | (~tall(X0) & ~curious(X0)))) [flattening 58]
60. ! [X0] : (((~humble(X0) & wise(X0)) | (brave(X0) | ~generous(X0))) & ((~brave(X0) & generous(X0)) | (humble(X0) | ~wise(X0)))) [nnf transformation 14]
61. ! [X0] : (((~humble(X0) & wise(X0)) | brave(X0) | ~generous(X0)) & ((~brave(X0) & generous(X0)) | humble(X0) | ~wise(X0))) [flattening 60]
78. wise(X0) | old(X0) | curious(X0) | generous(X0) [cnf transformation 44]
80. ~generous(X0) | ~old(X0) | curious(X0) [cnf transformation 44]
87. ~wise(X0) | brave(X0) | curious(X0) [cnf transformation 30]
99. strong(X0) | rich(X0) [cnf transformation 56]
104. funny(X0) | old(X0) [cnf transformation 34]
106. ~patient(X0) | funny(X0) [cnf transformation 34]
109. ~rich(X0) | ~curious(X0) [cnf transformation 59]
113. ~strong(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 38]
116. ~generous(X0) | brave(X0) | wise(X0) [cnf transformation 61]
119. ~brave(X0) | old(X0) [cnf transformation 39]
126. patient(alice) [cnf transformation 19]
136. generous(alice) [cnf transformation 25]
224. funny(alice) [resolution 106,126]
235. 17 <=> old(alice) [avatar definition]
236. ~old(alice) <- (~17) [avatar component clause 235]
239. 18 <=> curious(alice) [avatar definition]
245. ~old(alice) | curious(alice) [resolution 80,136]
283. ~funny(X0) | ~curious(X0) | rich(X0) [resolution 113,99]
328. 18 | ~17 [avatar split clause 245,235,239]
364. old(X1) | curious(X1) | generous(X1) | brave(X1) | curious(X1) [resolution 78,87]
372. old(X1) | curious(X1) | generous(X1) | brave(X1) [duplicate literal removal 364]
374. generous(X1) | curious(X1) | old(X1) [subsumption resolution 372,119]
430. curious(X0) | old(X0) | brave(X0) | wise(X0) [resolution 374,116]
435. curious(X0) | old(X0) | brave(X0) [subsumption resolution 430,87]
436. curious(X0) | old(X0) [subsumption resolution 435,119]
442. ~funny(X0) | ~curious(X0) [subsumption resolution 283,109]
489. ~curious(X0) | old(X0) [resolution 442,104]
490. ~curious(alice) [resolution 442,224]
491. old(X0) [subsumption resolution 489,436]
494. ~18 [avatar split clause 490,239]
495. $false <- (~17) [subsumption resolution 236,491]
496. 17 [avatar contradiction clause 495]
497. $false [avatar sat refutation 328,494,496]
% SZS output end Proof for 7407526885632722546930176
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not happy or rich then someone is not curious. Everyone who is old or not generous is either wise or funny and vice versa. If paul is quiet then someone is either creative or humble. Everyone who is not creative is not calm and vice versa. Everyone who is calm or not tall is both funny and wise. If someone is quiet then susan is both not creative and patient and vice versa. Everyone who is wise or not strong is either patient or funny. If someone is not happy or brave then paul is happy and vice versa. Everyone who is either kind or quiet is both not quiet and not strong and vice versa. If mary is wise or not rich then someone is either quiet or old. Everyone who is patient or humble is calm. If alice is both not humble and patient then john is either generous or tall and vice versa. Everyone who is either not quiet or not kind is either not strong or old. Everyone who is either strong or not funny is both not old and not calm. If paul is both kind and generous then someone is both not quiet and not funny. Everyone who is not wise is not strong and vice versa. Someone is either tall or not wise. Alice is both tall and generous. Paul is tall. Mary is happy or not rich. Lucy is not brave or old. Someone is either not strong or happy. | Lucy is patient. | contradiction | (((~happy(fred)|rich(fred)))=>(?[X]:(~curious(X))))&
(![X]:((old(X)|~generous(X))<=>(wise(X)<~>funny(X))))&
((quiet(paul))=>(?[X]:((creative(X)<~>humble(X)))))&
(![X]:(~creative(X)<=>~calm(X)))&
(![X]:((calm(X)|~tall(X))=>(funny(X)&wise(X))))&
((?[X]:(quiet(X)))<=>((~creative(susan)&patient(susan))))&
(![X]:((wise(X)|~strong(X))=>(patient(X)<~>funny(X))))&
((?[X]:((~happy(X)|brave(X))))<=>(happy(paul)))&
(![X]:((kind(X)<~>quiet(X))<=>(~quiet(X)&~strong(X))))&
(((wise(mary)|~rich(mary)))=>(?[X]:((quiet(X)<~>old(X)))))&
(![X]:((patient(X)|humble(X))=>calm(X)))&
(((~humble(alice)&patient(alice)))<=>((generous(john)<~>tall(john))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~strong(X)<~>old(X))))&
(![X]:((strong(X)<~>~funny(X))=>(~old(X)&~calm(X))))&
(((kind(paul)&generous(paul)))=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:(~wise(X)<=>~strong(X)))&
(?[X]:((tall(X)<~>~wise(X))))&
((tall(alice)&generous(alice)))&
(tall(paul))&
((happy(mary)|~rich(mary)))&
((~brave(lucy)|old(lucy)))&
(?[X]:((~strong(X)<~>happy(X)))) | patient(lucy) | [
"p4",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3423413348400599490342419
% SZS output start Proof for 3423413348400599490342419
5. ! [X0] : ((~tall(X0) | calm(X0)) => (wise(X0) & funny(X0))) [input p4]
7. ! [X0] : ((~strong(X0) | wise(X0)) => (patient(X0) <~> funny(X0))) [input p6]
11. ! [X0] : ((humble(X0) | patient(X0)) => calm(X0)) [input p10]
23. patient(lucy) [input hypothesis]
26. ! [X0] : ((wise(X0) & funny(X0)) | (tall(X0) & ~calm(X0))) [ennf transformation 5]
27. ! [X0] : ((patient(X0) <~> funny(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 7]
29. ! [X0] : (calm(X0) | (~humble(X0) & ~patient(X0))) [ennf transformation 11]
45. ! [X0] : (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | (strong(X0) & ~wise(X0))) [nnf transformation 27]
78. ~calm(X0) | funny(X0) [cnf transformation 26]
80. ~calm(X0) | wise(X0) [cnf transformation 26]
87. ~patient(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 45]
102. ~patient(X0) | calm(X0) [cnf transformation 29]
131. patient(lucy) [cnf transformation 23]
277. calm(lucy) [resolution 102,131]
279. wise(lucy) [resolution 277,80]
280. funny(lucy) [resolution 277,78]
361. ~funny(lucy) | ~wise(lucy) [resolution 87,131]
362. ~wise(lucy) [subsumption resolution 361,280]
363. $false [subsumption resolution 362,279]
% SZS output end Proof for 3423413348400599490342419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not kind and vice versa. Everyone who is humble is not curious and vice versa. Everyone who is kind is not funny or not generous and vice versa. Everyone who is both not wise and quiet is generous and vice versa. Everyone who is not tall is not brave or not strong and vice versa. Everyone who is either not strong or not calm is either tall or not strong. Everyone who is curious is either generous or not funny. If someone is rich then someone is strong. Everyone who is not happy or generous is generous and vice versa. Everyone who is either old or happy is not patient and vice versa. If someone is both not happy and generous then someone is strong or patient and vice versa. Everyone who is either quiet or not old is not kind. If someone is patient then someone is not creative or funny. Everyone who is both curious and not quiet is not strong or curious and vice versa. If someone is not rich then fred is old or strong and vice versa. Everyone who is old or tall is brave or quiet. Mary is not rich or not wise. Someone is both brave and old. Lucy is either wise or kind. Mary is humble or strong. Someone is either funny or calm. John is either calm or patient. Someone is old or kind. | Lucy is kind. | entailment | (![X]:(tall(X)<=>~kind(X)))&
(![X]:(humble(X)<=>~curious(X)))&
(![X]:(kind(X)<=>(~funny(X)|~generous(X))))&
(![X]:((~wise(X)&quiet(X))<=>generous(X)))&
(![X]:(~tall(X)<=>(~brave(X)|~strong(X))))&
(![X]:((~strong(X)<~>~calm(X))=>(tall(X)<~>~strong(X))))&
(![X]:(curious(X)=>(generous(X)<~>~funny(X))))&
((?[X]:(rich(X)))=>(?[X]:(strong(X))))&
(![X]:((~happy(X)|generous(X))<=>generous(X)))&
(![X]:((old(X)<~>happy(X))<=>~patient(X)))&
((?[X]:((~happy(X)&generous(X))))<=>(?[X]:((strong(X)|patient(X)))))&
(![X]:((quiet(X)<~>~old(X))=>~kind(X)))&
((?[X]:(patient(X)))=>(?[X]:((~creative(X)|funny(X)))))&
(![X]:((curious(X)&~quiet(X))<=>(~strong(X)|curious(X))))&
((?[X]:(~rich(X)))<=>((old(fred)|strong(fred))))&
(![X]:((old(X)|tall(X))=>(brave(X)|quiet(X))))&
((~rich(mary)|~wise(mary)))&
(?[X]:((brave(X)&old(X))))&
((wise(lucy)<~>kind(lucy)))&
((humble(mary)|strong(mary)))&
(?[X]:((funny(X)<~>calm(X))))&
((calm(john)<~>patient(john)))&
(?[X]:((old(X)|kind(X)))) | kind(lucy) | [
"p2",
"p3",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4298574623722237079827388
% SZS output start Proof for 4298574623722237079827388
3. ! [X0] : (kind(X0) <=> (~generous(X0) | ~funny(X0))) [input p2]
4. ! [X0] : ((quiet(X0) & ~wise(X0)) <=> generous(X0)) [input p3]
19. wise(lucy) <~> kind(lucy) [input p18]
24. ~kind(lucy) [input hypothesis]
38. ! [X0] : ((kind(X0) | (generous(X0) & funny(X0))) & ((~generous(X0) | ~funny(X0)) | ~kind(X0))) [nnf transformation 3]
39. ! [X0] : ((kind(X0) | (generous(X0) & funny(X0))) & (~generous(X0) | ~funny(X0) | ~kind(X0))) [flattening 38]
40. ! [X0] : (((quiet(X0) & ~wise(X0)) | ~generous(X0)) & (generous(X0) | (~quiet(X0) | wise(X0)))) [nnf transformation 4]
41. ! [X0] : (((quiet(X0) & ~wise(X0)) | ~generous(X0)) & (generous(X0) | ~quiet(X0) | wise(X0))) [flattening 40]
67. (~kind(lucy) | ~wise(lucy)) & (kind(lucy) | wise(lucy)) [nnf transformation 19]
79. generous(X0) | kind(X0) [cnf transformation 39]
81. ~wise(X0) | ~generous(X0) [cnf transformation 41]
120. kind(lucy) | wise(lucy) [cnf transformation 67]
128. ~kind(lucy) [cnf transformation 24]
198. 16 <=> wise(lucy) [avatar definition]
199. wise(lucy) <- (16) [avatar component clause 198]
202. 17 <=> kind(lucy) [avatar definition]
204. ~kind(lucy) <- (~17) [avatar component clause 202]
206. 16 | 17 [avatar split clause 120,202,198]
245. ~17 [avatar split clause 128,202]
250. ~generous(lucy) <- (16) [resolution 81,199]
251. kind(lucy) <- (16) [resolution 250,79]
252. $false <- (16, ~17) [subsumption resolution 251,204]
253. ~16 | 17 [avatar contradiction clause 252]
254. $false [avatar sat refutation 206,245,253]
% SZS output end Proof for 4298574623722237079827388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not tall is either happy or not creative.
Everyone who is both not calm and happy is rich.
Everyone who is both rich and kind is generous or not old and vice versa.
If susan is either humble or not curious then someone is both not quiet and quiet and vice versa.
If someone is both not funny and not wise then someone is either not generous or not happy and vice versa.
Everyone who is not curious is either humble or not strong.
If someone is not humble or not quiet then alice is both not brave and not happy and vice versa.
If mary is either not old or wise then mary is creative or calm and vice versa.
If someone is not happy or not strong then someone is not patient or tall.
Everyone who is both old and not calm is either not brave or not quiet and vice versa.
If someone is quiet then alice is both not patient and not happy and vice versa.
Everyone who is either not brave or not happy is humble.
If someone is both old and quiet then paul is funny.
Everyone who is not creative or brave is either not curious or quiet.
Everyone who is both not rich and not happy is creative or rich and vice versa.
If someone is not old or old then paul is both not funny and not generous and vice versa.
Someone is not kind or curious.
Alice is both not generous and not kind.
Someone is either not creative or humble.
Alice is not funny.
Someone is not tall or happy.
Someone is both not funny and strong.
John is either patient or not strong. | John is not rich. | entailment | (![X]:((quiet(X)&~tall(X))=>(happy(X)<~>~creative(X))))&
(![X]:((~calm(X)&happy(X))=>rich(X)))&
(![X]:((rich(X)&kind(X))<=>(generous(X)|~old(X))))&
(((humble(susan)<~>~curious(susan)))<=>(?[X]:((~quiet(X)&quiet(X)))))&
((?[X]:((~funny(X)&~wise(X))))<=>(?[X]:((~generous(X)<~>~happy(X)))))&
(![X]:(~curious(X)=>(humble(X)<~>~strong(X))))&
((?[X]:((~humble(X)|~quiet(X))))<=>((~brave(alice)&~happy(alice))))&
(((~old(mary)<~>wise(mary)))<=>((creative(mary)|calm(mary))))&
((?[X]:((~happy(X)|~strong(X))))=>(?[X]:((~patient(X)|tall(X)))))&
(![X]:((old(X)&~calm(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:(quiet(X)))<=>((~patient(alice)&~happy(alice))))&
(![X]:((~brave(X)<~>~happy(X))=>humble(X)))&
((?[X]:((old(X)&quiet(X))))=>(funny(paul)))&
(![X]:((~creative(X)|brave(X))=>(~curious(X)<~>quiet(X))))&
(![X]:((~rich(X)&~happy(X))<=>(creative(X)|rich(X))))&
((?[X]:((~old(X)|old(X))))<=>((~funny(paul)&~generous(paul))))&
(?[X]:((~kind(X)|curious(X))))&
((~generous(alice)&~kind(alice)))&
(?[X]:((~creative(X)<~>humble(X))))&
(~funny(alice))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:((~funny(X)&strong(X))))&
((patient(john)<~>~strong(john))) | ~rich(john) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2412254689737896964981095
% SZS output start Proof for 2412254689737896964981095
15. ! [X0] : ((~happy(X0) & ~rich(X0)) <=> (rich(X0) | creative(X0))) [input p14]
24. rich(john) [input hypothesis]
68. ! [X0] : (((~happy(X0) & ~rich(X0)) | (~rich(X0) & ~creative(X0))) & ((rich(X0) | creative(X0)) | (happy(X0) | rich(X0)))) [nnf transformation 15]
69. ! [X0] : (((~happy(X0) & ~rich(X0)) | (~rich(X0) & ~creative(X0))) & (rich(X0) | creative(X0) | happy(X0) | rich(X0))) [flattening 68]
138. ~rich(X0) | ~rich(X0) [cnf transformation 69]
157. rich(john) [cnf transformation 24]
159. ~rich(X0) [duplicate literal removal 138]
347. $false [subsumption resolution 157,159]
% SZS output end Proof for 2412254689737896964981095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both funny and strong then someone is either old or not curious.
If someone is not creative or creative then john is both curious and brave and vice versa.
If someone is either happy or rich then paul is humble or not quiet and vice versa.
Everyone who is either not wise or patient is tall or brave.
If mary is either not patient or not curious then someone is either not calm or not creative and vice versa.
Everyone who is not humble is strong or not kind.
Everyone who is rich is not quiet or not kind and vice versa.
Everyone who is creative is either not humble or not rich.
If alice is both rich and happy then john is both not strong and funny.
If someone is creative or not happy then susan is both not calm and quiet.
Everyone who is not humble is funny or not tall.
If mary is funny or happy then lucy is old or not calm and vice versa.
If lucy is both wise and quiet then someone is either quiet or kind and vice versa.
If mary is either kind or not generous then john is not rich or not funny.
Everyone who is both patient and not funny is both not brave and not humble.
Everyone who is wise or humble is not old or creative.
John is not kind.
Someone is both not calm and wise.
Alice is either generous or humble.
Someone is both tall and humble.
Someone is not funny.
Susan is patient or not rich.
Someone is calm.
Paul is not wise or calm. | Alice is rich. | neutral | (((funny(john)&strong(john)))=>(?[X]:((old(X)<~>~curious(X)))))&
((?[X]:((~creative(X)|creative(X))))<=>((curious(john)&brave(john))))&
((?[X]:((happy(X)<~>rich(X))))<=>((humble(paul)|~quiet(paul))))&
(![X]:((~wise(X)<~>patient(X))=>(tall(X)|brave(X))))&
(((~patient(mary)<~>~curious(mary)))<=>(?[X]:((~calm(X)<~>~creative(X)))))&
(![X]:(~humble(X)=>(strong(X)|~kind(X))))&
(![X]:(rich(X)<=>(~quiet(X)|~kind(X))))&
(![X]:(creative(X)=>(~humble(X)<~>~rich(X))))&
(((rich(alice)&happy(alice)))=>((~strong(john)&funny(john))))&
((?[X]:((creative(X)|~happy(X))))=>((~calm(susan)&quiet(susan))))&
(![X]:(~humble(X)=>(funny(X)|~tall(X))))&
(((funny(mary)|happy(mary)))<=>((old(lucy)|~calm(lucy))))&
(((wise(lucy)&quiet(lucy)))<=>(?[X]:((quiet(X)<~>kind(X)))))&
(((kind(mary)<~>~generous(mary)))=>((~rich(john)|~funny(john))))&
(![X]:((patient(X)&~funny(X))=>(~brave(X)&~humble(X))))&
(![X]:((wise(X)|humble(X))=>(~old(X)|creative(X))))&
(~kind(john))&
(?[X]:((~calm(X)&wise(X))))&
((generous(alice)<~>humble(alice)))&
(?[X]:((tall(X)&humble(X))))&
(?[X]:(~funny(X)))&
((patient(susan)|~rich(susan)))&
(?[X]:(calm(X)))&
((~wise(paul)|calm(paul))) | rich(alice) | [] | null | 0 |
Everyone who is both humble and not quiet is tall and vice versa.
If someone is patient or not rich then someone is either not curious or not quiet.
Everyone who is either patient or not kind is brave or not creative.
If someone is creative then someone is either creative or funny.
If someone is both tall and calm then alice is either not humble or not strong and vice versa.
If someone is both rich and not happy then someone is both not curious and not generous.
If mary is old or tall then john is both creative and quiet and vice versa.
Everyone who is both kind and curious is not brave or kind and vice versa.
Everyone who is not creative or tall is both not patient and not rich.
Everyone who is generous or not brave is not wise or kind.
Everyone who is not rich or generous is tall and vice versa.
If alice is both tall and rich then someone is brave or not happy and vice versa.
Everyone who is both not curious and not happy is both curious and not quiet.
Everyone who is either not quiet or not generous is either not strong or old.
If john is both kind and not happy then lucy is not kind.
Everyone who is either strong or not generous is not old and vice versa.
Someone is kind.
Someone is calm or not creative.
Someone is either not generous or generous.
Mary is either rich or not quiet.
Paul is either not creative or generous.
Susan is not brave or not calm.
Someone is happy or not wise.
Fred is not generous. | Susan is not happy. | contradiction | (![X]:((humble(X)&~quiet(X))<=>tall(X)))&
((?[X]:((patient(X)|~rich(X))))=>(?[X]:((~curious(X)<~>~quiet(X)))))&
(![X]:((patient(X)<~>~kind(X))=>(brave(X)|~creative(X))))&
((?[X]:(creative(X)))=>(?[X]:((creative(X)<~>funny(X)))))&
((?[X]:((tall(X)&calm(X))))<=>((~humble(alice)<~>~strong(alice))))&
((?[X]:((rich(X)&~happy(X))))=>(?[X]:((~curious(X)&~generous(X)))))&
(((old(mary)|tall(mary)))<=>((creative(john)&quiet(john))))&
(![X]:((kind(X)&curious(X))<=>(~brave(X)|kind(X))))&
(![X]:((~creative(X)|tall(X))=>(~patient(X)&~rich(X))))&
(![X]:((generous(X)|~brave(X))=>(~wise(X)|kind(X))))&
(![X]:((~rich(X)|generous(X))<=>tall(X)))&
(((tall(alice)&rich(alice)))<=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((~curious(X)&~happy(X))=>(curious(X)&~quiet(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>(~strong(X)<~>old(X))))&
(((kind(john)&~happy(john)))=>(~kind(lucy)))&
(![X]:((strong(X)<~>~generous(X))<=>~old(X)))&
(?[X]:(kind(X)))&
(?[X]:((calm(X)|~creative(X))))&
(?[X]:((~generous(X)<~>generous(X))))&
((rich(mary)<~>~quiet(mary)))&
((~creative(paul)<~>generous(paul)))&
((~brave(susan)|~calm(susan)))&
(?[X]:((happy(X)|~wise(X))))&
(~generous(fred)) | ~happy(susan) | [
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 965381010568550896450355
% SZS output start Proof for 965381010568550896450355
9. ! [X0] : ((tall(X0) | ~creative(X0)) => (~rich(X0) & ~patient(X0))) [input p8]
12. (rich(alice) & tall(alice)) <=> ? [X0] : (~happy(X0) | brave(X0)) [input p11]
25. ~happy(susan) [input hypothesis]
36. ! [X0] : ((~rich(X0) & ~patient(X0)) | (~tall(X0) & creative(X0))) [ennf transformation 9]
66. ((rich(alice) & tall(alice)) | ! [X0] : (happy(X0) & ~brave(X0))) & (? [X0] : (~happy(X0) | brave(X0)) | (~rich(alice) | ~tall(alice))) [nnf transformation 12]
67. ((rich(alice) & tall(alice)) | ! [X0] : (happy(X0) & ~brave(X0))) & (? [X0] : (~happy(X0) | brave(X0)) | ~rich(alice) | ~tall(alice)) [flattening 66]
68. ((rich(alice) & tall(alice)) | ! [X0] : (happy(X0) & ~brave(X0))) & (? [X1] : (~happy(X1) | brave(X1)) | ~rich(alice) | ~tall(alice)) [rectify 67]
69. ? [X1] : (~happy(X1) | brave(X1)) => (~happy(sK4) | brave(sK4)) [choice axiom]
70. ((rich(alice) & tall(alice)) | ! [X0] : (happy(X0) & ~brave(X0))) & ((~happy(sK4) | brave(sK4)) | ~rich(alice) | ~tall(alice)) [skolemisation 68,69]
114. ~rich(X0) | ~tall(X0) [cnf transformation 36]
120. tall(alice) | happy(X0) [cnf transformation 70]
122. rich(alice) | happy(X0) [cnf transformation 70]
144. ~happy(susan) [cnf transformation 25]
237. 20 <=> ! [X0] : happy(X0) [avatar definition]
238. happy(X0) <- (20) [avatar component clause 237]
240. 21 <=> rich(alice) [avatar definition]
242. rich(alice) <- (21) [avatar component clause 240]
243. 20 | 21 [avatar split clause 122,240,237]
249. 23 <=> tall(alice) [avatar definition]
251. tall(alice) <- (23) [avatar component clause 249]
252. 20 | 23 [avatar split clause 120,249,237]
305. $false <- (20) [resolution 238,144]
306. ~20 [avatar contradiction clause 305]
326. ~tall(alice) <- (21) [resolution 114,242]
327. $false <- (21, 23) [subsumption resolution 326,251]
328. ~21 | ~23 [avatar contradiction clause 327]
329. $false [avatar sat refutation 243,252,306,328]
% SZS output end Proof for 965381010568550896450355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not strong is calm and vice versa.
If alice is not wise then alice is curious or not humble.
Everyone who is both not kind and patient is not strong or not quiet.
Everyone who is patient or happy is brave or not funny.
If someone is either quiet or generous then fred is either calm or tall and vice versa.
If someone is both patient and not creative then fred is kind.
If susan is both kind and happy then lucy is either generous or not humble and vice versa.
Everyone who is not tall or strong is either strong or curious.
Everyone who is both generous and rich is wise or not tall and vice versa.
Everyone who is not kind is both generous and not wise.
If mary is either patient or rich then mary is not curious or strong.
Everyone who is rich or not calm is both generous and brave and vice versa.
Everyone who is either quiet or humble is not brave and vice versa.
Everyone who is calm is rich or old and vice versa.
Everyone who is both calm and not old is either not funny or not curious.
If lucy is not kind then susan is kind and vice versa.
Someone is not old.
Someone is both patient and calm.
Someone is not strong.
Lucy is not patient.
Alice is both not happy and not funny.
Someone is both not wise and brave.
Susan is kind. | Susan is happy. | neutral | (![X]:((curious(X)|~strong(X))<=>calm(X)))&
((~wise(alice))=>((curious(alice)|~humble(alice))))&
(![X]:((~kind(X)&patient(X))=>(~strong(X)|~quiet(X))))&
(![X]:((patient(X)|happy(X))=>(brave(X)|~funny(X))))&
((?[X]:((quiet(X)<~>generous(X))))<=>((calm(fred)<~>tall(fred))))&
((?[X]:((patient(X)&~creative(X))))=>(kind(fred)))&
(((kind(susan)&happy(susan)))<=>((generous(lucy)<~>~humble(lucy))))&
(![X]:((~tall(X)|strong(X))=>(strong(X)<~>curious(X))))&
(![X]:((generous(X)&rich(X))<=>(wise(X)|~tall(X))))&
(![X]:(~kind(X)=>(generous(X)&~wise(X))))&
(((patient(mary)<~>rich(mary)))=>((~curious(mary)|strong(mary))))&
(![X]:((rich(X)|~calm(X))<=>(generous(X)&brave(X))))&
(![X]:((quiet(X)<~>humble(X))<=>~brave(X)))&
(![X]:(calm(X)<=>(rich(X)|old(X))))&
(![X]:((calm(X)&~old(X))=>(~funny(X)<~>~curious(X))))&
((~kind(lucy))<=>(kind(susan)))&
(?[X]:(~old(X)))&
(?[X]:((patient(X)&calm(X))))&
(?[X]:(~strong(X)))&
(~patient(lucy))&
((~happy(alice)&~funny(alice)))&
(?[X]:((~wise(X)&brave(X))))&
(kind(susan)) | happy(susan) | [] | null | 0 |
Everyone who is both wise and happy is curious or not brave.
If fred is both generous and not patient then someone is both humble and generous.
Everyone who is not generous or not strong is both wise and not funny and vice versa.
Everyone who is not curious or not creative is either rich or curious and vice versa.
Everyone who is both not old and not generous is either generous or not creative and vice versa.
If paul is both tall and quiet then someone is both strong and not curious.
If someone is humble or not funny then someone is curious and vice versa.
Everyone who is quiet is both kind and tall.
Everyone who is either not funny or not humble is both not creative and strong.
Everyone who is both not happy and calm is either quiet or not funny and vice versa.
Everyone who is tall is humble or strong and vice versa.
If someone is not generous then paul is funny and vice versa.
Everyone who is either strong or kind is not calm or not rich.
If mary is both rich and patient then susan is creative or old.
Everyone who is not brave or not strong is both quiet and tall.
If someone is not calm then someone is either quiet or not calm.
Someone is not quiet or happy.
Mary is both not humble and not kind.
Someone is both not brave and happy.
Someone is either not curious or quiet.
Mary is either calm or not strong.
Someone is not rich or humble.
Paul is either not funny or wise. | Fred is strong. | entailment | (![X]:((wise(X)&happy(X))=>(curious(X)|~brave(X))))&
(((generous(fred)&~patient(fred)))=>(?[X]:((humble(X)&generous(X)))))&
(![X]:((~generous(X)|~strong(X))<=>(wise(X)&~funny(X))))&
(![X]:((~curious(X)|~creative(X))<=>(rich(X)<~>curious(X))))&
(![X]:((~old(X)&~generous(X))<=>(generous(X)<~>~creative(X))))&
(((tall(paul)&quiet(paul)))=>(?[X]:((strong(X)&~curious(X)))))&
((?[X]:((humble(X)|~funny(X))))<=>(?[X]:(curious(X))))&
(![X]:(quiet(X)=>(kind(X)&tall(X))))&
(![X]:((~funny(X)<~>~humble(X))=>(~creative(X)&strong(X))))&
(![X]:((~happy(X)&calm(X))<=>(quiet(X)<~>~funny(X))))&
(![X]:(tall(X)<=>(humble(X)|strong(X))))&
((?[X]:(~generous(X)))<=>(funny(paul)))&
(![X]:((strong(X)<~>kind(X))=>(~calm(X)|~rich(X))))&
(((rich(mary)&patient(mary)))=>((creative(susan)|old(susan))))&
(![X]:((~brave(X)|~strong(X))=>(quiet(X)&tall(X))))&
((?[X]:(~calm(X)))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(?[X]:((~quiet(X)|happy(X))))&
((~humble(mary)&~kind(mary)))&
(?[X]:((~brave(X)&happy(X))))&
(?[X]:((~curious(X)<~>quiet(X))))&
((calm(mary)<~>~strong(mary)))&
(?[X]:((~rich(X)|humble(X))))&
((~funny(paul)<~>wise(paul))) | strong(fred) | [
"p2",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4085979105519329618190756
% SZS output start Proof for 4085979105519329618190756
3. ! [X0] : ((~strong(X0) | ~generous(X0)) <=> (~funny(X0) & wise(X0))) [input p2]
9. ! [X0] : ((~funny(X0) <~> ~humble(X0)) => (strong(X0) & ~creative(X0))) [input p8]
11. ! [X0] : (tall(X0) <=> (strong(X0) | humble(X0))) [input p10]
15. ! [X0] : ((~strong(X0) | ~brave(X0)) => (tall(X0) & quiet(X0))) [input p14]
24. ~strong(fred) [input hypothesis]
34. ! [X0] : ((strong(X0) & ~creative(X0)) | (~funny(X0) <=> ~humble(X0))) [ennf transformation 9]
39. ! [X0] : ((tall(X0) & quiet(X0)) | (strong(X0) & brave(X0))) [ennf transformation 15]
43. ! [X0] : (((~strong(X0) | ~generous(X0)) | (funny(X0) | ~wise(X0))) & ((~funny(X0) & wise(X0)) | (strong(X0) & generous(X0)))) [nnf transformation 3]
44. ! [X0] : ((~strong(X0) | ~generous(X0) | funny(X0) | ~wise(X0)) & ((~funny(X0) & wise(X0)) | (strong(X0) & generous(X0)))) [flattening 43]
56. ! [X0] : ((strong(X0) & ~creative(X0)) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0)))) [nnf transformation 34]
59. ! [X0] : ((tall(X0) | (~strong(X0) & ~humble(X0))) & ((strong(X0) | humble(X0)) | ~tall(X0))) [nnf transformation 11]
60. ! [X0] : ((tall(X0) | (~strong(X0) & ~humble(X0))) & (strong(X0) | humble(X0) | ~tall(X0))) [flattening 59]
87. ~funny(X0) | strong(X0) [cnf transformation 44]
110. strong(X0) | ~humble(X0) | funny(X0) [cnf transformation 56]
118. strong(X0) | humble(X0) | ~tall(X0) [cnf transformation 60]
120. ~strong(X0) | tall(X0) [cnf transformation 60]
129. tall(X0) | strong(X0) [cnf transformation 39]
144. ~strong(fred) [cnf transformation 24]
210. ~humble(X0) | strong(X0) [subsumption resolution 110,87]
211. ~tall(X0) | strong(X0) [subsumption resolution 118,210]
239. tall(X0) [subsumption resolution 129,120]
324. strong(X0) [resolution 211,239]
330. $false [resolution 324,144]
% SZS output end Proof for 4085979105519329618190756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or quiet is both not happy and not humble. Everyone who is both not creative and not funny is creative. If someone is both tall and humble then susan is either not old or not curious. If paul is either generous or tall then someone is wise. If someone is funny or wise then someone is calm. Everyone who is happy is humble or not happy and vice versa. If lucy is happy or calm then someone is both not creative and not curious and vice versa. Everyone who is brave is both humble and generous and vice versa. If someone is not brave then someone is humble or old. If mary is not old or tall then someone is not generous or not tall and vice versa. If someone is not old then someone is calm or not generous and vice versa. Everyone who is patient is strong. If paul is either humble or not brave then mary is either calm or patient and vice versa. If someone is both not tall and funny then alice is not tall. Everyone who is not happy or not wise is patient. Everyone who is not wise is both tall and funny. Alice is not creative or curious. Someone is either kind or not strong. Someone is both happy and tall. Lucy is not kind or patient. Paul is both generous and not kind. Someone is not funny. Someone is brave. Paul is not tall or not wise. | Lucy is funny. | neutral | (![X]:((~strong(X)|quiet(X))=>(~happy(X)&~humble(X))))&
(![X]:((~creative(X)&~funny(X))=>creative(X)))&
((?[X]:((tall(X)&humble(X))))=>((~old(susan)<~>~curious(susan))))&
(((generous(paul)<~>tall(paul)))=>(?[X]:(wise(X))))&
((?[X]:((funny(X)|wise(X))))=>(?[X]:(calm(X))))&
(![X]:(happy(X)<=>(humble(X)|~happy(X))))&
(((happy(lucy)|calm(lucy)))<=>(?[X]:((~creative(X)&~curious(X)))))&
(![X]:(brave(X)<=>(humble(X)&generous(X))))&
((?[X]:(~brave(X)))=>(?[X]:((humble(X)|old(X)))))&
(((~old(mary)|tall(mary)))<=>(?[X]:((~generous(X)|~tall(X)))))&
((?[X]:(~old(X)))<=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:(patient(X)=>strong(X)))&
(((humble(paul)<~>~brave(paul)))<=>((calm(mary)<~>patient(mary))))&
((?[X]:((~tall(X)&funny(X))))=>(~tall(alice)))&
(![X]:((~happy(X)|~wise(X))=>patient(X)))&
(![X]:(~wise(X)=>(tall(X)&funny(X))))&
((~creative(alice)|curious(alice)))&
(?[X]:((kind(X)<~>~strong(X))))&
(?[X]:((happy(X)&tall(X))))&
((~kind(lucy)|patient(lucy)))&
((generous(paul)&~kind(paul)))&
(?[X]:(~funny(X)))&
(?[X]:(brave(X)))&
((~tall(paul)|~wise(paul))) | funny(lucy) | [] | null | 0 |
If susan is both strong and rich then someone is either kind or not curious and vice versa.
If someone is both happy and not wise then fred is not tall.
If mary is both not quiet and not generous then someone is not tall or strong.
Everyone who is creative or curious is tall.
If someone is kind or generous then someone is both not calm and not patient and vice versa.
If lucy is wise then susan is creative.
Everyone who is either not funny or humble is both not happy and not brave and vice versa.
Everyone who is not tall is both brave and rich.
Everyone who is kind or not calm is tall or not kind and vice versa.
Everyone who is old is both old and not tall.
If someone is either brave or happy then someone is rich or strong.
If susan is not curious then alice is both brave and calm and vice versa.
If alice is brave or not old then someone is not humble.
If someone is creative then someone is not old and vice versa.
If mary is both tall and not wise then someone is happy or generous and vice versa.
If mary is either old or curious then someone is both not kind and tall.
John is happy.
Fred is both not patient and not creative.
Someone is not calm or not kind.
Mary is happy.
Someone is either old or kind.
Mary is happy or not generous.
Lucy is patient or tall. | Fred is kind. | contradiction | (((strong(susan)&rich(susan)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
((?[X]:((happy(X)&~wise(X))))=>(~tall(fred)))&
(((~quiet(mary)&~generous(mary)))=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((creative(X)|curious(X))=>tall(X)))&
((?[X]:((kind(X)|generous(X))))<=>(?[X]:((~calm(X)&~patient(X)))))&
((wise(lucy))=>(creative(susan)))&
(![X]:((~funny(X)<~>humble(X))<=>(~happy(X)&~brave(X))))&
(![X]:(~tall(X)=>(brave(X)&rich(X))))&
(![X]:((kind(X)|~calm(X))<=>(tall(X)|~kind(X))))&
(![X]:(old(X)=>(old(X)&~tall(X))))&
((?[X]:((brave(X)<~>happy(X))))=>(?[X]:((rich(X)|strong(X)))))&
((~curious(susan))<=>((brave(alice)&calm(alice))))&
(((brave(alice)|~old(alice)))=>(?[X]:(~humble(X))))&
((?[X]:(creative(X)))<=>(?[X]:(~old(X))))&
(((tall(mary)&~wise(mary)))<=>(?[X]:((happy(X)|generous(X)))))&
(((old(mary)<~>curious(mary)))=>(?[X]:((~kind(X)&tall(X)))))&
(happy(john))&
((~patient(fred)&~creative(fred)))&
(?[X]:((~calm(X)|~kind(X))))&
(happy(mary))&
(?[X]:((old(X)<~>kind(X))))&
((happy(mary)|~generous(mary)))&
((patient(lucy)|tall(lucy))) | kind(fred) | [
"p1",
"p8",
"p14",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 621289787492905689185567
% SZS output start Proof for 621289787492905689185567
2. ? [X0] : (~wise(X0) & happy(X0)) => ~tall(fred) [input p1]
9. ! [X0] : ((~calm(X0) | kind(X0)) <=> (~kind(X0) | tall(X0))) [input p8]
15. (~wise(mary) & tall(mary)) <=> ? [X0] : (generous(X0) | happy(X0)) [input p14]
17. happy(john) [input p16]
20. happy(mary) [input p19]
24. kind(fred) [input hypothesis]
29. ~tall(fred) | ! [X0] : (wise(X0) | ~happy(X0)) [ennf transformation 2]
49. ! [X0] : (((~calm(X0) | kind(X0)) | (kind(X0) & ~tall(X0))) & ((~kind(X0) | tall(X0)) | (calm(X0) & ~kind(X0)))) [nnf transformation 9]
50. ! [X0] : ((~calm(X0) | kind(X0) | (kind(X0) & ~tall(X0))) & (~kind(X0) | tall(X0) | (calm(X0) & ~kind(X0)))) [flattening 49]
64. ((~wise(mary) & tall(mary)) | ! [X0] : (~generous(X0) & ~happy(X0))) & (? [X0] : (generous(X0) | happy(X0)) | (wise(mary) | ~tall(mary))) [nnf transformation 15]
65. ((~wise(mary) & tall(mary)) | ! [X0] : (~generous(X0) & ~happy(X0))) & (? [X0] : (generous(X0) | happy(X0)) | wise(mary) | ~tall(mary)) [flattening 64]
66. ((~wise(mary) & tall(mary)) | ! [X0] : (~generous(X0) & ~happy(X0))) & (? [X1] : (generous(X1) | happy(X1)) | wise(mary) | ~tall(mary)) [rectify 65]
67. ? [X1] : (generous(X1) | happy(X1)) => (generous(sK7) | happy(sK7)) [choice axiom]
68. ((~wise(mary) & tall(mary)) | ! [X0] : (~generous(X0) & ~happy(X0))) & ((generous(sK7) | happy(sK7)) | wise(mary) | ~tall(mary)) [skolemisation 66,67]
83. ~tall(fred) | wise(X0) | ~happy(X0) [cnf transformation 29]
100. ~kind(X0) | tall(X0) | ~kind(X0) [cnf transformation 50]
118. ~wise(mary) | ~happy(X0) [cnf transformation 68]
124. happy(john) [cnf transformation 17]
128. happy(mary) [cnf transformation 20]
133. kind(fred) [cnf transformation 24]
134. ~kind(X0) | tall(X0) [duplicate literal removal 100]
165. 7 <=> ! [X0] : (wise(X0) | ~happy(X0)) [avatar definition]
166. ~happy(X0) | wise(X0) <- (7) [avatar component clause 165]
168. 8 <=> tall(fred) [avatar definition]
171. 7 | ~8 [avatar split clause 83,168,165]
269. 31 <=> wise(mary) [avatar definition]
271. ~wise(mary) <- (~31) [avatar component clause 269]
274. 32 <=> ! [X0] : ~happy(X0) [avatar definition]
275. ~happy(X0) <- (32) [avatar component clause 274]
276. 32 | ~31 [avatar split clause 118,269,274]
334. $false <- (32) [resolution 275,124]
337. ~32 [avatar contradiction clause 334]
341. tall(fred) [resolution 134,133]
344. 8 [avatar split clause 341,168]
348. wise(mary) <- (7) [resolution 166,128]
350. $false <- (7, ~31) [subsumption resolution 348,271]
351. ~7 | 31 [avatar contradiction clause 350]
352. $false [avatar sat refutation 171,276,337,344,351]
% SZS output end Proof for 621289787492905689185567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then fred is either not old or curious and vice versa.
If fred is both not kind and not creative then someone is not funny and vice versa.
If paul is either not wise or not quiet then fred is both not happy and tall.
Everyone who is either tall or humble is creative or not creative.
If someone is either generous or not creative then paul is not brave or not wise.
Everyone who is both brave and calm is not rich or not calm and vice versa.
Everyone who is both calm and not humble is curious and vice versa.
Everyone who is either curious or tall is not wise.
Everyone who is either brave or wise is patient or humble and vice versa.
If lucy is creative then lucy is not old or not patient.
If susan is both not creative and not tall then fred is creative and vice versa.
Everyone who is either not quiet or creative is both strong and funny.
Everyone who is not old or not happy is both not rich and not calm.
Everyone who is both brave and not strong is not tall and vice versa.
If someone is both wise and not curious then someone is both generous and tall and vice versa.
If alice is both not generous and kind then fred is curious or not patient and vice versa.
Mary is not kind.
Someone is curious.
Someone is not wise or not quiet.
Paul is either kind or not generous.
Someone is either rich or not quiet.
Someone is not kind.
Alice is not quiet or not old.
Someone is humble or not calm. | Lucy is old. | entailment | ((?[X]:(~wise(X)))<=>((~old(fred)<~>curious(fred))))&
(((~kind(fred)&~creative(fred)))<=>(?[X]:(~funny(X))))&
(((~wise(paul)<~>~quiet(paul)))=>((~happy(fred)&tall(fred))))&
(![X]:((tall(X)<~>humble(X))=>(creative(X)|~creative(X))))&
((?[X]:((generous(X)<~>~creative(X))))=>((~brave(paul)|~wise(paul))))&
(![X]:((brave(X)&calm(X))<=>(~rich(X)|~calm(X))))&
(![X]:((calm(X)&~humble(X))<=>curious(X)))&
(![X]:((curious(X)<~>tall(X))=>~wise(X)))&
(![X]:((brave(X)<~>wise(X))<=>(patient(X)|humble(X))))&
((creative(lucy))=>((~old(lucy)|~patient(lucy))))&
(((~creative(susan)&~tall(susan)))<=>(creative(fred)))&
(![X]:((~quiet(X)<~>creative(X))=>(strong(X)&funny(X))))&
(![X]:((~old(X)|~happy(X))=>(~rich(X)&~calm(X))))&
(![X]:((brave(X)&~strong(X))<=>~tall(X)))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((generous(X)&tall(X)))))&
(((~generous(alice)&kind(alice)))<=>((curious(fred)|~patient(fred))))&
(~kind(mary))&
(?[X]:(curious(X)))&
(?[X]:((~wise(X)|~quiet(X))))&
((kind(paul)<~>~generous(paul)))&
(?[X]:((rich(X)<~>~quiet(X))))&
(?[X]:(~kind(X)))&
((~quiet(alice)|~old(alice)))&
(?[X]:((humble(X)|~calm(X)))) | old(lucy) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 585651348510146899997104
% SZS output start Proof for 585651348510146899997104
6. ! [X0] : ((calm(X0) & brave(X0)) <=> (~calm(X0) | ~rich(X0))) [input p5]
13. ! [X0] : ((~happy(X0) | ~old(X0)) => (~calm(X0) & ~rich(X0))) [input p12]
25. ~old(lucy) [input hypothesis]
36. ! [X0] : ((~calm(X0) & ~rich(X0)) | (happy(X0) & old(X0))) [ennf transformation 13]
49. ! [X0] : (((calm(X0) & brave(X0)) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | (~calm(X0) | ~brave(X0)))) [nnf transformation 6]
50. ! [X0] : (((calm(X0) & brave(X0)) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | ~calm(X0) | ~brave(X0))) [flattening 49]
99. calm(X0) | calm(X0) [cnf transformation 50]
121. ~calm(X0) | old(X0) [cnf transformation 36]
145. ~old(lucy) [cnf transformation 25]
147. calm(X0) [duplicate literal removal 99]
244. old(X0) [subsumption resolution 121,147]
319. $false [subsumption resolution 145,244]
% SZS output end Proof for 585651348510146899997104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not rich.
If someone is not tall then someone is not happy or not funny.
Everyone who is not happy or not tall is not humble.
Everyone who is creative or wise is both patient and wise.
Everyone who is rich is both strong and not quiet and vice versa.
Everyone who is not brave is patient.
Everyone who is either humble or curious is both not generous and not brave and vice versa.
Everyone who is not rich or not humble is creative.
Everyone who is tall is either not calm or funny.
Everyone who is either not brave or wise is either old or kind.
If mary is patient or brave then someone is either wise or not strong and vice versa.
If alice is either not kind or kind then someone is brave.
If someone is both old and creative then someone is not generous or old.
If mary is tall or creative then mary is both not rich and humble and vice versa.
If someone is both rich and not wise then mary is both generous and old.
Everyone who is quiet or not patient is both kind and wise and vice versa.
Someone is either calm or not old.
Someone is both generous and old.
Mary is calm.
Fred is both brave and not curious.
Susan is either not brave or not patient.
Someone is not rich. | Alice is calm. | neutral | (![X]:(tall(X)=>~rich(X)))&
((?[X]:(~tall(X)))=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~happy(X)|~tall(X))=>~humble(X)))&
(![X]:((creative(X)|wise(X))=>(patient(X)&wise(X))))&
(![X]:(rich(X)<=>(strong(X)&~quiet(X))))&
(![X]:(~brave(X)=>patient(X)))&
(![X]:((humble(X)<~>curious(X))<=>(~generous(X)&~brave(X))))&
(![X]:((~rich(X)|~humble(X))=>creative(X)))&
(![X]:(tall(X)=>(~calm(X)<~>funny(X))))&
(![X]:((~brave(X)<~>wise(X))=>(old(X)<~>kind(X))))&
(((patient(mary)|brave(mary)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~kind(alice)<~>kind(alice)))=>(?[X]:(brave(X))))&
((?[X]:((old(X)&creative(X))))=>(?[X]:((~generous(X)|old(X)))))&
(((tall(mary)|creative(mary)))<=>((~rich(mary)&humble(mary))))&
((?[X]:((rich(X)&~wise(X))))=>((generous(mary)&old(mary))))&
(![X]:((quiet(X)|~patient(X))<=>(kind(X)&wise(X))))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((generous(X)&old(X))))&
(calm(mary))&
((brave(fred)&~curious(fred)))&
((~brave(susan)<~>~patient(susan)))&
(?[X]:(~rich(X))) | calm(alice) | [] | null | 0 |
Everyone who is either not humble or humble is patient or not curious and vice versa. Everyone who is both happy and brave is not happy and vice versa. Everyone who is both not kind and tall is both calm and not old and vice versa. If paul is both not creative and funny then fred is rich and vice versa. If someone is either generous or not happy then john is either humble or happy. Everyone who is not curious is either not kind or kind and vice versa. If someone is both not old and old then mary is both old and humble and vice versa. Everyone who is not creative or quiet is either not creative or not old and vice versa. If someone is not wise or funny then someone is strong and vice versa. If alice is funny or not tall then someone is not tall or calm. Everyone who is not old or not patient is either tall or humble and vice versa. If john is either kind or not curious then susan is both not brave and not funny. If someone is either not happy or rich then fred is not creative or not tall. Everyone who is both wise and patient is funny. If susan is humble or brave then susan is both patient and not wise. Everyone who is either not humble or wise is not calm or happy and vice versa. Mary is either kind or old. John is either strong or not funny. Lucy is tall or not kind. Alice is old. Someone is creative. John is strong. Someone is either not generous or strong. Someone is not patient. | Alice is not happy. | contradiction | (![X]:((~humble(X)<~>humble(X))<=>(patient(X)|~curious(X))))&
(![X]:((happy(X)&brave(X))<=>~happy(X)))&
(![X]:((~kind(X)&tall(X))<=>(calm(X)&~old(X))))&
(((~creative(paul)&funny(paul)))<=>(rich(fred)))&
((?[X]:((generous(X)<~>~happy(X))))=>((humble(john)<~>happy(john))))&
(![X]:(~curious(X)<=>(~kind(X)<~>kind(X))))&
((?[X]:((~old(X)&old(X))))<=>((old(mary)&humble(mary))))&
(![X]:((~creative(X)|quiet(X))<=>(~creative(X)<~>~old(X))))&
((?[X]:((~wise(X)|funny(X))))<=>(?[X]:(strong(X))))&
(((funny(alice)|~tall(alice)))=>(?[X]:((~tall(X)|calm(X)))))&
(![X]:((~old(X)|~patient(X))<=>(tall(X)<~>humble(X))))&
(((kind(john)<~>~curious(john)))=>((~brave(susan)&~funny(susan))))&
((?[X]:((~happy(X)<~>rich(X))))=>((~creative(fred)|~tall(fred))))&
(![X]:((wise(X)&patient(X))=>funny(X)))&
(((humble(susan)|brave(susan)))=>((patient(susan)&~wise(susan))))&
(![X]:((~humble(X)<~>wise(X))<=>(~calm(X)|happy(X))))&
((kind(mary)<~>old(mary)))&
((strong(john)<~>~funny(john)))&
((tall(lucy)|~kind(lucy)))&
(old(alice))&
(?[X]:(creative(X)))&
(strong(john))&
(?[X]:((~generous(X)<~>strong(X))))&
(?[X]:(~patient(X))) | ~happy(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1002696298947653264844486
% SZS output start Proof for 1002696298947653264844486
2. ! [X0] : ((brave(X0) & happy(X0)) <=> ~happy(X0)) [input p1]
25. ~happy(alice) [input hypothesis]
37. ! [X0] : (((brave(X0) & happy(X0)) | happy(X0)) & (~happy(X0) | (~brave(X0) | ~happy(X0)))) [nnf transformation 2]
38. ! [X0] : (((brave(X0) & happy(X0)) | happy(X0)) & (~happy(X0) | ~brave(X0) | ~happy(X0))) [flattening 37]
81. happy(X0) | happy(X0) [cnf transformation 38]
147. ~happy(alice) [cnf transformation 25]
153. happy(X0) [duplicate literal removal 81]
315. $false [subsumption resolution 147,153]
% SZS output end Proof for 1002696298947653264844486
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not curious is wise or not tall and vice versa.
Everyone who is either patient or calm is not strong.
Everyone who is not patient is not curious or not brave.
Everyone who is either curious or not generous is either old or not quiet.
Everyone who is either quiet or not curious is both not brave and not old and vice versa.
Everyone who is happy or quiet is both quiet and not funny.
If someone is either tall or calm then alice is not quiet or not patient.
If someone is both tall and not happy then susan is calm.
If someone is either not creative or strong then john is either wise or not curious.
If someone is not wise then john is both not funny and brave and vice versa.
If someone is not calm or happy then susan is not tall and vice versa.
Everyone who is wise is either not funny or quiet and vice versa.
If lucy is calm or creative then paul is not wise and vice versa.
If paul is both not rich and old then someone is happy and vice versa.
Everyone who is both funny and not rich is happy or rich and vice versa.
Everyone who is both not strong and funny is not wise or generous and vice versa.
Someone is not rich or not quiet.
Susan is either creative or not brave.
Someone is not quiet.
Someone is both tall and strong.
Someone is either not generous or not calm.
Alice is humble. | Lucy is not quiet. | entailment | (![X]:((brave(X)<~>~curious(X))<=>(wise(X)|~tall(X))))&
(![X]:((patient(X)<~>calm(X))=>~strong(X)))&
(![X]:(~patient(X)=>(~curious(X)|~brave(X))))&
(![X]:((curious(X)<~>~generous(X))=>(old(X)<~>~quiet(X))))&
(![X]:((quiet(X)<~>~curious(X))<=>(~brave(X)&~old(X))))&
(![X]:((happy(X)|quiet(X))=>(quiet(X)&~funny(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~quiet(alice)|~patient(alice))))&
((?[X]:((tall(X)&~happy(X))))=>(calm(susan)))&
((?[X]:((~creative(X)<~>strong(X))))=>((wise(john)<~>~curious(john))))&
((?[X]:(~wise(X)))<=>((~funny(john)&brave(john))))&
((?[X]:((~calm(X)|happy(X))))<=>(~tall(susan)))&
(![X]:(wise(X)<=>(~funny(X)<~>quiet(X))))&
(((calm(lucy)|creative(lucy)))<=>(~wise(paul)))&
(((~rich(paul)&old(paul)))<=>(?[X]:(happy(X))))&
(![X]:((funny(X)&~rich(X))<=>(happy(X)|rich(X))))&
(![X]:((~strong(X)&funny(X))<=>(~wise(X)|generous(X))))&
(?[X]:((~rich(X)|~quiet(X))))&
((creative(susan)<~>~brave(susan)))&
(?[X]:(~quiet(X)))&
(?[X]:((tall(X)&strong(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(humble(alice)) | ~quiet(lucy) | [
"p5",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 42640292504394306006137
% SZS output start Proof for 42640292504394306006137
6. ! [X0] : ((quiet(X0) | happy(X0)) => (~funny(X0) & quiet(X0))) [input p5]
12. ! [X0] : (wise(X0) <=> (~funny(X0) <~> quiet(X0))) [input p11]
15. ! [X0] : ((~rich(X0) & funny(X0)) <=> (rich(X0) | happy(X0))) [input p14]
16. ! [X0] : ((funny(X0) & ~strong(X0)) <=> (generous(X0) | ~wise(X0))) [input p15]
23. quiet(lucy) [input hypothesis]
29. ! [X0] : ((~funny(X0) & quiet(X0)) | (~quiet(X0) & ~happy(X0))) [ennf transformation 6]
51. ! [X0] : ((wise(X0) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0)))) & (((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | ~wise(X0))) [nnf transformation 12]
59. ! [X0] : (((~rich(X0) & funny(X0)) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | (rich(X0) | ~funny(X0)))) [nnf transformation 15]
60. ! [X0] : (((~rich(X0) & funny(X0)) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | rich(X0) | ~funny(X0))) [flattening 59]
61. ! [X0] : (((funny(X0) & ~strong(X0)) | (~generous(X0) & wise(X0))) & ((generous(X0) | ~wise(X0)) | (~funny(X0) | strong(X0)))) [nnf transformation 16]
62. ! [X0] : (((funny(X0) & ~strong(X0)) | (~generous(X0) & wise(X0))) & (generous(X0) | ~wise(X0) | ~funny(X0) | strong(X0))) [flattening 61]
94. ~funny(X0) | ~happy(X0) [cnf transformation 29]
95. ~funny(X0) | ~quiet(X0) [cnf transformation 29]
110. ~quiet(X0) | funny(X0) | ~wise(X0) [cnf transformation 51]
119. rich(X0) | happy(X0) | rich(X0) | ~funny(X0) [cnf transformation 60]
123. ~rich(X0) | ~rich(X0) [cnf transformation 60]
127. funny(X0) | wise(X0) [cnf transformation 62]
137. quiet(lucy) [cnf transformation 23]
138. rich(X0) | happy(X0) | ~funny(X0) [duplicate literal removal 119]
139. ~rich(X0) [duplicate literal removal 123]
196. 14 <=> ! [X1] : wise(X1) [avatar definition]
197. wise(X1) <- (14) [avatar component clause 196]
221. ~quiet(X0) | ~wise(X0) [subsumption resolution 110,95]
255. happy(X0) | ~funny(X0) [subsumption resolution 138,139]
256. ~funny(X0) [subsumption resolution 255,94]
258. wise(X0) [subsumption resolution 127,256]
259. 14 [avatar split clause 258,196]
279. ~wise(lucy) [resolution 221,137]
280. $false <- (14) [subsumption resolution 279,197]
281. ~14 [avatar contradiction clause 280]
282. $false [avatar sat refutation 259,281]
% SZS output end Proof for 42640292504394306006137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or funny is either calm or funny. Everyone who is both strong and not patient is happy. Everyone who is humble or not generous is not curious or not tall. Everyone who is not creative is calm and vice versa. If susan is rich then someone is either not patient or old. If someone is both quiet and curious then john is both not generous and not quiet and vice versa. Everyone who is not calm or curious is creative or not generous and vice versa. If someone is calm then alice is either not happy or not patient and vice versa. If someone is not generous then someone is either not kind or happy and vice versa. Everyone who is both not old and not creative is not calm and vice versa. If mary is wise then john is calm. Everyone who is both not humble and strong is not generous or quiet. Everyone who is not old is either not rich or tall. Everyone who is both not kind and not wise is both old and patient and vice versa. If someone is both not strong and not tall then someone is either tall or not generous. Someone is either curious or generous. Someone is not brave or not funny. Mary is not quiet or funny. Susan is either old or strong. Lucy is both wise and curious. | Lucy is not brave. | neutral | (![X]:((~calm(X)|funny(X))=>(calm(X)<~>funny(X))))&
(![X]:((strong(X)&~patient(X))=>happy(X)))&
(![X]:((humble(X)|~generous(X))=>(~curious(X)|~tall(X))))&
(![X]:(~creative(X)<=>calm(X)))&
((rich(susan))=>(?[X]:((~patient(X)<~>old(X)))))&
((?[X]:((quiet(X)&curious(X))))<=>((~generous(john)&~quiet(john))))&
(![X]:((~calm(X)|curious(X))<=>(creative(X)|~generous(X))))&
((?[X]:(calm(X)))<=>((~happy(alice)<~>~patient(alice))))&
((?[X]:(~generous(X)))<=>(?[X]:((~kind(X)<~>happy(X)))))&
(![X]:((~old(X)&~creative(X))<=>~calm(X)))&
((wise(mary))=>(calm(john)))&
(![X]:((~humble(X)&strong(X))=>(~generous(X)|quiet(X))))&
(![X]:(~old(X)=>(~rich(X)<~>tall(X))))&
(![X]:((~kind(X)&~wise(X))<=>(old(X)&patient(X))))&
((?[X]:((~strong(X)&~tall(X))))=>(?[X]:((tall(X)<~>~generous(X)))))&
(?[X]:((curious(X)<~>generous(X))))&
(?[X]:((~brave(X)|~funny(X))))&
((~quiet(mary)|funny(mary)))&
((old(susan)<~>strong(susan)))&
((wise(lucy)&curious(lucy))) | ~brave(lucy) | [] | null | 0 |
If mary is both old and not patient then john is either brave or not generous and vice versa.
Everyone who is either creative or patient is old or not funny and vice versa.
Everyone who is calm is both patient and not strong and vice versa.
Everyone who is strong is either happy or not calm.
Everyone who is both not patient and not happy is strong or not generous.
If john is both not humble and wise then someone is not strong or brave.
If someone is both not tall and not rich then fred is both funny and quiet and vice versa.
Everyone who is either not brave or tall is not funny or strong and vice versa.
Everyone who is patient or not rich is both happy and rich and vice versa.
Everyone who is both wise and creative is curious or tall and vice versa.
If someone is tall then susan is either curious or not patient and vice versa.
Everyone who is not brave is strong.
Everyone who is not happy or not old is not wise and vice versa.
If lucy is either tall or not quiet then paul is wise.
If john is not brave or calm then fred is both not strong and not kind.
Everyone who is both quiet and creative is not funny and vice versa.
Someone is old or not funny.
Someone is either brave or funny.
Paul is not kind.
Someone is either not happy or not quiet.
Fred is not kind or rich.
Someone is old or not happy. | Mary is not rich. | contradiction | (((old(mary)&~patient(mary)))<=>((brave(john)<~>~generous(john))))&
(![X]:((creative(X)<~>patient(X))<=>(old(X)|~funny(X))))&
(![X]:(calm(X)<=>(patient(X)&~strong(X))))&
(![X]:(strong(X)=>(happy(X)<~>~calm(X))))&
(![X]:((~patient(X)&~happy(X))=>(strong(X)|~generous(X))))&
(((~humble(john)&wise(john)))=>(?[X]:((~strong(X)|brave(X)))))&
((?[X]:((~tall(X)&~rich(X))))<=>((funny(fred)&quiet(fred))))&
(![X]:((~brave(X)<~>tall(X))<=>(~funny(X)|strong(X))))&
(![X]:((patient(X)|~rich(X))<=>(happy(X)&rich(X))))&
(![X]:((wise(X)&creative(X))<=>(curious(X)|tall(X))))&
((?[X]:(tall(X)))<=>((curious(susan)<~>~patient(susan))))&
(![X]:(~brave(X)=>strong(X)))&
(![X]:((~happy(X)|~old(X))<=>~wise(X)))&
(((tall(lucy)<~>~quiet(lucy)))=>(wise(paul)))&
(((~brave(john)|calm(john)))=>((~strong(fred)&~kind(fred))))&
(![X]:((quiet(X)&creative(X))<=>~funny(X)))&
(?[X]:((old(X)|~funny(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(~kind(paul))&
(?[X]:((~happy(X)<~>~quiet(X))))&
((~kind(fred)|rich(fred)))&
(?[X]:((old(X)|~happy(X)))) | ~rich(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1618639735219788495614229
% SZS output start Proof for 1618639735219788495614229
9. ! [X0] : ((~rich(X0) | patient(X0)) <=> (rich(X0) & happy(X0))) [input p8]
23. ~rich(mary) [input hypothesis]
48. ! [X0] : (((~rich(X0) | patient(X0)) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | (rich(X0) & ~patient(X0)))) [nnf transformation 9]
49. ! [X0] : ((~rich(X0) | patient(X0) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | (rich(X0) & ~patient(X0)))) [flattening 48]
102. rich(X0) | rich(X0) [cnf transformation 49]
130. ~rich(mary) [cnf transformation 23]
131. rich(X0) [duplicate literal removal 102]
260. $false [subsumption resolution 130,131]
% SZS output end Proof for 1618639735219788495614229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is either kind or curious.
If mary is rich or not wise then someone is both patient and not tall.
If someone is tall then susan is curious.
If someone is not brave or generous then alice is either not old or not tall and vice versa.
If fred is both tall and not kind then susan is creative and vice versa.
Everyone who is happy is not quiet.
Everyone who is both patient and kind is not patient or patient.
Everyone who is both not tall and not humble is not wise and vice versa.
Everyone who is not happy or not patient is both not happy and generous.
If mary is patient then someone is both creative and not kind and vice versa.
Everyone who is not patient is wise and vice versa.
Everyone who is not strong or not generous is not strong or not brave and vice versa.
If someone is generous then someone is not funny or generous and vice versa.
Everyone who is not wise or calm is brave and vice versa.
If mary is either not patient or not brave then someone is happy or rich and vice versa.
Everyone who is tall is generous or brave.
Someone is quiet or not generous.
Paul is both not tall and not brave.
Fred is either curious or not generous.
Alice is both not patient and not rich.
Someone is not old.
Someone is not strong. | Mary is creative. | neutral | (![X]:(~brave(X)=>(kind(X)<~>curious(X))))&
(((rich(mary)|~wise(mary)))=>(?[X]:((patient(X)&~tall(X)))))&
((?[X]:(tall(X)))=>(curious(susan)))&
((?[X]:((~brave(X)|generous(X))))<=>((~old(alice)<~>~tall(alice))))&
(((tall(fred)&~kind(fred)))<=>(creative(susan)))&
(![X]:(happy(X)=>~quiet(X)))&
(![X]:((patient(X)&kind(X))=>(~patient(X)|patient(X))))&
(![X]:((~tall(X)&~humble(X))<=>~wise(X)))&
(![X]:((~happy(X)|~patient(X))=>(~happy(X)&generous(X))))&
((patient(mary))<=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:(~patient(X)<=>wise(X)))&
(![X]:((~strong(X)|~generous(X))<=>(~strong(X)|~brave(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((~wise(X)|calm(X))<=>brave(X)))&
(((~patient(mary)<~>~brave(mary)))<=>(?[X]:((happy(X)|rich(X)))))&
(![X]:(tall(X)=>(generous(X)|brave(X))))&
(?[X]:((quiet(X)|~generous(X))))&
((~tall(paul)&~brave(paul)))&
((curious(fred)<~>~generous(fred)))&
((~patient(alice)&~rich(alice)))&
(?[X]:(~old(X)))&
(?[X]:(~strong(X))) | creative(mary) | [] | null | 0 |
If susan is not curious then someone is both not quiet and tall and vice versa.
Everyone who is either curious or calm is either calm or not curious.
Everyone who is both kind and patient is either not calm or strong and vice versa.
Everyone who is both not brave and calm is brave and vice versa.
If john is both not curious and not happy then lucy is both not rich and generous.
If someone is not funny then susan is strong.
If someone is tall or not funny then lucy is both not curious and tall.
Everyone who is not old or not quiet is rich or not calm and vice versa.
Everyone who is both humble and not curious is either patient or not old.
Everyone who is both not patient and not curious is both rich and not funny and vice versa.
If someone is either calm or wise then someone is either humble or tall and vice versa.
If mary is both quiet and calm then someone is both happy and not brave and vice versa.
If someone is both old and not humble then paul is calm or wise.
If someone is either not wise or creative then someone is either not wise or humble and vice versa.
If alice is either not generous or not tall then alice is wise.
Everyone who is tall or not humble is either kind or brave.
Someone is both kind and not wise.
Fred is both creative and not generous.
John is either generous or rich.
Someone is rich or calm.
Mary is wise or not calm.
Someone is rich.
Someone is either not generous or funny. | Alice is old. | neutral | ((~curious(susan))<=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((curious(X)<~>calm(X))=>(calm(X)<~>~curious(X))))&
(![X]:((kind(X)&patient(X))<=>(~calm(X)<~>strong(X))))&
(![X]:((~brave(X)&calm(X))<=>brave(X)))&
(((~curious(john)&~happy(john)))=>((~rich(lucy)&generous(lucy))))&
((?[X]:(~funny(X)))=>(strong(susan)))&
((?[X]:((tall(X)|~funny(X))))=>((~curious(lucy)&tall(lucy))))&
(![X]:((~old(X)|~quiet(X))<=>(rich(X)|~calm(X))))&
(![X]:((humble(X)&~curious(X))=>(patient(X)<~>~old(X))))&
(![X]:((~patient(X)&~curious(X))<=>(rich(X)&~funny(X))))&
((?[X]:((calm(X)<~>wise(X))))<=>(?[X]:((humble(X)<~>tall(X)))))&
(((quiet(mary)&calm(mary)))<=>(?[X]:((happy(X)&~brave(X)))))&
((?[X]:((old(X)&~humble(X))))=>((calm(paul)|wise(paul))))&
((?[X]:((~wise(X)<~>creative(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(((~generous(alice)<~>~tall(alice)))=>(wise(alice)))&
(![X]:((tall(X)|~humble(X))=>(kind(X)<~>brave(X))))&
(?[X]:((kind(X)&~wise(X))))&
((creative(fred)&~generous(fred)))&
((generous(john)<~>rich(john)))&
(?[X]:((rich(X)|calm(X))))&
((wise(mary)|~calm(mary)))&
(?[X]:(rich(X)))&
(?[X]:((~generous(X)<~>funny(X)))) | old(alice) | [] | null | 0 |
Everyone who is both not tall and old is either not tall or happy and vice versa.
Everyone who is either wise or happy is strong or tall and vice versa.
Everyone who is patient is both tall and not quiet and vice versa.
Everyone who is not happy or not generous is not quiet and vice versa.
If lucy is calm or not strong then someone is both kind and generous and vice versa.
If someone is either wise or not old then someone is either rich or not old.
If someone is not funny then someone is both humble and rich and vice versa.
If john is both not calm and not brave then someone is not funny and vice versa.
If someone is both not tall and patient then someone is calm or quiet.
Everyone who is tall is both not strong and not quiet and vice versa.
If paul is either generous or brave then someone is either patient or not rich and vice versa.
If someone is not creative or not wise then someone is either not funny or not wise.
Everyone who is rich is either not generous or not calm.
Everyone who is not rich is not kind.
Everyone who is not creative or funny is either not curious or humble.
Everyone who is happy or quiet is either old or tall and vice versa.
Someone is wise.
Someone is kind or quiet.
Someone is either not curious or quiet.
Lucy is either not patient or rich.
Someone is old.
Mary is not strong.
Someone is both not happy and not creative. | John is patient. | entailment | (![X]:((~tall(X)&old(X))<=>(~tall(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))<=>(strong(X)|tall(X))))&
(![X]:(patient(X)<=>(tall(X)&~quiet(X))))&
(![X]:((~happy(X)|~generous(X))<=>~quiet(X)))&
(((calm(lucy)|~strong(lucy)))<=>(?[X]:((kind(X)&generous(X)))))&
((?[X]:((wise(X)<~>~old(X))))=>(?[X]:((rich(X)<~>~old(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((humble(X)&rich(X)))))&
(((~calm(john)&~brave(john)))<=>(?[X]:(~funny(X))))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:(tall(X)<=>(~strong(X)&~quiet(X))))&
(((generous(paul)<~>brave(paul)))<=>(?[X]:((patient(X)<~>~rich(X)))))&
((?[X]:((~creative(X)|~wise(X))))=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:(rich(X)=>(~generous(X)<~>~calm(X))))&
(![X]:(~rich(X)=>~kind(X)))&
(![X]:((~creative(X)|funny(X))=>(~curious(X)<~>humble(X))))&
(![X]:((happy(X)|quiet(X))<=>(old(X)<~>tall(X))))&
(?[X]:(wise(X)))&
(?[X]:((kind(X)|quiet(X))))&
(?[X]:((~curious(X)<~>quiet(X))))&
((~patient(lucy)<~>rich(lucy)))&
(?[X]:(old(X)))&
(~strong(mary))&
(?[X]:((~happy(X)&~creative(X)))) | patient(john) | [
"p0",
"p2",
"p3",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4690584382592784579810659
% SZS output start Proof for 4690584382592784579810659
1. ! [X0] : ((old(X0) & ~tall(X0)) <=> (~tall(X0) <~> happy(X0))) [input p0]
3. ! [X0] : (patient(X0) <=> (~quiet(X0) & tall(X0))) [input p2]
4. ! [X0] : ((~generous(X0) | ~happy(X0)) <=> ~quiet(X0)) [input p3]
10. ! [X0] : (tall(X0) <=> (~quiet(X0) & ~strong(X0))) [input p9]
16. ! [X0] : ((quiet(X0) | happy(X0)) <=> (old(X0) <~> tall(X0))) [input p15]
24. ~patient(john) [input hypothesis]
35. ! [X0] : (((old(X0) & ~tall(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) & (((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | (~old(X0) | tall(X0)))) [nnf transformation 1]
36. ! [X0] : (((old(X0) & ~tall(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) & (((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | ~old(X0) | tall(X0))) [flattening 35]
39. ! [X0] : ((patient(X0) | (quiet(X0) | ~tall(X0))) & ((~quiet(X0) & tall(X0)) | ~patient(X0))) [nnf transformation 3]
40. ! [X0] : ((patient(X0) | quiet(X0) | ~tall(X0)) & ((~quiet(X0) & tall(X0)) | ~patient(X0))) [flattening 39]
41. ! [X0] : (((~generous(X0) | ~happy(X0)) | quiet(X0)) & (~quiet(X0) | (generous(X0) & happy(X0)))) [nnf transformation 4]
42. ! [X0] : ((~generous(X0) | ~happy(X0) | quiet(X0)) & (~quiet(X0) | (generous(X0) & happy(X0)))) [flattening 41]
65. ! [X0] : ((tall(X0) | (quiet(X0) | strong(X0))) & ((~quiet(X0) & ~strong(X0)) | ~tall(X0))) [nnf transformation 10]
66. ! [X0] : ((tall(X0) | quiet(X0) | strong(X0)) & ((~quiet(X0) & ~strong(X0)) | ~tall(X0))) [flattening 65]
77. ! [X0] : (((quiet(X0) | happy(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~quiet(X0) & ~happy(X0)))) [nnf transformation 16]
78. ! [X0] : ((quiet(X0) | happy(X0) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~quiet(X0) & ~happy(X0)))) [flattening 77]
92. ~happy(X0) | tall(X0) | ~old(X0) | tall(X0) [cnf transformation 36]
94. ~tall(X0) | ~tall(X0) | ~happy(X0) [cnf transformation 36]
95. happy(X0) | old(X0) | tall(X0) [cnf transformation 36]
96. ~happy(X0) | ~tall(X0) | old(X0) [cnf transformation 36]
105. ~tall(X0) | quiet(X0) | patient(X0) [cnf transformation 40]
106. ~quiet(X0) | happy(X0) [cnf transformation 42]
126. ~quiet(X0) | ~tall(X0) [cnf transformation 66]
147. tall(X0) | old(X0) | ~happy(X0) [cnf transformation 78]
151. quiet(X0) | happy(X0) | tall(X0) | ~old(X0) [cnf transformation 78]
152. quiet(X0) | happy(X0) | old(X0) | ~tall(X0) [cnf transformation 78]
163. ~patient(john) [cnf transformation 24]
164. ~happy(X0) | tall(X0) | ~old(X0) [duplicate literal removal 92]
165. ~happy(X0) | ~tall(X0) [duplicate literal removal 94]
166. ~happy(X0) | ~old(X0) [subsumption resolution 164,165]
295. quiet(X0) | happy(X0) | old(X0) [subsumption resolution 152,95]
296. happy(X0) | old(X0) [subsumption resolution 295,106]
297. ~old(X0) | tall(X0) | quiet(X0) [subsumption resolution 151,166]
299. old(X0) | ~happy(X0) [subsumption resolution 147,96]
300. ~happy(X0) [subsumption resolution 299,166]
338. old(X2) [resolution 296,300]
405. quiet(X0) | tall(X0) [resolution 297,338]
501. tall(X3) | happy(X3) [resolution 405,106]
504. tall(X3) [subsumption resolution 501,300]
525. quiet(X0) | patient(X0) [resolution 504,105]
532. patient(X1) | ~tall(X1) [resolution 525,126]
537. patient(X1) [subsumption resolution 532,504]
539. $false [resolution 537,163]
% SZS output end Proof for 4690584382592784579810659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is not old or humble and vice versa.
Everyone who is both generous and rich is not kind and vice versa.
Everyone who is either not kind or creative is not old or humble.
If susan is not curious then someone is either quiet or not creative.
If mary is either not calm or tall then alice is not kind or brave.
Everyone who is not humble or kind is quiet.
Everyone who is quiet or not generous is rich.
If someone is not strong or generous then someone is kind and vice versa.
If someone is either not patient or patient then mary is both generous and not kind.
If lucy is not generous then john is either wise or not curious and vice versa.
Everyone who is both quiet and not rich is either funny or not wise and vice versa.
Everyone who is both not curious and creative is strong.
Everyone who is either not strong or not humble is not funny.
If someone is not old or creative then paul is funny or not wise.
If mary is either not patient or curious then mary is either not patient or not old and vice versa.
Everyone who is not happy or funny is not creative or not wise and vice versa.
Alice is either rich or happy.
Alice is wise or brave.
Someone is both tall and not curious.
John is not tall.
Alice is both wise and not humble.
Someone is not happy.
Mary is kind or not creative. | Paul is humble. | neutral | (![X]:(~quiet(X)<=>(~old(X)|humble(X))))&
(![X]:((generous(X)&rich(X))<=>~kind(X)))&
(![X]:((~kind(X)<~>creative(X))=>(~old(X)|humble(X))))&
((~curious(susan))=>(?[X]:((quiet(X)<~>~creative(X)))))&
(((~calm(mary)<~>tall(mary)))=>((~kind(alice)|brave(alice))))&
(![X]:((~humble(X)|kind(X))=>quiet(X)))&
(![X]:((quiet(X)|~generous(X))=>rich(X)))&
((?[X]:((~strong(X)|generous(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~patient(X)<~>patient(X))))=>((generous(mary)&~kind(mary))))&
((~generous(lucy))<=>((wise(john)<~>~curious(john))))&
(![X]:((quiet(X)&~rich(X))<=>(funny(X)<~>~wise(X))))&
(![X]:((~curious(X)&creative(X))=>strong(X)))&
(![X]:((~strong(X)<~>~humble(X))=>~funny(X)))&
((?[X]:((~old(X)|creative(X))))=>((funny(paul)|~wise(paul))))&
(((~patient(mary)<~>curious(mary)))<=>((~patient(mary)<~>~old(mary))))&
(![X]:((~happy(X)|funny(X))<=>(~creative(X)|~wise(X))))&
((rich(alice)<~>happy(alice)))&
((wise(alice)|brave(alice)))&
(?[X]:((tall(X)&~curious(X))))&
(~tall(john))&
((wise(alice)&~humble(alice)))&
(?[X]:(~happy(X)))&
((kind(mary)|~creative(mary))) | humble(paul) | [] | null | 0 |
Everyone who is strong is either not creative or tall.
Everyone who is both not strong and generous is both creative and quiet.
Everyone who is both not tall and kind is both not curious and not rich.
Everyone who is not strong is humble or curious.
If someone is not old or not tall then john is either not generous or not curious.
If someone is both creative and rich then susan is both old and kind.
Everyone who is humble is either not brave or not rich and vice versa.
Everyone who is generous or not funny is not old and vice versa.
If someone is rich or kind then alice is both curious and humble.
Everyone who is strong is both rich and not old and vice versa.
If susan is not curious or brave then someone is both wise and not quiet.
Everyone who is either not humble or rich is patient or wise.
If someone is both quiet and not tall then someone is kind and vice versa.
If paul is creative or not quiet then someone is wise or calm and vice versa.
If someone is both not brave and not patient then john is both generous and not generous.
Everyone who is not funny is generous or not funny.
Paul is funny or kind.
Alice is both curious and happy.
Lucy is wise.
Someone is not calm or not strong.
Someone is either happy or not kind.
Someone is both not creative and tall.
Mary is both quiet and brave.
Susan is not old. | Susan is patient. | neutral | (![X]:(strong(X)=>(~creative(X)<~>tall(X))))&
(![X]:((~strong(X)&generous(X))=>(creative(X)&quiet(X))))&
(![X]:((~tall(X)&kind(X))=>(~curious(X)&~rich(X))))&
(![X]:(~strong(X)=>(humble(X)|curious(X))))&
((?[X]:((~old(X)|~tall(X))))=>((~generous(john)<~>~curious(john))))&
((?[X]:((creative(X)&rich(X))))=>((old(susan)&kind(susan))))&
(![X]:(humble(X)<=>(~brave(X)<~>~rich(X))))&
(![X]:((generous(X)|~funny(X))<=>~old(X)))&
((?[X]:((rich(X)|kind(X))))=>((curious(alice)&humble(alice))))&
(![X]:(strong(X)<=>(rich(X)&~old(X))))&
(((~curious(susan)|brave(susan)))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:((~humble(X)<~>rich(X))=>(patient(X)|wise(X))))&
((?[X]:((quiet(X)&~tall(X))))<=>(?[X]:(kind(X))))&
(((creative(paul)|~quiet(paul)))<=>(?[X]:((wise(X)|calm(X)))))&
((?[X]:((~brave(X)&~patient(X))))=>((generous(john)&~generous(john))))&
(![X]:(~funny(X)=>(generous(X)|~funny(X))))&
((funny(paul)|kind(paul)))&
((curious(alice)&happy(alice)))&
(wise(lucy))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:((happy(X)<~>~kind(X))))&
(?[X]:((~creative(X)&tall(X))))&
((quiet(mary)&brave(mary)))&
(~old(susan)) | patient(susan) | [] | null | 0 |
If someone is not tall then paul is not kind or generous and vice versa.
Everyone who is humble or not rich is rich or funny and vice versa.
Everyone who is both not curious and brave is not curious or strong.
If someone is generous then susan is either not happy or not patient.
If susan is both not brave and not kind then alice is both humble and brave.
If someone is either not generous or creative then someone is not happy.
Everyone who is rich or not kind is not curious or curious.
Everyone who is either not creative or patient is kind or not generous.
Everyone who is both old and not rich is both happy and patient and vice versa.
Everyone who is not patient is tall or strong.
Everyone who is not funny or not curious is not patient or tall.
Everyone who is not wise is not humble or kind and vice versa.
If susan is not funny or tall then someone is humble or not tall.
Everyone who is both not happy and not funny is tall.
Everyone who is not calm is both curious and not kind and vice versa.
Everyone who is either not strong or not wise is not brave or not tall.
Someone is not strong.
Alice is both not brave and not funny.
Someone is both not brave and humble.
Someone is both old and not quiet.
Paul is calm.
Someone is humble.
Alice is patient.
Someone is either funny or rich. | Paul is creative. | neutral | ((?[X]:(~tall(X)))<=>((~kind(paul)|generous(paul))))&
(![X]:((humble(X)|~rich(X))<=>(rich(X)|funny(X))))&
(![X]:((~curious(X)&brave(X))=>(~curious(X)|strong(X))))&
((?[X]:(generous(X)))=>((~happy(susan)<~>~patient(susan))))&
(((~brave(susan)&~kind(susan)))=>((humble(alice)&brave(alice))))&
((?[X]:((~generous(X)<~>creative(X))))=>(?[X]:(~happy(X))))&
(![X]:((rich(X)|~kind(X))=>(~curious(X)|curious(X))))&
(![X]:((~creative(X)<~>patient(X))=>(kind(X)|~generous(X))))&
(![X]:((old(X)&~rich(X))<=>(happy(X)&patient(X))))&
(![X]:(~patient(X)=>(tall(X)|strong(X))))&
(![X]:((~funny(X)|~curious(X))=>(~patient(X)|tall(X))))&
(![X]:(~wise(X)<=>(~humble(X)|kind(X))))&
(((~funny(susan)|tall(susan)))=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((~happy(X)&~funny(X))=>tall(X)))&
(![X]:(~calm(X)<=>(curious(X)&~kind(X))))&
(![X]:((~strong(X)<~>~wise(X))=>(~brave(X)|~tall(X))))&
(?[X]:(~strong(X)))&
((~brave(alice)&~funny(alice)))&
(?[X]:((~brave(X)&humble(X))))&
(?[X]:((old(X)&~quiet(X))))&
(calm(paul))&
(?[X]:(humble(X)))&
(patient(alice))&
(?[X]:((funny(X)<~>rich(X)))) | creative(paul) | [] | null | 0 |
Everyone who is not rich is both quiet and not creative and vice versa.
If someone is not patient then someone is happy.
Everyone who is both not calm and not generous is either not rich or calm.
Everyone who is both not creative and curious is old or curious and vice versa.
If paul is not brave or not creative then someone is either not kind or patient and vice versa.
Everyone who is not tall is not brave or not calm and vice versa.
Everyone who is not funny is both strong and humble.
Everyone who is wise or not tall is not humble and vice versa.
Everyone who is not wise or not happy is either not brave or creative and vice versa.
If john is not kind or curious then paul is either not funny or tall.
If someone is happy or not quiet then alice is both not humble and rich and vice versa.
If someone is both not brave and not humble then susan is not old.
Everyone who is not old is strong or not funny.
Everyone who is not brave is not kind.
If someone is either not curious or kind then mary is both kind and patient and vice versa.
Everyone who is not quiet is not brave or not rich.
Susan is either kind or old.
Someone is both not kind and not tall.
Someone is either not strong or not creative.
Mary is calm.
Someone is both not curious and not tall.
Someone is both old and quiet.
Mary is both not humble and not wise.
Susan is not tall or not generous. | Susan is old. | contradiction | (![X]:(~rich(X)<=>(quiet(X)&~creative(X))))&
((?[X]:(~patient(X)))=>(?[X]:(happy(X))))&
(![X]:((~calm(X)&~generous(X))=>(~rich(X)<~>calm(X))))&
(![X]:((~creative(X)&curious(X))<=>(old(X)|curious(X))))&
(((~brave(paul)|~creative(paul)))<=>(?[X]:((~kind(X)<~>patient(X)))))&
(![X]:(~tall(X)<=>(~brave(X)|~calm(X))))&
(![X]:(~funny(X)=>(strong(X)&humble(X))))&
(![X]:((wise(X)|~tall(X))<=>~humble(X)))&
(![X]:((~wise(X)|~happy(X))<=>(~brave(X)<~>creative(X))))&
(((~kind(john)|curious(john)))=>((~funny(paul)<~>tall(paul))))&
((?[X]:((happy(X)|~quiet(X))))<=>((~humble(alice)&rich(alice))))&
((?[X]:((~brave(X)&~humble(X))))=>(~old(susan)))&
(![X]:(~old(X)=>(strong(X)|~funny(X))))&
(![X]:(~brave(X)=>~kind(X)))&
((?[X]:((~curious(X)<~>kind(X))))<=>((kind(mary)&patient(mary))))&
(![X]:(~quiet(X)=>(~brave(X)|~rich(X))))&
((kind(susan)<~>old(susan)))&
(?[X]:((~kind(X)&~tall(X))))&
(?[X]:((~strong(X)<~>~creative(X))))&
(calm(mary))&
(?[X]:((~curious(X)&~tall(X))))&
(?[X]:((old(X)&quiet(X))))&
((~humble(mary)&~wise(mary)))&
((~tall(susan)|~generous(susan))) | old(susan) | [
"p5",
"p7",
"p11",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2741450948357579782164461
% SZS output start Proof for 2741450948357579782164461
6. ! [X0] : (~tall(X0) <=> (~calm(X0) | ~brave(X0))) [input p5]
8. ! [X0] : ((~tall(X0) | wise(X0)) <=> ~humble(X0)) [input p7]
12. ? [X0] : (~humble(X0) & ~brave(X0)) => ~old(susan) [input p11]
20. calm(mary) [input p19]
23. ~wise(mary) & ~humble(mary) [input p22]
25. old(susan) [input hypothesis]
32. ~old(susan) | ! [X0] : (humble(X0) | brave(X0)) [ennf transformation 12]
51. ! [X0] : ((~tall(X0) | (calm(X0) & brave(X0))) & ((~calm(X0) | ~brave(X0)) | tall(X0))) [nnf transformation 6]
52. ! [X0] : ((~tall(X0) | (calm(X0) & brave(X0))) & (~calm(X0) | ~brave(X0) | tall(X0))) [flattening 51]
53. ! [X0] : (((~tall(X0) | wise(X0)) | humble(X0)) & (~humble(X0) | (tall(X0) & ~wise(X0)))) [nnf transformation 8]
54. ! [X0] : ((~tall(X0) | wise(X0) | humble(X0)) & (~humble(X0) | (tall(X0) & ~wise(X0)))) [flattening 53]
95. ~brave(X0) | ~calm(X0) | tall(X0) [cnf transformation 52]
96. ~tall(X0) | brave(X0) [cnf transformation 52]
101. ~humble(X0) | tall(X0) [cnf transformation 54]
102. ~tall(X0) | wise(X0) | humble(X0) [cnf transformation 54]
118. ~old(susan) | humble(X0) | brave(X0) [cnf transformation 32]
134. calm(mary) [cnf transformation 20]
139. ~humble(mary) [cnf transformation 23]
140. ~wise(mary) [cnf transformation 23]
142. old(susan) [cnf transformation 25]
228. 19 <=> ! [X0] : (humble(X0) | brave(X0)) [avatar definition]
229. humble(X0) | brave(X0) <- (19) [avatar component clause 228]
231. 20 <=> old(susan) [avatar definition]
234. 19 | ~20 [avatar split clause 118,231,228]
290. 20 [avatar split clause 142,231]
304. brave(X0) | tall(X0) <- (19) [resolution 229,101]
305. brave(X0) <- (19) [subsumption resolution 304,96]
320. ~calm(X0) | tall(X0) <- (19) [resolution 95,305]
455. tall(mary) <- (19) [resolution 320,134]
457. wise(mary) | humble(mary) <- (19) [resolution 455,102]
460. humble(mary) <- (19) [subsumption resolution 457,140]
461. $false <- (19) [subsumption resolution 460,139]
462. ~19 [avatar contradiction clause 461]
463. $false [avatar sat refutation 234,290,462]
% SZS output end Proof for 2741450948357579782164461
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
If paul is patient or not curious then susan is not happy or happy.
Everyone who is not funny is either funny or not wise and vice versa.
If lucy is either not happy or quiet then john is generous.
Everyone who is both brave and rich is old or not wise and vice versa.
If someone is either curious or not creative then alice is tall.
Someone is either not wise or patient.
Fred is either tall or not humble.
Lucy is not humble.
Someone is quiet or not calm.
Someone is both not kind and old. | John is not quiet. | entailment | (![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
(((patient(paul)|~curious(paul)))=>((~happy(susan)|happy(susan))))&
(![X]:(~funny(X)<=>(funny(X)<~>~wise(X))))&
(((~happy(lucy)<~>quiet(lucy)))=>(generous(john)))&
(![X]:((brave(X)&rich(X))<=>(old(X)|~wise(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>(tall(alice)))&
(?[X]:((~wise(X)<~>patient(X))))&
((tall(fred)<~>~humble(fred)))&
(~humble(lucy))&
(?[X]:((quiet(X)|~calm(X))))&
(?[X]:((~kind(X)&old(X)))) | ~quiet(john) | [
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2854023148327078147942997
% SZS output start Proof for 2854023148327078147942997
3. ! [X0] : ((quiet(X0) <~> curious(X0)) <=> (happy(X0) & curious(X0))) [input p2]
5. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> strong(X0)) [input p4]
8. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X0] : curious(X0) [input p7]
22. quiet(john) [input hypothesis]
23. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X1] : curious(X1) [rectify 8]
37. ! [X0] : ((((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0))))) [nnf transformation 3]
38. ! [X0] : ((((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0))))) [flattening 37]
39. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [nnf transformation 5]
40. ! [X0] : ((~generous(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [flattening 39]
45. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (funny(X0) | ~generous(X0))) [nnf transformation 23]
46. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (funny(X3) | ~generous(X3))) [rectify 45]
47. ? [X0] : (~funny(X0) & generous(X0)) => (~funny(sK1) & generous(sK1)) [choice axiom]
48. ? [X2] : curious(X2) => curious(sK2) [choice axiom]
49. ((~funny(sK1) & generous(sK1)) | ! [X1] : ~curious(X1)) & (curious(sK2) | ! [X3] : (funny(X3) | ~generous(X3))) [skolemisation 46,48,47]
75. curious(X0) | curious(X0) | ~quiet(X0) [cnf transformation 38]
83. strong(X0) | strong(X0) [cnf transformation 40]
85. ~generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 40]
94. generous(sK1) | ~curious(X1) [cnf transformation 49]
130. quiet(john) [cnf transformation 22]
133. strong(X0) [duplicate literal removal 83]
134. ~strong(X0) | ~generous(X0) [duplicate literal removal 85]
135. ~quiet(X0) | curious(X0) [duplicate literal removal 75]
163. 6 <=> ! [X1] : ~curious(X1) [avatar definition]
164. ~curious(X1) <- (6) [avatar component clause 163]
171. 8 <=> generous(sK1) [avatar definition]
173. generous(sK1) <- (8) [avatar component clause 171]
174. 6 | 8 [avatar split clause 94,171,163]
260. ~generous(X1) [resolution 134,133]
261. curious(john) [resolution 135,130]
263. $false <- (6) [subsumption resolution 261,164]
264. ~6 [avatar contradiction clause 263]
267. $false <- (8) [subsumption resolution 173,260]
268. ~8 [avatar contradiction clause 267]
269. $false [avatar sat refutation 174,264,268]
% SZS output end Proof for 2854023148327078147942997
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and patient is either not strong or quiet and vice versa.
If john is strong or wise then someone is old or not patient and vice versa.
If mary is not wise then mary is not humble and vice versa.
Everyone who is not wise is either not tall or not humble.
Everyone who is both not old and not brave is creative or not tall and vice versa.
Everyone who is strong or creative is both not quiet and funny.
Everyone who is both not patient and not creative is not wise.
If someone is humble or not generous then susan is wise or not calm.
Everyone who is creative is both generous and not patient.
Everyone who is either funny or curious is not creative or not kind and vice versa.
If someone is rich or not strong then john is both strong and not funny and vice versa.
If lucy is old or rich then fred is both tall and brave and vice versa.
If lucy is calm or tall then someone is both strong and brave and vice versa.
Everyone who is not kind or not curious is both kind and not happy and vice versa.
Everyone who is either wise or not calm is both not wise and not humble.
Everyone who is either not old or old is not tall.
Someone is both not humble and not quiet.
Susan is generous.
Someone is both not quiet and funny.
Someone is either humble or not rich.
Someone is not tall.
Lucy is quiet or not rich.
Someone is either tall or curious. | Lucy is not curious. | contradiction | (![X]:((~rich(X)&patient(X))<=>(~strong(X)<~>quiet(X))))&
(((strong(john)|wise(john)))<=>(?[X]:((old(X)|~patient(X)))))&
((~wise(mary))<=>(~humble(mary)))&
(![X]:(~wise(X)=>(~tall(X)<~>~humble(X))))&
(![X]:((~old(X)&~brave(X))<=>(creative(X)|~tall(X))))&
(![X]:((strong(X)|creative(X))=>(~quiet(X)&funny(X))))&
(![X]:((~patient(X)&~creative(X))=>~wise(X)))&
((?[X]:((humble(X)|~generous(X))))=>((wise(susan)|~calm(susan))))&
(![X]:(creative(X)=>(generous(X)&~patient(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((rich(X)|~strong(X))))<=>((strong(john)&~funny(john))))&
(((old(lucy)|rich(lucy)))<=>((tall(fred)&brave(fred))))&
(((calm(lucy)|tall(lucy)))<=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(kind(X)&~happy(X))))&
(![X]:((wise(X)<~>~calm(X))=>(~wise(X)&~humble(X))))&
(![X]:((~old(X)<~>old(X))=>~tall(X)))&
(?[X]:((~humble(X)&~quiet(X))))&
(generous(susan))&
(?[X]:((~quiet(X)&funny(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:(~tall(X)))&
((quiet(lucy)|~rich(lucy)))&
(?[X]:((tall(X)<~>curious(X)))) | ~curious(lucy) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"p9",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2323722590881420437323781
% SZS output start Proof for 2323722590881420437323781
1. ! [X0] : ((patient(X0) & ~rich(X0)) <=> (~strong(X0) <~> quiet(X0))) [input p0]
4. ! [X0] : (~wise(X0) => (~tall(X0) <~> ~humble(X0))) [input p3]
5. ! [X0] : ((~brave(X0) & ~old(X0)) <=> (~tall(X0) | creative(X0))) [input p4]
6. ! [X0] : ((creative(X0) | strong(X0)) => (funny(X0) & ~quiet(X0))) [input p5]
7. ! [X0] : ((~creative(X0) & ~patient(X0)) => ~wise(X0)) [input p6]
10. ! [X0] : ((funny(X0) <~> curious(X0)) <=> (~kind(X0) | ~creative(X0))) [input p9]
11. ? [X0] : (~strong(X0) | rich(X0)) <=> (~funny(john) & strong(john)) [input p10]
13. (tall(lucy) | calm(lucy)) <=> ? [X0] : (brave(X0) & strong(X0)) [input p12]
14. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> (~happy(X0) & kind(X0))) [input p13]
15. ! [X0] : ((wise(X0) <~> ~calm(X0)) => (~humble(X0) & ~wise(X0))) [input p14]
16. ! [X0] : ((~old(X0) <~> old(X0)) => ~tall(X0)) [input p15]
24. ~curious(lucy) [input hypothesis]
28. ! [X0] : ((~tall(X0) <~> ~humble(X0)) | wise(X0)) [ennf transformation 4]
29. ! [X0] : ((funny(X0) & ~quiet(X0)) | (~creative(X0) & ~strong(X0))) [ennf transformation 6]
30. ! [X0] : (~wise(X0) | (creative(X0) | patient(X0))) [ennf transformation 7]
31. ! [X0] : (~wise(X0) | creative(X0) | patient(X0)) [flattening 30]
35. ! [X0] : ((~humble(X0) & ~wise(X0)) | (wise(X0) <=> ~calm(X0))) [ennf transformation 15]
36. ! [X0] : (~tall(X0) | (~old(X0) <=> old(X0))) [ennf transformation 16]
37. ! [X0] : (((patient(X0) & ~rich(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0)))) & (((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | (~patient(X0) | rich(X0)))) [nnf transformation 1]
38. ! [X0] : (((patient(X0) & ~rich(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0)))) & (((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | ~patient(X0) | rich(X0))) [flattening 37]
45. ! [X0] : (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | wise(X0)) [nnf transformation 28]
46. ! [X0] : (((~brave(X0) & ~old(X0)) | (tall(X0) & ~creative(X0))) & ((~tall(X0) | creative(X0)) | (brave(X0) | old(X0)))) [nnf transformation 5]
47. ! [X0] : (((~brave(X0) & ~old(X0)) | (tall(X0) & ~creative(X0))) & (~tall(X0) | creative(X0) | brave(X0) | old(X0))) [flattening 46]
48. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 10]
49. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [flattening 48]
50. (? [X0] : (~strong(X0) | rich(X0)) | (funny(john) | ~strong(john))) & ((~funny(john) & strong(john)) | ! [X0] : (strong(X0) & ~rich(X0))) [nnf transformation 11]
51. (? [X0] : (~strong(X0) | rich(X0)) | funny(john) | ~strong(john)) & ((~funny(john) & strong(john)) | ! [X0] : (strong(X0) & ~rich(X0))) [flattening 50]
52. (? [X0] : (~strong(X0) | rich(X0)) | funny(john) | ~strong(john)) & ((~funny(john) & strong(john)) | ! [X1] : (strong(X1) & ~rich(X1))) [rectify 51]
53. ? [X0] : (~strong(X0) | rich(X0)) => (~strong(sK1) | rich(sK1)) [choice axiom]
54. ((~strong(sK1) | rich(sK1)) | funny(john) | ~strong(john)) & ((~funny(john) & strong(john)) | ! [X1] : (strong(X1) & ~rich(X1))) [skolemisation 52,53]
57. ((tall(lucy) | calm(lucy)) | ! [X0] : (~brave(X0) | ~strong(X0))) & (? [X0] : (brave(X0) & strong(X0)) | (~tall(lucy) & ~calm(lucy))) [nnf transformation 13]
58. (tall(lucy) | calm(lucy) | ! [X0] : (~brave(X0) | ~strong(X0))) & (? [X0] : (brave(X0) & strong(X0)) | (~tall(lucy) & ~calm(lucy))) [flattening 57]
59. (tall(lucy) | calm(lucy) | ! [X0] : (~brave(X0) | ~strong(X0))) & (? [X1] : (brave(X1) & strong(X1)) | (~tall(lucy) & ~calm(lucy))) [rectify 58]
60. ? [X1] : (brave(X1) & strong(X1)) => (brave(sK2) & strong(sK2)) [choice axiom]
61. (tall(lucy) | calm(lucy) | ! [X0] : (~brave(X0) | ~strong(X0))) & ((brave(sK2) & strong(sK2)) | (~tall(lucy) & ~calm(lucy))) [skolemisation 59,60]
62. ! [X0] : (((~curious(X0) | ~kind(X0)) | (happy(X0) | ~kind(X0))) & ((~happy(X0) & kind(X0)) | (curious(X0) & kind(X0)))) [nnf transformation 14]
63. ! [X0] : ((~curious(X0) | ~kind(X0) | happy(X0) | ~kind(X0)) & ((~happy(X0) & kind(X0)) | (curious(X0) & kind(X0)))) [flattening 62]
64. ! [X0] : ((~humble(X0) & ~wise(X0)) | ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0)))) [nnf transformation 35]
65. ! [X0] : (~tall(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 36]
78. ~strong(X0) | quiet(X0) | ~patient(X0) | rich(X0) [cnf transformation 38]
91. tall(X0) | humble(X0) | wise(X0) [cnf transformation 45]
94. ~old(X0) | tall(X0) [cnf transformation 47]
96. ~brave(X0) | tall(X0) [cnf transformation 47]
97. ~quiet(X0) | ~strong(X0) [cnf transformation 29]
99. ~strong(X0) | funny(X0) [cnf transformation 29]
100. ~creative(X0) | funny(X0) [cnf transformation 29]
101. ~wise(X0) | creative(X0) | patient(X0) [cnf transformation 31]
104. ~kind(X0) | ~creative(X0) | curious(X0) | ~funny(X0) [cnf transformation 49]
106. curious(X0) | funny(X0) | creative(X0) [cnf transformation 49]
110. strong(john) | ~rich(X1) [cnf transformation 54]
111. strong(john) | strong(X1) [cnf transformation 54]
112. ~funny(john) | ~rich(X1) [cnf transformation 54]
113. ~funny(john) | strong(X1) [cnf transformation 54]
122. brave(sK2) | ~calm(lucy) [cnf transformation 61]
126. kind(X0) | curious(X0) [cnf transformation 63]
133. ~humble(X0) | wise(X0) | calm(X0) [cnf transformation 64]
134. ~tall(X0) | old(X0) | old(X0) [cnf transformation 65]
135. ~tall(X0) | ~old(X0) | ~old(X0) [cnf transformation 65]
146. ~curious(lucy) [cnf transformation 24]
147. ~tall(X0) | old(X0) [duplicate literal removal 134]
148. ~tall(X0) | ~old(X0) [duplicate literal removal 135]
156. 2 <=> strong(john) [avatar definition]
158. strong(john) <- (2) [avatar component clause 156]
165. 4 <=> ! [X0] : ~old(X0) [avatar definition]
166. ~old(X0) <- (4) [avatar component clause 165]
200. curious(X0) | funny(X0) [subsumption resolution 106,100]
201. ~kind(X0) | ~creative(X0) | curious(X0) [subsumption resolution 104,200]
203. 12 <=> ! [X1] : strong(X1) [avatar definition]
204. strong(X1) <- (12) [avatar component clause 203]
206. 13 <=> funny(john) [avatar definition]
209. 12 | ~13 [avatar split clause 113,206,203]
211. 14 <=> ! [X1] : ~rich(X1) [avatar definition]
212. ~rich(X1) <- (14) [avatar component clause 211]
213. 14 | ~13 [avatar split clause 112,206,211]
214. 12 | 2 [avatar split clause 111,156,203]
215. 14 | 2 [avatar split clause 110,156,211]
242. 20 <=> calm(lucy) [avatar definition]
243. ~calm(lucy) <- (~20) [avatar component clause 242]
251. 22 <=> brave(sK2) [avatar definition]
253. brave(sK2) <- (22) [avatar component clause 251]
255. ~20 | 22 [avatar split clause 122,251,242]
262. ~old(X0) [subsumption resolution 148,94]
263. 4 [avatar split clause 262,165]
275. 26 <=> quiet(lucy) [avatar definition]
277. quiet(lucy) <- (26) [avatar component clause 275]
289. funny(john) <- (2) [resolution 99,158]
292. 13 | ~2 [avatar split clause 289,156,206]
305. humble(X1) | wise(X1) | old(X1) [resolution 91,147]
310. humble(X1) | wise(X1) <- (4) [subsumption resolution 305,166]
359. wise(X0) | calm(X0) | wise(X0) <- (4) [resolution 133,310]
361. calm(X0) | wise(X0) <- (4) [duplicate literal removal 359]
367. ~creative(X1) | curious(X1) | curious(X1) [resolution 201,126]
369. ~creative(X1) | curious(X1) [duplicate literal removal 367]
373. quiet(X0) | ~patient(X0) | rich(X0) <- (12) [resolution 78,204]
384. ~patient(X0) | quiet(X0) <- (12, 14) [subsumption resolution 373,212]
421. wise(lucy) <- (4, ~20) [resolution 361,243]
454. creative(lucy) | patient(lucy) <- (4, ~20) [resolution 421,101]
456. 39 <=> patient(lucy) [avatar definition]
458. patient(lucy) <- (39) [avatar component clause 456]
460. 40 <=> creative(lucy) [avatar definition]
462. creative(lucy) <- (40) [avatar component clause 460]
463. 39 | 40 | ~4 | 20 [avatar split clause 454,242,165,460,456]
473. curious(lucy) <- (40) [resolution 462,369]
479. $false <- (40) [subsumption resolution 473,146]
480. ~40 [avatar contradiction clause 479]
483. quiet(lucy) <- (12, 14, 39) [resolution 458,384]
484. 26 | ~12 | ~14 | ~39 [avatar split clause 483,456,211,203,275]
498. tall(sK2) <- (22) [resolution 253,96]
503. old(sK2) <- (22) [resolution 498,147]
505. $false <- (4, 22) [subsumption resolution 503,166]
506. ~4 | ~22 [avatar contradiction clause 505]
515. ~strong(lucy) <- (26) [resolution 277,97]
516. $false <- (12, 26) [subsumption resolution 515,204]
517. ~12 | ~26 [avatar contradiction clause 516]
518. $false [avatar sat refutation 209,213,214,215,255,263,292,463,480,484,506,517]
% SZS output end Proof for 2323722590881420437323781
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is wise and vice versa. Everyone who is both not happy and not generous is curious and vice versa. Everyone who is not quiet or not creative is not tall and vice versa. If susan is either old or not calm then fred is either not strong or not tall. If mary is either not happy or not strong then someone is not humble and vice versa. If someone is funny or not happy then someone is either kind or brave and vice versa. Everyone who is funny or brave is either not old or not creative and vice versa. Everyone who is either not brave or strong is quiet and vice versa. Everyone who is humble is not calm and vice versa. Everyone who is both brave and not funny is either not quiet or not rich. If someone is happy then someone is not curious or not happy and vice versa. Everyone who is old or not brave is either not funny or not kind. If alice is both not humble and not funny then someone is both not patient and wise. Everyone who is not humble is either not happy or not humble and vice versa. If alice is either not funny or patient then mary is not patient. Everyone who is either humble or not old is either strong or not old and vice versa. Someone is both patient and not old. Fred is either not creative or not old. Susan is not generous or not creative. Susan is either patient or quiet. Paul is wise. Someone is either calm or not kind. Someone is either not old or generous. | Mary is not wise. | contradiction | (![X]:(~strong(X)<=>wise(X)))&
(![X]:((~happy(X)&~generous(X))<=>curious(X)))&
(![X]:((~quiet(X)|~creative(X))<=>~tall(X)))&
(((old(susan)<~>~calm(susan)))=>((~strong(fred)<~>~tall(fred))))&
(((~happy(mary)<~>~strong(mary)))<=>(?[X]:(~humble(X))))&
((?[X]:((funny(X)|~happy(X))))<=>(?[X]:((kind(X)<~>brave(X)))))&
(![X]:((funny(X)|brave(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>strong(X))<=>quiet(X)))&
(![X]:(humble(X)<=>~calm(X)))&
(![X]:((brave(X)&~funny(X))=>(~quiet(X)<~>~rich(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)|~happy(X)))))&
(![X]:((old(X)|~brave(X))=>(~funny(X)<~>~kind(X))))&
(((~humble(alice)&~funny(alice)))=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:(~humble(X)<=>(~happy(X)<~>~humble(X))))&
(((~funny(alice)<~>patient(alice)))=>(~patient(mary)))&
(![X]:((humble(X)<~>~old(X))<=>(strong(X)<~>~old(X))))&
(?[X]:((patient(X)&~old(X))))&
((~creative(fred)<~>~old(fred)))&
((~generous(susan)|~creative(susan)))&
((patient(susan)<~>quiet(susan)))&
(wise(paul))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((~old(X)<~>generous(X)))) | ~wise(mary) | [
"p0",
"p4",
"p8",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5928844804047419568880746
% SZS output start Proof for 5928844804047419568880746
1. ! [X0] : (~strong(X0) <=> wise(X0)) [input p0]
5. (~happy(mary) <~> ~strong(mary)) <=> ? [X0] : ~humble(X0) [input p4]
9. ! [X0] : (humble(X0) <=> ~calm(X0)) [input p8]
14. ! [X0] : (~humble(X0) <=> (~happy(X0) <~> ~humble(X0))) [input p13]
16. ! [X0] : ((humble(X0) <~> ~old(X0)) <=> (strong(X0) <~> ~old(X0))) [input p15]
21. wise(paul) [input p20]
24. ~wise(mary) [input hypothesis]
34. ! [X0] : ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))) [nnf transformation 1]
40. (((strong(mary) | happy(mary)) & (~strong(mary) | ~happy(mary))) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | ((~happy(mary) | strong(mary)) & (~strong(mary) | happy(mary)))) [nnf transformation 5]
41. (((strong(mary) | happy(mary)) & (~strong(mary) | ~happy(mary))) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | ((~happy(mary) | strong(mary)) & (~strong(mary) | happy(mary)))) [rectify 40]
42. ? [X1] : ~humble(X1) => ~humble(sK0) [choice axiom]
43. (((strong(mary) | happy(mary)) & (~strong(mary) | ~happy(mary))) | ! [X0] : humble(X0)) & (~humble(sK0) | ((~happy(mary) | strong(mary)) & (~strong(mary) | happy(mary)))) [skolemisation 41,42]
52. ! [X0] : ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))) [nnf transformation 9]
62. ! [X0] : ((~humble(X0) | ((~happy(X0) | humble(X0)) & (~humble(X0) | happy(X0)))) & (((humble(X0) | happy(X0)) & (~humble(X0) | ~happy(X0))) | humble(X0))) [nnf transformation 14]
64. ! [X0] : ((((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) & (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0))))) [nnf transformation 16]
75. wise(X0) | strong(X0) [cnf transformation 34]
76. ~wise(X0) | ~strong(X0) [cnf transformation 34]
89. ~strong(mary) | ~happy(mary) | humble(X0) [cnf transformation 43]
107. ~humble(X0) | ~calm(X0) [cnf transformation 52]
108. humble(X0) | calm(X0) [cnf transformation 52]
121. humble(X0) | happy(X0) | humble(X0) [cnf transformation 62]
122. ~humble(X0) | ~humble(X0) | happy(X0) [cnf transformation 62]
126. ~old(X0) | strong(X0) | ~old(X0) | ~humble(X0) [cnf transformation 64]
133. old(X0) | ~humble(X0) | strong(X0) | old(X0) [cnf transformation 64]
141. wise(paul) [cnf transformation 21]
146. ~wise(mary) [cnf transformation 24]
147. ~old(X0) | strong(X0) | ~humble(X0) [duplicate literal removal 126]
150. old(X0) | ~humble(X0) | strong(X0) [duplicate literal removal 133]
151. humble(X0) | happy(X0) [duplicate literal removal 121]
152. ~humble(X0) | happy(X0) [duplicate literal removal 122]
174. 5 <=> ! [X0] : humble(X0) [avatar definition]
175. humble(X0) <- (5) [avatar component clause 174]
177. 6 <=> happy(mary) [avatar definition]
178. ~happy(mary) <- (~6) [avatar component clause 177]
181. 7 <=> strong(mary) [avatar definition]
185. 5 | ~6 | ~7 [avatar split clause 89,181,177,174]
209. 13 <=> ! [X3] : happy(X3) [avatar definition]
210. happy(X3) <- (13) [avatar component clause 209]
253. happy(X0) [subsumption resolution 151,152]
254. 13 [avatar split clause 253,209]
266. ~humble(X0) | strong(X0) [subsumption resolution 147,150]
320. strong(mary) [resolution 75,146]
323. 7 [avatar split clause 320,181]
324. $false <- (~6, 13) [subsumption resolution 178,210]
325. 6 | ~13 [avatar contradiction clause 324]
326. ~strong(paul) [resolution 76,141]
329. ~calm(X0) <- (5) [resolution 107,175]
338. strong(X0) | calm(X0) [resolution 266,108]
341. strong(X0) <- (5) [subsumption resolution 338,329]
345. $false <- (5) [resolution 341,326]
347. ~5 [avatar contradiction clause 345]
348. $false [avatar sat refutation 185,254,323,325,347]
% SZS output end Proof for 5928844804047419568880746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or rich is either curious or not wise and vice versa. Everyone who is both not rich and not patient is both brave and humble. Everyone who is not brave is either brave or not rich and vice versa. Everyone who is either not patient or not brave is brave or old. Everyone who is either not patient or not curious is not creative or not calm and vice versa. Everyone who is both quiet and not creative is either quiet or funny. Everyone who is both not quiet and not brave is not funny. If mary is either brave or not kind then susan is not rich or not humble and vice versa. Everyone who is kind is not brave or not generous. If someone is funny or tall then mary is not quiet or rich and vice versa. Everyone who is old is strong or old. Everyone who is both humble and patient is happy. Everyone who is both not patient and not happy is not humble. Everyone who is not patient or generous is not wise. Everyone who is old or generous is not creative or humble. If someone is either rich or not generous then paul is both tall and brave. Someone is strong or not patient. Someone is not calm or not old. Someone is either not humble or brave. Someone is humble or not rich. Someone is both happy and wise. Someone is not curious. Paul is wise. Mary is not patient or not humble. | Susan is not quiet. | neutral | (![X]:((~calm(X)|rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((~rich(X)&~patient(X))=>(brave(X)&humble(X))))&
(![X]:(~brave(X)<=>(brave(X)<~>~rich(X))))&
(![X]:((~patient(X)<~>~brave(X))=>(brave(X)|old(X))))&
(![X]:((~patient(X)<~>~curious(X))<=>(~creative(X)|~calm(X))))&
(![X]:((quiet(X)&~creative(X))=>(quiet(X)<~>funny(X))))&
(![X]:((~quiet(X)&~brave(X))=>~funny(X)))&
(((brave(mary)<~>~kind(mary)))<=>((~rich(susan)|~humble(susan))))&
(![X]:(kind(X)=>(~brave(X)|~generous(X))))&
((?[X]:((funny(X)|tall(X))))<=>((~quiet(mary)|rich(mary))))&
(![X]:(old(X)=>(strong(X)|old(X))))&
(![X]:((humble(X)&patient(X))=>happy(X)))&
(![X]:((~patient(X)&~happy(X))=>~humble(X)))&
(![X]:((~patient(X)|generous(X))=>~wise(X)))&
(![X]:((old(X)|generous(X))=>(~creative(X)|humble(X))))&
((?[X]:((rich(X)<~>~generous(X))))=>((tall(paul)&brave(paul))))&
(?[X]:((strong(X)|~patient(X))))&
(?[X]:((~calm(X)|~old(X))))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((humble(X)|~rich(X))))&
(?[X]:((happy(X)&wise(X))))&
(?[X]:(~curious(X)))&
(wise(paul))&
((~patient(mary)|~humble(mary))) | ~quiet(susan) | [] | null | 0 |
If paul is both quiet and not wise then someone is either not tall or not humble and vice versa.
Everyone who is both not kind and kind is creative and vice versa.
Everyone who is calm or not rich is both brave and not generous and vice versa.
Everyone who is both not curious and not rich is either calm or creative.
If susan is both humble and not quiet then fred is both not patient and not happy and vice versa.
Everyone who is rich or not old is both not wise and not strong.
Everyone who is either not patient or kind is not creative or not generous and vice versa.
Everyone who is either not kind or kind is both not rich and not wise.
Everyone who is both not humble and kind is quiet or not patient.
If alice is both not brave and creative then alice is not calm and vice versa.
If someone is strong then susan is generous or creative and vice versa.
Everyone who is either not happy or happy is not strong or patient and vice versa.
If mary is rich or not wise then someone is both not humble and curious and vice versa.
Everyone who is both funny and patient is not rich and vice versa.
Everyone who is wise or not patient is either kind or not strong and vice versa.
Fred is either generous or brave.
Someone is either not wise or not patient.
Someone is either not curious or not funny.
John is calm or strong.
Paul is either not patient or brave. | Paul is not curious. | neutral | (((quiet(paul)&~wise(paul)))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((~kind(X)&kind(X))<=>creative(X)))&
(![X]:((calm(X)|~rich(X))<=>(brave(X)&~generous(X))))&
(![X]:((~curious(X)&~rich(X))=>(calm(X)<~>creative(X))))&
(((humble(susan)&~quiet(susan)))<=>((~patient(fred)&~happy(fred))))&
(![X]:((rich(X)|~old(X))=>(~wise(X)&~strong(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~creative(X)|~generous(X))))&
(![X]:((~kind(X)<~>kind(X))=>(~rich(X)&~wise(X))))&
(![X]:((~humble(X)&kind(X))=>(quiet(X)|~patient(X))))&
(((~brave(alice)&creative(alice)))<=>(~calm(alice)))&
((?[X]:(strong(X)))<=>((generous(susan)|creative(susan))))&
(![X]:((~happy(X)<~>happy(X))<=>(~strong(X)|patient(X))))&
(((rich(mary)|~wise(mary)))<=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:((funny(X)&patient(X))<=>~rich(X)))&
(![X]:((wise(X)|~patient(X))<=>(kind(X)<~>~strong(X))))&
((generous(fred)<~>brave(fred)))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
((calm(john)|strong(john)))&
((~patient(paul)<~>brave(paul))) | ~curious(paul) | [] | null | 0 |
Everyone who is quiet or not kind is not strong and vice versa. If susan is not curious or not tall then fred is brave or not generous and vice versa. Everyone who is both not happy and curious is curious or not creative and vice versa. If someone is both old and funny then someone is both rich and curious. Everyone who is not patient or not humble is either curious or not rich and vice versa. Everyone who is not wise or not patient is both wise and quiet and vice versa. If someone is both generous and not patient then susan is either humble or not wise and vice versa. Everyone who is generous or not tall is creative. If mary is both wise and not patient then mary is both not patient and creative and vice versa. Everyone who is patient is either kind or not old. Everyone who is both patient and not funny is both curious and wise. If someone is not wise then someone is both not calm and strong and vice versa. Everyone who is both not wise and not creative is calm or not quiet and vice versa. Everyone who is not calm or kind is either not calm or not rich. If someone is either not creative or old then someone is either rich or calm and vice versa. Everyone who is not old is both not strong and curious. Someone is either generous or not happy. Someone is either creative or not old. Fred is not calm. Someone is either patient or curious. Lucy is brave. Mary is not brave. | Fred is happy. | contradiction | (![X]:((quiet(X)|~kind(X))<=>~strong(X)))&
(((~curious(susan)|~tall(susan)))<=>((brave(fred)|~generous(fred))))&
(![X]:((~happy(X)&curious(X))<=>(curious(X)|~creative(X))))&
((?[X]:((old(X)&funny(X))))=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((~patient(X)|~humble(X))<=>(curious(X)<~>~rich(X))))&
(![X]:((~wise(X)|~patient(X))<=>(wise(X)&quiet(X))))&
((?[X]:((generous(X)&~patient(X))))<=>((humble(susan)<~>~wise(susan))))&
(![X]:((generous(X)|~tall(X))=>creative(X)))&
(((wise(mary)&~patient(mary)))<=>((~patient(mary)&creative(mary))))&
(![X]:(patient(X)=>(kind(X)<~>~old(X))))&
(![X]:((patient(X)&~funny(X))=>(curious(X)&wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)&strong(X)))))&
(![X]:((~wise(X)&~creative(X))<=>(calm(X)|~quiet(X))))&
(![X]:((~calm(X)|kind(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((rich(X)<~>calm(X)))))&
(![X]:(~old(X)=>(~strong(X)&curious(X))))&
(?[X]:((generous(X)<~>~happy(X))))&
(?[X]:((creative(X)<~>~old(X))))&
(~calm(fred))&
(?[X]:((patient(X)<~>curious(X))))&
(brave(lucy))&
(~brave(mary)) | happy(fred) | [
"p2",
"p4",
"p5",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 984797200593911376858219
% SZS output start Proof for 984797200593911376858219
3. ! [X0] : ((curious(X0) & ~happy(X0)) <=> (~creative(X0) | curious(X0))) [input p2]
5. ! [X0] : ((~humble(X0) | ~patient(X0)) <=> (curious(X0) <~> ~rich(X0))) [input p4]
6. ! [X0] : ((~patient(X0) | ~wise(X0)) <=> (quiet(X0) & wise(X0))) [input p5]
13. ! [X0] : ((~creative(X0) & ~wise(X0)) <=> (~quiet(X0) | calm(X0))) [input p12]
14. ! [X0] : ((kind(X0) | ~calm(X0)) => (~calm(X0) <~> ~rich(X0))) [input p13]
23. happy(fred) [input hypothesis]
32. ! [X0] : ((~calm(X0) <~> ~rich(X0)) | (~kind(X0) & calm(X0))) [ennf transformation 14]
38. ! [X0] : (((curious(X0) & ~happy(X0)) | (creative(X0) & ~curious(X0))) & ((~creative(X0) | curious(X0)) | (~curious(X0) | happy(X0)))) [nnf transformation 3]
39. ! [X0] : (((curious(X0) & ~happy(X0)) | (creative(X0) & ~curious(X0))) & (~creative(X0) | curious(X0) | ~curious(X0) | happy(X0))) [flattening 38]
43. ! [X0] : (((~humble(X0) | ~patient(X0)) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) & (((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | (humble(X0) & patient(X0)))) [nnf transformation 5]
44. ! [X0] : ((~humble(X0) | ~patient(X0) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) & (((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | (humble(X0) & patient(X0)))) [flattening 43]
45. ! [X0] : (((~patient(X0) | ~wise(X0)) | (~quiet(X0) | ~wise(X0))) & ((quiet(X0) & wise(X0)) | (patient(X0) & wise(X0)))) [nnf transformation 6]
46. ! [X0] : ((~patient(X0) | ~wise(X0) | ~quiet(X0) | ~wise(X0)) & ((quiet(X0) & wise(X0)) | (patient(X0) & wise(X0)))) [flattening 45]
59. ! [X0] : (((~creative(X0) & ~wise(X0)) | (quiet(X0) & ~calm(X0))) & ((~quiet(X0) | calm(X0)) | (creative(X0) | wise(X0)))) [nnf transformation 13]
60. ! [X0] : (((~creative(X0) & ~wise(X0)) | (quiet(X0) & ~calm(X0))) & (~quiet(X0) | calm(X0) | creative(X0) | wise(X0))) [flattening 59]
61. ! [X0] : (((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | (~kind(X0) & calm(X0))) [nnf transformation 32]
84. ~happy(X0) | ~curious(X0) [cnf transformation 39]
90. ~rich(X0) | curious(X0) | patient(X0) [cnf transformation 44]
96. wise(X0) | wise(X0) [cnf transformation 46]
100. ~patient(X0) | ~wise(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 46]
121. ~wise(X0) | ~calm(X0) [cnf transformation 60]
122. ~wise(X0) | quiet(X0) [cnf transformation 60]
127. rich(X0) | calm(X0) | calm(X0) [cnf transformation 61]
148. happy(fred) [cnf transformation 23]
149. rich(X0) | calm(X0) [duplicate literal removal 127]
150. wise(X0) [duplicate literal removal 96]
151. ~wise(X0) | ~patient(X0) | ~quiet(X0) [duplicate literal removal 100]
217. quiet(X0) [subsumption resolution 122,150]
218. ~calm(X0) [subsumption resolution 121,150]
220. rich(X0) [subsumption resolution 149,218]
265. ~curious(fred) [resolution 84,148]
279. patient(X0) | curious(X0) [resolution 90,220]
336. ~patient(X2) | ~quiet(X2) [resolution 151,150]
337. ~patient(X2) [subsumption resolution 336,217]
341. curious(X0) [resolution 337,279]
353. $false [resolution 341,265]
% SZS output end Proof for 984797200593911376858219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or happy is either not strong or tall and vice versa.
Everyone who is both creative and not funny is calm and vice versa.
If paul is old or not funny then lucy is not funny or not tall.
If paul is either not patient or strong then fred is patient.
If fred is both brave and not quiet then someone is humble.
If paul is not quiet then someone is strong or rich and vice versa.
If someone is both not quiet and not generous then lucy is either not kind or quiet and vice versa.
If someone is generous then susan is calm.
Everyone who is not kind or not generous is both not old and not quiet.
Everyone who is either creative or tall is both happy and humble.
Everyone who is not patient or brave is either not calm or not happy and vice versa.
Everyone who is either generous or not funny is both not strong and quiet and vice versa.
Everyone who is old or strong is not patient or strong.
Everyone who is both kind and old is both humble and not rich.
Everyone who is either not generous or not tall is either tall or calm and vice versa.
Everyone who is humble is both not quiet and creative and vice versa.
Mary is not curious or tall.
John is not happy.
Lucy is not strong or not old.
Alice is quiet.
Someone is both kind and not funny.
Lucy is both quiet and not old.
Susan is not happy or not quiet. | Lucy is tall. | entailment | (![X]:((~strong(X)<~>happy(X))<=>(~strong(X)<~>tall(X))))&
(![X]:((creative(X)&~funny(X))<=>calm(X)))&
(((old(paul)|~funny(paul)))=>((~funny(lucy)|~tall(lucy))))&
(((~patient(paul)<~>strong(paul)))=>(patient(fred)))&
(((brave(fred)&~quiet(fred)))=>(?[X]:(humble(X))))&
((~quiet(paul))<=>(?[X]:((strong(X)|rich(X)))))&
((?[X]:((~quiet(X)&~generous(X))))<=>((~kind(lucy)<~>quiet(lucy))))&
((?[X]:(generous(X)))=>(calm(susan)))&
(![X]:((~kind(X)|~generous(X))=>(~old(X)&~quiet(X))))&
(![X]:((creative(X)<~>tall(X))=>(happy(X)&humble(X))))&
(![X]:((~patient(X)|brave(X))<=>(~calm(X)<~>~happy(X))))&
(![X]:((generous(X)<~>~funny(X))<=>(~strong(X)&quiet(X))))&
(![X]:((old(X)|strong(X))=>(~patient(X)|strong(X))))&
(![X]:((kind(X)&old(X))=>(humble(X)&~rich(X))))&
(![X]:((~generous(X)<~>~tall(X))<=>(tall(X)<~>calm(X))))&
(![X]:(humble(X)<=>(~quiet(X)&creative(X))))&
((~curious(mary)|tall(mary)))&
(~happy(john))&
((~strong(lucy)|~old(lucy)))&
(quiet(alice))&
(?[X]:((kind(X)&~funny(X))))&
((quiet(lucy)&~old(lucy)))&
((~happy(susan)|~quiet(susan))) | tall(lucy) | [
"p0",
"p1",
"p8",
"p9",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3222790732773115964643318
% SZS output start Proof for 3222790732773115964643318
1. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> (~strong(X0) <~> tall(X0))) [input p0]
2. ! [X0] : ((~funny(X0) & creative(X0)) <=> calm(X0)) [input p1]
9. ! [X0] : ((~generous(X0) | ~kind(X0)) => (~quiet(X0) & ~old(X0))) [input p8]
10. ! [X0] : ((creative(X0) <~> tall(X0)) => (humble(X0) & happy(X0))) [input p9]
15. ! [X0] : ((~generous(X0) <~> ~tall(X0)) <=> (tall(X0) <~> calm(X0))) [input p14]
22. ~old(lucy) & quiet(lucy) [input p21]
24. ~tall(lucy) [input hypothesis]
29. ! [X0] : ((~generous(X0) | ~kind(X0)) => ~quiet(X0)) [pure predicate removal 9]
31. quiet(lucy) [pure predicate removal 22]
39. ! [X0] : (~quiet(X0) | (generous(X0) & kind(X0))) [ennf transformation 29]
40. ! [X0] : ((humble(X0) & happy(X0)) | (creative(X0) <=> tall(X0))) [ennf transformation 10]
44. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) & (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 1]
45. ! [X0] : (((~funny(X0) & creative(X0)) | ~calm(X0)) & (calm(X0) | (funny(X0) | ~creative(X0)))) [nnf transformation 2]
46. ! [X0] : (((~funny(X0) & creative(X0)) | ~calm(X0)) & (calm(X0) | funny(X0) | ~creative(X0))) [flattening 45]
58. ! [X0] : ((humble(X0) & happy(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) [nnf transformation 40]
63. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0)))) & (((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [nnf transformation 15]
67. tall(X0) | ~strong(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 44]
72. ~happy(X0) | strong(X0) | tall(X0) | strong(X0) [cnf transformation 44]
75. ~calm(X0) | creative(X0) [cnf transformation 46]
92. ~quiet(X0) | generous(X0) [cnf transformation 39]
93. happy(X0) | tall(X0) | ~creative(X0) [cnf transformation 58]
111. calm(X0) | tall(X0) | ~generous(X0) | tall(X0) [cnf transformation 63]
114. ~tall(X0) | ~generous(X0) | calm(X0) | ~tall(X0) [cnf transformation 63]
124. quiet(lucy) [cnf transformation 31]
126. ~tall(lucy) [cnf transformation 24]
127. calm(X0) | tall(X0) | ~generous(X0) [duplicate literal removal 111]
129. ~tall(X0) | ~generous(X0) | calm(X0) [duplicate literal removal 114]
131. tall(X0) | ~strong(X0) | ~happy(X0) [duplicate literal removal 67]
134. ~happy(X0) | strong(X0) | tall(X0) [duplicate literal removal 72]
136. ~happy(X0) | tall(X0) [subsumption resolution 131,134]
146. 3 <=> tall(lucy) [avatar definition]
148. ~tall(lucy) <- (~3) [avatar component clause 146]
199. 15 <=> quiet(lucy) [avatar definition]
200. quiet(lucy) <- (15) [avatar component clause 199]
231. ~creative(X0) | tall(X0) [subsumption resolution 93,136]
235. ~generous(X0) | calm(X0) [subsumption resolution 127,129]
236. 15 [avatar split clause 124,199]
246. ~3 [avatar split clause 126,146]
254. generous(lucy) <- (15) [resolution 92,200]
268. calm(lucy) <- (15) [resolution 235,254]
280. creative(lucy) <- (15) [resolution 268,75]
292. tall(lucy) <- (15) [resolution 280,231]
294. $false <- (~3, 15) [subsumption resolution 292,148]
295. 3 | ~15 [avatar contradiction clause 294]
296. $false [avatar sat refutation 236,246,295]
% SZS output end Proof for 3222790732773115964643318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or kind then someone is either not wise or humble and vice versa.
Everyone who is happy is not old and vice versa.
Everyone who is not happy is both generous and calm.
Everyone who is old or rich is kind.
Everyone who is funny is not creative or not kind.
Everyone who is not humble or old is rich or not curious.
If lucy is curious then fred is either strong or creative.
Everyone who is both humble and generous is both kind and happy.
Everyone who is either not generous or not curious is either not brave or not tall and vice versa.
Everyone who is not creative is tall or not old and vice versa.
Everyone who is humble or generous is humble.
Everyone who is both happy and not rich is funny.
Everyone who is not wise is quiet or not kind and vice versa.
If lucy is either patient or not funny then someone is both not patient and not tall and vice versa.
If susan is both quiet and not creative then lucy is both curious and not calm.
If someone is not generous then john is either not tall or not patient and vice versa.
Someone is not happy or not quiet.
John is both not brave and not humble.
John is either tall or not generous.
Someone is not wise.
Lucy is both patient and not funny.
Susan is either not happy or not humble.
Someone is not calm.
Mary is not wise. | Susan is old. | contradiction | ((?[X]:((funny(X)|kind(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(happy(X)<=>~old(X)))&
(![X]:(~happy(X)=>(generous(X)&calm(X))))&
(![X]:((old(X)|rich(X))=>kind(X)))&
(![X]:(funny(X)=>(~creative(X)|~kind(X))))&
(![X]:((~humble(X)|old(X))=>(rich(X)|~curious(X))))&
((curious(lucy))=>((strong(fred)<~>creative(fred))))&
(![X]:((humble(X)&generous(X))=>(kind(X)&happy(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(tall(X)|~old(X))))&
(![X]:((humble(X)|generous(X))=>humble(X)))&
(![X]:((happy(X)&~rich(X))=>funny(X)))&
(![X]:(~wise(X)<=>(quiet(X)|~kind(X))))&
(((patient(lucy)<~>~funny(lucy)))<=>(?[X]:((~patient(X)&~tall(X)))))&
(((quiet(susan)&~creative(susan)))=>((curious(lucy)&~calm(lucy))))&
((?[X]:(~generous(X)))<=>((~tall(john)<~>~patient(john))))&
(?[X]:((~happy(X)|~quiet(X))))&
((~brave(john)&~humble(john)))&
((tall(john)<~>~generous(john)))&
(?[X]:(~wise(X)))&
((patient(lucy)&~funny(lucy)))&
((~happy(susan)<~>~humble(susan)))&
(?[X]:(~calm(X)))&
(~wise(mary)) | old(susan) | [
"p1",
"p2",
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9090926374690145743669157
% SZS output start Proof for 9090926374690145743669157
2. ! [X0] : (happy(X0) <=> ~old(X0)) [input p1]
3. ! [X0] : (~happy(X0) => (calm(X0) & generous(X0))) [input p2]
8. ! [X0] : ((generous(X0) & humble(X0)) => (happy(X0) & kind(X0))) [input p7]
22. ~happy(susan) <~> ~humble(susan) [input p21]
25. old(susan) [input hypothesis]
27. ! [X0] : ((calm(X0) & generous(X0)) | happy(X0)) [ennf transformation 3]
34. ! [X0] : ((happy(X0) & kind(X0)) | (~generous(X0) | ~humble(X0))) [ennf transformation 8]
35. ! [X0] : ((happy(X0) & kind(X0)) | ~generous(X0) | ~humble(X0)) [flattening 34]
46. ! [X0] : ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))) [nnf transformation 2]
66. (humble(susan) | happy(susan)) & (~humble(susan) | ~happy(susan)) [nnf transformation 22]
75. ~old(X0) | ~happy(X0) [cnf transformation 46]
77. generous(X0) | happy(X0) [cnf transformation 27]
87. happy(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 35]
126. humble(susan) | happy(susan) [cnf transformation 66]
129. old(susan) [cnf transformation 25]
178. happy(X0) | ~humble(X0) [subsumption resolution 87,77]
254. happy(susan) [subsumption resolution 126,178]
256. ~happy(susan) [resolution 75,129]
257. $false [subsumption resolution 256,254]
% SZS output end Proof for 9090926374690145743669157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or strong is not old.
Everyone who is either rich or not calm is not funny or not generous.
If someone is both funny and generous then someone is both not kind and quiet.
If fred is both funny and not strong then someone is either brave or not generous and vice versa.
Everyone who is not tall or not calm is either not happy or happy.
Everyone who is tall is either not rich or not funny and vice versa.
Everyone who is both brave and not generous is humble and vice versa.
If lucy is wise or not happy then fred is brave or not kind and vice versa.
Everyone who is strong is both humble and not brave and vice versa.
Everyone who is not generous is not wise or strong and vice versa.
If mary is both brave and not quiet then john is both funny and not kind.
Everyone who is wise is either humble or strong and vice versa.
If lucy is both not quiet and not happy then someone is either wise or not rich and vice versa.
If someone is not kind then john is either not kind or not tall.
If alice is not creative or calm then someone is not rich or old.
Someone is tall.
Someone is not wise.
Lucy is quiet.
John is either tall or calm.
Someone is humble or not curious.
Paul is either not patient or not curious.
Alice is either creative or not creative. | Lucy is not strong. | entailment | (![X]:((~funny(X)<~>strong(X))=>~old(X)))&
(![X]:((rich(X)<~>~calm(X))=>(~funny(X)|~generous(X))))&
((?[X]:((funny(X)&generous(X))))=>(?[X]:((~kind(X)&quiet(X)))))&
(((funny(fred)&~strong(fred)))<=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~tall(X)|~calm(X))=>(~happy(X)<~>happy(X))))&
(![X]:(tall(X)<=>(~rich(X)<~>~funny(X))))&
(![X]:((brave(X)&~generous(X))<=>humble(X)))&
(((wise(lucy)|~happy(lucy)))<=>((brave(fred)|~kind(fred))))&
(![X]:(strong(X)<=>(humble(X)&~brave(X))))&
(![X]:(~generous(X)<=>(~wise(X)|strong(X))))&
(((brave(mary)&~quiet(mary)))=>((funny(john)&~kind(john))))&
(![X]:(wise(X)<=>(humble(X)<~>strong(X))))&
(((~quiet(lucy)&~happy(lucy)))<=>(?[X]:((wise(X)<~>~rich(X)))))&
((?[X]:(~kind(X)))=>((~kind(john)<~>~tall(john))))&
(((~creative(alice)|calm(alice)))=>(?[X]:((~rich(X)|old(X)))))&
(?[X]:(tall(X)))&
(?[X]:(~wise(X)))&
(quiet(lucy))&
((tall(john)<~>calm(john)))&
(?[X]:((humble(X)|~curious(X))))&
((~patient(paul)<~>~curious(paul)))&
((creative(alice)<~>~creative(alice))) | ~strong(lucy) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 696776961755949256677773
% SZS output start Proof for 696776961755949256677773
7. ! [X0] : ((~generous(X0) & brave(X0)) <=> humble(X0)) [input p6]
9. ! [X0] : (strong(X0) <=> (~brave(X0) & humble(X0))) [input p8]
23. strong(lucy) [input hypothesis]
46. ! [X0] : (((~generous(X0) & brave(X0)) | ~humble(X0)) & (humble(X0) | (generous(X0) | ~brave(X0)))) [nnf transformation 7]
47. ! [X0] : (((~generous(X0) & brave(X0)) | ~humble(X0)) & (humble(X0) | generous(X0) | ~brave(X0))) [flattening 46]
50. ! [X0] : ((strong(X0) | (brave(X0) | ~humble(X0))) & ((~brave(X0) & humble(X0)) | ~strong(X0))) [nnf transformation 9]
51. ! [X0] : ((strong(X0) | brave(X0) | ~humble(X0)) & ((~brave(X0) & humble(X0)) | ~strong(X0))) [flattening 50]
93. ~humble(X0) | brave(X0) [cnf transformation 47]
99. ~strong(X0) | humble(X0) [cnf transformation 51]
100. ~brave(X0) | ~strong(X0) [cnf transformation 51]
131. strong(lucy) [cnf transformation 23]
290. humble(lucy) [resolution 99,131]
292. brave(lucy) [resolution 290,93]
293. ~strong(lucy) [resolution 292,100]
294. $false [subsumption resolution 293,131]
% SZS output end Proof for 696776961755949256677773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and generous is either not generous or rich and vice versa. If someone is either not quiet or not tall then someone is both not tall and not humble. If someone is funny then someone is happy and vice versa. Everyone who is both wise and not rich is funny. Everyone who is humble or not rich is not humble and vice versa. Everyone who is both curious and brave is kind and vice versa. If susan is either not calm or not funny then someone is generous or curious. If susan is not old then alice is calm and vice versa. Everyone who is not old is both calm and not calm and vice versa. Everyone who is either not generous or kind is either rich or happy and vice versa. Everyone who is either not humble or not funny is either curious or not old. Everyone who is patient or creative is not generous. Everyone who is not old or not curious is either patient or not brave and vice versa. Everyone who is both funny and not strong is both humble and calm. If paul is kind or happy then susan is either brave or not patient and vice versa. Alice is old or not brave. Someone is not calm or brave. John is both not quiet and happy. Lucy is not rich. Someone is either happy or creative. Someone is humble or not rich. Alice is happy. John is not old or not wise. | John is not old. | contradiction | (![X]:((~strong(X)&generous(X))<=>(~generous(X)<~>rich(X))))&
((?[X]:((~quiet(X)<~>~tall(X))))=>(?[X]:((~tall(X)&~humble(X)))))&
((?[X]:(funny(X)))<=>(?[X]:(happy(X))))&
(![X]:((wise(X)&~rich(X))=>funny(X)))&
(![X]:((humble(X)|~rich(X))<=>~humble(X)))&
(![X]:((curious(X)&brave(X))<=>kind(X)))&
(((~calm(susan)<~>~funny(susan)))=>(?[X]:((generous(X)|curious(X)))))&
((~old(susan))<=>(calm(alice)))&
(![X]:(~old(X)<=>(calm(X)&~calm(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(rich(X)<~>happy(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(curious(X)<~>~old(X))))&
(![X]:((patient(X)|creative(X))=>~generous(X)))&
(![X]:((~old(X)|~curious(X))<=>(patient(X)<~>~brave(X))))&
(![X]:((funny(X)&~strong(X))=>(humble(X)&calm(X))))&
(((kind(paul)|happy(paul)))<=>((brave(susan)<~>~patient(susan))))&
((old(alice)|~brave(alice)))&
(?[X]:((~calm(X)|brave(X))))&
((~quiet(john)&happy(john)))&
(~rich(lucy))&
(?[X]:((happy(X)<~>creative(X))))&
(?[X]:((humble(X)|~rich(X))))&
(happy(alice))&
((~old(john)|~wise(john))) | ~old(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7634748521404244769106072
% SZS output start Proof for 7634748521404244769106072
9. ! [X0] : (~old(X0) <=> (~calm(X0) & calm(X0))) [input p8]
24. ~old(john) [input hypothesis]
54. ! [X0] : ((~old(X0) | (calm(X0) | ~calm(X0))) & ((~calm(X0) & calm(X0)) | old(X0))) [nnf transformation 9]
55. ! [X0] : ((~old(X0) | calm(X0) | ~calm(X0)) & ((~calm(X0) & calm(X0)) | old(X0))) [flattening 54]
91. calm(X0) | old(X0) [cnf transformation 55]
92. ~calm(X0) | old(X0) [cnf transformation 55]
131. ~old(john) [cnf transformation 24]
199. old(X0) [subsumption resolution 91,92]
250. $false [subsumption resolution 131,199]
% SZS output end Proof for 7634748521404244769106072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and generous is either calm or quiet and vice versa.
Everyone who is either not funny or strong is either not wise or not strong and vice versa.
If john is not curious then someone is either not wise or not funny.
If someone is both not funny and rich then john is both curious and old and vice versa.
Everyone who is both strong and not brave is either funny or creative and vice versa.
Everyone who is either not happy or strong is brave or not kind and vice versa.
If someone is kind or not strong then someone is wise or not patient.
Everyone who is either not quiet or patient is either curious or tall and vice versa.
If someone is either not kind or not humble then someone is both not brave and calm.
Everyone who is not brave is old or patient and vice versa.
Everyone who is not patient or patient is not calm or not rich and vice versa.
If lucy is either not wise or quiet then someone is both generous and curious.
If mary is both funny and not funny then lucy is funny and vice versa.
Everyone who is funny is not brave or not happy.
If john is creative or not tall then someone is either quiet or not generous and vice versa.
If someone is creative or not kind then someone is patient or generous and vice versa.
Someone is not tall or not curious.
Someone is either not wise or kind.
Someone is not quiet or kind.
Someone is not quiet or not curious.
Someone is both not happy and kind.
Lucy is both not creative and patient.
Someone is old.
Mary is tall or old. | Lucy is not strong. | entailment | (![X]:((~funny(X)&generous(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((~funny(X)<~>strong(X))<=>(~wise(X)<~>~strong(X))))&
((~curious(john))=>(?[X]:((~wise(X)<~>~funny(X)))))&
((?[X]:((~funny(X)&rich(X))))<=>((curious(john)&old(john))))&
(![X]:((strong(X)&~brave(X))<=>(funny(X)<~>creative(X))))&
(![X]:((~happy(X)<~>strong(X))<=>(brave(X)|~kind(X))))&
((?[X]:((kind(X)|~strong(X))))=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((~quiet(X)<~>patient(X))<=>(curious(X)<~>tall(X))))&
((?[X]:((~kind(X)<~>~humble(X))))=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:(~brave(X)<=>(old(X)|patient(X))))&
(![X]:((~patient(X)|patient(X))<=>(~calm(X)|~rich(X))))&
(((~wise(lucy)<~>quiet(lucy)))=>(?[X]:((generous(X)&curious(X)))))&
(((funny(mary)&~funny(mary)))<=>(funny(lucy)))&
(![X]:(funny(X)=>(~brave(X)|~happy(X))))&
(((creative(john)|~tall(john)))<=>(?[X]:((quiet(X)<~>~generous(X)))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:((patient(X)|generous(X)))))&
(?[X]:((~tall(X)|~curious(X))))&
(?[X]:((~wise(X)<~>kind(X))))&
(?[X]:((~quiet(X)|kind(X))))&
(?[X]:((~quiet(X)|~curious(X))))&
(?[X]:((~happy(X)&kind(X))))&
((~creative(lucy)&patient(lucy)))&
(?[X]:(old(X)))&
((tall(mary)|old(mary))) | ~strong(lucy) | [
"p4",
"p9",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5775907694731496377584365
% SZS output start Proof for 5775907694731496377584365
5. ! [X0] : ((~brave(X0) & strong(X0)) <=> (funny(X0) <~> creative(X0))) [input p4]
10. ! [X0] : (~brave(X0) <=> (patient(X0) | old(X0))) [input p9]
13. (~funny(mary) & funny(mary)) <=> funny(lucy) [input p12]
22. patient(lucy) & ~creative(lucy) [input p21]
25. strong(lucy) [input hypothesis]
46. ! [X0] : (((~brave(X0) & strong(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (brave(X0) | ~strong(X0)))) [nnf transformation 5]
47. ! [X0] : (((~brave(X0) & strong(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | brave(X0) | ~strong(X0))) [flattening 46]
58. ! [X0] : ((~brave(X0) | (~patient(X0) & ~old(X0))) & ((patient(X0) | old(X0)) | brave(X0))) [nnf transformation 10]
59. ! [X0] : ((~brave(X0) | (~patient(X0) & ~old(X0))) & (patient(X0) | old(X0) | brave(X0))) [flattening 58]
65. ((~funny(mary) & funny(mary)) | ~funny(lucy)) & (funny(lucy) | (funny(mary) | ~funny(mary))) [nnf transformation 13]
66. ((~funny(mary) & funny(mary)) | ~funny(lucy)) & (funny(lucy) | funny(mary) | ~funny(mary)) [flattening 65]
110. ~strong(X0) | funny(X0) | brave(X0) | creative(X0) [cnf transformation 47]
138. ~patient(X0) | ~brave(X0) [cnf transformation 59]
148. funny(mary) | ~funny(lucy) [cnf transformation 66]
149. ~funny(mary) | ~funny(lucy) [cnf transformation 66]
168. ~creative(lucy) [cnf transformation 22]
169. patient(lucy) [cnf transformation 22]
172. strong(lucy) [cnf transformation 25]
258. 18 <=> funny(lucy) [avatar definition]
260. ~funny(lucy) <- (~18) [avatar component clause 258]
262. 19 <=> funny(mary) [avatar definition]
265. ~18 | ~19 [avatar split clause 149,262,258]
266. ~18 | 19 [avatar split clause 148,262,258]
373. ~brave(lucy) [resolution 138,169]
447. funny(lucy) | brave(lucy) | creative(lucy) [resolution 110,172]
448. brave(lucy) | creative(lucy) <- (~18) [subsumption resolution 447,260]
449. creative(lucy) <- (~18) [subsumption resolution 448,373]
450. $false <- (~18) [subsumption resolution 449,168]
451. 18 [avatar contradiction clause 450]
452. $false [avatar sat refutation 265,266,451]
% SZS output end Proof for 5775907694731496377584365
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either tall or generous then someone is not strong and vice versa.
Everyone who is either tall or not generous is curious.
If alice is both not tall and old then lucy is both not old and happy.
If someone is either not happy or not strong then someone is either rich or not brave and vice versa.
Everyone who is both not funny and not strong is both brave and not kind and vice versa.
Everyone who is funny is wise or humble.
If john is either not calm or not creative then someone is humble or not tall.
Everyone who is both patient and not rich is either not strong or humble and vice versa.
Everyone who is not curious is both creative and not happy and vice versa.
Everyone who is both brave and not wise is both calm and not calm and vice versa.
If someone is not curious or not tall then someone is humble or quiet.
If someone is patient then someone is both not brave and not quiet and vice versa.
If someone is not calm then fred is both quiet and not creative.
Everyone who is either not old or not kind is both not quiet and old.
Everyone who is both not curious and not quiet is both not curious and not strong and vice versa.
If susan is either not old or not happy then lucy is both patient and strong.
Paul is either not kind or curious.
Someone is not generous or curious.
Someone is generous.
Someone is both not wise and old.
Someone is either old or not calm.
Someone is both not generous and funny.
Someone is both not brave and wise. | Fred is not creative. | neutral | (((tall(john)<~>generous(john)))<=>(?[X]:(~strong(X))))&
(![X]:((tall(X)<~>~generous(X))=>curious(X)))&
(((~tall(alice)&old(alice)))=>((~old(lucy)&happy(lucy))))&
((?[X]:((~happy(X)<~>~strong(X))))<=>(?[X]:((rich(X)<~>~brave(X)))))&
(![X]:((~funny(X)&~strong(X))<=>(brave(X)&~kind(X))))&
(![X]:(funny(X)=>(wise(X)|humble(X))))&
(((~calm(john)<~>~creative(john)))=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((patient(X)&~rich(X))<=>(~strong(X)<~>humble(X))))&
(![X]:(~curious(X)<=>(creative(X)&~happy(X))))&
(![X]:((brave(X)&~wise(X))<=>(calm(X)&~calm(X))))&
((?[X]:((~curious(X)|~tall(X))))=>(?[X]:((humble(X)|quiet(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
((?[X]:(~calm(X)))=>((quiet(fred)&~creative(fred))))&
(![X]:((~old(X)<~>~kind(X))=>(~quiet(X)&old(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~curious(X)&~strong(X))))&
(((~old(susan)<~>~happy(susan)))=>((patient(lucy)&strong(lucy))))&
((~kind(paul)<~>curious(paul)))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:(generous(X)))&
(?[X]:((~wise(X)&old(X))))&
(?[X]:((old(X)<~>~calm(X))))&
(?[X]:((~generous(X)&funny(X))))&
(?[X]:((~brave(X)&wise(X)))) | ~creative(fred) | [] | null | 0 |
If someone is happy then mary is not kind or rich and vice versa.
If alice is either not brave or rich then someone is either creative or not quiet and vice versa.
If someone is brave then someone is either humble or not curious.
Everyone who is either not quiet or tall is either not tall or not brave and vice versa.
If someone is kind then paul is either curious or not generous.
Everyone who is not creative is rich.
If lucy is either not calm or curious then alice is strong or tall and vice versa.
Everyone who is both funny and patient is brave or not quiet and vice versa.
Everyone who is funny or not rich is either not patient or not kind.
Everyone who is both not generous and creative is generous and vice versa.
Everyone who is not tall is not curious.
Everyone who is not calm or not happy is strong or patient and vice versa.
Everyone who is not tall or happy is either rich or kind.
If someone is humble then fred is both rich and not kind and vice versa.
Everyone who is not wise is both not curious and not patient.
Everyone who is either rich or not rich is either not calm or not wise and vice versa.
Someone is both wise and happy.
Fred is not brave or generous.
Someone is either curious or quiet.
Someone is either not happy or kind.
Susan is both humble and brave.
Paul is not curious.
John is either not tall or humble. | Susan is calm. | contradiction | ((?[X]:(happy(X)))<=>((~kind(mary)|rich(mary))))&
(((~brave(alice)<~>rich(alice)))<=>(?[X]:((creative(X)<~>~quiet(X)))))&
((?[X]:(brave(X)))=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:((~quiet(X)<~>tall(X))<=>(~tall(X)<~>~brave(X))))&
((?[X]:(kind(X)))=>((curious(paul)<~>~generous(paul))))&
(![X]:(~creative(X)=>rich(X)))&
(((~calm(lucy)<~>curious(lucy)))<=>((strong(alice)|tall(alice))))&
(![X]:((funny(X)&patient(X))<=>(brave(X)|~quiet(X))))&
(![X]:((funny(X)|~rich(X))=>(~patient(X)<~>~kind(X))))&
(![X]:((~generous(X)&creative(X))<=>generous(X)))&
(![X]:(~tall(X)=>~curious(X)))&
(![X]:((~calm(X)|~happy(X))<=>(strong(X)|patient(X))))&
(![X]:((~tall(X)|happy(X))=>(rich(X)<~>kind(X))))&
((?[X]:(humble(X)))<=>((rich(fred)&~kind(fred))))&
(![X]:(~wise(X)=>(~curious(X)&~patient(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(~calm(X)<~>~wise(X))))&
(?[X]:((wise(X)&happy(X))))&
((~brave(fred)|generous(fred)))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
((humble(susan)&brave(susan)))&
(~curious(paul))&
((~tall(john)<~>humble(john))) | calm(susan) | [
"p7",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3647524715738667858484804
% SZS output start Proof for 3647524715738667858484804
8. ! [X0] : ((patient(X0) & funny(X0)) <=> (~quiet(X0) | brave(X0))) [input p7]
15. ! [X0] : (~wise(X0) => (~patient(X0) & ~curious(X0))) [input p14]
16. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> (~calm(X0) <~> ~wise(X0))) [input p15]
21. brave(susan) & humble(susan) [input p20]
24. calm(susan) [input hypothesis]
32. ! [X0] : ((~patient(X0) & ~curious(X0)) | wise(X0)) [ennf transformation 15]
50. ! [X0] : (((patient(X0) & funny(X0)) | (quiet(X0) & ~brave(X0))) & ((~quiet(X0) | brave(X0)) | (~patient(X0) | ~funny(X0)))) [nnf transformation 8]
51. ! [X0] : (((patient(X0) & funny(X0)) | (quiet(X0) & ~brave(X0))) & (~quiet(X0) | brave(X0) | ~patient(X0) | ~funny(X0))) [flattening 50]
63. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 16]
106. ~brave(X0) | patient(X0) [cnf transformation 51]
128. ~patient(X0) | wise(X0) [cnf transformation 32]
129. ~wise(X0) | ~calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
130. ~wise(X0) | ~calm(X0) | rich(X0) | rich(X0) [cnf transformation 63]
145. brave(susan) [cnf transformation 21]
149. calm(susan) [cnf transformation 24]
150. ~wise(X0) | ~calm(X0) | ~rich(X0) [duplicate literal removal 129]
151. ~wise(X0) | ~calm(X0) | rich(X0) [duplicate literal removal 130]
279. ~wise(X0) | ~calm(X0) [subsumption resolution 150,151]
317. patient(susan) [resolution 106,145]
321. wise(susan) [resolution 128,317]
332. ~calm(susan) [resolution 279,321]
335. $false [subsumption resolution 332,149]
% SZS output end Proof for 3647524715738667858484804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not calm is not wise.
If lucy is either curious or funny then fred is both not rich and not quiet.
Everyone who is both not old and brave is both brave and generous and vice versa.
Everyone who is curious or quiet is either creative or strong.
If fred is both not happy and quiet then lucy is both not kind and not patient and vice versa.
Everyone who is either not generous or happy is patient or funny and vice versa.
Everyone who is not wise or not brave is not rich or old.
If paul is calm then alice is both not generous and quiet and vice versa.
Everyone who is both not brave and quiet is both quiet and not creative.
If someone is both humble and happy then mary is not brave.
If paul is either generous or quiet then someone is curious or calm.
If fred is both wise and not strong then someone is not wise or kind.
If alice is either rich or brave then someone is humble.
Everyone who is both humble and strong is brave or rich and vice versa.
If someone is tall or not strong then someone is rich.
Everyone who is either creative or not strong is either creative or old and vice versa.
Someone is either not funny or calm.
Paul is both kind and not brave.
Someone is either kind or not happy.
Lucy is either calm or strong.
Someone is both tall and creative.
Susan is both old and not strong.
Fred is calm.
Lucy is strong. | Susan is strong. | contradiction | (![X]:((wise(X)<~>~calm(X))=>~wise(X)))&
(((curious(lucy)<~>funny(lucy)))=>((~rich(fred)&~quiet(fred))))&
(![X]:((~old(X)&brave(X))<=>(brave(X)&generous(X))))&
(![X]:((curious(X)|quiet(X))=>(creative(X)<~>strong(X))))&
(((~happy(fred)&quiet(fred)))<=>((~kind(lucy)&~patient(lucy))))&
(![X]:((~generous(X)<~>happy(X))<=>(patient(X)|funny(X))))&
(![X]:((~wise(X)|~brave(X))=>(~rich(X)|old(X))))&
((calm(paul))<=>((~generous(alice)&quiet(alice))))&
(![X]:((~brave(X)&quiet(X))=>(quiet(X)&~creative(X))))&
((?[X]:((humble(X)&happy(X))))=>(~brave(mary)))&
(((generous(paul)<~>quiet(paul)))=>(?[X]:((curious(X)|calm(X)))))&
(((wise(fred)&~strong(fred)))=>(?[X]:((~wise(X)|kind(X)))))&
(((rich(alice)<~>brave(alice)))=>(?[X]:(humble(X))))&
(![X]:((humble(X)&strong(X))<=>(brave(X)|rich(X))))&
((?[X]:((tall(X)|~strong(X))))=>(?[X]:(rich(X))))&
(![X]:((creative(X)<~>~strong(X))<=>(creative(X)<~>old(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
((kind(paul)&~brave(paul)))&
(?[X]:((kind(X)<~>~happy(X))))&
((calm(lucy)<~>strong(lucy)))&
(?[X]:((tall(X)&creative(X))))&
((old(susan)&~strong(susan)))&
(calm(fred))&
(strong(lucy)) | strong(susan) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2017799647466522225419525
% SZS output start Proof for 2017799647466522225419525
22. ~strong(susan) & old(susan) [input p21]
25. strong(susan) [input hypothesis]
137. ~strong(susan) [cnf transformation 22]
140. strong(susan) [cnf transformation 25]
299. $false [subsumption resolution 140,137]
% SZS output end Proof for 2017799647466522225419525
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not rich or not curious then someone is both not patient and not kind.
If paul is not humble or not strong then someone is funny or not humble.
Everyone who is both quiet and patient is funny and vice versa.
If alice is either not rich or not old then alice is both not generous and not quiet and vice versa.
Everyone who is either kind or not funny is both not humble and kind and vice versa.
Everyone who is funny or not wise is both rich and wise and vice versa.
If susan is either not humble or tall then someone is quiet and vice versa.
Everyone who is both humble and calm is either wise or calm.
If someone is both not rich and not curious then john is either not generous or brave and vice versa.
Everyone who is not creative or curious is not old.
If mary is brave then alice is not curious and vice versa.
Everyone who is either happy or not tall is not happy.
If lucy is not tall then someone is either not funny or not tall.
Everyone who is not kind is not old and vice versa.
If lucy is not funny or wise then someone is both humble and not generous and vice versa.
If someone is either not calm or not happy then someone is either calm or tall and vice versa.
John is not happy.
Someone is either not wise or not curious.
Lucy is both happy and not creative.
Someone is tall.
Fred is both patient and wise.
Someone is patient.
Someone is either not old or not rich.
Susan is not rich. | Lucy is old. | contradiction | (((~rich(fred)<~>~curious(fred)))=>(?[X]:((~patient(X)&~kind(X)))))&
(((~humble(paul)|~strong(paul)))=>(?[X]:((funny(X)|~humble(X)))))&
(![X]:((quiet(X)&patient(X))<=>funny(X)))&
(((~rich(alice)<~>~old(alice)))<=>((~generous(alice)&~quiet(alice))))&
(![X]:((kind(X)<~>~funny(X))<=>(~humble(X)&kind(X))))&
(![X]:((funny(X)|~wise(X))<=>(rich(X)&wise(X))))&
(((~humble(susan)<~>tall(susan)))<=>(?[X]:(quiet(X))))&
(![X]:((humble(X)&calm(X))=>(wise(X)<~>calm(X))))&
((?[X]:((~rich(X)&~curious(X))))<=>((~generous(john)<~>brave(john))))&
(![X]:((~creative(X)|curious(X))=>~old(X)))&
((brave(mary))<=>(~curious(alice)))&
(![X]:((happy(X)<~>~tall(X))=>~happy(X)))&
((~tall(lucy))=>(?[X]:((~funny(X)<~>~tall(X)))))&
(![X]:(~kind(X)<=>~old(X)))&
(((~funny(lucy)|wise(lucy)))<=>(?[X]:((humble(X)&~generous(X)))))&
((?[X]:((~calm(X)<~>~happy(X))))<=>(?[X]:((calm(X)<~>tall(X)))))&
(~happy(john))&
(?[X]:((~wise(X)<~>~curious(X))))&
((happy(lucy)&~creative(lucy)))&
(?[X]:(tall(X)))&
((patient(fred)&wise(fred)))&
(?[X]:(patient(X)))&
(?[X]:((~old(X)<~>~rich(X))))&
(~rich(susan)) | old(lucy) | [
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4037916479290371561155099
% SZS output start Proof for 4037916479290371561155099
10. ! [X0] : ((curious(X0) | ~creative(X0)) => ~old(X0)) [input p9]
19. ~creative(lucy) & happy(lucy) [input p18]
25. old(lucy) [input hypothesis]
32. ! [X0] : (~old(X0) | (~curious(X0) & creative(X0))) [ennf transformation 10]
120. ~old(X0) | creative(X0) [cnf transformation 32]
147. ~creative(lucy) [cnf transformation 19]
155. old(lucy) [cnf transformation 25]
335. creative(lucy) [resolution 120,155]
337. $false [subsumption resolution 335,147]
% SZS output end Proof for 4037916479290371561155099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and not generous then paul is both not creative and not wise. If someone is both strong and not calm then someone is rich and vice versa. If someone is either humble or not patient then alice is either wise or brave and vice versa. Everyone who is not funny is not funny or not tall. If fred is either strong or funny then someone is creative or not creative. Everyone who is creative or quiet is either old or tall and vice versa. Everyone who is both not tall and not calm is generous and vice versa. Everyone who is not calm is tall or wise and vice versa. Everyone who is both not kind and quiet is not generous or kind and vice versa. Everyone who is not funny or humble is either not tall or not quiet. If someone is both not strong and not rich then john is both not funny and not curious and vice versa. Everyone who is either tall or humble is not tall and vice versa. If john is quiet or happy then fred is strong and vice versa. If mary is not patient or curious then someone is either tall or calm. Everyone who is both old and not strong is either not kind or creative. Someone is either not quiet or not generous. Paul is not creative or wise. Someone is both curious and not patient. | Alice is not old. | contradiction | ((?[X]:((old(X)&~generous(X))))=>((~creative(paul)&~wise(paul))))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:(rich(X))))&
((?[X]:((humble(X)<~>~patient(X))))<=>((wise(alice)<~>brave(alice))))&
(![X]:(~funny(X)=>(~funny(X)|~tall(X))))&
(((strong(fred)<~>funny(fred)))=>(?[X]:((creative(X)|~creative(X)))))&
(![X]:((creative(X)|quiet(X))<=>(old(X)<~>tall(X))))&
(![X]:((~tall(X)&~calm(X))<=>generous(X)))&
(![X]:(~calm(X)<=>(tall(X)|wise(X))))&
(![X]:((~kind(X)&quiet(X))<=>(~generous(X)|kind(X))))&
(![X]:((~funny(X)|humble(X))=>(~tall(X)<~>~quiet(X))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~funny(john)&~curious(john))))&
(![X]:((tall(X)<~>humble(X))<=>~tall(X)))&
(((quiet(john)|happy(john)))<=>(strong(fred)))&
(((~patient(mary)|curious(mary)))=>(?[X]:((tall(X)<~>calm(X)))))&
(![X]:((old(X)&~strong(X))=>(~kind(X)<~>creative(X))))&
(?[X]:((~quiet(X)<~>~generous(X))))&
((~creative(paul)|wise(paul)))&
(?[X]:((curious(X)&~patient(X)))) | ~old(alice) | [
"p5",
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8443612897567494933938575
% SZS output start Proof for 8443612897567494933938575
6. ! [X0] : ((quiet(X0) | creative(X0)) <=> (old(X0) <~> tall(X0))) [input p5]
7. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> generous(X0)) [input p6]
9. ! [X0] : ((quiet(X0) & ~kind(X0)) <=> (kind(X0) | ~generous(X0))) [input p8]
10. ! [X0] : ((humble(X0) | ~funny(X0)) => (~tall(X0) <~> ~quiet(X0))) [input p9]
12. ! [X0] : ((tall(X0) <~> humble(X0)) <=> ~tall(X0)) [input p11]
19. ~old(alice) [input hypothesis]
25. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) | (~humble(X0) & funny(X0))) [ennf transformation 10]
41. ! [X0] : (((quiet(X0) | creative(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~quiet(X0) & ~creative(X0)))) [nnf transformation 6]
42. ! [X0] : ((quiet(X0) | creative(X0) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~quiet(X0) & ~creative(X0)))) [flattening 41]
43. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~generous(X0)) & (generous(X0) | (calm(X0) | tall(X0)))) [nnf transformation 7]
44. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~generous(X0)) & (generous(X0) | calm(X0) | tall(X0))) [flattening 43]
47. ! [X0] : (((quiet(X0) & ~kind(X0)) | (~kind(X0) & generous(X0))) & ((kind(X0) | ~generous(X0)) | (~quiet(X0) | kind(X0)))) [nnf transformation 9]
48. ! [X0] : (((quiet(X0) & ~kind(X0)) | (~kind(X0) & generous(X0))) & (kind(X0) | ~generous(X0) | ~quiet(X0) | kind(X0))) [flattening 47]
49. ! [X0] : (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | (~humble(X0) & funny(X0))) [nnf transformation 25]
55. ! [X0] : ((((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | tall(X0)) & (~tall(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))))) [nnf transformation 12]
84. ~quiet(X0) | old(X0) | tall(X0) [cnf transformation 42]
90. ~tall(X0) | ~generous(X0) [cnf transformation 44]
98. quiet(X0) | generous(X0) [cnf transformation 48]
101. ~quiet(X0) | ~tall(X0) | ~humble(X0) [cnf transformation 49]
103. ~humble(X0) | tall(X0) | quiet(X0) [cnf transformation 49]
108. ~tall(X0) | humble(X0) | ~tall(X0) [cnf transformation 55]
110. humble(X0) | tall(X0) | tall(X0) [cnf transformation 55]
126. ~old(alice) [cnf transformation 19]
127. ~tall(X0) | humble(X0) [duplicate literal removal 108]
128. tall(X0) | humble(X0) [duplicate literal removal 110]
219. humble(X0) [subsumption resolution 127,128]
293. ~tall(X0) | ~humble(X0) | generous(X0) [resolution 101,98]
294. ~tall(X0) | generous(X0) [subsumption resolution 293,219]
295. ~tall(X0) [subsumption resolution 294,90]
331. tall(X0) | quiet(X0) [resolution 103,219]
332. quiet(X0) [subsumption resolution 331,295]
342. old(X3) | tall(X3) [resolution 332,84]
344. old(X3) [subsumption resolution 342,295]
357. $false [resolution 344,126]
% SZS output end Proof for 8443612897567494933938575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not tall is not creative or rich.
Everyone who is wise is quiet or not curious.
Everyone who is either not wise or tall is both not patient and creative.
Everyone who is both patient and funny is both not old and not patient and vice versa.
Everyone who is not generous is kind or not wise and vice versa.
If someone is not happy then someone is either happy or funny.
Everyone who is not patient or not strong is either kind or rich.
If someone is not generous then john is not rich or rich and vice versa.
Everyone who is either old or not old is either humble or curious.
Everyone who is either not brave or not creative is not curious or happy and vice versa.
Everyone who is not creative is both not curious and not tall and vice versa.
Everyone who is both kind and quiet is either wise or not wise and vice versa.
Everyone who is rich or not curious is not funny or curious and vice versa.
If susan is both wise and not old then someone is both quiet and brave.
Everyone who is creative or not quiet is both not calm and not wise and vice versa.
Everyone who is calm or humble is either not quiet or happy.
Someone is calm or quiet.
Someone is not curious or tall.
Susan is generous or not generous.
Someone is kind or not rich. | Susan is not wise. | neutral | (![X]:((patient(X)<~>~tall(X))=>(~creative(X)|rich(X))))&
(![X]:(wise(X)=>(quiet(X)|~curious(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~patient(X)&creative(X))))&
(![X]:((patient(X)&funny(X))<=>(~old(X)&~patient(X))))&
(![X]:(~generous(X)<=>(kind(X)|~wise(X))))&
((?[X]:(~happy(X)))=>(?[X]:((happy(X)<~>funny(X)))))&
(![X]:((~patient(X)|~strong(X))=>(kind(X)<~>rich(X))))&
((?[X]:(~generous(X)))<=>((~rich(john)|rich(john))))&
(![X]:((old(X)<~>~old(X))=>(humble(X)<~>curious(X))))&
(![X]:((~brave(X)<~>~creative(X))<=>(~curious(X)|happy(X))))&
(![X]:(~creative(X)<=>(~curious(X)&~tall(X))))&
(![X]:((kind(X)&quiet(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((rich(X)|~curious(X))<=>(~funny(X)|curious(X))))&
(((wise(susan)&~old(susan)))=>(?[X]:((quiet(X)&brave(X)))))&
(![X]:((creative(X)|~quiet(X))<=>(~calm(X)&~wise(X))))&
(![X]:((calm(X)|humble(X))=>(~quiet(X)<~>happy(X))))&
(?[X]:((calm(X)|quiet(X))))&
(?[X]:((~curious(X)|tall(X))))&
((generous(susan)|~generous(susan)))&
(?[X]:((kind(X)|~rich(X)))) | ~wise(susan) | [] | null | 0 |
If mary is either strong or not curious then someone is both not calm and not old. Everyone who is not wise or rich is not brave or not quiet. Everyone who is either not tall or quiet is humble. Everyone who is creative is either not kind or not curious and vice versa. If john is both not kind and not brave then fred is both not wise and curious and vice versa. If fred is both not tall and not curious then someone is not strong. If lucy is not creative or not tall then paul is both not strong and not tall and vice versa. Everyone who is not patient or not wise is either not tall or not brave and vice versa. If susan is not quiet then paul is either not funny or funny and vice versa. If someone is funny then someone is either wise or not funny and vice versa. Everyone who is humble or not humble is both not tall and calm. If susan is not creative or calm then lucy is either not humble or not curious. If mary is strong then john is kind and vice versa. Everyone who is either brave or not rich is not kind. Everyone who is not humble is either tall or not creative and vice versa. Everyone who is rich or not creative is not strong or not calm and vice versa. Susan is either not curious or wise. Someone is both not tall and creative. Someone is not rich or not curious. Mary is not patient. Someone is not creative or not strong. Someone is both not generous and quiet. Lucy is both generous and calm. | Paul is not strong. | entailment | (((strong(mary)<~>~curious(mary)))=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((~wise(X)|rich(X))=>(~brave(X)|~quiet(X))))&
(![X]:((~tall(X)<~>quiet(X))=>humble(X)))&
(![X]:(creative(X)<=>(~kind(X)<~>~curious(X))))&
(((~kind(john)&~brave(john)))<=>((~wise(fred)&curious(fred))))&
(((~tall(fred)&~curious(fred)))=>(?[X]:(~strong(X))))&
(((~creative(lucy)|~tall(lucy)))<=>((~strong(paul)&~tall(paul))))&
(![X]:((~patient(X)|~wise(X))<=>(~tall(X)<~>~brave(X))))&
((~quiet(susan))<=>((~funny(paul)<~>funny(paul))))&
((?[X]:(funny(X)))<=>(?[X]:((wise(X)<~>~funny(X)))))&
(![X]:((humble(X)|~humble(X))=>(~tall(X)&calm(X))))&
(((~creative(susan)|calm(susan)))=>((~humble(lucy)<~>~curious(lucy))))&
((strong(mary))<=>(kind(john)))&
(![X]:((brave(X)<~>~rich(X))=>~kind(X)))&
(![X]:(~humble(X)<=>(tall(X)<~>~creative(X))))&
(![X]:((rich(X)|~creative(X))<=>(~strong(X)|~calm(X))))&
((~curious(susan)<~>wise(susan)))&
(?[X]:((~tall(X)&creative(X))))&
(?[X]:((~rich(X)|~curious(X))))&
(~patient(mary))&
(?[X]:((~creative(X)|~strong(X))))&
(?[X]:((~generous(X)&quiet(X))))&
((generous(lucy)&calm(lucy))) | ~strong(paul) | [
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1476488968321290899199548
% SZS output start Proof for 1476488968321290899199548
7. (~tall(lucy) | ~creative(lucy)) <=> (~tall(paul) & ~strong(paul)) [input p6]
11. ! [X0] : ((~humble(X0) | humble(X0)) => (calm(X0) & ~tall(X0))) [input p10]
24. strong(paul) [input hypothesis]
33. ! [X0] : ((calm(X0) & ~tall(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 11]
45. ((~tall(lucy) | ~creative(lucy)) | (tall(paul) | strong(paul))) & ((~tall(paul) & ~strong(paul)) | (tall(lucy) & creative(lucy))) [nnf transformation 7]
46. (~tall(lucy) | ~creative(lucy) | tall(paul) | strong(paul)) & ((~tall(paul) & ~strong(paul)) | (tall(lucy) & creative(lucy))) [flattening 45]
86. ~strong(paul) | tall(lucy) [cnf transformation 46]
104. ~tall(X0) | ~humble(X0) [cnf transformation 33]
105. ~tall(X0) | humble(X0) [cnf transformation 33]
135. strong(paul) [cnf transformation 24]
182. 10 <=> strong(paul) [avatar definition]
194. 13 <=> tall(lucy) [avatar definition]
195. tall(lucy) <- (13) [avatar component clause 194]
200. 13 | ~10 [avatar split clause 86,182,194]
238. ~tall(X0) [subsumption resolution 104,105]
283. 10 [avatar split clause 135,182]
284. $false <- (13) [subsumption resolution 195,238]
285. ~13 [avatar contradiction clause 284]
288. $false [avatar sat refutation 200,283,285]
% SZS output end Proof for 1476488968321290899199548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not humble is either old or not old. Everyone who is old or not generous is curious or patient. Everyone who is either not brave or generous is both happy and not creative and vice versa. Everyone who is not creative is either not humble or not calm and vice versa. If someone is either not calm or not rich then mary is old or not quiet. If paul is not tall or kind then alice is both funny and old. Everyone who is old or happy is either not brave or not old and vice versa. If fred is generous or tall then someone is both not old and not strong. Everyone who is not wise is old or brave and vice versa. Everyone who is either quiet or not quiet is both not quiet and not curious. If john is either strong or old then alice is either not wise or patient and vice versa. If mary is kind then someone is either not funny or calm and vice versa. Everyone who is tall is not humble or not funny and vice versa. If someone is either not kind or not brave then fred is both creative and rich. Everyone who is not strong or not quiet is not old or not creative. If alice is both creative and generous then paul is both not tall and generous and vice versa. Lucy is old or creative. Paul is not patient. Someone is not brave. Alice is not funny. Someone is not rich. Someone is not old or happy. Lucy is strong or tall. John is either wise or patient. | Mary is not curious. | entailment | (![X]:((calm(X)<~>~humble(X))=>(old(X)<~>~old(X))))&
(![X]:((old(X)|~generous(X))=>(curious(X)|patient(X))))&
(![X]:((~brave(X)<~>generous(X))<=>(happy(X)&~creative(X))))&
(![X]:(~creative(X)<=>(~humble(X)<~>~calm(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>((old(mary)|~quiet(mary))))&
(((~tall(paul)|kind(paul)))=>((funny(alice)&old(alice))))&
(![X]:((old(X)|happy(X))<=>(~brave(X)<~>~old(X))))&
(((generous(fred)|tall(fred)))=>(?[X]:((~old(X)&~strong(X)))))&
(![X]:(~wise(X)<=>(old(X)|brave(X))))&
(![X]:((quiet(X)<~>~quiet(X))=>(~quiet(X)&~curious(X))))&
(((strong(john)<~>old(john)))<=>((~wise(alice)<~>patient(alice))))&
((kind(mary))<=>(?[X]:((~funny(X)<~>calm(X)))))&
(![X]:(tall(X)<=>(~humble(X)|~funny(X))))&
((?[X]:((~kind(X)<~>~brave(X))))=>((creative(fred)&rich(fred))))&
(![X]:((~strong(X)|~quiet(X))=>(~old(X)|~creative(X))))&
(((creative(alice)&generous(alice)))<=>((~tall(paul)&generous(paul))))&
((old(lucy)|creative(lucy)))&
(~patient(paul))&
(?[X]:(~brave(X)))&
(~funny(alice))&
(?[X]:(~rich(X)))&
(?[X]:((~old(X)|happy(X))))&
((strong(lucy)|tall(lucy)))&
((wise(john)<~>patient(john))) | ~curious(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 445477115529654636937245
% SZS output start Proof for 445477115529654636937245
10. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) => (~curious(X0) & ~quiet(X0))) [input p9]
25. curious(mary) [input hypothesis]
33. ! [X0] : ((~curious(X0) & ~quiet(X0)) | (quiet(X0) <=> ~quiet(X0))) [ennf transformation 10]
48. ! [X0] : ((~curious(X0) & ~quiet(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) [nnf transformation 33]
103. ~curious(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 48]
104. ~curious(X0) | quiet(X0) | quiet(X0) [cnf transformation 48]
139. curious(mary) [cnf transformation 25]
142. ~curious(X0) | ~quiet(X0) [duplicate literal removal 103]
143. ~curious(X0) | quiet(X0) [duplicate literal removal 104]
202. ~curious(X0) [subsumption resolution 142,143]
322. $false [subsumption resolution 139,202]
% SZS output end Proof for 445477115529654636937245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then paul is not patient. If alice is both funny and generous then someone is curious or patient. Everyone who is not creative is either not brave or rich and vice versa. If someone is either creative or patient then someone is not old or tall and vice versa. If someone is kind or not creative then someone is not rich or not curious. Everyone who is not kind or not calm is both not generous and not quiet. If someone is either strong or not patient then mary is either quiet or not kind and vice versa. Everyone who is not kind or quiet is both rich and not wise and vice versa. Everyone who is not patient is strong and vice versa. Everyone who is not strong or strong is both not patient and not wise. Everyone who is old or not tall is not rich or patient and vice versa. Everyone who is either rich or not rich is not humble or patient. If mary is not funny or brave then john is both not kind and happy. If lucy is kind then someone is not calm or not old. If susan is both not wise and not calm then lucy is either brave or wise. Everyone who is generous is not patient. John is both strong and creative. Someone is not creative. Mary is old or kind. Someone is either calm or not tall. Susan is both generous and not curious. | Alice is not calm. | neutral | ((?[X]:(kind(X)))=>(~patient(paul)))&
(((funny(alice)&generous(alice)))=>(?[X]:((curious(X)|patient(X)))))&
(![X]:(~creative(X)<=>(~brave(X)<~>rich(X))))&
((?[X]:((creative(X)<~>patient(X))))<=>(?[X]:((~old(X)|tall(X)))))&
((?[X]:((kind(X)|~creative(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((~kind(X)|~calm(X))=>(~generous(X)&~quiet(X))))&
((?[X]:((strong(X)<~>~patient(X))))<=>((quiet(mary)<~>~kind(mary))))&
(![X]:((~kind(X)|quiet(X))<=>(rich(X)&~wise(X))))&
(![X]:(~patient(X)<=>strong(X)))&
(![X]:((~strong(X)|strong(X))=>(~patient(X)&~wise(X))))&
(![X]:((old(X)|~tall(X))<=>(~rich(X)|patient(X))))&
(![X]:((rich(X)<~>~rich(X))=>(~humble(X)|patient(X))))&
(((~funny(mary)|brave(mary)))=>((~kind(john)&happy(john))))&
((kind(lucy))=>(?[X]:((~calm(X)|~old(X)))))&
(((~wise(susan)&~calm(susan)))=>((brave(lucy)<~>wise(lucy))))&
(![X]:(generous(X)=>~patient(X)))&
((strong(john)&creative(john)))&
(?[X]:(~creative(X)))&
((old(mary)|kind(mary)))&
(?[X]:((calm(X)<~>~tall(X))))&
((generous(susan)&~curious(susan))) | ~calm(alice) | [] | null | 0 |
Everyone who is not kind or kind is either not rich or generous and vice versa. Everyone who is both kind and humble is not wise and vice versa. Everyone who is either not creative or not strong is strong and vice versa. If john is not calm then someone is tall or not patient. If someone is both not curious and not wise then someone is either not tall or not strong and vice versa. Everyone who is not funny or not curious is not strong or old and vice versa. If someone is happy then someone is either not patient or kind and vice versa. Everyone who is generous or brave is both happy and not strong. Everyone who is wise is patient and vice versa. Everyone who is rich or not old is both creative and curious and vice versa. Everyone who is tall or not quiet is quiet and vice versa. Everyone who is old is both calm and not curious and vice versa. Everyone who is either calm or not happy is generous or not generous and vice versa. If fred is either not quiet or wise then someone is both not humble and old. If lucy is not strong then someone is not strong. Fred is quiet. Susan is either tall or not funny. Someone is either not creative or not tall. Someone is both humble and brave. Paul is both not funny and strong. Someone is curious or humble. | Fred is happy. | entailment | (![X]:((~kind(X)|kind(X))<=>(~rich(X)<~>generous(X))))&
(![X]:((kind(X)&humble(X))<=>~wise(X)))&
(![X]:((~creative(X)<~>~strong(X))<=>strong(X)))&
((~calm(john))=>(?[X]:((tall(X)|~patient(X)))))&
((?[X]:((~curious(X)&~wise(X))))<=>(?[X]:((~tall(X)<~>~strong(X)))))&
(![X]:((~funny(X)|~curious(X))<=>(~strong(X)|old(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((generous(X)|brave(X))=>(happy(X)&~strong(X))))&
(![X]:(wise(X)<=>patient(X)))&
(![X]:((rich(X)|~old(X))<=>(creative(X)&curious(X))))&
(![X]:((tall(X)|~quiet(X))<=>quiet(X)))&
(![X]:(old(X)<=>(calm(X)&~curious(X))))&
(![X]:((calm(X)<~>~happy(X))<=>(generous(X)|~generous(X))))&
(((~quiet(fred)<~>wise(fred)))=>(?[X]:((~humble(X)&old(X)))))&
((~strong(lucy))=>(?[X]:(~strong(X))))&
(quiet(fred))&
((tall(susan)<~>~funny(susan)))&
(?[X]:((~creative(X)<~>~tall(X))))&
(?[X]:((humble(X)&brave(X))))&
((~funny(paul)&strong(paul)))&
(?[X]:((curious(X)|humble(X)))) | happy(fred) | [
"p2",
"p7",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4676331845376211910175229
% SZS output start Proof for 4676331845376211910175229
3. ! [X0] : ((~creative(X0) <~> ~strong(X0)) <=> strong(X0)) [input p2]
8. ! [X0] : ((brave(X0) | generous(X0)) => (~strong(X0) & happy(X0))) [input p7]
10. ! [X0] : ((~old(X0) | rich(X0)) <=> (curious(X0) & creative(X0))) [input p9]
12. ! [X0] : (old(X0) <=> (~curious(X0) & calm(X0))) [input p11]
13. ! [X0] : ((calm(X0) <~> ~happy(X0)) <=> (~generous(X0) | generous(X0))) [input p12]
22. ~happy(fred) [input hypothesis]
26. ! [X0] : ((~strong(X0) & happy(X0)) | (~brave(X0) & ~generous(X0))) [ennf transformation 8]
33. ! [X0] : ((((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | ~strong(X0)) & (strong(X0) | ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0))))) [nnf transformation 3]
49. ! [X0] : (((~old(X0) | rich(X0)) | (~curious(X0) | ~creative(X0))) & ((curious(X0) & creative(X0)) | (old(X0) & ~rich(X0)))) [nnf transformation 10]
50. ! [X0] : ((~old(X0) | rich(X0) | ~curious(X0) | ~creative(X0)) & ((curious(X0) & creative(X0)) | (old(X0) & ~rich(X0)))) [flattening 49]
53. ! [X0] : ((old(X0) | (curious(X0) | ~calm(X0))) & ((~curious(X0) & calm(X0)) | ~old(X0))) [nnf transformation 12]
54. ! [X0] : ((old(X0) | curious(X0) | ~calm(X0)) & ((~curious(X0) & calm(X0)) | ~old(X0))) [flattening 53]
55. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (generous(X0) & ~generous(X0))) & ((~generous(X0) | generous(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [nnf transformation 13]
56. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (generous(X0) & ~generous(X0))) & (~generous(X0) | generous(X0) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [flattening 55]
80. strong(X0) | ~creative(X0) | strong(X0) [cnf transformation 33]
81. ~strong(X0) | ~creative(X0) | ~strong(X0) [cnf transformation 33]
98. happy(X0) | ~generous(X0) [cnf transformation 26]
105. creative(X0) | old(X0) [cnf transformation 50]
112. calm(X0) | ~old(X0) [cnf transformation 54]
120. happy(X0) | ~calm(X0) | generous(X0) [cnf transformation 56]
136. ~happy(fred) [cnf transformation 22]
139. strong(X0) | ~creative(X0) [duplicate literal removal 80]
140. ~strong(X0) | ~creative(X0) [duplicate literal removal 81]
143. ~creative(X0) [subsumption resolution 139,140]
213. old(X0) [subsumption resolution 105,143]
216. calm(X0) [subsumption resolution 112,213]
217. happy(X0) | generous(X0) [subsumption resolution 120,216]
218. happy(X0) [subsumption resolution 217,98]
250. $false [subsumption resolution 136,218]
% SZS output end Proof for 4676331845376211910175229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or curious is either not kind or not old and vice versa.
Everyone who is both not wise and not funny is both patient and tall and vice versa.
Everyone who is either not old or not generous is not creative.
If mary is patient then someone is either kind or happy.
Everyone who is humble or not funny is not kind or rich and vice versa.
Everyone who is both tall and calm is both not humble and brave and vice versa.
If mary is both not rich and not brave then someone is both kind and old and vice versa.
If mary is both not happy and patient then someone is either not wise or not kind and vice versa.
If someone is either patient or strong then someone is not kind.
If fred is not humble or creative then someone is both calm and strong.
Everyone who is not calm is both quiet and not brave.
Everyone who is not brave or patient is either not quiet or old and vice versa.
If mary is either not strong or wise then susan is either kind or wise and vice versa.
If susan is humble or not old then mary is both not rich and quiet.
If someone is not generous or not brave then someone is either not kind or rich.
Everyone who is both not kind and creative is patient or not strong and vice versa.
Fred is either not funny or not quiet.
Someone is rich or not humble.
Mary is both not generous and brave.
Paul is both not patient and brave.
Alice is patient or old.
Lucy is patient.
Someone is either calm or not strong. | Lucy is not quiet. | contradiction | (![X]:((~curious(X)|curious(X))<=>(~kind(X)<~>~old(X))))&
(![X]:((~wise(X)&~funny(X))<=>(patient(X)&tall(X))))&
(![X]:((~old(X)<~>~generous(X))=>~creative(X)))&
((patient(mary))=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((humble(X)|~funny(X))<=>(~kind(X)|rich(X))))&
(![X]:((tall(X)&calm(X))<=>(~humble(X)&brave(X))))&
(((~rich(mary)&~brave(mary)))<=>(?[X]:((kind(X)&old(X)))))&
(((~happy(mary)&patient(mary)))<=>(?[X]:((~wise(X)<~>~kind(X)))))&
((?[X]:((patient(X)<~>strong(X))))=>(?[X]:(~kind(X))))&
(((~humble(fred)|creative(fred)))=>(?[X]:((calm(X)&strong(X)))))&
(![X]:(~calm(X)=>(quiet(X)&~brave(X))))&
(![X]:((~brave(X)|patient(X))<=>(~quiet(X)<~>old(X))))&
(((~strong(mary)<~>wise(mary)))<=>((kind(susan)<~>wise(susan))))&
(((humble(susan)|~old(susan)))=>((~rich(mary)&quiet(mary))))&
((?[X]:((~generous(X)|~brave(X))))=>(?[X]:((~kind(X)<~>rich(X)))))&
(![X]:((~kind(X)&creative(X))<=>(patient(X)|~strong(X))))&
((~funny(fred)<~>~quiet(fred)))&
(?[X]:((rich(X)|~humble(X))))&
((~generous(mary)&brave(mary)))&
((~patient(paul)&brave(paul)))&
((patient(alice)|old(alice)))&
(patient(lucy))&
(?[X]:((calm(X)<~>~strong(X)))) | ~quiet(lucy) | [
"p0",
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2816456874079742724881372
% SZS output start Proof for 2816456874079742724881372
1. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~kind(X0) <~> ~old(X0))) [input p0]
12. ! [X0] : ((patient(X0) | ~brave(X0)) <=> (~quiet(X0) <~> old(X0))) [input p11]
16. ! [X0] : ((creative(X0) & ~kind(X0)) <=> (~strong(X0) | patient(X0))) [input p15]
22. patient(lucy) [input p21]
24. ~quiet(lucy) [input hypothesis]
34. ! [X0] : (((curious(X0) | ~curious(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0)))) & (((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | (~curious(X0) & curious(X0)))) [nnf transformation 1]
35. ! [X0] : ((curious(X0) | ~curious(X0) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0)))) & (((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | (~curious(X0) & curious(X0)))) [flattening 34]
62. ! [X0] : (((patient(X0) | ~brave(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~patient(X0) & brave(X0)))) [nnf transformation 12]
63. ! [X0] : ((patient(X0) | ~brave(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~patient(X0) & brave(X0)))) [flattening 62]
69. ! [X0] : (((creative(X0) & ~kind(X0)) | (strong(X0) & ~patient(X0))) & ((~strong(X0) | patient(X0)) | (~creative(X0) | kind(X0)))) [nnf transformation 16]
70. ! [X0] : (((creative(X0) & ~kind(X0)) | (strong(X0) & ~patient(X0))) & (~strong(X0) | patient(X0) | ~creative(X0) | kind(X0))) [flattening 69]
79. old(X0) | kind(X0) | curious(X0) [cnf transformation 35]
80. ~curious(X0) | kind(X0) | old(X0) [cnf transformation 35]
120. ~patient(X0) | quiet(X0) | ~old(X0) [cnf transformation 63]
140. ~patient(X0) | ~kind(X0) [cnf transformation 70]
152. patient(lucy) [cnf transformation 22]
155. ~quiet(lucy) [cnf transformation 24]
156. old(X0) | kind(X0) [subsumption resolution 79,80]
347. ~kind(lucy) [resolution 140,152]
394. 42 <=> old(lucy) [avatar definition]
395. ~old(lucy) <- (~42) [avatar component clause 394]
396. old(lucy) <- (42) [avatar component clause 394]
549. kind(lucy) <- (~42) [resolution 395,156]
550. $false <- (~42) [subsumption resolution 549,347]
551. 42 [avatar contradiction clause 550]
624. quiet(lucy) | ~old(lucy) [resolution 120,152]
628. ~old(lucy) [subsumption resolution 624,155]
629. $false <- (42) [subsumption resolution 628,396]
630. ~42 [avatar contradiction clause 629]
631. $false [avatar sat refutation 551,630]
% SZS output end Proof for 2816456874079742724881372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or kind is not patient and vice versa. If john is generous then mary is kind or strong and vice versa. If someone is tall or funny then susan is tall and vice versa. Everyone who is curious is both creative and not generous. Everyone who is not curious or old is either rich or not happy. Everyone who is old is either not wise or not creative and vice versa. If mary is not strong or generous then someone is both funny and not strong. Everyone who is either not creative or wise is not brave or brave and vice versa. Everyone who is calm or not quiet is not patient and vice versa. If susan is not calm then fred is both not rich and curious and vice versa. Everyone who is both not brave and rich is either not generous or not calm. Everyone who is quiet or generous is either strong or not generous and vice versa. Everyone who is rich is both not tall and generous and vice versa. If someone is both not tall and quiet then john is not happy or curious and vice versa. If someone is either not strong or not kind then lucy is both not wise and not tall and vice versa. Everyone who is either not wise or quiet is calm or not strong and vice versa. Someone is not strong or funny. Alice is both not quiet and calm. Someone is not quiet or not humble. Paul is either humble or not generous. Someone is both not patient and tall. Lucy is both not brave and not rich. Lucy is either humble or kind. | Paul is quiet. | neutral | (![X]:((~quiet(X)|kind(X))<=>~patient(X)))&
((generous(john))<=>((kind(mary)|strong(mary))))&
((?[X]:((tall(X)|funny(X))))<=>(tall(susan)))&
(![X]:(curious(X)=>(creative(X)&~generous(X))))&
(![X]:((~curious(X)|old(X))=>(rich(X)<~>~happy(X))))&
(![X]:(old(X)<=>(~wise(X)<~>~creative(X))))&
(((~strong(mary)|generous(mary)))=>(?[X]:((funny(X)&~strong(X)))))&
(![X]:((~creative(X)<~>wise(X))<=>(~brave(X)|brave(X))))&
(![X]:((calm(X)|~quiet(X))<=>~patient(X)))&
((~calm(susan))<=>((~rich(fred)&curious(fred))))&
(![X]:((~brave(X)&rich(X))=>(~generous(X)<~>~calm(X))))&
(![X]:((quiet(X)|generous(X))<=>(strong(X)<~>~generous(X))))&
(![X]:(rich(X)<=>(~tall(X)&generous(X))))&
((?[X]:((~tall(X)&quiet(X))))<=>((~happy(john)|curious(john))))&
((?[X]:((~strong(X)<~>~kind(X))))<=>((~wise(lucy)&~tall(lucy))))&
(![X]:((~wise(X)<~>quiet(X))<=>(calm(X)|~strong(X))))&
(?[X]:((~strong(X)|funny(X))))&
((~quiet(alice)&calm(alice)))&
(?[X]:((~quiet(X)|~humble(X))))&
((humble(paul)<~>~generous(paul)))&
(?[X]:((~patient(X)&tall(X))))&
((~brave(lucy)&~rich(lucy)))&
((humble(lucy)<~>kind(lucy))) | quiet(paul) | [] | null | 0 |
Everyone who is both not strong and wise is either not generous or not calm and vice versa.
If someone is both generous and humble then john is not old and vice versa.
Everyone who is not calm is both tall and calm.
Everyone who is both not happy and quiet is not rich or curious and vice versa.
If fred is happy then someone is either not creative or tall.
Everyone who is not happy is rich and vice versa.
If someone is either not creative or curious then someone is not generous or curious and vice versa.
If someone is strong or not rich then fred is either not wise or not happy and vice versa.
If lucy is rich then paul is either not calm or curious.
If fred is both calm and not creative then alice is either generous or not patient and vice versa.
Everyone who is both not rich and not patient is not brave or not curious and vice versa.
If john is either patient or tall then mary is happy or rich.
If lucy is both humble and not wise then paul is not kind or not wise.
Everyone who is funny or creative is both creative and not humble and vice versa.
If someone is either not tall or not rich then someone is either tall or patient.
If someone is generous then john is either not funny or rich.
Someone is both funny and not patient.
Someone is not patient.
Alice is both not humble and not patient.
John is creative.
Mary is humble or not strong.
Fred is patient or not quiet. | Fred is brave. | entailment | (![X]:((~strong(X)&wise(X))<=>(~generous(X)<~>~calm(X))))&
((?[X]:((generous(X)&humble(X))))<=>(~old(john)))&
(![X]:(~calm(X)=>(tall(X)&calm(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~rich(X)|curious(X))))&
((happy(fred))=>(?[X]:((~creative(X)<~>tall(X)))))&
(![X]:(~happy(X)<=>rich(X)))&
((?[X]:((~creative(X)<~>curious(X))))<=>(?[X]:((~generous(X)|curious(X)))))&
((?[X]:((strong(X)|~rich(X))))<=>((~wise(fred)<~>~happy(fred))))&
((rich(lucy))=>((~calm(paul)<~>curious(paul))))&
(((calm(fred)&~creative(fred)))<=>((generous(alice)<~>~patient(alice))))&
(![X]:((~rich(X)&~patient(X))<=>(~brave(X)|~curious(X))))&
(((patient(john)<~>tall(john)))=>((happy(mary)|rich(mary))))&
(((humble(lucy)&~wise(lucy)))=>((~kind(paul)|~wise(paul))))&
(![X]:((funny(X)|creative(X))<=>(creative(X)&~humble(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>(?[X]:((tall(X)<~>patient(X)))))&
((?[X]:(generous(X)))=>((~funny(john)<~>rich(john))))&
(?[X]:((funny(X)&~patient(X))))&
(?[X]:(~patient(X)))&
((~humble(alice)&~patient(alice)))&
(creative(john))&
((humble(mary)|~strong(mary)))&
((patient(fred)|~quiet(fred))) | brave(fred) | [
"p3",
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2261417086373012680364571
% SZS output start Proof for 2261417086373012680364571
4. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (curious(X0) | ~rich(X0))) [input p3]
6. ! [X0] : (~happy(X0) <=> rich(X0)) [input p5]
11. ! [X0] : ((~patient(X0) & ~rich(X0)) <=> (~curious(X0) | ~brave(X0))) [input p10]
23. ~brave(fred) [input hypothesis]
40. ! [X0] : (((quiet(X0) & ~happy(X0)) | (~curious(X0) & rich(X0))) & ((curious(X0) | ~rich(X0)) | (~quiet(X0) | happy(X0)))) [nnf transformation 4]
41. ! [X0] : (((quiet(X0) & ~happy(X0)) | (~curious(X0) & rich(X0))) & (curious(X0) | ~rich(X0) | ~quiet(X0) | happy(X0))) [flattening 40]
45. ! [X0] : ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))) [nnf transformation 6]
58. ! [X0] : (((~patient(X0) & ~rich(X0)) | (curious(X0) & brave(X0))) & ((~curious(X0) | ~brave(X0)) | (patient(X0) | rich(X0)))) [nnf transformation 11]
59. ! [X0] : (((~patient(X0) & ~rich(X0)) | (curious(X0) & brave(X0))) & (~curious(X0) | ~brave(X0) | patient(X0) | rich(X0))) [flattening 58]
84. ~happy(X0) | rich(X0) [cnf transformation 41]
90. rich(X0) | happy(X0) [cnf transformation 45]
91. ~happy(X0) | ~rich(X0) [cnf transformation 45]
113. ~rich(X0) | brave(X0) [cnf transformation 59]
138. ~brave(fred) [cnf transformation 23]
172. ~happy(X0) [subsumption resolution 91,84]
173. rich(X0) [subsumption resolution 90,172]
245. brave(X0) [subsumption resolution 113,173]
289. $false [subsumption resolution 138,245]
% SZS output end Proof for 2261417086373012680364571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or not rich is wise or quiet and vice versa. Everyone who is tall is rich and vice versa. Everyone who is patient is tall or not generous. If mary is old then lucy is both humble and tall and vice versa. Everyone who is either humble or not brave is both not patient and curious and vice versa. Everyone who is either not humble or not rich is both rich and not rich and vice versa. Everyone who is not funny is not calm. Everyone who is not wise is either patient or tall. Everyone who is both strong and wise is both not strong and generous and vice versa. If susan is either funny or creative then someone is tall. If someone is either not rich or funny then fred is either patient or not creative and vice versa. If paul is both not old and brave then susan is humble or not wise and vice versa. If someone is happy then someone is not calm. Everyone who is both generous and wise is not wise and vice versa. If paul is tall then someone is patient or curious. If alice is both funny and not brave then mary is either not patient or not rich. Someone is funny or creative. Fred is brave or calm. Someone is both not generous and calm. Fred is happy or patient. Someone is both not curious and not quiet. Someone is not brave or funny. Someone is either calm or not funny. | Susan is rich. | neutral | (![X]:((rich(X)<~>~rich(X))<=>(wise(X)|quiet(X))))&
(![X]:(tall(X)<=>rich(X)))&
(![X]:(patient(X)=>(tall(X)|~generous(X))))&
((old(mary))<=>((humble(lucy)&tall(lucy))))&
(![X]:((humble(X)<~>~brave(X))<=>(~patient(X)&curious(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(rich(X)&~rich(X))))&
(![X]:(~funny(X)=>~calm(X)))&
(![X]:(~wise(X)=>(patient(X)<~>tall(X))))&
(![X]:((strong(X)&wise(X))<=>(~strong(X)&generous(X))))&
(((funny(susan)<~>creative(susan)))=>(?[X]:(tall(X))))&
((?[X]:((~rich(X)<~>funny(X))))<=>((patient(fred)<~>~creative(fred))))&
(((~old(paul)&brave(paul)))<=>((humble(susan)|~wise(susan))))&
((?[X]:(happy(X)))=>(?[X]:(~calm(X))))&
(![X]:((generous(X)&wise(X))<=>~wise(X)))&
((tall(paul))=>(?[X]:((patient(X)|curious(X)))))&
(((funny(alice)&~brave(alice)))=>((~patient(mary)<~>~rich(mary))))&
(?[X]:((funny(X)|creative(X))))&
((brave(fred)|calm(fred)))&
(?[X]:((~generous(X)&calm(X))))&
((happy(fred)|patient(fred)))&
(?[X]:((~curious(X)&~quiet(X))))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((calm(X)<~>~funny(X)))) | rich(susan) | [] | null | 0 |
If someone is not happy or patient then john is both not tall and curious and vice versa. If john is not funny or humble then john is not wise or wise and vice versa. Everyone who is both not happy and not curious is either not funny or not patient and vice versa. Everyone who is not tall or not generous is both tall and not old and vice versa. Everyone who is tall or generous is both not generous and rich. Everyone who is strong or not quiet is either generous or not strong and vice versa. If fred is not humble or not generous then mary is either not wise or patient. Everyone who is not rich is funny and vice versa. Everyone who is not creative is old or not happy and vice versa. If someone is both humble and kind then lucy is not strong or tall and vice versa. Everyone who is either generous or not humble is both generous and curious and vice versa. If mary is kind or not curious then mary is either not strong or not rich and vice versa. Everyone who is both not rich and not happy is not kind and vice versa. If someone is both humble and not generous then someone is not wise and vice versa. Someone is curious. Someone is funny or not strong. Someone is not wise. Paul is not strong. | Fred is quiet. | contradiction | ((?[X]:((~happy(X)|patient(X))))<=>((~tall(john)&curious(john))))&
(((~funny(john)|humble(john)))<=>((~wise(john)|wise(john))))&
(![X]:((~happy(X)&~curious(X))<=>(~funny(X)<~>~patient(X))))&
(![X]:((~tall(X)|~generous(X))<=>(tall(X)&~old(X))))&
(![X]:((tall(X)|generous(X))=>(~generous(X)&rich(X))))&
(![X]:((strong(X)|~quiet(X))<=>(generous(X)<~>~strong(X))))&
(((~humble(fred)|~generous(fred)))=>((~wise(mary)<~>patient(mary))))&
(![X]:(~rich(X)<=>funny(X)))&
(![X]:(~creative(X)<=>(old(X)|~happy(X))))&
((?[X]:((humble(X)&kind(X))))<=>((~strong(lucy)|tall(lucy))))&
(![X]:((generous(X)<~>~humble(X))<=>(generous(X)&curious(X))))&
(((kind(mary)|~curious(mary)))<=>((~strong(mary)<~>~rich(mary))))&
(![X]:((~rich(X)&~happy(X))<=>~kind(X)))&
((?[X]:((humble(X)&~generous(X))))<=>(?[X]:(~wise(X))))&
(?[X]:(curious(X)))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:(~wise(X)))&
(~strong(paul)) | quiet(fred) | [
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7709251877636946004535213
% SZS output start Proof for 7709251877636946004535213
5. ! [X0] : ((generous(X0) | tall(X0)) => (rich(X0) & ~generous(X0))) [input p4]
6. ! [X0] : ((~quiet(X0) | strong(X0)) <=> (generous(X0) <~> ~strong(X0))) [input p5]
19. quiet(fred) [input hypothesis]
21. ! [X0] : ((rich(X0) & ~generous(X0)) | (~generous(X0) & ~tall(X0))) [ennf transformation 5]
34. ! [X0] : (((~quiet(X0) | strong(X0)) | ((generous(X0) | strong(X0)) & (~strong(X0) | ~generous(X0)))) & (((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) | (quiet(X0) & ~strong(X0)))) [nnf transformation 6]
35. ! [X0] : ((~quiet(X0) | strong(X0) | ((generous(X0) | strong(X0)) & (~strong(X0) | ~generous(X0)))) & (((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) | (quiet(X0) & ~strong(X0)))) [flattening 34]
81. ~generous(X0) | ~generous(X0) [cnf transformation 21]
84. ~strong(X0) | generous(X0) | ~strong(X0) [cnf transformation 35]
89. ~quiet(X0) | strong(X0) | generous(X0) | strong(X0) [cnf transformation 35]
123. quiet(fred) [cnf transformation 19]
126. ~strong(X0) | generous(X0) [duplicate literal removal 84]
127. ~quiet(X0) | strong(X0) | generous(X0) [duplicate literal removal 89]
128. ~generous(X0) [duplicate literal removal 81]
173. ~quiet(X0) | strong(X0) [subsumption resolution 127,128]
175. ~strong(X0) [subsumption resolution 126,128]
220. strong(fred) [resolution 173,123]
221. $false [subsumption resolution 220,175]
% SZS output end Proof for 7709251877636946004535213
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not strong or not creative then someone is not funny or funny. If susan is both not quiet and not wise then mary is both old and not creative. Everyone who is generous or creative is either wise or curious and vice versa. Everyone who is both kind and creative is both rich and strong. If mary is both kind and not happy then lucy is calm and vice versa. If mary is not generous then john is either funny or not curious. Everyone who is not kind or not humble is not brave or not funny. Everyone who is both brave and funny is not curious or not strong. If someone is funny then lucy is creative. If john is kind or not strong then someone is humble and vice versa. If alice is both rich and kind then john is both humble and not generous. If john is not wise or not brave then john is both not patient and kind. Everyone who is either calm or strong is not strong and vice versa. If someone is either brave or not brave then john is either generous or not old. Everyone who is either generous or not generous is not wise. If someone is not calm or not tall then someone is creative or not calm and vice versa. Someone is not happy. Someone is either not patient or quiet. Paul is not strong. Mary is either quiet or brave. Susan is either not curious or curious. Someone is either not brave or not funny. Someone is both calm and funny. | Lucy is creative. | entailment | (((~strong(susan)<~>~creative(susan)))=>(?[X]:((~funny(X)|funny(X)))))&
(((~quiet(susan)&~wise(susan)))=>((old(mary)&~creative(mary))))&
(![X]:((generous(X)|creative(X))<=>(wise(X)<~>curious(X))))&
(![X]:((kind(X)&creative(X))=>(rich(X)&strong(X))))&
(((kind(mary)&~happy(mary)))<=>(calm(lucy)))&
((~generous(mary))=>((funny(john)<~>~curious(john))))&
(![X]:((~kind(X)|~humble(X))=>(~brave(X)|~funny(X))))&
(![X]:((brave(X)&funny(X))=>(~curious(X)|~strong(X))))&
((?[X]:(funny(X)))=>(creative(lucy)))&
(((kind(john)|~strong(john)))<=>(?[X]:(humble(X))))&
(((rich(alice)&kind(alice)))=>((humble(john)&~generous(john))))&
(((~wise(john)|~brave(john)))=>((~patient(john)&kind(john))))&
(![X]:((calm(X)<~>strong(X))<=>~strong(X)))&
((?[X]:((brave(X)<~>~brave(X))))=>((generous(john)<~>~old(john))))&
(![X]:((generous(X)<~>~generous(X))=>~wise(X)))&
((?[X]:((~calm(X)|~tall(X))))<=>(?[X]:((creative(X)|~calm(X)))))&
(?[X]:(~happy(X)))&
(?[X]:((~patient(X)<~>quiet(X))))&
(~strong(paul))&
((quiet(mary)<~>brave(mary)))&
((~curious(susan)<~>curious(susan)))&
(?[X]:((~brave(X)<~>~funny(X))))&
(?[X]:((calm(X)&funny(X)))) | creative(lucy) | [
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2062490954842334366455435
% SZS output start Proof for 2062490954842334366455435
9. ? [X0] : funny(X0) => creative(lucy) [input p8]
23. ? [X0] : (funny(X0) & calm(X0)) [input p22]
24. ~creative(lucy) [input hypothesis]
36. creative(lucy) | ! [X0] : ~funny(X0) [ennf transformation 9]
73. ? [X0] : (funny(X0) & calm(X0)) => (funny(sK7) & calm(sK7)) [choice axiom]
74. funny(sK7) & calm(sK7) [skolemisation 23,73]
95. creative(lucy) | ~funny(X0) [cnf transformation 36]
130. funny(sK7) [cnf transformation 74]
131. ~creative(lucy) [cnf transformation 24]
188. 11 <=> ! [X0] : ~funny(X0) [avatar definition]
189. ~funny(X0) <- (11) [avatar component clause 188]
191. 12 <=> creative(lucy) [avatar definition]
194. 11 | 12 [avatar split clause 95,191,188]
311. ~12 [avatar split clause 131,191]
318. $false <- (11) [resolution 189,130]
319. ~11 [avatar contradiction clause 318]
320. $false [avatar sat refutation 194,311,319]
% SZS output end Proof for 2062490954842334366455435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or funny is not strong and vice versa.
If someone is either not brave or curious then someone is calm.
If someone is both wise and quiet then someone is not kind or generous.
Everyone who is not tall is either quiet or not patient.
If paul is funny or quiet then lucy is either not rich or not strong and vice versa.
Everyone who is both not tall and funny is not old and vice versa.
Everyone who is generous is not generous or old and vice versa.
If paul is both calm and not calm then someone is kind or funny.
If someone is either patient or kind then lucy is either not wise or strong and vice versa.
If mary is not quiet or happy then someone is both creative and not rich.
Everyone who is both funny and kind is both brave and not tall and vice versa.
If paul is calm then someone is not rich or humble and vice versa.
If someone is both not brave and not calm then someone is happy or humble and vice versa.
Everyone who is both not kind and not funny is not quiet and vice versa.
Everyone who is not creative is both not happy and not calm.
Everyone who is tall or not calm is both not brave and humble.
John is either not humble or not happy.
Someone is not wise.
Someone is both not kind and not tall.
Susan is not tall or creative.
Someone is creative or wise. | John is patient. | neutral | (![X]:((kind(X)<~>funny(X))<=>~strong(X)))&
((?[X]:((~brave(X)<~>curious(X))))=>(?[X]:(calm(X))))&
((?[X]:((wise(X)&quiet(X))))=>(?[X]:((~kind(X)|generous(X)))))&
(![X]:(~tall(X)=>(quiet(X)<~>~patient(X))))&
(((funny(paul)|quiet(paul)))<=>((~rich(lucy)<~>~strong(lucy))))&
(![X]:((~tall(X)&funny(X))<=>~old(X)))&
(![X]:(generous(X)<=>(~generous(X)|old(X))))&
(((calm(paul)&~calm(paul)))=>(?[X]:((kind(X)|funny(X)))))&
((?[X]:((patient(X)<~>kind(X))))<=>((~wise(lucy)<~>strong(lucy))))&
(((~quiet(mary)|happy(mary)))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((funny(X)&kind(X))<=>(brave(X)&~tall(X))))&
((calm(paul))<=>(?[X]:((~rich(X)|humble(X)))))&
((?[X]:((~brave(X)&~calm(X))))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((~kind(X)&~funny(X))<=>~quiet(X)))&
(![X]:(~creative(X)=>(~happy(X)&~calm(X))))&
(![X]:((tall(X)|~calm(X))=>(~brave(X)&humble(X))))&
((~humble(john)<~>~happy(john)))&
(?[X]:(~wise(X)))&
(?[X]:((~kind(X)&~tall(X))))&
((~tall(susan)|creative(susan)))&
(?[X]:((creative(X)|wise(X)))) | patient(john) | [] | null | 0 |
Everyone who is either not funny or old is not old and vice versa. If mary is both not wise and creative then someone is not strong and vice versa. Everyone who is not generous or not wise is wise or not creative and vice versa. If lucy is quiet or not creative then paul is creative or not funny and vice versa. Everyone who is generous or not old is not tall or generous and vice versa. Everyone who is generous or calm is either happy or tall. If someone is either not curious or rich then paul is creative or not curious and vice versa. Everyone who is either creative or old is not patient or quiet. If susan is curious or not generous then fred is both not patient and tall and vice versa. Everyone who is either not generous or not happy is either not creative or brave and vice versa. Everyone who is calm or rich is both not creative and not strong and vice versa. Everyone who is not old or not generous is both happy and wise. Everyone who is either not patient or not funny is either creative or calm and vice versa. If alice is either not wise or patient then john is not generous or not calm and vice versa. Everyone who is either not patient or creative is both kind and strong and vice versa. Fred is generous. Someone is both not brave and not quiet. Lucy is wise or not calm. Someone is either quiet or curious. Susan is humble or not funny. Lucy is both quiet and not brave. Someone is both not humble and not wise. | Paul is not calm. | entailment | (![X]:((~funny(X)<~>old(X))<=>~old(X)))&
(((~wise(mary)&creative(mary)))<=>(?[X]:(~strong(X))))&
(![X]:((~generous(X)|~wise(X))<=>(wise(X)|~creative(X))))&
(((quiet(lucy)|~creative(lucy)))<=>((creative(paul)|~funny(paul))))&
(![X]:((generous(X)|~old(X))<=>(~tall(X)|generous(X))))&
(![X]:((generous(X)|calm(X))=>(happy(X)<~>tall(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((creative(paul)|~curious(paul))))&
(![X]:((creative(X)<~>old(X))=>(~patient(X)|quiet(X))))&
(((curious(susan)|~generous(susan)))<=>((~patient(fred)&tall(fred))))&
(![X]:((~generous(X)<~>~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)&~strong(X))))&
(![X]:((~old(X)|~generous(X))=>(happy(X)&wise(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(creative(X)<~>calm(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~generous(john)|~calm(john))))&
(![X]:((~patient(X)<~>creative(X))<=>(kind(X)&strong(X))))&
(generous(fred))&
(?[X]:((~brave(X)&~quiet(X))))&
((wise(lucy)|~calm(lucy)))&
(?[X]:((quiet(X)<~>curious(X))))&
((humble(susan)|~funny(susan)))&
((quiet(lucy)&~brave(lucy)))&
(?[X]:((~humble(X)&~wise(X)))) | ~calm(paul) | [
"p1",
"p2",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4090156000161906610352546
% SZS output start Proof for 4090156000161906610352546
2. (creative(mary) & ~wise(mary)) <=> ? [X0] : ~strong(X0) [input p1]
3. ! [X0] : ((~wise(X0) | ~generous(X0)) <=> (~creative(X0) | wise(X0))) [input p2]
11. ! [X0] : ((rich(X0) | calm(X0)) <=> (~strong(X0) & ~creative(X0))) [input p10]
23. calm(paul) [input hypothesis]
29. ((creative(mary) & ~wise(mary)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | (~creative(mary) | wise(mary))) [nnf transformation 2]
30. ((creative(mary) & ~wise(mary)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | ~creative(mary) | wise(mary)) [flattening 29]
31. ((creative(mary) & ~wise(mary)) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | ~creative(mary) | wise(mary)) [rectify 30]
32. ? [X1] : ~strong(X1) => ~strong(sK0) [choice axiom]
33. ((creative(mary) & ~wise(mary)) | ! [X0] : strong(X0)) & (~strong(sK0) | ~creative(mary) | wise(mary)) [skolemisation 31,32]
34. ! [X0] : (((~wise(X0) | ~generous(X0)) | (creative(X0) & ~wise(X0))) & ((~creative(X0) | wise(X0)) | (wise(X0) & generous(X0)))) [nnf transformation 3]
35. ! [X0] : ((~wise(X0) | ~generous(X0) | (creative(X0) & ~wise(X0))) & (~creative(X0) | wise(X0) | (wise(X0) & generous(X0)))) [flattening 34]
50. ! [X0] : (((rich(X0) | calm(X0)) | (strong(X0) | creative(X0))) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 11]
51. ! [X0] : ((rich(X0) | calm(X0) | strong(X0) | creative(X0)) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 50]
69. ~wise(mary) | strong(X0) [cnf transformation 33]
70. creative(mary) | strong(X0) [cnf transformation 33]
72. ~creative(X0) | wise(X0) | wise(X0) [cnf transformation 35]
110. ~calm(X0) | ~strong(X0) [cnf transformation 51]
148. calm(paul) [cnf transformation 23]
149. ~creative(X0) | wise(X0) [duplicate literal removal 72]
155. 1 <=> ! [X0] : strong(X0) [avatar definition]
156. strong(X0) <- (1) [avatar component clause 155]
158. 2 <=> creative(mary) [avatar definition]
160. creative(mary) <- (2) [avatar component clause 158]
161. 1 | 2 [avatar split clause 70,158,155]
163. 3 <=> wise(mary) [avatar definition]
165. ~wise(mary) <- (~3) [avatar component clause 163]
166. 1 | ~3 [avatar split clause 69,163,155]
284. ~strong(paul) [resolution 110,148]
289. wise(mary) <- (2) [resolution 149,160]
290. $false <- (2, ~3) [subsumption resolution 289,165]
291. ~2 | 3 [avatar contradiction clause 290]
293. $false <- (1) [resolution 156,284]
294. ~1 [avatar contradiction clause 293]
296. $false [avatar sat refutation 161,166,291,294]
% SZS output end Proof for 4090156000161906610352546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or brave is either tall or patient.
Everyone who is not wise or not strong is both funny and not strong and vice versa.
If someone is generous then paul is both patient and not strong.
Everyone who is both not happy and not humble is both not happy and rich and vice versa.
Everyone who is both happy and brave is either kind or not humble.
If lucy is not patient then paul is quiet.
If someone is either not tall or funny then fred is both not quiet and generous.
Everyone who is not quiet or not rich is either not old or calm and vice versa.
If someone is both quiet and not old then someone is quiet and vice versa.
Everyone who is kind is not funny and vice versa.
Everyone who is either not generous or humble is both not patient and old.
Everyone who is either not humble or kind is strong or humble and vice versa.
If alice is not quiet or not wise then someone is either not strong or old and vice versa.
Everyone who is not creative or not curious is not brave or not rich and vice versa.
Everyone who is patient is not wise.
If alice is either brave or not brave then john is not tall or humble and vice versa.
Someone is both not patient and strong.
Mary is strong.
Someone is tall or not rich.
Someone is not old.
Someone is not quiet. | Mary is humble. | entailment | (![X]:((funny(X)|brave(X))=>(tall(X)<~>patient(X))))&
(![X]:((~wise(X)|~strong(X))<=>(funny(X)&~strong(X))))&
((?[X]:(generous(X)))=>((patient(paul)&~strong(paul))))&
(![X]:((~happy(X)&~humble(X))<=>(~happy(X)&rich(X))))&
(![X]:((happy(X)&brave(X))=>(kind(X)<~>~humble(X))))&
((~patient(lucy))=>(quiet(paul)))&
((?[X]:((~tall(X)<~>funny(X))))=>((~quiet(fred)&generous(fred))))&
(![X]:((~quiet(X)|~rich(X))<=>(~old(X)<~>calm(X))))&
((?[X]:((quiet(X)&~old(X))))<=>(?[X]:(quiet(X))))&
(![X]:(kind(X)<=>~funny(X)))&
(![X]:((~generous(X)<~>humble(X))=>(~patient(X)&old(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(strong(X)|humble(X))))&
(((~quiet(alice)|~wise(alice)))<=>(?[X]:((~strong(X)<~>old(X)))))&
(![X]:((~creative(X)|~curious(X))<=>(~brave(X)|~rich(X))))&
(![X]:(patient(X)=>~wise(X)))&
(((brave(alice)<~>~brave(alice)))<=>((~tall(john)|humble(john))))&
(?[X]:((~patient(X)&strong(X))))&
(strong(mary))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:(~old(X)))&
(?[X]:(~quiet(X))) | humble(mary) | [
"p0",
"p1",
"p2",
"p6",
"p9",
"p11",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8972167185986375478165362
% SZS output start Proof for 8972167185986375478165362
1. ! [X0] : ((brave(X0) | funny(X0)) => (tall(X0) <~> patient(X0))) [input p0]
2. ! [X0] : ((~strong(X0) | ~wise(X0)) <=> (~strong(X0) & funny(X0))) [input p1]
3. ? [X0] : generous(X0) => (~strong(paul) & patient(paul)) [input p2]
7. ? [X0] : (~tall(X0) <~> funny(X0)) => (generous(fred) & ~quiet(fred)) [input p6]
10. ! [X0] : (kind(X0) <=> ~funny(X0)) [input p9]
12. ! [X0] : ((~humble(X0) <~> kind(X0)) <=> (humble(X0) | strong(X0))) [input p11]
15. ! [X0] : (patient(X0) => ~wise(X0)) [input p14]
18. strong(mary) [input p17]
22. ~humble(mary) [input hypothesis]
24. ! [X0] : ((tall(X0) <~> patient(X0)) | (~brave(X0) & ~funny(X0))) [ennf transformation 1]
25. (~strong(paul) & patient(paul)) | ! [X0] : ~generous(X0) [ennf transformation 3]
29. (generous(fred) & ~quiet(fred)) | ! [X0] : (~tall(X0) <=> funny(X0)) [ennf transformation 7]
31. ! [X0] : (~wise(X0) | ~patient(X0)) [ennf transformation 15]
32. ! [X0] : (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (~brave(X0) & ~funny(X0))) [nnf transformation 24]
33. ! [X0] : (((~strong(X0) | ~wise(X0)) | (strong(X0) | ~funny(X0))) & ((~strong(X0) & funny(X0)) | (strong(X0) & wise(X0)))) [nnf transformation 2]
34. ! [X0] : ((~strong(X0) | ~wise(X0) | strong(X0) | ~funny(X0)) & ((~strong(X0) & funny(X0)) | (strong(X0) & wise(X0)))) [flattening 33]
38. (generous(fred) & ~quiet(fred)) | ! [X0] : ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))) [nnf transformation 29]
46. ! [X0] : ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0))) [nnf transformation 10]
48. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [nnf transformation 12]
49. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [flattening 48]
67. ~funny(X0) | tall(X0) | patient(X0) [cnf transformation 32]
72. strong(X0) | funny(X0) [cnf transformation 34]
73. ~strong(X0) | wise(X0) [cnf transformation 34]
76. patient(paul) | ~generous(X0) [cnf transformation 25]
88. generous(fred) | ~tall(X0) | ~funny(X0) [cnf transformation 38]
98. ~kind(X0) | ~funny(X0) [cnf transformation 46]
99. kind(X0) | funny(X0) [cnf transformation 46]
104. humble(X0) | strong(X0) | kind(X0) | humble(X0) [cnf transformation 49]
107. kind(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 49]
108. ~kind(X0) | humble(X0) | ~strong(X0) [cnf transformation 49]
120. ~wise(X0) | ~patient(X0) [cnf transformation 31]
129. strong(mary) [cnf transformation 18]
133. ~humble(mary) [cnf transformation 22]
136. humble(X0) | strong(X0) | kind(X0) [duplicate literal removal 104]
137. ~humble(X0) | kind(X0) [duplicate literal removal 107]
139. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
140. ~generous(X0) <- (1) [avatar component clause 139]
147. 3 <=> patient(paul) [avatar definition]
149. patient(paul) <- (3) [avatar component clause 147]
150. 1 | 3 [avatar split clause 76,147,139]
161. 6 <=> ! [X0] : (~tall(X0) | ~funny(X0)) [avatar definition]
162. ~tall(X0) | ~funny(X0) <- (6) [avatar component clause 161]
164. 7 <=> generous(fred) [avatar definition]
166. generous(fred) <- (7) [avatar component clause 164]
167. 6 | 7 [avatar split clause 88,164,161]
199. kind(X0) | strong(X0) [subsumption resolution 136,137]
254. wise(mary) [resolution 73,129]
259. ~patient(mary) [resolution 120,254]
260. strong(X0) | ~funny(X0) [resolution 199,98]
261. strong(X0) [subsumption resolution 260,72]
264. wise(X0) [resolution 261,73]
270. $false <- (1, 7) [resolution 140,166]
271. ~1 | ~7 [avatar contradiction clause 270]
275. ~patient(X0) [resolution 264,120]
287. $false <- (3) [resolution 275,149]
290. ~3 [avatar contradiction clause 287]
322. humble(X1) | ~strong(X1) | funny(X1) [resolution 108,99]
345. humble(X1) | funny(X1) [subsumption resolution 322,261]
516. funny(mary) [resolution 345,133]
539. tall(mary) | patient(mary) [resolution 516,67]
540. tall(mary) [subsumption resolution 539,259]
560. ~funny(mary) <- (6) [resolution 540,162]
561. $false <- (6) [subsumption resolution 560,516]
562. ~6 [avatar contradiction clause 561]
563. $false [avatar sat refutation 150,167,271,290,562]
% SZS output end Proof for 8972167185986375478165362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or old then mary is patient or not generous and vice versa.
Everyone who is either not rich or not patient is either wise or not strong and vice versa.
Everyone who is either calm or old is both funny and not brave and vice versa.
Everyone who is curious is not curious.
If paul is not funny then someone is not patient or strong.
Everyone who is either not rich or funny is either wise or rich and vice versa.
If someone is either not quiet or old then susan is both happy and old.
Everyone who is humble or quiet is not curious.
Everyone who is either not tall or not strong is not generous.
Everyone who is old is both quiet and not humble and vice versa.
If someone is old or not strong then someone is generous.
If mary is both not old and creative then lucy is both quiet and happy.
Everyone who is both not old and not patient is both not strong and not curious.
Everyone who is not happy or happy is either creative or not funny.
If someone is not old then lucy is strong or not brave.
Everyone who is generous is not funny or creative and vice versa.
Susan is brave or happy.
Mary is either not strong or rich.
Lucy is either not patient or humble.
Someone is both not strong and calm.
Alice is either happy or not kind.
Someone is kind or creative.
Someone is both not calm and not quiet.
Fred is either not quiet or generous. | Mary is not patient. | contradiction | ((?[X]:((~calm(X)<~>old(X))))<=>((patient(mary)|~generous(mary))))&
(![X]:((~rich(X)<~>~patient(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((calm(X)<~>old(X))<=>(funny(X)&~brave(X))))&
(![X]:(curious(X)=>~curious(X)))&
((~funny(paul))=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((~rich(X)<~>funny(X))<=>(wise(X)<~>rich(X))))&
((?[X]:((~quiet(X)<~>old(X))))=>((happy(susan)&old(susan))))&
(![X]:((humble(X)|quiet(X))=>~curious(X)))&
(![X]:((~tall(X)<~>~strong(X))=>~generous(X)))&
(![X]:(old(X)<=>(quiet(X)&~humble(X))))&
((?[X]:((old(X)|~strong(X))))=>(?[X]:(generous(X))))&
(((~old(mary)&creative(mary)))=>((quiet(lucy)&happy(lucy))))&
(![X]:((~old(X)&~patient(X))=>(~strong(X)&~curious(X))))&
(![X]:((~happy(X)|happy(X))=>(creative(X)<~>~funny(X))))&
((?[X]:(~old(X)))=>((strong(lucy)|~brave(lucy))))&
(![X]:(generous(X)<=>(~funny(X)|creative(X))))&
((brave(susan)|happy(susan)))&
((~strong(mary)<~>rich(mary)))&
((~patient(lucy)<~>humble(lucy)))&
(?[X]:((~strong(X)&calm(X))))&
((happy(alice)<~>~kind(alice)))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:((~calm(X)&~quiet(X))))&
((~quiet(fred)<~>generous(fred))) | ~patient(mary) | [
"p0",
"p9",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7568635980455986421229255
% SZS output start Proof for 7568635980455986421229255
1. ? [X0] : (~calm(X0) <~> old(X0)) <=> (~generous(mary) | patient(mary)) [input p0]
10. ! [X0] : (old(X0) <=> (~humble(X0) & quiet(X0))) [input p9]
14. ! [X0] : ((happy(X0) | ~happy(X0)) => (creative(X0) <~> ~funny(X0))) [input p13]
16. ! [X0] : (generous(X0) <=> (creative(X0) | ~funny(X0))) [input p15]
23. ? [X0] : (~quiet(X0) & ~calm(X0)) [input p22]
25. ~patient(mary) [input hypothesis]
38. ! [X0] : ((creative(X0) <~> ~funny(X0)) | (~happy(X0) & happy(X0))) [ennf transformation 14]
41. (? [X0] : ((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | (generous(mary) & ~patient(mary))) & ((~generous(mary) | patient(mary)) | ! [X0] : ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) [nnf transformation 1]
42. (? [X0] : ((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | (generous(mary) & ~patient(mary))) & (~generous(mary) | patient(mary) | ! [X0] : ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) [flattening 41]
43. (? [X0] : ((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | (generous(mary) & ~patient(mary))) & (~generous(mary) | patient(mary) | ! [X1] : ((~calm(X1) | ~old(X1)) & (old(X1) | calm(X1)))) [rectify 42]
44. ? [X0] : ((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) => ((~old(sK0) | calm(sK0)) & (old(sK0) | ~calm(sK0))) [choice axiom]
45. (((~old(sK0) | calm(sK0)) & (old(sK0) | ~calm(sK0))) | (generous(mary) & ~patient(mary))) & (~generous(mary) | patient(mary) | ! [X1] : ((~calm(X1) | ~old(X1)) & (old(X1) | calm(X1)))) [skolemisation 43,44]
54. ! [X0] : ((old(X0) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | ~old(X0))) [nnf transformation 10]
55. ! [X0] : ((old(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | ~old(X0))) [flattening 54]
59. ! [X0] : (((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | (~happy(X0) & happy(X0))) [nnf transformation 38]
60. ! [X0] : ((generous(X0) | (~creative(X0) & funny(X0))) & ((creative(X0) | ~funny(X0)) | ~generous(X0))) [nnf transformation 16]
61. ! [X0] : ((generous(X0) | (~creative(X0) & funny(X0))) & (creative(X0) | ~funny(X0) | ~generous(X0))) [flattening 60]
69. ? [X0] : (~quiet(X0) & ~calm(X0)) => (~quiet(sK5) & ~calm(sK5)) [choice axiom]
70. ~quiet(sK5) & ~calm(sK5) [skolemisation 23,69]
72. ~generous(mary) | patient(mary) | old(X1) | calm(X1) [cnf transformation 45]
107. ~old(X0) | quiet(X0) [cnf transformation 55]
115. ~funny(X0) | creative(X0) | happy(X0) [cnf transformation 59]
116. ~happy(X0) | creative(X0) | ~funny(X0) [cnf transformation 59]
121. funny(X0) | generous(X0) [cnf transformation 61]
122. ~creative(X0) | generous(X0) [cnf transformation 61]
133. ~calm(sK5) [cnf transformation 70]
134. ~quiet(sK5) [cnf transformation 70]
137. ~patient(mary) [cnf transformation 25]
143. 1 <=> generous(mary) [avatar definition]
144. ~generous(mary) <- (~1) [avatar component clause 143]
156. 4 <=> patient(mary) [avatar definition]
167. 6 <=> ! [X1] : (old(X1) | calm(X1)) [avatar definition]
168. old(X1) | calm(X1) <- (6) [avatar component clause 167]
169. 6 | 4 | ~1 [avatar split clause 72,143,156,167]
234. ~funny(X0) | creative(X0) [subsumption resolution 115,116]
301. ~4 [avatar split clause 137,156]
306. creative(X1) | generous(X1) [resolution 234,121]
307. generous(X1) [subsumption resolution 306,122]
308. $false <- (~1) [resolution 307,144]
311. 1 [avatar contradiction clause 308]
315. quiet(X1) | calm(X1) <- (6) [resolution 168,107]
370. calm(sK5) <- (6) [resolution 315,134]
372. $false <- (6) [subsumption resolution 370,133]
373. ~6 [avatar contradiction clause 372]
374. $false [avatar sat refutation 169,301,311,373]
% SZS output end Proof for 7568635980455986421229255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not brave is both tall and not calm.
Everyone who is either not funny or brave is either not humble or happy.
Everyone who is both old and calm is quiet and vice versa.
Everyone who is either not funny or not patient is both not kind and kind.
Everyone who is not creative is funny.
Everyone who is both funny and wise is either not kind or not happy and vice versa.
If someone is either not kind or rich then paul is both not quiet and not creative.
If mary is rich then someone is either not tall or happy and vice versa.
Everyone who is both wise and old is quiet.
If lucy is funny then john is both calm and rich and vice versa.
Everyone who is not rich or calm is wise.
Everyone who is either not tall or not creative is both not humble and strong and vice versa.
Everyone who is either brave or curious is not creative and vice versa.
Everyone who is humble or patient is both not old and not happy and vice versa.
Everyone who is either curious or not funny is not old and vice versa.
Everyone who is either creative or not humble is humble or not generous and vice versa.
Fred is not tall.
Someone is not tall or not funny.
Someone is either patient or not creative.
Susan is either curious or humble.
Someone is not old.
John is not quiet or not happy. | John is quiet. | contradiction | (![X]:((~humble(X)<~>~brave(X))=>(tall(X)&~calm(X))))&
(![X]:((~funny(X)<~>brave(X))=>(~humble(X)<~>happy(X))))&
(![X]:((old(X)&calm(X))<=>quiet(X)))&
(![X]:((~funny(X)<~>~patient(X))=>(~kind(X)&kind(X))))&
(![X]:(~creative(X)=>funny(X)))&
(![X]:((funny(X)&wise(X))<=>(~kind(X)<~>~happy(X))))&
((?[X]:((~kind(X)<~>rich(X))))=>((~quiet(paul)&~creative(paul))))&
((rich(mary))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((wise(X)&old(X))=>quiet(X)))&
((funny(lucy))<=>((calm(john)&rich(john))))&
(![X]:((~rich(X)|calm(X))=>wise(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>(~humble(X)&strong(X))))&
(![X]:((brave(X)<~>curious(X))<=>~creative(X)))&
(![X]:((humble(X)|patient(X))<=>(~old(X)&~happy(X))))&
(![X]:((curious(X)<~>~funny(X))<=>~old(X)))&
(![X]:((creative(X)<~>~humble(X))<=>(humble(X)|~generous(X))))&
(~tall(fred))&
(?[X]:((~tall(X)|~funny(X))))&
(?[X]:((patient(X)<~>~creative(X))))&
((curious(susan)<~>humble(susan)))&
(?[X]:(~old(X)))&
((~quiet(john)|~happy(john))) | quiet(john) | [
"p0",
"p2",
"p3",
"p4",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2687894217207292590816802
% SZS output start Proof for 2687894217207292590816802
1. ! [X0] : ((~humble(X0) <~> ~brave(X0)) => (~calm(X0) & tall(X0))) [input p0]
3. ! [X0] : ((calm(X0) & old(X0)) <=> quiet(X0)) [input p2]
4. ! [X0] : ((~funny(X0) <~> ~patient(X0)) => (kind(X0) & ~kind(X0))) [input p3]
5. ! [X0] : (~creative(X0) => funny(X0)) [input p4]
13. ! [X0] : ((brave(X0) <~> curious(X0)) <=> ~creative(X0)) [input p12]
14. ! [X0] : ((patient(X0) | humble(X0)) <=> (~happy(X0) & ~old(X0))) [input p13]
15. ! [X0] : ((curious(X0) <~> ~funny(X0)) <=> ~old(X0)) [input p14]
23. quiet(john) [input hypothesis]
24. ! [X0] : ((~calm(X0) & tall(X0)) | (~humble(X0) <=> ~brave(X0))) [ennf transformation 1]
26. ! [X0] : ((kind(X0) & ~kind(X0)) | (~funny(X0) <=> ~patient(X0))) [ennf transformation 4]
27. ! [X0] : (funny(X0) | creative(X0)) [ennf transformation 5]
32. ! [X0] : ((~calm(X0) & tall(X0)) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) [nnf transformation 24]
34. ! [X0] : (((calm(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) | ~old(X0)))) [nnf transformation 3]
35. ! [X0] : (((calm(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | ~calm(X0) | ~old(X0))) [flattening 34]
36. ! [X0] : ((kind(X0) & ~kind(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) [nnf transformation 26]
48. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | creative(X0)) & (~creative(X0) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [nnf transformation 13]
49. ! [X0] : (((patient(X0) | humble(X0)) | (happy(X0) | old(X0))) & ((~happy(X0) & ~old(X0)) | (~patient(X0) & ~humble(X0)))) [nnf transformation 14]
50. ! [X0] : ((patient(X0) | humble(X0) | happy(X0) | old(X0)) & ((~happy(X0) & ~old(X0)) | (~patient(X0) & ~humble(X0)))) [flattening 49]
51. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | old(X0)) & (~old(X0) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [nnf transformation 15]
64. ~calm(X0) | ~brave(X0) | humble(X0) [cnf transformation 32]
71. ~quiet(X0) | old(X0) [cnf transformation 35]
72. ~quiet(X0) | calm(X0) [cnf transformation 35]
74. ~kind(X0) | ~funny(X0) | patient(X0) [cnf transformation 36]
76. ~funny(X0) | kind(X0) | patient(X0) [cnf transformation 36]
77. creative(X0) | funny(X0) [cnf transformation 27]
105. ~curious(X0) | brave(X0) | ~creative(X0) [cnf transformation 48]
106. curious(X0) | brave(X0) | creative(X0) [cnf transformation 48]
108. ~old(X0) | ~humble(X0) [cnf transformation 50]
109. ~patient(X0) | ~old(X0) [cnf transformation 50]
113. ~curious(X0) | ~funny(X0) | ~old(X0) [cnf transformation 51]
114. ~old(X0) | curious(X0) | funny(X0) [cnf transformation 51]
131. quiet(john) [cnf transformation 23]
134. ~funny(X0) | patient(X0) [subsumption resolution 74,76]
177. 10 <=> calm(john) [avatar definition]
178. calm(john) <- (10) [avatar component clause 177]
222. 19 <=> quiet(john) [avatar definition]
223. quiet(john) <- (19) [avatar component clause 222]
230. 19 [avatar split clause 131,222]
231. old(john) <- (19) [resolution 71,223]
232. calm(john) <- (19) [resolution 72,223]
233. 10 | ~19 [avatar split clause 232,222,177]
238. ~humble(john) <- (19) [resolution 108,231]
250. ~brave(john) | humble(john) <- (10) [resolution 64,178]
251. ~brave(john) <- (10, 19) [subsumption resolution 250,238]
309. ~funny(X0) | ~old(X0) | brave(X0) | creative(X0) [resolution 113,106]
311. ~old(X0) | brave(X0) | creative(X0) [subsumption resolution 309,77]
312. curious(john) | funny(john) <- (19) [resolution 114,231]
314. 28 <=> funny(john) [avatar definition]
316. funny(john) <- (28) [avatar component clause 314]
318. 29 <=> curious(john) [avatar definition]
320. curious(john) <- (29) [avatar component clause 318]
321. 28 | 29 | ~19 [avatar split clause 312,222,318,314]
431. patient(john) <- (28) [resolution 316,134]
433. 42 <=> patient(john) [avatar definition]
435. patient(john) <- (42) [avatar component clause 433]
441. 42 | ~28 [avatar split clause 431,314,433]
464. ~old(john) <- (42) [resolution 435,109]
465. $false <- (19, 42) [subsumption resolution 464,231]
466. ~19 | ~42 [avatar contradiction clause 465]
469. brave(john) | creative(john) <- (19) [resolution 311,231]
471. creative(john) <- (10, 19) [subsumption resolution 469,251]
475. brave(john) | ~creative(john) <- (29) [resolution 320,105]
476. ~creative(john) <- (10, 19, 29) [subsumption resolution 475,251]
477. $false <- (10, 19, 29) [subsumption resolution 476,471]
478. ~10 | ~19 | ~29 [avatar contradiction clause 477]
479. $false [avatar sat refutation 230,233,321,441,466,478]
% SZS output end Proof for 2687894217207292590816802
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both quiet and not tall then someone is both generous and not kind.
If someone is not quiet or not kind then fred is not curious or happy and vice versa.
If someone is humble then someone is either not tall or not patient.
Everyone who is both rich and not wise is patient or not old.
Everyone who is humble is both rich and not humble and vice versa.
Everyone who is strong or not generous is either not funny or not rich.
If susan is not funny or calm then someone is not quiet.
If susan is not generous or generous then someone is not creative and vice versa.
If someone is either not old or not patient then someone is both not kind and happy.
Everyone who is funny or wise is either not wise or not old.
Everyone who is wise or not funny is both happy and calm and vice versa.
Everyone who is either creative or not wise is not humble and vice versa.
Everyone who is both strong and not tall is not generous and vice versa.
Everyone who is both quiet and brave is both not calm and not curious and vice versa.
Everyone who is both rich and generous is not old or curious and vice versa.
Alice is either not kind or kind.
Someone is both brave and not happy.
Alice is curious or not humble.
Someone is not rich or brave.
Paul is either curious or not brave. | Paul is curious. | contradiction | (((quiet(alice)&~tall(alice)))=>(?[X]:((generous(X)&~kind(X)))))&
((?[X]:((~quiet(X)|~kind(X))))<=>((~curious(fred)|happy(fred))))&
((?[X]:(humble(X)))=>(?[X]:((~tall(X)<~>~patient(X)))))&
(![X]:((rich(X)&~wise(X))=>(patient(X)|~old(X))))&
(![X]:(humble(X)<=>(rich(X)&~humble(X))))&
(![X]:((strong(X)|~generous(X))=>(~funny(X)<~>~rich(X))))&
(((~funny(susan)|calm(susan)))=>(?[X]:(~quiet(X))))&
(((~generous(susan)|generous(susan)))<=>(?[X]:(~creative(X))))&
((?[X]:((~old(X)<~>~patient(X))))=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((funny(X)|wise(X))=>(~wise(X)<~>~old(X))))&
(![X]:((wise(X)|~funny(X))<=>(happy(X)&calm(X))))&
(![X]:((creative(X)<~>~wise(X))<=>~humble(X)))&
(![X]:((strong(X)&~tall(X))<=>~generous(X)))&
(![X]:((quiet(X)&brave(X))<=>(~calm(X)&~curious(X))))&
(![X]:((rich(X)&generous(X))<=>(~old(X)|curious(X))))&
((~kind(alice)<~>kind(alice)))&
(?[X]:((brave(X)&~happy(X))))&
((curious(alice)|~humble(alice)))&
(?[X]:((~rich(X)|brave(X))))&
((curious(paul)<~>~brave(paul))) | curious(paul) | [
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3989013800257032496762741
% SZS output start Proof for 3989013800257032496762741
5. ! [X0] : (humble(X0) <=> (~humble(X0) & rich(X0))) [input p4]
15. ! [X0] : ((generous(X0) & rich(X0)) <=> (curious(X0) | ~old(X0))) [input p14]
21. curious(paul) [input hypothesis]
44. ! [X0] : ((humble(X0) | (humble(X0) | ~rich(X0))) & ((~humble(X0) & rich(X0)) | ~humble(X0))) [nnf transformation 5]
45. ! [X0] : ((humble(X0) | humble(X0) | ~rich(X0)) & ((~humble(X0) & rich(X0)) | ~humble(X0))) [flattening 44]
66. ! [X0] : (((generous(X0) & rich(X0)) | (~curious(X0) & old(X0))) & ((curious(X0) | ~old(X0)) | (~generous(X0) | ~rich(X0)))) [nnf transformation 15]
67. ! [X0] : (((generous(X0) & rich(X0)) | (~curious(X0) & old(X0))) & (curious(X0) | ~old(X0) | ~generous(X0) | ~rich(X0))) [flattening 66]
84. ~humble(X0) | ~humble(X0) [cnf transformation 45]
85. humble(X0) | humble(X0) | ~rich(X0) [cnf transformation 45]
121. ~curious(X0) | rich(X0) [cnf transformation 67]
132. curious(paul) [cnf transformation 21]
134. ~humble(X0) [duplicate literal removal 84]
135. ~rich(X0) | humble(X0) [duplicate literal removal 85]
181. 11 <=> ! [X1] : ~humble(X1) [avatar definition]
182. ~humble(X1) <- (11) [avatar component clause 181]
193. 11 [avatar split clause 134,181]
255. 27 <=> curious(paul) [avatar definition]
256. curious(paul) <- (27) [avatar component clause 255]
264. 27 [avatar split clause 132,255]
265. rich(paul) <- (27) [resolution 121,256]
269. humble(paul) <- (27) [resolution 135,265]
270. $false <- (11, 27) [subsumption resolution 269,182]
271. ~11 | ~27 [avatar contradiction clause 270]
272. $false [avatar sat refutation 193,264,271]
% SZS output end Proof for 3989013800257032496762741
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then susan is not creative or curious.
If someone is not quiet then fred is either not wise or not generous and vice versa.
If someone is both not brave and brave then someone is calm.
If alice is humble or curious then john is either not kind or not calm and vice versa.
Everyone who is happy is humble.
If someone is not creative then susan is tall.
If susan is not kind then john is not humble or rich.
If someone is not kind or not curious then paul is either funny or strong and vice versa.
Everyone who is brave is either not tall or creative and vice versa.
Everyone who is not old or not rich is not brave.
Everyone who is patient or not old is both calm and creative and vice versa.
Everyone who is kind or funny is either not wise or happy and vice versa.
Everyone who is calm is either not funny or not generous and vice versa.
Everyone who is funny or rich is either strong or not kind.
Everyone who is not funny or funny is not curious and vice versa.
Everyone who is either wise or humble is tall or happy and vice versa.
Paul is either not wise or not brave.
Mary is not funny.
Someone is either old or happy.
Lucy is either not humble or wise.
Fred is both generous and patient.
Fred is happy.
Someone is not funny. | Mary is not tall. | neutral | ((?[X]:(generous(X)))=>((~creative(susan)|curious(susan))))&
((?[X]:(~quiet(X)))<=>((~wise(fred)<~>~generous(fred))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:(calm(X))))&
(((humble(alice)|curious(alice)))<=>((~kind(john)<~>~calm(john))))&
(![X]:(happy(X)=>humble(X)))&
((?[X]:(~creative(X)))=>(tall(susan)))&
((~kind(susan))=>((~humble(john)|rich(john))))&
((?[X]:((~kind(X)|~curious(X))))<=>((funny(paul)<~>strong(paul))))&
(![X]:(brave(X)<=>(~tall(X)<~>creative(X))))&
(![X]:((~old(X)|~rich(X))=>~brave(X)))&
(![X]:((patient(X)|~old(X))<=>(calm(X)&creative(X))))&
(![X]:((kind(X)|funny(X))<=>(~wise(X)<~>happy(X))))&
(![X]:(calm(X)<=>(~funny(X)<~>~generous(X))))&
(![X]:((funny(X)|rich(X))=>(strong(X)<~>~kind(X))))&
(![X]:((~funny(X)|funny(X))<=>~curious(X)))&
(![X]:((wise(X)<~>humble(X))<=>(tall(X)|happy(X))))&
((~wise(paul)<~>~brave(paul)))&
(~funny(mary))&
(?[X]:((old(X)<~>happy(X))))&
((~humble(lucy)<~>wise(lucy)))&
((generous(fred)&patient(fred)))&
(happy(fred))&
(?[X]:(~funny(X))) | ~tall(mary) | [] | null | 0 |
Everyone who is either old or curious is both not strong and calm and vice versa.
Everyone who is either not strong or strong is either strong or not strong.
If someone is not humble then someone is creative.
Everyone who is both tall and not old is not generous or not quiet.
Everyone who is both generous and not happy is either not happy or not rich.
Everyone who is either kind or rich is not old or not funny and vice versa.
Everyone who is strong or not wise is either kind or wise and vice versa.
If someone is either not quiet or not happy then john is both not generous and not creative.
Everyone who is not strong or quiet is calm and vice versa.
Everyone who is calm is both generous and curious and vice versa.
Everyone who is both tall and not generous is either not kind or not patient.
If susan is both not funny and wise then fred is both not wise and not old and vice versa.
Everyone who is brave is both not old and generous and vice versa.
If someone is not funny then someone is not patient and vice versa.
Everyone who is either creative or not curious is either generous or happy.
Everyone who is not brave is either kind or not quiet and vice versa.
Someone is brave.
Fred is both not happy and not humble.
Someone is not rich.
Mary is either tall or not kind.
Someone is either rich or patient.
Lucy is both rich and patient.
Someone is not generous.
Paul is strong. | John is not wise. | contradiction | (![X]:((old(X)<~>curious(X))<=>(~strong(X)&calm(X))))&
(![X]:((~strong(X)<~>strong(X))=>(strong(X)<~>~strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(creative(X))))&
(![X]:((tall(X)&~old(X))=>(~generous(X)|~quiet(X))))&
(![X]:((generous(X)&~happy(X))=>(~happy(X)<~>~rich(X))))&
(![X]:((kind(X)<~>rich(X))<=>(~old(X)|~funny(X))))&
(![X]:((strong(X)|~wise(X))<=>(kind(X)<~>wise(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))=>((~generous(john)&~creative(john))))&
(![X]:((~strong(X)|quiet(X))<=>calm(X)))&
(![X]:(calm(X)<=>(generous(X)&curious(X))))&
(![X]:((tall(X)&~generous(X))=>(~kind(X)<~>~patient(X))))&
(((~funny(susan)&wise(susan)))<=>((~wise(fred)&~old(fred))))&
(![X]:(brave(X)<=>(~old(X)&generous(X))))&
((?[X]:(~funny(X)))<=>(?[X]:(~patient(X))))&
(![X]:((creative(X)<~>~curious(X))=>(generous(X)<~>happy(X))))&
(![X]:(~brave(X)<=>(kind(X)<~>~quiet(X))))&
(?[X]:(brave(X)))&
((~happy(fred)&~humble(fred)))&
(?[X]:(~rich(X)))&
((tall(mary)<~>~kind(mary)))&
(?[X]:((rich(X)<~>patient(X))))&
((rich(lucy)&patient(lucy)))&
(?[X]:(~generous(X)))&
(strong(paul)) | ~wise(john) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8070129164785527887835535
% SZS output start Proof for 8070129164785527887835535
1. ! [X0] : ((old(X0) <~> curious(X0)) <=> (calm(X0) & ~strong(X0))) [input p0]
5. ! [X0] : ((~happy(X0) & generous(X0)) => (~happy(X0) <~> ~rich(X0))) [input p4]
6. ! [X0] : ((kind(X0) <~> rich(X0)) <=> (~funny(X0) | ~old(X0))) [input p5]
7. ! [X0] : ((~wise(X0) | strong(X0)) <=> (kind(X0) <~> wise(X0))) [input p6]
8. ? [X0] : (~quiet(X0) <~> ~happy(X0)) => (~creative(john) & ~generous(john)) [input p7]
9. ! [X0] : ((quiet(X0) | ~strong(X0)) <=> calm(X0)) [input p8]
10. ! [X0] : (calm(X0) <=> (curious(X0) & generous(X0))) [input p9]
13. ! [X0] : (brave(X0) <=> (generous(X0) & ~old(X0))) [input p12]
16. ! [X0] : (~brave(X0) <=> (kind(X0) <~> ~quiet(X0))) [input p15]
17. ? [X0] : brave(X0) [input p16]
25. ~wise(john) [input hypothesis]
32. ! [X0] : ((~happy(X0) <~> ~rich(X0)) | (happy(X0) | ~generous(X0))) [ennf transformation 5]
33. ! [X0] : ((~happy(X0) <~> ~rich(X0)) | happy(X0) | ~generous(X0)) [flattening 32]
34. (~creative(john) & ~generous(john)) | ! [X0] : (~quiet(X0) <=> ~happy(X0)) [ennf transformation 8]
38. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | (~calm(X0) | strong(X0))) & ((calm(X0) & ~strong(X0)) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [nnf transformation 1]
39. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | ~calm(X0) | strong(X0)) & ((calm(X0) & ~strong(X0)) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [flattening 38]
44. ! [X0] : (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | happy(X0) | ~generous(X0)) [nnf transformation 33]
45. ! [X0] : ((((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | (funny(X0) & old(X0))) & ((~funny(X0) | ~old(X0)) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0))))) [nnf transformation 6]
46. ! [X0] : ((((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | (funny(X0) & old(X0))) & (~funny(X0) | ~old(X0) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0))))) [flattening 45]
47. ! [X0] : (((~wise(X0) | strong(X0)) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0)))) & (((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (wise(X0) & ~strong(X0)))) [nnf transformation 7]
48. ! [X0] : ((~wise(X0) | strong(X0) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0)))) & (((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (wise(X0) & ~strong(X0)))) [flattening 47]
49. (~creative(john) & ~generous(john)) | ! [X0] : ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0))) [nnf transformation 34]
50. ! [X0] : (((quiet(X0) | ~strong(X0)) | ~calm(X0)) & (calm(X0) | (~quiet(X0) & strong(X0)))) [nnf transformation 9]
51. ! [X0] : ((quiet(X0) | ~strong(X0) | ~calm(X0)) & (calm(X0) | (~quiet(X0) & strong(X0)))) [flattening 50]
52. ! [X0] : ((calm(X0) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | ~calm(X0))) [nnf transformation 10]
53. ! [X0] : ((calm(X0) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | ~calm(X0))) [flattening 52]
57. ! [X0] : ((brave(X0) | (~generous(X0) | old(X0))) & ((generous(X0) & ~old(X0)) | ~brave(X0))) [nnf transformation 13]
58. ! [X0] : ((brave(X0) | ~generous(X0) | old(X0)) & ((generous(X0) & ~old(X0)) | ~brave(X0))) [flattening 57]
65. ! [X0] : ((~brave(X0) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0)))) & (((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | brave(X0))) [nnf transformation 16]
66. ? [X0] : brave(X0) => brave(sK3) [choice axiom]
67. brave(sK3) [skolemisation 17,66]
77. ~strong(X0) | old(X0) | ~curious(X0) [cnf transformation 39]
89. rich(X0) | happy(X0) | happy(X0) | ~generous(X0) [cnf transformation 44]
94. ~kind(X0) | ~rich(X0) | old(X0) [cnf transformation 46]
97. wise(X0) | kind(X0) | wise(X0) [cnf transformation 48]
101. ~wise(X0) | strong(X0) | kind(X0) | ~wise(X0) [cnf transformation 48]
102. ~generous(john) | ~happy(X0) | quiet(X0) [cnf transformation 49]
107. ~quiet(X0) | calm(X0) [cnf transformation 51]
109. ~calm(X0) | generous(X0) [cnf transformation 53]
110. ~calm(X0) | curious(X0) [cnf transformation 53]
118. ~brave(X0) | ~old(X0) [cnf transformation 58]
119. ~brave(X0) | generous(X0) [cnf transformation 58]
128. ~kind(X0) | quiet(X0) | brave(X0) [cnf transformation 65]
129. ~brave(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 65]
130. ~brave(X0) | kind(X0) | quiet(X0) [cnf transformation 65]
131. brave(sK3) [cnf transformation 67]
143. ~wise(john) [cnf transformation 25]
144. wise(X0) | kind(X0) [duplicate literal removal 97]
145. ~wise(X0) | strong(X0) | kind(X0) [duplicate literal removal 101]
146. ~generous(X0) | happy(X0) | rich(X0) [duplicate literal removal 89]
168. 5 <=> ! [X0] : (~happy(X0) | quiet(X0)) [avatar definition]
169. ~happy(X0) | quiet(X0) <- (5) [avatar component clause 168]
172. 6 <=> generous(john) [avatar definition]
174. ~generous(john) <- (~6) [avatar component clause 172]
176. 5 | ~6 [avatar split clause 102,172,168]
235. ~old(sK3) [resolution 118,131]
236. generous(sK3) [resolution 119,131]
237. kind(john) [resolution 144,143]
341. 34 <=> calm(sK3) [avatar definition]
343. calm(sK3) <- (34) [avatar component clause 341]
345. 35 <=> curious(sK3) [avatar definition]
346. curious(sK3) <- (35) [avatar component clause 345]
352. quiet(john) | brave(john) [resolution 128,237]
356. 36 <=> brave(john) [avatar definition]
358. brave(john) <- (36) [avatar component clause 356]
360. 37 <=> quiet(john) [avatar definition]
362. quiet(john) <- (37) [avatar component clause 360]
363. 36 | 37 [avatar split clause 352,360,356]
401. ~quiet(sK3) | ~kind(sK3) [resolution 129,131]
403. 44 <=> kind(sK3) [avatar definition]
404. kind(sK3) <- (44) [avatar component clause 403]
405. ~kind(sK3) <- (~44) [avatar component clause 403]
407. 45 <=> quiet(sK3) [avatar definition]
408. quiet(sK3) <- (45) [avatar component clause 407]
410. ~44 | ~45 [avatar split clause 401,407,403]
411. kind(sK3) | quiet(sK3) [resolution 130,131]
414. 45 | 44 [avatar split clause 411,403,407]
415. strong(X0) | kind(X0) | kind(X0) [resolution 145,144]
418. kind(X0) | strong(X0) [duplicate literal removal 415]
421. ~rich(sK3) | old(sK3) <- (44) [resolution 404,94]
427. 47 <=> rich(sK3) [avatar definition]
429. ~rich(sK3) <- (~47) [avatar component clause 427]
431. ~rich(sK3) <- (44) [subsumption resolution 421,235]
432. ~47 | ~44 [avatar split clause 431,403,427]
433. happy(sK3) | rich(sK3) [resolution 146,236]
435. happy(sK3) <- (~47) [subsumption resolution 433,429]
440. generous(john) <- (36) [resolution 358,119]
444. $false <- (~6, 36) [subsumption resolution 440,174]
445. 6 | ~36 [avatar contradiction clause 444]
451. calm(john) <- (37) [resolution 362,107]
600. generous(john) <- (37) [resolution 451,109]
605. 6 | ~37 [avatar split clause 600,360,172]
630. quiet(sK3) <- (5, ~47) [resolution 169,435]
634. 45 | ~5 | 47 [avatar split clause 630,427,168,407]
635. strong(sK3) <- (~44) [resolution 405,418]
650. calm(sK3) <- (45) [resolution 408,107]
654. 34 | ~45 [avatar split clause 650,407,341]
658. curious(sK3) <- (34) [resolution 343,110]
662. 35 | ~34 [avatar split clause 658,341,345]
671. old(sK3) | ~curious(sK3) <- (~44) [resolution 635,77]
673. ~curious(sK3) <- (~44) [subsumption resolution 671,235]
674. $false <- (35, ~44) [subsumption resolution 673,346]
675. ~35 | 44 [avatar contradiction clause 674]
676. $false [avatar sat refutation 176,363,410,414,432,445,605,634,654,662,675]
% SZS output end Proof for 8070129164785527887835535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not kind is both not kind and not strong and vice versa.
Everyone who is rich is wise.
Everyone who is brave is both funny and humble and vice versa.
Everyone who is either not humble or brave is not happy or curious.
If fred is both rich and not calm then someone is either generous or not humble.
Everyone who is either not quiet or not creative is either kind or not rich and vice versa.
If lucy is either not brave or not strong then someone is both wise and humble and vice versa.
If someone is not tall then someone is calm and vice versa.
Everyone who is both patient and tall is generous.
Everyone who is either creative or strong is either funny or not humble.
If lucy is both humble and creative then fred is patient.
Everyone who is both tall and not strong is both wise and not humble and vice versa.
Everyone who is either brave or not wise is rich.
If someone is either tall or not old then lucy is not humble.
Everyone who is curious or not old is not calm or generous and vice versa.
Everyone who is not strong or brave is tall or not kind and vice versa.
Mary is happy.
Alice is both old and not strong.
Someone is either humble or not kind.
John is either not strong or happy.
Fred is both generous and not patient.
Fred is both wise and humble.
Someone is brave.
Mary is tall. | Alice is tall. | contradiction | (![X]:((~calm(X)<~>~kind(X))<=>(~kind(X)&~strong(X))))&
(![X]:(rich(X)=>wise(X)))&
(![X]:(brave(X)<=>(funny(X)&humble(X))))&
(![X]:((~humble(X)<~>brave(X))=>(~happy(X)|curious(X))))&
(((rich(fred)&~calm(fred)))=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(kind(X)<~>~rich(X))))&
(((~brave(lucy)<~>~strong(lucy)))<=>(?[X]:((wise(X)&humble(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:(calm(X))))&
(![X]:((patient(X)&tall(X))=>generous(X)))&
(![X]:((creative(X)<~>strong(X))=>(funny(X)<~>~humble(X))))&
(((humble(lucy)&creative(lucy)))=>(patient(fred)))&
(![X]:((tall(X)&~strong(X))<=>(wise(X)&~humble(X))))&
(![X]:((brave(X)<~>~wise(X))=>rich(X)))&
((?[X]:((tall(X)<~>~old(X))))=>(~humble(lucy)))&
(![X]:((curious(X)|~old(X))<=>(~calm(X)|generous(X))))&
(![X]:((~strong(X)|brave(X))<=>(tall(X)|~kind(X))))&
(happy(mary))&
((old(alice)&~strong(alice)))&
(?[X]:((humble(X)<~>~kind(X))))&
((~strong(john)<~>happy(john)))&
((generous(fred)&~patient(fred)))&
((wise(fred)&humble(fred)))&
(?[X]:(brave(X)))&
(tall(mary)) | tall(alice) | [
"p1",
"p2",
"p6",
"p11",
"p12",
"p13",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8442935211477084411513293
% SZS output start Proof for 8442935211477084411513293
2. ! [X0] : (rich(X0) => wise(X0)) [input p1]
3. ! [X0] : (brave(X0) <=> (humble(X0) & funny(X0))) [input p2]
7. (~brave(lucy) <~> ~strong(lucy)) <=> ? [X0] : (humble(X0) & wise(X0)) [input p6]
12. ! [X0] : ((~strong(X0) & tall(X0)) <=> (~humble(X0) & wise(X0))) [input p11]
13. ! [X0] : ((brave(X0) <~> ~wise(X0)) => rich(X0)) [input p12]
14. ? [X0] : (tall(X0) <~> ~old(X0)) => ~humble(lucy) [input p13]
18. ~strong(alice) & old(alice) [input p17]
22. humble(fred) & wise(fred) [input p21]
25. tall(alice) [input hypothesis]
27. ! [X0] : (wise(X0) | ~rich(X0)) [ennf transformation 2]
37. ! [X0] : (rich(X0) | (brave(X0) <=> ~wise(X0))) [ennf transformation 13]
38. ~humble(lucy) | ! [X0] : (tall(X0) <=> ~old(X0)) [ennf transformation 14]
41. ! [X0] : ((brave(X0) | (~humble(X0) | ~funny(X0))) & ((humble(X0) & funny(X0)) | ~brave(X0))) [nnf transformation 3]
42. ! [X0] : ((brave(X0) | ~humble(X0) | ~funny(X0)) & ((humble(X0) & funny(X0)) | ~brave(X0))) [flattening 41]
48. (((strong(lucy) | brave(lucy)) & (~strong(lucy) | ~brave(lucy))) | ! [X0] : (~humble(X0) | ~wise(X0))) & (? [X0] : (humble(X0) & wise(X0)) | ((~brave(lucy) | strong(lucy)) & (~strong(lucy) | brave(lucy)))) [nnf transformation 7]
49. (((strong(lucy) | brave(lucy)) & (~strong(lucy) | ~brave(lucy))) | ! [X0] : (~humble(X0) | ~wise(X0))) & (? [X1] : (humble(X1) & wise(X1)) | ((~brave(lucy) | strong(lucy)) & (~strong(lucy) | brave(lucy)))) [rectify 48]
50. ? [X1] : (humble(X1) & wise(X1)) => (humble(sK1) & wise(sK1)) [choice axiom]
51. (((strong(lucy) | brave(lucy)) & (~strong(lucy) | ~brave(lucy))) | ! [X0] : (~humble(X0) | ~wise(X0))) & ((humble(sK1) & wise(sK1)) | ((~brave(lucy) | strong(lucy)) & (~strong(lucy) | brave(lucy)))) [skolemisation 49,50]
58. ! [X0] : (((~strong(X0) & tall(X0)) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | (strong(X0) | ~tall(X0)))) [nnf transformation 12]
59. ! [X0] : (((~strong(X0) & tall(X0)) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | strong(X0) | ~tall(X0))) [flattening 58]
60. ! [X0] : (rich(X0) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0)))) [nnf transformation 37]
61. ~humble(lucy) | ! [X0] : ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0))) [nnf transformation 38]
78. ~rich(X0) | wise(X0) [cnf transformation 27]
80. ~brave(X0) | humble(X0) [cnf transformation 42]
99. strong(lucy) | brave(lucy) | ~humble(X0) | ~wise(X0) [cnf transformation 51]
111. ~wise(X0) | humble(X0) | ~strong(X0) [cnf transformation 59]
113. rich(X0) | brave(X0) | wise(X0) [cnf transformation 60]
114. ~humble(lucy) | ~old(X0) | ~tall(X0) [cnf transformation 61]
125. old(alice) [cnf transformation 18]
133. wise(fred) [cnf transformation 22]
134. humble(fred) [cnf transformation 22]
137. tall(alice) [cnf transformation 25]
161. 5 <=> ! [X0] : (~humble(X0) | ~wise(X0)) [avatar definition]
162. ~humble(X0) | ~wise(X0) <- (5) [avatar component clause 161]
164. 6 <=> brave(lucy) [avatar definition]
165. ~brave(lucy) <- (~6) [avatar component clause 164]
166. brave(lucy) <- (6) [avatar component clause 164]
168. 7 <=> strong(lucy) [avatar definition]
170. strong(lucy) <- (7) [avatar component clause 168]
171. 5 | 6 | 7 [avatar split clause 99,168,164,161]
202. 14 <=> humble(lucy) [avatar definition]
204. ~humble(lucy) <- (~14) [avatar component clause 202]
214. brave(X0) | wise(X0) [subsumption resolution 113,78]
220. 18 <=> ! [X0] : (~old(X0) | ~tall(X0)) [avatar definition]
221. ~old(X0) | ~tall(X0) <- (18) [avatar component clause 220]
222. 18 | ~14 [avatar split clause 114,202,220]
248. ~wise(fred) <- (5) [resolution 162,134]
250. $false <- (5) [subsumption resolution 248,133]
251. ~5 [avatar contradiction clause 250]
252. humble(lucy) <- (6) [resolution 166,80]
256. 14 | ~6 [avatar split clause 252,164,202]
264. ~tall(alice) <- (18) [resolution 221,125]
266. $false <- (18) [subsumption resolution 264,137]
267. ~18 [avatar contradiction clause 266]
268. wise(lucy) <- (~6) [resolution 165,214]
332. humble(lucy) | ~strong(lucy) <- (~6) [resolution 111,268]
336. ~strong(lucy) <- (~6, ~14) [subsumption resolution 332,204]
337. $false <- (~6, 7, ~14) [subsumption resolution 336,170]
338. 6 | ~7 | 14 [avatar contradiction clause 337]
341. $false [avatar sat refutation 171,222,251,256,267,338]
% SZS output end Proof for 8442935211477084411513293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or strong then paul is both funny and strong and vice versa.
Everyone who is both creative and rich is generous or not tall.
Everyone who is not tall or not happy is tall and vice versa.
Everyone who is not generous or humble is both not calm and not old and vice versa.
If someone is both not funny and not quiet then someone is both brave and generous and vice versa.
Everyone who is rich is not patient or old and vice versa.
If fred is not tall then mary is not humble or not strong.
If john is either not tall or kind then fred is either not wise or not kind.
Everyone who is both strong and not patient is patient and vice versa.
If someone is either not tall or not brave then fred is not curious and vice versa.
Everyone who is either kind or not happy is both brave and not generous.
Everyone who is rich is not strong and vice versa.
Everyone who is not brave is either quiet or happy.
Everyone who is not old or not kind is both not old and not happy.
If someone is both quiet and happy then john is both not tall and not kind.
Everyone who is either not curious or not funny is either brave or calm and vice versa.
Lucy is both not wise and not quiet.
John is not quiet.
Mary is both kind and quiet.
Someone is tall.
Mary is not calm.
Alice is both not happy and curious.
John is either wise or not strong. | Lucy is kind. | neutral | ((?[X]:((creative(X)|strong(X))))<=>((funny(paul)&strong(paul))))&
(![X]:((creative(X)&rich(X))=>(generous(X)|~tall(X))))&
(![X]:((~tall(X)|~happy(X))<=>tall(X)))&
(![X]:((~generous(X)|humble(X))<=>(~calm(X)&~old(X))))&
((?[X]:((~funny(X)&~quiet(X))))<=>(?[X]:((brave(X)&generous(X)))))&
(![X]:(rich(X)<=>(~patient(X)|old(X))))&
((~tall(fred))=>((~humble(mary)|~strong(mary))))&
(((~tall(john)<~>kind(john)))=>((~wise(fred)<~>~kind(fred))))&
(![X]:((strong(X)&~patient(X))<=>patient(X)))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(~curious(fred)))&
(![X]:((kind(X)<~>~happy(X))=>(brave(X)&~generous(X))))&
(![X]:(rich(X)<=>~strong(X)))&
(![X]:(~brave(X)=>(quiet(X)<~>happy(X))))&
(![X]:((~old(X)|~kind(X))=>(~old(X)&~happy(X))))&
((?[X]:((quiet(X)&happy(X))))=>((~tall(john)&~kind(john))))&
(![X]:((~curious(X)<~>~funny(X))<=>(brave(X)<~>calm(X))))&
((~wise(lucy)&~quiet(lucy)))&
(~quiet(john))&
((kind(mary)&quiet(mary)))&
(?[X]:(tall(X)))&
(~calm(mary))&
((~happy(alice)&curious(alice)))&
((wise(john)<~>~strong(john))) | kind(lucy) | [] | null | 0 |
Everyone who is either not generous or strong is both not generous and not rich and vice versa. If lucy is either curious or not calm then mary is not tall or creative and vice versa. Everyone who is not creative is either not happy or happy and vice versa. If fred is not generous then alice is not curious or not strong and vice versa. Everyone who is humble is quiet and vice versa. If someone is not old or not generous then someone is not rich. Everyone who is both not funny and humble is both not creative and not calm and vice versa. Everyone who is not funny or not kind is either not curious or funny and vice versa. If someone is both patient and not tall then someone is both not generous and not strong and vice versa. If someone is not creative or not humble then susan is both not strong and brave. Everyone who is kind is rich or tall. Everyone who is both not wise and rich is wise. Everyone who is both not curious and generous is rich and vice versa. Everyone who is both old and not rich is not humble and vice versa. If john is both not strong and not quiet then john is not rich or not brave. If mary is either not strong or funny then mary is wise or patient and vice versa. Susan is both not rich and humble. Someone is either not funny or not happy. John is not calm. Someone is both generous and brave. Someone is both not humble and generous. Someone is not patient or calm. Someone is not curious or not brave. | Mary is creative. | contradiction | (![X]:((~generous(X)<~>strong(X))<=>(~generous(X)&~rich(X))))&
(((curious(lucy)<~>~calm(lucy)))<=>((~tall(mary)|creative(mary))))&
(![X]:(~creative(X)<=>(~happy(X)<~>happy(X))))&
((~generous(fred))<=>((~curious(alice)|~strong(alice))))&
(![X]:(humble(X)<=>quiet(X)))&
((?[X]:((~old(X)|~generous(X))))=>(?[X]:(~rich(X))))&
(![X]:((~funny(X)&humble(X))<=>(~creative(X)&~calm(X))))&
(![X]:((~funny(X)|~kind(X))<=>(~curious(X)<~>funny(X))))&
((?[X]:((patient(X)&~tall(X))))<=>(?[X]:((~generous(X)&~strong(X)))))&
((?[X]:((~creative(X)|~humble(X))))=>((~strong(susan)&brave(susan))))&
(![X]:(kind(X)=>(rich(X)|tall(X))))&
(![X]:((~wise(X)&rich(X))=>wise(X)))&
(![X]:((~curious(X)&generous(X))<=>rich(X)))&
(![X]:((old(X)&~rich(X))<=>~humble(X)))&
(((~strong(john)&~quiet(john)))=>((~rich(john)|~brave(john))))&
(((~strong(mary)<~>funny(mary)))<=>((wise(mary)|patient(mary))))&
((~rich(susan)&humble(susan)))&
(?[X]:((~funny(X)<~>~happy(X))))&
(~calm(john))&
(?[X]:((generous(X)&brave(X))))&
(?[X]:((~humble(X)&generous(X))))&
(?[X]:((~patient(X)|calm(X))))&
(?[X]:((~curious(X)|~brave(X)))) | creative(mary) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7646362539843258794908411
% SZS output start Proof for 7646362539843258794908411
3. ! [X0] : (~creative(X0) <=> (~happy(X0) <~> happy(X0))) [input p2]
24. creative(mary) [input hypothesis]
39. ! [X0] : ((~creative(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | creative(X0))) [nnf transformation 3]
86. ~creative(X0) | happy(X0) | happy(X0) [cnf transformation 39]
87. ~creative(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 39]
139. creative(mary) [cnf transformation 24]
143. ~creative(X0) | happy(X0) [duplicate literal removal 86]
144. ~creative(X0) | ~happy(X0) [duplicate literal removal 87]
169. ~creative(X0) [subsumption resolution 143,144]
309. $false [subsumption resolution 139,169]
% SZS output end Proof for 7646362539843258794908411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both not quiet and curious. If fred is not quiet or not kind then someone is both happy and creative and vice versa. If susan is both strong and not patient then someone is either curious or quiet. Everyone who is creative is funny. Everyone who is not brave is either brave or not happy and vice versa. Everyone who is not old is either generous or not patient. If lucy is both patient and not happy then paul is either quiet or not humble. Everyone who is rich is patient and vice versa. Everyone who is both not wise and not generous is both happy and generous. If someone is strong or not quiet then someone is curious or not tall. If paul is either brave or not calm then mary is not kind or not humble and vice versa. Everyone who is both not rich and brave is both brave and not calm and vice versa. If paul is both not curious and old then lucy is not kind and vice versa. If someone is both not humble and not patient then someone is not generous. If someone is not generous or patient then someone is either strong or happy. Everyone who is either quiet or curious is curious. Someone is strong or not humble. Someone is not generous. Someone is not strong or not happy. Fred is not old. Lucy is either not generous or not happy. John is not quiet or not kind. | John is kind. | neutral | (![X]:(funny(X)=>(~quiet(X)&curious(X))))&
(((~quiet(fred)|~kind(fred)))<=>(?[X]:((happy(X)&creative(X)))))&
(((strong(susan)&~patient(susan)))=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:(creative(X)=>funny(X)))&
(![X]:(~brave(X)<=>(brave(X)<~>~happy(X))))&
(![X]:(~old(X)=>(generous(X)<~>~patient(X))))&
(((patient(lucy)&~happy(lucy)))=>((quiet(paul)<~>~humble(paul))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((~wise(X)&~generous(X))=>(happy(X)&generous(X))))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((curious(X)|~tall(X)))))&
(((brave(paul)<~>~calm(paul)))<=>((~kind(mary)|~humble(mary))))&
(![X]:((~rich(X)&brave(X))<=>(brave(X)&~calm(X))))&
(((~curious(paul)&old(paul)))<=>(~kind(lucy)))&
((?[X]:((~humble(X)&~patient(X))))=>(?[X]:(~generous(X))))&
((?[X]:((~generous(X)|patient(X))))=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:((quiet(X)<~>curious(X))=>curious(X)))&
(?[X]:((strong(X)|~humble(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~strong(X)|~happy(X))))&
(~old(fred))&
((~generous(lucy)<~>~happy(lucy)))&
((~quiet(john)|~kind(john))) | kind(john) | [] | null | 0 |
Everyone who is either not calm or not quiet is not brave and vice versa.
If lucy is both not wise and wise then paul is both quiet and not rich and vice versa.
Everyone who is both not funny and not kind is both not creative and happy.
If susan is patient or generous then someone is kind and vice versa.
If fred is rich or kind then mary is not humble or calm.
If someone is kind then someone is quiet and vice versa.
If someone is not brave or not old then someone is curious.
Everyone who is kind is not kind.
If someone is either not curious or quiet then someone is tall or brave and vice versa.
Everyone who is both not quiet and kind is humble or not curious and vice versa.
If mary is either creative or tall then alice is not creative or rich and vice versa.
If someone is not quiet or quiet then lucy is either not humble or creative.
If someone is either not rich or tall then fred is curious or not happy.
If someone is either not old or humble then someone is either kind or calm.
Everyone who is humble is wise.
Someone is either not funny or not calm.
Someone is either happy or not tall.
Someone is either not wise or not humble.
Someone is either rich or quiet.
Mary is either strong or not wise.
Alice is either not happy or not patient. | Susan is not brave. | entailment | (![X]:((~calm(X)<~>~quiet(X))<=>~brave(X)))&
(((~wise(lucy)&wise(lucy)))<=>((quiet(paul)&~rich(paul))))&
(![X]:((~funny(X)&~kind(X))=>(~creative(X)&happy(X))))&
(((patient(susan)|generous(susan)))<=>(?[X]:(kind(X))))&
(((rich(fred)|kind(fred)))=>((~humble(mary)|calm(mary))))&
((?[X]:(kind(X)))<=>(?[X]:(quiet(X))))&
((?[X]:((~brave(X)|~old(X))))=>(?[X]:(curious(X))))&
(![X]:(kind(X)=>~kind(X)))&
((?[X]:((~curious(X)<~>quiet(X))))<=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~quiet(X)&kind(X))<=>(humble(X)|~curious(X))))&
(((creative(mary)<~>tall(mary)))<=>((~creative(alice)|rich(alice))))&
((?[X]:((~quiet(X)|quiet(X))))=>((~humble(lucy)<~>creative(lucy))))&
((?[X]:((~rich(X)<~>tall(X))))=>((curious(fred)|~happy(fred))))&
((?[X]:((~old(X)<~>humble(X))))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:(humble(X)=>wise(X)))&
(?[X]:((~funny(X)<~>~calm(X))))&
(?[X]:((happy(X)<~>~tall(X))))&
(?[X]:((~wise(X)<~>~humble(X))))&
(?[X]:((rich(X)<~>quiet(X))))&
((strong(mary)<~>~wise(mary)))&
((~happy(alice)<~>~patient(alice))) | ~brave(susan) | [
"p5",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1498638212519864337339413
% SZS output start Proof for 1498638212519864337339413
6. ? [X0] : kind(X0) <=> ? [X0] : quiet(X0) [input p5]
8. ! [X0] : (kind(X0) => ~kind(X0)) [input p7]
9. ? [X0] : (~curious(X0) <~> quiet(X0)) <=> ? [X0] : (brave(X0) | tall(X0)) [input p8]
10. ! [X0] : ((kind(X0) & ~quiet(X0)) <=> (~curious(X0) | humble(X0))) [input p9]
22. brave(susan) [input hypothesis]
23. ? [X0] : kind(X0) <=> ? [X1] : quiet(X1) [rectify 6]
25. ? [X0] : (~curious(X0) <~> quiet(X0)) <=> ? [X1] : (brave(X1) | tall(X1)) [rectify 9]
32. ! [X0] : (~kind(X0) | ~kind(X0)) [ennf transformation 8]
46. (? [X0] : kind(X0) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : ~kind(X0)) [nnf transformation 23]
47. (? [X0] : kind(X0) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : ~kind(X3)) [rectify 46]
48. ? [X0] : kind(X0) => kind(sK1) [choice axiom]
49. ? [X2] : quiet(X2) => quiet(sK2) [choice axiom]
50. (kind(sK1) | ! [X1] : ~quiet(X1)) & (quiet(sK2) | ! [X3] : ~kind(X3)) [skolemisation 47,49,48]
54. (? [X0] : ((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ! [X1] : (~brave(X1) & ~tall(X1))) & (? [X1] : (brave(X1) | tall(X1)) | ! [X0] : ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0)))) [nnf transformation 25]
55. (? [X0] : ((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ! [X1] : (~brave(X1) & ~tall(X1))) & (? [X2] : (brave(X2) | tall(X2)) | ! [X3] : ((~curious(X3) | ~quiet(X3)) & (quiet(X3) | curious(X3)))) [rectify 54]
56. ? [X0] : ((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) => ((~quiet(sK4) | curious(sK4)) & (quiet(sK4) | ~curious(sK4))) [choice axiom]
57. ? [X2] : (brave(X2) | tall(X2)) => (brave(sK5) | tall(sK5)) [choice axiom]
58. (((~quiet(sK4) | curious(sK4)) & (quiet(sK4) | ~curious(sK4))) | ! [X1] : (~brave(X1) & ~tall(X1))) & ((brave(sK5) | tall(sK5)) | ! [X3] : ((~curious(X3) | ~quiet(X3)) & (quiet(X3) | curious(X3)))) [skolemisation 55,57,56]
59. ! [X0] : (((kind(X0) & ~quiet(X0)) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | (~kind(X0) | quiet(X0)))) [nnf transformation 10]
60. ! [X0] : (((kind(X0) & ~quiet(X0)) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | ~kind(X0) | quiet(X0))) [flattening 59]
99. kind(sK1) | ~quiet(X1) [cnf transformation 50]
102. ~kind(X0) | ~kind(X0) [cnf transformation 32]
106. quiet(sK4) | ~curious(sK4) | ~brave(X1) [cnf transformation 58]
113. curious(X0) | kind(X0) [cnf transformation 60]
143. brave(susan) [cnf transformation 22]
144. ~kind(X0) [duplicate literal removal 102]
160. 4 <=> ! [X0] : ~kind(X0) [avatar definition]
161. ~kind(X0) <- (4) [avatar component clause 160]
196. 12 <=> ! [X1] : ~quiet(X1) [avatar definition]
197. ~quiet(X1) <- (12) [avatar component clause 196]
199. 13 <=> kind(sK1) [avatar definition]
201. kind(sK1) <- (13) [avatar component clause 199]
202. 12 | 13 [avatar split clause 99,199,196]
220. 4 [avatar split clause 144,160]
222. 18 <=> ! [X1] : ~brave(X1) [avatar definition]
223. ~brave(X1) <- (18) [avatar component clause 222]
225. 19 <=> curious(sK4) [avatar definition]
226. ~curious(sK4) <- (~19) [avatar component clause 225]
229. 20 <=> quiet(sK4) [avatar definition]
230. quiet(sK4) <- (20) [avatar component clause 229]
237. 18 | ~19 | 20 [avatar split clause 106,229,225,222]
380. kind(sK4) <- (~19) [resolution 113,226]
381. $false <- (4, ~19) [subsumption resolution 380,161]
382. ~4 | 19 [avatar contradiction clause 381]
383. $false <- (12, 20) [subsumption resolution 230,197]
384. ~12 | ~20 [avatar contradiction clause 383]
385. $false <- (4, 13) [subsumption resolution 201,161]
386. ~4 | ~13 [avatar contradiction clause 385]
387. $false <- (18) [resolution 223,143]
388. ~18 [avatar contradiction clause 387]
389. $false [avatar sat refutation 202,220,237,382,384,386,388]
% SZS output end Proof for 1498638212519864337339413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or old is both strong and not tall. Everyone who is patient or not calm is both not wise and old. If john is funny or curious then lucy is either generous or tall. If someone is not patient then someone is not generous. If someone is kind then someone is either not happy or not strong. Everyone who is either old or not humble is both not curious and not patient and vice versa. If lucy is both curious and creative then someone is either not rich or not generous. If mary is rich then mary is both generous and not calm. Everyone who is curious or calm is not wise. Everyone who is both strong and not wise is patient or wise and vice versa. If someone is rich then someone is both not funny and not calm and vice versa. Everyone who is curious or not wise is creative or tall. Everyone who is both not kind and not calm is both strong and not quiet. Everyone who is rich is not patient or happy and vice versa. If someone is both curious and not old then alice is calm or not brave and vice versa. Everyone who is brave is either not brave or not generous and vice versa. Fred is not curious or not kind. Someone is both not rich and not happy. Someone is either not happy or not tall. Someone is not calm or tall. Someone is strong. Alice is not humble. | Mary is not tall. | entailment | (![X]:((~strong(X)<~>old(X))=>(strong(X)&~tall(X))))&
(![X]:((patient(X)|~calm(X))=>(~wise(X)&old(X))))&
(((funny(john)|curious(john)))=>((generous(lucy)<~>tall(lucy))))&
((?[X]:(~patient(X)))=>(?[X]:(~generous(X))))&
((?[X]:(kind(X)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((old(X)<~>~humble(X))<=>(~curious(X)&~patient(X))))&
(((curious(lucy)&creative(lucy)))=>(?[X]:((~rich(X)<~>~generous(X)))))&
((rich(mary))=>((generous(mary)&~calm(mary))))&
(![X]:((curious(X)|calm(X))=>~wise(X)))&
(![X]:((strong(X)&~wise(X))<=>(patient(X)|wise(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~funny(X)&~calm(X)))))&
(![X]:((curious(X)|~wise(X))=>(creative(X)|tall(X))))&
(![X]:((~kind(X)&~calm(X))=>(strong(X)&~quiet(X))))&
(![X]:(rich(X)<=>(~patient(X)|happy(X))))&
((?[X]:((curious(X)&~old(X))))<=>((calm(alice)|~brave(alice))))&
(![X]:(brave(X)<=>(~brave(X)<~>~generous(X))))&
((~curious(fred)|~kind(fred)))&
(?[X]:((~rich(X)&~happy(X))))&
(?[X]:((~happy(X)<~>~tall(X))))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:(strong(X)))&
(~humble(alice)) | ~tall(mary) | [
"p0",
"p1",
"p7",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 174250829396319682565482
% SZS output start Proof for 174250829396319682565482
1. ! [X0] : ((~strong(X0) <~> old(X0)) => (~tall(X0) & strong(X0))) [input p0]
2. ! [X0] : ((~calm(X0) | patient(X0)) => (old(X0) & ~wise(X0))) [input p1]
8. rich(mary) => (~calm(mary) & generous(mary)) [input p7]
10. ! [X0] : ((~wise(X0) & strong(X0)) <=> (wise(X0) | patient(X0))) [input p9]
14. ! [X0] : (rich(X0) <=> (happy(X0) | ~patient(X0))) [input p13]
16. ! [X0] : (brave(X0) <=> (~brave(X0) <~> ~generous(X0))) [input p15]
23. tall(mary) [input hypothesis]
28. ! [X0] : ((~tall(X0) & strong(X0)) | (~strong(X0) <=> old(X0))) [ennf transformation 1]
29. ! [X0] : ((old(X0) & ~wise(X0)) | (calm(X0) & ~patient(X0))) [ennf transformation 2]
35. (~calm(mary) & generous(mary)) | ~rich(mary) [ennf transformation 8]
41. ! [X0] : ((~tall(X0) & strong(X0)) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) [nnf transformation 28]
55. ! [X0] : (((~wise(X0) & strong(X0)) | (~wise(X0) & ~patient(X0))) & ((wise(X0) | patient(X0)) | (wise(X0) | ~strong(X0)))) [nnf transformation 10]
56. ! [X0] : (((~wise(X0) & strong(X0)) | (~wise(X0) & ~patient(X0))) & (wise(X0) | patient(X0) | wise(X0) | ~strong(X0))) [flattening 55]
62. ! [X0] : ((rich(X0) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | ~rich(X0))) [nnf transformation 14]
63. ! [X0] : ((rich(X0) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | ~rich(X0))) [flattening 62]
69. ! [X0] : ((brave(X0) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | ~brave(X0))) [nnf transformation 16]
82. ~tall(X0) | ~strong(X0) | ~old(X0) [cnf transformation 41]
85. ~patient(X0) | old(X0) [cnf transformation 29]
102. generous(mary) | ~rich(mary) [cnf transformation 35]
107. ~patient(X0) | strong(X0) [cnf transformation 56]
118. rich(X0) | patient(X0) [cnf transformation 63]
125. ~generous(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 69]
127. brave(X0) | ~generous(X0) | brave(X0) [cnf transformation 69]
137. tall(mary) [cnf transformation 23]
138. ~generous(X0) | ~brave(X0) [duplicate literal removal 125]
139. ~generous(X0) | brave(X0) [duplicate literal removal 127]
205. 14 <=> rich(mary) [avatar definition]
207. ~rich(mary) <- (~14) [avatar component clause 205]
214. 16 <=> generous(mary) [avatar definition]
216. generous(mary) <- (16) [avatar component clause 214]
217. ~14 | 16 [avatar split clause 102,214,205]
266. ~generous(X0) [subsumption resolution 138,139]
298. patient(mary) <- (~14) [resolution 118,207]
302. strong(mary) <- (~14) [resolution 298,107]
303. old(mary) <- (~14) [resolution 298,85]
315. ~strong(mary) | ~old(mary) [resolution 82,137]
316. ~old(mary) <- (~14) [subsumption resolution 315,302]
317. $false <- (~14) [subsumption resolution 316,303]
318. 14 [avatar contradiction clause 317]
328. $false <- (16) [subsumption resolution 216,266]
329. ~16 [avatar contradiction clause 328]
330. $false [avatar sat refutation 217,318,329]
% SZS output end Proof for 174250829396319682565482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not generous is not kind or not old and vice versa.
If someone is not creative then fred is not curious.
If paul is rich or not creative then someone is either not tall or not creative.
If alice is not strong or not humble then alice is rich or not curious.
If someone is wise or generous then john is either not humble or rich and vice versa.
Everyone who is creative or not wise is rich and vice versa.
Everyone who is curious or not happy is not tall or not happy and vice versa.
Everyone who is either not curious or brave is both funny and tall and vice versa.
Everyone who is not curious is not kind or humble and vice versa.
Everyone who is old is humble or rich.
Everyone who is creative is either humble or not wise and vice versa.
Everyone who is either not tall or not generous is not happy or strong and vice versa.
If someone is both not strong and not humble then susan is either not generous or not quiet.
If john is both tall and not generous then someone is either brave or not wise and vice versa.
Everyone who is both not rich and not humble is both brave and not old and vice versa.
Everyone who is wise or not generous is either not curious or rich.
Someone is either calm or tall.
Fred is not tall.
Someone is old or not brave.
John is both not old and not calm.
Someone is not tall or generous. | Paul is brave. | contradiction | (![X]:((kind(X)|~generous(X))<=>(~kind(X)|~old(X))))&
((?[X]:(~creative(X)))=>(~curious(fred)))&
(((rich(paul)|~creative(paul)))=>(?[X]:((~tall(X)<~>~creative(X)))))&
(((~strong(alice)|~humble(alice)))=>((rich(alice)|~curious(alice))))&
((?[X]:((wise(X)|generous(X))))<=>((~humble(john)<~>rich(john))))&
(![X]:((creative(X)|~wise(X))<=>rich(X)))&
(![X]:((curious(X)|~happy(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~curious(X)<~>brave(X))<=>(funny(X)&tall(X))))&
(![X]:(~curious(X)<=>(~kind(X)|humble(X))))&
(![X]:(old(X)=>(humble(X)|rich(X))))&
(![X]:(creative(X)<=>(humble(X)<~>~wise(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~happy(X)|strong(X))))&
((?[X]:((~strong(X)&~humble(X))))=>((~generous(susan)<~>~quiet(susan))))&
(((tall(john)&~generous(john)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(brave(X)&~old(X))))&
(![X]:((wise(X)|~generous(X))=>(~curious(X)<~>rich(X))))&
(?[X]:((calm(X)<~>tall(X))))&
(~tall(fred))&
(?[X]:((old(X)|~brave(X))))&
((~old(john)&~calm(john)))&
(?[X]:((~tall(X)|generous(X)))) | brave(paul) | [
"p0",
"p1",
"p5",
"p6",
"p7",
"p8",
"p11",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4908929122737405158965623
% SZS output start Proof for 4908929122737405158965623
1. ! [X0] : ((~generous(X0) | kind(X0)) <=> (~old(X0) | ~kind(X0))) [input p0]
2. ? [X0] : ~creative(X0) => ~curious(fred) [input p1]
6. ! [X0] : ((~wise(X0) | creative(X0)) <=> rich(X0)) [input p5]
7. ! [X0] : ((~happy(X0) | curious(X0)) <=> (~happy(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((~curious(X0) <~> brave(X0)) <=> (tall(X0) & funny(X0))) [input p7]
9. ! [X0] : (~curious(X0) <=> (humble(X0) | ~kind(X0))) [input p8]
12. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (strong(X0) | ~happy(X0))) [input p11]
15. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (~old(X0) & brave(X0))) [input p14]
16. ! [X0] : ((~generous(X0) | wise(X0)) => (~curious(X0) <~> rich(X0))) [input p15]
18. ~tall(fred) [input p17]
22. brave(paul) [input hypothesis]
23. ~curious(fred) | ! [X0] : creative(X0) [ennf transformation 2]
30. ! [X0] : ((~curious(X0) <~> rich(X0)) | (generous(X0) & ~wise(X0))) [ennf transformation 16]
31. ! [X0] : (((~generous(X0) | kind(X0)) | (old(X0) & kind(X0))) & ((~old(X0) | ~kind(X0)) | (generous(X0) & ~kind(X0)))) [nnf transformation 1]
32. ! [X0] : ((~generous(X0) | kind(X0) | (old(X0) & kind(X0))) & (~old(X0) | ~kind(X0) | (generous(X0) & ~kind(X0)))) [flattening 31]
40. ! [X0] : (((~wise(X0) | creative(X0)) | ~rich(X0)) & (rich(X0) | (wise(X0) & ~creative(X0)))) [nnf transformation 6]
41. ! [X0] : ((~wise(X0) | creative(X0) | ~rich(X0)) & (rich(X0) | (wise(X0) & ~creative(X0)))) [flattening 40]
42. ! [X0] : (((~happy(X0) | curious(X0)) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | (happy(X0) & ~curious(X0)))) [nnf transformation 7]
43. ! [X0] : ((~happy(X0) | curious(X0) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | (happy(X0) & ~curious(X0)))) [flattening 42]
44. ! [X0] : ((((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (~tall(X0) | ~funny(X0))) & ((tall(X0) & funny(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0))))) [nnf transformation 8]
45. ! [X0] : ((((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | ~tall(X0) | ~funny(X0)) & ((tall(X0) & funny(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0))))) [flattening 44]
46. ! [X0] : ((~curious(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | curious(X0))) [nnf transformation 9]
47. ! [X0] : ((~curious(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | curious(X0))) [flattening 46]
49. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 12]
50. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [flattening 49]
57. ! [X0] : (((~humble(X0) & ~rich(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (humble(X0) | rich(X0)))) [nnf transformation 15]
58. ! [X0] : (((~humble(X0) & ~rich(X0)) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | humble(X0) | rich(X0))) [flattening 57]
59. ! [X0] : (((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | (generous(X0) & ~wise(X0))) [nnf transformation 30]
67. ~old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 32]
69. ~generous(X0) | kind(X0) | kind(X0) [cnf transformation 32]
71. ~curious(fred) | creative(X0) [cnf transformation 23]
84. ~creative(X0) | rich(X0) [cnf transformation 41]
89. ~happy(X0) | curious(X0) | tall(X0) [cnf transformation 43]
93. brave(X0) | tall(X0) | curious(X0) [cnf transformation 45]
97. ~kind(X0) | humble(X0) | curious(X0) [cnf transformation 47]
98. ~curious(X0) | kind(X0) [cnf transformation 47]
99. ~humble(X0) | ~curious(X0) [cnf transformation 47]
109. happy(X0) | tall(X0) | generous(X0) [cnf transformation 50]
121. ~brave(X0) | old(X0) | ~rich(X0) [cnf transformation 58]
122. ~brave(X0) | old(X0) | ~humble(X0) [cnf transformation 58]
126. ~rich(X0) | curious(X0) | generous(X0) [cnf transformation 59]
129. ~tall(fred) [cnf transformation 18]
134. brave(paul) [cnf transformation 22]
135. ~old(X0) | ~kind(X0) [duplicate literal removal 67]
136. ~generous(X0) | kind(X0) [duplicate literal removal 69]
138. 1 <=> ! [X0] : creative(X0) [avatar definition]
139. creative(X0) <- (1) [avatar component clause 138]
141. 2 <=> curious(fred) [avatar definition]
143. ~curious(fred) <- (~2) [avatar component clause 141]
144. 1 | ~2 [avatar split clause 71,141,138]
159. 6 <=> rich(paul) [avatar definition]
160. rich(paul) <- (6) [avatar component clause 159]
161. ~rich(paul) <- (~6) [avatar component clause 159]
317. 37 <=> curious(paul) [avatar definition]
318. curious(paul) <- (37) [avatar component clause 317]
319. ~curious(paul) <- (~37) [avatar component clause 317]
395. tall(X0) | generous(X0) | curious(X0) | tall(X0) [resolution 109,89]
397. tall(X0) | generous(X0) | curious(X0) [duplicate literal removal 395]
474. old(paul) | ~rich(paul) [resolution 121,134]
477. old(paul) <- (6) [subsumption resolution 474,160]
490. old(X1) | ~humble(X1) | tall(X1) | curious(X1) [resolution 122,93]
491. ~humble(X1) | old(X1) | tall(X1) [subsumption resolution 490,99]
495. ~kind(paul) <- (6) [resolution 477,135]
497. 54 <=> generous(paul) [avatar definition]
499. generous(paul) <- (54) [avatar component clause 497]
501. 55 <=> kind(paul) [avatar definition]
503. ~kind(paul) <- (~55) [avatar component clause 501]
505. ~55 | ~6 [avatar split clause 495,159,501]
513. curious(paul) | generous(paul) <- (6) [resolution 126,160]
524. generous(paul) <- (6, ~37) [subsumption resolution 513,319]
525. 54 | ~6 | 37 [avatar split clause 524,317,159,497]
542. kind(paul) <- (54) [resolution 499,136]
553. 55 | ~54 [avatar split clause 542,497,501]
600. generous(fred) | curious(fred) [resolution 397,129]
605. generous(fred) <- (~2) [subsumption resolution 600,143]
656. kind(fred) <- (~2) [resolution 605,136]
658. 66 <=> old(fred) [avatar definition]
660. old(fred) <- (66) [avatar component clause 658]
662. 67 <=> kind(fred) [avatar definition]
664. kind(fred) <- (67) [avatar component clause 662]
666. 67 | 2 [avatar split clause 656,141,662]
696. humble(fred) | curious(fred) <- (67) [resolution 664,97]
697. humble(fred) <- (~2, 67) [subsumption resolution 696,143]
717. old(fred) | tall(fred) <- (~2, 67) [resolution 697,491]
721. old(fred) <- (~2, 67) [subsumption resolution 717,129]
722. 66 | 2 | ~67 [avatar split clause 721,662,141,658]
742. rich(X0) <- (1) [resolution 139,84]
765. $false <- (1, ~6) [resolution 742,161]
770. ~1 | 6 [avatar contradiction clause 765]
790. ~kind(fred) <- (66) [resolution 660,135]
798. ~67 | ~66 [avatar split clause 790,658,662]
863. kind(paul) <- (37) [resolution 318,98]
864. $false <- (37, ~55) [subsumption resolution 863,503]
865. ~37 | 55 [avatar contradiction clause 864]
866. $false [avatar sat refutation 144,505,525,553,666,722,770,798,865]
% SZS output end Proof for 4908929122737405158965623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not brave or not happy then someone is both strong and rich and vice versa.
If lucy is both not happy and not curious then john is both old and not kind and vice versa.
Everyone who is either humble or kind is both brave and humble.
Everyone who is funny or not strong is not patient or not creative.
Everyone who is either not strong or kind is generous or not curious and vice versa.
If alice is either humble or strong then lucy is not quiet.
If mary is either not generous or not kind then lucy is both not creative and not rich and vice versa.
Everyone who is wise or funny is not calm or patient and vice versa.
If paul is not brave then someone is calm or not happy.
Everyone who is both rich and patient is creative or kind.
Everyone who is both not creative and not strong is patient and vice versa.
Everyone who is happy is both wise and not tall.
If someone is brave then someone is both not calm and curious.
Everyone who is either humble or not creative is not funny or calm.
Everyone who is either not humble or funny is quiet or rich.
If someone is both not brave and happy then susan is both not old and strong and vice versa.
Someone is either strong or not brave.
Someone is either not calm or not creative.
Mary is either old or not strong.
Mary is either not funny or not patient.
Paul is both not old and not tall.
Someone is not tall.
Fred is both calm and creative.
Paul is quiet or not patient. | Fred is wise. | contradiction | (((~brave(lucy)|~happy(lucy)))<=>(?[X]:((strong(X)&rich(X)))))&
(((~happy(lucy)&~curious(lucy)))<=>((old(john)&~kind(john))))&
(![X]:((humble(X)<~>kind(X))=>(brave(X)&humble(X))))&
(![X]:((funny(X)|~strong(X))=>(~patient(X)|~creative(X))))&
(![X]:((~strong(X)<~>kind(X))<=>(generous(X)|~curious(X))))&
(((humble(alice)<~>strong(alice)))=>(~quiet(lucy)))&
(((~generous(mary)<~>~kind(mary)))<=>((~creative(lucy)&~rich(lucy))))&
(![X]:((wise(X)|funny(X))<=>(~calm(X)|patient(X))))&
((~brave(paul))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((rich(X)&patient(X))=>(creative(X)|kind(X))))&
(![X]:((~creative(X)&~strong(X))<=>patient(X)))&
(![X]:(happy(X)=>(wise(X)&~tall(X))))&
((?[X]:(brave(X)))=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:((humble(X)<~>~creative(X))=>(~funny(X)|calm(X))))&
(![X]:((~humble(X)<~>funny(X))=>(quiet(X)|rich(X))))&
((?[X]:((~brave(X)&happy(X))))<=>((~old(susan)&strong(susan))))&
(?[X]:((strong(X)<~>~brave(X))))&
(?[X]:((~calm(X)<~>~creative(X))))&
((old(mary)<~>~strong(mary)))&
((~funny(mary)<~>~patient(mary)))&
((~old(paul)&~tall(paul)))&
(?[X]:(~tall(X)))&
((calm(fred)&creative(fred)))&
((quiet(paul)|~patient(paul))) | wise(fred) | [
"p7",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8731522607978802828182203
% SZS output start Proof for 8731522607978802828182203
8. ! [X0] : ((funny(X0) | wise(X0)) <=> (patient(X0) | ~calm(X0))) [input p7]
11. ! [X0] : ((~strong(X0) & ~creative(X0)) <=> patient(X0)) [input p10]
23. creative(fred) & calm(fred) [input p22]
25. wise(fred) [input hypothesis]
56. ! [X0] : (((funny(X0) | wise(X0)) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | (~funny(X0) & ~wise(X0)))) [nnf transformation 8]
57. ! [X0] : ((funny(X0) | wise(X0) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | (~funny(X0) & ~wise(X0)))) [flattening 56]
60. ! [X0] : (((~strong(X0) & ~creative(X0)) | ~patient(X0)) & (patient(X0) | (strong(X0) | creative(X0)))) [nnf transformation 11]
61. ! [X0] : (((~strong(X0) & ~creative(X0)) | ~patient(X0)) & (patient(X0) | strong(X0) | creative(X0))) [flattening 60]
109. ~calm(X0) | patient(X0) | ~wise(X0) [cnf transformation 57]
116. ~creative(X0) | ~patient(X0) [cnf transformation 61]
138. calm(fred) [cnf transformation 23]
139. creative(fred) [cnf transformation 23]
141. wise(fred) [cnf transformation 25]
317. ~patient(fred) [resolution 116,139]
357. patient(fred) | ~wise(fred) [resolution 109,138]
359. ~wise(fred) [subsumption resolution 357,317]
360. $false [subsumption resolution 359,141]
% SZS output end Proof for 8731522607978802828182203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or funny is both not humble and not old.
If john is either not humble or wise then someone is not wise or not generous.
If alice is either not creative or kind then someone is either not brave or not strong and vice versa.
If someone is either not curious or not wise then mary is both wise and not wise.
Everyone who is tall or humble is patient or old and vice versa.
Everyone who is not humble or not brave is not curious or not happy.
If paul is not brave or not patient then john is both tall and not quiet and vice versa.
Everyone who is not quiet or not strong is patient or not humble and vice versa.
If someone is either quiet or calm then someone is both not creative and generous.
Everyone who is both wise and brave is both not brave and not humble.
If fred is both curious and old then alice is both creative and strong and vice versa.
Everyone who is generous is both funny and not funny.
If paul is both calm and quiet then someone is either funny or brave and vice versa.
Everyone who is both kind and funny is both not kind and strong.
Everyone who is generous is both humble and happy.
If someone is either not strong or brave then alice is both not happy and not curious and vice versa.
Someone is either strong or rich.
Susan is happy or not humble.
Someone is old or not old.
Someone is not strong or not old.
Someone is both not wise and not happy.
Someone is rich.
Fred is both not calm and strong.
Someone is not tall. | Fred is not calm. | entailment | (![X]:((~happy(X)<~>funny(X))=>(~humble(X)&~old(X))))&
(((~humble(john)<~>wise(john)))=>(?[X]:((~wise(X)|~generous(X)))))&
(((~creative(alice)<~>kind(alice)))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
((?[X]:((~curious(X)<~>~wise(X))))=>((wise(mary)&~wise(mary))))&
(![X]:((tall(X)|humble(X))<=>(patient(X)|old(X))))&
(![X]:((~humble(X)|~brave(X))=>(~curious(X)|~happy(X))))&
(((~brave(paul)|~patient(paul)))<=>((tall(john)&~quiet(john))))&
(![X]:((~quiet(X)|~strong(X))<=>(patient(X)|~humble(X))))&
((?[X]:((quiet(X)<~>calm(X))))=>(?[X]:((~creative(X)&generous(X)))))&
(![X]:((wise(X)&brave(X))=>(~brave(X)&~humble(X))))&
(((curious(fred)&old(fred)))<=>((creative(alice)&strong(alice))))&
(![X]:(generous(X)=>(funny(X)&~funny(X))))&
(((calm(paul)&quiet(paul)))<=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:((kind(X)&funny(X))=>(~kind(X)&strong(X))))&
(![X]:(generous(X)=>(humble(X)&happy(X))))&
((?[X]:((~strong(X)<~>brave(X))))<=>((~happy(alice)&~curious(alice))))&
(?[X]:((strong(X)<~>rich(X))))&
((happy(susan)|~humble(susan)))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~strong(X)|~old(X))))&
(?[X]:((~wise(X)&~happy(X))))&
(?[X]:(rich(X)))&
((~calm(fred)&strong(fred)))&
(?[X]:(~tall(X))) | ~calm(fred) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 707257649980764409362354
% SZS output start Proof for 707257649980764409362354
23. strong(fred) & ~calm(fred) [input p22]
25. calm(fred) [input hypothesis]
152. ~calm(fred) [cnf transformation 23]
155. calm(fred) [cnf transformation 25]
360. $false [subsumption resolution 155,152]
% SZS output end Proof for 707257649980764409362354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or funny is not humble and vice versa. Everyone who is both not creative and not humble is not creative and vice versa. If someone is both calm and rich then someone is kind or not rich and vice versa. If someone is both funny and patient then mary is both not wise and not brave and vice versa. Everyone who is either not kind or not wise is either calm or funny. Everyone who is funny or not old is either not funny or not old and vice versa. If someone is either not wise or not curious then mary is either humble or not funny. If paul is either curious or not rich then paul is both not humble and not funny and vice versa. Everyone who is kind or not strong is both not rich and not creative. If susan is patient then someone is not curious or not calm and vice versa. If alice is either tall or not generous then john is either happy or not wise. If susan is either not creative or not curious then someone is funny. If someone is either creative or funny then mary is not tall or funny and vice versa. If lucy is both funny and not rich then someone is both not creative and funny and vice versa. Everyone who is not tall or happy is humble. Someone is either not strong or quiet. Someone is both tall and strong. Mary is either not kind or creative. Mary is either not kind or quiet. Someone is not rich or not humble. Someone is both tall and curious. Someone is not tall or not calm. Someone is not quiet or humble. | John is not tall. | contradiction | (![X]:((~patient(X)|funny(X))<=>~humble(X)))&
(![X]:((~creative(X)&~humble(X))<=>~creative(X)))&
((?[X]:((calm(X)&rich(X))))<=>(?[X]:((kind(X)|~rich(X)))))&
((?[X]:((funny(X)&patient(X))))<=>((~wise(mary)&~brave(mary))))&
(![X]:((~kind(X)<~>~wise(X))=>(calm(X)<~>funny(X))))&
(![X]:((funny(X)|~old(X))<=>(~funny(X)<~>~old(X))))&
((?[X]:((~wise(X)<~>~curious(X))))=>((humble(mary)<~>~funny(mary))))&
(((curious(paul)<~>~rich(paul)))<=>((~humble(paul)&~funny(paul))))&
(![X]:((kind(X)|~strong(X))=>(~rich(X)&~creative(X))))&
((patient(susan))<=>(?[X]:((~curious(X)|~calm(X)))))&
(((tall(alice)<~>~generous(alice)))=>((happy(john)<~>~wise(john))))&
(((~creative(susan)<~>~curious(susan)))=>(?[X]:(funny(X))))&
((?[X]:((creative(X)<~>funny(X))))<=>((~tall(mary)|funny(mary))))&
(((funny(lucy)&~rich(lucy)))<=>(?[X]:((~creative(X)&funny(X)))))&
(![X]:((~tall(X)|happy(X))=>humble(X)))&
(?[X]:((~strong(X)<~>quiet(X))))&
(?[X]:((tall(X)&strong(X))))&
((~kind(mary)<~>creative(mary)))&
((~kind(mary)<~>quiet(mary)))&
(?[X]:((~rich(X)|~humble(X))))&
(?[X]:((tall(X)&curious(X))))&
(?[X]:((~tall(X)|~calm(X))))&
(?[X]:((~quiet(X)|humble(X)))) | ~tall(john) | [
"p0",
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 682941789505453539644048
% SZS output start Proof for 682941789505453539644048
1. ! [X0] : ((funny(X0) | ~patient(X0)) <=> ~humble(X0)) [input p0]
6. ! [X0] : ((~old(X0) | funny(X0)) <=> (~funny(X0) <~> ~old(X0))) [input p5]
15. ! [X0] : ((happy(X0) | ~tall(X0)) => humble(X0)) [input p14]
24. ~tall(john) [input hypothesis]
31. ! [X0] : (humble(X0) | (~happy(X0) & tall(X0))) [ennf transformation 15]
32. ! [X0] : (((funny(X0) | ~patient(X0)) | humble(X0)) & (~humble(X0) | (~funny(X0) & patient(X0)))) [nnf transformation 1]
33. ! [X0] : ((funny(X0) | ~patient(X0) | humble(X0)) & (~humble(X0) | (~funny(X0) & patient(X0)))) [flattening 32]
47. ! [X0] : (((~old(X0) | funny(X0)) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0)))) & (((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (old(X0) & ~funny(X0)))) [nnf transformation 6]
48. ! [X0] : ((~old(X0) | funny(X0) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0)))) & (((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (old(X0) & ~funny(X0)))) [flattening 47]
86. ~humble(X0) | ~funny(X0) [cnf transformation 33]
107. old(X0) | funny(X0) | old(X0) [cnf transformation 48]
108. ~old(X0) | funny(X0) | ~old(X0) | funny(X0) [cnf transformation 48]
143. tall(X0) | humble(X0) [cnf transformation 31]
158. ~tall(john) [cnf transformation 24]
160. old(X0) | funny(X0) [duplicate literal removal 107]
161. ~old(X0) | funny(X0) [duplicate literal removal 108]
215. funny(X0) [subsumption resolution 160,161]
353. humble(john) [resolution 143,158]
357. ~funny(john) [resolution 353,86]
359. $false [subsumption resolution 357,215]
% SZS output end Proof for 682941789505453539644048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is kind and vice versa.
If susan is both old and kind then someone is both not strong and not creative and vice versa.
Everyone who is not quiet is not creative or not generous.
Everyone who is both curious and not patient is both brave and rich.
Everyone who is generous is either not old or quiet.
Everyone who is both humble and not calm is happy or kind and vice versa.
If someone is both generous and not wise then someone is not tall and vice versa.
Everyone who is funny or not strong is either not strong or not old and vice versa.
Everyone who is either creative or quiet is not tall or not wise and vice versa.
If mary is both brave and not generous then someone is both old and not tall and vice versa.
Everyone who is not humble or not tall is either not generous or not rich and vice versa.
If paul is brave or kind then paul is both not tall and not generous.
If someone is generous then susan is not quiet.
Everyone who is patient is creative and vice versa.
Everyone who is not humble is either kind or brave.
Everyone who is generous is not kind.
Someone is both brave and funny.
Someone is not brave.
Mary is not curious.
John is either strong or creative.
Fred is either not happy or kind.
Mary is both not wise and not rich. | Fred is not wise. | neutral | (![X]:(quiet(X)<=>kind(X)))&
(((old(susan)&kind(susan)))<=>(?[X]:((~strong(X)&~creative(X)))))&
(![X]:(~quiet(X)=>(~creative(X)|~generous(X))))&
(![X]:((curious(X)&~patient(X))=>(brave(X)&rich(X))))&
(![X]:(generous(X)=>(~old(X)<~>quiet(X))))&
(![X]:((humble(X)&~calm(X))<=>(happy(X)|kind(X))))&
((?[X]:((generous(X)&~wise(X))))<=>(?[X]:(~tall(X))))&
(![X]:((funny(X)|~strong(X))<=>(~strong(X)<~>~old(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(~tall(X)|~wise(X))))&
(((brave(mary)&~generous(mary)))<=>(?[X]:((old(X)&~tall(X)))))&
(![X]:((~humble(X)|~tall(X))<=>(~generous(X)<~>~rich(X))))&
(((brave(paul)|kind(paul)))=>((~tall(paul)&~generous(paul))))&
((?[X]:(generous(X)))=>(~quiet(susan)))&
(![X]:(patient(X)<=>creative(X)))&
(![X]:(~humble(X)=>(kind(X)<~>brave(X))))&
(![X]:(generous(X)=>~kind(X)))&
(?[X]:((brave(X)&funny(X))))&
(?[X]:(~brave(X)))&
(~curious(mary))&
((strong(john)<~>creative(john)))&
((~happy(fred)<~>kind(fred)))&
((~wise(mary)&~rich(mary))) | ~wise(fred) | [] | null | 0 |
If john is not creative then john is kind.
Everyone who is happy or generous is both not brave and not old.
Everyone who is not strong or not happy is both not tall and not old and vice versa.
If someone is creative or not kind then someone is either not patient or funny.
If mary is not strong then susan is not wise or not strong and vice versa.
If someone is either patient or creative then someone is not happy and vice versa.
If lucy is either rich or not happy then alice is not funny and vice versa.
Everyone who is both brave and not wise is either not patient or kind.
If fred is either kind or quiet then susan is not strong and vice versa.
If john is both happy and not calm then someone is not rich or strong and vice versa.
If lucy is wise or strong then someone is either tall or not funny.
Everyone who is tall or not tall is either patient or brave and vice versa.
Everyone who is either not wise or calm is not strong and vice versa.
If someone is both tall and old then alice is either not curious or not strong.
If fred is not quiet or humble then lucy is either not brave or not creative and vice versa.
Everyone who is either not strong or strong is either not humble or strong and vice versa.
Paul is happy or curious.
Susan is humble or calm.
Someone is creative or tall.
Someone is tall or humble.
Paul is either not patient or not generous.
Mary is either not old or not humble.
John is either patient or humble. | Mary is not kind. | neutral | ((~creative(john))=>(kind(john)))&
(![X]:((happy(X)|generous(X))=>(~brave(X)&~old(X))))&
(![X]:((~strong(X)|~happy(X))<=>(~tall(X)&~old(X))))&
((?[X]:((creative(X)|~kind(X))))=>(?[X]:((~patient(X)<~>funny(X)))))&
((~strong(mary))<=>((~wise(susan)|~strong(susan))))&
((?[X]:((patient(X)<~>creative(X))))<=>(?[X]:(~happy(X))))&
(((rich(lucy)<~>~happy(lucy)))<=>(~funny(alice)))&
(![X]:((brave(X)&~wise(X))=>(~patient(X)<~>kind(X))))&
(((kind(fred)<~>quiet(fred)))<=>(~strong(susan)))&
(((happy(john)&~calm(john)))<=>(?[X]:((~rich(X)|strong(X)))))&
(((wise(lucy)|strong(lucy)))=>(?[X]:((tall(X)<~>~funny(X)))))&
(![X]:((tall(X)|~tall(X))<=>(patient(X)<~>brave(X))))&
(![X]:((~wise(X)<~>calm(X))<=>~strong(X)))&
((?[X]:((tall(X)&old(X))))=>((~curious(alice)<~>~strong(alice))))&
(((~quiet(fred)|humble(fred)))<=>((~brave(lucy)<~>~creative(lucy))))&
(![X]:((~strong(X)<~>strong(X))<=>(~humble(X)<~>strong(X))))&
((happy(paul)|curious(paul)))&
((humble(susan)|calm(susan)))&
(?[X]:((creative(X)|tall(X))))&
(?[X]:((tall(X)|humble(X))))&
((~patient(paul)<~>~generous(paul)))&
((~old(mary)<~>~humble(mary)))&
((patient(john)<~>humble(john))) | ~kind(mary) | [] | null | 0 |
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