premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
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sequencelengths 0
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| proof
stringlengths 684
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⌀ | rule_concentration
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|---|---|---|---|---|---|---|---|
Everyone who is either curious or not humble is both patient and old and vice versa.
Everyone who is both not calm and not rich is curious.
If alice is either brave or not humble then someone is not calm.
If someone is either happy or tall then susan is not tall.
If paul is both kind and rich then someone is either curious or not happy.
Everyone who is quiet or not tall is not happy and vice versa.
Everyone who is not brave is both rich and creative and vice versa.
Everyone who is kind or not calm is both not humble and creative.
Everyone who is old is not creative.
Everyone who is both not creative and not happy is either brave or rich.
Everyone who is not creative or not wise is either not wise or calm.
Everyone who is brave is both strong and happy and vice versa.
If fred is humble then mary is rich.
Everyone who is rich is both not curious and not calm.
If someone is either rich or not strong then paul is both not old and humble and vice versa.
If someone is strong then mary is not wise.
Someone is creative.
Mary is generous or not calm.
Someone is old or wise.
Lucy is both tall and generous.
Someone is kind.
Alice is either not wise or wise. | Susan is not happy. | contradiction | (![X]:((curious(X)<~>~humble(X))<=>(patient(X)&old(X))))&
(![X]:((~calm(X)&~rich(X))=>curious(X)))&
(((brave(alice)<~>~humble(alice)))=>(?[X]:(~calm(X))))&
((?[X]:((happy(X)<~>tall(X))))=>(~tall(susan)))&
(((kind(paul)&rich(paul)))=>(?[X]:((curious(X)<~>~happy(X)))))&
(![X]:((quiet(X)|~tall(X))<=>~happy(X)))&
(![X]:(~brave(X)<=>(rich(X)&creative(X))))&
(![X]:((kind(X)|~calm(X))=>(~humble(X)&creative(X))))&
(![X]:(old(X)=>~creative(X)))&
(![X]:((~creative(X)&~happy(X))=>(brave(X)<~>rich(X))))&
(![X]:((~creative(X)|~wise(X))=>(~wise(X)<~>calm(X))))&
(![X]:(brave(X)<=>(strong(X)&happy(X))))&
((humble(fred))=>(rich(mary)))&
(![X]:(rich(X)=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)<~>~strong(X))))<=>((~old(paul)&humble(paul))))&
((?[X]:(strong(X)))=>(~wise(mary)))&
(?[X]:(creative(X)))&
((generous(mary)|~calm(mary)))&
(?[X]:((old(X)|wise(X))))&
((tall(lucy)&generous(lucy)))&
(?[X]:(kind(X)))&
((~wise(alice)<~>wise(alice))) | ~happy(susan) | [
"p0",
"p6",
"p7",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6105440395351403127933126
% SZS output start Proof for 6105440395351403127933126
1. ! [X0] : ((curious(X0) <~> ~humble(X0)) <=> (old(X0) & patient(X0))) [input p0]
7. ! [X0] : (~brave(X0) <=> (creative(X0) & rich(X0))) [input p6]
8. ! [X0] : ((~calm(X0) | kind(X0)) => (creative(X0) & ~humble(X0))) [input p7]
9. ! [X0] : (old(X0) => ~creative(X0)) [input p8]
12. ! [X0] : (brave(X0) <=> (happy(X0) & strong(X0))) [input p11]
14. ! [X0] : (rich(X0) => (~calm(X0) & ~curious(X0))) [input p13]
23. ~happy(susan) [input hypothesis]
32. ! [X0] : ((creative(X0) & ~humble(X0)) | (calm(X0) & ~kind(X0))) [ennf transformation 8]
33. ! [X0] : (~creative(X0) | ~old(X0)) [ennf transformation 9]
38. ! [X0] : ((~calm(X0) & ~curious(X0)) | ~rich(X0)) [ennf transformation 14]
40. ! [X0] : ((((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | (~old(X0) | ~patient(X0))) & ((old(X0) & patient(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0))))) [nnf transformation 1]
41. ! [X0] : ((((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | ~old(X0) | ~patient(X0)) & ((old(X0) & patient(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0))))) [flattening 40]
51. ! [X0] : ((~brave(X0) | (~creative(X0) | ~rich(X0))) & ((creative(X0) & rich(X0)) | brave(X0))) [nnf transformation 7]
52. ! [X0] : ((~brave(X0) | ~creative(X0) | ~rich(X0)) & ((creative(X0) & rich(X0)) | brave(X0))) [flattening 51]
55. ! [X0] : ((brave(X0) | (~happy(X0) | ~strong(X0))) & ((happy(X0) & strong(X0)) | ~brave(X0))) [nnf transformation 12]
56. ! [X0] : ((brave(X0) | ~happy(X0) | ~strong(X0)) & ((happy(X0) & strong(X0)) | ~brave(X0))) [flattening 55]
72. old(X0) | curious(X0) | humble(X0) [cnf transformation 41]
85. brave(X0) | rich(X0) [cnf transformation 52]
89. ~humble(X0) | calm(X0) [cnf transformation 32]
91. creative(X0) | calm(X0) [cnf transformation 32]
92. ~creative(X0) | ~old(X0) [cnf transformation 33]
100. ~brave(X0) | happy(X0) [cnf transformation 56]
103. ~rich(X0) | ~curious(X0) [cnf transformation 38]
104. ~rich(X0) | ~calm(X0) [cnf transformation 38]
118. ~happy(susan) [cnf transformation 23]
224. ~old(X0) | calm(X0) [resolution 92,91]
229. happy(X0) | rich(X0) [resolution 100,85]
342. calm(X0) | curious(X0) | humble(X0) [resolution 224,72]
343. calm(X0) | curious(X0) [subsumption resolution 342,89]
351. rich(susan) [resolution 229,118]
361. ~calm(susan) [resolution 351,104]
362. ~curious(susan) [resolution 351,103]
397. curious(susan) [resolution 361,343]
398. $false [subsumption resolution 397,362]
% SZS output end Proof for 6105440395351403127933126
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or funny then someone is both rich and old.
If someone is funny or humble then someone is not tall and vice versa.
Everyone who is not strong or not wise is brave and vice versa.
Everyone who is both rich and strong is both not generous and not old.
If lucy is either calm or tall then someone is either creative or not brave and vice versa.
Everyone who is either not kind or not patient is either humble or not rich and vice versa.
Everyone who is not brave or generous is strong or not patient.
If mary is not patient then someone is either humble or wise and vice versa.
Everyone who is tall is not calm or not generous and vice versa.
Everyone who is not funny is not funny or not tall.
Everyone who is not tall or quiet is either not creative or humble and vice versa.
Everyone who is humble or quiet is wise or creative.
If someone is not calm or not strong then mary is both not curious and not creative.
If someone is both funny and wise then mary is both not brave and not funny and vice versa.
Everyone who is patient or not old is either not quiet or old.
If john is either not funny or not kind then lucy is either not creative or not wise.
Paul is not old.
Susan is either calm or brave.
Someone is both not old and not patient.
Paul is not quiet or not creative.
Lucy is not funny.
Alice is both not patient and not wise.
Mary is old or rich. | Susan is not generous. | neutral | ((?[X]:((creative(X)|funny(X))))=>(?[X]:((rich(X)&old(X)))))&
((?[X]:((funny(X)|humble(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~strong(X)|~wise(X))<=>brave(X)))&
(![X]:((rich(X)&strong(X))=>(~generous(X)&~old(X))))&
(((calm(lucy)<~>tall(lucy)))<=>(?[X]:((creative(X)<~>~brave(X)))))&
(![X]:((~kind(X)<~>~patient(X))<=>(humble(X)<~>~rich(X))))&
(![X]:((~brave(X)|generous(X))=>(strong(X)|~patient(X))))&
((~patient(mary))<=>(?[X]:((humble(X)<~>wise(X)))))&
(![X]:(tall(X)<=>(~calm(X)|~generous(X))))&
(![X]:(~funny(X)=>(~funny(X)|~tall(X))))&
(![X]:((~tall(X)|quiet(X))<=>(~creative(X)<~>humble(X))))&
(![X]:((humble(X)|quiet(X))=>(wise(X)|creative(X))))&
((?[X]:((~calm(X)|~strong(X))))=>((~curious(mary)&~creative(mary))))&
((?[X]:((funny(X)&wise(X))))<=>((~brave(mary)&~funny(mary))))&
(![X]:((patient(X)|~old(X))=>(~quiet(X)<~>old(X))))&
(((~funny(john)<~>~kind(john)))=>((~creative(lucy)<~>~wise(lucy))))&
(~old(paul))&
((calm(susan)<~>brave(susan)))&
(?[X]:((~old(X)&~patient(X))))&
((~quiet(paul)|~creative(paul)))&
(~funny(lucy))&
((~patient(alice)&~wise(alice)))&
((old(mary)|rich(mary))) | ~generous(susan) | [] | null | 0 |
If john is wise then someone is both creative and not creative.
Everyone who is both brave and happy is not calm and vice versa.
If alice is either funny or patient then someone is both not strong and creative.
Everyone who is both not patient and patient is rich or funny.
Everyone who is not calm or old is not funny or not rich and vice versa.
Everyone who is either not humble or not tall is both funny and not humble.
Everyone who is not happy or not funny is both not calm and creative and vice versa.
Everyone who is either humble or brave is either happy or creative.
If someone is patient then someone is both humble and tall.
Everyone who is happy is both tall and not calm.
If someone is both not patient and not funny then mary is not patient.
Everyone who is old or happy is not funny.
Everyone who is both not happy and not curious is not curious or generous.
If mary is not creative or rich then alice is funny or not calm and vice versa.
Everyone who is not humble or humble is not calm or not funny and vice versa.
Someone is humble.
Someone is not patient.
Someone is patient.
Someone is either not kind or kind.
Alice is not old.
Mary is generous or old.
Someone is curious. | John is not calm. | entailment | ((wise(john))=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((brave(X)&happy(X))<=>~calm(X)))&
(((funny(alice)<~>patient(alice)))=>(?[X]:((~strong(X)&creative(X)))))&
(![X]:((~patient(X)&patient(X))=>(rich(X)|funny(X))))&
(![X]:((~calm(X)|old(X))<=>(~funny(X)|~rich(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(funny(X)&~humble(X))))&
(![X]:((~happy(X)|~funny(X))<=>(~calm(X)&creative(X))))&
(![X]:((humble(X)<~>brave(X))=>(happy(X)<~>creative(X))))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)&tall(X)))))&
(![X]:(happy(X)=>(tall(X)&~calm(X))))&
((?[X]:((~patient(X)&~funny(X))))=>(~patient(mary)))&
(![X]:((old(X)|happy(X))=>~funny(X)))&
(![X]:((~happy(X)&~curious(X))=>(~curious(X)|generous(X))))&
(((~creative(mary)|rich(mary)))<=>((funny(alice)|~calm(alice))))&
(![X]:((~humble(X)|humble(X))<=>(~calm(X)|~funny(X))))&
(?[X]:(humble(X)))&
(?[X]:(~patient(X)))&
(?[X]:(patient(X)))&
(?[X]:((~kind(X)<~>kind(X))))&
(~old(alice))&
((generous(mary)|old(mary)))&
(?[X]:(curious(X))) | ~calm(john) | [
"p1",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3363189467630882937435644
% SZS output start Proof for 3363189467630882937435644
2. ! [X0] : ((happy(X0) & brave(X0)) <=> ~calm(X0)) [input p1]
7. ! [X0] : ((~funny(X0) | ~happy(X0)) <=> (creative(X0) & ~calm(X0))) [input p6]
10. ! [X0] : (happy(X0) => (~calm(X0) & tall(X0))) [input p9]
23. calm(john) [input hypothesis]
36. ! [X0] : ((~calm(X0) & tall(X0)) | ~happy(X0)) [ennf transformation 10]
39. ! [X0] : (((happy(X0) & brave(X0)) | calm(X0)) & (~calm(X0) | (~happy(X0) | ~brave(X0)))) [nnf transformation 2]
40. ! [X0] : (((happy(X0) & brave(X0)) | calm(X0)) & (~calm(X0) | ~happy(X0) | ~brave(X0))) [flattening 39]
47. ! [X0] : (((~funny(X0) | ~happy(X0)) | (~creative(X0) | calm(X0))) & ((creative(X0) & ~calm(X0)) | (funny(X0) & happy(X0)))) [nnf transformation 7]
48. ! [X0] : ((~funny(X0) | ~happy(X0) | ~creative(X0) | calm(X0)) & ((creative(X0) & ~calm(X0)) | (funny(X0) & happy(X0)))) [flattening 47]
68. happy(X0) | calm(X0) [cnf transformation 40]
80. ~calm(X0) | happy(X0) [cnf transformation 48]
92. ~calm(X0) | ~happy(X0) [cnf transformation 36]
110. calm(john) [cnf transformation 23]
127. happy(X0) [subsumption resolution 80,68]
143. ~calm(X0) [subsumption resolution 92,127]
164. $false [subsumption resolution 110,143]
% SZS output end Proof for 3363189467630882937435644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or quiet is both quiet and old and vice versa. If alice is both old and not tall then susan is both generous and not old and vice versa. Everyone who is either quiet or not brave is either not curious or not rich and vice versa. Everyone who is not happy is either not old or not brave. If paul is both generous and not tall then mary is both kind and generous and vice versa. Everyone who is either not kind or not calm is not quiet. Everyone who is not creative or funny is kind. Everyone who is both quiet and not tall is either not patient or not old. If fred is curious then lucy is old or wise. If someone is not tall then alice is either not funny or not old and vice versa. If fred is either not generous or brave then someone is brave or not rich and vice versa. If someone is both quiet and not strong then someone is kind and vice versa. Everyone who is both not wise and patient is either not rich or strong and vice versa. Everyone who is both not patient and not tall is happy or humble and vice versa. Everyone who is rich or not wise is either quiet or not funny and vice versa. Everyone who is either not strong or generous is wise or not patient and vice versa. Someone is both not funny and humble. Someone is both not funny and not quiet. Fred is both not curious and calm. Someone is both not happy and tall. Someone is either quiet or kind. Susan is not curious or not strong. Alice is both not strong and funny. Mary is not rich. | Paul is not strong. | neutral | (![X]:((~old(X)<~>quiet(X))<=>(quiet(X)&old(X))))&
(((old(alice)&~tall(alice)))<=>((generous(susan)&~old(susan))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~curious(X)<~>~rich(X))))&
(![X]:(~happy(X)=>(~old(X)<~>~brave(X))))&
(((generous(paul)&~tall(paul)))<=>((kind(mary)&generous(mary))))&
(![X]:((~kind(X)<~>~calm(X))=>~quiet(X)))&
(![X]:((~creative(X)|funny(X))=>kind(X)))&
(![X]:((quiet(X)&~tall(X))=>(~patient(X)<~>~old(X))))&
((curious(fred))=>((old(lucy)|wise(lucy))))&
((?[X]:(~tall(X)))<=>((~funny(alice)<~>~old(alice))))&
(((~generous(fred)<~>brave(fred)))<=>(?[X]:((brave(X)|~rich(X)))))&
((?[X]:((quiet(X)&~strong(X))))<=>(?[X]:(kind(X))))&
(![X]:((~wise(X)&patient(X))<=>(~rich(X)<~>strong(X))))&
(![X]:((~patient(X)&~tall(X))<=>(happy(X)|humble(X))))&
(![X]:((rich(X)|~wise(X))<=>(quiet(X)<~>~funny(X))))&
(![X]:((~strong(X)<~>generous(X))<=>(wise(X)|~patient(X))))&
(?[X]:((~funny(X)&humble(X))))&
(?[X]:((~funny(X)&~quiet(X))))&
((~curious(fred)&calm(fred)))&
(?[X]:((~happy(X)&tall(X))))&
(?[X]:((quiet(X)<~>kind(X))))&
((~curious(susan)|~strong(susan)))&
((~strong(alice)&funny(alice)))&
(~rich(mary)) | ~strong(paul) | [] | null | 0 |
If susan is creative or generous then fred is either patient or humble and vice versa. If john is either curious or not calm then paul is either not generous or not funny. Everyone who is both tall and not funny is either not tall or wise. Everyone who is both not humble and rich is old or strong and vice versa. If someone is either not happy or not quiet then paul is not tall or not funny and vice versa. Everyone who is both brave and strong is not brave or patient. Everyone who is calm or patient is humble and vice versa. Everyone who is both not curious and not generous is kind and vice versa. If alice is either not happy or not brave then someone is not rich or tall and vice versa. Everyone who is funny is not kind and vice versa. Everyone who is either wise or not brave is either creative or not funny and vice versa. Everyone who is both happy and not quiet is either brave or not funny and vice versa. Everyone who is not rich is not wise and vice versa. Everyone who is either tall or happy is calm and vice versa. If someone is not quiet or wise then someone is both not tall and not humble. If someone is either tall or not patient then someone is both not funny and not strong and vice versa. Fred is funny. Mary is not strong. Paul is rich. Susan is not wise or not happy. Someone is calm or brave. Someone is humble. Mary is generous. Someone is not rich or kind. | Susan is not wise. | neutral | (((creative(susan)|generous(susan)))<=>((patient(fred)<~>humble(fred))))&
(((curious(john)<~>~calm(john)))=>((~generous(paul)<~>~funny(paul))))&
(![X]:((tall(X)&~funny(X))=>(~tall(X)<~>wise(X))))&
(![X]:((~humble(X)&rich(X))<=>(old(X)|strong(X))))&
((?[X]:((~happy(X)<~>~quiet(X))))<=>((~tall(paul)|~funny(paul))))&
(![X]:((brave(X)&strong(X))=>(~brave(X)|patient(X))))&
(![X]:((calm(X)|patient(X))<=>humble(X)))&
(![X]:((~curious(X)&~generous(X))<=>kind(X)))&
(((~happy(alice)<~>~brave(alice)))<=>(?[X]:((~rich(X)|tall(X)))))&
(![X]:(funny(X)<=>~kind(X)))&
(![X]:((wise(X)<~>~brave(X))<=>(creative(X)<~>~funny(X))))&
(![X]:((happy(X)&~quiet(X))<=>(brave(X)<~>~funny(X))))&
(![X]:(~rich(X)<=>~wise(X)))&
(![X]:((tall(X)<~>happy(X))<=>calm(X)))&
((?[X]:((~quiet(X)|wise(X))))=>(?[X]:((~tall(X)&~humble(X)))))&
((?[X]:((tall(X)<~>~patient(X))))<=>(?[X]:((~funny(X)&~strong(X)))))&
(funny(fred))&
(~strong(mary))&
(rich(paul))&
((~wise(susan)|~happy(susan)))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:(humble(X)))&
(generous(mary))&
(?[X]:((~rich(X)|kind(X)))) | ~wise(susan) | [] | null | 0 |
If lucy is either tall or patient then someone is not generous or not brave and vice versa. If alice is not creative then paul is both not rich and wise and vice versa. If someone is not creative then someone is both kind and tall and vice versa. Everyone who is wise is either not tall or not curious. If susan is both not old and not patient then someone is funny or brave and vice versa. Everyone who is both brave and not curious is either happy or not humble. Everyone who is curious is not old or creative. Everyone who is kind or calm is patient. Everyone who is either not calm or not funny is both not generous and creative and vice versa. If fred is old or happy then fred is calm and vice versa. If someone is both tall and patient then alice is both not creative and not tall and vice versa. Everyone who is kind is both not curious and not calm. If paul is not old then fred is wise. Everyone who is both not humble and funny is both generous and rich and vice versa. If mary is old or creative then fred is wise and vice versa. Everyone who is not old or not strong is not rich or not quiet and vice versa. Someone is generous or not creative. Mary is either not rich or tall. Someone is both not happy and old. Paul is not creative. Someone is brave. Someone is old or not happy. Someone is patient or curious. Paul is either not curious or not creative. | Fred is wise. | entailment | (((tall(lucy)<~>patient(lucy)))<=>(?[X]:((~generous(X)|~brave(X)))))&
((~creative(alice))<=>((~rich(paul)&wise(paul))))&
((?[X]:(~creative(X)))<=>(?[X]:((kind(X)&tall(X)))))&
(![X]:(wise(X)=>(~tall(X)<~>~curious(X))))&
(((~old(susan)&~patient(susan)))<=>(?[X]:((funny(X)|brave(X)))))&
(![X]:((brave(X)&~curious(X))=>(happy(X)<~>~humble(X))))&
(![X]:(curious(X)=>(~old(X)|creative(X))))&
(![X]:((kind(X)|calm(X))=>patient(X)))&
(![X]:((~calm(X)<~>~funny(X))<=>(~generous(X)&creative(X))))&
(((old(fred)|happy(fred)))<=>(calm(fred)))&
((?[X]:((tall(X)&patient(X))))<=>((~creative(alice)&~tall(alice))))&
(![X]:(kind(X)=>(~curious(X)&~calm(X))))&
((~old(paul))=>(wise(fred)))&
(![X]:((~humble(X)&funny(X))<=>(generous(X)&rich(X))))&
(((old(mary)|creative(mary)))<=>(wise(fred)))&
(![X]:((~old(X)|~strong(X))<=>(~rich(X)|~quiet(X))))&
(?[X]:((generous(X)|~creative(X))))&
((~rich(mary)<~>tall(mary)))&
(?[X]:((~happy(X)&old(X))))&
(~creative(paul))&
(?[X]:(brave(X)))&
(?[X]:((old(X)|~happy(X))))&
(?[X]:((patient(X)|curious(X))))&
((~curious(paul)<~>~creative(paul))) | wise(fred) | [
"p6",
"p12",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5884629143356934479378573
% SZS output start Proof for 5884629143356934479378573
7. ! [X0] : (curious(X0) => (creative(X0) | ~old(X0))) [input p6]
13. ~old(paul) => wise(fred) [input p12]
20. ~creative(paul) [input p19]
24. ~curious(paul) <~> ~creative(paul) [input p23]
25. ~wise(fred) [input hypothesis]
30. ! [X0] : ((creative(X0) | ~old(X0)) | ~curious(X0)) [ennf transformation 7]
31. ! [X0] : (creative(X0) | ~old(X0) | ~curious(X0)) [flattening 30]
34. wise(fred) | old(paul) [ennf transformation 13]
79. (creative(paul) | curious(paul)) & (~creative(paul) | ~curious(paul)) [nnf transformation 24]
101. ~old(X0) | creative(X0) | ~curious(X0) [cnf transformation 31]
119. wise(fred) | old(paul) [cnf transformation 34]
136. ~creative(paul) [cnf transformation 20]
141. creative(paul) | curious(paul) [cnf transformation 79]
142. ~wise(fred) [cnf transformation 25]
269. 28 <=> old(paul) [avatar definition]
271. old(paul) <- (28) [avatar component clause 269]
273. 29 <=> wise(fred) [avatar definition]
276. 28 | 29 [avatar split clause 119,273,269]
325. curious(paul) [subsumption resolution 141,136]
326. ~29 [avatar split clause 142,273]
341. creative(paul) | ~curious(paul) <- (28) [resolution 101,271]
351. ~curious(paul) <- (28) [subsumption resolution 341,136]
352. $false <- (28) [subsumption resolution 351,325]
353. ~28 [avatar contradiction clause 352]
354. $false [avatar sat refutation 276,326,353]
% SZS output end Proof for 5884629143356934479378573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or tall is wise.
Everyone who is not old is not strong or not creative.
Everyone who is happy or not happy is not brave.
Everyone who is either generous or rich is tall or not tall and vice versa.
If someone is both not wise and rich then lucy is not calm or not kind and vice versa.
Everyone who is both humble and creative is not happy and vice versa.
If someone is strong or not kind then someone is not generous or strong.
Everyone who is patient is not brave or curious and vice versa.
Everyone who is not brave or generous is either funny or strong.
If susan is either not strong or quiet then someone is not quiet or not creative and vice versa.
Everyone who is not rich is either not rich or not funny.
If john is not patient then paul is not old or creative.
Everyone who is both not creative and not tall is not kind or not humble.
If someone is both wise and funny then someone is both tall and not strong.
Everyone who is not wise is not tall or wise.
Everyone who is either humble or creative is either not humble or not patient.
Paul is both calm and not tall.
Someone is either not brave or wise.
Someone is humble or not tall.
Someone is tall.
Susan is both old and not curious.
Someone is both wise and tall.
Someone is not generous.
Paul is not old. | Lucy is not wise. | neutral | (![X]:((~rich(X)<~>tall(X))=>wise(X)))&
(![X]:(~old(X)=>(~strong(X)|~creative(X))))&
(![X]:((happy(X)|~happy(X))=>~brave(X)))&
(![X]:((generous(X)<~>rich(X))<=>(tall(X)|~tall(X))))&
((?[X]:((~wise(X)&rich(X))))<=>((~calm(lucy)|~kind(lucy))))&
(![X]:((humble(X)&creative(X))<=>~happy(X)))&
((?[X]:((strong(X)|~kind(X))))=>(?[X]:((~generous(X)|strong(X)))))&
(![X]:(patient(X)<=>(~brave(X)|curious(X))))&
(![X]:((~brave(X)|generous(X))=>(funny(X)<~>strong(X))))&
(((~strong(susan)<~>quiet(susan)))<=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:(~rich(X)=>(~rich(X)<~>~funny(X))))&
((~patient(john))=>((~old(paul)|creative(paul))))&
(![X]:((~creative(X)&~tall(X))=>(~kind(X)|~humble(X))))&
((?[X]:((wise(X)&funny(X))))=>(?[X]:((tall(X)&~strong(X)))))&
(![X]:(~wise(X)=>(~tall(X)|wise(X))))&
(![X]:((humble(X)<~>creative(X))=>(~humble(X)<~>~patient(X))))&
((calm(paul)&~tall(paul)))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:(tall(X)))&
((old(susan)&~curious(susan)))&
(?[X]:((wise(X)&tall(X))))&
(?[X]:(~generous(X)))&
(~old(paul)) | ~wise(lucy) | [] | null | 0 |
If someone is rich then someone is either strong or not strong. If alice is either not quiet or old then someone is both wise and not calm and vice versa. Everyone who is generous or not tall is either not calm or not humble and vice versa. Everyone who is either not rich or creative is both brave and creative. If alice is both not humble and curious then someone is both old and strong and vice versa. If someone is both quiet and not funny then someone is calm or wise and vice versa. Everyone who is both not strong and happy is tall. If john is either not old or not kind then fred is not creative and vice versa. Everyone who is either not creative or not tall is calm. Everyone who is wise or calm is either not humble or not happy and vice versa. If someone is tall then someone is creative or not brave and vice versa. Everyone who is either not strong or patient is not creative and vice versa. Everyone who is both not happy and humble is either not strong or brave. If someone is not brave or funny then fred is both funny and humble. Everyone who is both generous and not old is not kind. Everyone who is strong is both not strong and quiet and vice versa. Someone is either kind or brave. Fred is kind or not brave. Someone is not calm or not curious. Someone is not curious or not brave. Paul is humble. Someone is both curious and not rich. | John is not tall. | contradiction | ((?[X]:(rich(X)))=>(?[X]:((strong(X)<~>~strong(X)))))&
(((~quiet(alice)<~>old(alice)))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((generous(X)|~tall(X))<=>(~calm(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>creative(X))=>(brave(X)&creative(X))))&
(((~humble(alice)&curious(alice)))<=>(?[X]:((old(X)&strong(X)))))&
((?[X]:((quiet(X)&~funny(X))))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:((~strong(X)&happy(X))=>tall(X)))&
(((~old(john)<~>~kind(john)))<=>(~creative(fred)))&
(![X]:((~creative(X)<~>~tall(X))=>calm(X)))&
(![X]:((wise(X)|calm(X))<=>(~humble(X)<~>~happy(X))))&
((?[X]:(tall(X)))<=>(?[X]:((creative(X)|~brave(X)))))&
(![X]:((~strong(X)<~>patient(X))<=>~creative(X)))&
(![X]:((~happy(X)&humble(X))=>(~strong(X)<~>brave(X))))&
((?[X]:((~brave(X)|funny(X))))=>((funny(fred)&humble(fred))))&
(![X]:((generous(X)&~old(X))=>~kind(X)))&
(![X]:(strong(X)<=>(~strong(X)&quiet(X))))&
(?[X]:((kind(X)<~>brave(X))))&
((kind(fred)|~brave(fred)))&
(?[X]:((~calm(X)|~curious(X))))&
(?[X]:((~curious(X)|~brave(X))))&
(humble(paul))&
(?[X]:((curious(X)&~rich(X)))) | ~tall(john) | [
"p2",
"p5",
"p6",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5948044362763042630801539
% SZS output start Proof for 5948044362763042630801539
3. ! [X0] : ((~tall(X0) | generous(X0)) <=> (~calm(X0) <~> ~humble(X0))) [input p2]
6. ? [X0] : (~funny(X0) & quiet(X0)) <=> ? [X0] : (wise(X0) | calm(X0)) [input p5]
7. ! [X0] : ((happy(X0) & ~strong(X0)) => tall(X0)) [input p6]
10. ! [X0] : ((calm(X0) | wise(X0)) <=> (~humble(X0) <~> ~happy(X0))) [input p9]
16. ! [X0] : (strong(X0) <=> (quiet(X0) & ~strong(X0))) [input p15]
23. ~tall(john) [input hypothesis]
25. ? [X0] : (~funny(X0) & quiet(X0)) <=> ? [X1] : (wise(X1) | calm(X1)) [rectify 6]
29. ! [X0] : (tall(X0) | (~happy(X0) | strong(X0))) [ennf transformation 7]
30. ! [X0] : (tall(X0) | ~happy(X0) | strong(X0)) [flattening 29]
45. ! [X0] : (((~tall(X0) | generous(X0)) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) & (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (tall(X0) & ~generous(X0)))) [nnf transformation 3]
46. ! [X0] : ((~tall(X0) | generous(X0) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) & (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (tall(X0) & ~generous(X0)))) [flattening 45]
53. (? [X0] : (~funny(X0) & quiet(X0)) | ! [X1] : (~wise(X1) & ~calm(X1))) & (? [X1] : (wise(X1) | calm(X1)) | ! [X0] : (funny(X0) | ~quiet(X0))) [nnf transformation 25]
54. (? [X0] : (~funny(X0) & quiet(X0)) | ! [X1] : (~wise(X1) & ~calm(X1))) & (? [X2] : (wise(X2) | calm(X2)) | ! [X3] : (funny(X3) | ~quiet(X3))) [rectify 53]
55. ? [X0] : (~funny(X0) & quiet(X0)) => (~funny(sK3) & quiet(sK3)) [choice axiom]
56. ? [X2] : (wise(X2) | calm(X2)) => (wise(sK4) | calm(sK4)) [choice axiom]
57. ((~funny(sK3) & quiet(sK3)) | ! [X1] : (~wise(X1) & ~calm(X1))) & ((wise(sK4) | calm(sK4)) | ! [X3] : (funny(X3) | ~quiet(X3))) [skolemisation 54,56,55]
60. ! [X0] : (((calm(X0) | wise(X0)) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | (~calm(X0) & ~wise(X0)))) [nnf transformation 10]
61. ! [X0] : ((calm(X0) | wise(X0) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | (~calm(X0) & ~wise(X0)))) [flattening 60]
69. ! [X0] : ((strong(X0) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | ~strong(X0))) [nnf transformation 16]
70. ! [X0] : ((strong(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | ~strong(X0))) [flattening 69]
91. humble(X0) | calm(X0) | tall(X0) [cnf transformation 46]
103. quiet(sK3) | ~calm(X1) [cnf transformation 57]
104. quiet(sK3) | ~wise(X1) [cnf transformation 57]
107. ~happy(X0) | tall(X0) | strong(X0) [cnf transformation 30]
119. ~humble(X0) | wise(X0) | calm(X0) | happy(X0) [cnf transformation 61]
134. ~strong(X0) | ~strong(X0) [cnf transformation 70]
136. strong(X0) | ~quiet(X0) | strong(X0) [cnf transformation 70]
145. ~tall(john) [cnf transformation 23]
146. ~strong(X0) [duplicate literal removal 134]
147. ~quiet(X0) | strong(X0) [duplicate literal removal 136]
198. 11 <=> ! [X1] : ~wise(X1) [avatar definition]
199. ~wise(X1) <- (11) [avatar component clause 198]
206. 13 <=> ! [X1] : ~calm(X1) [avatar definition]
207. ~calm(X1) <- (13) [avatar component clause 206]
210. 14 <=> quiet(sK3) [avatar definition]
212. quiet(sK3) <- (14) [avatar component clause 210]
213. 11 | 14 [avatar split clause 104,210,198]
214. 13 | 14 [avatar split clause 103,210,206]
338. strong(sK3) <- (14) [resolution 147,212]
339. $false <- (14) [subsumption resolution 338,146]
340. ~14 [avatar contradiction clause 339]
406. wise(X0) | calm(X0) | happy(X0) | calm(X0) | tall(X0) [resolution 119,91]
407. wise(X0) | calm(X0) | happy(X0) | tall(X0) [duplicate literal removal 406]
410. calm(X0) | happy(X0) | tall(X0) <- (11) [subsumption resolution 407,199]
411. happy(X0) | tall(X0) <- (11, 13) [subsumption resolution 410,207]
436. tall(X3) | tall(X3) | strong(X3) <- (11, 13) [resolution 411,107]
437. tall(X3) | strong(X3) <- (11, 13) [duplicate literal removal 436]
438. tall(X3) <- (11, 13) [subsumption resolution 437,146]
439. $false <- (11, 13) [resolution 438,145]
442. ~11 | ~13 [avatar contradiction clause 439]
444. $false [avatar sat refutation 213,214,340,442]
% SZS output end Proof for 5948044362763042630801539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or wise is not funny. If fred is either not funny or strong then someone is not happy or quiet. Everyone who is quiet is not calm or not kind and vice versa. If someone is either not brave or strong then someone is not old. If someone is not patient or patient then lucy is both wise and old and vice versa. If susan is both not creative and quiet then someone is patient and vice versa. Everyone who is not funny is not wise and vice versa. Everyone who is either not curious or not generous is not brave or brave. If someone is either not old or humble then alice is not funny and vice versa. If someone is patient then someone is not patient and vice versa. Everyone who is happy is either not brave or not patient. Everyone who is not old or old is either not quiet or patient. Everyone who is either kind or curious is kind and vice versa. Everyone who is both not funny and not patient is either not rich or calm and vice versa. Everyone who is either curious or humble is patient or not wise. If paul is funny or tall then someone is not kind. John is wise. Alice is not creative or not quiet. Someone is both quiet and happy. Someone is both funny and calm. Susan is either old or not brave. Fred is strong or happy. Paul is either tall or not humble. | Fred is kind. | neutral | (![X]:((creative(X)<~>wise(X))=>~funny(X)))&
(((~funny(fred)<~>strong(fred)))=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:(quiet(X)<=>(~calm(X)|~kind(X))))&
((?[X]:((~brave(X)<~>strong(X))))=>(?[X]:(~old(X))))&
((?[X]:((~patient(X)|patient(X))))<=>((wise(lucy)&old(lucy))))&
(((~creative(susan)&quiet(susan)))<=>(?[X]:(patient(X))))&
(![X]:(~funny(X)<=>~wise(X)))&
(![X]:((~curious(X)<~>~generous(X))=>(~brave(X)|brave(X))))&
((?[X]:((~old(X)<~>humble(X))))<=>(~funny(alice)))&
((?[X]:(patient(X)))<=>(?[X]:(~patient(X))))&
(![X]:(happy(X)=>(~brave(X)<~>~patient(X))))&
(![X]:((~old(X)|old(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((kind(X)<~>curious(X))<=>kind(X)))&
(![X]:((~funny(X)&~patient(X))<=>(~rich(X)<~>calm(X))))&
(![X]:((curious(X)<~>humble(X))=>(patient(X)|~wise(X))))&
(((funny(paul)|tall(paul)))=>(?[X]:(~kind(X))))&
(wise(john))&
((~creative(alice)|~quiet(alice)))&
(?[X]:((quiet(X)&happy(X))))&
(?[X]:((funny(X)&calm(X))))&
((old(susan)<~>~brave(susan)))&
((strong(fred)|happy(fred)))&
((tall(paul)<~>~humble(paul))) | kind(fred) | [] | null | 0 |
If lucy is either not generous or not calm then mary is not brave. If someone is strong then mary is either funny or not tall and vice versa. Everyone who is both calm and tall is not happy and vice versa. Everyone who is kind or humble is both tall and not calm. Everyone who is not old is not patient. If susan is tall then someone is either not humble or not kind and vice versa. If mary is either not tall or not brave then someone is either generous or not patient. Everyone who is either generous or not quiet is either tall or generous. Everyone who is not wise or strong is both not calm and not kind. Everyone who is generous is both not tall and rich. If mary is humble then alice is not wise or not generous and vice versa. If paul is not funny or not kind then someone is both not funny and not happy. Everyone who is either not funny or funny is either not generous or not rich and vice versa. If someone is old then someone is creative. Everyone who is either tall or not funny is not tall. If someone is not funny or brave then someone is creative or not creative and vice versa. Paul is either generous or humble. Someone is rich. Someone is not quiet. Alice is rich. Paul is either not brave or kind. Susan is either not tall or not happy. Someone is either funny or strong. Someone is not generous. | Alice is generous. | contradiction | (((~generous(lucy)<~>~calm(lucy)))=>(~brave(mary)))&
((?[X]:(strong(X)))<=>((funny(mary)<~>~tall(mary))))&
(![X]:((calm(X)&tall(X))<=>~happy(X)))&
(![X]:((kind(X)|humble(X))=>(tall(X)&~calm(X))))&
(![X]:(~old(X)=>~patient(X)))&
((tall(susan))<=>(?[X]:((~humble(X)<~>~kind(X)))))&
(((~tall(mary)<~>~brave(mary)))=>(?[X]:((generous(X)<~>~patient(X)))))&
(![X]:((generous(X)<~>~quiet(X))=>(tall(X)<~>generous(X))))&
(![X]:((~wise(X)|strong(X))=>(~calm(X)&~kind(X))))&
(![X]:(generous(X)=>(~tall(X)&rich(X))))&
((humble(mary))<=>((~wise(alice)|~generous(alice))))&
(((~funny(paul)|~kind(paul)))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~generous(X)<~>~rich(X))))&
((?[X]:(old(X)))=>(?[X]:(creative(X))))&
(![X]:((tall(X)<~>~funny(X))=>~tall(X)))&
((?[X]:((~funny(X)|brave(X))))<=>(?[X]:((creative(X)|~creative(X)))))&
((generous(paul)<~>humble(paul)))&
(?[X]:(rich(X)))&
(?[X]:(~quiet(X)))&
(rich(alice))&
((~brave(paul)<~>kind(paul)))&
((~tall(susan)<~>~happy(susan)))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:(~generous(X))) | generous(alice) | [
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4982666674912971409864917
% SZS output start Proof for 4982666674912971409864917
10. ! [X0] : (generous(X0) => (rich(X0) & ~tall(X0))) [input p9]
13. ! [X0] : ((~funny(X0) <~> funny(X0)) <=> (~generous(X0) <~> ~rich(X0))) [input p12]
25. generous(alice) [input hypothesis]
34. ! [X0] : ((rich(X0) & ~tall(X0)) | ~generous(X0)) [ennf transformation 10]
57. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0)))) & (((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [nnf transformation 13]
110. rich(X0) | ~generous(X0) [cnf transformation 34]
118. ~rich(X0) | ~generous(X0) | funny(X0) | funny(X0) [cnf transformation 57]
119. ~rich(X0) | ~generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 57]
120. rich(X0) | generous(X0) | funny(X0) | funny(X0) [cnf transformation 57]
121. rich(X0) | generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 57]
145. generous(alice) [cnf transformation 25]
147. ~rich(X0) | ~generous(X0) | funny(X0) [duplicate literal removal 118]
148. ~rich(X0) | ~generous(X0) | ~funny(X0) [duplicate literal removal 119]
149. rich(X0) | generous(X0) | funny(X0) [duplicate literal removal 120]
150. rich(X0) | generous(X0) | ~funny(X0) [duplicate literal removal 121]
255. rich(X0) | ~funny(X0) [subsumption resolution 150,110]
256. rich(X0) | funny(X0) [subsumption resolution 149,110]
257. rich(X0) [subsumption resolution 256,255]
258. ~generous(X0) | ~funny(X0) [subsumption resolution 148,257]
259. ~generous(X0) | funny(X0) [subsumption resolution 147,257]
260. ~generous(X0) [subsumption resolution 259,258]
307. $false [subsumption resolution 145,260]
% SZS output end Proof for 4982666674912971409864917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not calm is either not strong or not wise.
Everyone who is either rich or generous is both kind and not curious.
Everyone who is happy or patient is both not brave and brave and vice versa.
If john is either not wise or not calm then someone is patient or quiet.
If mary is humble then alice is generous or happy and vice versa.
Everyone who is either wise or not old is not humble or kind and vice versa.
If fred is not old or not patient then susan is both not strong and curious.
If mary is not generous then fred is not wise or happy and vice versa.
If someone is tall then susan is not old or humble.
If paul is not wise or not tall then paul is both not funny and wise.
If someone is creative then someone is happy or not quiet and vice versa.
If someone is not calm or brave then lucy is both kind and old and vice versa.
Everyone who is either not quiet or kind is not tall or not rich and vice versa.
If fred is not creative or curious then someone is both not creative and tall.
If someone is both not brave and creative then susan is both tall and not generous and vice versa.
If someone is generous or not kind then someone is either not curious or not humble and vice versa.
John is either not generous or generous.
Someone is tall or generous.
Someone is not tall.
Someone is either calm or tall.
Someone is both not quiet and calm.
Lucy is not happy.
Someone is both not calm and funny.
Alice is both not patient and not wise. | Fred is patient. | contradiction | (![X]:((~generous(X)<~>~calm(X))=>(~strong(X)<~>~wise(X))))&
(![X]:((rich(X)<~>generous(X))=>(kind(X)&~curious(X))))&
(![X]:((happy(X)|patient(X))<=>(~brave(X)&brave(X))))&
(((~wise(john)<~>~calm(john)))=>(?[X]:((patient(X)|quiet(X)))))&
((humble(mary))<=>((generous(alice)|happy(alice))))&
(![X]:((wise(X)<~>~old(X))<=>(~humble(X)|kind(X))))&
(((~old(fred)|~patient(fred)))=>((~strong(susan)&curious(susan))))&
((~generous(mary))<=>((~wise(fred)|happy(fred))))&
((?[X]:(tall(X)))=>((~old(susan)|humble(susan))))&
(((~wise(paul)|~tall(paul)))=>((~funny(paul)&wise(paul))))&
((?[X]:(creative(X)))<=>(?[X]:((happy(X)|~quiet(X)))))&
((?[X]:((~calm(X)|brave(X))))<=>((kind(lucy)&old(lucy))))&
(![X]:((~quiet(X)<~>kind(X))<=>(~tall(X)|~rich(X))))&
(((~creative(fred)|curious(fred)))=>(?[X]:((~creative(X)&tall(X)))))&
((?[X]:((~brave(X)&creative(X))))<=>((tall(susan)&~generous(susan))))&
((?[X]:((generous(X)|~kind(X))))<=>(?[X]:((~curious(X)<~>~humble(X)))))&
((~generous(john)<~>generous(john)))&
(?[X]:((tall(X)|generous(X))))&
(?[X]:(~tall(X)))&
(?[X]:((calm(X)<~>tall(X))))&
(?[X]:((~quiet(X)&calm(X))))&
(~happy(lucy))&
(?[X]:((~calm(X)&funny(X))))&
((~patient(alice)&~wise(alice))) | patient(fred) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 9001713764372372347548615
% SZS output start Proof for 9001713764372372347548615
3. ! [X0] : ((patient(X0) | happy(X0)) <=> (brave(X0) & ~brave(X0))) [input p2]
25. patient(fred) [input hypothesis]
38. ! [X0] : (((patient(X0) | happy(X0)) | (~brave(X0) | brave(X0))) & ((brave(X0) & ~brave(X0)) | (~patient(X0) & ~happy(X0)))) [nnf transformation 3]
39. ! [X0] : ((patient(X0) | happy(X0) | ~brave(X0) | brave(X0)) & ((brave(X0) & ~brave(X0)) | (~patient(X0) & ~happy(X0)))) [flattening 38]
94. ~brave(X0) | ~patient(X0) [cnf transformation 39]
96. brave(X0) | ~patient(X0) [cnf transformation 39]
162. patient(fred) [cnf transformation 25]
164. ~patient(X0) [subsumption resolution 94,96]
374. $false [subsumption resolution 162,164]
% SZS output end Proof for 9001713764372372347548615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not curious is either happy or not curious and vice versa.
If alice is not generous then lucy is not wise or curious.
Everyone who is both old and not humble is either not generous or old and vice versa.
If mary is either generous or strong then someone is humble or funny and vice versa.
If mary is funny then someone is both not strong and not patient.
Everyone who is humble is both calm and creative and vice versa.
Everyone who is kind is not wise or not creative.
If john is not humble then alice is either not old or old.
If mary is not calm or not brave then susan is tall.
Everyone who is either old or not strong is tall.
If susan is not kind or kind then john is not strong.
If alice is both humble and not happy then fred is strong.
Everyone who is not wise is either calm or not funny.
If lucy is not funny then someone is creative or not funny and vice versa.
Everyone who is wise or not humble is either old or not brave and vice versa.
Lucy is not tall.
Mary is humble.
Someone is both creative and tall.
John is both creative and funny.
Mary is either curious or not funny.
Someone is not calm or funny.
Someone is kind. | John is not humble. | neutral | (![X]:((strong(X)|~curious(X))<=>(happy(X)<~>~curious(X))))&
((~generous(alice))=>((~wise(lucy)|curious(lucy))))&
(![X]:((old(X)&~humble(X))<=>(~generous(X)<~>old(X))))&
(((generous(mary)<~>strong(mary)))<=>(?[X]:((humble(X)|funny(X)))))&
((funny(mary))=>(?[X]:((~strong(X)&~patient(X)))))&
(![X]:(humble(X)<=>(calm(X)&creative(X))))&
(![X]:(kind(X)=>(~wise(X)|~creative(X))))&
((~humble(john))=>((~old(alice)<~>old(alice))))&
(((~calm(mary)|~brave(mary)))=>(tall(susan)))&
(![X]:((old(X)<~>~strong(X))=>tall(X)))&
(((~kind(susan)|kind(susan)))=>(~strong(john)))&
(((humble(alice)&~happy(alice)))=>(strong(fred)))&
(![X]:(~wise(X)=>(calm(X)<~>~funny(X))))&
((~funny(lucy))<=>(?[X]:((creative(X)|~funny(X)))))&
(![X]:((wise(X)|~humble(X))<=>(old(X)<~>~brave(X))))&
(~tall(lucy))&
(humble(mary))&
(?[X]:((creative(X)&tall(X))))&
((creative(john)&funny(john)))&
((curious(mary)<~>~funny(mary)))&
(?[X]:((~calm(X)|funny(X))))&
(?[X]:(kind(X))) | ~humble(john) | [] | null | 0 |
Everyone who is both brave and strong is either not wise or not calm.
Everyone who is not calm is both not calm and kind and vice versa.
If someone is curious or not happy then fred is calm or not generous.
If someone is both not happy and not old then someone is both not creative and not humble.
Everyone who is not kind or not calm is both not patient and wise and vice versa.
Everyone who is not humble or funny is either creative or curious and vice versa.
Everyone who is either not kind or not humble is both not brave and not calm and vice versa.
Everyone who is both calm and not humble is both brave and not calm and vice versa.
If someone is curious or strong then someone is either not tall or not strong and vice versa.
Everyone who is not rich or strong is curious or not brave and vice versa.
Everyone who is either humble or quiet is curious and vice versa.
Everyone who is either wise or not brave is not old or brave.
If someone is happy then lucy is patient or not happy and vice versa.
Everyone who is both kind and calm is strong.
Everyone who is old or patient is not brave or not calm and vice versa.
Everyone who is not happy or strong is either kind or not rich.
Lucy is both calm and not funny.
Someone is both kind and not patient.
Someone is wise.
Someone is not old.
Someone is either happy or strong.
Mary is both humble and old.
Someone is either old or strong.
Alice is curious. | Fred is not creative. | neutral | (![X]:((brave(X)&strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:(~calm(X)<=>(~calm(X)&kind(X))))&
((?[X]:((curious(X)|~happy(X))))=>((calm(fred)|~generous(fred))))&
((?[X]:((~happy(X)&~old(X))))=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((~kind(X)|~calm(X))<=>(~patient(X)&wise(X))))&
(![X]:((~humble(X)|funny(X))<=>(creative(X)<~>curious(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~brave(X)&~calm(X))))&
(![X]:((calm(X)&~humble(X))<=>(brave(X)&~calm(X))))&
((?[X]:((curious(X)|strong(X))))<=>(?[X]:((~tall(X)<~>~strong(X)))))&
(![X]:((~rich(X)|strong(X))<=>(curious(X)|~brave(X))))&
(![X]:((humble(X)<~>quiet(X))<=>curious(X)))&
(![X]:((wise(X)<~>~brave(X))=>(~old(X)|brave(X))))&
((?[X]:(happy(X)))<=>((patient(lucy)|~happy(lucy))))&
(![X]:((kind(X)&calm(X))=>strong(X)))&
(![X]:((old(X)|patient(X))<=>(~brave(X)|~calm(X))))&
(![X]:((~happy(X)|strong(X))=>(kind(X)<~>~rich(X))))&
((calm(lucy)&~funny(lucy)))&
(?[X]:((kind(X)&~patient(X))))&
(?[X]:(wise(X)))&
(?[X]:(~old(X)))&
(?[X]:((happy(X)<~>strong(X))))&
((humble(mary)&old(mary)))&
(?[X]:((old(X)<~>strong(X))))&
(curious(alice)) | ~creative(fred) | [] | null | 0 |
If someone is not old or not humble then someone is either wise or funny and vice versa.
If someone is both curious and wise then someone is both brave and not happy and vice versa.
If mary is either not happy or not creative then mary is either not patient or not strong.
Everyone who is not kind is either not quiet or old and vice versa.
If john is either not quiet or tall then someone is patient.
Everyone who is not generous or not calm is not old or not quiet and vice versa.
If someone is not strong or not tall then mary is calm and vice versa.
Everyone who is both not strong and kind is either not old or tall and vice versa.
Everyone who is creative is either rich or not humble.
Everyone who is calm or kind is both not wise and rich and vice versa.
Everyone who is happy or curious is not kind.
Everyone who is either quiet or humble is both not calm and curious.
If paul is both wise and humble then someone is both not strong and curious.
If someone is happy then paul is not generous or not brave.
Everyone who is either not calm or not brave is patient and vice versa.
If someone is kind or old then someone is either brave or tall and vice versa.
John is both not humble and not kind.
Someone is tall.
Mary is patient or not humble.
Someone is generous or not generous.
Someone is not calm or curious.
Someone is not curious or brave.
Paul is both happy and quiet.
Someone is not creative. | John is not old. | entailment | ((?[X]:((~old(X)|~humble(X))))<=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((curious(X)&wise(X))))<=>(?[X]:((brave(X)&~happy(X)))))&
(((~happy(mary)<~>~creative(mary)))=>((~patient(mary)<~>~strong(mary))))&
(![X]:(~kind(X)<=>(~quiet(X)<~>old(X))))&
(((~quiet(john)<~>tall(john)))=>(?[X]:(patient(X))))&
(![X]:((~generous(X)|~calm(X))<=>(~old(X)|~quiet(X))))&
((?[X]:((~strong(X)|~tall(X))))<=>(calm(mary)))&
(![X]:((~strong(X)&kind(X))<=>(~old(X)<~>tall(X))))&
(![X]:(creative(X)=>(rich(X)<~>~humble(X))))&
(![X]:((calm(X)|kind(X))<=>(~wise(X)&rich(X))))&
(![X]:((happy(X)|curious(X))=>~kind(X)))&
(![X]:((quiet(X)<~>humble(X))=>(~calm(X)&curious(X))))&
(((wise(paul)&humble(paul)))=>(?[X]:((~strong(X)&curious(X)))))&
((?[X]:(happy(X)))=>((~generous(paul)|~brave(paul))))&
(![X]:((~calm(X)<~>~brave(X))<=>patient(X)))&
((?[X]:((kind(X)|old(X))))<=>(?[X]:((brave(X)<~>tall(X)))))&
((~humble(john)&~kind(john)))&
(?[X]:(tall(X)))&
((patient(mary)|~humble(mary)))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((~calm(X)|curious(X))))&
(?[X]:((~curious(X)|brave(X))))&
((happy(paul)&quiet(paul)))&
(?[X]:(~creative(X))) | ~old(john) | [
"p3",
"p5",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7891765954296268768962937
% SZS output start Proof for 7891765954296268768962937
4. ! [X0] : (~kind(X0) <=> (~quiet(X0) <~> old(X0))) [input p3]
6. ! [X0] : ((~calm(X0) | ~generous(X0)) <=> (~quiet(X0) | ~old(X0))) [input p5]
12. ! [X0] : ((quiet(X0) <~> humble(X0)) => (curious(X0) & ~calm(X0))) [input p11]
17. ~kind(john) & ~humble(john) [input p16]
25. old(john) [input hypothesis]
33. ! [X0] : ((curious(X0) & ~calm(X0)) | (quiet(X0) <=> humble(X0))) [ennf transformation 12]
49. ! [X0] : ((~kind(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | kind(X0))) [nnf transformation 4]
53. ! [X0] : (((~calm(X0) | ~generous(X0)) | (quiet(X0) & old(X0))) & ((~quiet(X0) | ~old(X0)) | (calm(X0) & generous(X0)))) [nnf transformation 6]
54. ! [X0] : ((~calm(X0) | ~generous(X0) | (quiet(X0) & old(X0))) & (~quiet(X0) | ~old(X0) | (calm(X0) & generous(X0)))) [flattening 53]
64. ! [X0] : ((curious(X0) & ~calm(X0)) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0)))) [nnf transformation 33]
98. ~old(X0) | quiet(X0) | kind(X0) [cnf transformation 49]
104. ~quiet(X0) | ~old(X0) | calm(X0) [cnf transformation 54]
125. ~calm(X0) | humble(X0) | ~quiet(X0) [cnf transformation 64]
142. ~humble(john) [cnf transformation 17]
143. ~kind(john) [cnf transformation 17]
152. old(john) [cnf transformation 25]
238. 20 <=> quiet(john) [avatar definition]
239. quiet(john) <- (20) [avatar component clause 238]
378. quiet(john) | kind(john) [resolution 98,152]
382. quiet(john) [subsumption resolution 378,143]
383. 20 [avatar split clause 382,238]
403. ~old(john) | calm(john) <- (20) [resolution 104,239]
405. calm(john) <- (20) [subsumption resolution 403,152]
489. humble(john) | ~quiet(john) <- (20) [resolution 125,405]
493. ~quiet(john) <- (20) [subsumption resolution 489,142]
494. $false <- (20) [subsumption resolution 493,239]
495. ~20 [avatar contradiction clause 494]
496. $false [avatar sat refutation 383,495]
% SZS output end Proof for 7891765954296268768962937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not funny then john is both not rich and not kind and vice versa.
Everyone who is not brave is not generous or generous and vice versa.
Everyone who is both not brave and funny is patient.
If someone is both generous and happy then someone is old or humble and vice versa.
Everyone who is both not wise and tall is both humble and calm.
If someone is creative then someone is both patient and not rich.
Everyone who is not brave or not generous is funny and vice versa.
If someone is old or not generous then someone is not patient and vice versa.
If someone is both not strong and not old then someone is both not wise and not patient.
If susan is either funny or not rich then someone is either not tall or tall.
Everyone who is both not strong and not rich is either brave or not wise.
If john is both humble and not curious then lucy is either not calm or not strong and vice versa.
If fred is either not generous or funny then alice is calm or patient.
If susan is not calm or quiet then someone is not funny or curious and vice versa.
Everyone who is both not funny and not humble is both not old and strong.
If fred is either not tall or kind then someone is not patient.
Alice is old or funny.
Someone is happy.
Fred is either creative or happy.
Someone is calm or funny.
Susan is either not curious or tall.
Susan is either not generous or wise.
Someone is humble or strong. | Alice is not old. | entailment | ((?[X]:((~quiet(X)&~funny(X))))<=>((~rich(john)&~kind(john))))&
(![X]:(~brave(X)<=>(~generous(X)|generous(X))))&
(![X]:((~brave(X)&funny(X))=>patient(X)))&
((?[X]:((generous(X)&happy(X))))<=>(?[X]:((old(X)|humble(X)))))&
(![X]:((~wise(X)&tall(X))=>(humble(X)&calm(X))))&
((?[X]:(creative(X)))=>(?[X]:((patient(X)&~rich(X)))))&
(![X]:((~brave(X)|~generous(X))<=>funny(X)))&
((?[X]:((old(X)|~generous(X))))<=>(?[X]:(~patient(X))))&
((?[X]:((~strong(X)&~old(X))))=>(?[X]:((~wise(X)&~patient(X)))))&
(((funny(susan)<~>~rich(susan)))=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((~strong(X)&~rich(X))=>(brave(X)<~>~wise(X))))&
(((humble(john)&~curious(john)))<=>((~calm(lucy)<~>~strong(lucy))))&
(((~generous(fred)<~>funny(fred)))=>((calm(alice)|patient(alice))))&
(((~calm(susan)|quiet(susan)))<=>(?[X]:((~funny(X)|curious(X)))))&
(![X]:((~funny(X)&~humble(X))=>(~old(X)&strong(X))))&
(((~tall(fred)<~>kind(fred)))=>(?[X]:(~patient(X))))&
((old(alice)|funny(alice)))&
(?[X]:(happy(X)))&
((creative(fred)<~>happy(fred)))&
(?[X]:((calm(X)|funny(X))))&
((~curious(susan)<~>tall(susan)))&
((~generous(susan)<~>wise(susan)))&
(?[X]:((humble(X)|strong(X)))) | ~old(alice) | [
"p1",
"p2",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 350033147332074913825882
% SZS output start Proof for 350033147332074913825882
2. ! [X0] : (~brave(X0) <=> (generous(X0) | ~generous(X0))) [input p1]
3. ! [X0] : ((funny(X0) & ~brave(X0)) => patient(X0)) [input p2]
7. ! [X0] : ((~generous(X0) | ~brave(X0)) <=> funny(X0)) [input p6]
8. ? [X0] : (~generous(X0) | old(X0)) <=> ? [X0] : ~patient(X0) [input p7]
24. old(alice) [input hypothesis]
27. ? [X0] : (~generous(X0) | old(X0)) <=> ? [X1] : ~patient(X1) [rectify 8]
29. ! [X0] : (patient(X0) | (~funny(X0) | brave(X0))) [ennf transformation 3]
30. ! [X0] : (patient(X0) | ~funny(X0) | brave(X0)) [flattening 29]
48. ! [X0] : ((~brave(X0) | (~generous(X0) & generous(X0))) & ((generous(X0) | ~generous(X0)) | brave(X0))) [nnf transformation 2]
49. ! [X0] : ((~brave(X0) | (~generous(X0) & generous(X0))) & (generous(X0) | ~generous(X0) | brave(X0))) [flattening 48]
58. ! [X0] : (((~generous(X0) | ~brave(X0)) | ~funny(X0)) & (funny(X0) | (generous(X0) & brave(X0)))) [nnf transformation 7]
59. ! [X0] : ((~generous(X0) | ~brave(X0) | ~funny(X0)) & (funny(X0) | (generous(X0) & brave(X0)))) [flattening 58]
60. (? [X0] : (~generous(X0) | old(X0)) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : (generous(X0) & ~old(X0))) [nnf transformation 27]
61. (? [X0] : (~generous(X0) | old(X0)) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : (generous(X3) & ~old(X3))) [rectify 60]
62. ? [X0] : (~generous(X0) | old(X0)) => (~generous(sK4) | old(sK4)) [choice axiom]
63. ? [X2] : ~patient(X2) => ~patient(sK5) [choice axiom]
64. ((~generous(sK4) | old(sK4)) | ! [X1] : patient(X1)) & (~patient(sK5) | ! [X3] : (generous(X3) & ~old(X3))) [skolemisation 61,63,62]
97. ~brave(X0) | generous(X0) [cnf transformation 49]
98. ~generous(X0) | ~brave(X0) [cnf transformation 49]
99. patient(X0) | ~funny(X0) | brave(X0) [cnf transformation 30]
109. funny(X0) | brave(X0) [cnf transformation 59]
112. ~patient(sK5) | ~old(X3) [cnf transformation 64]
149. old(alice) [cnf transformation 24]
173. ~brave(X0) [subsumption resolution 97,98]
174. ~funny(X0) | patient(X0) [subsumption resolution 99,173]
184. 8 <=> ! [X1] : ~old(X1) [avatar definition]
185. ~old(X1) <- (8) [avatar component clause 184]
218. funny(X0) [subsumption resolution 109,173]
220. 16 <=> ! [X1] : patient(X1) [avatar definition]
221. patient(X1) <- (16) [avatar component clause 220]
235. 20 <=> patient(sK5) [avatar definition]
237. ~patient(sK5) <- (~20) [avatar component clause 235]
239. 8 | ~20 [avatar split clause 112,235,184]
365. $false <- (8) [resolution 185,149]
366. ~8 [avatar contradiction clause 365]
376. patient(X0) [resolution 174,218]
377. 16 [avatar split clause 376,220]
378. $false <- (16, ~20) [resolution 221,237]
383. ~16 | 20 [avatar contradiction clause 378]
384. $false [avatar sat refutation 239,366,377,383]
% SZS output end Proof for 350033147332074913825882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet and not tall is either patient or funny.
Everyone who is not rich or not brave is either not calm or not creative and vice versa.
If mary is either creative or quiet then john is both tall and calm and vice versa.
If someone is either not tall or wise then someone is funny or patient and vice versa.
Everyone who is either strong or not curious is not rich.
Everyone who is both not quiet and not brave is either not tall or not funny and vice versa.
If someone is both strong and not patient then john is not happy.
Everyone who is both calm and tall is patient or humble and vice versa.
Everyone who is either not tall or rich is either not old or not patient and vice versa.
If john is humble then fred is tall.
Everyone who is not wise is rich.
Everyone who is either not strong or not kind is not humble or not creative and vice versa.
Everyone who is either quiet or not calm is both not tall and tall and vice versa.
If someone is quiet then someone is either calm or brave and vice versa.
Everyone who is both not tall and calm is not strong.
John is both not funny and not kind.
Fred is not happy or not creative.
Alice is either creative or quiet.
Fred is not generous.
Mary is wise or tall.
Someone is either generous or rich.
Mary is both not kind and quiet.
Susan is wise. | John is not strong. | contradiction | (![X]:((~quiet(X)&~tall(X))=>(patient(X)<~>funny(X))))&
(![X]:((~rich(X)|~brave(X))<=>(~calm(X)<~>~creative(X))))&
(((creative(mary)<~>quiet(mary)))<=>((tall(john)&calm(john))))&
((?[X]:((~tall(X)<~>wise(X))))<=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((strong(X)<~>~curious(X))=>~rich(X)))&
(![X]:((~quiet(X)&~brave(X))<=>(~tall(X)<~>~funny(X))))&
((?[X]:((strong(X)&~patient(X))))=>(~happy(john)))&
(![X]:((calm(X)&tall(X))<=>(patient(X)|humble(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(~old(X)<~>~patient(X))))&
((humble(john))=>(tall(fred)))&
(![X]:(~wise(X)=>rich(X)))&
(![X]:((~strong(X)<~>~kind(X))<=>(~humble(X)|~creative(X))))&
(![X]:((quiet(X)<~>~calm(X))<=>(~tall(X)&tall(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((calm(X)<~>brave(X)))))&
(![X]:((~tall(X)&calm(X))=>~strong(X)))&
((~funny(john)&~kind(john)))&
((~happy(fred)|~creative(fred)))&
((creative(alice)<~>quiet(alice)))&
(~generous(fred))&
((wise(mary)|tall(mary)))&
(?[X]:((generous(X)<~>rich(X))))&
((~kind(mary)&quiet(mary)))&
(wise(susan)) | ~strong(john) | [
"p1",
"p5",
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7958515492902463269580118
% SZS output start Proof for 7958515492902463269580118
2. ! [X0] : ((~brave(X0) | ~rich(X0)) <=> (~calm(X0) <~> ~creative(X0))) [input p1]
6. ! [X0] : ((~brave(X0) & ~quiet(X0)) <=> (~tall(X0) <~> ~funny(X0))) [input p5]
8. ! [X0] : ((tall(X0) & calm(X0)) <=> (humble(X0) | patient(X0))) [input p7]
12. ! [X0] : ((~strong(X0) <~> ~kind(X0)) <=> (~creative(X0) | ~humble(X0))) [input p11]
16. ~kind(john) & ~funny(john) [input p15]
24. ~strong(john) [input hypothesis]
37. ! [X0] : (((~brave(X0) | ~rich(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0)))) & (((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (brave(X0) & rich(X0)))) [nnf transformation 2]
38. ! [X0] : ((~brave(X0) | ~rich(X0) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0)))) & (((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (brave(X0) & rich(X0)))) [flattening 37]
47. ! [X0] : (((~brave(X0) & ~quiet(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0)))) & (((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | (brave(X0) | quiet(X0)))) [nnf transformation 6]
48. ! [X0] : (((~brave(X0) & ~quiet(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0)))) & (((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | brave(X0) | quiet(X0))) [flattening 47]
49. ! [X0] : (((tall(X0) & calm(X0)) | (~humble(X0) & ~patient(X0))) & ((humble(X0) | patient(X0)) | (~tall(X0) | ~calm(X0)))) [nnf transformation 8]
50. ! [X0] : (((tall(X0) & calm(X0)) | (~humble(X0) & ~patient(X0))) & (humble(X0) | patient(X0) | ~tall(X0) | ~calm(X0))) [flattening 49]
52. ! [X0] : ((((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | (creative(X0) & humble(X0))) & ((~creative(X0) | ~humble(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0))))) [nnf transformation 12]
53. ! [X0] : ((((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | (creative(X0) & humble(X0))) & (~creative(X0) | ~humble(X0) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0))))) [flattening 52]
68. ~creative(X0) | ~calm(X0) | brave(X0) [cnf transformation 38]
92. ~brave(X0) | ~tall(X0) | funny(X0) [cnf transformation 48]
95. ~humble(X0) | calm(X0) [cnf transformation 50]
97. ~humble(X0) | tall(X0) [cnf transformation 50]
112. kind(X0) | strong(X0) | humble(X0) [cnf transformation 53]
113. kind(X0) | strong(X0) | creative(X0) [cnf transformation 53]
125. ~funny(john) [cnf transformation 16]
126. ~kind(john) [cnf transformation 16]
136. ~strong(john) [cnf transformation 24]
138. 1 <=> tall(john) [avatar definition]
139. tall(john) <- (1) [avatar component clause 138]
142. 2 <=> calm(john) [avatar definition]
143. calm(john) <- (2) [avatar component clause 142]
198. 13 <=> humble(john) [avatar definition]
199. humble(john) <- (13) [avatar component clause 198]
372. strong(john) | humble(john) [resolution 112,126]
377. humble(john) [subsumption resolution 372,136]
389. 13 [avatar split clause 377,198]
390. tall(john) <- (13) [resolution 199,97]
391. calm(john) <- (13) [resolution 199,95]
392. 1 | ~13 [avatar split clause 390,198,138]
395. 2 | ~13 [avatar split clause 391,198,142]
414. strong(john) | creative(john) [resolution 113,126]
419. creative(john) [subsumption resolution 414,136]
438. ~calm(john) | brave(john) [resolution 419,68]
440. brave(john) <- (2) [subsumption resolution 438,143]
465. ~tall(john) | funny(john) <- (2) [resolution 440,92]
467. funny(john) <- (1, 2) [subsumption resolution 465,139]
468. $false <- (1, 2) [subsumption resolution 467,125]
469. ~1 | ~2 [avatar contradiction clause 468]
470. $false [avatar sat refutation 389,392,395,469]
% SZS output end Proof for 7958515492902463269580118
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then lucy is either not calm or not funny. If someone is both creative and not curious then paul is not quiet and vice versa. Everyone who is not calm or old is creative or kind and vice versa. Everyone who is either strong or quiet is not quiet or creative. If susan is funny then fred is both rich and brave. If susan is brave then paul is not patient or not strong and vice versa. Everyone who is not old or not wise is humble or not funny and vice versa. If someone is either not patient or patient then someone is either kind or not funny and vice versa. If someone is both happy and not calm then susan is not tall. Everyone who is either not rich or kind is strong. If susan is not tall then susan is not strong and vice versa. Everyone who is not happy is not creative and vice versa. Everyone who is not brave or not old is either strong or old. Everyone who is either generous or wise is not generous or not patient and vice versa. Everyone who is both strong and funny is not calm. Everyone who is either not tall or happy is both humble and kind and vice versa. Someone is both kind and not patient. Lucy is not kind. John is either humble or not strong. Someone is not funny. Someone is both not strong and not kind. Lucy is either wise or not quiet. Someone is not brave. Someone is both not brave and wise. | Paul is not strong. | neutral | ((?[X]:(happy(X)))=>((~calm(lucy)<~>~funny(lucy))))&
((?[X]:((creative(X)&~curious(X))))<=>(~quiet(paul)))&
(![X]:((~calm(X)|old(X))<=>(creative(X)|kind(X))))&
(![X]:((strong(X)<~>quiet(X))=>(~quiet(X)|creative(X))))&
((funny(susan))=>((rich(fred)&brave(fred))))&
((brave(susan))<=>((~patient(paul)|~strong(paul))))&
(![X]:((~old(X)|~wise(X))<=>(humble(X)|~funny(X))))&
((?[X]:((~patient(X)<~>patient(X))))<=>(?[X]:((kind(X)<~>~funny(X)))))&
((?[X]:((happy(X)&~calm(X))))=>(~tall(susan)))&
(![X]:((~rich(X)<~>kind(X))=>strong(X)))&
((~tall(susan))<=>(~strong(susan)))&
(![X]:(~happy(X)<=>~creative(X)))&
(![X]:((~brave(X)|~old(X))=>(strong(X)<~>old(X))))&
(![X]:((generous(X)<~>wise(X))<=>(~generous(X)|~patient(X))))&
(![X]:((strong(X)&funny(X))=>~calm(X)))&
(![X]:((~tall(X)<~>happy(X))<=>(humble(X)&kind(X))))&
(?[X]:((kind(X)&~patient(X))))&
(~kind(lucy))&
((humble(john)<~>~strong(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~strong(X)&~kind(X))))&
((wise(lucy)<~>~quiet(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)&wise(X)))) | ~strong(paul) | [] | null | 0 |
Everyone who is both quiet and not kind is not humble or curious and vice versa.
If susan is not generous or happy then someone is either creative or not wise.
Everyone who is not calm or curious is either humble or funny and vice versa.
Everyone who is both not tall and brave is both not old and not curious and vice versa.
Everyone who is not creative is both old and quiet and vice versa.
If susan is either happy or not rich then john is patient or humble.
Everyone who is not generous or calm is both not creative and not happy.
Everyone who is either humble or creative is either not strong or not humble and vice versa.
If someone is both rich and not strong then someone is happy and vice versa.
If someone is quiet then someone is not kind or not tall and vice versa.
Everyone who is both humble and not happy is both wise and strong and vice versa.
If someone is not old then someone is not humble or brave and vice versa.
Everyone who is both curious and brave is either not funny or old and vice versa.
Everyone who is both generous and not strong is both not brave and humble.
If john is tall then someone is tall or rich.
Everyone who is patient is humble.
Mary is both quiet and patient.
Someone is both generous and happy.
Someone is either quiet or tall.
Someone is either not creative or not wise.
Fred is either old or creative.
Someone is both not brave and not kind.
Someone is both calm and not tall.
Someone is both funny and brave. | Mary is generous. | entailment | (![X]:((quiet(X)&~kind(X))<=>(~humble(X)|curious(X))))&
(((~generous(susan)|happy(susan)))=>(?[X]:((creative(X)<~>~wise(X)))))&
(![X]:((~calm(X)|curious(X))<=>(humble(X)<~>funny(X))))&
(![X]:((~tall(X)&brave(X))<=>(~old(X)&~curious(X))))&
(![X]:(~creative(X)<=>(old(X)&quiet(X))))&
(((happy(susan)<~>~rich(susan)))=>((patient(john)|humble(john))))&
(![X]:((~generous(X)|calm(X))=>(~creative(X)&~happy(X))))&
(![X]:((humble(X)<~>creative(X))<=>(~strong(X)<~>~humble(X))))&
((?[X]:((rich(X)&~strong(X))))<=>(?[X]:(happy(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((~kind(X)|~tall(X)))))&
(![X]:((humble(X)&~happy(X))<=>(wise(X)&strong(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~humble(X)|brave(X)))))&
(![X]:((curious(X)&brave(X))<=>(~funny(X)<~>old(X))))&
(![X]:((generous(X)&~strong(X))=>(~brave(X)&humble(X))))&
((tall(john))=>(?[X]:((tall(X)|rich(X)))))&
(![X]:(patient(X)=>humble(X)))&
((quiet(mary)&patient(mary)))&
(?[X]:((generous(X)&happy(X))))&
(?[X]:((quiet(X)<~>tall(X))))&
(?[X]:((~creative(X)<~>~wise(X))))&
((old(fred)<~>creative(fred)))&
(?[X]:((~brave(X)&~kind(X))))&
(?[X]:((calm(X)&~tall(X))))&
(?[X]:((funny(X)&brave(X)))) | generous(mary) | [
"p6",
"p7",
"p10",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2385371109694366695915330
% SZS output start Proof for 2385371109694366695915330
7. ! [X0] : ((calm(X0) | ~generous(X0)) => (~happy(X0) & ~creative(X0))) [input p6]
8. ! [X0] : ((humble(X0) <~> creative(X0)) <=> (~strong(X0) <~> ~humble(X0))) [input p7]
11. ! [X0] : ((~happy(X0) & humble(X0)) <=> (strong(X0) & wise(X0))) [input p10]
16. ! [X0] : (patient(X0) => humble(X0)) [input p15]
17. patient(mary) & quiet(mary) [input p16]
25. ~generous(mary) [input hypothesis]
32. ! [X0] : ((~happy(X0) & ~creative(X0)) | (~calm(X0) & generous(X0))) [ennf transformation 7]
36. ! [X0] : (humble(X0) | ~patient(X0)) [ennf transformation 16]
49. ! [X0] : ((((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))))) [nnf transformation 8]
60. ! [X0] : (((~happy(X0) & humble(X0)) | (~strong(X0) | ~wise(X0))) & ((strong(X0) & wise(X0)) | (happy(X0) | ~humble(X0)))) [nnf transformation 11]
61. ! [X0] : (((~happy(X0) & humble(X0)) | ~strong(X0) | ~wise(X0)) & ((strong(X0) & wise(X0)) | happy(X0) | ~humble(X0))) [flattening 60]
110. ~creative(X0) | generous(X0) [cnf transformation 32]
112. ~happy(X0) | generous(X0) [cnf transformation 32]
114. ~humble(X0) | ~strong(X0) | creative(X0) | ~humble(X0) [cnf transformation 49]
119. creative(X0) | humble(X0) | ~strong(X0) | humble(X0) [cnf transformation 49]
129. ~humble(X0) | happy(X0) | strong(X0) [cnf transformation 61]
144. ~patient(X0) | humble(X0) [cnf transformation 36]
146. patient(mary) [cnf transformation 17]
161. ~generous(mary) [cnf transformation 25]
162. ~humble(X0) | ~strong(X0) | creative(X0) [duplicate literal removal 114]
164. ~strong(X0) | humble(X0) | creative(X0) [duplicate literal removal 119]
201. ~strong(X0) | creative(X0) [subsumption resolution 162,164]
326. humble(mary) [resolution 144,146]
398. 42 <=> happy(mary) [avatar definition]
400. happy(mary) <- (42) [avatar component clause 398]
403. happy(mary) | strong(mary) [resolution 129,326]
405. 43 <=> strong(mary) [avatar definition]
407. strong(mary) <- (43) [avatar component clause 405]
408. 43 | 42 [avatar split clause 403,398,405]
413. generous(mary) <- (42) [resolution 400,112]
414. $false <- (42) [subsumption resolution 413,161]
415. ~42 [avatar contradiction clause 414]
443. creative(mary) <- (43) [resolution 407,201]
731. generous(mary) <- (43) [resolution 443,110]
746. $false <- (43) [subsumption resolution 731,161]
747. ~43 [avatar contradiction clause 746]
748. $false [avatar sat refutation 408,415,747]
% SZS output end Proof for 2385371109694366695915330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not curious or not humble then someone is either happy or not creative and vice versa.
Everyone who is either not funny or old is happy or not kind.
If john is both rich and brave then someone is either not strong or happy.
If someone is not old then fred is either calm or not kind and vice versa.
Everyone who is not kind is not wise.
Everyone who is both patient and strong is both not happy and generous and vice versa.
Everyone who is either not funny or generous is either not calm or humble and vice versa.
Everyone who is both not rich and not brave is both calm and brave and vice versa.
Everyone who is brave or creative is not patient and vice versa.
Everyone who is funny is both old and wise.
Everyone who is either not calm or not old is both old and patient and vice versa.
If susan is either not humble or not rich then susan is not patient.
If susan is both not calm and not creative then someone is not creative or not generous and vice versa.
Everyone who is humble or not humble is not calm and vice versa.
Everyone who is not quiet or rich is not creative or not calm and vice versa.
Everyone who is both not wise and humble is not wise or creative and vice versa.
Someone is not creative.
Lucy is both not old and not generous.
Someone is either not wise or humble.
Someone is humble or not patient.
Paul is strong or patient.
Someone is rich.
Fred is either not tall or not rich.
Someone is not old or humble. | Susan is creative. | contradiction | (((~curious(john)<~>~humble(john)))<=>(?[X]:((happy(X)<~>~creative(X)))))&
(![X]:((~funny(X)<~>old(X))=>(happy(X)|~kind(X))))&
(((rich(john)&brave(john)))=>(?[X]:((~strong(X)<~>happy(X)))))&
((?[X]:(~old(X)))<=>((calm(fred)<~>~kind(fred))))&
(![X]:(~kind(X)=>~wise(X)))&
(![X]:((patient(X)&strong(X))<=>(~happy(X)&generous(X))))&
(![X]:((~funny(X)<~>generous(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((~rich(X)&~brave(X))<=>(calm(X)&brave(X))))&
(![X]:((brave(X)|creative(X))<=>~patient(X)))&
(![X]:(funny(X)=>(old(X)&wise(X))))&
(![X]:((~calm(X)<~>~old(X))<=>(old(X)&patient(X))))&
(((~humble(susan)<~>~rich(susan)))=>(~patient(susan)))&
(((~calm(susan)&~creative(susan)))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((humble(X)|~humble(X))<=>~calm(X)))&
(![X]:((~quiet(X)|rich(X))<=>(~creative(X)|~calm(X))))&
(![X]:((~wise(X)&humble(X))<=>(~wise(X)|creative(X))))&
(?[X]:(~creative(X)))&
((~old(lucy)&~generous(lucy)))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:((humble(X)|~patient(X))))&
((strong(paul)|patient(paul)))&
(?[X]:(rich(X)))&
((~tall(fred)<~>~rich(fred)))&
(?[X]:((~old(X)|humble(X)))) | creative(susan) | [
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 373895866341674185217349
% SZS output start Proof for 373895866341674185217349
13. (~creative(susan) & ~calm(susan)) <=> ? [X0] : (~generous(X0) | ~creative(X0)) [input p12]
18. ~generous(lucy) & ~old(lucy) [input p17]
25. creative(susan) [input hypothesis]
55. ((~creative(susan) & ~calm(susan)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | (creative(susan) | calm(susan))) [nnf transformation 13]
56. ((~creative(susan) & ~calm(susan)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | creative(susan) | calm(susan)) [flattening 55]
57. ((~creative(susan) & ~calm(susan)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X1] : (~generous(X1) | ~creative(X1)) | creative(susan) | calm(susan)) [rectify 56]
58. ? [X1] : (~generous(X1) | ~creative(X1)) => (~generous(sK3) | ~creative(sK3)) [choice axiom]
59. ((~creative(susan) & ~calm(susan)) | ! [X0] : (generous(X0) & creative(X0))) & ((~generous(sK3) | ~creative(sK3)) | creative(susan) | calm(susan)) [skolemisation 57,58]
128. ~creative(susan) | generous(X0) [cnf transformation 59]
143. ~generous(lucy) [cnf transformation 18]
152. creative(susan) [cnf transformation 25]
239. 18 <=> ! [X0] : generous(X0) [avatar definition]
240. generous(X0) <- (18) [avatar component clause 239]
242. 19 <=> creative(susan) [avatar definition]
245. 18 | ~19 [avatar split clause 128,242,239]
306. 19 [avatar split clause 152,242]
309. $false <- (18) [resolution 240,143]
310. ~18 [avatar contradiction clause 309]
311. $false [avatar sat refutation 245,306,310]
% SZS output end Proof for 373895866341674185217349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not wise is both patient and not generous. Everyone who is not quiet is not tall and vice versa. If lucy is humble then someone is both quiet and not tall and vice versa. Everyone who is both not quiet and strong is both not rich and not generous. Everyone who is creative is either not strong or generous. Everyone who is either not old or not quiet is creative or not kind. Everyone who is either kind or curious is not rich and vice versa. If someone is both not rich and funny then someone is either creative or not kind. Everyone who is both curious and not brave is not funny and vice versa. Everyone who is not old or not humble is either not creative or funny and vice versa. If john is either not quiet or not funny then mary is either patient or not strong. Everyone who is both not strong and not generous is either not humble or not curious and vice versa. Everyone who is not calm or funny is funny or tall. Everyone who is both funny and creative is not brave or not generous. Everyone who is not curious or creative is not kind and vice versa. If someone is humble or generous then john is both not patient and not strong. Someone is either generous or not old. Someone is both not quiet and not happy. Alice is not calm. | Lucy is not curious. | contradiction | (![X]:((wise(X)|~wise(X))=>(patient(X)&~generous(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
((humble(lucy))<=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((~quiet(X)&strong(X))=>(~rich(X)&~generous(X))))&
(![X]:(creative(X)=>(~strong(X)<~>generous(X))))&
(![X]:((~old(X)<~>~quiet(X))=>(creative(X)|~kind(X))))&
(![X]:((kind(X)<~>curious(X))<=>~rich(X)))&
((?[X]:((~rich(X)&funny(X))))=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((curious(X)&~brave(X))<=>~funny(X)))&
(![X]:((~old(X)|~humble(X))<=>(~creative(X)<~>funny(X))))&
(((~quiet(john)<~>~funny(john)))=>((patient(mary)<~>~strong(mary))))&
(![X]:((~strong(X)&~generous(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~calm(X)|funny(X))=>(funny(X)|tall(X))))&
(![X]:((funny(X)&creative(X))=>(~brave(X)|~generous(X))))&
(![X]:((~curious(X)|creative(X))<=>~kind(X)))&
((?[X]:((humble(X)|generous(X))))=>((~patient(john)&~strong(john))))&
(?[X]:((generous(X)<~>~old(X))))&
(?[X]:((~quiet(X)&~happy(X))))&
(~calm(alice)) | ~curious(lucy) | [
"p0",
"p4",
"p8",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3323070450061387812244153
% SZS output start Proof for 3323070450061387812244153
1. ! [X0] : ((~wise(X0) | wise(X0)) => (~generous(X0) & patient(X0))) [input p0]
5. ! [X0] : (creative(X0) => (~strong(X0) <~> generous(X0))) [input p4]
9. ! [X0] : ((~brave(X0) & curious(X0)) <=> ~funny(X0)) [input p8]
10. ! [X0] : ((~humble(X0) | ~old(X0)) <=> (~creative(X0) <~> funny(X0))) [input p9]
12. ! [X0] : ((~generous(X0) & ~strong(X0)) <=> (~humble(X0) <~> ~curious(X0))) [input p11]
16. ? [X0] : (generous(X0) | humble(X0)) => (~strong(john) & ~patient(john)) [input p15]
20. ~curious(lucy) [input hypothesis]
23. ! [X0] : ((~generous(X0) & patient(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 1]
26. ! [X0] : ((~strong(X0) <~> generous(X0)) | ~creative(X0)) [ennf transformation 5]
35. (~strong(john) & ~patient(john)) | ! [X0] : (~generous(X0) & ~humble(X0)) [ennf transformation 16]
41. ! [X0] : (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ~creative(X0)) [nnf transformation 26]
48. ! [X0] : (((~brave(X0) & curious(X0)) | funny(X0)) & (~funny(X0) | (brave(X0) | ~curious(X0)))) [nnf transformation 9]
49. ! [X0] : (((~brave(X0) & curious(X0)) | funny(X0)) & (~funny(X0) | brave(X0) | ~curious(X0))) [flattening 48]
50. ! [X0] : (((~humble(X0) | ~old(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (humble(X0) & old(X0)))) [nnf transformation 10]
51. ! [X0] : ((~humble(X0) | ~old(X0) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (humble(X0) & old(X0)))) [flattening 50]
53. ! [X0] : (((~generous(X0) & ~strong(X0)) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) & (((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | (generous(X0) | strong(X0)))) [nnf transformation 12]
54. ! [X0] : (((~generous(X0) & ~strong(X0)) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) & (((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | generous(X0) | strong(X0))) [flattening 53]
62. patient(X0) | ~wise(X0) [cnf transformation 23]
63. patient(X0) | wise(X0) [cnf transformation 23]
64. ~generous(X0) | ~wise(X0) [cnf transformation 23]
65. ~generous(X0) | wise(X0) [cnf transformation 23]
73. generous(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 41]
84. funny(X0) | curious(X0) [cnf transformation 49]
89. ~funny(X0) | creative(X0) | humble(X0) [cnf transformation 51]
97. curious(X0) | humble(X0) | generous(X0) | strong(X0) [cnf transformation 54]
98. ~curious(X0) | ~strong(X0) | humble(X0) [cnf transformation 54]
108. ~patient(john) | ~humble(X0) [cnf transformation 35]
116. ~curious(lucy) [cnf transformation 20]
117. ~generous(X0) [subsumption resolution 64,65]
118. patient(X0) [subsumption resolution 62,63]
133. ~creative(X0) | ~strong(X0) [subsumption resolution 73,117]
163. curious(X0) | humble(X0) | strong(X0) [subsumption resolution 97,117]
166. 10 <=> ! [X0] : ~humble(X0) [avatar definition]
167. ~humble(X0) <- (10) [avatar component clause 166]
173. ~humble(X0) [subsumption resolution 108,118]
174. 10 [avatar split clause 173,166]
216. creative(X0) | humble(X0) | curious(X0) [resolution 89,84]
217. curious(X0) | creative(X0) <- (10) [subsumption resolution 216,167]
224. creative(X0) | ~strong(X0) | humble(X0) <- (10) [resolution 217,98]
227. creative(X0) | ~strong(X0) <- (10) [subsumption resolution 224,167]
228. ~strong(X0) <- (10) [subsumption resolution 227,133]
251. humble(lucy) | strong(lucy) [resolution 163,116]
257. strong(lucy) <- (10) [subsumption resolution 251,167]
262. $false <- (10) [subsumption resolution 257,228]
263. ~10 [avatar contradiction clause 262]
266. $false [avatar sat refutation 174,263]
% SZS output end Proof for 3323070450061387812244153
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not strong and strong then someone is both calm and not brave and vice versa.
If mary is either not tall or not funny then mary is both happy and not humble.
Everyone who is calm or not tall is both rich and not old.
If someone is patient or generous then lucy is both generous and not funny.
If paul is both not calm and not patient then someone is either strong or curious and vice versa.
Everyone who is either not curious or not brave is either creative or not happy.
If fred is either not humble or not creative then lucy is both not generous and humble.
Everyone who is creative or not tall is not happy.
Everyone who is both not old and strong is either calm or brave and vice versa.
If someone is both brave and not calm then someone is either not wise or creative and vice versa.
Everyone who is both not strong and not curious is creative and vice versa.
If paul is both brave and not kind then someone is not old or not funny and vice versa.
Everyone who is generous or strong is both rich and kind.
If fred is brave or generous then mary is generous or calm.
Someone is not wise.
Someone is happy or not generous.
Someone is not brave or not rich.
Someone is either not quiet or not funny.
Someone is either not happy or not tall.
Someone is wise or humble. | Lucy is old. | entailment | ((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((calm(X)&~brave(X)))))&
(((~tall(mary)<~>~funny(mary)))=>((happy(mary)&~humble(mary))))&
(![X]:((calm(X)|~tall(X))=>(rich(X)&~old(X))))&
((?[X]:((patient(X)|generous(X))))=>((generous(lucy)&~funny(lucy))))&
(((~calm(paul)&~patient(paul)))<=>(?[X]:((strong(X)<~>curious(X)))))&
(![X]:((~curious(X)<~>~brave(X))=>(creative(X)<~>~happy(X))))&
(((~humble(fred)<~>~creative(fred)))=>((~generous(lucy)&humble(lucy))))&
(![X]:((creative(X)|~tall(X))=>~happy(X)))&
(![X]:((~old(X)&strong(X))<=>(calm(X)<~>brave(X))))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((~wise(X)<~>creative(X)))))&
(![X]:((~strong(X)&~curious(X))<=>creative(X)))&
(((brave(paul)&~kind(paul)))<=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((generous(X)|strong(X))=>(rich(X)&kind(X))))&
(((brave(fred)|generous(fred)))=>((generous(mary)|calm(mary))))&
(?[X]:(~wise(X)))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:((~happy(X)<~>~tall(X))))&
(?[X]:((wise(X)|humble(X)))) | old(lucy) | [
"p4",
"p5",
"p7",
"p8",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6533449285750169603998613
% SZS output start Proof for 6533449285750169603998613
5. (~patient(paul) & ~calm(paul)) <=> ? [X0] : (strong(X0) <~> curious(X0)) [input p4]
6. ! [X0] : ((~curious(X0) <~> ~brave(X0)) => (creative(X0) <~> ~happy(X0))) [input p5]
8. ! [X0] : ((~tall(X0) | creative(X0)) => ~happy(X0)) [input p7]
9. ! [X0] : ((strong(X0) & ~old(X0)) <=> (calm(X0) <~> brave(X0))) [input p8]
11. ! [X0] : ((~curious(X0) & ~strong(X0)) <=> creative(X0)) [input p10]
12. (~kind(paul) & brave(paul)) <=> ? [X0] : (~funny(X0) | ~old(X0)) [input p11]
13. ! [X0] : ((strong(X0) | generous(X0)) => (kind(X0) & rich(X0))) [input p12]
21. ~old(lucy) [input hypothesis]
27. ! [X0] : ((creative(X0) <~> ~happy(X0)) | (~curious(X0) <=> ~brave(X0))) [ennf transformation 6]
29. ! [X0] : (~happy(X0) | (tall(X0) & ~creative(X0))) [ennf transformation 8]
30. ! [X0] : ((kind(X0) & rich(X0)) | (~strong(X0) & ~generous(X0))) [ennf transformation 13]
39. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (patient(paul) | calm(paul))) [nnf transformation 5]
40. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | patient(paul) | calm(paul)) [flattening 39]
41. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X1] : ((~curious(X1) | ~strong(X1)) & (curious(X1) | strong(X1))) | patient(paul) | calm(paul)) [rectify 40]
42. ? [X1] : ((~curious(X1) | ~strong(X1)) & (curious(X1) | strong(X1))) => ((~curious(sK2) | ~strong(sK2)) & (curious(sK2) | strong(sK2))) [choice axiom]
43. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (((~curious(sK2) | ~strong(sK2)) & (curious(sK2) | strong(sK2))) | patient(paul) | calm(paul)) [skolemisation 41,42]
44. ! [X0] : (((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) [nnf transformation 27]
46. ! [X0] : (((strong(X0) & ~old(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~strong(X0) | old(X0)))) [nnf transformation 9]
47. ! [X0] : (((strong(X0) & ~old(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | ~strong(X0) | old(X0))) [flattening 46]
53. ! [X0] : (((~curious(X0) & ~strong(X0)) | ~creative(X0)) & (creative(X0) | (curious(X0) | strong(X0)))) [nnf transformation 11]
54. ! [X0] : (((~curious(X0) & ~strong(X0)) | ~creative(X0)) & (creative(X0) | curious(X0) | strong(X0))) [flattening 53]
55. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X0] : (~funny(X0) | ~old(X0)) | (kind(paul) | ~brave(paul))) [nnf transformation 12]
56. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X0] : (~funny(X0) | ~old(X0)) | kind(paul) | ~brave(paul)) [flattening 55]
57. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X1] : (~funny(X1) | ~old(X1)) | kind(paul) | ~brave(paul)) [rectify 56]
58. ? [X1] : (~funny(X1) | ~old(X1)) => (~funny(sK5) | ~old(sK5)) [choice axiom]
59. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & ((~funny(sK5) | ~old(sK5)) | kind(paul) | ~brave(paul)) [skolemisation 57,58]
92. ~calm(paul) | curious(X0) | ~strong(X0) [cnf transformation 43]
93. ~calm(paul) | strong(X0) | ~curious(X0) [cnf transformation 43]
98. ~creative(X0) | happy(X0) | ~brave(X0) | curious(X0) [cnf transformation 44]
104. ~creative(X0) | ~happy(X0) [cnf transformation 29]
111. ~brave(X0) | calm(X0) | strong(X0) [cnf transformation 47]
118. creative(X0) | curious(X0) | strong(X0) [cnf transformation 54]
122. brave(paul) | old(X0) [cnf transformation 59]
124. ~kind(paul) | old(X0) [cnf transformation 59]
129. ~strong(X0) | kind(X0) [cnf transformation 30]
140. ~old(lucy) [cnf transformation 21]
189. 11 <=> ! [X0] : (strong(X0) | ~curious(X0)) [avatar definition]
190. ~curious(X0) | strong(X0) <- (11) [avatar component clause 189]
197. 13 <=> ! [X0] : (curious(X0) | ~strong(X0)) [avatar definition]
198. ~strong(X0) | curious(X0) <- (13) [avatar component clause 197]
201. 14 <=> calm(paul) [avatar definition]
204. 11 | ~14 [avatar split clause 93,201,189]
205. 13 | ~14 [avatar split clause 92,201,197]
269. 28 <=> kind(paul) [avatar definition]
271. ~kind(paul) <- (~28) [avatar component clause 269]
274. 29 <=> ! [X0] : old(X0) [avatar definition]
275. old(X0) <- (29) [avatar component clause 274]
276. 29 | ~28 [avatar split clause 124,269,274]
278. 30 <=> brave(paul) [avatar definition]
280. brave(paul) <- (30) [avatar component clause 278]
282. 29 | 30 [avatar split clause 122,278,274]
351. $false <- (29) [resolution 275,140]
352. ~29 [avatar contradiction clause 351]
381. calm(paul) | strong(paul) <- (30) [resolution 111,280]
386. curious(X2) | strong(X2) | ~happy(X2) [resolution 118,104]
389. ~happy(X2) | curious(X2) <- (13) [subsumption resolution 386,198]
420. happy(X0) | ~brave(X0) | curious(X0) | curious(X0) | strong(X0) [resolution 98,118]
421. happy(X0) | ~brave(X0) | curious(X0) | strong(X0) [duplicate literal removal 420]
424. happy(X0) | ~brave(X0) | curious(X0) <- (13) [subsumption resolution 421,198]
425. ~brave(X0) | curious(X0) <- (13) [subsumption resolution 424,389]
478. 55 <=> strong(paul) [avatar definition]
479. strong(paul) <- (55) [avatar component clause 478]
480. ~strong(paul) <- (~55) [avatar component clause 478]
482. 55 | 14 | ~30 [avatar split clause 381,278,201,478]
502. kind(paul) <- (55) [resolution 479,129]
504. $false <- (~28, 55) [subsumption resolution 502,271]
505. 28 | ~55 [avatar contradiction clause 504]
513. curious(paul) <- (13, 30) [resolution 425,280]
517. strong(paul) <- (11, 13, 30) [resolution 513,190]
519. $false <- (11, 13, 30, ~55) [subsumption resolution 517,480]
520. ~11 | ~13 | ~30 | 55 [avatar contradiction clause 519]
521. $false [avatar sat refutation 204,205,276,282,352,482,505,520]
% SZS output end Proof for 6533449285750169603998613
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not humble and quiet then mary is not generous.
Everyone who is both creative and not curious is not kind or not wise and vice versa.
Everyone who is either not curious or patient is either not calm or not happy and vice versa.
If susan is not kind or generous then someone is both not happy and not brave and vice versa.
If alice is humble or not kind then someone is both not quiet and rich and vice versa.
If someone is not calm then john is wise and vice versa.
Everyone who is not quiet or generous is kind or not old.
If fred is not brave or brave then fred is not curious or funny.
If someone is either rich or not creative then mary is both not patient and not funny and vice versa.
If alice is either not humble or brave then alice is both not funny and not strong.
If john is old or generous then someone is either not tall or happy and vice versa.
Everyone who is both not calm and strong is either patient or wise.
If paul is either not tall or calm then paul is strong or humble.
Everyone who is not creative or generous is either rich or tall and vice versa.
Everyone who is both not happy and calm is both strong and not funny.
If lucy is not curious then someone is both not quiet and not humble.
Alice is strong or not rich.
Someone is both not creative and patient.
Someone is wise or not curious.
Someone is humble or not humble.
Mary is either rich or wise.
Someone is not funny or tall.
Fred is both not calm and funny.
Alice is both not strong and quiet. | Alice is quiet. | entailment | (((~humble(paul)&quiet(paul)))=>(~generous(mary)))&
(![X]:((creative(X)&~curious(X))<=>(~kind(X)|~wise(X))))&
(![X]:((~curious(X)<~>patient(X))<=>(~calm(X)<~>~happy(X))))&
(((~kind(susan)|generous(susan)))<=>(?[X]:((~happy(X)&~brave(X)))))&
(((humble(alice)|~kind(alice)))<=>(?[X]:((~quiet(X)&rich(X)))))&
((?[X]:(~calm(X)))<=>(wise(john)))&
(![X]:((~quiet(X)|generous(X))=>(kind(X)|~old(X))))&
(((~brave(fred)|brave(fred)))=>((~curious(fred)|funny(fred))))&
((?[X]:((rich(X)<~>~creative(X))))<=>((~patient(mary)&~funny(mary))))&
(((~humble(alice)<~>brave(alice)))=>((~funny(alice)&~strong(alice))))&
(((old(john)|generous(john)))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~calm(X)&strong(X))=>(patient(X)<~>wise(X))))&
(((~tall(paul)<~>calm(paul)))=>((strong(paul)|humble(paul))))&
(![X]:((~creative(X)|generous(X))<=>(rich(X)<~>tall(X))))&
(![X]:((~happy(X)&calm(X))=>(strong(X)&~funny(X))))&
((~curious(lucy))=>(?[X]:((~quiet(X)&~humble(X)))))&
((strong(alice)|~rich(alice)))&
(?[X]:((~creative(X)&patient(X))))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:((humble(X)|~humble(X))))&
((rich(mary)<~>wise(mary)))&
(?[X]:((~funny(X)|tall(X))))&
((~calm(fred)&funny(fred)))&
((~strong(alice)&quiet(alice))) | quiet(alice) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6600295670952855281849229
% SZS output start Proof for 6600295670952855281849229
24. quiet(alice) & ~strong(alice) [input p23]
25. ~quiet(alice) [input hypothesis]
154. quiet(alice) [cnf transformation 24]
155. ~quiet(alice) [cnf transformation 25]
370. $false [subsumption resolution 155,154]
% SZS output end Proof for 6600295670952855281849229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or not happy is kind or not humble.
If someone is not wise then fred is either tall or generous.
If fred is either not generous or creative then someone is not quiet and vice versa.
Everyone who is quiet or not strong is both not creative and not rich and vice versa.
If someone is happy or not strong then susan is strong or not generous.
If someone is humble then someone is not old or wise and vice versa.
Everyone who is both quiet and not patient is either brave or not wise and vice versa.
Everyone who is either not curious or wise is either not rich or not wise and vice versa.
If paul is both rich and patient then someone is either brave or old and vice versa.
Everyone who is patient or funny is not old or funny.
If fred is wise or not generous then someone is both not old and not wise and vice versa.
If someone is not generous then someone is both not happy and quiet.
Everyone who is patient or not curious is both brave and not curious.
If mary is either not old or not quiet then someone is either patient or not quiet and vice versa.
Everyone who is not strong or humble is either happy or not patient and vice versa.
Everyone who is not strong is funny.
Mary is either patient or quiet.
Someone is humble or not curious.
Someone is either not quiet or patient.
Someone is not brave or rich.
Someone is rich.
Lucy is not calm or happy.
Mary is not patient.
Someone is either brave or not wise. | Mary is not rich. | entailment | (![X]:((patient(X)<~>~happy(X))=>(kind(X)|~humble(X))))&
((?[X]:(~wise(X)))=>((tall(fred)<~>generous(fred))))&
(((~generous(fred)<~>creative(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)|~strong(X))<=>(~creative(X)&~rich(X))))&
((?[X]:((happy(X)|~strong(X))))=>((strong(susan)|~generous(susan))))&
((?[X]:(humble(X)))<=>(?[X]:((~old(X)|wise(X)))))&
(![X]:((quiet(X)&~patient(X))<=>(brave(X)<~>~wise(X))))&
(![X]:((~curious(X)<~>wise(X))<=>(~rich(X)<~>~wise(X))))&
(((rich(paul)&patient(paul)))<=>(?[X]:((brave(X)<~>old(X)))))&
(![X]:((patient(X)|funny(X))=>(~old(X)|funny(X))))&
(((wise(fred)|~generous(fred)))<=>(?[X]:((~old(X)&~wise(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((~happy(X)&quiet(X)))))&
(![X]:((patient(X)|~curious(X))=>(brave(X)&~curious(X))))&
(((~old(mary)<~>~quiet(mary)))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
(![X]:((~strong(X)|humble(X))<=>(happy(X)<~>~patient(X))))&
(![X]:(~strong(X)=>funny(X)))&
((patient(mary)<~>quiet(mary)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:(rich(X)))&
((~calm(lucy)|happy(lucy)))&
(~patient(mary))&
(?[X]:((brave(X)<~>~wise(X)))) | ~rich(mary) | [
"p3",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 285009998941619174631871
% SZS output start Proof for 285009998941619174631871
4. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (~rich(X0) & ~creative(X0))) [input p3]
17. patient(mary) <~> quiet(mary) [input p16]
23. ~patient(mary) [input p22]
25. rich(mary) [input hypothesis]
43. ! [X0] : (((~strong(X0) | quiet(X0)) | (rich(X0) | creative(X0))) & ((~rich(X0) & ~creative(X0)) | (strong(X0) & ~quiet(X0)))) [nnf transformation 4]
44. ! [X0] : ((~strong(X0) | quiet(X0) | rich(X0) | creative(X0)) & ((~rich(X0) & ~creative(X0)) | (strong(X0) & ~quiet(X0)))) [flattening 43]
72. (~quiet(mary) | ~patient(mary)) & (quiet(mary) | patient(mary)) [nnf transformation 17]
93. ~rich(X0) | ~quiet(X0) [cnf transformation 44]
149. quiet(mary) | patient(mary) [cnf transformation 72]
156. ~patient(mary) [cnf transformation 23]
159. rich(mary) [cnf transformation 25]
303. 32 <=> quiet(mary) [avatar definition]
305. quiet(mary) <- (32) [avatar component clause 303]
326. 36 <=> patient(mary) [avatar definition]
330. 36 | 32 [avatar split clause 149,303,326]
359. ~36 [avatar split clause 156,326]
377. ~quiet(mary) [resolution 93,159]
378. $false <- (32) [subsumption resolution 377,305]
379. ~32 [avatar contradiction clause 378]
380. $false [avatar sat refutation 330,359,379]
% SZS output end Proof for 285009998941619174631871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then lucy is creative and vice versa.
If fred is both not happy and not calm then john is curious or wise and vice versa.
Everyone who is both creative and curious is both happy and tall and vice versa.
Everyone who is either not brave or rich is both not wise and not brave and vice versa.
Everyone who is not tall is not wise or rich.
If alice is either not strong or not kind then fred is both brave and tall and vice versa.
If someone is patient or wise then john is either not strong or not tall.
Everyone who is not curious is generous or not old.
If alice is either brave or not rich then someone is both brave and funny and vice versa.
If alice is curious or generous then someone is both patient and quiet.
Everyone who is wise or rich is patient and vice versa.
If mary is either funny or not patient then lucy is either not tall or kind.
Everyone who is not rich is funny.
Everyone who is either humble or brave is not happy.
If john is either not curious or creative then susan is both calm and tall and vice versa.
If someone is both generous and curious then fred is both calm and not generous and vice versa.
Someone is both not funny and not kind.
Lucy is either not happy or humble.
Someone is both wise and not humble.
Someone is both curious and quiet.
John is not wise.
Fred is both not calm and brave.
Someone is both rich and not humble.
Mary is either kind or creative. | Lucy is curious. | neutral | ((?[X]:(~generous(X)))<=>(creative(lucy)))&
(((~happy(fred)&~calm(fred)))<=>((curious(john)|wise(john))))&
(![X]:((creative(X)&curious(X))<=>(happy(X)&tall(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~wise(X)&~brave(X))))&
(![X]:(~tall(X)=>(~wise(X)|rich(X))))&
(((~strong(alice)<~>~kind(alice)))<=>((brave(fred)&tall(fred))))&
((?[X]:((patient(X)|wise(X))))=>((~strong(john)<~>~tall(john))))&
(![X]:(~curious(X)=>(generous(X)|~old(X))))&
(((brave(alice)<~>~rich(alice)))<=>(?[X]:((brave(X)&funny(X)))))&
(((curious(alice)|generous(alice)))=>(?[X]:((patient(X)&quiet(X)))))&
(![X]:((wise(X)|rich(X))<=>patient(X)))&
(((funny(mary)<~>~patient(mary)))=>((~tall(lucy)<~>kind(lucy))))&
(![X]:(~rich(X)=>funny(X)))&
(![X]:((humble(X)<~>brave(X))=>~happy(X)))&
(((~curious(john)<~>creative(john)))<=>((calm(susan)&tall(susan))))&
((?[X]:((generous(X)&curious(X))))<=>((calm(fred)&~generous(fred))))&
(?[X]:((~funny(X)&~kind(X))))&
((~happy(lucy)<~>humble(lucy)))&
(?[X]:((wise(X)&~humble(X))))&
(?[X]:((curious(X)&quiet(X))))&
(~wise(john))&
((~calm(fred)&brave(fred)))&
(?[X]:((rich(X)&~humble(X))))&
((kind(mary)<~>creative(mary))) | curious(lucy) | [] | null | 0 |
If lucy is not rich or quiet then paul is tall. If someone is not rich or not brave then john is old and vice versa. If alice is funny or not rich then john is wise. If mary is not wise then john is both curious and brave. Everyone who is both not generous and wise is either brave or not brave and vice versa. If paul is both creative and not wise then someone is either not calm or funny. If alice is either tall or not creative then someone is not kind or strong and vice versa. If fred is both happy and not generous then someone is not funny and vice versa. Everyone who is humble or generous is both not humble and funny. Everyone who is not patient or not brave is not strong. Everyone who is either wise or funny is either happy or brave and vice versa. Everyone who is curious or funny is wise and vice versa. Everyone who is curious is rich. Everyone who is both not funny and creative is not generous or not tall and vice versa. Everyone who is either not brave or not old is either tall or brave and vice versa. Everyone who is either not quiet or not generous is both not old and not creative and vice versa. Someone is rich or not creative. Alice is either strong or tall. Someone is wise or creative. Someone is both not old and creative. Mary is both not calm and not old. Someone is not old or not wise. | Alice is funny. | contradiction | (((~rich(lucy)|quiet(lucy)))=>(tall(paul)))&
((?[X]:((~rich(X)|~brave(X))))<=>(old(john)))&
(((funny(alice)|~rich(alice)))=>(wise(john)))&
((~wise(mary))=>((curious(john)&brave(john))))&
(![X]:((~generous(X)&wise(X))<=>(brave(X)<~>~brave(X))))&
(((creative(paul)&~wise(paul)))=>(?[X]:((~calm(X)<~>funny(X)))))&
(((tall(alice)<~>~creative(alice)))<=>(?[X]:((~kind(X)|strong(X)))))&
(((happy(fred)&~generous(fred)))<=>(?[X]:(~funny(X))))&
(![X]:((humble(X)|generous(X))=>(~humble(X)&funny(X))))&
(![X]:((~patient(X)|~brave(X))=>~strong(X)))&
(![X]:((wise(X)<~>funny(X))<=>(happy(X)<~>brave(X))))&
(![X]:((curious(X)|funny(X))<=>wise(X)))&
(![X]:(curious(X)=>rich(X)))&
(![X]:((~funny(X)&creative(X))<=>(~generous(X)|~tall(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(tall(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~old(X)&~creative(X))))&
(?[X]:((rich(X)|~creative(X))))&
((strong(alice)<~>tall(alice)))&
(?[X]:((wise(X)|creative(X))))&
(?[X]:((~old(X)&creative(X))))&
((~calm(mary)&~old(mary)))&
(?[X]:((~old(X)|~wise(X)))) | funny(alice) | [
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2513290216156039010106753
% SZS output start Proof for 2513290216156039010106753
5. ! [X0] : ((wise(X0) & ~generous(X0)) <=> (brave(X0) <~> ~brave(X0))) [input p4]
14. ! [X0] : ((creative(X0) & ~funny(X0)) <=> (~tall(X0) | ~generous(X0))) [input p13]
23. funny(alice) [input hypothesis]
38. ! [X0] : (((wise(X0) & ~generous(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (~wise(X0) | generous(X0)))) [nnf transformation 5]
39. ! [X0] : (((wise(X0) & ~generous(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | ~wise(X0) | generous(X0))) [flattening 38]
55. ! [X0] : (((creative(X0) & ~funny(X0)) | (tall(X0) & generous(X0))) & ((~tall(X0) | ~generous(X0)) | (~creative(X0) | funny(X0)))) [nnf transformation 14]
56. ! [X0] : (((creative(X0) & ~funny(X0)) | (tall(X0) & generous(X0))) & (~tall(X0) | ~generous(X0) | ~creative(X0) | funny(X0))) [flattening 55]
80. ~generous(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 39]
81. ~generous(X0) | brave(X0) | brave(X0) [cnf transformation 39]
110. ~funny(X0) | generous(X0) [cnf transformation 56]
137. funny(alice) [cnf transformation 23]
142. ~generous(X0) | ~brave(X0) [duplicate literal removal 80]
143. ~generous(X0) | brave(X0) [duplicate literal removal 81]
210. ~generous(X0) [subsumption resolution 142,143]
259. ~funny(X0) [subsumption resolution 110,210]
272. $false [subsumption resolution 137,259]
% SZS output end Proof for 2513290216156039010106753
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not humble is either brave or not humble and vice versa.
Everyone who is not wise or not quiet is kind.
Everyone who is both not generous and not funny is either wise or humble and vice versa.
If john is both curious and not strong then lucy is calm or strong and vice versa.
Everyone who is not calm is both not happy and not wise and vice versa.
Everyone who is not rich or quiet is not rich or old.
Everyone who is both not old and patient is either not kind or generous.
If someone is tall or old then someone is either not funny or curious.
Everyone who is not strong or not calm is both calm and quiet.
If fred is both not curious and patient then lucy is either not brave or generous.
Everyone who is either rich or wise is curious.
If fred is patient or not humble then susan is both not curious and not funny and vice versa.
Everyone who is both generous and wise is not quiet or not generous and vice versa.
If someone is not calm or calm then mary is not strong and vice versa.
If fred is not generous then fred is either not tall or patient and vice versa.
Someone is not brave or happy.
Susan is not patient.
Fred is calm.
Alice is both kind and humble.
Someone is both kind and patient. | Susan is not curious. | neutral | (![X]:((~tall(X)<~>~humble(X))<=>(brave(X)<~>~humble(X))))&
(![X]:((~wise(X)|~quiet(X))=>kind(X)))&
(![X]:((~generous(X)&~funny(X))<=>(wise(X)<~>humble(X))))&
(((curious(john)&~strong(john)))<=>((calm(lucy)|strong(lucy))))&
(![X]:(~calm(X)<=>(~happy(X)&~wise(X))))&
(![X]:((~rich(X)|quiet(X))=>(~rich(X)|old(X))))&
(![X]:((~old(X)&patient(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((tall(X)|old(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~strong(X)|~calm(X))=>(calm(X)&quiet(X))))&
(((~curious(fred)&patient(fred)))=>((~brave(lucy)<~>generous(lucy))))&
(![X]:((rich(X)<~>wise(X))=>curious(X)))&
(((patient(fred)|~humble(fred)))<=>((~curious(susan)&~funny(susan))))&
(![X]:((generous(X)&wise(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(~strong(mary)))&
((~generous(fred))<=>((~tall(fred)<~>patient(fred))))&
(?[X]:((~brave(X)|happy(X))))&
(~patient(susan))&
(calm(fred))&
((kind(alice)&humble(alice)))&
(?[X]:((kind(X)&patient(X)))) | ~curious(susan) | [] | null | 0 |
Everyone who is not funny or not old is generous and vice versa. If fred is either humble or not humble then someone is both quiet and wise. Everyone who is either old or not creative is both funny and not strong and vice versa. Everyone who is either not creative or creative is either happy or not wise. If someone is either happy or calm then susan is humble or not rich. Everyone who is tall is either not tall or funny and vice versa. If fred is brave then john is humble and vice versa. If fred is calm then someone is both kind and not tall. If someone is rich then susan is either not old or not rich and vice versa. Everyone who is kind is both strong and not tall. Everyone who is quiet is either not happy or brave. If alice is not rich then mary is both not creative and happy. Everyone who is creative or brave is both not kind and happy. If someone is both not funny and tall then fred is either tall or happy and vice versa. Everyone who is both quiet and humble is wise. Everyone who is not patient is either wise or not curious. Someone is both curious and creative. Lucy is either old or curious. Susan is not wise. Lucy is patient. Alice is either not calm or happy. Paul is both rich and curious. Fred is funny or brave. Mary is not patient or humble. | John is not humble. | neutral | (![X]:((~funny(X)|~old(X))<=>generous(X)))&
(((humble(fred)<~>~humble(fred)))=>(?[X]:((quiet(X)&wise(X)))))&
(![X]:((old(X)<~>~creative(X))<=>(funny(X)&~strong(X))))&
(![X]:((~creative(X)<~>creative(X))=>(happy(X)<~>~wise(X))))&
((?[X]:((happy(X)<~>calm(X))))=>((humble(susan)|~rich(susan))))&
(![X]:(tall(X)<=>(~tall(X)<~>funny(X))))&
((brave(fred))<=>(humble(john)))&
((calm(fred))=>(?[X]:((kind(X)&~tall(X)))))&
((?[X]:(rich(X)))<=>((~old(susan)<~>~rich(susan))))&
(![X]:(kind(X)=>(strong(X)&~tall(X))))&
(![X]:(quiet(X)=>(~happy(X)<~>brave(X))))&
((~rich(alice))=>((~creative(mary)&happy(mary))))&
(![X]:((creative(X)|brave(X))=>(~kind(X)&happy(X))))&
((?[X]:((~funny(X)&tall(X))))<=>((tall(fred)<~>happy(fred))))&
(![X]:((quiet(X)&humble(X))=>wise(X)))&
(![X]:(~patient(X)=>(wise(X)<~>~curious(X))))&
(?[X]:((curious(X)&creative(X))))&
((old(lucy)<~>curious(lucy)))&
(~wise(susan))&
(patient(lucy))&
((~calm(alice)<~>happy(alice)))&
((rich(paul)&curious(paul)))&
((funny(fred)|brave(fred)))&
((~patient(mary)|humble(mary))) | ~humble(john) | [] | null | 0 |
If someone is not calm then someone is either not calm or tall. If someone is old or not patient then someone is both not old and humble. Everyone who is not patient or not generous is either not calm or not wise. If susan is generous or not strong then someone is not funny. If someone is either not patient or not curious then someone is both wise and not calm and vice versa. If mary is both not kind and not old then someone is either not kind or strong and vice versa. Everyone who is either patient or not kind is old and vice versa. Everyone who is not funny is either not tall or not brave and vice versa. Everyone who is both wise and not patient is both humble and generous and vice versa. If someone is not old then someone is either not wise or not brave. If someone is not calm or not patient then lucy is both kind and not old and vice versa. Everyone who is either brave or humble is either not creative or happy and vice versa. If someone is not rich or not tall then someone is wise or not creative and vice versa. Everyone who is humble is brave or humble. Everyone who is both not curious and not old is rich or calm. Everyone who is either not patient or not generous is either funny or not quiet. Lucy is both not creative and not quiet. Someone is not wise. Someone is calm or not tall. Someone is both not wise and kind. Someone is funny or quiet. John is both not curious and not strong. John is not calm or not funny. | Susan is kind. | neutral | ((?[X]:(~calm(X)))=>(?[X]:((~calm(X)<~>tall(X)))))&
((?[X]:((old(X)|~patient(X))))=>(?[X]:((~old(X)&humble(X)))))&
(![X]:((~patient(X)|~generous(X))=>(~calm(X)<~>~wise(X))))&
(((generous(susan)|~strong(susan)))=>(?[X]:(~funny(X))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:((wise(X)&~calm(X)))))&
(((~kind(mary)&~old(mary)))<=>(?[X]:((~kind(X)<~>strong(X)))))&
(![X]:((patient(X)<~>~kind(X))<=>old(X)))&
(![X]:(~funny(X)<=>(~tall(X)<~>~brave(X))))&
(![X]:((wise(X)&~patient(X))<=>(humble(X)&generous(X))))&
((?[X]:(~old(X)))=>(?[X]:((~wise(X)<~>~brave(X)))))&
((?[X]:((~calm(X)|~patient(X))))<=>((kind(lucy)&~old(lucy))))&
(![X]:((brave(X)<~>humble(X))<=>(~creative(X)<~>happy(X))))&
((?[X]:((~rich(X)|~tall(X))))<=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:(humble(X)=>(brave(X)|humble(X))))&
(![X]:((~curious(X)&~old(X))=>(rich(X)|calm(X))))&
(![X]:((~patient(X)<~>~generous(X))=>(funny(X)<~>~quiet(X))))&
((~creative(lucy)&~quiet(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:((calm(X)|~tall(X))))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((funny(X)|quiet(X))))&
((~curious(john)&~strong(john)))&
((~calm(john)|~funny(john))) | kind(susan) | [] | null | 0 |
If someone is both not humble and not creative then lucy is not old or kind and vice versa. If paul is not patient or not curious then someone is calm or brave and vice versa. If someone is happy or not funny then someone is both not old and not humble. If someone is both brave and not curious then someone is both generous and not strong. If someone is both not kind and not strong then susan is either not creative or strong. If lucy is not curious or not calm then paul is not happy. Everyone who is both funny and not strong is either not creative or happy and vice versa. If susan is patient then someone is not old. If fred is not happy or not old then lucy is either rich or creative and vice versa. If someone is both not humble and not calm then lucy is funny or not creative and vice versa. Everyone who is happy or kind is both not tall and not funny and vice versa. If susan is either not calm or humble then alice is either not rich or strong and vice versa. Everyone who is not brave is not wise and vice versa. Everyone who is not creative is creative. Everyone who is old or humble is not quiet. Everyone who is kind or humble is either not wise or not patient and vice versa. Someone is not quiet or humble. Paul is not patient. Lucy is humble. Paul is either not quiet or not funny. Susan is funny. Someone is either generous or not kind. Alice is either patient or not generous. Alice is both humble and tall. | Lucy is creative. | entailment | ((?[X]:((~humble(X)&~creative(X))))<=>((~old(lucy)|kind(lucy))))&
(((~patient(paul)|~curious(paul)))<=>(?[X]:((calm(X)|brave(X)))))&
((?[X]:((happy(X)|~funny(X))))=>(?[X]:((~old(X)&~humble(X)))))&
((?[X]:((brave(X)&~curious(X))))=>(?[X]:((generous(X)&~strong(X)))))&
((?[X]:((~kind(X)&~strong(X))))=>((~creative(susan)<~>strong(susan))))&
(((~curious(lucy)|~calm(lucy)))=>(~happy(paul)))&
(![X]:((funny(X)&~strong(X))<=>(~creative(X)<~>happy(X))))&
((patient(susan))=>(?[X]:(~old(X))))&
(((~happy(fred)|~old(fred)))<=>((rich(lucy)<~>creative(lucy))))&
((?[X]:((~humble(X)&~calm(X))))<=>((funny(lucy)|~creative(lucy))))&
(![X]:((happy(X)|kind(X))<=>(~tall(X)&~funny(X))))&
(((~calm(susan)<~>humble(susan)))<=>((~rich(alice)<~>strong(alice))))&
(![X]:(~brave(X)<=>~wise(X)))&
(![X]:(~creative(X)=>creative(X)))&
(![X]:((old(X)|humble(X))=>~quiet(X)))&
(![X]:((kind(X)|humble(X))<=>(~wise(X)<~>~patient(X))))&
(?[X]:((~quiet(X)|humble(X))))&
(~patient(paul))&
(humble(lucy))&
((~quiet(paul)<~>~funny(paul)))&
(funny(susan))&
(?[X]:((generous(X)<~>~kind(X))))&
((patient(alice)<~>~generous(alice)))&
((humble(alice)&tall(alice))) | creative(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8372646262766538325637205
% SZS output start Proof for 8372646262766538325637205
14. ! [X0] : (~creative(X0) => creative(X0)) [input p13]
25. ~creative(lucy) [input hypothesis]
33. ! [X0] : (creative(X0) | creative(X0)) [ennf transformation 14]
128. creative(X0) | creative(X0) [cnf transformation 33]
149. ~creative(lucy) [cnf transformation 25]
150. creative(X0) [duplicate literal removal 128]
366. $false [subsumption resolution 149,150]
% SZS output end Proof for 8372646262766538325637205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not kind is both quiet and not creative and vice versa.
If someone is either quiet or tall then lucy is not rich and vice versa.
Everyone who is both creative and not tall is not quiet or not generous.
If susan is both happy and not tall then alice is rich and vice versa.
If someone is not creative or not wise then lucy is both not curious and patient.
If paul is either not funny or not kind then paul is rich or not creative.
Everyone who is tall or not happy is either curious or wise and vice versa.
Everyone who is both not creative and wise is strong and vice versa.
Everyone who is not funny or not happy is both not rich and not strong and vice versa.
Everyone who is not patient or not quiet is old or calm and vice versa.
Everyone who is happy is both funny and not old.
Everyone who is humble is either strong or not patient.
Everyone who is either not happy or brave is not old or funny and vice versa.
Everyone who is either brave or not old is wise or kind and vice versa.
Everyone who is either funny or creative is both rich and humble and vice versa.
If mary is not generous or not rich then someone is wise.
Susan is both happy and humble.
Alice is both tall and not old.
Someone is not old or not generous.
Fred is rich.
Alice is not generous or not kind.
Paul is curious.
Someone is not humble. | Lucy is patient. | entailment | (![X]:((~calm(X)&~kind(X))<=>(quiet(X)&~creative(X))))&
((?[X]:((quiet(X)<~>tall(X))))<=>(~rich(lucy)))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~tall(susan)))<=>(rich(alice)))&
((?[X]:((~creative(X)|~wise(X))))=>((~curious(lucy)&patient(lucy))))&
(((~funny(paul)<~>~kind(paul)))=>((rich(paul)|~creative(paul))))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)&wise(X))<=>strong(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(old(X)|calm(X))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
(![X]:((funny(X)<~>creative(X))<=>(rich(X)&humble(X))))&
(((~generous(mary)|~rich(mary)))=>(?[X]:(wise(X))))&
((happy(susan)&humble(susan)))&
((tall(alice)&~old(alice)))&
(?[X]:((~old(X)|~generous(X))))&
(rich(fred))&
((~generous(alice)|~kind(alice)))&
(curious(paul))&
(?[X]:(~humble(X))) | patient(lucy) | [
"p4",
"p10",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 441989662527779991489990
% SZS output start Proof for 441989662527779991489990
5. ? [X0] : (~wise(X0) | ~creative(X0)) => (patient(lucy) & ~curious(lucy)) [input p4]
11. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p10]
13. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (funny(X0) | ~old(X0))) [input p12]
14. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> (kind(X0) | wise(X0))) [input p13]
17. humble(susan) & happy(susan) [input p16]
24. ~patient(lucy) [input hypothesis]
27. (patient(lucy) & ~curious(lucy)) | ! [X0] : (wise(X0) & creative(X0)) [ennf transformation 5]
30. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 11]
51. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 13]
52. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 51]
53. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 14]
54. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [flattening 53]
78. patient(lucy) | wise(X0) [cnf transformation 27]
99. ~happy(X0) | funny(X0) [cnf transformation 30]
100. ~old(X0) | ~happy(X0) [cnf transformation 30]
106. brave(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 52]
113. ~brave(X0) | old(X0) | ~wise(X0) [cnf transformation 54]
123. happy(susan) [cnf transformation 17]
132. ~patient(lucy) [cnf transformation 24]
165. 8 <=> happy(susan) [avatar definition]
167. happy(susan) <- (8) [avatar component clause 165]
171. 9 <=> ! [X0] : wise(X0) [avatar definition]
172. wise(X0) <- (9) [avatar component clause 171]
174. 10 <=> patient(lucy) [avatar definition]
177. 9 | 10 [avatar split clause 78,174,171]
206. ~happy(X0) | brave(X0) [subsumption resolution 106,99]
224. 8 [avatar split clause 123,165]
243. ~10 [avatar split clause 132,174]
253. brave(susan) <- (8) [resolution 206,167]
327. old(susan) | ~wise(susan) <- (8) [resolution 113,253]
331. old(susan) <- (8, 9) [subsumption resolution 327,172]
341. ~happy(susan) <- (8, 9) [resolution 331,100]
342. $false <- (8, 9) [subsumption resolution 341,167]
343. ~8 | ~9 [avatar contradiction clause 342]
344. $false [avatar sat refutation 177,224,243,343]
% SZS output end Proof for 441989662527779991489990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not patient then someone is both brave and not patient.
Everyone who is either not strong or not brave is either humble or quiet and vice versa.
Everyone who is either not brave or strong is either not calm or tall and vice versa.
Everyone who is humble is both rich and creative.
If alice is not funny then lucy is not kind or funny and vice versa.
Everyone who is either not kind or not rich is calm or not strong.
If someone is not humble then john is both not humble and not wise and vice versa.
Everyone who is quiet is not curious and vice versa.
If someone is tall or not calm then someone is kind or not brave.
Everyone who is either not funny or not generous is humble or strong and vice versa.
If john is not rich then someone is either not old or patient.
If mary is not rich or curious then alice is either not patient or not funny.
Everyone who is either funny or strong is not patient or curious and vice versa.
If fred is tall or not creative then mary is patient or strong.
Everyone who is both not generous and tall is either quiet or calm and vice versa.
Everyone who is either not funny or tall is both funny and kind.
Someone is either funny or not happy.
Alice is both not quiet and not wise.
Someone is kind or generous.
Someone is both happy and generous.
Someone is not curious.
Someone is either not happy or not rich.
Someone is either not generous or not old.
John is not calm. | Alice is not generous. | contradiction | ((~patient(susan))=>(?[X]:((brave(X)&~patient(X)))))&
(![X]:((~strong(X)<~>~brave(X))<=>(humble(X)<~>quiet(X))))&
(![X]:((~brave(X)<~>strong(X))<=>(~calm(X)<~>tall(X))))&
(![X]:(humble(X)=>(rich(X)&creative(X))))&
((~funny(alice))<=>((~kind(lucy)|funny(lucy))))&
(![X]:((~kind(X)<~>~rich(X))=>(calm(X)|~strong(X))))&
((?[X]:(~humble(X)))<=>((~humble(john)&~wise(john))))&
(![X]:(quiet(X)<=>~curious(X)))&
((?[X]:((tall(X)|~calm(X))))=>(?[X]:((kind(X)|~brave(X)))))&
(![X]:((~funny(X)<~>~generous(X))<=>(humble(X)|strong(X))))&
((~rich(john))=>(?[X]:((~old(X)<~>patient(X)))))&
(((~rich(mary)|curious(mary)))=>((~patient(alice)<~>~funny(alice))))&
(![X]:((funny(X)<~>strong(X))<=>(~patient(X)|curious(X))))&
(((tall(fred)|~creative(fred)))=>((patient(mary)|strong(mary))))&
(![X]:((~generous(X)&tall(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~funny(X)<~>tall(X))=>(funny(X)&kind(X))))&
(?[X]:((funny(X)<~>~happy(X))))&
((~quiet(alice)&~wise(alice)))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((happy(X)&generous(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~happy(X)<~>~rich(X))))&
(?[X]:((~generous(X)<~>~old(X))))&
(~calm(john)) | ~generous(alice) | [
"p1",
"p2",
"p7",
"p9",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 433466525577487467054021
% SZS output start Proof for 433466525577487467054021
2. ! [X0] : ((~strong(X0) <~> ~brave(X0)) <=> (humble(X0) <~> quiet(X0))) [input p1]
3. ! [X0] : ((~brave(X0) <~> strong(X0)) <=> (~calm(X0) <~> tall(X0))) [input p2]
8. ! [X0] : (quiet(X0) <=> ~curious(X0)) [input p7]
10. ! [X0] : ((~funny(X0) <~> ~generous(X0)) <=> (strong(X0) | humble(X0))) [input p9]
13. ! [X0] : ((funny(X0) <~> strong(X0)) <=> (curious(X0) | ~patient(X0))) [input p12]
15. ! [X0] : ((tall(X0) & ~generous(X0)) <=> (quiet(X0) <~> calm(X0))) [input p14]
18. ~wise(alice) & ~quiet(alice) [input p17]
25. ~generous(alice) [input hypothesis]
41. ! [X0] : ((((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0))))) [nnf transformation 2]
42. ! [X0] : ((((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0)))) & (((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0))))) [nnf transformation 3]
51. ! [X0] : ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0))) [nnf transformation 8]
55. ! [X0] : ((((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | (~strong(X0) & ~humble(X0))) & ((strong(X0) | humble(X0)) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0))))) [nnf transformation 10]
56. ! [X0] : ((((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | (~strong(X0) & ~humble(X0))) & (strong(X0) | humble(X0) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0))))) [flattening 55]
61. ! [X0] : ((((~strong(X0) | ~funny(X0)) & (strong(X0) | funny(X0))) | (~curious(X0) & patient(X0))) & ((curious(X0) | ~patient(X0)) | ((funny(X0) | ~strong(X0)) & (strong(X0) | ~funny(X0))))) [nnf transformation 13]
62. ! [X0] : ((((~strong(X0) | ~funny(X0)) & (strong(X0) | funny(X0))) | (~curious(X0) & patient(X0))) & (curious(X0) | ~patient(X0) | ((funny(X0) | ~strong(X0)) & (strong(X0) | ~funny(X0))))) [flattening 61]
63. ! [X0] : (((tall(X0) & ~generous(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~tall(X0) | generous(X0)))) [nnf transformation 15]
64. ! [X0] : (((tall(X0) & ~generous(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | ~tall(X0) | generous(X0))) [flattening 63]
89. ~humble(X0) | strong(X0) | quiet(X0) | brave(X0) [cnf transformation 41]
95. ~brave(X0) | strong(X0) | tall(X0) | calm(X0) [cnf transformation 42]
96. ~tall(X0) | ~brave(X0) | ~calm(X0) | strong(X0) [cnf transformation 42]
109. curious(X0) | quiet(X0) [cnf transformation 51]
113. ~funny(X0) | humble(X0) | strong(X0) | generous(X0) [cnf transformation 56]
117. ~strong(X0) | funny(X0) | generous(X0) [cnf transformation 56]
127. ~curious(X0) | funny(X0) | strong(X0) [cnf transformation 62]
129. ~curious(X0) | ~funny(X0) | ~strong(X0) [cnf transformation 62]
131. ~tall(X0) | quiet(X0) | calm(X0) | generous(X0) [cnf transformation 64]
136. ~calm(X0) | quiet(X0) | tall(X0) [cnf transformation 64]
143. ~quiet(alice) [cnf transformation 18]
154. ~generous(alice) [cnf transformation 25]
175. 5 <=> funny(alice) [avatar definition]
176. funny(alice) <- (5) [avatar component clause 175]
177. ~funny(alice) <- (~5) [avatar component clause 175]
373. funny(X0) | strong(X0) | quiet(X0) [resolution 127,109]
382. ~funny(X0) | ~strong(X0) | quiet(X0) [resolution 129,109]
510. 64 <=> brave(alice) [avatar definition]
512. brave(alice) <- (64) [avatar component clause 510]
514. 65 <=> strong(alice) [avatar definition]
515. ~strong(alice) <- (~65) [avatar component clause 514]
516. strong(alice) <- (65) [avatar component clause 514]
518. 66 <=> calm(alice) [avatar definition]
520. calm(alice) <- (66) [avatar component clause 518]
527. 67 <=> tall(alice) [avatar definition]
528. tall(alice) <- (67) [avatar component clause 527]
529. ~tall(alice) <- (~67) [avatar component clause 527]
578. ~brave(alice) | ~calm(alice) | strong(alice) <- (67) [resolution 528,96]
685. quiet(alice) | calm(alice) | generous(alice) <- (67) [resolution 131,528]
686. calm(alice) | generous(alice) <- (67) [subsumption resolution 685,143]
692. ~brave(alice) | ~calm(alice) <- (~65, 67) [subsumption resolution 578,515]
693. ~66 | ~64 | 65 | ~67 [avatar split clause 692,527,514,510,518]
694. calm(alice) <- (67) [subsumption resolution 686,154]
695. 66 | ~67 [avatar split clause 694,527,518]
720. strong(alice) | quiet(alice) <- (~5) [resolution 373,177]
726. strong(alice) <- (~5) [subsumption resolution 720,143]
727. 65 | 5 [avatar split clause 726,175,514]
736. strong(alice) | tall(alice) | calm(alice) <- (64) [resolution 512,95]
752. funny(alice) | generous(alice) <- (65) [resolution 516,117]
758. funny(alice) <- (65) [subsumption resolution 752,154]
759. 5 | ~65 [avatar split clause 758,514,175]
768. ~strong(alice) | quiet(alice) <- (5) [resolution 176,382]
770. humble(alice) | strong(alice) | generous(alice) <- (5) [resolution 176,113]
776. humble(alice) | strong(alice) <- (5) [subsumption resolution 770,154]
778. 86 <=> humble(alice) [avatar definition]
780. humble(alice) <- (86) [avatar component clause 778]
781. 65 | 86 | ~5 [avatar split clause 776,175,778,514]
784. ~strong(alice) <- (5) [subsumption resolution 768,143]
785. ~65 | ~5 [avatar split clause 784,175,514]
810. strong(alice) | quiet(alice) | brave(alice) <- (86) [resolution 780,89]
854. quiet(alice) | tall(alice) <- (66) [resolution 520,136]
855. tall(alice) <- (66) [subsumption resolution 854,143]
856. $false <- (66, ~67) [subsumption resolution 855,529]
857. ~66 | 67 [avatar contradiction clause 856]
858. tall(alice) | calm(alice) <- (64, ~65) [subsumption resolution 736,515]
859. calm(alice) <- (64, ~65, ~67) [subsumption resolution 858,529]
860. 66 | ~64 | 65 | 67 [avatar split clause 859,527,514,510,518]
861. quiet(alice) | brave(alice) <- (~65, 86) [subsumption resolution 810,515]
862. brave(alice) <- (~65, 86) [subsumption resolution 861,143]
863. 64 | 65 | ~86 [avatar split clause 862,778,514,510]
864. $false [avatar sat refutation 693,695,727,759,781,785,857,860,863]
% SZS output end Proof for 433466525577487467054021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is either not funny or not curious and vice versa.
If someone is both not rich and not tall then someone is both curious and not generous.
If someone is both happy and curious then susan is wise or curious.
Everyone who is happy or curious is either curious or tall and vice versa.
Everyone who is both not calm and old is both funny and brave and vice versa.
Everyone who is either tall or not old is either calm or not wise.
If someone is both not kind and quiet then someone is not funny and vice versa.
Everyone who is brave or funny is not curious.
If someone is both quiet and curious then someone is either not wise or strong.
Everyone who is generous or old is patient or not calm and vice versa.
Everyone who is happy or not old is either not brave or not calm.
Everyone who is either not patient or not creative is not strong and vice versa.
Everyone who is both not calm and kind is both not generous and not funny and vice versa.
Everyone who is not quiet or not strong is not generous.
If susan is not brave or not wise then someone is both not creative and not calm and vice versa.
Everyone who is both not brave and rich is both not brave and not kind and vice versa.
Alice is either not patient or tall.
Paul is not funny.
Someone is wise.
Someone is not quiet or not brave.
Fred is not patient.
Paul is not curious or rich.
Someone is funny or strong.
Paul is not calm or tall. | Susan is wise. | neutral | (![X]:(rich(X)<=>(~funny(X)<~>~curious(X))))&
((?[X]:((~rich(X)&~tall(X))))=>(?[X]:((curious(X)&~generous(X)))))&
((?[X]:((happy(X)&curious(X))))=>((wise(susan)|curious(susan))))&
(![X]:((happy(X)|curious(X))<=>(curious(X)<~>tall(X))))&
(![X]:((~calm(X)&old(X))<=>(funny(X)&brave(X))))&
(![X]:((tall(X)<~>~old(X))=>(calm(X)<~>~wise(X))))&
((?[X]:((~kind(X)&quiet(X))))<=>(?[X]:(~funny(X))))&
(![X]:((brave(X)|funny(X))=>~curious(X)))&
((?[X]:((quiet(X)&curious(X))))=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:((generous(X)|old(X))<=>(patient(X)|~calm(X))))&
(![X]:((happy(X)|~old(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>~strong(X)))&
(![X]:((~calm(X)&kind(X))<=>(~generous(X)&~funny(X))))&
(![X]:((~quiet(X)|~strong(X))=>~generous(X)))&
(((~brave(susan)|~wise(susan)))<=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((~brave(X)&rich(X))<=>(~brave(X)&~kind(X))))&
((~patient(alice)<~>tall(alice)))&
(~funny(paul))&
(?[X]:(wise(X)))&
(?[X]:((~quiet(X)|~brave(X))))&
(~patient(fred))&
((~curious(paul)|rich(paul)))&
(?[X]:((funny(X)|strong(X))))&
((~calm(paul)|tall(paul))) | wise(susan) | [] | null | 0 |
Everyone who is not rich is generous and vice versa.
Everyone who is happy is not strong or not wise.
Everyone who is not tall or not old is kind and vice versa.
If someone is happy then alice is both not tall and not calm.
Everyone who is happy is both not generous and not patient.
Everyone who is not kind or not strong is either calm or rich.
Everyone who is not happy or not tall is both rich and creative and vice versa.
Everyone who is either tall or generous is both rich and not humble.
If mary is not patient or happy then someone is wise.
If someone is either not patient or tall then someone is both generous and patient and vice versa.
Everyone who is not funny or not rich is either quiet or old and vice versa.
Everyone who is not wise or wise is both kind and not tall.
Everyone who is both calm and generous is curious or old and vice versa.
If someone is either not curious or not humble then fred is not creative or not humble.
Everyone who is not quiet is tall and vice versa.
If fred is not funny then someone is quiet or calm.
Someone is both not funny and rich.
Someone is either not calm or wise.
Lucy is wise.
Mary is either generous or creative.
Alice is not funny or not quiet.
Susan is creative.
Someone is not strong. | Lucy is not generous. | entailment | (![X]:(~rich(X)<=>generous(X)))&
(![X]:(happy(X)=>(~strong(X)|~wise(X))))&
(![X]:((~tall(X)|~old(X))<=>kind(X)))&
((?[X]:(happy(X)))=>((~tall(alice)&~calm(alice))))&
(![X]:(happy(X)=>(~generous(X)&~patient(X))))&
(![X]:((~kind(X)|~strong(X))=>(calm(X)<~>rich(X))))&
(![X]:((~happy(X)|~tall(X))<=>(rich(X)&creative(X))))&
(![X]:((tall(X)<~>generous(X))=>(rich(X)&~humble(X))))&
(((~patient(mary)|happy(mary)))=>(?[X]:(wise(X))))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((generous(X)&patient(X)))))&
(![X]:((~funny(X)|~rich(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~wise(X)|wise(X))=>(kind(X)&~tall(X))))&
(![X]:((calm(X)&generous(X))<=>(curious(X)|old(X))))&
((?[X]:((~curious(X)<~>~humble(X))))=>((~creative(fred)|~humble(fred))))&
(![X]:(~quiet(X)<=>tall(X)))&
((~funny(fred))=>(?[X]:((quiet(X)|calm(X)))))&
(?[X]:((~funny(X)&rich(X))))&
(?[X]:((~calm(X)<~>wise(X))))&
(wise(lucy))&
((generous(mary)<~>creative(mary)))&
((~funny(alice)|~quiet(alice)))&
(creative(susan))&
(?[X]:(~strong(X))) | ~generous(lucy) | [
"p0",
"p4",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7464292587096381554559488
% SZS output start Proof for 7464292587096381554559488
1. ! [X0] : (~rich(X0) <=> generous(X0)) [input p0]
5. ! [X0] : (happy(X0) => (~patient(X0) & ~generous(X0))) [input p4]
7. ! [X0] : ((~tall(X0) | ~happy(X0)) <=> (creative(X0) & rich(X0))) [input p6]
10. ? [X0] : (~patient(X0) <~> tall(X0)) <=> ? [X0] : (patient(X0) & generous(X0)) [input p9]
12. ! [X0] : ((wise(X0) | ~wise(X0)) => (~tall(X0) & kind(X0))) [input p11]
24. generous(lucy) [input hypothesis]
25. ? [X0] : (~patient(X0) <~> tall(X0)) <=> ? [X1] : (patient(X1) & generous(X1)) [rectify 10]
32. ! [X0] : ((~patient(X0) & ~generous(X0)) | ~happy(X0)) [ennf transformation 5]
36. ! [X0] : ((~tall(X0) & kind(X0)) | (~wise(X0) & wise(X0))) [ennf transformation 12]
40. ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))) [nnf transformation 1]
42. ! [X0] : (((~tall(X0) | ~happy(X0)) | (~creative(X0) | ~rich(X0))) & ((creative(X0) & rich(X0)) | (tall(X0) & happy(X0)))) [nnf transformation 7]
43. ! [X0] : ((~tall(X0) | ~happy(X0) | ~creative(X0) | ~rich(X0)) & ((creative(X0) & rich(X0)) | (tall(X0) & happy(X0)))) [flattening 42]
47. (? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | ! [X1] : (~patient(X1) | ~generous(X1))) & (? [X1] : (patient(X1) & generous(X1)) | ! [X0] : ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0)))) [nnf transformation 25]
48. (? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | ! [X1] : (~patient(X1) | ~generous(X1))) & (? [X2] : (patient(X2) & generous(X2)) | ! [X3] : ((~patient(X3) | ~tall(X3)) & (tall(X3) | patient(X3)))) [rectify 47]
49. ? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) => ((~tall(sK1) | patient(sK1)) & (tall(sK1) | ~patient(sK1))) [choice axiom]
50. ? [X2] : (patient(X2) & generous(X2)) => (patient(sK2) & generous(sK2)) [choice axiom]
51. (((~tall(sK1) | patient(sK1)) & (tall(sK1) | ~patient(sK1))) | ! [X1] : (~patient(X1) | ~generous(X1))) & ((patient(sK2) & generous(sK2)) | ! [X3] : ((~patient(X3) | ~tall(X3)) & (tall(X3) | patient(X3)))) [skolemisation 48,50,49]
69. ~generous(X0) | ~rich(X0) [cnf transformation 40]
75. ~patient(X0) | ~happy(X0) [cnf transformation 32]
80. happy(X0) | rich(X0) [cnf transformation 43]
91. generous(sK2) | tall(X3) | patient(X3) [cnf transformation 51]
93. patient(sK2) | tall(X3) | patient(X3) [cnf transformation 51]
95. tall(sK1) | ~patient(sK1) | ~patient(X1) | ~generous(X1) [cnf transformation 51]
105. ~tall(X0) | wise(X0) [cnf transformation 36]
106. ~tall(X0) | ~wise(X0) [cnf transformation 36]
127. generous(lucy) [cnf transformation 24]
156. 7 <=> ! [X1] : (~patient(X1) | ~generous(X1)) [avatar definition]
157. ~patient(X1) | ~generous(X1) <- (7) [avatar component clause 156]
159. 8 <=> patient(sK1) [avatar definition]
160. ~patient(sK1) <- (~8) [avatar component clause 159]
163. 9 <=> tall(sK1) [avatar definition]
164. tall(sK1) <- (9) [avatar component clause 163]
167. 7 | ~8 | 9 [avatar split clause 95,163,159,156]
172. 11 <=> patient(sK2) [avatar definition]
174. patient(sK2) <- (11) [avatar component clause 172]
177. 12 <=> ! [X3] : (tall(X3) | patient(X3)) [avatar definition]
178. tall(X3) | patient(X3) <- (12) [avatar component clause 177]
179. 12 | 11 [avatar split clause 93,172,177]
181. 13 <=> generous(sK2) [avatar definition]
183. generous(sK2) <- (13) [avatar component clause 181]
185. 12 | 13 [avatar split clause 91,181,177]
186. ~tall(X0) [subsumption resolution 105,106]
226. patient(X3) <- (12) [subsumption resolution 178,186]
227. $false <- (~8, 12) [subsumption resolution 160,226]
228. 8 | ~12 [avatar contradiction clause 227]
229. ~generous(X1) <- (7, 12) [subsumption resolution 157,226]
230. $false <- (7, 12) [resolution 229,127]
233. ~7 | ~12 [avatar contradiction clause 230]
234. $false <- (9) [subsumption resolution 164,186]
235. ~9 [avatar contradiction clause 234]
239. ~rich(sK2) <- (13) [resolution 69,183]
240. ~happy(sK2) <- (11) [resolution 75,174]
243. rich(sK2) <- (11) [resolution 240,80]
244. $false <- (11, 13) [subsumption resolution 243,239]
245. ~11 | ~13 [avatar contradiction clause 244]
246. $false [avatar sat refutation 167,179,185,228,233,235,245]
% SZS output end Proof for 7464292587096381554559488
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not funny and not patient then someone is either tall or not generous and vice versa.
If susan is not rich then someone is either not strong or humble and vice versa.
Everyone who is either not brave or not funny is both brave and not tall and vice versa.
Everyone who is either not humble or strong is either not old or not quiet and vice versa.
If someone is humble or rich then someone is either wise or old and vice versa.
If lucy is not wise then someone is either not old or not tall and vice versa.
If someone is not rich then someone is both tall and patient.
Everyone who is not old or not wise is kind.
If someone is old then someone is both rich and strong and vice versa.
Everyone who is either not tall or not wise is strong.
Everyone who is curious or quiet is tall and vice versa.
If fred is either not strong or not tall then someone is either humble or strong.
Everyone who is wise is either not funny or not curious.
Everyone who is either not humble or not generous is wise and vice versa.
Everyone who is either quiet or happy is both humble and not patient and vice versa.
If fred is patient then john is either patient or humble and vice versa.
Someone is both funny and not old.
Susan is both not strong and humble.
Someone is either not tall or rich.
Someone is both generous and curious.
Mary is both happy and wise.
John is either not humble or wise.
Alice is funny or not wise. | Fred is funny. | contradiction | (((~funny(fred)&~patient(fred)))<=>(?[X]:((tall(X)<~>~generous(X)))))&
((~rich(susan))<=>(?[X]:((~strong(X)<~>humble(X)))))&
(![X]:((~brave(X)<~>~funny(X))<=>(brave(X)&~tall(X))))&
(![X]:((~humble(X)<~>strong(X))<=>(~old(X)<~>~quiet(X))))&
((?[X]:((humble(X)|rich(X))))<=>(?[X]:((wise(X)<~>old(X)))))&
((~wise(lucy))<=>(?[X]:((~old(X)<~>~tall(X)))))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)&patient(X)))))&
(![X]:((~old(X)|~wise(X))=>kind(X)))&
((?[X]:(old(X)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((~tall(X)<~>~wise(X))=>strong(X)))&
(![X]:((curious(X)|quiet(X))<=>tall(X)))&
(((~strong(fred)<~>~tall(fred)))=>(?[X]:((humble(X)<~>strong(X)))))&
(![X]:(wise(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>wise(X)))&
(![X]:((quiet(X)<~>happy(X))<=>(humble(X)&~patient(X))))&
((patient(fred))<=>((patient(john)<~>humble(john))))&
(?[X]:((funny(X)&~old(X))))&
((~strong(susan)&humble(susan)))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:((generous(X)&curious(X))))&
((happy(mary)&wise(mary)))&
((~humble(john)<~>wise(john)))&
((funny(alice)|~wise(alice))) | funny(fred) | [
"p0",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6195838620723941845933971
% SZS output start Proof for 6195838620723941845933971
1. (~patient(fred) & ~funny(fred)) <=> ? [X0] : (tall(X0) <~> ~generous(X0)) [input p0]
11. ! [X0] : ((quiet(X0) | curious(X0)) <=> tall(X0)) [input p10]
20. ? [X0] : (curious(X0) & generous(X0)) [input p19]
24. funny(fred) [input hypothesis]
33. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) & (? [X0] : ((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (patient(fred) | funny(fred))) [nnf transformation 1]
34. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) & (? [X0] : ((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | patient(fred) | funny(fred)) [flattening 33]
35. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) & (? [X1] : ((generous(X1) | ~tall(X1)) & (~generous(X1) | tall(X1))) | patient(fred) | funny(fred)) [rectify 34]
36. ? [X1] : ((generous(X1) | ~tall(X1)) & (~generous(X1) | tall(X1))) => ((generous(sK0) | ~tall(sK0)) & (~generous(sK0) | tall(sK0))) [choice axiom]
37. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) & (((generous(sK0) | ~tall(sK0)) & (~generous(sK0) | tall(sK0))) | patient(fred) | funny(fred)) [skolemisation 35,36]
63. ! [X0] : (((quiet(X0) | curious(X0)) | ~tall(X0)) & (tall(X0) | (~quiet(X0) & ~curious(X0)))) [nnf transformation 11]
64. ! [X0] : ((quiet(X0) | curious(X0) | ~tall(X0)) & (tall(X0) | (~quiet(X0) & ~curious(X0)))) [flattening 63]
78. ? [X0] : (curious(X0) & generous(X0)) => (curious(sK11) & generous(sK11)) [choice axiom]
79. curious(sK11) & generous(sK11) [skolemisation 20,78]
83. ~funny(fred) | ~generous(X0) | ~tall(X0) [cnf transformation 37]
122. ~curious(X0) | tall(X0) [cnf transformation 64]
151. generous(sK11) [cnf transformation 79]
152. curious(sK11) [cnf transformation 79]
158. funny(fred) [cnf transformation 24]
170. 3 <=> ! [X0] : (~generous(X0) | ~tall(X0)) [avatar definition]
171. ~generous(X0) | ~tall(X0) <- (3) [avatar component clause 170]
174. 4 <=> funny(fred) [avatar definition]
178. 3 | ~4 [avatar split clause 83,174,170]
358. 4 [avatar split clause 158,174]
369. tall(sK11) [resolution 122,152]
372. ~tall(sK11) <- (3) [resolution 171,151]
374. $false <- (3) [subsumption resolution 372,369]
375. ~3 [avatar contradiction clause 374]
376. $false [avatar sat refutation 178,358,375]
% SZS output end Proof for 6195838620723941845933971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or tall is both not rich and kind.
Everyone who is rich is both old and not generous and vice versa.
Everyone who is not old or kind is either patient or not rich.
Everyone who is not strong or not kind is both not strong and quiet and vice versa.
Everyone who is kind is patient.
If lucy is calm or not happy then alice is not strong or rich.
Everyone who is not wise or patient is funny and vice versa.
If someone is old then paul is either not generous or not strong and vice versa.
Everyone who is either happy or not brave is creative.
Everyone who is not funny is brave or not old.
Everyone who is not kind or not wise is both creative and quiet and vice versa.
If someone is not calm or happy then fred is not humble or not quiet and vice versa.
Everyone who is not tall is generous or not quiet.
If someone is both generous and happy then someone is calm and vice versa.
If someone is either creative or happy then john is creative or not creative.
If john is not tall then lucy is either happy or not rich.
Someone is humble.
Someone is either not humble or not brave.
Someone is strong or not patient.
Susan is tall or not rich.
Alice is not strong.
Paul is not funny or not rich.
Someone is not strong or kind. | John is not happy. | neutral | (![X]:((kind(X)|tall(X))=>(~rich(X)&kind(X))))&
(![X]:(rich(X)<=>(old(X)&~generous(X))))&
(![X]:((~old(X)|kind(X))=>(patient(X)<~>~rich(X))))&
(![X]:((~strong(X)|~kind(X))<=>(~strong(X)&quiet(X))))&
(![X]:(kind(X)=>patient(X)))&
(((calm(lucy)|~happy(lucy)))=>((~strong(alice)|rich(alice))))&
(![X]:((~wise(X)|patient(X))<=>funny(X)))&
((?[X]:(old(X)))<=>((~generous(paul)<~>~strong(paul))))&
(![X]:((happy(X)<~>~brave(X))=>creative(X)))&
(![X]:(~funny(X)=>(brave(X)|~old(X))))&
(![X]:((~kind(X)|~wise(X))<=>(creative(X)&quiet(X))))&
((?[X]:((~calm(X)|happy(X))))<=>((~humble(fred)|~quiet(fred))))&
(![X]:(~tall(X)=>(generous(X)|~quiet(X))))&
((?[X]:((generous(X)&happy(X))))<=>(?[X]:(calm(X))))&
((?[X]:((creative(X)<~>happy(X))))=>((creative(john)|~creative(john))))&
((~tall(john))=>((happy(lucy)<~>~rich(lucy))))&
(?[X]:(humble(X)))&
(?[X]:((~humble(X)<~>~brave(X))))&
(?[X]:((strong(X)|~patient(X))))&
((tall(susan)|~rich(susan)))&
(~strong(alice))&
((~funny(paul)|~rich(paul)))&
(?[X]:((~strong(X)|kind(X)))) | ~happy(john) | [] | null | 0 |
Everyone who is either not curious or generous is humble and vice versa.
Everyone who is old is either happy or not creative.
Everyone who is both old and not happy is generous or not rich and vice versa.
If someone is wise then lucy is both creative and happy and vice versa.
Everyone who is either strong or happy is both quiet and not quiet.
If someone is happy then someone is both not strong and not happy.
Everyone who is both funny and not curious is both not rich and funny.
Everyone who is strong is both not wise and creative.
Everyone who is not rich or not quiet is not tall or not old and vice versa.
If someone is not wise then fred is both creative and not funny and vice versa.
If alice is rich or not creative then fred is both not patient and brave and vice versa.
If mary is both tall and not patient then someone is either not strong or not funny.
If john is not patient or not rich then someone is both not kind and kind and vice versa.
If someone is not wise then someone is either not calm or not quiet and vice versa.
If paul is either patient or not kind then someone is both tall and not creative.
Someone is calm.
John is both calm and brave.
Alice is funny.
Mary is either not brave or tall.
Someone is both not kind and humble.
Someone is not tall or not wise.
Paul is not kind or curious.
John is quiet or not strong. | Fred is brave. | entailment | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((old(X)&~happy(X))<=>(generous(X)|~rich(X))))&
((?[X]:(wise(X)))<=>((creative(lucy)&happy(lucy))))&
(![X]:((strong(X)<~>happy(X))=>(quiet(X)&~quiet(X))))&
((?[X]:(happy(X)))=>(?[X]:((~strong(X)&~happy(X)))))&
(![X]:((funny(X)&~curious(X))=>(~rich(X)&funny(X))))&
(![X]:(strong(X)=>(~wise(X)&creative(X))))&
(![X]:((~rich(X)|~quiet(X))<=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(?[X]:(calm(X)))&
((calm(john)&brave(john)))&
(funny(alice))&
((~brave(mary)<~>tall(mary)))&
(?[X]:((~kind(X)&humble(X))))&
(?[X]:((~tall(X)|~wise(X))))&
((~kind(paul)|curious(paul)))&
((quiet(john)|~strong(john))) | brave(fred) | [
"p1",
"p2",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5949577621114698316521827
% SZS output start Proof for 5949577621114698316521827
2. ! [X0] : (old(X0) => (happy(X0) <~> ~creative(X0))) [input p1]
3. ! [X0] : ((~happy(X0) & old(X0)) <=> (~rich(X0) | generous(X0))) [input p2]
11. (~creative(alice) | rich(alice)) <=> (brave(fred) & ~patient(fred)) [input p10]
24. ~brave(fred) [input hypothesis]
29. ! [X0] : ((happy(X0) <~> ~creative(X0)) | ~old(X0)) [ennf transformation 2]
39. ! [X0] : (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ~old(X0)) [nnf transformation 29]
40. ! [X0] : (((~happy(X0) & old(X0)) | (rich(X0) & ~generous(X0))) & ((~rich(X0) | generous(X0)) | (happy(X0) | ~old(X0)))) [nnf transformation 3]
41. ! [X0] : (((~happy(X0) & old(X0)) | (rich(X0) & ~generous(X0))) & (~rich(X0) | generous(X0) | happy(X0) | ~old(X0))) [flattening 40]
58. ((~creative(alice) | rich(alice)) | (~brave(fred) | patient(fred))) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [nnf transformation 11]
59. (~creative(alice) | rich(alice) | ~brave(fred) | patient(fred)) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [flattening 58]
85. ~creative(X0) | happy(X0) | ~old(X0) [cnf transformation 39]
89. rich(X0) | old(X0) [cnf transformation 41]
91. ~happy(X0) | rich(X0) [cnf transformation 41]
114. brave(fred) | ~rich(alice) [cnf transformation 59]
115. brave(fred) | creative(alice) [cnf transformation 59]
143. ~brave(fred) [cnf transformation 24]
202. 13 <=> brave(fred) [avatar definition]
206. 14 <=> rich(alice) [avatar definition]
207. ~rich(alice) <- (~14) [avatar component clause 206]
210. 15 <=> creative(alice) [avatar definition]
211. creative(alice) <- (15) [avatar component clause 210]
214. 15 | 13 [avatar split clause 115,202,210]
215. ~14 | 13 [avatar split clause 114,202,206]
323. ~13 [avatar split clause 143,202]
330. old(alice) <- (~14) [resolution 89,207]
359. happy(alice) | ~old(alice) <- (15) [resolution 85,211]
361. happy(alice) <- (~14, 15) [subsumption resolution 359,330]
372. rich(alice) <- (~14, 15) [resolution 361,91]
374. $false <- (~14, 15) [subsumption resolution 372,207]
375. 14 | ~15 [avatar contradiction clause 374]
376. $false [avatar sat refutation 214,215,323,375]
% SZS output end Proof for 5949577621114698316521827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or not calm then someone is not rich.
If paul is strong then someone is either brave or generous and vice versa.
Everyone who is humble is strong or creative.
Everyone who is kind or happy is either not curious or not patient.
Everyone who is either rich or calm is either quiet or curious and vice versa.
Everyone who is not old or not creative is either wise or funny.
If lucy is wise then mary is either not patient or happy and vice versa.
Everyone who is either not curious or quiet is either old or calm and vice versa.
If john is both strong and patient then someone is calm and vice versa.
If someone is calm or curious then fred is either not humble or not calm and vice versa.
If someone is both tall and not strong then someone is both calm and rich.
If paul is tall then someone is either tall or not humble and vice versa.
Everyone who is both funny and not rich is not wise or not funny and vice versa.
If alice is either calm or not wise then someone is not calm and vice versa.
If someone is not tall then susan is not generous and vice versa.
Everyone who is not rich is old and vice versa.
Mary is either not quiet or not curious.
Someone is either happy or rich.
Someone is not strong.
Paul is both funny and creative.
Susan is either strong or not rich.
Someone is strong.
Someone is either tall or not curious.
Someone is either not calm or not curious. | Lucy is rich. | contradiction | ((?[X]:((~quiet(X)<~>~calm(X))))=>(?[X]:(~rich(X))))&
((strong(paul))<=>(?[X]:((brave(X)<~>generous(X)))))&
(![X]:(humble(X)=>(strong(X)|creative(X))))&
(![X]:((kind(X)|happy(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((rich(X)<~>calm(X))<=>(quiet(X)<~>curious(X))))&
(![X]:((~old(X)|~creative(X))=>(wise(X)<~>funny(X))))&
((wise(lucy))<=>((~patient(mary)<~>happy(mary))))&
(![X]:((~curious(X)<~>quiet(X))<=>(old(X)<~>calm(X))))&
(((strong(john)&patient(john)))<=>(?[X]:(calm(X))))&
((?[X]:((calm(X)|curious(X))))<=>((~humble(fred)<~>~calm(fred))))&
((?[X]:((tall(X)&~strong(X))))=>(?[X]:((calm(X)&rich(X)))))&
((tall(paul))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:((funny(X)&~rich(X))<=>(~wise(X)|~funny(X))))&
(((calm(alice)<~>~wise(alice)))<=>(?[X]:(~calm(X))))&
((?[X]:(~tall(X)))<=>(~generous(susan)))&
(![X]:(~rich(X)<=>old(X)))&
((~quiet(mary)<~>~curious(mary)))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:(~strong(X)))&
((funny(paul)&creative(paul)))&
((strong(susan)<~>~rich(susan)))&
(?[X]:(strong(X)))&
(?[X]:((tall(X)<~>~curious(X))))&
(?[X]:((~calm(X)<~>~curious(X)))) | rich(lucy) | [
"p5",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7065043695292961176352066
% SZS output start Proof for 7065043695292961176352066
6. ! [X0] : ((~creative(X0) | ~old(X0)) => (wise(X0) <~> funny(X0))) [input p5]
13. ! [X0] : ((~rich(X0) & funny(X0)) <=> (~funny(X0) | ~wise(X0))) [input p12]
16. ! [X0] : (~rich(X0) <=> old(X0)) [input p15]
25. rich(lucy) [input hypothesis]
30. ! [X0] : (~old(X0) => (wise(X0) <~> funny(X0))) [pure predicate removal 6]
34. ! [X0] : ((wise(X0) <~> funny(X0)) | old(X0)) [ennf transformation 30]
46. ! [X0] : (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | old(X0)) [nnf transformation 34]
65. ! [X0] : (((~rich(X0) & funny(X0)) | (funny(X0) & wise(X0))) & ((~funny(X0) | ~wise(X0)) | (rich(X0) | ~funny(X0)))) [nnf transformation 13]
66. ! [X0] : (((~rich(X0) & funny(X0)) | (funny(X0) & wise(X0))) & (~funny(X0) | ~wise(X0) | rich(X0) | ~funny(X0))) [flattening 65]
75. ! [X0] : ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0))) [nnf transformation 16]
108. ~funny(X0) | ~wise(X0) | old(X0) [cnf transformation 46]
138. funny(X0) | funny(X0) [cnf transformation 66]
139. ~rich(X0) | wise(X0) [cnf transformation 66]
148. ~old(X0) | ~rich(X0) [cnf transformation 75]
162. rich(lucy) [cnf transformation 25]
164. funny(X0) [duplicate literal removal 138]
208. 11 <=> wise(lucy) [avatar definition]
210. wise(lucy) <- (11) [avatar component clause 208]
378. wise(lucy) [resolution 139,162]
381. 11 [avatar split clause 378,208]
407. ~wise(X1) | old(X1) [resolution 108,164]
587. old(lucy) <- (11) [resolution 407,210]
615. ~rich(lucy) <- (11) [resolution 587,148]
620. $false <- (11) [subsumption resolution 615,162]
621. ~11 [avatar contradiction clause 620]
622. $false [avatar sat refutation 381,621]
% SZS output end Proof for 7065043695292961176352066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is quiet then someone is both not tall and not generous.
Everyone who is humble or not funny is both not humble and quiet and vice versa.
Everyone who is either old or not curious is both quiet and not rich.
If mary is either quiet or patient then someone is strong or wise.
Everyone who is humble or curious is strong or not funny and vice versa.
Everyone who is old or not brave is both funny and not kind and vice versa.
If someone is both not old and not patient then susan is not patient.
Everyone who is not humble or happy is either wise or humble.
Everyone who is both curious and not kind is rich and vice versa.
If john is either curious or not wise then someone is creative and vice versa.
Everyone who is not creative is both old and kind.
Everyone who is generous or not brave is funny and vice versa.
If lucy is either not brave or not quiet then someone is either not funny or tall.
If someone is both not strong and not rich then someone is not quiet or not happy.
If paul is both not rich and kind then someone is either not wise or not brave and vice versa.
If someone is not curious then lucy is both not patient and curious and vice versa.
Susan is patient.
Alice is strong.
Mary is not old or not rich.
Someone is either strong or curious.
Paul is either not creative or not calm.
Someone is calm or not brave.
Lucy is either not creative or brave. | Lucy is old. | contradiction | ((quiet(lucy))=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((humble(X)|~funny(X))<=>(~humble(X)&quiet(X))))&
(![X]:((old(X)<~>~curious(X))=>(quiet(X)&~rich(X))))&
(((quiet(mary)<~>patient(mary)))=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((humble(X)|curious(X))<=>(strong(X)|~funny(X))))&
(![X]:((old(X)|~brave(X))<=>(funny(X)&~kind(X))))&
((?[X]:((~old(X)&~patient(X))))=>(~patient(susan)))&
(![X]:((~humble(X)|happy(X))=>(wise(X)<~>humble(X))))&
(![X]:((curious(X)&~kind(X))<=>rich(X)))&
(((curious(john)<~>~wise(john)))<=>(?[X]:(creative(X))))&
(![X]:(~creative(X)=>(old(X)&kind(X))))&
(![X]:((generous(X)|~brave(X))<=>funny(X)))&
(((~brave(lucy)<~>~quiet(lucy)))=>(?[X]:((~funny(X)<~>tall(X)))))&
((?[X]:((~strong(X)&~rich(X))))=>(?[X]:((~quiet(X)|~happy(X)))))&
(((~rich(paul)&kind(paul)))<=>(?[X]:((~wise(X)<~>~brave(X)))))&
((?[X]:(~curious(X)))<=>((~patient(lucy)&curious(lucy))))&
(patient(susan))&
(strong(alice))&
((~old(mary)|~rich(mary)))&
(?[X]:((strong(X)<~>curious(X))))&
((~creative(paul)<~>~calm(paul)))&
(?[X]:((calm(X)|~brave(X))))&
((~creative(lucy)<~>brave(lucy))) | old(lucy) | [
"p1",
"p2",
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7851883599974136642168454
% SZS output start Proof for 7851883599974136642168454
2. ! [X0] : ((~funny(X0) | humble(X0)) <=> (quiet(X0) & ~humble(X0))) [input p1]
3. ! [X0] : ((old(X0) <~> ~curious(X0)) => (~rich(X0) & quiet(X0))) [input p2]
6. ! [X0] : ((~brave(X0) | old(X0)) <=> (~kind(X0) & funny(X0))) [input p5]
16. ? [X0] : ~curious(X0) <=> (curious(lucy) & ~patient(lucy)) [input p15]
24. old(lucy) [input hypothesis]
29. ! [X0] : ((~rich(X0) & quiet(X0)) | (old(X0) <=> ~curious(X0))) [ennf transformation 3]
37. ! [X0] : (((~funny(X0) | humble(X0)) | (~quiet(X0) | humble(X0))) & ((quiet(X0) & ~humble(X0)) | (funny(X0) & ~humble(X0)))) [nnf transformation 2]
38. ! [X0] : ((~funny(X0) | humble(X0) | ~quiet(X0) | humble(X0)) & ((quiet(X0) & ~humble(X0)) | (funny(X0) & ~humble(X0)))) [flattening 37]
39. ! [X0] : ((~rich(X0) & quiet(X0)) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0)))) [nnf transformation 29]
45. ! [X0] : (((~brave(X0) | old(X0)) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | (brave(X0) & ~old(X0)))) [nnf transformation 6]
46. ! [X0] : ((~brave(X0) | old(X0) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | (brave(X0) & ~old(X0)))) [flattening 45]
64. (? [X0] : ~curious(X0) | (~curious(lucy) | patient(lucy))) & ((curious(lucy) & ~patient(lucy)) | ! [X0] : curious(X0)) [nnf transformation 16]
65. (? [X0] : ~curious(X0) | ~curious(lucy) | patient(lucy)) & ((curious(lucy) & ~patient(lucy)) | ! [X0] : curious(X0)) [flattening 64]
66. (? [X0] : ~curious(X0) | ~curious(lucy) | patient(lucy)) & ((curious(lucy) & ~patient(lucy)) | ! [X1] : curious(X1)) [rectify 65]
67. ? [X0] : ~curious(X0) => ~curious(sK5) [choice axiom]
68. (~curious(sK5) | ~curious(lucy) | patient(lucy)) & ((curious(lucy) & ~patient(lucy)) | ! [X1] : curious(X1)) [skolemisation 66,67]
78. ~humble(X0) | ~humble(X0) [cnf transformation 38]
82. ~funny(X0) | humble(X0) | ~quiet(X0) | humble(X0) [cnf transformation 38]
83. ~curious(X0) | quiet(X0) | ~old(X0) [cnf transformation 39]
93. ~old(X0) | funny(X0) [cnf transformation 46]
124. curious(lucy) | curious(X1) [cnf transformation 68]
136. old(lucy) [cnf transformation 24]
138. ~humble(X0) [duplicate literal removal 78]
139. ~funny(X0) | humble(X0) | ~quiet(X0) [duplicate literal removal 82]
141. 1 <=> quiet(lucy) [avatar definition]
142. quiet(lucy) <- (1) [avatar component clause 141]
143. ~quiet(lucy) <- (~1) [avatar component clause 141]
241. 21 <=> curious(lucy) [avatar definition]
242. curious(lucy) <- (21) [avatar component clause 241]
243. ~curious(lucy) <- (~21) [avatar component clause 241]
250. 23 <=> ! [X1] : curious(X1) [avatar definition]
251. curious(X1) <- (23) [avatar component clause 250]
252. 23 | 21 [avatar split clause 124,241,250]
295. funny(lucy) [resolution 93,136]
318. quiet(lucy) | ~old(lucy) <- (21) [resolution 83,242]
322. ~old(lucy) <- (~1, 21) [subsumption resolution 318,143]
323. $false <- (~1, 21) [subsumption resolution 322,136]
324. 1 | ~21 [avatar contradiction clause 323]
352. $false <- (~21, 23) [subsumption resolution 243,251]
353. 21 | ~23 [avatar contradiction clause 352]
395. humble(lucy) | ~quiet(lucy) [resolution 139,295]
398. ~quiet(lucy) [subsumption resolution 395,138]
399. $false <- (1) [subsumption resolution 398,142]
400. ~1 [avatar contradiction clause 399]
403. $false [avatar sat refutation 252,324,353,400]
% SZS output end Proof for 7851883599974136642168454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not patient is not patient or not rich and vice versa.
If someone is happy then mary is both not kind and not brave and vice versa.
If john is not rich then someone is not humble or not strong.
Everyone who is happy is not strong or not humble and vice versa.
If someone is both not calm and not kind then susan is both not brave and curious and vice versa.
If someone is either humble or not old then someone is both not generous and happy.
If someone is either not wise or not brave then someone is both not quiet and creative.
Everyone who is either not kind or not brave is either quiet or strong.
Everyone who is either not kind or not curious is either not patient or not creative and vice versa.
If lucy is creative then mary is either happy or tall.
Everyone who is not creative is both quiet and not calm and vice versa.
Everyone who is not creative is not humble and vice versa.
Everyone who is both kind and not kind is calm or not old.
Everyone who is either not curious or not generous is either creative or curious and vice versa.
Everyone who is both generous and not tall is both happy and not wise and vice versa.
Everyone who is old is either not humble or kind and vice versa.
Someone is both calm and old.
Lucy is both calm and not tall.
Someone is either not quiet or old.
Someone is either not patient or not humble.
Susan is either not kind or humble.
John is not rich or funny.
Someone is both not happy and not old. | Susan is quiet. | neutral | (![X]:((happy(X)<~>~patient(X))<=>(~patient(X)|~rich(X))))&
((?[X]:(happy(X)))<=>((~kind(mary)&~brave(mary))))&
((~rich(john))=>(?[X]:((~humble(X)|~strong(X)))))&
(![X]:(happy(X)<=>(~strong(X)|~humble(X))))&
((?[X]:((~calm(X)&~kind(X))))<=>((~brave(susan)&curious(susan))))&
((?[X]:((humble(X)<~>~old(X))))=>(?[X]:((~generous(X)&happy(X)))))&
((?[X]:((~wise(X)<~>~brave(X))))=>(?[X]:((~quiet(X)&creative(X)))))&
(![X]:((~kind(X)<~>~brave(X))=>(quiet(X)<~>strong(X))))&
(![X]:((~kind(X)<~>~curious(X))<=>(~patient(X)<~>~creative(X))))&
((creative(lucy))=>((happy(mary)<~>tall(mary))))&
(![X]:(~creative(X)<=>(quiet(X)&~calm(X))))&
(![X]:(~creative(X)<=>~humble(X)))&
(![X]:((kind(X)&~kind(X))=>(calm(X)|~old(X))))&
(![X]:((~curious(X)<~>~generous(X))<=>(creative(X)<~>curious(X))))&
(![X]:((generous(X)&~tall(X))<=>(happy(X)&~wise(X))))&
(![X]:(old(X)<=>(~humble(X)<~>kind(X))))&
(?[X]:((calm(X)&old(X))))&
((calm(lucy)&~tall(lucy)))&
(?[X]:((~quiet(X)<~>old(X))))&
(?[X]:((~patient(X)<~>~humble(X))))&
((~kind(susan)<~>humble(susan)))&
((~rich(john)|funny(john)))&
(?[X]:((~happy(X)&~old(X)))) | quiet(susan) | [] | null | 0 |
If someone is not curious or not kind then mary is strong and vice versa.
Everyone who is either funny or generous is not strong or not old and vice versa.
If someone is not funny then susan is not wise.
Everyone who is kind or strong is either not strong or humble and vice versa.
If someone is either not patient or humble then lucy is either humble or not tall and vice versa.
If alice is tall or not patient then john is not brave.
Everyone who is not old is not generous or funny and vice versa.
If susan is not tall then john is either not curious or funny and vice versa.
Everyone who is both not happy and strong is both rich and strong and vice versa.
If someone is both not patient and not quiet then lucy is both not strong and not rich.
Everyone who is either funny or not tall is patient and vice versa.
If mary is tall or not calm then lucy is not old or not rich and vice versa.
Everyone who is either funny or not strong is not generous or not creative.
Everyone who is wise or generous is not wise or not tall.
Everyone who is kind or not brave is curious or old and vice versa.
If paul is both not humble and not kind then someone is generous.
Alice is funny.
Paul is both curious and strong.
Lucy is both not curious and kind.
Alice is not generous or patient.
John is both calm and happy.
Lucy is either wise or not generous.
Someone is not quiet or strong.
Fred is either not quiet or creative. | Paul is humble. | entailment | ((?[X]:((~curious(X)|~kind(X))))<=>(strong(mary)))&
(![X]:((funny(X)<~>generous(X))<=>(~strong(X)|~old(X))))&
((?[X]:(~funny(X)))=>(~wise(susan)))&
(![X]:((kind(X)|strong(X))<=>(~strong(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>humble(X))))<=>((humble(lucy)<~>~tall(lucy))))&
(((tall(alice)|~patient(alice)))=>(~brave(john)))&
(![X]:(~old(X)<=>(~generous(X)|funny(X))))&
((~tall(susan))<=>((~curious(john)<~>funny(john))))&
(![X]:((~happy(X)&strong(X))<=>(rich(X)&strong(X))))&
((?[X]:((~patient(X)&~quiet(X))))=>((~strong(lucy)&~rich(lucy))))&
(![X]:((funny(X)<~>~tall(X))<=>patient(X)))&
(((tall(mary)|~calm(mary)))<=>((~old(lucy)|~rich(lucy))))&
(![X]:((funny(X)<~>~strong(X))=>(~generous(X)|~creative(X))))&
(![X]:((wise(X)|generous(X))=>(~wise(X)|~tall(X))))&
(![X]:((kind(X)|~brave(X))<=>(curious(X)|old(X))))&
(((~humble(paul)&~kind(paul)))=>(?[X]:(generous(X))))&
(funny(alice))&
((curious(paul)&strong(paul)))&
((~curious(lucy)&kind(lucy)))&
((~generous(alice)|patient(alice)))&
((calm(john)&happy(john)))&
((wise(lucy)<~>~generous(lucy)))&
(?[X]:((~quiet(X)|strong(X))))&
((~quiet(fred)<~>creative(fred))) | humble(paul) | [
"p3",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3320454238010628615186115
% SZS output start Proof for 3320454238010628615186115
4. ! [X0] : ((strong(X0) | kind(X0)) <=> (~strong(X0) <~> humble(X0))) [input p3]
18. strong(paul) & curious(paul) [input p17]
25. ~humble(paul) [input hypothesis]
41. ! [X0] : (((strong(X0) | kind(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | (~strong(X0) & ~kind(X0)))) [nnf transformation 4]
42. ! [X0] : ((strong(X0) | kind(X0) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | (~strong(X0) & ~kind(X0)))) [flattening 41]
75. humble(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 42]
122. strong(paul) [cnf transformation 18]
133. ~humble(paul) [cnf transformation 25]
135. ~strong(X0) | humble(X0) [duplicate literal removal 75]
259. 26 <=> humble(paul) [avatar definition]
260. ~humble(paul) <- (~26) [avatar component clause 259]
305. ~26 [avatar split clause 133,259]
308. humble(paul) [resolution 135,122]
310. $false <- (~26) [subsumption resolution 308,260]
311. 26 [avatar contradiction clause 310]
312. $false [avatar sat refutation 305,311]
% SZS output end Proof for 3320454238010628615186115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not happy or not patient then someone is not calm and vice versa.
If someone is creative then someone is either not humble or patient.
Everyone who is not brave is calm and vice versa.
If someone is generous then someone is both not creative and not wise and vice versa.
If someone is not generous or calm then susan is both not happy and not generous and vice versa.
If paul is not funny then someone is either funny or calm and vice versa.
Everyone who is wise is not wise or not quiet and vice versa.
If fred is either not rich or not strong then someone is not creative.
Everyone who is either funny or not funny is calm and vice versa.
If someone is happy or not funny then lucy is not patient or not generous.
If someone is not rich then someone is both strong and funny and vice versa.
If someone is not funny or wise then someone is both not patient and rich.
If someone is either not old or not tall then lucy is not kind.
Everyone who is both happy and humble is not old.
Everyone who is either not funny or happy is not calm or tall and vice versa.
If paul is both not curious and not humble then lucy is either funny or brave.
Someone is both not tall and not quiet.
Someone is both funny and humble.
Someone is quiet or creative.
Lucy is wise or not funny.
Someone is either curious or not strong.
Someone is not creative or not calm.
Someone is not kind or not strong. | Susan is not brave. | entailment | (((~happy(alice)<~>~patient(alice)))<=>(?[X]:(~calm(X))))&
((?[X]:(creative(X)))=>(?[X]:((~humble(X)<~>patient(X)))))&
(![X]:(~brave(X)<=>calm(X)))&
((?[X]:(generous(X)))<=>(?[X]:((~creative(X)&~wise(X)))))&
((?[X]:((~generous(X)|calm(X))))<=>((~happy(susan)&~generous(susan))))&
((~funny(paul))<=>(?[X]:((funny(X)<~>calm(X)))))&
(![X]:(wise(X)<=>(~wise(X)|~quiet(X))))&
(((~rich(fred)<~>~strong(fred)))=>(?[X]:(~creative(X))))&
(![X]:((funny(X)<~>~funny(X))<=>calm(X)))&
((?[X]:((happy(X)|~funny(X))))=>((~patient(lucy)|~generous(lucy))))&
((?[X]:(~rich(X)))<=>(?[X]:((strong(X)&funny(X)))))&
((?[X]:((~funny(X)|wise(X))))=>(?[X]:((~patient(X)&rich(X)))))&
((?[X]:((~old(X)<~>~tall(X))))=>(~kind(lucy)))&
(![X]:((happy(X)&humble(X))=>~old(X)))&
(![X]:((~funny(X)<~>happy(X))<=>(~calm(X)|tall(X))))&
(((~curious(paul)&~humble(paul)))=>((funny(lucy)<~>brave(lucy))))&
(?[X]:((~tall(X)&~quiet(X))))&
(?[X]:((funny(X)&humble(X))))&
(?[X]:((quiet(X)|creative(X))))&
((wise(lucy)|~funny(lucy)))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~creative(X)|~calm(X))))&
(?[X]:((~kind(X)|~strong(X)))) | ~brave(susan) | [
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5914796701005711694366896
% SZS output start Proof for 5914796701005711694366896
3. ! [X0] : (~brave(X0) <=> calm(X0)) [input p2]
9. ! [X0] : ((funny(X0) <~> ~funny(X0)) <=> calm(X0)) [input p8]
24. brave(susan) [input hypothesis]
47. ! [X0] : ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0))) [nnf transformation 3]
67. ! [X0] : ((((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | ~calm(X0)) & (calm(X0) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0))))) [nnf transformation 9]
97. ~brave(X0) | ~calm(X0) [cnf transformation 47]
115. calm(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 67]
116. calm(X0) | funny(X0) | funny(X0) [cnf transformation 67]
145. brave(susan) [cnf transformation 24]
146. calm(X0) | ~funny(X0) [duplicate literal removal 115]
147. calm(X0) | funny(X0) [duplicate literal removal 116]
151. 1 <=> ! [X0] : calm(X0) [avatar definition]
152. calm(X0) <- (1) [avatar component clause 151]
267. calm(X0) [subsumption resolution 146,147]
268. 1 [avatar split clause 267,151]
362. ~calm(susan) [resolution 97,145]
364. $false <- (1) [subsumption resolution 362,152]
365. ~1 [avatar contradiction clause 364]
366. $false [avatar sat refutation 268,365]
% SZS output end Proof for 5914796701005711694366896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not wise is both generous and rich and vice versa. Everyone who is not rich or funny is both not funny and not wise. Everyone who is not rich or tall is happy. Everyone who is patient is both not brave and not quiet. Everyone who is both not rich and not funny is both not kind and not tall. Everyone who is curious or patient is both creative and generous and vice versa. Everyone who is either curious or generous is both happy and calm and vice versa. Everyone who is not rich is either not generous or not old. If someone is both not tall and tall then mary is not generous or not kind. If lucy is both not kind and not wise then someone is either not old or curious and vice versa. If alice is not funny then susan is creative and vice versa. If susan is not funny then fred is either humble or generous. Everyone who is both funny and generous is not old. Everyone who is either happy or funny is wise and vice versa. If someone is not patient then someone is strong and vice versa. Fred is both generous and not wise. Someone is either calm or funny. Someone is either not brave or not humble. Alice is curious. Someone is calm. | Susan is not happy. | neutral | (![X]:((humble(X)|~wise(X))<=>(generous(X)&rich(X))))&
(![X]:((~rich(X)|funny(X))=>(~funny(X)&~wise(X))))&
(![X]:((~rich(X)|tall(X))=>happy(X)))&
(![X]:(patient(X)=>(~brave(X)&~quiet(X))))&
(![X]:((~rich(X)&~funny(X))=>(~kind(X)&~tall(X))))&
(![X]:((curious(X)|patient(X))<=>(creative(X)&generous(X))))&
(![X]:((curious(X)<~>generous(X))<=>(happy(X)&calm(X))))&
(![X]:(~rich(X)=>(~generous(X)<~>~old(X))))&
((?[X]:((~tall(X)&tall(X))))=>((~generous(mary)|~kind(mary))))&
(((~kind(lucy)&~wise(lucy)))<=>(?[X]:((~old(X)<~>curious(X)))))&
((~funny(alice))<=>(creative(susan)))&
((~funny(susan))=>((humble(fred)<~>generous(fred))))&
(![X]:((funny(X)&generous(X))=>~old(X)))&
(![X]:((happy(X)<~>funny(X))<=>wise(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(strong(X))))&
((generous(fred)&~wise(fred)))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:((~brave(X)<~>~humble(X))))&
(curious(alice))&
(?[X]:(calm(X))) | ~happy(susan) | [] | null | 0 |
If someone is both humble and generous then mary is both brave and not quiet and vice versa. Everyone who is not strong is not wise and vice versa. Everyone who is not quiet or not happy is both creative and not funny. If someone is both quiet and not patient then fred is not humble. Everyone who is both creative and tall is not kind or not happy and vice versa. Everyone who is generous or not quiet is both not patient and wise. If lucy is funny or not creative then someone is either not curious or not brave and vice versa. Everyone who is either creative or rich is not funny or old and vice versa. Everyone who is either not tall or not kind is both not strong and not patient and vice versa. If susan is both curious and generous then someone is curious and vice versa. Everyone who is both generous and not humble is not strong and vice versa. Everyone who is either creative or old is both tall and humble and vice versa. Everyone who is either strong or creative is both generous and curious. If someone is either not wise or not rich then someone is rich or not funny. Someone is not happy. Someone is not quiet or not old. Mary is either not patient or not wise. Someone is not funny or kind. Alice is strong. | Lucy is kind. | entailment | ((?[X]:((humble(X)&generous(X))))<=>((brave(mary)&~quiet(mary))))&
(![X]:(~strong(X)<=>~wise(X)))&
(![X]:((~quiet(X)|~happy(X))=>(creative(X)&~funny(X))))&
((?[X]:((quiet(X)&~patient(X))))=>(~humble(fred)))&
(![X]:((creative(X)&tall(X))<=>(~kind(X)|~happy(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
((?[X]:((~wise(X)<~>~rich(X))))=>(?[X]:((rich(X)|~funny(X)))))&
(?[X]:(~happy(X)))&
(?[X]:((~quiet(X)|~old(X))))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X))))&
(strong(alice)) | kind(lucy) | [
"p1",
"p4",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 881358663091548716925678
% SZS output start Proof for 881358663091548716925678
2. ! [X0] : (~strong(X0) <=> ~wise(X0)) [input p1]
5. ! [X0] : ((tall(X0) & creative(X0)) <=> (~happy(X0) | ~kind(X0))) [input p4]
6. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p5]
9. ! [X0] : ((~tall(X0) <~> ~kind(X0)) <=> (~patient(X0) & ~strong(X0))) [input p8]
11. ! [X0] : ((~humble(X0) & generous(X0)) <=> ~strong(X0)) [input p10]
20. ~kind(lucy) [input hypothesis]
24. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 6]
32. ! [X0] : ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0))) [nnf transformation 2]
33. ! [X0] : (((tall(X0) & creative(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~tall(X0) | ~creative(X0)))) [nnf transformation 5]
34. ! [X0] : (((tall(X0) & creative(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~tall(X0) | ~creative(X0))) [flattening 33]
42. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [nnf transformation 9]
43. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [flattening 42]
49. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 11]
50. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | humble(X0) | ~generous(X0))) [flattening 49]
69. ~wise(X0) | strong(X0) [cnf transformation 32]
70. ~strong(X0) | wise(X0) [cnf transformation 32]
79. kind(X0) | tall(X0) [cnf transformation 34]
83. ~generous(X0) | wise(X0) [cnf transformation 24]
98. ~strong(X0) | ~tall(X0) | kind(X0) [cnf transformation 43]
107. strong(X0) | generous(X0) [cnf transformation 50]
127. ~kind(lucy) [cnf transformation 20]
189. ~strong(X0) | kind(X0) [subsumption resolution 98,79]
265. generous(X0) | wise(X0) [resolution 107,70]
266. wise(X0) [subsumption resolution 265,83]
267. strong(X0) [resolution 266,69]
271. kind(X0) [resolution 189,267]
279. $false [resolution 271,127]
% SZS output end Proof for 881358663091548716925678
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not funny or strong then someone is funny and vice versa. If john is both curious and not tall then someone is both happy and not rich and vice versa. If someone is not quiet or not tall then someone is either not patient or patient. If mary is rich or not rich then lucy is not old or not funny and vice versa. Everyone who is both not quiet and old is patient or rich. Everyone who is either curious or not strong is both generous and not brave. Everyone who is strong or not tall is both funny and not strong. If someone is both wise and funny then alice is either not rich or strong and vice versa. If john is both not wise and not quiet then john is tall. If alice is either not kind or not old then john is either creative or wise and vice versa. Everyone who is rich or not creative is both not patient and not funny. Everyone who is both not calm and not humble is creative and vice versa. Everyone who is either quiet or kind is funny or not creative and vice versa. Everyone who is funny or brave is old. Everyone who is not kind or funny is either not happy or strong. Everyone who is either not old or generous is not happy and vice versa. John is either not kind or patient. Mary is not wise or generous. Paul is not tall or calm. Alice is not curious or generous. Fred is either rich or calm. Someone is not old or happy. Susan is wise. | Mary is wise. | neutral | ((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:(funny(X))))&
(((curious(john)&~tall(john)))<=>(?[X]:((happy(X)&~rich(X)))))&
((?[X]:((~quiet(X)|~tall(X))))=>(?[X]:((~patient(X)<~>patient(X)))))&
(((rich(mary)|~rich(mary)))<=>((~old(lucy)|~funny(lucy))))&
(![X]:((~quiet(X)&old(X))=>(patient(X)|rich(X))))&
(![X]:((curious(X)<~>~strong(X))=>(generous(X)&~brave(X))))&
(![X]:((strong(X)|~tall(X))=>(funny(X)&~strong(X))))&
((?[X]:((wise(X)&funny(X))))<=>((~rich(alice)<~>strong(alice))))&
(((~wise(john)&~quiet(john)))=>(tall(john)))&
(((~kind(alice)<~>~old(alice)))<=>((creative(john)<~>wise(john))))&
(![X]:((rich(X)|~creative(X))=>(~patient(X)&~funny(X))))&
(![X]:((~calm(X)&~humble(X))<=>creative(X)))&
(![X]:((quiet(X)<~>kind(X))<=>(funny(X)|~creative(X))))&
(![X]:((funny(X)|brave(X))=>old(X)))&
(![X]:((~kind(X)|funny(X))=>(~happy(X)<~>strong(X))))&
(![X]:((~old(X)<~>generous(X))<=>~happy(X)))&
((~kind(john)<~>patient(john)))&
((~wise(mary)|generous(mary)))&
((~tall(paul)|calm(paul)))&
((~curious(alice)|generous(alice)))&
((rich(fred)<~>calm(fred)))&
(?[X]:((~old(X)|happy(X))))&
(wise(susan)) | wise(mary) | [] | null | 0 |
Everyone who is not generous or not wise is both not rich and curious.
Everyone who is either tall or brave is both not brave and curious.
Everyone who is both happy and kind is kind.
Everyone who is not patient or wise is not rich.
If john is brave or strong then lucy is both patient and brave and vice versa.
Everyone who is both not rich and not brave is patient.
Everyone who is either rich or not old is not rich and vice versa.
If someone is either patient or funny then someone is either creative or not quiet and vice versa.
If someone is happy then someone is either not calm or not tall.
Everyone who is either wise or old is not creative.
Everyone who is both patient and not brave is either not calm or old and vice versa.
If paul is not creative or patient then john is both generous and not curious and vice versa.
Everyone who is wise is old or generous and vice versa.
If fred is not funny or curious then someone is either not happy or not quiet and vice versa.
Someone is not wise.
Someone is both not wise and not patient.
Someone is both not tall and funny. | John is quiet. | neutral | (![X]:((~generous(X)|~wise(X))=>(~rich(X)&curious(X))))&
(![X]:((tall(X)<~>brave(X))=>(~brave(X)&curious(X))))&
(![X]:((happy(X)&kind(X))=>kind(X)))&
(![X]:((~patient(X)|wise(X))=>~rich(X)))&
(((brave(john)|strong(john)))<=>((patient(lucy)&brave(lucy))))&
(![X]:((~rich(X)&~brave(X))=>patient(X)))&
(![X]:((rich(X)<~>~old(X))<=>~rich(X)))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((creative(X)<~>~quiet(X)))))&
((?[X]:(happy(X)))=>(?[X]:((~calm(X)<~>~tall(X)))))&
(![X]:((wise(X)<~>old(X))=>~creative(X)))&
(![X]:((patient(X)&~brave(X))<=>(~calm(X)<~>old(X))))&
(((~creative(paul)|patient(paul)))<=>((generous(john)&~curious(john))))&
(![X]:(wise(X)<=>(old(X)|generous(X))))&
(((~funny(fred)|curious(fred)))<=>(?[X]:((~happy(X)<~>~quiet(X)))))&
(?[X]:(~wise(X)))&
(?[X]:((~wise(X)&~patient(X))))&
(?[X]:((~tall(X)&funny(X)))) | quiet(john) | [] | null | 0 |
If someone is either strong or funny then fred is old or strong.
If someone is both not rich and brave then john is old or not patient.
Everyone who is not wise or not humble is not quiet.
If alice is tall then fred is both rich and not curious and vice versa.
Everyone who is humble or creative is both generous and not brave and vice versa.
Everyone who is not kind is either not creative or rich and vice versa.
If mary is not kind then susan is either generous or not calm.
Everyone who is both not calm and old is not rich.
If fred is both not happy and old then alice is generous or kind and vice versa.
Everyone who is quiet is both old and rich and vice versa.
Everyone who is both not old and not funny is generous and vice versa.
Everyone who is rich or not tall is both kind and patient and vice versa.
Everyone who is both not rich and not strong is both not humble and not old.
If someone is tall then lucy is either not kind or not old and vice versa.
If someone is patient then mary is both patient and tall.
Susan is either not old or tall.
Fred is creative or not creative.
Mary is either not brave or not wise.
Someone is not creative.
Susan is not old.
Someone is kind or not wise. | Lucy is not tall. | neutral | ((?[X]:((strong(X)<~>funny(X))))=>((old(fred)|strong(fred))))&
((?[X]:((~rich(X)&brave(X))))=>((old(john)|~patient(john))))&
(![X]:((~wise(X)|~humble(X))=>~quiet(X)))&
((tall(alice))<=>((rich(fred)&~curious(fred))))&
(![X]:((humble(X)|creative(X))<=>(generous(X)&~brave(X))))&
(![X]:(~kind(X)<=>(~creative(X)<~>rich(X))))&
((~kind(mary))=>((generous(susan)<~>~calm(susan))))&
(![X]:((~calm(X)&old(X))=>~rich(X)))&
(((~happy(fred)&old(fred)))<=>((generous(alice)|kind(alice))))&
(![X]:(quiet(X)<=>(old(X)&rich(X))))&
(![X]:((~old(X)&~funny(X))<=>generous(X)))&
(![X]:((rich(X)|~tall(X))<=>(kind(X)&patient(X))))&
(![X]:((~rich(X)&~strong(X))=>(~humble(X)&~old(X))))&
((?[X]:(tall(X)))<=>((~kind(lucy)<~>~old(lucy))))&
((?[X]:(patient(X)))=>((patient(mary)&tall(mary))))&
((~old(susan)<~>tall(susan)))&
((creative(fred)|~creative(fred)))&
((~brave(mary)<~>~wise(mary)))&
(?[X]:(~creative(X)))&
(~old(susan))&
(?[X]:((kind(X)|~wise(X)))) | ~tall(lucy) | [] | null | 0 |
If mary is not wise or creative then someone is not curious or rich.
Everyone who is not wise or calm is both not humble and not patient.
Everyone who is either strong or calm is not kind or patient.
If someone is both old and calm then someone is not funny.
Everyone who is generous is either generous or old and vice versa.
Everyone who is either rich or not curious is generous.
Everyone who is either quiet or not funny is both not funny and generous and vice versa.
Everyone who is both kind and not quiet is quiet or not old.
If lucy is both humble and not happy then someone is wise or generous.
Everyone who is not brave or strong is not kind.
Everyone who is not generous is not creative or not rich and vice versa.
If paul is kind then fred is not curious or not humble and vice versa.
If someone is both not calm and not funny then paul is not curious or not funny and vice versa.
Everyone who is both not generous and quiet is not wise or not happy and vice versa.
If someone is brave or not kind then someone is both not humble and patient and vice versa.
If lucy is not generous or not rich then paul is both not creative and humble.
Someone is not wise.
Alice is either not patient or not curious.
Fred is both not generous and tall.
Someone is both not generous and not funny.
Someone is both not calm and not strong.
Alice is either not brave or creative.
Mary is rich.
Susan is both quiet and not tall. | Fred is not old. | entailment | (((~wise(mary)|creative(mary)))=>(?[X]:((~curious(X)|rich(X)))))&
(![X]:((~wise(X)|calm(X))=>(~humble(X)&~patient(X))))&
(![X]:((strong(X)<~>calm(X))=>(~kind(X)|patient(X))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:(~funny(X))))&
(![X]:(generous(X)<=>(generous(X)<~>old(X))))&
(![X]:((rich(X)<~>~curious(X))=>generous(X)))&
(![X]:((quiet(X)<~>~funny(X))<=>(~funny(X)&generous(X))))&
(![X]:((kind(X)&~quiet(X))=>(quiet(X)|~old(X))))&
(((humble(lucy)&~happy(lucy)))=>(?[X]:((wise(X)|generous(X)))))&
(![X]:((~brave(X)|strong(X))=>~kind(X)))&
(![X]:(~generous(X)<=>(~creative(X)|~rich(X))))&
((kind(paul))<=>((~curious(fred)|~humble(fred))))&
((?[X]:((~calm(X)&~funny(X))))<=>((~curious(paul)|~funny(paul))))&
(![X]:((~generous(X)&quiet(X))<=>(~wise(X)|~happy(X))))&
((?[X]:((brave(X)|~kind(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~generous(lucy)|~rich(lucy)))=>((~creative(paul)&humble(paul))))&
(?[X]:(~wise(X)))&
((~patient(alice)<~>~curious(alice)))&
((~generous(fred)&tall(fred)))&
(?[X]:((~generous(X)&~funny(X))))&
(?[X]:((~calm(X)&~strong(X))))&
((~brave(alice)<~>creative(alice)))&
(rich(mary))&
((quiet(susan)&~tall(susan))) | ~old(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6565242335146431593765840
% SZS output start Proof for 6565242335146431593765840
5. ! [X0] : (generous(X0) <=> (generous(X0) <~> old(X0))) [input p4]
25. old(fred) [input hypothesis]
46. ! [X0] : ((generous(X0) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0)))) & (((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | ~generous(X0))) [nnf transformation 5]
86. ~old(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 46]
88. generous(X0) | generous(X0) | ~old(X0) [cnf transformation 46]
140. old(fred) [cnf transformation 25]
144. ~old(X0) | ~generous(X0) [duplicate literal removal 86]
145. generous(X0) | ~old(X0) [duplicate literal removal 88]
173. ~old(X0) [subsumption resolution 144,145]
288. $false [subsumption resolution 140,173]
% SZS output end Proof for 6565242335146431593765840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not brave is happy. If john is not funny or rich then someone is either funny or not humble. If someone is either not generous or wise then someone is both kind and calm. Everyone who is both generous and not creative is strong or not funny and vice versa. Everyone who is both not old and not patient is rich. Everyone who is both not strong and calm is not calm and vice versa. If susan is strong then someone is old. If someone is both not rich and strong then someone is either brave or not generous. Everyone who is both not happy and not creative is not humble. If someone is kind or humble then paul is both not quiet and humble. If someone is both kind and brave then someone is not patient and vice versa. Everyone who is either not wise or tall is either not tall or kind and vice versa. Everyone who is either patient or not creative is not curious or brave and vice versa. If john is either not quiet or old then susan is old. Everyone who is either brave or tall is generous. Mary is either patient or not rich. Lucy is either generous or kind. Lucy is both not rich and not quiet. Mary is either generous or not curious. Mary is either patient or not funny. Someone is either not rich or funny. Fred is not patient. Someone is both strong and tall. | Mary is not patient. | neutral | (![X]:((brave(X)<~>~brave(X))=>happy(X)))&
(((~funny(john)|rich(john)))=>(?[X]:((funny(X)<~>~humble(X)))))&
((?[X]:((~generous(X)<~>wise(X))))=>(?[X]:((kind(X)&calm(X)))))&
(![X]:((generous(X)&~creative(X))<=>(strong(X)|~funny(X))))&
(![X]:((~old(X)&~patient(X))=>rich(X)))&
(![X]:((~strong(X)&calm(X))<=>~calm(X)))&
((strong(susan))=>(?[X]:(old(X))))&
((?[X]:((~rich(X)&strong(X))))=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~happy(X)&~creative(X))=>~humble(X)))&
((?[X]:((kind(X)|humble(X))))=>((~quiet(paul)&humble(paul))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~wise(X)<~>tall(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~curious(X)|brave(X))))&
(((~quiet(john)<~>old(john)))=>(old(susan)))&
(![X]:((brave(X)<~>tall(X))=>generous(X)))&
((patient(mary)<~>~rich(mary)))&
((generous(lucy)<~>kind(lucy)))&
((~rich(lucy)&~quiet(lucy)))&
((generous(mary)<~>~curious(mary)))&
((patient(mary)<~>~funny(mary)))&
(?[X]:((~rich(X)<~>funny(X))))&
(~patient(fred))&
(?[X]:((strong(X)&tall(X)))) | ~patient(mary) | [] | null | 0 |
If someone is both not generous and not curious then susan is humble and vice versa. Everyone who is not wise is both not rich and not brave and vice versa. Everyone who is not creative is not kind or brave and vice versa. If someone is both creative and curious then someone is rich or not strong. If paul is funny then fred is either patient or not wise. Everyone who is both not brave and creative is either not humble or creative and vice versa. If mary is both not kind and old then someone is both not calm and tall and vice versa. Everyone who is both old and happy is not wise and vice versa. Everyone who is kind is not brave or generous and vice versa. If john is kind or rich then someone is both not calm and not quiet and vice versa. If fred is either not creative or not brave then lucy is rich and vice versa. If paul is both brave and not kind then someone is either not humble or calm and vice versa. Everyone who is not brave is not kind. Everyone who is not rich or tall is both wise and not kind and vice versa. Everyone who is both not curious and creative is either not wise or old and vice versa. If john is not humble or patient then someone is calm. Someone is wise or calm. Someone is generous or rich. Someone is both not generous and not tall. Someone is old or rich. Paul is both not calm and not kind. Lucy is both not old and rich. Someone is either not creative or not wise. Alice is patient. | Paul is tall. | contradiction | ((?[X]:((~generous(X)&~curious(X))))<=>(humble(susan)))&
(![X]:(~wise(X)<=>(~rich(X)&~brave(X))))&
(![X]:(~creative(X)<=>(~kind(X)|brave(X))))&
((?[X]:((creative(X)&curious(X))))=>(?[X]:((rich(X)|~strong(X)))))&
((funny(paul))=>((patient(fred)<~>~wise(fred))))&
(![X]:((~brave(X)&creative(X))<=>(~humble(X)<~>creative(X))))&
(((~kind(mary)&old(mary)))<=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((old(X)&happy(X))<=>~wise(X)))&
(![X]:(kind(X)<=>(~brave(X)|generous(X))))&
(((kind(john)|rich(john)))<=>(?[X]:((~calm(X)&~quiet(X)))))&
(((~creative(fred)<~>~brave(fred)))<=>(rich(lucy)))&
(((brave(paul)&~kind(paul)))<=>(?[X]:((~humble(X)<~>calm(X)))))&
(![X]:(~brave(X)=>~kind(X)))&
(![X]:((~rich(X)|tall(X))<=>(wise(X)&~kind(X))))&
(![X]:((~curious(X)&creative(X))<=>(~wise(X)<~>old(X))))&
(((~humble(john)|patient(john)))=>(?[X]:(calm(X))))&
(?[X]:((wise(X)|calm(X))))&
(?[X]:((generous(X)|rich(X))))&
(?[X]:((~generous(X)&~tall(X))))&
(?[X]:((old(X)|rich(X))))&
((~calm(paul)&~kind(paul)))&
((~old(lucy)&rich(lucy)))&
(?[X]:((~creative(X)<~>~wise(X))))&
(patient(alice)) | tall(paul) | [
"p1",
"p2",
"p6",
"p8",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3868011794955580480981535
% SZS output start Proof for 3868011794955580480981535
2. ! [X0] : (~wise(X0) <=> (~brave(X0) & ~rich(X0))) [input p1]
3. ! [X0] : (~creative(X0) <=> (brave(X0) | ~kind(X0))) [input p2]
7. (old(mary) & ~kind(mary)) <=> ? [X0] : (tall(X0) & ~calm(X0)) [input p6]
9. ! [X0] : (kind(X0) <=> (generous(X0) | ~brave(X0))) [input p8]
13. ! [X0] : (~brave(X0) => ~kind(X0)) [input p12]
14. ! [X0] : ((tall(X0) | ~rich(X0)) <=> (~kind(X0) & wise(X0))) [input p13]
15. ! [X0] : ((creative(X0) & ~curious(X0)) <=> (~wise(X0) <~> old(X0))) [input p14]
21. ~kind(paul) & ~calm(paul) [input p20]
25. tall(paul) [input hypothesis]
29. ! [X0] : (~kind(X0) | brave(X0)) [ennf transformation 13]
35. ! [X0] : ((~wise(X0) | (brave(X0) | rich(X0))) & ((~brave(X0) & ~rich(X0)) | wise(X0))) [nnf transformation 2]
36. ! [X0] : ((~wise(X0) | brave(X0) | rich(X0)) & ((~brave(X0) & ~rich(X0)) | wise(X0))) [flattening 35]
37. ! [X0] : ((~creative(X0) | (~brave(X0) & kind(X0))) & ((brave(X0) | ~kind(X0)) | creative(X0))) [nnf transformation 3]
38. ! [X0] : ((~creative(X0) | (~brave(X0) & kind(X0))) & (brave(X0) | ~kind(X0) | creative(X0))) [flattening 37]
41. ((old(mary) & ~kind(mary)) | ! [X0] : (~tall(X0) | calm(X0))) & (? [X0] : (tall(X0) & ~calm(X0)) | (~old(mary) | kind(mary))) [nnf transformation 7]
42. ((old(mary) & ~kind(mary)) | ! [X0] : (~tall(X0) | calm(X0))) & (? [X0] : (tall(X0) & ~calm(X0)) | ~old(mary) | kind(mary)) [flattening 41]
43. ((old(mary) & ~kind(mary)) | ! [X0] : (~tall(X0) | calm(X0))) & (? [X1] : (tall(X1) & ~calm(X1)) | ~old(mary) | kind(mary)) [rectify 42]
44. ? [X1] : (tall(X1) & ~calm(X1)) => (tall(sK1) & ~calm(sK1)) [choice axiom]
45. ((old(mary) & ~kind(mary)) | ! [X0] : (~tall(X0) | calm(X0))) & ((tall(sK1) & ~calm(sK1)) | ~old(mary) | kind(mary)) [skolemisation 43,44]
48. ! [X0] : ((kind(X0) | (~generous(X0) & brave(X0))) & ((generous(X0) | ~brave(X0)) | ~kind(X0))) [nnf transformation 9]
49. ! [X0] : ((kind(X0) | (~generous(X0) & brave(X0))) & (generous(X0) | ~brave(X0) | ~kind(X0))) [flattening 48]
61. ! [X0] : (((tall(X0) | ~rich(X0)) | (kind(X0) | ~wise(X0))) & ((~kind(X0) & wise(X0)) | (~tall(X0) & rich(X0)))) [nnf transformation 14]
62. ! [X0] : ((tall(X0) | ~rich(X0) | kind(X0) | ~wise(X0)) & ((~kind(X0) & wise(X0)) | (~tall(X0) & rich(X0)))) [flattening 61]
63. ! [X0] : (((creative(X0) & ~curious(X0)) | ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) & (((~old(X0) | wise(X0)) & (old(X0) | ~wise(X0))) | (~creative(X0) | curious(X0)))) [nnf transformation 15]
64. ! [X0] : (((creative(X0) & ~curious(X0)) | ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) & (((~old(X0) | wise(X0)) & (old(X0) | ~wise(X0))) | ~creative(X0) | curious(X0))) [flattening 63]
81. ~rich(X0) | wise(X0) [cnf transformation 36]
86. ~creative(X0) | ~brave(X0) [cnf transformation 38]
96. old(mary) | ~tall(X0) | calm(X0) [cnf transformation 45]
101. kind(X0) | brave(X0) [cnf transformation 49]
118. ~kind(X0) | brave(X0) [cnf transformation 29]
119. wise(X0) | rich(X0) [cnf transformation 62]
129. creative(X0) | ~wise(X0) | ~old(X0) [cnf transformation 64]
137. ~calm(paul) [cnf transformation 21]
144. tall(paul) [cnf transformation 25]
167. 5 <=> ! [X0] : (~tall(X0) | calm(X0)) [avatar definition]
168. ~tall(X0) | calm(X0) <- (5) [avatar component clause 167]
170. 6 <=> old(mary) [avatar definition]
172. old(mary) <- (6) [avatar component clause 170]
173. 5 | 6 [avatar split clause 96,170,167]
260. brave(X0) [subsumption resolution 118,101]
262. wise(X0) [subsumption resolution 119,81]
263. ~old(X0) | creative(X0) [subsumption resolution 129,262]
331. calm(paul) <- (5) [resolution 168,144]
332. $false <- (5) [subsumption resolution 331,137]
333. ~5 [avatar contradiction clause 332]
348. creative(mary) <- (6) [resolution 263,172]
357. ~brave(mary) <- (6) [resolution 348,86]
359. $false <- (6) [subsumption resolution 357,260]
360. ~6 [avatar contradiction clause 359]
363. $false [avatar sat refutation 173,333,360]
% SZS output end Proof for 3868011794955580480981535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not wise is not old or not calm.
If someone is strong or happy then susan is not kind.
Everyone who is humble is both generous and not rich.
Everyone who is old or brave is both not brave and brave.
If someone is curious or not generous then lucy is quiet or generous and vice versa.
If alice is both brave and not curious then paul is old or not funny.
Everyone who is not calm is not quiet and vice versa.
If alice is either not happy or not old then someone is both not rich and not patient.
Everyone who is not rich is curious or not curious and vice versa.
Everyone who is not happy or funny is either generous or rich.
If john is tall then someone is not curious or not old and vice versa.
If someone is either not wise or patient then susan is rich and vice versa.
If susan is either not tall or calm then mary is either not curious or not funny.
If someone is calm then someone is either tall or not patient.
Everyone who is kind is either not happy or strong and vice versa.
If fred is not old or not rich then susan is both not curious and wise and vice versa.
Someone is both humble and not quiet.
Susan is tall or rich.
Someone is either not happy or not tall.
Fred is both wise and strong.
Someone is both calm and not curious.
Fred is not quiet or not old. | Alice is not rich. | entailment | (![X]:((strong(X)|~wise(X))=>(~old(X)|~calm(X))))&
((?[X]:((strong(X)|happy(X))))=>(~kind(susan)))&
(![X]:(humble(X)=>(generous(X)&~rich(X))))&
(![X]:((old(X)|brave(X))=>(~brave(X)&brave(X))))&
((?[X]:((curious(X)|~generous(X))))<=>((quiet(lucy)|generous(lucy))))&
(((brave(alice)&~curious(alice)))=>((old(paul)|~funny(paul))))&
(![X]:(~calm(X)<=>~quiet(X)))&
(((~happy(alice)<~>~old(alice)))=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:(~rich(X)<=>(curious(X)|~curious(X))))&
(![X]:((~happy(X)|funny(X))=>(generous(X)<~>rich(X))))&
((tall(john))<=>(?[X]:((~curious(X)|~old(X)))))&
((?[X]:((~wise(X)<~>patient(X))))<=>(rich(susan)))&
(((~tall(susan)<~>calm(susan)))=>((~curious(mary)<~>~funny(mary))))&
((?[X]:(calm(X)))=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:(kind(X)<=>(~happy(X)<~>strong(X))))&
(((~old(fred)|~rich(fred)))<=>((~curious(susan)&wise(susan))))&
(?[X]:((humble(X)&~quiet(X))))&
((tall(susan)|rich(susan)))&
(?[X]:((~happy(X)<~>~tall(X))))&
((wise(fred)&strong(fred)))&
(?[X]:((calm(X)&~curious(X))))&
((~quiet(fred)|~old(fred))) | ~rich(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8776649858654676334976315
% SZS output start Proof for 8776649858654676334976315
9. ! [X0] : (~rich(X0) <=> (~curious(X0) | curious(X0))) [input p8]
23. rich(alice) [input hypothesis]
47. ! [X0] : ((~rich(X0) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | rich(X0))) [nnf transformation 9]
48. ! [X0] : ((~rich(X0) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | rich(X0))) [flattening 47]
95. ~rich(X0) | ~curious(X0) [cnf transformation 48]
96. ~rich(X0) | curious(X0) [cnf transformation 48]
131. rich(alice) [cnf transformation 23]
191. ~rich(X0) [subsumption resolution 95,96]
273. $false [subsumption resolution 131,191]
% SZS output end Proof for 8776649858654676334976315
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is curious then john is brave.
If mary is both strong and not tall then someone is patient.
Everyone who is creative or not humble is either not curious or rich.
Everyone who is happy or rich is not kind.
Everyone who is both not curious and brave is humble or not quiet and vice versa.
If someone is both not strong and humble then someone is patient.
If someone is both creative and not patient then mary is both happy and old.
If paul is both not strong and not rich then someone is either not quiet or happy.
If lucy is not creative or not generous then someone is either calm or not quiet and vice versa.
Everyone who is either curious or not creative is happy or not patient and vice versa.
Everyone who is not calm or not creative is not quiet and vice versa.
If susan is both not curious and not generous then someone is generous or patient and vice versa.
If john is not rich then lucy is kind.
Everyone who is not calm is happy or not calm and vice versa.
If someone is wise or generous then paul is not funny or not tall and vice versa.
If lucy is either not creative or strong then someone is either not brave or curious.
Mary is funny.
Someone is both not calm and not curious.
Fred is either not old or calm.
Susan is creative.
Fred is wise.
Mary is rich.
Paul is either funny or quiet.
Someone is wise or not strong. | Mary is not brave. | contradiction | ((curious(alice))=>(brave(john)))&
(((strong(mary)&~tall(mary)))=>(?[X]:(patient(X))))&
(![X]:((creative(X)|~humble(X))=>(~curious(X)<~>rich(X))))&
(![X]:((happy(X)|rich(X))=>~kind(X)))&
(![X]:((~curious(X)&brave(X))<=>(humble(X)|~quiet(X))))&
((?[X]:((~strong(X)&humble(X))))=>(?[X]:(patient(X))))&
((?[X]:((creative(X)&~patient(X))))=>((happy(mary)&old(mary))))&
(((~strong(paul)&~rich(paul)))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(((~creative(lucy)|~generous(lucy)))<=>(?[X]:((calm(X)<~>~quiet(X)))))&
(![X]:((curious(X)<~>~creative(X))<=>(happy(X)|~patient(X))))&
(![X]:((~calm(X)|~creative(X))<=>~quiet(X)))&
(((~curious(susan)&~generous(susan)))<=>(?[X]:((generous(X)|patient(X)))))&
((~rich(john))=>(kind(lucy)))&
(![X]:(~calm(X)<=>(happy(X)|~calm(X))))&
((?[X]:((wise(X)|generous(X))))<=>((~funny(paul)|~tall(paul))))&
(((~creative(lucy)<~>strong(lucy)))=>(?[X]:((~brave(X)<~>curious(X)))))&
(funny(mary))&
(?[X]:((~calm(X)&~curious(X))))&
((~old(fred)<~>calm(fred)))&
(creative(susan))&
(wise(fred))&
(rich(mary))&
((funny(paul)<~>quiet(paul)))&
(?[X]:((wise(X)|~strong(X)))) | ~brave(mary) | [
"p2",
"p4",
"p6",
"p9",
"p10",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3759448613896956866315029
% SZS output start Proof for 3759448613896956866315029
3. ! [X0] : ((~humble(X0) | creative(X0)) => (~curious(X0) <~> rich(X0))) [input p2]
5. ! [X0] : ((brave(X0) & ~curious(X0)) <=> (~quiet(X0) | humble(X0))) [input p4]
7. ? [X0] : (~patient(X0) & creative(X0)) => (old(mary) & happy(mary)) [input p6]
10. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> (~patient(X0) | happy(X0))) [input p9]
11. ! [X0] : ((~creative(X0) | ~calm(X0)) <=> ~quiet(X0)) [input p10]
14. ! [X0] : (~calm(X0) <=> (~calm(X0) | happy(X0))) [input p13]
22. rich(mary) [input p21]
25. ~brave(mary) [input hypothesis]
30. ! [X0] : ((~curious(X0) <~> rich(X0)) | (humble(X0) & ~creative(X0))) [ennf transformation 3]
33. (old(mary) & happy(mary)) | ! [X0] : (patient(X0) | ~creative(X0)) [ennf transformation 7]
40. ! [X0] : (((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | (humble(X0) & ~creative(X0))) [nnf transformation 30]
41. ! [X0] : (((brave(X0) & ~curious(X0)) | (quiet(X0) & ~humble(X0))) & ((~quiet(X0) | humble(X0)) | (~brave(X0) | curious(X0)))) [nnf transformation 5]
42. ! [X0] : (((brave(X0) & ~curious(X0)) | (quiet(X0) & ~humble(X0))) & (~quiet(X0) | humble(X0) | ~brave(X0) | curious(X0))) [flattening 41]
54. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | (patient(X0) & ~happy(X0))) & ((~patient(X0) | happy(X0)) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 10]
55. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | (patient(X0) & ~happy(X0))) & (~patient(X0) | happy(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [flattening 54]
56. ! [X0] : (((~creative(X0) | ~calm(X0)) | quiet(X0)) & (~quiet(X0) | (creative(X0) & calm(X0)))) [nnf transformation 11]
57. ! [X0] : ((~creative(X0) | ~calm(X0) | quiet(X0)) & (~quiet(X0) | (creative(X0) & calm(X0)))) [flattening 56]
63. ! [X0] : ((~calm(X0) | (calm(X0) & ~happy(X0))) & ((~calm(X0) | happy(X0)) | calm(X0))) [nnf transformation 14]
64. ! [X0] : ((~calm(X0) | (calm(X0) & ~happy(X0))) & (~calm(X0) | happy(X0) | calm(X0))) [flattening 63]
83. ~rich(X0) | curious(X0) | ~creative(X0) [cnf transformation 40]
91. quiet(X0) | brave(X0) [cnf transformation 42]
93. happy(mary) | patient(X0) | ~creative(X0) [cnf transformation 33]
103. ~creative(X0) | happy(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 55]
108. ~curious(X0) | creative(X0) | patient(X0) [cnf transformation 55]
109. ~quiet(X0) | calm(X0) [cnf transformation 57]
110. ~quiet(X0) | creative(X0) [cnf transformation 57]
119. ~calm(X0) | ~happy(X0) [cnf transformation 64]
136. rich(mary) [cnf transformation 22]
140. ~brave(mary) [cnf transformation 25]
172. 8 <=> ! [X0] : (patient(X0) | ~creative(X0)) [avatar definition]
173. ~creative(X0) | patient(X0) <- (8) [avatar component clause 172]
180. 10 <=> happy(mary) [avatar definition]
182. happy(mary) <- (10) [avatar component clause 180]
183. 8 | 10 [avatar split clause 93,180,172]
340. calm(X0) | brave(X0) [resolution 109,91]
342. creative(X0) | brave(X0) [resolution 110,91]
347. curious(mary) | ~creative(mary) [resolution 83,136]
351. 42 <=> creative(mary) [avatar definition]
352. creative(mary) <- (42) [avatar component clause 351]
353. ~creative(mary) <- (~42) [avatar component clause 351]
355. 43 <=> curious(mary) [avatar definition]
357. curious(mary) <- (43) [avatar component clause 355]
358. ~42 | 43 [avatar split clause 347,355,351]
405. creative(mary) | patient(mary) <- (43) [resolution 108,357]
413. patient(mary) <- (8, 43) [subsumption resolution 405,173]
427. happy(mary) | ~patient(mary) | ~curious(mary) <- (42) [resolution 103,352]
432. happy(mary) | ~curious(mary) <- (8, 42, 43) [subsumption resolution 427,413]
433. happy(mary) <- (8, 42, 43) [subsumption resolution 432,357]
434. 10 | ~8 | ~42 | ~43 [avatar split clause 433,355,351,172,180]
470. ~happy(X1) | brave(X1) [resolution 340,119]
484. brave(mary) <- (10) [resolution 470,182]
486. $false <- (10) [subsumption resolution 484,140]
487. ~10 [avatar contradiction clause 486]
489. brave(mary) <- (~42) [resolution 353,342]
490. $false <- (~42) [subsumption resolution 489,140]
491. 42 [avatar contradiction clause 490]
492. $false [avatar sat refutation 183,358,434,487,491]
% SZS output end Proof for 3759448613896956866315029
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not kind or tall then someone is not curious or brave and vice versa. Everyone who is creative or not tall is both quiet and old. If someone is both curious and not old then fred is both quiet and not funny and vice versa. Everyone who is either not curious or not wise is quiet or not brave. If alice is either tall or quiet then someone is kind. Everyone who is not humble is either funny or not generous and vice versa. If someone is both humble and not brave then someone is either patient or not rich. Everyone who is not wise is happy or old and vice versa. If paul is humble then someone is either not patient or not happy. Everyone who is both happy and generous is both not creative and brave and vice versa. Everyone who is both brave and strong is wise. If alice is rich then someone is not calm or kind and vice versa. If someone is creative then susan is generous or kind. Everyone who is kind or not wise is both not quiet and not kind and vice versa. Everyone who is tall or not wise is not humble. Everyone who is not patient is not rich or not happy. Alice is either brave or quiet. Someone is not quiet or not patient. Someone is both not strong and not humble. Paul is either brave or not happy. Alice is not kind. Someone is funny or not creative. | Fred is not humble. | entailment | (((~kind(paul)|tall(paul)))<=>(?[X]:((~curious(X)|brave(X)))))&
(![X]:((creative(X)|~tall(X))=>(quiet(X)&old(X))))&
((?[X]:((curious(X)&~old(X))))<=>((quiet(fred)&~funny(fred))))&
(![X]:((~curious(X)<~>~wise(X))=>(quiet(X)|~brave(X))))&
(((tall(alice)<~>quiet(alice)))=>(?[X]:(kind(X))))&
(![X]:(~humble(X)<=>(funny(X)<~>~generous(X))))&
((?[X]:((humble(X)&~brave(X))))=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:(~wise(X)<=>(happy(X)|old(X))))&
((humble(paul))=>(?[X]:((~patient(X)<~>~happy(X)))))&
(![X]:((happy(X)&generous(X))<=>(~creative(X)&brave(X))))&
(![X]:((brave(X)&strong(X))=>wise(X)))&
((rich(alice))<=>(?[X]:((~calm(X)|kind(X)))))&
((?[X]:(creative(X)))=>((generous(susan)|kind(susan))))&
(![X]:((kind(X)|~wise(X))<=>(~quiet(X)&~kind(X))))&
(![X]:((tall(X)|~wise(X))=>~humble(X)))&
(![X]:(~patient(X)=>(~rich(X)|~happy(X))))&
((brave(alice)<~>quiet(alice)))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((~strong(X)&~humble(X))))&
((brave(paul)<~>~happy(paul)))&
(~kind(alice))&
(?[X]:((funny(X)|~creative(X)))) | ~humble(fred) | [
"p1",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6368243334625326253234782
% SZS output start Proof for 6368243334625326253234782
2. ! [X0] : ((~tall(X0) | creative(X0)) => (old(X0) & quiet(X0))) [input p1]
8. ! [X0] : (~wise(X0) <=> (old(X0) | happy(X0))) [input p7]
14. ! [X0] : ((~wise(X0) | kind(X0)) <=> (~kind(X0) & ~quiet(X0))) [input p13]
15. ! [X0] : ((~wise(X0) | tall(X0)) => ~humble(X0)) [input p14]
23. humble(fred) [input hypothesis]
27. ! [X0] : ((old(X0) & quiet(X0)) | (tall(X0) & ~creative(X0))) [ennf transformation 2]
35. ! [X0] : (~humble(X0) | (wise(X0) & ~tall(X0))) [ennf transformation 15]
57. ! [X0] : ((~wise(X0) | (~old(X0) & ~happy(X0))) & ((old(X0) | happy(X0)) | wise(X0))) [nnf transformation 8]
58. ! [X0] : ((~wise(X0) | (~old(X0) & ~happy(X0))) & (old(X0) | happy(X0) | wise(X0))) [flattening 57]
68. ! [X0] : (((~wise(X0) | kind(X0)) | (kind(X0) | quiet(X0))) & ((~kind(X0) & ~quiet(X0)) | (wise(X0) & ~kind(X0)))) [nnf transformation 14]
69. ! [X0] : ((~wise(X0) | kind(X0) | kind(X0) | quiet(X0)) & ((~kind(X0) & ~quiet(X0)) | (wise(X0) & ~kind(X0)))) [flattening 68]
83. quiet(X0) | tall(X0) [cnf transformation 27]
85. old(X0) | tall(X0) [cnf transformation 27]
102. ~wise(X0) | ~old(X0) [cnf transformation 58]
114. ~quiet(X0) | wise(X0) [cnf transformation 69]
118. ~humble(X0) | ~tall(X0) [cnf transformation 35]
129. humble(fred) [cnf transformation 23]
159. 7 <=> quiet(fred) [avatar definition]
160. quiet(fred) <- (7) [avatar component clause 159]
161. ~quiet(fred) <- (~7) [avatar component clause 159]
296. wise(fred) <- (7) [resolution 114,160]
299. ~old(fred) <- (7) [resolution 296,102]
300. ~tall(fred) [resolution 118,129]
303. tall(fred) <- (7) [resolution 299,85]
304. $false <- (7) [subsumption resolution 303,300]
305. ~7 [avatar contradiction clause 304]
306. tall(fred) <- (~7) [resolution 161,83]
307. $false <- (~7) [subsumption resolution 306,300]
308. 7 [avatar contradiction clause 307]
309. $false [avatar sat refutation 305,308]
% SZS output end Proof for 6368243334625326253234782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not curious is not tall and vice versa.
Everyone who is old is either humble or not wise.
If someone is not kind then john is both rich and not curious and vice versa.
If someone is calm or not calm then lucy is both creative and not generous and vice versa.
If someone is not generous or not curious then fred is not wise and vice versa.
Everyone who is either not calm or not happy is not calm and vice versa.
If someone is not curious then someone is kind or not happy.
Everyone who is either not kind or not rich is tall and vice versa.
Everyone who is not generous or not rich is curious.
If john is either humble or kind then john is either not kind or not brave.
Everyone who is not patient is old or calm.
Everyone who is not generous or not brave is both old and kind.
Everyone who is not brave is not curious and vice versa.
If lucy is not creative or happy then someone is not calm.
If someone is not funny then someone is not quiet or calm and vice versa.
If mary is rich then paul is calm and vice versa.
Susan is curious.
Someone is either old or not tall.
Mary is both creative and patient.
Someone is either not rich or funny.
Someone is not old.
Paul is curious. | Susan is not kind. | contradiction | (![X]:((~happy(X)&~curious(X))<=>~tall(X)))&
(![X]:(old(X)=>(humble(X)<~>~wise(X))))&
((?[X]:(~kind(X)))<=>((rich(john)&~curious(john))))&
((?[X]:((calm(X)|~calm(X))))<=>((creative(lucy)&~generous(lucy))))&
((?[X]:((~generous(X)|~curious(X))))<=>(~wise(fred)))&
(![X]:((~calm(X)<~>~happy(X))<=>~calm(X)))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((~kind(X)<~>~rich(X))<=>tall(X)))&
(![X]:((~generous(X)|~rich(X))=>curious(X)))&
(((humble(john)<~>kind(john)))=>((~kind(john)<~>~brave(john))))&
(![X]:(~patient(X)=>(old(X)|calm(X))))&
(![X]:((~generous(X)|~brave(X))=>(old(X)&kind(X))))&
(![X]:(~brave(X)<=>~curious(X)))&
(((~creative(lucy)|happy(lucy)))=>(?[X]:(~calm(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~quiet(X)|calm(X)))))&
((rich(mary))<=>(calm(paul)))&
(curious(susan))&
(?[X]:((old(X)<~>~tall(X))))&
((creative(mary)&patient(mary)))&
(?[X]:((~rich(X)<~>funny(X))))&
(?[X]:(~old(X)))&
(curious(paul)) | ~kind(susan) | [
"p0",
"p2",
"p5",
"p7",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 471425600772945995076571
% SZS output start Proof for 471425600772945995076571
1. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> ~tall(X0)) [input p0]
3. ? [X0] : ~kind(X0) <=> (~curious(john) & rich(john)) [input p2]
6. ! [X0] : ((~calm(X0) <~> ~happy(X0)) <=> ~calm(X0)) [input p5]
8. ! [X0] : ((~kind(X0) <~> ~rich(X0)) <=> tall(X0)) [input p7]
9. ! [X0] : ((~rich(X0) | ~generous(X0)) => curious(X0)) [input p8]
12. ! [X0] : ((~brave(X0) | ~generous(X0)) => (kind(X0) & old(X0))) [input p11]
13. ! [X0] : (~brave(X0) <=> ~curious(X0)) [input p12]
23. ~kind(susan) [input hypothesis]
30. ! [X0] : (curious(X0) | (rich(X0) & generous(X0))) [ennf transformation 9]
32. ! [X0] : ((kind(X0) & old(X0)) | (brave(X0) & generous(X0))) [ennf transformation 12]
34. ! [X0] : (((~curious(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) | happy(X0)))) [nnf transformation 1]
35. ! [X0] : (((~curious(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | curious(X0) | happy(X0))) [flattening 34]
37. (? [X0] : ~kind(X0) | (curious(john) | ~rich(john))) & ((~curious(john) & rich(john)) | ! [X0] : kind(X0)) [nnf transformation 3]
38. (? [X0] : ~kind(X0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X0] : kind(X0)) [flattening 37]
39. (? [X0] : ~kind(X0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X1] : kind(X1)) [rectify 38]
40. ? [X0] : ~kind(X0) => ~kind(sK0) [choice axiom]
41. (~kind(sK0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X1] : kind(X1)) [skolemisation 39,40]
51. ! [X0] : ((((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | calm(X0)) & (~calm(X0) | ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0))))) [nnf transformation 6]
55. ! [X0] : ((((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | ~tall(X0)) & (tall(X0) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0))))) [nnf transformation 8]
57. ! [X0] : ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))) [nnf transformation 13]
75. ~happy(X0) | tall(X0) [cnf transformation 35]
80. ~curious(john) | kind(X1) [cnf transformation 41]
91. ~calm(X0) | ~calm(X0) | happy(X0) [cnf transformation 51]
93. happy(X0) | calm(X0) | calm(X0) [cnf transformation 51]
97. ~rich(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 55]
100. rich(X0) | curious(X0) [cnf transformation 30]
108. brave(X0) | kind(X0) [cnf transformation 32]
110. ~brave(X0) | curious(X0) [cnf transformation 57]
126. ~kind(susan) [cnf transformation 23]
129. ~calm(X0) | happy(X0) [duplicate literal removal 91]
130. calm(X0) | happy(X0) [duplicate literal removal 93]
136. 2 <=> curious(john) [avatar definition]
137. ~curious(john) <- (~2) [avatar component clause 136]
145. 4 <=> ! [X1] : kind(X1) [avatar definition]
146. kind(X1) <- (4) [avatar component clause 145]
147. 4 | ~2 [avatar split clause 80,136,145]
181. 12 <=> ! [X1] : curious(X1) [avatar definition]
182. curious(X1) <- (12) [avatar component clause 181]
188. happy(X0) [subsumption resolution 129,130]
267. $false <- (4) [resolution 146,126]
268. ~4 [avatar contradiction clause 267]
269. $false <- (~2, 12) [subsumption resolution 137,182]
270. 2 | ~12 [avatar contradiction clause 269]
273. tall(X0) [resolution 75,188]
296. kind(X0) | curious(X0) [resolution 110,108]
322. ~kind(X0) | ~tall(X0) | curious(X0) [resolution 97,100]
326. ~kind(X0) | curious(X0) [subsumption resolution 322,273]
327. curious(X0) [subsumption resolution 326,296]
328. 12 [avatar split clause 327,181]
329. $false [avatar sat refutation 147,268,270,328]
% SZS output end Proof for 471425600772945995076571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both kind and creative.
If someone is both not brave and kind then someone is both not strong and happy.
If lucy is both not patient and not wise then mary is creative.
Everyone who is both not tall and not wise is both quiet and strong.
Everyone who is not rich is either not happy or calm and vice versa.
Everyone who is both not rich and not wise is old.
If john is either not generous or not calm then someone is both not wise and kind and vice versa.
If alice is not old or not kind then someone is both not strong and not funny and vice versa.
If john is both not patient and curious then someone is either rich or not old and vice versa.
Everyone who is patient or not old is both not strong and not calm and vice versa.
Everyone who is both humble and not kind is either not calm or kind.
Everyone who is either quiet or calm is not quiet or kind and vice versa.
If someone is either not funny or creative then someone is either not curious or funny.
Everyone who is either not wise or calm is both quiet and not brave.
If mary is both not old and not calm then someone is either wise or not tall and vice versa.
If lucy is not creative then someone is both not calm and generous.
Someone is both tall and happy.
Someone is brave.
Alice is not creative or not humble.
Someone is not calm or funny.
John is either not curious or funny.
Paul is quiet or not kind. | Paul is not kind. | contradiction | (![X]:(~humble(X)=>(kind(X)&creative(X))))&
((?[X]:((~brave(X)&kind(X))))=>(?[X]:((~strong(X)&happy(X)))))&
(((~patient(lucy)&~wise(lucy)))=>(creative(mary)))&
(![X]:((~tall(X)&~wise(X))=>(quiet(X)&strong(X))))&
(![X]:(~rich(X)<=>(~happy(X)<~>calm(X))))&
(![X]:((~rich(X)&~wise(X))=>old(X)))&
(((~generous(john)<~>~calm(john)))<=>(?[X]:((~wise(X)&kind(X)))))&
(((~old(alice)|~kind(alice)))<=>(?[X]:((~strong(X)&~funny(X)))))&
(((~patient(john)&curious(john)))<=>(?[X]:((rich(X)<~>~old(X)))))&
(![X]:((patient(X)|~old(X))<=>(~strong(X)&~calm(X))))&
(![X]:((humble(X)&~kind(X))=>(~calm(X)<~>kind(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(~quiet(X)|kind(X))))&
((?[X]:((~funny(X)<~>creative(X))))=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:((~wise(X)<~>calm(X))=>(quiet(X)&~brave(X))))&
(((~old(mary)&~calm(mary)))<=>(?[X]:((wise(X)<~>~tall(X)))))&
((~creative(lucy))=>(?[X]:((~calm(X)&generous(X)))))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:(brave(X)))&
((~creative(alice)|~humble(alice)))&
(?[X]:((~calm(X)|funny(X))))&
((~curious(john)<~>funny(john)))&
((quiet(paul)|~kind(paul))) | ~kind(paul) | [
"p0",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5912371402985616238854398
% SZS output start Proof for 5912371402985616238854398
1. ! [X0] : (~humble(X0) => (creative(X0) & kind(X0))) [input p0]
11. ! [X0] : ((~kind(X0) & humble(X0)) => (~calm(X0) <~> kind(X0))) [input p10]
12. ! [X0] : ((quiet(X0) <~> calm(X0)) <=> (kind(X0) | ~quiet(X0))) [input p11]
23. ~kind(paul) [input hypothesis]
26. ! [X0] : ((creative(X0) & kind(X0)) | humble(X0)) [ennf transformation 1]
34. ! [X0] : ((~calm(X0) <~> kind(X0)) | (kind(X0) | ~humble(X0))) [ennf transformation 11]
35. ! [X0] : ((~calm(X0) <~> kind(X0)) | kind(X0) | ~humble(X0)) [flattening 34]
59. ! [X0] : (((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | kind(X0) | ~humble(X0)) [nnf transformation 35]
60. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [nnf transformation 12]
61. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [flattening 60]
81. kind(X0) | humble(X0) [cnf transformation 26]
115. kind(X0) | ~calm(X0) | kind(X0) | ~humble(X0) [cnf transformation 59]
117. kind(X0) | ~quiet(X0) | calm(X0) | ~quiet(X0) [cnf transformation 61]
119. calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 61]
147. ~kind(paul) [cnf transformation 23]
148. kind(X0) | ~quiet(X0) | calm(X0) [duplicate literal removal 117]
149. calm(X0) | quiet(X0) [duplicate literal removal 119]
150. kind(X0) | ~calm(X0) | ~humble(X0) [duplicate literal removal 115]
254. kind(X0) | ~calm(X0) [subsumption resolution 150,81]
256. kind(X0) | calm(X0) [subsumption resolution 148,149]
257. kind(X0) [subsumption resolution 256,254]
346. $false [subsumption resolution 147,257]
% SZS output end Proof for 5912371402985616238854398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or quiet then someone is not wise or not rich and vice versa. If someone is both not generous and brave then someone is either rich or generous and vice versa. If fred is funny then fred is either not calm or not strong and vice versa. If alice is both brave and not kind then john is both not tall and not strong. Everyone who is not funny is not rich or curious. If someone is generous or calm then susan is both not calm and curious and vice versa. Everyone who is not brave or tall is not quiet or generous and vice versa. Everyone who is not wise or not rich is not creative. If lucy is not happy or strong then lucy is not quiet or not generous and vice versa. If someone is either creative or tall then someone is calm or quiet and vice versa. If someone is both rich and not brave then paul is happy or strong. If john is not tall or strong then paul is both not patient and old and vice versa. Everyone who is either old or rich is both not brave and brave. If john is both not brave and tall then someone is patient or strong and vice versa. If someone is both not brave and tall then mary is not humble or not creative. If fred is either brave or not happy then someone is either patient or not strong. Someone is generous. Susan is not funny. Alice is both creative and not tall. Someone is either not curious or not generous. Paul is not tall or tall. Paul is both not calm and not humble. Lucy is either tall or not curious. Someone is not creative or not calm. | Paul is calm. | contradiction | ((?[X]:((calm(X)|quiet(X))))<=>(?[X]:((~wise(X)|~rich(X)))))&
((?[X]:((~generous(X)&brave(X))))<=>(?[X]:((rich(X)<~>generous(X)))))&
((funny(fred))<=>((~calm(fred)<~>~strong(fred))))&
(((brave(alice)&~kind(alice)))=>((~tall(john)&~strong(john))))&
(![X]:(~funny(X)=>(~rich(X)|curious(X))))&
((?[X]:((generous(X)|calm(X))))<=>((~calm(susan)&curious(susan))))&
(![X]:((~brave(X)|tall(X))<=>(~quiet(X)|generous(X))))&
(![X]:((~wise(X)|~rich(X))=>~creative(X)))&
(((~happy(lucy)|strong(lucy)))<=>((~quiet(lucy)|~generous(lucy))))&
((?[X]:((creative(X)<~>tall(X))))<=>(?[X]:((calm(X)|quiet(X)))))&
((?[X]:((rich(X)&~brave(X))))=>((happy(paul)|strong(paul))))&
(((~tall(john)|strong(john)))<=>((~patient(paul)&old(paul))))&
(![X]:((old(X)<~>rich(X))=>(~brave(X)&brave(X))))&
(((~brave(john)&tall(john)))<=>(?[X]:((patient(X)|strong(X)))))&
((?[X]:((~brave(X)&tall(X))))=>((~humble(mary)|~creative(mary))))&
(((brave(fred)<~>~happy(fred)))=>(?[X]:((patient(X)<~>~strong(X)))))&
(?[X]:(generous(X)))&
(~funny(susan))&
((creative(alice)&~tall(alice)))&
(?[X]:((~curious(X)<~>~generous(X))))&
((~tall(paul)|tall(paul)))&
((~calm(paul)&~humble(paul)))&
((tall(lucy)<~>~curious(lucy)))&
(?[X]:((~creative(X)|~calm(X)))) | calm(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5497053271812451245445810
% SZS output start Proof for 5497053271812451245445810
22. ~humble(paul) & ~calm(paul) [input p21]
25. calm(paul) [input hypothesis]
30. ~calm(paul) [pure predicate removal 22]
145. ~calm(paul) [cnf transformation 30]
149. calm(paul) [cnf transformation 25]
408. $false [subsumption resolution 149,145]
% SZS output end Proof for 5497053271812451245445810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not curious or not wise then someone is both not old and calm.
Everyone who is not kind is both kind and not curious.
Everyone who is either not calm or strong is not generous and vice versa.
Everyone who is either rich or not humble is not funny or patient.
If alice is brave then fred is kind and vice versa.
If lucy is both brave and patient then someone is either calm or strong and vice versa.
If susan is rich then someone is not old or not funny.
If paul is either not generous or old then fred is both not happy and quiet and vice versa.
If lucy is both old and not wise then alice is either not wise or generous.
Everyone who is either wise or not funny is either not brave or not strong and vice versa.
Everyone who is either not strong or not quiet is rich or not creative and vice versa.
Everyone who is either wise or tall is both not brave and not calm and vice versa.
Everyone who is both generous and strong is both not brave and calm and vice versa.
Everyone who is not calm or tall is both old and not curious.
If fred is either not funny or old then someone is either patient or not tall.
If paul is both happy and not calm then someone is kind or rich.
Someone is either not tall or generous.
Someone is not creative.
Someone is old or not creative.
John is rich or funny.
Someone is not wise.
Someone is both patient and not old.
Someone is not rich.
Someone is kind or not rich. | John is not kind. | contradiction | (((~curious(paul)|~wise(paul)))=>(?[X]:((~old(X)&calm(X)))))&
(![X]:(~kind(X)=>(kind(X)&~curious(X))))&
(![X]:((~calm(X)<~>strong(X))<=>~generous(X)))&
(![X]:((rich(X)<~>~humble(X))=>(~funny(X)|patient(X))))&
((brave(alice))<=>(kind(fred)))&
(((brave(lucy)&patient(lucy)))<=>(?[X]:((calm(X)<~>strong(X)))))&
((rich(susan))=>(?[X]:((~old(X)|~funny(X)))))&
(((~generous(paul)<~>old(paul)))<=>((~happy(fred)&quiet(fred))))&
(((old(lucy)&~wise(lucy)))=>((~wise(alice)<~>generous(alice))))&
(![X]:((wise(X)<~>~funny(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(rich(X)|~creative(X))))&
(![X]:((wise(X)<~>tall(X))<=>(~brave(X)&~calm(X))))&
(![X]:((generous(X)&strong(X))<=>(~brave(X)&calm(X))))&
(![X]:((~calm(X)|tall(X))=>(old(X)&~curious(X))))&
(((~funny(fred)<~>old(fred)))=>(?[X]:((patient(X)<~>~tall(X)))))&
(((happy(paul)&~calm(paul)))=>(?[X]:((kind(X)|rich(X)))))&
(?[X]:((~tall(X)<~>generous(X))))&
(?[X]:(~creative(X)))&
(?[X]:((old(X)|~creative(X))))&
((rich(john)|funny(john)))&
(?[X]:(~wise(X)))&
(?[X]:((patient(X)&~old(X))))&
(?[X]:(~rich(X)))&
(?[X]:((kind(X)|~rich(X)))) | ~kind(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 40769826461014517678266
% SZS output start Proof for 40769826461014517678266
2. ! [X0] : (~kind(X0) => (~curious(X0) & kind(X0))) [input p1]
25. ~kind(john) [input hypothesis]
27. ! [X0] : ((~curious(X0) & kind(X0)) | kind(X0)) [ennf transformation 2]
83. kind(X0) | kind(X0) [cnf transformation 27]
151. ~kind(john) [cnf transformation 25]
152. kind(X0) [duplicate literal removal 83]
304. $false [subsumption resolution 151,152]
% SZS output end Proof for 40769826461014517678266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is either brave or not kind. If someone is humble or wise then someone is either tall or brave and vice versa. If fred is not calm then someone is not humble or not funny and vice versa. Everyone who is both not brave and not rich is not old and vice versa. Everyone who is either quiet or strong is not strong or not humble and vice versa. Everyone who is not wise is both funny and old and vice versa. Everyone who is either tall or not tall is not brave. Everyone who is either generous or not rich is either not strong or brave and vice versa. Everyone who is not quiet or curious is generous. If fred is both wise and not brave then paul is curious. If alice is either not wise or not calm then someone is either wise or creative. If someone is creative then alice is humble or not patient. Everyone who is generous or not creative is either not funny or not rich and vice versa. If paul is both patient and not old then mary is funny. Everyone who is either curious or not calm is not tall and vice versa. John is either not strong or not happy. Someone is not brave. Someone is either brave or not kind. John is not wise. Someone is patient. Susan is not curious or calm. Lucy is not creative. | Paul is not old. | neutral | (![X]:(~brave(X)=>(brave(X)<~>~kind(X))))&
((?[X]:((humble(X)|wise(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
((~calm(fred))<=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:((~brave(X)&~rich(X))<=>~old(X)))&
(![X]:((quiet(X)<~>strong(X))<=>(~strong(X)|~humble(X))))&
(![X]:(~wise(X)<=>(funny(X)&old(X))))&
(![X]:((tall(X)<~>~tall(X))=>~brave(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(~strong(X)<~>brave(X))))&
(![X]:((~quiet(X)|curious(X))=>generous(X)))&
(((wise(fred)&~brave(fred)))=>(curious(paul)))&
(((~wise(alice)<~>~calm(alice)))=>(?[X]:((wise(X)<~>creative(X)))))&
((?[X]:(creative(X)))=>((humble(alice)|~patient(alice))))&
(![X]:((generous(X)|~creative(X))<=>(~funny(X)<~>~rich(X))))&
(((patient(paul)&~old(paul)))=>(funny(mary)))&
(![X]:((curious(X)<~>~calm(X))<=>~tall(X)))&
((~strong(john)<~>~happy(john)))&
(?[X]:(~brave(X)))&
(?[X]:((brave(X)<~>~kind(X))))&
(~wise(john))&
(?[X]:(patient(X)))&
((~curious(susan)|calm(susan)))&
(~creative(lucy)) | ~old(paul) | [] | null | 0 |
Everyone who is not generous is tall or not creative and vice versa.
If someone is either patient or curious then susan is both not brave and humble.
If lucy is rich then alice is not curious and vice versa.
If john is happy or not tall then someone is not quiet.
Everyone who is not curious or curious is either strong or not generous and vice versa.
If mary is either quiet or tall then lucy is tall or wise and vice versa.
Everyone who is not quiet is not funny.
If someone is calm or not funny then someone is not curious or not humble.
Everyone who is not wise or old is either not curious or kind and vice versa.
If someone is not quiet then someone is either curious or not strong.
If someone is not creative or wise then someone is both not generous and generous.
Everyone who is either not tall or not kind is not curious or generous.
If lucy is not rich or strong then someone is tall or not kind.
If mary is not humble then alice is both generous and funny and vice versa.
If someone is both wise and not patient then someone is patient and vice versa.
If someone is either old or not brave then mary is both not brave and happy.
Lucy is not strong or not curious.
Susan is either wise or strong.
Someone is either not rich or not humble.
Someone is happy or not tall.
Alice is not patient or not rich.
Alice is not happy.
Someone is both humble and not funny.
Someone is creative. | Susan is not wise. | entailment | (![X]:(~generous(X)<=>(tall(X)|~creative(X))))&
((?[X]:((patient(X)<~>curious(X))))=>((~brave(susan)&humble(susan))))&
((rich(lucy))<=>(~curious(alice)))&
(((happy(john)|~tall(john)))=>(?[X]:(~quiet(X))))&
(![X]:((~curious(X)|curious(X))<=>(strong(X)<~>~generous(X))))&
(((quiet(mary)<~>tall(mary)))<=>((tall(lucy)|wise(lucy))))&
(![X]:(~quiet(X)=>~funny(X)))&
((?[X]:((calm(X)|~funny(X))))=>(?[X]:((~curious(X)|~humble(X)))))&
(![X]:((~wise(X)|old(X))<=>(~curious(X)<~>kind(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((curious(X)<~>~strong(X)))))&
((?[X]:((~creative(X)|wise(X))))=>(?[X]:((~generous(X)&generous(X)))))&
(![X]:((~tall(X)<~>~kind(X))=>(~curious(X)|generous(X))))&
(((~rich(lucy)|strong(lucy)))=>(?[X]:((tall(X)|~kind(X)))))&
((~humble(mary))<=>((generous(alice)&funny(alice))))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:(patient(X))))&
((?[X]:((old(X)<~>~brave(X))))=>((~brave(mary)&happy(mary))))&
((~strong(lucy)|~curious(lucy)))&
((wise(susan)<~>strong(susan)))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:((happy(X)|~tall(X))))&
((~patient(alice)|~rich(alice)))&
(~happy(alice))&
(?[X]:((humble(X)&~funny(X))))&
(?[X]:(creative(X))) | ~wise(susan) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 671003071838596364557468
% SZS output start Proof for 671003071838596364557468
11. ? [X0] : (wise(X0) | ~creative(X0)) => ? [X0] : (generous(X0) & ~generous(X0)) [input p10]
25. wise(susan) [input hypothesis]
28. ? [X0] : (wise(X0) | ~creative(X0)) => ? [X1] : (generous(X1) & ~generous(X1)) [rectify 11]
36. ? [X1] : (generous(X1) & ~generous(X1)) | ! [X0] : (~wise(X0) & creative(X0)) [ennf transformation 28]
60. ? [X0] : (generous(X0) & ~generous(X0)) | ! [X1] : (~wise(X1) & creative(X1)) [rectify 36]
61. ? [X0] : (generous(X0) & ~generous(X0)) => (generous(sK3) & ~generous(sK3)) [choice axiom]
62. (generous(sK3) & ~generous(sK3)) | ! [X1] : (~wise(X1) & creative(X1)) [skolemisation 60,61]
118. ~generous(sK3) | ~wise(X1) [cnf transformation 62]
120. generous(sK3) | ~wise(X1) [cnf transformation 62]
146. wise(susan) [cnf transformation 25]
239. 20 <=> ! [X1] : ~wise(X1) [avatar definition]
240. ~wise(X1) <- (20) [avatar component clause 239]
242. 21 <=> generous(sK3) [avatar definition]
245. 20 | 21 [avatar split clause 120,242,239]
250. 20 | ~21 [avatar split clause 118,242,239]
327. 39 <=> wise(susan) [avatar definition]
328. wise(susan) <- (39) [avatar component clause 327]
364. 39 [avatar split clause 146,327]
365. $false <- (20, 39) [resolution 328,240]
366. ~20 | ~39 [avatar contradiction clause 365]
367. $false [avatar sat refutation 245,250,364,366]
% SZS output end Proof for 671003071838596364557468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then john is not kind or generous and vice versa. If someone is either quiet or creative then susan is curious and vice versa. Everyone who is brave is both not old and not curious and vice versa. Everyone who is patient or not creative is calm and vice versa. Everyone who is not strong is both humble and patient and vice versa. Everyone who is both not brave and not old is creative. If someone is not humble or funny then someone is both tall and not wise and vice versa. If someone is both not brave and not wise then alice is either not quiet or calm. Everyone who is quiet or humble is either not old or kind and vice versa. If alice is happy or not quiet then someone is either quiet or not quiet and vice versa. Everyone who is both strong and not calm is not quiet and vice versa. Everyone who is not brave or calm is not patient or humble. Everyone who is not kind or tall is both kind and not quiet. If someone is both not tall and patient then alice is rich and vice versa. Everyone who is both not generous and not brave is not calm and vice versa. Everyone who is not calm or not kind is both humble and strong. Someone is either strong or not generous. Paul is both creative and not brave. Alice is not curious or calm. Someone is not brave or quiet. John is either happy or wise. Mary is generous. | Paul is humble. | entailment | ((?[X]:(kind(X)))<=>((~kind(john)|generous(john))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(curious(susan)))&
(![X]:(brave(X)<=>(~old(X)&~curious(X))))&
(![X]:((patient(X)|~creative(X))<=>calm(X)))&
(![X]:(~strong(X)<=>(humble(X)&patient(X))))&
(![X]:((~brave(X)&~old(X))=>creative(X)))&
((?[X]:((~humble(X)|funny(X))))<=>(?[X]:((tall(X)&~wise(X)))))&
((?[X]:((~brave(X)&~wise(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((quiet(X)|humble(X))<=>(~old(X)<~>kind(X))))&
(((happy(alice)|~quiet(alice)))<=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((strong(X)&~calm(X))<=>~quiet(X)))&
(![X]:((~brave(X)|calm(X))=>(~patient(X)|humble(X))))&
(![X]:((~kind(X)|tall(X))=>(kind(X)&~quiet(X))))&
((?[X]:((~tall(X)&patient(X))))<=>(rich(alice)))&
(![X]:((~generous(X)&~brave(X))<=>~calm(X)))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)&strong(X))))&
(?[X]:((strong(X)<~>~generous(X))))&
((creative(paul)&~brave(paul)))&
((~curious(alice)|calm(alice)))&
(?[X]:((~brave(X)|quiet(X))))&
((happy(john)<~>wise(john)))&
(generous(mary)) | humble(paul) | [
"p3",
"p11",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4890687117881014358447080
% SZS output start Proof for 4890687117881014358447080
4. ! [X0] : ((~creative(X0) | patient(X0)) <=> calm(X0)) [input p3]
12. ! [X0] : ((calm(X0) | ~brave(X0)) => (humble(X0) | ~patient(X0))) [input p11]
16. ! [X0] : ((~kind(X0) | ~calm(X0)) => (strong(X0) & humble(X0))) [input p15]
18. ~brave(paul) & creative(paul) [input p17]
23. ~humble(paul) [input hypothesis]
28. ! [X0] : ((humble(X0) | ~patient(X0)) | (~calm(X0) & brave(X0))) [ennf transformation 12]
29. ! [X0] : (humble(X0) | ~patient(X0) | (~calm(X0) & brave(X0))) [flattening 28]
31. ! [X0] : ((strong(X0) & humble(X0)) | (kind(X0) & calm(X0))) [ennf transformation 16]
43. ! [X0] : (((~creative(X0) | patient(X0)) | ~calm(X0)) & (calm(X0) | (creative(X0) & ~patient(X0)))) [nnf transformation 4]
44. ! [X0] : ((~creative(X0) | patient(X0) | ~calm(X0)) & (calm(X0) | (creative(X0) & ~patient(X0)))) [flattening 43]
84. ~patient(X0) | calm(X0) [cnf transformation 44]
86. ~calm(X0) | patient(X0) | ~creative(X0) [cnf transformation 44]
114. humble(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 29]
125. humble(X0) | calm(X0) [cnf transformation 31]
131. creative(paul) [cnf transformation 18]
138. ~humble(paul) [cnf transformation 23]
237. ~patient(X0) | humble(X0) [subsumption resolution 114,84]
315. calm(paul) [resolution 125,138]
330. patient(paul) | ~creative(paul) [resolution 86,315]
344. patient(paul) [subsumption resolution 330,131]
450. humble(paul) [resolution 344,237]
452. $false [subsumption resolution 450,138]
% SZS output end Proof for 4890687117881014358447080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or patient is either funny or not quiet and vice versa.
If someone is both happy and not rich then john is kind.
If someone is rich then someone is strong and vice versa.
If fred is either patient or curious then someone is humble and vice versa.
If alice is curious or generous then someone is either not rich or humble and vice versa.
Everyone who is not kind or not wise is not curious or not quiet.
Everyone who is patient is both not brave and not calm.
If someone is both quiet and not happy then someone is creative and vice versa.
If someone is strong or not wise then someone is both not old and calm.
If john is both old and tall then someone is either funny or tall and vice versa.
If alice is not tall or humble then someone is either happy or not quiet.
Everyone who is wise or generous is both funny and kind.
Everyone who is not kind is both not patient and calm and vice versa.
Everyone who is either not calm or not funny is both not happy and not funny.
If lucy is both not curious and not patient then alice is both not creative and brave.
If fred is either strong or curious then mary is strong.
Paul is either creative or not curious.
Someone is either tall or patient.
Someone is not humble.
Paul is not brave or not calm.
John is not strong or not old.
Someone is not strong or rich.
Fred is either not kind or not wise.
Alice is not rich. | John is generous. | contradiction | (![X]:((~humble(X)<~>patient(X))<=>(funny(X)<~>~quiet(X))))&
((?[X]:((happy(X)&~rich(X))))=>(kind(john)))&
((?[X]:(rich(X)))<=>(?[X]:(strong(X))))&
(((patient(fred)<~>curious(fred)))<=>(?[X]:(humble(X))))&
(((curious(alice)|generous(alice)))<=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((~kind(X)|~wise(X))=>(~curious(X)|~quiet(X))))&
(![X]:(patient(X)=>(~brave(X)&~calm(X))))&
((?[X]:((quiet(X)&~happy(X))))<=>(?[X]:(creative(X))))&
((?[X]:((strong(X)|~wise(X))))=>(?[X]:((~old(X)&calm(X)))))&
(((old(john)&tall(john)))<=>(?[X]:((funny(X)<~>tall(X)))))&
(((~tall(alice)|humble(alice)))=>(?[X]:((happy(X)<~>~quiet(X)))))&
(![X]:((wise(X)|generous(X))=>(funny(X)&kind(X))))&
(![X]:(~kind(X)<=>(~patient(X)&calm(X))))&
(![X]:((~calm(X)<~>~funny(X))=>(~happy(X)&~funny(X))))&
(((~curious(lucy)&~patient(lucy)))=>((~creative(alice)&brave(alice))))&
(((strong(fred)<~>curious(fred)))=>(strong(mary)))&
((creative(paul)<~>~curious(paul)))&
(?[X]:((tall(X)<~>patient(X))))&
(?[X]:(~humble(X)))&
((~brave(paul)|~calm(paul)))&
((~strong(john)|~old(john)))&
(?[X]:((~strong(X)|rich(X))))&
((~kind(fred)<~>~wise(fred)))&
(~rich(alice)) | generous(john) | [
"p6",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2804297978307911775761730
% SZS output start Proof for 2804297978307911775761730
7. ! [X0] : (patient(X0) => (~calm(X0) & ~brave(X0))) [input p6]
12. ! [X0] : ((generous(X0) | wise(X0)) => (kind(X0) & funny(X0))) [input p11]
13. ! [X0] : (~kind(X0) <=> (calm(X0) & ~patient(X0))) [input p12]
14. ! [X0] : ((~calm(X0) <~> ~funny(X0)) => (~funny(X0) & ~happy(X0))) [input p13]
25. generous(john) [input hypothesis]
32. ! [X0] : ((~calm(X0) & ~brave(X0)) | ~patient(X0)) [ennf transformation 7]
35. ! [X0] : ((kind(X0) & funny(X0)) | (~generous(X0) & ~wise(X0))) [ennf transformation 12]
36. ! [X0] : ((~funny(X0) & ~happy(X0)) | (~calm(X0) <=> ~funny(X0))) [ennf transformation 14]
71. ! [X0] : ((~kind(X0) | (~calm(X0) | patient(X0))) & ((calm(X0) & ~patient(X0)) | kind(X0))) [nnf transformation 13]
72. ! [X0] : ((~kind(X0) | ~calm(X0) | patient(X0)) & ((calm(X0) & ~patient(X0)) | kind(X0))) [flattening 71]
73. ! [X0] : ((~funny(X0) & ~happy(X0)) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0)))) [nnf transformation 36]
108. ~calm(X0) | ~patient(X0) [cnf transformation 32]
127. ~generous(X0) | funny(X0) [cnf transformation 35]
129. ~generous(X0) | kind(X0) [cnf transformation 35]
132. ~kind(X0) | ~calm(X0) | patient(X0) [cnf transformation 72]
135. ~funny(X0) | ~funny(X0) | calm(X0) [cnf transformation 73]
152. generous(john) [cnf transformation 25]
153. ~funny(X0) | calm(X0) [duplicate literal removal 135]
158. 2 <=> kind(john) [avatar definition]
309. ~calm(X0) | ~kind(X0) [subsumption resolution 132,108]
386. funny(john) [resolution 127,152]
387. kind(john) [resolution 129,152]
389. calm(john) [resolution 153,386]
399. ~kind(john) [resolution 309,389]
402. ~2 [avatar split clause 399,158]
403. 2 [avatar split clause 387,158]
405. $false [avatar sat refutation 402,403]
% SZS output end Proof for 2804297978307911775761730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not calm is not calm or strong.
Everyone who is both patient and brave is either curious or rich and vice versa.
Everyone who is either brave or old is either not happy or not funny and vice versa.
If fred is kind then someone is not generous and vice versa.
If someone is either patient or not curious then lucy is either not curious or not quiet and vice versa.
If john is not creative then mary is both not wise and old and vice versa.
If susan is either old or not wise then susan is either tall or not happy.
If fred is strong or not creative then someone is both not rich and rich and vice versa.
If paul is either not rich or not funny then john is rich or not creative.
If someone is not funny or not creative then someone is not old or not funny and vice versa.
Everyone who is both not old and old is rich and vice versa.
Everyone who is either calm or brave is either not old or happy.
Everyone who is patient is not patient or brave and vice versa.
If susan is either not tall or calm then alice is not humble and vice versa.
Everyone who is both old and not humble is both not tall and quiet.
Everyone who is both not kind and wise is both not curious and not brave and vice versa.
Someone is both not humble and not quiet.
Someone is both calm and not strong.
Someone is either happy or not strong.
Mary is creative.
Someone is creative or not happy.
Fred is not curious or kind.
Someone is both not tall and calm.
Mary is creative or not quiet. | John is wise. | neutral | (![X]:((tall(X)<~>~calm(X))=>(~calm(X)|strong(X))))&
(![X]:((patient(X)&brave(X))<=>(curious(X)<~>rich(X))))&
(![X]:((brave(X)<~>old(X))<=>(~happy(X)<~>~funny(X))))&
((kind(fred))<=>(?[X]:(~generous(X))))&
((?[X]:((patient(X)<~>~curious(X))))<=>((~curious(lucy)<~>~quiet(lucy))))&
((~creative(john))<=>((~wise(mary)&old(mary))))&
(((old(susan)<~>~wise(susan)))=>((tall(susan)<~>~happy(susan))))&
(((strong(fred)|~creative(fred)))<=>(?[X]:((~rich(X)&rich(X)))))&
(((~rich(paul)<~>~funny(paul)))=>((rich(john)|~creative(john))))&
((?[X]:((~funny(X)|~creative(X))))<=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((~old(X)&old(X))<=>rich(X)))&
(![X]:((calm(X)<~>brave(X))=>(~old(X)<~>happy(X))))&
(![X]:(patient(X)<=>(~patient(X)|brave(X))))&
(((~tall(susan)<~>calm(susan)))<=>(~humble(alice)))&
(![X]:((old(X)&~humble(X))=>(~tall(X)&quiet(X))))&
(![X]:((~kind(X)&wise(X))<=>(~curious(X)&~brave(X))))&
(?[X]:((~humble(X)&~quiet(X))))&
(?[X]:((calm(X)&~strong(X))))&
(?[X]:((happy(X)<~>~strong(X))))&
(creative(mary))&
(?[X]:((creative(X)|~happy(X))))&
((~curious(fred)|kind(fred)))&
(?[X]:((~tall(X)&calm(X))))&
((creative(mary)|~quiet(mary))) | wise(john) | [] | null | 0 |
If someone is both tall and not curious then lucy is humble. If someone is old or wise then someone is both patient and not strong. Everyone who is both not tall and wise is generous. Everyone who is both not brave and not calm is not tall. If alice is rich then someone is either rich or brave and vice versa. Everyone who is either creative or generous is either humble or old and vice versa. Everyone who is both quiet and not wise is both wise and not creative and vice versa. If someone is humble then lucy is either not curious or not funny and vice versa. Everyone who is both rich and not funny is either brave or not kind. Everyone who is funny is brave or curious and vice versa. Everyone who is both not kind and calm is tall. Everyone who is not kind is both generous and not funny. Everyone who is old is not humble or not funny. If mary is calm then someone is either brave or not patient and vice versa. If susan is funny then susan is not rich or tall. Everyone who is brave is both not kind and rich. Fred is both not rich and not happy. Susan is humble or not kind. Someone is not brave or patient. Someone is both not funny and not creative. Someone is either happy or patient. Someone is creative or not brave. Mary is creative. | Lucy is not curious. | neutral | ((?[X]:((tall(X)&~curious(X))))=>(humble(lucy)))&
((?[X]:((old(X)|wise(X))))=>(?[X]:((patient(X)&~strong(X)))))&
(![X]:((~tall(X)&wise(X))=>generous(X)))&
(![X]:((~brave(X)&~calm(X))=>~tall(X)))&
((rich(alice))<=>(?[X]:((rich(X)<~>brave(X)))))&
(![X]:((creative(X)<~>generous(X))<=>(humble(X)<~>old(X))))&
(![X]:((quiet(X)&~wise(X))<=>(wise(X)&~creative(X))))&
((?[X]:(humble(X)))<=>((~curious(lucy)<~>~funny(lucy))))&
(![X]:((rich(X)&~funny(X))=>(brave(X)<~>~kind(X))))&
(![X]:(funny(X)<=>(brave(X)|curious(X))))&
(![X]:((~kind(X)&calm(X))=>tall(X)))&
(![X]:(~kind(X)=>(generous(X)&~funny(X))))&
(![X]:(old(X)=>(~humble(X)|~funny(X))))&
((calm(mary))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((funny(susan))=>((~rich(susan)|tall(susan))))&
(![X]:(brave(X)=>(~kind(X)&rich(X))))&
((~rich(fred)&~happy(fred)))&
((humble(susan)|~kind(susan)))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((~funny(X)&~creative(X))))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((creative(X)|~brave(X))))&
(creative(mary)) | ~curious(lucy) | [] | null | 0 |
If john is either happy or calm then alice is both wise and not funny and vice versa. Everyone who is brave or old is happy and vice versa. If someone is not happy then paul is both not brave and strong and vice versa. Everyone who is both not quiet and not old is both creative and rich and vice versa. If someone is both brave and calm then someone is both not quiet and generous and vice versa. If someone is calm or not calm then someone is patient. If someone is either tall or not brave then alice is either not calm or not curious and vice versa. Everyone who is either brave or wise is not brave. Everyone who is either not tall or not patient is not old and vice versa. If lucy is rich or not funny then someone is both not kind and funny. Everyone who is quiet or not funny is both not curious and wise. If paul is not funny then mary is either not happy or patient. If susan is either not funny or not creative then alice is not generous or not patient. If lucy is either not creative or not patient then someone is both brave and not funny and vice versa. Everyone who is both not wise and creative is either patient or not happy and vice versa. Someone is either rich or humble. Someone is humble or kind. Paul is both tall and not calm. Someone is either creative or not wise. Someone is not patient or humble. Lucy is humble or funny. Lucy is not happy. | Paul is funny. | entailment | (((happy(john)<~>calm(john)))<=>((wise(alice)&~funny(alice))))&
(![X]:((brave(X)|old(X))<=>happy(X)))&
((?[X]:(~happy(X)))<=>((~brave(paul)&strong(paul))))&
(![X]:((~quiet(X)&~old(X))<=>(creative(X)&rich(X))))&
((?[X]:((brave(X)&calm(X))))<=>(?[X]:((~quiet(X)&generous(X)))))&
((?[X]:((calm(X)|~calm(X))))=>(?[X]:(patient(X))))&
((?[X]:((tall(X)<~>~brave(X))))<=>((~calm(alice)<~>~curious(alice))))&
(![X]:((brave(X)<~>wise(X))=>~brave(X)))&
(![X]:((~tall(X)<~>~patient(X))<=>~old(X)))&
(((rich(lucy)|~funny(lucy)))=>(?[X]:((~kind(X)&funny(X)))))&
(![X]:((quiet(X)|~funny(X))=>(~curious(X)&wise(X))))&
((~funny(paul))=>((~happy(mary)<~>patient(mary))))&
(((~funny(susan)<~>~creative(susan)))=>((~generous(alice)|~patient(alice))))&
(((~creative(lucy)<~>~patient(lucy)))<=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:((~wise(X)&creative(X))<=>(patient(X)<~>~happy(X))))&
(?[X]:((rich(X)<~>humble(X))))&
(?[X]:((humble(X)|kind(X))))&
((tall(paul)&~calm(paul)))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((~patient(X)|humble(X))))&
((humble(lucy)|funny(lucy)))&
(~happy(lucy)) | funny(paul) | [
"p1",
"p2",
"p8",
"p10",
"p14",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5258916842765208436916909
% SZS output start Proof for 5258916842765208436916909
2. ! [X0] : ((old(X0) | brave(X0)) <=> happy(X0)) [input p1]
3. ? [X0] : ~happy(X0) <=> (strong(paul) & ~brave(paul)) [input p2]
9. ! [X0] : ((~tall(X0) <~> ~patient(X0)) <=> ~old(X0)) [input p8]
11. ! [X0] : ((~funny(X0) | quiet(X0)) => (wise(X0) & ~curious(X0))) [input p10]
15. ! [X0] : ((creative(X0) & ~wise(X0)) <=> (patient(X0) <~> ~happy(X0))) [input p14]
18. ~calm(paul) & tall(paul) [input p17]
22. ~happy(lucy) [input p21]
23. ~funny(paul) [input hypothesis]
29. ! [X0] : ((wise(X0) & ~curious(X0)) | (funny(X0) & ~quiet(X0))) [ennf transformation 11]
35. ! [X0] : (((old(X0) | brave(X0)) | ~happy(X0)) & (happy(X0) | (~old(X0) & ~brave(X0)))) [nnf transformation 2]
36. ! [X0] : ((old(X0) | brave(X0) | ~happy(X0)) & (happy(X0) | (~old(X0) & ~brave(X0)))) [flattening 35]
37. (? [X0] : ~happy(X0) | (~strong(paul) | brave(paul))) & ((strong(paul) & ~brave(paul)) | ! [X0] : happy(X0)) [nnf transformation 3]
38. (? [X0] : ~happy(X0) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X0] : happy(X0)) [flattening 37]
39. (? [X0] : ~happy(X0) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X1] : happy(X1)) [rectify 38]
40. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
41. (~happy(sK0) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X1] : happy(X1)) [skolemisation 39,40]
57. ! [X0] : ((((patient(X0) | tall(X0)) & (~patient(X0) | ~tall(X0))) | old(X0)) & (~old(X0) | ((~tall(X0) | patient(X0)) & (~patient(X0) | tall(X0))))) [nnf transformation 9]
66. ! [X0] : (((creative(X0) & ~wise(X0)) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (~creative(X0) | wise(X0)))) [nnf transformation 15]
67. ! [X0] : (((creative(X0) & ~wise(X0)) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | ~creative(X0) | wise(X0))) [flattening 66]
85. ~old(X0) | happy(X0) [cnf transformation 36]
86. ~happy(X0) | brave(X0) | old(X0) [cnf transformation 36]
87. ~brave(paul) | happy(X1) [cnf transformation 41]
111. ~tall(X0) | ~old(X0) | patient(X0) [cnf transformation 57]
112. ~tall(X0) | ~patient(X0) | old(X0) [cnf transformation 57]
121. funny(X0) | wise(X0) [cnf transformation 29]
134. ~patient(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 67]
135. ~wise(X0) | patient(X0) | happy(X0) [cnf transformation 67]
141. tall(paul) [cnf transformation 18]
147. ~happy(lucy) [cnf transformation 22]
148. ~funny(paul) [cnf transformation 23]
173. 5 <=> brave(paul) [avatar definition]
186. 8 <=> ! [X1] : happy(X1) [avatar definition]
187. happy(X1) <- (8) [avatar component clause 186]
189. 8 | ~5 [avatar split clause 87,173,186]
279. 28 <=> funny(paul) [avatar definition]
280. ~funny(paul) <- (~28) [avatar component clause 279]
378. ~28 [avatar split clause 148,279]
382. wise(paul) <- (~28) [resolution 121,280]
440. ~old(paul) | patient(paul) [resolution 111,141]
442. 58 <=> patient(paul) [avatar definition]
443. ~patient(paul) <- (~58) [avatar component clause 442]
444. patient(paul) <- (58) [avatar component clause 442]
446. 59 <=> old(paul) [avatar definition]
447. old(paul) <- (59) [avatar component clause 446]
448. ~old(paul) <- (~59) [avatar component clause 446]
449. 58 | ~59 [avatar split clause 440,446,442]
450. ~patient(paul) | old(paul) [resolution 112,141]
486. patient(paul) | happy(paul) <- (~28) [resolution 135,382]
488. happy(paul) <- (~28, ~58) [subsumption resolution 486,443]
579. brave(paul) | old(paul) <- (~28, ~58) [resolution 488,86]
583. brave(paul) <- (~28, ~58, ~59) [subsumption resolution 579,448]
584. 5 | 28 | 58 | 59 [avatar split clause 583,446,442,279,173]
604. $false <- (8) [resolution 187,147]
613. ~8 [avatar contradiction clause 604]
616. 75 <=> happy(paul) [avatar definition]
617. ~happy(paul) <- (~75) [avatar component clause 616]
619. 75 | 58 | 28 [avatar split clause 486,279,442,616]
620. 59 | ~58 [avatar split clause 450,442,446]
634. ~happy(paul) | ~wise(paul) <- (58) [resolution 444,134]
641. ~happy(paul) <- (~28, 58) [subsumption resolution 634,382]
642. ~75 | 28 | ~58 [avatar split clause 641,442,279,616]
643. happy(paul) <- (59) [resolution 447,85]
644. $false <- (59, ~75) [subsumption resolution 643,617]
645. ~59 | 75 [avatar contradiction clause 644]
646. $false [avatar sat refutation 189,378,449,584,613,619,620,642,645]
% SZS output end Proof for 5258916842765208436916909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or humble then fred is both not funny and not rich.
Everyone who is either rich or not rich is both old and quiet and vice versa.
Everyone who is tall is not funny or not quiet and vice versa.
If someone is brave or quiet then someone is either calm or wise.
Everyone who is curious is either patient or not humble and vice versa.
If lucy is generous or not tall then someone is either not creative or not generous.
If paul is not generous then susan is calm.
If someone is both not brave and old then someone is happy or old and vice versa.
Everyone who is both not curious and not kind is either generous or not funny and vice versa.
If mary is old then someone is either not rich or creative and vice versa.
Everyone who is tall is not curious and vice versa.
Everyone who is both not rich and not patient is either rich or brave and vice versa.
If paul is not patient or strong then someone is not rich and vice versa.
Everyone who is either generous or curious is both not calm and calm.
Everyone who is both tall and brave is both wise and not tall and vice versa.
Everyone who is creative is not calm or wise and vice versa.
Someone is not funny.
Someone is either creative or not quiet.
Someone is not brave. | Paul is not brave. | entailment | ((?[X]:((kind(X)|humble(X))))=>((~funny(fred)&~rich(fred))))&
(![X]:((rich(X)<~>~rich(X))<=>(old(X)&quiet(X))))&
(![X]:(tall(X)<=>(~funny(X)|~quiet(X))))&
((?[X]:((brave(X)|quiet(X))))=>(?[X]:((calm(X)<~>wise(X)))))&
(![X]:(curious(X)<=>(patient(X)<~>~humble(X))))&
(((generous(lucy)|~tall(lucy)))=>(?[X]:((~creative(X)<~>~generous(X)))))&
((~generous(paul))=>(calm(susan)))&
((?[X]:((~brave(X)&old(X))))<=>(?[X]:((happy(X)|old(X)))))&
(![X]:((~curious(X)&~kind(X))<=>(generous(X)<~>~funny(X))))&
((old(mary))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:(tall(X)<=>~curious(X)))&
(![X]:((~rich(X)&~patient(X))<=>(rich(X)<~>brave(X))))&
(((~patient(paul)|strong(paul)))<=>(?[X]:(~rich(X))))&
(![X]:((generous(X)<~>curious(X))=>(~calm(X)&calm(X))))&
(![X]:((tall(X)&brave(X))<=>(wise(X)&~tall(X))))&
(![X]:(creative(X)<=>(~calm(X)|wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)<~>~quiet(X))))&
(?[X]:(~brave(X))) | ~brave(paul) | [
"p2",
"p8",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3326315513788433041624066
% SZS output start Proof for 3326315513788433041624066
3. ! [X0] : (tall(X0) <=> (~quiet(X0) | ~funny(X0))) [input p2]
9. ! [X0] : ((~kind(X0) & ~curious(X0)) <=> (generous(X0) <~> ~funny(X0))) [input p8]
11. ! [X0] : (tall(X0) <=> ~curious(X0)) [input p10]
14. ! [X0] : ((generous(X0) <~> curious(X0)) => (calm(X0) & ~calm(X0))) [input p13]
15. ! [X0] : ((brave(X0) & tall(X0)) <=> (~tall(X0) & wise(X0))) [input p14]
20. brave(paul) [input hypothesis]
27. ! [X0] : ((calm(X0) & ~calm(X0)) | (generous(X0) <=> curious(X0))) [ennf transformation 14]
30. ! [X0] : ((tall(X0) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | ~tall(X0))) [nnf transformation 3]
31. ! [X0] : ((tall(X0) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~tall(X0))) [flattening 30]
45. ! [X0] : (((~kind(X0) & ~curious(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (kind(X0) | curious(X0)))) [nnf transformation 9]
46. ! [X0] : (((~kind(X0) & ~curious(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | kind(X0) | curious(X0))) [flattening 45]
51. ! [X0] : ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))) [nnf transformation 11]
59. ! [X0] : ((calm(X0) & ~calm(X0)) | ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) [nnf transformation 27]
60. ! [X0] : (((brave(X0) & tall(X0)) | (tall(X0) | ~wise(X0))) & ((~tall(X0) & wise(X0)) | (~brave(X0) | ~tall(X0)))) [nnf transformation 15]
61. ! [X0] : (((brave(X0) & tall(X0)) | tall(X0) | ~wise(X0)) & ((~tall(X0) & wise(X0)) | ~brave(X0) | ~tall(X0))) [flattening 60]
82. tall(X0) | funny(X0) [cnf transformation 31]
104. ~generous(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 46]
113. curious(X0) | tall(X0) [cnf transformation 51]
124. ~calm(X0) | generous(X0) | ~curious(X0) [cnf transformation 59]
126. calm(X0) | generous(X0) | ~curious(X0) [cnf transformation 59]
128. ~tall(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 61]
138. brave(paul) [cnf transformation 20]
139. ~brave(X0) | ~tall(X0) [duplicate literal removal 128]
246. ~curious(X0) | generous(X0) [subsumption resolution 124,126]
251. ~tall(paul) [resolution 139,138]
256. generous(X0) | tall(X0) [resolution 246,113]
273. ~funny(X0) | ~curious(X0) | tall(X0) [resolution 104,256]
277. ~curious(X0) | tall(X0) [subsumption resolution 273,82]
278. tall(X0) [subsumption resolution 277,113]
303. $false [resolution 278,251]
% SZS output end Proof for 3326315513788433041624066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or funny is either not creative or not old and vice versa.
Everyone who is wise or not humble is happy or curious.
If alice is rich then someone is rich or not wise.
Everyone who is creative is not humble.
If fred is not generous or not brave then someone is not patient or not old.
If alice is not rich or not patient then someone is both not happy and wise.
Everyone who is not wise is both happy and wise.
Everyone who is generous or not wise is happy and vice versa.
Everyone who is not funny is both not patient and not calm.
Everyone who is old or not wise is either not calm or curious and vice versa.
If paul is both strong and brave then alice is brave or not brave.
Everyone who is curious is either creative or funny and vice versa.
Everyone who is either kind or not creative is both tall and not creative and vice versa.
If someone is either not humble or not strong then susan is not curious.
Everyone who is not curious is either kind or creative and vice versa.
If fred is not patient then someone is either not rich or patient.
Someone is brave.
Someone is not patient or strong.
Someone is both tall and not brave.
John is creative.
Lucy is tall.
Someone is not strong. | Alice is not funny. | contradiction | (![X]:((creative(X)<~>funny(X))<=>(~creative(X)<~>~old(X))))&
(![X]:((wise(X)|~humble(X))=>(happy(X)|curious(X))))&
((rich(alice))=>(?[X]:((rich(X)|~wise(X)))))&
(![X]:(creative(X)=>~humble(X)))&
(((~generous(fred)|~brave(fred)))=>(?[X]:((~patient(X)|~old(X)))))&
(((~rich(alice)|~patient(alice)))=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:(~wise(X)=>(happy(X)&wise(X))))&
(![X]:((generous(X)|~wise(X))<=>happy(X)))&
(![X]:(~funny(X)=>(~patient(X)&~calm(X))))&
(![X]:((old(X)|~wise(X))<=>(~calm(X)<~>curious(X))))&
(((strong(paul)&brave(paul)))=>((brave(alice)|~brave(alice))))&
(![X]:(curious(X)<=>(creative(X)<~>funny(X))))&
(![X]:((kind(X)<~>~creative(X))<=>(tall(X)&~creative(X))))&
((?[X]:((~humble(X)<~>~strong(X))))=>(~curious(susan)))&
(![X]:(~curious(X)<=>(kind(X)<~>creative(X))))&
((~patient(fred))=>(?[X]:((~rich(X)<~>patient(X)))))&
(?[X]:(brave(X)))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((tall(X)&~brave(X))))&
(creative(john))&
(tall(lucy))&
(?[X]:(~strong(X))) | ~funny(alice) | [
"p0",
"p6",
"p8",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3713313642886036928849357
% SZS output start Proof for 3713313642886036928849357
1. ! [X0] : ((creative(X0) <~> funny(X0)) <=> (~creative(X0) <~> ~old(X0))) [input p0]
7. ! [X0] : (~wise(X0) => (wise(X0) & happy(X0))) [input p6]
9. ! [X0] : (~funny(X0) => (~calm(X0) & ~patient(X0))) [input p8]
10. ! [X0] : ((~wise(X0) | old(X0)) <=> (~calm(X0) <~> curious(X0))) [input p9]
12. ! [X0] : (curious(X0) <=> (creative(X0) <~> funny(X0))) [input p11]
13. ! [X0] : ((kind(X0) <~> ~creative(X0)) <=> (~creative(X0) & tall(X0))) [input p12]
15. ! [X0] : (~curious(X0) <=> (kind(X0) <~> creative(X0))) [input p14]
23. ~funny(alice) [input hypothesis]
30. ! [X0] : ((wise(X0) & happy(X0)) | wise(X0)) [ennf transformation 7]
31. ! [X0] : ((~calm(X0) & ~patient(X0)) | funny(X0)) [ennf transformation 9]
36. ! [X0] : ((((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) & (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0))))) [nnf transformation 1]
45. ! [X0] : (((~wise(X0) | old(X0)) | ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0)))) & (((~curious(X0) | calm(X0)) & (curious(X0) | ~calm(X0))) | (wise(X0) & ~old(X0)))) [nnf transformation 10]
46. ! [X0] : ((~wise(X0) | old(X0) | ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0)))) & (((~curious(X0) | calm(X0)) & (curious(X0) | ~calm(X0))) | (wise(X0) & ~old(X0)))) [flattening 45]
47. ! [X0] : ((curious(X0) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0)))) & (((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | ~curious(X0))) [nnf transformation 12]
48. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | (creative(X0) | ~tall(X0))) & ((~creative(X0) & tall(X0)) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [nnf transformation 13]
49. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | creative(X0) | ~tall(X0)) & ((~creative(X0) & tall(X0)) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [flattening 48]
51. ! [X0] : ((~curious(X0) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) & (((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | curious(X0))) [nnf transformation 15]
63. ~old(X0) | ~creative(X0) | funny(X0) | ~creative(X0) [cnf transformation 36]
67. funny(X0) | creative(X0) | ~old(X0) | creative(X0) [cnf transformation 36]
82. wise(X0) | wise(X0) [cnf transformation 30]
87. ~calm(X0) | funny(X0) [cnf transformation 31]
92. ~wise(X0) | old(X0) | curious(X0) | calm(X0) [cnf transformation 46]
95. ~curious(X0) | creative(X0) | funny(X0) [cnf transformation 47]
101. ~creative(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 49]
110. ~curious(X0) | kind(X0) | ~creative(X0) [cnf transformation 51]
120. ~funny(alice) [cnf transformation 23]
121. ~kind(X0) | ~creative(X0) [duplicate literal removal 101]
123. wise(X0) [duplicate literal removal 82]
124. ~old(X0) | ~creative(X0) | funny(X0) [duplicate literal removal 63]
126. ~old(X0) | creative(X0) | funny(X0) [duplicate literal removal 67]
129. ~old(X0) | funny(X0) [subsumption resolution 124,126]
179. calm(X0) | curious(X0) | old(X0) [subsumption resolution 92,123]
192. ~curious(X0) | ~creative(X0) [subsumption resolution 110,121]
332. curious(X2) | old(X2) | funny(X2) [resolution 179,87]
335. curious(X2) | funny(X2) [subsumption resolution 332,129]
339. funny(X1) | creative(X1) | funny(X1) [resolution 335,95]
341. funny(X3) | ~creative(X3) [resolution 335,192]
345. funny(X1) | creative(X1) [duplicate literal removal 339]
346. funny(X3) [subsumption resolution 341,345]
366. $false [resolution 346,120]
% SZS output end Proof for 3713313642886036928849357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not tall is either not quiet or not funny and vice versa.
If lucy is not patient then someone is both not patient and creative and vice versa.
Everyone who is kind or strong is quiet.
If someone is both not funny and not humble then mary is not kind and vice versa.
Everyone who is funny is not funny or wise and vice versa.
Everyone who is not strong or patient is not funny or brave and vice versa.
If paul is not happy then someone is either not tall or not old and vice versa.
Everyone who is both not quiet and not kind is tall and vice versa.
Everyone who is either not curious or not tall is both not quiet and curious and vice versa.
If someone is either happy or not calm then someone is both not brave and tall and vice versa.
If alice is both not wise and brave then someone is not kind.
If paul is either not calm or not rich then someone is not rich or not old.
If mary is either not quiet or not strong then susan is both not happy and funny.
If paul is both not wise and not curious then someone is curious.
Everyone who is both kind and not kind is either not funny or brave.
Someone is either not brave or not wise.
Someone is not humble.
Someone is both not creative and not rich.
Mary is either rich or not happy.
Someone is calm or brave.
Fred is either not brave or tall.
Alice is happy. | Paul is not curious. | entailment | (![X]:((quiet(X)<~>~tall(X))<=>(~quiet(X)<~>~funny(X))))&
((~patient(lucy))<=>(?[X]:((~patient(X)&creative(X)))))&
(![X]:((kind(X)|strong(X))=>quiet(X)))&
((?[X]:((~funny(X)&~humble(X))))<=>(~kind(mary)))&
(![X]:(funny(X)<=>(~funny(X)|wise(X))))&
(![X]:((~strong(X)|patient(X))<=>(~funny(X)|brave(X))))&
((~happy(paul))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:((~quiet(X)&~kind(X))<=>tall(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(((~wise(alice)&brave(alice)))=>(?[X]:(~kind(X))))&
(((~calm(paul)<~>~rich(paul)))=>(?[X]:((~rich(X)|~old(X)))))&
(((~quiet(mary)<~>~strong(mary)))=>((~happy(susan)&funny(susan))))&
(((~wise(paul)&~curious(paul)))=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))=>(~funny(X)<~>brave(X))))&
(?[X]:((~brave(X)<~>~wise(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)&~rich(X))))&
((rich(mary)<~>~happy(mary)))&
(?[X]:((calm(X)|brave(X))))&
((~brave(fred)<~>tall(fred)))&
(happy(alice)) | ~curious(paul) | [
"p0",
"p2",
"p4",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5854961956536304301218193
% SZS output start Proof for 5854961956536304301218193
1. ! [X0] : ((quiet(X0) <~> ~tall(X0)) <=> (~quiet(X0) <~> ~funny(X0))) [input p0]
3. ! [X0] : ((strong(X0) | kind(X0)) => quiet(X0)) [input p2]
5. ! [X0] : (funny(X0) <=> (wise(X0) | ~funny(X0))) [input p4]
8. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> tall(X0)) [input p7]
9. ! [X0] : ((~curious(X0) <~> ~tall(X0)) <=> (curious(X0) & ~quiet(X0))) [input p8]
23. curious(paul) [input hypothesis]
25. ! [X0] : (quiet(X0) | (~strong(X0) & ~kind(X0))) [ennf transformation 3]
34. ! [X0] : ((((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | ((~quiet(X0) | funny(X0)) & (~funny(X0) | quiet(X0)))) & (((funny(X0) | quiet(X0)) & (~funny(X0) | ~quiet(X0))) | ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0))))) [nnf transformation 1]
43. ! [X0] : ((funny(X0) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 5]
44. ! [X0] : ((funny(X0) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~funny(X0))) [flattening 43]
51. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | (kind(X0) | quiet(X0)))) [nnf transformation 8]
52. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | kind(X0) | quiet(X0))) [flattening 51]
53. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~curious(X0) | quiet(X0))) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [nnf transformation 9]
54. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | ~curious(X0) | quiet(X0)) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [flattening 53]
80. ~funny(X0) | ~quiet(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 34]
84. ~tall(X0) | quiet(X0) | ~funny(X0) | quiet(X0) [cnf transformation 34]
91. ~kind(X0) | quiet(X0) [cnf transformation 25]
97. funny(X0) | funny(X0) [cnf transformation 44]
107. tall(X0) | kind(X0) | quiet(X0) [cnf transformation 52]
111. ~quiet(X0) | ~curious(X0) | tall(X0) [cnf transformation 54]
143. curious(paul) [cnf transformation 23]
147. funny(X0) [duplicate literal removal 97]
148. ~funny(X0) | ~quiet(X0) | ~tall(X0) [duplicate literal removal 80]
150. ~tall(X0) | quiet(X0) | ~funny(X0) [duplicate literal removal 84]
153. ~funny(X0) | ~tall(X0) [subsumption resolution 148,150]
215. tall(X0) | quiet(X0) [subsumption resolution 107,91]
217. ~curious(X0) | tall(X0) [subsumption resolution 111,215]
319. ~tall(X1) [resolution 153,147]
335. tall(paul) [resolution 217,143]
336. $false [subsumption resolution 335,319]
% SZS output end Proof for 5854961956536304301218193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not strong then someone is happy or not quiet.
If susan is both not generous and strong then mary is not tall and vice versa.
Everyone who is not happy or patient is both curious and not creative.
If john is not strong then lucy is not old or not generous.
Everyone who is happy is either not strong or not funny and vice versa.
Everyone who is curious or not old is curious.
Everyone who is not happy or happy is strong.
If someone is not strong or not quiet then someone is both not funny and patient.
Everyone who is not tall or kind is curious and vice versa.
Everyone who is both brave and not quiet is both quiet and not rich and vice versa.
Everyone who is happy is not happy or not kind and vice versa.
If someone is both kind and generous then someone is both wise and not tall and vice versa.
Everyone who is not creative or not rich is wise or not happy.
Everyone who is either not funny or humble is patient.
If paul is either not tall or humble then someone is either happy or not humble.
If lucy is not wise then lucy is either not kind or rich and vice versa.
Lucy is not funny or not strong.
Fred is both happy and not tall.
Someone is happy.
Paul is either funny or not curious.
Someone is not generous or not happy.
Fred is not old.
Someone is either generous or wise.
Someone is creative. | Lucy is not patient. | entailment | ((?[X]:((kind(X)<~>~strong(X))))=>(?[X]:((happy(X)|~quiet(X)))))&
(((~generous(susan)&strong(susan)))<=>(~tall(mary)))&
(![X]:((~happy(X)|patient(X))=>(curious(X)&~creative(X))))&
((~strong(john))=>((~old(lucy)|~generous(lucy))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
((~wise(lucy))<=>((~kind(lucy)<~>rich(lucy))))&
((~funny(lucy)|~strong(lucy)))&
((happy(fred)&~tall(fred)))&
(?[X]:(happy(X)))&
((funny(paul)<~>~curious(paul)))&
(?[X]:((~generous(X)|~happy(X))))&
(~old(fred))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:(creative(X))) | ~patient(lucy) | [
"p2",
"p8",
"p10",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6451620294797235792531028
% SZS output start Proof for 6451620294797235792531028
3. ! [X0] : ((patient(X0) | ~happy(X0)) => (~creative(X0) & curious(X0))) [input p2]
9. ! [X0] : ((kind(X0) | ~tall(X0)) <=> curious(X0)) [input p8]
11. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p10]
12. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X0] : (~tall(X0) & wise(X0)) [input p11]
13. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~happy(X0) | wise(X0))) [input p12]
16. ~wise(lucy) <=> (~kind(lucy) <~> rich(lucy)) [input p15]
25. patient(lucy) [input hypothesis]
28. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X1] : (~tall(X1) & wise(X1)) [rectify 12]
30. ! [X0] : ((~creative(X0) & curious(X0)) | (~patient(X0) & happy(X0))) [ennf transformation 3]
36. ! [X0] : ((~happy(X0) | wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 13]
37. ! [X0] : (~happy(X0) | wise(X0) | (rich(X0) & creative(X0))) [flattening 36]
50. ! [X0] : (((kind(X0) | ~tall(X0)) | ~curious(X0)) & (curious(X0) | (~kind(X0) & tall(X0)))) [nnf transformation 9]
51. ! [X0] : ((kind(X0) | ~tall(X0) | ~curious(X0)) & (curious(X0) | (~kind(X0) & tall(X0)))) [flattening 50]
54. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 11]
55. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 54]
56. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X1] : (~tall(X1) & wise(X1)) | ! [X0] : (~generous(X0) | ~kind(X0))) [nnf transformation 28]
57. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X2] : (~tall(X2) & wise(X2)) | ! [X3] : (~generous(X3) | ~kind(X3))) [rectify 56]
58. ? [X0] : (generous(X0) & kind(X0)) => (generous(sK2) & kind(sK2)) [choice axiom]
59. ? [X2] : (~tall(X2) & wise(X2)) => (~tall(sK3) & wise(sK3)) [choice axiom]
60. ((generous(sK2) & kind(sK2)) | ! [X1] : (tall(X1) | ~wise(X1))) & ((~tall(sK3) & wise(sK3)) | ! [X3] : (~generous(X3) | ~kind(X3))) [skolemisation 57,59,58]
65. (~wise(lucy) | ((~kind(lucy) | ~rich(lucy)) & (rich(lucy) | kind(lucy)))) & (((~rich(lucy) | kind(lucy)) & (rich(lucy) | ~kind(lucy))) | wise(lucy)) [nnf transformation 16]
82. ~patient(X0) | curious(X0) [cnf transformation 30]
100. ~curious(X0) | ~tall(X0) | kind(X0) [cnf transformation 51]
105. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 55]
106. happy(X0) | happy(X0) [cnf transformation 55]
110. kind(sK2) | tall(X1) | ~wise(X1) [cnf transformation 60]
113. ~happy(X0) | wise(X0) | rich(X0) [cnf transformation 37]
121. ~rich(lucy) | kind(lucy) | wise(lucy) [cnf transformation 65]
122. ~wise(lucy) | rich(lucy) | kind(lucy) [cnf transformation 65]
135. patient(lucy) [cnf transformation 25]
136. ~kind(X0) | ~happy(X0) [duplicate literal removal 105]
137. happy(X0) [duplicate literal removal 106]
198. ~kind(X0) [subsumption resolution 136,137]
200. 14 <=> ! [X1] : (tall(X1) | ~wise(X1)) [avatar definition]
201. ~wise(X1) | tall(X1) <- (14) [avatar component clause 200]
207. tall(X1) | ~wise(X1) [subsumption resolution 110,198]
208. 14 [avatar split clause 207,200]
209. wise(X0) | rich(X0) [subsumption resolution 113,137]
227. ~wise(lucy) | rich(lucy) [subsumption resolution 122,198]
228. rich(lucy) [subsumption resolution 227,209]
229. kind(lucy) | wise(lucy) [subsumption resolution 121,228]
230. wise(lucy) [subsumption resolution 229,198]
258. curious(lucy) [resolution 82,135]
269. tall(lucy) <- (14) [resolution 201,230]
283. ~tall(lucy) | kind(lucy) [resolution 100,258]
286. kind(lucy) <- (14) [subsumption resolution 283,269]
287. $false <- (14) [subsumption resolution 286,198]
288. ~14 [avatar contradiction clause 287]
290. $false [avatar sat refutation 208,288]
% SZS output end Proof for 6451620294797235792531028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not patient or kind then alice is humble and vice versa. If someone is funny then alice is strong or curious. Everyone who is both not curious and not patient is tall. Everyone who is strong or brave is both not old and not rich and vice versa. Everyone who is patient or quiet is both not tall and tall and vice versa. Everyone who is not creative is either not wise or not kind. Everyone who is curious is creative. If someone is patient or wise then susan is not brave or generous. Everyone who is not old or not generous is creative or not tall and vice versa. If john is both not strong and funny then someone is both generous and not rich and vice versa. Everyone who is not old is both not tall and not kind and vice versa. Everyone who is either not rich or calm is not patient or generous and vice versa. If someone is strong then someone is either not creative or not patient. Everyone who is funny is either generous or not quiet. If paul is rich then someone is not patient. If john is wise then someone is both not patient and wise. Someone is wise. Someone is either not old or humble. Someone is both tall and not curious. Fred is not curious or not tall. Someone is brave. Lucy is rich. | Paul is calm. | neutral | (((~patient(lucy)<~>kind(lucy)))<=>(humble(alice)))&
((?[X]:(funny(X)))=>((strong(alice)|curious(alice))))&
(![X]:((~curious(X)&~patient(X))=>tall(X)))&
(![X]:((strong(X)|brave(X))<=>(~old(X)&~rich(X))))&
(![X]:((patient(X)|quiet(X))<=>(~tall(X)&tall(X))))&
(![X]:(~creative(X)=>(~wise(X)<~>~kind(X))))&
(![X]:(curious(X)=>creative(X)))&
((?[X]:((patient(X)|wise(X))))=>((~brave(susan)|generous(susan))))&
(![X]:((~old(X)|~generous(X))<=>(creative(X)|~tall(X))))&
(((~strong(john)&funny(john)))<=>(?[X]:((generous(X)&~rich(X)))))&
(![X]:(~old(X)<=>(~tall(X)&~kind(X))))&
(![X]:((~rich(X)<~>calm(X))<=>(~patient(X)|generous(X))))&
((?[X]:(strong(X)))=>(?[X]:((~creative(X)<~>~patient(X)))))&
(![X]:(funny(X)=>(generous(X)<~>~quiet(X))))&
((rich(paul))=>(?[X]:(~patient(X))))&
((wise(john))=>(?[X]:((~patient(X)&wise(X)))))&
(?[X]:(wise(X)))&
(?[X]:((~old(X)<~>humble(X))))&
(?[X]:((tall(X)&~curious(X))))&
((~curious(fred)|~tall(fred)))&
(?[X]:(brave(X)))&
(rich(lucy)) | calm(paul) | [] | null | 0 |
Everyone who is not generous is curious and vice versa.
If john is not old then paul is both creative and not brave.
Everyone who is both not quiet and not strong is not generous or humble and vice versa.
Everyone who is not strong or not curious is both not humble and not strong and vice versa.
Everyone who is either not creative or curious is curious and vice versa.
Everyone who is strong is calm or kind.
If someone is not tall then someone is humble or happy and vice versa.
If someone is curious or creative then lucy is either humble or curious and vice versa.
If someone is strong or not tall then someone is not kind and vice versa.
Everyone who is not patient or not kind is both creative and rich and vice versa.
Everyone who is either not creative or generous is funny and vice versa.
If alice is patient then someone is not kind.
Everyone who is either not brave or not wise is quiet or not calm and vice versa.
Everyone who is either not funny or patient is not generous.
Everyone who is either brave or generous is both wise and not kind.
Everyone who is both happy and not funny is both kind and not funny and vice versa.
Someone is not happy or wise.
Fred is either quiet or not happy.
Someone is generous.
Paul is either curious or not brave.
Susan is either not kind or not calm.
Someone is either happy or not happy. | Lucy is kind. | neutral | (![X]:(~generous(X)<=>curious(X)))&
((~old(john))=>((creative(paul)&~brave(paul))))&
(![X]:((~quiet(X)&~strong(X))<=>(~generous(X)|humble(X))))&
(![X]:((~strong(X)|~curious(X))<=>(~humble(X)&~strong(X))))&
(![X]:((~creative(X)<~>curious(X))<=>curious(X)))&
(![X]:(strong(X)=>(calm(X)|kind(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((humble(X)|happy(X)))))&
((?[X]:((curious(X)|creative(X))))<=>((humble(lucy)<~>curious(lucy))))&
((?[X]:((strong(X)|~tall(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~patient(X)|~kind(X))<=>(creative(X)&rich(X))))&
(![X]:((~creative(X)<~>generous(X))<=>funny(X)))&
((patient(alice))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(quiet(X)|~calm(X))))&
(![X]:((~funny(X)<~>patient(X))=>~generous(X)))&
(![X]:((brave(X)<~>generous(X))=>(wise(X)&~kind(X))))&
(![X]:((happy(X)&~funny(X))<=>(kind(X)&~funny(X))))&
(?[X]:((~happy(X)|wise(X))))&
((quiet(fred)<~>~happy(fred)))&
(?[X]:(generous(X)))&
((curious(paul)<~>~brave(paul)))&
((~kind(susan)<~>~calm(susan)))&
(?[X]:((happy(X)<~>~happy(X)))) | kind(lucy) | [] | null | 0 |
If someone is creative or not happy then someone is calm.
Everyone who is not tall or wise is quiet.
If someone is not brave or wise then susan is strong or old.
Everyone who is not tall is happy or not funny.
Everyone who is either wise or quiet is not brave.
Everyone who is both not humble and generous is brave or not tall and vice versa.
Everyone who is not quiet or not generous is both not generous and rich and vice versa.
If mary is brave then someone is not old and vice versa.
Everyone who is either happy or not happy is either not generous or not brave.
Everyone who is either creative or brave is not generous.
Everyone who is both happy and not humble is either humble or not humble and vice versa.
If paul is both old and brave then paul is either not quiet or not happy and vice versa.
Everyone who is either not calm or tall is both wise and rich.
Everyone who is both old and rich is either humble or not kind and vice versa.
Everyone who is both not kind and old is not old.
If someone is not rich then susan is not wise and vice versa.
Someone is not kind or not humble.
Someone is not brave.
Paul is both strong and funny.
Someone is not old or not curious.
Paul is either not creative or brave.
Paul is quiet or old. | Susan is not wise. | entailment | ((?[X]:((creative(X)|~happy(X))))=>(?[X]:(calm(X))))&
(![X]:((~tall(X)|wise(X))=>quiet(X)))&
((?[X]:((~brave(X)|wise(X))))=>((strong(susan)|old(susan))))&
(![X]:(~tall(X)=>(happy(X)|~funny(X))))&
(![X]:((wise(X)<~>quiet(X))=>~brave(X)))&
(![X]:((~humble(X)&generous(X))<=>(brave(X)|~tall(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(~generous(X)&rich(X))))&
((brave(mary))<=>(?[X]:(~old(X))))&
(![X]:((happy(X)<~>~happy(X))=>(~generous(X)<~>~brave(X))))&
(![X]:((creative(X)<~>brave(X))=>~generous(X)))&
(![X]:((happy(X)&~humble(X))<=>(humble(X)<~>~humble(X))))&
(((old(paul)&brave(paul)))<=>((~quiet(paul)<~>~happy(paul))))&
(![X]:((~calm(X)<~>tall(X))=>(wise(X)&rich(X))))&
(![X]:((old(X)&rich(X))<=>(humble(X)<~>~kind(X))))&
(![X]:((~kind(X)&old(X))=>~old(X)))&
((?[X]:(~rich(X)))<=>(~wise(susan)))&
(?[X]:((~kind(X)|~humble(X))))&
(?[X]:(~brave(X)))&
((strong(paul)&funny(paul)))&
(?[X]:((~old(X)|~curious(X))))&
((~creative(paul)<~>brave(paul)))&
((quiet(paul)|old(paul))) | ~wise(susan) | [
"p5",
"p7",
"p8",
"p10",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1574970837180792325120252
% SZS output start Proof for 1574970837180792325120252
6. ! [X0] : ((generous(X0) & ~humble(X0)) <=> (~tall(X0) | brave(X0))) [input p5]
8. brave(mary) <=> ? [X0] : ~old(X0) [input p7]
9. ! [X0] : ((happy(X0) <~> ~happy(X0)) => (~generous(X0) <~> ~brave(X0))) [input p8]
11. ! [X0] : ((~humble(X0) & happy(X0)) <=> (humble(X0) <~> ~humble(X0))) [input p10]
14. ! [X0] : ((rich(X0) & old(X0)) <=> (humble(X0) <~> ~kind(X0))) [input p13]
15. ! [X0] : ((old(X0) & ~kind(X0)) => ~old(X0)) [input p14]
16. ? [X0] : ~rich(X0) <=> ~wise(susan) [input p15]
23. wise(susan) [input hypothesis]
33. ! [X0] : ((~generous(X0) <~> ~brave(X0)) | (happy(X0) <=> ~happy(X0))) [ennf transformation 9]
36. ! [X0] : (~old(X0) | (~old(X0) | kind(X0))) [ennf transformation 15]
37. ! [X0] : (~old(X0) | ~old(X0) | kind(X0)) [flattening 36]
42. ! [X0] : (((generous(X0) & ~humble(X0)) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | (~generous(X0) | humble(X0)))) [nnf transformation 6]
43. ! [X0] : (((generous(X0) & ~humble(X0)) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | ~generous(X0) | humble(X0))) [flattening 42]
46. (brave(mary) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~brave(mary)) [nnf transformation 8]
47. (brave(mary) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~brave(mary)) [rectify 46]
48. ? [X1] : ~old(X1) => ~old(sK1) [choice axiom]
49. (brave(mary) | ! [X0] : old(X0)) & (~old(sK1) | ~brave(mary)) [skolemisation 47,48]
50. ! [X0] : (((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 33]
52. ! [X0] : (((~humble(X0) & happy(X0)) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) & (((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | (humble(X0) | ~happy(X0)))) [nnf transformation 11]
53. ! [X0] : (((~humble(X0) & happy(X0)) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) & (((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | humble(X0) | ~happy(X0))) [flattening 52]
57. ! [X0] : (((rich(X0) & old(X0)) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) & (((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | (~rich(X0) | ~old(X0)))) [nnf transformation 14]
58. ! [X0] : (((rich(X0) & old(X0)) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) & (((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | ~rich(X0) | ~old(X0))) [flattening 57]
59. (? [X0] : ~rich(X0) | wise(susan)) & (~wise(susan) | ! [X0] : rich(X0)) [nnf transformation 16]
60. (? [X0] : ~rich(X0) | wise(susan)) & (~wise(susan) | ! [X1] : rich(X1)) [rectify 59]
61. ? [X0] : ~rich(X0) => ~rich(sK2) [choice axiom]
62. (~rich(sK2) | wise(susan)) & (~wise(susan) | ! [X1] : rich(X1)) [skolemisation 60,61]
78. ~brave(X0) | generous(X0) [cnf transformation 43]
86. brave(mary) | old(X0) [cnf transformation 49]
87. ~brave(X0) | ~generous(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 50]
88. ~brave(X0) | ~generous(X0) | happy(X0) | happy(X0) [cnf transformation 50]
89. brave(X0) | generous(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 50]
90. brave(X0) | generous(X0) | happy(X0) | happy(X0) [cnf transformation 50]
97. ~humble(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 53]
109. ~kind(X0) | humble(X0) | ~rich(X0) | ~old(X0) [cnf transformation 58]
112. old(X0) | humble(X0) | kind(X0) [cnf transformation 58]
115. ~old(X0) | ~old(X0) | kind(X0) [cnf transformation 37]
116. ~wise(susan) | rich(X1) [cnf transformation 62]
124. wise(susan) [cnf transformation 23]
125. ~old(X0) | kind(X0) [duplicate literal removal 115]
130. ~humble(X0) [duplicate literal removal 97]
132. ~brave(X0) | ~generous(X0) | ~happy(X0) [duplicate literal removal 87]
133. ~brave(X0) | ~generous(X0) | happy(X0) [duplicate literal removal 88]
134. brave(X0) | generous(X0) | ~happy(X0) [duplicate literal removal 89]
135. brave(X0) | generous(X0) | happy(X0) [duplicate literal removal 90]
149. 4 <=> ! [X0] : old(X0) [avatar definition]
150. old(X0) <- (4) [avatar component clause 149]
152. 5 <=> brave(mary) [avatar definition]
154. brave(mary) <- (5) [avatar component clause 152]
155. 4 | 5 [avatar split clause 86,152,149]
161. generous(X0) | happy(X0) [subsumption resolution 135,78]
162. generous(X0) | ~happy(X0) [subsumption resolution 134,78]
163. generous(X0) [subsumption resolution 162,161]
164. ~brave(X0) | happy(X0) [subsumption resolution 133,163]
165. ~brave(X0) | ~happy(X0) [subsumption resolution 132,163]
166. ~brave(X0) [subsumption resolution 165,164]
191. kind(X0) | old(X0) [subsumption resolution 112,130]
192. ~kind(X0) | ~rich(X0) | ~old(X0) [subsumption resolution 109,130]
193. kind(X0) [subsumption resolution 125,191]
195. 10 <=> wise(susan) [avatar definition]
204. 12 <=> ! [X1] : rich(X1) [avatar definition]
205. rich(X1) <- (12) [avatar component clause 204]
206. 12 | ~10 [avatar split clause 116,195,204]
209. 10 [avatar split clause 124,195]
220. ~rich(X2) | ~old(X2) [resolution 192,193]
221. ~old(X2) <- (12) [subsumption resolution 220,205]
222. $false <- (4, 12) [subsumption resolution 221,150]
223. ~4 | ~12 [avatar contradiction clause 222]
224. $false <- (5) [subsumption resolution 154,166]
225. ~5 [avatar contradiction clause 224]
226. $false [avatar sat refutation 155,206,209,223,225]
% SZS output end Proof for 1574970837180792325120252
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is creative or not brave.
Everyone who is both rich and not curious is strong.
Everyone who is either quiet or patient is both not generous and not curious and vice versa.
Everyone who is not curious or not strong is funny.
Everyone who is wise or brave is both not wise and not humble and vice versa.
Everyone who is not generous is not strong or quiet and vice versa.
Everyone who is not tall or humble is both kind and not rich and vice versa.
If alice is both not brave and not humble then someone is either curious or brave.
Everyone who is either tall or not old is not calm.
If someone is brave then someone is not calm.
If someone is either not happy or humble then lucy is wise or quiet and vice versa.
Everyone who is not happy is both curious and humble.
Everyone who is patient or funny is both not patient and rich and vice versa.
If someone is generous or not generous then susan is not patient and vice versa.
Everyone who is both not kind and not funny is generous or not curious and vice versa.
Everyone who is brave or not funny is both not old and curious.
Alice is brave.
Someone is both brave and not generous.
Fred is not creative or calm.
Someone is not kind.
Fred is either calm or quiet.
Alice is either kind or rich.
Someone is either not humble or quiet. | Alice is not quiet. | entailment | (![X]:(strong(X)=>(creative(X)|~brave(X))))&
(![X]:((rich(X)&~curious(X))=>strong(X)))&
(![X]:((quiet(X)<~>patient(X))<=>(~generous(X)&~curious(X))))&
(![X]:((~curious(X)|~strong(X))=>funny(X)))&
(![X]:((wise(X)|brave(X))<=>(~wise(X)&~humble(X))))&
(![X]:(~generous(X)<=>(~strong(X)|quiet(X))))&
(![X]:((~tall(X)|humble(X))<=>(kind(X)&~rich(X))))&
(((~brave(alice)&~humble(alice)))=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:((tall(X)<~>~old(X))=>~calm(X)))&
((?[X]:(brave(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~happy(X)<~>humble(X))))<=>((wise(lucy)|quiet(lucy))))&
(![X]:(~happy(X)=>(curious(X)&humble(X))))&
(![X]:((patient(X)|funny(X))<=>(~patient(X)&rich(X))))&
((?[X]:((generous(X)|~generous(X))))<=>(~patient(susan)))&
(![X]:((~kind(X)&~funny(X))<=>(generous(X)|~curious(X))))&
(![X]:((brave(X)|~funny(X))=>(~old(X)&curious(X))))&
(brave(alice))&
(?[X]:((brave(X)&~generous(X))))&
((~creative(fred)|calm(fred)))&
(?[X]:(~kind(X)))&
((calm(fred)<~>quiet(fred)))&
((kind(alice)<~>rich(alice)))&
(?[X]:((~humble(X)<~>quiet(X)))) | ~quiet(alice) | [
"p2",
"p3",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 595834650251190810859587
% SZS output start Proof for 595834650251190810859587
3. ! [X0] : ((quiet(X0) <~> patient(X0)) <=> (~curious(X0) & ~generous(X0))) [input p2]
4. ! [X0] : ((~strong(X0) | ~curious(X0)) => funny(X0)) [input p3]
13. ! [X0] : ((funny(X0) | patient(X0)) <=> (rich(X0) & ~patient(X0))) [input p12]
15. ! [X0] : ((~funny(X0) & ~kind(X0)) <=> (~curious(X0) | generous(X0))) [input p14]
24. quiet(alice) [input hypothesis]
30. ! [X0] : (funny(X0) | (strong(X0) & curious(X0))) [ennf transformation 4]
37. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [nnf transformation 3]
38. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [flattening 37]
57. ! [X0] : (((funny(X0) | patient(X0)) | (~rich(X0) | patient(X0))) & ((rich(X0) & ~patient(X0)) | (~funny(X0) & ~patient(X0)))) [nnf transformation 13]
58. ! [X0] : ((funny(X0) | patient(X0) | ~rich(X0) | patient(X0)) & ((rich(X0) & ~patient(X0)) | (~funny(X0) & ~patient(X0)))) [flattening 57]
63. ! [X0] : (((~funny(X0) & ~kind(X0)) | (curious(X0) & ~generous(X0))) & ((~curious(X0) | generous(X0)) | (funny(X0) | kind(X0)))) [nnf transformation 15]
64. ! [X0] : (((~funny(X0) & ~kind(X0)) | (curious(X0) & ~generous(X0))) & (~curious(X0) | generous(X0) | funny(X0) | kind(X0))) [flattening 63]
78. ~quiet(X0) | patient(X0) | ~curious(X0) [cnf transformation 38]
82. funny(X0) | curious(X0) [cnf transformation 30]
110. ~patient(X0) | ~patient(X0) [cnf transformation 58]
122. ~funny(X0) | curious(X0) [cnf transformation 64]
138. quiet(alice) [cnf transformation 24]
139. ~patient(X0) [duplicate literal removal 110]
194. curious(X0) [subsumption resolution 122,82]
270. patient(alice) | ~curious(alice) [resolution 78,138]
272. ~curious(alice) [subsumption resolution 270,139]
273. $false [subsumption resolution 272,194]
% SZS output end Proof for 595834650251190810859587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then someone is either not quiet or not curious and vice versa.
If someone is not generous or kind then someone is funny.
Everyone who is not patient or strong is either happy or old and vice versa.
Everyone who is either not funny or not strong is both not brave and not patient and vice versa.
If someone is calm or creative then someone is not humble and vice versa.
If alice is either strong or creative then someone is either kind or quiet.
Everyone who is patient is not patient.
Everyone who is both not kind and not brave is either wise or brave and vice versa.
Everyone who is not calm is both not wise and not happy.
Everyone who is humble or old is not patient.
Everyone who is funny or not curious is both curious and wise and vice versa.
Everyone who is either rich or old is both not patient and not old and vice versa.
If john is either not tall or happy then someone is generous or not funny.
If fred is not funny or tall then susan is funny or not strong and vice versa.
If paul is either curious or not generous then susan is not patient or not brave.
If susan is either not calm or not patient then john is both not brave and old.
Alice is both funny and humble.
Mary is happy.
Mary is either not generous or not rich.
Paul is both not humble and not wise.
Someone is either rich or not calm.
Paul is both not quiet and strong.
Fred is not curious or not old. | Mary is curious. | entailment | ((?[X]:(~wise(X)))<=>(?[X]:((~quiet(X)<~>~curious(X)))))&
((?[X]:((~generous(X)|kind(X))))=>(?[X]:(funny(X))))&
(![X]:((~patient(X)|strong(X))<=>(happy(X)<~>old(X))))&
(![X]:((~funny(X)<~>~strong(X))<=>(~brave(X)&~patient(X))))&
((?[X]:((calm(X)|creative(X))))<=>(?[X]:(~humble(X))))&
(((strong(alice)<~>creative(alice)))=>(?[X]:((kind(X)<~>quiet(X)))))&
(![X]:(patient(X)=>~patient(X)))&
(![X]:((~kind(X)&~brave(X))<=>(wise(X)<~>brave(X))))&
(![X]:(~calm(X)=>(~wise(X)&~happy(X))))&
(![X]:((humble(X)|old(X))=>~patient(X)))&
(![X]:((funny(X)|~curious(X))<=>(curious(X)&wise(X))))&
(![X]:((rich(X)<~>old(X))<=>(~patient(X)&~old(X))))&
(((~tall(john)<~>happy(john)))=>(?[X]:((generous(X)|~funny(X)))))&
(((~funny(fred)|tall(fred)))<=>((funny(susan)|~strong(susan))))&
(((curious(paul)<~>~generous(paul)))=>((~patient(susan)|~brave(susan))))&
(((~calm(susan)<~>~patient(susan)))=>((~brave(john)&old(john))))&
((funny(alice)&humble(alice)))&
(happy(mary))&
((~generous(mary)<~>~rich(mary)))&
((~humble(paul)&~wise(paul)))&
(?[X]:((rich(X)<~>~calm(X))))&
((~quiet(paul)&strong(paul)))&
((~curious(fred)|~old(fred))) | curious(mary) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8160552250551152013576280
% SZS output start Proof for 8160552250551152013576280
11. ! [X0] : ((~curious(X0) | funny(X0)) <=> (wise(X0) & curious(X0))) [input p10]
24. ~curious(mary) [input hypothesis]
59. ! [X0] : (((~curious(X0) | funny(X0)) | (~wise(X0) | ~curious(X0))) & ((wise(X0) & curious(X0)) | (curious(X0) & ~funny(X0)))) [nnf transformation 11]
60. ! [X0] : ((~curious(X0) | funny(X0) | ~wise(X0) | ~curious(X0)) & ((wise(X0) & curious(X0)) | (curious(X0) & ~funny(X0)))) [flattening 59]
111. curious(X0) | curious(X0) [cnf transformation 60]
145. ~curious(mary) [cnf transformation 24]
148. curious(X0) [duplicate literal removal 111]
294. $false [subsumption resolution 145,148]
% SZS output end Proof for 8160552250551152013576280
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not old or quiet then someone is quiet or not funny and vice versa.
Everyone who is not quiet is calm and vice versa.
If fred is either kind or not generous then mary is patient.
Everyone who is not calm is both tall and wise.
Everyone who is old is both creative and funny.
Everyone who is both patient and tall is not happy and vice versa.
Everyone who is either not quiet or not wise is both creative and not calm and vice versa.
Everyone who is not kind or creative is not rich or not happy.
If lucy is both not creative and not wise then someone is both rich and not calm.
If someone is not curious or curious then someone is not tall or not happy.
If alice is wise then someone is not tall or funny and vice versa.
If someone is either not rich or kind then someone is old.
Everyone who is both tall and not patient is either rich or kind.
If fred is both creative and not humble then fred is not patient and vice versa.
Everyone who is both kind and not old is both not creative and curious.
Everyone who is patient or brave is both not wise and not kind and vice versa.
Someone is both generous and kind.
Someone is not kind.
Someone is not humble.
Someone is happy or funny.
Someone is happy or not rich.
Mary is calm.
Someone is not generous.
John is curious. | Susan is not old. | entailment | (((~old(susan)<~>quiet(susan)))<=>(?[X]:((quiet(X)|~funny(X)))))&
(![X]:(~quiet(X)<=>calm(X)))&
(((kind(fred)<~>~generous(fred)))=>(patient(mary)))&
(![X]:(~calm(X)=>(tall(X)&wise(X))))&
(![X]:(old(X)=>(creative(X)&funny(X))))&
(![X]:((patient(X)&tall(X))<=>~happy(X)))&
(![X]:((~quiet(X)<~>~wise(X))<=>(creative(X)&~calm(X))))&
(![X]:((~kind(X)|creative(X))=>(~rich(X)|~happy(X))))&
(((~creative(lucy)&~wise(lucy)))=>(?[X]:((rich(X)&~calm(X)))))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:((~tall(X)|~happy(X)))))&
((wise(alice))<=>(?[X]:((~tall(X)|funny(X)))))&
((?[X]:((~rich(X)<~>kind(X))))=>(?[X]:(old(X))))&
(![X]:((tall(X)&~patient(X))=>(rich(X)<~>kind(X))))&
(((creative(fred)&~humble(fred)))<=>(~patient(fred)))&
(![X]:((kind(X)&~old(X))=>(~creative(X)&curious(X))))&
(![X]:((patient(X)|brave(X))<=>(~wise(X)&~kind(X))))&
(?[X]:((generous(X)&kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~humble(X)))&
(?[X]:((happy(X)|funny(X))))&
(?[X]:((happy(X)|~rich(X))))&
(calm(mary))&
(?[X]:(~generous(X)))&
(curious(john)) | ~old(susan) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7716614321307774253369311
% SZS output start Proof for 7716614321307774253369311
1. (~old(susan) <~> quiet(susan)) <=> ? [X0] : (~funny(X0) | quiet(X0)) [input p0]
2. ! [X0] : (~quiet(X0) <=> calm(X0)) [input p1]
4. ! [X0] : (~calm(X0) => (wise(X0) & tall(X0))) [input p3]
5. ! [X0] : (old(X0) => (funny(X0) & creative(X0))) [input p4]
7. ! [X0] : ((~quiet(X0) <~> ~wise(X0)) <=> (~calm(X0) & creative(X0))) [input p6]
11. wise(alice) <=> ? [X0] : (funny(X0) | ~tall(X0)) [input p10]
25. old(susan) [input hypothesis]
29. ! [X0] : ((wise(X0) & tall(X0)) | calm(X0)) [ennf transformation 4]
30. ! [X0] : ((funny(X0) & creative(X0)) | ~old(X0)) [ennf transformation 5]
41. (((~quiet(susan) | old(susan)) & (quiet(susan) | ~old(susan))) | ! [X0] : (funny(X0) & ~quiet(X0))) & (? [X0] : (~funny(X0) | quiet(X0)) | ((~old(susan) | ~quiet(susan)) & (quiet(susan) | old(susan)))) [nnf transformation 1]
42. (((~quiet(susan) | old(susan)) & (quiet(susan) | ~old(susan))) | ! [X0] : (funny(X0) & ~quiet(X0))) & (? [X1] : (~funny(X1) | quiet(X1)) | ((~old(susan) | ~quiet(susan)) & (quiet(susan) | old(susan)))) [rectify 41]
43. ? [X1] : (~funny(X1) | quiet(X1)) => (~funny(sK0) | quiet(sK0)) [choice axiom]
44. (((~quiet(susan) | old(susan)) & (quiet(susan) | ~old(susan))) | ! [X0] : (funny(X0) & ~quiet(X0))) & ((~funny(sK0) | quiet(sK0)) | ((~old(susan) | ~quiet(susan)) & (quiet(susan) | old(susan)))) [skolemisation 42,43]
45. ! [X0] : ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))) [nnf transformation 2]
49. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | (calm(X0) | ~creative(X0))) & ((~calm(X0) & creative(X0)) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [nnf transformation 7]
50. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | calm(X0) | ~creative(X0)) & ((~calm(X0) & creative(X0)) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [flattening 49]
56. (wise(alice) | ! [X0] : (~funny(X0) & tall(X0))) & (? [X0] : (funny(X0) | ~tall(X0)) | ~wise(alice)) [nnf transformation 11]
57. (wise(alice) | ! [X0] : (~funny(X0) & tall(X0))) & (? [X1] : (funny(X1) | ~tall(X1)) | ~wise(alice)) [rectify 56]
58. ? [X1] : (funny(X1) | ~tall(X1)) => (funny(sK3) | ~tall(sK3)) [choice axiom]
59. (wise(alice) | ! [X0] : (~funny(X0) & tall(X0))) & ((funny(sK3) | ~tall(sK3)) | ~wise(alice)) [skolemisation 57,58]
83. quiet(susan) | ~old(susan) | ~quiet(X0) [cnf transformation 44]
84. quiet(susan) | ~old(susan) | funny(X0) [cnf transformation 44]
87. calm(X0) | quiet(X0) [cnf transformation 45]
88. ~calm(X0) | ~quiet(X0) [cnf transformation 45]
92. wise(X0) | calm(X0) [cnf transformation 29]
93. ~old(X0) | creative(X0) [cnf transformation 30]
100. ~calm(X0) | ~wise(X0) | quiet(X0) [cnf transformation 50]
102. ~wise(X0) | ~quiet(X0) | calm(X0) | ~creative(X0) [cnf transformation 50]
112. wise(alice) | ~funny(X0) [cnf transformation 59]
136. old(susan) [cnf transformation 25]
138. 1 <=> ! [X0] : funny(X0) [avatar definition]
139. funny(X0) <- (1) [avatar component clause 138]
141. 2 <=> old(susan) [avatar definition]
143. old(susan) <- (2) [avatar component clause 141]
145. 3 <=> quiet(susan) [avatar definition]
150. 4 <=> ! [X0] : ~quiet(X0) [avatar definition]
151. ~quiet(X0) <- (4) [avatar component clause 150]
153. 1 | ~2 | 3 [avatar split clause 84,145,141,138]
154. 4 | ~2 | 3 [avatar split clause 83,145,141,150]
179. ~wise(X0) | calm(X0) | ~creative(X0) [subsumption resolution 102,87]
180. ~creative(X0) | calm(X0) [subsumption resolution 179,92]
181. ~wise(X0) | ~calm(X0) [subsumption resolution 100,88]
217. 18 <=> ! [X0] : ~funny(X0) [avatar definition]
218. ~funny(X0) <- (18) [avatar component clause 217]
220. 19 <=> wise(alice) [avatar definition]
222. wise(alice) <- (19) [avatar component clause 220]
223. 18 | 19 [avatar split clause 112,220,217]
282. 2 [avatar split clause 136,141]
287. creative(susan) <- (2) [resolution 93,143]
299. calm(susan) <- (2) [resolution 180,287]
302. ~calm(alice) <- (19) [resolution 181,222]
304. quiet(alice) <- (19) [resolution 302,87]
320. ~quiet(susan) <- (2) [resolution 299,88]
323. ~3 | ~2 [avatar split clause 320,141,145]
352. $false <- (4, 19) [resolution 304,151]
354. ~4 | ~19 [avatar contradiction clause 352]
355. $false <- (1, 18) [subsumption resolution 218,139]
356. ~1 | ~18 [avatar contradiction clause 355]
357. $false [avatar sat refutation 153,154,223,282,323,354,356]
% SZS output end Proof for 7716614321307774253369311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or creative is both not strong and humble. If susan is not tall or funny then john is both happy and funny and vice versa. Everyone who is not rich or not funny is both kind and wise and vice versa. If lucy is both not funny and not strong then someone is rich and vice versa. Everyone who is patient or not strong is either not quiet or not rich. Everyone who is creative is either tall or not generous and vice versa. Everyone who is not calm is tall or not calm. Everyone who is not quiet is not brave. Everyone who is quiet is both not calm and not curious and vice versa. Everyone who is curious is either not kind or not generous. Everyone who is not funny or tall is either not calm or quiet. Everyone who is not calm is not wise or brave. If alice is either not wise or happy then mary is calm. Everyone who is either curious or calm is not kind. If mary is both not tall and calm then john is either quiet or funny. Everyone who is not quiet is both old and kind. Someone is both not patient and not creative. Someone is either happy or brave. Someone is calm or not humble. Susan is either not wise or happy. Someone is patient. Someone is both not curious and generous. | Lucy is strong. | neutral | (![X]:((~happy(X)<~>creative(X))=>(~strong(X)&humble(X))))&
(((~tall(susan)|funny(susan)))<=>((happy(john)&funny(john))))&
(![X]:((~rich(X)|~funny(X))<=>(kind(X)&wise(X))))&
(((~funny(lucy)&~strong(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((patient(X)|~strong(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:(creative(X)<=>(tall(X)<~>~generous(X))))&
(![X]:(~calm(X)=>(tall(X)|~calm(X))))&
(![X]:(~quiet(X)=>~brave(X)))&
(![X]:(quiet(X)<=>(~calm(X)&~curious(X))))&
(![X]:(curious(X)=>(~kind(X)<~>~generous(X))))&
(![X]:((~funny(X)|tall(X))=>(~calm(X)<~>quiet(X))))&
(![X]:(~calm(X)=>(~wise(X)|brave(X))))&
(((~wise(alice)<~>happy(alice)))=>(calm(mary)))&
(![X]:((curious(X)<~>calm(X))=>~kind(X)))&
(((~tall(mary)&calm(mary)))=>((quiet(john)<~>funny(john))))&
(![X]:(~quiet(X)=>(old(X)&kind(X))))&
(?[X]:((~patient(X)&~creative(X))))&
(?[X]:((happy(X)<~>brave(X))))&
(?[X]:((calm(X)|~humble(X))))&
((~wise(susan)<~>happy(susan)))&
(?[X]:(patient(X)))&
(?[X]:((~curious(X)&generous(X)))) | strong(lucy) | [] | null | 0 |
If lucy is either not calm or generous then fred is both curious and not old and vice versa.
Everyone who is either kind or not wise is not happy or calm.
Everyone who is both not curious and not funny is not wise or not tall and vice versa.
Everyone who is both not strong and not curious is both not wise and brave.
Everyone who is either creative or kind is both not curious and not kind.
If someone is both wise and not creative then someone is brave or not generous.
If someone is not brave then susan is both not rich and not generous.
If fred is either rich or strong then someone is funny and vice versa.
Everyone who is not strong is both happy and not calm.
If lucy is both quiet and not rich then mary is both tall and not happy.
Everyone who is not patient or not tall is curious.
Everyone who is both not wise and happy is not wise or funny and vice versa.
Everyone who is either not humble or not happy is strong or not patient.
If someone is patient or strong then susan is either generous or not kind and vice versa.
If mary is both not calm and not generous then lucy is not funny.
If someone is kind then lucy is happy and vice versa.
Someone is either wise or not happy.
Someone is not generous or rich.
Someone is either old or happy.
Someone is both not creative and wise.
Someone is not patient or brave.
Someone is strong or not old.
Lucy is both creative and not calm. | Lucy is tall. | entailment | (((~calm(lucy)<~>generous(lucy)))<=>((curious(fred)&~old(fred))))&
(![X]:((kind(X)<~>~wise(X))=>(~happy(X)|calm(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~wise(X)|~tall(X))))&
(![X]:((~strong(X)&~curious(X))=>(~wise(X)&brave(X))))&
(![X]:((creative(X)<~>kind(X))=>(~curious(X)&~kind(X))))&
((?[X]:((wise(X)&~creative(X))))=>(?[X]:((brave(X)|~generous(X)))))&
((?[X]:(~brave(X)))=>((~rich(susan)&~generous(susan))))&
(((rich(fred)<~>strong(fred)))<=>(?[X]:(funny(X))))&
(![X]:(~strong(X)=>(happy(X)&~calm(X))))&
(((quiet(lucy)&~rich(lucy)))=>((tall(mary)&~happy(mary))))&
(![X]:((~patient(X)|~tall(X))=>curious(X)))&
(![X]:((~wise(X)&happy(X))<=>(~wise(X)|funny(X))))&
(![X]:((~humble(X)<~>~happy(X))=>(strong(X)|~patient(X))))&
((?[X]:((patient(X)|strong(X))))<=>((generous(susan)<~>~kind(susan))))&
(((~calm(mary)&~generous(mary)))=>(~funny(lucy)))&
((?[X]:(kind(X)))<=>(happy(lucy)))&
(?[X]:((wise(X)<~>~happy(X))))&
(?[X]:((~generous(X)|rich(X))))&
(?[X]:((old(X)<~>happy(X))))&
(?[X]:((~creative(X)&wise(X))))&
(?[X]:((~patient(X)|brave(X))))&
(?[X]:((strong(X)|~old(X))))&
((creative(lucy)&~calm(lucy))) | tall(lucy) | [
"p2",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 112346728292155283563521
% SZS output start Proof for 112346728292155283563521
3. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (~tall(X0) | ~wise(X0))) [input p2]
11. ! [X0] : ((~tall(X0) | ~patient(X0)) => curious(X0)) [input p10]
24. ~tall(lucy) [input hypothesis]
37. ! [X0] : (curious(X0) | (tall(X0) & patient(X0))) [ennf transformation 11]
45. ! [X0] : (((~funny(X0) & ~curious(X0)) | (tall(X0) & wise(X0))) & ((~tall(X0) | ~wise(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 3]
46. ! [X0] : (((~funny(X0) & ~curious(X0)) | (tall(X0) & wise(X0))) & (~tall(X0) | ~wise(X0) | funny(X0) | curious(X0))) [flattening 45]
85. ~curious(X0) | tall(X0) [cnf transformation 46]
100. curious(X0) | tall(X0) [cnf transformation 37]
127. ~tall(lucy) [cnf transformation 24]
170. tall(X0) [subsumption resolution 100,85]
259. $false [subsumption resolution 127,170]
% SZS output end Proof for 112346728292155283563521
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or tall is either creative or kind.
Everyone who is patient or generous is brave or not rich.
If someone is tall or not wise then mary is not rich or not wise and vice versa.
Everyone who is not brave or humble is old and vice versa.
If someone is either quiet or funny then someone is not strong or generous.
If someone is either brave or curious then lucy is either old or not patient and vice versa.
Everyone who is old or calm is either not curious or humble.
Everyone who is kind or creative is either kind or not old and vice versa.
If lucy is either not quiet or strong then paul is not curious.
If someone is either not wise or not old then someone is not brave.
Everyone who is not patient is both not tall and not creative and vice versa.
Everyone who is both not happy and not quiet is both happy and not wise.
Everyone who is either not curious or creative is old and vice versa.
If mary is not kind then mary is both not tall and not creative.
Everyone who is both not creative and not calm is either not wise or not funny.
Everyone who is brave is either kind or not calm.
Someone is either not old or not kind.
John is not wise or not funny.
Lucy is both not creative and happy.
Paul is both happy and generous.
John is both strong and kind.
Lucy is not brave or humble.
Someone is both not curious and not wise.
Someone is both not patient and not curious. | Lucy is strong. | neutral | (![X]:((funny(X)|tall(X))=>(creative(X)<~>kind(X))))&
(![X]:((patient(X)|generous(X))=>(brave(X)|~rich(X))))&
((?[X]:((tall(X)|~wise(X))))<=>((~rich(mary)|~wise(mary))))&
(![X]:((~brave(X)|humble(X))<=>old(X)))&
((?[X]:((quiet(X)<~>funny(X))))=>(?[X]:((~strong(X)|generous(X)))))&
((?[X]:((brave(X)<~>curious(X))))<=>((old(lucy)<~>~patient(lucy))))&
(![X]:((old(X)|calm(X))=>(~curious(X)<~>humble(X))))&
(![X]:((kind(X)|creative(X))<=>(kind(X)<~>~old(X))))&
(((~quiet(lucy)<~>strong(lucy)))=>(~curious(paul)))&
((?[X]:((~wise(X)<~>~old(X))))=>(?[X]:(~brave(X))))&
(![X]:(~patient(X)<=>(~tall(X)&~creative(X))))&
(![X]:((~happy(X)&~quiet(X))=>(happy(X)&~wise(X))))&
(![X]:((~curious(X)<~>creative(X))<=>old(X)))&
((~kind(mary))=>((~tall(mary)&~creative(mary))))&
(![X]:((~creative(X)&~calm(X))=>(~wise(X)<~>~funny(X))))&
(![X]:(brave(X)=>(kind(X)<~>~calm(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
((~wise(john)|~funny(john)))&
((~creative(lucy)&happy(lucy)))&
((happy(paul)&generous(paul)))&
((strong(john)&kind(john)))&
((~brave(lucy)|humble(lucy)))&
(?[X]:((~curious(X)&~wise(X))))&
(?[X]:((~patient(X)&~curious(X)))) | strong(lucy) | [] | null | 0 |
If lucy is old or not generous then lucy is not brave or not happy.
If someone is both not strong and not quiet then mary is not happy or not calm and vice versa.
Everyone who is either creative or not calm is not curious or not patient.
If alice is both not curious and not kind then someone is both not wise and not brave.
Everyone who is calm is quiet or strong and vice versa.
Everyone who is both humble and not wise is both not quiet and tall.
Everyone who is both not happy and happy is both not patient and funny and vice versa.
Everyone who is either not brave or not kind is not old.
If lucy is either not funny or rich then lucy is kind or generous and vice versa.
If someone is not strong then alice is not wise and vice versa.
Everyone who is not happy is funny.
If someone is either not curious or not patient then mary is either not curious or brave.
Everyone who is either generous or not curious is not curious.
If someone is not wise then someone is not tall or not rich and vice versa.
Everyone who is either humble or rich is quiet.
Everyone who is tall or not rich is generous or not kind and vice versa.
Someone is either not curious or tall.
Someone is strong or not patient.
Alice is either not curious or creative.
Someone is either tall or not generous.
Someone is not happy.
Paul is either funny or rich.
Someone is both quiet and brave.
Someone is not quiet or not wise. | Lucy is quiet. | neutral | (((old(lucy)|~generous(lucy)))=>((~brave(lucy)|~happy(lucy))))&
((?[X]:((~strong(X)&~quiet(X))))<=>((~happy(mary)|~calm(mary))))&
(![X]:((creative(X)<~>~calm(X))=>(~curious(X)|~patient(X))))&
(((~curious(alice)&~kind(alice)))=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:(calm(X)<=>(quiet(X)|strong(X))))&
(![X]:((humble(X)&~wise(X))=>(~quiet(X)&tall(X))))&
(![X]:((~happy(X)&happy(X))<=>(~patient(X)&funny(X))))&
(![X]:((~brave(X)<~>~kind(X))=>~old(X)))&
(((~funny(lucy)<~>rich(lucy)))<=>((kind(lucy)|generous(lucy))))&
((?[X]:(~strong(X)))<=>(~wise(alice)))&
(![X]:(~happy(X)=>funny(X)))&
((?[X]:((~curious(X)<~>~patient(X))))=>((~curious(mary)<~>brave(mary))))&
(![X]:((generous(X)<~>~curious(X))=>~curious(X)))&
((?[X]:(~wise(X)))<=>(?[X]:((~tall(X)|~rich(X)))))&
(![X]:((humble(X)<~>rich(X))=>quiet(X)))&
(![X]:((tall(X)|~rich(X))<=>(generous(X)|~kind(X))))&
(?[X]:((~curious(X)<~>tall(X))))&
(?[X]:((strong(X)|~patient(X))))&
((~curious(alice)<~>creative(alice)))&
(?[X]:((tall(X)<~>~generous(X))))&
(?[X]:(~happy(X)))&
((funny(paul)<~>rich(paul)))&
(?[X]:((quiet(X)&brave(X))))&
(?[X]:((~quiet(X)|~wise(X)))) | quiet(lucy) | [] | null | 0 |
If someone is quiet then john is not rich or not wise.
If someone is either happy or not old then paul is both calm and not humble.
Everyone who is strong or not patient is brave and vice versa.
Everyone who is both rich and creative is old and vice versa.
Everyone who is patient or brave is either kind or not humble.
If paul is not patient or humble then john is either calm or funny and vice versa.
If someone is both quiet and not brave then someone is either not wise or tall and vice versa.
If someone is not creative then paul is either old or kind and vice versa.
Everyone who is not brave or strong is humble or not brave.
If paul is not quiet or not tall then fred is not creative or not brave.
If mary is both kind and brave then john is both kind and wise.
Everyone who is tall or not calm is not curious.
If susan is old or kind then someone is both not kind and not happy and vice versa.
Everyone who is not curious is both not patient and patient.
Everyone who is either not humble or kind is either not calm or not brave and vice versa.
If alice is both not funny and not quiet then fred is either not brave or old.
Someone is not creative.
Alice is both generous and not happy.
Lucy is quiet.
Someone is either patient or not wise.
Someone is either funny or not patient.
Someone is either old or not quiet.
Mary is not generous or not kind. | Lucy is tall. | contradiction | ((?[X]:(quiet(X)))=>((~rich(john)|~wise(john))))&
((?[X]:((happy(X)<~>~old(X))))=>((calm(paul)&~humble(paul))))&
(![X]:((strong(X)|~patient(X))<=>brave(X)))&
(![X]:((rich(X)&creative(X))<=>old(X)))&
(![X]:((patient(X)|brave(X))=>(kind(X)<~>~humble(X))))&
(((~patient(paul)|humble(paul)))<=>((calm(john)<~>funny(john))))&
((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((?[X]:(~creative(X)))<=>((old(paul)<~>kind(paul))))&
(![X]:((~brave(X)|strong(X))=>(humble(X)|~brave(X))))&
(((~quiet(paul)|~tall(paul)))=>((~creative(fred)|~brave(fred))))&
(((kind(mary)&brave(mary)))=>((kind(john)&wise(john))))&
(![X]:((tall(X)|~calm(X))=>~curious(X)))&
(((old(susan)|kind(susan)))<=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:(~curious(X)=>(~patient(X)&patient(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(~calm(X)<~>~brave(X))))&
(((~funny(alice)&~quiet(alice)))=>((~brave(fred)<~>old(fred))))&
(?[X]:(~creative(X)))&
((generous(alice)&~happy(alice)))&
(quiet(lucy))&
(?[X]:((patient(X)<~>~wise(X))))&
(?[X]:((funny(X)<~>~patient(X))))&
(?[X]:((old(X)<~>~quiet(X))))&
((~generous(mary)|~kind(mary))) | tall(lucy) | [
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6703994925010245268830844
% SZS output start Proof for 6703994925010245268830844
12. ! [X0] : ((~calm(X0) | tall(X0)) => ~curious(X0)) [input p11]
14. ! [X0] : (~curious(X0) => (patient(X0) & ~patient(X0))) [input p13]
24. tall(lucy) [input hypothesis]
36. ! [X0] : (~curious(X0) | (calm(X0) & ~tall(X0))) [ennf transformation 12]
37. ! [X0] : ((patient(X0) & ~patient(X0)) | curious(X0)) [ennf transformation 14]
112. ~curious(X0) | ~tall(X0) [cnf transformation 36]
119. ~patient(X0) | curious(X0) [cnf transformation 37]
120. patient(X0) | curious(X0) [cnf transformation 37]
142. tall(lucy) [cnf transformation 24]
298. curious(X0) [subsumption resolution 119,120]
354. ~tall(X0) [resolution 112,298]
356. $false [resolution 354,142]
% SZS output end Proof for 6703994925010245268830844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and humble is both happy and tall and vice versa.
Everyone who is calm is either not wise or happy and vice versa.
Everyone who is kind or not calm is not generous and vice versa.
If someone is not happy then paul is creative or not creative.
If someone is creative or not curious then someone is both humble and strong.
Everyone who is both kind and not generous is creative.
If someone is both calm and wise then someone is both curious and not calm and vice versa.
If mary is both creative and not creative then someone is either not strong or calm and vice versa.
Everyone who is not rich is rich.
If someone is both patient and not old then someone is both not wise and kind and vice versa.
Everyone who is wise or patient is both not wise and not generous.
Everyone who is either not funny or calm is both funny and not rich.
Everyone who is both brave and not quiet is both generous and not calm and vice versa.
If susan is not tall then someone is either not happy or not old and vice versa.
Everyone who is not calm or not old is not happy.
If someone is humble or old then someone is both happy and not calm and vice versa.
Fred is quiet.
Someone is either not quiet or strong.
Mary is tall or not funny.
Paul is either curious or humble. | Paul is humble. | contradiction | (![X]:((~patient(X)&humble(X))<=>(happy(X)&tall(X))))&
(![X]:(calm(X)<=>(~wise(X)<~>happy(X))))&
(![X]:((kind(X)|~calm(X))<=>~generous(X)))&
((?[X]:(~happy(X)))=>((creative(paul)|~creative(paul))))&
((?[X]:((creative(X)|~curious(X))))=>(?[X]:((humble(X)&strong(X)))))&
(![X]:((kind(X)&~generous(X))=>creative(X)))&
((?[X]:((calm(X)&wise(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(((creative(mary)&~creative(mary)))<=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:(~rich(X)=>rich(X)))&
((?[X]:((patient(X)&~old(X))))<=>(?[X]:((~wise(X)&kind(X)))))&
(![X]:((wise(X)|patient(X))=>(~wise(X)&~generous(X))))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(quiet(fred))&
(?[X]:((~quiet(X)<~>strong(X))))&
((tall(mary)|~funny(mary)))&
((curious(paul)<~>humble(paul))) | humble(paul) | [
"p4",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5330590339811515584996206
% SZS output start Proof for 5330590339811515584996206
5. ? [X0] : (~curious(X0) | creative(X0)) => ? [X0] : (strong(X0) & humble(X0)) [input p4]
15. ! [X0] : ((~old(X0) | ~calm(X0)) => ~happy(X0)) [input p14]
16. ? [X0] : (old(X0) | humble(X0)) <=> ? [X0] : (~calm(X0) & happy(X0)) [input p15]
20. curious(paul) <~> humble(paul) [input p19]
21. humble(paul) [input hypothesis]
22. ? [X0] : (~curious(X0) | creative(X0)) => ? [X1] : (strong(X1) & humble(X1)) [rectify 5]
25. ? [X0] : (old(X0) | humble(X0)) <=> ? [X1] : (~calm(X1) & happy(X1)) [rectify 16]
28. ? [X1] : (strong(X1) & humble(X1)) | ! [X0] : (curious(X0) & ~creative(X0)) [ennf transformation 22]
34. ! [X0] : (~happy(X0) | (old(X0) & calm(X0))) [ennf transformation 15]
40. ? [X0] : (strong(X0) & humble(X0)) | ! [X1] : (curious(X1) & ~creative(X1)) [rectify 28]
41. ? [X0] : (strong(X0) & humble(X0)) => (strong(sK0) & humble(sK0)) [choice axiom]
42. (strong(sK0) & humble(sK0)) | ! [X1] : (curious(X1) & ~creative(X1)) [skolemisation 40,41]
65. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X1] : (~calm(X1) & happy(X1)) | ! [X0] : (~old(X0) & ~humble(X0))) [nnf transformation 25]
66. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X2] : (~calm(X2) & happy(X2)) | ! [X3] : (~old(X3) & ~humble(X3))) [rectify 65]
67. ? [X0] : (old(X0) | humble(X0)) => (old(sK7) | humble(sK7)) [choice axiom]
68. ? [X2] : (~calm(X2) & happy(X2)) => (~calm(sK8) & happy(sK8)) [choice axiom]
69. ((old(sK7) | humble(sK7)) | ! [X1] : (calm(X1) | ~happy(X1))) & ((~calm(sK8) & happy(sK8)) | ! [X3] : (~old(X3) & ~humble(X3))) [skolemisation 66,68,67]
73. (~humble(paul) | ~curious(paul)) & (humble(paul) | curious(paul)) [nnf transformation 20]
87. humble(sK0) | curious(X1) [cnf transformation 42]
122. ~happy(X0) | calm(X0) [cnf transformation 34]
124. happy(sK8) | ~humble(X3) [cnf transformation 69]
126. ~calm(sK8) | ~humble(X3) [cnf transformation 69]
134. ~humble(paul) | ~curious(paul) [cnf transformation 73]
135. humble(paul) [cnf transformation 21]
140. 1 <=> ! [X1] : curious(X1) [avatar definition]
141. curious(X1) <- (1) [avatar component clause 140]
152. 4 <=> humble(sK0) [avatar definition]
154. humble(sK0) <- (4) [avatar component clause 152]
155. 1 | 4 [avatar split clause 87,152,140]
253. 26 <=> calm(sK8) [avatar definition]
255. ~calm(sK8) <- (~26) [avatar component clause 253]
258. 27 <=> ! [X3] : ~humble(X3) [avatar definition]
259. ~humble(X3) <- (27) [avatar component clause 258]
260. 27 | ~26 [avatar split clause 126,253,258]
262. 28 <=> happy(sK8) [avatar definition]
264. happy(sK8) <- (28) [avatar component clause 262]
266. 27 | 28 [avatar split clause 124,262,258]
287. 33 <=> curious(paul) [avatar definition]
289. ~curious(paul) <- (~33) [avatar component clause 287]
291. 34 <=> humble(paul) [avatar definition]
294. ~33 | ~34 [avatar split clause 134,291,287]
296. 34 [avatar split clause 135,291]
300. $false <- (4, 27) [subsumption resolution 154,259]
301. ~4 | ~27 [avatar contradiction clause 300]
302. $false <- (1, ~33) [resolution 289,141]
303. ~1 | 33 [avatar contradiction clause 302]
306. calm(sK8) <- (28) [resolution 122,264]
307. $false <- (~26, 28) [subsumption resolution 306,255]
308. 26 | ~28 [avatar contradiction clause 307]
309. $false [avatar sat refutation 155,260,266,294,296,301,303,308]
% SZS output end Proof for 5330590339811515584996206
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny is patient or not kind. If someone is not generous then fred is rich. If someone is both not patient and tall then mary is both not humble and not generous. Everyone who is not calm or rich is both funny and not quiet and vice versa. Everyone who is funny is not quiet and vice versa. If someone is both strong and quiet then someone is not old and vice versa. Everyone who is both not creative and creative is tall and vice versa. If alice is creative or not tall then someone is both old and not humble and vice versa. Everyone who is not strong is both not tall and not humble and vice versa. Everyone who is either not quiet or not happy is rich or happy. Everyone who is not calm or not old is both wise and tall. If someone is both strong and not patient then john is either not quiet or not creative and vice versa. If fred is either funny or not creative then someone is both not calm and funny. If alice is kind or funny then fred is either not curious or not tall. Everyone who is not quiet or not patient is both not strong and not funny and vice versa. Everyone who is either not patient or not brave is both funny and not tall. Someone is not tall or not kind. Mary is both not curious and not funny. Alice is not creative. Someone is not funny or curious. | Alice is not brave. | entailment | (![X]:(~funny(X)=>(patient(X)|~kind(X))))&
((?[X]:(~generous(X)))=>(rich(fred)))&
((?[X]:((~patient(X)&tall(X))))=>((~humble(mary)&~generous(mary))))&
(![X]:((~calm(X)|rich(X))<=>(funny(X)&~quiet(X))))&
(![X]:(funny(X)<=>~quiet(X)))&
((?[X]:((strong(X)&quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)&creative(X))<=>tall(X)))&
(((creative(alice)|~tall(alice)))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:(~strong(X)<=>(~tall(X)&~humble(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>(rich(X)|happy(X))))&
(![X]:((~calm(X)|~old(X))=>(wise(X)&tall(X))))&
((?[X]:((strong(X)&~patient(X))))<=>((~quiet(john)<~>~creative(john))))&
(((funny(fred)<~>~creative(fred)))=>(?[X]:((~calm(X)&funny(X)))))&
(((kind(alice)|funny(alice)))=>((~curious(fred)<~>~tall(fred))))&
(![X]:((~quiet(X)|~patient(X))<=>(~strong(X)&~funny(X))))&
(![X]:((~patient(X)<~>~brave(X))=>(funny(X)&~tall(X))))&
(?[X]:((~tall(X)|~kind(X))))&
((~curious(mary)&~funny(mary)))&
(~creative(alice))&
(?[X]:((~funny(X)|curious(X)))) | ~brave(alice) | [
"p4",
"p5",
"p6",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1398075009026464193757805
% SZS output start Proof for 1398075009026464193757805
5. ! [X0] : (funny(X0) <=> ~quiet(X0)) [input p4]
6. ? [X0] : (quiet(X0) & strong(X0)) <=> ? [X0] : ~old(X0) [input p5]
7. ! [X0] : ((creative(X0) & ~creative(X0)) <=> tall(X0)) [input p6]
11. ! [X0] : ((~old(X0) | ~calm(X0)) => (tall(X0) & wise(X0))) [input p10]
15. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (~funny(X0) & ~strong(X0))) [input p14]
16. ! [X0] : ((~patient(X0) <~> ~brave(X0)) => (~tall(X0) & funny(X0))) [input p15]
21. brave(alice) [input hypothesis]
22. ? [X0] : (quiet(X0) & strong(X0)) <=> ? [X1] : ~old(X1) [rectify 6]
23. ! [X0] : ((~old(X0) | ~calm(X0)) => tall(X0)) [pure predicate removal 11]
31. ! [X0] : (tall(X0) | (old(X0) & calm(X0))) [ennf transformation 23]
34. ! [X0] : ((~tall(X0) & funny(X0)) | (~patient(X0) <=> ~brave(X0))) [ennf transformation 16]
37. ! [X0] : ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))) [nnf transformation 5]
38. (? [X0] : (quiet(X0) & strong(X0)) | ! [X1] : old(X1)) & (? [X1] : ~old(X1) | ! [X0] : (~quiet(X0) | ~strong(X0))) [nnf transformation 22]
39. (? [X0] : (quiet(X0) & strong(X0)) | ! [X1] : old(X1)) & (? [X2] : ~old(X2) | ! [X3] : (~quiet(X3) | ~strong(X3))) [rectify 38]
40. ? [X0] : (quiet(X0) & strong(X0)) => (quiet(sK0) & strong(sK0)) [choice axiom]
41. ? [X2] : ~old(X2) => ~old(sK1) [choice axiom]
42. ((quiet(sK0) & strong(sK0)) | ! [X1] : old(X1)) & (~old(sK1) | ! [X3] : (~quiet(X3) | ~strong(X3))) [skolemisation 39,41,40]
43. ! [X0] : (((creative(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | (~creative(X0) | creative(X0)))) [nnf transformation 7]
44. ! [X0] : (((creative(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | ~creative(X0) | creative(X0))) [flattening 43]
61. ! [X0] : (((~patient(X0) | ~quiet(X0)) | (funny(X0) | strong(X0))) & ((~funny(X0) & ~strong(X0)) | (patient(X0) & quiet(X0)))) [nnf transformation 15]
62. ! [X0] : ((~patient(X0) | ~quiet(X0) | funny(X0) | strong(X0)) & ((~funny(X0) & ~strong(X0)) | (patient(X0) & quiet(X0)))) [flattening 61]
63. ! [X0] : ((~tall(X0) & funny(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) [nnf transformation 34]
74. ~quiet(X0) | ~funny(X0) [cnf transformation 37]
75. quiet(X0) | funny(X0) [cnf transformation 37]
76. ~old(sK1) | ~quiet(X3) | ~strong(X3) [cnf transformation 42]
80. ~creative(X0) | ~tall(X0) [cnf transformation 44]
81. ~tall(X0) | creative(X0) [cnf transformation 44]
93. tall(X0) | old(X0) [cnf transformation 31]
108. ~funny(X0) | quiet(X0) [cnf transformation 62]
109. ~funny(X0) | patient(X0) [cnf transformation 62]
110. ~patient(X0) | ~quiet(X0) | funny(X0) | strong(X0) [cnf transformation 62]
111. funny(X0) | ~brave(X0) | patient(X0) [cnf transformation 63]
119. brave(alice) [cnf transformation 21]
143. 6 <=> ! [X1] : old(X1) [avatar definition]
144. old(X1) <- (6) [avatar component clause 143]
156. 9 <=> ! [X3] : (~quiet(X3) | ~strong(X3)) [avatar definition]
157. ~quiet(X3) | ~strong(X3) <- (9) [avatar component clause 156]
159. 10 <=> old(sK1) [avatar definition]
161. ~old(sK1) <- (~10) [avatar component clause 159]
162. 9 | ~10 [avatar split clause 76,159,156]
163. ~tall(X0) [subsumption resolution 80,81]
168. old(X0) [subsumption resolution 93,163]
169. 6 [avatar split clause 168,143]
224. ~quiet(X0) | ~patient(X0) | strong(X0) [subsumption resolution 110,74]
225. quiet(X0) [subsumption resolution 108,75]
227. ~brave(X0) | patient(X0) [subsumption resolution 111,109]
239. $false <- (6, ~10) [resolution 161,144]
240. ~6 | 10 [avatar contradiction clause 239]
241. ~strong(X3) <- (9) [subsumption resolution 157,225]
252. ~funny(X0) [resolution 74,225]
261. patient(alice) [resolution 227,119]
263. ~patient(X0) | strong(X0) | funny(X0) [resolution 224,75]
265. ~patient(X0) | funny(X0) <- (9) [subsumption resolution 263,241]
266. ~patient(X0) <- (9) [subsumption resolution 265,252]
269. $false <- (9) [resolution 266,261]
270. ~9 [avatar contradiction clause 269]
271. $false [avatar sat refutation 162,169,240,270]
% SZS output end Proof for 1398075009026464193757805
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then mary is strong or not calm.
Everyone who is either not tall or not patient is both not brave and not quiet.
If mary is tall then someone is not tall or not brave and vice versa.
If someone is both calm and not old then paul is strong and vice versa.
Everyone who is both calm and not old is not curious.
If someone is wise then someone is both not calm and not brave and vice versa.
Everyone who is generous or rich is calm and vice versa.
Everyone who is both not calm and happy is not quiet or happy and vice versa.
If lucy is either not quiet or old then john is either not creative or not old and vice versa.
Everyone who is both not strong and kind is not patient.
If someone is not quiet then alice is both rich and not rich and vice versa.
If someone is either not brave or wise then fred is both not rich and not strong and vice versa.
If someone is both funny and generous then someone is both old and not curious.
Everyone who is either not tall or calm is either not kind or tall and vice versa.
If someone is either not old or not generous then mary is curious or not generous.
Everyone who is generous is either strong or not humble.
Someone is rich or wise.
Fred is both not funny and not humble.
Someone is not funny.
Fred is either strong or not creative.
Someone is both humble and kind.
Paul is curious.
Lucy is strong.
Mary is kind or not funny. | Lucy is not quiet. | contradiction | ((?[X]:(happy(X)))=>((strong(mary)|~calm(mary))))&
(![X]:((~tall(X)<~>~patient(X))=>(~brave(X)&~quiet(X))))&
((tall(mary))<=>(?[X]:((~tall(X)|~brave(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(strong(paul)))&
(![X]:((calm(X)&~old(X))=>~curious(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((generous(X)|rich(X))<=>calm(X)))&
(![X]:((~calm(X)&happy(X))<=>(~quiet(X)|happy(X))))&
(((~quiet(lucy)<~>old(lucy)))<=>((~creative(john)<~>~old(john))))&
(![X]:((~strong(X)&kind(X))=>~patient(X)))&
((?[X]:(~quiet(X)))<=>((rich(alice)&~rich(alice))))&
((?[X]:((~brave(X)<~>wise(X))))<=>((~rich(fred)&~strong(fred))))&
((?[X]:((funny(X)&generous(X))))=>(?[X]:((old(X)&~curious(X)))))&
(![X]:((~tall(X)<~>calm(X))<=>(~kind(X)<~>tall(X))))&
((?[X]:((~old(X)<~>~generous(X))))=>((curious(mary)|~generous(mary))))&
(![X]:(generous(X)=>(strong(X)<~>~humble(X))))&
(?[X]:((rich(X)|wise(X))))&
((~funny(fred)&~humble(fred)))&
(?[X]:(~funny(X)))&
((strong(fred)<~>~creative(fred)))&
(?[X]:((humble(X)&kind(X))))&
(curious(paul))&
(strong(lucy))&
((kind(mary)|~funny(mary))) | ~quiet(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3105193050245764542745928
% SZS output start Proof for 3105193050245764542745928
11. ? [X0] : ~quiet(X0) <=> (~rich(alice) & rich(alice)) [input p10]
25. ~quiet(lucy) [input hypothesis]
61. (? [X0] : ~quiet(X0) | (rich(alice) | ~rich(alice))) & ((~rich(alice) & rich(alice)) | ! [X0] : quiet(X0)) [nnf transformation 11]
62. (? [X0] : ~quiet(X0) | rich(alice) | ~rich(alice)) & ((~rich(alice) & rich(alice)) | ! [X0] : quiet(X0)) [flattening 61]
63. (? [X0] : ~quiet(X0) | rich(alice) | ~rich(alice)) & ((~rich(alice) & rich(alice)) | ! [X1] : quiet(X1)) [rectify 62]
64. ? [X0] : ~quiet(X0) => ~quiet(sK4) [choice axiom]
65. (~quiet(sK4) | rich(alice) | ~rich(alice)) & ((~rich(alice) & rich(alice)) | ! [X1] : quiet(X1)) [skolemisation 63,64]
111. rich(alice) | quiet(X1) [cnf transformation 65]
112. ~rich(alice) | quiet(X1) [cnf transformation 65]
140. ~quiet(lucy) [cnf transformation 25]
226. 20 <=> quiet(lucy) [avatar definition]
227. ~quiet(lucy) <- (~20) [avatar component clause 226]
242. 22 <=> ! [X1] : quiet(X1) [avatar definition]
243. quiet(X1) <- (22) [avatar component clause 242]
245. 23 <=> rich(alice) [avatar definition]
248. 22 | ~23 [avatar split clause 112,245,242]
249. 22 | 23 [avatar split clause 111,245,242]
311. ~20 [avatar split clause 140,226]
312. $false <- (~20, 22) [subsumption resolution 227,243]
313. 20 | ~22 [avatar contradiction clause 312]
314. $false [avatar sat refutation 248,249,311,313]
% SZS output end Proof for 3105193050245764542745928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both old and not creative.
Everyone who is old or humble is both old and patient.
Everyone who is both not old and not strong is both calm and tall.
Everyone who is either not wise or happy is either quiet or not curious.
Everyone who is both tall and calm is not calm and vice versa.
If someone is either funny or tall then alice is either happy or kind.
Everyone who is not tall is either wise or not rich.
Everyone who is not generous is not strong or not humble.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
If paul is not creative or not strong then someone is strong and vice versa.
John is not patient or humble.
John is brave or not funny.
Someone is not old.
Lucy is both not old and not rich.
Someone is brave.
Lucy is patient or calm. | Mary is not strong. | neutral | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|humble(X))=>(old(X)&patient(X))))&
(![X]:((~old(X)&~strong(X))=>(calm(X)&tall(X))))&
(![X]:((~wise(X)<~>happy(X))=>(quiet(X)<~>~curious(X))))&
(![X]:((tall(X)&calm(X))<=>~calm(X)))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(alice)<~>kind(alice))))&
(![X]:(~tall(X)=>(wise(X)<~>~rich(X))))&
(![X]:(~generous(X)=>(~strong(X)|~humble(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
((~patient(john)|humble(john)))&
((brave(john)|~funny(john)))&
(?[X]:(~old(X)))&
((~old(lucy)&~rich(lucy)))&
(?[X]:(brave(X)))&
((patient(lucy)|calm(lucy))) | ~strong(mary) | [] | null | 0 |
If alice is either not quiet or not creative then someone is both not tall and strong. Everyone who is both not kind and not creative is either not patient or not funny and vice versa. Everyone who is either not happy or generous is both not quiet and brave. If paul is both not creative and quiet then john is strong or rich and vice versa. If susan is quiet then alice is not rich. Everyone who is both rich and not brave is not brave or not strong. Everyone who is kind is either brave or not brave and vice versa. Everyone who is humble is either not patient or kind and vice versa. Everyone who is curious or not generous is both not calm and strong and vice versa. Everyone who is not generous or not wise is both tall and not brave. Everyone who is not wise or humble is not curious and vice versa. If someone is both curious and tall then john is not patient or not tall and vice versa. If someone is not curious or not brave then someone is either not strong or not old and vice versa. Everyone who is rich or patient is curious or not rich and vice versa. If paul is not rich or not wise then someone is either not quiet or patient. If fred is rich then alice is both quiet and funny and vice versa. Paul is both brave and kind. Someone is either not quiet or not old. Someone is brave. Someone is both generous and funny. Someone is both patient and tall. Someone is either not curious or old. Someone is not wise or brave. Paul is not funny. | Paul is not rich. | contradiction | (((~quiet(alice)<~>~creative(alice)))=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((~kind(X)&~creative(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((~happy(X)<~>generous(X))=>(~quiet(X)&brave(X))))&
(((~creative(paul)&quiet(paul)))<=>((strong(john)|rich(john))))&
((quiet(susan))=>(~rich(alice)))&
(![X]:((rich(X)&~brave(X))=>(~brave(X)|~strong(X))))&
(![X]:(kind(X)<=>(brave(X)<~>~brave(X))))&
(![X]:(humble(X)<=>(~patient(X)<~>kind(X))))&
(![X]:((curious(X)|~generous(X))<=>(~calm(X)&strong(X))))&
(![X]:((~generous(X)|~wise(X))=>(tall(X)&~brave(X))))&
(![X]:((~wise(X)|humble(X))<=>~curious(X)))&
((?[X]:((curious(X)&tall(X))))<=>((~patient(john)|~tall(john))))&
((?[X]:((~curious(X)|~brave(X))))<=>(?[X]:((~strong(X)<~>~old(X)))))&
(![X]:((rich(X)|patient(X))<=>(curious(X)|~rich(X))))&
(((~rich(paul)|~wise(paul)))=>(?[X]:((~quiet(X)<~>patient(X)))))&
((rich(fred))<=>((quiet(alice)&funny(alice))))&
((brave(paul)&kind(paul)))&
(?[X]:((~quiet(X)<~>~old(X))))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((patient(X)&tall(X))))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:((~wise(X)|brave(X))))&
(~funny(paul)) | ~rich(paul) | [
"p1",
"p6",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4601243080169418879964658
% SZS output start Proof for 4601243080169418879964658
2. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (~patient(X0) <~> ~funny(X0))) [input p1]
7. ! [X0] : (kind(X0) <=> (brave(X0) <~> ~brave(X0))) [input p6]
14. ! [X0] : ((patient(X0) | rich(X0)) <=> (~rich(X0) | curious(X0))) [input p13]
24. ~funny(paul) [input p23]
25. ~rich(paul) [input hypothesis]
37. ! [X0] : (((~creative(X0) & ~kind(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (creative(X0) | kind(X0)))) [nnf transformation 2]
38. ! [X0] : (((~creative(X0) & ~kind(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | creative(X0) | kind(X0))) [flattening 37]
42. ! [X0] : ((kind(X0) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | ~kind(X0))) [nnf transformation 7]
58. ! [X0] : (((patient(X0) | rich(X0)) | (rich(X0) & ~curious(X0))) & ((~rich(X0) | curious(X0)) | (~patient(X0) & ~rich(X0)))) [nnf transformation 14]
59. ! [X0] : ((patient(X0) | rich(X0) | (rich(X0) & ~curious(X0))) & (~rich(X0) | curious(X0) | (~patient(X0) & ~rich(X0)))) [flattening 58]
86. ~patient(X0) | ~kind(X0) | funny(X0) [cnf transformation 38]
102. kind(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 42]
103. kind(X0) | brave(X0) | brave(X0) [cnf transformation 42]
134. patient(X0) | rich(X0) | rich(X0) [cnf transformation 59]
154. ~funny(paul) [cnf transformation 24]
155. ~rich(paul) [cnf transformation 25]
157. rich(X0) | patient(X0) [duplicate literal removal 134]
158. kind(X0) | ~brave(X0) [duplicate literal removal 102]
159. brave(X0) | kind(X0) [duplicate literal removal 103]
210. kind(X0) [subsumption resolution 158,159]
285. 27 <=> rich(paul) [avatar definition]
286. ~rich(paul) <- (~27) [avatar component clause 285]
331. ~27 [avatar split clause 155,285]
342. patient(paul) <- (~27) [resolution 157,286]
355. ~kind(paul) | funny(paul) <- (~27) [resolution 86,342]
359. funny(paul) <- (~27) [subsumption resolution 355,210]
360. $false <- (~27) [subsumption resolution 359,154]
361. 27 [avatar contradiction clause 360]
365. $false [avatar sat refutation 331,361]
% SZS output end Proof for 4601243080169418879964658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is happy or old then someone is creative. Everyone who is rich is not kind or not generous. If mary is kind then someone is not generous or generous and vice versa. Everyone who is quiet or not humble is both creative and strong and vice versa. Everyone who is either not creative or strong is not quiet. Everyone who is not old or tall is kind or not wise and vice versa. Everyone who is either creative or kind is generous or not strong and vice versa. If mary is generous or patient then someone is wise or not calm. Everyone who is calm or not generous is not quiet. If paul is not rich or calm then someone is either creative or not curious and vice versa. If alice is rich or not patient then someone is both curious and quiet and vice versa. Everyone who is either not calm or not happy is not humble and vice versa. Everyone who is rich or not funny is either not wise or funny and vice versa. If mary is quiet then someone is either not brave or creative and vice versa. If someone is kind then paul is either generous or humble. If someone is creative or old then someone is both not curious and kind. Someone is either not patient or not quiet. Someone is not humble or not brave. Someone is calm. Fred is both brave and not curious. John is not strong or not happy. Someone is happy. Someone is rich. Someone is not old or not quiet. | Alice is not rich. | entailment | (((happy(john)|old(john)))=>(?[X]:(creative(X))))&
(![X]:(rich(X)=>(~kind(X)|~generous(X))))&
((kind(mary))<=>(?[X]:((~generous(X)|generous(X)))))&
(![X]:((quiet(X)|~humble(X))<=>(creative(X)&strong(X))))&
(![X]:((~creative(X)<~>strong(X))=>~quiet(X)))&
(![X]:((~old(X)|tall(X))<=>(kind(X)|~wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>(generous(X)|~strong(X))))&
(((generous(mary)|patient(mary)))=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:((calm(X)|~generous(X))=>~quiet(X)))&
(((~rich(paul)|calm(paul)))<=>(?[X]:((creative(X)<~>~curious(X)))))&
(((rich(alice)|~patient(alice)))<=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((~calm(X)<~>~happy(X))<=>~humble(X)))&
(![X]:((rich(X)|~funny(X))<=>(~wise(X)<~>funny(X))))&
((quiet(mary))<=>(?[X]:((~brave(X)<~>creative(X)))))&
((?[X]:(kind(X)))=>((generous(paul)<~>humble(paul))))&
((?[X]:((creative(X)|old(X))))=>(?[X]:((~curious(X)&kind(X)))))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:(calm(X)))&
((brave(fred)&~curious(fred)))&
((~strong(john)|~happy(john)))&
(?[X]:(happy(X)))&
(?[X]:(rich(X)))&
(?[X]:((~old(X)|~quiet(X)))) | ~rich(alice) | [
"p3",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 523247498823439030912063
% SZS output start Proof for 523247498823439030912063
4. ! [X0] : ((~humble(X0) | quiet(X0)) <=> (strong(X0) & creative(X0))) [input p3]
5. ! [X0] : ((~creative(X0) <~> strong(X0)) => ~quiet(X0)) [input p4]
11. (~patient(alice) | rich(alice)) <=> ? [X0] : (quiet(X0) & curious(X0)) [input p10]
25. rich(alice) [input hypothesis]
30. ! [X0] : (~quiet(X0) | (~creative(X0) <=> strong(X0))) [ennf transformation 5]
41. ! [X0] : (((~humble(X0) | quiet(X0)) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | (humble(X0) & ~quiet(X0)))) [nnf transformation 4]
42. ! [X0] : ((~humble(X0) | quiet(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | (humble(X0) & ~quiet(X0)))) [flattening 41]
43. ! [X0] : (~quiet(X0) | ((~creative(X0) | ~strong(X0)) & (strong(X0) | creative(X0)))) [nnf transformation 30]
55. ((~patient(alice) | rich(alice)) | ! [X0] : (~quiet(X0) | ~curious(X0))) & (? [X0] : (quiet(X0) & curious(X0)) | (patient(alice) & ~rich(alice))) [nnf transformation 11]
56. (~patient(alice) | rich(alice) | ! [X0] : (~quiet(X0) | ~curious(X0))) & (? [X0] : (quiet(X0) & curious(X0)) | (patient(alice) & ~rich(alice))) [flattening 55]
57. (~patient(alice) | rich(alice) | ! [X0] : (~quiet(X0) | ~curious(X0))) & (? [X1] : (quiet(X1) & curious(X1)) | (patient(alice) & ~rich(alice))) [rectify 56]
58. ? [X1] : (quiet(X1) & curious(X1)) => (quiet(sK4) & curious(sK4)) [choice axiom]
59. (~patient(alice) | rich(alice) | ! [X0] : (~quiet(X0) | ~curious(X0))) & ((quiet(sK4) & curious(sK4)) | (patient(alice) & ~rich(alice))) [skolemisation 57,58]
90. creative(X0) | ~quiet(X0) [cnf transformation 42]
92. strong(X0) | ~quiet(X0) [cnf transformation 42]
96. ~quiet(X0) | ~creative(X0) | ~strong(X0) [cnf transformation 43]
119. quiet(sK4) | ~rich(alice) [cnf transformation 59]
152. rich(alice) [cnf transformation 25]
181. ~quiet(X0) | ~creative(X0) [subsumption resolution 96,92]
182. ~quiet(X0) [subsumption resolution 181,90]
230. ~rich(alice) [subsumption resolution 119,182]
279. $false [subsumption resolution 152,230]
% SZS output end Proof for 523247498823439030912063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not wise or not quiet then mary is funny and vice versa.
Everyone who is not patient is not tall or not strong and vice versa.
If someone is both strong and creative then someone is both calm and not humble and vice versa.
If someone is either not creative or patient then someone is quiet or calm.
Everyone who is both calm and not tall is strong.
Everyone who is funny is either quiet or happy.
Everyone who is not patient or quiet is either not quiet or not rich.
If someone is quiet or not kind then lucy is either happy or old and vice versa.
Everyone who is not calm or happy is wise or not humble and vice versa.
Everyone who is both not generous and creative is both quiet and not generous and vice versa.
Everyone who is patient is not wise or humble and vice versa.
Everyone who is patient or not kind is old.
If someone is happy then someone is not patient and vice versa.
Everyone who is both not old and not humble is either not curious or not brave and vice versa.
Everyone who is either calm or not wise is strong or kind.
Everyone who is not kind or not calm is either not generous or not calm and vice versa.
Someone is both not kind and funny.
Paul is funny.
Alice is curious.
Someone is wise or not quiet.
Fred is either kind or calm.
Someone is humble or strong.
Alice is not kind or not generous.
Someone is either calm or brave. | Alice is not brave. | contradiction | (((~wise(susan)|~quiet(susan)))<=>(funny(mary)))&
(![X]:(~patient(X)<=>(~tall(X)|~strong(X))))&
((?[X]:((strong(X)&creative(X))))<=>(?[X]:((calm(X)&~humble(X)))))&
((?[X]:((~creative(X)<~>patient(X))))=>(?[X]:((quiet(X)|calm(X)))))&
(![X]:((calm(X)&~tall(X))=>strong(X)))&
(![X]:(funny(X)=>(quiet(X)<~>happy(X))))&
(![X]:((~patient(X)|quiet(X))=>(~quiet(X)<~>~rich(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((happy(lucy)<~>old(lucy))))&
(![X]:((~calm(X)|happy(X))<=>(wise(X)|~humble(X))))&
(![X]:((~generous(X)&creative(X))<=>(quiet(X)&~generous(X))))&
(![X]:(patient(X)<=>(~wise(X)|humble(X))))&
(![X]:((patient(X)|~kind(X))=>old(X)))&
((?[X]:(happy(X)))<=>(?[X]:(~patient(X))))&
(![X]:((~old(X)&~humble(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((calm(X)<~>~wise(X))=>(strong(X)|kind(X))))&
(![X]:((~kind(X)|~calm(X))<=>(~generous(X)<~>~calm(X))))&
(?[X]:((~kind(X)&funny(X))))&
(funny(paul))&
(curious(alice))&
(?[X]:((wise(X)|~quiet(X))))&
((kind(fred)<~>calm(fred)))&
(?[X]:((humble(X)|strong(X))))&
((~kind(alice)|~generous(alice)))&
(?[X]:((calm(X)<~>brave(X)))) | ~brave(alice) | [
"p11",
"p13",
"p15",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5273811276019938278252576
% SZS output start Proof for 5273811276019938278252576
12. ! [X0] : ((~kind(X0) | patient(X0)) => old(X0)) [input p11]
14. ! [X0] : ((~humble(X0) & ~old(X0)) <=> (~curious(X0) <~> ~brave(X0))) [input p13]
16. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> (~generous(X0) <~> ~calm(X0))) [input p15]
19. curious(alice) [input p18]
23. ~generous(alice) | ~kind(alice) [input p22]
25. ~brave(alice) [input hypothesis]
34. ! [X0] : (old(X0) | (kind(X0) & ~patient(X0))) [ennf transformation 12]
67. ! [X0] : (((~humble(X0) & ~old(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) & (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (humble(X0) | old(X0)))) [nnf transformation 14]
68. ! [X0] : (((~humble(X0) & ~old(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) & (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | humble(X0) | old(X0))) [flattening 67]
70. ! [X0] : (((~calm(X0) | ~kind(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (calm(X0) & kind(X0)))) [nnf transformation 16]
71. ! [X0] : ((~calm(X0) | ~kind(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (calm(X0) & kind(X0)))) [flattening 70]
119. old(X0) | kind(X0) [cnf transformation 34]
125. ~curious(X0) | ~old(X0) | brave(X0) [cnf transformation 68]
133. calm(X0) | generous(X0) | calm(X0) [cnf transformation 71]
134. ~calm(X0) | ~kind(X0) | ~calm(X0) | generous(X0) [cnf transformation 71]
139. curious(alice) [cnf transformation 19]
144. ~generous(alice) | ~kind(alice) [cnf transformation 23]
147. ~brave(alice) [cnf transformation 25]
148. generous(X0) | calm(X0) [duplicate literal removal 133]
149. ~kind(X0) | ~calm(X0) | generous(X0) [duplicate literal removal 134]
281. 30 <=> kind(alice) [avatar definition]
282. kind(alice) <- (30) [avatar component clause 281]
285. 31 <=> generous(alice) [avatar definition]
287. ~generous(alice) <- (~31) [avatar component clause 285]
288. ~30 | ~31 [avatar split clause 144,285,281]
502. ~old(alice) | brave(alice) [resolution 125,139]
503. ~old(alice) [subsumption resolution 502,147]
504. kind(alice) [resolution 503,119]
507. 30 [avatar split clause 504,281]
508. calm(alice) <- (~31) [resolution 287,148]
572. ~calm(alice) | generous(alice) <- (30) [resolution 149,282]
573. generous(alice) <- (30, ~31) [subsumption resolution 572,508]
574. $false <- (30, ~31) [subsumption resolution 573,287]
575. ~30 | 31 [avatar contradiction clause 574]
576. $false [avatar sat refutation 288,507,575]
% SZS output end Proof for 5273811276019938278252576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or calm is funny.
Everyone who is not happy or happy is both not tall and creative.
Everyone who is either rich or not wise is calm or rich and vice versa.
Everyone who is both not brave and not wise is both calm and not wise.
If someone is humble then someone is both calm and patient.
If paul is both not patient and not wise then someone is not wise and vice versa.
Everyone who is both calm and patient is either not happy or not creative and vice versa.
Everyone who is either humble or not funny is happy or patient and vice versa.
If fred is either not creative or not patient then alice is either generous or not happy.
If someone is either not creative or quiet then susan is generous or not happy and vice versa.
If fred is either not patient or kind then mary is both generous and old.
If alice is brave then alice is either not strong or generous and vice versa.
Everyone who is both not patient and quiet is either calm or strong and vice versa.
If someone is either not generous or old then someone is old or strong and vice versa.
Paul is happy.
Someone is either not rich or not wise.
Someone is rich or not happy.
Alice is not old.
Fred is not generous or not curious.
Alice is not calm. | Susan is not kind. | neutral | (![X]:((~funny(X)|calm(X))=>funny(X)))&
(![X]:((~happy(X)|happy(X))=>(~tall(X)&creative(X))))&
(![X]:((rich(X)<~>~wise(X))<=>(calm(X)|rich(X))))&
(![X]:((~brave(X)&~wise(X))=>(calm(X)&~wise(X))))&
((?[X]:(humble(X)))=>(?[X]:((calm(X)&patient(X)))))&
(((~patient(paul)&~wise(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((calm(X)&patient(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:((humble(X)<~>~funny(X))<=>(happy(X)|patient(X))))&
(((~creative(fred)<~>~patient(fred)))=>((generous(alice)<~>~happy(alice))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>((generous(susan)|~happy(susan))))&
(((~patient(fred)<~>kind(fred)))=>((generous(mary)&old(mary))))&
((brave(alice))<=>((~strong(alice)<~>generous(alice))))&
(![X]:((~patient(X)&quiet(X))<=>(calm(X)<~>strong(X))))&
((?[X]:((~generous(X)<~>old(X))))<=>(?[X]:((old(X)|strong(X)))))&
(happy(paul))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:((rich(X)|~happy(X))))&
(~old(alice))&
((~generous(fred)|~curious(fred)))&
(~calm(alice)) | ~kind(susan) | [] | null | 0 |
Everyone who is not quiet or strong is both happy and rich. Everyone who is funny is not old or not humble and vice versa. If mary is old or not creative then alice is strong or calm. If someone is humble or not calm then someone is humble and vice versa. If someone is either calm or wise then lucy is wise or humble and vice versa. If john is not kind then someone is both happy and not tall and vice versa. Everyone who is either not strong or not funny is patient and vice versa. If susan is quiet then john is not brave or patient. Everyone who is either not curious or not happy is either humble or quiet and vice versa. If alice is not curious or not old then someone is not quiet or strong. Everyone who is both not happy and not calm is curious and vice versa. If someone is not happy or not calm then alice is both not tall and not rich. If susan is not rich or not kind then someone is brave. Everyone who is not funny is either not happy or calm. If mary is both not old and not calm then someone is not patient and vice versa. Everyone who is either old or not funny is both not funny and old. Alice is both not funny and not brave. Someone is both quiet and wise. Someone is either calm or not patient. Someone is strong or not generous. Susan is either not creative or not funny. Someone is creative. Someone is patient. | Mary is creative. | neutral | (![X]:((~quiet(X)|strong(X))=>(happy(X)&rich(X))))&
(![X]:(funny(X)<=>(~old(X)|~humble(X))))&
(((old(mary)|~creative(mary)))=>((strong(alice)|calm(alice))))&
((?[X]:((humble(X)|~calm(X))))<=>(?[X]:(humble(X))))&
((?[X]:((calm(X)<~>wise(X))))<=>((wise(lucy)|humble(lucy))))&
((~kind(john))<=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:((~strong(X)<~>~funny(X))<=>patient(X)))&
((quiet(susan))=>((~brave(john)|patient(john))))&
(![X]:((~curious(X)<~>~happy(X))<=>(humble(X)<~>quiet(X))))&
(((~curious(alice)|~old(alice)))=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:((~happy(X)&~calm(X))<=>curious(X)))&
((?[X]:((~happy(X)|~calm(X))))=>((~tall(alice)&~rich(alice))))&
(((~rich(susan)|~kind(susan)))=>(?[X]:(brave(X))))&
(![X]:(~funny(X)=>(~happy(X)<~>calm(X))))&
(((~old(mary)&~calm(mary)))<=>(?[X]:(~patient(X))))&
(![X]:((old(X)<~>~funny(X))=>(~funny(X)&old(X))))&
((~funny(alice)&~brave(alice)))&
(?[X]:((quiet(X)&wise(X))))&
(?[X]:((calm(X)<~>~patient(X))))&
(?[X]:((strong(X)|~generous(X))))&
((~creative(susan)<~>~funny(susan)))&
(?[X]:(creative(X)))&
(?[X]:(patient(X))) | creative(mary) | [] | null | 0 |
Everyone who is either tall or kind is both curious and calm.
If someone is not old or not generous then alice is either not old or not calm.
If mary is both not quiet and tall then paul is either not happy or quiet.
Everyone who is either strong or not tall is not funny.
If someone is both not tall and happy then alice is both funny and happy.
Everyone who is either generous or old is both not wise and not happy and vice versa.
Everyone who is either not calm or not patient is both rich and calm.
Everyone who is tall or not tall is not creative.
If someone is either not wise or not humble then someone is both not funny and not brave and vice versa.
If someone is curious then someone is not brave.
Everyone who is either not generous or curious is both not old and rich.
If someone is both not calm and kind then paul is not tall and vice versa.
If susan is both not curious and not calm then susan is not humble and vice versa.
If someone is happy or not creative then alice is not curious or generous and vice versa.
Everyone who is rich is not brave or creative and vice versa.
If mary is not brave or not patient then fred is humble and vice versa.
Fred is both happy and rich.
Fred is not tall or strong.
Lucy is both generous and not calm.
Someone is not kind.
Someone is either brave or kind.
Lucy is both not calm and kind.
Someone is not rich or not generous.
Someone is both not quiet and strong. | Paul is tall. | contradiction | (![X]:((tall(X)<~>kind(X))=>(curious(X)&calm(X))))&
((?[X]:((~old(X)|~generous(X))))=>((~old(alice)<~>~calm(alice))))&
(((~quiet(mary)&tall(mary)))=>((~happy(paul)<~>quiet(paul))))&
(![X]:((strong(X)<~>~tall(X))=>~funny(X)))&
((?[X]:((~tall(X)&happy(X))))=>((funny(alice)&happy(alice))))&
(![X]:((generous(X)<~>old(X))<=>(~wise(X)&~happy(X))))&
(![X]:((~calm(X)<~>~patient(X))=>(rich(X)&calm(X))))&
(![X]:((tall(X)|~tall(X))=>~creative(X)))&
((?[X]:((~wise(X)<~>~humble(X))))<=>(?[X]:((~funny(X)&~brave(X)))))&
((?[X]:(curious(X)))=>(?[X]:(~brave(X))))&
(![X]:((~generous(X)<~>curious(X))=>(~old(X)&rich(X))))&
((?[X]:((~calm(X)&kind(X))))<=>(~tall(paul)))&
(((~curious(susan)&~calm(susan)))<=>(~humble(susan)))&
((?[X]:((happy(X)|~creative(X))))<=>((~curious(alice)|generous(alice))))&
(![X]:(rich(X)<=>(~brave(X)|creative(X))))&
(((~brave(mary)|~patient(mary)))<=>(humble(fred)))&
((happy(fred)&rich(fred)))&
((~tall(fred)|strong(fred)))&
((generous(lucy)&~calm(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((brave(X)<~>kind(X))))&
((~calm(lucy)&kind(lucy)))&
(?[X]:((~rich(X)|~generous(X))))&
(?[X]:((~quiet(X)&strong(X)))) | tall(paul) | [
"p11",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3955953605812393876868395
% SZS output start Proof for 3955953605812393876868395
12. ? [X0] : (kind(X0) & ~calm(X0)) <=> ~tall(paul) [input p11]
19. ~calm(lucy) & generous(lucy) [input p18]
22. kind(lucy) & ~calm(lucy) [input p21]
25. tall(paul) [input hypothesis]
54. (? [X0] : (kind(X0) & ~calm(X0)) | tall(paul)) & (~tall(paul) | ! [X0] : (~kind(X0) | calm(X0))) [nnf transformation 12]
55. (? [X0] : (kind(X0) & ~calm(X0)) | tall(paul)) & (~tall(paul) | ! [X1] : (~kind(X1) | calm(X1))) [rectify 54]
56. ? [X0] : (kind(X0) & ~calm(X0)) => (kind(sK3) & ~calm(sK3)) [choice axiom]
57. ((kind(sK3) & ~calm(sK3)) | tall(paul)) & (~tall(paul) | ! [X1] : (~kind(X1) | calm(X1))) [skolemisation 55,56]
115. ~tall(paul) | ~kind(X1) | calm(X1) [cnf transformation 57]
135. ~calm(lucy) [cnf transformation 19]
140. kind(lucy) [cnf transformation 22]
144. tall(paul) [cnf transformation 25]
236. 21 <=> tall(paul) [avatar definition]
250. 24 <=> ! [X1] : (~kind(X1) | calm(X1)) [avatar definition]
251. ~kind(X1) | calm(X1) <- (24) [avatar component clause 250]
252. 24 | ~21 [avatar split clause 115,236,250]
326. 21 [avatar split clause 144,236]
336. calm(lucy) <- (24) [resolution 251,140]
337. $false <- (24) [subsumption resolution 336,135]
338. ~24 [avatar contradiction clause 337]
339. $false [avatar sat refutation 252,326,338]
% SZS output end Proof for 3955953605812393876868395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or quiet is both not generous and creative and vice versa.
Everyone who is both not rich and not wise is not calm.
If paul is both not kind and rich then fred is not old or kind and vice versa.
If john is either tall or not happy then susan is generous and vice versa.
Everyone who is not tall is strong and vice versa.
If john is either kind or not creative then paul is either not humble or old.
Everyone who is both creative and patient is either not tall or happy.
If susan is not tall then someone is both not calm and generous and vice versa.
Everyone who is either rich or old is both old and not calm and vice versa.
Everyone who is creative or not quiet is either not wise or not tall.
Everyone who is either humble or rich is either rich or happy and vice versa.
Everyone who is both happy and not generous is not funny.
If someone is either calm or not rich then someone is strong or generous.
If susan is both not funny and not curious then paul is both not strong and not brave and vice versa.
If paul is either humble or happy then someone is either not generous or calm.
Everyone who is either not humble or not curious is either wise or not curious.
Fred is generous.
Paul is not creative.
Someone is not patient.
Paul is funny or tall.
Someone is not quiet.
John is not quiet.
Someone is either not rich or not happy.
Mary is tall. | Mary is wise. | contradiction | (![X]:((tall(X)|quiet(X))<=>(~generous(X)&creative(X))))&
(![X]:((~rich(X)&~wise(X))=>~calm(X)))&
(((~kind(paul)&rich(paul)))<=>((~old(fred)|kind(fred))))&
(((tall(john)<~>~happy(john)))<=>(generous(susan)))&
(![X]:(~tall(X)<=>strong(X)))&
(((kind(john)<~>~creative(john)))=>((~humble(paul)<~>old(paul))))&
(![X]:((creative(X)&patient(X))=>(~tall(X)<~>happy(X))))&
((~tall(susan))<=>(?[X]:((~calm(X)&generous(X)))))&
(![X]:((rich(X)<~>old(X))<=>(old(X)&~calm(X))))&
(![X]:((creative(X)|~quiet(X))=>(~wise(X)<~>~tall(X))))&
(![X]:((humble(X)<~>rich(X))<=>(rich(X)<~>happy(X))))&
(![X]:((happy(X)&~generous(X))=>~funny(X)))&
((?[X]:((calm(X)<~>~rich(X))))=>(?[X]:((strong(X)|generous(X)))))&
(((~funny(susan)&~curious(susan)))<=>((~strong(paul)&~brave(paul))))&
(((humble(paul)<~>happy(paul)))=>(?[X]:((~generous(X)<~>calm(X)))))&
(![X]:((~humble(X)<~>~curious(X))=>(wise(X)<~>~curious(X))))&
(generous(fred))&
(~creative(paul))&
(?[X]:(~patient(X)))&
((funny(paul)|tall(paul)))&
(?[X]:(~quiet(X)))&
(~quiet(john))&
(?[X]:((~rich(X)<~>~happy(X))))&
(tall(mary)) | wise(mary) | [
"p0",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8596218881898934965844355
% SZS output start Proof for 8596218881898934965844355
1. ! [X0] : ((quiet(X0) | tall(X0)) <=> (creative(X0) & ~generous(X0))) [input p0]
10. ! [X0] : ((~quiet(X0) | creative(X0)) => (~wise(X0) <~> ~tall(X0))) [input p9]
24. tall(mary) [input p23]
25. wise(mary) [input hypothesis]
32. ! [X0] : ((~wise(X0) <~> ~tall(X0)) | (quiet(X0) & ~creative(X0))) [ennf transformation 10]
38. ! [X0] : (((quiet(X0) | tall(X0)) | (~creative(X0) | generous(X0))) & ((creative(X0) & ~generous(X0)) | (~quiet(X0) & ~tall(X0)))) [nnf transformation 1]
39. ! [X0] : ((quiet(X0) | tall(X0) | ~creative(X0) | generous(X0)) & ((creative(X0) & ~generous(X0)) | (~quiet(X0) & ~tall(X0)))) [flattening 38]
51. ! [X0] : (((tall(X0) | wise(X0)) & (~tall(X0) | ~wise(X0))) | (quiet(X0) & ~creative(X0))) [nnf transformation 32]
70. ~tall(X0) | creative(X0) [cnf transformation 39]
98. ~tall(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 51]
132. tall(mary) [cnf transformation 24]
133. wise(mary) [cnf transformation 25]
217. ~wise(X0) | ~tall(X0) [subsumption resolution 98,70]
297. ~tall(mary) [resolution 217,133]
298. $false [subsumption resolution 297,132]
% SZS output end Proof for 8596218881898934965844355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or funny is both strong and kind.
Everyone who is not rich or not brave is either patient or not kind.
If someone is not wise or not tall then someone is not wise or rich.
If john is both not quiet and not kind then someone is either not quiet or humble.
If someone is happy then someone is both not tall and curious.
If alice is both not strong and old then someone is rich or humble and vice versa.
Everyone who is kind or rich is both not old and kind.
Everyone who is brave or not old is brave or not rich and vice versa.
If alice is not kind then lucy is creative or not calm.
If someone is either not creative or strong then someone is rich and vice versa.
Everyone who is not old or rich is kind or curious and vice versa.
Everyone who is either not kind or not old is both rich and not quiet.
Everyone who is not wise or happy is rich or funny.
If susan is either rich or not patient then fred is both not kind and brave.
If someone is either not funny or not humble then susan is both not tall and tall.
Mary is generous.
Susan is not strong or tall.
Fred is not patient or not brave.
Paul is not curious or generous. | John is not wise. | contradiction | (![X]:((strong(X)|funny(X))=>(strong(X)&kind(X))))&
(![X]:((~rich(X)|~brave(X))=>(patient(X)<~>~kind(X))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((~wise(X)|rich(X)))))&
(((~quiet(john)&~kind(john)))=>(?[X]:((~quiet(X)<~>humble(X)))))&
((?[X]:(happy(X)))=>(?[X]:((~tall(X)&curious(X)))))&
(((~strong(alice)&old(alice)))<=>(?[X]:((rich(X)|humble(X)))))&
(![X]:((kind(X)|rich(X))=>(~old(X)&kind(X))))&
(![X]:((brave(X)|~old(X))<=>(brave(X)|~rich(X))))&
((~kind(alice))=>((creative(lucy)|~calm(lucy))))&
((?[X]:((~creative(X)<~>strong(X))))<=>(?[X]:(rich(X))))&
(![X]:((~old(X)|rich(X))<=>(kind(X)|curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(rich(X)&~quiet(X))))&
(![X]:((~wise(X)|happy(X))=>(rich(X)|funny(X))))&
(((rich(susan)<~>~patient(susan)))=>((~kind(fred)&brave(fred))))&
((?[X]:((~funny(X)<~>~humble(X))))=>((~tall(susan)&tall(susan))))&
(generous(mary))&
((~strong(susan)|tall(susan)))&
((~patient(fred)|~brave(fred)))&
((~curious(paul)|generous(paul))) | ~wise(john) | [
"p5",
"p6",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5485836111584088732250553
% SZS output start Proof for 5485836111584088732250553
6. (old(alice) & ~strong(alice)) <=> ? [X0] : (humble(X0) | rich(X0)) [input p5]
7. ! [X0] : ((rich(X0) | kind(X0)) => (kind(X0) & ~old(X0))) [input p6]
12. ! [X0] : ((~kind(X0) <~> ~old(X0)) => (~quiet(X0) & rich(X0))) [input p11]
13. ! [X0] : ((happy(X0) | ~wise(X0)) => (funny(X0) | rich(X0))) [input p12]
15. ? [X0] : (~funny(X0) <~> ~humble(X0)) => (tall(susan) & ~tall(susan)) [input p14]
20. ~wise(john) [input hypothesis]
28. ! [X0] : (~wise(X0) => (funny(X0) | rich(X0))) [pure predicate removal 13]
34. ! [X0] : ((kind(X0) & ~old(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 7]
35. ! [X0] : ((~quiet(X0) & rich(X0)) | (~kind(X0) <=> ~old(X0))) [ennf transformation 12]
36. ! [X0] : ((funny(X0) | rich(X0)) | wise(X0)) [ennf transformation 28]
37. ! [X0] : (funny(X0) | rich(X0) | wise(X0)) [flattening 36]
39. (tall(susan) & ~tall(susan)) | ! [X0] : (~funny(X0) <=> ~humble(X0)) [ennf transformation 15]
47. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X0] : (humble(X0) | rich(X0)) | (~old(alice) | strong(alice))) [nnf transformation 6]
48. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X0] : (humble(X0) | rich(X0)) | ~old(alice) | strong(alice)) [flattening 47]
49. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X1] : (humble(X1) | rich(X1)) | ~old(alice) | strong(alice)) [rectify 48]
50. ? [X1] : (humble(X1) | rich(X1)) => (humble(sK2) | rich(sK2)) [choice axiom]
51. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & ((humble(sK2) | rich(sK2)) | ~old(alice) | strong(alice)) [skolemisation 49,50]
61. ! [X0] : ((~quiet(X0) & rich(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0)))) [nnf transformation 35]
63. (tall(susan) & ~tall(susan)) | ! [X0] : ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0))) [nnf transformation 39]
79. old(alice) | ~rich(X0) [cnf transformation 51]
80. old(alice) | ~humble(X0) [cnf transformation 51]
81. ~old(X0) | ~kind(X0) [cnf transformation 34]
82. ~old(X0) | ~rich(X0) [cnf transformation 34]
97. rich(X0) | ~old(X0) | kind(X0) [cnf transformation 61]
101. wise(X0) | rich(X0) | funny(X0) [cnf transformation 37]
107. ~tall(susan) | ~funny(X0) | humble(X0) [cnf transformation 63]
109. tall(susan) | ~funny(X0) | humble(X0) [cnf transformation 63]
112. ~wise(john) [cnf transformation 20]
148. 9 <=> ! [X0] : ~humble(X0) [avatar definition]
149. ~humble(X0) <- (9) [avatar component clause 148]
151. 10 <=> old(alice) [avatar definition]
153. old(alice) <- (10) [avatar component clause 151]
154. 9 | 10 [avatar split clause 80,151,148]
156. 11 <=> ! [X0] : ~rich(X0) [avatar definition]
157. ~rich(X0) <- (11) [avatar component clause 156]
158. 11 | 10 [avatar split clause 79,151,156]
202. ~old(X0) | kind(X0) [subsumption resolution 97,82]
203. ~old(X0) [subsumption resolution 202,81]
225. 24 <=> ! [X0] : (~funny(X0) | humble(X0)) [avatar definition]
226. ~funny(X0) | humble(X0) <- (24) [avatar component clause 225]
228. 25 <=> tall(susan) [avatar definition]
231. 24 | 25 [avatar split clause 109,228,225]
236. 24 | ~25 [avatar split clause 107,228,225]
250. $false <- (10) [subsumption resolution 153,203]
251. ~10 [avatar contradiction clause 250]
276. rich(john) | funny(john) [resolution 101,112]
278. funny(john) <- (11) [subsumption resolution 276,157]
280. humble(john) <- (11, 24) [resolution 278,226]
283. $false <- (9, 11, 24) [subsumption resolution 280,149]
284. ~9 | ~11 | ~24 [avatar contradiction clause 283]
286. $false [avatar sat refutation 154,158,231,236,251,284]
% SZS output end Proof for 5485836111584088732250553
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not funny then mary is not creative and vice versa.
Everyone who is either calm or not rich is not old.
If someone is both not funny and not patient then someone is not kind or tall.
If someone is either funny or wise then someone is either not kind or not strong.
Everyone who is curious is not funny or tall and vice versa.
Everyone who is curious or not calm is both wise and creative.
If alice is not generous then someone is not humble or not strong and vice versa.
Everyone who is either old or patient is both not humble and happy.
Everyone who is not generous or funny is both curious and not tall and vice versa.
Everyone who is not creative or not wise is not rich or not kind and vice versa.
If paul is either brave or not wise then someone is both not rich and tall and vice versa.
If someone is either not brave or calm then someone is patient or humble and vice versa.
Everyone who is both not strong and curious is either happy or not creative.
Everyone who is creative or quiet is either not calm or quiet.
Everyone who is not calm or not old is wise or not creative.
Everyone who is generous or quiet is not quiet or calm.
Someone is either not calm or strong.
Someone is either tall or funny.
Lucy is quiet.
Someone is both patient and creative.
Alice is either not curious or old.
Someone is either not humble or not brave.
Someone is both creative and not old.
Someone is not funny or not creative. | Lucy is rich. | entailment | (((wise(john)<~>~funny(john)))<=>(~creative(mary)))&
(![X]:((calm(X)<~>~rich(X))=>~old(X)))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:((~kind(X)|tall(X)))))&
((?[X]:((funny(X)<~>wise(X))))=>(?[X]:((~kind(X)<~>~strong(X)))))&
(![X]:(curious(X)<=>(~funny(X)|tall(X))))&
(![X]:((curious(X)|~calm(X))=>(wise(X)&creative(X))))&
((~generous(alice))<=>(?[X]:((~humble(X)|~strong(X)))))&
(![X]:((old(X)<~>patient(X))=>(~humble(X)&happy(X))))&
(![X]:((~generous(X)|funny(X))<=>(curious(X)&~tall(X))))&
(![X]:((~creative(X)|~wise(X))<=>(~rich(X)|~kind(X))))&
(((brave(paul)<~>~wise(paul)))<=>(?[X]:((~rich(X)&tall(X)))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((patient(X)|humble(X)))))&
(![X]:((~strong(X)&curious(X))=>(happy(X)<~>~creative(X))))&
(![X]:((creative(X)|quiet(X))=>(~calm(X)<~>quiet(X))))&
(![X]:((~calm(X)|~old(X))=>(wise(X)|~creative(X))))&
(![X]:((generous(X)|quiet(X))=>(~quiet(X)|calm(X))))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(quiet(lucy))&
(?[X]:((patient(X)&creative(X))))&
((~curious(alice)<~>old(alice)))&
(?[X]:((~humble(X)<~>~brave(X))))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:((~funny(X)|~creative(X)))) | rich(lucy) | [
"p4",
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6871541692159170847206821
% SZS output start Proof for 6871541692159170847206821
5. ! [X0] : (curious(X0) <=> (tall(X0) | ~funny(X0))) [input p4]
6. ! [X0] : ((~calm(X0) | curious(X0)) => (creative(X0) & wise(X0))) [input p5]
9. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (~tall(X0) & curious(X0))) [input p8]
10. ! [X0] : ((~wise(X0) | ~creative(X0)) <=> (~kind(X0) | ~rich(X0))) [input p9]
25. ~rich(lucy) [input hypothesis]
32. ! [X0] : ((creative(X0) & wise(X0)) | (calm(X0) & ~curious(X0))) [ennf transformation 6]
50. ! [X0] : ((curious(X0) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | ~curious(X0))) [nnf transformation 5]
51. ! [X0] : ((curious(X0) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~curious(X0))) [flattening 50]
57. ! [X0] : (((funny(X0) | ~generous(X0)) | (tall(X0) | ~curious(X0))) & ((~tall(X0) & curious(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 9]
58. ! [X0] : ((funny(X0) | ~generous(X0) | tall(X0) | ~curious(X0)) & ((~tall(X0) & curious(X0)) | (~funny(X0) & generous(X0)))) [flattening 57]
59. ! [X0] : (((~wise(X0) | ~creative(X0)) | (kind(X0) & rich(X0))) & ((~kind(X0) | ~rich(X0)) | (wise(X0) & creative(X0)))) [nnf transformation 10]
60. ! [X0] : ((~wise(X0) | ~creative(X0) | (kind(X0) & rich(X0))) & (~kind(X0) | ~rich(X0) | (wise(X0) & creative(X0)))) [flattening 59]
100. curious(X0) | funny(X0) [cnf transformation 51]
102. ~curious(X0) | wise(X0) [cnf transformation 32]
104. ~curious(X0) | creative(X0) [cnf transformation 32]
114. curious(X0) | ~funny(X0) [cnf transformation 58]
120. ~creative(X0) | ~wise(X0) | rich(X0) [cnf transformation 60]
158. ~rich(lucy) [cnf transformation 25]
229. curious(X0) [subsumption resolution 114,100]
331. wise(X1) [resolution 102,229]
339. creative(X1) [resolution 104,229]
421. ~wise(X0) | rich(X0) [resolution 120,339]
424. rich(X0) [subsumption resolution 421,331]
444. $false [resolution 424,158]
% SZS output end Proof for 6871541692159170847206821
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either rich or calm then susan is brave or patient. Everyone who is not old or patient is both not generous and old and vice versa. Everyone who is not quiet or not wise is both not kind and quiet and vice versa. Everyone who is either rich or happy is not strong and vice versa. If mary is wise or creative then fred is both curious and not curious and vice versa. Everyone who is not happy or kind is not creative or not happy and vice versa. If someone is not rich or happy then john is both not old and patient and vice versa. Everyone who is both humble and not happy is either not creative or brave and vice versa. Everyone who is both brave and tall is either not strong or kind. Everyone who is both curious and brave is not patient and vice versa. If someone is both calm and not old then john is rich or not brave. Everyone who is either curious or brave is not happy and vice versa. Everyone who is both wise and not old is either generous or not quiet and vice versa. Everyone who is strong is both patient and not generous. Everyone who is happy is either not creative or not curious. Everyone who is not calm is both old and brave. Someone is either quiet or not patient. Susan is not happy or not rich. Someone is both not calm and not funny. Lucy is not brave. Someone is either brave or not tall. Someone is not wise. | Susan is not strong. | entailment | ((?[X]:((rich(X)<~>calm(X))))=>((brave(susan)|patient(susan))))&
(![X]:((~old(X)|patient(X))<=>(~generous(X)&old(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~kind(X)&quiet(X))))&
(![X]:((rich(X)<~>happy(X))<=>~strong(X)))&
(((wise(mary)|creative(mary)))<=>((curious(fred)&~curious(fred))))&
(![X]:((~happy(X)|kind(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((~old(john)&patient(john))))&
(![X]:((humble(X)&~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((brave(X)&tall(X))=>(~strong(X)<~>kind(X))))&
(![X]:((curious(X)&brave(X))<=>~patient(X)))&
((?[X]:((calm(X)&~old(X))))=>((rich(john)|~brave(john))))&
(![X]:((curious(X)<~>brave(X))<=>~happy(X)))&
(![X]:((wise(X)&~old(X))<=>(generous(X)<~>~quiet(X))))&
(![X]:(strong(X)=>(patient(X)&~generous(X))))&
(![X]:(happy(X)=>(~creative(X)<~>~curious(X))))&
(![X]:(~calm(X)=>(old(X)&brave(X))))&
(?[X]:((quiet(X)<~>~patient(X))))&
((~happy(susan)|~rich(susan)))&
(?[X]:((~calm(X)&~funny(X))))&
(~brave(lucy))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:(~wise(X))) | ~strong(susan) | [
"p1",
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1119238790651437000960730
% SZS output start Proof for 1119238790651437000960730
2. ! [X0] : ((patient(X0) | ~old(X0)) <=> (old(X0) & ~generous(X0))) [input p1]
4. ! [X0] : ((rich(X0) <~> happy(X0)) <=> ~strong(X0)) [input p3]
7. ? [X0] : (happy(X0) | ~rich(X0)) <=> (patient(john) & ~old(john)) [input p6]
23. strong(susan) [input hypothesis]
35. ! [X0] : (((patient(X0) | ~old(X0)) | (~old(X0) | generous(X0))) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [nnf transformation 2]
36. ! [X0] : ((patient(X0) | ~old(X0) | ~old(X0) | generous(X0)) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [flattening 35]
39. ! [X0] : ((((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | strong(X0)) & (~strong(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0))))) [nnf transformation 4]
44. (? [X0] : (happy(X0) | ~rich(X0)) | (~patient(john) | old(john))) & ((patient(john) & ~old(john)) | ! [X0] : (~happy(X0) & rich(X0))) [nnf transformation 7]
45. (? [X0] : (happy(X0) | ~rich(X0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X0] : (~happy(X0) & rich(X0))) [flattening 44]
46. (? [X0] : (happy(X0) | ~rich(X0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X1] : (~happy(X1) & rich(X1))) [rectify 45]
47. ? [X0] : (happy(X0) | ~rich(X0)) => (happy(sK0) | ~rich(sK0)) [choice axiom]
48. ((happy(sK0) | ~rich(sK0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X1] : (~happy(X1) & rich(X1))) [skolemisation 46,47]
72. old(X0) | old(X0) [cnf transformation 36]
80. ~strong(X0) | happy(X0) | ~rich(X0) [cnf transformation 39]
93. ~old(john) | rich(X1) [cnf transformation 48]
94. ~old(john) | ~happy(X1) [cnf transformation 48]
134. strong(susan) [cnf transformation 23]
137. old(X0) [duplicate literal removal 72]
172. 8 <=> ! [X1] : ~happy(X1) [avatar definition]
173. ~happy(X1) <- (8) [avatar component clause 172]
180. 10 <=> ! [X1] : rich(X1) [avatar definition]
181. rich(X1) <- (10) [avatar component clause 180]
183. ~happy(X1) [subsumption resolution 94,137]
184. 8 [avatar split clause 183,172]
185. rich(X1) [subsumption resolution 93,137]
186. 10 [avatar split clause 185,180]
220. happy(susan) | ~rich(susan) [resolution 80,134]
221. ~rich(susan) <- (8) [subsumption resolution 220,173]
222. $false <- (8, 10) [subsumption resolution 221,181]
223. ~8 | ~10 [avatar contradiction clause 222]
224. $false [avatar sat refutation 184,186,223]
% SZS output end Proof for 1119238790651437000960730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet is both not generous and kind.
Everyone who is either not funny or not wise is rich.
Everyone who is patient is either happy or not funny and vice versa.
If susan is not happy or not creative then someone is either calm or kind.
If susan is patient or curious then alice is not funny or not humble.
If someone is either not rich or not wise then lucy is not wise and vice versa.
Everyone who is not tall or happy is not old or not humble and vice versa.
Everyone who is both not curious and happy is not rich or not funny and vice versa.
Everyone who is both not wise and not curious is quiet.
Everyone who is not calm or wise is not patient or not creative.
Everyone who is tall or not rich is kind.
Everyone who is happy or not wise is both not rich and funny.
Everyone who is either not humble or tall is not strong.
If susan is both not strong and not old then someone is generous.
Everyone who is brave or funny is either not old or funny.
Everyone who is not generous or not tall is kind.
John is rich or not strong.
Someone is not brave or not old.
Someone is tall or not generous.
Mary is not happy or humble.
Fred is either not calm or not brave.
Someone is either not brave or not quiet. | Lucy is not curious. | neutral | (![X]:((~curious(X)|~quiet(X))=>(~generous(X)&kind(X))))&
(![X]:((~funny(X)<~>~wise(X))=>rich(X)))&
(![X]:(patient(X)<=>(happy(X)<~>~funny(X))))&
(((~happy(susan)|~creative(susan)))=>(?[X]:((calm(X)<~>kind(X)))))&
(((patient(susan)|curious(susan)))=>((~funny(alice)|~humble(alice))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(~wise(lucy)))&
(![X]:((~tall(X)|happy(X))<=>(~old(X)|~humble(X))))&
(![X]:((~curious(X)&happy(X))<=>(~rich(X)|~funny(X))))&
(![X]:((~wise(X)&~curious(X))=>quiet(X)))&
(![X]:((~calm(X)|wise(X))=>(~patient(X)|~creative(X))))&
(![X]:((tall(X)|~rich(X))=>kind(X)))&
(![X]:((happy(X)|~wise(X))=>(~rich(X)&funny(X))))&
(![X]:((~humble(X)<~>tall(X))=>~strong(X)))&
(((~strong(susan)&~old(susan)))=>(?[X]:(generous(X))))&
(![X]:((brave(X)|funny(X))=>(~old(X)<~>funny(X))))&
(![X]:((~generous(X)|~tall(X))=>kind(X)))&
((rich(john)|~strong(john)))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:((tall(X)|~generous(X))))&
((~happy(mary)|humble(mary)))&
((~calm(fred)<~>~brave(fred)))&
(?[X]:((~brave(X)<~>~quiet(X)))) | ~curious(lucy) | [] | null | 0 |
If someone is curious then someone is not quiet or quiet and vice versa.
Everyone who is either patient or not rich is wise or not curious and vice versa.
If mary is either not kind or kind then someone is humble or calm and vice versa.
Everyone who is both not quiet and not generous is not funny or creative and vice versa.
If someone is not patient then lucy is tall or kind.
Everyone who is not creative or not kind is either not generous or not funny.
Everyone who is either funny or brave is both not old and not quiet and vice versa.
Everyone who is not calm is both generous and not tall.
Everyone who is either not kind or not generous is both not rich and not quiet and vice versa.
Everyone who is both calm and rich is either patient or calm.
Everyone who is not creative is curious or wise and vice versa.
Everyone who is either not creative or not old is either kind or not rich and vice versa.
Everyone who is either generous or happy is both funny and not happy.
Everyone who is humble is either not wise or not patient.
If someone is either not happy or old then someone is not tall or not wise and vice versa.
If someone is calm or not tall then mary is not calm or humble and vice versa.
Susan is both rich and not tall.
Someone is either not curious or not quiet.
John is either not creative or not wise.
Susan is either quiet or not calm.
Someone is either not rich or not happy.
Someone is not quiet.
Someone is both calm and not wise. | John is patient. | contradiction | ((?[X]:(curious(X)))<=>(?[X]:((~quiet(X)|quiet(X)))))&
(![X]:((patient(X)<~>~rich(X))<=>(wise(X)|~curious(X))))&
(((~kind(mary)<~>kind(mary)))<=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((~quiet(X)&~generous(X))<=>(~funny(X)|creative(X))))&
((?[X]:(~patient(X)))=>((tall(lucy)|kind(lucy))))&
(![X]:((~creative(X)|~kind(X))=>(~generous(X)<~>~funny(X))))&
(![X]:((funny(X)<~>brave(X))<=>(~old(X)&~quiet(X))))&
(![X]:(~calm(X)=>(generous(X)&~tall(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(~rich(X)&~quiet(X))))&
(![X]:((calm(X)&rich(X))=>(patient(X)<~>calm(X))))&
(![X]:(~creative(X)<=>(curious(X)|wise(X))))&
(![X]:((~creative(X)<~>~old(X))<=>(kind(X)<~>~rich(X))))&
(![X]:((generous(X)<~>happy(X))=>(funny(X)&~happy(X))))&
(![X]:(humble(X)=>(~wise(X)<~>~patient(X))))&
((?[X]:((~happy(X)<~>old(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
((?[X]:((calm(X)|~tall(X))))<=>((~calm(mary)|humble(mary))))&
((rich(susan)&~tall(susan)))&
(?[X]:((~curious(X)<~>~quiet(X))))&
((~creative(john)<~>~wise(john)))&
((quiet(susan)<~>~calm(susan)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((calm(X)&~wise(X)))) | patient(john) | [
"p1",
"p3",
"p5",
"p7",
"p9",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7470743388714383579429512
% SZS output start Proof for 7470743388714383579429512
2. ! [X0] : ((patient(X0) <~> ~rich(X0)) <=> (~curious(X0) | wise(X0))) [input p1]
4. ! [X0] : ((~generous(X0) & ~quiet(X0)) <=> (creative(X0) | ~funny(X0))) [input p3]
6. ! [X0] : ((~kind(X0) | ~creative(X0)) => (~generous(X0) <~> ~funny(X0))) [input p5]
8. ! [X0] : (~calm(X0) => (~tall(X0) & generous(X0))) [input p7]
10. ! [X0] : ((rich(X0) & calm(X0)) => (patient(X0) <~> calm(X0))) [input p9]
11. ! [X0] : (~creative(X0) <=> (wise(X0) | curious(X0))) [input p10]
19. ~creative(john) <~> ~wise(john) [input p18]
24. patient(john) [input hypothesis]
29. ! [X0] : ((~generous(X0) <~> ~funny(X0)) | (kind(X0) & creative(X0))) [ennf transformation 6]
30. ! [X0] : ((~tall(X0) & generous(X0)) | calm(X0)) [ennf transformation 8]
31. ! [X0] : ((patient(X0) <~> calm(X0)) | (~rich(X0) | ~calm(X0))) [ennf transformation 10]
32. ! [X0] : ((patient(X0) <~> calm(X0)) | ~rich(X0) | ~calm(X0)) [flattening 31]
40. ! [X0] : ((((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | (curious(X0) & ~wise(X0))) & ((~curious(X0) | wise(X0)) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))))) [nnf transformation 2]
41. ! [X0] : ((((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | (curious(X0) & ~wise(X0))) & (~curious(X0) | wise(X0) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))))) [flattening 40]
46. ! [X0] : (((~generous(X0) & ~quiet(X0)) | (~creative(X0) & funny(X0))) & ((creative(X0) | ~funny(X0)) | (generous(X0) | quiet(X0)))) [nnf transformation 4]
47. ! [X0] : (((~generous(X0) & ~quiet(X0)) | (~creative(X0) & funny(X0))) & (creative(X0) | ~funny(X0) | generous(X0) | quiet(X0))) [flattening 46]
48. ! [X0] : (((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | (kind(X0) & creative(X0))) [nnf transformation 29]
53. ! [X0] : (((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | ~rich(X0) | ~calm(X0)) [nnf transformation 32]
54. ! [X0] : ((~creative(X0) | (~wise(X0) & ~curious(X0))) & ((wise(X0) | curious(X0)) | creative(X0))) [nnf transformation 11]
55. ! [X0] : ((~creative(X0) | (~wise(X0) & ~curious(X0))) & (wise(X0) | curious(X0) | creative(X0))) [flattening 54]
72. (wise(john) | creative(john)) & (~wise(john) | ~creative(john)) [nnf transformation 19]
88. ~wise(X0) | ~patient(X0) | rich(X0) [cnf transformation 41]
89. ~patient(X0) | rich(X0) | curious(X0) [cnf transformation 41]
99. ~generous(X0) | funny(X0) [cnf transformation 47]
100. ~creative(X0) | ~generous(X0) [cnf transformation 47]
102. ~funny(X0) | ~generous(X0) | creative(X0) [cnf transformation 48]
104. funny(X0) | generous(X0) | creative(X0) [cnf transformation 48]
112. generous(X0) | calm(X0) [cnf transformation 30]
121. ~calm(X0) | ~patient(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 53]
123. ~creative(X0) | ~curious(X0) [cnf transformation 55]
154. wise(john) | creative(john) [cnf transformation 72]
162. patient(john) [cnf transformation 24]
164. ~calm(X0) | ~patient(X0) | ~rich(X0) [duplicate literal removal 121]
206. creative(X0) | funny(X0) [subsumption resolution 104,99]
208. ~generous(X0) | creative(X0) [subsumption resolution 102,206]
209. ~generous(X0) [subsumption resolution 208,100]
212. calm(X0) [subsumption resolution 112,209]
216. ~rich(X0) | ~patient(X0) [subsumption resolution 164,212]
269. 19 <=> creative(john) [avatar definition]
271. creative(john) <- (19) [avatar component clause 269]
273. 20 <=> wise(john) [avatar definition]
275. wise(john) <- (20) [avatar component clause 273]
276. 19 | 20 [avatar split clause 154,273,269]
282. ~curious(john) <- (19) [resolution 123,271]
301. rich(john) | curious(john) [resolution 89,162]
302. rich(john) <- (19) [subsumption resolution 301,282]
304. ~patient(john) <- (19) [resolution 302,216]
305. $false <- (19) [subsumption resolution 304,162]
306. ~19 [avatar contradiction clause 305]
312. 22 <=> rich(john) [avatar definition]
314. rich(john) <- (22) [avatar component clause 312]
317. ~patient(john) | rich(john) <- (20) [resolution 275,88]
320. ~patient(john) <- (22) [resolution 314,216]
321. $false <- (22) [subsumption resolution 320,162]
322. ~22 [avatar contradiction clause 321]
323. rich(john) <- (20) [subsumption resolution 317,162]
324. 22 | ~20 [avatar split clause 323,273,312]
325. $false [avatar sat refutation 276,306,322,324]
% SZS output end Proof for 7470743388714383579429512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is both not old and generous.
If susan is either wise or calm then alice is rich and vice versa.
If someone is creative then someone is both not curious and not old and vice versa.
If fred is either not rich or happy then alice is not wise or brave.
If someone is not kind or generous then someone is both brave and not brave.
Everyone who is both generous and creative is humble and vice versa.
If fred is strong or not patient then someone is not humble or brave.
Everyone who is not wise or patient is wise.
Everyone who is generous or not patient is old or quiet.
If fred is wise then lucy is calm and vice versa.
If alice is not old then someone is either kind or happy and vice versa.
Everyone who is both wise and rich is rich and vice versa.
If someone is not tall or calm then mary is humble or quiet.
Everyone who is either quiet or not generous is either not calm or not brave and vice versa.
If paul is happy then someone is not happy and vice versa.
Everyone who is patient is either not rich or not generous and vice versa.
Someone is not calm.
Susan is not humble.
Susan is both not tall and not old.
Someone is both not curious and happy.
Someone is either strong or not quiet.
Someone is not old or wise. | Susan is not curious. | contradiction | (![X]:(creative(X)=>(~old(X)&generous(X))))&
(((wise(susan)<~>calm(susan)))<=>(rich(alice)))&
((?[X]:(creative(X)))<=>(?[X]:((~curious(X)&~old(X)))))&
(((~rich(fred)<~>happy(fred)))=>((~wise(alice)|brave(alice))))&
((?[X]:((~kind(X)|generous(X))))=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:((generous(X)&creative(X))<=>humble(X)))&
(((strong(fred)|~patient(fred)))=>(?[X]:((~humble(X)|brave(X)))))&
(![X]:((~wise(X)|patient(X))=>wise(X)))&
(![X]:((generous(X)|~patient(X))=>(old(X)|quiet(X))))&
((wise(fred))<=>(calm(lucy)))&
((~old(alice))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((wise(X)&rich(X))<=>rich(X)))&
((?[X]:((~tall(X)|calm(X))))=>((humble(mary)|quiet(mary))))&
(![X]:((quiet(X)<~>~generous(X))<=>(~calm(X)<~>~brave(X))))&
((happy(paul))<=>(?[X]:(~happy(X))))&
(![X]:(patient(X)<=>(~rich(X)<~>~generous(X))))&
(?[X]:(~calm(X)))&
(~humble(susan))&
((~tall(susan)&~old(susan)))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:((strong(X)<~>~quiet(X))))&
(?[X]:((~old(X)|wise(X)))) | ~curious(susan) | [
"p0",
"p2",
"p4",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1504751529990160406794254
% SZS output start Proof for 1504751529990160406794254
1. ! [X0] : (creative(X0) => (generous(X0) & ~old(X0))) [input p0]
3. ? [X0] : creative(X0) <=> ? [X0] : (~old(X0) & ~curious(X0)) [input p2]
5. ? [X0] : (generous(X0) | ~kind(X0)) => ? [X0] : (~brave(X0) & brave(X0)) [input p4]
19. ~old(susan) & ~tall(susan) [input p18]
23. ~curious(susan) [input hypothesis]
24. ? [X0] : creative(X0) <=> ? [X1] : (~old(X1) & ~curious(X1)) [rectify 3]
25. ? [X0] : (generous(X0) | ~kind(X0)) => ? [X1] : (~brave(X1) & brave(X1)) [rectify 5]
26. ! [X0] : ((generous(X0) & ~old(X0)) | ~creative(X0)) [ennf transformation 1]
29. ? [X1] : (~brave(X1) & brave(X1)) | ! [X0] : (~generous(X0) & kind(X0)) [ennf transformation 25]
37. (? [X0] : creative(X0) | ! [X1] : (old(X1) | curious(X1))) & (? [X1] : (~old(X1) & ~curious(X1)) | ! [X0] : ~creative(X0)) [nnf transformation 24]
38. (? [X0] : creative(X0) | ! [X1] : (old(X1) | curious(X1))) & (? [X2] : (~old(X2) & ~curious(X2)) | ! [X3] : ~creative(X3)) [rectify 37]
39. ? [X0] : creative(X0) => creative(sK0) [choice axiom]
40. ? [X2] : (~old(X2) & ~curious(X2)) => (~old(sK1) & ~curious(sK1)) [choice axiom]
41. (creative(sK0) | ! [X1] : (old(X1) | curious(X1))) & ((~old(sK1) & ~curious(sK1)) | ! [X3] : ~creative(X3)) [skolemisation 38,40,39]
43. ? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : (~generous(X1) & kind(X1)) [rectify 29]
44. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK2) & brave(sK2)) [choice axiom]
45. (~brave(sK2) & brave(sK2)) | ! [X1] : (~generous(X1) & kind(X1)) [skolemisation 43,44]
73. ~creative(X0) | generous(X0) [cnf transformation 26]
80. creative(sK0) | old(X1) | curious(X1) [cnf transformation 41]
84. brave(sK2) | ~generous(X1) [cnf transformation 45]
86. ~brave(sK2) | ~generous(X1) [cnf transformation 45]
124. ~old(susan) [cnf transformation 19]
130. ~curious(susan) [cnf transformation 23]
149. 4 <=> ! [X1] : (old(X1) | curious(X1)) [avatar definition]
150. curious(X1) | old(X1) <- (4) [avatar component clause 149]
152. 5 <=> creative(sK0) [avatar definition]
154. creative(sK0) <- (5) [avatar component clause 152]
155. 4 | 5 [avatar split clause 80,152,149]
188. 13 <=> ! [X1] : ~generous(X1) [avatar definition]
189. ~generous(X1) <- (13) [avatar component clause 188]
191. 14 <=> brave(sK2) [avatar definition]
194. 13 | ~14 [avatar split clause 86,191,188]
199. 13 | 14 [avatar split clause 84,191,188]
300. old(susan) <- (4) [resolution 150,130]
302. $false <- (4) [subsumption resolution 300,124]
303. ~4 [avatar contradiction clause 302]
306. generous(sK0) <- (5) [resolution 154,73]
307. $false <- (5, 13) [subsumption resolution 306,189]
308. ~5 | ~13 [avatar contradiction clause 307]
309. $false [avatar sat refutation 155,194,199,303,308]
% SZS output end Proof for 1504751529990160406794254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient or not patient then someone is both quiet and wise.
If someone is either creative or not creative then alice is not patient and vice versa.
If someone is creative or brave then lucy is either not rich or patient.
Everyone who is not humble is both wise and patient.
If susan is not calm then someone is not quiet and vice versa.
Everyone who is not curious is not funny or generous and vice versa.
Everyone who is strong or not patient is humble or not generous.
Everyone who is either generous or not humble is brave and vice versa.
If someone is not generous or calm then someone is both creative and not quiet.
Everyone who is both creative and not funny is not kind or humble.
If alice is either brave or not brave then someone is either not old or generous.
If someone is not brave then someone is not strong.
Everyone who is either happy or not funny is both creative and tall.
If someone is either not old or old then someone is tall.
Everyone who is either not patient or not calm is both not happy and not funny and vice versa.
If someone is either patient or not strong then john is creative or not funny and vice versa.
Susan is not rich or rich.
Susan is both curious and rich.
Paul is either happy or not humble.
Fred is not generous.
Fred is curious or tall.
Someone is not strong.
Paul is either humble or not strong.
Someone is tall. | Susan is patient. | contradiction | ((?[X]:((patient(X)|~patient(X))))=>(?[X]:((quiet(X)&wise(X)))))&
((?[X]:((creative(X)<~>~creative(X))))<=>(~patient(alice)))&
((?[X]:((creative(X)|brave(X))))=>((~rich(lucy)<~>patient(lucy))))&
(![X]:(~humble(X)=>(wise(X)&patient(X))))&
((~calm(susan))<=>(?[X]:(~quiet(X))))&
(![X]:(~curious(X)<=>(~funny(X)|generous(X))))&
(![X]:((strong(X)|~patient(X))=>(humble(X)|~generous(X))))&
(![X]:((generous(X)<~>~humble(X))<=>brave(X)))&
((?[X]:((~generous(X)|calm(X))))=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:((creative(X)&~funny(X))=>(~kind(X)|humble(X))))&
(((brave(alice)<~>~brave(alice)))=>(?[X]:((~old(X)<~>generous(X)))))&
((?[X]:(~brave(X)))=>(?[X]:(~strong(X))))&
(![X]:((happy(X)<~>~funny(X))=>(creative(X)&tall(X))))&
((?[X]:((~old(X)<~>old(X))))=>(?[X]:(tall(X))))&
(![X]:((~patient(X)<~>~calm(X))<=>(~happy(X)&~funny(X))))&
((?[X]:((patient(X)<~>~strong(X))))<=>((creative(john)|~funny(john))))&
((~rich(susan)|rich(susan)))&
((curious(susan)&rich(susan)))&
((happy(paul)<~>~humble(paul)))&
(~generous(fred))&
((curious(fred)|tall(fred)))&
(?[X]:(~strong(X)))&
((humble(paul)<~>~strong(paul)))&
(?[X]:(tall(X))) | patient(susan) | [
"p4",
"p5",
"p8",
"p14",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6110002878327974129221398
% SZS output start Proof for 6110002878327974129221398
5. ~calm(susan) <=> ? [X0] : ~quiet(X0) [input p4]
6. ! [X0] : (~curious(X0) <=> (generous(X0) | ~funny(X0))) [input p5]
9. ? [X0] : (calm(X0) | ~generous(X0)) => ? [X0] : (~quiet(X0) & creative(X0)) [input p8]
15. ! [X0] : ((~patient(X0) <~> ~calm(X0)) <=> (~funny(X0) & ~happy(X0))) [input p14]
18. rich(susan) & curious(susan) [input p17]
20. ~generous(fred) [input p19]
25. patient(susan) [input hypothesis]
27. ? [X0] : (calm(X0) | ~generous(X0)) => ? [X1] : (~quiet(X1) & creative(X1)) [rectify 9]
30. ! [X0] : ((generous(X0) | ~funny(X0)) => ~curious(X0)) [unused predicate definition removal 6]
41. ! [X0] : (~curious(X0) | (~generous(X0) & funny(X0))) [ennf transformation 30]
44. ? [X1] : (~quiet(X1) & creative(X1)) | ! [X0] : (~calm(X0) & generous(X0)) [ennf transformation 27]
56. (~calm(susan) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | calm(susan)) [nnf transformation 5]
57. (~calm(susan) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | calm(susan)) [rectify 56]
58. ? [X1] : ~quiet(X1) => ~quiet(sK2) [choice axiom]
59. (~calm(susan) | ! [X0] : quiet(X0)) & (~quiet(sK2) | calm(susan)) [skolemisation 57,58]
61. ? [X0] : (~quiet(X0) & creative(X0)) | ! [X1] : (~calm(X1) & generous(X1)) [rectify 44]
62. ? [X0] : (~quiet(X0) & creative(X0)) => (~quiet(sK3) & creative(sK3)) [choice axiom]
63. (~quiet(sK3) & creative(sK3)) | ! [X1] : (~calm(X1) & generous(X1)) [skolemisation 61,62]
71. ! [X0] : ((((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (funny(X0) | happy(X0))) & ((~funny(X0) & ~happy(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0))))) [nnf transformation 15]
72. ! [X0] : ((((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | funny(X0) | happy(X0)) & ((~funny(X0) & ~happy(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0))))) [flattening 71]
94. ~calm(susan) | quiet(X0) [cnf transformation 59]
95. ~curious(X0) | funny(X0) [cnf transformation 41]
105. ~quiet(sK3) | generous(X1) [cnf transformation 63]
117. ~funny(X0) | ~patient(X0) | calm(X0) [cnf transformation 72]
127. curious(susan) [cnf transformation 18]
131. ~generous(fred) [cnf transformation 20]
135. patient(susan) [cnf transformation 25]
182. 10 <=> ! [X0] : quiet(X0) [avatar definition]
183. quiet(X0) <- (10) [avatar component clause 182]
185. 11 <=> calm(susan) [avatar definition]
188. 10 | ~11 [avatar split clause 94,185,182]
198. 14 <=> quiet(sK3) [avatar definition]
200. ~quiet(sK3) <- (~14) [avatar component clause 198]
203. 15 <=> ! [X1] : generous(X1) [avatar definition]
204. generous(X1) <- (15) [avatar component clause 203]
205. 15 | ~14 [avatar split clause 105,198,203]
280. $false <- (15) [resolution 204,131]
281. ~15 [avatar contradiction clause 280]
283. funny(susan) [resolution 95,127]
337. ~patient(susan) | calm(susan) [resolution 117,283]
339. calm(susan) [subsumption resolution 337,135]
345. 11 [avatar split clause 339,185]
349. $false <- (10, ~14) [resolution 183,200]
350. ~10 | 14 [avatar contradiction clause 349]
352. $false [avatar sat refutation 188,205,281,345,350]
% SZS output end Proof for 6110002878327974129221398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either happy or not patient. Everyone who is not old is either patient or not kind and vice versa. If paul is not funny or strong then someone is rich or not strong. Everyone who is patient is not rich and vice versa. If someone is both not old and not rich then someone is both not old and not strong and vice versa. If lucy is strong then lucy is either tall or calm. If john is either not patient or not curious then someone is either patient or not funny and vice versa. If someone is calm then someone is either not quiet or strong. Everyone who is not old is both rich and not old. Everyone who is either not brave or not curious is not kind or not calm and vice versa. If susan is quiet or creative then someone is kind. If lucy is both not old and not kind then someone is both not wise and creative and vice versa. If someone is not rich or not creative then john is patient. Everyone who is both brave and rich is both calm and not wise. If someone is either generous or happy then john is either humble or not creative. Everyone who is not wise is both not tall and not creative and vice versa. Lucy is rich. Someone is either not quiet or not strong. John is both wise and not strong. Someone is either not rich or curious. Someone is not rich. Someone is rich. Paul is not patient. Lucy is either generous or brave. | John is not happy. | contradiction | (![X]:(wise(X)=>(happy(X)<~>~patient(X))))&
(![X]:(~old(X)<=>(patient(X)<~>~kind(X))))&
(((~funny(paul)|strong(paul)))=>(?[X]:((rich(X)|~strong(X)))))&
(![X]:(patient(X)<=>~rich(X)))&
((?[X]:((~old(X)&~rich(X))))<=>(?[X]:((~old(X)&~strong(X)))))&
((strong(lucy))=>((tall(lucy)<~>calm(lucy))))&
(((~patient(john)<~>~curious(john)))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:(calm(X)))=>(?[X]:((~quiet(X)<~>strong(X)))))&
(![X]:(~old(X)=>(rich(X)&~old(X))))&
(![X]:((~brave(X)<~>~curious(X))<=>(~kind(X)|~calm(X))))&
(((quiet(susan)|creative(susan)))=>(?[X]:(kind(X))))&
(((~old(lucy)&~kind(lucy)))<=>(?[X]:((~wise(X)&creative(X)))))&
((?[X]:((~rich(X)|~creative(X))))=>(patient(john)))&
(![X]:((brave(X)&rich(X))=>(calm(X)&~wise(X))))&
((?[X]:((generous(X)<~>happy(X))))=>((humble(john)<~>~creative(john))))&
(![X]:(~wise(X)<=>(~tall(X)&~creative(X))))&
(rich(lucy))&
(?[X]:((~quiet(X)<~>~strong(X))))&
((wise(john)&~strong(john)))&
(?[X]:((~rich(X)<~>curious(X))))&
(?[X]:(~rich(X)))&
(?[X]:(rich(X)))&
(~patient(paul))&
((generous(lucy)<~>brave(lucy))) | ~happy(john) | [
"p0",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 988444802000157704658910
% SZS output start Proof for 988444802000157704658910
1. ! [X0] : (wise(X0) => (happy(X0) <~> ~patient(X0))) [input p0]
13. ? [X0] : (~creative(X0) | ~rich(X0)) => patient(john) [input p12]
19. ~strong(john) & wise(john) [input p18]
21. ? [X0] : ~rich(X0) [input p20]
25. ~happy(john) [input hypothesis]
28. ! [X0] : ((happy(X0) <~> ~patient(X0)) | ~wise(X0)) [ennf transformation 1]
34. patient(john) | ! [X0] : (creative(X0) & rich(X0)) [ennf transformation 13]
38. ! [X0] : (((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | ~wise(X0)) [nnf transformation 28]
75. ? [X0] : ~rich(X0) => ~rich(sK9) [choice axiom]
76. ~rich(sK9) [skolemisation 21,75]
80. ~patient(X0) | happy(X0) | ~wise(X0) [cnf transformation 38]
120. patient(john) | rich(X0) [cnf transformation 34]
134. wise(john) [cnf transformation 19]
138. ~rich(sK9) [cnf transformation 76]
143. ~happy(john) [cnf transformation 25]
206. 15 <=> patient(john) [avatar definition]
208. patient(john) <- (15) [avatar component clause 206]
288. 32 <=> ! [X0] : rich(X0) [avatar definition]
289. rich(X0) <- (32) [avatar component clause 288]
290. 32 | 15 [avatar split clause 120,206,288]
360. happy(john) | ~wise(john) <- (15) [resolution 80,208]
363. ~wise(john) <- (15) [subsumption resolution 360,143]
364. $false <- (15) [subsumption resolution 363,134]
365. ~15 [avatar contradiction clause 364]
391. $false <- (32) [resolution 289,138]
392. ~32 [avatar contradiction clause 391]
394. $false [avatar sat refutation 290,365,392]
% SZS output end Proof for 988444802000157704658910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is not humble or wise then lucy is either not quiet or patient and vice versa.
If someone is not strong or not rich then lucy is either not creative or wise.
Everyone who is both not strong and humble is both not curious and not calm and vice versa.
Everyone who is not strong is patient or tall and vice versa.
If someone is both not quiet and tall then someone is either not brave or not funny and vice versa.
If fred is either rich or not happy then lucy is either funny or old.
Everyone who is either generous or curious is either brave or not generous.
Everyone who is creative is both generous and calm and vice versa.
If someone is both tall and strong then alice is either generous or not tall.
If susan is kind then someone is either wise or not creative.
If fred is tall or generous then someone is either curious or not old and vice versa.
If alice is either not rich or not tall then john is both patient and not brave.
Everyone who is not quiet is patient.
If mary is happy or not tall then someone is either generous or not generous.
If someone is either not humble or brave then john is not calm and vice versa.
Everyone who is either not humble or not patient is not old.
Paul is either not kind or brave.
Someone is both not creative and not humble.
Someone is either not rich or not strong.
John is either not wise or humble.
Someone is either not quiet or quiet.
Mary is tall or not brave.
Someone is either not tall or brave.
Alice is not happy. | Lucy is patient. | entailment | (((~humble(john)|wise(john)))<=>((~quiet(lucy)<~>patient(lucy))))&
((?[X]:((~strong(X)|~rich(X))))=>((~creative(lucy)<~>wise(lucy))))&
(![X]:((~strong(X)&humble(X))<=>(~curious(X)&~calm(X))))&
(![X]:(~strong(X)<=>(patient(X)|tall(X))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(((rich(fred)<~>~happy(fred)))=>((funny(lucy)<~>old(lucy))))&
(![X]:((generous(X)<~>curious(X))=>(brave(X)<~>~generous(X))))&
(![X]:(creative(X)<=>(generous(X)&calm(X))))&
((?[X]:((tall(X)&strong(X))))=>((generous(alice)<~>~tall(alice))))&
((kind(susan))=>(?[X]:((wise(X)<~>~creative(X)))))&
(((tall(fred)|generous(fred)))<=>(?[X]:((curious(X)<~>~old(X)))))&
(((~rich(alice)<~>~tall(alice)))=>((patient(john)&~brave(john))))&
(![X]:(~quiet(X)=>patient(X)))&
(((happy(mary)|~tall(mary)))=>(?[X]:((generous(X)<~>~generous(X)))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(~calm(john)))&
(![X]:((~humble(X)<~>~patient(X))=>~old(X)))&
((~kind(paul)<~>brave(paul)))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:((~rich(X)<~>~strong(X))))&
((~wise(john)<~>humble(john)))&
(?[X]:((~quiet(X)<~>quiet(X))))&
((tall(mary)|~brave(mary)))&
(?[X]:((~tall(X)<~>brave(X))))&
(~happy(alice)) | patient(lucy) | [
"p0",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5383644920243453808992671
% SZS output start Proof for 5383644920243453808992671
1. (wise(john) | ~humble(john)) <=> (~quiet(lucy) <~> patient(lucy)) [input p0]
13. ! [X0] : (~quiet(X0) => patient(X0)) [input p12]
20. ~wise(john) <~> humble(john) [input p19]
25. ~patient(lucy) [input hypothesis]
33. ! [X0] : (patient(X0) | quiet(X0)) [ennf transformation 13]
36. ((wise(john) | ~humble(john)) | ((~quiet(lucy) | ~patient(lucy)) & (patient(lucy) | quiet(lucy)))) & (((~patient(lucy) | quiet(lucy)) & (patient(lucy) | ~quiet(lucy))) | (~wise(john) & humble(john))) [nnf transformation 1]
37. (wise(john) | ~humble(john) | ((~quiet(lucy) | ~patient(lucy)) & (patient(lucy) | quiet(lucy)))) & (((~patient(lucy) | quiet(lucy)) & (patient(lucy) | ~quiet(lucy))) | (~wise(john) & humble(john))) [flattening 36]
76. (~humble(john) | wise(john)) & (humble(john) | ~wise(john)) [nnf transformation 20]
83. patient(lucy) | ~quiet(lucy) | humble(john) [cnf transformation 37]
84. patient(lucy) | ~quiet(lucy) | ~wise(john) [cnf transformation 37]
131. patient(X0) | quiet(X0) [cnf transformation 33]
149. ~humble(john) | wise(john) [cnf transformation 76]
156. ~patient(lucy) [cnf transformation 25]
160. 1 <=> patient(lucy) [avatar definition]
162. ~patient(lucy) <- (~1) [avatar component clause 160]
164. 2 <=> quiet(lucy) [avatar definition]
166. ~quiet(lucy) <- (~2) [avatar component clause 164]
168. 3 <=> humble(john) [avatar definition]
172. 4 <=> wise(john) [avatar definition]
179. ~4 | ~2 | 1 [avatar split clause 84,160,164,172]
180. 3 | ~2 | 1 [avatar split clause 83,160,164,168]
354. 4 | ~3 [avatar split clause 149,168,172]
375. ~1 [avatar split clause 156,160]
378. quiet(lucy) <- (~1) [resolution 131,162]
379. $false <- (~1, ~2) [subsumption resolution 378,166]
380. 1 | 2 [avatar contradiction clause 379]
381. $false [avatar sat refutation 179,180,354,375,380]
% SZS output end Proof for 5383644920243453808992671
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is either not happy or humble.
If john is both not curious and not happy then mary is not humble or not kind and vice versa.
Everyone who is either not brave or not tall is not old or calm and vice versa.
Everyone who is not happy or not creative is strong or not humble.
Everyone who is both kind and old is both curious and generous and vice versa.
Everyone who is both not old and not curious is not funny and vice versa.
Everyone who is funny or happy is not brave or quiet and vice versa.
Everyone who is funny or not rich is either not quiet or wise.
Everyone who is either not creative or not patient is not creative and vice versa.
If alice is not curious then someone is not humble.
Everyone who is not brave is either humble or not kind.
If fred is either funny or not strong then someone is either tall or patient and vice versa.
Everyone who is quiet is brave.
Everyone who is either not creative or not kind is either not old or not kind.
If someone is either not brave or wise then someone is not patient and vice versa.
If someone is humble then susan is calm.
Fred is not creative or not strong.
Alice is either not humble or not old.
Someone is either not old or wise.
Mary is either quiet or not strong.
Someone is not kind or curious.
Lucy is humble or not humble.
Someone is not happy or not old.
Mary is rich. | John is not curious. | entailment | (![X]:(~patient(X)=>(~happy(X)<~>humble(X))))&
(((~curious(john)&~happy(john)))<=>((~humble(mary)|~kind(mary))))&
(![X]:((~brave(X)<~>~tall(X))<=>(~old(X)|calm(X))))&
(![X]:((~happy(X)|~creative(X))=>(strong(X)|~humble(X))))&
(![X]:((kind(X)&old(X))<=>(curious(X)&generous(X))))&
(![X]:((~old(X)&~curious(X))<=>~funny(X)))&
(![X]:((funny(X)|happy(X))<=>(~brave(X)|quiet(X))))&
(![X]:((funny(X)|~rich(X))=>(~quiet(X)<~>wise(X))))&
(![X]:((~creative(X)<~>~patient(X))<=>~creative(X)))&
((~curious(alice))=>(?[X]:(~humble(X))))&
(![X]:(~brave(X)=>(humble(X)<~>~kind(X))))&
(((funny(fred)<~>~strong(fred)))<=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:(quiet(X)=>brave(X)))&
(![X]:((~creative(X)<~>~kind(X))=>(~old(X)<~>~kind(X))))&
((?[X]:((~brave(X)<~>wise(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(humble(X)))=>(calm(susan)))&
((~creative(fred)|~strong(fred)))&
((~humble(alice)<~>~old(alice)))&
(?[X]:((~old(X)<~>wise(X))))&
((quiet(mary)<~>~strong(mary)))&
(?[X]:((~kind(X)|curious(X))))&
((humble(lucy)|~humble(lucy)))&
(?[X]:((~happy(X)|~old(X))))&
(rich(mary)) | ~curious(john) | [
"p5",
"p6",
"p7",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 824074798251751455257942
% SZS output start Proof for 824074798251751455257942
6. ! [X0] : ((~curious(X0) & ~old(X0)) <=> ~funny(X0)) [input p5]
7. ! [X0] : ((happy(X0) | funny(X0)) <=> (quiet(X0) | ~brave(X0))) [input p6]
8. ! [X0] : ((~rich(X0) | funny(X0)) => (~quiet(X0) <~> wise(X0))) [input p7]
9. ! [X0] : ((~creative(X0) <~> ~patient(X0)) <=> ~creative(X0)) [input p8]
13. ! [X0] : (quiet(X0) => brave(X0)) [input p12]
15. ? [X0] : (~brave(X0) <~> wise(X0)) <=> ? [X0] : ~patient(X0) [input p14]
25. curious(john) [input hypothesis]
26. ? [X0] : (~brave(X0) <~> wise(X0)) <=> ? [X1] : ~patient(X1) [rectify 15]
27. ! [X0] : (funny(X0) => (~quiet(X0) <~> wise(X0))) [pure predicate removal 8]
32. ! [X0] : ((~quiet(X0) <~> wise(X0)) | ~funny(X0)) [ennf transformation 27]
35. ! [X0] : (brave(X0) | ~quiet(X0)) [ennf transformation 13]
45. ! [X0] : (((~curious(X0) & ~old(X0)) | funny(X0)) & (~funny(X0) | (curious(X0) | old(X0)))) [nnf transformation 6]
46. ! [X0] : (((~curious(X0) & ~old(X0)) | funny(X0)) & (~funny(X0) | curious(X0) | old(X0))) [flattening 45]
47. ! [X0] : (((happy(X0) | funny(X0)) | (~quiet(X0) & brave(X0))) & ((quiet(X0) | ~brave(X0)) | (~happy(X0) & ~funny(X0)))) [nnf transformation 7]
48. ! [X0] : ((happy(X0) | funny(X0) | (~quiet(X0) & brave(X0))) & (quiet(X0) | ~brave(X0) | (~happy(X0) & ~funny(X0)))) [flattening 47]
49. ! [X0] : (((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~funny(X0)) [nnf transformation 32]
50. ! [X0] : ((((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | creative(X0)) & (~creative(X0) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0))))) [nnf transformation 9]
59. (? [X0] : ((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) [nnf transformation 26]
60. (? [X0] : ((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : ((~brave(X3) | ~wise(X3)) & (wise(X3) | brave(X3)))) [rectify 59]
61. ? [X0] : ((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) => ((~wise(sK2) | brave(sK2)) & (wise(sK2) | ~brave(sK2))) [choice axiom]
62. ? [X2] : ~patient(X2) => ~patient(sK3) [choice axiom]
63. (((~wise(sK2) | brave(sK2)) & (wise(sK2) | ~brave(sK2))) | ! [X1] : patient(X1)) & (~patient(sK3) | ! [X3] : ((~brave(X3) | ~wise(X3)) & (wise(X3) | brave(X3)))) [skolemisation 60,62,61]
94. ~curious(X0) | funny(X0) [cnf transformation 46]
95. ~funny(X0) | ~brave(X0) | quiet(X0) [cnf transformation 48]
99. ~quiet(X0) | wise(X0) | ~funny(X0) [cnf transformation 49]
100. ~wise(X0) | quiet(X0) | ~funny(X0) [cnf transformation 49]
102. ~creative(X0) | ~creative(X0) | patient(X0) [cnf transformation 50]
104. patient(X0) | creative(X0) | creative(X0) [cnf transformation 50]
116. ~quiet(X0) | brave(X0) [cnf transformation 35]
121. ~patient(sK3) | wise(X3) | brave(X3) [cnf transformation 63]
122. ~patient(sK3) | ~brave(X3) | ~wise(X3) [cnf transformation 63]
136. curious(john) [cnf transformation 25]
139. ~creative(X0) | patient(X0) [duplicate literal removal 102]
140. creative(X0) | patient(X0) [duplicate literal removal 104]
156. 4 <=> curious(john) [avatar definition]
157. curious(john) <- (4) [avatar component clause 156]
162. patient(X0) [subsumption resolution 139,140]
195. ~wise(X3) | ~brave(X3) [subsumption resolution 122,162]
196. wise(X3) | brave(X3) [subsumption resolution 121,162]
258. 4 [avatar split clause 136,156]
261. funny(john) <- (4) [resolution 94,157]
313. 29 <=> quiet(john) [avatar definition]
315. quiet(john) <- (29) [avatar component clause 313]
317. 30 <=> brave(john) [avatar definition]
318. brave(john) <- (30) [avatar component clause 317]
368. quiet(X0) | ~funny(X0) | brave(X0) [resolution 100,196]
369. ~funny(X0) | quiet(X0) [subsumption resolution 368,95]
371. quiet(john) <- (4) [resolution 369,261]
374. 29 | ~4 [avatar split clause 371,156,313]
402. wise(john) | ~funny(john) <- (29) [resolution 315,99]
404. brave(john) <- (29) [resolution 315,116]
405. wise(john) <- (4, 29) [subsumption resolution 402,261]
408. 30 | ~29 [avatar split clause 404,313,317]
429. ~brave(john) <- (4, 29) [resolution 405,195]
430. $false <- (4, 29, 30) [subsumption resolution 429,318]
431. ~4 | ~29 | ~30 [avatar contradiction clause 430]
432. $false [avatar sat refutation 258,374,408,431]
% SZS output end Proof for 824074798251751455257942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then someone is not humble or happy and vice versa.
If someone is brave or not curious then someone is both patient and humble.
If paul is humble or wise then fred is both not kind and not humble and vice versa.
If john is happy then mary is kind.
Everyone who is either patient or not happy is either not curious or curious and vice versa.
If john is not tall then someone is either not wise or not generous and vice versa.
Everyone who is not funny or old is either not creative or curious and vice versa.
Everyone who is not humble is either not creative or old and vice versa.
Everyone who is both calm and not patient is patient or funny and vice versa.
Everyone who is wise is either not kind or not humble and vice versa.
If fred is both quiet and calm then someone is patient.
If someone is generous or tall then susan is not humble or old and vice versa.
If someone is not happy then lucy is both tall and creative and vice versa.
Everyone who is either not old or not creative is funny and vice versa.
If fred is strong then mary is not wise or kind and vice versa.
Fred is not quiet.
Someone is quiet or calm.
Mary is not kind or brave.
Susan is not brave.
Paul is either happy or not calm.
Someone is either kind or funny. | Mary is funny. | contradiction | ((?[X]:(~tall(X)))<=>(?[X]:((~humble(X)|happy(X)))))&
((?[X]:((brave(X)|~curious(X))))=>(?[X]:((patient(X)&humble(X)))))&
(((humble(paul)|wise(paul)))<=>((~kind(fred)&~humble(fred))))&
((happy(john))=>(kind(mary)))&
(![X]:((patient(X)<~>~happy(X))<=>(~curious(X)<~>curious(X))))&
((~tall(john))<=>(?[X]:((~wise(X)<~>~generous(X)))))&
(![X]:((~funny(X)|old(X))<=>(~creative(X)<~>curious(X))))&
(![X]:(~humble(X)<=>(~creative(X)<~>old(X))))&
(![X]:((calm(X)&~patient(X))<=>(patient(X)|funny(X))))&
(![X]:(wise(X)<=>(~kind(X)<~>~humble(X))))&
(((quiet(fred)&calm(fred)))=>(?[X]:(patient(X))))&
((?[X]:((generous(X)|tall(X))))<=>((~humble(susan)|old(susan))))&
((?[X]:(~happy(X)))<=>((tall(lucy)&creative(lucy))))&
(![X]:((~old(X)<~>~creative(X))<=>funny(X)))&
((strong(fred))<=>((~wise(mary)|kind(mary))))&
(~quiet(fred))&
(?[X]:((quiet(X)|calm(X))))&
((~kind(mary)|brave(mary)))&
(~brave(susan))&
((happy(paul)<~>~calm(paul)))&
(?[X]:((kind(X)<~>funny(X)))) | funny(mary) | [
"p1",
"p6",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7473541795845549226567414
% SZS output start Proof for 7473541795845549226567414
2. ? [X0] : (~curious(X0) | brave(X0)) => ? [X0] : (humble(X0) & patient(X0)) [input p1]
7. ! [X0] : ((old(X0) | ~funny(X0)) <=> (~creative(X0) <~> curious(X0))) [input p6]
9. ! [X0] : ((~patient(X0) & calm(X0)) <=> (funny(X0) | patient(X0))) [input p8]
14. ! [X0] : ((~old(X0) <~> ~creative(X0)) <=> funny(X0)) [input p13]
22. funny(mary) [input hypothesis]
24. ? [X0] : (~curious(X0) | brave(X0)) => ? [X1] : (humble(X1) & patient(X1)) [rectify 2]
25. ? [X1] : (humble(X1) & patient(X1)) | ! [X0] : (curious(X0) & ~brave(X0)) [ennf transformation 24]
34. ? [X0] : (humble(X0) & patient(X0)) | ! [X1] : (curious(X1) & ~brave(X1)) [rectify 25]
35. ? [X0] : (humble(X0) & patient(X0)) => (humble(sK2) & patient(sK2)) [choice axiom]
36. (humble(sK2) & patient(sK2)) | ! [X1] : (curious(X1) & ~brave(X1)) [skolemisation 34,35]
44. ! [X0] : (((old(X0) | ~funny(X0)) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | (~old(X0) & funny(X0)))) [nnf transformation 7]
45. ! [X0] : ((old(X0) | ~funny(X0) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | (~old(X0) & funny(X0)))) [flattening 44]
47. ! [X0] : (((~patient(X0) & calm(X0)) | (~funny(X0) & ~patient(X0))) & ((funny(X0) | patient(X0)) | (patient(X0) | ~calm(X0)))) [nnf transformation 9]
48. ! [X0] : (((~patient(X0) & calm(X0)) | (~funny(X0) & ~patient(X0))) & (funny(X0) | patient(X0) | patient(X0) | ~calm(X0))) [flattening 47]
62. ! [X0] : ((((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | ~funny(X0)) & (funny(X0) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))))) [nnf transformation 14]
75. patient(sK2) | curious(X1) [cnf transformation 36]
99. ~old(X0) | creative(X0) | ~curious(X0) [cnf transformation 45]
101. ~creative(X0) | ~funny(X0) | old(X0) | ~curious(X0) [cnf transformation 45]
109. ~patient(X0) | ~patient(X0) [cnf transformation 48]
125. ~creative(X0) | ~old(X0) | ~funny(X0) [cnf transformation 62]
126. ~funny(X0) | old(X0) | creative(X0) [cnf transformation 62]
138. funny(mary) [cnf transformation 22]
140. ~patient(X0) [duplicate literal removal 109]
170. 7 <=> ! [X1] : curious(X1) [avatar definition]
171. curious(X1) <- (7) [avatar component clause 170]
182. 10 <=> patient(sK2) [avatar definition]
184. patient(sK2) <- (10) [avatar component clause 182]
185. 7 | 10 [avatar split clause 75,182,170]
465. old(mary) | creative(mary) [resolution 126,138]
468. 56 <=> creative(mary) [avatar definition]
469. ~creative(mary) <- (~56) [avatar component clause 468]
470. creative(mary) <- (56) [avatar component clause 468]
472. 57 <=> old(mary) [avatar definition]
473. ~old(mary) <- (~57) [avatar component clause 472]
474. old(mary) <- (57) [avatar component clause 472]
475. 56 | 57 [avatar split clause 465,472,468]
490. ~old(mary) | ~funny(mary) <- (56) [resolution 470,125]
496. ~old(mary) <- (56) [subsumption resolution 490,138]
497. ~57 | ~56 [avatar split clause 496,468,472]
508. creative(mary) | ~curious(mary) <- (57) [resolution 474,99]
511. ~curious(mary) <- (~56, 57) [subsumption resolution 508,469]
512. $false <- (7, ~56, 57) [subsumption resolution 511,171]
513. ~7 | 56 | ~57 [avatar contradiction clause 512]
515. $false <- (10) [subsumption resolution 184,140]
516. ~10 [avatar contradiction clause 515]
551. ~funny(mary) | old(mary) | ~curious(mary) <- (56) [resolution 101,470]
552. old(mary) | ~curious(mary) <- (56) [subsumption resolution 551,138]
553. ~curious(mary) <- (56, ~57) [subsumption resolution 552,473]
554. $false <- (7, 56, ~57) [subsumption resolution 553,171]
555. ~7 | ~56 | 57 [avatar contradiction clause 554]
556. $false [avatar sat refutation 185,475,497,513,516,555]
% SZS output end Proof for 7473541795845549226567414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
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