premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If someone is not patient or not creative then susan is both tall and humble and vice versa. Everyone who is happy is strong or not quiet. If paul is strong or not tall then someone is not funny. If alice is happy or old then mary is patient and vice versa. Everyone who is not strong is either not strong or not quiet and vice versa. Everyone who is both not brave and not tall is generous and vice versa. If someone is not strong then someone is not quiet and vice versa. If susan is both not old and rich then mary is either not wise or not generous. Everyone who is either not creative or wise is creative and vice versa. If someone is not funny or patient then lucy is old or tall. Everyone who is both quiet and rich is humble or rich. If someone is happy or not wise then john is both wise and not creative. Everyone who is not rich or not patient is brave or not generous. Everyone who is not calm or generous is not generous. If someone is funny then paul is both strong and not creative. Everyone who is both curious and kind is either kind or tall. Susan is not funny. Paul is brave. Fred is quiet or not creative. Someone is not funny or not wise. Paul is both patient and not generous. | John is calm. | neutral | ((?[X]:((~patient(X)|~creative(X))))<=>((tall(susan)&humble(susan))))&
(![X]:(happy(X)=>(strong(X)|~quiet(X))))&
(((strong(paul)|~tall(paul)))=>(?[X]:(~funny(X))))&
(((happy(alice)|old(alice)))<=>(patient(mary)))&
(![X]:(~strong(X)<=>(~strong(X)<~>~quiet(X))))&
(![X]:((~brave(X)&~tall(X))<=>generous(X)))&
((?[X]:(~strong(X)))<=>(?[X]:(~quiet(X))))&
(((~old(susan)&rich(susan)))=>((~wise(mary)<~>~generous(mary))))&
(![X]:((~creative(X)<~>wise(X))<=>creative(X)))&
((?[X]:((~funny(X)|patient(X))))=>((old(lucy)|tall(lucy))))&
(![X]:((quiet(X)&rich(X))=>(humble(X)|rich(X))))&
((?[X]:((happy(X)|~wise(X))))=>((wise(john)&~creative(john))))&
(![X]:((~rich(X)|~patient(X))=>(brave(X)|~generous(X))))&
(![X]:((~calm(X)|generous(X))=>~generous(X)))&
((?[X]:(funny(X)))=>((strong(paul)&~creative(paul))))&
(![X]:((curious(X)&kind(X))=>(kind(X)<~>tall(X))))&
(~funny(susan))&
(brave(paul))&
((quiet(fred)|~creative(fred)))&
(?[X]:((~funny(X)|~wise(X))))&
((patient(paul)&~generous(paul))) | calm(john) | [] | null | 0 |
Everyone who is both strong and creative is both not kind and humble and vice versa. Everyone who is not curious or strong is both not curious and wise. Everyone who is not curious is funny and vice versa. Everyone who is quiet is either funny or old and vice versa. Everyone who is either not generous or wise is both not patient and brave. If someone is either patient or wise then someone is both not happy and curious and vice versa. If susan is either strong or kind then someone is either not tall or rich. Everyone who is both not curious and quiet is both patient and not tall. Everyone who is wise is either kind or not creative. Everyone who is both not brave and kind is either kind or quiet and vice versa. Everyone who is not patient or not kind is calm or strong and vice versa. If someone is funny or not funny then susan is both generous and not tall. Everyone who is funny is both not old and not funny and vice versa. If someone is both not creative and not brave then someone is both old and not creative and vice versa. If john is not generous then someone is either not curious or kind and vice versa. Everyone who is both not calm and not patient is funny and vice versa. John is either not happy or not funny. Fred is not funny. John is either calm or tall. Someone is creative or not brave. Someone is not wise. Paul is both not tall and quiet. | Paul is not tall. | entailment | (![X]:((strong(X)&creative(X))<=>(~kind(X)&humble(X))))&
(![X]:((~curious(X)|strong(X))=>(~curious(X)&wise(X))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:(quiet(X)<=>(funny(X)<~>old(X))))&
(![X]:((~generous(X)<~>wise(X))=>(~patient(X)&brave(X))))&
((?[X]:((patient(X)<~>wise(X))))<=>(?[X]:((~happy(X)&curious(X)))))&
(((strong(susan)<~>kind(susan)))=>(?[X]:((~tall(X)<~>rich(X)))))&
(![X]:((~curious(X)&quiet(X))=>(patient(X)&~tall(X))))&
(![X]:(wise(X)=>(kind(X)<~>~creative(X))))&
(![X]:((~brave(X)&kind(X))<=>(kind(X)<~>quiet(X))))&
(![X]:((~patient(X)|~kind(X))<=>(calm(X)|strong(X))))&
((?[X]:((funny(X)|~funny(X))))=>((generous(susan)&~tall(susan))))&
(![X]:(funny(X)<=>(~old(X)&~funny(X))))&
((?[X]:((~creative(X)&~brave(X))))<=>(?[X]:((old(X)&~creative(X)))))&
((~generous(john))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((~calm(X)&~patient(X))<=>funny(X)))&
((~happy(john)<~>~funny(john)))&
(~funny(fred))&
((calm(john)<~>tall(john)))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:(~wise(X)))&
((~tall(paul)&quiet(paul))) | ~tall(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 663912148270079922402458
% SZS output start Proof for 663912148270079922402458
22. quiet(paul) & ~tall(paul) [input p21]
23. tall(paul) [input hypothesis]
137. ~tall(paul) [cnf transformation 22]
139. tall(paul) [cnf transformation 23]
292. $false [subsumption resolution 139,137]
% SZS output end Proof for 663912148270079922402458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is either not generous or curious. Everyone who is both rich and quiet is either not calm or tall and vice versa. Everyone who is not generous or not happy is not happy and vice versa. If lucy is both not creative and not funny then someone is strong or rich. If someone is not rich or tall then someone is both brave and tall and vice versa. Everyone who is both not old and not rich is not tall or creative and vice versa. Everyone who is not strong or old is either funny or happy and vice versa. If mary is not brave or quiet then someone is either calm or tall and vice versa. Everyone who is not wise or not generous is both rich and not funny. If paul is both old and not quiet then john is both kind and not old and vice versa. If someone is either not generous or tall then someone is not curious and vice versa. Everyone who is not wise is not happy or not old and vice versa. Everyone who is either not creative or patient is patient or not funny. If mary is curious or not old then someone is rich. If someone is both humble and quiet then someone is both not curious and not humble and vice versa. Everyone who is patient or generous is both rich and funny and vice versa. Someone is both quiet and kind. Alice is not old or not strong. Someone is not kind or tall. Alice is not generous or not humble. | Paul is generous. | contradiction | (![X]:(~strong(X)=>(~generous(X)<~>curious(X))))&
(![X]:((rich(X)&quiet(X))<=>(~calm(X)<~>tall(X))))&
(![X]:((~generous(X)|~happy(X))<=>~happy(X)))&
(((~creative(lucy)&~funny(lucy)))=>(?[X]:((strong(X)|rich(X)))))&
((?[X]:((~rich(X)|tall(X))))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((~old(X)&~rich(X))<=>(~tall(X)|creative(X))))&
(![X]:((~strong(X)|old(X))<=>(funny(X)<~>happy(X))))&
(((~brave(mary)|quiet(mary)))<=>(?[X]:((calm(X)<~>tall(X)))))&
(![X]:((~wise(X)|~generous(X))=>(rich(X)&~funny(X))))&
(((old(paul)&~quiet(paul)))<=>((kind(john)&~old(john))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:(~curious(X))))&
(![X]:(~wise(X)<=>(~happy(X)|~old(X))))&
(![X]:((~creative(X)<~>patient(X))=>(patient(X)|~funny(X))))&
(((curious(mary)|~old(mary)))=>(?[X]:(rich(X))))&
((?[X]:((humble(X)&quiet(X))))<=>(?[X]:((~curious(X)&~humble(X)))))&
(![X]:((patient(X)|generous(X))<=>(rich(X)&funny(X))))&
(?[X]:((quiet(X)&kind(X))))&
((~old(alice)|~strong(alice)))&
(?[X]:((~kind(X)|tall(X))))&
((~generous(alice)|~humble(alice))) | generous(paul) | [
"p6",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 694887885338080784338645
% SZS output start Proof for 694887885338080784338645
7. ! [X0] : ((old(X0) | ~strong(X0)) <=> (funny(X0) <~> happy(X0))) [input p6]
9. ! [X0] : ((~generous(X0) | ~wise(X0)) => (~funny(X0) & rich(X0))) [input p8]
12. ! [X0] : (~wise(X0) <=> (~old(X0) | ~happy(X0))) [input p11]
16. ! [X0] : ((generous(X0) | patient(X0)) <=> (funny(X0) & rich(X0))) [input p15]
21. generous(paul) [input hypothesis]
25. ! [X0] : ((~old(X0) | ~happy(X0)) => ~wise(X0)) [unused predicate definition removal 12]
29. ! [X0] : ((~funny(X0) & rich(X0)) | (generous(X0) & wise(X0))) [ennf transformation 9]
30. ! [X0] : (~wise(X0) | (old(X0) & happy(X0))) [ennf transformation 25]
48. ! [X0] : (((old(X0) | ~strong(X0)) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~old(X0) & strong(X0)))) [nnf transformation 7]
49. ! [X0] : ((old(X0) | ~strong(X0) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~old(X0) & strong(X0)))) [flattening 48]
70. ! [X0] : (((generous(X0) | patient(X0)) | (~funny(X0) | ~rich(X0))) & ((funny(X0) & rich(X0)) | (~generous(X0) & ~patient(X0)))) [nnf transformation 16]
71. ! [X0] : ((generous(X0) | patient(X0) | ~funny(X0) | ~rich(X0)) & ((funny(X0) & rich(X0)) | (~generous(X0) & ~patient(X0)))) [flattening 70]
101. ~old(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 49]
112. ~funny(X0) | wise(X0) [cnf transformation 29]
122. ~wise(X0) | happy(X0) [cnf transformation 30]
123. ~wise(X0) | old(X0) [cnf transformation 30]
135. ~generous(X0) | funny(X0) [cnf transformation 71]
142. generous(paul) [cnf transformation 21]
233. 21 <=> old(paul) [avatar definition]
235. old(paul) <- (21) [avatar component clause 233]
359. funny(paul) [resolution 135,142]
369. wise(paul) [resolution 359,112]
380. old(paul) [resolution 369,123]
381. happy(paul) [resolution 369,122]
384. 21 [avatar split clause 380,233]
491. ~funny(paul) | ~happy(paul) <- (21) [resolution 101,235]
492. ~happy(paul) <- (21) [subsumption resolution 491,359]
493. $false <- (21) [subsumption resolution 492,381]
494. ~21 [avatar contradiction clause 493]
495. $false [avatar sat refutation 384,494]
% SZS output end Proof for 694887885338080784338645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not funny is not quiet and vice versa.
If someone is both calm and creative then paul is humble or not quiet and vice versa.
If someone is both not strong and not patient then susan is either funny or patient.
If someone is strong then someone is both creative and funny.
Everyone who is either not tall or not humble is either quiet or not generous and vice versa.
Everyone who is not strong or not brave is old or curious and vice versa.
If someone is both humble and not funny then alice is not wise or not generous and vice versa.
Everyone who is both brave and not humble is both calm and happy and vice versa.
Everyone who is either patient or not generous is either creative or not kind and vice versa.
Everyone who is generous or tall is funny or old.
Everyone who is both not funny and kind is curious.
If someone is either not funny or curious then someone is either not brave or not quiet.
Everyone who is both not tall and tall is not quiet or not happy and vice versa.
If alice is either calm or not wise then susan is not wise and vice versa.
Everyone who is either humble or not tall is not kind or not calm and vice versa.
If someone is happy or not kind then someone is either generous or not curious.
John is both not creative and not wise.
John is not wise or rich.
Alice is not old or not brave.
Someone is either strong or brave.
Someone is either wise or not curious.
Someone is either curious or not tall.
Paul is quiet. | Paul is curious. | neutral | (![X]:((~strong(X)|~funny(X))<=>~quiet(X)))&
((?[X]:((calm(X)&creative(X))))<=>((humble(paul)|~quiet(paul))))&
((?[X]:((~strong(X)&~patient(X))))=>((funny(susan)<~>patient(susan))))&
((?[X]:(strong(X)))=>(?[X]:((creative(X)&funny(X)))))&
(![X]:((~tall(X)<~>~humble(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:((~strong(X)|~brave(X))<=>(old(X)|curious(X))))&
((?[X]:((humble(X)&~funny(X))))<=>((~wise(alice)|~generous(alice))))&
(![X]:((brave(X)&~humble(X))<=>(calm(X)&happy(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((generous(X)|tall(X))=>(funny(X)|old(X))))&
(![X]:((~funny(X)&kind(X))=>curious(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((~tall(X)&tall(X))<=>(~quiet(X)|~happy(X))))&
(((calm(alice)<~>~wise(alice)))<=>(~wise(susan)))&
(![X]:((humble(X)<~>~tall(X))<=>(~kind(X)|~calm(X))))&
((?[X]:((happy(X)|~kind(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
((~creative(john)&~wise(john)))&
((~wise(john)|rich(john)))&
((~old(alice)|~brave(alice)))&
(?[X]:((strong(X)<~>brave(X))))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:((curious(X)<~>~tall(X))))&
(quiet(paul)) | curious(paul) | [] | null | 0 |
If someone is both not rich and not patient then paul is quiet.
If paul is brave then john is either quiet or not wise.
If someone is happy then alice is brave or not tall.
Everyone who is either kind or wise is either old or brave.
Everyone who is rich or creative is not funny and vice versa.
If susan is either not happy or not funny then someone is both not brave and calm.
If susan is both not calm and tall then someone is both happy and strong and vice versa.
Everyone who is not happy is both happy and quiet and vice versa.
Everyone who is not humble or not curious is not calm or not curious and vice versa.
Everyone who is either not generous or not humble is creative or patient.
Everyone who is both tall and not old is both not patient and not curious and vice versa.
Everyone who is either not wise or generous is creative or not humble and vice versa.
If someone is both not creative and happy then paul is old and vice versa.
Everyone who is both brave and wise is happy or brave.
Everyone who is not quiet or old is both not kind and not old and vice versa.
John is either wise or calm.
Alice is either not kind or patient.
Someone is both creative and not funny.
Someone is either not quiet or not curious.
Paul is either not old or not brave.
Someone is both not kind and tall.
Someone is not calm or calm.
Someone is curious or not rich. | Alice is not funny. | entailment | ((?[X]:((~rich(X)&~patient(X))))=>(quiet(paul)))&
((brave(paul))=>((quiet(john)<~>~wise(john))))&
((?[X]:(happy(X)))=>((brave(alice)|~tall(alice))))&
(![X]:((kind(X)<~>wise(X))=>(old(X)<~>brave(X))))&
(![X]:((rich(X)|creative(X))<=>~funny(X)))&
(((~happy(susan)<~>~funny(susan)))=>(?[X]:((~brave(X)&calm(X)))))&
(((~calm(susan)&tall(susan)))<=>(?[X]:((happy(X)&strong(X)))))&
(![X]:(~happy(X)<=>(happy(X)&quiet(X))))&
(![X]:((~humble(X)|~curious(X))<=>(~calm(X)|~curious(X))))&
(![X]:((~generous(X)<~>~humble(X))=>(creative(X)|patient(X))))&
(![X]:((tall(X)&~old(X))<=>(~patient(X)&~curious(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(creative(X)|~humble(X))))&
((?[X]:((~creative(X)&happy(X))))<=>(old(paul)))&
(![X]:((brave(X)&wise(X))=>(happy(X)|brave(X))))&
(![X]:((~quiet(X)|old(X))<=>(~kind(X)&~old(X))))&
((wise(john)<~>calm(john)))&
((~kind(alice)<~>patient(alice)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((~quiet(X)<~>~curious(X))))&
((~old(paul)<~>~brave(paul)))&
(?[X]:((~kind(X)&tall(X))))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((curious(X)|~rich(X)))) | ~funny(alice) | [
"p4",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1711119811125954986949936
% SZS output start Proof for 1711119811125954986949936
5. ! [X0] : ((creative(X0) | rich(X0)) <=> ~funny(X0)) [input p4]
8. ! [X0] : (~happy(X0) <=> (quiet(X0) & happy(X0))) [input p7]
13. ? [X0] : (happy(X0) & ~creative(X0)) <=> old(paul) [input p12]
15. ! [X0] : ((old(X0) | ~quiet(X0)) <=> (~old(X0) & ~kind(X0))) [input p14]
24. funny(alice) [input hypothesis]
37. ! [X0] : (((creative(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (~creative(X0) & ~rich(X0)))) [nnf transformation 5]
38. ! [X0] : ((creative(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (~creative(X0) & ~rich(X0)))) [flattening 37]
47. ! [X0] : ((~happy(X0) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | happy(X0))) [nnf transformation 8]
48. ! [X0] : ((~happy(X0) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | happy(X0))) [flattening 47]
56. (? [X0] : (happy(X0) & ~creative(X0)) | ~old(paul)) & (old(paul) | ! [X0] : (~happy(X0) | creative(X0))) [nnf transformation 13]
57. (? [X0] : (happy(X0) & ~creative(X0)) | ~old(paul)) & (old(paul) | ! [X1] : (~happy(X1) | creative(X1))) [rectify 56]
58. ? [X0] : (happy(X0) & ~creative(X0)) => (happy(sK2) & ~creative(sK2)) [choice axiom]
59. ((happy(sK2) & ~creative(sK2)) | ~old(paul)) & (old(paul) | ! [X1] : (~happy(X1) | creative(X1))) [skolemisation 57,58]
60. ! [X0] : (((old(X0) | ~quiet(X0)) | (old(X0) | kind(X0))) & ((~old(X0) & ~kind(X0)) | (~old(X0) & quiet(X0)))) [nnf transformation 15]
61. ! [X0] : ((old(X0) | ~quiet(X0) | old(X0) | kind(X0)) & ((~old(X0) & ~kind(X0)) | (~old(X0) & quiet(X0)))) [flattening 60]
85. ~funny(X0) | ~creative(X0) [cnf transformation 38]
95. happy(X0) | happy(X0) [cnf transformation 48]
114. old(paul) | ~happy(X1) | creative(X1) [cnf transformation 59]
121. ~old(X0) | ~old(X0) [cnf transformation 61]
137. funny(alice) [cnf transformation 24]
138. ~old(X0) [duplicate literal removal 121]
140. happy(X0) [duplicate literal removal 95]
220. 18 <=> old(paul) [avatar definition]
221. old(paul) <- (18) [avatar component clause 220]
228. old(paul) | creative(X1) [subsumption resolution 114,140]
230. 20 <=> ! [X1] : creative(X1) [avatar definition]
231. creative(X1) <- (20) [avatar component clause 230]
232. 20 | 18 [avatar split clause 228,220,230]
270. $false <- (18) [subsumption resolution 221,138]
271. ~18 [avatar contradiction clause 270]
279. ~creative(alice) [resolution 85,137]
281. $false <- (20) [subsumption resolution 279,231]
282. ~20 [avatar contradiction clause 281]
285. $false [avatar sat refutation 232,271,282]
% SZS output end Proof for 1711119811125954986949936
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not quiet then lucy is not rich and vice versa.
If john is either not generous or not wise then someone is both not brave and not tall.
If someone is old then someone is both kind and not wise and vice versa.
Everyone who is not tall is kind or wise and vice versa.
Everyone who is both funny and not rich is funny or not rich and vice versa.
Everyone who is not generous or not humble is strong or creative.
Everyone who is not patient or humble is either funny or not humble and vice versa.
Everyone who is either wise or not calm is not kind or not curious and vice versa.
Everyone who is quiet or brave is either not brave or humble.
Everyone who is creative is old or happy and vice versa.
Everyone who is both creative and humble is not old.
If someone is either not creative or not humble then mary is not rich or patient and vice versa.
If john is both not wise and brave then someone is both not curious and not happy and vice versa.
Everyone who is not rich is both kind and funny and vice versa.
Everyone who is both funny and not kind is strong and vice versa.
Everyone who is both not rich and not happy is not patient or creative.
Someone is either not tall or not happy.
Someone is either not old or creative.
Someone is kind.
Someone is both humble and kind.
Lucy is happy.
Someone is both not strong and not generous.
Someone is both kind and not brave.
Someone is not patient or not curious. | John is not wise. | neutral | ((~quiet(paul))<=>(~rich(lucy)))&
(((~generous(john)<~>~wise(john)))=>(?[X]:((~brave(X)&~tall(X)))))&
((?[X]:(old(X)))<=>(?[X]:((kind(X)&~wise(X)))))&
(![X]:(~tall(X)<=>(kind(X)|wise(X))))&
(![X]:((funny(X)&~rich(X))<=>(funny(X)|~rich(X))))&
(![X]:((~generous(X)|~humble(X))=>(strong(X)|creative(X))))&
(![X]:((~patient(X)|humble(X))<=>(funny(X)<~>~humble(X))))&
(![X]:((wise(X)<~>~calm(X))<=>(~kind(X)|~curious(X))))&
(![X]:((quiet(X)|brave(X))=>(~brave(X)<~>humble(X))))&
(![X]:(creative(X)<=>(old(X)|happy(X))))&
(![X]:((creative(X)&humble(X))=>~old(X)))&
((?[X]:((~creative(X)<~>~humble(X))))<=>((~rich(mary)|patient(mary))))&
(((~wise(john)&brave(john)))<=>(?[X]:((~curious(X)&~happy(X)))))&
(![X]:(~rich(X)<=>(kind(X)&funny(X))))&
(![X]:((funny(X)&~kind(X))<=>strong(X)))&
(![X]:((~rich(X)&~happy(X))=>(~patient(X)|creative(X))))&
(?[X]:((~tall(X)<~>~happy(X))))&
(?[X]:((~old(X)<~>creative(X))))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&kind(X))))&
(happy(lucy))&
(?[X]:((~strong(X)&~generous(X))))&
(?[X]:((kind(X)&~brave(X))))&
(?[X]:((~patient(X)|~curious(X)))) | ~wise(john) | [] | null | 0 |
Everyone who is not kind is not tall or not strong. If john is old then someone is not patient and vice versa. Everyone who is either tall or strong is either not creative or not old. Everyone who is brave or creative is both generous and not rich. If john is either not wise or patient then someone is both not calm and not curious and vice versa. If alice is both wise and not humble then someone is not funny or quiet. If someone is either not brave or quiet then someone is not old or quiet and vice versa. If someone is either brave or not curious then mary is both strong and not brave and vice versa. Everyone who is both not humble and funny is either not humble or not creative. If someone is either happy or not happy then susan is funny. Everyone who is old or generous is both rich and not wise. Everyone who is not kind or generous is curious or not patient. If lucy is quiet then fred is calm or not creative and vice versa. Everyone who is either not rich or rich is not creative or not old and vice versa. If paul is not generous then someone is both creative and not rich. If john is brave then someone is not generous or not happy and vice versa. Susan is either brave or not wise. Fred is not old. Fred is both not tall and not creative. Someone is brave or generous. Someone is either not calm or not creative. Someone is curious or not calm. Alice is both patient and humble. Someone is not patient or not strong. | Lucy is wise. | contradiction | (![X]:(~kind(X)=>(~tall(X)|~strong(X))))&
((old(john))<=>(?[X]:(~patient(X))))&
(![X]:((tall(X)<~>strong(X))=>(~creative(X)<~>~old(X))))&
(![X]:((brave(X)|creative(X))=>(generous(X)&~rich(X))))&
(((~wise(john)<~>patient(john)))<=>(?[X]:((~calm(X)&~curious(X)))))&
(((wise(alice)&~humble(alice)))=>(?[X]:((~funny(X)|quiet(X)))))&
((?[X]:((~brave(X)<~>quiet(X))))<=>(?[X]:((~old(X)|quiet(X)))))&
((?[X]:((brave(X)<~>~curious(X))))<=>((strong(mary)&~brave(mary))))&
(![X]:((~humble(X)&funny(X))=>(~humble(X)<~>~creative(X))))&
((?[X]:((happy(X)<~>~happy(X))))=>(funny(susan)))&
(![X]:((old(X)|generous(X))=>(rich(X)&~wise(X))))&
(![X]:((~kind(X)|generous(X))=>(curious(X)|~patient(X))))&
((quiet(lucy))<=>((calm(fred)|~creative(fred))))&
(![X]:((~rich(X)<~>rich(X))<=>(~creative(X)|~old(X))))&
((~generous(paul))=>(?[X]:((creative(X)&~rich(X)))))&
((brave(john))<=>(?[X]:((~generous(X)|~happy(X)))))&
((brave(susan)<~>~wise(susan)))&
(~old(fred))&
((~tall(fred)&~creative(fred)))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:((~calm(X)<~>~creative(X))))&
(?[X]:((curious(X)|~calm(X))))&
((patient(alice)&humble(alice)))&
(?[X]:((~patient(X)|~strong(X)))) | wise(lucy) | [
"p3",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 507901082093295885333322
% SZS output start Proof for 507901082093295885333322
4. ! [X0] : ((creative(X0) | brave(X0)) => (~rich(X0) & generous(X0))) [input p3]
11. ! [X0] : ((generous(X0) | old(X0)) => (~wise(X0) & rich(X0))) [input p10]
16. brave(john) <=> ? [X0] : (~happy(X0) | ~generous(X0)) [input p15]
25. wise(lucy) [input hypothesis]
30. ! [X0] : ((~rich(X0) & generous(X0)) | (~creative(X0) & ~brave(X0))) [ennf transformation 4]
36. ! [X0] : ((~wise(X0) & rich(X0)) | (~generous(X0) & ~old(X0))) [ennf transformation 11]
69. (brave(john) | ! [X0] : (happy(X0) & generous(X0))) & (? [X0] : (~happy(X0) | ~generous(X0)) | ~brave(john)) [nnf transformation 16]
70. (brave(john) | ! [X0] : (happy(X0) & generous(X0))) & (? [X1] : (~happy(X1) | ~generous(X1)) | ~brave(john)) [rectify 69]
71. ? [X1] : (~happy(X1) | ~generous(X1)) => (~happy(sK7) | ~generous(sK7)) [choice axiom]
72. (brave(john) | ! [X0] : (happy(X0) & generous(X0))) & ((~happy(sK7) | ~generous(sK7)) | ~brave(john)) [skolemisation 70,71]
89. ~brave(X0) | generous(X0) [cnf transformation 30]
91. ~rich(X0) | ~brave(X0) [cnf transformation 30]
117. ~generous(X0) | rich(X0) [cnf transformation 36]
119. ~wise(X0) | ~generous(X0) [cnf transformation 36]
133. brave(john) | generous(X0) [cnf transformation 72]
147. wise(lucy) [cnf transformation 25]
312. 36 <=> brave(john) [avatar definition]
314. brave(john) <- (36) [avatar component clause 312]
317. 37 <=> ! [X0] : generous(X0) [avatar definition]
318. generous(X0) <- (37) [avatar component clause 317]
319. 37 | 36 [avatar split clause 133,312,317]
388. ~generous(lucy) [resolution 119,147]
389. $false <- (37) [subsumption resolution 388,318]
390. ~37 [avatar contradiction clause 389]
401. generous(john) <- (36) [resolution 314,89]
430. rich(john) <- (36) [resolution 401,117]
452. ~brave(john) <- (36) [resolution 430,91]
453. $false <- (36) [subsumption resolution 452,314]
454. ~36 [avatar contradiction clause 453]
455. $false [avatar sat refutation 319,390,454]
% SZS output end Proof for 507901082093295885333322
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or calm is not happy.
If someone is both not generous and brave then lucy is old and vice versa.
Everyone who is both not wise and not rich is both curious and quiet and vice versa.
Everyone who is both not tall and quiet is tall or creative and vice versa.
Everyone who is rich or not funny is either not wise or not funny and vice versa.
If someone is either wise or funny then someone is not kind or funny.
If someone is either calm or not humble then lucy is both funny and not calm and vice versa.
Everyone who is either happy or not strong is both wise and not rich and vice versa.
If someone is not funny then fred is either not quiet or kind and vice versa.
Everyone who is not creative is generous or strong and vice versa.
If susan is both not curious and not rich then alice is not old and vice versa.
Everyone who is not generous or not wise is both old and wise and vice versa.
If someone is old then fred is humble.
If someone is either calm or generous then mary is not generous or creative.
Everyone who is either not rich or patient is not generous.
Alice is funny or not funny.
Someone is both calm and curious.
Mary is either not old or humble.
Susan is both rich and not old.
Paul is both not kind and not creative.
Someone is either not calm or wise.
John is not rich or not curious.
John is not patient. | Paul is tall. | contradiction | (![X]:((~calm(X)<~>calm(X))=>~happy(X)))&
((?[X]:((~generous(X)&brave(X))))<=>(old(lucy)))&
(![X]:((~wise(X)&~rich(X))<=>(curious(X)&quiet(X))))&
(![X]:((~tall(X)&quiet(X))<=>(tall(X)|creative(X))))&
(![X]:((rich(X)|~funny(X))<=>(~wise(X)<~>~funny(X))))&
((?[X]:((wise(X)<~>funny(X))))=>(?[X]:((~kind(X)|funny(X)))))&
((?[X]:((calm(X)<~>~humble(X))))<=>((funny(lucy)&~calm(lucy))))&
(![X]:((happy(X)<~>~strong(X))<=>(wise(X)&~rich(X))))&
((?[X]:(~funny(X)))<=>((~quiet(fred)<~>kind(fred))))&
(![X]:(~creative(X)<=>(generous(X)|strong(X))))&
(((~curious(susan)&~rich(susan)))<=>(~old(alice)))&
(![X]:((~generous(X)|~wise(X))<=>(old(X)&wise(X))))&
((?[X]:(old(X)))=>(humble(fred)))&
((?[X]:((calm(X)<~>generous(X))))=>((~generous(mary)|creative(mary))))&
(![X]:((~rich(X)<~>patient(X))=>~generous(X)))&
((funny(alice)|~funny(alice)))&
(?[X]:((calm(X)&curious(X))))&
((~old(mary)<~>humble(mary)))&
((rich(susan)&~old(susan)))&
((~kind(paul)&~creative(paul)))&
(?[X]:((~calm(X)<~>wise(X))))&
((~rich(john)|~curious(john)))&
(~patient(john)) | tall(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2240498383584217794996012
% SZS output start Proof for 2240498383584217794996012
4. ! [X0] : ((quiet(X0) & ~tall(X0)) <=> (creative(X0) | tall(X0))) [input p3]
24. tall(paul) [input hypothesis]
39. ! [X0] : (((quiet(X0) & ~tall(X0)) | (~creative(X0) & ~tall(X0))) & ((creative(X0) | tall(X0)) | (~quiet(X0) | tall(X0)))) [nnf transformation 4]
40. ! [X0] : (((quiet(X0) & ~tall(X0)) | (~creative(X0) & ~tall(X0))) & (creative(X0) | tall(X0) | ~quiet(X0) | tall(X0))) [flattening 39]
82. ~tall(X0) | ~tall(X0) [cnf transformation 40]
139. tall(paul) [cnf transformation 24]
145. ~tall(X0) [duplicate literal removal 82]
301. $false [subsumption resolution 139,145]
% SZS output end Proof for 2240498383584217794996012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either patient or old then someone is humble or not humble. If someone is both funny and not tall then lucy is both generous and curious. Everyone who is either calm or not happy is not kind or happy and vice versa. Everyone who is not patient or patient is both not humble and not funny and vice versa. Everyone who is not old is both not funny and not calm and vice versa. Everyone who is either not kind or happy is either not brave or not generous. Everyone who is either not humble or not rich is either not tall or funny and vice versa. Everyone who is not old or patient is not creative. If someone is both not generous and funny then fred is both funny and not generous and vice versa. If someone is rich then someone is not quiet and vice versa. Everyone who is not old is both wise and strong and vice versa. Everyone who is both not tall and not wise is both not brave and curious and vice versa. Everyone who is not tall is either not generous or not funny and vice versa. Everyone who is calm is funny and vice versa. Everyone who is not humble or not rich is both patient and not old. If someone is not calm then lucy is not tall or not kind and vice versa. Fred is either not tall or calm. Paul is either kind or curious. Paul is strong or not curious. | Lucy is funny. | contradiction | (((patient(alice)<~>old(alice)))=>(?[X]:((humble(X)|~humble(X)))))&
((?[X]:((funny(X)&~tall(X))))=>((generous(lucy)&curious(lucy))))&
(![X]:((calm(X)<~>~happy(X))<=>(~kind(X)|happy(X))))&
(![X]:((~patient(X)|patient(X))<=>(~humble(X)&~funny(X))))&
(![X]:(~old(X)<=>(~funny(X)&~calm(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~tall(X)<~>funny(X))))&
(![X]:((~old(X)|patient(X))=>~creative(X)))&
((?[X]:((~generous(X)&funny(X))))<=>((funny(fred)&~generous(fred))))&
((?[X]:(rich(X)))<=>(?[X]:(~quiet(X))))&
(![X]:(~old(X)<=>(wise(X)&strong(X))))&
(![X]:((~tall(X)&~wise(X))<=>(~brave(X)&curious(X))))&
(![X]:(~tall(X)<=>(~generous(X)<~>~funny(X))))&
(![X]:(calm(X)<=>funny(X)))&
(![X]:((~humble(X)|~rich(X))=>(patient(X)&~old(X))))&
((?[X]:(~calm(X)))<=>((~tall(lucy)|~kind(lucy))))&
((~tall(fred)<~>calm(fred)))&
((kind(paul)<~>curious(paul)))&
((strong(paul)|~curious(paul))) | funny(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1825493247707887593724032
% SZS output start Proof for 1825493247707887593724032
4. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~funny(X0) & ~humble(X0))) [input p3]
20. funny(lucy) [input hypothesis]
32. ! [X0] : (((patient(X0) | ~patient(X0)) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 4]
33. ! [X0] : ((patient(X0) | ~patient(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [flattening 32]
73. ~funny(X0) | patient(X0) [cnf transformation 33]
74. ~funny(X0) | ~patient(X0) [cnf transformation 33]
122. funny(lucy) [cnf transformation 20]
139. ~funny(X0) [subsumption resolution 73,74]
193. $false [subsumption resolution 122,139]
% SZS output end Proof for 1825493247707887593724032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or creative is either not patient or not humble.
If lucy is both not calm and not happy then fred is not creative and vice versa.
If someone is creative then someone is both calm and not calm and vice versa.
Everyone who is quiet is funny or patient.
Everyone who is not happy is either not rich or brave and vice versa.
If someone is either quiet or brave then susan is not patient or not brave.
If someone is both curious and not tall then paul is either not curious or not brave and vice versa.
Everyone who is both not rich and kind is either not funny or creative.
If paul is both not old and quiet then someone is both not quiet and patient.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
If someone is patient or brave then someone is either not patient or not old and vice versa.
Everyone who is quiet or old is patient and vice versa.
Alice is either wise or curious.
Someone is not creative or not strong.
Susan is both not tall and not generous.
Alice is either not funny or strong.
Someone is either tall or quiet. | Lucy is old. | contradiction | (![X]:((~wise(X)<~>creative(X))=>(~patient(X)<~>~humble(X))))&
(((~calm(lucy)&~happy(lucy)))<=>(~creative(fred)))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(![X]:((quiet(X)|old(X))<=>patient(X)))&
((wise(alice)<~>curious(alice)))&
(?[X]:((~creative(X)|~strong(X))))&
((~tall(susan)&~generous(susan)))&
((~funny(alice)<~>strong(alice)))&
(?[X]:((tall(X)<~>quiet(X)))) | old(lucy) | [
"p2",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1633276364600363006611510
% SZS output start Proof for 1633276364600363006611510
3. ? [X0] : creative(X0) <=> ? [X0] : (~calm(X0) & calm(X0)) [input p2]
10. ! [X0] : (quiet(X0) <=> creative(X0)) [input p9]
15. ? [X0] : (brave(X0) | patient(X0)) <=> ? [X0] : (~patient(X0) <~> ~old(X0)) [input p14]
16. ! [X0] : ((old(X0) | quiet(X0)) <=> patient(X0)) [input p15]
22. old(lucy) [input hypothesis]
23. ? [X0] : creative(X0) <=> ? [X1] : (~calm(X1) & calm(X1)) [rectify 3]
24. ? [X0] : (brave(X0) | patient(X0)) <=> ? [X1] : (~patient(X1) <~> ~old(X1)) [rectify 15]
40. (? [X0] : creative(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X1] : (~calm(X1) & calm(X1)) | ! [X0] : ~creative(X0)) [nnf transformation 23]
41. (? [X0] : creative(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X2] : (~calm(X2) & calm(X2)) | ! [X3] : ~creative(X3)) [rectify 40]
42. ? [X0] : creative(X0) => creative(sK0) [choice axiom]
43. ? [X2] : (~calm(X2) & calm(X2)) => (~calm(sK1) & calm(sK1)) [choice axiom]
44. (creative(sK0) | ! [X1] : (calm(X1) | ~calm(X1))) & ((~calm(sK1) & calm(sK1)) | ! [X3] : ~creative(X3)) [skolemisation 41,43,42]
53. ! [X0] : ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))) [nnf transformation 10]
56. (? [X0] : (brave(X0) | patient(X0)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (? [X1] : ((old(X1) | patient(X1)) & (~old(X1) | ~patient(X1))) | ! [X0] : (~brave(X0) & ~patient(X0))) [nnf transformation 24]
57. (? [X0] : (brave(X0) | patient(X0)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (? [X2] : ((old(X2) | patient(X2)) & (~old(X2) | ~patient(X2))) | ! [X3] : (~brave(X3) & ~patient(X3))) [rectify 56]
58. ? [X0] : (brave(X0) | patient(X0)) => (brave(sK4) | patient(sK4)) [choice axiom]
59. ? [X2] : ((old(X2) | patient(X2)) & (~old(X2) | ~patient(X2))) => ((old(sK5) | patient(sK5)) & (~old(sK5) | ~patient(sK5))) [choice axiom]
60. ((brave(sK4) | patient(sK4)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (((old(sK5) | patient(sK5)) & (~old(sK5) | ~patient(sK5))) | ! [X3] : (~brave(X3) & ~patient(X3))) [skolemisation 57,59,58]
61. ! [X0] : (((old(X0) | quiet(X0)) | ~patient(X0)) & (patient(X0) | (~old(X0) & ~quiet(X0)))) [nnf transformation 16]
62. ! [X0] : ((old(X0) | quiet(X0) | ~patient(X0)) & (patient(X0) | (~old(X0) & ~quiet(X0)))) [flattening 61]
77. calm(sK1) | ~creative(X3) [cnf transformation 44]
78. ~calm(sK1) | ~creative(X3) [cnf transformation 44]
95. ~quiet(X0) | creative(X0) [cnf transformation 53]
108. ~old(sK5) | ~patient(sK5) | ~patient(X3) [cnf transformation 60]
110. old(sK5) | patient(sK5) | ~patient(X3) [cnf transformation 60]
115. patient(X0) | ~old(X0) [cnf transformation 62]
116. ~patient(X0) | quiet(X0) | old(X0) [cnf transformation 62]
125. old(lucy) [cnf transformation 22]
142. 4 <=> ! [X3] : ~creative(X3) [avatar definition]
143. ~creative(X3) <- (4) [avatar component clause 142]
145. 5 <=> calm(sK1) [avatar definition]
148. 4 | ~5 [avatar split clause 78,145,142]
149. 4 | 5 [avatar split clause 77,145,142]
235. 25 <=> ! [X1] : (~old(X1) | patient(X1)) [avatar definition]
236. ~old(X1) | patient(X1) <- (25) [avatar component clause 235]
242. 27 <=> patient(sK5) [avatar definition]
244. patient(sK5) <- (27) [avatar component clause 242]
246. 28 <=> old(sK5) [avatar definition]
247. ~old(sK5) <- (~28) [avatar component clause 246]
248. old(sK5) <- (28) [avatar component clause 246]
251. 29 <=> ! [X3] : ~patient(X3) [avatar definition]
252. ~patient(X3) <- (29) [avatar component clause 251]
253. 29 | 27 | 28 [avatar split clause 110,246,242,251]
255. 29 | ~27 | ~28 [avatar split clause 108,246,242,251]
256. 25 [avatar split clause 115,235]
304. patient(lucy) <- (25) [resolution 236,125]
345. quiet(sK5) | old(sK5) <- (27) [resolution 116,244]
348. quiet(sK5) <- (27, ~28) [subsumption resolution 345,247]
360. creative(sK5) <- (27, ~28) [resolution 348,95]
361. $false <- (4, 27, ~28) [subsumption resolution 360,143]
362. ~4 | ~27 | 28 [avatar contradiction clause 361]
367. patient(sK5) <- (25, 28) [resolution 248,236]
370. 27 | ~25 | ~28 [avatar split clause 367,246,235,242]
380. $false <- (25, 29) [resolution 252,304]
383. ~25 | ~29 [avatar contradiction clause 380]
384. $false [avatar sat refutation 148,149,253,255,256,362,370,383]
% SZS output end Proof for 1633276364600363006611510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either funny or patient then john is old or not funny.
Everyone who is not patient is not calm or funny.
Everyone who is either not strong or strong is both old and not strong and vice versa.
If someone is not patient or wise then john is wise.
If lucy is either curious or not quiet then mary is not curious.
Everyone who is not humble or creative is either not happy or not creative and vice versa.
Everyone who is either wise or not humble is either not generous or not funny.
Everyone who is either curious or creative is generous or tall.
If someone is patient or creative then someone is calm or quiet and vice versa.
Everyone who is both not humble and quiet is not brave.
Everyone who is calm or creative is both not quiet and not funny.
Everyone who is old is both calm and not kind.
If alice is either rich or not patient then john is either not generous or humble and vice versa.
If someone is humble or wise then someone is both not strong and patient.
Everyone who is either not wise or not generous is either not patient or kind.
Everyone who is wise is patient.
Alice is either not old or not rich.
Lucy is calm or humble.
Someone is tall or not generous.
Lucy is brave or humble.
Someone is not humble.
Someone is patient or brave. | John is quiet. | contradiction | (((funny(alice)<~>patient(alice)))=>((old(john)|~funny(john))))&
(![X]:(~patient(X)=>(~calm(X)|funny(X))))&
(![X]:((~strong(X)<~>strong(X))<=>(old(X)&~strong(X))))&
((?[X]:((~patient(X)|wise(X))))=>(wise(john)))&
(((curious(lucy)<~>~quiet(lucy)))=>(~curious(mary)))&
(![X]:((~humble(X)|creative(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:((wise(X)<~>~humble(X))=>(~generous(X)<~>~funny(X))))&
(![X]:((curious(X)<~>creative(X))=>(generous(X)|tall(X))))&
((?[X]:((patient(X)|creative(X))))<=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:((~humble(X)&quiet(X))=>~brave(X)))&
(![X]:((calm(X)|creative(X))=>(~quiet(X)&~funny(X))))&
(![X]:(old(X)=>(calm(X)&~kind(X))))&
(((rich(alice)<~>~patient(alice)))<=>((~generous(john)<~>humble(john))))&
((?[X]:((humble(X)|wise(X))))=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~patient(X)<~>kind(X))))&
(![X]:(wise(X)=>patient(X)))&
((~old(alice)<~>~rich(alice)))&
((calm(lucy)|humble(lucy)))&
(?[X]:((tall(X)|~generous(X))))&
((brave(lucy)|humble(lucy)))&
(?[X]:(~humble(X)))&
(?[X]:((patient(X)|brave(X)))) | quiet(john) | [
"p2",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3892338935044767381542254
% SZS output start Proof for 3892338935044767381542254
3. ! [X0] : ((~strong(X0) <~> strong(X0)) <=> (~strong(X0) & old(X0))) [input p2]
11. ! [X0] : ((creative(X0) | calm(X0)) => (~funny(X0) & ~quiet(X0))) [input p10]
12. ! [X0] : (old(X0) => (~kind(X0) & calm(X0))) [input p11]
23. quiet(john) [input hypothesis]
37. ! [X0] : ((~funny(X0) & ~quiet(X0)) | (~creative(X0) & ~calm(X0))) [ennf transformation 11]
38. ! [X0] : ((~kind(X0) & calm(X0)) | ~old(X0)) [ennf transformation 12]
43. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (strong(X0) | ~old(X0))) & ((~strong(X0) & old(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [nnf transformation 3]
44. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | strong(X0) | ~old(X0)) & ((~strong(X0) & old(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [flattening 43]
67. old(X0) | strong(X0) | strong(X0) [cnf transformation 44]
70. ~strong(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 44]
92. ~quiet(X0) | ~calm(X0) [cnf transformation 37]
96. calm(X0) | ~old(X0) [cnf transformation 38]
121. quiet(john) [cnf transformation 23]
124. old(X0) | strong(X0) [duplicate literal removal 67]
127. ~strong(X0) [duplicate literal removal 70]
148. old(X0) [subsumption resolution 124,127]
208. calm(X0) [subsumption resolution 96,148]
260. ~calm(john) [resolution 92,121]
261. $false [subsumption resolution 260,208]
% SZS output end Proof for 3892338935044767381542254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or strong is happy. Everyone who is both humble and not wise is both not kind and rich. If someone is both generous and tall then someone is either not funny or not quiet and vice versa. Everyone who is both rich and not generous is not strong. If susan is either brave or tall then paul is both not curious and not generous and vice versa. If someone is wise then john is not wise or generous. If someone is either not funny or strong then someone is curious and vice versa. If paul is either not generous or not old then susan is not brave. Everyone who is quiet or kind is not patient or old. Everyone who is both not tall and happy is not rich or kind and vice versa. If someone is either creative or quiet then someone is not generous or funny and vice versa. Everyone who is curious is either not brave or not funny and vice versa. If lucy is either brave or humble then someone is both brave and old and vice versa. If someone is either patient or not kind then susan is both strong and kind and vice versa. Everyone who is not calm is both not creative and quiet and vice versa. Everyone who is not strong is not quiet and vice versa. Fred is not old. Alice is either not creative or funny. John is not patient. Someone is both creative and kind. Someone is curious. Mary is not quiet. Susan is both not strong and not humble. Someone is not creative. | Susan is calm. | entailment | (![X]:((~kind(X)|strong(X))=>happy(X)))&
(![X]:((humble(X)&~wise(X))=>(~kind(X)&rich(X))))&
((?[X]:((generous(X)&tall(X))))<=>(?[X]:((~funny(X)<~>~quiet(X)))))&
(![X]:((rich(X)&~generous(X))=>~strong(X)))&
(((brave(susan)<~>tall(susan)))<=>((~curious(paul)&~generous(paul))))&
((?[X]:(wise(X)))=>((~wise(john)|generous(john))))&
((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:(curious(X))))&
(((~generous(paul)<~>~old(paul)))=>(~brave(susan)))&
(![X]:((quiet(X)|kind(X))=>(~patient(X)|old(X))))&
(![X]:((~tall(X)&happy(X))<=>(~rich(X)|kind(X))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:((~generous(X)|funny(X)))))&
(![X]:(curious(X)<=>(~brave(X)<~>~funny(X))))&
(((brave(lucy)<~>humble(lucy)))<=>(?[X]:((brave(X)&old(X)))))&
((?[X]:((patient(X)<~>~kind(X))))<=>((strong(susan)&kind(susan))))&
(![X]:(~calm(X)<=>(~creative(X)&quiet(X))))&
(![X]:(~strong(X)<=>~quiet(X)))&
(~old(fred))&
((~creative(alice)<~>funny(alice)))&
(~patient(john))&
(?[X]:((creative(X)&kind(X))))&
(?[X]:(curious(X)))&
(~quiet(mary))&
((~strong(susan)&~humble(susan)))&
(?[X]:(~creative(X))) | calm(susan) | [
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4676951558347447854534562
% SZS output start Proof for 4676951558347447854534562
15. ! [X0] : (~calm(X0) <=> (quiet(X0) & ~creative(X0))) [input p14]
16. ! [X0] : (~strong(X0) <=> ~quiet(X0)) [input p15]
23. ~humble(susan) & ~strong(susan) [input p22]
25. ~calm(susan) [input hypothesis]
29. ! [X0] : (~calm(X0) => (quiet(X0) & ~creative(X0))) [unused predicate definition removal 15]
40. ! [X0] : ((quiet(X0) & ~creative(X0)) | calm(X0)) [ennf transformation 29]
71. ! [X0] : ((~strong(X0) | quiet(X0)) & (~quiet(X0) | strong(X0))) [nnf transformation 16]
133. calm(X0) | quiet(X0) [cnf transformation 40]
134. ~quiet(X0) | strong(X0) [cnf transformation 71]
144. ~strong(susan) [cnf transformation 23]
147. ~calm(susan) [cnf transformation 25]
306. 35 <=> strong(susan) [avatar definition]
308. ~strong(susan) <- (~35) [avatar component clause 306]
343. ~35 [avatar split clause 144,306]
348. quiet(susan) [resolution 133,147]
349. strong(susan) [resolution 348,134]
350. $false <- (~35) [subsumption resolution 349,308]
351. 35 [avatar contradiction clause 350]
352. $false [avatar sat refutation 343,351]
% SZS output end Proof for 4676951558347447854534562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not tall is both generous and not rich.
If someone is not creative then someone is either not humble or not curious.
Everyone who is either not generous or not happy is tall or not old.
If alice is quiet or patient then alice is not kind.
Everyone who is both not humble and not kind is either happy or not generous.
Everyone who is not brave or not strong is either not patient or not strong and vice versa.
Everyone who is either tall or rich is both strong and wise and vice versa.
If susan is not calm then someone is humble and vice versa.
Everyone who is happy or not curious is either funny or rich and vice versa.
Everyone who is not tall is either old or happy and vice versa.
Everyone who is curious or not curious is kind or happy and vice versa.
If alice is not quiet or not brave then paul is either funny or generous.
If someone is calm or kind then someone is either rich or curious.
Everyone who is not happy or generous is not rich or not kind and vice versa.
If john is either brave or not generous then someone is either not humble or quiet and vice versa.
Everyone who is either generous or not wise is either rich or curious and vice versa.
Mary is not brave.
Mary is either patient or rich.
Someone is strong or not old.
Alice is both humble and wise.
Someone is not funny or calm.
Mary is either wise or not humble.
Mary is kind.
Alice is both brave and creative. | Alice is kind. | contradiction | (![X]:((~humble(X)<~>~tall(X))=>(generous(X)&~rich(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((~generous(X)<~>~happy(X))=>(tall(X)|~old(X))))&
(((quiet(alice)|patient(alice)))=>(~kind(alice)))&
(![X]:((~humble(X)&~kind(X))=>(happy(X)<~>~generous(X))))&
(![X]:((~brave(X)|~strong(X))<=>(~patient(X)<~>~strong(X))))&
(![X]:((tall(X)<~>rich(X))<=>(strong(X)&wise(X))))&
((~calm(susan))<=>(?[X]:(humble(X))))&
(![X]:((happy(X)|~curious(X))<=>(funny(X)<~>rich(X))))&
(![X]:(~tall(X)<=>(old(X)<~>happy(X))))&
(![X]:((curious(X)|~curious(X))<=>(kind(X)|happy(X))))&
(((~quiet(alice)|~brave(alice)))=>((funny(paul)<~>generous(paul))))&
((?[X]:((calm(X)|kind(X))))=>(?[X]:((rich(X)<~>curious(X)))))&
(![X]:((~happy(X)|generous(X))<=>(~rich(X)|~kind(X))))&
(((brave(john)<~>~generous(john)))<=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:((generous(X)<~>~wise(X))<=>(rich(X)<~>curious(X))))&
(~brave(mary))&
((patient(mary)<~>rich(mary)))&
(?[X]:((strong(X)|~old(X))))&
((humble(alice)&wise(alice)))&
(?[X]:((~funny(X)|calm(X))))&
((wise(mary)<~>~humble(mary)))&
(kind(mary))&
((brave(alice)&creative(alice))) | kind(alice) | [
"p3",
"p5",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 21519706612234708314226
% SZS output start Proof for 21519706612234708314226
4. (patient(alice) | quiet(alice)) => ~kind(alice) [input p3]
6. ! [X0] : ((~strong(X0) | ~brave(X0)) <=> (~patient(X0) <~> ~strong(X0))) [input p5]
24. creative(alice) & brave(alice) [input p23]
25. kind(alice) [input hypothesis]
29. brave(alice) [pure predicate removal 24]
33. ~kind(alice) | (~patient(alice) & ~quiet(alice)) [ennf transformation 4]
41. ! [X0] : (((~strong(X0) | ~brave(X0)) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | (strong(X0) & brave(X0)))) [nnf transformation 6]
42. ! [X0] : ((~strong(X0) | ~brave(X0) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | (strong(X0) & brave(X0)))) [flattening 41]
79. ~kind(alice) | ~patient(alice) [cnf transformation 33]
85. strong(X0) | patient(X0) | strong(X0) [cnf transformation 42]
86. ~strong(X0) | ~brave(X0) | ~strong(X0) | patient(X0) [cnf transformation 42]
148. brave(alice) [cnf transformation 29]
149. kind(alice) [cnf transformation 25]
150. strong(X0) | patient(X0) [duplicate literal removal 85]
151. ~strong(X0) | ~brave(X0) | patient(X0) [duplicate literal removal 86]
153. 1 <=> patient(alice) [avatar definition]
155. ~patient(alice) <- (~1) [avatar component clause 153]
157. 2 <=> kind(alice) [avatar definition]
160. ~1 | ~2 [avatar split clause 79,157,153]
181. 7 <=> brave(alice) [avatar definition]
183. brave(alice) <- (7) [avatar component clause 181]
284. 7 [avatar split clause 148,181]
285. 2 [avatar split clause 149,157]
420. ~brave(X0) | patient(X0) | patient(X0) [resolution 151,150]
423. ~brave(X0) | patient(X0) [duplicate literal removal 420]
424. patient(alice) <- (7) [resolution 423,183]
425. $false <- (~1, 7) [subsumption resolution 424,155]
426. 1 | ~7 [avatar contradiction clause 425]
427. $false [avatar sat refutation 160,284,285,426]
% SZS output end Proof for 21519706612234708314226
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both not old and not calm then susan is either not quiet or generous.
Everyone who is not quiet or not curious is not wise and vice versa.
Everyone who is curious or old is not creative or wise and vice versa.
If susan is either calm or not brave then someone is patient or not tall.
If someone is both old and not kind then mary is not generous.
Everyone who is both not brave and kind is creative or not happy and vice versa.
Everyone who is not patient is both not wise and not humble and vice versa.
Everyone who is both not kind and not wise is funny and vice versa.
Everyone who is old or quiet is funny or kind and vice versa.
Everyone who is not creative or humble is both brave and not patient and vice versa.
If someone is not calm then someone is not funny.
If someone is creative then john is creative and vice versa.
Everyone who is both not calm and kind is either not patient or quiet.
If someone is either old or wise then someone is both brave and not happy.
If paul is humble then lucy is both patient and quiet.
Alice is either not patient or not rich.
Someone is either not patient or not kind.
Someone is kind.
Mary is quiet or curious. | John is calm. | neutral | (((~old(john)&~calm(john)))=>((~quiet(susan)<~>generous(susan))))&
(![X]:((~quiet(X)|~curious(X))<=>~wise(X)))&
(![X]:((curious(X)|old(X))<=>(~creative(X)|wise(X))))&
(((calm(susan)<~>~brave(susan)))=>(?[X]:((patient(X)|~tall(X)))))&
((?[X]:((old(X)&~kind(X))))=>(~generous(mary)))&
(![X]:((~brave(X)&kind(X))<=>(creative(X)|~happy(X))))&
(![X]:(~patient(X)<=>(~wise(X)&~humble(X))))&
(![X]:((~kind(X)&~wise(X))<=>funny(X)))&
(![X]:((old(X)|quiet(X))<=>(funny(X)|kind(X))))&
(![X]:((~creative(X)|humble(X))<=>(brave(X)&~patient(X))))&
((?[X]:(~calm(X)))=>(?[X]:(~funny(X))))&
((?[X]:(creative(X)))<=>(creative(john)))&
(![X]:((~calm(X)&kind(X))=>(~patient(X)<~>quiet(X))))&
((?[X]:((old(X)<~>wise(X))))=>(?[X]:((brave(X)&~happy(X)))))&
((humble(paul))=>((patient(lucy)&quiet(lucy))))&
((~patient(alice)<~>~rich(alice)))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:(kind(X)))&
((quiet(mary)|curious(mary))) | calm(john) | [] | null | 0 |
Everyone who is both humble and not rich is both quiet and not humble. If someone is both not calm and humble then lucy is not calm or generous and vice versa. Everyone who is patient or tall is happy or not old and vice versa. Everyone who is either not quiet or old is either curious or not kind. If john is not humble or not wise then someone is either not brave or not kind. Everyone who is kind or not generous is either curious or not tall and vice versa. If paul is both brave and humble then someone is funny or strong. If someone is both curious and wise then someone is not kind and vice versa. Everyone who is patient is quiet or strong and vice versa. Everyone who is not patient is both not rich and creative. If someone is either generous or strong then someone is both not quiet and not generous and vice versa. If susan is funny then susan is calm. If someone is not tall or generous then someone is not humble or kind and vice versa. If someone is both not patient and not funny then someone is both rich and curious. Everyone who is either kind or not strong is not patient. Everyone who is strong is happy. John is calm or not tall. Someone is both not creative and quiet. John is both not tall and humble. Mary is happy. Paul is both generous and not happy. Lucy is both not quiet and rich. Fred is not old or not brave. Someone is either not generous or not funny. | John is not rich. | contradiction | (![X]:((humble(X)&~rich(X))=>(quiet(X)&~humble(X))))&
((?[X]:((~calm(X)&humble(X))))<=>((~calm(lucy)|generous(lucy))))&
(![X]:((patient(X)|tall(X))<=>(happy(X)|~old(X))))&
(![X]:((~quiet(X)<~>old(X))=>(curious(X)<~>~kind(X))))&
(((~humble(john)|~wise(john)))=>(?[X]:((~brave(X)<~>~kind(X)))))&
(![X]:((kind(X)|~generous(X))<=>(curious(X)<~>~tall(X))))&
(((brave(paul)&humble(paul)))=>(?[X]:((funny(X)|strong(X)))))&
((?[X]:((curious(X)&wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:(patient(X)<=>(quiet(X)|strong(X))))&
(![X]:(~patient(X)=>(~rich(X)&creative(X))))&
((?[X]:((generous(X)<~>strong(X))))<=>(?[X]:((~quiet(X)&~generous(X)))))&
((funny(susan))=>(calm(susan)))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:((~humble(X)|kind(X)))))&
((?[X]:((~patient(X)&~funny(X))))=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((kind(X)<~>~strong(X))=>~patient(X)))&
(![X]:(strong(X)=>happy(X)))&
((calm(john)|~tall(john)))&
(?[X]:((~creative(X)&quiet(X))))&
((~tall(john)&humble(john)))&
(happy(mary))&
((generous(paul)&~happy(paul)))&
((~quiet(lucy)&rich(lucy)))&
((~old(fred)|~brave(fred)))&
(?[X]:((~generous(X)<~>~funny(X)))) | ~rich(john) | [
"p0",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1734496327437700042474761
% SZS output start Proof for 1734496327437700042474761
1. ! [X0] : ((~rich(X0) & humble(X0)) => (~humble(X0) & quiet(X0))) [input p0]
19. humble(john) & ~tall(john) [input p18]
25. ~rich(john) [input hypothesis]
30. ! [X0] : ((~humble(X0) & quiet(X0)) | (rich(X0) | ~humble(X0))) [ennf transformation 1]
31. ! [X0] : ((~humble(X0) & quiet(X0)) | rich(X0) | ~humble(X0)) [flattening 30]
83. ~humble(X0) | rich(X0) | ~humble(X0) [cnf transformation 31]
136. humble(john) [cnf transformation 19]
145. ~rich(john) [cnf transformation 25]
146. ~humble(X0) | rich(X0) [duplicate literal removal 83]
185. 9 <=> humble(john) [avatar definition]
187. humble(john) <- (9) [avatar component clause 185]
324. 9 [avatar split clause 136,185]
351. rich(john) <- (9) [resolution 146,187]
352. $false <- (9) [subsumption resolution 351,145]
353. ~9 [avatar contradiction clause 352]
354. $false [avatar sat refutation 324,353]
% SZS output end Proof for 1734496327437700042474761
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then someone is both not funny and not strong and vice versa.
If someone is either wise or generous then someone is either not tall or not humble.
Everyone who is both not curious and not old is not creative or humble and vice versa.
Everyone who is not strong is tall and vice versa.
If susan is generous then susan is wise and vice versa.
If john is both patient and humble then someone is either not strong or funny and vice versa.
Everyone who is not humble or not wise is both humble and not tall.
Everyone who is quiet or not funny is brave and vice versa.
Everyone who is not brave is both not brave and calm and vice versa.
If someone is not rich then someone is not strong and vice versa.
Everyone who is humble or not humble is both not brave and not strong and vice versa.
If alice is not creative or tall then alice is not happy or not tall.
If john is either humble or strong then john is either not creative or creative and vice versa.
Someone is patient or not humble.
Someone is either calm or not generous.
Lucy is not creative or calm.
Someone is patient or not strong.
Fred is funny.
Someone is either kind or brave. | Alice is not creative. | neutral | ((?[X]:(~funny(X)))<=>(?[X]:((~funny(X)&~strong(X)))))&
((?[X]:((wise(X)<~>generous(X))))=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((~curious(X)&~old(X))<=>(~creative(X)|humble(X))))&
(![X]:(~strong(X)<=>tall(X)))&
((generous(susan))<=>(wise(susan)))&
(((patient(john)&humble(john)))<=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((~humble(X)|~wise(X))=>(humble(X)&~tall(X))))&
(![X]:((quiet(X)|~funny(X))<=>brave(X)))&
(![X]:(~brave(X)<=>(~brave(X)&calm(X))))&
((?[X]:(~rich(X)))<=>(?[X]:(~strong(X))))&
(![X]:((humble(X)|~humble(X))<=>(~brave(X)&~strong(X))))&
(((~creative(alice)|tall(alice)))=>((~happy(alice)|~tall(alice))))&
(((humble(john)<~>strong(john)))<=>((~creative(john)<~>creative(john))))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((calm(X)<~>~generous(X))))&
((~creative(lucy)|calm(lucy)))&
(?[X]:((patient(X)|~strong(X))))&
(funny(fred))&
(?[X]:((kind(X)<~>brave(X)))) | ~creative(alice) | [] | null | 0 |
If mary is not wise then susan is not brave and vice versa. Everyone who is either not quiet or humble is both happy and kind and vice versa. If fred is both not calm and curious then alice is not kind and vice versa. Everyone who is tall is either calm or not humble. Everyone who is either not generous or curious is both not rich and not generous. Everyone who is either not kind or brave is both not patient and not happy and vice versa. Everyone who is not brave is both not kind and patient. Everyone who is curious or humble is not happy or funny and vice versa. If someone is not creative then someone is both not tall and not old. Everyone who is not funny is either not kind or not rich. If someone is not wise then fred is either tall or not quiet and vice versa. Everyone who is not humble is both not calm and not quiet. Everyone who is both happy and curious is not quiet or happy and vice versa. Everyone who is both not wise and not kind is not tall. Everyone who is wise is not old or not happy. John is rich or not tall. Someone is not curious or not strong. Fred is either humble or creative. | Alice is patient. | neutral | ((~wise(mary))<=>(~brave(susan)))&
(![X]:((~quiet(X)<~>humble(X))<=>(happy(X)&kind(X))))&
(((~calm(fred)&curious(fred)))<=>(~kind(alice)))&
(![X]:(tall(X)=>(calm(X)<~>~humble(X))))&
(![X]:((~generous(X)<~>curious(X))=>(~rich(X)&~generous(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(~patient(X)&~happy(X))))&
(![X]:(~brave(X)=>(~kind(X)&patient(X))))&
(![X]:((curious(X)|humble(X))<=>(~happy(X)|funny(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:(~funny(X)=>(~kind(X)<~>~rich(X))))&
((?[X]:(~wise(X)))<=>((tall(fred)<~>~quiet(fred))))&
(![X]:(~humble(X)=>(~calm(X)&~quiet(X))))&
(![X]:((happy(X)&curious(X))<=>(~quiet(X)|happy(X))))&
(![X]:((~wise(X)&~kind(X))=>~tall(X)))&
(![X]:(wise(X)=>(~old(X)|~happy(X))))&
((rich(john)|~tall(john)))&
(?[X]:((~curious(X)|~strong(X))))&
((humble(fred)<~>creative(fred))) | patient(alice) | [] | null | 0 |
If john is not rich or not creative then someone is both tall and not wise and vice versa. If someone is both not patient and not kind then john is both generous and not happy. If paul is not calm then susan is not patient or not quiet and vice versa. If mary is patient then lucy is not humble. If someone is either not patient or not kind then fred is both not creative and not old. Everyone who is both tall and curious is calm and vice versa. If someone is patient or not happy then someone is both generous and happy and vice versa. Everyone who is both strong and not generous is curious and vice versa. Everyone who is wise or humble is both not creative and happy and vice versa. Everyone who is either not rich or happy is kind or not generous and vice versa. Everyone who is not funny or calm is old or not old. If someone is both not humble and not funny then someone is not funny. Everyone who is wise is old or tall. If someone is creative then susan is not calm and vice versa. Everyone who is either rich or not wise is not generous and vice versa. Everyone who is not generous or happy is either not creative or rich. Someone is wise or old. Paul is both not creative and not curious. Someone is quiet or not funny. Someone is both not quiet and strong. Someone is both creative and not quiet. Someone is not tall or not old. Lucy is either strong or tall. Fred is both rich and not patient. | Paul is not funny. | neutral | (((~rich(john)|~creative(john)))<=>(?[X]:((tall(X)&~wise(X)))))&
((?[X]:((~patient(X)&~kind(X))))=>((generous(john)&~happy(john))))&
((~calm(paul))<=>((~patient(susan)|~quiet(susan))))&
((patient(mary))=>(~humble(lucy)))&
((?[X]:((~patient(X)<~>~kind(X))))=>((~creative(fred)&~old(fred))))&
(![X]:((tall(X)&curious(X))<=>calm(X)))&
((?[X]:((patient(X)|~happy(X))))<=>(?[X]:((generous(X)&happy(X)))))&
(![X]:((strong(X)&~generous(X))<=>curious(X)))&
(![X]:((wise(X)|humble(X))<=>(~creative(X)&happy(X))))&
(![X]:((~rich(X)<~>happy(X))<=>(kind(X)|~generous(X))))&
(![X]:((~funny(X)|calm(X))=>(old(X)|~old(X))))&
((?[X]:((~humble(X)&~funny(X))))=>(?[X]:(~funny(X))))&
(![X]:(wise(X)=>(old(X)|tall(X))))&
((?[X]:(creative(X)))<=>(~calm(susan)))&
(![X]:((rich(X)<~>~wise(X))<=>~generous(X)))&
(![X]:((~generous(X)|happy(X))=>(~creative(X)<~>rich(X))))&
(?[X]:((wise(X)|old(X))))&
((~creative(paul)&~curious(paul)))&
(?[X]:((quiet(X)|~funny(X))))&
(?[X]:((~quiet(X)&strong(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(?[X]:((~tall(X)|~old(X))))&
((strong(lucy)<~>tall(lucy)))&
((rich(fred)&~patient(fred))) | ~funny(paul) | [] | null | 0 |
If fred is both not curious and creative then john is both not rich and old.
Everyone who is either wise or not kind is either not happy or funny and vice versa.
Everyone who is either not humble or not calm is both creative and not creative.
Everyone who is not old or curious is both not brave and not patient.
If someone is both rich and not patient then someone is either not curious or generous and vice versa.
Everyone who is calm is both not creative and not generous.
If fred is old then paul is humble.
If paul is both not humble and not creative then someone is both generous and not old and vice versa.
Everyone who is not brave or not patient is either not happy or not tall.
If someone is rich or humble then fred is either not generous or not humble.
Everyone who is either not wise or old is both not patient and not curious and vice versa.
If john is kind then someone is rich.
If alice is old or not strong then someone is both not old and rich.
If paul is kind then someone is both calm and not patient.
Everyone who is kind is both not kind and not calm.
Everyone who is kind or quiet is patient.
John is brave or not humble.
Fred is either not happy or old.
Someone is funny.
Alice is not kind or tall.
Someone is both happy and not strong.
John is strong.
Someone is generous or humble.
Someone is either calm or happy. | Paul is kind. | contradiction | (((~curious(fred)&creative(fred)))=>((~rich(john)&old(john))))&
(![X]:((wise(X)<~>~kind(X))<=>(~happy(X)<~>funny(X))))&
(![X]:((~humble(X)<~>~calm(X))=>(creative(X)&~creative(X))))&
(![X]:((~old(X)|curious(X))=>(~brave(X)&~patient(X))))&
((?[X]:((rich(X)&~patient(X))))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:(calm(X)=>(~creative(X)&~generous(X))))&
((old(fred))=>(humble(paul)))&
(((~humble(paul)&~creative(paul)))<=>(?[X]:((generous(X)&~old(X)))))&
(![X]:((~brave(X)|~patient(X))=>(~happy(X)<~>~tall(X))))&
((?[X]:((rich(X)|humble(X))))=>((~generous(fred)<~>~humble(fred))))&
(![X]:((~wise(X)<~>old(X))<=>(~patient(X)&~curious(X))))&
((kind(john))=>(?[X]:(rich(X))))&
(((old(alice)|~strong(alice)))=>(?[X]:((~old(X)&rich(X)))))&
((kind(paul))=>(?[X]:((calm(X)&~patient(X)))))&
(![X]:(kind(X)=>(~kind(X)&~calm(X))))&
(![X]:((kind(X)|quiet(X))=>patient(X)))&
((brave(john)|~humble(john)))&
((~happy(fred)<~>old(fred)))&
(?[X]:(funny(X)))&
((~kind(alice)|tall(alice)))&
(?[X]:((happy(X)&~strong(X))))&
(strong(john))&
(?[X]:((generous(X)|humble(X))))&
(?[X]:((calm(X)<~>happy(X)))) | kind(paul) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1562773150087706800547048
% SZS output start Proof for 1562773150087706800547048
15. ! [X0] : (kind(X0) => (~calm(X0) & ~kind(X0))) [input p14]
25. kind(paul) [input hypothesis]
39. ! [X0] : ((~calm(X0) & ~kind(X0)) | ~kind(X0)) [ennf transformation 15]
125. ~kind(X0) | ~kind(X0) [cnf transformation 39]
139. kind(paul) [cnf transformation 25]
140. ~kind(X0) [duplicate literal removal 125]
317. $false [subsumption resolution 139,140]
% SZS output end Proof for 1562773150087706800547048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not wise is tall.
Everyone who is either not brave or not generous is old or not happy and vice versa.
Everyone who is both generous and not creative is either kind or not kind.
If someone is not generous or humble then alice is both not happy and creative.
If paul is either generous or not generous then lucy is either not old or not calm.
If someone is either not generous or not brave then susan is either not quiet or not patient and vice versa.
If john is either brave or not brave then someone is both not strong and not wise.
Everyone who is either generous or rich is either tall or brave and vice versa.
If someone is not tall then someone is kind or not creative.
If lucy is strong then mary is both tall and curious.
Everyone who is not wise is both not curious and not wise and vice versa.
Everyone who is not quiet is wise.
Everyone who is funny or old is both not creative and funny.
Everyone who is either calm or not brave is either calm or not old and vice versa.
Everyone who is not happy is not generous or not tall.
If mary is not patient then susan is either wise or not humble.
Someone is either not calm or creative.
Susan is either calm or funny.
Someone is not generous.
Someone is either happy or funny.
Someone is not patient or not curious.
Paul is not strong or not happy.
Mary is brave or not funny. | Susan is calm. | neutral | (![X]:((quiet(X)<~>~wise(X))=>tall(X)))&
(![X]:((~brave(X)<~>~generous(X))<=>(old(X)|~happy(X))))&
(![X]:((generous(X)&~creative(X))=>(kind(X)<~>~kind(X))))&
((?[X]:((~generous(X)|humble(X))))=>((~happy(alice)&creative(alice))))&
(((generous(paul)<~>~generous(paul)))=>((~old(lucy)<~>~calm(lucy))))&
((?[X]:((~generous(X)<~>~brave(X))))<=>((~quiet(susan)<~>~patient(susan))))&
(((brave(john)<~>~brave(john)))=>(?[X]:((~strong(X)&~wise(X)))))&
(![X]:((generous(X)<~>rich(X))<=>(tall(X)<~>brave(X))))&
((?[X]:(~tall(X)))=>(?[X]:((kind(X)|~creative(X)))))&
((strong(lucy))=>((tall(mary)&curious(mary))))&
(![X]:(~wise(X)<=>(~curious(X)&~wise(X))))&
(![X]:(~quiet(X)=>wise(X)))&
(![X]:((funny(X)|old(X))=>(~creative(X)&funny(X))))&
(![X]:((calm(X)<~>~brave(X))<=>(calm(X)<~>~old(X))))&
(![X]:(~happy(X)=>(~generous(X)|~tall(X))))&
((~patient(mary))=>((wise(susan)<~>~humble(susan))))&
(?[X]:((~calm(X)<~>creative(X))))&
((calm(susan)<~>funny(susan)))&
(?[X]:(~generous(X)))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~patient(X)|~curious(X))))&
((~strong(paul)|~happy(paul)))&
((brave(mary)|~funny(mary))) | calm(susan) | [] | null | 0 |
If someone is either funny or not creative then someone is either not old or humble and vice versa. If fred is either strong or not curious then paul is either not brave or wise and vice versa. If alice is either tall or quiet then someone is either kind or not kind and vice versa. If susan is both creative and not creative then someone is either rich or not calm. If john is not kind then john is not patient or not old. If someone is either not humble or not patient then someone is not creative and vice versa. If alice is tall or not strong then paul is both happy and creative and vice versa. If someone is either kind or humble then lucy is both not tall and kind. Everyone who is either quiet or kind is calm or not tall. Everyone who is both not happy and curious is either not kind or not rich. Everyone who is either not generous or strong is both patient and wise. Everyone who is old or not brave is both funny and not strong and vice versa. Everyone who is both not kind and creative is both not wise and not patient and vice versa. Everyone who is not tall or funny is both not humble and not brave. If someone is not tall or not patient then lucy is both not calm and old and vice versa. If john is calm or not kind then someone is old. Lucy is both not quiet and brave. Someone is not humble or not patient. Susan is happy. Someone is either strong or kind. Someone is either calm or kind. Someone is quiet. Mary is either creative or not strong. Mary is not strong or old. | Alice is not quiet. | entailment | ((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:((~old(X)<~>humble(X)))))&
(((strong(fred)<~>~curious(fred)))<=>((~brave(paul)<~>wise(paul))))&
(((tall(alice)<~>quiet(alice)))<=>(?[X]:((kind(X)<~>~kind(X)))))&
(((creative(susan)&~creative(susan)))=>(?[X]:((rich(X)<~>~calm(X)))))&
((~kind(john))=>((~patient(john)|~old(john))))&
((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:(~creative(X))))&
(((tall(alice)|~strong(alice)))<=>((happy(paul)&creative(paul))))&
((?[X]:((kind(X)<~>humble(X))))=>((~tall(lucy)&kind(lucy))))&
(![X]:((quiet(X)<~>kind(X))=>(calm(X)|~tall(X))))&
(![X]:((~happy(X)&curious(X))=>(~kind(X)<~>~rich(X))))&
(![X]:((~generous(X)<~>strong(X))=>(patient(X)&wise(X))))&
(![X]:((old(X)|~brave(X))<=>(funny(X)&~strong(X))))&
(![X]:((~kind(X)&creative(X))<=>(~wise(X)&~patient(X))))&
(![X]:((~tall(X)|funny(X))=>(~humble(X)&~brave(X))))&
((?[X]:((~tall(X)|~patient(X))))<=>((~calm(lucy)&old(lucy))))&
(((calm(john)|~kind(john)))=>(?[X]:(old(X))))&
((~quiet(lucy)&brave(lucy)))&
(?[X]:((~humble(X)|~patient(X))))&
(happy(susan))&
(?[X]:((strong(X)<~>kind(X))))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:(quiet(X)))&
((creative(mary)<~>~strong(mary)))&
((~strong(mary)|old(mary))) | ~quiet(alice) | [
"p2",
"p11",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 784514915230453263810267
% SZS output start Proof for 784514915230453263810267
3. (tall(alice) <~> quiet(alice)) <=> ? [X0] : (kind(X0) <~> ~kind(X0)) [input p2]
12. ! [X0] : ((~brave(X0) | old(X0)) <=> (~strong(X0) & funny(X0))) [input p11]
14. ! [X0] : ((funny(X0) | ~tall(X0)) => (~brave(X0) & ~humble(X0))) [input p13]
15. ? [X0] : (~patient(X0) | ~tall(X0)) <=> (old(lucy) & ~calm(lucy)) [input p14]
17. brave(lucy) & ~quiet(lucy) [input p16]
25. quiet(alice) [input hypothesis]
38. ! [X0] : ((~brave(X0) & ~humble(X0)) | (~funny(X0) & tall(X0))) [ennf transformation 14]
46. (((~quiet(alice) | ~tall(alice)) & (quiet(alice) | tall(alice))) | ! [X0] : ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (? [X0] : ((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((tall(alice) | ~quiet(alice)) & (quiet(alice) | ~tall(alice)))) [nnf transformation 3]
47. (((~quiet(alice) | ~tall(alice)) & (quiet(alice) | tall(alice))) | ! [X0] : ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (? [X1] : ((kind(X1) | ~kind(X1)) & (~kind(X1) | kind(X1))) | ((tall(alice) | ~quiet(alice)) & (quiet(alice) | ~tall(alice)))) [rectify 46]
48. ? [X1] : ((kind(X1) | ~kind(X1)) & (~kind(X1) | kind(X1))) => ((kind(sK2) | ~kind(sK2)) & (~kind(sK2) | kind(sK2))) [choice axiom]
49. (((~quiet(alice) | ~tall(alice)) & (quiet(alice) | tall(alice))) | ! [X0] : ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(sK2) | ~kind(sK2)) & (~kind(sK2) | kind(sK2))) | ((tall(alice) | ~quiet(alice)) & (quiet(alice) | ~tall(alice)))) [skolemisation 47,48]
64. ! [X0] : (((~brave(X0) | old(X0)) | (strong(X0) | ~funny(X0))) & ((~strong(X0) & funny(X0)) | (brave(X0) & ~old(X0)))) [nnf transformation 12]
65. ! [X0] : ((~brave(X0) | old(X0) | strong(X0) | ~funny(X0)) & ((~strong(X0) & funny(X0)) | (brave(X0) & ~old(X0)))) [flattening 64]
68. (? [X0] : (~patient(X0) | ~tall(X0)) | (~old(lucy) | calm(lucy))) & ((old(lucy) & ~calm(lucy)) | ! [X0] : (patient(X0) & tall(X0))) [nnf transformation 15]
69. (? [X0] : (~patient(X0) | ~tall(X0)) | ~old(lucy) | calm(lucy)) & ((old(lucy) & ~calm(lucy)) | ! [X0] : (patient(X0) & tall(X0))) [flattening 68]
70. (? [X0] : (~patient(X0) | ~tall(X0)) | ~old(lucy) | calm(lucy)) & ((old(lucy) & ~calm(lucy)) | ! [X1] : (patient(X1) & tall(X1))) [rectify 69]
71. ? [X0] : (~patient(X0) | ~tall(X0)) => (~patient(sK6) | ~tall(sK6)) [choice axiom]
72. ((~patient(sK6) | ~tall(sK6)) | ~old(lucy) | calm(lucy)) & ((old(lucy) & ~calm(lucy)) | ! [X1] : (patient(X1) & tall(X1))) [skolemisation 70,71]
108. ~quiet(alice) | ~tall(alice) | ~kind(X0) | ~kind(X0) [cnf transformation 49]
109. ~quiet(alice) | ~tall(alice) | kind(X0) | kind(X0) [cnf transformation 49]
134. ~old(X0) | funny(X0) [cnf transformation 65]
146. ~brave(X0) | ~funny(X0) [cnf transformation 38]
149. old(lucy) | tall(X1) [cnf transformation 72]
155. brave(lucy) [cnf transformation 17]
166. quiet(alice) [cnf transformation 25]
169. ~quiet(alice) | ~tall(alice) | ~kind(X0) [duplicate literal removal 108]
170. ~quiet(alice) | ~tall(alice) | kind(X0) [duplicate literal removal 109]
232. 13 <=> ! [X0] : kind(X0) [avatar definition]
233. kind(X0) <- (13) [avatar component clause 232]
235. 14 <=> tall(alice) [avatar definition]
237. ~tall(alice) <- (~14) [avatar component clause 235]
239. 15 <=> quiet(alice) [avatar definition]
242. 13 | ~14 | ~15 [avatar split clause 170,239,235,232]
244. 16 <=> ! [X0] : ~kind(X0) [avatar definition]
245. ~kind(X0) <- (16) [avatar component clause 244]
246. 16 | ~14 | ~15 [avatar split clause 169,239,235,244]
327. 34 <=> old(lucy) [avatar definition]
328. old(lucy) <- (34) [avatar component clause 327]
344. 38 <=> ! [X1] : tall(X1) [avatar definition]
345. tall(X1) <- (38) [avatar component clause 344]
346. 38 | 34 [avatar split clause 149,327,344]
400. 15 [avatar split clause 166,239]
403. funny(lucy) <- (34) [resolution 134,328]
415. ~funny(lucy) [resolution 146,155]
418. $false <- (34) [subsumption resolution 415,403]
419. ~34 [avatar contradiction clause 418]
426. $false <- (~14, 38) [resolution 345,237]
427. 14 | ~38 [avatar contradiction clause 426]
428. $false <- (13, 16) [subsumption resolution 233,245]
429. ~13 | ~16 [avatar contradiction clause 428]
430. $false [avatar sat refutation 242,246,346,400,419,427,429]
% SZS output end Proof for 784514915230453263810267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not quiet is old.
If paul is brave or generous then lucy is either not funny or wise.
If paul is both funny and tall then paul is either brave or happy and vice versa.
Everyone who is not funny or creative is not rich or not brave.
Everyone who is either not kind or calm is both not creative and old and vice versa.
If lucy is calm then paul is not kind or not wise and vice versa.
Everyone who is generous is calm.
If someone is patient or curious then susan is both generous and not patient.
If susan is not calm or creative then fred is not patient or not humble and vice versa.
If someone is strong then someone is patient.
Everyone who is not wise is both not creative and tall and vice versa.
Everyone who is either not rich or kind is either creative or not brave.
If susan is either not rich or not old then alice is wise and vice versa.
Everyone who is not wise is not curious or not rich.
Everyone who is not curious is not patient or generous.
Everyone who is not rich or brave is both curious and patient and vice versa.
Someone is not rich or tall.
Alice is either not funny or not strong.
Lucy is either funny or old.
Mary is not curious.
Someone is either tall or not wise.
Alice is not old or quiet.
Alice is curious. | Lucy is creative. | neutral | (![X]:((~calm(X)<~>~quiet(X))=>old(X)))&
(((brave(paul)|generous(paul)))=>((~funny(lucy)<~>wise(lucy))))&
(((funny(paul)&tall(paul)))<=>((brave(paul)<~>happy(paul))))&
(![X]:((~funny(X)|creative(X))=>(~rich(X)|~brave(X))))&
(![X]:((~kind(X)<~>calm(X))<=>(~creative(X)&old(X))))&
((calm(lucy))<=>((~kind(paul)|~wise(paul))))&
(![X]:(generous(X)=>calm(X)))&
((?[X]:((patient(X)|curious(X))))=>((generous(susan)&~patient(susan))))&
(((~calm(susan)|creative(susan)))<=>((~patient(fred)|~humble(fred))))&
((?[X]:(strong(X)))=>(?[X]:(patient(X))))&
(![X]:(~wise(X)<=>(~creative(X)&tall(X))))&
(![X]:((~rich(X)<~>kind(X))=>(creative(X)<~>~brave(X))))&
(((~rich(susan)<~>~old(susan)))<=>(wise(alice)))&
(![X]:(~wise(X)=>(~curious(X)|~rich(X))))&
(![X]:(~curious(X)=>(~patient(X)|generous(X))))&
(![X]:((~rich(X)|brave(X))<=>(curious(X)&patient(X))))&
(?[X]:((~rich(X)|tall(X))))&
((~funny(alice)<~>~strong(alice)))&
((funny(lucy)<~>old(lucy)))&
(~curious(mary))&
(?[X]:((tall(X)<~>~wise(X))))&
((~old(alice)|quiet(alice)))&
(curious(alice)) | creative(lucy) | [] | null | 0 |
If someone is both happy and not generous then someone is strong or not wise and vice versa.
If fred is tall or not patient then lucy is not strong or creative.
If alice is tall or not patient then someone is both humble and patient.
Everyone who is either not wise or not creative is either not funny or not tall.
If someone is either not tall or not humble then someone is either not kind or funny.
If someone is happy or brave then someone is old or funny and vice versa.
Everyone who is curious is not brave or strong.
If someone is not wise or funny then mary is both old and tall and vice versa.
If someone is not old then paul is both not generous and tall.
If someone is rich or creative then paul is old and vice versa.
Everyone who is wise or strong is not old or not wise.
Everyone who is either funny or not patient is not kind or not old.
Everyone who is happy or old is both brave and wise.
Everyone who is generous or not kind is curious.
If someone is either not patient or kind then someone is wise or not happy.
Someone is wise.
Paul is not strong or strong. | Lucy is old. | contradiction | ((?[X]:((happy(X)&~generous(X))))<=>(?[X]:((strong(X)|~wise(X)))))&
(((tall(fred)|~patient(fred)))=>((~strong(lucy)|creative(lucy))))&
(((tall(alice)|~patient(alice)))=>(?[X]:((humble(X)&patient(X)))))&
(![X]:((~wise(X)<~>~creative(X))=>(~funny(X)<~>~tall(X))))&
((?[X]:((~tall(X)<~>~humble(X))))=>(?[X]:((~kind(X)<~>funny(X)))))&
((?[X]:((happy(X)|brave(X))))<=>(?[X]:((old(X)|funny(X)))))&
(![X]:(curious(X)=>(~brave(X)|strong(X))))&
((?[X]:((~wise(X)|funny(X))))<=>((old(mary)&tall(mary))))&
((?[X]:(~old(X)))=>((~generous(paul)&tall(paul))))&
((?[X]:((rich(X)|creative(X))))<=>(old(paul)))&
(![X]:((wise(X)|strong(X))=>(~old(X)|~wise(X))))&
(![X]:((funny(X)<~>~patient(X))=>(~kind(X)|~old(X))))&
(![X]:((happy(X)|old(X))=>(brave(X)&wise(X))))&
(![X]:((generous(X)|~kind(X))=>curious(X)))&
((?[X]:((~patient(X)<~>kind(X))))=>(?[X]:((wise(X)|~happy(X)))))&
(?[X]:(wise(X)))&
((~strong(paul)|strong(paul))) | old(lucy) | [
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 862614847605357500974413
% SZS output start Proof for 862614847605357500974413
11. ! [X0] : ((strong(X0) | wise(X0)) => (~wise(X0) | ~old(X0))) [input p10]
13. ! [X0] : ((old(X0) | happy(X0)) => (wise(X0) & brave(X0))) [input p12]
18. old(lucy) [input hypothesis]
31. ! [X0] : ((~wise(X0) | ~old(X0)) | (~strong(X0) & ~wise(X0))) [ennf transformation 11]
32. ! [X0] : (~wise(X0) | ~old(X0) | (~strong(X0) & ~wise(X0))) [flattening 31]
35. ! [X0] : ((wise(X0) & brave(X0)) | (~old(X0) & ~happy(X0))) [ennf transformation 13]
105. ~wise(X0) | ~old(X0) | ~wise(X0) [cnf transformation 32]
112. wise(X0) | ~old(X0) [cnf transformation 35]
119. old(lucy) [cnf transformation 18]
120. ~wise(X0) | ~old(X0) [duplicate literal removal 105]
220. 23 <=> ! [X1] : ~old(X1) [avatar definition]
221. ~old(X1) <- (23) [avatar component clause 220]
294. ~old(X0) [subsumption resolution 112,120]
295. 23 [avatar split clause 294,220]
306. $false <- (23) [resolution 221,119]
307. ~23 [avatar contradiction clause 306]
308. $false [avatar sat refutation 295,307]
% SZS output end Proof for 862614847605357500974413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative is both old and not rich.
Everyone who is either funny or not humble is not humble.
Everyone who is rich is both patient and wise.
Everyone who is funny or not funny is either not strong or rich.
If someone is both not patient and not happy then someone is curious or happy and vice versa.
Everyone who is either tall or not creative is either not kind or not old.
Everyone who is either not humble or not kind is either kind or not happy and vice versa.
Everyone who is both curious and not wise is either calm or old.
Everyone who is tall is either not rich or wise.
If someone is either not brave or not curious then mary is strong and vice versa.
If someone is not curious then susan is not wise or creative.
Everyone who is not rich or not wise is not funny.
Everyone who is patient is either not strong or not wise and vice versa.
Everyone who is both not old and happy is patient.
Everyone who is both happy and not tall is not calm or not quiet and vice versa.
Alice is kind.
Mary is either generous or creative.
John is either not creative or patient.
Someone is not funny or not strong.
John is calm.
Mary is not strong or not funny.
Someone is both humble and not kind.
Alice is either not rich or old. | John is rich. | contradiction | (![X]:(~creative(X)=>(old(X)&~rich(X))))&
(![X]:((funny(X)<~>~humble(X))=>~humble(X)))&
(![X]:(rich(X)=>(patient(X)&wise(X))))&
(![X]:((funny(X)|~funny(X))=>(~strong(X)<~>rich(X))))&
((?[X]:((~patient(X)&~happy(X))))<=>(?[X]:((curious(X)|happy(X)))))&
(![X]:((tall(X)<~>~creative(X))=>(~kind(X)<~>~old(X))))&
(![X]:((~humble(X)<~>~kind(X))<=>(kind(X)<~>~happy(X))))&
(![X]:((curious(X)&~wise(X))=>(calm(X)<~>old(X))))&
(![X]:(tall(X)=>(~rich(X)<~>wise(X))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>(strong(mary)))&
((?[X]:(~curious(X)))=>((~wise(susan)|creative(susan))))&
(![X]:((~rich(X)|~wise(X))=>~funny(X)))&
(![X]:(patient(X)<=>(~strong(X)<~>~wise(X))))&
(![X]:((~old(X)&happy(X))=>patient(X)))&
(![X]:((happy(X)&~tall(X))<=>(~calm(X)|~quiet(X))))&
(kind(alice))&
((generous(mary)<~>creative(mary)))&
((~creative(john)<~>patient(john)))&
(?[X]:((~funny(X)|~strong(X))))&
(calm(john))&
((~strong(mary)|~funny(mary)))&
(?[X]:((humble(X)&~kind(X))))&
((~rich(alice)<~>old(alice))) | rich(john) | [
"p0",
"p2",
"p3",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2878433344621419271624063
% SZS output start Proof for 2878433344621419271624063
1. ! [X0] : (~creative(X0) => (~rich(X0) & old(X0))) [input p0]
3. ! [X0] : (rich(X0) => (wise(X0) & patient(X0))) [input p2]
4. ! [X0] : ((~funny(X0) | funny(X0)) => (~strong(X0) <~> rich(X0))) [input p3]
13. ! [X0] : (patient(X0) <=> (~strong(X0) <~> ~wise(X0))) [input p12]
18. ~creative(john) <~> patient(john) [input p17]
24. rich(john) [input hypothesis]
26. ! [X0] : ((~rich(X0) & old(X0)) | creative(X0)) [ennf transformation 1]
28. ! [X0] : ((wise(X0) & patient(X0)) | ~rich(X0)) [ennf transformation 3]
29. ! [X0] : ((~strong(X0) <~> rich(X0)) | (funny(X0) & ~funny(X0))) [ennf transformation 4]
40. ! [X0] : (((~rich(X0) | strong(X0)) & (rich(X0) | ~strong(X0))) | (funny(X0) & ~funny(X0))) [nnf transformation 29]
54. ! [X0] : ((patient(X0) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) & (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | ~patient(X0))) [nnf transformation 13]
58. (~patient(john) | creative(john)) & (patient(john) | ~creative(john)) [nnf transformation 18]
65. ~rich(X0) | creative(X0) [cnf transformation 26]
69. ~rich(X0) | wise(X0) [cnf transformation 28]
72. ~rich(X0) | strong(X0) | ~funny(X0) [cnf transformation 40]
73. ~rich(X0) | strong(X0) | funny(X0) [cnf transformation 40]
102. ~strong(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 54]
115. patient(john) | ~creative(john) [cnf transformation 58]
124. rich(john) [cnf transformation 24]
130. ~rich(X0) | strong(X0) [subsumption resolution 72,73]
211. 18 <=> creative(john) [avatar definition]
215. 19 <=> patient(john) [avatar definition]
216. patient(john) <- (19) [avatar component clause 215]
219. ~18 | 19 [avatar split clause 115,215,211]
245. creative(john) [resolution 65,124]
248. 18 [avatar split clause 245,211]
250. wise(john) [resolution 69,124]
252. strong(john) [resolution 130,124]
276. ~wise(john) | ~patient(john) [resolution 102,252]
277. ~patient(john) [subsumption resolution 276,250]
278. $false <- (19) [subsumption resolution 277,216]
279. ~19 [avatar contradiction clause 278]
280. $false [avatar sat refutation 219,248,279]
% SZS output end Proof for 2878433344621419271624063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is brave then someone is both not generous and quiet.
Everyone who is both not creative and old is both generous and not creative and vice versa.
Everyone who is patient is old or not kind and vice versa.
If paul is either not quiet or not wise then someone is quiet or not old and vice versa.
Everyone who is calm is both not old and wise and vice versa.
If paul is not wise then someone is not strong or patient.
If john is both calm and rich then someone is either not quiet or happy and vice versa.
Everyone who is either not humble or not strong is either happy or not happy.
Everyone who is both tall and not wise is both curious and not patient.
If someone is quiet or not calm then someone is both not strong and not old.
If someone is either not calm or not tall then someone is generous.
If someone is humble or generous then someone is curious or not kind.
If someone is funny then susan is either not happy or strong and vice versa.
Everyone who is kind or calm is either not happy or brave and vice versa.
If someone is both not brave and quiet then someone is kind or brave and vice versa.
Everyone who is both kind and not happy is kind or patient and vice versa.
Mary is not calm.
Someone is either not funny or not quiet.
Mary is both not generous and not wise.
John is both wise and not calm.
Someone is either creative or not patient. | Paul is kind. | entailment | ((brave(mary))=>(?[X]:((~generous(X)&quiet(X)))))&
(![X]:((~creative(X)&old(X))<=>(generous(X)&~creative(X))))&
(![X]:(patient(X)<=>(old(X)|~kind(X))))&
(((~quiet(paul)<~>~wise(paul)))<=>(?[X]:((quiet(X)|~old(X)))))&
(![X]:(calm(X)<=>(~old(X)&wise(X))))&
((~wise(paul))=>(?[X]:((~strong(X)|patient(X)))))&
(((calm(john)&rich(john)))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((~humble(X)<~>~strong(X))=>(happy(X)<~>~happy(X))))&
(![X]:((tall(X)&~wise(X))=>(curious(X)&~patient(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(?[X]:((~strong(X)&~old(X)))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(?[X]:(generous(X))))&
((?[X]:((humble(X)|generous(X))))=>(?[X]:((curious(X)|~kind(X)))))&
((?[X]:(funny(X)))<=>((~happy(susan)<~>strong(susan))))&
(![X]:((kind(X)|calm(X))<=>(~happy(X)<~>brave(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((kind(X)&~happy(X))<=>(kind(X)|patient(X))))&
(~calm(mary))&
(?[X]:((~funny(X)<~>~quiet(X))))&
((~generous(mary)&~wise(mary)))&
((wise(john)&~calm(john)))&
(?[X]:((creative(X)<~>~patient(X)))) | kind(paul) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 155127514099987356045008
% SZS output start Proof for 155127514099987356045008
3. ! [X0] : (patient(X0) <=> (~kind(X0) | old(X0))) [input p2]
16. ! [X0] : ((~happy(X0) & kind(X0)) <=> (patient(X0) | kind(X0))) [input p15]
22. ~kind(paul) [input hypothesis]
40. ! [X0] : ((patient(X0) | (kind(X0) & ~old(X0))) & ((~kind(X0) | old(X0)) | ~patient(X0))) [nnf transformation 3]
41. ! [X0] : ((patient(X0) | (kind(X0) & ~old(X0))) & (~kind(X0) | old(X0) | ~patient(X0))) [flattening 40]
74. ! [X0] : (((~happy(X0) & kind(X0)) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | (happy(X0) | ~kind(X0)))) [nnf transformation 16]
75. ! [X0] : (((~happy(X0) & kind(X0)) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | happy(X0) | ~kind(X0))) [flattening 74]
90. patient(X0) | kind(X0) [cnf transformation 41]
135. kind(X0) | ~patient(X0) [cnf transformation 75]
147. ~kind(paul) [cnf transformation 22]
303. kind(X0) [subsumption resolution 135,90]
325. $false [subsumption resolution 147,303]
% SZS output end Proof for 155127514099987356045008
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either old or curious then alice is both patient and not tall and vice versa.
If alice is both not strong and not old then someone is either rich or wise.
Everyone who is both brave and not rich is calm and vice versa.
If someone is funny then mary is both happy and calm.
Everyone who is either not wise or not curious is both not quiet and humble.
Everyone who is either not tall or not strong is not happy.
If someone is not curious then someone is rich and vice versa.
Everyone who is not brave or patient is funny and vice versa.
If someone is not wise or not curious then susan is old or patient and vice versa.
If paul is both not calm and rich then lucy is both rich and calm.
Everyone who is not strong or humble is not creative or not funny.
Everyone who is not rich or humble is both patient and not tall.
If someone is both not kind and rich then paul is creative and vice versa.
Everyone who is tall is either calm or not happy.
If fred is either old or not patient then fred is not wise and vice versa.
Someone is kind.
Someone is not calm.
Someone is not happy or generous.
John is creative.
Susan is both not funny and not strong.
Alice is not funny or kind. | Paul is not strong. | neutral | (((old(lucy)<~>curious(lucy)))<=>((patient(alice)&~tall(alice))))&
(((~strong(alice)&~old(alice)))=>(?[X]:((rich(X)<~>wise(X)))))&
(![X]:((brave(X)&~rich(X))<=>calm(X)))&
((?[X]:(funny(X)))=>((happy(mary)&calm(mary))))&
(![X]:((~wise(X)<~>~curious(X))=>(~quiet(X)&humble(X))))&
(![X]:((~tall(X)<~>~strong(X))=>~happy(X)))&
((?[X]:(~curious(X)))<=>(?[X]:(rich(X))))&
(![X]:((~brave(X)|patient(X))<=>funny(X)))&
((?[X]:((~wise(X)|~curious(X))))<=>((old(susan)|patient(susan))))&
(((~calm(paul)&rich(paul)))=>((rich(lucy)&calm(lucy))))&
(![X]:((~strong(X)|humble(X))=>(~creative(X)|~funny(X))))&
(![X]:((~rich(X)|humble(X))=>(patient(X)&~tall(X))))&
((?[X]:((~kind(X)&rich(X))))<=>(creative(paul)))&
(![X]:(tall(X)=>(calm(X)<~>~happy(X))))&
(((old(fred)<~>~patient(fred)))<=>(~wise(fred)))&
(?[X]:(kind(X)))&
(?[X]:(~calm(X)))&
(?[X]:((~happy(X)|generous(X))))&
(creative(john))&
((~funny(susan)&~strong(susan)))&
((~funny(alice)|kind(alice))) | ~strong(paul) | [] | null | 0 |
If paul is generous or old then paul is not wise or brave and vice versa. If mary is either not kind or not tall then someone is both not patient and not brave and vice versa. If mary is either not funny or tall then alice is both not humble and not tall and vice versa. Everyone who is not kind is both not funny and not creative and vice versa. If someone is both happy and not rich then someone is not curious. If alice is either not rich or not curious then susan is not creative. Everyone who is quiet or not funny is both not generous and not funny and vice versa. Everyone who is either not curious or rich is old. If paul is not brave or not strong then fred is not brave or not happy and vice versa. If someone is both old and quiet then someone is kind or tall and vice versa. If paul is either funny or curious then fred is both kind and not happy. Everyone who is both quiet and kind is both humble and not generous. If alice is not wise or not curious then john is not creative or not brave and vice versa. If someone is both calm and not patient then someone is either not generous or not wise. If mary is either creative or not calm then lucy is not funny or not wise and vice versa. If someone is not creative then susan is not curious or not wise. Someone is not strong. John is both not humble and not curious. Paul is not funny. Alice is either calm or curious. Lucy is not strong or not wise. Someone is humble. Lucy is either not humble or not happy. Susan is not patient. | Alice is rich. | neutral | (((generous(paul)|old(paul)))<=>((~wise(paul)|brave(paul))))&
(((~kind(mary)<~>~tall(mary)))<=>(?[X]:((~patient(X)&~brave(X)))))&
(((~funny(mary)<~>tall(mary)))<=>((~humble(alice)&~tall(alice))))&
(![X]:(~kind(X)<=>(~funny(X)&~creative(X))))&
((?[X]:((happy(X)&~rich(X))))=>(?[X]:(~curious(X))))&
(((~rich(alice)<~>~curious(alice)))=>(~creative(susan)))&
(![X]:((quiet(X)|~funny(X))<=>(~generous(X)&~funny(X))))&
(![X]:((~curious(X)<~>rich(X))=>old(X)))&
(((~brave(paul)|~strong(paul)))<=>((~brave(fred)|~happy(fred))))&
((?[X]:((old(X)&quiet(X))))<=>(?[X]:((kind(X)|tall(X)))))&
(((funny(paul)<~>curious(paul)))=>((kind(fred)&~happy(fred))))&
(![X]:((quiet(X)&kind(X))=>(humble(X)&~generous(X))))&
(((~wise(alice)|~curious(alice)))<=>((~creative(john)|~brave(john))))&
((?[X]:((calm(X)&~patient(X))))=>(?[X]:((~generous(X)<~>~wise(X)))))&
(((creative(mary)<~>~calm(mary)))<=>((~funny(lucy)|~wise(lucy))))&
((?[X]:(~creative(X)))=>((~curious(susan)|~wise(susan))))&
(?[X]:(~strong(X)))&
((~humble(john)&~curious(john)))&
(~funny(paul))&
((calm(alice)<~>curious(alice)))&
((~strong(lucy)|~wise(lucy)))&
(?[X]:(humble(X)))&
((~humble(lucy)<~>~happy(lucy)))&
(~patient(susan)) | rich(alice) | [] | null | 0 |
Everyone who is not curious or patient is either not brave or wise.
Everyone who is brave or wise is not wise.
If someone is quiet or rich then someone is not calm.
If someone is not tall then someone is not creative or not old.
If paul is either not quiet or not calm then someone is both rich and creative.
Everyone who is calm is either not quiet or not happy.
If mary is either tall or strong then lucy is both not kind and not wise and vice versa.
Everyone who is happy or creative is both not brave and wise.
Everyone who is both humble and wise is both strong and brave and vice versa.
Everyone who is not brave or happy is either not patient or brave.
If fred is not quiet or old then someone is either not funny or not curious.
If someone is either funny or creative then john is both not curious and creative and vice versa.
If susan is kind then someone is not generous or kind.
If someone is either quiet or brave then someone is both curious and wise and vice versa.
Everyone who is not creative or humble is both strong and not tall and vice versa.
Fred is not kind or not tall.
Paul is either patient or strong.
Someone is not creative. | Mary is quiet. | contradiction | (![X]:((~curious(X)|patient(X))=>(~brave(X)<~>wise(X))))&
(![X]:((brave(X)|wise(X))=>~wise(X)))&
((?[X]:((quiet(X)|rich(X))))=>(?[X]:(~calm(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~creative(X)|~old(X)))))&
(((~quiet(paul)<~>~calm(paul)))=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(calm(X)=>(~quiet(X)<~>~happy(X))))&
(((tall(mary)<~>strong(mary)))<=>((~kind(lucy)&~wise(lucy))))&
(![X]:((happy(X)|creative(X))=>(~brave(X)&wise(X))))&
(![X]:((humble(X)&wise(X))<=>(strong(X)&brave(X))))&
(![X]:((~brave(X)|happy(X))=>(~patient(X)<~>brave(X))))&
(((~quiet(fred)|old(fred)))=>(?[X]:((~funny(X)<~>~curious(X)))))&
((?[X]:((funny(X)<~>creative(X))))<=>((~curious(john)&creative(john))))&
((kind(susan))=>(?[X]:((~generous(X)|kind(X)))))&
((?[X]:((quiet(X)<~>brave(X))))<=>(?[X]:((curious(X)&wise(X)))))&
(![X]:((~creative(X)|humble(X))<=>(strong(X)&~tall(X))))&
((~kind(fred)|~tall(fred)))&
((patient(paul)<~>strong(paul)))&
(?[X]:(~creative(X))) | quiet(mary) | [
"p1",
"p7",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 384164533070662160227349
% SZS output start Proof for 384164533070662160227349
2. ! [X0] : ((wise(X0) | brave(X0)) => ~wise(X0)) [input p1]
8. ! [X0] : ((creative(X0) | happy(X0)) => (wise(X0) & ~brave(X0))) [input p7]
9. ! [X0] : ((wise(X0) & humble(X0)) <=> (brave(X0) & strong(X0))) [input p8]
14. ? [X0] : (quiet(X0) <~> brave(X0)) <=> ? [X0] : (wise(X0) & curious(X0)) [input p13]
15. ! [X0] : ((humble(X0) | ~creative(X0)) <=> (~tall(X0) & strong(X0))) [input p14]
19. quiet(mary) [input hypothesis]
22. ? [X0] : (quiet(X0) <~> brave(X0)) <=> ? [X1] : (wise(X1) & curious(X1)) [rectify 14]
27. ! [X0] : (~wise(X0) | (~wise(X0) & ~brave(X0))) [ennf transformation 2]
31. ! [X0] : ((wise(X0) & ~brave(X0)) | (~creative(X0) & ~happy(X0))) [ennf transformation 8]
44. ! [X0] : (((wise(X0) & humble(X0)) | (~brave(X0) | ~strong(X0))) & ((brave(X0) & strong(X0)) | (~wise(X0) | ~humble(X0)))) [nnf transformation 9]
45. ! [X0] : (((wise(X0) & humble(X0)) | ~brave(X0) | ~strong(X0)) & ((brave(X0) & strong(X0)) | ~wise(X0) | ~humble(X0))) [flattening 44]
55. (? [X0] : ((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ! [X1] : (~wise(X1) | ~curious(X1))) & (? [X1] : (wise(X1) & curious(X1)) | ! [X0] : ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) [nnf transformation 22]
56. (? [X0] : ((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ! [X1] : (~wise(X1) | ~curious(X1))) & (? [X2] : (wise(X2) & curious(X2)) | ! [X3] : ((quiet(X3) | ~brave(X3)) & (brave(X3) | ~quiet(X3)))) [rectify 55]
57. ? [X0] : ((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) => ((~brave(sK4) | ~quiet(sK4)) & (brave(sK4) | quiet(sK4))) [choice axiom]
58. ? [X2] : (wise(X2) & curious(X2)) => (wise(sK5) & curious(sK5)) [choice axiom]
59. (((~brave(sK4) | ~quiet(sK4)) & (brave(sK4) | quiet(sK4))) | ! [X1] : (~wise(X1) | ~curious(X1))) & ((wise(sK5) & curious(sK5)) | ! [X3] : ((quiet(X3) | ~brave(X3)) & (brave(X3) | ~quiet(X3)))) [skolemisation 56,58,57]
60. ! [X0] : (((humble(X0) | ~creative(X0)) | (tall(X0) | ~strong(X0))) & ((~tall(X0) & strong(X0)) | (~humble(X0) & creative(X0)))) [nnf transformation 15]
61. ! [X0] : ((humble(X0) | ~creative(X0) | tall(X0) | ~strong(X0)) & ((~tall(X0) & strong(X0)) | (~humble(X0) & creative(X0)))) [flattening 60]
70. ~wise(X0) | ~wise(X0) [cnf transformation 27]
88. wise(X0) | ~creative(X0) [cnf transformation 31]
92. wise(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 45]
107. wise(sK5) | brave(X3) | ~quiet(X3) [cnf transformation 59]
111. strong(X0) | creative(X0) [cnf transformation 61]
120. quiet(mary) [cnf transformation 19]
122. ~wise(X0) [duplicate literal removal 70]
173. ~creative(X0) [subsumption resolution 88,122]
175. ~strong(X0) | ~brave(X0) [subsumption resolution 92,122]
193. ~quiet(X3) | brave(X3) [subsumption resolution 107,122]
195. strong(X0) [subsumption resolution 111,173]
199. ~brave(X0) [resolution 175,195]
200. brave(mary) [resolution 193,120]
202. $false [subsumption resolution 200,199]
% SZS output end Proof for 384164533070662160227349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or tall is brave and vice versa.
If lucy is both not calm and calm then someone is humble and vice versa.
Everyone who is calm is not tall or not wise and vice versa.
Everyone who is both happy and not creative is either not patient or old and vice versa.
Everyone who is quiet is calm.
Everyone who is both calm and not quiet is both not generous and patient and vice versa.
Everyone who is generous is either rich or humble.
If someone is either curious or calm then lucy is strong or not brave and vice versa.
Everyone who is both quiet and not happy is happy or old.
Everyone who is not patient is either humble or not curious and vice versa.
Everyone who is both not quiet and old is both not strong and not rich.
If susan is both brave and rich then fred is both rich and not wise and vice versa.
Everyone who is either tall or not generous is both not old and patient.
If someone is calm or not generous then susan is old or humble.
Everyone who is both wise and not old is either strong or not curious.
Everyone who is not creative or patient is not calm.
John is not tall or strong.
Susan is funny or not brave.
Mary is old.
Mary is either patient or not wise.
Mary is not calm or not rich.
Someone is either calm or not calm.
Susan is not brave or creative. | Mary is not rich. | entailment | (![X]:((creative(X)|tall(X))<=>brave(X)))&
(((~calm(lucy)&calm(lucy)))<=>(?[X]:(humble(X))))&
(![X]:(calm(X)<=>(~tall(X)|~wise(X))))&
(![X]:((happy(X)&~creative(X))<=>(~patient(X)<~>old(X))))&
(![X]:(quiet(X)=>calm(X)))&
(![X]:((calm(X)&~quiet(X))<=>(~generous(X)&patient(X))))&
(![X]:(generous(X)=>(rich(X)<~>humble(X))))&
((?[X]:((curious(X)<~>calm(X))))<=>((strong(lucy)|~brave(lucy))))&
(![X]:((quiet(X)&~happy(X))=>(happy(X)|old(X))))&
(![X]:(~patient(X)<=>(humble(X)<~>~curious(X))))&
(![X]:((~quiet(X)&old(X))=>(~strong(X)&~rich(X))))&
(((brave(susan)&rich(susan)))<=>((rich(fred)&~wise(fred))))&
(![X]:((tall(X)<~>~generous(X))=>(~old(X)&patient(X))))&
((?[X]:((calm(X)|~generous(X))))=>((old(susan)|humble(susan))))&
(![X]:((wise(X)&~old(X))=>(strong(X)<~>~curious(X))))&
(![X]:((~creative(X)|patient(X))=>~calm(X)))&
((~tall(john)|strong(john)))&
((funny(susan)|~brave(susan)))&
(old(mary))&
((patient(mary)<~>~wise(mary)))&
((~calm(mary)|~rich(mary)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~brave(susan)|creative(susan))) | ~rich(mary) | [
"p2",
"p5",
"p12",
"p18",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2046174521019584196233270
% SZS output start Proof for 2046174521019584196233270
3. ! [X0] : (calm(X0) <=> (~wise(X0) | ~tall(X0))) [input p2]
6. ! [X0] : ((~quiet(X0) & calm(X0)) <=> (patient(X0) & ~generous(X0))) [input p5]
13. ! [X0] : ((tall(X0) <~> ~generous(X0)) => (patient(X0) & ~old(X0))) [input p12]
19. old(mary) [input p18]
20. patient(mary) <~> ~wise(mary) [input p19]
21. ~rich(mary) | ~calm(mary) [input p20]
24. rich(mary) [input hypothesis]
32. ! [X0] : ((patient(X0) & ~old(X0)) | (tall(X0) <=> ~generous(X0))) [ennf transformation 13]
45. ! [X0] : ((calm(X0) | (wise(X0) & tall(X0))) & ((~wise(X0) | ~tall(X0)) | ~calm(X0))) [nnf transformation 3]
46. ! [X0] : ((calm(X0) | (wise(X0) & tall(X0))) & (~wise(X0) | ~tall(X0) | ~calm(X0))) [flattening 45]
49. ! [X0] : (((~quiet(X0) & calm(X0)) | (~patient(X0) | generous(X0))) & ((patient(X0) & ~generous(X0)) | (quiet(X0) | ~calm(X0)))) [nnf transformation 6]
50. ! [X0] : (((~quiet(X0) & calm(X0)) | ~patient(X0) | generous(X0)) & ((patient(X0) & ~generous(X0)) | quiet(X0) | ~calm(X0))) [flattening 49]
60. ! [X0] : ((patient(X0) & ~old(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) [nnf transformation 32]
62. (wise(mary) | ~patient(mary)) & (~wise(mary) | patient(mary)) [nnf transformation 20]
73. calm(X0) | tall(X0) [cnf transformation 46]
74. wise(X0) | calm(X0) [cnf transformation 46]
84. ~patient(X0) | calm(X0) | generous(X0) [cnf transformation 50]
105. ~generous(X0) | ~old(X0) | ~tall(X0) [cnf transformation 60]
116. old(mary) [cnf transformation 19]
117. ~wise(mary) | patient(mary) [cnf transformation 62]
119. ~rich(mary) | ~calm(mary) [cnf transformation 21]
123. rich(mary) [cnf transformation 24]
208. 19 <=> patient(mary) [avatar definition]
209. patient(mary) <- (19) [avatar component clause 208]
212. 20 <=> wise(mary) [avatar definition]
213. ~wise(mary) <- (~20) [avatar component clause 212]
216. 19 | ~20 [avatar split clause 117,212,208]
218. 21 <=> calm(mary) [avatar definition]
220. ~calm(mary) <- (~21) [avatar component clause 218]
222. 22 <=> rich(mary) [avatar definition]
225. ~21 | ~22 [avatar split clause 119,222,218]
231. 22 [avatar split clause 123,222]
233. tall(mary) <- (~21) [resolution 73,220]
235. calm(mary) <- (~20) [resolution 74,213]
236. $false <- (~20, ~21) [subsumption resolution 235,220]
237. 20 | 21 [avatar contradiction clause 236]
292. calm(mary) | generous(mary) <- (19) [resolution 84,209]
293. generous(mary) <- (19, ~21) [subsumption resolution 292,220]
348. ~old(mary) | ~tall(mary) <- (19, ~21) [resolution 105,293]
349. ~tall(mary) <- (19, ~21) [subsumption resolution 348,116]
350. $false <- (19, ~21) [subsumption resolution 349,233]
351. ~19 | 21 [avatar contradiction clause 350]
352. $false [avatar sat refutation 216,225,231,237,351]
% SZS output end Proof for 2046174521019584196233270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or brave is both not curious and not rich and vice versa.
Everyone who is either not old or funny is not brave and vice versa.
Everyone who is not funny or old is both generous and creative.
If john is either calm or not strong then alice is funny.
Everyone who is not old is both not quiet and not generous and vice versa.
Everyone who is either wise or curious is not brave or not strong and vice versa.
Everyone who is generous is either kind or patient.
Everyone who is both not generous and not tall is wise or not old and vice versa.
Everyone who is curious is both humble and not rich.
If mary is old or not funny then susan is either not wise or happy and vice versa.
Everyone who is not kind or not strong is rich and vice versa.
If alice is not wise or calm then mary is both not calm and not funny and vice versa.
Everyone who is either not generous or wise is kind and vice versa.
If susan is both not humble and creative then fred is not humble or generous.
If paul is both quiet and rich then lucy is generous or rich.
Someone is quiet or funny.
Someone is strong or wise.
Lucy is both not strong and not humble.
Someone is humble. | Fred is tall. | contradiction | (![X]:((~creative(X)<~>brave(X))<=>(~curious(X)&~rich(X))))&
(![X]:((~old(X)<~>funny(X))<=>~brave(X)))&
(![X]:((~funny(X)|old(X))=>(generous(X)&creative(X))))&
(((calm(john)<~>~strong(john)))=>(funny(alice)))&
(![X]:(~old(X)<=>(~quiet(X)&~generous(X))))&
(![X]:((wise(X)<~>curious(X))<=>(~brave(X)|~strong(X))))&
(![X]:(generous(X)=>(kind(X)<~>patient(X))))&
(![X]:((~generous(X)&~tall(X))<=>(wise(X)|~old(X))))&
(![X]:(curious(X)=>(humble(X)&~rich(X))))&
(((old(mary)|~funny(mary)))<=>((~wise(susan)<~>happy(susan))))&
(![X]:((~kind(X)|~strong(X))<=>rich(X)))&
(((~wise(alice)|calm(alice)))<=>((~calm(mary)&~funny(mary))))&
(![X]:((~generous(X)<~>wise(X))<=>kind(X)))&
(((~humble(susan)&creative(susan)))=>((~humble(fred)|generous(fred))))&
(((quiet(paul)&rich(paul)))=>((generous(lucy)|rich(lucy))))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:((strong(X)|wise(X))))&
((~strong(lucy)&~humble(lucy)))&
(?[X]:(humble(X))) | tall(fred) | [
"p0",
"p2",
"p5",
"p7",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7634536614328605645773471
% SZS output start Proof for 7634536614328605645773471
1. ! [X0] : ((~creative(X0) <~> brave(X0)) <=> (~rich(X0) & ~curious(X0))) [input p0]
3. ! [X0] : ((old(X0) | ~funny(X0)) => (creative(X0) & generous(X0))) [input p2]
6. ! [X0] : ((wise(X0) <~> curious(X0)) <=> (~strong(X0) | ~brave(X0))) [input p5]
8. ! [X0] : ((~tall(X0) & ~generous(X0)) <=> (~old(X0) | wise(X0))) [input p7]
9. ! [X0] : (curious(X0) => (~rich(X0) & humble(X0))) [input p8]
11. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> rich(X0)) [input p10]
13. ! [X0] : ((~generous(X0) <~> wise(X0)) <=> kind(X0)) [input p12]
20. tall(fred) [input hypothesis]
21. ! [X0] : ((creative(X0) & generous(X0)) | (~old(X0) & funny(X0))) [ennf transformation 3]
24. ! [X0] : ((~rich(X0) & humble(X0)) | ~curious(X0)) [ennf transformation 9]
29. ! [X0] : ((((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (rich(X0) | curious(X0))) & ((~rich(X0) & ~curious(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0))))) [nnf transformation 1]
30. ! [X0] : ((((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | rich(X0) | curious(X0)) & ((~rich(X0) & ~curious(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0))))) [flattening 29]
35. ! [X0] : ((((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | (strong(X0) & brave(X0))) & ((~strong(X0) | ~brave(X0)) | ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0))))) [nnf transformation 6]
36. ! [X0] : ((((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | (strong(X0) & brave(X0))) & (~strong(X0) | ~brave(X0) | ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0))))) [flattening 35]
38. ! [X0] : (((~tall(X0) & ~generous(X0)) | (old(X0) & ~wise(X0))) & ((~old(X0) | wise(X0)) | (tall(X0) | generous(X0)))) [nnf transformation 8]
39. ! [X0] : (((~tall(X0) & ~generous(X0)) | (old(X0) & ~wise(X0))) & (~old(X0) | wise(X0) | tall(X0) | generous(X0))) [flattening 38]
42. ! [X0] : (((~strong(X0) | ~kind(X0)) | ~rich(X0)) & (rich(X0) | (strong(X0) & kind(X0)))) [nnf transformation 11]
43. ! [X0] : ((~strong(X0) | ~kind(X0) | ~rich(X0)) & (rich(X0) | (strong(X0) & kind(X0)))) [flattening 42]
46. ! [X0] : ((((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | ~kind(X0)) & (kind(X0) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0))))) [nnf transformation 13]
56. ~rich(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 30]
64. ~old(X0) | generous(X0) [cnf transformation 21]
66. ~old(X0) | creative(X0) [cnf transformation 21]
74. wise(X0) | curious(X0) | brave(X0) [cnf transformation 36]
81. ~wise(X0) | ~generous(X0) [cnf transformation 39]
83. ~tall(X0) | ~wise(X0) [cnf transformation 39]
84. ~tall(X0) | old(X0) [cnf transformation 39]
86. ~rich(X0) | ~curious(X0) [cnf transformation 24]
93. kind(X0) | rich(X0) [cnf transformation 43]
103. wise(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 46]
104. ~wise(X0) | generous(X0) | ~kind(X0) [cnf transformation 46]
112. tall(fred) [cnf transformation 20]
166. ~kind(X0) | ~wise(X0) [subsumption resolution 104,81]
167. ~kind(X0) | ~generous(X0) [subsumption resolution 103,166]
181. 14 <=> generous(fred) [avatar definition]
183. generous(fred) <- (14) [avatar component clause 181]
225. ~wise(fred) [resolution 83,112]
226. old(fred) [resolution 84,112]
227. creative(fred) [resolution 226,66]
228. generous(fred) [resolution 226,64]
229. 14 [avatar split clause 228,181]
238. ~generous(X0) | rich(X0) [resolution 167,93]
288. 30 <=> brave(fred) [avatar definition]
310. curious(fred) | brave(fred) [resolution 74,225]
340. 36 <=> curious(fred) [avatar definition]
438. rich(fred) <- (14) [resolution 238,183]
457. ~creative(fred) | ~brave(fred) <- (14) [resolution 438,56]
459. ~curious(fred) <- (14) [resolution 438,86]
460. ~brave(fred) <- (14) [subsumption resolution 457,227]
463. ~36 | ~14 [avatar split clause 459,181,340]
464. ~30 | ~14 [avatar split clause 460,181,288]
465. 30 | 36 [avatar split clause 310,340,288]
466. $false [avatar sat refutation 229,463,464,465]
% SZS output end Proof for 7634536614328605645773471
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If john is both creative and not creative then alice is humble or not quiet and vice versa. If someone is not wise then fred is rich or not quiet. If john is both wise and not happy then paul is not brave or tall and vice versa. If someone is both not brave and strong then fred is both kind and not rich and vice versa. If alice is both not old and not rich then someone is not old. Everyone who is both not curious and not strong is patient and vice versa. Everyone who is generous or wise is both strong and not quiet. Everyone who is tall is both rich and not humble and vice versa. If someone is not funny or not tall then someone is either not creative or funny and vice versa. If someone is calm or patient then lucy is strong or kind. If someone is both creative and not curious then mary is either not calm or old. Everyone who is either not brave or not tall is not old and vice versa. If mary is not calm then john is either not patient or curious and vice versa. Everyone who is not rich or old is not calm and vice versa. Everyone who is either not tall or wise is old and vice versa. If someone is calm or not brave then lucy is curious or wise. John is either happy or quiet. Lucy is generous. Mary is not tall or quiet. Someone is not happy or not wise. Paul is either quiet or not humble. Someone is strong or rich. Paul is both creative and kind. Someone is both generous and rich. | Paul is strong. | entailment | (((creative(john)&~creative(john)))<=>((humble(alice)|~quiet(alice))))&
((?[X]:(~wise(X)))=>((rich(fred)|~quiet(fred))))&
(((wise(john)&~happy(john)))<=>((~brave(paul)|tall(paul))))&
((?[X]:((~brave(X)&strong(X))))<=>((kind(fred)&~rich(fred))))&
(((~old(alice)&~rich(alice)))=>(?[X]:(~old(X))))&
(![X]:((~curious(X)&~strong(X))<=>patient(X)))&
(![X]:((generous(X)|wise(X))=>(strong(X)&~quiet(X))))&
(![X]:(tall(X)<=>(rich(X)&~humble(X))))&
((?[X]:((~funny(X)|~tall(X))))<=>(?[X]:((~creative(X)<~>funny(X)))))&
((?[X]:((calm(X)|patient(X))))=>((strong(lucy)|kind(lucy))))&
((?[X]:((creative(X)&~curious(X))))=>((~calm(mary)<~>old(mary))))&
(![X]:((~brave(X)<~>~tall(X))<=>~old(X)))&
((~calm(mary))<=>((~patient(john)<~>curious(john))))&
(![X]:((~rich(X)|old(X))<=>~calm(X)))&
(![X]:((~tall(X)<~>wise(X))<=>old(X)))&
((?[X]:((calm(X)|~brave(X))))=>((curious(lucy)|wise(lucy))))&
((happy(john)<~>quiet(john)))&
(generous(lucy))&
((~tall(mary)|quiet(mary)))&
(?[X]:((~happy(X)|~wise(X))))&
((quiet(paul)<~>~humble(paul)))&
(?[X]:((strong(X)|rich(X))))&
((creative(paul)&kind(paul)))&
(?[X]:((generous(X)&rich(X)))) | strong(paul) | [
"p2",
"p6",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6921282245680091148962228
% SZS output start Proof for 6921282245680091148962228
3. (~happy(john) & wise(john)) <=> (tall(paul) | ~brave(paul)) [input p2]
7. ! [X0] : ((wise(X0) | generous(X0)) => (~quiet(X0) & strong(X0))) [input p6]
12. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> ~old(X0)) [input p11]
15. ! [X0] : ((~tall(X0) <~> wise(X0)) <=> old(X0)) [input p14]
17. happy(john) <~> quiet(john) [input p16]
25. ~strong(paul) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & strong(X0)) | (~wise(X0) & ~generous(X0))) [ennf transformation 7]
39. ((~happy(john) & wise(john)) | (~tall(paul) & brave(paul))) & ((tall(paul) | ~brave(paul)) | (happy(john) | ~wise(john))) [nnf transformation 3]
40. ((~happy(john) & wise(john)) | (~tall(paul) & brave(paul))) & (tall(paul) | ~brave(paul) | happy(john) | ~wise(john)) [flattening 39]
58. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | old(X0)) & (~old(X0) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 12]
62. ! [X0] : ((((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | ~old(X0)) & (old(X0) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0))))) [nnf transformation 15]
63. (~quiet(john) | ~happy(john)) & (quiet(john) | happy(john)) [nnf transformation 17]
78. wise(john) | brave(paul) [cnf transformation 40]
79. wise(john) | ~tall(paul) [cnf transformation 40]
80. ~happy(john) | brave(paul) [cnf transformation 40]
81. ~happy(john) | ~tall(paul) [cnf transformation 40]
91. ~wise(X0) | strong(X0) [cnf transformation 31]
93. ~wise(X0) | ~quiet(X0) [cnf transformation 31]
108. ~old(X0) | ~brave(X0) | tall(X0) [cnf transformation 58]
118. old(X0) | wise(X0) | tall(X0) [cnf transformation 62]
124. quiet(john) | happy(john) [cnf transformation 63]
136. ~strong(paul) [cnf transformation 25]
166. 7 <=> tall(paul) [avatar definition]
168. ~tall(paul) <- (~7) [avatar component clause 166]
170. 8 <=> happy(john) [avatar definition]
173. ~7 | ~8 [avatar split clause 81,170,166]
175. 9 <=> brave(paul) [avatar definition]
177. brave(paul) <- (9) [avatar component clause 175]
178. 9 | ~8 [avatar split clause 80,170,175]
180. 10 <=> wise(john) [avatar definition]
182. wise(john) <- (10) [avatar component clause 180]
183. ~7 | 10 [avatar split clause 79,180,166]
184. 9 | 10 [avatar split clause 78,180,175]
308. 38 <=> quiet(john) [avatar definition]
309. quiet(john) <- (38) [avatar component clause 308]
312. 8 | 38 [avatar split clause 124,308,170]
396. wise(X0) | tall(X0) | ~brave(X0) | tall(X0) [resolution 118,108]
398. ~brave(X0) | tall(X0) | wise(X0) [duplicate literal removal 396]
464. tall(paul) | wise(paul) <- (9) [resolution 398,177]
469. wise(paul) <- (~7, 9) [subsumption resolution 464,168]
677. strong(paul) <- (~7, 9) [resolution 469,91]
678. $false <- (~7, 9) [subsumption resolution 677,136]
679. 7 | ~9 [avatar contradiction clause 678]
681. ~quiet(john) <- (10) [resolution 182,93]
683. $false <- (10, 38) [subsumption resolution 681,309]
684. ~10 | ~38 [avatar contradiction clause 683]
685. $false [avatar sat refutation 173,178,183,184,312,679,684]
% SZS output end Proof for 6921282245680091148962228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not humble is strong or quiet and vice versa.
If susan is quiet then lucy is not old or not generous.
If mary is both generous and not strong then someone is not happy or calm and vice versa.
If paul is kind then someone is both not wise and not funny.
If mary is either calm or not wise then alice is patient or not creative and vice versa.
Everyone who is generous is not kind.
Everyone who is not creative or funny is not funny or tall and vice versa.
Everyone who is curious is either not happy or happy.
Everyone who is either not patient or not creative is either brave or rich and vice versa.
If someone is curious or not rich then susan is happy or not generous.
If susan is not patient or calm then someone is either not happy or wise and vice versa.
If lucy is either not brave or strong then someone is curious.
Everyone who is either funny or strong is not wise or old and vice versa.
Everyone who is both brave and not calm is either not tall or old.
Everyone who is not curious is humble or wise and vice versa.
Everyone who is curious is either not old or not calm and vice versa.
Alice is not generous or humble.
Paul is not generous.
Lucy is not old.
Someone is both not quiet and not funny.
Someone is both not rich and not generous.
Someone is both not kind and calm.
Someone is happy. | Susan is calm. | neutral | (![X]:((~old(X)<~>~humble(X))<=>(strong(X)|quiet(X))))&
((quiet(susan))=>((~old(lucy)|~generous(lucy))))&
(((generous(mary)&~strong(mary)))<=>(?[X]:((~happy(X)|calm(X)))))&
((kind(paul))=>(?[X]:((~wise(X)&~funny(X)))))&
(((calm(mary)<~>~wise(mary)))<=>((patient(alice)|~creative(alice))))&
(![X]:(generous(X)=>~kind(X)))&
(![X]:((~creative(X)|funny(X))<=>(~funny(X)|tall(X))))&
(![X]:(curious(X)=>(~happy(X)<~>happy(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>(brave(X)<~>rich(X))))&
((?[X]:((curious(X)|~rich(X))))=>((happy(susan)|~generous(susan))))&
(((~patient(susan)|calm(susan)))<=>(?[X]:((~happy(X)<~>wise(X)))))&
(((~brave(lucy)<~>strong(lucy)))=>(?[X]:(curious(X))))&
(![X]:((funny(X)<~>strong(X))<=>(~wise(X)|old(X))))&
(![X]:((brave(X)&~calm(X))=>(~tall(X)<~>old(X))))&
(![X]:(~curious(X)<=>(humble(X)|wise(X))))&
(![X]:(curious(X)<=>(~old(X)<~>~calm(X))))&
((~generous(alice)|humble(alice)))&
(~generous(paul))&
(~old(lucy))&
(?[X]:((~quiet(X)&~funny(X))))&
(?[X]:((~rich(X)&~generous(X))))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:(happy(X))) | calm(susan) | [] | null | 0 |
Everyone who is both patient and not quiet is not strong and vice versa.
Everyone who is not curious or not strong is both brave and old and vice versa.
If john is either not curious or rich then susan is not quiet or not happy.
If someone is not funny or not patient then someone is not strong and vice versa.
Everyone who is either humble or not calm is either generous or not rich.
If someone is funny or not kind then someone is either not quiet or brave.
If john is either not generous or wise then mary is tall.
Everyone who is not curious is either not rich or happy.
Everyone who is not curious or brave is either not creative or old.
If lucy is creative or not curious then susan is curious.
Everyone who is humble is curious or kind and vice versa.
Everyone who is not strong or not wise is either generous or not generous and vice versa.
Everyone who is both not wise and not tall is not calm.
If alice is both kind and not patient then someone is not quiet or not humble and vice versa.
Everyone who is curious or not patient is happy and vice versa.
Everyone who is both not old and not patient is generous or tall and vice versa.
Alice is not quiet or rich.
John is happy or not creative.
Paul is not brave or not patient.
Susan is rich or not patient.
Alice is both not creative and not tall.
Someone is not kind or not patient.
Someone is either generous or not strong.
Someone is either not brave or not happy. | Alice is not happy. | contradiction | (![X]:((patient(X)&~quiet(X))<=>~strong(X)))&
(![X]:((~curious(X)|~strong(X))<=>(brave(X)&old(X))))&
(((~curious(john)<~>rich(john)))=>((~quiet(susan)|~happy(susan))))&
((?[X]:((~funny(X)|~patient(X))))<=>(?[X]:(~strong(X))))&
(![X]:((humble(X)<~>~calm(X))=>(generous(X)<~>~rich(X))))&
((?[X]:((funny(X)|~kind(X))))=>(?[X]:((~quiet(X)<~>brave(X)))))&
(((~generous(john)<~>wise(john)))=>(tall(mary)))&
(![X]:(~curious(X)=>(~rich(X)<~>happy(X))))&
(![X]:((~curious(X)|brave(X))=>(~creative(X)<~>old(X))))&
(((creative(lucy)|~curious(lucy)))=>(curious(susan)))&
(![X]:(humble(X)<=>(curious(X)|kind(X))))&
(![X]:((~strong(X)|~wise(X))<=>(generous(X)<~>~generous(X))))&
(![X]:((~wise(X)&~tall(X))=>~calm(X)))&
(((kind(alice)&~patient(alice)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:((curious(X)|~patient(X))<=>happy(X)))&
(![X]:((~old(X)&~patient(X))<=>(generous(X)|tall(X))))&
((~quiet(alice)|rich(alice)))&
((happy(john)|~creative(john)))&
((~brave(paul)|~patient(paul)))&
((rich(susan)|~patient(susan)))&
((~creative(alice)&~tall(alice)))&
(?[X]:((~kind(X)|~patient(X))))&
(?[X]:((generous(X)<~>~strong(X))))&
(?[X]:((~brave(X)<~>~happy(X)))) | ~happy(alice) | [
"p0",
"p3",
"p13",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5369378151320677224748018
% SZS output start Proof for 5369378151320677224748018
1. ! [X0] : ((~quiet(X0) & patient(X0)) <=> ~strong(X0)) [input p0]
4. ? [X0] : (~patient(X0) | ~funny(X0)) <=> ? [X0] : ~strong(X0) [input p3]
14. (~patient(alice) & kind(alice)) <=> ? [X0] : (~humble(X0) | ~quiet(X0)) [input p13]
15. ! [X0] : ((~patient(X0) | curious(X0)) <=> happy(X0)) [input p14]
16. ! [X0] : ((~patient(X0) & ~old(X0)) <=> (tall(X0) | generous(X0))) [input p15]
23. ? [X0] : (generous(X0) <~> ~strong(X0)) [input p22]
25. ~happy(alice) [input hypothesis]
26. ? [X0] : (~patient(X0) | ~funny(X0)) <=> ? [X1] : ~strong(X1) [rectify 4]
38. ! [X0] : (((~quiet(X0) & patient(X0)) | strong(X0)) & (~strong(X0) | (quiet(X0) | ~patient(X0)))) [nnf transformation 1]
39. ! [X0] : (((~quiet(X0) & patient(X0)) | strong(X0)) & (~strong(X0) | quiet(X0) | ~patient(X0))) [flattening 38]
43. (? [X0] : (~patient(X0) | ~funny(X0)) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : (patient(X0) & funny(X0))) [nnf transformation 26]
44. (? [X0] : (~patient(X0) | ~funny(X0)) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : (patient(X3) & funny(X3))) [rectify 43]
45. ? [X0] : (~patient(X0) | ~funny(X0)) => (~patient(sK0) | ~funny(sK0)) [choice axiom]
46. ? [X2] : ~strong(X2) => ~strong(sK1) [choice axiom]
47. ((~patient(sK0) | ~funny(sK0)) | ! [X1] : strong(X1)) & (~strong(sK1) | ! [X3] : (patient(X3) & funny(X3))) [skolemisation 44,46,45]
60. ((~patient(alice) & kind(alice)) | ! [X0] : (humble(X0) & quiet(X0))) & (? [X0] : (~humble(X0) | ~quiet(X0)) | (patient(alice) | ~kind(alice))) [nnf transformation 14]
61. ((~patient(alice) & kind(alice)) | ! [X0] : (humble(X0) & quiet(X0))) & (? [X0] : (~humble(X0) | ~quiet(X0)) | patient(alice) | ~kind(alice)) [flattening 60]
62. ((~patient(alice) & kind(alice)) | ! [X0] : (humble(X0) & quiet(X0))) & (? [X1] : (~humble(X1) | ~quiet(X1)) | patient(alice) | ~kind(alice)) [rectify 61]
63. ? [X1] : (~humble(X1) | ~quiet(X1)) => (~humble(sK3) | ~quiet(sK3)) [choice axiom]
64. ((~patient(alice) & kind(alice)) | ! [X0] : (humble(X0) & quiet(X0))) & ((~humble(sK3) | ~quiet(sK3)) | patient(alice) | ~kind(alice)) [skolemisation 62,63]
65. ! [X0] : (((~patient(X0) | curious(X0)) | ~happy(X0)) & (happy(X0) | (patient(X0) & ~curious(X0)))) [nnf transformation 15]
66. ! [X0] : ((~patient(X0) | curious(X0) | ~happy(X0)) & (happy(X0) | (patient(X0) & ~curious(X0)))) [flattening 65]
67. ! [X0] : (((~patient(X0) & ~old(X0)) | (~tall(X0) & ~generous(X0))) & ((tall(X0) | generous(X0)) | (patient(X0) | old(X0)))) [nnf transformation 16]
68. ! [X0] : (((~patient(X0) & ~old(X0)) | (~tall(X0) & ~generous(X0))) & (tall(X0) | generous(X0) | patient(X0) | old(X0))) [flattening 67]
71. ? [X0] : ((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) [nnf transformation 23]
72. ? [X0] : ((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) => ((strong(sK5) | ~generous(sK5)) & (~strong(sK5) | generous(sK5))) [choice axiom]
73. (strong(sK5) | ~generous(sK5)) & (~strong(sK5) | generous(sK5)) [skolemisation 71,72]
79. ~quiet(X0) | strong(X0) [cnf transformation 39]
88. ~strong(sK1) | patient(X3) [cnf transformation 47]
121. ~patient(alice) | quiet(X0) [cnf transformation 64]
124. happy(X0) | patient(X0) [cnf transformation 66]
129. ~generous(X0) | ~patient(X0) [cnf transformation 68]
138. ~strong(sK5) | generous(sK5) [cnf transformation 73]
142. ~happy(alice) [cnf transformation 25]
164. 5 <=> ! [X1] : strong(X1) [avatar definition]
165. strong(X1) <- (5) [avatar component clause 164]
176. 8 <=> ! [X3] : patient(X3) [avatar definition]
177. patient(X3) <- (8) [avatar component clause 176]
179. 9 <=> strong(sK1) [avatar definition]
181. ~strong(sK1) <- (~9) [avatar component clause 179]
182. 8 | ~9 [avatar split clause 88,179,176]
239. 22 <=> patient(alice) [avatar definition]
244. 23 <=> ! [X0] : quiet(X0) [avatar definition]
245. quiet(X0) <- (23) [avatar component clause 244]
246. 23 | ~22 [avatar split clause 121,239,244]
308. 37 <=> generous(sK5) [avatar definition]
309. generous(sK5) <- (37) [avatar component clause 308]
312. 38 <=> strong(sK5) [avatar definition]
313. ~strong(sK5) <- (~38) [avatar component clause 312]
316. 37 | ~38 [avatar split clause 138,312,308]
339. patient(alice) [resolution 124,142]
346. 22 [avatar split clause 339,239]
350. strong(X0) <- (23) [resolution 245,79]
351. 5 | ~23 [avatar split clause 350,244,164]
352. $false <- (5, ~9) [resolution 165,181]
353. $false <- (5, ~38) [resolution 165,313]
354. ~5 | 38 [avatar contradiction clause 353]
355. ~5 | 9 [avatar contradiction clause 352]
368. ~patient(sK5) <- (37) [resolution 129,309]
369. $false <- (8, 37) [subsumption resolution 368,177]
370. ~8 | ~37 [avatar contradiction clause 369]
371. $false [avatar sat refutation 182,246,316,346,351,354,355,370]
% SZS output end Proof for 5369378151320677224748018
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is not wise or brave and vice versa. Everyone who is not strong or funny is both not quiet and not funny and vice versa. If someone is generous or not curious then lucy is both not old and not humble and vice versa. If someone is either not quiet or brave then susan is either patient or not funny and vice versa. Everyone who is both humble and not quiet is kind. If someone is rich then alice is happy or not old and vice versa. If lucy is either creative or not humble then someone is curious or creative. If fred is both not tall and strong then fred is either creative or kind and vice versa. Everyone who is not generous is not creative or kind and vice versa. Everyone who is rich is either not strong or not brave. If susan is not funny or strong then someone is both calm and humble. Everyone who is both tall and quiet is either not humble or not happy and vice versa. Everyone who is either not patient or not rich is old. Everyone who is both not generous and brave is either not quiet or not calm. If someone is not quiet or not humble then alice is either creative or not old. If someone is not funny then paul is both not strong and not quiet. Mary is not strong. Someone is quiet or funny. Paul is rich. Someone is either not generous or generous. Someone is not curious. Mary is not generous. Susan is both quiet and generous. Lucy is either quiet or not old. | Paul is not tall. | entailment | (![X]:(~tall(X)<=>(~wise(X)|brave(X))))&
(![X]:((~strong(X)|funny(X))<=>(~quiet(X)&~funny(X))))&
((?[X]:((generous(X)|~curious(X))))<=>((~old(lucy)&~humble(lucy))))&
((?[X]:((~quiet(X)<~>brave(X))))<=>((patient(susan)<~>~funny(susan))))&
(![X]:((humble(X)&~quiet(X))=>kind(X)))&
((?[X]:(rich(X)))<=>((happy(alice)|~old(alice))))&
(((creative(lucy)<~>~humble(lucy)))=>(?[X]:((curious(X)|creative(X)))))&
(((~tall(fred)&strong(fred)))<=>((creative(fred)<~>kind(fred))))&
(![X]:(~generous(X)<=>(~creative(X)|kind(X))))&
(![X]:(rich(X)=>(~strong(X)<~>~brave(X))))&
(((~funny(susan)|strong(susan)))=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((tall(X)&quiet(X))<=>(~humble(X)<~>~happy(X))))&
(![X]:((~patient(X)<~>~rich(X))=>old(X)))&
(![X]:((~generous(X)&brave(X))=>(~quiet(X)<~>~calm(X))))&
((?[X]:((~quiet(X)|~humble(X))))=>((creative(alice)<~>~old(alice))))&
((?[X]:(~funny(X)))=>((~strong(paul)&~quiet(paul))))&
(~strong(mary))&
(?[X]:((quiet(X)|funny(X))))&
(rich(paul))&
(?[X]:((~generous(X)<~>generous(X))))&
(?[X]:(~curious(X)))&
(~generous(mary))&
((quiet(susan)&generous(susan)))&
((quiet(lucy)<~>~old(lucy))) | ~tall(paul) | [
"p0",
"p1",
"p9",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2745442425979123531764075
% SZS output start Proof for 2745442425979123531764075
1. ! [X0] : (~tall(X0) <=> (brave(X0) | ~wise(X0))) [input p0]
2. ! [X0] : ((funny(X0) | ~strong(X0)) <=> (~funny(X0) & ~quiet(X0))) [input p1]
10. ! [X0] : (rich(X0) => (~strong(X0) <~> ~brave(X0))) [input p9]
16. ? [X0] : ~funny(X0) => (~quiet(paul) & ~strong(paul)) [input p15]
19. rich(paul) [input p18]
25. tall(paul) [input hypothesis]
29. ! [X0] : ((~strong(X0) <~> ~brave(X0)) | ~rich(X0)) [ennf transformation 10]
35. (~quiet(paul) & ~strong(paul)) | ! [X0] : funny(X0) [ennf transformation 16]
36. ! [X0] : ((~tall(X0) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | tall(X0))) [nnf transformation 1]
37. ! [X0] : ((~tall(X0) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | tall(X0))) [flattening 36]
38. ! [X0] : (((funny(X0) | ~strong(X0)) | (funny(X0) | quiet(X0))) & ((~funny(X0) & ~quiet(X0)) | (~funny(X0) & strong(X0)))) [nnf transformation 2]
39. ! [X0] : ((funny(X0) | ~strong(X0) | funny(X0) | quiet(X0)) & ((~funny(X0) & ~quiet(X0)) | (~funny(X0) & strong(X0)))) [flattening 38]
61. ! [X0] : (((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | ~rich(X0)) [nnf transformation 29]
79. ~brave(X0) | ~tall(X0) [cnf transformation 37]
83. ~funny(X0) | ~funny(X0) [cnf transformation 39]
114. ~rich(X0) | strong(X0) | brave(X0) [cnf transformation 61]
133. ~strong(paul) | funny(X0) [cnf transformation 35]
137. rich(paul) [cnf transformation 19]
146. tall(paul) [cnf transformation 25]
147. ~funny(X0) [duplicate literal removal 83]
289. ~strong(paul) [subsumption resolution 133,147]
340. strong(paul) | brave(paul) [resolution 114,137]
342. brave(paul) [subsumption resolution 340,289]
349. ~tall(paul) [resolution 342,79]
350. $false [subsumption resolution 349,146]
% SZS output end Proof for 2745442425979123531764075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either not funny or not quiet then someone is both not creative and humble and vice versa. Everyone who is either not strong or not quiet is calm. If someone is either not kind or not tall then alice is both kind and not happy and vice versa. Everyone who is wise is both rich and not happy. If alice is wise then someone is not patient or rich. If mary is either not humble or generous then someone is strong. Everyone who is strong is not tall or not generous. Everyone who is not wise is not funny or patient. Everyone who is not tall or not strong is old. Everyone who is either humble or not humble is both funny and quiet. If someone is either not rich or funny then alice is either strong or happy and vice versa. Everyone who is strong is patient. If lucy is both quiet and not tall then someone is kind or patient. If someone is both not generous and wise then paul is not tall. Everyone who is not old or generous is not quiet. Everyone who is both wise and calm is not generous or humble and vice versa. Fred is wise. Someone is wise or not brave. Someone is both not happy and not curious. John is not patient or happy. Someone is either not happy or generous. Someone is both creative and not generous. Someone is both not happy and funny. Someone is not creative. | John is not strong. | entailment | ((?[X]:((~funny(X)<~>~quiet(X))))<=>(?[X]:((~creative(X)&humble(X)))))&
(![X]:((~strong(X)<~>~quiet(X))=>calm(X)))&
((?[X]:((~kind(X)<~>~tall(X))))<=>((kind(alice)&~happy(alice))))&
(![X]:(wise(X)=>(rich(X)&~happy(X))))&
((wise(alice))=>(?[X]:((~patient(X)|rich(X)))))&
(((~humble(mary)<~>generous(mary)))=>(?[X]:(strong(X))))&
(![X]:(strong(X)=>(~tall(X)|~generous(X))))&
(![X]:(~wise(X)=>(~funny(X)|patient(X))))&
(![X]:((~tall(X)|~strong(X))=>old(X)))&
(![X]:((humble(X)<~>~humble(X))=>(funny(X)&quiet(X))))&
((?[X]:((~rich(X)<~>funny(X))))<=>((strong(alice)<~>happy(alice))))&
(![X]:(strong(X)=>patient(X)))&
(((quiet(lucy)&~tall(lucy)))=>(?[X]:((kind(X)|patient(X)))))&
((?[X]:((~generous(X)&wise(X))))=>(~tall(paul)))&
(![X]:((~old(X)|generous(X))=>~quiet(X)))&
(![X]:((wise(X)&calm(X))<=>(~generous(X)|humble(X))))&
(wise(fred))&
(?[X]:((wise(X)|~brave(X))))&
(?[X]:((~happy(X)&~curious(X))))&
((~patient(john)|happy(john)))&
(?[X]:((~happy(X)<~>generous(X))))&
(?[X]:((creative(X)&~generous(X))))&
(?[X]:((~happy(X)&funny(X))))&
(?[X]:(~creative(X))) | ~strong(john) | [
"p3",
"p9",
"p11",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7290203881361009734995291
% SZS output start Proof for 7290203881361009734995291
4. ! [X0] : (wise(X0) => (~happy(X0) & rich(X0))) [input p3]
10. ! [X0] : ((humble(X0) <~> ~humble(X0)) => (quiet(X0) & funny(X0))) [input p9]
12. ! [X0] : (strong(X0) => patient(X0)) [input p11]
15. ! [X0] : ((generous(X0) | ~old(X0)) => ~quiet(X0)) [input p14]
16. ! [X0] : ((calm(X0) & wise(X0)) <=> (humble(X0) | ~generous(X0))) [input p15]
20. happy(john) | ~patient(john) [input p19]
25. strong(john) [input hypothesis]
30. ! [X0] : (generous(X0) => ~quiet(X0)) [pure predicate removal 15]
32. ! [X0] : ((~happy(X0) & rich(X0)) | ~wise(X0)) [ennf transformation 4]
39. ! [X0] : ((quiet(X0) & funny(X0)) | (humble(X0) <=> ~humble(X0))) [ennf transformation 10]
40. ! [X0] : (patient(X0) | ~strong(X0)) [ennf transformation 12]
44. ! [X0] : (~quiet(X0) | ~generous(X0)) [ennf transformation 30]
61. ! [X0] : ((quiet(X0) & funny(X0)) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) [nnf transformation 39]
68. ! [X0] : (((calm(X0) & wise(X0)) | (~humble(X0) & generous(X0))) & ((humble(X0) | ~generous(X0)) | (~calm(X0) | ~wise(X0)))) [nnf transformation 16]
69. ! [X0] : (((calm(X0) & wise(X0)) | (~humble(X0) & generous(X0))) & (humble(X0) | ~generous(X0) | ~calm(X0) | ~wise(X0))) [flattening 68]
96. ~wise(X0) | ~happy(X0) [cnf transformation 32]
104. quiet(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 61]
105. quiet(X0) | humble(X0) | humble(X0) [cnf transformation 61]
114. ~strong(X0) | patient(X0) [cnf transformation 40]
117. ~quiet(X0) | ~generous(X0) [cnf transformation 44]
119. wise(X0) | generous(X0) [cnf transformation 69]
125. happy(john) | ~patient(john) [cnf transformation 20]
133. strong(john) [cnf transformation 25]
136. quiet(X0) | ~humble(X0) [duplicate literal removal 104]
137. quiet(X0) | humble(X0) [duplicate literal removal 105]
224. quiet(X0) [subsumption resolution 136,137]
267. ~generous(X0) [subsumption resolution 117,224]
269. wise(X0) [subsumption resolution 119,267]
271. 28 <=> patient(john) [avatar definition]
275. 29 <=> happy(john) [avatar definition]
277. happy(john) <- (29) [avatar component clause 275]
278. ~28 | 29 [avatar split clause 125,275,271]
285. ~happy(X0) [resolution 96,269]
288. patient(john) [resolution 114,133]
293. 28 [avatar split clause 288,271]
294. $false <- (29) [subsumption resolution 277,285]
295. ~29 [avatar contradiction clause 294]
296. $false [avatar sat refutation 278,293,295]
% SZS output end Proof for 7290203881361009734995291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not creative is both quiet and not brave.
If mary is not kind or wise then paul is either not funny or not brave.
Everyone who is not rich is both not happy and not funny and vice versa.
If someone is not tall then paul is not creative.
If john is either not rich or not wise then fred is either not old or generous.
Everyone who is both not wise and generous is not patient.
If someone is both not brave and not wise then lucy is both rich and not calm and vice versa.
Everyone who is both not tall and happy is not quiet and vice versa.
If susan is both not old and creative then john is humble or not old and vice versa.
Everyone who is either curious or wise is wise or not patient.
Everyone who is not creative or not humble is both humble and not patient.
If mary is both generous and funny then mary is humble or calm.
Everyone who is tall is either not calm or quiet and vice versa.
If fred is happy or not curious then someone is not old or tall and vice versa.
Everyone who is wise or not brave is both wise and not quiet and vice versa.
Everyone who is either patient or tall is curious or not curious.
Someone is generous.
Alice is either patient or creative.
Someone is either tall or strong.
Fred is generous or not rich.
Lucy is not wise or not happy.
Alice is not brave or humble.
Someone is both funny and not curious. | John is calm. | entailment | (![X]:((~kind(X)|~creative(X))=>(quiet(X)&~brave(X))))&
(((~kind(mary)|wise(mary)))=>((~funny(paul)<~>~brave(paul))))&
(![X]:(~rich(X)<=>(~happy(X)&~funny(X))))&
((?[X]:(~tall(X)))=>(~creative(paul)))&
(((~rich(john)<~>~wise(john)))=>((~old(fred)<~>generous(fred))))&
(![X]:((~wise(X)&generous(X))=>~patient(X)))&
((?[X]:((~brave(X)&~wise(X))))<=>((rich(lucy)&~calm(lucy))))&
(![X]:((~tall(X)&happy(X))<=>~quiet(X)))&
(((~old(susan)&creative(susan)))<=>((humble(john)|~old(john))))&
(![X]:((curious(X)<~>wise(X))=>(wise(X)|~patient(X))))&
(![X]:((~creative(X)|~humble(X))=>(humble(X)&~patient(X))))&
(((generous(mary)&funny(mary)))=>((humble(mary)|calm(mary))))&
(![X]:(tall(X)<=>(~calm(X)<~>quiet(X))))&
(((happy(fred)|~curious(fred)))<=>(?[X]:((~old(X)|tall(X)))))&
(![X]:((wise(X)|~brave(X))<=>(wise(X)&~quiet(X))))&
(![X]:((patient(X)<~>tall(X))=>(curious(X)|~curious(X))))&
(?[X]:(generous(X)))&
((patient(alice)<~>creative(alice)))&
(?[X]:((tall(X)<~>strong(X))))&
((generous(fred)|~rich(fred)))&
((~wise(lucy)|~happy(lucy)))&
((~brave(alice)|humble(alice)))&
(?[X]:((funny(X)&~curious(X)))) | calm(john) | [
"p0",
"p3",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2144508982481923988164792
% SZS output start Proof for 2144508982481923988164792
1. ! [X0] : ((~creative(X0) | ~kind(X0)) => (~brave(X0) & quiet(X0))) [input p0]
4. ? [X0] : ~tall(X0) => ~creative(paul) [input p3]
8. ! [X0] : ((happy(X0) & ~tall(X0)) <=> ~quiet(X0)) [input p7]
13. ! [X0] : (tall(X0) <=> (~calm(X0) <~> quiet(X0))) [input p12]
15. ! [X0] : ((~brave(X0) | wise(X0)) <=> (~quiet(X0) & wise(X0))) [input p14]
24. ~calm(john) [input hypothesis]
26. ! [X0] : (~creative(X0) => (~brave(X0) & quiet(X0))) [pure predicate removal 1]
27. ! [X0] : ((~brave(X0) & quiet(X0)) | creative(X0)) [ennf transformation 26]
29. ~creative(paul) | ! [X0] : tall(X0) [ennf transformation 4]
49. ! [X0] : (((happy(X0) & ~tall(X0)) | quiet(X0)) & (~quiet(X0) | (~happy(X0) | tall(X0)))) [nnf transformation 8]
50. ! [X0] : (((happy(X0) & ~tall(X0)) | quiet(X0)) & (~quiet(X0) | ~happy(X0) | tall(X0))) [flattening 49]
54. ! [X0] : ((tall(X0) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | ~tall(X0))) [nnf transformation 13]
60. ! [X0] : (((~brave(X0) | wise(X0)) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | (brave(X0) & ~wise(X0)))) [nnf transformation 15]
61. ! [X0] : ((~brave(X0) | wise(X0) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | (brave(X0) & ~wise(X0)))) [flattening 60]
71. quiet(X0) | creative(X0) [cnf transformation 27]
72. ~brave(X0) | creative(X0) [cnf transformation 27]
78. ~creative(paul) | tall(X0) [cnf transformation 29]
89. ~tall(X0) | quiet(X0) [cnf transformation 50]
104. ~quiet(X0) | calm(X0) | ~tall(X0) [cnf transformation 54]
114. ~quiet(X0) | brave(X0) [cnf transformation 61]
128. ~calm(john) [cnf transformation 24]
146. 4 <=> ! [X0] : tall(X0) [avatar definition]
147. tall(X0) <- (4) [avatar component clause 146]
149. 5 <=> creative(paul) [avatar definition]
151. ~creative(paul) <- (~5) [avatar component clause 149]
152. 4 | ~5 [avatar split clause 78,149,146]
218. ~tall(X0) | calm(X0) [subsumption resolution 104,89]
278. brave(X0) | creative(X0) [resolution 114,71]
281. creative(X0) [subsumption resolution 278,72]
282. $false <- (~5) [resolution 281,151]
283. 5 [avatar contradiction clause 282]
292. calm(X0) <- (4) [resolution 218,147]
294. $false <- (4) [resolution 292,128]
295. ~4 [avatar contradiction clause 294]
296. $false [avatar sat refutation 152,283,295]
% SZS output end Proof for 2144508982481923988164792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not strong and not creative then someone is not strong or wise.
If paul is not curious or not humble then lucy is not humble and vice versa.
If mary is either not kind or not funny then someone is not old.
If paul is not brave then alice is kind or not creative.
Everyone who is either funny or not quiet is creative or curious and vice versa.
Everyone who is both not generous and funny is not rich.
Everyone who is wise is both funny and not quiet and vice versa.
Everyone who is both not kind and curious is not quiet.
Everyone who is either strong or kind is wise and vice versa.
Everyone who is strong is old.
If someone is either curious or not old then someone is either not tall or not kind and vice versa.
Everyone who is not wise or old is not quiet and vice versa.
Everyone who is generous is strong.
Everyone who is not creative or kind is wise and vice versa.
Everyone who is either not brave or not kind is either not quiet or happy and vice versa.
Everyone who is both not creative and not calm is both happy and not creative.
Someone is not old or wise.
Someone is both not kind and humble.
Paul is patient or generous.
Someone is not old.
Alice is patient or quiet.
Someone is both old and not calm.
Paul is funny.
Susan is not humble or strong. | Lucy is humble. | contradiction | (((~strong(alice)&~creative(alice)))=>(?[X]:((~strong(X)|wise(X)))))&
(((~curious(paul)|~humble(paul)))<=>(~humble(lucy)))&
(((~kind(mary)<~>~funny(mary)))=>(?[X]:(~old(X))))&
((~brave(paul))=>((kind(alice)|~creative(alice))))&
(![X]:((funny(X)<~>~quiet(X))<=>(creative(X)|curious(X))))&
(![X]:((~generous(X)&funny(X))=>~rich(X)))&
(![X]:(wise(X)<=>(funny(X)&~quiet(X))))&
(![X]:((~kind(X)&curious(X))=>~quiet(X)))&
(![X]:((strong(X)<~>kind(X))<=>wise(X)))&
(![X]:(strong(X)=>old(X)))&
((?[X]:((curious(X)<~>~old(X))))<=>(?[X]:((~tall(X)<~>~kind(X)))))&
(![X]:((~wise(X)|old(X))<=>~quiet(X)))&
(![X]:(generous(X)=>strong(X)))&
(![X]:((~creative(X)|kind(X))<=>wise(X)))&
(![X]:((~brave(X)<~>~kind(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:((~creative(X)&~calm(X))=>(happy(X)&~creative(X))))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:((~kind(X)&humble(X))))&
((patient(paul)|generous(paul)))&
(?[X]:(~old(X)))&
((patient(alice)|quiet(alice)))&
(?[X]:((old(X)&~calm(X))))&
(funny(paul))&
((~humble(susan)|strong(susan))) | humble(lucy) | [
"p1",
"p4",
"p6",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4009588048272777108735332
% SZS output start Proof for 4009588048272777108735332
2. (~humble(paul) | ~curious(paul)) <=> ~humble(lucy) [input p1]
5. ! [X0] : ((funny(X0) <~> ~quiet(X0)) <=> (curious(X0) | creative(X0))) [input p4]
7. ! [X0] : (wise(X0) <=> (~quiet(X0) & funny(X0))) [input p6]
12. ! [X0] : ((old(X0) | ~wise(X0)) <=> ~quiet(X0)) [input p11]
23. funny(paul) [input p22]
25. humble(lucy) [input hypothesis]
43. ((~humble(paul) | ~curious(paul)) | humble(lucy)) & (~humble(lucy) | (humble(paul) & curious(paul))) [nnf transformation 2]
44. (~humble(paul) | ~curious(paul) | humble(lucy)) & (~humble(lucy) | (humble(paul) & curious(paul))) [flattening 43]
48. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (~curious(X0) & ~creative(X0))) & ((curious(X0) | creative(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [nnf transformation 5]
49. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (~curious(X0) & ~creative(X0))) & (curious(X0) | creative(X0) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [flattening 48]
50. ! [X0] : ((wise(X0) | (quiet(X0) | ~funny(X0))) & ((~quiet(X0) & funny(X0)) | ~wise(X0))) [nnf transformation 7]
51. ! [X0] : ((wise(X0) | quiet(X0) | ~funny(X0)) & ((~quiet(X0) & funny(X0)) | ~wise(X0))) [flattening 50]
58. ! [X0] : (((old(X0) | ~wise(X0)) | quiet(X0)) & (~quiet(X0) | (~old(X0) & wise(X0)))) [nnf transformation 12]
59. ! [X0] : ((old(X0) | ~wise(X0) | quiet(X0)) & (~quiet(X0) | (~old(X0) & wise(X0)))) [flattening 58]
72. ~humble(lucy) | curious(paul) [cnf transformation 44]
83. ~funny(X0) | quiet(X0) | ~curious(X0) [cnf transformation 49]
85. ~quiet(X0) | ~wise(X0) [cnf transformation 51]
101. ~quiet(X0) | wise(X0) [cnf transformation 59]
123. funny(paul) [cnf transformation 23]
125. humble(lucy) [cnf transformation 25]
144. 5 <=> humble(lucy) [avatar definition]
148. 6 <=> curious(paul) [avatar definition]
149. curious(paul) <- (6) [avatar component clause 148]
157. 6 | ~5 [avatar split clause 72,144,148]
218. ~quiet(X0) [subsumption resolution 101,85]
241. 5 [avatar split clause 125,144]
251. quiet(paul) | ~curious(paul) [resolution 83,123]
253. ~curious(paul) [subsumption resolution 251,218]
254. $false <- (6) [subsumption resolution 253,149]
255. ~6 [avatar contradiction clause 254]
257. $false [avatar sat refutation 157,241,255]
% SZS output end Proof for 4009588048272777108735332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old then paul is not wise or humble and vice versa.
If fred is not generous or not quiet then john is either strong or funny and vice versa.
Everyone who is either kind or humble is both not creative and not strong and vice versa.
If fred is not brave then lucy is both not old and patient and vice versa.
If john is creative or not strong then john is happy or not strong and vice versa.
Everyone who is not creative or not humble is either not funny or not wise and vice versa.
If alice is both not strong and brave then lucy is either not kind or patient.
If fred is both wise and not generous then someone is both brave and rich and vice versa.
Everyone who is both not happy and not quiet is both not curious and not calm and vice versa.
Everyone who is not humble is generous or not curious.
Everyone who is not strong is either not funny or wise.
Everyone who is rich or brave is either not creative or rich and vice versa.
If lucy is not curious then lucy is wise and vice versa.
If john is not curious then someone is not kind or not humble.
If someone is either not generous or not funny then someone is both not creative and not tall.
Everyone who is either not kind or not humble is not old.
Someone is not generous or funny.
Someone is kind or funny.
Someone is either rich or strong.
Someone is either not happy or not calm.
Paul is not generous or funny.
Someone is not wise or not quiet.
Susan is either not calm or patient.
Alice is both strong and not old. | John is happy. | neutral | ((~old(alice))<=>((~wise(paul)|humble(paul))))&
(((~generous(fred)|~quiet(fred)))<=>((strong(john)<~>funny(john))))&
(![X]:((kind(X)<~>humble(X))<=>(~creative(X)&~strong(X))))&
((~brave(fred))<=>((~old(lucy)&patient(lucy))))&
(((creative(john)|~strong(john)))<=>((happy(john)|~strong(john))))&
(![X]:((~creative(X)|~humble(X))<=>(~funny(X)<~>~wise(X))))&
(((~strong(alice)&brave(alice)))=>((~kind(lucy)<~>patient(lucy))))&
(((wise(fred)&~generous(fred)))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:((~happy(X)&~quiet(X))<=>(~curious(X)&~calm(X))))&
(![X]:(~humble(X)=>(generous(X)|~curious(X))))&
(![X]:(~strong(X)=>(~funny(X)<~>wise(X))))&
(![X]:((rich(X)|brave(X))<=>(~creative(X)<~>rich(X))))&
((~curious(lucy))<=>(wise(lucy)))&
((~curious(john))=>(?[X]:((~kind(X)|~humble(X)))))&
((?[X]:((~generous(X)<~>~funny(X))))=>(?[X]:((~creative(X)&~tall(X)))))&
(![X]:((~kind(X)<~>~humble(X))=>~old(X)))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((~happy(X)<~>~calm(X))))&
((~generous(paul)|funny(paul)))&
(?[X]:((~wise(X)|~quiet(X))))&
((~calm(susan)<~>patient(susan)))&
((strong(alice)&~old(alice))) | happy(john) | [] | null | 0 |
Everyone who is quiet is either not patient or funny and vice versa.
If fred is patient or humble then someone is quiet and vice versa.
If lucy is either not kind or kind then someone is both not humble and not strong.
If alice is happy or not happy then john is not wise or rich and vice versa.
If someone is not wise or tall then susan is not wise.
Everyone who is not patient is both not patient and not generous.
If someone is not funny or not old then someone is either not creative or generous and vice versa.
Everyone who is creative is not generous and vice versa.
If someone is both patient and not happy then alice is both strong and not humble.
Everyone who is both generous and not curious is funny and vice versa.
If someone is either patient or tall then john is either not kind or not generous and vice versa.
Everyone who is either not wise or curious is humble or generous and vice versa.
If susan is wise or not strong then mary is not humble or not wise and vice versa.
If someone is rich then fred is happy or not creative and vice versa.
Everyone who is not strong is either not wise or not calm.
Everyone who is either rich or not creative is not patient and vice versa.
Lucy is wise or kind.
Fred is funny.
Susan is either not curious or brave.
Someone is either not patient or patient.
Someone is both not humble and strong. | Susan is wise. | contradiction | (![X]:(quiet(X)<=>(~patient(X)<~>funny(X))))&
(((patient(fred)|humble(fred)))<=>(?[X]:(quiet(X))))&
(((~kind(lucy)<~>kind(lucy)))=>(?[X]:((~humble(X)&~strong(X)))))&
(((happy(alice)|~happy(alice)))<=>((~wise(john)|rich(john))))&
((?[X]:((~wise(X)|tall(X))))=>(~wise(susan)))&
(![X]:(~patient(X)=>(~patient(X)&~generous(X))))&
((?[X]:((~funny(X)|~old(X))))<=>(?[X]:((~creative(X)<~>generous(X)))))&
(![X]:(creative(X)<=>~generous(X)))&
((?[X]:((patient(X)&~happy(X))))=>((strong(alice)&~humble(alice))))&
(![X]:((generous(X)&~curious(X))<=>funny(X)))&
((?[X]:((patient(X)<~>tall(X))))<=>((~kind(john)<~>~generous(john))))&
(![X]:((~wise(X)<~>curious(X))<=>(humble(X)|generous(X))))&
(((wise(susan)|~strong(susan)))<=>((~humble(mary)|~wise(mary))))&
((?[X]:(rich(X)))<=>((happy(fred)|~creative(fred))))&
(![X]:(~strong(X)=>(~wise(X)<~>~calm(X))))&
(![X]:((rich(X)<~>~creative(X))<=>~patient(X)))&
((wise(lucy)|kind(lucy)))&
(funny(fred))&
((~curious(susan)<~>brave(susan)))&
(?[X]:((~patient(X)<~>patient(X))))&
(?[X]:((~humble(X)&strong(X)))) | wise(susan) | [
"p4",
"p6",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 824574326580137007136597
% SZS output start Proof for 824574326580137007136597
5. ? [X0] : (tall(X0) | ~wise(X0)) => ~wise(susan) [input p4]
7. ? [X0] : (~old(X0) | ~funny(X0)) <=> ? [X0] : (~creative(X0) <~> generous(X0)) [input p6]
8. ! [X0] : (creative(X0) <=> ~generous(X0)) [input p7]
10. ! [X0] : ((~curious(X0) & generous(X0)) <=> funny(X0)) [input p9]
12. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (generous(X0) | humble(X0))) [input p11]
22. wise(susan) [input hypothesis]
23. ? [X0] : (~old(X0) | ~funny(X0)) <=> ? [X1] : (~creative(X1) <~> generous(X1)) [rectify 7]
25. ~wise(susan) | ! [X0] : (~tall(X0) & wise(X0)) [ennf transformation 5]
40. (? [X0] : (~old(X0) | ~funny(X0)) | ! [X1] : ((~creative(X1) | ~generous(X1)) & (generous(X1) | creative(X1)))) & (? [X1] : ((~generous(X1) | creative(X1)) & (generous(X1) | ~creative(X1))) | ! [X0] : (old(X0) & funny(X0))) [nnf transformation 23]
41. (? [X0] : (~old(X0) | ~funny(X0)) | ! [X1] : ((~creative(X1) | ~generous(X1)) & (generous(X1) | creative(X1)))) & (? [X2] : ((~generous(X2) | creative(X2)) & (generous(X2) | ~creative(X2))) | ! [X3] : (old(X3) & funny(X3))) [rectify 40]
42. ? [X0] : (~old(X0) | ~funny(X0)) => (~old(sK2) | ~funny(sK2)) [choice axiom]
43. ? [X2] : ((~generous(X2) | creative(X2)) & (generous(X2) | ~creative(X2))) => ((~generous(sK3) | creative(sK3)) & (generous(sK3) | ~creative(sK3))) [choice axiom]
44. ((~old(sK2) | ~funny(sK2)) | ! [X1] : ((~creative(X1) | ~generous(X1)) & (generous(X1) | creative(X1)))) & (((~generous(sK3) | creative(sK3)) & (generous(sK3) | ~creative(sK3))) | ! [X3] : (old(X3) & funny(X3))) [skolemisation 41,43,42]
45. ! [X0] : ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0))) [nnf transformation 8]
46. ! [X0] : (((~curious(X0) & generous(X0)) | ~funny(X0)) & (funny(X0) | (curious(X0) | ~generous(X0)))) [nnf transformation 10]
47. ! [X0] : (((~curious(X0) & generous(X0)) | ~funny(X0)) & (funny(X0) | curious(X0) | ~generous(X0))) [flattening 46]
52. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 12]
53. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [flattening 52]
84. ~wise(susan) | wise(X0) [cnf transformation 25]
88. generous(sK3) | ~creative(sK3) | funny(X3) [cnf transformation 44]
90. ~generous(sK3) | creative(sK3) | funny(X3) [cnf transformation 44]
94. ~generous(X0) | ~creative(X0) [cnf transformation 45]
95. creative(X0) | generous(X0) [cnf transformation 45]
99. ~funny(X0) | generous(X0) [cnf transformation 47]
100. ~curious(X0) | ~funny(X0) [cnf transformation 47]
112. ~generous(X0) | ~wise(X0) | curious(X0) [cnf transformation 53]
136. wise(susan) [cnf transformation 22]
193. 12 <=> wise(susan) [avatar definition]
198. 13 <=> ! [X0] : wise(X0) [avatar definition]
199. wise(X0) <- (13) [avatar component clause 198]
200. 13 | ~12 [avatar split clause 84,193,198]
202. 14 <=> ! [X1] : (~creative(X1) | ~generous(X1)) [avatar definition]
203. ~creative(X1) | ~generous(X1) <- (14) [avatar component clause 202]
214. 17 <=> ! [X1] : (generous(X1) | creative(X1)) [avatar definition]
215. creative(X1) | generous(X1) <- (17) [avatar component clause 214]
221. 19 <=> creative(sK3) [avatar definition]
222. ~creative(sK3) <- (~19) [avatar component clause 221]
223. creative(sK3) <- (19) [avatar component clause 221]
225. 20 <=> generous(sK3) [avatar definition]
227. ~generous(sK3) <- (~20) [avatar component clause 225]
230. 21 <=> ! [X3] : funny(X3) [avatar definition]
231. funny(X3) <- (21) [avatar component clause 230]
232. 21 | 19 | ~20 [avatar split clause 90,225,221,230]
234. 21 | ~19 | 20 [avatar split clause 88,225,221,230]
235. 17 [avatar split clause 95,214]
236. 14 [avatar split clause 94,202]
251. 25 <=> generous(john) [avatar definition]
252. ~generous(john) <- (~25) [avatar component clause 251]
253. generous(john) <- (25) [avatar component clause 251]
329. 12 [avatar split clause 136,193]
338. generous(sK3) <- (17, ~19) [resolution 215,222]
341. $false <- (17, ~19, ~20) [subsumption resolution 338,227]
342. ~17 | 19 | 20 [avatar contradiction clause 341]
343. ~generous(sK3) <- (14, 19) [resolution 223,203]
346. ~20 | ~14 | ~19 [avatar split clause 343,221,202,225]
347. generous(X0) <- (21) [resolution 231,99]
375. ~wise(john) | curious(john) <- (25) [resolution 112,253]
378. curious(john) <- (13, 25) [subsumption resolution 375,199]
381. ~funny(john) <- (13, 25) [resolution 378,100]
382. $false <- (13, 21, 25) [subsumption resolution 381,231]
383. ~13 | ~21 | ~25 [avatar contradiction clause 382]
384. $false <- (21, ~25) [subsumption resolution 252,347]
385. ~21 | 25 [avatar contradiction clause 384]
386. $false [avatar sat refutation 200,232,234,235,236,329,342,346,383,385]
% SZS output end Proof for 824574326580137007136597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not funny and not quiet then someone is old or not strong and vice versa. If mary is not curious then john is not funny or kind and vice versa. If someone is calm then lucy is either happy or strong. If alice is either not happy or not wise then someone is not creative. If mary is wise then paul is either not calm or not creative. Everyone who is either tall or not old is either not old or funny. Everyone who is both not humble and not generous is either quiet or not happy and vice versa. Everyone who is either strong or humble is strong or not old and vice versa. Everyone who is either not curious or quiet is not strong or brave. Everyone who is not rich or not old is either not strong or happy and vice versa. Everyone who is either creative or strong is either patient or tall and vice versa. If someone is either not happy or not tall then someone is not kind or patient and vice versa. If paul is either not brave or not curious then someone is not wise or patient and vice versa. Everyone who is either humble or not funny is patient or not happy. Everyone who is patient is either not old or not curious. Everyone who is not calm or not brave is either wise or not calm and vice versa. Someone is either generous or brave. Someone is not rich or not calm. Someone is humble or generous. Someone is both not brave and not funny. Someone is old or not strong. Mary is happy. John is curious. | Mary is rich. | neutral | ((?[X]:((~funny(X)&~quiet(X))))<=>(?[X]:((old(X)|~strong(X)))))&
((~curious(mary))<=>((~funny(john)|kind(john))))&
((?[X]:(calm(X)))=>((happy(lucy)<~>strong(lucy))))&
(((~happy(alice)<~>~wise(alice)))=>(?[X]:(~creative(X))))&
((wise(mary))=>((~calm(paul)<~>~creative(paul))))&
(![X]:((tall(X)<~>~old(X))=>(~old(X)<~>funny(X))))&
(![X]:((~humble(X)&~generous(X))<=>(quiet(X)<~>~happy(X))))&
(![X]:((strong(X)<~>humble(X))<=>(strong(X)|~old(X))))&
(![X]:((~curious(X)<~>quiet(X))=>(~strong(X)|brave(X))))&
(![X]:((~rich(X)|~old(X))<=>(~strong(X)<~>happy(X))))&
(![X]:((creative(X)<~>strong(X))<=>(patient(X)<~>tall(X))))&
((?[X]:((~happy(X)<~>~tall(X))))<=>(?[X]:((~kind(X)|patient(X)))))&
(((~brave(paul)<~>~curious(paul)))<=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((humble(X)<~>~funny(X))=>(patient(X)|~happy(X))))&
(![X]:(patient(X)=>(~old(X)<~>~curious(X))))&
(![X]:((~calm(X)|~brave(X))<=>(wise(X)<~>~calm(X))))&
(?[X]:((generous(X)<~>brave(X))))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((~brave(X)&~funny(X))))&
(?[X]:((old(X)|~strong(X))))&
(happy(mary))&
(curious(john)) | rich(mary) | [] | null | 0 |
Everyone who is not happy is either not tall or patient and vice versa.
Everyone who is not funny or tall is both not patient and happy.
If lucy is not tall then john is strong and vice versa.
Everyone who is not strong or strong is either not curious or brave.
Everyone who is both not curious and funny is both quiet and not tall and vice versa.
Everyone who is both calm and not calm is either patient or not calm and vice versa.
Everyone who is not quiet or not rich is humble or not kind and vice versa.
Everyone who is either quiet or happy is either funny or creative and vice versa.
If someone is either wise or not calm then john is not generous and vice versa.
If someone is both not patient and not quiet then paul is not calm.
Everyone who is both calm and quiet is not kind or happy.
Everyone who is curious or not humble is not patient or curious.
If someone is not patient or not strong then someone is either not tall or not patient and vice versa.
Everyone who is patient is either generous or not generous and vice versa.
If someone is either happy or not strong then someone is both not rich and not humble and vice versa.
If someone is funny then someone is generous or funny and vice versa.
Someone is either curious or creative.
Lucy is curious.
Someone is creative or brave.
Someone is not wise.
Mary is both not calm and creative.
Someone is not funny or quiet.
Susan is both kind and not tall. | Mary is not curious. | entailment | (![X]:(~happy(X)<=>(~tall(X)<~>patient(X))))&
(![X]:((~funny(X)|tall(X))=>(~patient(X)&happy(X))))&
((~tall(lucy))<=>(strong(john)))&
(![X]:((~strong(X)|strong(X))=>(~curious(X)<~>brave(X))))&
(![X]:((~curious(X)&funny(X))<=>(quiet(X)&~tall(X))))&
(![X]:((calm(X)&~calm(X))<=>(patient(X)<~>~calm(X))))&
(![X]:((~quiet(X)|~rich(X))<=>(humble(X)|~kind(X))))&
(![X]:((quiet(X)<~>happy(X))<=>(funny(X)<~>creative(X))))&
((?[X]:((wise(X)<~>~calm(X))))<=>(~generous(john)))&
((?[X]:((~patient(X)&~quiet(X))))=>(~calm(paul)))&
(![X]:((calm(X)&quiet(X))=>(~kind(X)|happy(X))))&
(![X]:((curious(X)|~humble(X))=>(~patient(X)|curious(X))))&
((?[X]:((~patient(X)|~strong(X))))<=>(?[X]:((~tall(X)<~>~patient(X)))))&
(![X]:(patient(X)<=>(generous(X)<~>~generous(X))))&
((?[X]:((happy(X)<~>~strong(X))))<=>(?[X]:((~rich(X)&~humble(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((generous(X)|funny(X)))))&
(?[X]:((curious(X)<~>creative(X))))&
(curious(lucy))&
(?[X]:((creative(X)|brave(X))))&
(?[X]:(~wise(X)))&
((~calm(mary)&creative(mary)))&
(?[X]:((~funny(X)|quiet(X))))&
((kind(susan)&~tall(susan))) | ~curious(mary) | [
"p0",
"p1",
"p4",
"p7",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2314779266035693980195130
% SZS output start Proof for 2314779266035693980195130
1. ! [X0] : (~happy(X0) <=> (~tall(X0) <~> patient(X0))) [input p0]
2. ! [X0] : ((tall(X0) | ~funny(X0)) => (happy(X0) & ~patient(X0))) [input p1]
5. ! [X0] : ((funny(X0) & ~curious(X0)) <=> (~tall(X0) & quiet(X0))) [input p4]
8. ! [X0] : ((quiet(X0) <~> happy(X0)) <=> (funny(X0) <~> creative(X0))) [input p7]
14. ! [X0] : (patient(X0) <=> (generous(X0) <~> ~generous(X0))) [input p13]
21. creative(mary) & ~calm(mary) [input p20]
24. curious(mary) [input hypothesis]
28. ! [X0] : ((happy(X0) & ~patient(X0)) | (~tall(X0) & funny(X0))) [ennf transformation 2]
35. ! [X0] : ((~happy(X0) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) & (((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | happy(X0))) [nnf transformation 1]
38. ! [X0] : (((funny(X0) & ~curious(X0)) | (tall(X0) | ~quiet(X0))) & ((~tall(X0) & quiet(X0)) | (~funny(X0) | curious(X0)))) [nnf transformation 5]
39. ! [X0] : (((funny(X0) & ~curious(X0)) | tall(X0) | ~quiet(X0)) & ((~tall(X0) & quiet(X0)) | ~funny(X0) | curious(X0))) [flattening 38]
44. ! [X0] : ((((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0))))) [nnf transformation 8]
54. ! [X0] : ((patient(X0) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | ~patient(X0))) [nnf transformation 14]
75. ~patient(X0) | tall(X0) | happy(X0) [cnf transformation 35]
78. ~patient(X0) | funny(X0) [cnf transformation 28]
79. ~patient(X0) | ~tall(X0) [cnf transformation 28]
90. ~quiet(X0) | tall(X0) | ~curious(X0) [cnf transformation 39]
105. ~creative(X0) | ~funny(X0) | quiet(X0) | ~happy(X0) [cnf transformation 44]
126. patient(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 54]
127. patient(X0) | generous(X0) | generous(X0) [cnf transformation 54]
143. creative(mary) [cnf transformation 21]
147. curious(mary) [cnf transformation 24]
148. patient(X0) | ~generous(X0) [duplicate literal removal 126]
149. generous(X0) | patient(X0) [duplicate literal removal 127]
202. 10 <=> ! [X1] : ~tall(X1) [avatar definition]
203. ~tall(X1) <- (10) [avatar component clause 202]
231. 17 <=> ! [X3] : patient(X3) [avatar definition]
232. patient(X3) <- (17) [avatar component clause 231]
234. patient(X0) [subsumption resolution 148,149]
235. 17 [avatar split clause 234,231]
322. funny(X0) <- (17) [resolution 78,232]
327. ~tall(X0) <- (17) [resolution 79,232]
328. 10 | ~17 [avatar split clause 327,231,202]
344. tall(X0) | happy(X0) <- (17) [resolution 75,232]
345. happy(X0) <- (10, 17) [subsumption resolution 344,203]
431. ~funny(mary) | quiet(mary) | ~happy(mary) [resolution 105,143]
437. quiet(mary) | ~happy(mary) <- (17) [subsumption resolution 431,322]
438. quiet(mary) <- (10, 17) [subsumption resolution 437,345]
452. tall(mary) | ~curious(mary) <- (10, 17) [resolution 438,90]
453. ~curious(mary) <- (10, 17) [subsumption resolution 452,203]
454. $false <- (10, 17) [subsumption resolution 453,147]
455. ~10 | ~17 [avatar contradiction clause 454]
456. $false [avatar sat refutation 235,328,455]
% SZS output end Proof for 2314779266035693980195130
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or not old then someone is rich or generous.
Everyone who is not kind is either not brave or rich.
Everyone who is curious or quiet is either calm or creative.
If someone is kind then someone is rich or creative and vice versa.
If john is both not happy and not rich then lucy is generous or tall and vice versa.
If fred is not creative or creative then john is not patient or not happy and vice versa.
Everyone who is not brave or not creative is either not tall or happy.
Everyone who is both not brave and not kind is either strong or quiet and vice versa.
If someone is both not calm and curious then susan is quiet or not old.
Everyone who is either old or kind is strong or not tall and vice versa.
If someone is both not happy and not calm then someone is either not patient or brave and vice versa.
If john is strong then lucy is either not quiet or not calm and vice versa.
If someone is creative then john is calm or not brave.
Everyone who is not tall is not rich and vice versa.
Everyone who is quiet is not rich or not kind.
Everyone who is both kind and creative is both not humble and brave and vice versa.
Someone is both creative and not quiet.
Someone is either not strong or not generous.
Lucy is not creative or rich.
Someone is not funny.
Someone is both strong and not creative.
Someone is brave or creative.
Someone is brave.
Fred is either wise or not quiet. | John is generous. | neutral | ((?[X]:((strong(X)|~old(X))))=>(?[X]:((rich(X)|generous(X)))))&
(![X]:(~kind(X)=>(~brave(X)<~>rich(X))))&
(![X]:((curious(X)|quiet(X))=>(calm(X)<~>creative(X))))&
((?[X]:(kind(X)))<=>(?[X]:((rich(X)|creative(X)))))&
(((~happy(john)&~rich(john)))<=>((generous(lucy)|tall(lucy))))&
(((~creative(fred)|creative(fred)))<=>((~patient(john)|~happy(john))))&
(![X]:((~brave(X)|~creative(X))=>(~tall(X)<~>happy(X))))&
(![X]:((~brave(X)&~kind(X))<=>(strong(X)<~>quiet(X))))&
((?[X]:((~calm(X)&curious(X))))=>((quiet(susan)|~old(susan))))&
(![X]:((old(X)<~>kind(X))<=>(strong(X)|~tall(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>(?[X]:((~patient(X)<~>brave(X)))))&
((strong(john))<=>((~quiet(lucy)<~>~calm(lucy))))&
((?[X]:(creative(X)))=>((calm(john)|~brave(john))))&
(![X]:(~tall(X)<=>~rich(X)))&
(![X]:(quiet(X)=>(~rich(X)|~kind(X))))&
(![X]:((kind(X)&creative(X))<=>(~humble(X)&brave(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(?[X]:((~strong(X)<~>~generous(X))))&
((~creative(lucy)|rich(lucy)))&
(?[X]:(~funny(X)))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((brave(X)|creative(X))))&
(?[X]:(brave(X)))&
((wise(fred)<~>~quiet(fred))) | generous(john) | [] | null | 0 |
Everyone who is either brave or not brave is not quiet or generous and vice versa.
If someone is calm or not brave then someone is both wise and brave.
Everyone who is not happy is either funny or not happy.
If someone is both not happy and wise then alice is both not patient and calm.
If susan is both rich and not tall then someone is both humble and wise and vice versa.
If someone is either brave or kind then someone is both brave and tall and vice versa.
Everyone who is both calm and curious is not wise or wise.
Everyone who is not creative is both tall and wise and vice versa.
Everyone who is not curious or wise is calm or tall and vice versa.
Everyone who is not strong or not patient is both quiet and kind and vice versa.
If lucy is strong then susan is not generous.
If mary is rich or not brave then lucy is both not funny and patient.
Everyone who is not happy or not tall is tall or curious and vice versa.
Everyone who is both not curious and not generous is either wise or old and vice versa.
If susan is generous or tall then someone is not rich or not kind.
If susan is both kind and tall then paul is both funny and not happy.
Someone is calm.
Someone is either not humble or strong.
Someone is not curious.
Someone is both not wise and not calm.
Paul is curious or rich.
Someone is not patient.
Mary is both rich and humble.
Paul is old or not old. | Lucy is not generous. | neutral | (![X]:((brave(X)<~>~brave(X))<=>(~quiet(X)|generous(X))))&
((?[X]:((calm(X)|~brave(X))))=>(?[X]:((wise(X)&brave(X)))))&
(![X]:(~happy(X)=>(funny(X)<~>~happy(X))))&
((?[X]:((~happy(X)&wise(X))))=>((~patient(alice)&calm(alice))))&
(((rich(susan)&~tall(susan)))<=>(?[X]:((humble(X)&wise(X)))))&
((?[X]:((brave(X)<~>kind(X))))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((calm(X)&curious(X))=>(~wise(X)|wise(X))))&
(![X]:(~creative(X)<=>(tall(X)&wise(X))))&
(![X]:((~curious(X)|wise(X))<=>(calm(X)|tall(X))))&
(![X]:((~strong(X)|~patient(X))<=>(quiet(X)&kind(X))))&
((strong(lucy))=>(~generous(susan)))&
(((rich(mary)|~brave(mary)))=>((~funny(lucy)&patient(lucy))))&
(![X]:((~happy(X)|~tall(X))<=>(tall(X)|curious(X))))&
(![X]:((~curious(X)&~generous(X))<=>(wise(X)<~>old(X))))&
(((generous(susan)|tall(susan)))=>(?[X]:((~rich(X)|~kind(X)))))&
(((kind(susan)&tall(susan)))=>((funny(paul)&~happy(paul))))&
(?[X]:(calm(X)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~wise(X)&~calm(X))))&
((curious(paul)|rich(paul)))&
(?[X]:(~patient(X)))&
((rich(mary)&humble(mary)))&
((old(paul)|~old(paul))) | ~generous(lucy) | [] | null | 0 |
If paul is either not tall or curious then someone is either rich or happy. Everyone who is either wise or strong is not quiet. If someone is not happy then lucy is both not patient and not generous and vice versa. Everyone who is tall is both not happy and rich and vice versa. Everyone who is both strong and happy is not wise or not quiet. If someone is either funny or curious then alice is both not generous and generous. Everyone who is generous is either not creative or not tall and vice versa. Everyone who is not tall or kind is not brave or old. Everyone who is both happy and brave is both patient and not patient and vice versa. Everyone who is not curious is both not kind and funny and vice versa. If paul is not old or not kind then mary is not rich or wise and vice versa. If someone is not curious or strong then john is either quiet or not wise. If lucy is either not tall or not curious then lucy is not kind and vice versa. If someone is both curious and not funny then lucy is both quiet and tall. Everyone who is either happy or patient is both patient and not humble. Susan is old. Mary is calm or old. Susan is patient. Someone is both not old and not calm. Alice is both strong and old. Alice is strong or not old. | John is kind. | entailment | (((~tall(paul)<~>curious(paul)))=>(?[X]:((rich(X)<~>happy(X)))))&
(![X]:((wise(X)<~>strong(X))=>~quiet(X)))&
((?[X]:(~happy(X)))<=>((~patient(lucy)&~generous(lucy))))&
(![X]:(tall(X)<=>(~happy(X)&rich(X))))&
(![X]:((strong(X)&happy(X))=>(~wise(X)|~quiet(X))))&
((?[X]:((funny(X)<~>curious(X))))=>((~generous(alice)&generous(alice))))&
(![X]:(generous(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:((~tall(X)|kind(X))=>(~brave(X)|old(X))))&
(![X]:((happy(X)&brave(X))<=>(patient(X)&~patient(X))))&
(![X]:(~curious(X)<=>(~kind(X)&funny(X))))&
(((~old(paul)|~kind(paul)))<=>((~rich(mary)|wise(mary))))&
((?[X]:((~curious(X)|strong(X))))=>((quiet(john)<~>~wise(john))))&
(((~tall(lucy)<~>~curious(lucy)))<=>(~kind(lucy)))&
((?[X]:((curious(X)&~funny(X))))=>((quiet(lucy)&tall(lucy))))&
(![X]:((happy(X)<~>patient(X))=>(patient(X)&~humble(X))))&
(old(susan))&
((calm(mary)|old(mary)))&
(patient(susan))&
(?[X]:((~old(X)&~calm(X))))&
((strong(alice)&old(alice)))&
((strong(alice)|~old(alice))) | kind(john) | [
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 281405501020339827596921
% SZS output start Proof for 281405501020339827596921
6. ? [X0] : (funny(X0) <~> curious(X0)) => (generous(alice) & ~generous(alice)) [input p5]
10. ! [X0] : (~curious(X0) <=> (funny(X0) & ~kind(X0))) [input p9]
22. ~kind(john) [input hypothesis]
28. (generous(alice) & ~generous(alice)) | ! [X0] : (funny(X0) <=> curious(X0)) [ennf transformation 6]
45. (generous(alice) & ~generous(alice)) | ! [X0] : ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))) [nnf transformation 28]
49. ! [X0] : ((~curious(X0) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | curious(X0))) [nnf transformation 10]
50. ! [X0] : ((~curious(X0) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | curious(X0))) [flattening 49]
71. ~generous(alice) | curious(X0) | ~funny(X0) [cnf transformation 45]
72. ~generous(alice) | funny(X0) | ~curious(X0) [cnf transformation 45]
73. generous(alice) | curious(X0) | ~funny(X0) [cnf transformation 45]
74. generous(alice) | funny(X0) | ~curious(X0) [cnf transformation 45]
86. funny(X0) | curious(X0) [cnf transformation 50]
87. ~funny(X0) | ~curious(X0) | kind(X0) [cnf transformation 50]
112. ~kind(john) [cnf transformation 22]
154. 9 <=> ! [X0] : (funny(X0) | ~curious(X0)) [avatar definition]
155. funny(X0) | ~curious(X0) <- (9) [avatar component clause 154]
157. 10 <=> generous(alice) [avatar definition]
160. 9 | 10 [avatar split clause 74,157,154]
162. 11 <=> ! [X0] : (curious(X0) | ~funny(X0)) [avatar definition]
163. curious(X0) | ~funny(X0) <- (11) [avatar component clause 162]
164. 11 | 10 [avatar split clause 73,157,162]
165. 9 | ~10 [avatar split clause 72,157,154]
166. 11 | ~10 [avatar split clause 71,157,162]
201. 19 <=> ! [X0] : curious(X0) [avatar definition]
202. curious(X0) <- (19) [avatar component clause 201]
225. 23 <=> ! [X0] : funny(X0) [avatar definition]
226. funny(X0) <- (23) [avatar component clause 225]
248. ~curious(X1) | kind(X1) <- (23) [resolution 87,226]
249. kind(X1) <- (19, 23) [subsumption resolution 248,202]
250. $false <- (19, 23) [resolution 249,112]
254. ~19 | ~23 [avatar contradiction clause 250]
255. funny(X0) <- (9, 19) [subsumption resolution 155,202]
256. 23 | ~9 | ~19 [avatar split clause 255,201,154,225]
257. curious(X0) <- (11) [subsumption resolution 163,86]
258. 19 | ~11 [avatar split clause 257,162,201]
261. $false [avatar sat refutation 160,164,165,166,254,256,258]
% SZS output end Proof for 281405501020339827596921
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not humble or not quiet then someone is strong or not tall. If paul is strong then someone is either old or curious and vice versa. Everyone who is not happy is not brave. Everyone who is either not curious or rich is kind or not happy and vice versa. If someone is funny or not quiet then fred is both not creative and not kind and vice versa. If john is old or not rich then john is either patient or not funny and vice versa. Everyone who is either not wise or not curious is curious and vice versa. Everyone who is kind or tall is not rich. Everyone who is both funny and patient is both rich and brave. If alice is not happy then mary is not old or generous and vice versa. Everyone who is either not old or not generous is patient or quiet and vice versa. Everyone who is either humble or happy is rich and vice versa. Everyone who is not humble or not rich is humble. If someone is either quiet or wise then fred is old or funny and vice versa. If someone is both calm and quiet then someone is both not creative and brave and vice versa. If someone is not patient then fred is either not patient or not kind. Alice is not creative. Lucy is either funny or not quiet. Someone is either not tall or funny. Fred is both happy and generous. Someone is calm or not curious. Susan is either not happy or strong. Someone is either not creative or patient. | Fred is not quiet. | entailment | (((~humble(paul)|~quiet(paul)))=>(?[X]:((strong(X)|~tall(X)))))&
((strong(paul))<=>(?[X]:((old(X)<~>curious(X)))))&
(![X]:(~happy(X)=>~brave(X)))&
(![X]:((~curious(X)<~>rich(X))<=>(kind(X)|~happy(X))))&
((?[X]:((funny(X)|~quiet(X))))<=>((~creative(fred)&~kind(fred))))&
(((old(john)|~rich(john)))<=>((patient(john)<~>~funny(john))))&
(![X]:((~wise(X)<~>~curious(X))<=>curious(X)))&
(![X]:((kind(X)|tall(X))=>~rich(X)))&
(![X]:((funny(X)&patient(X))=>(rich(X)&brave(X))))&
((~happy(alice))<=>((~old(mary)|generous(mary))))&
(![X]:((~old(X)<~>~generous(X))<=>(patient(X)|quiet(X))))&
(![X]:((humble(X)<~>happy(X))<=>rich(X)))&
(![X]:((~humble(X)|~rich(X))=>humble(X)))&
((?[X]:((quiet(X)<~>wise(X))))<=>((old(fred)|funny(fred))))&
((?[X]:((calm(X)&quiet(X))))<=>(?[X]:((~creative(X)&brave(X)))))&
((?[X]:(~patient(X)))=>((~patient(fred)<~>~kind(fred))))&
(~creative(alice))&
((funny(lucy)<~>~quiet(lucy)))&
(?[X]:((~tall(X)<~>funny(X))))&
((happy(fred)&generous(fred)))&
(?[X]:((calm(X)|~curious(X))))&
((~happy(susan)<~>strong(susan)))&
(?[X]:((~creative(X)<~>patient(X)))) | ~quiet(fred) | [
"p4",
"p6",
"p8",
"p10",
"p11",
"p12",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7558295762554070629905192
% SZS output start Proof for 7558295762554070629905192
5. ? [X0] : (~quiet(X0) | funny(X0)) <=> (~kind(fred) & ~creative(fred)) [input p4]
7. ! [X0] : ((~wise(X0) <~> ~curious(X0)) <=> curious(X0)) [input p6]
9. ! [X0] : ((patient(X0) & funny(X0)) => (brave(X0) & rich(X0))) [input p8]
11. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> (quiet(X0) | patient(X0))) [input p10]
12. ! [X0] : ((humble(X0) <~> happy(X0)) <=> rich(X0)) [input p11]
13. ! [X0] : ((~rich(X0) | ~humble(X0)) => humble(X0)) [input p12]
14. ? [X0] : (quiet(X0) <~> wise(X0)) <=> (funny(fred) | old(fred)) [input p13]
16. ? [X0] : ~patient(X0) => (~patient(fred) <~> ~kind(fred)) [input p15]
20. generous(fred) & happy(fred) [input p19]
24. quiet(fred) [input hypothesis]
29. ! [X0] : ((brave(X0) & rich(X0)) | (~patient(X0) | ~funny(X0))) [ennf transformation 9]
30. ! [X0] : ((brave(X0) & rich(X0)) | ~patient(X0) | ~funny(X0)) [flattening 29]
31. ! [X0] : (humble(X0) | (rich(X0) & humble(X0))) [ennf transformation 13]
32. (~patient(fred) <~> ~kind(fred)) | ! [X0] : patient(X0) [ennf transformation 16]
41. (? [X0] : (~quiet(X0) | funny(X0)) | (kind(fred) | creative(fred))) & ((~kind(fred) & ~creative(fred)) | ! [X0] : (quiet(X0) & ~funny(X0))) [nnf transformation 5]
42. (? [X0] : (~quiet(X0) | funny(X0)) | kind(fred) | creative(fred)) & ((~kind(fred) & ~creative(fred)) | ! [X0] : (quiet(X0) & ~funny(X0))) [flattening 41]
43. (? [X0] : (~quiet(X0) | funny(X0)) | kind(fred) | creative(fred)) & ((~kind(fred) & ~creative(fred)) | ! [X1] : (quiet(X1) & ~funny(X1))) [rectify 42]
44. ? [X0] : (~quiet(X0) | funny(X0)) => (~quiet(sK2) | funny(sK2)) [choice axiom]
45. ((~quiet(sK2) | funny(sK2)) | kind(fred) | creative(fred)) & ((~kind(fred) & ~creative(fred)) | ! [X1] : (quiet(X1) & ~funny(X1))) [skolemisation 43,44]
48. ! [X0] : ((((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | ~curious(X0)) & (curious(X0) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0))))) [nnf transformation 7]
51. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 11]
52. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [flattening 51]
53. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ~rich(X0)) & (rich(X0) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [nnf transformation 12]
54. (? [X0] : ((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (~funny(fred) & ~old(fred))) & ((funny(fred) | old(fred)) | ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) [nnf transformation 14]
55. (? [X0] : ((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (~funny(fred) & ~old(fred))) & (funny(fred) | old(fred) | ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) [flattening 54]
56. (? [X0] : ((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (~funny(fred) & ~old(fred))) & (funny(fred) | old(fred) | ! [X1] : ((quiet(X1) | ~wise(X1)) & (wise(X1) | ~quiet(X1)))) [rectify 55]
57. ? [X0] : ((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) => ((~wise(sK3) | ~quiet(sK3)) & (wise(sK3) | quiet(sK3))) [choice axiom]
58. (((~wise(sK3) | ~quiet(sK3)) & (wise(sK3) | quiet(sK3))) | (~funny(fred) & ~old(fred))) & (funny(fred) | old(fred) | ! [X1] : ((quiet(X1) | ~wise(X1)) & (wise(X1) | ~quiet(X1)))) [skolemisation 56,57]
64. ((kind(fred) | patient(fred)) & (~kind(fred) | ~patient(fred))) | ! [X0] : patient(X0) [nnf transformation 32]
90. ~kind(fred) | ~funny(X1) [cnf transformation 45]
100. curious(X0) | ~wise(X0) | curious(X0) [cnf transformation 48]
101. ~curious(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 48]
105. ~patient(X0) | rich(X0) | ~funny(X0) [cnf transformation 30]
113. ~generous(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 52]
119. ~rich(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 53]
120. humble(X0) | humble(X0) [cnf transformation 31]
122. funny(fred) | old(fred) | wise(X1) | ~quiet(X1) [cnf transformation 58]
133. kind(fred) | patient(fred) | patient(X0) [cnf transformation 64]
139. happy(fred) [cnf transformation 20]
140. generous(fred) [cnf transformation 20]
146. quiet(fred) [cnf transformation 24]
147. humble(X0) [duplicate literal removal 120]
148. curious(X0) | ~wise(X0) [duplicate literal removal 100]
149. ~wise(X0) | ~curious(X0) [duplicate literal removal 101]
195. 11 <=> kind(fred) [avatar definition]
212. 15 <=> ! [X1] : ~funny(X1) [avatar definition]
213. ~funny(X1) <- (15) [avatar component clause 212]
214. 15 | ~11 [avatar split clause 90,195,212]
239. ~wise(X0) [subsumption resolution 148,149]
257. 23 <=> funny(fred) [avatar definition]
258. funny(fred) <- (23) [avatar component clause 257]
267. 25 <=> old(fred) [avatar definition]
271. funny(fred) | old(fred) | ~quiet(X1) [subsumption resolution 122,239]
273. 26 <=> ! [X1] : ~quiet(X1) [avatar definition]
274. ~quiet(X1) <- (26) [avatar component clause 273]
275. 26 | 25 | 23 [avatar split clause 271,257,267,273]
303. 33 <=> ! [X0] : patient(X0) [avatar definition]
304. patient(X0) <- (33) [avatar component clause 303]
306. 34 <=> patient(fred) [avatar definition]
308. patient(fred) <- (34) [avatar component clause 306]
309. 33 | 34 | 11 [avatar split clause 133,195,306,303]
360. $false <- (15, 23) [resolution 258,213]
361. ~15 | ~23 [avatar contradiction clause 360]
388. ~funny(X0) | rich(X0) <- (33) [resolution 105,304]
396. $false <- (26) [resolution 274,146]
399. ~26 [avatar contradiction clause 396]
400. ~old(fred) | ~quiet(fred) [resolution 113,140]
401. rich(fred) <- (23, 33) [resolution 388,258]
427. ~humble(fred) | ~happy(fred) <- (23, 33) [resolution 119,401]
431. ~happy(fred) <- (23, 33) [subsumption resolution 427,147]
432. $false <- (23, 33) [subsumption resolution 431,139]
433. ~23 | ~33 [avatar contradiction clause 432]
434. ~old(fred) [subsumption resolution 400,146]
435. ~25 [avatar split clause 434,267]
462. rich(fred) | ~funny(fred) <- (34) [resolution 308,105]
464. rich(fred) <- (23, 34) [subsumption resolution 462,258]
559. ~humble(fred) | ~happy(fred) <- (23, 34) [resolution 464,119]
565. ~happy(fred) <- (23, 34) [subsumption resolution 559,147]
566. $false <- (23, 34) [subsumption resolution 565,139]
567. ~23 | ~34 [avatar contradiction clause 566]
568. $false [avatar sat refutation 214,275,309,361,399,433,435,567]
% SZS output end Proof for 7558295762554070629905192
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or old is either not old or humble. Everyone who is either humble or not old is generous or strong and vice versa. If someone is either not patient or not humble then someone is old or wise and vice versa. Everyone who is old or not wise is both not humble and not creative and vice versa. If someone is either kind or not creative then susan is not kind and vice versa. Everyone who is both not patient and old is both old and not brave and vice versa. Everyone who is either generous or happy is funny. If someone is either not funny or funny then paul is not happy or not strong. If someone is brave or creative then someone is both calm and not creative. Everyone who is both wise and not tall is not kind and vice versa. If someone is either brave or curious then someone is both quiet and not humble. If alice is not strong or not brave then someone is both not brave and not rich and vice versa. Everyone who is both patient and generous is not wise. If someone is not calm then susan is both not brave and old. If someone is both happy and rich then someone is either not creative or creative. Everyone who is patient is creative or generous and vice versa. John is both not curious and not patient. Someone is either not wise or old. Paul is not rich or not tall. Mary is both not tall and creative. Someone is either strong or not happy. Paul is either brave or kind. Someone is both not brave and not humble. Someone is not wise or wise. | John is generous. | contradiction | (![X]:((curious(X)<~>old(X))=>(~old(X)<~>humble(X))))&
(![X]:((humble(X)<~>~old(X))<=>(generous(X)|strong(X))))&
((?[X]:((~patient(X)<~>~humble(X))))<=>(?[X]:((old(X)|wise(X)))))&
(![X]:((old(X)|~wise(X))<=>(~humble(X)&~creative(X))))&
((?[X]:((kind(X)<~>~creative(X))))<=>(~kind(susan)))&
(![X]:((~patient(X)&old(X))<=>(old(X)&~brave(X))))&
(![X]:((generous(X)<~>happy(X))=>funny(X)))&
((?[X]:((~funny(X)<~>funny(X))))=>((~happy(paul)|~strong(paul))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:((calm(X)&~creative(X)))))&
(![X]:((wise(X)&~tall(X))<=>~kind(X)))&
((?[X]:((brave(X)<~>curious(X))))=>(?[X]:((quiet(X)&~humble(X)))))&
(((~strong(alice)|~brave(alice)))<=>(?[X]:((~brave(X)&~rich(X)))))&
(![X]:((patient(X)&generous(X))=>~wise(X)))&
((?[X]:(~calm(X)))=>((~brave(susan)&old(susan))))&
((?[X]:((happy(X)&rich(X))))=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:(patient(X)<=>(creative(X)|generous(X))))&
((~curious(john)&~patient(john)))&
(?[X]:((~wise(X)<~>old(X))))&
((~rich(paul)|~tall(paul)))&
((~tall(mary)&creative(mary)))&
(?[X]:((strong(X)<~>~happy(X))))&
((brave(paul)<~>kind(paul)))&
(?[X]:((~brave(X)&~humble(X))))&
(?[X]:((~wise(X)|wise(X)))) | generous(john) | [
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7373497786958525559847424
% SZS output start Proof for 7373497786958525559847424
16. ! [X0] : (patient(X0) <=> (generous(X0) | creative(X0))) [input p15]
17. ~patient(john) & ~curious(john) [input p16]
25. generous(john) [input hypothesis]
78. ! [X0] : ((patient(X0) | (~generous(X0) & ~creative(X0))) & ((generous(X0) | creative(X0)) | ~patient(X0))) [nnf transformation 16]
79. ! [X0] : ((patient(X0) | (~generous(X0) & ~creative(X0))) & (generous(X0) | creative(X0) | ~patient(X0))) [flattening 78]
141. ~generous(X0) | patient(X0) [cnf transformation 79]
143. ~patient(john) [cnf transformation 17]
156. generous(john) [cnf transformation 25]
326. patient(john) [resolution 141,156]
327. $false [subsumption resolution 326,143]
% SZS output end Proof for 7373497786958525559847424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not calm is kind or tall and vice versa. Everyone who is curious or not kind is creative. Everyone who is either curious or kind is not brave or not strong. Everyone who is either brave or not rich is either old or creative and vice versa. If susan is either not generous or strong then susan is both not rich and not patient and vice versa. If someone is both old and patient then lucy is either not happy or not quiet and vice versa. If fred is both wise and not curious then someone is not calm and vice versa. If mary is either quiet or not tall then someone is not happy. If someone is either old or not old then fred is not calm and vice versa. If someone is tall or not quiet then someone is kind. Everyone who is brave or quiet is both not humble and rich and vice versa. If someone is not brave or not tall then someone is both tall and not brave. If mary is either wise or not generous then fred is not happy or not rich. If someone is either not quiet or not rich then fred is not wise and vice versa. If someone is wise then fred is both patient and not strong. Everyone who is not patient is not happy or not patient and vice versa. Fred is either not happy or brave. Someone is both rich and quiet. Paul is either not curious or not calm. Paul is both tall and patient. Someone is either quiet or not strong. Someone is tall or not happy. Paul is either not tall or not kind. | Susan is calm. | contradiction | (![X]:((brave(X)&~calm(X))<=>(kind(X)|tall(X))))&
(![X]:((curious(X)|~kind(X))=>creative(X)))&
(![X]:((curious(X)<~>kind(X))=>(~brave(X)|~strong(X))))&
(![X]:((brave(X)<~>~rich(X))<=>(old(X)<~>creative(X))))&
(((~generous(susan)<~>strong(susan)))<=>((~rich(susan)&~patient(susan))))&
((?[X]:((old(X)&patient(X))))<=>((~happy(lucy)<~>~quiet(lucy))))&
(((wise(fred)&~curious(fred)))<=>(?[X]:(~calm(X))))&
(((quiet(mary)<~>~tall(mary)))=>(?[X]:(~happy(X))))&
((?[X]:((old(X)<~>~old(X))))<=>(~calm(fred)))&
((?[X]:((tall(X)|~quiet(X))))=>(?[X]:(kind(X))))&
(![X]:((brave(X)|quiet(X))<=>(~humble(X)&rich(X))))&
((?[X]:((~brave(X)|~tall(X))))=>(?[X]:((tall(X)&~brave(X)))))&
(((wise(mary)<~>~generous(mary)))=>((~happy(fred)|~rich(fred))))&
((?[X]:((~quiet(X)<~>~rich(X))))<=>(~wise(fred)))&
((?[X]:(wise(X)))=>((patient(fred)&~strong(fred))))&
(![X]:(~patient(X)<=>(~happy(X)|~patient(X))))&
((~happy(fred)<~>brave(fred)))&
(?[X]:((rich(X)&quiet(X))))&
((~curious(paul)<~>~calm(paul)))&
((tall(paul)&patient(paul)))&
(?[X]:((quiet(X)<~>~strong(X))))&
(?[X]:((tall(X)|~happy(X))))&
((~tall(paul)<~>~kind(paul))) | calm(susan) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3578568831204561883554068
% SZS output start Proof for 3578568831204561883554068
1. ! [X0] : ((~calm(X0) & brave(X0)) <=> (tall(X0) | kind(X0))) [input p0]
12. ? [X0] : (~tall(X0) | ~brave(X0)) => ? [X0] : (~brave(X0) & tall(X0)) [input p11]
24. calm(susan) [input hypothesis]
26. ? [X0] : (~tall(X0) | ~brave(X0)) => ? [X1] : (~brave(X1) & tall(X1)) [rectify 12]
32. ? [X1] : (~brave(X1) & tall(X1)) | ! [X0] : (tall(X0) & brave(X0)) [ennf transformation 26]
36. ! [X0] : (((~calm(X0) & brave(X0)) | (~tall(X0) & ~kind(X0))) & ((tall(X0) | kind(X0)) | (calm(X0) | ~brave(X0)))) [nnf transformation 1]
37. ! [X0] : (((~calm(X0) & brave(X0)) | (~tall(X0) & ~kind(X0))) & (tall(X0) | kind(X0) | calm(X0) | ~brave(X0))) [flattening 36]
63. ? [X0] : (~brave(X0) & tall(X0)) | ! [X1] : (tall(X1) & brave(X1)) [rectify 32]
64. ? [X0] : (~brave(X0) & tall(X0)) => (~brave(sK5) & tall(sK5)) [choice axiom]
65. (~brave(sK5) & tall(sK5)) | ! [X1] : (tall(X1) & brave(X1)) [skolemisation 63,64]
85. ~tall(X0) | brave(X0) [cnf transformation 37]
87. ~tall(X0) | ~calm(X0) [cnf transformation 37]
129. tall(sK5) | tall(X1) [cnf transformation 65]
131. ~brave(sK5) | tall(X1) [cnf transformation 65]
156. calm(susan) [cnf transformation 24]
264. 23 <=> ! [X1] : tall(X1) [avatar definition]
265. tall(X1) <- (23) [avatar component clause 264]
267. 24 <=> brave(sK5) [avatar definition]
269. ~brave(sK5) <- (~24) [avatar component clause 267]
270. 23 | ~24 [avatar split clause 131,267,264]
276. 26 <=> tall(sK5) [avatar definition]
278. tall(sK5) <- (26) [avatar component clause 276]
279. 23 | 26 [avatar split clause 129,276,264]
377. ~calm(X0) <- (23) [resolution 87,265]
379. $false <- (23) [resolution 377,156]
380. ~23 [avatar contradiction clause 379]
384. brave(sK5) <- (26) [resolution 278,85]
385. $false <- (~24, 26) [subsumption resolution 384,269]
386. 24 | ~26 [avatar contradiction clause 385]
387. $false [avatar sat refutation 270,279,380,386]
% SZS output end Proof for 3578568831204561883554068
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not old or not curious then john is not wise or not quiet. Everyone who is strong or calm is both calm and tall and vice versa. If lucy is not wise or not patient then someone is both quiet and brave and vice versa. Everyone who is not quiet or generous is both calm and not happy and vice versa. Everyone who is rich is strong or not humble and vice versa. Everyone who is not brave or funny is either not calm or not patient and vice versa. Everyone who is not humble is either not funny or not brave. If someone is not rich then fred is either wise or funny. Everyone who is not happy or old is not tall and vice versa. Everyone who is both not patient and not tall is either strong or not tall. Everyone who is patient or curious is wise and vice versa. Everyone who is both funny and not rich is not calm or patient and vice versa. If paul is not strong or not old then someone is both funny and brave. Everyone who is both rich and happy is not brave or strong and vice versa. Everyone who is both not generous and strong is either tall or funny. Everyone who is not creative is not funny or not creative and vice versa. Someone is both not funny and not curious. Someone is curious or not funny. John is not generous or creative. Someone is old. Someone is both strong and not brave. John is happy or not brave. Susan is kind. Mary is either rich or not creative. | Lucy is calm. | entailment | (((~old(susan)|~curious(susan)))=>((~wise(john)|~quiet(john))))&
(![X]:((strong(X)|calm(X))<=>(calm(X)&tall(X))))&
(((~wise(lucy)|~patient(lucy)))<=>(?[X]:((quiet(X)&brave(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(calm(X)&~happy(X))))&
(![X]:(rich(X)<=>(strong(X)|~humble(X))))&
(![X]:((~brave(X)|funny(X))<=>(~calm(X)<~>~patient(X))))&
(![X]:(~humble(X)=>(~funny(X)<~>~brave(X))))&
((?[X]:(~rich(X)))=>((wise(fred)<~>funny(fred))))&
(![X]:((~happy(X)|old(X))<=>~tall(X)))&
(![X]:((~patient(X)&~tall(X))=>(strong(X)<~>~tall(X))))&
(![X]:((patient(X)|curious(X))<=>wise(X)))&
(![X]:((funny(X)&~rich(X))<=>(~calm(X)|patient(X))))&
(((~strong(paul)|~old(paul)))=>(?[X]:((funny(X)&brave(X)))))&
(![X]:((rich(X)&happy(X))<=>(~brave(X)|strong(X))))&
(![X]:((~generous(X)&strong(X))=>(tall(X)<~>funny(X))))&
(![X]:(~creative(X)<=>(~funny(X)|~creative(X))))&
(?[X]:((~funny(X)&~curious(X))))&
(?[X]:((curious(X)|~funny(X))))&
((~generous(john)|creative(john)))&
(?[X]:(old(X)))&
(?[X]:((strong(X)&~brave(X))))&
((happy(john)|~brave(john)))&
(kind(susan))&
((rich(mary)<~>~creative(mary))) | calm(lucy) | [
"p2",
"p3",
"p5",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1716688728566377918848886
% SZS output start Proof for 1716688728566377918848886
3. (~patient(lucy) | ~wise(lucy)) <=> ? [X0] : (brave(X0) & quiet(X0)) [input p2]
4. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (~happy(X0) & calm(X0))) [input p3]
6. ! [X0] : ((funny(X0) | ~brave(X0)) <=> (~calm(X0) <~> ~patient(X0))) [input p5]
11. ! [X0] : ((curious(X0) | patient(X0)) <=> wise(X0)) [input p10]
12. ! [X0] : ((~rich(X0) & funny(X0)) <=> (patient(X0) | ~calm(X0))) [input p11]
14. ! [X0] : ((happy(X0) & rich(X0)) <=> (strong(X0) | ~brave(X0))) [input p13]
25. ~calm(lucy) [input hypothesis]
38. ((~patient(lucy) | ~wise(lucy)) | ! [X0] : (~brave(X0) | ~quiet(X0))) & (? [X0] : (brave(X0) & quiet(X0)) | (patient(lucy) & wise(lucy))) [nnf transformation 3]
39. (~patient(lucy) | ~wise(lucy) | ! [X0] : (~brave(X0) | ~quiet(X0))) & (? [X0] : (brave(X0) & quiet(X0)) | (patient(lucy) & wise(lucy))) [flattening 38]
40. (~patient(lucy) | ~wise(lucy) | ! [X0] : (~brave(X0) | ~quiet(X0))) & (? [X1] : (brave(X1) & quiet(X1)) | (patient(lucy) & wise(lucy))) [rectify 39]
41. ? [X1] : (brave(X1) & quiet(X1)) => (brave(sK0) & quiet(sK0)) [choice axiom]
42. (~patient(lucy) | ~wise(lucy) | ! [X0] : (~brave(X0) | ~quiet(X0))) & ((brave(sK0) & quiet(sK0)) | (patient(lucy) & wise(lucy))) [skolemisation 40,41]
43. ! [X0] : (((generous(X0) | ~quiet(X0)) | (happy(X0) | ~calm(X0))) & ((~happy(X0) & calm(X0)) | (~generous(X0) & quiet(X0)))) [nnf transformation 4]
44. ! [X0] : ((generous(X0) | ~quiet(X0) | happy(X0) | ~calm(X0)) & ((~happy(X0) & calm(X0)) | (~generous(X0) & quiet(X0)))) [flattening 43]
47. ! [X0] : (((funny(X0) | ~brave(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (~funny(X0) & brave(X0)))) [nnf transformation 6]
48. ! [X0] : ((funny(X0) | ~brave(X0) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (~funny(X0) & brave(X0)))) [flattening 47]
54. ! [X0] : (((curious(X0) | patient(X0)) | ~wise(X0)) & (wise(X0) | (~curious(X0) & ~patient(X0)))) [nnf transformation 11]
55. ! [X0] : ((curious(X0) | patient(X0) | ~wise(X0)) & (wise(X0) | (~curious(X0) & ~patient(X0)))) [flattening 54]
56. ! [X0] : (((~rich(X0) & funny(X0)) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | (rich(X0) | ~funny(X0)))) [nnf transformation 12]
57. ! [X0] : (((~rich(X0) & funny(X0)) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | rich(X0) | ~funny(X0))) [flattening 56]
60. ! [X0] : (((happy(X0) & rich(X0)) | (~strong(X0) & brave(X0))) & ((strong(X0) | ~brave(X0)) | (~happy(X0) | ~rich(X0)))) [nnf transformation 14]
61. ! [X0] : (((happy(X0) & rich(X0)) | (~strong(X0) & brave(X0))) & (strong(X0) | ~brave(X0) | ~happy(X0) | ~rich(X0))) [flattening 60]
85. ~patient(lucy) | ~wise(lucy) | ~brave(X0) | ~quiet(X0) [cnf transformation 42]
86. calm(X0) | quiet(X0) [cnf transformation 44]
97. ~funny(X0) | calm(X0) | patient(X0) [cnf transformation 48]
109. ~patient(X0) | wise(X0) [cnf transformation 55]
112. patient(X0) | ~calm(X0) | rich(X0) | ~funny(X0) [cnf transformation 57]
113. funny(X0) | calm(X0) [cnf transformation 57]
115. ~rich(X0) | calm(X0) [cnf transformation 57]
122. rich(X0) | brave(X0) [cnf transformation 61]
141. ~calm(lucy) [cnf transformation 25]
162. 5 <=> ! [X0] : (~brave(X0) | ~quiet(X0)) [avatar definition]
163. ~brave(X0) | ~quiet(X0) <- (5) [avatar component clause 162]
165. 6 <=> wise(lucy) [avatar definition]
167. ~wise(lucy) <- (~6) [avatar component clause 165]
169. 7 <=> patient(lucy) [avatar definition]
170. patient(lucy) <- (7) [avatar component clause 169]
171. ~patient(lucy) <- (~7) [avatar component clause 169]
172. 5 | ~6 | ~7 [avatar split clause 85,169,165,162]
198. ~funny(X0) | rich(X0) | patient(X0) [subsumption resolution 112,97]
257. quiet(lucy) [resolution 86,141]
289. brave(X1) | calm(X1) [resolution 122,115]
333. 26 <=> brave(lucy) [avatar definition]
334. brave(lucy) <- (26) [avatar component clause 333]
335. ~brave(lucy) <- (~26) [avatar component clause 333]
421. rich(X1) | patient(X1) | calm(X1) [resolution 198,113]
536. ~quiet(lucy) <- (5, 26) [resolution 334,163]
537. $false <- (5, 26) [subsumption resolution 536,257]
538. ~5 | ~26 [avatar contradiction clause 537]
555. patient(X1) | calm(X1) [subsumption resolution 421,115]
587. calm(lucy) <- (~26) [resolution 335,289]
589. $false <- (~26) [subsumption resolution 587,141]
590. 26 [avatar contradiction clause 589]
606. calm(lucy) <- (~7) [resolution 555,171]
611. $false <- (~7) [subsumption resolution 606,141]
612. 7 [avatar contradiction clause 611]
617. wise(lucy) <- (7) [resolution 170,109]
618. $false <- (~6, 7) [subsumption resolution 617,167]
619. 6 | ~7 [avatar contradiction clause 618]
620. $false [avatar sat refutation 172,538,590,612,619]
% SZS output end Proof for 1716688728566377918848886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not funny is kind. Everyone who is both not happy and quiet is not happy or humble and vice versa. If someone is either humble or not brave then paul is either not happy or funny and vice versa. Everyone who is either not patient or kind is rich. If someone is not calm then fred is both not funny and not curious and vice versa. If someone is strong then someone is patient or not happy and vice versa. If someone is both kind and not humble then alice is both not generous and kind and vice versa. Everyone who is not funny or not wise is either patient or funny and vice versa. If someone is calm then fred is not old or not quiet and vice versa. If john is either patient or not patient then someone is not tall or happy. If someone is either strong or not rich then john is both not wise and curious and vice versa. If someone is funny then paul is both kind and not happy and vice versa. Everyone who is either quiet or rich is either not wise or not quiet and vice versa. Everyone who is rich is not tall. Everyone who is calm is both humble and not patient and vice versa. If someone is calm then someone is funny. Someone is either brave or not humble. Someone is not calm or not patient. Someone is wise or not curious. Someone is both not rich and tall. Someone is either wise or not kind. Someone is both not humble and not strong. Alice is either not generous or generous. Someone is creative or wise. | Fred is not wise. | contradiction | (![X]:((~strong(X)|~funny(X))=>kind(X)))&
(![X]:((~happy(X)&quiet(X))<=>(~happy(X)|humble(X))))&
((?[X]:((humble(X)<~>~brave(X))))<=>((~happy(paul)<~>funny(paul))))&
(![X]:((~patient(X)<~>kind(X))=>rich(X)))&
((?[X]:(~calm(X)))<=>((~funny(fred)&~curious(fred))))&
((?[X]:(strong(X)))<=>(?[X]:((patient(X)|~happy(X)))))&
((?[X]:((kind(X)&~humble(X))))<=>((~generous(alice)&kind(alice))))&
(![X]:((~funny(X)|~wise(X))<=>(patient(X)<~>funny(X))))&
((?[X]:(calm(X)))<=>((~old(fred)|~quiet(fred))))&
(((patient(john)<~>~patient(john)))=>(?[X]:((~tall(X)|happy(X)))))&
((?[X]:((strong(X)<~>~rich(X))))<=>((~wise(john)&curious(john))))&
((?[X]:(funny(X)))<=>((kind(paul)&~happy(paul))))&
(![X]:((quiet(X)<~>rich(X))<=>(~wise(X)<~>~quiet(X))))&
(![X]:(rich(X)=>~tall(X)))&
(![X]:(calm(X)<=>(humble(X)&~patient(X))))&
((?[X]:(calm(X)))=>(?[X]:(funny(X))))&
(?[X]:((brave(X)<~>~humble(X))))&
(?[X]:((~calm(X)|~patient(X))))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~generous(alice)<~>generous(alice)))&
(?[X]:((creative(X)|wise(X)))) | ~wise(fred) | [
"p0",
"p3",
"p4",
"p7",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6654183402885025084753892
% SZS output start Proof for 6654183402885025084753892
1. ! [X0] : ((~funny(X0) | ~strong(X0)) => kind(X0)) [input p0]
4. ! [X0] : ((~patient(X0) <~> kind(X0)) => rich(X0)) [input p3]
5. ? [X0] : ~calm(X0) <=> (~curious(fred) & ~funny(fred)) [input p4]
8. ! [X0] : ((~wise(X0) | ~funny(X0)) <=> (patient(X0) <~> funny(X0))) [input p7]
13. ! [X0] : ((quiet(X0) <~> rich(X0)) <=> (~wise(X0) <~> ~quiet(X0))) [input p12]
15. ! [X0] : (calm(X0) <=> (~patient(X0) & humble(X0))) [input p14]
22. ? [X0] : (~strong(X0) & ~humble(X0)) [input p21]
25. ~wise(fred) [input hypothesis]
29. ! [X0] : (kind(X0) | (funny(X0) & strong(X0))) [ennf transformation 1]
30. ! [X0] : (rich(X0) | (~patient(X0) <=> kind(X0))) [ennf transformation 4]
40. ! [X0] : (rich(X0) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0)))) [nnf transformation 30]
41. (? [X0] : ~calm(X0) | (curious(fred) | funny(fred))) & ((~curious(fred) & ~funny(fred)) | ! [X0] : calm(X0)) [nnf transformation 5]
42. (? [X0] : ~calm(X0) | curious(fred) | funny(fred)) & ((~curious(fred) & ~funny(fred)) | ! [X0] : calm(X0)) [flattening 41]
43. (? [X0] : ~calm(X0) | curious(fred) | funny(fred)) & ((~curious(fred) & ~funny(fred)) | ! [X1] : calm(X1)) [rectify 42]
44. ? [X0] : ~calm(X0) => ~calm(sK1) [choice axiom]
45. (~calm(sK1) | curious(fred) | funny(fred)) & ((~curious(fred) & ~funny(fred)) | ! [X1] : calm(X1)) [skolemisation 43,44]
56. ! [X0] : (((~wise(X0) | ~funny(X0)) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0)))) & (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | (wise(X0) & funny(X0)))) [nnf transformation 8]
57. ! [X0] : ((~wise(X0) | ~funny(X0) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0)))) & (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | (wise(X0) & funny(X0)))) [flattening 56]
76. ! [X0] : ((((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))))) [nnf transformation 13]
77. ! [X0] : ((calm(X0) | (patient(X0) | ~humble(X0))) & ((~patient(X0) & humble(X0)) | ~calm(X0))) [nnf transformation 15]
78. ! [X0] : ((calm(X0) | patient(X0) | ~humble(X0)) & ((~patient(X0) & humble(X0)) | ~calm(X0))) [flattening 77]
94. ? [X0] : (~strong(X0) & ~humble(X0)) => (~strong(sK15) & ~humble(sK15)) [choice axiom]
95. ~strong(sK15) & ~humble(sK15) [skolemisation 22,94]
98. kind(X0) | funny(X0) [cnf transformation 29]
113. ~patient(X0) | rich(X0) | ~kind(X0) [cnf transformation 40]
114. ~funny(fred) | calm(X1) [cnf transformation 45]
124. funny(X0) | patient(X0) | funny(X0) [cnf transformation 57]
147. quiet(X0) | wise(X0) | quiet(X0) | ~rich(X0) [cnf transformation 76]
150. ~rich(X0) | ~quiet(X0) | ~quiet(X0) | wise(X0) [cnf transformation 76]
153. ~calm(X0) | humble(X0) [cnf transformation 78]
165. ~humble(sK15) [cnf transformation 95]
169. ~wise(fred) [cnf transformation 25]
171. quiet(X0) | wise(X0) | ~rich(X0) [duplicate literal removal 147]
173. ~rich(X0) | ~quiet(X0) | wise(X0) [duplicate literal removal 150]
176. patient(X0) | funny(X0) [duplicate literal removal 124]
209. 7 <=> funny(fred) [avatar definition]
222. 10 <=> ! [X1] : calm(X1) [avatar definition]
223. calm(X1) <- (10) [avatar component clause 222]
225. 10 | ~7 [avatar split clause 114,209,222]
347. ~rich(X0) | wise(X0) [subsumption resolution 171,173]
410. rich(X0) | ~kind(X0) | funny(X0) [resolution 113,176]
412. rich(X0) | funny(X0) [subsumption resolution 410,98]
444. wise(X1) | funny(X1) [resolution 412,347]
448. funny(fred) [resolution 444,169]
453. 7 [avatar split clause 448,209]
459. humble(X1) <- (10) [resolution 223,153]
473. $false <- (10) [resolution 459,165]
474. ~10 [avatar contradiction clause 473]
478. $false [avatar sat refutation 225,453,474]
% SZS output end Proof for 6654183402885025084753892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is old then alice is both calm and not strong.
If someone is both curious and not strong then alice is not rich or not patient.
Everyone who is either curious or calm is patient.
Everyone who is either not wise or rich is tall.
Everyone who is quiet is either not patient or not strong and vice versa.
If someone is not wise or not humble then someone is both not kind and not quiet and vice versa.
If susan is either patient or not funny then someone is not brave and vice versa.
If someone is not quiet or calm then lucy is either tall or not brave.
If someone is wise or not tall then paul is happy and vice versa.
If alice is either wise or generous then fred is either curious or old and vice versa.
Everyone who is both not wise and kind is rich.
Everyone who is rich or not generous is both happy and not brave.
If susan is either not brave or brave then someone is either not quiet or not strong and vice versa.
If mary is old or not quiet then fred is old.
Everyone who is not creative is not patient or not happy.
Everyone who is both not old and old is not quiet and vice versa.
Lucy is calm.
Someone is not kind.
Alice is curious or funny.
Someone is not generous.
Someone is old.
Someone is either not happy or not creative. | Susan is not quiet. | contradiction | ((old(mary))=>((calm(alice)&~strong(alice))))&
((?[X]:((curious(X)&~strong(X))))=>((~rich(alice)|~patient(alice))))&
(![X]:((curious(X)<~>calm(X))=>patient(X)))&
(![X]:((~wise(X)<~>rich(X))=>tall(X)))&
(![X]:(quiet(X)<=>(~patient(X)<~>~strong(X))))&
((?[X]:((~wise(X)|~humble(X))))<=>(?[X]:((~kind(X)&~quiet(X)))))&
(((patient(susan)<~>~funny(susan)))<=>(?[X]:(~brave(X))))&
((?[X]:((~quiet(X)|calm(X))))=>((tall(lucy)<~>~brave(lucy))))&
((?[X]:((wise(X)|~tall(X))))<=>(happy(paul)))&
(((wise(alice)<~>generous(alice)))<=>((curious(fred)<~>old(fred))))&
(![X]:((~wise(X)&kind(X))=>rich(X)))&
(![X]:((rich(X)|~generous(X))=>(happy(X)&~brave(X))))&
(((~brave(susan)<~>brave(susan)))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(((old(mary)|~quiet(mary)))=>(old(fred)))&
(![X]:(~creative(X)=>(~patient(X)|~happy(X))))&
(![X]:((~old(X)&old(X))<=>~quiet(X)))&
(calm(lucy))&
(?[X]:(~kind(X)))&
((curious(alice)|funny(alice)))&
(?[X]:(~generous(X)))&
(?[X]:(old(X)))&
(?[X]:((~happy(X)<~>~creative(X)))) | ~quiet(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 413658006756127181540420
% SZS output start Proof for 413658006756127181540420
16. ! [X0] : ((old(X0) & ~old(X0)) <=> ~quiet(X0)) [input p15]
23. ~quiet(susan) [input hypothesis]
59. ! [X0] : (((old(X0) & ~old(X0)) | quiet(X0)) & (~quiet(X0) | (~old(X0) | old(X0)))) [nnf transformation 16]
60. ! [X0] : (((old(X0) & ~old(X0)) | quiet(X0)) & (~quiet(X0) | ~old(X0) | old(X0))) [flattening 59]
122. ~old(X0) | quiet(X0) [cnf transformation 60]
123. old(X0) | quiet(X0) [cnf transformation 60]
131. ~quiet(susan) [cnf transformation 23]
224. 21 <=> ! [X0] : quiet(X0) [avatar definition]
225. quiet(X0) <- (21) [avatar component clause 224]
296. quiet(X0) [subsumption resolution 122,123]
297. 21 [avatar split clause 296,224]
323. $false <- (21) [resolution 225,131]
324. ~21 [avatar contradiction clause 323]
325. $false [avatar sat refutation 297,324]
% SZS output end Proof for 413658006756127181540420
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny.
If someone is both humble and curious then alice is either happy or not happy.
If fred is not generous then someone is not humble or not strong and vice versa.
If susan is not strong then john is kind.
If lucy is creative then someone is both happy and funny.
Everyone who is both quiet and humble is both not old and not funny and vice versa.
Everyone who is old is both humble and not tall and vice versa.
If mary is not curious or funny then john is either wise or kind and vice versa.
If alice is both wise and not calm then alice is funny.
Everyone who is calm is both not generous and curious and vice versa.
If someone is quiet then paul is generous or humble and vice versa.
Everyone who is quiet or not wise is old and vice versa.
Everyone who is not creative or creative is not old or quiet and vice versa.
Everyone who is quiet is curious or not brave and vice versa.
Everyone who is creative or not kind is not wise or not curious.
If lucy is wise or not brave then someone is not happy or not funny and vice versa.
Someone is not quiet or old.
Paul is funny.
Alice is either not wise or not kind.
Someone is tall.
Someone is either curious or humble. | Mary is not brave. | contradiction | (![X]:(wise(X)=>funny(X)))&
((?[X]:((humble(X)&curious(X))))=>((happy(alice)<~>~happy(alice))))&
((~generous(fred))<=>(?[X]:((~humble(X)|~strong(X)))))&
((~strong(susan))=>(kind(john)))&
((creative(lucy))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((quiet(X)&humble(X))<=>(~old(X)&~funny(X))))&
(![X]:(old(X)<=>(humble(X)&~tall(X))))&
(((~curious(mary)|funny(mary)))<=>((wise(john)<~>kind(john))))&
(((wise(alice)&~calm(alice)))=>(funny(alice)))&
(![X]:(calm(X)<=>(~generous(X)&curious(X))))&
((?[X]:(quiet(X)))<=>((generous(paul)|humble(paul))))&
(![X]:((quiet(X)|~wise(X))<=>old(X)))&
(![X]:((~creative(X)|creative(X))<=>(~old(X)|quiet(X))))&
(![X]:(quiet(X)<=>(curious(X)|~brave(X))))&
(![X]:((creative(X)|~kind(X))=>(~wise(X)|~curious(X))))&
(((wise(lucy)|~brave(lucy)))<=>(?[X]:((~happy(X)|~funny(X)))))&
(?[X]:((~quiet(X)|old(X))))&
(funny(paul))&
((~wise(alice)<~>~kind(alice)))&
(?[X]:(tall(X)))&
(?[X]:((curious(X)<~>humble(X)))) | ~brave(mary) | [
"p5",
"p6",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 518330563325941422015404
% SZS output start Proof for 518330563325941422015404
6. ! [X0] : ((humble(X0) & quiet(X0)) <=> (~funny(X0) & ~old(X0))) [input p5]
7. ! [X0] : (old(X0) <=> (~tall(X0) & humble(X0))) [input p6]
11. ? [X0] : quiet(X0) <=> (humble(paul) | generous(paul)) [input p10]
12. ! [X0] : ((~wise(X0) | quiet(X0)) <=> old(X0)) [input p11]
14. ! [X0] : (quiet(X0) <=> (~brave(X0) | curious(X0))) [input p13]
22. ~brave(mary) [input hypothesis]
40. ! [X0] : (((humble(X0) & quiet(X0)) | (funny(X0) | old(X0))) & ((~funny(X0) & ~old(X0)) | (~humble(X0) | ~quiet(X0)))) [nnf transformation 6]
41. ! [X0] : (((humble(X0) & quiet(X0)) | funny(X0) | old(X0)) & ((~funny(X0) & ~old(X0)) | ~humble(X0) | ~quiet(X0))) [flattening 40]
42. ! [X0] : ((old(X0) | (tall(X0) | ~humble(X0))) & ((~tall(X0) & humble(X0)) | ~old(X0))) [nnf transformation 7]
43. ! [X0] : ((old(X0) | tall(X0) | ~humble(X0)) & ((~tall(X0) & humble(X0)) | ~old(X0))) [flattening 42]
46. (? [X0] : quiet(X0) | (~humble(paul) & ~generous(paul))) & ((humble(paul) | generous(paul)) | ! [X0] : ~quiet(X0)) [nnf transformation 11]
47. (? [X0] : quiet(X0) | (~humble(paul) & ~generous(paul))) & (humble(paul) | generous(paul) | ! [X0] : ~quiet(X0)) [flattening 46]
48. (? [X0] : quiet(X0) | (~humble(paul) & ~generous(paul))) & (humble(paul) | generous(paul) | ! [X1] : ~quiet(X1)) [rectify 47]
49. ? [X0] : quiet(X0) => quiet(sK2) [choice axiom]
50. (quiet(sK2) | (~humble(paul) & ~generous(paul))) & (humble(paul) | generous(paul) | ! [X1] : ~quiet(X1)) [skolemisation 48,49]
51. ! [X0] : (((~wise(X0) | quiet(X0)) | ~old(X0)) & (old(X0) | (wise(X0) & ~quiet(X0)))) [nnf transformation 12]
52. ! [X0] : ((~wise(X0) | quiet(X0) | ~old(X0)) & (old(X0) | (wise(X0) & ~quiet(X0)))) [flattening 51]
55. ! [X0] : ((quiet(X0) | (brave(X0) & ~curious(X0))) & ((~brave(X0) | curious(X0)) | ~quiet(X0))) [nnf transformation 14]
56. ! [X0] : ((quiet(X0) | (brave(X0) & ~curious(X0))) & (~brave(X0) | curious(X0) | ~quiet(X0))) [flattening 55]
79. ~old(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 41]
83. ~old(X0) | humble(X0) [cnf transformation 43]
95. humble(paul) | generous(paul) | ~quiet(X1) [cnf transformation 50]
96. quiet(sK2) | ~generous(paul) [cnf transformation 50]
97. quiet(sK2) | ~humble(paul) [cnf transformation 50]
98. ~quiet(X0) | old(X0) [cnf transformation 52]
107. brave(X0) | quiet(X0) [cnf transformation 56]
121. ~brave(mary) [cnf transformation 22]
185. 14 <=> humble(paul) [avatar definition]
189. 15 <=> quiet(sK2) [avatar definition]
191. quiet(sK2) <- (15) [avatar component clause 189]
192. ~14 | 15 [avatar split clause 97,189,185]
194. 16 <=> generous(paul) [avatar definition]
197. ~16 | 15 [avatar split clause 96,189,194]
199. 17 <=> ! [X1] : ~quiet(X1) [avatar definition]
200. ~quiet(X1) <- (17) [avatar component clause 199]
201. 17 | 16 | 14 [avatar split clause 95,185,194,199]
251. old(sK2) <- (15) [resolution 98,191]
254. humble(sK2) <- (15) [resolution 251,83]
257. quiet(mary) [resolution 107,121]
264. ~humble(sK2) | ~quiet(sK2) <- (15) [resolution 79,251]
267. ~quiet(sK2) <- (15) [subsumption resolution 264,254]
268. $false <- (15) [subsumption resolution 267,191]
269. ~15 [avatar contradiction clause 268]
271. $false <- (17) [resolution 200,257]
274. ~17 [avatar contradiction clause 271]
276. $false [avatar sat refutation 192,197,201,269,274]
% SZS output end Proof for 518330563325941422015404
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or strong is both wise and rich and vice versa.
If alice is not creative then someone is generous and vice versa.
Everyone who is both curious and not strong is not wise.
If someone is either not patient or old then someone is not rich and vice versa.
Everyone who is not curious is kind or patient.
If fred is both not strong and not creative then someone is not calm or not wise.
Everyone who is curious or not happy is not humble and vice versa.
If alice is tall or strong then someone is not kind or curious.
If mary is funny then someone is not calm and vice versa.
If someone is not tall or not creative then someone is both not patient and not old and vice versa.
If john is both strong and patient then someone is not calm or not wise.
Everyone who is both quiet and curious is not creative and vice versa.
If lucy is either not old or not generous then mary is both wise and calm and vice versa.
If fred is brave then someone is either tall or quiet and vice versa.
If someone is not calm then susan is both not brave and not patient and vice versa.
Everyone who is either humble or not happy is rich or not funny.
Paul is not tall or not quiet.
Alice is strong.
Someone is not kind or not happy.
Susan is both not old and not brave.
Paul is both tall and calm.
Someone is either not tall or funny. | John is strong. | neutral | (![X]:((~strong(X)|strong(X))<=>(wise(X)&rich(X))))&
((~creative(alice))<=>(?[X]:(generous(X))))&
(![X]:((curious(X)&~strong(X))=>~wise(X)))&
((?[X]:((~patient(X)<~>old(X))))<=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)=>(kind(X)|patient(X))))&
(((~strong(fred)&~creative(fred)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((curious(X)|~happy(X))<=>~humble(X)))&
(((tall(alice)|strong(alice)))=>(?[X]:((~kind(X)|curious(X)))))&
((funny(mary))<=>(?[X]:(~calm(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(((strong(john)&patient(john)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((quiet(X)&curious(X))<=>~creative(X)))&
(((~old(lucy)<~>~generous(lucy)))<=>((wise(mary)&calm(mary))))&
((brave(fred))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))<=>((~brave(susan)&~patient(susan))))&
(![X]:((humble(X)<~>~happy(X))=>(rich(X)|~funny(X))))&
((~tall(paul)|~quiet(paul)))&
(strong(alice))&
(?[X]:((~kind(X)|~happy(X))))&
((~old(susan)&~brave(susan)))&
((tall(paul)&calm(paul)))&
(?[X]:((~tall(X)<~>funny(X)))) | strong(john) | [] | null | 0 |
Everyone who is not humble or generous is not wise or quiet.
If someone is funny or not tall then someone is either kind or strong and vice versa.
If fred is either not tall or brave then john is happy.
Everyone who is either not funny or not strong is either patient or creative.
Everyone who is tall or creative is both rich and tall and vice versa.
If alice is either not kind or not wise then someone is not curious or curious and vice versa.
If john is both not humble and humble then susan is generous.
If someone is either happy or patient then someone is not quiet or rich and vice versa.
If alice is either not old or funny then someone is not humble.
Everyone who is either not rich or not strong is not rich.
Everyone who is both not tall and strong is either patient or humble and vice versa.
Everyone who is generous or quiet is not quiet and vice versa.
Everyone who is not old is both happy and not humble.
If susan is not generous or not patient then lucy is not tall or not curious and vice versa.
Everyone who is not patient is either not curious or tall and vice versa.
Everyone who is not tall is either not quiet or not happy.
Alice is both kind and strong.
Someone is both humble and kind.
Someone is not happy.
Lucy is wise or not calm.
John is either wise or not old.
Susan is either not rich or rich. | John is wise. | contradiction | (![X]:((~humble(X)|generous(X))=>(~wise(X)|quiet(X))))&
((?[X]:((funny(X)|~tall(X))))<=>(?[X]:((kind(X)<~>strong(X)))))&
(((~tall(fred)<~>brave(fred)))=>(happy(john)))&
(![X]:((~funny(X)<~>~strong(X))=>(patient(X)<~>creative(X))))&
(![X]:((tall(X)|creative(X))<=>(rich(X)&tall(X))))&
(((~kind(alice)<~>~wise(alice)))<=>(?[X]:((~curious(X)|curious(X)))))&
(((~humble(john)&humble(john)))=>(generous(susan)))&
((?[X]:((happy(X)<~>patient(X))))<=>(?[X]:((~quiet(X)|rich(X)))))&
(((~old(alice)<~>funny(alice)))=>(?[X]:(~humble(X))))&
(![X]:((~rich(X)<~>~strong(X))=>~rich(X)))&
(![X]:((~tall(X)&strong(X))<=>(patient(X)<~>humble(X))))&
(![X]:((generous(X)|quiet(X))<=>~quiet(X)))&
(![X]:(~old(X)=>(happy(X)&~humble(X))))&
(((~generous(susan)|~patient(susan)))<=>((~tall(lucy)|~curious(lucy))))&
(![X]:(~patient(X)<=>(~curious(X)<~>tall(X))))&
(![X]:(~tall(X)=>(~quiet(X)<~>~happy(X))))&
((kind(alice)&strong(alice)))&
(?[X]:((humble(X)&kind(X))))&
(?[X]:(~happy(X)))&
((wise(lucy)|~calm(lucy)))&
((wise(john)<~>~old(john)))&
((~rich(susan)<~>rich(susan))) | wise(john) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4234243132064236564237576
% SZS output start Proof for 4234243132064236564237576
1. ! [X0] : ((generous(X0) | ~humble(X0)) => (quiet(X0) | ~wise(X0))) [input p0]
12. ! [X0] : ((quiet(X0) | generous(X0)) <=> ~quiet(X0)) [input p11]
23. wise(john) [input hypothesis]
27. ! [X0] : ((quiet(X0) | ~wise(X0)) | (~generous(X0) & humble(X0))) [ennf transformation 1]
28. ! [X0] : (quiet(X0) | ~wise(X0) | (~generous(X0) & humble(X0))) [flattening 27]
61. ! [X0] : (((quiet(X0) | generous(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~generous(X0)))) [nnf transformation 12]
62. ! [X0] : ((quiet(X0) | generous(X0) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~generous(X0)))) [flattening 61]
74. ~wise(X0) | quiet(X0) | ~generous(X0) [cnf transformation 28]
116. ~quiet(X0) | ~quiet(X0) [cnf transformation 62]
117. quiet(X0) | generous(X0) | quiet(X0) [cnf transformation 62]
139. wise(john) [cnf transformation 23]
140. ~quiet(X0) [duplicate literal removal 116]
141. quiet(X0) | generous(X0) [duplicate literal removal 117]
280. 31 <=> wise(john) [avatar definition]
281. wise(john) <- (31) [avatar component clause 280]
289. 31 [avatar split clause 139,280]
291. generous(X0) [resolution 141,140]
296. quiet(john) | ~generous(john) <- (31) [resolution 74,281]
297. ~generous(john) <- (31) [subsumption resolution 296,140]
298. $false <- (31) [subsumption resolution 297,291]
299. ~31 [avatar contradiction clause 298]
300. $false [avatar sat refutation 289,299]
% SZS output end Proof for 4234243132064236564237576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is both curious and not quiet and vice versa.
If someone is old or not old then someone is quiet and vice versa.
Everyone who is not funny or not rich is both humble and not curious and vice versa.
If someone is not creative or strong then mary is not strong or not funny and vice versa.
Everyone who is either happy or wise is both kind and not patient and vice versa.
Everyone who is either not happy or not creative is not funny and vice versa.
Everyone who is not strong is both creative and kind and vice versa.
Everyone who is both not patient and not creative is curious or not curious.
If mary is either not strong or not wise then fred is not wise or strong and vice versa.
If mary is strong or not strong then paul is either not tall or brave and vice versa.
Everyone who is kind is both not patient and quiet and vice versa.
If someone is either not calm or quiet then someone is wise.
If lucy is both not calm and happy then fred is both not patient and funny.
If paul is not funny then someone is either not kind or not funny and vice versa.
John is either quiet or not wise.
Someone is not patient.
Fred is both not calm and not generous.
Someone is either rich or old.
Someone is both not generous and not brave.
Someone is patient or old.
Someone is creative. | Lucy is not strong. | neutral | (![X]:(strong(X)<=>(curious(X)&~quiet(X))))&
((?[X]:((old(X)|~old(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~funny(X)|~rich(X))<=>(humble(X)&~curious(X))))&
((?[X]:((~creative(X)|strong(X))))<=>((~strong(mary)|~funny(mary))))&
(![X]:((happy(X)<~>wise(X))<=>(kind(X)&~patient(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>~funny(X)))&
(![X]:(~strong(X)<=>(creative(X)&kind(X))))&
(![X]:((~patient(X)&~creative(X))=>(curious(X)|~curious(X))))&
(((~strong(mary)<~>~wise(mary)))<=>((~wise(fred)|strong(fred))))&
(((strong(mary)|~strong(mary)))<=>((~tall(paul)<~>brave(paul))))&
(![X]:(kind(X)<=>(~patient(X)&quiet(X))))&
((?[X]:((~calm(X)<~>quiet(X))))=>(?[X]:(wise(X))))&
(((~calm(lucy)&happy(lucy)))=>((~patient(fred)&funny(fred))))&
((~funny(paul))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
((quiet(john)<~>~wise(john)))&
(?[X]:(~patient(X)))&
((~calm(fred)&~generous(fred)))&
(?[X]:((rich(X)<~>old(X))))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:(creative(X))) | ~strong(lucy) | [] | null | 0 |
Everyone who is either not rich or creative is patient. Everyone who is both not wise and not generous is quiet or creative and vice versa. If someone is not rich or generous then fred is either calm or wise. Everyone who is both not curious and not rich is either happy or not tall. If someone is either tall or funny then someone is not humble. Everyone who is humble is either not humble or not happy. Everyone who is either creative or old is both not old and quiet and vice versa. Everyone who is not happy is both not funny and funny and vice versa. Everyone who is both not humble and tall is quiet. If someone is either not quiet or humble then someone is both not curious and not happy and vice versa. If someone is either calm or not quiet then susan is either generous or rich and vice versa. Everyone who is generous or not funny is not funny. If mary is funny or not humble then someone is happy and vice versa. Someone is both strong and brave. Someone is not patient or not wise. Susan is rich or not curious. Someone is either kind or happy. Alice is not happy or quiet. Alice is strong. Someone is either generous or curious. | Fred is not patient. | neutral | (![X]:((~rich(X)<~>creative(X))=>patient(X)))&
(![X]:((~wise(X)&~generous(X))<=>(quiet(X)|creative(X))))&
((?[X]:((~rich(X)|generous(X))))=>((calm(fred)<~>wise(fred))))&
(![X]:((~curious(X)&~rich(X))=>(happy(X)<~>~tall(X))))&
((?[X]:((tall(X)<~>funny(X))))=>(?[X]:(~humble(X))))&
(![X]:(humble(X)=>(~humble(X)<~>~happy(X))))&
(![X]:((creative(X)<~>old(X))<=>(~old(X)&quiet(X))))&
(![X]:(~happy(X)<=>(~funny(X)&funny(X))))&
(![X]:((~humble(X)&tall(X))=>quiet(X)))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(?[X]:((~curious(X)&~happy(X)))))&
((?[X]:((calm(X)<~>~quiet(X))))<=>((generous(susan)<~>rich(susan))))&
(![X]:((generous(X)|~funny(X))=>~funny(X)))&
(((funny(mary)|~humble(mary)))<=>(?[X]:(happy(X))))&
(?[X]:((strong(X)&brave(X))))&
(?[X]:((~patient(X)|~wise(X))))&
((rich(susan)|~curious(susan)))&
(?[X]:((kind(X)<~>happy(X))))&
((~happy(alice)|quiet(alice)))&
(strong(alice))&
(?[X]:((generous(X)<~>curious(X)))) | ~patient(fred) | [] | null | 0 |
If someone is wise then fred is both patient and not creative and vice versa.
Everyone who is humble or not wise is either kind or not curious and vice versa.
Everyone who is not funny or not calm is funny.
If lucy is both not creative and not kind then someone is either old or humble and vice versa.
If john is both rich and not funny then fred is humble or not tall and vice versa.
If someone is both not strong and humble then fred is old or humble and vice versa.
If paul is either strong or not strong then alice is both tall and curious.
Everyone who is not strong is kind.
If someone is either not strong or humble then john is not funny and vice versa.
Everyone who is not calm is creative or kind and vice versa.
Everyone who is not generous or generous is either rich or generous and vice versa.
Everyone who is wise or quiet is not kind and vice versa.
If susan is not brave or old then mary is not rich or patient.
Everyone who is not strong is not calm or rich.
Everyone who is not wise is both not rich and not calm and vice versa.
Everyone who is not calm is patient or strong.
John is both old and not wise.
John is old.
Mary is either tall or not strong.
Someone is either not patient or wise.
Fred is not patient or strong. | Lucy is not creative. | entailment | ((?[X]:(wise(X)))<=>((patient(fred)&~creative(fred))))&
(![X]:((humble(X)|~wise(X))<=>(kind(X)<~>~curious(X))))&
(![X]:((~funny(X)|~calm(X))=>funny(X)))&
(((~creative(lucy)&~kind(lucy)))<=>(?[X]:((old(X)<~>humble(X)))))&
(((rich(john)&~funny(john)))<=>((humble(fred)|~tall(fred))))&
((?[X]:((~strong(X)&humble(X))))<=>((old(fred)|humble(fred))))&
(((strong(paul)<~>~strong(paul)))=>((tall(alice)&curious(alice))))&
(![X]:(~strong(X)=>kind(X)))&
((?[X]:((~strong(X)<~>humble(X))))<=>(~funny(john)))&
(![X]:(~calm(X)<=>(creative(X)|kind(X))))&
(![X]:((~generous(X)|generous(X))<=>(rich(X)<~>generous(X))))&
(![X]:((wise(X)|quiet(X))<=>~kind(X)))&
(((~brave(susan)|old(susan)))=>((~rich(mary)|patient(mary))))&
(![X]:(~strong(X)=>(~calm(X)|rich(X))))&
(![X]:(~wise(X)<=>(~rich(X)&~calm(X))))&
(![X]:(~calm(X)=>(patient(X)|strong(X))))&
((old(john)&~wise(john)))&
(old(john))&
((tall(mary)<~>~strong(mary)))&
(?[X]:((~patient(X)<~>wise(X))))&
((~patient(fred)|strong(fred))) | ~creative(lucy) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7507846991622008824285240
% SZS output start Proof for 7507846991622008824285240
3. ! [X0] : ((~calm(X0) | ~funny(X0)) => funny(X0)) [input p2]
4. (~kind(lucy) & ~creative(lucy)) <=> ? [X0] : (old(X0) <~> humble(X0)) [input p3]
5. (~funny(john) & rich(john)) <=> (~tall(fred) | humble(fred)) [input p4]
6. ? [X0] : (humble(X0) & ~strong(X0)) <=> (humble(fred) | old(fred)) [input p5]
9. ? [X0] : (~strong(X0) <~> humble(X0)) <=> ~funny(john) [input p8]
17. ~wise(john) & old(john) [input p16]
22. creative(lucy) [input hypothesis]
24. ! [X0] : (funny(X0) | (calm(X0) & funny(X0))) [ennf transformation 3]
40. ((~kind(lucy) & ~creative(lucy)) | ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (? [X0] : ((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (kind(lucy) | creative(lucy))) [nnf transformation 4]
41. ((~kind(lucy) & ~creative(lucy)) | ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (? [X0] : ((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | kind(lucy) | creative(lucy)) [flattening 40]
42. ((~kind(lucy) & ~creative(lucy)) | ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (? [X1] : ((~humble(X1) | ~old(X1)) & (humble(X1) | old(X1))) | kind(lucy) | creative(lucy)) [rectify 41]
43. ? [X1] : ((~humble(X1) | ~old(X1)) & (humble(X1) | old(X1))) => ((~humble(sK1) | ~old(sK1)) & (humble(sK1) | old(sK1))) [choice axiom]
44. ((~kind(lucy) & ~creative(lucy)) | ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (((~humble(sK1) | ~old(sK1)) & (humble(sK1) | old(sK1))) | kind(lucy) | creative(lucy)) [skolemisation 42,43]
45. ((~funny(john) & rich(john)) | (tall(fred) & ~humble(fred))) & ((~tall(fred) | humble(fred)) | (funny(john) | ~rich(john))) [nnf transformation 5]
46. ((~funny(john) & rich(john)) | (tall(fred) & ~humble(fred))) & (~tall(fred) | humble(fred) | funny(john) | ~rich(john)) [flattening 45]
47. (? [X0] : (humble(X0) & ~strong(X0)) | (~humble(fred) & ~old(fred))) & ((humble(fred) | old(fred)) | ! [X0] : (~humble(X0) | strong(X0))) [nnf transformation 6]
48. (? [X0] : (humble(X0) & ~strong(X0)) | (~humble(fred) & ~old(fred))) & (humble(fred) | old(fred) | ! [X0] : (~humble(X0) | strong(X0))) [flattening 47]
49. (? [X0] : (humble(X0) & ~strong(X0)) | (~humble(fred) & ~old(fred))) & (humble(fred) | old(fred) | ! [X1] : (~humble(X1) | strong(X1))) [rectify 48]
50. ? [X0] : (humble(X0) & ~strong(X0)) => (humble(sK2) & ~strong(sK2)) [choice axiom]
51. ((humble(sK2) & ~strong(sK2)) | (~humble(fred) & ~old(fred))) & (humble(fred) | old(fred) | ! [X1] : (~humble(X1) | strong(X1))) [skolemisation 49,50]
53. (? [X0] : ((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | funny(john)) & (~funny(john) | ! [X0] : ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) [nnf transformation 9]
54. (? [X0] : ((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | funny(john)) & (~funny(john) | ! [X1] : ((~strong(X1) | ~humble(X1)) & (humble(X1) | strong(X1)))) [rectify 53]
55. ? [X0] : ((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) => ((~humble(sK3) | strong(sK3)) & (humble(sK3) | ~strong(sK3))) [choice axiom]
56. (((~humble(sK3) | strong(sK3)) & (humble(sK3) | ~strong(sK3))) | funny(john)) & (~funny(john) | ! [X1] : ((~strong(X1) | ~humble(X1)) & (humble(X1) | strong(X1)))) [skolemisation 54,55]
78. funny(X0) | funny(X0) [cnf transformation 24]
82. ~creative(lucy) | humble(X0) | ~old(X0) [cnf transformation 44]
89. ~funny(john) | ~humble(fred) [cnf transformation 46]
91. humble(fred) | old(fred) | ~humble(X1) | strong(X1) [cnf transformation 51]
101. ~funny(john) | humble(X1) | strong(X1) [cnf transformation 56]
102. ~funny(john) | ~strong(X1) | ~humble(X1) [cnf transformation 56]
123. old(john) [cnf transformation 17]
131. creative(lucy) [cnf transformation 22]
140. funny(X0) [duplicate literal removal 78]
168. 7 <=> ! [X0] : (humble(X0) | ~old(X0)) [avatar definition]
169. ~old(X0) | humble(X0) <- (7) [avatar component clause 168]
172. 8 <=> creative(lucy) [avatar definition]
176. 7 | ~8 [avatar split clause 82,172,168]
188. ~humble(fred) [subsumption resolution 89,140]
190. 11 <=> old(fred) [avatar definition]
191. old(fred) <- (11) [avatar component clause 190]
203. old(fred) | ~humble(X1) | strong(X1) [subsumption resolution 91,188]
205. 14 <=> ! [X1] : (~humble(X1) | strong(X1)) [avatar definition]
206. ~humble(X1) | strong(X1) <- (14) [avatar component clause 205]
207. 14 | 11 [avatar split clause 203,190,205]
224. ~strong(X1) | ~humble(X1) [subsumption resolution 102,140]
225. strong(X1) | humble(X1) [subsumption resolution 101,140]
264. 8 [avatar split clause 131,172]
274. humble(john) <- (7) [resolution 169,123]
275. humble(fred) <- (7, 11) [resolution 169,191]
276. $false <- (7, 11) [subsumption resolution 275,188]
277. ~7 | ~11 [avatar contradiction clause 276]
278. strong(X1) <- (14) [subsumption resolution 206,225]
283. ~humble(X0) <- (14) [resolution 224,278]
290. $false <- (7, 14) [resolution 283,274]
291. ~7 | ~14 [avatar contradiction clause 290]
293. $false [avatar sat refutation 176,207,264,277,291]
% SZS output end Proof for 7507846991622008824285240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both tall and not curious then susan is both kind and patient and vice versa.
If mary is wise or not curious then someone is creative and vice versa.
Everyone who is not funny or generous is humble or not patient and vice versa.
Everyone who is quiet or not generous is not tall.
Everyone who is both not generous and calm is not patient or not quiet and vice versa.
If someone is not funny then fred is both tall and not curious and vice versa.
If lucy is not curious then mary is wise and vice versa.
If lucy is either curious or brave then alice is both not generous and quiet.
Everyone who is brave or funny is either not strong or generous.
Everyone who is happy or not rich is both happy and not rich and vice versa.
Everyone who is both tall and not brave is both calm and rich.
If someone is not kind or not patient then john is not curious.
Everyone who is rich or happy is kind or wise and vice versa.
Everyone who is both rich and not strong is not patient and vice versa.
Everyone who is both creative and curious is both not brave and not rich.
If susan is tall then alice is not brave.
Someone is either not rich or not kind.
Susan is wise or not generous.
Alice is generous or not curious.
Someone is either funny or not wise.
Someone is not old or tall.
Alice is both not creative and happy.
Lucy is either brave or not quiet. | John is patient. | entailment | (((tall(alice)&~curious(alice)))<=>((kind(susan)&patient(susan))))&
(((wise(mary)|~curious(mary)))<=>(?[X]:(creative(X))))&
(![X]:((~funny(X)|generous(X))<=>(humble(X)|~patient(X))))&
(![X]:((quiet(X)|~generous(X))=>~tall(X)))&
(![X]:((~generous(X)&calm(X))<=>(~patient(X)|~quiet(X))))&
((?[X]:(~funny(X)))<=>((tall(fred)&~curious(fred))))&
((~curious(lucy))<=>(wise(mary)))&
(((curious(lucy)<~>brave(lucy)))=>((~generous(alice)&quiet(alice))))&
(![X]:((brave(X)|funny(X))=>(~strong(X)<~>generous(X))))&
(![X]:((happy(X)|~rich(X))<=>(happy(X)&~rich(X))))&
(![X]:((tall(X)&~brave(X))=>(calm(X)&rich(X))))&
((?[X]:((~kind(X)|~patient(X))))=>(~curious(john)))&
(![X]:((rich(X)|happy(X))<=>(kind(X)|wise(X))))&
(![X]:((rich(X)&~strong(X))<=>~patient(X)))&
(![X]:((creative(X)&curious(X))=>(~brave(X)&~rich(X))))&
((tall(susan))=>(~brave(alice)))&
(?[X]:((~rich(X)<~>~kind(X))))&
((wise(susan)|~generous(susan)))&
((generous(alice)|~curious(alice)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((~old(X)|tall(X))))&
((~creative(alice)&happy(alice)))&
((brave(lucy)<~>~quiet(lucy))) | patient(john) | [
"p2",
"p3",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4298871708506372397404414
% SZS output start Proof for 4298871708506372397404414
3. ! [X0] : ((generous(X0) | ~funny(X0)) <=> (~patient(X0) | humble(X0))) [input p2]
4. ! [X0] : ((~generous(X0) | quiet(X0)) => ~tall(X0)) [input p3]
5. ! [X0] : ((calm(X0) & ~generous(X0)) <=> (~quiet(X0) | ~patient(X0))) [input p4]
6. ? [X0] : ~funny(X0) <=> (~curious(fred) & tall(fred)) [input p5]
24. ~patient(john) [input hypothesis]
26. ! [X0] : (~tall(X0) | (generous(X0) & ~quiet(X0))) [ennf transformation 4]
42. ! [X0] : (((generous(X0) | ~funny(X0)) | (patient(X0) & ~humble(X0))) & ((~patient(X0) | humble(X0)) | (~generous(X0) & funny(X0)))) [nnf transformation 3]
43. ! [X0] : ((generous(X0) | ~funny(X0) | (patient(X0) & ~humble(X0))) & (~patient(X0) | humble(X0) | (~generous(X0) & funny(X0)))) [flattening 42]
44. ! [X0] : (((calm(X0) & ~generous(X0)) | (quiet(X0) & patient(X0))) & ((~quiet(X0) | ~patient(X0)) | (~calm(X0) | generous(X0)))) [nnf transformation 5]
45. ! [X0] : (((calm(X0) & ~generous(X0)) | (quiet(X0) & patient(X0))) & (~quiet(X0) | ~patient(X0) | ~calm(X0) | generous(X0))) [flattening 44]
46. (? [X0] : ~funny(X0) | (curious(fred) | ~tall(fred))) & ((~curious(fred) & tall(fred)) | ! [X0] : funny(X0)) [nnf transformation 6]
47. (? [X0] : ~funny(X0) | curious(fred) | ~tall(fred)) & ((~curious(fred) & tall(fred)) | ! [X0] : funny(X0)) [flattening 46]
48. (? [X0] : ~funny(X0) | curious(fred) | ~tall(fred)) & ((~curious(fred) & tall(fred)) | ! [X1] : funny(X1)) [rectify 47]
49. ? [X0] : ~funny(X0) => ~funny(sK1) [choice axiom]
50. (~funny(sK1) | curious(fred) | ~tall(fred)) & ((~curious(fred) & tall(fred)) | ! [X1] : funny(X1)) [skolemisation 48,49]
77. ~funny(X0) | generous(X0) | patient(X0) [cnf transformation 43]
78. ~quiet(X0) | ~tall(X0) [cnf transformation 26]
79. ~tall(X0) | generous(X0) [cnf transformation 26]
81. ~generous(X0) | patient(X0) [cnf transformation 45]
82. ~generous(X0) | quiet(X0) [cnf transformation 45]
85. tall(fred) | funny(X1) [cnf transformation 50]
127. ~patient(john) [cnf transformation 24]
167. 9 <=> tall(fred) [avatar definition]
168. tall(fred) <- (9) [avatar component clause 167]
180. 12 <=> ! [X1] : funny(X1) [avatar definition]
181. funny(X1) <- (12) [avatar component clause 180]
183. 12 | 9 [avatar split clause 85,167,180]
207. 17 <=> ! [X0] : patient(X0) [avatar definition]
208. patient(X0) <- (17) [avatar component clause 207]
263. generous(fred) <- (9) [resolution 79,168]
265. quiet(fred) <- (9) [resolution 82,263]
266. ~tall(fred) <- (9) [resolution 265,78]
267. $false <- (9) [subsumption resolution 266,168]
268. ~9 [avatar contradiction clause 267]
278. generous(X0) | patient(X0) <- (12) [resolution 77,181]
279. patient(X0) <- (12) [subsumption resolution 278,81]
280. 17 | ~12 [avatar split clause 279,180,207]
281. $false <- (17) [resolution 208,127]
283. ~17 [avatar contradiction clause 281]
284. $false [avatar sat refutation 183,268,280,283]
% SZS output end Proof for 4298871708506372397404414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is calm and vice versa.
Everyone who is both patient and not happy is not happy or not old.
If alice is either not old or not happy then someone is either generous or not funny and vice versa.
If susan is both funny and generous then lucy is generous and vice versa.
If someone is not strong or funny then someone is both curious and not strong.
Everyone who is either wise or not calm is quiet and vice versa.
Everyone who is not humble is either not creative or not happy.
Everyone who is either not humble or not tall is both happy and wise.
Everyone who is not brave is curious or not rich.
Everyone who is generous or not rich is not kind.
Everyone who is both not happy and calm is either brave or not brave and vice versa.
Everyone who is not old or rich is both curious and wise and vice versa.
Everyone who is either not rich or not generous is not old or calm and vice versa.
If someone is happy then someone is both not old and not happy and vice versa.
If lucy is not patient then lucy is wise and vice versa.
Everyone who is not funny or curious is either not brave or calm.
Fred is both not curious and generous.
Someone is either quiet or not funny.
Someone is either quiet or not curious.
Someone is quiet or not strong.
Someone is strong.
Mary is not generous or rich.
Someone is not patient or creative. | Lucy is not strong. | neutral | (![X]:(old(X)<=>calm(X)))&
(![X]:((patient(X)&~happy(X))=>(~happy(X)|~old(X))))&
(((~old(alice)<~>~happy(alice)))<=>(?[X]:((generous(X)<~>~funny(X)))))&
(((funny(susan)&generous(susan)))<=>(generous(lucy)))&
((?[X]:((~strong(X)|funny(X))))=>(?[X]:((curious(X)&~strong(X)))))&
(![X]:((wise(X)<~>~calm(X))<=>quiet(X)))&
(![X]:(~humble(X)=>(~creative(X)<~>~happy(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(happy(X)&wise(X))))&
(![X]:(~brave(X)=>(curious(X)|~rich(X))))&
(![X]:((generous(X)|~rich(X))=>~kind(X)))&
(![X]:((~happy(X)&calm(X))<=>(brave(X)<~>~brave(X))))&
(![X]:((~old(X)|rich(X))<=>(curious(X)&wise(X))))&
(![X]:((~rich(X)<~>~generous(X))<=>(~old(X)|calm(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~old(X)&~happy(X)))))&
((~patient(lucy))<=>(wise(lucy)))&
(![X]:((~funny(X)|curious(X))=>(~brave(X)<~>calm(X))))&
((~curious(fred)&generous(fred)))&
(?[X]:((quiet(X)<~>~funny(X))))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:(strong(X)))&
((~generous(mary)|rich(mary)))&
(?[X]:((~patient(X)|creative(X)))) | ~strong(lucy) | [] | null | 0 |
Everyone who is not wise or old is tall or not old and vice versa.
Everyone who is either humble or not funny is both not brave and not wise and vice versa.
If someone is both not tall and not brave then john is not kind or brave and vice versa.
Everyone who is either creative or funny is strong and vice versa.
If someone is both strong and not old then someone is both not humble and not strong.
If fred is both not rich and generous then someone is not wise or not kind.
If fred is both brave and not curious then alice is tall.
If lucy is either humble or happy then paul is both not humble and not kind.
Everyone who is not wise or not tall is either tall or wise and vice versa.
If someone is generous or not old then mary is creative and vice versa.
Everyone who is both generous and humble is either creative or not funny and vice versa.
If someone is rich or not wise then paul is not old.
If lucy is not kind or not patient then someone is not happy or not strong.
If fred is not quiet or not patient then paul is either not patient or not quiet and vice versa.
Everyone who is tall is strong.
Someone is happy or not wise.
Susan is either generous or rich.
Alice is generous or calm.
Someone is either patient or tall.
Lucy is not wise or not funny.
Someone is either not quiet or not wise. | John is old. | entailment | (![X]:((~wise(X)|old(X))<=>(tall(X)|~old(X))))&
(![X]:((humble(X)<~>~funny(X))<=>(~brave(X)&~wise(X))))&
((?[X]:((~tall(X)&~brave(X))))<=>((~kind(john)|brave(john))))&
(![X]:((creative(X)<~>funny(X))<=>strong(X)))&
((?[X]:((strong(X)&~old(X))))=>(?[X]:((~humble(X)&~strong(X)))))&
(((~rich(fred)&generous(fred)))=>(?[X]:((~wise(X)|~kind(X)))))&
(((brave(fred)&~curious(fred)))=>(tall(alice)))&
(((humble(lucy)<~>happy(lucy)))=>((~humble(paul)&~kind(paul))))&
(![X]:((~wise(X)|~tall(X))<=>(tall(X)<~>wise(X))))&
((?[X]:((generous(X)|~old(X))))<=>(creative(mary)))&
(![X]:((generous(X)&humble(X))<=>(creative(X)<~>~funny(X))))&
((?[X]:((rich(X)|~wise(X))))=>(~old(paul)))&
(((~kind(lucy)|~patient(lucy)))=>(?[X]:((~happy(X)|~strong(X)))))&
(((~quiet(fred)|~patient(fred)))<=>((~patient(paul)<~>~quiet(paul))))&
(![X]:(tall(X)=>strong(X)))&
(?[X]:((happy(X)|~wise(X))))&
((generous(susan)<~>rich(susan)))&
((generous(alice)|calm(alice)))&
(?[X]:((patient(X)<~>tall(X))))&
((~wise(lucy)|~funny(lucy)))&
(?[X]:((~quiet(X)<~>~wise(X)))) | old(john) | [
"p0",
"p4",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5912566089822307606963379
% SZS output start Proof for 5912566089822307606963379
1. ! [X0] : ((old(X0) | ~wise(X0)) <=> (~old(X0) | tall(X0))) [input p0]
5. ? [X0] : (~old(X0) & strong(X0)) => ? [X0] : (~strong(X0) & ~humble(X0)) [input p4]
9. ! [X0] : ((~tall(X0) | ~wise(X0)) <=> (tall(X0) <~> wise(X0))) [input p8]
15. ! [X0] : (tall(X0) => strong(X0)) [input p14]
22. ~old(john) [input hypothesis]
23. ? [X0] : (~old(X0) & strong(X0)) => ? [X1] : (~strong(X1) & ~humble(X1)) [rectify 5]
26. ? [X1] : (~strong(X1) & ~humble(X1)) | ! [X0] : (old(X0) | ~strong(X0)) [ennf transformation 23]
32. ! [X0] : (strong(X0) | ~tall(X0)) [ennf transformation 15]
33. ! [X0] : (((old(X0) | ~wise(X0)) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | (~old(X0) & wise(X0)))) [nnf transformation 1]
34. ! [X0] : ((old(X0) | ~wise(X0) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | (~old(X0) & wise(X0)))) [flattening 33]
43. ? [X0] : (~strong(X0) & ~humble(X0)) | ! [X1] : (old(X1) | ~strong(X1)) [rectify 26]
44. ? [X0] : (~strong(X0) & ~humble(X0)) => (~strong(sK1) & ~humble(sK1)) [choice axiom]
45. (~strong(sK1) & ~humble(sK1)) | ! [X1] : (old(X1) | ~strong(X1)) [skolemisation 43,44]
49. ! [X0] : (((~tall(X0) | ~wise(X0)) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (tall(X0) & wise(X0)))) [nnf transformation 9]
50. ! [X0] : ((~tall(X0) | ~wise(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (tall(X0) & wise(X0)))) [flattening 49]
71. ~old(X0) | tall(X0) | ~old(X0) [cnf transformation 34]
73. old(X0) | ~wise(X0) | old(X0) [cnf transformation 34]
90. ~strong(sK1) | old(X1) | ~strong(X1) [cnf transformation 45]
97. wise(X0) | tall(X0) | tall(X0) [cnf transformation 50]
121. ~tall(X0) | strong(X0) [cnf transformation 32]
130. ~old(john) [cnf transformation 22]
132. tall(X0) | wise(X0) [duplicate literal removal 97]
135. ~old(X0) | tall(X0) [duplicate literal removal 71]
136. ~wise(X0) | old(X0) [duplicate literal removal 73]
162. 6 <=> ! [X1] : (old(X1) | ~strong(X1)) [avatar definition]
163. ~strong(X1) | old(X1) <- (6) [avatar component clause 162]
165. 7 <=> strong(sK1) [avatar definition]
167. ~strong(sK1) <- (~7) [avatar component clause 165]
168. 6 | ~7 [avatar split clause 90,165,162]
225. 20 <=> ! [X1] : old(X1) [avatar definition]
226. old(X1) <- (20) [avatar component clause 225]
334. strong(X0) | wise(X0) [resolution 132,121]
350. wise(sK1) <- (~7) [resolution 334,167]
362. $false <- (20) [resolution 226,130]
367. ~20 [avatar contradiction clause 362]
372. old(sK1) <- (~7) [resolution 350,136]
450. tall(sK1) <- (~7) [resolution 372,135]
623. strong(sK1) <- (~7) [resolution 450,121]
624. $false <- (~7) [subsumption resolution 623,167]
625. 7 [avatar contradiction clause 624]
654. old(X2) | wise(X2) <- (6) [resolution 163,334]
662. old(X2) <- (6) [subsumption resolution 654,136]
663. 20 | ~6 [avatar split clause 662,162,225]
666. $false [avatar sat refutation 168,367,625,663]
% SZS output end Proof for 5912566089822307606963379
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not strong or not happy then mary is humble or not patient.
If someone is either brave or not quiet then someone is either not happy or not curious.
Everyone who is quiet is either not funny or old.
Everyone who is not quiet or wise is both not old and funny.
Everyone who is either not tall or rich is curious or generous and vice versa.
Everyone who is not humble or not brave is brave and vice versa.
If someone is humble then paul is wise or not funny.
Everyone who is both not funny and calm is both happy and not kind.
If fred is either generous or not brave then someone is happy or patient and vice versa.
Everyone who is either not quiet or patient is not patient or funny and vice versa.
Everyone who is not generous or strong is either wise or humble and vice versa.
If someone is humble then someone is strong or not humble.
Everyone who is either kind or rich is humble.
Everyone who is not wise is either quiet or not tall.
Everyone who is both curious and not calm is both patient and not calm.
If someone is curious then someone is rich.
John is strong.
Someone is both creative and not wise.
Someone is curious.
Fred is either not generous or happy.
Paul is kind.
Fred is strong. | John is not funny. | contradiction | (((~strong(john)|~happy(john)))=>((humble(mary)|~patient(mary))))&
((?[X]:((brave(X)<~>~quiet(X))))=>(?[X]:((~happy(X)<~>~curious(X)))))&
(![X]:(quiet(X)=>(~funny(X)<~>old(X))))&
(![X]:((~quiet(X)|wise(X))=>(~old(X)&funny(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(curious(X)|generous(X))))&
(![X]:((~humble(X)|~brave(X))<=>brave(X)))&
((?[X]:(humble(X)))=>((wise(paul)|~funny(paul))))&
(![X]:((~funny(X)&calm(X))=>(happy(X)&~kind(X))))&
(((generous(fred)<~>~brave(fred)))<=>(?[X]:((happy(X)|patient(X)))))&
(![X]:((~quiet(X)<~>patient(X))<=>(~patient(X)|funny(X))))&
(![X]:((~generous(X)|strong(X))<=>(wise(X)<~>humble(X))))&
((?[X]:(humble(X)))=>(?[X]:((strong(X)|~humble(X)))))&
(![X]:((kind(X)<~>rich(X))=>humble(X)))&
(![X]:(~wise(X)=>(quiet(X)<~>~tall(X))))&
(![X]:((curious(X)&~calm(X))=>(patient(X)&~calm(X))))&
((?[X]:(curious(X)))=>(?[X]:(rich(X))))&
(strong(john))&
(?[X]:((creative(X)&~wise(X))))&
(?[X]:(curious(X)))&
((~generous(fred)<~>happy(fred)))&
(kind(paul))&
(strong(fred)) | ~funny(john) | [
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4857562634266946060302263
% SZS output start Proof for 4857562634266946060302263
4. ! [X0] : ((wise(X0) | ~quiet(X0)) => (funny(X0) & ~old(X0))) [input p3]
10. ! [X0] : ((~quiet(X0) <~> patient(X0)) <=> (funny(X0) | ~patient(X0))) [input p9]
23. ~funny(john) [input hypothesis]
32. ! [X0] : ((funny(X0) & ~old(X0)) | (~wise(X0) & quiet(X0))) [ennf transformation 4]
56. ! [X0] : ((((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) | (~funny(X0) & patient(X0))) & ((funny(X0) | ~patient(X0)) | ((~quiet(X0) | ~patient(X0)) & (patient(X0) | quiet(X0))))) [nnf transformation 10]
57. ! [X0] : ((((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) | (~funny(X0) & patient(X0))) & (funny(X0) | ~patient(X0) | ((~quiet(X0) | ~patient(X0)) & (patient(X0) | quiet(X0))))) [flattening 56]
83. funny(X0) | quiet(X0) [cnf transformation 32]
104. funny(X0) | ~patient(X0) | ~quiet(X0) | ~patient(X0) [cnf transformation 57]
105. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 57]
108. ~patient(X0) | quiet(X0) | ~funny(X0) [cnf transformation 57]
130. ~funny(john) [cnf transformation 23]
131. funny(X0) | ~patient(X0) | ~quiet(X0) [duplicate literal removal 104]
132. ~quiet(X0) | patient(X0) [duplicate literal removal 105]
207. ~patient(X0) | quiet(X0) [subsumption resolution 108,83]
208. ~patient(X0) | funny(X0) [subsumption resolution 131,207]
237. quiet(john) [resolution 83,130]
239. patient(john) [resolution 132,237]
252. funny(john) [resolution 208,239]
253. $false [subsumption resolution 252,130]
% SZS output end Proof for 4857562634266946060302263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not wise or patient then someone is either not quiet or not patient.
If someone is not curious or not kind then someone is both not kind and not brave and vice versa.
Everyone who is not strong or generous is calm or generous and vice versa.
If john is both not quiet and funny then someone is either not kind or not tall and vice versa.
If lucy is both not humble and not old then someone is wise and vice versa.
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.
Someone is either not tall or not creative.
Someone is both humble and creative.
Someone is not calm or strong.
Someone is either not funny or old.
Alice is brave or patient.
Susan is both generous and not wise.
Someone is either tall or creative. | Susan is curious. | entailment | (((~wise(mary)|patient(mary)))=>(?[X]:((~quiet(X)<~>~patient(X)))))&
((?[X]:((~curious(X)|~kind(X))))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((~strong(X)|generous(X))<=>(calm(X)|generous(X))))&
(((~quiet(john)&funny(john)))<=>(?[X]:((~kind(X)<~>~tall(X)))))&
(((~humble(lucy)&~old(lucy)))<=>(?[X]:(wise(X))))&
(![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)))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((~funny(X)<~>old(X))))&
((brave(alice)|patient(alice)))&
((generous(susan)&~wise(susan)))&
(?[X]:((tall(X)<~>creative(X)))) | curious(susan) | [
"p3",
"p5",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4607265164973944707855874
% SZS output start Proof for 4607265164973944707855874
4. (funny(john) & ~quiet(john)) <=> ? [X0] : (~kind(X0) <~> ~tall(X0)) [input p3]
6. ! [X0] : (happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p5]
8. ! [X0] : ((happy(X0) | ~happy(X0)) => strong(X0)) [input p7]
10. ! [X0] : ((kind(X0) | ~tall(X0)) <=> curious(X0)) [input p9]
12. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p11]
24. ~curious(susan) [input hypothesis]
30. ! [X0] : (strong(X0) | (~happy(X0) & happy(X0))) [ennf transformation 8]
46. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X0] : ((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | (~funny(john) | quiet(john))) [nnf transformation 4]
47. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X0] : ((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | ~funny(john) | quiet(john)) [flattening 46]
48. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X1] : ((tall(X1) | kind(X1)) & (~tall(X1) | ~kind(X1))) | ~funny(john) | quiet(john)) [rectify 47]
49. ? [X1] : ((tall(X1) | kind(X1)) & (~tall(X1) | ~kind(X1))) => ((tall(sK3) | kind(sK3)) & (~tall(sK3) | ~kind(sK3))) [choice axiom]
50. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (((tall(sK3) | kind(sK3)) & (~tall(sK3) | ~kind(sK3))) | ~funny(john) | quiet(john)) [skolemisation 48,49]
56. ! [X0] : ((happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ~happy(X0))) [nnf transformation 6]
60. ! [X0] : (((kind(X0) | ~tall(X0)) | ~curious(X0)) & (curious(X0) | (~kind(X0) & tall(X0)))) [nnf transformation 10]
61. ! [X0] : ((kind(X0) | ~tall(X0) | ~curious(X0)) & (curious(X0) | (~kind(X0) & tall(X0)))) [flattening 60]
64. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 12]
65. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 64]
105. funny(john) | ~tall(X0) | kind(X0) [cnf transformation 50]
110. ~happy(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 56]
116. strong(X0) | happy(X0) [cnf transformation 30]
117. ~happy(X0) | strong(X0) [cnf transformation 30]
122. tall(X0) | curious(X0) [cnf transformation 61]
129. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 65]
130. happy(X0) | happy(X0) [cnf transformation 65]
131. happy(X0) | kind(X0) [cnf transformation 65]
156. ~curious(susan) [cnf transformation 24]
157. ~kind(X0) | ~happy(X0) [duplicate literal removal 129]
158. happy(X0) [duplicate literal removal 130]
202. 10 <=> ! [X3] : curious(X3) [avatar definition]
203. curious(X3) <- (10) [avatar component clause 202]
215. 13 <=> funny(john) [avatar definition]
217. funny(john) <- (13) [avatar component clause 215]
220. 14 <=> ! [X0] : (~tall(X0) | kind(X0)) [avatar definition]
221. ~tall(X0) | kind(X0) <- (14) [avatar component clause 220]
222. 14 | 13 [avatar split clause 105,215,220]
257. strong(X0) [subsumption resolution 116,117]
271. ~kind(X0) [subsumption resolution 157,158]
367. ~strong(X0) | ~funny(X0) | kind(X0) [resolution 110,131]
369. ~funny(X0) | kind(X0) [subsumption resolution 367,257]
370. ~funny(X0) [subsumption resolution 369,271]
373. $false <- (13) [resolution 370,217]
374. ~13 [avatar contradiction clause 373]
375. ~tall(X0) <- (14) [subsumption resolution 221,271]
378. curious(X0) <- (14) [resolution 375,122]
383. 10 | ~14 [avatar split clause 378,220,202]
384. $false <- (10) [resolution 203,156]
387. ~10 [avatar contradiction clause 384]
388. $false [avatar sat refutation 222,374,383,387]
% SZS output end Proof for 4607265164973944707855874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is tall and vice versa.
If alice is either not quiet or wise then john is either kind or tall.
Everyone who is not calm or brave is both quiet and not strong.
Everyone who is both not happy and not quiet is either generous or rich and vice versa.
Everyone who is both not old and not funny is happy or wise and vice versa.
Everyone who is both not generous and not quiet is both quiet and generous.
Everyone who is either old or calm is generous.
Everyone who is curious is either kind or not funny and vice versa.
Everyone who is both not curious and quiet is both not old and not wise.
Everyone who is either not kind or creative is both brave and not tall.
Everyone who is both not curious and not brave is not strong and vice versa.
Everyone who is both not old and not calm is not generous or creative and vice versa.
Everyone who is both not generous and humble is both wise and strong.
If someone is both kind and not old then someone is not tall or not strong and vice versa.
Everyone who is tall is either not creative or not quiet.
If mary is brave then someone is either generous or strong and vice versa.
Someone is both quiet and not curious.
Someone is both not old and not creative.
Someone is either generous or not strong.
Someone is not brave.
John is either not kind or not calm. | Alice is creative. | neutral | (![X]:(wise(X)<=>tall(X)))&
(((~quiet(alice)<~>wise(alice)))=>((kind(john)<~>tall(john))))&
(![X]:((~calm(X)|brave(X))=>(quiet(X)&~strong(X))))&
(![X]:((~happy(X)&~quiet(X))<=>(generous(X)<~>rich(X))))&
(![X]:((~old(X)&~funny(X))<=>(happy(X)|wise(X))))&
(![X]:((~generous(X)&~quiet(X))=>(quiet(X)&generous(X))))&
(![X]:((old(X)<~>calm(X))=>generous(X)))&
(![X]:(curious(X)<=>(kind(X)<~>~funny(X))))&
(![X]:((~curious(X)&quiet(X))=>(~old(X)&~wise(X))))&
(![X]:((~kind(X)<~>creative(X))=>(brave(X)&~tall(X))))&
(![X]:((~curious(X)&~brave(X))<=>~strong(X)))&
(![X]:((~old(X)&~calm(X))<=>(~generous(X)|creative(X))))&
(![X]:((~generous(X)&humble(X))=>(wise(X)&strong(X))))&
((?[X]:((kind(X)&~old(X))))<=>(?[X]:((~tall(X)|~strong(X)))))&
(![X]:(tall(X)=>(~creative(X)<~>~quiet(X))))&
((brave(mary))<=>(?[X]:((generous(X)<~>strong(X)))))&
(?[X]:((quiet(X)&~curious(X))))&
(?[X]:((~old(X)&~creative(X))))&
(?[X]:((generous(X)<~>~strong(X))))&
(?[X]:(~brave(X)))&
((~kind(john)<~>~calm(john))) | creative(alice) | [] | null | 0 |
If lucy is not strong or wise then alice is not happy.
Everyone who is not old or not happy is not humble or not rich and vice versa.
Everyone who is not humble is either patient or quiet and vice versa.
Everyone who is strong is both not wise and strong.
Everyone who is not humble is not quiet or not old.
Everyone who is curious or creative is tall.
Everyone who is generous is curious and vice versa.
Everyone who is both not generous and not calm is not happy or not generous and vice versa.
Everyone who is not generous or not old is both quiet and calm.
If alice is both not calm and wise then paul is old.
If someone is either not patient or tall then someone is not tall or not curious and vice versa.
Everyone who is either not tall or generous is not calm or not generous.
Everyone who is both not strong and not tall is funny or not humble and vice versa.
If someone is both generous and not calm then someone is either not funny or not wise and vice versa.
If lucy is not generous then mary is not rich or not funny.
Everyone who is either generous or rich is either creative or old.
John is either brave or not calm.
Mary is strong or not happy.
John is rich or creative.
Someone is either not tall or not patient.
Fred is brave or not humble. | Mary is not funny. | entailment | (((~strong(lucy)|wise(lucy)))=>(~happy(alice)))&
(![X]:((~old(X)|~happy(X))<=>(~humble(X)|~rich(X))))&
(![X]:(~humble(X)<=>(patient(X)<~>quiet(X))))&
(![X]:(strong(X)=>(~wise(X)&strong(X))))&
(![X]:(~humble(X)=>(~quiet(X)|~old(X))))&
(![X]:((curious(X)|creative(X))=>tall(X)))&
(![X]:(generous(X)<=>curious(X)))&
(![X]:((~generous(X)&~calm(X))<=>(~happy(X)|~generous(X))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&calm(X))))&
(((~calm(alice)&wise(alice)))=>(old(paul)))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((~tall(X)<~>generous(X))=>(~calm(X)|~generous(X))))&
(![X]:((~strong(X)&~tall(X))<=>(funny(X)|~humble(X))))&
((?[X]:((generous(X)&~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
((~generous(lucy))=>((~rich(mary)|~funny(mary))))&
(![X]:((generous(X)<~>rich(X))=>(creative(X)<~>old(X))))&
((brave(john)<~>~calm(john)))&
((strong(mary)|~happy(mary)))&
((rich(john)|creative(john)))&
(?[X]:((~tall(X)<~>~patient(X))))&
((brave(fred)|~humble(fred))) | ~funny(mary) | [
"p7",
"p8",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1965111386413186665972318
% SZS output start Proof for 1965111386413186665972318
8. ! [X0] : ((~calm(X0) & ~generous(X0)) <=> (~generous(X0) | ~happy(X0))) [input p7]
9. ! [X0] : ((~old(X0) | ~generous(X0)) => (calm(X0) & quiet(X0))) [input p8]
13. ! [X0] : ((~tall(X0) & ~strong(X0)) <=> (~humble(X0) | funny(X0))) [input p12]
18. ~happy(mary) | strong(mary) [input p17]
22. funny(mary) [input hypothesis]
30. ! [X0] : ((calm(X0) & quiet(X0)) | (old(X0) & generous(X0))) [ennf transformation 9]
42. ! [X0] : (((~calm(X0) & ~generous(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (calm(X0) | generous(X0)))) [nnf transformation 8]
43. ! [X0] : (((~calm(X0) & ~generous(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | calm(X0) | generous(X0))) [flattening 42]
50. ! [X0] : (((~tall(X0) & ~strong(X0)) | (humble(X0) & ~funny(X0))) & ((~humble(X0) | funny(X0)) | (tall(X0) | strong(X0)))) [nnf transformation 13]
51. ! [X0] : (((~tall(X0) & ~strong(X0)) | (humble(X0) & ~funny(X0))) & (~humble(X0) | funny(X0) | tall(X0) | strong(X0))) [flattening 50]
80. ~generous(X0) | happy(X0) [cnf transformation 43]
83. ~calm(X0) | generous(X0) [cnf transformation 43]
86. calm(X0) | generous(X0) [cnf transformation 30]
98. ~funny(X0) | ~strong(X0) [cnf transformation 51]
115. ~happy(mary) | strong(mary) [cnf transformation 18]
120. funny(mary) [cnf transformation 22]
136. generous(X0) [subsumption resolution 86,83]
223. 22 <=> strong(mary) [avatar definition]
225. strong(mary) <- (22) [avatar component clause 223]
227. 23 <=> happy(mary) [avatar definition]
229. ~happy(mary) <- (~23) [avatar component clause 227]
230. 22 | ~23 [avatar split clause 115,227,223]
272. happy(X0) [resolution 80,136]
274. $false <- (~23) [resolution 272,229]
275. 23 [avatar contradiction clause 274]
282. ~strong(mary) [resolution 98,120]
284. $false <- (22) [subsumption resolution 282,225]
285. ~22 [avatar contradiction clause 284]
286. $false [avatar sat refutation 230,275,285]
% SZS output end Proof for 1965111386413186665972318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and not generous then paul is both not funny and old and vice versa.
Everyone who is wise or strong is rich or not patient and vice versa.
Everyone who is kind is either curious or not generous and vice versa.
If paul is either not quiet or generous then john is either strong or calm.
Everyone who is not rich is either patient or happy and vice versa.
If paul is wise then lucy is rich.
Everyone who is kind is both not strong and patient.
Everyone who is old is not creative and vice versa.
If mary is both curious and humble then someone is not wise or patient and vice versa.
If mary is old then alice is either not rich or not tall and vice versa.
Everyone who is not creative or humble is both happy and not quiet and vice versa.
Everyone who is humble or calm is not quiet and vice versa.
If susan is not generous or not brave then someone is both not calm and funny and vice versa.
Everyone who is calm or curious is not brave or not humble.
Everyone who is both creative and calm is creative or calm.
Everyone who is either not kind or not curious is both not old and calm and vice versa.
Someone is both not tall and quiet.
Mary is both not curious and happy.
Someone is both curious and not generous.
Alice is both not quiet and not rich.
Mary is both not creative and brave.
Someone is either not patient or not happy.
Mary is quiet or not curious. | Susan is curious. | neutral | ((?[X]:((~humble(X)&~generous(X))))<=>((~funny(paul)&old(paul))))&
(![X]:((wise(X)|strong(X))<=>(rich(X)|~patient(X))))&
(![X]:(kind(X)<=>(curious(X)<~>~generous(X))))&
(((~quiet(paul)<~>generous(paul)))=>((strong(john)<~>calm(john))))&
(![X]:(~rich(X)<=>(patient(X)<~>happy(X))))&
((wise(paul))=>(rich(lucy)))&
(![X]:(kind(X)=>(~strong(X)&patient(X))))&
(![X]:(old(X)<=>~creative(X)))&
(((curious(mary)&humble(mary)))<=>(?[X]:((~wise(X)|patient(X)))))&
((old(mary))<=>((~rich(alice)<~>~tall(alice))))&
(![X]:((~creative(X)|humble(X))<=>(happy(X)&~quiet(X))))&
(![X]:((humble(X)|calm(X))<=>~quiet(X)))&
(((~generous(susan)|~brave(susan)))<=>(?[X]:((~calm(X)&funny(X)))))&
(![X]:((calm(X)|curious(X))=>(~brave(X)|~humble(X))))&
(![X]:((creative(X)&calm(X))=>(creative(X)|calm(X))))&
(![X]:((~kind(X)<~>~curious(X))<=>(~old(X)&calm(X))))&
(?[X]:((~tall(X)&quiet(X))))&
((~curious(mary)&happy(mary)))&
(?[X]:((curious(X)&~generous(X))))&
((~quiet(alice)&~rich(alice)))&
((~creative(mary)&brave(mary)))&
(?[X]:((~patient(X)<~>~happy(X))))&
((quiet(mary)|~curious(mary))) | curious(susan) | [] | null | 0 |
Everyone who is not brave or not creative is wise.
If paul is either generous or not calm then someone is kind or generous and vice versa.
If alice is not calm or calm then someone is not calm.
Everyone who is both creative and happy is both wise and not happy.
Everyone who is either wise or creative is either calm or not brave and vice versa.
Everyone who is wise is creative and vice versa.
If susan is both not kind and not quiet then someone is either calm or patient and vice versa.
Everyone who is not wise or not happy is not curious or kind and vice versa.
Everyone who is not strong or happy is not brave or not humble and vice versa.
If someone is not old then someone is quiet.
Everyone who is either not happy or not strong is both kind and rich and vice versa.
Everyone who is either creative or curious is both calm and not wise and vice versa.
If someone is calm then someone is not tall or brave and vice versa.
If lucy is quiet or brave then someone is not brave or brave.
If paul is calm or funny then someone is quiet or calm.
If paul is not wise then someone is both old and patient.
Someone is happy or old.
Someone is old or not creative.
Mary is either not kind or not tall.
Lucy is both not old and generous.
Someone is either not curious or not brave.
Lucy is not quiet.
Someone is patient or not happy.
Someone is either rich or not happy. | Alice is happy. | contradiction | (![X]:((~brave(X)|~creative(X))=>wise(X)))&
(((generous(paul)<~>~calm(paul)))<=>(?[X]:((kind(X)|generous(X)))))&
(((~calm(alice)|calm(alice)))=>(?[X]:(~calm(X))))&
(![X]:((creative(X)&happy(X))=>(wise(X)&~happy(X))))&
(![X]:((wise(X)<~>creative(X))<=>(calm(X)<~>~brave(X))))&
(![X]:(wise(X)<=>creative(X)))&
(((~kind(susan)&~quiet(susan)))<=>(?[X]:((calm(X)<~>patient(X)))))&
(![X]:((~wise(X)|~happy(X))<=>(~curious(X)|kind(X))))&
(![X]:((~strong(X)|happy(X))<=>(~brave(X)|~humble(X))))&
((?[X]:(~old(X)))=>(?[X]:(quiet(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>(kind(X)&rich(X))))&
(![X]:((creative(X)<~>curious(X))<=>(calm(X)&~wise(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~tall(X)|brave(X)))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:((~brave(X)|brave(X)))))&
(((calm(paul)|funny(paul)))=>(?[X]:((quiet(X)|calm(X)))))&
((~wise(paul))=>(?[X]:((old(X)&patient(X)))))&
(?[X]:((happy(X)|old(X))))&
(?[X]:((old(X)|~creative(X))))&
((~kind(mary)<~>~tall(mary)))&
((~old(lucy)&generous(lucy)))&
(?[X]:((~curious(X)<~>~brave(X))))&
(~quiet(lucy))&
(?[X]:((patient(X)|~happy(X))))&
(?[X]:((rich(X)<~>~happy(X)))) | happy(alice) | [
"p0",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6036320779520381729672787
% SZS output start Proof for 6036320779520381729672787
1. ! [X0] : ((~creative(X0) | ~brave(X0)) => wise(X0)) [input p0]
4. ! [X0] : ((happy(X0) & creative(X0)) => (~happy(X0) & wise(X0))) [input p3]
6. ! [X0] : (wise(X0) <=> creative(X0)) [input p5]
25. happy(alice) [input hypothesis]
29. ! [X0] : (wise(X0) | (creative(X0) & brave(X0))) [ennf transformation 1]
31. ! [X0] : ((~happy(X0) & wise(X0)) | (~happy(X0) | ~creative(X0))) [ennf transformation 4]
32. ! [X0] : ((~happy(X0) & wise(X0)) | ~happy(X0) | ~creative(X0)) [flattening 31]
44. ! [X0] : ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))) [nnf transformation 6]
86. wise(X0) | creative(X0) [cnf transformation 29]
96. ~happy(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 32]
105. creative(X0) | ~wise(X0) [cnf transformation 44]
106. wise(X0) | ~creative(X0) [cnf transformation 44]
154. happy(alice) [cnf transformation 25]
155. ~happy(X0) | ~creative(X0) [duplicate literal removal 96]
199. wise(X0) [subsumption resolution 106,86]
200. creative(X0) [subsumption resolution 105,199]
318. ~creative(alice) [resolution 155,154]
320. $false [subsumption resolution 318,200]
% SZS output end Proof for 6036320779520381729672787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is both brave and not kind and vice versa.
Everyone who is both not rich and not brave is not old or old and vice versa.
Everyone who is either not calm or humble is not old or funny.
If john is old then alice is either rich or not brave.
If alice is either old or not kind then alice is not happy or happy.
If fred is either rich or old then john is both not humble and funny.
If susan is both not patient and not wise then alice is both not humble and curious.
If someone is not patient then someone is brave or not generous and vice versa.
If paul is tall or not humble then someone is not rich or not quiet and vice versa.
Everyone who is happy or not kind is both tall and not strong.
Everyone who is either not generous or not funny is humble or not calm.
If mary is either brave or not strong then lucy is happy and vice versa.
If someone is generous or humble then paul is not old and vice versa.
If paul is old then someone is both rich and not creative.
If fred is kind or not old then fred is both not brave and creative.
Everyone who is both not brave and not humble is brave.
Lucy is either not quiet or creative.
Someone is either not strong or rich.
Someone is either not quiet or creative.
Fred is either brave or quiet.
Someone is both old and not funny. | Fred is old. | contradiction | (![X]:(~creative(X)<=>(brave(X)&~kind(X))))&
(![X]:((~rich(X)&~brave(X))<=>(~old(X)|old(X))))&
(![X]:((~calm(X)<~>humble(X))=>(~old(X)|funny(X))))&
((old(john))=>((rich(alice)<~>~brave(alice))))&
(((old(alice)<~>~kind(alice)))=>((~happy(alice)|happy(alice))))&
(((rich(fred)<~>old(fred)))=>((~humble(john)&funny(john))))&
(((~patient(susan)&~wise(susan)))=>((~humble(alice)&curious(alice))))&
((?[X]:(~patient(X)))<=>(?[X]:((brave(X)|~generous(X)))))&
(((tall(paul)|~humble(paul)))<=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((happy(X)|~kind(X))=>(tall(X)&~strong(X))))&
(![X]:((~generous(X)<~>~funny(X))=>(humble(X)|~calm(X))))&
(((brave(mary)<~>~strong(mary)))<=>(happy(lucy)))&
((?[X]:((generous(X)|humble(X))))<=>(~old(paul)))&
((old(paul))=>(?[X]:((rich(X)&~creative(X)))))&
(((kind(fred)|~old(fred)))=>((~brave(fred)&creative(fred))))&
(![X]:((~brave(X)&~humble(X))=>brave(X)))&
((~quiet(lucy)<~>creative(lucy)))&
(?[X]:((~strong(X)<~>rich(X))))&
(?[X]:((~quiet(X)<~>creative(X))))&
((brave(fred)<~>quiet(fred)))&
(?[X]:((old(X)&~funny(X)))) | old(fred) | [
"p1",
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3066058506538862020482565
% SZS output start Proof for 3066058506538862020482565
2. ! [X0] : ((~brave(X0) & ~rich(X0)) <=> (old(X0) | ~old(X0))) [input p1]
6. (rich(fred) <~> old(fred)) => (funny(john) & ~humble(john)) [input p5]
16. ! [X0] : ((~humble(X0) & ~brave(X0)) => brave(X0)) [input p15]
22. old(fred) [input hypothesis]
31. (funny(john) & ~humble(john)) | (rich(fred) <=> old(fred)) [ennf transformation 6]
37. ! [X0] : (brave(X0) | (humble(X0) | brave(X0))) [ennf transformation 16]
38. ! [X0] : (brave(X0) | humble(X0) | brave(X0)) [flattening 37]
41. ! [X0] : (((~brave(X0) & ~rich(X0)) | (~old(X0) & old(X0))) & ((old(X0) | ~old(X0)) | (brave(X0) | rich(X0)))) [nnf transformation 2]
42. ! [X0] : (((~brave(X0) & ~rich(X0)) | (~old(X0) & old(X0))) & (old(X0) | ~old(X0) | brave(X0) | rich(X0))) [flattening 41]
46. (funny(john) & ~humble(john)) | ((rich(fred) | ~old(fred)) & (old(fred) | ~rich(fred))) [nnf transformation 31]
79. ~rich(X0) | old(X0) [cnf transformation 42]
80. ~rich(X0) | ~old(X0) [cnf transformation 42]
81. ~brave(X0) | old(X0) [cnf transformation 42]
82. ~brave(X0) | ~old(X0) [cnf transformation 42]
90. ~humble(john) | rich(fred) | ~old(fred) [cnf transformation 46]
119. brave(X0) | humble(X0) | brave(X0) [cnf transformation 38]
130. old(fred) [cnf transformation 22]
131. brave(X0) | humble(X0) [duplicate literal removal 119]
132. ~brave(X0) [subsumption resolution 81,82]
133. ~rich(X0) [subsumption resolution 79,80]
136. 1 <=> old(fred) [avatar definition]
144. ~humble(john) | ~old(fred) [subsumption resolution 90,133]
146. 3 <=> humble(john) [avatar definition]
148. ~humble(john) <- (~3) [avatar component clause 146]
149. ~1 | ~3 [avatar split clause 144,146,136]
226. humble(X0) [subsumption resolution 131,132]
249. 1 [avatar split clause 130,136]
252. $false <- (~3) [subsumption resolution 148,226]
253. 3 [avatar contradiction clause 252]
254. $false [avatar sat refutation 149,249,253]
% SZS output end Proof for 3066058506538862020482565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not happy is both patient and quiet. Everyone who is not humble or funny is both not quiet and not humble. If someone is old or quiet then someone is generous or not wise. Everyone who is either creative or not happy is not calm and vice versa. Everyone who is both patient and not strong is either not wise or brave. If lucy is not happy then someone is not creative or not calm. Everyone who is either not humble or not strong is old and vice versa. Everyone who is either not tall or not creative is not curious or not funny and vice versa. Everyone who is patient or not tall is both old and tall. If someone is either strong or not happy then mary is either quiet or curious. Everyone who is funny or tall is not generous and vice versa. Everyone who is calm is not kind or quiet. Everyone who is not funny or old is generous or funny. Everyone who is either rich or not humble is kind. Everyone who is tall or not brave is both patient and not generous. Someone is generous or kind. John is rich. Susan is both funny and not generous. Alice is both wise and tall. | John is not calm. | neutral | (![X]:((kind(X)<~>~happy(X))=>(patient(X)&quiet(X))))&
(![X]:((~humble(X)|funny(X))=>(~quiet(X)&~humble(X))))&
((?[X]:((old(X)|quiet(X))))=>(?[X]:((generous(X)|~wise(X)))))&
(![X]:((creative(X)<~>~happy(X))<=>~calm(X)))&
(![X]:((patient(X)&~strong(X))=>(~wise(X)<~>brave(X))))&
((~happy(lucy))=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:((~humble(X)<~>~strong(X))<=>old(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>(~curious(X)|~funny(X))))&
(![X]:((patient(X)|~tall(X))=>(old(X)&tall(X))))&
((?[X]:((strong(X)<~>~happy(X))))=>((quiet(mary)<~>curious(mary))))&
(![X]:((funny(X)|tall(X))<=>~generous(X)))&
(![X]:(calm(X)=>(~kind(X)|quiet(X))))&
(![X]:((~funny(X)|old(X))=>(generous(X)|funny(X))))&
(![X]:((rich(X)<~>~humble(X))=>kind(X)))&
(![X]:((tall(X)|~brave(X))=>(patient(X)&~generous(X))))&
(?[X]:((generous(X)|kind(X))))&
(rich(john))&
((funny(susan)&~generous(susan)))&
((wise(alice)&tall(alice))) | ~calm(john) | [] | null | 0 |
Everyone who is either humble or patient is either humble or not strong and vice versa.
Everyone who is both quiet and not wise is wise.
Everyone who is either creative or calm is not generous or calm.
Everyone who is calm or not happy is either not rich or not generous.
If someone is either not humble or rich then someone is brave and vice versa.
If alice is not happy then mary is not calm.
If someone is kind or quiet then someone is either humble or not kind.
Everyone who is funny or patient is either not calm or not rich.
If someone is quiet or curious then someone is either not curious or creative.
If someone is either not patient or wise then lucy is both generous and not calm and vice versa.
Everyone who is not wise is quiet or tall and vice versa.
Everyone who is not brave is either calm or not happy and vice versa.
Everyone who is not old or not wise is wise or not calm and vice versa.
If john is calm then alice is both not creative and not brave and vice versa.
Everyone who is either quiet or kind is not curious and vice versa.
Everyone who is not happy is either not happy or funny and vice versa.
Fred is rich.
John is both not brave and not humble.
Someone is not funny or generous.
Someone is wise.
Someone is strong.
Someone is old.
Lucy is either brave or not generous. | Fred is not strong. | neutral | (![X]:((humble(X)<~>patient(X))<=>(humble(X)<~>~strong(X))))&
(![X]:((quiet(X)&~wise(X))=>wise(X)))&
(![X]:((creative(X)<~>calm(X))=>(~generous(X)|calm(X))))&
(![X]:((calm(X)|~happy(X))=>(~rich(X)<~>~generous(X))))&
((?[X]:((~humble(X)<~>rich(X))))<=>(?[X]:(brave(X))))&
((~happy(alice))=>(~calm(mary)))&
((?[X]:((kind(X)|quiet(X))))=>(?[X]:((humble(X)<~>~kind(X)))))&
(![X]:((funny(X)|patient(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:((quiet(X)|curious(X))))=>(?[X]:((~curious(X)<~>creative(X)))))&
((?[X]:((~patient(X)<~>wise(X))))<=>((generous(lucy)&~calm(lucy))))&
(![X]:(~wise(X)<=>(quiet(X)|tall(X))))&
(![X]:(~brave(X)<=>(calm(X)<~>~happy(X))))&
(![X]:((~old(X)|~wise(X))<=>(wise(X)|~calm(X))))&
((calm(john))<=>((~creative(alice)&~brave(alice))))&
(![X]:((quiet(X)<~>kind(X))<=>~curious(X)))&
(![X]:(~happy(X)<=>(~happy(X)<~>funny(X))))&
(rich(fred))&
((~brave(john)&~humble(john)))&
(?[X]:((~funny(X)|generous(X))))&
(?[X]:(wise(X)))&
(?[X]:(strong(X)))&
(?[X]:(old(X)))&
((brave(lucy)<~>~generous(lucy))) | ~strong(fred) | [] | null | 0 |
If paul is not funny or patient then paul is not old or curious. Everyone who is generous or rich is both humble and not brave and vice versa. If fred is both not happy and not old then fred is either generous or not curious and vice versa. Everyone who is not rich or not generous is either brave or not kind and vice versa. If alice is not humble then someone is either not patient or funny and vice versa. If mary is not patient then susan is generous and vice versa. Everyone who is either rich or not wise is not generous or calm. Everyone who is not strong or strong is not creative or not happy. If fred is old then someone is both not funny and not generous and vice versa. Everyone who is both not humble and not generous is both curious and not humble and vice versa. Everyone who is not brave or humble is wise or not calm and vice versa. Everyone who is either brave or not tall is not kind. Everyone who is either calm or not patient is either brave or not old. Everyone who is not kind or old is patient or brave and vice versa. Everyone who is either not rich or rich is brave and vice versa. If someone is either wise or funny then someone is quiet and vice versa. Mary is either not creative or not rich. Someone is strong. Someone is either funny or not patient. Someone is either not generous or tall. Someone is creative. | Mary is not calm. | neutral | (((~funny(paul)|patient(paul)))=>((~old(paul)|curious(paul))))&
(![X]:((generous(X)|rich(X))<=>(humble(X)&~brave(X))))&
(((~happy(fred)&~old(fred)))<=>((generous(fred)<~>~curious(fred))))&
(![X]:((~rich(X)|~generous(X))<=>(brave(X)<~>~kind(X))))&
((~humble(alice))<=>(?[X]:((~patient(X)<~>funny(X)))))&
((~patient(mary))<=>(generous(susan)))&
(![X]:((rich(X)<~>~wise(X))=>(~generous(X)|calm(X))))&
(![X]:((~strong(X)|strong(X))=>(~creative(X)|~happy(X))))&
((old(fred))<=>(?[X]:((~funny(X)&~generous(X)))))&
(![X]:((~humble(X)&~generous(X))<=>(curious(X)&~humble(X))))&
(![X]:((~brave(X)|humble(X))<=>(wise(X)|~calm(X))))&
(![X]:((brave(X)<~>~tall(X))=>~kind(X)))&
(![X]:((calm(X)<~>~patient(X))=>(brave(X)<~>~old(X))))&
(![X]:((~kind(X)|old(X))<=>(patient(X)|brave(X))))&
(![X]:((~rich(X)<~>rich(X))<=>brave(X)))&
((?[X]:((wise(X)<~>funny(X))))<=>(?[X]:(quiet(X))))&
((~creative(mary)<~>~rich(mary)))&
(?[X]:(strong(X)))&
(?[X]:((funny(X)<~>~patient(X))))&
(?[X]:((~generous(X)<~>tall(X))))&
(?[X]:(creative(X))) | ~calm(mary) | [] | null | 0 |
Everyone who is both not generous and not curious is funny and vice versa. Everyone who is generous is not humble. Everyone who is creative or not creative is not humble and vice versa. If someone is not happy then fred is not tall. If someone is not happy then lucy is either not calm or tall and vice versa. If someone is both not rich and not curious then someone is old or quiet and vice versa. If someone is both funny and rich then someone is kind and vice versa. If someone is either not tall or quiet then alice is not kind or rich. Everyone who is wise or not funny is either creative or not rich and vice versa. Everyone who is not patient or not happy is not funny. Everyone who is either calm or not tall is strong or humble. If mary is not wise or not funny then someone is either creative or not generous. Everyone who is calm is not patient or not quiet. Everyone who is either wise or funny is either happy or not rich and vice versa. Everyone who is not generous is not wise or not happy and vice versa. Everyone who is either not creative or not wise is not tall or not humble. Paul is calm. Paul is not quiet. Someone is either not funny or funny. Lucy is not humble or tall. Someone is either not brave or not wise. John is not rich. | John is humble. | contradiction | (![X]:((~generous(X)&~curious(X))<=>funny(X)))&
(![X]:(generous(X)=>~humble(X)))&
(![X]:((creative(X)|~creative(X))<=>~humble(X)))&
((?[X]:(~happy(X)))=>(~tall(fred)))&
((?[X]:(~happy(X)))<=>((~calm(lucy)<~>tall(lucy))))&
((?[X]:((~rich(X)&~curious(X))))<=>(?[X]:((old(X)|quiet(X)))))&
((?[X]:((funny(X)&rich(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~tall(X)<~>quiet(X))))=>((~kind(alice)|rich(alice))))&
(![X]:((wise(X)|~funny(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((~patient(X)|~happy(X))=>~funny(X)))&
(![X]:((calm(X)<~>~tall(X))=>(strong(X)|humble(X))))&
(((~wise(mary)|~funny(mary)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(calm(X)=>(~patient(X)|~quiet(X))))&
(![X]:((wise(X)<~>funny(X))<=>(happy(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(~wise(X)|~happy(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(~tall(X)|~humble(X))))&
(calm(paul))&
(~quiet(paul))&
(?[X]:((~funny(X)<~>funny(X))))&
((~humble(lucy)|tall(lucy)))&
(?[X]:((~brave(X)<~>~wise(X))))&
(~rich(john)) | humble(john) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 2970830772650385150852552
% SZS output start Proof for 2970830772650385150852552
3. ! [X0] : ((~creative(X0) | creative(X0)) <=> ~humble(X0)) [input p2]
23. humble(john) [input hypothesis]
39. ! [X0] : (((~creative(X0) | creative(X0)) | humble(X0)) & (~humble(X0) | (creative(X0) & ~creative(X0)))) [nnf transformation 3]
40. ! [X0] : ((~creative(X0) | creative(X0) | humble(X0)) & (~humble(X0) | (creative(X0) & ~creative(X0)))) [flattening 39]
75. ~humble(X0) | ~creative(X0) [cnf transformation 40]
76. ~humble(X0) | creative(X0) [cnf transformation 40]
127. humble(john) [cnf transformation 23]
128. ~humble(X0) [subsumption resolution 75,76]
254. $false [subsumption resolution 127,128]
% SZS output end Proof for 2970830772650385150852552
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not calm and quiet then someone is both not rich and not strong.
Everyone who is strong is either not old or tall and vice versa.
If fred is either not calm or not quiet then lucy is both not funny and strong and vice versa.
Everyone who is both curious and not kind is either not generous or brave.
Everyone who is not brave or funny is either not creative or tall and vice versa.
If someone is either funny or not calm then someone is either not old or humble and vice versa.
Everyone who is not generous is not quiet and vice versa.
If someone is either calm or not generous then someone is both not old and not rich.
If susan is either not curious or rich then someone is both brave and patient.
If susan is either not tall or generous then someone is both creative and not strong and vice versa.
Everyone who is both not quiet and not tall is both not generous and not curious and vice versa.
Everyone who is generous is kind and vice versa.
Everyone who is both not old and not wise is curious or not wise and vice versa.
If someone is both tall and generous then someone is both not tall and creative.
Everyone who is not generous is both not quiet and not wise and vice versa.
If john is not tall or not funny then someone is not strong or not wise.
Fred is either not kind or brave.
Mary is kind or not old.
Someone is wise.
Lucy is not curious or not creative.
Someone is tall or not calm.
Susan is strong or not brave.
Lucy is not strong or calm. | Susan is not creative. | neutral | (((~calm(susan)&quiet(susan)))=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:(strong(X)<=>(~old(X)<~>tall(X))))&
(((~calm(fred)<~>~quiet(fred)))<=>((~funny(lucy)&strong(lucy))))&
(![X]:((curious(X)&~kind(X))=>(~generous(X)<~>brave(X))))&
(![X]:((~brave(X)|funny(X))<=>(~creative(X)<~>tall(X))))&
((?[X]:((funny(X)<~>~calm(X))))<=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:(~generous(X)<=>~quiet(X)))&
((?[X]:((calm(X)<~>~generous(X))))=>(?[X]:((~old(X)&~rich(X)))))&
(((~curious(susan)<~>rich(susan)))=>(?[X]:((brave(X)&patient(X)))))&
(((~tall(susan)<~>generous(susan)))<=>(?[X]:((creative(X)&~strong(X)))))&
(![X]:((~quiet(X)&~tall(X))<=>(~generous(X)&~curious(X))))&
(![X]:(generous(X)<=>kind(X)))&
(![X]:((~old(X)&~wise(X))<=>(curious(X)|~wise(X))))&
((?[X]:((tall(X)&generous(X))))=>(?[X]:((~tall(X)&creative(X)))))&
(![X]:(~generous(X)<=>(~quiet(X)&~wise(X))))&
(((~tall(john)|~funny(john)))=>(?[X]:((~strong(X)|~wise(X)))))&
((~kind(fred)<~>brave(fred)))&
((kind(mary)|~old(mary)))&
(?[X]:(wise(X)))&
((~curious(lucy)|~creative(lucy)))&
(?[X]:((tall(X)|~calm(X))))&
((strong(susan)|~brave(susan)))&
((~strong(lucy)|calm(lucy))) | ~creative(susan) | [] | null | 0 |
Everyone who is tall or not creative is both not quiet and not patient and vice versa. If john is not quiet then lucy is generous or not strong and vice versa. If fred is not patient or not kind then paul is tall and vice versa. Everyone who is not humble is either kind or not funny and vice versa. Everyone who is old or not humble is happy or kind. Everyone who is not generous is not strong and vice versa. Everyone who is rich is both tall and not curious. Everyone who is either not happy or not quiet is strong or old. Everyone who is humble is either curious or not humble and vice versa. Everyone who is wise or not strong is patient or not patient and vice versa. Everyone who is both quiet and kind is either wise or not patient and vice versa. Everyone who is both quiet and not tall is strong or generous. Everyone who is either not rich or curious is curious. If someone is not funny or humble then someone is both not happy and not kind and vice versa. If susan is not wise then someone is patient or calm. If someone is not curious then alice is either not creative or old. Alice is quiet. Someone is not rich. Someone is either not happy or not brave. Lucy is not calm or quiet. Paul is either humble or calm. John is not humble or not strong. Mary is not calm. Someone is not wise. | Alice is wise. | entailment | (![X]:((tall(X)|~creative(X))<=>(~quiet(X)&~patient(X))))&
((~quiet(john))<=>((generous(lucy)|~strong(lucy))))&
(((~patient(fred)|~kind(fred)))<=>(tall(paul)))&
(![X]:(~humble(X)<=>(kind(X)<~>~funny(X))))&
(![X]:((old(X)|~humble(X))=>(happy(X)|kind(X))))&
(![X]:(~generous(X)<=>~strong(X)))&
(![X]:(rich(X)=>(tall(X)&~curious(X))))&
(![X]:((~happy(X)<~>~quiet(X))=>(strong(X)|old(X))))&
(![X]:(humble(X)<=>(curious(X)<~>~humble(X))))&
(![X]:((wise(X)|~strong(X))<=>(patient(X)|~patient(X))))&
(![X]:((quiet(X)&kind(X))<=>(wise(X)<~>~patient(X))))&
(![X]:((quiet(X)&~tall(X))=>(strong(X)|generous(X))))&
(![X]:((~rich(X)<~>curious(X))=>curious(X)))&
((?[X]:((~funny(X)|humble(X))))<=>(?[X]:((~happy(X)&~kind(X)))))&
((~wise(susan))=>(?[X]:((patient(X)|calm(X)))))&
((?[X]:(~curious(X)))=>((~creative(alice)<~>old(alice))))&
(quiet(alice))&
(?[X]:(~rich(X)))&
(?[X]:((~happy(X)<~>~brave(X))))&
((~calm(lucy)|quiet(lucy)))&
((humble(paul)<~>calm(paul)))&
((~humble(john)|~strong(john)))&
(~calm(mary))&
(?[X]:(~wise(X))) | wise(alice) | [
"p0",
"p5",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4046125355722996578648155
% SZS output start Proof for 4046125355722996578648155
1. ! [X0] : ((~creative(X0) | tall(X0)) <=> (~patient(X0) & ~quiet(X0))) [input p0]
6. ! [X0] : (~generous(X0) <=> ~strong(X0)) [input p5]
10. ! [X0] : ((~strong(X0) | wise(X0)) <=> (~patient(X0) | patient(X0))) [input p9]
12. ! [X0] : ((~tall(X0) & quiet(X0)) => (generous(X0) | strong(X0))) [input p11]
17. quiet(alice) [input p16]
25. ~wise(alice) [input hypothesis]
32. ! [X0] : ((generous(X0) | strong(X0)) | (tall(X0) | ~quiet(X0))) [ennf transformation 12]
33. ! [X0] : (generous(X0) | strong(X0) | tall(X0) | ~quiet(X0)) [flattening 32]
37. ! [X0] : (((~creative(X0) | tall(X0)) | (patient(X0) | quiet(X0))) & ((~patient(X0) & ~quiet(X0)) | (creative(X0) & ~tall(X0)))) [nnf transformation 1]
38. ! [X0] : ((~creative(X0) | tall(X0) | patient(X0) | quiet(X0)) & ((~patient(X0) & ~quiet(X0)) | (creative(X0) & ~tall(X0)))) [flattening 37]
44. ! [X0] : ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))) [nnf transformation 6]
47. ! [X0] : (((~strong(X0) | wise(X0)) | (patient(X0) & ~patient(X0))) & ((~patient(X0) | patient(X0)) | (strong(X0) & ~wise(X0)))) [nnf transformation 10]
48. ! [X0] : ((~strong(X0) | wise(X0) | (patient(X0) & ~patient(X0))) & (~patient(X0) | patient(X0) | (strong(X0) & ~wise(X0)))) [flattening 47]
68. ~quiet(X0) | ~tall(X0) [cnf transformation 38]
86. ~generous(X0) | strong(X0) [cnf transformation 44]
97. ~strong(X0) | wise(X0) | ~patient(X0) [cnf transformation 48]
98. ~strong(X0) | wise(X0) | patient(X0) [cnf transformation 48]
105. generous(X0) | strong(X0) | tall(X0) | ~quiet(X0) [cnf transformation 33]
116. quiet(alice) [cnf transformation 17]
126. ~wise(alice) [cnf transformation 25]
161. ~strong(X0) | wise(X0) [subsumption resolution 97,98]
162. strong(X0) | tall(X0) | ~quiet(X0) [subsumption resolution 105,86]
163. ~quiet(X0) | strong(X0) [subsumption resolution 162,68]
249. strong(alice) [resolution 163,116]
250. wise(alice) [resolution 249,161]
252. $false [subsumption resolution 250,126]
% SZS output end Proof for 4046125355722996578648155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong then someone is wise. Everyone who is not humble is not strong. Everyone who is either funny or kind is both not brave and tall. Everyone who is patient is either not funny or not tall and vice versa. Everyone who is patient is both not kind and humble and vice versa. Everyone who is tall or not rich is strong. If someone is not patient then someone is either creative or not generous. Everyone who is not generous is not wise. Everyone who is both not rich and tall is not generous. Everyone who is either not funny or rich is patient. Everyone who is both kind and not generous is either not calm or rich and vice versa. Everyone who is not generous is patient and vice versa. Everyone who is creative is either rich or not quiet and vice versa. If someone is kind or not happy then someone is both not generous and not humble and vice versa. Everyone who is either generous or strong is both not wise and not brave and vice versa. Everyone who is both curious and not wise is not generous and vice versa. Someone is quiet or generous. Someone is not happy or not quiet. Alice is humble or funny. Someone is not wise or quiet. | Alice is calm. | neutral | ((?[X]:((creative(X)|~strong(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)=>~strong(X)))&
(![X]:((funny(X)<~>kind(X))=>(~brave(X)&tall(X))))&
(![X]:(patient(X)<=>(~funny(X)<~>~tall(X))))&
(![X]:(patient(X)<=>(~kind(X)&humble(X))))&
(![X]:((tall(X)|~rich(X))=>strong(X)))&
((?[X]:(~patient(X)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:((~funny(X)<~>rich(X))=>patient(X)))&
(![X]:((kind(X)&~generous(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(creative(X)<=>(rich(X)<~>~quiet(X))))&
((?[X]:((kind(X)|~happy(X))))<=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((generous(X)<~>strong(X))<=>(~wise(X)&~brave(X))))&
(![X]:((curious(X)&~wise(X))<=>~generous(X)))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((~happy(X)|~quiet(X))))&
((humble(alice)|funny(alice)))&
(?[X]:((~wise(X)|quiet(X)))) | calm(alice) | [] | null | 0 |
Everyone who is either not kind or humble is either not calm or humble and vice versa.
If someone is either rich or not curious then susan is both calm and rich and vice versa.
Everyone who is either not strong or not brave is both patient and not calm.
Everyone who is calm or strong is either kind or not humble.
If someone is happy then someone is either happy or not generous.
Everyone who is both not humble and not patient is patient or not kind and vice versa.
If alice is both old and happy then someone is not patient or strong and vice versa.
Everyone who is both rich and patient is both strong and not patient.
Everyone who is both tall and not quiet is both not patient and patient and vice versa.
If mary is either not wise or old then mary is either not happy or rich.
If someone is humble or happy then mary is not brave.
Everyone who is not creative is both not kind and patient.
Everyone who is not rich is either not brave or creative and vice versa.
Everyone who is tall or quiet is creative or not humble and vice versa.
Everyone who is not calm or quiet is both not funny and happy.
Everyone who is generous or not kind is either not wise or not patient.
Someone is not rich or curious.
Someone is either kind or not kind.
Someone is wise.
Someone is either old or not kind.
Someone is both curious and creative.
John is tall.
Someone is either not quiet or not rich. | Susan is not happy. | contradiction | (![X]:((~kind(X)<~>humble(X))<=>(~calm(X)<~>humble(X))))&
((?[X]:((rich(X)<~>~curious(X))))<=>((calm(susan)&rich(susan))))&
(![X]:((~strong(X)<~>~brave(X))=>(patient(X)&~calm(X))))&
(![X]:((calm(X)|strong(X))=>(kind(X)<~>~humble(X))))&
((?[X]:(happy(X)))=>(?[X]:((happy(X)<~>~generous(X)))))&
(![X]:((~humble(X)&~patient(X))<=>(patient(X)|~kind(X))))&
(((old(alice)&happy(alice)))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((rich(X)&patient(X))=>(strong(X)&~patient(X))))&
(![X]:((tall(X)&~quiet(X))<=>(~patient(X)&patient(X))))&
(((~wise(mary)<~>old(mary)))=>((~happy(mary)<~>rich(mary))))&
((?[X]:((humble(X)|happy(X))))=>(~brave(mary)))&
(![X]:(~creative(X)=>(~kind(X)&patient(X))))&
(![X]:(~rich(X)<=>(~brave(X)<~>creative(X))))&
(![X]:((tall(X)|quiet(X))<=>(creative(X)|~humble(X))))&
(![X]:((~calm(X)|quiet(X))=>(~funny(X)&happy(X))))&
(![X]:((generous(X)|~kind(X))=>(~wise(X)<~>~patient(X))))&
(?[X]:((~rich(X)|curious(X))))&
(?[X]:((kind(X)<~>~kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((old(X)<~>~kind(X))))&
(?[X]:((curious(X)&creative(X))))&
(tall(john))&
(?[X]:((~quiet(X)<~>~rich(X)))) | ~happy(susan) | [
"p5",
"p8",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6779313086027699945898590
% SZS output start Proof for 6779313086027699945898590
6. ! [X0] : ((~patient(X0) & ~humble(X0)) <=> (~kind(X0) | patient(X0))) [input p5]
9. ! [X0] : ((~quiet(X0) & tall(X0)) <=> (patient(X0) & ~patient(X0))) [input p8]
12. ! [X0] : (~creative(X0) => (patient(X0) & ~kind(X0))) [input p11]
14. ! [X0] : ((quiet(X0) | tall(X0)) <=> (~humble(X0) | creative(X0))) [input p13]
15. ! [X0] : ((quiet(X0) | ~calm(X0)) => (happy(X0) & ~funny(X0))) [input p14]
24. ~happy(susan) [input hypothesis]
26. ! [X0] : ((quiet(X0) | ~calm(X0)) => happy(X0)) [pure predicate removal 15]
34. ! [X0] : ((patient(X0) & ~kind(X0)) | creative(X0)) [ennf transformation 12]
35. ! [X0] : (happy(X0) | (~quiet(X0) & calm(X0))) [ennf transformation 26]
49. ! [X0] : (((~patient(X0) & ~humble(X0)) | (kind(X0) & ~patient(X0))) & ((~kind(X0) | patient(X0)) | (patient(X0) | humble(X0)))) [nnf transformation 6]
50. ! [X0] : (((~patient(X0) & ~humble(X0)) | (kind(X0) & ~patient(X0))) & (~kind(X0) | patient(X0) | patient(X0) | humble(X0))) [flattening 49]
56. ! [X0] : (((~quiet(X0) & tall(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (quiet(X0) | ~tall(X0)))) [nnf transformation 9]
57. ! [X0] : (((~quiet(X0) & tall(X0)) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | quiet(X0) | ~tall(X0))) [flattening 56]
60. ! [X0] : (((quiet(X0) | tall(X0)) | (humble(X0) & ~creative(X0))) & ((~humble(X0) | creative(X0)) | (~quiet(X0) & ~tall(X0)))) [nnf transformation 14]
61. ! [X0] : ((quiet(X0) | tall(X0) | (humble(X0) & ~creative(X0))) & (~humble(X0) | creative(X0) | (~quiet(X0) & ~tall(X0)))) [flattening 60]
105. ~patient(X0) | ~patient(X0) [cnf transformation 50]
115. patient(X0) | quiet(X0) | ~tall(X0) [cnf transformation 57]
125. patient(X0) | creative(X0) [cnf transformation 34]
132. quiet(X0) | tall(X0) | ~creative(X0) [cnf transformation 61]
135. happy(X0) | ~quiet(X0) [cnf transformation 35]
151. ~happy(susan) [cnf transformation 24]
154. ~patient(X0) [duplicate literal removal 105]
221. quiet(X0) | ~tall(X0) [subsumption resolution 115,154]
251. creative(X0) [subsumption resolution 125,154]
255. quiet(X0) | tall(X0) [subsumption resolution 132,251]
256. quiet(X0) [subsumption resolution 255,221]
257. happy(X0) [subsumption resolution 135,256]
280. $false [subsumption resolution 151,257]
% SZS output end Proof for 6779313086027699945898590
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious then someone is not wise or not kind and vice versa. If someone is not generous then susan is old and vice versa. Everyone who is either tall or not creative is not quiet and vice versa. If alice is both not calm and not generous then susan is either generous or not strong and vice versa. Everyone who is either rich or not rich is either patient or rich and vice versa. Everyone who is either happy or wise is patient and vice versa. Everyone who is quiet or happy is not curious. If lucy is both not brave and calm then mary is either not patient or not quiet. If someone is either curious or not strong then someone is not funny or not brave and vice versa. If susan is either not old or not calm then someone is not kind or curious. Everyone who is both not quiet and not old is both generous and wise and vice versa. Everyone who is either patient or tall is not rich or not curious and vice versa. Everyone who is not tall is not quiet. If fred is either not rich or tall then someone is not funny or generous. If someone is not generous or not humble then paul is not creative. Everyone who is either funny or not wise is not rich or not calm. Someone is both not tall and not kind. Paul is calm or patient. Mary is brave. John is either old or tall. Someone is not wise or quiet. Paul is not creative. Mary is not wise or not curious. | Susan is generous. | neutral | ((?[X]:(~curious(X)))<=>(?[X]:((~wise(X)|~kind(X)))))&
((?[X]:(~generous(X)))<=>(old(susan)))&
(![X]:((tall(X)<~>~creative(X))<=>~quiet(X)))&
(((~calm(alice)&~generous(alice)))<=>((generous(susan)<~>~strong(susan))))&
(![X]:((rich(X)<~>~rich(X))<=>(patient(X)<~>rich(X))))&
(![X]:((happy(X)<~>wise(X))<=>patient(X)))&
(![X]:((quiet(X)|happy(X))=>~curious(X)))&
(((~brave(lucy)&calm(lucy)))=>((~patient(mary)<~>~quiet(mary))))&
((?[X]:((curious(X)<~>~strong(X))))<=>(?[X]:((~funny(X)|~brave(X)))))&
(((~old(susan)<~>~calm(susan)))=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~quiet(X)&~old(X))<=>(generous(X)&wise(X))))&
(![X]:((patient(X)<~>tall(X))<=>(~rich(X)|~curious(X))))&
(![X]:(~tall(X)=>~quiet(X)))&
(((~rich(fred)<~>tall(fred)))=>(?[X]:((~funny(X)|generous(X)))))&
((?[X]:((~generous(X)|~humble(X))))=>(~creative(paul)))&
(![X]:((funny(X)<~>~wise(X))=>(~rich(X)|~calm(X))))&
(?[X]:((~tall(X)&~kind(X))))&
((calm(paul)|patient(paul)))&
(brave(mary))&
((old(john)<~>tall(john)))&
(?[X]:((~wise(X)|quiet(X))))&
(~creative(paul))&
((~wise(mary)|~curious(mary))) | generous(susan) | [] | null | 0 |
Everyone who is either not calm or generous is either happy or old and vice versa. Everyone who is curious or patient is either strong or kind. If fred is both curious and happy then susan is funny and vice versa. Everyone who is curious or creative is both not kind and generous. Everyone who is happy or not kind is not curious. Everyone who is not brave is both not happy and not brave. Everyone who is both happy and not tall is generous and vice versa. If someone is not calm or not humble then mary is not strong or calm and vice versa. If someone is not creative then someone is not strong or not creative and vice versa. Everyone who is not humble is both not kind and not brave. If john is either old or tall then someone is not happy. If someone is both not kind and patient then susan is tall or humble and vice versa. If someone is either wise or not happy then someone is either not calm or strong. Everyone who is either not humble or generous is both not funny and old and vice versa. Everyone who is either not quiet or not happy is kind or happy and vice versa. Everyone who is happy or not tall is both not calm and not generous. Someone is either not wise or not funny. Alice is either not tall or old. Someone is not patient or not generous. Lucy is not creative or not curious. Someone is either wise or funny. Someone is either calm or not kind. | Alice is old. | entailment | (![X]:((~calm(X)<~>generous(X))<=>(happy(X)<~>old(X))))&
(![X]:((curious(X)|patient(X))=>(strong(X)<~>kind(X))))&
(((curious(fred)&happy(fred)))<=>(funny(susan)))&
(![X]:((curious(X)|creative(X))=>(~kind(X)&generous(X))))&
(![X]:((happy(X)|~kind(X))=>~curious(X)))&
(![X]:(~brave(X)=>(~happy(X)&~brave(X))))&
(![X]:((happy(X)&~tall(X))<=>generous(X)))&
((?[X]:((~calm(X)|~humble(X))))<=>((~strong(mary)|calm(mary))))&
((?[X]:(~creative(X)))<=>(?[X]:((~strong(X)|~creative(X)))))&
(![X]:(~humble(X)=>(~kind(X)&~brave(X))))&
(((old(john)<~>tall(john)))=>(?[X]:(~happy(X))))&
((?[X]:((~kind(X)&patient(X))))<=>((tall(susan)|humble(susan))))&
((?[X]:((wise(X)<~>~happy(X))))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((~humble(X)<~>generous(X))<=>(~funny(X)&old(X))))&
(![X]:((~quiet(X)<~>~happy(X))<=>(kind(X)|happy(X))))&
(![X]:((happy(X)|~tall(X))=>(~calm(X)&~generous(X))))&
(?[X]:((~wise(X)<~>~funny(X))))&
((~tall(alice)<~>old(alice)))&
(?[X]:((~patient(X)|~generous(X))))&
((~creative(lucy)|~curious(lucy)))&
(?[X]:((wise(X)<~>funny(X))))&
(?[X]:((calm(X)<~>~kind(X)))) | old(alice) | [
"p0",
"p6",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 907935703915313639981447
% SZS output start Proof for 907935703915313639981447
1. ! [X0] : ((~calm(X0) <~> generous(X0)) <=> (happy(X0) <~> old(X0))) [input p0]
7. ! [X0] : ((~tall(X0) & happy(X0)) <=> generous(X0)) [input p6]
16. ! [X0] : ((~tall(X0) | happy(X0)) => (~generous(X0) & ~calm(X0))) [input p15]
18. ~tall(alice) <~> old(alice) [input p17]
23. ~old(alice) [input hypothesis]
33. ! [X0] : ((~generous(X0) & ~calm(X0)) | (tall(X0) & ~happy(X0))) [ennf transformation 16]
34. ! [X0] : ((((~generous(X0) | calm(X0)) & (generous(X0) | ~calm(X0))) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0)))) & (((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0))))) [nnf transformation 1]
38. ! [X0] : (((~tall(X0) & happy(X0)) | ~generous(X0)) & (generous(X0) | (tall(X0) | ~happy(X0)))) [nnf transformation 7]
39. ! [X0] : (((~tall(X0) & happy(X0)) | ~generous(X0)) & (generous(X0) | tall(X0) | ~happy(X0))) [flattening 38]
69. (~old(alice) | tall(alice)) & (old(alice) | ~tall(alice)) [nnf transformation 18]
78. old(X0) | happy(X0) | generous(X0) | calm(X0) [cnf transformation 34]
101. ~happy(X0) | tall(X0) | generous(X0) [cnf transformation 39]
103. ~tall(X0) | ~generous(X0) [cnf transformation 39]
137. ~calm(X0) | tall(X0) [cnf transformation 33]
139. ~generous(X0) | tall(X0) [cnf transformation 33]
142. old(alice) | ~tall(alice) [cnf transformation 69]
150. ~old(alice) [cnf transformation 23]
273. ~generous(X0) [subsumption resolution 139,103]
285. 29 <=> tall(alice) [avatar definition]
286. ~tall(alice) <- (~29) [avatar component clause 285]
289. 30 <=> old(alice) [avatar definition]
291. ~old(alice) <- (~30) [avatar component clause 289]
293. ~29 | 30 [avatar split clause 142,289,285]
314. ~30 [avatar split clause 150,289]
322. happy(alice) | generous(alice) | calm(alice) <- (~30) [resolution 78,291]
323. happy(alice) | calm(alice) <- (~30) [subsumption resolution 322,273]
325. 35 <=> calm(alice) [avatar definition]
327. calm(alice) <- (35) [avatar component clause 325]
329. 36 <=> happy(alice) [avatar definition]
331. happy(alice) <- (36) [avatar component clause 329]
332. 35 | 36 | 30 [avatar split clause 323,289,329,325]
333. tall(alice) <- (35) [resolution 327,137]
334. $false <- (~29, 35) [subsumption resolution 333,286]
335. 29 | ~35 [avatar contradiction clause 334]
338. tall(alice) | generous(alice) <- (36) [resolution 331,101]
341. generous(alice) <- (~29, 36) [subsumption resolution 338,286]
342. $false <- (~29, 36) [subsumption resolution 341,273]
343. 29 | ~36 [avatar contradiction clause 342]
344. $false [avatar sat refutation 293,314,332,335,343]
% SZS output end Proof for 907935703915313639981447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or rich is not curious and vice versa.
Everyone who is not happy is not creative.
Everyone who is either not curious or not calm is both kind and curious and vice versa.
If alice is either not humble or not generous then someone is either creative or generous and vice versa.
Everyone who is generous is both not strong and not brave.
If lucy is either old or not creative then someone is either rich or tall and vice versa.
Everyone who is humble is patient and vice versa.
If fred is humble then susan is not curious and vice versa.
If someone is both quiet and not curious then lucy is funny or not old.
If someone is tall or not strong then fred is not quiet or not creative and vice versa.
If someone is wise or not humble then someone is either not humble or not brave.
Everyone who is both patient and rich is either wise or not kind.
Everyone who is either quiet or tall is both funny and not curious and vice versa.
Everyone who is funny is not humble or not rich.
Everyone who is strong or not wise is not creative and vice versa.
Everyone who is both not rich and not kind is either not strong or not happy and vice versa.
Alice is either not creative or rich.
Mary is strong or tall.
Fred is either curious or brave.
Someone is either rich or not creative.
Mary is either generous or curious.
Paul is either not generous or not funny. | Mary is creative. | neutral | (![X]:((tall(X)<~>rich(X))<=>~curious(X)))&
(![X]:(~happy(X)=>~creative(X)))&
(![X]:((~curious(X)<~>~calm(X))<=>(kind(X)&curious(X))))&
(((~humble(alice)<~>~generous(alice)))<=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:(generous(X)=>(~strong(X)&~brave(X))))&
(((old(lucy)<~>~creative(lucy)))<=>(?[X]:((rich(X)<~>tall(X)))))&
(![X]:(humble(X)<=>patient(X)))&
((humble(fred))<=>(~curious(susan)))&
((?[X]:((quiet(X)&~curious(X))))=>((funny(lucy)|~old(lucy))))&
((?[X]:((tall(X)|~strong(X))))<=>((~quiet(fred)|~creative(fred))))&
((?[X]:((wise(X)|~humble(X))))=>(?[X]:((~humble(X)<~>~brave(X)))))&
(![X]:((patient(X)&rich(X))=>(wise(X)<~>~kind(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(funny(X)&~curious(X))))&
(![X]:(funny(X)=>(~humble(X)|~rich(X))))&
(![X]:((strong(X)|~wise(X))<=>~creative(X)))&
(![X]:((~rich(X)&~kind(X))<=>(~strong(X)<~>~happy(X))))&
((~creative(alice)<~>rich(alice)))&
((strong(mary)|tall(mary)))&
((curious(fred)<~>brave(fred)))&
(?[X]:((rich(X)<~>~creative(X))))&
((generous(mary)<~>curious(mary)))&
((~generous(paul)<~>~funny(paul))) | creative(mary) | [] | null | 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 tall. | 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)))) | tall(fred) | [
"p1",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5599726935775086124598084
% SZS output start Proof for 5599726935775086124598084
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]
23. ~tall(fred) [input hypothesis]
28. ! [X0] : ((old(X0) & quiet(X0)) | (tall(X0) & ~creative(X0))) [ennf transformation 2]
59. ! [X0] : ((~wise(X0) | (~old(X0) & ~happy(X0))) & ((old(X0) | happy(X0)) | wise(X0))) [nnf transformation 8]
60. ! [X0] : ((~wise(X0) | (~old(X0) & ~happy(X0))) & (old(X0) | happy(X0) | wise(X0))) [flattening 59]
70. ! [X0] : (((~wise(X0) | kind(X0)) | (kind(X0) | quiet(X0))) & ((~kind(X0) & ~quiet(X0)) | (wise(X0) & ~kind(X0)))) [nnf transformation 14]
71. ! [X0] : ((~wise(X0) | kind(X0) | kind(X0) | quiet(X0)) & ((~kind(X0) & ~quiet(X0)) | (wise(X0) & ~kind(X0)))) [flattening 70]
85. quiet(X0) | tall(X0) [cnf transformation 28]
87. old(X0) | tall(X0) [cnf transformation 28]
102. ~wise(X0) | ~old(X0) [cnf transformation 60]
114. ~quiet(X0) | wise(X0) [cnf transformation 71]
129. ~tall(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]
301. tall(fred) <- (7) [resolution 299,87]
302. $false <- (7) [subsumption resolution 301,129]
303. ~7 [avatar contradiction clause 302]
304. tall(fred) <- (~7) [resolution 161,85]
305. $false <- (~7) [subsumption resolution 304,129]
306. 7 [avatar contradiction clause 305]
307. $false [avatar sat refutation 303,306]
% SZS output end Proof for 5599726935775086124598084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and generous is either patient or generous and vice versa.
Everyone who is not brave or old is either not rich or old.
If someone is both strong and brave then someone is not rich.
If someone is both not creative and not calm then someone is either happy or not tall and vice versa.
If someone is not generous then susan is both not old and brave and vice versa.
Everyone who is old or not rich is brave or not old and vice versa.
Everyone who is happy is quiet.
Everyone who is not patient or not generous is generous and vice versa.
If mary is either kind or rich then someone is both not calm and generous.
If paul is patient or kind then someone is not creative.
If someone is both not happy and happy then someone is patient.
If alice is both happy and not calm then someone is not old or brave.
Everyone who is both humble and not calm is not calm and vice versa.
If someone is both not humble and tall then lucy is either happy or kind.
If alice is both generous and patient then someone is either not calm or not quiet and vice versa.
Everyone who is not quiet or wise is not rich or patient and vice versa.
Someone is both not quiet and not calm.
Paul is both not quiet and not patient.
Someone is both brave and not calm.
John is tall.
Paul is either quiet or not creative.
Alice is tall or not quiet.
John is both happy and not old. | Paul is not happy. | entailment | (![X]:((strong(X)&generous(X))<=>(patient(X)<~>generous(X))))&
(![X]:((~brave(X)|old(X))=>(~rich(X)<~>old(X))))&
((?[X]:((strong(X)&brave(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~creative(X)&~calm(X))))<=>(?[X]:((happy(X)<~>~tall(X)))))&
((?[X]:(~generous(X)))<=>((~old(susan)&brave(susan))))&
(![X]:((old(X)|~rich(X))<=>(brave(X)|~old(X))))&
(![X]:(happy(X)=>quiet(X)))&
(![X]:((~patient(X)|~generous(X))<=>generous(X)))&
(((kind(mary)<~>rich(mary)))=>(?[X]:((~calm(X)&generous(X)))))&
(((patient(paul)|kind(paul)))=>(?[X]:(~creative(X))))&
((?[X]:((~happy(X)&happy(X))))=>(?[X]:(patient(X))))&
(((happy(alice)&~calm(alice)))=>(?[X]:((~old(X)|brave(X)))))&
(![X]:((humble(X)&~calm(X))<=>~calm(X)))&
((?[X]:((~humble(X)&tall(X))))=>((happy(lucy)<~>kind(lucy))))&
(((generous(alice)&patient(alice)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:((~quiet(X)|wise(X))<=>(~rich(X)|patient(X))))&
(?[X]:((~quiet(X)&~calm(X))))&
((~quiet(paul)&~patient(paul)))&
(?[X]:((brave(X)&~calm(X))))&
(tall(john))&
((quiet(paul)<~>~creative(paul)))&
((tall(alice)|~quiet(alice)))&
((happy(john)&~old(john))) | ~happy(paul) | [
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8797008252651569623511478
% SZS output start Proof for 8797008252651569623511478
7. ! [X0] : (happy(X0) => quiet(X0)) [input p6]
18. ~patient(paul) & ~quiet(paul) [input p17]
24. happy(paul) [input hypothesis]
30. ! [X0] : (quiet(X0) | ~happy(X0)) [ennf transformation 7]
106. ~happy(X0) | quiet(X0) [cnf transformation 30]
135. ~quiet(paul) [cnf transformation 18]
145. happy(paul) [cnf transformation 24]
274. quiet(paul) [resolution 106,145]
275. $false [subsumption resolution 274,135]
% SZS output end Proof for 8797008252651569623511478
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is strong.
If someone is funny then someone is either tall or calm.
If someone is not calm or not tall then someone is either not patient or not tall.
If someone is either quiet or not curious then susan is both calm and not generous and vice versa.
Everyone who is kind or quiet is wise or rich and vice versa.
If someone is either brave or not generous then mary is not calm or kind and vice versa.
Everyone who is both not wise and patient is both not creative and not calm.
If lucy is not brave or generous then someone is brave or calm.
Everyone who is either not wise or quiet is not rich.
Everyone who is not calm is happy.
If mary is generous or calm then someone is humble and vice versa.
Everyone who is both not tall and not strong is either strong or rich and vice versa.
If someone is both not quiet and wise then fred is happy or old and vice versa.
If someone is both not rich and calm then someone is old or not quiet and vice versa.
If lucy is patient or not patient then someone is either creative or quiet and vice versa.
If john is not strong or not wise then someone is both not generous and not old and vice versa.
Someone is either not curious or not patient.
Susan is both not old and quiet.
Someone is not calm.
Susan is either not old or not strong.
Someone is both brave and strong.
Lucy is both not happy and curious.
Someone is not wise.
Someone is both not funny and not brave. | Mary is quiet. | entailment | (![X]:(~strong(X)=>strong(X)))&
((?[X]:(funny(X)))=>(?[X]:((tall(X)<~>calm(X)))))&
((?[X]:((~calm(X)|~tall(X))))=>(?[X]:((~patient(X)<~>~tall(X)))))&
((?[X]:((quiet(X)<~>~curious(X))))<=>((calm(susan)&~generous(susan))))&
(![X]:((kind(X)|quiet(X))<=>(wise(X)|rich(X))))&
((?[X]:((brave(X)<~>~generous(X))))<=>((~calm(mary)|kind(mary))))&
(![X]:((~wise(X)&patient(X))=>(~creative(X)&~calm(X))))&
(((~brave(lucy)|generous(lucy)))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~wise(X)<~>quiet(X))=>~rich(X)))&
(![X]:(~calm(X)=>happy(X)))&
(((generous(mary)|calm(mary)))<=>(?[X]:(humble(X))))&
(![X]:((~tall(X)&~strong(X))<=>(strong(X)<~>rich(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((happy(fred)|old(fred))))&
((?[X]:((~rich(X)&calm(X))))<=>(?[X]:((old(X)|~quiet(X)))))&
(((patient(lucy)|~patient(lucy)))<=>(?[X]:((creative(X)<~>quiet(X)))))&
(((~strong(john)|~wise(john)))<=>(?[X]:((~generous(X)&~old(X)))))&
(?[X]:((~curious(X)<~>~patient(X))))&
((~old(susan)&quiet(susan)))&
(?[X]:(~calm(X)))&
((~old(susan)<~>~strong(susan)))&
(?[X]:((brave(X)&strong(X))))&
((~happy(lucy)&curious(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:((~funny(X)&~brave(X)))) | quiet(mary) | [
"p0",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2247312445744200055160927
% SZS output start Proof for 2247312445744200055160927
1. ! [X0] : (~strong(X0) => strong(X0)) [input p0]
12. ! [X0] : ((~strong(X0) & ~tall(X0)) <=> (strong(X0) <~> rich(X0))) [input p11]
14. ? [X0] : (calm(X0) & ~rich(X0)) <=> ? [X0] : (~quiet(X0) | old(X0)) [input p13]
25. ~quiet(mary) [input hypothesis]
28. ? [X0] : (calm(X0) & ~rich(X0)) <=> ? [X1] : (~quiet(X1) | old(X1)) [rectify 14]
31. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 1]
62. ! [X0] : (((~strong(X0) & ~tall(X0)) | ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0)))) & (((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | (strong(X0) | tall(X0)))) [nnf transformation 12]
63. ! [X0] : (((~strong(X0) & ~tall(X0)) | ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0)))) & (((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | strong(X0) | tall(X0))) [flattening 62]
69. (? [X0] : (calm(X0) & ~rich(X0)) | ! [X1] : (quiet(X1) & ~old(X1))) & (? [X1] : (~quiet(X1) | old(X1)) | ! [X0] : (~calm(X0) | rich(X0))) [nnf transformation 28]
70. (? [X0] : (calm(X0) & ~rich(X0)) | ! [X1] : (quiet(X1) & ~old(X1))) & (? [X2] : (~quiet(X2) | old(X2)) | ! [X3] : (~calm(X3) | rich(X3))) [rectify 69]
71. ? [X0] : (calm(X0) & ~rich(X0)) => (calm(sK6) & ~rich(sK6)) [choice axiom]
72. ? [X2] : (~quiet(X2) | old(X2)) => (~quiet(sK7) | old(sK7)) [choice axiom]
73. ((calm(sK6) & ~rich(sK6)) | ! [X1] : (quiet(X1) & ~old(X1))) & ((~quiet(sK7) | old(sK7)) | ! [X3] : (~calm(X3) | rich(X3))) [skolemisation 70,72,71]
96. strong(X0) | strong(X0) [cnf transformation 31]
131. ~strong(X0) | rich(X0) | ~strong(X0) [cnf transformation 63]
140. ~rich(sK6) | quiet(X1) [cnf transformation 73]
167. ~quiet(mary) [cnf transformation 25]
169. ~strong(X0) | rich(X0) [duplicate literal removal 131]
170. strong(X0) [duplicate literal removal 96]
277. rich(X0) [subsumption resolution 169,170]
303. 29 <=> ! [X1] : quiet(X1) [avatar definition]
304. quiet(X1) <- (29) [avatar component clause 303]
314. quiet(X1) [subsumption resolution 140,277]
315. 29 [avatar split clause 314,303]
369. $false <- (29) [resolution 304,167]
370. ~29 [avatar contradiction clause 369]
371. $false [avatar sat refutation 315,370]
% SZS output end Proof for 2247312445744200055160927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not creative is either not curious or not brave and vice versa. If fred is either not humble or generous then fred is both not strong and not happy. If john is kind then mary is quiet or tall. If someone is not kind or not patient then fred is generous or patient. Everyone who is not rich or not humble is either not tall or not quiet and vice versa. If susan is either wise or not curious then lucy is brave. Everyone who is both old and generous is either not calm or not creative and vice versa. Everyone who is not tall is either not strong or not brave. If lucy is not humble or not patient then lucy is not rich or not wise and vice versa. Everyone who is strong is either not rich or calm and vice versa. If alice is not calm or calm then lucy is not rich and vice versa. If someone is both old and humble then someone is not generous or wise. Everyone who is happy or calm is both not creative and kind. Everyone who is both happy and kind is not curious. Everyone who is kind is either not curious or not creative. Everyone who is not quiet is calm. Paul is not curious. Paul is both generous and not wise. Fred is not patient. Fred is both not curious and not creative. Someone is both funny and curious. Alice is funny. John is not wise or funny. Mary is not creative. | Fred is old. | contradiction | (![X]:((calm(X)<~>~creative(X))<=>(~curious(X)<~>~brave(X))))&
(((~humble(fred)<~>generous(fred)))=>((~strong(fred)&~happy(fred))))&
((kind(john))=>((quiet(mary)|tall(mary))))&
((?[X]:((~kind(X)|~patient(X))))=>((generous(fred)|patient(fred))))&
(![X]:((~rich(X)|~humble(X))<=>(~tall(X)<~>~quiet(X))))&
(((wise(susan)<~>~curious(susan)))=>(brave(lucy)))&
(![X]:((old(X)&generous(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:(~tall(X)=>(~strong(X)<~>~brave(X))))&
(((~humble(lucy)|~patient(lucy)))<=>((~rich(lucy)|~wise(lucy))))&
(![X]:(strong(X)<=>(~rich(X)<~>calm(X))))&
(((~calm(alice)|calm(alice)))<=>(~rich(lucy)))&
((?[X]:((old(X)&humble(X))))=>(?[X]:((~generous(X)|wise(X)))))&
(![X]:((happy(X)|calm(X))=>(~creative(X)&kind(X))))&
(![X]:((happy(X)&kind(X))=>~curious(X)))&
(![X]:(kind(X)=>(~curious(X)<~>~creative(X))))&
(![X]:(~quiet(X)=>calm(X)))&
(~curious(paul))&
((generous(paul)&~wise(paul)))&
(~patient(fred))&
((~curious(fred)&~creative(fred)))&
(?[X]:((funny(X)&curious(X))))&
(funny(alice))&
((~wise(john)|funny(john)))&
(~creative(mary)) | old(fred) | [
"p3",
"p6",
"p12",
"p14",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 577928458513794549767170
% SZS output start Proof for 577928458513794549767170
4. ? [X0] : (~patient(X0) | ~kind(X0)) => (patient(fred) | generous(fred)) [input p3]
7. ! [X0] : ((generous(X0) & old(X0)) <=> (~calm(X0) <~> ~creative(X0))) [input p6]
13. ! [X0] : ((calm(X0) | happy(X0)) => (kind(X0) & ~creative(X0))) [input p12]
15. ! [X0] : (kind(X0) => (~curious(X0) <~> ~creative(X0))) [input p14]
19. ~patient(fred) [input p18]
20. ~creative(fred) & ~curious(fred) [input p19]
25. old(fred) [input hypothesis]
32. ! [X0] : (calm(X0) => (kind(X0) & ~creative(X0))) [pure predicate removal 13]
36. (patient(fred) | generous(fred)) | ! [X0] : (patient(X0) & kind(X0)) [ennf transformation 4]
37. patient(fred) | generous(fred) | ! [X0] : (patient(X0) & kind(X0)) [flattening 36]
41. ! [X0] : ((kind(X0) & ~creative(X0)) | ~calm(X0)) [ennf transformation 32]
42. ! [X0] : ((~curious(X0) <~> ~creative(X0)) | ~kind(X0)) [ennf transformation 15]
49. ! [X0] : (((generous(X0) & old(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0)))) & (((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (~generous(X0) | ~old(X0)))) [nnf transformation 7]
50. ! [X0] : (((generous(X0) & old(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0)))) & (((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | ~generous(X0) | ~old(X0))) [flattening 49]
60. ! [X0] : (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | ~kind(X0)) [nnf transformation 42]
74. patient(fred) | generous(fred) | kind(X0) [cnf transformation 37]
85. ~old(X0) | calm(X0) | ~generous(X0) | creative(X0) [cnf transformation 50]
105. ~calm(X0) | kind(X0) [cnf transformation 41]
107. ~kind(X0) | curious(X0) | creative(X0) [cnf transformation 60]
112. ~patient(fred) [cnf transformation 19]
113. ~curious(fred) [cnf transformation 20]
114. ~creative(fred) [cnf transformation 20]
117. old(fred) [cnf transformation 25]
119. 1 <=> generous(fred) [avatar definition]
120. generous(fred) <- (1) [avatar component clause 119]
149. 8 <=> patient(fred) [avatar definition]
154. 9 <=> ! [X0] : kind(X0) [avatar definition]
155. kind(X0) <- (9) [avatar component clause 154]
156. 9 | 1 | 8 [avatar split clause 74,149,119,154]
209. ~8 [avatar split clause 112,149]
252. curious(X0) | creative(X0) <- (9) [resolution 107,155]
256. creative(fred) <- (9) [resolution 252,113]
258. $false <- (9) [subsumption resolution 256,114]
259. ~9 [avatar contradiction clause 258]
366. calm(fred) | ~generous(fred) | creative(fred) [resolution 85,117]
367. calm(fred) | creative(fred) <- (1) [subsumption resolution 366,120]
368. calm(fred) <- (1) [subsumption resolution 367,114]
371. kind(fred) <- (1) [resolution 368,105]
401. curious(fred) | creative(fred) <- (1) [resolution 371,107]
403. creative(fred) <- (1) [subsumption resolution 401,113]
404. $false <- (1) [subsumption resolution 403,114]
405. ~1 [avatar contradiction clause 404]
406. $false [avatar sat refutation 156,209,259,405]
% SZS output end Proof for 577928458513794549767170
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not brave and rich then someone is not creative. If someone is not creative then someone is both not creative and not strong and vice versa. Everyone who is not creative or not generous is either not tall or not curious and vice versa. Everyone who is both not brave and old is either not humble or not curious and vice versa. Everyone who is strong or wise is not calm. Everyone who is both humble and not humble is not wise or not patient and vice versa. Everyone who is either not old or brave is not kind and vice versa. If susan is either not brave or quiet then john is both not brave and creative. If mary is either tall or not rich then susan is either not quiet or not patient. If someone is brave or calm then someone is not happy. If mary is not strong or not rich then susan is either humble or strong. Everyone who is creative is both brave and not kind. Everyone who is both not humble and humble is calm and vice versa. If paul is generous then someone is not tall. Everyone who is both old and not patient is generous and vice versa. Someone is not curious or not brave. Someone is both quiet and not kind. John is either generous or not curious. Susan is not wise or not funny. Someone is either calm or brave. Someone is either not brave or tall. Paul is patient. | Susan is calm. | contradiction | ((?[X]:((~brave(X)&rich(X))))=>(?[X]:(~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~creative(X)&~strong(X)))))&
(![X]:((~creative(X)|~generous(X))<=>(~tall(X)<~>~curious(X))))&
(![X]:((~brave(X)&old(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((strong(X)|wise(X))=>~calm(X)))&
(![X]:((humble(X)&~humble(X))<=>(~wise(X)|~patient(X))))&
(![X]:((~old(X)<~>brave(X))<=>~kind(X)))&
(((~brave(susan)<~>quiet(susan)))=>((~brave(john)&creative(john))))&
(((tall(mary)<~>~rich(mary)))=>((~quiet(susan)<~>~patient(susan))))&
((?[X]:((brave(X)|calm(X))))=>(?[X]:(~happy(X))))&
(((~strong(mary)|~rich(mary)))=>((humble(susan)<~>strong(susan))))&
(![X]:(creative(X)=>(brave(X)&~kind(X))))&
(![X]:((~humble(X)&humble(X))<=>calm(X)))&
((generous(paul))=>(?[X]:(~tall(X))))&
(![X]:((old(X)&~patient(X))<=>generous(X)))&
(?[X]:((~curious(X)|~brave(X))))&
(?[X]:((quiet(X)&~kind(X))))&
((generous(john)<~>~curious(john)))&
((~wise(susan)|~funny(susan)))&
(?[X]:((calm(X)<~>brave(X))))&
(?[X]:((~brave(X)<~>tall(X))))&
(patient(paul)) | calm(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 755013844306632204530368
% SZS output start Proof for 755013844306632204530368
13. ! [X0] : ((humble(X0) & ~humble(X0)) <=> calm(X0)) [input p12]
23. calm(susan) [input hypothesis]
56. ! [X0] : (((humble(X0) & ~humble(X0)) | ~calm(X0)) & (calm(X0) | (~humble(X0) | humble(X0)))) [nnf transformation 13]
57. ! [X0] : (((humble(X0) & ~humble(X0)) | ~calm(X0)) & (calm(X0) | ~humble(X0) | humble(X0))) [flattening 56]
113. ~humble(X0) | ~calm(X0) [cnf transformation 57]
114. humble(X0) | ~calm(X0) [cnf transformation 57]
129. calm(susan) [cnf transformation 23]
209. ~calm(X0) [subsumption resolution 113,114]
241. $false [subsumption resolution 129,209]
% SZS output end Proof for 755013844306632204530368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not calm then someone is humble and vice versa.
If someone is patient or not old then someone is rich.
If someone is not kind then someone is both not happy and not old.
Everyone who is patient or not quiet is both humble and wise.
Everyone who is not rich or not generous is either not funny or happy.
Everyone who is not creative or funny is both happy and not patient and vice versa.
If fred is not funny or not quiet then someone is not patient and vice versa.
Everyone who is both not kind and not brave is both generous and not generous and vice versa.
If someone is generous or not kind then lucy is either quiet or not quiet and vice versa.
Everyone who is both not brave and not calm is not wise or wise and vice versa.
Everyone who is not calm or old is both not funny and not curious and vice versa.
If someone is either curious or wise then someone is not strong and vice versa.
Everyone who is not happy is both not kind and not curious and vice versa.
If alice is not patient then someone is both brave and funny and vice versa.
Everyone who is either not rich or brave is either happy or wise.
Everyone who is both calm and patient is both not old and kind.
Alice is rich or not wise.
Someone is kind or happy.
Susan is not old.
Someone is either not humble or humble. | Lucy is not kind. | contradiction | ((?[X]:((~quiet(X)&~calm(X))))<=>(?[X]:(humble(X))))&
((?[X]:((patient(X)|~old(X))))=>(?[X]:(rich(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~happy(X)&~old(X)))))&
(![X]:((patient(X)|~quiet(X))=>(humble(X)&wise(X))))&
(![X]:((~rich(X)|~generous(X))=>(~funny(X)<~>happy(X))))&
(![X]:((~creative(X)|funny(X))<=>(happy(X)&~patient(X))))&
(((~funny(fred)|~quiet(fred)))<=>(?[X]:(~patient(X))))&
(![X]:((~kind(X)&~brave(X))<=>(generous(X)&~generous(X))))&
((?[X]:((generous(X)|~kind(X))))<=>((quiet(lucy)<~>~quiet(lucy))))&
(![X]:((~brave(X)&~calm(X))<=>(~wise(X)|wise(X))))&
(![X]:((~calm(X)|old(X))<=>(~funny(X)&~curious(X))))&
((?[X]:((curious(X)<~>wise(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~happy(X)<=>(~kind(X)&~curious(X))))&
((~patient(alice))<=>(?[X]:((brave(X)&funny(X)))))&
(![X]:((~rich(X)<~>brave(X))=>(happy(X)<~>wise(X))))&
(![X]:((calm(X)&patient(X))=>(~old(X)&kind(X))))&
((rich(alice)|~wise(alice)))&
(?[X]:((kind(X)|happy(X))))&
(~old(susan))&
(?[X]:((~humble(X)<~>humble(X)))) | ~kind(lucy) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7814200716108899814345321
% SZS output start Proof for 7814200716108899814345321
8. ! [X0] : ((~brave(X0) & ~kind(X0)) <=> (~generous(X0) & generous(X0))) [input p7]
10. ! [X0] : ((~calm(X0) & ~brave(X0)) <=> (wise(X0) | ~wise(X0))) [input p9]
21. ~kind(lucy) [input hypothesis]
52. ! [X0] : (((~brave(X0) & ~kind(X0)) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | (brave(X0) | kind(X0)))) [nnf transformation 8]
53. ! [X0] : (((~brave(X0) & ~kind(X0)) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | brave(X0) | kind(X0))) [flattening 52]
58. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | (calm(X0) | brave(X0)))) [nnf transformation 10]
59. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | calm(X0) | brave(X0))) [flattening 58]
102. generous(X0) | brave(X0) | kind(X0) [cnf transformation 53]
103. ~generous(X0) | brave(X0) | kind(X0) [cnf transformation 53]
113. ~brave(X0) | wise(X0) [cnf transformation 59]
114. ~brave(X0) | ~wise(X0) [cnf transformation 59]
143. ~kind(lucy) [cnf transformation 21]
180. 9 <=> ! [X1] : kind(X1) [avatar definition]
181. kind(X1) <- (9) [avatar component clause 180]
210. brave(X0) | kind(X0) [subsumption resolution 102,103]
226. ~brave(X0) [subsumption resolution 113,114]
278. kind(X1) [resolution 210,226]
279. 9 [avatar split clause 278,180]
280. $false <- (9) [resolution 181,143]
284. ~9 [avatar contradiction clause 280]
285. $false [avatar sat refutation 279,284]
% SZS output end Proof for 7814200716108899814345321
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is kind or not strong.
If alice is not kind then someone is both wise and curious and vice versa.
Everyone who is both not quiet and not wise is not rich and vice versa.
Everyone who is curious is both not generous and not humble.
Everyone who is not quiet is patient or generous and vice versa.
Everyone who is not calm or quiet is not old or not wise and vice versa.
Everyone who is calm is not tall or calm and vice versa.
Everyone who is generous or not generous is both not patient and curious.
If someone is not patient or not funny then mary is tall and vice versa.
If john is generous then someone is both not creative and not happy and vice versa.
If john is both not curious and wise then someone is strong or not curious and vice versa.
If fred is either not creative or not curious then someone is both patient and wise.
Everyone who is humble is quiet.
If alice is not kind or old then someone is both old and curious and vice versa.
Everyone who is both not brave and patient is either rich or funny and vice versa.
If lucy is both not happy and not brave then someone is not kind and vice versa.
John is both quiet and kind.
Someone is not happy or humble.
Someone is either not humble or not old.
Someone is either tall or not humble.
Someone is calm or not generous.
Someone is either funny or old.
John is either not creative or not rich. | Lucy is not quiet. | contradiction | (![X]:(~humble(X)=>(kind(X)|~strong(X))))&
((~kind(alice))<=>(?[X]:((wise(X)&curious(X)))))&
(![X]:((~quiet(X)&~wise(X))<=>~rich(X)))&
(![X]:(curious(X)=>(~generous(X)&~humble(X))))&
(![X]:(~quiet(X)<=>(patient(X)|generous(X))))&
(![X]:((~calm(X)|quiet(X))<=>(~old(X)|~wise(X))))&
(![X]:(calm(X)<=>(~tall(X)|calm(X))))&
(![X]:((generous(X)|~generous(X))=>(~patient(X)&curious(X))))&
((?[X]:((~patient(X)|~funny(X))))<=>(tall(mary)))&
((generous(john))<=>(?[X]:((~creative(X)&~happy(X)))))&
(((~curious(john)&wise(john)))<=>(?[X]:((strong(X)|~curious(X)))))&
(((~creative(fred)<~>~curious(fred)))=>(?[X]:((patient(X)&wise(X)))))&
(![X]:(humble(X)=>quiet(X)))&
(((~kind(alice)|old(alice)))<=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~brave(X)&patient(X))<=>(rich(X)<~>funny(X))))&
(((~happy(lucy)&~brave(lucy)))<=>(?[X]:(~kind(X))))&
((quiet(john)&kind(john)))&
(?[X]:((~happy(X)|humble(X))))&
(?[X]:((~humble(X)<~>~old(X))))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:((calm(X)|~generous(X))))&
(?[X]:((funny(X)<~>old(X))))&
((~creative(john)<~>~rich(john))) | ~quiet(lucy) | [
"p3",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6842973134939903719960021
% SZS output start Proof for 6842973134939903719960021
4. ! [X0] : (curious(X0) => (~humble(X0) & ~generous(X0))) [input p3]
5. ! [X0] : (~quiet(X0) <=> (generous(X0) | patient(X0))) [input p4]
8. ! [X0] : ((~generous(X0) | generous(X0)) => (curious(X0) & ~patient(X0))) [input p7]
24. ~quiet(lucy) [input hypothesis]
27. ! [X0] : ((~humble(X0) & ~generous(X0)) | ~curious(X0)) [ennf transformation 4]
28. ! [X0] : ((curious(X0) & ~patient(X0)) | (generous(X0) & ~generous(X0))) [ennf transformation 8]
37. ! [X0] : ((~quiet(X0) | (~generous(X0) & ~patient(X0))) & ((generous(X0) | patient(X0)) | quiet(X0))) [nnf transformation 5]
38. ! [X0] : ((~quiet(X0) | (~generous(X0) & ~patient(X0))) & (generous(X0) | patient(X0) | quiet(X0))) [flattening 37]
92. ~generous(X0) | ~curious(X0) [cnf transformation 27]
94. patient(X0) | generous(X0) | quiet(X0) [cnf transformation 38]
105. ~patient(X0) | generous(X0) [cnf transformation 28]
106. curious(X0) | ~generous(X0) [cnf transformation 28]
150. ~quiet(lucy) [cnf transformation 24]
169. ~generous(X0) [subsumption resolution 106,92]
170. ~patient(X0) [subsumption resolution 105,169]
360. generous(X1) | quiet(X1) [resolution 94,170]
361. quiet(X1) [subsumption resolution 360,169]
362. $false [resolution 361,150]
% SZS output end Proof for 6842973134939903719960021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise then lucy is both not happy and not quiet.
Everyone who is both quiet and rich is rich or generous.
Everyone who is either generous or not curious is not tall or not strong and vice versa.
Everyone who is patient or not happy is either generous or not wise and vice versa.
Everyone who is brave is either generous or not wise.
Everyone who is both creative and not brave is both not brave and wise and vice versa.
If paul is tall then someone is curious or not quiet and vice versa.
If someone is both not strong and not calm then alice is not calm or not rich.
Everyone who is either not quiet or not funny is creative or tall and vice versa.
Everyone who is not strong or quiet is rich or not tall.
Everyone who is creative or not quiet is old.
Everyone who is not old or quiet is either not old or strong and vice versa.
Everyone who is not creative or humble is happy or not tall.
Everyone who is not curious is both generous and not quiet.
Everyone who is not quiet is curious.
If lucy is happy or not quiet then john is both not patient and happy.
Someone is not tall or brave.
Alice is patient or happy.
Paul is wise or generous.
Someone is either not tall or not kind.
Someone is wise or generous.
Someone is strong.
Someone is both curious and funny.
Someone is tall or not humble. | Alice is not rich. | neutral | ((wise(alice))=>((~happy(lucy)&~quiet(lucy))))&
(![X]:((quiet(X)&rich(X))=>(rich(X)|generous(X))))&
(![X]:((generous(X)<~>~curious(X))<=>(~tall(X)|~strong(X))))&
(![X]:((patient(X)|~happy(X))<=>(generous(X)<~>~wise(X))))&
(![X]:(brave(X)=>(generous(X)<~>~wise(X))))&
(![X]:((creative(X)&~brave(X))<=>(~brave(X)&wise(X))))&
((tall(paul))<=>(?[X]:((curious(X)|~quiet(X)))))&
((?[X]:((~strong(X)&~calm(X))))=>((~calm(alice)|~rich(alice))))&
(![X]:((~quiet(X)<~>~funny(X))<=>(creative(X)|tall(X))))&
(![X]:((~strong(X)|quiet(X))=>(rich(X)|~tall(X))))&
(![X]:((creative(X)|~quiet(X))=>old(X)))&
(![X]:((~old(X)|quiet(X))<=>(~old(X)<~>strong(X))))&
(![X]:((~creative(X)|humble(X))=>(happy(X)|~tall(X))))&
(![X]:(~curious(X)=>(generous(X)&~quiet(X))))&
(![X]:(~quiet(X)=>curious(X)))&
(((happy(lucy)|~quiet(lucy)))=>((~patient(john)&happy(john))))&
(?[X]:((~tall(X)|brave(X))))&
((patient(alice)|happy(alice)))&
((wise(paul)|generous(paul)))&
(?[X]:((~tall(X)<~>~kind(X))))&
(?[X]:((wise(X)|generous(X))))&
(?[X]:(strong(X)))&
(?[X]:((curious(X)&funny(X))))&
(?[X]:((tall(X)|~humble(X)))) | ~rich(alice) | [] | null | 0 |
Everyone who is both not happy and not kind is either not humble or not quiet and vice versa. Everyone who is calm is not creative and vice versa. Everyone who is either not humble or generous is both not generous and not brave and vice versa. Everyone who is both creative and funny is either not humble or not old and vice versa. Everyone who is either not rich or not strong is both humble and funny and vice versa. Everyone who is quiet or not brave is not old or not patient and vice versa. If paul is brave then someone is either quiet or creative and vice versa. Everyone who is not wise or not old is both not funny and patient. Everyone who is both quiet and old is either not curious or rich and vice versa. Everyone who is curious or not generous is both curious and strong and vice versa. If mary is both not kind and happy then lucy is either not tall or quiet. Everyone who is strong or not kind is not humble and vice versa. If paul is either rich or strong then someone is either not wise or not happy and vice versa. Everyone who is humble or patient is not humble. If someone is generous then mary is either not funny or not wise. If someone is both not funny and rich then john is both calm and quiet and vice versa. Someone is not curious or generous. Someone is patient. Paul is funny or rich. Mary is either not wise or not quiet. Mary is not curious. Someone is both not creative and patient. Lucy is kind. | Paul is not rich. | contradiction | (![X]:((~happy(X)&~kind(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:(calm(X)<=>~creative(X)))&
(![X]:((~humble(X)<~>generous(X))<=>(~generous(X)&~brave(X))))&
(![X]:((creative(X)&funny(X))<=>(~humble(X)<~>~old(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>(humble(X)&funny(X))))&
(![X]:((quiet(X)|~brave(X))<=>(~old(X)|~patient(X))))&
((brave(paul))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((~wise(X)|~old(X))=>(~funny(X)&patient(X))))&
(![X]:((quiet(X)&old(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((curious(X)|~generous(X))<=>(curious(X)&strong(X))))&
(((~kind(mary)&happy(mary)))=>((~tall(lucy)<~>quiet(lucy))))&
(![X]:((strong(X)|~kind(X))<=>~humble(X)))&
(((rich(paul)<~>strong(paul)))<=>(?[X]:((~wise(X)<~>~happy(X)))))&
(![X]:((humble(X)|patient(X))=>~humble(X)))&
((?[X]:(generous(X)))=>((~funny(mary)<~>~wise(mary))))&
((?[X]:((~funny(X)&rich(X))))<=>((calm(john)&quiet(john))))&
(?[X]:((~curious(X)|generous(X))))&
(?[X]:(patient(X)))&
((funny(paul)|rich(paul)))&
((~wise(mary)<~>~quiet(mary)))&
(~curious(mary))&
(?[X]:((~creative(X)&patient(X))))&
(kind(lucy)) | ~rich(paul) | [
"p0",
"p4",
"p7",
"p8",
"p9",
"p12",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 154708032907301276803800
% SZS output start Proof for 154708032907301276803800
1. ! [X0] : ((~kind(X0) & ~happy(X0)) <=> (~humble(X0) <~> ~quiet(X0))) [input p0]
5. ! [X0] : ((~rich(X0) <~> ~strong(X0)) <=> (funny(X0) & humble(X0))) [input p4]
8. ! [X0] : ((~old(X0) | ~wise(X0)) => (patient(X0) & ~funny(X0))) [input p7]
9. ! [X0] : ((old(X0) & quiet(X0)) <=> (~curious(X0) <~> rich(X0))) [input p8]
10. ! [X0] : ((~generous(X0) | curious(X0)) <=> (strong(X0) & curious(X0))) [input p9]
13. (rich(paul) <~> strong(paul)) <=> ? [X0] : (~wise(X0) <~> ~happy(X0)) [input p12]
14. ! [X0] : ((patient(X0) | humble(X0)) => ~humble(X0)) [input p13]
19. rich(paul) | funny(paul) [input p18]
24. ~rich(paul) [input hypothesis]
25. ! [X0] : ((patient(X0) & ~funny(X0)) | (old(X0) & wise(X0))) [ennf transformation 8]
28. ! [X0] : (~humble(X0) | (~patient(X0) & ~humble(X0))) [ennf transformation 14]
30. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0)))) & (((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | (kind(X0) | happy(X0)))) [nnf transformation 1]
31. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0)))) & (((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | kind(X0) | happy(X0))) [flattening 30]
37. ! [X0] : ((((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))))) [nnf transformation 5]
38. ! [X0] : ((((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))))) [flattening 37]
45. ! [X0] : (((old(X0) & quiet(X0)) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) & (((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | (~old(X0) | ~quiet(X0)))) [nnf transformation 9]
46. ! [X0] : (((old(X0) & quiet(X0)) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) & (((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | ~old(X0) | ~quiet(X0))) [flattening 45]
47. ! [X0] : (((~generous(X0) | curious(X0)) | (~strong(X0) | ~curious(X0))) & ((strong(X0) & curious(X0)) | (generous(X0) & ~curious(X0)))) [nnf transformation 10]
48. ! [X0] : ((~generous(X0) | curious(X0) | ~strong(X0) | ~curious(X0)) & ((strong(X0) & curious(X0)) | (generous(X0) & ~curious(X0)))) [flattening 47]
52. (((~strong(paul) | ~rich(paul)) & (strong(paul) | rich(paul))) | ! [X0] : ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (? [X0] : ((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | ((rich(paul) | ~strong(paul)) & (strong(paul) | ~rich(paul)))) [nnf transformation 13]
53. (((~strong(paul) | ~rich(paul)) & (strong(paul) | rich(paul))) | ! [X0] : ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (? [X1] : ((happy(X1) | wise(X1)) & (~happy(X1) | ~wise(X1))) | ((rich(paul) | ~strong(paul)) & (strong(paul) | ~rich(paul)))) [rectify 52]
54. ? [X1] : ((happy(X1) | wise(X1)) & (~happy(X1) | ~wise(X1))) => ((happy(sK1) | wise(sK1)) & (~happy(sK1) | ~wise(sK1))) [choice axiom]
55. (((~strong(paul) | ~rich(paul)) & (strong(paul) | rich(paul))) | ! [X0] : ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (((happy(sK1) | wise(sK1)) & (~happy(sK1) | ~wise(sK1))) | ((rich(paul) | ~strong(paul)) & (strong(paul) | ~rich(paul)))) [skolemisation 53,54]
71. ~quiet(X0) | ~happy(X0) | humble(X0) [cnf transformation 31]
89. ~strong(X0) | humble(X0) | rich(X0) [cnf transformation 38]
103. ~funny(X0) | wise(X0) [cnf transformation 25]
109. curious(X0) | rich(X0) | quiet(X0) [cnf transformation 46]
115. ~curious(X0) | strong(X0) [cnf transformation 48]
128. strong(paul) | rich(paul) | ~wise(X0) | happy(X0) [cnf transformation 55]
131. ~humble(X0) | ~humble(X0) [cnf transformation 28]
141. rich(paul) | funny(paul) [cnf transformation 19]
148. ~rich(paul) [cnf transformation 24]
149. ~humble(X0) [duplicate literal removal 131]
193. 10 <=> ! [X0] : (~wise(X0) | happy(X0)) [avatar definition]
194. ~wise(X0) | happy(X0) <- (10) [avatar component clause 193]
196. 11 <=> rich(paul) [avatar definition]
198. ~rich(paul) <- (~11) [avatar component clause 196]
200. 12 <=> strong(paul) [avatar definition]
201. strong(paul) <- (12) [avatar component clause 200]
202. ~strong(paul) <- (~12) [avatar component clause 200]
208. 10 | 11 | 12 [avatar split clause 128,200,196,193]
262. 24 <=> funny(paul) [avatar definition]
264. funny(paul) <- (24) [avatar component clause 262]
265. 24 | 11 [avatar split clause 141,196,262]
272. ~11 [avatar split clause 148,196]
276. wise(paul) <- (24) [resolution 103,264]
290. happy(paul) <- (10, 24) [resolution 194,276]
361. 32 <=> quiet(paul) [avatar definition]
362. ~quiet(paul) <- (~32) [avatar component clause 361]
363. quiet(paul) <- (32) [avatar component clause 361]
383. strong(X0) | quiet(X0) | rich(X0) [resolution 109,115]
555. quiet(paul) | rich(paul) <- (~12) [resolution 383,202]
562. rich(paul) <- (~12, ~32) [subsumption resolution 555,362]
563. $false <- (~11, ~12, ~32) [subsumption resolution 562,198]
564. 11 | 12 | 32 [avatar contradiction clause 563]
569. humble(paul) | rich(paul) <- (12) [resolution 201,89]
571. rich(paul) <- (12) [subsumption resolution 569,149]
572. $false <- (~11, 12) [subsumption resolution 571,198]
573. 11 | ~12 [avatar contradiction clause 572]
586. ~happy(paul) | humble(paul) <- (32) [resolution 363,71]
588. humble(paul) <- (10, 24, 32) [subsumption resolution 586,290]
589. $false <- (10, 24, 32) [subsumption resolution 588,149]
590. ~10 | ~24 | ~32 [avatar contradiction clause 589]
591. $false [avatar sat refutation 208,265,272,564,573,590]
% SZS output end Proof for 154708032907301276803800
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not kind is either not funny or not brave and vice versa.
Everyone who is strong is old and vice versa.
If someone is not strong then someone is calm.
Everyone who is both not tall and wise is either not quiet or tall and vice versa.
Everyone who is patient or not rich is not patient and vice versa.
Everyone who is either calm or not funny is not brave or generous and vice versa.
Everyone who is wise is not strong or brave and vice versa.
Everyone who is both not creative and not wise is either not kind or rich and vice versa.
Everyone who is not old or not calm is creative or not humble and vice versa.
If paul is old or generous then mary is both not old and not calm and vice versa.
Everyone who is both not rich and creative is strong and vice versa.
Everyone who is both not generous and creative is quiet or brave.
Everyone who is old or tall is happy and vice versa.
If someone is both not wise and not strong then fred is curious and vice versa.
Susan is not tall or not patient.
Alice is curious.
Someone is funny or generous.
Paul is either not funny or not happy. | Paul is not tall. | neutral | (![X]:((~old(X)&~kind(X))<=>(~funny(X)<~>~brave(X))))&
(![X]:(strong(X)<=>old(X)))&
((?[X]:(~strong(X)))=>(?[X]:(calm(X))))&
(![X]:((~tall(X)&wise(X))<=>(~quiet(X)<~>tall(X))))&
(![X]:((patient(X)|~rich(X))<=>~patient(X)))&
(![X]:((calm(X)<~>~funny(X))<=>(~brave(X)|generous(X))))&
(![X]:(wise(X)<=>(~strong(X)|brave(X))))&
(![X]:((~creative(X)&~wise(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((~old(X)|~calm(X))<=>(creative(X)|~humble(X))))&
(((old(paul)|generous(paul)))<=>((~old(mary)&~calm(mary))))&
(![X]:((~rich(X)&creative(X))<=>strong(X)))&
(![X]:((~generous(X)&creative(X))=>(quiet(X)|brave(X))))&
(![X]:((old(X)|tall(X))<=>happy(X)))&
((?[X]:((~wise(X)&~strong(X))))<=>(curious(fred)))&
((~tall(susan)|~patient(susan)))&
(curious(alice))&
(?[X]:((funny(X)|generous(X))))&
((~funny(paul)<~>~happy(paul))) | ~tall(paul) | [] | null | 0 |
Everyone who is both wise and not wise is not patient or quiet. If someone is either not curious or not rich then someone is either not creative or not kind. Everyone who is either happy or old is rich or happy and vice versa. If someone is not wise then someone is either not wise or old. Everyone who is happy 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. If lucy is both not wise and tall then someone is not tall or generous and vice versa. If paul is not wise or not strong then someone is either not creative or brave. If susan is not funny or strong then alice is not kind or not generous. If someone is calm or not brave then someone is not old or wise. If susan is not rich then someone is quiet or kind. Someone is humble or not humble. Alice is not brave or curious. Someone is patient or humble. Someone is not funny. Lucy is happy or calm. Mary is tall. Someone is both brave and not wise. John is both not brave and old. | Susan is old. | entailment | (![X]:((wise(X)&~wise(X))=>(~patient(X)|quiet(X))))&
((?[X]:((~curious(X)<~>~rich(X))))=>(?[X]:((~creative(X)<~>~kind(X)))))&
(![X]:((happy(X)<~>old(X))<=>(rich(X)|happy(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:(happy(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))))&
(((~wise(lucy)&tall(lucy)))<=>(?[X]:((~tall(X)|generous(X)))))&
(((~wise(paul)|~strong(paul)))=>(?[X]:((~creative(X)<~>brave(X)))))&
(((~funny(susan)|strong(susan)))=>((~kind(alice)|~generous(alice))))&
((?[X]:((calm(X)|~brave(X))))=>(?[X]:((~old(X)|wise(X)))))&
((~rich(susan))=>(?[X]:((quiet(X)|kind(X)))))&
(?[X]:((humble(X)|~humble(X))))&
((~brave(alice)|curious(alice)))&
(?[X]:((patient(X)|humble(X))))&
(?[X]:(~funny(X)))&
((happy(lucy)|calm(lucy)))&
(tall(mary))&
(?[X]:((brave(X)&~wise(X))))&
((~brave(john)&old(john))) | old(susan) | [
"p2",
"p4",
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4004129350802726689551310
% SZS output start Proof for 4004129350802726689551310
3. ! [X0] : ((happy(X0) <~> old(X0)) <=> (happy(X0) | rich(X0))) [input p2]
5. ! [X0] : (happy(X0) <=> (~generous(X0) & quiet(X0))) [input p4]
7. ! [X0] : ((~kind(X0) | patient(X0)) => old(X0)) [input p6]
8. ? [X0] : happy(X0) <=> ? [X0] : ~patient(X0) [input p7]
11. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> (~generous(X0) <~> ~calm(X0))) [input p10]
25. ~old(susan) [input hypothesis]
28. ? [X0] : happy(X0) <=> ? [X1] : ~patient(X1) [rectify 8]
34. ! [X0] : (old(X0) | (kind(X0) & ~patient(X0))) [ennf transformation 7]
46. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (~happy(X0) & ~rich(X0))) & ((happy(X0) | rich(X0)) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [nnf transformation 3]
47. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (~happy(X0) & ~rich(X0))) & (happy(X0) | rich(X0) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [flattening 46]
52. ! [X0] : ((happy(X0) | (generous(X0) | ~quiet(X0))) & ((~generous(X0) & quiet(X0)) | ~happy(X0))) [nnf transformation 5]
53. ! [X0] : ((happy(X0) | generous(X0) | ~quiet(X0)) & ((~generous(X0) & quiet(X0)) | ~happy(X0))) [flattening 52]
56. (? [X0] : happy(X0) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : ~happy(X0)) [nnf transformation 28]
57. (? [X0] : happy(X0) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : ~happy(X3)) [rectify 56]
58. ? [X0] : happy(X0) => happy(sK2) [choice axiom]
59. ? [X2] : ~patient(X2) => ~patient(sK3) [choice axiom]
60. (happy(sK2) | ! [X1] : patient(X1)) & (~patient(sK3) | ! [X3] : ~happy(X3)) [skolemisation 57,59,58]
64. ! [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 11]
65. ! [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 64]
97. ~old(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 47]
101. ~generous(X0) | ~happy(X0) [cnf transformation 53]
106. ~patient(X0) | old(X0) [cnf transformation 34]
107. old(X0) | kind(X0) [cnf transformation 34]
109. happy(sK2) | patient(X1) [cnf transformation 60]
121. calm(X0) | generous(X0) | calm(X0) [cnf transformation 65]
122. ~calm(X0) | ~kind(X0) | ~calm(X0) | generous(X0) [cnf transformation 65]
148. ~old(susan) [cnf transformation 25]
149. calm(X0) | generous(X0) [duplicate literal removal 121]
150. ~calm(X0) | ~kind(X0) | generous(X0) [duplicate literal removal 122]
152. ~old(X0) | ~happy(X0) [duplicate literal removal 97]
186. 8 <=> ! [X1] : patient(X1) [avatar definition]
187. patient(X1) <- (8) [avatar component clause 186]
189. 9 <=> happy(sK2) [avatar definition]
191. happy(sK2) <- (9) [avatar component clause 189]
192. 8 | 9 [avatar split clause 109,189,186]
325. ~happy(X0) | kind(X0) [resolution 152,107]
378. ~kind(X0) | generous(X0) | generous(X0) [resolution 150,149]
379. ~kind(X0) | generous(X0) [duplicate literal removal 378]
456. kind(sK2) <- (9) [resolution 325,191]
498. generous(sK2) <- (9) [resolution 456,379]
549. ~happy(sK2) <- (9) [resolution 498,101]
550. $false <- (9) [subsumption resolution 549,191]
551. ~9 [avatar contradiction clause 550]
553. old(X1) <- (8) [resolution 187,106]
559. $false <- (8) [resolution 553,148]
564. ~8 [avatar contradiction clause 559]
565. $false [avatar sat refutation 192,551,564]
% SZS output end Proof for 4004129350802726689551310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not humble is both happy and generous and vice versa.
If someone is either old or not tall then susan is either tall or wise.
Everyone who is quiet or not funny is not funny and vice versa.
Everyone who is either funny or happy is both not tall and humble.
If fred is either tall or funny then someone is either not patient or not creative.
Everyone who is both not brave and brave is not creative and vice versa.
Everyone who is both not curious and not brave is either not patient or creative.
Everyone who is not wise or happy is either not quiet or not curious and vice versa.
If someone is both not kind and not wise then someone is both not calm and generous and vice versa.
Everyone who is not strong is both strong and humble and vice versa.
If someone is either not happy or humble then someone is either not tall or not creative.
Everyone who is either not strong or generous is either rich or curious and vice versa.
Everyone who is happy is either not quiet or kind.
Everyone who is both not quiet and rich is not old and vice versa.
Everyone who is not kind is curious or funny.
If someone is calm or not quiet then someone is both not generous and not patient.
Someone is either tall or humble.
Mary is curious or patient.
Someone is both tall and not humble.
Lucy is happy or not happy.
Paul is not calm or strong. | Paul is not curious. | contradiction | (![X]:((happy(X)<~>~humble(X))<=>(happy(X)&generous(X))))&
((?[X]:((old(X)<~>~tall(X))))=>((tall(susan)<~>wise(susan))))&
(![X]:((quiet(X)|~funny(X))<=>~funny(X)))&
(![X]:((funny(X)<~>happy(X))=>(~tall(X)&humble(X))))&
(((tall(fred)<~>funny(fred)))=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:((~brave(X)&brave(X))<=>~creative(X)))&
(![X]:((~curious(X)&~brave(X))=>(~patient(X)<~>creative(X))))&
(![X]:((~wise(X)|happy(X))<=>(~quiet(X)<~>~curious(X))))&
((?[X]:((~kind(X)&~wise(X))))<=>(?[X]:((~calm(X)&generous(X)))))&
(![X]:(~strong(X)<=>(strong(X)&humble(X))))&
((?[X]:((~happy(X)<~>humble(X))))=>(?[X]:((~tall(X)<~>~creative(X)))))&
(![X]:((~strong(X)<~>generous(X))<=>(rich(X)<~>curious(X))))&
(![X]:(happy(X)=>(~quiet(X)<~>kind(X))))&
(![X]:((~quiet(X)&rich(X))<=>~old(X)))&
(![X]:(~kind(X)=>(curious(X)|funny(X))))&
((?[X]:((calm(X)|~quiet(X))))=>(?[X]:((~generous(X)&~patient(X)))))&
(?[X]:((tall(X)<~>humble(X))))&
((curious(mary)|patient(mary)))&
(?[X]:((tall(X)&~humble(X))))&
((happy(lucy)|~happy(lucy)))&
((~calm(paul)|strong(paul))) | ~curious(paul) | [
"p0",
"p2",
"p3",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8067809169272525709559399
% SZS output start Proof for 8067809169272525709559399
1. ! [X0] : ((happy(X0) <~> ~humble(X0)) <=> (generous(X0) & happy(X0))) [input p0]
3. ! [X0] : ((~funny(X0) | quiet(X0)) <=> ~funny(X0)) [input p2]
4. ! [X0] : ((funny(X0) <~> happy(X0)) => (humble(X0) & ~tall(X0))) [input p3]
8. ! [X0] : ((happy(X0) | ~wise(X0)) <=> (~quiet(X0) <~> ~curious(X0))) [input p7]
10. ! [X0] : (~strong(X0) <=> (humble(X0) & strong(X0))) [input p9]
22. ~curious(paul) [input hypothesis]
27. ! [X0] : ((humble(X0) & ~tall(X0)) | (funny(X0) <=> happy(X0))) [ennf transformation 4]
36. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [nnf transformation 1]
37. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [flattening 36]
39. ! [X0] : (((~funny(X0) | quiet(X0)) | funny(X0)) & (~funny(X0) | (funny(X0) & ~quiet(X0)))) [nnf transformation 3]
40. ! [X0] : ((~funny(X0) | quiet(X0) | funny(X0)) & (~funny(X0) | (funny(X0) & ~quiet(X0)))) [flattening 39]
41. ! [X0] : ((humble(X0) & ~tall(X0)) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) [nnf transformation 27]
48. ! [X0] : (((happy(X0) | ~wise(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) & (((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~happy(X0) & wise(X0)))) [nnf transformation 8]
49. ! [X0] : ((happy(X0) | ~wise(X0) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) & (((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~happy(X0) & wise(X0)))) [flattening 48]
55. ! [X0] : ((~strong(X0) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | strong(X0))) [nnf transformation 10]
56. ! [X0] : ((~strong(X0) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | strong(X0))) [flattening 55]
74. happy(X0) | happy(X0) | humble(X0) [cnf transformation 37]
83. ~funny(X0) | ~quiet(X0) [cnf transformation 40]
89. humble(X0) | funny(X0) | ~happy(X0) [cnf transformation 41]
102. ~happy(X0) | quiet(X0) | curious(X0) [cnf transformation 49]
109. strong(X0) | strong(X0) [cnf transformation 56]
111. ~strong(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 56]
141. ~curious(paul) [cnf transformation 22]
142. strong(X0) [duplicate literal removal 109]
143. ~strong(X0) | ~humble(X0) [duplicate literal removal 111]
144. humble(X0) | happy(X0) [duplicate literal removal 74]
164. funny(X0) | humble(X0) [subsumption resolution 89,144]
264. ~humble(X1) [resolution 143,142]
267. happy(X0) [resolution 264,144]
269. humble(X0) | ~quiet(X0) [resolution 164,83]
272. ~quiet(X0) [subsumption resolution 269,264]
305. quiet(X0) | curious(X0) [resolution 102,267]
308. curious(X0) [subsumption resolution 305,272]
322. $false [resolution 308,141]
% SZS output end Proof for 8067809169272525709559399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or brave is both not brave and not old and vice versa. If someone is humble or happy then mary is either tall or not creative. Everyone who is not brave or kind is not funny and vice versa. Everyone who is rich is wise or not tall. Everyone who is either not curious or not calm is curious and vice versa. Everyone who is both tall and not generous is either wise or not happy. Everyone who is not rich is both not calm and calm and vice versa. If someone is humble or brave then someone is not rich. Everyone who is either not curious or humble is both not patient and tall. Everyone who is old is not kind. If someone is not creative or humble then john is both quiet and not strong and vice versa. If john is both creative and not happy then paul is not strong. If mary is brave or not strong then someone is either strong or not patient and vice versa. Everyone who is either quiet or calm is both not wise and funny and vice versa. If someone is both humble and curious then someone is either humble or not creative and vice versa. Fred is either not generous or old. Alice is either patient or rich. Lucy is both tall and not curious. Someone is either not calm or generous. Susan is either not wise or rich. Someone is either not calm or funny. Someone is not tall. | John is not creative. | contradiction | (![X]:((~old(X)|brave(X))<=>(~brave(X)&~old(X))))&
((?[X]:((humble(X)|happy(X))))=>((tall(mary)<~>~creative(mary))))&
(![X]:((~brave(X)|kind(X))<=>~funny(X)))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~wise(X)&funny(X))))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((~generous(fred)<~>old(fred)))&
((patient(alice)<~>rich(alice)))&
((tall(lucy)&~curious(lucy)))&
(?[X]:((~calm(X)<~>generous(X))))&
((~wise(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>funny(X))))&
(?[X]:(~tall(X))) | ~creative(john) | [
"p0",
"p2",
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7336455439928787161832740
% SZS output start Proof for 7336455439928787161832740
1. ! [X0] : ((brave(X0) | ~old(X0)) <=> (~old(X0) & ~brave(X0))) [input p0]
3. ! [X0] : ((kind(X0) | ~brave(X0)) <=> ~funny(X0)) [input p2]
5. ! [X0] : ((~curious(X0) <~> ~calm(X0)) <=> curious(X0)) [input p4]
11. ? [X0] : (humble(X0) | ~creative(X0)) <=> (~strong(john) & quiet(john)) [input p10]
14. ! [X0] : ((quiet(X0) <~> calm(X0)) <=> (funny(X0) & ~wise(X0))) [input p13]
23. ~creative(john) [input hypothesis]
36. ! [X0] : (((brave(X0) | ~old(X0)) | (old(X0) | brave(X0))) & ((~old(X0) & ~brave(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 1]
37. ! [X0] : ((brave(X0) | ~old(X0) | old(X0) | brave(X0)) & ((~old(X0) & ~brave(X0)) | (~brave(X0) & old(X0)))) [flattening 36]
39. ! [X0] : (((kind(X0) | ~brave(X0)) | funny(X0)) & (~funny(X0) | (~kind(X0) & brave(X0)))) [nnf transformation 3]
40. ! [X0] : ((kind(X0) | ~brave(X0) | funny(X0)) & (~funny(X0) | (~kind(X0) & brave(X0)))) [flattening 39]
41. ! [X0] : ((((calm(X0) | curious(X0)) & (~calm(X0) | ~curious(X0))) | ~curious(X0)) & (curious(X0) | ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))))) [nnf transformation 5]
49. (? [X0] : (humble(X0) | ~creative(X0)) | (strong(john) | ~quiet(john))) & ((~strong(john) & quiet(john)) | ! [X0] : (~humble(X0) & creative(X0))) [nnf transformation 11]
50. (? [X0] : (humble(X0) | ~creative(X0)) | strong(john) | ~quiet(john)) & ((~strong(john) & quiet(john)) | ! [X0] : (~humble(X0) & creative(X0))) [flattening 49]
51. (? [X0] : (humble(X0) | ~creative(X0)) | strong(john) | ~quiet(john)) & ((~strong(john) & quiet(john)) | ! [X1] : (~humble(X1) & creative(X1))) [rectify 50]
52. ? [X0] : (humble(X0) | ~creative(X0)) => (humble(sK1) | ~creative(sK1)) [choice axiom]
53. ((humble(sK1) | ~creative(sK1)) | strong(john) | ~quiet(john)) & ((~strong(john) & quiet(john)) | ! [X1] : (~humble(X1) & creative(X1))) [skolemisation 51,52]
59. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~funny(X0) | wise(X0))) & ((funny(X0) & ~wise(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [nnf transformation 14]
60. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | ~funny(X0) | wise(X0)) & ((funny(X0) & ~wise(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [flattening 59]
78. ~brave(X0) | ~brave(X0) [cnf transformation 37]
86. ~funny(X0) | brave(X0) [cnf transformation 40]
90. curious(X0) | ~calm(X0) | curious(X0) [cnf transformation 41]
92. ~calm(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 41]
106. quiet(john) | creative(X1) [cnf transformation 53]
120. funny(X0) | calm(X0) | ~quiet(X0) [cnf transformation 60]
143. ~creative(john) [cnf transformation 23]
144. curious(X0) | ~calm(X0) [duplicate literal removal 90]
145. ~calm(X0) | ~curious(X0) [duplicate literal removal 92]
146. ~brave(X0) [duplicate literal removal 78]
166. ~funny(X0) [subsumption resolution 86,146]
167. ~calm(X0) [subsumption resolution 144,145]
172. 5 <=> quiet(john) [avatar definition]
173. quiet(john) <- (5) [avatar component clause 172]
190. 9 <=> ! [X1] : creative(X1) [avatar definition]
191. creative(X1) <- (9) [avatar component clause 190]
194. 9 | 5 [avatar split clause 106,172,190]
196. 10 <=> creative(john) [avatar definition]
198. ~creative(john) <- (~10) [avatar component clause 196]
232. calm(X0) | ~quiet(X0) [subsumption resolution 120,166]
233. ~quiet(X0) [subsumption resolution 232,167]
278. ~10 [avatar split clause 143,196]
279. $false <- (5) [subsumption resolution 173,233]
280. ~5 [avatar contradiction clause 279]
285. $false <- (9, ~10) [resolution 198,191]
286. ~9 | 10 [avatar contradiction clause 285]
287. $false [avatar sat refutation 194,278,280,286]
% SZS output end Proof for 7336455439928787161832740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not humble is both not quiet and brave and vice versa. If someone is both calm and humble then someone is creative and vice versa. If someone is quiet then fred is calm or not quiet. Everyone who is not creative is either creative or humble. If fred is funny or generous then someone is not curious. If john is both not calm and not tall then susan is either strong or humble and vice versa. If susan is both not quiet and funny then someone is either strong or creative and vice versa. Everyone who is either curious or generous is not tall or not brave. If someone is both old and happy then someone is kind and vice versa. Everyone who is creative is not rich. If someone is not brave then someone is either not kind or kind. If paul is both humble and happy then susan is either kind or not generous. Everyone who is both not humble and rich is generous and vice versa. Everyone who is either funny or not brave is brave and vice versa. Lucy is not happy or not strong. Someone is not happy or not wise. Alice is both calm and not rich. Someone is either not tall or generous. Paul is both not quiet and tall. Someone is not wise or brave. Someone is calm or not generous. | Lucy is not happy. | neutral | (![X]:((happy(X)<~>~humble(X))<=>(~quiet(X)&brave(X))))&
((?[X]:((calm(X)&humble(X))))<=>(?[X]:(creative(X))))&
((?[X]:(quiet(X)))=>((calm(fred)|~quiet(fred))))&
(![X]:(~creative(X)=>(creative(X)<~>humble(X))))&
(((funny(fred)|generous(fred)))=>(?[X]:(~curious(X))))&
(((~calm(john)&~tall(john)))<=>((strong(susan)<~>humble(susan))))&
(((~quiet(susan)&funny(susan)))<=>(?[X]:((strong(X)<~>creative(X)))))&
(![X]:((curious(X)<~>generous(X))=>(~tall(X)|~brave(X))))&
((?[X]:((old(X)&happy(X))))<=>(?[X]:(kind(X))))&
(![X]:(creative(X)=>~rich(X)))&
((?[X]:(~brave(X)))=>(?[X]:((~kind(X)<~>kind(X)))))&
(((humble(paul)&happy(paul)))=>((kind(susan)<~>~generous(susan))))&
(![X]:((~humble(X)&rich(X))<=>generous(X)))&
(![X]:((funny(X)<~>~brave(X))<=>brave(X)))&
((~happy(lucy)|~strong(lucy)))&
(?[X]:((~happy(X)|~wise(X))))&
((calm(alice)&~rich(alice)))&
(?[X]:((~tall(X)<~>generous(X))))&
((~quiet(paul)&tall(paul)))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:((calm(X)|~generous(X)))) | ~happy(lucy) | [] | null | 0 |
Everyone who is strong is not generous and vice versa.
If john is not rich or not calm then someone is not strong or not wise.
Everyone who is not calm or not strong is both not wise and not happy and vice versa.
If lucy is both not creative and not generous then paul is not kind or not tall and vice versa.
If someone is generous then mary is both not brave and brave and vice versa.
Everyone who is both not kind and not happy is either not kind or patient.
Everyone who is both kind and not quiet is wise.
If someone is generous or funny then john is not kind or curious and vice versa.
If someone is not calm then someone is both tall and not generous and vice versa.
If fred is either not generous or not tall then someone is calm and vice versa.
If someone is either not creative or not curious then alice is happy and vice versa.
If someone is either not generous or patient then susan is tall or not curious and vice versa.
Everyone who is both not tall and not wise is either strong or not strong.
If fred is either not strong or tall then alice is both not quiet and old and vice versa.
Someone is not strong or not funny.
Someone is not tall or not creative.
Susan is both not patient and not brave.
John is creative.
Paul is not quiet.
Someone is either humble or happy.
Someone is both happy and not brave.
Mary is either calm or not brave. | John is wise. | neutral | (![X]:(strong(X)<=>~generous(X)))&
(((~rich(john)|~calm(john)))=>(?[X]:((~strong(X)|~wise(X)))))&
(![X]:((~calm(X)|~strong(X))<=>(~wise(X)&~happy(X))))&
(((~creative(lucy)&~generous(lucy)))<=>((~kind(paul)|~tall(paul))))&
((?[X]:(generous(X)))<=>((~brave(mary)&brave(mary))))&
(![X]:((~kind(X)&~happy(X))=>(~kind(X)<~>patient(X))))&
(![X]:((kind(X)&~quiet(X))=>wise(X)))&
((?[X]:((generous(X)|funny(X))))<=>((~kind(john)|curious(john))))&
((?[X]:(~calm(X)))<=>(?[X]:((tall(X)&~generous(X)))))&
(((~generous(fred)<~>~tall(fred)))<=>(?[X]:(calm(X))))&
((?[X]:((~creative(X)<~>~curious(X))))<=>(happy(alice)))&
((?[X]:((~generous(X)<~>patient(X))))<=>((tall(susan)|~curious(susan))))&
(![X]:((~tall(X)&~wise(X))=>(strong(X)<~>~strong(X))))&
(((~strong(fred)<~>tall(fred)))<=>((~quiet(alice)&old(alice))))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:((~tall(X)|~creative(X))))&
((~patient(susan)&~brave(susan)))&
(creative(john))&
(~quiet(paul))&
(?[X]:((humble(X)<~>happy(X))))&
(?[X]:((happy(X)&~brave(X))))&
((calm(mary)<~>~brave(mary))) | wise(john) | [] | null | 0 |
Everyone who is either not generous or brave is not quiet and vice versa.
Everyone who is either funny or not tall is funny or not tall and vice versa.
Everyone who is both tall and not curious is calm.
Everyone who is not generous or not brave is humble and vice versa.
Everyone who is both not generous and brave is rich and vice versa.
Everyone who is old is generous.
Everyone who is both creative and happy is happy or curious and vice versa.
Everyone who is either not calm or not wise is wise.
Everyone who is both strong and humble is either not creative or not quiet and vice versa.
If fred is both not quiet and tall then someone is curious.
Everyone who is kind is not calm and vice versa.
If susan is either patient or not wise then mary is not wise or curious.
If mary is not funny or not calm then susan is not curious.
If someone is not strong then fred is both generous and kind and vice versa.
Everyone who is both not quiet and creative is funny or happy.
If someone is not old or not rich then someone is either not quiet or kind.
Someone is both rich and tall.
Someone is not kind or wise.
Alice is either old or tall.
Someone is curious or kind.
Alice is both not calm and tall.
Alice is either kind or rich.
Someone is calm or not calm.
Someone is calm or not kind. | Alice is humble. | entailment | (![X]:((~generous(X)<~>brave(X))<=>~quiet(X)))&
(![X]:((funny(X)<~>~tall(X))<=>(funny(X)|~tall(X))))&
(![X]:((tall(X)&~curious(X))=>calm(X)))&
(![X]:((~generous(X)|~brave(X))<=>humble(X)))&
(![X]:((~generous(X)&brave(X))<=>rich(X)))&
(![X]:(old(X)=>generous(X)))&
(![X]:((creative(X)&happy(X))<=>(happy(X)|curious(X))))&
(![X]:((~calm(X)<~>~wise(X))=>wise(X)))&
(![X]:((strong(X)&humble(X))<=>(~creative(X)<~>~quiet(X))))&
(((~quiet(fred)&tall(fred)))=>(?[X]:(curious(X))))&
(![X]:(kind(X)<=>~calm(X)))&
(((patient(susan)<~>~wise(susan)))=>((~wise(mary)|curious(mary))))&
(((~funny(mary)|~calm(mary)))=>(~curious(susan)))&
((?[X]:(~strong(X)))<=>((generous(fred)&kind(fred))))&
(![X]:((~quiet(X)&creative(X))=>(funny(X)|happy(X))))&
((?[X]:((~old(X)|~rich(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((~kind(X)|wise(X))))&
((old(alice)<~>tall(alice)))&
(?[X]:((curious(X)|kind(X))))&
((~calm(alice)&tall(alice)))&
((kind(alice)<~>rich(alice)))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((calm(X)|~kind(X)))) | humble(alice) | [
"p0",
"p2",
"p3",
"p6",
"p8",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7785342522099733079874190
% SZS output start Proof for 7785342522099733079874190
1. ! [X0] : ((~generous(X0) <~> brave(X0)) <=> ~quiet(X0)) [input p0]
3. ! [X0] : ((~curious(X0) & tall(X0)) => calm(X0)) [input p2]
4. ! [X0] : ((~brave(X0) | ~generous(X0)) <=> humble(X0)) [input p3]
7. ! [X0] : ((happy(X0) & creative(X0)) <=> (curious(X0) | happy(X0))) [input p6]
9. ! [X0] : ((humble(X0) & strong(X0)) <=> (~creative(X0) <~> ~quiet(X0))) [input p8]
21. tall(alice) & ~calm(alice) [input p20]
25. ~humble(alice) [input hypothesis]
27. ! [X0] : (calm(X0) | (curious(X0) | ~tall(X0))) [ennf transformation 3]
28. ! [X0] : (calm(X0) | curious(X0) | ~tall(X0)) [flattening 27]
39. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | quiet(X0)) & (~quiet(X0) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [nnf transformation 1]
42. ! [X0] : (((~brave(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (brave(X0) & generous(X0)))) [nnf transformation 4]
43. ! [X0] : ((~brave(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (brave(X0) & generous(X0)))) [flattening 42]
46. ! [X0] : (((happy(X0) & creative(X0)) | (~curious(X0) & ~happy(X0))) & ((curious(X0) | happy(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 7]
47. ! [X0] : (((happy(X0) & creative(X0)) | (~curious(X0) & ~happy(X0))) & (curious(X0) | happy(X0) | ~happy(X0) | ~creative(X0))) [flattening 46]
49. ! [X0] : (((humble(X0) & strong(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~humble(X0) | ~strong(X0)))) [nnf transformation 9]
50. ! [X0] : (((humble(X0) & strong(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~humble(X0) | ~strong(X0))) [flattening 49]
77. ~quiet(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 39]
86. ~tall(X0) | curious(X0) | calm(X0) [cnf transformation 28]
87. humble(X0) | generous(X0) [cnf transformation 43]
88. humble(X0) | brave(X0) [cnf transformation 43]
96. ~curious(X0) | creative(X0) [cnf transformation 47]
106. ~creative(X0) | humble(X0) | quiet(X0) [cnf transformation 50]
128. ~calm(alice) [cnf transformation 21]
129. tall(alice) [cnf transformation 21]
134. ~humble(alice) [cnf transformation 25]
235. 22 <=> tall(alice) [avatar definition]
236. tall(alice) <- (22) [avatar component clause 235]
249. 22 [avatar split clause 129,235]
261. generous(alice) [resolution 87,134]
262. brave(alice) [resolution 88,134]
295. curious(alice) | calm(alice) <- (22) [resolution 86,236]
305. curious(alice) <- (22) [subsumption resolution 295,128]
310. creative(alice) <- (22) [resolution 305,96]
348. humble(alice) | quiet(alice) <- (22) [resolution 310,106]
350. quiet(alice) <- (22) [subsumption resolution 348,134]
357. ~generous(alice) | ~brave(alice) <- (22) [resolution 350,77]
359. ~brave(alice) <- (22) [subsumption resolution 357,261]
360. $false <- (22) [subsumption resolution 359,262]
361. ~22 [avatar contradiction clause 360]
362. $false [avatar sat refutation 249,361]
% SZS output end Proof for 7785342522099733079874190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or patient then someone is curious.
Everyone who is curious is both patient and old.
Everyone who is creative is not wise or not creative.
If fred is not creative or calm then mary is either funny or not rich and vice versa.
Everyone who is either not quiet or creative is not generous.
Everyone who is creative or calm is either not happy or creative and vice versa.
Everyone who is not strong is not wise or not patient and vice versa.
If someone is either not brave or patient then paul is both not humble and not rich and vice versa.
Everyone who is quiet is not quiet or not funny and vice versa.
Everyone who is either curious or humble is both not brave and not humble and vice versa.
Everyone who is either generous or calm is both not calm and wise and vice versa.
If someone is not tall then someone is both not brave and not calm and vice versa.
Everyone who is not strong is not brave or not curious.
Everyone who is not rich is not old or happy and vice versa.
If someone is either strong or not wise then someone is not calm and vice versa.
Everyone who is both wise and rich is either old or humble and vice versa.
Someone is both wise and humble.
Someone is either brave or not wise.
Susan is both quiet and happy.
Susan is either not happy or not curious.
Paul is either calm or not humble.
Paul is either curious or wise.
Someone is funny or brave.
Someone is funny or not patient. | Mary is quiet. | entailment | ((?[X]:((strong(X)<~>patient(X))))=>(?[X]:(curious(X))))&
(![X]:(curious(X)=>(patient(X)&old(X))))&
(![X]:(creative(X)=>(~wise(X)|~creative(X))))&
(((~creative(fred)|calm(fred)))<=>((funny(mary)<~>~rich(mary))))&
(![X]:((~quiet(X)<~>creative(X))=>~generous(X)))&
(![X]:((creative(X)|calm(X))<=>(~happy(X)<~>creative(X))))&
(![X]:(~strong(X)<=>(~wise(X)|~patient(X))))&
((?[X]:((~brave(X)<~>patient(X))))<=>((~humble(paul)&~rich(paul))))&
(![X]:(quiet(X)<=>(~quiet(X)|~funny(X))))&
(![X]:((curious(X)<~>humble(X))<=>(~brave(X)&~humble(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~calm(X)&wise(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~brave(X)&~calm(X)))))&
(![X]:(~strong(X)=>(~brave(X)|~curious(X))))&
(![X]:(~rich(X)<=>(~old(X)|happy(X))))&
((?[X]:((strong(X)<~>~wise(X))))<=>(?[X]:(~calm(X))))&
(![X]:((wise(X)&rich(X))<=>(old(X)<~>humble(X))))&
(?[X]:((wise(X)&humble(X))))&
(?[X]:((brave(X)<~>~wise(X))))&
((quiet(susan)&happy(susan)))&
((~happy(susan)<~>~curious(susan)))&
((calm(paul)<~>~humble(paul)))&
((curious(paul)<~>wise(paul)))&
(?[X]:((funny(X)|brave(X))))&
(?[X]:((funny(X)|~patient(X)))) | quiet(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 955201581798521837801408
% SZS output start Proof for 955201581798521837801408
9. ! [X0] : (quiet(X0) <=> (~funny(X0) | ~quiet(X0))) [input p8]
25. ~quiet(mary) [input hypothesis]
52. ! [X0] : ((quiet(X0) | (funny(X0) & quiet(X0))) & ((~funny(X0) | ~quiet(X0)) | ~quiet(X0))) [nnf transformation 9]
53. ! [X0] : ((quiet(X0) | (funny(X0) & quiet(X0))) & (~funny(X0) | ~quiet(X0) | ~quiet(X0))) [flattening 52]
113. quiet(X0) | quiet(X0) [cnf transformation 53]
158. ~quiet(mary) [cnf transformation 25]
164. quiet(X0) [duplicate literal removal 113]
310. $false [subsumption resolution 158,164]
% SZS output end Proof for 955201581798521837801408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is both not brave and not calm.
If mary is not kind or rich then susan is either happy or wise and vice versa.
If someone is either humble or rich then susan is both not wise and not rich and vice versa.
Everyone who is wise is wise or not patient and vice versa.
If alice is calm then someone is quiet.
If lucy is both not calm and not brave then alice is funny or tall.
Everyone who is calm is both not kind and old.
Everyone who is funny is not strong.
Everyone who is either not patient or not old is both strong and tall.
Everyone who is not creative is either funny or not calm and vice versa.
If mary is rich then someone is not rich and vice versa.
If paul is not tall then paul is both rich and humble and vice versa.
If susan is creative then susan is quiet or not wise and vice versa.
If alice is not quiet then someone is kind or not creative and vice versa.
Everyone who is humble or quiet is not kind or not happy and vice versa.
If susan is humble then john is patient or not brave.
John is calm or not wise.
Alice is brave.
Someone is either rich or not creative.
Someone is both not curious and brave.
Fred is either not curious or not old.
Fred is both not humble and not patient.
Mary is not curious.
Lucy is curious or not kind. | Lucy is not creative. | contradiction | (![X]:(~quiet(X)=>(~brave(X)&~calm(X))))&
(((~kind(mary)|rich(mary)))<=>((happy(susan)<~>wise(susan))))&
((?[X]:((humble(X)<~>rich(X))))<=>((~wise(susan)&~rich(susan))))&
(![X]:(wise(X)<=>(wise(X)|~patient(X))))&
((calm(alice))=>(?[X]:(quiet(X))))&
(((~calm(lucy)&~brave(lucy)))=>((funny(alice)|tall(alice))))&
(![X]:(calm(X)=>(~kind(X)&old(X))))&
(![X]:(funny(X)=>~strong(X)))&
(![X]:((~patient(X)<~>~old(X))=>(strong(X)&tall(X))))&
(![X]:(~creative(X)<=>(funny(X)<~>~calm(X))))&
((rich(mary))<=>(?[X]:(~rich(X))))&
((~tall(paul))<=>((rich(paul)&humble(paul))))&
((creative(susan))<=>((quiet(susan)|~wise(susan))))&
((~quiet(alice))<=>(?[X]:((kind(X)|~creative(X)))))&
(![X]:((humble(X)|quiet(X))<=>(~kind(X)|~happy(X))))&
((humble(susan))=>((patient(john)|~brave(john))))&
((calm(john)|~wise(john)))&
(brave(alice))&
(?[X]:((rich(X)<~>~creative(X))))&
(?[X]:((~curious(X)&brave(X))))&
((~curious(fred)<~>~old(fred)))&
((~humble(fred)&~patient(fred)))&
(~curious(mary))&
((curious(lucy)|~kind(lucy))) | ~creative(lucy) | [
"p0",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3891413453359763697354944
% SZS output start Proof for 3891413453359763697354944
1. ! [X0] : (~quiet(X0) => (~calm(X0) & ~brave(X0))) [input p0]
14. ~quiet(alice) <=> ? [X0] : (~creative(X0) | kind(X0)) [input p13]
18. brave(alice) [input p17]
25. ~creative(lucy) [input hypothesis]
26. ! [X0] : ((~calm(X0) & ~brave(X0)) | quiet(X0)) [ennf transformation 1]
56. (~quiet(alice) | ! [X0] : (creative(X0) & ~kind(X0))) & (? [X0] : (~creative(X0) | kind(X0)) | quiet(alice)) [nnf transformation 14]
57. (~quiet(alice) | ! [X0] : (creative(X0) & ~kind(X0))) & (? [X1] : (~creative(X1) | kind(X1)) | quiet(alice)) [rectify 56]
58. ? [X1] : (~creative(X1) | kind(X1)) => (~creative(sK3) | kind(sK3)) [choice axiom]
59. (~quiet(alice) | ! [X0] : (creative(X0) & ~kind(X0))) & ((~creative(sK3) | kind(sK3)) | quiet(alice)) [skolemisation 57,58]
68. ~brave(X0) | quiet(X0) [cnf transformation 26]
108. ~quiet(alice) | creative(X0) [cnf transformation 59]
115. brave(alice) [cnf transformation 18]
126. ~creative(lucy) [cnf transformation 25]
235. 23 <=> ! [X0] : creative(X0) [avatar definition]
236. creative(X0) <- (23) [avatar component clause 235]
238. 24 <=> quiet(alice) [avatar definition]
241. 23 | ~24 [avatar split clause 108,238,235]
306. quiet(alice) [resolution 68,115]
310. 24 [avatar split clause 306,238]
311. $false <- (23) [resolution 236,126]
316. ~23 [avatar contradiction clause 311]
317. $false [avatar sat refutation 241,310,316]
% SZS output end Proof for 3891413453359763697354944
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not kind is either not tall or not strong.
If mary is either creative or not strong then someone is either not humble or curious.
If lucy is both not happy and not brave then susan is calm.
Everyone who is both curious and old is quiet or not patient.
Everyone who is not wise is either not kind or not funny.
Everyone who is brave or tall is either rich or not curious.
Everyone who is either calm or tall is either rich or not wise and vice versa.
Everyone who is not wise is both not curious and not rich and vice versa.
Everyone who is either not generous or calm is either old or not happy and vice versa.
Everyone who is both patient and not calm is both not funny and not kind.
If paul is both quiet and not tall then someone is either kind or humble.
Everyone who is both not rich and not happy is either not strong or humble and vice versa.
Everyone who is generous or not happy is not happy.
If paul is wise then someone is either not kind or creative.
If alice is funny or wise then susan is not quiet or humble.
If alice is both not brave and not creative then paul is old.
Lucy is calm or not funny.
Mary is not happy or generous.
Someone is happy or not old.
Lucy is either quiet or not patient.
Paul is not tall or not wise.
Someone is either not calm or not quiet.
Alice is not wise. | Paul is not calm. | neutral | (![X]:((~strong(X)&~kind(X))=>(~tall(X)<~>~strong(X))))&
(((creative(mary)<~>~strong(mary)))=>(?[X]:((~humble(X)<~>curious(X)))))&
(((~happy(lucy)&~brave(lucy)))=>(calm(susan)))&
(![X]:((curious(X)&old(X))=>(quiet(X)|~patient(X))))&
(![X]:(~wise(X)=>(~kind(X)<~>~funny(X))))&
(![X]:((brave(X)|tall(X))=>(rich(X)<~>~curious(X))))&
(![X]:((calm(X)<~>tall(X))<=>(rich(X)<~>~wise(X))))&
(![X]:(~wise(X)<=>(~curious(X)&~rich(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(old(X)<~>~happy(X))))&
(![X]:((patient(X)&~calm(X))=>(~funny(X)&~kind(X))))&
(((quiet(paul)&~tall(paul)))=>(?[X]:((kind(X)<~>humble(X)))))&
(![X]:((~rich(X)&~happy(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((generous(X)|~happy(X))=>~happy(X)))&
((wise(paul))=>(?[X]:((~kind(X)<~>creative(X)))))&
(((funny(alice)|wise(alice)))=>((~quiet(susan)|humble(susan))))&
(((~brave(alice)&~creative(alice)))=>(old(paul)))&
((calm(lucy)|~funny(lucy)))&
((~happy(mary)|generous(mary)))&
(?[X]:((happy(X)|~old(X))))&
((quiet(lucy)<~>~patient(lucy)))&
((~tall(paul)|~wise(paul)))&
(?[X]:((~calm(X)<~>~quiet(X))))&
(~wise(alice)) | ~calm(paul) | [] | null | 0 |
If susan is both not rich and not tall then someone is both not rich and not creative.
If someone is not humble or patient then john is either not rich or old and vice versa.
Everyone who is not brave is both not happy and rich and vice versa.
Everyone who is either not generous or old is either creative or not humble.
Everyone who is both tall and rich is patient or not patient and vice versa.
If paul is either humble or not wise then john is quiet.
Everyone who is not happy is both not funny and not happy.
Everyone who is either not wise or kind is not wise or not calm and vice versa.
Everyone who is either not humble or wise is generous or not kind.
Everyone who is both not calm and funny is not rich or not creative.
If mary is either quiet or not happy then mary is either patient or not patient.
Everyone who is not brave or generous is either not calm or not old and vice versa.
If someone is both not funny and not curious then someone is either generous or not humble and vice versa.
If someone is both kind and not strong then susan is both not kind and old.
Everyone who is both kind and not patient is either not quiet or not wise and vice versa.
Everyone who is not wise or kind is either humble or funny.
Someone is both wise and happy.
Paul is both not calm and not patient.
Paul is old or not strong.
Mary is both not kind and funny.
Paul is either creative or not brave.
Lucy is patient or not quiet.
Alice is not old or funny. | Lucy is old. | neutral | (((~rich(susan)&~tall(susan)))=>(?[X]:((~rich(X)&~creative(X)))))&
((?[X]:((~humble(X)|patient(X))))<=>((~rich(john)<~>old(john))))&
(![X]:(~brave(X)<=>(~happy(X)&rich(X))))&
(![X]:((~generous(X)<~>old(X))=>(creative(X)<~>~humble(X))))&
(![X]:((tall(X)&rich(X))<=>(patient(X)|~patient(X))))&
(((humble(paul)<~>~wise(paul)))=>(quiet(john)))&
(![X]:(~happy(X)=>(~funny(X)&~happy(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(~wise(X)|~calm(X))))&
(![X]:((~humble(X)<~>wise(X))=>(generous(X)|~kind(X))))&
(![X]:((~calm(X)&funny(X))=>(~rich(X)|~creative(X))))&
(((quiet(mary)<~>~happy(mary)))=>((patient(mary)<~>~patient(mary))))&
(![X]:((~brave(X)|generous(X))<=>(~calm(X)<~>~old(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:((generous(X)<~>~humble(X)))))&
((?[X]:((kind(X)&~strong(X))))=>((~kind(susan)&old(susan))))&
(![X]:((kind(X)&~patient(X))<=>(~quiet(X)<~>~wise(X))))&
(![X]:((~wise(X)|kind(X))=>(humble(X)<~>funny(X))))&
(?[X]:((wise(X)&happy(X))))&
((~calm(paul)&~patient(paul)))&
((old(paul)|~strong(paul)))&
((~kind(mary)&funny(mary)))&
((creative(paul)<~>~brave(paul)))&
((patient(lucy)|~quiet(lucy)))&
((~old(alice)|funny(alice))) | old(lucy) | [] | null | 0 |
If someone is strong or not tall then fred is not strong.
Everyone who is not calm or patient is not tall or happy and vice versa.
If someone is strong then lucy is either humble or not patient.
If john is humble or not creative then someone is not old or not patient and vice versa.
If fred is not generous or not calm then someone is funny and vice versa.
If lucy is funny then someone is both not tall and funny and vice versa.
If mary is either rich or humble then fred is happy or not brave.
Everyone who is not patient or wise is rich and vice versa.
If paul is quiet then john is both not tall and not humble.
If someone is both old and not curious then fred is either not quiet or not brave.
If someone is old or wise then alice is not strong and vice versa.
Everyone who is wise or curious is both rich and not tall.
If someone is either not happy or quiet then someone is not generous and vice versa.
If someone is both not funny and not patient then someone is both not calm and not funny.
Everyone who is either curious or generous is not brave.
If john is either not wise or generous then john is kind.
Someone is not happy or not tall.
Fred is both not rich and not old.
Someone is either not patient or not brave.
Fred is either not humble or curious.
John is brave or not brave.
Lucy is generous.
Lucy is not rich.
Lucy is either not strong or not brave. | Lucy is wise. | contradiction | ((?[X]:((strong(X)|~tall(X))))=>(~strong(fred)))&
(![X]:((~calm(X)|patient(X))<=>(~tall(X)|happy(X))))&
((?[X]:(strong(X)))=>((humble(lucy)<~>~patient(lucy))))&
(((humble(john)|~creative(john)))<=>(?[X]:((~old(X)|~patient(X)))))&
(((~generous(fred)|~calm(fred)))<=>(?[X]:(funny(X))))&
((funny(lucy))<=>(?[X]:((~tall(X)&funny(X)))))&
(((rich(mary)<~>humble(mary)))=>((happy(fred)|~brave(fred))))&
(![X]:((~patient(X)|wise(X))<=>rich(X)))&
((quiet(paul))=>((~tall(john)&~humble(john))))&
((?[X]:((old(X)&~curious(X))))=>((~quiet(fred)<~>~brave(fred))))&
((?[X]:((old(X)|wise(X))))<=>(~strong(alice)))&
(![X]:((wise(X)|curious(X))=>(rich(X)&~tall(X))))&
((?[X]:((~happy(X)<~>quiet(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((curious(X)<~>generous(X))=>~brave(X)))&
(((~wise(john)<~>generous(john)))=>(kind(john)))&
(?[X]:((~happy(X)|~tall(X))))&
((~rich(fred)&~old(fred)))&
(?[X]:((~patient(X)<~>~brave(X))))&
((~humble(fred)<~>curious(fred)))&
((brave(john)|~brave(john)))&
(generous(lucy))&
(~rich(lucy))&
((~strong(lucy)<~>~brave(lucy))) | wise(lucy) | [
"p7",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5312843701653579062583294
% SZS output start Proof for 5312843701653579062583294
8. ! [X0] : ((wise(X0) | ~patient(X0)) <=> rich(X0)) [input p7]
23. ~rich(lucy) [input p22]
25. wise(lucy) [input hypothesis]
56. ! [X0] : (((wise(X0) | ~patient(X0)) | ~rich(X0)) & (rich(X0) | (~wise(X0) & patient(X0)))) [nnf transformation 8]
57. ! [X0] : ((wise(X0) | ~patient(X0) | ~rich(X0)) & (rich(X0) | (~wise(X0) & patient(X0)))) [flattening 56]
100. ~wise(X0) | rich(X0) [cnf transformation 57]
130. ~rich(lucy) [cnf transformation 23]
133. wise(lucy) [cnf transformation 25]
359. rich(lucy) [resolution 100,133]
360. $false [subsumption resolution 359,130]
% SZS output end Proof for 5312843701653579062583294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both generous and brave then alice is not wise or not kind and vice versa.
If someone is both not rich and quiet then paul is old and vice versa.
Everyone who is both not funny and not humble is both not strong and wise and vice versa.
If someone is both strong and not generous then someone is not patient or quiet and vice versa.
Everyone who is either not strong or not quiet is strong and vice versa.
Everyone who is calm or not wise is not wise or strong and vice versa.
Everyone who is both kind and generous is calm.
Everyone who is both wise and creative is not tall or tall and vice versa.
If someone is not humble then someone is not strong or strong.
Everyone who is funny is either not rich or not curious.
If someone is both not calm and happy then someone is not tall or not funny and vice versa.
Everyone who is not humble is both funny and not kind and vice versa.
If susan is both not brave and not quiet then lucy is both not generous and not tall and vice versa.
If fred is both old and calm then someone is either not tall or not wise and vice versa.
If someone is both brave and rich then fred is humble and vice versa.
Mary is either creative or rich.
Paul is either generous or not old.
Someone is creative or not happy.
Mary is both not kind and calm.
Someone is both generous and not kind. | Susan is not tall. | contradiction | (((generous(mary)&brave(mary)))<=>((~wise(alice)|~kind(alice))))&
((?[X]:((~rich(X)&quiet(X))))<=>(old(paul)))&
(![X]:((~funny(X)&~humble(X))<=>(~strong(X)&wise(X))))&
((?[X]:((strong(X)&~generous(X))))<=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((~strong(X)<~>~quiet(X))<=>strong(X)))&
(![X]:((calm(X)|~wise(X))<=>(~wise(X)|strong(X))))&
(![X]:((kind(X)&generous(X))=>calm(X)))&
(![X]:((wise(X)&creative(X))<=>(~tall(X)|tall(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~strong(X)|strong(X)))))&
(![X]:(funny(X)=>(~rich(X)<~>~curious(X))))&
((?[X]:((~calm(X)&happy(X))))<=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:(~humble(X)<=>(funny(X)&~kind(X))))&
(((~brave(susan)&~quiet(susan)))<=>((~generous(lucy)&~tall(lucy))))&
(((old(fred)&calm(fred)))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((brave(X)&rich(X))))<=>(humble(fred)))&
((creative(mary)<~>rich(mary)))&
((generous(paul)<~>~old(paul)))&
(?[X]:((creative(X)|~happy(X))))&
((~kind(mary)&calm(mary)))&
(?[X]:((generous(X)&~kind(X)))) | ~tall(susan) | [
"p2",
"p5",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4681549830047995020167846
% SZS output start Proof for 4681549830047995020167846
3. ! [X0] : ((~humble(X0) & ~funny(X0)) <=> (wise(X0) & ~strong(X0))) [input p2]
6. ! [X0] : ((~wise(X0) | calm(X0)) <=> (strong(X0) | ~wise(X0))) [input p5]
8. ! [X0] : ((creative(X0) & wise(X0)) <=> (tall(X0) | ~tall(X0))) [input p7]
11. ? [X0] : (happy(X0) & ~calm(X0)) <=> ? [X0] : (~funny(X0) | ~tall(X0)) [input p10]
12. ! [X0] : (~humble(X0) <=> (~kind(X0) & funny(X0))) [input p11]
21. ~tall(susan) [input hypothesis]
24. ? [X0] : (happy(X0) & ~calm(X0)) <=> ? [X1] : (~funny(X1) | ~tall(X1)) [rectify 11]
35. ! [X0] : (((~humble(X0) & ~funny(X0)) | (~wise(X0) | strong(X0))) & ((wise(X0) & ~strong(X0)) | (humble(X0) | funny(X0)))) [nnf transformation 3]
36. ! [X0] : (((~humble(X0) & ~funny(X0)) | ~wise(X0) | strong(X0)) & ((wise(X0) & ~strong(X0)) | humble(X0) | funny(X0))) [flattening 35]
43. ! [X0] : (((~wise(X0) | calm(X0)) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | (wise(X0) & ~calm(X0)))) [nnf transformation 6]
44. ! [X0] : ((~wise(X0) | calm(X0) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | (wise(X0) & ~calm(X0)))) [flattening 43]
45. ! [X0] : (((creative(X0) & wise(X0)) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | (~creative(X0) | ~wise(X0)))) [nnf transformation 8]
46. ! [X0] : (((creative(X0) & wise(X0)) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | ~creative(X0) | ~wise(X0))) [flattening 45]
51. (? [X0] : (happy(X0) & ~calm(X0)) | ! [X1] : (funny(X1) & tall(X1))) & (? [X1] : (~funny(X1) | ~tall(X1)) | ! [X0] : (~happy(X0) | calm(X0))) [nnf transformation 24]
52. (? [X0] : (happy(X0) & ~calm(X0)) | ! [X1] : (funny(X1) & tall(X1))) & (? [X2] : (~funny(X2) | ~tall(X2)) | ! [X3] : (~happy(X3) | calm(X3))) [rectify 51]
53. ? [X0] : (happy(X0) & ~calm(X0)) => (happy(sK4) & ~calm(sK4)) [choice axiom]
54. ? [X2] : (~funny(X2) | ~tall(X2)) => (~funny(sK5) | ~tall(sK5)) [choice axiom]
55. ((happy(sK4) & ~calm(sK4)) | ! [X1] : (funny(X1) & tall(X1))) & ((~funny(sK5) | ~tall(sK5)) | ! [X3] : (~happy(X3) | calm(X3))) [skolemisation 52,54,53]
56. ! [X0] : ((~humble(X0) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | humble(X0))) [nnf transformation 12]
57. ! [X0] : ((~humble(X0) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | humble(X0))) [flattening 56]
85. ~funny(X0) | ~wise(X0) | strong(X0) [cnf transformation 36]
86. ~humble(X0) | ~wise(X0) | strong(X0) [cnf transformation 36]
99. ~strong(X0) | calm(X0) | ~wise(X0) [cnf transformation 44]
102. wise(X0) | tall(X0) [cnf transformation 46]
103. ~tall(X0) | wise(X0) [cnf transformation 46]
110. ~calm(sK4) | tall(X1) [cnf transformation 55]
114. humble(X0) | funny(X0) [cnf transformation 57]
139. ~tall(susan) [cnf transformation 21]
214. wise(X0) [subsumption resolution 102,103]
224. 18 <=> ! [X1] : tall(X1) [avatar definition]
225. tall(X1) <- (18) [avatar component clause 224]
228. 19 <=> calm(sK4) [avatar definition]
230. ~calm(sK4) <- (~19) [avatar component clause 228]
232. 18 | ~19 [avatar split clause 110,228,224]
312. $false <- (18) [resolution 225,139]
313. ~18 [avatar contradiction clause 312]
320. ~wise(X1) | strong(X1) | funny(X1) [resolution 86,114]
322. strong(X1) | funny(X1) [subsumption resolution 320,214]
335. funny(X0) | calm(X0) | ~wise(X0) [resolution 322,99]
339. calm(X0) | funny(X0) [subsumption resolution 335,214]
340. funny(sK4) <- (~19) [resolution 339,230]
343. ~wise(sK4) | strong(sK4) <- (~19) [resolution 340,85]
353. strong(sK4) <- (~19) [subsumption resolution 343,214]
369. calm(sK4) | ~wise(sK4) <- (~19) [resolution 353,99]
372. ~wise(sK4) <- (~19) [subsumption resolution 369,230]
373. $false <- (~19) [subsumption resolution 372,214]
374. 19 [avatar contradiction clause 373]
375. $false [avatar sat refutation 232,313,374]
% SZS output end Proof for 4681549830047995020167846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not patient or humble then fred is kind or humble and vice versa. If alice is not strong or not curious then lucy is either wise or not rich. If someone is either generous or not generous then lucy is not happy. Everyone who is both funny and wise is strong or not rich and vice versa. Everyone who is brave is either creative or not rich and vice versa. Everyone who is either not rich or funny is not strong or creative and vice versa. Everyone who is not calm or rich is either not strong or tall and vice versa. If someone is either not happy or humble then someone is both not patient and quiet. Everyone who is either kind or not patient is both rich and brave and vice versa. Everyone who is both kind and not generous is not curious and vice versa. If alice is not patient or not calm then someone is not kind and vice versa. Everyone who is happy is both not creative and not brave. If mary is old then susan is either not funny or old and vice versa. If john is either not tall or curious then someone is both humble and wise. Everyone who is generous or funny is not kind. Someone is both quiet and funny. Someone is both not humble and not strong. John is both not calm and brave. Someone is both not old and generous. Someone is not kind. John is either creative or not rich. Lucy is either not curious or not tall. | Mary is funny. | entailment | (((~patient(paul)<~>humble(paul)))<=>((kind(fred)|humble(fred))))&
(((~strong(alice)|~curious(alice)))=>((wise(lucy)<~>~rich(lucy))))&
((?[X]:((generous(X)<~>~generous(X))))=>(~happy(lucy)))&
(![X]:((funny(X)&wise(X))<=>(strong(X)|~rich(X))))&
(![X]:(brave(X)<=>(creative(X)<~>~rich(X))))&
(![X]:((~rich(X)<~>funny(X))<=>(~strong(X)|creative(X))))&
(![X]:((~calm(X)|rich(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:((~happy(X)<~>humble(X))))=>(?[X]:((~patient(X)&quiet(X)))))&
(![X]:((kind(X)<~>~patient(X))<=>(rich(X)&brave(X))))&
(![X]:((kind(X)&~generous(X))<=>~curious(X)))&
(((~patient(alice)|~calm(alice)))<=>(?[X]:(~kind(X))))&
(![X]:(happy(X)=>(~creative(X)&~brave(X))))&
((old(mary))<=>((~funny(susan)<~>old(susan))))&
(((~tall(john)<~>curious(john)))=>(?[X]:((humble(X)&wise(X)))))&
(![X]:((generous(X)|funny(X))=>~kind(X)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~calm(john)&brave(john)))&
(?[X]:((~old(X)&generous(X))))&
(?[X]:(~kind(X)))&
((creative(john)<~>~rich(john)))&
((~curious(lucy)<~>~tall(lucy))) | funny(mary) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 899009224082342436390604
% SZS output start Proof for 899009224082342436390604
4. ! [X0] : ((wise(X0) & funny(X0)) <=> (~rich(X0) | strong(X0))) [input p3]
6. ! [X0] : ((~rich(X0) <~> funny(X0)) <=> (creative(X0) | ~strong(X0))) [input p5]
23. ~funny(mary) [input hypothesis]
37. ! [X0] : (((wise(X0) & funny(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (~wise(X0) | ~funny(X0)))) [nnf transformation 4]
38. ! [X0] : (((wise(X0) & funny(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | ~wise(X0) | ~funny(X0))) [flattening 37]
40. ! [X0] : ((((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (~creative(X0) & strong(X0))) & ((creative(X0) | ~strong(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0))))) [nnf transformation 6]
41. ! [X0] : ((((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (~creative(X0) & strong(X0))) & (creative(X0) | ~strong(X0) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0))))) [flattening 40]
84. funny(X0) | ~strong(X0) [cnf transformation 38]
85. funny(X0) | rich(X0) [cnf transformation 38]
94. funny(X0) | ~rich(X0) | strong(X0) [cnf transformation 41]
96. ~funny(X0) | rich(X0) | strong(X0) [cnf transformation 41]
142. ~funny(mary) [cnf transformation 23]
200. rich(X0) | strong(X0) [subsumption resolution 96,85]
202. funny(X0) | strong(X0) [subsumption resolution 94,200]
203. funny(X0) [subsumption resolution 202,84]
289. $false [subsumption resolution 142,203]
% SZS output end Proof for 899009224082342436390604
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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