premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is either not creative or generous then susan is both tall and happy.
Everyone who is creative is either quiet or not tall.
If alice is both not strong and not old then someone is calm or tall and vice versa.
Everyone who is rich is either funny or strong.
If alice is both quiet and not calm then someone is rich or calm and vice versa.
Everyone who is both patient and not tall is both creative and not strong and vice versa.
If lucy is either kind or brave then john is strong or funny and vice versa.
If someone is both generous and not humble then fred is quiet or not humble.
Everyone who is not calm is not quiet and vice versa.
Everyone who is old or tall is not patient or humble and vice versa.
Everyone who is either funny or not strong is humble and vice versa.
Everyone who is not humble is curious or not calm.
If paul is either curious or strong then paul is not old or happy and vice versa.
Everyone who is not quiet or strong is not kind and vice versa.
If lucy is brave then someone is either tall or not creative.
If fred is generous or funny then john is both kind and not humble and vice versa.
Someone is either not wise or not curious.
Susan is not quiet or not generous.
Mary is both not quiet and tall.
Someone is not quiet or patient.
Mary is kind or not brave.
Susan is strong or not funny.
Susan is both not funny and strong. | Susan is not generous. | neutral | ((?[X]:((~creative(X)<~>generous(X))))=>((tall(susan)&happy(susan))))&
(![X]:(creative(X)=>(quiet(X)<~>~tall(X))))&
(((~strong(alice)&~old(alice)))<=>(?[X]:((calm(X)|tall(X)))))&
(![X]:(rich(X)=>(funny(X)<~>strong(X))))&
(((quiet(alice)&~calm(alice)))<=>(?[X]:((rich(X)|calm(X)))))&
(![X]:((patient(X)&~tall(X))<=>(creative(X)&~strong(X))))&
(((kind(lucy)<~>brave(lucy)))<=>((strong(john)|funny(john))))&
((?[X]:((generous(X)&~humble(X))))=>((quiet(fred)|~humble(fred))))&
(![X]:(~calm(X)<=>~quiet(X)))&
(![X]:((old(X)|tall(X))<=>(~patient(X)|humble(X))))&
(![X]:((funny(X)<~>~strong(X))<=>humble(X)))&
(![X]:(~humble(X)=>(curious(X)|~calm(X))))&
(((curious(paul)<~>strong(paul)))<=>((~old(paul)|happy(paul))))&
(![X]:((~quiet(X)|strong(X))<=>~kind(X)))&
((brave(lucy))=>(?[X]:((tall(X)<~>~creative(X)))))&
(((generous(fred)|funny(fred)))<=>((kind(john)&~humble(john))))&
(?[X]:((~wise(X)<~>~curious(X))))&
((~quiet(susan)|~generous(susan)))&
((~quiet(mary)&tall(mary)))&
(?[X]:((~quiet(X)|patient(X))))&
((kind(mary)|~brave(mary)))&
((strong(susan)|~funny(susan)))&
((~funny(susan)&strong(susan))) | ~generous(susan) | [] | null | 0 |
If someone is not humble or not creative then someone is both curious and not old.
Everyone who is either not rich or not quiet is either calm or not old and vice versa.
If someone is either generous or not curious then fred is patient or tall and vice versa.
If fred is either humble or old then someone is quiet or not patient and vice versa.
Everyone who is either brave or kind is quiet or curious and vice versa.
Everyone who is old is not strong.
Everyone who is calm or not happy is both strong and not funny and vice versa.
Everyone who is not curious or tall is not brave or not strong and vice versa.
If someone is both tall and brave then mary is not generous or not tall.
Everyone who is either not kind or not old is strong and vice versa.
Everyone who is kind or not kind is either quiet or strong.
Everyone who is both not wise and strong is either not wise or not calm.
Everyone who is both patient and quiet is either calm or not quiet.
Everyone who is both calm and not strong is tall and vice versa.
If someone is not creative or humble then someone is not old.
Someone is either not old or wise.
Someone is both brave and funny.
Someone is both kind and not funny.
Someone is either not tall or rich.
Someone is either not tall or not humble. | Mary is not strong. | entailment | ((?[X]:((~humble(X)|~creative(X))))=>(?[X]:((curious(X)&~old(X)))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(calm(X)<~>~old(X))))&
((?[X]:((generous(X)<~>~curious(X))))<=>((patient(fred)|tall(fred))))&
(((humble(fred)<~>old(fred)))<=>(?[X]:((quiet(X)|~patient(X)))))&
(![X]:((brave(X)<~>kind(X))<=>(quiet(X)|curious(X))))&
(![X]:(old(X)=>~strong(X)))&
(![X]:((calm(X)|~happy(X))<=>(strong(X)&~funny(X))))&
(![X]:((~curious(X)|tall(X))<=>(~brave(X)|~strong(X))))&
((?[X]:((tall(X)&brave(X))))=>((~generous(mary)|~tall(mary))))&
(![X]:((~kind(X)<~>~old(X))<=>strong(X)))&
(![X]:((kind(X)|~kind(X))=>(quiet(X)<~>strong(X))))&
(![X]:((~wise(X)&strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((patient(X)&quiet(X))=>(calm(X)<~>~quiet(X))))&
(![X]:((calm(X)&~strong(X))<=>tall(X)))&
((?[X]:((~creative(X)|humble(X))))=>(?[X]:(~old(X))))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:((brave(X)&funny(X))))&
(?[X]:((kind(X)&~funny(X))))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:((~tall(X)<~>~humble(X)))) | ~strong(mary) | [
"p4",
"p5",
"p7",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3901016900453727265142285
% SZS output start Proof for 3901016900453727265142285
5. ! [X0] : ((brave(X0) <~> kind(X0)) <=> (curious(X0) | quiet(X0))) [input p4]
6. ! [X0] : (old(X0) => ~strong(X0)) [input p5]
8. ! [X0] : ((tall(X0) | ~curious(X0)) <=> (~strong(X0) | ~brave(X0))) [input p7]
10. ! [X0] : ((~kind(X0) <~> ~old(X0)) <=> strong(X0)) [input p9]
11. ! [X0] : ((~kind(X0) | kind(X0)) => (quiet(X0) <~> strong(X0))) [input p10]
14. ! [X0] : ((~strong(X0) & calm(X0)) <=> tall(X0)) [input p13]
21. strong(mary) [input hypothesis]
27. ! [X0] : (~strong(X0) | ~old(X0)) [ennf transformation 6]
30. ! [X0] : ((quiet(X0) <~> strong(X0)) | (kind(X0) & ~kind(X0))) [ennf transformation 11]
49. ! [X0] : ((((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0))))) [nnf transformation 5]
50. ! [X0] : ((((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0))))) [flattening 49]
53. ! [X0] : (((tall(X0) | ~curious(X0)) | (strong(X0) & brave(X0))) & ((~strong(X0) | ~brave(X0)) | (~tall(X0) & curious(X0)))) [nnf transformation 8]
54. ! [X0] : ((tall(X0) | ~curious(X0) | (strong(X0) & brave(X0))) & (~strong(X0) | ~brave(X0) | (~tall(X0) & curious(X0)))) [flattening 53]
55. ! [X0] : ((((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | ~strong(X0)) & (strong(X0) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0))))) [nnf transformation 10]
56. ! [X0] : (((~strong(X0) | ~quiet(X0)) & (strong(X0) | quiet(X0))) | (kind(X0) & ~kind(X0))) [nnf transformation 30]
59. ! [X0] : (((~strong(X0) & calm(X0)) | ~tall(X0)) & (tall(X0) | (strong(X0) | ~calm(X0)))) [nnf transformation 14]
60. ! [X0] : (((~strong(X0) & calm(X0)) | ~tall(X0)) & (tall(X0) | strong(X0) | ~calm(X0))) [flattening 59]
100. ~kind(X0) | quiet(X0) | brave(X0) | curious(X0) [cnf transformation 50]
104. ~kind(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 50]
105. ~strong(X0) | ~old(X0) [cnf transformation 27]
111. ~strong(X0) | ~brave(X0) | curious(X0) [cnf transformation 54]
113. ~curious(X0) | tall(X0) | brave(X0) [cnf transformation 54]
119. old(X0) | kind(X0) | ~strong(X0) [cnf transformation 55]
120. strong(X0) | quiet(X0) | ~kind(X0) [cnf transformation 56]
121. strong(X0) | quiet(X0) | kind(X0) [cnf transformation 56]
122. ~strong(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 56]
130. ~strong(X0) | ~tall(X0) [cnf transformation 60]
142. strong(mary) [cnf transformation 21]
222. 18 <=> tall(mary) [avatar definition]
226. ~strong(X0) | kind(X0) [subsumption resolution 119,105]
228. ~strong(X0) | ~quiet(X0) [subsumption resolution 122,226]
229. kind(X0) | quiet(X0) [subsumption resolution 121,226]
230. strong(X0) | quiet(X0) [subsumption resolution 120,229]
275. ~tall(mary) [resolution 130,142]
277. kind(mary) [resolution 226,142]
283. ~quiet(mary) [resolution 228,142]
322. ~brave(X0) | ~curious(X0) | quiet(X0) [resolution 104,229]
323. ~brave(mary) | ~curious(mary) [resolution 104,277]
327. 32 <=> curious(mary) [avatar definition]
328. curious(mary) <- (32) [avatar component clause 327]
331. 33 <=> brave(mary) [avatar definition]
333. ~brave(mary) <- (~33) [avatar component clause 331]
334. ~32 | ~33 [avatar split clause 323,331,327]
336. ~brave(X0) | curious(X0) | quiet(X0) [resolution 111,230]
339. ~brave(X0) | quiet(X0) [subsumption resolution 336,322]
486. quiet(X0) | brave(X0) | curious(X0) | quiet(X0) [resolution 100,229]
489. quiet(X0) | brave(X0) | curious(X0) [duplicate literal removal 486]
490. quiet(X0) | curious(X0) [subsumption resolution 489,339]
499. curious(mary) [resolution 490,283]
504. 32 [avatar split clause 499,327]
506. tall(mary) | brave(mary) <- (32) [resolution 328,113]
511. tall(mary) <- (32, ~33) [subsumption resolution 506,333]
512. 18 | ~32 | 33 [avatar split clause 511,331,327,222]
513. ~18 [avatar split clause 275,222]
514. $false [avatar sat refutation 334,504,512,513]
% SZS output end Proof for 3901016900453727265142285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not curious is rich and vice versa.
Everyone who is curious is both old and not brave and vice versa.
If fred is either not brave or wise then someone is either not brave or not old.
If someone is either not calm or not patient then alice is both not old and calm and vice versa.
If someone is curious or not humble then someone is calm.
Everyone who is not patient is either not quiet or not generous and vice versa.
Everyone who is not calm is either strong or funny and vice versa.
If someone is quiet or not brave then paul is humble.
If john is both rich and tall then someone is patient and vice versa.
Everyone who is either not creative or humble is not strong or not patient and vice versa.
Everyone who is either patient or kind is either strong or happy.
Everyone who is either wise or happy is happy.
If someone is not rich or kind then lucy is curious and vice versa.
Everyone who is either not strong or not quiet is not rich and vice versa.
If someone is curious or not wise then someone is not rich.
Everyone who is not curious is creative or not patient and vice versa.
Someone is not tall or old.
John is either not humble or patient.
Someone is either funny or not kind.
Alice is funny or old.
Lucy is either not curious or brave.
Susan is either funny or not calm.
Fred is not kind.
Paul is tall or brave. | Alice is not tall. | contradiction | (![X]:((tall(X)&~curious(X))<=>rich(X)))&
(![X]:(curious(X)<=>(old(X)&~brave(X))))&
(((~brave(fred)<~>wise(fred)))=>(?[X]:((~brave(X)<~>~old(X)))))&
((?[X]:((~calm(X)<~>~patient(X))))<=>((~old(alice)&calm(alice))))&
((?[X]:((curious(X)|~humble(X))))=>(?[X]:(calm(X))))&
(![X]:(~patient(X)<=>(~quiet(X)<~>~generous(X))))&
(![X]:(~calm(X)<=>(strong(X)<~>funny(X))))&
((?[X]:((quiet(X)|~brave(X))))=>(humble(paul)))&
(((rich(john)&tall(john)))<=>(?[X]:(patient(X))))&
(![X]:((~creative(X)<~>humble(X))<=>(~strong(X)|~patient(X))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(?[X]:((~tall(X)|old(X))))&
((~humble(john)<~>patient(john)))&
(?[X]:((funny(X)<~>~kind(X))))&
((funny(alice)|old(alice)))&
((~curious(lucy)<~>brave(lucy)))&
((funny(susan)<~>~calm(susan)))&
(~kind(fred))&
((tall(paul)|brave(paul))) | ~tall(alice) | [
"p0",
"p1",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3492682807355841699814426
% SZS output start Proof for 3492682807355841699814426
1. ! [X0] : ((~curious(X0) & tall(X0)) <=> rich(X0)) [input p0]
2. ! [X0] : (curious(X0) <=> (~brave(X0) & old(X0))) [input p1]
13. ? [X0] : (kind(X0) | ~rich(X0)) <=> curious(lucy) [input p12]
21. ~curious(lucy) <~> brave(lucy) [input p20]
25. ~tall(alice) [input hypothesis]
34. ! [X0] : (((~curious(X0) & tall(X0)) | ~rich(X0)) & (rich(X0) | (curious(X0) | ~tall(X0)))) [nnf transformation 1]
35. ! [X0] : (((~curious(X0) & tall(X0)) | ~rich(X0)) & (rich(X0) | curious(X0) | ~tall(X0))) [flattening 34]
36. ! [X0] : ((curious(X0) | (brave(X0) | ~old(X0))) & ((~brave(X0) & old(X0)) | ~curious(X0))) [nnf transformation 2]
37. ! [X0] : ((curious(X0) | brave(X0) | ~old(X0)) & ((~brave(X0) & old(X0)) | ~curious(X0))) [flattening 36]
60. (? [X0] : (kind(X0) | ~rich(X0)) | ~curious(lucy)) & (curious(lucy) | ! [X0] : (~kind(X0) & rich(X0))) [nnf transformation 13]
61. (? [X0] : (kind(X0) | ~rich(X0)) | ~curious(lucy)) & (curious(lucy) | ! [X1] : (~kind(X1) & rich(X1))) [rectify 60]
62. ? [X0] : (kind(X0) | ~rich(X0)) => (kind(sK4) | ~rich(sK4)) [choice axiom]
63. ((kind(sK4) | ~rich(sK4)) | ~curious(lucy)) & (curious(lucy) | ! [X1] : (~kind(X1) & rich(X1))) [skolemisation 61,62]
76. (~brave(lucy) | curious(lucy)) & (brave(lucy) | ~curious(lucy)) [nnf transformation 21]
79. ~rich(X0) | tall(X0) [cnf transformation 35]
82. ~brave(X0) | ~curious(X0) [cnf transformation 37]
121. curious(lucy) | rich(X1) [cnf transformation 63]
139. brave(lucy) | ~curious(lucy) [cnf transformation 76]
140. ~brave(lucy) | curious(lucy) [cnf transformation 76]
145. ~tall(alice) [cnf transformation 25]
239. 21 <=> curious(lucy) [avatar definition]
256. 25 <=> ! [X1] : rich(X1) [avatar definition]
257. rich(X1) <- (25) [avatar component clause 256]
258. 25 | 21 [avatar split clause 121,239,256]
302. ~brave(lucy) [subsumption resolution 140,82]
303. ~curious(lucy) [subsumption resolution 139,302]
304. ~21 [avatar split clause 303,239]
333. tall(X0) <- (25) [resolution 79,257]
335. $false <- (25) [resolution 333,145]
338. ~25 [avatar contradiction clause 335]
339. $false [avatar sat refutation 258,304,338]
% SZS output end Proof for 3492682807355841699814426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is both brave and not kind.
Everyone who is both not generous and wise is calm and vice versa.
Everyone who is either not calm or not tall is either humble or brave and vice versa.
Everyone who is either not rich or not generous is both not old and not rich.
If someone is either not quiet or not humble then someone is both not calm and not funny and vice versa.
Everyone who is either brave or not rich is not funny and vice versa.
Everyone who is brave is either creative or rich and vice versa.
If paul is not kind then susan is either not creative or humble.
Everyone who is either not creative or creative is patient or not rich and vice versa.
Everyone who is calm is both not creative and not quiet.
Everyone who is both not curious and not humble is both not humble and not strong and vice versa.
If someone is either not rich or calm then alice is either not happy or not patient.
If lucy is both not calm and not quiet then susan is both not curious and strong and vice versa.
If someone is not kind then someone is not curious.
If paul is not kind or not calm then alice is funny or not tall and vice versa.
If someone is either old or brave then someone is both not happy and humble.
Someone is either not patient or tall.
Alice is both strong and rich.
Someone is not rich or happy.
Fred is not strong or strong.
Someone is not creative or not tall.
Mary is both patient and not tall.
Someone is not humble.
Paul is both not calm and not patient. | Paul is funny. | entailment | (![X]:(~rich(X)=>(brave(X)&~kind(X))))&
(![X]:((~generous(X)&wise(X))<=>calm(X)))&
(![X]:((~calm(X)<~>~tall(X))<=>(humble(X)<~>brave(X))))&
(![X]:((~rich(X)<~>~generous(X))=>(~old(X)&~rich(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))<=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((brave(X)<~>~rich(X))<=>~funny(X)))&
(![X]:(brave(X)<=>(creative(X)<~>rich(X))))&
((~kind(paul))=>((~creative(susan)<~>humble(susan))))&
(![X]:((~creative(X)<~>creative(X))<=>(patient(X)|~rich(X))))&
(![X]:(calm(X)=>(~creative(X)&~quiet(X))))&
(![X]:((~curious(X)&~humble(X))<=>(~humble(X)&~strong(X))))&
((?[X]:((~rich(X)<~>calm(X))))=>((~happy(alice)<~>~patient(alice))))&
(((~calm(lucy)&~quiet(lucy)))<=>((~curious(susan)&strong(susan))))&
((?[X]:(~kind(X)))=>(?[X]:(~curious(X))))&
(((~kind(paul)|~calm(paul)))<=>((funny(alice)|~tall(alice))))&
((?[X]:((old(X)<~>brave(X))))=>(?[X]:((~happy(X)&humble(X)))))&
(?[X]:((~patient(X)<~>tall(X))))&
((strong(alice)&rich(alice)))&
(?[X]:((~rich(X)|happy(X))))&
((~strong(fred)|strong(fred)))&
(?[X]:((~creative(X)|~tall(X))))&
((patient(mary)&~tall(mary)))&
(?[X]:(~humble(X)))&
((~calm(paul)&~patient(paul))) | funny(paul) | [
"p0",
"p5",
"p6",
"p8",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 729900441718790754356349
% SZS output start Proof for 729900441718790754356349
1. ! [X0] : (~rich(X0) => (~kind(X0) & brave(X0))) [input p0]
6. ! [X0] : ((brave(X0) <~> ~rich(X0)) <=> ~funny(X0)) [input p5]
7. ! [X0] : (brave(X0) <=> (creative(X0) <~> rich(X0))) [input p6]
9. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (~rich(X0) | patient(X0))) [input p8]
24. ~patient(paul) & ~calm(paul) [input p23]
25. ~funny(paul) [input hypothesis]
29. ! [X0] : ((~kind(X0) & brave(X0)) | rich(X0)) [ennf transformation 1]
45. ! [X0] : ((((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | funny(X0)) & (~funny(X0) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))))) [nnf transformation 6]
46. ! [X0] : ((brave(X0) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0)))) & (((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | ~brave(X0))) [nnf transformation 7]
48. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (rich(X0) & ~patient(X0))) & ((~rich(X0) | patient(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 9]
49. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (rich(X0) & ~patient(X0))) & (~rich(X0) | patient(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 48]
73. brave(X0) | rich(X0) [cnf transformation 29]
98. ~rich(X0) | brave(X0) | funny(X0) [cnf transformation 45]
99. rich(X0) | ~brave(X0) | funny(X0) [cnf transformation 45]
100. rich(X0) | creative(X0) | ~brave(X0) [cnf transformation 46]
101. ~creative(X0) | ~rich(X0) | ~brave(X0) [cnf transformation 46]
103. brave(X0) | creative(X0) | ~rich(X0) [cnf transformation 46]
106. ~rich(X0) | patient(X0) | creative(X0) | creative(X0) [cnf transformation 49]
146. ~patient(paul) [cnf transformation 24]
147. ~funny(paul) [cnf transformation 25]
148. ~rich(X0) | patient(X0) | creative(X0) [duplicate literal removal 106]
182. funny(X0) | rich(X0) [subsumption resolution 99,73]
183. funny(X0) | brave(X0) [subsumption resolution 98,182]
184. creative(X0) | brave(X0) [subsumption resolution 103,73]
185. creative(X0) | rich(X0) [subsumption resolution 100,184]
200. patient(X0) | creative(X0) [subsumption resolution 148,185]
312. rich(paul) [resolution 182,147]
315. brave(paul) [resolution 183,147]
322. creative(paul) [resolution 200,146]
332. ~rich(paul) | ~brave(paul) [resolution 101,322]
334. ~brave(paul) [subsumption resolution 332,312]
335. $false [subsumption resolution 334,315]
% SZS output end Proof for 729900441718790754356349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or generous is creative.
If someone is not quiet then john is not tall or quiet and vice versa.
Everyone who is either not old or rich is not tall and vice versa.
Everyone who is either humble or not rich is not strong or quiet and vice versa.
Everyone who is not calm or not creative is not tall.
Everyone who is wise is either not strong or calm.
Everyone who is not brave or creative is either humble or not creative.
If someone is not funny then john is humble or tall and vice versa.
Everyone who is both rich and not creative is funny or not tall.
If someone is quiet then lucy is tall.
Everyone who is not calm is not quiet or happy.
Everyone who is tall is curious and vice versa.
Everyone who is either tall or humble is curious and vice versa.
If paul is not happy or wise then paul is either humble or not strong and vice versa.
If lucy is either not kind or not funny then fred is both wise and not rich and vice versa.
If john is both not strong and strong then someone is both happy and not happy.
Someone is brave.
Someone is both brave and not kind.
Susan is not generous or not funny.
Susan is rich or not generous.
Someone is not humble or not tall.
Someone is calm.
Fred is either calm or not humble. | Susan is quiet. | contradiction | (![X]:((humble(X)|generous(X))=>creative(X)))&
((?[X]:(~quiet(X)))<=>((~tall(john)|quiet(john))))&
(![X]:((~old(X)<~>rich(X))<=>~tall(X)))&
(![X]:((humble(X)<~>~rich(X))<=>(~strong(X)|quiet(X))))&
(![X]:((~calm(X)|~creative(X))=>~tall(X)))&
(![X]:(wise(X)=>(~strong(X)<~>calm(X))))&
(![X]:((~brave(X)|creative(X))=>(humble(X)<~>~creative(X))))&
((?[X]:(~funny(X)))<=>((humble(john)|tall(john))))&
(![X]:((rich(X)&~creative(X))=>(funny(X)|~tall(X))))&
((?[X]:(quiet(X)))=>(tall(lucy)))&
(![X]:(~calm(X)=>(~quiet(X)|happy(X))))&
(![X]:(tall(X)<=>curious(X)))&
(![X]:((tall(X)<~>humble(X))<=>curious(X)))&
(((~happy(paul)|wise(paul)))<=>((humble(paul)<~>~strong(paul))))&
(((~kind(lucy)<~>~funny(lucy)))<=>((wise(fred)&~rich(fred))))&
(((~strong(john)&strong(john)))=>(?[X]:((happy(X)&~happy(X)))))&
(?[X]:(brave(X)))&
(?[X]:((brave(X)&~kind(X))))&
((~generous(susan)|~funny(susan)))&
((rich(susan)|~generous(susan)))&
(?[X]:((~humble(X)|~tall(X))))&
(?[X]:(calm(X)))&
((calm(fred)<~>~humble(fred))) | quiet(susan) | [
"p4",
"p6",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 130605905885212898142046
% SZS output start Proof for 130605905885212898142046
5. ! [X0] : ((~creative(X0) | ~calm(X0)) => ~tall(X0)) [input p4]
7. ! [X0] : ((creative(X0) | ~brave(X0)) => (humble(X0) <~> ~creative(X0))) [input p6]
10. ? [X0] : quiet(X0) => tall(lucy) [input p9]
12. ! [X0] : (tall(X0) <=> curious(X0)) [input p11]
13. ! [X0] : ((tall(X0) <~> humble(X0)) <=> curious(X0)) [input p12]
24. quiet(susan) [input hypothesis]
26. ! [X0] : (creative(X0) => (humble(X0) <~> ~creative(X0))) [pure predicate removal 7]
32. ! [X0] : (~tall(X0) | (creative(X0) & calm(X0))) [ennf transformation 5]
34. ! [X0] : ((humble(X0) <~> ~creative(X0)) | ~creative(X0)) [ennf transformation 26]
37. tall(lucy) | ! [X0] : ~quiet(X0) [ennf transformation 10]
51. ! [X0] : (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | ~creative(X0)) [nnf transformation 34]
57. ! [X0] : ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0))) [nnf transformation 12]
58. ! [X0] : ((((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ~curious(X0)) & (curious(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))))) [nnf transformation 13]
87. ~tall(X0) | creative(X0) [cnf transformation 32]
90. ~creative(X0) | humble(X0) | ~creative(X0) [cnf transformation 51]
96. tall(lucy) | ~quiet(X0) [cnf transformation 37]
98. ~tall(X0) | curious(X0) [cnf transformation 57]
99. ~curious(X0) | tall(X0) [cnf transformation 57]
101. curious(X0) | tall(X0) | ~humble(X0) [cnf transformation 58]
103. ~humble(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 58]
123. quiet(susan) [cnf transformation 24]
124. ~creative(X0) | humble(X0) [duplicate literal removal 90]
158. 8 <=> ! [X0] : ~quiet(X0) [avatar definition]
159. ~quiet(X0) <- (8) [avatar component clause 158]
161. 9 <=> tall(lucy) [avatar definition]
163. tall(lucy) <- (9) [avatar component clause 161]
164. 8 | 9 [avatar split clause 96,161,158]
165. ~humble(X0) | ~curious(X0) [subsumption resolution 103,99]
166. curious(X0) | ~humble(X0) [subsumption resolution 101,98]
167. ~humble(X0) [subsumption resolution 166,165]
215. $false <- (8) [resolution 159,123]
216. ~8 [avatar contradiction clause 215]
220. creative(lucy) <- (9) [resolution 87,163]
223. humble(lucy) <- (9) [resolution 124,220]
224. $false <- (9) [subsumption resolution 223,167]
225. ~9 [avatar contradiction clause 224]
226. $false [avatar sat refutation 164,216,225]
% SZS output end Proof for 130605905885212898142046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both brave and not tall then someone is both creative and not creative and vice versa.
Everyone who is quiet or calm is either not humble or calm and vice versa.
If someone is curious or not strong then paul is not quiet.
If someone is both creative and not wise then someone is old or not kind and vice versa.
If someone is creative then someone is generous or not patient.
Everyone who is either not brave or not tall is both curious and wise.
Everyone who is not old or not brave is not humble.
If someone is not kind or quiet then someone is either wise or not curious.
If someone is creative or not kind then someone is either not happy or not patient and vice versa.
Everyone who is not calm or brave is both not creative and not wise.
Everyone who is not curious or strong is tall.
Everyone who is brave is strong and vice versa.
If susan is both not brave and not patient then john is either not strong or creative.
If someone is not calm or humble then someone is both not happy and not creative and vice versa.
Everyone who is either kind or not old is both not generous and not tall.
Someone is either not quiet or brave.
Someone is not wise or not quiet.
Someone is either not rich or not happy.
Someone is both not funny and not happy.
Someone is either not patient or not strong. | John is not strong. | contradiction | (((brave(paul)&~tall(paul)))<=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((quiet(X)|calm(X))<=>(~humble(X)<~>calm(X))))&
((?[X]:((curious(X)|~strong(X))))=>(~quiet(paul)))&
((?[X]:((creative(X)&~wise(X))))<=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:(creative(X)))=>(?[X]:((generous(X)|~patient(X)))))&
(![X]:((~brave(X)<~>~tall(X))=>(curious(X)&wise(X))))&
(![X]:((~old(X)|~brave(X))=>~humble(X)))&
((?[X]:((~kind(X)|quiet(X))))=>(?[X]:((wise(X)<~>~curious(X)))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:((~calm(X)|brave(X))=>(~creative(X)&~wise(X))))&
(![X]:((~curious(X)|strong(X))=>tall(X)))&
(![X]:(brave(X)<=>strong(X)))&
(((~brave(susan)&~patient(susan)))=>((~strong(john)<~>creative(john))))&
((?[X]:((~calm(X)|humble(X))))<=>(?[X]:((~happy(X)&~creative(X)))))&
(![X]:((kind(X)<~>~old(X))=>(~generous(X)&~tall(X))))&
(?[X]:((~quiet(X)<~>brave(X))))&
(?[X]:((~wise(X)|~quiet(X))))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((~funny(X)&~happy(X))))&
(?[X]:((~patient(X)<~>~strong(X)))) | ~strong(john) | [
"p1",
"p2",
"p3",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7786670203942669725201644
% SZS output start Proof for 7786670203942669725201644
2. ! [X0] : ((calm(X0) | quiet(X0)) <=> (~humble(X0) <~> calm(X0))) [input p1]
3. ? [X0] : (~strong(X0) | curious(X0)) => ~quiet(paul) [input p2]
4. ? [X0] : (~wise(X0) & creative(X0)) <=> ? [X0] : (~kind(X0) | old(X0)) [input p3]
7. ! [X0] : ((~brave(X0) | ~old(X0)) => ~humble(X0)) [input p6]
10. ! [X0] : ((brave(X0) | ~calm(X0)) => (~wise(X0) & ~creative(X0))) [input p9]
21. ~strong(john) [input hypothesis]
22. ? [X0] : (~wise(X0) & creative(X0)) <=> ? [X1] : (~kind(X1) | old(X1)) [rectify 4]
28. ~quiet(paul) | ! [X0] : (strong(X0) & ~curious(X0)) [ennf transformation 3]
31. ! [X0] : (~humble(X0) | (brave(X0) & old(X0))) [ennf transformation 7]
33. ! [X0] : ((~wise(X0) & ~creative(X0)) | (~brave(X0) & calm(X0))) [ennf transformation 10]
43. ! [X0] : (((calm(X0) | quiet(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0)))) & (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (~calm(X0) & ~quiet(X0)))) [nnf transformation 2]
44. ! [X0] : ((calm(X0) | quiet(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0)))) & (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (~calm(X0) & ~quiet(X0)))) [flattening 43]
45. (? [X0] : (~wise(X0) & creative(X0)) | ! [X1] : (kind(X1) & ~old(X1))) & (? [X1] : (~kind(X1) | old(X1)) | ! [X0] : (wise(X0) | ~creative(X0))) [nnf transformation 22]
46. (? [X0] : (~wise(X0) & creative(X0)) | ! [X1] : (kind(X1) & ~old(X1))) & (? [X2] : (~kind(X2) | old(X2)) | ! [X3] : (wise(X3) | ~creative(X3))) [rectify 45]
47. ? [X0] : (~wise(X0) & creative(X0)) => (~wise(sK1) & creative(sK1)) [choice axiom]
48. ? [X2] : (~kind(X2) | old(X2)) => (~kind(sK2) | old(sK2)) [choice axiom]
49. ((~wise(sK1) & creative(sK1)) | ! [X1] : (kind(X1) & ~old(X1))) & ((~kind(sK2) | old(sK2)) | ! [X3] : (wise(X3) | ~creative(X3))) [skolemisation 46,48,47]
91. ~calm(X0) | humble(X0) | ~calm(X0) [cnf transformation 44]
92. calm(X0) | quiet(X0) | calm(X0) | humble(X0) [cnf transformation 44]
95. ~quiet(paul) | strong(X0) [cnf transformation 28]
97. creative(sK1) | ~old(X1) [cnf transformation 49]
106. ~humble(X0) | old(X0) [cnf transformation 31]
107. ~humble(X0) | brave(X0) [cnf transformation 31]
118. ~creative(X0) | calm(X0) [cnf transformation 33]
119. ~creative(X0) | ~brave(X0) [cnf transformation 33]
145. ~strong(john) [cnf transformation 21]
146. ~calm(X0) | humble(X0) [duplicate literal removal 91]
147. humble(X0) | quiet(X0) | calm(X0) [duplicate literal removal 92]
163. 4 <=> ! [X0] : strong(X0) [avatar definition]
164. strong(X0) <- (4) [avatar component clause 163]
166. 5 <=> quiet(paul) [avatar definition]
168. ~quiet(paul) <- (~5) [avatar component clause 166]
169. 4 | ~5 [avatar split clause 95,166,163]
183. 9 <=> ! [X1] : ~old(X1) [avatar definition]
184. ~old(X1) <- (9) [avatar component clause 183]
187. 10 <=> creative(sK1) [avatar definition]
189. creative(sK1) <- (10) [avatar component clause 187]
191. 9 | 10 [avatar split clause 97,187,183]
268. 28 <=> strong(john) [avatar definition]
269. ~strong(john) <- (~28) [avatar component clause 268]
334. ~28 [avatar split clause 145,268]
356. quiet(X2) | calm(X2) | old(X2) [resolution 147,106]
358. calm(X2) | quiet(X2) <- (9) [subsumption resolution 356,184]
359. humble(X0) | quiet(X0) <- (9) [resolution 358,146]
363. quiet(X2) | old(X2) <- (9) [resolution 359,106]
364. quiet(X2) <- (9) [subsumption resolution 363,184]
365. $false <- (~5, 9) [resolution 364,168]
370. 5 | ~9 [avatar contradiction clause 365]
374. ~brave(sK1) <- (10) [resolution 189,119]
375. calm(sK1) <- (10) [resolution 189,118]
386. $false <- (4, ~28) [resolution 164,269]
391. ~4 | 28 [avatar contradiction clause 386]
396. humble(sK1) <- (10) [resolution 375,146]
408. brave(sK1) <- (10) [resolution 396,107]
410. $false <- (10) [subsumption resolution 408,374]
411. ~10 [avatar contradiction clause 410]
412. $false [avatar sat refutation 169,191,334,370,391,411]
% SZS output end Proof for 7786670203942669725201644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and strong then someone is both creative and not tall and vice versa.
If someone is not strong then john is creative and vice versa.
If paul is tall or not patient then someone is tall or not humble.
Everyone who is both humble and not wise is either creative or humble and vice versa.
If someone is not funny or funny then susan is either brave or creative.
If paul is either not quiet or quiet then susan is strong.
Everyone who is either not quiet or calm is generous.
Everyone who is both brave and not quiet is funny or wise and vice versa.
If someone is calm then someone is both strong and wise.
Everyone who is either funny or tall is either generous or not kind.
If someone is both happy and not curious then paul is humble.
Everyone who is either not tall or quiet is either not funny or patient and vice versa.
Everyone who is both brave and tall is both old and not funny.
John is both not curious and tall.
Someone is either not humble or not wise.
Susan is not rich.
Alice is happy or not rich.
Someone is either not funny or humble.
Alice is not tall. | Paul is brave. | neutral | ((?[X]:((funny(X)&strong(X))))<=>(?[X]:((creative(X)&~tall(X)))))&
((?[X]:(~strong(X)))<=>(creative(john)))&
(((tall(paul)|~patient(paul)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((humble(X)&~wise(X))<=>(creative(X)<~>humble(X))))&
((?[X]:((~funny(X)|funny(X))))=>((brave(susan)<~>creative(susan))))&
(((~quiet(paul)<~>quiet(paul)))=>(strong(susan)))&
(![X]:((~quiet(X)<~>calm(X))=>generous(X)))&
(![X]:((brave(X)&~quiet(X))<=>(funny(X)|wise(X))))&
((?[X]:(calm(X)))=>(?[X]:((strong(X)&wise(X)))))&
(![X]:((funny(X)<~>tall(X))=>(generous(X)<~>~kind(X))))&
((?[X]:((happy(X)&~curious(X))))=>(humble(paul)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((brave(X)&tall(X))=>(old(X)&~funny(X))))&
((~curious(john)&tall(john)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(~rich(susan))&
((happy(alice)|~rich(alice)))&
(?[X]:((~funny(X)<~>humble(X))))&
(~tall(alice)) | brave(paul) | [] | null | 0 |
If susan is not wise or strong then someone is kind or not rich and vice versa. If someone is not curious or strong then fred is curious or not funny and vice versa. If someone is quiet or not calm then fred is both curious and not quiet and vice versa. If alice is either not calm or not quiet then fred is not quiet or happy. Everyone who is both curious and not strong is both not wise and not happy. If lucy is both calm and quiet then lucy is either not tall or not old. If someone is both not calm and not wise then someone is both not patient and wise and vice versa. Everyone who is both not curious and not humble is patient or not quiet and vice versa. If alice is both not kind and not calm then susan is old or not kind. If someone is both not rich and not strong then someone is both strong and happy and vice versa. If lucy is either quiet or calm then alice is either not patient or not wise. Everyone who is wise is not curious or not funny. Everyone who is not patient or generous is either rich or not tall and vice versa. Everyone who is either funny or not humble is either brave or not wise and vice versa. If someone is strong then lucy is either not humble or not quiet. If someone is either not humble or curious then someone is kind or not generous and vice versa. Susan is brave or not old. Someone is humble or not tall. Someone is not patient. Alice is not generous or not brave. Paul is not kind or not old. | Susan is not happy. | neutral | (((~wise(susan)|strong(susan)))<=>(?[X]:((kind(X)|~rich(X)))))&
((?[X]:((~curious(X)|strong(X))))<=>((curious(fred)|~funny(fred))))&
((?[X]:((quiet(X)|~calm(X))))<=>((curious(fred)&~quiet(fred))))&
(((~calm(alice)<~>~quiet(alice)))=>((~quiet(fred)|happy(fred))))&
(![X]:((curious(X)&~strong(X))=>(~wise(X)&~happy(X))))&
(((calm(lucy)&quiet(lucy)))=>((~tall(lucy)<~>~old(lucy))))&
((?[X]:((~calm(X)&~wise(X))))<=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:((~curious(X)&~humble(X))<=>(patient(X)|~quiet(X))))&
(((~kind(alice)&~calm(alice)))=>((old(susan)|~kind(susan))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:((strong(X)&happy(X)))))&
(((quiet(lucy)<~>calm(lucy)))=>((~patient(alice)<~>~wise(alice))))&
(![X]:(wise(X)=>(~curious(X)|~funny(X))))&
(![X]:((~patient(X)|generous(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((funny(X)<~>~humble(X))<=>(brave(X)<~>~wise(X))))&
((?[X]:(strong(X)))=>((~humble(lucy)<~>~quiet(lucy))))&
((?[X]:((~humble(X)<~>curious(X))))<=>(?[X]:((kind(X)|~generous(X)))))&
((brave(susan)|~old(susan)))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:(~patient(X)))&
((~generous(alice)|~brave(alice)))&
((~kind(paul)|~old(paul))) | ~happy(susan) | [] | null | 0 |
If someone is not kind then someone is not happy or calm.
Everyone who is either not generous or not tall is either quiet or not patient.
Everyone who is both not calm and not rich is quiet.
If paul is tall then someone is either not creative or not happy and vice versa.
Everyone who is not funny is either not funny or not quiet and vice versa.
If lucy is quiet or wise then someone is either not patient or not old and vice versa.
If someone is wise then someone is calm or not wise and vice versa.
If someone is funny or not wise then someone is both generous and creative.
Everyone who is either not strong or calm is both not old and not kind.
If lucy is rich then someone is both not creative and not strong.
If lucy is not happy or brave then someone is not old or not tall and vice versa.
If someone is tall then someone is generous and vice versa.
Everyone who is calm is either not tall or not creative.
If someone is not tall then someone is both not old and not generous.
Everyone who is not tall is funny or not curious.
If alice is patient then someone is both patient and calm.
Someone is both not kind and rich.
Someone is not rich or not tall.
Mary is kind or not tall.
Someone is not happy or not generous.
Someone is either not old or not wise.
Someone is both strong and not kind.
John is both not rich and creative.
Lucy is either happy or not strong. | Lucy is funny. | neutral | ((?[X]:(~kind(X)))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((~generous(X)<~>~tall(X))=>(quiet(X)<~>~patient(X))))&
(![X]:((~calm(X)&~rich(X))=>quiet(X)))&
((tall(paul))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
(![X]:(~funny(X)<=>(~funny(X)<~>~quiet(X))))&
(((quiet(lucy)|wise(lucy)))<=>(?[X]:((~patient(X)<~>~old(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((calm(X)|~wise(X)))))&
((?[X]:((funny(X)|~wise(X))))=>(?[X]:((generous(X)&creative(X)))))&
(![X]:((~strong(X)<~>calm(X))=>(~old(X)&~kind(X))))&
((rich(lucy))=>(?[X]:((~creative(X)&~strong(X)))))&
(((~happy(lucy)|brave(lucy)))<=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:(tall(X)))<=>(?[X]:(generous(X))))&
(![X]:(calm(X)=>(~tall(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~old(X)&~generous(X)))))&
(![X]:(~tall(X)=>(funny(X)|~curious(X))))&
((patient(alice))=>(?[X]:((patient(X)&calm(X)))))&
(?[X]:((~kind(X)&rich(X))))&
(?[X]:((~rich(X)|~tall(X))))&
((kind(mary)|~tall(mary)))&
(?[X]:((~happy(X)|~generous(X))))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:((strong(X)&~kind(X))))&
((~rich(john)&creative(john)))&
((happy(lucy)<~>~strong(lucy))) | funny(lucy) | [] | null | 0 |
Everyone who is either not generous or funny is both not quiet and not creative and vice versa.
Everyone who is rich or not funny is either creative or not funny.
Everyone who is curious is tall and vice versa.
If someone is either calm or not strong then fred is not creative or curious and vice versa.
Everyone who is either creative or quiet is not patient or not rich and vice versa.
If someone is both old and quiet then someone is both tall and not kind.
If someone is either generous or not wise then mary is not happy and vice versa.
Everyone who is not wise or not rich is kind and vice versa.
If alice is creative or not generous then paul is not rich.
Everyone who is both not happy and not humble is not happy.
Everyone who is both creative and not funny is not strong.
Everyone who is not calm or not old is both not patient and creative and vice versa.
If fred is not humble then john is old or curious.
If someone is either not patient or rich then someone is humble.
Everyone who is not curious is both not kind and brave.
Everyone who is either strong or kind is both strong and patient.
Someone is not strong or not kind.
Someone is either not humble or happy.
Alice is either not generous or not old.
Someone is wise.
John is not rich or not tall.
Lucy is both not humble and not wise.
Someone is either not curious or happy.
Fred is brave. | Paul is not strong. | contradiction | (![X]:((~generous(X)<~>funny(X))<=>(~quiet(X)&~creative(X))))&
(![X]:((rich(X)|~funny(X))=>(creative(X)<~>~funny(X))))&
(![X]:(curious(X)<=>tall(X)))&
((?[X]:((calm(X)<~>~strong(X))))<=>((~creative(fred)|curious(fred))))&
(![X]:((creative(X)<~>quiet(X))<=>(~patient(X)|~rich(X))))&
((?[X]:((old(X)&quiet(X))))=>(?[X]:((tall(X)&~kind(X)))))&
((?[X]:((generous(X)<~>~wise(X))))<=>(~happy(mary)))&
(![X]:((~wise(X)|~rich(X))<=>kind(X)))&
(((creative(alice)|~generous(alice)))=>(~rich(paul)))&
(![X]:((~happy(X)&~humble(X))=>~happy(X)))&
(![X]:((creative(X)&~funny(X))=>~strong(X)))&
(![X]:((~calm(X)|~old(X))<=>(~patient(X)&creative(X))))&
((~humble(fred))=>((old(john)|curious(john))))&
((?[X]:((~patient(X)<~>rich(X))))=>(?[X]:(humble(X))))&
(![X]:(~curious(X)=>(~kind(X)&brave(X))))&
(![X]:((strong(X)<~>kind(X))=>(strong(X)&patient(X))))&
(?[X]:((~strong(X)|~kind(X))))&
(?[X]:((~humble(X)<~>happy(X))))&
((~generous(alice)<~>~old(alice)))&
(?[X]:(wise(X)))&
((~rich(john)|~tall(john)))&
((~humble(lucy)&~wise(lucy)))&
(?[X]:((~curious(X)<~>happy(X))))&
(brave(fred)) | ~strong(paul) | [
"p7",
"p8",
"p11",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5962562502797120564634536
% SZS output start Proof for 5962562502797120564634536
8. ! [X0] : ((~rich(X0) | ~wise(X0)) <=> kind(X0)) [input p7]
9. (~generous(alice) | creative(alice)) => ~rich(paul) [input p8]
12. ! [X0] : ((~old(X0) | ~calm(X0)) <=> (creative(X0) & ~patient(X0))) [input p11]
16. ! [X0] : ((strong(X0) <~> kind(X0)) => (patient(X0) & strong(X0))) [input p15]
19. ~generous(alice) <~> ~old(alice) [input p18]
25. ~strong(paul) [input hypothesis]
32. ~rich(paul) | (generous(alice) & ~creative(alice)) [ennf transformation 9]
41. ! [X0] : ((patient(X0) & strong(X0)) | (strong(X0) <=> kind(X0))) [ennf transformation 16]
60. ! [X0] : (((~rich(X0) | ~wise(X0)) | ~kind(X0)) & (kind(X0) | (rich(X0) & wise(X0)))) [nnf transformation 8]
61. ! [X0] : ((~rich(X0) | ~wise(X0) | ~kind(X0)) & (kind(X0) | (rich(X0) & wise(X0)))) [flattening 60]
62. ! [X0] : (((~old(X0) | ~calm(X0)) | (~creative(X0) | patient(X0))) & ((creative(X0) & ~patient(X0)) | (old(X0) & calm(X0)))) [nnf transformation 12]
63. ! [X0] : ((~old(X0) | ~calm(X0) | ~creative(X0) | patient(X0)) & ((creative(X0) & ~patient(X0)) | (old(X0) & calm(X0)))) [flattening 62]
68. ! [X0] : ((patient(X0) & strong(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) [nnf transformation 41]
74. (old(alice) | generous(alice)) & (~old(alice) | ~generous(alice)) [nnf transformation 19]
111. kind(X0) | rich(X0) [cnf transformation 61]
113. ~rich(paul) | ~creative(alice) [cnf transformation 32]
114. ~rich(paul) | generous(alice) [cnf transformation 32]
120. old(X0) | creative(X0) [cnf transformation 63]
127. strong(X0) | strong(X0) | ~kind(X0) [cnf transformation 68]
133. ~old(alice) | ~generous(alice) [cnf transformation 74]
141. ~strong(paul) [cnf transformation 25]
142. ~kind(X0) | strong(X0) [duplicate literal removal 127]
208. 15 <=> generous(alice) [avatar definition]
212. 16 <=> rich(paul) [avatar definition]
214. ~rich(paul) <- (~16) [avatar component clause 212]
215. 15 | ~16 [avatar split clause 114,212,208]
217. 17 <=> creative(alice) [avatar definition]
220. ~17 | ~16 [avatar split clause 113,212,217]
258. 26 <=> old(alice) [avatar definition]
259. ~old(alice) <- (~26) [avatar component clause 258]
262. ~15 | ~26 [avatar split clause 133,258,208]
286. creative(alice) <- (~26) [resolution 120,259]
287. 17 | 26 [avatar split clause 286,258,217]
292. strong(X0) | rich(X0) [resolution 142,111]
468. rich(paul) [resolution 292,141]
471. $false <- (~16) [subsumption resolution 468,214]
472. 16 [avatar contradiction clause 471]
473. $false [avatar sat refutation 215,220,262,287,472]
% SZS output end Proof for 5962562502797120564634536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not calm is either not funny or tall and vice versa.
Everyone who is happy is either not creative or generous and vice versa.
Everyone who is both not creative and not generous is curious.
If someone is both not funny and quiet then someone is both funny and creative and vice versa.
Everyone who is generous is either not tall or quiet.
Everyone who is both kind and not funny is not humble or rich and vice versa.
If someone is kind or not kind then mary is either not humble or quiet and vice versa.
If lucy is old then alice is not funny.
Everyone who is not strong or humble is either not curious or not kind and vice versa.
Everyone who is quiet is generous or not humble and vice versa.
Everyone who is not old or not rich is not quiet and vice versa.
If someone is kind or not kind then mary is not tall or brave and vice versa.
If lucy is either not quiet or funny then mary is not funny.
Everyone who is either happy or brave is both not quiet and not rich.
Everyone who is both humble and not humble is both kind and creative.
Alice is not brave or funny.
Lucy is not kind or not brave.
Paul is both calm and not old.
Someone is creative or not generous.
Someone is humble or not calm.
Susan is strong. | Mary is generous. | entailment | (![X]:((~curious(X)<~>~calm(X))<=>(~funny(X)<~>tall(X))))&
(![X]:(happy(X)<=>(~creative(X)<~>generous(X))))&
(![X]:((~creative(X)&~generous(X))=>curious(X)))&
((?[X]:((~funny(X)&quiet(X))))<=>(?[X]:((funny(X)&creative(X)))))&
(![X]:(generous(X)=>(~tall(X)<~>quiet(X))))&
(![X]:((kind(X)&~funny(X))<=>(~humble(X)|rich(X))))&
((?[X]:((kind(X)|~kind(X))))<=>((~humble(mary)<~>quiet(mary))))&
((old(lucy))=>(~funny(alice)))&
(![X]:((~strong(X)|humble(X))<=>(~curious(X)<~>~kind(X))))&
(![X]:(quiet(X)<=>(generous(X)|~humble(X))))&
(![X]:((~old(X)|~rich(X))<=>~quiet(X)))&
((?[X]:((kind(X)|~kind(X))))<=>((~tall(mary)|brave(mary))))&
(((~quiet(lucy)<~>funny(lucy)))=>(~funny(mary)))&
(![X]:((happy(X)<~>brave(X))=>(~quiet(X)&~rich(X))))&
(![X]:((humble(X)&~humble(X))=>(kind(X)&creative(X))))&
((~brave(alice)|funny(alice)))&
((~kind(lucy)|~brave(lucy)))&
((calm(paul)&~old(paul)))&
(?[X]:((creative(X)|~generous(X))))&
(?[X]:((humble(X)|~calm(X))))&
(strong(susan)) | generous(mary) | [
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5260175652714357693196293
% SZS output start Proof for 5260175652714357693196293
7. ? [X0] : (~kind(X0) | kind(X0)) <=> (~humble(mary) <~> quiet(mary)) [input p6]
10. ! [X0] : (quiet(X0) <=> (~humble(X0) | generous(X0))) [input p9]
22. ~generous(mary) [input hypothesis]
42. (? [X0] : (~kind(X0) | kind(X0)) | ((~humble(mary) | ~quiet(mary)) & (quiet(mary) | humble(mary)))) & (((~quiet(mary) | humble(mary)) & (quiet(mary) | ~humble(mary))) | ! [X0] : (kind(X0) & ~kind(X0))) [nnf transformation 7]
43. (? [X0] : (~kind(X0) | kind(X0)) | ((~humble(mary) | ~quiet(mary)) & (quiet(mary) | humble(mary)))) & (((~quiet(mary) | humble(mary)) & (quiet(mary) | ~humble(mary))) | ! [X1] : (kind(X1) & ~kind(X1))) [rectify 42]
44. ? [X0] : (~kind(X0) | kind(X0)) => (~kind(sK2) | kind(sK2)) [choice axiom]
45. ((~kind(sK2) | kind(sK2)) | ((~humble(mary) | ~quiet(mary)) & (quiet(mary) | humble(mary)))) & (((~quiet(mary) | humble(mary)) & (quiet(mary) | ~humble(mary))) | ! [X1] : (kind(X1) & ~kind(X1))) [skolemisation 43,44]
48. ! [X0] : ((quiet(X0) | (humble(X0) & ~generous(X0))) & ((~humble(X0) | generous(X0)) | ~quiet(X0))) [nnf transformation 10]
49. ! [X0] : ((quiet(X0) | (humble(X0) & ~generous(X0))) & (~humble(X0) | generous(X0) | ~quiet(X0))) [flattening 48]
87. quiet(mary) | ~humble(mary) | ~kind(X1) [cnf transformation 45]
88. quiet(mary) | ~humble(mary) | kind(X1) [cnf transformation 45]
89. ~quiet(mary) | humble(mary) | ~kind(X1) [cnf transformation 45]
90. ~quiet(mary) | humble(mary) | kind(X1) [cnf transformation 45]
100. ~humble(X0) | generous(X0) | ~quiet(X0) [cnf transformation 49]
102. humble(X0) | quiet(X0) [cnf transformation 49]
125. ~generous(mary) [cnf transformation 22]
153. 7 <=> ! [X1] : kind(X1) [avatar definition]
154. kind(X1) <- (7) [avatar component clause 153]
156. 8 <=> humble(mary) [avatar definition]
157. ~humble(mary) <- (~8) [avatar component clause 156]
158. humble(mary) <- (8) [avatar component clause 156]
160. 9 <=> quiet(mary) [avatar definition]
162. ~quiet(mary) <- (~9) [avatar component clause 160]
163. 7 | 8 | ~9 [avatar split clause 90,160,156,153]
165. 10 <=> ! [X1] : ~kind(X1) [avatar definition]
166. ~kind(X1) <- (10) [avatar component clause 165]
167. 10 | 8 | ~9 [avatar split clause 89,160,156,165]
168. 7 | ~8 | 9 [avatar split clause 88,160,156,153]
169. 10 | ~8 | 9 [avatar split clause 87,160,156,165]
238. quiet(mary) <- (~8) [resolution 102,157]
239. $false <- (~8, ~9) [subsumption resolution 238,162]
240. 8 | 9 [avatar contradiction clause 239]
358. generous(mary) | ~quiet(mary) <- (8) [resolution 100,158]
360. ~quiet(mary) <- (8) [subsumption resolution 358,125]
368. ~9 | ~8 [avatar split clause 360,156,160]
369. $false <- (7, 10) [subsumption resolution 154,166]
370. ~7 | ~10 [avatar contradiction clause 369]
371. $false [avatar sat refutation 163,167,168,169,240,368,370]
% SZS output end Proof for 5260175652714357693196293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is strong or quiet and vice versa. Everyone who is quiet or tall is both creative and not quiet and vice versa. Everyone who is both not happy and not calm is either calm or not creative and vice versa. Everyone who is both rich and not tall is either not curious or wise. Everyone who is either happy or not funny is not humble and vice versa. Everyone who is both humble and creative is not quiet or funny. Everyone who is not calm or quiet is generous and vice versa. If someone is either curious or not old then someone is not patient or calm and vice versa. If someone is both calm and not quiet then someone is not rich and vice versa. If mary is either kind or not kind then someone is not patient or creative and vice versa. If someone is either not old or rich then susan is either rich or happy. Everyone who is either not curious or old is either quiet or not old. If paul is either tall or not calm then someone is humble or not quiet. Everyone who is both generous and strong is both not humble and not happy. Everyone who is not rich or strong is funny. Everyone who is both not rich and brave is tall and vice versa. Someone is strong. Mary is either happy or not quiet. Paul is either not happy or rich. Alice is both strong and not old. Lucy is both rich and not tall. Someone is both generous and rich. Paul is kind. Susan is both not happy and not calm. | Alice is not creative. | entailment | (![X]:(humble(X)<=>(strong(X)|quiet(X))))&
(![X]:((quiet(X)|tall(X))<=>(creative(X)&~quiet(X))))&
(![X]:((~happy(X)&~calm(X))<=>(calm(X)<~>~creative(X))))&
(![X]:((rich(X)&~tall(X))=>(~curious(X)<~>wise(X))))&
(![X]:((happy(X)<~>~funny(X))<=>~humble(X)))&
(![X]:((humble(X)&creative(X))=>(~quiet(X)|funny(X))))&
(![X]:((~calm(X)|quiet(X))<=>generous(X)))&
((?[X]:((curious(X)<~>~old(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
((?[X]:((calm(X)&~quiet(X))))<=>(?[X]:(~rich(X))))&
(((kind(mary)<~>~kind(mary)))<=>(?[X]:((~patient(X)|creative(X)))))&
((?[X]:((~old(X)<~>rich(X))))=>((rich(susan)<~>happy(susan))))&
(![X]:((~curious(X)<~>old(X))=>(quiet(X)<~>~old(X))))&
(((tall(paul)<~>~calm(paul)))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:((generous(X)&strong(X))=>(~humble(X)&~happy(X))))&
(![X]:((~rich(X)|strong(X))=>funny(X)))&
(![X]:((~rich(X)&brave(X))<=>tall(X)))&
(?[X]:(strong(X)))&
((happy(mary)<~>~quiet(mary)))&
((~happy(paul)<~>rich(paul)))&
((strong(alice)&~old(alice)))&
((rich(lucy)&~tall(lucy)))&
(?[X]:((generous(X)&rich(X))))&
(kind(paul))&
((~happy(susan)&~calm(susan))) | ~creative(alice) | [
"p0",
"p2",
"p4",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3244072955642372224900842
% SZS output start Proof for 3244072955642372224900842
1. ! [X0] : (humble(X0) <=> (quiet(X0) | strong(X0))) [input p0]
3. ! [X0] : ((~calm(X0) & ~happy(X0)) <=> (calm(X0) <~> ~creative(X0))) [input p2]
5. ! [X0] : ((happy(X0) <~> ~funny(X0)) <=> ~humble(X0)) [input p4]
15. ! [X0] : ((strong(X0) | ~rich(X0)) => funny(X0)) [input p14]
20. ~old(alice) & strong(alice) [input p19]
25. creative(alice) [input hypothesis]
37. ! [X0] : (funny(X0) | (~strong(X0) & rich(X0))) [ennf transformation 15]
38. ! [X0] : ((humble(X0) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | ~humble(X0))) [nnf transformation 1]
39. ! [X0] : ((humble(X0) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | ~humble(X0))) [flattening 38]
42. ! [X0] : (((~calm(X0) & ~happy(X0)) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) & (((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | (calm(X0) | happy(X0)))) [nnf transformation 3]
43. ! [X0] : (((~calm(X0) & ~happy(X0)) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) & (((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | calm(X0) | happy(X0))) [flattening 42]
45. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | humble(X0)) & (~humble(X0) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [nnf transformation 5]
76. ~strong(X0) | humble(X0) [cnf transformation 39]
83. ~creative(X0) | calm(X0) | calm(X0) | happy(X0) [cnf transformation 43]
87. ~calm(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 43]
91. ~funny(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 45]
127. ~strong(X0) | funny(X0) [cnf transformation 37]
136. strong(alice) [cnf transformation 20]
145. creative(alice) [cnf transformation 25]
150. ~creative(X0) | calm(X0) | happy(X0) [duplicate literal removal 83]
151. ~calm(X0) | ~creative(X0) [duplicate literal removal 87]
154. ~creative(X0) | happy(X0) [subsumption resolution 150,151]
254. humble(alice) [resolution 76,136]
256. funny(alice) [resolution 127,136]
261. happy(alice) [resolution 154,145]
274. ~humble(alice) | ~happy(alice) [resolution 91,256]
276. ~happy(alice) [subsumption resolution 274,254]
277. $false [subsumption resolution 276,261]
% SZS output end Proof for 3244072955642372224900842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or wise is both old and not rich. Everyone who is not humble or quiet is not humble. Everyone who is not kind is both old and funny and vice versa. If susan is not tall or tall then someone is funny or kind. If someone is rich or not wise then john is not funny or not humble and vice versa. Everyone who is both calm and not creative is either not funny or not strong and vice versa. If john is either rich or not funny then someone is not old or not humble and vice versa. Everyone who is not patient is both calm and generous and vice versa. Everyone who is both not curious and funny is either not humble or happy and vice versa. Everyone who is both not patient and not strong is either not tall or funny. If john is both not rich and curious then someone is both kind and not strong. Everyone who is brave or humble is not old and vice versa. If someone is wise then someone is both creative and old and vice versa. Everyone who is both rich and tall is either patient or not curious. If alice is either creative or generous then paul is calm or not calm and vice versa. Everyone who is calm is not humble or not brave and vice versa. Someone is funny or not calm. Someone is funny. Someone is kind or not brave. Someone is generous or quiet. Someone is both not funny and old. Susan is calm or wise. Alice is not calm. | Alice is not wise. | entailment | (![X]:((~patient(X)|wise(X))=>(old(X)&~rich(X))))&
(![X]:((~humble(X)|quiet(X))=>~humble(X)))&
(![X]:(~kind(X)<=>(old(X)&funny(X))))&
(((~tall(susan)|tall(susan)))=>(?[X]:((funny(X)|kind(X)))))&
((?[X]:((rich(X)|~wise(X))))<=>((~funny(john)|~humble(john))))&
(![X]:((calm(X)&~creative(X))<=>(~funny(X)<~>~strong(X))))&
(((rich(john)<~>~funny(john)))<=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:(~patient(X)<=>(calm(X)&generous(X))))&
(![X]:((~curious(X)&funny(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((~patient(X)&~strong(X))=>(~tall(X)<~>funny(X))))&
(((~rich(john)&curious(john)))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((brave(X)|humble(X))<=>~old(X)))&
((?[X]:(wise(X)))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:((rich(X)&tall(X))=>(patient(X)<~>~curious(X))))&
(((creative(alice)<~>generous(alice)))<=>((calm(paul)|~calm(paul))))&
(![X]:(calm(X)<=>(~humble(X)|~brave(X))))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:((generous(X)|quiet(X))))&
(?[X]:((~funny(X)&old(X))))&
((calm(susan)|wise(susan)))&
(~calm(alice)) | ~wise(alice) | [
"p0",
"p11",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4092647975269796828215365
% SZS output start Proof for 4092647975269796828215365
1. ! [X0] : ((wise(X0) | ~patient(X0)) => (~rich(X0) & old(X0))) [input p0]
12. ! [X0] : ((humble(X0) | brave(X0)) <=> ~old(X0)) [input p11]
16. ! [X0] : (calm(X0) <=> (~brave(X0) | ~humble(X0))) [input p15]
23. ~calm(alice) [input p22]
24. wise(alice) [input hypothesis]
27. ! [X0] : ((~rich(X0) & old(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 1]
58. ! [X0] : (((humble(X0) | brave(X0)) | old(X0)) & (~old(X0) | (~humble(X0) & ~brave(X0)))) [nnf transformation 12]
59. ! [X0] : ((humble(X0) | brave(X0) | old(X0)) & (~old(X0) | (~humble(X0) & ~brave(X0)))) [flattening 58]
68. ! [X0] : ((calm(X0) | (brave(X0) & humble(X0))) & ((~brave(X0) | ~humble(X0)) | ~calm(X0))) [nnf transformation 16]
69. ! [X0] : ((calm(X0) | (brave(X0) & humble(X0))) & (~brave(X0) | ~humble(X0) | ~calm(X0))) [flattening 68]
81. ~wise(X0) | old(X0) [cnf transformation 27]
119. ~humble(X0) | ~old(X0) [cnf transformation 59]
133. calm(X0) | humble(X0) [cnf transformation 69]
142. ~calm(alice) [cnf transformation 23]
143. wise(alice) [cnf transformation 24]
296. old(alice) [resolution 81,143]
300. humble(alice) [resolution 133,142]
304. ~old(alice) [resolution 300,119]
305. $false [subsumption resolution 304,296]
% SZS output end Proof for 4092647975269796828215365
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not patient is not kind or not brave and vice versa.
If someone is both generous and creative then fred is either not old or not funny.
Everyone who is patient is either strong or generous.
Everyone who is both curious and patient is both wise and patient and vice versa.
Everyone who is brave is either old or not generous.
If someone is brave then susan is both generous and not wise and vice versa.
Everyone who is not patient or creative is both not tall and not wise and vice versa.
If someone is either brave or calm then someone is either not happy or not rich.
If someone is humble or not wise then someone is not patient.
If susan is both strong and not generous then someone is brave.
If someone is brave or kind then someone is not humble or not curious.
If fred is either not kind or wise then susan is both patient and not humble.
Everyone who is both not old and wise is both not happy and not curious and vice versa.
Everyone who is either not rich or not patient is either not quiet or not curious.
If someone is tall then someone is old and vice versa.
Everyone who is both not calm and not humble is either curious or not wise and vice versa.
Someone is kind or creative.
Someone is both not funny and happy.
Someone is not happy.
Mary is both brave and tall.
Someone is not patient.
Someone is generous.
Mary is either not rich or not calm.
Susan is either generous or happy. | Susan is not patient. | entailment | (![X]:((wise(X)&~patient(X))<=>(~kind(X)|~brave(X))))&
((?[X]:((generous(X)&creative(X))))=>((~old(fred)<~>~funny(fred))))&
(![X]:(patient(X)=>(strong(X)<~>generous(X))))&
(![X]:((curious(X)&patient(X))<=>(wise(X)&patient(X))))&
(![X]:(brave(X)=>(old(X)<~>~generous(X))))&
((?[X]:(brave(X)))<=>((generous(susan)&~wise(susan))))&
(![X]:((~patient(X)|creative(X))<=>(~tall(X)&~wise(X))))&
((?[X]:((brave(X)<~>calm(X))))=>(?[X]:((~happy(X)<~>~rich(X)))))&
((?[X]:((humble(X)|~wise(X))))=>(?[X]:(~patient(X))))&
(((strong(susan)&~generous(susan)))=>(?[X]:(brave(X))))&
((?[X]:((brave(X)|kind(X))))=>(?[X]:((~humble(X)|~curious(X)))))&
(((~kind(fred)<~>wise(fred)))=>((patient(susan)&~humble(susan))))&
(![X]:((~old(X)&wise(X))<=>(~happy(X)&~curious(X))))&
(![X]:((~rich(X)<~>~patient(X))=>(~quiet(X)<~>~curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:(old(X))))&
(![X]:((~calm(X)&~humble(X))<=>(curious(X)<~>~wise(X))))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:((~funny(X)&happy(X))))&
(?[X]:(~happy(X)))&
((brave(mary)&tall(mary)))&
(?[X]:(~patient(X)))&
(?[X]:(generous(X)))&
((~rich(mary)<~>~calm(mary)))&
((generous(susan)<~>happy(susan))) | ~patient(susan) | [
"p0",
"p3",
"p4",
"p5",
"p12",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3450333193935861830397341
% SZS output start Proof for 3450333193935861830397341
1. ! [X0] : ((~patient(X0) & wise(X0)) <=> (~brave(X0) | ~kind(X0))) [input p0]
4. ! [X0] : ((patient(X0) & curious(X0)) <=> (patient(X0) & wise(X0))) [input p3]
5. ! [X0] : (brave(X0) => (old(X0) <~> ~generous(X0))) [input p4]
6. ? [X0] : brave(X0) <=> (~wise(susan) & generous(susan)) [input p5]
13. ! [X0] : ((wise(X0) & ~old(X0)) <=> (~curious(X0) & ~happy(X0))) [input p12]
20. tall(mary) & brave(mary) [input p19]
24. generous(susan) <~> happy(susan) [input p23]
25. patient(susan) [input hypothesis]
32. ! [X0] : ((old(X0) <~> ~generous(X0)) | ~brave(X0)) [ennf transformation 5]
40. ! [X0] : (((~patient(X0) & wise(X0)) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | (patient(X0) | ~wise(X0)))) [nnf transformation 1]
41. ! [X0] : (((~patient(X0) & wise(X0)) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | patient(X0) | ~wise(X0))) [flattening 40]
44. ! [X0] : (((patient(X0) & curious(X0)) | (~patient(X0) | ~wise(X0))) & ((patient(X0) & wise(X0)) | (~patient(X0) | ~curious(X0)))) [nnf transformation 4]
45. ! [X0] : (((patient(X0) & curious(X0)) | ~patient(X0) | ~wise(X0)) & ((patient(X0) & wise(X0)) | ~patient(X0) | ~curious(X0))) [flattening 44]
46. ! [X0] : (((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | ~brave(X0)) [nnf transformation 32]
47. (? [X0] : brave(X0) | (wise(susan) | ~generous(susan))) & ((~wise(susan) & generous(susan)) | ! [X0] : ~brave(X0)) [nnf transformation 6]
48. (? [X0] : brave(X0) | wise(susan) | ~generous(susan)) & ((~wise(susan) & generous(susan)) | ! [X0] : ~brave(X0)) [flattening 47]
49. (? [X0] : brave(X0) | wise(susan) | ~generous(susan)) & ((~wise(susan) & generous(susan)) | ! [X1] : ~brave(X1)) [rectify 48]
50. ? [X0] : brave(X0) => brave(sK0) [choice axiom]
51. (brave(sK0) | wise(susan) | ~generous(susan)) & ((~wise(susan) & generous(susan)) | ! [X1] : ~brave(X1)) [skolemisation 49,50]
67. ! [X0] : (((wise(X0) & ~old(X0)) | (curious(X0) | happy(X0))) & ((~curious(X0) & ~happy(X0)) | (~wise(X0) | old(X0)))) [nnf transformation 13]
68. ! [X0] : (((wise(X0) & ~old(X0)) | curious(X0) | happy(X0)) & ((~curious(X0) & ~happy(X0)) | ~wise(X0) | old(X0))) [flattening 67]
88. (~happy(susan) | ~generous(susan)) & (happy(susan) | generous(susan)) [nnf transformation 24]
93. ~patient(X0) | brave(X0) [cnf transformation 41]
98. ~curious(X0) | ~patient(X0) | wise(X0) [cnf transformation 45]
102. ~generous(X0) | old(X0) | ~brave(X0) [cnf transformation 46]
104. generous(susan) | ~brave(X1) [cnf transformation 51]
105. ~wise(susan) | ~brave(X1) [cnf transformation 51]
127. ~old(X0) | curious(X0) | happy(X0) [cnf transformation 68]
145. brave(mary) [cnf transformation 20]
152. ~happy(susan) | ~generous(susan) [cnf transformation 88]
153. patient(susan) [cnf transformation 25]
168. 4 <=> generous(susan) [avatar definition]
169. generous(susan) <- (4) [avatar component clause 168]
172. 5 <=> wise(susan) [avatar definition]
173. ~wise(susan) <- (~5) [avatar component clause 172]
181. 7 <=> ! [X1] : ~brave(X1) [avatar definition]
182. ~brave(X1) <- (7) [avatar component clause 181]
183. 7 | ~5 [avatar split clause 105,172,181]
184. 7 | 4 [avatar split clause 104,168,181]
251. 23 <=> patient(susan) [avatar definition]
253. patient(susan) <- (23) [avatar component clause 251]
291. 32 <=> happy(susan) [avatar definition]
293. ~happy(susan) <- (~32) [avatar component clause 291]
294. ~4 | ~32 [avatar split clause 152,291,168]
296. 23 [avatar split clause 153,251]
304. brave(susan) <- (23) [resolution 93,253]
380. old(susan) | ~brave(susan) <- (4) [resolution 102,169]
390. old(susan) <- (4, 23) [subsumption resolution 380,304]
425. curious(susan) | happy(susan) <- (4, 23) [resolution 127,390]
435. curious(susan) <- (4, 23, ~32) [subsumption resolution 425,293]
475. $false <- (7) [resolution 182,145]
478. ~7 [avatar contradiction clause 475]
560. ~patient(susan) | wise(susan) <- (4, 23, ~32) [resolution 435,98]
567. wise(susan) <- (4, 23, ~32) [subsumption resolution 560,253]
568. $false <- (4, ~5, 23, ~32) [subsumption resolution 567,173]
569. ~4 | 5 | ~23 | 32 [avatar contradiction clause 568]
570. $false [avatar sat refutation 183,184,294,296,478,569]
% SZS output end Proof for 3450333193935861830397341
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either humble or not rich then susan is not patient and vice versa.
If someone is not quiet or generous then alice is not happy or wise.
Everyone who is humble is calm.
Everyone who is patient is both strong and old.
If someone is both quiet and not quiet then someone is both wise and not curious and vice versa.
If susan is either strong or patient then john is calm.
If someone is both tall and not happy then alice is either not brave or not curious.
If someone is strong then someone is not funny.
Everyone who is not happy is both not creative and patient and vice versa.
Everyone who is both creative and not funny is both patient and not calm and vice versa.
Everyone who is either curious or not creative is kind and vice versa.
If alice is generous or funny then someone is either happy or strong.
Everyone who is both creative and not quiet is either calm or not tall.
Everyone who is both quiet and not creative is both generous and not rich and vice versa.
If someone is both brave and calm then paul is patient and vice versa.
If someone is either creative or calm then fred is both creative and strong and vice versa.
Paul is strong.
Someone is either not patient or creative.
John is either not patient or not humble.
Lucy is tall.
Lucy is either rich or curious.
Susan is both happy and not rich.
Lucy is creative.
Someone is not tall or curious. | Susan is not calm. | neutral | ((?[X]:((humble(X)<~>~rich(X))))<=>(~patient(susan)))&
((?[X]:((~quiet(X)|generous(X))))=>((~happy(alice)|wise(alice))))&
(![X]:(humble(X)=>calm(X)))&
(![X]:(patient(X)=>(strong(X)&old(X))))&
((?[X]:((quiet(X)&~quiet(X))))<=>(?[X]:((wise(X)&~curious(X)))))&
(((strong(susan)<~>patient(susan)))=>(calm(john)))&
((?[X]:((tall(X)&~happy(X))))=>((~brave(alice)<~>~curious(alice))))&
((?[X]:(strong(X)))=>(?[X]:(~funny(X))))&
(![X]:(~happy(X)<=>(~creative(X)&patient(X))))&
(![X]:((creative(X)&~funny(X))<=>(patient(X)&~calm(X))))&
(![X]:((curious(X)<~>~creative(X))<=>kind(X)))&
(((generous(alice)|funny(alice)))=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:((creative(X)&~quiet(X))=>(calm(X)<~>~tall(X))))&
(![X]:((quiet(X)&~creative(X))<=>(generous(X)&~rich(X))))&
((?[X]:((brave(X)&calm(X))))<=>(patient(paul)))&
((?[X]:((creative(X)<~>calm(X))))<=>((creative(fred)&strong(fred))))&
(strong(paul))&
(?[X]:((~patient(X)<~>creative(X))))&
((~patient(john)<~>~humble(john)))&
(tall(lucy))&
((rich(lucy)<~>curious(lucy)))&
((happy(susan)&~rich(susan)))&
(creative(lucy))&
(?[X]:((~tall(X)|curious(X)))) | ~calm(susan) | [] | null | 0 |
Everyone who is not strong or not quiet is brave and vice versa.
Everyone who is either humble or not strong is both generous and funny.
Everyone who is either not happy or rich is not generous or happy and vice versa.
Everyone who is both creative and not generous is rich.
If paul is both not strong and quiet then susan is brave or not humble and vice versa.
If someone is quiet then someone is not creative.
If paul is not calm then fred is either not curious or not happy and vice versa.
Everyone who is not quiet or not funny is either funny or not happy.
If susan is either creative or generous then fred is both wise and happy and vice versa.
Everyone who is either kind or not rich is quiet.
If someone is either rich or not funny then susan is both happy and not brave.
Everyone who is either not brave or not kind is both old and not wise.
Everyone who is not wise or strong is both not kind and rich and vice versa.
Everyone who is patient is either strong or wise.
If john is both quiet and not calm then someone is kind and vice versa.
If lucy is not calm or not creative then someone is not generous or patient and vice versa.
Susan is kind.
Someone is either tall or not creative.
Someone is humble or funny.
Someone is strong.
Lucy is not generous. | Paul is not patient. | neutral | (![X]:((~strong(X)|~quiet(X))<=>brave(X)))&
(![X]:((humble(X)<~>~strong(X))=>(generous(X)&funny(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~generous(X)|happy(X))))&
(![X]:((creative(X)&~generous(X))=>rich(X)))&
(((~strong(paul)&quiet(paul)))<=>((brave(susan)|~humble(susan))))&
((?[X]:(quiet(X)))=>(?[X]:(~creative(X))))&
((~calm(paul))<=>((~curious(fred)<~>~happy(fred))))&
(![X]:((~quiet(X)|~funny(X))=>(funny(X)<~>~happy(X))))&
(((creative(susan)<~>generous(susan)))<=>((wise(fred)&happy(fred))))&
(![X]:((kind(X)<~>~rich(X))=>quiet(X)))&
((?[X]:((rich(X)<~>~funny(X))))=>((happy(susan)&~brave(susan))))&
(![X]:((~brave(X)<~>~kind(X))=>(old(X)&~wise(X))))&
(![X]:((~wise(X)|strong(X))<=>(~kind(X)&rich(X))))&
(![X]:(patient(X)=>(strong(X)<~>wise(X))))&
(((quiet(john)&~calm(john)))<=>(?[X]:(kind(X))))&
(((~calm(lucy)|~creative(lucy)))<=>(?[X]:((~generous(X)|patient(X)))))&
(kind(susan))&
(?[X]:((tall(X)<~>~creative(X))))&
(?[X]:((humble(X)|funny(X))))&
(?[X]:(strong(X)))&
(~generous(lucy)) | ~patient(paul) | [] | null | 0 |
Everyone who is not brave or funny is either happy or not generous and vice versa. Everyone who is both happy and generous is not tall or not humble and vice versa. If mary is either not wise or quiet then someone is not old or not humble and vice versa. If someone is not brave or happy then someone is not curious and vice versa. Everyone who is rich is not generous and vice versa. If someone is not rich or curious then someone is patient and vice versa. Everyone who is either creative or not patient is happy or not kind and vice versa. If someone is both not quiet and not wise then someone is humble or strong. If alice is both not creative and funny then lucy is creative and vice versa. Everyone who is not patient or rich is humble and vice versa. Everyone who is not quiet is either patient or calm and vice versa. If someone is not patient then someone is both rich and funny. If someone is funny then someone is old or not calm. If fred is either not generous or not humble then alice is not brave. Everyone who is patient is both curious and not brave and vice versa. Everyone who is either not old or brave is brave. Someone is either not calm or not rich. Susan is either not creative or rich. Someone is both not kind and curious. Fred is happy. Someone is generous or not funny. Someone is not kind. Someone is both generous and not creative. Someone is both not patient and strong. | Susan is humble. | entailment | (![X]:((~brave(X)|funny(X))<=>(happy(X)<~>~generous(X))))&
(![X]:((happy(X)&generous(X))<=>(~tall(X)|~humble(X))))&
(((~wise(mary)<~>quiet(mary)))<=>(?[X]:((~old(X)|~humble(X)))))&
((?[X]:((~brave(X)|happy(X))))<=>(?[X]:(~curious(X))))&
(![X]:(rich(X)<=>~generous(X)))&
((?[X]:((~rich(X)|curious(X))))<=>(?[X]:(patient(X))))&
(![X]:((creative(X)<~>~patient(X))<=>(happy(X)|~kind(X))))&
((?[X]:((~quiet(X)&~wise(X))))=>(?[X]:((humble(X)|strong(X)))))&
(((~creative(alice)&funny(alice)))<=>(creative(lucy)))&
(![X]:((~patient(X)|rich(X))<=>humble(X)))&
(![X]:(~quiet(X)<=>(patient(X)<~>calm(X))))&
((?[X]:(~patient(X)))=>(?[X]:((rich(X)&funny(X)))))&
((?[X]:(funny(X)))=>(?[X]:((old(X)|~calm(X)))))&
(((~generous(fred)<~>~humble(fred)))=>(~brave(alice)))&
(![X]:(patient(X)<=>(curious(X)&~brave(X))))&
(![X]:((~old(X)<~>brave(X))=>brave(X)))&
(?[X]:((~calm(X)<~>~rich(X))))&
((~creative(susan)<~>rich(susan)))&
(?[X]:((~kind(X)&curious(X))))&
(happy(fred))&
(?[X]:((generous(X)|~funny(X))))&
(?[X]:(~kind(X)))&
(?[X]:((generous(X)&~creative(X))))&
(?[X]:((~patient(X)&strong(X)))) | humble(susan) | [
"p1",
"p4",
"p6",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 584351251723410670189092
% SZS output start Proof for 584351251723410670189092
2. ! [X0] : ((generous(X0) & happy(X0)) <=> (~humble(X0) | ~tall(X0))) [input p1]
5. ! [X0] : (rich(X0) <=> ~generous(X0)) [input p4]
7. ! [X0] : ((creative(X0) <~> ~patient(X0)) <=> (~kind(X0) | happy(X0))) [input p6]
10. ! [X0] : ((rich(X0) | ~patient(X0)) <=> humble(X0)) [input p9]
18. ~creative(susan) <~> rich(susan) [input p17]
25. ~humble(susan) [input hypothesis]
39. ! [X0] : (((generous(X0) & happy(X0)) | (humble(X0) & tall(X0))) & ((~humble(X0) | ~tall(X0)) | (~generous(X0) | ~happy(X0)))) [nnf transformation 2]
40. ! [X0] : (((generous(X0) & happy(X0)) | (humble(X0) & tall(X0))) & (~humble(X0) | ~tall(X0) | ~generous(X0) | ~happy(X0))) [flattening 39]
50. ! [X0] : ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))) [nnf transformation 5]
56. ! [X0] : ((((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0))))) [nnf transformation 7]
57. ! [X0] : ((((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0))))) [flattening 56]
60. ! [X0] : (((rich(X0) | ~patient(X0)) | ~humble(X0)) & (humble(X0) | (~rich(X0) & patient(X0)))) [nnf transformation 10]
61. ! [X0] : ((rich(X0) | ~patient(X0) | ~humble(X0)) & (humble(X0) | (~rich(X0) & patient(X0)))) [flattening 60]
76. (~rich(susan) | creative(susan)) & (rich(susan) | ~creative(susan)) [nnf transformation 18]
95. humble(X0) | happy(X0) [cnf transformation 40]
97. humble(X0) | generous(X0) [cnf transformation 40]
107. ~rich(X0) | ~generous(X0) [cnf transformation 50]
114. ~patient(X0) | creative(X0) | ~happy(X0) [cnf transformation 57]
121. patient(X0) | humble(X0) [cnf transformation 61]
140. rich(susan) | ~creative(susan) [cnf transformation 76]
150. ~humble(susan) [cnf transformation 25]
295. 33 <=> creative(susan) [avatar definition]
296. ~creative(susan) <- (~33) [avatar component clause 295]
299. 34 <=> rich(susan) [avatar definition]
300. rich(susan) <- (34) [avatar component clause 299]
303. ~33 | 34 [avatar split clause 140,299,295]
316. generous(susan) [resolution 97,150]
388. creative(X0) | ~happy(X0) | humble(X0) [resolution 114,121]
398. creative(X0) | humble(X0) [subsumption resolution 388,95]
624. humble(susan) <- (~33) [resolution 398,296]
626. $false <- (~33) [subsumption resolution 624,150]
627. 33 [avatar contradiction clause 626]
642. ~generous(susan) <- (34) [resolution 300,107]
645. $false <- (34) [subsumption resolution 642,316]
646. ~34 [avatar contradiction clause 645]
647. $false [avatar sat refutation 303,627,646]
% SZS output end Proof for 584351251723410670189092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or humble is wise and vice versa. If paul is both creative and not rich then someone is not old and vice versa. Everyone who is either not old or not curious is not funny. If someone is either not wise or not brave then alice is either not patient or not funny and vice versa. Everyone who is not kind or strong is both creative and happy and vice versa. Everyone who is either patient or rich is both humble and not quiet. If fred is both happy and not old then john is not generous or not tall and vice versa. If someone is either funny or not rich then alice is either not strong or not creative and vice versa. Everyone who is strong or not wise is not generous and vice versa. If lucy is both not curious and not rich then fred is not patient and vice versa. If someone is not strong then someone is curious and vice versa. Everyone who is calm is both calm and rich and vice versa. Everyone who is either not strong or strong is both kind and not happy and vice versa. If someone is both not generous and not quiet then someone is not humble. Everyone who is either curious or funny is calm and vice versa. Someone is humble. John is creative. Someone is either not calm or curious. Alice is not funny or patient. Someone is either not patient or not strong. Susan is not strong or not humble. Fred is either humble or old. | Alice is patient. | neutral | (![X]:((~old(X)|humble(X))<=>wise(X)))&
(((creative(paul)&~rich(paul)))<=>(?[X]:(~old(X))))&
(![X]:((~old(X)<~>~curious(X))=>~funny(X)))&
((?[X]:((~wise(X)<~>~brave(X))))<=>((~patient(alice)<~>~funny(alice))))&
(![X]:((~kind(X)|strong(X))<=>(creative(X)&happy(X))))&
(![X]:((patient(X)<~>rich(X))=>(humble(X)&~quiet(X))))&
(((happy(fred)&~old(fred)))<=>((~generous(john)|~tall(john))))&
((?[X]:((funny(X)<~>~rich(X))))<=>((~strong(alice)<~>~creative(alice))))&
(![X]:((strong(X)|~wise(X))<=>~generous(X)))&
(((~curious(lucy)&~rich(lucy)))<=>(~patient(fred)))&
((?[X]:(~strong(X)))<=>(?[X]:(curious(X))))&
(![X]:(calm(X)<=>(calm(X)&rich(X))))&
(![X]:((~strong(X)<~>strong(X))<=>(kind(X)&~happy(X))))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:(~humble(X))))&
(![X]:((curious(X)<~>funny(X))<=>calm(X)))&
(?[X]:(humble(X)))&
(creative(john))&
(?[X]:((~calm(X)<~>curious(X))))&
((~funny(alice)|patient(alice)))&
(?[X]:((~patient(X)<~>~strong(X))))&
((~strong(susan)|~humble(susan)))&
((humble(fred)<~>old(fred))) | patient(alice) | [] | null | 0 |
If someone is both not creative and generous then alice is both tall and not old.
Everyone who is rich or wise is not kind and vice versa.
Everyone who is both generous and not old is not patient or happy and vice versa.
Everyone who is both not curious and not rich is both not rich and not calm.
Everyone who is funny or old is rich and vice versa.
If someone is happy then someone is either curious or not creative.
Everyone who is both brave and not humble is both old and happy and vice versa.
If lucy is old then fred is not creative or wise and vice versa.
Everyone who is both kind and not kind is both not wise and happy and vice versa.
Everyone who is tall is not quiet and vice versa.
Everyone who is happy is tall.
Everyone who is both rich and humble is not creative or not generous and vice versa.
Everyone who is both generous and not creative is both patient and rich and vice versa.
Everyone who is not kind is not rich or humble and vice versa.
If fred is calm then alice is happy and vice versa.
Lucy is humble or quiet.
Lucy is either not tall or not creative.
Paul is not brave.
Susan is not wise or creative.
Someone is either not happy or humble.
Mary is humble or not generous.
Someone is both not quiet and not happy. | Lucy is calm. | neutral | ((?[X]:((~creative(X)&generous(X))))=>((tall(alice)&~old(alice))))&
(![X]:((rich(X)|wise(X))<=>~kind(X)))&
(![X]:((generous(X)&~old(X))<=>(~patient(X)|happy(X))))&
(![X]:((~curious(X)&~rich(X))=>(~rich(X)&~calm(X))))&
(![X]:((funny(X)|old(X))<=>rich(X)))&
((?[X]:(happy(X)))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((brave(X)&~humble(X))<=>(old(X)&happy(X))))&
((old(lucy))<=>((~creative(fred)|wise(fred))))&
(![X]:((kind(X)&~kind(X))<=>(~wise(X)&happy(X))))&
(![X]:(tall(X)<=>~quiet(X)))&
(![X]:(happy(X)=>tall(X)))&
(![X]:((rich(X)&humble(X))<=>(~creative(X)|~generous(X))))&
(![X]:((generous(X)&~creative(X))<=>(patient(X)&rich(X))))&
(![X]:(~kind(X)<=>(~rich(X)|humble(X))))&
((calm(fred))<=>(happy(alice)))&
((humble(lucy)|quiet(lucy)))&
((~tall(lucy)<~>~creative(lucy)))&
(~brave(paul))&
((~wise(susan)|creative(susan)))&
(?[X]:((~happy(X)<~>humble(X))))&
((humble(mary)|~generous(mary)))&
(?[X]:((~quiet(X)&~happy(X)))) | calm(lucy) | [] | null | 0 |
Everyone who is either not calm or creative is strong.
If someone is not calm then mary is both old and generous.
Everyone who is both rich and not curious is tall.
If someone is not curious or not strong then susan is either not tall or quiet.
If someone is either kind or not humble then john is either brave or not generous and vice versa.
If someone is funny or not old then someone is not quiet or not creative.
Everyone who is strong or quiet is either not humble or funny.
Everyone who is either old or strong is not old or not funny and vice versa.
If someone is either not happy or calm then lucy is not curious or generous and vice versa.
Everyone who is both humble and kind is both not old and happy and vice versa.
Everyone who is humble is patient and vice versa.
Everyone who is either quiet or not brave is either not strong or generous and vice versa.
If someone is not kind then someone is not brave.
If mary is quiet then john is both calm and not kind and vice versa.
Everyone who is either generous or funny is not generous or tall and vice versa.
If paul is tall then someone is either tall or calm and vice versa.
Someone is patient or not kind.
Someone is tall.
Lucy is both not brave and not funny.
Someone is both generous and not brave.
Someone is either not patient or curious.
Someone is humble or not calm.
Alice is both funny and not calm.
Someone is not happy or funny. | Lucy is patient. | contradiction | (![X]:((~calm(X)<~>creative(X))=>strong(X)))&
((?[X]:(~calm(X)))=>((old(mary)&generous(mary))))&
(![X]:((rich(X)&~curious(X))=>tall(X)))&
((?[X]:((~curious(X)|~strong(X))))=>((~tall(susan)<~>quiet(susan))))&
((?[X]:((kind(X)<~>~humble(X))))<=>((brave(john)<~>~generous(john))))&
((?[X]:((funny(X)|~old(X))))=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:((strong(X)|quiet(X))=>(~humble(X)<~>funny(X))))&
(![X]:((old(X)<~>strong(X))<=>(~old(X)|~funny(X))))&
((?[X]:((~happy(X)<~>calm(X))))<=>((~curious(lucy)|generous(lucy))))&
(![X]:((humble(X)&kind(X))<=>(~old(X)&happy(X))))&
(![X]:(humble(X)<=>patient(X)))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~brave(X))))&
((quiet(mary))<=>((calm(john)&~kind(john))))&
(![X]:((generous(X)<~>funny(X))<=>(~generous(X)|tall(X))))&
((tall(paul))<=>(?[X]:((tall(X)<~>calm(X)))))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:(tall(X)))&
((~brave(lucy)&~funny(lucy)))&
(?[X]:((generous(X)&~brave(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((humble(X)|~calm(X))))&
((funny(alice)&~calm(alice)))&
(?[X]:((~happy(X)|funny(X)))) | patient(lucy) | [
"p6",
"p7",
"p10",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7327383482700420836341162
% SZS output start Proof for 7327383482700420836341162
7. ! [X0] : ((quiet(X0) | strong(X0)) => (~humble(X0) <~> funny(X0))) [input p6]
8. ! [X0] : ((old(X0) <~> strong(X0)) <=> (~funny(X0) | ~old(X0))) [input p7]
11. ! [X0] : (humble(X0) <=> patient(X0)) [input p10]
12. ! [X0] : ((quiet(X0) <~> ~brave(X0)) <=> (~strong(X0) <~> generous(X0))) [input p11]
15. ! [X0] : ((generous(X0) <~> funny(X0)) <=> (tall(X0) | ~generous(X0))) [input p14]
19. ~funny(lucy) & ~brave(lucy) [input p18]
25. patient(lucy) [input hypothesis]
33. ! [X0] : ((~humble(X0) <~> funny(X0)) | (~quiet(X0) & ~strong(X0))) [ennf transformation 7]
44. ! [X0] : (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~quiet(X0) & ~strong(X0))) [nnf transformation 33]
45. ! [X0] : ((((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (funny(X0) & old(X0))) & ((~funny(X0) | ~old(X0)) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (funny(X0) & old(X0))) & (~funny(X0) | ~old(X0) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))))) [flattening 45]
54. ! [X0] : ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))) [nnf transformation 11]
55. ! [X0] : ((((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0))))) [nnf transformation 12]
61. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | (~tall(X0) & generous(X0))) & ((tall(X0) | ~generous(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [nnf transformation 15]
62. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | (~tall(X0) & generous(X0))) & (tall(X0) | ~generous(X0) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [flattening 61]
98. ~humble(X0) | funny(X0) | ~strong(X0) [cnf transformation 44]
99. ~humble(X0) | funny(X0) | ~quiet(X0) [cnf transformation 44]
102. ~funny(X0) | ~old(X0) | strong(X0) | ~old(X0) [cnf transformation 46]
104. strong(X0) | old(X0) | old(X0) [cnf transformation 46]
119. ~patient(X0) | humble(X0) [cnf transformation 54]
123. ~generous(X0) | strong(X0) | quiet(X0) | brave(X0) [cnf transformation 55]
134. funny(X0) | generous(X0) | generous(X0) [cnf transformation 62]
144. ~brave(lucy) [cnf transformation 19]
145. ~funny(lucy) [cnf transformation 19]
154. patient(lucy) [cnf transformation 25]
156. funny(X0) | generous(X0) [duplicate literal removal 134]
157. ~funny(X0) | ~old(X0) | strong(X0) [duplicate literal removal 102]
158. old(X0) | strong(X0) [duplicate literal removal 104]
236. ~funny(X0) | strong(X0) [subsumption resolution 157,158]
348. humble(lucy) [resolution 119,154]
355. generous(X0) | strong(X0) [resolution 236,156]
363. funny(lucy) | ~strong(lucy) [resolution 98,348]
364. ~strong(lucy) [subsumption resolution 363,145]
365. funny(lucy) | ~quiet(lucy) [resolution 99,348]
366. ~quiet(lucy) [subsumption resolution 365,145]
490. strong(X0) | quiet(X0) | brave(X0) | strong(X0) [resolution 123,355]
495. brave(X0) | quiet(X0) | strong(X0) [duplicate literal removal 490]
606. quiet(lucy) | strong(lucy) [resolution 495,144]
612. strong(lucy) [subsumption resolution 606,366]
613. $false [subsumption resolution 612,364]
% SZS output end Proof for 7327383482700420836341162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is happy then alice is either not funny or calm.
Everyone who is either not happy or happy is not funny or quiet.
Everyone who is either curious or not creative is wise or old.
Everyone who is both not happy and not strong is not funny or patient and vice versa.
If alice is either not humble or not wise then lucy is either not tall or tall.
Everyone who is either not strong or not rich is not kind or not old and vice versa.
Everyone who is not quiet is calm and vice versa.
Everyone who is funny or not curious is both not old and generous.
If john is either not funny or not kind then someone is generous or humble and vice versa.
If paul is funny or not happy then someone is both happy and brave.
Everyone who is both not curious and funny is either funny or tall.
Everyone who is either not humble or not patient is not rich or not tall.
If susan is either not generous or not patient then someone is kind or not wise and vice versa.
If someone is either not rich or not strong then someone is happy and vice versa.
If someone is quiet or curious then someone is wise or not humble.
Everyone who is patient is wise and vice versa.
Someone is quiet.
Someone is quiet or not curious.
Someone is humble or not quiet.
John is either curious or not curious.
Someone is generous or not wise.
Lucy is funny.
Someone is creative or not funny.
Alice is either not rich or not curious. | Lucy is not calm. | entailment | ((happy(lucy))=>((~funny(alice)<~>calm(alice))))&
(![X]:((~happy(X)<~>happy(X))=>(~funny(X)|quiet(X))))&
(![X]:((curious(X)<~>~creative(X))=>(wise(X)|old(X))))&
(![X]:((~happy(X)&~strong(X))<=>(~funny(X)|patient(X))))&
(((~humble(alice)<~>~wise(alice)))=>((~tall(lucy)<~>tall(lucy))))&
(![X]:((~strong(X)<~>~rich(X))<=>(~kind(X)|~old(X))))&
(![X]:(~quiet(X)<=>calm(X)))&
(![X]:((funny(X)|~curious(X))=>(~old(X)&generous(X))))&
(((~funny(john)<~>~kind(john)))<=>(?[X]:((generous(X)|humble(X)))))&
(((funny(paul)|~happy(paul)))=>(?[X]:((happy(X)&brave(X)))))&
(![X]:((~curious(X)&funny(X))=>(funny(X)<~>tall(X))))&
(![X]:((~humble(X)<~>~patient(X))=>(~rich(X)|~tall(X))))&
(((~generous(susan)<~>~patient(susan)))<=>(?[X]:((kind(X)|~wise(X)))))&
((?[X]:((~rich(X)<~>~strong(X))))<=>(?[X]:(happy(X))))&
((?[X]:((quiet(X)|curious(X))))=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:(patient(X)<=>wise(X)))&
(?[X]:(quiet(X)))&
(?[X]:((quiet(X)|~curious(X))))&
(?[X]:((humble(X)|~quiet(X))))&
((curious(john)<~>~curious(john)))&
(?[X]:((generous(X)|~wise(X))))&
(funny(lucy))&
(?[X]:((creative(X)|~funny(X))))&
((~rich(alice)<~>~curious(alice))) | ~calm(lucy) | [
"p1",
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8819756447549409259340490
% SZS output start Proof for 8819756447549409259340490
2. ! [X0] : ((~happy(X0) <~> happy(X0)) => (quiet(X0) | ~funny(X0))) [input p1]
7. ! [X0] : (~quiet(X0) <=> calm(X0)) [input p6]
22. funny(lucy) [input p21]
25. calm(lucy) [input hypothesis]
30. ! [X0] : ((quiet(X0) | ~funny(X0)) | (~happy(X0) <=> happy(X0))) [ennf transformation 2]
31. ! [X0] : (quiet(X0) | ~funny(X0) | (~happy(X0) <=> happy(X0))) [flattening 30]
43. ! [X0] : (quiet(X0) | ~funny(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 31]
50. ! [X0] : ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))) [nnf transformation 7]
86. quiet(X0) | ~funny(X0) | happy(X0) | happy(X0) [cnf transformation 43]
87. quiet(X0) | ~funny(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 43]
106. ~quiet(X0) | ~calm(X0) [cnf transformation 50]
143. funny(lucy) [cnf transformation 22]
147. calm(lucy) [cnf transformation 25]
149. quiet(X0) | ~funny(X0) | happy(X0) [duplicate literal removal 86]
150. quiet(X0) | ~funny(X0) | ~happy(X0) [duplicate literal removal 87]
165. ~funny(X0) | quiet(X0) [subsumption resolution 149,150]
350. quiet(lucy) [resolution 165,143]
353. ~calm(lucy) [resolution 350,106]
354. $false [subsumption resolution 353,147]
% SZS output end Proof for 8819756447549409259340490
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not calm or tall then someone is both brave and not humble and vice versa.
Everyone who is not humble is not wise.
If someone is strong then susan is humble or happy.
If fred is curious or happy then someone is old and vice versa.
If someone is both not funny and not patient then someone is both curious and not wise.
Everyone who is either patient or not humble is either tall or curious and vice versa.
If someone is both tall and not humble then someone is not creative and vice versa.
Everyone who is creative or not calm is both not quiet and quiet and vice versa.
Everyone who is humble or not calm is either not wise or not patient.
If john is either strong or not patient then susan is both strong and wise and vice versa.
If fred is not quiet or not generous then someone is not calm or not tall.
If mary is rich then someone is either tall or curious.
Everyone who is both not old and not humble is not calm.
Everyone who is both rich and curious is not wise or not brave.
If someone is humble then someone is either quiet or kind.
Everyone who is both wise and not kind is not quiet and vice versa.
Fred is generous or kind.
Fred is either kind or not humble.
Someone is either not funny or not quiet.
John is not tall or not patient.
Lucy is both not rich and not strong.
Someone is either not generous or not old.
Someone is not happy or rich.
Someone is both generous and funny. | Lucy is not calm. | contradiction | (((~calm(alice)|tall(alice)))<=>(?[X]:((brave(X)&~humble(X)))))&
(![X]:(~humble(X)=>~wise(X)))&
((?[X]:(strong(X)))=>((humble(susan)|happy(susan))))&
(((curious(fred)|happy(fred)))<=>(?[X]:(old(X))))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:((curious(X)&~wise(X)))))&
(![X]:((patient(X)<~>~humble(X))<=>(tall(X)<~>curious(X))))&
((?[X]:((tall(X)&~humble(X))))<=>(?[X]:(~creative(X))))&
(![X]:((creative(X)|~calm(X))<=>(~quiet(X)&quiet(X))))&
(![X]:((humble(X)|~calm(X))=>(~wise(X)<~>~patient(X))))&
(((strong(john)<~>~patient(john)))<=>((strong(susan)&wise(susan))))&
(((~quiet(fred)|~generous(fred)))=>(?[X]:((~calm(X)|~tall(X)))))&
((rich(mary))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:((~old(X)&~humble(X))=>~calm(X)))&
(![X]:((rich(X)&curious(X))=>(~wise(X)|~brave(X))))&
((?[X]:(humble(X)))=>(?[X]:((quiet(X)<~>kind(X)))))&
(![X]:((wise(X)&~kind(X))<=>~quiet(X)))&
((generous(fred)|kind(fred)))&
((kind(fred)<~>~humble(fred)))&
(?[X]:((~funny(X)<~>~quiet(X))))&
((~tall(john)|~patient(john)))&
((~rich(lucy)&~strong(lucy)))&
(?[X]:((~generous(X)<~>~old(X))))&
(?[X]:((~happy(X)|rich(X))))&
(?[X]:((generous(X)&funny(X)))) | ~calm(lucy) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5926421896973868536969161
% SZS output start Proof for 5926421896973868536969161
8. ! [X0] : ((~calm(X0) | creative(X0)) <=> (quiet(X0) & ~quiet(X0))) [input p7]
25. ~calm(lucy) [input hypothesis]
60. ! [X0] : (((~calm(X0) | creative(X0)) | (~quiet(X0) | quiet(X0))) & ((quiet(X0) & ~quiet(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 8]
61. ! [X0] : ((~calm(X0) | creative(X0) | ~quiet(X0) | quiet(X0)) & ((quiet(X0) & ~quiet(X0)) | (calm(X0) & ~creative(X0)))) [flattening 60]
111. ~quiet(X0) | calm(X0) [cnf transformation 61]
113. quiet(X0) | calm(X0) [cnf transformation 61]
149. ~calm(lucy) [cnf transformation 25]
238. calm(X0) [subsumption resolution 111,113]
352. $false [subsumption resolution 149,238]
% SZS output end Proof for 5926421896973868536969161
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then fred is brave.
If someone is both not wise and patient then someone is not funny or generous and vice versa.
Everyone who is brave or not brave is not brave and vice versa.
Everyone who is not quiet or not happy is both wise and strong.
Everyone who is not tall or creative is creative or not patient and vice versa.
Everyone who is both not rich and quiet is either not brave or not humble.
Everyone who is not patient is both quiet and not rich.
Everyone who is quiet is both tall and funny.
Everyone who is not patient is funny or generous.
If someone is either happy or wise then paul is either curious or patient and vice versa.
If alice is either not tall or creative then someone is humble and vice versa.
If someone is not rich or not humble then someone is humble or not kind and vice versa.
Everyone who is both not strong and not brave is not tall and vice versa.
Everyone who is wise or humble is patient or creative.
Everyone who is quiet or not quiet is both not calm and not wise and vice versa.
Everyone who is not tall is both not strong and creative and vice versa.
Someone is either not happy or not generous.
Someone is not old or old.
Fred is both not generous and creative. | Paul is not tall. | contradiction | ((?[X]:(generous(X)))=>(brave(fred)))&
((?[X]:((~wise(X)&patient(X))))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((brave(X)|~brave(X))<=>~brave(X)))&
(![X]:((~quiet(X)|~happy(X))=>(wise(X)&strong(X))))&
(![X]:((~tall(X)|creative(X))<=>(creative(X)|~patient(X))))&
(![X]:((~rich(X)&quiet(X))=>(~brave(X)<~>~humble(X))))&
(![X]:(~patient(X)=>(quiet(X)&~rich(X))))&
(![X]:(quiet(X)=>(tall(X)&funny(X))))&
(![X]:(~patient(X)=>(funny(X)|generous(X))))&
((?[X]:((happy(X)<~>wise(X))))<=>((curious(paul)<~>patient(paul))))&
(((~tall(alice)<~>creative(alice)))<=>(?[X]:(humble(X))))&
((?[X]:((~rich(X)|~humble(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~strong(X)&~brave(X))<=>~tall(X)))&
(![X]:((wise(X)|humble(X))=>(patient(X)|creative(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~calm(X)&~wise(X))))&
(![X]:(~tall(X)<=>(~strong(X)&creative(X))))&
(?[X]:((~happy(X)<~>~generous(X))))&
(?[X]:((~old(X)|old(X))))&
((~generous(fred)&creative(fred))) | ~tall(paul) | [
"p3",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 20987558170452255128423
% SZS output start Proof for 20987558170452255128423
4. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (strong(X0) & wise(X0))) [input p3]
8. ! [X0] : (quiet(X0) => (funny(X0) & tall(X0))) [input p7]
15. ! [X0] : ((~quiet(X0) | quiet(X0)) <=> (~wise(X0) & ~calm(X0))) [input p14]
20. ~tall(paul) [input hypothesis]
24. ! [X0] : ((strong(X0) & wise(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 4]
28. ! [X0] : ((funny(X0) & tall(X0)) | ~quiet(X0)) [ennf transformation 8]
58. ! [X0] : (((~quiet(X0) | quiet(X0)) | (wise(X0) | calm(X0))) & ((~wise(X0) & ~calm(X0)) | (quiet(X0) & ~quiet(X0)))) [nnf transformation 15]
59. ! [X0] : ((~quiet(X0) | quiet(X0) | wise(X0) | calm(X0)) & ((~wise(X0) & ~calm(X0)) | (quiet(X0) & ~quiet(X0)))) [flattening 58]
76. quiet(X0) | wise(X0) [cnf transformation 24]
88. ~quiet(X0) | tall(X0) [cnf transformation 28]
114. ~wise(X0) | ~quiet(X0) [cnf transformation 59]
115. ~wise(X0) | quiet(X0) [cnf transformation 59]
125. ~tall(paul) [cnf transformation 20]
245. quiet(X0) [subsumption resolution 115,76]
246. ~wise(X0) [subsumption resolution 114,245]
261. tall(X1) | wise(X1) [resolution 88,76]
263. tall(X1) [subsumption resolution 261,246]
264. $false [resolution 263,125]
% SZS output end Proof for 20987558170452255128423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not quiet and not happy is either kind or not generous and vice versa.
Everyone who is not brave is not creative and vice versa.
Everyone who is either not calm or happy is brave and vice versa.
If mary is not patient or not creative then someone is both not curious and not humble.
If alice is not brave or not funny then lucy is either not patient or curious.
Everyone who is creative or funny is both humble and strong and vice versa.
Everyone who is brave or not curious is both tall and not curious and vice versa.
If someone is calm then someone is both not curious and not calm.
If someone is both wise and generous then someone is either happy or not strong.
Everyone who is humble is either not patient or wise.
If someone is not kind then susan is both tall and not funny and vice versa.
Everyone who is either strong or not brave is kind.
If someone is happy then lucy is humble or not creative.
If mary is not brave or not funny then fred is either happy or wise and vice versa.
If someone is either wise or not funny then susan is not humble or not curious.
If someone is brave then susan is both old and not quiet and vice versa.
Susan is not kind.
Someone is both not brave and kind.
Someone is both happy and not calm.
Someone is both not generous and not calm.
Someone is both not old and not patient.
John is generous.
Someone is either not funny or not curious.
John is not calm. | Susan is funny. | contradiction | (![X]:((~quiet(X)&~happy(X))<=>(kind(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((~calm(X)<~>happy(X))<=>brave(X)))&
(((~patient(mary)|~creative(mary)))=>(?[X]:((~curious(X)&~humble(X)))))&
(((~brave(alice)|~funny(alice)))=>((~patient(lucy)<~>curious(lucy))))&
(![X]:((creative(X)|funny(X))<=>(humble(X)&strong(X))))&
(![X]:((brave(X)|~curious(X))<=>(tall(X)&~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(humble(X)=>(~patient(X)<~>wise(X))))&
((?[X]:(~kind(X)))<=>((tall(susan)&~funny(susan))))&
(![X]:((strong(X)<~>~brave(X))=>kind(X)))&
((?[X]:(happy(X)))=>((humble(lucy)|~creative(lucy))))&
(((~brave(mary)|~funny(mary)))<=>((happy(fred)<~>wise(fred))))&
((?[X]:((wise(X)<~>~funny(X))))=>((~humble(susan)|~curious(susan))))&
((?[X]:(brave(X)))<=>((old(susan)&~quiet(susan))))&
(~kind(susan))&
(?[X]:((~brave(X)&kind(X))))&
(?[X]:((happy(X)&~calm(X))))&
(?[X]:((~generous(X)&~calm(X))))&
(?[X]:((~old(X)&~patient(X))))&
(generous(john))&
(?[X]:((~funny(X)<~>~curious(X))))&
(~calm(john)) | funny(susan) | [
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2298962107005985045129730
% SZS output start Proof for 2298962107005985045129730
11. ? [X0] : ~kind(X0) <=> (~funny(susan) & tall(susan)) [input p10]
17. ~kind(susan) [input p16]
25. funny(susan) [input hypothesis]
57. (? [X0] : ~kind(X0) | (funny(susan) | ~tall(susan))) & ((~funny(susan) & tall(susan)) | ! [X0] : kind(X0)) [nnf transformation 11]
58. (? [X0] : ~kind(X0) | funny(susan) | ~tall(susan)) & ((~funny(susan) & tall(susan)) | ! [X0] : kind(X0)) [flattening 57]
59. (? [X0] : ~kind(X0) | funny(susan) | ~tall(susan)) & ((~funny(susan) & tall(susan)) | ! [X1] : kind(X1)) [rectify 58]
60. ? [X0] : ~kind(X0) => ~kind(sK3) [choice axiom]
61. (~kind(sK3) | funny(susan) | ~tall(susan)) & ((~funny(susan) & tall(susan)) | ! [X1] : kind(X1)) [skolemisation 59,60]
119. ~funny(susan) | kind(X1) [cnf transformation 61]
135. ~kind(susan) [cnf transformation 17]
148. funny(susan) [cnf transformation 25]
220. 16 <=> funny(susan) [avatar definition]
229. 18 <=> ! [X1] : kind(X1) [avatar definition]
230. kind(X1) <- (18) [avatar component clause 229]
231. 18 | ~16 [avatar split clause 119,220,229]
299. 16 [avatar split clause 148,220]
300. $false <- (18) [resolution 230,135]
301. ~18 [avatar contradiction clause 300]
302. $false [avatar sat refutation 231,299,301]
% SZS output end Proof for 2298962107005985045129730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is rich or not humble then paul is not humble and vice versa.
Everyone who is either not funny or not tall is either humble or not brave.
If someone is not creative then someone is kind or tall.
Everyone who is happy or not old is funny and vice versa.
Everyone who is not rich is rich.
Everyone who is both not old and strong is not wise or wise.
If someone is either not old or tall then someone is not quiet.
If fred is either not quiet or generous then someone is both old and not quiet.
If alice is both generous and curious then susan is either brave or humble and vice versa.
If someone is both happy and kind then mary is brave and vice versa.
Everyone who is quiet is both curious and not calm.
If someone is happy or not humble then mary is both calm and wise.
If john is not kind then fred is not brave or calm.
Everyone who is quiet is both not quiet and not rich and vice versa.
Everyone who is not brave is not rich.
If someone is either brave or calm then someone is both not strong and not quiet and vice versa.
Susan is humble or patient.
John is patient or humble.
Lucy is either curious or tall.
Someone is both patient and humble.
Someone is not calm.
Someone is humble.
Someone is not generous.
Mary is funny or not strong. | Mary is not calm. | contradiction | (((rich(john)|~humble(john)))<=>(~humble(paul)))&
(![X]:((~funny(X)<~>~tall(X))=>(humble(X)<~>~brave(X))))&
((?[X]:(~creative(X)))=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((happy(X)|~old(X))<=>funny(X)))&
(![X]:(~rich(X)=>rich(X)))&
(![X]:((~old(X)&strong(X))=>(~wise(X)|wise(X))))&
((?[X]:((~old(X)<~>tall(X))))=>(?[X]:(~quiet(X))))&
(((~quiet(fred)<~>generous(fred)))=>(?[X]:((old(X)&~quiet(X)))))&
(((generous(alice)&curious(alice)))<=>((brave(susan)<~>humble(susan))))&
((?[X]:((happy(X)&kind(X))))<=>(brave(mary)))&
(![X]:(quiet(X)=>(curious(X)&~calm(X))))&
((?[X]:((happy(X)|~humble(X))))=>((calm(mary)&wise(mary))))&
((~kind(john))=>((~brave(fred)|calm(fred))))&
(![X]:(quiet(X)<=>(~quiet(X)&~rich(X))))&
(![X]:(~brave(X)=>~rich(X)))&
((?[X]:((brave(X)<~>calm(X))))<=>(?[X]:((~strong(X)&~quiet(X)))))&
((humble(susan)|patient(susan)))&
((patient(john)|humble(john)))&
((curious(lucy)<~>tall(lucy)))&
(?[X]:((patient(X)&humble(X))))&
(?[X]:(~calm(X)))&
(?[X]:(humble(X)))&
(?[X]:(~generous(X)))&
((funny(mary)|~strong(mary))) | ~calm(mary) | [
"p4",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2079072991616387842917571
% SZS output start Proof for 2079072991616387842917571
5. ! [X0] : (~rich(X0) => rich(X0)) [input p4]
10. ? [X0] : (kind(X0) & happy(X0)) <=> brave(mary) [input p9]
12. ? [X0] : (~humble(X0) | happy(X0)) => (wise(mary) & calm(mary)) [input p11]
15. ! [X0] : (~brave(X0) => ~rich(X0)) [input p14]
25. ~calm(mary) [input hypothesis]
34. ! [X0] : (rich(X0) | rich(X0)) [ennf transformation 5]
40. (wise(mary) & calm(mary)) | ! [X0] : (humble(X0) & ~happy(X0)) [ennf transformation 12]
43. ! [X0] : (~rich(X0) | brave(X0)) [ennf transformation 15]
58. (? [X0] : (kind(X0) & happy(X0)) | ~brave(mary)) & (brave(mary) | ! [X0] : (~kind(X0) | ~happy(X0))) [nnf transformation 10]
59. (? [X0] : (kind(X0) & happy(X0)) | ~brave(mary)) & (brave(mary) | ! [X1] : (~kind(X1) | ~happy(X1))) [rectify 58]
60. ? [X0] : (kind(X0) & happy(X0)) => (kind(sK2) & happy(sK2)) [choice axiom]
61. ((kind(sK2) & happy(sK2)) | ~brave(mary)) & (brave(mary) | ! [X1] : (~kind(X1) | ~happy(X1))) [skolemisation 59,60]
88. rich(X0) | rich(X0) [cnf transformation 34]
103. happy(sK2) | ~brave(mary) [cnf transformation 61]
107. calm(mary) | ~happy(X0) [cnf transformation 40]
115. ~rich(X0) | brave(X0) [cnf transformation 43]
129. ~calm(mary) [cnf transformation 25]
132. rich(X0) [duplicate literal removal 88]
203. 15 <=> brave(mary) [avatar definition]
205. ~brave(mary) <- (~15) [avatar component clause 203]
212. 17 <=> happy(sK2) [avatar definition]
214. happy(sK2) <- (17) [avatar component clause 212]
215. ~15 | 17 [avatar split clause 103,212,203]
229. 21 <=> ! [X0] : ~happy(X0) [avatar definition]
230. ~happy(X0) <- (21) [avatar component clause 229]
233. 22 <=> calm(mary) [avatar definition]
237. 21 | 22 [avatar split clause 107,233,229]
252. brave(X0) [subsumption resolution 115,132]
291. ~22 [avatar split clause 129,233]
294. $false <- (17, 21) [subsumption resolution 214,230]
295. ~17 | ~21 [avatar contradiction clause 294]
304. $false <- (~15) [subsumption resolution 205,252]
305. 15 [avatar contradiction clause 304]
308. $false [avatar sat refutation 215,237,291,295,305]
% SZS output end Proof for 2079072991616387842917571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or funny then fred is not quiet or not funny and vice versa. Everyone who is both not happy and not creative is both brave and tall and vice versa. Everyone who is not creative or not brave is creative. Everyone who is either not happy or calm is not creative. If alice is both not happy and not funny then lucy is not strong or quiet and vice versa. Everyone who is not curious or quiet is calm. Everyone who is both brave and generous is not calm or quiet. Everyone who is both not brave and happy is quiet and vice versa. If someone is either curious or not wise then someone is not old or not tall. If someone is either wise or strong then someone is not humble. If alice is both not humble and brave then someone is both not happy and calm. Everyone who is patient is either not quiet or strong and vice versa. Everyone who is funny or wise is happy. Everyone who is both patient and rich is not funny and vice versa. If lucy is not humble or happy then susan is either not wise or happy and vice versa. If someone is not brave or brave then lucy is either not quiet or curious. Susan is either not tall or not happy. Lucy is both not generous and tall. Lucy is not kind. Someone is both funny and not calm. Someone is either wise or not rich. Lucy is not rich or not generous. Susan is either strong or generous. Paul is not kind. | Lucy is not calm. | contradiction | ((?[X]:((happy(X)<~>funny(X))))<=>((~quiet(fred)|~funny(fred))))&
(![X]:((~happy(X)&~creative(X))<=>(brave(X)&tall(X))))&
(![X]:((~creative(X)|~brave(X))=>creative(X)))&
(![X]:((~happy(X)<~>calm(X))=>~creative(X)))&
(((~happy(alice)&~funny(alice)))<=>((~strong(lucy)|quiet(lucy))))&
(![X]:((~curious(X)|quiet(X))=>calm(X)))&
(![X]:((brave(X)&generous(X))=>(~calm(X)|quiet(X))))&
(![X]:((~brave(X)&happy(X))<=>quiet(X)))&
((?[X]:((curious(X)<~>~wise(X))))=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:((wise(X)<~>strong(X))))=>(?[X]:(~humble(X))))&
(((~humble(alice)&brave(alice)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(((~humble(lucy)|happy(lucy)))<=>((~wise(susan)<~>happy(susan))))&
((?[X]:((~brave(X)|brave(X))))=>((~quiet(lucy)<~>curious(lucy))))&
((~tall(susan)<~>~happy(susan)))&
((~generous(lucy)&tall(lucy)))&
(~kind(lucy))&
(?[X]:((funny(X)&~calm(X))))&
(?[X]:((wise(X)<~>~rich(X))))&
((~rich(lucy)|~generous(lucy)))&
((strong(susan)<~>generous(susan)))&
(~kind(paul)) | ~calm(lucy) | [
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5203575725573595487615697
% SZS output start Proof for 5203575725573595487615697
6. ! [X0] : ((quiet(X0) | ~curious(X0)) => calm(X0)) [input p5]
16. ? [X0] : (brave(X0) | ~brave(X0)) => (~quiet(lucy) <~> curious(lucy)) [input p15]
25. ~calm(lucy) [input hypothesis]
33. ! [X0] : (calm(X0) | (~quiet(X0) & curious(X0))) [ennf transformation 6]
40. (~quiet(lucy) <~> curious(lucy)) | ! [X0] : (~brave(X0) & brave(X0)) [ennf transformation 16]
64. ((~curious(lucy) | quiet(lucy)) & (curious(lucy) | ~quiet(lucy))) | ! [X0] : (~brave(X0) & brave(X0)) [nnf transformation 40]
91. curious(X0) | calm(X0) [cnf transformation 33]
92. ~quiet(X0) | calm(X0) [cnf transformation 33]
118. ~curious(lucy) | quiet(lucy) | brave(X0) [cnf transformation 64]
119. ~curious(lucy) | quiet(lucy) | ~brave(X0) [cnf transformation 64]
131. ~calm(lucy) [cnf transformation 25]
164. 7 <=> quiet(lucy) [avatar definition]
165. quiet(lucy) <- (7) [avatar component clause 164]
238. 22 <=> ! [X0] : ~brave(X0) [avatar definition]
239. ~brave(X0) <- (22) [avatar component clause 238]
241. 23 <=> curious(lucy) [avatar definition]
243. ~curious(lucy) <- (~23) [avatar component clause 241]
244. 22 | 7 | ~23 [avatar split clause 119,241,164,238]
246. 24 <=> ! [X0] : brave(X0) [avatar definition]
247. brave(X0) <- (24) [avatar component clause 246]
248. 24 | 7 | ~23 [avatar split clause 118,241,164,246]
278. calm(lucy) <- (~23) [resolution 91,243]
279. $false <- (~23) [subsumption resolution 278,131]
280. 23 [avatar contradiction clause 279]
281. calm(lucy) <- (7) [resolution 92,165]
282. $false <- (7) [subsumption resolution 281,131]
283. ~7 [avatar contradiction clause 282]
284. $false <- (22, 24) [subsumption resolution 239,247]
285. ~22 | ~24 [avatar contradiction clause 284]
286. $false [avatar sat refutation 244,248,280,283,285]
% SZS output end Proof for 5203575725573595487615697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both not curious and curious.
If paul is both not quiet and happy then someone is either rich or not creative and vice versa.
Everyone who is either not rich or not strong is strong and vice versa.
If susan is both not brave and not quiet then someone is either brave or not strong.
If someone is not humble then someone is both funny and not brave.
Everyone who is both not tall and generous is either strong or kind.
Everyone who is either patient or old is kind or not creative and vice versa.
Everyone who is not tall is both not funny and not calm.
If lucy is not funny then paul is not curious.
Everyone who is both curious and strong is brave and vice versa.
Everyone who is either rich or tall is happy and vice versa.
Everyone who is humble or not generous is old and vice versa.
Everyone who is either not curious or generous is either old or not quiet and vice versa.
Everyone who is either humble or not wise is either happy or not rich.
If lucy is both wise and not wise then fred is both not strong and not generous.
Everyone who is not creative is strong and vice versa.
Someone is both curious and not kind.
Someone is either not curious or quiet.
Lucy is either not happy or calm.
Someone is not generous.
Fred is either not quiet or not rich. | Susan is not generous. | neutral | (![X]:(happy(X)=>(~curious(X)&curious(X))))&
(((~quiet(paul)&happy(paul)))<=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:((~rich(X)<~>~strong(X))<=>strong(X)))&
(((~brave(susan)&~quiet(susan)))=>(?[X]:((brave(X)<~>~strong(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((funny(X)&~brave(X)))))&
(![X]:((~tall(X)&generous(X))=>(strong(X)<~>kind(X))))&
(![X]:((patient(X)<~>old(X))<=>(kind(X)|~creative(X))))&
(![X]:(~tall(X)=>(~funny(X)&~calm(X))))&
((~funny(lucy))=>(~curious(paul)))&
(![X]:((curious(X)&strong(X))<=>brave(X)))&
(![X]:((rich(X)<~>tall(X))<=>happy(X)))&
(![X]:((humble(X)|~generous(X))<=>old(X)))&
(![X]:((~curious(X)<~>generous(X))<=>(old(X)<~>~quiet(X))))&
(![X]:((humble(X)<~>~wise(X))=>(happy(X)<~>~rich(X))))&
(((wise(lucy)&~wise(lucy)))=>((~strong(fred)&~generous(fred))))&
(![X]:(~creative(X)<=>strong(X)))&
(?[X]:((curious(X)&~kind(X))))&
(?[X]:((~curious(X)<~>quiet(X))))&
((~happy(lucy)<~>calm(lucy)))&
(?[X]:(~generous(X)))&
((~quiet(fred)<~>~rich(fred))) | ~generous(susan) | [] | null | 0 |
If paul is both patient and rich then someone is not generous or funny. Everyone who is both strong and not kind is not tall or patient. Everyone who is both not patient and not funny is not tall and vice versa. Everyone who is not old is not patient or not quiet and vice versa. If someone is both not quiet and not brave then lucy is both rich and not patient. Everyone who is kind is both curious and not old and vice versa. Everyone who is not happy or humble is humble and vice versa. If someone is not rich or wise then someone is either strong or tall and vice versa. Everyone who is not funny is tall or not happy. Everyone who is both not funny and not curious is tall. If fred is both not patient and not tall then lucy is rich and vice versa. Everyone who is both calm and creative is tall or brave and vice versa. Everyone who is happy or calm is not generous and vice versa. Everyone who is both calm and not patient is both not old and tall. If fred is both old and not old then someone is not generous and vice versa. Susan is not strong or strong. Mary is either not old or rich. Someone is not calm or not brave. | Mary is patient. | contradiction | (((patient(paul)&rich(paul)))=>(?[X]:((~generous(X)|funny(X)))))&
(![X]:((strong(X)&~kind(X))=>(~tall(X)|patient(X))))&
(![X]:((~patient(X)&~funny(X))<=>~tall(X)))&
(![X]:(~old(X)<=>(~patient(X)|~quiet(X))))&
((?[X]:((~quiet(X)&~brave(X))))=>((rich(lucy)&~patient(lucy))))&
(![X]:(kind(X)<=>(curious(X)&~old(X))))&
(![X]:((~happy(X)|humble(X))<=>humble(X)))&
((?[X]:((~rich(X)|wise(X))))<=>(?[X]:((strong(X)<~>tall(X)))))&
(![X]:(~funny(X)=>(tall(X)|~happy(X))))&
(![X]:((~funny(X)&~curious(X))=>tall(X)))&
(((~patient(fred)&~tall(fred)))<=>(rich(lucy)))&
(![X]:((calm(X)&creative(X))<=>(tall(X)|brave(X))))&
(![X]:((happy(X)|calm(X))<=>~generous(X)))&
(![X]:((calm(X)&~patient(X))=>(~old(X)&tall(X))))&
(((old(fred)&~old(fred)))<=>(?[X]:(~generous(X))))&
((~strong(susan)|strong(susan)))&
((~old(mary)<~>rich(mary)))&
(?[X]:((~calm(X)|~brave(X)))) | patient(mary) | [
"p2",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6150243225559250433492470
% SZS output start Proof for 6150243225559250433492470
3. ! [X0] : ((~funny(X0) & ~patient(X0)) <=> ~tall(X0)) [input p2]
12. ! [X0] : ((creative(X0) & calm(X0)) <=> (brave(X0) | tall(X0))) [input p11]
13. ! [X0] : ((calm(X0) | happy(X0)) <=> ~generous(X0)) [input p12]
15. (~old(fred) & old(fred)) <=> ? [X0] : ~generous(X0) [input p14]
19. patient(mary) [input hypothesis]
36. ! [X0] : (((~funny(X0) & ~patient(X0)) | tall(X0)) & (~tall(X0) | (funny(X0) | patient(X0)))) [nnf transformation 3]
37. ! [X0] : (((~funny(X0) & ~patient(X0)) | tall(X0)) & (~tall(X0) | funny(X0) | patient(X0))) [flattening 36]
49. ! [X0] : (((creative(X0) & calm(X0)) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | (~creative(X0) | ~calm(X0)))) [nnf transformation 12]
50. ! [X0] : (((creative(X0) & calm(X0)) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | ~creative(X0) | ~calm(X0))) [flattening 49]
51. ! [X0] : (((calm(X0) | happy(X0)) | generous(X0)) & (~generous(X0) | (~calm(X0) & ~happy(X0)))) [nnf transformation 13]
52. ! [X0] : ((calm(X0) | happy(X0) | generous(X0)) & (~generous(X0) | (~calm(X0) & ~happy(X0)))) [flattening 51]
53. ((~old(fred) & old(fred)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (old(fred) | ~old(fred))) [nnf transformation 15]
54. ((~old(fred) & old(fred)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | old(fred) | ~old(fred)) [flattening 53]
55. ((~old(fred) & old(fred)) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | old(fred) | ~old(fred)) [rectify 54]
56. ? [X1] : ~generous(X1) => ~generous(sK3) [choice axiom]
57. ((~old(fred) & old(fred)) | ! [X0] : generous(X0)) & (~generous(sK3) | old(fred) | ~old(fred)) [skolemisation 55,56]
64. ~patient(X0) | tall(X0) [cnf transformation 37]
86. ~tall(X0) | calm(X0) [cnf transformation 50]
91. ~calm(X0) | ~generous(X0) [cnf transformation 52]
96. old(fred) | generous(X0) [cnf transformation 57]
97. ~old(fred) | generous(X0) [cnf transformation 57]
102. patient(mary) [cnf transformation 19]
182. 18 <=> ! [X0] : generous(X0) [avatar definition]
183. generous(X0) <- (18) [avatar component clause 182]
185. 19 <=> old(fred) [avatar definition]
188. 18 | ~19 [avatar split clause 97,185,182]
189. 18 | 19 [avatar split clause 96,185,182]
203. tall(mary) [resolution 64,102]
204. calm(mary) [resolution 86,203]
206. ~generous(mary) [resolution 91,204]
207. $false <- (18) [subsumption resolution 206,183]
208. ~18 [avatar contradiction clause 207]
209. $false [avatar sat refutation 188,189,208]
% SZS output end Proof for 6150243225559250433492470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or rich is both patient and not patient and vice versa.
If someone is generous or not strong then fred is both not rich and not happy.
Everyone who is either not generous or calm is either strong or quiet and vice versa.
Everyone who is happy is both quiet and not funny and vice versa.
If someone is creative then someone is both rich and creative and vice versa.
Everyone who is not kind or not curious is not quiet and vice versa.
Everyone who is not quiet or not generous is not brave or not patient and vice versa.
If someone is either old or kind then someone is not happy or not calm.
If lucy is not old then someone is both not old and patient and vice versa.
If john is either not brave or creative then someone is generous.
If susan is either kind or tall then paul is both wise and quiet and vice versa.
Everyone who is not happy is strong and vice versa.
If john is not generous then fred is either not curious or not patient.
Everyone who is either not kind or not rich is either happy or wise.
Everyone who is either curious or patient is not tall and vice versa.
Everyone who is either not funny or kind is rich or not old and vice versa.
Someone is either old or not humble.
John is curious.
Lucy is both quiet and tall.
Paul is happy.
Someone is creative or old.
Lucy is not old or not tall.
Alice is either happy or quiet. | Paul is happy. | entailment | (![X]:((calm(X)|rich(X))<=>(patient(X)&~patient(X))))&
((?[X]:((generous(X)|~strong(X))))=>((~rich(fred)&~happy(fred))))&
(![X]:((~generous(X)<~>calm(X))<=>(strong(X)<~>quiet(X))))&
(![X]:(happy(X)<=>(quiet(X)&~funny(X))))&
((?[X]:(creative(X)))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:((~kind(X)|~curious(X))<=>~quiet(X)))&
(![X]:((~quiet(X)|~generous(X))<=>(~brave(X)|~patient(X))))&
((?[X]:((old(X)<~>kind(X))))=>(?[X]:((~happy(X)|~calm(X)))))&
((~old(lucy))<=>(?[X]:((~old(X)&patient(X)))))&
(((~brave(john)<~>creative(john)))=>(?[X]:(generous(X))))&
(((kind(susan)<~>tall(susan)))<=>((wise(paul)&quiet(paul))))&
(![X]:(~happy(X)<=>strong(X)))&
((~generous(john))=>((~curious(fred)<~>~patient(fred))))&
(![X]:((~kind(X)<~>~rich(X))=>(happy(X)<~>wise(X))))&
(![X]:((curious(X)<~>patient(X))<=>~tall(X)))&
(![X]:((~funny(X)<~>kind(X))<=>(rich(X)|~old(X))))&
(?[X]:((old(X)<~>~humble(X))))&
(curious(john))&
((quiet(lucy)&tall(lucy)))&
(happy(paul))&
(?[X]:((creative(X)|old(X))))&
((~old(lucy)|~tall(lucy)))&
((happy(alice)<~>quiet(alice))) | happy(paul) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 719664114477819163509614
% SZS output start Proof for 719664114477819163509614
20. happy(paul) [input p19]
24. ~happy(paul) [input hypothesis]
137. happy(paul) [cnf transformation 20]
142. ~happy(paul) [cnf transformation 24]
266. $false [subsumption resolution 142,137]
% SZS output end Proof for 719664114477819163509614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or funny is both old and not creative. Everyone who is old or humble is creative. If someone is not curious then mary is either creative or not funny and vice versa. Everyone who is rich or old is both old and not curious and vice versa. Everyone who is both not old and not strong is both calm and tall. Everyone who is either not wise or happy is either quiet or not curious. Everyone who is both tall and calm is not calm and vice versa. If someone is either funny or tall then alice is either happy or kind. Everyone who is not tall is either wise or not rich. Everyone who is not generous is not strong or not humble. Everyone who is not curious or calm is both not humble and kind and vice versa. If john is humble then alice is either not rich or not quiet. If john is both creative and funny then susan is either not quiet or brave and vice versa. If mary is kind then paul is creative or curious and vice versa. Everyone who is both not generous and not kind is both not happy and not creative. If fred is both old and not humble then someone is either old or not tall and vice versa. Someone is not quiet or patient. Paul is old. John is creative. Alice is not humble. Someone is not humble or humble. Someone is not brave. | Fred is creative. | entailment | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|humble(X))=>creative(X)))&
((?[X]:(~curious(X)))<=>((creative(mary)<~>~funny(mary))))&
(![X]:((rich(X)|old(X))<=>(old(X)&~curious(X))))&
(![X]:((~old(X)&~strong(X))=>(calm(X)&tall(X))))&
(![X]:((~wise(X)<~>happy(X))=>(quiet(X)<~>~curious(X))))&
(![X]:((tall(X)&calm(X))<=>~calm(X)))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(alice)<~>kind(alice))))&
(![X]:(~tall(X)=>(wise(X)<~>~rich(X))))&
(![X]:(~generous(X)=>(~strong(X)|~humble(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(?[X]:((~quiet(X)|patient(X))))&
(old(paul))&
(creative(john))&
(~humble(alice))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:(~brave(X))) | creative(fred) | [
"p1",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4790405963875394199389246
% SZS output start Proof for 4790405963875394199389246
2. ! [X0] : ((humble(X0) | old(X0)) => creative(X0)) [input p1]
7. ! [X0] : ((calm(X0) & tall(X0)) <=> ~calm(X0)) [input p6]
16. (~humble(fred) & old(fred)) <=> ? [X0] : (old(X0) <~> ~tall(X0)) [input p15]
23. ~creative(fred) [input hypothesis]
29. ! [X0] : (creative(X0) | (~humble(X0) & ~old(X0))) [ennf transformation 2]
42. ! [X0] : (((calm(X0) & tall(X0)) | calm(X0)) & (~calm(X0) | (~calm(X0) | ~tall(X0)))) [nnf transformation 7]
43. ! [X0] : (((calm(X0) & tall(X0)) | calm(X0)) & (~calm(X0) | ~calm(X0) | ~tall(X0))) [flattening 42]
53. ((~humble(fred) & old(fred)) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (? [X0] : ((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (humble(fred) | ~old(fred))) [nnf transformation 16]
54. ((~humble(fred) & old(fred)) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (? [X0] : ((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | humble(fred) | ~old(fred)) [flattening 53]
55. ((~humble(fred) & old(fred)) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (? [X1] : ((tall(X1) | ~old(X1)) & (~tall(X1) | old(X1))) | humble(fred) | ~old(fred)) [rectify 54]
56. ? [X1] : ((tall(X1) | ~old(X1)) & (~tall(X1) | old(X1))) => ((tall(sK1) | ~old(sK1)) & (~tall(sK1) | old(sK1))) [choice axiom]
57. ((~humble(fred) & old(fred)) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(sK1) | ~old(sK1)) & (~tall(sK1) | old(sK1))) | humble(fred) | ~old(fred)) [skolemisation 55,56]
66. ~old(X0) | creative(X0) [cnf transformation 29]
81. ~calm(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 43]
83. calm(X0) | calm(X0) [cnf transformation 43]
109. old(fred) | old(X0) | tall(X0) [cnf transformation 57]
117. ~creative(fred) [cnf transformation 23]
118. ~calm(X0) | ~tall(X0) [duplicate literal removal 81]
119. calm(X0) [duplicate literal removal 83]
139. ~tall(X0) [subsumption resolution 118,119]
191. old(fred) | old(X0) [subsumption resolution 109,139]
193. 14 <=> ! [X0] : old(X0) [avatar definition]
194. old(X0) <- (14) [avatar component clause 193]
196. 15 <=> old(fred) [avatar definition]
197. ~old(fred) <- (~15) [avatar component clause 196]
198. old(fred) <- (15) [avatar component clause 196]
199. 14 | 15 [avatar split clause 191,196,193]
208. $false <- (14, ~15) [resolution 197,194]
209. ~14 | 15 [avatar contradiction clause 208]
213. creative(fred) <- (15) [resolution 66,198]
214. $false <- (15) [subsumption resolution 213,117]
215. ~15 [avatar contradiction clause 214]
216. $false [avatar sat refutation 199,209,215]
% SZS output end Proof for 4790405963875394199389246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or not funny is both not happy and not brave.
If someone is both not tall and not calm then someone is both calm and not funny and vice versa.
Everyone who is either not patient or not happy is either generous or creative and vice versa.
Everyone who is happy is either happy or not kind.
Everyone who is humble is funny or creative.
If someone is old then alice is either humble or not calm.
Everyone who is both not patient and not humble is either strong or not kind and vice versa.
Everyone who is either not humble or not strong is either not happy or funny and vice versa.
Everyone who is either not tall or generous is both not creative and not tall and vice versa.
Everyone who is both not generous and wise is either calm or not curious.
If someone is wise or not creative then someone is either curious or not happy and vice versa.
Everyone who is not kind is both quiet and not creative.
If john is happy then fred is both not funny and not curious.
If someone is not tall or strong then someone is strong and vice versa.
If someone is curious or old then someone is either rich or creative and vice versa.
If mary is brave or not generous then susan is both humble and not calm.
Someone is both rich and creative.
Someone is both not humble and not patient.
Someone is curious or not brave.
John is not humble or not brave.
Susan is not humble.
Susan is both not creative and not patient.
Someone is wise.
Lucy is not generous. | Mary is not kind. | contradiction | (![X]:((~happy(X)<~>~funny(X))=>(~happy(X)&~brave(X))))&
((?[X]:((~tall(X)&~calm(X))))<=>(?[X]:((calm(X)&~funny(X)))))&
(![X]:((~patient(X)<~>~happy(X))<=>(generous(X)<~>creative(X))))&
(![X]:(happy(X)=>(happy(X)<~>~kind(X))))&
(![X]:(humble(X)=>(funny(X)|creative(X))))&
((?[X]:(old(X)))=>((humble(alice)<~>~calm(alice))))&
(![X]:((~patient(X)&~humble(X))<=>(strong(X)<~>~kind(X))))&
(![X]:((~humble(X)<~>~strong(X))<=>(~happy(X)<~>funny(X))))&
(![X]:((~tall(X)<~>generous(X))<=>(~creative(X)&~tall(X))))&
(![X]:((~generous(X)&wise(X))=>(calm(X)<~>~curious(X))))&
((?[X]:((wise(X)|~creative(X))))<=>(?[X]:((curious(X)<~>~happy(X)))))&
(![X]:(~kind(X)=>(quiet(X)&~creative(X))))&
((happy(john))=>((~funny(fred)&~curious(fred))))&
((?[X]:((~tall(X)|strong(X))))<=>(?[X]:(strong(X))))&
((?[X]:((curious(X)|old(X))))<=>(?[X]:((rich(X)<~>creative(X)))))&
(((brave(mary)|~generous(mary)))=>((humble(susan)&~calm(susan))))&
(?[X]:((rich(X)&creative(X))))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((curious(X)|~brave(X))))&
((~humble(john)|~brave(john)))&
(~humble(susan))&
((~creative(susan)&~patient(susan)))&
(?[X]:(wise(X)))&
(~generous(lucy)) | ~kind(mary) | [
"p8",
"p11",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8055748933697137558648524
% SZS output start Proof for 8055748933697137558648524
9. ! [X0] : ((~tall(X0) <~> generous(X0)) <=> (~tall(X0) & ~creative(X0))) [input p8]
12. ! [X0] : (~kind(X0) => (~creative(X0) & quiet(X0))) [input p11]
16. (~generous(mary) | brave(mary)) => (~calm(susan) & humble(susan)) [input p15]
21. ~humble(susan) [input p20]
25. ~kind(mary) [input hypothesis]
30. ! [X0] : (~kind(X0) => ~creative(X0)) [pure predicate removal 12]
33. ~generous(mary) => (~calm(susan) & humble(susan)) [pure predicate removal 16]
42. ! [X0] : (~creative(X0) | kind(X0)) [ennf transformation 30]
44. (~calm(susan) & humble(susan)) | generous(mary) [ennf transformation 33]
57. ! [X0] : ((((~generous(X0) | tall(X0)) & (generous(X0) | ~tall(X0))) | (tall(X0) | creative(X0))) & ((~tall(X0) & ~creative(X0)) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0))))) [nnf transformation 9]
58. ! [X0] : ((((~generous(X0) | tall(X0)) & (generous(X0) | ~tall(X0))) | tall(X0) | creative(X0)) & ((~tall(X0) & ~creative(X0)) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0))))) [flattening 57]
117. ~tall(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 58]
119. ~generous(X0) | tall(X0) | tall(X0) | creative(X0) [cnf transformation 58]
128. ~creative(X0) | kind(X0) [cnf transformation 42]
140. humble(susan) | generous(mary) [cnf transformation 44]
146. ~humble(susan) [cnf transformation 21]
151. ~kind(mary) [cnf transformation 25]
152. ~generous(X0) | ~tall(X0) [duplicate literal removal 117]
153. ~generous(X0) | tall(X0) | creative(X0) [duplicate literal removal 119]
300. 33 <=> generous(mary) [avatar definition]
302. generous(mary) <- (33) [avatar component clause 300]
309. 35 <=> humble(susan) [avatar definition]
312. 33 | 35 [avatar split clause 140,309,300]
313. ~35 [avatar split clause 146,309]
315. ~tall(mary) <- (33) [resolution 152,302]
346. tall(mary) | creative(mary) <- (33) [resolution 153,302]
347. creative(mary) <- (33) [subsumption resolution 346,315]
349. kind(mary) <- (33) [resolution 347,128]
350. $false <- (33) [subsumption resolution 349,151]
351. ~33 [avatar contradiction clause 350]
352. $false [avatar sat refutation 312,313,351]
% SZS output end Proof for 8055748933697137558648524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either funny or happy then susan is both not old and not calm and vice versa. Everyone who is either quiet or funny is both funny and not old. Everyone who is not strong is funny or not strong. If alice is tall or not calm then susan is both creative and tall. Everyone who is either not funny or calm is not funny. Everyone who is both curious and not brave is either not funny or not strong and vice versa. Everyone who is not calm or not generous is either not strong or not patient. If someone is either not old or not curious then someone is both not kind and not curious. Everyone who is either not happy or creative is either not kind or not generous. Everyone who is both tall and not calm is tall or rich. Everyone who is either wise or creative is either not kind or not generous and vice versa. Everyone who is generous is both brave and old and vice versa. If someone is either tall or not curious then someone is either strong or humble. Everyone who is either not kind or not funny is funny and vice versa. Everyone who is not quiet or not brave is both not wise and creative. Everyone who is not quiet is not generous or not brave and vice versa. Someone is not quiet or not patient. Paul is either not kind or not humble. Someone is both creative and quiet. Mary is not curious. Someone is generous. | Alice is not old. | contradiction | (((funny(susan)<~>happy(susan)))<=>((~old(susan)&~calm(susan))))&
(![X]:((quiet(X)<~>funny(X))=>(funny(X)&~old(X))))&
(![X]:(~strong(X)=>(funny(X)|~strong(X))))&
(((tall(alice)|~calm(alice)))=>((creative(susan)&tall(susan))))&
(![X]:((~funny(X)<~>calm(X))=>~funny(X)))&
(![X]:((curious(X)&~brave(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:((~calm(X)|~generous(X))=>(~strong(X)<~>~patient(X))))&
((?[X]:((~old(X)<~>~curious(X))))=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((tall(X)&~calm(X))=>(tall(X)|rich(X))))&
(![X]:((wise(X)<~>creative(X))<=>(~kind(X)<~>~generous(X))))&
(![X]:(generous(X)<=>(brave(X)&old(X))))&
((?[X]:((tall(X)<~>~curious(X))))=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((~kind(X)<~>~funny(X))<=>funny(X)))&
(![X]:((~quiet(X)|~brave(X))=>(~wise(X)&creative(X))))&
(![X]:(~quiet(X)<=>(~generous(X)|~brave(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
((~kind(paul)<~>~humble(paul)))&
(?[X]:((creative(X)&quiet(X))))&
(~curious(mary))&
(?[X]:(generous(X))) | ~old(alice) | [
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8930448695802279843436534
% SZS output start Proof for 8930448695802279843436534
11. ! [X0] : ((wise(X0) <~> creative(X0)) <=> (~kind(X0) <~> ~generous(X0))) [input p10]
12. ! [X0] : (generous(X0) <=> (old(X0) & brave(X0))) [input p11]
14. ! [X0] : ((~kind(X0) <~> ~funny(X0)) <=> funny(X0)) [input p13]
15. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (creative(X0) & ~wise(X0))) [input p14]
16. ! [X0] : (~quiet(X0) <=> (~brave(X0) | ~generous(X0))) [input p15]
22. ~old(alice) [input hypothesis]
35. ! [X0] : ((creative(X0) & ~wise(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 15]
48. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | ((~kind(X0) | generous(X0)) & (~generous(X0) | kind(X0)))) & (((generous(X0) | kind(X0)) & (~generous(X0) | ~kind(X0))) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [nnf transformation 11]
49. ! [X0] : ((generous(X0) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | ~generous(X0))) [nnf transformation 12]
50. ! [X0] : ((generous(X0) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | ~generous(X0))) [flattening 49]
55. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~funny(X0)) & (funny(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [nnf transformation 14]
56. ! [X0] : ((~quiet(X0) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | quiet(X0))) [nnf transformation 16]
57. ! [X0] : ((~quiet(X0) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | quiet(X0))) [flattening 56]
103. ~creative(X0) | kind(X0) | wise(X0) | generous(X0) [cnf transformation 48]
108. ~generous(X0) | brave(X0) [cnf transformation 50]
109. ~generous(X0) | old(X0) [cnf transformation 50]
116. funny(X0) | ~kind(X0) | funny(X0) [cnf transformation 55]
117. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 55]
119. ~wise(X0) | quiet(X0) [cnf transformation 35]
121. creative(X0) | quiet(X0) [cnf transformation 35]
123. ~brave(X0) | ~generous(X0) | quiet(X0) [cnf transformation 57]
124. ~quiet(X0) | generous(X0) [cnf transformation 57]
133. ~old(alice) [cnf transformation 22]
134. funny(X0) | ~kind(X0) [duplicate literal removal 116]
135. ~kind(X0) | ~funny(X0) [duplicate literal removal 117]
216. ~kind(X0) [subsumption resolution 134,135]
217. ~generous(X0) | quiet(X0) [subsumption resolution 123,108]
315. kind(X1) | wise(X1) | generous(X1) | quiet(X1) [resolution 103,121]
318. wise(X1) | generous(X1) | quiet(X1) [subsumption resolution 315,216]
319. generous(X1) | quiet(X1) [subsumption resolution 318,119]
320. quiet(X1) [subsumption resolution 319,217]
325. generous(X3) [resolution 320,124]
384. old(X2) [resolution 325,109]
391. $false [resolution 384,133]
% SZS output end Proof for 8930448695802279843436534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not tall then someone is both patient and generous.
Everyone who is both not old and not strong is both tall and funny and vice versa.
Everyone who is either not creative or not wise is either not old or tall.
Everyone who is either old or tall is not brave.
Everyone who is happy is not patient and vice versa.
Everyone who is happy or not old is not curious.
Everyone who is both brave and happy is both rich and not funny and vice versa.
If someone is both not patient and not rich then someone is generous.
Everyone who is not kind is funny and vice versa.
Everyone who is humble is either old or not brave and vice versa.
If someone is either not humble or not rich then someone is both not humble and humble.
If john is brave then someone is both generous and creative and vice versa.
If john is not patient then lucy is funny and vice versa.
If fred is either tall or strong then someone is not curious and vice versa.
Everyone who is both happy and not old is creative and vice versa.
Everyone who is either old or not creative is not curious or not brave and vice versa.
Paul is either not strong or strong.
Someone is either not quiet or wise.
Someone is either not creative or wise.
Someone is happy or not kind.
Someone is humble.
Someone is patient or generous.
Lucy is not old.
John is not strong or generous. | Lucy is not kind. | contradiction | ((~tall(mary))=>(?[X]:((patient(X)&generous(X)))))&
(![X]:((~old(X)&~strong(X))<=>(tall(X)&funny(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(~old(X)<~>tall(X))))&
(![X]:((old(X)<~>tall(X))=>~brave(X)))&
(![X]:(happy(X)<=>~patient(X)))&
(![X]:((happy(X)|~old(X))=>~curious(X)))&
(![X]:((brave(X)&happy(X))<=>(rich(X)&~funny(X))))&
((?[X]:((~patient(X)&~rich(X))))=>(?[X]:(generous(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:(humble(X)<=>(old(X)<~>~brave(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>(?[X]:((~humble(X)&humble(X)))))&
((brave(john))<=>(?[X]:((generous(X)&creative(X)))))&
((~patient(john))<=>(funny(lucy)))&
(((tall(fred)<~>strong(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((happy(X)&~old(X))<=>creative(X)))&
(![X]:((old(X)<~>~creative(X))<=>(~curious(X)|~brave(X))))&
((~strong(paul)<~>strong(paul)))&
(?[X]:((~quiet(X)<~>wise(X))))&
(?[X]:((~creative(X)<~>wise(X))))&
(?[X]:((happy(X)|~kind(X))))&
(?[X]:(humble(X)))&
(?[X]:((patient(X)|generous(X))))&
(~old(lucy))&
((~strong(john)|generous(john))) | ~kind(lucy) | [
"p4",
"p5",
"p8",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 861784946832213444450936
% SZS output start Proof for 861784946832213444450936
5. ! [X0] : (happy(X0) <=> ~patient(X0)) [input p4]
6. ! [X0] : ((~old(X0) | happy(X0)) => ~curious(X0)) [input p5]
9. ! [X0] : (~kind(X0) <=> funny(X0)) [input p8]
12. brave(john) <=> ? [X0] : (creative(X0) & generous(X0)) [input p11]
13. ~patient(john) <=> funny(lucy) [input p12]
15. ! [X0] : ((~old(X0) & happy(X0)) <=> creative(X0)) [input p14]
16. ! [X0] : ((old(X0) <~> ~creative(X0)) <=> (~brave(X0) | ~curious(X0))) [input p15]
25. ~kind(lucy) [input hypothesis]
28. ! [X0] : (~kind(X0) => funny(X0)) [unused predicate definition removal 9]
32. ! [X0] : (~curious(X0) | (old(X0) & ~happy(X0))) [ennf transformation 6]
34. ! [X0] : (funny(X0) | kind(X0)) [ennf transformation 28]
42. ! [X0] : ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))) [nnf transformation 5]
53. (brave(john) | ! [X0] : (~creative(X0) | ~generous(X0))) & (? [X0] : (creative(X0) & generous(X0)) | ~brave(john)) [nnf transformation 12]
54. (brave(john) | ! [X0] : (~creative(X0) | ~generous(X0))) & (? [X1] : (creative(X1) & generous(X1)) | ~brave(john)) [rectify 53]
55. ? [X1] : (creative(X1) & generous(X1)) => (creative(sK3) & generous(sK3)) [choice axiom]
56. (brave(john) | ! [X0] : (~creative(X0) | ~generous(X0))) & ((creative(sK3) & generous(sK3)) | ~brave(john)) [skolemisation 54,55]
57. (~patient(john) | ~funny(lucy)) & (funny(lucy) | patient(john)) [nnf transformation 13]
62. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 15]
63. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | old(X0) | ~happy(X0))) [flattening 62]
64. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & ((~brave(X0) | ~curious(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [nnf transformation 16]
65. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & (~brave(X0) | ~curious(X0) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [flattening 64]
92. happy(X0) | patient(X0) [cnf transformation 42]
93. ~curious(X0) | ~happy(X0) [cnf transformation 32]
100. kind(X0) | funny(X0) [cnf transformation 34]
110. creative(sK3) | ~brave(john) [cnf transformation 56]
113. ~patient(john) | ~funny(lucy) [cnf transformation 57]
118. ~happy(X0) | old(X0) | creative(X0) [cnf transformation 63]
119. ~creative(X0) | happy(X0) [cnf transformation 63]
120. ~creative(X0) | ~old(X0) [cnf transformation 63]
123. ~creative(X0) | old(X0) | curious(X0) [cnf transformation 65]
124. ~creative(X0) | old(X0) | brave(X0) [cnf transformation 65]
125. creative(X0) | ~old(X0) | curious(X0) [cnf transformation 65]
126. creative(X0) | ~old(X0) | brave(X0) [cnf transformation 65]
138. ~kind(lucy) [cnf transformation 25]
179. 10 <=> brave(john) [avatar definition]
180. ~brave(john) <- (~10) [avatar component clause 179]
184. 11 <=> creative(sK3) [avatar definition]
186. creative(sK3) <- (11) [avatar component clause 184]
187. ~10 | 11 [avatar split clause 110,184,179]
194. 13 <=> funny(lucy) [avatar definition]
198. 14 <=> patient(john) [avatar definition]
201. ~13 | ~14 [avatar split clause 113,198,194]
222. ~old(X0) | brave(X0) [subsumption resolution 126,120]
223. ~old(X0) | curious(X0) [subsumption resolution 125,120]
224. ~creative(X0) | brave(X0) [subsumption resolution 124,222]
225. ~creative(X0) | curious(X0) [subsumption resolution 123,223]
276. funny(lucy) [resolution 100,138]
369. creative(X0) | old(X0) | patient(X0) [resolution 118,92]
398. old(X5) | patient(X5) | brave(X5) [resolution 369,224]
410. brave(X5) | patient(X5) [subsumption resolution 398,222]
441. patient(john) <- (~10) [resolution 410,180]
450. 13 [avatar split clause 276,194]
451. 14 | 10 [avatar split clause 441,179,198]
465. happy(sK3) <- (11) [resolution 186,119]
469. curious(sK3) <- (11) [resolution 186,225]
500. ~happy(sK3) <- (11) [resolution 469,93]
503. $false <- (11) [subsumption resolution 500,465]
504. ~11 [avatar contradiction clause 503]
505. $false [avatar sat refutation 187,201,450,451,504]
% SZS output end Proof for 861784946832213444450936
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not calm is not kind or quiet and vice versa.
Everyone who is both wise and not happy is both quiet and not funny and vice versa.
Everyone who is kind is either strong or not wise.
Everyone who is not calm or humble is old or not tall and vice versa.
Everyone who is curious is not quiet or funny and vice versa.
Everyone who is either wise or quiet is either curious or calm and vice versa.
If alice is either happy or calm then someone is not creative or not kind.
Everyone who is either not funny or not humble is either creative or kind.
Everyone who is both patient and old is not generous or kind.
If someone is not strong or strong then someone is either tall or generous and vice versa.
If fred is either not generous or creative then someone is not quiet and vice versa.
Everyone who is quiet or not strong is both not creative and not rich and vice versa.
If someone is happy or not strong then susan is strong or not generous.
If someone is humble then someone is not old or wise and vice versa.
Everyone who is both quiet and not patient is either brave or not wise and vice versa.
Everyone who is either not curious or wise is either not rich or not wise and vice versa.
John is rich or patient.
Someone is either brave or old.
John is both funny and generous.
Paul is both tall and not kind.
Susan is not creative or curious.
Someone is not old.
John is not quiet or not strong. | Alice is quiet. | contradiction | (![X]:((wise(X)&~calm(X))<=>(~kind(X)|quiet(X))))&
(![X]:((wise(X)&~happy(X))<=>(quiet(X)&~funny(X))))&
(![X]:(kind(X)=>(strong(X)<~>~wise(X))))&
(![X]:((~calm(X)|humble(X))<=>(old(X)|~tall(X))))&
(![X]:(curious(X)<=>(~quiet(X)|funny(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(curious(X)<~>calm(X))))&
(((happy(alice)<~>calm(alice)))=>(?[X]:((~creative(X)|~kind(X)))))&
(![X]:((~funny(X)<~>~humble(X))=>(creative(X)<~>kind(X))))&
(![X]:((patient(X)&old(X))=>(~generous(X)|kind(X))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((tall(X)<~>generous(X)))))&
(((~generous(fred)<~>creative(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)|~strong(X))<=>(~creative(X)&~rich(X))))&
((?[X]:((happy(X)|~strong(X))))=>((strong(susan)|~generous(susan))))&
((?[X]:(humble(X)))<=>(?[X]:((~old(X)|wise(X)))))&
(![X]:((quiet(X)&~patient(X))<=>(brave(X)<~>~wise(X))))&
(![X]:((~curious(X)<~>wise(X))<=>(~rich(X)<~>~wise(X))))&
((rich(john)|patient(john)))&
(?[X]:((brave(X)<~>old(X))))&
((funny(john)&generous(john)))&
((tall(paul)&~kind(paul)))&
((~creative(susan)|curious(susan)))&
(?[X]:(~old(X)))&
((~quiet(john)|~strong(john))) | quiet(alice) | [
"p0",
"p4",
"p5",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8741742944526434781665669
% SZS output start Proof for 8741742944526434781665669
1. ! [X0] : ((~calm(X0) & wise(X0)) <=> (quiet(X0) | ~kind(X0))) [input p0]
5. ! [X0] : (curious(X0) <=> (funny(X0) | ~quiet(X0))) [input p4]
6. ! [X0] : ((wise(X0) <~> quiet(X0)) <=> (curious(X0) <~> calm(X0))) [input p5]
12. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (~rich(X0) & ~creative(X0))) [input p11]
16. ! [X0] : ((~curious(X0) <~> wise(X0)) <=> (~rich(X0) <~> ~wise(X0))) [input p15]
24. quiet(alice) [input hypothesis]
34. ! [X0] : (((~calm(X0) & wise(X0)) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | (calm(X0) | ~wise(X0)))) [nnf transformation 1]
35. ! [X0] : (((~calm(X0) & wise(X0)) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | calm(X0) | ~wise(X0))) [flattening 34]
41. ! [X0] : ((curious(X0) | (~funny(X0) & quiet(X0))) & ((funny(X0) | ~quiet(X0)) | ~curious(X0))) [nnf transformation 5]
42. ! [X0] : ((curious(X0) | (~funny(X0) & quiet(X0))) & (funny(X0) | ~quiet(X0) | ~curious(X0))) [flattening 41]
43. ! [X0] : ((((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) & (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0))))) [nnf transformation 6]
57. ! [X0] : (((~strong(X0) | quiet(X0)) | (rich(X0) | creative(X0))) & ((~rich(X0) & ~creative(X0)) | (strong(X0) & ~quiet(X0)))) [nnf transformation 12]
58. ! [X0] : ((~strong(X0) | quiet(X0) | rich(X0) | creative(X0)) & ((~rich(X0) & ~creative(X0)) | (strong(X0) & ~quiet(X0)))) [flattening 57]
66. ! [X0] : ((((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0))))) [nnf transformation 16]
74. ~quiet(X0) | wise(X0) [cnf transformation 35]
76. ~quiet(X0) | ~calm(X0) [cnf transformation 35]
88. curious(X0) | quiet(X0) [cnf transformation 42]
96. ~quiet(X0) | ~wise(X0) | calm(X0) | ~curious(X0) [cnf transformation 43]
117. ~rich(X0) | ~quiet(X0) [cnf transformation 58]
133. wise(X0) | rich(X0) | wise(X0) | curious(X0) [cnf transformation 66]
137. ~wise(X0) | curious(X0) | ~wise(X0) | rich(X0) [cnf transformation 66]
149. quiet(alice) [cnf transformation 24]
151. wise(X0) | rich(X0) | curious(X0) [duplicate literal removal 133]
153. ~wise(X0) | curious(X0) | rich(X0) [duplicate literal removal 137]
155. ~quiet(X0) | ~wise(X0) | ~curious(X0) [subsumption resolution 96,76]
156. ~curious(X0) | ~quiet(X0) [subsumption resolution 155,74]
253. rich(X0) | curious(X0) [subsumption resolution 151,153]
306. curious(X1) | ~quiet(X1) [resolution 253,117]
308. curious(X1) [subsumption resolution 306,88]
309. ~quiet(X0) [resolution 308,156]
311. $false [resolution 309,149]
% SZS output end Proof for 8741742944526434781665669
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or not tall then mary is both not strong and not rich and vice versa. Everyone who is either not humble or not calm is calm or not funny. Everyone who is not old is both not old and rich and vice versa. If alice is rich or not brave then mary is not brave or generous and vice versa. If someone is patient or not kind then someone is not rich or not wise. If someone is not calm then someone is calm or not tall. Everyone who is not strong or happy is either not strong or happy. Everyone who is either not strong or rich is either not kind or brave and vice versa. If susan is tall then someone is not happy or tall and vice versa. Everyone who is either not old or not brave is not old or not curious. Everyone who is not happy or not creative is not humble. If someone is either calm or curious then someone is old. If someone is both happy and not patient then john is both not quiet and strong and vice versa. If someone is both not strong and wise then someone is either not patient or not creative and vice versa. Everyone who is either not funny or not humble is strong and vice versa. If someone is wise or curious then someone is strong and vice versa. Someone is not brave or not wise. Someone is both rich and not wise. Mary is either not patient or generous. John is both tall and kind. Someone is not brave. Susan is tall or humble. Someone is either not wise or not strong. Someone is both not strong and not happy. | Susan is not generous. | neutral | ((?[X]:((~kind(X)<~>~tall(X))))<=>((~strong(mary)&~rich(mary))))&
(![X]:((~humble(X)<~>~calm(X))=>(calm(X)|~funny(X))))&
(![X]:(~old(X)<=>(~old(X)&rich(X))))&
(((rich(alice)|~brave(alice)))<=>((~brave(mary)|generous(mary))))&
((?[X]:((patient(X)|~kind(X))))=>(?[X]:((~rich(X)|~wise(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((calm(X)|~tall(X)))))&
(![X]:((~strong(X)|happy(X))=>(~strong(X)<~>happy(X))))&
(![X]:((~strong(X)<~>rich(X))<=>(~kind(X)<~>brave(X))))&
((tall(susan))<=>(?[X]:((~happy(X)|tall(X)))))&
(![X]:((~old(X)<~>~brave(X))=>(~old(X)|~curious(X))))&
(![X]:((~happy(X)|~creative(X))=>~humble(X)))&
((?[X]:((calm(X)<~>curious(X))))=>(?[X]:(old(X))))&
((?[X]:((happy(X)&~patient(X))))<=>((~quiet(john)&strong(john))))&
((?[X]:((~strong(X)&wise(X))))<=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:((~funny(X)<~>~humble(X))<=>strong(X)))&
((?[X]:((wise(X)|curious(X))))<=>(?[X]:(strong(X))))&
(?[X]:((~brave(X)|~wise(X))))&
(?[X]:((rich(X)&~wise(X))))&
((~patient(mary)<~>generous(mary)))&
((tall(john)&kind(john)))&
(?[X]:(~brave(X)))&
((tall(susan)|humble(susan)))&
(?[X]:((~wise(X)<~>~strong(X))))&
(?[X]:((~strong(X)&~happy(X)))) | ~generous(susan) | [] | null | 0 |
Everyone who is not calm is either generous or humble. If someone is both funny and generous then someone is funny. Everyone who is not rich or brave is either not calm or not curious. Everyone who is either happy or not brave is funny or not wise. If someone is strong then susan is not patient or happy. Everyone who is either not patient or not happy is both not wise and not funny. If john is either patient or not quiet then someone is either not funny or not patient. Everyone who is humble is not wise and vice versa. If someone is humble or not quiet then someone is not happy. Everyone who is not old is both happy and not happy. Everyone who is not happy is happy or brave and vice versa. Everyone who is both not strong and funny is not patient and vice versa. If susan is either wise or curious then someone is not rich. Everyone who is generous is either not wise or not old. Everyone who is either funny or not patient is either not quiet or curious and vice versa. If alice is not tall or generous then someone is both not patient and not brave. Someone is kind. Someone is both generous and not patient. Alice is happy or curious. Someone is not patient. Someone is patient. Someone is old or kind. Mary is either not quiet or old. | Alice is humble. | entailment | (![X]:(~calm(X)=>(generous(X)<~>humble(X))))&
((?[X]:((funny(X)&generous(X))))=>(?[X]:(funny(X))))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)<~>~curious(X))))&
(![X]:((happy(X)<~>~brave(X))=>(funny(X)|~wise(X))))&
((?[X]:(strong(X)))=>((~patient(susan)|happy(susan))))&
(![X]:((~patient(X)<~>~happy(X))=>(~wise(X)&~funny(X))))&
(((patient(john)<~>~quiet(john)))=>(?[X]:((~funny(X)<~>~patient(X)))))&
(![X]:(humble(X)<=>~wise(X)))&
((?[X]:((humble(X)|~quiet(X))))=>(?[X]:(~happy(X))))&
(![X]:(~old(X)=>(happy(X)&~happy(X))))&
(![X]:(~happy(X)<=>(happy(X)|brave(X))))&
(![X]:((~strong(X)&funny(X))<=>~patient(X)))&
(((wise(susan)<~>curious(susan)))=>(?[X]:(~rich(X))))&
(![X]:(generous(X)=>(~wise(X)<~>~old(X))))&
(![X]:((funny(X)<~>~patient(X))<=>(~quiet(X)<~>curious(X))))&
(((~tall(alice)|generous(alice)))=>(?[X]:((~patient(X)&~brave(X)))))&
(?[X]:(kind(X)))&
(?[X]:((generous(X)&~patient(X))))&
((happy(alice)|curious(alice)))&
(?[X]:(~patient(X)))&
(?[X]:(patient(X)))&
(?[X]:((old(X)|kind(X))))&
((~quiet(mary)<~>old(mary))) | humble(alice) | [
"p0",
"p2",
"p10",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9059362280541625555704829
% SZS output start Proof for 9059362280541625555704829
1. ! [X0] : (~calm(X0) => (generous(X0) <~> humble(X0))) [input p0]
3. ! [X0] : ((brave(X0) | ~rich(X0)) => (~calm(X0) <~> ~curious(X0))) [input p2]
11. ! [X0] : (~happy(X0) <=> (brave(X0) | happy(X0))) [input p10]
16. (generous(alice) | ~tall(alice)) => ? [X0] : (~brave(X0) & ~patient(X0)) [input p15]
19. curious(alice) | happy(alice) [input p18]
24. ~humble(alice) [input hypothesis]
29. generous(alice) => ? [X0] : (~brave(X0) & ~patient(X0)) [pure predicate removal 16]
30. ! [X0] : ((generous(X0) <~> humble(X0)) | calm(X0)) [ennf transformation 1]
32. ! [X0] : ((~calm(X0) <~> ~curious(X0)) | (~brave(X0) & rich(X0))) [ennf transformation 3]
43. ? [X0] : (~brave(X0) & ~patient(X0)) | ~generous(alice) [ennf transformation 29]
44. ! [X0] : (((~humble(X0) | ~generous(X0)) & (humble(X0) | generous(X0))) | calm(X0)) [nnf transformation 30]
48. ! [X0] : (((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (~brave(X0) & rich(X0))) [nnf transformation 32]
58. ! [X0] : ((~happy(X0) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | happy(X0))) [nnf transformation 11]
59. ! [X0] : ((~happy(X0) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | happy(X0))) [flattening 58]
67. ? [X0] : (~brave(X0) & ~patient(X0)) => (~brave(sK4) & ~patient(sK4)) [choice axiom]
68. (~brave(sK4) & ~patient(sK4)) | ~generous(alice) [skolemisation 43,67]
76. humble(X0) | generous(X0) | calm(X0) [cnf transformation 44]
80. ~curious(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 48]
100. brave(X0) | happy(X0) | happy(X0) [cnf transformation 59]
101. ~happy(X0) | ~happy(X0) [cnf transformation 59]
119. ~brave(sK4) | ~generous(alice) [cnf transformation 68]
122. curious(alice) | happy(alice) [cnf transformation 19]
127. ~humble(alice) [cnf transformation 24]
128. brave(X0) | happy(X0) [duplicate literal removal 100]
129. ~happy(X0) [duplicate literal removal 101]
183. brave(X0) [subsumption resolution 128,129]
203. ~generous(alice) [subsumption resolution 119,183]
204. curious(alice) [subsumption resolution 122,129]
212. generous(alice) | calm(alice) [resolution 76,127]
213. calm(alice) [subsumption resolution 212,203]
218. ~calm(alice) | ~brave(alice) [resolution 80,204]
219. ~brave(alice) [subsumption resolution 218,213]
220. $false [subsumption resolution 219,183]
% SZS output end Proof for 9059362280541625555704829
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is either not funny or not quiet and vice versa.
Everyone who is not happy or not quiet is calm.
If someone is tall then someone is both curious and calm.
Everyone who is both wise and patient is not happy and vice versa.
If mary is creative then someone is either tall or not strong and vice versa.
If someone is kind then someone is either wise or rich.
If someone is generous then someone is wise or humble and vice versa.
Everyone who is both happy and not rich is either old or not happy and vice versa.
Everyone who is quiet is creative and vice versa.
If fred is happy or not quiet then someone is either strong or patient and vice versa.
Everyone who is funny is either not curious or happy and vice versa.
Everyone who is calm is both strong and generous and vice versa.
Everyone who is not patient is both humble and not funny.
If lucy is happy then someone is funny or patient.
Everyone who is old or not kind is both old and not curious.
Everyone who is not calm or tall is both creative and not kind and vice versa.
Paul is either strong or quiet.
Mary is either not funny or not calm.
Lucy is either patient or funny.
Someone is tall or old.
Paul is either generous or humble.
Paul is not quiet.
Someone is not patient or not humble. | Lucy is creative. | contradiction | (![X]:(wise(X)<=>(~funny(X)<~>~quiet(X))))&
(![X]:((~happy(X)|~quiet(X))=>calm(X)))&
((?[X]:(tall(X)))=>(?[X]:((curious(X)&calm(X)))))&
(![X]:((wise(X)&patient(X))<=>~happy(X)))&
((creative(mary))<=>(?[X]:((tall(X)<~>~strong(X)))))&
((?[X]:(kind(X)))=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((happy(X)&~rich(X))<=>(old(X)<~>~happy(X))))&
(![X]:(quiet(X)<=>creative(X)))&
(((happy(fred)|~quiet(fred)))<=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:(funny(X)<=>(~curious(X)<~>happy(X))))&
(![X]:(calm(X)<=>(strong(X)&generous(X))))&
(![X]:(~patient(X)=>(humble(X)&~funny(X))))&
((happy(lucy))=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((old(X)|~kind(X))=>(old(X)&~curious(X))))&
(![X]:((~calm(X)|tall(X))<=>(creative(X)&~kind(X))))&
((strong(paul)<~>quiet(paul)))&
((~funny(mary)<~>~calm(mary)))&
((patient(lucy)<~>funny(lucy)))&
(?[X]:((tall(X)|old(X))))&
((generous(paul)<~>humble(paul)))&
(~quiet(paul))&
(?[X]:((~patient(X)|~humble(X)))) | creative(lucy) | [
"p0",
"p3",
"p7",
"p8",
"p10",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4605735026624633482832943
% SZS output start Proof for 4605735026624633482832943
1. ! [X0] : (wise(X0) <=> (~funny(X0) <~> ~quiet(X0))) [input p0]
4. ! [X0] : ((patient(X0) & wise(X0)) <=> ~happy(X0)) [input p3]
8. ! [X0] : ((~rich(X0) & happy(X0)) <=> (old(X0) <~> ~happy(X0))) [input p7]
9. ! [X0] : (quiet(X0) <=> creative(X0)) [input p8]
11. ! [X0] : (funny(X0) <=> (~curious(X0) <~> happy(X0))) [input p10]
13. ! [X0] : (~patient(X0) => (~funny(X0) & humble(X0))) [input p12]
15. ! [X0] : ((~kind(X0) | old(X0)) => (~curious(X0) & old(X0))) [input p14]
19. patient(lucy) <~> funny(lucy) [input p18]
24. creative(lucy) [input hypothesis]
31. ! [X0] : ((~funny(X0) & humble(X0)) | patient(X0)) [ennf transformation 13]
33. ! [X0] : ((~curious(X0) & old(X0)) | (kind(X0) & ~old(X0))) [ennf transformation 15]
34. ! [X0] : ((wise(X0) | ((~funny(X0) | quiet(X0)) & (~quiet(X0) | funny(X0)))) & (((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | ~wise(X0))) [nnf transformation 1]
38. ! [X0] : (((patient(X0) & wise(X0)) | happy(X0)) & (~happy(X0) | (~patient(X0) | ~wise(X0)))) [nnf transformation 4]
39. ! [X0] : (((patient(X0) & wise(X0)) | happy(X0)) & (~happy(X0) | ~patient(X0) | ~wise(X0))) [flattening 38]
53. ! [X0] : (((~rich(X0) & happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | (rich(X0) | ~happy(X0)))) [nnf transformation 8]
54. ! [X0] : (((~rich(X0) & happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | rich(X0) | ~happy(X0))) [flattening 53]
55. ! [X0] : ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))) [nnf transformation 9]
61. ! [X0] : ((funny(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) & (((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | ~funny(X0))) [nnf transformation 11]
70. (~funny(lucy) | ~patient(lucy)) & (funny(lucy) | patient(lucy)) [nnf transformation 19]
78. ~quiet(X0) | wise(X0) | funny(X0) [cnf transformation 34]
84. ~patient(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 39]
99. happy(X0) | old(X0) | happy(X0) [cnf transformation 54]
103. ~creative(X0) | quiet(X0) [cnf transformation 55]
112. curious(X0) | happy(X0) | funny(X0) [cnf transformation 61]
118. ~funny(X0) | patient(X0) [cnf transformation 31]
122. ~old(X0) | ~curious(X0) [cnf transformation 33]
133. funny(lucy) | patient(lucy) [cnf transformation 70]
134. ~funny(lucy) | ~patient(lucy) [cnf transformation 70]
140. creative(lucy) [cnf transformation 24]
142. old(X0) | happy(X0) [duplicate literal removal 99]
246. 24 <=> happy(lucy) [avatar definition]
248. ~happy(lucy) <- (~24) [avatar component clause 246]
274. ~funny(lucy) [subsumption resolution 134,118]
275. patient(lucy) [subsumption resolution 133,274]
318. quiet(lucy) [resolution 103,140]
343. ~curious(X0) | happy(X0) [resolution 142,122]
373. wise(lucy) | funny(lucy) [resolution 78,318]
382. ~happy(lucy) | ~wise(lucy) [resolution 84,275]
488. 51 <=> wise(lucy) [avatar definition]
491. ~51 | ~24 [avatar split clause 382,246,488]
492. wise(lucy) [subsumption resolution 373,274]
493. 51 [avatar split clause 492,488]
621. happy(X0) | happy(X0) | funny(X0) [resolution 343,112]
624. happy(X0) | funny(X0) [duplicate literal removal 621]
804. funny(lucy) <- (~24) [resolution 624,248]
808. $false <- (~24) [subsumption resolution 804,274]
809. 24 [avatar contradiction clause 808]
812. $false [avatar sat refutation 491,493,809]
% SZS output end Proof for 4605735026624633482832943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then alice is either rich or not patient. Everyone who is creative or funny is either not brave or not humble and vice versa. If someone is both creative and happy then someone is either happy or not humble and vice versa. Everyone who is curious or tall is brave. Everyone who is creative or not funny is not creative and vice versa. If someone is not funny or not strong then someone is either not funny or creative. Everyone who is not generous or not curious is humble and vice versa. Everyone who is either calm or not happy is both humble and not kind. If john is either not old or not brave then someone is not happy or rich and vice versa. Everyone who is not wise or tall is either not generous or not strong and vice versa. If mary is both not curious and generous then someone is not creative and vice versa. Everyone who is either not curious or not funny is either not calm or humble. Everyone who is both wise and calm is not brave. Everyone who is patient is both generous and not humble. If fred is both tall and brave then someone is either wise or not strong and vice versa. If susan is either not calm or curious then someone is either not funny or not rich. Someone is kind. Someone is not happy. Someone is either rich or happy. Paul is not strong or curious. Someone is generous or humble. | John is old. | contradiction | ((?[X]:(~quiet(X)))=>((rich(alice)<~>~patient(alice))))&
(![X]:((creative(X)|funny(X))<=>(~brave(X)<~>~humble(X))))&
((?[X]:((creative(X)&happy(X))))<=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:((curious(X)|tall(X))=>brave(X)))&
(![X]:((creative(X)|~funny(X))<=>~creative(X)))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:((~funny(X)<~>creative(X)))))&
(![X]:((~generous(X)|~curious(X))<=>humble(X)))&
(![X]:((calm(X)<~>~happy(X))=>(humble(X)&~kind(X))))&
(((~old(john)<~>~brave(john)))<=>(?[X]:((~happy(X)|rich(X)))))&
(![X]:((~wise(X)|tall(X))<=>(~generous(X)<~>~strong(X))))&
(((~curious(mary)&generous(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)<~>~funny(X))=>(~calm(X)<~>humble(X))))&
(![X]:((wise(X)&calm(X))=>~brave(X)))&
(![X]:(patient(X)=>(generous(X)&~humble(X))))&
(((tall(fred)&brave(fred)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(susan)<~>curious(susan)))=>(?[X]:((~funny(X)<~>~rich(X)))))&
(?[X]:(kind(X)))&
(?[X]:(~happy(X)))&
(?[X]:((rich(X)<~>happy(X))))&
((~strong(paul)|curious(paul)))&
(?[X]:((generous(X)|humble(X)))) | old(john) | [
"p1",
"p3",
"p4",
"p6",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2249382886810290153230755
% SZS output start Proof for 2249382886810290153230755
2. ! [X0] : ((funny(X0) | creative(X0)) <=> (~brave(X0) <~> ~humble(X0))) [input p1]
4. ! [X0] : ((tall(X0) | curious(X0)) => brave(X0)) [input p3]
5. ! [X0] : ((~funny(X0) | creative(X0)) <=> ~creative(X0)) [input p4]
7. ! [X0] : ((~curious(X0) | ~generous(X0)) <=> humble(X0)) [input p6]
9. (~old(john) <~> ~brave(john)) <=> ? [X0] : (rich(X0) | ~happy(X0)) [input p8]
18. ? [X0] : ~happy(X0) [input p17]
22. old(john) [input hypothesis]
27. ! [X0] : (brave(X0) | (~tall(X0) & ~curious(X0))) [ennf transformation 4]
34. ! [X0] : (((funny(X0) | creative(X0)) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0)))) & (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | (~funny(X0) & ~creative(X0)))) [nnf transformation 2]
35. ! [X0] : ((funny(X0) | creative(X0) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0)))) & (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | (~funny(X0) & ~creative(X0)))) [flattening 34]
41. ! [X0] : (((~funny(X0) | creative(X0)) | creative(X0)) & (~creative(X0) | (funny(X0) & ~creative(X0)))) [nnf transformation 5]
42. ! [X0] : ((~funny(X0) | creative(X0) | creative(X0)) & (~creative(X0) | (funny(X0) & ~creative(X0)))) [flattening 41]
47. ! [X0] : (((~curious(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (curious(X0) & generous(X0)))) [nnf transformation 7]
48. ! [X0] : ((~curious(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (curious(X0) & generous(X0)))) [flattening 47]
50. (((brave(john) | old(john)) & (~brave(john) | ~old(john))) | ! [X0] : (~rich(X0) & happy(X0))) & (? [X0] : (rich(X0) | ~happy(X0)) | ((~old(john) | brave(john)) & (~brave(john) | old(john)))) [nnf transformation 9]
51. (((brave(john) | old(john)) & (~brave(john) | ~old(john))) | ! [X0] : (~rich(X0) & happy(X0))) & (? [X1] : (rich(X1) | ~happy(X1)) | ((~old(john) | brave(john)) & (~brave(john) | old(john)))) [rectify 50]
52. ? [X1] : (rich(X1) | ~happy(X1)) => (rich(sK3) | ~happy(sK3)) [choice axiom]
53. (((brave(john) | old(john)) & (~brave(john) | ~old(john))) | ! [X0] : (~rich(X0) & happy(X0))) & ((rich(sK3) | ~happy(sK3)) | ((~old(john) | brave(john)) & (~brave(john) | old(john)))) [skolemisation 51,52]
72. ? [X0] : ~happy(X0) => ~happy(sK8) [choice axiom]
73. ~happy(sK8) [skolemisation 18,72]
83. ~humble(X0) | creative(X0) | funny(X0) | brave(X0) [cnf transformation 35]
91. ~curious(X0) | brave(X0) [cnf transformation 27]
93. ~creative(X0) | ~creative(X0) [cnf transformation 42]
95. ~funny(X0) | creative(X0) | creative(X0) [cnf transformation 42]
101. curious(X0) | humble(X0) [cnf transformation 48]
109. ~brave(john) | ~old(john) | happy(X0) [cnf transformation 53]
138. ~happy(sK8) [cnf transformation 73]
143. old(john) [cnf transformation 22]
144. ~creative(X0) [duplicate literal removal 93]
145. ~funny(X0) | creative(X0) [duplicate literal removal 95]
181. 9 <=> old(john) [avatar definition]
185. 10 <=> brave(john) [avatar definition]
186. ~brave(john) <- (~10) [avatar component clause 185]
190. 11 <=> ! [X0] : happy(X0) [avatar definition]
191. happy(X0) <- (11) [avatar component clause 190]
194. 11 | ~9 | ~10 [avatar split clause 109,185,181,190]
278. 9 [avatar split clause 143,181]
283. humble(X0) | brave(X0) [resolution 101,91]
384. creative(X0) | funny(X0) | brave(X0) | brave(X0) [resolution 83,283]
389. creative(X0) | funny(X0) | brave(X0) [duplicate literal removal 384]
390. brave(X0) | funny(X0) [subsumption resolution 389,144]
585. funny(john) <- (~10) [resolution 390,186]
639. creative(john) <- (~10) [resolution 585,145]
649. $false <- (~10) [subsumption resolution 639,144]
650. 10 [avatar contradiction clause 649]
660. $false <- (11) [resolution 191,138]
661. ~11 [avatar contradiction clause 660]
665. $false [avatar sat refutation 194,278,650,661]
% SZS output end Proof for 2249382886810290153230755
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or kind is either not humble or not quiet and vice versa.
Everyone who is rich or strong is both not calm and calm and vice versa.
Everyone who is calm or not brave is either patient or old.
If fred is strong or old then someone is not kind.
Everyone who is both not brave and not humble is both not calm and strong.
Everyone who is either not curious or funny is both curious and creative and vice versa.
Everyone who is both not kind and not curious is both not strong and humble and vice versa.
Everyone who is patient is both brave and not quiet and vice versa.
If mary is brave or quiet then mary is either rich or not patient and vice versa.
Everyone who is both generous and not patient is both not kind and humble.
If someone is either strong or tall then alice is humble.
Everyone who is both not calm and not curious is old or rich and vice versa.
If someone is funny or not brave then someone is not curious or not kind and vice versa.
If someone is not wise or not old then lucy is curious or not calm and vice versa.
If alice is both not humble and funny then someone is not curious and vice versa.
Fred is brave or not humble.
Paul is not curious.
Paul is humble.
Someone is either calm or brave.
Someone is either happy or funny.
Someone is not quiet or strong.
Lucy is not calm or brave. | Paul is not humble. | contradiction | (![X]:((~calm(X)<~>kind(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((rich(X)|strong(X))<=>(~calm(X)&calm(X))))&
(![X]:((calm(X)|~brave(X))=>(patient(X)<~>old(X))))&
(((strong(fred)|old(fred)))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)&~humble(X))=>(~calm(X)&strong(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(curious(X)&creative(X))))&
(![X]:((~kind(X)&~curious(X))<=>(~strong(X)&humble(X))))&
(![X]:(patient(X)<=>(brave(X)&~quiet(X))))&
(((brave(mary)|quiet(mary)))<=>((rich(mary)<~>~patient(mary))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((brave(fred)|~humble(fred)))&
(~curious(paul))&
(humble(paul))&
(?[X]:((calm(X)<~>brave(X))))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy))) | ~humble(paul) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1164816459509250317284779
% SZS output start Proof for 1164816459509250317284779
18. humble(paul) [input p17]
23. ~humble(paul) [input hypothesis]
131. humble(paul) [cnf transformation 18]
138. ~humble(paul) [cnf transformation 23]
275. $false [subsumption resolution 138,131]
% SZS output end Proof for 1164816459509250317284779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not creative or not curious then someone is either not tall or old.
If someone is not kind or kind then mary is not generous or rich and vice versa.
Everyone who is generous is not funny and vice versa.
If paul is not old or generous then someone is wise and vice versa.
If paul is creative then john is not generous or not kind.
If mary is either tall or not patient then fred is brave.
If someone is rich then someone is quiet.
Everyone who is either not old or not brave is tall or not strong and vice versa.
If someone is both funny and patient then paul is curious.
If someone is both not strong and not old then mary is both not happy and not quiet and vice versa.
If susan is old or rich then someone is both rich and not curious.
Everyone who is both wise and calm is either not humble or not happy and vice versa.
If someone is either not kind or funny then alice is both happy and wise.
Everyone who is not curious is both creative and rich and vice versa.
If someone is both strong and wise then susan is either wise or funny and vice versa.
Everyone who is not strong or strong is both funny and patient.
Someone is brave.
Someone is tall.
Someone is happy.
Lucy is funny.
Lucy is humble.
John is not curious.
Susan is rich. | Lucy is not generous. | entailment | (((~creative(paul)|~curious(paul)))=>(?[X]:((~tall(X)<~>old(X)))))&
((?[X]:((~kind(X)|kind(X))))<=>((~generous(mary)|rich(mary))))&
(![X]:(generous(X)<=>~funny(X)))&
(((~old(paul)|generous(paul)))<=>(?[X]:(wise(X))))&
((creative(paul))=>((~generous(john)|~kind(john))))&
(((tall(mary)<~>~patient(mary)))=>(brave(fred)))&
((?[X]:(rich(X)))=>(?[X]:(quiet(X))))&
(![X]:((~old(X)<~>~brave(X))<=>(tall(X)|~strong(X))))&
((?[X]:((funny(X)&patient(X))))=>(curious(paul)))&
((?[X]:((~strong(X)&~old(X))))<=>((~happy(mary)&~quiet(mary))))&
(((old(susan)|rich(susan)))=>(?[X]:((rich(X)&~curious(X)))))&
(![X]:((wise(X)&calm(X))<=>(~humble(X)<~>~happy(X))))&
((?[X]:((~kind(X)<~>funny(X))))=>((happy(alice)&wise(alice))))&
(![X]:(~curious(X)<=>(creative(X)&rich(X))))&
((?[X]:((strong(X)&wise(X))))<=>((wise(susan)<~>funny(susan))))&
(![X]:((~strong(X)|strong(X))=>(funny(X)&patient(X))))&
(?[X]:(brave(X)))&
(?[X]:(tall(X)))&
(?[X]:(happy(X)))&
(funny(lucy))&
(humble(lucy))&
(~curious(john))&
(rich(susan)) | ~generous(lucy) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6404595108329890947501320
% SZS output start Proof for 6404595108329890947501320
3. ! [X0] : (generous(X0) <=> ~funny(X0)) [input p2]
16. ! [X0] : ((strong(X0) | ~strong(X0)) => (patient(X0) & funny(X0))) [input p15]
24. generous(lucy) [input hypothesis]
34. ! [X0] : ((patient(X0) & funny(X0)) | (~strong(X0) & strong(X0))) [ennf transformation 16]
43. ! [X0] : ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))) [nnf transformation 3]
85. ~funny(X0) | ~generous(X0) [cnf transformation 43]
128. funny(X0) | strong(X0) [cnf transformation 34]
129. funny(X0) | ~strong(X0) [cnf transformation 34]
139. generous(lucy) [cnf transformation 24]
316. funny(X0) [subsumption resolution 128,129]
329. ~generous(X0) [resolution 85,316]
331. $false [resolution 329,139]
% SZS output end Proof for 6404595108329890947501320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and strong is kind or not humble and vice versa.
Everyone who is not strong is old or not curious.
If susan is both wise and quiet then mary is quiet or strong and vice versa.
Everyone who is strong or rich is either not wise or not kind and vice versa.
If lucy is either not wise or old then john is both not brave and generous.
Everyone who is not calm or creative is kind and vice versa.
Everyone who is not curious or wise is both not generous and not creative.
If john is not old then john is creative or humble and vice versa.
If someone is creative then someone is either quiet or not happy and vice versa.
Everyone who is not brave or not rich is either creative or not calm and vice versa.
Everyone who is funny or not quiet is quiet or generous and vice versa.
If someone is curious or not funny then mary is either not wise or not humble.
Everyone who is both not generous and kind is not patient or not wise and vice versa.
If someone is either generous or strong then mary is not happy or not creative and vice versa.
If someone is not calm then john is either wise or tall and vice versa.
If john is not strong then mary is patient or not old and vice versa.
Someone is calm.
Someone is both not old and not wise.
Paul is not strong.
Mary is both rich and not happy.
Someone is humble.
Mary is both old and not curious.
Lucy is funny or not humble.
Someone is funny or not generous. | John is wise. | entailment | (![X]:((~tall(X)&strong(X))<=>(kind(X)|~humble(X))))&
(![X]:(~strong(X)=>(old(X)|~curious(X))))&
(((wise(susan)&quiet(susan)))<=>((quiet(mary)|strong(mary))))&
(![X]:((strong(X)|rich(X))<=>(~wise(X)<~>~kind(X))))&
(((~wise(lucy)<~>old(lucy)))=>((~brave(john)&generous(john))))&
(![X]:((~calm(X)|creative(X))<=>kind(X)))&
(![X]:((~curious(X)|wise(X))=>(~generous(X)&~creative(X))))&
((~old(john))<=>((creative(john)|humble(john))))&
((?[X]:(creative(X)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
(![X]:((~brave(X)|~rich(X))<=>(creative(X)<~>~calm(X))))&
(![X]:((funny(X)|~quiet(X))<=>(quiet(X)|generous(X))))&
((?[X]:((curious(X)|~funny(X))))=>((~wise(mary)<~>~humble(mary))))&
(![X]:((~generous(X)&kind(X))<=>(~patient(X)|~wise(X))))&
((?[X]:((generous(X)<~>strong(X))))<=>((~happy(mary)|~creative(mary))))&
((?[X]:(~calm(X)))<=>((wise(john)<~>tall(john))))&
((~strong(john))<=>((patient(mary)|~old(mary))))&
(?[X]:(calm(X)))&
(?[X]:((~old(X)&~wise(X))))&
(~strong(paul))&
((rich(mary)&~happy(mary)))&
(?[X]:(humble(X)))&
((old(mary)&~curious(mary)))&
((funny(lucy)|~humble(lucy)))&
(?[X]:((funny(X)|~generous(X)))) | wise(john) | [
"p0",
"p5",
"p6",
"p12",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5582049154816437550749058
% SZS output start Proof for 5582049154816437550749058
1. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (~humble(X0) | kind(X0))) [input p0]
6. ! [X0] : ((creative(X0) | ~calm(X0)) <=> kind(X0)) [input p5]
7. ! [X0] : ((wise(X0) | ~curious(X0)) => (~creative(X0) & ~generous(X0))) [input p6]
13. ! [X0] : ((kind(X0) & ~generous(X0)) <=> (~wise(X0) | ~patient(X0))) [input p12]
15. ? [X0] : ~calm(X0) <=> (wise(john) <~> tall(john)) [input p14]
16. ~strong(john) <=> (~old(mary) | patient(mary)) [input p15]
22. ~curious(mary) & old(mary) [input p21]
25. ~wise(john) [input hypothesis]
30. ! [X0] : ((~creative(X0) & ~generous(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 7]
32. ! [X0] : (((strong(X0) & ~tall(X0)) | (humble(X0) & ~kind(X0))) & ((~humble(X0) | kind(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 1]
33. ! [X0] : (((strong(X0) & ~tall(X0)) | (humble(X0) & ~kind(X0))) & (~humble(X0) | kind(X0) | ~strong(X0) | tall(X0))) [flattening 32]
39. ! [X0] : (((creative(X0) | ~calm(X0)) | ~kind(X0)) & (kind(X0) | (~creative(X0) & calm(X0)))) [nnf transformation 6]
40. ! [X0] : ((creative(X0) | ~calm(X0) | ~kind(X0)) & (kind(X0) | (~creative(X0) & calm(X0)))) [flattening 39]
53. ! [X0] : (((kind(X0) & ~generous(X0)) | (wise(X0) & patient(X0))) & ((~wise(X0) | ~patient(X0)) | (~kind(X0) | generous(X0)))) [nnf transformation 13]
54. ! [X0] : (((kind(X0) & ~generous(X0)) | (wise(X0) & patient(X0))) & (~wise(X0) | ~patient(X0) | ~kind(X0) | generous(X0))) [flattening 53]
60. (? [X0] : ~calm(X0) | ((wise(john) | ~tall(john)) & (tall(john) | ~wise(john)))) & (((~tall(john) | ~wise(john)) & (tall(john) | wise(john))) | ! [X0] : calm(X0)) [nnf transformation 15]
61. (? [X0] : ~calm(X0) | ((wise(john) | ~tall(john)) & (tall(john) | ~wise(john)))) & (((~tall(john) | ~wise(john)) & (tall(john) | wise(john))) | ! [X1] : calm(X1)) [rectify 60]
62. ? [X0] : ~calm(X0) => ~calm(sK3) [choice axiom]
63. (~calm(sK3) | ((wise(john) | ~tall(john)) & (tall(john) | ~wise(john)))) & (((~tall(john) | ~wise(john)) & (tall(john) | wise(john))) | ! [X1] : calm(X1)) [skolemisation 61,62]
64. (~strong(john) | (old(mary) & ~patient(mary))) & ((~old(mary) | patient(mary)) | strong(john)) [nnf transformation 16]
65. (~strong(john) | (old(mary) & ~patient(mary))) & (~old(mary) | patient(mary) | strong(john)) [flattening 64]
75. ~kind(X0) | ~tall(X0) [cnf transformation 33]
77. ~kind(X0) | strong(X0) [cnf transformation 33]
97. ~calm(X0) | creative(X0) | ~kind(X0) [cnf transformation 40]
100. ~creative(X0) | curious(X0) [cnf transformation 30]
126. patient(X0) | kind(X0) [cnf transformation 54]
127. wise(X0) | kind(X0) [cnf transformation 54]
134. tall(john) | wise(john) | calm(X1) [cnf transformation 63]
139. ~strong(john) | ~patient(mary) [cnf transformation 65]
149. ~curious(mary) [cnf transformation 22]
152. ~wise(john) [cnf transformation 25]
259. 22 <=> creative(mary) [avatar definition]
261. creative(mary) <- (22) [avatar component clause 259]
279. 26 <=> tall(john) [avatar definition]
283. 27 <=> wise(john) [avatar definition]
284. ~wise(john) <- (~27) [avatar component clause 283]
293. 29 <=> ! [X1] : calm(X1) [avatar definition]
294. calm(X1) <- (29) [avatar component clause 293]
296. 29 | 27 | 26 [avatar split clause 134,279,283,293]
302. 31 <=> strong(john) [avatar definition]
307. 32 <=> patient(mary) [avatar definition]
309. ~patient(mary) <- (~32) [avatar component clause 307]
310. ~32 | ~31 [avatar split clause 139,302,307]
323. ~27 [avatar split clause 152,283]
344. kind(john) <- (~27) [resolution 127,284]
359. strong(john) <- (~27) [resolution 344,77]
360. ~tall(john) <- (~27) [resolution 344,75]
365. ~26 | 27 [avatar split clause 360,283,279]
366. 31 | 27 [avatar split clause 359,283,302]
369. kind(mary) <- (~32) [resolution 309,126]
411. ~kind(X0) | creative(X0) <- (29) [resolution 97,294]
499. creative(mary) <- (29, ~32) [resolution 411,369]
504. 22 | ~29 | 32 [avatar split clause 499,307,293,259]
522. curious(mary) <- (22) [resolution 261,100]
526. $false <- (22) [subsumption resolution 522,149]
527. ~22 [avatar contradiction clause 526]
528. $false [avatar sat refutation 296,310,323,365,366,504,527]
% SZS output end Proof for 5582049154816437550749058
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and not tall is humble and vice versa. Everyone who is not wise or not generous is either not quiet or not patient and vice versa. If someone is wise then susan is not funny. Everyone who is either not quiet or not generous is not funny. If someone is strong or brave then someone is both not rich and not creative and vice versa. Everyone who is either kind or wise is not strong. Everyone who is wise is not calm or not brave and vice versa. Everyone who is strong is both not funny and wise. If someone is both not wise and kind then john is either not rich or calm and vice versa. If someone is either not tall or quiet then susan is old and vice versa. Everyone who is not kind or not humble is either generous or curious. If john is either happy or generous then someone is either not quiet or not calm and vice versa. If someone is patient or not old then alice is humble and vice versa. Everyone who is not quiet or not wise is both generous and calm. Everyone who is either not curious or not patient is either rich or old. If susan is both funny and not creative then lucy is not happy or humble. Someone is either not brave or not funny. Fred is both not humble and not old. Someone is either not humble or generous. Fred is rich. Susan is not tall or not old. Someone is both not rich and not patient. John is calm or not humble. Someone is either tall or not quiet. | Alice is not tall. | entailment | (![X]:((~happy(X)&~tall(X))<=>humble(X)))&
(![X]:((~wise(X)|~generous(X))<=>(~quiet(X)<~>~patient(X))))&
((?[X]:(wise(X)))=>(~funny(susan)))&
(![X]:((~quiet(X)<~>~generous(X))=>~funny(X)))&
((?[X]:((strong(X)|brave(X))))<=>(?[X]:((~rich(X)&~creative(X)))))&
(![X]:((kind(X)<~>wise(X))=>~strong(X)))&
(![X]:(wise(X)<=>(~calm(X)|~brave(X))))&
(![X]:(strong(X)=>(~funny(X)&wise(X))))&
((?[X]:((~wise(X)&kind(X))))<=>((~rich(john)<~>calm(john))))&
((?[X]:((~tall(X)<~>quiet(X))))<=>(old(susan)))&
(![X]:((~kind(X)|~humble(X))=>(generous(X)<~>curious(X))))&
(((happy(john)<~>generous(john)))<=>(?[X]:((~quiet(X)<~>~calm(X)))))&
((?[X]:((patient(X)|~old(X))))<=>(humble(alice)))&
(![X]:((~quiet(X)|~wise(X))=>(generous(X)&calm(X))))&
(![X]:((~curious(X)<~>~patient(X))=>(rich(X)<~>old(X))))&
(((funny(susan)&~creative(susan)))=>((~happy(lucy)|humble(lucy))))&
(?[X]:((~brave(X)<~>~funny(X))))&
((~humble(fred)&~old(fred)))&
(?[X]:((~humble(X)<~>generous(X))))&
(rich(fred))&
((~tall(susan)|~old(susan)))&
(?[X]:((~rich(X)&~patient(X))))&
((calm(john)|~humble(john)))&
(?[X]:((tall(X)<~>~quiet(X)))) | ~tall(alice) | [
"p0",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 471866818684566802660382
% SZS output start Proof for 471866818684566802660382
1. ! [X0] : ((~tall(X0) & ~happy(X0)) <=> humble(X0)) [input p0]
13. ? [X0] : (~old(X0) | patient(X0)) <=> humble(alice) [input p12]
18. ~old(fred) & ~humble(fred) [input p17]
25. tall(alice) [input hypothesis]
36. ! [X0] : (((~tall(X0) & ~happy(X0)) | ~humble(X0)) & (humble(X0) | (tall(X0) | happy(X0)))) [nnf transformation 1]
37. ! [X0] : (((~tall(X0) & ~happy(X0)) | ~humble(X0)) & (humble(X0) | tall(X0) | happy(X0))) [flattening 36]
62. (? [X0] : (~old(X0) | patient(X0)) | ~humble(alice)) & (humble(alice) | ! [X0] : (old(X0) & ~patient(X0))) [nnf transformation 13]
63. (? [X0] : (~old(X0) | patient(X0)) | ~humble(alice)) & (humble(alice) | ! [X1] : (old(X1) & ~patient(X1))) [rectify 62]
64. ? [X0] : (~old(X0) | patient(X0)) => (~old(sK5) | patient(sK5)) [choice axiom]
65. ((~old(sK5) | patient(sK5)) | ~humble(alice)) & (humble(alice) | ! [X1] : (old(X1) & ~patient(X1))) [skolemisation 63,64]
80. ~humble(X0) | ~tall(X0) [cnf transformation 37]
125. humble(alice) | old(X1) [cnf transformation 65]
139. ~old(fred) [cnf transformation 18]
149. tall(alice) [cnf transformation 25]
266. 26 <=> humble(alice) [avatar definition]
267. humble(alice) <- (26) [avatar component clause 266]
279. 29 <=> ! [X1] : old(X1) [avatar definition]
280. old(X1) <- (29) [avatar component clause 279]
281. 29 | 26 [avatar split clause 125,266,279]
347. ~tall(alice) <- (26) [resolution 80,267]
348. $false <- (26) [subsumption resolution 347,149]
349. ~26 [avatar contradiction clause 348]
350. $false <- (29) [resolution 280,139]
353. ~29 [avatar contradiction clause 350]
354. $false [avatar sat refutation 281,349,353]
% SZS output end Proof for 471866818684566802660382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and not wise then someone is both funny and not funny and vice versa.
Everyone who is either rich or not humble is not curious.
If fred is not humble then john is not generous and vice versa.
If john is both funny and wise then fred is funny or patient.
Everyone who is either happy or wise is not tall.
Everyone who is both not creative and not quiet is not creative or generous and vice versa.
Everyone who is not old or generous is patient and vice versa.
Everyone who is either not kind or not old is both brave and not humble.
Everyone who is both not quiet and brave is both not curious and not patient and vice versa.
If john is tall or not humble then someone is not kind or not brave and vice versa.
Everyone who is both strong and old is either rich or generous and vice versa.
If john is both not quiet and wise then someone is either not strong or not brave and vice versa.
Everyone who is not rich is either not patient or not quiet.
If someone is not humble then someone is either patient or creative.
If paul is either humble or not funny then fred is both not rich and not wise.
Everyone who is not quiet is patient and vice versa.
Susan is either not rich or happy.
Mary is tall.
Someone is kind.
Fred is rich.
Someone is not funny or rich.
Lucy is both not patient and not kind.
Lucy is rich.
Mary is wise. | Lucy is humble. | contradiction | ((?[X]:((kind(X)&~wise(X))))<=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((rich(X)<~>~humble(X))=>~curious(X)))&
((~humble(fred))<=>(~generous(john)))&
(((funny(john)&wise(john)))=>((funny(fred)|patient(fred))))&
(![X]:((happy(X)<~>wise(X))=>~tall(X)))&
(![X]:((~creative(X)&~quiet(X))<=>(~creative(X)|generous(X))))&
(![X]:((~old(X)|generous(X))<=>patient(X)))&
(![X]:((~kind(X)<~>~old(X))=>(brave(X)&~humble(X))))&
(![X]:((~quiet(X)&brave(X))<=>(~curious(X)&~patient(X))))&
(((tall(john)|~humble(john)))<=>(?[X]:((~kind(X)|~brave(X)))))&
(![X]:((strong(X)&old(X))<=>(rich(X)<~>generous(X))))&
(((~quiet(john)&wise(john)))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:(~rich(X)=>(~patient(X)<~>~quiet(X))))&
((?[X]:(~humble(X)))=>(?[X]:((patient(X)<~>creative(X)))))&
(((humble(paul)<~>~funny(paul)))=>((~rich(fred)&~wise(fred))))&
(![X]:(~quiet(X)<=>patient(X)))&
((~rich(susan)<~>happy(susan)))&
(tall(mary))&
(?[X]:(kind(X)))&
(rich(fred))&
(?[X]:((~funny(X)|rich(X))))&
((~patient(lucy)&~kind(lucy)))&
(rich(lucy))&
(wise(mary)) | humble(lucy) | [
"p6",
"p7",
"p10",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1537821842302347276236062
% SZS output start Proof for 1537821842302347276236062
7. ! [X0] : ((generous(X0) | ~old(X0)) <=> patient(X0)) [input p6]
8. ! [X0] : ((~kind(X0) <~> ~old(X0)) => (~humble(X0) & brave(X0))) [input p7]
11. ! [X0] : ((old(X0) & strong(X0)) <=> (rich(X0) <~> generous(X0))) [input p10]
22. ~kind(lucy) & ~patient(lucy) [input p21]
23. rich(lucy) [input p22]
25. humble(lucy) [input hypothesis]
32. ! [X0] : ((~humble(X0) & brave(X0)) | (~kind(X0) <=> ~old(X0))) [ennf transformation 8]
46. ! [X0] : (((generous(X0) | ~old(X0)) | ~patient(X0)) & (patient(X0) | (~generous(X0) & old(X0)))) [nnf transformation 7]
47. ! [X0] : ((generous(X0) | ~old(X0) | ~patient(X0)) & (patient(X0) | (~generous(X0) & old(X0)))) [flattening 46]
48. ! [X0] : ((~humble(X0) & brave(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0)))) [nnf transformation 32]
56. ! [X0] : (((old(X0) & strong(X0)) | ((rich(X0) | ~generous(X0)) & (generous(X0) | ~rich(X0)))) & (((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) | (~old(X0) | ~strong(X0)))) [nnf transformation 11]
57. ! [X0] : (((old(X0) & strong(X0)) | ((rich(X0) | ~generous(X0)) & (generous(X0) | ~rich(X0)))) & (((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) | ~old(X0) | ~strong(X0))) [flattening 56]
92. ~generous(X0) | patient(X0) [cnf transformation 47]
96. ~old(X0) | ~humble(X0) | kind(X0) [cnf transformation 48]
110. ~rich(X0) | generous(X0) | old(X0) [cnf transformation 57]
134. ~patient(lucy) [cnf transformation 22]
135. ~kind(lucy) [cnf transformation 22]
136. rich(lucy) [cnf transformation 23]
138. humble(lucy) [cnf transformation 25]
358. 40 <=> generous(lucy) [avatar definition]
360. generous(lucy) <- (40) [avatar component clause 358]
383. generous(lucy) | old(lucy) [resolution 110,136]
386. 45 <=> old(lucy) [avatar definition]
388. old(lucy) <- (45) [avatar component clause 386]
389. 45 | 40 [avatar split clause 383,358,386]
397. patient(lucy) <- (40) [resolution 360,92]
398. $false <- (40) [subsumption resolution 397,134]
399. ~40 [avatar contradiction clause 398]
401. ~humble(lucy) | kind(lucy) <- (45) [resolution 388,96]
404. kind(lucy) <- (45) [subsumption resolution 401,138]
405. $false <- (45) [subsumption resolution 404,135]
406. ~45 [avatar contradiction clause 405]
407. $false [avatar sat refutation 389,399,406]
% SZS output end Proof for 1537821842302347276236062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not generous is not tall. If paul is both not wise and creative then someone is either tall or brave and vice versa. If fred is either quiet or humble then someone is both not kind and kind and vice versa. If john is either not quiet or not calm then john is humble or calm. If paul is not curious then someone is either creative or rich. Everyone who is not generous is kind. Everyone who is either not old or rich is humble. Everyone who is kind or not humble is brave or old and vice versa. Everyone who is patient or not strong is curious or kind. Everyone who is both calm and funny is either not rich or wise. Everyone who is wise is kind. Everyone who is not calm or rich is both humble and not happy and vice versa. If paul is both humble and not brave then mary is both brave and not strong and vice versa. Everyone who is both quiet and humble is either curious or not creative. Everyone who is both not curious and brave is creative or strong and vice versa. If mary is both not patient and not kind then someone is not generous and vice versa. Someone is not rich or not calm. John is not wise or calm. Someone is rich. Fred is either strong or quiet. Someone is either calm or brave. Fred is both not creative and patient. Mary is not strong or not tall. | Fred is happy. | neutral | (![X]:((funny(X)|~generous(X))=>~tall(X)))&
(((~wise(paul)&creative(paul)))<=>(?[X]:((tall(X)<~>brave(X)))))&
(((quiet(fred)<~>humble(fred)))<=>(?[X]:((~kind(X)&kind(X)))))&
(((~quiet(john)<~>~calm(john)))=>((humble(john)|calm(john))))&
((~curious(paul))=>(?[X]:((creative(X)<~>rich(X)))))&
(![X]:(~generous(X)=>kind(X)))&
(![X]:((~old(X)<~>rich(X))=>humble(X)))&
(![X]:((kind(X)|~humble(X))<=>(brave(X)|old(X))))&
(![X]:((patient(X)|~strong(X))=>(curious(X)|kind(X))))&
(![X]:((calm(X)&funny(X))=>(~rich(X)<~>wise(X))))&
(![X]:(wise(X)=>kind(X)))&
(![X]:((~calm(X)|rich(X))<=>(humble(X)&~happy(X))))&
(((humble(paul)&~brave(paul)))<=>((brave(mary)&~strong(mary))))&
(![X]:((quiet(X)&humble(X))=>(curious(X)<~>~creative(X))))&
(![X]:((~curious(X)&brave(X))<=>(creative(X)|strong(X))))&
(((~patient(mary)&~kind(mary)))<=>(?[X]:(~generous(X))))&
(?[X]:((~rich(X)|~calm(X))))&
((~wise(john)|calm(john)))&
(?[X]:(rich(X)))&
((strong(fred)<~>quiet(fred)))&
(?[X]:((calm(X)<~>brave(X))))&
((~creative(fred)&patient(fred)))&
((~strong(mary)|~tall(mary))) | happy(fred) | [] | null | 0 |
If fred is either not humble or not wise then someone is both brave and not generous.
If someone is either tall or rich then john is kind and vice versa.
If someone is generous then someone is both not brave and not curious and vice versa.
Everyone who is not happy or not brave is either kind or not brave and vice versa.
If someone is both not humble and not patient then someone is either rich or funny.
Everyone who is both not kind and curious is either not tall or strong and vice versa.
If susan is creative or not kind then lucy is rich or not brave and vice versa.
If someone is both patient and not kind then someone is both happy and not rich.
Everyone who is wise or creative is not creative or not brave and vice versa.
Everyone who is not strong is either strong or not generous and vice versa.
If someone is wise or not rich then mary is tall or curious.
If mary is kind then someone is not old or not curious and vice versa.
If someone is either not quiet or old then susan is either not wise or brave.
If paul is generous then someone is generous or not kind and vice versa.
Everyone who is either not kind or not strong is quiet or not rich and vice versa.
Everyone who is either not creative or old is either calm or not strong and vice versa.
Susan is not rich.
Someone is not calm or calm.
Fred is either not calm or funny.
Someone is either not rich or not humble.
Susan is not strong. | Fred is not brave. | contradiction | (((~humble(fred)<~>~wise(fred)))=>(?[X]:((brave(X)&~generous(X)))))&
((?[X]:((tall(X)<~>rich(X))))<=>(kind(john)))&
((?[X]:(generous(X)))<=>(?[X]:((~brave(X)&~curious(X)))))&
(![X]:((~happy(X)|~brave(X))<=>(kind(X)<~>~brave(X))))&
((?[X]:((~humble(X)&~patient(X))))=>(?[X]:((rich(X)<~>funny(X)))))&
(![X]:((~kind(X)&curious(X))<=>(~tall(X)<~>strong(X))))&
(((creative(susan)|~kind(susan)))<=>((rich(lucy)|~brave(lucy))))&
((?[X]:((patient(X)&~kind(X))))=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((wise(X)|creative(X))<=>(~creative(X)|~brave(X))))&
(![X]:(~strong(X)<=>(strong(X)<~>~generous(X))))&
((?[X]:((wise(X)|~rich(X))))=>((tall(mary)|curious(mary))))&
((kind(mary))<=>(?[X]:((~old(X)|~curious(X)))))&
((?[X]:((~quiet(X)<~>old(X))))=>((~wise(susan)<~>brave(susan))))&
((generous(paul))<=>(?[X]:((generous(X)|~kind(X)))))&
(![X]:((~kind(X)<~>~strong(X))<=>(quiet(X)|~rich(X))))&
(![X]:((~creative(X)<~>old(X))<=>(calm(X)<~>~strong(X))))&
(~rich(susan))&
(?[X]:((~calm(X)|calm(X))))&
((~calm(fred)<~>funny(fred)))&
(?[X]:((~rich(X)<~>~humble(X))))&
(~strong(susan)) | ~brave(fred) | [
"p3",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 198095285618193025211795
% SZS output start Proof for 198095285618193025211795
4. ! [X0] : ((~brave(X0) | ~happy(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p3]
10. ! [X0] : (~strong(X0) <=> (strong(X0) <~> ~generous(X0))) [input p9]
14. generous(paul) <=> ? [X0] : (~kind(X0) | generous(X0)) [input p13]
22. ~brave(fred) [input hypothesis]
44. ! [X0] : (((~brave(X0) | ~happy(X0)) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (brave(X0) & happy(X0)))) [nnf transformation 4]
45. ! [X0] : ((~brave(X0) | ~happy(X0) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (brave(X0) & happy(X0)))) [flattening 44]
59. ! [X0] : ((~strong(X0) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0)))) & (((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | strong(X0))) [nnf transformation 10]
65. (generous(paul) | ! [X0] : (kind(X0) & ~generous(X0))) & (? [X0] : (~kind(X0) | generous(X0)) | ~generous(paul)) [nnf transformation 14]
66. (generous(paul) | ! [X0] : (kind(X0) & ~generous(X0))) & (? [X1] : (~kind(X1) | generous(X1)) | ~generous(paul)) [rectify 65]
67. ? [X1] : (~kind(X1) | generous(X1)) => (~kind(sK7) | generous(sK7)) [choice axiom]
68. (generous(paul) | ! [X0] : (kind(X0) & ~generous(X0))) & ((~kind(sK7) | generous(sK7)) | ~generous(paul)) [skolemisation 66,67]
92. brave(X0) | ~kind(X0) | brave(X0) [cnf transformation 45]
113. ~generous(X0) | strong(X0) | strong(X0) [cnf transformation 59]
115. ~strong(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 59]
128. generous(paul) | kind(X0) [cnf transformation 68]
150. ~brave(fred) [cnf transformation 22]
151. ~generous(X0) | strong(X0) [duplicate literal removal 113]
152. ~strong(X0) | ~generous(X0) [duplicate literal removal 115]
155. ~kind(X0) | brave(X0) [duplicate literal removal 92]
208. 12 <=> ! [X3] : ~generous(X3) [avatar definition]
209. ~generous(X3) <- (12) [avatar component clause 208]
266. ~generous(X0) [subsumption resolution 151,152]
267. 12 [avatar split clause 266,208]
324. 38 <=> ! [X0] : kind(X0) [avatar definition]
325. kind(X0) <- (38) [avatar component clause 324]
327. 39 <=> generous(paul) [avatar definition]
329. generous(paul) <- (39) [avatar component clause 327]
330. 38 | 39 [avatar split clause 128,327,324]
365. $false <- (12, 39) [subsumption resolution 329,209]
366. ~12 | ~39 [avatar contradiction clause 365]
369. brave(X0) <- (38) [resolution 155,325]
374. $false <- (38) [resolution 369,150]
379. ~38 [avatar contradiction clause 374]
380. $false [avatar sat refutation 267,330,366,379]
% SZS output end Proof for 198095285618193025211795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not brave then fred is tall or not calm. If lucy is not wise then paul is both not funny and wise and vice versa. If someone is tall or generous then fred is not curious and vice versa. Everyone who is both generous and wise is either wise or kind. If someone is not wise then someone is not rich or wise. Everyone who is both not funny and happy is funny and vice versa. If someone is both not kind and humble then someone is not curious or quiet and vice versa. If someone is either rich or creative then john is not generous. Everyone who is either not patient or not happy is not brave. If someone is not patient or quiet then john is either not calm or happy. If fred is old then john is not patient or calm and vice versa. If someone is both not old and strong then mary is either not funny or wise. Everyone who is both wise and not kind is not kind. Everyone who is either not old or kind is either kind or tall. If someone is rich or not generous then john is not humble or not tall. Everyone who is either not generous or calm is both not calm and funny and vice versa. Mary is not rich or happy. Alice is either brave or quiet. Someone is either rich or curious. Paul is strong or calm. Someone is not generous or curious. Alice is old. Susan is not wise or not brave. | Susan is not happy. | entailment | ((~brave(lucy))=>((tall(fred)|~calm(fred))))&
((~wise(lucy))<=>((~funny(paul)&wise(paul))))&
((?[X]:((tall(X)|generous(X))))<=>(~curious(fred)))&
(![X]:((generous(X)&wise(X))=>(wise(X)<~>kind(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~rich(X)|wise(X)))))&
(![X]:((~funny(X)&happy(X))<=>funny(X)))&
((?[X]:((~kind(X)&humble(X))))<=>(?[X]:((~curious(X)|quiet(X)))))&
((?[X]:((rich(X)<~>creative(X))))=>(~generous(john)))&
(![X]:((~patient(X)<~>~happy(X))=>~brave(X)))&
((?[X]:((~patient(X)|quiet(X))))=>((~calm(john)<~>happy(john))))&
((old(fred))<=>((~patient(john)|calm(john))))&
((?[X]:((~old(X)&strong(X))))=>((~funny(mary)<~>wise(mary))))&
(![X]:((wise(X)&~kind(X))=>~kind(X)))&
(![X]:((~old(X)<~>kind(X))=>(kind(X)<~>tall(X))))&
((?[X]:((rich(X)|~generous(X))))=>((~humble(john)|~tall(john))))&
(![X]:((~generous(X)<~>calm(X))<=>(~calm(X)&funny(X))))&
((~rich(mary)|happy(mary)))&
((brave(alice)<~>quiet(alice)))&
(?[X]:((rich(X)<~>curious(X))))&
((strong(paul)|calm(paul)))&
(?[X]:((~generous(X)|curious(X))))&
(old(alice))&
((~wise(susan)|~brave(susan))) | ~happy(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1837842532046930683964643
% SZS output start Proof for 1837842532046930683964643
6. ! [X0] : ((happy(X0) & ~funny(X0)) <=> funny(X0)) [input p5]
24. happy(susan) [input hypothesis]
51. ! [X0] : (((happy(X0) & ~funny(X0)) | ~funny(X0)) & (funny(X0) | (~happy(X0) | funny(X0)))) [nnf transformation 6]
52. ! [X0] : (((happy(X0) & ~funny(X0)) | ~funny(X0)) & (funny(X0) | ~happy(X0) | funny(X0))) [flattening 51]
83. funny(X0) | ~happy(X0) | funny(X0) [cnf transformation 52]
84. ~funny(X0) | ~funny(X0) [cnf transformation 52]
126. happy(susan) [cnf transformation 24]
131. funny(X0) | ~happy(X0) [duplicate literal removal 83]
132. ~funny(X0) [duplicate literal removal 84]
195. ~happy(X0) [subsumption resolution 131,132]
336. $false [subsumption resolution 126,195]
% SZS output end Proof for 1837842532046930683964643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not rich is either not generous or not old.
Everyone who is happy is either tall or not quiet.
Everyone who is either not brave or not creative is either not humble or kind.
If someone is not curious then someone is both funny and creative.
Everyone who is not creative or not kind is not patient and vice versa.
Everyone who is not rich or rich is not strong.
If fred is happy or quiet then susan is both not quiet and not old.
Everyone who is not happy is not quiet or funny.
Everyone who is funny or humble is not calm or kind and vice versa.
Everyone who is both not generous and generous is both not calm and not strong and vice versa.
Everyone who is patient is either not kind or not patient.
If someone is kind or not funny then someone is not brave.
Everyone who is old is not kind or not humble and vice versa.
If mary is either not strong or not quiet then someone is not strong or funny.
Everyone who is either not rich or patient is funny or strong.
Everyone who is not strong or strong is not old and vice versa.
Someone is wise.
Lucy is either not old or rich.
Someone is humble or patient.
Someone is both humble and calm.
Fred is either not kind or funny. | Fred is not humble. | contradiction | (![X]:((~generous(X)&~rich(X))=>(~generous(X)<~>~old(X))))&
(![X]:(happy(X)=>(tall(X)<~>~quiet(X))))&
(![X]:((~brave(X)<~>~creative(X))=>(~humble(X)<~>kind(X))))&
((?[X]:(~curious(X)))=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((~creative(X)|~kind(X))<=>~patient(X)))&
(![X]:((~rich(X)|rich(X))=>~strong(X)))&
(((happy(fred)|quiet(fred)))=>((~quiet(susan)&~old(susan))))&
(![X]:(~happy(X)=>(~quiet(X)|funny(X))))&
(![X]:((funny(X)|humble(X))<=>(~calm(X)|kind(X))))&
(![X]:((~generous(X)&generous(X))<=>(~calm(X)&~strong(X))))&
(![X]:(patient(X)=>(~kind(X)<~>~patient(X))))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>(~kind(X)|~humble(X))))&
(((~strong(mary)<~>~quiet(mary)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~rich(X)<~>patient(X))=>(funny(X)|strong(X))))&
(![X]:((~strong(X)|strong(X))<=>~old(X)))&
(?[X]:(wise(X)))&
((~old(lucy)<~>rich(lucy)))&
(?[X]:((humble(X)|patient(X))))&
(?[X]:((humble(X)&calm(X))))&
((~kind(fred)<~>funny(fred))) | ~humble(fred) | [
"p5",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 356403599614633595767145
% SZS output start Proof for 356403599614633595767145
6. ! [X0] : ((rich(X0) | ~rich(X0)) => ~strong(X0)) [input p5]
13. ! [X0] : (old(X0) <=> (~humble(X0) | ~kind(X0))) [input p12]
16. ! [X0] : ((strong(X0) | ~strong(X0)) <=> ~old(X0)) [input p15]
22. ~humble(fred) [input hypothesis]
31. ! [X0] : (~strong(X0) | (~rich(X0) & rich(X0))) [ennf transformation 6]
53. ! [X0] : ((old(X0) | (humble(X0) & kind(X0))) & ((~humble(X0) | ~kind(X0)) | ~old(X0))) [nnf transformation 13]
54. ! [X0] : ((old(X0) | (humble(X0) & kind(X0))) & (~humble(X0) | ~kind(X0) | ~old(X0))) [flattening 53]
59. ! [X0] : (((strong(X0) | ~strong(X0)) | old(X0)) & (~old(X0) | (~strong(X0) & strong(X0)))) [nnf transformation 16]
60. ! [X0] : ((strong(X0) | ~strong(X0) | old(X0)) & (~old(X0) | (~strong(X0) & strong(X0)))) [flattening 59]
78. ~strong(X0) | rich(X0) [cnf transformation 31]
79. ~strong(X0) | ~rich(X0) [cnf transformation 31]
99. humble(X0) | old(X0) [cnf transformation 54]
104. ~old(X0) | strong(X0) [cnf transformation 60]
114. ~humble(fred) [cnf transformation 22]
117. ~strong(X0) [subsumption resolution 78,79]
156. ~old(X0) [subsumption resolution 104,117]
172. old(fred) [resolution 99,114]
173. $false [subsumption resolution 172,156]
% SZS output end Proof for 356403599614633595767145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and not creative then someone is not old and vice versa. If alice is either not wise or calm then paul is both not patient and creative. If someone is both kind and curious then john is not generous or curious and vice versa. If someone is not generous then john is either wise or strong. Everyone who is not creative or not wise is both curious and creative and vice versa. If someone is not rich or calm then paul is not calm or not generous. Everyone who is kind or not funny is not tall and vice versa. Everyone who is both not old and humble is not rich or curious and vice versa. Everyone who is both strong and kind is either not quiet or funny and vice versa. If someone is strong or not old then someone is kind. Everyone who is either not quiet or not generous is both not curious and not calm and vice versa. If fred is not strong or not generous then someone is not creative or not brave. If susan is tall or quiet then alice is both rich and calm and vice versa. If someone is not humble then susan is both not patient and not curious. If john is both brave and calm then someone is either not rich or not humble and vice versa. Everyone who is both not rich and not tall is kind or not quiet. Fred is not generous. Fred is wise or not patient. Fred is old. Susan is not funny. Alice is both rich and not strong. | Paul is wise. | entailment | ((?[X]:((happy(X)&~creative(X))))<=>(?[X]:(~old(X))))&
(((~wise(alice)<~>calm(alice)))=>((~patient(paul)&creative(paul))))&
((?[X]:((kind(X)&curious(X))))<=>((~generous(john)|curious(john))))&
((?[X]:(~generous(X)))=>((wise(john)<~>strong(john))))&
(![X]:((~creative(X)|~wise(X))<=>(curious(X)&creative(X))))&
((?[X]:((~rich(X)|calm(X))))=>((~calm(paul)|~generous(paul))))&
(![X]:((kind(X)|~funny(X))<=>~tall(X)))&
(![X]:((~old(X)&humble(X))<=>(~rich(X)|curious(X))))&
(![X]:((strong(X)&kind(X))<=>(~quiet(X)<~>funny(X))))&
((?[X]:((strong(X)|~old(X))))=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~curious(X)&~calm(X))))&
(((~strong(fred)|~generous(fred)))=>(?[X]:((~creative(X)|~brave(X)))))&
(((tall(susan)|quiet(susan)))<=>((rich(alice)&calm(alice))))&
((?[X]:(~humble(X)))=>((~patient(susan)&~curious(susan))))&
(((brave(john)&calm(john)))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~rich(X)&~tall(X))=>(kind(X)|~quiet(X))))&
(~generous(fred))&
((wise(fred)|~patient(fred)))&
(old(fred))&
(~funny(susan))&
((rich(alice)&~strong(alice))) | wise(paul) | [
"p0",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 34538354059453055303569
% SZS output start Proof for 34538354059453055303569
1. ? [X0] : (~creative(X0) & happy(X0)) <=> ? [X0] : ~old(X0) [input p0]
5. ! [X0] : ((~wise(X0) | ~creative(X0)) <=> (creative(X0) & curious(X0))) [input p4]
8. ! [X0] : ((humble(X0) & ~old(X0)) <=> (curious(X0) | ~rich(X0))) [input p7]
22. ~wise(paul) [input hypothesis]
23. ? [X0] : (~creative(X0) & happy(X0)) <=> ? [X1] : ~old(X1) [rectify 1]
37. (? [X0] : (~creative(X0) & happy(X0)) | ! [X1] : old(X1)) & (? [X1] : ~old(X1) | ! [X0] : (creative(X0) | ~happy(X0))) [nnf transformation 23]
38. (? [X0] : (~creative(X0) & happy(X0)) | ! [X1] : old(X1)) & (? [X2] : ~old(X2) | ! [X3] : (creative(X3) | ~happy(X3))) [rectify 37]
39. ? [X0] : (~creative(X0) & happy(X0)) => (~creative(sK0) & happy(sK0)) [choice axiom]
40. ? [X2] : ~old(X2) => ~old(sK1) [choice axiom]
41. ((~creative(sK0) & happy(sK0)) | ! [X1] : old(X1)) & (~old(sK1) | ! [X3] : (creative(X3) | ~happy(X3))) [skolemisation 38,40,39]
49. ! [X0] : (((~wise(X0) | ~creative(X0)) | (~creative(X0) | ~curious(X0))) & ((creative(X0) & curious(X0)) | (wise(X0) & creative(X0)))) [nnf transformation 5]
50. ! [X0] : ((~wise(X0) | ~creative(X0) | ~creative(X0) | ~curious(X0)) & ((creative(X0) & curious(X0)) | (wise(X0) & creative(X0)))) [flattening 49]
53. ! [X0] : (((humble(X0) & ~old(X0)) | (~curious(X0) & rich(X0))) & ((curious(X0) | ~rich(X0)) | (~humble(X0) | old(X0)))) [nnf transformation 8]
54. ! [X0] : (((humble(X0) & ~old(X0)) | (~curious(X0) & rich(X0))) & (curious(X0) | ~rich(X0) | ~humble(X0) | old(X0))) [flattening 53]
73. ~creative(sK0) | old(X1) [cnf transformation 41]
84. curious(X0) | wise(X0) [cnf transformation 50]
85. creative(X0) | creative(X0) [cnf transformation 50]
95. ~curious(X0) | ~old(X0) [cnf transformation 54]
132. ~wise(paul) [cnf transformation 22]
133. creative(X0) [duplicate literal removal 85]
136. 1 <=> ! [X1] : old(X1) [avatar definition]
137. old(X1) <- (1) [avatar component clause 136]
139. 2 <=> creative(sK0) [avatar definition]
141. ~creative(sK0) <- (~2) [avatar component clause 139]
142. 1 | ~2 [avatar split clause 73,139,136]
300. $false <- (~2) [subsumption resolution 141,133]
301. 2 [avatar contradiction clause 300]
315. ~old(X0) | wise(X0) [resolution 95,84]
320. wise(X0) <- (1) [subsumption resolution 315,137]
323. $false <- (1) [resolution 320,132]
324. ~1 [avatar contradiction clause 323]
325. $false [avatar sat refutation 142,301,324]
% SZS output end Proof for 34538354059453055303569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and curious is either not patient or happy.
If john is both humble and not kind then john is both kind and rich.
If someone is both not curious and not quiet then susan is either not kind or not wise and vice versa.
Everyone who is both creative and humble is both not quiet and not funny.
Everyone who is both curious and not curious is brave or not old.
Everyone who is not strong is both kind and generous.
If someone is both funny and not strong then lucy is either not kind or tall.
If someone is quiet then mary is both funny and not calm.
Everyone who is calm or not patient is either not calm or funny.
Everyone who is both not curious and not kind is both not kind and not tall and vice versa.
If someone is either rich or not calm then someone is funny or rich and vice versa.
If someone is either quiet or wise then someone is either brave or kind.
Everyone who is not humble or funny is either not patient or not humble and vice versa.
Everyone who is not generous is either not kind or calm.
Everyone who is both quiet and not patient is not strong or not kind and vice versa.
If alice is wise or brave then someone is tall or not generous.
Someone is either funny or wise.
Someone is not tall.
Lucy is both not kind and happy.
Someone is both old and curious.
Alice is old or tall.
Someone is both rich and not brave.
Someone is either kind or strong. | Lucy is tall. | contradiction | (![X]:((quiet(X)&curious(X))=>(~patient(X)<~>happy(X))))&
(((humble(john)&~kind(john)))=>((kind(john)&rich(john))))&
((?[X]:((~curious(X)&~quiet(X))))<=>((~kind(susan)<~>~wise(susan))))&
(![X]:((creative(X)&humble(X))=>(~quiet(X)&~funny(X))))&
(![X]:((curious(X)&~curious(X))=>(brave(X)|~old(X))))&
(![X]:(~strong(X)=>(kind(X)&generous(X))))&
((?[X]:((funny(X)&~strong(X))))=>((~kind(lucy)<~>tall(lucy))))&
((?[X]:(quiet(X)))=>((funny(mary)&~calm(mary))))&
(![X]:((calm(X)|~patient(X))=>(~calm(X)<~>funny(X))))&
(![X]:((~curious(X)&~kind(X))<=>(~kind(X)&~tall(X))))&
((?[X]:((rich(X)<~>~calm(X))))<=>(?[X]:((funny(X)|rich(X)))))&
((?[X]:((quiet(X)<~>wise(X))))=>(?[X]:((brave(X)<~>kind(X)))))&
(![X]:((~humble(X)|funny(X))<=>(~patient(X)<~>~humble(X))))&
(![X]:(~generous(X)=>(~kind(X)<~>calm(X))))&
(![X]:((quiet(X)&~patient(X))<=>(~strong(X)|~kind(X))))&
(((wise(alice)|brave(alice)))=>(?[X]:((tall(X)|~generous(X)))))&
(?[X]:((funny(X)<~>wise(X))))&
(?[X]:(~tall(X)))&
((~kind(lucy)&happy(lucy)))&
(?[X]:((old(X)&curious(X))))&
((old(alice)|tall(alice)))&
(?[X]:((rich(X)&~brave(X))))&
(?[X]:((kind(X)<~>strong(X)))) | tall(lucy) | [
"p0",
"p9",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8753169637860568386581891
% SZS output start Proof for 8753169637860568386581891
1. ! [X0] : ((curious(X0) & quiet(X0)) => (~patient(X0) <~> happy(X0))) [input p0]
10. ! [X0] : ((~kind(X0) & ~curious(X0)) <=> (~tall(X0) & ~kind(X0))) [input p9]
15. ! [X0] : ((~patient(X0) & quiet(X0)) <=> (~kind(X0) | ~strong(X0))) [input p14]
19. happy(lucy) & ~kind(lucy) [input p18]
24. tall(lucy) [input hypothesis]
28. ! [X0] : ((~patient(X0) <~> happy(X0)) | (~curious(X0) | ~quiet(X0))) [ennf transformation 1]
29. ! [X0] : ((~patient(X0) <~> happy(X0)) | ~curious(X0) | ~quiet(X0)) [flattening 28]
41. ! [X0] : (((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | ~curious(X0) | ~quiet(X0)) [nnf transformation 29]
48. ! [X0] : (((~kind(X0) & ~curious(X0)) | (tall(X0) | kind(X0))) & ((~tall(X0) & ~kind(X0)) | (kind(X0) | curious(X0)))) [nnf transformation 10]
49. ! [X0] : (((~kind(X0) & ~curious(X0)) | tall(X0) | kind(X0)) & ((~tall(X0) & ~kind(X0)) | kind(X0) | curious(X0))) [flattening 48]
62. ! [X0] : (((~patient(X0) & quiet(X0)) | (kind(X0) & strong(X0))) & ((~kind(X0) | ~strong(X0)) | (patient(X0) | ~quiet(X0)))) [nnf transformation 15]
63. ! [X0] : (((~patient(X0) & quiet(X0)) | (kind(X0) & strong(X0))) & (~kind(X0) | ~strong(X0) | patient(X0) | ~quiet(X0))) [flattening 62]
79. ~happy(X0) | patient(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 41]
100. ~tall(X0) | kind(X0) | curious(X0) [cnf transformation 49]
123. kind(X0) | quiet(X0) [cnf transformation 63]
125. ~patient(X0) | kind(X0) [cnf transformation 63]
131. ~kind(lucy) [cnf transformation 19]
132. happy(lucy) [cnf transformation 19]
140. tall(lucy) [cnf transformation 24]
188. 10 <=> kind(lucy) [avatar definition]
189. ~kind(lucy) <- (~10) [avatar component clause 188]
192. 11 <=> tall(lucy) [avatar definition]
193. tall(lucy) <- (11) [avatar component clause 192]
290. ~10 [avatar split clause 131,188]
309. 11 [avatar split clause 140,192]
317. quiet(lucy) <- (~10) [resolution 123,189]
348. kind(lucy) | curious(lucy) <- (11) [resolution 100,193]
349. curious(lucy) <- (~10, 11) [subsumption resolution 348,189]
431. patient(lucy) | ~curious(lucy) | ~quiet(lucy) [resolution 79,132]
432. patient(lucy) | ~quiet(lucy) <- (~10, 11) [subsumption resolution 431,349]
433. patient(lucy) <- (~10, 11) [subsumption resolution 432,317]
435. kind(lucy) <- (~10, 11) [resolution 433,125]
437. $false <- (~10, 11) [subsumption resolution 435,189]
438. 10 | ~11 [avatar contradiction clause 437]
439. $false [avatar sat refutation 290,309,438]
% SZS output end Proof for 8753169637860568386581891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not strong.
If lucy is not wise then someone is both happy and not wise.
Everyone who is either not brave or old is both wise and strong and vice versa.
Everyone who is either not brave or not humble is both not strong and not calm and vice versa.
Everyone who is not quiet is either strong or old.
Everyone who is either old or not humble is not creative or not tall.
Everyone who is not brave is either creative or not strong and vice versa.
Everyone who is generous is both not funny and funny.
Everyone who is not tall is kind or strong.
If fred is not calm then mary is not patient or happy.
If someone is both not happy and not old then fred is not brave and vice versa.
Everyone who is rich is not brave and vice versa.
Everyone who is patient or not brave is either tall or not wise and vice versa.
If lucy is generous then someone is not happy or calm.
Everyone who is either not brave or not strong is patient or not wise and vice versa.
Everyone who is both not happy and not tall is either not calm or quiet.
Someone is either wise or funny.
John is not calm or creative.
Someone is both not quiet and happy.
Someone is both brave and humble.
Alice is both tall and not generous.
Mary is not kind or not strong.
Someone is both old and tall.
Someone is not generous. | Alice is not old. | neutral | (![X]:(creative(X)=>~strong(X)))&
((~wise(lucy))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~brave(X)<~>old(X))<=>(wise(X)&strong(X))))&
(![X]:((~brave(X)<~>~humble(X))<=>(~strong(X)&~calm(X))))&
(![X]:(~quiet(X)=>(strong(X)<~>old(X))))&
(![X]:((old(X)<~>~humble(X))=>(~creative(X)|~tall(X))))&
(![X]:(~brave(X)<=>(creative(X)<~>~strong(X))))&
(![X]:(generous(X)=>(~funny(X)&funny(X))))&
(![X]:(~tall(X)=>(kind(X)|strong(X))))&
((~calm(fred))=>((~patient(mary)|happy(mary))))&
((?[X]:((~happy(X)&~old(X))))<=>(~brave(fred)))&
(![X]:(rich(X)<=>~brave(X)))&
(![X]:((patient(X)|~brave(X))<=>(tall(X)<~>~wise(X))))&
((generous(lucy))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((~brave(X)<~>~strong(X))<=>(patient(X)|~wise(X))))&
(![X]:((~happy(X)&~tall(X))=>(~calm(X)<~>quiet(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((~calm(john)|creative(john)))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:((brave(X)&humble(X))))&
((tall(alice)&~generous(alice)))&
((~kind(mary)|~strong(mary)))&
(?[X]:((old(X)&tall(X))))&
(?[X]:(~generous(X))) | ~old(alice) | [] | null | 0 |
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. Everyone who is both calm and rich is either not old or not patient and vice versa. Everyone who is happy is either not quiet or not tall. If someone is either not rich or creative then lucy is both brave and not humble and vice versa. Everyone who is funny or not calm is both not kind and not patient and vice versa. If someone is both wise and not wise then john is kind or not calm and vice versa. If paul is not creative then mary is quiet or wise. Everyone who is either happy or quiet is both not creative and not brave and vice versa. Everyone who is either not old or humble is both not calm and not brave. If lucy is not curious or wise then someone is both not funny and wise. If someone is either tall or brave then john is patient. Everyone who is either not happy or not quiet is rich or not rich and vice versa. Everyone who is both patient and not curious is rich or old. Everyone who is both not old and funny is both rich and not strong and vice versa. If lucy is either not brave or kind then mary is brave or not curious. Alice is both not patient and not happy. Someone is not generous. Someone is either not rich or old. Paul is not patient or creative. Mary is not rich or not patient. Someone is either funny or not humble. | Fred is curious. | neutral | (((~patient(susan)&~rich(susan)))<=>(kind(fred)))&
((~rich(paul))<=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(![X]:((calm(X)&rich(X))<=>(~old(X)<~>~patient(X))))&
(![X]:(happy(X)=>(~quiet(X)<~>~tall(X))))&
((?[X]:((~rich(X)<~>creative(X))))<=>((brave(lucy)&~humble(lucy))))&
(![X]:((funny(X)|~calm(X))<=>(~kind(X)&~patient(X))))&
((?[X]:((wise(X)&~wise(X))))<=>((kind(john)|~calm(john))))&
((~creative(paul))=>((quiet(mary)|wise(mary))))&
(![X]:((happy(X)<~>quiet(X))<=>(~creative(X)&~brave(X))))&
(![X]:((~old(X)<~>humble(X))=>(~calm(X)&~brave(X))))&
(((~curious(lucy)|wise(lucy)))=>(?[X]:((~funny(X)&wise(X)))))&
((?[X]:((tall(X)<~>brave(X))))=>(patient(john)))&
(![X]:((~happy(X)<~>~quiet(X))<=>(rich(X)|~rich(X))))&
(![X]:((patient(X)&~curious(X))=>(rich(X)|old(X))))&
(![X]:((~old(X)&funny(X))<=>(rich(X)&~strong(X))))&
(((~brave(lucy)<~>kind(lucy)))=>((brave(mary)|~curious(mary))))&
((~patient(alice)&~happy(alice)))&
(?[X]:(~generous(X)))&
(?[X]:((~rich(X)<~>old(X))))&
((~patient(paul)|creative(paul)))&
((~rich(mary)|~patient(mary)))&
(?[X]:((funny(X)<~>~humble(X)))) | curious(fred) | [] | null | 0 |
Everyone who is not patient or brave is quiet or rich and vice versa. Everyone who is both not patient and curious is kind. If lucy is old then lucy is both rich and not kind. Everyone who is both not rich and tall is both not generous and calm and vice versa. If someone is either strong or rich then someone is either not curious or not brave. If someone is both not wise and brave then susan is rich or patient. Everyone who is both not happy and not funny is either not tall or not wise and vice versa. If fred is old then paul is either not patient or humble and vice versa. Everyone who is either rich or not funny is both not happy and not quiet and vice versa. Everyone who is either tall or happy is not old or brave and vice versa. Everyone who is both brave and not creative is patient. Everyone who is not quiet or not brave is both humble and brave and vice versa. Everyone who is both not happy and not strong is funny. Everyone who is not creative is not happy or generous. If susan is both not quiet and generous then alice is both creative and not old. If someone is either quiet or calm then fred is tall or not tall and vice versa. Someone is kind or tall. Someone is wise or not quiet. Someone is not patient or kind. Someone is happy. Alice is both not creative and not happy. Susan is generous. Susan is not rich or strong. Alice is both strong and not creative. | Fred is not tall. | neutral | (![X]:((~patient(X)|brave(X))<=>(quiet(X)|rich(X))))&
(![X]:((~patient(X)&curious(X))=>kind(X)))&
((old(lucy))=>((rich(lucy)&~kind(lucy))))&
(![X]:((~rich(X)&tall(X))<=>(~generous(X)&calm(X))))&
((?[X]:((strong(X)<~>rich(X))))=>(?[X]:((~curious(X)<~>~brave(X)))))&
((?[X]:((~wise(X)&brave(X))))=>((rich(susan)|patient(susan))))&
(![X]:((~happy(X)&~funny(X))<=>(~tall(X)<~>~wise(X))))&
((old(fred))<=>((~patient(paul)<~>humble(paul))))&
(![X]:((rich(X)<~>~funny(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((tall(X)<~>happy(X))<=>(~old(X)|brave(X))))&
(![X]:((brave(X)&~creative(X))=>patient(X)))&
(![X]:((~quiet(X)|~brave(X))<=>(humble(X)&brave(X))))&
(![X]:((~happy(X)&~strong(X))=>funny(X)))&
(![X]:(~creative(X)=>(~happy(X)|generous(X))))&
(((~quiet(susan)&generous(susan)))=>((creative(alice)&~old(alice))))&
((?[X]:((quiet(X)<~>calm(X))))<=>((tall(fred)|~tall(fred))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:((wise(X)|~quiet(X))))&
(?[X]:((~patient(X)|kind(X))))&
(?[X]:(happy(X)))&
((~creative(alice)&~happy(alice)))&
(generous(susan))&
((~rich(susan)|strong(susan)))&
((strong(alice)&~creative(alice))) | ~tall(fred) | [] | null | 0 |
Everyone who is either calm or kind is generous.
Everyone who is brave or not humble is not old and vice versa.
If paul is not calm then john is happy or not strong and vice versa.
If someone is rich or not generous then someone is wise or strong and vice versa.
Everyone who is either not tall or happy is both quiet and not kind and vice versa.
If susan is quiet then someone is not quiet and vice versa.
If someone is tall then someone is either kind or not brave.
Everyone who is either not tall or not wise is either not kind or not funny.
Everyone who is both quiet and not tall is not rich or not generous.
Everyone who is not tall or tall is either happy or brave and vice versa.
Everyone who is either not brave or not rich is both happy and not creative and vice versa.
If paul is both tall and happy then paul is either not generous or tall.
If paul is not tall or quiet then alice is either not kind or kind and vice versa.
Everyone who is either not brave or not humble is brave and vice versa.
Everyone who is both kind and not old is curious or creative.
Everyone who is either humble or curious is not curious or curious.
Someone is both strong and not wise.
Someone is not wise.
Someone is generous or not humble.
Someone is both not humble and tall.
Lucy is kind or funny.
Mary is both not funny and not calm. | Lucy is not creative. | neutral | (![X]:((calm(X)<~>kind(X))=>generous(X)))&
(![X]:((brave(X)|~humble(X))<=>~old(X)))&
((~calm(paul))<=>((happy(john)|~strong(john))))&
((?[X]:((rich(X)|~generous(X))))<=>(?[X]:((wise(X)|strong(X)))))&
(![X]:((~tall(X)<~>happy(X))<=>(quiet(X)&~kind(X))))&
((quiet(susan))<=>(?[X]:(~quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((~tall(X)<~>~wise(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((quiet(X)&~tall(X))=>(~rich(X)|~generous(X))))&
(![X]:((~tall(X)|tall(X))<=>(happy(X)<~>brave(X))))&
(![X]:((~brave(X)<~>~rich(X))<=>(happy(X)&~creative(X))))&
(((tall(paul)&happy(paul)))=>((~generous(paul)<~>tall(paul))))&
(((~tall(paul)|quiet(paul)))<=>((~kind(alice)<~>kind(alice))))&
(![X]:((~brave(X)<~>~humble(X))<=>brave(X)))&
(![X]:((kind(X)&~old(X))=>(curious(X)|creative(X))))&
(![X]:((humble(X)<~>curious(X))=>(~curious(X)|curious(X))))&
(?[X]:((strong(X)&~wise(X))))&
(?[X]:(~wise(X)))&
(?[X]:((generous(X)|~humble(X))))&
(?[X]:((~humble(X)&tall(X))))&
((kind(lucy)|funny(lucy)))&
((~funny(mary)&~calm(mary))) | ~creative(lucy) | [] | 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 creative. | entailment | (![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))) | creative(mary) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6111281968706054386665496
% SZS output start Proof for 6111281968706054386665496
6. ! [X0] : ((funny(X0) | ~quiet(X0)) <=> (creative(X0) & ~tall(X0))) [input p5]
13. (funny(mary) | creative(mary)) <=> ? [X0] : (quiet(X0) & ~creative(X0)) [input p12]
23. ~creative(mary) [input hypothesis]
43. ! [X0] : (((funny(X0) | ~quiet(X0)) | (~creative(X0) | tall(X0))) & ((creative(X0) & ~tall(X0)) | (~funny(X0) & quiet(X0)))) [nnf transformation 6]
44. ! [X0] : ((funny(X0) | ~quiet(X0) | ~creative(X0) | tall(X0)) & ((creative(X0) & ~tall(X0)) | (~funny(X0) & quiet(X0)))) [flattening 43]
55. ((funny(mary) | creative(mary)) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X0] : (quiet(X0) & ~creative(X0)) | (~funny(mary) & ~creative(mary))) [nnf transformation 13]
56. (funny(mary) | creative(mary) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X0] : (quiet(X0) & ~creative(X0)) | (~funny(mary) & ~creative(mary))) [flattening 55]
57. (funny(mary) | creative(mary) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X1] : (quiet(X1) & ~creative(X1)) | (~funny(mary) & ~creative(mary))) [rectify 56]
58. ? [X1] : (quiet(X1) & ~creative(X1)) => (quiet(sK3) & ~creative(sK3)) [choice axiom]
59. (funny(mary) | creative(mary) | ! [X0] : (~quiet(X0) | creative(X0))) & ((quiet(sK3) & ~creative(sK3)) | (~funny(mary) & ~creative(mary))) [skolemisation 57,58]
92. creative(X0) | quiet(X0) [cnf transformation 44]
93. creative(X0) | ~funny(X0) [cnf transformation 44]
114. funny(mary) | creative(mary) | ~quiet(X0) | creative(X0) [cnf transformation 59]
129. ~creative(mary) [cnf transformation 23]
167. 7 <=> ! [X0] : creative(X0) [avatar definition]
168. creative(X0) <- (7) [avatar component clause 167]
211. funny(mary) | creative(mary) | creative(X0) [subsumption resolution 114,92]
212. creative(mary) | creative(X0) [subsumption resolution 211,93]
214. 17 <=> creative(mary) [avatar definition]
215. ~creative(mary) <- (~17) [avatar component clause 214]
217. 7 | 17 [avatar split clause 212,214,167]
246. ~17 [avatar split clause 129,214]
249. $false <- (7, ~17) [resolution 215,168]
250. ~7 | 17 [avatar contradiction clause 249]
251. $false [avatar sat refutation 217,246,250]
% SZS output end Proof for 6111281968706054386665496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and calm is both not tall and not happy.
Everyone who is funny is not kind.
Everyone who is tall is kind.
Everyone who is either not creative or not happy is quiet or rich and vice versa.
Everyone who is not happy or quiet is not creative or quiet.
Everyone who is not humble is both not strong and generous.
If someone is happy then someone is both curious and not patient.
If someone is both curious and calm then paul is happy and vice versa.
If john is not tall or not quiet then paul is either not wise or calm and vice versa.
If alice is either calm or not wise then someone is either creative or not quiet.
Everyone who is quiet or not humble is not patient or happy.
Everyone who is not wise or not old is both not tall and funny and vice versa.
If alice is either rich or humble then someone is brave.
Everyone who is not strong or tall is strong.
If someone is both not old and humble then someone is calm.
Everyone who is not wise or creative is quiet or not old and vice versa.
Lucy is not creative or rich.
Paul is both not old and not brave.
Someone is both strong and tall.
Someone is both brave and curious.
Alice is calm.
Someone is funny or brave.
Someone is creative or funny.
Fred is brave. | Paul is wise. | neutral | (![X]:((~brave(X)&calm(X))=>(~tall(X)&~happy(X))))&
(![X]:(funny(X)=>~kind(X)))&
(![X]:(tall(X)=>kind(X)))&
(![X]:((~creative(X)<~>~happy(X))<=>(quiet(X)|rich(X))))&
(![X]:((~happy(X)|quiet(X))=>(~creative(X)|quiet(X))))&
(![X]:(~humble(X)=>(~strong(X)&generous(X))))&
((?[X]:(happy(X)))=>(?[X]:((curious(X)&~patient(X)))))&
((?[X]:((curious(X)&calm(X))))<=>(happy(paul)))&
(((~tall(john)|~quiet(john)))<=>((~wise(paul)<~>calm(paul))))&
(((calm(alice)<~>~wise(alice)))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((quiet(X)|~humble(X))=>(~patient(X)|happy(X))))&
(![X]:((~wise(X)|~old(X))<=>(~tall(X)&funny(X))))&
(((rich(alice)<~>humble(alice)))=>(?[X]:(brave(X))))&
(![X]:((~strong(X)|tall(X))=>strong(X)))&
((?[X]:((~old(X)&humble(X))))=>(?[X]:(calm(X))))&
(![X]:((~wise(X)|creative(X))<=>(quiet(X)|~old(X))))&
((~creative(lucy)|rich(lucy)))&
((~old(paul)&~brave(paul)))&
(?[X]:((strong(X)&tall(X))))&
(?[X]:((brave(X)&curious(X))))&
(calm(alice))&
(?[X]:((funny(X)|brave(X))))&
(?[X]:((creative(X)|funny(X))))&
(brave(fred)) | wise(paul) | [] | null | 0 |
If alice is quiet or generous then someone is both quiet and patient.
Everyone who is both not patient and not humble is generous or not quiet and vice versa.
If fred is not rich or calm then alice is not humble and vice versa.
Everyone who is both not calm and kind is quiet or happy and vice versa.
If fred is both not quiet and wise then someone is not kind.
Everyone who is either not calm or not wise is rich.
If someone is not happy then mary is both not funny and not wise.
If fred is both rich and strong then mary is not strong or kind and vice versa.
Everyone who is both curious and rich is not old.
If someone is either quiet or not happy then someone is not humble or not creative.
If someone is not old or not happy then john is both strong and not wise.
If someone is not patient then fred is either kind or happy.
If someone is either not wise or funny then someone is wise or rich.
Everyone who is generous is both kind and old and vice versa.
Everyone who is either not kind or brave is patient or generous and vice versa.
Everyone who is not strong or rich is patient and vice versa.
Someone is either generous or not calm.
Someone is not old or not strong.
Fred is not kind or not patient.
Someone is rich or creative.
Paul is not humble.
Someone is not kind.
Mary is not wise or not patient.
Someone is quiet or curious. | Mary is rich. | contradiction | (((quiet(alice)|generous(alice)))=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:((~patient(X)&~humble(X))<=>(generous(X)|~quiet(X))))&
(((~rich(fred)|calm(fred)))<=>(~humble(alice)))&
(![X]:((~calm(X)&kind(X))<=>(quiet(X)|happy(X))))&
(((~quiet(fred)&wise(fred)))=>(?[X]:(~kind(X))))&
(![X]:((~calm(X)<~>~wise(X))=>rich(X)))&
((?[X]:(~happy(X)))=>((~funny(mary)&~wise(mary))))&
(((rich(fred)&strong(fred)))<=>((~strong(mary)|kind(mary))))&
(![X]:((curious(X)&rich(X))=>~old(X)))&
((?[X]:((quiet(X)<~>~happy(X))))=>(?[X]:((~humble(X)|~creative(X)))))&
((?[X]:((~old(X)|~happy(X))))=>((strong(john)&~wise(john))))&
((?[X]:(~patient(X)))=>((kind(fred)<~>happy(fred))))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((wise(X)|rich(X)))))&
(![X]:(generous(X)<=>(kind(X)&old(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(patient(X)|generous(X))))&
(![X]:((~strong(X)|rich(X))<=>patient(X)))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((~old(X)|~strong(X))))&
((~kind(fred)|~patient(fred)))&
(?[X]:((rich(X)|creative(X))))&
(~humble(paul))&
(?[X]:(~kind(X)))&
((~wise(mary)|~patient(mary)))&
(?[X]:((quiet(X)|curious(X)))) | rich(mary) | [
"p1",
"p3",
"p7",
"p11",
"p15",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4271125201089895942314499
% SZS output start Proof for 4271125201089895942314499
2. ! [X0] : ((~humble(X0) & ~patient(X0)) <=> (~quiet(X0) | generous(X0))) [input p1]
4. ! [X0] : ((kind(X0) & ~calm(X0)) <=> (happy(X0) | quiet(X0))) [input p3]
8. (strong(fred) & rich(fred)) <=> (kind(mary) | ~strong(mary)) [input p7]
12. ? [X0] : ~patient(X0) => (kind(fred) <~> happy(fred)) [input p11]
16. ! [X0] : ((rich(X0) | ~strong(X0)) <=> patient(X0)) [input p15]
19. ~patient(fred) | ~kind(fred) [input p18]
22. ? [X0] : ~kind(X0) [input p21]
25. rich(mary) [input hypothesis]
37. (kind(fred) <~> happy(fred)) | ! [X0] : patient(X0) [ennf transformation 12]
41. ! [X0] : (((~humble(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) & ((~quiet(X0) | generous(X0)) | (humble(X0) | patient(X0)))) [nnf transformation 2]
42. ! [X0] : (((~humble(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) & (~quiet(X0) | generous(X0) | humble(X0) | patient(X0))) [flattening 41]
45. ! [X0] : (((kind(X0) & ~calm(X0)) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | (~kind(X0) | calm(X0)))) [nnf transformation 4]
46. ! [X0] : (((kind(X0) & ~calm(X0)) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~kind(X0) | calm(X0))) [flattening 45]
50. ((strong(fred) & rich(fred)) | (~kind(mary) & strong(mary))) & ((kind(mary) | ~strong(mary)) | (~strong(fred) | ~rich(fred))) [nnf transformation 8]
51. ((strong(fred) & rich(fred)) | (~kind(mary) & strong(mary))) & (kind(mary) | ~strong(mary) | ~strong(fred) | ~rich(fred)) [flattening 50]
56. ((~happy(fred) | ~kind(fred)) & (happy(fred) | kind(fred))) | ! [X0] : patient(X0) [nnf transformation 37]
65. ! [X0] : (((rich(X0) | ~strong(X0)) | ~patient(X0)) & (patient(X0) | (~rich(X0) & strong(X0)))) [nnf transformation 16]
66. ! [X0] : ((rich(X0) | ~strong(X0) | ~patient(X0)) & (patient(X0) | (~rich(X0) & strong(X0)))) [flattening 65]
74. ? [X0] : ~kind(X0) => ~kind(sK7) [choice axiom]
75. ~kind(sK7) [skolemisation 22,74]
84. ~patient(X0) | quiet(X0) [cnf transformation 42]
93. ~quiet(X0) | kind(X0) [cnf transformation 46]
94. ~happy(X0) | kind(X0) [cnf transformation 46]
102. rich(fred) | ~kind(mary) [cnf transformation 51]
112. happy(fred) | kind(fred) | patient(X0) [cnf transformation 56]
126. ~rich(X0) | patient(X0) [cnf transformation 66]
131. ~patient(fred) | ~kind(fred) [cnf transformation 19]
134. ~kind(sK7) [cnf transformation 75]
137. rich(mary) [cnf transformation 25]
163. 6 <=> rich(fred) [avatar definition]
164. rich(fred) <- (6) [avatar component clause 163]
200. 14 <=> kind(mary) [avatar definition]
213. ~14 | 6 [avatar split clause 102,163,200]
249. 24 <=> ! [X0] : patient(X0) [avatar definition]
250. patient(X0) <- (24) [avatar component clause 249]
256. kind(fred) | patient(X0) [subsumption resolution 112,94]
258. 26 <=> kind(fred) [avatar definition]
261. 24 | 26 [avatar split clause 256,258,249]
300. 35 <=> patient(fred) [avatar definition]
302. ~patient(fred) <- (~35) [avatar component clause 300]
303. ~26 | ~35 [avatar split clause 131,300,258]
314. 38 <=> patient(mary) [avatar definition]
315. patient(mary) <- (38) [avatar component clause 314]
346. patient(mary) [resolution 126,137]
347. patient(fred) <- (6) [resolution 126,164]
351. $false <- (6, ~35) [subsumption resolution 347,302]
352. ~6 | 35 [avatar contradiction clause 351]
353. 38 [avatar split clause 346,314]
354. quiet(mary) <- (38) [resolution 315,84]
365. kind(mary) <- (38) [resolution 354,93]
368. 14 | ~38 [avatar split clause 365,314,200]
373. quiet(X0) <- (24) [resolution 250,84]
379. kind(X0) <- (24) [resolution 373,93]
416. $false <- (24) [resolution 379,134]
417. ~24 [avatar contradiction clause 416]
421. $false [avatar sat refutation 213,261,303,352,353,368,417]
% SZS output end Proof for 4271125201089895942314499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not rich or creative is either wise or creative and vice versa.
Everyone who is both not patient and not calm is not kind.
Everyone who is brave is not patient or generous and vice versa.
If john is not funny then someone is either not brave or not happy.
Everyone who is not kind or calm is not curious or humble.
Everyone who is not patient is not tall or not kind and vice versa.
If someone is both not patient and kind then someone is both not curious and funny and vice versa.
Everyone who is either generous or old is both not rich and not wise.
If someone is curious then someone is not curious or not rich.
Everyone who is rich is old and vice versa.
Everyone who is either happy or not happy is not curious or not wise and vice versa.
If alice is old or calm then lucy is both not wise and not strong and vice versa.
Everyone who is both not brave and wise is either not curious or not creative and vice versa.
If someone is both funny and not creative then someone is either curious or not tall.
Everyone who is not rich is both funny and not creative and vice versa.
John is tall or quiet.
Someone is both not kind and rich.
Someone is calm.
Mary is strong.
Paul is either not humble or generous.
Susan is tall or patient.
Someone is happy.
Someone is old or not creative. | Lucy is strong. | neutral | (![X]:((~rich(X)<~>creative(X))<=>(wise(X)<~>creative(X))))&
(![X]:((~patient(X)&~calm(X))=>~kind(X)))&
(![X]:(brave(X)<=>(~patient(X)|generous(X))))&
((~funny(john))=>(?[X]:((~brave(X)<~>~happy(X)))))&
(![X]:((~kind(X)|calm(X))=>(~curious(X)|humble(X))))&
(![X]:(~patient(X)<=>(~tall(X)|~kind(X))))&
((?[X]:((~patient(X)&kind(X))))<=>(?[X]:((~curious(X)&funny(X)))))&
(![X]:((generous(X)<~>old(X))=>(~rich(X)&~wise(X))))&
((?[X]:(curious(X)))=>(?[X]:((~curious(X)|~rich(X)))))&
(![X]:(rich(X)<=>old(X)))&
(![X]:((happy(X)<~>~happy(X))<=>(~curious(X)|~wise(X))))&
(((old(alice)|calm(alice)))<=>((~wise(lucy)&~strong(lucy))))&
(![X]:((~brave(X)&wise(X))<=>(~curious(X)<~>~creative(X))))&
((?[X]:((funny(X)&~creative(X))))=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:(~rich(X)<=>(funny(X)&~creative(X))))&
((tall(john)|quiet(john)))&
(?[X]:((~kind(X)&rich(X))))&
(?[X]:(calm(X)))&
(strong(mary))&
((~humble(paul)<~>generous(paul)))&
((tall(susan)|patient(susan)))&
(?[X]:(happy(X)))&
(?[X]:((old(X)|~creative(X)))) | strong(lucy) | [] | null | 0 |
Everyone who is either not curious or not funny is both not tall and funny.
If someone is not wise or not kind then someone is not rich.
If someone is brave or curious then fred is either not happy or not brave.
If john is both patient and not funny then someone is not old or not tall and vice versa.
Everyone who is both not brave and happy is humble or not tall and vice versa.
If john is both brave and generous then susan is not funny.
Everyone who is both not humble and not strong is kind and vice versa.
If john is either tall or not funny then someone is old.
If someone is not old then fred is happy or patient.
Everyone who is not generous is patient or not old and vice versa.
Everyone who is either kind or not creative is not humble and vice versa.
Everyone who is either strong or happy is creative and vice versa.
If susan is patient then someone is both not curious and not rich and vice versa.
If someone is both not rich and old then someone is wise and vice versa.
If paul is patient or not generous then paul is not patient or not wise.
Everyone who is not generous or not quiet is either not wise or not kind.
Someone is not humble.
Someone is both quiet and creative.
Someone is both not strong and wise.
John is both not patient and curious.
Lucy is not generous or kind. | Susan is brave. | neutral | (![X]:((~curious(X)<~>~funny(X))=>(~tall(X)&funny(X))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)|curious(X))))=>((~happy(fred)<~>~brave(fred))))&
(((patient(john)&~funny(john)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~brave(X)&happy(X))<=>(humble(X)|~tall(X))))&
(((brave(john)&generous(john)))=>(~funny(susan)))&
(![X]:((~humble(X)&~strong(X))<=>kind(X)))&
(((tall(john)<~>~funny(john)))=>(?[X]:(old(X))))&
((?[X]:(~old(X)))=>((happy(fred)|patient(fred))))&
(![X]:(~generous(X)<=>(patient(X)|~old(X))))&
(![X]:((kind(X)<~>~creative(X))<=>~humble(X)))&
(![X]:((strong(X)<~>happy(X))<=>creative(X)))&
((patient(susan))<=>(?[X]:((~curious(X)&~rich(X)))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:(wise(X))))&
(((patient(paul)|~generous(paul)))=>((~patient(paul)|~wise(paul))))&
(![X]:((~generous(X)|~quiet(X))=>(~wise(X)<~>~kind(X))))&
(?[X]:(~humble(X)))&
(?[X]:((quiet(X)&creative(X))))&
(?[X]:((~strong(X)&wise(X))))&
((~patient(john)&curious(john)))&
((~generous(lucy)|kind(lucy))) | brave(susan) | [] | null | 0 |
If alice is either not wise or rich then someone is not strong and vice versa.
Everyone who is either wise or not quiet is either not quiet or not funny and vice versa.
Everyone who is either creative or old is both funny and not curious.
Everyone who is old or brave is either calm or not patient and vice versa.
If someone is both not old and wise then someone is not funny or strong and vice versa.
Everyone who is tall is either generous or old.
Everyone who is not rich or not tall is patient or not calm and vice versa.
Everyone who is both generous and calm is both quiet and wise and vice versa.
Everyone who is either not calm or calm is brave and vice versa.
If someone is either not humble or brave then someone is both old and patient.
Everyone who is both creative and kind is humble or generous and vice versa.
If paul is wise then mary is not creative.
If someone is both not happy and not wise then someone is not humble.
If someone is either brave or not old then someone is generous.
If paul is rich then fred is both not creative and not rich and vice versa.
Everyone who is both brave and humble is not curious or not rich.
Alice is quiet or rich.
Someone is not humble.
John is both brave and not generous.
John is not kind.
John is both not humble and not calm.
Lucy is not old or not generous.
Fred is not old.
Someone is both curious and not wise. | Mary is not brave. | contradiction | (((~wise(alice)<~>rich(alice)))<=>(?[X]:(~strong(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~quiet(X)<~>~funny(X))))&
(![X]:((creative(X)<~>old(X))=>(funny(X)&~curious(X))))&
(![X]:((old(X)|brave(X))<=>(calm(X)<~>~patient(X))))&
((?[X]:((~old(X)&wise(X))))<=>(?[X]:((~funny(X)|strong(X)))))&
(![X]:(tall(X)=>(generous(X)<~>old(X))))&
(![X]:((~rich(X)|~tall(X))<=>(patient(X)|~calm(X))))&
(![X]:((generous(X)&calm(X))<=>(quiet(X)&wise(X))))&
(![X]:((~calm(X)<~>calm(X))<=>brave(X)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((old(X)&patient(X)))))&
(![X]:((creative(X)&kind(X))<=>(humble(X)|generous(X))))&
((wise(paul))=>(~creative(mary)))&
((?[X]:((~happy(X)&~wise(X))))=>(?[X]:(~humble(X))))&
((?[X]:((brave(X)<~>~old(X))))=>(?[X]:(generous(X))))&
((rich(paul))<=>((~creative(fred)&~rich(fred))))&
(![X]:((brave(X)&humble(X))=>(~curious(X)|~rich(X))))&
((quiet(alice)|rich(alice)))&
(?[X]:(~humble(X)))&
((brave(john)&~generous(john)))&
(~kind(john))&
((~humble(john)&~calm(john)))&
((~old(lucy)|~generous(lucy)))&
(~old(fred))&
(?[X]:((curious(X)&~wise(X)))) | ~brave(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7664908115621055803862766
% SZS output start Proof for 7664908115621055803862766
9. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> brave(X0)) [input p8]
25. ~brave(mary) [input hypothesis]
56. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~brave(X0)) & (brave(X0) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 9]
110. brave(X0) | calm(X0) | calm(X0) [cnf transformation 56]
111. brave(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 56]
141. ~brave(mary) [cnf transformation 25]
142. brave(X0) | calm(X0) [duplicate literal removal 110]
143. brave(X0) | ~calm(X0) [duplicate literal removal 111]
199. brave(X0) [subsumption resolution 142,143]
263. $false [subsumption resolution 141,199]
% SZS output end Proof for 7664908115621055803862766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and curious is patient and vice versa.
Everyone who is either not humble or not calm is brave and vice versa.
Everyone who is both happy and not strong is both strong and funny.
Everyone who is old or funny is not brave or curious and vice versa.
If someone is both not funny and creative then paul is either curious or patient.
Everyone who is both not kind and not strong is either rich or calm and vice versa.
If alice is creative or old then someone is curious or not quiet and vice versa.
If fred is both patient and not humble then susan is both not curious and calm and vice versa.
Everyone who is strong or not patient is not kind or not calm and vice versa.
Everyone who is both happy and not kind is both not creative and not humble.
If paul is creative or not funny then someone is rich and vice versa.
If lucy is either not brave or not patient then someone is humble or calm and vice versa.
Everyone who is calm or not wise is both happy and not funny and vice versa.
Everyone who is either patient or not funny is both strong and funny and vice versa.
If someone is not humble or wise then john is either old or not old and vice versa.
If lucy is both humble and not wise then fred is not kind.
Someone is not rich or wise.
Someone is not generous or patient.
Someone is not brave or not tall.
Someone is not calm. | Paul is old. | neutral | (![X]:((~strong(X)&curious(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~calm(X))<=>brave(X)))&
(![X]:((happy(X)&~strong(X))=>(strong(X)&funny(X))))&
(![X]:((old(X)|funny(X))<=>(~brave(X)|curious(X))))&
((?[X]:((~funny(X)&creative(X))))=>((curious(paul)<~>patient(paul))))&
(![X]:((~kind(X)&~strong(X))<=>(rich(X)<~>calm(X))))&
(((creative(alice)|old(alice)))<=>(?[X]:((curious(X)|~quiet(X)))))&
(((patient(fred)&~humble(fred)))<=>((~curious(susan)&calm(susan))))&
(![X]:((strong(X)|~patient(X))<=>(~kind(X)|~calm(X))))&
(![X]:((happy(X)&~kind(X))=>(~creative(X)&~humble(X))))&
(((creative(paul)|~funny(paul)))<=>(?[X]:(rich(X))))&
(((~brave(lucy)<~>~patient(lucy)))<=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((calm(X)|~wise(X))<=>(happy(X)&~funny(X))))&
(![X]:((patient(X)<~>~funny(X))<=>(strong(X)&funny(X))))&
((?[X]:((~humble(X)|wise(X))))<=>((old(john)<~>~old(john))))&
(((humble(lucy)&~wise(lucy)))=>(~kind(fred)))&
(?[X]:((~rich(X)|wise(X))))&
(?[X]:((~generous(X)|patient(X))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:(~calm(X))) | old(paul) | [] | null | 0 |
Everyone who is either not rich or not humble is either patient or not creative. Everyone who is both not strong and rich is not humble. Everyone who is calm is not patient or not strong. If someone is quiet or brave then susan is tall. Everyone who is patient or not patient is happy or humble and vice versa. Everyone who is both not strong and patient is strong or not strong and vice versa. Everyone who is either not calm or not humble is wise and vice versa. Everyone who is both not strong and generous is quiet or not brave and vice versa. If fred is either patient or generous then fred is either not patient or not tall. Everyone who is not calm is both calm and not creative. Everyone who is generous is strong or wise and vice versa. Everyone who is either generous or not calm is both patient and funny. Everyone who is not brave is not wise or rich and vice versa. If susan is funny or humble then paul is either curious or strong. If fred is either strong or happy then fred is either tall or not quiet and vice versa. Everyone who is rich is both humble and brave. Someone is both not old and not tall. Someone is not humble or not creative. Someone is either not curious or old. Someone is either not brave or calm. Someone is not funny or not rich. Mary is either not generous or curious. Alice is either not tall or not wise. Someone is either not funny or calm. | Paul is not generous. | contradiction | (![X]:((~rich(X)<~>~humble(X))=>(patient(X)<~>~creative(X))))&
(![X]:((~strong(X)&rich(X))=>~humble(X)))&
(![X]:(calm(X)=>(~patient(X)|~strong(X))))&
((?[X]:((quiet(X)|brave(X))))=>(tall(susan)))&
(![X]:((patient(X)|~patient(X))<=>(happy(X)|humble(X))))&
(![X]:((~strong(X)&patient(X))<=>(strong(X)|~strong(X))))&
(![X]:((~calm(X)<~>~humble(X))<=>wise(X)))&
(![X]:((~strong(X)&generous(X))<=>(quiet(X)|~brave(X))))&
(((patient(fred)<~>generous(fred)))=>((~patient(fred)<~>~tall(fred))))&
(![X]:(~calm(X)=>(calm(X)&~creative(X))))&
(![X]:(generous(X)<=>(strong(X)|wise(X))))&
(![X]:((generous(X)<~>~calm(X))=>(patient(X)&funny(X))))&
(![X]:(~brave(X)<=>(~wise(X)|rich(X))))&
(((funny(susan)|humble(susan)))=>((curious(paul)<~>strong(paul))))&
(((strong(fred)<~>happy(fred)))<=>((tall(fred)<~>~quiet(fred))))&
(![X]:(rich(X)=>(humble(X)&brave(X))))&
(?[X]:((~old(X)&~tall(X))))&
(?[X]:((~humble(X)|~creative(X))))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:((~brave(X)<~>calm(X))))&
(?[X]:((~funny(X)|~rich(X))))&
((~generous(mary)<~>curious(mary)))&
((~tall(alice)<~>~wise(alice)))&
(?[X]:((~funny(X)<~>calm(X)))) | ~generous(paul) | [
"p5",
"p7",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4973084049277546550587118
% SZS output start Proof for 4973084049277546550587118
6. ! [X0] : ((patient(X0) & ~strong(X0)) <=> (~strong(X0) | strong(X0))) [input p5]
8. ! [X0] : ((generous(X0) & ~strong(X0)) <=> (~brave(X0) | quiet(X0))) [input p7]
11. ! [X0] : (generous(X0) <=> (wise(X0) | strong(X0))) [input p10]
13. ! [X0] : (~brave(X0) <=> (rich(X0) | ~wise(X0))) [input p12]
25. ~generous(paul) [input hypothesis]
40. ! [X0] : (((patient(X0) & ~strong(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~patient(X0) | strong(X0)))) [nnf transformation 6]
41. ! [X0] : (((patient(X0) & ~strong(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~patient(X0) | strong(X0))) [flattening 40]
43. ! [X0] : (((generous(X0) & ~strong(X0)) | (brave(X0) & ~quiet(X0))) & ((~brave(X0) | quiet(X0)) | (~generous(X0) | strong(X0)))) [nnf transformation 8]
44. ! [X0] : (((generous(X0) & ~strong(X0)) | (brave(X0) & ~quiet(X0))) & (~brave(X0) | quiet(X0) | ~generous(X0) | strong(X0))) [flattening 43]
46. ! [X0] : ((generous(X0) | (~wise(X0) & ~strong(X0))) & ((wise(X0) | strong(X0)) | ~generous(X0))) [nnf transformation 11]
47. ! [X0] : ((generous(X0) | (~wise(X0) & ~strong(X0))) & (wise(X0) | strong(X0) | ~generous(X0))) [flattening 46]
49. ! [X0] : ((~brave(X0) | (~rich(X0) & wise(X0))) & ((rich(X0) | ~wise(X0)) | brave(X0))) [nnf transformation 13]
50. ! [X0] : ((~brave(X0) | (~rich(X0) & wise(X0))) & (rich(X0) | ~wise(X0) | brave(X0))) [flattening 49]
83. ~strong(X0) | ~strong(X0) [cnf transformation 41]
95. generous(X0) | brave(X0) [cnf transformation 44]
102. wise(X0) | strong(X0) | ~generous(X0) [cnf transformation 47]
104. ~wise(X0) | generous(X0) [cnf transformation 47]
110. ~brave(X0) | wise(X0) [cnf transformation 50]
140. ~generous(paul) [cnf transformation 25]
145. ~strong(X0) [duplicate literal removal 83]
171. ~generous(X0) | wise(X0) [subsumption resolution 102,145]
259. wise(X0) | brave(X0) [resolution 171,95]
260. wise(X0) [subsumption resolution 259,110]
265. generous(X0) [resolution 260,104]
275. $false [resolution 265,140]
% SZS output end Proof for 4973084049277546550587118
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or wise then someone is not old or strong.
If someone is not tall or not rich then paul is patient or not humble and vice versa.
Everyone who is either brave or not humble is brave or rich and vice versa.
Everyone who is strong or not kind is not curious or not rich and vice versa.
Everyone who is both brave and old is either old or not quiet and vice versa.
If fred is either not old or not calm then someone is either not happy or tall and vice versa.
Everyone who is both happy and not happy is both not creative and kind and vice versa.
If john is either rich or humble then fred is tall and vice versa.
If someone is not curious or not tall then paul is not kind and vice versa.
Everyone who is curious or creative is both calm and not brave.
Everyone who is both creative and not kind is both not happy and not strong.
Everyone who is either generous or not wise is not happy and vice versa.
Everyone who is not old is both not calm and not humble and vice versa.
If someone is calm then someone is either not quiet or not generous and vice versa.
Everyone who is both not rich and funny is not rich or not calm and vice versa.
If john is creative then someone is either kind or not curious.
John is not generous.
Someone is both not kind and generous.
Someone is calm.
Alice is either not brave or not tall.
Paul is either patient or funny.
Someone is not calm.
Someone is both not funny and not wise. | John is not wise. | neutral | ((?[X]:((~quiet(X)<~>wise(X))))=>(?[X]:((~old(X)|strong(X)))))&
((?[X]:((~tall(X)|~rich(X))))<=>((patient(paul)|~humble(paul))))&
(![X]:((brave(X)<~>~humble(X))<=>(brave(X)|rich(X))))&
(![X]:((strong(X)|~kind(X))<=>(~curious(X)|~rich(X))))&
(![X]:((brave(X)&old(X))<=>(old(X)<~>~quiet(X))))&
(((~old(fred)<~>~calm(fred)))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(![X]:((happy(X)&~happy(X))<=>(~creative(X)&kind(X))))&
(((rich(john)<~>humble(john)))<=>(tall(fred)))&
((?[X]:((~curious(X)|~tall(X))))<=>(~kind(paul)))&
(![X]:((curious(X)|creative(X))=>(calm(X)&~brave(X))))&
(![X]:((creative(X)&~kind(X))=>(~happy(X)&~strong(X))))&
(![X]:((generous(X)<~>~wise(X))<=>~happy(X)))&
(![X]:(~old(X)<=>(~calm(X)&~humble(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:((~rich(X)&funny(X))<=>(~rich(X)|~calm(X))))&
((creative(john))=>(?[X]:((kind(X)<~>~curious(X)))))&
(~generous(john))&
(?[X]:((~kind(X)&generous(X))))&
(?[X]:(calm(X)))&
((~brave(alice)<~>~tall(alice)))&
((patient(paul)<~>funny(paul)))&
(?[X]:(~calm(X)))&
(?[X]:((~funny(X)&~wise(X)))) | ~wise(john) | [] | null | 0 |
Everyone who is both patient and not curious is not humble or kind and vice versa.
If paul is patient then fred is creative or not wise and vice versa.
Everyone who is not old is rich and vice versa.
If someone is old then someone is both funny and creative and vice versa.
Everyone who is either wise or not humble is curious.
If mary is funny or generous then someone is brave or not kind.
Everyone who is humble or curious is not calm or not strong and vice versa.
Everyone who is either quiet or generous is rich.
If someone is kind then someone is either quiet or not strong and vice versa.
Everyone who is not kind is either humble or not curious.
If mary is not quiet or brave then someone is curious or not calm and vice versa.
Everyone who is not creative is not old.
Everyone who is either tall or not generous is both not generous and not quiet and vice versa.
If someone is not brave or brave then someone is not rich.
Everyone who is both old and not creative is both funny and patient and vice versa.
Everyone who is both creative and old is both not kind and wise.
Fred is both patient and not humble.
Mary is either quiet or not humble.
Mary is either not old or kind.
Paul is both not curious and not rich.
Paul is generous.
Lucy is both not curious and creative.
Someone is either not patient or brave.
Susan is both humble and not tall. | Lucy is funny. | contradiction | (![X]:((patient(X)&~curious(X))<=>(~humble(X)|kind(X))))&
((patient(paul))<=>((creative(fred)|~wise(fred))))&
(![X]:(~old(X)<=>rich(X)))&
((?[X]:(old(X)))<=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((wise(X)<~>~humble(X))=>curious(X)))&
(((funny(mary)|generous(mary)))=>(?[X]:((brave(X)|~kind(X)))))&
(![X]:((humble(X)|curious(X))<=>(~calm(X)|~strong(X))))&
(![X]:((quiet(X)<~>generous(X))=>rich(X)))&
((?[X]:(kind(X)))<=>(?[X]:((quiet(X)<~>~strong(X)))))&
(![X]:(~kind(X)=>(humble(X)<~>~curious(X))))&
(((~quiet(mary)|brave(mary)))<=>(?[X]:((curious(X)|~calm(X)))))&
(![X]:(~creative(X)=>~old(X)))&
(![X]:((tall(X)<~>~generous(X))<=>(~generous(X)&~quiet(X))))&
((?[X]:((~brave(X)|brave(X))))=>(?[X]:(~rich(X))))&
(![X]:((old(X)&~creative(X))<=>(funny(X)&patient(X))))&
(![X]:((creative(X)&old(X))=>(~kind(X)&wise(X))))&
((patient(fred)&~humble(fred)))&
((quiet(mary)<~>~humble(mary)))&
((~old(mary)<~>kind(mary)))&
((~curious(paul)&~rich(paul)))&
(generous(paul))&
((~curious(lucy)&creative(lucy)))&
(?[X]:((~patient(X)<~>brave(X))))&
((humble(susan)&~tall(susan))) | funny(lucy) | [
"p0",
"p9",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4870834647945149370372699
% SZS output start Proof for 4870834647945149370372699
1. ! [X0] : ((~curious(X0) & patient(X0)) <=> (kind(X0) | ~humble(X0))) [input p0]
10. ! [X0] : (~kind(X0) => (humble(X0) <~> ~curious(X0))) [input p9]
15. ! [X0] : ((~creative(X0) & old(X0)) <=> (patient(X0) & funny(X0))) [input p14]
22. creative(lucy) & ~curious(lucy) [input p21]
25. funny(lucy) [input hypothesis]
32. ! [X0] : ((humble(X0) <~> ~curious(X0)) | kind(X0)) [ennf transformation 10]
37. ! [X0] : (((~curious(X0) & patient(X0)) | (~kind(X0) & humble(X0))) & ((kind(X0) | ~humble(X0)) | (curious(X0) | ~patient(X0)))) [nnf transformation 1]
38. ! [X0] : (((~curious(X0) & patient(X0)) | (~kind(X0) & humble(X0))) & (kind(X0) | ~humble(X0) | curious(X0) | ~patient(X0))) [flattening 37]
58. ! [X0] : (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | kind(X0)) [nnf transformation 32]
69. ! [X0] : (((~creative(X0) & old(X0)) | (~patient(X0) | ~funny(X0))) & ((patient(X0) & funny(X0)) | (creative(X0) | ~old(X0)))) [nnf transformation 15]
70. ! [X0] : (((~creative(X0) & old(X0)) | ~patient(X0) | ~funny(X0)) & ((patient(X0) & funny(X0)) | creative(X0) | ~old(X0))) [flattening 69]
77. humble(X0) | patient(X0) [cnf transformation 38]
78. ~kind(X0) | patient(X0) [cnf transformation 38]
104. ~humble(X0) | curious(X0) | kind(X0) [cnf transformation 58]
121. ~funny(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 70]
133. ~curious(lucy) [cnf transformation 22]
134. creative(lucy) [cnf transformation 22]
139. funny(lucy) [cnf transformation 25]
342. curious(X0) | kind(X0) | patient(X0) [resolution 104,77]
346. curious(X0) | patient(X0) [subsumption resolution 342,78]
418. 45 <=> patient(lucy) [avatar definition]
431. ~patient(lucy) | ~creative(lucy) [resolution 121,139]
450. patient(lucy) [resolution 346,133]
456. 45 [avatar split clause 450,418]
457. ~patient(lucy) [subsumption resolution 431,134]
458. ~45 [avatar split clause 457,418]
459. $false [avatar sat refutation 456,458]
% SZS output end Proof for 4870834647945149370372699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both strong and not funny then john is either funny or not strong and vice versa.
If someone is both not humble and not rich then someone is both brave and not quiet and vice versa.
Everyone who is either not wise or not kind is old and vice versa.
If paul is either not rich or patient then someone is not rich or not humble.
If susan is not rich then fred is either strong or not creative.
Everyone who is not humble is old or not rich.
If someone is quiet then alice is both not curious and tall.
Everyone who is both not wise and tall is creative or generous.
If someone is not tall then susan is either not strong or quiet and vice versa.
If susan is not brave or not funny then someone is both rich and old.
If mary is either not funny or kind then someone is kind and vice versa.
If someone is not quiet or not generous then someone is quiet and vice versa.
If alice is both not funny and quiet then someone is either brave or happy and vice versa.
Everyone who is both happy and quiet is both happy and not rich and vice versa.
Everyone who is not rich is not wise or not strong and vice versa.
If alice is both not patient and not quiet then someone is brave or funny.
Fred is both not happy and brave.
John is not brave.
Paul is not quiet.
Someone is not patient or not strong.
Paul is not old or not happy.
Fred is not creative.
Susan is either wise or not curious.
Alice is both not old and happy. | Fred is not brave. | contradiction | (((strong(lucy)&~funny(lucy)))<=>((funny(john)<~>~strong(john))))&
((?[X]:((~humble(X)&~rich(X))))<=>(?[X]:((brave(X)&~quiet(X)))))&
(![X]:((~wise(X)<~>~kind(X))<=>old(X)))&
(((~rich(paul)<~>patient(paul)))=>(?[X]:((~rich(X)|~humble(X)))))&
((~rich(susan))=>((strong(fred)<~>~creative(fred))))&
(![X]:(~humble(X)=>(old(X)|~rich(X))))&
((?[X]:(quiet(X)))=>((~curious(alice)&tall(alice))))&
(![X]:((~wise(X)&tall(X))=>(creative(X)|generous(X))))&
((?[X]:(~tall(X)))<=>((~strong(susan)<~>quiet(susan))))&
(((~brave(susan)|~funny(susan)))=>(?[X]:((rich(X)&old(X)))))&
(((~funny(mary)<~>kind(mary)))<=>(?[X]:(kind(X))))&
((?[X]:((~quiet(X)|~generous(X))))<=>(?[X]:(quiet(X))))&
(((~funny(alice)&quiet(alice)))<=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:((happy(X)&quiet(X))<=>(happy(X)&~rich(X))))&
(![X]:(~rich(X)<=>(~wise(X)|~strong(X))))&
(((~patient(alice)&~quiet(alice)))=>(?[X]:((brave(X)|funny(X)))))&
((~happy(fred)&brave(fred)))&
(~brave(john))&
(~quiet(paul))&
(?[X]:((~patient(X)|~strong(X))))&
((~old(paul)|~happy(paul)))&
(~creative(fred))&
((wise(susan)<~>~curious(susan)))&
((~old(alice)&happy(alice))) | ~brave(fred) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6593589991856346448307397
% SZS output start Proof for 6593589991856346448307397
17. brave(fred) & ~happy(fred) [input p16]
25. ~brave(fred) [input hypothesis]
131. brave(fred) [cnf transformation 17]
141. ~brave(fred) [cnf transformation 25]
384. $false [subsumption resolution 141,131]
% SZS output end Proof for 6593589991856346448307397
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or quiet is either not strong or patient and vice versa. Everyone who is calm is kind and vice versa. If someone is either not rich or calm then someone is either not wise or rich. If paul is both creative and not creative then someone is either funny or not quiet and vice versa. Everyone who is either curious or quiet is either not humble or quiet and vice versa. Everyone who is both quiet and not creative is both not curious and not happy and vice versa. If someone is happy or humble then someone is not curious or old. Everyone who is both patient and not creative is not strong or old and vice versa. If fred is either brave or generous then susan is calm or not strong and vice versa. If someone is happy then alice is both not tall and generous. If fred is not kind then paul is both not funny and calm. Everyone who is either brave or wise is tall. Everyone who is both not patient and not funny is not calm and vice versa. If mary is not quiet then john is both not quiet and not patient and vice versa. If mary is either not quiet or not humble then john is both strong and not old. If susan is happy then paul is either not wise or happy. Someone is strong or brave. Susan is tall. Mary is not happy. Mary is brave or wise. Someone is both happy and not tall. Alice is either generous or not creative. Someone is humble. Someone is both not old and curious. | Susan is patient. | entailment | (![X]:((~quiet(X)|quiet(X))<=>(~strong(X)<~>patient(X))))&
(![X]:(calm(X)<=>kind(X)))&
((?[X]:((~rich(X)<~>calm(X))))=>(?[X]:((~wise(X)<~>rich(X)))))&
(((creative(paul)&~creative(paul)))<=>(?[X]:((funny(X)<~>~quiet(X)))))&
(![X]:((curious(X)<~>quiet(X))<=>(~humble(X)<~>quiet(X))))&
(![X]:((quiet(X)&~creative(X))<=>(~curious(X)&~happy(X))))&
((?[X]:((happy(X)|humble(X))))=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((patient(X)&~creative(X))<=>(~strong(X)|old(X))))&
(((brave(fred)<~>generous(fred)))<=>((calm(susan)|~strong(susan))))&
((?[X]:(happy(X)))=>((~tall(alice)&generous(alice))))&
((~kind(fred))=>((~funny(paul)&calm(paul))))&
(![X]:((brave(X)<~>wise(X))=>tall(X)))&
(![X]:((~patient(X)&~funny(X))<=>~calm(X)))&
((~quiet(mary))<=>((~quiet(john)&~patient(john))))&
(((~quiet(mary)<~>~humble(mary)))=>((strong(john)&~old(john))))&
((happy(susan))=>((~wise(paul)<~>happy(paul))))&
(?[X]:((strong(X)|brave(X))))&
(tall(susan))&
(~happy(mary))&
((brave(mary)|wise(mary)))&
(?[X]:((happy(X)&~tall(X))))&
((generous(alice)<~>~creative(alice)))&
(?[X]:(humble(X)))&
(?[X]:((~old(X)&curious(X)))) | patient(susan) | [
"p0",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2550831371921075770564288
% SZS output start Proof for 2550831371921075770564288
1. ! [X0] : ((quiet(X0) | ~quiet(X0)) <=> (~strong(X0) <~> patient(X0))) [input p0]
8. ! [X0] : ((~creative(X0) & patient(X0)) <=> (old(X0) | ~strong(X0))) [input p7]
25. ~patient(susan) [input hypothesis]
35. ! [X0] : (((quiet(X0) | ~quiet(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~quiet(X0) & quiet(X0)))) [nnf transformation 1]
36. ! [X0] : ((quiet(X0) | ~quiet(X0) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~quiet(X0) & quiet(X0)))) [flattening 35]
53. ! [X0] : (((~creative(X0) & patient(X0)) | (~old(X0) & strong(X0))) & ((old(X0) | ~strong(X0)) | (creative(X0) | ~patient(X0)))) [nnf transformation 8]
54. ! [X0] : (((~creative(X0) & patient(X0)) | (~old(X0) & strong(X0))) & (old(X0) | ~strong(X0) | creative(X0) | ~patient(X0))) [flattening 53]
73. patient(X0) | ~strong(X0) | quiet(X0) [cnf transformation 36]
74. patient(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 36]
106. patient(X0) | strong(X0) [cnf transformation 54]
145. ~patient(susan) [cnf transformation 25]
151. patient(X0) | ~strong(X0) [subsumption resolution 73,74]
202. patient(X0) [subsumption resolution 106,151]
306. $false [subsumption resolution 145,202]
% SZS output end Proof for 2550831371921075770564288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or not patient then someone is calm and vice versa.
If someone is either not strong or not patient then paul is both generous and rich and vice versa.
Everyone who is both not kind and tall is not calm or rich.
If someone is not humble then someone is kind or not tall.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
If paul is patient or not curious then susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Susan is not kind or curious.
Someone is old. | John is kind. | neutral | ((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:(calm(X))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>((generous(paul)&rich(paul))))&
(![X]:((~kind(X)&tall(X))=>(~calm(X)|rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
(((patient(paul)|~curious(paul)))=>((~happy(susan)|happy(susan))))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
((~kind(susan)|curious(susan)))&
(?[X]:(old(X))) | kind(john) | [] | null | 0 |
If mary is not tall then someone is both patient and generous. Everyone who is both not old and not strong is both tall and funny and vice versa. If alice is either generous or wise then john is both wise and old. Everyone who is both not humble and humble is tall or not curious and vice versa. Everyone who is both brave and happy is both rich and not funny and vice versa. If someone is both not patient and not rich then someone is generous. Everyone who is not kind is funny and vice versa. Everyone who is humble is either old or not brave and vice versa. If someone is either not humble or not rich then someone is both not humble and humble. If john is brave then someone is both generous and creative and vice versa. If john is not patient then lucy is funny and vice versa. If fred is either tall or strong then someone is not curious and vice versa. Everyone who is both happy and not old is creative and vice versa. Everyone who is either old or not creative is not curious or not brave and vice versa. If someone is either not strong or strong then someone is either not quiet or wise. If someone is not kind then alice is curious and vice versa. Someone is not wise. Lucy is not funny or curious. Paul is calm or happy. Susan is calm or patient. Someone is curious. Susan is kind or creative. Alice is either happy or humble. Someone is not quiet. | Susan is not kind. | contradiction | ((~tall(mary))=>(?[X]:((patient(X)&generous(X)))))&
(![X]:((~old(X)&~strong(X))<=>(tall(X)&funny(X))))&
(((generous(alice)<~>wise(alice)))=>((wise(john)&old(john))))&
(![X]:((~humble(X)&humble(X))<=>(tall(X)|~curious(X))))&
(![X]:((brave(X)&happy(X))<=>(rich(X)&~funny(X))))&
((?[X]:((~patient(X)&~rich(X))))=>(?[X]:(generous(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:(humble(X)<=>(old(X)<~>~brave(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>(?[X]:((~humble(X)&humble(X)))))&
((brave(john))<=>(?[X]:((generous(X)&creative(X)))))&
((~patient(john))<=>(funny(lucy)))&
(((tall(fred)<~>strong(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((happy(X)&~old(X))<=>creative(X)))&
(![X]:((old(X)<~>~creative(X))<=>(~curious(X)|~brave(X))))&
((?[X]:((~strong(X)<~>strong(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:(~kind(X)))<=>(curious(alice)))&
(?[X]:(~wise(X)))&
((~funny(lucy)|curious(lucy)))&
((calm(paul)|happy(paul)))&
((calm(susan)|patient(susan)))&
(?[X]:(curious(X)))&
((kind(susan)|creative(susan)))&
((happy(alice)<~>humble(alice)))&
(?[X]:(~quiet(X))) | ~kind(susan) | [
"p4",
"p6",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3555641259382416570899998
% SZS output start Proof for 3555641259382416570899998
5. ! [X0] : ((happy(X0) & brave(X0)) <=> (~funny(X0) & rich(X0))) [input p4]
7. ! [X0] : (~kind(X0) <=> funny(X0)) [input p6]
13. ! [X0] : ((~old(X0) & happy(X0)) <=> creative(X0)) [input p12]
14. ! [X0] : ((old(X0) <~> ~creative(X0)) <=> (~brave(X0) | ~curious(X0))) [input p13]
22. creative(susan) | kind(susan) [input p21]
25. ~kind(susan) [input hypothesis]
43. ! [X0] : (((happy(X0) & brave(X0)) | (funny(X0) | ~rich(X0))) & ((~funny(X0) & rich(X0)) | (~happy(X0) | ~brave(X0)))) [nnf transformation 5]
44. ! [X0] : (((happy(X0) & brave(X0)) | funny(X0) | ~rich(X0)) & ((~funny(X0) & rich(X0)) | ~happy(X0) | ~brave(X0))) [flattening 43]
48. ! [X0] : ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0))) [nnf transformation 7]
63. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 13]
64. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | old(X0) | ~happy(X0))) [flattening 63]
65. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & ((~brave(X0) | ~curious(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [nnf transformation 14]
66. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & (~brave(X0) | ~curious(X0) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [flattening 65]
98. ~happy(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 44]
102. kind(X0) | funny(X0) [cnf transformation 48]
122. ~creative(X0) | happy(X0) [cnf transformation 64]
123. ~creative(X0) | ~old(X0) [cnf transformation 64]
127. ~creative(X0) | old(X0) | brave(X0) [cnf transformation 66]
129. creative(X0) | ~old(X0) | brave(X0) [cnf transformation 66]
139. creative(susan) | kind(susan) [cnf transformation 22]
143. ~kind(susan) [cnf transformation 25]
236. ~old(X0) | brave(X0) [subsumption resolution 129,123]
237. ~creative(X0) | brave(X0) [subsumption resolution 127,236]
259. 23 <=> kind(susan) [avatar definition]
260. ~kind(susan) <- (~23) [avatar component clause 259]
263. 24 <=> creative(susan) [avatar definition]
265. creative(susan) <- (24) [avatar component clause 263]
266. 23 | 24 [avatar split clause 139,263,259]
277. ~23 [avatar split clause 143,259]
279. funny(susan) <- (~23) [resolution 102,260]
281. happy(susan) <- (24) [resolution 122,265]
285. brave(susan) <- (24) [resolution 237,265]
312. ~funny(susan) | ~brave(susan) <- (24) [resolution 98,281]
313. ~brave(susan) <- (~23, 24) [subsumption resolution 312,279]
314. $false <- (~23, 24) [subsumption resolution 313,285]
315. 23 | ~24 [avatar contradiction clause 314]
316. $false [avatar sat refutation 266,277,315]
% SZS output end Proof for 3555641259382416570899998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not humble is patient.
If someone is either not brave or rich then someone is not happy or not quiet and vice versa.
Everyone who is both not old and not curious is not quiet or not tall.
Everyone who is not kind or wise is both happy and rich.
Everyone who is both not funny and rich is strong.
Everyone who is quiet is either not tall or rich and vice versa.
Everyone who is quiet or rich is kind or strong.
If someone is kind or not patient then someone is either not quiet or wise and vice versa.
If someone is not strong or not rich then mary is brave or curious and vice versa.
Everyone who is quiet or funny is not wise.
Everyone who is both funny and not old is either not kind or quiet and vice versa.
If someone is either tall or humble then someone is not brave and vice versa.
Everyone who is either not humble or not kind is either curious or calm and vice versa.
Everyone who is not funny or tall is not brave and vice versa.
If someone is creative then someone is either not funny or old.
If someone is both not patient and calm then someone is both generous and kind and vice versa.
Someone is both not kind and not funny.
Someone is either not old or rich.
Fred is strong or not kind.
John is brave or not wise.
Someone is both humble and not happy.
Susan is either not curious or not quiet.
Someone is not wise or creative.
Someone is not wise. | Susan is generous. | neutral | (![X]:((~curious(X)&~humble(X))=>patient(X)))&
((?[X]:((~brave(X)<~>rich(X))))<=>(?[X]:((~happy(X)|~quiet(X)))))&
(![X]:((~old(X)&~curious(X))=>(~quiet(X)|~tall(X))))&
(![X]:((~kind(X)|wise(X))=>(happy(X)&rich(X))))&
(![X]:((~funny(X)&rich(X))=>strong(X)))&
(![X]:(quiet(X)<=>(~tall(X)<~>rich(X))))&
(![X]:((quiet(X)|rich(X))=>(kind(X)|strong(X))))&
((?[X]:((kind(X)|~patient(X))))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:((~strong(X)|~rich(X))))<=>((brave(mary)|curious(mary))))&
(![X]:((quiet(X)|funny(X))=>~wise(X)))&
(![X]:((funny(X)&~old(X))<=>(~kind(X)<~>quiet(X))))&
((?[X]:((tall(X)<~>humble(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~humble(X)<~>~kind(X))<=>(curious(X)<~>calm(X))))&
(![X]:((~funny(X)|tall(X))<=>~brave(X)))&
((?[X]:(creative(X)))=>(?[X]:((~funny(X)<~>old(X)))))&
((?[X]:((~patient(X)&calm(X))))<=>(?[X]:((generous(X)&kind(X)))))&
(?[X]:((~kind(X)&~funny(X))))&
(?[X]:((~old(X)<~>rich(X))))&
((strong(fred)|~kind(fred)))&
((brave(john)|~wise(john)))&
(?[X]:((humble(X)&~happy(X))))&
((~curious(susan)<~>~quiet(susan)))&
(?[X]:((~wise(X)|creative(X))))&
(?[X]:(~wise(X))) | generous(susan) | [] | null | 0 |
Everyone who is either not curious or generous is wise and vice versa.
Everyone who is either not wise or not strong is not creative or rich.
Everyone who is generous or not calm is either patient or not humble and vice versa.
If lucy is either not happy or calm then someone is either curious or not curious and vice versa.
If alice is happy then someone is wise or not happy and vice versa.
If susan is not creative then someone is not calm or not humble and vice versa.
Everyone who is either strong or not funny is old and vice versa.
If someone is not quiet or humble then john is both not kind and rich.
If someone is both not generous and curious then mary is curious or quiet and vice versa.
If mary is funny then lucy is both funny and not patient.
If someone is old or rich then fred is both generous and not calm.
If susan is tall then lucy is not brave.
Everyone who is curious or not rich is wise.
Everyone who is brave or not brave is not funny or not wise.
Everyone who is wise is not humble.
Everyone who is both strong and not generous is not humble or wise and vice versa.
Someone is not brave or patient.
Susan is not generous.
John is both not generous and patient.
Susan is not brave. | Susan is curious. | contradiction | (![X]:((~curious(X)<~>generous(X))<=>wise(X)))&
(![X]:((~wise(X)<~>~strong(X))=>(~creative(X)|rich(X))))&
(![X]:((generous(X)|~calm(X))<=>(patient(X)<~>~humble(X))))&
(((~happy(lucy)<~>calm(lucy)))<=>(?[X]:((curious(X)<~>~curious(X)))))&
((happy(alice))<=>(?[X]:((wise(X)|~happy(X)))))&
((~creative(susan))<=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:((strong(X)<~>~funny(X))<=>old(X)))&
((?[X]:((~quiet(X)|humble(X))))=>((~kind(john)&rich(john))))&
((?[X]:((~generous(X)&curious(X))))<=>((curious(mary)|quiet(mary))))&
((funny(mary))=>((funny(lucy)&~patient(lucy))))&
((?[X]:((old(X)|rich(X))))=>((generous(fred)&~calm(fred))))&
((tall(susan))=>(~brave(lucy)))&
(![X]:((curious(X)|~rich(X))=>wise(X)))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|~wise(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((strong(X)&~generous(X))<=>(~humble(X)|wise(X))))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan))&
((~generous(john)&patient(john)))&
(~brave(susan)) | curious(susan) | [
"p0",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2500315384598453513494801
% SZS output start Proof for 2500315384598453513494801
1. ! [X0] : ((~curious(X0) <~> generous(X0)) <=> wise(X0)) [input p0]
13. ! [X0] : ((~rich(X0) | curious(X0)) => wise(X0)) [input p12]
18. ~generous(susan) [input p17]
21. curious(susan) [input hypothesis]
31. ! [X0] : (wise(X0) | (rich(X0) & ~curious(X0))) [ennf transformation 13]
35. ! [X0] : ((((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | ~wise(X0)) & (wise(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0))))) [nnf transformation 1]
63. ~wise(X0) | ~curious(X0) | generous(X0) [cnf transformation 35]
102. ~curious(X0) | wise(X0) [cnf transformation 31]
113. ~generous(susan) [cnf transformation 18]
117. curious(susan) [cnf transformation 21]
263. wise(susan) [resolution 102,117]
276. ~curious(susan) | generous(susan) [resolution 63,263]
281. generous(susan) [subsumption resolution 276,117]
282. $false [subsumption resolution 281,113]
% SZS output end Proof for 2500315384598453513494801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and wise then susan is both not kind and not humble and vice versa.
Everyone who is either quiet or tall is both curious and not rich.
If someone is not kind or brave then paul is either strong or brave and vice versa.
If paul is not curious then paul is not old.
Everyone who is either quiet or not humble is both tall and strong and vice versa.
Everyone who is either old or calm is both old and kind.
Everyone who is old or not quiet is either not strong or tall.
Everyone who is not creative or generous is either brave or happy and vice versa.
Everyone who is both not calm and wise is quiet or not quiet.
Everyone who is not happy or strong is both not funny and not kind.
Everyone who is either old or not strong is not calm.
Everyone who is curious is both patient and not curious and vice versa.
If mary is both not creative and tall then someone is both happy and quiet.
If lucy is both not old and strong then someone is both not old and patient.
Everyone who is not strong is not curious.
Everyone who is funny or quiet is humble or wise and vice versa.
Someone is creative or tall.
Paul is wise or quiet.
Mary is not wise.
Someone is both not curious and not patient.
Mary is either kind or not funny.
Lucy is brave.
Paul is wise. | Lucy is generous. | neutral | ((?[X]:((~patient(X)&wise(X))))<=>((~kind(susan)&~humble(susan))))&
(![X]:((quiet(X)<~>tall(X))=>(curious(X)&~rich(X))))&
((?[X]:((~kind(X)|brave(X))))<=>((strong(paul)<~>brave(paul))))&
((~curious(paul))=>(~old(paul)))&
(![X]:((quiet(X)<~>~humble(X))<=>(tall(X)&strong(X))))&
(![X]:((old(X)<~>calm(X))=>(old(X)&kind(X))))&
(![X]:((old(X)|~quiet(X))=>(~strong(X)<~>tall(X))))&
(![X]:((~creative(X)|generous(X))<=>(brave(X)<~>happy(X))))&
(![X]:((~calm(X)&wise(X))=>(quiet(X)|~quiet(X))))&
(![X]:((~happy(X)|strong(X))=>(~funny(X)&~kind(X))))&
(![X]:((old(X)<~>~strong(X))=>~calm(X)))&
(![X]:(curious(X)<=>(patient(X)&~curious(X))))&
(((~creative(mary)&tall(mary)))=>(?[X]:((happy(X)&quiet(X)))))&
(((~old(lucy)&strong(lucy)))=>(?[X]:((~old(X)&patient(X)))))&
(![X]:(~strong(X)=>~curious(X)))&
(![X]:((funny(X)|quiet(X))<=>(humble(X)|wise(X))))&
(?[X]:((creative(X)|tall(X))))&
((wise(paul)|quiet(paul)))&
(~wise(mary))&
(?[X]:((~curious(X)&~patient(X))))&
((kind(mary)<~>~funny(mary)))&
(brave(lucy))&
(wise(paul)) | generous(lucy) | [] | null | 0 |
Everyone who is not tall or happy is either not creative or not humble.
If paul is creative or not humble then john is either strong or humble.
Everyone who is generous is not funny and vice versa.
Everyone who is both not creative and not calm is not brave.
Everyone who is not generous or not rich is either tall or funny and vice versa.
If alice is both not brave and not happy then someone is quiet or not old.
If john is both calm and happy then someone is creative or not brave.
If someone is either not creative or rich then fred is either old or not humble and vice versa.
If someone is both not humble and not old then alice is both not rich and old and vice versa.
Everyone who is not funny is not happy and vice versa.
If someone is both not funny and quiet then someone is either not tall or not wise.
Everyone who is both not curious and not brave is not quiet.
If someone is not happy then someone is strong or not generous.
Everyone who is generous is either not curious or not tall.
If someone is either not funny or not wise then alice is both rich and old and vice versa.
Someone is not rich or brave.
Fred is both not wise and humble.
Someone is generous or strong.
Fred is either happy or not brave.
Someone is either not brave or not rich.
Someone is both strong and not kind.
Someone is both not calm and old.
Someone is either not happy or not calm. | Alice is not brave. | neutral | (![X]:((~tall(X)|happy(X))=>(~creative(X)<~>~humble(X))))&
(((creative(paul)|~humble(paul)))=>((strong(john)<~>humble(john))))&
(![X]:(generous(X)<=>~funny(X)))&
(![X]:((~creative(X)&~calm(X))=>~brave(X)))&
(![X]:((~generous(X)|~rich(X))<=>(tall(X)<~>funny(X))))&
(((~brave(alice)&~happy(alice)))=>(?[X]:((quiet(X)|~old(X)))))&
(((calm(john)&happy(john)))=>(?[X]:((creative(X)|~brave(X)))))&
((?[X]:((~creative(X)<~>rich(X))))<=>((old(fred)<~>~humble(fred))))&
((?[X]:((~humble(X)&~old(X))))<=>((~rich(alice)&old(alice))))&
(![X]:(~funny(X)<=>~happy(X)))&
((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((~tall(X)<~>~wise(X)))))&
(![X]:((~curious(X)&~brave(X))=>~quiet(X)))&
((?[X]:(~happy(X)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:(generous(X)=>(~curious(X)<~>~tall(X))))&
((?[X]:((~funny(X)<~>~wise(X))))<=>((rich(alice)&old(alice))))&
(?[X]:((~rich(X)|brave(X))))&
((~wise(fred)&humble(fred)))&
(?[X]:((generous(X)|strong(X))))&
((happy(fred)<~>~brave(fred)))&
(?[X]:((~brave(X)<~>~rich(X))))&
(?[X]:((strong(X)&~kind(X))))&
(?[X]:((~calm(X)&old(X))))&
(?[X]:((~happy(X)<~>~calm(X)))) | ~brave(alice) | [] | null | 0 |
If alice is not tall then alice is not creative and vice versa.
If lucy is either not quiet or tall then susan is both not tall and not kind.
Everyone who is either not curious or not calm is either strong or not generous.
Everyone who is either tall or not quiet is either not funny or old and vice versa.
Everyone who is not humble or strong is not curious and vice versa.
Everyone who is generous or not curious is not rich or kind.
Everyone who is either not generous or not happy is both not calm and humble.
If someone is tall then susan is humble and vice versa.
Everyone who is curious or humble is generous or funny and vice versa.
If someone is strong then someone is either humble or curious and vice versa.
If someone is both rich and not old then someone is not kind.
If someone is curious or not calm then paul is both not patient and old and vice versa.
If someone is old or not kind then someone is rich.
If lucy is both not rich and rich then someone is both not rich and humble.
Everyone who is both kind and strong is either humble or funny and vice versa.
Everyone who is strong or not humble is both not kind and not calm and vice versa.
Someone is creative or strong.
Someone is brave.
Mary is not curious.
Someone is both quiet and calm.
Fred is not strong.
Someone is either patient or not quiet.
Someone is not strong.
Someone is not tall. | Mary is not rich. | entailment | ((~tall(alice))<=>(~creative(alice)))&
(((~quiet(lucy)<~>tall(lucy)))=>((~tall(susan)&~kind(susan))))&
(![X]:((~curious(X)<~>~calm(X))=>(strong(X)<~>~generous(X))))&
(![X]:((tall(X)<~>~quiet(X))<=>(~funny(X)<~>old(X))))&
(![X]:((~humble(X)|strong(X))<=>~curious(X)))&
(![X]:((generous(X)|~curious(X))=>(~rich(X)|kind(X))))&
(![X]:((~generous(X)<~>~happy(X))=>(~calm(X)&humble(X))))&
((?[X]:(tall(X)))<=>(humble(susan)))&
(![X]:((curious(X)|humble(X))<=>(generous(X)|funny(X))))&
((?[X]:(strong(X)))<=>(?[X]:((humble(X)<~>curious(X)))))&
((?[X]:((rich(X)&~old(X))))=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)|~calm(X))))<=>((~patient(paul)&old(paul))))&
((?[X]:((old(X)|~kind(X))))=>(?[X]:(rich(X))))&
(((~rich(lucy)&rich(lucy)))=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((kind(X)&strong(X))<=>(humble(X)<~>funny(X))))&
(![X]:((strong(X)|~humble(X))<=>(~kind(X)&~calm(X))))&
(?[X]:((creative(X)|strong(X))))&
(?[X]:(brave(X)))&
(~curious(mary))&
(?[X]:((quiet(X)&calm(X))))&
(~strong(fred))&
(?[X]:((patient(X)<~>~quiet(X))))&
(?[X]:(~strong(X)))&
(?[X]:(~tall(X))) | ~rich(mary) | [
"p4",
"p5",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2286327921514178375509602
% SZS output start Proof for 2286327921514178375509602
5. ! [X0] : ((strong(X0) | ~humble(X0)) <=> ~curious(X0)) [input p4]
6. ! [X0] : ((~curious(X0) | generous(X0)) => (kind(X0) | ~rich(X0))) [input p5]
16. ! [X0] : ((~humble(X0) | strong(X0)) <=> (~calm(X0) & ~kind(X0))) [input p15]
19. ~curious(mary) [input p18]
25. rich(mary) [input hypothesis]
32. ! [X0] : ((kind(X0) | ~rich(X0)) | (curious(X0) & ~generous(X0))) [ennf transformation 6]
33. ! [X0] : (kind(X0) | ~rich(X0) | (curious(X0) & ~generous(X0))) [flattening 32]
43. ! [X0] : (((strong(X0) | ~humble(X0)) | curious(X0)) & (~curious(X0) | (~strong(X0) & humble(X0)))) [nnf transformation 5]
44. ! [X0] : ((strong(X0) | ~humble(X0) | curious(X0)) & (~curious(X0) | (~strong(X0) & humble(X0)))) [flattening 43]
72. ! [X0] : (((~humble(X0) | strong(X0)) | (calm(X0) | kind(X0))) & ((~calm(X0) & ~kind(X0)) | (humble(X0) & ~strong(X0)))) [nnf transformation 16]
73. ! [X0] : ((~humble(X0) | strong(X0) | calm(X0) | kind(X0)) & ((~calm(X0) & ~kind(X0)) | (humble(X0) & ~strong(X0)))) [flattening 72]
105. ~humble(X0) | strong(X0) | curious(X0) [cnf transformation 44]
107. ~rich(X0) | kind(X0) | curious(X0) [cnf transformation 33]
138. ~strong(X0) | ~kind(X0) [cnf transformation 73]
139. ~kind(X0) | humble(X0) [cnf transformation 73]
144. ~curious(mary) [cnf transformation 19]
152. rich(mary) [cnf transformation 25]
302. 31 <=> kind(mary) [avatar definition]
304. kind(mary) <- (31) [avatar component clause 302]
315. kind(mary) | curious(mary) [resolution 107,152]
317. kind(mary) [subsumption resolution 315,144]
318. 31 [avatar split clause 317,302]
360. humble(mary) <- (31) [resolution 304,139]
533. strong(mary) | curious(mary) <- (31) [resolution 360,105]
535. 57 <=> strong(mary) [avatar definition]
537. strong(mary) <- (57) [avatar component clause 535]
545. strong(mary) <- (31) [subsumption resolution 533,144]
546. 57 | ~31 [avatar split clause 545,302,535]
758. ~kind(mary) <- (57) [resolution 537,138]
762. $false <- (31, 57) [subsumption resolution 758,304]
763. ~31 | ~57 [avatar contradiction clause 762]
764. $false [avatar sat refutation 318,546,763]
% SZS output end Proof for 2286327921514178375509602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or strong then someone is both funny and not strong. If lucy is both curious and not calm then john is either not generous or quiet and vice versa. Everyone who is generous or not rich is not quiet or rich and vice versa. Everyone who is either strong or kind is either not strong or wise. If mary is humble or not creative then mary is generous or curious and vice versa. If someone is either not curious or not quiet then john is not happy or wise and vice versa. If someone is both not calm and not strong then someone is both kind and curious. Everyone who is quiet is not curious or funny and vice versa. Everyone who is patient or tall is both not generous and tall. If someone is humble or not quiet then john is either not old or not creative and vice versa. Everyone who is funny or not funny is generous. If john is either not happy or not kind then fred is both calm and humble and vice versa. Everyone who is patient or wise is creative and vice versa. Everyone who is wise or brave is not old or patient. Everyone who is not creative is quiet. If alice is either not happy or wise then mary is not happy or brave. John is both not strong and calm. Someone is both not old and quiet. Paul is either not humble or creative. Someone is both not humble and quiet. Susan is patient or creative. Someone is calm or not brave. Someone is either calm or quiet. Someone is both curious and quiet. | Susan is not old. | entailment | ((?[X]:((wise(X)|strong(X))))=>(?[X]:((funny(X)&~strong(X)))))&
(((curious(lucy)&~calm(lucy)))<=>((~generous(john)<~>quiet(john))))&
(![X]:((generous(X)|~rich(X))<=>(~quiet(X)|rich(X))))&
(![X]:((strong(X)<~>kind(X))=>(~strong(X)<~>wise(X))))&
(((humble(mary)|~creative(mary)))<=>((generous(mary)|curious(mary))))&
((?[X]:((~curious(X)<~>~quiet(X))))<=>((~happy(john)|wise(john))))&
((?[X]:((~calm(X)&~strong(X))))=>(?[X]:((kind(X)&curious(X)))))&
(![X]:(quiet(X)<=>(~curious(X)|funny(X))))&
(![X]:((patient(X)|tall(X))=>(~generous(X)&tall(X))))&
((?[X]:((humble(X)|~quiet(X))))<=>((~old(john)<~>~creative(john))))&
(![X]:((funny(X)|~funny(X))=>generous(X)))&
(((~happy(john)<~>~kind(john)))<=>((calm(fred)&humble(fred))))&
(![X]:((patient(X)|wise(X))<=>creative(X)))&
(![X]:((wise(X)|brave(X))=>(~old(X)|patient(X))))&
(![X]:(~creative(X)=>quiet(X)))&
(((~happy(alice)<~>wise(alice)))=>((~happy(mary)|brave(mary))))&
((~strong(john)&calm(john)))&
(?[X]:((~old(X)&quiet(X))))&
((~humble(paul)<~>creative(paul)))&
(?[X]:((~humble(X)&quiet(X))))&
((patient(susan)|creative(susan)))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((curious(X)&quiet(X)))) | ~old(susan) | [
"p8",
"p10",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6680566634979539022437340
% SZS output start Proof for 6680566634979539022437340
9. ! [X0] : ((tall(X0) | patient(X0)) => (tall(X0) & ~generous(X0))) [input p8]
11. ! [X0] : ((~funny(X0) | funny(X0)) => generous(X0)) [input p10]
13. ! [X0] : ((wise(X0) | patient(X0)) <=> creative(X0)) [input p12]
14. ! [X0] : ((brave(X0) | wise(X0)) => (patient(X0) | ~old(X0))) [input p13]
21. creative(susan) | patient(susan) [input p20]
25. old(susan) [input hypothesis]
31. ! [X0] : ((tall(X0) & ~generous(X0)) | (~tall(X0) & ~patient(X0))) [ennf transformation 9]
32. ! [X0] : (generous(X0) | (funny(X0) & ~funny(X0))) [ennf transformation 11]
33. ! [X0] : ((patient(X0) | ~old(X0)) | (~brave(X0) & ~wise(X0))) [ennf transformation 14]
34. ! [X0] : (patient(X0) | ~old(X0) | (~brave(X0) & ~wise(X0))) [flattening 33]
64. ! [X0] : (((wise(X0) | patient(X0)) | ~creative(X0)) & (creative(X0) | (~wise(X0) & ~patient(X0)))) [nnf transformation 13]
65. ! [X0] : ((wise(X0) | patient(X0) | ~creative(X0)) & (creative(X0) | (~wise(X0) & ~patient(X0)))) [flattening 64]
112. ~patient(X0) | ~generous(X0) [cnf transformation 31]
122. generous(X0) | ~funny(X0) [cnf transformation 32]
123. generous(X0) | funny(X0) [cnf transformation 32]
130. ~patient(X0) | creative(X0) [cnf transformation 65]
132. ~creative(X0) | patient(X0) | wise(X0) [cnf transformation 65]
133. ~old(X0) | patient(X0) | ~wise(X0) [cnf transformation 34]
146. creative(susan) | patient(susan) [cnf transformation 21]
152. old(susan) [cnf transformation 25]
286. generous(X0) [subsumption resolution 122,123]
333. creative(susan) [subsumption resolution 146,130]
408. patient(susan) | wise(susan) [resolution 132,333]
412. 47 <=> wise(susan) [avatar definition]
414. wise(susan) <- (47) [avatar component clause 412]
416. 48 <=> patient(susan) [avatar definition]
418. patient(susan) <- (48) [avatar component clause 416]
419. 47 | 48 [avatar split clause 408,416,412]
421. patient(susan) | ~wise(susan) [resolution 133,152]
422. patient(susan) <- (47) [subsumption resolution 421,414]
423. 48 | ~47 [avatar split clause 422,412,416]
439. ~generous(susan) <- (48) [resolution 418,112]
440. $false <- (48) [subsumption resolution 439,286]
441. ~48 [avatar contradiction clause 440]
442. $false [avatar sat refutation 419,423,441]
% SZS output end Proof for 6680566634979539022437340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous then fred is not tall or happy and vice versa. If someone is not brave or not generous then susan is old and vice versa. Everyone who is either not generous or funny is humble or not generous and vice versa. Everyone who is wise or not strong is both not wise and not old. If susan is either not curious or strong then mary is not funny or not generous. Everyone who is either creative or humble is both not calm and not curious and vice versa. If susan is both creative and curious then john is not patient or quiet and vice versa. Everyone who is generous is not tall. Everyone who is not generous is rich. Everyone who is calm is not brave. Everyone who is both not kind and humble is either creative or not rich and vice versa. If someone is brave or not creative then someone is not rich and vice versa. Everyone who is either not patient or tall is both wise and calm. If paul is both not old and not humble then someone is both rich and not curious and vice versa. If john is happy then someone is not happy or humble. If alice is either not calm or not rich then someone is either quiet or wise. Someone is both not quiet and happy. Mary is both not patient and not wise. Susan is both not brave and not kind. Someone is not tall or generous. Paul is not strong or not tall. Fred is either tall or not happy. Someone is either humble or not funny. Someone is not creative. | Alice is calm. | neutral | ((?[X]:(~generous(X)))<=>((~tall(fred)|happy(fred))))&
((?[X]:((~brave(X)|~generous(X))))<=>(old(susan)))&
(![X]:((~generous(X)<~>funny(X))<=>(humble(X)|~generous(X))))&
(![X]:((wise(X)|~strong(X))=>(~wise(X)&~old(X))))&
(((~curious(susan)<~>strong(susan)))=>((~funny(mary)|~generous(mary))))&
(![X]:((creative(X)<~>humble(X))<=>(~calm(X)&~curious(X))))&
(((creative(susan)&curious(susan)))<=>((~patient(john)|quiet(john))))&
(![X]:(generous(X)=>~tall(X)))&
(![X]:(~generous(X)=>rich(X)))&
(![X]:(calm(X)=>~brave(X)))&
(![X]:((~kind(X)&humble(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((brave(X)|~creative(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~patient(X)<~>tall(X))=>(wise(X)&calm(X))))&
(((~old(paul)&~humble(paul)))<=>(?[X]:((rich(X)&~curious(X)))))&
((happy(john))=>(?[X]:((~happy(X)|humble(X)))))&
(((~calm(alice)<~>~rich(alice)))=>(?[X]:((quiet(X)<~>wise(X)))))&
(?[X]:((~quiet(X)&happy(X))))&
((~patient(mary)&~wise(mary)))&
((~brave(susan)&~kind(susan)))&
(?[X]:((~tall(X)|generous(X))))&
((~strong(paul)|~tall(paul)))&
((tall(fred)<~>~happy(fred)))&
(?[X]:((humble(X)<~>~funny(X))))&
(?[X]:(~creative(X))) | calm(alice) | [] | null | 0 |
Everyone who is not happy or not humble is calm and vice versa.
Everyone who is both not quiet and not generous is both not quiet and not kind and vice versa.
Everyone who is not generous is not calm or not brave.
If john is either not brave or not old then someone is both quiet and calm and vice versa.
If alice is both not wise and creative then john is either happy or strong and vice versa.
If someone is either not generous or not humble then susan is not creative or creative.
If susan is humble or not wise then someone is strong or tall.
Everyone who is creative or happy is not tall or generous.
Everyone who is either not generous or wise is either strong or humble and vice versa.
Everyone who is either humble or calm is both not creative and quiet and vice versa.
Everyone who is either not humble or not strong is not happy.
If paul is strong or creative then fred is not brave.
If john is not humble then someone is not calm or not happy.
If john is kind or creative then someone is humble.
Everyone who is not brave or not wise is either brave or not old.
If mary is both old and tall then someone is not quiet or not happy.
Someone is not happy.
Paul is kind.
Fred is not humble or brave.
Someone is calm or not happy.
Lucy is either not rich or happy.
Alice is both not generous and not strong.
Lucy is old or not rich.
Paul is not generous. | John is not old. | entailment | (![X]:((~happy(X)|~humble(X))<=>calm(X)))&
(![X]:((~quiet(X)&~generous(X))<=>(~quiet(X)&~kind(X))))&
(![X]:(~generous(X)=>(~calm(X)|~brave(X))))&
(((~brave(john)<~>~old(john)))<=>(?[X]:((quiet(X)&calm(X)))))&
(((~wise(alice)&creative(alice)))<=>((happy(john)<~>strong(john))))&
((?[X]:((~generous(X)<~>~humble(X))))=>((~creative(susan)|creative(susan))))&
(((humble(susan)|~wise(susan)))=>(?[X]:((strong(X)|tall(X)))))&
(![X]:((creative(X)|happy(X))=>(~tall(X)|generous(X))))&
(![X]:((~generous(X)<~>wise(X))<=>(strong(X)<~>humble(X))))&
(![X]:((humble(X)<~>calm(X))<=>(~creative(X)&quiet(X))))&
(![X]:((~humble(X)<~>~strong(X))=>~happy(X)))&
(((strong(paul)|creative(paul)))=>(~brave(fred)))&
((~humble(john))=>(?[X]:((~calm(X)|~happy(X)))))&
(((kind(john)|creative(john)))=>(?[X]:(humble(X))))&
(![X]:((~brave(X)|~wise(X))=>(brave(X)<~>~old(X))))&
(((old(mary)&tall(mary)))=>(?[X]:((~quiet(X)|~happy(X)))))&
(?[X]:(~happy(X)))&
(kind(paul))&
((~humble(fred)|brave(fred)))&
(?[X]:((calm(X)|~happy(X))))&
((~rich(lucy)<~>happy(lucy)))&
((~generous(alice)&~strong(alice)))&
((old(lucy)|~rich(lucy)))&
(~generous(paul)) | ~old(john) | [
"p0",
"p1",
"p3",
"p9",
"p10",
"p11",
"p14",
"p17",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 259878781190755501818554
% SZS output start Proof for 259878781190755501818554
1. ! [X0] : ((~humble(X0) | ~happy(X0)) <=> calm(X0)) [input p0]
2. ! [X0] : ((~generous(X0) & ~quiet(X0)) <=> (~kind(X0) & ~quiet(X0))) [input p1]
4. (~brave(john) <~> ~old(john)) <=> ? [X0] : (calm(X0) & quiet(X0)) [input p3]
10. ! [X0] : ((humble(X0) <~> calm(X0)) <=> (quiet(X0) & ~creative(X0))) [input p9]
11. ! [X0] : ((~humble(X0) <~> ~strong(X0)) => ~happy(X0)) [input p10]
12. (creative(paul) | strong(paul)) => ~brave(fred) [input p11]
15. ! [X0] : ((~wise(X0) | ~brave(X0)) => (brave(X0) <~> ~old(X0))) [input p14]
18. kind(paul) [input p17]
19. brave(fred) | ~humble(fred) [input p18]
24. ~generous(paul) [input p23]
25. old(john) [input hypothesis]
33. ! [X0] : (~happy(X0) | (~humble(X0) <=> ~strong(X0))) [ennf transformation 11]
34. ~brave(fred) | (~creative(paul) & ~strong(paul)) [ennf transformation 12]
37. ! [X0] : ((brave(X0) <~> ~old(X0)) | (wise(X0) & brave(X0))) [ennf transformation 15]
40. ! [X0] : (((~humble(X0) | ~happy(X0)) | ~calm(X0)) & (calm(X0) | (humble(X0) & happy(X0)))) [nnf transformation 1]
41. ! [X0] : ((~humble(X0) | ~happy(X0) | ~calm(X0)) & (calm(X0) | (humble(X0) & happy(X0)))) [flattening 40]
42. ! [X0] : (((~generous(X0) & ~quiet(X0)) | (kind(X0) | quiet(X0))) & ((~kind(X0) & ~quiet(X0)) | (generous(X0) | quiet(X0)))) [nnf transformation 2]
43. ! [X0] : (((~generous(X0) & ~quiet(X0)) | kind(X0) | quiet(X0)) & ((~kind(X0) & ~quiet(X0)) | generous(X0) | quiet(X0))) [flattening 42]
44. (((old(john) | brave(john)) & (~old(john) | ~brave(john))) | ! [X0] : (~calm(X0) | ~quiet(X0))) & (? [X0] : (calm(X0) & quiet(X0)) | ((~brave(john) | old(john)) & (~old(john) | brave(john)))) [nnf transformation 4]
45. (((old(john) | brave(john)) & (~old(john) | ~brave(john))) | ! [X0] : (~calm(X0) | ~quiet(X0))) & (? [X1] : (calm(X1) & quiet(X1)) | ((~brave(john) | old(john)) & (~old(john) | brave(john)))) [rectify 44]
46. ? [X1] : (calm(X1) & quiet(X1)) => (calm(sK0) & quiet(sK0)) [choice axiom]
47. (((old(john) | brave(john)) & (~old(john) | ~brave(john))) | ! [X0] : (~calm(X0) | ~quiet(X0))) & ((calm(sK0) & quiet(sK0)) | ((~brave(john) | old(john)) & (~old(john) | brave(john)))) [skolemisation 45,46]
54. ! [X0] : ((((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | (~quiet(X0) | creative(X0))) & ((quiet(X0) & ~creative(X0)) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0))))) [nnf transformation 10]
55. ! [X0] : ((((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | ~quiet(X0) | creative(X0)) & ((quiet(X0) & ~creative(X0)) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0))))) [flattening 54]
56. ! [X0] : (~happy(X0) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) [nnf transformation 33]
61. ! [X0] : (((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (wise(X0) & brave(X0))) [nnf transformation 37]
69. calm(X0) | happy(X0) [cnf transformation 41]
70. calm(X0) | humble(X0) [cnf transformation 41]
73. ~kind(X0) | generous(X0) | quiet(X0) [cnf transformation 43]
81. ~old(john) | ~brave(john) | ~calm(X0) | ~quiet(X0) [cnf transformation 47]
106. quiet(X0) | humble(X0) | ~calm(X0) [cnf transformation 55]
110. ~humble(X0) | ~happy(X0) | strong(X0) [cnf transformation 56]
111. ~brave(fred) | ~strong(paul) [cnf transformation 34]
116. ~old(X0) | brave(X0) | brave(X0) [cnf transformation 61]
122. kind(paul) [cnf transformation 18]
123. brave(fred) | ~humble(fred) [cnf transformation 19]
130. ~generous(paul) [cnf transformation 24]
131. old(john) [cnf transformation 25]
132. ~old(X0) | brave(X0) [duplicate literal removal 116]
134. 1 <=> ! [X0] : (~calm(X0) | ~quiet(X0)) [avatar definition]
135. ~quiet(X0) | ~calm(X0) <- (1) [avatar component clause 134]
137. 2 <=> brave(john) [avatar definition]
141. 3 <=> old(john) [avatar definition]
143. old(john) <- (3) [avatar component clause 141]
145. 1 | ~2 | ~3 [avatar split clause 81,141,137,134]
198. quiet(X0) | humble(X0) [subsumption resolution 106,70]
207. 15 <=> brave(fred) [avatar definition]
212. 16 <=> strong(paul) [avatar definition]
214. ~strong(paul) <- (~16) [avatar component clause 212]
215. ~16 | ~15 [avatar split clause 111,207,212]
261. 27 <=> humble(fred) [avatar definition]
263. ~humble(fred) <- (~27) [avatar component clause 261]
264. ~27 | 15 [avatar split clause 123,207,261]
281. 3 [avatar split clause 131,141]
284. brave(john) <- (3) [resolution 132,143]
287. 2 | ~3 [avatar split clause 284,141,137]
295. humble(X0) | ~calm(X0) <- (1) [resolution 198,135]
296. humble(X0) <- (1) [subsumption resolution 295,70]
300. $false <- (1, ~27) [resolution 296,263]
301. ~1 | 27 [avatar contradiction clause 300]
311. generous(paul) | quiet(paul) [resolution 73,122]
312. quiet(paul) [subsumption resolution 311,130]
313. ~calm(paul) <- (1) [resolution 312,135]
315. happy(paul) <- (1) [resolution 313,69]
348. ~happy(X0) | strong(X0) <- (1) [resolution 110,296]
381. strong(paul) <- (1) [resolution 348,315]
382. $false <- (1, ~16) [subsumption resolution 381,214]
383. ~1 | 16 [avatar contradiction clause 382]
384. $false [avatar sat refutation 145,215,264,281,287,301,383]
% SZS output end Proof for 259878781190755501818554
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not curious or not funny then susan is both not quiet and rich and vice versa. Everyone who is both funny and tall is either kind or not happy. Everyone who is both tall and not quiet is not strong. Everyone who is both rich and not old is tall or not quiet and vice versa. Everyone who is both funny and not generous is not brave. Everyone who is either not humble or not funny is either kind or not generous. If someone is both not rich and not wise then someone is either calm or curious. Everyone who is calm or not creative is humble or not humble. Everyone who is not rich or quiet is not patient and vice versa. Everyone who is both not generous and not old is not funny and vice versa. Everyone who is either happy or not kind is not wise or strong. If someone is either not calm or not rich then someone is kind or not kind and vice versa. Everyone who is either curious or not old is both creative and humble and vice versa. Everyone who is both not brave and generous is not rich and vice versa. If someone is either not quiet or creative then someone is patient and vice versa. Everyone who is not funny or strong is strong or not generous and vice versa. Lucy is either not quiet or not funny. Susan is both not rich and happy. Someone is not brave or not curious. John is not creative or generous. Fred is both not generous and brave. Susan is not strong or creative. Fred is both happy and not curious. | Lucy is not rich. | contradiction | (((~curious(alice)<~>~funny(alice)))<=>((~quiet(susan)&rich(susan))))&
(![X]:((funny(X)&tall(X))=>(kind(X)<~>~happy(X))))&
(![X]:((tall(X)&~quiet(X))=>~strong(X)))&
(![X]:((rich(X)&~old(X))<=>(tall(X)|~quiet(X))))&
(![X]:((funny(X)&~generous(X))=>~brave(X)))&
(![X]:((~humble(X)<~>~funny(X))=>(kind(X)<~>~generous(X))))&
((?[X]:((~rich(X)&~wise(X))))=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:((calm(X)|~creative(X))=>(humble(X)|~humble(X))))&
(![X]:((~rich(X)|quiet(X))<=>~patient(X)))&
(![X]:((~generous(X)&~old(X))<=>~funny(X)))&
(![X]:((happy(X)<~>~kind(X))=>(~wise(X)|strong(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((curious(X)<~>~old(X))<=>(creative(X)&humble(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)|strong(X))<=>(strong(X)|~generous(X))))&
((~quiet(lucy)<~>~funny(lucy)))&
((~rich(susan)&happy(susan)))&
(?[X]:((~brave(X)|~curious(X))))&
((~creative(john)|generous(john)))&
((~generous(fred)&brave(fred)))&
((~strong(susan)|creative(susan)))&
((happy(fred)&~curious(fred))) | ~rich(lucy) | [
"p3",
"p9",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2828653116705795284310907
% SZS output start Proof for 2828653116705795284310907
4. ! [X0] : ((~old(X0) & rich(X0)) <=> (~quiet(X0) | tall(X0))) [input p3]
10. ! [X0] : ((~old(X0) & ~generous(X0)) <=> ~funny(X0)) [input p9]
14. ! [X0] : ((generous(X0) & ~brave(X0)) <=> ~rich(X0)) [input p13]
17. ~quiet(lucy) <~> ~funny(lucy) [input p16]
24. ~rich(lucy) [input hypothesis]
43. ! [X0] : (((~old(X0) & rich(X0)) | (quiet(X0) & ~tall(X0))) & ((~quiet(X0) | tall(X0)) | (old(X0) | ~rich(X0)))) [nnf transformation 4]
44. ! [X0] : (((~old(X0) & rich(X0)) | (quiet(X0) & ~tall(X0))) & (~quiet(X0) | tall(X0) | old(X0) | ~rich(X0))) [flattening 43]
52. ! [X0] : (((~old(X0) & ~generous(X0)) | funny(X0)) & (~funny(X0) | (old(X0) | generous(X0)))) [nnf transformation 10]
53. ! [X0] : (((~old(X0) & ~generous(X0)) | funny(X0)) & (~funny(X0) | old(X0) | generous(X0))) [flattening 52]
62. ! [X0] : (((generous(X0) & ~brave(X0)) | rich(X0)) & (~rich(X0) | (~generous(X0) | brave(X0)))) [nnf transformation 14]
63. ! [X0] : (((generous(X0) & ~brave(X0)) | rich(X0)) & (~rich(X0) | ~generous(X0) | brave(X0))) [flattening 62]
71. (funny(lucy) | quiet(lucy)) & (~funny(lucy) | ~quiet(lucy)) [nnf transformation 17]
85. rich(X0) | quiet(X0) [cnf transformation 44]
101. ~generous(X0) | funny(X0) [cnf transformation 53]
119. generous(X0) | rich(X0) [cnf transformation 63]
128. ~funny(lucy) | ~quiet(lucy) [cnf transformation 71]
139. ~rich(lucy) [cnf transformation 24]
220. 18 <=> quiet(lucy) [avatar definition]
224. 19 <=> funny(lucy) [avatar definition]
228. ~18 | ~19 [avatar split clause 128,224,220]
257. quiet(lucy) [resolution 85,139]
267. rich(X0) | funny(X0) [resolution 119,101]
270. funny(lucy) [resolution 267,139]
275. 18 [avatar split clause 257,220]
276. 19 [avatar split clause 270,224]
277. $false [avatar sat refutation 228,275,276]
% SZS output end Proof for 2828653116705795284310907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either tall or not curious then susan is not happy or kind.
Everyone who is generous is tall and vice versa.
If fred is not brave then someone is either creative or not happy and vice versa.
If paul is both not strong and not old then someone is not tall or not brave and vice versa.
Everyone who is not rich is strong and vice versa.
If alice is both not creative and not wise then alice is not rich or humble and vice versa.
If someone is calm or happy then fred is either not wise or not generous.
Everyone who is both not wise and not kind is quiet and vice versa.
If fred is not wise or not humble then alice is either strong or patient.
Everyone who is both not patient and tall is both not curious and not calm.
If someone is not happy then paul is both rich and not happy.
If someone is either not brave or not strong then someone is rich or quiet.
Everyone who is both not quiet and strong is not brave or creative and vice versa.
Everyone who is brave or not quiet is not wise.
Everyone who is either happy or not brave is both not curious and quiet.
If someone is not brave then alice is both not happy and wise and vice versa.
Fred is rich or not generous.
Someone is generous.
Lucy is not curious or not tall.
Someone is either creative or not creative.
Someone is not kind or not generous. | Lucy is brave. | entailment | (((tall(susan)<~>~curious(susan)))=>((~happy(susan)|kind(susan))))&
(![X]:(generous(X)<=>tall(X)))&
((~brave(fred))<=>(?[X]:((creative(X)<~>~happy(X)))))&
(((~strong(paul)&~old(paul)))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(~rich(X)<=>strong(X)))&
(((~creative(alice)&~wise(alice)))<=>((~rich(alice)|humble(alice))))&
((?[X]:((calm(X)|happy(X))))=>((~wise(fred)<~>~generous(fred))))&
(![X]:((~wise(X)&~kind(X))<=>quiet(X)))&
(((~wise(fred)|~humble(fred)))=>((strong(alice)<~>patient(alice))))&
(![X]:((~patient(X)&tall(X))=>(~curious(X)&~calm(X))))&
((?[X]:(~happy(X)))=>((rich(paul)&~happy(paul))))&
((?[X]:((~brave(X)<~>~strong(X))))=>(?[X]:((rich(X)|quiet(X)))))&
(![X]:((~quiet(X)&strong(X))<=>(~brave(X)|creative(X))))&
(![X]:((brave(X)|~quiet(X))=>~wise(X)))&
(![X]:((happy(X)<~>~brave(X))=>(~curious(X)&quiet(X))))&
((?[X]:(~brave(X)))<=>((~happy(alice)&wise(alice))))&
((rich(fred)|~generous(fred)))&
(?[X]:(generous(X)))&
((~curious(lucy)|~tall(lucy)))&
(?[X]:((creative(X)<~>~creative(X))))&
(?[X]:((~kind(X)|~generous(X)))) | brave(lucy) | [
"p7",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 12927717078887983133658
% SZS output start Proof for 12927717078887983133658
8. ! [X0] : ((~kind(X0) & ~wise(X0)) <=> quiet(X0)) [input p7]
14. ! [X0] : ((~quiet(X0) | brave(X0)) => ~wise(X0)) [input p13]
16. ? [X0] : ~brave(X0) <=> (wise(alice) & ~happy(alice)) [input p15]
22. ~brave(lucy) [input hypothesis]
34. ! [X0] : (~wise(X0) | (quiet(X0) & ~brave(X0))) [ennf transformation 14]
51. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | (kind(X0) | wise(X0)))) [nnf transformation 8]
52. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | kind(X0) | wise(X0))) [flattening 51]
61. (? [X0] : ~brave(X0) | (~wise(alice) | happy(alice))) & ((wise(alice) & ~happy(alice)) | ! [X0] : brave(X0)) [nnf transformation 16]
62. (? [X0] : ~brave(X0) | ~wise(alice) | happy(alice)) & ((wise(alice) & ~happy(alice)) | ! [X0] : brave(X0)) [flattening 61]
63. (? [X0] : ~brave(X0) | ~wise(alice) | happy(alice)) & ((wise(alice) & ~happy(alice)) | ! [X1] : brave(X1)) [rectify 62]
64. ? [X0] : ~brave(X0) => ~brave(sK3) [choice axiom]
65. (~brave(sK3) | ~wise(alice) | happy(alice)) & ((wise(alice) & ~happy(alice)) | ! [X1] : brave(X1)) [skolemisation 63,64]
96. ~wise(X0) | ~quiet(X0) [cnf transformation 52]
113. ~wise(X0) | quiet(X0) [cnf transformation 34]
119. wise(alice) | brave(X1) [cnf transformation 65]
127. ~brave(lucy) [cnf transformation 22]
169. 10 <=> ! [X0] : brave(X0) [avatar definition]
170. brave(X0) <- (10) [avatar component clause 169]
274. ~wise(X0) [subsumption resolution 113,96]
276. brave(X1) [subsumption resolution 119,274]
277. 10 [avatar split clause 276,169]
317. $false <- (10) [resolution 170,127]
318. ~10 [avatar contradiction clause 317]
319. $false [avatar sat refutation 277,318]
% SZS output end Proof for 12927717078887983133658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or kind is both calm and not kind and vice versa.
Everyone who is both not calm and calm is either not quiet or not creative and vice versa.
If mary is both not strong and not funny then lucy is either wise or rich and vice versa.
If mary is both calm and not brave then paul is either not quiet or patient and vice versa.
If fred is both not humble and calm then someone is not brave or not kind and vice versa.
Everyone who is both happy and not quiet is either not brave or not humble and vice versa.
Everyone who is both not brave and creative is not kind or not generous and vice versa.
If someone is both curious and not kind then paul is either not creative or not brave.
If alice is both not humble and rich then someone is tall.
If john is either not rich or not generous then john is not happy or not funny.
If someone is both not happy and tall then paul is either not happy or happy.
Everyone who is both curious and old is both happy and not curious and vice versa.
If paul is both not calm and curious then lucy is either not old or not rich.
Everyone who is not old is either not patient or not calm.
If paul is both patient and strong then someone is funny and vice versa.
Everyone who is not creative is not rich.
Mary is quiet.
Alice is happy or not calm.
Fred is creative or not happy.
Fred is either quiet or not calm.
Paul is both not curious and generous.
Someone is either humble or not funny. | Paul is not rich. | neutral | (![X]:((~strong(X)|kind(X))<=>(calm(X)&~kind(X))))&
(![X]:((~calm(X)&calm(X))<=>(~quiet(X)<~>~creative(X))))&
(((~strong(mary)&~funny(mary)))<=>((wise(lucy)<~>rich(lucy))))&
(((calm(mary)&~brave(mary)))<=>((~quiet(paul)<~>patient(paul))))&
(((~humble(fred)&calm(fred)))<=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((happy(X)&~quiet(X))<=>(~brave(X)<~>~humble(X))))&
(![X]:((~brave(X)&creative(X))<=>(~kind(X)|~generous(X))))&
((?[X]:((curious(X)&~kind(X))))=>((~creative(paul)<~>~brave(paul))))&
(((~humble(alice)&rich(alice)))=>(?[X]:(tall(X))))&
(((~rich(john)<~>~generous(john)))=>((~happy(john)|~funny(john))))&
((?[X]:((~happy(X)&tall(X))))=>((~happy(paul)<~>happy(paul))))&
(![X]:((curious(X)&old(X))<=>(happy(X)&~curious(X))))&
(((~calm(paul)&curious(paul)))=>((~old(lucy)<~>~rich(lucy))))&
(![X]:(~old(X)=>(~patient(X)<~>~calm(X))))&
(((patient(paul)&strong(paul)))<=>(?[X]:(funny(X))))&
(![X]:(~creative(X)=>~rich(X)))&
(quiet(mary))&
((happy(alice)|~calm(alice)))&
((creative(fred)|~happy(fred)))&
((quiet(fred)<~>~calm(fred)))&
((~curious(paul)&generous(paul)))&
(?[X]:((humble(X)<~>~funny(X)))) | ~rich(paul) | [] | null | 0 |
Everyone who is brave or funny is both not happy and not tall.
If lucy is either not generous or old then mary is not curious and vice versa.
If someone is both happy and not humble then fred is not tall or generous.
Everyone who is kind or humble is both tall and generous.
Everyone who is either funny or kind is not rich or not quiet and vice versa.
If alice is not curious or not rich then someone is both happy and generous and vice versa.
Everyone who is both not funny and not kind is not quiet or curious and vice versa.
Everyone who is happy or kind is both not wise and funny and vice versa.
If someone is either not calm or brave then someone is tall or not generous and vice versa.
Everyone who is wise or not brave is either not tall or wise and vice versa.
If someone is either not kind or rich then someone is not patient or calm and vice versa.
If someone is strong then mary is not funny or not creative.
If someone is calm then someone is not generous and vice versa.
Everyone who is both strong and not calm is curious.
Everyone who is not wise is kind and vice versa.
Everyone who is curious or not strong is either strong or patient.
Someone is quiet or generous.
Susan is funny or wise.
Someone is either not humble or not calm.
Someone is quiet or not wise.
John is both tall and patient.
Someone is either calm or not calm.
Alice is both not creative and patient.
Someone is not generous or patient. | Lucy is calm. | contradiction | (![X]:((brave(X)|funny(X))=>(~happy(X)&~tall(X))))&
(((~generous(lucy)<~>old(lucy)))<=>(~curious(mary)))&
((?[X]:((happy(X)&~humble(X))))=>((~tall(fred)|generous(fred))))&
(![X]:((kind(X)|humble(X))=>(tall(X)&generous(X))))&
(![X]:((funny(X)<~>kind(X))<=>(~rich(X)|~quiet(X))))&
(((~curious(alice)|~rich(alice)))<=>(?[X]:((happy(X)&generous(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(~quiet(X)|curious(X))))&
(![X]:((happy(X)|kind(X))<=>(~wise(X)&funny(X))))&
((?[X]:((~calm(X)<~>brave(X))))<=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:((wise(X)|~brave(X))<=>(~tall(X)<~>wise(X))))&
((?[X]:((~kind(X)<~>rich(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
((?[X]:(strong(X)))=>((~funny(mary)|~creative(mary))))&
((?[X]:(calm(X)))<=>(?[X]:(~generous(X))))&
(![X]:((strong(X)&~calm(X))=>curious(X)))&
(![X]:(~wise(X)<=>kind(X)))&
(![X]:((curious(X)|~strong(X))=>(strong(X)<~>patient(X))))&
(?[X]:((quiet(X)|generous(X))))&
((funny(susan)|wise(susan)))&
(?[X]:((~humble(X)<~>~calm(X))))&
(?[X]:((quiet(X)|~wise(X))))&
((tall(john)&patient(john)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~creative(alice)&patient(alice)))&
(?[X]:((~generous(X)|patient(X)))) | calm(lucy) | [
"p0",
"p3",
"p4",
"p7",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7664465881407639224292891
% SZS output start Proof for 7664465881407639224292891
1. ! [X0] : ((funny(X0) | brave(X0)) => (~tall(X0) & ~happy(X0))) [input p0]
4. ! [X0] : ((humble(X0) | kind(X0)) => (generous(X0) & tall(X0))) [input p3]
5. ! [X0] : ((funny(X0) <~> kind(X0)) <=> (~quiet(X0) | ~rich(X0))) [input p4]
8. ! [X0] : ((kind(X0) | happy(X0)) <=> (funny(X0) & ~wise(X0))) [input p7]
10. ! [X0] : ((~brave(X0) | wise(X0)) <=> (~tall(X0) <~> wise(X0))) [input p9]
11. ? [X0] : (~kind(X0) <~> rich(X0)) <=> ? [X0] : (calm(X0) | ~patient(X0)) [input p10]
15. ! [X0] : (~wise(X0) <=> kind(X0)) [input p14]
25. calm(lucy) [input hypothesis]
27. ? [X0] : (~kind(X0) <~> rich(X0)) <=> ? [X1] : (calm(X1) | ~patient(X1)) [rectify 11]
31. ! [X0] : ((~tall(X0) & ~happy(X0)) | (~funny(X0) & ~brave(X0))) [ennf transformation 1]
34. ! [X0] : ((generous(X0) & tall(X0)) | (~humble(X0) & ~kind(X0))) [ennf transformation 4]
39. ! [X0] : ((((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))))) [nnf transformation 5]
40. ! [X0] : ((((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))))) [flattening 39]
48. ! [X0] : (((kind(X0) | happy(X0)) | (~funny(X0) | wise(X0))) & ((funny(X0) & ~wise(X0)) | (~kind(X0) & ~happy(X0)))) [nnf transformation 8]
49. ! [X0] : ((kind(X0) | happy(X0) | ~funny(X0) | wise(X0)) & ((funny(X0) & ~wise(X0)) | (~kind(X0) & ~happy(X0)))) [flattening 48]
55. ! [X0] : (((~brave(X0) | wise(X0)) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0)))) & (((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | (brave(X0) & ~wise(X0)))) [nnf transformation 10]
56. ! [X0] : ((~brave(X0) | wise(X0) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0)))) & (((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | (brave(X0) & ~wise(X0)))) [flattening 55]
57. (? [X0] : ((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | ! [X1] : (~calm(X1) & patient(X1))) & (? [X1] : (calm(X1) | ~patient(X1)) | ! [X0] : ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) [nnf transformation 27]
58. (? [X0] : ((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | ! [X1] : (~calm(X1) & patient(X1))) & (? [X2] : (calm(X2) | ~patient(X2)) | ! [X3] : ((~kind(X3) | ~rich(X3)) & (rich(X3) | kind(X3)))) [rectify 57]
59. ? [X0] : ((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) => ((~rich(sK3) | kind(sK3)) & (rich(sK3) | ~kind(sK3))) [choice axiom]
60. ? [X2] : (calm(X2) | ~patient(X2)) => (calm(sK4) | ~patient(sK4)) [choice axiom]
61. (((~rich(sK3) | kind(sK3)) & (rich(sK3) | ~kind(sK3))) | ! [X1] : (~calm(X1) & patient(X1))) & ((calm(sK4) | ~patient(sK4)) | ! [X3] : ((~kind(X3) | ~rich(X3)) & (rich(X3) | kind(X3)))) [skolemisation 58,60,59]
67. ! [X0] : ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))) [nnf transformation 15]
84. ~tall(X0) | ~funny(X0) [cnf transformation 31]
90. ~kind(X0) | tall(X0) [cnf transformation 34]
96. rich(X0) | funny(X0) | kind(X0) [cnf transformation 40]
113. ~kind(X0) | funny(X0) [cnf transformation 49]
123. ~wise(X0) | tall(X0) | ~wise(X0) [cnf transformation 56]
132. ~rich(sK3) | kind(sK3) | ~calm(X1) [cnf transformation 61]
136. wise(X0) | kind(X0) [cnf transformation 67]
153. calm(lucy) [cnf transformation 25]
155. ~wise(X0) | tall(X0) [duplicate literal removal 123]
249. 20 <=> ! [X1] : ~calm(X1) [avatar definition]
250. ~calm(X1) <- (20) [avatar component clause 249]
252. 21 <=> kind(sK3) [avatar definition]
253. ~kind(sK3) <- (~21) [avatar component clause 252]
254. kind(sK3) <- (21) [avatar component clause 252]
256. 22 <=> rich(sK3) [avatar definition]
258. ~rich(sK3) <- (~22) [avatar component clause 256]
259. 20 | 21 | ~22 [avatar split clause 132,256,252,249]
357. tall(X0) | kind(X0) [resolution 155,136]
358. tall(X0) [subsumption resolution 357,90]
360. ~funny(X0) [resolution 358,84]
368. funny(sK3) | kind(sK3) <- (~22) [resolution 96,258]
369. kind(sK3) <- (~22) [subsumption resolution 368,360]
370. $false <- (~21, ~22) [subsumption resolution 369,253]
371. 21 | 22 [avatar contradiction clause 370]
372. funny(sK3) <- (21) [resolution 254,113]
377. $false <- (21) [subsumption resolution 372,360]
378. ~21 [avatar contradiction clause 377]
379. $false <- (20) [resolution 250,153]
382. ~20 [avatar contradiction clause 379]
383. $false [avatar sat refutation 259,371,378,382]
% SZS output end Proof for 7664465881407639224292891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or funny is strong and vice versa. If paul is either not old or brave then fred is either creative or happy. Everyone who is wise is not curious or quiet and vice versa. If paul is happy then someone is not humble. Everyone who is either happy or not rich is creative or not tall. If alice is happy then mary is not wise. Everyone who is rich or kind is either generous or not funny. If someone is both creative and not calm then alice is either strong or quiet. Everyone who is not calm is both old and not generous and vice versa. If someone is old or not happy then lucy is not kind and vice versa. Everyone who is not old is quiet or funny and vice versa. If lucy is either not curious or not old then someone is not wise or strong. If alice is old then someone is strong. Everyone who is not strong or not patient is creative or not quiet and vice versa. Everyone who is not humble or old is both tall and patient. Everyone who is both not generous and not patient is not patient or wise and vice versa. Someone is not funny. Someone is not funny or curious. Someone is either calm or happy. Someone is strong or not brave. Paul is not tall or rich. Lucy is not happy. Lucy is not brave. | Paul is generous. | neutral | (![X]:((patient(X)<~>funny(X))<=>strong(X)))&
(((~old(paul)<~>brave(paul)))=>((creative(fred)<~>happy(fred))))&
(![X]:(wise(X)<=>(~curious(X)|quiet(X))))&
((happy(paul))=>(?[X]:(~humble(X))))&
(![X]:((happy(X)<~>~rich(X))=>(creative(X)|~tall(X))))&
((happy(alice))=>(~wise(mary)))&
(![X]:((rich(X)|kind(X))=>(generous(X)<~>~funny(X))))&
((?[X]:((creative(X)&~calm(X))))=>((strong(alice)<~>quiet(alice))))&
(![X]:(~calm(X)<=>(old(X)&~generous(X))))&
((?[X]:((old(X)|~happy(X))))<=>(~kind(lucy)))&
(![X]:(~old(X)<=>(quiet(X)|funny(X))))&
(((~curious(lucy)<~>~old(lucy)))=>(?[X]:((~wise(X)|strong(X)))))&
((old(alice))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)|~patient(X))<=>(creative(X)|~quiet(X))))&
(![X]:((~humble(X)|old(X))=>(tall(X)&patient(X))))&
(![X]:((~generous(X)&~patient(X))<=>(~patient(X)|wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~funny(X)|curious(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((strong(X)|~brave(X))))&
((~tall(paul)|rich(paul)))&
(~happy(lucy))&
(~brave(lucy)) | generous(paul) | [] | null | 0 |
Everyone who is both not strong and rich is both not curious and not strong and vice versa.
Everyone who is happy or funny is either not strong or patient.
Everyone who is strong or patient is not wise and vice versa.
Everyone who is not patient or not kind is both funny and not happy and vice versa.
Everyone who is either not old or not rich is both not creative and old and vice versa.
Everyone who is both not happy and quiet is not wise.
If paul is quiet then susan is both rich and humble.
Everyone who is either not curious or not quiet is happy.
Everyone who is generous is creative or not happy and vice versa.
If mary is both creative and not quiet then someone is either not generous or not humble.
If lucy is quiet or brave then someone is both not humble and quiet and vice versa.
If lucy is both not kind and not brave then alice is either happy or old and vice versa.
Everyone who is either generous or not old is either rich or quiet and vice versa.
Everyone who is not generous is both happy and not curious.
Everyone who is happy is either not tall or humble.
Alice is not patient or brave.
Someone is curious or not quiet.
Lucy is wise.
Someone is brave or not rich.
Alice is not strong.
Fred is not patient.
John is either funny or not humble.
Someone is not curious or strong. | Lucy is not funny. | contradiction | (![X]:((~strong(X)&rich(X))<=>(~curious(X)&~strong(X))))&
(![X]:((happy(X)|funny(X))=>(~strong(X)<~>patient(X))))&
(![X]:((strong(X)|patient(X))<=>~wise(X)))&
(![X]:((~patient(X)|~kind(X))<=>(funny(X)&~happy(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(~creative(X)&old(X))))&
(![X]:((~happy(X)&quiet(X))=>~wise(X)))&
((quiet(paul))=>((rich(susan)&humble(susan))))&
(![X]:((~curious(X)<~>~quiet(X))=>happy(X)))&
(![X]:(generous(X)<=>(creative(X)|~happy(X))))&
(((creative(mary)&~quiet(mary)))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(((quiet(lucy)|brave(lucy)))<=>(?[X]:((~humble(X)&quiet(X)))))&
(((~kind(lucy)&~brave(lucy)))<=>((happy(alice)<~>old(alice))))&
(![X]:((generous(X)<~>~old(X))<=>(rich(X)<~>quiet(X))))&
(![X]:(~generous(X)=>(happy(X)&~curious(X))))&
(![X]:(happy(X)=>(~tall(X)<~>humble(X))))&
((~patient(alice)|brave(alice)))&
(?[X]:((curious(X)|~quiet(X))))&
(wise(lucy))&
(?[X]:((brave(X)|~rich(X))))&
(~strong(alice))&
(~patient(fred))&
((funny(john)<~>~humble(john)))&
(?[X]:((~curious(X)|strong(X)))) | ~funny(lucy) | [
"p2",
"p3",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8085724983905830609471782
% SZS output start Proof for 8085724983905830609471782
3. ! [X0] : ((patient(X0) | strong(X0)) <=> ~wise(X0)) [input p2]
4. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (~happy(X0) & funny(X0))) [input p3]
18. wise(lucy) [input p17]
24. ~funny(lucy) [input hypothesis]
37. ! [X0] : (((patient(X0) | strong(X0)) | wise(X0)) & (~wise(X0) | (~patient(X0) & ~strong(X0)))) [nnf transformation 3]
38. ! [X0] : ((patient(X0) | strong(X0) | wise(X0)) & (~wise(X0) | (~patient(X0) & ~strong(X0)))) [flattening 37]
39. ! [X0] : (((~kind(X0) | ~patient(X0)) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | (kind(X0) & patient(X0)))) [nnf transformation 4]
40. ! [X0] : ((~kind(X0) | ~patient(X0) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | (kind(X0) & patient(X0)))) [flattening 39]
74. ~wise(X0) | ~patient(X0) [cnf transformation 38]
76. patient(X0) | funny(X0) [cnf transformation 40]
122. wise(lucy) [cnf transformation 18]
129. ~funny(lucy) [cnf transformation 24]
257. ~patient(lucy) [resolution 74,122]
260. funny(lucy) [resolution 76,257]
261. $false [subsumption resolution 260,129]
% SZS output end Proof for 8085724983905830609471782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not calm is tall.
Everyone who is not tall is either not tall or not quiet and vice versa.
If fred is either not brave or not quiet then someone is both not old and not kind.
Everyone who is humble is not rich or wise and vice versa.
Everyone who is not rich or rich is happy or curious.
If someone is curious or not generous then someone is not brave and vice versa.
If alice is not wise or wise then someone is either generous or rich.
If someone is strong then john is either funny or not generous.
Everyone who is either humble or not brave is either humble or calm and vice versa.
Everyone who is either funny or not generous is both not calm and not curious and vice versa.
Everyone who is wise or quiet is not curious and vice versa.
Everyone who is not calm or tall is either not wise or not creative.
If alice is both kind and brave then paul is not generous and vice versa.
If someone is calm or strong then mary is both curious and tall and vice versa.
Everyone who is old is both not rich and kind.
Everyone who is not quiet or not creative is generous and vice versa.
Fred is curious or brave.
Someone is either not funny or old.
Someone is either curious or not curious.
Mary is brave.
Someone is both not patient and tall.
Susan is either not curious or not humble. | Fred is humble. | entailment | (![X]:((patient(X)<~>~calm(X))=>tall(X)))&
(![X]:(~tall(X)<=>(~tall(X)<~>~quiet(X))))&
(((~brave(fred)<~>~quiet(fred)))=>(?[X]:((~old(X)&~kind(X)))))&
(![X]:(humble(X)<=>(~rich(X)|wise(X))))&
(![X]:((~rich(X)|rich(X))=>(happy(X)|curious(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(?[X]:(~brave(X))))&
(((~wise(alice)|wise(alice)))=>(?[X]:((generous(X)<~>rich(X)))))&
((?[X]:(strong(X)))=>((funny(john)<~>~generous(john))))&
(![X]:((humble(X)<~>~brave(X))<=>(humble(X)<~>calm(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~calm(X)&~curious(X))))&
(![X]:((wise(X)|quiet(X))<=>~curious(X)))&
(![X]:((~calm(X)|tall(X))=>(~wise(X)<~>~creative(X))))&
(((kind(alice)&brave(alice)))<=>(~generous(paul)))&
((?[X]:((calm(X)|strong(X))))<=>((curious(mary)&tall(mary))))&
(![X]:(old(X)=>(~rich(X)&kind(X))))&
(![X]:((~quiet(X)|~creative(X))<=>generous(X)))&
((curious(fred)|brave(fred)))&
(?[X]:((~funny(X)<~>old(X))))&
(?[X]:((curious(X)<~>~curious(X))))&
(brave(mary))&
(?[X]:((~patient(X)&tall(X))))&
((~curious(susan)<~>~humble(susan))) | humble(fred) | [
"p1",
"p3",
"p5",
"p8",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3951306107463031728139540
% SZS output start Proof for 3951306107463031728139540
2. ! [X0] : (~tall(X0) <=> (~tall(X0) <~> ~quiet(X0))) [input p1]
4. ! [X0] : (humble(X0) <=> (wise(X0) | ~rich(X0))) [input p3]
6. ? [X0] : (~generous(X0) | curious(X0)) <=> ? [X0] : ~brave(X0) [input p5]
9. ! [X0] : ((humble(X0) <~> ~brave(X0)) <=> (humble(X0) <~> calm(X0))) [input p8]
11. ! [X0] : ((quiet(X0) | wise(X0)) <=> ~curious(X0)) [input p10]
12. ! [X0] : ((tall(X0) | ~calm(X0)) => (~wise(X0) <~> ~creative(X0))) [input p11]
14. ? [X0] : (strong(X0) | calm(X0)) <=> (tall(mary) & curious(mary)) [input p13]
16. ! [X0] : ((~creative(X0) | ~quiet(X0)) <=> generous(X0)) [input p15]
23. ~humble(fred) [input hypothesis]
24. ? [X0] : (~generous(X0) | curious(X0)) <=> ? [X1] : ~brave(X1) [rectify 6]
30. ! [X0] : ((~wise(X0) <~> ~creative(X0)) | (~tall(X0) & calm(X0))) [ennf transformation 12]
33. ! [X0] : ((~tall(X0) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | tall(X0))) [nnf transformation 2]
37. ! [X0] : ((humble(X0) | (~wise(X0) & rich(X0))) & ((wise(X0) | ~rich(X0)) | ~humble(X0))) [nnf transformation 4]
38. ! [X0] : ((humble(X0) | (~wise(X0) & rich(X0))) & (wise(X0) | ~rich(X0) | ~humble(X0))) [flattening 37]
39. (? [X0] : (~generous(X0) | curious(X0)) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : (generous(X0) & ~curious(X0))) [nnf transformation 24]
40. (? [X0] : (~generous(X0) | curious(X0)) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : (generous(X3) & ~curious(X3))) [rectify 39]
41. ? [X0] : (~generous(X0) | curious(X0)) => (~generous(sK1) | curious(sK1)) [choice axiom]
42. ? [X2] : ~brave(X2) => ~brave(sK2) [choice axiom]
43. ((~generous(sK1) | curious(sK1)) | ! [X1] : brave(X1)) & (~brave(sK2) | ! [X3] : (generous(X3) & ~curious(X3))) [skolemisation 40,42,41]
48. ! [X0] : ((((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) & (((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | ((humble(X0) | brave(X0)) & (~brave(X0) | ~humble(X0))))) [nnf transformation 9]
51. ! [X0] : (((quiet(X0) | wise(X0)) | curious(X0)) & (~curious(X0) | (~quiet(X0) & ~wise(X0)))) [nnf transformation 11]
52. ! [X0] : ((quiet(X0) | wise(X0) | curious(X0)) & (~curious(X0) | (~quiet(X0) & ~wise(X0)))) [flattening 51]
53. ! [X0] : (((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | (~tall(X0) & calm(X0))) [nnf transformation 30]
56. (? [X0] : (strong(X0) | calm(X0)) | (~tall(mary) | ~curious(mary))) & ((tall(mary) & curious(mary)) | ! [X0] : (~strong(X0) & ~calm(X0))) [nnf transformation 14]
57. (? [X0] : (strong(X0) | calm(X0)) | ~tall(mary) | ~curious(mary)) & ((tall(mary) & curious(mary)) | ! [X0] : (~strong(X0) & ~calm(X0))) [flattening 56]
58. (? [X0] : (strong(X0) | calm(X0)) | ~tall(mary) | ~curious(mary)) & ((tall(mary) & curious(mary)) | ! [X1] : (~strong(X1) & ~calm(X1))) [rectify 57]
59. ? [X0] : (strong(X0) | calm(X0)) => (strong(sK4) | calm(sK4)) [choice axiom]
60. ((strong(sK4) | calm(sK4)) | ~tall(mary) | ~curious(mary)) & ((tall(mary) & curious(mary)) | ! [X1] : (~strong(X1) & ~calm(X1))) [skolemisation 58,59]
61. ! [X0] : (((~creative(X0) | ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (creative(X0) & quiet(X0)))) [nnf transformation 16]
62. ! [X0] : ((~creative(X0) | ~quiet(X0) | ~generous(X0)) & (generous(X0) | (creative(X0) & quiet(X0)))) [flattening 61]
75. quiet(X0) | tall(X0) | tall(X0) [cnf transformation 33]
77. ~tall(X0) | ~tall(X0) | quiet(X0) [cnf transformation 33]
84. ~wise(X0) | humble(X0) [cnf transformation 38]
86. ~brave(sK2) | generous(X3) [cnf transformation 43]
95. calm(X0) | humble(X0) | humble(X0) | brave(X0) [cnf transformation 48]
100. brave(X0) | ~humble(X0) | calm(X0) | ~humble(X0) [cnf transformation 48]
109. ~curious(X0) | ~quiet(X0) [cnf transformation 52]
113. creative(X0) | wise(X0) | calm(X0) [cnf transformation 53]
118. curious(mary) | ~calm(X1) [cnf transformation 60]
127. ~creative(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 62]
138. ~humble(fred) [cnf transformation 23]
139. calm(X0) | humble(X0) | brave(X0) [duplicate literal removal 95]
142. brave(X0) | ~humble(X0) | calm(X0) [duplicate literal removal 100]
143. quiet(X0) | tall(X0) [duplicate literal removal 75]
144. ~tall(X0) | quiet(X0) [duplicate literal removal 77]
145. quiet(X0) [subsumption resolution 143,144]
175. 7 <=> ! [X3] : generous(X3) [avatar definition]
176. generous(X3) <- (7) [avatar component clause 175]
178. 8 <=> brave(sK2) [avatar definition]
180. ~brave(sK2) <- (~8) [avatar component clause 178]
181. 7 | ~8 [avatar split clause 86,178,175]
183. 9 <=> ! [X3] : ~curious(X3) [avatar definition]
184. ~curious(X3) <- (9) [avatar component clause 183]
216. brave(X0) | calm(X0) [subsumption resolution 139,142]
217. ~curious(X0) [subsumption resolution 109,145]
218. 9 [avatar split clause 217,183]
235. 19 <=> curious(mary) [avatar definition]
236. curious(mary) <- (19) [avatar component clause 235]
253. 23 <=> ! [X1] : ~calm(X1) [avatar definition]
254. ~calm(X1) <- (23) [avatar component clause 253]
257. 23 | 19 [avatar split clause 118,235,253]
258. ~creative(X0) | ~generous(X0) [subsumption resolution 127,145]
284. $false <- (9, 19) [resolution 236,184]
285. ~9 | ~19 [avatar contradiction clause 284]
298. calm(sK2) <- (~8) [resolution 216,180]
300. $false <- (~8, 23) [subsumption resolution 298,254]
301. 8 | ~23 [avatar contradiction clause 300]
317. wise(X2) | calm(X2) | ~generous(X2) [resolution 113,258]
319. wise(X2) | ~generous(X2) <- (23) [subsumption resolution 317,254]
320. wise(X2) <- (7, 23) [subsumption resolution 319,176]
325. humble(X0) <- (7, 23) [resolution 320,84]
332. $false <- (7, 23) [resolution 325,138]
333. ~7 | ~23 [avatar contradiction clause 332]
334. $false [avatar sat refutation 181,218,257,285,301,333]
% SZS output end Proof for 3951306107463031728139540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not funny and not old then someone is either humble or not quiet.
Everyone who is either rich or not generous is not rich or happy and vice versa.
If someone is both brave and not funny then alice is creative and vice versa.
Everyone who is either kind or wise is old.
Everyone who is wise is not wise or patient.
If someone is not generous then susan is either not generous or old and vice versa.
If someone is both not strong and not curious then mary is generous or not calm and vice versa.
Everyone who is not generous or humble is both quiet and not kind.
If someone is both strong and curious then alice is not humble or humble.
If someone is quiet then someone is funny and vice versa.
Everyone who is either creative or not kind is either happy or not humble.
Everyone who is not tall or old is either quiet or kind.
Everyone who is either not happy or tall is both old and creative and vice versa.
If susan is both wise and brave then lucy is old or happy and vice versa.
Everyone who is brave or quiet is not creative and vice versa.
If paul is kind or not wise then fred is brave and vice versa.
Alice is either happy or not quiet.
Susan is either not old or not rich.
Fred is both generous and rich.
Someone is either generous or not strong.
Fred is either wise or funny.
Someone is kind.
Someone is either curious or not happy. | Alice is not creative. | entailment | (((~funny(alice)&~old(alice)))=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:((rich(X)<~>~generous(X))<=>(~rich(X)|happy(X))))&
((?[X]:((brave(X)&~funny(X))))<=>(creative(alice)))&
(![X]:((kind(X)<~>wise(X))=>old(X)))&
(![X]:(wise(X)=>(~wise(X)|patient(X))))&
((?[X]:(~generous(X)))<=>((~generous(susan)<~>old(susan))))&
((?[X]:((~strong(X)&~curious(X))))<=>((generous(mary)|~calm(mary))))&
(![X]:((~generous(X)|humble(X))=>(quiet(X)&~kind(X))))&
((?[X]:((strong(X)&curious(X))))=>((~humble(alice)|humble(alice))))&
((?[X]:(quiet(X)))<=>(?[X]:(funny(X))))&
(![X]:((creative(X)<~>~kind(X))=>(happy(X)<~>~humble(X))))&
(![X]:((~tall(X)|old(X))=>(quiet(X)<~>kind(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(old(X)&creative(X))))&
(((wise(susan)&brave(susan)))<=>((old(lucy)|happy(lucy))))&
(![X]:((brave(X)|quiet(X))<=>~creative(X)))&
(((kind(paul)|~wise(paul)))<=>(brave(fred)))&
((happy(alice)<~>~quiet(alice)))&
((~old(susan)<~>~rich(susan)))&
((generous(fred)&rich(fred)))&
(?[X]:((generous(X)<~>~strong(X))))&
((wise(fred)<~>funny(fred)))&
(?[X]:(kind(X)))&
(?[X]:((curious(X)<~>~happy(X)))) | ~creative(alice) | [
"p1",
"p7",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8360135203391330000286780
% SZS output start Proof for 8360135203391330000286780
2. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (happy(X0) | ~rich(X0))) [input p1]
8. ! [X0] : ((humble(X0) | ~generous(X0)) => (~kind(X0) & quiet(X0))) [input p7]
15. ! [X0] : ((quiet(X0) | brave(X0)) <=> ~creative(X0)) [input p14]
17. happy(alice) <~> ~quiet(alice) [input p16]
24. creative(alice) [input hypothesis]
30. ! [X0] : ((~kind(X0) & quiet(X0)) | (~humble(X0) & generous(X0))) [ennf transformation 8]
38. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 2]
39. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [flattening 38]
65. ! [X0] : (((quiet(X0) | brave(X0)) | creative(X0)) & (~creative(X0) | (~quiet(X0) & ~brave(X0)))) [nnf transformation 15]
66. ! [X0] : ((quiet(X0) | brave(X0) | creative(X0)) & (~creative(X0) | (~quiet(X0) & ~brave(X0)))) [flattening 65]
69. (quiet(alice) | ~happy(alice)) & (~quiet(alice) | happy(alice)) [nnf transformation 17]
82. happy(X0) | ~rich(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 39]
84. ~generous(X0) | rich(X0) | rich(X0) [cnf transformation 39]
102. generous(X0) | quiet(X0) [cnf transformation 30]
129. ~creative(X0) | ~quiet(X0) [cnf transformation 66]
135. quiet(alice) | ~happy(alice) [cnf transformation 69]
147. creative(alice) [cnf transformation 24]
148. happy(X0) | ~rich(X0) | ~generous(X0) [duplicate literal removal 82]
149. ~generous(X0) | rich(X0) [duplicate literal removal 84]
168. ~generous(X0) | happy(X0) [subsumption resolution 148,149]
170. 5 <=> creative(alice) [avatar definition]
171. creative(alice) <- (5) [avatar component clause 170]
285. 29 <=> happy(alice) [avatar definition]
287. ~happy(alice) <- (~29) [avatar component clause 285]
289. 30 <=> quiet(alice) [avatar definition]
290. ~quiet(alice) <- (~30) [avatar component clause 289]
292. ~29 | 30 [avatar split clause 135,289,285]
330. 5 [avatar split clause 147,170]
345. ~quiet(alice) <- (5) [resolution 129,171]
362. happy(X1) | quiet(X1) [resolution 168,102]
371. ~30 | ~5 [avatar split clause 345,170,289]
558. quiet(alice) <- (~29) [resolution 362,287]
561. $false <- (~29, ~30) [subsumption resolution 558,290]
562. 29 | 30 [avatar contradiction clause 561]
563. $false [avatar sat refutation 292,330,371,562]
% SZS output end Proof for 8360135203391330000286780
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not wise and rich then susan is not tall or kind and vice versa.
Everyone who is creative or not happy is both not rich and not old.
Everyone who is either creative or not tall is both strong and not old.
If susan is both not funny and wise then john is either not happy or brave.
Everyone who is both humble and not strong is either not old or not creative and vice versa.
Everyone who is either brave or not tall is both not brave and not humble.
If john is either old or not kind then someone is either strong or brave.
If mary is both not kind and curious then someone is tall or not brave and vice versa.
Everyone who is either strong or not patient is either tall or wise and vice versa.
Everyone who is not brave is not wise or funny and vice versa.
If paul is both not calm and curious then fred is quiet or not strong.
Everyone who is not wise is not kind.
Everyone who is not funny or not humble is curious or not old.
Everyone who is both not funny and not old is both not funny and not tall and vice versa.
Everyone who is not humble is not old and vice versa.
Everyone who is both not creative and generous is happy or not brave.
Someone is not patient.
Someone is not curious.
Fred is not curious or not generous.
Someone is both not creative and calm.
Someone is both patient and not happy.
Fred is either kind or wise.
Someone is either not tall or not generous.
Fred is either funny or wise. | Fred is not kind. | entailment | (((~wise(mary)&rich(mary)))<=>((~tall(susan)|kind(susan))))&
(![X]:((creative(X)|~happy(X))=>(~rich(X)&~old(X))))&
(![X]:((creative(X)<~>~tall(X))=>(strong(X)&~old(X))))&
(((~funny(susan)&wise(susan)))=>((~happy(john)<~>brave(john))))&
(![X]:((humble(X)&~strong(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((brave(X)<~>~tall(X))=>(~brave(X)&~humble(X))))&
(((old(john)<~>~kind(john)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~kind(mary)&curious(mary)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((strong(X)<~>~patient(X))<=>(tall(X)<~>wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)|funny(X))))&
(((~calm(paul)&curious(paul)))=>((quiet(fred)|~strong(fred))))&
(![X]:(~wise(X)=>~kind(X)))&
(![X]:((~funny(X)|~humble(X))=>(curious(X)|~old(X))))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&~tall(X))))&
(![X]:(~humble(X)<=>~old(X)))&
(![X]:((~creative(X)&generous(X))=>(happy(X)|~brave(X))))&
(?[X]:(~patient(X)))&
(?[X]:(~curious(X)))&
((~curious(fred)|~generous(fred)))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>wise(fred)))&
(?[X]:((~tall(X)<~>~generous(X))))&
((funny(fred)<~>wise(fred))) | ~kind(fred) | [
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7913801707267723011990311
% SZS output start Proof for 7913801707267723011990311
12. ! [X0] : (~wise(X0) => ~kind(X0)) [input p11]
22. kind(fred) <~> wise(fred) [input p21]
25. kind(fred) [input hypothesis]
34. ! [X0] : (~kind(X0) | wise(X0)) [ennf transformation 12]
68. (~wise(fred) | ~kind(fred)) & (wise(fred) | kind(fred)) [nnf transformation 22]
118. ~kind(X0) | wise(X0) [cnf transformation 34]
135. ~wise(fred) | ~kind(fred) [cnf transformation 68]
140. kind(fred) [cnf transformation 25]
239. ~kind(fred) [subsumption resolution 135,118]
252. $false [subsumption resolution 140,239]
% SZS output end Proof for 7913801707267723011990311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not strong is either rich or not humble and vice versa. If someone is not strong or not rich then susan is either not creative or humble. If alice is brave or not creative then someone is both not old and happy. Everyone who is both generous and patient is both not calm and not strong. If alice is either wise or calm then someone is either kind or not patient and vice versa. If someone is both humble and happy then mary is not rich. Everyone who is both not tall and not strong is either curious or not happy. Everyone who is either generous or brave is funny or tall and vice versa. If susan is both patient and strong then someone is both rich and generous and vice versa. Everyone who is not strong or creative is generous or creative. If someone is both not funny and not humble then alice is either funny or not creative. Everyone who is not creative is rich or not tall and vice versa. Everyone who is happy is either creative or strong. Everyone who is either generous or happy is not rich and vice versa. Everyone who is curious is not kind or happy. Everyone who is not strong is both not generous and happy and vice versa. Mary is either not strong or not quiet. Someone is either rich or not curious. Someone is not tall. Someone is both calm and funny. Paul is not humble or curious. Paul is tall. Susan is either creative or not strong. Someone is humble or tall. | Susan is rich. | contradiction | (![X]:((old(X)|~strong(X))<=>(rich(X)<~>~humble(X))))&
((?[X]:((~strong(X)|~rich(X))))=>((~creative(susan)<~>humble(susan))))&
(((brave(alice)|~creative(alice)))=>(?[X]:((~old(X)&happy(X)))))&
(![X]:((generous(X)&patient(X))=>(~calm(X)&~strong(X))))&
(((wise(alice)<~>calm(alice)))<=>(?[X]:((kind(X)<~>~patient(X)))))&
((?[X]:((humble(X)&happy(X))))=>(~rich(mary)))&
(![X]:((~tall(X)&~strong(X))=>(curious(X)<~>~happy(X))))&
(![X]:((generous(X)<~>brave(X))<=>(funny(X)|tall(X))))&
(((patient(susan)&strong(susan)))<=>(?[X]:((rich(X)&generous(X)))))&
(![X]:((~strong(X)|creative(X))=>(generous(X)|creative(X))))&
((?[X]:((~funny(X)&~humble(X))))=>((funny(alice)<~>~creative(alice))))&
(![X]:(~creative(X)<=>(rich(X)|~tall(X))))&
(![X]:(happy(X)=>(creative(X)<~>strong(X))))&
(![X]:((generous(X)<~>happy(X))<=>~rich(X)))&
(![X]:(curious(X)=>(~kind(X)|happy(X))))&
(![X]:(~strong(X)<=>(~generous(X)&happy(X))))&
((~strong(mary)<~>~quiet(mary)))&
(?[X]:((rich(X)<~>~curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((calm(X)&funny(X))))&
((~humble(paul)|curious(paul)))&
(tall(paul))&
((creative(susan)<~>~strong(susan)))&
(?[X]:((humble(X)|tall(X)))) | rich(susan) | [
"p0",
"p1",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4930420312633906011945524
% SZS output start Proof for 4930420312633906011945524
1. ! [X0] : ((~strong(X0) | old(X0)) <=> (rich(X0) <~> ~humble(X0))) [input p0]
2. ? [X0] : (~rich(X0) | ~strong(X0)) => (~creative(susan) <~> humble(susan)) [input p1]
12. ! [X0] : (~creative(X0) <=> (~tall(X0) | rich(X0))) [input p11]
23. creative(susan) <~> ~strong(susan) [input p22]
25. rich(susan) [input hypothesis]
26. (~creative(susan) <~> humble(susan)) | ! [X0] : (rich(X0) & strong(X0)) [ennf transformation 2]
39. ! [X0] : (((~strong(X0) | old(X0)) | ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | (strong(X0) & ~old(X0)))) [nnf transformation 1]
40. ! [X0] : ((~strong(X0) | old(X0) | ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | (strong(X0) & ~old(X0)))) [flattening 39]
41. ((~humble(susan) | creative(susan)) & (humble(susan) | ~creative(susan))) | ! [X0] : (rich(X0) & strong(X0)) [nnf transformation 26]
57. ! [X0] : ((~creative(X0) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | creative(X0))) [nnf transformation 12]
58. ! [X0] : ((~creative(X0) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | creative(X0))) [flattening 57]
71. (strong(susan) | ~creative(susan)) & (~strong(susan) | creative(susan)) [nnf transformation 23]
77. ~rich(X0) | humble(X0) | strong(X0) [cnf transformation 40]
82. ~humble(susan) | creative(susan) | strong(X0) [cnf transformation 41]
116. ~creative(X0) | ~rich(X0) [cnf transformation 58]
137. ~strong(susan) | creative(susan) [cnf transformation 71]
140. rich(susan) [cnf transformation 25]
145. 2 <=> creative(susan) [avatar definition]
147. creative(susan) <- (2) [avatar component clause 145]
149. 3 <=> humble(susan) [avatar definition]
154. 4 <=> ! [X0] : strong(X0) [avatar definition]
155. strong(X0) <- (4) [avatar component clause 154]
156. 4 | 2 | ~3 [avatar split clause 82,149,145,154]
221. 18 <=> strong(susan) [avatar definition]
222. ~strong(susan) <- (~18) [avatar component clause 221]
279. 2 | ~18 [avatar split clause 137,221,145]
307. humble(susan) | strong(susan) [resolution 77,140]
311. 18 | 3 [avatar split clause 307,149,221]
318. ~rich(susan) <- (2) [resolution 147,116]
319. $false <- (2) [subsumption resolution 318,140]
320. ~2 [avatar contradiction clause 319]
329. $false <- (4, ~18) [resolution 222,155]
330. ~4 | 18 [avatar contradiction clause 329]
331. $false [avatar sat refutation 156,279,311,320,330]
% SZS output end Proof for 4930420312633906011945524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or tall is both not curious and old.
If someone is not creative then someone is both not tall and humble.
If someone is both old and funny then someone is either tall or not brave and vice versa.
If someone is tall then someone is old.
Everyone who is either patient or creative is not creative or not rich and vice versa.
Everyone who is happy is not happy.
If alice is not kind then someone is not happy or not funny.
If john is either kind or not generous then someone is quiet or not tall and vice versa.
If someone is happy then someone is either not funny or tall.
If john is both creative and not generous then someone is not tall or happy.
If someone is either tall or not old then someone is either not old or rich and vice versa.
Everyone who is funny or not quiet is not patient.
If someone is not quiet then alice is not tall or happy and vice versa.
If someone is generous or quiet then someone is not tall or quiet.
Everyone who is not humble or happy is either brave or happy and vice versa.
Everyone who is both not patient and quiet is not curious or not happy and vice versa.
John is both creative and not tall.
Someone is either tall or strong.
Someone is not creative or kind.
Someone is not humble.
Paul is both not calm and not old.
Fred is either not quiet or not strong.
Someone is either wise or quiet.
John is either brave or not curious. | Paul is creative. | entailment | (![X]:((generous(X)|tall(X))=>(~curious(X)&old(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~tall(X)&humble(X)))))&
((?[X]:((old(X)&funny(X))))<=>(?[X]:((tall(X)<~>~brave(X)))))&
((?[X]:(tall(X)))=>(?[X]:(old(X))))&
(![X]:((patient(X)<~>creative(X))<=>(~creative(X)|~rich(X))))&
(![X]:(happy(X)=>~happy(X)))&
((~kind(alice))=>(?[X]:((~happy(X)|~funny(X)))))&
(((kind(john)<~>~generous(john)))<=>(?[X]:((quiet(X)|~tall(X)))))&
((?[X]:(happy(X)))=>(?[X]:((~funny(X)<~>tall(X)))))&
(((creative(john)&~generous(john)))=>(?[X]:((~tall(X)|happy(X)))))&
((?[X]:((tall(X)<~>~old(X))))<=>(?[X]:((~old(X)<~>rich(X)))))&
(![X]:((funny(X)|~quiet(X))=>~patient(X)))&
((?[X]:(~quiet(X)))<=>((~tall(alice)|happy(alice))))&
((?[X]:((generous(X)|quiet(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
(![X]:((~humble(X)|happy(X))<=>(brave(X)<~>happy(X))))&
(![X]:((~patient(X)&quiet(X))<=>(~curious(X)|~happy(X))))&
((creative(john)&~tall(john)))&
(?[X]:((tall(X)<~>strong(X))))&
(?[X]:((~creative(X)|kind(X))))&
(?[X]:(~humble(X)))&
((~calm(paul)&~old(paul)))&
((~quiet(fred)<~>~strong(fred)))&
(?[X]:((wise(X)<~>quiet(X))))&
((brave(john)<~>~curious(john))) | creative(paul) | [
"p4",
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4422470722011148961886409
% SZS output start Proof for 4422470722011148961886409
5. ! [X0] : ((patient(X0) <~> creative(X0)) <=> (~rich(X0) | ~creative(X0))) [input p4]
6. ! [X0] : (happy(X0) => ~happy(X0)) [input p5]
16. ! [X0] : ((quiet(X0) & ~patient(X0)) <=> (~happy(X0) | ~curious(X0))) [input p15]
25. ~creative(paul) [input hypothesis]
36. ! [X0] : (~happy(X0) | ~happy(X0)) [ennf transformation 6]
54. ! [X0] : ((((~creative(X0) | ~patient(X0)) & (creative(X0) | patient(X0))) | (rich(X0) & creative(X0))) & ((~rich(X0) | ~creative(X0)) | ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))))) [nnf transformation 5]
55. ! [X0] : ((((~creative(X0) | ~patient(X0)) & (creative(X0) | patient(X0))) | (rich(X0) & creative(X0))) & (~rich(X0) | ~creative(X0) | ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))))) [flattening 54]
83. ! [X0] : (((quiet(X0) & ~patient(X0)) | (happy(X0) & curious(X0))) & ((~happy(X0) | ~curious(X0)) | (~quiet(X0) | patient(X0)))) [nnf transformation 16]
84. ! [X0] : (((quiet(X0) & ~patient(X0)) | (happy(X0) & curious(X0))) & (~happy(X0) | ~curious(X0) | ~quiet(X0) | patient(X0))) [flattening 83]
112. creative(X0) | patient(X0) | creative(X0) [cnf transformation 55]
116. ~happy(X0) | ~happy(X0) [cnf transformation 36]
150. ~patient(X0) | happy(X0) [cnf transformation 84]
166. ~creative(paul) [cnf transformation 25]
169. ~happy(X0) [duplicate literal removal 116]
171. patient(X0) | creative(X0) [duplicate literal removal 112]
173. 1 <=> ! [X1] : creative(X1) [avatar definition]
174. creative(X1) <- (1) [avatar component clause 173]
329. ~patient(X0) [subsumption resolution 150,169]
391. creative(X2) [resolution 171,329]
392. 1 [avatar split clause 391,173]
393. $false <- (1) [resolution 174,166]
396. ~1 [avatar contradiction clause 393]
397. $false [avatar sat refutation 392,396]
% SZS output end Proof for 4422470722011148961886409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not happy or not old then someone is either not brave or not generous and vice versa. If someone is happy or not creative then alice is not old. If someone is not tall or not generous then someone is both kind and curious. Everyone who is not happy or brave is not creative and vice versa. Everyone who is either not creative or funny is both kind and patient. If someone is not patient then someone is not calm. If mary is not kind or not patient then someone is old or patient and vice versa. If someone is both quiet and not funny then someone is both wise and not wise. Everyone who is not kind or old is both not quiet and not wise. If someone is both not calm and calm then someone is either not quiet or patient and vice versa. Everyone who is both humble and quiet is either not rich or humble. Everyone who is wise is either brave or rich. Everyone who is both not tall and old is either happy or not rich. If mary is both not curious and tall then fred is not old and vice versa. If someone is funny then someone is both rich and not generous. Everyone who is kind is both brave and creative. Someone is either not wise or kind. Susan is either old or not strong. Alice is either not brave or not happy. Someone is either not kind or not humble. Lucy is not calm or kind. Someone is not rich. | Mary is not happy. | contradiction | (((~happy(fred)|~old(fred)))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((?[X]:((happy(X)|~creative(X))))=>(~old(alice)))&
((?[X]:((~tall(X)|~generous(X))))=>(?[X]:((kind(X)&curious(X)))))&
(![X]:((~happy(X)|brave(X))<=>~creative(X)))&
(![X]:((~creative(X)<~>funny(X))=>(kind(X)&patient(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~calm(X))))&
(((~kind(mary)|~patient(mary)))<=>(?[X]:((old(X)|patient(X)))))&
((?[X]:((quiet(X)&~funny(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~kind(X)|old(X))=>(~quiet(X)&~wise(X))))&
((?[X]:((~calm(X)&calm(X))))<=>(?[X]:((~quiet(X)<~>patient(X)))))&
(![X]:((humble(X)&quiet(X))=>(~rich(X)<~>humble(X))))&
(![X]:(wise(X)=>(brave(X)<~>rich(X))))&
(![X]:((~tall(X)&old(X))=>(happy(X)<~>~rich(X))))&
(((~curious(mary)&tall(mary)))<=>(~old(fred)))&
((?[X]:(funny(X)))=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:(kind(X)=>(brave(X)&creative(X))))&
(?[X]:((~wise(X)<~>kind(X))))&
((old(susan)<~>~strong(susan)))&
((~brave(alice)<~>~happy(alice)))&
(?[X]:((~kind(X)<~>~humble(X))))&
((~calm(lucy)|kind(lucy)))&
(?[X]:(~rich(X))) | ~happy(mary) | [
"p2",
"p3",
"p4",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4364591396199364422144347
% SZS output start Proof for 4364591396199364422144347
3. ? [X0] : (~generous(X0) | ~tall(X0)) => ? [X0] : (curious(X0) & kind(X0)) [input p2]
4. ! [X0] : ((brave(X0) | ~happy(X0)) <=> ~creative(X0)) [input p3]
5. ! [X0] : ((~creative(X0) <~> funny(X0)) => (patient(X0) & kind(X0))) [input p4]
15. ? [X0] : funny(X0) => ? [X0] : (~generous(X0) & rich(X0)) [input p14]
16. ! [X0] : (kind(X0) => (creative(X0) & brave(X0))) [input p15]
23. ~happy(mary) [input hypothesis]
24. ? [X0] : (~generous(X0) | ~tall(X0)) => ? [X1] : (curious(X1) & kind(X1)) [rectify 3]
28. ? [X0] : funny(X0) => ? [X1] : (~generous(X1) & rich(X1)) [rectify 15]
30. ? [X1] : (curious(X1) & kind(X1)) | ! [X0] : (generous(X0) & tall(X0)) [ennf transformation 24]
31. ! [X0] : ((patient(X0) & kind(X0)) | (~creative(X0) <=> funny(X0))) [ennf transformation 5]
40. ? [X1] : (~generous(X1) & rich(X1)) | ! [X0] : ~funny(X0) [ennf transformation 28]
41. ! [X0] : ((creative(X0) & brave(X0)) | ~kind(X0)) [ennf transformation 16]
47. ? [X0] : (curious(X0) & kind(X0)) | ! [X1] : (generous(X1) & tall(X1)) [rectify 30]
48. ? [X0] : (curious(X0) & kind(X0)) => (curious(sK1) & kind(sK1)) [choice axiom]
49. (curious(sK1) & kind(sK1)) | ! [X1] : (generous(X1) & tall(X1)) [skolemisation 47,48]
50. ! [X0] : (((brave(X0) | ~happy(X0)) | creative(X0)) & (~creative(X0) | (~brave(X0) & happy(X0)))) [nnf transformation 4]
51. ! [X0] : ((brave(X0) | ~happy(X0) | creative(X0)) & (~creative(X0) | (~brave(X0) & happy(X0)))) [flattening 50]
52. ! [X0] : ((patient(X0) & kind(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) [nnf transformation 31]
74. ? [X0] : (~generous(X0) & rich(X0)) | ! [X1] : ~funny(X1) [rectify 40]
75. ? [X0] : (~generous(X0) & rich(X0)) => (~generous(sK7) & rich(sK7)) [choice axiom]
76. (~generous(sK7) & rich(sK7)) | ! [X1] : ~funny(X1) [skolemisation 74,75]
96. kind(sK1) | generous(X1) [cnf transformation 49]
99. ~creative(X0) | happy(X0) [cnf transformation 51]
100. ~creative(X0) | ~brave(X0) [cnf transformation 51]
102. funny(X0) | kind(X0) | creative(X0) [cnf transformation 52]
133. ~generous(sK7) | ~funny(X1) [cnf transformation 76]
134. ~kind(X0) | brave(X0) [cnf transformation 41]
135. ~kind(X0) | creative(X0) [cnf transformation 41]
146. ~happy(mary) [cnf transformation 23]
177. 7 <=> ! [X0] : creative(X0) [avatar definition]
178. creative(X0) <- (7) [avatar component clause 177]
189. 10 <=> ! [X1] : generous(X1) [avatar definition]
190. generous(X1) <- (10) [avatar component clause 189]
201. 13 <=> kind(sK1) [avatar definition]
203. kind(sK1) <- (13) [avatar component clause 201]
204. 10 | 13 [avatar split clause 96,201,189]
275. 29 <=> ! [X1] : ~funny(X1) [avatar definition]
276. ~funny(X1) <- (29) [avatar component clause 275]
278. 30 <=> generous(sK7) [avatar definition]
280. ~generous(sK7) <- (~30) [avatar component clause 278]
281. 29 | ~30 [avatar split clause 133,278,275]
338. brave(sK1) <- (13) [resolution 134,203]
341. creative(sK1) <- (13) [resolution 135,203]
348. ~brave(sK1) <- (13) [resolution 341,100]
350. $false <- (13) [subsumption resolution 348,338]
351. ~13 [avatar contradiction clause 350]
369. $false <- (10, ~30) [subsumption resolution 280,190]
370. ~10 | 30 [avatar contradiction clause 369]
386. kind(X0) | creative(X0) <- (29) [resolution 102,276]
387. creative(X0) <- (29) [subsumption resolution 386,135]
388. 7 | ~29 [avatar split clause 387,275,177]
390. happy(X1) <- (7) [resolution 178,99]
401. $false <- (7) [resolution 390,146]
403. ~7 [avatar contradiction clause 401]
404. $false [avatar sat refutation 204,281,351,370,388,403]
% SZS output end Proof for 4364591396199364422144347
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either kind or rich then fred is happy or brave.
If paul is brave then someone is both calm and patient and vice versa.
Everyone who is not tall is not kind and vice versa.
If someone is either not curious or not strong then john is either not happy or wise.
Everyone who is not happy or kind is both not rich and happy and vice versa.
If susan is not tall or not old then someone is not creative or old.
If someone is either brave or not tall then someone is curious and vice versa.
Everyone who is creative or old is either not wise or calm.
Everyone who is both quiet and not creative is either not quiet or strong.
If fred is not funny then someone is both not creative and not calm.
Everyone who is brave or not creative is either quiet or not patient and vice versa.
Everyone who is brave or rich is funny or old and vice versa.
Everyone who is not patient or humble is not brave or not wise.
If someone is not brave or kind then someone is both rich and not old.
Everyone who is not strong is patient or not happy and vice versa.
Everyone who is generous is both kind and not generous and vice versa.
Susan is either happy or wise.
Someone is not quiet.
Paul is not generous.
Paul is either not strong or wise.
Someone is both brave and patient. | Susan is not wise. | entailment | (((kind(lucy)<~>rich(lucy)))=>((happy(fred)|brave(fred))))&
((brave(paul))<=>(?[X]:((calm(X)&patient(X)))))&
(![X]:(~tall(X)<=>~kind(X)))&
((?[X]:((~curious(X)<~>~strong(X))))=>((~happy(john)<~>wise(john))))&
(![X]:((~happy(X)|kind(X))<=>(~rich(X)&happy(X))))&
(((~tall(susan)|~old(susan)))=>(?[X]:((~creative(X)|old(X)))))&
((?[X]:((brave(X)<~>~tall(X))))<=>(?[X]:(curious(X))))&
(![X]:((creative(X)|old(X))=>(~wise(X)<~>calm(X))))&
(![X]:((quiet(X)&~creative(X))=>(~quiet(X)<~>strong(X))))&
((~funny(fred))=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((brave(X)|~creative(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:((brave(X)|rich(X))<=>(funny(X)|old(X))))&
(![X]:((~patient(X)|humble(X))=>(~brave(X)|~wise(X))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((rich(X)&~old(X)))))&
(![X]:(~strong(X)<=>(patient(X)|~happy(X))))&
(![X]:(generous(X)<=>(kind(X)&~generous(X))))&
((happy(susan)<~>wise(susan)))&
(?[X]:(~quiet(X)))&
(~generous(paul))&
((~strong(paul)<~>wise(paul)))&
(?[X]:((brave(X)&patient(X)))) | ~wise(susan) | [
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4435904481279034477113534
% SZS output start Proof for 4435904481279034477113534
5. ! [X0] : ((kind(X0) | ~happy(X0)) <=> (happy(X0) & ~rich(X0))) [input p4]
17. happy(susan) <~> wise(susan) [input p16]
22. wise(susan) [input hypothesis]
44. ! [X0] : (((kind(X0) | ~happy(X0)) | (~happy(X0) | rich(X0))) & ((happy(X0) & ~rich(X0)) | (~kind(X0) & happy(X0)))) [nnf transformation 5]
45. ! [X0] : ((kind(X0) | ~happy(X0) | ~happy(X0) | rich(X0)) & ((happy(X0) & ~rich(X0)) | (~kind(X0) & happy(X0)))) [flattening 44]
68. (~wise(susan) | ~happy(susan)) & (wise(susan) | happy(susan)) [nnf transformation 17]
87. happy(X0) | happy(X0) [cnf transformation 45]
126. ~wise(susan) | ~happy(susan) [cnf transformation 68]
133. wise(susan) [cnf transformation 22]
137. happy(X0) [duplicate literal removal 87]
269. ~wise(susan) [subsumption resolution 126,137]
280. $false [subsumption resolution 133,269]
% SZS output end Proof for 4435904481279034477113534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or brave then someone is not generous or tall.
If someone is not tall then someone is either generous or curious and vice versa.
Everyone who is quiet or not wise is not calm and vice versa.
Everyone who is humble or wise is both not kind and patient.
Everyone who is either old or not curious is quiet or not quiet and vice versa.
Everyone who is not patient is both brave and not patient.
If someone is either quiet or not funny then someone is curious and vice versa.
Everyone who is old is both generous and not kind.
If someone is both not funny and funny then lucy is either tall or not quiet and vice versa.
Everyone who is either not old or curious is not humble.
If someone is not patient or strong then mary is not brave.
Everyone who is old or calm is either generous or not calm and vice versa.
Everyone who is both not rich and not happy is strong.
Everyone who is either not funny or strong is both funny and not kind and vice versa.
If paul is either strong or not old then someone is both humble and calm.
Everyone who is both humble and strong is both tall and not rich and vice versa.
Someone is curious.
Alice is either not calm or not wise.
Someone is either not quiet or patient.
Someone is wise or not rich.
Mary is generous.
Someone is not curious. | Alice is not old. | entailment | ((?[X]:((~patient(X)|brave(X))))=>(?[X]:((~generous(X)|tall(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((quiet(X)|~wise(X))<=>~calm(X)))&
(![X]:((humble(X)|wise(X))=>(~kind(X)&patient(X))))&
(![X]:((old(X)<~>~curious(X))<=>(quiet(X)|~quiet(X))))&
(![X]:(~patient(X)=>(brave(X)&~patient(X))))&
((?[X]:((quiet(X)<~>~funny(X))))<=>(?[X]:(curious(X))))&
(![X]:(old(X)=>(generous(X)&~kind(X))))&
((?[X]:((~funny(X)&funny(X))))<=>((tall(lucy)<~>~quiet(lucy))))&
(![X]:((~old(X)<~>curious(X))=>~humble(X)))&
((?[X]:((~patient(X)|strong(X))))=>(~brave(mary)))&
(![X]:((old(X)|calm(X))<=>(generous(X)<~>~calm(X))))&
(![X]:((~rich(X)&~happy(X))=>strong(X)))&
(![X]:((~funny(X)<~>strong(X))<=>(funny(X)&~kind(X))))&
(((strong(paul)<~>~old(paul)))=>(?[X]:((humble(X)&calm(X)))))&
(![X]:((humble(X)&strong(X))<=>(tall(X)&~rich(X))))&
(?[X]:(curious(X)))&
((~calm(alice)<~>~wise(alice)))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:((wise(X)|~rich(X))))&
(generous(mary))&
(?[X]:(~curious(X))) | ~old(alice) | [
"p2",
"p7",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6267466234580333230715458
% SZS output start Proof for 6267466234580333230715458
3. ! [X0] : ((~wise(X0) | quiet(X0)) <=> ~calm(X0)) [input p2]
8. ! [X0] : (old(X0) => (~kind(X0) & generous(X0))) [input p7]
12. ! [X0] : ((calm(X0) | old(X0)) <=> (generous(X0) <~> ~calm(X0))) [input p11]
18. ~calm(alice) <~> ~wise(alice) [input p17]
23. old(alice) [input hypothesis]
31. ! [X0] : ((~kind(X0) & generous(X0)) | ~old(X0)) [ennf transformation 8]
43. ! [X0] : (((~wise(X0) | quiet(X0)) | calm(X0)) & (~calm(X0) | (wise(X0) & ~quiet(X0)))) [nnf transformation 3]
44. ! [X0] : ((~wise(X0) | quiet(X0) | calm(X0)) & (~calm(X0) | (wise(X0) & ~quiet(X0)))) [flattening 43]
57. ! [X0] : (((calm(X0) | old(X0)) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) & (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (~calm(X0) & ~old(X0)))) [nnf transformation 12]
58. ! [X0] : ((calm(X0) | old(X0) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) & (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (~calm(X0) & ~old(X0)))) [flattening 57]
68. (wise(alice) | calm(alice)) & (~wise(alice) | ~calm(alice)) [nnf transformation 18]
83. ~calm(X0) | wise(X0) [cnf transformation 44]
101. ~old(X0) | generous(X0) [cnf transformation 31]
115. calm(X0) | ~generous(X0) | ~old(X0) [cnf transformation 58]
134. ~wise(alice) | ~calm(alice) [cnf transformation 68]
135. wise(alice) | calm(alice) [cnf transformation 68]
141. old(alice) [cnf transformation 23]
242. ~old(X0) | calm(X0) [subsumption resolution 115,101]
264. wise(alice) [subsumption resolution 135,83]
265. ~calm(alice) [subsumption resolution 134,264]
317. calm(alice) [resolution 242,141]
320. $false [subsumption resolution 317,265]
% SZS output end Proof for 6267466234580333230715458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or kind is either not curious or not humble and vice versa. If susan is both humble and quiet then mary is creative or kind and vice versa. Everyone who is either brave or not brave is both not strong and generous. Everyone who is both not old and not curious is not happy or curious and vice versa. Everyone who is either happy or generous is either funny or not patient. If someone is either not kind or brave then susan is either humble or creative. Everyone who is both funny and not creative is either rich or not patient and vice versa. Everyone who is both generous and not patient is both not kind and humble. If someone is either strong or tall then alice is humble. Everyone who is both not calm and not curious is old or rich and vice versa. If someone is funny or not brave then someone is not curious or not kind and vice versa. If someone is not wise or not old then lucy is curious or not calm and vice versa. Everyone who is not calm is old. If alice is both not humble and funny then someone is not curious and vice versa. If susan is not strong then someone is not happy or curious and vice versa. Everyone who is wise is not patient. Someone is brave. Someone is either happy or funny. Someone is not quiet or strong. Lucy is not calm or brave. Mary is old. Lucy is either not rich or quiet. John is both funny and not kind. | Mary is tall. | contradiction | (![X]:((~calm(X)<~>kind(X))<=>(~curious(X)<~>~humble(X))))&
(((humble(susan)&quiet(susan)))<=>((creative(mary)|kind(mary))))&
(![X]:((brave(X)<~>~brave(X))=>(~strong(X)&generous(X))))&
(![X]:((~old(X)&~curious(X))<=>(~happy(X)|curious(X))))&
(![X]:((happy(X)<~>generous(X))=>(funny(X)<~>~patient(X))))&
((?[X]:((~kind(X)<~>brave(X))))=>((humble(susan)<~>creative(susan))))&
(![X]:((funny(X)&~creative(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(![X]:(~calm(X)=>old(X)))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((~strong(susan))<=>(?[X]:((~happy(X)|curious(X)))))&
(![X]:(wise(X)=>~patient(X)))&
(?[X]:(brave(X)))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy)))&
(old(mary))&
((~rich(lucy)<~>quiet(lucy)))&
((funny(john)&~kind(john))) | tall(mary) | [
"p2",
"p3",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5944290137891688859193237
% SZS output start Proof for 5944290137891688859193237
3. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (generous(X0) & ~strong(X0))) [input p2]
4. ! [X0] : ((~curious(X0) & ~old(X0)) <=> (curious(X0) | ~happy(X0))) [input p3]
9. ? [X0] : (strong(X0) <~> tall(X0)) => humble(alice) [input p8]
14. (funny(alice) & ~humble(alice)) <=> ? [X0] : ~curious(X0) [input p13]
24. tall(mary) [input hypothesis]
26. ! [X0] : ((generous(X0) & ~strong(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 3]
31. humble(alice) | ! [X0] : (strong(X0) <=> tall(X0)) [ennf transformation 9]
37. ! [X0] : ((generous(X0) & ~strong(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 26]
38. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | (curious(X0) | old(X0)))) [nnf transformation 4]
39. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | curious(X0) | old(X0))) [flattening 38]
44. humble(alice) | ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))) [nnf transformation 31]
57. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~funny(alice) | humble(alice))) [nnf transformation 14]
58. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ~funny(alice) | humble(alice)) [flattening 57]
59. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ~funny(alice) | humble(alice)) [rectify 58]
60. ? [X1] : ~curious(X1) => ~curious(sK3) [choice axiom]
61. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (~curious(sK3) | ~funny(alice) | humble(alice)) [skolemisation 59,60]
87. ~strong(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 37]
88. ~strong(X0) | brave(X0) | brave(X0) [cnf transformation 37]
95. ~curious(X0) | ~curious(X0) [cnf transformation 39]
113. humble(alice) | strong(X0) | ~tall(X0) [cnf transformation 44]
129. ~humble(alice) | curious(X0) [cnf transformation 61]
145. tall(mary) [cnf transformation 24]
147. ~curious(X0) [duplicate literal removal 95]
148. ~strong(X0) | ~brave(X0) [duplicate literal removal 87]
149. ~strong(X0) | brave(X0) [duplicate literal removal 88]
174. ~strong(X0) [subsumption resolution 148,149]
194. humble(alice) | ~tall(X0) [subsumption resolution 113,174]
196. 8 <=> ! [X0] : ~tall(X0) [avatar definition]
197. ~tall(X0) <- (8) [avatar component clause 196]
199. 9 <=> humble(alice) [avatar definition]
202. 8 | 9 [avatar split clause 194,199,196]
242. ~humble(alice) [subsumption resolution 129,147]
243. ~9 [avatar split clause 242,199]
272. $false <- (8) [resolution 197,145]
273. ~8 [avatar contradiction clause 272]
274. $false [avatar sat refutation 202,243,273]
% SZS output end Proof for 5944290137891688859193237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or not old then someone is not happy.
Everyone who is not brave or calm is brave or not funny and vice versa.
Everyone who is not creative is rich or patient.
If someone is both generous and not brave then someone is both creative and quiet.
If fred is not strong or not funny then paul is old and vice versa.
Everyone who is not happy is both wise and not old and vice versa.
Everyone who is rich is strong and vice versa.
Everyone who is either not brave or wise is either not creative or brave and vice versa.
If someone is not happy then someone is both kind and not happy.
If susan is both not creative and patient then someone is not strong or quiet and vice versa.
If susan is either strong or kind then alice is both humble and not creative and vice versa.
Everyone who is either not generous or not rich is either not happy or not calm and vice versa.
Everyone who is not tall or happy is brave and vice versa.
Everyone who is strong is humble or not rich and vice versa.
If someone is either brave or strong then someone is both not wise and old.
If fred is either not generous or not old then someone is not old.
John is both not funny and not creative.
Susan is both not funny and not happy.
Susan is humble or not curious.
Someone is either humble or tall.
Mary is both strong and not curious.
Someone is creative or funny.
Mary is both not tall and rich. | John is not quiet. | entailment | ((?[X]:((quiet(X)<~>~old(X))))=>(?[X]:(~happy(X))))&
(![X]:((~brave(X)|calm(X))<=>(brave(X)|~funny(X))))&
(![X]:(~creative(X)=>(rich(X)|patient(X))))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:((creative(X)&quiet(X)))))&
(((~strong(fred)|~funny(fred)))<=>(old(paul)))&
(![X]:(~happy(X)<=>(wise(X)&~old(X))))&
(![X]:(rich(X)<=>strong(X)))&
(![X]:((~brave(X)<~>wise(X))<=>(~creative(X)<~>brave(X))))&
((?[X]:(~happy(X)))=>(?[X]:((kind(X)&~happy(X)))))&
(((~creative(susan)&patient(susan)))<=>(?[X]:((~strong(X)|quiet(X)))))&
(((strong(susan)<~>kind(susan)))<=>((humble(alice)&~creative(alice))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~happy(X)<~>~calm(X))))&
(![X]:((~tall(X)|happy(X))<=>brave(X)))&
(![X]:(strong(X)<=>(humble(X)|~rich(X))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((~wise(X)&old(X)))))&
(((~generous(fred)<~>~old(fred)))=>(?[X]:(~old(X))))&
((~funny(john)&~creative(john)))&
((~funny(susan)&~happy(susan)))&
((humble(susan)|~curious(susan)))&
(?[X]:((humble(X)<~>tall(X))))&
((strong(mary)&~curious(mary)))&
(?[X]:((creative(X)|funny(X))))&
((~tall(mary)&rich(mary))) | ~quiet(john) | [
"p5",
"p7",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2507913935996659501907931
% SZS output start Proof for 2507913935996659501907931
6. ! [X0] : (~happy(X0) <=> (~old(X0) & wise(X0))) [input p5]
8. ! [X0] : ((~brave(X0) <~> wise(X0)) <=> (~creative(X0) <~> brave(X0))) [input p7]
10. (patient(susan) & ~creative(susan)) <=> ? [X0] : (quiet(X0) | ~strong(X0)) [input p9]
18. ~happy(susan) & ~funny(susan) [input p17]
24. quiet(john) [input hypothesis]
49. ! [X0] : ((~happy(X0) | (old(X0) | ~wise(X0))) & ((~old(X0) & wise(X0)) | happy(X0))) [nnf transformation 6]
50. ! [X0] : ((~happy(X0) | old(X0) | ~wise(X0)) & ((~old(X0) & wise(X0)) | happy(X0))) [flattening 49]
52. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [nnf transformation 8]
56. ((patient(susan) & ~creative(susan)) | ! [X0] : (~quiet(X0) & strong(X0))) & (? [X0] : (quiet(X0) | ~strong(X0)) | (~patient(susan) | creative(susan))) [nnf transformation 10]
57. ((patient(susan) & ~creative(susan)) | ! [X0] : (~quiet(X0) & strong(X0))) & (? [X0] : (quiet(X0) | ~strong(X0)) | ~patient(susan) | creative(susan)) [flattening 56]
58. ((patient(susan) & ~creative(susan)) | ! [X0] : (~quiet(X0) & strong(X0))) & (? [X1] : (quiet(X1) | ~strong(X1)) | ~patient(susan) | creative(susan)) [rectify 57]
59. ? [X1] : (quiet(X1) | ~strong(X1)) => (quiet(sK3) | ~strong(sK3)) [choice axiom]
60. ((patient(susan) & ~creative(susan)) | ! [X0] : (~quiet(X0) & strong(X0))) & ((quiet(sK3) | ~strong(sK3)) | ~patient(susan) | creative(susan)) [skolemisation 58,59]
92. wise(X0) | happy(X0) [cnf transformation 50]
100. ~brave(X0) | creative(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 52]
103. ~wise(X0) | brave(X0) | brave(X0) | creative(X0) [cnf transformation 52]
109. ~creative(susan) | ~quiet(X0) [cnf transformation 60]
141. ~happy(susan) [cnf transformation 18]
148. quiet(john) [cnf transformation 24]
150. ~brave(X0) | creative(X0) | ~wise(X0) [duplicate literal removal 100]
152. ~wise(X0) | brave(X0) | creative(X0) [duplicate literal removal 103]
195. ~wise(X0) | creative(X0) [subsumption resolution 150,152]
211. 13 <=> ! [X0] : ~quiet(X0) [avatar definition]
212. ~quiet(X0) <- (13) [avatar component clause 211]
223. 16 <=> creative(susan) [avatar definition]
225. ~creative(susan) <- (~16) [avatar component clause 223]
226. 13 | ~16 [avatar split clause 109,223,211]
323. $false <- (13) [resolution 212,148]
324. ~13 [avatar contradiction clause 323]
337. creative(X0) | happy(X0) [resolution 195,92]
349. happy(susan) <- (~16) [resolution 337,225]
352. $false <- (~16) [subsumption resolution 349,141]
353. 16 [avatar contradiction clause 352]
354. $false [avatar sat refutation 226,324,353]
% SZS output end Proof for 2507913935996659501907931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and brave then fred is kind or strong. If lucy is both happy and old then someone is both happy and not quiet and vice versa. Everyone who is either not calm or strong is strong and vice versa. Everyone who is not wise or not kind is both quiet and not tall. Everyone who is old is both wise and not quiet. If someone is either not patient or patient then someone is funny and vice versa. Everyone who is patient or not calm is both not quiet and old and vice versa. Everyone who is both not kind and not curious is kind or not curious and vice versa. If mary is brave or not curious then paul is both quiet and not quiet. Everyone who is both not rich and kind is either strong or humble and vice versa. If mary is patient then fred is rich. Everyone who is both not brave and calm is tall or happy. If someone is both not generous and brave then someone is not funny or brave and vice versa. Everyone who is either not tall or not curious is not brave and vice versa. Everyone who is calm or old is not tall or humble and vice versa. Alice is not happy. Someone is both not patient and rich. Lucy is not creative or happy. Someone is either generous or not generous. Someone is both happy and not rich. John is either not wise or tall. | Mary is brave. | contradiction | ((?[X]:((rich(X)&brave(X))))=>((kind(fred)|strong(fred))))&
(((happy(lucy)&old(lucy)))<=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:((~calm(X)<~>strong(X))<=>strong(X)))&
(![X]:((~wise(X)|~kind(X))=>(quiet(X)&~tall(X))))&
(![X]:(old(X)=>(wise(X)&~quiet(X))))&
((?[X]:((~patient(X)<~>patient(X))))<=>(?[X]:(funny(X))))&
(![X]:((patient(X)|~calm(X))<=>(~quiet(X)&old(X))))&
(![X]:((~kind(X)&~curious(X))<=>(kind(X)|~curious(X))))&
(((brave(mary)|~curious(mary)))=>((quiet(paul)&~quiet(paul))))&
(![X]:((~rich(X)&kind(X))<=>(strong(X)<~>humble(X))))&
((patient(mary))=>(rich(fred)))&
(![X]:((~brave(X)&calm(X))=>(tall(X)|happy(X))))&
((?[X]:((~generous(X)&brave(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:((~tall(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((calm(X)|old(X))<=>(~tall(X)|humble(X))))&
(~happy(alice))&
(?[X]:((~patient(X)&rich(X))))&
((~creative(lucy)|happy(lucy)))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:((happy(X)&~rich(X))))&
((~wise(john)<~>tall(john))) | brave(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 617943727500795578434607
% SZS output start Proof for 617943727500795578434607
9. (~curious(mary) | brave(mary)) => (~quiet(paul) & quiet(paul)) [input p8]
22. brave(mary) [input hypothesis]
30. (~quiet(paul) & quiet(paul)) | (curious(mary) & ~brave(mary)) [ennf transformation 9]
96. quiet(paul) | ~brave(mary) [cnf transformation 30]
98. ~quiet(paul) | ~brave(mary) [cnf transformation 30]
130. brave(mary) [cnf transformation 22]
193. 13 <=> quiet(paul) [avatar definition]
198. 14 <=> brave(mary) [avatar definition]
201. ~14 | ~13 [avatar split clause 98,193,198]
203. ~14 | 13 [avatar split clause 96,193,198]
256. 14 [avatar split clause 130,198]
257. $false [avatar sat refutation 201,203,256]
% SZS output end Proof for 617943727500795578434607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is both not curious and not wise. Everyone who is brave or creative is either not creative or not humble. If john is both not rich and not happy then someone is either curious or happy. Everyone who is tall is both not creative and not quiet. Everyone who is patient is humble or not wise. Everyone who is not patient is curious or not calm. If someone is tall then john is either not wise or not kind and vice versa. If mary is not generous then susan is both rich and not happy and vice versa. If someone is both not wise and kind then lucy is either curious or not humble. Everyone who is either curious or old is both patient and not strong. Everyone who is wise is either not patient or kind and vice versa. If someone is both not brave and not old then someone is both not strong and not brave. Everyone who is not rich or creative is either humble or calm and vice versa. Everyone who is either strong or generous is calm and vice versa. If someone is both tall and not tall then fred is not brave or generous and vice versa. Everyone who is either not kind or not patient is not calm or tall and vice versa. Alice is brave. Someone is either not brave or generous. Fred is not rich or not brave. Paul is not generous. Someone is both old and happy. John is not wise. | Mary is not calm. | neutral | (![X]:(calm(X)=>(~curious(X)&~wise(X))))&
(![X]:((brave(X)|creative(X))=>(~creative(X)<~>~humble(X))))&
(((~rich(john)&~happy(john)))=>(?[X]:((curious(X)<~>happy(X)))))&
(![X]:(tall(X)=>(~creative(X)&~quiet(X))))&
(![X]:(patient(X)=>(humble(X)|~wise(X))))&
(![X]:(~patient(X)=>(curious(X)|~calm(X))))&
((?[X]:(tall(X)))<=>((~wise(john)<~>~kind(john))))&
((~generous(mary))<=>((rich(susan)&~happy(susan))))&
((?[X]:((~wise(X)&kind(X))))=>((curious(lucy)<~>~humble(lucy))))&
(![X]:((curious(X)<~>old(X))=>(patient(X)&~strong(X))))&
(![X]:(wise(X)<=>(~patient(X)<~>kind(X))))&
((?[X]:((~brave(X)&~old(X))))=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((~rich(X)|creative(X))<=>(humble(X)<~>calm(X))))&
(![X]:((strong(X)<~>generous(X))<=>calm(X)))&
((?[X]:((tall(X)&~tall(X))))<=>((~brave(fred)|generous(fred))))&
(![X]:((~kind(X)<~>~patient(X))<=>(~calm(X)|tall(X))))&
(brave(alice))&
(?[X]:((~brave(X)<~>generous(X))))&
((~rich(fred)|~brave(fred)))&
(~generous(paul))&
(?[X]:((old(X)&happy(X))))&
(~wise(john)) | ~calm(mary) | [] | null | 0 |
If someone is either not brave or funny then alice is both calm and not humble. If fred is creative or not wise then john is not patient. Everyone who is not quiet or tall is either brave or rich and vice versa. If fred is both not strong and not creative then someone is either not old or tall. Everyone who is patient is both not quiet and happy. If someone is curious then someone is calm. Everyone who is patient or not kind is happy or funny and vice versa. Everyone who is both not tall and strong is old. If someone is patient then someone is either calm or rich. Everyone who is tall or not funny is both happy and wise. Everyone who is not patient or patient is funny and vice versa. Everyone who is either not rich or patient is both not funny and kind and vice versa. If mary is curious then someone is not curious or generous and vice versa. Everyone who is not kind is either strong or not quiet and vice versa. Everyone who is not quiet or generous is both strong and generous and vice versa. Everyone who is either not generous or kind is strong or brave. Alice is patient or humble. Someone is either not funny or tall. Susan is both not calm and not quiet. Someone is curious. Paul is not strong or patient. Someone is not curious. Someone is not brave or curious. | Paul is not quiet. | entailment | ((?[X]:((~brave(X)<~>funny(X))))=>((calm(alice)&~humble(alice))))&
(((creative(fred)|~wise(fred)))=>(~patient(john)))&
(![X]:((~quiet(X)|tall(X))<=>(brave(X)<~>rich(X))))&
(((~strong(fred)&~creative(fred)))=>(?[X]:((~old(X)<~>tall(X)))))&
(![X]:(patient(X)=>(~quiet(X)&happy(X))))&
((?[X]:(curious(X)))=>(?[X]:(calm(X))))&
(![X]:((patient(X)|~kind(X))<=>(happy(X)|funny(X))))&
(![X]:((~tall(X)&strong(X))=>old(X)))&
((?[X]:(patient(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((tall(X)|~funny(X))=>(happy(X)&wise(X))))&
(![X]:((~patient(X)|patient(X))<=>funny(X)))&
(![X]:((~rich(X)<~>patient(X))<=>(~funny(X)&kind(X))))&
((curious(mary))<=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:(~kind(X)<=>(strong(X)<~>~quiet(X))))&
(![X]:((~quiet(X)|generous(X))<=>(strong(X)&generous(X))))&
(![X]:((~generous(X)<~>kind(X))=>(strong(X)|brave(X))))&
((patient(alice)|humble(alice)))&
(?[X]:((~funny(X)<~>tall(X))))&
((~calm(susan)&~quiet(susan)))&
(?[X]:(curious(X)))&
((~strong(paul)|patient(paul)))&
(?[X]:(~curious(X)))&
(?[X]:((~brave(X)|curious(X)))) | ~quiet(paul) | [
"p4",
"p6",
"p10",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3159655793507393713481639
% SZS output start Proof for 3159655793507393713481639
5. ! [X0] : (patient(X0) => (happy(X0) & ~quiet(X0))) [input p4]
7. ! [X0] : ((~kind(X0) | patient(X0)) <=> (funny(X0) | happy(X0))) [input p6]
11. ! [X0] : ((patient(X0) | ~patient(X0)) <=> funny(X0)) [input p10]
14. ! [X0] : (~kind(X0) <=> (strong(X0) <~> ~quiet(X0))) [input p13]
21. patient(paul) | ~strong(paul) [input p20]
24. quiet(paul) [input hypothesis]
33. ! [X0] : ((happy(X0) & ~quiet(X0)) | ~patient(X0)) [ennf transformation 5]
50. ! [X0] : (((~kind(X0) | patient(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (kind(X0) & ~patient(X0)))) [nnf transformation 7]
51. ! [X0] : ((~kind(X0) | patient(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (kind(X0) & ~patient(X0)))) [flattening 50]
56. ! [X0] : (((patient(X0) | ~patient(X0)) | ~funny(X0)) & (funny(X0) | (~patient(X0) & patient(X0)))) [nnf transformation 11]
57. ! [X0] : ((patient(X0) | ~patient(X0) | ~funny(X0)) & (funny(X0) | (~patient(X0) & patient(X0)))) [flattening 56]
64. ! [X0] : ((~kind(X0) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | kind(X0))) [nnf transformation 14]
90. ~quiet(X0) | ~patient(X0) [cnf transformation 33]
96. ~kind(X0) | patient(X0) | ~funny(X0) [cnf transformation 51]
102. funny(X0) | patient(X0) [cnf transformation 57]
103. ~patient(X0) | funny(X0) [cnf transformation 57]
114. ~quiet(X0) | strong(X0) | kind(X0) [cnf transformation 64]
131. patient(paul) | ~strong(paul) [cnf transformation 21]
134. quiet(paul) [cnf transformation 24]
197. funny(X0) [subsumption resolution 102,103]
229. 21 <=> strong(paul) [avatar definition]
231. ~strong(paul) <- (~21) [avatar component clause 229]
233. 22 <=> patient(paul) [avatar definition]
234. ~patient(paul) <- (~22) [avatar component clause 233]
236. ~21 | 22 [avatar split clause 131,233,229]
250. ~patient(paul) [resolution 90,134]
251. ~22 [avatar split clause 250,233]
310. strong(paul) | kind(paul) [resolution 114,134]
311. kind(paul) <- (~21) [subsumption resolution 310,231]
314. patient(paul) | ~funny(paul) <- (~21) [resolution 311,96]
316. ~funny(paul) <- (~21, ~22) [subsumption resolution 314,234]
317. $false <- (~21, ~22) [subsumption resolution 316,197]
318. 21 | 22 [avatar contradiction clause 317]
320. $false [avatar sat refutation 236,251,318]
% SZS output end Proof for 3159655793507393713481639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is strong or not generous then someone is funny.
If paul is curious then susan is either not happy or funny and vice versa.
Everyone who is either not brave or not kind is quiet.
Everyone who is not patient is both patient and not humble and vice versa.
If john is either quiet or curious then someone is either strong or not happy.
Everyone who is tall or calm is both curious and not generous and vice versa.
If alice is both not quiet and not funny then someone is not generous or patient and vice versa.
If fred is either rich or brave then someone is not rich or kind and vice versa.
Everyone who is not rich or not creative is both brave and not patient and vice versa.
Everyone who is both rich and not happy is both wise and tall.
If lucy is both not tall and not wise then alice is both not strong and curious.
If someone is calm or not old then someone is both strong and not humble.
If mary is either rich or funny then alice is both not generous and strong and vice versa.
If someone is either funny or happy then someone is both patient and strong.
Everyone who is not humble is strong and vice versa.
Someone is either not patient or not tall.
Paul is both curious and not generous.
Someone is either kind or not wise.
Someone is either not quiet or wise.
John is both not curious and patient.
Someone is not curious. | Lucy is strong. | contradiction | (((strong(lucy)|~generous(lucy)))=>(?[X]:(funny(X))))&
((curious(paul))<=>((~happy(susan)<~>funny(susan))))&
(![X]:((~brave(X)<~>~kind(X))=>quiet(X)))&
(![X]:(~patient(X)<=>(patient(X)&~humble(X))))&
(((quiet(john)<~>curious(john)))=>(?[X]:((strong(X)<~>~happy(X)))))&
(![X]:((tall(X)|calm(X))<=>(curious(X)&~generous(X))))&
(((~quiet(alice)&~funny(alice)))<=>(?[X]:((~generous(X)|patient(X)))))&
(((rich(fred)<~>brave(fred)))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~rich(X)|~creative(X))<=>(brave(X)&~patient(X))))&
(![X]:((rich(X)&~happy(X))=>(wise(X)&tall(X))))&
(((~tall(lucy)&~wise(lucy)))=>((~strong(alice)&curious(alice))))&
((?[X]:((calm(X)|~old(X))))=>(?[X]:((strong(X)&~humble(X)))))&
(((rich(mary)<~>funny(mary)))<=>((~generous(alice)&strong(alice))))&
((?[X]:((funny(X)<~>happy(X))))=>(?[X]:((patient(X)&strong(X)))))&
(![X]:(~humble(X)<=>strong(X)))&
(?[X]:((~patient(X)<~>~tall(X))))&
((curious(paul)&~generous(paul)))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:((~quiet(X)<~>wise(X))))&
((~curious(john)&patient(john)))&
(?[X]:(~curious(X))) | strong(lucy) | [
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3670948497353617761483462
% SZS output start Proof for 3670948497353617761483462
4. ! [X0] : (~patient(X0) <=> (~humble(X0) & patient(X0))) [input p3]
15. ! [X0] : (~humble(X0) <=> strong(X0)) [input p14]
22. strong(lucy) [input hypothesis]
39. ! [X0] : ((~patient(X0) | (humble(X0) | ~patient(X0))) & ((~humble(X0) & patient(X0)) | patient(X0))) [nnf transformation 4]
40. ! [X0] : ((~patient(X0) | humble(X0) | ~patient(X0)) & ((~humble(X0) & patient(X0)) | patient(X0))) [flattening 39]
66. ! [X0] : ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0))) [nnf transformation 15]
86. patient(X0) | patient(X0) [cnf transformation 40]
88. ~patient(X0) | humble(X0) | ~patient(X0) [cnf transformation 40]
131. ~humble(X0) | ~strong(X0) [cnf transformation 66]
143. strong(lucy) [cnf transformation 22]
144. patient(X0) [duplicate literal removal 86]
145. ~patient(X0) | humble(X0) [duplicate literal removal 88]
156. 3 <=> strong(lucy) [avatar definition]
157. strong(lucy) <- (3) [avatar component clause 156]
313. 3 [avatar split clause 143,156]
325. humble(X0) [resolution 145,144]
326. ~strong(X0) [resolution 325,131]
328. $false <- (3) [resolution 326,157]
333. ~3 [avatar contradiction clause 328]
334. $false [avatar sat refutation 313,333]
% SZS output end Proof for 3670948497353617761483462
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not kind is both not tall and not creative. If someone is creative then mary is both not humble and humble. Everyone who is strong or tall is funny and vice versa. If mary is either not creative or not quiet then someone is both creative and not curious. If paul is either not strong or brave then someone is not tall or happy. If lucy is either not brave or patient then lucy is either not generous or quiet and vice versa. Everyone who is either curious or calm is both funny and curious and vice versa. If paul is not curious then alice is both not quiet and not patient. Everyone who is creative is curious. Everyone who is both not quiet and not tall is strong or old and vice versa. Everyone who is not quiet or not curious is either patient or not rich and vice versa. Everyone who is both brave and not happy is either strong or patient. Everyone who is not old or not patient is either generous or not kind and vice versa. Everyone who is rich or calm is both rich and calm and vice versa. Everyone who is not calm or not curious is either strong or calm and vice versa. If john is not humble or not strong then susan is both strong and not wise and vice versa. Someone is either not patient or brave. Susan is either rich or not calm. Someone is not brave. Alice is either old or not humble. Someone is not brave or not tall. Mary is not quiet. John is not creative or wise. | Paul is patient. | contradiction | (![X]:((~brave(X)&~kind(X))=>(~tall(X)&~creative(X))))&
((?[X]:(creative(X)))=>((~humble(mary)&humble(mary))))&
(![X]:((strong(X)|tall(X))<=>funny(X)))&
(((~creative(mary)<~>~quiet(mary)))=>(?[X]:((creative(X)&~curious(X)))))&
(((~strong(paul)<~>brave(paul)))=>(?[X]:((~tall(X)|happy(X)))))&
(((~brave(lucy)<~>patient(lucy)))<=>((~generous(lucy)<~>quiet(lucy))))&
(![X]:((curious(X)<~>calm(X))<=>(funny(X)&curious(X))))&
((~curious(paul))=>((~quiet(alice)&~patient(alice))))&
(![X]:(creative(X)=>curious(X)))&
(![X]:((~quiet(X)&~tall(X))<=>(strong(X)|old(X))))&
(![X]:((~quiet(X)|~curious(X))<=>(patient(X)<~>~rich(X))))&
(![X]:((brave(X)&~happy(X))=>(strong(X)<~>patient(X))))&
(![X]:((~old(X)|~patient(X))<=>(generous(X)<~>~kind(X))))&
(![X]:((rich(X)|calm(X))<=>(rich(X)&calm(X))))&
(![X]:((~calm(X)|~curious(X))<=>(strong(X)<~>calm(X))))&
(((~humble(john)|~strong(john)))<=>((strong(susan)&~wise(susan))))&
(?[X]:((~patient(X)<~>brave(X))))&
((rich(susan)<~>~calm(susan)))&
(?[X]:(~brave(X)))&
((old(alice)<~>~humble(alice)))&
(?[X]:((~brave(X)|~tall(X))))&
(~quiet(mary))&
((~creative(john)|wise(john))) | patient(paul) | [
"p2",
"p6",
"p9",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8254774775247702464730333
% SZS output start Proof for 8254774775247702464730333
3. ! [X0] : ((tall(X0) | strong(X0)) <=> funny(X0)) [input p2]
7. ! [X0] : ((curious(X0) <~> calm(X0)) <=> (curious(X0) & funny(X0))) [input p6]
10. ! [X0] : ((~tall(X0) & ~quiet(X0)) <=> (old(X0) | strong(X0))) [input p9]
11. ! [X0] : ((~curious(X0) | ~quiet(X0)) <=> (patient(X0) <~> ~rich(X0))) [input p10]
14. ! [X0] : ((calm(X0) | rich(X0)) <=> (calm(X0) & rich(X0))) [input p13]
15. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (strong(X0) <~> calm(X0))) [input p14]
24. patient(paul) [input hypothesis]
33. ! [X0] : (((tall(X0) | strong(X0)) | ~funny(X0)) & (funny(X0) | (~tall(X0) & ~strong(X0)))) [nnf transformation 3]
34. ! [X0] : ((tall(X0) | strong(X0) | ~funny(X0)) & (funny(X0) | (~tall(X0) & ~strong(X0)))) [flattening 33]
39. ! [X0] : ((((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | (~curious(X0) | ~funny(X0))) & ((curious(X0) & funny(X0)) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0))))) [nnf transformation 7]
40. ! [X0] : ((((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ~curious(X0) | ~funny(X0)) & ((curious(X0) & funny(X0)) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0))))) [flattening 39]
41. ! [X0] : (((~tall(X0) & ~quiet(X0)) | (~old(X0) & ~strong(X0))) & ((old(X0) | strong(X0)) | (tall(X0) | quiet(X0)))) [nnf transformation 10]
42. ! [X0] : (((~tall(X0) & ~quiet(X0)) | (~old(X0) & ~strong(X0))) & (old(X0) | strong(X0) | tall(X0) | quiet(X0))) [flattening 41]
43. ! [X0] : (((~curious(X0) | ~quiet(X0)) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) & (((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | (curious(X0) & quiet(X0)))) [nnf transformation 11]
44. ! [X0] : ((~curious(X0) | ~quiet(X0) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) & (((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | (curious(X0) & quiet(X0)))) [flattening 43]
47. ! [X0] : (((calm(X0) | rich(X0)) | (~calm(X0) | ~rich(X0))) & ((calm(X0) & rich(X0)) | (~calm(X0) & ~rich(X0)))) [nnf transformation 14]
48. ! [X0] : ((calm(X0) | rich(X0) | ~calm(X0) | ~rich(X0)) & ((calm(X0) & rich(X0)) | (~calm(X0) & ~rich(X0)))) [flattening 47]
49. ! [X0] : (((~curious(X0) | ~calm(X0)) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) & (((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | (curious(X0) & calm(X0)))) [nnf transformation 15]
50. ! [X0] : ((~curious(X0) | ~calm(X0) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) & (((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | (curious(X0) & calm(X0)))) [flattening 49]
66. ~strong(X0) | funny(X0) [cnf transformation 34]
84. curious(X0) | curious(X0) | ~calm(X0) [cnf transformation 40]
86. ~calm(X0) | ~curious(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 40]
91. ~quiet(X0) | ~strong(X0) [cnf transformation 42]
97. ~patient(X0) | rich(X0) | quiet(X0) [cnf transformation 44]
109. ~rich(X0) | calm(X0) [cnf transformation 48]
112. calm(X0) | strong(X0) | calm(X0) [cnf transformation 50]
117. ~curious(X0) | ~calm(X0) | strong(X0) | ~calm(X0) [cnf transformation 50]
133. patient(paul) [cnf transformation 24]
134. calm(X0) | strong(X0) [duplicate literal removal 112]
135. ~curious(X0) | ~calm(X0) | strong(X0) [duplicate literal removal 117]
136. ~calm(X0) | curious(X0) [duplicate literal removal 84]
137. ~calm(X0) | ~curious(X0) | ~funny(X0) [duplicate literal removal 86]
192. 11 <=> curious(paul) [avatar definition]
205. ~calm(X0) | strong(X0) [subsumption resolution 135,136]
207. strong(X0) [subsumption resolution 134,205]
259. funny(X0) [resolution 66,207]
263. rich(paul) | quiet(paul) [resolution 97,133]
265. 24 <=> quiet(paul) [avatar definition]
267. quiet(paul) <- (24) [avatar component clause 265]
269. 25 <=> rich(paul) [avatar definition]
271. rich(paul) <- (25) [avatar component clause 269]
272. 24 | 25 [avatar split clause 263,269,265]
276. ~strong(paul) <- (24) [resolution 267,91]
277. $false <- (24) [subsumption resolution 276,207]
278. ~24 [avatar contradiction clause 277]
281. calm(paul) <- (25) [resolution 271,109]
283. curious(paul) <- (25) [resolution 281,136]
285. ~curious(paul) | ~funny(paul) <- (25) [resolution 137,281]
289. ~curious(paul) <- (25) [subsumption resolution 285,259]
290. ~11 | ~25 [avatar split clause 289,269,192]
291. 11 | ~25 [avatar split clause 283,269,192]
292. $false [avatar sat refutation 272,278,290,291]
% SZS output end Proof for 8254774775247702464730333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is humble or not strong and vice versa. Everyone who is not funny is not funny or not curious. Everyone who is quiet is old or not tall. Everyone who is wise is either happy or not calm. If someone is humble or not kind then someone is both rich and not calm. Everyone who is both tall and brave is both patient and strong. If fred is either not strong or not old then someone is not old. Everyone who is either tall or not creative is either not creative or not brave and vice versa. If mary is generous then fred is either quiet or generous. Everyone who is either creative or not strong is either tall or not happy and vice versa. Everyone who is both wise and happy is generous or funny and vice versa. Everyone who is both quiet and not generous is not patient or not funny. Everyone who is both not wise and quiet is tall or curious. If paul is generous or not funny then lucy is not wise or not brave. Everyone who is either not tall or wise is either not rich or wise and vice versa. Everyone who is either not creative or not tall is both not humble and tall. Lucy is kind or generous. Mary is both strong and creative. Someone is both not rich and generous. Lucy is creative. Someone is not curious. Fred is both not funny and not generous. Mary is both rich and funny. Someone is happy. | Lucy is tall. | entailment | (![X]:(~happy(X)<=>(humble(X)|~strong(X))))&
(![X]:(~funny(X)=>(~funny(X)|~curious(X))))&
(![X]:(quiet(X)=>(old(X)|~tall(X))))&
(![X]:(wise(X)=>(happy(X)<~>~calm(X))))&
((?[X]:((humble(X)|~kind(X))))=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((tall(X)&brave(X))=>(patient(X)&strong(X))))&
(((~strong(fred)<~>~old(fred)))=>(?[X]:(~old(X))))&
(![X]:((tall(X)<~>~creative(X))<=>(~creative(X)<~>~brave(X))))&
((generous(mary))=>((quiet(fred)<~>generous(fred))))&
(![X]:((creative(X)<~>~strong(X))<=>(tall(X)<~>~happy(X))))&
(![X]:((wise(X)&happy(X))<=>(generous(X)|funny(X))))&
(![X]:((quiet(X)&~generous(X))=>(~patient(X)|~funny(X))))&
(![X]:((~wise(X)&quiet(X))=>(tall(X)|curious(X))))&
(((generous(paul)|~funny(paul)))=>((~wise(lucy)|~brave(lucy))))&
(![X]:((~tall(X)<~>wise(X))<=>(~rich(X)<~>wise(X))))&
(![X]:((~creative(X)<~>~tall(X))=>(~humble(X)&tall(X))))&
((kind(lucy)|generous(lucy)))&
((strong(mary)&creative(mary)))&
(?[X]:((~rich(X)&generous(X))))&
(creative(lucy))&
(?[X]:(~curious(X)))&
((~funny(fred)&~generous(fred)))&
((rich(mary)&funny(mary)))&
(?[X]:(happy(X))) | tall(lucy) | [
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7033217050869444544526643
% SZS output start Proof for 7033217050869444544526643
16. ! [X0] : ((~creative(X0) <~> ~tall(X0)) => (tall(X0) & ~humble(X0))) [input p15]
20. creative(lucy) [input p19]
25. ~tall(lucy) [input hypothesis]
45. ! [X0] : ((tall(X0) & ~humble(X0)) | (~creative(X0) <=> ~tall(X0))) [ennf transformation 16]
61. ! [X0] : ((tall(X0) & ~humble(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) [nnf transformation 45]
119. tall(X0) | ~creative(X0) | tall(X0) [cnf transformation 61]
124. creative(lucy) [cnf transformation 20]
131. ~tall(lucy) [cnf transformation 25]
132. ~creative(X0) | tall(X0) [duplicate literal removal 119]
216. tall(lucy) [resolution 132,124]
217. $false [subsumption resolution 216,131]
% SZS output end Proof for 7033217050869444544526643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or generous is both calm and not strong and vice versa. If fred is not calm or calm then john is both happy and not old and vice versa. Everyone who is both generous and wise is either old or creative. If paul is either not happy or not creative then someone is both not quiet and brave and vice versa. If alice is funny or not funny then lucy is not humble or calm. If alice is either not wise or brave then alice is creative and vice versa. Everyone who is not calm is either not patient or quiet. If mary is patient then someone is both tall and curious and vice versa. If someone is old then john is both not tall and happy. Everyone who is both generous and quiet is both not curious and not funny. Everyone who is not humble is either not curious or brave and vice versa. Everyone who is creative is both tall and kind and vice versa. If paul is not rich or patient then fred is not old and vice versa. If someone is funny then lucy is both not happy and humble and vice versa. Everyone who is not creative or tall is both calm and not curious and vice versa. If susan is either calm or not kind then someone is both happy and not wise. Someone is strong. Someone is either calm or not tall. Someone is both not funny and not curious. Someone is funny. Someone is not strong or funny. John is both strong and wise. Paul is both wise and not old. | Fred is curious. | contradiction | (![X]:((~rich(X)<~>generous(X))<=>(calm(X)&~strong(X))))&
(((~calm(fred)|calm(fred)))<=>((happy(john)&~old(john))))&
(![X]:((generous(X)&wise(X))=>(old(X)<~>creative(X))))&
(((~happy(paul)<~>~creative(paul)))<=>(?[X]:((~quiet(X)&brave(X)))))&
(((funny(alice)|~funny(alice)))=>((~humble(lucy)|calm(lucy))))&
(((~wise(alice)<~>brave(alice)))<=>(creative(alice)))&
(![X]:(~calm(X)=>(~patient(X)<~>quiet(X))))&
((patient(mary))<=>(?[X]:((tall(X)&curious(X)))))&
((?[X]:(old(X)))=>((~tall(john)&happy(john))))&
(![X]:((generous(X)&quiet(X))=>(~curious(X)&~funny(X))))&
(![X]:(~humble(X)<=>(~curious(X)<~>brave(X))))&
(![X]:(creative(X)<=>(tall(X)&kind(X))))&
(((~rich(paul)|patient(paul)))<=>(~old(fred)))&
((?[X]:(funny(X)))<=>((~happy(lucy)&humble(lucy))))&
(![X]:((~creative(X)|tall(X))<=>(calm(X)&~curious(X))))&
(((calm(susan)<~>~kind(susan)))=>(?[X]:((happy(X)&~wise(X)))))&
(?[X]:(strong(X)))&
(?[X]:((calm(X)<~>~tall(X))))&
(?[X]:((~funny(X)&~curious(X))))&
(?[X]:(funny(X)))&
(?[X]:((~strong(X)|funny(X))))&
((strong(john)&wise(john)))&
((wise(paul)&~old(paul))) | curious(fred) | [
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1263848767513000409277040
% SZS output start Proof for 1263848767513000409277040
12. ! [X0] : (creative(X0) <=> (kind(X0) & tall(X0))) [input p11]
15. ! [X0] : ((tall(X0) | ~creative(X0)) <=> (~curious(X0) & calm(X0))) [input p14]
24. curious(fred) [input hypothesis]
50. ! [X0] : ((creative(X0) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | ~creative(X0))) [nnf transformation 12]
51. ! [X0] : ((creative(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | ~creative(X0))) [flattening 50]
59. ! [X0] : (((tall(X0) | ~creative(X0)) | (curious(X0) | ~calm(X0))) & ((~curious(X0) & calm(X0)) | (~tall(X0) & creative(X0)))) [nnf transformation 15]
60. ! [X0] : ((tall(X0) | ~creative(X0) | curious(X0) | ~calm(X0)) & ((~curious(X0) & calm(X0)) | (~tall(X0) & creative(X0)))) [flattening 59]
113. ~creative(X0) | tall(X0) [cnf transformation 51]
124. ~curious(X0) | creative(X0) [cnf transformation 60]
125. ~curious(X0) | ~tall(X0) [cnf transformation 60]
142. curious(fred) [cnf transformation 24]
215. 15 <=> ! [X0] : (~curious(X0) | ~tall(X0)) [avatar definition]
216. ~curious(X0) | ~tall(X0) <- (15) [avatar component clause 215]
270. 15 [avatar split clause 125,215]
318. creative(fred) [resolution 124,142]
324. ~tall(fred) <- (15) [resolution 216,142]
326. tall(fred) [resolution 318,113]
327. $false <- (15) [subsumption resolution 326,324]
328. ~15 [avatar contradiction clause 327]
329. $false [avatar sat refutation 270,328]
% SZS output end Proof for 1263848767513000409277040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or patient is either not tall or not patient.
If someone is not funny or generous then someone is either not rich or rich and vice versa.
Everyone who is not humble or brave is rich and vice versa.
If paul is both not patient and strong then someone is both happy and not curious.
If someone is both wise and not calm then paul is both not brave and not generous.
If john is not old or tall then paul is happy or brave and vice versa.
Everyone who is both old and curious is quiet and vice versa.
Everyone who is both not old and not kind is not curious or curious and vice versa.
Everyone who is humble is both not creative and generous.
If someone is both humble and strong then someone is tall or not wise and vice versa.
If fred is not tall then lucy is not tall or not patient and vice versa.
If john is strong then mary is both not quiet and humble.
If susan is not funny then fred is both not brave and not humble.
If paul is both rich and old then lucy is not happy and vice versa.
Everyone who is not funny or humble is not funny or calm and vice versa.
If someone is not wise then lucy is rich or not old.
Someone is generous.
Someone is either not rich or not funny.
Someone is creative.
Someone is both humble and curious.
Someone is either not brave or not patient.
Paul is not generous.
Someone is either quiet or not creative. | Fred is not kind. | entailment | (![X]:((tall(X)|patient(X))=>(~tall(X)<~>~patient(X))))&
((?[X]:((~funny(X)|generous(X))))<=>(?[X]:((~rich(X)<~>rich(X)))))&
(![X]:((~humble(X)|brave(X))<=>rich(X)))&
(((~patient(paul)&strong(paul)))=>(?[X]:((happy(X)&~curious(X)))))&
((?[X]:((wise(X)&~calm(X))))=>((~brave(paul)&~generous(paul))))&
(((~old(john)|tall(john)))<=>((happy(paul)|brave(paul))))&
(![X]:((old(X)&curious(X))<=>quiet(X)))&
(![X]:((~old(X)&~kind(X))<=>(~curious(X)|curious(X))))&
(![X]:(humble(X)=>(~creative(X)&generous(X))))&
((?[X]:((humble(X)&strong(X))))<=>(?[X]:((tall(X)|~wise(X)))))&
((~tall(fred))<=>((~tall(lucy)|~patient(lucy))))&
((strong(john))=>((~quiet(mary)&humble(mary))))&
((~funny(susan))=>((~brave(fred)&~humble(fred))))&
(((rich(paul)&old(paul)))<=>(~happy(lucy)))&
(![X]:((~funny(X)|humble(X))<=>(~funny(X)|calm(X))))&
((?[X]:(~wise(X)))=>((rich(lucy)|~old(lucy))))&
(?[X]:(generous(X)))&
(?[X]:((~rich(X)<~>~funny(X))))&
(?[X]:(creative(X)))&
(?[X]:((humble(X)&curious(X))))&
(?[X]:((~brave(X)<~>~patient(X))))&
(~generous(paul))&
(?[X]:((quiet(X)<~>~creative(X)))) | ~kind(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3899393369624548555860434
% SZS output start Proof for 3899393369624548555860434
8. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (curious(X0) | ~curious(X0))) [input p7]
24. kind(fred) [input hypothesis]
50. ! [X0] : (((~kind(X0) & ~old(X0)) | (~curious(X0) & curious(X0))) & ((curious(X0) | ~curious(X0)) | (kind(X0) | old(X0)))) [nnf transformation 8]
51. ! [X0] : (((~kind(X0) & ~old(X0)) | (~curious(X0) & curious(X0))) & (curious(X0) | ~curious(X0) | kind(X0) | old(X0))) [flattening 50]
105. ~kind(X0) | curious(X0) [cnf transformation 51]
106. ~kind(X0) | ~curious(X0) [cnf transformation 51]
140. kind(fred) [cnf transformation 24]
208. ~kind(X0) [subsumption resolution 105,106]
314. $false [subsumption resolution 140,208]
% SZS output end Proof for 3899393369624548555860434
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not wise or humble then mary is not wise or not humble.
If someone is either kind or old then fred is either not creative or patient and vice versa.
Everyone who is generous is not happy or not generous.
Everyone who is both not patient and not old is either calm or generous and vice versa.
Everyone who is rich is curious and vice versa.
Everyone who is not patient is calm or quiet.
If someone is either not tall or not calm then john is both not rich and not funny and vice versa.
Everyone who is both patient and not strong is either strong or funny and vice versa.
If someone is both tall and not strong then lucy is rich or not curious and vice versa.
Everyone who is funny is both not quiet and not patient and vice versa.
If mary is curious or not wise then paul is both generous and strong.
Everyone who is either tall or not happy is wise.
If someone is both rich and not rich then fred is either not curious or tall.
Everyone who is both not wise and not kind is not curious or funny.
If someone is both kind and humble then someone is both wise and generous.
If someone is both not old and not humble then someone is both not tall and tall and vice versa.
Someone is curious or not curious.
Someone is calm or kind.
Someone is not generous.
Someone is not funny.
Fred is either not strong or brave.
Someone is both generous and not happy.
Someone is not old or not rich.
Someone is humble or creative. | Mary is patient. | contradiction | (((~wise(paul)|humble(paul)))=>((~wise(mary)|~humble(mary))))&
((?[X]:((kind(X)<~>old(X))))<=>((~creative(fred)<~>patient(fred))))&
(![X]:(generous(X)=>(~happy(X)|~generous(X))))&
(![X]:((~patient(X)&~old(X))<=>(calm(X)<~>generous(X))))&
(![X]:(rich(X)<=>curious(X)))&
(![X]:(~patient(X)=>(calm(X)|quiet(X))))&
((?[X]:((~tall(X)<~>~calm(X))))<=>((~rich(john)&~funny(john))))&
(![X]:((patient(X)&~strong(X))<=>(strong(X)<~>funny(X))))&
((?[X]:((tall(X)&~strong(X))))<=>((rich(lucy)|~curious(lucy))))&
(![X]:(funny(X)<=>(~quiet(X)&~patient(X))))&
(((curious(mary)|~wise(mary)))=>((generous(paul)&strong(paul))))&
(![X]:((tall(X)<~>~happy(X))=>wise(X)))&
((?[X]:((rich(X)&~rich(X))))=>((~curious(fred)<~>tall(fred))))&
(![X]:((~wise(X)&~kind(X))=>(~curious(X)|funny(X))))&
((?[X]:((kind(X)&humble(X))))=>(?[X]:((wise(X)&generous(X)))))&
((?[X]:((~old(X)&~humble(X))))<=>(?[X]:((~tall(X)&tall(X)))))&
(?[X]:((curious(X)|~curious(X))))&
(?[X]:((calm(X)|kind(X))))&
(?[X]:(~generous(X)))&
(?[X]:(~funny(X)))&
((~strong(fred)<~>brave(fred)))&
(?[X]:((generous(X)&~happy(X))))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:((humble(X)|creative(X)))) | patient(mary) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2829251077580948592705374
% SZS output start Proof for 2829251077580948592705374
8. ! [X0] : ((~strong(X0) & patient(X0)) <=> (strong(X0) <~> funny(X0))) [input p7]
10. ! [X0] : (funny(X0) <=> (~patient(X0) & ~quiet(X0))) [input p9]
25. patient(mary) [input hypothesis]
52. ! [X0] : (((~strong(X0) & patient(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) & (((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | (strong(X0) | ~patient(X0)))) [nnf transformation 8]
53. ! [X0] : (((~strong(X0) & patient(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) & (((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | strong(X0) | ~patient(X0))) [flattening 52]
59. ! [X0] : ((funny(X0) | (patient(X0) | quiet(X0))) & ((~patient(X0) & ~quiet(X0)) | ~funny(X0))) [nnf transformation 10]
60. ! [X0] : ((funny(X0) | patient(X0) | quiet(X0)) & ((~patient(X0) & ~quiet(X0)) | ~funny(X0))) [flattening 59]
112. funny(X0) | strong(X0) | strong(X0) | ~patient(X0) [cnf transformation 53]
116. ~strong(X0) | funny(X0) | ~strong(X0) [cnf transformation 53]
124. ~patient(X0) | ~funny(X0) [cnf transformation 60]
151. patient(mary) [cnf transformation 25]
152. funny(X0) | strong(X0) | ~patient(X0) [duplicate literal removal 112]
153. ~strong(X0) | funny(X0) [duplicate literal removal 116]
231. funny(X0) | ~patient(X0) [subsumption resolution 152,153]
253. ~patient(X0) [subsumption resolution 124,231]
329. $false [subsumption resolution 151,253]
% SZS output end Proof for 2829251077580948592705374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
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