premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either happy or not patient is either not creative or not quiet.
If someone is either not generous or not wise then someone is patient or calm.
Everyone who is both calm and generous is both kind and not funny and vice versa.
Everyone who is either wise or not tall is either strong or curious.
If susan is either not rich or not kind then someone is either not rich or kind and vice versa.
Everyone who is both not quiet and not strong is both not calm and not generous and vice versa.
Everyone who is either generous or not funny is not strong.
Everyone who is either rich or not calm is not kind or not strong and vice versa.
If someone is both quiet and curious then lucy is not brave or not happy.
Everyone who is either funny or not rich is either rich or funny.
Everyone who is either not generous or creative is either not patient or not rich.
If someone is not generous then someone is not strong or tall.
Everyone who is not old is curious.
If someone is rich or not funny then someone is both calm and wise and vice versa.
Everyone who is either rich or curious is not happy or calm and vice versa.
Everyone who is not kind is tall and vice versa.
Mary is strong.
Alice is not calm.
Someone is not quiet.
Someone is both old and not creative.
Susan is not kind.
Lucy is not brave or not quiet.
Someone is not strong.
Someone is funny. | Mary is not curious. | contradiction | (![X]:((happy(X)<~>~patient(X))=>(~creative(X)<~>~quiet(X))))&
((?[X]:((~generous(X)<~>~wise(X))))=>(?[X]:((patient(X)|calm(X)))))&
(![X]:((calm(X)&generous(X))<=>(kind(X)&~funny(X))))&
(![X]:((wise(X)<~>~tall(X))=>(strong(X)<~>curious(X))))&
(((~rich(susan)<~>~kind(susan)))<=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:((~quiet(X)&~strong(X))<=>(~calm(X)&~generous(X))))&
(![X]:((generous(X)<~>~funny(X))=>~strong(X)))&
(![X]:((rich(X)<~>~calm(X))<=>(~kind(X)|~strong(X))))&
((?[X]:((quiet(X)&curious(X))))=>((~brave(lucy)|~happy(lucy))))&
(![X]:((funny(X)<~>~rich(X))=>(rich(X)<~>funny(X))))&
(![X]:((~generous(X)<~>creative(X))=>(~patient(X)<~>~rich(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~strong(X)|tall(X)))))&
(![X]:(~old(X)=>curious(X)))&
((?[X]:((rich(X)|~funny(X))))<=>(?[X]:((calm(X)&wise(X)))))&
(![X]:((rich(X)<~>curious(X))<=>(~happy(X)|calm(X))))&
(![X]:(~kind(X)<=>tall(X)))&
(strong(mary))&
(~calm(alice))&
(?[X]:(~quiet(X)))&
(?[X]:((old(X)&~creative(X))))&
(~kind(susan))&
((~brave(lucy)|~quiet(lucy)))&
(?[X]:(~strong(X)))&
(?[X]:(funny(X))) | ~curious(mary) | [
"p2",
"p5",
"p6",
"p7",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4256232433068535923343080
% SZS output start Proof for 4256232433068535923343080
3. ! [X0] : ((generous(X0) & calm(X0)) <=> (~funny(X0) & kind(X0))) [input p2]
6. ! [X0] : ((~strong(X0) & ~quiet(X0)) <=> (~generous(X0) & ~calm(X0))) [input p5]
7. ! [X0] : ((generous(X0) <~> ~funny(X0)) => ~strong(X0)) [input p6]
8. ! [X0] : ((rich(X0) <~> ~calm(X0)) <=> (~strong(X0) | ~kind(X0))) [input p7]
10. ! [X0] : ((funny(X0) <~> ~rich(X0)) => (rich(X0) <~> funny(X0))) [input p9]
15. ! [X0] : ((rich(X0) <~> curious(X0)) <=> (calm(X0) | ~happy(X0))) [input p14]
17. strong(mary) [input p16]
25. ~curious(mary) [input hypothesis]
36. ! [X0] : (~strong(X0) | (generous(X0) <=> ~funny(X0))) [ennf transformation 7]
37. ! [X0] : ((rich(X0) <~> funny(X0)) | (funny(X0) <=> ~rich(X0))) [ennf transformation 10]
45. ! [X0] : (((generous(X0) & calm(X0)) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | (~generous(X0) | ~calm(X0)))) [nnf transformation 3]
46. ! [X0] : (((generous(X0) & calm(X0)) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | ~generous(X0) | ~calm(X0))) [flattening 45]
52. ! [X0] : (((~strong(X0) & ~quiet(X0)) | (generous(X0) | calm(X0))) & ((~generous(X0) & ~calm(X0)) | (strong(X0) | quiet(X0)))) [nnf transformation 6]
53. ! [X0] : (((~strong(X0) & ~quiet(X0)) | generous(X0) | calm(X0)) & ((~generous(X0) & ~calm(X0)) | strong(X0) | quiet(X0))) [flattening 52]
54. ! [X0] : (~strong(X0) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) [nnf transformation 36]
55. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (strong(X0) & kind(X0))) & ((~strong(X0) | ~kind(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [nnf transformation 8]
56. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (strong(X0) & kind(X0))) & (~strong(X0) | ~kind(X0) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [flattening 55]
57. ! [X0] : (((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | ((funny(X0) | rich(X0)) & (~rich(X0) | ~funny(X0)))) [nnf transformation 37]
67. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (~calm(X0) & happy(X0))) & ((calm(X0) | ~happy(X0)) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [nnf transformation 15]
68. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (~calm(X0) & happy(X0))) & (calm(X0) | ~happy(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [flattening 67]
84. ~calm(X0) | ~generous(X0) | kind(X0) [cnf transformation 46]
86. ~kind(X0) | funny(X0) | calm(X0) [cnf transformation 46]
103. ~strong(X0) | generous(X0) | calm(X0) [cnf transformation 53]
104. ~strong(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 54]
105. ~strong(X0) | generous(X0) | funny(X0) [cnf transformation 54]
106. ~rich(X0) | ~kind(X0) | ~calm(X0) | ~strong(X0) [cnf transformation 56]
110. ~rich(X0) | calm(X0) | kind(X0) [cnf transformation 56]
113. funny(X0) | rich(X0) | funny(X0) | rich(X0) [cnf transformation 57]
114. ~funny(X0) | ~rich(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 57]
129. ~calm(X0) | rich(X0) | curious(X0) [cnf transformation 68]
134. strong(mary) [cnf transformation 17]
141. ~curious(mary) [cnf transformation 25]
142. rich(X0) | funny(X0) [duplicate literal removal 113]
143. ~rich(X0) | ~funny(X0) [duplicate literal removal 114]
309. generous(mary) | calm(mary) [resolution 103,134]
311. 28 <=> calm(mary) [avatar definition]
312. ~calm(mary) <- (~28) [avatar component clause 311]
313. calm(mary) <- (28) [avatar component clause 311]
315. 29 <=> generous(mary) [avatar definition]
317. generous(mary) <- (29) [avatar component clause 315]
318. 28 | 29 [avatar split clause 309,315,311]
320. ~funny(mary) | ~generous(mary) [resolution 104,134]
322. ~funny(mary) <- (29) [subsumption resolution 320,317]
324. generous(mary) | funny(mary) [resolution 105,134]
532. ~kind(X2) | ~calm(X2) | ~strong(X2) | funny(X2) [resolution 106,142]
537. ~strong(X2) | ~kind(X2) | funny(X2) [subsumption resolution 532,86]
563. 58 <=> rich(mary) [avatar definition]
564. ~rich(mary) <- (~58) [avatar component clause 563]
565. rich(mary) <- (58) [avatar component clause 563]
636. ~funny(mary) <- (58) [resolution 565,143]
639. 65 <=> kind(mary) [avatar definition]
641. ~kind(mary) <- (~65) [avatar component clause 639]
762. ~kind(mary) | funny(mary) [resolution 537,134]
766. ~kind(mary) <- (29) [subsumption resolution 762,322]
767. ~65 | ~29 [avatar split clause 766,315,639]
929. rich(mary) | curious(mary) <- (28) [resolution 313,129]
933. ~generous(mary) | kind(mary) <- (28) [resolution 313,84]
937. ~generous(mary) <- (28, ~65) [subsumption resolution 933,641]
938. ~29 | ~28 | 65 [avatar split clause 937,639,311,315]
939. generous(mary) <- (58) [subsumption resolution 324,636]
940. 29 | ~58 [avatar split clause 939,563,315]
942. rich(mary) <- (28) [subsumption resolution 929,141]
943. 58 | ~28 [avatar split clause 942,311,563]
964. 94 <=> funny(mary) [avatar definition]
965. ~funny(mary) <- (~94) [avatar component clause 964]
967. 94 | 29 [avatar split clause 324,315,964]
968. ~29 | ~94 [avatar split clause 320,964,315]
986. funny(mary) <- (~58) [resolution 564,142]
989. $false <- (~58, ~94) [subsumption resolution 986,965]
990. 58 | 94 [avatar contradiction clause 989]
992. calm(mary) | kind(mary) <- (58) [resolution 565,110]
1000. kind(mary) <- (~28, 58) [subsumption resolution 992,312]
1001. $false <- (~28, 58, ~65) [subsumption resolution 1000,641]
1002. 28 | ~58 | 65 [avatar contradiction clause 1001]
1003. $false [avatar sat refutation 318,767,938,940,943,967,968,990,1002]
% SZS output end Proof for 4256232433068535923343080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or generous then susan is both rich and not calm. If alice is either tall or creative then john is either kind or not brave and vice versa. Everyone who is both old and patient is creative or humble and vice versa. If susan is both strong and not happy then someone is both not strong and not brave. If someone is old then someone is either tall or not creative. If someone is not creative then paul is both not curious and generous. Everyone who is either old or calm is both not curious and funny and vice versa. Everyone who is both not funny and humble is not curious or wise and vice versa. Everyone who is quiet or not patient is curious. If alice is patient or not rich then someone is not curious or not calm and vice versa. If someone is both not old and not strong then susan is tall and vice versa. If alice is not humble or not tall then mary is either not kind or not humble. Everyone who is either patient or not strong is happy and vice versa. Everyone who is either not tall or not curious is brave and vice versa. John is both not tall and not strong. Susan is either not generous or not tall. Someone is not tall. Alice is either not tall or not wise. Lucy is not calm. | John is not patient. | neutral | ((?[X]:((~funny(X)|generous(X))))=>((rich(susan)&~calm(susan))))&
(((tall(alice)<~>creative(alice)))<=>((kind(john)<~>~brave(john))))&
(![X]:((old(X)&patient(X))<=>(creative(X)|humble(X))))&
(((strong(susan)&~happy(susan)))=>(?[X]:((~strong(X)&~brave(X)))))&
((?[X]:(old(X)))=>(?[X]:((tall(X)<~>~creative(X)))))&
((?[X]:(~creative(X)))=>((~curious(paul)&generous(paul))))&
(![X]:((old(X)<~>calm(X))<=>(~curious(X)&funny(X))))&
(![X]:((~funny(X)&humble(X))<=>(~curious(X)|wise(X))))&
(![X]:((quiet(X)|~patient(X))=>curious(X)))&
(((patient(alice)|~rich(alice)))<=>(?[X]:((~curious(X)|~calm(X)))))&
((?[X]:((~old(X)&~strong(X))))<=>(tall(susan)))&
(((~humble(alice)|~tall(alice)))=>((~kind(mary)<~>~humble(mary))))&
(![X]:((patient(X)<~>~strong(X))<=>happy(X)))&
(![X]:((~tall(X)<~>~curious(X))<=>brave(X)))&
((~tall(john)&~strong(john)))&
((~generous(susan)<~>~tall(susan)))&
(?[X]:(~tall(X)))&
((~tall(alice)<~>~wise(alice)))&
(~calm(lucy)) | ~patient(john) | [] | null | 0 |
Everyone who is not quiet or calm is creative.
If alice is patient then alice is not creative.
Everyone who is both not quiet and curious is both old and curious and vice versa.
If someone is either wise or not generous then alice is not calm.
Everyone who is both tall and rich is not old and vice versa.
If someone is generous or tall then lucy is either old or not strong.
If someone is either tall or funny then someone is either quiet or creative and vice versa.
Everyone who is either not humble or old is either not tall or not strong and vice versa.
If fred is not wise or old then someone is not brave and vice versa.
Everyone who is wise or not funny is generous or not calm and vice versa.
If lucy is not rich or generous then lucy is kind and vice versa.
Everyone who is both not rich and not calm is not strong or tall.
If john is not wise or not brave then someone is creative or not happy and vice versa.
Everyone who is not brave is quiet or not wise.
Everyone who is quiet is either not brave or brave and vice versa.
Everyone who is either generous or not humble is either not tall or kind.
Mary is funny or strong.
Fred is not rich.
Someone is not tall.
Someone is either calm or not patient.
John is either old or not rich.
Mary is either kind or not old.
Lucy is not brave or funny.
Someone is happy. | Alice is creative. | neutral | (![X]:((~quiet(X)|calm(X))=>creative(X)))&
((patient(alice))=>(~creative(alice)))&
(![X]:((~quiet(X)&curious(X))<=>(old(X)&curious(X))))&
((?[X]:((wise(X)<~>~generous(X))))=>(~calm(alice)))&
(![X]:((tall(X)&rich(X))<=>~old(X)))&
((?[X]:((generous(X)|tall(X))))=>((old(lucy)<~>~strong(lucy))))&
((?[X]:((tall(X)<~>funny(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((~humble(X)<~>old(X))<=>(~tall(X)<~>~strong(X))))&
(((~wise(fred)|old(fred)))<=>(?[X]:(~brave(X))))&
(![X]:((wise(X)|~funny(X))<=>(generous(X)|~calm(X))))&
(((~rich(lucy)|generous(lucy)))<=>(kind(lucy)))&
(![X]:((~rich(X)&~calm(X))=>(~strong(X)|tall(X))))&
(((~wise(john)|~brave(john)))<=>(?[X]:((creative(X)|~happy(X)))))&
(![X]:(~brave(X)=>(quiet(X)|~wise(X))))&
(![X]:(quiet(X)<=>(~brave(X)<~>brave(X))))&
(![X]:((generous(X)<~>~humble(X))=>(~tall(X)<~>kind(X))))&
((funny(mary)|strong(mary)))&
(~rich(fred))&
(?[X]:(~tall(X)))&
(?[X]:((calm(X)<~>~patient(X))))&
((old(john)<~>~rich(john)))&
((kind(mary)<~>~old(mary)))&
((~brave(lucy)|funny(lucy)))&
(?[X]:(happy(X))) | creative(alice) | [] | null | 0 |
Everyone who is either funny or curious is both creative and not old and vice versa. Everyone who is both old and kind is both generous and not curious. If someone is not calm then fred is calm or not humble. Everyone who is both not calm and wise is brave or not wise. If someone is not happy then someone is either wise or old and vice versa. Everyone who is both not rich and patient is both not generous and generous and vice versa. If someone is either not curious or not happy then alice is both patient and funny. Everyone who is both not quiet and brave is both humble and tall and vice versa. If someone is both not humble and rich then someone is patient or generous. Everyone who is either not brave or not old is not creative. Everyone who is not old or patient is both not curious and not creative and vice versa. Everyone who is both strong and old is quiet or not humble. Everyone who is either curious or calm is both not brave and not quiet. Everyone who is not old or brave is both curious and old and vice versa. Everyone who is not quiet is both curious and not old. If mary is not old or not generous then paul is strong or curious. Someone is either not kind or not creative. Someone is wise or curious. Someone is either quiet or not quiet. Someone is not patient. Mary is not rich. Paul is tall or not rich. Someone is brave or humble. | Mary is not funny. | contradiction | (![X]:((funny(X)<~>curious(X))<=>(creative(X)&~old(X))))&
(![X]:((old(X)&kind(X))=>(generous(X)&~curious(X))))&
((?[X]:(~calm(X)))=>((calm(fred)|~humble(fred))))&
(![X]:((~calm(X)&wise(X))=>(brave(X)|~wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((~rich(X)&patient(X))<=>(~generous(X)&generous(X))))&
((?[X]:((~curious(X)<~>~happy(X))))=>((patient(alice)&funny(alice))))&
(![X]:((~quiet(X)&brave(X))<=>(humble(X)&tall(X))))&
((?[X]:((~humble(X)&rich(X))))=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~brave(X)<~>~old(X))=>~creative(X)))&
(![X]:((~old(X)|patient(X))<=>(~curious(X)&~creative(X))))&
(![X]:((strong(X)&old(X))=>(quiet(X)|~humble(X))))&
(![X]:((curious(X)<~>calm(X))=>(~brave(X)&~quiet(X))))&
(![X]:((~old(X)|brave(X))<=>(curious(X)&old(X))))&
(![X]:(~quiet(X)=>(curious(X)&~old(X))))&
(((~old(mary)|~generous(mary)))=>((strong(paul)|curious(paul))))&
(?[X]:((~kind(X)<~>~creative(X))))&
(?[X]:((wise(X)|curious(X))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
(?[X]:(~patient(X)))&
(~rich(mary))&
((tall(paul)|~rich(paul)))&
(?[X]:((brave(X)|humble(X)))) | ~funny(mary) | [
"p0",
"p5",
"p9",
"p10",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7059885383352572862938907
% SZS output start Proof for 7059885383352572862938907
1. ! [X0] : ((funny(X0) <~> curious(X0)) <=> (~old(X0) & creative(X0))) [input p0]
6. ! [X0] : ((patient(X0) & ~rich(X0)) <=> (generous(X0) & ~generous(X0))) [input p5]
10. ! [X0] : ((~brave(X0) <~> ~old(X0)) => ~creative(X0)) [input p9]
11. ! [X0] : ((patient(X0) | ~old(X0)) <=> (~creative(X0) & ~curious(X0))) [input p10]
14. ! [X0] : ((brave(X0) | ~old(X0)) <=> (old(X0) & curious(X0))) [input p13]
21. ~rich(mary) [input p20]
24. ~funny(mary) [input hypothesis]
35. ! [X0] : (~creative(X0) | (~brave(X0) <=> ~old(X0))) [ennf transformation 10]
42. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | (old(X0) | ~creative(X0))) & ((~old(X0) & creative(X0)) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 1]
43. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | old(X0) | ~creative(X0)) & ((~old(X0) & creative(X0)) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [flattening 42]
49. ! [X0] : (((patient(X0) & ~rich(X0)) | (~generous(X0) | generous(X0))) & ((generous(X0) & ~generous(X0)) | (~patient(X0) | rich(X0)))) [nnf transformation 6]
50. ! [X0] : (((patient(X0) & ~rich(X0)) | ~generous(X0) | generous(X0)) & ((generous(X0) & ~generous(X0)) | ~patient(X0) | rich(X0))) [flattening 49]
57. ! [X0] : (~creative(X0) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) [nnf transformation 35]
58. ! [X0] : (((patient(X0) | ~old(X0)) | (creative(X0) | curious(X0))) & ((~creative(X0) & ~curious(X0)) | (~patient(X0) & old(X0)))) [nnf transformation 11]
59. ! [X0] : ((patient(X0) | ~old(X0) | creative(X0) | curious(X0)) & ((~creative(X0) & ~curious(X0)) | (~patient(X0) & old(X0)))) [flattening 58]
61. ! [X0] : (((brave(X0) | ~old(X0)) | (~old(X0) | ~curious(X0))) & ((old(X0) & curious(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 14]
62. ! [X0] : ((brave(X0) | ~old(X0) | ~old(X0) | ~curious(X0)) & ((old(X0) & curious(X0)) | (~brave(X0) & old(X0)))) [flattening 61]
78. ~old(X0) | funny(X0) | ~curious(X0) [cnf transformation 43]
89. ~generous(X0) | ~patient(X0) | rich(X0) [cnf transformation 50]
90. ~patient(X0) | generous(X0) | rich(X0) [cnf transformation 50]
102. ~old(X0) | ~creative(X0) | brave(X0) [cnf transformation 57]
108. ~old(X0) | patient(X0) | creative(X0) | curious(X0) [cnf transformation 59]
115. ~brave(X0) | curious(X0) [cnf transformation 62]
116. old(X0) | old(X0) [cnf transformation 62]
129. ~rich(mary) [cnf transformation 21]
132. ~funny(mary) [cnf transformation 24]
133. old(X0) [duplicate literal removal 116]
173. ~patient(X0) | rich(X0) [subsumption resolution 89,90]
288. ~curious(X0) | funny(X0) [resolution 78,133]
293. ~creative(X0) | brave(X0) [resolution 102,133]
319. patient(X0) | creative(X0) | curious(X0) [resolution 108,133]
340. rich(X1) | curious(X1) | creative(X1) [resolution 319,173]
361. curious(mary) | creative(mary) [resolution 340,129]
365. 34 <=> creative(mary) [avatar definition]
367. creative(mary) <- (34) [avatar component clause 365]
369. 35 <=> curious(mary) [avatar definition]
371. curious(mary) <- (35) [avatar component clause 369]
372. 34 | 35 [avatar split clause 361,369,365]
410. brave(mary) <- (34) [resolution 367,293]
417. curious(mary) <- (34) [resolution 410,115]
419. 35 | ~34 [avatar split clause 417,365,369]
421. funny(mary) <- (35) [resolution 371,288]
426. $false <- (35) [subsumption resolution 421,132]
427. ~35 [avatar contradiction clause 426]
428. $false [avatar sat refutation 372,419,427]
% SZS output end Proof for 7059885383352572862938907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not old then someone is either happy or not generous.
Everyone who is kind is both kind and not strong.
If lucy is both strong and rich then lucy is both creative and not quiet and vice versa.
Everyone who is both not humble and kind is patient or not brave and vice versa.
If someone is either not old or not patient then susan is wise or not humble.
Everyone who is either generous or happy is not old.
If someone is either quiet or humble then mary is both not patient and not wise and vice versa.
If someone is either not funny or not rich then someone is rich or wise.
Everyone who is kind or brave is both funny and wise.
Everyone who is either not happy or not generous is either strong or happy and vice versa.
If alice is not kind or not rich then john is both not rich and not wise.
If someone is either strong or not creative then mary is either rich or not kind and vice versa.
Everyone who is either quiet or not creative is either old or not strong.
If someone is not wise then someone is not patient or quiet.
Everyone who is not patient is either creative or funny and vice versa.
If lucy is not curious or not calm then someone is both not brave and not happy.
Someone is not creative.
John is not rich.
John is both not strong and not patient.
Mary is not humble.
Someone is rich.
Someone is both not calm and not strong.
Alice is brave or not brave. | Alice is brave. | neutral | ((?[X]:((~creative(X)<~>~old(X))))=>(?[X]:((happy(X)<~>~generous(X)))))&
(![X]:(kind(X)=>(kind(X)&~strong(X))))&
(((strong(lucy)&rich(lucy)))<=>((creative(lucy)&~quiet(lucy))))&
(![X]:((~humble(X)&kind(X))<=>(patient(X)|~brave(X))))&
((?[X]:((~old(X)<~>~patient(X))))=>((wise(susan)|~humble(susan))))&
(![X]:((generous(X)<~>happy(X))=>~old(X)))&
((?[X]:((quiet(X)<~>humble(X))))<=>((~patient(mary)&~wise(mary))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((kind(X)|brave(X))=>(funny(X)&wise(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(strong(X)<~>happy(X))))&
(((~kind(alice)|~rich(alice)))=>((~rich(john)&~wise(john))))&
((?[X]:((strong(X)<~>~creative(X))))<=>((rich(mary)<~>~kind(mary))))&
(![X]:((quiet(X)<~>~creative(X))=>(old(X)<~>~strong(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:(~patient(X)<=>(creative(X)<~>funny(X))))&
(((~curious(lucy)|~calm(lucy)))=>(?[X]:((~brave(X)&~happy(X)))))&
(?[X]:(~creative(X)))&
(~rich(john))&
((~strong(john)&~patient(john)))&
(~humble(mary))&
(?[X]:(rich(X)))&
(?[X]:((~calm(X)&~strong(X))))&
((brave(alice)|~brave(alice))) | brave(alice) | [] | null | 0 |
Everyone who is not funny or rich is either rich or brave.
Everyone who is both not generous and wise is both tall and not curious.
Everyone who is not brave or patient is humble.
Everyone who is happy or rich is either calm or creative.
If someone is humble or not funny then someone is not tall or wise and vice versa.
If john is both not kind and not tall then someone is not patient.
Everyone who is both creative and curious is either happy or strong.
Everyone who is not curious or not funny is rich and vice versa.
If someone is either rich or not funny then paul is both not generous and rich and vice versa.
If alice is not calm or strong then alice is either strong or not rich.
Everyone who is both brave and not old is not happy or calm and vice versa.
Everyone who is wise is either not generous or creative.
If fred is not wise then someone is not tall and vice versa.
Everyone who is rich is either not generous or happy and vice versa.
Everyone who is both not strong and happy is not calm or curious.
If someone is both tall and humble then lucy is either funny or calm and vice versa.
Fred is both kind and happy.
Someone is brave or quiet.
Paul is brave.
Alice is calm.
Lucy is not old or humble.
Susan is both not wise and not generous.
Someone is not humble or strong. | Alice is not humble. | neutral | (![X]:((~funny(X)|rich(X))=>(rich(X)<~>brave(X))))&
(![X]:((~generous(X)&wise(X))=>(tall(X)&~curious(X))))&
(![X]:((~brave(X)|patient(X))=>humble(X)))&
(![X]:((happy(X)|rich(X))=>(calm(X)<~>creative(X))))&
((?[X]:((humble(X)|~funny(X))))<=>(?[X]:((~tall(X)|wise(X)))))&
(((~kind(john)&~tall(john)))=>(?[X]:(~patient(X))))&
(![X]:((creative(X)&curious(X))=>(happy(X)<~>strong(X))))&
(![X]:((~curious(X)|~funny(X))<=>rich(X)))&
((?[X]:((rich(X)<~>~funny(X))))<=>((~generous(paul)&rich(paul))))&
(((~calm(alice)|strong(alice)))=>((strong(alice)<~>~rich(alice))))&
(![X]:((brave(X)&~old(X))<=>(~happy(X)|calm(X))))&
(![X]:(wise(X)=>(~generous(X)<~>creative(X))))&
((~wise(fred))<=>(?[X]:(~tall(X))))&
(![X]:(rich(X)<=>(~generous(X)<~>happy(X))))&
(![X]:((~strong(X)&happy(X))=>(~calm(X)|curious(X))))&
((?[X]:((tall(X)&humble(X))))<=>((funny(lucy)<~>calm(lucy))))&
((kind(fred)&happy(fred)))&
(?[X]:((brave(X)|quiet(X))))&
(brave(paul))&
(calm(alice))&
((~old(lucy)|humble(lucy)))&
((~wise(susan)&~generous(susan)))&
(?[X]:((~humble(X)|strong(X)))) | ~humble(alice) | [] | null | 0 |
Everyone who is both not patient and not strong is not humble or not quiet. If someone is either happy or strong then fred is curious or brave and vice versa. Everyone who is not rich is not tall or not wise. Everyone who is calm is both not quiet and calm and vice versa. If someone is both quiet and funny then someone is brave and vice versa. If someone is generous then mary is not curious and vice versa. Everyone who is strong or funny is both quiet and not curious. Everyone who is both not tall and old is both tall and not calm. Everyone who is not happy or not generous is generous or not tall. Everyone who is not generous is both not brave and not creative. Everyone who is not brave or not rich is both happy and calm. Everyone who is both funny and not wise is either not tall or not kind. Everyone who is either generous or not patient is both generous and quiet and vice versa. Everyone who is either wise or not kind is either not old or creative and vice versa. If mary is both wise and not kind then lucy is either wise or not brave. If mary is not tall or not kind then fred is not brave or patient and vice versa. Mary is humble or brave. Someone is both not old and not calm. Fred is wise. Someone is either calm or not patient. Lucy is curious. Someone is either kind or humble. Someone is both kind and wise. | Fred is patient. | neutral | (![X]:((~patient(X)&~strong(X))=>(~humble(X)|~quiet(X))))&
((?[X]:((happy(X)<~>strong(X))))<=>((curious(fred)|brave(fred))))&
(![X]:(~rich(X)=>(~tall(X)|~wise(X))))&
(![X]:(calm(X)<=>(~quiet(X)&calm(X))))&
((?[X]:((quiet(X)&funny(X))))<=>(?[X]:(brave(X))))&
((?[X]:(generous(X)))<=>(~curious(mary)))&
(![X]:((strong(X)|funny(X))=>(quiet(X)&~curious(X))))&
(![X]:((~tall(X)&old(X))=>(tall(X)&~calm(X))))&
(![X]:((~happy(X)|~generous(X))=>(generous(X)|~tall(X))))&
(![X]:(~generous(X)=>(~brave(X)&~creative(X))))&
(![X]:((~brave(X)|~rich(X))=>(happy(X)&calm(X))))&
(![X]:((funny(X)&~wise(X))=>(~tall(X)<~>~kind(X))))&
(![X]:((generous(X)<~>~patient(X))<=>(generous(X)&quiet(X))))&
(![X]:((wise(X)<~>~kind(X))<=>(~old(X)<~>creative(X))))&
(((wise(mary)&~kind(mary)))=>((wise(lucy)<~>~brave(lucy))))&
(((~tall(mary)|~kind(mary)))<=>((~brave(fred)|patient(fred))))&
((humble(mary)|brave(mary)))&
(?[X]:((~old(X)&~calm(X))))&
(wise(fred))&
(?[X]:((calm(X)<~>~patient(X))))&
(curious(lucy))&
(?[X]:((kind(X)<~>humble(X))))&
(?[X]:((kind(X)&wise(X)))) | patient(fred) | [] | null | 0 |
Everyone who is either rich or not calm is rich.
Everyone who is rich is not generous.
If susan is not strong then lucy is either not rich or not wise.
If someone is wise then john is both not patient and not calm and vice versa.
If someone is both curious and not curious then lucy is not rich and vice versa.
Everyone who is not tall or rich is both not tall and humble and vice versa.
Everyone who is calm is either not wise or tall.
If lucy is either not strong or wise then someone is curious or calm.
If someone is patient then paul is either tall or generous and vice versa.
Everyone who is both kind and not patient is not wise and vice versa.
If mary is either quiet or brave then someone is both not happy and calm.
Everyone who is either quiet or rich is not rich and vice versa.
Everyone who is not quiet is wise or not curious.
Everyone who is not rich or not generous is either not creative or tall and vice versa.
Everyone who is both quiet and not happy is curious or wise and vice versa.
Lucy is either patient or kind.
Someone is both funny and not happy.
Someone is old or not creative.
Someone is generous or not patient.
Someone is both not tall and humble.
Someone is funny or wise. | Susan is not old. | neutral | (![X]:((rich(X)<~>~calm(X))=>rich(X)))&
(![X]:(rich(X)=>~generous(X)))&
((~strong(susan))=>((~rich(lucy)<~>~wise(lucy))))&
((?[X]:(wise(X)))<=>((~patient(john)&~calm(john))))&
((?[X]:((curious(X)&~curious(X))))<=>(~rich(lucy)))&
(![X]:((~tall(X)|rich(X))<=>(~tall(X)&humble(X))))&
(![X]:(calm(X)=>(~wise(X)<~>tall(X))))&
(((~strong(lucy)<~>wise(lucy)))=>(?[X]:((curious(X)|calm(X)))))&
((?[X]:(patient(X)))<=>((tall(paul)<~>generous(paul))))&
(![X]:((kind(X)&~patient(X))<=>~wise(X)))&
(((quiet(mary)<~>brave(mary)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:((quiet(X)<~>rich(X))<=>~rich(X)))&
(![X]:(~quiet(X)=>(wise(X)|~curious(X))))&
(![X]:((~rich(X)|~generous(X))<=>(~creative(X)<~>tall(X))))&
(![X]:((quiet(X)&~happy(X))<=>(curious(X)|wise(X))))&
((patient(lucy)<~>kind(lucy)))&
(?[X]:((funny(X)&~happy(X))))&
(?[X]:((old(X)|~creative(X))))&
(?[X]:((generous(X)|~patient(X))))&
(?[X]:((~tall(X)&humble(X))))&
(?[X]:((funny(X)|wise(X)))) | ~old(susan) | [] | null | 0 |
Everyone who is either creative or not old is either humble or curious and vice versa.
If lucy is both not humble and tall then mary is both happy and humble.
If susan is not strong then someone is curious and vice versa.
If someone is both quiet and not rich then someone is not creative or not quiet and vice versa.
If fred is not quiet then lucy is strong or not tall and vice versa.
Everyone who is both kind and not calm is either not patient or not strong.
Everyone who is both not creative and not funny is rich or calm and vice versa.
If mary is calm or creative then someone is not rich or quiet.
If paul is generous then someone is not old or not generous.
Everyone who is quiet or creative is creative or rich.
If mary is tall then someone is not quiet and vice versa.
Everyone who is either not curious or strong is either not curious or not happy and vice versa.
If john is either patient or kind then fred is curious or calm.
Everyone who is strong is both not generous and not wise.
If lucy is not curious or not kind then someone is either not patient or tall.
If someone is not humble then lucy is both old and strong.
Someone is both not humble and funny.
Someone is either rich or tall.
Susan is tall.
Someone is not kind.
John is funny or tall.
Someone is either humble or not tall.
Someone is either patient or rich.
Someone is both rich and not kind. | Lucy is old. | entailment | (![X]:((creative(X)<~>~old(X))<=>(humble(X)<~>curious(X))))&
(((~humble(lucy)&tall(lucy)))=>((happy(mary)&humble(mary))))&
((~strong(susan))<=>(?[X]:(curious(X))))&
((?[X]:((quiet(X)&~rich(X))))<=>(?[X]:((~creative(X)|~quiet(X)))))&
((~quiet(fred))<=>((strong(lucy)|~tall(lucy))))&
(![X]:((kind(X)&~calm(X))=>(~patient(X)<~>~strong(X))))&
(![X]:((~creative(X)&~funny(X))<=>(rich(X)|calm(X))))&
(((calm(mary)|creative(mary)))=>(?[X]:((~rich(X)|quiet(X)))))&
((generous(paul))=>(?[X]:((~old(X)|~generous(X)))))&
(![X]:((quiet(X)|creative(X))=>(creative(X)|rich(X))))&
((tall(mary))<=>(?[X]:(~quiet(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(~curious(X)<~>~happy(X))))&
(((patient(john)<~>kind(john)))=>((curious(fred)|calm(fred))))&
(![X]:(strong(X)=>(~generous(X)&~wise(X))))&
(((~curious(lucy)|~kind(lucy)))=>(?[X]:((~patient(X)<~>tall(X)))))&
((?[X]:(~humble(X)))=>((old(lucy)&strong(lucy))))&
(?[X]:((~humble(X)&funny(X))))&
(?[X]:((rich(X)<~>tall(X))))&
(tall(susan))&
(?[X]:(~kind(X)))&
((funny(john)|tall(john)))&
(?[X]:((humble(X)<~>~tall(X))))&
(?[X]:((patient(X)<~>rich(X))))&
(?[X]:((rich(X)&~kind(X)))) | old(lucy) | [
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4756075814990914252180458
% SZS output start Proof for 4756075814990914252180458
16. ? [X0] : ~humble(X0) => (strong(lucy) & old(lucy)) [input p15]
17. ? [X0] : (funny(X0) & ~humble(X0)) [input p16]
25. ~old(lucy) [input hypothesis]
40. (strong(lucy) & old(lucy)) | ! [X0] : humble(X0) [ennf transformation 16]
67. ? [X0] : (funny(X0) & ~humble(X0)) => (funny(sK6) & ~humble(sK6)) [choice axiom]
68. funny(sK6) & ~humble(sK6) [skolemisation 17,67]
129. old(lucy) | humble(X0) [cnf transformation 40]
131. ~humble(sK6) [cnf transformation 68]
144. ~old(lucy) [cnf transformation 25]
290. 31 <=> ! [X0] : humble(X0) [avatar definition]
291. humble(X0) <- (31) [avatar component clause 290]
294. 32 <=> old(lucy) [avatar definition]
297. 31 | 32 [avatar split clause 129,294,290]
337. ~32 [avatar split clause 144,294]
344. $false <- (31) [resolution 291,131]
345. ~31 [avatar contradiction clause 344]
346. $false [avatar sat refutation 297,337,345]
% SZS output end Proof for 4756075814990914252180458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either tall or not humble and vice versa.
Everyone who is rich or curious is not happy and vice versa.
If someone is not creative or not patient then susan is not generous.
If paul is kind then someone is either tall or not patient.
Everyone who is not brave is wise.
If someone is both quiet and not brave then lucy is both not creative and not old.
If paul is rich or quiet then paul is either not calm or funny and vice versa.
Everyone who is not brave or rich is both not happy and not curious and vice versa.
If mary is either kind or wise then mary is quiet and vice versa.
If alice is kind or not calm then someone is both kind and not creative and vice versa.
Everyone who is both patient and not old is generous and vice versa.
Everyone who is generous is calm and vice versa.
Everyone who is either wise or funny is both not patient and patient.
Everyone who is not creative or not happy is either not quiet or curious and vice versa.
If someone is both rich and not creative then susan is both not curious and creative.
Everyone who is both not old and not patient is both patient and not wise and vice versa.
Someone is not funny or quiet.
Alice is patient or not quiet.
Someone is creative or not tall.
Someone is not wise.
Susan is strong or wise.
Paul is both not patient and creative.
Mary is either not curious or not old.
Someone is quiet. | Paul is quiet. | neutral | (![X]:(~quiet(X)<=>(tall(X)<~>~humble(X))))&
(![X]:((rich(X)|curious(X))<=>~happy(X)))&
((?[X]:((~creative(X)|~patient(X))))=>(~generous(susan)))&
((kind(paul))=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:(~brave(X)=>wise(X)))&
((?[X]:((quiet(X)&~brave(X))))=>((~creative(lucy)&~old(lucy))))&
(((rich(paul)|quiet(paul)))<=>((~calm(paul)<~>funny(paul))))&
(![X]:((~brave(X)|rich(X))<=>(~happy(X)&~curious(X))))&
(((kind(mary)<~>wise(mary)))<=>(quiet(mary)))&
(((kind(alice)|~calm(alice)))<=>(?[X]:((kind(X)&~creative(X)))))&
(![X]:((patient(X)&~old(X))<=>generous(X)))&
(![X]:(generous(X)<=>calm(X)))&
(![X]:((wise(X)<~>funny(X))=>(~patient(X)&patient(X))))&
(![X]:((~creative(X)|~happy(X))<=>(~quiet(X)<~>curious(X))))&
((?[X]:((rich(X)&~creative(X))))=>((~curious(susan)&creative(susan))))&
(![X]:((~old(X)&~patient(X))<=>(patient(X)&~wise(X))))&
(?[X]:((~funny(X)|quiet(X))))&
((patient(alice)|~quiet(alice)))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:(~wise(X)))&
((strong(susan)|wise(susan)))&
((~patient(paul)&creative(paul)))&
((~curious(mary)<~>~old(mary)))&
(?[X]:(quiet(X))) | quiet(paul) | [] | null | 0 |
Everyone who is not rich or tall is both happy and funny and vice versa. If someone is curious then alice is not curious or strong and vice versa. Everyone who is curious or not calm is either not quiet or not funny. Everyone who is not humble is either not curious or not patient. If someone is either not calm or not funny then paul is not brave. If mary is brave or rich then lucy is funny or not calm and vice versa. Everyone who is both not curious and generous is either not humble or calm and vice versa. Everyone who is either curious or not wise is strong and vice versa. If mary is not wise or not calm then mary is either not strong or not wise and vice versa. If someone is not calm then someone is both not calm and not funny and vice versa. If paul is both tall and old then john is patient or wise and vice versa. Everyone who is both humble and funny is not happy or not creative. If someone is either humble or funny then lucy is both not wise and curious and vice versa. Everyone who is old is happy and vice versa. Everyone who is either calm or strong is not patient. If lucy is tall then paul is creative or not wise and vice versa. Someone is either brave or not curious. Susan is either kind or patient. Someone is not quiet. Mary is not calm or not quiet. Alice is either not old or rich. Someone is both happy and not wise. Someone is both funny and not brave. | Alice is happy. | entailment | (![X]:((~rich(X)|tall(X))<=>(happy(X)&funny(X))))&
((?[X]:(curious(X)))<=>((~curious(alice)|strong(alice))))&
(![X]:((curious(X)|~calm(X))=>(~quiet(X)<~>~funny(X))))&
(![X]:(~humble(X)=>(~curious(X)<~>~patient(X))))&
((?[X]:((~calm(X)<~>~funny(X))))=>(~brave(paul)))&
(((brave(mary)|rich(mary)))<=>((funny(lucy)|~calm(lucy))))&
(![X]:((~curious(X)&generous(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((curious(X)<~>~wise(X))<=>strong(X)))&
(((~wise(mary)|~calm(mary)))<=>((~strong(mary)<~>~wise(mary))))&
((?[X]:(~calm(X)))<=>(?[X]:((~calm(X)&~funny(X)))))&
(((tall(paul)&old(paul)))<=>((patient(john)|wise(john))))&
(![X]:((humble(X)&funny(X))=>(~happy(X)|~creative(X))))&
((?[X]:((humble(X)<~>funny(X))))<=>((~wise(lucy)&curious(lucy))))&
(![X]:(old(X)<=>happy(X)))&
(![X]:((calm(X)<~>strong(X))=>~patient(X)))&
((tall(lucy))<=>((creative(paul)|~wise(paul))))&
(?[X]:((brave(X)<~>~curious(X))))&
((kind(susan)<~>patient(susan)))&
(?[X]:(~quiet(X)))&
((~calm(mary)|~quiet(mary)))&
((~old(alice)<~>rich(alice)))&
(?[X]:((happy(X)&~wise(X))))&
(?[X]:((funny(X)&~brave(X)))) | happy(alice) | [
"p0",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6509857227085051049421822
% SZS output start Proof for 6509857227085051049421822
1. ! [X0] : ((tall(X0) | ~rich(X0)) <=> (funny(X0) & happy(X0))) [input p0]
14. ! [X0] : (old(X0) <=> happy(X0)) [input p13]
21. ~old(alice) <~> rich(alice) [input p20]
24. ~happy(alice) [input hypothesis]
32. ! [X0] : (((tall(X0) | ~rich(X0)) | (~funny(X0) | ~happy(X0))) & ((funny(X0) & happy(X0)) | (~tall(X0) & rich(X0)))) [nnf transformation 1]
33. ! [X0] : ((tall(X0) | ~rich(X0) | ~funny(X0) | ~happy(X0)) & ((funny(X0) & happy(X0)) | (~tall(X0) & rich(X0)))) [flattening 32]
61. ! [X0] : ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))) [nnf transformation 14]
71. (~rich(alice) | old(alice)) & (rich(alice) | ~old(alice)) [nnf transformation 21]
76. happy(X0) | rich(X0) [cnf transformation 33]
127. ~old(X0) | happy(X0) [cnf transformation 61]
141. ~rich(alice) | old(alice) [cnf transformation 71]
146. ~happy(alice) [cnf transformation 24]
326. 38 <=> old(alice) [avatar definition]
328. old(alice) <- (38) [avatar component clause 326]
330. 39 <=> rich(alice) [avatar definition]
333. 38 | ~39 [avatar split clause 141,330,326]
335. rich(alice) [resolution 76,146]
338. 39 [avatar split clause 335,330]
342. happy(alice) <- (38) [resolution 127,328]
343. $false <- (38) [subsumption resolution 342,146]
344. ~38 [avatar contradiction clause 343]
345. $false [avatar sat refutation 333,338,344]
% SZS output end Proof for 6509857227085051049421822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both creative and not old then someone is not happy and vice versa. Everyone who is either rich or not calm is both happy and not old. Everyone who is both happy and not generous is either not old or patient. Everyone who is tall or brave is either happy or strong and vice versa. If someone is kind or calm then john is either rich or curious. If someone is tall or kind then alice is not creative. If paul is both not creative and quiet then someone is not humble and vice versa. Everyone who is kind or not creative is not strong. Everyone who is not strong is creative or strong and vice versa. Everyone who is not brave or rich is either curious or not funny. Everyone who is both not brave and strong is both not kind and funny and vice versa. Everyone who is not tall or not generous is generous or not humble and vice versa. Everyone who is either happy or kind is not tall or not strong and vice versa. If fred is either not brave or not kind then paul is both creative and patient and vice versa. Everyone who is either not generous or not humble is either funny or not creative and vice versa. Alice is not kind or happy. Someone is funny or not calm. Someone is either wise or not happy. Susan is both old and not quiet. | John is not brave. | contradiction | (((creative(fred)&~old(fred)))<=>(?[X]:(~happy(X))))&
(![X]:((rich(X)<~>~calm(X))=>(happy(X)&~old(X))))&
(![X]:((happy(X)&~generous(X))=>(~old(X)<~>patient(X))))&
(![X]:((tall(X)|brave(X))<=>(happy(X)<~>strong(X))))&
((?[X]:((kind(X)|calm(X))))=>((rich(john)<~>curious(john))))&
((?[X]:((tall(X)|kind(X))))=>(~creative(alice)))&
(((~creative(paul)&quiet(paul)))<=>(?[X]:(~humble(X))))&
(![X]:((kind(X)|~creative(X))=>~strong(X)))&
(![X]:(~strong(X)<=>(creative(X)|strong(X))))&
(![X]:((~brave(X)|rich(X))=>(curious(X)<~>~funny(X))))&
(![X]:((~brave(X)&strong(X))<=>(~kind(X)&funny(X))))&
(![X]:((~tall(X)|~generous(X))<=>(generous(X)|~humble(X))))&
(![X]:((happy(X)<~>kind(X))<=>(~tall(X)|~strong(X))))&
(((~brave(fred)<~>~kind(fred)))<=>((creative(paul)&patient(paul))))&
(![X]:((~generous(X)<~>~humble(X))<=>(funny(X)<~>~creative(X))))&
((~kind(alice)|happy(alice)))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:((wise(X)<~>~happy(X))))&
((old(susan)&~quiet(susan))) | ~brave(john) | [
"p3",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1644668078025112115294026
% SZS output start Proof for 1644668078025112115294026
4. ! [X0] : ((brave(X0) | tall(X0)) <=> (happy(X0) <~> strong(X0))) [input p3]
6. ? [X0] : (kind(X0) | tall(X0)) => ~creative(alice) [input p5]
9. ! [X0] : (~strong(X0) <=> (strong(X0) | creative(X0))) [input p8]
13. ! [X0] : ((happy(X0) <~> kind(X0)) <=> (~strong(X0) | ~tall(X0))) [input p12]
20. ~brave(john) [input hypothesis]
25. ~creative(alice) | ! [X0] : (~kind(X0) & ~tall(X0)) [ennf transformation 6]
35. ! [X0] : (((brave(X0) | tall(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (~brave(X0) & ~tall(X0)))) [nnf transformation 4]
36. ! [X0] : ((brave(X0) | tall(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (~brave(X0) & ~tall(X0)))) [flattening 35]
43. ! [X0] : ((~strong(X0) | (~strong(X0) & ~creative(X0))) & ((strong(X0) | creative(X0)) | strong(X0))) [nnf transformation 9]
44. ! [X0] : ((~strong(X0) | (~strong(X0) & ~creative(X0))) & (strong(X0) | creative(X0) | strong(X0))) [flattening 43]
50. ! [X0] : ((((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0))))) [nnf transformation 13]
51. ! [X0] : ((((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0))))) [flattening 50]
73. ~happy(X0) | tall(X0) | strong(X0) | brave(X0) [cnf transformation 36]
79. ~creative(alice) | ~tall(X0) [cnf transformation 25]
80. ~creative(alice) | ~kind(X0) [cnf transformation 25]
86. strong(X0) | creative(X0) | strong(X0) [cnf transformation 44]
88. ~strong(X0) | ~strong(X0) [cnf transformation 44]
104. kind(X0) | happy(X0) | strong(X0) [cnf transformation 51]
127. ~brave(john) [cnf transformation 20]
130. strong(X0) | creative(X0) [duplicate literal removal 86]
131. ~strong(X0) [duplicate literal removal 88]
133. 1 <=> ! [X0] : happy(X0) [avatar definition]
134. happy(X0) <- (1) [avatar component clause 133]
163. 8 <=> ! [X0] : ~kind(X0) [avatar definition]
164. ~kind(X0) <- (8) [avatar component clause 163]
169. 9 <=> creative(alice) [avatar definition]
171. ~creative(alice) <- (~9) [avatar component clause 169]
172. 8 | ~9 [avatar split clause 80,169,163]
174. 10 <=> ! [X0] : ~tall(X0) [avatar definition]
175. ~tall(X0) <- (10) [avatar component clause 174]
176. 10 | ~9 [avatar split clause 79,169,174]
195. creative(X0) [subsumption resolution 130,131]
198. kind(X0) | happy(X0) [subsumption resolution 104,131]
242. $false <- (~9) [subsumption resolution 171,195]
243. 9 [avatar contradiction clause 242]
252. happy(X2) <- (8) [resolution 198,164]
255. 1 | ~8 [avatar split clause 252,163,133]
298. tall(X0) | strong(X0) | brave(X0) <- (1) [resolution 73,134]
301. strong(X0) | brave(X0) <- (1, 10) [subsumption resolution 298,175]
302. brave(X0) <- (1, 10) [subsumption resolution 301,131]
303. $false <- (1, 10) [resolution 302,127]
307. ~1 | ~10 [avatar contradiction clause 303]
308. $false [avatar sat refutation 172,176,243,255,307]
% SZS output end Proof for 1644668078025112115294026
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not funny. Everyone who is either calm or creative is strong. Everyone who is either not rich or not strong is happy. If someone is both tall and not creative then someone is kind and vice versa. Everyone who is either funny or rich is either not curious or creative and vice versa. Everyone who is both not brave and not kind is either not patient or kind. Everyone who is either not happy or rich is humble or rich and vice versa. Everyone who is either kind or not old is both rich and patient and vice versa. Everyone who is brave or tall is either rich or not strong and vice versa. Everyone who is either brave or not rich is not brave. If lucy is not old or creative then someone is both tall and not rich and vice versa. Everyone who is patient or not kind is both not kind and kind and vice versa. Everyone who is either not happy or creative is either old or not calm and vice versa. Everyone who is either creative or not kind is patient. Everyone who is humble is wise or happy and vice versa. If alice is either quiet or not creative then someone is not strong. John is quiet or curious. Lucy is either humble or creative. Someone is either not curious or quiet. Fred is funny or not funny. Fred is either not kind or humble. Someone is not creative. | Alice is not strong. | neutral | (![X]:(curious(X)=>~funny(X)))&
(![X]:((calm(X)<~>creative(X))=>strong(X)))&
(![X]:((~rich(X)<~>~strong(X))=>happy(X)))&
((?[X]:((tall(X)&~creative(X))))<=>(?[X]:(kind(X))))&
(![X]:((funny(X)<~>rich(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((~brave(X)&~kind(X))=>(~patient(X)<~>kind(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(humble(X)|rich(X))))&
(![X]:((kind(X)<~>~old(X))<=>(rich(X)&patient(X))))&
(![X]:((brave(X)|tall(X))<=>(rich(X)<~>~strong(X))))&
(![X]:((brave(X)<~>~rich(X))=>~brave(X)))&
(((~old(lucy)|creative(lucy)))<=>(?[X]:((tall(X)&~rich(X)))))&
(![X]:((patient(X)|~kind(X))<=>(~kind(X)&kind(X))))&
(![X]:((~happy(X)<~>creative(X))<=>(old(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~kind(X))=>patient(X)))&
(![X]:(humble(X)<=>(wise(X)|happy(X))))&
(((quiet(alice)<~>~creative(alice)))=>(?[X]:(~strong(X))))&
((quiet(john)|curious(john)))&
((humble(lucy)<~>creative(lucy)))&
(?[X]:((~curious(X)<~>quiet(X))))&
((funny(fred)|~funny(fred)))&
((~kind(fred)<~>humble(fred)))&
(?[X]:(~creative(X))) | ~strong(alice) | [] | null | 0 |
Everyone who is not tall is tall or not kind and vice versa. If susan is both not calm and not quiet then someone is not old or not wise. Everyone who is not calm is wise or not tall and vice versa. If someone is not strong then john is either not curious or happy and vice versa. If alice is wise or patient then mary is both tall and old and vice versa. If someone is humble or not humble then someone is humble and vice versa. Everyone who is both tall and not old is both happy and strong. If fred is creative then someone is tall or not patient and vice versa. Everyone who is both generous and not humble is happy or creative and vice versa. If someone is not calm then someone is either patient or not creative. Everyone who is either kind or funny is calm and vice versa. Everyone who is not humble is either not tall or quiet and vice versa. If john is not rich or kind then someone is both brave and not creative. Everyone who is either generous or quiet is strong or brave and vice versa. Everyone who is both quiet and not happy is rich or quiet. Fred is both rich and wise. Someone is either generous or wise. Someone is brave. Mary is both not generous and not wise. | Fred is not generous. | contradiction | (![X]:(~tall(X)<=>(tall(X)|~kind(X))))&
(((~calm(susan)&~quiet(susan)))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:(~calm(X)<=>(wise(X)|~tall(X))))&
((?[X]:(~strong(X)))<=>((~curious(john)<~>happy(john))))&
(((wise(alice)|patient(alice)))<=>((tall(mary)&old(mary))))&
((?[X]:((humble(X)|~humble(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)&~old(X))=>(happy(X)&strong(X))))&
((creative(fred))<=>(?[X]:((tall(X)|~patient(X)))))&
(![X]:((generous(X)&~humble(X))<=>(happy(X)|creative(X))))&
((?[X]:(~calm(X)))=>(?[X]:((patient(X)<~>~creative(X)))))&
(![X]:((kind(X)<~>funny(X))<=>calm(X)))&
(![X]:(~humble(X)<=>(~tall(X)<~>quiet(X))))&
(((~rich(john)|kind(john)))=>(?[X]:((brave(X)&~creative(X)))))&
(![X]:((generous(X)<~>quiet(X))<=>(strong(X)|brave(X))))&
(![X]:((quiet(X)&~happy(X))=>(rich(X)|quiet(X))))&
((rich(fred)&wise(fred)))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:(brave(X)))&
((~generous(mary)&~wise(mary))) | ~generous(fred) | [
"p0",
"p4",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6088474570330322034362221
% SZS output start Proof for 6088474570330322034362221
1. ! [X0] : (~tall(X0) <=> (~kind(X0) | tall(X0))) [input p0]
5. (patient(alice) | wise(alice)) <=> (old(mary) & tall(mary)) [input p4]
8. creative(fred) <=> ? [X0] : (~patient(X0) | tall(X0)) [input p7]
9. ! [X0] : ((~humble(X0) & generous(X0)) <=> (creative(X0) | happy(X0))) [input p8]
20. ~generous(fred) [input hypothesis]
32. ! [X0] : ((~tall(X0) | (kind(X0) & ~tall(X0))) & ((~kind(X0) | tall(X0)) | tall(X0))) [nnf transformation 1]
33. ! [X0] : ((~tall(X0) | (kind(X0) & ~tall(X0))) & (~kind(X0) | tall(X0) | tall(X0))) [flattening 32]
42. ((patient(alice) | wise(alice)) | (~old(mary) | ~tall(mary))) & ((old(mary) & tall(mary)) | (~patient(alice) & ~wise(alice))) [nnf transformation 5]
43. (patient(alice) | wise(alice) | ~old(mary) | ~tall(mary)) & ((old(mary) & tall(mary)) | (~patient(alice) & ~wise(alice))) [flattening 42]
49. (creative(fred) | ! [X0] : (patient(X0) & ~tall(X0))) & (? [X0] : (~patient(X0) | tall(X0)) | ~creative(fred)) [nnf transformation 8]
50. (creative(fred) | ! [X0] : (patient(X0) & ~tall(X0))) & (? [X1] : (~patient(X1) | tall(X1)) | ~creative(fred)) [rectify 49]
51. ? [X1] : (~patient(X1) | tall(X1)) => (~patient(sK4) | tall(sK4)) [choice axiom]
52. (creative(fred) | ! [X0] : (patient(X0) & ~tall(X0))) & ((~patient(sK4) | tall(sK4)) | ~creative(fred)) [skolemisation 50,51]
53. ! [X0] : (((~humble(X0) & generous(X0)) | (~creative(X0) & ~happy(X0))) & ((creative(X0) | happy(X0)) | (humble(X0) | ~generous(X0)))) [nnf transformation 9]
54. ! [X0] : (((~humble(X0) & generous(X0)) | (~creative(X0) & ~happy(X0))) & (creative(X0) | happy(X0) | humble(X0) | ~generous(X0))) [flattening 53]
71. ~tall(X0) | ~tall(X0) [cnf transformation 33]
82. tall(mary) | ~patient(alice) [cnf transformation 43]
93. creative(fred) | patient(X0) [cnf transformation 52]
96. ~creative(X0) | generous(X0) [cnf transformation 54]
123. ~generous(fred) [cnf transformation 20]
125. ~tall(X0) [duplicate literal removal 71]
165. 9 <=> patient(alice) [avatar definition]
167. ~patient(alice) <- (~9) [avatar component clause 165]
178. ~patient(alice) [subsumption resolution 82,125]
179. ~9 [avatar split clause 178,165]
195. 15 <=> ! [X0] : patient(X0) [avatar definition]
196. patient(X0) <- (15) [avatar component clause 195]
198. 16 <=> creative(fred) [avatar definition]
200. creative(fred) <- (16) [avatar component clause 198]
201. 15 | 16 [avatar split clause 93,198,195]
234. $false <- (~9, 15) [subsumption resolution 167,196]
235. 9 | ~15 [avatar contradiction clause 234]
236. generous(fred) <- (16) [resolution 96,200]
237. $false <- (16) [subsumption resolution 236,123]
238. ~16 [avatar contradiction clause 237]
239. $false [avatar sat refutation 179,201,235,238]
% SZS output end Proof for 6088474570330322034362221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not funny and humble then someone is patient.
Everyone who is not kind is patient or not wise and vice versa.
If john is either not curious or brave then someone is brave.
Everyone who is not tall or not funny is both not funny and not tall.
Everyone who is not tall or old is happy and vice versa.
If someone is kind or happy then someone is not kind.
If fred is wise then mary is not patient or not tall.
If someone is both curious and brave then someone is either humble or not quiet.
Everyone who is either strong or generous is not curious or tall.
If someone is creative or strong then mary is both not quiet and not patient.
Everyone who is both not creative and not brave is both not funny and curious and vice versa.
Everyone who is not happy or not patient is both not kind and brave.
Everyone who is both kind and rich is quiet or funny.
Everyone who is both not tall and old is brave and vice versa.
If someone is not wise then lucy is not quiet and vice versa.
If john is not calm then someone is both not generous and not calm and vice versa.
Alice is either strong or not tall.
Paul is not quiet or not humble.
Someone is either kind or patient.
Someone is not calm.
Someone is curious.
Someone is rich.
Mary is either old or not funny.
John is either not creative or not curious. | Mary is curious. | entailment | (((~funny(john)&humble(john)))=>(?[X]:(patient(X))))&
(![X]:(~kind(X)<=>(patient(X)|~wise(X))))&
(((~curious(john)<~>brave(john)))=>(?[X]:(brave(X))))&
(![X]:((~tall(X)|~funny(X))=>(~funny(X)&~tall(X))))&
(![X]:((~tall(X)|old(X))<=>happy(X)))&
((?[X]:((kind(X)|happy(X))))=>(?[X]:(~kind(X))))&
((wise(fred))=>((~patient(mary)|~tall(mary))))&
((?[X]:((curious(X)&brave(X))))=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:((strong(X)<~>generous(X))=>(~curious(X)|tall(X))))&
((?[X]:((creative(X)|strong(X))))=>((~quiet(mary)&~patient(mary))))&
(![X]:((~creative(X)&~brave(X))<=>(~funny(X)&curious(X))))&
(![X]:((~happy(X)|~patient(X))=>(~kind(X)&brave(X))))&
(![X]:((kind(X)&rich(X))=>(quiet(X)|funny(X))))&
(![X]:((~tall(X)&old(X))<=>brave(X)))&
((?[X]:(~wise(X)))<=>(~quiet(lucy)))&
((~calm(john))<=>(?[X]:((~generous(X)&~calm(X)))))&
((strong(alice)<~>~tall(alice)))&
((~quiet(paul)|~humble(paul)))&
(?[X]:((kind(X)<~>patient(X))))&
(?[X]:(~calm(X)))&
(?[X]:(curious(X)))&
(?[X]:(rich(X)))&
((old(mary)<~>~funny(mary)))&
((~creative(john)<~>~curious(john))) | curious(mary) | [
"p3",
"p9",
"p10",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1755118863478904130819051
% SZS output start Proof for 1755118863478904130819051
4. ! [X0] : ((~funny(X0) | ~tall(X0)) => (~tall(X0) & ~funny(X0))) [input p3]
10. ? [X0] : (strong(X0) | creative(X0)) => (~patient(mary) & ~quiet(mary)) [input p9]
11. ! [X0] : ((~brave(X0) & ~creative(X0)) <=> (curious(X0) & ~funny(X0))) [input p10]
12. ! [X0] : ((~patient(X0) | ~happy(X0)) => (brave(X0) & ~kind(X0))) [input p11]
14. ! [X0] : ((old(X0) & ~tall(X0)) <=> brave(X0)) [input p13]
23. old(mary) <~> ~funny(mary) [input p22]
25. ~curious(mary) [input hypothesis]
31. ! [X0] : ((~tall(X0) & ~funny(X0)) | (funny(X0) & tall(X0))) [ennf transformation 4]
38. (~patient(mary) & ~quiet(mary)) | ! [X0] : (~strong(X0) & ~creative(X0)) [ennf transformation 10]
39. ! [X0] : ((brave(X0) & ~kind(X0)) | (patient(X0) & happy(X0))) [ennf transformation 12]
59. ! [X0] : (((~brave(X0) & ~creative(X0)) | (~curious(X0) | funny(X0))) & ((curious(X0) & ~funny(X0)) | (brave(X0) | creative(X0)))) [nnf transformation 11]
60. ! [X0] : (((~brave(X0) & ~creative(X0)) | ~curious(X0) | funny(X0)) & ((curious(X0) & ~funny(X0)) | brave(X0) | creative(X0))) [flattening 59]
61. ! [X0] : (((old(X0) & ~tall(X0)) | ~brave(X0)) & (brave(X0) | (~old(X0) | tall(X0)))) [nnf transformation 14]
62. ! [X0] : (((old(X0) & ~tall(X0)) | ~brave(X0)) & (brave(X0) | ~old(X0) | tall(X0))) [flattening 61]
81. (funny(mary) | ~old(mary)) & (~funny(mary) | old(mary)) [nnf transformation 23]
89. ~funny(X0) | tall(X0) [cnf transformation 31]
105. ~patient(mary) | ~creative(X0) [cnf transformation 38]
107. ~funny(X0) | brave(X0) | creative(X0) [cnf transformation 60]
108. creative(X0) | brave(X0) | curious(X0) [cnf transformation 60]
114. brave(X0) | patient(X0) [cnf transformation 39]
117. ~tall(X0) | ~brave(X0) [cnf transformation 62]
118. ~brave(X0) | old(X0) [cnf transformation 62]
133. funny(mary) | ~old(mary) [cnf transformation 81]
136. ~curious(mary) [cnf transformation 25]
181. 11 <=> patient(mary) [avatar definition]
185. 12 <=> tall(mary) [avatar definition]
186. tall(mary) <- (12) [avatar component clause 185]
207. 17 <=> ! [X0] : ~creative(X0) [avatar definition]
208. ~creative(X0) <- (17) [avatar component clause 207]
209. 17 | ~11 [avatar split clause 105,181,207]
278. 32 <=> old(mary) [avatar definition]
280. ~old(mary) <- (~32) [avatar component clause 278]
282. 33 <=> funny(mary) [avatar definition]
284. funny(mary) <- (33) [avatar component clause 282]
285. ~32 | 33 [avatar split clause 133,282,278]
296. old(X0) | patient(X0) [resolution 118,114]
297. patient(mary) <- (~32) [resolution 296,280]
301. 11 | 32 [avatar split clause 297,278,181]
307. brave(X0) | curious(X0) <- (17) [resolution 108,208]
309. old(X0) | curious(X0) <- (17) [resolution 307,118]
311. curious(mary) <- (17, ~32) [resolution 309,280]
313. $false <- (17, ~32) [subsumption resolution 311,136]
314. ~17 | 32 [avatar contradiction clause 313]
316. brave(mary) | creative(mary) <- (33) [resolution 284,107]
317. tall(mary) <- (33) [resolution 284,89]
319. 35 <=> creative(mary) [avatar definition]
321. creative(mary) <- (35) [avatar component clause 319]
323. 36 <=> brave(mary) [avatar definition]
324. ~brave(mary) <- (~36) [avatar component clause 323]
326. 35 | 36 | ~33 [avatar split clause 316,282,323,319]
327. 12 | ~33 [avatar split clause 317,282,185]
329. ~brave(mary) <- (12) [resolution 186,117]
333. ~36 | ~12 [avatar split clause 329,185,323]
339. patient(mary) <- (~36) [resolution 324,114]
342. 11 | 36 [avatar split clause 339,323,181]
344. $false <- (17, 35) [resolution 208,321]
345. ~17 | ~35 [avatar contradiction clause 344]
346. $false [avatar sat refutation 209,285,301,314,326,327,333,342,345]
% SZS output end Proof for 1755118863478904130819051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or strong is both generous and patient and vice versa. If someone is not calm then fred is not curious. Everyone who is generous or not old is humble or not funny and vice versa. Everyone who is both not curious and not rich is wise and vice versa. Everyone who is humble or wise is rich or funny. If alice is not brave then someone is both not wise and not patient and vice versa. Everyone who is both calm and old is not calm. If lucy is not strong then lucy is generous or creative and vice versa. If alice is both generous and not patient then someone is both not funny and not patient and vice versa. If someone is either wise or rich then lucy is either strong or tall. If lucy is either wise or quiet then someone is either not humble or funny and vice versa. Everyone who is either not creative or not humble is not wise or not curious and vice versa. If susan is both funny and not humble then someone is curious and vice versa. Everyone who is strong or humble is tall or kind and vice versa. If someone is not happy or patient then susan is happy or not happy. If mary is both not strong and calm then someone is both kind and not old. Someone is both not humble and generous. Someone is either wise or kind. Susan is either generous or not funny. Someone is either humble or old. Someone is not quiet. | Susan is kind. | neutral | (![X]:((~happy(X)|strong(X))<=>(generous(X)&patient(X))))&
((?[X]:(~calm(X)))=>(~curious(fred)))&
(![X]:((generous(X)|~old(X))<=>(humble(X)|~funny(X))))&
(![X]:((~curious(X)&~rich(X))<=>wise(X)))&
(![X]:((humble(X)|wise(X))=>(rich(X)|funny(X))))&
((~brave(alice))<=>(?[X]:((~wise(X)&~patient(X)))))&
(![X]:((calm(X)&old(X))=>~calm(X)))&
((~strong(lucy))<=>((generous(lucy)|creative(lucy))))&
(((generous(alice)&~patient(alice)))<=>(?[X]:((~funny(X)&~patient(X)))))&
((?[X]:((wise(X)<~>rich(X))))=>((strong(lucy)<~>tall(lucy))))&
(((wise(lucy)<~>quiet(lucy)))<=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~creative(X)<~>~humble(X))<=>(~wise(X)|~curious(X))))&
(((funny(susan)&~humble(susan)))<=>(?[X]:(curious(X))))&
(![X]:((strong(X)|humble(X))<=>(tall(X)|kind(X))))&
((?[X]:((~happy(X)|patient(X))))=>((happy(susan)|~happy(susan))))&
(((~strong(mary)&calm(mary)))=>(?[X]:((kind(X)&~old(X)))))&
(?[X]:((~humble(X)&generous(X))))&
(?[X]:((wise(X)<~>kind(X))))&
((generous(susan)<~>~funny(susan)))&
(?[X]:((humble(X)<~>old(X))))&
(?[X]:(~quiet(X))) | kind(susan) | [] | null | 0 |
If someone is either rich or not quiet then someone is not old or curious. If someone is both humble and brave then fred is both creative and not humble. Everyone who is both not patient and quiet is happy or tall. If lucy is quiet then someone is either old or strong and vice versa. Everyone who is not rich or brave is not happy or not calm and vice versa. If someone is either rich or funny then someone is funny or not kind and vice versa. Everyone who is old is both generous and not rich. Everyone who is not humble is either not patient or not happy and vice versa. Everyone who is tall or not creative is not patient and vice versa. Everyone who is calm is either not funny or calm and vice versa. Everyone who is either funny or happy is not rich or funny and vice versa. Everyone who is both happy and not funny is not wise or not funny. If fred is both funny and quiet then someone is either not wise or not curious. Everyone who is not wise or not strong is both tall and not generous and vice versa. If someone is either not curious or not brave then someone is not quiet. If mary is both not humble and strong then someone is either not creative or curious. Someone is either not curious or rich. Someone is rich or wise. Susan is patient. Paul is not kind or not strong. Fred is tall. Someone is generous or quiet. John is not brave or not calm. | John is happy. | contradiction | ((?[X]:((rich(X)<~>~quiet(X))))=>(?[X]:((~old(X)|curious(X)))))&
((?[X]:((humble(X)&brave(X))))=>((creative(fred)&~humble(fred))))&
(![X]:((~patient(X)&quiet(X))=>(happy(X)|tall(X))))&
((quiet(lucy))<=>(?[X]:((old(X)<~>strong(X)))))&
(![X]:((~rich(X)|brave(X))<=>(~happy(X)|~calm(X))))&
((?[X]:((rich(X)<~>funny(X))))<=>(?[X]:((funny(X)|~kind(X)))))&
(![X]:(old(X)=>(generous(X)&~rich(X))))&
(![X]:(~humble(X)<=>(~patient(X)<~>~happy(X))))&
(![X]:((tall(X)|~creative(X))<=>~patient(X)))&
(![X]:(calm(X)<=>(~funny(X)<~>calm(X))))&
(![X]:((funny(X)<~>happy(X))<=>(~rich(X)|funny(X))))&
(![X]:((happy(X)&~funny(X))=>(~wise(X)|~funny(X))))&
(((funny(fred)&quiet(fred)))=>(?[X]:((~wise(X)<~>~curious(X)))))&
(![X]:((~wise(X)|~strong(X))<=>(tall(X)&~generous(X))))&
((?[X]:((~curious(X)<~>~brave(X))))=>(?[X]:(~quiet(X))))&
(((~humble(mary)&strong(mary)))=>(?[X]:((~creative(X)<~>curious(X)))))&
(?[X]:((~curious(X)<~>rich(X))))&
(?[X]:((rich(X)|wise(X))))&
(patient(susan))&
((~kind(paul)|~strong(paul)))&
(tall(fred))&
(?[X]:((generous(X)|quiet(X))))&
((~brave(john)|~calm(john))) | happy(john) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7620535560480092069203106
% SZS output start Proof for 7620535560480092069203106
10. ! [X0] : (calm(X0) <=> (~funny(X0) <~> calm(X0))) [input p9]
11. ! [X0] : ((funny(X0) <~> happy(X0)) <=> (funny(X0) | ~rich(X0))) [input p10]
24. happy(john) [input hypothesis]
58. ! [X0] : ((calm(X0) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | ~calm(X0))) [nnf transformation 10]
59. ! [X0] : ((((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~funny(X0) & rich(X0))) & ((funny(X0) | ~rich(X0)) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0))))) [nnf transformation 11]
60. ! [X0] : ((((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~funny(X0) & rich(X0))) & (funny(X0) | ~rich(X0) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0))))) [flattening 59]
109. ~calm(X0) | funny(X0) | ~calm(X0) [cnf transformation 58]
110. calm(X0) | calm(X0) | funny(X0) [cnf transformation 58]
117. ~happy(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 60]
138. happy(john) [cnf transformation 24]
140. ~happy(X0) | ~funny(X0) [duplicate literal removal 117]
141. ~calm(X0) | funny(X0) [duplicate literal removal 109]
142. calm(X0) | funny(X0) [duplicate literal removal 110]
228. funny(X0) [subsumption resolution 141,142]
229. ~happy(X0) [subsumption resolution 140,228]
322. $false [subsumption resolution 138,229]
% SZS output end Proof for 7620535560480092069203106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and happy is happy and vice versa.
Everyone who is kind is both not patient and happy.
If lucy is not quiet or not tall then paul is either wise or brave and vice versa.
If paul is either wise or not happy then fred is not happy.
If someone is either happy or humble then someone is both not funny and strong and vice versa.
If mary is either not humble or patient then someone is kind or humble and vice versa.
Everyone who is quiet or patient is not tall or humble and vice versa.
Everyone who is not old is not quiet.
If someone is not kind or not rich then alice is not rich or not kind and vice versa.
Everyone who is both not curious and not happy is either not humble or happy and vice versa.
Everyone who is not brave or calm is wise.
If susan is both brave and not happy then someone is both not kind and patient and vice versa.
If someone is either not happy or not funny then paul is not quiet or not generous and vice versa.
Everyone who is quiet is calm or not kind and vice versa.
If someone is both kind and not curious then john is wise and vice versa.
Everyone who is calm is tall or not brave.
Someone is both old and not funny.
Fred is either wise or kind.
Susan is strong or not curious.
Someone is not generous.
Lucy is either tall or brave.
John is either not kind or wise.
Someone is not patient. | Alice is kind. | neutral | (![X]:((brave(X)&happy(X))<=>happy(X)))&
(![X]:(kind(X)=>(~patient(X)&happy(X))))&
(((~quiet(lucy)|~tall(lucy)))<=>((wise(paul)<~>brave(paul))))&
(((wise(paul)<~>~happy(paul)))=>(~happy(fred)))&
((?[X]:((happy(X)<~>humble(X))))<=>(?[X]:((~funny(X)&strong(X)))))&
(((~humble(mary)<~>patient(mary)))<=>(?[X]:((kind(X)|humble(X)))))&
(![X]:((quiet(X)|patient(X))<=>(~tall(X)|humble(X))))&
(![X]:(~old(X)=>~quiet(X)))&
((?[X]:((~kind(X)|~rich(X))))<=>((~rich(alice)|~kind(alice))))&
(![X]:((~curious(X)&~happy(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((~brave(X)|calm(X))=>wise(X)))&
(((brave(susan)&~happy(susan)))<=>(?[X]:((~kind(X)&patient(X)))))&
((?[X]:((~happy(X)<~>~funny(X))))<=>((~quiet(paul)|~generous(paul))))&
(![X]:(quiet(X)<=>(calm(X)|~kind(X))))&
((?[X]:((kind(X)&~curious(X))))<=>(wise(john)))&
(![X]:(calm(X)=>(tall(X)|~brave(X))))&
(?[X]:((old(X)&~funny(X))))&
((wise(fred)<~>kind(fred)))&
((strong(susan)|~curious(susan)))&
(?[X]:(~generous(X)))&
((tall(lucy)<~>brave(lucy)))&
((~kind(john)<~>wise(john)))&
(?[X]:(~patient(X))) | kind(alice) | [] | null | 0 |
Everyone who is generous is both not wise and calm and vice versa.
Everyone who is both kind and not brave is either not funny or rich and vice versa.
If alice is both generous and brave then someone is both not strong and happy.
Everyone who is either humble or not humble is either curious or calm.
If someone is either funny or not brave then paul is kind or not kind and vice versa.
Everyone who is quiet is not wise or not generous and vice versa.
Everyone who is creative is either not patient or not calm and vice versa.
If john is either not wise or not quiet then someone is tall and vice versa.
If someone is both rich and old then someone is wise or not tall.
If someone is not strong or kind then mary is not wise or not kind.
If paul is both happy and calm then someone is humble and vice versa.
If someone is both quiet and wise then someone is either not rich or funny.
If susan is not old or not patient then fred is brave and vice versa.
Everyone who is not strong or not calm is not quiet.
Everyone who is both brave and not strong is creative.
If mary is rich or generous then someone is not wise.
Alice is wise or patient.
Someone is not old or not curious.
Someone is both old and humble.
Susan is either not rich or rich.
Someone is creative or wise.
Paul is not generous.
Susan is humble.
Mary is either strong or not old. | Mary is curious. | contradiction | (![X]:(generous(X)<=>(~wise(X)&calm(X))))&
(![X]:((kind(X)&~brave(X))<=>(~funny(X)<~>rich(X))))&
(((generous(alice)&brave(alice)))=>(?[X]:((~strong(X)&happy(X)))))&
(![X]:((humble(X)<~>~humble(X))=>(curious(X)<~>calm(X))))&
((?[X]:((funny(X)<~>~brave(X))))<=>((kind(paul)|~kind(paul))))&
(![X]:(quiet(X)<=>(~wise(X)|~generous(X))))&
(![X]:(creative(X)<=>(~patient(X)<~>~calm(X))))&
(((~wise(john)<~>~quiet(john)))<=>(?[X]:(tall(X))))&
((?[X]:((rich(X)&old(X))))=>(?[X]:((wise(X)|~tall(X)))))&
((?[X]:((~strong(X)|kind(X))))=>((~wise(mary)|~kind(mary))))&
(((happy(paul)&calm(paul)))<=>(?[X]:(humble(X))))&
((?[X]:((quiet(X)&wise(X))))=>(?[X]:((~rich(X)<~>funny(X)))))&
(((~old(susan)|~patient(susan)))<=>(brave(fred)))&
(![X]:((~strong(X)|~calm(X))=>~quiet(X)))&
(![X]:((brave(X)&~strong(X))=>creative(X)))&
(((rich(mary)|generous(mary)))=>(?[X]:(~wise(X))))&
((wise(alice)|patient(alice)))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:((old(X)&humble(X))))&
((~rich(susan)<~>rich(susan)))&
(?[X]:((creative(X)|wise(X))))&
(~generous(paul))&
(humble(susan))&
((strong(mary)<~>~old(mary))) | curious(mary) | [
"p0",
"p3",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5809341229357117941796256
% SZS output start Proof for 5809341229357117941796256
1. ! [X0] : (generous(X0) <=> (calm(X0) & ~wise(X0))) [input p0]
4. ! [X0] : ((humble(X0) <~> ~humble(X0)) => (curious(X0) <~> calm(X0))) [input p3]
6. ! [X0] : (quiet(X0) <=> (~generous(X0) | ~wise(X0))) [input p5]
14. ! [X0] : ((~calm(X0) | ~strong(X0)) => ~quiet(X0)) [input p13]
25. curious(mary) [input hypothesis]
31. ! [X0] : ((curious(X0) <~> calm(X0)) | (humble(X0) <=> ~humble(X0))) [ennf transformation 4]
37. ! [X0] : (~quiet(X0) | (calm(X0) & strong(X0))) [ennf transformation 14]
41. ! [X0] : ((generous(X0) | (~calm(X0) | wise(X0))) & ((calm(X0) & ~wise(X0)) | ~generous(X0))) [nnf transformation 1]
42. ! [X0] : ((generous(X0) | ~calm(X0) | wise(X0)) & ((calm(X0) & ~wise(X0)) | ~generous(X0))) [flattening 41]
47. ! [X0] : (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) [nnf transformation 31]
53. ! [X0] : ((quiet(X0) | (generous(X0) & wise(X0))) & ((~generous(X0) | ~wise(X0)) | ~quiet(X0))) [nnf transformation 6]
54. ! [X0] : ((quiet(X0) | (generous(X0) & wise(X0))) & (~generous(X0) | ~wise(X0) | ~quiet(X0))) [flattening 53]
85. ~generous(X0) | calm(X0) [cnf transformation 42]
97. ~calm(X0) | ~curious(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 47]
98. ~calm(X0) | ~curious(X0) | humble(X0) | humble(X0) [cnf transformation 47]
107. quiet(X0) | generous(X0) [cnf transformation 54]
126. ~quiet(X0) | calm(X0) [cnf transformation 37]
141. curious(mary) [cnf transformation 25]
144. ~calm(X0) | ~curious(X0) | ~humble(X0) [duplicate literal removal 97]
145. ~calm(X0) | ~curious(X0) | humble(X0) [duplicate literal removal 98]
164. ~curious(X0) | ~calm(X0) [subsumption resolution 144,145]
337. calm(X0) | generous(X0) [resolution 126,107]
339. calm(X0) [subsumption resolution 337,85]
340. ~calm(mary) [resolution 164,141]
341. $false [subsumption resolution 340,339]
% SZS output end Proof for 5809341229357117941796256
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or wise then someone is either curious or not strong. If alice is either old or not creative then fred is both not rich and creative. Everyone who is not tall or kind is not happy or not old and vice versa. Everyone who is both strong and humble is not humble and vice versa. If mary is wise or strong then lucy is both curious and not rich and vice versa. If someone is both not tall and not wise then someone is not funny and vice versa. Everyone who is not strong or not generous is not old or patient. If someone is both not patient and happy then someone is either wise or happy. If mary is happy then mary is creative or not curious. If paul is patient or not wise then someone is not happy and vice versa. If susan is not happy or rich then john is not curious. Everyone who is creative is calm or strong. If john is quiet then john is not humble. Everyone who is either not curious or creative is both rich and not creative. Everyone who is generous or not quiet is both not tall and not rich and vice versa. Everyone who is funny is both quiet and wise. Someone is either not wise or creative. Someone is either rich or not calm. Fred is both not patient and not quiet. John is curious. Someone is not patient. Paul is old. Someone is not generous or not rich. | Lucy is curious. | neutral | ((?[X]:((creative(X)|wise(X))))=>(?[X]:((curious(X)<~>~strong(X)))))&
(((old(alice)<~>~creative(alice)))=>((~rich(fred)&creative(fred))))&
(![X]:((~tall(X)|kind(X))<=>(~happy(X)|~old(X))))&
(![X]:((strong(X)&humble(X))<=>~humble(X)))&
(((wise(mary)|strong(mary)))<=>((curious(lucy)&~rich(lucy))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~strong(X)|~generous(X))=>(~old(X)|patient(X))))&
((?[X]:((~patient(X)&happy(X))))=>(?[X]:((wise(X)<~>happy(X)))))&
((happy(mary))=>((creative(mary)|~curious(mary))))&
(((patient(paul)|~wise(paul)))<=>(?[X]:(~happy(X))))&
(((~happy(susan)|rich(susan)))=>(~curious(john)))&
(![X]:(creative(X)=>(calm(X)|strong(X))))&
((quiet(john))=>(~humble(john)))&
(![X]:((~curious(X)<~>creative(X))=>(rich(X)&~creative(X))))&
(![X]:((generous(X)|~quiet(X))<=>(~tall(X)&~rich(X))))&
(![X]:(funny(X)=>(quiet(X)&wise(X))))&
(?[X]:((~wise(X)<~>creative(X))))&
(?[X]:((rich(X)<~>~calm(X))))&
((~patient(fred)&~quiet(fred)))&
(curious(john))&
(?[X]:(~patient(X)))&
(old(paul))&
(?[X]:((~generous(X)|~rich(X)))) | curious(lucy) | [] | null | 0 |
If someone is not humble or not kind then lucy is both not humble and not funny.
Everyone who is not kind or strong is humble or quiet and vice versa.
If mary is old or generous then someone is tall and vice versa.
Everyone who is quiet or kind is brave and vice versa.
If paul is both humble and not strong then someone is old or kind and vice versa.
Everyone who is humble is either humble or not wise.
Everyone who is either not wise or quiet is not kind.
If susan is either tall or wise then paul is both quiet and old.
Everyone who is both rich and old is either not rich or not patient and vice versa.
Everyone who is not strong is tall and vice versa.
Everyone who is both curious and not patient is either patient or strong.
If someone is not strong then someone is either funny or not humble and vice versa.
Everyone who is not kind or calm is both not quiet and rich.
Everyone who is not brave is not quiet or old and vice versa.
Everyone who is either not patient or humble is not happy or not kind and vice versa.
If fred is either not wise or not calm then john is not generous or wise and vice versa.
Someone is not creative or not happy.
Paul is wise or not funny.
Someone is not patient.
Someone is both generous and calm.
John is not quiet.
Someone is either kind or funny.
Susan is either curious or rich.
Someone is not patient or not creative. | John is patient. | entailment | ((?[X]:((~humble(X)|~kind(X))))=>((~humble(lucy)&~funny(lucy))))&
(![X]:((~kind(X)|strong(X))<=>(humble(X)|quiet(X))))&
(((old(mary)|generous(mary)))<=>(?[X]:(tall(X))))&
(![X]:((quiet(X)|kind(X))<=>brave(X)))&
(((humble(paul)&~strong(paul)))<=>(?[X]:((old(X)|kind(X)))))&
(![X]:(humble(X)=>(humble(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>quiet(X))=>~kind(X)))&
(((tall(susan)<~>wise(susan)))=>((quiet(paul)&old(paul))))&
(![X]:((rich(X)&old(X))<=>(~rich(X)<~>~patient(X))))&
(![X]:(~strong(X)<=>tall(X)))&
(![X]:((curious(X)&~patient(X))=>(patient(X)<~>strong(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((funny(X)<~>~humble(X)))))&
(![X]:((~kind(X)|calm(X))=>(~quiet(X)&rich(X))))&
(![X]:(~brave(X)<=>(~quiet(X)|old(X))))&
(![X]:((~patient(X)<~>humble(X))<=>(~happy(X)|~kind(X))))&
(((~wise(fred)<~>~calm(fred)))<=>((~generous(john)|wise(john))))&
(?[X]:((~creative(X)|~happy(X))))&
((wise(paul)|~funny(paul)))&
(?[X]:(~patient(X)))&
(?[X]:((generous(X)&calm(X))))&
(~quiet(john))&
(?[X]:((kind(X)<~>funny(X))))&
((curious(susan)<~>rich(susan)))&
(?[X]:((~patient(X)|~creative(X)))) | patient(john) | [
"p1",
"p3",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4349687090829777793459903
% SZS output start Proof for 4349687090829777793459903
2. ! [X0] : ((strong(X0) | ~kind(X0)) <=> (quiet(X0) | humble(X0))) [input p1]
4. ! [X0] : ((kind(X0) | quiet(X0)) <=> brave(X0)) [input p3]
14. ! [X0] : (~brave(X0) <=> (old(X0) | ~quiet(X0))) [input p13]
15. ! [X0] : ((~patient(X0) <~> humble(X0)) <=> (~kind(X0) | ~happy(X0))) [input p14]
21. ~quiet(john) [input p20]
25. ~patient(john) [input hypothesis]
36. ! [X0] : (((strong(X0) | ~kind(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (~strong(X0) & kind(X0)))) [nnf transformation 2]
37. ! [X0] : ((strong(X0) | ~kind(X0) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | (~strong(X0) & kind(X0)))) [flattening 36]
43. ! [X0] : (((kind(X0) | quiet(X0)) | ~brave(X0)) & (brave(X0) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 4]
44. ! [X0] : ((kind(X0) | quiet(X0) | ~brave(X0)) & (brave(X0) | (~kind(X0) & ~quiet(X0)))) [flattening 43]
62. ! [X0] : ((~brave(X0) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | brave(X0))) [nnf transformation 14]
63. ! [X0] : ((~brave(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | brave(X0))) [flattening 62]
64. ! [X0] : ((((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0))))) [nnf transformation 15]
65. ! [X0] : ((((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0))))) [flattening 64]
80. quiet(X0) | humble(X0) | kind(X0) [cnf transformation 37]
88. ~kind(X0) | brave(X0) [cnf transformation 44]
122. ~brave(X0) | quiet(X0) [cnf transformation 63]
129. ~humble(X0) | patient(X0) | kind(X0) [cnf transformation 65]
140. ~quiet(john) [cnf transformation 21]
145. ~patient(john) [cnf transformation 25]
359. humble(john) | kind(john) [resolution 80,140]
382. 35 <=> kind(john) [avatar definition]
383. ~kind(john) <- (~35) [avatar component clause 382]
384. kind(john) <- (35) [avatar component clause 382]
386. 36 <=> humble(john) [avatar definition]
388. humble(john) <- (36) [avatar component clause 386]
389. 35 | 36 [avatar split clause 359,386,382]
413. brave(john) <- (35) [resolution 384,88]
606. quiet(john) <- (35) [resolution 413,122]
607. $false <- (35) [subsumption resolution 606,140]
608. ~35 [avatar contradiction clause 607]
615. patient(john) | kind(john) <- (36) [resolution 388,129]
618. kind(john) <- (36) [subsumption resolution 615,145]
619. $false <- (~35, 36) [subsumption resolution 618,383]
620. 35 | ~36 [avatar contradiction clause 619]
622. $false [avatar sat refutation 389,608,620]
% SZS output end Proof for 4349687090829777793459903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or brave is humble and vice versa. Everyone who is either not old or tall is both not quiet and wise and vice versa. Everyone who is both not brave and curious is either brave or wise. Everyone who is both rich and not generous is not curious and vice versa. If john is calm then someone is creative or not happy. If susan is funny then paul is quiet or not tall. Everyone who is not calm is happy or not creative and vice versa. Everyone who is either funny or generous is patient. Everyone who is not curious is both brave and not kind. Everyone who is both not wise and not humble is patient or rich and vice versa. If someone is not wise or brave then john is both strong and patient and vice versa. Everyone who is either not happy or wise is both not old and not humble. If someone is either tall or calm then lucy is happy and vice versa. If lucy is not wise then paul is not funny or not old and vice versa. Everyone who is not old is not tall or wise. Someone is both not happy and creative. Someone is either not strong or rich. Mary is either not humble or rich. Someone is generous or tall. Someone is not calm. | Paul is not happy. | entailment | (![X]:((funny(X)|brave(X))<=>humble(X)))&
(![X]:((~old(X)<~>tall(X))<=>(~quiet(X)&wise(X))))&
(![X]:((~brave(X)&curious(X))=>(brave(X)<~>wise(X))))&
(![X]:((rich(X)&~generous(X))<=>~curious(X)))&
((calm(john))=>(?[X]:((creative(X)|~happy(X)))))&
((funny(susan))=>((quiet(paul)|~tall(paul))))&
(![X]:(~calm(X)<=>(happy(X)|~creative(X))))&
(![X]:((funny(X)<~>generous(X))=>patient(X)))&
(![X]:(~curious(X)=>(brave(X)&~kind(X))))&
(![X]:((~wise(X)&~humble(X))<=>(patient(X)|rich(X))))&
((?[X]:((~wise(X)|brave(X))))<=>((strong(john)&patient(john))))&
(![X]:((~happy(X)<~>wise(X))=>(~old(X)&~humble(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(happy(lucy)))&
((~wise(lucy))<=>((~funny(paul)|~old(paul))))&
(![X]:(~old(X)=>(~tall(X)|wise(X))))&
(?[X]:((~happy(X)&creative(X))))&
(?[X]:((~strong(X)<~>rich(X))))&
((~humble(mary)<~>rich(mary)))&
(?[X]:((generous(X)|tall(X))))&
(?[X]:(~calm(X))) | ~happy(paul) | [
"p0",
"p2",
"p8",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 305632365204295867310242
% SZS output start Proof for 305632365204295867310242
1. ! [X0] : ((brave(X0) | funny(X0)) <=> humble(X0)) [input p0]
3. ! [X0] : ((curious(X0) & ~brave(X0)) => (brave(X0) <~> wise(X0))) [input p2]
9. ! [X0] : (~curious(X0) => (~kind(X0) & brave(X0))) [input p8]
10. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (rich(X0) | patient(X0))) [input p9]
11. ? [X0] : (brave(X0) | ~wise(X0)) <=> (patient(john) & strong(john)) [input p10]
12. ! [X0] : ((~happy(X0) <~> wise(X0)) => (~humble(X0) & ~old(X0))) [input p11]
14. ~wise(lucy) <=> (~old(paul) | ~funny(paul)) [input p13]
21. happy(paul) [input hypothesis]
22. ! [X0] : (~curious(X0) => brave(X0)) [pure predicate removal 9]
23. ! [X0] : ((brave(X0) <~> wise(X0)) | (~curious(X0) | brave(X0))) [ennf transformation 3]
24. ! [X0] : ((brave(X0) <~> wise(X0)) | ~curious(X0) | brave(X0)) [flattening 23]
29. ! [X0] : (brave(X0) | curious(X0)) [ennf transformation 22]
30. ! [X0] : ((~humble(X0) & ~old(X0)) | (~happy(X0) <=> wise(X0))) [ennf transformation 12]
33. ! [X0] : (((brave(X0) | funny(X0)) | ~humble(X0)) & (humble(X0) | (~brave(X0) & ~funny(X0)))) [nnf transformation 1]
34. ! [X0] : ((brave(X0) | funny(X0) | ~humble(X0)) & (humble(X0) | (~brave(X0) & ~funny(X0)))) [flattening 33]
37. ! [X0] : (((~wise(X0) | ~brave(X0)) & (wise(X0) | brave(X0))) | ~curious(X0) | brave(X0)) [nnf transformation 24]
45. ! [X0] : (((~humble(X0) & ~wise(X0)) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | (humble(X0) | wise(X0)))) [nnf transformation 10]
46. ! [X0] : (((~humble(X0) & ~wise(X0)) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | humble(X0) | wise(X0))) [flattening 45]
47. (? [X0] : (brave(X0) | ~wise(X0)) | (~patient(john) | ~strong(john))) & ((patient(john) & strong(john)) | ! [X0] : (~brave(X0) & wise(X0))) [nnf transformation 11]
48. (? [X0] : (brave(X0) | ~wise(X0)) | ~patient(john) | ~strong(john)) & ((patient(john) & strong(john)) | ! [X0] : (~brave(X0) & wise(X0))) [flattening 47]
49. (? [X0] : (brave(X0) | ~wise(X0)) | ~patient(john) | ~strong(john)) & ((patient(john) & strong(john)) | ! [X1] : (~brave(X1) & wise(X1))) [rectify 48]
50. ? [X0] : (brave(X0) | ~wise(X0)) => (brave(sK1) | ~wise(sK1)) [choice axiom]
51. ((brave(sK1) | ~wise(sK1)) | ~patient(john) | ~strong(john)) & ((patient(john) & strong(john)) | ! [X1] : (~brave(X1) & wise(X1))) [skolemisation 49,50]
52. ! [X0] : ((~humble(X0) & ~old(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0)))) [nnf transformation 30]
57. (~wise(lucy) | (old(paul) & funny(paul))) & ((~old(paul) | ~funny(paul)) | wise(lucy)) [nnf transformation 14]
58. (~wise(lucy) | (old(paul) & funny(paul))) & (~old(paul) | ~funny(paul) | wise(lucy)) [flattening 57]
70. ~brave(X0) | humble(X0) [cnf transformation 34]
78. wise(X0) | brave(X0) | ~curious(X0) | brave(X0) [cnf transformation 37]
90. curious(X0) | brave(X0) [cnf transformation 29]
92. ~patient(X0) | ~wise(X0) [cnf transformation 46]
94. ~patient(X0) | ~humble(X0) [cnf transformation 46]
98. patient(john) | wise(X1) [cnf transformation 51]
102. ~happy(X0) | ~old(X0) | ~wise(X0) [cnf transformation 52]
111. ~wise(lucy) | old(paul) [cnf transformation 58]
121. happy(paul) [cnf transformation 21]
122. ~curious(X0) | brave(X0) | wise(X0) [duplicate literal removal 78]
154. 8 <=> patient(john) [avatar definition]
155. patient(john) <- (8) [avatar component clause 154]
171. 12 <=> ! [X1] : wise(X1) [avatar definition]
172. wise(X1) <- (12) [avatar component clause 171]
173. 12 | 8 [avatar split clause 98,154,171]
199. 18 <=> old(paul) [avatar definition]
201. old(paul) <- (18) [avatar component clause 199]
203. 19 <=> wise(lucy) [avatar definition]
205. ~wise(lucy) <- (~19) [avatar component clause 203]
206. 18 | ~19 [avatar split clause 111,203,199]
296. $false <- (12, ~19) [subsumption resolution 205,172]
297. ~12 | 19 [avatar contradiction clause 296]
300. ~humble(john) <- (8) [resolution 155,94]
301. ~wise(john) <- (8) [resolution 155,92]
332. ~old(paul) | ~wise(paul) [resolution 102,121]
334. ~wise(paul) <- (18) [subsumption resolution 332,201]
341. brave(X0) | wise(X0) | brave(X0) [resolution 122,90]
345. wise(X0) | brave(X0) [duplicate literal removal 341]
401. brave(john) <- (8) [resolution 345,301]
408. humble(john) <- (8) [resolution 401,70]
409. $false <- (8) [subsumption resolution 408,300]
410. ~8 [avatar contradiction clause 409]
431. $false <- (12, 18) [resolution 172,334]
432. ~12 | ~18 [avatar contradiction clause 431]
433. $false [avatar sat refutation 173,206,297,410,432]
% SZS output end Proof for 305632365204295867310242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious or tall then paul is either patient or creative.
If alice is strong or not funny then john is both rich and not kind.
Everyone who is kind or not rich is both not tall and not quiet.
Everyone who is either not humble or strong is kind or brave and vice versa.
If someone is not kind or quiet then paul is both tall and not tall and vice versa.
If paul is both humble and not tall then john is humble or not calm and vice versa.
If someone is brave then someone is both not wise and calm and vice versa.
Everyone who is either funny or old is not tall and vice versa.
Everyone who is not humble is not creative or generous and vice versa.
If someone is not tall then someone is calm and vice versa.
If someone is either old or wise then mary is either tall or not calm.
Everyone who is not humble or generous is both kind and not patient.
If alice is both not old and not curious then susan is not quiet.
Everyone who is not happy or not quiet is both not happy and not wise and vice versa.
Everyone who is not tall or not brave is not quiet or not rich and vice versa.
Everyone who is not generous or calm is both not creative and generous.
Mary is either not creative or curious.
Mary is either not generous or rich.
Someone is not rich or not curious. | John is not rich. | neutral | ((?[X]:((curious(X)|tall(X))))=>((patient(paul)<~>creative(paul))))&
(((strong(alice)|~funny(alice)))=>((rich(john)&~kind(john))))&
(![X]:((kind(X)|~rich(X))=>(~tall(X)&~quiet(X))))&
(![X]:((~humble(X)<~>strong(X))<=>(kind(X)|brave(X))))&
((?[X]:((~kind(X)|quiet(X))))<=>((tall(paul)&~tall(paul))))&
(((humble(paul)&~tall(paul)))<=>((humble(john)|~calm(john))))&
((?[X]:(brave(X)))<=>(?[X]:((~wise(X)&calm(X)))))&
(![X]:((funny(X)<~>old(X))<=>~tall(X)))&
(![X]:(~humble(X)<=>(~creative(X)|generous(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(calm(X))))&
((?[X]:((old(X)<~>wise(X))))=>((tall(mary)<~>~calm(mary))))&
(![X]:((~humble(X)|generous(X))=>(kind(X)&~patient(X))))&
(((~old(alice)&~curious(alice)))=>(~quiet(susan)))&
(![X]:((~happy(X)|~quiet(X))<=>(~happy(X)&~wise(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~quiet(X)|~rich(X))))&
(![X]:((~generous(X)|calm(X))=>(~creative(X)&generous(X))))&
((~creative(mary)<~>curious(mary)))&
((~generous(mary)<~>rich(mary)))&
(?[X]:((~rich(X)|~curious(X)))) | ~rich(john) | [] | null | 0 |
If john is either generous or not old then someone is both humble and creative.
If someone is both not humble and not brave then fred is not creative or strong.
If susan is not humble then someone is not tall or calm and vice versa.
If someone is either not patient or kind then susan is both not rich and not wise.
If john is kind or old then mary is not kind or not curious and vice versa.
If someone is not calm or not tall then someone is both patient and not quiet and vice versa.
Everyone who is not creative or not happy is not funny or humble and vice versa.
If alice is curious then alice is not wise or tall.
If john is both not quiet and kind then someone is calm or not brave.
Everyone who is either not kind or creative is not generous or not brave.
If susan is both not curious and strong then paul is either not creative or not strong.
Everyone who is both not happy and not calm is rich or not calm and vice versa.
If alice is not creative or not wise then someone is either strong or funny.
If paul is either humble or curious then fred is both generous and happy.
If alice is not wise then someone is both not curious and calm.
If someone is both not strong and quiet then someone is both not calm and not rich.
John is not quiet or not tall.
John is both not happy and wise.
Someone is both creative and not funny.
Someone is either strong or not wise.
Mary is either not creative or not calm.
Someone is patient or generous.
Alice is both old and not wise.
Someone is either rich or quiet. | Fred is happy. | neutral | (((generous(john)<~>~old(john)))=>(?[X]:((humble(X)&creative(X)))))&
((?[X]:((~humble(X)&~brave(X))))=>((~creative(fred)|strong(fred))))&
((~humble(susan))<=>(?[X]:((~tall(X)|calm(X)))))&
((?[X]:((~patient(X)<~>kind(X))))=>((~rich(susan)&~wise(susan))))&
(((kind(john)|old(john)))<=>((~kind(mary)|~curious(mary))))&
((?[X]:((~calm(X)|~tall(X))))<=>(?[X]:((patient(X)&~quiet(X)))))&
(![X]:((~creative(X)|~happy(X))<=>(~funny(X)|humble(X))))&
((curious(alice))=>((~wise(alice)|tall(alice))))&
(((~quiet(john)&kind(john)))=>(?[X]:((calm(X)|~brave(X)))))&
(![X]:((~kind(X)<~>creative(X))=>(~generous(X)|~brave(X))))&
(((~curious(susan)&strong(susan)))=>((~creative(paul)<~>~strong(paul))))&
(![X]:((~happy(X)&~calm(X))<=>(rich(X)|~calm(X))))&
(((~creative(alice)|~wise(alice)))=>(?[X]:((strong(X)<~>funny(X)))))&
(((humble(paul)<~>curious(paul)))=>((generous(fred)&happy(fred))))&
((~wise(alice))=>(?[X]:((~curious(X)&calm(X)))))&
((?[X]:((~strong(X)&quiet(X))))=>(?[X]:((~calm(X)&~rich(X)))))&
((~quiet(john)|~tall(john)))&
((~happy(john)&wise(john)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((strong(X)<~>~wise(X))))&
((~creative(mary)<~>~calm(mary)))&
(?[X]:((patient(X)|generous(X))))&
((old(alice)&~wise(alice)))&
(?[X]:((rich(X)<~>quiet(X)))) | happy(fred) | [] | null | 0 |
Everyone who is both kind and funny is either not strong or creative. If fred is generous then paul is both old and patient. Everyone who is both not happy and wise is brave. Everyone who is either kind or not strong is either curious or funny and vice versa. If someone is tall or not strong then john is both not humble and curious. If someone is either not calm or not quiet then paul is both tall and not kind and vice versa. Everyone who is both generous and not strong is not patient or not humble and vice versa. If susan is not brave then paul is patient and vice versa. If alice is both not humble and quiet then someone is old and vice versa. Everyone who is old or strong is both not creative and not strong and vice versa. Everyone who is either funny or not rich is both not curious and generous and vice versa. If alice is not quiet or not funny then someone is not calm or quiet and vice versa. If someone is wise then lucy is either brave or quiet. If someone is both not humble and not tall then someone is either not tall or not quiet. Everyone who is both not kind and kind is not tall. If mary is either not curious or old then someone is both not brave and not quiet and vice versa. Someone is both generous and not strong. Alice is both not strong and not patient. Someone is not curious or not creative. Susan is either rich or not old. Someone is either patient or not generous. Paul is rich. Paul is curious. | Susan is curious. | neutral | (![X]:((kind(X)&funny(X))=>(~strong(X)<~>creative(X))))&
((generous(fred))=>((old(paul)&patient(paul))))&
(![X]:((~happy(X)&wise(X))=>brave(X)))&
(![X]:((kind(X)<~>~strong(X))<=>(curious(X)<~>funny(X))))&
((?[X]:((tall(X)|~strong(X))))=>((~humble(john)&curious(john))))&
((?[X]:((~calm(X)<~>~quiet(X))))<=>((tall(paul)&~kind(paul))))&
(![X]:((generous(X)&~strong(X))<=>(~patient(X)|~humble(X))))&
((~brave(susan))<=>(patient(paul)))&
(((~humble(alice)&quiet(alice)))<=>(?[X]:(old(X))))&
(![X]:((old(X)|strong(X))<=>(~creative(X)&~strong(X))))&
(![X]:((funny(X)<~>~rich(X))<=>(~curious(X)&generous(X))))&
(((~quiet(alice)|~funny(alice)))<=>(?[X]:((~calm(X)|quiet(X)))))&
((?[X]:(wise(X)))=>((brave(lucy)<~>quiet(lucy))))&
((?[X]:((~humble(X)&~tall(X))))=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(![X]:((~kind(X)&kind(X))=>~tall(X)))&
(((~curious(mary)<~>old(mary)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
(?[X]:((generous(X)&~strong(X))))&
((~strong(alice)&~patient(alice)))&
(?[X]:((~curious(X)|~creative(X))))&
((rich(susan)<~>~old(susan)))&
(?[X]:((patient(X)<~>~generous(X))))&
(rich(paul))&
(curious(paul)) | curious(susan) | [] | null | 0 |
Everyone who is patient is not funny and vice versa.
If someone is calm or brave then someone is not curious or not calm and vice versa.
Everyone who is not quiet is either not wise or not patient and vice versa.
Everyone who is happy or curious is either curious or not wise and vice versa.
Everyone who is either not calm or strong is tall or curious and vice versa.
If paul is either not old or not humble then someone is both not happy and not generous and vice versa.
Everyone who is rich is happy or not rich and vice versa.
If someone is brave or kind then mary is both funny and not patient and vice versa.
If lucy is not brave or not kind then someone is both creative and rich.
Everyone who is generous or kind is either not rich or not strong and vice versa.
If someone is either humble or not quiet then someone is patient or old.
If someone is both not tall and not strong then someone is not tall.
Everyone who is rich or funny is not happy or calm and vice versa.
Everyone who is either not strong or curious is either not quiet or not curious.
Everyone who is kind or not kind is kind.
Everyone who is humble is calm or kind and vice versa.
Someone is creative.
Fred is either not strong or creative.
Fred is brave.
Someone is not generous or not brave.
Someone is not humble or happy. | Fred is curious. | contradiction | (![X]:(patient(X)<=>~funny(X)))&
((?[X]:((calm(X)|brave(X))))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:(~quiet(X)<=>(~wise(X)<~>~patient(X))))&
(![X]:((happy(X)|curious(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((~calm(X)<~>strong(X))<=>(tall(X)|curious(X))))&
(((~old(paul)<~>~humble(paul)))<=>(?[X]:((~happy(X)&~generous(X)))))&
(![X]:(rich(X)<=>(happy(X)|~rich(X))))&
((?[X]:((brave(X)|kind(X))))<=>((funny(mary)&~patient(mary))))&
(((~brave(lucy)|~kind(lucy)))=>(?[X]:((creative(X)&rich(X)))))&
(![X]:((generous(X)|kind(X))<=>(~rich(X)<~>~strong(X))))&
((?[X]:((humble(X)<~>~quiet(X))))=>(?[X]:((patient(X)|old(X)))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:(~tall(X))))&
(![X]:((rich(X)|funny(X))<=>(~happy(X)|calm(X))))&
(![X]:((~strong(X)<~>curious(X))=>(~quiet(X)<~>~curious(X))))&
(![X]:((kind(X)|~kind(X))=>kind(X)))&
(![X]:(humble(X)<=>(calm(X)|kind(X))))&
(?[X]:(creative(X)))&
((~strong(fred)<~>creative(fred)))&
(brave(fred))&
(?[X]:((~generous(X)|~brave(X))))&
(?[X]:((~humble(X)|happy(X)))) | curious(fred) | [
"p4",
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 352654251130218852724260
% SZS output start Proof for 352654251130218852724260
5. ! [X0] : ((~calm(X0) <~> strong(X0)) <=> (curious(X0) | tall(X0))) [input p4]
7. ! [X0] : (rich(X0) <=> (~rich(X0) | happy(X0))) [input p6]
10. ! [X0] : ((kind(X0) | generous(X0)) <=> (~rich(X0) <~> ~strong(X0))) [input p9]
13. ! [X0] : ((funny(X0) | rich(X0)) <=> (calm(X0) | ~happy(X0))) [input p12]
15. ! [X0] : ((~kind(X0) | kind(X0)) => kind(X0)) [input p14]
22. curious(fred) [input hypothesis]
30. ! [X0] : (kind(X0) | (kind(X0) & ~kind(X0))) [ennf transformation 15]
40. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (~curious(X0) & ~tall(X0))) & ((curious(X0) | tall(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [nnf transformation 5]
41. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (~curious(X0) & ~tall(X0))) & (curious(X0) | tall(X0) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [flattening 40]
46. ! [X0] : ((rich(X0) | (rich(X0) & ~happy(X0))) & ((~rich(X0) | happy(X0)) | ~rich(X0))) [nnf transformation 7]
47. ! [X0] : ((rich(X0) | (rich(X0) & ~happy(X0))) & (~rich(X0) | happy(X0) | ~rich(X0))) [flattening 46]
55. ! [X0] : (((kind(X0) | generous(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~kind(X0) & ~generous(X0)))) [nnf transformation 10]
56. ! [X0] : ((kind(X0) | generous(X0) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~kind(X0) & ~generous(X0)))) [flattening 55]
64. ! [X0] : (((funny(X0) | rich(X0)) | (~calm(X0) & happy(X0))) & ((calm(X0) | ~happy(X0)) | (~funny(X0) & ~rich(X0)))) [nnf transformation 13]
65. ! [X0] : ((funny(X0) | rich(X0) | (~calm(X0) & happy(X0))) & (calm(X0) | ~happy(X0) | (~funny(X0) & ~rich(X0)))) [flattening 64]
95. ~curious(X0) | ~calm(X0) | strong(X0) [cnf transformation 41]
104. ~rich(X0) | happy(X0) | ~rich(X0) [cnf transformation 47]
106. rich(X0) | rich(X0) [cnf transformation 47]
117. ~strong(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 56]
125. calm(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 65]
134. kind(X0) | kind(X0) [cnf transformation 30]
144. curious(fred) [cnf transformation 22]
145. kind(X0) [duplicate literal removal 134]
148. ~rich(X0) | happy(X0) [duplicate literal removal 104]
149. rich(X0) [duplicate literal removal 106]
153. 1 <=> ! [X1] : calm(X1) [avatar definition]
154. calm(X1) <- (1) [avatar component clause 153]
209. happy(X0) [subsumption resolution 148,149]
250. ~kind(X0) | ~strong(X0) [subsumption resolution 117,149]
277. calm(X0) | ~rich(X0) [subsumption resolution 125,209]
278. calm(X0) [subsumption resolution 277,149]
279. 1 [avatar split clause 278,153]
307. ~strong(X0) [resolution 250,145]
330. ~calm(fred) | strong(fred) [resolution 95,144]
331. strong(fred) <- (1) [subsumption resolution 330,154]
334. $false <- (1) [subsumption resolution 331,307]
335. ~1 [avatar contradiction clause 334]
338. $false [avatar sat refutation 279,335]
% SZS output end Proof for 352654251130218852724260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is rich or humble then mary is not creative or rich and vice versa.
Everyone who is either not calm or patient is either not rich or humble and vice versa.
Everyone who is either patient or kind is either not funny or not kind and vice versa.
Everyone who is not patient is either not rich or not happy.
Everyone who is brave is either not wise or calm and vice versa.
Everyone who is brave is not patient or not wise.
Everyone who is either generous or old is both rich and creative.
Everyone who is kind is either kind or rich and vice versa.
Everyone who is strong is either not kind or not quiet.
Everyone who is both quiet and wise is both humble and not kind.
Everyone who is not creative or not brave is both generous and curious and vice versa.
Everyone who is either old or brave is wise or not creative and vice versa.
If john is not brave then someone is not brave or not curious and vice versa.
If someone is curious or not calm then someone is both happy and not old.
Everyone who is not funny or old is either funny or not quiet.
If someone is not tall then alice is either brave or not humble.
Someone is not humble.
Someone is old or not funny.
Paul is brave or generous.
Paul is either kind or wise.
Someone is both not wise and curious.
Someone is happy or kind.
Alice is not creative or happy. | John is old. | entailment | (((rich(john)|humble(john)))<=>((~creative(mary)|rich(mary))))&
(![X]:((~calm(X)<~>patient(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((patient(X)<~>kind(X))<=>(~funny(X)<~>~kind(X))))&
(![X]:(~patient(X)=>(~rich(X)<~>~happy(X))))&
(![X]:(brave(X)<=>(~wise(X)<~>calm(X))))&
(![X]:(brave(X)=>(~patient(X)|~wise(X))))&
(![X]:((generous(X)<~>old(X))=>(rich(X)&creative(X))))&
(![X]:(kind(X)<=>(kind(X)<~>rich(X))))&
(![X]:(strong(X)=>(~kind(X)<~>~quiet(X))))&
(![X]:((quiet(X)&wise(X))=>(humble(X)&~kind(X))))&
(![X]:((~creative(X)|~brave(X))<=>(generous(X)&curious(X))))&
(![X]:((old(X)<~>brave(X))<=>(wise(X)|~creative(X))))&
((~brave(john))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:((curious(X)|~calm(X))))=>(?[X]:((happy(X)&~old(X)))))&
(![X]:((~funny(X)|old(X))=>(funny(X)<~>~quiet(X))))&
((?[X]:(~tall(X)))=>((brave(alice)<~>~humble(alice))))&
(?[X]:(~humble(X)))&
(?[X]:((old(X)|~funny(X))))&
((brave(paul)|generous(paul)))&
((kind(paul)<~>wise(paul)))&
(?[X]:((~wise(X)&curious(X))))&
(?[X]:((happy(X)|kind(X))))&
((~creative(alice)|happy(alice))) | old(john) | [
"p4",
"p6",
"p7",
"p10",
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1112847460812465458494589
% SZS output start Proof for 1112847460812465458494589
5. ! [X0] : (brave(X0) <=> (~wise(X0) <~> calm(X0))) [input p4]
7. ! [X0] : ((generous(X0) <~> old(X0)) => (creative(X0) & rich(X0))) [input p6]
8. ! [X0] : (kind(X0) <=> (kind(X0) <~> rich(X0))) [input p7]
11. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (curious(X0) & generous(X0))) [input p10]
12. ! [X0] : ((old(X0) <~> brave(X0)) <=> (~creative(X0) | wise(X0))) [input p11]
13. ~brave(john) <=> ? [X0] : (~curious(X0) | ~brave(X0)) [input p12]
21. ? [X0] : (curious(X0) & ~wise(X0)) [input p20]
24. ~old(john) [input hypothesis]
31. ! [X0] : ((creative(X0) & rich(X0)) | (generous(X0) <=> old(X0))) [ennf transformation 7]
41. ! [X0] : ((brave(X0) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ~brave(X0))) [nnf transformation 5]
42. ! [X0] : ((creative(X0) & rich(X0)) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0)))) [nnf transformation 31]
43. ! [X0] : ((kind(X0) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0)))) & (((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 8]
44. ! [X0] : (((~brave(X0) | ~creative(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (brave(X0) & creative(X0)))) [nnf transformation 11]
45. ! [X0] : ((~brave(X0) | ~creative(X0) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | (brave(X0) & creative(X0)))) [flattening 44]
46. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (creative(X0) & ~wise(X0))) & ((~creative(X0) | wise(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [nnf transformation 12]
47. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (creative(X0) & ~wise(X0))) & (~creative(X0) | wise(X0) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [flattening 46]
48. (~brave(john) | ! [X0] : (curious(X0) & brave(X0))) & (? [X0] : (~curious(X0) | ~brave(X0)) | brave(john)) [nnf transformation 13]
49. (~brave(john) | ! [X0] : (curious(X0) & brave(X0))) & (? [X1] : (~curious(X1) | ~brave(X1)) | brave(john)) [rectify 48]
50. ? [X1] : (~curious(X1) | ~brave(X1)) => (~curious(sK0) | ~brave(sK0)) [choice axiom]
51. (~brave(john) | ! [X0] : (curious(X0) & brave(X0))) & ((~curious(sK0) | ~brave(sK0)) | brave(john)) [skolemisation 49,50]
61. ? [X0] : (curious(X0) & ~wise(X0)) => (curious(sK4) & ~wise(sK4)) [choice axiom]
62. curious(sK4) & ~wise(sK4) [skolemisation 21,61]
87. ~wise(X0) | calm(X0) | ~brave(X0) [cnf transformation 41]
88. ~brave(X0) | wise(X0) | ~calm(X0) [cnf transformation 41]
92. ~generous(X0) | old(X0) | rich(X0) [cnf transformation 42]
93. ~old(X0) | generous(X0) | rich(X0) [cnf transformation 42]
97. ~rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 43]
99. kind(X0) | kind(X0) | ~rich(X0) [cnf transformation 43]
102. generous(X0) | creative(X0) [cnf transformation 45]
103. generous(X0) | brave(X0) [cnf transformation 45]
106. ~curious(X0) | ~creative(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 45]
108. ~brave(X0) | wise(X0) | old(X0) | ~creative(X0) [cnf transformation 47]
112. ~old(X0) | ~brave(X0) | creative(X0) [cnf transformation 47]
114. ~brave(john) | brave(X0) [cnf transformation 51]
115. ~brave(john) | curious(X0) [cnf transformation 51]
129. ~wise(sK4) [cnf transformation 62]
133. ~old(john) [cnf transformation 24]
135. ~rich(X0) | ~kind(X0) [duplicate literal removal 97]
136. ~rich(X0) | kind(X0) [duplicate literal removal 99]
163. ~rich(X0) [subsumption resolution 135,136]
165. 5 <=> ! [X0] : curious(X0) [avatar definition]
166. curious(X0) <- (5) [avatar component clause 165]
168. 6 <=> brave(john) [avatar definition]
171. 5 | ~6 [avatar split clause 115,168,165]
173. 7 <=> ! [X0] : brave(X0) [avatar definition]
174. brave(X0) <- (7) [avatar component clause 173]
175. 7 | ~6 [avatar split clause 114,168,173]
186. 10 <=> ! [X1] : calm(X1) [avatar definition]
187. calm(X1) <- (10) [avatar component clause 186]
264. old(X0) | rich(X0) | brave(X0) [resolution 92,103]
265. old(X1) | rich(X1) | creative(X1) [resolution 92,102]
266. old(X0) | brave(X0) [subsumption resolution 264,163]
267. old(X1) | creative(X1) [subsumption resolution 265,163]
268. brave(john) [resolution 266,133]
272. 6 [avatar split clause 268,168]
275. ~calm(X0) | wise(X0) <- (7) [resolution 174,88]
276. wise(X0) <- (7, 10) [subsumption resolution 275,187]
278. $false <- (7, 10) [resolution 276,129]
284. ~7 | ~10 [avatar contradiction clause 278]
308. ~brave(X1) | creative(X1) | creative(X1) [resolution 112,267]
310. ~brave(X1) | creative(X1) [duplicate literal removal 308]
312. creative(X1) <- (7) [subsumption resolution 310,174]
324. ~creative(X0) | ~brave(X0) | ~generous(X0) <- (5) [resolution 106,166]
329. ~brave(X0) | ~generous(X0) <- (5, 7) [subsumption resolution 324,312]
330. ~generous(X0) <- (5, 7) [subsumption resolution 329,174]
339. wise(X0) | old(X0) | ~creative(X0) <- (7) [resolution 108,174]
351. old(X0) | wise(X0) <- (7) [subsumption resolution 339,312]
391. wise(X5) | generous(X5) | rich(X5) <- (7) [resolution 351,93]
396. wise(X5) | rich(X5) <- (5, 7) [subsumption resolution 391,330]
397. wise(X5) <- (5, 7) [subsumption resolution 396,163]
409. calm(X4) | ~brave(X4) <- (5, 7) [resolution 397,87]
413. calm(X4) <- (5, 7) [subsumption resolution 409,174]
414. 10 | ~5 | ~7 [avatar split clause 413,173,165,186]
415. $false [avatar sat refutation 171,175,272,284,414]
% SZS output end Proof for 1112847460812465458494589
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or humble then someone is both happy and kind.
If mary is either happy or not humble then someone is both rich and happy.
Everyone who is wise or not wise is both wise and not funny and vice versa.
Everyone who is brave is either not calm or strong.
Everyone who is old or curious is brave or not happy and vice versa.
Everyone who is not wise or not rich is creative.
If susan is both strong and not wise then someone is either calm or funny.
Everyone who is both not rich and not kind is not patient or not calm and vice versa.
If someone is not strong then someone is not patient or funny and vice versa.
If someone is both generous and not strong then john is funny or strong and vice versa.
Everyone who is both calm and not old is not patient and vice versa.
If paul is not strong then john is not happy.
Everyone who is not funny is either not funny or strong.
Everyone who is not creative is both not old and funny.
If john is either not creative or not old then someone is either quiet or not patient.
Someone is not humble or not curious.
Someone is either not funny or not calm.
Someone is both not quiet and not tall.
Lucy is either brave or not quiet.
Lucy is either calm or patient.
Alice is both patient and creative.
John is rich.
Susan is either kind or not kind. | Paul is generous. | contradiction | ((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:((happy(X)&kind(X)))))&
(((happy(mary)<~>~humble(mary)))=>(?[X]:((rich(X)&happy(X)))))&
(![X]:((wise(X)|~wise(X))<=>(wise(X)&~funny(X))))&
(![X]:(brave(X)=>(~calm(X)<~>strong(X))))&
(![X]:((old(X)|curious(X))<=>(brave(X)|~happy(X))))&
(![X]:((~wise(X)|~rich(X))=>creative(X)))&
(((strong(susan)&~wise(susan)))=>(?[X]:((calm(X)<~>funny(X)))))&
(![X]:((~rich(X)&~kind(X))<=>(~patient(X)|~calm(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~patient(X)|funny(X)))))&
((?[X]:((generous(X)&~strong(X))))<=>((funny(john)|strong(john))))&
(![X]:((calm(X)&~old(X))<=>~patient(X)))&
((~strong(paul))=>(~happy(john)))&
(![X]:(~funny(X)=>(~funny(X)<~>strong(X))))&
(![X]:(~creative(X)=>(~old(X)&funny(X))))&
(((~creative(john)<~>~old(john)))=>(?[X]:((quiet(X)<~>~patient(X)))))&
(?[X]:((~humble(X)|~curious(X))))&
(?[X]:((~funny(X)<~>~calm(X))))&
(?[X]:((~quiet(X)&~tall(X))))&
((brave(lucy)<~>~quiet(lucy)))&
((calm(lucy)<~>patient(lucy)))&
((patient(alice)&creative(alice)))&
(rich(john))&
((kind(susan)<~>~kind(susan))) | generous(paul) | [
"p2",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2171583758349726011268692
% SZS output start Proof for 2171583758349726011268692
3. ! [X0] : ((~wise(X0) | wise(X0)) <=> (~funny(X0) & wise(X0))) [input p2]
10. ? [X0] : (~strong(X0) & generous(X0)) <=> (strong(john) | funny(john)) [input p9]
13. ! [X0] : (~funny(X0) => (~funny(X0) <~> strong(X0))) [input p12]
24. generous(paul) [input hypothesis]
35. ! [X0] : ((~funny(X0) <~> strong(X0)) | funny(X0)) [ennf transformation 13]
45. ! [X0] : (((~wise(X0) | wise(X0)) | (funny(X0) | ~wise(X0))) & ((~funny(X0) & wise(X0)) | (wise(X0) & ~wise(X0)))) [nnf transformation 3]
46. ! [X0] : ((~wise(X0) | wise(X0) | funny(X0) | ~wise(X0)) & ((~funny(X0) & wise(X0)) | (wise(X0) & ~wise(X0)))) [flattening 45]
60. (? [X0] : (~strong(X0) & generous(X0)) | (~strong(john) & ~funny(john))) & ((strong(john) | funny(john)) | ! [X0] : (strong(X0) | ~generous(X0))) [nnf transformation 10]
61. (? [X0] : (~strong(X0) & generous(X0)) | (~strong(john) & ~funny(john))) & (strong(john) | funny(john) | ! [X0] : (strong(X0) | ~generous(X0))) [flattening 60]
62. (? [X0] : (~strong(X0) & generous(X0)) | (~strong(john) & ~funny(john))) & (strong(john) | funny(john) | ! [X1] : (strong(X1) | ~generous(X1))) [rectify 61]
63. ? [X0] : (~strong(X0) & generous(X0)) => (~strong(sK5) & generous(sK5)) [choice axiom]
64. ((~strong(sK5) & generous(sK5)) | (~strong(john) & ~funny(john))) & (strong(john) | funny(john) | ! [X1] : (strong(X1) | ~generous(X1))) [skolemisation 62,63]
67. ! [X0] : (((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | funny(X0)) [nnf transformation 35]
91. ~funny(X0) | ~wise(X0) [cnf transformation 46]
92. ~funny(X0) | wise(X0) [cnf transformation 46]
112. strong(john) | funny(john) | strong(X1) | ~generous(X1) [cnf transformation 64]
122. ~strong(X0) | funny(X0) | funny(X0) [cnf transformation 67]
142. generous(paul) [cnf transformation 24]
143. ~strong(X0) | funny(X0) [duplicate literal removal 122]
184. ~funny(X0) [subsumption resolution 91,92]
203. 13 <=> strong(john) [avatar definition]
204. strong(john) <- (13) [avatar component clause 203]
216. strong(john) | strong(X1) | ~generous(X1) [subsumption resolution 112,184]
218. 16 <=> ! [X1] : (strong(X1) | ~generous(X1)) [avatar definition]
219. strong(X1) | ~generous(X1) <- (16) [avatar component clause 218]
220. 16 | 13 [avatar split clause 216,203,218]
230. ~strong(X0) [subsumption resolution 143,184]
277. $false <- (13) [subsumption resolution 204,230]
278. ~13 [avatar contradiction clause 277]
279. ~generous(X1) <- (16) [subsumption resolution 219,230]
280. $false <- (16) [resolution 279,142]
283. ~16 [avatar contradiction clause 280]
284. $false [avatar sat refutation 220,278,283]
% SZS output end Proof for 2171583758349726011268692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then susan is not wise or strong. Everyone who is either not wise or calm is funny or not patient and vice versa. Everyone who is either not creative or generous is both not old and patient and vice versa. Everyone who is creative is not funny and vice versa. Everyone who is kind or creative is both creative and calm and vice versa. If alice is wise or not humble then john is either not wise or not curious. Everyone who is calm is brave or happy and vice versa. If someone is not wise then alice is wise and vice versa. Everyone who is both funny and tall is both strong and quiet. If susan is wise or not quiet then someone is both patient and old. Everyone who is either kind or not quiet is not quiet or not happy. If alice is both creative and strong then someone is both kind and humble and vice versa. If someone is either wise or not happy then fred is both patient and kind. If someone is funny or not creative then someone is not patient. Everyone who is both not calm and not rich is either creative or generous and vice versa. If mary is not wise then paul is both not generous and not brave and vice versa. Someone is either not calm or calm. Someone is calm or patient. Mary is either wise or not old. Someone is either quiet or tall. Someone is both creative and not brave. Alice is not curious or calm. Someone is not brave or quiet. John is either happy or wise. | Fred is not funny. | entailment | ((?[X]:(~kind(X)))=>((~wise(susan)|strong(susan))))&
(![X]:((~wise(X)<~>calm(X))<=>(funny(X)|~patient(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(~old(X)&patient(X))))&
(![X]:(creative(X)<=>~funny(X)))&
(![X]:((kind(X)|creative(X))<=>(creative(X)&calm(X))))&
(((wise(alice)|~humble(alice)))=>((~wise(john)<~>~curious(john))))&
(![X]:(calm(X)<=>(brave(X)|happy(X))))&
((?[X]:(~wise(X)))<=>(wise(alice)))&
(![X]:((funny(X)&tall(X))=>(strong(X)&quiet(X))))&
(((wise(susan)|~quiet(susan)))=>(?[X]:((patient(X)&old(X)))))&
(![X]:((kind(X)<~>~quiet(X))=>(~quiet(X)|~happy(X))))&
(((creative(alice)&strong(alice)))<=>(?[X]:((kind(X)&humble(X)))))&
((?[X]:((wise(X)<~>~happy(X))))=>((patient(fred)&kind(fred))))&
((?[X]:((funny(X)|~creative(X))))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)&~rich(X))<=>(creative(X)<~>generous(X))))&
((~wise(mary))<=>((~generous(paul)&~brave(paul))))&
(?[X]:((~calm(X)<~>calm(X))))&
(?[X]:((calm(X)|patient(X))))&
((wise(mary)<~>~old(mary)))&
(?[X]:((quiet(X)<~>tall(X))))&
(?[X]:((creative(X)&~brave(X))))&
((~curious(alice)|calm(alice)))&
(?[X]:((~brave(X)|quiet(X))))&
((happy(john)<~>wise(john))) | ~funny(fred) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8935732838831480755527412
% SZS output start Proof for 8935732838831480755527412
2. ! [X0] : ((~wise(X0) <~> calm(X0)) <=> (~patient(X0) | funny(X0))) [input p1]
3. ! [X0] : ((~creative(X0) <~> generous(X0)) <=> (patient(X0) & ~old(X0))) [input p2]
4. ! [X0] : (creative(X0) <=> ~funny(X0)) [input p3]
5. ! [X0] : ((creative(X0) | kind(X0)) <=> (calm(X0) & creative(X0))) [input p4]
7. ! [X0] : (calm(X0) <=> (happy(X0) | brave(X0))) [input p6]
13. ? [X0] : (wise(X0) <~> ~happy(X0)) => (kind(fred) & patient(fred)) [input p12]
14. ? [X0] : (~creative(X0) | funny(X0)) => ? [X0] : ~patient(X0) [input p13]
15. ! [X0] : ((~rich(X0) & ~calm(X0)) <=> (creative(X0) <~> generous(X0))) [input p14]
25. funny(fred) [input hypothesis]
26. ? [X0] : (~creative(X0) | funny(X0)) => ? [X1] : ~patient(X1) [rectify 14]
35. (kind(fred) & patient(fred)) | ! [X0] : (wise(X0) <=> ~happy(X0)) [ennf transformation 13]
36. ? [X1] : ~patient(X1) | ! [X0] : (creative(X0) & ~funny(X0)) [ennf transformation 26]
37. ! [X0] : ((((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | (patient(X0) & ~funny(X0))) & ((~patient(X0) | funny(X0)) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | (patient(X0) & ~funny(X0))) & (~patient(X0) | funny(X0) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0))))) [flattening 37]
39. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (~patient(X0) | old(X0))) & ((patient(X0) & ~old(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [nnf transformation 3]
40. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | ~patient(X0) | old(X0)) & ((patient(X0) & ~old(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [flattening 39]
41. ! [X0] : ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))) [nnf transformation 4]
42. ! [X0] : (((creative(X0) | kind(X0)) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | (~creative(X0) & ~kind(X0)))) [nnf transformation 5]
43. ! [X0] : ((creative(X0) | kind(X0) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | (~creative(X0) & ~kind(X0)))) [flattening 42]
45. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | ~calm(X0))) [nnf transformation 7]
46. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ~calm(X0))) [flattening 45]
59. (kind(fred) & patient(fred)) | ! [X0] : ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0))) [nnf transformation 35]
60. ? [X0] : ~patient(X0) | ! [X1] : (creative(X1) & ~funny(X1)) [rectify 36]
61. ? [X0] : ~patient(X0) => ~patient(sK3) [choice axiom]
62. ~patient(sK3) | ! [X1] : (creative(X1) & ~funny(X1)) [skolemisation 60,61]
63. ! [X0] : (((~rich(X0) & ~calm(X0)) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | (rich(X0) | calm(X0)))) [nnf transformation 15]
64. ! [X0] : (((~rich(X0) & ~calm(X0)) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | rich(X0) | calm(X0))) [flattening 63]
84. ~funny(X0) | ~wise(X0) | calm(X0) [cnf transformation 38]
90. generous(X0) | patient(X0) | creative(X0) [cnf transformation 40]
91. ~generous(X0) | ~creative(X0) | patient(X0) [cnf transformation 40]
94. ~creative(X0) | ~funny(X0) [cnf transformation 41]
95. creative(X0) | funny(X0) [cnf transformation 41]
96. ~kind(X0) | creative(X0) [cnf transformation 43]
99. ~creative(X0) | calm(X0) [cnf transformation 43]
107. ~happy(X0) | calm(X0) [cnf transformation 46]
125. kind(fred) | wise(X0) | happy(X0) [cnf transformation 59]
126. ~patient(sK3) | ~funny(X1) [cnf transformation 62]
130. ~calm(X0) | generous(X0) | ~creative(X0) [cnf transformation 64]
131. ~generous(X0) | creative(X0) | ~calm(X0) [cnf transformation 64]
150. funny(fred) [cnf transformation 25]
233. 18 <=> ! [X0] : (wise(X0) | happy(X0)) [avatar definition]
234. happy(X0) | wise(X0) <- (18) [avatar component clause 233]
236. 19 <=> kind(fred) [avatar definition]
238. kind(fred) <- (19) [avatar component clause 236]
239. 18 | 19 [avatar split clause 125,236,233]
254. 23 <=> patient(sK3) [avatar definition]
256. ~patient(sK3) <- (~23) [avatar component clause 254]
259. 24 <=> ! [X1] : ~funny(X1) [avatar definition]
260. ~funny(X1) <- (24) [avatar component clause 259]
261. 24 | ~23 [avatar split clause 126,254,259]
262. ~creative(X0) | generous(X0) [subsumption resolution 130,99]
331. funny(X0) | calm(X0) [resolution 99,95]
333. calm(X0) | wise(X0) <- (18) [resolution 234,107]
336. generous(X0) | funny(X0) [resolution 262,95]
460. creative(X0) | ~calm(X0) | patient(X0) | creative(X0) [resolution 131,90]
464. ~calm(X0) | creative(X0) | patient(X0) [duplicate literal removal 460]
527. calm(X1) | ~wise(X1) | calm(X1) [resolution 331,84]
528. calm(X1) | ~wise(X1) [duplicate literal removal 527]
529. calm(X1) <- (18) [subsumption resolution 528,333]
543. funny(X2) | ~creative(X2) | patient(X2) [resolution 336,91]
544. ~creative(X2) | patient(X2) [subsumption resolution 543,94]
569. creative(X0) | patient(X0) <- (18) [resolution 529,464]
576. patient(X0) <- (18) [subsumption resolution 569,544]
588. $false <- (18, ~23) [resolution 576,256]
591. ~18 | 23 [avatar contradiction clause 588]
623. creative(fred) <- (19) [resolution 238,96]
626. $false <- (24) [resolution 260,150]
627. ~24 [avatar contradiction clause 626]
652. ~funny(fred) <- (19) [resolution 623,94]
664. $false <- (19) [subsumption resolution 652,150]
665. ~19 [avatar contradiction clause 664]
666. $false [avatar sat refutation 239,261,591,627,665]
% SZS output end Proof for 8935732838831480755527412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not rich is both not kind and kind.
Everyone who is wise is not quiet or happy and vice versa.
If mary is not curious then someone is either not brave or not old and vice versa.
Everyone who is either not rich or funny is not funny or tall.
Everyone who is happy is both not kind and quiet.
If someone is not generous then mary is either wise or old.
Everyone who is either old or not curious is both curious and not curious.
If someone is either strong or brave then someone is kind and vice versa.
If someone is generous then someone is not curious.
Everyone who is not rich or calm is not creative.
Everyone who is quiet is not calm and vice versa.
Everyone who is not brave or not strong is calm or not quiet.
Everyone who is either rich or not generous is both creative and curious and vice versa.
Everyone who is either brave or funny is calm or not calm.
If someone is not calm then paul is patient and vice versa.
Everyone who is either funny or rich is brave or not happy.
Fred is creative.
Someone is either not patient or not humble.
Someone is kind or old.
Someone is curious or not funny.
Mary is happy or not funny.
John is either not happy or not funny.
Someone is both not old and strong.
Someone is creative or not quiet. | Mary is generous. | contradiction | (![X]:(~rich(X)=>(~kind(X)&kind(X))))&
(![X]:(wise(X)<=>(~quiet(X)|happy(X))))&
((~curious(mary))<=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((~rich(X)<~>funny(X))=>(~funny(X)|tall(X))))&
(![X]:(happy(X)=>(~kind(X)&quiet(X))))&
((?[X]:(~generous(X)))=>((wise(mary)<~>old(mary))))&
(![X]:((old(X)<~>~curious(X))=>(curious(X)&~curious(X))))&
((?[X]:((strong(X)<~>brave(X))))<=>(?[X]:(kind(X))))&
((?[X]:(generous(X)))=>(?[X]:(~curious(X))))&
(![X]:((~rich(X)|calm(X))=>~creative(X)))&
(![X]:(quiet(X)<=>~calm(X)))&
(![X]:((~brave(X)|~strong(X))=>(calm(X)|~quiet(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(creative(X)&curious(X))))&
(![X]:((brave(X)<~>funny(X))=>(calm(X)|~calm(X))))&
((?[X]:(~calm(X)))<=>(patient(paul)))&
(![X]:((funny(X)<~>rich(X))=>(brave(X)|~happy(X))))&
(creative(fred))&
(?[X]:((~patient(X)<~>~humble(X))))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((curious(X)|~funny(X))))&
((happy(mary)|~funny(mary)))&
((~happy(john)<~>~funny(john)))&
(?[X]:((~old(X)&strong(X))))&
(?[X]:((creative(X)|~quiet(X)))) | generous(mary) | [
"p0",
"p2",
"p6",
"p9",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8735556122544633413282718
% SZS output start Proof for 8735556122544633413282718
1. ! [X0] : (~rich(X0) => (kind(X0) & ~kind(X0))) [input p0]
3. ~curious(mary) <=> ? [X0] : (~brave(X0) <~> ~old(X0)) [input p2]
7. ! [X0] : ((old(X0) <~> ~curious(X0)) => (~curious(X0) & curious(X0))) [input p6]
10. ! [X0] : ((calm(X0) | ~rich(X0)) => ~creative(X0)) [input p9]
11. ! [X0] : (quiet(X0) <=> ~calm(X0)) [input p10]
12. ! [X0] : ((~strong(X0) | ~brave(X0)) => (~quiet(X0) | calm(X0))) [input p11]
13. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (curious(X0) & creative(X0))) [input p12]
25. generous(mary) [input hypothesis]
29. ! [X0] : ((kind(X0) & ~kind(X0)) | rich(X0)) [ennf transformation 1]
32. ! [X0] : ((~curious(X0) & curious(X0)) | (old(X0) <=> ~curious(X0))) [ennf transformation 7]
34. ! [X0] : (~creative(X0) | (~calm(X0) & rich(X0))) [ennf transformation 10]
35. ! [X0] : ((~quiet(X0) | calm(X0)) | (strong(X0) & brave(X0))) [ennf transformation 12]
36. ! [X0] : (~quiet(X0) | calm(X0) | (strong(X0) & brave(X0))) [flattening 35]
43. (~curious(mary) | ! [X0] : ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) & (? [X0] : ((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | curious(mary)) [nnf transformation 3]
44. (~curious(mary) | ! [X0] : ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) & (? [X1] : ((old(X1) | brave(X1)) & (~old(X1) | ~brave(X1))) | curious(mary)) [rectify 43]
45. ? [X1] : ((old(X1) | brave(X1)) & (~old(X1) | ~brave(X1))) => ((old(sK0) | brave(sK0)) & (~old(sK0) | ~brave(sK0))) [choice axiom]
46. (~curious(mary) | ! [X0] : ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) & (((old(sK0) | brave(sK0)) & (~old(sK0) | ~brave(sK0))) | curious(mary)) [skolemisation 44,45]
48. ! [X0] : ((~curious(X0) & curious(X0)) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0)))) [nnf transformation 32]
57. ! [X0] : ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))) [nnf transformation 11]
58. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (~curious(X0) | ~creative(X0))) & ((curious(X0) & creative(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 13]
59. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | ~curious(X0) | ~creative(X0)) & ((curious(X0) & creative(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [flattening 58]
78. ~kind(X0) | rich(X0) [cnf transformation 29]
79. kind(X0) | rich(X0) [cnf transformation 29]
86. ~curious(mary) | ~brave(X0) | old(X0) [cnf transformation 46]
93. ~curious(X0) | ~curious(X0) | ~old(X0) [cnf transformation 48]
101. ~creative(X0) | ~calm(X0) [cnf transformation 34]
103. calm(X0) | quiet(X0) [cnf transformation 57]
104. ~quiet(X0) | calm(X0) | brave(X0) [cnf transformation 36]
106. creative(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 59]
108. curious(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 59]
129. generous(mary) [cnf transformation 25]
131. ~old(X0) | ~curious(X0) [duplicate literal removal 93]
132. rich(X0) [subsumption resolution 78,79]
134. 1 <=> ! [X0] : (~brave(X0) | old(X0)) [avatar definition]
135. ~brave(X0) | old(X0) <- (1) [avatar component clause 134]
137. 2 <=> curious(mary) [avatar definition]
138. curious(mary) <- (2) [avatar component clause 137]
139. ~curious(mary) <- (~2) [avatar component clause 137]
140. 1 | ~2 [avatar split clause 86,137,134]
163. 8 <=> old(mary) [avatar definition]
164. old(mary) <- (8) [avatar component clause 163]
165. ~old(mary) <- (~8) [avatar component clause 163]
202. calm(X0) | brave(X0) [subsumption resolution 104,103]
204. ~generous(X0) | curious(X0) [subsumption resolution 108,132]
205. ~generous(X0) | creative(X0) [subsumption resolution 106,132]
296. curious(mary) [resolution 204,129]
298. $false <- (~2) [subsumption resolution 296,139]
299. 2 [avatar contradiction clause 298]
310. ~curious(mary) <- (8) [resolution 164,131]
311. $false <- (2, 8) [subsumption resolution 310,138]
312. ~2 | ~8 [avatar contradiction clause 311]
314. creative(mary) [resolution 205,129]
315. ~calm(mary) [resolution 314,101]
366. brave(mary) [resolution 315,202]
376. old(mary) <- (1) [resolution 366,135]
377. $false <- (1, ~8) [subsumption resolution 376,165]
378. ~1 | 8 [avatar contradiction clause 377]
379. $false [avatar sat refutation 140,299,312,378]
% SZS output end Proof for 8735556122544633413282718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and creative is both not tall and not humble and vice versa.
If someone is either not tall or not patient then fred is kind or humble.
Everyone who is not strong or quiet is not calm and vice versa.
If someone is either calm or curious then someone is both generous and curious.
If john is generous or not creative then paul is both not kind and not calm.
If mary is both strong and not brave then alice is either not humble or rich and vice versa.
Everyone who is not generous is either patient or not generous and vice versa.
Everyone who is not quiet is not patient.
If someone is brave then susan is both not strong and not funny and vice versa.
If lucy is rich then someone is either not tall or not old.
Everyone who is both not old and not strong is strong or not strong and vice versa.
If someone is calm then alice is strong or humble and vice versa.
If paul is either happy or not brave then john is both not funny and not old.
Everyone who is both brave and not patient is either not humble or strong and vice versa.
If someone is either not strong or kind then fred is either tall or not old.
Alice is either brave or not quiet.
Someone is rich.
Fred is both rich and not wise.
John is not tall or not humble.
Susan is both not old and not wise.
Mary is not brave.
Someone is not humble or not creative. | Mary is not patient. | entailment | (![X]:((kind(X)&creative(X))<=>(~tall(X)&~humble(X))))&
((?[X]:((~tall(X)<~>~patient(X))))=>((kind(fred)|humble(fred))))&
(![X]:((~strong(X)|quiet(X))<=>~calm(X)))&
((?[X]:((calm(X)<~>curious(X))))=>(?[X]:((generous(X)&curious(X)))))&
(((generous(john)|~creative(john)))=>((~kind(paul)&~calm(paul))))&
(((strong(mary)&~brave(mary)))<=>((~humble(alice)<~>rich(alice))))&
(![X]:(~generous(X)<=>(patient(X)<~>~generous(X))))&
(![X]:(~quiet(X)=>~patient(X)))&
((?[X]:(brave(X)))<=>((~strong(susan)&~funny(susan))))&
((rich(lucy))=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:((~old(X)&~strong(X))<=>(strong(X)|~strong(X))))&
((?[X]:(calm(X)))<=>((strong(alice)|humble(alice))))&
(((happy(paul)<~>~brave(paul)))=>((~funny(john)&~old(john))))&
(![X]:((brave(X)&~patient(X))<=>(~humble(X)<~>strong(X))))&
((?[X]:((~strong(X)<~>kind(X))))=>((tall(fred)<~>~old(fred))))&
((brave(alice)<~>~quiet(alice)))&
(?[X]:(rich(X)))&
((rich(fred)&~wise(fred)))&
((~tall(john)|~humble(john)))&
((~old(susan)&~wise(susan)))&
(~brave(mary))&
(?[X]:((~humble(X)|~creative(X)))) | ~patient(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2359678038893241968297409
% SZS output start Proof for 2359678038893241968297409
7. ! [X0] : (~generous(X0) <=> (patient(X0) <~> ~generous(X0))) [input p6]
23. patient(mary) [input hypothesis]
46. ! [X0] : ((~generous(X0) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | generous(X0))) [nnf transformation 7]
95. generous(X0) | ~patient(X0) | generous(X0) [cnf transformation 46]
96. ~generous(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 46]
134. patient(mary) [cnf transformation 23]
137. generous(X0) | ~patient(X0) [duplicate literal removal 95]
138. ~generous(X0) | ~patient(X0) [duplicate literal removal 96]
215. ~patient(X0) [subsumption resolution 137,138]
315. $false [subsumption resolution 134,215]
% SZS output end Proof for 2359678038893241968297409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is not old or not brave and vice versa. Everyone who is not brave is happy or old. Everyone who is not quiet is both creative and curious and vice versa. If paul is strong then paul is both not calm and not curious and vice versa. If john is not calm then someone is creative and vice versa. Everyone who is rich or kind is both old and not kind and vice versa. Everyone who is either not happy or rich is not kind or not calm and vice versa. Everyone who is funny is both not kind and strong and vice versa. If someone is both not humble and tall then someone is curious. Everyone who is both brave and not creative is both not brave and wise and vice versa. If someone is either not generous or generous then fred is both not old and not funny. If someone is either not tall or not brave then mary is curious and vice versa. Everyone who is both rich and not brave is both rich and not wise and vice versa. If susan is not wise then someone is not strong and vice versa. If john is not calm or not old then someone is happy or humble and vice versa. If paul is not happy or not quiet then fred is brave or not funny and vice versa. Fred is not humble. Someone is not calm. Mary is strong. Susan is not quiet or not rich. Paul is both curious and wise. Someone is both humble and funny. Mary is either not wise or humble. Someone is old or not happy. | Paul is calm. | neutral | (![X]:(~wise(X)<=>(~old(X)|~brave(X))))&
(![X]:(~brave(X)=>(happy(X)|old(X))))&
(![X]:(~quiet(X)<=>(creative(X)&curious(X))))&
((strong(paul))<=>((~calm(paul)&~curious(paul))))&
((~calm(john))<=>(?[X]:(creative(X))))&
(![X]:((rich(X)|kind(X))<=>(old(X)&~kind(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~kind(X)|~calm(X))))&
(![X]:(funny(X)<=>(~kind(X)&strong(X))))&
((?[X]:((~humble(X)&tall(X))))=>(?[X]:(curious(X))))&
(![X]:((brave(X)&~creative(X))<=>(~brave(X)&wise(X))))&
((?[X]:((~generous(X)<~>generous(X))))=>((~old(fred)&~funny(fred))))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(curious(mary)))&
(![X]:((rich(X)&~brave(X))<=>(rich(X)&~wise(X))))&
((~wise(susan))<=>(?[X]:(~strong(X))))&
(((~calm(john)|~old(john)))<=>(?[X]:((happy(X)|humble(X)))))&
(((~happy(paul)|~quiet(paul)))<=>((brave(fred)|~funny(fred))))&
(~humble(fred))&
(?[X]:(~calm(X)))&
(strong(mary))&
((~quiet(susan)|~rich(susan)))&
((curious(paul)&wise(paul)))&
(?[X]:((humble(X)&funny(X))))&
((~wise(mary)<~>humble(mary)))&
(?[X]:((old(X)|~happy(X)))) | calm(paul) | [] | null | 0 |
If someone is both generous and tall then someone is either old or wise and vice versa.
If someone is either not calm or not brave then someone is both happy and not rich and vice versa.
Everyone who is either not funny or rich is either not creative or humble and vice versa.
If someone is either not humble or generous then someone is both not brave and calm and vice versa.
Everyone who is either not funny or funny is not creative or strong and vice versa.
Everyone who is both calm and funny is both kind and not kind.
Everyone who is either not old or not kind is both not patient and not wise.
Everyone who is both patient and funny is not creative or not kind and vice versa.
If someone is both creative and happy then someone is either not kind or old.
If mary is both not generous and not funny then lucy is not funny or not tall.
If john is generous or not tall then someone is either not kind or not tall.
Everyone who is either humble or not funny is both not calm and not strong and vice versa.
Everyone who is either calm or wise is brave or strong and vice versa.
If susan is both rich and not generous then paul is either not wise or old.
Everyone who is not kind or not rich is both rich and not strong and vice versa.
If mary is creative then susan is humble and vice versa.
Someone is funny or humble.
Susan is quiet.
Someone is either not calm or not strong.
Someone is both not creative and old.
Paul is happy. | Mary is not funny. | contradiction | ((?[X]:((generous(X)&tall(X))))<=>(?[X]:((old(X)<~>wise(X)))))&
((?[X]:((~calm(X)<~>~brave(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((~funny(X)<~>rich(X))<=>(~creative(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~creative(X)|strong(X))))&
(![X]:((calm(X)&funny(X))=>(kind(X)&~kind(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~patient(X)&~wise(X))))&
(![X]:((patient(X)&funny(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((creative(X)&happy(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(((~generous(mary)&~funny(mary)))=>((~funny(lucy)|~tall(lucy))))&
(((generous(john)|~tall(john)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
(![X]:((humble(X)<~>~funny(X))<=>(~calm(X)&~strong(X))))&
(![X]:((calm(X)<~>wise(X))<=>(brave(X)|strong(X))))&
(((rich(susan)&~generous(susan)))=>((~wise(paul)<~>old(paul))))&
(![X]:((~kind(X)|~rich(X))<=>(rich(X)&~strong(X))))&
((creative(mary))<=>(humble(susan)))&
(?[X]:((funny(X)|humble(X))))&
(quiet(susan))&
(?[X]:((~calm(X)<~>~strong(X))))&
(?[X]:((~creative(X)&old(X))))&
(happy(paul)) | ~funny(mary) | [
"p2",
"p4",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1518644408934776417281879
% SZS output start Proof for 1518644408934776417281879
3. ! [X0] : ((~funny(X0) <~> rich(X0)) <=> (~creative(X0) <~> humble(X0))) [input p2]
5. ! [X0] : ((~funny(X0) <~> funny(X0)) <=> (strong(X0) | ~creative(X0))) [input p4]
8. ! [X0] : ((funny(X0) & patient(X0)) <=> (~kind(X0) | ~creative(X0))) [input p7]
12. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (~strong(X0) & ~calm(X0))) [input p11]
15. ! [X0] : ((~rich(X0) | ~kind(X0)) <=> (~strong(X0) & rich(X0))) [input p14]
22. ~funny(mary) [input hypothesis]
47. ! [X0] : ((((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0)))) & (((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0))))) [nnf transformation 3]
53. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | (~strong(X0) & creative(X0))) & ((strong(X0) | ~creative(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [nnf transformation 5]
54. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | (~strong(X0) & creative(X0))) & (strong(X0) | ~creative(X0) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [flattening 53]
56. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | (~funny(X0) | ~patient(X0)))) [nnf transformation 8]
57. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ~funny(X0) | ~patient(X0))) [flattening 56]
65. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (strong(X0) | calm(X0))) & ((~strong(X0) & ~calm(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 12]
66. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | strong(X0) | calm(X0)) & ((~strong(X0) & ~calm(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [flattening 65]
70. ! [X0] : (((~rich(X0) | ~kind(X0)) | (strong(X0) | ~rich(X0))) & ((~strong(X0) & rich(X0)) | (rich(X0) & kind(X0)))) [nnf transformation 15]
71. ! [X0] : ((~rich(X0) | ~kind(X0) | strong(X0) | ~rich(X0)) & ((~strong(X0) & rich(X0)) | (rich(X0) & kind(X0)))) [flattening 70]
99. ~humble(X0) | funny(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 47]
106. strong(X0) | ~creative(X0) | funny(X0) | funny(X0) [cnf transformation 54]
107. strong(X0) | ~creative(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 54]
121. creative(X0) | funny(X0) [cnf transformation 57]
133. ~strong(X0) | humble(X0) | funny(X0) [cnf transformation 66]
145. rich(X0) | rich(X0) [cnf transformation 71]
157. ~funny(mary) [cnf transformation 22]
158. rich(X0) [duplicate literal removal 145]
160. strong(X0) | ~creative(X0) | funny(X0) [duplicate literal removal 106]
161. ~creative(X0) | strong(X0) | ~funny(X0) [duplicate literal removal 107]
252. ~creative(X0) | strong(X0) [subsumption resolution 160,161]
272. 25 <=> funny(mary) [avatar definition]
273. ~funny(mary) <- (~25) [avatar component clause 272]
329. 37 <=> creative(mary) [avatar definition]
330. ~creative(mary) <- (~37) [avatar component clause 329]
331. creative(mary) <- (37) [avatar component clause 329]
353. ~25 [avatar split clause 157,272]
357. funny(mary) <- (~37) [resolution 121,330]
358. $false <- (~25, ~37) [subsumption resolution 357,273]
359. 25 | 37 [avatar contradiction clause 358]
381. strong(mary) <- (37) [resolution 252,331]
408. humble(mary) | funny(mary) <- (37) [resolution 133,381]
409. humble(mary) <- (~25, 37) [subsumption resolution 408,273]
566. funny(mary) | ~creative(mary) | ~rich(mary) <- (~25, 37) [resolution 99,409]
573. ~creative(mary) | ~rich(mary) <- (~25, 37) [subsumption resolution 566,273]
574. ~rich(mary) <- (~25, 37) [subsumption resolution 573,331]
575. $false <- (~25, 37) [subsumption resolution 574,158]
576. 25 | ~37 [avatar contradiction clause 575]
585. $false [avatar sat refutation 353,359,576]
% SZS output end Proof for 1518644408934776417281879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is not humble or not old.
Everyone who is not brave is both not patient and not wise and vice versa.
Everyone who is both not generous and patient is both funny and wise.
Everyone who is not curious is either not wise or calm.
If someone is not happy or not generous then someone is both brave and not brave.
If paul is not old then mary is not wise and vice versa.
If someone is not strong or calm then alice is not old or not brave and vice versa.
Everyone who is not happy or not quiet is kind and vice versa.
If susan is generous then john is both not wise and not calm.
If someone is brave or not rich then someone is either not calm or not quiet.
If someone is quiet then someone is not creative and vice versa.
Everyone who is both not old and not strong is either creative or not old and vice versa.
Everyone who is not strong or generous is either creative or humble.
Everyone who is not calm is funny or quiet.
Lucy is either quiet or humble.
Mary is not rich or not strong.
Paul is not creative.
Someone is both funny and not kind.
Someone is either not tall or not humble.
Mary is both calm and not tall.
Lucy is old or patient. | John is kind. | neutral | (![X]:(quiet(X)=>(~humble(X)|~old(X))))&
(![X]:(~brave(X)<=>(~patient(X)&~wise(X))))&
(![X]:((~generous(X)&patient(X))=>(funny(X)&wise(X))))&
(![X]:(~curious(X)=>(~wise(X)<~>calm(X))))&
((?[X]:((~happy(X)|~generous(X))))=>(?[X]:((brave(X)&~brave(X)))))&
((~old(paul))<=>(~wise(mary)))&
((?[X]:((~strong(X)|calm(X))))<=>((~old(alice)|~brave(alice))))&
(![X]:((~happy(X)|~quiet(X))<=>kind(X)))&
((generous(susan))=>((~wise(john)&~calm(john))))&
((?[X]:((brave(X)|~rich(X))))=>(?[X]:((~calm(X)<~>~quiet(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:(~creative(X))))&
(![X]:((~old(X)&~strong(X))<=>(creative(X)<~>~old(X))))&
(![X]:((~strong(X)|generous(X))=>(creative(X)<~>humble(X))))&
(![X]:(~calm(X)=>(funny(X)|quiet(X))))&
((quiet(lucy)<~>humble(lucy)))&
((~rich(mary)|~strong(mary)))&
(~creative(paul))&
(?[X]:((funny(X)&~kind(X))))&
(?[X]:((~tall(X)<~>~humble(X))))&
((calm(mary)&~tall(mary)))&
((old(lucy)|patient(lucy))) | kind(john) | [] | null | 0 |
If john is not rich then alice is not quiet.
Everyone who is not quiet is not generous.
Everyone who is not calm or not curious is both wise and not wise.
If mary is either not rich or curious then someone is either brave or happy.
Everyone who is either not brave or curious is both strong and kind.
Everyone who is not curious is both quiet and tall and vice versa.
If john is both brave and calm then someone is generous or not brave.
Everyone who is not patient or not creative is both not curious and kind and vice versa.
If paul is patient then someone is both strong and not quiet.
Everyone who is either rich or not tall is either generous or not rich and vice versa.
If mary is not wise then someone is either not rich or wise.
If someone is not humble then someone is both not tall and not rich and vice versa.
Everyone who is not quiet or generous is brave or humble and vice versa.
Everyone who is funny or generous is either strong or old.
Everyone who is either not humble or funny is kind or curious and vice versa.
Everyone who is either not tall or not humble is brave or creative and vice versa.
Mary is not quiet or not curious.
Lucy is either curious or not brave.
Susan is either creative or kind.
Susan is both funny and not quiet.
Someone is not tall or not generous. | John is creative. | entailment | ((~rich(john))=>(~quiet(alice)))&
(![X]:(~quiet(X)=>~generous(X)))&
(![X]:((~calm(X)|~curious(X))=>(wise(X)&~wise(X))))&
(((~rich(mary)<~>curious(mary)))=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:((~brave(X)<~>curious(X))=>(strong(X)&kind(X))))&
(![X]:(~curious(X)<=>(quiet(X)&tall(X))))&
(((brave(john)&calm(john)))=>(?[X]:((generous(X)|~brave(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(~curious(X)&kind(X))))&
((patient(paul))=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~tall(X))<=>(generous(X)<~>~rich(X))))&
((~wise(mary))=>(?[X]:((~rich(X)<~>wise(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((~tall(X)&~rich(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(brave(X)|humble(X))))&
(![X]:((funny(X)|generous(X))=>(strong(X)<~>old(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(kind(X)|curious(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(brave(X)|creative(X))))&
((~quiet(mary)|~curious(mary)))&
((curious(lucy)<~>~brave(lucy)))&
((creative(susan)<~>kind(susan)))&
((funny(susan)&~quiet(susan)))&
(?[X]:((~tall(X)|~generous(X)))) | creative(john) | [
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5582429120648883424461803
% SZS output start Proof for 5582429120648883424461803
3. ! [X0] : ((~curious(X0) | ~calm(X0)) => (~wise(X0) & wise(X0))) [input p2]
8. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (kind(X0) & ~curious(X0))) [input p7]
22. ~creative(john) [input hypothesis]
26. ! [X0] : ((~wise(X0) & wise(X0)) | (curious(X0) & calm(X0))) [ennf transformation 3]
42. ! [X0] : (((~creative(X0) | ~patient(X0)) | (~kind(X0) | curious(X0))) & ((kind(X0) & ~curious(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 8]
43. ! [X0] : ((~creative(X0) | ~patient(X0) | ~kind(X0) | curious(X0)) & ((kind(X0) & ~curious(X0)) | (creative(X0) & patient(X0)))) [flattening 42]
69. wise(X0) | curious(X0) [cnf transformation 26]
71. ~wise(X0) | curious(X0) [cnf transformation 26]
85. ~curious(X0) | creative(X0) [cnf transformation 43]
132. ~creative(john) [cnf transformation 22]
146. curious(X0) [subsumption resolution 69,71]
181. creative(X0) [subsumption resolution 85,146]
230. $false [subsumption resolution 132,181]
% SZS output end Proof for 5582429120648883424461803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is quiet then someone is both quiet and tall and vice versa.
If someone is both not patient and brave then someone is not creative or not funny and vice versa.
Everyone who is either brave or happy is kind.
If paul is both not strong and curious then someone is curious or calm and vice versa.
If someone is happy then susan is either not tall or funny and vice versa.
If someone is not kind then someone is not rich.
If someone is either not happy or brave then someone is either patient or not calm.
Everyone who is not calm or not brave is creative and vice versa.
Everyone who is not happy or brave is not funny or rich.
Everyone who is not happy or not calm is either not funny or not quiet.
Everyone who is either not wise or curious is either happy or patient and vice versa.
Everyone who is not wise is happy or quiet and vice versa.
Everyone who is not wise or wise is both not patient and curious.
If lucy is not creative then susan is either not kind or strong.
If someone is kind or quiet then susan is either curious or wise and vice versa.
If someone is either not brave or humble then someone is both not strong and strong.
Susan is both not patient and curious.
John is either not curious or strong.
Alice is quiet or funny.
Lucy is either funny or not creative.
Someone is either patient or kind.
Paul is both tall and humble. | Lucy is humble. | contradiction | ((quiet(lucy))<=>(?[X]:((quiet(X)&tall(X)))))&
((?[X]:((~patient(X)&brave(X))))<=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((brave(X)<~>happy(X))=>kind(X)))&
(((~strong(paul)&curious(paul)))<=>(?[X]:((curious(X)|calm(X)))))&
((?[X]:(happy(X)))<=>((~tall(susan)<~>funny(susan))))&
((?[X]:(~kind(X)))=>(?[X]:(~rich(X))))&
((?[X]:((~happy(X)<~>brave(X))))=>(?[X]:((patient(X)<~>~calm(X)))))&
(![X]:((~calm(X)|~brave(X))<=>creative(X)))&
(![X]:((~happy(X)|brave(X))=>(~funny(X)|rich(X))))&
(![X]:((~happy(X)|~calm(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(happy(X)<~>patient(X))))&
(![X]:(~wise(X)<=>(happy(X)|quiet(X))))&
(![X]:((~wise(X)|wise(X))=>(~patient(X)&curious(X))))&
((~creative(lucy))=>((~kind(susan)<~>strong(susan))))&
((?[X]:((kind(X)|quiet(X))))<=>((curious(susan)<~>wise(susan))))&
((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:((~strong(X)&strong(X)))))&
((~patient(susan)&curious(susan)))&
((~curious(john)<~>strong(john)))&
((quiet(alice)|funny(alice)))&
((funny(lucy)<~>~creative(lucy)))&
(?[X]:((patient(X)<~>kind(X))))&
((tall(paul)&humble(paul))) | humble(lucy) | [
"p0",
"p4",
"p7",
"p9",
"p10",
"p11",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 881905417006218507723922
% SZS output start Proof for 881905417006218507723922
1. quiet(lucy) <=> ? [X0] : (tall(X0) & quiet(X0)) [input p0]
5. ? [X0] : happy(X0) <=> (~tall(susan) <~> funny(susan)) [input p4]
8. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> creative(X0)) [input p7]
10. ! [X0] : ((~calm(X0) | ~happy(X0)) => (~funny(X0) <~> ~quiet(X0))) [input p9]
11. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (happy(X0) <~> patient(X0))) [input p10]
12. ! [X0] : (~wise(X0) <=> (quiet(X0) | happy(X0))) [input p11]
13. ! [X0] : ((wise(X0) | ~wise(X0)) => (curious(X0) & ~patient(X0))) [input p12]
16. ? [X0] : (~brave(X0) <~> humble(X0)) => ? [X0] : (strong(X0) & ~strong(X0)) [input p15]
20. funny(lucy) <~> ~creative(lucy) [input p19]
23. humble(lucy) [input hypothesis]
27. ? [X0] : (~brave(X0) <~> humble(X0)) => ? [X1] : (strong(X1) & ~strong(X1)) [rectify 16]
33. ! [X0] : ((~funny(X0) <~> ~quiet(X0)) | (calm(X0) & happy(X0))) [ennf transformation 10]
34. ! [X0] : ((curious(X0) & ~patient(X0)) | (~wise(X0) & wise(X0))) [ennf transformation 13]
36. ? [X1] : (strong(X1) & ~strong(X1)) | ! [X0] : (~brave(X0) <=> humble(X0)) [ennf transformation 27]
37. (quiet(lucy) | ! [X0] : (~tall(X0) | ~quiet(X0))) & (? [X0] : (tall(X0) & quiet(X0)) | ~quiet(lucy)) [nnf transformation 1]
38. (quiet(lucy) | ! [X0] : (~tall(X0) | ~quiet(X0))) & (? [X1] : (tall(X1) & quiet(X1)) | ~quiet(lucy)) [rectify 37]
39. ? [X1] : (tall(X1) & quiet(X1)) => (tall(sK0) & quiet(sK0)) [choice axiom]
40. (quiet(lucy) | ! [X0] : (~tall(X0) | ~quiet(X0))) & ((tall(sK0) & quiet(sK0)) | ~quiet(lucy)) [skolemisation 38,39]
52. (? [X0] : happy(X0) | ((~tall(susan) | ~funny(susan)) & (funny(susan) | tall(susan)))) & (((~funny(susan) | tall(susan)) & (funny(susan) | ~tall(susan))) | ! [X0] : ~happy(X0)) [nnf transformation 5]
53. (? [X0] : happy(X0) | ((~tall(susan) | ~funny(susan)) & (funny(susan) | tall(susan)))) & (((~funny(susan) | tall(susan)) & (funny(susan) | ~tall(susan))) | ! [X1] : ~happy(X1)) [rectify 52]
54. ? [X0] : happy(X0) => happy(sK4) [choice axiom]
55. (happy(sK4) | ((~tall(susan) | ~funny(susan)) & (funny(susan) | tall(susan)))) & (((~funny(susan) | tall(susan)) & (funny(susan) | ~tall(susan))) | ! [X1] : ~happy(X1)) [skolemisation 53,54]
63. ! [X0] : (((~brave(X0) | ~calm(X0)) | ~creative(X0)) & (creative(X0) | (brave(X0) & calm(X0)))) [nnf transformation 8]
64. ! [X0] : ((~brave(X0) | ~calm(X0) | ~creative(X0)) & (creative(X0) | (brave(X0) & calm(X0)))) [flattening 63]
65. ! [X0] : (((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | (calm(X0) & happy(X0))) [nnf transformation 33]
66. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0)))) & (((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 11]
67. ! [X0] : ((~wise(X0) | (~quiet(X0) & ~happy(X0))) & ((quiet(X0) | happy(X0)) | wise(X0))) [nnf transformation 12]
68. ! [X0] : ((~wise(X0) | (~quiet(X0) & ~happy(X0))) & (quiet(X0) | happy(X0) | wise(X0))) [flattening 67]
74. ? [X1] : (strong(X1) & ~strong(X1)) | ! [X0] : ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0))) [nnf transformation 36]
75. ? [X0] : (strong(X0) & ~strong(X0)) | ! [X1] : ((~brave(X1) | ~humble(X1)) & (humble(X1) | brave(X1))) [rectify 74]
76. ? [X0] : (strong(X0) & ~strong(X0)) => (strong(sK8) & ~strong(sK8)) [choice axiom]
77. (strong(sK8) & ~strong(sK8)) | ! [X1] : ((~brave(X1) | ~humble(X1)) & (humble(X1) | brave(X1))) [skolemisation 75,76]
79. (creative(lucy) | ~funny(lucy)) & (~creative(lucy) | funny(lucy)) [nnf transformation 20]
85. quiet(lucy) | ~tall(X0) | ~quiet(X0) [cnf transformation 40]
100. happy(sK4) | funny(susan) | tall(susan) [cnf transformation 55]
108. creative(X0) | brave(X0) [cnf transformation 64]
112. ~funny(X0) | ~quiet(X0) | happy(X0) [cnf transformation 65]
117. ~wise(X0) | happy(X0) | patient(X0) | ~curious(X0) [cnf transformation 66]
122. ~curious(X0) | wise(X0) | patient(X0) | ~happy(X0) [cnf transformation 66]
124. wise(X0) | happy(X0) | quiet(X0) [cnf transformation 68]
125. ~wise(X0) | ~happy(X0) [cnf transformation 68]
127. ~patient(X0) | wise(X0) [cnf transformation 34]
128. ~wise(X0) | ~patient(X0) [cnf transformation 34]
129. curious(X0) | wise(X0) [cnf transformation 34]
130. ~wise(X0) | curious(X0) [cnf transformation 34]
140. ~strong(sK8) | ~brave(X1) | ~humble(X1) [cnf transformation 77]
142. strong(sK8) | ~brave(X1) | ~humble(X1) [cnf transformation 77]
148. ~creative(lucy) | funny(lucy) [cnf transformation 79]
154. humble(lucy) [cnf transformation 23]
156. 1 <=> ! [X0] : (~tall(X0) | ~quiet(X0)) [avatar definition]
157. ~tall(X0) | ~quiet(X0) <- (1) [avatar component clause 156]
159. 2 <=> quiet(lucy) [avatar definition]
162. 1 | 2 [avatar split clause 85,159,156]
231. 18 <=> funny(susan) [avatar definition]
232. funny(susan) <- (18) [avatar component clause 231]
235. 19 <=> tall(susan) [avatar definition]
236. tall(susan) <- (19) [avatar component clause 235]
239. 20 <=> happy(sK4) [avatar definition]
241. happy(sK4) <- (20) [avatar component clause 239]
243. 19 | 18 | 20 [avatar split clause 100,239,231,235]
245. 21 <=> ! [X1] : ~happy(X1) [avatar definition]
246. ~happy(X1) <- (21) [avatar component clause 245]
275. curious(X0) [subsumption resolution 129,130]
276. ~patient(X0) [subsumption resolution 127,128]
278. 28 <=> creative(lucy) [avatar definition]
279. ~creative(lucy) <- (~28) [avatar component clause 278]
293. 31 <=> wise(susan) [avatar definition]
294. ~wise(susan) <- (~31) [avatar component clause 293]
295. wise(susan) <- (31) [avatar component clause 293]
316. 36 <=> ! [X1] : (~brave(X1) | ~humble(X1)) [avatar definition]
317. ~humble(X1) | ~brave(X1) <- (36) [avatar component clause 316]
319. 37 <=> strong(sK8) [avatar definition]
322. 36 | 37 [avatar split clause 142,319,316]
327. 36 | ~37 [avatar split clause 140,319,316]
340. 41 <=> funny(lucy) [avatar definition]
341. funny(lucy) <- (41) [avatar component clause 340]
344. 41 | ~28 [avatar split clause 148,278,340]
355. brave(lucy) <- (~28) [resolution 108,279]
357. ~brave(lucy) <- (36) [resolution 317,154]
358. $false <- (~28, 36) [subsumption resolution 357,355]
359. 28 | ~36 [avatar contradiction clause 358]
378. $false <- (20, 21) [resolution 246,241]
379. ~20 | ~21 [avatar contradiction clause 378]
398. ~quiet(lucy) | happy(lucy) <- (41) [resolution 112,341]
410. happy(susan) | quiet(susan) <- (~31) [resolution 124,294]
421. 46 <=> quiet(susan) [avatar definition]
423. quiet(susan) <- (46) [avatar component clause 421]
425. 47 <=> happy(susan) [avatar definition]
427. happy(susan) <- (47) [avatar component clause 425]
428. 46 | 47 | 31 [avatar split clause 410,293,425,421]
451. ~quiet(susan) | happy(susan) <- (18) [resolution 232,112]
455. happy(susan) <- (18, 46) [subsumption resolution 451,423]
456. 47 | ~18 | ~46 [avatar split clause 455,421,231,425]
519. wise(X0) | patient(X0) | ~happy(X0) [resolution 122,275]
520. wise(X0) | ~happy(X0) [subsumption resolution 519,276]
521. ~happy(X0) [subsumption resolution 520,125]
522. 21 [avatar split clause 521,245]
526. $false <- (21, 47) [resolution 246,427]
527. ~21 | ~47 [avatar contradiction clause 526]
532. ~quiet(lucy) <- (21, 41) [subsumption resolution 398,246]
533. ~2 | ~21 | ~41 [avatar split clause 532,340,245,159]
541. ~quiet(susan) <- (1, 19) [resolution 157,236]
547. ~46 | ~1 | ~19 [avatar split clause 541,235,156,421]
548. happy(susan) | patient(susan) | ~curious(susan) <- (31) [resolution 295,117]
556. patient(susan) | ~curious(susan) <- (21, 31) [subsumption resolution 548,246]
557. ~curious(susan) <- (21, 31) [subsumption resolution 556,276]
558. $false <- (21, 31) [subsumption resolution 557,275]
559. ~21 | ~31 [avatar contradiction clause 558]
560. $false [avatar sat refutation 162,243,322,327,344,359,379,428,456,522,527,533,547,559]
% SZS output end Proof for 881905417006218507723922
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either old or not wise and vice versa. If someone is either rich or calm then mary is rich or strong. Everyone who is not calm is both not old and calm. If mary is not tall or not brave then someone is kind or strong. If someone is both not kind and not wise then someone is funny or wise. If someone is calm then someone is wise and vice versa. Everyone who is both curious and not tall is rich and vice versa. If someone is either not wise or kind then mary is tall and vice versa. Everyone who is not curious or brave is not tall or curious and vice versa. Everyone who is either quiet or not brave is both not strong and funny and vice versa. Everyone who is either not calm or not tall is both not funny and not happy and vice versa. If fred is either not brave or not wise then someone is either creative or brave and vice versa. If susan is either curious or kind then mary is not creative and vice versa. Everyone who is humble or creative is both not tall and not old and vice versa. Everyone who is not generous is funny. Everyone who is not patient or calm is not tall and vice versa. Someone is both not curious and not old. Someone is not creative or not tall. Someone is tall or not creative. Someone is creative or humble. Alice is either not happy or kind. Someone is tall or not tall. Paul is brave or not creative. | Mary is not generous. | contradiction | (![X]:(~quiet(X)<=>(old(X)<~>~wise(X))))&
((?[X]:((rich(X)<~>calm(X))))=>((rich(mary)|strong(mary))))&
(![X]:(~calm(X)=>(~old(X)&calm(X))))&
(((~tall(mary)|~brave(mary)))=>(?[X]:((kind(X)|strong(X)))))&
((?[X]:((~kind(X)&~wise(X))))=>(?[X]:((funny(X)|wise(X)))))&
((?[X]:(calm(X)))<=>(?[X]:(wise(X))))&
(![X]:((curious(X)&~tall(X))<=>rich(X)))&
((?[X]:((~wise(X)<~>kind(X))))<=>(tall(mary)))&
(![X]:((~curious(X)|brave(X))<=>(~tall(X)|curious(X))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)&funny(X))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~funny(X)&~happy(X))))&
(((~brave(fred)<~>~wise(fred)))<=>(?[X]:((creative(X)<~>brave(X)))))&
(((curious(susan)<~>kind(susan)))<=>(~creative(mary)))&
(![X]:((humble(X)|creative(X))<=>(~tall(X)&~old(X))))&
(![X]:(~generous(X)=>funny(X)))&
(![X]:((~patient(X)|calm(X))<=>~tall(X)))&
(?[X]:((~curious(X)&~old(X))))&
(?[X]:((~creative(X)|~tall(X))))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:((creative(X)|humble(X))))&
((~happy(alice)<~>kind(alice)))&
(?[X]:((tall(X)|~tall(X))))&
((brave(paul)|~creative(paul))) | ~generous(mary) | [
"p2",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 779214639777039354383714
% SZS output start Proof for 779214639777039354383714
3. ! [X0] : (~calm(X0) => (calm(X0) & ~old(X0))) [input p2]
11. ! [X0] : ((~calm(X0) <~> ~tall(X0)) <=> (~happy(X0) & ~funny(X0))) [input p10]
15. ! [X0] : (~generous(X0) => funny(X0)) [input p14]
16. ! [X0] : ((calm(X0) | ~patient(X0)) <=> ~tall(X0)) [input p15]
24. ~generous(mary) [input hypothesis]
29. ! [X0] : ((calm(X0) & ~old(X0)) | calm(X0)) [ennf transformation 3]
32. ! [X0] : (funny(X0) | generous(X0)) [ennf transformation 15]
55. ! [X0] : ((((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0))))) [nnf transformation 11]
56. ! [X0] : ((((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0))))) [flattening 55]
64. ! [X0] : (((calm(X0) | ~patient(X0)) | tall(X0)) & (~tall(X0) | (~calm(X0) & patient(X0)))) [nnf transformation 16]
65. ! [X0] : ((calm(X0) | ~patient(X0) | tall(X0)) & (~tall(X0) | (~calm(X0) & patient(X0)))) [flattening 64]
84. calm(X0) | calm(X0) [cnf transformation 29]
108. ~funny(X0) | ~calm(X0) | tall(X0) [cnf transformation 56]
130. generous(X0) | funny(X0) [cnf transformation 32]
132. ~tall(X0) | ~calm(X0) [cnf transformation 65]
143. ~generous(mary) [cnf transformation 24]
146. calm(X0) [duplicate literal removal 84]
211. ~funny(X0) | tall(X0) [subsumption resolution 108,146]
258. ~tall(X0) [subsumption resolution 132,146]
294. funny(mary) [resolution 130,143]
303. tall(mary) [resolution 211,294]
304. $false [subsumption resolution 303,258]
% SZS output end Proof for 779214639777039354383714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both calm and not kind then someone is either rich or not brave and vice versa.
Everyone who is not wise or not quiet is generous or wise.
If paul is kind or rich then fred is both brave and tall and vice versa.
If someone is both not calm and humble then someone is either not strong or brave and vice versa.
Everyone who is either not kind or calm is not creative or wise and vice versa.
Everyone who is curious or generous is rich or not quiet.
Everyone who is both not kind and wise is both not wise and not rich and vice versa.
If someone is both not creative and not happy then someone is both not patient and not kind and vice versa.
Everyone who is calm is not old or quiet.
If someone is not calm then someone is both kind and strong.
Everyone who is strong is either not happy or not strong.
Everyone who is quiet or not patient is both not old and not calm.
Everyone who is not old is both humble and not happy.
Everyone who is either not happy or not funny is kind or not wise and vice versa.
If someone is both creative and wise then fred is not brave or not calm and vice versa.
Everyone who is either not funny or kind is happy or not strong.
Mary is generous or not wise.
Fred is not patient or not wise.
Someone is not patient or humble.
Someone is either rich or strong.
Someone is both brave and generous. | Mary is kind. | contradiction | ((?[X]:((calm(X)&~kind(X))))<=>(?[X]:((rich(X)<~>~brave(X)))))&
(![X]:((~wise(X)|~quiet(X))=>(generous(X)|wise(X))))&
(((kind(paul)|rich(paul)))<=>((brave(fred)&tall(fred))))&
((?[X]:((~calm(X)&humble(X))))<=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:((~kind(X)<~>calm(X))<=>(~creative(X)|wise(X))))&
(![X]:((curious(X)|generous(X))=>(rich(X)|~quiet(X))))&
(![X]:((~kind(X)&wise(X))<=>(~wise(X)&~rich(X))))&
((?[X]:((~creative(X)&~happy(X))))<=>(?[X]:((~patient(X)&~kind(X)))))&
(![X]:(calm(X)=>(~old(X)|quiet(X))))&
((?[X]:(~calm(X)))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:(strong(X)=>(~happy(X)<~>~strong(X))))&
(![X]:((quiet(X)|~patient(X))=>(~old(X)&~calm(X))))&
(![X]:(~old(X)=>(humble(X)&~happy(X))))&
(![X]:((~happy(X)<~>~funny(X))<=>(kind(X)|~wise(X))))&
((?[X]:((creative(X)&wise(X))))<=>((~brave(fred)|~calm(fred))))&
(![X]:((~funny(X)<~>kind(X))=>(happy(X)|~strong(X))))&
((generous(mary)|~wise(mary)))&
((~patient(fred)|~wise(fred)))&
(?[X]:((~patient(X)|humble(X))))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((brave(X)&generous(X)))) | kind(mary) | [
"p2",
"p4",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6080933589770169417464733
% SZS output start Proof for 6080933589770169417464733
3. (rich(paul) | kind(paul)) <=> (tall(fred) & brave(fred)) [input p2]
5. ! [X0] : ((~kind(X0) <~> calm(X0)) <=> (wise(X0) | ~creative(X0))) [input p4]
7. ! [X0] : ((wise(X0) & ~kind(X0)) <=> (~rich(X0) & ~wise(X0))) [input p6]
8. ? [X0] : (~happy(X0) & ~creative(X0)) <=> ? [X0] : (~kind(X0) & ~patient(X0)) [input p7]
9. ! [X0] : (calm(X0) => (quiet(X0) | ~old(X0))) [input p8]
10. ? [X0] : ~calm(X0) => ? [X0] : (strong(X0) & kind(X0)) [input p9]
11. ! [X0] : (strong(X0) => (~happy(X0) <~> ~strong(X0))) [input p10]
12. ! [X0] : ((~patient(X0) | quiet(X0)) => (~calm(X0) & ~old(X0))) [input p11]
13. ! [X0] : (~old(X0) => (~happy(X0) & humble(X0))) [input p12]
14. ! [X0] : ((~happy(X0) <~> ~funny(X0)) <=> (~wise(X0) | kind(X0))) [input p13]
15. ? [X0] : (wise(X0) & creative(X0)) <=> (~calm(fred) | ~brave(fred)) [input p14]
16. ! [X0] : ((~funny(X0) <~> kind(X0)) => (~strong(X0) | happy(X0))) [input p15]
22. kind(mary) [input hypothesis]
25. ? [X0] : (~happy(X0) & ~creative(X0)) <=> ? [X1] : (~kind(X1) & ~patient(X1)) [rectify 8]
26. ? [X0] : ~calm(X0) => ? [X1] : (strong(X1) & kind(X1)) [rectify 10]
32. ! [X0] : ((quiet(X0) | ~old(X0)) | ~calm(X0)) [ennf transformation 9]
33. ! [X0] : (quiet(X0) | ~old(X0) | ~calm(X0)) [flattening 32]
34. ? [X1] : (strong(X1) & kind(X1)) | ! [X0] : calm(X0) [ennf transformation 26]
35. ! [X0] : ((~happy(X0) <~> ~strong(X0)) | ~strong(X0)) [ennf transformation 11]
36. ! [X0] : ((~calm(X0) & ~old(X0)) | (patient(X0) & ~quiet(X0))) [ennf transformation 12]
37. ! [X0] : ((~happy(X0) & humble(X0)) | old(X0)) [ennf transformation 13]
38. ! [X0] : ((~strong(X0) | happy(X0)) | (~funny(X0) <=> kind(X0))) [ennf transformation 16]
39. ! [X0] : (~strong(X0) | happy(X0) | (~funny(X0) <=> kind(X0))) [flattening 38]
45. ((rich(paul) | kind(paul)) | (~tall(fred) | ~brave(fred))) & ((tall(fred) & brave(fred)) | (~rich(paul) & ~kind(paul))) [nnf transformation 3]
46. (rich(paul) | kind(paul) | ~tall(fred) | ~brave(fred)) & ((tall(fred) & brave(fred)) | (~rich(paul) & ~kind(paul))) [flattening 45]
52. ! [X0] : ((((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0))))) [nnf transformation 5]
53. ! [X0] : ((((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0))))) [flattening 52]
54. ! [X0] : (((wise(X0) & ~kind(X0)) | (rich(X0) | wise(X0))) & ((~rich(X0) & ~wise(X0)) | (~wise(X0) | kind(X0)))) [nnf transformation 7]
55. ! [X0] : (((wise(X0) & ~kind(X0)) | rich(X0) | wise(X0)) & ((~rich(X0) & ~wise(X0)) | ~wise(X0) | kind(X0))) [flattening 54]
56. (? [X0] : (~happy(X0) & ~creative(X0)) | ! [X1] : (kind(X1) | patient(X1))) & (? [X1] : (~kind(X1) & ~patient(X1)) | ! [X0] : (happy(X0) | creative(X0))) [nnf transformation 25]
57. (? [X0] : (~happy(X0) & ~creative(X0)) | ! [X1] : (kind(X1) | patient(X1))) & (? [X2] : (~kind(X2) & ~patient(X2)) | ! [X3] : (happy(X3) | creative(X3))) [rectify 56]
58. ? [X0] : (~happy(X0) & ~creative(X0)) => (~happy(sK4) & ~creative(sK4)) [choice axiom]
59. ? [X2] : (~kind(X2) & ~patient(X2)) => (~kind(sK5) & ~patient(sK5)) [choice axiom]
60. ((~happy(sK4) & ~creative(sK4)) | ! [X1] : (kind(X1) | patient(X1))) & ((~kind(sK5) & ~patient(sK5)) | ! [X3] : (happy(X3) | creative(X3))) [skolemisation 57,59,58]
61. ? [X0] : (strong(X0) & kind(X0)) | ! [X1] : calm(X1) [rectify 34]
62. ? [X0] : (strong(X0) & kind(X0)) => (strong(sK6) & kind(sK6)) [choice axiom]
63. (strong(sK6) & kind(sK6)) | ! [X1] : calm(X1) [skolemisation 61,62]
64. ! [X0] : (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | ~strong(X0)) [nnf transformation 35]
65. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (wise(X0) & ~kind(X0))) & ((~wise(X0) | kind(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [nnf transformation 14]
66. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (wise(X0) & ~kind(X0))) & (~wise(X0) | kind(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [flattening 65]
67. (? [X0] : (wise(X0) & creative(X0)) | (calm(fred) & brave(fred))) & ((~calm(fred) | ~brave(fred)) | ! [X0] : (~wise(X0) | ~creative(X0))) [nnf transformation 15]
68. (? [X0] : (wise(X0) & creative(X0)) | (calm(fred) & brave(fred))) & (~calm(fred) | ~brave(fred) | ! [X0] : (~wise(X0) | ~creative(X0))) [flattening 67]
69. (? [X0] : (wise(X0) & creative(X0)) | (calm(fred) & brave(fred))) & (~calm(fred) | ~brave(fred) | ! [X1] : (~wise(X1) | ~creative(X1))) [rectify 68]
70. ? [X0] : (wise(X0) & creative(X0)) => (wise(sK7) & creative(sK7)) [choice axiom]
71. ((wise(sK7) & creative(sK7)) | (calm(fred) & brave(fred))) & (~calm(fred) | ~brave(fred) | ! [X1] : (~wise(X1) | ~creative(X1))) [skolemisation 69,70]
72. ! [X0] : (~strong(X0) | happy(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) [nnf transformation 39]
88. brave(fred) | ~kind(paul) [cnf transformation 46]
89. brave(fred) | ~rich(paul) [cnf transformation 46]
100. ~creative(X0) | wise(X0) | ~kind(X0) | ~calm(X0) [cnf transformation 53]
106. ~wise(X0) | ~wise(X0) | kind(X0) [cnf transformation 55]
109. wise(X0) | rich(X0) | wise(X0) [cnf transformation 55]
110. ~patient(sK5) | happy(X3) | creative(X3) [cnf transformation 60]
114. ~old(X0) | quiet(X0) | ~calm(X0) [cnf transformation 33]
115. kind(sK6) | calm(X1) [cnf transformation 63]
116. strong(sK6) | calm(X1) [cnf transformation 63]
117. ~strong(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 64]
119. ~old(X0) | ~quiet(X0) [cnf transformation 36]
122. ~calm(X0) | patient(X0) [cnf transformation 36]
124. ~happy(X0) | old(X0) [cnf transformation 37]
127. ~funny(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 66]
129. ~kind(X0) | happy(X0) | funny(X0) [cnf transformation 66]
131. ~calm(fred) | ~brave(fred) | ~wise(X1) | ~creative(X1) [cnf transformation 71]
136. ~strong(X0) | happy(X0) | kind(X0) | funny(X0) [cnf transformation 72]
137. ~strong(X0) | happy(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 72]
145. kind(mary) [cnf transformation 22]
146. ~happy(X0) | ~strong(X0) [duplicate literal removal 117]
147. ~wise(X0) | kind(X0) [duplicate literal removal 106]
148. wise(X0) | rich(X0) [duplicate literal removal 109]
182. 8 <=> brave(fred) [avatar definition]
190. 10 <=> kind(paul) [avatar definition]
194. 11 <=> rich(paul) [avatar definition]
195. ~rich(paul) <- (~11) [avatar component clause 194]
200. ~11 | 8 [avatar split clause 89,182,194]
201. ~10 | 8 [avatar split clause 88,182,190]
247. 22 <=> ! [X3] : (happy(X3) | creative(X3)) [avatar definition]
248. happy(X3) | creative(X3) <- (22) [avatar component clause 247]
255. 24 <=> patient(sK5) [avatar definition]
257. ~patient(sK5) <- (~24) [avatar component clause 255]
258. 22 | ~24 [avatar split clause 110,255,247]
260. 25 <=> ! [X1] : calm(X1) [avatar definition]
261. calm(X1) <- (25) [avatar component clause 260]
263. 26 <=> strong(sK6) [avatar definition]
265. strong(sK6) <- (26) [avatar component clause 263]
266. 25 | 26 [avatar split clause 116,263,260]
268. 27 <=> kind(sK6) [avatar definition]
271. 25 | 27 [avatar split clause 115,268,260]
273. 28 <=> calm(fred) [avatar definition]
274. ~calm(fred) <- (~28) [avatar component clause 273]
289. 31 <=> ! [X1] : (~wise(X1) | ~creative(X1)) [avatar definition]
290. ~creative(X1) | ~wise(X1) <- (31) [avatar component clause 289]
291. 31 | ~8 | ~28 [avatar split clause 131,273,182,289]
292. ~funny(X0) | ~strong(X0) | ~kind(X0) [subsumption resolution 137,127]
293. ~strong(X0) | happy(X0) | funny(X0) [subsumption resolution 136,129]
294. ~strong(X0) | funny(X0) [subsumption resolution 293,146]
324. $false <- (25, ~28) [resolution 274,261]
325. ~25 | 28 [avatar contradiction clause 324]
330. rich(X0) | kind(X0) [resolution 148,147]
337. funny(sK6) <- (26) [resolution 294,265]
346. 38 <=> creative(mary) [avatar definition]
348. creative(mary) <- (38) [avatar component clause 346]
389. 44 <=> quiet(mary) [avatar definition]
412. 47 <=> happy(mary) [avatar definition]
413. ~happy(mary) <- (~47) [avatar component clause 412]
414. happy(mary) <- (47) [avatar component clause 412]
428. 50 <=> wise(mary) [avatar definition]
429. ~wise(mary) <- (~50) [avatar component clause 428]
437. ~strong(sK6) | ~kind(sK6) <- (26) [resolution 292,337]
440. ~kind(sK6) <- (26) [subsumption resolution 437,265]
445. ~27 | ~26 [avatar split clause 440,263,268]
459. patient(X1) <- (25) [resolution 261,122]
467. $false <- (~24, 25) [resolution 459,257]
472. 24 | ~25 [avatar contradiction clause 467]
477. creative(mary) <- (22, ~47) [resolution 248,413]
482. ~wise(mary) <- (31, 38) [resolution 290,348]
486. ~50 | ~31 | ~38 [avatar split clause 482,346,289,428]
496. wise(mary) | ~kind(mary) | ~calm(mary) <- (38) [resolution 100,348]
500. ~kind(mary) | ~calm(mary) <- (38, ~50) [subsumption resolution 496,429]
501. ~calm(mary) <- (38, ~50) [subsumption resolution 500,145]
502. $false <- (25, 38, ~50) [subsumption resolution 501,261]
503. ~25 | ~38 | 50 [avatar contradiction clause 502]
506. 38 | ~22 | 47 [avatar split clause 477,412,247,346]
509. old(mary) <- (47) [resolution 414,124]
536. kind(paul) <- (~11) [resolution 330,195]
539. 10 | 11 [avatar split clause 536,194,190]
577. quiet(mary) | ~calm(mary) <- (47) [resolution 509,114]
579. ~quiet(mary) <- (47) [resolution 509,119]
583. ~44 | ~47 [avatar split clause 579,412,389]
584. quiet(mary) <- (25, 47) [subsumption resolution 577,261]
585. 44 | ~25 | ~47 [avatar split clause 584,412,260,389]
586. $false [avatar sat refutation 200,201,258,266,271,291,325,445,472,486,503,506,539,583,585]
% SZS output end Proof for 6080933589770169417464733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not old then someone is either happy or not generous.
Everyone who is kind is both kind and not strong.
If lucy is both strong and rich then lucy is both creative and not quiet and vice versa.
Everyone who is both not humble and kind is patient or not brave and vice versa.
If someone is either not old or not patient then susan is wise or not humble.
Everyone who is either generous or happy is not old.
If someone is either quiet or humble then mary is both not patient and not wise and vice versa.
If someone is either not funny or not rich then someone is rich or wise.
Everyone who is kind or brave is both funny and wise.
Everyone who is either not happy or not generous is either strong or happy and vice versa.
If alice is not kind or not rich then john is both not rich and not wise.
If someone is either strong or not creative then mary is either rich or not kind and vice versa.
Everyone who is either quiet or not creative is either old or not strong.
If someone is not wise then someone is not patient or quiet.
Everyone who is not patient is either creative or funny and vice versa.
If lucy is not curious or not calm then someone is both not brave and not happy.
Someone is not creative.
John is not rich.
John is both not strong and not patient.
Mary is not humble.
Someone is rich.
Someone is both not calm and not strong.
Alice is brave or not brave. | Lucy is not quiet. | neutral | ((?[X]:((~creative(X)<~>~old(X))))=>(?[X]:((happy(X)<~>~generous(X)))))&
(![X]:(kind(X)=>(kind(X)&~strong(X))))&
(((strong(lucy)&rich(lucy)))<=>((creative(lucy)&~quiet(lucy))))&
(![X]:((~humble(X)&kind(X))<=>(patient(X)|~brave(X))))&
((?[X]:((~old(X)<~>~patient(X))))=>((wise(susan)|~humble(susan))))&
(![X]:((generous(X)<~>happy(X))=>~old(X)))&
((?[X]:((quiet(X)<~>humble(X))))<=>((~patient(mary)&~wise(mary))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((kind(X)|brave(X))=>(funny(X)&wise(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(strong(X)<~>happy(X))))&
(((~kind(alice)|~rich(alice)))=>((~rich(john)&~wise(john))))&
((?[X]:((strong(X)<~>~creative(X))))<=>((rich(mary)<~>~kind(mary))))&
(![X]:((quiet(X)<~>~creative(X))=>(old(X)<~>~strong(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:(~patient(X)<=>(creative(X)<~>funny(X))))&
(((~curious(lucy)|~calm(lucy)))=>(?[X]:((~brave(X)&~happy(X)))))&
(?[X]:(~creative(X)))&
(~rich(john))&
((~strong(john)&~patient(john)))&
(~humble(mary))&
(?[X]:(rich(X)))&
(?[X]:((~calm(X)&~strong(X))))&
((brave(alice)|~brave(alice))) | ~quiet(lucy) | [] | null | 0 |
If susan is kind then someone is either humble or not humble and vice versa.
Everyone who is either not strong or funny is both not patient and not quiet and vice versa.
If fred is both not happy and not strong then someone is either not humble or not rich and vice versa.
If someone is old or not quiet then someone is not calm.
Everyone who is not patient is both not strong and happy.
If paul is both kind and tall then someone is either not generous or creative.
Everyone who is brave is either not patient or not brave and vice versa.
Everyone who is either not kind or old is either not brave or not funny.
If someone is either not humble or not generous then paul is curious.
If someone is either not humble or not calm then someone is kind or not quiet.
Everyone who is either not brave or rich is either old or not strong and vice versa.
Everyone who is not funny or patient is old or not humble and vice versa.
If someone is happy then mary is old.
Everyone who is not rich or happy is both happy and rich.
Everyone who is not curious or not calm is both not creative and not generous.
Alice is either not calm or not brave.
Someone is brave or creative.
Fred is either rich or not tall.
Lucy is both quiet and rich.
Someone is both not brave and not wise. | Susan is humble. | entailment | ((kind(susan))<=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~strong(X)<~>funny(X))<=>(~patient(X)&~quiet(X))))&
(((~happy(fred)&~strong(fred)))<=>(?[X]:((~humble(X)<~>~rich(X)))))&
((?[X]:((old(X)|~quiet(X))))=>(?[X]:(~calm(X))))&
(![X]:(~patient(X)=>(~strong(X)&happy(X))))&
(((kind(paul)&tall(paul)))=>(?[X]:((~generous(X)<~>creative(X)))))&
(![X]:(brave(X)<=>(~patient(X)<~>~brave(X))))&
(![X]:((~kind(X)<~>old(X))=>(~brave(X)<~>~funny(X))))&
((?[X]:((~humble(X)<~>~generous(X))))=>(curious(paul)))&
((?[X]:((~humble(X)<~>~calm(X))))=>(?[X]:((kind(X)|~quiet(X)))))&
(![X]:((~brave(X)<~>rich(X))<=>(old(X)<~>~strong(X))))&
(![X]:((~funny(X)|patient(X))<=>(old(X)|~humble(X))))&
((?[X]:(happy(X)))=>(old(mary)))&
(![X]:((~rich(X)|happy(X))=>(happy(X)&rich(X))))&
(![X]:((~curious(X)|~calm(X))=>(~creative(X)&~generous(X))))&
((~calm(alice)<~>~brave(alice)))&
(?[X]:((brave(X)|creative(X))))&
((rich(fred)<~>~tall(fred)))&
((quiet(lucy)&rich(lucy)))&
(?[X]:((~brave(X)&~wise(X)))) | humble(susan) | [
"p2",
"p4",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8097633930872682860516081
% SZS output start Proof for 8097633930872682860516081
3. (~strong(fred) & ~happy(fred)) <=> ? [X0] : (~humble(X0) <~> ~rich(X0)) [input p2]
5. ! [X0] : (~patient(X0) => (happy(X0) & ~strong(X0))) [input p4]
7. ! [X0] : (brave(X0) <=> (~patient(X0) <~> ~brave(X0))) [input p6]
14. ! [X0] : ((happy(X0) | ~rich(X0)) => (rich(X0) & happy(X0))) [input p13]
21. ~humble(susan) [input hypothesis]
28. ! [X0] : ((happy(X0) & ~strong(X0)) | patient(X0)) [ennf transformation 5]
34. ! [X0] : ((rich(X0) & happy(X0)) | (~happy(X0) & rich(X0))) [ennf transformation 14]
42. ((~strong(fred) & ~happy(fred)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0)))) & (? [X0] : ((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | (strong(fred) | happy(fred))) [nnf transformation 3]
43. ((~strong(fred) & ~happy(fred)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0)))) & (? [X0] : ((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | strong(fred) | happy(fred)) [flattening 42]
44. ((~strong(fred) & ~happy(fred)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0)))) & (? [X1] : ((rich(X1) | humble(X1)) & (~rich(X1) | ~humble(X1))) | strong(fred) | happy(fred)) [rectify 43]
45. ? [X1] : ((rich(X1) | humble(X1)) & (~rich(X1) | ~humble(X1))) => ((rich(sK1) | humble(sK1)) & (~rich(sK1) | ~humble(sK1))) [choice axiom]
46. ((~strong(fred) & ~happy(fred)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0)))) & (((rich(sK1) | humble(sK1)) & (~rich(sK1) | ~humble(sK1))) | strong(fred) | happy(fred)) [skolemisation 44,45]
53. ! [X0] : ((brave(X0) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) & (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | ~brave(X0))) [nnf transformation 7]
80. ~happy(fred) | ~rich(X0) | humble(X0) [cnf transformation 46]
87. happy(X0) | patient(X0) [cnf transformation 28]
90. ~brave(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 53]
93. brave(X0) | ~patient(X0) | brave(X0) [cnf transformation 53]
115. rich(X0) | rich(X0) [cnf transformation 34]
127. ~humble(susan) [cnf transformation 21]
128. rich(X0) [duplicate literal removal 115]
129. ~brave(X0) | ~patient(X0) [duplicate literal removal 90]
130. brave(X0) | ~patient(X0) [duplicate literal removal 93]
134. 1 <=> ! [X0] : humble(X0) [avatar definition]
135. humble(X0) <- (1) [avatar component clause 134]
154. 6 <=> ! [X0] : (~rich(X0) | humble(X0)) [avatar definition]
155. ~rich(X0) | humble(X0) <- (6) [avatar component clause 154]
158. 7 <=> happy(fred) [avatar definition]
160. ~happy(fred) <- (~7) [avatar component clause 158]
162. 6 | ~7 [avatar split clause 80,158,154]
203. ~patient(X0) [subsumption resolution 129,130]
257. patient(fred) <- (~7) [resolution 160,87]
258. $false <- (~7) [subsumption resolution 257,203]
259. 7 [avatar contradiction clause 258]
260. humble(X0) <- (6) [subsumption resolution 155,128]
261. 1 | ~6 [avatar split clause 260,154,134]
262. $false <- (1) [resolution 135,127]
265. ~1 [avatar contradiction clause 262]
266. $false [avatar sat refutation 162,259,261,265]
% SZS output end Proof for 8097633930872682860516081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not quiet is happy or generous. If john is not creative then someone is brave and vice versa. If alice is both rich and not strong then lucy is creative. Everyone who is curious is both brave and not curious and vice versa. If paul is curious or generous then someone is not calm or creative. Everyone who is rich or brave is both brave and calm. If susan is not brave then lucy is either generous or not tall. If someone is not patient then someone is either not happy or not strong and vice versa. If lucy is strong or not quiet then mary is not kind or generous. If someone is not wise or quiet then susan is not humble. Everyone who is both not quiet and not brave is either not tall or brave. Everyone who is either brave or calm is both not happy and generous and vice versa. If someone is either not calm or not patient then john is not brave or kind. If someone is both creative and calm then someone is either wise or curious and vice versa. If mary is strong or creative then fred is either happy or creative and vice versa. If susan is funny or creative then paul is brave. Someone is both not old and humble. Mary is humble or brave. Paul is creative. Someone is either not tall or patient. John is either not generous or old. Someone is not strong. Fred is old. | Lucy is curious. | contradiction | (![X]:((~generous(X)|~quiet(X))=>(happy(X)|generous(X))))&
((~creative(john))<=>(?[X]:(brave(X))))&
(((rich(alice)&~strong(alice)))=>(creative(lucy)))&
(![X]:(curious(X)<=>(brave(X)&~curious(X))))&
(((curious(paul)|generous(paul)))=>(?[X]:((~calm(X)|creative(X)))))&
(![X]:((rich(X)|brave(X))=>(brave(X)&calm(X))))&
((~brave(susan))=>((generous(lucy)<~>~tall(lucy))))&
((?[X]:(~patient(X)))<=>(?[X]:((~happy(X)<~>~strong(X)))))&
(((strong(lucy)|~quiet(lucy)))=>((~kind(mary)|generous(mary))))&
((?[X]:((~wise(X)|quiet(X))))=>(~humble(susan)))&
(![X]:((~quiet(X)&~brave(X))=>(~tall(X)<~>brave(X))))&
(![X]:((brave(X)<~>calm(X))<=>(~happy(X)&generous(X))))&
((?[X]:((~calm(X)<~>~patient(X))))=>((~brave(john)|kind(john))))&
((?[X]:((creative(X)&calm(X))))<=>(?[X]:((wise(X)<~>curious(X)))))&
(((strong(mary)|creative(mary)))<=>((happy(fred)<~>creative(fred))))&
(((funny(susan)|creative(susan)))=>(brave(paul)))&
(?[X]:((~old(X)&humble(X))))&
((humble(mary)|brave(mary)))&
(creative(paul))&
(?[X]:((~tall(X)<~>patient(X))))&
((~generous(john)<~>old(john)))&
(?[X]:(~strong(X)))&
(old(fred)) | curious(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2061315260580777741685356
% SZS output start Proof for 2061315260580777741685356
4. ! [X0] : (curious(X0) <=> (~curious(X0) & brave(X0))) [input p3]
24. curious(lucy) [input hypothesis]
47. ! [X0] : ((curious(X0) | (curious(X0) | ~brave(X0))) & ((~curious(X0) & brave(X0)) | ~curious(X0))) [nnf transformation 4]
48. ! [X0] : ((curious(X0) | curious(X0) | ~brave(X0)) & ((~curious(X0) & brave(X0)) | ~curious(X0))) [flattening 47]
81. ~curious(X0) | ~curious(X0) [cnf transformation 48]
130. curious(lucy) [cnf transformation 24]
132. ~curious(X0) [duplicate literal removal 81]
334. $false [subsumption resolution 130,132]
% SZS output end Proof for 2061315260580777741685356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then fred is humble.
Everyone who is wise is both calm and brave.
Everyone who is both creative and old is not rich or not old and vice versa.
If someone is either not old or curious then fred is not calm.
If someone is either curious or not tall then fred is either wise or not curious.
If alice is calm or not tall then mary is both strong and not old.
Everyone who is not tall is not curious or kind.
Everyone who is both not old and strong is both not happy and not funny and vice versa.
Everyone who is wise or creative is both strong and funny.
If someone is either humble or kind then someone is both tall and not quiet.
Everyone who is both not rich and patient is either kind or wise and vice versa.
Everyone who is both not happy and not brave is either not humble or happy and vice versa.
If paul is tall then someone is not generous and vice versa.
If paul is wise then someone is both not curious and generous and vice versa.
If someone is either not patient or not humble then someone is patient and vice versa.
If paul is not funny then alice is not brave.
John is either not generous or calm.
Alice is either not kind or not patient.
Someone is both curious and brave.
John is both old and strong.
Fred is either calm or patient.
Lucy is calm or not curious.
Paul is either humble or not rich.
Lucy is old. | Fred is funny. | entailment | ((?[X]:(~kind(X)))=>(humble(fred)))&
(![X]:(wise(X)=>(calm(X)&brave(X))))&
(![X]:((creative(X)&old(X))<=>(~rich(X)|~old(X))))&
((?[X]:((~old(X)<~>curious(X))))=>(~calm(fred)))&
((?[X]:((curious(X)<~>~tall(X))))=>((wise(fred)<~>~curious(fred))))&
(((calm(alice)|~tall(alice)))=>((strong(mary)&~old(mary))))&
(![X]:(~tall(X)=>(~curious(X)|kind(X))))&
(![X]:((~old(X)&strong(X))<=>(~happy(X)&~funny(X))))&
(![X]:((wise(X)|creative(X))=>(strong(X)&funny(X))))&
((?[X]:((humble(X)<~>kind(X))))=>(?[X]:((tall(X)&~quiet(X)))))&
(![X]:((~rich(X)&patient(X))<=>(kind(X)<~>wise(X))))&
(![X]:((~happy(X)&~brave(X))<=>(~humble(X)<~>happy(X))))&
((tall(paul))<=>(?[X]:(~generous(X))))&
((wise(paul))<=>(?[X]:((~curious(X)&generous(X)))))&
((?[X]:((~patient(X)<~>~humble(X))))<=>(?[X]:(patient(X))))&
((~funny(paul))=>(~brave(alice)))&
((~generous(john)<~>calm(john)))&
((~kind(alice)<~>~patient(alice)))&
(?[X]:((curious(X)&brave(X))))&
((old(john)&strong(john)))&
((calm(fred)<~>patient(fred)))&
((calm(lucy)|~curious(lucy)))&
((humble(paul)<~>~rich(paul)))&
(old(lucy)) | funny(fred) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6215890374093564197999193
% SZS output start Proof for 6215890374093564197999193
1. ? [X0] : ~kind(X0) => humble(fred) [input p0]
2. ! [X0] : (wise(X0) => (brave(X0) & calm(X0))) [input p1]
3. ! [X0] : ((old(X0) & creative(X0)) <=> (~old(X0) | ~rich(X0))) [input p2]
6. (~tall(alice) | calm(alice)) => (~old(mary) & strong(mary)) [input p5]
8. ! [X0] : ((strong(X0) & ~old(X0)) <=> (~funny(X0) & ~happy(X0))) [input p7]
11. ! [X0] : ((patient(X0) & ~rich(X0)) <=> (kind(X0) <~> wise(X0))) [input p10]
12. ! [X0] : ((~brave(X0) & ~happy(X0)) <=> (~humble(X0) <~> happy(X0))) [input p11]
18. ~kind(alice) <~> ~patient(alice) [input p17]
25. ~funny(fred) [input hypothesis]
29. humble(fred) | ! [X0] : kind(X0) [ennf transformation 1]
30. ! [X0] : ((brave(X0) & calm(X0)) | ~wise(X0)) [ennf transformation 2]
33. (~old(mary) & strong(mary)) | (tall(alice) & ~calm(alice)) [ennf transformation 6]
39. ! [X0] : (((old(X0) & creative(X0)) | (old(X0) & rich(X0))) & ((~old(X0) | ~rich(X0)) | (~old(X0) | ~creative(X0)))) [nnf transformation 3]
40. ! [X0] : (((old(X0) & creative(X0)) | (old(X0) & rich(X0))) & (~old(X0) | ~rich(X0) | ~old(X0) | ~creative(X0))) [flattening 39]
43. ! [X0] : (((strong(X0) & ~old(X0)) | (funny(X0) | happy(X0))) & ((~funny(X0) & ~happy(X0)) | (~strong(X0) | old(X0)))) [nnf transformation 8]
44. ! [X0] : (((strong(X0) & ~old(X0)) | funny(X0) | happy(X0)) & ((~funny(X0) & ~happy(X0)) | ~strong(X0) | old(X0))) [flattening 43]
49. ! [X0] : (((patient(X0) & ~rich(X0)) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0)))) & (((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (~patient(X0) | rich(X0)))) [nnf transformation 11]
50. ! [X0] : (((patient(X0) & ~rich(X0)) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0)))) & (((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | ~patient(X0) | rich(X0))) [flattening 49]
51. ! [X0] : (((~brave(X0) & ~happy(X0)) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0)))) & (((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | (brave(X0) | happy(X0)))) [nnf transformation 12]
52. ! [X0] : (((~brave(X0) & ~happy(X0)) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0)))) & (((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | brave(X0) | happy(X0))) [flattening 51]
67. (patient(alice) | kind(alice)) & (~patient(alice) | ~kind(alice)) [nnf transformation 18]
72. humble(fred) | kind(X0) [cnf transformation 29]
73. ~wise(X0) | calm(X0) [cnf transformation 30]
79. old(X0) | old(X0) [cnf transformation 40]
88. ~old(mary) | ~calm(alice) [cnf transformation 33]
93. ~old(X0) | funny(X0) | happy(X0) [cnf transformation 44]
105. ~kind(X0) | wise(X0) | patient(X0) [cnf transformation 50]
110. ~happy(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 52]
125. ~patient(alice) | ~kind(alice) [cnf transformation 67]
137. ~funny(fred) [cnf transformation 25]
139. ~happy(X0) | ~humble(X0) [duplicate literal removal 110]
141. old(X0) [duplicate literal removal 79]
143. 1 <=> ! [X0] : kind(X0) [avatar definition]
144. kind(X0) <- (1) [avatar component clause 143]
146. 2 <=> humble(fred) [avatar definition]
149. 1 | 2 [avatar split clause 72,146,143]
179. ~calm(alice) [subsumption resolution 88,141]
180. funny(X0) | happy(X0) [subsumption resolution 93,141]
270. 29 <=> kind(alice) [avatar definition]
271. ~kind(alice) <- (~29) [avatar component clause 270]
272. kind(alice) <- (29) [avatar component clause 270]
274. 30 <=> patient(alice) [avatar definition]
275. ~patient(alice) <- (~30) [avatar component clause 274]
278. ~29 | ~30 [avatar split clause 125,274,270]
315. happy(fred) [resolution 180,137]
317. ~humble(fred) [resolution 315,139]
320. ~2 [avatar split clause 317,146]
330. wise(alice) | patient(alice) <- (29) [resolution 105,272]
332. wise(alice) <- (29, ~30) [subsumption resolution 330,275]
336. calm(alice) <- (29, ~30) [resolution 332,73]
339. $false <- (29, ~30) [subsumption resolution 336,179]
340. ~29 | 30 [avatar contradiction clause 339]
341. $false <- (1, ~29) [subsumption resolution 271,144]
342. ~1 | 29 [avatar contradiction clause 341]
343. $false [avatar sat refutation 149,278,320,340,342]
% SZS output end Proof for 6215890374093564197999193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is rich then someone is both generous and brave.
Everyone who is both generous and not funny is humble and vice versa.
If someone is either rich or old then lucy is brave.
Everyone who is either calm or humble is both rich and not tall.
If lucy is humble then someone is not old or not curious and vice versa.
If someone is tall or quiet then someone is not happy or not generous and vice versa.
Everyone who is strong is either strong or not quiet.
Everyone who is both not wise and humble is either patient or funny.
Everyone who is both tall and not old is either wise or creative and vice versa.
If someone is both curious and rich then lucy is not funny and vice versa.
Everyone who is not quiet is creative or quiet.
If someone is either not creative or old then someone is either old or not happy and vice versa.
Everyone who is both not quiet and not generous is either tall or not patient and vice versa.
Everyone who is humble or not strong is either not patient or not funny and vice versa.
Everyone who is both tall and calm is both not quiet and not kind.
If someone is both not tall and generous then fred is both generous and tall.
Someone is calm.
Mary is both old and patient.
Someone is not rich or wise.
Someone is not rich.
Alice is either strong or calm.
Susan is both not creative and humble.
Susan is not humble or humble. | Fred is not strong. | entailment | ((rich(fred))=>(?[X]:((generous(X)&brave(X)))))&
(![X]:((generous(X)&~funny(X))<=>humble(X)))&
((?[X]:((rich(X)<~>old(X))))=>(brave(lucy)))&
(![X]:((calm(X)<~>humble(X))=>(rich(X)&~tall(X))))&
((humble(lucy))<=>(?[X]:((~old(X)|~curious(X)))))&
((?[X]:((tall(X)|quiet(X))))<=>(?[X]:((~happy(X)|~generous(X)))))&
(![X]:(strong(X)=>(strong(X)<~>~quiet(X))))&
(![X]:((~wise(X)&humble(X))=>(patient(X)<~>funny(X))))&
(![X]:((tall(X)&~old(X))<=>(wise(X)<~>creative(X))))&
((?[X]:((curious(X)&rich(X))))<=>(~funny(lucy)))&
(![X]:(~quiet(X)=>(creative(X)|quiet(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:((~quiet(X)&~generous(X))<=>(tall(X)<~>~patient(X))))&
(![X]:((humble(X)|~strong(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((tall(X)&calm(X))=>(~quiet(X)&~kind(X))))&
((?[X]:((~tall(X)&generous(X))))=>((generous(fred)&tall(fred))))&
(?[X]:(calm(X)))&
((old(mary)&patient(mary)))&
(?[X]:((~rich(X)|wise(X))))&
(?[X]:(~rich(X)))&
((strong(alice)<~>calm(alice)))&
((~creative(susan)&humble(susan)))&
((~humble(susan)|humble(susan))) | ~strong(fred) | [
"p1",
"p3",
"p6",
"p10",
"p12",
"p13",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 539171233177527904897131
% SZS output start Proof for 539171233177527904897131
2. ! [X0] : ((~funny(X0) & generous(X0)) <=> humble(X0)) [input p1]
4. ! [X0] : ((calm(X0) <~> humble(X0)) => (~tall(X0) & rich(X0))) [input p3]
7. ! [X0] : (strong(X0) => (strong(X0) <~> ~quiet(X0))) [input p6]
11. ! [X0] : (~quiet(X0) => (quiet(X0) | creative(X0))) [input p10]
13. ! [X0] : ((~generous(X0) & ~quiet(X0)) <=> (tall(X0) <~> ~patient(X0))) [input p12]
14. ! [X0] : ((~strong(X0) | humble(X0)) <=> (~patient(X0) <~> ~funny(X0))) [input p13]
15. ! [X0] : ((calm(X0) & tall(X0)) => (~kind(X0) & ~quiet(X0))) [input p14]
16. ? [X0] : (generous(X0) & ~tall(X0)) => (tall(fred) & generous(fred)) [input p15]
22. humble(susan) & ~creative(susan) [input p21]
24. strong(fred) [input hypothesis]
27. ! [X0] : ((calm(X0) & tall(X0)) => ~quiet(X0)) [pure predicate removal 15]
31. ! [X0] : ((~tall(X0) & rich(X0)) | (calm(X0) <=> humble(X0))) [ennf transformation 4]
32. ! [X0] : ((strong(X0) <~> ~quiet(X0)) | ~strong(X0)) [ennf transformation 7]
35. ! [X0] : ((quiet(X0) | creative(X0)) | quiet(X0)) [ennf transformation 11]
36. ! [X0] : (quiet(X0) | creative(X0) | quiet(X0)) [flattening 35]
37. ! [X0] : (~quiet(X0) | (~calm(X0) | ~tall(X0))) [ennf transformation 27]
38. ! [X0] : (~quiet(X0) | ~calm(X0) | ~tall(X0)) [flattening 37]
39. (tall(fred) & generous(fred)) | ! [X0] : (~generous(X0) | tall(X0)) [ennf transformation 16]
42. ! [X0] : (((~funny(X0) & generous(X0)) | ~humble(X0)) & (humble(X0) | (funny(X0) | ~generous(X0)))) [nnf transformation 2]
43. ! [X0] : (((~funny(X0) & generous(X0)) | ~humble(X0)) & (humble(X0) | funny(X0) | ~generous(X0))) [flattening 42]
44. ! [X0] : ((~tall(X0) & rich(X0)) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) [nnf transformation 31]
54. ! [X0] : (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | ~strong(X0)) [nnf transformation 32]
67. ! [X0] : (((~generous(X0) & ~quiet(X0)) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0)))) & (((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | (generous(X0) | quiet(X0)))) [nnf transformation 13]
68. ! [X0] : (((~generous(X0) & ~quiet(X0)) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0)))) & (((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | generous(X0) | quiet(X0))) [flattening 67]
69. ! [X0] : (((~strong(X0) | humble(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (strong(X0) & ~humble(X0)))) [nnf transformation 14]
70. ! [X0] : ((~strong(X0) | humble(X0) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (strong(X0) & ~humble(X0)))) [flattening 69]
79. ~generous(X0) | funny(X0) | humble(X0) [cnf transformation 43]
80. ~humble(X0) | generous(X0) [cnf transformation 43]
81. ~humble(X0) | ~funny(X0) [cnf transformation 43]
85. ~tall(X0) | calm(X0) | ~humble(X0) [cnf transformation 44]
94. quiet(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 54]
106. quiet(X0) | creative(X0) | quiet(X0) [cnf transformation 36]
117. ~patient(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 68]
123. funny(X0) | patient(X0) | ~humble(X0) [cnf transformation 70]
125. ~strong(X0) | humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 70]
127. ~quiet(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 38]
128. generous(fred) | ~generous(X0) | tall(X0) [cnf transformation 39]
129. tall(fred) | ~generous(X0) | tall(X0) [cnf transformation 39]
137. ~creative(susan) [cnf transformation 22]
138. humble(susan) [cnf transformation 22]
140. strong(fred) [cnf transformation 24]
141. creative(X0) | quiet(X0) [duplicate literal removal 106]
142. ~strong(X0) | quiet(X0) [duplicate literal removal 94]
260. ~strong(X0) | ~funny(X0) | patient(X0) [subsumption resolution 125,81]
261. ~humble(X0) | patient(X0) [subsumption resolution 123,81]
263. 28 <=> ! [X0] : (~generous(X0) | tall(X0)) [avatar definition]
264. ~generous(X0) | tall(X0) <- (28) [avatar component clause 263]
266. 29 <=> tall(fred) [avatar definition]
268. tall(fred) <- (29) [avatar component clause 266]
269. 28 | 29 [avatar split clause 129,266,263]
271. 30 <=> generous(fred) [avatar definition]
273. generous(fred) <- (30) [avatar component clause 271]
274. 28 | 30 [avatar split clause 128,271,263]
294. generous(susan) [resolution 80,138]
298. quiet(susan) [resolution 141,137]
300. quiet(fred) [resolution 142,140]
302. patient(susan) [resolution 261,138]
304. tall(susan) <- (28) [resolution 264,294]
354. ~quiet(susan) | ~tall(susan) [resolution 117,302]
365. ~tall(susan) [subsumption resolution 354,298]
366. $false <- (28) [subsumption resolution 365,304]
367. ~28 [avatar contradiction clause 366]
378. calm(fred) | ~humble(fred) <- (29) [resolution 268,85]
381. 47 <=> humble(fred) [avatar definition]
383. ~humble(fred) <- (~47) [avatar component clause 381]
385. 48 <=> calm(fred) [avatar definition]
388. ~47 | 48 | ~29 [avatar split clause 378,266,385,381]
390. funny(fred) | humble(fred) <- (30) [resolution 273,79]
391. funny(fred) <- (30, ~47) [subsumption resolution 390,383]
453. ~calm(fred) | ~tall(fred) [resolution 127,300]
458. ~funny(fred) | patient(fred) [resolution 260,140]
460. patient(fred) <- (30, ~47) [subsumption resolution 458,391]
463. ~quiet(fred) | ~tall(fred) <- (30, ~47) [resolution 460,117]
467. ~tall(fred) <- (30, ~47) [subsumption resolution 463,300]
468. $false <- (29, 30, ~47) [subsumption resolution 467,268]
469. ~29 | ~30 | 47 [avatar contradiction clause 468]
480. ~calm(fred) <- (29) [subsumption resolution 453,268]
481. ~48 | ~29 [avatar split clause 480,266,385]
482. $false [avatar sat refutation 269,274,367,388,469,481]
% SZS output end Proof for 539171233177527904897131
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not wise and strong is curious or not kind and vice versa.
If someone is not tall or kind then someone is generous or not happy and vice versa.
Everyone who is not funny is creative.
Everyone who is both creative and happy is calm or not humble and vice versa.
Everyone who is either quiet or generous is creative or not curious and vice versa.
If someone is not generous then mary is not generous.
Everyone who is not happy is both not tall and not happy.
Everyone who is both not brave and not curious is brave or not calm.
Everyone who is both not kind and creative is both not calm and tall.
If mary is both strong and curious then someone is either quiet or not creative and vice versa.
Everyone who is quiet is both tall and not creative.
Everyone who is either not old or calm is both generous and old and vice versa.
If someone is funny or not calm then someone is not happy or funny and vice versa.
Everyone who is either kind or not curious is both humble and calm and vice versa.
If alice is kind or not funny then susan is either curious or not wise.
If susan is tall then someone is not humble or not strong and vice versa.
Susan is not strong or not tall.
Alice is either not brave or not creative.
Paul is both not humble and happy.
Lucy is either not old or brave.
Alice is happy.
Someone is either kind or rich.
Someone is not strong.
Lucy is both not old and not tall. | Paul is not creative. | contradiction | (![X]:((~wise(X)&strong(X))<=>(curious(X)|~kind(X))))&
((?[X]:((~tall(X)|kind(X))))<=>(?[X]:((generous(X)|~happy(X)))))&
(![X]:(~funny(X)=>creative(X)))&
(![X]:((creative(X)&happy(X))<=>(calm(X)|~humble(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(creative(X)|~curious(X))))&
((?[X]:(~generous(X)))=>(~generous(mary)))&
(![X]:(~happy(X)=>(~tall(X)&~happy(X))))&
(![X]:((~brave(X)&~curious(X))=>(brave(X)|~calm(X))))&
(![X]:((~kind(X)&creative(X))=>(~calm(X)&tall(X))))&
(((strong(mary)&curious(mary)))<=>(?[X]:((quiet(X)<~>~creative(X)))))&
(![X]:(quiet(X)=>(tall(X)&~creative(X))))&
(![X]:((~old(X)<~>calm(X))<=>(generous(X)&old(X))))&
((?[X]:((funny(X)|~calm(X))))<=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:((kind(X)<~>~curious(X))<=>(humble(X)&calm(X))))&
(((kind(alice)|~funny(alice)))=>((curious(susan)<~>~wise(susan))))&
((tall(susan))<=>(?[X]:((~humble(X)|~strong(X)))))&
((~strong(susan)|~tall(susan)))&
((~brave(alice)<~>~creative(alice)))&
((~humble(paul)&happy(paul)))&
((~old(lucy)<~>brave(lucy)))&
(happy(alice))&
(?[X]:((kind(X)<~>rich(X))))&
(?[X]:(~strong(X)))&
((~old(lucy)&~tall(lucy))) | ~creative(paul) | [
"p3",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7853760210620374368424501
% SZS output start Proof for 7853760210620374368424501
4. ! [X0] : ((happy(X0) & creative(X0)) <=> (~humble(X0) | calm(X0))) [input p3]
19. happy(paul) & ~humble(paul) [input p18]
25. ~creative(paul) [input hypothesis]
44. ! [X0] : (((happy(X0) & creative(X0)) | (humble(X0) & ~calm(X0))) & ((~humble(X0) | calm(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 4]
45. ! [X0] : (((happy(X0) & creative(X0)) | (humble(X0) & ~calm(X0))) & (~humble(X0) | calm(X0) | ~happy(X0) | ~creative(X0))) [flattening 44]
86. humble(X0) | creative(X0) [cnf transformation 45]
135. ~humble(paul) [cnf transformation 19]
145. ~creative(paul) [cnf transformation 25]
333. creative(paul) [resolution 86,135]
335. $false [subsumption resolution 333,145]
% SZS output end Proof for 7853760210620374368424501
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not brave is not tall or old and vice versa.
If fred is both strong and old then someone is either calm or curious.
If john is both wise and not patient then paul is either not creative or not kind.
If someone is humble then someone is both old and brave.
Everyone who is either happy or not wise is not strong or not funny and vice versa.
Everyone who is both not quiet and not humble is both not calm and not brave and vice versa.
Everyone who is curious is wise or not calm and vice versa.
Everyone who is both happy and not kind is either not funny or not wise.
Everyone who is either not curious or not creative is not strong.
Everyone who is either not happy or not kind is creative or not kind and vice versa.
Everyone who is wise is either humble or happy.
Everyone who is either wise or calm is both not curious and not wise and vice versa.
Everyone who is either not old or not funny is both not calm and funny and vice versa.
If someone is curious then someone is either not calm or tall.
Everyone who is either not patient or quiet is not generous.
Everyone who is not kind or rich is both not tall and not old and vice versa.
Paul is not generous.
Someone is not humble or not calm.
Someone is either quiet or humble.
Someone is either brave or calm.
Someone is not calm.
John is either creative or not brave.
Alice is both happy and old.
Mary is not humble or brave. | Alice is creative. | contradiction | (![X]:((~generous(X)<~>~brave(X))<=>(~tall(X)|old(X))))&
(((strong(fred)&old(fred)))=>(?[X]:((calm(X)<~>curious(X)))))&
(((wise(john)&~patient(john)))=>((~creative(paul)<~>~kind(paul))))&
((?[X]:(humble(X)))=>(?[X]:((old(X)&brave(X)))))&
(![X]:((happy(X)<~>~wise(X))<=>(~strong(X)|~funny(X))))&
(![X]:((~quiet(X)&~humble(X))<=>(~calm(X)&~brave(X))))&
(![X]:(curious(X)<=>(wise(X)|~calm(X))))&
(![X]:((happy(X)&~kind(X))=>(~funny(X)<~>~wise(X))))&
(![X]:((~curious(X)<~>~creative(X))=>~strong(X)))&
(![X]:((~happy(X)<~>~kind(X))<=>(creative(X)|~kind(X))))&
(![X]:(wise(X)=>(humble(X)<~>happy(X))))&
(![X]:((wise(X)<~>calm(X))<=>(~curious(X)&~wise(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(~calm(X)&funny(X))))&
((?[X]:(curious(X)))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:((~patient(X)<~>quiet(X))=>~generous(X)))&
(![X]:((~kind(X)|rich(X))<=>(~tall(X)&~old(X))))&
(~generous(paul))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((quiet(X)<~>humble(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(?[X]:(~calm(X)))&
((creative(john)<~>~brave(john)))&
((happy(alice)&old(alice)))&
((~humble(mary)|brave(mary))) | creative(alice) | [
"p9",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2127092956054555266719906
% SZS output start Proof for 2127092956054555266719906
10. ! [X0] : ((~happy(X0) <~> ~kind(X0)) <=> (~kind(X0) | creative(X0))) [input p9]
16. ! [X0] : ((rich(X0) | ~kind(X0)) <=> (~old(X0) & ~tall(X0))) [input p15]
23. old(alice) & happy(alice) [input p22]
25. creative(alice) [input hypothesis]
56. ! [X0] : ((((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (kind(X0) & ~creative(X0))) & ((~kind(X0) | creative(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0))))) [nnf transformation 10]
57. ! [X0] : ((((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (kind(X0) & ~creative(X0))) & (~kind(X0) | creative(X0) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0))))) [flattening 56]
68. ! [X0] : (((rich(X0) | ~kind(X0)) | (old(X0) | tall(X0))) & ((~old(X0) & ~tall(X0)) | (~rich(X0) & kind(X0)))) [nnf transformation 16]
69. ! [X0] : ((rich(X0) | ~kind(X0) | old(X0) | tall(X0)) & ((~old(X0) & ~tall(X0)) | (~rich(X0) & kind(X0)))) [flattening 68]
112. ~happy(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 57]
136. ~old(X0) | kind(X0) [cnf transformation 69]
148. happy(alice) [cnf transformation 23]
149. old(alice) [cnf transformation 23]
151. creative(alice) [cnf transformation 25]
269. kind(alice) [resolution 136,149]
420. ~kind(alice) | ~creative(alice) [resolution 112,148]
423. ~creative(alice) [subsumption resolution 420,269]
424. $false [subsumption resolution 423,151]
% SZS output end Proof for 2127092956054555266719906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not generous then someone is not creative or kind and vice versa.
Everyone who is either funny or not humble is patient or not generous and vice versa.
Everyone who is humble or kind is both calm and tall and vice versa.
Everyone who is both generous and not brave is either creative or not creative and vice versa.
If someone is either calm or wise then fred is both rich and not curious.
Everyone who is both not rich and not quiet is strong or not creative and vice versa.
If mary is not tall or funny then susan is both not happy and kind and vice versa.
Everyone who is humble is both rich and patient.
If someone is both not tall and not patient then someone is both curious and not rich and vice versa.
Everyone who is old or not calm is both not calm and humble.
Everyone who is both old and not curious is happy or not rich and vice versa.
If fred is both old and kind then someone is both tall and not brave.
Everyone who is either not old or rich is not kind or not rich and vice versa.
If susan is not wise then lucy is either calm or not curious and vice versa.
Everyone who is either not creative or not curious is patient.
Everyone who is rich is creative or not happy.
Lucy is not curious or rich.
Susan is both not old and calm.
Someone is both not funny and not brave.
John is either happy or not humble.
Paul is not tall or kind.
Someone is either calm or happy. | Susan is not generous. | contradiction | ((?[X]:((~old(X)|~generous(X))))<=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(patient(X)|~generous(X))))&
(![X]:((humble(X)|kind(X))<=>(calm(X)&tall(X))))&
(![X]:((generous(X)&~brave(X))<=>(creative(X)<~>~creative(X))))&
((?[X]:((calm(X)<~>wise(X))))=>((rich(fred)&~curious(fred))))&
(![X]:((~rich(X)&~quiet(X))<=>(strong(X)|~creative(X))))&
(((~tall(mary)|funny(mary)))<=>((~happy(susan)&kind(susan))))&
(![X]:(humble(X)=>(rich(X)&patient(X))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:((old(X)|~calm(X))=>(~calm(X)&humble(X))))&
(![X]:((old(X)&~curious(X))<=>(happy(X)|~rich(X))))&
(((old(fred)&kind(fred)))=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((~old(X)<~>rich(X))<=>(~kind(X)|~rich(X))))&
((~wise(susan))<=>((calm(lucy)<~>~curious(lucy))))&
(![X]:((~creative(X)<~>~curious(X))=>patient(X)))&
(![X]:(rich(X)=>(creative(X)|~happy(X))))&
((~curious(lucy)|rich(lucy)))&
((~old(susan)&calm(susan)))&
(?[X]:((~funny(X)&~brave(X))))&
((happy(john)<~>~humble(john)))&
((~tall(paul)|kind(paul)))&
(?[X]:((calm(X)<~>happy(X)))) | ~generous(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2687395471236708736415015
% SZS output start Proof for 2687395471236708736415015
4. ! [X0] : ((~brave(X0) & generous(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p3]
23. ~generous(susan) [input hypothesis]
43. ! [X0] : (((~brave(X0) & generous(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (brave(X0) | ~generous(X0)))) [nnf transformation 4]
44. ! [X0] : (((~brave(X0) & generous(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | brave(X0) | ~generous(X0))) [flattening 43]
86. generous(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 44]
87. generous(X0) | creative(X0) | creative(X0) [cnf transformation 44]
144. ~generous(susan) [cnf transformation 23]
147. generous(X0) | ~creative(X0) [duplicate literal removal 86]
148. generous(X0) | creative(X0) [duplicate literal removal 87]
168. 5 <=> ! [X3] : generous(X3) [avatar definition]
169. generous(X3) <- (5) [avatar component clause 168]
184. generous(X0) [subsumption resolution 147,148]
185. 5 [avatar split clause 184,168]
272. $false <- (5) [resolution 169,144]
273. ~5 [avatar contradiction clause 272]
274. $false [avatar sat refutation 185,273]
% SZS output end Proof for 2687395471236708736415015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or not kind is either tall or generous and vice versa. Everyone who is calm is old. Everyone who is not quiet or happy is both not strong and not humble and vice versa. Everyone who is humble or not patient is either not brave or not funny and vice versa. If susan is generous then someone is calm and vice versa. If alice is not brave then susan is not kind or not tall. Everyone who is both rich and creative is calm. Everyone who is either not brave or calm is either not patient or not strong and vice versa. If someone is strong then fred is not calm. Everyone who is strong is not curious or kind and vice versa. Everyone who is happy or curious is both old and not calm and vice versa. Everyone who is humble is not strong. Everyone who is both not happy and not humble is not tall and vice versa. If john is not brave or generous then someone is either tall or creative. Everyone who is not calm or wise is either not generous or kind. Everyone who is both brave and strong is not funny or tall and vice versa. Someone is either not brave or not happy. Someone is either calm or funny. Someone is not curious or not humble. Paul is wise. Fred is either creative or not generous. Mary is either quiet or not rich. | Susan is not quiet. | contradiction | (![X]:((rich(X)<~>~kind(X))<=>(tall(X)<~>generous(X))))&
(![X]:(calm(X)=>old(X)))&
(![X]:((~quiet(X)|happy(X))<=>(~strong(X)&~humble(X))))&
(![X]:((humble(X)|~patient(X))<=>(~brave(X)<~>~funny(X))))&
((generous(susan))<=>(?[X]:(calm(X))))&
((~brave(alice))=>((~kind(susan)|~tall(susan))))&
(![X]:((rich(X)&creative(X))=>calm(X)))&
(![X]:((~brave(X)<~>calm(X))<=>(~patient(X)<~>~strong(X))))&
((?[X]:(strong(X)))=>(~calm(fred)))&
(![X]:(strong(X)<=>(~curious(X)|kind(X))))&
(![X]:((happy(X)|curious(X))<=>(old(X)&~calm(X))))&
(![X]:(humble(X)=>~strong(X)))&
(![X]:((~happy(X)&~humble(X))<=>~tall(X)))&
(((~brave(john)|generous(john)))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((~calm(X)|wise(X))=>(~generous(X)<~>kind(X))))&
(![X]:((brave(X)&strong(X))<=>(~funny(X)|tall(X))))&
(?[X]:((~brave(X)<~>~happy(X))))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:((~curious(X)|~humble(X))))&
(wise(paul))&
((creative(fred)<~>~generous(fred)))&
((quiet(mary)<~>~rich(mary))) | ~quiet(susan) | [
"p2",
"p3",
"p4",
"p7",
"p9",
"p10",
"p11",
"p12",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7760408894249113108531949
% SZS output start Proof for 7760408894249113108531949
3. ! [X0] : ((happy(X0) | ~quiet(X0)) <=> (~humble(X0) & ~strong(X0))) [input p2]
4. ! [X0] : ((~patient(X0) | humble(X0)) <=> (~brave(X0) <~> ~funny(X0))) [input p3]
5. generous(susan) <=> ? [X0] : calm(X0) [input p4]
8. ! [X0] : ((~brave(X0) <~> calm(X0)) <=> (~patient(X0) <~> ~strong(X0))) [input p7]
10. ! [X0] : (strong(X0) <=> (kind(X0) | ~curious(X0))) [input p9]
11. ! [X0] : ((curious(X0) | happy(X0)) <=> (~calm(X0) & old(X0))) [input p10]
12. ! [X0] : (humble(X0) => ~strong(X0)) [input p11]
13. ! [X0] : ((~humble(X0) & ~happy(X0)) <=> ~tall(X0)) [input p12]
15. ! [X0] : ((wise(X0) | ~calm(X0)) => (~generous(X0) <~> kind(X0))) [input p14]
16. ! [X0] : ((strong(X0) & brave(X0)) <=> (tall(X0) | ~funny(X0))) [input p15]
17. ? [X0] : (~brave(X0) <~> ~happy(X0)) [input p16]
23. ~quiet(susan) [input hypothesis]
30. ! [X0] : (~strong(X0) | ~humble(X0)) [ennf transformation 12]
32. ! [X0] : ((~generous(X0) <~> kind(X0)) | (~wise(X0) & calm(X0))) [ennf transformation 15]
34. ! [X0] : (((happy(X0) | ~quiet(X0)) | (humble(X0) | strong(X0))) & ((~humble(X0) & ~strong(X0)) | (~happy(X0) & quiet(X0)))) [nnf transformation 3]
35. ! [X0] : ((happy(X0) | ~quiet(X0) | humble(X0) | strong(X0)) & ((~humble(X0) & ~strong(X0)) | (~happy(X0) & quiet(X0)))) [flattening 34]
36. ! [X0] : (((~patient(X0) | humble(X0)) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (patient(X0) & ~humble(X0)))) [nnf transformation 4]
37. ! [X0] : ((~patient(X0) | humble(X0) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (patient(X0) & ~humble(X0)))) [flattening 36]
38. (generous(susan) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ~generous(susan)) [nnf transformation 5]
39. (generous(susan) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ~generous(susan)) [rectify 38]
40. ? [X1] : calm(X1) => calm(sK0) [choice axiom]
41. (generous(susan) | ! [X0] : ~calm(X0)) & (calm(sK0) | ~generous(susan)) [skolemisation 39,40]
42. ! [X0] : ((((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0))))) [nnf transformation 8]
43. ! [X0] : ((strong(X0) | (~kind(X0) & curious(X0))) & ((kind(X0) | ~curious(X0)) | ~strong(X0))) [nnf transformation 10]
44. ! [X0] : ((strong(X0) | (~kind(X0) & curious(X0))) & (kind(X0) | ~curious(X0) | ~strong(X0))) [flattening 43]
45. ! [X0] : (((curious(X0) | happy(X0)) | (calm(X0) | ~old(X0))) & ((~calm(X0) & old(X0)) | (~curious(X0) & ~happy(X0)))) [nnf transformation 11]
46. ! [X0] : ((curious(X0) | happy(X0) | calm(X0) | ~old(X0)) & ((~calm(X0) & old(X0)) | (~curious(X0) & ~happy(X0)))) [flattening 45]
47. ! [X0] : (((~humble(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | (humble(X0) | happy(X0)))) [nnf transformation 13]
48. ! [X0] : (((~humble(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | humble(X0) | happy(X0))) [flattening 47]
52. ! [X0] : (((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (~wise(X0) & calm(X0))) [nnf transformation 32]
53. ! [X0] : (((strong(X0) & brave(X0)) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | (~strong(X0) | ~brave(X0)))) [nnf transformation 16]
54. ! [X0] : (((strong(X0) & brave(X0)) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~strong(X0) | ~brave(X0))) [flattening 53]
55. ? [X0] : ((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) [nnf transformation 17]
56. ? [X0] : ((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) => ((happy(sK2) | brave(sK2)) & (~happy(sK2) | ~brave(sK2))) [choice axiom]
57. (happy(sK2) | brave(sK2)) & (~happy(sK2) | ~brave(sK2)) [skolemisation 55,56]
74. ~strong(X0) | quiet(X0) [cnf transformation 35]
79. ~funny(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 37]
80. ~funny(X0) | ~brave(X0) | patient(X0) [cnf transformation 37]
84. ~brave(X0) | humble(X0) | ~patient(X0) | funny(X0) [cnf transformation 37]
86. generous(susan) | ~calm(X0) [cnf transformation 41]
93. ~brave(X0) | calm(X0) | ~strong(X0) | patient(X0) [cnf transformation 42]
94. ~brave(X0) | calm(X0) | ~patient(X0) | strong(X0) [cnf transformation 42]
99. curious(X0) | strong(X0) [cnf transformation 44]
100. ~kind(X0) | strong(X0) [cnf transformation 44]
104. ~curious(X0) | ~calm(X0) [cnf transformation 46]
106. ~humble(X0) | ~strong(X0) [cnf transformation 30]
107. ~tall(X0) | humble(X0) | happy(X0) [cnf transformation 48]
108. ~happy(X0) | tall(X0) [cnf transformation 48]
114. ~generous(X0) | kind(X0) | calm(X0) [cnf transformation 52]
118. ~funny(X0) | tall(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 54]
120. ~tall(X0) | brave(X0) [cnf transformation 54]
121. funny(X0) | strong(X0) [cnf transformation 54]
123. ~happy(sK2) | ~brave(sK2) [cnf transformation 57]
124. happy(sK2) | brave(sK2) [cnf transformation 57]
133. ~quiet(susan) [cnf transformation 23]
135. 1 <=> ! [X0] : ~calm(X0) [avatar definition]
136. ~calm(X0) <- (1) [avatar component clause 135]
138. 2 <=> generous(susan) [avatar definition]
140. generous(susan) <- (2) [avatar component clause 138]
141. 1 | 2 [avatar split clause 86,138,135]
152. 5 <=> kind(susan) [avatar definition]
153. kind(susan) <- (5) [avatar component clause 152]
189. 13 <=> brave(sK2) [avatar definition]
190. ~brave(sK2) <- (~13) [avatar component clause 189]
191. brave(sK2) <- (13) [avatar component clause 189]
193. 14 <=> happy(sK2) [avatar definition]
194. ~happy(sK2) <- (~14) [avatar component clause 193]
195. happy(sK2) <- (14) [avatar component clause 193]
196. 13 | 14 [avatar split clause 124,193,189]
197. ~13 | ~14 [avatar split clause 123,193,189]
240. ~calm(X0) | strong(X0) [resolution 104,99]
249. ~brave(X0) | ~humble(X0) | strong(X0) [resolution 79,121]
251. ~brave(X0) | ~humble(X0) [subsumption resolution 249,106]
252. ~brave(X0) | patient(X0) | strong(X0) [resolution 80,121]
282. kind(susan) | calm(susan) <- (2) [resolution 114,140]
284. 25 <=> calm(susan) [avatar definition]
286. calm(susan) <- (25) [avatar component clause 284]
287. 25 | 5 | ~2 [avatar split clause 282,138,152,284]
288. strong(susan) <- (5) [resolution 153,100]
301. quiet(susan) <- (5) [resolution 288,74]
302. $false <- (5) [subsumption resolution 301,133]
303. ~5 [avatar contradiction clause 302]
304. strong(susan) <- (25) [resolution 286,240]
397. quiet(susan) <- (25) [resolution 304,74]
398. $false <- (25) [subsumption resolution 397,133]
399. ~25 [avatar contradiction clause 398]
424. humble(sK2) | ~patient(sK2) | funny(sK2) <- (13) [resolution 84,191]
426. 37 <=> funny(sK2) [avatar definition]
428. funny(sK2) <- (37) [avatar component clause 426]
430. 38 <=> patient(sK2) [avatar definition]
431. patient(sK2) <- (38) [avatar component clause 430]
432. ~patient(sK2) <- (~38) [avatar component clause 430]
434. 39 <=> humble(sK2) [avatar definition]
435. ~humble(sK2) <- (~39) [avatar component clause 434]
437. 37 | ~38 | 39 | ~13 [avatar split clause 424,189,434,430,426]
453. calm(sK2) | ~strong(sK2) | patient(sK2) <- (13) [resolution 93,191]
456. ~strong(sK2) | patient(sK2) <- (1, 13) [subsumption resolution 453,136]
457. ~strong(sK2) <- (1, 13, ~38) [subsumption resolution 456,432]
494. ~humble(sK2) <- (13) [resolution 251,191]
496. ~39 | ~13 [avatar split clause 494,189,434]
499. patient(sK2) | strong(sK2) <- (13) [resolution 252,191]
502. strong(sK2) <- (13, ~38) [subsumption resolution 499,432]
503. $false <- (1, 13, ~38) [subsumption resolution 502,457]
504. ~1 | ~13 | 38 [avatar contradiction clause 503]
507. tall(sK2) <- (14) [resolution 195,108]
514. brave(sK2) <- (14) [resolution 507,120]
529. $false <- (~13, 14) [subsumption resolution 514,190]
530. 13 | ~14 [avatar contradiction clause 529]
535. calm(sK2) | ~patient(sK2) | strong(sK2) <- (13) [resolution 191,94]
538. ~patient(sK2) | strong(sK2) <- (1, 13) [subsumption resolution 535,136]
539. strong(sK2) <- (1, 13, 38) [subsumption resolution 538,431]
540. tall(sK2) | ~strong(sK2) | ~brave(sK2) <- (37) [resolution 428,118]
544. tall(sK2) | ~brave(sK2) <- (1, 13, 37, 38) [subsumption resolution 540,539]
545. tall(sK2) <- (1, 13, 37, 38) [subsumption resolution 544,191]
561. humble(sK2) | happy(sK2) <- (1, 13, 37, 38) [resolution 545,107]
566. happy(sK2) <- (1, 13, 37, 38, ~39) [subsumption resolution 561,435]
567. $false <- (1, 13, ~14, 37, 38, ~39) [subsumption resolution 566,194]
568. ~1 | ~13 | 14 | ~37 | ~38 | 39 [avatar contradiction clause 567]
569. $false [avatar sat refutation 141,196,197,287,303,399,437,496,504,530,568]
% SZS output end Proof for 7760408894249113108531949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is either not calm or not strong.
If john is both not patient and humble then someone is tall.
Everyone who is both quiet and strong is not tall or quiet.
Everyone who is not brave is strong and vice versa.
If fred is happy then fred is quiet.
If susan is either funny or tall then someone is not generous.
If paul is not happy then someone is both not rich and not creative.
Everyone who is either not brave or wise is both not patient and not brave.
If someone is brave then someone is either kind or not quiet and vice versa.
Everyone who is happy is patient or not calm.
Everyone who is either curious or not funny is both patient and not brave and vice versa.
If someone is not quiet then mary is strong and vice versa.
Everyone who is both funny and tall is calm or happy.
Everyone who is kind or old is both not humble and rich and vice versa.
If john is either old or not strong then paul is either patient or not happy.
Everyone who is both not creative and not strong is both not happy and old.
Alice is wise.
Someone is not brave or strong.
John is either not creative or not happy.
Lucy is both not humble and not tall.
Paul is quiet or not wise.
Mary is both not old and quiet. | Lucy is quiet. | neutral | (![X]:(~curious(X)=>(~calm(X)<~>~strong(X))))&
(((~patient(john)&humble(john)))=>(?[X]:(tall(X))))&
(![X]:((quiet(X)&strong(X))=>(~tall(X)|quiet(X))))&
(![X]:(~brave(X)<=>strong(X)))&
((happy(fred))=>(quiet(fred)))&
(((funny(susan)<~>tall(susan)))=>(?[X]:(~generous(X))))&
((~happy(paul))=>(?[X]:((~rich(X)&~creative(X)))))&
(![X]:((~brave(X)<~>wise(X))=>(~patient(X)&~brave(X))))&
((?[X]:(brave(X)))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:(happy(X)=>(patient(X)|~calm(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(patient(X)&~brave(X))))&
((?[X]:(~quiet(X)))<=>(strong(mary)))&
(![X]:((funny(X)&tall(X))=>(calm(X)|happy(X))))&
(![X]:((kind(X)|old(X))<=>(~humble(X)&rich(X))))&
(((old(john)<~>~strong(john)))=>((patient(paul)<~>~happy(paul))))&
(![X]:((~creative(X)&~strong(X))=>(~happy(X)&old(X))))&
(wise(alice))&
(?[X]:((~brave(X)|strong(X))))&
((~creative(john)<~>~happy(john)))&
((~humble(lucy)&~tall(lucy)))&
((quiet(paul)|~wise(paul)))&
((~old(mary)&quiet(mary))) | quiet(lucy) | [] | null | 0 |
If fred is brave or not kind then someone is both calm and not brave.
If fred is both humble and not quiet then someone is not funny or not humble and vice versa.
Everyone who is both not funny and not humble is either not brave or not tall and vice versa.
Everyone who is strong or not humble is both not curious and happy.
Everyone who is both not rich and not tall is not wise.
Everyone who is wise is strong or not wise and vice versa.
If someone is humble or funny then john is either not wise or not old and vice versa.
If susan is either rich or old then someone is wise or patient.
If lucy is both happy and not kind then someone is patient.
If john is both funny and not patient then someone is not funny and vice versa.
Everyone who is not strong is both quiet and funny.
Everyone who is not rich or not old is wise or not wise and vice versa.
Everyone who is either creative or not wise is not funny.
If someone is not patient or happy then fred is both tall and not kind and vice versa.
Everyone who is both old and not humble is either brave or not funny and vice versa.
Everyone who is either calm or kind is tall.
Someone is brave.
Someone is happy.
Paul is not brave.
Susan is not kind.
Someone is not generous.
Someone is old or quiet.
Alice is both strong and quiet. | Fred is quiet. | contradiction | (((brave(fred)|~kind(fred)))=>(?[X]:((calm(X)&~brave(X)))))&
(((humble(fred)&~quiet(fred)))<=>(?[X]:((~funny(X)|~humble(X)))))&
(![X]:((~funny(X)&~humble(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:((strong(X)|~humble(X))=>(~curious(X)&happy(X))))&
(![X]:((~rich(X)&~tall(X))=>~wise(X)))&
(![X]:(wise(X)<=>(strong(X)|~wise(X))))&
((?[X]:((humble(X)|funny(X))))<=>((~wise(john)<~>~old(john))))&
(((rich(susan)<~>old(susan)))=>(?[X]:((wise(X)|patient(X)))))&
(((happy(lucy)&~kind(lucy)))=>(?[X]:(patient(X))))&
(((funny(john)&~patient(john)))<=>(?[X]:(~funny(X))))&
(![X]:(~strong(X)=>(quiet(X)&funny(X))))&
(![X]:((~rich(X)|~old(X))<=>(wise(X)|~wise(X))))&
(![X]:((creative(X)<~>~wise(X))=>~funny(X)))&
((?[X]:((~patient(X)|happy(X))))<=>((tall(fred)&~kind(fred))))&
(![X]:((old(X)&~humble(X))<=>(brave(X)<~>~funny(X))))&
(![X]:((calm(X)<~>kind(X))=>tall(X)))&
(?[X]:(brave(X)))&
(?[X]:(happy(X)))&
(~brave(paul))&
(~kind(susan))&
(?[X]:(~generous(X)))&
(?[X]:((old(X)|quiet(X))))&
((strong(alice)&quiet(alice))) | quiet(fred) | [
"p1",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 455551173639979258677972
% SZS output start Proof for 455551173639979258677972
2. (~quiet(fred) & humble(fred)) <=> ? [X0] : (~humble(X0) | ~funny(X0)) [input p1]
15. ! [X0] : ((~humble(X0) & old(X0)) <=> (brave(X0) <~> ~funny(X0))) [input p14]
17. ? [X0] : brave(X0) [input p16]
24. quiet(fred) [input hypothesis]
39. ((~quiet(fred) & humble(fred)) | ! [X0] : (humble(X0) & funny(X0))) & (? [X0] : (~humble(X0) | ~funny(X0)) | (quiet(fred) | ~humble(fred))) [nnf transformation 2]
40. ((~quiet(fred) & humble(fred)) | ! [X0] : (humble(X0) & funny(X0))) & (? [X0] : (~humble(X0) | ~funny(X0)) | quiet(fred) | ~humble(fred)) [flattening 39]
41. ((~quiet(fred) & humble(fred)) | ! [X0] : (humble(X0) & funny(X0))) & (? [X1] : (~humble(X1) | ~funny(X1)) | quiet(fred) | ~humble(fred)) [rectify 40]
42. ? [X1] : (~humble(X1) | ~funny(X1)) => (~humble(sK1) | ~funny(sK1)) [choice axiom]
43. ((~quiet(fred) & humble(fred)) | ! [X0] : (humble(X0) & funny(X0))) & ((~humble(sK1) | ~funny(sK1)) | quiet(fred) | ~humble(fred)) [skolemisation 41,42]
70. ! [X0] : (((~humble(X0) & old(X0)) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0)))) & (((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | (humble(X0) | ~old(X0)))) [nnf transformation 15]
71. ! [X0] : (((~humble(X0) & old(X0)) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0)))) & (((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | humble(X0) | ~old(X0))) [flattening 70]
73. ? [X0] : brave(X0) => brave(sK7) [choice axiom]
74. brave(sK7) [skolemisation 17,73]
86. ~quiet(fred) | funny(X0) [cnf transformation 43]
87. ~quiet(fred) | humble(X0) [cnf transformation 43]
129. ~funny(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 71]
133. brave(sK7) [cnf transformation 74]
140. quiet(fred) [cnf transformation 24]
164. 5 <=> ! [X0] : humble(X0) [avatar definition]
165. humble(X0) <- (5) [avatar component clause 164]
167. 6 <=> quiet(fred) [avatar definition]
170. 5 | ~6 [avatar split clause 87,167,164]
172. 7 <=> ! [X0] : funny(X0) [avatar definition]
173. funny(X0) <- (7) [avatar component clause 172]
174. 7 | ~6 [avatar split clause 86,167,172]
277. 6 [avatar split clause 140,167]
306. ~humble(X0) | ~brave(X0) <- (7) [resolution 129,173]
307. ~brave(X0) <- (5, 7) [subsumption resolution 306,165]
308. $false <- (5, 7) [resolution 307,133]
313. ~5 | ~7 [avatar contradiction clause 308]
314. $false [avatar sat refutation 170,174,277,313]
% SZS output end Proof for 455551173639979258677972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or not curious is not calm or wise and vice versa. Everyone who is either not old or not wise is not rich or happy and vice versa. Everyone who is strong is both not tall and old and vice versa. Everyone who is calm or not patient is not kind or rich and vice versa. If mary is quiet then john is both brave and quiet. Everyone who is not brave is either not rich or not humble. Everyone who is either rich or curious is either funny or not creative and vice versa. Everyone who is not calm is curious or not strong and vice versa. Everyone who is old or creative is strong or not happy. If someone is either kind or not patient then someone is not old. If someone is either not quiet or rich then someone is not happy or generous and vice versa. If someone is not humble then someone is creative or funny and vice versa. Everyone who is either not curious or not tall is both strong and not tall and vice versa. If paul is not patient then lucy is either kind or rich and vice versa. Everyone who is both tall and not old is either rich or creative. If paul is either old or patient then alice is both not happy and not brave and vice versa. Lucy is both generous and not happy. Someone is old. John is not patient or not tall. Someone is not funny. Fred is creative or not old. Someone is either not humble or not funny. Someone is either not old or not creative. | John is quiet. | neutral | (![X]:((creative(X)<~>~curious(X))<=>(~calm(X)|wise(X))))&
(![X]:((~old(X)<~>~wise(X))<=>(~rich(X)|happy(X))))&
(![X]:(strong(X)<=>(~tall(X)&old(X))))&
(![X]:((calm(X)|~patient(X))<=>(~kind(X)|rich(X))))&
((quiet(mary))=>((brave(john)&quiet(john))))&
(![X]:(~brave(X)=>(~rich(X)<~>~humble(X))))&
(![X]:((rich(X)<~>curious(X))<=>(funny(X)<~>~creative(X))))&
(![X]:(~calm(X)<=>(curious(X)|~strong(X))))&
(![X]:((old(X)|creative(X))=>(strong(X)|~happy(X))))&
((?[X]:((kind(X)<~>~patient(X))))=>(?[X]:(~old(X))))&
((?[X]:((~quiet(X)<~>rich(X))))<=>(?[X]:((~happy(X)|generous(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((creative(X)|funny(X)))))&
(![X]:((~curious(X)<~>~tall(X))<=>(strong(X)&~tall(X))))&
((~patient(paul))<=>((kind(lucy)<~>rich(lucy))))&
(![X]:((tall(X)&~old(X))=>(rich(X)<~>creative(X))))&
(((old(paul)<~>patient(paul)))<=>((~happy(alice)&~brave(alice))))&
((generous(lucy)&~happy(lucy)))&
(?[X]:(old(X)))&
((~patient(john)|~tall(john)))&
(?[X]:(~funny(X)))&
((creative(fred)|~old(fred)))&
(?[X]:((~humble(X)<~>~funny(X))))&
(?[X]:((~old(X)<~>~creative(X)))) | quiet(john) | [] | null | 0 |
Everyone who is both creative and not calm is tall or not tall. Everyone who is not strong is both generous and strong. If alice is both funny and strong then mary is not creative. Everyone who is both funny and generous is not creative and vice versa. If someone is rich then susan is either not humble or not generous. Everyone who is both strong and brave is strong or not brave. If mary is rich then someone is patient. If someone is both rich and not tall then john is either not strong or not creative. Everyone who is not happy is not tall or not rich. Everyone who is not quiet or happy is both tall and old. If someone is generous or not quiet then someone is rich or creative and vice versa. Everyone who is not quiet or not brave is not generous and vice versa. If someone is not humble then alice is happy or not patient and vice versa. Everyone who is either creative or not old is not happy or rich and vice versa. Everyone who is quiet or wise is not quiet. Someone is either not patient or strong. Susan is both creative and humble. Someone is brave. Susan is rich. John is either not strong or not patient. | Mary is old. | entailment | (![X]:((creative(X)&~calm(X))=>(tall(X)|~tall(X))))&
(![X]:(~strong(X)=>(generous(X)&strong(X))))&
(((funny(alice)&strong(alice)))=>(~creative(mary)))&
(![X]:((funny(X)&generous(X))<=>~creative(X)))&
((?[X]:(rich(X)))=>((~humble(susan)<~>~generous(susan))))&
(![X]:((strong(X)&brave(X))=>(strong(X)|~brave(X))))&
((rich(mary))=>(?[X]:(patient(X))))&
((?[X]:((rich(X)&~tall(X))))=>((~strong(john)<~>~creative(john))))&
(![X]:(~happy(X)=>(~tall(X)|~rich(X))))&
(![X]:((~quiet(X)|happy(X))=>(tall(X)&old(X))))&
((?[X]:((generous(X)|~quiet(X))))<=>(?[X]:((rich(X)|creative(X)))))&
(![X]:((~quiet(X)|~brave(X))<=>~generous(X)))&
((?[X]:(~humble(X)))<=>((happy(alice)|~patient(alice))))&
(![X]:((creative(X)<~>~old(X))<=>(~happy(X)|rich(X))))&
(![X]:((quiet(X)|wise(X))=>~quiet(X)))&
(?[X]:((~patient(X)<~>strong(X))))&
((creative(susan)&humble(susan)))&
(?[X]:(brave(X)))&
(rich(susan))&
((~strong(john)<~>~patient(john))) | old(mary) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 455540988106964334729089
% SZS output start Proof for 455540988106964334729089
10. ! [X0] : ((happy(X0) | ~quiet(X0)) => (old(X0) & tall(X0))) [input p9]
15. ! [X0] : ((wise(X0) | quiet(X0)) => ~quiet(X0)) [input p14]
21. ~old(mary) [input hypothesis]
23. ! [X0] : (quiet(X0) => ~quiet(X0)) [pure predicate removal 15]
35. ! [X0] : ((old(X0) & tall(X0)) | (~happy(X0) & quiet(X0))) [ennf transformation 10]
36. ! [X0] : (~quiet(X0) | ~quiet(X0)) [ennf transformation 23]
78. old(X0) | quiet(X0) [cnf transformation 35]
96. ~quiet(X0) | ~quiet(X0) [cnf transformation 36]
105. ~old(mary) [cnf transformation 21]
106. ~quiet(X0) [duplicate literal removal 96]
205. quiet(mary) [resolution 78,105]
206. $false [subsumption resolution 205,106]
% SZS output end Proof for 455540988106964334729089
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy 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.
If susan is creative then paul is both not humble and calm and vice versa.
Everyone who is either humble or not happy is both not generous and not old.
If someone is not wise or funny then someone is not tall and vice versa.
Someone is calm.
Fred is either calm or not humble.
Someone is generous.
John is both wise and not quiet. | John is not generous. | neutral | (![X]:((~happy(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)))))&
((creative(susan))<=>((~humble(paul)&calm(paul))))&
(![X]:((humble(X)<~>~happy(X))=>(~generous(X)&~old(X))))&
((?[X]:((~wise(X)|funny(X))))<=>(?[X]:(~tall(X))))&
(?[X]:(calm(X)))&
((calm(fred)<~>~humble(fred)))&
(?[X]:(generous(X)))&
((wise(john)&~quiet(john))) | ~generous(john) | [] | null | 0 |
Everyone who is not curious or old is both humble and not old and vice versa.
If lucy is calm then someone is either kind or creative.
Everyone who is both not rich and happy is not strong or old and vice versa.
If mary is not rich or happy then someone is not calm or not quiet and vice versa.
Everyone who is both not generous and not rich is generous.
If someone is either wise or tall then alice is either patient or not quiet.
Everyone who is patient is creative or not tall and vice versa.
If lucy is not old or old then lucy is not patient and vice versa.
If someone is either not quiet or brave then lucy is brave or kind and vice versa.
Everyone who is rich or not generous is either not tall or creative.
Everyone who is both not wise and funny is either not generous or not rich and vice versa.
If fred is quiet then someone is patient or not rich.
If someone is both not funny and old then paul is either not quiet or kind and vice versa.
If someone is quiet then someone is brave and vice versa.
If someone is both not brave and not tall then someone is either not humble or wise and vice versa.
If someone is either not curious or not brave then john is not brave or quiet and vice versa.
Someone is both creative and not tall.
Lucy is either not strong or not creative.
Someone is not happy or not curious.
Mary is either tall or calm.
Someone is wise or not calm.
Someone is both strong and not patient.
Someone is not tall or funny.
Someone is both not quiet and patient. | Lucy is not happy. | entailment | (![X]:((~curious(X)|old(X))<=>(humble(X)&~old(X))))&
((calm(lucy))=>(?[X]:((kind(X)<~>creative(X)))))&
(![X]:((~rich(X)&happy(X))<=>(~strong(X)|old(X))))&
(((~rich(mary)|happy(mary)))<=>(?[X]:((~calm(X)|~quiet(X)))))&
(![X]:((~generous(X)&~rich(X))=>generous(X)))&
((?[X]:((wise(X)<~>tall(X))))=>((patient(alice)<~>~quiet(alice))))&
(![X]:(patient(X)<=>(creative(X)|~tall(X))))&
(((~old(lucy)|old(lucy)))<=>(~patient(lucy)))&
((?[X]:((~quiet(X)<~>brave(X))))<=>((brave(lucy)|kind(lucy))))&
(![X]:((rich(X)|~generous(X))=>(~tall(X)<~>creative(X))))&
(![X]:((~wise(X)&funny(X))<=>(~generous(X)<~>~rich(X))))&
((quiet(fred))=>(?[X]:((patient(X)|~rich(X)))))&
((?[X]:((~funny(X)&old(X))))<=>((~quiet(paul)<~>kind(paul))))&
((?[X]:(quiet(X)))<=>(?[X]:(brave(X))))&
((?[X]:((~brave(X)&~tall(X))))<=>(?[X]:((~humble(X)<~>wise(X)))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>((~brave(john)|quiet(john))))&
(?[X]:((creative(X)&~tall(X))))&
((~strong(lucy)<~>~creative(lucy)))&
(?[X]:((~happy(X)|~curious(X))))&
((tall(mary)<~>calm(mary)))&
(?[X]:((wise(X)|~calm(X))))&
(?[X]:((strong(X)&~patient(X))))&
(?[X]:((~tall(X)|funny(X))))&
(?[X]:((~quiet(X)&patient(X)))) | ~happy(lucy) | [
"p0",
"p2",
"p6",
"p7",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3964039842531963195185679
% SZS output start Proof for 3964039842531963195185679
1. ! [X0] : ((old(X0) | ~curious(X0)) <=> (~old(X0) & humble(X0))) [input p0]
3. ! [X0] : ((happy(X0) & ~rich(X0)) <=> (old(X0) | ~strong(X0))) [input p2]
7. ! [X0] : (patient(X0) <=> (~tall(X0) | creative(X0))) [input p6]
8. (old(lucy) | ~old(lucy)) <=> ~patient(lucy) [input p7]
10. ! [X0] : ((~generous(X0) | rich(X0)) => (~tall(X0) <~> creative(X0))) [input p9]
18. ~strong(lucy) <~> ~creative(lucy) [input p17]
25. happy(lucy) [input hypothesis]
32. ! [X0] : ((~tall(X0) <~> creative(X0)) | (generous(X0) & ~rich(X0))) [ennf transformation 10]
34. ! [X0] : (((old(X0) | ~curious(X0)) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | (~old(X0) & curious(X0)))) [nnf transformation 1]
35. ! [X0] : ((old(X0) | ~curious(X0) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | (~old(X0) & curious(X0)))) [flattening 34]
39. ! [X0] : (((happy(X0) & ~rich(X0)) | (~old(X0) & strong(X0))) & ((old(X0) | ~strong(X0)) | (~happy(X0) | rich(X0)))) [nnf transformation 3]
40. ! [X0] : (((happy(X0) & ~rich(X0)) | (~old(X0) & strong(X0))) & (old(X0) | ~strong(X0) | ~happy(X0) | rich(X0))) [flattening 39]
47. ! [X0] : ((patient(X0) | (tall(X0) & ~creative(X0))) & ((~tall(X0) | creative(X0)) | ~patient(X0))) [nnf transformation 7]
48. ! [X0] : ((patient(X0) | (tall(X0) & ~creative(X0))) & (~tall(X0) | creative(X0) | ~patient(X0))) [flattening 47]
49. ((old(lucy) | ~old(lucy)) | patient(lucy)) & (~patient(lucy) | (~old(lucy) & old(lucy))) [nnf transformation 8]
50. (old(lucy) | ~old(lucy) | patient(lucy)) & (~patient(lucy) | (~old(lucy) & old(lucy))) [flattening 49]
56. ! [X0] : (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | (generous(X0) & ~rich(X0))) [nnf transformation 32]
82. (creative(lucy) | strong(lucy)) & (~creative(lucy) | ~strong(lucy)) [nnf transformation 18]
97. ~old(X0) | ~old(X0) [cnf transformation 35]
101. old(X0) | ~strong(X0) | ~happy(X0) | rich(X0) [cnf transformation 40]
116. ~creative(X0) | patient(X0) [cnf transformation 48]
117. patient(X0) | tall(X0) [cnf transformation 48]
118. ~patient(lucy) | old(lucy) [cnf transformation 50]
127. ~tall(X0) | creative(X0) | ~rich(X0) [cnf transformation 56]
161. creative(lucy) | strong(lucy) [cnf transformation 82]
171. happy(lucy) [cnf transformation 25]
173. ~old(X0) [duplicate literal removal 97]
189. ~strong(X0) | ~happy(X0) | rich(X0) [subsumption resolution 101,173]
234. ~patient(lucy) [subsumption resolution 118,173]
374. 43 <=> strong(lucy) [avatar definition]
376. strong(lucy) <- (43) [avatar component clause 374]
378. 44 <=> creative(lucy) [avatar definition]
379. ~creative(lucy) <- (~44) [avatar component clause 378]
380. creative(lucy) <- (44) [avatar component clause 378]
381. 43 | 44 [avatar split clause 161,378,374]
424. tall(lucy) [resolution 117,234]
437. creative(lucy) | ~rich(lucy) [resolution 127,424]
441. ~rich(lucy) <- (~44) [subsumption resolution 437,379]
498. ~happy(lucy) | rich(lucy) <- (43) [resolution 189,376]
501. rich(lucy) <- (43) [subsumption resolution 498,171]
502. $false <- (43, ~44) [subsumption resolution 501,441]
503. ~43 | 44 [avatar contradiction clause 502]
516. patient(lucy) <- (44) [resolution 380,116]
517. $false <- (44) [subsumption resolution 516,234]
518. ~44 [avatar contradiction clause 517]
519. $false [avatar sat refutation 381,503,518]
% SZS output end Proof for 3964039842531963195185679
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and humble is either kind or not rich. Everyone who is quiet is either not generous or not funny and vice versa. If alice is not generous or not funny then lucy is both not humble and patient. If someone is patient or calm then mary is not strong or tall. Everyone who is both curious and not generous is both not creative and kind. Everyone who is either not humble or quiet is not humble or not brave and vice versa. If fred is both not funny and not generous then lucy is rich and vice versa. If someone is not curious then someone is both not strong and kind and vice versa. Everyone who is not old or not generous is not wise and vice versa. Everyone who is both not tall and curious is not old or not quiet. If john is both not strong and curious then fred is not generous. If paul is either humble or kind then someone is both happy and old. Everyone who is tall or not wise is creative or tall. If mary is not quiet or not calm then alice is either not quiet or patient. If someone is not humble then someone is not humble or not calm. Everyone who is not old is either humble or calm and vice versa. John is either not quiet or not wise. Someone is not kind. Someone is both curious and not quiet. Lucy is funny. Someone is funny. Paul is either calm or kind. Mary is either old or kind. Someone is funny or brave. | Lucy is patient. | neutral | (![X]:((~brave(X)&humble(X))=>(kind(X)<~>~rich(X))))&
(![X]:(quiet(X)<=>(~generous(X)<~>~funny(X))))&
(((~generous(alice)|~funny(alice)))=>((~humble(lucy)&patient(lucy))))&
((?[X]:((patient(X)|calm(X))))=>((~strong(mary)|tall(mary))))&
(![X]:((curious(X)&~generous(X))=>(~creative(X)&kind(X))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~humble(X)|~brave(X))))&
(((~funny(fred)&~generous(fred)))<=>(rich(lucy)))&
((?[X]:(~curious(X)))<=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~old(X)|~generous(X))<=>~wise(X)))&
(![X]:((~tall(X)&curious(X))=>(~old(X)|~quiet(X))))&
(((~strong(john)&curious(john)))=>(~generous(fred)))&
(((humble(paul)<~>kind(paul)))=>(?[X]:((happy(X)&old(X)))))&
(![X]:((tall(X)|~wise(X))=>(creative(X)|tall(X))))&
(((~quiet(mary)|~calm(mary)))=>((~quiet(alice)<~>patient(alice))))&
((?[X]:(~humble(X)))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:(~old(X)<=>(humble(X)<~>calm(X))))&
((~quiet(john)<~>~wise(john)))&
(?[X]:(~kind(X)))&
(?[X]:((curious(X)&~quiet(X))))&
(funny(lucy))&
(?[X]:(funny(X)))&
((calm(paul)<~>kind(paul)))&
((old(mary)<~>kind(mary)))&
(?[X]:((funny(X)|brave(X)))) | patient(lucy) | [] | null | 0 |
If john is either not funny or quiet then fred is happy.
If someone is brave or not wise then susan is both tall and not rich and vice versa.
If someone is humble then lucy is either humble or quiet.
Everyone who is strong is both not wise and strong.
Everyone who is not humble is not quiet or not old.
Everyone who is curious or creative is tall.
Everyone who is generous is curious and vice versa.
Everyone who is both not generous and not calm is not happy or not generous and vice versa.
Everyone who is not generous or not old is both quiet and calm.
If alice is both not calm and wise then paul is old.
If someone is either not patient or tall then someone is not tall or not curious and vice versa.
Everyone who is either not tall or generous is not calm or not generous.
Everyone who is both not strong and not tall is funny or not humble and vice versa.
If someone is both generous and not calm then someone is either not funny or not wise and vice versa.
If lucy is not generous then mary is not rich or not funny.
Everyone who is either generous or rich is either creative or old.
John is either brave or not calm.
Mary is strong or not happy.
John is rich or creative.
Someone is either not tall or not patient.
Fred is brave or not humble. | Fred is not happy. | contradiction | (((~funny(john)<~>quiet(john)))=>(happy(fred)))&
((?[X]:((brave(X)|~wise(X))))<=>((tall(susan)&~rich(susan))))&
((?[X]:(humble(X)))=>((humble(lucy)<~>quiet(lucy))))&
(![X]:(strong(X)=>(~wise(X)&strong(X))))&
(![X]:(~humble(X)=>(~quiet(X)|~old(X))))&
(![X]:((curious(X)|creative(X))=>tall(X)))&
(![X]:(generous(X)<=>curious(X)))&
(![X]:((~generous(X)&~calm(X))<=>(~happy(X)|~generous(X))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&calm(X))))&
(((~calm(alice)&wise(alice)))=>(old(paul)))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((~tall(X)<~>generous(X))=>(~calm(X)|~generous(X))))&
(![X]:((~strong(X)&~tall(X))<=>(funny(X)|~humble(X))))&
((?[X]:((generous(X)&~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
((~generous(lucy))=>((~rich(mary)|~funny(mary))))&
(![X]:((generous(X)<~>rich(X))=>(creative(X)<~>old(X))))&
((brave(john)<~>~calm(john)))&
((strong(mary)|~happy(mary)))&
((rich(john)|creative(john)))&
(?[X]:((~tall(X)<~>~patient(X))))&
((brave(fred)|~humble(fred))) | ~happy(fred) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7582976744217290306835047
% SZS output start Proof for 7582976744217290306835047
8. ! [X0] : ((~calm(X0) & ~generous(X0)) <=> (~generous(X0) | ~happy(X0))) [input p7]
9. ! [X0] : ((~old(X0) | ~generous(X0)) => (calm(X0) & quiet(X0))) [input p8]
22. ~happy(fred) [input hypothesis]
31. ! [X0] : ((calm(X0) & quiet(X0)) | (old(X0) & generous(X0))) [ennf transformation 9]
47. ! [X0] : (((~calm(X0) & ~generous(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (calm(X0) | generous(X0)))) [nnf transformation 8]
48. ! [X0] : (((~calm(X0) & ~generous(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | calm(X0) | generous(X0))) [flattening 47]
84. ~generous(X0) | happy(X0) [cnf transformation 48]
87. ~calm(X0) | generous(X0) [cnf transformation 48]
90. calm(X0) | generous(X0) [cnf transformation 31]
124. ~happy(fred) [cnf transformation 22]
135. 3 <=> happy(fred) [avatar definition]
136. ~happy(fred) <- (~3) [avatar component clause 135]
180. generous(X0) [subsumption resolution 90,87]
303. ~3 [avatar split clause 124,135]
317. happy(X0) [resolution 84,180]
319. $false <- (~3) [resolution 317,136]
322. 3 [avatar contradiction clause 319]
323. $false [avatar sat refutation 303,322]
% SZS output end Proof for 7582976744217290306835047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and not happy then alice is not happy. Everyone who is both not kind and not rich is tall and vice versa. Everyone who is humble or kind is both not calm and patient. If someone is both patient and not curious then alice is patient and vice versa. Everyone who is both not old and not generous is not patient. If someone is either not humble or tall then susan is either old or not brave. Everyone who is either not kind or not rich is both not old and funny. Everyone who is either calm or strong is not strong and vice versa. Everyone who is strong is not creative or not funny and vice versa. If someone is not brave then someone is either not happy or not strong. Everyone who is not happy or not funny is both happy and kind and vice versa. If alice is not quiet then someone is either not tall or not brave. If fred is both not curious and patient then john is patient. If susan is either not curious or not brave then alice is either brave or creative and vice versa. Everyone who is either brave or tall is either not brave or not quiet and vice versa. Someone is both calm and not wise. Lucy is either rich or not brave. Mary is rich. Paul is tall or not patient. Susan is either not rich or not strong. Someone is not creative. | Fred is not humble. | entailment | ((?[X]:((creative(X)&~happy(X))))=>(~happy(alice)))&
(![X]:((~kind(X)&~rich(X))<=>tall(X)))&
(![X]:((humble(X)|kind(X))=>(~calm(X)&patient(X))))&
((?[X]:((patient(X)&~curious(X))))<=>(patient(alice)))&
(![X]:((~old(X)&~generous(X))=>~patient(X)))&
((?[X]:((~humble(X)<~>tall(X))))=>((old(susan)<~>~brave(susan))))&
(![X]:((~kind(X)<~>~rich(X))=>(~old(X)&funny(X))))&
(![X]:((calm(X)<~>strong(X))<=>~strong(X)))&
(![X]:(strong(X)<=>(~creative(X)|~funny(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((~happy(X)|~funny(X))<=>(happy(X)&kind(X))))&
((~quiet(alice))=>(?[X]:((~tall(X)<~>~brave(X)))))&
(((~curious(fred)&patient(fred)))=>(patient(john)))&
(((~curious(susan)<~>~brave(susan)))<=>((brave(alice)<~>creative(alice))))&
(![X]:((brave(X)<~>tall(X))<=>(~brave(X)<~>~quiet(X))))&
(?[X]:((calm(X)&~wise(X))))&
((rich(lucy)<~>~brave(lucy)))&
(rich(mary))&
((tall(paul)|~patient(paul)))&
((~rich(susan)<~>~strong(susan)))&
(?[X]:(~creative(X))) | ~humble(fred) | [
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2264112910183163175880797
% SZS output start Proof for 2264112910183163175880797
3. ! [X0] : ((kind(X0) | humble(X0)) => (patient(X0) & ~calm(X0))) [input p2]
8. ! [X0] : ((calm(X0) <~> strong(X0)) <=> ~strong(X0)) [input p7]
22. humble(fred) [input hypothesis]
27. ! [X0] : ((patient(X0) & ~calm(X0)) | (~kind(X0) & ~humble(X0))) [ennf transformation 3]
42. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | strong(X0)) & (~strong(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [nnf transformation 8]
66. ~calm(X0) | ~humble(X0) [cnf transformation 27]
82. ~strong(X0) | calm(X0) | ~strong(X0) [cnf transformation 42]
83. strong(X0) | calm(X0) | strong(X0) [cnf transformation 42]
122. humble(fred) [cnf transformation 22]
129. ~strong(X0) | calm(X0) [duplicate literal removal 82]
130. strong(X0) | calm(X0) [duplicate literal removal 83]
175. calm(X0) [subsumption resolution 129,130]
271. ~humble(X0) [resolution 66,175]
272. $false [resolution 271,122]
% SZS output end Proof for 2264112910183163175880797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or quiet is both not quiet and not brave.
Everyone who is calm or brave is both not wise and brave and vice versa.
Everyone who is generous is both not rich and old and vice versa.
If someone is either funny or not creative then someone is not curious and vice versa.
If someone is both not generous and not tall then someone is not humble or not calm.
Everyone who is curious or generous is either not happy or calm and vice versa.
If someone is both tall and not wise then fred is both not wise and brave and vice versa.
If john is wise then alice is either not creative or humble.
Everyone who is calm or not funny is kind or not humble and vice versa.
If alice is both not generous and brave then fred is not brave.
Everyone who is not curious or funny is either not patient or not humble.
Everyone who is both not curious and not funny is not tall and vice versa.
If someone is not rich or not kind then john is either not patient or not old and vice versa.
If alice is either not brave or tall then someone is strong and vice versa.
Everyone who is rich is brave or happy and vice versa.
Everyone who is either not patient or not strong is happy or not kind.
Someone is calm or rich.
Alice is not happy.
Someone is both not curious and not quiet.
Susan is tall.
Someone is both not patient and wise.
Lucy is both not tall and patient. | Lucy is happy. | neutral | (![X]:((rich(X)|quiet(X))=>(~quiet(X)&~brave(X))))&
(![X]:((calm(X)|brave(X))<=>(~wise(X)&brave(X))))&
(![X]:(generous(X)<=>(~rich(X)&old(X))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((curious(X)|generous(X))<=>(~happy(X)<~>calm(X))))&
((?[X]:((tall(X)&~wise(X))))<=>((~wise(fred)&brave(fred))))&
((wise(john))=>((~creative(alice)<~>humble(alice))))&
(![X]:((calm(X)|~funny(X))<=>(kind(X)|~humble(X))))&
(((~generous(alice)&brave(alice)))=>(~brave(fred)))&
(![X]:((~curious(X)|funny(X))=>(~patient(X)<~>~humble(X))))&
(![X]:((~curious(X)&~funny(X))<=>~tall(X)))&
((?[X]:((~rich(X)|~kind(X))))<=>((~patient(john)<~>~old(john))))&
(((~brave(alice)<~>tall(alice)))<=>(?[X]:(strong(X))))&
(![X]:(rich(X)<=>(brave(X)|happy(X))))&
(![X]:((~patient(X)<~>~strong(X))=>(happy(X)|~kind(X))))&
(?[X]:((calm(X)|rich(X))))&
(~happy(alice))&
(?[X]:((~curious(X)&~quiet(X))))&
(tall(susan))&
(?[X]:((~patient(X)&wise(X))))&
((~tall(lucy)&patient(lucy))) | happy(lucy) | [] | null | 0 |
Everyone who is patient is wise and vice versa.
Everyone who is not old or wise is both not happy and not quiet and vice versa.
Everyone who is either not happy or brave is either not patient or not kind and vice versa.
If fred is not tall or happy then lucy is either not kind or happy and vice versa.
Everyone who is both not funny and not quiet is either not curious or not calm and vice versa.
Everyone who is both not quiet and brave is not generous and vice versa.
If someone is both generous and not rich then fred is not patient or rich and vice versa.
If paul is not patient then susan is not generous and vice versa.
If john is either funny or creative then someone is not old.
If john is not brave or curious then susan is happy.
Everyone who is either not wise or not curious is happy or not calm.
Everyone who is tall or not humble is not strong and vice versa.
If fred is both funny and tall then susan is both rich and not calm and vice versa.
If mary is humble then fred is both not calm and old and vice versa.
Everyone who is either not generous or creative is either not curious or creative.
If alice is both not generous and not quiet then alice is generous or not strong and vice versa.
Someone is quiet or generous.
Someone is calm or not wise.
Someone is not happy.
Fred is either not calm or wise.
Fred is both not tall and not calm.
Paul is both not old and not strong.
Paul is not happy. | Susan is not patient. | neutral | (![X]:(patient(X)<=>wise(X)))&
(![X]:((~old(X)|wise(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~patient(X)<~>~kind(X))))&
(((~tall(fred)|happy(fred)))<=>((~kind(lucy)<~>happy(lucy))))&
(![X]:((~funny(X)&~quiet(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((~quiet(X)&brave(X))<=>~generous(X)))&
((?[X]:((generous(X)&~rich(X))))<=>((~patient(fred)|rich(fred))))&
((~patient(paul))<=>(~generous(susan)))&
(((funny(john)<~>creative(john)))=>(?[X]:(~old(X))))&
(((~brave(john)|curious(john)))=>(happy(susan)))&
(![X]:((~wise(X)<~>~curious(X))=>(happy(X)|~calm(X))))&
(![X]:((tall(X)|~humble(X))<=>~strong(X)))&
(((funny(fred)&tall(fred)))<=>((rich(susan)&~calm(susan))))&
((humble(mary))<=>((~calm(fred)&old(fred))))&
(![X]:((~generous(X)<~>creative(X))=>(~curious(X)<~>creative(X))))&
(((~generous(alice)&~quiet(alice)))<=>((generous(alice)|~strong(alice))))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((calm(X)|~wise(X))))&
(?[X]:(~happy(X)))&
((~calm(fred)<~>wise(fred)))&
((~tall(fred)&~calm(fred)))&
((~old(paul)&~strong(paul)))&
(~happy(paul)) | ~patient(susan) | [] | null | 0 |
Everyone who is not humble is both curious and not patient. Everyone who is creative is either curious or not tall and vice versa. Everyone who is both old and not old is quiet and vice versa. If someone is patient or not strong then mary is either not brave or not wise and vice versa. If alice is either strong or creative then someone is not generous or curious and vice versa. Everyone who is happy or not generous is either not brave or kind and vice versa. If paul is both rich and not happy then someone is not calm or quiet. Everyone who is strong is not happy or brave. If someone is generous or not creative then john is either not rich or generous and vice versa. Everyone who is old is either creative or not wise. If someone is not happy or wise then lucy is not strong. Everyone who is both brave and not happy is not humble and vice versa. Everyone who is either not generous or happy is not tall and vice versa. If lucy is tall then someone is either not tall or kind and vice versa. If someone is not wise or not strong then someone is not rich or not happy. Someone is not kind or generous. Susan is both brave and calm. Someone is wise. Fred is either tall or not kind. Someone is tall or not brave. Someone is either not rich or not quiet. Lucy is not happy or funny. Someone is kind or old. | Alice is not quiet. | entailment | (![X]:(~humble(X)=>(curious(X)&~patient(X))))&
(![X]:(creative(X)<=>(curious(X)<~>~tall(X))))&
(![X]:((old(X)&~old(X))<=>quiet(X)))&
((?[X]:((patient(X)|~strong(X))))<=>((~brave(mary)<~>~wise(mary))))&
(((strong(alice)<~>creative(alice)))<=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((happy(X)|~generous(X))<=>(~brave(X)<~>kind(X))))&
(((rich(paul)&~happy(paul)))=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:(strong(X)=>(~happy(X)|brave(X))))&
((?[X]:((generous(X)|~creative(X))))<=>((~rich(john)<~>generous(john))))&
(![X]:(old(X)=>(creative(X)<~>~wise(X))))&
((?[X]:((~happy(X)|wise(X))))=>(~strong(lucy)))&
(![X]:((brave(X)&~happy(X))<=>~humble(X)))&
(![X]:((~generous(X)<~>happy(X))<=>~tall(X)))&
((tall(lucy))<=>(?[X]:((~tall(X)<~>kind(X)))))&
((?[X]:((~wise(X)|~strong(X))))=>(?[X]:((~rich(X)|~happy(X)))))&
(?[X]:((~kind(X)|generous(X))))&
((brave(susan)&calm(susan)))&
(?[X]:(wise(X)))&
((tall(fred)<~>~kind(fred)))&
(?[X]:((tall(X)|~brave(X))))&
(?[X]:((~rich(X)<~>~quiet(X))))&
((~happy(lucy)|funny(lucy)))&
(?[X]:((kind(X)|old(X)))) | ~quiet(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1724861502540447770153997
% SZS output start Proof for 1724861502540447770153997
3. ! [X0] : ((~old(X0) & old(X0)) <=> quiet(X0)) [input p2]
24. quiet(alice) [input hypothesis]
39. ! [X0] : (((~old(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | (old(X0) | ~old(X0)))) [nnf transformation 3]
40. ! [X0] : (((~old(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | old(X0) | ~old(X0))) [flattening 39]
85. old(X0) | ~quiet(X0) [cnf transformation 40]
86. ~old(X0) | ~quiet(X0) [cnf transformation 40]
138. quiet(alice) [cnf transformation 24]
139. ~quiet(X0) [subsumption resolution 85,86]
323. $false [subsumption resolution 138,139]
% SZS output end Proof for 1724861502540447770153997
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not kind or tall then someone is funny or not kind and vice versa. If lucy is not kind or patient then mary is both not tall and not wise. Everyone who is strong or wise is not strong and vice versa. If someone is either not funny or quiet then someone is not patient and vice versa. Everyone who is tall is both not kind and patient. If someone is not tall or not kind then paul is tall or not brave and vice versa. Everyone who is both brave and kind is either kind or happy. Everyone who is either not brave or tall is either generous or not humble. Everyone who is either not curious or not happy is not generous. If someone is not old or not tall then fred is either curious or not quiet and vice versa. Everyone who is not generous or tall is not patient and vice versa. Everyone who is either not old or patient is tall or not tall. Everyone who is both happy and not brave is not patient or not funny. Everyone who is either not calm or not strong is not old or not curious. If mary is either curious or brave then someone is old and vice versa. If someone is both not old and kind then mary is curious or happy. Susan is both not strong and not tall. Paul is both wise and kind. Susan is either old or not happy. Someone is not brave. Paul is either not funny or not humble. Someone is both calm and not old. Someone is wise or not rich. | Lucy is not rich. | neutral | (((~kind(paul)<~>tall(paul)))<=>(?[X]:((funny(X)|~kind(X)))))&
(((~kind(lucy)|patient(lucy)))=>((~tall(mary)&~wise(mary))))&
(![X]:((strong(X)|wise(X))<=>~strong(X)))&
((?[X]:((~funny(X)<~>quiet(X))))<=>(?[X]:(~patient(X))))&
(![X]:(tall(X)=>(~kind(X)&patient(X))))&
((?[X]:((~tall(X)|~kind(X))))<=>((tall(paul)|~brave(paul))))&
(![X]:((brave(X)&kind(X))=>(kind(X)<~>happy(X))))&
(![X]:((~brave(X)<~>tall(X))=>(generous(X)<~>~humble(X))))&
(![X]:((~curious(X)<~>~happy(X))=>~generous(X)))&
((?[X]:((~old(X)|~tall(X))))<=>((curious(fred)<~>~quiet(fred))))&
(![X]:((~generous(X)|tall(X))<=>~patient(X)))&
(![X]:((~old(X)<~>patient(X))=>(tall(X)|~tall(X))))&
(![X]:((happy(X)&~brave(X))=>(~patient(X)|~funny(X))))&
(![X]:((~calm(X)<~>~strong(X))=>(~old(X)|~curious(X))))&
(((curious(mary)<~>brave(mary)))<=>(?[X]:(old(X))))&
((?[X]:((~old(X)&kind(X))))=>((curious(mary)|happy(mary))))&
((~strong(susan)&~tall(susan)))&
((wise(paul)&kind(paul)))&
((old(susan)<~>~happy(susan)))&
(?[X]:(~brave(X)))&
((~funny(paul)<~>~humble(paul)))&
(?[X]:((calm(X)&~old(X))))&
(?[X]:((wise(X)|~rich(X)))) | ~rich(lucy) | [] | null | 0 |
If mary is not rich or brave then someone is not generous or not creative and vice versa. Everyone who is not generous or not kind is humble and vice versa. Everyone who is both creative and not humble is both not curious and brave and vice versa. Everyone who is brave is either patient or not creative and vice versa. Everyone who is not wise is quiet or not creative. If someone is generous or not curious then someone is both brave and not humble and vice versa. If mary is either not kind or happy then fred is not creative and vice versa. Everyone who is both not rich and not quiet is both not generous and tall. If someone is both not creative and not curious then someone is creative or kind and vice versa. If lucy is either not calm or not patient then someone is either not strong or not tall and vice versa. Everyone who is patient is not funny. Everyone who is either not wise or generous is both funny and not rich. If susan is either not brave or generous then someone is generous or not brave and vice versa. If someone is not strong or not calm then someone is tall or calm. If someone is either brave or not generous then fred is both not happy and happy. If fred is tall or funny then someone is calm or generous. Someone is happy. Someone is not tall. Fred is brave. Susan is both not quiet and strong. John is wise. Fred is both tall and curious. Mary is both not generous and not patient. | Lucy is not patient. | entailment | (((~rich(mary)|brave(mary)))<=>(?[X]:((~generous(X)|~creative(X)))))&
(![X]:((~generous(X)|~kind(X))<=>humble(X)))&
(![X]:((creative(X)&~humble(X))<=>(~curious(X)&brave(X))))&
(![X]:(brave(X)<=>(patient(X)<~>~creative(X))))&
(![X]:(~wise(X)=>(quiet(X)|~creative(X))))&
((?[X]:((generous(X)|~curious(X))))<=>(?[X]:((brave(X)&~humble(X)))))&
(((~kind(mary)<~>happy(mary)))<=>(~creative(fred)))&
(![X]:((~rich(X)&~quiet(X))=>(~generous(X)&tall(X))))&
((?[X]:((~creative(X)&~curious(X))))<=>(?[X]:((creative(X)|kind(X)))))&
(((~calm(lucy)<~>~patient(lucy)))<=>(?[X]:((~strong(X)<~>~tall(X)))))&
(![X]:(patient(X)=>~funny(X)))&
(![X]:((~wise(X)<~>generous(X))=>(funny(X)&~rich(X))))&
(((~brave(susan)<~>generous(susan)))<=>(?[X]:((generous(X)|~brave(X)))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:((tall(X)|calm(X)))))&
((?[X]:((brave(X)<~>~generous(X))))=>((~happy(fred)&happy(fred))))&
(((tall(fred)|funny(fred)))=>(?[X]:((calm(X)|generous(X)))))&
(?[X]:(happy(X)))&
(?[X]:(~tall(X)))&
(brave(fred))&
((~quiet(susan)&strong(susan)))&
(wise(john))&
((tall(fred)&curious(fred)))&
((~generous(mary)&~patient(mary))) | ~patient(lucy) | [
"p1",
"p3",
"p5",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2225634957194510307996968
% SZS output start Proof for 2225634957194510307996968
2. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> humble(X0)) [input p1]
4. ! [X0] : (brave(X0) <=> (patient(X0) <~> ~creative(X0))) [input p3]
6. ? [X0] : (~curious(X0) | generous(X0)) <=> ? [X0] : (~humble(X0) & brave(X0)) [input p5]
9. ? [X0] : (~curious(X0) & ~creative(X0)) <=> ? [X0] : (kind(X0) | creative(X0)) [input p8]
13. (~brave(susan) <~> generous(susan)) <=> ? [X0] : (~brave(X0) | generous(X0)) [input p12]
15. ? [X0] : (brave(X0) <~> ~generous(X0)) => (happy(fred) & ~happy(fred)) [input p14]
24. patient(lucy) [input hypothesis]
25. ? [X0] : (~curious(X0) | generous(X0)) <=> ? [X1] : (~humble(X1) & brave(X1)) [rectify 6]
26. ? [X0] : (~curious(X0) & ~creative(X0)) <=> ? [X1] : (kind(X1) | creative(X1)) [rectify 9]
35. (happy(fred) & ~happy(fred)) | ! [X0] : (brave(X0) <=> ~generous(X0)) [ennf transformation 15]
42. ! [X0] : (((~kind(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (kind(X0) & generous(X0)))) [nnf transformation 2]
43. ! [X0] : ((~kind(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (kind(X0) & generous(X0)))) [flattening 42]
46. ! [X0] : ((brave(X0) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) & (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | ~brave(X0))) [nnf transformation 4]
47. (? [X0] : (~curious(X0) | generous(X0)) | ! [X1] : (humble(X1) | ~brave(X1))) & (? [X1] : (~humble(X1) & brave(X1)) | ! [X0] : (curious(X0) & ~generous(X0))) [nnf transformation 25]
48. (? [X0] : (~curious(X0) | generous(X0)) | ! [X1] : (humble(X1) | ~brave(X1))) & (? [X2] : (~humble(X2) & brave(X2)) | ! [X3] : (curious(X3) & ~generous(X3))) [rectify 47]
49. ? [X0] : (~curious(X0) | generous(X0)) => (~curious(sK1) | generous(sK1)) [choice axiom]
50. ? [X2] : (~humble(X2) & brave(X2)) => (~humble(sK2) & brave(sK2)) [choice axiom]
51. ((~curious(sK1) | generous(sK1)) | ! [X1] : (humble(X1) | ~brave(X1))) & ((~humble(sK2) & brave(sK2)) | ! [X3] : (curious(X3) & ~generous(X3))) [skolemisation 48,50,49]
53. (? [X0] : (~curious(X0) & ~creative(X0)) | ! [X1] : (~kind(X1) & ~creative(X1))) & (? [X1] : (kind(X1) | creative(X1)) | ! [X0] : (curious(X0) | creative(X0))) [nnf transformation 26]
54. (? [X0] : (~curious(X0) & ~creative(X0)) | ! [X1] : (~kind(X1) & ~creative(X1))) & (? [X2] : (kind(X2) | creative(X2)) | ! [X3] : (curious(X3) | creative(X3))) [rectify 53]
55. ? [X0] : (~curious(X0) & ~creative(X0)) => (~curious(sK3) & ~creative(sK3)) [choice axiom]
56. ? [X2] : (kind(X2) | creative(X2)) => (kind(sK4) | creative(sK4)) [choice axiom]
57. ((~curious(sK3) & ~creative(sK3)) | ! [X1] : (~kind(X1) & ~creative(X1))) & ((kind(sK4) | creative(sK4)) | ! [X3] : (curious(X3) | creative(X3))) [skolemisation 54,56,55]
63. (((~generous(susan) | brave(susan)) & (generous(susan) | ~brave(susan))) | ! [X0] : (brave(X0) & ~generous(X0))) & (? [X0] : (~brave(X0) | generous(X0)) | ((~brave(susan) | ~generous(susan)) & (generous(susan) | brave(susan)))) [nnf transformation 13]
64. (((~generous(susan) | brave(susan)) & (generous(susan) | ~brave(susan))) | ! [X0] : (brave(X0) & ~generous(X0))) & (? [X1] : (~brave(X1) | generous(X1)) | ((~brave(susan) | ~generous(susan)) & (generous(susan) | brave(susan)))) [rectify 63]
65. ? [X1] : (~brave(X1) | generous(X1)) => (~brave(sK6) | generous(sK6)) [choice axiom]
66. (((~generous(susan) | brave(susan)) & (generous(susan) | ~brave(susan))) | ! [X0] : (brave(X0) & ~generous(X0))) & ((~brave(sK6) | generous(sK6)) | ((~brave(susan) | ~generous(susan)) & (generous(susan) | brave(susan)))) [skolemisation 64,65]
70. (happy(fred) & ~happy(fred)) | ! [X0] : ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0))) [nnf transformation 35]
81. humble(X0) | generous(X0) [cnf transformation 43]
89. ~patient(X0) | creative(X0) | ~brave(X0) [cnf transformation 46]
96. ~humble(sK2) | curious(X3) [cnf transformation 51]
107. ~curious(sK3) | ~creative(X1) [cnf transformation 57]
124. generous(susan) | ~brave(susan) | ~generous(X0) [cnf transformation 66]
125. generous(susan) | ~brave(susan) | brave(X0) [cnf transformation 66]
126. ~generous(susan) | brave(susan) | ~generous(X0) [cnf transformation 66]
127. ~generous(susan) | brave(susan) | brave(X0) [cnf transformation 66]
130. ~happy(fred) | ~generous(X0) | ~brave(X0) [cnf transformation 70]
131. ~happy(fred) | brave(X0) | generous(X0) [cnf transformation 70]
132. happy(fred) | ~generous(X0) | ~brave(X0) [cnf transformation 70]
133. happy(fred) | brave(X0) | generous(X0) [cnf transformation 70]
146. patient(lucy) [cnf transformation 24]
186. 10 <=> ! [X3] : curious(X3) [avatar definition]
187. curious(X3) <- (10) [avatar component clause 186]
189. 11 <=> humble(sK2) [avatar definition]
191. ~humble(sK2) <- (~11) [avatar component clause 189]
192. 10 | ~11 [avatar split clause 96,189,186]
194. 12 <=> ! [X3] : ~generous(X3) [avatar definition]
195. ~generous(X3) <- (12) [avatar component clause 194]
223. 18 <=> curious(sK3) [avatar definition]
225. ~curious(sK3) <- (~18) [avatar component clause 223]
228. 19 <=> ! [X1] : ~creative(X1) [avatar definition]
229. ~creative(X1) <- (19) [avatar component clause 228]
230. 19 | ~18 [avatar split clause 107,223,228]
257. 26 <=> patient(lucy) [avatar definition]
259. patient(lucy) <- (26) [avatar component clause 257]
280. 30 <=> ! [X0] : brave(X0) [avatar definition]
281. brave(X0) <- (30) [avatar component clause 280]
283. 31 <=> brave(susan) [avatar definition]
285. brave(susan) <- (31) [avatar component clause 283]
287. 32 <=> generous(susan) [avatar definition]
288. generous(susan) <- (32) [avatar component clause 287]
289. ~generous(susan) <- (~32) [avatar component clause 287]
290. 30 | 31 | ~32 [avatar split clause 127,287,283,280]
291. 12 | 31 | ~32 [avatar split clause 126,287,283,194]
292. 30 | ~31 | 32 [avatar split clause 125,287,283,280]
293. 12 | ~31 | 32 [avatar split clause 124,287,283,194]
321. 39 <=> ! [X0] : (brave(X0) | generous(X0)) [avatar definition]
322. generous(X0) | brave(X0) <- (39) [avatar component clause 321]
324. 40 <=> happy(fred) [avatar definition]
327. 39 | 40 [avatar split clause 133,324,321]
329. 41 <=> ! [X0] : (~generous(X0) | ~brave(X0)) [avatar definition]
330. ~generous(X0) | ~brave(X0) <- (41) [avatar component clause 329]
331. 41 | 40 [avatar split clause 132,324,329]
332. 39 | ~40 [avatar split clause 131,324,321]
333. 41 | ~40 [avatar split clause 130,324,329]
353. 26 [avatar split clause 146,257]
356. generous(sK2) <- (~11) [resolution 81,191]
357. $false <- (~11, 12) [subsumption resolution 356,195]
358. 11 | ~12 [avatar contradiction clause 357]
361. $false <- (10, ~18) [resolution 187,225]
362. ~10 | 18 [avatar contradiction clause 361]
378. brave(susan) <- (~32, 39) [resolution 322,289]
382. 31 | 32 | ~39 [avatar split clause 378,321,287,283]
395. ~brave(susan) <- (32, 41) [resolution 330,288]
396. $false <- (31, 32, 41) [subsumption resolution 395,285]
397. ~31 | ~32 | ~41 [avatar contradiction clause 396]
422. creative(lucy) | ~brave(lucy) <- (26) [resolution 89,259]
423. ~brave(lucy) <- (19, 26) [subsumption resolution 422,229]
424. $false <- (19, 26, 30) [subsumption resolution 423,281]
425. ~19 | ~26 | ~30 [avatar contradiction clause 424]
426. $false [avatar sat refutation 192,230,290,291,292,293,327,331,332,333,353,358,362,382,397,425]
% SZS output end Proof for 2225634957194510307996968
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet or not patient is not patient or generous.
Everyone who is happy or not patient is curious and vice versa.
Everyone who is creative is both strong and generous.
Everyone who is not creative or funny is kind or not funny.
Everyone who is either not quiet or old is not quiet or creative and vice versa.
If someone is either kind or not brave then someone is both happy and not rich and vice versa.
Everyone who is either not funny or rich is either not creative or humble and vice versa.
If someone is either not humble or generous then someone is both not brave and calm and vice versa.
Everyone who is either not funny or funny is not creative or strong and vice versa.
Everyone who is both calm and funny is both kind and not kind.
Everyone who is either not old or not kind is both not patient and not wise.
Everyone who is both patient and funny is not creative or not kind and vice versa.
If someone is both creative and happy then someone is either not kind or old.
If mary is both not generous and not funny then lucy is not funny or not tall.
If john is generous or not tall then someone is either not kind or not tall.
Everyone who is either humble or not funny is both not calm and not strong and vice versa.
Mary is either calm or humble.
Alice is generous.
Someone is not tall or not creative.
John is not happy.
Someone is curious.
Paul is both generous and old.
Paul is not calm. | Lucy is not strong. | contradiction | (![X]:((~quiet(X)|~patient(X))=>(~patient(X)|generous(X))))&
(![X]:((happy(X)|~patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(strong(X)&generous(X))))&
(![X]:((~creative(X)|funny(X))=>(kind(X)|~funny(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(~quiet(X)|creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((~funny(X)<~>rich(X))<=>(~creative(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~creative(X)|strong(X))))&
(![X]:((calm(X)&funny(X))=>(kind(X)&~kind(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~patient(X)&~wise(X))))&
(![X]:((patient(X)&funny(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((creative(X)&happy(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(((~generous(mary)&~funny(mary)))=>((~funny(lucy)|~tall(lucy))))&
(((generous(john)|~tall(john)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
(![X]:((humble(X)<~>~funny(X))<=>(~calm(X)&~strong(X))))&
((calm(mary)<~>humble(mary)))&
(generous(alice))&
(?[X]:((~tall(X)|~creative(X))))&
(~happy(john))&
(?[X]:(curious(X)))&
((generous(paul)&old(paul)))&
(~calm(paul)) | ~strong(lucy) | [
"p2",
"p3",
"p4",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5710119925823157186928464
% SZS output start Proof for 5710119925823157186928464
3. ! [X0] : (creative(X0) => (generous(X0) & strong(X0))) [input p2]
4. ! [X0] : ((funny(X0) | ~creative(X0)) => (~funny(X0) | kind(X0))) [input p3]
5. ! [X0] : ((~quiet(X0) <~> old(X0)) <=> (creative(X0) | ~quiet(X0))) [input p4]
11. ! [X0] : ((~old(X0) <~> ~kind(X0)) => (~wise(X0) & ~patient(X0))) [input p10]
12. ! [X0] : ((funny(X0) & patient(X0)) <=> (~kind(X0) | ~creative(X0))) [input p11]
24. ~strong(lucy) [input hypothesis]
29. ! [X0] : ((~old(X0) <~> ~kind(X0)) => ~patient(X0)) [pure predicate removal 11]
34. ! [X0] : ((generous(X0) & strong(X0)) | ~creative(X0)) [ennf transformation 3]
35. ! [X0] : ((~funny(X0) | kind(X0)) | (~funny(X0) & creative(X0))) [ennf transformation 4]
36. ! [X0] : (~funny(X0) | kind(X0) | (~funny(X0) & creative(X0))) [flattening 35]
39. ! [X0] : (~patient(X0) | (~old(X0) <=> ~kind(X0))) [ennf transformation 29]
44. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [nnf transformation 5]
45. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [flattening 44]
59. ! [X0] : (~patient(X0) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 39]
60. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | (~funny(X0) | ~patient(X0)))) [nnf transformation 12]
61. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ~funny(X0) | ~patient(X0))) [flattening 60]
79. ~creative(X0) | strong(X0) [cnf transformation 34]
82. ~funny(X0) | kind(X0) | ~funny(X0) [cnf transformation 36]
84. creative(X0) | ~quiet(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 45]
87. ~old(X0) | quiet(X0) | quiet(X0) [cnf transformation 45]
117. ~kind(X0) | ~patient(X0) | old(X0) [cnf transformation 59]
119. ~kind(X0) | ~creative(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 61]
120. creative(X0) | patient(X0) [cnf transformation 61]
122. funny(X0) | creative(X0) [cnf transformation 61]
123. funny(X0) | kind(X0) [cnf transformation 61]
146. ~strong(lucy) [cnf transformation 24]
149. creative(X0) | ~quiet(X0) | ~old(X0) [duplicate literal removal 84]
150. ~old(X0) | quiet(X0) [duplicate literal removal 87]
151. ~funny(X0) | kind(X0) [duplicate literal removal 82]
152. ~old(X0) | creative(X0) [subsumption resolution 149,150]
216. kind(X0) [subsumption resolution 123,151]
217. ~funny(X0) | ~creative(X0) | ~patient(X0) [subsumption resolution 119,216]
236. 19 <=> funny(lucy) [avatar definition]
237. funny(lucy) <- (19) [avatar component clause 236]
238. ~funny(lucy) <- (~19) [avatar component clause 236]
279. strong(X1) | patient(X1) [resolution 120,79]
280. creative(lucy) <- (~19) [resolution 122,238]
282. strong(lucy) <- (~19) [resolution 280,79]
283. $false <- (~19) [subsumption resolution 282,146]
284. 19 [avatar contradiction clause 283]
322. ~patient(X0) | old(X0) [resolution 117,216]
359. ~creative(lucy) | ~patient(lucy) <- (19) [resolution 217,237]
362. 35 <=> patient(lucy) [avatar definition]
363. patient(lucy) <- (35) [avatar component clause 362]
366. 36 <=> creative(lucy) [avatar definition]
368. ~creative(lucy) <- (~36) [avatar component clause 366]
369. ~35 | ~36 | ~19 [avatar split clause 359,236,366,362]
417. patient(lucy) [resolution 279,146]
422. 35 [avatar split clause 417,362]
465. old(lucy) <- (35) [resolution 322,363]
510. creative(lucy) <- (35) [resolution 465,152]
512. $false <- (35, ~36) [subsumption resolution 510,368]
513. ~35 | 36 [avatar contradiction clause 512]
514. $false [avatar sat refutation 284,369,422,513]
% SZS output end Proof for 5710119925823157186928464
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not tall is either not tall or not curious.
If mary is either not old or happy then paul is both happy and creative.
Everyone who is both not creative and not kind is not old and vice versa.
If paul is either not calm or not tall then someone is either not strong or not brave and vice versa.
Everyone who is not old is not happy and vice versa.
Everyone who is either not generous or not humble is either not old or quiet and vice versa.
Everyone who is creative or happy is not humble and vice versa.
Everyone who is either not kind or curious is either creative or humble.
If someone is generous or brave then mary is not curious and vice versa.
Everyone who is brave is either humble or not rich and vice versa.
If someone is both not rich and not humble then someone is generous and vice versa.
If someone is both not wise and not creative then someone is either brave or creative.
If alice is either brave or not generous then someone is brave and vice versa.
Everyone who is either old or humble is generous.
Everyone who is wise is both rich and not calm and vice versa.
Everyone who is strong is brave and vice versa.
Susan is not kind or humble.
Mary is both not creative and not brave.
Someone is happy or not calm.
Someone is either happy or strong.
Alice is either not curious or not kind. | Paul is quiet. | entailment | (![X]:((humble(X)&~tall(X))=>(~tall(X)<~>~curious(X))))&
(((~old(mary)<~>happy(mary)))=>((happy(paul)&creative(paul))))&
(![X]:((~creative(X)&~kind(X))<=>~old(X)))&
(((~calm(paul)<~>~tall(paul)))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:((~generous(X)<~>~humble(X))<=>(~old(X)<~>quiet(X))))&
(![X]:((creative(X)|happy(X))<=>~humble(X)))&
(![X]:((~kind(X)<~>curious(X))=>(creative(X)<~>humble(X))))&
((?[X]:((generous(X)|brave(X))))<=>(~curious(mary)))&
(![X]:(brave(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:((~rich(X)&~humble(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~wise(X)&~creative(X))))=>(?[X]:((brave(X)<~>creative(X)))))&
(((brave(alice)<~>~generous(alice)))<=>(?[X]:(brave(X))))&
(![X]:((old(X)<~>humble(X))=>generous(X)))&
(![X]:(wise(X)<=>(rich(X)&~calm(X))))&
(![X]:(strong(X)<=>brave(X)))&
((~kind(susan)|humble(susan)))&
((~creative(mary)&~brave(mary)))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((happy(X)<~>strong(X))))&
((~curious(alice)<~>~kind(alice))) | quiet(paul) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1033692721894000960720786
% SZS output start Proof for 1033692721894000960720786
2. (~old(mary) <~> happy(mary)) => (creative(paul) & happy(paul)) [input p1]
3. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> ~old(X0)) [input p2]
5. ! [X0] : (~old(X0) <=> ~happy(X0)) [input p4]
6. ! [X0] : ((~generous(X0) <~> ~humble(X0)) <=> (~old(X0) <~> quiet(X0))) [input p5]
7. ! [X0] : ((happy(X0) | creative(X0)) <=> ~humble(X0)) [input p6]
14. ! [X0] : ((old(X0) <~> humble(X0)) => generous(X0)) [input p13]
22. ~quiet(paul) [input hypothesis]
28. (creative(paul) & happy(paul)) | (~old(mary) <=> happy(mary)) [ennf transformation 2]
31. ! [X0] : (generous(X0) | (old(X0) <=> humble(X0))) [ennf transformation 14]
34. (creative(paul) & happy(paul)) | ((~old(mary) | ~happy(mary)) & (happy(mary) | old(mary))) [nnf transformation 28]
35. ! [X0] : (((~kind(X0) & ~creative(X0)) | old(X0)) & (~old(X0) | (kind(X0) | creative(X0)))) [nnf transformation 3]
36. ! [X0] : (((~kind(X0) & ~creative(X0)) | old(X0)) & (~old(X0) | kind(X0) | creative(X0))) [flattening 35]
41. ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))) [nnf transformation 5]
42. ! [X0] : ((((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0)))) & (((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0))))) [nnf transformation 6]
43. ! [X0] : (((happy(X0) | creative(X0)) | humble(X0)) & (~humble(X0) | (~happy(X0) & ~creative(X0)))) [nnf transformation 7]
44. ! [X0] : ((happy(X0) | creative(X0) | humble(X0)) & (~humble(X0) | (~happy(X0) & ~creative(X0)))) [flattening 43]
64. ! [X0] : (generous(X0) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) [nnf transformation 31]
76. creative(paul) | happy(mary) | old(mary) [cnf transformation 34]
77. creative(paul) | ~old(mary) | ~happy(mary) [cnf transformation 34]
79. ~creative(X0) | old(X0) [cnf transformation 36]
89. ~happy(X0) | old(X0) [cnf transformation 41]
90. ~old(X0) | happy(X0) [cnf transformation 41]
92. ~generous(X0) | ~old(X0) | quiet(X0) | humble(X0) [cnf transformation 42]
99. ~creative(X0) | ~humble(X0) [cnf transformation 44]
122. ~old(X0) | humble(X0) | generous(X0) [cnf transformation 64]
136. ~quiet(paul) [cnf transformation 22]
139. 1 <=> happy(mary) [avatar definition]
140. happy(mary) <- (1) [avatar component clause 139]
141. ~happy(mary) <- (~1) [avatar component clause 139]
143. 2 <=> old(mary) [avatar definition]
144. old(mary) <- (2) [avatar component clause 143]
145. ~old(mary) <- (~2) [avatar component clause 143]
147. 3 <=> creative(paul) [avatar definition]
149. creative(paul) <- (3) [avatar component clause 147]
150. ~1 | ~2 | 3 [avatar split clause 77,147,143,139]
151. 2 | 1 | 3 [avatar split clause 76,147,139,143]
300. happy(mary) <- (2) [resolution 90,144]
302. $false <- (~1, 2) [subsumption resolution 300,141]
303. 1 | ~2 [avatar contradiction clause 302]
304. old(mary) <- (1) [resolution 140,89]
305. $false <- (1, ~2) [subsumption resolution 304,145]
306. ~1 | 2 [avatar contradiction clause 305]
307. old(paul) <- (3) [resolution 149,79]
309. ~humble(paul) <- (3) [resolution 99,149]
394. humble(paul) | generous(paul) <- (3) [resolution 122,307]
398. generous(paul) <- (3) [subsumption resolution 394,309]
504. ~old(paul) | quiet(paul) | humble(paul) <- (3) [resolution 398,92]
505. quiet(paul) | humble(paul) <- (3) [subsumption resolution 504,307]
506. humble(paul) <- (3) [subsumption resolution 505,136]
507. $false <- (3) [subsumption resolution 506,309]
508. ~3 [avatar contradiction clause 507]
509. $false [avatar sat refutation 150,151,303,306,508]
% SZS output end Proof for 1033692721894000960720786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or strong is quiet and vice versa. If someone is either not patient or not happy then someone is not wise or not strong and vice versa. Everyone who is either wise or happy is brave or not old and vice versa. If someone is both not quiet and not rich then someone is strong or tall. If someone is calm then someone is kind and vice versa. If fred is not strong or not creative then someone is wise or patient and vice versa. If alice is either strong or kind then someone is either not happy or rich and vice versa. If someone is either not brave or not wise then someone is not generous or strong and vice versa. If paul is either curious or old then someone is not strong or not quiet. Everyone who is brave or kind is funny or not curious. If someone is not tall or not kind then mary is both wise and kind. If someone is either curious or brave then alice is either not generous or not quiet. If susan is both not wise and rich then mary is both calm and rich and vice versa. If someone is old then someone is not funny or not generous. If susan is not calm then someone is not creative and vice versa. Everyone who is not old is either old or not quiet and vice versa. Someone is not quiet. Someone is either not tall or patient. Someone is calm or not old. Someone is generous. Someone is both wise and creative. Someone is not strong. Someone is funny or generous. Someone is happy. | Mary is not brave. | neutral | (![X]:((wise(X)<~>strong(X))<=>quiet(X)))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:((wise(X)<~>happy(X))<=>(brave(X)|~old(X))))&
((?[X]:((~quiet(X)&~rich(X))))=>(?[X]:((strong(X)|tall(X)))))&
((?[X]:(calm(X)))<=>(?[X]:(kind(X))))&
(((~strong(fred)|~creative(fred)))<=>(?[X]:((wise(X)|patient(X)))))&
(((strong(alice)<~>kind(alice)))<=>(?[X]:((~happy(X)<~>rich(X)))))&
((?[X]:((~brave(X)<~>~wise(X))))<=>(?[X]:((~generous(X)|strong(X)))))&
(((curious(paul)<~>old(paul)))=>(?[X]:((~strong(X)|~quiet(X)))))&
(![X]:((brave(X)|kind(X))=>(funny(X)|~curious(X))))&
((?[X]:((~tall(X)|~kind(X))))=>((wise(mary)&kind(mary))))&
((?[X]:((curious(X)<~>brave(X))))=>((~generous(alice)<~>~quiet(alice))))&
(((~wise(susan)&rich(susan)))<=>((calm(mary)&rich(mary))))&
((?[X]:(old(X)))=>(?[X]:((~funny(X)|~generous(X)))))&
((~calm(susan))<=>(?[X]:(~creative(X))))&
(![X]:(~old(X)<=>(old(X)<~>~quiet(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~tall(X)<~>patient(X))))&
(?[X]:((calm(X)|~old(X))))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)&creative(X))))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)|generous(X))))&
(?[X]:(happy(X))) | ~brave(mary) | [] | null | 0 |
Everyone who is either not rich or not funny is not rich or not funny and vice versa.
Everyone who is old or not quiet is both curious and creative and vice versa.
Everyone who is either wise or quiet is either not creative or not humble.
Everyone who is not tall is not patient or rich.
Everyone who is generous is either not curious or not tall and vice versa.
Everyone who is strong is patient and vice versa.
If mary is both not old and not quiet then someone is wise or not creative.
Everyone who is not old or tall is rich or kind.
Everyone who is not kind is both happy and curious.
If someone is either kind or wise then lucy is either not strong or calm.
Everyone who is not humble or not happy is funny and vice versa.
Everyone who is both calm and funny is not brave or not creative.
Everyone who is either not generous or strong is tall or kind and vice versa.
If alice is funny or calm then alice is not creative and vice versa.
If someone is both quiet and not tall then someone is not generous and vice versa.
Everyone who is not quiet is not old.
Someone is patient.
Someone is old.
Someone is both generous and not patient.
Someone is either quiet or not humble.
Mary is not strong.
John is either old or not tall.
Alice is either creative or kind. | Lucy is not brave. | neutral | (![X]:((~rich(X)<~>~funny(X))<=>(~rich(X)|~funny(X))))&
(![X]:((old(X)|~quiet(X))<=>(curious(X)&creative(X))))&
(![X]:((wise(X)<~>quiet(X))=>(~creative(X)<~>~humble(X))))&
(![X]:(~tall(X)=>(~patient(X)|rich(X))))&
(![X]:(generous(X)<=>(~curious(X)<~>~tall(X))))&
(![X]:(strong(X)<=>patient(X)))&
(((~old(mary)&~quiet(mary)))=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:((~old(X)|tall(X))=>(rich(X)|kind(X))))&
(![X]:(~kind(X)=>(happy(X)&curious(X))))&
((?[X]:((kind(X)<~>wise(X))))=>((~strong(lucy)<~>calm(lucy))))&
(![X]:((~humble(X)|~happy(X))<=>funny(X)))&
(![X]:((calm(X)&funny(X))=>(~brave(X)|~creative(X))))&
(![X]:((~generous(X)<~>strong(X))<=>(tall(X)|kind(X))))&
(((funny(alice)|calm(alice)))<=>(~creative(alice)))&
((?[X]:((quiet(X)&~tall(X))))<=>(?[X]:(~generous(X))))&
(![X]:(~quiet(X)=>~old(X)))&
(?[X]:(patient(X)))&
(?[X]:(old(X)))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((quiet(X)<~>~humble(X))))&
(~strong(mary))&
((old(john)<~>~tall(john)))&
((creative(alice)<~>kind(alice))) | ~brave(lucy) | [] | null | 0 |
If mary is funny then fred is not humble and vice versa.
Everyone who is both not calm and not strong is not brave or generous and vice versa.
Everyone who is not curious is both brave and not tall and vice versa.
Everyone who is either not calm or not creative is not strong or calm and vice versa.
Everyone who is either not strong or kind is both not tall and not creative and vice versa.
If fred is either not curious or not funny then fred is either not humble or humble.
If someone is not generous or rich then john is creative or not brave.
If paul is both not generous and humble then john is not kind.
Everyone who is both generous and not calm is not kind and vice versa.
Everyone who is quiet is patient or curious.
If someone is either not strong or not creative then someone is either humble or not curious.
Everyone who is not curious is calm or patient and vice versa.
Everyone who is both old and not brave is either creative or not old and vice versa.
Everyone who is both creative and not generous is old and vice versa.
Everyone who is either old or not happy is not creative and vice versa.
John is funny or patient.
Susan is old or happy.
Someone is either not rich or humble.
Someone is not funny. | Fred is generous. | contradiction | ((funny(mary))<=>(~humble(fred)))&
(![X]:((~calm(X)&~strong(X))<=>(~brave(X)|generous(X))))&
(![X]:(~curious(X)<=>(brave(X)&~tall(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(~strong(X)|calm(X))))&
(![X]:((~strong(X)<~>kind(X))<=>(~tall(X)&~creative(X))))&
(((~curious(fred)<~>~funny(fred)))=>((~humble(fred)<~>humble(fred))))&
((?[X]:((~generous(X)|rich(X))))=>((creative(john)|~brave(john))))&
(((~generous(paul)&humble(paul)))=>(~kind(john)))&
(![X]:((generous(X)&~calm(X))<=>~kind(X)))&
(![X]:(quiet(X)=>(patient(X)|curious(X))))&
((?[X]:((~strong(X)<~>~creative(X))))=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:(~curious(X)<=>(calm(X)|patient(X))))&
(![X]:((old(X)&~brave(X))<=>(creative(X)<~>~old(X))))&
(![X]:((creative(X)&~generous(X))<=>old(X)))&
(![X]:((old(X)<~>~happy(X))<=>~creative(X)))&
((funny(john)|patient(john)))&
((old(susan)|happy(susan)))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:(~funny(X))) | generous(fred) | [
"p1",
"p3",
"p4",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7903472386070368641827814
% SZS output start Proof for 7903472386070368641827814
2. ! [X0] : ((~strong(X0) & ~calm(X0)) <=> (generous(X0) | ~brave(X0))) [input p1]
4. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> (calm(X0) | ~strong(X0))) [input p3]
5. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (~creative(X0) & ~tall(X0))) [input p4]
9. ! [X0] : ((~calm(X0) & generous(X0)) <=> ~kind(X0)) [input p8]
13. ! [X0] : ((~brave(X0) & old(X0)) <=> (creative(X0) <~> ~old(X0))) [input p12]
14. ! [X0] : ((~generous(X0) & creative(X0)) <=> old(X0)) [input p13]
20. generous(fred) [input hypothesis]
30. ! [X0] : (((~strong(X0) & ~calm(X0)) | (~generous(X0) & brave(X0))) & ((generous(X0) | ~brave(X0)) | (strong(X0) | calm(X0)))) [nnf transformation 2]
31. ! [X0] : (((~strong(X0) & ~calm(X0)) | (~generous(X0) & brave(X0))) & (generous(X0) | ~brave(X0) | strong(X0) | calm(X0))) [flattening 30]
34. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 4]
35. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [flattening 34]
36. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (creative(X0) | tall(X0))) & ((~creative(X0) & ~tall(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | creative(X0) | tall(X0)) & ((~creative(X0) & ~tall(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [flattening 36]
39. ! [X0] : (((~calm(X0) & generous(X0)) | kind(X0)) & (~kind(X0) | (calm(X0) | ~generous(X0)))) [nnf transformation 9]
40. ! [X0] : (((~calm(X0) & generous(X0)) | kind(X0)) & (~kind(X0) | calm(X0) | ~generous(X0))) [flattening 39]
47. ! [X0] : (((~brave(X0) & old(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | (brave(X0) | ~old(X0)))) [nnf transformation 13]
48. ! [X0] : (((~brave(X0) & old(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | brave(X0) | ~old(X0))) [flattening 47]
49. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | (generous(X0) | ~creative(X0)))) [nnf transformation 14]
50. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | generous(X0) | ~creative(X0))) [flattening 49]
61. ~generous(X0) | ~calm(X0) [cnf transformation 31]
67. calm(X0) | ~strong(X0) | ~creative(X0) | calm(X0) [cnf transformation 35]
70. ~creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 35]
75. ~creative(X0) | kind(X0) | strong(X0) [cnf transformation 37]
86. ~kind(X0) | calm(X0) | ~generous(X0) [cnf transformation 40]
99. old(X0) | creative(X0) | old(X0) [cnf transformation 48]
103. creative(X0) | ~old(X0) [cnf transformation 50]
114. generous(fred) [cnf transformation 20]
116. old(X0) | creative(X0) [duplicate literal removal 99]
117. calm(X0) | ~strong(X0) | ~creative(X0) [duplicate literal removal 67]
118. ~creative(X0) | ~calm(X0) [duplicate literal removal 70]
129. ~creative(X0) | ~strong(X0) [subsumption resolution 117,118]
131. ~creative(X0) | kind(X0) [subsumption resolution 75,129]
161. ~kind(X0) | ~generous(X0) [subsumption resolution 86,61]
185. creative(X0) [subsumption resolution 103,116]
219. kind(X0) [resolution 131,185]
222. ~generous(X0) [resolution 219,161]
224. $false [resolution 222,114]
% SZS output end Proof for 7903472386070368641827814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and calm is old. If someone is both not quiet and not calm then fred is not old or calm and vice versa. Everyone who is both not creative and kind is not calm or rich and vice versa. If alice is both old and not calm then someone is quiet or happy and vice versa. Everyone who is kind is both quiet and generous. If someone is both not kind and not calm then someone is both not curious and not tall and vice versa. If someone is not humble or not calm then lucy is strong or not patient. Everyone who is both not rich and happy is curious and vice versa. Everyone who is strong is both funny and strong and vice versa. If fred is either not tall or not creative then fred is not rich or not funny. Everyone who is not brave or funny is not tall and vice versa. If someone is either not kind or curious then paul is both not quiet and not generous. Everyone who is happy or not calm is not brave. Everyone who is either not wise or not curious is not patient and vice versa. Everyone who is both not brave and not old is both not calm and tall. If lucy is both curious and not brave then alice is both rich and patient and vice versa. Lucy is humble. Susan is brave. Someone is either strong or not calm. Alice is quiet or creative. Someone is generous or not old. Susan is both patient and calm. | Lucy is curious. | contradiction | (![X]:((creative(X)&calm(X))=>old(X)))&
((?[X]:((~quiet(X)&~calm(X))))<=>((~old(fred)|calm(fred))))&
(![X]:((~creative(X)&kind(X))<=>(~calm(X)|rich(X))))&
(((old(alice)&~calm(alice)))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:(kind(X)=>(quiet(X)&generous(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
((?[X]:((~humble(X)|~calm(X))))=>((strong(lucy)|~patient(lucy))))&
(![X]:((~rich(X)&happy(X))<=>curious(X)))&
(![X]:(strong(X)<=>(funny(X)&strong(X))))&
(((~tall(fred)<~>~creative(fred)))=>((~rich(fred)|~funny(fred))))&
(![X]:((~brave(X)|funny(X))<=>~tall(X)))&
((?[X]:((~kind(X)<~>curious(X))))=>((~quiet(paul)&~generous(paul))))&
(![X]:((happy(X)|~calm(X))=>~brave(X)))&
(![X]:((~wise(X)<~>~curious(X))<=>~patient(X)))&
(![X]:((~brave(X)&~old(X))=>(~calm(X)&tall(X))))&
(((curious(lucy)&~brave(lucy)))<=>((rich(alice)&patient(alice))))&
(humble(lucy))&
(brave(susan))&
(?[X]:((strong(X)<~>~calm(X))))&
((quiet(alice)|creative(alice)))&
(?[X]:((generous(X)|~old(X))))&
((patient(susan)&calm(susan))) | curious(lucy) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6394693168916503767629089
% SZS output start Proof for 6394693168916503767629089
3. ! [X0] : ((kind(X0) & ~creative(X0)) <=> (rich(X0) | ~calm(X0))) [input p2]
4. (~calm(alice) & old(alice)) <=> ? [X0] : (happy(X0) | quiet(X0)) [input p3]
6. ? [X0] : (~calm(X0) & ~kind(X0)) <=> ? [X0] : (~tall(X0) & ~curious(X0)) [input p5]
8. ! [X0] : ((happy(X0) & ~rich(X0)) <=> curious(X0)) [input p7]
11. ! [X0] : ((funny(X0) | ~brave(X0)) <=> ~tall(X0)) [input p10]
13. ! [X0] : ((~calm(X0) | happy(X0)) => ~brave(X0)) [input p12]
16. (~brave(lucy) & curious(lucy)) <=> (patient(alice) & rich(alice)) [input p15]
20. creative(alice) | quiet(alice) [input p19]
23. curious(lucy) [input hypothesis]
24. ? [X0] : (~calm(X0) & ~kind(X0)) <=> ? [X1] : (~tall(X1) & ~curious(X1)) [rectify 6]
35. ! [X0] : (~brave(X0) | (calm(X0) & ~happy(X0))) [ennf transformation 13]
43. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~kind(X0) | creative(X0)))) [nnf transformation 3]
44. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~kind(X0) | creative(X0))) [flattening 43]
45. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | (calm(alice) | ~old(alice))) [nnf transformation 4]
46. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | calm(alice) | ~old(alice)) [flattening 45]
47. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X1] : (happy(X1) | quiet(X1)) | calm(alice) | ~old(alice)) [rectify 46]
48. ? [X1] : (happy(X1) | quiet(X1)) => (happy(sK1) | quiet(sK1)) [choice axiom]
49. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & ((happy(sK1) | quiet(sK1)) | calm(alice) | ~old(alice)) [skolemisation 47,48]
50. (? [X0] : (~calm(X0) & ~kind(X0)) | ! [X1] : (tall(X1) | curious(X1))) & (? [X1] : (~tall(X1) & ~curious(X1)) | ! [X0] : (calm(X0) | kind(X0))) [nnf transformation 24]
51. (? [X0] : (~calm(X0) & ~kind(X0)) | ! [X1] : (tall(X1) | curious(X1))) & (? [X2] : (~tall(X2) & ~curious(X2)) | ! [X3] : (calm(X3) | kind(X3))) [rectify 50]
52. ? [X0] : (~calm(X0) & ~kind(X0)) => (~calm(sK2) & ~kind(sK2)) [choice axiom]
53. ? [X2] : (~tall(X2) & ~curious(X2)) => (~tall(sK3) & ~curious(sK3)) [choice axiom]
54. ((~calm(sK2) & ~kind(sK2)) | ! [X1] : (tall(X1) | curious(X1))) & ((~tall(sK3) & ~curious(sK3)) | ! [X3] : (calm(X3) | kind(X3))) [skolemisation 51,53,52]
55. ! [X0] : (((happy(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | (~happy(X0) | rich(X0)))) [nnf transformation 8]
56. ! [X0] : (((happy(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | ~happy(X0) | rich(X0))) [flattening 55]
60. ! [X0] : (((funny(X0) | ~brave(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) & brave(X0)))) [nnf transformation 11]
61. ! [X0] : ((funny(X0) | ~brave(X0) | tall(X0)) & (~tall(X0) | (~funny(X0) & brave(X0)))) [flattening 60]
64. ((~brave(lucy) & curious(lucy)) | (~patient(alice) | ~rich(alice))) & ((patient(alice) & rich(alice)) | (brave(lucy) | ~curious(lucy))) [nnf transformation 16]
65. ((~brave(lucy) & curious(lucy)) | ~patient(alice) | ~rich(alice)) & ((patient(alice) & rich(alice)) | brave(lucy) | ~curious(lucy)) [flattening 64]
79. ~rich(X0) | ~creative(X0) [cnf transformation 44]
80. kind(X0) | calm(X0) [cnf transformation 44]
85. ~calm(alice) | ~quiet(X0) [cnf transformation 49]
91. ~kind(sK2) | tall(X1) | curious(X1) [cnf transformation 54]
92. ~calm(sK2) | tall(X1) | curious(X1) [cnf transformation 54]
95. ~curious(X0) | ~rich(X0) [cnf transformation 56]
96. ~curious(X0) | happy(X0) [cnf transformation 56]
102. ~tall(X0) | brave(X0) [cnf transformation 61]
109. ~brave(X0) | ~happy(X0) [cnf transformation 35]
110. ~brave(X0) | calm(X0) [cnf transformation 35]
117. rich(alice) | brave(lucy) | ~curious(lucy) [cnf transformation 65]
124. creative(alice) | quiet(alice) [cnf transformation 20]
128. curious(lucy) [cnf transformation 23]
157. 7 <=> calm(alice) [avatar definition]
159. ~calm(alice) <- (~7) [avatar component clause 157]
162. 8 <=> ! [X0] : ~quiet(X0) [avatar definition]
163. ~quiet(X0) <- (8) [avatar component clause 162]
164. 8 | ~7 [avatar split clause 85,157,162]
181. 12 <=> ! [X1] : (tall(X1) | curious(X1)) [avatar definition]
182. tall(X1) | curious(X1) <- (12) [avatar component clause 181]
184. 13 <=> calm(sK2) [avatar definition]
187. 12 | ~13 [avatar split clause 92,184,181]
189. 14 <=> kind(sK2) [avatar definition]
191. ~kind(sK2) <- (~14) [avatar component clause 189]
192. 12 | ~14 [avatar split clause 91,189,181]
239. 25 <=> rich(alice) [avatar definition]
240. rich(alice) <- (25) [avatar component clause 239]
247. 27 <=> brave(lucy) [avatar definition]
248. brave(lucy) <- (27) [avatar component clause 247]
252. 28 <=> curious(lucy) [avatar definition]
254. curious(lucy) <- (28) [avatar component clause 252]
257. ~28 | 27 | 25 [avatar split clause 117,239,247,252]
269. 31 <=> quiet(alice) [avatar definition]
271. quiet(alice) <- (31) [avatar component clause 269]
273. 32 <=> creative(alice) [avatar definition]
276. 31 | 32 [avatar split clause 124,273,269]
286. 28 [avatar split clause 128,252]
287. $false <- (8, 31) [resolution 271,163]
288. ~8 | ~31 [avatar contradiction clause 287]
289. ~creative(alice) <- (25) [resolution 79,240]
290. ~32 | ~25 [avatar split clause 289,239,273]
291. calm(sK2) <- (~14) [resolution 80,191]
294. 13 | 14 [avatar split clause 291,189,184]
302. happy(lucy) <- (28) [resolution 96,254]
312. brave(X0) | curious(X0) <- (12) [resolution 182,102]
384. 48 <=> curious(alice) [avatar definition]
385. curious(alice) <- (48) [avatar component clause 384]
386. ~curious(alice) <- (~48) [avatar component clause 384]
398. curious(X1) | calm(X1) <- (12) [resolution 312,110]
408. calm(alice) <- (12, ~48) [resolution 398,386]
409. $false <- (~7, 12, ~48) [subsumption resolution 408,159]
410. 7 | ~12 | 48 [avatar contradiction clause 409]
423. ~rich(alice) <- (48) [resolution 385,95]
426. ~25 | ~48 [avatar split clause 423,384,239]
429. ~happy(lucy) <- (27) [resolution 248,109]
439. $false <- (27, 28) [subsumption resolution 429,302]
440. ~27 | ~28 [avatar contradiction clause 439]
441. $false [avatar sat refutation 164,187,192,257,276,286,288,290,294,410,426,440]
% SZS output end Proof for 6394693168916503767629089
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or tall is both calm and not old and vice versa.
If someone is either not calm or not generous then john is either rich or calm.
Everyone who is either generous or not patient is either not happy or not curious and vice versa.
Everyone who is calm is not wise or not calm.
If someone is both tall and generous then someone is both not creative and generous and vice versa.
If mary is both not kind and not wise then john is not calm.
Everyone who is either not strong or not tall is not tall and vice versa.
Everyone who is quiet or not generous is patient or not kind and vice versa.
If someone is not humble or not tall then someone is not funny or not happy.
If susan is both patient and happy then mary is both tall and not brave and vice versa.
If someone is generous or brave then lucy is either not generous or not strong.
If fred is both not creative and not rich then susan is not quiet or not rich.
Everyone who is not kind is happy and vice versa.
Everyone who is either tall or not old is either not brave or funny.
Everyone who is kind is rich or strong and vice versa.
Everyone who is not humble is both generous and old and vice versa.
Someone is either not old or funny.
Lucy is not generous.
Susan is either strong or not wise.
Susan is both not calm and patient.
Someone is calm.
Mary is either not patient or not strong.
Susan is either not brave or old. | Mary is not curious. | entailment | (![X]:((~rich(X)|tall(X))<=>(calm(X)&~old(X))))&
((?[X]:((~calm(X)<~>~generous(X))))=>((rich(john)<~>calm(john))))&
(![X]:((generous(X)<~>~patient(X))<=>(~happy(X)<~>~curious(X))))&
(![X]:(calm(X)=>(~wise(X)|~calm(X))))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((~creative(X)&generous(X)))))&
(((~kind(mary)&~wise(mary)))=>(~calm(john)))&
(![X]:((~strong(X)<~>~tall(X))<=>~tall(X)))&
(![X]:((quiet(X)|~generous(X))<=>(patient(X)|~kind(X))))&
((?[X]:((~humble(X)|~tall(X))))=>(?[X]:((~funny(X)|~happy(X)))))&
(((patient(susan)&happy(susan)))<=>((tall(mary)&~brave(mary))))&
((?[X]:((generous(X)|brave(X))))=>((~generous(lucy)<~>~strong(lucy))))&
(((~creative(fred)&~rich(fred)))=>((~quiet(susan)|~rich(susan))))&
(![X]:(~kind(X)<=>happy(X)))&
(![X]:((tall(X)<~>~old(X))=>(~brave(X)<~>funny(X))))&
(![X]:(kind(X)<=>(rich(X)|strong(X))))&
(![X]:(~humble(X)<=>(generous(X)&old(X))))&
(?[X]:((~old(X)<~>funny(X))))&
(~generous(lucy))&
((strong(susan)<~>~wise(susan)))&
((~calm(susan)&patient(susan)))&
(?[X]:(calm(X)))&
((~patient(mary)<~>~strong(mary)))&
((~brave(susan)<~>old(susan))) | ~curious(mary) | [
"p2",
"p6",
"p7",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 236505165746188550726383
% SZS output start Proof for 236505165746188550726383
3. ! [X0] : ((generous(X0) <~> ~patient(X0)) <=> (~happy(X0) <~> ~curious(X0))) [input p2]
7. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> ~tall(X0)) [input p6]
8. ! [X0] : ((~generous(X0) | quiet(X0)) <=> (~kind(X0) | patient(X0))) [input p7]
13. ! [X0] : (~kind(X0) <=> happy(X0)) [input p12]
15. ! [X0] : (kind(X0) <=> (strong(X0) | rich(X0))) [input p14]
22. ~patient(mary) <~> ~strong(mary) [input p21]
24. curious(mary) [input hypothesis]
43. ! [X0] : ((((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0)))) & (((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0))))) [nnf transformation 3]
49. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | tall(X0)) & (~tall(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 7]
50. ! [X0] : (((~generous(X0) | quiet(X0)) | (kind(X0) & ~patient(X0))) & ((~kind(X0) | patient(X0)) | (generous(X0) & ~quiet(X0)))) [nnf transformation 8]
51. ! [X0] : ((~generous(X0) | quiet(X0) | (kind(X0) & ~patient(X0))) & (~kind(X0) | patient(X0) | (generous(X0) & ~quiet(X0)))) [flattening 50]
58. ! [X0] : ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0))) [nnf transformation 13]
60. ! [X0] : ((kind(X0) | (~strong(X0) & ~rich(X0))) & ((strong(X0) | rich(X0)) | ~kind(X0))) [nnf transformation 15]
61. ! [X0] : ((kind(X0) | (~strong(X0) & ~rich(X0))) & (strong(X0) | rich(X0) | ~kind(X0))) [flattening 60]
68. (strong(mary) | patient(mary)) & (~strong(mary) | ~patient(mary)) [nnf transformation 22]
85. ~curious(X0) | ~generous(X0) | patient(X0) | happy(X0) [cnf transformation 43]
93. ~tall(X0) | ~tall(X0) | strong(X0) [cnf transformation 49]
96. tall(X0) | strong(X0) | tall(X0) [cnf transformation 49]
98. ~kind(X0) | patient(X0) | generous(X0) [cnf transformation 51]
112. kind(X0) | happy(X0) [cnf transformation 58]
113. ~kind(X0) | ~happy(X0) [cnf transformation 58]
120. kind(X0) | ~strong(X0) [cnf transformation 61]
130. ~strong(mary) | ~patient(mary) [cnf transformation 68]
134. curious(mary) [cnf transformation 24]
135. ~tall(X0) | strong(X0) [duplicate literal removal 93]
136. strong(X0) | tall(X0) [duplicate literal removal 96]
189. strong(X0) [subsumption resolution 135,136]
257. kind(X0) [subsumption resolution 120,189]
271. ~patient(mary) [subsumption resolution 130,189]
287. ~happy(X1) [resolution 113,257]
289. patient(X0) | generous(X0) | happy(X0) [resolution 98,112]
291. patient(X0) | generous(X0) [subsumption resolution 289,287]
292. generous(mary) [resolution 291,271]
325. ~generous(mary) | patient(mary) | happy(mary) [resolution 85,134]
328. patient(mary) | happy(mary) [subsumption resolution 325,292]
329. happy(mary) [subsumption resolution 328,271]
330. $false [subsumption resolution 329,287]
% SZS output end Proof for 236505165746188550726383
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is quiet or not happy.
If lucy is either creative or generous then someone is quiet or creative.
Everyone who is not calm is both not calm and not funny.
If someone is both happy and not strong then someone is not curious and vice versa.
Everyone who is either generous or funny is both not rich and curious.
Everyone who is either tall or not patient is both generous and not curious and vice versa.
Everyone who is calm or not creative is not brave or creative and vice versa.
If someone is either old or brave then alice is happy or not strong.
If someone is brave then susan is old.
Everyone who is not patient is both not calm and not creative and vice versa.
Everyone who is either not kind or quiet is both not creative and not wise.
Everyone who is both generous and patient is either humble or funny and vice versa.
Everyone who is humble is rich or not strong.
If mary is both not quiet and funny then someone is not brave or not kind.
If lucy is either not wise or not creative then susan is either quiet or funny and vice versa.
Everyone who is either not rich or curious is humble and vice versa.
John is either humble or tall.
Someone is either patient or not curious.
John is both happy and not creative.
Someone is either not happy or generous.
Someone is either wise or old.
Someone is not old.
Someone is both creative and funny.
Someone is both curious and old. | John is not tall. | contradiction | (![X]:(patient(X)=>(quiet(X)|~happy(X))))&
(((creative(lucy)<~>generous(lucy)))=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:(~calm(X)=>(~calm(X)&~funny(X))))&
((?[X]:((happy(X)&~strong(X))))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)<~>funny(X))=>(~rich(X)&curious(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(generous(X)&~curious(X))))&
(![X]:((calm(X)|~creative(X))<=>(~brave(X)|creative(X))))&
((?[X]:((old(X)<~>brave(X))))=>((happy(alice)|~strong(alice))))&
((?[X]:(brave(X)))=>(old(susan)))&
(![X]:(~patient(X)<=>(~calm(X)&~creative(X))))&
(![X]:((~kind(X)<~>quiet(X))=>(~creative(X)&~wise(X))))&
(![X]:((generous(X)&patient(X))<=>(humble(X)<~>funny(X))))&
(![X]:(humble(X)=>(rich(X)|~strong(X))))&
(((~quiet(mary)&funny(mary)))=>(?[X]:((~brave(X)|~kind(X)))))&
(((~wise(lucy)<~>~creative(lucy)))<=>((quiet(susan)<~>funny(susan))))&
(![X]:((~rich(X)<~>curious(X))<=>humble(X)))&
((humble(john)<~>tall(john)))&
(?[X]:((patient(X)<~>~curious(X))))&
((happy(john)&~creative(john)))&
(?[X]:((~happy(X)<~>generous(X))))&
(?[X]:((wise(X)<~>old(X))))&
(?[X]:(~old(X)))&
(?[X]:((creative(X)&funny(X))))&
(?[X]:((curious(X)&old(X)))) | ~tall(john) | [
"p2",
"p4",
"p5",
"p9",
"p11",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1442375976295240803581583
% SZS output start Proof for 1442375976295240803581583
3. ! [X0] : (~calm(X0) => (~funny(X0) & ~calm(X0))) [input p2]
5. ! [X0] : ((generous(X0) <~> funny(X0)) => (curious(X0) & ~rich(X0))) [input p4]
6. ! [X0] : ((tall(X0) <~> ~patient(X0)) <=> (~curious(X0) & generous(X0))) [input p5]
10. ! [X0] : (~patient(X0) <=> (~creative(X0) & ~calm(X0))) [input p9]
12. ! [X0] : ((patient(X0) & generous(X0)) <=> (humble(X0) <~> funny(X0))) [input p11]
16. ! [X0] : ((~rich(X0) <~> curious(X0)) <=> humble(X0)) [input p15]
17. humble(john) <~> tall(john) [input p16]
25. ~tall(john) [input hypothesis]
30. ! [X0] : ((~funny(X0) & ~calm(X0)) | calm(X0)) [ennf transformation 3]
31. ! [X0] : ((curious(X0) & ~rich(X0)) | (generous(X0) <=> funny(X0))) [ennf transformation 5]
48. ! [X0] : ((curious(X0) & ~rich(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0)))) [nnf transformation 31]
49. ! [X0] : ((((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | (curious(X0) | ~generous(X0))) & ((~curious(X0) & generous(X0)) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0))))) [nnf transformation 6]
50. ! [X0] : ((((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | curious(X0) | ~generous(X0)) & ((~curious(X0) & generous(X0)) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0))))) [flattening 49]
54. ! [X0] : ((~patient(X0) | (creative(X0) | calm(X0))) & ((~creative(X0) & ~calm(X0)) | patient(X0))) [nnf transformation 10]
55. ! [X0] : ((~patient(X0) | creative(X0) | calm(X0)) & ((~creative(X0) & ~calm(X0)) | patient(X0))) [flattening 54]
57. ! [X0] : (((patient(X0) & generous(X0)) | ((humble(X0) | ~funny(X0)) & (funny(X0) | ~humble(X0)))) & (((~funny(X0) | ~humble(X0)) & (funny(X0) | humble(X0))) | (~patient(X0) | ~generous(X0)))) [nnf transformation 12]
58. ! [X0] : (((patient(X0) & generous(X0)) | ((humble(X0) | ~funny(X0)) & (funny(X0) | ~humble(X0)))) & (((~funny(X0) | ~humble(X0)) & (funny(X0) | humble(X0))) | ~patient(X0) | ~generous(X0))) [flattening 57]
62. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | ~humble(X0)) & (humble(X0) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [nnf transformation 16]
63. (~tall(john) | ~humble(john)) & (tall(john) | humble(john)) [nnf transformation 17]
83. ~funny(X0) | calm(X0) [cnf transformation 30]
87. ~rich(X0) | funny(X0) | ~generous(X0) [cnf transformation 48]
88. ~rich(X0) | generous(X0) | ~funny(X0) [cnf transformation 48]
89. ~generous(X0) | funny(X0) | curious(X0) [cnf transformation 48]
90. ~funny(X0) | generous(X0) | curious(X0) [cnf transformation 48]
92. tall(X0) | generous(X0) | patient(X0) [cnf transformation 50]
95. ~generous(X0) | tall(X0) | curious(X0) | ~patient(X0) [cnf transformation 50]
104. ~calm(X0) | patient(X0) [cnf transformation 55]
112. ~humble(X0) | ~funny(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 58]
113. ~humble(X0) | funny(X0) | generous(X0) [cnf transformation 58]
130. ~humble(X0) | rich(X0) | ~curious(X0) [cnf transformation 62]
131. tall(john) | humble(john) [cnf transformation 63]
146. ~tall(john) [cnf transformation 25]
251. 23 <=> humble(john) [avatar definition]
252. humble(john) <- (23) [avatar component clause 251]
255. 24 <=> tall(john) [avatar definition]
257. ~tall(john) <- (~24) [avatar component clause 255]
259. 23 | 24 [avatar split clause 131,255,251]
290. ~24 [avatar split clause 146,255]
301. 31 <=> patient(john) [avatar definition]
302. patient(john) <- (31) [avatar component clause 301]
303. ~patient(john) <- (~31) [avatar component clause 301]
328. generous(john) | patient(john) <- (~24) [resolution 92,257]
331. generous(john) <- (~24, ~31) [subsumption resolution 328,303]
333. funny(john) | curious(john) <- (~24, ~31) [resolution 331,89]
335. 37 <=> curious(john) [avatar definition]
339. 38 <=> funny(john) [avatar definition]
341. funny(john) <- (38) [avatar component clause 339]
342. 37 | 38 | 24 | 31 [avatar split clause 333,301,255,339,335]
344. 39 <=> generous(john) [avatar definition]
346. generous(john) <- (39) [avatar component clause 344]
384. funny(john) | generous(john) <- (23) [resolution 113,252]
385. 39 | 38 | ~23 [avatar split clause 384,251,339,344]
386. generous(john) | curious(john) <- (38) [resolution 341,90]
387. calm(john) <- (38) [resolution 341,83]
388. 37 | 39 | ~38 [avatar split clause 386,339,344,335]
408. 48 <=> rich(john) [avatar definition]
410. rich(john) <- (48) [avatar component clause 408]
421. rich(john) | ~curious(john) <- (23) [resolution 130,252]
426. ~37 | 48 | ~23 [avatar split clause 421,251,408,335]
430. tall(john) | curious(john) | ~patient(john) <- (39) [resolution 95,346]
431. curious(john) | ~patient(john) <- (~24, 39) [subsumption resolution 430,257]
440. ~funny(john) | ~patient(john) | ~generous(john) <- (23) [resolution 112,252]
444. patient(john) <- (38) [resolution 387,104]
447. 31 | ~38 [avatar split clause 444,339,301]
451. ~31 | 37 | 24 | ~39 [avatar split clause 431,344,255,335,301]
452. ~funny(john) | ~generous(john) <- (23, 31) [subsumption resolution 440,302]
457. generous(john) | ~funny(john) <- (48) [resolution 410,88]
458. funny(john) | ~generous(john) <- (48) [resolution 410,87]
462. ~39 | 38 | ~48 [avatar split clause 458,408,339,344]
463. ~38 | 39 | ~48 [avatar split clause 457,408,344,339]
464. ~39 | ~38 | ~23 | ~31 [avatar split clause 452,301,251,339,344]
465. $false [avatar sat refutation 259,290,342,385,388,426,447,451,462,463,464]
% SZS output end Proof for 1442375976295240803581583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or calm is both not happy and not patient.
If someone is tall or not creative then someone is both not wise and not curious and vice versa.
Everyone who is humble or not tall is not patient.
Everyone who is both not quiet and funny is old and vice versa.
Everyone who is kind is either strong or kind and vice versa.
Everyone who is not calm or not tall is either old or not quiet.
Everyone who is not calm or tall is both not tall and generous and vice versa.
Everyone who is not curious is generous.
If someone is not creative then mary is rich and vice versa.
Everyone who is both not strong and strong is not kind and vice versa.
If mary is rich or not humble then john is kind or not rich.
If someone is curious or kind then someone is generous or not old and vice versa.
If someone is either not strong or not kind then someone is not patient or not brave.
If someone is either brave or patient then paul is not patient or strong and vice versa.
Everyone who is not curious is both not brave and not generous and vice versa.
Someone is calm or not happy.
Someone is brave or rich.
Lucy is generous.
Someone is not quiet or happy.
Someone is both not calm and not wise.
Someone is kind. | John is funny. | contradiction | (![X]:((quiet(X)<~>calm(X))=>(~happy(X)&~patient(X))))&
((?[X]:((tall(X)|~creative(X))))<=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:((humble(X)|~tall(X))=>~patient(X)))&
(![X]:((~quiet(X)&funny(X))<=>old(X)))&
(![X]:(kind(X)<=>(strong(X)<~>kind(X))))&
(![X]:((~calm(X)|~tall(X))=>(old(X)<~>~quiet(X))))&
(![X]:((~calm(X)|tall(X))<=>(~tall(X)&generous(X))))&
(![X]:(~curious(X)=>generous(X)))&
((?[X]:(~creative(X)))<=>(rich(mary)))&
(![X]:((~strong(X)&strong(X))<=>~kind(X)))&
(((rich(mary)|~humble(mary)))=>((kind(john)|~rich(john))))&
((?[X]:((curious(X)|kind(X))))<=>(?[X]:((generous(X)|~old(X)))))&
((?[X]:((~strong(X)<~>~kind(X))))=>(?[X]:((~patient(X)|~brave(X)))))&
((?[X]:((brave(X)<~>patient(X))))<=>((~patient(paul)|strong(paul))))&
(![X]:(~curious(X)<=>(~brave(X)&~generous(X))))&
(?[X]:((calm(X)|~happy(X))))&
(?[X]:((brave(X)|rich(X))))&
(generous(lucy))&
(?[X]:((~quiet(X)|happy(X))))&
(?[X]:((~calm(X)&~wise(X))))&
(?[X]:(kind(X))) | funny(john) | [
"p3",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2955046443068571398874435
% SZS output start Proof for 2955046443068571398874435
4. ! [X0] : ((funny(X0) & ~quiet(X0)) <=> old(X0)) [input p3]
6. ! [X0] : ((~tall(X0) | ~calm(X0)) => (old(X0) <~> ~quiet(X0))) [input p5]
7. ! [X0] : ((tall(X0) | ~calm(X0)) <=> (generous(X0) & ~tall(X0))) [input p6]
22. funny(john) [input hypothesis]
28. ! [X0] : ((old(X0) <~> ~quiet(X0)) | (tall(X0) & calm(X0))) [ennf transformation 6]
39. ! [X0] : (((funny(X0) & ~quiet(X0)) | ~old(X0)) & (old(X0) | (~funny(X0) | quiet(X0)))) [nnf transformation 4]
40. ! [X0] : (((funny(X0) & ~quiet(X0)) | ~old(X0)) & (old(X0) | ~funny(X0) | quiet(X0))) [flattening 39]
42. ! [X0] : (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (tall(X0) & calm(X0))) [nnf transformation 28]
43. ! [X0] : (((tall(X0) | ~calm(X0)) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | (~tall(X0) & calm(X0)))) [nnf transformation 7]
44. ! [X0] : ((tall(X0) | ~calm(X0) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | (~tall(X0) & calm(X0)))) [flattening 43]
88. ~funny(X0) | old(X0) | quiet(X0) [cnf transformation 40]
89. ~old(X0) | ~quiet(X0) [cnf transformation 40]
96. ~quiet(X0) | old(X0) | tall(X0) [cnf transformation 42]
98. quiet(X0) | ~old(X0) | tall(X0) [cnf transformation 42]
100. ~tall(X0) | ~tall(X0) [cnf transformation 44]
134. funny(john) [cnf transformation 22]
135. ~tall(X0) [duplicate literal removal 100]
160. 6 <=> ! [X3] : ~tall(X3) [avatar definition]
161. ~tall(X3) <- (6) [avatar component clause 160]
170. ~old(X0) | tall(X0) [subsumption resolution 98,89]
172. ~quiet(X0) | tall(X0) [subsumption resolution 96,170]
174. 6 [avatar split clause 135,160]
272. old(john) | quiet(john) [resolution 88,134]
274. 26 <=> quiet(john) [avatar definition]
276. quiet(john) <- (26) [avatar component clause 274]
278. 27 <=> old(john) [avatar definition]
280. old(john) <- (27) [avatar component clause 278]
281. 26 | 27 [avatar split clause 272,278,274]
283. tall(john) <- (26) [resolution 276,172]
284. $false <- (6, 26) [subsumption resolution 283,161]
285. ~6 | ~26 [avatar contradiction clause 284]
291. tall(john) <- (27) [resolution 280,170]
294. $false <- (6, 27) [subsumption resolution 291,161]
295. ~6 | ~27 [avatar contradiction clause 294]
296. $false [avatar sat refutation 174,281,285,295]
% SZS output end Proof for 2955046443068571398874435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and not old then susan is either wise or funny.
If someone is generous or not old then alice is not rich or funny.
Everyone who is not brave is either not tall or strong and vice versa.
If susan is not funny or not happy then paul is both not strong and humble and vice versa.
If someone is either not patient or strong then john is not creative and vice versa.
Everyone who is generous is both not tall and not quiet.
Everyone who is strong or tall is both old and quiet and vice versa.
If someone is either not kind or not humble then someone is patient and vice versa.
If someone is not curious or not creative then someone is curious.
If someone is either not generous or not patient then someone is not old and vice versa.
If someone is strong then paul is either patient or not kind.
If alice is both curious and not quiet then lucy is happy or not patient and vice versa.
If alice is both not brave and not tall then someone is either rich or curious and vice versa.
Everyone who is both not old and strong is either not quiet or brave and vice versa.
Everyone who is humble is not wise or not funny.
If paul is not calm then alice is both happy and generous.
Mary is quiet or happy.
Someone is not happy.
Someone is brave or curious.
Someone is both not rich and not kind.
Someone is both calm and strong.
Paul is either kind or happy.
Mary is both not curious and not calm.
Fred is both patient and funny. | Lucy is not patient. | contradiction | ((?[X]:((old(X)&~old(X))))=>((wise(susan)<~>funny(susan))))&
((?[X]:((generous(X)|~old(X))))=>((~rich(alice)|funny(alice))))&
(![X]:(~brave(X)<=>(~tall(X)<~>strong(X))))&
(((~funny(susan)|~happy(susan)))<=>((~strong(paul)&humble(paul))))&
((?[X]:((~patient(X)<~>strong(X))))<=>(~creative(john)))&
(![X]:(generous(X)=>(~tall(X)&~quiet(X))))&
(![X]:((strong(X)|tall(X))<=>(old(X)&quiet(X))))&
((?[X]:((~kind(X)<~>~humble(X))))<=>(?[X]:(patient(X))))&
((?[X]:((~curious(X)|~creative(X))))=>(?[X]:(curious(X))))&
((?[X]:((~generous(X)<~>~patient(X))))<=>(?[X]:(~old(X))))&
((?[X]:(strong(X)))=>((patient(paul)<~>~kind(paul))))&
(((curious(alice)&~quiet(alice)))<=>((happy(lucy)|~patient(lucy))))&
(((~brave(alice)&~tall(alice)))<=>(?[X]:((rich(X)<~>curious(X)))))&
(![X]:((~old(X)&strong(X))<=>(~quiet(X)<~>brave(X))))&
(![X]:(humble(X)=>(~wise(X)|~funny(X))))&
((~calm(paul))=>((happy(alice)&generous(alice))))&
((quiet(mary)|happy(mary)))&
(?[X]:(~happy(X)))&
(?[X]:((brave(X)|curious(X))))&
(?[X]:((~rich(X)&~kind(X))))&
(?[X]:((calm(X)&strong(X))))&
((kind(paul)<~>happy(paul)))&
((~curious(mary)&~calm(mary)))&
((patient(fred)&funny(fred))) | ~patient(lucy) | [
"p2",
"p6",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2953249503847332671821
% SZS output start Proof for 2953249503847332671821
3. ! [X0] : (~brave(X0) <=> (~tall(X0) <~> strong(X0))) [input p2]
7. ! [X0] : ((tall(X0) | strong(X0)) <=> (quiet(X0) & old(X0))) [input p6]
12. (~quiet(alice) & curious(alice)) <=> (~patient(lucy) | happy(lucy)) [input p11]
14. ! [X0] : ((strong(X0) & ~old(X0)) <=> (~quiet(X0) <~> brave(X0))) [input p13]
25. ~patient(lucy) [input hypothesis]
39. ! [X0] : ((~brave(X0) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0)))) & (((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | brave(X0))) [nnf transformation 3]
46. ! [X0] : (((tall(X0) | strong(X0)) | (~quiet(X0) | ~old(X0))) & ((quiet(X0) & old(X0)) | (~tall(X0) & ~strong(X0)))) [nnf transformation 7]
47. ! [X0] : ((tall(X0) | strong(X0) | ~quiet(X0) | ~old(X0)) & ((quiet(X0) & old(X0)) | (~tall(X0) & ~strong(X0)))) [flattening 46]
62. ((~quiet(alice) & curious(alice)) | (patient(lucy) & ~happy(lucy))) & ((~patient(lucy) | happy(lucy)) | (quiet(alice) | ~curious(alice))) [nnf transformation 12]
63. ((~quiet(alice) & curious(alice)) | (patient(lucy) & ~happy(lucy))) & (~patient(lucy) | happy(lucy) | quiet(alice) | ~curious(alice)) [flattening 62]
69. ! [X0] : (((strong(X0) & ~old(X0)) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0)))) & (((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | (~strong(X0) | old(X0)))) [nnf transformation 14]
70. ! [X0] : (((strong(X0) & ~old(X0)) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0)))) & (((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | ~strong(X0) | old(X0))) [flattening 69]
86. ~brave(X0) | strong(X0) | tall(X0) [cnf transformation 39]
101. ~strong(X0) | quiet(X0) [cnf transformation 47]
102. ~tall(X0) | quiet(X0) [cnf transformation 47]
120. ~quiet(alice) | patient(lucy) [cnf transformation 63]
131. strong(X0) | brave(X0) | quiet(X0) [cnf transformation 70]
149. ~patient(lucy) [cnf transformation 25]
282. 31 <=> patient(lucy) [avatar definition]
286. 32 <=> quiet(alice) [avatar definition]
288. ~quiet(alice) <- (~32) [avatar component clause 286]
289. 31 | ~32 [avatar split clause 120,286,282]
306. 36 <=> tall(alice) [avatar definition]
307. tall(alice) <- (36) [avatar component clause 306]
308. ~tall(alice) <- (~36) [avatar component clause 306]
315. 38 <=> brave(alice) [avatar definition]
316. brave(alice) <- (38) [avatar component clause 315]
330. quiet(X0) | brave(X0) [subsumption resolution 131,101]
369. ~31 [avatar split clause 149,282]
381. quiet(alice) <- (36) [resolution 102,307]
382. $false <- (~32, 36) [subsumption resolution 381,288]
383. 32 | ~36 [avatar contradiction clause 382]
391. brave(alice) <- (~32) [resolution 330,288]
395. 38 | 32 [avatar split clause 391,286,315]
411. strong(alice) | tall(alice) <- (38) [resolution 86,316]
415. strong(alice) <- (~36, 38) [subsumption resolution 411,308]
436. quiet(alice) <- (~36, 38) [resolution 415,101]
438. $false <- (~32, ~36, 38) [subsumption resolution 436,288]
439. 32 | 36 | ~38 [avatar contradiction clause 438]
440. $false [avatar sat refutation 289,369,383,395,439]
% SZS output end Proof for 2953249503847332671821
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not generous is not generous.
Everyone who is brave is happy or brave.
Everyone who is either humble or happy is strong or humble.
If paul is either not kind or not happy then someone is both brave and happy and vice versa.
If someone is both not kind and brave then someone is calm or not happy.
Everyone who is curious or not quiet is either not brave or not calm and vice versa.
If someone is both not brave and not rich then someone is both not creative and generous and vice versa.
If mary is both kind and not tall then susan is curious and vice versa.
If lucy is creative then fred is either curious or not wise and vice versa.
If someone is quiet then mary is both not creative and not wise.
If mary is strong or curious then someone is calm and vice versa.
Everyone who is wise is calm or wise.
Everyone who is not quiet or not funny is either not wise or not rich.
If someone is both curious and funny then paul is either not funny or rich.
Everyone who is either not calm or calm is both curious and calm.
Everyone who is not kind is wise and vice versa.
Fred is not kind.
Susan is both not wise and not generous.
Someone is both generous and happy.
Mary is either happy or not generous.
Fred is strong or brave.
Someone is tall or not brave.
Someone is not happy. | Susan is quiet. | neutral | (![X]:((~patient(X)|~generous(X))=>~generous(X)))&
(![X]:(brave(X)=>(happy(X)|brave(X))))&
(![X]:((humble(X)<~>happy(X))=>(strong(X)|humble(X))))&
(((~kind(paul)<~>~happy(paul)))<=>(?[X]:((brave(X)&happy(X)))))&
((?[X]:((~kind(X)&brave(X))))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((curious(X)|~quiet(X))<=>(~brave(X)<~>~calm(X))))&
((?[X]:((~brave(X)&~rich(X))))<=>(?[X]:((~creative(X)&generous(X)))))&
(((kind(mary)&~tall(mary)))<=>(curious(susan)))&
((creative(lucy))<=>((curious(fred)<~>~wise(fred))))&
((?[X]:(quiet(X)))=>((~creative(mary)&~wise(mary))))&
(((strong(mary)|curious(mary)))<=>(?[X]:(calm(X))))&
(![X]:(wise(X)=>(calm(X)|wise(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~wise(X)<~>~rich(X))))&
((?[X]:((curious(X)&funny(X))))=>((~funny(paul)<~>rich(paul))))&
(![X]:((~calm(X)<~>calm(X))=>(curious(X)&calm(X))))&
(![X]:(~kind(X)<=>wise(X)))&
(~kind(fred))&
((~wise(susan)&~generous(susan)))&
(?[X]:((generous(X)&happy(X))))&
((happy(mary)<~>~generous(mary)))&
((strong(fred)|brave(fred)))&
(?[X]:((tall(X)|~brave(X))))&
(?[X]:(~happy(X))) | quiet(susan) | [] | null | 0 |
Everyone who is either not kind or not brave is both not creative and humble and vice versa.
If paul is either not kind or not patient then someone is both not rich and not kind and vice versa.
Everyone who is strong is tall and vice versa.
Everyone who is either brave or not strong is both strong and not old.
If paul is both generous and happy then lucy is both tall and not wise.
If paul is not calm or not curious then paul is either brave or quiet and vice versa.
Everyone who is generous is either not calm or not creative.
Everyone who is both not humble and not brave is tall or not wise and vice versa.
Everyone who is brave is both not creative and not brave and vice versa.
Everyone who is either happy or not rich is kind and vice versa.
If mary is rich or brave then someone is either not quiet or kind and vice versa.
If someone is not humble then someone is either not generous or not brave and vice versa.
If someone is calm then someone is both not old and not tall.
Everyone who is both old and not quiet is both not rich and not funny and vice versa.
Everyone who is either not generous or not kind is either funny or not strong.
Someone is curious or not old.
Someone is both patient and not curious.
Someone is either not quiet or rich.
Someone is not wise or not generous.
Someone is either not rich or not brave.
Alice is quiet.
Susan is either not happy or not quiet.
John is either calm or not curious. | Alice is not calm. | entailment | (![X]:((~kind(X)<~>~brave(X))<=>(~creative(X)&humble(X))))&
(((~kind(paul)<~>~patient(paul)))<=>(?[X]:((~rich(X)&~kind(X)))))&
(![X]:(strong(X)<=>tall(X)))&
(![X]:((brave(X)<~>~strong(X))=>(strong(X)&~old(X))))&
(((generous(paul)&happy(paul)))=>((tall(lucy)&~wise(lucy))))&
(((~calm(paul)|~curious(paul)))<=>((brave(paul)<~>quiet(paul))))&
(![X]:(generous(X)=>(~calm(X)<~>~creative(X))))&
(![X]:((~humble(X)&~brave(X))<=>(tall(X)|~wise(X))))&
(![X]:(brave(X)<=>(~creative(X)&~brave(X))))&
(![X]:((happy(X)<~>~rich(X))<=>kind(X)))&
(((rich(mary)|brave(mary)))<=>(?[X]:((~quiet(X)<~>kind(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
((?[X]:(calm(X)))=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((old(X)&~quiet(X))<=>(~rich(X)&~funny(X))))&
(![X]:((~generous(X)<~>~kind(X))=>(funny(X)<~>~strong(X))))&
(?[X]:((curious(X)|~old(X))))&
(?[X]:((patient(X)&~curious(X))))&
(?[X]:((~quiet(X)<~>rich(X))))&
(?[X]:((~wise(X)|~generous(X))))&
(?[X]:((~rich(X)<~>~brave(X))))&
(quiet(alice))&
((~happy(susan)<~>~quiet(susan)))&
((calm(john)<~>~curious(john))) | ~calm(alice) | [
"p2",
"p3",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5089191140193114687859631
% SZS output start Proof for 5089191140193114687859631
3. ! [X0] : (strong(X0) <=> tall(X0)) [input p2]
4. ! [X0] : ((brave(X0) <~> ~strong(X0)) => (~old(X0) & strong(X0))) [input p3]
9. ! [X0] : (brave(X0) <=> (~brave(X0) & ~creative(X0))) [input p8]
13. ? [X0] : calm(X0) => ? [X0] : (~tall(X0) & ~old(X0)) [input p12]
24. calm(alice) [input hypothesis]
26. ? [X0] : calm(X0) => ? [X1] : (~tall(X1) & ~old(X1)) [rectify 13]
27. ! [X0] : ((~old(X0) & strong(X0)) | (brave(X0) <=> ~strong(X0))) [ennf transformation 4]
31. ? [X1] : (~tall(X1) & ~old(X1)) | ! [X0] : ~calm(X0) [ennf transformation 26]
39. ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))) [nnf transformation 3]
40. ! [X0] : ((~old(X0) & strong(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0)))) [nnf transformation 27]
46. ! [X0] : ((brave(X0) | (brave(X0) | creative(X0))) & ((~brave(X0) & ~creative(X0)) | ~brave(X0))) [nnf transformation 9]
47. ! [X0] : ((brave(X0) | brave(X0) | creative(X0)) & ((~brave(X0) & ~creative(X0)) | ~brave(X0))) [flattening 46]
59. ? [X0] : (~tall(X0) & ~old(X0)) | ! [X1] : ~calm(X1) [rectify 31]
60. ? [X0] : (~tall(X0) & ~old(X0)) => (~tall(sK4) & ~old(sK4)) [choice axiom]
61. (~tall(sK4) & ~old(sK4)) | ! [X1] : ~calm(X1) [skolemisation 59,60]
91. ~strong(X0) | tall(X0) [cnf transformation 39]
94. strong(X0) | brave(X0) | strong(X0) [cnf transformation 40]
113. ~brave(X0) | ~brave(X0) [cnf transformation 47]
130. ~tall(sK4) | ~calm(X1) [cnf transformation 61]
152. calm(alice) [cnf transformation 24]
153. ~brave(X0) [duplicate literal removal 113]
155. strong(X0) | brave(X0) [duplicate literal removal 94]
264. 23 <=> ! [X1] : ~calm(X1) [avatar definition]
265. ~calm(X1) <- (23) [avatar component clause 264]
267. 24 <=> tall(sK4) [avatar definition]
269. ~tall(sK4) <- (~24) [avatar component clause 267]
270. 23 | ~24 [avatar split clause 130,267,264]
328. brave(X0) | tall(X0) [resolution 155,91]
329. tall(X0) [subsumption resolution 328,153]
331. $false <- (~24) [resolution 329,269]
335. 24 [avatar contradiction clause 331]
342. $false <- (23) [resolution 265,152]
343. ~23 [avatar contradiction clause 342]
344. $false [avatar sat refutation 270,335,343]
% SZS output end Proof for 5089191140193114687859631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both calm and not happy and vice versa.
Everyone who is either calm or not funny is either not humble or not kind and vice versa.
If paul is rich then someone is both not happy and not generous.
Everyone who is rich or not rich is old.
Everyone who is either tall or funny is either quiet or curious.
Everyone who is both calm and quiet is creative or not creative and vice versa.
If someone is not patient then fred is either not patient or not kind.
Everyone who is curious is not old or not rich and vice versa.
If paul is not funny then someone is both brave and not tall and vice versa.
Everyone who is both not brave and humble is either brave or not kind and vice versa.
If someone is both kind and not humble then someone is both calm and humble and vice versa.
Everyone who is either quiet or not wise is not calm or not happy.
Everyone who is both generous and old is both not quiet and creative and vice versa.
Everyone who is old or not happy is either funny or not patient.
Everyone who is both quiet and not quiet is either not creative or not old.
Someone is not patient or not curious.
Someone is not rich or strong.
Someone is both not generous and not kind.
Someone is humble or calm. | Fred is patient. | entailment | (![X]:(~funny(X)<=>(calm(X)&~happy(X))))&
(![X]:((calm(X)<~>~funny(X))<=>(~humble(X)<~>~kind(X))))&
((rich(paul))=>(?[X]:((~happy(X)&~generous(X)))))&
(![X]:((rich(X)|~rich(X))=>old(X)))&
(![X]:((tall(X)<~>funny(X))=>(quiet(X)<~>curious(X))))&
(![X]:((calm(X)&quiet(X))<=>(creative(X)|~creative(X))))&
((?[X]:(~patient(X)))=>((~patient(fred)<~>~kind(fred))))&
(![X]:(curious(X)<=>(~old(X)|~rich(X))))&
((~funny(paul))<=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((~brave(X)&humble(X))<=>(brave(X)<~>~kind(X))))&
((?[X]:((kind(X)&~humble(X))))<=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((quiet(X)<~>~wise(X))=>(~calm(X)|~happy(X))))&
(![X]:((generous(X)&old(X))<=>(~quiet(X)&creative(X))))&
(![X]:((old(X)|~happy(X))=>(funny(X)<~>~patient(X))))&
(![X]:((quiet(X)&~quiet(X))=>(~creative(X)<~>~old(X))))&
(?[X]:((~patient(X)|~curious(X))))&
(?[X]:((~rich(X)|strong(X))))&
(?[X]:((~generous(X)&~kind(X))))&
(?[X]:((humble(X)|calm(X)))) | patient(fred) | [
"p0",
"p1",
"p3",
"p6",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 44608136442893455910418
% SZS output start Proof for 44608136442893455910418
1. ! [X0] : (~funny(X0) <=> (~happy(X0) & calm(X0))) [input p0]
2. ! [X0] : ((calm(X0) <~> ~funny(X0)) <=> (~humble(X0) <~> ~kind(X0))) [input p1]
4. ! [X0] : ((~rich(X0) | rich(X0)) => old(X0)) [input p3]
7. ? [X0] : ~patient(X0) => (~patient(fred) <~> ~kind(fred)) [input p6]
10. ! [X0] : ((humble(X0) & ~brave(X0)) <=> (brave(X0) <~> ~kind(X0))) [input p9]
14. ! [X0] : ((~happy(X0) | old(X0)) => (funny(X0) <~> ~patient(X0))) [input p13]
20. ~patient(fred) [input hypothesis]
24. ! [X0] : (old(X0) | (rich(X0) & ~rich(X0))) [ennf transformation 4]
26. (~patient(fred) <~> ~kind(fred)) | ! [X0] : patient(X0) [ennf transformation 7]
29. ! [X0] : ((funny(X0) <~> ~patient(X0)) | (happy(X0) & ~old(X0))) [ennf transformation 14]
32. ! [X0] : ((~funny(X0) | (happy(X0) | ~calm(X0))) & ((~happy(X0) & calm(X0)) | funny(X0))) [nnf transformation 1]
33. ! [X0] : ((~funny(X0) | happy(X0) | ~calm(X0)) & ((~happy(X0) & calm(X0)) | funny(X0))) [flattening 32]
34. ! [X0] : ((((funny(X0) | ~calm(X0)) & (~funny(X0) | calm(X0))) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0)))) & (((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0))))) [nnf transformation 2]
40. ((kind(fred) | patient(fred)) & (~kind(fred) | ~patient(fred))) | ! [X0] : patient(X0) [nnf transformation 26]
47. ! [X0] : (((humble(X0) & ~brave(X0)) | ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0)))) & (((kind(X0) | ~brave(X0)) & (~kind(X0) | brave(X0))) | (~humble(X0) | brave(X0)))) [nnf transformation 10]
48. ! [X0] : (((humble(X0) & ~brave(X0)) | ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0)))) & (((kind(X0) | ~brave(X0)) & (~kind(X0) | brave(X0))) | ~humble(X0) | brave(X0))) [flattening 47]
57. ! [X0] : (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (happy(X0) & ~old(X0))) [nnf transformation 29]
65. calm(X0) | funny(X0) [cnf transformation 33]
74. funny(X0) | ~calm(X0) | ~kind(X0) | humble(X0) [cnf transformation 34]
78. old(X0) | ~rich(X0) [cnf transformation 24]
79. old(X0) | rich(X0) [cnf transformation 24]
90. kind(fred) | patient(fred) | patient(X0) [cnf transformation 40]
97. ~kind(X0) | brave(X0) | ~humble(X0) | brave(X0) [cnf transformation 48]
99. ~brave(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 48]
115. patient(X0) | ~funny(X0) | ~old(X0) [cnf transformation 57]
123. ~patient(fred) [cnf transformation 20]
124. ~kind(X0) | brave(X0) | ~humble(X0) [duplicate literal removal 97]
125. ~brave(X0) | ~kind(X0) [duplicate literal removal 99]
127. ~kind(X0) | funny(X0) | humble(X0) [subsumption resolution 74,65]
144. old(X0) [subsumption resolution 78,79]
148. 4 <=> ! [X0] : patient(X0) [avatar definition]
149. patient(X0) <- (4) [avatar component clause 148]
151. 5 <=> patient(fred) [avatar definition]
152. ~patient(fred) <- (~5) [avatar component clause 151]
155. 6 <=> kind(fred) [avatar definition]
157. kind(fred) <- (6) [avatar component clause 155]
158. 4 | 5 | 6 [avatar split clause 90,155,151,148]
179. ~kind(X0) | ~humble(X0) [subsumption resolution 124,125]
209. ~funny(X0) | patient(X0) [subsumption resolution 115,144]
220. ~5 [avatar split clause 123,151]
221. $false <- (4, ~5) [resolution 152,149]
222. ~4 | 5 [avatar contradiction clause 221]
229. ~humble(fred) <- (6) [resolution 179,157]
255. funny(fred) | humble(fred) <- (6) [resolution 127,157]
257. funny(fred) <- (6) [subsumption resolution 255,229]
278. patient(fred) <- (6) [resolution 257,209]
280. $false <- (~5, 6) [subsumption resolution 278,152]
281. 5 | ~6 [avatar contradiction clause 280]
282. $false [avatar sat refutation 158,220,222,281]
% SZS output end Proof for 44608136442893455910418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then someone is either old or not calm and vice versa.
If someone is both tall and creative then paul is not strong or brave and vice versa.
If someone is either funny or calm then someone is both creative and quiet.
If someone is either brave or strong then someone is not tall or not wise.
Everyone who is wise is not humble.
Everyone who is humble or wise is either not funny or not strong and vice versa.
If someone is not rich then someone is both not rich and old and vice versa.
Everyone who is quiet or funny is either not creative or brave and vice versa.
Everyone who is both not tall and not humble is not happy or not brave and vice versa.
Everyone who is quiet is tall and vice versa.
Everyone who is strong is not old and vice versa.
If someone is either not funny or not generous then someone is not calm.
Everyone who is both not rich and not curious is either not funny or creative.
Everyone who is brave is not patient or not funny.
If someone is either not old or not wise then fred is not generous and vice versa.
Everyone who is generous is both funny and rich.
Someone is either happy or old.
Someone is either generous or funny.
Alice is either not funny or not strong.
Lucy is either old or generous.
Alice is not old or not creative.
Someone is either calm or not creative.
Someone is not wise or not brave.
Paul is wise. | Paul is not humble. | entailment | ((?[X]:(curious(X)))<=>(?[X]:((old(X)<~>~calm(X)))))&
((?[X]:((tall(X)&creative(X))))<=>((~strong(paul)|brave(paul))))&
((?[X]:((funny(X)<~>calm(X))))=>(?[X]:((creative(X)&quiet(X)))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((~tall(X)|~wise(X)))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((humble(X)|wise(X))<=>(~funny(X)<~>~strong(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~rich(X)&old(X)))))&
(![X]:((quiet(X)|funny(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~happy(X)|~brave(X))))&
(![X]:(quiet(X)<=>tall(X)))&
(![X]:(strong(X)<=>~old(X)))&
((?[X]:((~funny(X)<~>~generous(X))))=>(?[X]:(~calm(X))))&
(![X]:((~rich(X)&~curious(X))=>(~funny(X)<~>creative(X))))&
(![X]:(brave(X)=>(~patient(X)|~funny(X))))&
((?[X]:((~old(X)<~>~wise(X))))<=>(~generous(fred)))&
(![X]:(generous(X)=>(funny(X)&rich(X))))&
(?[X]:((happy(X)<~>old(X))))&
(?[X]:((generous(X)<~>funny(X))))&
((~funny(alice)<~>~strong(alice)))&
((old(lucy)<~>generous(lucy)))&
((~old(alice)|~creative(alice)))&
(?[X]:((calm(X)<~>~creative(X))))&
(?[X]:((~wise(X)|~brave(X))))&
(wise(paul)) | ~humble(paul) | [
"p4",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3082818489064160399442063
% SZS output start Proof for 3082818489064160399442063
5. ! [X0] : (wise(X0) => ~humble(X0)) [input p4]
24. wise(paul) [input p23]
25. humble(paul) [input hypothesis]
34. ! [X0] : (~humble(X0) | ~wise(X0)) [ennf transformation 5]
107. ~humble(X0) | ~wise(X0) [cnf transformation 34]
154. wise(paul) [cnf transformation 24]
155. humble(paul) [cnf transformation 25]
365. ~wise(paul) [resolution 107,155]
366. $false [subsumption resolution 365,154]
% SZS output end Proof for 3082818489064160399442063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall or not kind then someone is both brave and patient and vice versa.
If fred is not calm or not humble then alice is both not funny and not happy and vice versa.
Everyone who is both not quiet and curious is not creative and vice versa.
Everyone who is quiet is both not funny and not brave.
If someone is either calm or brave then susan is not generous and vice versa.
Everyone who is not calm or not funny is funny or not kind and vice versa.
If john is not quiet then john is either humble or not happy.
If someone is happy or patient then paul is rich or not rich.
Everyone who is happy or not curious is both not brave and wise and vice versa.
If paul is not strong or curious then someone is not happy or not old and vice versa.
Everyone who is either wise or not happy is either kind or not rich and vice versa.
If someone is not generous then someone is not old and vice versa.
If someone is creative or calm then alice is either not strong or calm.
If someone is creative then mary is not wise.
If someone is patient or humble then someone is not rich or rich and vice versa.
Everyone who is not brave is strong.
Someone is both not curious and not patient.
Mary is either wise or quiet.
Someone is not calm or curious.
Susan is both humble and brave.
Someone is both wise and kind.
Alice is either kind or funny.
Fred is not generous. | Mary is not rich. | entailment | ((?[X]:((tall(X)|~kind(X))))<=>(?[X]:((brave(X)&patient(X)))))&
(((~calm(fred)|~humble(fred)))<=>((~funny(alice)&~happy(alice))))&
(![X]:((~quiet(X)&curious(X))<=>~creative(X)))&
(![X]:(quiet(X)=>(~funny(X)&~brave(X))))&
((?[X]:((calm(X)<~>brave(X))))<=>(~generous(susan)))&
(![X]:((~calm(X)|~funny(X))<=>(funny(X)|~kind(X))))&
((~quiet(john))=>((humble(john)<~>~happy(john))))&
((?[X]:((happy(X)|patient(X))))=>((rich(paul)|~rich(paul))))&
(![X]:((happy(X)|~curious(X))<=>(~brave(X)&wise(X))))&
(((~strong(paul)|curious(paul)))<=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:((wise(X)<~>~happy(X))<=>(kind(X)<~>~rich(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~old(X))))&
((?[X]:((creative(X)|calm(X))))=>((~strong(alice)<~>calm(alice))))&
((?[X]:(creative(X)))=>(~wise(mary)))&
((?[X]:((patient(X)|humble(X))))<=>(?[X]:((~rich(X)|rich(X)))))&
(![X]:(~brave(X)=>strong(X)))&
(?[X]:((~curious(X)&~patient(X))))&
((wise(mary)<~>quiet(mary)))&
(?[X]:((~calm(X)|curious(X))))&
((humble(susan)&brave(susan)))&
(?[X]:((wise(X)&kind(X))))&
((kind(alice)<~>funny(alice)))&
(~generous(fred)) | ~rich(mary) | [
"p2",
"p3",
"p5",
"p8",
"p10",
"p13",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6444998212044189157531412
% SZS output start Proof for 6444998212044189157531412
3. ! [X0] : ((curious(X0) & ~quiet(X0)) <=> ~creative(X0)) [input p2]
4. ! [X0] : (quiet(X0) => (~brave(X0) & ~funny(X0))) [input p3]
6. ! [X0] : ((~funny(X0) | ~calm(X0)) <=> (~kind(X0) | funny(X0))) [input p5]
9. ! [X0] : ((~curious(X0) | happy(X0)) <=> (wise(X0) & ~brave(X0))) [input p8]
11. ! [X0] : ((wise(X0) <~> ~happy(X0)) <=> (kind(X0) <~> ~rich(X0))) [input p10]
14. ? [X0] : creative(X0) => ~wise(mary) [input p13]
17. ? [X0] : (~patient(X0) & ~curious(X0)) [input p16]
18. wise(mary) <~> quiet(mary) [input p17]
24. rich(mary) [input hypothesis]
28. ! [X0] : (~creative(X0) => (curious(X0) & ~quiet(X0))) [unused predicate definition removal 3]
29. ! [X0] : ((curious(X0) & ~quiet(X0)) | creative(X0)) [ennf transformation 28]
30. ! [X0] : ((~brave(X0) & ~funny(X0)) | ~quiet(X0)) [ennf transformation 4]
35. ~wise(mary) | ! [X0] : ~creative(X0) [ennf transformation 14]
48. ! [X0] : (((~funny(X0) | ~calm(X0)) | (kind(X0) & ~funny(X0))) & ((~kind(X0) | funny(X0)) | (funny(X0) & calm(X0)))) [nnf transformation 6]
49. ! [X0] : ((~funny(X0) | ~calm(X0) | (kind(X0) & ~funny(X0))) & (~kind(X0) | funny(X0) | (funny(X0) & calm(X0)))) [flattening 48]
51. ! [X0] : (((~curious(X0) | happy(X0)) | (~wise(X0) | brave(X0))) & ((wise(X0) & ~brave(X0)) | (curious(X0) & ~happy(X0)))) [nnf transformation 9]
52. ! [X0] : ((~curious(X0) | happy(X0) | ~wise(X0) | brave(X0)) & ((wise(X0) & ~brave(X0)) | (curious(X0) & ~happy(X0)))) [flattening 51]
58. ! [X0] : ((((happy(X0) | ~wise(X0)) & (~happy(X0) | wise(X0))) | ((kind(X0) | rich(X0)) & (~rich(X0) | ~kind(X0)))) & (((rich(X0) | ~kind(X0)) & (~rich(X0) | kind(X0))) | ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0))))) [nnf transformation 11]
70. ? [X0] : (~patient(X0) & ~curious(X0)) => (~patient(sK8) & ~curious(sK8)) [choice axiom]
71. ~patient(sK8) & ~curious(sK8) [skolemisation 17,70]
72. (~quiet(mary) | ~wise(mary)) & (quiet(mary) | wise(mary)) [nnf transformation 18]
89. creative(X0) | curious(X0) [cnf transformation 29]
90. ~quiet(X0) | ~funny(X0) [cnf transformation 30]
97. ~kind(X0) | funny(X0) | funny(X0) [cnf transformation 49]
106. ~happy(X0) | wise(X0) [cnf transformation 52]
114. ~rich(X0) | kind(X0) | wise(X0) | happy(X0) [cnf transformation 58]
127. ~wise(mary) | ~creative(X0) [cnf transformation 35]
133. ~curious(sK8) [cnf transformation 71]
135. quiet(mary) | wise(mary) [cnf transformation 72]
145. rich(mary) [cnf transformation 24]
146. ~kind(X0) | funny(X0) [duplicate literal removal 97]
263. ~rich(X0) | kind(X0) | wise(X0) [subsumption resolution 114,106]
291. 32 <=> ! [X0] : ~creative(X0) [avatar definition]
292. ~creative(X0) <- (32) [avatar component clause 291]
297. 33 <=> wise(mary) [avatar definition]
299. ~wise(mary) <- (~33) [avatar component clause 297]
300. 32 | ~33 [avatar split clause 127,297,291]
318. 38 <=> quiet(mary) [avatar definition]
319. quiet(mary) <- (38) [avatar component clause 318]
322. 33 | 38 [avatar split clause 135,318,297]
337. curious(X0) <- (32) [resolution 89,292]
338. $false <- (32) [resolution 337,133]
339. ~32 [avatar contradiction clause 338]
341. ~funny(mary) <- (38) [resolution 90,319]
357. kind(mary) | wise(mary) [resolution 263,145]
358. kind(mary) <- (~33) [subsumption resolution 357,299]
360. funny(mary) <- (~33) [resolution 358,146]
361. $false <- (~33, 38) [subsumption resolution 360,341]
362. 33 | ~38 [avatar contradiction clause 361]
363. $false [avatar sat refutation 300,322,339,362]
% SZS output end Proof for 6444998212044189157531412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then mary is both kind and not brave.
If someone is either not generous or not brave then paul is old and vice versa.
If someone is curious then someone is both strong and not tall.
Everyone who is both not wise and not calm is creative and vice versa.
Everyone who is creative is either not kind or not rich and vice versa.
If paul is brave or old then mary is either rich or not funny and vice versa.
Everyone who is rich or not rich is either calm or funny.
Everyone who is quiet is tall or quiet.
Everyone who is both not curious and not quiet is not happy.
If someone is wise then fred is not generous and vice versa.
If lucy is not calm then someone is either not creative or not rich.
If someone is both not patient and wise then someone is wise or funny and vice versa.
If lucy is not rich then lucy is both not old and calm.
If someone is not kind then someone is either curious or creative and vice versa.
If fred is strong or not generous then paul is not rich and vice versa.
If susan is both not brave and not quiet then someone is not calm or not humble.
Someone is either happy or wise.
Mary is both not strong and not funny.
Someone is tall or strong.
Paul is both not rich and kind.
Someone is both kind and happy.
Someone is not wise or humble. | Paul is not brave. | entailment | ((?[X]:(~calm(X)))=>((kind(mary)&~brave(mary))))&
((?[X]:((~generous(X)<~>~brave(X))))<=>(old(paul)))&
((?[X]:(curious(X)))=>(?[X]:((strong(X)&~tall(X)))))&
(![X]:((~wise(X)&~calm(X))<=>creative(X)))&
(![X]:(creative(X)<=>(~kind(X)<~>~rich(X))))&
(((brave(paul)|old(paul)))<=>((rich(mary)<~>~funny(mary))))&
(![X]:((rich(X)|~rich(X))=>(calm(X)<~>funny(X))))&
(![X]:(quiet(X)=>(tall(X)|quiet(X))))&
(![X]:((~curious(X)&~quiet(X))=>~happy(X)))&
((?[X]:(wise(X)))<=>(~generous(fred)))&
((~calm(lucy))=>(?[X]:((~creative(X)<~>~rich(X)))))&
((?[X]:((~patient(X)&wise(X))))<=>(?[X]:((wise(X)|funny(X)))))&
((~rich(lucy))=>((~old(lucy)&calm(lucy))))&
((?[X]:(~kind(X)))<=>(?[X]:((curious(X)<~>creative(X)))))&
(((strong(fred)|~generous(fred)))<=>(~rich(paul)))&
(((~brave(susan)&~quiet(susan)))=>(?[X]:((~calm(X)|~humble(X)))))&
(?[X]:((happy(X)<~>wise(X))))&
((~strong(mary)&~funny(mary)))&
(?[X]:((tall(X)|strong(X))))&
((~rich(paul)&kind(paul)))&
(?[X]:((kind(X)&happy(X))))&
(?[X]:((~wise(X)|humble(X)))) | ~brave(paul) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5086872435606124896242393
% SZS output start Proof for 5086872435606124896242393
1. ? [X0] : ~calm(X0) => (~brave(mary) & kind(mary)) [input p0]
4. ! [X0] : ((~calm(X0) & ~wise(X0)) <=> creative(X0)) [input p3]
5. ! [X0] : (creative(X0) <=> (~kind(X0) <~> ~rich(X0))) [input p4]
6. (old(paul) | brave(paul)) <=> (rich(mary) <~> ~funny(mary)) [input p5]
7. ! [X0] : ((~rich(X0) | rich(X0)) => (calm(X0) <~> funny(X0))) [input p6]
18. ~funny(mary) & ~strong(mary) [input p17]
20. kind(paul) & ~rich(paul) [input p19]
23. brave(paul) [input hypothesis]
27. (~brave(mary) & kind(mary)) | ! [X0] : calm(X0) [ennf transformation 1]
29. ! [X0] : ((calm(X0) <~> funny(X0)) | (rich(X0) & ~rich(X0))) [ennf transformation 7]
45. ! [X0] : (((~calm(X0) & ~wise(X0)) | ~creative(X0)) & (creative(X0) | (calm(X0) | wise(X0)))) [nnf transformation 4]
46. ! [X0] : (((~calm(X0) & ~wise(X0)) | ~creative(X0)) & (creative(X0) | calm(X0) | wise(X0))) [flattening 45]
47. ! [X0] : ((creative(X0) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | ~creative(X0))) [nnf transformation 5]
48. ((old(paul) | brave(paul)) | ((rich(mary) | funny(mary)) & (~funny(mary) | ~rich(mary)))) & (((funny(mary) | ~rich(mary)) & (~funny(mary) | rich(mary))) | (~old(paul) & ~brave(paul))) [nnf transformation 6]
49. (old(paul) | brave(paul) | ((rich(mary) | funny(mary)) & (~funny(mary) | ~rich(mary)))) & (((funny(mary) | ~rich(mary)) & (~funny(mary) | rich(mary))) | (~old(paul) & ~brave(paul))) [flattening 48]
50. ! [X0] : (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | (rich(X0) & ~rich(X0))) [nnf transformation 29]
81. kind(mary) | calm(X0) [cnf transformation 27]
91. ~creative(X0) | ~calm(X0) [cnf transformation 46]
95. ~kind(X0) | creative(X0) | rich(X0) [cnf transformation 47]
98. funny(mary) | ~rich(mary) | ~brave(paul) [cnf transformation 49]
102. funny(X0) | calm(X0) | ~rich(X0) [cnf transformation 50]
103. funny(X0) | calm(X0) | rich(X0) [cnf transformation 50]
130. ~funny(mary) [cnf transformation 18]
132. ~rich(paul) [cnf transformation 20]
133. kind(paul) [cnf transformation 20]
137. brave(paul) [cnf transformation 23]
139. 1 <=> ! [X0] : calm(X0) [avatar definition]
140. calm(X0) <- (1) [avatar component clause 139]
147. 3 <=> kind(mary) [avatar definition]
149. kind(mary) <- (3) [avatar component clause 147]
150. 1 | 3 [avatar split clause 81,147,139]
187. 12 <=> funny(mary) [avatar definition]
188. ~funny(mary) <- (~12) [avatar component clause 187]
191. 13 <=> rich(mary) [avatar definition]
192. ~rich(mary) <- (~13) [avatar component clause 191]
195. 14 <=> brave(paul) [avatar definition]
201. ~14 | ~13 | 12 [avatar split clause 98,187,191,195]
205. funny(X0) | calm(X0) [subsumption resolution 102,103]
296. 35 <=> rich(paul) [avatar definition]
297. ~rich(paul) <- (~35) [avatar component clause 296]
333. ~12 [avatar split clause 130,187]
343. ~35 [avatar split clause 132,296]
353. 14 [avatar split clause 137,195]
362. calm(mary) <- (~12) [resolution 188,205]
373. creative(paul) | rich(paul) [resolution 95,133]
395. creative(paul) <- (~35) [subsumption resolution 373,297]
405. creative(mary) | rich(mary) <- (3) [resolution 149,95]
406. creative(mary) <- (3, ~13) [subsumption resolution 405,192]
450. ~calm(paul) <- (~35) [resolution 395,91]
497. ~calm(mary) <- (3, ~13) [resolution 406,91]
499. $false <- (3, ~12, ~13) [subsumption resolution 497,362]
500. ~3 | 12 | 13 [avatar contradiction clause 499]
510. $false <- (1, ~35) [resolution 450,140]
511. ~1 | 35 [avatar contradiction clause 510]
512. $false [avatar sat refutation 150,201,333,343,353,500,511]
% SZS output end Proof for 5086872435606124896242393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then mary is not brave. Everyone who is either quiet or not wise is either not tall or humble. Everyone who is either not old or strong is not creative and vice versa. Everyone who is either calm or not humble is patient or not humble and vice versa. If someone is not quiet or strong then someone is either happy or humble and vice versa. Everyone who is either not calm or old is either creative or kind and vice versa. If susan is rich or not wise then alice is both strong and not wise and vice versa. Everyone who is not humble or not brave is not patient and vice versa. If mary is either old or not happy then someone is happy. Everyone who is both not brave and not rich is both brave and not generous and vice versa. If someone is not curious then susan is both not brave and not tall. If john is not generous then someone is both strong and not quiet and vice versa. If someone is both rich and not generous then someone is both not tall and not generous and vice versa. Everyone who is both wise and not rich is either strong or curious and vice versa. If someone is either curious or wise then someone is either not humble or generous and vice versa. If someone is not strong or not patient then someone is both not humble and not brave. Fred is either not old or not wise. Lucy is not brave. Alice is both wise and not humble. Lucy is not quiet. Someone is either rich or not rich. Alice is either humble or not humble. Lucy is both not generous and not humble. Susan is rich or not strong. | Fred is curious. | entailment | ((?[X]:(~old(X)))=>(~brave(mary)))&
(![X]:((quiet(X)<~>~wise(X))=>(~tall(X)<~>humble(X))))&
(![X]:((~old(X)<~>strong(X))<=>~creative(X)))&
(![X]:((calm(X)<~>~humble(X))<=>(patient(X)|~humble(X))))&
((?[X]:((~quiet(X)|strong(X))))<=>(?[X]:((happy(X)<~>humble(X)))))&
(![X]:((~calm(X)<~>old(X))<=>(creative(X)<~>kind(X))))&
(((rich(susan)|~wise(susan)))<=>((strong(alice)&~wise(alice))))&
(![X]:((~humble(X)|~brave(X))<=>~patient(X)))&
(((old(mary)<~>~happy(mary)))=>(?[X]:(happy(X))))&
(![X]:((~brave(X)&~rich(X))<=>(brave(X)&~generous(X))))&
((?[X]:(~curious(X)))=>((~brave(susan)&~tall(susan))))&
((~generous(john))<=>(?[X]:((strong(X)&~quiet(X)))))&
((?[X]:((rich(X)&~generous(X))))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((wise(X)&~rich(X))<=>(strong(X)<~>curious(X))))&
((?[X]:((curious(X)<~>wise(X))))<=>(?[X]:((~humble(X)<~>generous(X)))))&
((?[X]:((~strong(X)|~patient(X))))=>(?[X]:((~humble(X)&~brave(X)))))&
((~old(fred)<~>~wise(fred)))&
(~brave(lucy))&
((wise(alice)&~humble(alice)))&
(~quiet(lucy))&
(?[X]:((rich(X)<~>~rich(X))))&
((humble(alice)<~>~humble(alice)))&
((~generous(lucy)&~humble(lucy)))&
((rich(susan)|~strong(susan))) | curious(fred) | [
"p6",
"p9",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 565396541075935666317967
% SZS output start Proof for 565396541075935666317967
7. (~wise(susan) | rich(susan)) <=> (~wise(alice) & strong(alice)) [input p6]
10. ! [X0] : ((~rich(X0) & ~brave(X0)) <=> (~generous(X0) & brave(X0))) [input p9]
11. ? [X0] : ~curious(X0) => (~tall(susan) & ~brave(susan)) [input p10]
19. ~humble(alice) & wise(alice) [input p18]
25. ~curious(fred) [input hypothesis]
33. (~tall(susan) & ~brave(susan)) | ! [X0] : curious(X0) [ennf transformation 11]
45. ((~wise(susan) | rich(susan)) | (wise(alice) | ~strong(alice))) & ((~wise(alice) & strong(alice)) | (wise(susan) & ~rich(susan))) [nnf transformation 7]
46. (~wise(susan) | rich(susan) | wise(alice) | ~strong(alice)) & ((~wise(alice) & strong(alice)) | (wise(susan) & ~rich(susan))) [flattening 45]
52. ! [X0] : (((~rich(X0) & ~brave(X0)) | (generous(X0) | ~brave(X0))) & ((~generous(X0) & brave(X0)) | (rich(X0) | brave(X0)))) [nnf transformation 10]
53. ! [X0] : (((~rich(X0) & ~brave(X0)) | generous(X0) | ~brave(X0)) & ((~generous(X0) & brave(X0)) | rich(X0) | brave(X0))) [flattening 52]
109. ~wise(alice) | ~rich(susan) [cnf transformation 46]
117. brave(X0) | rich(X0) | brave(X0) [cnf transformation 53]
121. ~brave(susan) | curious(X0) [cnf transformation 33]
151. wise(alice) [cnf transformation 19]
161. ~curious(fred) [cnf transformation 25]
162. rich(X0) | brave(X0) [duplicate literal removal 117]
214. 12 <=> wise(alice) [avatar definition]
218. 13 <=> rich(susan) [avatar definition]
219. ~rich(susan) <- (~13) [avatar component clause 218]
227. ~13 | ~12 [avatar split clause 109,214,218]
245. 18 <=> ! [X0] : curious(X0) [avatar definition]
246. curious(X0) <- (18) [avatar component clause 245]
253. 20 <=> brave(susan) [avatar definition]
256. 18 | ~20 [avatar split clause 121,253,245]
365. 12 [avatar split clause 151,214]
371. brave(susan) <- (~13) [resolution 162,219]
374. 20 | 13 [avatar split clause 371,218,253]
375. $false <- (18) [resolution 246,161]
376. ~18 [avatar contradiction clause 375]
377. $false [avatar sat refutation 227,256,365,374,376]
% SZS output end Proof for 565396541075935666317967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then alice is funny or curious.
Everyone who is not curious is wise.
If someone is brave then john is either not calm or not tall.
Everyone who is both strong and curious is not calm or wise.
If john is not calm then someone is either patient or wise and vice versa.
If paul is quiet or old then someone is both not wise and not funny.
Everyone who is brave or not strong is both generous and not humble and vice versa.
If john is not calm or happy then someone is either not kind or not generous and vice versa.
Everyone who is not wise or not brave is not old and vice versa.
Everyone who is both strong and humble is both not brave and wise.
If fred is either not humble or happy then paul is either creative or not generous.
Everyone who is tall is both generous and calm.
Everyone who is tall or curious is not generous or calm and vice versa.
Everyone who is not wise or creative is either not quiet or generous and vice versa.
Everyone who is kind is either not patient or not quiet and vice versa.
If mary is either not tall or not strong then mary is either generous or not rich.
Alice is not rich.
Alice is both kind and old.
Mary is not kind or wise.
Someone is not funny.
Lucy is both humble and generous.
Paul is not generous. | Alice is not patient. | contradiction | ((?[X]:(~strong(X)))=>((funny(alice)|curious(alice))))&
(![X]:(~curious(X)=>wise(X)))&
((?[X]:(brave(X)))=>((~calm(john)<~>~tall(john))))&
(![X]:((strong(X)&curious(X))=>(~calm(X)|wise(X))))&
((~calm(john))<=>(?[X]:((patient(X)<~>wise(X)))))&
(((quiet(paul)|old(paul)))=>(?[X]:((~wise(X)&~funny(X)))))&
(![X]:((brave(X)|~strong(X))<=>(generous(X)&~humble(X))))&
(((~calm(john)|happy(john)))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
(![X]:((~wise(X)|~brave(X))<=>~old(X)))&
(![X]:((strong(X)&humble(X))=>(~brave(X)&wise(X))))&
(((~humble(fred)<~>happy(fred)))=>((creative(paul)<~>~generous(paul))))&
(![X]:(tall(X)=>(generous(X)&calm(X))))&
(![X]:((tall(X)|curious(X))<=>(~generous(X)|calm(X))))&
(![X]:((~wise(X)|creative(X))<=>(~quiet(X)<~>generous(X))))&
(![X]:(kind(X)<=>(~patient(X)<~>~quiet(X))))&
(((~tall(mary)<~>~strong(mary)))=>((generous(mary)<~>~rich(mary))))&
(~rich(alice))&
((kind(alice)&old(alice)))&
((~kind(mary)|wise(mary)))&
(?[X]:(~funny(X)))&
((humble(lucy)&generous(lucy)))&
(~generous(paul)) | ~patient(alice) | [
"p2",
"p4",
"p8",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5176283015720246715162530
% SZS output start Proof for 5176283015720246715162530
3. ? [X0] : brave(X0) => (~calm(john) <~> ~tall(john)) [input p2]
5. ~calm(john) <=> ? [X0] : (patient(X0) <~> wise(X0)) [input p4]
9. ! [X0] : ((~brave(X0) | ~wise(X0)) <=> ~old(X0)) [input p8]
12. ! [X0] : (tall(X0) => (calm(X0) & generous(X0))) [input p11]
18. old(alice) & kind(alice) [input p17]
23. ~patient(alice) [input hypothesis]
27. (~calm(john) <~> ~tall(john)) | ! [X0] : ~brave(X0) [ennf transformation 3]
34. ! [X0] : ((calm(X0) & generous(X0)) | ~tall(X0)) [ennf transformation 12]
36. ((tall(john) | calm(john)) & (~tall(john) | ~calm(john))) | ! [X0] : ~brave(X0) [nnf transformation 27]
37. (~calm(john) | ! [X0] : ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) & (? [X0] : ((~wise(X0) | ~patient(X0)) & (wise(X0) | patient(X0))) | calm(john)) [nnf transformation 5]
38. (~calm(john) | ! [X0] : ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) & (? [X1] : ((~wise(X1) | ~patient(X1)) & (wise(X1) | patient(X1))) | calm(john)) [rectify 37]
39. ? [X1] : ((~wise(X1) | ~patient(X1)) & (wise(X1) | patient(X1))) => ((~wise(sK0) | ~patient(sK0)) & (wise(sK0) | patient(sK0))) [choice axiom]
40. (~calm(john) | ! [X0] : ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) & (((~wise(sK0) | ~patient(sK0)) & (wise(sK0) | patient(sK0))) | calm(john)) [skolemisation 38,39]
50. ! [X0] : (((~brave(X0) | ~wise(X0)) | old(X0)) & (~old(X0) | (brave(X0) & wise(X0)))) [nnf transformation 9]
51. ! [X0] : ((~brave(X0) | ~wise(X0) | old(X0)) & (~old(X0) | (brave(X0) & wise(X0)))) [flattening 50]
64. tall(john) | calm(john) | ~brave(X0) [cnf transformation 36]
69. ~calm(john) | patient(X0) | ~wise(X0) [cnf transformation 40]
85. ~old(X0) | wise(X0) [cnf transformation 51]
86. ~old(X0) | brave(X0) [cnf transformation 51]
95. ~tall(X0) | calm(X0) [cnf transformation 34]
116. old(alice) [cnf transformation 18]
122. ~patient(alice) [cnf transformation 23]
136. 4 <=> ! [X0] : ~brave(X0) [avatar definition]
137. ~brave(X0) <- (4) [avatar component clause 136]
139. 5 <=> calm(john) [avatar definition]
140. ~calm(john) <- (~5) [avatar component clause 139]
143. 6 <=> tall(john) [avatar definition]
145. tall(john) <- (6) [avatar component clause 143]
146. 4 | 5 | 6 [avatar split clause 64,143,139,136]
150. 7 <=> ! [X0] : (patient(X0) | ~wise(X0)) [avatar definition]
151. ~wise(X0) | patient(X0) <- (7) [avatar component clause 150]
152. 7 | ~5 [avatar split clause 69,139,150]
270. wise(alice) [resolution 85,116]
271. brave(alice) [resolution 86,116]
274. patient(alice) <- (7) [resolution 151,270]
275. $false <- (7) [subsumption resolution 274,122]
276. ~7 [avatar contradiction clause 275]
277. $false <- (4) [resolution 137,271]
278. ~4 [avatar contradiction clause 277]
279. calm(john) <- (6) [resolution 145,95]
281. $false <- (~5, 6) [subsumption resolution 279,140]
282. 5 | ~6 [avatar contradiction clause 281]
283. $false [avatar sat refutation 146,152,276,278,282]
% SZS output end Proof for 5176283015720246715162530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or brave is not old or curious.
Everyone who is either kind or wise is either old or generous and vice versa.
Everyone who is both brave and patient is not happy and vice versa.
Everyone who is not funny or creative is wise or creative.
Everyone who is not generous is not old and vice versa.
Everyone who is both calm and not funny is quiet.
If someone is calm then someone is not humble and vice versa.
If someone is both not happy and old then mary is either not rich or strong and vice versa.
Everyone who is not curious is strong.
Everyone who is generous or not creative is not patient or strong.
Everyone who is strong or funny is strong or wise and vice versa.
Everyone who is either old or strong is not calm and vice versa.
Everyone who is not funny is either not calm or not humble and vice versa.
Everyone who is not funny is either not old or not generous and vice versa.
If someone is both not curious and generous then lucy is not generous or old and vice versa.
Everyone who is either not quiet or not rich is funny or not funny.
Susan is wise or quiet.
Someone is both patient and not quiet.
Fred is both brave and not old.
Someone is either not humble or quiet.
Someone is either not patient or funny.
Someone is both tall and wise.
Someone is not kind.
Lucy is not humble. | Susan is not happy. | neutral | (![X]:((~humble(X)|brave(X))=>(~old(X)|curious(X))))&
(![X]:((kind(X)<~>wise(X))<=>(old(X)<~>generous(X))))&
(![X]:((brave(X)&patient(X))<=>~happy(X)))&
(![X]:((~funny(X)|creative(X))=>(wise(X)|creative(X))))&
(![X]:(~generous(X)<=>~old(X)))&
(![X]:((calm(X)&~funny(X))=>quiet(X)))&
((?[X]:(calm(X)))<=>(?[X]:(~humble(X))))&
((?[X]:((~happy(X)&old(X))))<=>((~rich(mary)<~>strong(mary))))&
(![X]:(~curious(X)=>strong(X)))&
(![X]:((generous(X)|~creative(X))=>(~patient(X)|strong(X))))&
(![X]:((strong(X)|funny(X))<=>(strong(X)|wise(X))))&
(![X]:((old(X)<~>strong(X))<=>~calm(X)))&
(![X]:(~funny(X)<=>(~calm(X)<~>~humble(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>~generous(X))))&
((?[X]:((~curious(X)&generous(X))))<=>((~generous(lucy)|old(lucy))))&
(![X]:((~quiet(X)<~>~rich(X))=>(funny(X)|~funny(X))))&
((wise(susan)|quiet(susan)))&
(?[X]:((patient(X)&~quiet(X))))&
((brave(fred)&~old(fred)))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((tall(X)&wise(X))))&
(?[X]:(~kind(X)))&
(~humble(lucy)) | ~happy(susan) | [] | null | 0 |
If susan is both not patient and not tall then paul is either not strong or not kind and vice versa. If someone is not calm or not creative then alice is either kind or not curious. Everyone who is either not happy or funny is both quiet and not calm and vice versa. If fred is either calm or wise then someone is both wise and funny and vice versa. If someone is both creative and happy then someone is not generous or not wise. Everyone who is happy or humble is both not brave and not calm and vice versa. If someone is not brave or not happy then someone is old or generous and vice versa. If lucy is not old then susan is not wise and vice versa. If someone is not curious then someone is both strong and generous and vice versa. If someone is not strong then paul is either creative or generous and vice versa. If someone is funny or not curious then alice is not generous. If someone is funny then mary is either not quiet or humble and vice versa. If susan is both curious and not old then susan is both not rich and calm and vice versa. If john is either not creative or creative then someone is either kind or strong. If paul is either not creative or not tall then fred is either creative or not patient. If someone is not brave or rich then lucy is either funny or not rich and vice versa. Someone is not happy. John is not rich or wise. Paul is either not humble or not patient. Susan is both humble and happy. Someone is not quiet. John is either strong or not tall. | Mary is not humble. | neutral | (((~patient(susan)&~tall(susan)))<=>((~strong(paul)<~>~kind(paul))))&
((?[X]:((~calm(X)|~creative(X))))=>((kind(alice)<~>~curious(alice))))&
(![X]:((~happy(X)<~>funny(X))<=>(quiet(X)&~calm(X))))&
(((calm(fred)<~>wise(fred)))<=>(?[X]:((wise(X)&funny(X)))))&
((?[X]:((creative(X)&happy(X))))=>(?[X]:((~generous(X)|~wise(X)))))&
(![X]:((happy(X)|humble(X))<=>(~brave(X)&~calm(X))))&
((?[X]:((~brave(X)|~happy(X))))<=>(?[X]:((old(X)|generous(X)))))&
((~old(lucy))<=>(~wise(susan)))&
((?[X]:(~curious(X)))<=>(?[X]:((strong(X)&generous(X)))))&
((?[X]:(~strong(X)))<=>((creative(paul)<~>generous(paul))))&
((?[X]:((funny(X)|~curious(X))))=>(~generous(alice)))&
((?[X]:(funny(X)))<=>((~quiet(mary)<~>humble(mary))))&
(((curious(susan)&~old(susan)))<=>((~rich(susan)&calm(susan))))&
(((~creative(john)<~>creative(john)))=>(?[X]:((kind(X)<~>strong(X)))))&
(((~creative(paul)<~>~tall(paul)))=>((creative(fred)<~>~patient(fred))))&
((?[X]:((~brave(X)|rich(X))))<=>((funny(lucy)<~>~rich(lucy))))&
(?[X]:(~happy(X)))&
((~rich(john)|wise(john)))&
((~humble(paul)<~>~patient(paul)))&
((humble(susan)&happy(susan)))&
(?[X]:(~quiet(X)))&
((strong(john)<~>~tall(john))) | ~humble(mary) | [] | null | 0 |
If someone is both tall and strong then alice is both not patient and not rich. Everyone who is both generous and not generous is either creative or not happy. If paul is both not tall and not old then someone is either not curious or not calm. Everyone who is calm is strong. Everyone who is not patient or not tall is both not generous and wise and vice versa. If someone is not calm or not curious then someone is funny and vice versa. Everyone who is either brave or not brave is both not brave and not tall. If lucy is either not quiet or not funny then someone is kind or not brave. Everyone who is both not brave and humble is not curious. If someone is not curious or not brave then someone is not happy or not old and vice versa. Everyone who is quiet or not wise is either funny or strong. If someone is not generous or not brave then fred is either not calm or not generous and vice versa. If someone is curious or not tall then alice is both curious and strong and vice versa. If alice is humble or not funny then john is not curious and vice versa. If fred is either not brave or not generous then alice is either quiet or not tall. Someone is not patient. Susan is either not wise or not calm. Someone is not curious or rich. Fred is tall or not patient. Mary is either wise or strong. Someone is not brave or not happy. Someone is brave or not happy. | John is funny. | neutral | ((?[X]:((tall(X)&strong(X))))=>((~patient(alice)&~rich(alice))))&
(![X]:((generous(X)&~generous(X))=>(creative(X)<~>~happy(X))))&
(((~tall(paul)&~old(paul)))=>(?[X]:((~curious(X)<~>~calm(X)))))&
(![X]:(calm(X)=>strong(X)))&
(![X]:((~patient(X)|~tall(X))<=>(~generous(X)&wise(X))))&
((?[X]:((~calm(X)|~curious(X))))<=>(?[X]:(funny(X))))&
(![X]:((brave(X)<~>~brave(X))=>(~brave(X)&~tall(X))))&
(((~quiet(lucy)<~>~funny(lucy)))=>(?[X]:((kind(X)|~brave(X)))))&
(![X]:((~brave(X)&humble(X))=>~curious(X)))&
((?[X]:((~curious(X)|~brave(X))))<=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:((quiet(X)|~wise(X))=>(funny(X)<~>strong(X))))&
((?[X]:((~generous(X)|~brave(X))))<=>((~calm(fred)<~>~generous(fred))))&
((?[X]:((curious(X)|~tall(X))))<=>((curious(alice)&strong(alice))))&
(((humble(alice)|~funny(alice)))<=>(~curious(john)))&
(((~brave(fred)<~>~generous(fred)))=>((quiet(alice)<~>~tall(alice))))&
(?[X]:(~patient(X)))&
((~wise(susan)<~>~calm(susan)))&
(?[X]:((~curious(X)|rich(X))))&
((tall(fred)|~patient(fred)))&
((wise(mary)<~>strong(mary)))&
(?[X]:((~brave(X)|~happy(X))))&
(?[X]:((brave(X)|~happy(X)))) | funny(john) | [] | null | 0 |
Everyone who is not rich or humble is patient or wise.
If alice is tall or not patient then someone is both quiet and patient and vice versa.
Everyone who is not calm is both not patient and curious and vice versa.
If lucy is both not wise and wise then someone is wise or not quiet and vice versa.
Everyone who is both not humble and not tall is both calm and not funny and vice versa.
Everyone who is either curious or not quiet is either not old or calm and vice versa.
If someone is not strong or not creative then someone is humble and vice versa.
If fred is both calm and old then someone is not old or not humble.
Everyone who is either not humble or patient is not wise.
Everyone who is either not rich or not tall is tall or calm and vice versa.
Everyone who is both not happy and not wise is not calm and vice versa.
If someone is not patient then susan is both rich and not tall and vice versa.
Everyone who is tall is either not rich or quiet.
If someone is either wise or curious then someone is not funny or not curious.
Everyone who is not brave or not curious is not kind and vice versa.
If someone is curious then someone is either not creative or tall.
Someone is curious or tall.
Someone is not wise.
Someone is brave or not kind.
Someone is either not funny or curious.
Alice is not strong. | Lucy is quiet. | entailment | (![X]:((~rich(X)|humble(X))=>(patient(X)|wise(X))))&
(((tall(alice)|~patient(alice)))<=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:(~calm(X)<=>(~patient(X)&curious(X))))&
(((~wise(lucy)&wise(lucy)))<=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((~humble(X)&~tall(X))<=>(calm(X)&~funny(X))))&
(![X]:((curious(X)<~>~quiet(X))<=>(~old(X)<~>calm(X))))&
((?[X]:((~strong(X)|~creative(X))))<=>(?[X]:(humble(X))))&
(((calm(fred)&old(fred)))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~humble(X)<~>patient(X))=>~wise(X)))&
(![X]:((~rich(X)<~>~tall(X))<=>(tall(X)|calm(X))))&
(![X]:((~happy(X)&~wise(X))<=>~calm(X)))&
((?[X]:(~patient(X)))<=>((rich(susan)&~tall(susan))))&
(![X]:(tall(X)=>(~rich(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>curious(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((~brave(X)|~curious(X))<=>~kind(X)))&
((?[X]:(curious(X)))=>(?[X]:((~creative(X)<~>tall(X)))))&
(?[X]:((curious(X)|tall(X))))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)|~kind(X))))&
(?[X]:((~funny(X)<~>curious(X))))&
(~strong(alice)) | quiet(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 291934959717146133472951
% SZS output start Proof for 291934959717146133472951
4. (wise(lucy) & ~wise(lucy)) <=> ? [X0] : (~quiet(X0) | wise(X0)) [input p3]
22. ~quiet(lucy) [input hypothesis]
44. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X0] : (~quiet(X0) | wise(X0)) | (~wise(lucy) | wise(lucy))) [nnf transformation 4]
45. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X0] : (~quiet(X0) | wise(X0)) | ~wise(lucy) | wise(lucy)) [flattening 44]
46. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X1] : (~quiet(X1) | wise(X1)) | ~wise(lucy) | wise(lucy)) [rectify 45]
47. ? [X1] : (~quiet(X1) | wise(X1)) => (~quiet(sK1) | wise(sK1)) [choice axiom]
48. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & ((~quiet(sK1) | wise(sK1)) | ~wise(lucy) | wise(lucy)) [skolemisation 46,47]
99. ~wise(lucy) | quiet(X0) [cnf transformation 48]
101. wise(lucy) | quiet(X0) [cnf transformation 48]
145. ~quiet(lucy) [cnf transformation 22]
173. 6 <=> ! [X0] : quiet(X0) [avatar definition]
174. quiet(X0) <- (6) [avatar component clause 173]
176. 7 <=> wise(lucy) [avatar definition]
179. 6 | 7 [avatar split clause 101,176,173]
184. 6 | ~7 [avatar split clause 99,176,173]
309. $false <- (6) [resolution 174,145]
310. ~6 [avatar contradiction clause 309]
311. $false [avatar sat refutation 179,184,310]
% SZS output end Proof for 291934959717146133472951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is patient then someone is not brave and vice versa.
Everyone who is wise or kind is both not quiet and curious and vice versa.
Everyone who is not old or not kind is not happy.
If someone is both not strong and not curious then paul is either not humble or not happy.
Everyone who is strong or curious is both brave and creative.
If lucy is either funny or tall then someone is either quiet or patient and vice versa.
Everyone who is patient is not humble and vice versa.
If john is tall then alice is either rich or not patient and vice versa.
Everyone who is calm is either not brave or funny and vice versa.
Everyone who is humble is either not curious or not quiet.
Everyone who is not patient is old or not quiet.
Everyone who is not humble is either not kind or not brave and vice versa.
If someone is either calm or not quiet then someone is generous or not humble and vice versa.
If alice is not old then susan is both quiet and not tall.
If mary is tall then lucy is both kind and not wise and vice versa.
Susan is both not quiet and not wise.
Paul is not funny.
John is humble or not rich.
Alice is humble or not kind.
Lucy is both not wise and patient.
Fred is both generous and not calm. | Mary is creative. | neutral | ((patient(john))<=>(?[X]:(~brave(X))))&
(![X]:((wise(X)|kind(X))<=>(~quiet(X)&curious(X))))&
(![X]:((~old(X)|~kind(X))=>~happy(X)))&
((?[X]:((~strong(X)&~curious(X))))=>((~humble(paul)<~>~happy(paul))))&
(![X]:((strong(X)|curious(X))=>(brave(X)&creative(X))))&
(((funny(lucy)<~>tall(lucy)))<=>(?[X]:((quiet(X)<~>patient(X)))))&
(![X]:(patient(X)<=>~humble(X)))&
((tall(john))<=>((rich(alice)<~>~patient(alice))))&
(![X]:(calm(X)<=>(~brave(X)<~>funny(X))))&
(![X]:(humble(X)=>(~curious(X)<~>~quiet(X))))&
(![X]:(~patient(X)=>(old(X)|~quiet(X))))&
(![X]:(~humble(X)<=>(~kind(X)<~>~brave(X))))&
((?[X]:((calm(X)<~>~quiet(X))))<=>(?[X]:((generous(X)|~humble(X)))))&
((~old(alice))=>((quiet(susan)&~tall(susan))))&
((tall(mary))<=>((kind(lucy)&~wise(lucy))))&
((~quiet(susan)&~wise(susan)))&
(~funny(paul))&
((humble(john)|~rich(john)))&
((humble(alice)|~kind(alice)))&
((~wise(lucy)&patient(lucy)))&
((generous(fred)&~calm(fred))) | creative(mary) | [] | null | 0 |
If fred is either not quiet or patient then susan is rich. If someone is patient or not creative then someone is both old and not tall. Everyone who is both brave and wise is either not humble or quiet. Everyone who is not patient or strong is either rich or not calm. If paul is either creative or not calm then someone is not calm or rich. Everyone who is both patient and not generous is not happy and vice versa. Everyone who is both brave and not funny is brave. Everyone who is both rich and not patient is both not humble and strong and vice versa. Everyone who is calm is not generous or strong. If someone is both creative and quiet then john is either wise or not old. Everyone who is not generous or generous is not old or not kind. Everyone who is either happy or not quiet is either not patient or creative. Everyone who is both quiet and not humble is not curious and vice versa. If someone is either generous or not wise then someone is curious and vice versa. Everyone who is quiet or not wise is patient. If susan is both generous and humble then paul is either patient or brave. Fred is both not happy and wise. Alice is both not old and not funny. Lucy is both strong and not funny. Alice is not kind. Mary is not humble or funny. Alice is happy or not funny. Someone is not calm or calm. John is both wise and calm. | Mary is quiet. | neutral | (((~quiet(fred)<~>patient(fred)))=>(rich(susan)))&
((?[X]:((patient(X)|~creative(X))))=>(?[X]:((old(X)&~tall(X)))))&
(![X]:((brave(X)&wise(X))=>(~humble(X)<~>quiet(X))))&
(![X]:((~patient(X)|strong(X))=>(rich(X)<~>~calm(X))))&
(((creative(paul)<~>~calm(paul)))=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:((patient(X)&~generous(X))<=>~happy(X)))&
(![X]:((brave(X)&~funny(X))=>brave(X)))&
(![X]:((rich(X)&~patient(X))<=>(~humble(X)&strong(X))))&
(![X]:(calm(X)=>(~generous(X)|strong(X))))&
((?[X]:((creative(X)&quiet(X))))=>((wise(john)<~>~old(john))))&
(![X]:((~generous(X)|generous(X))=>(~old(X)|~kind(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(~patient(X)<~>creative(X))))&
(![X]:((quiet(X)&~humble(X))<=>~curious(X)))&
((?[X]:((generous(X)<~>~wise(X))))<=>(?[X]:(curious(X))))&
(![X]:((quiet(X)|~wise(X))=>patient(X)))&
(((generous(susan)&humble(susan)))=>((patient(paul)<~>brave(paul))))&
((~happy(fred)&wise(fred)))&
((~old(alice)&~funny(alice)))&
((strong(lucy)&~funny(lucy)))&
(~kind(alice))&
((~humble(mary)|funny(mary)))&
((happy(alice)|~funny(alice)))&
(?[X]:((~calm(X)|calm(X))))&
((wise(john)&calm(john))) | quiet(mary) | [] | null | 0 |
If alice is curious or brave then john is both not creative and not quiet.
If someone is not happy or rich then alice is both calm and not calm and vice versa.
If susan is kind then alice is creative or funny and vice versa.
Everyone who is both not rich and not funny is humble or patient and vice versa.
Everyone who is not kind is either strong or wise and vice versa.
Everyone who is calm is either rich or not humble and vice versa.
Everyone who is brave or humble is strong or generous.
If someone is old or kind then john is both not wise and funny.
Everyone who is both funny and not rich is not kind or quiet.
Everyone who is both curious and brave is both tall and not calm.
Everyone who is either calm or rich is not wise or not funny.
Everyone who is either not happy or calm is either not brave or not quiet.
Everyone who is both rich and not quiet is not humble and vice versa.
If someone is not humble then alice is not wise.
Everyone who is both not brave and calm is both creative and brave and vice versa.
If susan is generous or kind then john is both tall and funny.
Mary is curious or patient.
Alice is brave or strong.
Someone is not calm.
Fred is patient or not generous.
Alice is not old or curious.
Mary is not happy or not quiet. | Susan is not curious. | neutral | (((curious(alice)|brave(alice)))=>((~creative(john)&~quiet(john))))&
((?[X]:((~happy(X)|rich(X))))<=>((calm(alice)&~calm(alice))))&
((kind(susan))<=>((creative(alice)|funny(alice))))&
(![X]:((~rich(X)&~funny(X))<=>(humble(X)|patient(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>wise(X))))&
(![X]:(calm(X)<=>(rich(X)<~>~humble(X))))&
(![X]:((brave(X)|humble(X))=>(strong(X)|generous(X))))&
((?[X]:((old(X)|kind(X))))=>((~wise(john)&funny(john))))&
(![X]:((funny(X)&~rich(X))=>(~kind(X)|quiet(X))))&
(![X]:((curious(X)&brave(X))=>(tall(X)&~calm(X))))&
(![X]:((calm(X)<~>rich(X))=>(~wise(X)|~funny(X))))&
(![X]:((~happy(X)<~>calm(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((rich(X)&~quiet(X))<=>~humble(X)))&
((?[X]:(~humble(X)))=>(~wise(alice)))&
(![X]:((~brave(X)&calm(X))<=>(creative(X)&brave(X))))&
(((generous(susan)|kind(susan)))=>((tall(john)&funny(john))))&
((curious(mary)|patient(mary)))&
((brave(alice)|strong(alice)))&
(?[X]:(~calm(X)))&
((patient(fred)|~generous(fred)))&
((~old(alice)|curious(alice)))&
((~happy(mary)|~quiet(mary))) | ~curious(susan) | [] | null | 0 |
If someone is both not generous and not calm then mary is both not happy and rich and vice versa. Everyone who is either patient or generous is not generous and vice versa. Everyone who is either not calm or not brave is not old or not tall. If someone is either curious or quiet then fred is not kind or not calm. Everyone who is both not quiet and not rich is not wise. If someone is quiet or brave then mary is happy or rich. If mary is not wise or not curious then someone is not creative. Everyone who is not funny or old is both quiet and creative. If someone is not curious then someone is both not creative and wise. Everyone who is either not creative or old is not calm or not quiet. If someone is both rich and humble then someone is not wise or not humble and vice versa. If john is either not strong or not happy then someone is either not rich or not funny and vice versa. Everyone who is not old or not generous is not wise. Everyone who is not wise or humble is both not strong and rich and vice versa. Everyone who is not happy or creative is both not creative and not brave. Everyone who is both quiet and not tall is both not funny and not creative and vice versa. Someone is both not quiet and not generous. Alice is curious or calm. Lucy is not brave. Mary is not quiet or not happy. Someone is both not happy and humble. Alice is rich or not strong. Someone is brave. | Mary is not rich. | contradiction | ((?[X]:((~generous(X)&~calm(X))))<=>((~happy(mary)&rich(mary))))&
(![X]:((patient(X)<~>generous(X))<=>~generous(X)))&
(![X]:((~calm(X)<~>~brave(X))=>(~old(X)|~tall(X))))&
((?[X]:((curious(X)<~>quiet(X))))=>((~kind(fred)|~calm(fred))))&
(![X]:((~quiet(X)&~rich(X))=>~wise(X)))&
((?[X]:((quiet(X)|brave(X))))=>((happy(mary)|rich(mary))))&
(((~wise(mary)|~curious(mary)))=>(?[X]:(~creative(X))))&
(![X]:((~funny(X)|old(X))=>(quiet(X)&creative(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~creative(X)&wise(X)))))&
(![X]:((~creative(X)<~>old(X))=>(~calm(X)|~quiet(X))))&
((?[X]:((rich(X)&humble(X))))<=>(?[X]:((~wise(X)|~humble(X)))))&
(((~strong(john)<~>~happy(john)))<=>(?[X]:((~rich(X)<~>~funny(X)))))&
(![X]:((~old(X)|~generous(X))=>~wise(X)))&
(![X]:((~wise(X)|humble(X))<=>(~strong(X)&rich(X))))&
(![X]:((~happy(X)|creative(X))=>(~creative(X)&~brave(X))))&
(![X]:((quiet(X)&~tall(X))<=>(~funny(X)&~creative(X))))&
(?[X]:((~quiet(X)&~generous(X))))&
((curious(alice)|calm(alice)))&
(~brave(lucy))&
((~quiet(mary)|~happy(mary)))&
(?[X]:((~happy(X)&humble(X))))&
((rich(alice)|~strong(alice)))&
(?[X]:(brave(X))) | ~rich(mary) | [
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2693074259756394280778423
% SZS output start Proof for 2693074259756394280778423
8. ! [X0] : ((old(X0) | ~funny(X0)) => (creative(X0) & quiet(X0))) [input p7]
13. ! [X0] : ((~generous(X0) | ~old(X0)) => ~wise(X0)) [input p12]
14. ! [X0] : ((humble(X0) | ~wise(X0)) <=> (rich(X0) & ~strong(X0))) [input p13]
15. ! [X0] : ((creative(X0) | ~happy(X0)) => (~brave(X0) & ~creative(X0))) [input p14]
24. ~rich(mary) [input hypothesis]
38. ! [X0] : ((creative(X0) & quiet(X0)) | (~old(X0) & funny(X0))) [ennf transformation 8]
41. ! [X0] : (~wise(X0) | (generous(X0) & old(X0))) [ennf transformation 13]
42. ! [X0] : ((~brave(X0) & ~creative(X0)) | (~creative(X0) & happy(X0))) [ennf transformation 15]
62. ! [X0] : (((humble(X0) | ~wise(X0)) | (~rich(X0) | strong(X0))) & ((rich(X0) & ~strong(X0)) | (~humble(X0) & wise(X0)))) [nnf transformation 14]
63. ! [X0] : ((humble(X0) | ~wise(X0) | ~rich(X0) | strong(X0)) & ((rich(X0) & ~strong(X0)) | (~humble(X0) & wise(X0)))) [flattening 62]
89. ~old(X0) | creative(X0) [cnf transformation 38]
105. ~wise(X0) | old(X0) [cnf transformation 41]
109. wise(X0) | rich(X0) [cnf transformation 63]
113. ~creative(X0) | ~creative(X0) [cnf transformation 42]
128. ~rich(mary) [cnf transformation 24]
129. ~creative(X0) [duplicate literal removal 113]
137. 2 <=> rich(mary) [avatar definition]
139. ~rich(mary) <- (~2) [avatar component clause 137]
250. ~2 [avatar split clause 128,137]
272. old(X1) | rich(X1) [resolution 109,105]
342. rich(X1) | creative(X1) [resolution 272,89]
344. rich(X1) [subsumption resolution 342,129]
349. $false <- (~2) [resolution 344,139]
352. 2 [avatar contradiction clause 349]
353. $false [avatar sat refutation 250,352]
% SZS output end Proof for 2693074259756394280778423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or strong then john is both strong and not tall and vice versa. If someone is either old or not rich then someone is creative. If someone is either not brave or creative then someone is brave. Everyone who is either not quiet or not happy is either quiet or strong and vice versa. If someone is both brave and not happy then someone is both patient and tall and vice versa. Everyone who is either old or humble is either patient or not quiet. Everyone who is not calm or generous is both wise and not old. Everyone who is either humble or generous is both not wise and generous and vice versa. Everyone who is kind is not rich and vice versa. Everyone who is creative or strong is not brave or not old and vice versa. If someone is kind or not kind then someone is not happy or tall and vice versa. Everyone who is not rich is both curious and not curious. If lucy is either strong or not rich then someone is strong or not curious. Everyone who is kind or old is either not calm or calm. If someone is both tall and kind then fred is old and vice versa. If someone is calm or happy then lucy is either not tall or calm and vice versa. Someone is both strong and not creative. Someone is curious or not tall. Someone is not creative. Someone is both not tall and calm. Lucy is both not wise and not generous. Someone is either tall or curious. Someone is funny. John is humble or happy. | Lucy is not tall. | contradiction | ((?[X]:((calm(X)<~>strong(X))))<=>((strong(john)&~tall(john))))&
((?[X]:((old(X)<~>~rich(X))))=>(?[X]:(creative(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)<~>~happy(X))<=>(quiet(X)<~>strong(X))))&
((?[X]:((brave(X)&~happy(X))))<=>(?[X]:((patient(X)&tall(X)))))&
(![X]:((old(X)<~>humble(X))=>(patient(X)<~>~quiet(X))))&
(![X]:((~calm(X)|generous(X))=>(wise(X)&~old(X))))&
(![X]:((humble(X)<~>generous(X))<=>(~wise(X)&generous(X))))&
(![X]:(kind(X)<=>~rich(X)))&
(![X]:((creative(X)|strong(X))<=>(~brave(X)|~old(X))))&
((?[X]:((kind(X)|~kind(X))))<=>(?[X]:((~happy(X)|tall(X)))))&
(![X]:(~rich(X)=>(curious(X)&~curious(X))))&
(((strong(lucy)<~>~rich(lucy)))=>(?[X]:((strong(X)|~curious(X)))))&
(![X]:((kind(X)|old(X))=>(~calm(X)<~>calm(X))))&
((?[X]:((tall(X)&kind(X))))<=>(old(fred)))&
((?[X]:((calm(X)|happy(X))))<=>((~tall(lucy)<~>calm(lucy))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~tall(X)&calm(X))))&
((~wise(lucy)&~generous(lucy)))&
(?[X]:((tall(X)<~>curious(X))))&
(?[X]:(funny(X)))&
((humble(john)|happy(john))) | ~tall(lucy) | [
"p6",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 736085661226720202198805
% SZS output start Proof for 736085661226720202198805
7. ! [X0] : ((generous(X0) | ~calm(X0)) => (~old(X0) & wise(X0))) [input p6]
16. ? [X0] : (happy(X0) | calm(X0)) <=> (~tall(lucy) <~> calm(lucy)) [input p15]
21. ~generous(lucy) & ~wise(lucy) [input p20]
25. ~tall(lucy) [input hypothesis]
34. ! [X0] : ((~old(X0) & wise(X0)) | (~generous(X0) & calm(X0))) [ennf transformation 7]
76. (? [X0] : (happy(X0) | calm(X0)) | ((~tall(lucy) | ~calm(lucy)) & (calm(lucy) | tall(lucy)))) & (((~calm(lucy) | tall(lucy)) & (calm(lucy) | ~tall(lucy))) | ! [X0] : (~happy(X0) & ~calm(X0))) [nnf transformation 16]
77. (? [X0] : (happy(X0) | calm(X0)) | ((~tall(lucy) | ~calm(lucy)) & (calm(lucy) | tall(lucy)))) & (((~calm(lucy) | tall(lucy)) & (calm(lucy) | ~tall(lucy))) | ! [X1] : (~happy(X1) & ~calm(X1))) [rectify 76]
78. ? [X0] : (happy(X0) | calm(X0)) => (happy(sK9) | calm(sK9)) [choice axiom]
79. ((happy(sK9) | calm(sK9)) | ((~tall(lucy) | ~calm(lucy)) & (calm(lucy) | tall(lucy)))) & (((~calm(lucy) | tall(lucy)) & (calm(lucy) | ~tall(lucy))) | ! [X1] : (~happy(X1) & ~calm(X1))) [skolemisation 77,78]
117. wise(X0) | calm(X0) [cnf transformation 34]
150. ~calm(lucy) | tall(lucy) | ~calm(X1) [cnf transformation 79]
160. ~wise(lucy) [cnf transformation 21]
165. ~tall(lucy) [cnf transformation 25]
303. 30 <=> calm(lucy) [avatar definition]
304. calm(lucy) <- (30) [avatar component clause 303]
307. 31 <=> tall(lucy) [avatar definition]
325. 35 <=> ! [X1] : ~calm(X1) [avatar definition]
326. ~calm(X1) <- (35) [avatar component clause 325]
327. 35 | 31 | ~30 [avatar split clause 150,303,307,325]
358. ~31 [avatar split clause 165,307]
359. calm(lucy) [resolution 117,160]
362. 30 [avatar split clause 359,303]
363. $false <- (30, 35) [subsumption resolution 304,326]
364. ~30 | ~35 [avatar contradiction clause 363]
365. $false [avatar sat refutation 327,358,362,364]
% SZS output end Proof for 736085661226720202198805
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not strong or patient then alice is both curious and strong and vice versa. Everyone who is calm or not brave is both humble and not funny. Everyone who is both funny and not curious is wise and vice versa. If someone is either kind or not rich then susan is humble and vice versa. If alice is both kind and tall then someone is either funny or not strong and vice versa. Everyone who is both not creative and funny is both happy and not quiet and vice versa. If fred is both not kind and not generous then paul is patient. Everyone who is either not kind or patient is either quiet or not happy and vice versa. Everyone who is both funny and not wise is either rich or tall and vice versa. Everyone who is not rich or not quiet is both not old and calm. If someone is not tall then someone is either not brave or not happy and vice versa. If susan is either humble or patient then alice is both not rich and generous. Everyone who is either generous or calm is not patient or funny. Everyone who is either not calm or rich is either funny or humble. Everyone who is happy is both not humble and not quiet. Everyone who is brave or calm is not happy or happy. Someone is both brave and curious. Someone is either not kind or curious. Fred is not generous or not kind. John is not tall or curious. Mary is either not calm or funny. Fred is either wise or strong. Someone is both kind and wise. Someone is not kind. | Susan is humble. | entailment | (((~strong(fred)|patient(fred)))<=>((curious(alice)&strong(alice))))&
(![X]:((calm(X)|~brave(X))=>(humble(X)&~funny(X))))&
(![X]:((funny(X)&~curious(X))<=>wise(X)))&
((?[X]:((kind(X)<~>~rich(X))))<=>(humble(susan)))&
(((kind(alice)&tall(alice)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
(![X]:((~creative(X)&funny(X))<=>(happy(X)&~quiet(X))))&
(((~kind(fred)&~generous(fred)))=>(patient(paul)))&
(![X]:((~kind(X)<~>patient(X))<=>(quiet(X)<~>~happy(X))))&
(![X]:((funny(X)&~wise(X))<=>(rich(X)<~>tall(X))))&
(![X]:((~rich(X)|~quiet(X))=>(~old(X)&calm(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
(((humble(susan)<~>patient(susan)))=>((~rich(alice)&generous(alice))))&
(![X]:((generous(X)<~>calm(X))=>(~patient(X)|funny(X))))&
(![X]:((~calm(X)<~>rich(X))=>(funny(X)<~>humble(X))))&
(![X]:(happy(X)=>(~humble(X)&~quiet(X))))&
(![X]:((brave(X)|calm(X))=>(~happy(X)|happy(X))))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((~kind(X)<~>curious(X))))&
((~generous(fred)|~kind(fred)))&
((~tall(john)|curious(john)))&
((~calm(mary)<~>funny(mary)))&
((wise(fred)<~>strong(fred)))&
(?[X]:((kind(X)&wise(X))))&
(?[X]:(~kind(X))) | humble(susan) | [
"p1",
"p2",
"p3",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9038703499378158817547420
% SZS output start Proof for 9038703499378158817547420
2. ! [X0] : ((~brave(X0) | calm(X0)) => (~funny(X0) & humble(X0))) [input p1]
3. ! [X0] : ((~curious(X0) & funny(X0)) <=> wise(X0)) [input p2]
4. ? [X0] : (kind(X0) <~> ~rich(X0)) <=> humble(susan) [input p3]
10. ! [X0] : ((~quiet(X0) | ~rich(X0)) => (calm(X0) & ~old(X0))) [input p9]
23. ? [X0] : (wise(X0) & kind(X0)) [input p22]
25. ~humble(susan) [input hypothesis]
27. ! [X0] : ((~quiet(X0) | ~rich(X0)) => calm(X0)) [pure predicate removal 10]
28. ! [X0] : ((~funny(X0) & humble(X0)) | (brave(X0) & ~calm(X0))) [ennf transformation 2]
31. ! [X0] : (calm(X0) | (quiet(X0) & rich(X0))) [ennf transformation 27]
41. ! [X0] : (((~curious(X0) & funny(X0)) | ~wise(X0)) & (wise(X0) | (curious(X0) | ~funny(X0)))) [nnf transformation 3]
42. ! [X0] : (((~curious(X0) & funny(X0)) | ~wise(X0)) & (wise(X0) | curious(X0) | ~funny(X0))) [flattening 41]
43. (? [X0] : ((rich(X0) | ~kind(X0)) & (~rich(X0) | kind(X0))) | ~humble(susan)) & (humble(susan) | ! [X0] : ((kind(X0) | rich(X0)) & (~rich(X0) | ~kind(X0)))) [nnf transformation 4]
44. (? [X0] : ((rich(X0) | ~kind(X0)) & (~rich(X0) | kind(X0))) | ~humble(susan)) & (humble(susan) | ! [X1] : ((kind(X1) | rich(X1)) & (~rich(X1) | ~kind(X1)))) [rectify 43]
45. ? [X0] : ((rich(X0) | ~kind(X0)) & (~rich(X0) | kind(X0))) => ((rich(sK0) | ~kind(sK0)) & (~rich(sK0) | kind(sK0))) [choice axiom]
46. (((rich(sK0) | ~kind(sK0)) & (~rich(sK0) | kind(sK0))) | ~humble(susan)) & (humble(susan) | ! [X1] : ((kind(X1) | rich(X1)) & (~rich(X1) | ~kind(X1)))) [skolemisation 44,45]
72. ? [X0] : (wise(X0) & kind(X0)) => (wise(sK6) & kind(sK6)) [choice axiom]
73. wise(sK6) & kind(sK6) [skolemisation 23,72]
83. ~funny(X0) | ~calm(X0) [cnf transformation 28]
86. ~wise(X0) | funny(X0) [cnf transformation 42]
88. humble(susan) | ~rich(X1) | ~kind(X1) [cnf transformation 46]
117. rich(X0) | calm(X0) [cnf transformation 31]
147. kind(sK6) [cnf transformation 73]
148. wise(sK6) [cnf transformation 73]
150. ~humble(susan) [cnf transformation 25]
173. 5 <=> humble(susan) [avatar definition]
191. 9 <=> ! [X1] : (~rich(X1) | ~kind(X1)) [avatar definition]
192. ~rich(X1) | ~kind(X1) <- (9) [avatar component clause 191]
193. 9 | 5 [avatar split clause 88,173,191]
305. ~5 [avatar split clause 150,173]
311. funny(sK6) [resolution 86,148]
314. ~calm(sK6) [resolution 311,83]
317. ~kind(X1) | calm(X1) <- (9) [resolution 192,117]
344. calm(sK6) <- (9) [resolution 317,147]
346. $false <- (9) [subsumption resolution 344,314]
347. ~9 [avatar contradiction clause 346]
348. $false [avatar sat refutation 193,305,347]
% SZS output end Proof for 9038703499378158817547420
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is not funny or funny and vice versa.
If someone is happy or tall then someone is both quiet and happy and vice versa.
Everyone who is both old and humble is not kind or not patient and vice versa.
If someone is not generous or not patient then someone is either not wise or not generous.
Everyone who is both calm and not strong is not old or not calm.
If someone is old then fred is both patient and not funny and vice versa.
If someone is either not humble or brave then someone is kind or old and vice versa.
If alice is either old or strong then someone is either not wise or curious.
If mary is both not patient and not quiet then alice is either creative or quiet and vice versa.
Everyone who is both funny and not tall is both funny and wise.
Everyone who is both tall and not generous is humble.
If someone is calm or not funny then someone is rich.
If alice is both not strong and not brave then alice is either kind or brave and vice versa.
Everyone who is old or not calm is either not funny or not humble.
Everyone who is not kind or not generous is both not humble and strong.
If someone is not tall then lucy is rich or not curious and vice versa.
Mary is both not brave and not happy.
Someone is both not rich and creative.
Someone is both not quiet and funny.
Lucy is either wise or brave.
Someone is both not tall and not calm.
Susan is either not generous or funny. | Fred is strong. | neutral | (![X]:(~quiet(X)<=>(~funny(X)|funny(X))))&
((?[X]:((happy(X)|tall(X))))<=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((old(X)&humble(X))<=>(~kind(X)|~patient(X))))&
((?[X]:((~generous(X)|~patient(X))))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(![X]:((calm(X)&~strong(X))=>(~old(X)|~calm(X))))&
((?[X]:(old(X)))<=>((patient(fred)&~funny(fred))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((kind(X)|old(X)))))&
(((old(alice)<~>strong(alice)))=>(?[X]:((~wise(X)<~>curious(X)))))&
(((~patient(mary)&~quiet(mary)))<=>((creative(alice)<~>quiet(alice))))&
(![X]:((funny(X)&~tall(X))=>(funny(X)&wise(X))))&
(![X]:((tall(X)&~generous(X))=>humble(X)))&
((?[X]:((calm(X)|~funny(X))))=>(?[X]:(rich(X))))&
(((~strong(alice)&~brave(alice)))<=>((kind(alice)<~>brave(alice))))&
(![X]:((old(X)|~calm(X))=>(~funny(X)<~>~humble(X))))&
(![X]:((~kind(X)|~generous(X))=>(~humble(X)&strong(X))))&
((?[X]:(~tall(X)))<=>((rich(lucy)|~curious(lucy))))&
((~brave(mary)&~happy(mary)))&
(?[X]:((~rich(X)&creative(X))))&
(?[X]:((~quiet(X)&funny(X))))&
((wise(lucy)<~>brave(lucy)))&
(?[X]:((~tall(X)&~calm(X))))&
((~generous(susan)<~>funny(susan))) | strong(fred) | [] | null | 0 |
Everyone who is either not strong or not quiet is either not quiet or not old.
If someone is not curious or not wise then someone is either generous or not brave and vice versa.
Everyone who is both not humble and quiet is not funny.
If someone is not generous or not tall then susan is both kind and old and vice versa.
Everyone who is both patient and not patient is not brave.
Everyone who is not kind or strong is rich and vice versa.
Everyone who is both generous and not patient is either calm or not funny.
Everyone who is either generous or strong is both patient and funny and vice versa.
Everyone who is not generous or funny is both quiet and happy and vice versa.
Everyone who is not strong or not funny is tall or not rich.
If someone is both strong and not tall then someone is either kind or funny.
If john is both not patient and not curious then someone is both humble and not strong and vice versa.
If someone is either calm or not kind then someone is old or curious and vice versa.
Everyone who is either not creative or not tall is not calm and vice versa.
Everyone who is not creative or generous is wise or not curious and vice versa.
Everyone who is curious is both patient and funny and vice versa.
Someone is not funny.
Mary is not kind.
Someone is either not kind or humble.
Susan is calm or not quiet.
Someone is both not funny and not wise.
Mary is quiet.
Paul is not quiet or brave.
Paul is not quiet. | John is patient. | neutral | (![X]:((~strong(X)<~>~quiet(X))=>(~quiet(X)<~>~old(X))))&
((?[X]:((~curious(X)|~wise(X))))<=>(?[X]:((generous(X)<~>~brave(X)))))&
(![X]:((~humble(X)&quiet(X))=>~funny(X)))&
((?[X]:((~generous(X)|~tall(X))))<=>((kind(susan)&old(susan))))&
(![X]:((patient(X)&~patient(X))=>~brave(X)))&
(![X]:((~kind(X)|strong(X))<=>rich(X)))&
(![X]:((generous(X)&~patient(X))=>(calm(X)<~>~funny(X))))&
(![X]:((generous(X)<~>strong(X))<=>(patient(X)&funny(X))))&
(![X]:((~generous(X)|funny(X))<=>(quiet(X)&happy(X))))&
(![X]:((~strong(X)|~funny(X))=>(tall(X)|~rich(X))))&
((?[X]:((strong(X)&~tall(X))))=>(?[X]:((kind(X)<~>funny(X)))))&
(((~patient(john)&~curious(john)))<=>(?[X]:((humble(X)&~strong(X)))))&
((?[X]:((calm(X)<~>~kind(X))))<=>(?[X]:((old(X)|curious(X)))))&
(![X]:((~creative(X)<~>~tall(X))<=>~calm(X)))&
(![X]:((~creative(X)|generous(X))<=>(wise(X)|~curious(X))))&
(![X]:(curious(X)<=>(patient(X)&funny(X))))&
(?[X]:(~funny(X)))&
(~kind(mary))&
(?[X]:((~kind(X)<~>humble(X))))&
((calm(susan)|~quiet(susan)))&
(?[X]:((~funny(X)&~wise(X))))&
(quiet(mary))&
((~quiet(paul)|brave(paul)))&
(~quiet(paul)) | patient(john) | [] | null | 0 |
Everyone who is either not rich or not quiet is tall and vice versa.
Everyone who is not rich is not curious and vice versa.
Everyone who is patient is calm or rich.
Everyone who is not creative or strong is either not quiet or not patient.
Everyone who is patient or not wise is strong or not old and vice versa.
If someone is both not kind and not strong then lucy is either not funny or not creative and vice versa.
If alice is brave or happy then lucy is both kind and curious and vice versa.
Everyone who is calm or old is not humble or strong.
Everyone who is not brave is both calm and not wise.
Everyone who is brave or tall is both not kind and old.
If someone is not strong or not calm then someone is not tall.
If someone is not creative then someone is not strong and vice versa.
Everyone who is not curious or tall is either humble or kind and vice versa.
If someone is tall or creative then someone is both not humble and not calm and vice versa.
If lucy is both not humble and patient then mary is either not strong or patient and vice versa.
If alice is brave then someone is brave.
Mary is either calm or not wise.
Lucy is either strong or creative.
Fred is both not rich and funny.
Paul is creative or not quiet.
Susan is both not humble and quiet.
Someone is both happy and not old.
Someone is not old or old.
Mary is either happy or funny. | Lucy is creative. | neutral | (![X]:((~rich(X)<~>~quiet(X))<=>tall(X)))&
(![X]:(~rich(X)<=>~curious(X)))&
(![X]:(patient(X)=>(calm(X)|rich(X))))&
(![X]:((~creative(X)|strong(X))=>(~quiet(X)<~>~patient(X))))&
(![X]:((patient(X)|~wise(X))<=>(strong(X)|~old(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>((~funny(lucy)<~>~creative(lucy))))&
(((brave(alice)|happy(alice)))<=>((kind(lucy)&curious(lucy))))&
(![X]:((calm(X)|old(X))=>(~humble(X)|strong(X))))&
(![X]:(~brave(X)=>(calm(X)&~wise(X))))&
(![X]:((brave(X)|tall(X))=>(~kind(X)&old(X))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:(~tall(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)|tall(X))<=>(humble(X)<~>kind(X))))&
((?[X]:((tall(X)|creative(X))))<=>(?[X]:((~humble(X)&~calm(X)))))&
(((~humble(lucy)&patient(lucy)))<=>((~strong(mary)<~>patient(mary))))&
((brave(alice))=>(?[X]:(brave(X))))&
((calm(mary)<~>~wise(mary)))&
((strong(lucy)<~>creative(lucy)))&
((~rich(fred)&funny(fred)))&
((creative(paul)|~quiet(paul)))&
((~humble(susan)&quiet(susan)))&
(?[X]:((happy(X)&~old(X))))&
(?[X]:((~old(X)|old(X))))&
((happy(mary)<~>funny(mary))) | creative(lucy) | [] | null | 0 |
Everyone who is either not quiet or not strong is calm or not rich. Everyone who is not calm is wise and vice versa. If someone is not rich or kind then susan is either brave or not brave and vice versa. Everyone who is both old and tall is not strong or not happy and vice versa. Everyone who is both generous and not generous is either not quiet or patient and vice versa. Everyone who is both kind and not patient is either not patient or funny and vice versa. Everyone who is not old or curious is both not brave and not creative. Everyone who is creative is not quiet or tall and vice versa. If someone is not kind then someone is not brave or curious. If fred is rich or not humble then john is quiet or not kind and vice versa. If mary is both not kind and not tall then someone is both not humble and not happy and vice versa. Everyone who is not strong or not old is not old. If someone is both not generous and creative then lucy is either wise or not happy and vice versa. Everyone who is not quiet or patient is patient. If mary is patient then mary is both not happy and not calm. Everyone who is not quiet or generous is happy and vice versa. Susan is not wise or brave. Lucy is generous. John is not quiet. Someone is brave. Someone is brave or not rich. Alice is not rich or not patient. Someone is not generous. | Alice is happy. | neutral | (![X]:((~quiet(X)<~>~strong(X))=>(calm(X)|~rich(X))))&
(![X]:(~calm(X)<=>wise(X)))&
((?[X]:((~rich(X)|kind(X))))<=>((brave(susan)<~>~brave(susan))))&
(![X]:((old(X)&tall(X))<=>(~strong(X)|~happy(X))))&
(![X]:((generous(X)&~generous(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((kind(X)&~patient(X))<=>(~patient(X)<~>funny(X))))&
(![X]:((~old(X)|curious(X))=>(~brave(X)&~creative(X))))&
(![X]:(creative(X)<=>(~quiet(X)|tall(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~brave(X)|curious(X)))))&
(((rich(fred)|~humble(fred)))<=>((quiet(john)|~kind(john))))&
(((~kind(mary)&~tall(mary)))<=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((~strong(X)|~old(X))=>~old(X)))&
((?[X]:((~generous(X)&creative(X))))<=>((wise(lucy)<~>~happy(lucy))))&
(![X]:((~quiet(X)|patient(X))=>patient(X)))&
((patient(mary))=>((~happy(mary)&~calm(mary))))&
(![X]:((~quiet(X)|generous(X))<=>happy(X)))&
((~wise(susan)|brave(susan)))&
(generous(lucy))&
(~quiet(john))&
(?[X]:(brave(X)))&
(?[X]:((brave(X)|~rich(X))))&
((~rich(alice)|~patient(alice)))&
(?[X]:(~generous(X))) | happy(alice) | [] | null | 0 |
Everyone who is not creative or not kind is both curious and old and vice versa. If lucy is strong then mary is both not rich and brave and vice versa. Everyone who is either not curious or not tall is either patient or tall. Everyone who is not brave or not curious is tall. Everyone who is both not calm and strong is either not generous or not patient. If someone is either not tall or not old then mary is either wise or calm and vice versa. Everyone who is happy is funny or humble. Everyone who is old or not old is either wise or not curious and vice versa. Everyone who is not rich or patient is both not humble and old and vice versa. Everyone who is either quiet or not calm is either funny or not funny. If someone is curious or not kind then susan is generous or not generous and vice versa. Everyone who is old or funny is rich or not kind and vice versa. If someone is not tall then mary is not old or not calm. Everyone who is not rich is either not wise or not creative. Everyone who is patient or happy is both creative and not brave. If someone is old or not kind then fred is not tall. Alice is wise or tall. Lucy is either patient or happy. Someone is creative. Mary is rich or not rich. Paul is either not brave or generous. Alice is both tall and quiet. Someone is not humble or calm. | Alice is strong. | neutral | (![X]:((~creative(X)|~kind(X))<=>(curious(X)&old(X))))&
((strong(lucy))<=>((~rich(mary)&brave(mary))))&
(![X]:((~curious(X)<~>~tall(X))=>(patient(X)<~>tall(X))))&
(![X]:((~brave(X)|~curious(X))=>tall(X)))&
(![X]:((~calm(X)&strong(X))=>(~generous(X)<~>~patient(X))))&
((?[X]:((~tall(X)<~>~old(X))))<=>((wise(mary)<~>calm(mary))))&
(![X]:(happy(X)=>(funny(X)|humble(X))))&
(![X]:((old(X)|~old(X))<=>(wise(X)<~>~curious(X))))&
(![X]:((~rich(X)|patient(X))<=>(~humble(X)&old(X))))&
(![X]:((quiet(X)<~>~calm(X))=>(funny(X)<~>~funny(X))))&
((?[X]:((curious(X)|~kind(X))))<=>((generous(susan)|~generous(susan))))&
(![X]:((old(X)|funny(X))<=>(rich(X)|~kind(X))))&
((?[X]:(~tall(X)))=>((~old(mary)|~calm(mary))))&
(![X]:(~rich(X)=>(~wise(X)<~>~creative(X))))&
(![X]:((patient(X)|happy(X))=>(creative(X)&~brave(X))))&
((?[X]:((old(X)|~kind(X))))=>(~tall(fred)))&
((wise(alice)|tall(alice)))&
((patient(lucy)<~>happy(lucy)))&
(?[X]:(creative(X)))&
((rich(mary)|~rich(mary)))&
((~brave(paul)<~>generous(paul)))&
((tall(alice)&quiet(alice)))&
(?[X]:((~humble(X)|calm(X)))) | strong(alice) | [] | null | 0 |
Everyone who is either old or tall is calm or not rich and vice versa.
If paul is funny then someone is both calm and kind.
If someone is either wise or not quiet then lucy is both calm and not curious and vice versa.
Everyone who is both strong and not calm is humble or funny and vice versa.
If someone is not happy or not patient then someone is either old or strong.
If john is both creative and not quiet then someone is not rich or quiet and vice versa.
If paul is both humble and not quiet then paul is not patient and vice versa.
If paul is either calm or funny then someone is both humble and not old and vice versa.
If alice is strong or curious then lucy is either old or not quiet.
If someone is both funny and not happy then someone is both not creative and creative.
If someone is both not strong and old then susan is not rich or not old and vice versa.
If fred is generous then alice is tall or curious and vice versa.
Everyone who is not happy or not calm is strong.
If mary is either generous or not curious then someone is not quiet and vice versa.
If someone is either not creative or funny then someone is either not calm or creative and vice versa.
Someone is either quiet or generous.
Mary is creative or not curious.
Susan is not tall.
Susan is patient or quiet.
Someone is both funny and patient.
Mary is either strong or not generous.
Someone is creative or not rich. | Mary is not rich. | neutral | (![X]:((old(X)<~>tall(X))<=>(calm(X)|~rich(X))))&
((funny(paul))=>(?[X]:((calm(X)&kind(X)))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((calm(lucy)&~curious(lucy))))&
(![X]:((strong(X)&~calm(X))<=>(humble(X)|funny(X))))&
((?[X]:((~happy(X)|~patient(X))))=>(?[X]:((old(X)<~>strong(X)))))&
(((creative(john)&~quiet(john)))<=>(?[X]:((~rich(X)|quiet(X)))))&
(((humble(paul)&~quiet(paul)))<=>(~patient(paul)))&
(((calm(paul)<~>funny(paul)))<=>(?[X]:((humble(X)&~old(X)))))&
(((strong(alice)|curious(alice)))=>((old(lucy)<~>~quiet(lucy))))&
((?[X]:((funny(X)&~happy(X))))=>(?[X]:((~creative(X)&creative(X)))))&
((?[X]:((~strong(X)&old(X))))<=>((~rich(susan)|~old(susan))))&
((generous(fred))<=>((tall(alice)|curious(alice))))&
(![X]:((~happy(X)|~calm(X))=>strong(X)))&
(((generous(mary)<~>~curious(mary)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~creative(X)<~>funny(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(?[X]:((quiet(X)<~>generous(X))))&
((creative(mary)|~curious(mary)))&
(~tall(susan))&
((patient(susan)|quiet(susan)))&
(?[X]:((funny(X)&patient(X))))&
((strong(mary)<~>~generous(mary)))&
(?[X]:((creative(X)|~rich(X)))) | ~rich(mary) | [] | null | 0 |
Everyone who is quiet is not patient or not strong.
Everyone who is not brave or patient is kind or quiet and vice versa.
If someone is rich then john is wise.
If mary is not wise then paul is not old and vice versa.
If someone is generous then susan is brave and vice versa.
Everyone who is either wise or not humble is old or not tall and vice versa.
If someone is both not quiet and creative then paul is both rich and old and vice versa.
Everyone who is funny or creative is either quiet or not kind and vice versa.
If alice is either creative or not brave then alice is either creative or curious and vice versa.
If mary is either not kind or not humble then susan is either not old or not tall.
Everyone who is not strong or strong is creative.
Everyone who is strong or not patient is either not calm or curious and vice versa.
If someone is wise then someone is either not brave or not quiet.
If someone is both kind and not creative then fred is not curious and vice versa.
If someone is not generous or not kind then paul is either not patient or old.
Everyone who is not patient is both humble and wise.
Someone is calm or humble.
Someone is both not calm and not rich.
Susan is both not kind and tall.
Lucy is either brave or not creative.
Paul is kind or not old.
Paul is either not kind or not wise.
Fred is both calm and not rich.
Someone is both not kind and happy. | Susan is not old. | contradiction | (![X]:(quiet(X)=>(~patient(X)|~strong(X))))&
(![X]:((~brave(X)|patient(X))<=>(kind(X)|quiet(X))))&
((?[X]:(rich(X)))=>(wise(john)))&
((~wise(mary))<=>(~old(paul)))&
((?[X]:(generous(X)))<=>(brave(susan)))&
(![X]:((wise(X)<~>~humble(X))<=>(old(X)|~tall(X))))&
((?[X]:((~quiet(X)&creative(X))))<=>((rich(paul)&old(paul))))&
(![X]:((funny(X)|creative(X))<=>(quiet(X)<~>~kind(X))))&
(((creative(alice)<~>~brave(alice)))<=>((creative(alice)<~>curious(alice))))&
(((~kind(mary)<~>~humble(mary)))=>((~old(susan)<~>~tall(susan))))&
(![X]:((~strong(X)|strong(X))=>creative(X)))&
(![X]:((strong(X)|~patient(X))<=>(~calm(X)<~>curious(X))))&
((?[X]:(wise(X)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
((?[X]:((kind(X)&~creative(X))))<=>(~curious(fred)))&
((?[X]:((~generous(X)|~kind(X))))=>((~patient(paul)<~>old(paul))))&
(![X]:(~patient(X)=>(humble(X)&wise(X))))&
(?[X]:((calm(X)|humble(X))))&
(?[X]:((~calm(X)&~rich(X))))&
((~kind(susan)&tall(susan)))&
((brave(lucy)<~>~creative(lucy)))&
((kind(paul)|~old(paul)))&
((~kind(paul)<~>~wise(paul)))&
((calm(fred)&~rich(fred)))&
(?[X]:((~kind(X)&happy(X)))) | ~old(susan) | [
"p1",
"p5",
"p7",
"p10",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6261918408744591680254378
% SZS output start Proof for 6261918408744591680254378
2. ! [X0] : ((patient(X0) | ~brave(X0)) <=> (quiet(X0) | kind(X0))) [input p1]
6. ! [X0] : ((wise(X0) <~> ~humble(X0)) <=> (~tall(X0) | old(X0))) [input p5]
8. ! [X0] : ((creative(X0) | funny(X0)) <=> (quiet(X0) <~> ~kind(X0))) [input p7]
11. ! [X0] : ((strong(X0) | ~strong(X0)) => creative(X0)) [input p10]
16. ! [X0] : (~patient(X0) => (wise(X0) & humble(X0))) [input p15]
19. tall(susan) & ~kind(susan) [input p18]
25. ~old(susan) [input hypothesis]
32. ! [X0] : (creative(X0) | (~strong(X0) & strong(X0))) [ennf transformation 11]
35. ! [X0] : ((wise(X0) & humble(X0)) | patient(X0)) [ennf transformation 16]
36. ! [X0] : (((patient(X0) | ~brave(X0)) | (~quiet(X0) & ~kind(X0))) & ((quiet(X0) | kind(X0)) | (~patient(X0) & brave(X0)))) [nnf transformation 2]
37. ! [X0] : ((patient(X0) | ~brave(X0) | (~quiet(X0) & ~kind(X0))) & (quiet(X0) | kind(X0) | (~patient(X0) & brave(X0)))) [flattening 36]
43. ! [X0] : ((((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | (tall(X0) & ~old(X0))) & ((~tall(X0) | old(X0)) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0))))) [nnf transformation 6]
44. ! [X0] : ((((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | (tall(X0) & ~old(X0))) & (~tall(X0) | old(X0) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0))))) [flattening 43]
50. ! [X0] : (((creative(X0) | funny(X0)) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (~creative(X0) & ~funny(X0)))) [nnf transformation 8]
51. ! [X0] : ((creative(X0) | funny(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (~creative(X0) & ~funny(X0)))) [flattening 50]
75. ~patient(X0) | kind(X0) | quiet(X0) [cnf transformation 37]
83. ~tall(X0) | old(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 44]
96. ~creative(X0) | ~quiet(X0) | kind(X0) [cnf transformation 51]
111. creative(X0) | strong(X0) [cnf transformation 32]
112. ~strong(X0) | creative(X0) [cnf transformation 32]
128. humble(X0) | patient(X0) [cnf transformation 35]
129. wise(X0) | patient(X0) [cnf transformation 35]
133. ~kind(susan) [cnf transformation 19]
134. tall(susan) [cnf transformation 19]
143. ~old(susan) [cnf transformation 25]
223. 17 <=> old(susan) [avatar definition]
224. ~old(susan) <- (~17) [avatar component clause 223]
227. 18 <=> tall(susan) [avatar definition]
229. tall(susan) <- (18) [avatar component clause 227]
234. creative(X0) [subsumption resolution 111,112]
272. 18 [avatar split clause 134,227]
285. ~17 [avatar split clause 143,223]
332. ~quiet(X0) | kind(X0) [resolution 96,234]
351. 34 <=> quiet(susan) [avatar definition]
352. quiet(susan) <- (34) [avatar component clause 351]
355. 35 <=> patient(susan) [avatar definition]
357. patient(susan) <- (35) [avatar component clause 355]
439. old(susan) | ~humble(susan) | ~wise(susan) <- (18) [resolution 83,229]
441. ~humble(susan) | ~wise(susan) <- (~17, 18) [subsumption resolution 439,224]
443. 49 <=> wise(susan) [avatar definition]
445. ~wise(susan) <- (~49) [avatar component clause 443]
447. 50 <=> humble(susan) [avatar definition]
449. ~humble(susan) <- (~50) [avatar component clause 447]
450. ~49 | ~50 | 17 | ~18 [avatar split clause 441,227,223,447,443]
515. patient(susan) <- (~50) [resolution 449,128]
516. 35 | 50 [avatar split clause 515,447,355]
518. patient(susan) <- (~49) [resolution 445,129]
519. 35 | 49 [avatar split clause 518,443,355]
521. kind(susan) | quiet(susan) <- (35) [resolution 357,75]
535. quiet(susan) <- (35) [subsumption resolution 521,133]
538. 34 | ~35 [avatar split clause 535,355,351]
567. kind(susan) <- (34) [resolution 332,352]
569. $false <- (34) [subsumption resolution 567,133]
570. ~34 [avatar contradiction clause 569]
571. $false [avatar sat refutation 272,285,450,516,519,538,570]
% SZS output end Proof for 6261918408744591680254378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both brave and old and vice versa.
Everyone who is both old and not generous is both not creative and curious.
Everyone who is humble or strong is both not creative and not funny.
Everyone who is wise or not generous is both not rich and not patient.
If john is brave or not funny then someone is either rich or not quiet and vice versa.
Everyone who is either wise or not wise is either not rich or funny and vice versa.
Everyone who is both not old and old is not kind and vice versa.
Everyone who is either not calm or quiet is both not calm and not old.
If mary is not kind or happy then lucy is either not creative or quiet.
If someone is both not strong and not old then someone is both curious and not funny.
Everyone who is either not strong or not creative is both not tall and creative.
If mary is either not funny or not rich then someone is funny.
Everyone who is curious is either not creative or curious and vice versa.
If john is not curious or not wise then someone is either old or not funny.
If someone is both not patient and not calm then mary is curious or patient.
Someone is not patient or kind.
Alice is either brave or not brave.
Lucy is either not brave or not old.
Fred is patient or not humble.
John is both curious and not wise.
Alice is not quiet or happy.
Someone is strong or old.
John is generous or patient. | Mary is humble. | contradiction | (![X]:(~curious(X)<=>(brave(X)&old(X))))&
(![X]:((old(X)&~generous(X))=>(~creative(X)&curious(X))))&
(![X]:((humble(X)|strong(X))=>(~creative(X)&~funny(X))))&
(![X]:((wise(X)|~generous(X))=>(~rich(X)&~patient(X))))&
(((brave(john)|~funny(john)))<=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((wise(X)<~>~wise(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((~old(X)&old(X))<=>~kind(X)))&
(![X]:((~calm(X)<~>quiet(X))=>(~calm(X)&~old(X))))&
(((~kind(mary)|happy(mary)))=>((~creative(lucy)<~>quiet(lucy))))&
((?[X]:((~strong(X)&~old(X))))=>(?[X]:((curious(X)&~funny(X)))))&
(![X]:((~strong(X)<~>~creative(X))=>(~tall(X)&creative(X))))&
(((~funny(mary)<~>~rich(mary)))=>(?[X]:(funny(X))))&
(![X]:(curious(X)<=>(~creative(X)<~>curious(X))))&
(((~curious(john)|~wise(john)))=>(?[X]:((old(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~calm(X))))=>((curious(mary)|patient(mary))))&
(?[X]:((~patient(X)|kind(X))))&
((brave(alice)<~>~brave(alice)))&
((~brave(lucy)<~>~old(lucy)))&
((patient(fred)|~humble(fred)))&
((curious(john)&~wise(john)))&
((~quiet(alice)|happy(alice)))&
(?[X]:((strong(X)|old(X))))&
((generous(john)|patient(john))) | humble(mary) | [
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8648080078554014786123107
% SZS output start Proof for 8648080078554014786123107
3. ! [X0] : ((strong(X0) | humble(X0)) => (~funny(X0) & ~creative(X0))) [input p2]
13. ! [X0] : (curious(X0) <=> (~creative(X0) <~> curious(X0))) [input p12]
24. humble(mary) [input hypothesis]
31. ! [X0] : ((~funny(X0) & ~creative(X0)) | (~strong(X0) & ~humble(X0))) [ennf transformation 3]
60. ! [X0] : ((curious(X0) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | ~curious(X0))) [nnf transformation 13]
73. ~humble(X0) | ~creative(X0) [cnf transformation 31]
109. ~curious(X0) | creative(X0) | ~curious(X0) [cnf transformation 60]
110. curious(X0) | curious(X0) | creative(X0) [cnf transformation 60]
127. humble(mary) [cnf transformation 24]
128. ~curious(X0) | creative(X0) [duplicate literal removal 109]
129. curious(X0) | creative(X0) [duplicate literal removal 110]
213. creative(X0) [subsumption resolution 128,129]
296. ~creative(mary) [resolution 73,127]
297. $false [subsumption resolution 296,213]
% SZS output end Proof for 8648080078554014786123107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If paul is not humble then lucy is both not creative and not calm and vice versa.
If paul is creative or not generous then someone is both old and strong.
If paul is not funny then paul is humble or not quiet.
If john is generous then mary is strong and vice versa.
Everyone who is both not wise and generous is not kind or not brave and vice versa.
If lucy is either tall or not humble then someone is either curious or tall and vice versa.
Everyone who is either not funny or creative is not tall and vice versa.
If fred is both not happy and old then john is both brave and not brave.
If mary is not calm then fred is not creative.
If mary is curious then someone is not generous and vice versa.
If someone is either not happy or not old then john is not creative and vice versa.
Everyone who is tall is either old or quiet.
Everyone who is not creative is both not wise and curious.
Everyone who is both quiet and generous is creative and vice versa.
Everyone who is either not funny or generous is both wise and kind and vice versa.
Everyone who is not kind is wise and vice versa.
Fred is either not creative or not old.
Mary is kind or not generous.
Someone is curious.
Paul is either not generous or creative.
Someone is either funny or generous.
Someone is not generous or wise.
John is happy. | Mary is generous. | neutral | ((~humble(paul))<=>((~creative(lucy)&~calm(lucy))))&
(((creative(paul)|~generous(paul)))=>(?[X]:((old(X)&strong(X)))))&
((~funny(paul))=>((humble(paul)|~quiet(paul))))&
((generous(john))<=>(strong(mary)))&
(![X]:((~wise(X)&generous(X))<=>(~kind(X)|~brave(X))))&
(((tall(lucy)<~>~humble(lucy)))<=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((~funny(X)<~>creative(X))<=>~tall(X)))&
(((~happy(fred)&old(fred)))=>((brave(john)&~brave(john))))&
((~calm(mary))=>(~creative(fred)))&
((curious(mary))<=>(?[X]:(~generous(X))))&
((?[X]:((~happy(X)<~>~old(X))))<=>(~creative(john)))&
(![X]:(tall(X)=>(old(X)<~>quiet(X))))&
(![X]:(~creative(X)=>(~wise(X)&curious(X))))&
(![X]:((quiet(X)&generous(X))<=>creative(X)))&
(![X]:((~funny(X)<~>generous(X))<=>(wise(X)&kind(X))))&
(![X]:(~kind(X)<=>wise(X)))&
((~creative(fred)<~>~old(fred)))&
((kind(mary)|~generous(mary)))&
(?[X]:(curious(X)))&
((~generous(paul)<~>creative(paul)))&
(?[X]:((funny(X)<~>generous(X))))&
(?[X]:((~generous(X)|wise(X))))&
(happy(john)) | generous(mary) | [] | null | 0 |
Everyone who is both kind and not funny is both not humble and generous.
Everyone who is either wise or not old is humble and vice versa.
If susan is both generous and not generous then someone is both humble and not funny.
If someone is either creative or strong then susan is not strong and vice versa.
Everyone who is both not tall and rich is either not happy or brave and vice versa.
If john is not funny then fred is either not humble or wise and vice versa.
If john is either not calm or not wise then lucy is calm and vice versa.
Everyone who is both humble and not creative is curious or happy.
Everyone who is funny or not humble is either not generous or not rich and vice versa.
Everyone who is not calm or old is not wise or patient.
Everyone who is not funny is either not patient or not quiet and vice versa.
If alice is curious then mary is strong and vice versa.
If someone is both not happy and not humble then someone is not creative or kind.
Everyone who is either humble or happy is kind and vice versa.
If someone is either curious or not happy then mary is both brave and not wise and vice versa.
If someone is not tall or patient then susan is both not patient and not happy.
Someone is not kind or not calm.
Paul is either quiet or creative.
Mary is curious or funny.
Paul is old.
John is not tall or not creative.
Someone is curious.
Someone is either not strong or not curious.
Someone is humble or calm. | Fred is quiet. | neutral | (![X]:((kind(X)&~funny(X))=>(~humble(X)&generous(X))))&
(![X]:((wise(X)<~>~old(X))<=>humble(X)))&
(((generous(susan)&~generous(susan)))=>(?[X]:((humble(X)&~funny(X)))))&
((?[X]:((creative(X)<~>strong(X))))<=>(~strong(susan)))&
(![X]:((~tall(X)&rich(X))<=>(~happy(X)<~>brave(X))))&
((~funny(john))<=>((~humble(fred)<~>wise(fred))))&
(((~calm(john)<~>~wise(john)))<=>(calm(lucy)))&
(![X]:((humble(X)&~creative(X))=>(curious(X)|happy(X))))&
(![X]:((funny(X)|~humble(X))<=>(~generous(X)<~>~rich(X))))&
(![X]:((~calm(X)|old(X))=>(~wise(X)|patient(X))))&
(![X]:(~funny(X)<=>(~patient(X)<~>~quiet(X))))&
((curious(alice))<=>(strong(mary)))&
((?[X]:((~happy(X)&~humble(X))))=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((humble(X)<~>happy(X))<=>kind(X)))&
((?[X]:((curious(X)<~>~happy(X))))<=>((brave(mary)&~wise(mary))))&
((?[X]:((~tall(X)|patient(X))))=>((~patient(susan)&~happy(susan))))&
(?[X]:((~kind(X)|~calm(X))))&
((quiet(paul)<~>creative(paul)))&
((curious(mary)|funny(mary)))&
(old(paul))&
((~tall(john)|~creative(john)))&
(?[X]:(curious(X)))&
(?[X]:((~strong(X)<~>~curious(X))))&
(?[X]:((humble(X)|calm(X)))) | quiet(fred) | [] | null | 0 |
Everyone who is either tall or not creative is either not funny or strong.
If paul is not humble or tall then someone is quiet.
Everyone who is not brave or not calm is both not tall and calm and vice versa.
Everyone who is both not tall and not brave is both not curious and not creative and vice versa.
If susan is either rich or not patient then someone is either not funny or quiet.
If someone is both not creative and calm then susan is both patient and not quiet and vice versa.
Everyone who is creative is either kind or calm.
If fred is quiet then mary is either not strong or not curious and vice versa.
If john is both not funny and not kind then john is both happy and not patient and vice versa.
If susan is not curious or not tall then someone is not strong or old.
Everyone who is not happy or humble is quiet and vice versa.
If someone is either brave or quiet then someone is brave.
Everyone who is not kind is calm.
If paul is both strong and not quiet then susan is both old and tall.
Everyone who is both not calm and happy is not quiet and vice versa.
Everyone who is not strong is either not patient or not quiet and vice versa.
Susan is not old or not happy.
Alice is both generous and not kind.
Someone is both tall and calm.
Someone is either curious or old.
Mary is both not funny and generous.
Susan is either not brave or not rich.
Alice is patient or calm. | Susan is tall. | entailment | (![X]:((tall(X)<~>~creative(X))=>(~funny(X)<~>strong(X))))&
(((~humble(paul)|tall(paul)))=>(?[X]:(quiet(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~tall(X)&calm(X))))&
(![X]:((~tall(X)&~brave(X))<=>(~curious(X)&~creative(X))))&
(((rich(susan)<~>~patient(susan)))=>(?[X]:((~funny(X)<~>quiet(X)))))&
((?[X]:((~creative(X)&calm(X))))<=>((patient(susan)&~quiet(susan))))&
(![X]:(creative(X)=>(kind(X)<~>calm(X))))&
((quiet(fred))<=>((~strong(mary)<~>~curious(mary))))&
(((~funny(john)&~kind(john)))<=>((happy(john)&~patient(john))))&
(((~curious(susan)|~tall(susan)))=>(?[X]:((~strong(X)|old(X)))))&
(![X]:((~happy(X)|humble(X))<=>quiet(X)))&
((?[X]:((brave(X)<~>quiet(X))))=>(?[X]:(brave(X))))&
(![X]:(~kind(X)=>calm(X)))&
(((strong(paul)&~quiet(paul)))=>((old(susan)&tall(susan))))&
(![X]:((~calm(X)&happy(X))<=>~quiet(X)))&
(![X]:(~strong(X)<=>(~patient(X)<~>~quiet(X))))&
((~old(susan)|~happy(susan)))&
((generous(alice)&~kind(alice)))&
(?[X]:((tall(X)&calm(X))))&
(?[X]:((curious(X)<~>old(X))))&
((~funny(mary)&generous(mary)))&
((~brave(susan)<~>~rich(susan)))&
((patient(alice)|calm(alice))) | tall(susan) | [
"p2",
"p3",
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 853072161364733466028911
% SZS output start Proof for 853072161364733466028911
3. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> (calm(X0) & ~tall(X0))) [input p2]
4. ! [X0] : ((~brave(X0) & ~tall(X0)) <=> (~creative(X0) & ~curious(X0))) [input p3]
6. ? [X0] : (calm(X0) & ~creative(X0)) <=> (~quiet(susan) & patient(susan)) [input p5]
15. ! [X0] : ((happy(X0) & ~calm(X0)) <=> ~quiet(X0)) [input p14]
24. ~tall(susan) [input hypothesis]
40. ! [X0] : (((~calm(X0) | ~brave(X0)) | (~calm(X0) | tall(X0))) & ((calm(X0) & ~tall(X0)) | (calm(X0) & brave(X0)))) [nnf transformation 3]
41. ! [X0] : ((~calm(X0) | ~brave(X0) | ~calm(X0) | tall(X0)) & ((calm(X0) & ~tall(X0)) | (calm(X0) & brave(X0)))) [flattening 40]
42. ! [X0] : (((~brave(X0) & ~tall(X0)) | (creative(X0) | curious(X0))) & ((~creative(X0) & ~curious(X0)) | (brave(X0) | tall(X0)))) [nnf transformation 4]
43. ! [X0] : (((~brave(X0) & ~tall(X0)) | creative(X0) | curious(X0)) & ((~creative(X0) & ~curious(X0)) | brave(X0) | tall(X0))) [flattening 42]
47. (? [X0] : (calm(X0) & ~creative(X0)) | (quiet(susan) | ~patient(susan))) & ((~quiet(susan) & patient(susan)) | ! [X0] : (~calm(X0) | creative(X0))) [nnf transformation 6]
48. (? [X0] : (calm(X0) & ~creative(X0)) | quiet(susan) | ~patient(susan)) & ((~quiet(susan) & patient(susan)) | ! [X0] : (~calm(X0) | creative(X0))) [flattening 47]
49. (? [X0] : (calm(X0) & ~creative(X0)) | quiet(susan) | ~patient(susan)) & ((~quiet(susan) & patient(susan)) | ! [X1] : (~calm(X1) | creative(X1))) [rectify 48]
50. ? [X0] : (calm(X0) & ~creative(X0)) => (calm(sK2) & ~creative(sK2)) [choice axiom]
51. ((calm(sK2) & ~creative(sK2)) | quiet(susan) | ~patient(susan)) & ((~quiet(susan) & patient(susan)) | ! [X1] : (~calm(X1) | creative(X1))) [skolemisation 49,50]
64. ! [X0] : (((happy(X0) & ~calm(X0)) | quiet(X0)) & (~quiet(X0) | (~happy(X0) | calm(X0)))) [nnf transformation 15]
65. ! [X0] : (((happy(X0) & ~calm(X0)) | quiet(X0)) & (~quiet(X0) | ~happy(X0) | calm(X0))) [flattening 64]
79. ~tall(X0) | brave(X0) [cnf transformation 41]
82. calm(X0) | calm(X0) [cnf transformation 41]
83. ~calm(X0) | ~brave(X0) | ~calm(X0) | tall(X0) [cnf transformation 41]
85. ~creative(X0) | brave(X0) | tall(X0) [cnf transformation 43]
93. ~quiet(susan) | ~calm(X1) | creative(X1) [cnf transformation 51]
117. ~calm(X0) | quiet(X0) [cnf transformation 65]
133. ~tall(susan) [cnf transformation 24]
134. calm(X0) [duplicate literal removal 82]
135. ~calm(X0) | ~brave(X0) | tall(X0) [duplicate literal removal 83]
150. ~creative(X0) | brave(X0) [subsumption resolution 85,79]
173. 8 <=> quiet(susan) [avatar definition]
174. ~quiet(susan) <- (~8) [avatar component clause 173]
181. ~quiet(susan) | creative(X1) [subsumption resolution 93,134]
183. 10 <=> ! [X1] : creative(X1) [avatar definition]
184. creative(X1) <- (10) [avatar component clause 183]
185. 10 | ~8 [avatar split clause 181,173,183]
226. 18 <=> tall(susan) [avatar definition]
227. ~tall(susan) <- (~18) [avatar component clause 226]
269. quiet(X0) [subsumption resolution 117,134]
293. ~18 [avatar split clause 133,226]
296. $false <- (~8) [subsumption resolution 174,269]
297. 8 [avatar contradiction clause 296]
304. brave(X0) <- (10) [resolution 150,184]
318. ~brave(X0) | tall(X0) [resolution 135,134]
319. tall(X0) <- (10) [subsumption resolution 318,304]
324. $false <- (10, ~18) [resolution 319,227]
327. ~10 | 18 [avatar contradiction clause 324]
328. $false [avatar sat refutation 185,293,297,327]
% SZS output end Proof for 853072161364733466028911
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
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