premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not calm is not funny or not patient and vice versa.
If john is either not quiet or not patient then lucy is tall or not tall and vice versa.
If someone is not brave then fred is not rich or not wise.
If fred is calm or tall then someone is both wise and calm and vice versa.
If susan is both quiet and not quiet then someone is both not strong and curious.
If someone is generous or funny then someone is not creative and vice versa.
Everyone who is not generous or not strong is patient and vice versa.
If someone is either not happy or kind then john is not funny or strong and vice versa.
Everyone who is both not kind and generous is both not rich and not old and vice versa.
Everyone who is wise is creative.
Everyone who is creative is either not strong or creative and vice versa.
If someone is both patient and not funny then john is either patient or tall and vice versa.
If someone is both not calm and kind then someone is not generous or curious and vice versa.
If john is wise or not strong then someone is either not quiet or humble and vice versa.
If susan is not generous then someone is not funny.
Everyone who is generous or tall is not wise or not old.
Someone is not brave or not calm.
Mary is not curious.
Fred is either curious or funny.
Someone is not calm or tall.
Someone is either not creative or not old.
Someone is not rich or patient.
Mary is either not curious or not funny. | Susan is not wise. | neutral | (![X]:(~calm(X)<=>(~funny(X)|~patient(X))))&
(((~quiet(john)<~>~patient(john)))<=>((tall(lucy)|~tall(lucy))))&
((?[X]:(~brave(X)))=>((~rich(fred)|~wise(fred))))&
(((calm(fred)|tall(fred)))<=>(?[X]:((wise(X)&calm(X)))))&
(((quiet(susan)&~quiet(susan)))=>(?[X]:((~strong(X)&curious(X)))))&
((?[X]:((generous(X)|funny(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~generous(X)|~strong(X))<=>patient(X)))&
((?[X]:((~happy(X)<~>kind(X))))<=>((~funny(john)|strong(john))))&
(![X]:((~kind(X)&generous(X))<=>(~rich(X)&~old(X))))&
(![X]:(wise(X)=>creative(X)))&
(![X]:(creative(X)<=>(~strong(X)<~>creative(X))))&
((?[X]:((patient(X)&~funny(X))))<=>((patient(john)<~>tall(john))))&
((?[X]:((~calm(X)&kind(X))))<=>(?[X]:((~generous(X)|curious(X)))))&
(((wise(john)|~strong(john)))<=>(?[X]:((~quiet(X)<~>humble(X)))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|tall(X))=>(~wise(X)|~old(X))))&
(?[X]:((~brave(X)|~calm(X))))&
(~curious(mary))&
((curious(fred)<~>funny(fred)))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:((~creative(X)<~>~old(X))))&
(?[X]:((~rich(X)|patient(X))))&
((~curious(mary)<~>~funny(mary))) | ~wise(susan) | []
| null | 0 |
Everyone who is not funny or wise is either rich or creative.
If someone is humble then mary is both not strong and old and vice versa.
If someone is calm then paul is either strong or old.
Everyone who is not kind is both not patient and not old and vice versa.
Everyone who is not rich is both not creative and rich and vice versa.
If susan is both not quiet and quiet then fred is humble or strong.
Everyone who is not strong is creative or not brave and vice versa.
If someone is tall or humble then susan is not creative or not rich.
If someone is not generous then someone is not curious or strong.
If someone is both not happy and not kind then mary is not tall.
If someone is not brave then someone is either not brave or calm and vice versa.
If someone is not generous then someone is either curious or creative.
If someone is both patient and not kind then alice is both old and generous and vice versa.
If someone is not happy or strong then fred is both not generous and not quiet and vice versa.
Everyone who is happy or not rich is either quiet or patient.
Someone is either humble or old.
Alice is kind.
Someone is either old or not funny.
Fred is either patient or rich.
Alice is both creative and not calm.
Someone is either not happy or old.
Someone is curious or generous. | Alice is not rich. | contradiction | (![X]:((~funny(X)|wise(X))=>(rich(X)<~>creative(X))))&
((?[X]:(humble(X)))<=>((~strong(mary)&old(mary))))&
((?[X]:(calm(X)))=>((strong(paul)<~>old(paul))))&
(![X]:(~kind(X)<=>(~patient(X)&~old(X))))&
(![X]:(~rich(X)<=>(~creative(X)&rich(X))))&
(((~quiet(susan)&quiet(susan)))=>((humble(fred)|strong(fred))))&
(![X]:(~strong(X)<=>(creative(X)|~brave(X))))&
((?[X]:((tall(X)|humble(X))))=>((~creative(susan)|~rich(susan))))&
((?[X]:(~generous(X)))=>(?[X]:((~curious(X)|strong(X)))))&
((?[X]:((~happy(X)&~kind(X))))=>(~tall(mary)))&
((?[X]:(~brave(X)))<=>(?[X]:((~brave(X)<~>calm(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((curious(X)<~>creative(X)))))&
((?[X]:((patient(X)&~kind(X))))<=>((old(alice)&generous(alice))))&
((?[X]:((~happy(X)|strong(X))))<=>((~generous(fred)&~quiet(fred))))&
(![X]:((happy(X)|~rich(X))=>(quiet(X)<~>patient(X))))&
(?[X]:((humble(X)<~>old(X))))&
(kind(alice))&
(?[X]:((old(X)<~>~funny(X))))&
((patient(fred)<~>rich(fred)))&
((creative(alice)&~calm(alice)))&
(?[X]:((~happy(X)<~>old(X))))&
(?[X]:((curious(X)|generous(X)))) | ~rich(alice) | [
"p4",
"hypothesis"
]
| % SZS status Unsatisfiable for 3871817501228581754267582
% SZS output start Proof for 3871817501228581754267582
5. ! [X0] : (~rich(X0) <=> (rich(X0) & ~creative(X0))) [input p4]
23. ~rich(alice) [input hypothesis]
48. ! [X0] : ((~rich(X0) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | rich(X0))) [nnf transformation 5]
49. ! [X0] : ((~rich(X0) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | rich(X0))) [flattening 48]
98. rich(X0) | rich(X0) [cnf transformation 49]
137. ~rich(alice) [cnf transformation 23]
138. rich(X0) [duplicate literal removal 98]
309. $false [subsumption resolution 137,138]
% SZS output end Proof for 3871817501228581754267582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not curious is brave or old.
If someone is either not generous or quiet then mary is calm.
If someone is either brave or not quiet then paul is not brave and vice versa.
Everyone who is curious or calm is not happy or not brave and vice versa.
If alice is humble or not humble then someone is not happy or not old.
Everyone who is not funny or curious is not strong and vice versa.
Everyone who is not funny is both not tall and not patient.
Everyone who is both not tall and generous is not humble or brave and vice versa.
If someone is both not old and kind then someone is old or not brave.
Everyone who is happy or not strong is not calm and vice versa.
Everyone who is old is wise and vice versa.
Everyone who is both wise and not curious is either patient or not happy and vice versa.
If someone is not tall or not wise then someone is both patient and not wise.
Everyone who is either humble or not old is both brave and funny and vice versa.
Everyone who is funny is both not kind and humble.
If someone is either not wise or not brave then paul is not humble and vice versa.
Someone is old or curious.
Susan is brave or not wise.
Lucy is either not rich or not kind.
Someone is either curious or not kind.
Susan is strong or not creative.
Paul is not curious.
Someone is either quiet or funny. | Paul is not humble. | contradiction | (![X]:((brave(X)&~curious(X))=>(brave(X)|old(X))))&
((?[X]:((~generous(X)<~>quiet(X))))=>(calm(mary)))&
((?[X]:((brave(X)<~>~quiet(X))))<=>(~brave(paul)))&
(![X]:((curious(X)|calm(X))<=>(~happy(X)|~brave(X))))&
(((humble(alice)|~humble(alice)))=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:((~funny(X)|curious(X))<=>~strong(X)))&
(![X]:(~funny(X)=>(~tall(X)&~patient(X))))&
(![X]:((~tall(X)&generous(X))<=>(~humble(X)|brave(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>~calm(X)))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((wise(X)&~curious(X))<=>(patient(X)<~>~happy(X))))&
((?[X]:((~tall(X)|~wise(X))))=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((humble(X)<~>~old(X))<=>(brave(X)&funny(X))))&
(![X]:(funny(X)=>(~kind(X)&humble(X))))&
((?[X]:((~wise(X)<~>~brave(X))))<=>(~humble(paul)))&
(?[X]:((old(X)|curious(X))))&
((brave(susan)|~wise(susan)))&
((~rich(lucy)<~>~kind(lucy)))&
(?[X]:((curious(X)<~>~kind(X))))&
((strong(susan)|~creative(susan)))&
(~curious(paul))&
(?[X]:((quiet(X)<~>funny(X)))) | ~humble(paul) | [
"p3",
"p5",
"p6",
"p9",
"p10",
"p11",
"p13",
"p14",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 5070964010078742174185827
% SZS output start Proof for 5070964010078742174185827
4. ! [X0] : ((calm(X0) | curious(X0)) <=> (~brave(X0) | ~happy(X0))) [input p3]
6. ! [X0] : ((curious(X0) | ~funny(X0)) <=> ~strong(X0)) [input p5]
7. ! [X0] : (~funny(X0) => (~patient(X0) & ~tall(X0))) [input p6]
10. ! [X0] : ((~strong(X0) | happy(X0)) <=> ~calm(X0)) [input p9]
11. ! [X0] : (old(X0) <=> wise(X0)) [input p10]
12. ! [X0] : ((~curious(X0) & wise(X0)) <=> (patient(X0) <~> ~happy(X0))) [input p11]
14. ! [X0] : ((humble(X0) <~> ~old(X0)) <=> (funny(X0) & brave(X0))) [input p13]
15. ! [X0] : (funny(X0) => (humble(X0) & ~kind(X0))) [input p14]
22. ~curious(paul) [input p21]
24. ~humble(paul) [input hypothesis]
32. ! [X0] : ((~patient(X0) & ~tall(X0)) | funny(X0)) [ennf transformation 7]
35. ! [X0] : ((humble(X0) & ~kind(X0)) | ~funny(X0)) [ennf transformation 15]
41. ! [X0] : (((calm(X0) | curious(X0)) | (brave(X0) & happy(X0))) & ((~brave(X0) | ~happy(X0)) | (~calm(X0) & ~curious(X0)))) [nnf transformation 4]
42. ! [X0] : ((calm(X0) | curious(X0) | (brave(X0) & happy(X0))) & (~brave(X0) | ~happy(X0) | (~calm(X0) & ~curious(X0)))) [flattening 41]
45. ! [X0] : (((curious(X0) | ~funny(X0)) | strong(X0)) & (~strong(X0) | (~curious(X0) & funny(X0)))) [nnf transformation 6]
46. ! [X0] : ((curious(X0) | ~funny(X0) | strong(X0)) & (~strong(X0) | (~curious(X0) & funny(X0)))) [flattening 45]
52. ! [X0] : (((~strong(X0) | happy(X0)) | calm(X0)) & (~calm(X0) | (strong(X0) & ~happy(X0)))) [nnf transformation 10]
53. ! [X0] : ((~strong(X0) | happy(X0) | calm(X0)) & (~calm(X0) | (strong(X0) & ~happy(X0)))) [flattening 52]
54. ! [X0] : ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))) [nnf transformation 11]
55. ! [X0] : (((~curious(X0) & wise(X0)) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (curious(X0) | ~wise(X0)))) [nnf transformation 12]
56. ! [X0] : (((~curious(X0) & wise(X0)) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | curious(X0) | ~wise(X0))) [flattening 55]
60. ! [X0] : ((((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | (~funny(X0) | ~brave(X0))) & ((funny(X0) & brave(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0))))) [nnf transformation 14]
61. ! [X0] : ((((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | ~funny(X0) | ~brave(X0)) & ((funny(X0) & brave(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0))))) [flattening 60]
84. happy(X0) | curious(X0) | calm(X0) [cnf transformation 42]
88. ~strong(X0) | funny(X0) [cnf transformation 46]
92. ~patient(X0) | funny(X0) [cnf transformation 32]
100. ~calm(X0) | strong(X0) [cnf transformation 53]
102. ~old(X0) | wise(X0) [cnf transformation 54]
104. ~wise(X0) | patient(X0) | curious(X0) | ~happy(X0) [cnf transformation 56]
117. funny(X0) | humble(X0) | old(X0) [cnf transformation 61]
121. ~funny(X0) | humble(X0) [cnf transformation 35]
132. ~curious(paul) [cnf transformation 22]
135. ~humble(paul) [cnf transformation 24]
215. 19 <=> humble(paul) [avatar definition]
216. ~humble(paul) <- (~19) [avatar component clause 215]
284. ~19 [avatar split clause 135,215]
393. humble(X1) | old(X1) | humble(X1) [resolution 117,121]
395. humble(X1) | old(X1) [duplicate literal removal 393]
533. 58 <=> happy(paul) [avatar definition]
534. ~happy(paul) <- (~58) [avatar component clause 533]
535. happy(paul) <- (58) [avatar component clause 533]
537. 59 <=> patient(paul) [avatar definition]
538. patient(paul) <- (59) [avatar component clause 537]
543. old(paul) <- (~19) [resolution 395,216]
698. curious(paul) | calm(paul) <- (~58) [resolution 534,84]
699. calm(paul) <- (~58) [subsumption resolution 698,132]
751. strong(paul) <- (~58) [resolution 699,100]
759. funny(paul) <- (~58) [resolution 751,88]
771. humble(paul) <- (~58) [resolution 759,121]
776. $false <- (~19, ~58) [subsumption resolution 771,216]
777. 19 | 58 [avatar contradiction clause 776]
779. 72 <=> old(paul) [avatar definition]
781. old(paul) <- (72) [avatar component clause 779]
783. 72 | 19 [avatar split clause 543,215,779]
791. wise(paul) <- (72) [resolution 781,102]
794. patient(paul) | curious(paul) | ~happy(paul) <- (72) [resolution 791,104]
800. patient(paul) | ~happy(paul) <- (72) [subsumption resolution 794,132]
801. patient(paul) <- (58, 72) [subsumption resolution 800,535]
802. 59 | ~58 | ~72 [avatar split clause 801,779,533,537]
805. funny(paul) <- (59) [resolution 538,92]
809. humble(paul) <- (59) [resolution 805,121]
815. $false <- (~19, 59) [subsumption resolution 809,216]
816. 19 | ~59 [avatar contradiction clause 815]
817. $false [avatar sat refutation 284,777,783,802,816]
% SZS output end Proof for 5070964010078742174185827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not curious then someone is quiet or tall and vice versa.
Everyone who is not curious or not calm is both not creative and quiet.
If paul is not kind then alice is quiet.
If someone is both generous and quiet then fred is patient or not kind and vice versa.
Everyone who is not funny or creative is both not old and strong.
If someone is brave or not kind then someone is both not tall and not kind.
If someone is both tall and not strong then someone is not strong or not happy.
Everyone who is either not rich or not old is not wise and vice versa.
If someone is not creative or not old then susan is both creative and not wise and vice versa.
Everyone who is either not tall or brave is not old or kind.
If fred is not strong or not kind then someone is calm and vice versa.
If lucy is not kind then someone is not humble and vice versa.
Everyone who is generous or not quiet is both not happy and not wise and vice versa.
If lucy is not humble then someone is either rich or not tall.
If someone is either not tall or calm then alice is brave and vice versa.
Everyone who is either humble or wise is not old or not generous.
Fred is not humble.
Fred is either rich or tall.
Alice is patient or rich.
Someone is either generous or wise.
Someone is both not patient and brave.
Fred is not happy or strong.
John is both not happy and not tall.
Someone is either not calm or generous. | Susan is strong. | entailment | ((~curious(paul))<=>(?[X]:((quiet(X)|tall(X)))))&
(![X]:((~curious(X)|~calm(X))=>(~creative(X)&quiet(X))))&
((~kind(paul))=>(quiet(alice)))&
((?[X]:((generous(X)&quiet(X))))<=>((patient(fred)|~kind(fred))))&
(![X]:((~funny(X)|creative(X))=>(~old(X)&strong(X))))&
((?[X]:((brave(X)|~kind(X))))=>(?[X]:((~tall(X)&~kind(X)))))&
((?[X]:((tall(X)&~strong(X))))=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:((~rich(X)<~>~old(X))<=>~wise(X)))&
((?[X]:((~creative(X)|~old(X))))<=>((creative(susan)&~wise(susan))))&
(![X]:((~tall(X)<~>brave(X))=>(~old(X)|kind(X))))&
(((~strong(fred)|~kind(fred)))<=>(?[X]:(calm(X))))&
((~kind(lucy))<=>(?[X]:(~humble(X))))&
(![X]:((generous(X)|~quiet(X))<=>(~happy(X)&~wise(X))))&
((~humble(lucy))=>(?[X]:((rich(X)<~>~tall(X)))))&
((?[X]:((~tall(X)<~>calm(X))))<=>(brave(alice)))&
(![X]:((humble(X)<~>wise(X))=>(~old(X)|~generous(X))))&
(~humble(fred))&
((rich(fred)<~>tall(fred)))&
((patient(alice)|rich(alice)))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:((~patient(X)&brave(X))))&
((~happy(fred)|strong(fred)))&
((~happy(john)&~tall(john)))&
(?[X]:((~calm(X)<~>generous(X)))) | strong(susan) | [
"p4",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 6680337529087340715739267
% SZS output start Proof for 6680337529087340715739267
5. ! [X0] : ((creative(X0) | ~funny(X0)) => (strong(X0) & ~old(X0))) [input p4]
9. ? [X0] : (~old(X0) | ~creative(X0)) <=> (~wise(susan) & creative(susan)) [input p8]
25. ~strong(susan) [input hypothesis]
28. ! [X0] : (creative(X0) => (strong(X0) & ~old(X0))) [pure predicate removal 5]
31. ! [X0] : ((strong(X0) & ~old(X0)) | ~creative(X0)) [ennf transformation 28]
55. (? [X0] : (~old(X0) | ~creative(X0)) | (wise(susan) | ~creative(susan))) & ((~wise(susan) & creative(susan)) | ! [X0] : (old(X0) & creative(X0))) [nnf transformation 9]
56. (? [X0] : (~old(X0) | ~creative(X0)) | wise(susan) | ~creative(susan)) & ((~wise(susan) & creative(susan)) | ! [X0] : (old(X0) & creative(X0))) [flattening 55]
57. (? [X0] : (~old(X0) | ~creative(X0)) | wise(susan) | ~creative(susan)) & ((~wise(susan) & creative(susan)) | ! [X1] : (old(X1) & creative(X1))) [rectify 56]
58. ? [X0] : (~old(X0) | ~creative(X0)) => (~old(sK4) | ~creative(sK4)) [choice axiom]
59. ((~old(sK4) | ~creative(sK4)) | wise(susan) | ~creative(susan)) & ((~wise(susan) & creative(susan)) | ! [X1] : (old(X1) & creative(X1))) [skolemisation 57,58]
102. ~old(X0) | ~creative(X0) [cnf transformation 31]
103. ~creative(X0) | strong(X0) [cnf transformation 31]
113. creative(susan) | creative(X1) [cnf transformation 59]
114. creative(susan) | old(X1) [cnf transformation 59]
151. ~strong(susan) [cnf transformation 25]
237. 20 <=> ! [X1] : old(X1) [avatar definition]
238. old(X1) <- (20) [avatar component clause 237]
245. 22 <=> ! [X1] : creative(X1) [avatar definition]
246. creative(X1) <- (22) [avatar component clause 245]
249. 23 <=> creative(susan) [avatar definition]
251. creative(susan) <- (23) [avatar component clause 249]
252. 20 | 23 [avatar split clause 114,249,237]
253. 22 | 23 [avatar split clause 113,249,245]
370. ~creative(X0) <- (20) [resolution 102,238]
371. strong(susan) <- (23) [resolution 103,251]
372. $false <- (23) [subsumption resolution 371,151]
373. ~23 [avatar contradiction clause 372]
374. $false <- (20, 22) [subsumption resolution 246,370]
375. ~20 | ~22 [avatar contradiction clause 374]
376. $false [avatar sat refutation 252,253,373,375]
% SZS output end Proof for 6680337529087340715739267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not quiet is kind and vice versa. If john is both patient and not quiet then paul is not calm or not quiet. Everyone who is either not rich or creative is not humble and vice versa. If susan is rich then someone is not curious or not generous. If someone is curious then someone is not strong or brave and vice versa. Everyone who is not funny is brave or not kind. Everyone who is either not humble or not strong is generous. Everyone who is both creative and not brave is kind or not quiet. Everyone who is humble or generous is either not brave or not happy. Everyone who is rich or creative is not generous. If someone is not quiet or not happy then someone is not kind and vice versa. Everyone who is not old is not kind or creative and vice versa. If lucy is calm then someone is creative. If susan is curious then someone is both happy and brave. Everyone who is both calm and not generous is not creative and vice versa. If lucy is not humble or brave then someone is not brave or not quiet. Someone is either calm or not curious. John is creative or not tall. Paul is both not curious and funny. Paul is quiet or brave. Someone is either not kind or creative. Someone is either happy or not kind. Alice is either creative or calm. Someone is either humble or happy. | Alice is patient. | neutral | (![X]:((calm(X)|~quiet(X))<=>kind(X)))&
(((patient(john)&~quiet(john)))=>((~calm(paul)|~quiet(paul))))&
(![X]:((~rich(X)<~>creative(X))<=>~humble(X)))&
((rich(susan))=>(?[X]:((~curious(X)|~generous(X)))))&
((?[X]:(curious(X)))<=>(?[X]:((~strong(X)|brave(X)))))&
(![X]:(~funny(X)=>(brave(X)|~kind(X))))&
(![X]:((~humble(X)<~>~strong(X))=>generous(X)))&
(![X]:((creative(X)&~brave(X))=>(kind(X)|~quiet(X))))&
(![X]:((humble(X)|generous(X))=>(~brave(X)<~>~happy(X))))&
(![X]:((rich(X)|creative(X))=>~generous(X)))&
((?[X]:((~quiet(X)|~happy(X))))<=>(?[X]:(~kind(X))))&
(![X]:(~old(X)<=>(~kind(X)|creative(X))))&
((calm(lucy))=>(?[X]:(creative(X))))&
((curious(susan))=>(?[X]:((happy(X)&brave(X)))))&
(![X]:((calm(X)&~generous(X))<=>~creative(X)))&
(((~humble(lucy)|brave(lucy)))=>(?[X]:((~brave(X)|~quiet(X)))))&
(?[X]:((calm(X)<~>~curious(X))))&
((creative(john)|~tall(john)))&
((~curious(paul)&funny(paul)))&
((quiet(paul)|brave(paul)))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((happy(X)<~>~kind(X))))&
((creative(alice)<~>calm(alice)))&
(?[X]:((humble(X)<~>happy(X)))) | patient(alice) | []
| null | 0 |
If john is both not generous and not happy then someone is either brave or not wise.
Everyone who is either patient or not wise is rich.
Everyone who is not generous is not patient.
Everyone who is both not old and strong is either not kind or tall.
Everyone who is both generous and creative is not tall or not generous and vice versa.
If susan is not rich or not curious then mary is both not quiet and not kind and vice versa.
Everyone who is either not tall or funny is either not curious or humble.
Everyone who is both calm and not funny is not quiet or not wise.
If someone is either not humble or not tall then mary is not strong or not tall and vice versa.
If lucy is both wise and rich then someone is wise.
If fred is not wise then mary is not curious or not tall and vice versa.
If mary is funny or not funny then someone is tall or not curious.
If fred is both kind and strong then mary is quiet or calm and vice versa.
Everyone who is not calm or old is not patient.
If someone is brave or not generous then someone is not curious or patient.
Everyone who is not strong is not curious or humble.
Lucy is either happy or not kind.
Susan is not kind or creative.
Lucy is not rich or wise.
Mary is both strong and wise.
John is not tall.
Lucy is both not happy and not calm.
Someone is humble. | Mary is not curious. | neutral | (((~generous(john)&~happy(john)))=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
(![X]:(~generous(X)=>~patient(X)))&
(![X]:((~old(X)&strong(X))=>(~kind(X)<~>tall(X))))&
(![X]:((generous(X)&creative(X))<=>(~tall(X)|~generous(X))))&
(((~rich(susan)|~curious(susan)))<=>((~quiet(mary)&~kind(mary))))&
(![X]:((~tall(X)<~>funny(X))=>(~curious(X)<~>humble(X))))&
(![X]:((calm(X)&~funny(X))=>(~quiet(X)|~wise(X))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>((~strong(mary)|~tall(mary))))&
(((wise(lucy)&rich(lucy)))=>(?[X]:(wise(X))))&
((~wise(fred))<=>((~curious(mary)|~tall(mary))))&
(((funny(mary)|~funny(mary)))=>(?[X]:((tall(X)|~curious(X)))))&
(((kind(fred)&strong(fred)))<=>((quiet(mary)|calm(mary))))&
(![X]:((~calm(X)|old(X))=>~patient(X)))&
((?[X]:((brave(X)|~generous(X))))=>(?[X]:((~curious(X)|patient(X)))))&
(![X]:(~strong(X)=>(~curious(X)|humble(X))))&
((happy(lucy)<~>~kind(lucy)))&
((~kind(susan)|creative(susan)))&
((~rich(lucy)|wise(lucy)))&
((strong(mary)&wise(mary)))&
(~tall(john))&
((~happy(lucy)&~calm(lucy)))&
(?[X]:(humble(X))) | ~curious(mary) | []
| null | 0 |
Everyone who is both curious and not rich is not creative or not tall.
Everyone who is not humble or not wise is old.
If alice is both funny and not curious then fred is both quiet and wise and vice versa.
Everyone who is not generous is both creative and not humble.
Everyone who is both generous and not old is both calm and kind.
Everyone who is not quiet or not generous is either happy or generous.
If susan is both kind and creative then fred is both happy and not curious and vice versa.
If someone is happy then someone is either happy or not curious.
If lucy is funny or patient then susan is not tall.
If mary is curious then mary is both generous and patient and vice versa.
Everyone who is both kind and happy is either strong or quiet and vice versa.
Everyone who is both curious and not calm is both wise and not kind and vice versa.
If mary is calm or not happy then lucy is either not funny or happy.
If fred is both humble and not kind then someone is not quiet.
Everyone who is not rich is not patient or generous and vice versa.
Everyone who is either calm or not happy is not creative or rich.
Lucy is not rich or not wise.
John is either tall or calm.
Someone is either not quiet or tall.
Someone is not patient.
Mary is both not humble and old.
Lucy is either not kind or strong.
Susan is not strong or not tall.
Lucy is both quiet and not old. | Alice is not creative. | neutral | (![X]:((curious(X)&~rich(X))=>(~creative(X)|~tall(X))))&
(![X]:((~humble(X)|~wise(X))=>old(X)))&
(((funny(alice)&~curious(alice)))<=>((quiet(fred)&wise(fred))))&
(![X]:(~generous(X)=>(creative(X)&~humble(X))))&
(![X]:((generous(X)&~old(X))=>(calm(X)&kind(X))))&
(![X]:((~quiet(X)|~generous(X))=>(happy(X)<~>generous(X))))&
(((kind(susan)&creative(susan)))<=>((happy(fred)&~curious(fred))))&
((?[X]:(happy(X)))=>(?[X]:((happy(X)<~>~curious(X)))))&
(((funny(lucy)|patient(lucy)))=>(~tall(susan)))&
((curious(mary))<=>((generous(mary)&patient(mary))))&
(![X]:((kind(X)&happy(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((curious(X)&~calm(X))<=>(wise(X)&~kind(X))))&
(((calm(mary)|~happy(mary)))=>((~funny(lucy)<~>happy(lucy))))&
(((humble(fred)&~kind(fred)))=>(?[X]:(~quiet(X))))&
(![X]:(~rich(X)<=>(~patient(X)|generous(X))))&
(![X]:((calm(X)<~>~happy(X))=>(~creative(X)|rich(X))))&
((~rich(lucy)|~wise(lucy)))&
((tall(john)<~>calm(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(?[X]:(~patient(X)))&
((~humble(mary)&old(mary)))&
((~kind(lucy)<~>strong(lucy)))&
((~strong(susan)|~tall(susan)))&
((quiet(lucy)&~old(lucy))) | ~creative(alice) | []
| null | 0 |
If someone is not humble or quiet then alice is tall or not generous.
Everyone who is not patient or not kind is old.
Everyone who is both not curious and not happy is curious or not rich.
Everyone who is tall is not funny.
If someone is either not quiet or happy then someone is not generous.
Everyone who is both humble and not wise is brave or wise.
Everyone who is calm or not rich is not curious or not wise.
Everyone who is not kind or rich is either not generous or quiet.
Everyone who is both not strong and not creative is calm.
If someone is not brave or patient then someone is both not brave and funny.
Everyone who is not humble or happy is either not tall or not humble and vice versa.
Everyone who is either not rich or not old is both strong and funny and vice versa.
If john is strong or creative then susan is not brave or not old and vice versa.
Everyone who is brave or calm is not kind.
Everyone who is quiet or not quiet is both wise and funny and vice versa.
Everyone who is not old is brave or not brave.
Lucy is not generous or not strong.
Someone is not creative or curious.
John is both not generous and brave.
Someone is either generous or not calm.
Someone is both not tall and not kind.
Mary is either not quiet or humble.
John is not patient or not curious. | John is not creative. | neutral | ((?[X]:((~humble(X)|quiet(X))))=>((tall(alice)|~generous(alice))))&
(![X]:((~patient(X)|~kind(X))=>old(X)))&
(![X]:((~curious(X)&~happy(X))=>(curious(X)|~rich(X))))&
(![X]:(tall(X)=>~funny(X)))&
((?[X]:((~quiet(X)<~>happy(X))))=>(?[X]:(~generous(X))))&
(![X]:((humble(X)&~wise(X))=>(brave(X)|wise(X))))&
(![X]:((calm(X)|~rich(X))=>(~curious(X)|~wise(X))))&
(![X]:((~kind(X)|rich(X))=>(~generous(X)<~>quiet(X))))&
(![X]:((~strong(X)&~creative(X))=>calm(X)))&
((?[X]:((~brave(X)|patient(X))))=>(?[X]:((~brave(X)&funny(X)))))&
(![X]:((~humble(X)|happy(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>~old(X))<=>(strong(X)&funny(X))))&
(((strong(john)|creative(john)))<=>((~brave(susan)|~old(susan))))&
(![X]:((brave(X)|calm(X))=>~kind(X)))&
(![X]:((quiet(X)|~quiet(X))<=>(wise(X)&funny(X))))&
(![X]:(~old(X)=>(brave(X)|~brave(X))))&
((~generous(lucy)|~strong(lucy)))&
(?[X]:((~creative(X)|curious(X))))&
((~generous(john)&brave(john)))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((~tall(X)&~kind(X))))&
((~quiet(mary)<~>humble(mary)))&
((~patient(john)|~curious(john))) | ~creative(john) | []
| null | 0 |
Everyone who is not quiet or not calm is either not rich or brave and vice versa.
Everyone who is both not tall and wise is not wise.
Everyone who is kind or not rich is quiet and vice versa.
If someone is quiet or not rich then someone is not rich.
Everyone who is not generous is not quiet or not patient.
If mary is either not creative or kind then paul is not rich or curious.
Everyone who is either not quiet or wise is wise and vice versa.
Everyone who is not wise or not funny is not calm and vice versa.
Everyone who is either not happy or wise is both creative and wise and vice versa.
If someone is either not quiet or patient then someone is either not quiet or not generous and vice versa.
Everyone who is not old or old is quiet or wise and vice versa.
Everyone who is either brave or patient is brave and vice versa.
Everyone who is not kind is both not tall and not happy.
Everyone who is not tall or kind is rich or curious and vice versa.
If susan is both not patient and not rich then fred is kind and vice versa.
If paul is not rich then someone is either not quiet or not wise and vice versa.
Someone is happy.
Someone is calm or rich.
John is not patient.
Someone is tall.
Someone is not rich or not creative.
Someone is both not curious and not calm.
Someone is not calm. | Fred is not kind. | contradiction | (![X]:((~quiet(X)|~calm(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~tall(X)&wise(X))=>~wise(X)))&
(![X]:((kind(X)|~rich(X))<=>quiet(X)))&
((?[X]:((quiet(X)|~rich(X))))=>(?[X]:(~rich(X))))&
(![X]:(~generous(X)=>(~quiet(X)|~patient(X))))&
(((~creative(mary)<~>kind(mary)))=>((~rich(paul)|curious(paul))))&
(![X]:((~quiet(X)<~>wise(X))<=>wise(X)))&
(![X]:((~wise(X)|~funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(creative(X)&wise(X))))&
((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:((~old(X)|old(X))<=>(quiet(X)|wise(X))))&
(![X]:((brave(X)<~>patient(X))<=>brave(X)))&
(![X]:(~kind(X)=>(~tall(X)&~happy(X))))&
(![X]:((~tall(X)|kind(X))<=>(rich(X)|curious(X))))&
(((~patient(susan)&~rich(susan)))<=>(kind(fred)))&
((~rich(paul))<=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(?[X]:(happy(X)))&
(?[X]:((calm(X)|rich(X))))&
(~patient(john))&
(?[X]:(tall(X)))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((~curious(X)&~calm(X))))&
(?[X]:(~calm(X))) | ~kind(fred) | [
"p1",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 5526031208114798473202348
% SZS output start Proof for 5526031208114798473202348
2. ! [X0] : ((wise(X0) & ~tall(X0)) => ~wise(X0)) [input p1]
9. ! [X0] : ((~happy(X0) <~> wise(X0)) <=> (wise(X0) & creative(X0))) [input p8]
13. ! [X0] : (~kind(X0) => (~happy(X0) & ~tall(X0))) [input p12]
24. ~kind(fred) [input hypothesis]
27. ! [X0] : (~wise(X0) | (~wise(X0) | tall(X0))) [ennf transformation 2]
28. ! [X0] : (~wise(X0) | ~wise(X0) | tall(X0)) [flattening 27]
34. ! [X0] : ((~happy(X0) & ~tall(X0)) | kind(X0)) [ennf transformation 13]
46. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (~wise(X0) | ~creative(X0))) & ((wise(X0) & creative(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | ~wise(X0) | ~creative(X0)) & ((wise(X0) & creative(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [flattening 46]
82. ~wise(X0) | ~wise(X0) | tall(X0) [cnf transformation 28]
100. wise(X0) | wise(X0) | happy(X0) [cnf transformation 47]
120. ~tall(X0) | kind(X0) [cnf transformation 34]
121. ~happy(X0) | kind(X0) [cnf transformation 34]
141. ~kind(fred) [cnf transformation 24]
144. happy(X0) | wise(X0) [duplicate literal removal 100]
148. ~wise(X0) | tall(X0) [duplicate literal removal 82]
203. 12 <=> kind(fred) [avatar definition]
205. ~kind(fred) <- (~12) [avatar component clause 203]
246. ~12 [avatar split clause 141,203]
256. kind(X0) | wise(X0) [resolution 144,121]
352. wise(fred) <- (~12) [resolution 256,205]
358. tall(fred) <- (~12) [resolution 352,148]
361. kind(fred) <- (~12) [resolution 358,120]
362. $false <- (~12) [subsumption resolution 361,205]
363. 12 [avatar contradiction clause 362]
364. $false [avatar sat refutation 246,363]
% SZS output end Proof for 5526031208114798473202348
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not tall or not patient is patient or not old. Everyone who is not quiet or wise is calm. If someone is not calm or quiet then alice is both generous and humble. Everyone who is either curious or tall is either not wise or not quiet. If someone is either kind or not kind then alice is kind or not happy. If mary is either not brave or tall then alice is either wise or tall and vice versa. If susan is both old and calm then paul is either not kind or not quiet and vice versa. Everyone who is either not patient or not old is either not calm or not old. If someone is calm then someone is either not brave or not generous and vice versa. If alice is old then someone is either not calm or not happy and vice versa. Everyone who is either tall or old is not tall or kind and vice versa. If someone is either humble or not kind then someone is not patient or not tall and vice versa. Everyone who is not calm or not curious is both patient and wise. If susan is either not strong or not happy then someone is either not wise or not old. Everyone who is both not generous and creative is either not patient or humble and vice versa. Someone is both curious and not strong. Mary is either quiet or curious. Mary is either tall or brave. Someone is creative. Mary is either not rich or happy. John is not wise or not kind. | Susan is tall. | neutral | (![X]:((~tall(X)<~>~patient(X))=>(patient(X)|~old(X))))&
(![X]:((~quiet(X)|wise(X))=>calm(X)))&
((?[X]:((~calm(X)|quiet(X))))=>((generous(alice)&humble(alice))))&
(![X]:((curious(X)<~>tall(X))=>(~wise(X)<~>~quiet(X))))&
((?[X]:((kind(X)<~>~kind(X))))=>((kind(alice)|~happy(alice))))&
(((~brave(mary)<~>tall(mary)))<=>((wise(alice)<~>tall(alice))))&
(((old(susan)&calm(susan)))<=>((~kind(paul)<~>~quiet(paul))))&
(![X]:((~patient(X)<~>~old(X))=>(~calm(X)<~>~old(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((old(alice))<=>(?[X]:((~calm(X)<~>~happy(X)))))&
(![X]:((tall(X)<~>old(X))<=>(~tall(X)|kind(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:((~calm(X)|~curious(X))=>(patient(X)&wise(X))))&
(((~strong(susan)<~>~happy(susan)))=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>humble(X))))&
(?[X]:((curious(X)&~strong(X))))&
((quiet(mary)<~>curious(mary)))&
((tall(mary)<~>brave(mary)))&
(?[X]:(creative(X)))&
((~rich(mary)<~>happy(mary)))&
((~wise(john)|~kind(john))) | tall(susan) | []
| null | 0 |
Everyone who is not generous or not wise is not humble.
Everyone who is both brave and kind is not creative and vice versa.
If john is both old and curious then someone is not humble or not curious.
If someone is not creative or not happy then alice is both not strong and not brave.
If someone is both not old and not creative then susan is both not wise and creative and vice versa.
Everyone who is both not kind and not humble is not rich.
Everyone who is not generous is either kind or not funny and vice versa.
Everyone who is not brave is funny or not calm and vice versa.
Everyone who is not generous is not kind and vice versa.
If someone is humble or creative then paul is not quiet and vice versa.
Everyone who is creative or curious is happy.
If paul is not funny or brave then someone is both not patient and curious and vice versa.
If lucy is humble then someone is either not creative or patient and vice versa.
If john is both not humble and creative then fred is both not brave and not humble and vice versa.
Everyone who is quiet is generous and vice versa.
If someone is both rich and not funny then someone is either rich or not strong and vice versa.
Someone is either wise or curious.
Someone is tall or not humble.
Mary is not generous or not creative.
John is both not strong and not happy.
Lucy is old.
Fred is either not curious or not rich. | Alice is not calm. | entailment | (![X]:((~generous(X)|~wise(X))=>~humble(X)))&
(![X]:((brave(X)&kind(X))<=>~creative(X)))&
(((old(john)&curious(john)))=>(?[X]:((~humble(X)|~curious(X)))))&
((?[X]:((~creative(X)|~happy(X))))=>((~strong(alice)&~brave(alice))))&
((?[X]:((~old(X)&~creative(X))))<=>((~wise(susan)&creative(susan))))&
(![X]:((~kind(X)&~humble(X))=>~rich(X)))&
(![X]:(~generous(X)<=>(kind(X)<~>~funny(X))))&
(![X]:(~brave(X)<=>(funny(X)|~calm(X))))&
(![X]:(~generous(X)<=>~kind(X)))&
((?[X]:((humble(X)|creative(X))))<=>(~quiet(paul)))&
(![X]:((creative(X)|curious(X))=>happy(X)))&
(((~funny(paul)|brave(paul)))<=>(?[X]:((~patient(X)&curious(X)))))&
((humble(lucy))<=>(?[X]:((~creative(X)<~>patient(X)))))&
(((~humble(john)&creative(john)))<=>((~brave(fred)&~humble(fred))))&
(![X]:(quiet(X)<=>generous(X)))&
((?[X]:((rich(X)&~funny(X))))<=>(?[X]:((rich(X)<~>~strong(X)))))&
(?[X]:((wise(X)<~>curious(X))))&
(?[X]:((tall(X)|~humble(X))))&
((~generous(mary)|~creative(mary)))&
((~strong(john)&~happy(john)))&
(old(lucy))&
((~curious(fred)<~>~rich(fred))) | ~calm(alice) | [
"p3",
"p6",
"p7",
"p8",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 2699744844521481223469564
% SZS output start Proof for 2699744844521481223469564
4. ? [X0] : (~happy(X0) | ~creative(X0)) => (~brave(alice) & ~strong(alice)) [input p3]
7. ! [X0] : (~generous(X0) <=> (kind(X0) <~> ~funny(X0))) [input p6]
8. ! [X0] : (~brave(X0) <=> (~calm(X0) | funny(X0))) [input p7]
9. ! [X0] : (~generous(X0) <=> ~kind(X0)) [input p8]
20. ~happy(john) & ~strong(john) [input p19]
23. calm(alice) [input hypothesis]
29. (~brave(alice) & ~strong(alice)) | ! [X0] : (happy(X0) & creative(X0)) [ennf transformation 4]
42. ! [X0] : ((~generous(X0) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0)))) & (((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | generous(X0))) [nnf transformation 7]
43. ! [X0] : ((~brave(X0) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | brave(X0))) [nnf transformation 8]
44. ! [X0] : ((~brave(X0) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | brave(X0))) [flattening 43]
45. ! [X0] : ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))) [nnf transformation 9]
80. ~brave(alice) | happy(X0) [cnf transformation 29]
86. ~funny(X0) | kind(X0) | generous(X0) [cnf transformation 42]
88. ~funny(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 42]
90. ~calm(X0) | funny(X0) | brave(X0) [cnf transformation 44]
93. ~kind(X0) | generous(X0) [cnf transformation 45]
94. ~generous(X0) | kind(X0) [cnf transformation 45]
125. ~happy(john) [cnf transformation 20]
129. calm(alice) [cnf transformation 23]
148. 5 <=> ! [X0] : happy(X0) [avatar definition]
149. happy(X0) <- (5) [avatar component clause 148]
151. 6 <=> brave(alice) [avatar definition]
153. ~brave(alice) <- (~6) [avatar component clause 151]
154. 5 | ~6 [avatar split clause 80,151,148]
424. funny(alice) | brave(alice) [resolution 90,129]
428. funny(alice) <- (~6) [subsumption resolution 424,153]
429. ~generous(alice) | ~kind(alice) <- (~6) [resolution 428,88]
430. kind(alice) | generous(alice) <- (~6) [resolution 428,86]
432. ~kind(alice) <- (~6) [subsumption resolution 429,93]
433. generous(alice) <- (~6) [subsumption resolution 430,432]
465. kind(alice) <- (~6) [resolution 433,94]
466. $false <- (~6) [subsumption resolution 465,432]
467. 6 [avatar contradiction clause 466]
482. $false <- (5) [resolution 149,125]
483. ~5 [avatar contradiction clause 482]
484. $false [avatar sat refutation 154,467,483]
% SZS output end Proof for 2699744844521481223469564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not quiet is humble and vice versa. Everyone who is old is either curious or not happy and vice versa. Everyone who is not wise is either strong or brave and vice versa. If susan is not old or not tall then john is both not happy and not humble. Everyone who is not happy is either quiet or generous. Everyone who is creative or not tall is both not funny and not happy and vice versa. If paul is both humble and not tall then someone is not rich or not generous and vice versa. If lucy is either not old or not patient then susan is not quiet or kind and vice versa. Everyone who is either not happy or not quiet is creative or not tall and vice versa. Everyone who is both not strong and patient is either not kind or old. Everyone who is both brave and not old is both not calm and not creative. Everyone who is both not happy and kind is either not brave or not patient. If someone is either not strong or generous then mary is humble and vice versa. Everyone who is not kind or creative is either not wise or not humble and vice versa. If someone is both not curious and brave then susan is either not generous or not creative and vice versa. If someone is quiet or patient then someone is not patient. Someone is curious or quiet. John is strong. Someone is either kind or calm. Fred is either patient or tall. Someone is old. Someone is either not curious or not humble. | Mary is happy. | contradiction | (![X]:((curious(X)&~quiet(X))<=>humble(X)))&
(![X]:(old(X)<=>(curious(X)<~>~happy(X))))&
(![X]:(~wise(X)<=>(strong(X)<~>brave(X))))&
(((~old(susan)|~tall(susan)))=>((~happy(john)&~humble(john))))&
(![X]:(~happy(X)=>(quiet(X)<~>generous(X))))&
(![X]:((creative(X)|~tall(X))<=>(~funny(X)&~happy(X))))&
(((humble(paul)&~tall(paul)))<=>(?[X]:((~rich(X)|~generous(X)))))&
(((~old(lucy)<~>~patient(lucy)))<=>((~quiet(susan)|kind(susan))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(creative(X)|~tall(X))))&
(![X]:((~strong(X)&patient(X))=>(~kind(X)<~>old(X))))&
(![X]:((brave(X)&~old(X))=>(~calm(X)&~creative(X))))&
(![X]:((~happy(X)&kind(X))=>(~brave(X)<~>~patient(X))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(humble(mary)))&
(![X]:((~kind(X)|creative(X))<=>(~wise(X)<~>~humble(X))))&
((?[X]:((~curious(X)&brave(X))))<=>((~generous(susan)<~>~creative(susan))))&
((?[X]:((quiet(X)|patient(X))))=>(?[X]:(~patient(X))))&
(?[X]:((curious(X)|quiet(X))))&
(strong(john))&
(?[X]:((kind(X)<~>calm(X))))&
((patient(fred)<~>tall(fred)))&
(?[X]:(old(X)))&
(?[X]:((~curious(X)<~>~humble(X)))) | happy(mary) | [
"p0",
"p5",
"p6",
"p8",
"p12",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 297877338712334634498388
% SZS output start Proof for 297877338712334634498388
1. ! [X0] : ((~quiet(X0) & curious(X0)) <=> humble(X0)) [input p0]
6. ! [X0] : ((~tall(X0) | creative(X0)) <=> (~happy(X0) & ~funny(X0))) [input p5]
7. (~tall(paul) & humble(paul)) <=> ? [X0] : (~generous(X0) | ~rich(X0)) [input p6]
9. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) <=> (~tall(X0) | creative(X0))) [input p8]
13. ? [X0] : (~strong(X0) <~> generous(X0)) <=> humble(mary) [input p12]
18. strong(john) [input p17]
23. happy(mary) [input hypothesis]
34. ! [X0] : (((~quiet(X0) & curious(X0)) | ~humble(X0)) & (humble(X0) | (quiet(X0) | ~curious(X0)))) [nnf transformation 1]
35. ! [X0] : (((~quiet(X0) & curious(X0)) | ~humble(X0)) & (humble(X0) | quiet(X0) | ~curious(X0))) [flattening 34]
39. ! [X0] : (((~tall(X0) | creative(X0)) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | (tall(X0) & ~creative(X0)))) [nnf transformation 6]
40. ! [X0] : ((~tall(X0) | creative(X0) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | (tall(X0) & ~creative(X0)))) [flattening 39]
41. ((~tall(paul) & humble(paul)) | ! [X0] : (generous(X0) & rich(X0))) & (? [X0] : (~generous(X0) | ~rich(X0)) | (tall(paul) | ~humble(paul))) [nnf transformation 7]
42. ((~tall(paul) & humble(paul)) | ! [X0] : (generous(X0) & rich(X0))) & (? [X0] : (~generous(X0) | ~rich(X0)) | tall(paul) | ~humble(paul)) [flattening 41]
43. ((~tall(paul) & humble(paul)) | ! [X0] : (generous(X0) & rich(X0))) & (? [X1] : (~generous(X1) | ~rich(X1)) | tall(paul) | ~humble(paul)) [rectify 42]
44. ? [X1] : (~generous(X1) | ~rich(X1)) => (~generous(sK0) | ~rich(sK0)) [choice axiom]
45. ((~tall(paul) & humble(paul)) | ! [X0] : (generous(X0) & rich(X0))) & ((~generous(sK0) | ~rich(sK0)) | tall(paul) | ~humble(paul)) [skolemisation 43,44]
48. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (tall(X0) & ~creative(X0))) & ((~tall(X0) | creative(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [nnf transformation 9]
49. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (tall(X0) & ~creative(X0))) & (~tall(X0) | creative(X0) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [flattening 48]
52. (? [X0] : ((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ~humble(mary)) & (humble(mary) | ! [X0] : ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) [nnf transformation 13]
53. (? [X0] : ((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ~humble(mary)) & (humble(mary) | ! [X1] : ((~strong(X1) | ~generous(X1)) & (generous(X1) | strong(X1)))) [rectify 52]
54. ? [X0] : ((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) => ((~generous(sK1) | strong(sK1)) & (generous(sK1) | ~strong(sK1))) [choice axiom]
55. (((~generous(sK1) | strong(sK1)) & (generous(sK1) | ~strong(sK1))) | ~humble(mary)) & (humble(mary) | ! [X1] : ((~strong(X1) | ~generous(X1)) & (generous(X1) | strong(X1)))) [skolemisation 53,54]
78. ~humble(X0) | ~quiet(X0) [cnf transformation 35]
95. ~creative(X0) | ~happy(X0) [cnf transformation 40]
96. ~happy(X0) | tall(X0) [cnf transformation 40]
100. humble(paul) | generous(X0) [cnf transformation 45]
102. ~tall(paul) | generous(X0) [cnf transformation 45]
110. ~tall(X0) | creative(X0) | ~happy(X0) | quiet(X0) [cnf transformation 49]
113. quiet(X0) | happy(X0) | ~creative(X0) [cnf transformation 49]
114. quiet(X0) | happy(X0) | tall(X0) [cnf transformation 49]
122. humble(mary) | ~strong(X1) | ~generous(X1) [cnf transformation 55]
140. strong(john) [cnf transformation 18]
148. happy(mary) [cnf transformation 23]
170. 5 <=> ! [X0] : generous(X0) [avatar definition]
171. generous(X0) <- (5) [avatar component clause 170]
173. 6 <=> tall(paul) [avatar definition]
175. ~tall(paul) <- (~6) [avatar component clause 173]
176. 5 | ~6 [avatar split clause 102,173,170]
182. 8 <=> humble(paul) [avatar definition]
184. humble(paul) <- (8) [avatar component clause 182]
185. 5 | 8 [avatar split clause 100,182,170]
218. tall(X0) | quiet(X0) [subsumption resolution 114,96]
219. ~creative(X0) | quiet(X0) [subsumption resolution 113,95]
220. creative(X0) | ~happy(X0) | quiet(X0) [subsumption resolution 110,218]
221. ~happy(X0) | quiet(X0) [subsumption resolution 220,219]
223. 15 <=> humble(mary) [avatar definition]
224. humble(mary) <- (15) [avatar component clause 223]
237. 18 <=> ! [X1] : (~strong(X1) | ~generous(X1)) [avatar definition]
238. ~strong(X1) | ~generous(X1) <- (18) [avatar component clause 237]
239. 18 | 15 [avatar split clause 122,223,237]
318. ~quiet(mary) <- (15) [resolution 78,224]
319. ~quiet(paul) <- (8) [resolution 78,184]
322. quiet(paul) <- (~6) [resolution 218,175]
324. $false <- (~6, 8) [subsumption resolution 322,319]
325. 6 | ~8 [avatar contradiction clause 324]
332. quiet(mary) [resolution 221,148]
333. $false <- (15) [subsumption resolution 332,318]
334. ~15 [avatar contradiction clause 333]
335. ~strong(X1) <- (5, 18) [subsumption resolution 238,171]
336. $false <- (5, 18) [resolution 335,140]
339. ~5 | ~18 [avatar contradiction clause 336]
340. $false [avatar sat refutation 176,185,239,325,334,339]
% SZS output end Proof for 297877338712334634498388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is quiet or tall then someone is not rich or old.
If lucy is either not generous or strong then someone is either not creative or not happy.
If someone is both tall and not generous then paul is not happy and vice versa.
Everyone who is both patient and not strong is not kind or tall and vice versa.
If someone is not strong or not happy then someone is both not strong and not brave and vice versa.
Everyone who is both strong and not curious is rich and vice versa.
Everyone who is both not creative and happy is not generous.
Everyone who is either wise or not calm is calm and vice versa.
Everyone who is both not old and not creative is either curious or not wise.
Everyone who is not calm or not happy is not happy.
If someone is not curious then paul is quiet and vice versa.
Everyone who is both not old and not kind is both rich and funny.
Everyone who is generous is happy and vice versa.
Everyone who is either tall or happy is either humble or strong.
Everyone who is not rich is not brave or tall.
If someone is not calm or generous then paul is both not kind and wise.
Someone is not patient.
Someone is either not calm or not kind.
Paul is not strong.
Paul is not curious.
Paul is not patient.
Someone is either not creative or not brave.
Paul is both humble and not happy.
Someone is either quiet or patient. | Alice is not calm. | contradiction | (((quiet(alice)|tall(alice)))=>(?[X]:((~rich(X)|old(X)))))&
(((~generous(lucy)<~>strong(lucy)))=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:((tall(X)&~generous(X))))<=>(~happy(paul)))&
(![X]:((patient(X)&~strong(X))<=>(~kind(X)|tall(X))))&
((?[X]:((~strong(X)|~happy(X))))<=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((strong(X)&~curious(X))<=>rich(X)))&
(![X]:((~creative(X)&happy(X))=>~generous(X)))&
(![X]:((wise(X)<~>~calm(X))<=>calm(X)))&
(![X]:((~old(X)&~creative(X))=>(curious(X)<~>~wise(X))))&
(![X]:((~calm(X)|~happy(X))=>~happy(X)))&
((?[X]:(~curious(X)))<=>(quiet(paul)))&
(![X]:((~old(X)&~kind(X))=>(rich(X)&funny(X))))&
(![X]:(generous(X)<=>happy(X)))&
(![X]:((tall(X)<~>happy(X))=>(humble(X)<~>strong(X))))&
(![X]:(~rich(X)=>(~brave(X)|tall(X))))&
((?[X]:((~calm(X)|generous(X))))=>((~kind(paul)&wise(paul))))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)<~>~kind(X))))&
(~strong(paul))&
(~curious(paul))&
(~patient(paul))&
(?[X]:((~creative(X)<~>~brave(X))))&
((humble(paul)&~happy(paul)))&
(?[X]:((quiet(X)<~>patient(X)))) | ~calm(alice) | [
"p3",
"p15",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 673808953859526978533682
% SZS output start Proof for 673808953859526978533682
4. ! [X0] : ((~strong(X0) & patient(X0)) <=> (tall(X0) | ~kind(X0))) [input p3]
16. ? [X0] : (generous(X0) | ~calm(X0)) => (wise(paul) & ~kind(paul)) [input p15]
21. ~patient(paul) [input p20]
25. ~calm(alice) [input hypothesis]
40. (wise(paul) & ~kind(paul)) | ! [X0] : (~generous(X0) & calm(X0)) [ennf transformation 16]
48. ! [X0] : (((~strong(X0) & patient(X0)) | (~tall(X0) & kind(X0))) & ((tall(X0) | ~kind(X0)) | (strong(X0) | ~patient(X0)))) [nnf transformation 4]
49. ! [X0] : (((~strong(X0) & patient(X0)) | (~tall(X0) & kind(X0))) & (tall(X0) | ~kind(X0) | strong(X0) | ~patient(X0))) [flattening 48]
81. kind(X0) | patient(X0) [cnf transformation 49]
108. ~kind(paul) | calm(X0) [cnf transformation 40]
117. ~patient(paul) [cnf transformation 21]
124. ~calm(alice) [cnf transformation 25]
215. 20 <=> kind(paul) [avatar definition]
217. ~kind(paul) <- (~20) [avatar component clause 215]
220. 21 <=> ! [X0] : calm(X0) [avatar definition]
221. calm(X0) <- (21) [avatar component clause 220]
222. 21 | ~20 [avatar split clause 108,215,220]
254. patient(paul) <- (~20) [resolution 81,217]
256. $false <- (~20) [subsumption resolution 254,117]
257. 20 [avatar contradiction clause 256]
260. $false <- (21) [resolution 221,124]
261. ~21 [avatar contradiction clause 260]
262. $false [avatar sat refutation 222,257,261]
% SZS output end Proof for 673808953859526978533682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is either not strong or not patient and vice versa.
If susan is brave then someone is not generous or happy and vice versa.
Everyone who is either not old or wise is both strong and not creative and vice versa.
Everyone who is not happy is both generous and wise.
If someone is both not funny and happy then someone is not wise.
Everyone who is kind is both not curious and generous.
Everyone who is either not calm or calm is both not patient and brave and vice versa.
Everyone who is brave or not rich is calm.
Everyone who is quiet or humble is generous or not creative and vice versa.
Everyone who is both kind and not old is patient or not calm.
If lucy is not curious then someone is not quiet.
Everyone who is either happy or not strong is either creative or happy and vice versa.
If someone is both not brave and not tall then someone is not kind.
Everyone who is not quiet or rich is both not old and not calm.
If john is either not strong or not funny then john is both creative and not old and vice versa.
Everyone who is not old or humble is not generous and vice versa.
Someone is kind or generous.
Someone is either wise or creative.
Paul is not tall or kind.
Alice is either rich or not kind. | Paul is not humble. | entailment | (![X]:(rich(X)<=>(~strong(X)<~>~patient(X))))&
((brave(susan))<=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~old(X)<~>wise(X))<=>(strong(X)&~creative(X))))&
(![X]:(~happy(X)=>(generous(X)&wise(X))))&
((?[X]:((~funny(X)&happy(X))))=>(?[X]:(~wise(X))))&
(![X]:(kind(X)=>(~curious(X)&generous(X))))&
(![X]:((~calm(X)<~>calm(X))<=>(~patient(X)&brave(X))))&
(![X]:((brave(X)|~rich(X))=>calm(X)))&
(![X]:((quiet(X)|humble(X))<=>(generous(X)|~creative(X))))&
(![X]:((kind(X)&~old(X))=>(patient(X)|~calm(X))))&
((~curious(lucy))=>(?[X]:(~quiet(X))))&
(![X]:((happy(X)<~>~strong(X))<=>(creative(X)<~>happy(X))))&
((?[X]:((~brave(X)&~tall(X))))=>(?[X]:(~kind(X))))&
(![X]:((~quiet(X)|rich(X))=>(~old(X)&~calm(X))))&
(((~strong(john)<~>~funny(john)))<=>((creative(john)&~old(john))))&
(![X]:((~old(X)|humble(X))<=>~generous(X)))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((wise(X)<~>creative(X))))&
((~tall(paul)|kind(paul)))&
((rich(alice)<~>~kind(alice))) | ~humble(paul) | [
"p0",
"p6",
"p7",
"p8",
"p11",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 1324838204856656372717471
% SZS output start Proof for 1324838204856656372717471
1. ! [X0] : (rich(X0) <=> (~strong(X0) <~> ~patient(X0))) [input p0]
7. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> (brave(X0) & ~patient(X0))) [input p6]
8. ! [X0] : ((~rich(X0) | brave(X0)) => calm(X0)) [input p7]
9. ! [X0] : ((humble(X0) | quiet(X0)) <=> (~creative(X0) | generous(X0))) [input p8]
12. ! [X0] : ((happy(X0) <~> ~strong(X0)) <=> (creative(X0) <~> happy(X0))) [input p11]
14. ! [X0] : ((rich(X0) | ~quiet(X0)) => (~calm(X0) & ~old(X0))) [input p13]
16. ! [X0] : ((humble(X0) | ~old(X0)) <=> ~generous(X0)) [input p15]
21. humble(paul) [input hypothesis]
27. ! [X0] : (calm(X0) | (rich(X0) & ~brave(X0))) [ennf transformation 8]
32. ! [X0] : ((~calm(X0) & ~old(X0)) | (~rich(X0) & quiet(X0))) [ennf transformation 14]
33. ! [X0] : ((rich(X0) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) & (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~rich(X0))) [nnf transformation 1]
43. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~brave(X0) | patient(X0))) & ((brave(X0) & ~patient(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 7]
44. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~brave(X0) | patient(X0)) & ((brave(X0) & ~patient(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [flattening 43]
45. ! [X0] : (((humble(X0) | quiet(X0)) | (creative(X0) & ~generous(X0))) & ((~creative(X0) | generous(X0)) | (~humble(X0) & ~quiet(X0)))) [nnf transformation 9]
46. ! [X0] : ((humble(X0) | quiet(X0) | (creative(X0) & ~generous(X0))) & (~creative(X0) | generous(X0) | (~humble(X0) & ~quiet(X0)))) [flattening 45]
49. ! [X0] : ((((strong(X0) | ~happy(X0)) & (~strong(X0) | happy(X0))) | ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0)))) & (((~happy(X0) | ~creative(X0)) & (happy(X0) | creative(X0))) | ((happy(X0) | strong(X0)) & (~strong(X0) | ~happy(X0))))) [nnf transformation 12]
55. ! [X0] : (((humble(X0) | ~old(X0)) | generous(X0)) & (~generous(X0) | (~humble(X0) & old(X0)))) [nnf transformation 16]
56. ! [X0] : ((humble(X0) | ~old(X0) | generous(X0)) & (~generous(X0) | (~humble(X0) & old(X0)))) [flattening 55]
66. ~strong(X0) | rich(X0) | patient(X0) [cnf transformation 33]
81. ~patient(X0) | calm(X0) | calm(X0) [cnf transformation 44]
82. ~patient(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 44]
83. brave(X0) | calm(X0) | calm(X0) [cnf transformation 44]
84. brave(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 44]
87. calm(X0) | ~brave(X0) [cnf transformation 27]
89. ~quiet(X0) | generous(X0) | ~creative(X0) [cnf transformation 46]
96. happy(X0) | creative(X0) | happy(X0) | strong(X0) [cnf transformation 49]
102. strong(X0) | ~happy(X0) | creative(X0) | ~happy(X0) [cnf transformation 49]
106. ~calm(X0) | quiet(X0) [cnf transformation 32]
107. ~calm(X0) | ~rich(X0) [cnf transformation 32]
115. ~humble(X0) | ~generous(X0) [cnf transformation 56]
123. humble(paul) [cnf transformation 21]
124. happy(X0) | creative(X0) | strong(X0) [duplicate literal removal 96]
127. ~happy(X0) | strong(X0) | creative(X0) [duplicate literal removal 102]
128. ~patient(X0) | calm(X0) [duplicate literal removal 81]
129. ~calm(X0) | ~patient(X0) [duplicate literal removal 82]
130. brave(X0) | calm(X0) [duplicate literal removal 83]
131. ~calm(X0) | brave(X0) [duplicate literal removal 84]
161. brave(X0) [subsumption resolution 130,131]
162. ~patient(X0) [subsumption resolution 128,129]
163. calm(X0) [subsumption resolution 87,161]
176. creative(X0) | strong(X0) [subsumption resolution 124,127]
177. ~rich(X0) [subsumption resolution 107,163]
178. quiet(X0) [subsumption resolution 106,163]
227. ~generous(paul) [resolution 115,123]
267. ~creative(X0) | generous(X0) [resolution 89,178]
306. generous(X0) | strong(X0) [resolution 267,176]
416. strong(paul) [resolution 306,227]
419. rich(paul) | patient(paul) [resolution 416,66]
429. patient(paul) [subsumption resolution 419,177]
430. $false [subsumption resolution 429,162]
% SZS output end Proof for 1324838204856656372717471
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both not quiet and not strong.
If someone is either not curious or not wise then someone is not tall or tall.
If john is happy then mary is quiet.
If someone is either calm or not brave then someone is not old and vice versa.
If someone is patient or not funny then someone is both not humble and not calm.
If paul is both not generous and quiet then john is not old.
Everyone who is both not kind and not wise is not brave or quiet.
If someone is not brave or kind then lucy is both tall and wise and vice versa.
If someone is both calm and not brave then susan is humble and vice versa.
If someone is tall then alice is creative or not curious and vice versa.
If someone is not curious or not creative then someone is not humble and vice versa.
If lucy is either not creative or not happy then susan is both happy and not patient and vice versa.
If paul is funny then someone is not curious or humble.
If someone is either wise or generous then someone is either funny or not funny and vice versa.
If alice is not quiet then someone is not funny or not rich.
If susan is not patient or not quiet then someone is both old and not brave.
Lucy is either not quiet or tall.
Someone is both not quiet and strong.
Someone is happy.
Mary is quiet.
Someone is rich.
Susan is both not quiet and not happy.
Someone is brave or not creative.
Mary is not kind. | Mary is not calm. | entailment | (![X]:(calm(X)=>(~quiet(X)&~strong(X))))&
((?[X]:((~curious(X)<~>~wise(X))))=>(?[X]:((~tall(X)|tall(X)))))&
((happy(john))=>(quiet(mary)))&
((?[X]:((calm(X)<~>~brave(X))))<=>(?[X]:(~old(X))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~humble(X)&~calm(X)))))&
(((~generous(paul)&quiet(paul)))=>(~old(john)))&
(![X]:((~kind(X)&~wise(X))=>(~brave(X)|quiet(X))))&
((?[X]:((~brave(X)|kind(X))))<=>((tall(lucy)&wise(lucy))))&
((?[X]:((calm(X)&~brave(X))))<=>(humble(susan)))&
((?[X]:(tall(X)))<=>((creative(alice)|~curious(alice))))&
((?[X]:((~curious(X)|~creative(X))))<=>(?[X]:(~humble(X))))&
(((~creative(lucy)<~>~happy(lucy)))<=>((happy(susan)&~patient(susan))))&
((funny(paul))=>(?[X]:((~curious(X)|humble(X)))))&
((?[X]:((wise(X)<~>generous(X))))<=>(?[X]:((funny(X)<~>~funny(X)))))&
((~quiet(alice))=>(?[X]:((~funny(X)|~rich(X)))))&
(((~patient(susan)|~quiet(susan)))=>(?[X]:((old(X)&~brave(X)))))&
((~quiet(lucy)<~>tall(lucy)))&
(?[X]:((~quiet(X)&strong(X))))&
(?[X]:(happy(X)))&
(quiet(mary))&
(?[X]:(rich(X)))&
((~quiet(susan)&~happy(susan)))&
(?[X]:((brave(X)|~creative(X))))&
(~kind(mary)) | ~calm(mary) | [
"p0",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 7043722325055084727766226
% SZS output start Proof for 7043722325055084727766226
1. ! [X0] : (calm(X0) => (~strong(X0) & ~quiet(X0))) [input p0]
20. quiet(mary) [input p19]
25. calm(mary) [input hypothesis]
31. ! [X0] : ((~strong(X0) & ~quiet(X0)) | ~calm(X0)) [ennf transformation 1]
95. ~quiet(X0) | ~calm(X0) [cnf transformation 31]
149. quiet(mary) [cnf transformation 20]
155. calm(mary) [cnf transformation 25]
165. 2 <=> quiet(mary) [avatar definition]
167. quiet(mary) <- (2) [avatar component clause 165]
397. 2 [avatar split clause 149,165]
415. ~calm(mary) <- (2) [resolution 95,167]
417. $false <- (2) [subsumption resolution 415,155]
418. ~2 [avatar contradiction clause 417]
419. $false [avatar sat refutation 397,418]
% SZS output end Proof for 7043722325055084727766226
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and generous is both not patient and not strong and vice versa.
If someone is either not brave or not patient then paul is not funny or not quiet.
Everyone who is both not happy and curious is patient and vice versa.
If mary is tall then someone is either not kind or not generous and vice versa.
If mary is not generous or not patient then someone is patient or not humble and vice versa.
Everyone who is both brave and not rich is either kind or not calm.
Everyone who is either not happy or not curious is old.
Everyone who is old is old or not strong and vice versa.
Everyone who is not kind is not patient and vice versa.
Everyone who is not patient is both not humble and brave.
Everyone who is both not happy and curious is happy and vice versa.
Everyone who is funny or patient is not happy.
If paul is wise then someone is not kind and vice versa.
If someone is curious or not wise then john is calm or patient and vice versa.
Everyone who is quiet is either curious or rich.
Someone is not tall or humble.
Someone is either funny or strong.
Someone is not tall or quiet.
Someone is either curious or generous.
Paul is either generous or not quiet. | Paul is wise. | entailment | (![X]:((wise(X)&generous(X))<=>(~patient(X)&~strong(X))))&
((?[X]:((~brave(X)<~>~patient(X))))=>((~funny(paul)|~quiet(paul))))&
(![X]:((~happy(X)&curious(X))<=>patient(X)))&
((tall(mary))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
(((~generous(mary)|~patient(mary)))<=>(?[X]:((patient(X)|~humble(X)))))&
(![X]:((brave(X)&~rich(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~happy(X)<~>~curious(X))=>old(X)))&
(![X]:(old(X)<=>(old(X)|~strong(X))))&
(![X]:(~kind(X)<=>~patient(X)))&
(![X]:(~patient(X)=>(~humble(X)&brave(X))))&
(![X]:((~happy(X)&curious(X))<=>happy(X)))&
(![X]:((funny(X)|patient(X))=>~happy(X)))&
((wise(paul))<=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)|~wise(X))))<=>((calm(john)|patient(john))))&
(![X]:(quiet(X)=>(curious(X)<~>rich(X))))&
(?[X]:((~tall(X)|humble(X))))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:((~tall(X)|quiet(X))))&
(?[X]:((curious(X)<~>generous(X))))&
((generous(paul)<~>~quiet(paul))) | wise(paul) | [
"p2",
"p8",
"p10",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 80981227516921406195306
% SZS output start Proof for 80981227516921406195306
3. ! [X0] : ((curious(X0) & ~happy(X0)) <=> patient(X0)) [input p2]
9. ! [X0] : (~kind(X0) <=> ~patient(X0)) [input p8]
11. ! [X0] : ((curious(X0) & ~happy(X0)) <=> happy(X0)) [input p10]
13. wise(paul) <=> ? [X0] : ~kind(X0) [input p12]
21. ~wise(paul) [input hypothesis]
33. ! [X0] : (((curious(X0) & ~happy(X0)) | ~patient(X0)) & (patient(X0) | (~curious(X0) | happy(X0)))) [nnf transformation 3]
34. ! [X0] : (((curious(X0) & ~happy(X0)) | ~patient(X0)) & (patient(X0) | ~curious(X0) | happy(X0))) [flattening 33]
48. ! [X0] : ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0))) [nnf transformation 9]
49. ! [X0] : (((curious(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | (~curious(X0) | happy(X0)))) [nnf transformation 11]
50. ! [X0] : (((curious(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | ~curious(X0) | happy(X0))) [flattening 49]
51. (wise(paul) | ! [X0] : kind(X0)) & (? [X0] : ~kind(X0) | ~wise(paul)) [nnf transformation 13]
52. (wise(paul) | ! [X0] : kind(X0)) & (? [X1] : ~kind(X1) | ~wise(paul)) [rectify 51]
53. ? [X1] : ~kind(X1) => ~kind(sK2) [choice axiom]
54. (wise(paul) | ! [X0] : kind(X0)) & (~kind(sK2) | ~wise(paul)) [skolemisation 52,53]
80. ~patient(X0) | curious(X0) [cnf transformation 34]
97. ~kind(X0) | patient(X0) [cnf transformation 48]
100. happy(X0) | ~curious(X0) | happy(X0) [cnf transformation 50]
101. ~happy(X0) | ~happy(X0) [cnf transformation 50]
106. wise(paul) | kind(X0) [cnf transformation 54]
121. ~wise(paul) [cnf transformation 21]
122. happy(X0) | ~curious(X0) [duplicate literal removal 100]
123. ~happy(X0) [duplicate literal removal 101]
188. ~curious(X0) [subsumption resolution 122,123]
190. 16 <=> ! [X0] : kind(X0) [avatar definition]
191. kind(X0) <- (16) [avatar component clause 190]
193. 17 <=> wise(paul) [avatar definition]
196. 16 | 17 [avatar split clause 106,193,190]
258. ~17 [avatar split clause 121,193]
267. patient(X0) <- (16) [resolution 97,191]
269. curious(X1) <- (16) [resolution 267,80]
272. $false <- (16) [subsumption resolution 269,188]
273. ~16 [avatar contradiction clause 272]
274. $false [avatar sat refutation 196,258,273]
% SZS output end Proof for 80981227516921406195306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not humble and creative then someone is tall or creative.
If someone is either brave or not wise then someone is either not humble or humble and vice versa.
Everyone who is not curious is either strong or not funny.
Everyone who is both calm and funny is both not calm and not kind and vice versa.
Everyone who is rich is either not generous or rich and vice versa.
Everyone who is not kind is either not kind or not rich and vice versa.
Everyone who is both old and funny is either strong or not funny.
Everyone who is either wise or not calm is not calm or not strong.
If someone is old or not happy then someone is both strong and patient.
Everyone who is old or not old is humble or not humble.
If susan is either not patient or curious then john is both not calm and creative.
If alice is not generous or brave then lucy is not curious and vice versa.
If lucy is brave or kind then susan is not rich or kind.
If someone is brave or not humble then someone is both not wise and happy.
If alice is either tall or generous then lucy is quiet and vice versa.
Everyone who is both curious and strong is not creative or funny and vice versa.
Someone is happy.
John is not curious or not rich.
Alice is either rich or not strong.
Alice is either not curious or rich.
Lucy is either humble or tall.
Fred is generous or not tall.
Someone is old. | Lucy is not rich. | contradiction | (((~humble(mary)&creative(mary)))=>(?[X]:((tall(X)|creative(X)))))&
((?[X]:((brave(X)<~>~wise(X))))<=>(?[X]:((~humble(X)<~>humble(X)))))&
(![X]:(~curious(X)=>(strong(X)<~>~funny(X))))&
(![X]:((calm(X)&funny(X))<=>(~calm(X)&~kind(X))))&
(![X]:(rich(X)<=>(~generous(X)<~>rich(X))))&
(![X]:(~kind(X)<=>(~kind(X)<~>~rich(X))))&
(![X]:((old(X)&funny(X))=>(strong(X)<~>~funny(X))))&
(![X]:((wise(X)<~>~calm(X))=>(~calm(X)|~strong(X))))&
((?[X]:((old(X)|~happy(X))))=>(?[X]:((strong(X)&patient(X)))))&
(![X]:((old(X)|~old(X))=>(humble(X)|~humble(X))))&
(((~patient(susan)<~>curious(susan)))=>((~calm(john)&creative(john))))&
(((~generous(alice)|brave(alice)))<=>(~curious(lucy)))&
(((brave(lucy)|kind(lucy)))=>((~rich(susan)|kind(susan))))&
((?[X]:((brave(X)|~humble(X))))=>(?[X]:((~wise(X)&happy(X)))))&
(((tall(alice)<~>generous(alice)))<=>(quiet(lucy)))&
(![X]:((curious(X)&strong(X))<=>(~creative(X)|funny(X))))&
(?[X]:(happy(X)))&
((~curious(john)|~rich(john)))&
((rich(alice)<~>~strong(alice)))&
((~curious(alice)<~>rich(alice)))&
((humble(lucy)<~>tall(lucy)))&
((generous(fred)|~tall(fred)))&
(?[X]:(old(X))) | ~rich(lucy) | [
"p5",
"hypothesis"
]
| % SZS status Unsatisfiable for 4889544134917937755451995
% SZS output start Proof for 4889544134917937755451995
6. ! [X0] : (~kind(X0) <=> (~kind(X0) <~> ~rich(X0))) [input p5]
24. ~rich(lucy) [input hypothesis]
56. ! [X0] : ((~kind(X0) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | kind(X0))) [nnf transformation 6]
96. rich(X0) | kind(X0) | kind(X0) [cnf transformation 56]
98. ~kind(X0) | ~kind(X0) | rich(X0) [cnf transformation 56]
136. ~rich(lucy) [cnf transformation 24]
139. rich(X0) | kind(X0) [duplicate literal removal 96]
140. ~kind(X0) | rich(X0) [duplicate literal removal 98]
185. rich(X0) [subsumption resolution 139,140]
281. $false [subsumption resolution 136,185]
% SZS output end Proof for 4889544134917937755451995
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or humble then fred is both not funny and not rich.
Everyone who is either rich or not rich is both old and quiet and vice versa.
Everyone who is tall is not funny or not quiet and vice versa.
If someone is brave or quiet then someone is either calm or wise.
Everyone who is curious is either patient or not humble and vice versa.
If lucy is generous or not tall then someone is either not creative or not generous.
If paul is not generous then susan is calm.
If someone is both not brave and old then someone is happy or old and vice versa.
Everyone who is both not curious and not kind is either generous or not funny and vice versa.
If mary is old then someone is either not rich or creative and vice versa.
Everyone who is tall is not curious and vice versa.
Everyone who is both not rich and not patient is either rich or brave and vice versa.
If paul is not patient or strong then someone is not rich and vice versa.
Everyone who is either generous or curious is both not calm and calm.
Everyone who is both tall and brave is both wise and not tall and vice versa.
Everyone who is creative is not calm or wise and vice versa.
Someone is not funny.
Someone is either creative or not quiet.
Someone is not brave. | Mary is not funny. | entailment | ((?[X]:((kind(X)|humble(X))))=>((~funny(fred)&~rich(fred))))&
(![X]:((rich(X)<~>~rich(X))<=>(old(X)&quiet(X))))&
(![X]:(tall(X)<=>(~funny(X)|~quiet(X))))&
((?[X]:((brave(X)|quiet(X))))=>(?[X]:((calm(X)<~>wise(X)))))&
(![X]:(curious(X)<=>(patient(X)<~>~humble(X))))&
(((generous(lucy)|~tall(lucy)))=>(?[X]:((~creative(X)<~>~generous(X)))))&
((~generous(paul))=>(calm(susan)))&
((?[X]:((~brave(X)&old(X))))<=>(?[X]:((happy(X)|old(X)))))&
(![X]:((~curious(X)&~kind(X))<=>(generous(X)<~>~funny(X))))&
((old(mary))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:(tall(X)<=>~curious(X)))&
(![X]:((~rich(X)&~patient(X))<=>(rich(X)<~>brave(X))))&
(((~patient(paul)|strong(paul)))<=>(?[X]:(~rich(X))))&
(![X]:((generous(X)<~>curious(X))=>(~calm(X)&calm(X))))&
(![X]:((tall(X)&brave(X))<=>(wise(X)&~tall(X))))&
(![X]:(creative(X)<=>(~calm(X)|wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)<~>~quiet(X))))&
(?[X]:(~brave(X))) | ~funny(mary) | [
"p1",
"p2",
"p8",
"p10",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 91570444652617932794182
% SZS output start Proof for 91570444652617932794182
2. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> (quiet(X0) & old(X0))) [input p1]
3. ! [X0] : (tall(X0) <=> (~quiet(X0) | ~funny(X0))) [input p2]
9. ! [X0] : ((~kind(X0) & ~curious(X0)) <=> (generous(X0) <~> ~funny(X0))) [input p8]
11. ! [X0] : (tall(X0) <=> ~curious(X0)) [input p10]
14. ! [X0] : ((generous(X0) <~> curious(X0)) => (calm(X0) & ~calm(X0))) [input p13]
20. funny(mary) [input hypothesis]
27. ! [X0] : ((calm(X0) & ~calm(X0)) | (generous(X0) <=> curious(X0))) [ennf transformation 14]
28. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | (~quiet(X0) | ~old(X0))) & ((quiet(X0) & old(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 2]
29. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ~quiet(X0) | ~old(X0)) & ((quiet(X0) & old(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [flattening 28]
30. ! [X0] : ((tall(X0) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | ~tall(X0))) [nnf transformation 3]
31. ! [X0] : ((tall(X0) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~tall(X0))) [flattening 30]
45. ! [X0] : (((~kind(X0) & ~curious(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (kind(X0) | curious(X0)))) [nnf transformation 9]
46. ! [X0] : (((~kind(X0) & ~curious(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | kind(X0) | curious(X0))) [flattening 45]
51. ! [X0] : ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))) [nnf transformation 11]
59. ! [X0] : ((calm(X0) & ~calm(X0)) | ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) [nnf transformation 27]
77. quiet(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 29]
78. quiet(X0) | rich(X0) | rich(X0) [cnf transformation 29]
81. ~quiet(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 31]
82. tall(X0) | funny(X0) [cnf transformation 31]
104. ~generous(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 46]
113. curious(X0) | tall(X0) [cnf transformation 51]
124. ~calm(X0) | generous(X0) | ~curious(X0) [cnf transformation 59]
126. calm(X0) | generous(X0) | ~curious(X0) [cnf transformation 59]
138. funny(mary) [cnf transformation 20]
145. quiet(X0) | ~rich(X0) [duplicate literal removal 77]
146. quiet(X0) | rich(X0) [duplicate literal removal 78]
165. quiet(X0) [subsumption resolution 145,146]
167. ~tall(X0) | ~funny(X0) [subsumption resolution 81,165]
246. ~curious(X0) | generous(X0) [subsumption resolution 124,126]
255. generous(X0) | tall(X0) [resolution 246,113]
273. ~funny(X0) | ~curious(X0) | tall(X0) [resolution 104,255]
277. ~curious(X0) | tall(X0) [subsumption resolution 273,82]
278. tall(X0) [subsumption resolution 277,113]
303. ~funny(X0) [resolution 278,167]
304. $false [resolution 303,138]
% SZS output end Proof for 91570444652617932794182
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not creative then paul is not tall. Everyone who is both quiet and not humble is tall or not curious and vice versa. Everyone who is either not patient or humble is not generous or not brave and vice versa. If someone is not kind then someone is curious or humble. If someone is either funny or not generous then someone is both not curious and not brave and vice versa. Everyone who is not old or not generous is funny or calm and vice versa. Everyone who is quiet or not creative is curious. Everyone who is either funny or not generous is either wise or not creative and vice versa. Everyone who is strong or wise is wise or curious. Everyone who is both not kind and funny is not curious or funny and vice versa. Everyone who is not quiet is tall. If susan is happy or not tall then someone is either generous or not curious. If john is either humble or not calm then someone is not curious or not patient. Everyone who is not creative or not happy is both old and wise. If paul is not happy or strong then john is patient or not tall and vice versa. Everyone who is happy or not creative is both not brave and tall. John is tall. Paul is rich or not rich. Lucy is either creative or patient. Someone is either not happy or not strong. Someone is not patient or not brave. | Susan is not brave. | entailment | (((humble(mary)|~creative(mary)))=>(~tall(paul)))&
(![X]:((quiet(X)&~humble(X))<=>(tall(X)|~curious(X))))&
(![X]:((~patient(X)<~>humble(X))<=>(~generous(X)|~brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((curious(X)|humble(X)))))&
((?[X]:((funny(X)<~>~generous(X))))<=>(?[X]:((~curious(X)&~brave(X)))))&
(![X]:((~old(X)|~generous(X))<=>(funny(X)|calm(X))))&
(![X]:((quiet(X)|~creative(X))=>curious(X)))&
(![X]:((funny(X)<~>~generous(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((strong(X)|wise(X))=>(wise(X)|curious(X))))&
(![X]:((~kind(X)&funny(X))<=>(~curious(X)|funny(X))))&
(![X]:(~quiet(X)=>tall(X)))&
(((happy(susan)|~tall(susan)))=>(?[X]:((generous(X)<~>~curious(X)))))&
(((humble(john)<~>~calm(john)))=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:((~creative(X)|~happy(X))=>(old(X)&wise(X))))&
(((~happy(paul)|strong(paul)))<=>((patient(john)|~tall(john))))&
(![X]:((happy(X)|~creative(X))=>(~brave(X)&tall(X))))&
(tall(john))&
((rich(paul)|~rich(paul)))&
((creative(lucy)<~>patient(lucy)))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((~patient(X)|~brave(X)))) | ~brave(susan) | [
"p1",
"p4",
"p6",
"p7",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 7606061656057583085597330
% SZS output start Proof for 7606061656057583085597330
2. ! [X0] : ((~humble(X0) & quiet(X0)) <=> (~curious(X0) | tall(X0))) [input p1]
5. ? [X0] : (funny(X0) <~> ~generous(X0)) <=> ? [X0] : (~brave(X0) & ~curious(X0)) [input p4]
7. ! [X0] : ((~creative(X0) | quiet(X0)) => curious(X0)) [input p6]
8. ! [X0] : ((funny(X0) <~> ~generous(X0)) <=> (wise(X0) <~> ~creative(X0))) [input p7]
14. ! [X0] : ((~happy(X0) | ~creative(X0)) => (wise(X0) & old(X0))) [input p13]
16. ! [X0] : ((~creative(X0) | happy(X0)) => (tall(X0) & ~brave(X0))) [input p15]
22. brave(susan) [input hypothesis]
24. ? [X0] : (funny(X0) <~> ~generous(X0)) <=> ? [X1] : (~brave(X1) & ~curious(X1)) [rectify 5]
27. ! [X0] : (curious(X0) | (creative(X0) & ~quiet(X0))) [ennf transformation 7]
33. ! [X0] : ((wise(X0) & old(X0)) | (happy(X0) & creative(X0))) [ennf transformation 14]
34. ! [X0] : ((tall(X0) & ~brave(X0)) | (creative(X0) & ~happy(X0))) [ennf transformation 16]
35. ! [X0] : (((~humble(X0) & quiet(X0)) | (curious(X0) & ~tall(X0))) & ((~curious(X0) | tall(X0)) | (humble(X0) | ~quiet(X0)))) [nnf transformation 2]
36. ! [X0] : (((~humble(X0) & quiet(X0)) | (curious(X0) & ~tall(X0))) & (~curious(X0) | tall(X0) | humble(X0) | ~quiet(X0))) [flattening 35]
42. (? [X0] : ((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | ! [X1] : (brave(X1) | curious(X1))) & (? [X1] : (~brave(X1) & ~curious(X1)) | ! [X0] : ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0)))) [nnf transformation 24]
43. (? [X0] : ((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | ! [X1] : (brave(X1) | curious(X1))) & (? [X2] : (~brave(X2) & ~curious(X2)) | ! [X3] : ((funny(X3) | generous(X3)) & (~generous(X3) | ~funny(X3)))) [rectify 42]
44. ? [X0] : ((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) => ((generous(sK1) | ~funny(sK1)) & (~generous(sK1) | funny(sK1))) [choice axiom]
45. ? [X2] : (~brave(X2) & ~curious(X2)) => (~brave(sK2) & ~curious(sK2)) [choice axiom]
46. (((generous(sK1) | ~funny(sK1)) & (~generous(sK1) | funny(sK1))) | ! [X1] : (brave(X1) | curious(X1))) & ((~brave(sK2) & ~curious(sK2)) | ! [X3] : ((funny(X3) | generous(X3)) & (~generous(X3) | ~funny(X3)))) [skolemisation 43,45,44]
49. ! [X0] : ((((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | ((wise(X0) | creative(X0)) & (~creative(X0) | ~wise(X0)))) & (((creative(X0) | ~wise(X0)) & (~creative(X0) | wise(X0))) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0))))) [nnf transformation 8]
70. curious(X0) | quiet(X0) [cnf transformation 36]
80. ~curious(sK2) | ~generous(X3) | ~funny(X3) [cnf transformation 46]
81. ~curious(sK2) | funny(X3) | generous(X3) [cnf transformation 46]
90. curious(X0) | ~quiet(X0) [cnf transformation 27]
96. ~wise(X0) | funny(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 49]
98. ~wise(X0) | ~funny(X0) | ~creative(X0) | generous(X0) [cnf transformation 49]
117. happy(X0) | wise(X0) [cnf transformation 33]
122. ~happy(X0) | ~brave(X0) [cnf transformation 34]
123. ~brave(X0) | creative(X0) [cnf transformation 34]
133. brave(susan) [cnf transformation 22]
171. 9 <=> ! [X3] : (funny(X3) | generous(X3)) [avatar definition]
172. funny(X3) | generous(X3) <- (9) [avatar component clause 171]
179. 11 <=> ! [X3] : (~generous(X3) | ~funny(X3)) [avatar definition]
180. ~funny(X3) | ~generous(X3) <- (11) [avatar component clause 179]
183. 12 <=> curious(sK2) [avatar definition]
185. ~curious(sK2) <- (~12) [avatar component clause 183]
186. 9 | ~12 [avatar split clause 81,183,171]
187. 11 | ~12 [avatar split clause 80,183,179]
188. curious(X0) [subsumption resolution 90,70]
202. 15 <=> happy(susan) [avatar definition]
203. happy(susan) <- (15) [avatar component clause 202]
204. ~happy(susan) <- (~15) [avatar component clause 202]
272. $false <- (~12) [subsumption resolution 185,188]
273. 12 [avatar contradiction clause 272]
280. wise(susan) <- (~15) [resolution 117,204]
285. creative(susan) [resolution 123,133]
359. funny(susan) | ~creative(susan) | ~generous(susan) <- (~15) [resolution 96,280]
365. funny(susan) | ~generous(susan) <- (~15) [subsumption resolution 359,285]
404. ~generous(susan) <- (11, ~15) [subsumption resolution 365,180]
417. ~funny(susan) | ~creative(susan) | generous(susan) <- (~15) [resolution 98,280]
421. ~funny(susan) | generous(susan) <- (~15) [subsumption resolution 417,285]
422. ~funny(susan) <- (11, ~15) [subsumption resolution 421,404]
427. generous(susan) <- (9, 11, ~15) [resolution 422,172]
428. $false <- (9, 11, ~15) [subsumption resolution 427,404]
429. ~9 | ~11 | 15 [avatar contradiction clause 428]
442. ~brave(susan) <- (15) [resolution 203,122]
443. $false <- (15) [subsumption resolution 442,133]
444. ~15 [avatar contradiction clause 443]
445. $false [avatar sat refutation 186,187,273,429,444]
% SZS output end Proof for 7606061656057583085597330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not creative and patient is either not strong or rich and vice versa. Everyone who is both not curious and not calm is either creative or not humble and vice versa. If someone is wise or rich then alice is tall or creative and vice versa. If alice is not humble or not creative then someone is either quiet or not strong. Everyone who is happy is not humble or not old and vice versa. Everyone who is either curious or tall is calm or happy. If fred is not generous then alice is brave or not humble and vice versa. Everyone who is not humble is both not creative and not curious. If someone is both tall and brave then someone is generous or wise. Everyone who is either not humble or kind is both kind and not humble and vice versa. If someone is not curious or happy then someone is kind and vice versa. If someone is not calm then someone is not brave or kind and vice versa. Everyone who is rich or wise is either not rich or not tall. If john is not quiet or funny then someone is curious or not old. Everyone who is both not wise and happy is both tall and not rich and vice versa. Someone is either patient or happy. Paul is not quiet or strong. Lucy is both humble and not happy. Fred is both not strong and not creative. Someone is both strong and not happy. Someone is calm or creative. Someone is either quiet or not strong. | Alice is brave. | entailment | (![X]:((~creative(X)&patient(X))<=>(~strong(X)<~>rich(X))))&
(![X]:((~curious(X)&~calm(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:((wise(X)|rich(X))))<=>((tall(alice)|creative(alice))))&
(((~humble(alice)|~creative(alice)))=>(?[X]:((quiet(X)<~>~strong(X)))))&
(![X]:(happy(X)<=>(~humble(X)|~old(X))))&
(![X]:((curious(X)<~>tall(X))=>(calm(X)|happy(X))))&
((~generous(fred))<=>((brave(alice)|~humble(alice))))&
(![X]:(~humble(X)=>(~creative(X)&~curious(X))))&
((?[X]:((tall(X)&brave(X))))=>(?[X]:((generous(X)|wise(X)))))&
(![X]:((~humble(X)<~>kind(X))<=>(kind(X)&~humble(X))))&
((?[X]:((~curious(X)|happy(X))))<=>(?[X]:(kind(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((rich(X)|wise(X))=>(~rich(X)<~>~tall(X))))&
(((~quiet(john)|funny(john)))=>(?[X]:((curious(X)|~old(X)))))&
(![X]:((~wise(X)&happy(X))<=>(tall(X)&~rich(X))))&
(?[X]:((patient(X)<~>happy(X))))&
((~quiet(paul)|strong(paul)))&
((humble(lucy)&~happy(lucy)))&
((~strong(fred)&~creative(fred)))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:((quiet(X)<~>~strong(X)))) | brave(alice) | [
"p5",
"p9",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 619145487640936247045311
% SZS output start Proof for 619145487640936247045311
6. ! [X0] : ((curious(X0) <~> tall(X0)) => (happy(X0) | calm(X0))) [input p5]
10. ! [X0] : ((~humble(X0) <~> kind(X0)) <=> (~humble(X0) & kind(X0))) [input p9]
11. ? [X0] : (happy(X0) | ~curious(X0)) <=> ? [X0] : kind(X0) [input p10]
12. ? [X0] : ~calm(X0) <=> ? [X0] : (kind(X0) | ~brave(X0)) [input p11]
13. ! [X0] : ((wise(X0) | rich(X0)) => (~rich(X0) <~> ~tall(X0))) [input p12]
15. ! [X0] : ((happy(X0) & ~wise(X0)) <=> (~rich(X0) & tall(X0))) [input p14]
23. ~brave(alice) [input hypothesis]
25. ? [X0] : (happy(X0) | ~curious(X0)) <=> ? [X1] : kind(X1) [rectify 11]
26. ? [X0] : ~calm(X0) <=> ? [X1] : (kind(X1) | ~brave(X1)) [rectify 12]
29. ! [X0] : ((happy(X0) | calm(X0)) | (curious(X0) <=> tall(X0))) [ennf transformation 6]
30. ! [X0] : (happy(X0) | calm(X0) | (curious(X0) <=> tall(X0))) [flattening 29]
33. ! [X0] : ((~rich(X0) <~> ~tall(X0)) | (~wise(X0) & ~rich(X0))) [ennf transformation 13]
49. ! [X0] : (happy(X0) | calm(X0) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) [nnf transformation 30]
55. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (humble(X0) | ~kind(X0))) & ((~humble(X0) & kind(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [nnf transformation 10]
56. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | humble(X0) | ~kind(X0)) & ((~humble(X0) & kind(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [flattening 55]
57. (? [X0] : (happy(X0) | ~curious(X0)) | ! [X1] : ~kind(X1)) & (? [X1] : kind(X1) | ! [X0] : (~happy(X0) & curious(X0))) [nnf transformation 25]
58. (? [X0] : (happy(X0) | ~curious(X0)) | ! [X1] : ~kind(X1)) & (? [X2] : kind(X2) | ! [X3] : (~happy(X3) & curious(X3))) [rectify 57]
59. ? [X0] : (happy(X0) | ~curious(X0)) => (happy(sK3) | ~curious(sK3)) [choice axiom]
60. ? [X2] : kind(X2) => kind(sK4) [choice axiom]
61. ((happy(sK3) | ~curious(sK3)) | ! [X1] : ~kind(X1)) & (kind(sK4) | ! [X3] : (~happy(X3) & curious(X3))) [skolemisation 58,60,59]
62. (? [X0] : ~calm(X0) | ! [X1] : (~kind(X1) & brave(X1))) & (? [X1] : (kind(X1) | ~brave(X1)) | ! [X0] : calm(X0)) [nnf transformation 26]
63. (? [X0] : ~calm(X0) | ! [X1] : (~kind(X1) & brave(X1))) & (? [X2] : (kind(X2) | ~brave(X2)) | ! [X3] : calm(X3)) [rectify 62]
64. ? [X0] : ~calm(X0) => ~calm(sK5) [choice axiom]
65. ? [X2] : (kind(X2) | ~brave(X2)) => (kind(sK6) | ~brave(sK6)) [choice axiom]
66. (~calm(sK5) | ! [X1] : (~kind(X1) & brave(X1))) & ((kind(sK6) | ~brave(sK6)) | ! [X3] : calm(X3)) [skolemisation 63,65,64]
67. ! [X0] : (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~wise(X0) & ~rich(X0))) [nnf transformation 33]
70. ! [X0] : (((happy(X0) & ~wise(X0)) | (rich(X0) | ~tall(X0))) & ((~rich(X0) & tall(X0)) | (~happy(X0) | wise(X0)))) [nnf transformation 15]
71. ! [X0] : (((happy(X0) & ~wise(X0)) | rich(X0) | ~tall(X0)) & ((~rich(X0) & tall(X0)) | ~happy(X0) | wise(X0))) [flattening 70]
105. ~curious(X0) | calm(X0) | tall(X0) | happy(X0) [cnf transformation 49]
116. ~humble(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 56]
118. ~kind(X0) | humble(X0) | humble(X0) | ~kind(X0) [cnf transformation 56]
119. kind(sK4) | curious(X3) [cnf transformation 61]
120. kind(sK4) | ~happy(X3) [cnf transformation 61]
123. ~calm(sK5) | brave(X1) [cnf transformation 66]
125. ~tall(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 67]
133. happy(X0) | rich(X0) | ~tall(X0) [cnf transformation 71]
146. ~brave(alice) [cnf transformation 23]
147. ~tall(X0) | ~rich(X0) [duplicate literal removal 125]
149. ~humble(X0) | ~kind(X0) [duplicate literal removal 116]
150. ~kind(X0) | humble(X0) [duplicate literal removal 118]
199. 11 <=> brave(alice) [avatar definition]
201. ~brave(alice) <- (~11) [avatar component clause 199]
216. ~kind(X0) [subsumption resolution 149,150]
218. ~happy(X3) [subsumption resolution 120,216]
219. curious(X3) [subsumption resolution 119,216]
221. 15 <=> ! [X1] : brave(X1) [avatar definition]
222. brave(X1) <- (15) [avatar component clause 221]
224. 16 <=> calm(sK5) [avatar definition]
226. ~calm(sK5) <- (~16) [avatar component clause 224]
227. 15 | ~16 [avatar split clause 123,224,221]
230. 17 <=> ! [X3] : calm(X3) [avatar definition]
231. calm(X3) <- (17) [avatar component clause 230]
237. rich(X0) | ~tall(X0) [subsumption resolution 133,218]
238. ~tall(X0) [subsumption resolution 237,147]
268. ~11 [avatar split clause 146,199]
297. calm(X0) | tall(X0) | happy(X0) [resolution 105,219]
298. calm(X0) | happy(X0) [subsumption resolution 297,238]
299. calm(X0) [subsumption resolution 298,218]
300. 17 [avatar split clause 299,230]
301. $false <- (~16, 17) [resolution 231,226]
303. 16 | ~17 [avatar contradiction clause 301]
304. $false <- (~11, 15) [resolution 222,201]
307. 11 | ~15 [avatar contradiction clause 304]
308. $false [avatar sat refutation 227,268,300,303,307]
% SZS output end Proof for 619145487640936247045311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not happy then someone is not creative and vice versa. If paul is both curious and quiet then someone is curious or not brave and vice versa. Everyone who is either quiet or not funny is both not rich and funny and vice versa. If someone is calm or happy then someone is kind or funny. If fred is either not patient or not quiet then mary is both tall and brave. Everyone who is both not wise and old is old. Everyone who is not rich or happy is brave. If alice is both not funny and not happy then someone is happy. Everyone who is either humble or not happy is brave. If someone is not kind then someone is both brave and not funny. Everyone who is not old is both not old and not brave and vice versa. If someone is not rich or not creative then someone is either old or wise and vice versa. Everyone who is either funny or patient is either rich or not brave and vice versa. Everyone who is not brave or not rich is not funny or wise and vice versa. Everyone who is both not funny and creative is tall and vice versa. If susan is either not brave or not tall then someone is not curious and vice versa. Someone is either humble or generous. Lucy is either not tall or wise. Someone is not old. John is not rich. Someone is both curious and old. Alice is not kind or not brave. Paul is both brave and not kind. Susan is wise or not old. | Paul is not old. | contradiction | ((?[X]:((~brave(X)|~happy(X))))<=>(?[X]:(~creative(X))))&
(((curious(paul)&quiet(paul)))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:((quiet(X)<~>~funny(X))<=>(~rich(X)&funny(X))))&
((?[X]:((calm(X)|happy(X))))=>(?[X]:((kind(X)|funny(X)))))&
(((~patient(fred)<~>~quiet(fred)))=>((tall(mary)&brave(mary))))&
(![X]:((~wise(X)&old(X))=>old(X)))&
(![X]:((~rich(X)|happy(X))=>brave(X)))&
(((~funny(alice)&~happy(alice)))=>(?[X]:(happy(X))))&
(![X]:((humble(X)<~>~happy(X))=>brave(X)))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:(~old(X)<=>(~old(X)&~brave(X))))&
((?[X]:((~rich(X)|~creative(X))))<=>(?[X]:((old(X)<~>wise(X)))))&
(![X]:((funny(X)<~>patient(X))<=>(rich(X)<~>~brave(X))))&
(![X]:((~brave(X)|~rich(X))<=>(~funny(X)|wise(X))))&
(![X]:((~funny(X)&creative(X))<=>tall(X)))&
(((~brave(susan)<~>~tall(susan)))<=>(?[X]:(~curious(X))))&
(?[X]:((humble(X)<~>generous(X))))&
((~tall(lucy)<~>wise(lucy)))&
(?[X]:(~old(X)))&
(~rich(john))&
(?[X]:((curious(X)&old(X))))&
((~kind(alice)|~brave(alice)))&
((brave(paul)&~kind(paul)))&
((wise(susan)|~old(susan))) | ~old(paul) | [
"p10",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 911132683353040832440618
% SZS output start Proof for 911132683353040832440618
11. ! [X0] : (~old(X0) <=> (~brave(X0) & ~old(X0))) [input p10]
23. ~kind(paul) & brave(paul) [input p22]
25. ~old(paul) [input hypothesis]
62. ! [X0] : ((~old(X0) | (brave(X0) | old(X0))) & ((~brave(X0) & ~old(X0)) | old(X0))) [nnf transformation 11]
63. ! [X0] : ((~old(X0) | brave(X0) | old(X0)) & ((~brave(X0) & ~old(X0)) | old(X0))) [flattening 62]
114. ~brave(X0) | old(X0) [cnf transformation 63]
150. brave(paul) [cnf transformation 23]
153. ~old(paul) [cnf transformation 25]
364. old(paul) [resolution 114,150]
368. $false [subsumption resolution 364,153]
% SZS output end Proof for 911132683353040832440618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is wise or calm. If mary is both patient and creative then someone is old or curious. Everyone who is not funny is both creative and not creative. If someone is kind then someone is not kind or curious. Everyone who is both not wise and quiet is both not quiet and not rich. Everyone who is not rich or not happy is not happy or tall. Everyone who is generous or kind is both not kind and creative. If someone is both not calm and not funny then someone is humble or not funny. If someone is wise or not tall then lucy is humble. If someone is both not rich and not patient then lucy is both rich and funny. Everyone who is either not quiet or not old is either not wise or generous. Everyone who is both not creative and not quiet is both generous and tall. If mary is both not tall and not generous then someone is humble or creative and vice versa. Everyone who is either kind or not generous is not wise or not calm. Everyone who is either not rich or wise is creative. Lucy is strong. Someone is humble or not generous. Susan is not curious. Someone is not creative. Mary is either wise or old. Someone is either not creative or not rich. | Mary is not quiet. | entailment | ((?[X]:(~creative(X)))=>(?[X]:((wise(X)|calm(X)))))&
(((patient(mary)&creative(mary)))=>(?[X]:((old(X)|curious(X)))))&
(![X]:(~funny(X)=>(creative(X)&~creative(X))))&
((?[X]:(kind(X)))=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~wise(X)&quiet(X))=>(~quiet(X)&~rich(X))))&
(![X]:((~rich(X)|~happy(X))=>(~happy(X)|tall(X))))&
(![X]:((generous(X)|kind(X))=>(~kind(X)&creative(X))))&
((?[X]:((~calm(X)&~funny(X))))=>(?[X]:((humble(X)|~funny(X)))))&
((?[X]:((wise(X)|~tall(X))))=>(humble(lucy)))&
((?[X]:((~rich(X)&~patient(X))))=>((rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)<~>~old(X))=>(~wise(X)<~>generous(X))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)&tall(X))))&
(((~tall(mary)&~generous(mary)))<=>(?[X]:((humble(X)|creative(X)))))&
(![X]:((kind(X)<~>~generous(X))=>(~wise(X)|~calm(X))))&
(![X]:((~rich(X)<~>wise(X))=>creative(X)))&
(strong(lucy))&
(?[X]:((humble(X)|~generous(X))))&
(~curious(susan))&
(?[X]:(~creative(X)))&
((wise(mary)<~>old(mary)))&
(?[X]:((~creative(X)<~>~rich(X)))) | ~quiet(mary) | [
"p4",
"p6",
"p8",
"p10",
"p11",
"p12",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 412367388655752109271532
% SZS output start Proof for 412367388655752109271532
5. ! [X0] : ((quiet(X0) & ~wise(X0)) => (~rich(X0) & ~quiet(X0))) [input p4]
7. ! [X0] : ((kind(X0) | generous(X0)) => (creative(X0) & ~kind(X0))) [input p6]
9. ? [X0] : (~tall(X0) | wise(X0)) => humble(lucy) [input p8]
11. ! [X0] : ((~quiet(X0) <~> ~old(X0)) => (~wise(X0) <~> generous(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) & ~creative(X0)) => (tall(X0) & generous(X0))) [input p11]
13. (~generous(mary) & ~tall(mary)) <=> ? [X0] : (creative(X0) | humble(X0)) [input p12]
20. wise(mary) <~> old(mary) [input p19]
22. quiet(mary) [input hypothesis]
32. ! [X0] : ((~rich(X0) & ~quiet(X0)) | (~quiet(X0) | wise(X0))) [ennf transformation 5]
33. ! [X0] : ((~rich(X0) & ~quiet(X0)) | ~quiet(X0) | wise(X0)) [flattening 32]
36. ! [X0] : ((creative(X0) & ~kind(X0)) | (~kind(X0) & ~generous(X0))) [ennf transformation 7]
38. humble(lucy) | ! [X0] : (tall(X0) & ~wise(X0)) [ennf transformation 9]
40. ! [X0] : ((~wise(X0) <~> generous(X0)) | (~quiet(X0) <=> ~old(X0))) [ennf transformation 11]
41. ! [X0] : ((tall(X0) & generous(X0)) | (quiet(X0) | creative(X0))) [ennf transformation 12]
42. ! [X0] : ((tall(X0) & generous(X0)) | quiet(X0) | creative(X0)) [flattening 41]
57. ! [X0] : (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0)))) [nnf transformation 40]
58. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & (? [X0] : (creative(X0) | humble(X0)) | (generous(mary) | tall(mary))) [nnf transformation 13]
59. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & (? [X0] : (creative(X0) | humble(X0)) | generous(mary) | tall(mary)) [flattening 58]
60. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & (? [X1] : (creative(X1) | humble(X1)) | generous(mary) | tall(mary)) [rectify 59]
61. ? [X1] : (creative(X1) | humble(X1)) => (creative(sK4) | humble(sK4)) [choice axiom]
62. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & ((creative(sK4) | humble(sK4)) | generous(mary) | tall(mary)) [skolemisation 60,61]
69. (~old(mary) | ~wise(mary)) & (old(mary) | wise(mary)) [nnf transformation 20]
78. ~quiet(X0) | ~quiet(X0) | wise(X0) [cnf transformation 33]
84. ~generous(X0) | creative(X0) [cnf transformation 36]
87. humble(lucy) | ~wise(X0) [cnf transformation 38]
92. generous(X0) | ~wise(X0) | ~quiet(X0) | old(X0) [cnf transformation 57]
95. generous(X0) | quiet(X0) | creative(X0) [cnf transformation 42]
100. ~generous(mary) | ~humble(X0) [cnf transformation 62]
101. ~generous(mary) | ~creative(X0) [cnf transformation 62]
110. ~old(mary) | ~wise(mary) [cnf transformation 69]
113. quiet(mary) [cnf transformation 22]
115. ~quiet(X0) | wise(X0) [duplicate literal removal 78]
163. 12 <=> humble(lucy) [avatar definition]
165. humble(lucy) <- (12) [avatar component clause 163]
168. 13 <=> ! [X0] : ~wise(X0) [avatar definition]
169. ~wise(X0) <- (13) [avatar component clause 168]
170. 13 | 12 [avatar split clause 87,163,168]
180. ~quiet(X0) | generous(X0) | old(X0) [subsumption resolution 92,115]
181. quiet(X0) | creative(X0) [subsumption resolution 95,84]
183. 16 <=> ! [X0] : ~creative(X0) [avatar definition]
184. ~creative(X0) <- (16) [avatar component clause 183]
186. 17 <=> generous(mary) [avatar definition]
189. 16 | ~17 [avatar split clause 101,186,183]
191. 18 <=> ! [X0] : ~humble(X0) [avatar definition]
192. ~humble(X0) <- (18) [avatar component clause 191]
193. 18 | ~17 [avatar split clause 100,186,191]
219. 24 <=> wise(mary) [avatar definition]
223. 25 <=> old(mary) [avatar definition]
226. ~24 | ~25 [avatar split clause 110,223,219]
238. $false <- (12, 18) [subsumption resolution 165,192]
239. ~12 | ~18 [avatar contradiction clause 238]
247. wise(mary) [resolution 115,113]
249. wise(X0) | creative(X0) [resolution 181,115]
265. generous(mary) | old(mary) [resolution 180,113]
271. 24 [avatar split clause 247,219]
273. 25 | 17 [avatar split clause 265,186,223]
274. creative(X0) <- (13) [resolution 169,249]
275. $false <- (13, 16) [subsumption resolution 274,184]
276. ~13 | ~16 [avatar contradiction clause 275]
277. $false [avatar sat refutation 170,189,193,226,239,271,273,276]
% SZS output end Proof for 412367388655752109271532
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and not funny then paul is either not old or not calm and vice versa. If someone is both not old and not rich then someone is both quiet and kind. If alice is both creative and quiet then someone is not humble or old and vice versa. Everyone who is either not humble or humble is rich. If fred is both funny and not humble then mary is not kind or curious and vice versa. If lucy is either strong or old then someone is not tall or funny and vice versa. Everyone who is both not brave and not generous is not old. If susan is either not wise or not curious then someone is rich or not rich. Everyone who is both not quiet and strong is both old and happy. If someone is humble or rich then someone is either not quiet or old. Everyone who is either not humble or not curious is old or brave and vice versa. If john is not humble then someone is calm or not strong. Everyone who is either strong or curious is either not generous or not calm. Everyone who is both curious and not patient is either rich or curious and vice versa. Everyone who is either happy or not calm is either not rich or quiet. If someone is either wise or creative then someone is both not strong and not quiet. Someone is curious or not calm. Mary is not brave. Fred is old. Someone is either not brave or not humble. Someone is either creative or not wise. Someone is kind or not tall. Someone is humble or not rich. | John is not rich. | contradiction | ((?[X]:((~happy(X)&~funny(X))))<=>((~old(paul)<~>~calm(paul))))&
((?[X]:((~old(X)&~rich(X))))=>(?[X]:((quiet(X)&kind(X)))))&
(((creative(alice)&quiet(alice)))<=>(?[X]:((~humble(X)|old(X)))))&
(![X]:((~humble(X)<~>humble(X))=>rich(X)))&
(((funny(fred)&~humble(fred)))<=>((~kind(mary)|curious(mary))))&
(((strong(lucy)<~>old(lucy)))<=>(?[X]:((~tall(X)|funny(X)))))&
(![X]:((~brave(X)&~generous(X))=>~old(X)))&
(((~wise(susan)<~>~curious(susan)))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:((~quiet(X)&strong(X))=>(old(X)&happy(X))))&
((?[X]:((humble(X)|rich(X))))=>(?[X]:((~quiet(X)<~>old(X)))))&
(![X]:((~humble(X)<~>~curious(X))<=>(old(X)|brave(X))))&
((~humble(john))=>(?[X]:((calm(X)|~strong(X)))))&
(![X]:((strong(X)<~>curious(X))=>(~generous(X)<~>~calm(X))))&
(![X]:((curious(X)&~patient(X))<=>(rich(X)<~>curious(X))))&
(![X]:((happy(X)<~>~calm(X))=>(~rich(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>creative(X))))=>(?[X]:((~strong(X)&~quiet(X)))))&
(?[X]:((curious(X)|~calm(X))))&
(~brave(mary))&
(old(fred))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((kind(X)|~tall(X))))&
(?[X]:((humble(X)|~rich(X)))) | ~rich(john) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 7686225235860371347921676
% SZS output start Proof for 7686225235860371347921676
4. ! [X0] : ((~humble(X0) <~> humble(X0)) => rich(X0)) [input p3]
24. ~rich(john) [input hypothesis]
29. ! [X0] : (rich(X0) | (~humble(X0) <=> humble(X0))) [ennf transformation 4]
52. ! [X0] : (rich(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 29]
103. rich(X0) | humble(X0) | humble(X0) [cnf transformation 52]
104. rich(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 52]
159. ~rich(john) [cnf transformation 24]
162. rich(X0) | humble(X0) [duplicate literal removal 103]
163. rich(X0) | ~humble(X0) [duplicate literal removal 104]
229. rich(X0) [subsumption resolution 162,163]
363. $false [subsumption resolution 159,229]
% SZS output end Proof for 7686225235860371347921676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is strong or old then john is patient.
Everyone who is both generous and not calm is funny or tall.
Everyone who is both calm and strong is not patient and vice versa.
If someone is tall then fred is generous or brave.
Everyone who is either not wise or not brave is either not wise or not generous and vice versa.
If someone is quiet then someone is not strong or generous.
If someone is not generous or not funny then someone is either humble or brave and vice versa.
Everyone who is not tall is curious or not old.
Everyone who is not calm is both not rich and not curious.
If someone is both not old and curious then someone is either not funny or generous.
If someone is not calm then someone is not patient.
Everyone who is patient or not happy is either humble or not humble.
If someone is not kind or tall then someone is wise or not funny and vice versa.
Everyone who is strong is not brave and vice versa.
Everyone who is both strong and calm is both not quiet and not patient.
If someone is not calm or brave then someone is not calm or not rich.
Susan is not generous.
Fred is either not generous or not wise.
Alice is both not wise and generous.
Someone is humble or tall.
Paul is either tall or creative.
Someone is quiet.
Fred is generous.
Someone is creative. | Fred is not strong. | entailment | (((strong(alice)|old(alice)))=>(patient(john)))&
(![X]:((generous(X)&~calm(X))=>(funny(X)|tall(X))))&
(![X]:((calm(X)&strong(X))<=>~patient(X)))&
((?[X]:(tall(X)))=>((generous(fred)|brave(fred))))&
(![X]:((~wise(X)<~>~brave(X))<=>(~wise(X)<~>~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~strong(X)|generous(X)))))&
((?[X]:((~generous(X)|~funny(X))))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~tall(X)=>(curious(X)|~old(X))))&
(![X]:(~calm(X)=>(~rich(X)&~curious(X))))&
((?[X]:((~old(X)&curious(X))))=>(?[X]:((~funny(X)<~>generous(X)))))&
((?[X]:(~calm(X)))=>(?[X]:(~patient(X))))&
(![X]:((patient(X)|~happy(X))=>(humble(X)<~>~humble(X))))&
((?[X]:((~kind(X)|tall(X))))<=>(?[X]:((wise(X)|~funny(X)))))&
(![X]:(strong(X)<=>~brave(X)))&
(![X]:((strong(X)&calm(X))=>(~quiet(X)&~patient(X))))&
((?[X]:((~calm(X)|brave(X))))=>(?[X]:((~calm(X)|~rich(X)))))&
(~generous(susan))&
((~generous(fred)<~>~wise(fred)))&
((~wise(alice)&generous(alice)))&
(?[X]:((humble(X)|tall(X))))&
((tall(paul)<~>creative(paul)))&
(?[X]:(quiet(X)))&
(generous(fred))&
(?[X]:(creative(X))) | ~strong(fred) | [
"p4",
"p13",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 334670398597499875111830
% SZS output start Proof for 334670398597499875111830
5. ! [X0] : ((~wise(X0) <~> ~brave(X0)) <=> (~wise(X0) <~> ~generous(X0))) [input p4]
14. ! [X0] : (strong(X0) <=> ~brave(X0)) [input p13]
23. generous(fred) [input p22]
25. strong(fred) [input hypothesis]
51. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) & (((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [nnf transformation 5]
73. ! [X0] : ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0))) [nnf transformation 14]
90. ~generous(X0) | ~wise(X0) | ~wise(X0) | brave(X0) [cnf transformation 51]
95. brave(X0) | wise(X0) | ~generous(X0) | wise(X0) [cnf transformation 51]
115. ~brave(X0) | ~strong(X0) [cnf transformation 73]
128. generous(fred) [cnf transformation 23]
130. strong(fred) [cnf transformation 25]
131. ~generous(X0) | ~wise(X0) | brave(X0) [duplicate literal removal 90]
134. brave(X0) | wise(X0) | ~generous(X0) [duplicate literal removal 95]
153. 5 <=> generous(fred) [avatar definition]
155. generous(fred) <- (5) [avatar component clause 153]
157. 6 <=> brave(fred) [avatar definition]
159. brave(fred) <- (6) [avatar component clause 157]
162. ~generous(X0) | brave(X0) [subsumption resolution 131,134]
281. 5 [avatar split clause 128,153]
287. brave(fred) <- (5) [resolution 162,155]
288. 6 | ~5 [avatar split clause 287,153,157]
290. ~strong(fred) <- (6) [resolution 159,115]
291. $false <- (6) [subsumption resolution 290,130]
292. ~6 [avatar contradiction clause 291]
293. $false [avatar sat refutation 281,288,292]
% SZS output end Proof for 334670398597499875111830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then someone is both not funny and not old.
Everyone who is either wise or generous is creative.
Everyone who is not patient is either not tall or kind and vice versa.
Everyone who is curious is either rich or not wise.
Everyone who is either creative or not brave is calm and vice versa.
If someone is either quiet or not calm then someone is patient or not funny.
If alice is either not creative or not quiet then susan is not kind and vice versa.
Everyone who is not creative or not rich is not quiet and vice versa.
If john is both creative and humble then fred is both not rich and funny.
Everyone who is both old and tall is either creative or not creative and vice versa.
Everyone who is not brave is either not old or patient and vice versa.
Everyone who is rich is either not kind or quiet.
If someone is both curious and generous then someone is both curious and rich.
If john is patient then someone is both patient and not brave.
Everyone who is not calm or calm is generous or rich.
Everyone who is either brave or not patient is generous or funny.
Fred is not funny or patient.
John is old.
Someone is generous.
John is either humble or creative.
John is not kind or humble.
Someone is both not rich and brave.
Susan is patient.
Someone is kind or strong. | Susan is not quiet. | entailment | ((?[X]:(strong(X)))=>(?[X]:((~funny(X)&~old(X)))))&
(![X]:((wise(X)<~>generous(X))=>creative(X)))&
(![X]:(~patient(X)<=>(~tall(X)<~>kind(X))))&
(![X]:(curious(X)=>(rich(X)<~>~wise(X))))&
(![X]:((creative(X)<~>~brave(X))<=>calm(X)))&
((?[X]:((quiet(X)<~>~calm(X))))=>(?[X]:((patient(X)|~funny(X)))))&
(((~creative(alice)<~>~quiet(alice)))<=>(~kind(susan)))&
(![X]:((~creative(X)|~rich(X))<=>~quiet(X)))&
(((creative(john)&humble(john)))=>((~rich(fred)&funny(fred))))&
(![X]:((old(X)&tall(X))<=>(creative(X)<~>~creative(X))))&
(![X]:(~brave(X)<=>(~old(X)<~>patient(X))))&
(![X]:(rich(X)=>(~kind(X)<~>quiet(X))))&
((?[X]:((curious(X)&generous(X))))=>(?[X]:((curious(X)&rich(X)))))&
((patient(john))=>(?[X]:((patient(X)&~brave(X)))))&
(![X]:((~calm(X)|calm(X))=>(generous(X)|rich(X))))&
(![X]:((brave(X)<~>~patient(X))=>(generous(X)|funny(X))))&
((~funny(fred)|patient(fred)))&
(old(john))&
(?[X]:(generous(X)))&
((humble(john)<~>creative(john)))&
((~kind(john)|humble(john)))&
(?[X]:((~rich(X)&brave(X))))&
(patient(susan))&
(?[X]:((kind(X)|strong(X)))) | ~quiet(susan) | [
"p2",
"p7",
"p9",
"p11",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 115589347766256667865933
% SZS output start Proof for 115589347766256667865933
3. ! [X0] : (~patient(X0) <=> (~tall(X0) <~> kind(X0))) [input p2]
8. ! [X0] : ((~rich(X0) | ~creative(X0)) <=> ~quiet(X0)) [input p7]
10. ! [X0] : ((tall(X0) & old(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p9]
12. ! [X0] : (rich(X0) => (~kind(X0) <~> quiet(X0))) [input p11]
23. patient(susan) [input p22]
25. quiet(susan) [input hypothesis]
35. ! [X0] : ((~kind(X0) <~> quiet(X0)) | ~rich(X0)) [ennf transformation 12]
46. ! [X0] : ((~patient(X0) | ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0)))) & (((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | patient(X0))) [nnf transformation 3]
54. ! [X0] : (((~rich(X0) | ~creative(X0)) | quiet(X0)) & (~quiet(X0) | (rich(X0) & creative(X0)))) [nnf transformation 8]
55. ! [X0] : ((~rich(X0) | ~creative(X0) | quiet(X0)) & (~quiet(X0) | (rich(X0) & creative(X0)))) [flattening 54]
56. ! [X0] : (((tall(X0) & old(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~tall(X0) | ~old(X0)))) [nnf transformation 10]
57. ! [X0] : (((tall(X0) & old(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~tall(X0) | ~old(X0))) [flattening 56]
59. ! [X0] : (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | ~rich(X0)) [nnf transformation 35]
80. ~kind(X0) | ~tall(X0) | ~patient(X0) [cnf transformation 46]
94. ~quiet(X0) | rich(X0) [cnf transformation 55]
102. tall(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 57]
103. tall(X0) | creative(X0) | creative(X0) [cnf transformation 57]
109. ~quiet(X0) | kind(X0) | ~rich(X0) [cnf transformation 59]
126. patient(susan) [cnf transformation 23]
128. quiet(susan) [cnf transformation 25]
131. tall(X0) | ~creative(X0) [duplicate literal removal 102]
132. tall(X0) | creative(X0) [duplicate literal removal 103]
163. 8 <=> kind(susan) [avatar definition]
165. kind(susan) <- (8) [avatar component clause 163]
196. tall(X0) [subsumption resolution 131,132]
200. ~quiet(X0) | kind(X0) [subsumption resolution 109,94]
257. kind(susan) [resolution 200,128]
293. ~tall(susan) | ~patient(susan) <- (8) [resolution 80,165]
296. ~patient(susan) <- (8) [subsumption resolution 293,196]
297. $false <- (8) [subsumption resolution 296,126]
298. ~8 [avatar contradiction clause 297]
300. 8 [avatar split clause 257,163]
301. $false [avatar sat refutation 298,300]
% SZS output end Proof for 115589347766256667865933
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not kind.
Everyone who is rich is either wise or not calm and vice versa.
If lucy is humble then lucy is both happy and not wise.
Everyone who is both not patient and not kind is not calm and vice versa.
If someone is curious or wise then someone is strong and vice versa.
Everyone who is either tall or not wise is not old or old and vice versa.
Everyone who is both patient and funny is brave and vice versa.
If alice is strong or not curious then lucy is both happy and not kind.
Everyone who is tall is not quiet or kind and vice versa.
Everyone who is quiet or not strong is not humble and vice versa.
Everyone who is both not calm and calm is tall or humble and vice versa.
If someone is both not old and not quiet then someone is not kind or creative.
If someone is both not patient and not quiet then paul is calm or not happy.
If susan is both not brave and tall then susan is both kind and tall and vice versa.
Everyone who is either not quiet or not patient is either happy or wise and vice versa.
Everyone who is both not quiet and not wise is funny.
John is both not generous and old.
Mary is either kind or not creative.
Someone is either not tall or not rich.
Lucy is quiet.
Lucy is not wise or not patient.
Someone is patient.
John is either funny or not calm. | Alice is not patient. | neutral | (![X]:(funny(X)=>~kind(X)))&
(![X]:(rich(X)<=>(wise(X)<~>~calm(X))))&
((humble(lucy))=>((happy(lucy)&~wise(lucy))))&
(![X]:((~patient(X)&~kind(X))<=>~calm(X)))&
((?[X]:((curious(X)|wise(X))))<=>(?[X]:(strong(X))))&
(![X]:((tall(X)<~>~wise(X))<=>(~old(X)|old(X))))&
(![X]:((patient(X)&funny(X))<=>brave(X)))&
(((strong(alice)|~curious(alice)))=>((happy(lucy)&~kind(lucy))))&
(![X]:(tall(X)<=>(~quiet(X)|kind(X))))&
(![X]:((quiet(X)|~strong(X))<=>~humble(X)))&
(![X]:((~calm(X)&calm(X))<=>(tall(X)|humble(X))))&
((?[X]:((~old(X)&~quiet(X))))=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:((~patient(X)&~quiet(X))))=>((calm(paul)|~happy(paul))))&
(((~brave(susan)&tall(susan)))<=>((kind(susan)&tall(susan))))&
(![X]:((~quiet(X)<~>~patient(X))<=>(happy(X)<~>wise(X))))&
(![X]:((~quiet(X)&~wise(X))=>funny(X)))&
((~generous(john)&old(john)))&
((kind(mary)<~>~creative(mary)))&
(?[X]:((~tall(X)<~>~rich(X))))&
(quiet(lucy))&
((~wise(lucy)|~patient(lucy)))&
(?[X]:(patient(X)))&
((funny(john)<~>~calm(john))) | ~patient(alice) | []
| null | 0 |
If someone is either wise or not generous then john is either calm or not calm and vice versa.
If mary is either not strong or not old then alice is either tall or patient and vice versa.
Everyone who is either not curious or not kind is both not brave and not funny and vice versa.
Everyone who is not wise or not curious is not old and vice versa.
Everyone who is funny or not patient is funny or curious and vice versa.
If someone is either not creative or tall then susan is not brave and vice versa.
Everyone who is both not humble and strong is calm or not generous and vice versa.
Everyone who is old is calm or not old and vice versa.
Everyone who is both not creative and not wise is not generous or tall.
If someone is both kind and wise then lucy is either not creative or not old.
Everyone who is either curious or brave is both not quiet and not kind and vice versa.
If fred is both calm and not happy then someone is not rich and vice versa.
If alice is tall then someone is brave or humble.
Everyone who is either not funny or not calm is either tall or not humble.
Everyone who is either not quiet or not generous is not rich.
Everyone who is both not calm and not funny is both not wise and generous and vice versa.
Someone is rich or not creative.
Fred is either old or not patient.
Fred is either not calm or calm.
Someone is not creative.
Someone is either not funny or not creative.
Someone is both curious and not patient.
Susan is not humble or not old. | Mary is not calm. | contradiction | ((?[X]:((wise(X)<~>~generous(X))))<=>((calm(john)<~>~calm(john))))&
(((~strong(mary)<~>~old(mary)))<=>((tall(alice)<~>patient(alice))))&
(![X]:((~curious(X)<~>~kind(X))<=>(~brave(X)&~funny(X))))&
(![X]:((~wise(X)|~curious(X))<=>~old(X)))&
(![X]:((funny(X)|~patient(X))<=>(funny(X)|curious(X))))&
((?[X]:((~creative(X)<~>tall(X))))<=>(~brave(susan)))&
(![X]:((~humble(X)&strong(X))<=>(calm(X)|~generous(X))))&
(![X]:(old(X)<=>(calm(X)|~old(X))))&
(![X]:((~creative(X)&~wise(X))=>(~generous(X)|tall(X))))&
((?[X]:((kind(X)&wise(X))))=>((~creative(lucy)<~>~old(lucy))))&
(![X]:((curious(X)<~>brave(X))<=>(~quiet(X)&~kind(X))))&
(((calm(fred)&~happy(fred)))<=>(?[X]:(~rich(X))))&
((tall(alice))=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~funny(X)<~>~calm(X))=>(tall(X)<~>~humble(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>~rich(X)))&
(![X]:((~calm(X)&~funny(X))<=>(~wise(X)&generous(X))))&
(?[X]:((rich(X)|~creative(X))))&
((old(fred)<~>~patient(fred)))&
((~calm(fred)<~>calm(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)<~>~creative(X))))&
(?[X]:((curious(X)&~patient(X))))&
((~humble(susan)|~old(susan))) | ~calm(mary) | [
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 6382893628045667359877976
% SZS output start Proof for 6382893628045667359877976
8. ! [X0] : (old(X0) <=> (~old(X0) | calm(X0))) [input p7]
24. ~calm(mary) [input hypothesis]
48. ! [X0] : ((old(X0) | (old(X0) & ~calm(X0))) & ((~old(X0) | calm(X0)) | ~old(X0))) [nnf transformation 8]
49. ! [X0] : ((old(X0) | (old(X0) & ~calm(X0))) & (~old(X0) | calm(X0) | ~old(X0))) [flattening 48]
113. ~old(X0) | calm(X0) | ~old(X0) [cnf transformation 49]
115. old(X0) | old(X0) [cnf transformation 49]
150. ~calm(mary) [cnf transformation 24]
151. ~old(X0) | calm(X0) [duplicate literal removal 113]
152. old(X0) [duplicate literal removal 115]
219. calm(X0) [subsumption resolution 151,152]
275. $false [subsumption resolution 150,219]
% SZS output end Proof for 6382893628045667359877976
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not patient then paul is curious and vice versa.
Everyone who is not creative is either not generous or funny and vice versa.
If someone is both curious and rich then someone is both patient and not tall and vice versa.
Everyone who is not curious is old and vice versa.
Everyone who is either not old or not happy is strong.
If someone is either not creative or not strong then fred is both generous and creative and vice versa.
If paul is both curious and not humble then lucy is not funny.
Everyone who is either humble or tall is not brave or not tall and vice versa.
Everyone who is patient or calm is old or brave.
Everyone who is not curious or not generous is either not generous or not happy.
If someone is rich then someone is both not patient and not rich.
Everyone who is either not humble or kind is both strong and old.
Everyone who is not happy is either not patient or not calm and vice versa.
If mary is either not tall or not wise then john is not humble or kind and vice versa.
If paul is kind then someone is brave or calm and vice versa.
Everyone who is both not funny and not calm is patient and vice versa.
Susan is wise or calm.
Someone is both not brave and not generous.
Someone is not funny.
Someone is both not rich and kind.
Someone is either not humble or not old.
Someone is wise or kind.
Someone is creative.
Fred is either not patient or not calm. | Paul is patient. | contradiction | ((?[X]:((quiet(X)|~patient(X))))<=>(curious(paul)))&
(![X]:(~creative(X)<=>(~generous(X)<~>funny(X))))&
((?[X]:((curious(X)&rich(X))))<=>(?[X]:((patient(X)&~tall(X)))))&
(![X]:(~curious(X)<=>old(X)))&
(![X]:((~old(X)<~>~happy(X))=>strong(X)))&
((?[X]:((~creative(X)<~>~strong(X))))<=>((generous(fred)&creative(fred))))&
(((curious(paul)&~humble(paul)))=>(~funny(lucy)))&
(![X]:((humble(X)<~>tall(X))<=>(~brave(X)|~tall(X))))&
(![X]:((patient(X)|calm(X))=>(old(X)|brave(X))))&
(![X]:((~curious(X)|~generous(X))=>(~generous(X)<~>~happy(X))))&
((?[X]:(rich(X)))=>(?[X]:((~patient(X)&~rich(X)))))&
(![X]:((~humble(X)<~>kind(X))=>(strong(X)&old(X))))&
(![X]:(~happy(X)<=>(~patient(X)<~>~calm(X))))&
(((~tall(mary)<~>~wise(mary)))<=>((~humble(john)|kind(john))))&
((kind(paul))<=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~funny(X)&~calm(X))<=>patient(X)))&
((wise(susan)|calm(susan)))&
(?[X]:((~brave(X)&~generous(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~rich(X)&kind(X))))&
(?[X]:((~humble(X)<~>~old(X))))&
(?[X]:((wise(X)|kind(X))))&
(?[X]:(creative(X)))&
((~patient(fred)<~>~calm(fred))) | patient(paul) | [
"p0",
"p3",
"p7",
"p8",
"p9",
"p11",
"p12",
"p14",
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 1037462057472883978519535
% SZS output start Proof for 1037462057472883978519535
1. ? [X0] : (~patient(X0) | quiet(X0)) <=> curious(paul) [input p0]
4. ! [X0] : (~curious(X0) <=> old(X0)) [input p3]
8. ! [X0] : ((humble(X0) <~> tall(X0)) <=> (~tall(X0) | ~brave(X0))) [input p7]
9. ! [X0] : ((calm(X0) | patient(X0)) => (brave(X0) | old(X0))) [input p8]
10. ! [X0] : ((~generous(X0) | ~curious(X0)) => (~generous(X0) <~> ~happy(X0))) [input p9]
12. ! [X0] : ((~humble(X0) <~> kind(X0)) => (old(X0) & strong(X0))) [input p11]
13. ! [X0] : (~happy(X0) <=> (~patient(X0) <~> ~calm(X0))) [input p12]
15. kind(paul) <=> ? [X0] : (calm(X0) | brave(X0)) [input p14]
16. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> patient(X0)) [input p15]
18. ? [X0] : (~generous(X0) & ~brave(X0)) [input p17]
25. patient(paul) [input hypothesis]
31. ! [X0] : ((brave(X0) | old(X0)) | (~calm(X0) & ~patient(X0))) [ennf transformation 9]
32. ! [X0] : (brave(X0) | old(X0) | (~calm(X0) & ~patient(X0))) [flattening 31]
33. ! [X0] : ((~generous(X0) <~> ~happy(X0)) | (generous(X0) & curious(X0))) [ennf transformation 10]
35. ! [X0] : ((old(X0) & strong(X0)) | (~humble(X0) <=> kind(X0))) [ennf transformation 12]
36. (? [X0] : (~patient(X0) | quiet(X0)) | ~curious(paul)) & (curious(paul) | ! [X0] : (patient(X0) & ~quiet(X0))) [nnf transformation 1]
37. (? [X0] : (~patient(X0) | quiet(X0)) | ~curious(paul)) & (curious(paul) | ! [X1] : (patient(X1) & ~quiet(X1))) [rectify 36]
38. ? [X0] : (~patient(X0) | quiet(X0)) => (~patient(sK0) | quiet(sK0)) [choice axiom]
39. ((~patient(sK0) | quiet(sK0)) | ~curious(paul)) & (curious(paul) | ! [X1] : (patient(X1) & ~quiet(X1))) [skolemisation 37,38]
46. ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0))) [nnf transformation 4]
53. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (tall(X0) & brave(X0))) & ((~tall(X0) | ~brave(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [nnf transformation 8]
54. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (tall(X0) & brave(X0))) & (~tall(X0) | ~brave(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [flattening 53]
55. ! [X0] : (((happy(X0) | generous(X0)) & (~happy(X0) | ~generous(X0))) | (generous(X0) & curious(X0))) [nnf transformation 33]
59. ! [X0] : ((old(X0) & strong(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0)))) [nnf transformation 35]
60. ! [X0] : ((~happy(X0) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | happy(X0))) [nnf transformation 13]
63. (kind(paul) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X0] : (calm(X0) | brave(X0)) | ~kind(paul)) [nnf transformation 15]
64. (kind(paul) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X1] : (calm(X1) | brave(X1)) | ~kind(paul)) [rectify 63]
65. ? [X1] : (calm(X1) | brave(X1)) => (calm(sK5) | brave(sK5)) [choice axiom]
66. (kind(paul) | ! [X0] : (~calm(X0) & ~brave(X0))) & ((calm(sK5) | brave(sK5)) | ~kind(paul)) [skolemisation 64,65]
67. ! [X0] : (((~calm(X0) & ~funny(X0)) | ~patient(X0)) & (patient(X0) | (calm(X0) | funny(X0)))) [nnf transformation 16]
68. ! [X0] : (((~calm(X0) & ~funny(X0)) | ~patient(X0)) & (patient(X0) | calm(X0) | funny(X0))) [flattening 67]
69. ? [X0] : (~generous(X0) & ~brave(X0)) => (~generous(sK6) & ~brave(sK6)) [choice axiom]
70. ~generous(sK6) & ~brave(sK6) [skolemisation 18,69]
84. curious(paul) | patient(X1) [cnf transformation 39]
95. ~old(X0) | ~curious(X0) [cnf transformation 46]
106. ~tall(X0) | ~brave(X0) | humble(X0) | ~tall(X0) [cnf transformation 54]
108. tall(X0) | humble(X0) | tall(X0) [cnf transformation 54]
111. ~patient(X0) | old(X0) | brave(X0) [cnf transformation 32]
116. happy(X0) | generous(X0) | generous(X0) [cnf transformation 55]
122. ~kind(X0) | ~humble(X0) | old(X0) [cnf transformation 59]
126. ~happy(X0) | ~patient(X0) | calm(X0) [cnf transformation 60]
134. kind(paul) | ~brave(X0) [cnf transformation 66]
138. ~calm(X0) | ~patient(X0) [cnf transformation 68]
141. ~generous(sK6) [cnf transformation 70]
151. patient(paul) [cnf transformation 25]
152. happy(X0) | generous(X0) [duplicate literal removal 116]
153. ~tall(X0) | ~brave(X0) | humble(X0) [duplicate literal removal 106]
154. humble(X0) | tall(X0) [duplicate literal removal 108]
156. 1 <=> curious(paul) [avatar definition]
157. curious(paul) <- (1) [avatar component clause 156]
169. 4 <=> ! [X1] : patient(X1) [avatar definition]
170. patient(X1) <- (4) [avatar component clause 169]
171. 4 | 1 [avatar split clause 84,156,169]
231. 18 <=> humble(paul) [avatar definition]
233. humble(paul) <- (18) [avatar component clause 231]
239. ~brave(X0) | humble(X0) [subsumption resolution 153,154]
279. 28 <=> kind(paul) [avatar definition]
281. kind(paul) <- (28) [avatar component clause 279]
284. 29 <=> ! [X0] : ~brave(X0) [avatar definition]
285. ~brave(X0) <- (29) [avatar component clause 284]
286. 29 | 28 [avatar split clause 134,279,284]
372. old(paul) | brave(paul) [resolution 111,151]
376. 44 <=> brave(paul) [avatar definition]
378. brave(paul) <- (44) [avatar component clause 376]
380. 45 <=> old(paul) [avatar definition]
382. old(paul) <- (45) [avatar component clause 380]
383. 44 | 45 [avatar split clause 372,380,376]
387. humble(paul) <- (44) [resolution 378,239]
388. 18 | ~44 [avatar split clause 387,376,231]
456. ~humble(paul) | old(paul) <- (28) [resolution 122,281]
460. old(paul) <- (18, 28) [subsumption resolution 456,233]
461. 45 | ~18 | ~28 [avatar split clause 460,279,231,380]
463. ~curious(paul) <- (45) [resolution 382,95]
464. $false <- (1, 45) [subsumption resolution 463,157]
465. ~1 | ~45 [avatar contradiction clause 464]
468. $false <- (29, 44) [resolution 285,378]
473. ~29 | ~44 [avatar contradiction clause 468]
495. ~patient(X0) | calm(X0) | generous(X0) [resolution 126,152]
496. calm(X0) | generous(X0) <- (4) [subsumption resolution 495,170]
517. generous(X3) | ~patient(X3) <- (4) [resolution 496,138]
519. generous(X3) <- (4) [subsumption resolution 517,170]
523. $false <- (4) [resolution 519,141]
525. ~4 [avatar contradiction clause 523]
526. $false [avatar sat refutation 171,286,383,388,461,465,473,525]
% SZS output end Proof for 1037462057472883978519535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | John is not old. | contradiction | (((~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))) | ~old(john) | [
"p5",
"p6",
"p7",
"p8",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 381300305544013891420404
% SZS output start Proof for 381300305544013891420404
6. ! [X0] : ((creative(X0) | curious(X0)) => tall(X0)) [input p5]
7. ! [X0] : (generous(X0) <=> curious(X0)) [input p6]
8. ! [X0] : ((~calm(X0) & ~generous(X0)) <=> (~generous(X0) | ~happy(X0))) [input p7]
9. ! [X0] : ((~old(X0) | ~generous(X0)) => (calm(X0) & quiet(X0))) [input p8]
12. ! [X0] : ((~tall(X0) <~> generous(X0)) => (~generous(X0) | ~calm(X0))) [input p11]
22. ~old(john) [input hypothesis]
29. ! [X0] : (tall(X0) | (~creative(X0) & ~curious(X0))) [ennf transformation 6]
30. ! [X0] : ((calm(X0) & quiet(X0)) | (old(X0) & generous(X0))) [ennf transformation 9]
33. ! [X0] : ((~generous(X0) | ~calm(X0)) | (~tall(X0) <=> generous(X0))) [ennf transformation 12]
34. ! [X0] : (~generous(X0) | ~calm(X0) | (~tall(X0) <=> generous(X0))) [flattening 33]
41. ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0))) [nnf transformation 7]
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]
49. ! [X0] : (~generous(X0) | ~calm(X0) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0)))) [nnf transformation 34]
75. ~curious(X0) | tall(X0) [cnf transformation 29]
77. ~generous(X0) | curious(X0) [cnf transformation 41]
83. ~calm(X0) | generous(X0) [cnf transformation 43]
86. calm(X0) | generous(X0) [cnf transformation 30]
87. calm(X0) | old(X0) [cnf transformation 30]
96. ~generous(X0) | ~calm(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 49]
120. ~old(john) [cnf transformation 22]
121. ~generous(X0) | ~calm(X0) | ~tall(X0) [duplicate literal removal 96]
136. generous(X0) [subsumption resolution 86,83]
151. 7 <=> ! [X1] : curious(X1) [avatar definition]
152. curious(X1) <- (7) [avatar component clause 151]
163. 10 <=> ! [X1] : tall(X1) [avatar definition]
164. tall(X1) <- (10) [avatar component clause 163]
182. ~calm(X0) | ~tall(X0) [subsumption resolution 121,136]
217. 21 <=> calm(john) [avatar definition]
218. ~calm(john) <- (~21) [avatar component clause 217]
219. calm(john) <- (21) [avatar component clause 217]
263. curious(X0) [resolution 77,136]
264. 7 [avatar split clause 263,151]
266. tall(X0) <- (7) [resolution 152,75]
268. 10 | ~7 [avatar split clause 266,151,163]
279. old(john) <- (~21) [resolution 87,218]
282. $false <- (~21) [subsumption resolution 279,120]
283. 21 [avatar contradiction clause 282]
305. ~tall(john) <- (21) [resolution 182,219]
311. $false <- (10, 21) [subsumption resolution 305,164]
312. ~10 | ~21 [avatar contradiction clause 311]
313. $false [avatar sat refutation 264,268,283,312]
% SZS output end Proof for 381300305544013891420404
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not creative or funny then someone is either not brave or tall.
If someone is wise or patient then someone is both funny and rich.
Everyone who is both strong and creative is brave or not happy and vice versa.
Everyone who is both not funny and funny is not tall and vice versa.
Everyone who is not tall is quiet or not humble.
If mary is not tall then someone is not rich or not brave and vice versa.
If john is either calm or not strong then someone is not wise or quiet.
If someone is not curious or not wise then someone is curious or not creative.
Everyone who is quiet is either creative or quiet.
Everyone who is either rich or not humble is not patient and vice versa.
Everyone who is either strong or not brave is creative and vice versa.
Everyone who is either strong or humble is either generous or calm and vice versa.
Everyone who is either not happy or not curious is either brave or strong.
If someone is curious then paul is not happy or generous.
Everyone who is either creative or not kind is humble and vice versa.
Everyone who is not curious or not kind is both not tall and rich.
Someone is both humble and not patient.
Alice is either humble or quiet.
Someone is either not happy or generous.
Lucy is not quiet or creative.
Someone is creative.
Someone is either not curious or generous. | Lucy is not patient. | entailment | (((~creative(susan)<~>funny(susan)))=>(?[X]:((~brave(X)<~>tall(X)))))&
((?[X]:((wise(X)|patient(X))))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((strong(X)&creative(X))<=>(brave(X)|~happy(X))))&
(![X]:((~funny(X)&funny(X))<=>~tall(X)))&
(![X]:(~tall(X)=>(quiet(X)|~humble(X))))&
((~tall(mary))<=>(?[X]:((~rich(X)|~brave(X)))))&
(((calm(john)<~>~strong(john)))=>(?[X]:((~wise(X)|quiet(X)))))&
((?[X]:((~curious(X)|~wise(X))))=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:(quiet(X)=>(creative(X)<~>quiet(X))))&
(![X]:((rich(X)<~>~humble(X))<=>~patient(X)))&
(![X]:((strong(X)<~>~brave(X))<=>creative(X)))&
(![X]:((strong(X)<~>humble(X))<=>(generous(X)<~>calm(X))))&
(![X]:((~happy(X)<~>~curious(X))=>(brave(X)<~>strong(X))))&
((?[X]:(curious(X)))=>((~happy(paul)|generous(paul))))&
(![X]:((creative(X)<~>~kind(X))<=>humble(X)))&
(![X]:((~curious(X)|~kind(X))=>(~tall(X)&rich(X))))&
(?[X]:((humble(X)&~patient(X))))&
((humble(alice)<~>quiet(alice)))&
(?[X]:((~happy(X)<~>generous(X))))&
((~quiet(lucy)|creative(lucy)))&
(?[X]:(creative(X)))&
(?[X]:((~curious(X)<~>generous(X)))) | ~patient(lucy) | [
"p2",
"p3",
"p5",
"p9",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 2237208160800350008651178
% SZS output start Proof for 2237208160800350008651178
3. ! [X0] : ((creative(X0) & strong(X0)) <=> (~happy(X0) | brave(X0))) [input p2]
4. ! [X0] : ((funny(X0) & ~funny(X0)) <=> ~tall(X0)) [input p3]
6. ~tall(mary) <=> ? [X0] : (~brave(X0) | ~rich(X0)) [input p5]
10. ! [X0] : ((rich(X0) <~> ~humble(X0)) <=> ~patient(X0)) [input p9]
15. ! [X0] : ((creative(X0) <~> ~kind(X0)) <=> humble(X0)) [input p14]
16. ! [X0] : ((~kind(X0) | ~curious(X0)) => (rich(X0) & ~tall(X0))) [input p15]
23. patient(lucy) [input hypothesis]
36. ! [X0] : ((rich(X0) & ~tall(X0)) | (kind(X0) & curious(X0))) [ennf transformation 16]
43. ! [X0] : (((creative(X0) & strong(X0)) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | (~creative(X0) | ~strong(X0)))) [nnf transformation 3]
44. ! [X0] : (((creative(X0) & strong(X0)) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | ~creative(X0) | ~strong(X0))) [flattening 43]
45. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) | funny(X0)))) [nnf transformation 4]
46. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | ~funny(X0) | funny(X0))) [flattening 45]
47. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X0] : (~brave(X0) | ~rich(X0)) | tall(mary)) [nnf transformation 6]
48. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X1] : (~brave(X1) | ~rich(X1)) | tall(mary)) [rectify 47]
49. ? [X1] : (~brave(X1) | ~rich(X1)) => (~brave(sK2) | ~rich(sK2)) [choice axiom]
50. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & ((~brave(sK2) | ~rich(sK2)) | tall(mary)) [skolemisation 48,49]
58. ! [X0] : ((((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | patient(X0)) & (~patient(X0) | ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0))))) [nnf transformation 10]
62. ! [X0] : ((((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | ~humble(X0)) & (humble(X0) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0))))) [nnf transformation 15]
85. ~brave(X0) | creative(X0) [cnf transformation 44]
88. ~funny(X0) | tall(X0) [cnf transformation 46]
89. tall(X0) | funny(X0) [cnf transformation 46]
92. ~tall(mary) | rich(X0) [cnf transformation 50]
93. ~tall(mary) | brave(X0) [cnf transformation 50]
100. ~patient(X0) | ~humble(X0) | ~rich(X0) [cnf transformation 58]
121. ~kind(X0) | humble(X0) | ~creative(X0) [cnf transformation 62]
126. ~tall(X0) | kind(X0) [cnf transformation 36]
139. patient(lucy) [cnf transformation 23]
162. 5 <=> ! [X1] : ~patient(X1) [avatar definition]
163. ~patient(X1) <- (5) [avatar component clause 162]
179. tall(X0) [subsumption resolution 88,89]
180. brave(X0) [subsumption resolution 93,179]
181. rich(X0) [subsumption resolution 92,179]
217. ~humble(X0) | ~patient(X0) [subsumption resolution 100,181]
233. kind(X0) [subsumption resolution 126,179]
271. $false <- (5) [resolution 163,139]
272. ~5 [avatar contradiction clause 271]
278. creative(X0) [resolution 85,180]
293. humble(X0) | ~creative(X0) [resolution 121,233]
294. humble(X0) [subsumption resolution 293,278]
303. ~patient(X0) [resolution 294,217]
304. 5 [avatar split clause 303,162]
305. $false [avatar sat refutation 272,304]
% SZS output end Proof for 2237208160800350008651178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not generous is wise or funny and vice versa.
Everyone who is both not curious and tall is either happy or creative and vice versa.
Everyone who is not calm or strong is either not happy or not calm and vice versa.
If someone is funny or not tall then alice is both humble and curious and vice versa.
Everyone who is both not generous and strong is not rich or not curious and vice versa.
If susan is either not curious or not funny then fred is not patient or kind.
If someone is quiet or funny then someone is either humble or not brave.
Everyone who is either not rich or humble is both not tall and not curious.
Everyone who is brave is not old.
Everyone who is wise or not rich is both rich and generous.
Everyone who is either not wise or funny is kind.
Everyone who is funny or wise is humble.
Everyone who is either calm or happy is not curious or not creative.
Everyone who is both not funny and patient is both not old and not kind and vice versa.
Susan is either not old or not rich.
Mary is not happy or curious.
Susan is quiet.
Someone is patient or not brave.
Someone is generous or not wise. | Mary is patient. | contradiction | (![X]:((patient(X)|~generous(X))<=>(wise(X)|funny(X))))&
(![X]:((~curious(X)&tall(X))<=>(happy(X)<~>creative(X))))&
(![X]:((~calm(X)|strong(X))<=>(~happy(X)<~>~calm(X))))&
((?[X]:((funny(X)|~tall(X))))<=>((humble(alice)&curious(alice))))&
(![X]:((~generous(X)&strong(X))<=>(~rich(X)|~curious(X))))&
(((~curious(susan)<~>~funny(susan)))=>((~patient(fred)|kind(fred))))&
((?[X]:((quiet(X)|funny(X))))=>(?[X]:((humble(X)<~>~brave(X)))))&
(![X]:((~rich(X)<~>humble(X))=>(~tall(X)&~curious(X))))&
(![X]:(brave(X)=>~old(X)))&
(![X]:((wise(X)|~rich(X))=>(rich(X)&generous(X))))&
(![X]:((~wise(X)<~>funny(X))=>kind(X)))&
(![X]:((funny(X)|wise(X))=>humble(X)))&
(![X]:((calm(X)<~>happy(X))=>(~curious(X)|~creative(X))))&
(![X]:((~funny(X)&patient(X))<=>(~old(X)&~kind(X))))&
((~old(susan)<~>~rich(susan)))&
((~happy(mary)|curious(mary)))&
(quiet(susan))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:((generous(X)|~wise(X)))) | patient(mary) | [
"p0",
"p3",
"p4",
"p7",
"p9",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 6436385898801216782511175
% SZS output start Proof for 6436385898801216782511175
1. ! [X0] : ((~generous(X0) | patient(X0)) <=> (funny(X0) | wise(X0))) [input p0]
4. ? [X0] : (~tall(X0) | funny(X0)) <=> (curious(alice) & humble(alice)) [input p3]
5. ! [X0] : ((strong(X0) & ~generous(X0)) <=> (~curious(X0) | ~rich(X0))) [input p4]
8. ! [X0] : ((~rich(X0) <~> humble(X0)) => (~curious(X0) & ~tall(X0))) [input p7]
10. ! [X0] : ((~rich(X0) | wise(X0)) => (generous(X0) & rich(X0))) [input p9]
12. ! [X0] : ((wise(X0) | funny(X0)) => humble(X0)) [input p11]
20. patient(mary) [input hypothesis]
25. ! [X0] : ((~curious(X0) & ~tall(X0)) | (~rich(X0) <=> humble(X0))) [ennf transformation 8]
27. ! [X0] : ((generous(X0) & rich(X0)) | (rich(X0) & ~wise(X0))) [ennf transformation 10]
29. ! [X0] : (humble(X0) | (~wise(X0) & ~funny(X0))) [ennf transformation 12]
32. ! [X0] : (((~generous(X0) | patient(X0)) | (~funny(X0) & ~wise(X0))) & ((funny(X0) | wise(X0)) | (generous(X0) & ~patient(X0)))) [nnf transformation 1]
33. ! [X0] : ((~generous(X0) | patient(X0) | (~funny(X0) & ~wise(X0))) & (funny(X0) | wise(X0) | (generous(X0) & ~patient(X0)))) [flattening 32]
38. (? [X0] : (~tall(X0) | funny(X0)) | (~curious(alice) | ~humble(alice))) & ((curious(alice) & humble(alice)) | ! [X0] : (tall(X0) & ~funny(X0))) [nnf transformation 4]
39. (? [X0] : (~tall(X0) | funny(X0)) | ~curious(alice) | ~humble(alice)) & ((curious(alice) & humble(alice)) | ! [X0] : (tall(X0) & ~funny(X0))) [flattening 38]
40. (? [X0] : (~tall(X0) | funny(X0)) | ~curious(alice) | ~humble(alice)) & ((curious(alice) & humble(alice)) | ! [X1] : (tall(X1) & ~funny(X1))) [rectify 39]
41. ? [X0] : (~tall(X0) | funny(X0)) => (~tall(sK0) | funny(sK0)) [choice axiom]
42. ((~tall(sK0) | funny(sK0)) | ~curious(alice) | ~humble(alice)) & ((curious(alice) & humble(alice)) | ! [X1] : (tall(X1) & ~funny(X1))) [skolemisation 40,41]
43. ! [X0] : (((strong(X0) & ~generous(X0)) | (curious(X0) & rich(X0))) & ((~curious(X0) | ~rich(X0)) | (~strong(X0) | generous(X0)))) [nnf transformation 5]
44. ! [X0] : (((strong(X0) & ~generous(X0)) | (curious(X0) & rich(X0))) & (~curious(X0) | ~rich(X0) | ~strong(X0) | generous(X0))) [flattening 43]
50. ! [X0] : ((~curious(X0) & ~tall(X0)) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) [nnf transformation 25]
60. ~patient(X0) | wise(X0) | funny(X0) [cnf transformation 33]
61. funny(X0) | wise(X0) | generous(X0) [cnf transformation 33]
76. humble(alice) | ~funny(X1) [cnf transformation 42]
78. curious(alice) | ~funny(X1) [cnf transformation 42]
82. ~generous(X0) | rich(X0) [cnf transformation 44]
83. ~generous(X0) | curious(X0) [cnf transformation 44]
95. ~rich(X0) | ~curious(X0) | ~humble(X0) [cnf transformation 50]
99. ~wise(X0) | generous(X0) [cnf transformation 27]
100. generous(X0) | rich(X0) [cnf transformation 27]
104. ~wise(X0) | humble(X0) [cnf transformation 29]
117. patient(mary) [cnf transformation 20]
122. 1 <=> humble(alice) [avatar definition]
123. humble(alice) <- (1) [avatar component clause 122]
126. 2 <=> curious(alice) [avatar definition]
127. curious(alice) <- (2) [avatar component clause 126]
143. 6 <=> ! [X1] : ~funny(X1) [avatar definition]
144. ~funny(X1) <- (6) [avatar component clause 143]
145. 6 | 2 [avatar split clause 78,126,143]
147. 6 | 1 [avatar split clause 76,122,143]
181. rich(X0) [subsumption resolution 100,82]
203. wise(mary) | funny(mary) [resolution 60,117]
204. wise(mary) <- (6) [subsumption resolution 203,144]
206. wise(X1) | generous(X1) <- (6) [resolution 61,144]
208. generous(X1) <- (6) [subsumption resolution 206,99]
209. humble(mary) <- (6) [resolution 204,104]
212. curious(X0) <- (6) [resolution 208,83]
232. ~humble(X1) | ~curious(X1) [resolution 95,181]
234. ~humble(X1) <- (6) [subsumption resolution 232,212]
235. $false <- (6) [resolution 234,209]
239. ~6 [avatar contradiction clause 235]
316. ~curious(alice) <- (1) [resolution 232,123]
319. $false <- (1, 2) [subsumption resolution 316,127]
320. ~1 | ~2 [avatar contradiction clause 319]
323. $false [avatar sat refutation 145,147,239,320]
% SZS output end Proof for 6436385898801216782511175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not brave is not calm or humble and vice versa.
If someone is creative then someone is both not calm and humble.
Everyone who is funny is both happy and calm and vice versa.
Everyone who is either not curious or patient is both not quiet and old and vice versa.
If paul is funny then john is not rich or rich.
If someone is funny then alice is either not kind or curious.
If someone is both not funny and not wise then alice is not generous or calm.
Everyone who is either calm or not kind is both generous and patient and vice versa.
If someone is rich or not rich then paul is both happy and not humble and vice versa.
If lucy is not patient or brave then someone is either not patient or not strong and vice versa.
If mary is brave then paul is either not tall or not quiet and vice versa.
If susan is funny or kind then alice is strong or wise.
Everyone who is either patient or old is not brave and vice versa.
If someone is curious then fred is both wise and humble and vice versa.
Everyone who is both curious and generous is either patient or not funny and vice versa.
John is both quiet and not humble.
Someone is creative.
Paul is kind.
Alice is kind.
Susan is old or not old.
Susan is both strong and not generous.
Someone is either not generous or tall.
Someone is not patient. | Fred is wise. | entailment | (![X]:((~calm(X)<~>~brave(X))<=>(~calm(X)|humble(X))))&
((?[X]:(creative(X)))=>(?[X]:((~calm(X)&humble(X)))))&
(![X]:(funny(X)<=>(happy(X)&calm(X))))&
(![X]:((~curious(X)<~>patient(X))<=>(~quiet(X)&old(X))))&
((funny(paul))=>((~rich(john)|rich(john))))&
((?[X]:(funny(X)))=>((~kind(alice)<~>curious(alice))))&
((?[X]:((~funny(X)&~wise(X))))=>((~generous(alice)|calm(alice))))&
(![X]:((calm(X)<~>~kind(X))<=>(generous(X)&patient(X))))&
((?[X]:((rich(X)|~rich(X))))<=>((happy(paul)&~humble(paul))))&
(((~patient(lucy)|brave(lucy)))<=>(?[X]:((~patient(X)<~>~strong(X)))))&
((brave(mary))<=>((~tall(paul)<~>~quiet(paul))))&
(((funny(susan)|kind(susan)))=>((strong(alice)|wise(alice))))&
(![X]:((patient(X)<~>old(X))<=>~brave(X)))&
((?[X]:(curious(X)))<=>((wise(fred)&humble(fred))))&
(![X]:((curious(X)&generous(X))<=>(patient(X)<~>~funny(X))))&
((quiet(john)&~humble(john)))&
(?[X]:(creative(X)))&
(kind(paul))&
(kind(alice))&
((old(susan)|~old(susan)))&
((strong(susan)&~generous(susan)))&
(?[X]:((~generous(X)<~>tall(X))))&
(?[X]:(~patient(X))) | wise(fred) | [
"p5",
"p13",
"p14",
"p18",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 837017186051643042724187
% SZS output start Proof for 837017186051643042724187
6. ? [X0] : funny(X0) => (~kind(alice) <~> curious(alice)) [input p5]
14. ? [X0] : curious(X0) <=> (humble(fred) & wise(fred)) [input p13]
15. ! [X0] : ((generous(X0) & curious(X0)) <=> (patient(X0) <~> ~funny(X0))) [input p14]
19. kind(alice) [input p18]
23. ? [X0] : ~patient(X0) [input p22]
24. ~wise(fred) [input hypothesis]
29. (~kind(alice) <~> curious(alice)) | ! [X0] : ~funny(X0) [ennf transformation 6]
43. ((~curious(alice) | kind(alice)) & (curious(alice) | ~kind(alice))) | ! [X0] : ~funny(X0) [nnf transformation 29]
58. (? [X0] : curious(X0) | (~humble(fred) | ~wise(fred))) & ((humble(fred) & wise(fred)) | ! [X0] : ~curious(X0)) [nnf transformation 14]
59. (? [X0] : curious(X0) | ~humble(fred) | ~wise(fred)) & ((humble(fred) & wise(fred)) | ! [X0] : ~curious(X0)) [flattening 58]
60. (? [X0] : curious(X0) | ~humble(fred) | ~wise(fred)) & ((humble(fred) & wise(fred)) | ! [X1] : ~curious(X1)) [rectify 59]
61. ? [X0] : curious(X0) => curious(sK3) [choice axiom]
62. (curious(sK3) | ~humble(fred) | ~wise(fred)) & ((humble(fred) & wise(fred)) | ! [X1] : ~curious(X1)) [skolemisation 60,61]
63. ! [X0] : (((generous(X0) & curious(X0)) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | (~generous(X0) | ~curious(X0)))) [nnf transformation 15]
64. ! [X0] : (((generous(X0) & curious(X0)) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ~generous(X0) | ~curious(X0))) [flattening 63]
70. ? [X0] : ~patient(X0) => ~patient(sK6) [choice axiom]
71. ~patient(sK6) [skolemisation 23,70]
90. curious(alice) | ~kind(alice) | ~funny(X0) [cnf transformation 43]
120. wise(fred) | ~curious(X1) [cnf transformation 62]
126. patient(X0) | curious(X0) | funny(X0) [cnf transformation 64]
133. kind(alice) [cnf transformation 19]
139. ~patient(sK6) [cnf transformation 71]
140. ~wise(fred) [cnf transformation 24]
158. 4 <=> ! [X0] : ~funny(X0) [avatar definition]
159. ~funny(X0) <- (4) [avatar component clause 158]
161. 5 <=> kind(alice) [avatar definition]
165. 6 <=> curious(alice) [avatar definition]
166. curious(alice) <- (6) [avatar component clause 165]
169. 4 | ~5 | 6 [avatar split clause 90,165,161,158]
263. 27 <=> wise(fred) [avatar definition]
276. 30 <=> ! [X1] : ~curious(X1) [avatar definition]
277. ~curious(X1) <- (30) [avatar component clause 276]
279. 30 | 27 [avatar split clause 120,263,276]
280. 5 [avatar split clause 133,161]
291. ~27 [avatar split clause 140,263]
376. curious(sK6) | funny(sK6) [resolution 126,139]
382. funny(sK6) <- (30) [subsumption resolution 376,277]
383. $false <- (4, 30) [subsumption resolution 382,159]
384. ~4 | ~30 [avatar contradiction clause 383]
403. $false <- (6, 30) [subsumption resolution 166,277]
404. ~6 | ~30 [avatar contradiction clause 403]
405. $false [avatar sat refutation 169,279,280,291,384,404]
% SZS output end Proof for 837017186051643042724187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either humble or not happy then someone is both creative and not tall and vice versa.
Everyone who is either tall or kind is either wise or not generous and vice versa.
Everyone who is both patient and brave is not old and vice versa.
Everyone who is not strong or not brave is not rich and vice versa.
If susan is either rich or not rich then paul is both tall and rich.
Everyone who is not curious or strong is humble.
If lucy is humble or creative then someone is both humble and not kind.
If alice is patient or not strong then someone is both calm and not curious.
If someone is either rich or not kind then someone is both kind and wise.
Everyone who is old is both not quiet and not generous and vice versa.
If john is not creative then susan is both creative and humble.
If john is not generous then someone is either not strong or not quiet.
Everyone who is not rich or curious is both not happy and strong.
If someone is either curious or not generous then john is either creative or generous.
If susan is wise or strong then someone is both not curious and funny.
Everyone who is both humble and old is quiet.
Someone is funny or not strong.
Someone is either old or not creative.
Fred is patient.
Someone is rich or patient.
Someone is both wise and not tall. | John is old. | contradiction | (((humble(paul)<~>~happy(paul)))<=>(?[X]:((creative(X)&~tall(X)))))&
(![X]:((tall(X)<~>kind(X))<=>(wise(X)<~>~generous(X))))&
(![X]:((patient(X)&brave(X))<=>~old(X)))&
(![X]:((~strong(X)|~brave(X))<=>~rich(X)))&
(((rich(susan)<~>~rich(susan)))=>((tall(paul)&rich(paul))))&
(![X]:((~curious(X)|strong(X))=>humble(X)))&
(((humble(lucy)|creative(lucy)))=>(?[X]:((humble(X)&~kind(X)))))&
(((patient(alice)|~strong(alice)))=>(?[X]:((calm(X)&~curious(X)))))&
((?[X]:((rich(X)<~>~kind(X))))=>(?[X]:((kind(X)&wise(X)))))&
(![X]:(old(X)<=>(~quiet(X)&~generous(X))))&
((~creative(john))=>((creative(susan)&humble(susan))))&
((~generous(john))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((~rich(X)|curious(X))=>(~happy(X)&strong(X))))&
((?[X]:((curious(X)<~>~generous(X))))=>((creative(john)<~>generous(john))))&
(((wise(susan)|strong(susan)))=>(?[X]:((~curious(X)&funny(X)))))&
(![X]:((humble(X)&old(X))=>quiet(X)))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((old(X)<~>~creative(X))))&
(patient(fred))&
(?[X]:((rich(X)|patient(X))))&
(?[X]:((wise(X)&~tall(X)))) | old(john) | [
"p3",
"p5",
"p9",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 4178738563419740306898887
% SZS output start Proof for 4178738563419740306898887
4. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> ~rich(X0)) [input p3]
6. ! [X0] : ((strong(X0) | ~curious(X0)) => humble(X0)) [input p5]
10. ! [X0] : (old(X0) <=> (~generous(X0) & ~quiet(X0))) [input p9]
13. ! [X0] : ((curious(X0) | ~rich(X0)) => (strong(X0) & ~happy(X0))) [input p12]
16. ! [X0] : ((old(X0) & humble(X0)) => quiet(X0)) [input p15]
22. old(john) [input hypothesis]
28. ! [X0] : (humble(X0) | (~strong(X0) & curious(X0))) [ennf transformation 6]
34. ! [X0] : ((strong(X0) & ~happy(X0)) | (~curious(X0) & rich(X0))) [ennf transformation 13]
37. ! [X0] : (quiet(X0) | (~old(X0) | ~humble(X0))) [ennf transformation 16]
38. ! [X0] : (quiet(X0) | ~old(X0) | ~humble(X0)) [flattening 37]
46. ! [X0] : (((~brave(X0) | ~strong(X0)) | rich(X0)) & (~rich(X0) | (brave(X0) & strong(X0)))) [nnf transformation 4]
47. ! [X0] : ((~brave(X0) | ~strong(X0) | rich(X0)) & (~rich(X0) | (brave(X0) & strong(X0)))) [flattening 46]
57. ! [X0] : ((old(X0) | (generous(X0) | quiet(X0))) & ((~generous(X0) & ~quiet(X0)) | ~old(X0))) [nnf transformation 10]
58. ! [X0] : ((old(X0) | generous(X0) | quiet(X0)) & ((~generous(X0) & ~quiet(X0)) | ~old(X0))) [flattening 57]
89. ~rich(X0) | strong(X0) [cnf transformation 47]
97. ~strong(X0) | humble(X0) [cnf transformation 28]
108. ~quiet(X0) | ~old(X0) [cnf transformation 58]
117. strong(X0) | rich(X0) [cnf transformation 34]
125. quiet(X0) | ~old(X0) | ~humble(X0) [cnf transformation 38]
132. old(john) [cnf transformation 22]
258. strong(X0) [subsumption resolution 117,89]
270. ~old(X0) | ~humble(X0) [subsumption resolution 125,108]
298. humble(X0) [resolution 97,258]
316. ~humble(john) [resolution 270,132]
319. $false [subsumption resolution 316,298]
% SZS output end Proof for 4178738563419740306898887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not funny or not tall then susan is either not old or generous.
Everyone who is old or calm is humble and vice versa.
If susan is not wise or tall then paul is not tall or tall.
Everyone who is not kind is quiet or kind and vice versa.
Everyone who is not creative is both calm and brave and vice versa.
If paul is strong then paul is old or not rich.
Everyone who is either not strong or not happy is not patient.
If someone is not kind or wise then mary is brave.
If fred is both creative and not funny then someone is humble and vice versa.
If someone is not old then someone is creative and vice versa.
Everyone who is either not generous or not humble is either quiet or funny.
Everyone who is not strong or not patient is not patient and vice versa.
Everyone who is both patient and rich is both tall and generous and vice versa.
If susan is old then someone is not patient or not curious.
If someone is calm or curious then john is brave or not rich.
If someone is not creative then john is quiet and vice versa.
Paul is either generous or not generous.
Someone is not wise or kind.
Someone is both not wise and not calm.
Someone is curious.
Paul is curious.
Lucy is either patient or brave.
Someone is rich or strong.
Someone is funny. | Paul is strong. | neutral | (((~funny(mary)|~tall(mary)))=>((~old(susan)<~>generous(susan))))&
(![X]:((old(X)|calm(X))<=>humble(X)))&
(((~wise(susan)|tall(susan)))=>((~tall(paul)|tall(paul))))&
(![X]:(~kind(X)<=>(quiet(X)|kind(X))))&
(![X]:(~creative(X)<=>(calm(X)&brave(X))))&
((strong(paul))=>((old(paul)|~rich(paul))))&
(![X]:((~strong(X)<~>~happy(X))=>~patient(X)))&
((?[X]:((~kind(X)|wise(X))))=>(brave(mary)))&
(((creative(fred)&~funny(fred)))<=>(?[X]:(humble(X))))&
((?[X]:(~old(X)))<=>(?[X]:(creative(X))))&
(![X]:((~generous(X)<~>~humble(X))=>(quiet(X)<~>funny(X))))&
(![X]:((~strong(X)|~patient(X))<=>~patient(X)))&
(![X]:((patient(X)&rich(X))<=>(tall(X)&generous(X))))&
((old(susan))=>(?[X]:((~patient(X)|~curious(X)))))&
((?[X]:((calm(X)|curious(X))))=>((brave(john)|~rich(john))))&
((?[X]:(~creative(X)))<=>(quiet(john)))&
((generous(paul)<~>~generous(paul)))&
(?[X]:((~wise(X)|kind(X))))&
(?[X]:((~wise(X)&~calm(X))))&
(?[X]:(curious(X)))&
(curious(paul))&
((patient(lucy)<~>brave(lucy)))&
(?[X]:((rich(X)|strong(X))))&
(?[X]:(funny(X))) | strong(paul) | []
| null | 0 |
If alice is not humble then fred is either humble or not tall and vice versa.
Everyone who is both not old and not strong is both not brave and not rich and vice versa.
Everyone who is not quiet or not creative is either not tall or patient.
If fred is not creative or generous then someone is both happy and patient.
If someone is either not funny or not humble then alice is either not creative or tall.
If mary is quiet then someone is patient or not funny and vice versa.
Everyone who is both not creative and creative is not patient and vice versa.
If john is either funny or not funny then susan is quiet and vice versa.
Everyone who is funny is both patient and generous and vice versa.
Everyone who is not tall or not strong is happy or humble.
Everyone who is not humble or not old is not patient.
Everyone who is both humble and funny is both wise and old.
Everyone who is funny is not patient and vice versa.
If someone is both not strong and not humble then someone is either not tall or not generous.
Everyone who is not funny is either not kind or not humble and vice versa.
Someone is not generous or not kind.
Mary is quiet.
Someone is either not curious or tall.
Someone is both not happy and wise.
Paul is not funny or patient.
Mary is not quiet or tall.
Someone is funny or old.
Someone is not calm or not humble. | Mary is not kind. | entailment | ((~humble(alice))<=>((humble(fred)<~>~tall(fred))))&
(![X]:((~old(X)&~strong(X))<=>(~brave(X)&~rich(X))))&
(![X]:((~quiet(X)|~creative(X))=>(~tall(X)<~>patient(X))))&
(((~creative(fred)|generous(fred)))=>(?[X]:((happy(X)&patient(X)))))&
((?[X]:((~funny(X)<~>~humble(X))))=>((~creative(alice)<~>tall(alice))))&
((quiet(mary))<=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((~creative(X)&creative(X))<=>~patient(X)))&
(((funny(john)<~>~funny(john)))<=>(quiet(susan)))&
(![X]:(funny(X)<=>(patient(X)&generous(X))))&
(![X]:((~tall(X)|~strong(X))=>(happy(X)|humble(X))))&
(![X]:((~humble(X)|~old(X))=>~patient(X)))&
(![X]:((humble(X)&funny(X))=>(wise(X)&old(X))))&
(![X]:(funny(X)<=>~patient(X)))&
((?[X]:((~strong(X)&~humble(X))))=>(?[X]:((~tall(X)<~>~generous(X)))))&
(![X]:(~funny(X)<=>(~kind(X)<~>~humble(X))))&
(?[X]:((~generous(X)|~kind(X))))&
(quiet(mary))&
(?[X]:((~curious(X)<~>tall(X))))&
(?[X]:((~happy(X)&wise(X))))&
((~funny(paul)|patient(paul)))&
((~quiet(mary)|tall(mary)))&
(?[X]:((funny(X)|old(X))))&
(?[X]:((~calm(X)|~humble(X)))) | ~kind(mary) | [
"p6",
"p10",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 309747772685524526598424
% SZS output start Proof for 309747772685524526598424
7. ! [X0] : ((creative(X0) & ~creative(X0)) <=> ~patient(X0)) [input p6]
11. ! [X0] : ((~old(X0) | ~humble(X0)) => ~patient(X0)) [input p10]
13. ! [X0] : (funny(X0) <=> ~patient(X0)) [input p12]
15. ! [X0] : (~funny(X0) <=> (~kind(X0) <~> ~humble(X0))) [input p14]
24. kind(mary) [input hypothesis]
34. ! [X0] : (~patient(X0) | (old(X0) & humble(X0))) [ennf transformation 11]
49. ! [X0] : (((creative(X0) & ~creative(X0)) | patient(X0)) & (~patient(X0) | (~creative(X0) | creative(X0)))) [nnf transformation 7]
50. ! [X0] : (((creative(X0) & ~creative(X0)) | patient(X0)) & (~patient(X0) | ~creative(X0) | creative(X0))) [flattening 49]
54. ! [X0] : ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0))) [nnf transformation 13]
59. ! [X0] : ((~funny(X0) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | funny(X0))) [nnf transformation 15]
93. ~creative(X0) | patient(X0) [cnf transformation 50]
94. creative(X0) | patient(X0) [cnf transformation 50]
104. ~patient(X0) | humble(X0) [cnf transformation 34]
107. ~patient(X0) | ~funny(X0) [cnf transformation 54]
111. ~humble(X0) | ~kind(X0) | funny(X0) [cnf transformation 59]
123. kind(mary) [cnf transformation 24]
201. patient(X0) [subsumption resolution 93,94]
214. humble(X0) [subsumption resolution 104,201]
215. ~funny(X0) [subsumption resolution 107,201]
216. ~kind(X0) | funny(X0) [subsumption resolution 111,214]
217. ~kind(X0) [subsumption resolution 216,215]
234. $false [subsumption resolution 123,217]
% SZS output end Proof for 309747772685524526598424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and patient then someone is both rich and old and vice versa. Everyone who is both kind and not wise is either quiet or creative and vice versa. Everyone who is strong is both patient and not happy and vice versa. Everyone who is not funny is both not humble and not curious and vice versa. Everyone who is funny is not quiet or creative and vice versa. Everyone who is either funny or not creative is generous or kind. Everyone who is either not strong or not old is calm. Everyone who is rich or not calm is not patient. If mary is strong or generous then paul is either rich or not kind. Everyone who is not patient or not rich is both not wise and not quiet. Everyone who is not tall or calm is either not creative or not wise and vice versa. If someone is patient or not funny then someone is not patient. Everyone who is strong is humble. If someone is not happy or funny then mary is not tall. Everyone who is quiet is either not tall or not curious. If someone is either rich or not generous then someone is not patient or rich and vice versa. Alice is both not quiet and not tall. Someone is either not calm or not creative. Lucy is not humble or not rich. Fred is not calm or patient. John is both not happy and not rich. Someone is patient or old. Someone is either not quiet or not brave. | Fred is funny. | entailment | ((?[X]:((~happy(X)&patient(X))))<=>(?[X]:((rich(X)&old(X)))))&
(![X]:((kind(X)&~wise(X))<=>(quiet(X)<~>creative(X))))&
(![X]:(strong(X)<=>(patient(X)&~happy(X))))&
(![X]:(~funny(X)<=>(~humble(X)&~curious(X))))&
(![X]:(funny(X)<=>(~quiet(X)|creative(X))))&
(![X]:((funny(X)<~>~creative(X))=>(generous(X)|kind(X))))&
(![X]:((~strong(X)<~>~old(X))=>calm(X)))&
(![X]:((rich(X)|~calm(X))=>~patient(X)))&
(((strong(mary)|generous(mary)))=>((rich(paul)<~>~kind(paul))))&
(![X]:((~patient(X)|~rich(X))=>(~wise(X)&~quiet(X))))&
(![X]:((~tall(X)|calm(X))<=>(~creative(X)<~>~wise(X))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:(~patient(X))))&
(![X]:(strong(X)=>humble(X)))&
((?[X]:((~happy(X)|funny(X))))=>(~tall(mary)))&
(![X]:(quiet(X)=>(~tall(X)<~>~curious(X))))&
((?[X]:((rich(X)<~>~generous(X))))<=>(?[X]:((~patient(X)|rich(X)))))&
((~quiet(alice)&~tall(alice)))&
(?[X]:((~calm(X)<~>~creative(X))))&
((~humble(lucy)|~rich(lucy)))&
((~calm(fred)|patient(fred)))&
((~happy(john)&~rich(john)))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((~quiet(X)<~>~brave(X)))) | funny(fred) | [
"p4",
"p7",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 9002063664968226287292063
% SZS output start Proof for 9002063664968226287292063
5. ! [X0] : (funny(X0) <=> (creative(X0) | ~quiet(X0))) [input p4]
8. ! [X0] : ((~calm(X0) | rich(X0)) => ~patient(X0)) [input p7]
10. ! [X0] : ((~rich(X0) | ~patient(X0)) => (~quiet(X0) & ~wise(X0))) [input p9]
24. ~funny(fred) [input hypothesis]
31. ! [X0] : (~patient(X0) | (calm(X0) & ~rich(X0))) [ennf transformation 8]
33. ! [X0] : ((~quiet(X0) & ~wise(X0)) | (rich(X0) & patient(X0))) [ennf transformation 10]
49. ! [X0] : ((funny(X0) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ~funny(X0))) [nnf transformation 5]
50. ! [X0] : ((funny(X0) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ~funny(X0))) [flattening 49]
90. funny(X0) | quiet(X0) [cnf transformation 50]
96. ~rich(X0) | ~patient(X0) [cnf transformation 31]
104. ~quiet(X0) | patient(X0) [cnf transformation 33]
105. ~quiet(X0) | rich(X0) [cnf transformation 33]
136. ~funny(fred) [cnf transformation 24]
265. 29 <=> patient(fred) [avatar definition]
267. patient(fred) <- (29) [avatar component clause 265]
288. quiet(fred) [resolution 90,136]
292. patient(fred) [resolution 104,288]
293. 29 [avatar split clause 292,265]
299. rich(fred) [resolution 105,288]
319. ~patient(fred) [resolution 299,96]
320. $false <- (29) [subsumption resolution 319,267]
321. ~29 [avatar contradiction clause 320]
322. $false [avatar sat refutation 293,321]
% SZS output end Proof for 9002063664968226287292063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or quiet is not humble or patient and vice versa. Everyone who is both strong and calm is not tall and vice versa. If someone is patient or not brave then john is tall. Everyone who is calm is both not creative and old and vice versa. If someone is both calm and tall then someone is either calm or not patient. If mary is either not tall or strong then someone is both not rich and patient and vice versa. If someone is both not quiet and quiet then someone is both brave and happy. Everyone who is tall or quiet is both generous and not rich. If someone is both not calm and not curious then john is either not tall or brave and vice versa. Everyone who is calm or wise is funny. If john is humble then paul is not curious or creative and vice versa. If someone is either creative or generous then lucy is not rich or happy and vice versa. If someone is rich or not patient then someone is either not curious or funny and vice versa. If someone is both strong and not funny then someone is both not patient and happy and vice versa. Everyone who is not quiet is brave and vice versa. If someone is both not strong and patient then someone is both not strong and tall. Paul is calm. Lucy is not wise. Mary is creative. Someone is either not funny or not generous. Alice is either kind or brave. Mary is quiet. Someone is kind or not old. John is either not wise or patient. | Mary is rich. | contradiction | (![X]:((~patient(X)|quiet(X))<=>(~humble(X)|patient(X))))&
(![X]:((strong(X)&calm(X))<=>~tall(X)))&
((?[X]:((patient(X)|~brave(X))))=>(tall(john)))&
(![X]:(calm(X)<=>(~creative(X)&old(X))))&
((?[X]:((calm(X)&tall(X))))=>(?[X]:((calm(X)<~>~patient(X)))))&
(((~tall(mary)<~>strong(mary)))<=>(?[X]:((~rich(X)&patient(X)))))&
((?[X]:((~quiet(X)&quiet(X))))=>(?[X]:((brave(X)&happy(X)))))&
(![X]:((tall(X)|quiet(X))=>(generous(X)&~rich(X))))&
((?[X]:((~calm(X)&~curious(X))))<=>((~tall(john)<~>brave(john))))&
(![X]:((calm(X)|wise(X))=>funny(X)))&
((humble(john))<=>((~curious(paul)|creative(paul))))&
((?[X]:((creative(X)<~>generous(X))))<=>((~rich(lucy)|happy(lucy))))&
((?[X]:((rich(X)|~patient(X))))<=>(?[X]:((~curious(X)<~>funny(X)))))&
((?[X]:((strong(X)&~funny(X))))<=>(?[X]:((~patient(X)&happy(X)))))&
(![X]:(~quiet(X)<=>brave(X)))&
((?[X]:((~strong(X)&patient(X))))=>(?[X]:((~strong(X)&tall(X)))))&
(calm(paul))&
(~wise(lucy))&
(creative(mary))&
(?[X]:((~funny(X)<~>~generous(X))))&
((kind(alice)<~>brave(alice)))&
(quiet(mary))&
(?[X]:((kind(X)|~old(X))))&
((~wise(john)<~>patient(john))) | rich(mary) | [
"p1",
"p3",
"p7",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 660277096285233623539040
% SZS output start Proof for 660277096285233623539040
2. ! [X0] : ((calm(X0) & strong(X0)) <=> ~tall(X0)) [input p1]
4. ! [X0] : (calm(X0) <=> (old(X0) & ~creative(X0))) [input p3]
8. ! [X0] : ((quiet(X0) | tall(X0)) => (~rich(X0) & generous(X0))) [input p7]
19. creative(mary) [input p18]
25. rich(mary) [input hypothesis]
34. ! [X0] : ((~rich(X0) & generous(X0)) | (~quiet(X0) & ~tall(X0))) [ennf transformation 8]
39. ! [X0] : (((calm(X0) & strong(X0)) | tall(X0)) & (~tall(X0) | (~calm(X0) | ~strong(X0)))) [nnf transformation 2]
40. ! [X0] : (((calm(X0) & strong(X0)) | tall(X0)) & (~tall(X0) | ~calm(X0) | ~strong(X0))) [flattening 39]
41. ! [X0] : ((calm(X0) | (~old(X0) | creative(X0))) & ((old(X0) & ~creative(X0)) | ~calm(X0))) [nnf transformation 4]
42. ! [X0] : ((calm(X0) | ~old(X0) | creative(X0)) & ((old(X0) & ~creative(X0)) | ~calm(X0))) [flattening 41]
92. tall(X0) | calm(X0) [cnf transformation 40]
95. ~creative(X0) | ~calm(X0) [cnf transformation 42]
110. ~rich(X0) | ~tall(X0) [cnf transformation 34]
145. creative(mary) [cnf transformation 19]
154. rich(mary) [cnf transformation 25]
187. 8 <=> tall(mary) [avatar definition]
188. ~tall(mary) <- (~8) [avatar component clause 187]
385. ~calm(mary) [resolution 95,145]
393. ~tall(mary) [resolution 110,154]
396. ~8 [avatar split clause 393,187]
397. calm(mary) <- (~8) [resolution 188,92]
399. $false <- (~8) [subsumption resolution 397,385]
400. 8 [avatar contradiction clause 399]
401. $false [avatar sat refutation 396,400]
% SZS output end Proof for 660277096285233623539040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not wise is kind or not tall and vice versa.
Everyone who is either generous or tall is either curious or wise.
If someone is both not generous and kind then someone is creative or not calm and vice versa.
Everyone who is either not old or patient is not rich and vice versa.
Everyone who is either not strong or not calm is either not wise or happy.
If mary is both not patient and not quiet then someone is both happy and rich.
If someone is both tall and humble then someone is not rich or curious.
Everyone who is both wise and not brave is either not happy or wise and vice versa.
If paul is not funny or not calm then alice is either not patient or not brave and vice versa.
Everyone who is both not quiet and rich is both not brave and not funny.
Everyone who is either not wise or not strong is not happy or not wise and vice versa.
Everyone who is not brave is either not strong or not happy and vice versa.
If someone is not happy or not curious then someone is not tall or not calm and vice versa.
If alice is either happy or wise then susan is either happy or funny.
If someone is either not kind or generous then lucy is not rich or brave.
Everyone who is not kind or not humble is both not happy and strong and vice versa.
Lucy is not old or wise.
Mary is quiet or happy.
John is either creative or happy.
Someone is not patient or not happy.
Fred is not generous. | Alice is not happy. | contradiction | (![X]:((rich(X)&~wise(X))<=>(kind(X)|~tall(X))))&
(![X]:((generous(X)<~>tall(X))=>(curious(X)<~>wise(X))))&
((?[X]:((~generous(X)&kind(X))))<=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((~old(X)<~>patient(X))<=>~rich(X)))&
(![X]:((~strong(X)<~>~calm(X))=>(~wise(X)<~>happy(X))))&
(((~patient(mary)&~quiet(mary)))=>(?[X]:((happy(X)&rich(X)))))&
((?[X]:((tall(X)&humble(X))))=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((wise(X)&~brave(X))<=>(~happy(X)<~>wise(X))))&
(((~funny(paul)|~calm(paul)))<=>((~patient(alice)<~>~brave(alice))))&
(![X]:((~quiet(X)&rich(X))=>(~brave(X)&~funny(X))))&
(![X]:((~wise(X)<~>~strong(X))<=>(~happy(X)|~wise(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~happy(X))))&
((?[X]:((~happy(X)|~curious(X))))<=>(?[X]:((~tall(X)|~calm(X)))))&
(((happy(alice)<~>wise(alice)))=>((happy(susan)<~>funny(susan))))&
((?[X]:((~kind(X)<~>generous(X))))=>((~rich(lucy)|brave(lucy))))&
(![X]:((~kind(X)|~humble(X))<=>(~happy(X)&strong(X))))&
((~old(lucy)|wise(lucy)))&
((quiet(mary)|happy(mary)))&
((creative(john)<~>happy(john)))&
(?[X]:((~patient(X)|~happy(X))))&
(~generous(fred)) | ~happy(alice) | [
"p0",
"p7",
"p10",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 1785976718462189251558145
% SZS output start Proof for 1785976718462189251558145
1. ! [X0] : ((~wise(X0) & rich(X0)) <=> (~tall(X0) | kind(X0))) [input p0]
8. ! [X0] : ((~brave(X0) & wise(X0)) <=> (~happy(X0) <~> wise(X0))) [input p7]
11. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~wise(X0) | ~happy(X0))) [input p10]
16. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> (strong(X0) & ~happy(X0))) [input p15]
22. ~happy(alice) [input hypothesis]
35. ! [X0] : (((~wise(X0) & rich(X0)) | (tall(X0) & ~kind(X0))) & ((~tall(X0) | kind(X0)) | (wise(X0) | ~rich(X0)))) [nnf transformation 1]
36. ! [X0] : (((~wise(X0) & rich(X0)) | (tall(X0) & ~kind(X0))) & (~tall(X0) | kind(X0) | wise(X0) | ~rich(X0))) [flattening 35]
48. ! [X0] : (((~brave(X0) & wise(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0)))) & (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (brave(X0) | ~wise(X0)))) [nnf transformation 8]
49. ! [X0] : (((~brave(X0) & wise(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0)))) & (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | brave(X0) | ~wise(X0))) [flattening 48]
52. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (wise(X0) & happy(X0))) & ((~wise(X0) | ~happy(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 11]
53. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (wise(X0) & happy(X0))) & (~wise(X0) | ~happy(X0) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [flattening 52]
62. ! [X0] : (((~humble(X0) | ~kind(X0)) | (~strong(X0) | happy(X0))) & ((strong(X0) & ~happy(X0)) | (humble(X0) & kind(X0)))) [nnf transformation 16]
63. ! [X0] : ((~humble(X0) | ~kind(X0) | ~strong(X0) | happy(X0)) & ((strong(X0) & ~happy(X0)) | (humble(X0) & kind(X0)))) [flattening 62]
70. ~kind(X0) | ~wise(X0) [cnf transformation 36]
92. wise(X0) | wise(X0) | happy(X0) [cnf transformation 49]
104. ~strong(X0) | ~wise(X0) | happy(X0) [cnf transformation 53]
122. ~happy(X0) | kind(X0) [cnf transformation 63]
124. strong(X0) | kind(X0) [cnf transformation 63]
132. ~happy(alice) [cnf transformation 22]
136. happy(X0) | wise(X0) [duplicate literal removal 92]
204. ~strong(X0) | happy(X0) [subsumption resolution 104,136]
238. 22 <=> happy(alice) [avatar definition]
239. ~happy(alice) <- (~22) [avatar component clause 238]
252. 25 <=> wise(alice) [avatar definition]
254. wise(alice) <- (25) [avatar component clause 252]
304. ~22 [avatar split clause 132,238]
314. wise(alice) <- (~22) [resolution 136,239]
317. 25 | 22 [avatar split clause 314,238,252]
322. happy(X1) | kind(X1) [resolution 204,124]
323. kind(X1) [subsumption resolution 322,122]
326. ~wise(X0) [resolution 323,70]
409. $false <- (25) [resolution 326,254]
412. ~25 [avatar contradiction clause 409]
413. $false [avatar sat refutation 304,317,412]
% SZS output end Proof for 1785976718462189251558145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not brave or rich then paul is not rich or not old and vice versa.
If someone is generous or not creative then someone is happy or generous.
Everyone who is not patient or old is quiet or happy.
If john is not brave or not creative then someone is tall.
If mary is either calm or creative then someone is not tall or curious and vice versa.
Everyone who is both not generous and old is not curious.
If mary is both strong and not creative then someone is curious or not kind and vice versa.
If someone is brave then someone is either not quiet or not creative and vice versa.
If alice is both not old and not humble then someone is either wise or quiet.
Everyone who is either not patient or not creative is either curious or quiet.
Everyone who is both not creative and strong is not curious or curious and vice versa.
Everyone who is either funny or wise is kind.
If alice is funny then alice is tall or not tall and vice versa.
If paul is either not patient or not funny then someone is not old.
Everyone who is rich or calm is tall or not patient.
Everyone who is both curious and strong is not happy or not calm and vice versa.
Someone is not generous.
Someone is not rich or quiet.
Mary is either wise or not strong.
Alice is not humble.
Lucy is either not rich or generous.
Someone is either not old or quiet.
John is happy.
Someone is either old or not brave. | Fred is rich. | neutral | (((~brave(fred)|rich(fred)))<=>((~rich(paul)|~old(paul))))&
((?[X]:((generous(X)|~creative(X))))=>(?[X]:((happy(X)|generous(X)))))&
(![X]:((~patient(X)|old(X))=>(quiet(X)|happy(X))))&
(((~brave(john)|~creative(john)))=>(?[X]:(tall(X))))&
(((calm(mary)<~>creative(mary)))<=>(?[X]:((~tall(X)|curious(X)))))&
(![X]:((~generous(X)&old(X))=>~curious(X)))&
(((strong(mary)&~creative(mary)))<=>(?[X]:((curious(X)|~kind(X)))))&
((?[X]:(brave(X)))<=>(?[X]:((~quiet(X)<~>~creative(X)))))&
(((~old(alice)&~humble(alice)))=>(?[X]:((wise(X)<~>quiet(X)))))&
(![X]:((~patient(X)<~>~creative(X))=>(curious(X)<~>quiet(X))))&
(![X]:((~creative(X)&strong(X))<=>(~curious(X)|curious(X))))&
(![X]:((funny(X)<~>wise(X))=>kind(X)))&
((funny(alice))<=>((tall(alice)|~tall(alice))))&
(((~patient(paul)<~>~funny(paul)))=>(?[X]:(~old(X))))&
(![X]:((rich(X)|calm(X))=>(tall(X)|~patient(X))))&
(![X]:((curious(X)&strong(X))<=>(~happy(X)|~calm(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~rich(X)|quiet(X))))&
((wise(mary)<~>~strong(mary)))&
(~humble(alice))&
((~rich(lucy)<~>generous(lucy)))&
(?[X]:((~old(X)<~>quiet(X))))&
(happy(john))&
(?[X]:((old(X)<~>~brave(X)))) | rich(fred) | []
| null | 0 |
Everyone who is either not humble or happy is curious or not creative.
Everyone who is both calm and not funny is either old or quiet.
If susan is either not rich or not patient then someone is both not rich and not tall.
Everyone who is not wise is both not calm and brave and vice versa.
Everyone who is either not quiet or patient is happy and vice versa.
If john is not happy then lucy is either creative or humble.
If someone is not quiet or not curious then lucy is curious or rich and vice versa.
Everyone who is patient or funny is either not calm or generous and vice versa.
Everyone who is either wise or patient is either not tall or not brave and vice versa.
If lucy is not wise or not happy then someone is not happy or happy.
Everyone who is both not calm and not quiet is either strong or wise and vice versa.
Everyone who is both not curious and not brave is both not funny and happy and vice versa.
If alice is generous or not brave then someone is funny or not old and vice versa.
Everyone who is curious or not funny is calm and vice versa.
Everyone who is funny is both happy and not tall and vice versa.
Lucy is patient or not calm.
Fred is funny or calm.
Lucy is not old or calm.
Someone is either not brave or not quiet.
John is both patient and not brave.
Someone is either not quiet or old.
Paul is not humble.
John is not tall. | Fred is tall. | neutral | (![X]:((~humble(X)<~>happy(X))=>(curious(X)|~creative(X))))&
(![X]:((calm(X)&~funny(X))=>(old(X)<~>quiet(X))))&
(((~rich(susan)<~>~patient(susan)))=>(?[X]:((~rich(X)&~tall(X)))))&
(![X]:(~wise(X)<=>(~calm(X)&brave(X))))&
(![X]:((~quiet(X)<~>patient(X))<=>happy(X)))&
((~happy(john))=>((creative(lucy)<~>humble(lucy))))&
((?[X]:((~quiet(X)|~curious(X))))<=>((curious(lucy)|rich(lucy))))&
(![X]:((patient(X)|funny(X))<=>(~calm(X)<~>generous(X))))&
(![X]:((wise(X)<~>patient(X))<=>(~tall(X)<~>~brave(X))))&
(((~wise(lucy)|~happy(lucy)))=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((~calm(X)&~quiet(X))<=>(strong(X)<~>wise(X))))&
(![X]:((~curious(X)&~brave(X))<=>(~funny(X)&happy(X))))&
(((generous(alice)|~brave(alice)))<=>(?[X]:((funny(X)|~old(X)))))&
(![X]:((curious(X)|~funny(X))<=>calm(X)))&
(![X]:(funny(X)<=>(happy(X)&~tall(X))))&
((patient(lucy)|~calm(lucy)))&
((funny(fred)|calm(fred)))&
((~old(lucy)|calm(lucy)))&
(?[X]:((~brave(X)<~>~quiet(X))))&
((patient(john)&~brave(john)))&
(?[X]:((~quiet(X)<~>old(X))))&
(~humble(paul))&
(~tall(john)) | tall(fred) | []
| null | 0 |
If someone is both not generous and happy then mary is either not brave or old. If someone is not rich or not tall then mary is not old. If someone is both generous and not old then lucy is either not curious or not generous. Everyone who is either tall or kind is either kind or not kind and vice versa. Everyone who is either patient or not strong is not patient or old and vice versa. Everyone who is either calm or not strong is either kind or not brave and vice versa. Everyone who is both not patient and not funny is both old and not quiet. Everyone who is not quiet or wise is not strong or funny and vice versa. If someone is either curious or tall then someone is either not calm or rich. If lucy is creative then someone is not quiet. Everyone who is creative or not brave is not funny or patient and vice versa. Everyone who is either not calm or curious is both not tall and wise. Everyone who is kind or not creative is either not curious or not quiet and vice versa. Everyone who is wise or not humble is not creative or not calm and vice versa. Everyone who is either calm or not quiet is not quiet or kind and vice versa. Everyone who is tall or not patient is either creative or quiet. Mary is both funny and brave. Mary is either not happy or not generous. Someone is not wise. Someone is quiet. Lucy is not humble. Someone is funny. Someone is either not calm or not tall. | Lucy is strong. | neutral | ((?[X]:((~generous(X)&happy(X))))=>((~brave(mary)<~>old(mary))))&
((?[X]:((~rich(X)|~tall(X))))=>(~old(mary)))&
((?[X]:((generous(X)&~old(X))))=>((~curious(lucy)<~>~generous(lucy))))&
(![X]:((tall(X)<~>kind(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~patient(X)|old(X))))&
(![X]:((calm(X)<~>~strong(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~patient(X)&~funny(X))=>(old(X)&~quiet(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~strong(X)|funny(X))))&
((?[X]:((curious(X)<~>tall(X))))=>(?[X]:((~calm(X)<~>rich(X)))))&
((creative(lucy))=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)|~brave(X))<=>(~funny(X)|patient(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~tall(X)&wise(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)<~>~quiet(X))))&
(![X]:((wise(X)|~humble(X))<=>(~creative(X)|~calm(X))))&
(![X]:((calm(X)<~>~quiet(X))<=>(~quiet(X)|kind(X))))&
(![X]:((tall(X)|~patient(X))=>(creative(X)<~>quiet(X))))&
((funny(mary)&brave(mary)))&
((~happy(mary)<~>~generous(mary)))&
(?[X]:(~wise(X)))&
(?[X]:(quiet(X)))&
(~humble(lucy))&
(?[X]:(funny(X)))&
(?[X]:((~calm(X)<~>~tall(X)))) | strong(lucy) | []
| null | 0 |
Everyone who is not old is both not quiet and generous.
Everyone who is either calm or not creative is not brave or generous.
If someone is both humble and not quiet then lucy is either old or not funny and vice versa.
Everyone who is not calm is not strong.
If someone is not rich or curious then alice is not patient or tall.
Everyone who is not humble is both humble and generous.
Everyone who is not tall is either not old or brave and vice versa.
Everyone who is not wise or not quiet is both not tall and quiet.
If alice is both rich and kind then someone is not rich and vice versa.
If someone is not wise or wise then fred is not generous and vice versa.
If alice is not kind then fred is not rich.
If someone is either wise or old then someone is either rich or not curious.
Everyone who is humble or funny is strong and vice versa.
If fred is wise or tall then someone is both not happy and not wise and vice versa.
Everyone who is not quiet is not tall.
Paul is not rich.
Someone is not rich or not patient.
Fred is either not wise or not generous.
Someone is both not tall and rich.
Someone is quiet or kind.
John is both wise and not rich. | Fred is curious. | neutral | (![X]:(~old(X)=>(~quiet(X)&generous(X))))&
(![X]:((calm(X)<~>~creative(X))=>(~brave(X)|generous(X))))&
((?[X]:((humble(X)&~quiet(X))))<=>((old(lucy)<~>~funny(lucy))))&
(![X]:(~calm(X)=>~strong(X)))&
((?[X]:((~rich(X)|curious(X))))=>((~patient(alice)|tall(alice))))&
(![X]:(~humble(X)=>(humble(X)&generous(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>brave(X))))&
(![X]:((~wise(X)|~quiet(X))=>(~tall(X)&quiet(X))))&
(((rich(alice)&kind(alice)))<=>(?[X]:(~rich(X))))&
((?[X]:((~wise(X)|wise(X))))<=>(~generous(fred)))&
((~kind(alice))=>(~rich(fred)))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:((humble(X)|funny(X))<=>strong(X)))&
(((wise(fred)|tall(fred)))<=>(?[X]:((~happy(X)&~wise(X)))))&
(![X]:(~quiet(X)=>~tall(X)))&
(~rich(paul))&
(?[X]:((~rich(X)|~patient(X))))&
((~wise(fred)<~>~generous(fred)))&
(?[X]:((~tall(X)&rich(X))))&
(?[X]:((quiet(X)|kind(X))))&
((wise(john)&~rich(john))) | curious(fred) | []
| null | 0 |
Everyone who is old is not funny.
Everyone who is curious is calm.
Everyone who is both strong and brave is wise or not old and vice versa.
Everyone who is kind or curious is either not creative or old and vice versa.
If fred is not calm then john is either not brave or kind and vice versa.
Everyone who is kind or quiet is both not humble and happy.
Everyone who is not quiet is generous.
Everyone who is not calm is both humble and kind.
If someone is not wise or brave then someone is patient and vice versa.
If someone is not curious then susan is either funny or not wise.
Everyone who is both tall and happy is either not curious or not rich.
If mary is either creative or wise then someone is not quiet or curious and vice versa.
Everyone who is both not happy and strong is either not generous or old.
If someone is not happy then someone is generous.
Everyone who is either not creative or not brave is either happy or not calm and vice versa.
If someone is not calm then john is either kind or not rich.
Lucy is either not funny or quiet.
Someone is both not humble and generous.
Someone is either not wise or funny.
Alice is either not rich or not wise.
Someone is both not curious and tall.
Alice is not old.
Someone is both brave and not kind.
Someone is either strong or not wise. | Alice is happy. | entailment | (![X]:(old(X)=>~funny(X)))&
(![X]:(curious(X)=>calm(X)))&
(![X]:((strong(X)&brave(X))<=>(wise(X)|~old(X))))&
(![X]:((kind(X)|curious(X))<=>(~creative(X)<~>old(X))))&
((~calm(fred))<=>((~brave(john)<~>kind(john))))&
(![X]:((kind(X)|quiet(X))=>(~humble(X)&happy(X))))&
(![X]:(~quiet(X)=>generous(X)))&
(![X]:(~calm(X)=>(humble(X)&kind(X))))&
((?[X]:((~wise(X)|brave(X))))<=>(?[X]:(patient(X))))&
((?[X]:(~curious(X)))=>((funny(susan)<~>~wise(susan))))&
(![X]:((tall(X)&happy(X))=>(~curious(X)<~>~rich(X))))&
(((creative(mary)<~>wise(mary)))<=>(?[X]:((~quiet(X)|curious(X)))))&
(![X]:((~happy(X)&strong(X))=>(~generous(X)<~>old(X))))&
((?[X]:(~happy(X)))=>(?[X]:(generous(X))))&
(![X]:((~creative(X)<~>~brave(X))<=>(happy(X)<~>~calm(X))))&
((?[X]:(~calm(X)))=>((kind(john)<~>~rich(john))))&
((~funny(lucy)<~>quiet(lucy)))&
(?[X]:((~humble(X)&generous(X))))&
(?[X]:((~wise(X)<~>funny(X))))&
((~rich(alice)<~>~wise(alice)))&
(?[X]:((~curious(X)&tall(X))))&
(~old(alice))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:((strong(X)<~>~wise(X)))) | happy(alice) | [
"p2",
"p5",
"p6",
"p12",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 1147154136813479340290544
% SZS output start Proof for 1147154136813479340290544
3. ! [X0] : ((brave(X0) & strong(X0)) <=> (~old(X0) | wise(X0))) [input p2]
6. ! [X0] : ((quiet(X0) | kind(X0)) => (happy(X0) & ~humble(X0))) [input p5]
7. ! [X0] : (~quiet(X0) => generous(X0)) [input p6]
13. ! [X0] : ((strong(X0) & ~happy(X0)) => (~generous(X0) <~> old(X0))) [input p12]
22. ~old(alice) [input p21]
25. ~happy(alice) [input hypothesis]
30. ! [X0] : ((happy(X0) & ~humble(X0)) | (~quiet(X0) & ~kind(X0))) [ennf transformation 6]
31. ! [X0] : (generous(X0) | quiet(X0)) [ennf transformation 7]
36. ! [X0] : ((~generous(X0) <~> old(X0)) | (~strong(X0) | happy(X0))) [ennf transformation 13]
37. ! [X0] : ((~generous(X0) <~> old(X0)) | ~strong(X0) | happy(X0)) [flattening 36]
40. ! [X0] : (((brave(X0) & strong(X0)) | (old(X0) & ~wise(X0))) & ((~old(X0) | wise(X0)) | (~brave(X0) | ~strong(X0)))) [nnf transformation 3]
41. ! [X0] : (((brave(X0) & strong(X0)) | (old(X0) & ~wise(X0))) & (~old(X0) | wise(X0) | ~brave(X0) | ~strong(X0))) [flattening 40]
56. ! [X0] : (((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | ~strong(X0) | happy(X0)) [nnf transformation 37]
80. strong(X0) | old(X0) [cnf transformation 41]
96. ~quiet(X0) | happy(X0) [cnf transformation 30]
97. generous(X0) | quiet(X0) [cnf transformation 31]
113. old(X0) | ~generous(X0) | ~strong(X0) | happy(X0) [cnf transformation 56]
136. ~old(alice) [cnf transformation 22]
141. ~happy(alice) [cnf transformation 25]
211. ~generous(X0) | old(X0) | happy(X0) [subsumption resolution 113,80]
302. old(X0) | happy(X0) | quiet(X0) [resolution 211,97]
321. happy(X0) | old(X0) [subsumption resolution 302,96]
507. old(alice) [resolution 321,141]
513. $false [subsumption resolution 507,136]
% SZS output end Proof for 1147154136813479340290544
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not strong is creative or not creative and vice versa. Everyone who is both not quiet and generous is either tall or strong and vice versa. Everyone who is not curious or not calm is either strong or not humble. If someone is not happy then john is either not happy or tall and vice versa. If someone is either not kind or tall then someone is not humble. Everyone who is both humble and not funny is either not strong or not happy and vice versa. Everyone who is both not kind and creative is calm. If someone is both patient and calm then lucy is brave or quiet. If someone is both not creative and wise then mary is both wise and not old and vice versa. Everyone who is not strong or not calm is curious or not strong and vice versa. If susan is not generous then someone is not funny. Everyone who is generous or not generous is both not brave and not wise and vice versa. Everyone who is funny is both not strong and not kind and vice versa. If someone is either happy or not old then paul is both not quiet and not kind. Everyone who is kind or not strong is both not funny and not humble. John is both not wise and not tall. Alice is rich or calm. Mary is happy or not creative. Someone is calm. Fred is strong or not generous. Someone is either humble or not curious. | Susan is not old. | contradiction | (![X]:((brave(X)|~strong(X))<=>(creative(X)|~creative(X))))&
(![X]:((~quiet(X)&generous(X))<=>(tall(X)<~>strong(X))))&
(![X]:((~curious(X)|~calm(X))=>(strong(X)<~>~humble(X))))&
((?[X]:(~happy(X)))<=>((~happy(john)<~>tall(john))))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:(~humble(X))))&
(![X]:((humble(X)&~funny(X))<=>(~strong(X)<~>~happy(X))))&
(![X]:((~kind(X)&creative(X))=>calm(X)))&
((?[X]:((patient(X)&calm(X))))=>((brave(lucy)|quiet(lucy))))&
((?[X]:((~creative(X)&wise(X))))<=>((wise(mary)&~old(mary))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)|~strong(X))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|~generous(X))<=>(~brave(X)&~wise(X))))&
(![X]:(funny(X)<=>(~strong(X)&~kind(X))))&
((?[X]:((happy(X)<~>~old(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)&~humble(X))))&
((~wise(john)&~tall(john)))&
((rich(alice)|calm(alice)))&
((happy(mary)|~creative(mary)))&
(?[X]:(calm(X)))&
((strong(fred)|~generous(fred)))&
(?[X]:((humble(X)<~>~curious(X)))) | ~old(susan) | [
"p0",
"p5",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 26076346347177317056356
% SZS output start Proof for 26076346347177317056356
1. ! [X0] : ((~strong(X0) | brave(X0)) <=> (~creative(X0) | creative(X0))) [input p0]
6. ! [X0] : ((~funny(X0) & humble(X0)) <=> (~strong(X0) <~> ~happy(X0))) [input p5]
12. ! [X0] : ((~generous(X0) | generous(X0)) <=> (~wise(X0) & ~brave(X0))) [input p11]
13. ! [X0] : (funny(X0) <=> (~kind(X0) & ~strong(X0))) [input p12]
14. ? [X0] : (happy(X0) <~> ~old(X0)) => (~kind(paul) & ~quiet(paul)) [input p13]
15. ! [X0] : ((~strong(X0) | kind(X0)) => (~humble(X0) & ~funny(X0))) [input p14]
22. ~old(susan) [input hypothesis]
31. (~kind(paul) & ~quiet(paul)) | ! [X0] : (happy(X0) <=> ~old(X0)) [ennf transformation 14]
32. ! [X0] : ((~humble(X0) & ~funny(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 15]
33. ! [X0] : (((~strong(X0) | brave(X0)) | (creative(X0) & ~creative(X0))) & ((~creative(X0) | creative(X0)) | (strong(X0) & ~brave(X0)))) [nnf transformation 1]
34. ! [X0] : ((~strong(X0) | brave(X0) | (creative(X0) & ~creative(X0))) & (~creative(X0) | creative(X0) | (strong(X0) & ~brave(X0)))) [flattening 33]
46. ! [X0] : (((~funny(X0) & humble(X0)) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | (funny(X0) | ~humble(X0)))) [nnf transformation 6]
47. ! [X0] : (((~funny(X0) & humble(X0)) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | funny(X0) | ~humble(X0))) [flattening 46]
57. ! [X0] : (((~generous(X0) | generous(X0)) | (wise(X0) | brave(X0))) & ((~wise(X0) & ~brave(X0)) | (generous(X0) & ~generous(X0)))) [nnf transformation 12]
58. ! [X0] : ((~generous(X0) | generous(X0) | wise(X0) | brave(X0)) & ((~wise(X0) & ~brave(X0)) | (generous(X0) & ~generous(X0)))) [flattening 57]
59. ! [X0] : ((funny(X0) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | ~funny(X0))) [nnf transformation 13]
60. ! [X0] : ((funny(X0) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | ~funny(X0))) [flattening 59]
61. (~kind(paul) & ~quiet(paul)) | ! [X0] : ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))) [nnf transformation 31]
69. ~strong(X0) | brave(X0) | ~creative(X0) [cnf transformation 34]
70. ~strong(X0) | brave(X0) | creative(X0) [cnf transformation 34]
89. ~happy(X0) | humble(X0) | strong(X0) [cnf transformation 47]
103. ~brave(X0) | ~generous(X0) [cnf transformation 58]
104. ~brave(X0) | generous(X0) [cnf transformation 58]
108. ~funny(X0) | ~strong(X0) [cnf transformation 60]
110. funny(X0) | kind(X0) | strong(X0) [cnf transformation 60]
114. ~kind(paul) | happy(X0) | old(X0) [cnf transformation 61]
116. ~funny(X0) | strong(X0) [cnf transformation 32]
118. ~humble(X0) | strong(X0) [cnf transformation 32]
126. ~old(susan) [cnf transformation 22]
127. ~strong(X0) | brave(X0) [subsumption resolution 69,70]
192. ~brave(X0) [subsumption resolution 103,104]
194. 15 <=> ! [X0] : (happy(X0) | old(X0)) [avatar definition]
195. old(X0) | happy(X0) <- (15) [avatar component clause 194]
197. 16 <=> kind(paul) [avatar definition]
199. ~kind(paul) <- (~16) [avatar component clause 197]
200. 15 | ~16 [avatar split clause 114,197,194]
211. ~funny(X0) [subsumption resolution 116,108]
259. kind(X4) | strong(X4) [resolution 110,211]
261. strong(paul) <- (~16) [resolution 259,199]
269. brave(paul) <- (~16) [resolution 261,127]
300. $false <- (~16) [subsumption resolution 269,192]
301. 16 [avatar contradiction clause 300]
304. happy(susan) <- (15) [resolution 195,126]
310. humble(susan) | strong(susan) <- (15) [resolution 304,89]
311. strong(susan) <- (15) [subsumption resolution 310,118]
321. brave(susan) <- (15) [resolution 311,127]
330. $false <- (15) [subsumption resolution 321,192]
331. ~15 [avatar contradiction clause 330]
332. $false [avatar sat refutation 200,301,331]
% SZS output end Proof for 26076346347177317056356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then someone is either quiet or not tall. Everyone who is not quiet or not brave is not kind or funny. If someone is both not happy and quiet then fred is tall or brave. Everyone who is not wise or patient is not tall. Everyone who is not tall or funny is calm and vice versa. If someone is either not funny or brave then someone is quiet and vice versa. Everyone who is either patient or not rich is both not tall and not old. Everyone who is either rich or not rich is funny or patient and vice versa. Everyone who is curious is not generous. Everyone who is calm is happy and vice versa. If someone is both humble and not humble then someone is either not creative or not kind. Everyone who is both not quiet and not old is not funny or not wise. Everyone who is not curious or wise is wise or happy. If fred is either happy or strong then someone is both not strong and kind and vice versa. Everyone who is both not quiet and curious is not wise. If someone is both patient and not calm then someone is both not old and not kind. Someone is not kind or brave. Lucy is old or not wise. Someone is both not wise and generous. Susan is both not brave and rich. Someone is both not tall and patient. Someone is not generous. Someone is both quiet and happy. | Susan is calm. | entailment | ((?[X]:(funny(X)))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:((~quiet(X)|~brave(X))=>(~kind(X)|funny(X))))&
((?[X]:((~happy(X)&quiet(X))))=>((tall(fred)|brave(fred))))&
(![X]:((~wise(X)|patient(X))=>~tall(X)))&
(![X]:((~tall(X)|funny(X))<=>calm(X)))&
((?[X]:((~funny(X)<~>brave(X))))<=>(?[X]:(quiet(X))))&
(![X]:((patient(X)<~>~rich(X))=>(~tall(X)&~old(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(funny(X)|patient(X))))&
(![X]:(curious(X)=>~generous(X)))&
(![X]:(calm(X)<=>happy(X)))&
((?[X]:((humble(X)&~humble(X))))=>(?[X]:((~creative(X)<~>~kind(X)))))&
(![X]:((~quiet(X)&~old(X))=>(~funny(X)|~wise(X))))&
(![X]:((~curious(X)|wise(X))=>(wise(X)|happy(X))))&
(((happy(fred)<~>strong(fred)))<=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~quiet(X)&curious(X))=>~wise(X)))&
((?[X]:((patient(X)&~calm(X))))=>(?[X]:((~old(X)&~kind(X)))))&
(?[X]:((~kind(X)|brave(X))))&
((old(lucy)|~wise(lucy)))&
(?[X]:((~wise(X)&generous(X))))&
((~brave(susan)&rich(susan)))&
(?[X]:((~tall(X)&patient(X))))&
(?[X]:(~generous(X)))&
(?[X]:((quiet(X)&happy(X)))) | calm(susan) | [
"p3",
"p4",
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 4991461680774017853232423
% SZS output start Proof for 4991461680774017853232423
4. ! [X0] : ((patient(X0) | ~wise(X0)) => ~tall(X0)) [input p3]
5. ! [X0] : ((funny(X0) | ~tall(X0)) <=> calm(X0)) [input p4]
8. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> (patient(X0) | funny(X0))) [input p7]
24. ~calm(susan) [input hypothesis]
34. ! [X0] : (~tall(X0) | (~patient(X0) & wise(X0))) [ennf transformation 4]
49. ! [X0] : (((funny(X0) | ~tall(X0)) | ~calm(X0)) & (calm(X0) | (~funny(X0) & tall(X0)))) [nnf transformation 5]
50. ! [X0] : ((funny(X0) | ~tall(X0) | ~calm(X0)) & (calm(X0) | (~funny(X0) & tall(X0)))) [flattening 49]
57. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | (~patient(X0) & ~funny(X0))) & ((patient(X0) | funny(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 8]
58. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | (~patient(X0) & ~funny(X0))) & (patient(X0) | funny(X0) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [flattening 57]
87. ~patient(X0) | ~tall(X0) [cnf transformation 34]
88. calm(X0) | tall(X0) [cnf transformation 50]
89. ~funny(X0) | calm(X0) [cnf transformation 50]
99. patient(X0) | funny(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
100. patient(X0) | funny(X0) | rich(X0) | rich(X0) [cnf transformation 58]
133. ~calm(susan) [cnf transformation 24]
134. patient(X0) | funny(X0) | ~rich(X0) [duplicate literal removal 99]
135. patient(X0) | funny(X0) | rich(X0) [duplicate literal removal 100]
187. patient(X0) | funny(X0) [subsumption resolution 134,135]
245. tall(susan) [resolution 88,133]
255. ~tall(X0) | funny(X0) [resolution 187,87]
262. funny(susan) [resolution 255,245]
267. calm(susan) [resolution 262,89]
268. $false [subsumption resolution 267,133]
% SZS output end Proof for 4991461680774017853232423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or kind then someone is not humble.
If someone is both not happy and not funny then someone is both wise and not kind and vice versa.
If mary is not happy then alice is either not tall or humble.
Everyone who is either quiet or kind is not wise and vice versa.
If paul is not curious or funny then someone is not quiet and vice versa.
Everyone who is happy is both creative and not strong and vice versa.
Everyone who is quiet is creative or not generous.
If paul is not kind then fred is both curious and not happy.
If someone is quiet or not generous then someone is both not old and not tall and vice versa.
Everyone who is curious or strong is both not wise and not humble and vice versa.
If someone is both not generous and not humble then susan is not generous.
If paul is creative or wise then lucy is rich or happy and vice versa.
Everyone who is both calm and not quiet is not rich or not wise.
Everyone who is patient or wise is quiet and vice versa.
Everyone who is both tall and generous is not tall or not creative and vice versa.
Mary is funny or not wise.
Someone is not curious.
Mary is both not wise and kind.
Mary is not quiet or curious.
Someone is kind or not rich.
John is not curious or old.
Someone is either strong or not kind. | Paul is wise. | contradiction | ((?[X]:((~wise(X)|kind(X))))=>(?[X]:(~humble(X))))&
((?[X]:((~happy(X)&~funny(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
((~happy(mary))=>((~tall(alice)<~>humble(alice))))&
(![X]:((quiet(X)<~>kind(X))<=>~wise(X)))&
(((~curious(paul)|funny(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(happy(X)<=>(creative(X)&~strong(X))))&
(![X]:(quiet(X)=>(creative(X)|~generous(X))))&
((~kind(paul))=>((curious(fred)&~happy(fred))))&
((?[X]:((quiet(X)|~generous(X))))<=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
(((creative(paul)|wise(paul)))<=>((rich(lucy)|happy(lucy))))&
(![X]:((calm(X)&~quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(![X]:((tall(X)&generous(X))<=>(~tall(X)|~creative(X))))&
((funny(mary)|~wise(mary)))&
(?[X]:(~curious(X)))&
((~wise(mary)&kind(mary)))&
((~quiet(mary)|curious(mary)))&
(?[X]:((kind(X)|~rich(X))))&
((~curious(john)|old(john)))&
(?[X]:((strong(X)<~>~kind(X)))) | wise(paul) | [
"p8",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3549997803451977597870432
% SZS output start Proof for 3549997803451977597870432
9. ? [X0] : (~generous(X0) | quiet(X0)) <=> ? [X0] : (~tall(X0) & ~old(X0)) [input p8]
14. ! [X0] : ((wise(X0) | patient(X0)) <=> quiet(X0)) [input p13]
15. ! [X0] : ((generous(X0) & tall(X0)) <=> (~creative(X0) | ~tall(X0))) [input p14]
23. wise(paul) [input hypothesis]
26. ? [X0] : (~generous(X0) | quiet(X0)) <=> ? [X1] : (~tall(X1) & ~old(X1)) [rectify 9]
51. (? [X0] : (~generous(X0) | quiet(X0)) | ! [X1] : (tall(X1) | old(X1))) & (? [X1] : (~tall(X1) & ~old(X1)) | ! [X0] : (generous(X0) & ~quiet(X0))) [nnf transformation 26]
52. (? [X0] : (~generous(X0) | quiet(X0)) | ! [X1] : (tall(X1) | old(X1))) & (? [X2] : (~tall(X2) & ~old(X2)) | ! [X3] : (generous(X3) & ~quiet(X3))) [rectify 51]
53. ? [X0] : (~generous(X0) | quiet(X0)) => (~generous(sK4) | quiet(sK4)) [choice axiom]
54. ? [X2] : (~tall(X2) & ~old(X2)) => (~tall(sK5) & ~old(sK5)) [choice axiom]
55. ((~generous(sK4) | quiet(sK4)) | ! [X1] : (tall(X1) | old(X1))) & ((~tall(sK5) & ~old(sK5)) | ! [X3] : (generous(X3) & ~quiet(X3))) [skolemisation 52,54,53]
60. ! [X0] : (((wise(X0) | patient(X0)) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [nnf transformation 14]
61. ! [X0] : ((wise(X0) | patient(X0) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [flattening 60]
62. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 15]
63. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | ~generous(X0) | ~tall(X0))) [flattening 62]
94. ~tall(sK5) | ~quiet(X3) [cnf transformation 55]
108. ~wise(X0) | quiet(X0) [cnf transformation 61]
111. tall(X0) | tall(X0) [cnf transformation 63]
124. wise(paul) [cnf transformation 23]
126. tall(X0) [duplicate literal removal 111]
227. 24 <=> tall(sK5) [avatar definition]
229. ~tall(sK5) <- (~24) [avatar component clause 227]
232. 25 <=> ! [X3] : ~quiet(X3) [avatar definition]
233. ~quiet(X3) <- (25) [avatar component clause 232]
234. 25 | ~24 [avatar split clause 94,227,232]
258. 31 <=> wise(paul) [avatar definition]
260. wise(paul) <- (31) [avatar component clause 258]
317. 31 [avatar split clause 124,258]
318. $false <- (~24) [subsumption resolution 229,126]
319. 24 [avatar contradiction clause 318]
328. quiet(paul) <- (31) [resolution 108,260]
329. $false <- (25, 31) [subsumption resolution 328,233]
330. ~25 | ~31 [avatar contradiction clause 329]
331. $false [avatar sat refutation 234,317,319,330]
% SZS output end Proof for 3549997803451977597870432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both creative and not creative then mary is either curious or tall. If john is not tall then alice is happy. Everyone who is not quiet is not generous. Everyone who is old or not patient is patient and vice versa. If someone is both not rich and not calm then someone is tall or calm. If mary is either rich or not generous then paul is both not curious and strong. Everyone who is not brave or patient is either not old or not quiet. If someone is not generous or not creative then someone is not wise. If lucy is either not funny or not patient then paul is both not kind and not happy. Everyone who is either not generous or calm is both not patient and happy. Everyone who is both calm and old is tall. If someone is brave then someone is either quiet or not brave and vice versa. If someone is either strong or rich then alice is both creative and not funny and vice versa. If fred is not kind then someone is either strong or creative and vice versa. If someone is either creative or patient then lucy is not calm or curious and vice versa. John is calm. Alice is both not humble and brave. Someone is both not quiet and not strong. Someone is either generous or rich. Someone is either kind or not calm. Someone is patient. Fred is not curious or not calm. | Fred is tall. | entailment | (((creative(mary)&~creative(mary)))=>((curious(mary)<~>tall(mary))))&
((~tall(john))=>(happy(alice)))&
(![X]:(~quiet(X)=>~generous(X)))&
(![X]:((old(X)|~patient(X))<=>patient(X)))&
((?[X]:((~rich(X)&~calm(X))))=>(?[X]:((tall(X)|calm(X)))))&
(((rich(mary)<~>~generous(mary)))=>((~curious(paul)&strong(paul))))&
(![X]:((~brave(X)|patient(X))=>(~old(X)<~>~quiet(X))))&
((?[X]:((~generous(X)|~creative(X))))=>(?[X]:(~wise(X))))&
(((~funny(lucy)<~>~patient(lucy)))=>((~kind(paul)&~happy(paul))))&
(![X]:((~generous(X)<~>calm(X))=>(~patient(X)&happy(X))))&
(![X]:((calm(X)&old(X))=>tall(X)))&
((?[X]:(brave(X)))<=>(?[X]:((quiet(X)<~>~brave(X)))))&
((?[X]:((strong(X)<~>rich(X))))<=>((creative(alice)&~funny(alice))))&
((~kind(fred))<=>(?[X]:((strong(X)<~>creative(X)))))&
((?[X]:((creative(X)<~>patient(X))))<=>((~calm(lucy)|curious(lucy))))&
(calm(john))&
((~humble(alice)&brave(alice)))&
(?[X]:((~quiet(X)&~strong(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:((kind(X)<~>~calm(X))))&
(?[X]:(patient(X)))&
((~curious(fred)|~calm(fred))) | tall(fred) | [
"p2",
"p3",
"p6",
"p9",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 6690041171582957121216546
% SZS output start Proof for 6690041171582957121216546
3. ! [X0] : (~quiet(X0) => ~generous(X0)) [input p2]
4. ! [X0] : ((~patient(X0) | old(X0)) <=> patient(X0)) [input p3]
7. ! [X0] : ((patient(X0) | ~brave(X0)) => (~old(X0) <~> ~quiet(X0))) [input p6]
10. ! [X0] : ((~generous(X0) <~> calm(X0)) => (happy(X0) & ~patient(X0))) [input p9]
11. ! [X0] : ((old(X0) & calm(X0)) => tall(X0)) [input p10]
23. ~tall(fred) [input hypothesis]
32. ! [X0] : (~generous(X0) | quiet(X0)) [ennf transformation 3]
35. ! [X0] : ((~old(X0) <~> ~quiet(X0)) | (~patient(X0) & brave(X0))) [ennf transformation 7]
37. ! [X0] : ((happy(X0) & ~patient(X0)) | (~generous(X0) <=> calm(X0))) [ennf transformation 10]
38. ! [X0] : (tall(X0) | (~old(X0) | ~calm(X0))) [ennf transformation 11]
39. ! [X0] : (tall(X0) | ~old(X0) | ~calm(X0)) [flattening 38]
41. ! [X0] : (((~patient(X0) | old(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) & ~old(X0)))) [nnf transformation 4]
42. ! [X0] : ((~patient(X0) | old(X0) | ~patient(X0)) & (patient(X0) | (patient(X0) & ~old(X0)))) [flattening 41]
47. ! [X0] : (((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | (~patient(X0) & brave(X0))) [nnf transformation 35]
49. ! [X0] : ((happy(X0) & ~patient(X0)) | ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0)))) [nnf transformation 37]
82. ~generous(X0) | quiet(X0) [cnf transformation 32]
84. patient(X0) | patient(X0) [cnf transformation 42]
85. ~patient(X0) | old(X0) | ~patient(X0) [cnf transformation 42]
92. ~quiet(X0) | ~old(X0) | ~patient(X0) [cnf transformation 47]
99. ~patient(X0) | calm(X0) | generous(X0) [cnf transformation 49]
103. ~calm(X0) | ~old(X0) | tall(X0) [cnf transformation 39]
134. ~tall(fred) [cnf transformation 23]
135. patient(X0) [duplicate literal removal 84]
136. ~patient(X0) | old(X0) [duplicate literal removal 85]
178. ~old(X0) | ~quiet(X0) [subsumption resolution 92,135]
196. calm(X0) | generous(X0) [subsumption resolution 99,135]
318. 39 <=> calm(fred) [avatar definition]
319. calm(fred) <- (39) [avatar component clause 318]
320. ~calm(fred) <- (~39) [avatar component clause 318]
324. old(X0) [resolution 136,135]
328. ~quiet(X0) [resolution 324,178]
333. generous(fred) <- (~39) [resolution 196,320]
345. quiet(fred) <- (~39) [resolution 333,82]
346. $false <- (~39) [subsumption resolution 345,328]
347. 39 [avatar contradiction clause 346]
376. ~old(fred) | tall(fred) <- (39) [resolution 103,319]
384. tall(fred) <- (39) [subsumption resolution 376,324]
385. $false <- (39) [subsumption resolution 384,134]
386. ~39 [avatar contradiction clause 385]
388. $false [avatar sat refutation 347,386]
% SZS output end Proof for 6690041171582957121216546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both curious and strong.
Everyone who is not generous is either not brave or not happy.
Everyone who is both not rich and generous is not kind and vice versa.
Everyone who is kind or not generous is either creative or not humble and vice versa.
If someone is not brave then someone is both curious and not creative.
If lucy is either quiet or happy then mary is calm or wise.
If someone is both tall and generous then someone is both not tall and funny and vice versa.
If lucy is funny then susan is not strong and vice versa.
Everyone who is both brave and creative is either not humble or not old and vice versa.
If someone is either tall or not strong then lucy is not creative and vice versa.
Everyone who is happy or patient is not humble.
If fred is either curious or calm then someone is both strong and creative and vice versa.
Everyone who is either tall or brave is tall or patient and vice versa.
Everyone who is not old or brave is happy and vice versa.
Everyone who is brave or not wise is humble.
Everyone who is either not old or kind is both generous and not kind.
Someone is creative.
Alice is both generous and humble.
Paul is generous.
Fred is quiet or happy.
Susan is either not quiet or not happy.
Mary is both not brave and humble. | Susan is not curious. | neutral | (![X]:(~humble(X)=>(curious(X)&strong(X))))&
(![X]:(~generous(X)=>(~brave(X)<~>~happy(X))))&
(![X]:((~rich(X)&generous(X))<=>~kind(X)))&
(![X]:((kind(X)|~generous(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:(~brave(X)))=>(?[X]:((curious(X)&~creative(X)))))&
(((quiet(lucy)<~>happy(lucy)))=>((calm(mary)|wise(mary))))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((~tall(X)&funny(X)))))&
((funny(lucy))<=>(~strong(susan)))&
(![X]:((brave(X)&creative(X))<=>(~humble(X)<~>~old(X))))&
((?[X]:((tall(X)<~>~strong(X))))<=>(~creative(lucy)))&
(![X]:((happy(X)|patient(X))=>~humble(X)))&
(((curious(fred)<~>calm(fred)))<=>(?[X]:((strong(X)&creative(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(tall(X)|patient(X))))&
(![X]:((~old(X)|brave(X))<=>happy(X)))&
(![X]:((brave(X)|~wise(X))=>humble(X)))&
(![X]:((~old(X)<~>kind(X))=>(generous(X)&~kind(X))))&
(?[X]:(creative(X)))&
((generous(alice)&humble(alice)))&
(generous(paul))&
((quiet(fred)|happy(fred)))&
((~quiet(susan)<~>~happy(susan)))&
((~brave(mary)&humble(mary))) | ~curious(susan) | []
| null | 0 |
If someone is not generous or not happy then someone is not old.
Everyone who is both creative and not humble is both not brave and wise and vice versa.
Everyone who is both patient and not rich is both not old and old.
Everyone who is both not rich and not funny is both not calm and not wise and vice versa.
If mary is not creative then someone is both not kind and not quiet and vice versa.
Everyone who is both not kind and old is quiet and vice versa.
If fred is either old or generous then someone is happy or calm.
Everyone who is either creative or not curious is not creative or happy.
Everyone who is either humble or not quiet is not patient or not curious and vice versa.
Everyone who is both not happy and wise is both strong and rich and vice versa.
Everyone who is not old is kind or not generous and vice versa.
If someone is old then alice is both not brave and funny and vice versa.
Everyone who is both funny and calm is either tall or not tall and vice versa.
If someone is kind or not generous then someone is both not curious and curious and vice versa.
Everyone who is generous or calm is not patient or brave and vice versa.
Everyone who is not old or strong is both not humble and not generous and vice versa.
Someone is either not funny or not wise.
Susan is not wise or not patient.
Alice is humble.
Susan is rich or tall.
Susan is generous. | Alice is old. | entailment | ((?[X]:((~generous(X)|~happy(X))))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~humble(X))<=>(~brave(X)&wise(X))))&
(![X]:((patient(X)&~rich(X))=>(~old(X)&old(X))))&
(![X]:((~rich(X)&~funny(X))<=>(~calm(X)&~wise(X))))&
((~creative(mary))<=>(?[X]:((~kind(X)&~quiet(X)))))&
(![X]:((~kind(X)&old(X))<=>quiet(X)))&
(((old(fred)<~>generous(fred)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((creative(X)<~>~curious(X))=>(~creative(X)|happy(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(~patient(X)|~curious(X))))&
(![X]:((~happy(X)&wise(X))<=>(strong(X)&rich(X))))&
(![X]:(~old(X)<=>(kind(X)|~generous(X))))&
((?[X]:(old(X)))<=>((~brave(alice)&funny(alice))))&
(![X]:((funny(X)&calm(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((kind(X)|~generous(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|strong(X))<=>(~humble(X)&~generous(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
((~wise(susan)|~patient(susan)))&
(humble(alice))&
((rich(susan)|tall(susan)))&
(generous(susan)) | old(alice) | [
"p15",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 341665898679844619438693
% SZS output start Proof for 341665898679844619438693
16. ! [X0] : ((strong(X0) | ~old(X0)) <=> (~generous(X0) & ~humble(X0))) [input p15]
19. humble(alice) [input p18]
22. ~old(alice) [input hypothesis]
68. ! [X0] : (((strong(X0) | ~old(X0)) | (generous(X0) | humble(X0))) & ((~generous(X0) & ~humble(X0)) | (~strong(X0) & old(X0)))) [nnf transformation 16]
69. ! [X0] : ((strong(X0) | ~old(X0) | generous(X0) | humble(X0)) & ((~generous(X0) & ~humble(X0)) | (~strong(X0) & old(X0)))) [flattening 68]
126. ~humble(X0) | old(X0) [cnf transformation 69]
134. humble(alice) [cnf transformation 19]
137. ~old(alice) [cnf transformation 22]
247. old(alice) [resolution 126,134]
248. $false [subsumption resolution 247,137]
% SZS output end Proof for 341665898679844619438693
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or rich is funny or strong and vice versa.
If mary is not generous then paul is both not rich and wise and vice versa.
If susan is both not curious and patient then someone is not strong or funny.
Everyone who is either not old or not creative is both wise and tall.
Everyone who is either not rich or not happy is both curious and generous and vice versa.
If someone is not happy or not kind then john is happy or generous and vice versa.
If someone is either not curious or old then john is both not patient and wise and vice versa.
Everyone who is old or not generous is brave.
Everyone who is both not kind and not tall is not tall or rich and vice versa.
Everyone who is both not calm and brave is not funny and vice versa.
Everyone who is not kind is not old or tall.
Everyone who is not rich or wise is either rich or not curious and vice versa.
Everyone who is kind is both patient and not funny and vice versa.
Everyone who is either not rich or quiet is tall or creative and vice versa.
If someone is both curious and strong then susan is either generous or kind.
If someone is curious then mary is not happy.
Someone is calm.
Susan is either happy or not rich.
Someone is both not curious and patient.
Fred is either generous or patient.
Paul is quiet.
Mary is not quiet.
Lucy is kind.
Someone is not brave or not patient. | John is patient. | contradiction | (![X]:((brave(X)|rich(X))<=>(funny(X)|strong(X))))&
((~generous(mary))<=>((~rich(paul)&wise(paul))))&
(((~curious(susan)&patient(susan)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~old(X)<~>~creative(X))=>(wise(X)&tall(X))))&
(![X]:((~rich(X)<~>~happy(X))<=>(curious(X)&generous(X))))&
((?[X]:((~happy(X)|~kind(X))))<=>((happy(john)|generous(john))))&
((?[X]:((~curious(X)<~>old(X))))<=>((~patient(john)&wise(john))))&
(![X]:((old(X)|~generous(X))=>brave(X)))&
(![X]:((~kind(X)&~tall(X))<=>(~tall(X)|rich(X))))&
(![X]:((~calm(X)&brave(X))<=>~funny(X)))&
(![X]:(~kind(X)=>(~old(X)|tall(X))))&
(![X]:((~rich(X)|wise(X))<=>(rich(X)<~>~curious(X))))&
(![X]:(kind(X)<=>(patient(X)&~funny(X))))&
(![X]:((~rich(X)<~>quiet(X))<=>(tall(X)|creative(X))))&
((?[X]:((curious(X)&strong(X))))=>((generous(susan)<~>kind(susan))))&
((?[X]:(curious(X)))=>(~happy(mary)))&
(?[X]:(calm(X)))&
((happy(susan)<~>~rich(susan)))&
(?[X]:((~curious(X)&patient(X))))&
((generous(fred)<~>patient(fred)))&
(quiet(paul))&
(~quiet(mary))&
(kind(lucy))&
(?[X]:((~brave(X)|~patient(X)))) | patient(john) | [
"p3",
"p6",
"p8",
"p10",
"p11",
"p13",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 28389173522886241555239
% SZS output start Proof for 28389173522886241555239
4. ! [X0] : ((~old(X0) <~> ~creative(X0)) => (tall(X0) & wise(X0))) [input p3]
7. ? [X0] : (~curious(X0) <~> old(X0)) <=> (wise(john) & ~patient(john)) [input p6]
9. ! [X0] : ((~tall(X0) & ~kind(X0)) <=> (rich(X0) | ~tall(X0))) [input p8]
11. ! [X0] : (~kind(X0) => (tall(X0) | ~old(X0))) [input p10]
12. ! [X0] : ((wise(X0) | ~rich(X0)) <=> (rich(X0) <~> ~curious(X0))) [input p11]
14. ! [X0] : ((~rich(X0) <~> quiet(X0)) <=> (creative(X0) | tall(X0))) [input p13]
21. quiet(paul) [input p20]
25. patient(john) [input hypothesis]
28. ! [X0] : ((tall(X0) & wise(X0)) | (~old(X0) <=> ~creative(X0))) [ennf transformation 4]
30. ! [X0] : ((tall(X0) | ~old(X0)) | kind(X0)) [ennf transformation 11]
31. ! [X0] : (tall(X0) | ~old(X0) | kind(X0)) [flattening 30]
40. ! [X0] : ((tall(X0) & wise(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) [nnf transformation 28]
48. (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | (~wise(john) | patient(john))) & ((wise(john) & ~patient(john)) | ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) [nnf transformation 7]
49. (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ~wise(john) | patient(john)) & ((wise(john) & ~patient(john)) | ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) [flattening 48]
50. (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ~wise(john) | patient(john)) & ((wise(john) & ~patient(john)) | ! [X1] : ((~curious(X1) | ~old(X1)) & (old(X1) | curious(X1)))) [rectify 49]
51. ? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) => ((~old(sK2) | curious(sK2)) & (old(sK2) | ~curious(sK2))) [choice axiom]
52. (((~old(sK2) | curious(sK2)) & (old(sK2) | ~curious(sK2))) | ~wise(john) | patient(john)) & ((wise(john) & ~patient(john)) | ! [X1] : ((~curious(X1) | ~old(X1)) & (old(X1) | curious(X1)))) [skolemisation 50,51]
53. ! [X0] : (((~tall(X0) & ~kind(X0)) | (~rich(X0) & tall(X0))) & ((rich(X0) | ~tall(X0)) | (tall(X0) | kind(X0)))) [nnf transformation 9]
54. ! [X0] : (((~tall(X0) & ~kind(X0)) | (~rich(X0) & tall(X0))) & (rich(X0) | ~tall(X0) | tall(X0) | kind(X0))) [flattening 53]
57. ! [X0] : (((wise(X0) | ~rich(X0)) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (~wise(X0) & rich(X0)))) [nnf transformation 12]
58. ! [X0] : ((wise(X0) | ~rich(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (~wise(X0) & rich(X0)))) [flattening 57]
61. ! [X0] : ((((~quiet(X0) | rich(X0)) & (quiet(X0) | ~rich(X0))) | (~creative(X0) & ~tall(X0))) & ((creative(X0) | tall(X0)) | ((~rich(X0) | ~quiet(X0)) & (quiet(X0) | rich(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~quiet(X0) | rich(X0)) & (quiet(X0) | ~rich(X0))) | (~creative(X0) & ~tall(X0))) & (creative(X0) | tall(X0) | ((~rich(X0) | ~quiet(X0)) & (quiet(X0) | rich(X0))))) [flattening 61]
82. ~creative(X0) | tall(X0) | old(X0) [cnf transformation 40]
94. ~patient(john) | old(X1) | curious(X1) [cnf transformation 52]
103. ~kind(X0) | tall(X0) [cnf transformation 54]
106. ~tall(X0) | ~rich(X0) [cnf transformation 54]
110. tall(X0) | ~old(X0) | kind(X0) [cnf transformation 31]
111. ~curious(X0) | rich(X0) | rich(X0) [cnf transformation 58]
121. creative(X0) | tall(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 62]
124. ~quiet(X0) | rich(X0) | ~tall(X0) [cnf transformation 62]
136. quiet(paul) [cnf transformation 21]
140. patient(john) [cnf transformation 25]
141. ~curious(X0) | rich(X0) [duplicate literal removal 111]
144. 1 <=> rich(paul) [avatar definition]
146. rich(paul) <- (1) [avatar component clause 144]
202. 14 <=> patient(john) [avatar definition]
224. 19 <=> ! [X1] : (old(X1) | curious(X1)) [avatar definition]
225. old(X1) | curious(X1) <- (19) [avatar component clause 224]
228. 19 | ~14 [avatar split clause 94,202,224]
229. ~old(X0) | tall(X0) [subsumption resolution 110,103]
230. ~quiet(X0) | ~tall(X0) [subsumption resolution 124,106]
231. ~quiet(X0) | ~rich(X0) | creative(X0) [subsumption resolution 121,230]
282. 14 [avatar split clause 140,202]
293. tall(X0) | curious(X0) <- (19) [resolution 229,225]
294. ~tall(paul) [resolution 230,136]
340. curious(paul) <- (19) [resolution 293,294]
342. rich(paul) <- (19) [resolution 340,141]
346. 1 | ~19 [avatar split clause 342,224,144]
426. ~rich(paul) | creative(paul) [resolution 231,136]
427. creative(paul) <- (1) [subsumption resolution 426,146]
429. tall(paul) | old(paul) <- (1) [resolution 427,82]
431. old(paul) <- (1) [subsumption resolution 429,294]
526. tall(paul) <- (1) [resolution 431,229]
529. $false <- (1) [subsumption resolution 526,294]
530. ~1 [avatar contradiction clause 529]
533. $false [avatar sat refutation 228,282,346,530]
% SZS output end Proof for 28389173522886241555239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not funny or not quiet then someone is generous. If john is either quiet or not wise then someone is quiet and vice versa. Everyone who is both not strong and funny is both generous and strong and vice versa. Everyone who is both creative and wise is brave. If someone is both not creative and patient then someone is either not kind or patient and vice versa. Everyone who is either patient or quiet is kind or not quiet and vice versa. If someone is either not wise or patient then lucy is both not happy and not brave and vice versa. If susan is both kind and not quiet then someone is either humble or not wise and vice versa. If mary is generous or wise then mary is both not kind and not creative and vice versa. Everyone who is either not humble or quiet is both funny and not tall. Everyone who is patient or not creative is not curious and vice versa. If mary is not strong or not quiet then alice is not funny or not curious and vice versa. If someone is generous then john is brave. Everyone who is either not tall or not funny is not kind. Everyone who is not rich is both not quiet and curious. Everyone who is both kind and happy is not calm or not brave and vice versa. Someone is calm or not tall. Paul is not humble or not calm. Paul is both happy and not kind. Someone is either generous or not curious. John is both not creative and not wise. Mary is both not funny and patient. John is not wise or rich. Alice is not old or not brave. | Susan is not rich. | contradiction | (((~funny(fred)|~quiet(fred)))=>(?[X]:(generous(X))))&
(((quiet(john)<~>~wise(john)))<=>(?[X]:(quiet(X))))&
(![X]:((~strong(X)&funny(X))<=>(generous(X)&strong(X))))&
(![X]:((creative(X)&wise(X))=>brave(X)))&
((?[X]:((~creative(X)&patient(X))))<=>(?[X]:((~kind(X)<~>patient(X)))))&
(![X]:((patient(X)<~>quiet(X))<=>(kind(X)|~quiet(X))))&
((?[X]:((~wise(X)<~>patient(X))))<=>((~happy(lucy)&~brave(lucy))))&
(((kind(susan)&~quiet(susan)))<=>(?[X]:((humble(X)<~>~wise(X)))))&
(((generous(mary)|wise(mary)))<=>((~kind(mary)&~creative(mary))))&
(![X]:((~humble(X)<~>quiet(X))=>(funny(X)&~tall(X))))&
(![X]:((patient(X)|~creative(X))<=>~curious(X)))&
(((~strong(mary)|~quiet(mary)))<=>((~funny(alice)|~curious(alice))))&
((?[X]:(generous(X)))=>(brave(john)))&
(![X]:((~tall(X)<~>~funny(X))=>~kind(X)))&
(![X]:(~rich(X)=>(~quiet(X)&curious(X))))&
(![X]:((kind(X)&happy(X))<=>(~calm(X)|~brave(X))))&
(?[X]:((calm(X)|~tall(X))))&
((~humble(paul)|~calm(paul)))&
((happy(paul)&~kind(paul)))&
(?[X]:((generous(X)<~>~curious(X))))&
((~creative(john)&~wise(john)))&
((~funny(mary)&patient(mary)))&
((~wise(john)|rich(john)))&
((~old(alice)|~brave(alice))) | ~rich(susan) | [
"p5",
"p6",
"p7",
"p10",
"p14",
"p15",
"p17",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 5945985090979674081885551
% SZS output start Proof for 5945985090979674081885551
6. ! [X0] : ((patient(X0) <~> quiet(X0)) <=> (~quiet(X0) | kind(X0))) [input p5]
7. ? [X0] : (~wise(X0) <~> patient(X0)) <=> (~brave(lucy) & ~happy(lucy)) [input p6]
8. (~quiet(susan) & kind(susan)) <=> ? [X0] : (humble(X0) <~> ~wise(X0)) [input p7]
11. ! [X0] : ((~creative(X0) | patient(X0)) <=> ~curious(X0)) [input p10]
15. ! [X0] : (~rich(X0) => (curious(X0) & ~quiet(X0))) [input p14]
16. ! [X0] : ((happy(X0) & kind(X0)) <=> (~brave(X0) | ~calm(X0))) [input p15]
18. ~calm(paul) | ~humble(paul) [input p17]
19. ~kind(paul) & happy(paul) [input p18]
25. ~rich(susan) [input hypothesis]
34. ! [X0] : ((curious(X0) & ~quiet(X0)) | rich(X0)) [ennf transformation 15]
48. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (quiet(X0) & ~kind(X0))) & ((~quiet(X0) | kind(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [nnf transformation 6]
49. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (quiet(X0) & ~kind(X0))) & (~quiet(X0) | kind(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [flattening 48]
50. (? [X0] : ((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | (brave(lucy) | happy(lucy))) & ((~brave(lucy) & ~happy(lucy)) | ! [X0] : ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0)))) [nnf transformation 7]
51. (? [X0] : ((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | brave(lucy) | happy(lucy)) & ((~brave(lucy) & ~happy(lucy)) | ! [X0] : ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0)))) [flattening 50]
52. (? [X0] : ((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | brave(lucy) | happy(lucy)) & ((~brave(lucy) & ~happy(lucy)) | ! [X1] : ((~wise(X1) | ~patient(X1)) & (patient(X1) | wise(X1)))) [rectify 51]
53. ? [X0] : ((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) => ((~patient(sK4) | wise(sK4)) & (patient(sK4) | ~wise(sK4))) [choice axiom]
54. (((~patient(sK4) | wise(sK4)) & (patient(sK4) | ~wise(sK4))) | brave(lucy) | happy(lucy)) & ((~brave(lucy) & ~happy(lucy)) | ! [X1] : ((~wise(X1) | ~patient(X1)) & (patient(X1) | wise(X1)))) [skolemisation 52,53]
55. ((~quiet(susan) & kind(susan)) | ! [X0] : ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (? [X0] : ((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | (quiet(susan) | ~kind(susan))) [nnf transformation 8]
56. ((~quiet(susan) & kind(susan)) | ! [X0] : ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (? [X0] : ((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | quiet(susan) | ~kind(susan)) [flattening 55]
57. ((~quiet(susan) & kind(susan)) | ! [X0] : ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (? [X1] : ((wise(X1) | ~humble(X1)) & (~wise(X1) | humble(X1))) | quiet(susan) | ~kind(susan)) [rectify 56]
58. ? [X1] : ((wise(X1) | ~humble(X1)) & (~wise(X1) | humble(X1))) => ((wise(sK5) | ~humble(sK5)) & (~wise(sK5) | humble(sK5))) [choice axiom]
59. ((~quiet(susan) & kind(susan)) | ! [X0] : ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (((wise(sK5) | ~humble(sK5)) & (~wise(sK5) | humble(sK5))) | quiet(susan) | ~kind(susan)) [skolemisation 57,58]
63. ! [X0] : (((~creative(X0) | patient(X0)) | curious(X0)) & (~curious(X0) | (creative(X0) & ~patient(X0)))) [nnf transformation 11]
64. ! [X0] : ((~creative(X0) | patient(X0) | curious(X0)) & (~curious(X0) | (creative(X0) & ~patient(X0)))) [flattening 63]
68. ! [X0] : (((happy(X0) & kind(X0)) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | (~happy(X0) | ~kind(X0)))) [nnf transformation 16]
69. ! [X0] : (((happy(X0) & kind(X0)) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | ~happy(X0) | ~kind(X0))) [flattening 68]
93. ~quiet(X0) | kind(X0) | patient(X0) | ~quiet(X0) [cnf transformation 49]
95. quiet(X0) | patient(X0) | quiet(X0) [cnf transformation 49]
99. ~happy(lucy) | ~wise(X1) | ~patient(X1) [cnf transformation 54]
101. ~brave(lucy) | ~wise(X1) | ~patient(X1) [cnf transformation 54]
109. ~quiet(susan) | humble(X0) | wise(X0) [cnf transformation 59]
119. ~curious(X0) | ~patient(X0) [cnf transformation 64]
130. rich(X0) | curious(X0) [cnf transformation 34]
132. calm(X0) | kind(X0) [cnf transformation 69]
135. happy(X0) | brave(X0) [cnf transformation 69]
137. ~calm(paul) | ~humble(paul) [cnf transformation 18]
139. ~kind(paul) [cnf transformation 19]
147. ~rich(susan) [cnf transformation 25]
148. ~quiet(X0) | kind(X0) | patient(X0) [duplicate literal removal 93]
149. patient(X0) | quiet(X0) [duplicate literal removal 95]
194. 10 <=> ! [X1] : (patient(X1) | kind(X1)) [avatar definition]
195. kind(X1) | patient(X1) <- (10) [avatar component clause 194]
216. kind(X0) | patient(X0) [subsumption resolution 148,149]
217. 10 [avatar split clause 216,194]
219. 15 <=> happy(lucy) [avatar definition]
220. ~happy(lucy) <- (~15) [avatar component clause 219]
223. 16 <=> brave(lucy) [avatar definition]
237. 19 <=> ! [X1] : (~wise(X1) | ~patient(X1)) [avatar definition]
238. ~patient(X1) | ~wise(X1) <- (19) [avatar component clause 237]
239. 19 | ~16 [avatar split clause 101,223,237]
244. 19 | ~15 [avatar split clause 99,219,237]
247. 21 <=> ! [X0] : (humble(X0) | wise(X0)) [avatar definition]
248. humble(X0) | wise(X0) <- (21) [avatar component clause 247]
250. 22 <=> quiet(susan) [avatar definition]
252. ~quiet(susan) <- (~22) [avatar component clause 250]
253. 21 | ~22 [avatar split clause 109,250,247]
333. 39 <=> humble(paul) [avatar definition]
335. ~humble(paul) <- (~39) [avatar component clause 333]
337. 40 <=> calm(paul) [avatar definition]
339. ~calm(paul) <- (~40) [avatar component clause 337]
340. ~39 | ~40 [avatar split clause 137,337,333]
364. curious(susan) [resolution 130,147]
365. kind(paul) <- (~40) [resolution 132,339]
366. $false <- (~40) [subsumption resolution 365,139]
367. 40 [avatar contradiction clause 366]
369. ~patient(susan) [resolution 364,119]
373. brave(lucy) <- (~15) [resolution 135,220]
376. 16 | 15 [avatar split clause 373,219,223]
386. patient(paul) <- (10) [resolution 195,139]
402. ~wise(paul) <- (10, 19) [resolution 238,386]
410. wise(paul) <- (21, ~39) [resolution 248,335]
412. $false <- (10, 19, 21, ~39) [subsumption resolution 410,402]
413. ~10 | ~19 | ~21 | 39 [avatar contradiction clause 412]
417. quiet(susan) [resolution 369,149]
418. $false <- (~22) [subsumption resolution 417,252]
419. 22 [avatar contradiction clause 418]
420. $false [avatar sat refutation 217,239,244,253,340,367,376,413,419]
% SZS output end Proof for 5945985090979674081885551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not curious is not tall and vice versa.
Everyone who is old is either humble or not wise.
If someone is not kind then john is both rich and not curious and vice versa.
If someone is calm or not calm then lucy is both creative and not generous and vice versa.
If someone is not generous or not curious then fred is not wise and vice versa.
Everyone who is either not calm or not happy is not calm and vice versa.
If someone is not curious then someone is kind or not happy.
Everyone who is either not kind or not rich is tall and vice versa.
Everyone who is not generous or not rich is curious.
If john is either humble or kind then john is either not kind or not brave.
Everyone who is not patient is old or calm.
Everyone who is not generous or not brave is both old and kind.
Everyone who is not brave is not curious and vice versa.
If lucy is not creative or happy then someone is not calm.
If someone is not funny then someone is not quiet or calm and vice versa.
If mary is rich then paul is calm and vice versa.
Susan is curious.
Someone is either old or not tall.
Mary is both creative and patient.
Someone is either not rich or funny.
Someone is not old.
Paul is curious. | Susan is not kind. | contradiction | (![X]:((~happy(X)&~curious(X))<=>~tall(X)))&
(![X]:(old(X)=>(humble(X)<~>~wise(X))))&
((?[X]:(~kind(X)))<=>((rich(john)&~curious(john))))&
((?[X]:((calm(X)|~calm(X))))<=>((creative(lucy)&~generous(lucy))))&
((?[X]:((~generous(X)|~curious(X))))<=>(~wise(fred)))&
(![X]:((~calm(X)<~>~happy(X))<=>~calm(X)))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((~kind(X)<~>~rich(X))<=>tall(X)))&
(![X]:((~generous(X)|~rich(X))=>curious(X)))&
(((humble(john)<~>kind(john)))=>((~kind(john)<~>~brave(john))))&
(![X]:(~patient(X)=>(old(X)|calm(X))))&
(![X]:((~generous(X)|~brave(X))=>(old(X)&kind(X))))&
(![X]:(~brave(X)<=>~curious(X)))&
(((~creative(lucy)|happy(lucy)))=>(?[X]:(~calm(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~quiet(X)|calm(X)))))&
((rich(mary))<=>(calm(paul)))&
(curious(susan))&
(?[X]:((old(X)<~>~tall(X))))&
((creative(mary)&patient(mary)))&
(?[X]:((~rich(X)<~>funny(X))))&
(?[X]:(~old(X)))&
(curious(paul)) | ~kind(susan) | [
"p0",
"p2",
"p5",
"p7",
"p8",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 4714256007729459950356842
% SZS output start Proof for 4714256007729459950356842
1. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> ~tall(X0)) [input p0]
3. ? [X0] : ~kind(X0) <=> (~curious(john) & rich(john)) [input p2]
6. ! [X0] : ((~calm(X0) <~> ~happy(X0)) <=> ~calm(X0)) [input p5]
8. ! [X0] : ((~kind(X0) <~> ~rich(X0)) <=> tall(X0)) [input p7]
9. ! [X0] : ((~rich(X0) | ~generous(X0)) => curious(X0)) [input p8]
12. ! [X0] : ((~brave(X0) | ~generous(X0)) => (kind(X0) & old(X0))) [input p11]
13. ! [X0] : (~brave(X0) <=> ~curious(X0)) [input p12]
23. ~kind(susan) [input hypothesis]
30. ! [X0] : (curious(X0) | (rich(X0) & generous(X0))) [ennf transformation 9]
32. ! [X0] : ((kind(X0) & old(X0)) | (brave(X0) & generous(X0))) [ennf transformation 12]
34. ! [X0] : (((~curious(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) | happy(X0)))) [nnf transformation 1]
35. ! [X0] : (((~curious(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | curious(X0) | happy(X0))) [flattening 34]
37. (? [X0] : ~kind(X0) | (curious(john) | ~rich(john))) & ((~curious(john) & rich(john)) | ! [X0] : kind(X0)) [nnf transformation 3]
38. (? [X0] : ~kind(X0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X0] : kind(X0)) [flattening 37]
39. (? [X0] : ~kind(X0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X1] : kind(X1)) [rectify 38]
40. ? [X0] : ~kind(X0) => ~kind(sK0) [choice axiom]
41. (~kind(sK0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X1] : kind(X1)) [skolemisation 39,40]
51. ! [X0] : ((((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | calm(X0)) & (~calm(X0) | ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0))))) [nnf transformation 6]
55. ! [X0] : ((((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | ~tall(X0)) & (tall(X0) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0))))) [nnf transformation 8]
57. ! [X0] : ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))) [nnf transformation 13]
75. ~happy(X0) | tall(X0) [cnf transformation 35]
80. ~curious(john) | kind(X1) [cnf transformation 41]
91. ~calm(X0) | ~calm(X0) | happy(X0) [cnf transformation 51]
93. happy(X0) | calm(X0) | calm(X0) [cnf transformation 51]
97. ~rich(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 55]
100. rich(X0) | curious(X0) [cnf transformation 30]
108. brave(X0) | kind(X0) [cnf transformation 32]
110. ~brave(X0) | curious(X0) [cnf transformation 57]
126. ~kind(susan) [cnf transformation 23]
129. ~calm(X0) | happy(X0) [duplicate literal removal 91]
130. calm(X0) | happy(X0) [duplicate literal removal 93]
136. 2 <=> curious(john) [avatar definition]
137. ~curious(john) <- (~2) [avatar component clause 136]
145. 4 <=> ! [X1] : kind(X1) [avatar definition]
146. kind(X1) <- (4) [avatar component clause 145]
147. 4 | ~2 [avatar split clause 80,136,145]
181. 12 <=> ! [X1] : curious(X1) [avatar definition]
182. curious(X1) <- (12) [avatar component clause 181]
188. happy(X0) [subsumption resolution 129,130]
267. $false <- (4) [resolution 146,126]
268. ~4 [avatar contradiction clause 267]
269. $false <- (~2, 12) [subsumption resolution 137,182]
270. 2 | ~12 [avatar contradiction clause 269]
273. tall(X0) [resolution 75,188]
296. kind(X0) | curious(X0) [resolution 110,108]
322. ~kind(X0) | ~tall(X0) | curious(X0) [resolution 97,100]
326. ~kind(X0) | curious(X0) [subsumption resolution 322,273]
327. curious(X0) [subsumption resolution 326,296]
328. 12 [avatar split clause 327,181]
329. $false [avatar sat refutation 147,268,270,328]
% SZS output end Proof for 4714256007729459950356842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is both funny and patient.
Everyone who is calm is either not humble or happy and vice versa.
If lucy is either kind or tall then someone is both brave and strong.
If someone is happy or strong then someone is not brave.
Everyone who is either not rich or not old is curious or not tall.
Everyone who is either not curious or tall is tall and vice versa.
Everyone who is both kind and old is either tall or not funny.
Everyone who is both happy and calm is either not humble or wise and vice versa.
If mary is both quiet and not funny then mary is both not creative and calm and vice versa.
If susan is both wise and not tall then someone is both not tall and strong.
Everyone who is not brave or not generous is either not tall or humble.
Everyone who is both not strong and creative is both not generous and creative.
If someone is both curious and not brave then alice is both happy and generous.
Everyone who is not generous or not strong is generous and vice versa.
Everyone who is not curious is either not quiet or patient.
Everyone who is not wise is curious or not rich and vice versa.
Someone is both funny and tall.
Lucy is either not calm or not quiet. | Mary is quiet. | neutral | (![X]:(~creative(X)=>(funny(X)&patient(X))))&
(![X]:(calm(X)<=>(~humble(X)<~>happy(X))))&
(((kind(lucy)<~>tall(lucy)))=>(?[X]:((brave(X)&strong(X)))))&
((?[X]:((happy(X)|strong(X))))=>(?[X]:(~brave(X))))&
(![X]:((~rich(X)<~>~old(X))=>(curious(X)|~tall(X))))&
(![X]:((~curious(X)<~>tall(X))<=>tall(X)))&
(![X]:((kind(X)&old(X))=>(tall(X)<~>~funny(X))))&
(![X]:((happy(X)&calm(X))<=>(~humble(X)<~>wise(X))))&
(((quiet(mary)&~funny(mary)))<=>((~creative(mary)&calm(mary))))&
(((wise(susan)&~tall(susan)))=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((~brave(X)|~generous(X))=>(~tall(X)<~>humble(X))))&
(![X]:((~strong(X)&creative(X))=>(~generous(X)&creative(X))))&
((?[X]:((curious(X)&~brave(X))))=>((happy(alice)&generous(alice))))&
(![X]:((~generous(X)|~strong(X))<=>generous(X)))&
(![X]:(~curious(X)=>(~quiet(X)<~>patient(X))))&
(![X]:(~wise(X)<=>(curious(X)|~rich(X))))&
(?[X]:((funny(X)&tall(X))))&
((~calm(lucy)<~>~quiet(lucy))) | quiet(mary) | []
| null | 0 |
Everyone who is either old or not kind is humble or not patient and vice versa.
If someone is either not creative or kind then fred is not generous or funny.
Everyone who is both not curious and not brave is creative or not rich and vice versa.
If someone is not curious or rich then someone is both not creative and old and vice versa.
If alice is either old or tall then alice is both not tall and not curious and vice versa.
Everyone who is both happy and not patient is not strong and vice versa.
Everyone who is not calm or generous is not old or rich.
Everyone who is patient or calm is both not old and calm.
If john is kind or old then john is not wise.
If lucy is not generous then someone is both brave and strong.
Everyone who is not curious is not tall or not curious.
If someone is either not tall or funny then someone is old.
If john is both not humble and kind then susan is both not brave and not curious.
If someone is both not happy and not creative then alice is funny and vice versa.
If lucy is both old and quiet then someone is both not creative and not rich and vice versa.
If lucy is old then someone is either not creative or not patient and vice versa.
Someone is both not happy and not brave.
Someone is funny.
John is not kind.
Someone is both funny and calm.
Mary is old or quiet.
Paul is both tall and creative.
Someone is not generous.
Someone is either not calm or not kind. | Alice is not rich. | contradiction | (![X]:((old(X)<~>~kind(X))<=>(humble(X)|~patient(X))))&
((?[X]:((~creative(X)<~>kind(X))))=>((~generous(fred)|funny(fred))))&
(![X]:((~curious(X)&~brave(X))<=>(creative(X)|~rich(X))))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((~creative(X)&old(X)))))&
(((old(alice)<~>tall(alice)))<=>((~tall(alice)&~curious(alice))))&
(![X]:((happy(X)&~patient(X))<=>~strong(X)))&
(![X]:((~calm(X)|generous(X))=>(~old(X)|rich(X))))&
(![X]:((patient(X)|calm(X))=>(~old(X)&calm(X))))&
(((kind(john)|old(john)))=>(~wise(john)))&
((~generous(lucy))=>(?[X]:((brave(X)&strong(X)))))&
(![X]:(~curious(X)=>(~tall(X)|~curious(X))))&
((?[X]:((~tall(X)<~>funny(X))))=>(?[X]:(old(X))))&
(((~humble(john)&kind(john)))=>((~brave(susan)&~curious(susan))))&
((?[X]:((~happy(X)&~creative(X))))<=>(funny(alice)))&
(((old(lucy)&quiet(lucy)))<=>(?[X]:((~creative(X)&~rich(X)))))&
((old(lucy))<=>(?[X]:((~creative(X)<~>~patient(X)))))&
(?[X]:((~happy(X)&~brave(X))))&
(?[X]:(funny(X)))&
(~kind(john))&
(?[X]:((funny(X)&calm(X))))&
((old(mary)|quiet(mary)))&
((tall(paul)&creative(paul)))&
(?[X]:(~generous(X)))&
(?[X]:((~calm(X)<~>~kind(X)))) | ~rich(alice) | [
"p2",
"p4",
"p6",
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 1484242270531654343532787
% SZS output start Proof for 1484242270531654343532787
3. ! [X0] : ((~brave(X0) & ~curious(X0)) <=> (~rich(X0) | creative(X0))) [input p2]
5. (old(alice) <~> tall(alice)) <=> (~curious(alice) & ~tall(alice)) [input p4]
7. ! [X0] : ((generous(X0) | ~calm(X0)) => (rich(X0) | ~old(X0))) [input p6]
8. ! [X0] : ((calm(X0) | patient(X0)) => (calm(X0) & ~old(X0))) [input p7]
25. ~rich(alice) [input hypothesis]
34. ! [X0] : ((rich(X0) | ~old(X0)) | (~generous(X0) & calm(X0))) [ennf transformation 7]
35. ! [X0] : (rich(X0) | ~old(X0) | (~generous(X0) & calm(X0))) [flattening 34]
36. ! [X0] : ((calm(X0) & ~old(X0)) | (~calm(X0) & ~patient(X0))) [ennf transformation 8]
46. ! [X0] : (((~brave(X0) & ~curious(X0)) | (rich(X0) & ~creative(X0))) & ((~rich(X0) | creative(X0)) | (brave(X0) | curious(X0)))) [nnf transformation 3]
47. ! [X0] : (((~brave(X0) & ~curious(X0)) | (rich(X0) & ~creative(X0))) & (~rich(X0) | creative(X0) | brave(X0) | curious(X0))) [flattening 46]
53. (((~tall(alice) | ~old(alice)) & (tall(alice) | old(alice))) | (curious(alice) | tall(alice))) & ((~curious(alice) & ~tall(alice)) | ((old(alice) | ~tall(alice)) & (tall(alice) | ~old(alice)))) [nnf transformation 5]
54. (((~tall(alice) | ~old(alice)) & (tall(alice) | old(alice))) | curious(alice) | tall(alice)) & ((~curious(alice) & ~tall(alice)) | ((old(alice) | ~tall(alice)) & (tall(alice) | ~old(alice)))) [flattening 53]
95. ~curious(X0) | rich(X0) [cnf transformation 47]
104. ~tall(alice) | old(alice) | ~tall(alice) [cnf transformation 54]
107. tall(alice) | old(alice) | curious(alice) | tall(alice) [cnf transformation 54]
110. ~old(X0) | rich(X0) | calm(X0) [cnf transformation 35]
113. ~calm(X0) | ~old(X0) [cnf transformation 36]
146. ~rich(alice) [cnf transformation 25]
147. ~tall(alice) | old(alice) [duplicate literal removal 104]
148. tall(alice) | old(alice) | curious(alice) [duplicate literal removal 107]
184. 9 <=> curious(alice) [avatar definition]
186. curious(alice) <- (9) [avatar component clause 184]
188. 10 <=> old(alice) [avatar definition]
190. old(alice) <- (10) [avatar component clause 188]
192. 11 <=> tall(alice) [avatar definition]
195. 9 | 10 | 11 [avatar split clause 148,192,188,184]
198. 10 | ~11 [avatar split clause 147,192,188]
323. rich(alice) <- (9) [resolution 95,186]
324. $false <- (9) [subsumption resolution 323,146]
325. ~9 [avatar contradiction clause 324]
403. rich(alice) | calm(alice) <- (10) [resolution 110,190]
407. calm(alice) <- (10) [subsumption resolution 403,146]
482. ~old(alice) <- (10) [resolution 407,113]
483. $false <- (10) [subsumption resolution 482,190]
484. ~10 [avatar contradiction clause 483]
485. $false [avatar sat refutation 195,198,325,484]
% SZS output end Proof for 1484242270531654343532787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not rich is not curious or not funny.
Everyone who is not funny is funny or not generous and vice versa.
Everyone who is rich is either not strong or kind.
If mary is not old or wise then alice is creative.
If susan is either calm or patient then someone is not patient and vice versa.
If someone is either not tall or rich then someone is not creative or not calm and vice versa.
Everyone who is wise is either not patient or patient and vice versa.
Everyone who is either not brave or not calm is either happy or creative and vice versa.
If fred is either funny or patient then lucy is both funny and patient.
Everyone who is both not calm and patient is both not creative and old and vice versa.
If someone is either not brave or wise then someone is both funny and rich.
If someone is either not calm or strong then lucy is not calm or wise and vice versa.
Everyone who is brave is either not strong or kind.
If lucy is not old then someone is either patient or not quiet and vice versa.
Everyone who is both not patient and generous is not happy and vice versa.
If someone is calm then susan is not kind or not creative and vice versa.
Someone is either quiet or not tall.
Lucy is not tall or not kind.
John is either calm or not patient.
Someone is creative or tall.
Someone is both patient and not funny.
Alice is either humble or not patient. | Fred is not rich. | neutral | (![X]:((~funny(X)|~rich(X))=>(~curious(X)|~funny(X))))&
(![X]:(~funny(X)<=>(funny(X)|~generous(X))))&
(![X]:(rich(X)=>(~strong(X)<~>kind(X))))&
(((~old(mary)|wise(mary)))=>(creative(alice)))&
(((calm(susan)<~>patient(susan)))<=>(?[X]:(~patient(X))))&
((?[X]:((~tall(X)<~>rich(X))))<=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:(wise(X)<=>(~patient(X)<~>patient(X))))&
(![X]:((~brave(X)<~>~calm(X))<=>(happy(X)<~>creative(X))))&
(((funny(fred)<~>patient(fred)))=>((funny(lucy)&patient(lucy))))&
(![X]:((~calm(X)&patient(X))<=>(~creative(X)&old(X))))&
((?[X]:((~brave(X)<~>wise(X))))=>(?[X]:((funny(X)&rich(X)))))&
((?[X]:((~calm(X)<~>strong(X))))<=>((~calm(lucy)|wise(lucy))))&
(![X]:(brave(X)=>(~strong(X)<~>kind(X))))&
((~old(lucy))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
(![X]:((~patient(X)&generous(X))<=>~happy(X)))&
((?[X]:(calm(X)))<=>((~kind(susan)|~creative(susan))))&
(?[X]:((quiet(X)<~>~tall(X))))&
((~tall(lucy)|~kind(lucy)))&
((calm(john)<~>~patient(john)))&
(?[X]:((creative(X)|tall(X))))&
(?[X]:((patient(X)&~funny(X))))&
((humble(alice)<~>~patient(alice))) | ~rich(fred) | []
| null | 0 |
Everyone who is not tall is either not rich or wise and vice versa.
Everyone who is generous is both strong and not old and vice versa.
If someone is either strong or happy then paul is both wise and not humble.
If mary is either rich or curious then someone is both not strong and humble.
If someone is patient or wise then susan is not funny or not strong.
If someone is either not happy or not quiet then mary is happy and vice versa.
Everyone who is curious or not patient is both not generous and kind and vice versa.
Everyone who is both funny and not strong is not generous and vice versa.
Everyone who is either not quiet or kind is kind and vice versa.
Everyone who is both not happy and not strong is either old or not funny.
Everyone who is both generous and kind is either quiet or patient.
Everyone who is not kind or kind is humble and vice versa.
If susan is brave then someone is either curious or not creative and vice versa.
If someone is both strong and not wise then someone is either not quiet or brave and vice versa.
If someone is either brave or not quiet then alice is both funny and not humble and vice versa.
Everyone who is both not humble and not old is both not kind and not curious.
Someone is both not rich and wise.
Fred is both tall and happy.
Someone is kind or not tall.
John is either not funny or not humble.
Someone is either not rich or not old.
Someone is both not patient and old.
Someone is both generous and not calm. | Mary is not humble. | contradiction | (![X]:(~tall(X)<=>(~rich(X)<~>wise(X))))&
(![X]:(generous(X)<=>(strong(X)&~old(X))))&
((?[X]:((strong(X)<~>happy(X))))=>((wise(paul)&~humble(paul))))&
(((rich(mary)<~>curious(mary)))=>(?[X]:((~strong(X)&humble(X)))))&
((?[X]:((patient(X)|wise(X))))=>((~funny(susan)|~strong(susan))))&
((?[X]:((~happy(X)<~>~quiet(X))))<=>(happy(mary)))&
(![X]:((curious(X)|~patient(X))<=>(~generous(X)&kind(X))))&
(![X]:((funny(X)&~strong(X))<=>~generous(X)))&
(![X]:((~quiet(X)<~>kind(X))<=>kind(X)))&
(![X]:((~happy(X)&~strong(X))=>(old(X)<~>~funny(X))))&
(![X]:((generous(X)&kind(X))=>(quiet(X)<~>patient(X))))&
(![X]:((~kind(X)|kind(X))<=>humble(X)))&
((brave(susan))<=>(?[X]:((curious(X)<~>~creative(X)))))&
((?[X]:((strong(X)&~wise(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((brave(X)<~>~quiet(X))))<=>((funny(alice)&~humble(alice))))&
(![X]:((~humble(X)&~old(X))=>(~kind(X)&~curious(X))))&
(?[X]:((~rich(X)&wise(X))))&
((tall(fred)&happy(fred)))&
(?[X]:((kind(X)|~tall(X))))&
((~funny(john)<~>~humble(john)))&
(?[X]:((~rich(X)<~>~old(X))))&
(?[X]:((~patient(X)&old(X))))&
(?[X]:((generous(X)&~calm(X)))) | ~humble(mary) | [
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 3220736242167300563623430
% SZS output start Proof for 3220736242167300563623430
12. ! [X0] : ((kind(X0) | ~kind(X0)) <=> humble(X0)) [input p11]
24. ~humble(mary) [input hypothesis]
55. ! [X0] : (((kind(X0) | ~kind(X0)) | ~humble(X0)) & (humble(X0) | (~kind(X0) & kind(X0)))) [nnf transformation 12]
56. ! [X0] : ((kind(X0) | ~kind(X0) | ~humble(X0)) & (humble(X0) | (~kind(X0) & kind(X0)))) [flattening 55]
120. humble(X0) | kind(X0) [cnf transformation 56]
121. humble(X0) | ~kind(X0) [cnf transformation 56]
153. ~humble(mary) [cnf transformation 24]
235. humble(X0) [subsumption resolution 120,121]
311. $false [subsumption resolution 153,235]
% SZS output end Proof for 3220736242167300563623430
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not funny is either not old or old and vice versa. If john is not quiet or not happy then alice is wise. Everyone who is either happy or not kind is not strong or brave. Everyone who is either not happy or not curious is either not quiet or happy and vice versa. Everyone who is both curious and not curious is both not curious and calm. Everyone who is either creative or humble is not wise or quiet and vice versa. Everyone who is both not strong and not kind is quiet or not quiet and vice versa. Everyone who is curious is either funny or not wise and vice versa. Everyone who is either quiet or not rich is either wise or kind and vice versa. If someone is humble then someone is rich or happy. If susan is either tall or not tall then fred is both old and not calm and vice versa. Everyone who is either not rich or not old is either old or not kind and vice versa. Everyone who is either curious or humble is both happy and calm. If lucy is rich then alice is either quiet or creative and vice versa. Everyone who is both rich and not wise is strong and vice versa. Everyone who is not tall is not funny. Alice is either curious or generous. Mary is happy or old. Fred is not strong or humble. Someone is both creative and happy. Mary is not strong or not brave. Someone is not happy or not creative. Alice is both quiet and not funny. | Alice is not humble. | contradiction | (![X]:((~calm(X)|~funny(X))<=>(~old(X)<~>old(X))))&
(((~quiet(john)|~happy(john)))=>(wise(alice)))&
(![X]:((happy(X)<~>~kind(X))=>(~strong(X)|brave(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:((curious(X)&~curious(X))=>(~curious(X)&calm(X))))&
(![X]:((creative(X)<~>humble(X))<=>(~wise(X)|quiet(X))))&
(![X]:((~strong(X)&~kind(X))<=>(quiet(X)|~quiet(X))))&
(![X]:(curious(X)<=>(funny(X)<~>~wise(X))))&
(![X]:((quiet(X)<~>~rich(X))<=>(wise(X)<~>kind(X))))&
((?[X]:(humble(X)))=>(?[X]:((rich(X)|happy(X)))))&
(((tall(susan)<~>~tall(susan)))<=>((old(fred)&~calm(fred))))&
(![X]:((~rich(X)<~>~old(X))<=>(old(X)<~>~kind(X))))&
(![X]:((curious(X)<~>humble(X))=>(happy(X)&calm(X))))&
((rich(lucy))<=>((quiet(alice)<~>creative(alice))))&
(![X]:((rich(X)&~wise(X))<=>strong(X)))&
(![X]:(~tall(X)=>~funny(X)))&
((curious(alice)<~>generous(alice)))&
((happy(mary)|old(mary)))&
((~strong(fred)|humble(fred)))&
(?[X]:((creative(X)&happy(X))))&
((~strong(mary)|~brave(mary)))&
(?[X]:((~happy(X)|~creative(X))))&
((quiet(alice)&~funny(alice))) | ~humble(alice) | [
"p5",
"p6",
"p11",
"p13",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 8675017790797431148364403
% SZS output start Proof for 8675017790797431148364403
6. ! [X0] : ((creative(X0) <~> humble(X0)) <=> (quiet(X0) | ~wise(X0))) [input p5]
7. ! [X0] : ((~kind(X0) & ~strong(X0)) <=> (~quiet(X0) | quiet(X0))) [input p6]
12. ! [X0] : ((~rich(X0) <~> ~old(X0)) <=> (old(X0) <~> ~kind(X0))) [input p11]
14. rich(lucy) <=> (quiet(alice) <~> creative(alice)) [input p13]
23. ~funny(alice) & quiet(alice) [input p22]
24. ~humble(alice) [input hypothesis]
38. ! [X0] : ((((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | (~quiet(X0) & wise(X0))) & ((quiet(X0) | ~wise(X0)) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0))))) [nnf transformation 6]
39. ! [X0] : ((((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | (~quiet(X0) & wise(X0))) & (quiet(X0) | ~wise(X0) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0))))) [flattening 38]
40. ! [X0] : (((~kind(X0) & ~strong(X0)) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | (kind(X0) | strong(X0)))) [nnf transformation 7]
41. ! [X0] : (((~kind(X0) & ~strong(X0)) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | kind(X0) | strong(X0))) [flattening 40]
49. ! [X0] : ((((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))))) [nnf transformation 12]
51. (rich(lucy) | ((quiet(alice) | ~creative(alice)) & (creative(alice) | ~quiet(alice)))) & (((~creative(alice) | ~quiet(alice)) & (creative(alice) | quiet(alice))) | ~rich(lucy)) [nnf transformation 14]
82. ~quiet(X0) | creative(X0) | humble(X0) [cnf transformation 39]
88. ~kind(X0) | ~quiet(X0) [cnf transformation 41]
89. ~kind(X0) | quiet(X0) [cnf transformation 41]
111. kind(X0) | ~old(X0) | ~old(X0) | rich(X0) [cnf transformation 49]
116. old(X0) | rich(X0) | old(X0) | kind(X0) [cnf transformation 49]
122. ~creative(alice) | ~quiet(alice) | ~rich(lucy) [cnf transformation 51]
137. quiet(alice) [cnf transformation 23]
139. ~humble(alice) [cnf transformation 24]
141. kind(X0) | ~old(X0) | rich(X0) [duplicate literal removal 111]
143. old(X0) | rich(X0) | kind(X0) [duplicate literal removal 116]
172. ~kind(X0) [subsumption resolution 88,89]
206. rich(X0) | old(X0) [subsumption resolution 143,172]
207. ~old(X0) | rich(X0) [subsumption resolution 141,172]
208. rich(X0) [subsumption resolution 207,206]
209. ~creative(alice) | ~quiet(alice) [subsumption resolution 122,208]
211. 10 <=> quiet(alice) [avatar definition]
212. quiet(alice) <- (10) [avatar component clause 211]
215. 11 <=> creative(alice) [avatar definition]
217. ~creative(alice) <- (~11) [avatar component clause 215]
218. ~10 | ~11 [avatar split clause 209,215,211]
251. 10 [avatar split clause 137,211]
258. creative(alice) | humble(alice) <- (10) [resolution 82,212]
259. humble(alice) <- (10, ~11) [subsumption resolution 258,217]
260. $false <- (10, ~11) [subsumption resolution 259,139]
261. ~10 | 11 [avatar contradiction clause 260]
262. $false [avatar sat refutation 218,251,261]
% SZS output end Proof for 8675017790797431148364403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or patient is both curious and not curious. If lucy is kind or not rich then someone is either tall or kind and vice versa. Everyone who is either not curious or humble is both funny and curious. Everyone who is not generous or funny is both not creative and not quiet. Everyone who is brave or curious is not humble or not tall and vice versa. Everyone who is not patient is old or happy. If john is strong or not brave then someone is either not happy or not strong. Everyone who is not quiet is patient. If someone is curious then alice is both creative and generous. If someone is either calm or quiet then mary is curious or not creative. If john is not happy then someone is happy and vice versa. Everyone who is both creative and wise is not funny or strong and vice versa. Everyone who is both patient and not humble is humble and vice versa. Everyone who is either creative or brave is either rich or not happy and vice versa. Paul is either not strong or not generous. Someone is not kind. Someone is both not calm and not old. Someone is both not patient and generous. | Paul is creative. | entailment | (![X]:((rich(X)|patient(X))=>(curious(X)&~curious(X))))&
(((kind(lucy)|~rich(lucy)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((patient(X)&~humble(X))<=>humble(X)))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
((~strong(paul)<~>~generous(paul)))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)&~old(X))))&
(?[X]:((~patient(X)&generous(X)))) | creative(paul) | [
"p0",
"p3",
"p7",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 8507279259297927177497564
% SZS output start Proof for 8507279259297927177497564
1. ! [X0] : ((patient(X0) | rich(X0)) => (~curious(X0) & curious(X0))) [input p0]
4. ! [X0] : ((funny(X0) | ~generous(X0)) => (~quiet(X0) & ~creative(X0))) [input p3]
8. ! [X0] : (~quiet(X0) => patient(X0)) [input p7]
12. ! [X0] : ((wise(X0) & creative(X0)) <=> (strong(X0) | ~funny(X0))) [input p11]
19. ~creative(paul) [input hypothesis]
20. ! [X0] : ((~curious(X0) & curious(X0)) | (~patient(X0) & ~rich(X0))) [ennf transformation 1]
22. ! [X0] : ((~quiet(X0) & ~creative(X0)) | (~funny(X0) & generous(X0))) [ennf transformation 4]
26. ! [X0] : (patient(X0) | quiet(X0)) [ennf transformation 8]
46. ! [X0] : (((wise(X0) & creative(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (~wise(X0) | ~creative(X0)))) [nnf transformation 12]
47. ! [X0] : (((wise(X0) & creative(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | ~wise(X0) | ~creative(X0))) [flattening 46]
59. curious(X0) | ~patient(X0) [cnf transformation 20]
61. ~curious(X0) | ~patient(X0) [cnf transformation 20]
75. ~quiet(X0) | ~funny(X0) [cnf transformation 22]
85. patient(X0) | quiet(X0) [cnf transformation 26]
93. creative(X0) | funny(X0) [cnf transformation 47]
115. ~creative(paul) [cnf transformation 19]
119. ~patient(X0) [subsumption resolution 59,61]
160. quiet(X0) [subsumption resolution 85,119]
221. ~funny(X0) [resolution 75,160]
222. funny(paul) [resolution 93,115]
226. $false [subsumption resolution 222,221]
% SZS output end Proof for 8507279259297927177497564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and calm then susan is either not happy or not kind and vice versa.
Everyone who is either not old or not creative is not quiet and vice versa.
Everyone who is not wise or not patient is both tall and not kind and vice versa.
Everyone who is kind is not kind or humble and vice versa.
Everyone who is either old or brave is both tall and brave and vice versa.
Everyone who is either not wise or not rich is generous and vice versa.
Everyone who is quiet is both not patient and calm.
Everyone who is either brave or funny is quiet.
If someone is not calm or old then someone is both not kind and generous.
Everyone who is either not brave or wise is either not creative or not generous.
Everyone who is both not kind and old is quiet and vice versa.
If susan is both not quiet and not strong then someone is patient and vice versa.
If fred is creative then susan is not quiet or patient and vice versa.
Everyone who is not creative is not humble or tall and vice versa.
Everyone who is either rich or not curious is both not old and curious.
Someone is happy or old.
Mary is kind.
Someone is not brave or patient.
Someone is both not strong and calm.
Paul is humble or quiet. | Paul is strong. | neutral | ((?[X]:((~rich(X)&calm(X))))<=>((~happy(susan)<~>~kind(susan))))&
(![X]:((~old(X)<~>~creative(X))<=>~quiet(X)))&
(![X]:((~wise(X)|~patient(X))<=>(tall(X)&~kind(X))))&
(![X]:(kind(X)<=>(~kind(X)|humble(X))))&
(![X]:((old(X)<~>brave(X))<=>(tall(X)&brave(X))))&
(![X]:((~wise(X)<~>~rich(X))<=>generous(X)))&
(![X]:(quiet(X)=>(~patient(X)&calm(X))))&
(![X]:((brave(X)<~>funny(X))=>quiet(X)))&
((?[X]:((~calm(X)|old(X))))=>(?[X]:((~kind(X)&generous(X)))))&
(![X]:((~brave(X)<~>wise(X))=>(~creative(X)<~>~generous(X))))&
(![X]:((~kind(X)&old(X))<=>quiet(X)))&
(((~quiet(susan)&~strong(susan)))<=>(?[X]:(patient(X))))&
((creative(fred))<=>((~quiet(susan)|patient(susan))))&
(![X]:(~creative(X)<=>(~humble(X)|tall(X))))&
(![X]:((rich(X)<~>~curious(X))=>(~old(X)&curious(X))))&
(?[X]:((happy(X)|old(X))))&
(kind(mary))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((~strong(X)&calm(X))))&
((humble(paul)|quiet(paul))) | strong(paul) | []
| null | 0 |
Everyone who is creative is not wise.
If someone is either not creative or tall then someone is old.
Everyone who is patient or not generous is both strong and generous and vice versa.
Everyone who is not tall or humble is either creative or quiet and vice versa.
Everyone who is not calm is both old and generous and vice versa.
Everyone who is strong or calm is both tall and funny and vice versa.
Everyone who is curious or not calm is not rich or happy.
If someone is patient then mary is both rich and not kind.
Everyone who is wise or rich is not generous and vice versa.
Everyone who is either generous or patient is either not tall or humble.
Everyone who is not strong is both happy and humble.
Everyone who is either calm or funny is either tall or not calm and vice versa.
If someone is either wise or rich then alice is not kind and vice versa.
Everyone who is either not old or calm is not tall.
Everyone who is both generous and tall is not brave.
Someone is either kind or not generous.
Someone is not happy or not creative.
Mary is not patient.
Someone is not funny or not wise.
Fred is either not brave or curious. | Alice is brave. | contradiction | (![X]:(creative(X)=>~wise(X)))&
((?[X]:((~creative(X)<~>tall(X))))=>(?[X]:(old(X))))&
(![X]:((patient(X)|~generous(X))<=>(strong(X)&generous(X))))&
(![X]:((~tall(X)|humble(X))<=>(creative(X)<~>quiet(X))))&
(![X]:(~calm(X)<=>(old(X)&generous(X))))&
(![X]:((strong(X)|calm(X))<=>(tall(X)&funny(X))))&
(![X]:((curious(X)|~calm(X))=>(~rich(X)|happy(X))))&
((?[X]:(patient(X)))=>((rich(mary)&~kind(mary))))&
(![X]:((wise(X)|rich(X))<=>~generous(X)))&
(![X]:((generous(X)<~>patient(X))=>(~tall(X)<~>humble(X))))&
(![X]:(~strong(X)=>(happy(X)&humble(X))))&
(![X]:((calm(X)<~>funny(X))<=>(tall(X)<~>~calm(X))))&
((?[X]:((wise(X)<~>rich(X))))<=>(~kind(alice)))&
(![X]:((~old(X)<~>calm(X))=>~tall(X)))&
(![X]:((generous(X)&tall(X))=>~brave(X)))&
(?[X]:((kind(X)<~>~generous(X))))&
(?[X]:((~happy(X)|~creative(X))))&
(~patient(mary))&
(?[X]:((~funny(X)|~wise(X))))&
((~brave(fred)<~>curious(fred))) | brave(alice) | [
"p2",
"p5",
"p7",
"p8",
"p9",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2796085521794747600231941
% SZS output start Proof for 2796085521794747600231941
3. ! [X0] : ((~generous(X0) | patient(X0)) <=> (generous(X0) & strong(X0))) [input p2]
6. ! [X0] : ((calm(X0) | strong(X0)) <=> (funny(X0) & tall(X0))) [input p5]
8. ? [X0] : patient(X0) => (~kind(mary) & rich(mary)) [input p7]
9. ! [X0] : ((rich(X0) | wise(X0)) <=> ~generous(X0)) [input p8]
10. ! [X0] : ((generous(X0) <~> patient(X0)) => (~tall(X0) <~> humble(X0))) [input p9]
11. ! [X0] : (~strong(X0) => (humble(X0) & happy(X0))) [input p10]
15. ! [X0] : ((tall(X0) & generous(X0)) => ~brave(X0)) [input p14]
21. brave(alice) [input hypothesis]
27. (~kind(mary) & rich(mary)) | ! [X0] : ~patient(X0) [ennf transformation 8]
28. ! [X0] : ((~tall(X0) <~> humble(X0)) | (generous(X0) <=> patient(X0))) [ennf transformation 10]
29. ! [X0] : ((humble(X0) & happy(X0)) | strong(X0)) [ennf transformation 11]
31. ! [X0] : (~brave(X0) | (~tall(X0) | ~generous(X0))) [ennf transformation 15]
32. ! [X0] : (~brave(X0) | ~tall(X0) | ~generous(X0)) [flattening 31]
37. ! [X0] : (((~generous(X0) | patient(X0)) | (~generous(X0) | ~strong(X0))) & ((generous(X0) & strong(X0)) | (generous(X0) & ~patient(X0)))) [nnf transformation 3]
38. ! [X0] : ((~generous(X0) | patient(X0) | ~generous(X0) | ~strong(X0)) & ((generous(X0) & strong(X0)) | (generous(X0) & ~patient(X0)))) [flattening 37]
43. ! [X0] : (((calm(X0) | strong(X0)) | (~funny(X0) | ~tall(X0))) & ((funny(X0) & tall(X0)) | (~calm(X0) & ~strong(X0)))) [nnf transformation 6]
44. ! [X0] : ((calm(X0) | strong(X0) | ~funny(X0) | ~tall(X0)) & ((funny(X0) & tall(X0)) | (~calm(X0) & ~strong(X0)))) [flattening 43]
45. ! [X0] : (((rich(X0) | wise(X0)) | generous(X0)) & (~generous(X0) | (~rich(X0) & ~wise(X0)))) [nnf transformation 9]
46. ! [X0] : ((rich(X0) | wise(X0) | generous(X0)) & (~generous(X0) | (~rich(X0) & ~wise(X0)))) [flattening 45]
47. ! [X0] : (((~humble(X0) | tall(X0)) & (humble(X0) | ~tall(X0))) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0)))) [nnf transformation 28]
68. generous(X0) | generous(X0) [cnf transformation 38]
79. ~strong(X0) | tall(X0) [cnf transformation 44]
86. rich(mary) | ~patient(X0) [cnf transformation 27]
89. ~generous(X0) | ~rich(X0) [cnf transformation 46]
93. ~humble(X0) | tall(X0) | patient(X0) | ~generous(X0) [cnf transformation 47]
96. humble(X0) | strong(X0) [cnf transformation 29]
111. ~brave(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 32]
119. brave(alice) [cnf transformation 21]
124. generous(X0) [duplicate literal removal 68]
140. 4 <=> ! [X0] : ~patient(X0) [avatar definition]
141. ~patient(X0) <- (4) [avatar component clause 140]
148. 6 <=> rich(mary) [avatar definition]
150. rich(mary) <- (6) [avatar component clause 148]
151. 4 | 6 [avatar split clause 86,148,140]
152. ~rich(X0) [subsumption resolution 89,124]
154. ~humble(X0) | tall(X0) | patient(X0) [subsumption resolution 93,124]
162. ~brave(X0) | ~tall(X0) [subsumption resolution 111,124]
188. ~tall(alice) [resolution 162,119]
193. tall(X0) | patient(X0) | strong(X0) [resolution 154,96]
194. tall(X0) | strong(X0) <- (4) [subsumption resolution 193,141]
195. tall(X0) <- (4) [subsumption resolution 194,79]
196. $false <- (4) [resolution 195,188]
197. ~4 [avatar contradiction clause 196]
200. $false <- (6) [subsumption resolution 150,152]
201. ~6 [avatar contradiction clause 200]
202. $false [avatar sat refutation 151,197,201]
% SZS output end Proof for 2796085521794747600231941
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or creative is both wise and not tall and vice versa.
Everyone who is not kind or humble is not funny or quiet.
Everyone who is both not rich and not quiet is both not humble and not patient and vice versa.
Everyone who is not funny or not happy is either rich or not generous and vice versa.
If susan is both not rich and strong then fred is calm or not calm.
If paul is not curious then alice is either not curious or happy and vice versa.
Everyone who is both creative and quiet is quiet or happy and vice versa.
If susan is either creative or not rich then lucy is both kind and not brave and vice versa.
Everyone who is either not rich or funny is both patient and not patient and vice versa.
Everyone who is not kind or funny is both not brave and not patient and vice versa.
If someone is not wise or old then mary is not rich or patient and vice versa.
If alice is both old and kind then john is creative and vice versa.
If john is both not brave and not creative then alice is both not kind and wise.
If someone is quiet or not creative then someone is either not funny or not curious.
If fred is not funny or humble then someone is not happy or quiet and vice versa.
Everyone who is both kind and old is not tall or humble.
Someone is creative.
Someone is old or patient.
Fred is not curious.
Someone is both rich and generous.
Someone is old or happy.
Susan is curious.
Lucy is both not humble and creative.
John is both not quiet and not tall. | Fred is not wise. | contradiction | (![X]:((~curious(X)|creative(X))<=>(wise(X)&~tall(X))))&
(![X]:((~kind(X)|humble(X))=>(~funny(X)|quiet(X))))&
(![X]:((~rich(X)&~quiet(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~funny(X)|~happy(X))<=>(rich(X)<~>~generous(X))))&
(((~rich(susan)&strong(susan)))=>((calm(fred)|~calm(fred))))&
((~curious(paul))<=>((~curious(alice)<~>happy(alice))))&
(![X]:((creative(X)&quiet(X))<=>(quiet(X)|happy(X))))&
(((creative(susan)<~>~rich(susan)))<=>((kind(lucy)&~brave(lucy))))&
(![X]:((~rich(X)<~>funny(X))<=>(patient(X)&~patient(X))))&
(![X]:((~kind(X)|funny(X))<=>(~brave(X)&~patient(X))))&
((?[X]:((~wise(X)|old(X))))<=>((~rich(mary)|patient(mary))))&
(((old(alice)&kind(alice)))<=>(creative(john)))&
(((~brave(john)&~creative(john)))=>((~kind(alice)&wise(alice))))&
((?[X]:((quiet(X)|~creative(X))))=>(?[X]:((~funny(X)<~>~curious(X)))))&
(((~funny(fred)|humble(fred)))<=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:((kind(X)&old(X))=>(~tall(X)|humble(X))))&
(?[X]:(creative(X)))&
(?[X]:((old(X)|patient(X))))&
(~curious(fred))&
(?[X]:((rich(X)&generous(X))))&
(?[X]:((old(X)|happy(X))))&
(curious(susan))&
((~humble(lucy)&creative(lucy)))&
((~quiet(john)&~tall(john))) | ~wise(fred) | [
"p0",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 6655960175260143255458172
% SZS output start Proof for 6655960175260143255458172
1. ! [X0] : ((creative(X0) | ~curious(X0)) <=> (~tall(X0) & wise(X0))) [input p0]
19. ~curious(fred) [input p18]
25. ~wise(fred) [input hypothesis]
35. ! [X0] : (((creative(X0) | ~curious(X0)) | (tall(X0) | ~wise(X0))) & ((~tall(X0) & wise(X0)) | (~creative(X0) & curious(X0)))) [nnf transformation 1]
36. ! [X0] : ((creative(X0) | ~curious(X0) | tall(X0) | ~wise(X0)) & ((~tall(X0) & wise(X0)) | (~creative(X0) & curious(X0)))) [flattening 35]
74. wise(X0) | curious(X0) [cnf transformation 36]
137. ~curious(fred) [cnf transformation 19]
146. ~wise(fred) [cnf transformation 25]
287. curious(fred) [resolution 74,146]
289. $false [subsumption resolution 287,137]
% SZS output end Proof for 6655960175260143255458172
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is either not old or not calm. If john is quiet or not tall then someone is not curious or tall. Everyone who is either not creative or patient is not rich. If paul is not tall or not strong then alice is both not patient and happy and vice versa. If someone is calm then alice is both happy and not calm and vice versa. If alice is not calm or not patient then lucy is not old or not brave and vice versa. Everyone who is both not calm and patient is either tall or not creative. If someone is both not tall and not funny then someone is not strong or not funny and vice versa. Everyone who is brave is happy. Everyone who is calm or strong is both brave and creative and vice versa. Everyone who is both tall and curious is either strong or not strong and vice versa. Everyone who is strong is either tall or not brave and vice versa. Everyone who is not tall is not patient or not humble. Everyone who is not patient is not old or not generous. If susan is both calm and not humble then fred is either not strong or not calm and vice versa. If mary is either wise or not creative then someone is kind and vice versa. Fred is kind or not strong. Someone is either not calm or not happy. John is not old or not creative. Someone is either not funny or funny. Someone is creative. | Mary is not rich. | neutral | (![X]:(~curious(X)=>(~old(X)<~>~calm(X))))&
(((quiet(john)|~tall(john)))=>(?[X]:((~curious(X)|tall(X)))))&
(![X]:((~creative(X)<~>patient(X))=>~rich(X)))&
(((~tall(paul)|~strong(paul)))<=>((~patient(alice)&happy(alice))))&
((?[X]:(calm(X)))<=>((happy(alice)&~calm(alice))))&
(((~calm(alice)|~patient(alice)))<=>((~old(lucy)|~brave(lucy))))&
(![X]:((~calm(X)&patient(X))=>(tall(X)<~>~creative(X))))&
((?[X]:((~tall(X)&~funny(X))))<=>(?[X]:((~strong(X)|~funny(X)))))&
(![X]:(brave(X)=>happy(X)))&
(![X]:((calm(X)|strong(X))<=>(brave(X)&creative(X))))&
(![X]:((tall(X)&curious(X))<=>(strong(X)<~>~strong(X))))&
(![X]:(strong(X)<=>(tall(X)<~>~brave(X))))&
(![X]:(~tall(X)=>(~patient(X)|~humble(X))))&
(![X]:(~patient(X)=>(~old(X)|~generous(X))))&
(((calm(susan)&~humble(susan)))<=>((~strong(fred)<~>~calm(fred))))&
(((wise(mary)<~>~creative(mary)))<=>(?[X]:(kind(X))))&
((kind(fred)|~strong(fred)))&
(?[X]:((~calm(X)<~>~happy(X))))&
((~old(john)|~creative(john)))&
(?[X]:((~funny(X)<~>funny(X))))&
(?[X]:(creative(X))) | ~rich(mary) | []
| null | 0 |
If someone is not strong or curious then alice is both old and not patient and vice versa.
Everyone who is both quiet and calm is both not brave and not happy.
Everyone who is either creative or old is not old.
Everyone who is both not creative and curious is either humble or not curious and vice versa.
If lucy is not humble then paul is not kind or not creative.
If someone is either humble or not calm then someone is not curious and vice versa.
Everyone who is generous is both not generous and funny.
If fred is creative or not happy then lucy is not curious or not humble and vice versa.
If someone is humble then mary is both not calm and curious and vice versa.
Everyone who is not funny is brave.
Everyone who is either not brave or not rich is both not patient and not generous.
Everyone who is both tall and not brave is not tall and vice versa.
Everyone who is not creative or wise is calm or rich and vice versa.
Everyone who is brave or strong is both happy and kind.
If someone is both generous and creative then someone is quiet and vice versa.
If susan is wise then susan is not happy and vice versa.
Someone is either not old or wise.
John is not kind or not funny.
Paul is not generous.
Mary is either not happy or rich.
Paul is not calm.
Susan is creative or not curious. | Fred is patient. | neutral | ((?[X]:((~strong(X)|curious(X))))<=>((old(alice)&~patient(alice))))&
(![X]:((quiet(X)&calm(X))=>(~brave(X)&~happy(X))))&
(![X]:((creative(X)<~>old(X))=>~old(X)))&
(![X]:((~creative(X)&curious(X))<=>(humble(X)<~>~curious(X))))&
((~humble(lucy))=>((~kind(paul)|~creative(paul))))&
((?[X]:((humble(X)<~>~calm(X))))<=>(?[X]:(~curious(X))))&
(![X]:(generous(X)=>(~generous(X)&funny(X))))&
(((creative(fred)|~happy(fred)))<=>((~curious(lucy)|~humble(lucy))))&
((?[X]:(humble(X)))<=>((~calm(mary)&curious(mary))))&
(![X]:(~funny(X)=>brave(X)))&
(![X]:((~brave(X)<~>~rich(X))=>(~patient(X)&~generous(X))))&
(![X]:((tall(X)&~brave(X))<=>~tall(X)))&
(![X]:((~creative(X)|wise(X))<=>(calm(X)|rich(X))))&
(![X]:((brave(X)|strong(X))=>(happy(X)&kind(X))))&
((?[X]:((generous(X)&creative(X))))<=>(?[X]:(quiet(X))))&
((wise(susan))<=>(~happy(susan)))&
(?[X]:((~old(X)<~>wise(X))))&
((~kind(john)|~funny(john)))&
(~generous(paul))&
((~happy(mary)<~>rich(mary)))&
(~calm(paul))&
((creative(susan)|~curious(susan))) | patient(fred) | []
| null | 0 |
If fred is either not humble or not rich then paul is both happy and tall and vice versa.
If someone is either patient or not happy then paul is either not old or not brave.
Everyone who is not tall or not brave is calm or not curious.
If someone is both not brave and calm then fred is not calm or not generous.
Everyone who is either not quiet or strong is either patient or brave.
Everyone who is curious or creative is either rich or curious.
If susan is funny or wise then someone is not generous or not funny.
Everyone who is both generous and not kind is not curious or generous and vice versa.
Everyone who is not calm is both tall and curious.
Everyone who is either generous or rich is either generous or not patient.
If paul is both curious and old then someone is not tall or old.
Everyone who is not patient is either brave or not curious and vice versa.
Everyone who is both calm and not quiet is either brave or not humble and vice versa.
If someone is not humble or funny then someone is humble or creative.
If lucy is either not tall or happy then someone is both rich and not curious and vice versa.
Everyone who is not creative is not kind or not old.
Paul is generous or brave.
Someone is not creative.
Someone is funny or creative.
Alice is wise or not curious.
Mary is funny.
Susan is either brave or wise.
Fred is patient.
Someone is not tall or not creative. | Fred is not calm. | contradiction | (((~humble(fred)<~>~rich(fred)))<=>((happy(paul)&tall(paul))))&
((?[X]:((patient(X)<~>~happy(X))))=>((~old(paul)<~>~brave(paul))))&
(![X]:((~tall(X)|~brave(X))=>(calm(X)|~curious(X))))&
((?[X]:((~brave(X)&calm(X))))=>((~calm(fred)|~generous(fred))))&
(![X]:((~quiet(X)<~>strong(X))=>(patient(X)<~>brave(X))))&
(![X]:((curious(X)|creative(X))=>(rich(X)<~>curious(X))))&
(((funny(susan)|wise(susan)))=>(?[X]:((~generous(X)|~funny(X)))))&
(![X]:((generous(X)&~kind(X))<=>(~curious(X)|generous(X))))&
(![X]:(~calm(X)=>(tall(X)&curious(X))))&
(![X]:((generous(X)<~>rich(X))=>(generous(X)<~>~patient(X))))&
(((curious(paul)&old(paul)))=>(?[X]:((~tall(X)|old(X)))))&
(![X]:(~patient(X)<=>(brave(X)<~>~curious(X))))&
(![X]:((calm(X)&~quiet(X))<=>(brave(X)<~>~humble(X))))&
((?[X]:((~humble(X)|funny(X))))=>(?[X]:((humble(X)|creative(X)))))&
(((~tall(lucy)<~>happy(lucy)))<=>(?[X]:((rich(X)&~curious(X)))))&
(![X]:(~creative(X)=>(~kind(X)|~old(X))))&
((generous(paul)|brave(paul)))&
(?[X]:(~creative(X)))&
(?[X]:((funny(X)|creative(X))))&
((wise(alice)|~curious(alice)))&
(funny(mary))&
((brave(susan)<~>wise(susan)))&
(patient(fred))&
(?[X]:((~tall(X)|~creative(X)))) | ~calm(fred) | [
"p2",
"p8",
"p11",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 7726294260611925042927977
% SZS output start Proof for 7726294260611925042927977
3. ! [X0] : ((~brave(X0) | ~tall(X0)) => (~curious(X0) | calm(X0))) [input p2]
9. ! [X0] : (~calm(X0) => (curious(X0) & tall(X0))) [input p8]
12. ! [X0] : (~patient(X0) <=> (brave(X0) <~> ~curious(X0))) [input p11]
23. patient(fred) [input p22]
25. ~calm(fred) [input hypothesis]
28. ! [X0] : ((~curious(X0) | calm(X0)) | (brave(X0) & tall(X0))) [ennf transformation 3]
29. ! [X0] : (~curious(X0) | calm(X0) | (brave(X0) & tall(X0))) [flattening 28]
35. ! [X0] : ((curious(X0) & tall(X0)) | calm(X0)) [ennf transformation 9]
54. ! [X0] : ((~patient(X0) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0)))) & (((curious(X0) | ~brave(X0)) & (~curious(X0) | brave(X0))) | patient(X0))) [nnf transformation 12]
82. ~curious(X0) | calm(X0) | brave(X0) [cnf transformation 29]
100. curious(X0) | calm(X0) [cnf transformation 35]
108. ~curious(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 54]
132. patient(fred) [cnf transformation 23]
134. ~calm(fred) [cnf transformation 25]
182. 10 <=> calm(fred) [avatar definition]
184. ~calm(fred) <- (~10) [avatar component clause 182]
302. ~10 [avatar split clause 134,182]
312. calm(X0) | brave(X0) | calm(X0) [resolution 82,100]
313. calm(X0) | brave(X0) [duplicate literal removal 312]
336. ~patient(X0) | ~brave(X0) | calm(X0) [resolution 108,100]
338. ~patient(X0) | calm(X0) [subsumption resolution 336,313]
354. calm(fred) [resolution 338,132]
355. $false <- (~10) [subsumption resolution 354,184]
356. 10 [avatar contradiction clause 355]
357. $false [avatar sat refutation 302,356]
% SZS output end Proof for 7726294260611925042927977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is 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 not generous. | entailment | (![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 8628539289420386469386429
% SZS output start Proof for 8628539289420386469386429
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 8628539289420386469386429
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet then mary is not funny or not quiet.
Everyone who is either not kind or curious is either tall or not humble and vice versa.
If someone is tall then someone is not brave or not wise.
If john is humble or not rich then lucy is both not old and wise and vice versa.
Everyone who is tall or creative is both not curious and not rich and vice versa.
Everyone who is humble or curious is happy or not funny and vice versa.
If someone is both kind and not kind then susan is funny.
Everyone who is both old and not strong is either brave or wise and vice versa.
Everyone who is both not wise and not kind is either not patient or quiet.
Everyone who is old is both patient and kind.
Everyone who is either not funny or generous is either quiet or not patient and vice versa.
Everyone who is calm or not wise is not rich or humble.
Everyone who is either quiet or funny is not wise or generous and vice versa.
If someone is brave then someone is not happy and vice versa.
Everyone who is either not tall or not rich is happy or wise.
Everyone who is both not funny and happy is not funny and vice versa.
Fred is old.
Someone is not strong.
Susan is either kind or not humble.
Someone is either kind or not happy.
Susan is either not calm or not funny.
Someone is happy or old. | John is rich. | neutral | ((~quiet(alice))=>((~funny(mary)|~quiet(mary))))&
(![X]:((~kind(X)<~>curious(X))<=>(tall(X)<~>~humble(X))))&
((?[X]:(tall(X)))=>(?[X]:((~brave(X)|~wise(X)))))&
(((humble(john)|~rich(john)))<=>((~old(lucy)&wise(lucy))))&
(![X]:((tall(X)|creative(X))<=>(~curious(X)&~rich(X))))&
(![X]:((humble(X)|curious(X))<=>(happy(X)|~funny(X))))&
((?[X]:((kind(X)&~kind(X))))=>(funny(susan)))&
(![X]:((old(X)&~strong(X))<=>(brave(X)<~>wise(X))))&
(![X]:((~wise(X)&~kind(X))=>(~patient(X)<~>quiet(X))))&
(![X]:(old(X)=>(patient(X)&kind(X))))&
(![X]:((~funny(X)<~>generous(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:((calm(X)|~wise(X))=>(~rich(X)|humble(X))))&
(![X]:((quiet(X)<~>funny(X))<=>(~wise(X)|generous(X))))&
((?[X]:(brave(X)))<=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)<~>~rich(X))=>(happy(X)|wise(X))))&
(![X]:((~funny(X)&happy(X))<=>~funny(X)))&
(old(fred))&
(?[X]:(~strong(X)))&
((kind(susan)<~>~humble(susan)))&
(?[X]:((kind(X)<~>~happy(X))))&
((~calm(susan)<~>~funny(susan)))&
(?[X]:((happy(X)|old(X)))) | rich(john) | []
| null | 0 |
Everyone who is either not old or tall is both humble and not humble and vice versa. If susan is both quiet and brave then someone is either not rich or rich. If someone is calm then mary is both not kind and not rich. Everyone who is either curious or rich is either calm or not calm and vice versa. Everyone who is calm is wise. Everyone who is not quiet or funny is both not tall and creative and vice versa. If fred is not old then alice is both calm and not kind. If alice is not kind or not curious then someone is rich or not creative and vice versa. If someone is both not tall and old then someone is not kind. If someone is either humble or kind then lucy is not quiet or creative. Everyone who is wise is both not wise and not strong. Everyone who is not brave is either not old or quiet and vice versa. If mary is creative or funny then someone is both not creative and quiet and vice versa. Everyone who is curious is either not quiet or brave and vice versa. Everyone who is not old or not wise is brave. Paul is either wise or creative. Someone is both quiet and not humble. Someone is patient or calm. Someone is quiet or not wise. Lucy is not generous. Someone is either rich or strong. Someone is curious. | Mary is not rich. | neutral | (![X]:((~old(X)<~>tall(X))<=>(humble(X)&~humble(X))))&
(((quiet(susan)&brave(susan)))=>(?[X]:((~rich(X)<~>rich(X)))))&
((?[X]:(calm(X)))=>((~kind(mary)&~rich(mary))))&
(![X]:((curious(X)<~>rich(X))<=>(calm(X)<~>~calm(X))))&
(![X]:(calm(X)=>wise(X)))&
(![X]:((~quiet(X)|funny(X))<=>(~tall(X)&creative(X))))&
((~old(fred))=>((calm(alice)&~kind(alice))))&
(((~kind(alice)|~curious(alice)))<=>(?[X]:((rich(X)|~creative(X)))))&
((?[X]:((~tall(X)&old(X))))=>(?[X]:(~kind(X))))&
((?[X]:((humble(X)<~>kind(X))))=>((~quiet(lucy)|creative(lucy))))&
(![X]:(wise(X)=>(~wise(X)&~strong(X))))&
(![X]:(~brave(X)<=>(~old(X)<~>quiet(X))))&
(((creative(mary)|funny(mary)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:(curious(X)<=>(~quiet(X)<~>brave(X))))&
(![X]:((~old(X)|~wise(X))=>brave(X)))&
((wise(paul)<~>creative(paul)))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((patient(X)|calm(X))))&
(?[X]:((quiet(X)|~wise(X))))&
(~generous(lucy))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:(curious(X))) | ~rich(mary) | []
| null | 0 |
Everyone who is either humble or curious is not curious or happy. If susan is calm or humble then john is not curious or not tall and vice versa. Everyone who is both not tall and wise is funny or old. Everyone who is both wise and not creative is generous or brave. Everyone who is old or not kind is both not calm and wise and vice versa. Everyone who is either strong or not funny is both not humble and rich and vice versa. If someone is not patient or curious then someone is not funny or humble and vice versa. If someone is either not tall or funny then mary is either not humble or not quiet and vice versa. Everyone who is patient or not brave is not tall or happy and vice versa. If someone is curious or generous then someone is not tall. Everyone who is either not humble or wise is not kind and vice versa. Everyone who is both brave and not calm is wise. Everyone who is humble is not strong. If someone is not calm or not quiet then paul is kind or funny and vice versa. If john is not kind then someone is humble or not old and vice versa. If someone is either funny or kind then paul is brave. Lucy is curious or not old. Someone is either not brave or not calm. Someone is both quiet and creative. Someone is both quiet and not funny. Someone is either not patient or not wise. Someone is strong or not old. Mary is either brave or tall. Someone is either humble or not funny. | Susan is not creative. | neutral | (![X]:((humble(X)<~>curious(X))=>(~curious(X)|happy(X))))&
(((calm(susan)|humble(susan)))<=>((~curious(john)|~tall(john))))&
(![X]:((~tall(X)&wise(X))=>(funny(X)|old(X))))&
(![X]:((wise(X)&~creative(X))=>(generous(X)|brave(X))))&
(![X]:((old(X)|~kind(X))<=>(~calm(X)&wise(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~humble(X)&rich(X))))&
((?[X]:((~patient(X)|curious(X))))<=>(?[X]:((~funny(X)|humble(X)))))&
((?[X]:((~tall(X)<~>funny(X))))<=>((~humble(mary)<~>~quiet(mary))))&
(![X]:((patient(X)|~brave(X))<=>(~tall(X)|happy(X))))&
((?[X]:((curious(X)|generous(X))))=>(?[X]:(~tall(X))))&
(![X]:((~humble(X)<~>wise(X))<=>~kind(X)))&
(![X]:((brave(X)&~calm(X))=>wise(X)))&
(![X]:(humble(X)=>~strong(X)))&
((?[X]:((~calm(X)|~quiet(X))))<=>((kind(paul)|funny(paul))))&
((~kind(john))<=>(?[X]:((humble(X)|~old(X)))))&
((?[X]:((funny(X)<~>kind(X))))=>(brave(paul)))&
((curious(lucy)|~old(lucy)))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((quiet(X)&creative(X))))&
(?[X]:((quiet(X)&~funny(X))))&
(?[X]:((~patient(X)<~>~wise(X))))&
(?[X]:((strong(X)|~old(X))))&
((brave(mary)<~>tall(mary)))&
(?[X]:((humble(X)<~>~funny(X)))) | ~creative(susan) | []
| null | 0 |
Everyone who is not creative is not generous and vice versa.
Everyone who is both not curious and humble is not funny or not strong and vice versa.
If alice is either not funny or not quiet then someone is wise.
Everyone who is both rich and generous is either old or not creative and vice versa.
Everyone who is calm or patient is both patient and not curious.
Everyone who is rich is either tall or humble.
If fred is brave then someone is not happy.
If someone is not old or not kind then alice is both patient and wise.
Everyone who is both old and happy is either not curious or brave.
Everyone who is not humble or not strong is not patient and vice versa.
Everyone who is not tall or not calm is curious.
If paul is either happy or old then lucy is both not patient and tall and vice versa.
If paul is not creative then someone is not humble or kind.
If paul is rich or generous then fred is both not humble and not generous.
Everyone who is wise is calm.
If lucy is tall or not strong then someone is not humble or not generous.
John is not strong or calm.
Someone is both not wise and not calm.
Susan is not old.
Paul is either wise or not tall.
Someone is either wise or humble.
Someone is either not calm or strong.
Lucy is both not quiet and creative.
Someone is both not kind and not funny. | Fred is humble. | neutral | (![X]:(~creative(X)<=>~generous(X)))&
(![X]:((~curious(X)&humble(X))<=>(~funny(X)|~strong(X))))&
(((~funny(alice)<~>~quiet(alice)))=>(?[X]:(wise(X))))&
(![X]:((rich(X)&generous(X))<=>(old(X)<~>~creative(X))))&
(![X]:((calm(X)|patient(X))=>(patient(X)&~curious(X))))&
(![X]:(rich(X)=>(tall(X)<~>humble(X))))&
((brave(fred))=>(?[X]:(~happy(X))))&
((?[X]:((~old(X)|~kind(X))))=>((patient(alice)&wise(alice))))&
(![X]:((old(X)&happy(X))=>(~curious(X)<~>brave(X))))&
(![X]:((~humble(X)|~strong(X))<=>~patient(X)))&
(![X]:((~tall(X)|~calm(X))=>curious(X)))&
(((happy(paul)<~>old(paul)))<=>((~patient(lucy)&tall(lucy))))&
((~creative(paul))=>(?[X]:((~humble(X)|kind(X)))))&
(((rich(paul)|generous(paul)))=>((~humble(fred)&~generous(fred))))&
(![X]:(wise(X)=>calm(X)))&
(((tall(lucy)|~strong(lucy)))=>(?[X]:((~humble(X)|~generous(X)))))&
((~strong(john)|calm(john)))&
(?[X]:((~wise(X)&~calm(X))))&
(~old(susan))&
((wise(paul)<~>~tall(paul)))&
(?[X]:((wise(X)<~>humble(X))))&
(?[X]:((~calm(X)<~>strong(X))))&
((~quiet(lucy)&creative(lucy)))&
(?[X]:((~kind(X)&~funny(X)))) | humble(fred) | []
| null | 0 |
Everyone who is wise or not quiet is happy and vice versa.
If someone is old then lucy is either happy or not happy and vice versa.
If someone is patient then mary is funny and vice versa.
If someone is not old or not kind then someone is not calm.
Everyone who is both brave and not patient is either patient or not happy and vice versa.
If alice is either not curious or quiet then someone is not rich.
If john is generous then someone is either not humble or rich.
If someone is brave or humble then susan is either happy or not kind.
Everyone who is both happy and not quiet is not old or not tall.
If john is either rich or not brave then mary is not brave.
Everyone who is tall is both not happy and generous and vice versa.
If someone is not kind then fred is wise or not creative.
Everyone who is either not creative or strong is funny and vice versa.
If someone is not generous or not strong then someone is either not rich or humble.
Everyone who is not wise or not tall is both not curious and not creative.
Everyone who is both wise and not creative is both not patient and happy and vice versa.
Alice is not brave.
Susan is both not patient and generous.
Someone is not quiet or not kind.
Mary is either brave or quiet.
Alice is either happy or not happy.
Someone is both calm and not patient.
Lucy is not patient. | Mary is not creative. | entailment | (![X]:((wise(X)|~quiet(X))<=>happy(X)))&
((?[X]:(old(X)))<=>((happy(lucy)<~>~happy(lucy))))&
((?[X]:(patient(X)))<=>(funny(mary)))&
((?[X]:((~old(X)|~kind(X))))=>(?[X]:(~calm(X))))&
(![X]:((brave(X)&~patient(X))<=>(patient(X)<~>~happy(X))))&
(((~curious(alice)<~>quiet(alice)))=>(?[X]:(~rich(X))))&
((generous(john))=>(?[X]:((~humble(X)<~>rich(X)))))&
((?[X]:((brave(X)|humble(X))))=>((happy(susan)<~>~kind(susan))))&
(![X]:((happy(X)&~quiet(X))=>(~old(X)|~tall(X))))&
(((rich(john)<~>~brave(john)))=>(~brave(mary)))&
(![X]:(tall(X)<=>(~happy(X)&generous(X))))&
((?[X]:(~kind(X)))=>((wise(fred)|~creative(fred))))&
(![X]:((~creative(X)<~>strong(X))<=>funny(X)))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((~wise(X)|~tall(X))=>(~curious(X)&~creative(X))))&
(![X]:((wise(X)&~creative(X))<=>(~patient(X)&happy(X))))&
(~brave(alice))&
((~patient(susan)&generous(susan)))&
(?[X]:((~quiet(X)|~kind(X))))&
((brave(mary)<~>quiet(mary)))&
((happy(alice)<~>~happy(alice)))&
(?[X]:((calm(X)&~patient(X))))&
(~patient(lucy)) | ~creative(mary) | [
"p0",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 64262262536413517996024
% SZS output start Proof for 64262262536413517996024
1. ! [X0] : ((~quiet(X0) | wise(X0)) <=> happy(X0)) [input p0]
11. ! [X0] : (tall(X0) <=> (generous(X0) & ~happy(X0))) [input p10]
15. ! [X0] : ((~tall(X0) | ~wise(X0)) => (~creative(X0) & ~curious(X0))) [input p14]
24. creative(mary) [input hypothesis]
37. ! [X0] : ((~creative(X0) & ~curious(X0)) | (tall(X0) & wise(X0))) [ennf transformation 15]
38. ! [X0] : (((~quiet(X0) | wise(X0)) | ~happy(X0)) & (happy(X0) | (quiet(X0) & ~wise(X0)))) [nnf transformation 1]
39. ! [X0] : ((~quiet(X0) | wise(X0) | ~happy(X0)) & (happy(X0) | (quiet(X0) & ~wise(X0)))) [flattening 38]
61. ! [X0] : ((tall(X0) | (~generous(X0) | happy(X0))) & ((generous(X0) & ~happy(X0)) | ~tall(X0))) [nnf transformation 11]
62. ! [X0] : ((tall(X0) | ~generous(X0) | happy(X0)) & ((generous(X0) & ~happy(X0)) | ~tall(X0))) [flattening 61]
76. ~wise(X0) | happy(X0) [cnf transformation 39]
104. ~tall(X0) | ~happy(X0) [cnf transformation 62]
118. ~creative(X0) | wise(X0) [cnf transformation 37]
119. ~creative(X0) | tall(X0) [cnf transformation 37]
135. creative(mary) [cnf transformation 24]
282. wise(mary) [resolution 118,135]
283. tall(mary) [resolution 119,135]
284. happy(mary) [resolution 282,76]
287. ~happy(mary) [resolution 283,104]
288. $false [subsumption resolution 287,284]
% SZS output end Proof for 64262262536413517996024
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is both rich and not strong and vice versa.
Everyone who is both not rich and curious is either not kind or not humble and vice versa.
Everyone who is both calm and not rich is both quiet and rich and vice versa.
If susan is not kind or humble then lucy is both not calm and not creative and vice versa.
If someone is not happy then lucy is both happy and wise and vice versa.
If paul is quiet or not wise then someone is not strong.
Everyone who is either not kind or rich is not old or not wise and vice versa.
Everyone who is brave is not brave.
Everyone who is quiet or not old is either not rich or not wise and vice versa.
Everyone who is not quiet or wise is both not rich and not kind and vice versa.
If fred is not happy then susan is not wise or calm.
If mary is not curious or not generous then someone is both not wise and not brave and vice versa.
If mary is either not funny or not humble then mary is not old or strong.
Everyone who is either not humble or not rich is both curious and not patient.
Everyone who is not brave or calm is not humble or not old.
If someone is both creative and calm then mary is either not curious or humble.
Someone is both not tall and not patient.
John is not generous.
Alice is not quiet or not rich.
John is both not patient and not tall. | John is curious. | contradiction | (![X]:(~old(X)<=>(rich(X)&~strong(X))))&
(![X]:((~rich(X)&curious(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((calm(X)&~rich(X))<=>(quiet(X)&rich(X))))&
(((~kind(susan)|humble(susan)))<=>((~calm(lucy)&~creative(lucy))))&
((?[X]:(~happy(X)))<=>((happy(lucy)&wise(lucy))))&
(((quiet(paul)|~wise(paul)))=>(?[X]:(~strong(X))))&
(![X]:((~kind(X)<~>rich(X))<=>(~old(X)|~wise(X))))&
(![X]:(brave(X)=>~brave(X)))&
(![X]:((quiet(X)|~old(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~rich(X)&~kind(X))))&
((~happy(fred))=>((~wise(susan)|calm(susan))))&
(((~curious(mary)|~generous(mary)))<=>(?[X]:((~wise(X)&~brave(X)))))&
(((~funny(mary)<~>~humble(mary)))=>((~old(mary)|strong(mary))))&
(![X]:((~humble(X)<~>~rich(X))=>(curious(X)&~patient(X))))&
(![X]:((~brave(X)|calm(X))=>(~humble(X)|~old(X))))&
((?[X]:((creative(X)&calm(X))))=>((~curious(mary)<~>humble(mary))))&
(?[X]:((~tall(X)&~patient(X))))&
(~generous(john))&
((~quiet(alice)|~rich(alice)))&
((~patient(john)&~tall(john))) | curious(john) | [
"p0",
"p1",
"p2",
"p6",
"p7",
"p9",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 8598053254547523390643585
% SZS output start Proof for 8598053254547523390643585
1. ! [X0] : (~old(X0) <=> (~strong(X0) & rich(X0))) [input p0]
2. ! [X0] : ((curious(X0) & ~rich(X0)) <=> (~kind(X0) <~> ~humble(X0))) [input p1]
3. ! [X0] : ((~rich(X0) & calm(X0)) <=> (rich(X0) & quiet(X0))) [input p2]
7. ! [X0] : ((~kind(X0) <~> rich(X0)) <=> (~wise(X0) | ~old(X0))) [input p6]
8. ! [X0] : (brave(X0) => ~brave(X0)) [input p7]
10. ! [X0] : ((wise(X0) | ~quiet(X0)) <=> (~kind(X0) & ~rich(X0))) [input p9]
15. ! [X0] : ((calm(X0) | ~brave(X0)) => (~old(X0) | ~humble(X0))) [input p14]
21. curious(john) [input hypothesis]
28. ! [X0] : (~brave(X0) | ~brave(X0)) [ennf transformation 8]
34. ! [X0] : ((~old(X0) | ~humble(X0)) | (~calm(X0) & brave(X0))) [ennf transformation 15]
35. ! [X0] : (~old(X0) | ~humble(X0) | (~calm(X0) & brave(X0))) [flattening 34]
37. ! [X0] : ((~old(X0) | (strong(X0) | ~rich(X0))) & ((~strong(X0) & rich(X0)) | old(X0))) [nnf transformation 1]
38. ! [X0] : ((~old(X0) | strong(X0) | ~rich(X0)) & ((~strong(X0) & rich(X0)) | old(X0))) [flattening 37]
39. ! [X0] : (((curious(X0) & ~rich(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | (~curious(X0) | rich(X0)))) [nnf transformation 2]
40. ! [X0] : (((curious(X0) & ~rich(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | ~curious(X0) | rich(X0))) [flattening 39]
41. ! [X0] : (((~rich(X0) & calm(X0)) | (~rich(X0) | ~quiet(X0))) & ((rich(X0) & quiet(X0)) | (rich(X0) | ~calm(X0)))) [nnf transformation 3]
42. ! [X0] : (((~rich(X0) & calm(X0)) | ~rich(X0) | ~quiet(X0)) & ((rich(X0) & quiet(X0)) | rich(X0) | ~calm(X0))) [flattening 41]
52. ! [X0] : ((((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (wise(X0) & old(X0))) & ((~wise(X0) | ~old(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))))) [nnf transformation 7]
53. ! [X0] : ((((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (wise(X0) & old(X0))) & (~wise(X0) | ~old(X0) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))))) [flattening 52]
56. ! [X0] : (((wise(X0) | ~quiet(X0)) | (kind(X0) | rich(X0))) & ((~kind(X0) & ~rich(X0)) | (~wise(X0) & quiet(X0)))) [nnf transformation 10]
57. ! [X0] : ((wise(X0) | ~quiet(X0) | kind(X0) | rich(X0)) & ((~kind(X0) & ~rich(X0)) | (~wise(X0) & quiet(X0)))) [flattening 56]
66. rich(X0) | old(X0) [cnf transformation 38]
70. ~curious(X0) | kind(X0) | humble(X0) | rich(X0) [cnf transformation 40]
78. ~rich(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 42]
92. ~kind(X0) | rich(X0) | wise(X0) [cnf transformation 53]
95. ~brave(X0) | ~brave(X0) [cnf transformation 28]
102. ~rich(X0) | quiet(X0) [cnf transformation 57]
105. ~wise(X0) | ~kind(X0) [cnf transformation 57]
117. ~old(X0) | ~humble(X0) | brave(X0) [cnf transformation 35]
123. curious(john) [cnf transformation 21]
124. ~brave(X0) [duplicate literal removal 95]
126. ~quiet(X0) | ~rich(X0) [duplicate literal removal 78]
186. ~rich(X0) [subsumption resolution 102,126]
238. ~humble(X0) | ~old(X0) [subsumption resolution 117,124]
243. old(X0) [resolution 66,186]
264. kind(john) | humble(john) | rich(john) [resolution 70,123]
265. kind(john) | humble(john) [subsumption resolution 264,186]
267. 24 <=> humble(john) [avatar definition]
269. humble(john) <- (24) [avatar component clause 267]
271. 25 <=> kind(john) [avatar definition]
273. kind(john) <- (25) [avatar component clause 271]
274. 24 | 25 [avatar split clause 265,271,267]
278. ~old(john) <- (24) [resolution 269,238]
283. $false <- (24) [subsumption resolution 278,243]
284. ~24 [avatar contradiction clause 283]
285. rich(john) | wise(john) <- (25) [resolution 273,92]
289. wise(john) <- (25) [subsumption resolution 285,186]
296. ~kind(john) <- (25) [resolution 289,105]
298. $false <- (25) [subsumption resolution 296,273]
299. ~25 [avatar contradiction clause 298]
300. $false [avatar sat refutation 274,284,299]
% SZS output end Proof for 8598053254547523390643585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If john is not calm then someone is either calm or not funny and vice versa.
If susan is not old or not brave then fred is either not generous or kind.
If someone is either humble or tall then someone is either not patient or not funny.
If someone is either kind or rich then someone is tall or strong.
If fred is not happy then john is either not kind or not brave.
Everyone who is both not creative and not old is either not strong or calm and vice versa.
Everyone who is both creative and not kind is creative and vice versa.
Everyone who is both funny and calm is curious or not creative and vice versa.
If john is not humble or not brave then someone is either not curious or wise and vice versa.
If alice is either tall or humble then lucy is both not brave and not funny and vice versa.
If someone is rich or strong then john is not happy.
Everyone who is not quiet or patient is both happy and rich and vice versa.
Everyone who is funny or not curious is both humble and not kind.
Everyone who is not calm is either not generous or not creative.
Everyone who is not patient or rich is either generous or old.
Everyone who is happy is not funny or creative and vice versa.
Someone is generous or brave.
John is not creative or not strong.
Someone is either calm or not wise.
Lucy is either creative or patient. | Alice is calm. | entailment | ((~calm(john))<=>(?[X]:((calm(X)<~>~funny(X)))))&
(((~old(susan)|~brave(susan)))=>((~generous(fred)<~>kind(fred))))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:((~patient(X)<~>~funny(X)))))&
((?[X]:((kind(X)<~>rich(X))))=>(?[X]:((tall(X)|strong(X)))))&
((~happy(fred))=>((~kind(john)<~>~brave(john))))&
(![X]:((~creative(X)&~old(X))<=>(~strong(X)<~>calm(X))))&
(![X]:((creative(X)&~kind(X))<=>creative(X)))&
(![X]:((funny(X)&calm(X))<=>(curious(X)|~creative(X))))&
(((~humble(john)|~brave(john)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(((tall(alice)<~>humble(alice)))<=>((~brave(lucy)&~funny(lucy))))&
((?[X]:((rich(X)|strong(X))))=>(~happy(john)))&
(![X]:((~quiet(X)|patient(X))<=>(happy(X)&rich(X))))&
(![X]:((funny(X)|~curious(X))=>(humble(X)&~kind(X))))&
(![X]:(~calm(X)=>(~generous(X)<~>~creative(X))))&
(![X]:((~patient(X)|rich(X))=>(generous(X)<~>old(X))))&
(![X]:(happy(X)<=>(~funny(X)|creative(X))))&
(?[X]:((generous(X)|brave(X))))&
((~creative(john)|~strong(john)))&
(?[X]:((calm(X)<~>~wise(X))))&
((creative(lucy)<~>patient(lucy))) | calm(alice) | [
"p0",
"p5",
"p7",
"p10",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 514652149366608531823817
% SZS output start Proof for 514652149366608531823817
1. ~calm(john) <=> ? [X0] : (calm(X0) <~> ~funny(X0)) [input p0]
6. ! [X0] : ((~old(X0) & ~creative(X0)) <=> (~strong(X0) <~> calm(X0))) [input p5]
8. ! [X0] : ((calm(X0) & funny(X0)) <=> (~creative(X0) | curious(X0))) [input p7]
11. ? [X0] : (strong(X0) | rich(X0)) => ~happy(john) [input p10]
16. ! [X0] : (happy(X0) <=> (creative(X0) | ~funny(X0))) [input p15]
21. ~calm(alice) [input hypothesis]
28. ~happy(john) | ! [X0] : (~strong(X0) & ~rich(X0)) [ennf transformation 11]
32. (~calm(john) | ! [X0] : ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0)))) & (? [X0] : ((funny(X0) | ~calm(X0)) & (~funny(X0) | calm(X0))) | calm(john)) [nnf transformation 1]
33. (~calm(john) | ! [X0] : ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0)))) & (? [X1] : ((funny(X1) | ~calm(X1)) & (~funny(X1) | calm(X1))) | calm(john)) [rectify 32]
34. ? [X1] : ((funny(X1) | ~calm(X1)) & (~funny(X1) | calm(X1))) => ((funny(sK0) | ~calm(sK0)) & (~funny(sK0) | calm(sK0))) [choice axiom]
35. (~calm(john) | ! [X0] : ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0)))) & (((funny(sK0) | ~calm(sK0)) & (~funny(sK0) | calm(sK0))) | calm(john)) [skolemisation 33,34]
46. ! [X0] : (((~old(X0) & ~creative(X0)) | ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | (old(X0) | creative(X0)))) [nnf transformation 6]
47. ! [X0] : (((~old(X0) & ~creative(X0)) | ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | old(X0) | creative(X0))) [flattening 46]
50. ! [X0] : (((calm(X0) & funny(X0)) | (creative(X0) & ~curious(X0))) & ((~creative(X0) | curious(X0)) | (~calm(X0) | ~funny(X0)))) [nnf transformation 8]
51. ! [X0] : (((calm(X0) & funny(X0)) | (creative(X0) & ~curious(X0))) & (~creative(X0) | curious(X0) | ~calm(X0) | ~funny(X0))) [flattening 50]
63. ! [X0] : ((happy(X0) | (~creative(X0) & funny(X0))) & ((creative(X0) | ~funny(X0)) | ~happy(X0))) [nnf transformation 16]
64. ! [X0] : ((happy(X0) | (~creative(X0) & funny(X0))) & (creative(X0) | ~funny(X0) | ~happy(X0))) [flattening 63]
73. ~calm(john) | ~funny(X0) | ~calm(X0) [cnf transformation 35]
89. ~creative(X0) | calm(X0) | strong(X0) [cnf transformation 47]
100. creative(X0) | calm(X0) [cnf transformation 51]
114. ~happy(john) | ~strong(X0) [cnf transformation 28]
131. happy(X0) | funny(X0) [cnf transformation 64]
132. ~creative(X0) | happy(X0) [cnf transformation 64]
139. ~calm(alice) [cnf transformation 21]
144. 2 <=> calm(john) [avatar definition]
145. calm(john) <- (2) [avatar component clause 144]
146. ~calm(john) <- (~2) [avatar component clause 144]
149. 3 <=> ! [X0] : (~funny(X0) | ~calm(X0)) [avatar definition]
150. ~funny(X0) | ~calm(X0) <- (3) [avatar component clause 149]
151. 3 | ~2 [avatar split clause 73,144,149]
277. 30 <=> ! [X0] : ~strong(X0) [avatar definition]
278. ~strong(X0) <- (30) [avatar component clause 277]
280. 31 <=> happy(john) [avatar definition]
282. ~happy(john) <- (~31) [avatar component clause 280]
283. 30 | ~31 [avatar split clause 114,280,277]
342. happy(X0) | calm(X0) [resolution 132,100]
351. calm(X0) | strong(X0) | calm(X0) [resolution 89,100]
353. strong(X0) | calm(X0) [duplicate literal removal 351]
448. calm(john) <- (~31) [resolution 342,282]
450. $false <- (~2, ~31) [subsumption resolution 448,146]
451. 2 | 31 [avatar contradiction clause 450]
469. calm(X0) <- (30) [resolution 353,278]
477. 53 <=> funny(john) [avatar definition]
478. funny(john) <- (53) [avatar component clause 477]
497. $false <- (30) [resolution 469,139]
504. ~30 [avatar contradiction clause 497]
512. funny(john) <- (~31) [resolution 282,131]
515. 53 | 31 [avatar split clause 512,280,477]
546. ~calm(john) <- (3, 53) [resolution 150,478]
547. $false <- (2, 3, 53) [subsumption resolution 546,145]
548. ~2 | ~3 | ~53 [avatar contradiction clause 547]
549. $false [avatar sat refutation 151,283,451,504,515,548]
% SZS output end Proof for 514652149366608531823817
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not kind is not generous or patient.
Everyone who is either curious or not rich is either tall or rich.
If mary is not generous or patient then john is not kind.
If someone is happy then alice is creative or funny.
Everyone who is either creative or not brave is not brave or not tall.
If mary is either curious or not generous then paul is either not generous or not wise.
Everyone who is not funny or not happy is generous.
Everyone who is either funny or not creative is both creative and not wise and vice versa.
Everyone who is not wise is quiet or not patient.
Everyone who is both not wise and not old is strong and vice versa.
Everyone who is either not creative or not brave is either not strong or strong and vice versa.
Everyone who is patient or calm is both creative and not tall and vice versa.
Everyone who is both not wise and not kind is rich or not creative.
Everyone who is not calm or not tall is happy and vice versa.
If alice is both not kind and not tall then alice is not brave.
If paul is not happy or not tall then someone is both not quiet and rich.
Lucy is not calm or not funny.
Someone is rich.
Someone is either not quiet or not kind.
Someone is both strong and calm.
Someone is both not brave and strong.
John is kind or wise.
Alice is brave.
Someone is either not rich or quiet. | Alice is strong. | neutral | (![X]:((~brave(X)&~kind(X))=>(~generous(X)|patient(X))))&
(![X]:((curious(X)<~>~rich(X))=>(tall(X)<~>rich(X))))&
(((~generous(mary)|patient(mary)))=>(~kind(john)))&
((?[X]:(happy(X)))=>((creative(alice)|funny(alice))))&
(![X]:((creative(X)<~>~brave(X))=>(~brave(X)|~tall(X))))&
(((curious(mary)<~>~generous(mary)))=>((~generous(paul)<~>~wise(paul))))&
(![X]:((~funny(X)|~happy(X))=>generous(X)))&
(![X]:((funny(X)<~>~creative(X))<=>(creative(X)&~wise(X))))&
(![X]:(~wise(X)=>(quiet(X)|~patient(X))))&
(![X]:((~wise(X)&~old(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))&
(![X]:((~calm(X)|~tall(X))<=>happy(X)))&
(((~kind(alice)&~tall(alice)))=>(~brave(alice)))&
(((~happy(paul)|~tall(paul)))=>(?[X]:((~quiet(X)&rich(X)))))&
((~calm(lucy)|~funny(lucy)))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:((strong(X)&calm(X))))&
(?[X]:((~brave(X)&strong(X))))&
((kind(john)|wise(john)))&
(brave(alice))&
(?[X]:((~rich(X)<~>quiet(X)))) | strong(alice) | []
| null | 0 |
If someone is happy then someone is wise. Everyone who is not tall is either not happy or tall. If mary is either quiet or not tall then lucy is both not funny and rich and vice versa. If someone is either not funny or not tall then paul is not rich. Everyone who is not happy or quiet is both not brave and funny. Everyone who is both not creative and not humble is not calm or not rich. Everyone who is either curious or not funny is not rich or rich and vice versa. Everyone who is not creative or wise is not creative. Everyone who is not strong is either not quiet or rich. Everyone who is curious or happy is not rich and vice versa. Everyone who is not creative is either strong or not patient. If fred is creative or funny then someone is not brave or not funny. Everyone who is not kind or not brave is both not quiet and creative. Everyone who is patient is both not rich and not patient. Everyone who is not brave or not old is either not wise or tall. If fred is both not humble and funny then someone is either not happy or not generous and vice versa. Lucy is not patient. Paul is either happy or quiet. Paul is creative or not happy. Susan is not old or not strong. Someone is curious. Lucy is either calm or funny. Mary is not creative. Someone is funny or not quiet. | Mary is kind. | entailment | ((?[X]:(happy(X)))=>(?[X]:(wise(X))))&
(![X]:(~tall(X)=>(~happy(X)<~>tall(X))))&
(((quiet(mary)<~>~tall(mary)))<=>((~funny(lucy)&rich(lucy))))&
((?[X]:((~funny(X)<~>~tall(X))))=>(~rich(paul)))&
(![X]:((~happy(X)|quiet(X))=>(~brave(X)&funny(X))))&
(![X]:((~creative(X)&~humble(X))=>(~calm(X)|~rich(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(~rich(X)|rich(X))))&
(![X]:((~creative(X)|wise(X))=>~creative(X)))&
(![X]:(~strong(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((curious(X)|happy(X))<=>~rich(X)))&
(![X]:(~creative(X)=>(strong(X)<~>~patient(X))))&
(((creative(fred)|funny(fred)))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((~kind(X)|~brave(X))=>(~quiet(X)&creative(X))))&
(![X]:(patient(X)=>(~rich(X)&~patient(X))))&
(![X]:((~brave(X)|~old(X))=>(~wise(X)<~>tall(X))))&
(((~humble(fred)&funny(fred)))<=>(?[X]:((~happy(X)<~>~generous(X)))))&
(~patient(lucy))&
((happy(paul)<~>quiet(paul)))&
((creative(paul)|~happy(paul)))&
((~old(susan)|~strong(susan)))&
(?[X]:(curious(X)))&
((calm(lucy)<~>funny(lucy)))&
(~creative(mary))&
(?[X]:((funny(X)|~quiet(X)))) | kind(mary) | [
"p12",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4350219481595335813791999
% SZS output start Proof for 4350219481595335813791999
13. ! [X0] : ((~brave(X0) | ~kind(X0)) => (creative(X0) & ~quiet(X0))) [input p12]
23. ~creative(mary) [input p22]
25. ~kind(mary) [input hypothesis]
37. ! [X0] : ((creative(X0) & ~quiet(X0)) | (brave(X0) & kind(X0))) [ennf transformation 13]
102. kind(X0) | creative(X0) [cnf transformation 37]
124. ~creative(mary) [cnf transformation 23]
126. ~kind(mary) [cnf transformation 25]
238. creative(mary) [resolution 102,126]
239. $false [subsumption resolution 238,124]
% SZS output end Proof for 4350219481595335813791999
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not funny and vice versa. If fred is both not curious and kind then alice is both not kind and not happy. If someone is funny then lucy is brave and vice versa. Everyone who is rich is both not rich and not creative and vice versa. If someone is old or not kind then someone is not strong and vice versa. Everyone who is both wise and not happy is both rich and kind. Everyone who is either not creative or quiet is calm and vice versa. If mary is not wise then mary is both not strong and not quiet. Everyone who is either not funny or not brave is funny. If someone is creative then someone is not strong or wise and vice versa. If someone is not humble or not rich then someone is not wise and vice versa. If fred is both not funny and not calm then alice is kind or old. If mary is not curious or not happy then susan is not patient or not happy and vice versa. If mary is both quiet and tall then someone is not generous and vice versa. Everyone who is both not rich and not kind is old and vice versa. Everyone who is both creative and old is both kind and tall and vice versa. Someone is either not happy or patient. Susan is both not rich and not curious. Someone is not humble. Paul is either not wise or happy. Alice is not humble or not quiet. Someone is not quiet or curious. Susan is funny or rich. | Fred is creative. | entailment | (![X]:(~calm(X)<=>~funny(X)))&
(((~curious(fred)&kind(fred)))=>((~kind(alice)&~happy(alice))))&
((?[X]:(funny(X)))<=>(brave(lucy)))&
(![X]:(rich(X)<=>(~rich(X)&~creative(X))))&
((?[X]:((old(X)|~kind(X))))<=>(?[X]:(~strong(X))))&
(![X]:((wise(X)&~happy(X))=>(rich(X)&kind(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>calm(X)))&
((~wise(mary))=>((~strong(mary)&~quiet(mary))))&
(![X]:((~funny(X)<~>~brave(X))=>funny(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~strong(X)|wise(X)))))&
((?[X]:((~humble(X)|~rich(X))))<=>(?[X]:(~wise(X))))&
(((~funny(fred)&~calm(fred)))=>((kind(alice)|old(alice))))&
(((~curious(mary)|~happy(mary)))<=>((~patient(susan)|~happy(susan))))&
(((quiet(mary)&tall(mary)))<=>(?[X]:(~generous(X))))&
(![X]:((~rich(X)&~kind(X))<=>old(X)))&
(![X]:((creative(X)&old(X))<=>(kind(X)&tall(X))))&
(?[X]:((~happy(X)<~>patient(X))))&
((~rich(susan)&~curious(susan)))&
(?[X]:(~humble(X)))&
((~wise(paul)<~>happy(paul)))&
((~humble(alice)|~quiet(alice)))&
(?[X]:((~quiet(X)|curious(X))))&
((funny(susan)|rich(susan))) | creative(fred) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 3782691684028883331223916
% SZS output start Proof for 3782691684028883331223916
4. ! [X0] : (rich(X0) <=> (~creative(X0) & ~rich(X0))) [input p3]
24. ~creative(fred) [input hypothesis]
41. ! [X0] : ((rich(X0) | (creative(X0) | rich(X0))) & ((~creative(X0) & ~rich(X0)) | ~rich(X0))) [nnf transformation 4]
42. ! [X0] : ((rich(X0) | creative(X0) | rich(X0)) & ((~creative(X0) & ~rich(X0)) | ~rich(X0))) [flattening 41]
85. ~rich(X0) | ~rich(X0) [cnf transformation 42]
87. rich(X0) | creative(X0) | rich(X0) [cnf transformation 42]
132. ~creative(fred) [cnf transformation 24]
134. ~rich(X0) [duplicate literal removal 85]
135. creative(X0) | rich(X0) [duplicate literal removal 87]
324. rich(fred) [resolution 135,132]
326. $false [subsumption resolution 324,134]
% SZS output end Proof for 3782691684028883331223916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is happy or strong.
If someone is curious or not tall then mary is kind or not patient.
If mary is creative or not quiet then lucy is humble or generous.
Everyone who is either strong or wise is wise or not calm.
Everyone who is not funny or brave is both brave and not calm.
If fred is both not old and tall then someone is creative or funny and vice versa.
Everyone who is either rich or not wise is either not tall or wise and vice versa.
Everyone who is not curious or not funny is kind or not curious.
Everyone who is both happy and not tall is humble or not wise and vice versa.
Everyone who is both curious and quiet is brave.
Everyone who is either calm or curious is generous or not rich and vice versa.
If someone is both not creative and curious then mary is not strong or creative.
If fred is wise or not calm then fred is both not rich and strong and vice versa.
If someone is generous or not old then alice is not rich or funny.
Everyone who is not brave is either not tall or strong and vice versa.
Susan is either brave or strong.
John is not creative.
Susan is not calm.
Someone is both old and generous.
Someone is not wise or tall.
Someone is either not patient or tall.
Someone is not humble. | Susan is funny. | contradiction | (![X]:(brave(X)=>(happy(X)|strong(X))))&
((?[X]:((curious(X)|~tall(X))))=>((kind(mary)|~patient(mary))))&
(((creative(mary)|~quiet(mary)))=>((humble(lucy)|generous(lucy))))&
(![X]:((strong(X)<~>wise(X))=>(wise(X)|~calm(X))))&
(![X]:((~funny(X)|brave(X))=>(brave(X)&~calm(X))))&
(((~old(fred)&tall(fred)))<=>(?[X]:((creative(X)|funny(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~curious(X)|~funny(X))=>(kind(X)|~curious(X))))&
(![X]:((happy(X)&~tall(X))<=>(humble(X)|~wise(X))))&
(![X]:((curious(X)&quiet(X))=>brave(X)))&
(![X]:((calm(X)<~>curious(X))<=>(generous(X)|~rich(X))))&
((?[X]:((~creative(X)&curious(X))))=>((~strong(mary)|creative(mary))))&
(((wise(fred)|~calm(fred)))<=>((~rich(fred)&strong(fred))))&
((?[X]:((generous(X)|~old(X))))=>((~rich(alice)|funny(alice))))&
(![X]:(~brave(X)<=>(~tall(X)<~>strong(X))))&
((brave(susan)<~>strong(susan)))&
(~creative(john))&
(~calm(susan))&
(?[X]:((old(X)&generous(X))))&
(?[X]:((~wise(X)|tall(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
(?[X]:(~humble(X))) | funny(susan) | [
"p5",
"p6",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 6215041369349346154439958
% SZS output start Proof for 6215041369349346154439958
6. (tall(fred) & ~old(fred)) <=> ? [X0] : (funny(X0) | creative(X0)) [input p5]
7. ! [X0] : ((rich(X0) <~> ~wise(X0)) <=> (~tall(X0) <~> wise(X0))) [input p6]
9. ! [X0] : ((~tall(X0) & happy(X0)) <=> (~wise(X0) | humble(X0))) [input p8]
13. (~calm(fred) | wise(fred)) <=> (strong(fred) & ~rich(fred)) [input p12]
23. funny(susan) [input hypothesis]
40. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | (~tall(fred) | old(fred))) [nnf transformation 6]
41. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | ~tall(fred) | old(fred)) [flattening 40]
42. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X1] : (funny(X1) | creative(X1)) | ~tall(fred) | old(fred)) [rectify 41]
43. ? [X1] : (funny(X1) | creative(X1)) => (funny(sK0) | creative(sK0)) [choice axiom]
44. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & ((funny(sK0) | creative(sK0)) | ~tall(fred) | old(fred)) [skolemisation 42,43]
45. ! [X0] : ((((wise(X0) | ~rich(X0)) & (~wise(X0) | rich(X0))) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0)))) & (((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))))) [nnf transformation 7]
46. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | (tall(X0) | ~happy(X0)))) [nnf transformation 9]
47. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | tall(X0) | ~happy(X0))) [flattening 46]
50. ((~calm(fred) | wise(fred)) | (~strong(fred) | rich(fred))) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [nnf transformation 13]
51. (~calm(fred) | wise(fred) | ~strong(fred) | rich(fred)) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [flattening 50]
76. tall(fred) | ~funny(X0) [cnf transformation 44]
78. wise(X0) | ~tall(X0) | rich(X0) | wise(X0) [cnf transformation 45]
82. ~wise(X0) | rich(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 45]
89. ~tall(X0) | wise(X0) [cnf transformation 47]
98. ~rich(fred) | ~wise(fred) [cnf transformation 51]
119. funny(susan) [cnf transformation 23]
120. wise(X0) | ~tall(X0) | rich(X0) [duplicate literal removal 78]
122. ~wise(X0) | rich(X0) | ~tall(X0) [duplicate literal removal 82]
144. 5 <=> ! [X0] : ~funny(X0) [avatar definition]
145. ~funny(X0) <- (5) [avatar component clause 144]
147. 6 <=> tall(fred) [avatar definition]
149. tall(fred) <- (6) [avatar component clause 147]
150. 5 | 6 [avatar split clause 76,147,144]
171. ~tall(X0) | rich(X0) [subsumption resolution 120,122]
190. 15 <=> wise(fred) [avatar definition]
195. 16 <=> rich(fred) [avatar definition]
197. ~rich(fred) <- (~16) [avatar component clause 195]
199. ~15 | ~16 [avatar split clause 98,195,190]
245. $false <- (5) [resolution 145,119]
246. ~5 [avatar contradiction clause 245]
255. wise(fred) <- (6) [resolution 89,149]
258. 15 | ~6 [avatar split clause 255,147,190]
259. rich(fred) <- (6) [resolution 171,149]
260. $false <- (6, ~16) [subsumption resolution 259,197]
261. ~6 | 16 [avatar contradiction clause 260]
262. $false [avatar sat refutation 150,199,246,258,261]
% SZS output end Proof for 6215041369349346154439958
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not funny is both curious and not brave and vice versa.
Everyone who is not kind or kind is not kind and vice versa.
If someone is not patient then someone is either not kind or not funny and vice versa.
Everyone who is old or brave is funny.
Everyone who is either not happy or curious is both tall and not quiet.
Everyone who is not curious or not humble is brave.
Everyone who is either not happy or rich is not strong.
Everyone who is calm or not old is either not humble or not quiet.
If someone is not calm then susan is happy or not generous.
Everyone who is both not funny and not strong is either not tall or wise and vice versa.
Everyone who is generous or not generous is both not tall and not creative.
Everyone who is not humble or strong is not tall or not funny.
If someone is funny then someone is not humble or not old and vice versa.
If someone is patient then someone is brave or not wise and vice versa.
Everyone who is both calm and not humble is both not creative and not patient and vice versa.
Paul is old.
Someone is either not rich or patient.
Someone is both not strong and patient.
Someone is not strong.
Mary is curious or wise.
Someone is either generous or not curious.
Someone is funny or not funny. | Susan is not patient. | neutral | (![X]:((patient(X)<~>~funny(X))<=>(curious(X)&~brave(X))))&
(![X]:((~kind(X)|kind(X))<=>~kind(X)))&
((?[X]:(~patient(X)))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
(![X]:((old(X)|brave(X))=>funny(X)))&
(![X]:((~happy(X)<~>curious(X))=>(tall(X)&~quiet(X))))&
(![X]:((~curious(X)|~humble(X))=>brave(X)))&
(![X]:((~happy(X)<~>rich(X))=>~strong(X)))&
(![X]:((calm(X)|~old(X))=>(~humble(X)<~>~quiet(X))))&
((?[X]:(~calm(X)))=>((happy(susan)|~generous(susan))))&
(![X]:((~funny(X)&~strong(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((generous(X)|~generous(X))=>(~tall(X)&~creative(X))))&
(![X]:((~humble(X)|strong(X))=>(~tall(X)|~funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~humble(X)|~old(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((brave(X)|~wise(X)))))&
(![X]:((calm(X)&~humble(X))<=>(~creative(X)&~patient(X))))&
(old(paul))&
(?[X]:((~rich(X)<~>patient(X))))&
(?[X]:((~strong(X)&patient(X))))&
(?[X]:(~strong(X)))&
((curious(mary)|wise(mary)))&
(?[X]:((generous(X)<~>~curious(X))))&
(?[X]:((funny(X)|~funny(X)))) | ~patient(susan) | []
| null | 0 |
Everyone who is strong or not curious is either happy or not curious and vice versa.
If alice is both not strong and not patient then someone is not creative.
Everyone who is both kind and not kind is both old and not wise.
If someone is either quiet or not patient then someone is both generous and not brave and vice versa.
If someone is calm or curious then paul is kind or rich.
If someone is not quiet or wise then someone is both strong and brave.
If mary is both happy and curious then susan is not curious.
Everyone who is not patient or not old is either generous or rich and vice versa.
If mary is either creative or humble then someone is patient or not funny.
Everyone who is wise or not humble is either old or not brave and vice versa.
Everyone who is old or not old is both not generous and not curious.
Everyone who is humble or generous is either not generous or not strong.
If someone is either not patient or rich then mary is both not quiet and not strong.
Everyone who is both not curious and not old is not quiet and vice versa.
Everyone who is old is kind.
If mary is not patient or old then paul is not happy or strong.
Someone is not strong or not tall.
Mary is both rich and not humble.
Fred is not strong or creative.
Someone is either quiet or generous.
Mary is not wise or calm.
Someone is either humble or strong.
Lucy is kind or not rich. | Mary is not wise. | neutral | (![X]:((strong(X)|~curious(X))<=>(happy(X)<~>~curious(X))))&
(((~strong(alice)&~patient(alice)))=>(?[X]:(~creative(X))))&
(![X]:((kind(X)&~kind(X))=>(old(X)&~wise(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((calm(X)|curious(X))))=>((kind(paul)|rich(paul))))&
((?[X]:((~quiet(X)|wise(X))))=>(?[X]:((strong(X)&brave(X)))))&
(((happy(mary)&curious(mary)))=>(~curious(susan)))&
(![X]:((~patient(X)|~old(X))<=>(generous(X)<~>rich(X))))&
(((creative(mary)<~>humble(mary)))=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((wise(X)|~humble(X))<=>(old(X)<~>~brave(X))))&
(![X]:((old(X)|~old(X))=>(~generous(X)&~curious(X))))&
(![X]:((humble(X)|generous(X))=>(~generous(X)<~>~strong(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~quiet(mary)&~strong(mary))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
(![X]:(old(X)=>kind(X)))&
(((~patient(mary)|old(mary)))=>((~happy(paul)|strong(paul))))&
(?[X]:((~strong(X)|~tall(X))))&
((rich(mary)&~humble(mary)))&
((~strong(fred)|creative(fred)))&
(?[X]:((quiet(X)<~>generous(X))))&
((~wise(mary)|calm(mary)))&
(?[X]:((humble(X)<~>strong(X))))&
((kind(lucy)|~rich(lucy))) | ~wise(mary) | []
| null | 0 |
Everyone who is patient or not calm is both not tall and not curious. Everyone who is either strong or wise is not wise or not kind and vice versa. If someone is calm then susan is both rich and wise. If someone is not calm then john is kind or quiet. Everyone who is either not humble or not strong is both tall and funny and vice versa. If lucy is old or generous then mary is both not humble and strong and vice versa. Everyone who is not calm or tall is not calm or curious and vice versa. Everyone who is both not tall and strong is quiet or strong and vice versa. If alice is tall or not patient then fred is not rich and vice versa. If fred is both wise and not creative then someone is not creative or not strong and vice versa. If someone is either old or not generous then fred is not wise. If someone is rich then paul is humble. If lucy is both not strong and curious then mary is either not strong or not wise. Everyone who is kind is both tall and brave and vice versa. If lucy is wise then someone is quiet. Everyone who is either not quiet or kind is not old. Someone is both creative and not brave. Susan is either generous or tall. Paul is either not kind or not brave. Lucy is either generous or humble. Someone is both not kind and not old. Susan is either patient or rich. | Mary is not strong. | contradiction | (![X]:((patient(X)|~calm(X))=>(~tall(X)&~curious(X))))&
(![X]:((strong(X)<~>wise(X))<=>(~wise(X)|~kind(X))))&
((?[X]:(calm(X)))=>((rich(susan)&wise(susan))))&
((?[X]:(~calm(X)))=>((kind(john)|quiet(john))))&
(![X]:((~humble(X)<~>~strong(X))<=>(tall(X)&funny(X))))&
(((old(lucy)|generous(lucy)))<=>((~humble(mary)&strong(mary))))&
(![X]:((~calm(X)|tall(X))<=>(~calm(X)|curious(X))))&
(![X]:((~tall(X)&strong(X))<=>(quiet(X)|strong(X))))&
(((tall(alice)|~patient(alice)))<=>(~rich(fred)))&
(((wise(fred)&~creative(fred)))<=>(?[X]:((~creative(X)|~strong(X)))))&
((?[X]:((old(X)<~>~generous(X))))=>(~wise(fred)))&
((?[X]:(rich(X)))=>(humble(paul)))&
(((~strong(lucy)&curious(lucy)))=>((~strong(mary)<~>~wise(mary))))&
(![X]:(kind(X)<=>(tall(X)&brave(X))))&
((wise(lucy))=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)<~>kind(X))=>~old(X)))&
(?[X]:((creative(X)&~brave(X))))&
((generous(susan)<~>tall(susan)))&
((~kind(paul)<~>~brave(paul)))&
((generous(lucy)<~>humble(lucy)))&
(?[X]:((~kind(X)&~old(X))))&
((patient(susan)<~>rich(susan))) | ~strong(mary) | [
"p5",
"p9",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 2708895315657151744129206
% SZS output start Proof for 2708895315657151744129206
6. (generous(lucy) | old(lucy)) <=> (strong(mary) & ~humble(mary)) [input p5]
10. (~creative(fred) & wise(fred)) <=> ? [X0] : (~strong(X0) | ~creative(X0)) [input p9]
11. ? [X0] : (old(X0) <~> ~generous(X0)) => ~wise(fred) [input p10]
23. ~strong(mary) [input hypothesis]
28. ~wise(fred) | ! [X0] : (old(X0) <=> ~generous(X0)) [ennf transformation 11]
38. ((generous(lucy) | old(lucy)) | (~strong(mary) | humble(mary))) & ((strong(mary) & ~humble(mary)) | (~generous(lucy) & ~old(lucy))) [nnf transformation 6]
39. (generous(lucy) | old(lucy) | ~strong(mary) | humble(mary)) & ((strong(mary) & ~humble(mary)) | (~generous(lucy) & ~old(lucy))) [flattening 38]
46. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X0] : (~strong(X0) | ~creative(X0)) | (creative(fred) | ~wise(fred))) [nnf transformation 10]
47. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X0] : (~strong(X0) | ~creative(X0)) | creative(fred) | ~wise(fred)) [flattening 46]
48. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X1] : (~strong(X1) | ~creative(X1)) | creative(fred) | ~wise(fred)) [rectify 47]
49. ? [X1] : (~strong(X1) | ~creative(X1)) => (~strong(sK0) | ~creative(sK0)) [choice axiom]
50. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & ((~strong(sK0) | ~creative(sK0)) | creative(fred) | ~wise(fred)) [skolemisation 48,49]
51. ~wise(fred) | ! [X0] : ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0))) [nnf transformation 28]
87. strong(mary) | ~old(lucy) [cnf transformation 39]
88. strong(mary) | ~generous(lucy) [cnf transformation 39]
104. wise(fred) | strong(X0) [cnf transformation 50]
108. ~wise(fred) | old(X0) | generous(X0) [cnf transformation 51]
130. ~strong(mary) [cnf transformation 23]
164. 8 <=> strong(mary) [avatar definition]
166. ~strong(mary) <- (~8) [avatar component clause 164]
168. 9 <=> old(lucy) [avatar definition]
169. ~old(lucy) <- (~9) [avatar component clause 168]
172. 10 <=> generous(lucy) [avatar definition]
173. ~generous(lucy) <- (~10) [avatar component clause 172]
176. ~10 | 8 [avatar split clause 88,164,172]
177. ~9 | 8 [avatar split clause 87,164,168]
199. 14 <=> ! [X0] : strong(X0) [avatar definition]
200. strong(X0) <- (14) [avatar component clause 199]
211. 17 <=> wise(fred) [avatar definition]
214. 14 | 17 [avatar split clause 104,211,199]
226. 20 <=> ! [X0] : (old(X0) | generous(X0)) [avatar definition]
227. generous(X0) | old(X0) <- (20) [avatar component clause 226]
228. 20 | ~17 [avatar split clause 108,211,226]
287. ~8 [avatar split clause 130,164]
290. $false <- (~8, 14) [subsumption resolution 166,200]
291. 8 | ~14 [avatar contradiction clause 290]
297. old(lucy) <- (~10, 20) [resolution 227,173]
298. $false <- (~9, ~10, 20) [subsumption resolution 297,169]
299. 9 | 10 | ~20 [avatar contradiction clause 298]
300. $false [avatar sat refutation 176,177,214,228,287,291,299]
% SZS output end Proof for 2708895315657151744129206
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny is both generous and not calm.
If john is either wise or funny then alice is both curious and strong.
Everyone who is not creative or funny is both not curious and not rich and vice versa.
Everyone who is not curious is not happy or not calm and vice versa.
Everyone who is old is both not old and rich.
If paul is both not wise and not humble then someone is not tall and vice versa.
Everyone who is patient is not wise or not curious and vice versa.
If someone is curious or not quiet then someone is not creative and vice versa.
Everyone who is both not funny and tall is tall or old.
Everyone who is strong is calm and vice versa.
If paul is both curious and generous then someone is kind or not wise and vice versa.
Everyone who is either strong or happy is not curious.
If someone is either not tall or not calm then someone is not brave and vice versa.
Everyone who is not funny is either rich or not strong.
Everyone who is either brave or creative is not curious and vice versa.
Someone is not old or not quiet.
Mary is not rich.
Susan is both not humble and not creative.
Paul is either strong or funny.
Someone is either not curious or not patient.
Someone is not quiet or calm. | Alice is kind. | contradiction | (![X]:(~funny(X)=>(generous(X)&~calm(X))))&
(((wise(john)<~>funny(john)))=>((curious(alice)&strong(alice))))&
(![X]:((~creative(X)|funny(X))<=>(~curious(X)&~rich(X))))&
(![X]:(~curious(X)<=>(~happy(X)|~calm(X))))&
(![X]:(old(X)=>(~old(X)&rich(X))))&
(((~wise(paul)&~humble(paul)))<=>(?[X]:(~tall(X))))&
(![X]:(patient(X)<=>(~wise(X)|~curious(X))))&
((?[X]:((curious(X)|~quiet(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~funny(X)&tall(X))=>(tall(X)|old(X))))&
(![X]:(strong(X)<=>calm(X)))&
(((curious(paul)&generous(paul)))<=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((strong(X)<~>happy(X))=>~curious(X)))&
((?[X]:((~tall(X)<~>~calm(X))))<=>(?[X]:(~brave(X))))&
(![X]:(~funny(X)=>(rich(X)<~>~strong(X))))&
(![X]:((brave(X)<~>creative(X))<=>~curious(X)))&
(?[X]:((~old(X)|~quiet(X))))&
(~rich(mary))&
((~humble(susan)&~creative(susan)))&
((strong(paul)<~>funny(paul)))&
(?[X]:((~curious(X)<~>~patient(X))))&
(?[X]:((~quiet(X)|calm(X)))) | kind(alice) | [
"p0",
"p2",
"p3",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 139034967011029857377590
% SZS output start Proof for 139034967011029857377590
1. ! [X0] : (~funny(X0) => (~calm(X0) & generous(X0))) [input p0]
3. ! [X0] : ((funny(X0) | ~creative(X0)) <=> (~rich(X0) & ~curious(X0))) [input p2]
4. ! [X0] : (~curious(X0) <=> (~calm(X0) | ~happy(X0))) [input p3]
11. (generous(paul) & curious(paul)) <=> ? [X0] : (~wise(X0) | kind(X0)) [input p10]
22. kind(alice) [input hypothesis]
25. ! [X0] : ((~calm(X0) & generous(X0)) | funny(X0)) [ennf transformation 1]
33. ! [X0] : (((funny(X0) | ~creative(X0)) | (rich(X0) | curious(X0))) & ((~rich(X0) & ~curious(X0)) | (~funny(X0) & creative(X0)))) [nnf transformation 3]
34. ! [X0] : ((funny(X0) | ~creative(X0) | rich(X0) | curious(X0)) & ((~rich(X0) & ~curious(X0)) | (~funny(X0) & creative(X0)))) [flattening 33]
35. ! [X0] : ((~curious(X0) | (calm(X0) & happy(X0))) & ((~calm(X0) | ~happy(X0)) | curious(X0))) [nnf transformation 4]
36. ! [X0] : ((~curious(X0) | (calm(X0) & happy(X0))) & (~calm(X0) | ~happy(X0) | curious(X0))) [flattening 35]
50. ((generous(paul) & curious(paul)) | ! [X0] : (wise(X0) & ~kind(X0))) & (? [X0] : (~wise(X0) | kind(X0)) | (~generous(paul) | ~curious(paul))) [nnf transformation 11]
51. ((generous(paul) & curious(paul)) | ! [X0] : (wise(X0) & ~kind(X0))) & (? [X0] : (~wise(X0) | kind(X0)) | ~generous(paul) | ~curious(paul)) [flattening 50]
52. ((generous(paul) & curious(paul)) | ! [X0] : (wise(X0) & ~kind(X0))) & (? [X1] : (~wise(X1) | kind(X1)) | ~generous(paul) | ~curious(paul)) [rectify 51]
53. ? [X1] : (~wise(X1) | kind(X1)) => (~wise(sK3) | kind(sK3)) [choice axiom]
54. ((generous(paul) & curious(paul)) | ! [X0] : (wise(X0) & ~kind(X0))) & ((~wise(sK3) | kind(sK3)) | ~generous(paul) | ~curious(paul)) [skolemisation 52,53]
72. ~calm(X0) | funny(X0) [cnf transformation 25]
78. ~curious(X0) | ~funny(X0) [cnf transformation 34]
84. ~curious(X0) | calm(X0) [cnf transformation 36]
100. curious(paul) | ~kind(X0) [cnf transformation 54]
125. kind(alice) [cnf transformation 22]
198. 17 <=> ! [X0] : ~kind(X0) [avatar definition]
199. ~kind(X0) <- (17) [avatar component clause 198]
202. 18 <=> curious(paul) [avatar definition]
204. curious(paul) <- (18) [avatar component clause 202]
206. 17 | 18 [avatar split clause 100,202,198]
250. 28 <=> funny(paul) [avatar definition]
277. $false <- (17) [resolution 199,125]
278. ~17 [avatar contradiction clause 277]
282. ~funny(paul) <- (18) [resolution 78,204]
284. calm(paul) <- (18) [resolution 84,204]
285. funny(paul) <- (18) [resolution 284,72]
288. 28 | ~18 [avatar split clause 285,202,250]
289. ~28 | ~18 [avatar split clause 282,202,250]
290. $false [avatar sat refutation 206,278,288,289]
% SZS output end Proof for 139034967011029857377590
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or happy then someone is either not wise or not funny and vice versa.
Everyone who is both not strong and not old is both generous and kind and vice versa.
If someone is not generous then john is both not tall and creative and vice versa.
If someone is either not wise or rich then someone is either not calm or generous and vice versa.
Everyone who is either not generous or not humble is patient or not tall.
Everyone who is not tall is both old and not generous.
If someone is rich or not tall then someone is not generous or not old and vice versa.
If someone is either not calm or calm then john is not happy.
Everyone who is calm or humble is either creative or generous and vice versa.
Everyone who is either not kind or old is curious or generous.
If alice is not happy or curious then alice is not old or tall and vice versa.
If someone is creative or not funny then someone is wise or humble.
Everyone who is either not quiet or not kind is both tall and not old and vice versa.
Everyone who is both not funny and not rich is both not curious and not rich.
Everyone who is tall or patient is not tall or calm and vice versa.
Everyone who is either not rich or humble is either calm or humble.
Alice is either funny or not happy.
Someone is either not curious or not quiet.
Susan is calm or kind.
Someone is either not calm or not generous.
Fred is not creative.
Fred is not strong or rich.
Mary is either not patient or curious. | Fred is creative. | contradiction | ((?[X]:((~wise(X)<~>happy(X))))<=>(?[X]:((~wise(X)<~>~funny(X)))))&
(![X]:((~strong(X)&~old(X))<=>(generous(X)&kind(X))))&
((?[X]:(~generous(X)))<=>((~tall(john)&creative(john))))&
((?[X]:((~wise(X)<~>rich(X))))<=>(?[X]:((~calm(X)<~>generous(X)))))&
(![X]:((~generous(X)<~>~humble(X))=>(patient(X)|~tall(X))))&
(![X]:(~tall(X)=>(old(X)&~generous(X))))&
((?[X]:((rich(X)|~tall(X))))<=>(?[X]:((~generous(X)|~old(X)))))&
((?[X]:((~calm(X)<~>calm(X))))=>(~happy(john)))&
(![X]:((calm(X)|humble(X))<=>(creative(X)<~>generous(X))))&
(![X]:((~kind(X)<~>old(X))=>(curious(X)|generous(X))))&
(((~happy(alice)|curious(alice)))<=>((~old(alice)|tall(alice))))&
((?[X]:((creative(X)|~funny(X))))=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(tall(X)&~old(X))))&
(![X]:((~funny(X)&~rich(X))=>(~curious(X)&~rich(X))))&
(![X]:((tall(X)|patient(X))<=>(~tall(X)|calm(X))))&
(![X]:((~rich(X)<~>humble(X))=>(calm(X)<~>humble(X))))&
((funny(alice)<~>~happy(alice)))&
(?[X]:((~curious(X)<~>~quiet(X))))&
((calm(susan)|kind(susan)))&
(?[X]:((~calm(X)<~>~generous(X))))&
(~creative(fred))&
((~strong(fred)|rich(fred)))&
((~patient(mary)<~>curious(mary))) | creative(fred) | [
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 930389347691008119672609
% SZS output start Proof for 930389347691008119672609
21. ~creative(fred) [input p20]
24. creative(fred) [input hypothesis]
154. ~creative(fred) [cnf transformation 21]
158. creative(fred) [cnf transformation 24]
391. $false [subsumption resolution 158,154]
% SZS output end Proof for 930389347691008119672609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not patient then paul is calm or strong and vice versa.
Everyone who is both not kind and not calm is either creative or wise and vice versa.
Everyone who is strong or tall is both generous and not generous.
Everyone who is both funny and not patient is not funny or quiet and vice versa.
If someone is both wise and tall then fred is either brave or not wise.
If mary is both humble and kind then alice is rich or generous.
Everyone who is not funny or funny is curious or not humble.
Everyone who is kind is both not humble and funny.
If someone is both quiet and curious then someone is either happy or brave and vice versa.
Everyone who is rich or not strong is strong or not humble.
If someone is brave or curious then paul is either not curious or not generous.
Everyone who is either humble or not funny is not wise.
If alice is not funny then alice is either happy or not quiet.
If susan is not generous or patient then someone is both kind and not funny.
If someone is either rich or kind then someone is not wise.
Everyone who is both not tall and tall is tall and vice versa.
Someone is either not calm or not tall.
Someone is either creative or not old.
Mary is not tall.
John is wise.
Someone is calm.
Someone is not tall.
Lucy is both not strong and not brave.
Lucy is patient. | Lucy is patient. | entailment | ((~patient(fred))<=>((calm(paul)|strong(paul))))&
(![X]:((~kind(X)&~calm(X))<=>(creative(X)<~>wise(X))))&
(![X]:((strong(X)|tall(X))=>(generous(X)&~generous(X))))&
(![X]:((funny(X)&~patient(X))<=>(~funny(X)|quiet(X))))&
((?[X]:((wise(X)&tall(X))))=>((brave(fred)<~>~wise(fred))))&
(((humble(mary)&kind(mary)))=>((rich(alice)|generous(alice))))&
(![X]:((~funny(X)|funny(X))=>(curious(X)|~humble(X))))&
(![X]:(kind(X)=>(~humble(X)&funny(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((rich(X)|~strong(X))=>(strong(X)|~humble(X))))&
((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((humble(X)<~>~funny(X))=>~wise(X)))&
((~funny(alice))=>((happy(alice)<~>~quiet(alice))))&
(((~generous(susan)|patient(susan)))=>(?[X]:((kind(X)&~funny(X)))))&
((?[X]:((rich(X)<~>kind(X))))=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>tall(X)))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((creative(X)<~>~old(X))))&
(~tall(mary))&
(wise(john))&
(?[X]:(calm(X)))&
(?[X]:(~tall(X)))&
((~strong(lucy)&~brave(lucy)))&
(patient(lucy)) | patient(lucy) | [
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 13640456153329945283296
% SZS output start Proof for 13640456153329945283296
24. patient(lucy) [input p23]
25. ~patient(lucy) [input hypothesis]
135. patient(lucy) [cnf transformation 24]
136. ~patient(lucy) [cnf transformation 25]
253. $false [subsumption resolution 136,135]
% SZS output end Proof for 13640456153329945283296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either tall or happy then lucy is both not creative and not patient and vice versa.
Everyone who is quiet or curious is either not kind or not curious and vice versa.
Everyone who is curious or old is both calm and patient.
Everyone who is either not rich or brave is tall and vice versa.
Everyone who is not wise is both rich and not generous and vice versa.
Everyone who is either old or not old is rich.
If someone is quiet then lucy is either creative or not generous and vice versa.
Everyone who is not wise or curious is either tall or not patient and vice versa.
If paul is both rich and generous then someone is either generous or not tall and vice versa.
If lucy is both not tall and not wise then john is both not happy and brave and vice versa.
Everyone who is not creative or not patient is calm.
Everyone who is not funny is both tall and not kind.
If fred is either not creative or generous then mary is brave or generous.
If someone is curious then john is either not funny or not patient.
Everyone who is either kind or not curious is not curious.
If alice is not brave or not happy then someone is not kind or patient and vice versa.
Someone is kind or funny.
Susan is not quiet or curious.
Mary is funny or generous.
Paul is not funny or rich.
John is wise or rich.
Alice is either not rich or curious. | Mary is old. | neutral | ((?[X]:((tall(X)<~>happy(X))))<=>((~creative(lucy)&~patient(lucy))))&
(![X]:((quiet(X)|curious(X))<=>(~kind(X)<~>~curious(X))))&
(![X]:((curious(X)|old(X))=>(calm(X)&patient(X))))&
(![X]:((~rich(X)<~>brave(X))<=>tall(X)))&
(![X]:(~wise(X)<=>(rich(X)&~generous(X))))&
(![X]:((old(X)<~>~old(X))=>rich(X)))&
((?[X]:(quiet(X)))<=>((creative(lucy)<~>~generous(lucy))))&
(![X]:((~wise(X)|curious(X))<=>(tall(X)<~>~patient(X))))&
(((rich(paul)&generous(paul)))<=>(?[X]:((generous(X)<~>~tall(X)))))&
(((~tall(lucy)&~wise(lucy)))<=>((~happy(john)&brave(john))))&
(![X]:((~creative(X)|~patient(X))=>calm(X)))&
(![X]:(~funny(X)=>(tall(X)&~kind(X))))&
(((~creative(fred)<~>generous(fred)))=>((brave(mary)|generous(mary))))&
((?[X]:(curious(X)))=>((~funny(john)<~>~patient(john))))&
(![X]:((kind(X)<~>~curious(X))=>~curious(X)))&
(((~brave(alice)|~happy(alice)))<=>(?[X]:((~kind(X)|patient(X)))))&
(?[X]:((kind(X)|funny(X))))&
((~quiet(susan)|curious(susan)))&
((funny(mary)|generous(mary)))&
((~funny(paul)|rich(paul)))&
((wise(john)|rich(john)))&
((~rich(alice)<~>curious(alice))) | old(mary) | []
| null | 0 |
Everyone who is creative or not brave is not funny.
If someone is not curious then fred is not generous and vice versa.
If someone is not funny or calm then someone is both not happy and not quiet.
If fred is either brave or not quiet then someone is not generous.
Everyone who is not quiet or not rich is rich or not old and vice versa.
If someone is either not humble or calm then someone is both tall and not curious.
Everyone who is brave or not funny is either not quiet or not brave and vice versa.
Everyone who is either not happy or creative is either not calm or happy.
Everyone who is both kind and happy is both not strong and quiet.
Everyone who is not humble or calm is either creative or happy and vice versa.
Everyone who is both calm and not humble is not rich and vice versa.
Everyone who is happy is not rich or not calm and vice versa.
If someone is both not funny and creative then someone is both not calm and not old.
Everyone who is both kind and old is both funny and not wise.
Everyone who is kind is both not kind and not strong.
Someone is not quiet or not patient.
John is both not old and not patient.
John is either creative or not curious.
Someone is not creative or not rich.
Someone is not rich or humble. | John is not funny. | neutral | (![X]:((creative(X)|~brave(X))=>~funny(X)))&
((?[X]:(~curious(X)))<=>(~generous(fred)))&
((?[X]:((~funny(X)|calm(X))))=>(?[X]:((~happy(X)&~quiet(X)))))&
(((brave(fred)<~>~quiet(fred)))=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|~rich(X))<=>(rich(X)|~old(X))))&
((?[X]:((~humble(X)<~>calm(X))))=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:((brave(X)|~funny(X))<=>(~quiet(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>creative(X))=>(~calm(X)<~>happy(X))))&
(![X]:((kind(X)&happy(X))=>(~strong(X)&quiet(X))))&
(![X]:((~humble(X)|calm(X))<=>(creative(X)<~>happy(X))))&
(![X]:((calm(X)&~humble(X))<=>~rich(X)))&
(![X]:(happy(X)<=>(~rich(X)|~calm(X))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((kind(X)&old(X))=>(funny(X)&~wise(X))))&
(![X]:(kind(X)=>(~kind(X)&~strong(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
((~old(john)&~patient(john)))&
((creative(john)<~>~curious(john)))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:((~rich(X)|humble(X)))) | ~funny(john) | []
| null | 0 |
Everyone who is calm or creative is not funny or not calm and vice versa.
If someone is either not calm or curious then someone is not tall or not strong and vice versa.
Everyone who is not old or wise is not patient or not humble.
Everyone who is wise or not funny is wise and vice versa.
If paul is both not creative and patient then someone is either patient or not happy and vice versa.
Everyone who is both brave and not rich is either brave or not rich.
If someone is either not happy or not curious then someone is not kind or not happy.
Everyone who is creative is not happy.
Everyone who is either not tall or not creative is both not rich and not kind and vice versa.
If someone is both kind and not creative then someone is not rich and vice versa.
Everyone who is kind is not rich or rich.
Everyone who is either not creative or not old is not old or not strong.
If someone is patient or not strong then someone is either generous or not old and vice versa.
Everyone who is either patient or calm is both brave and not strong.
Everyone who is not quiet is both humble and not quiet.
If someone is either happy or not creative then alice is both not creative and curious.
Someone is not patient.
Someone is both not calm and patient.
Paul is either calm or not tall.
Someone is not calm.
Someone is either wise or humble.
Someone is both not tall and not creative.
Alice is not generous or rich.
Paul is both not strong and not old. | Paul is quiet. | entailment | (![X]:((calm(X)|creative(X))<=>(~funny(X)|~calm(X))))&
((?[X]:((~calm(X)<~>curious(X))))<=>(?[X]:((~tall(X)|~strong(X)))))&
(![X]:((~old(X)|wise(X))=>(~patient(X)|~humble(X))))&
(![X]:((wise(X)|~funny(X))<=>wise(X)))&
(((~creative(paul)&patient(paul)))<=>(?[X]:((patient(X)<~>~happy(X)))))&
(![X]:((brave(X)&~rich(X))=>(brave(X)<~>~rich(X))))&
((?[X]:((~happy(X)<~>~curious(X))))=>(?[X]:((~kind(X)|~happy(X)))))&
(![X]:(creative(X)=>~happy(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>(~rich(X)&~kind(X))))&
((?[X]:((kind(X)&~creative(X))))<=>(?[X]:(~rich(X))))&
(![X]:(kind(X)=>(~rich(X)|rich(X))))&
(![X]:((~creative(X)<~>~old(X))=>(~old(X)|~strong(X))))&
((?[X]:((patient(X)|~strong(X))))<=>(?[X]:((generous(X)<~>~old(X)))))&
(![X]:((patient(X)<~>calm(X))=>(brave(X)&~strong(X))))&
(![X]:(~quiet(X)=>(humble(X)&~quiet(X))))&
((?[X]:((happy(X)<~>~creative(X))))=>((~creative(alice)&curious(alice))))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)&patient(X))))&
((calm(paul)<~>~tall(paul)))&
(?[X]:(~calm(X)))&
(?[X]:((wise(X)<~>humble(X))))&
(?[X]:((~tall(X)&~creative(X))))&
((~generous(alice)|rich(alice)))&
((~strong(paul)&~old(paul))) | quiet(paul) | [
"p0",
"p2",
"p4",
"p5",
"p7",
"p8",
"p13",
"p14",
"p18",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 2364729171373170442868289
% SZS output start Proof for 2364729171373170442868289
1. ! [X0] : ((creative(X0) | calm(X0)) <=> (~calm(X0) | ~funny(X0))) [input p0]
3. ! [X0] : ((wise(X0) | ~old(X0)) => (~humble(X0) | ~patient(X0))) [input p2]
5. (patient(paul) & ~creative(paul)) <=> ? [X0] : (patient(X0) <~> ~happy(X0)) [input p4]
6. ! [X0] : ((~rich(X0) & brave(X0)) => (brave(X0) <~> ~rich(X0))) [input p5]
8. ! [X0] : (creative(X0) => ~happy(X0)) [input p7]
9. ! [X0] : ((~tall(X0) <~> ~creative(X0)) <=> (~kind(X0) & ~rich(X0))) [input p8]
14. ! [X0] : ((patient(X0) <~> calm(X0)) => (~strong(X0) & brave(X0))) [input p13]
15. ! [X0] : (~quiet(X0) => (~quiet(X0) & humble(X0))) [input p14]
19. calm(paul) <~> ~tall(paul) [input p18]
24. ~old(paul) & ~strong(paul) [input p23]
25. ~quiet(paul) [input hypothesis]
30. ! [X0] : ((~humble(X0) | ~patient(X0)) | (~wise(X0) & old(X0))) [ennf transformation 3]
31. ! [X0] : (~humble(X0) | ~patient(X0) | (~wise(X0) & old(X0))) [flattening 30]
32. ! [X0] : ((brave(X0) <~> ~rich(X0)) | (rich(X0) | ~brave(X0))) [ennf transformation 6]
33. ! [X0] : ((brave(X0) <~> ~rich(X0)) | rich(X0) | ~brave(X0)) [flattening 32]
35. ! [X0] : (~happy(X0) | ~creative(X0)) [ennf transformation 8]
40. ! [X0] : ((~strong(X0) & brave(X0)) | (patient(X0) <=> calm(X0))) [ennf transformation 14]
41. ! [X0] : ((~quiet(X0) & humble(X0)) | quiet(X0)) [ennf transformation 15]
43. ! [X0] : (((creative(X0) | calm(X0)) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | (~creative(X0) & ~calm(X0)))) [nnf transformation 1]
44. ! [X0] : ((creative(X0) | calm(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | (~creative(X0) & ~calm(X0)))) [flattening 43]
52. ((patient(paul) & ~creative(paul)) | ! [X0] : ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (? [X0] : ((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (~patient(paul) | creative(paul))) [nnf transformation 5]
53. ((patient(paul) & ~creative(paul)) | ! [X0] : ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (? [X0] : ((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | ~patient(paul) | creative(paul)) [flattening 52]
54. ((patient(paul) & ~creative(paul)) | ! [X0] : ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (? [X1] : ((happy(X1) | ~patient(X1)) & (~happy(X1) | patient(X1))) | ~patient(paul) | creative(paul)) [rectify 53]
55. ? [X1] : ((happy(X1) | ~patient(X1)) & (~happy(X1) | patient(X1))) => ((happy(sK2) | ~patient(sK2)) & (~happy(sK2) | patient(sK2))) [choice axiom]
56. ((patient(paul) & ~creative(paul)) | ! [X0] : ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (((happy(sK2) | ~patient(sK2)) & (~happy(sK2) | patient(sK2))) | ~patient(paul) | creative(paul)) [skolemisation 54,55]
57. ! [X0] : (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | rich(X0) | ~brave(X0)) [nnf transformation 33]
62. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (kind(X0) | rich(X0))) & ((~kind(X0) & ~rich(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [nnf transformation 9]
63. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | kind(X0) | rich(X0)) & ((~kind(X0) & ~rich(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [flattening 62]
75. ! [X0] : ((~strong(X0) & brave(X0)) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0)))) [nnf transformation 40]
81. (tall(paul) | ~calm(paul)) & (~tall(paul) | calm(paul)) [nnf transformation 19]
92. creative(X0) | calm(X0) | calm(X0) [cnf transformation 44]
99. ~humble(X0) | ~patient(X0) | old(X0) [cnf transformation 31]
107. ~creative(paul) | patient(X0) | happy(X0) [cnf transformation 56]
111. rich(X0) | ~brave(X0) | rich(X0) | ~brave(X0) [cnf transformation 57]
114. ~happy(X0) | ~creative(X0) [cnf transformation 35]
116. ~rich(X0) | ~tall(X0) | creative(X0) [cnf transformation 63]
134. ~calm(X0) | patient(X0) | brave(X0) [cnf transformation 75]
137. quiet(X0) | humble(X0) [cnf transformation 41]
147. tall(paul) | ~calm(paul) [cnf transformation 81]
155. ~old(paul) [cnf transformation 24]
156. ~quiet(paul) [cnf transformation 25]
158. ~brave(X0) | rich(X0) [duplicate literal removal 111]
160. creative(X0) | calm(X0) [duplicate literal removal 92]
196. 9 <=> ! [X0] : (patient(X0) | happy(X0)) [avatar definition]
197. happy(X0) | patient(X0) <- (9) [avatar component clause 196]
199. 10 <=> patient(paul) [avatar definition]
200. ~patient(paul) <- (~10) [avatar component clause 199]
208. 12 <=> creative(paul) [avatar definition]
209. creative(paul) <- (12) [avatar component clause 208]
210. ~creative(paul) <- (~12) [avatar component clause 208]
211. 9 | ~12 [avatar split clause 107,208,196]
305. 34 <=> calm(paul) [avatar definition]
306. calm(paul) <- (34) [avatar component clause 305]
307. ~calm(paul) <- (~34) [avatar component clause 305]
309. 35 <=> tall(paul) [avatar definition]
311. tall(paul) <- (35) [avatar component clause 309]
312. ~34 | 35 [avatar split clause 147,309,305]
335. humble(paul) [resolution 137,156]
337. calm(paul) <- (~12) [resolution 160,210]
339. $false <- (~12, ~34) [subsumption resolution 337,307]
340. 12 | 34 [avatar contradiction clause 339]
342. ~creative(X0) | patient(X0) <- (9) [resolution 197,114]
350. ~patient(paul) | old(paul) [resolution 99,335]
354. ~patient(paul) [subsumption resolution 350,155]
355. ~10 [avatar split clause 354,199]
358. patient(paul) <- (9, 12) [resolution 342,209]
360. $false <- (9, ~10, 12) [subsumption resolution 358,200]
361. ~9 | 10 | ~12 [avatar contradiction clause 360]
399. patient(paul) | brave(paul) <- (34) [resolution 134,306]
403. brave(paul) <- (~10, 34) [subsumption resolution 399,200]
442. rich(paul) <- (~10, 34) [resolution 403,158]
518. ~tall(paul) | creative(paul) <- (~10, 34) [resolution 442,116]
520. creative(paul) <- (~10, 34, 35) [subsumption resolution 518,311]
521. $false <- (~10, ~12, 34, 35) [subsumption resolution 520,210]
522. 10 | 12 | ~34 | ~35 [avatar contradiction clause 521]
523. $false [avatar sat refutation 211,312,340,355,361,522]
% SZS output end Proof for 2364729171373170442868289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not creative and not kind is both not curious and happy and vice versa.
If susan is both generous and not humble then someone is either calm or not rich and vice versa.
Everyone who is kind or not old is either funny or wise and vice versa.
Everyone who is either not patient or happy is both calm and not generous and vice versa.
Everyone who is either strong or funny is either happy or not happy.
If someone is both not calm and wise then someone is either calm or tall and vice versa.
If someone is both tall and not strong then someone is happy or not old and vice versa.
Everyone who is both not old and funny is not rich.
If susan is strong then susan is generous.
If susan is humble then someone is both calm and tall and vice versa.
If fred is quiet or calm then someone is funny or wise and vice versa.
Everyone who is curious or not happy is either humble or happy.
Everyone who is strong is not wise and vice versa.
If paul is brave then someone is rich and vice versa.
Everyone who is both not tall and not humble is not rich.
If someone is not quiet or not curious then someone is both old and curious.
Paul is humble.
Paul is not calm.
Someone is kind or not curious.
Someone is either humble or not calm.
Someone is not quiet or not humble.
Alice is either tall or kind.
Lucy is either rich or not kind. | Fred is not creative. | neutral | (![X]:((~creative(X)&~kind(X))<=>(~curious(X)&happy(X))))&
(((generous(susan)&~humble(susan)))<=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:((kind(X)|~old(X))<=>(funny(X)<~>wise(X))))&
(![X]:((~patient(X)<~>happy(X))<=>(calm(X)&~generous(X))))&
(![X]:((strong(X)<~>funny(X))=>(happy(X)<~>~happy(X))))&
((?[X]:((~calm(X)&wise(X))))<=>(?[X]:((calm(X)<~>tall(X)))))&
((?[X]:((tall(X)&~strong(X))))<=>(?[X]:((happy(X)|~old(X)))))&
(![X]:((~old(X)&funny(X))=>~rich(X)))&
((strong(susan))=>(generous(susan)))&
((humble(susan))<=>(?[X]:((calm(X)&tall(X)))))&
(((quiet(fred)|calm(fred)))<=>(?[X]:((funny(X)|wise(X)))))&
(![X]:((curious(X)|~happy(X))=>(humble(X)<~>happy(X))))&
(![X]:(strong(X)<=>~wise(X)))&
((brave(paul))<=>(?[X]:(rich(X))))&
(![X]:((~tall(X)&~humble(X))=>~rich(X)))&
((?[X]:((~quiet(X)|~curious(X))))=>(?[X]:((old(X)&curious(X)))))&
(humble(paul))&
(~calm(paul))&
(?[X]:((kind(X)|~curious(X))))&
(?[X]:((humble(X)<~>~calm(X))))&
(?[X]:((~quiet(X)|~humble(X))))&
((tall(alice)<~>kind(alice)))&
((rich(lucy)<~>~kind(lucy))) | ~creative(fred) | []
| null | 0 |
If john is not old or brave then susan is both not calm and humble.
Everyone who is old or calm is not wise and vice versa.
Everyone who is not patient is either creative or not calm.
If lucy is not happy then alice is not creative or not generous.
Everyone who is not curious is both not rich and funny and vice versa.
If mary is not happy then someone is not wise or not rich.
If someone is not happy then someone is brave or not quiet.
Everyone who is brave or strong is either not creative or not humble.
Everyone who is strong or not wise is both patient and not brave and vice versa.
If john is both not quiet and humble then mary is either funny or not calm and vice versa.
If someone is both generous and funny then lucy is patient.
Everyone who is not rich or not old is not funny.
Everyone who is either not kind or not generous is not old or not strong and vice versa.
Everyone who is both curious and not calm is rich or curious and vice versa.
Everyone who is brave or rich is both not quiet and quiet.
Fred is both old and not tall.
Susan is happy.
Someone is both wise and tall.
Paul is not generous.
Mary is not old.
Someone is either funny or humble. | Fred is brave. | contradiction | (((~old(john)|brave(john)))=>((~calm(susan)&humble(susan))))&
(![X]:((old(X)|calm(X))<=>~wise(X)))&
(![X]:(~patient(X)=>(creative(X)<~>~calm(X))))&
((~happy(lucy))=>((~creative(alice)|~generous(alice))))&
(![X]:(~curious(X)<=>(~rich(X)&funny(X))))&
((~happy(mary))=>(?[X]:((~wise(X)|~rich(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((brave(X)|strong(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((strong(X)|~wise(X))<=>(patient(X)&~brave(X))))&
(((~quiet(john)&humble(john)))<=>((funny(mary)<~>~calm(mary))))&
((?[X]:((generous(X)&funny(X))))=>(patient(lucy)))&
(![X]:((~rich(X)|~old(X))=>~funny(X)))&
(![X]:((~kind(X)<~>~generous(X))<=>(~old(X)|~strong(X))))&
(![X]:((curious(X)&~calm(X))<=>(rich(X)|curious(X))))&
(![X]:((brave(X)|rich(X))=>(~quiet(X)&quiet(X))))&
((old(fred)&~tall(fred)))&
(happy(susan))&
(?[X]:((wise(X)&tall(X))))&
(~generous(paul))&
(~old(mary))&
(?[X]:((funny(X)<~>humble(X)))) | brave(fred) | [
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2475959230031710274169076
% SZS output start Proof for 2475959230031710274169076
15. ! [X0] : ((rich(X0) | brave(X0)) => (quiet(X0) & ~quiet(X0))) [input p14]
22. brave(fred) [input hypothesis]
33. ! [X0] : ((quiet(X0) & ~quiet(X0)) | (~rich(X0) & ~brave(X0))) [ennf transformation 15]
94. ~quiet(X0) | ~brave(X0) [cnf transformation 33]
96. quiet(X0) | ~brave(X0) [cnf transformation 33]
106. brave(fred) [cnf transformation 22]
158. ~brave(X0) [subsumption resolution 94,96]
169. $false [subsumption resolution 106,158]
% SZS output end Proof for 2475959230031710274169076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not creative is both not patient and wise and vice versa.
If someone is not kind then someone is kind and vice versa.
If fred is both creative and not humble then someone is curious or patient and vice versa.
Everyone who is both not funny and not strong is patient or curious and vice versa.
If someone is both wise and calm then fred is both patient and not brave.
If john is not humble or not quiet then someone is either not kind or old.
Everyone who is both not humble and creative is either not funny or not patient and vice versa.
If someone is both not happy and not calm then mary is quiet or patient and vice versa.
If someone is not humble then fred is not kind or generous and vice versa.
Everyone who is both not creative and not rich is curious or rich.
Everyone who is not calm or not brave is either not rich or rich and vice versa.
Everyone who is not humble is either brave or calm and vice versa.
If fred is both not tall and calm then someone is both patient and not creative.
Everyone who is either funny or not humble is strong or not patient and vice versa.
Everyone who is either humble or not strong is humble and vice versa.
Everyone who is both curious and not generous is either not quiet or rich and vice versa.
Someone is either not happy or not generous.
Someone is both not creative and not calm.
Someone is not quiet.
Someone is rich or not brave. | Mary is brave. | entailment | (![X]:((~generous(X)|~creative(X))<=>(~patient(X)&wise(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(kind(X))))&
(((creative(fred)&~humble(fred)))<=>(?[X]:((curious(X)|patient(X)))))&
(![X]:((~funny(X)&~strong(X))<=>(patient(X)|curious(X))))&
((?[X]:((wise(X)&calm(X))))=>((patient(fred)&~brave(fred))))&
(((~humble(john)|~quiet(john)))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((~humble(X)&creative(X))<=>(~funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>((quiet(mary)|patient(mary))))&
((?[X]:(~humble(X)))<=>((~kind(fred)|generous(fred))))&
(![X]:((~creative(X)&~rich(X))=>(curious(X)|rich(X))))&
(![X]:((~calm(X)|~brave(X))<=>(~rich(X)<~>rich(X))))&
(![X]:(~humble(X)<=>(brave(X)<~>calm(X))))&
(((~tall(fred)&calm(fred)))=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(strong(X)|~patient(X))))&
(![X]:((humble(X)<~>~strong(X))<=>humble(X)))&
(![X]:((curious(X)&~generous(X))<=>(~quiet(X)<~>rich(X))))&
(?[X]:((~happy(X)<~>~generous(X))))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((rich(X)|~brave(X)))) | brave(mary) | [
"p0",
"p3",
"p4",
"p6",
"p11",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 7141022594734590101717701
% SZS output start Proof for 7141022594734590101717701
1. ! [X0] : ((~creative(X0) | ~generous(X0)) <=> (wise(X0) & ~patient(X0))) [input p0]
4. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (curious(X0) | patient(X0))) [input p3]
5. ? [X0] : (calm(X0) & wise(X0)) => (~brave(fred) & patient(fred)) [input p4]
7. ! [X0] : ((creative(X0) & ~humble(X0)) <=> (~funny(X0) <~> ~patient(X0))) [input p6]
12. ! [X0] : (~humble(X0) <=> (brave(X0) <~> calm(X0))) [input p11]
14. ! [X0] : ((funny(X0) <~> ~humble(X0)) <=> (~patient(X0) | strong(X0))) [input p13]
21. ~brave(mary) [input hypothesis]
24. (~brave(fred) & patient(fred)) | ! [X0] : (~calm(X0) | ~wise(X0)) [ennf transformation 5]
28. ! [X0] : (((~creative(X0) | ~generous(X0)) | (~wise(X0) | patient(X0))) & ((wise(X0) & ~patient(X0)) | (creative(X0) & generous(X0)))) [nnf transformation 1]
29. ! [X0] : ((~creative(X0) | ~generous(X0) | ~wise(X0) | patient(X0)) & ((wise(X0) & ~patient(X0)) | (creative(X0) & generous(X0)))) [flattening 28]
40. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | (strong(X0) | funny(X0)))) [nnf transformation 4]
41. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | strong(X0) | funny(X0))) [flattening 40]
45. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | (~creative(X0) | humble(X0)))) [nnf transformation 7]
46. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | ~creative(X0) | humble(X0))) [flattening 45]
59. ! [X0] : ((~humble(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | humble(X0))) [nnf transformation 12]
60. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & ((~patient(X0) | strong(X0)) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [nnf transformation 14]
61. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & (~patient(X0) | strong(X0) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [flattening 60]
77. wise(X0) | creative(X0) [cnf transformation 29]
87. ~funny(X0) | ~patient(X0) [cnf transformation 41]
89. ~strong(X0) | ~patient(X0) [cnf transformation 41]
91. patient(fred) | ~calm(X0) | ~wise(X0) [cnf transformation 24]
98. ~creative(X0) | funny(X0) | patient(X0) | humble(X0) [cnf transformation 46]
99. ~humble(X0) | ~patient(X0) | funny(X0) [cnf transformation 46]
100. ~humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 46]
118. brave(X0) | calm(X0) | humble(X0) [cnf transformation 59]
123. ~patient(X0) | strong(X0) | funny(X0) | humble(X0) [cnf transformation 61]
125. ~humble(X0) | funny(X0) | patient(X0) [cnf transformation 61]
127. humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 61]
144. ~brave(mary) [cnf transformation 21]
167. 5 <=> ! [X0] : ~patient(X0) [avatar definition]
168. ~patient(X0) <- (5) [avatar component clause 167]
194. 11 <=> ! [X0] : (~calm(X0) | ~wise(X0)) [avatar definition]
195. ~calm(X0) | ~wise(X0) <- (11) [avatar component clause 194]
202. 13 <=> patient(fred) [avatar definition]
204. patient(fred) <- (13) [avatar component clause 202]
205. 11 | 13 [avatar split clause 91,202,194]
227. ~funny(X0) | ~humble(X0) [subsumption resolution 100,87]
228. ~humble(X0) | ~patient(X0) [subsumption resolution 99,227]
274. humble(X0) | ~funny(X0) [subsumption resolution 127,87]
275. ~funny(X0) [subsumption resolution 274,227]
276. ~humble(X0) | patient(X0) [subsumption resolution 125,275]
277. ~humble(X0) [subsumption resolution 276,228]
278. ~patient(X0) | strong(X0) | humble(X0) [subsumption resolution 123,275]
279. ~patient(X0) | strong(X0) [subsumption resolution 278,277]
280. ~patient(X0) [subsumption resolution 279,89]
281. 5 [avatar split clause 280,167]
310. calm(mary) | humble(mary) [resolution 118,144]
314. calm(mary) [subsumption resolution 310,277]
317. ~wise(mary) <- (11) [resolution 314,195]
322. creative(mary) <- (11) [resolution 317,77]
345. funny(mary) | patient(mary) | humble(mary) <- (11) [resolution 98,322]
347. patient(mary) | humble(mary) <- (11) [subsumption resolution 345,275]
348. humble(mary) <- (5, 11) [subsumption resolution 347,168]
349. $false <- (5, 11) [subsumption resolution 348,277]
350. ~5 | ~11 [avatar contradiction clause 349]
355. $false <- (5, 13) [subsumption resolution 204,168]
356. ~5 | ~13 [avatar contradiction clause 355]
357. $false [avatar sat refutation 205,281,350,356]
% SZS output end Proof for 7141022594734590101717701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not tall or not kind then paul is creative or brave and vice versa.
Everyone who is not curious or funny is both brave and not strong and vice versa.
Everyone who is humble or not strong is funny and vice versa.
Everyone who is generous is not old or quiet and vice versa.
If someone is not humble then john is either not funny or funny.
Everyone who is wise is not happy.
Everyone who is both wise and funny is both patient and not generous and vice versa.
If someone is curious or not calm then mary is strong.
If susan is both not patient and not quiet then mary is either not strong or not curious and vice versa.
Everyone who is both humble and not strong is rich or not funny and vice versa.
Everyone who is either not generous or not happy is curious and vice versa.
Everyone who is not generous or not kind is not creative and vice versa.
If someone is either not quiet or creative then susan is not happy or not creative.
Everyone who is both calm and not tall is not humble and vice versa.
If someone is either not wise or not rich then fred is humble or funny.
If alice is either not wise or not creative then someone is either quiet or brave and vice versa.
Someone is not strong.
Alice is not kind or quiet.
Someone is not humble or patient.
Mary is creative.
Susan is either rich or not funny.
Mary is either strong or generous. | Fred is not calm. | contradiction | (((~tall(fred)<~>~kind(fred)))<=>((creative(paul)|brave(paul))))&
(![X]:((~curious(X)|funny(X))<=>(brave(X)&~strong(X))))&
(![X]:((humble(X)|~strong(X))<=>funny(X)))&
(![X]:(generous(X)<=>(~old(X)|quiet(X))))&
((?[X]:(~humble(X)))=>((~funny(john)<~>funny(john))))&
(![X]:(wise(X)=>~happy(X)))&
(![X]:((wise(X)&funny(X))<=>(patient(X)&~generous(X))))&
((?[X]:((curious(X)|~calm(X))))=>(strong(mary)))&
(((~patient(susan)&~quiet(susan)))<=>((~strong(mary)<~>~curious(mary))))&
(![X]:((humble(X)&~strong(X))<=>(rich(X)|~funny(X))))&
(![X]:((~generous(X)<~>~happy(X))<=>curious(X)))&
(![X]:((~generous(X)|~kind(X))<=>~creative(X)))&
((?[X]:((~quiet(X)<~>creative(X))))=>((~happy(susan)|~creative(susan))))&
(![X]:((calm(X)&~tall(X))<=>~humble(X)))&
((?[X]:((~wise(X)<~>~rich(X))))=>((humble(fred)|funny(fred))))&
(((~wise(alice)<~>~creative(alice)))<=>(?[X]:((quiet(X)<~>brave(X)))))&
(?[X]:(~strong(X)))&
((~kind(alice)|quiet(alice)))&
(?[X]:((~humble(X)|patient(X))))&
(creative(mary))&
((rich(susan)<~>~funny(susan)))&
((strong(mary)<~>generous(mary))) | ~calm(fred) | [
"p1",
"p2",
"p7",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 8232325878815069377408919
% SZS output start Proof for 8232325878815069377408919
2. ! [X0] : ((funny(X0) | ~curious(X0)) <=> (~strong(X0) & brave(X0))) [input p1]
3. ! [X0] : ((~strong(X0) | humble(X0)) <=> funny(X0)) [input p2]
8. ? [X0] : (~calm(X0) | curious(X0)) => strong(mary) [input p7]
10. ! [X0] : ((~strong(X0) & humble(X0)) <=> (~funny(X0) | rich(X0))) [input p9]
23. ~calm(fred) [input hypothesis]
26. strong(mary) | ! [X0] : (calm(X0) & ~curious(X0)) [ennf transformation 8]
33. ! [X0] : (((funny(X0) | ~curious(X0)) | (strong(X0) | ~brave(X0))) & ((~strong(X0) & brave(X0)) | (~funny(X0) & curious(X0)))) [nnf transformation 2]
34. ! [X0] : ((funny(X0) | ~curious(X0) | strong(X0) | ~brave(X0)) & ((~strong(X0) & brave(X0)) | (~funny(X0) & curious(X0)))) [flattening 33]
35. ! [X0] : (((~strong(X0) | humble(X0)) | ~funny(X0)) & (funny(X0) | (strong(X0) & ~humble(X0)))) [nnf transformation 3]
36. ! [X0] : ((~strong(X0) | humble(X0) | ~funny(X0)) & (funny(X0) | (strong(X0) & ~humble(X0)))) [flattening 35]
44. ! [X0] : (((~strong(X0) & humble(X0)) | (funny(X0) & ~rich(X0))) & ((~funny(X0) | rich(X0)) | (strong(X0) | ~humble(X0)))) [nnf transformation 10]
45. ! [X0] : (((~strong(X0) & humble(X0)) | (funny(X0) & ~rich(X0))) & (~funny(X0) | rich(X0) | strong(X0) | ~humble(X0))) [flattening 44]
72. ~strong(X0) | ~funny(X0) [cnf transformation 34]
75. funny(X0) | strong(X0) [cnf transformation 36]
88. strong(mary) | calm(X0) [cnf transformation 26]
99. ~strong(X0) | funny(X0) [cnf transformation 45]
130. ~calm(fred) [cnf transformation 23]
154. 5 <=> ! [X0] : calm(X0) [avatar definition]
155. calm(X0) <- (5) [avatar component clause 154]
157. 6 <=> strong(mary) [avatar definition]
159. strong(mary) <- (6) [avatar component clause 157]
160. 5 | 6 [avatar split clause 88,157,154]
183. funny(X0) [subsumption resolution 99,75]
259. ~funny(mary) <- (6) [resolution 72,159]
260. $false <- (6) [subsumption resolution 259,183]
261. ~6 [avatar contradiction clause 260]
262. $false <- (5) [resolution 155,130]
263. ~5 [avatar contradiction clause 262]
264. $false [avatar sat refutation 160,261,263]
% SZS output end Proof for 8232325878815069377408919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and not funny then someone is not brave and vice versa. Everyone who is either not wise or not old is generous or not strong. Everyone who is not curious or not rich is either not strong or not patient and vice versa. Everyone who is funny is brave or not generous and vice versa. If someone is not rich then lucy is not curious. If paul is happy then alice is calm or curious and vice versa. If someone is either not curious or kind then someone is either curious or calm. Everyone who is both not quiet and rich is both happy and kind. Everyone who is happy or old is both not quiet and not strong and vice versa. Everyone who is either not happy or not kind is funny and vice versa. If paul is either tall or not curious then paul is both brave and not strong and vice versa. Everyone who is both not happy and curious is generous or curious and vice versa. If paul is either not funny or tall then john is not calm and vice versa. If someone is both curious and not curious then paul is both not humble and tall and vice versa. If paul is not funny or not patient then someone is both quiet and funny and vice versa. If someone is both not creative and happy then mary is either curious or creative. Someone is both not old and not humble. Lucy is both not wise and patient. Someone is either kind or calm. John is both not generous and rich. Lucy is not brave. Someone is either rich or not generous. Someone is both not wise and calm. | John is old. | contradiction | ((?[X]:((tall(X)&~funny(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~wise(X)<~>~old(X))=>(generous(X)|~strong(X))))&
(![X]:((~curious(X)|~rich(X))<=>(~strong(X)<~>~patient(X))))&
(![X]:(funny(X)<=>(brave(X)|~generous(X))))&
((?[X]:(~rich(X)))=>(~curious(lucy)))&
((happy(paul))<=>((calm(alice)|curious(alice))))&
((?[X]:((~curious(X)<~>kind(X))))=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((~quiet(X)&rich(X))=>(happy(X)&kind(X))))&
(![X]:((happy(X)|old(X))<=>(~quiet(X)&~strong(X))))&
(![X]:((~happy(X)<~>~kind(X))<=>funny(X)))&
(((tall(paul)<~>~curious(paul)))<=>((brave(paul)&~strong(paul))))&
(![X]:((~happy(X)&curious(X))<=>(generous(X)|curious(X))))&
(((~funny(paul)<~>tall(paul)))<=>(~calm(john)))&
((?[X]:((curious(X)&~curious(X))))<=>((~humble(paul)&tall(paul))))&
(((~funny(paul)|~patient(paul)))<=>(?[X]:((quiet(X)&funny(X)))))&
((?[X]:((~creative(X)&happy(X))))=>((curious(mary)<~>creative(mary))))&
(?[X]:((~old(X)&~humble(X))))&
((~wise(lucy)&patient(lucy)))&
(?[X]:((kind(X)<~>calm(X))))&
((~generous(john)&rich(john)))&
(~brave(lucy))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:((~wise(X)&calm(X)))) | old(john) | [
"p3",
"p7",
"p8",
"p9",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 7721219424648010191941044
% SZS output start Proof for 7721219424648010191941044
4. ! [X0] : (funny(X0) <=> (~generous(X0) | brave(X0))) [input p3]
8. ! [X0] : ((rich(X0) & ~quiet(X0)) => (kind(X0) & happy(X0))) [input p7]
9. ! [X0] : ((old(X0) | happy(X0)) <=> (~strong(X0) & ~quiet(X0))) [input p8]
10. ! [X0] : ((~happy(X0) <~> ~kind(X0)) <=> funny(X0)) [input p9]
20. rich(john) & ~generous(john) [input p19]
24. old(john) [input hypothesis]
31. ! [X0] : ((kind(X0) & happy(X0)) | (~rich(X0) | quiet(X0))) [ennf transformation 8]
32. ! [X0] : ((kind(X0) & happy(X0)) | ~rich(X0) | quiet(X0)) [flattening 31]
42. ! [X0] : ((funny(X0) | (generous(X0) & ~brave(X0))) & ((~generous(X0) | brave(X0)) | ~funny(X0))) [nnf transformation 4]
43. ! [X0] : ((funny(X0) | (generous(X0) & ~brave(X0))) & (~generous(X0) | brave(X0) | ~funny(X0))) [flattening 42]
50. ! [X0] : (((old(X0) | happy(X0)) | (strong(X0) | quiet(X0))) & ((~strong(X0) & ~quiet(X0)) | (~old(X0) & ~happy(X0)))) [nnf transformation 9]
51. ! [X0] : ((old(X0) | happy(X0) | strong(X0) | quiet(X0)) & ((~strong(X0) & ~quiet(X0)) | (~old(X0) & ~happy(X0)))) [flattening 50]
52. ! [X0] : ((((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | ~funny(X0)) & (funny(X0) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0))))) [nnf transformation 10]
92. generous(X0) | funny(X0) [cnf transformation 43]
101. ~rich(X0) | happy(X0) | quiet(X0) [cnf transformation 32]
102. ~rich(X0) | kind(X0) | quiet(X0) [cnf transformation 32]
104. ~quiet(X0) | ~old(X0) [cnf transformation 51]
110. ~kind(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 52]
144. ~generous(john) [cnf transformation 20]
145. rich(john) [cnf transformation 20]
151. old(john) [cnf transformation 24]
312. funny(john) [resolution 92,144]
330. happy(john) | quiet(john) [resolution 101,145]
332. 34 <=> quiet(john) [avatar definition]
334. quiet(john) <- (34) [avatar component clause 332]
336. 35 <=> happy(john) [avatar definition]
338. happy(john) <- (35) [avatar component clause 336]
339. 34 | 35 [avatar split clause 330,336,332]
340. kind(john) | quiet(john) [resolution 102,145]
342. ~old(john) <- (34) [resolution 334,104]
346. $false <- (34) [subsumption resolution 342,151]
347. ~34 [avatar contradiction clause 346]
350. 36 <=> kind(john) [avatar definition]
352. kind(john) <- (36) [avatar component clause 350]
353. 34 | 36 [avatar split clause 340,350,332]
369. ~happy(john) | ~funny(john) <- (36) [resolution 352,110]
371. ~funny(john) <- (35, 36) [subsumption resolution 369,338]
372. $false <- (35, 36) [subsumption resolution 371,312]
373. ~35 | ~36 [avatar contradiction clause 372]
374. $false [avatar sat refutation 339,347,353,373]
% SZS output end Proof for 7721219424648010191941044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or humble then someone is kind.
Everyone who is either calm or not curious is not tall.
Everyone who is either humble or not happy is either quiet or not tall and vice versa.
If fred is not humble or humble then lucy is not curious or curious and vice versa.
If susan is tall or not creative then mary is either not wise or rich.
Everyone who is not creative or quiet is either not happy or not brave.
Everyone who is either not tall or not humble is creative or not humble and vice versa.
If someone is creative or not creative then alice is both not creative and not wise and vice versa.
If susan is curious then paul is strong or not creative and vice versa.
Everyone who is strong or not quiet is funny or wise.
Everyone who is both curious and not kind is patient and vice versa.
Everyone who is both not generous and not brave is not kind.
Everyone who is both rich and not patient is both brave and happy and vice versa.
Everyone who is either not strong or not patient is not quiet and vice versa.
Everyone who is not brave is funny or not funny and vice versa.
If fred is either not curious or quiet then someone is either not old or humble and vice versa.
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.
Someone is old or not generous.
Someone is curious or not happy.
Paul is either rich or not humble. | Alice is not happy. | contradiction | ((?[X]:((wise(X)|humble(X))))=>(?[X]:(kind(X))))&
(![X]:((calm(X)<~>~curious(X))=>~tall(X)))&
(![X]:((humble(X)<~>~happy(X))<=>(quiet(X)<~>~tall(X))))&
(((~humble(fred)|humble(fred)))<=>((~curious(lucy)|curious(lucy))))&
(((tall(susan)|~creative(susan)))=>((~wise(mary)<~>rich(mary))))&
(![X]:((~creative(X)|quiet(X))=>(~happy(X)<~>~brave(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(creative(X)|~humble(X))))&
((?[X]:((creative(X)|~creative(X))))<=>((~creative(alice)&~wise(alice))))&
((curious(susan))<=>((strong(paul)|~creative(paul))))&
(![X]:((strong(X)|~quiet(X))=>(funny(X)|wise(X))))&
(![X]:((curious(X)&~kind(X))<=>patient(X)))&
(![X]:((~generous(X)&~brave(X))=>~kind(X)))&
(![X]:((rich(X)&~patient(X))<=>(brave(X)&happy(X))))&
(![X]:((~strong(X)<~>~patient(X))<=>~quiet(X)))&
(![X]:(~brave(X)<=>(funny(X)|~funny(X))))&
(((~curious(fred)<~>quiet(fred)))<=>(?[X]:((~old(X)<~>humble(X)))))&
((rich(susan)&~old(susan)))&
((~kind(paul)&~creative(paul)))&
(?[X]:((~calm(X)<~>wise(X))))&
((~rich(john)|~curious(john)))&
(~patient(john))&
(?[X]:((old(X)|~generous(X))))&
(?[X]:((curious(X)|~happy(X))))&
((rich(paul)<~>~humble(paul))) | ~happy(alice) | [
"p5",
"p7",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 282855417610409668193319
% SZS output start Proof for 282855417610409668193319
6. ! [X0] : ((quiet(X0) | ~creative(X0)) => (~happy(X0) <~> ~brave(X0))) [input p5]
8. ? [X0] : (~creative(X0) | creative(X0)) <=> (~wise(alice) & ~creative(alice)) [input p7]
15. ! [X0] : (~brave(X0) <=> (~funny(X0) | funny(X0))) [input p14]
25. ~happy(alice) [input hypothesis]
30. ! [X0] : ((~happy(X0) <~> ~brave(X0)) | (~quiet(X0) & creative(X0))) [ennf transformation 6]
43. ! [X0] : (((brave(X0) | happy(X0)) & (~brave(X0) | ~happy(X0))) | (~quiet(X0) & creative(X0))) [nnf transformation 30]
46. (? [X0] : (~creative(X0) | creative(X0)) | (wise(alice) | creative(alice))) & ((~wise(alice) & ~creative(alice)) | ! [X0] : (creative(X0) & ~creative(X0))) [nnf transformation 8]
47. (? [X0] : (~creative(X0) | creative(X0)) | wise(alice) | creative(alice)) & ((~wise(alice) & ~creative(alice)) | ! [X0] : (creative(X0) & ~creative(X0))) [flattening 46]
48. (? [X0] : (~creative(X0) | creative(X0)) | wise(alice) | creative(alice)) & ((~wise(alice) & ~creative(alice)) | ! [X1] : (creative(X1) & ~creative(X1))) [rectify 47]
49. ? [X0] : (~creative(X0) | creative(X0)) => (~creative(sK1) | creative(sK1)) [choice axiom]
50. ((~creative(sK1) | creative(sK1)) | wise(alice) | creative(alice)) & ((~wise(alice) & ~creative(alice)) | ! [X1] : (creative(X1) & ~creative(X1))) [skolemisation 48,49]
58. ! [X0] : ((~brave(X0) | (funny(X0) & ~funny(X0))) & ((~funny(X0) | funny(X0)) | brave(X0))) [nnf transformation 15]
59. ! [X0] : ((~brave(X0) | (funny(X0) & ~funny(X0))) & (~funny(X0) | funny(X0) | brave(X0))) [flattening 58]
94. brave(X0) | happy(X0) | creative(X0) [cnf transformation 43]
102. ~creative(alice) | ~creative(X1) [cnf transformation 50]
103. ~creative(alice) | creative(X1) [cnf transformation 50]
125. ~brave(X0) | ~funny(X0) [cnf transformation 59]
126. ~brave(X0) | funny(X0) [cnf transformation 59]
147. ~happy(alice) [cnf transformation 25]
184. 8 <=> ! [X1] : creative(X1) [avatar definition]
185. creative(X1) <- (8) [avatar component clause 184]
192. 10 <=> ! [X1] : ~creative(X1) [avatar definition]
193. ~creative(X1) <- (10) [avatar component clause 192]
196. 11 <=> creative(alice) [avatar definition]
198. ~creative(alice) <- (~11) [avatar component clause 196]
199. 8 | ~11 [avatar split clause 103,196,184]
200. 10 | ~11 [avatar split clause 102,196,192]
216. ~brave(X0) [subsumption resolution 125,126]
312. $false <- (8, 10) [subsumption resolution 185,193]
313. ~8 | ~10 [avatar contradiction clause 312]
334. creative(X3) | happy(X3) [resolution 94,216]
338. happy(alice) <- (~11) [resolution 334,198]
340. $false <- (~11) [subsumption resolution 338,147]
341. 11 [avatar contradiction clause 340]
342. $false [avatar sat refutation 199,200,313,341]
% SZS output end Proof for 282855417610409668193319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or humble then alice is both calm and happy and vice versa.
If fred is either not calm or not brave then someone is not funny or not generous.
If someone is both not quiet and not tall then someone is creative or not calm and vice versa.
Everyone who is curious or not happy is either curious or humble.
If paul is not old then paul is both brave and not strong.
If someone is either tall or curious then john is not rich or creative and vice versa.
Everyone who is generous is both not calm and not brave and vice versa.
If someone is both creative and not creative then paul is not creative or calm.
Everyone who is both calm and not calm is not funny or quiet and vice versa.
Everyone who is both calm and tall is either curious or not wise and vice versa.
If john is not kind then mary is either funny or strong.
If someone is either not funny or old then someone is rich or not creative.
If someone is either generous or old then fred is not brave and vice versa.
If someone is either calm or not funny then someone is both generous and patient and vice versa.
Everyone who is both funny and happy is curious.
If someone is both strong and calm then mary is not patient or brave.
Paul is either not happy or not calm.
Someone is either not humble or not generous.
Fred is not creative.
Lucy is both kind and happy.
John is curious or patient.
Someone is both happy and brave.
Someone is both strong and happy. | Lucy is happy. | entailment | ((?[X]:((patient(X)<~>humble(X))))<=>((calm(alice)&happy(alice))))&
(((~calm(fred)<~>~brave(fred)))=>(?[X]:((~funny(X)|~generous(X)))))&
((?[X]:((~quiet(X)&~tall(X))))<=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((curious(X)|~happy(X))=>(curious(X)<~>humble(X))))&
((~old(paul))=>((brave(paul)&~strong(paul))))&
((?[X]:((tall(X)<~>curious(X))))<=>((~rich(john)|creative(john))))&
(![X]:(generous(X)<=>(~calm(X)&~brave(X))))&
((?[X]:((creative(X)&~creative(X))))=>((~creative(paul)|calm(paul))))&
(![X]:((calm(X)&~calm(X))<=>(~funny(X)|quiet(X))))&
(![X]:((calm(X)&tall(X))<=>(curious(X)<~>~wise(X))))&
((~kind(john))=>((funny(mary)<~>strong(mary))))&
((?[X]:((~funny(X)<~>old(X))))=>(?[X]:((rich(X)|~creative(X)))))&
((?[X]:((generous(X)<~>old(X))))<=>(~brave(fred)))&
((?[X]:((calm(X)<~>~funny(X))))<=>(?[X]:((generous(X)&patient(X)))))&
(![X]:((funny(X)&happy(X))=>curious(X)))&
((?[X]:((strong(X)&calm(X))))=>((~patient(mary)|brave(mary))))&
((~happy(paul)<~>~calm(paul)))&
(?[X]:((~humble(X)<~>~generous(X))))&
(~creative(fred))&
((kind(lucy)&happy(lucy)))&
((curious(john)|patient(john)))&
(?[X]:((happy(X)&brave(X))))&
(?[X]:((strong(X)&happy(X)))) | happy(lucy) | [
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 440983747080059052443654
% SZS output start Proof for 440983747080059052443654
20. happy(lucy) & kind(lucy) [input p19]
24. ~happy(lucy) [input hypothesis]
29. happy(lucy) [pure predicate removal 20]
145. happy(lucy) [cnf transformation 29]
151. ~happy(lucy) [cnf transformation 24]
370. $false [subsumption resolution 151,145]
% SZS output end Proof for 440983747080059052443654
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong then someone is not tall or not calm. If fred is both not happy and old then someone is either not creative or funny. Everyone who is not funny is not calm and vice versa. Everyone who is either curious or patient is not calm. Everyone who is not rich is either creative or not calm. Everyone who is either funny or brave is either not generous or not tall. If someone is either not tall or patient then someone is not curious. Everyone who is happy or generous is not brave or generous. If paul is wise or not calm then alice is creative or humble and vice versa. Everyone who is both happy and not patient is curious or not strong. Everyone who is not wise is curious or not brave. Everyone who is not generous or curious is both funny and not humble and vice versa. Everyone who is either patient or not curious is both not generous and not rich. If fred is not kind then someone is not rich or not generous. If someone is both creative and not creative then paul is either not funny or creative and vice versa. If someone is both not strong and not happy then mary is not calm or not tall. Alice is either calm or tall. Someone is not happy. Paul is both not curious and generous. Someone is both not calm and generous. John is not patient. Paul is not tall. Someone is patient. Someone is either rich or not curious. | John is not generous. | entailment | ((~strong(mary))=>(?[X]:((~tall(X)|~calm(X)))))&
(((~happy(fred)&old(fred)))=>(?[X]:((~creative(X)<~>funny(X)))))&
(![X]:(~funny(X)<=>~calm(X)))&
(![X]:((curious(X)<~>patient(X))=>~calm(X)))&
(![X]:(~rich(X)=>(creative(X)<~>~calm(X))))&
(![X]:((funny(X)<~>brave(X))=>(~generous(X)<~>~tall(X))))&
((?[X]:((~tall(X)<~>patient(X))))=>(?[X]:(~curious(X))))&
(![X]:((happy(X)|generous(X))=>(~brave(X)|generous(X))))&
(((wise(paul)|~calm(paul)))<=>((creative(alice)|humble(alice))))&
(![X]:((happy(X)&~patient(X))=>(curious(X)|~strong(X))))&
(![X]:(~wise(X)=>(curious(X)|~brave(X))))&
(![X]:((~generous(X)|curious(X))<=>(funny(X)&~humble(X))))&
(![X]:((patient(X)<~>~curious(X))=>(~generous(X)&~rich(X))))&
((~kind(fred))=>(?[X]:((~rich(X)|~generous(X)))))&
((?[X]:((creative(X)&~creative(X))))<=>((~funny(paul)<~>creative(paul))))&
((?[X]:((~strong(X)&~happy(X))))=>((~calm(mary)|~tall(mary))))&
((calm(alice)<~>tall(alice)))&
(?[X]:(~happy(X)))&
((~curious(paul)&generous(paul)))&
(?[X]:((~calm(X)&generous(X))))&
(~patient(john))&
(~tall(paul))&
(?[X]:(patient(X)))&
(?[X]:((rich(X)<~>~curious(X)))) | ~generous(john) | [
"p2",
"p3",
"p11",
"p12",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 2424197882442007733278313
% SZS output start Proof for 2424197882442007733278313
3. ! [X0] : (~funny(X0) <=> ~calm(X0)) [input p2]
4. ! [X0] : ((curious(X0) <~> patient(X0)) => ~calm(X0)) [input p3]
12. ! [X0] : ((curious(X0) | ~generous(X0)) <=> (~humble(X0) & funny(X0))) [input p11]
13. ! [X0] : ((patient(X0) <~> ~curious(X0)) => (~rich(X0) & ~generous(X0))) [input p12]
21. ~patient(john) [input p20]
25. generous(john) [input hypothesis]
30. ! [X0] : (~calm(X0) | (curious(X0) <=> patient(X0))) [ennf transformation 4]
40. ! [X0] : ((~rich(X0) & ~generous(X0)) | (patient(X0) <=> ~curious(X0))) [ennf transformation 13]
45. ! [X0] : ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0))) [nnf transformation 3]
46. ! [X0] : (~calm(X0) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0)))) [nnf transformation 30]
55. ! [X0] : (((curious(X0) | ~generous(X0)) | (humble(X0) | ~funny(X0))) & ((~humble(X0) & funny(X0)) | (~curious(X0) & generous(X0)))) [nnf transformation 12]
56. ! [X0] : ((curious(X0) | ~generous(X0) | humble(X0) | ~funny(X0)) & ((~humble(X0) & funny(X0)) | (~curious(X0) & generous(X0)))) [flattening 55]
57. ! [X0] : ((~rich(X0) & ~generous(X0)) | ((patient(X0) | curious(X0)) & (~curious(X0) | ~patient(X0)))) [nnf transformation 40]
74. ~funny(X0) | calm(X0) [cnf transformation 45]
75. ~curious(X0) | patient(X0) | ~calm(X0) [cnf transformation 46]
94. ~curious(X0) | funny(X0) [cnf transformation 56]
99. ~generous(X0) | patient(X0) | curious(X0) [cnf transformation 57]
116. ~patient(john) [cnf transformation 21]
121. generous(john) [cnf transformation 25]
255. patient(john) | curious(john) [resolution 99,121]
260. curious(john) [subsumption resolution 255,116]
274. 26 <=> funny(john) [avatar definition]
275. funny(john) <- (26) [avatar component clause 274]
299. patient(john) | ~calm(john) [resolution 260,75]
300. funny(john) [resolution 260,94]
301. ~calm(john) [subsumption resolution 299,116]
304. 26 [avatar split clause 300,274]
311. calm(john) <- (26) [resolution 275,74]
312. $false <- (26) [subsumption resolution 311,301]
313. ~26 [avatar contradiction clause 312]
314. $false [avatar sat refutation 304,313]
% SZS output end Proof for 2424197882442007733278313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is either quiet or funny and vice versa.
Everyone who is both not happy and old is tall.
Everyone who is both quiet and happy is rich or not rich and vice versa.
If someone is patient or not calm then someone is both quiet and not happy.
Everyone who is both not funny and wise is both strong and brave and vice versa.
If someone is tall or not wise then lucy is both not kind and quiet and vice versa.
If someone is both patient and kind then paul is either not old or calm and vice versa.
If fred is not wise then someone is either brave or creative.
If someone is not happy or old then alice is not rich or not curious and vice versa.
If fred is not rich then paul is not humble.
Everyone who is not quiet is not creative and vice versa.
Everyone who is either curious or rich is either not curious or not creative and vice versa.
Everyone who is not wise or creative is not tall.
Everyone who is calm is either not curious or tall and vice versa.
If lucy is kind then susan is not quiet and vice versa.
Someone is not calm or strong.
Paul is both brave and calm.
Someone is old.
Someone is either curious or not brave.
Someone is not strong.
John is quiet.
John is both creative and humble. | Alice is not tall. | entailment | (![X]:(kind(X)<=>(quiet(X)<~>funny(X))))&
(![X]:((~happy(X)&old(X))=>tall(X)))&
(![X]:((quiet(X)&happy(X))<=>(rich(X)|~rich(X))))&
((?[X]:((patient(X)|~calm(X))))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:((~funny(X)&wise(X))<=>(strong(X)&brave(X))))&
((?[X]:((tall(X)|~wise(X))))<=>((~kind(lucy)&quiet(lucy))))&
((?[X]:((patient(X)&kind(X))))<=>((~old(paul)<~>calm(paul))))&
((~wise(fred))=>(?[X]:((brave(X)<~>creative(X)))))&
((?[X]:((~happy(X)|old(X))))<=>((~rich(alice)|~curious(alice))))&
((~rich(fred))=>(~humble(paul)))&
(![X]:(~quiet(X)<=>~creative(X)))&
(![X]:((curious(X)<~>rich(X))<=>(~curious(X)<~>~creative(X))))&
(![X]:((~wise(X)|creative(X))=>~tall(X)))&
(![X]:(calm(X)<=>(~curious(X)<~>tall(X))))&
((kind(lucy))<=>(~quiet(susan)))&
(?[X]:((~calm(X)|strong(X))))&
((brave(paul)&calm(paul)))&
(?[X]:(old(X)))&
(?[X]:((curious(X)<~>~brave(X))))&
(?[X]:(~strong(X)))&
(quiet(john))&
((creative(john)&humble(john))) | ~tall(alice) | [
"p2",
"p10",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 378424492289205079386504
% SZS output start Proof for 378424492289205079386504
3. ! [X0] : ((happy(X0) & quiet(X0)) <=> (~rich(X0) | rich(X0))) [input p2]
11. ! [X0] : (~quiet(X0) <=> ~creative(X0)) [input p10]
13. ! [X0] : ((creative(X0) | ~wise(X0)) => ~tall(X0)) [input p12]
23. tall(alice) [input hypothesis]
30. ! [X0] : (~tall(X0) | (~creative(X0) & wise(X0))) [ennf transformation 13]
32. ! [X0] : (((happy(X0) & quiet(X0)) | (rich(X0) & ~rich(X0))) & ((~rich(X0) | rich(X0)) | (~happy(X0) | ~quiet(X0)))) [nnf transformation 3]
33. ! [X0] : (((happy(X0) & quiet(X0)) | (rich(X0) & ~rich(X0))) & (~rich(X0) | rich(X0) | ~happy(X0) | ~quiet(X0))) [flattening 32]
56. ! [X0] : ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0))) [nnf transformation 11]
75. quiet(X0) | ~rich(X0) [cnf transformation 33]
76. quiet(X0) | rich(X0) [cnf transformation 33]
106. ~quiet(X0) | creative(X0) [cnf transformation 56]
116. ~tall(X0) | ~creative(X0) [cnf transformation 30]
133. tall(alice) [cnf transformation 23]
139. quiet(X0) [subsumption resolution 75,76]
161. 5 <=> ! [X1] : ~tall(X1) [avatar definition]
162. ~tall(X1) <- (5) [avatar component clause 161]
220. creative(X0) [subsumption resolution 106,139]
224. ~tall(X0) [subsumption resolution 116,220]
225. 5 [avatar split clause 224,161]
243. $false <- (5) [resolution 162,133]
244. ~5 [avatar contradiction clause 243]
245. $false [avatar sat refutation 225,244]
% SZS output end Proof for 378424492289205079386504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not calm and curious then someone is either rich or not kind. If john is strong then someone is strong or not tall. Everyone who is either not creative or not quiet is generous and vice versa. Everyone who is both not tall and funny is both not brave and not tall and vice versa. Everyone who is not generous or old is both not tall and kind. Everyone who is quiet is not funny or wise. If someone is both wise and quiet then someone is both not quiet and generous. If someone is either not quiet or strong then someone is not wise. If someone is both strong and not tall then john is not funny and vice versa. If lucy is both strong and quiet then fred is not wise or curious and vice versa. If someone is quiet or rich then alice is kind and vice versa. Everyone who is not humble or quiet is either generous or old and vice versa. Everyone who is either curious or not tall is either not patient or generous. Everyone who is both happy and curious is rich or humble. Everyone who is either not old or not wise is not generous and vice versa. If alice is both brave and not generous then someone is tall or strong and vice versa. Someone is not patient. John is brave. Paul is both not quiet and wise. Someone is either quiet or not happy. Fred is not generous or strong. Someone is funny or old. Someone is old or not happy. | Alice is funny. | contradiction | (((~calm(lucy)&curious(lucy)))=>(?[X]:((rich(X)<~>~kind(X)))))&
((strong(john))=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((~creative(X)<~>~quiet(X))<=>generous(X)))&
(![X]:((~tall(X)&funny(X))<=>(~brave(X)&~tall(X))))&
(![X]:((~generous(X)|old(X))=>(~tall(X)&kind(X))))&
(![X]:(quiet(X)=>(~funny(X)|wise(X))))&
((?[X]:((wise(X)&quiet(X))))=>(?[X]:((~quiet(X)&generous(X)))))&
((?[X]:((~quiet(X)<~>strong(X))))=>(?[X]:(~wise(X))))&
((?[X]:((strong(X)&~tall(X))))<=>(~funny(john)))&
(((strong(lucy)&quiet(lucy)))<=>((~wise(fred)|curious(fred))))&
((?[X]:((quiet(X)|rich(X))))<=>(kind(alice)))&
(![X]:((~humble(X)|quiet(X))<=>(generous(X)<~>old(X))))&
(![X]:((curious(X)<~>~tall(X))=>(~patient(X)<~>generous(X))))&
(![X]:((happy(X)&curious(X))=>(rich(X)|humble(X))))&
(![X]:((~old(X)<~>~wise(X))<=>~generous(X)))&
(((brave(alice)&~generous(alice)))<=>(?[X]:((tall(X)|strong(X)))))&
(?[X]:(~patient(X)))&
(brave(john))&
((~quiet(paul)&wise(paul)))&
(?[X]:((quiet(X)<~>~happy(X))))&
((~generous(fred)|strong(fred)))&
(?[X]:((funny(X)|old(X))))&
(?[X]:((old(X)|~happy(X)))) | funny(alice) | [
"p3",
"p4",
"p8",
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 7670814635158253950314599
% SZS output start Proof for 7670814635158253950314599
4. ! [X0] : ((funny(X0) & ~tall(X0)) <=> (~tall(X0) & ~brave(X0))) [input p3]
5. ! [X0] : ((old(X0) | ~generous(X0)) => (kind(X0) & ~tall(X0))) [input p4]
9. ? [X0] : (~tall(X0) & strong(X0)) <=> ~funny(john) [input p8]
16. (~generous(alice) & brave(alice)) <=> ? [X0] : (strong(X0) | tall(X0)) [input p15]
18. brave(john) [input p17]
24. funny(alice) [input hypothesis]
29. ! [X0] : ((kind(X0) & ~tall(X0)) | (~old(X0) & generous(X0))) [ennf transformation 5]
40. ! [X0] : (((funny(X0) & ~tall(X0)) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | (~funny(X0) | tall(X0)))) [nnf transformation 4]
41. ! [X0] : (((funny(X0) & ~tall(X0)) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | ~funny(X0) | tall(X0))) [flattening 40]
49. (? [X0] : (~tall(X0) & strong(X0)) | funny(john)) & (~funny(john) | ! [X0] : (tall(X0) | ~strong(X0))) [nnf transformation 9]
50. (? [X0] : (~tall(X0) & strong(X0)) | funny(john)) & (~funny(john) | ! [X1] : (tall(X1) | ~strong(X1))) [rectify 49]
51. ? [X0] : (~tall(X0) & strong(X0)) => (~tall(sK3) & strong(sK3)) [choice axiom]
52. ((~tall(sK3) & strong(sK3)) | funny(john)) & (~funny(john) | ! [X1] : (tall(X1) | ~strong(X1))) [skolemisation 50,51]
63. ((~generous(alice) & brave(alice)) | ! [X0] : (~strong(X0) & ~tall(X0))) & (? [X0] : (strong(X0) | tall(X0)) | (generous(alice) | ~brave(alice))) [nnf transformation 16]
64. ((~generous(alice) & brave(alice)) | ! [X0] : (~strong(X0) & ~tall(X0))) & (? [X0] : (strong(X0) | tall(X0)) | generous(alice) | ~brave(alice)) [flattening 63]
65. ((~generous(alice) & brave(alice)) | ! [X0] : (~strong(X0) & ~tall(X0))) & (? [X1] : (strong(X1) | tall(X1)) | generous(alice) | ~brave(alice)) [rectify 64]
66. ? [X1] : (strong(X1) | tall(X1)) => (strong(sK5) | tall(sK5)) [choice axiom]
67. ((~generous(alice) & brave(alice)) | ! [X0] : (~strong(X0) & ~tall(X0))) & ((strong(sK5) | tall(sK5)) | generous(alice) | ~brave(alice)) [skolemisation 65,66]
82. ~brave(X0) | ~funny(X0) | tall(X0) [cnf transformation 41]
86. ~tall(X0) | generous(X0) [cnf transformation 29]
96. strong(sK3) | funny(john) [cnf transformation 52]
122. brave(alice) | ~tall(X0) [cnf transformation 67]
123. brave(alice) | ~strong(X0) [cnf transformation 67]
124. ~generous(alice) | ~tall(X0) [cnf transformation 67]
127. brave(john) [cnf transformation 18]
135. funny(alice) [cnf transformation 24]
175. 10 <=> funny(john) [avatar definition]
184. 12 <=> strong(sK3) [avatar definition]
186. strong(sK3) <- (12) [avatar component clause 184]
187. 10 | 12 [avatar split clause 96,184,175]
237. 23 <=> ! [X0] : ~strong(X0) [avatar definition]
238. ~strong(X0) <- (23) [avatar component clause 237]
240. 24 <=> generous(alice) [avatar definition]
242. ~generous(alice) <- (~24) [avatar component clause 240]
245. 25 <=> ! [X0] : ~tall(X0) [avatar definition]
246. ~tall(X0) <- (25) [avatar component clause 245]
247. 25 | ~24 [avatar split clause 124,240,245]
249. 26 <=> brave(alice) [avatar definition]
251. brave(alice) <- (26) [avatar component clause 249]
252. 23 | 26 [avatar split clause 123,249,237]
253. 25 | 26 [avatar split clause 122,249,245]
300. $false <- (12, 23) [subsumption resolution 186,238]
301. ~12 | ~23 [avatar contradiction clause 300]
318. ~funny(john) | tall(john) [resolution 82,127]
322. ~funny(john) <- (25) [subsumption resolution 318,246]
323. ~10 | ~25 [avatar split clause 322,245,175]
328. ~funny(alice) | tall(alice) <- (26) [resolution 251,82]
329. tall(alice) <- (26) [subsumption resolution 328,135]
330. $false <- (25, 26) [subsumption resolution 329,246]
331. ~25 | ~26 [avatar contradiction clause 330]
332. generous(alice) <- (26) [resolution 329,86]
333. $false <- (~24, 26) [subsumption resolution 332,242]
334. 24 | ~26 [avatar contradiction clause 333]
335. $false [avatar sat refutation 187,247,252,253,301,323,331,334]
% SZS output end Proof for 7670814635158253950314599
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or humble then someone is not creative or not quiet.
Everyone who is curious is both not rich and not brave and vice versa.
If someone is strong or not rich then susan is both not generous and patient.
Everyone who is both not brave and kind is not curious and vice versa.
If someone is not generous then alice is not happy and vice versa.
If someone is calm or not curious then someone is either kind or rich and vice versa.
Everyone who is both old and not calm is either old or wise.
If someone is either wise or tall then lucy is either quiet or old and vice versa.
Everyone who is either not funny or happy is not quiet or quiet.
If mary is either not wise or tall then someone is not humble and vice versa.
If someone is both creative and not funny then susan is both not wise and not happy and vice versa.
Everyone who is kind or curious is either not humble or not quiet.
Everyone who is not patient is either tall or not humble.
If susan is both not creative and humble then alice is humble and vice versa.
Alice is either rich or not old.
Lucy is both not quiet and generous.
Susan is not tall.
Someone is patient.
Someone is both not quiet and not funny.
Susan is not creative. | Susan is not quiet. | neutral | ((?[X]:((brave(X)|humble(X))))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:(curious(X)<=>(~rich(X)&~brave(X))))&
((?[X]:((strong(X)|~rich(X))))=>((~generous(susan)&patient(susan))))&
(![X]:((~brave(X)&kind(X))<=>~curious(X)))&
((?[X]:(~generous(X)))<=>(~happy(alice)))&
((?[X]:((calm(X)|~curious(X))))<=>(?[X]:((kind(X)<~>rich(X)))))&
(![X]:((old(X)&~calm(X))=>(old(X)<~>wise(X))))&
((?[X]:((wise(X)<~>tall(X))))<=>((quiet(lucy)<~>old(lucy))))&
(![X]:((~funny(X)<~>happy(X))=>(~quiet(X)|quiet(X))))&
(((~wise(mary)<~>tall(mary)))<=>(?[X]:(~humble(X))))&
((?[X]:((creative(X)&~funny(X))))<=>((~wise(susan)&~happy(susan))))&
(![X]:((kind(X)|curious(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:(~patient(X)=>(tall(X)<~>~humble(X))))&
(((~creative(susan)&humble(susan)))<=>(humble(alice)))&
((rich(alice)<~>~old(alice)))&
((~quiet(lucy)&generous(lucy)))&
(~tall(susan))&
(?[X]:(patient(X)))&
(?[X]:((~quiet(X)&~funny(X))))&
(~creative(susan)) | ~quiet(susan) | []
| null | 0 |
Everyone who is funny or humble is humble and vice versa.
Everyone who is not creative or humble is both not rich and tall.
If someone is both not kind and funny then someone is not wise and vice versa.
Everyone who is tall is either funny or quiet.
Everyone who is either old or not tall is funny or old and vice versa.
If lucy is both not humble and not creative then mary is not rich or patient.
If paul is both not creative and funny then someone is humble or calm.
Everyone who is not calm is rich and vice versa.
Everyone who is either quiet or not generous is both not curious and not wise.
If fred is both quiet and happy then john is either generous or not wise.
Everyone who is tall is not kind or patient.
Everyone who is not tall or calm is calm.
Everyone who is not kind is both not calm and calm and vice versa.
If paul is not calm then someone is either creative or not calm.
Everyone who is either quiet or not rich is both rich and generous and vice versa.
Everyone who is generous or not rich is either tall or not patient and vice versa.
Paul is either not kind or patient.
John is both not rich and not funny.
Someone is both tall and not strong. | John is humble. | neutral | (![X]:((funny(X)|humble(X))<=>humble(X)))&
(![X]:((~creative(X)|humble(X))=>(~rich(X)&tall(X))))&
((?[X]:((~kind(X)&funny(X))))<=>(?[X]:(~wise(X))))&
(![X]:(tall(X)=>(funny(X)<~>quiet(X))))&
(![X]:((old(X)<~>~tall(X))<=>(funny(X)|old(X))))&
(((~humble(lucy)&~creative(lucy)))=>((~rich(mary)|patient(mary))))&
(((~creative(paul)&funny(paul)))=>(?[X]:((humble(X)|calm(X)))))&
(![X]:(~calm(X)<=>rich(X)))&
(![X]:((quiet(X)<~>~generous(X))=>(~curious(X)&~wise(X))))&
(((quiet(fred)&happy(fred)))=>((generous(john)<~>~wise(john))))&
(![X]:(tall(X)=>(~kind(X)|patient(X))))&
(![X]:((~tall(X)|calm(X))=>calm(X)))&
(![X]:(~kind(X)<=>(~calm(X)&calm(X))))&
((~calm(paul))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>(rich(X)&generous(X))))&
(![X]:((generous(X)|~rich(X))<=>(tall(X)<~>~patient(X))))&
((~kind(paul)<~>patient(paul)))&
((~rich(john)&~funny(john)))&
(?[X]:((tall(X)&~strong(X)))) | humble(john) | []
| null | 0 |
If mary is not quiet or quiet then mary is either not tall or strong.
Everyone who is either funny or humble is not creative.
Everyone who is curious is humble or not old.
If paul is both generous and not generous then alice is not humble.
Everyone who is both old and curious is old or not old and vice versa.
If someone is curious or not humble then someone is humble and vice versa.
Everyone who is not funny or kind is generous or strong.
If susan is either old or quiet then someone is rich.
Everyone who is both not old and humble is calm and vice versa.
Everyone who is either wise or not curious is both tall and not curious and vice versa.
If susan is either not rich or strong then someone is both calm and not humble and vice versa.
If someone is curious then mary is kind.
Everyone who is either tall or not patient is either patient or creative.
Everyone who is not humble is both happy and not strong.
If someone is not curious then susan is not creative.
Everyone who is both not calm and not funny is tall.
Someone is not creative.
Someone is humble or not rich.
Someone is happy or not wise.
Someone is not brave or not generous.
Mary is not creative or strong.
Someone is either rich or not tall. | Paul is old. | entailment | (((~quiet(mary)|quiet(mary)))=>((~tall(mary)<~>strong(mary))))&
(![X]:((funny(X)<~>humble(X))=>~creative(X)))&
(![X]:(curious(X)=>(humble(X)|~old(X))))&
(((generous(paul)&~generous(paul)))=>(~humble(alice)))&
(![X]:((old(X)&curious(X))<=>(old(X)|~old(X))))&
((?[X]:((curious(X)|~humble(X))))<=>(?[X]:(humble(X))))&
(![X]:((~funny(X)|kind(X))=>(generous(X)|strong(X))))&
(((old(susan)<~>quiet(susan)))=>(?[X]:(rich(X))))&
(![X]:((~old(X)&humble(X))<=>calm(X)))&
(![X]:((wise(X)<~>~curious(X))<=>(tall(X)&~curious(X))))&
(((~rich(susan)<~>strong(susan)))<=>(?[X]:((calm(X)&~humble(X)))))&
((?[X]:(curious(X)))=>(kind(mary)))&
(![X]:((tall(X)<~>~patient(X))=>(patient(X)<~>creative(X))))&
(![X]:(~humble(X)=>(happy(X)&~strong(X))))&
((?[X]:(~curious(X)))=>(~creative(susan)))&
(![X]:((~calm(X)&~funny(X))=>tall(X)))&
(?[X]:(~creative(X)))&
(?[X]:((humble(X)|~rich(X))))&
(?[X]:((happy(X)|~wise(X))))&
(?[X]:((~brave(X)|~generous(X))))&
((~creative(mary)|strong(mary)))&
(?[X]:((rich(X)<~>~tall(X)))) | old(paul) | [
"p4",
"hypothesis"
]
| % SZS status Unsatisfiable for 8267742271614969843413775
% SZS output start Proof for 8267742271614969843413775
5. ! [X0] : ((curious(X0) & old(X0)) <=> (~old(X0) | old(X0))) [input p4]
23. ~old(paul) [input hypothesis]
45. ! [X0] : (((curious(X0) & old(X0)) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | (~curious(X0) | ~old(X0)))) [nnf transformation 5]
46. ! [X0] : (((curious(X0) & old(X0)) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~curious(X0) | ~old(X0))) [flattening 45]
81. old(X0) | old(X0) [cnf transformation 46]
119. ~old(paul) [cnf transformation 23]
125. old(X0) [duplicate literal removal 81]
209. $false [subsumption resolution 119,125]
% SZS output end Proof for 8267742271614969843413775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not rich or not quiet then someone is curious or not quiet and vice versa.
Everyone who is either curious or not wise is either not kind or not old.
If paul is either not happy or not calm then john is both not curious and happy and vice versa.
If someone is generous then mary is both not quiet and kind.
If lucy is not rich or not patient then mary is not humble and vice versa.
Everyone who is either not curious or old is not calm or not creative.
If someone is both not brave and strong then someone is either kind or curious.
Everyone who is both not kind and not wise is either tall or not rich.
Everyone who is both brave and creative is either not curious or creative and vice versa.
Everyone who is both not calm and not rich is not funny.
Everyone who is either brave or patient is humble.
If mary is not rich or quiet then someone is either rich or not brave.
Everyone who is either brave or not curious is quiet.
If someone is either humble or not creative then john is not rich or happy and vice versa.
If john is kind or not kind then someone is both not old and not brave and vice versa.
If alice is either not strong or not quiet then someone is quiet or not old.
John is either tall or not curious.
Mary is both not happy and patient.
Paul is generous or old.
Someone is either not happy or not strong.
Someone is brave or not humble.
Alice is both calm and not kind.
Paul is both not rich and not old. | John is not wise. | neutral | (((~rich(john)|~quiet(john)))<=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:((curious(X)<~>~wise(X))=>(~kind(X)<~>~old(X))))&
(((~happy(paul)<~>~calm(paul)))<=>((~curious(john)&happy(john))))&
((?[X]:(generous(X)))=>((~quiet(mary)&kind(mary))))&
(((~rich(lucy)|~patient(lucy)))<=>(~humble(mary)))&
(![X]:((~curious(X)<~>old(X))=>(~calm(X)|~creative(X))))&
((?[X]:((~brave(X)&strong(X))))=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:((~kind(X)&~wise(X))=>(tall(X)<~>~rich(X))))&
(![X]:((brave(X)&creative(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((~calm(X)&~rich(X))=>~funny(X)))&
(![X]:((brave(X)<~>patient(X))=>humble(X)))&
(((~rich(mary)|quiet(mary)))=>(?[X]:((rich(X)<~>~brave(X)))))&
(![X]:((brave(X)<~>~curious(X))=>quiet(X)))&
((?[X]:((humble(X)<~>~creative(X))))<=>((~rich(john)|happy(john))))&
(((kind(john)|~kind(john)))<=>(?[X]:((~old(X)&~brave(X)))))&
(((~strong(alice)<~>~quiet(alice)))=>(?[X]:((quiet(X)|~old(X)))))&
((tall(john)<~>~curious(john)))&
((~happy(mary)&patient(mary)))&
((generous(paul)|old(paul)))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((brave(X)|~humble(X))))&
((calm(alice)&~kind(alice)))&
((~rich(paul)&~old(paul))) | ~wise(john) | []
| null | 0 |
If someone is both quiet and not funny then paul is either not tall or curious and vice versa. Everyone who is either quiet or not creative is both tall and not strong. If someone is either not happy or kind then lucy is either generous or creative. If someone is either not brave or not curious then someone is both not kind and not quiet. If someone is curious or not rich then someone is either strong or not strong and vice versa. If lucy is old or generous then someone is either creative or not brave and vice versa. Everyone who is not funny is either not strong or funny and vice versa. If susan is both not creative and wise then someone is not quiet or 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 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. Paul is patient. Someone is either funny or rich. Someone is not creative. Alice is not rich or not patient. Someone is brave or not generous. Fred is both tall and funny. Someone is both not generous and not creative. | Mary is not strong. | entailment | ((?[X]:((quiet(X)&~funny(X))))<=>((~tall(paul)<~>curious(paul))))&
(![X]:((quiet(X)<~>~creative(X))=>(tall(X)&~strong(X))))&
((?[X]:((~happy(X)<~>kind(X))))=>((generous(lucy)<~>creative(lucy))))&
((?[X]:((~brave(X)<~>~curious(X))))=>(?[X]:((~kind(X)&~quiet(X)))))&
((?[X]:((curious(X)|~rich(X))))<=>(?[X]:((strong(X)<~>~strong(X)))))&
(((old(lucy)|generous(lucy)))<=>(?[X]:((creative(X)<~>~brave(X)))))&
(![X]:(~funny(X)<=>(~strong(X)<~>funny(X))))&
(((~creative(susan)&wise(susan)))=>(?[X]:((~quiet(X)|~funny(X)))))&
(((happy(alice)|old(alice)))<=>(patient(mary)))&
(![X]:(~strong(X)<=>(~strong(X)<~>~quiet(X))))&
(![X]:((~brave(X)&~tall(X))<=>generous(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))))&
(patient(paul))&
(?[X]:((funny(X)<~>rich(X))))&
(?[X]:(~creative(X)))&
((~rich(alice)|~patient(alice)))&
(?[X]:((brave(X)|~generous(X))))&
((tall(fred)&funny(fred)))&
(?[X]:((~generous(X)&~creative(X)))) | ~strong(mary) | [
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 5874732955439692999220078
% SZS output start Proof for 5874732955439692999220078
7. ! [X0] : (~funny(X0) <=> (~strong(X0) <~> funny(X0))) [input p6]
23. strong(mary) [input hypothesis]
56. ! [X0] : ((~funny(X0) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) & (((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | funny(X0))) [nnf transformation 7]
105. funny(X0) | ~strong(X0) | funny(X0) [cnf transformation 56]
108. ~funny(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 56]
138. strong(mary) [cnf transformation 23]
143. funny(X0) | ~strong(X0) [duplicate literal removal 105]
144. ~funny(X0) | ~strong(X0) [duplicate literal removal 108]
221. 17 <=> ! [X1] : ~strong(X1) [avatar definition]
222. ~strong(X1) <- (17) [avatar component clause 221]
248. ~strong(X0) [subsumption resolution 143,144]
249. 17 [avatar split clause 248,221]
336. $false <- (17) [resolution 222,138]
337. ~17 [avatar contradiction clause 336]
338. $false [avatar sat refutation 249,337]
% SZS output end Proof for 5874732955439692999220078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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