premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is not happy is both not calm and creative and vice versa.
If john is either quiet or not kind then paul is either brave or not strong.
Everyone who is either not happy or not quiet is generous or tall.
Everyone who is either generous or not tall is rich and vice versa.
If susan is not kind or humble then someone is either not tall or not quiet and vice versa.
If fred is either not humble or wise then someone is either not creative or patient and vice versa.
Everyone who is either wise or rich is not kind or patient and vice versa.
Everyone who is both creative and happy is both tall and humble and vice versa.
If susan is not kind or not patient then someone is either not quiet or happy and vice versa.
If paul is not quiet then someone is not brave or not generous.
If someone is either not strong or not rich then someone is either tall or not curious.
Everyone who is not happy is either not kind or funny and vice versa.
If john is both patient and not quiet then someone is both not brave and quiet and vice versa.
If lucy is happy then alice is not calm or rich.
Everyone who is not happy or not curious is both tall and brave.
If someone is not happy then someone is both not brave and wise and vice versa.
Someone is humble or not strong.
Mary is not happy.
John is quiet.
Fred is not funny.
Alice is either not humble or generous.
Mary is curious or funny.
Alice is either not brave or not wise.
Alice is either not kind or not rich. | Mary is humble. | contradiction | (![X]:(~happy(X)<=>(~calm(X)&creative(X))))&
(((quiet(john)<~>~kind(john)))=>((brave(paul)<~>~strong(paul))))&
(![X]:((~happy(X)<~>~quiet(X))=>(generous(X)|tall(X))))&
(![X]:((generous(X)<~>~tall(X))<=>rich(X)))&
(((~kind(susan)|humble(susan)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(((~humble(fred)<~>wise(fred)))<=>(?[X]:((~creative(X)<~>patient(X)))))&
(![X]:((wise(X)<~>rich(X))<=>(~kind(X)|patient(X))))&
(![X]:((creative(X)&happy(X))<=>(tall(X)&humble(X))))&
(((~kind(susan)|~patient(susan)))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
((~quiet(paul))=>(?[X]:((~brave(X)|~generous(X)))))&
((?[X]:((~strong(X)<~>~rich(X))))=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:(~happy(X)<=>(~kind(X)<~>funny(X))))&
(((patient(john)&~quiet(john)))<=>(?[X]:((~brave(X)&quiet(X)))))&
((happy(lucy))=>((~calm(alice)|rich(alice))))&
(![X]:((~happy(X)|~curious(X))=>(tall(X)&brave(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~brave(X)&wise(X)))))&
(?[X]:((humble(X)|~strong(X))))&
(~happy(mary))&
(quiet(john))&
(~funny(fred))&
((~humble(alice)<~>generous(alice)))&
((curious(mary)|funny(mary)))&
((~brave(alice)<~>~wise(alice)))&
((~kind(alice)<~>~rich(alice))) | humble(mary) | [
"p7",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1414226419861130073199588
% SZS output start Proof for 1414226419861130073199588
8. ! [X0] : ((happy(X0) & creative(X0)) <=> (humble(X0) & tall(X0))) [input p7]
15. ! [X0] : ((~curious(X0) | ~happy(X0)) => (brave(X0) & tall(X0))) [input p14]
18. ~happy(mary) [input p17]
25. humble(mary) [input hypothesis]
35. ! [X0] : ((brave(X0) & tall(X0)) | (curious(X0) & happy(X0))) [ennf transformation 15]
52. ! [X0] : (((happy(X0) & creative(X0)) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 8]
53. ! [X0] : (((happy(X0) & creative(X0)) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | ~happy(X0) | ~creative(X0))) [flattening 52]
117. ~humble(X0) | happy(X0) | ~tall(X0) [cnf transformation 53]
138. tall(X0) | happy(X0) [cnf transformation 35]
146. ~happy(mary) [cnf transformation 18]
156. humble(mary) [cnf transformation 25]
513. 64 <=> tall(mary) [avatar definition]
514. tall(mary) <- (64) [avatar component clause 513]
515. ~tall(mary) <- (~64) [avatar component clause 513]
521. happy(mary) <- (~64) [resolution 515,138]
522. $false <- (~64) [subsumption resolution 521,146]
523. 64 [avatar contradiction clause 522]
524. happy(mary) | ~tall(mary) [resolution 117,156]
525. ~tall(mary) [subsumption resolution 524,146]
526. $false <- (64) [subsumption resolution 525,514]
527. ~64 [avatar contradiction clause 526]
528. $false [avatar sat refutation 523,527]
% SZS output end Proof for 1414226419861130073199588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and not strong is both happy and not tall and vice versa.
If lucy is either not generous or creative then someone is both not kind and not quiet.
If alice is either not rich or not patient then someone is not strong and vice versa.
Everyone who is either not curious or tall is not curious or not strong.
If susan is not funny or quiet then someone is not rich.
Everyone who is either not quiet or brave is patient.
If paul is either not wise or not curious then someone is either not humble or brave and vice versa.
If someone is both creative and not happy then alice is both generous and not calm.
Everyone who is either kind or not patient is both not funny and not creative and vice versa.
If someone is quiet or not calm then someone is not happy and vice versa.
If lucy is happy or not patient then someone is either humble or old.
If someone is either calm or happy then paul is not funny and vice versa.
Everyone who is either calm or not brave is tall.
If john is either tall or not tall then lucy is not calm or rich.
Everyone who is not strong or creative is either not creative or not generous.
If someone is humble or not curious then susan is humble or not curious and vice versa.
Alice is not wise or wise.
Susan is both not patient and brave.
Someone is not tall or not strong.
Someone is either not kind or not creative.
Mary is either wise or patient.
Fred is both happy and not brave.
Someone is both not creative and not strong. | John is not brave. | neutral | (![X]:((~creative(X)&~strong(X))<=>(happy(X)&~tall(X))))&
(((~generous(lucy)<~>creative(lucy)))=>(?[X]:((~kind(X)&~quiet(X)))))&
(((~rich(alice)<~>~patient(alice)))<=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)<~>tall(X))=>(~curious(X)|~strong(X))))&
(((~funny(susan)|quiet(susan)))=>(?[X]:(~rich(X))))&
(![X]:((~quiet(X)<~>brave(X))=>patient(X)))&
(((~wise(paul)<~>~curious(paul)))<=>(?[X]:((~humble(X)<~>brave(X)))))&
((?[X]:((creative(X)&~happy(X))))=>((generous(alice)&~calm(alice))))&
(![X]:((kind(X)<~>~patient(X))<=>(~funny(X)&~creative(X))))&
((?[X]:((quiet(X)|~calm(X))))<=>(?[X]:(~happy(X))))&
(((happy(lucy)|~patient(lucy)))=>(?[X]:((humble(X)<~>old(X)))))&
((?[X]:((calm(X)<~>happy(X))))<=>(~funny(paul)))&
(![X]:((calm(X)<~>~brave(X))=>tall(X)))&
(((tall(john)<~>~tall(john)))=>((~calm(lucy)|rich(lucy))))&
(![X]:((~strong(X)|creative(X))=>(~creative(X)<~>~generous(X))))&
((?[X]:((humble(X)|~curious(X))))<=>((humble(susan)|~curious(susan))))&
((~wise(alice)|wise(alice)))&
((~patient(susan)&brave(susan)))&
(?[X]:((~tall(X)|~strong(X))))&
(?[X]:((~kind(X)<~>~creative(X))))&
((wise(mary)<~>patient(mary)))&
((happy(fred)&~brave(fred)))&
(?[X]:((~creative(X)&~strong(X)))) | ~brave(john) | [] | null | 0 |
If someone is humble or brave then someone is creative and vice versa.
If lucy is both not patient and not creative then susan is not calm or not funny and vice versa.
Everyone who is not brave or not wise is not strong or wise.
Everyone who is both not calm and calm is funny or patient and vice versa.
Everyone who is not curious or generous is funny or quiet.
If someone is wise or not rich then someone is either calm or tall and vice versa.
If someone is funny or happy then someone is either strong or calm.
Everyone who is not patient or kind is both not quiet and tall.
If fred is not strong then someone is creative.
If someone is both curious and strong then lucy is not kind.
If someone is patient then someone is humble or brave and vice versa.
If mary is both not strong and not curious then susan is both not curious and wise and vice versa.
Everyone who is funny is both not rich and not patient and vice versa.
Someone is either calm or not patient.
Someone is either not wise or not calm.
Mary is not humble.
Someone is wise or old. | Fred is curious. | entailment | ((?[X]:((humble(X)|brave(X))))<=>(?[X]:(creative(X))))&
(((~patient(lucy)&~creative(lucy)))<=>((~calm(susan)|~funny(susan))))&
(![X]:((~brave(X)|~wise(X))=>(~strong(X)|wise(X))))&
(![X]:((~calm(X)&calm(X))<=>(funny(X)|patient(X))))&
(![X]:((~curious(X)|generous(X))=>(funny(X)|quiet(X))))&
((?[X]:((wise(X)|~rich(X))))<=>(?[X]:((calm(X)<~>tall(X)))))&
((?[X]:((funny(X)|happy(X))))=>(?[X]:((strong(X)<~>calm(X)))))&
(![X]:((~patient(X)|kind(X))=>(~quiet(X)&tall(X))))&
((~strong(fred))=>(?[X]:(creative(X))))&
((?[X]:((curious(X)&strong(X))))=>(~kind(lucy)))&
((?[X]:(patient(X)))<=>(?[X]:((humble(X)|brave(X)))))&
(((~strong(mary)&~curious(mary)))<=>((~curious(susan)&wise(susan))))&
(![X]:(funny(X)<=>(~rich(X)&~patient(X))))&
(?[X]:((calm(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>~calm(X))))&
(~humble(mary))&
(?[X]:((wise(X)|old(X)))) | curious(fred) | [
"p3",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3272894561642336211851028
% SZS output start Proof for 3272894561642336211851028
4. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (patient(X0) | funny(X0))) [input p3]
5. ! [X0] : ((generous(X0) | ~curious(X0)) => (quiet(X0) | funny(X0))) [input p4]
8. ! [X0] : ((kind(X0) | ~patient(X0)) => (tall(X0) & ~quiet(X0))) [input p7]
18. ~curious(fred) [input hypothesis]
25. ! [X0] : (~patient(X0) => (tall(X0) & ~quiet(X0))) [pure predicate removal 8]
27. ! [X0] : (~curious(X0) => (quiet(X0) | funny(X0))) [pure predicate removal 5]
30. ! [X0] : ((quiet(X0) | funny(X0)) | curious(X0)) [ennf transformation 27]
31. ! [X0] : (quiet(X0) | funny(X0) | curious(X0)) [flattening 30]
33. ! [X0] : ((tall(X0) & ~quiet(X0)) | patient(X0)) [ennf transformation 25]
42. ! [X0] : (((calm(X0) & ~calm(X0)) | (~patient(X0) & ~funny(X0))) & ((patient(X0) | funny(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 4]
43. ! [X0] : (((calm(X0) & ~calm(X0)) | (~patient(X0) & ~funny(X0))) & (patient(X0) | funny(X0) | ~calm(X0) | calm(X0))) [flattening 42]
81. ~calm(X0) | ~funny(X0) [cnf transformation 43]
82. ~calm(X0) | ~patient(X0) [cnf transformation 43]
83. ~funny(X0) | calm(X0) [cnf transformation 43]
84. ~patient(X0) | calm(X0) [cnf transformation 43]
85. quiet(X0) | funny(X0) | curious(X0) [cnf transformation 31]
94. ~quiet(X0) | patient(X0) [cnf transformation 33]
112. ~curious(fred) [cnf transformation 18]
159. ~patient(X0) [subsumption resolution 82,84]
160. ~funny(X0) [subsumption resolution 81,83]
161. quiet(X0) | curious(X0) [subsumption resolution 85,160]
197. ~quiet(X0) [subsumption resolution 94,159]
254. curious(X0) [resolution 161,197]
255. $false [resolution 254,112]
% SZS output end Proof for 3272894561642336211851028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not funny is not old and vice versa.
Everyone who is not happy or creative is funny or not brave and vice versa.
Everyone who is kind is either happy or not humble and vice versa.
If someone is not patient or quiet then alice is curious or creative and vice versa.
If alice is both strong and not kind then someone is either quiet or not curious.
Everyone who is both not humble and not curious is either not happy or not patient and vice versa.
If someone is both not rich and not tall then fred is happy or not happy and vice versa.
If someone is humble or old then alice is not quiet.
Everyone who is both not wise and not humble is either not happy or rich and vice versa.
Everyone who is calm is both patient and kind.
Everyone who is both not creative and not brave is kind and vice versa.
Everyone who is humble is not happy and vice versa.
If someone is happy or creative then alice is not wise or humble and vice versa.
Everyone who is either not tall or calm is either not brave or not quiet.
Everyone who is either kind or patient is either not brave or humble.
Everyone who is either not old or not tall is both not curious and old.
Someone is rich.
Fred is both funny and rich.
Someone is funny.
Someone is strong or not rich.
Someone is not kind.
Someone is generous or not humble.
Someone is either not strong or not happy.
Paul is not humble. | Alice is rich. | entailment | (![X]:((~old(X)<~>~funny(X))<=>~old(X)))&
(![X]:((~happy(X)|creative(X))<=>(funny(X)|~brave(X))))&
(![X]:(kind(X)<=>(happy(X)<~>~humble(X))))&
((?[X]:((~patient(X)|quiet(X))))<=>((curious(alice)|creative(alice))))&
(((strong(alice)&~kind(alice)))=>(?[X]:((quiet(X)<~>~curious(X)))))&
(![X]:((~humble(X)&~curious(X))<=>(~happy(X)<~>~patient(X))))&
((?[X]:((~rich(X)&~tall(X))))<=>((happy(fred)|~happy(fred))))&
((?[X]:((humble(X)|old(X))))=>(~quiet(alice)))&
(![X]:((~wise(X)&~humble(X))<=>(~happy(X)<~>rich(X))))&
(![X]:(calm(X)=>(patient(X)&kind(X))))&
(![X]:((~creative(X)&~brave(X))<=>kind(X)))&
(![X]:(humble(X)<=>~happy(X)))&
((?[X]:((happy(X)|creative(X))))<=>((~wise(alice)|humble(alice))))&
(![X]:((~tall(X)<~>calm(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>patient(X))=>(~brave(X)<~>humble(X))))&
(![X]:((~old(X)<~>~tall(X))=>(~curious(X)&old(X))))&
(?[X]:(rich(X)))&
((funny(fred)&rich(fred)))&
(?[X]:(funny(X)))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:((generous(X)|~humble(X))))&
(?[X]:((~strong(X)<~>~happy(X))))&
(~humble(paul)) | rich(alice) | [
"p0",
"p1",
"p2",
"p8",
"p11",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7360425713694863473649872
% SZS output start Proof for 7360425713694863473649872
1. ! [X0] : ((~old(X0) <~> ~funny(X0)) <=> ~old(X0)) [input p0]
2. ! [X0] : ((creative(X0) | ~happy(X0)) <=> (~brave(X0) | funny(X0))) [input p1]
3. ! [X0] : (kind(X0) <=> (happy(X0) <~> ~humble(X0))) [input p2]
9. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (~happy(X0) <~> rich(X0))) [input p8]
12. ! [X0] : (humble(X0) <=> ~happy(X0)) [input p11]
13. ? [X0] : (creative(X0) | happy(X0)) <=> (humble(alice) | ~wise(alice)) [input p12]
24. ~humble(paul) [input p23]
25. ~rich(alice) [input hypothesis]
34. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | old(X0)) & (~old(X0) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [nnf transformation 1]
35. ! [X0] : (((creative(X0) | ~happy(X0)) | (brave(X0) & ~funny(X0))) & ((~brave(X0) | funny(X0)) | (~creative(X0) & happy(X0)))) [nnf transformation 2]
36. ! [X0] : ((creative(X0) | ~happy(X0) | (brave(X0) & ~funny(X0))) & (~brave(X0) | funny(X0) | (~creative(X0) & happy(X0)))) [flattening 35]
37. ! [X0] : ((kind(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) & (((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | ~kind(X0))) [nnf transformation 3]
53. ! [X0] : (((~humble(X0) & ~wise(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (humble(X0) | wise(X0)))) [nnf transformation 9]
54. ! [X0] : (((~humble(X0) & ~wise(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | humble(X0) | wise(X0))) [flattening 53]
57. ! [X0] : ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0))) [nnf transformation 12]
58. (? [X0] : (creative(X0) | happy(X0)) | (~humble(alice) & wise(alice))) & ((humble(alice) | ~wise(alice)) | ! [X0] : (~creative(X0) & ~happy(X0))) [nnf transformation 13]
59. (? [X0] : (creative(X0) | happy(X0)) | (~humble(alice) & wise(alice))) & (humble(alice) | ~wise(alice) | ! [X0] : (~creative(X0) & ~happy(X0))) [flattening 58]
60. (? [X0] : (creative(X0) | happy(X0)) | (~humble(alice) & wise(alice))) & (humble(alice) | ~wise(alice) | ! [X1] : (~creative(X1) & ~happy(X1))) [rectify 59]
61. ? [X0] : (creative(X0) | happy(X0)) => (creative(sK3) | happy(sK3)) [choice axiom]
62. ((creative(sK3) | happy(sK3)) | (~humble(alice) & wise(alice))) & (humble(alice) | ~wise(alice) | ! [X1] : (~creative(X1) & ~happy(X1))) [skolemisation 60,61]
78. ~old(X0) | ~old(X0) | funny(X0) [cnf transformation 34]
80. funny(X0) | old(X0) | old(X0) [cnf transformation 34]
83. creative(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 36]
85. ~humble(X0) | happy(X0) | ~kind(X0) [cnf transformation 37]
88. humble(X0) | happy(X0) | kind(X0) [cnf transformation 37]
108. ~happy(X0) | rich(X0) | humble(X0) | wise(X0) [cnf transformation 54]
112. ~humble(X0) | rich(X0) | happy(X0) [cnf transformation 54]
119. ~humble(X0) | ~happy(X0) [cnf transformation 57]
120. humble(X0) | happy(X0) [cnf transformation 57]
122. humble(alice) | ~wise(alice) | ~creative(X1) [cnf transformation 62]
145. ~humble(paul) [cnf transformation 24]
146. ~rich(alice) [cnf transformation 25]
148. ~old(X0) | funny(X0) [duplicate literal removal 78]
149. funny(X0) | old(X0) [duplicate literal removal 80]
150. funny(X0) [subsumption resolution 148,149]
151. ~happy(X0) | creative(X0) [subsumption resolution 83,150]
226. 17 <=> humble(alice) [avatar definition]
227. humble(alice) <- (17) [avatar component clause 226]
236. 19 <=> wise(alice) [avatar definition]
241. 20 <=> ! [X1] : ~creative(X1) [avatar definition]
242. ~creative(X1) <- (20) [avatar component clause 241]
243. 20 | ~19 | 17 [avatar split clause 122,226,236,241]
269. happy(paul) [resolution 120,145]
271. creative(paul) [resolution 151,269]
273. happy(X0) | ~kind(X0) | happy(X0) [resolution 85,120]
274. ~kind(X0) | happy(X0) [duplicate literal removal 273]
286. 26 <=> happy(alice) [avatar definition]
288. happy(alice) <- (26) [avatar component clause 286]
297. rich(X0) | happy(X0) | happy(X0) | kind(X0) [resolution 112,88]
300. rich(X0) | happy(X0) | kind(X0) [duplicate literal removal 297]
301. rich(X0) | happy(X0) [subsumption resolution 300,274]
305. happy(alice) [resolution 301,146]
310. 26 [avatar split clause 305,286]
367. rich(alice) | humble(alice) | wise(alice) <- (26) [resolution 108,288]
371. humble(alice) | wise(alice) <- (26) [subsumption resolution 367,146]
409. ~happy(alice) <- (17) [resolution 227,119]
412. $false <- (17, 26) [subsumption resolution 409,288]
413. ~17 | ~26 [avatar contradiction clause 412]
414. 19 | 17 | ~26 [avatar split clause 371,286,226,236]
420. $false <- (20) [resolution 242,271]
425. ~20 [avatar contradiction clause 420]
427. $false [avatar sat refutation 243,310,413,414,425]
% SZS output end Proof for 7360425713694863473649872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and not kind is not patient or wise.
Everyone who is kind is both not generous and creative and vice versa.
Everyone who is not quiet or not curious is both not funny and not strong.
If someone is strong or quiet then mary is both rich and tall.
Everyone who is both funny and happy is both not happy and not calm and vice versa.
Everyone who is both happy and funny is both happy and not rich.
Everyone who is funny or not calm is both quiet and creative and vice versa.
Everyone who is not tall or old is both humble and not old.
If someone is both wise and brave then alice is kind.
Everyone who is both quiet and not rich is either quiet or brave and vice versa.
If someone is curious or not generous then alice is not rich and vice versa.
Everyone who is both old and patient is wise.
If someone is either not brave or not wise then alice is not curious or rich.
Everyone who is either not generous or not calm is either quiet or not patient.
Everyone who is both funny and generous is both not curious and not quiet and vice versa.
If fred is humble then someone is old or not happy and vice versa.
Someone is calm or funny.
Someone is both not quiet and not strong.
Someone is tall.
Mary is not curious.
John is kind or not curious.
Fred is either not curious or not creative.
Fred is both kind and humble.
Someone is both not humble and not generous. | Mary is not humble. | neutral | (![X]:((~creative(X)&~kind(X))=>(~patient(X)|wise(X))))&
(![X]:(kind(X)<=>(~generous(X)&creative(X))))&
(![X]:((~quiet(X)|~curious(X))=>(~funny(X)&~strong(X))))&
((?[X]:((strong(X)|quiet(X))))=>((rich(mary)&tall(mary))))&
(![X]:((funny(X)&happy(X))<=>(~happy(X)&~calm(X))))&
(![X]:((happy(X)&funny(X))=>(happy(X)&~rich(X))))&
(![X]:((funny(X)|~calm(X))<=>(quiet(X)&creative(X))))&
(![X]:((~tall(X)|old(X))=>(humble(X)&~old(X))))&
((?[X]:((wise(X)&brave(X))))=>(kind(alice)))&
(![X]:((quiet(X)&~rich(X))<=>(quiet(X)<~>brave(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(~rich(alice)))&
(![X]:((old(X)&patient(X))=>wise(X)))&
((?[X]:((~brave(X)<~>~wise(X))))=>((~curious(alice)|rich(alice))))&
(![X]:((~generous(X)<~>~calm(X))=>(quiet(X)<~>~patient(X))))&
(![X]:((funny(X)&generous(X))<=>(~curious(X)&~quiet(X))))&
((humble(fred))<=>(?[X]:((old(X)|~happy(X)))))&
(?[X]:((calm(X)|funny(X))))&
(?[X]:((~quiet(X)&~strong(X))))&
(?[X]:(tall(X)))&
(~curious(mary))&
((kind(john)|~curious(john)))&
((~curious(fred)<~>~creative(fred)))&
((kind(fred)&humble(fred)))&
(?[X]:((~humble(X)&~generous(X)))) | ~humble(mary) | [] | null | 0 |
If someone is wise or not quiet then someone is tall and vice versa.
Everyone who is both curious and not calm is both not creative and not rich and vice versa.
Everyone who is not tall is either generous or brave.
If susan is either not rich or rich then john is not kind and vice versa.
If someone is either not curious or rich then someone is kind and vice versa.
Everyone who is either tall or humble is not rich and vice versa.
Everyone who is both kind and curious is either generous or not strong and vice versa.
If mary is not happy then someone is both rich and not patient.
If fred is curious or not brave then john is both old and not patient.
If someone is both not tall and not calm then someone is not strong and vice versa.
Everyone who is both tall and curious is quiet and vice versa.
Everyone who is both not wise and quiet is generous or creative.
Everyone who is either not brave or generous is not quiet and vice versa.
If someone is both not rich and not patient then someone is not quiet.
If paul is rich or quiet then someone is generous or quiet and vice versa.
If someone is either wise or not wise then alice is not generous.
Susan is both rich and calm.
Mary is humble.
Mary is either not old or strong.
Fred is not wise or happy.
Someone is either wise or not brave.
Someone is either not strong or old.
Someone is either generous or kind. | Mary is not old. | contradiction | ((?[X]:((wise(X)|~quiet(X))))<=>(?[X]:(tall(X))))&
(![X]:((curious(X)&~calm(X))<=>(~creative(X)&~rich(X))))&
(![X]:(~tall(X)=>(generous(X)<~>brave(X))))&
(((~rich(susan)<~>rich(susan)))<=>(~kind(john)))&
((?[X]:((~curious(X)<~>rich(X))))<=>(?[X]:(kind(X))))&
(![X]:((tall(X)<~>humble(X))<=>~rich(X)))&
(![X]:((kind(X)&curious(X))<=>(generous(X)<~>~strong(X))))&
((~happy(mary))=>(?[X]:((rich(X)&~patient(X)))))&
(((curious(fred)|~brave(fred)))=>((old(john)&~patient(john))))&
((?[X]:((~tall(X)&~calm(X))))<=>(?[X]:(~strong(X))))&
(![X]:((tall(X)&curious(X))<=>quiet(X)))&
(![X]:((~wise(X)&quiet(X))=>(generous(X)|creative(X))))&
(![X]:((~brave(X)<~>generous(X))<=>~quiet(X)))&
((?[X]:((~rich(X)&~patient(X))))=>(?[X]:(~quiet(X))))&
(((rich(paul)|quiet(paul)))<=>(?[X]:((generous(X)|quiet(X)))))&
((?[X]:((wise(X)<~>~wise(X))))=>(~generous(alice)))&
((rich(susan)&calm(susan)))&
(humble(mary))&
((~old(mary)<~>strong(mary)))&
((~wise(fred)|happy(fred)))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((~strong(X)<~>old(X))))&
(?[X]:((generous(X)<~>kind(X)))) | ~old(mary) | [
"p2",
"p9",
"p10",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6562566613649868738792553
% SZS output start Proof for 6562566613649868738792553
3. ! [X0] : (~tall(X0) => (generous(X0) <~> brave(X0))) [input p2]
10. ? [X0] : (~calm(X0) & ~tall(X0)) <=> ? [X0] : ~strong(X0) [input p9]
11. ! [X0] : ((curious(X0) & tall(X0)) <=> quiet(X0)) [input p10]
13. ! [X0] : ((~brave(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p12]
19. ~old(mary) <~> strong(mary) [input p18]
24. ~old(mary) [input hypothesis]
27. ? [X0] : (~calm(X0) & ~tall(X0)) <=> ? [X1] : ~strong(X1) [rectify 10]
31. ! [X0] : ((generous(X0) <~> brave(X0)) | tall(X0)) [ennf transformation 3]
44. ! [X0] : (((~brave(X0) | ~generous(X0)) & (brave(X0) | generous(X0))) | tall(X0)) [nnf transformation 31]
54. (? [X0] : (~calm(X0) & ~tall(X0)) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : (calm(X0) | tall(X0))) [nnf transformation 27]
55. (? [X0] : (~calm(X0) & ~tall(X0)) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : (calm(X3) | tall(X3))) [rectify 54]
56. ? [X0] : (~calm(X0) & ~tall(X0)) => (~calm(sK4) & ~tall(sK4)) [choice axiom]
57. ? [X2] : ~strong(X2) => ~strong(sK5) [choice axiom]
58. ((~calm(sK4) & ~tall(sK4)) | ! [X1] : strong(X1)) & (~strong(sK5) | ! [X3] : (calm(X3) | tall(X3))) [skolemisation 55,57,56]
59. ! [X0] : (((curious(X0) & tall(X0)) | ~quiet(X0)) & (quiet(X0) | (~curious(X0) | ~tall(X0)))) [nnf transformation 11]
60. ! [X0] : (((curious(X0) & tall(X0)) | ~quiet(X0)) & (quiet(X0) | ~curious(X0) | ~tall(X0))) [flattening 59]
61. ! [X0] : ((((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | quiet(X0)) & (~quiet(X0) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0))))) [nnf transformation 13]
71. (~strong(mary) | old(mary)) & (strong(mary) | ~old(mary)) [nnf transformation 19]
88. brave(X0) | generous(X0) | tall(X0) [cnf transformation 44]
89. ~brave(X0) | ~generous(X0) | tall(X0) [cnf transformation 44]
113. ~tall(sK4) | strong(X1) [cnf transformation 58]
116. ~quiet(X0) | tall(X0) [cnf transformation 60]
121. ~brave(X0) | generous(X0) | quiet(X0) [cnf transformation 61]
122. ~generous(X0) | brave(X0) | quiet(X0) [cnf transformation 61]
134. ~strong(mary) | old(mary) [cnf transformation 71]
141. ~old(mary) [cnf transformation 24]
226. 19 <=> ! [X1] : strong(X1) [avatar definition]
227. strong(X1) <- (19) [avatar component clause 226]
234. 21 <=> tall(sK4) [avatar definition]
236. ~tall(sK4) <- (~21) [avatar component clause 234]
237. 19 | ~21 [avatar split clause 113,234,226]
291. 34 <=> old(mary) [avatar definition]
295. 35 <=> strong(mary) [avatar definition]
297. ~strong(mary) <- (~35) [avatar component clause 295]
298. 34 | ~35 [avatar split clause 134,295,291]
330. ~34 [avatar split clause 141,291]
468. generous(X0) | quiet(X0) | generous(X0) | tall(X0) [resolution 121,88]
469. generous(X0) | quiet(X0) | tall(X0) [duplicate literal removal 468]
471. generous(X0) | tall(X0) [subsumption resolution 469,116]
523. $false <- (19, ~35) [resolution 227,297]
526. ~19 | 35 [avatar contradiction clause 523]
624. tall(X0) | brave(X0) | quiet(X0) [resolution 471,122]
631. brave(X0) | tall(X0) [subsumption resolution 624,116]
799. tall(X2) | ~generous(X2) | tall(X2) [resolution 631,89]
800. tall(X2) | ~generous(X2) [duplicate literal removal 799]
801. tall(X2) [subsumption resolution 800,471]
849. $false <- (~21) [resolution 801,236]
853. 21 [avatar contradiction clause 849]
854. $false [avatar sat refutation 237,298,330,526,853]
% SZS output end Proof for 6562566613649868738792553
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not happy or not funny is both quiet and not kind.
Everyone who is wise or not brave is tall or not rich.
Everyone who is both not curious and patient is both patient and curious and vice versa.
If paul is not happy or not curious then someone is either not funny or strong.
Everyone who is either not creative or not generous is not strong or generous.
Everyone who is either brave or not wise is not kind or funny.
Everyone who is strong or funny is either not curious or not happy and vice versa.
If someone is wise then susan is funny or generous and vice versa.
Everyone who is either not creative or humble is not strong or curious.
If paul is both not calm and not patient then someone is not rich and vice versa.
If someone is either brave or not happy then fred is not funny or not happy and vice versa.
Everyone who is not generous or not strong is either not calm or curious.
If alice is not generous or quiet then susan is either not rich or not brave and vice versa.
If alice is both not patient and kind then someone is both not happy and not quiet and vice versa.
Everyone who is both not generous and funny is either not quiet or not humble.
If john is both not wise and curious then someone is both not quiet and not happy and vice versa.
John is not creative or generous.
Someone is both not quiet and tall.
Someone is not rich or not patient.
Someone is strong or quiet.
Someone is not tall.
Someone is humble. | John is not rich. | neutral | (![X]:((~happy(X)|~funny(X))=>(quiet(X)&~kind(X))))&
(![X]:((wise(X)|~brave(X))=>(tall(X)|~rich(X))))&
(![X]:((~curious(X)&patient(X))<=>(patient(X)&curious(X))))&
(((~happy(paul)|~curious(paul)))=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:((~creative(X)<~>~generous(X))=>(~strong(X)|generous(X))))&
(![X]:((brave(X)<~>~wise(X))=>(~kind(X)|funny(X))))&
(![X]:((strong(X)|funny(X))<=>(~curious(X)<~>~happy(X))))&
((?[X]:(wise(X)))<=>((funny(susan)|generous(susan))))&
(![X]:((~creative(X)<~>humble(X))=>(~strong(X)|curious(X))))&
(((~calm(paul)&~patient(paul)))<=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)<~>~happy(X))))<=>((~funny(fred)|~happy(fred))))&
(![X]:((~generous(X)|~strong(X))=>(~calm(X)<~>curious(X))))&
(((~generous(alice)|quiet(alice)))<=>((~rich(susan)<~>~brave(susan))))&
(((~patient(alice)&kind(alice)))<=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:((~generous(X)&funny(X))=>(~quiet(X)<~>~humble(X))))&
(((~wise(john)&curious(john)))<=>(?[X]:((~quiet(X)&~happy(X)))))&
((~creative(john)|generous(john)))&
(?[X]:((~quiet(X)&tall(X))))&
(?[X]:((~rich(X)|~patient(X))))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:(~tall(X)))&
(?[X]:(humble(X))) | ~rich(john) | [] | null | 0 |
Everyone who is quiet is both not patient and quiet. Everyone who is calm is quiet. If alice is strong then paul is either calm or not funny and vice versa. Everyone who is both not tall and rich is both kind and patient. If mary is not generous then fred is calm. Everyone who is both not calm and patient is brave. Everyone who is either not old or old is funny or not generous. Everyone who is not curious is patient. If lucy is rich then someone is patient. If someone is not humble then lucy is both not happy and tall and vice versa. Everyone who is not calm is patient and vice versa. Everyone who is either tall or not happy is not tall or not patient and vice versa. If john is not wise then someone is not patient. Everyone who is not creative is either not calm or not wise. If lucy is curious then alice is not patient and vice versa. Everyone who is both not patient and not tall is generous or not curious and vice versa. Lucy is either creative or not wise. Someone is quiet or tall. Fred is either calm or kind. Fred is not rich or not creative. Alice is not funny. Someone is both strong and curious. Fred is both not happy and strong. | Lucy is wise. | neutral | (![X]:(quiet(X)=>(~patient(X)&quiet(X))))&
(![X]:(calm(X)=>quiet(X)))&
((strong(alice))<=>((calm(paul)<~>~funny(paul))))&
(![X]:((~tall(X)&rich(X))=>(kind(X)&patient(X))))&
((~generous(mary))=>(calm(fred)))&
(![X]:((~calm(X)&patient(X))=>brave(X)))&
(![X]:((~old(X)<~>old(X))=>(funny(X)|~generous(X))))&
(![X]:(~curious(X)=>patient(X)))&
((rich(lucy))=>(?[X]:(patient(X))))&
((?[X]:(~humble(X)))<=>((~happy(lucy)&tall(lucy))))&
(![X]:(~calm(X)<=>patient(X)))&
(![X]:((tall(X)<~>~happy(X))<=>(~tall(X)|~patient(X))))&
((~wise(john))=>(?[X]:(~patient(X))))&
(![X]:(~creative(X)=>(~calm(X)<~>~wise(X))))&
((curious(lucy))<=>(~patient(alice)))&
(![X]:((~patient(X)&~tall(X))<=>(generous(X)|~curious(X))))&
((creative(lucy)<~>~wise(lucy)))&
(?[X]:((quiet(X)|tall(X))))&
((calm(fred)<~>kind(fred)))&
((~rich(fred)|~creative(fred)))&
(~funny(alice))&
(?[X]:((strong(X)&curious(X))))&
((~happy(fred)&strong(fred))) | wise(lucy) | [] | null | 0 |
If paul is either happy or not quiet then lucy is rich or tall and vice versa.
Everyone who is either not humble or not strong is either calm or not old.
Everyone who is either not generous or rich is not old or not patient.
Everyone who is both funny and not funny is humble or not curious and vice versa.
If mary is strong or not creative then someone is either not patient or not generous and vice versa.
Everyone who is both not old and not calm is creative and vice versa.
Everyone who is both calm and wise is happy.
Everyone who is not tall is both funny and curious and vice versa.
Everyone who is either not humble or not patient is tall.
If susan is both not happy and brave then someone is old or not rich.
Everyone who is not tall or funny is either generous or not rich and vice versa.
Everyone who is calm is both generous and not old and vice versa.
Everyone who is either strong or not quiet is rich or kind and vice versa.
Everyone who is either kind or humble is creative or not patient and vice versa.
If john is kind then susan is not kind or calm.
Everyone who is tall is both quiet and tall and vice versa.
Lucy is strong.
Susan is both not funny and old.
Someone is strong.
Someone is both funny and not quiet.
Someone is not funny.
Someone is not wise or not brave.
Paul is both not kind and brave. | Paul is not strong. | entailment | (((happy(paul)<~>~quiet(paul)))<=>((rich(lucy)|tall(lucy))))&
(![X]:((~humble(X)<~>~strong(X))=>(calm(X)<~>~old(X))))&
(![X]:((~generous(X)<~>rich(X))=>(~old(X)|~patient(X))))&
(![X]:((funny(X)&~funny(X))<=>(humble(X)|~curious(X))))&
(((strong(mary)|~creative(mary)))<=>(?[X]:((~patient(X)<~>~generous(X)))))&
(![X]:((~old(X)&~calm(X))<=>creative(X)))&
(![X]:((calm(X)&wise(X))=>happy(X)))&
(![X]:(~tall(X)<=>(funny(X)&curious(X))))&
(![X]:((~humble(X)<~>~patient(X))=>tall(X)))&
(((~happy(susan)&brave(susan)))=>(?[X]:((old(X)|~rich(X)))))&
(![X]:((~tall(X)|funny(X))<=>(generous(X)<~>~rich(X))))&
(![X]:(calm(X)<=>(generous(X)&~old(X))))&
(![X]:((strong(X)<~>~quiet(X))<=>(rich(X)|kind(X))))&
(![X]:((kind(X)<~>humble(X))<=>(creative(X)|~patient(X))))&
((kind(john))=>((~kind(susan)|calm(susan))))&
(![X]:(tall(X)<=>(quiet(X)&tall(X))))&
(strong(lucy))&
((~funny(susan)&old(susan)))&
(?[X]:(strong(X)))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~wise(X)|~brave(X))))&
((~kind(paul)&brave(paul))) | ~strong(paul) | [
"p1",
"p2",
"p3",
"p5",
"p8",
"p11",
"p12",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3074646624818222980708055
% SZS output start Proof for 3074646624818222980708055
2. ! [X0] : ((~humble(X0) <~> ~strong(X0)) => (calm(X0) <~> ~old(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> rich(X0)) => (~patient(X0) | ~old(X0))) [input p2]
4. ! [X0] : ((~funny(X0) & funny(X0)) <=> (~curious(X0) | humble(X0))) [input p3]
6. ! [X0] : ((~calm(X0) & ~old(X0)) <=> creative(X0)) [input p5]
9. ! [X0] : ((~humble(X0) <~> ~patient(X0)) => tall(X0)) [input p8]
12. ! [X0] : (calm(X0) <=> (~old(X0) & generous(X0))) [input p11]
13. ! [X0] : ((strong(X0) <~> ~quiet(X0)) <=> (kind(X0) | rich(X0))) [input p12]
14. ! [X0] : ((kind(X0) <~> humble(X0)) <=> (~patient(X0) | creative(X0))) [input p13]
16. ! [X0] : (tall(X0) <=> (tall(X0) & quiet(X0))) [input p15]
23. brave(paul) & ~kind(paul) [input p22]
24. strong(paul) [input hypothesis]
27. ! [X0] : ((calm(X0) <~> ~old(X0)) | (~humble(X0) <=> ~strong(X0))) [ennf transformation 2]
28. ! [X0] : ((~patient(X0) | ~old(X0)) | (~generous(X0) <=> rich(X0))) [ennf transformation 3]
29. ! [X0] : (~patient(X0) | ~old(X0) | (~generous(X0) <=> rich(X0))) [flattening 28]
30. ! [X0] : (tall(X0) | (~humble(X0) <=> ~patient(X0))) [ennf transformation 9]
37. ! [X0] : (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) [nnf transformation 27]
38. ! [X0] : (~patient(X0) | ~old(X0) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) [nnf transformation 29]
39. ! [X0] : (((~funny(X0) & funny(X0)) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | (funny(X0) | ~funny(X0)))) [nnf transformation 4]
40. ! [X0] : (((~funny(X0) & funny(X0)) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | funny(X0) | ~funny(X0))) [flattening 39]
46. ! [X0] : (((~calm(X0) & ~old(X0)) | ~creative(X0)) & (creative(X0) | (calm(X0) | old(X0)))) [nnf transformation 6]
47. ! [X0] : (((~calm(X0) & ~old(X0)) | ~creative(X0)) & (creative(X0) | calm(X0) | old(X0))) [flattening 46]
50. ! [X0] : (tall(X0) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) [nnf transformation 30]
55. ! [X0] : ((calm(X0) | (old(X0) | ~generous(X0))) & ((~old(X0) & generous(X0)) | ~calm(X0))) [nnf transformation 12]
56. ! [X0] : ((calm(X0) | old(X0) | ~generous(X0)) & ((~old(X0) & generous(X0)) | ~calm(X0))) [flattening 55]
57. ! [X0] : ((((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (~kind(X0) & ~rich(X0))) & ((kind(X0) | rich(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0))))) [nnf transformation 13]
58. ! [X0] : ((((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (~kind(X0) & ~rich(X0))) & (kind(X0) | rich(X0) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0))))) [flattening 57]
59. ! [X0] : ((((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0))))) [nnf transformation 14]
60. ! [X0] : ((((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0))))) [flattening 59]
61. ! [X0] : ((tall(X0) | (~tall(X0) | ~quiet(X0))) & ((tall(X0) & quiet(X0)) | ~tall(X0))) [nnf transformation 16]
62. ! [X0] : ((tall(X0) | ~tall(X0) | ~quiet(X0)) & ((tall(X0) & quiet(X0)) | ~tall(X0))) [flattening 61]
75. ~old(X0) | calm(X0) | ~strong(X0) | humble(X0) [cnf transformation 37]
77. ~calm(X0) | old(X0) | ~strong(X0) | humble(X0) [cnf transformation 37]
80. ~patient(X0) | ~old(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 38]
82. funny(X0) | ~humble(X0) [cnf transformation 40]
84. ~funny(X0) | ~humble(X0) [cnf transformation 40]
92. creative(X0) | calm(X0) | old(X0) [cnf transformation 47]
98. tall(X0) | ~patient(X0) | humble(X0) [cnf transformation 50]
107. ~calm(X0) | generous(X0) [cnf transformation 56]
110. ~strong(X0) | rich(X0) | ~quiet(X0) | kind(X0) [cnf transformation 58]
118. humble(X0) | kind(X0) | ~creative(X0) [cnf transformation 60]
119. humble(X0) | kind(X0) | patient(X0) [cnf transformation 60]
123. ~tall(X0) | quiet(X0) [cnf transformation 62]
133. ~kind(paul) [cnf transformation 23]
135. strong(paul) [cnf transformation 24]
145. 3 <=> quiet(paul) [avatar definition]
147. quiet(paul) <- (3) [avatar component clause 145]
159. ~humble(X0) [subsumption resolution 82,84]
189. ~patient(X0) | tall(X0) [subsumption resolution 98,159]
209. kind(X0) | patient(X0) [subsumption resolution 119,159]
210. ~creative(X0) | kind(X0) [subsumption resolution 118,159]
239. patient(paul) [resolution 209,133]
241. tall(paul) [resolution 239,189]
246. kind(X0) | old(X0) | calm(X0) [resolution 92,210]
249. quiet(paul) [resolution 241,123]
252. 3 [avatar split clause 249,145]
296. 23 <=> calm(paul) [avatar definition]
297. ~calm(paul) <- (~23) [avatar component clause 296]
298. calm(paul) <- (23) [avatar component clause 296]
300. 24 <=> old(paul) [avatar definition]
301. ~old(paul) <- (~24) [avatar component clause 300]
302. old(paul) <- (24) [avatar component clause 300]
395. ~old(paul) | ~generous(paul) | ~rich(paul) [resolution 80,239]
399. rich(paul) | ~quiet(paul) | kind(paul) [resolution 110,135]
410. rich(paul) | kind(paul) <- (3) [subsumption resolution 399,147]
411. rich(paul) <- (3) [subsumption resolution 410,133]
412. ~old(paul) | ~generous(paul) <- (3) [subsumption resolution 395,411]
414. 38 <=> generous(paul) [avatar definition]
417. ~38 | ~24 | ~3 [avatar split clause 412,145,300,414]
461. old(paul) | calm(paul) [resolution 246,133]
505. old(paul) | ~strong(paul) | humble(paul) <- (23) [resolution 298,77]
506. generous(paul) <- (23) [resolution 298,107]
507. ~strong(paul) | humble(paul) <- (23, ~24) [subsumption resolution 505,301]
508. humble(paul) <- (23, ~24) [subsumption resolution 507,135]
509. $false <- (23, ~24) [subsumption resolution 508,159]
510. ~23 | 24 [avatar contradiction clause 509]
511. 38 | ~23 [avatar split clause 506,296,414]
514. old(paul) <- (~23) [subsumption resolution 461,297]
515. 24 | 23 [avatar split clause 514,296,300]
522. calm(paul) | ~strong(paul) | humble(paul) <- (24) [resolution 302,75]
524. ~strong(paul) | humble(paul) <- (~23, 24) [subsumption resolution 522,297]
525. humble(paul) <- (~23, 24) [subsumption resolution 524,135]
526. $false <- (~23, 24) [subsumption resolution 525,159]
527. 23 | ~24 [avatar contradiction clause 526]
528. $false [avatar sat refutation 252,417,510,511,515,527]
% SZS output end Proof for 3074646624818222980708055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not quiet or not strong then lucy is calm. If someone is both calm and rich then susan is not strong or not rich. Everyone who is both not strong and not funny is not creative. Everyone who is either not patient or not brave is either not funny or brave. Everyone who is not old is humble. If mary is not kind then alice is both strong and creative and vice versa. Everyone who is either not kind or not brave is either rich or not curious and vice versa. If susan is tall or not old then fred is both not happy and wise. Everyone who is either curious or funny is generous or not tall. Everyone who is both not happy and patient is not curious. If mary is calm then alice is not brave and vice versa. If someone is either curious or not wise then someone is not brave and vice versa. If someone is kind or not brave then someone is humble or not calm. Everyone who is not generous is not funny. If someone is funny then mary is either not kind or creative and vice versa. Everyone who is creative or kind is both not curious and quiet. Paul is both not happy and not patient. Lucy is not rich. Someone is curious. Someone is generous. Fred is old. Someone is either not rich or patient. Someone is not calm or not old. | Susan is strong. | neutral | (((~quiet(alice)<~>~strong(alice)))=>(calm(lucy)))&
((?[X]:((calm(X)&rich(X))))=>((~strong(susan)|~rich(susan))))&
(![X]:((~strong(X)&~funny(X))=>~creative(X)))&
(![X]:((~patient(X)<~>~brave(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~old(X)=>humble(X)))&
((~kind(mary))<=>((strong(alice)&creative(alice))))&
(![X]:((~kind(X)<~>~brave(X))<=>(rich(X)<~>~curious(X))))&
(((tall(susan)|~old(susan)))=>((~happy(fred)&wise(fred))))&
(![X]:((curious(X)<~>funny(X))=>(generous(X)|~tall(X))))&
(![X]:((~happy(X)&patient(X))=>~curious(X)))&
((calm(mary))<=>(~brave(alice)))&
((?[X]:((curious(X)<~>~wise(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((kind(X)|~brave(X))))=>(?[X]:((humble(X)|~calm(X)))))&
(![X]:(~generous(X)=>~funny(X)))&
((?[X]:(funny(X)))<=>((~kind(mary)<~>creative(mary))))&
(![X]:((creative(X)|kind(X))=>(~curious(X)&quiet(X))))&
((~happy(paul)&~patient(paul)))&
(~rich(lucy))&
(?[X]:(curious(X)))&
(?[X]:(generous(X)))&
(old(fred))&
(?[X]:((~rich(X)<~>patient(X))))&
(?[X]:((~calm(X)|~old(X)))) | strong(susan) | [] | null | 0 |
Everyone who is funny or calm is either not calm or not curious. Everyone who is calm is either curious or rich. Everyone who is either brave or not generous is old and vice versa. If someone is either not kind or curious then someone is not creative and vice versa. Everyone who is not curious or creative is either not calm or calm. If someone is either generous or not brave then mary is both not creative and tall. If john is both kind and not wise then someone is kind. If john is either not wise or not kind then someone is happy and vice versa. If someone is both not kind and rich then lucy is both patient and not kind. If fred is either not strong or strong then someone is either not patient or not funny and vice versa. If alice is not strong then lucy is not wise and vice versa. Everyone who is rich is both not funny and not wise. Everyone who is both not generous and brave is either kind or not curious. Everyone who is both not happy and curious is either not patient or not creative and vice versa. If someone is not brave or strong then lucy is both humble and not calm. Everyone who is either not curious or funny is both quiet and rich. Someone is not tall. Someone is not creative. Someone is brave. Someone is both creative and brave. Someone is not funny. Someone is not wise or not creative. Susan is both wise and generous. Someone is not brave. | Lucy is not humble. | contradiction | (![X]:((funny(X)|calm(X))=>(~calm(X)<~>~curious(X))))&
(![X]:(calm(X)=>(curious(X)<~>rich(X))))&
(![X]:((brave(X)<~>~generous(X))<=>old(X)))&
((?[X]:((~kind(X)<~>curious(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)|creative(X))=>(~calm(X)<~>calm(X))))&
((?[X]:((generous(X)<~>~brave(X))))=>((~creative(mary)&tall(mary))))&
(((kind(john)&~wise(john)))=>(?[X]:(kind(X))))&
(((~wise(john)<~>~kind(john)))<=>(?[X]:(happy(X))))&
((?[X]:((~kind(X)&rich(X))))=>((patient(lucy)&~kind(lucy))))&
(((~strong(fred)<~>strong(fred)))<=>(?[X]:((~patient(X)<~>~funny(X)))))&
((~strong(alice))<=>(~wise(lucy)))&
(![X]:(rich(X)=>(~funny(X)&~wise(X))))&
(![X]:((~generous(X)&brave(X))=>(kind(X)<~>~curious(X))))&
(![X]:((~happy(X)&curious(X))<=>(~patient(X)<~>~creative(X))))&
((?[X]:((~brave(X)|strong(X))))=>((humble(lucy)&~calm(lucy))))&
(![X]:((~curious(X)<~>funny(X))=>(quiet(X)&rich(X))))&
(?[X]:(~tall(X)))&
(?[X]:(~creative(X)))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)&brave(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~wise(X)|~creative(X))))&
((wise(susan)&generous(susan)))&
(?[X]:(~brave(X))) | ~humble(lucy) | [
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6218589840568764804237539
% SZS output start Proof for 6218589840568764804237539
15. ? [X0] : (strong(X0) | ~brave(X0)) => (~calm(lucy) & humble(lucy)) [input p14]
24. ? [X0] : ~brave(X0) [input p23]
25. ~humble(lucy) [input hypothesis]
38. (~calm(lucy) & humble(lucy)) | ! [X0] : (~strong(X0) & brave(X0)) [ennf transformation 15]
76. ? [X0] : ~brave(X0) => ~brave(sK11) [choice axiom]
77. ~brave(sK11) [skolemisation 24,76]
123. humble(lucy) | brave(X0) [cnf transformation 38]
138. ~brave(sK11) [cnf transformation 77]
139. ~humble(lucy) [cnf transformation 25]
261. 26 <=> ! [X0] : brave(X0) [avatar definition]
262. brave(X0) <- (26) [avatar component clause 261]
265. 27 <=> humble(lucy) [avatar definition]
269. 26 | 27 [avatar split clause 123,265,261]
280. ~27 [avatar split clause 139,265]
282. $false <- (26) [resolution 262,138]
283. ~26 [avatar contradiction clause 282]
284. $false [avatar sat refutation 269,280,283]
% SZS output end Proof for 6218589840568764804237539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If mary is quiet then lucy is not calm and vice versa.
If someone is not old then susan is either funny or not funny and vice versa.
If someone is not tall then someone is quiet or not creative and vice versa.
If someone is not patient then john is either not happy or old.
Everyone who is both not tall and old is not calm and vice versa.
Everyone who is not humble is kind.
Everyone who is both generous and not funny is either not patient or quiet.
Everyone who is both not quiet and curious is both happy and not quiet and vice versa.
If someone is either rich or creative then someone is either not tall or old and vice versa.
Everyone who is curious is both funny and not patient.
Everyone who is both creative and not tall is not calm or not kind.
If someone is strong then susan is not funny or patient.
If someone is not curious then mary is not creative or not rich.
If someone is both creative and not funny then fred is generous.
Everyone who is both not humble and not calm is patient and vice versa.
Everyone who is not patient or not curious is not creative.
Lucy is not tall.
Someone is both not curious and brave.
Someone is not brave.
Fred is either not funny or not rich.
Lucy is not brave.
Susan is not patient.
Someone is either rich or not humble.
Susan is either not happy or kind. | Lucy is calm. | neutral | ((quiet(mary))<=>(~calm(lucy)))&
((?[X]:(~old(X)))<=>((funny(susan)<~>~funny(susan))))&
((?[X]:(~tall(X)))<=>(?[X]:((quiet(X)|~creative(X)))))&
((?[X]:(~patient(X)))=>((~happy(john)<~>old(john))))&
(![X]:((~tall(X)&old(X))<=>~calm(X)))&
(![X]:(~humble(X)=>kind(X)))&
(![X]:((generous(X)&~funny(X))=>(~patient(X)<~>quiet(X))))&
(![X]:((~quiet(X)&curious(X))<=>(happy(X)&~quiet(X))))&
((?[X]:((rich(X)<~>creative(X))))<=>(?[X]:((~tall(X)<~>old(X)))))&
(![X]:(curious(X)=>(funny(X)&~patient(X))))&
(![X]:((creative(X)&~tall(X))=>(~calm(X)|~kind(X))))&
((?[X]:(strong(X)))=>((~funny(susan)|patient(susan))))&
((?[X]:(~curious(X)))=>((~creative(mary)|~rich(mary))))&
((?[X]:((creative(X)&~funny(X))))=>(generous(fred)))&
(![X]:((~humble(X)&~calm(X))<=>patient(X)))&
(![X]:((~patient(X)|~curious(X))=>~creative(X)))&
(~tall(lucy))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:(~brave(X)))&
((~funny(fred)<~>~rich(fred)))&
(~brave(lucy))&
(~patient(susan))&
(?[X]:((rich(X)<~>~humble(X))))&
((~happy(susan)<~>kind(susan))) | calm(lucy) | [] | null | 0 |
Everyone who is not patient or not curious is wise or rich and vice versa.
Everyone who is either quiet or not calm is wise and vice versa.
If paul is curious or not calm then alice is either not wise or kind.
Everyone who is not generous or not humble is old.
Everyone who is both not strong and not rich is either not quiet or not brave.
Everyone who is either not happy or not strong is both tall and not strong.
Everyone who is calm is either funny or creative and vice versa.
If susan is both patient and not tall then someone is both curious and quiet.
If someone is kind or not old then someone is either generous or not funny and vice versa.
Everyone who is not old is either not humble or funny and vice versa.
If someone is quiet then someone is either not calm or not funny.
If someone is not creative then someone is old or generous and vice versa.
Everyone who is either creative or not creative is either kind or not patient and vice versa.
Everyone who is not tall or not patient is either old or not tall and vice versa.
Everyone who is curious is tall or curious.
If someone is both not kind and curious then someone is either tall or not generous.
Lucy is funny.
Fred is either kind or not quiet.
Someone is both creative and not old.
Someone is creative.
Someone is both not generous and not strong.
Lucy is not happy or humble.
Lucy is both curious and happy.
Someone is humble. | Lucy is not humble. | contradiction | (![X]:((~patient(X)|~curious(X))<=>(wise(X)|rich(X))))&
(![X]:((quiet(X)<~>~calm(X))<=>wise(X)))&
(((curious(paul)|~calm(paul)))=>((~wise(alice)<~>kind(alice))))&
(![X]:((~generous(X)|~humble(X))=>old(X)))&
(![X]:((~strong(X)&~rich(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>~strong(X))=>(tall(X)&~strong(X))))&
(![X]:(calm(X)<=>(funny(X)<~>creative(X))))&
(((patient(susan)&~tall(susan)))=>(?[X]:((curious(X)&quiet(X)))))&
((?[X]:((kind(X)|~old(X))))<=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:(~old(X)<=>(~humble(X)<~>funny(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)<~>~funny(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((old(X)|generous(X)))))&
(![X]:((creative(X)<~>~creative(X))<=>(kind(X)<~>~patient(X))))&
(![X]:((~tall(X)|~patient(X))<=>(old(X)<~>~tall(X))))&
(![X]:(curious(X)=>(tall(X)|curious(X))))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:((tall(X)<~>~generous(X)))))&
(funny(lucy))&
((kind(fred)<~>~quiet(fred)))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:(creative(X)))&
(?[X]:((~generous(X)&~strong(X))))&
((~happy(lucy)|humble(lucy)))&
((curious(lucy)&happy(lucy)))&
(?[X]:(humble(X))) | ~humble(lucy) | [
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6454720996365144675997392
% SZS output start Proof for 6454720996365144675997392
22. humble(lucy) | ~happy(lucy) [input p21]
23. happy(lucy) & curious(lucy) [input p22]
25. ~humble(lucy) [input hypothesis]
147. humble(lucy) | ~happy(lucy) [cnf transformation 22]
149. happy(lucy) [cnf transformation 23]
151. ~humble(lucy) [cnf transformation 25]
284. 28 <=> happy(lucy) [avatar definition]
288. 29 <=> humble(lucy) [avatar definition]
291. ~28 | 29 [avatar split clause 147,288,284]
292. 28 [avatar split clause 149,284]
293. ~29 [avatar split clause 151,288]
294. $false [avatar sat refutation 291,292,293]
% SZS output end Proof for 6454720996365144675997392
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and funny then john is either creative or not brave. If mary is patient or wise then paul is creative. Everyone who is both calm and patient is not humble and vice versa. Everyone who is either old or not humble is not quiet or not curious. If someone is generous then someone is both creative and strong and vice versa. Everyone who is both strong and calm is both not calm and not humble. If susan is both not humble and rich then john is not kind and vice versa. If someone is quiet or patient then lucy is calm and vice versa. If someone is either curious or wise then someone is either patient or brave. If someone is not strong or quiet then john is both not happy and funny. Everyone who is either wise or not happy is either not strong or strong and vice versa. Everyone who is not creative is either not quiet or not kind. If paul is both old and not strong then someone is not kind or not patient and vice versa. If someone is tall or not funny then lucy is humble and vice versa. Everyone who is either not strong or generous is calm. Everyone who is both kind and not calm is generous. Someone is both humble and generous. Mary is both humble and not patient. Paul is both funny and generous. Fred is either not patient or not creative. Fred is not generous or creative. John is not creative. Alice is creative. Fred is both happy and not generous. | John is not funny. | contradiction | ((?[X]:((strong(X)&funny(X))))=>((creative(john)<~>~brave(john))))&
(((patient(mary)|wise(mary)))=>(creative(paul)))&
(![X]:((calm(X)&patient(X))<=>~humble(X)))&
(![X]:((old(X)<~>~humble(X))=>(~quiet(X)|~curious(X))))&
((?[X]:(generous(X)))<=>(?[X]:((creative(X)&strong(X)))))&
(![X]:((strong(X)&calm(X))=>(~calm(X)&~humble(X))))&
(((~humble(susan)&rich(susan)))<=>(~kind(john)))&
((?[X]:((quiet(X)|patient(X))))<=>(calm(lucy)))&
((?[X]:((curious(X)<~>wise(X))))=>(?[X]:((patient(X)<~>brave(X)))))&
((?[X]:((~strong(X)|quiet(X))))=>((~happy(john)&funny(john))))&
(![X]:((wise(X)<~>~happy(X))<=>(~strong(X)<~>strong(X))))&
(![X]:(~creative(X)=>(~quiet(X)<~>~kind(X))))&
(((old(paul)&~strong(paul)))<=>(?[X]:((~kind(X)|~patient(X)))))&
((?[X]:((tall(X)|~funny(X))))<=>(humble(lucy)))&
(![X]:((~strong(X)<~>generous(X))=>calm(X)))&
(![X]:((kind(X)&~calm(X))=>generous(X)))&
(?[X]:((humble(X)&generous(X))))&
((humble(mary)&~patient(mary)))&
((funny(paul)&generous(paul)))&
((~patient(fred)<~>~creative(fred)))&
((~generous(fred)|creative(fred)))&
(~creative(john))&
(creative(alice))&
((happy(fred)&~generous(fred))) | ~funny(john) | [
"p9",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2567766057262975432649819
% SZS output start Proof for 2567766057262975432649819
10. ? [X0] : (quiet(X0) | ~strong(X0)) => (funny(john) & ~happy(john)) [input p9]
13. (~strong(paul) & old(paul)) <=> ? [X0] : (~patient(X0) | ~kind(X0)) [input p12]
18. ~patient(mary) & humble(mary) [input p17]
25. ~funny(john) [input hypothesis]
35. (funny(john) & ~happy(john)) | ! [X0] : (~quiet(X0) & strong(X0)) [ennf transformation 10]
61. ((~strong(paul) & old(paul)) | ! [X0] : (patient(X0) & kind(X0))) & (? [X0] : (~patient(X0) | ~kind(X0)) | (strong(paul) | ~old(paul))) [nnf transformation 13]
62. ((~strong(paul) & old(paul)) | ! [X0] : (patient(X0) & kind(X0))) & (? [X0] : (~patient(X0) | ~kind(X0)) | strong(paul) | ~old(paul)) [flattening 61]
63. ((~strong(paul) & old(paul)) | ! [X0] : (patient(X0) & kind(X0))) & (? [X1] : (~patient(X1) | ~kind(X1)) | strong(paul) | ~old(paul)) [rectify 62]
64. ? [X1] : (~patient(X1) | ~kind(X1)) => (~patient(sK4) | ~kind(sK4)) [choice axiom]
65. ((~strong(paul) & old(paul)) | ! [X0] : (patient(X0) & kind(X0))) & ((~patient(sK4) | ~kind(sK4)) | strong(paul) | ~old(paul)) [skolemisation 63,64]
100. funny(john) | strong(X0) [cnf transformation 35]
116. ~strong(paul) | patient(X0) [cnf transformation 65]
126. ~patient(mary) [cnf transformation 18]
136. ~funny(john) [cnf transformation 25]
165. 6 <=> patient(mary) [avatar definition]
167. ~patient(mary) <- (~6) [avatar component clause 165]
245. 24 <=> funny(john) [avatar definition]
250. 25 <=> ! [X0] : strong(X0) [avatar definition]
251. strong(X0) <- (25) [avatar component clause 250]
252. 25 | 24 [avatar split clause 100,245,250]
262. 27 <=> ! [X0] : patient(X0) [avatar definition]
263. patient(X0) <- (27) [avatar component clause 262]
265. 28 <=> strong(paul) [avatar definition]
267. ~strong(paul) <- (~28) [avatar component clause 265]
268. 27 | ~28 [avatar split clause 116,265,262]
310. ~6 [avatar split clause 126,165]
328. ~24 [avatar split clause 136,245]
332. $false <- (~6, 27) [subsumption resolution 167,263]
333. 6 | ~27 [avatar contradiction clause 332]
334. $false <- (25, ~28) [subsumption resolution 267,251]
335. ~25 | 28 [avatar contradiction clause 334]
336. $false [avatar sat refutation 252,268,310,328,333,335]
% SZS output end Proof for 2567766057262975432649819
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is not old or generous then someone is patient or not strong and vice versa.
Everyone who is generous or funny is both not humble and patient and vice versa.
Everyone who is either curious or not generous is not curious and vice versa.
Everyone who is both not rich and not patient is either patient or not curious.
If someone is calm or not creative then alice is not brave.
Everyone who is not strong or not curious is either funny or not curious and vice versa.
If mary is both not kind and not humble then someone is not rich and vice versa.
Everyone who is both not humble and not rich is not strong and vice versa.
If lucy is either quiet or not humble then mary is either old or generous and vice versa.
If someone is either not calm or kind then john is tall or not rich.
If john is happy or strong then someone is both not calm and wise and vice versa.
If someone is either wise or patient then fred is not kind.
If someone is not old then someone is either not patient or not wise.
Everyone who is both brave and not wise is not brave or not kind and vice versa.
Everyone who is not wise or not brave is quiet or calm.
Someone is not funny.
Someone is not tall or not curious.
Mary is not tall or funny.
Someone is either patient or not humble.
Lucy is either not funny or wise.
Someone is tall or not tall. | Fred is not calm. | entailment | (((~old(john)|generous(john)))<=>(?[X]:((patient(X)|~strong(X)))))&
(![X]:((generous(X)|funny(X))<=>(~humble(X)&patient(X))))&
(![X]:((curious(X)<~>~generous(X))<=>~curious(X)))&
(![X]:((~rich(X)&~patient(X))=>(patient(X)<~>~curious(X))))&
((?[X]:((calm(X)|~creative(X))))=>(~brave(alice)))&
(![X]:((~strong(X)|~curious(X))<=>(funny(X)<~>~curious(X))))&
(((~kind(mary)&~humble(mary)))<=>(?[X]:(~rich(X))))&
(![X]:((~humble(X)&~rich(X))<=>~strong(X)))&
(((quiet(lucy)<~>~humble(lucy)))<=>((old(mary)<~>generous(mary))))&
((?[X]:((~calm(X)<~>kind(X))))=>((tall(john)|~rich(john))))&
(((happy(john)|strong(john)))<=>(?[X]:((~calm(X)&wise(X)))))&
((?[X]:((wise(X)<~>patient(X))))=>(~kind(fred)))&
((?[X]:(~old(X)))=>(?[X]:((~patient(X)<~>~wise(X)))))&
(![X]:((brave(X)&~wise(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~wise(X)|~brave(X))=>(quiet(X)|calm(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~tall(X)|~curious(X))))&
((~tall(mary)|funny(mary)))&
(?[X]:((patient(X)<~>~humble(X))))&
((~funny(lucy)<~>wise(lucy)))&
(?[X]:((tall(X)|~tall(X)))) | ~calm(fred) | [
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4249591175571127348163451
% SZS output start Proof for 4249591175571127348163451
5. ? [X0] : (~creative(X0) | calm(X0)) => ~brave(alice) [input p4]
14. ! [X0] : ((~wise(X0) & brave(X0)) <=> (~kind(X0) | ~brave(X0))) [input p13]
22. calm(fred) [input hypothesis]
24. ? [X0] : calm(X0) => ~brave(alice) [pure predicate removal 5]
27. ~brave(alice) | ! [X0] : ~calm(X0) [ennf transformation 24]
64. ! [X0] : (((~wise(X0) & brave(X0)) | (kind(X0) & brave(X0))) & ((~kind(X0) | ~brave(X0)) | (wise(X0) | ~brave(X0)))) [nnf transformation 14]
65. ! [X0] : (((~wise(X0) & brave(X0)) | (kind(X0) & brave(X0))) & (~kind(X0) | ~brave(X0) | wise(X0) | ~brave(X0))) [flattening 64]
91. ~brave(alice) | ~calm(X0) [cnf transformation 27]
124. brave(X0) | brave(X0) [cnf transformation 65]
138. calm(fred) [cnf transformation 22]
140. brave(X0) [duplicate literal removal 124]
174. 7 <=> ! [X0] : ~calm(X0) [avatar definition]
175. ~calm(X0) <- (7) [avatar component clause 174]
177. 8 <=> brave(alice) [avatar definition]
179. ~brave(alice) <- (~8) [avatar component clause 177]
180. 7 | ~8 [avatar split clause 91,177,174]
323. $false <- (~8) [subsumption resolution 179,140]
324. 8 [avatar contradiction clause 323]
327. $false <- (7) [resolution 175,138]
328. ~7 [avatar contradiction clause 327]
329. $false [avatar sat refutation 180,324,328]
% SZS output end Proof for 4249591175571127348163451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and generous is either not generous or rich and vice versa. If someone is either not quiet or not tall then someone is both not tall and not humble. If someone is funny then someone is happy and vice versa. Everyone who is both wise and not rich is funny. Everyone who is humble or not rich is not humble and vice versa. Everyone who is both curious and brave is kind and vice versa. If susan is either not calm or not funny then someone is generous or curious. If susan is not old then alice is calm and vice versa. Everyone who is not old is both calm and not calm and vice versa. Everyone who is either not generous or kind is either rich or happy and vice versa. Everyone who is either not humble or not funny is either curious or not old. Everyone who is patient or creative is not generous. Everyone who is not old or not curious is either patient or not brave and vice versa. Everyone who is both funny and not strong is both humble and calm. If paul is kind or happy then susan is either brave or not patient and vice versa. Alice is old or not brave. Someone is not calm or brave. John is both not quiet and happy. Lucy is not rich. Someone is either happy or creative. Someone is humble or not rich. Alice is happy. John is not old or not wise. | John is kind. | entailment | (![X]:((~strong(X)&generous(X))<=>(~generous(X)<~>rich(X))))&
((?[X]:((~quiet(X)<~>~tall(X))))=>(?[X]:((~tall(X)&~humble(X)))))&
((?[X]:(funny(X)))<=>(?[X]:(happy(X))))&
(![X]:((wise(X)&~rich(X))=>funny(X)))&
(![X]:((humble(X)|~rich(X))<=>~humble(X)))&
(![X]:((curious(X)&brave(X))<=>kind(X)))&
(((~calm(susan)<~>~funny(susan)))=>(?[X]:((generous(X)|curious(X)))))&
((~old(susan))<=>(calm(alice)))&
(![X]:(~old(X)<=>(calm(X)&~calm(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(rich(X)<~>happy(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(curious(X)<~>~old(X))))&
(![X]:((patient(X)|creative(X))=>~generous(X)))&
(![X]:((~old(X)|~curious(X))<=>(patient(X)<~>~brave(X))))&
(![X]:((funny(X)&~strong(X))=>(humble(X)&calm(X))))&
(((kind(paul)|happy(paul)))<=>((brave(susan)<~>~patient(susan))))&
((old(alice)|~brave(alice)))&
(?[X]:((~calm(X)|brave(X))))&
((~quiet(john)&happy(john)))&
(~rich(lucy))&
(?[X]:((happy(X)<~>creative(X))))&
(?[X]:((humble(X)|~rich(X))))&
(happy(alice))&
((~old(john)|~wise(john))) | kind(john) | [
"p0",
"p4",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1551598658421265510891160
% SZS output start Proof for 1551598658421265510891160
1. ! [X0] : ((generous(X0) & ~strong(X0)) <=> (~generous(X0) <~> rich(X0))) [input p0]
5. ! [X0] : ((~rich(X0) | humble(X0)) <=> ~humble(X0)) [input p4]
10. ! [X0] : ((~generous(X0) <~> kind(X0)) <=> (rich(X0) <~> happy(X0))) [input p9]
18. happy(john) & ~quiet(john) [input p17]
24. ~kind(john) [input hypothesis]
35. ! [X0] : (((generous(X0) & ~strong(X0)) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | (~generous(X0) | strong(X0)))) [nnf transformation 1]
36. ! [X0] : (((generous(X0) & ~strong(X0)) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | ~generous(X0) | strong(X0))) [flattening 35]
46. ! [X0] : (((~rich(X0) | humble(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) & ~humble(X0)))) [nnf transformation 5]
47. ! [X0] : ((~rich(X0) | humble(X0) | humble(X0)) & (~humble(X0) | (rich(X0) & ~humble(X0)))) [flattening 46]
56. ! [X0] : ((((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))))) [nnf transformation 10]
69. rich(X0) | ~generous(X0) | ~generous(X0) | strong(X0) [cnf transformation 36]
72. ~rich(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 36]
73. generous(X0) | rich(X0) | generous(X0) [cnf transformation 36]
81. ~humble(X0) | ~humble(X0) [cnf transformation 47]
83. ~rich(X0) | humble(X0) | humble(X0) [cnf transformation 47]
99. kind(X0) | ~generous(X0) | rich(X0) | ~happy(X0) [cnf transformation 56]
125. happy(john) [cnf transformation 18]
131. ~kind(john) [cnf transformation 24]
132. ~humble(X0) [duplicate literal removal 81]
133. ~rich(X0) | humble(X0) [duplicate literal removal 83]
134. rich(X0) | ~generous(X0) | strong(X0) [duplicate literal removal 69]
135. rich(X0) | generous(X0) [duplicate literal removal 73]
136. rich(X0) | strong(X0) [subsumption resolution 134,135]
201. ~happy(X0) | rich(X0) | kind(X0) [subsumption resolution 99,135]
260. generous(X0) | humble(X0) [resolution 135,133]
261. generous(X0) [subsumption resolution 260,132]
263. strong(X0) | humble(X0) [resolution 136,133]
264. strong(X0) [subsumption resolution 263,132]
292. rich(john) | kind(john) [resolution 201,125]
304. rich(john) [subsumption resolution 292,131]
334. ~generous(john) | ~strong(john) [resolution 304,72]
336. ~strong(john) [subsumption resolution 334,261]
337. $false [subsumption resolution 336,264]
% SZS output end Proof for 1551598658421265510891160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either rich or not curious and vice versa. If someone is tall or not funny then fred is both not brave and calm and vice versa. If john is not happy or not curious then someone is not brave or funny and vice versa. If lucy is either calm or happy then mary is either not creative or not tall and vice versa. If alice is either not calm or not humble then someone is either rich or brave. Everyone who is either not quiet or brave is not quiet or creative and vice versa. If alice is rich then susan is either wise or generous. Everyone who is calm or not patient is both rich and not happy and vice versa. Everyone who is not calm is not wise or not humble. Everyone who is not rich or rich is either not tall or brave and vice versa. If mary is both not patient and curious then someone is brave or not old. Everyone who is both funny and not creative is both not curious and not humble and vice versa. Everyone who is not wise is either calm or not tall and vice versa. If someone is brave or rich then fred is strong and vice versa. Everyone who is either not rich or not patient is either patient or not calm and vice versa. If someone is not patient then alice is humble or not humble and vice versa. Paul is either curious or not brave. Someone is not generous. Lucy is happy. Someone is either not old or not wise. Someone is happy or not old. Someone is not wise or not humble. Someone is either not kind or not brave. Alice is tall or humble. | Alice is not old. | neutral | (![X]:(~happy(X)<=>(rich(X)<~>~curious(X))))&
((?[X]:((tall(X)|~funny(X))))<=>((~brave(fred)&calm(fred))))&
(((~happy(john)|~curious(john)))<=>(?[X]:((~brave(X)|funny(X)))))&
(((calm(lucy)<~>happy(lucy)))<=>((~creative(mary)<~>~tall(mary))))&
(((~calm(alice)<~>~humble(alice)))=>(?[X]:((rich(X)<~>brave(X)))))&
(![X]:((~quiet(X)<~>brave(X))<=>(~quiet(X)|creative(X))))&
((rich(alice))=>((wise(susan)<~>generous(susan))))&
(![X]:((calm(X)|~patient(X))<=>(rich(X)&~happy(X))))&
(![X]:(~calm(X)=>(~wise(X)|~humble(X))))&
(![X]:((~rich(X)|rich(X))<=>(~tall(X)<~>brave(X))))&
(((~patient(mary)&curious(mary)))=>(?[X]:((brave(X)|~old(X)))))&
(![X]:((funny(X)&~creative(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~wise(X)<=>(calm(X)<~>~tall(X))))&
((?[X]:((brave(X)|rich(X))))<=>(strong(fred)))&
(![X]:((~rich(X)<~>~patient(X))<=>(patient(X)<~>~calm(X))))&
((?[X]:(~patient(X)))<=>((humble(alice)|~humble(alice))))&
((curious(paul)<~>~brave(paul)))&
(?[X]:(~generous(X)))&
(happy(lucy))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:((happy(X)|~old(X))))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((~kind(X)<~>~brave(X))))&
((tall(alice)|humble(alice))) | ~old(alice) | [] | null | 0 |
If someone is both not kind and rich then lucy is rich.
If someone is creative then susan is curious or happy.
If paul is either not tall or not calm then paul is funny.
Everyone who is either tall or generous is not strong or not creative.
If someone is either happy or tall then fred is both strong and humble and vice versa.
If someone is either not rich or not funny then someone is both creative and not patient.
If susan is either old or not happy then someone is wise or kind and vice versa.
If john is not patient or quiet then alice is not generous or not kind and vice versa.
If mary is not brave then lucy is rich.
Everyone who is both not rich and humble is wise or not generous and vice versa.
Everyone who is both not calm and generous is both kind and not creative.
Everyone who is either not strong or not rich is both not calm and not humble.
If someone is both creative and quiet then fred is quiet and vice versa.
Everyone who is either not humble or not creative is both tall and quiet and vice versa.
Everyone who is not calm or curious is either not humble or curious.
Everyone who is either generous or not creative is not generous or not humble and vice versa.
Someone is both wise and not curious.
Lucy is either not brave or curious.
Someone is curious.
Someone is both not happy and wise.
Lucy is strong.
Paul is either patient or old.
John is either not curious or not humble.
Someone is either wise or calm. | Fred is creative. | contradiction | ((?[X]:((~kind(X)&rich(X))))=>(rich(lucy)))&
((?[X]:(creative(X)))=>((curious(susan)|happy(susan))))&
(((~tall(paul)<~>~calm(paul)))=>(funny(paul)))&
(![X]:((tall(X)<~>generous(X))=>(~strong(X)|~creative(X))))&
((?[X]:((happy(X)<~>tall(X))))<=>((strong(fred)&humble(fred))))&
((?[X]:((~rich(X)<~>~funny(X))))=>(?[X]:((creative(X)&~patient(X)))))&
(((old(susan)<~>~happy(susan)))<=>(?[X]:((wise(X)|kind(X)))))&
(((~patient(john)|quiet(john)))<=>((~generous(alice)|~kind(alice))))&
((~brave(mary))=>(rich(lucy)))&
(![X]:((~rich(X)&humble(X))<=>(wise(X)|~generous(X))))&
(![X]:((~calm(X)&generous(X))=>(kind(X)&~creative(X))))&
(![X]:((~strong(X)<~>~rich(X))=>(~calm(X)&~humble(X))))&
((?[X]:((creative(X)&quiet(X))))<=>(quiet(fred)))&
(![X]:((~humble(X)<~>~creative(X))<=>(tall(X)&quiet(X))))&
(![X]:((~calm(X)|curious(X))=>(~humble(X)<~>curious(X))))&
(![X]:((generous(X)<~>~creative(X))<=>(~generous(X)|~humble(X))))&
(?[X]:((wise(X)&~curious(X))))&
((~brave(lucy)<~>curious(lucy)))&
(?[X]:(curious(X)))&
(?[X]:((~happy(X)&wise(X))))&
(strong(lucy))&
((patient(paul)<~>old(paul)))&
((~curious(john)<~>~humble(john)))&
(?[X]:((wise(X)<~>calm(X)))) | creative(fred) | [
"p4",
"p9",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3018985215843986389318964
% SZS output start Proof for 3018985215843986389318964
5. ? [X0] : (happy(X0) <~> tall(X0)) <=> (humble(fred) & strong(fred)) [input p4]
10. ! [X0] : ((humble(X0) & ~rich(X0)) <=> (~generous(X0) | wise(X0))) [input p9]
14. ! [X0] : ((~humble(X0) <~> ~creative(X0)) <=> (quiet(X0) & tall(X0))) [input p13]
16. ! [X0] : ((generous(X0) <~> ~creative(X0)) <=> (~humble(X0) | ~generous(X0))) [input p15]
20. ? [X0] : (wise(X0) & ~happy(X0)) [input p19]
25. creative(fred) [input hypothesis]
41. (? [X0] : ((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | (~humble(fred) | ~strong(fred))) & ((humble(fred) & strong(fred)) | ! [X0] : ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0)))) [nnf transformation 5]
42. (? [X0] : ((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | ~humble(fred) | ~strong(fred)) & ((humble(fred) & strong(fred)) | ! [X0] : ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0)))) [flattening 41]
43. (? [X0] : ((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | ~humble(fred) | ~strong(fred)) & ((humble(fred) & strong(fred)) | ! [X1] : ((happy(X1) | ~tall(X1)) & (tall(X1) | ~happy(X1)))) [rectify 42]
44. ? [X0] : ((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) => ((~tall(sK0) | ~happy(sK0)) & (tall(sK0) | happy(sK0))) [choice axiom]
45. (((~tall(sK0) | ~happy(sK0)) & (tall(sK0) | happy(sK0))) | ~humble(fred) | ~strong(fred)) & ((humble(fred) & strong(fred)) | ! [X1] : ((happy(X1) | ~tall(X1)) & (tall(X1) | ~happy(X1)))) [skolemisation 43,44]
56. ! [X0] : (((humble(X0) & ~rich(X0)) | (generous(X0) & ~wise(X0))) & ((~generous(X0) | wise(X0)) | (~humble(X0) | rich(X0)))) [nnf transformation 10]
57. ! [X0] : (((humble(X0) & ~rich(X0)) | (generous(X0) & ~wise(X0))) & (~generous(X0) | wise(X0) | ~humble(X0) | rich(X0))) [flattening 56]
63. ! [X0] : ((((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0))))) [nnf transformation 14]
64. ! [X0] : ((((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0))))) [flattening 63]
66. ! [X0] : ((((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | (humble(X0) & generous(X0))) & ((~humble(X0) | ~generous(X0)) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0))))) [nnf transformation 16]
67. ! [X0] : ((((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | (humble(X0) & generous(X0))) & (~humble(X0) | ~generous(X0) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0))))) [flattening 66]
73. ? [X0] : (wise(X0) & ~happy(X0)) => (wise(sK6) & ~happy(sK6)) [choice axiom]
74. wise(sK6) & ~happy(sK6) [skolemisation 20,73]
89. humble(fred) | happy(X1) | ~tall(X1) [cnf transformation 45]
110. ~wise(X0) | humble(X0) [cnf transformation 57]
111. humble(X0) | generous(X0) [cnf transformation 57]
122. ~humble(X0) | tall(X0) | creative(X0) [cnf transformation 64]
131. ~humble(X0) | ~generous(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 67]
133. ~creative(X0) | generous(X0) | generous(X0) [cnf transformation 67]
136. creative(X0) | ~generous(X0) | humble(X0) [cnf transformation 67]
142. ~happy(sK6) [cnf transformation 74]
143. wise(sK6) [cnf transformation 74]
151. creative(fred) [cnf transformation 25]
152. ~humble(X0) | ~generous(X0) | ~creative(X0) [duplicate literal removal 131]
153. ~creative(X0) | generous(X0) [duplicate literal removal 133]
194. 10 <=> humble(fred) [avatar definition]
195. humble(fred) <- (10) [avatar component clause 194]
208. 13 <=> ! [X1] : (happy(X1) | ~tall(X1)) [avatar definition]
209. ~tall(X1) | happy(X1) <- (13) [avatar component clause 208]
210. 13 | 10 [avatar split clause 89,194,208]
302. humble(X0) | creative(X0) [subsumption resolution 136,111]
303. ~humble(X0) | ~creative(X0) [subsumption resolution 152,153]
349. humble(sK6) [resolution 110,143]
358. ~creative(fred) <- (10) [resolution 303,195]
361. ~creative(sK6) [resolution 303,349]
363. $false <- (10) [subsumption resolution 358,151]
364. ~10 [avatar contradiction clause 363]
482. tall(X0) | creative(X0) | creative(X0) [resolution 122,302]
490. tall(X0) | creative(X0) [duplicate literal removal 482]
610. happy(X0) | creative(X0) <- (13) [resolution 490,209]
741. creative(sK6) <- (13) [resolution 610,142]
744. $false <- (13) [subsumption resolution 741,361]
745. ~13 [avatar contradiction clause 744]
748. $false [avatar sat refutation 210,364,745]
% SZS output end Proof for 3018985215843986389318964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either tall or not happy then mary is both tall and funny and vice versa.
If alice is both curious and not happy then susan is both not creative and not rich.
Everyone who is either not happy or happy is not creative.
If susan is either tall or happy then someone is both not kind and strong and vice versa.
If someone is not strong then fred is either generous or not strong and vice versa.
Everyone who is curious is either tall or not curious and vice versa.
If fred is either not curious or not kind then someone is either curious or not generous.
If lucy is both rich and generous then paul is both not quiet and not wise.
If fred is either curious or not funny then paul is both not old and calm.
Everyone who is both not tall and not calm is either generous or quiet and vice versa.
If someone is wise or not wise then paul is either not tall or humble and vice versa.
If someone is brave or not brave then john is tall or curious and vice versa.
If lucy is not quiet then susan is not generous or not rich and vice versa.
If alice is not quiet or generous then mary is wise or kind and vice versa.
Everyone who is curious or not calm is both not humble and tall.
Everyone who is not funny or not brave is not humble.
Susan is either curious or not kind.
Susan is curious.
Fred is either creative or not happy.
Someone is both quiet and not calm.
Susan is old.
John is either wise or not rich. | Paul is kind. | neutral | ((?[X]:((tall(X)<~>~happy(X))))<=>((tall(mary)&funny(mary))))&
(((curious(alice)&~happy(alice)))=>((~creative(susan)&~rich(susan))))&
(![X]:((~happy(X)<~>happy(X))=>~creative(X)))&
(((tall(susan)<~>happy(susan)))<=>(?[X]:((~kind(X)&strong(X)))))&
((?[X]:(~strong(X)))<=>((generous(fred)<~>~strong(fred))))&
(![X]:(curious(X)<=>(tall(X)<~>~curious(X))))&
(((~curious(fred)<~>~kind(fred)))=>(?[X]:((curious(X)<~>~generous(X)))))&
(((rich(lucy)&generous(lucy)))=>((~quiet(paul)&~wise(paul))))&
(((curious(fred)<~>~funny(fred)))=>((~old(paul)&calm(paul))))&
(![X]:((~tall(X)&~calm(X))<=>(generous(X)<~>quiet(X))))&
((?[X]:((wise(X)|~wise(X))))<=>((~tall(paul)<~>humble(paul))))&
((?[X]:((brave(X)|~brave(X))))<=>((tall(john)|curious(john))))&
((~quiet(lucy))<=>((~generous(susan)|~rich(susan))))&
(((~quiet(alice)|generous(alice)))<=>((wise(mary)|kind(mary))))&
(![X]:((curious(X)|~calm(X))=>(~humble(X)&tall(X))))&
(![X]:((~funny(X)|~brave(X))=>~humble(X)))&
((curious(susan)<~>~kind(susan)))&
(curious(susan))&
((creative(fred)<~>~happy(fred)))&
(?[X]:((quiet(X)&~calm(X))))&
(old(susan))&
((wise(john)<~>~rich(john))) | kind(paul) | [] | null | 0 |
If someone is both not humble and humble then paul is calm and vice versa.
Everyone who is both quiet and not wise is not curious or quiet and vice versa.
Everyone who is quiet or humble is not quiet and vice versa.
Everyone who is not generous or not tall is both not rich and kind and vice versa.
If alice is either not brave or not patient then someone is both wise and not generous.
Everyone who is not humble is not funny and vice versa.
If someone is both kind and not happy then susan is both kind and quiet.
Everyone who is brave or not patient is either not curious or not generous and vice versa.
Everyone who is either funny or creative is either curious or not strong and vice versa.
If someone is not kind or quiet then susan is curious or generous.
Everyone who is both creative and curious is brave and vice versa.
Everyone who is not tall is either not kind or rich.
If someone is humble then paul is curious or not happy and vice versa.
If alice is both not tall and not funny then someone is funny.
Everyone who is both not brave and tall is either not patient or not curious.
Someone is wise.
Someone is both not wise and not generous.
Someone is not rich.
Lucy is not creative or brave.
Susan is strong. | Susan is not funny. | contradiction | ((?[X]:((~humble(X)&humble(X))))<=>(calm(paul)))&
(![X]:((quiet(X)&~wise(X))<=>(~curious(X)|quiet(X))))&
(![X]:((quiet(X)|humble(X))<=>~quiet(X)))&
(![X]:((~generous(X)|~tall(X))<=>(~rich(X)&kind(X))))&
(((~brave(alice)<~>~patient(alice)))=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:(~humble(X)<=>~funny(X)))&
((?[X]:((kind(X)&~happy(X))))=>((kind(susan)&quiet(susan))))&
(![X]:((brave(X)|~patient(X))<=>(~curious(X)<~>~generous(X))))&
(![X]:((funny(X)<~>creative(X))<=>(curious(X)<~>~strong(X))))&
((?[X]:((~kind(X)|quiet(X))))=>((curious(susan)|generous(susan))))&
(![X]:((creative(X)&curious(X))<=>brave(X)))&
(![X]:(~tall(X)=>(~kind(X)<~>rich(X))))&
((?[X]:(humble(X)))<=>((curious(paul)|~happy(paul))))&
(((~tall(alice)&~funny(alice)))=>(?[X]:(funny(X))))&
(![X]:((~brave(X)&tall(X))=>(~patient(X)<~>~curious(X))))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)&~generous(X))))&
(?[X]:(~rich(X)))&
((~creative(lucy)|brave(lucy)))&
(strong(susan)) | ~funny(susan) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7870476254306685079490420
% SZS output start Proof for 7870476254306685079490420
3. ! [X0] : ((humble(X0) | quiet(X0)) <=> ~quiet(X0)) [input p2]
6. ! [X0] : (~humble(X0) <=> ~funny(X0)) [input p5]
21. ~funny(susan) [input hypothesis]
37. ! [X0] : (((humble(X0) | quiet(X0)) | quiet(X0)) & (~quiet(X0) | (~humble(X0) & ~quiet(X0)))) [nnf transformation 3]
38. ! [X0] : ((humble(X0) | quiet(X0) | quiet(X0)) & (~quiet(X0) | (~humble(X0) & ~quiet(X0)))) [flattening 37]
44. ! [X0] : ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))) [nnf transformation 6]
73. ~quiet(X0) | ~quiet(X0) [cnf transformation 38]
75. humble(X0) | quiet(X0) | quiet(X0) [cnf transformation 38]
86. ~humble(X0) | funny(X0) [cnf transformation 44]
122. ~funny(susan) [cnf transformation 21]
123. ~quiet(X0) [duplicate literal removal 73]
124. quiet(X0) | humble(X0) [duplicate literal removal 75]
205. humble(X1) [resolution 124,123]
206. funny(X0) [resolution 205,86]
212. $false [resolution 206,122]
% SZS output end Proof for 7870476254306685079490420
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not strong or not rich then paul is strong. If john is wise then fred is calm or strong. Everyone who is curious or not kind is quiet. If someone is quiet or calm then fred is both not curious and quiet and vice versa. If someone is not curious then someone is not funny or not brave. If someone is not brave or calm then someone is either generous or not calm. Everyone who is quiet or humble is both not happy and patient and vice versa. If alice is either not kind or not brave then someone is either not funny or not humble. If someone is tall then lucy is either not old or not strong. If someone is both creative and not kind then someone is both tall and funny. Everyone who is not old or not wise is rich and vice versa. Everyone who is rich is both not tall and wise. Everyone who is either not patient or patient is both strong and not curious and vice versa. If someone is calm or humble then someone is both wise and calm. If someone is not creative or not strong then lucy is both kind and brave. Everyone who is kind is both not kind and not strong. Fred is both wise and calm. Someone is not calm. Someone is wise or calm. John is not calm. | Alice is wise. | entailment | (((~strong(alice)<~>~rich(alice)))=>(strong(paul)))&
((wise(john))=>((calm(fred)|strong(fred))))&
(![X]:((curious(X)|~kind(X))=>quiet(X)))&
((?[X]:((quiet(X)|calm(X))))<=>((~curious(fred)&quiet(fred))))&
((?[X]:(~curious(X)))=>(?[X]:((~funny(X)|~brave(X)))))&
((?[X]:((~brave(X)|calm(X))))=>(?[X]:((generous(X)<~>~calm(X)))))&
(![X]:((quiet(X)|humble(X))<=>(~happy(X)&patient(X))))&
(((~kind(alice)<~>~brave(alice)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
((?[X]:(tall(X)))=>((~old(lucy)<~>~strong(lucy))))&
((?[X]:((creative(X)&~kind(X))))=>(?[X]:((tall(X)&funny(X)))))&
(![X]:((~old(X)|~wise(X))<=>rich(X)))&
(![X]:(rich(X)=>(~tall(X)&wise(X))))&
(![X]:((~patient(X)<~>patient(X))<=>(strong(X)&~curious(X))))&
((?[X]:((calm(X)|humble(X))))=>(?[X]:((wise(X)&calm(X)))))&
((?[X]:((~creative(X)|~strong(X))))=>((kind(lucy)&brave(lucy))))&
(![X]:(kind(X)=>(~kind(X)&~strong(X))))&
((wise(fred)&calm(fred)))&
(?[X]:(~calm(X)))&
(?[X]:((wise(X)|calm(X))))&
(~calm(john)) | wise(alice) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 794209446507978703161426
% SZS output start Proof for 794209446507978703161426
11. ! [X0] : ((~wise(X0) | ~old(X0)) <=> rich(X0)) [input p10]
12. ! [X0] : (rich(X0) => (wise(X0) & ~tall(X0))) [input p11]
21. ~wise(alice) [input hypothesis]
35. ! [X0] : ((wise(X0) & ~tall(X0)) | ~rich(X0)) [ennf transformation 12]
61. ! [X0] : (((~wise(X0) | ~old(X0)) | ~rich(X0)) & (rich(X0) | (wise(X0) & old(X0)))) [nnf transformation 11]
62. ! [X0] : ((~wise(X0) | ~old(X0) | ~rich(X0)) & (rich(X0) | (wise(X0) & old(X0)))) [flattening 61]
101. rich(X0) | wise(X0) [cnf transformation 62]
104. wise(X0) | ~rich(X0) [cnf transformation 35]
126. ~wise(alice) [cnf transformation 21]
259. wise(X0) [subsumption resolution 104,101]
286. $false [subsumption resolution 126,259]
% SZS output end Proof for 794209446507978703161426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not creative is not patient and vice versa.
If someone is old then mary is both humble and not quiet and vice versa.
If john is both strong and curious then paul is either not old or not rich and vice versa.
Everyone who is either generous or humble is either calm or not curious.
Everyone who is not generous or rich is kind and vice versa.
Everyone who is either not patient or creative is creative.
If someone is not rich then susan is brave.
Everyone who is humble or funny is not old and vice versa.
Everyone who is not kind is rich or not old and vice versa.
Everyone who is either not brave or not rich is either not calm or curious.
If someone is either humble or tall then someone is both rich and brave and vice versa.
Everyone who is either not creative or tall is generous.
If mary is both not happy and not creative then lucy is both brave and old and vice versa.
Everyone who is not humble or not curious is not calm and vice versa.
Everyone who is kind is patient.
Everyone who is kind or generous is creative.
Someone is tall or patient.
Fred is both not old and curious.
Mary is both not strong and tall.
Susan is either happy or quiet.
Paul is either not kind or tall.
Someone is not strong.
John is both humble and patient.
Someone is wise or calm. | Fred is not tall. | contradiction | (![X]:((~tall(X)<~>~creative(X))<=>~patient(X)))&
((?[X]:(old(X)))<=>((humble(mary)&~quiet(mary))))&
(((strong(john)&curious(john)))<=>((~old(paul)<~>~rich(paul))))&
(![X]:((generous(X)<~>humble(X))=>(calm(X)<~>~curious(X))))&
(![X]:((~generous(X)|rich(X))<=>kind(X)))&
(![X]:((~patient(X)<~>creative(X))=>creative(X)))&
((?[X]:(~rich(X)))=>(brave(susan)))&
(![X]:((humble(X)|funny(X))<=>~old(X)))&
(![X]:(~kind(X)<=>(rich(X)|~old(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(~calm(X)<~>curious(X))))&
((?[X]:((humble(X)<~>tall(X))))<=>(?[X]:((rich(X)&brave(X)))))&
(![X]:((~creative(X)<~>tall(X))=>generous(X)))&
(((~happy(mary)&~creative(mary)))<=>((brave(lucy)&old(lucy))))&
(![X]:((~humble(X)|~curious(X))<=>~calm(X)))&
(![X]:(kind(X)=>patient(X)))&
(![X]:((kind(X)|generous(X))=>creative(X)))&
(?[X]:((tall(X)|patient(X))))&
((~old(fred)&curious(fred)))&
((~strong(mary)&tall(mary)))&
((happy(susan)<~>quiet(susan)))&
((~kind(paul)<~>tall(paul)))&
(?[X]:(~strong(X)))&
((humble(john)&patient(john)))&
(?[X]:((wise(X)|calm(X)))) | ~tall(fred) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p8",
"p10",
"p11",
"p13",
"p14",
"p15",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 613827486984717272987517
% SZS output start Proof for 613827486984717272987517
1. ! [X0] : ((~tall(X0) <~> ~creative(X0)) <=> ~patient(X0)) [input p0]
2. ? [X0] : old(X0) <=> (~quiet(mary) & humble(mary)) [input p1]
4. ! [X0] : ((generous(X0) <~> humble(X0)) => (calm(X0) <~> ~curious(X0))) [input p3]
5. ! [X0] : ((rich(X0) | ~generous(X0)) <=> kind(X0)) [input p4]
6. ! [X0] : ((~patient(X0) <~> creative(X0)) => creative(X0)) [input p5]
9. ! [X0] : (~kind(X0) <=> (~old(X0) | rich(X0))) [input p8]
11. ? [X0] : (humble(X0) <~> tall(X0)) <=> ? [X0] : (brave(X0) & rich(X0)) [input p10]
12. ! [X0] : ((~creative(X0) <~> tall(X0)) => generous(X0)) [input p11]
14. ! [X0] : ((~curious(X0) | ~humble(X0)) <=> ~calm(X0)) [input p13]
15. ! [X0] : (kind(X0) => patient(X0)) [input p14]
16. ! [X0] : ((generous(X0) | kind(X0)) => creative(X0)) [input p15]
18. curious(fred) & ~old(fred) [input p17]
19. tall(mary) & ~strong(mary) [input p18]
25. ~tall(fred) [input hypothesis]
26. ? [X0] : (humble(X0) <~> tall(X0)) <=> ? [X1] : (brave(X1) & rich(X1)) [rectify 11]
28. ! [X0] : ((calm(X0) <~> ~curious(X0)) | (generous(X0) <=> humble(X0))) [ennf transformation 4]
29. ! [X0] : (creative(X0) | (~patient(X0) <=> creative(X0))) [ennf transformation 6]
32. ! [X0] : (generous(X0) | (~creative(X0) <=> tall(X0))) [ennf transformation 12]
33. ! [X0] : (patient(X0) | ~kind(X0)) [ennf transformation 15]
34. ! [X0] : (creative(X0) | (~generous(X0) & ~kind(X0))) [ennf transformation 16]
35. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | patient(X0)) & (~patient(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [nnf transformation 1]
36. (? [X0] : old(X0) | (quiet(mary) | ~humble(mary))) & ((~quiet(mary) & humble(mary)) | ! [X0] : ~old(X0)) [nnf transformation 2]
37. (? [X0] : old(X0) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X0] : ~old(X0)) [flattening 36]
38. (? [X0] : old(X0) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X1] : ~old(X1)) [rectify 37]
39. ? [X0] : old(X0) => old(sK0) [choice axiom]
40. (old(sK0) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X1] : ~old(X1)) [skolemisation 38,39]
43. ! [X0] : (((curious(X0) | ~calm(X0)) & (~curious(X0) | calm(X0))) | ((generous(X0) | ~humble(X0)) & (humble(X0) | ~generous(X0)))) [nnf transformation 28]
44. ! [X0] : (((rich(X0) | ~generous(X0)) | ~kind(X0)) & (kind(X0) | (~rich(X0) & generous(X0)))) [nnf transformation 5]
45. ! [X0] : ((rich(X0) | ~generous(X0) | ~kind(X0)) & (kind(X0) | (~rich(X0) & generous(X0)))) [flattening 44]
46. ! [X0] : (creative(X0) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) [nnf transformation 29]
49. ! [X0] : ((~kind(X0) | (old(X0) & ~rich(X0))) & ((~old(X0) | rich(X0)) | kind(X0))) [nnf transformation 9]
50. ! [X0] : ((~kind(X0) | (old(X0) & ~rich(X0))) & (~old(X0) | rich(X0) | kind(X0))) [flattening 49]
52. (? [X0] : ((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ! [X1] : (~brave(X1) | ~rich(X1))) & (? [X1] : (brave(X1) & rich(X1)) | ! [X0] : ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) [nnf transformation 26]
53. (? [X0] : ((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ! [X1] : (~brave(X1) | ~rich(X1))) & (? [X2] : (brave(X2) & rich(X2)) | ! [X3] : ((humble(X3) | ~tall(X3)) & (tall(X3) | ~humble(X3)))) [rectify 52]
54. ? [X0] : ((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) => ((~tall(sK1) | ~humble(sK1)) & (tall(sK1) | humble(sK1))) [choice axiom]
55. ? [X2] : (brave(X2) & rich(X2)) => (brave(sK2) & rich(sK2)) [choice axiom]
56. (((~tall(sK1) | ~humble(sK1)) & (tall(sK1) | humble(sK1))) | ! [X1] : (~brave(X1) | ~rich(X1))) & ((brave(sK2) & rich(sK2)) | ! [X3] : ((humble(X3) | ~tall(X3)) & (tall(X3) | ~humble(X3)))) [skolemisation 53,55,54]
57. ! [X0] : (generous(X0) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) [nnf transformation 32]
60. ! [X0] : (((~curious(X0) | ~humble(X0)) | calm(X0)) & (~calm(X0) | (curious(X0) & humble(X0)))) [nnf transformation 14]
61. ! [X0] : ((~curious(X0) | ~humble(X0) | calm(X0)) & (~calm(X0) | (curious(X0) & humble(X0)))) [flattening 60]
68. ~patient(X0) | ~creative(X0) | tall(X0) [cnf transformation 35]
69. ~patient(X0) | ~tall(X0) | creative(X0) [cnf transformation 35]
73. ~quiet(mary) | ~old(X1) [cnf transformation 40]
74. old(sK0) | quiet(mary) | ~humble(mary) [cnf transformation 40]
81. ~generous(X0) | calm(X0) | humble(X0) | ~curious(X0) [cnf transformation 43]
85. kind(X0) | generous(X0) [cnf transformation 45]
86. ~rich(X0) | kind(X0) [cnf transformation 45]
87. ~kind(X0) | ~generous(X0) | rich(X0) [cnf transformation 45]
88. creative(X0) | creative(X0) | patient(X0) [cnf transformation 46]
94. ~old(X0) | rich(X0) | kind(X0) [cnf transformation 50]
95. ~kind(X0) | ~rich(X0) [cnf transformation 50]
96. ~kind(X0) | old(X0) [cnf transformation 50]
101. rich(sK2) | tall(X3) | ~humble(X3) [cnf transformation 56]
102. rich(sK2) | humble(X3) | ~tall(X3) [cnf transformation 56]
107. generous(X0) | tall(X0) | creative(X0) [cnf transformation 57]
108. ~creative(X0) | generous(X0) | ~tall(X0) [cnf transformation 57]
113. ~calm(X0) | humble(X0) [cnf transformation 61]
116. ~kind(X0) | patient(X0) [cnf transformation 33]
118. ~generous(X0) | creative(X0) [cnf transformation 34]
121. curious(fred) [cnf transformation 18]
123. tall(mary) [cnf transformation 19]
131. ~tall(fred) [cnf transformation 25]
132. patient(X0) | creative(X0) [duplicate literal removal 88]
134. 1 <=> humble(mary) [avatar definition]
138. 2 <=> quiet(mary) [avatar definition]
142. 3 <=> old(sK0) [avatar definition]
144. old(sK0) <- (3) [avatar component clause 142]
145. ~1 | 2 | 3 [avatar split clause 74,142,138,134]
147. 4 <=> ! [X1] : ~old(X1) [avatar definition]
148. ~old(X1) <- (4) [avatar component clause 147]
149. 4 | ~2 [avatar split clause 73,138,147]
181. ~rich(X0) [subsumption resolution 95,86]
182. ~old(X0) | kind(X0) [subsumption resolution 94,181]
186. 11 <=> ! [X3] : (humble(X3) | ~tall(X3)) [avatar definition]
187. ~tall(X3) | humble(X3) <- (11) [avatar component clause 186]
194. 13 <=> ! [X3] : (tall(X3) | ~humble(X3)) [avatar definition]
195. ~humble(X3) | tall(X3) <- (13) [avatar component clause 194]
197. humble(X3) | ~tall(X3) [subsumption resolution 102,181]
198. 11 [avatar split clause 197,186]
199. tall(X3) | ~humble(X3) [subsumption resolution 101,181]
200. 13 [avatar split clause 199,194]
256. generous(X0) | old(X0) [resolution 96,85]
257. generous(X0) <- (4) [subsumption resolution 256,148]
262. humble(mary) <- (11) [resolution 187,123]
266. 1 | ~11 [avatar split clause 262,186,134]
278. ~tall(X0) | creative(X0) | creative(X0) [resolution 69,132]
279. ~tall(X0) | creative(X0) [duplicate literal removal 278]
298. tall(X0) | creative(X0) | creative(X0) [resolution 107,118]
299. creative(X0) | tall(X0) [duplicate literal removal 298]
309. 25 <=> humble(fred) [avatar definition]
310. humble(fred) <- (25) [avatar component clause 309]
337. calm(X1) | humble(X1) | ~curious(X1) <- (4) [resolution 81,257]
348. ~curious(X1) | humble(X1) <- (4) [subsumption resolution 337,113]
350. humble(fred) <- (4) [resolution 348,121]
353. 25 | ~4 [avatar split clause 350,147,309]
358. tall(fred) <- (13, 25) [resolution 310,195]
360. $false <- (13, 25) [subsumption resolution 358,131]
361. ~13 | ~25 [avatar contradiction clause 360]
366. creative(X0) [subsumption resolution 279,299]
368. kind(sK0) <- (3) [resolution 144,182]
374. ~tall(X0) | generous(X0) [resolution 366,108]
376. ~generous(sK0) | rich(sK0) <- (3) [resolution 368,87]
378. patient(sK0) <- (3) [resolution 368,116]
380. ~generous(sK0) <- (3) [subsumption resolution 376,181]
392. ~creative(sK0) | tall(sK0) <- (3) [resolution 378,68]
393. tall(sK0) <- (3) [subsumption resolution 392,366]
401. generous(sK0) <- (3) [resolution 393,374]
403. $false <- (3) [subsumption resolution 401,380]
404. ~3 [avatar contradiction clause 403]
405. $false [avatar sat refutation 145,149,198,200,266,353,361,404]
% SZS output end Proof for 613827486984717272987517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either strong or brave then someone is both curious and strong.
If fred is happy then lucy is not strong or rich.
If john is strong or generous then fred is either old or not old and vice versa.
Everyone who is either calm or not strong is tall.
Everyone who is either not wise or not brave is kind or not curious and vice versa.
If someone is both happy and creative then fred is both generous and patient and vice versa.
If susan is happy or funny then someone is not generous.
If paul is not rich or old then someone is both funny and not funny and vice versa.
If lucy is not curious then someone is both not old and tall and vice versa.
If someone is humble or not calm then someone is tall or not rich.
If alice is creative or rich then someone is either creative or not kind.
Everyone who is both not happy and humble is both not humble and not strong.
Everyone who is either not old or not quiet is strong or not generous.
If someone is both brave and kind then someone is not brave or wise and vice versa.
Everyone who is brave is creative or not old and vice versa.
If someone is both wise and humble then someone is not calm or not strong and vice versa.
Fred is both creative and tall.
Someone is both not kind and not happy.
Alice is either not humble or humble.
Someone is both not quiet and not humble.
Someone is both funny and generous.
Someone is patient or not generous.
Someone is not rich or humble.
Alice is either calm or not patient. | Paul is brave. | entailment | (((strong(lucy)<~>brave(lucy)))=>(?[X]:((curious(X)&strong(X)))))&
((happy(fred))=>((~strong(lucy)|rich(lucy))))&
(((strong(john)|generous(john)))<=>((old(fred)<~>~old(fred))))&
(![X]:((calm(X)<~>~strong(X))=>tall(X)))&
(![X]:((~wise(X)<~>~brave(X))<=>(kind(X)|~curious(X))))&
((?[X]:((happy(X)&creative(X))))<=>((generous(fred)&patient(fred))))&
(((happy(susan)|funny(susan)))=>(?[X]:(~generous(X))))&
(((~rich(paul)|old(paul)))<=>(?[X]:((funny(X)&~funny(X)))))&
((~curious(lucy))<=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:((humble(X)|~calm(X))))=>(?[X]:((tall(X)|~rich(X)))))&
(((creative(alice)|rich(alice)))=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((~happy(X)&humble(X))=>(~humble(X)&~strong(X))))&
(![X]:((~old(X)<~>~quiet(X))=>(strong(X)|~generous(X))))&
((?[X]:((brave(X)&kind(X))))<=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:(brave(X)<=>(creative(X)|~old(X))))&
((?[X]:((wise(X)&humble(X))))<=>(?[X]:((~calm(X)|~strong(X)))))&
((creative(fred)&tall(fred)))&
(?[X]:((~kind(X)&~happy(X))))&
((~humble(alice)<~>humble(alice)))&
(?[X]:((~quiet(X)&~humble(X))))&
(?[X]:((funny(X)&generous(X))))&
(?[X]:((patient(X)|~generous(X))))&
(?[X]:((~rich(X)|humble(X))))&
((calm(alice)<~>~patient(alice))) | brave(paul) | [
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9841415419189119163552
% SZS output start Proof for 9841415419189119163552
8. (old(paul) | ~rich(paul)) <=> ? [X0] : (~funny(X0) & funny(X0)) [input p7]
15. ! [X0] : (brave(X0) <=> (~old(X0) | creative(X0))) [input p14]
25. ~brave(paul) [input hypothesis]
55. ((old(paul) | ~rich(paul)) | ! [X0] : (funny(X0) | ~funny(X0))) & (? [X0] : (~funny(X0) & funny(X0)) | (~old(paul) & rich(paul))) [nnf transformation 8]
56. (old(paul) | ~rich(paul) | ! [X0] : (funny(X0) | ~funny(X0))) & (? [X0] : (~funny(X0) & funny(X0)) | (~old(paul) & rich(paul))) [flattening 55]
57. (old(paul) | ~rich(paul) | ! [X0] : (funny(X0) | ~funny(X0))) & (? [X1] : (~funny(X1) & funny(X1)) | (~old(paul) & rich(paul))) [rectify 56]
58. ? [X1] : (~funny(X1) & funny(X1)) => (~funny(sK3) & funny(sK3)) [choice axiom]
59. (old(paul) | ~rich(paul) | ! [X0] : (funny(X0) | ~funny(X0))) & ((~funny(sK3) & funny(sK3)) | (~old(paul) & rich(paul))) [skolemisation 57,58]
76. ! [X0] : ((brave(X0) | (old(X0) & ~creative(X0))) & ((~old(X0) | creative(X0)) | ~brave(X0))) [nnf transformation 15]
77. ! [X0] : ((brave(X0) | (old(X0) & ~creative(X0))) & (~old(X0) | creative(X0) | ~brave(X0))) [flattening 76]
121. funny(sK3) | ~old(paul) [cnf transformation 59]
123. ~funny(sK3) | ~old(paul) [cnf transformation 59]
145. old(X0) | brave(X0) [cnf transformation 77]
165. ~brave(paul) [cnf transformation 25]
250. 18 <=> old(paul) [avatar definition]
252. ~old(paul) <- (~18) [avatar component clause 250]
254. 19 <=> funny(sK3) [avatar definition]
257. ~18 | ~19 [avatar split clause 123,254,250]
263. ~18 | 19 [avatar split clause 121,254,250]
418. brave(paul) <- (~18) [resolution 145,252]
419. $false <- (~18) [subsumption resolution 418,165]
420. 18 [avatar contradiction clause 419]
421. $false [avatar sat refutation 257,263,420]
% SZS output end Proof for 9841415419189119163552
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or tall is both funny and not funny. Everyone who is not strong or not generous is rich. Everyone who is not humble is both brave and not tall and vice versa. Everyone who is either happy or not quiet is not brave or calm and vice versa. Everyone who is not calm is both not curious and patient and vice versa. Everyone who is both curious and not generous is both not wise and not kind and vice versa. If someone is both not calm and wise then someone is not brave. Everyone who is not quiet is kind and vice versa. If susan is both not kind and calm then john is both tall and funny. If alice is strong then alice is both not old and not curious and vice versa. If alice is not curious then alice is either curious or not quiet and vice versa. If alice is either not happy or humble then mary is either rich or not strong. If someone is calm then someone is creative. Everyone who is both not brave and not rich is both not creative and not old and vice versa. Everyone who is both creative and not calm is not old or not happy and vice versa. Someone is generous. Someone is generous or not happy. Someone is either not curious or wise. Someone is quiet or not rich. Susan is not brave or not rich. | Alice is not strong. | entailment | (![X]:((creative(X)|tall(X))=>(funny(X)&~funny(X))))&
(![X]:((~strong(X)|~generous(X))=>rich(X)))&
(![X]:(~humble(X)<=>(brave(X)&~tall(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(~brave(X)|calm(X))))&
(![X]:(~calm(X)<=>(~curious(X)&patient(X))))&
(![X]:((curious(X)&~generous(X))<=>(~wise(X)&~kind(X))))&
((?[X]:((~calm(X)&wise(X))))=>(?[X]:(~brave(X))))&
(![X]:(~quiet(X)<=>kind(X)))&
(((~kind(susan)&calm(susan)))=>((tall(john)&funny(john))))&
((strong(alice))<=>((~old(alice)&~curious(alice))))&
((~curious(alice))<=>((curious(alice)<~>~quiet(alice))))&
(((~happy(alice)<~>humble(alice)))=>((rich(mary)<~>~strong(mary))))&
((?[X]:(calm(X)))=>(?[X]:(creative(X))))&
(![X]:((~brave(X)&~rich(X))<=>(~creative(X)&~old(X))))&
(![X]:((creative(X)&~calm(X))<=>(~old(X)|~happy(X))))&
(?[X]:(generous(X)))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
(?[X]:((quiet(X)|~rich(X))))&
((~brave(susan)|~rich(susan))) | ~strong(alice) | [
"p0",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4488189831274856206660526
% SZS output start Proof for 4488189831274856206660526
1. ! [X0] : ((tall(X0) | creative(X0)) => (~funny(X0) & funny(X0))) [input p0]
10. strong(alice) <=> (~curious(alice) & ~old(alice)) [input p9]
15. ! [X0] : ((~calm(X0) & creative(X0)) <=> (~happy(X0) | ~old(X0))) [input p14]
21. strong(alice) [input hypothesis]
24. ! [X0] : ((~funny(X0) & funny(X0)) | (~tall(X0) & ~creative(X0))) [ennf transformation 1]
43. (strong(alice) | (curious(alice) | old(alice))) & ((~curious(alice) & ~old(alice)) | ~strong(alice)) [nnf transformation 10]
44. (strong(alice) | curious(alice) | old(alice)) & ((~curious(alice) & ~old(alice)) | ~strong(alice)) [flattening 43]
52. ! [X0] : (((~calm(X0) & creative(X0)) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | (calm(X0) | ~creative(X0)))) [nnf transformation 15]
53. ! [X0] : (((~calm(X0) & creative(X0)) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | calm(X0) | ~creative(X0))) [flattening 52]
63. funny(X0) | ~creative(X0) [cnf transformation 24]
65. ~funny(X0) | ~creative(X0) [cnf transformation 24]
90. ~old(alice) | ~strong(alice) [cnf transformation 44]
107. creative(X0) | old(X0) [cnf transformation 53]
117. strong(alice) [cnf transformation 21]
121. ~creative(X0) [subsumption resolution 63,65]
147. 6 <=> old(alice) [avatar definition]
148. ~old(alice) <- (~6) [avatar component clause 147]
155. 8 <=> strong(alice) [avatar definition]
160. ~8 | ~6 [avatar split clause 90,147,155]
195. old(X0) [subsumption resolution 107,121]
225. 8 [avatar split clause 117,155]
228. $false <- (~6) [subsumption resolution 148,195]
229. 6 [avatar contradiction clause 228]
230. $false [avatar sat refutation 160,225,229]
% SZS output end Proof for 4488189831274856206660526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or not kind is both not calm and not quiet and vice versa.
Everyone who is both patient and happy is either not quiet or not happy.
Everyone who is not curious or tall is not strong or not quiet.
Everyone who is old is brave or quiet.
If lucy is not old then fred is not creative.
If someone is either old or not wise then alice is both calm and not humble.
Everyone who is not tall or quiet is both creative and not brave.
Everyone who is either quiet or not creative is either quiet or not old.
If john is not calm then mary is not wise or not creative.
If someone is either not tall or happy then mary is not creative or generous and vice versa.
If someone is old then john is both creative and happy and vice versa.
If someone is either not curious or humble then someone is either not rich or patient.
Everyone who is not tall is either not brave or not humble.
If mary is not happy or not funny then alice is funny or not calm.
If someone is not rich then someone is both not funny and patient.
If mary is both not kind and not brave then mary is either not humble or humble and vice versa.
Someone is curious or not happy.
Lucy is both funny and not rich.
Someone is not calm.
Fred is either not brave or strong.
Someone is kind.
Fred is both not patient and quiet.
Paul is either not patient or not wise.
Someone is not humble. | Lucy is not old. | contradiction | (![X]:((creative(X)<~>~kind(X))<=>(~calm(X)&~quiet(X))))&
(![X]:((patient(X)&happy(X))=>(~quiet(X)<~>~happy(X))))&
(![X]:((~curious(X)|tall(X))=>(~strong(X)|~quiet(X))))&
(![X]:(old(X)=>(brave(X)|quiet(X))))&
((~old(lucy))=>(~creative(fred)))&
((?[X]:((old(X)<~>~wise(X))))=>((calm(alice)&~humble(alice))))&
(![X]:((~tall(X)|quiet(X))=>(creative(X)&~brave(X))))&
(![X]:((quiet(X)<~>~creative(X))=>(quiet(X)<~>~old(X))))&
((~calm(john))=>((~wise(mary)|~creative(mary))))&
((?[X]:((~tall(X)<~>happy(X))))<=>((~creative(mary)|generous(mary))))&
((?[X]:(old(X)))<=>((creative(john)&happy(john))))&
((?[X]:((~curious(X)<~>humble(X))))=>(?[X]:((~rich(X)<~>patient(X)))))&
(![X]:(~tall(X)=>(~brave(X)<~>~humble(X))))&
(((~happy(mary)|~funny(mary)))=>((funny(alice)|~calm(alice))))&
((?[X]:(~rich(X)))=>(?[X]:((~funny(X)&patient(X)))))&
(((~kind(mary)&~brave(mary)))<=>((~humble(mary)<~>humble(mary))))&
(?[X]:((curious(X)|~happy(X))))&
((funny(lucy)&~rich(lucy)))&
(?[X]:(~calm(X)))&
((~brave(fred)<~>strong(fred)))&
(?[X]:(kind(X)))&
((~patient(fred)&quiet(fred)))&
((~patient(paul)<~>~wise(paul)))&
(?[X]:(~humble(X))) | ~old(lucy) | [
"p4",
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7454875689288384725905852
% SZS output start Proof for 7454875689288384725905852
5. ~old(lucy) => ~creative(fred) [input p4]
7. ! [X0] : ((quiet(X0) | ~tall(X0)) => (~brave(X0) & creative(X0))) [input p6]
22. quiet(fred) & ~patient(fred) [input p21]
25. ~old(lucy) [input hypothesis]
34. ~creative(fred) | old(lucy) [ennf transformation 5]
36. ! [X0] : ((~brave(X0) & creative(X0)) | (~quiet(X0) & tall(X0))) [ennf transformation 7]
91. ~creative(fred) | old(lucy) [cnf transformation 34]
97. ~quiet(X0) | creative(X0) [cnf transformation 36]
138. quiet(fred) [cnf transformation 22]
142. ~old(lucy) [cnf transformation 25]
151. 1 <=> old(lucy) [avatar definition]
155. 2 <=> creative(fred) [avatar definition]
157. ~creative(fred) <- (~2) [avatar component clause 155]
158. 1 | ~2 [avatar split clause 91,155,151]
325. ~1 [avatar split clause 142,151]
331. creative(fred) [resolution 97,138]
332. $false <- (~2) [subsumption resolution 331,157]
333. 2 [avatar contradiction clause 332]
334. $false [avatar sat refutation 158,325,333]
% SZS output end Proof for 7454875689288384725905852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is patient then john is both not curious and kind and vice versa.
Everyone who is not calm is not wise or not old.
If someone is both calm and old then susan is either calm or not funny.
If someone is both strong and not rich then alice is either not kind or rich and vice versa.
If john is both rich and humble then someone is not happy or quiet.
Everyone who is rich or humble is either not curious or not tall and vice versa.
If someone is both not wise and not old then john is creative or not strong.
Everyone who is not humble or humble is either not tall or curious.
If someone is both strong and calm then someone is either not kind or not happy.
If someone is not brave or curious then lucy is rich and vice versa.
If someone is both not patient and happy then someone is not humble and vice versa.
Everyone who is either wise or rich is generous or not kind and vice versa.
If someone is both calm and creative then susan is both not happy and kind and vice versa.
Everyone who is not kind is not tall and vice versa.
Lucy is either not old or not humble.
Fred is either calm or not strong.
Someone is not kind or not quiet.
Fred is brave. | Alice is creative. | neutral | ((patient(susan))<=>((~curious(john)&kind(john))))&
(![X]:(~calm(X)=>(~wise(X)|~old(X))))&
((?[X]:((calm(X)&old(X))))=>((calm(susan)<~>~funny(susan))))&
((?[X]:((strong(X)&~rich(X))))<=>((~kind(alice)<~>rich(alice))))&
(((rich(john)&humble(john)))=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:((rich(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
((?[X]:((~wise(X)&~old(X))))=>((creative(john)|~strong(john))))&
(![X]:((~humble(X)|humble(X))=>(~tall(X)<~>curious(X))))&
((?[X]:((strong(X)&calm(X))))=>(?[X]:((~kind(X)<~>~happy(X)))))&
((?[X]:((~brave(X)|curious(X))))<=>(rich(lucy)))&
((?[X]:((~patient(X)&happy(X))))<=>(?[X]:(~humble(X))))&
(![X]:((wise(X)<~>rich(X))<=>(generous(X)|~kind(X))))&
((?[X]:((calm(X)&creative(X))))<=>((~happy(susan)&kind(susan))))&
(![X]:(~kind(X)<=>~tall(X)))&
((~old(lucy)<~>~humble(lucy)))&
((calm(fred)<~>~strong(fred)))&
(?[X]:((~kind(X)|~quiet(X))))&
(brave(fred)) | creative(alice) | [] | null | 0 |
Everyone who is brave is either not wise or not kind and vice versa.
Everyone who is either not wise or not curious is both kind and strong and vice versa.
If someone is not brave or funny then someone is not brave.
If mary is not strong or strong then john is calm or generous.
Everyone who is both not happy and tall is either not humble or not old.
If mary is not rich then someone is both not happy and old.
Everyone who is generous is both strong and not patient.
Everyone who is quiet or kind is happy or funny and vice versa.
Everyone who is both generous and wise is not humble and vice versa.
If someone is both not tall and not old then someone is brave or not generous and vice versa.
If susan is kind then someone is both funny and patient and vice versa.
Everyone who is not quiet is both creative and funny and vice versa.
Everyone who is not kind or not humble is not generous or not curious.
If john is not curious then someone is wise or not rich.
If someone is kind then someone is both curious and not kind.
Everyone who is kind or quiet is both strong and patient and vice versa.
Alice is either not curious or not wise.
Paul is not creative.
Someone is not tall.
Fred is not kind.
Paul is both not generous and not creative.
Alice is not creative.
Someone is not calm. | Alice is not humble. | contradiction | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(kind(X)&strong(X))))&
((?[X]:((~brave(X)|funny(X))))=>(?[X]:(~brave(X))))&
(((~strong(mary)|strong(mary)))=>((calm(john)|generous(john))))&
(![X]:((~happy(X)&tall(X))=>(~humble(X)<~>~old(X))))&
((~rich(mary))=>(?[X]:((~happy(X)&old(X)))))&
(![X]:(generous(X)=>(strong(X)&~patient(X))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))&
(![X]:((generous(X)&wise(X))<=>~humble(X)))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))&
((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
((~curious(alice)<~>~wise(alice)))&
(~creative(paul))&
(?[X]:(~tall(X)))&
(~kind(fred))&
((~generous(paul)&~creative(paul)))&
(~creative(alice))&
(?[X]:(~calm(X))) | ~humble(alice) | [
"p6",
"p8",
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1222578346283042389712545
% SZS output start Proof for 1222578346283042389712545
7. ! [X0] : (generous(X0) => (~patient(X0) & strong(X0))) [input p6]
9. ! [X0] : ((wise(X0) & generous(X0)) <=> ~humble(X0)) [input p8]
12. ! [X0] : (~quiet(X0) <=> (funny(X0) & creative(X0))) [input p11]
16. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p15]
22. ~creative(alice) [input p21]
24. ~humble(alice) [input hypothesis]
34. ! [X0] : ((~patient(X0) & strong(X0)) | ~generous(X0)) [ennf transformation 7]
50. ! [X0] : (((wise(X0) & generous(X0)) | humble(X0)) & (~humble(X0) | (~wise(X0) | ~generous(X0)))) [nnf transformation 9]
51. ! [X0] : (((wise(X0) & generous(X0)) | humble(X0)) & (~humble(X0) | ~wise(X0) | ~generous(X0))) [flattening 50]
61. ! [X0] : ((~quiet(X0) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | quiet(X0))) [nnf transformation 12]
62. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | quiet(X0))) [flattening 61]
68. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 16]
69. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 68]
94. ~patient(X0) | ~generous(X0) [cnf transformation 34]
100. humble(X0) | generous(X0) [cnf transformation 51]
110. creative(X0) | quiet(X0) [cnf transformation 62]
121. ~quiet(X0) | patient(X0) [cnf transformation 69]
130. ~creative(alice) [cnf transformation 22]
132. ~humble(alice) [cnf transformation 24]
258. generous(alice) [resolution 100,132]
265. quiet(alice) [resolution 110,130]
271. patient(alice) [resolution 121,265]
275. ~generous(alice) [resolution 271,94]
276. $false [subsumption resolution 275,258]
% SZS output end Proof for 1222578346283042389712545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is patient or creative and vice versa.
Everyone who is calm or not brave is brave.
If someone is quiet then john is not old and vice versa.
Everyone who is happy or generous is patient and vice versa.
Everyone who is either humble or not tall is either strong or not curious.
If someone is either not kind or brave then someone is not wise or not creative.
If someone is not patient or not creative then someone is rich and vice versa.
If someone is curious then someone is not funny and vice versa.
Everyone who is strong is both not creative and patient and vice versa.
If someone is not creative or humble then paul is both strong and not happy and vice versa.
If alice is both not humble and quiet then someone is either old or not kind and vice versa.
Everyone who is either old or patient is curious.
Everyone who is not kind or generous is happy.
If john is both patient and not happy then someone is both kind and not strong.
If john is both not strong and brave then someone is both brave and not funny.
Everyone who is either rich or curious is not quiet or not curious and vice versa.
Lucy is happy.
Someone is either tall or not rich.
Alice is either kind or not happy.
Susan is either not strong or not old.
Paul is either curious or not strong.
Someone is not patient. | Paul is not rich. | contradiction | ((?[X]:((creative(X)|wise(X))))<=>((patient(john)|creative(john))))&
(![X]:((calm(X)|~brave(X))=>brave(X)))&
((?[X]:(quiet(X)))<=>(~old(john)))&
(![X]:((happy(X)|generous(X))<=>patient(X)))&
(![X]:((humble(X)<~>~tall(X))=>(strong(X)<~>~curious(X))))&
((?[X]:((~kind(X)<~>brave(X))))=>(?[X]:((~wise(X)|~creative(X)))))&
((?[X]:((~patient(X)|~creative(X))))<=>(?[X]:(rich(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~funny(X))))&
(![X]:(strong(X)<=>(~creative(X)&patient(X))))&
((?[X]:((~creative(X)|humble(X))))<=>((strong(paul)&~happy(paul))))&
(((~humble(alice)&quiet(alice)))<=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:((old(X)<~>patient(X))=>curious(X)))&
(![X]:((~kind(X)|generous(X))=>happy(X)))&
(((patient(john)&~happy(john)))=>(?[X]:((kind(X)&~strong(X)))))&
(((~strong(john)&brave(john)))=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:((rich(X)<~>curious(X))<=>(~quiet(X)|~curious(X))))&
(happy(lucy))&
(?[X]:((tall(X)<~>~rich(X))))&
((kind(alice)<~>~happy(alice)))&
((~strong(susan)<~>~old(susan)))&
((curious(paul)<~>~strong(paul)))&
(?[X]:(~patient(X))) | ~rich(paul) | [
"p3",
"p8",
"p9",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2403374726457594961944740
% SZS output start Proof for 2403374726457594961944740
4. ! [X0] : ((generous(X0) | happy(X0)) <=> patient(X0)) [input p3]
9. ! [X0] : (strong(X0) <=> (patient(X0) & ~creative(X0))) [input p8]
10. ? [X0] : (humble(X0) | ~creative(X0)) <=> (~happy(paul) & strong(paul)) [input p9]
13. ! [X0] : ((generous(X0) | ~kind(X0)) => happy(X0)) [input p12]
16. ! [X0] : ((rich(X0) <~> curious(X0)) <=> (~curious(X0) | ~quiet(X0))) [input p15]
21. curious(paul) <~> ~strong(paul) [input p20]
23. ~rich(paul) [input hypothesis]
32. ! [X0] : (happy(X0) | (~generous(X0) & kind(X0))) [ennf transformation 13]
46. ! [X0] : (((generous(X0) | happy(X0)) | ~patient(X0)) & (patient(X0) | (~generous(X0) & ~happy(X0)))) [nnf transformation 4]
47. ! [X0] : ((generous(X0) | happy(X0) | ~patient(X0)) & (patient(X0) | (~generous(X0) & ~happy(X0)))) [flattening 46]
63. ! [X0] : ((strong(X0) | (~patient(X0) | creative(X0))) & ((patient(X0) & ~creative(X0)) | ~strong(X0))) [nnf transformation 9]
64. ! [X0] : ((strong(X0) | ~patient(X0) | creative(X0)) & ((patient(X0) & ~creative(X0)) | ~strong(X0))) [flattening 63]
65. (? [X0] : (humble(X0) | ~creative(X0)) | (happy(paul) | ~strong(paul))) & ((~happy(paul) & strong(paul)) | ! [X0] : (~humble(X0) & creative(X0))) [nnf transformation 10]
66. (? [X0] : (humble(X0) | ~creative(X0)) | happy(paul) | ~strong(paul)) & ((~happy(paul) & strong(paul)) | ! [X0] : (~humble(X0) & creative(X0))) [flattening 65]
67. (? [X0] : (humble(X0) | ~creative(X0)) | happy(paul) | ~strong(paul)) & ((~happy(paul) & strong(paul)) | ! [X1] : (~humble(X1) & creative(X1))) [rectify 66]
68. ? [X0] : (humble(X0) | ~creative(X0)) => (humble(sK7) | ~creative(sK7)) [choice axiom]
69. ((humble(sK7) | ~creative(sK7)) | happy(paul) | ~strong(paul)) & ((~happy(paul) & strong(paul)) | ! [X1] : (~humble(X1) & creative(X1))) [skolemisation 67,68]
80. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (curious(X0) & quiet(X0))) & ((~curious(X0) | ~quiet(X0)) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [nnf transformation 16]
81. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (curious(X0) & quiet(X0))) & (~curious(X0) | ~quiet(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [flattening 80]
87. (strong(paul) | ~curious(paul)) & (~strong(paul) | curious(paul)) [nnf transformation 21]
99. ~patient(X0) | happy(X0) | generous(X0) [cnf transformation 47]
111. ~strong(X0) | ~creative(X0) [cnf transformation 64]
112. ~strong(X0) | patient(X0) [cnf transformation 64]
116. ~happy(paul) | creative(X1) [cnf transformation 69]
128. ~generous(X0) | happy(X0) [cnf transformation 32]
136. curious(X0) | rich(X0) | curious(X0) [cnf transformation 81]
147. strong(paul) | ~curious(paul) [cnf transformation 87]
149. ~rich(paul) [cnf transformation 23]
151. rich(X0) | curious(X0) [duplicate literal removal 136]
218. 16 <=> ! [X3] : creative(X3) [avatar definition]
219. creative(X3) <- (16) [avatar component clause 218]
246. 23 <=> strong(paul) [avatar definition]
247. strong(paul) <- (23) [avatar component clause 246]
250. 24 <=> happy(paul) [avatar definition]
266. 16 | ~24 [avatar split clause 116,250,218]
345. 43 <=> curious(paul) [avatar definition]
348. ~43 | 23 [avatar split clause 147,246,345]
362. ~creative(paul) <- (23) [resolution 111,247]
364. patient(paul) <- (23) [resolution 112,247]
367. curious(paul) [resolution 151,149]
372. happy(paul) | generous(paul) <- (23) [resolution 99,364]
443. happy(paul) <- (23) [subsumption resolution 372,128]
444. 24 | ~23 [avatar split clause 443,246,250]
471. $false <- (16, 23) [resolution 362,219]
472. ~16 | ~23 [avatar contradiction clause 471]
473. 43 [avatar split clause 367,345]
474. $false [avatar sat refutation 266,348,444,472,473]
% SZS output end Proof for 2403374726457594961944740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and rich then john is both old and tall.
If susan is both rich and not calm then mary is not old and vice versa.
If someone is either happy or not funny then paul is happy and vice versa.
If someone is curious or kind then someone is both not quiet and curious.
If lucy is not quiet then someone is either not happy or not wise and vice versa.
Everyone who is calm or rich is either not curious or not strong and vice versa.
Everyone who is not patient or not quiet is not rich or calm.
Everyone who is both wise and not old is quiet or creative.
If someone is quiet then someone is not brave or not strong.
Everyone who is both wise and generous is not strong or patient.
Everyone who is both strong and not curious is either strong or curious and vice versa.
If fred is not rich or patient then mary is calm and vice versa.
Everyone who is both not creative and happy is either not old or wise.
If someone is not rich then someone is both not curious and not rich and vice versa.
Everyone who is not funny or curious is old or not rich.
Everyone who is not quiet is either patient or not generous.
Someone is old.
Someone is both quiet and strong.
Someone is either not calm or not patient.
Someone is happy.
Someone is both wise and brave.
John is both old and happy.
Mary is both humble and not quiet.
Susan is either wise or not kind. | John is not rich. | neutral | ((?[X]:((~calm(X)&rich(X))))=>((old(john)&tall(john))))&
(((rich(susan)&~calm(susan)))<=>(~old(mary)))&
((?[X]:((happy(X)<~>~funny(X))))<=>(happy(paul)))&
((?[X]:((curious(X)|kind(X))))=>(?[X]:((~quiet(X)&curious(X)))))&
((~quiet(lucy))<=>(?[X]:((~happy(X)<~>~wise(X)))))&
(![X]:((calm(X)|rich(X))<=>(~curious(X)<~>~strong(X))))&
(![X]:((~patient(X)|~quiet(X))=>(~rich(X)|calm(X))))&
(![X]:((wise(X)&~old(X))=>(quiet(X)|creative(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~brave(X)|~strong(X)))))&
(![X]:((wise(X)&generous(X))=>(~strong(X)|patient(X))))&
(![X]:((strong(X)&~curious(X))<=>(strong(X)<~>curious(X))))&
(((~rich(fred)|patient(fred)))<=>(calm(mary)))&
(![X]:((~creative(X)&happy(X))=>(~old(X)<~>wise(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~curious(X)&~rich(X)))))&
(![X]:((~funny(X)|curious(X))=>(old(X)|~rich(X))))&
(![X]:(~quiet(X)=>(patient(X)<~>~generous(X))))&
(?[X]:(old(X)))&
(?[X]:((quiet(X)&strong(X))))&
(?[X]:((~calm(X)<~>~patient(X))))&
(?[X]:(happy(X)))&
(?[X]:((wise(X)&brave(X))))&
((old(john)&happy(john)))&
((humble(mary)&~quiet(mary)))&
((wise(susan)<~>~kind(susan))) | ~rich(john) | [] | null | 0 |
If someone is old then someone is not tall.
If someone is not patient or happy then someone is both not tall and patient and vice versa.
If lucy is quiet or calm then paul is both not old and not curious and vice versa.
If lucy is not tall then someone is either not calm or not rich.
If mary is patient then someone is both tall and not curious.
Everyone who is old or not calm is both strong and kind.
If someone is brave or strong then mary is not quiet or not old.
If mary is not wise or not generous then someone is both not tall and not calm and vice versa.
If mary is both calm and not generous then john is both not strong and humble.
Everyone who is not strong or strong is both tall and funny and vice versa.
If someone is tall then someone is both quiet and not strong.
If alice is kind or creative then mary is not happy and vice versa.
If someone is not funny or wise then someone is brave or not patient and vice versa.
If someone is both quiet and not patient then someone is tall.
Everyone who is either creative or tall is not curious or wise.
Mary is generous or rich.
Alice is quiet or not kind.
Someone is not happy.
Someone is creative or tall.
Lucy is kind or not happy.
Someone is not kind.
Paul is wise or not tall. | Lucy is not old. | entailment | ((?[X]:(old(X)))=>(?[X]:(~tall(X))))&
((?[X]:((~patient(X)|happy(X))))<=>(?[X]:((~tall(X)&patient(X)))))&
(((quiet(lucy)|calm(lucy)))<=>((~old(paul)&~curious(paul))))&
((~tall(lucy))=>(?[X]:((~calm(X)<~>~rich(X)))))&
((patient(mary))=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:((old(X)|~calm(X))=>(strong(X)&kind(X))))&
((?[X]:((brave(X)|strong(X))))=>((~quiet(mary)|~old(mary))))&
(((~wise(mary)|~generous(mary)))<=>(?[X]:((~tall(X)&~calm(X)))))&
(((calm(mary)&~generous(mary)))=>((~strong(john)&humble(john))))&
(![X]:((~strong(X)|strong(X))<=>(tall(X)&funny(X))))&
((?[X]:(tall(X)))=>(?[X]:((quiet(X)&~strong(X)))))&
(((kind(alice)|creative(alice)))<=>(~happy(mary)))&
((?[X]:((~funny(X)|wise(X))))<=>(?[X]:((brave(X)|~patient(X)))))&
((?[X]:((quiet(X)&~patient(X))))=>(?[X]:(tall(X))))&
(![X]:((creative(X)<~>tall(X))=>(~curious(X)|wise(X))))&
((generous(mary)|rich(mary)))&
((quiet(alice)|~kind(alice)))&
(?[X]:(~happy(X)))&
(?[X]:((creative(X)|tall(X))))&
((kind(lucy)|~happy(lucy)))&
(?[X]:(~kind(X)))&
((wise(paul)|~tall(paul))) | ~old(lucy) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2060244636161370246984336
% SZS output start Proof for 2060244636161370246984336
1. ? [X0] : old(X0) => ? [X0] : ~tall(X0) [input p0]
10. ! [X0] : ((strong(X0) | ~strong(X0)) <=> (funny(X0) & tall(X0))) [input p9]
23. old(lucy) [input hypothesis]
24. ? [X0] : old(X0) => ? [X1] : ~tall(X1) [rectify 1]
30. ? [X1] : ~tall(X1) | ! [X0] : ~old(X0) [ennf transformation 24]
42. ? [X0] : ~tall(X0) | ! [X1] : ~old(X1) [rectify 30]
43. ? [X0] : ~tall(X0) => ~tall(sK0) [choice axiom]
44. ~tall(sK0) | ! [X1] : ~old(X1) [skolemisation 42,43]
62. ! [X0] : (((strong(X0) | ~strong(X0)) | (~funny(X0) | ~tall(X0))) & ((funny(X0) & tall(X0)) | (~strong(X0) & strong(X0)))) [nnf transformation 10]
63. ! [X0] : ((strong(X0) | ~strong(X0) | ~funny(X0) | ~tall(X0)) & ((funny(X0) & tall(X0)) | (~strong(X0) & strong(X0)))) [flattening 62]
84. ~tall(sK0) | ~old(X1) [cnf transformation 44]
111. tall(X0) | strong(X0) [cnf transformation 63]
112. tall(X0) | ~strong(X0) [cnf transformation 63]
135. old(lucy) [cnf transformation 23]
137. 1 <=> ! [X1] : ~old(X1) [avatar definition]
138. ~old(X1) <- (1) [avatar component clause 137]
140. 2 <=> tall(sK0) [avatar definition]
142. ~tall(sK0) <- (~2) [avatar component clause 140]
143. 1 | ~2 [avatar split clause 84,140,137]
273. tall(X0) [subsumption resolution 111,112]
336. $false <- (~2) [subsumption resolution 142,273]
337. 2 [avatar contradiction clause 336]
342. $false <- (1) [resolution 138,135]
343. ~1 [avatar contradiction clause 342]
344. $false [avatar sat refutation 143,337,343]
% SZS output end Proof for 2060244636161370246984336
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then someone is brave or quiet and vice versa.
Everyone who is either not old or creative is not funny and vice versa.
If mary is either not curious or funny then someone is either not wise or tall and vice versa.
If lucy is not creative then someone is quiet and vice versa.
Everyone who is not old or tall is both not generous and not creative and vice versa.
If someone is both humble and wise then someone is calm.
Everyone who is both old and strong is brave or not curious and vice versa.
Everyone who is not funny or not creative is not quiet and vice versa.
If alice is humble or not strong then someone is either not curious or not generous and vice versa.
Everyone who is both not wise and not kind is not quiet or not rich and vice versa.
Everyone who is both not happy and not old is brave or not strong.
If someone is curious then someone is both not quiet and brave.
If someone is both quiet and not old then someone is either tall or not old and vice versa.
If fred is not strong or not generous then john is not tall or not kind and vice versa.
If lucy is not rich then someone is not patient and vice versa.
Everyone who is not curious or patient is not humble.
Someone is not generous or not rich.
Someone is not kind or patient.
Someone is not calm.
Lucy is not quiet.
Fred is both not brave and rich.
Lucy is either not brave or curious. | Lucy is not brave. | entailment | ((?[X]:(quiet(X)))<=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:((~old(X)<~>creative(X))<=>~funny(X)))&
(((~curious(mary)<~>funny(mary)))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((~creative(lucy))<=>(?[X]:(quiet(X))))&
(![X]:((~old(X)|tall(X))<=>(~generous(X)&~creative(X))))&
((?[X]:((humble(X)&wise(X))))=>(?[X]:(calm(X))))&
(![X]:((old(X)&strong(X))<=>(brave(X)|~curious(X))))&
(![X]:((~funny(X)|~creative(X))<=>~quiet(X)))&
(((humble(alice)|~strong(alice)))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
(![X]:((~wise(X)&~kind(X))<=>(~quiet(X)|~rich(X))))&
(![X]:((~happy(X)&~old(X))=>(brave(X)|~strong(X))))&
((?[X]:(curious(X)))=>(?[X]:((~quiet(X)&brave(X)))))&
((?[X]:((quiet(X)&~old(X))))<=>(?[X]:((tall(X)<~>~old(X)))))&
(((~strong(fred)|~generous(fred)))<=>((~tall(john)|~kind(john))))&
((~rich(lucy))<=>(?[X]:(~patient(X))))&
(![X]:((~curious(X)|patient(X))=>~humble(X)))&
(?[X]:((~generous(X)|~rich(X))))&
(?[X]:((~kind(X)|patient(X))))&
(?[X]:(~calm(X)))&
(~quiet(lucy))&
((~brave(fred)&rich(fred)))&
((~brave(lucy)<~>curious(lucy))) | ~brave(lucy) | [
"p0",
"p1",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4947323749099996353741144
% SZS output start Proof for 4947323749099996353741144
1. ? [X0] : quiet(X0) <=> ? [X0] : (quiet(X0) | brave(X0)) [input p0]
2. ! [X0] : ((~old(X0) <~> creative(X0)) <=> ~funny(X0)) [input p1]
5. ! [X0] : ((tall(X0) | ~old(X0)) <=> (~creative(X0) & ~generous(X0))) [input p4]
8. ! [X0] : ((~creative(X0) | ~funny(X0)) <=> ~quiet(X0)) [input p7]
23. brave(lucy) [input hypothesis]
24. ? [X0] : quiet(X0) <=> ? [X1] : (quiet(X1) | brave(X1)) [rectify 1]
32. (? [X0] : quiet(X0) | ! [X1] : (~quiet(X1) & ~brave(X1))) & (? [X1] : (quiet(X1) | brave(X1)) | ! [X0] : ~quiet(X0)) [nnf transformation 24]
33. (? [X0] : quiet(X0) | ! [X1] : (~quiet(X1) & ~brave(X1))) & (? [X2] : (quiet(X2) | brave(X2)) | ! [X3] : ~quiet(X3)) [rectify 32]
34. ? [X0] : quiet(X0) => quiet(sK0) [choice axiom]
35. ? [X2] : (quiet(X2) | brave(X2)) => (quiet(sK1) | brave(sK1)) [choice axiom]
36. (quiet(sK0) | ! [X1] : (~quiet(X1) & ~brave(X1))) & ((quiet(sK1) | brave(sK1)) | ! [X3] : ~quiet(X3)) [skolemisation 33,35,34]
37. ! [X0] : ((((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | funny(X0)) & (~funny(X0) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0))))) [nnf transformation 2]
46. ! [X0] : (((tall(X0) | ~old(X0)) | (creative(X0) | generous(X0))) & ((~creative(X0) & ~generous(X0)) | (~tall(X0) & old(X0)))) [nnf transformation 5]
47. ! [X0] : ((tall(X0) | ~old(X0) | creative(X0) | generous(X0)) & ((~creative(X0) & ~generous(X0)) | (~tall(X0) & old(X0)))) [flattening 46]
53. ! [X0] : (((~creative(X0) | ~funny(X0)) | quiet(X0)) & (~quiet(X0) | (creative(X0) & funny(X0)))) [nnf transformation 8]
54. ! [X0] : ((~creative(X0) | ~funny(X0) | quiet(X0)) & (~quiet(X0) | (creative(X0) & funny(X0)))) [flattening 53]
84. quiet(sK0) | ~brave(X1) [cnf transformation 36]
87. ~funny(X0) | ~old(X0) | ~creative(X0) [cnf transformation 37]
102. ~creative(X0) | old(X0) [cnf transformation 47]
111. ~quiet(X0) | funny(X0) [cnf transformation 54]
112. ~quiet(X0) | creative(X0) [cnf transformation 54]
149. brave(lucy) [cnf transformation 23]
154. 2 <=> quiet(sK0) [avatar definition]
156. quiet(sK0) <- (2) [avatar component clause 154]
159. 3 <=> ! [X1] : ~brave(X1) [avatar definition]
160. ~brave(X1) <- (3) [avatar component clause 159]
161. 3 | 2 [avatar split clause 84,154,159]
343. 43 <=> brave(lucy) [avatar definition]
345. brave(lucy) <- (43) [avatar component clause 343]
352. 43 [avatar split clause 149,343]
364. funny(sK0) <- (2) [resolution 111,156]
366. creative(sK0) <- (2) [resolution 112,156]
368. old(sK0) <- (2) [resolution 366,102]
398. ~old(sK0) | ~creative(sK0) <- (2) [resolution 87,364]
401. ~creative(sK0) <- (2) [subsumption resolution 398,368]
402. $false <- (2) [subsumption resolution 401,366]
403. ~2 [avatar contradiction clause 402]
411. $false <- (3, 43) [resolution 160,345]
414. ~3 | ~43 [avatar contradiction clause 411]
416. $false [avatar sat refutation 161,352,403,414]
% SZS output end Proof for 4947323749099996353741144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either not patient or old then someone is either not creative or humble.
Everyone who is both not wise and not patient is either strong or old and vice versa.
Everyone who is calm or not creative is either not old or not curious.
Everyone who is both not wise and not old is both not humble and not kind.
Everyone who is not brave or not funny is not calm.
If someone is not generous or not kind then lucy is not funny and vice versa.
If paul is not patient or humble then someone is patient or not funny and vice versa.
Everyone who is both happy and not wise is both rich and happy.
Everyone who is both not curious and not creative is generous.
If paul is either brave or not quiet then susan is not rich or not strong and vice versa.
Everyone who is either creative or not happy is not tall or wise and vice versa.
If susan is not wise then someone is not strong or not patient.
If someone is either not old or not quiet then someone is both funny and not curious and vice versa.
If fred is both not wise and patient then alice is either strong or not wise and vice versa.
Everyone who is both quiet and not kind is brave or not happy and vice versa.
Someone is either not happy or kind.
Paul is old.
John is not happy or not calm.
Mary is either not tall or generous.
Mary is brave.
Someone is not old.
John is tall.
Alice is both not old and humble. | Mary is not kind. | entailment | (((~patient(john)<~>old(john)))=>(?[X]:((~creative(X)<~>humble(X)))))&
(![X]:((~wise(X)&~patient(X))<=>(strong(X)<~>old(X))))&
(![X]:((calm(X)|~creative(X))=>(~old(X)<~>~curious(X))))&
(![X]:((~wise(X)&~old(X))=>(~humble(X)&~kind(X))))&
(![X]:((~brave(X)|~funny(X))=>~calm(X)))&
((?[X]:((~generous(X)|~kind(X))))<=>(~funny(lucy)))&
(((~patient(paul)|humble(paul)))<=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((happy(X)&~wise(X))=>(rich(X)&happy(X))))&
(![X]:((~curious(X)&~creative(X))=>generous(X)))&
(((brave(paul)<~>~quiet(paul)))<=>((~rich(susan)|~strong(susan))))&
(![X]:((creative(X)<~>~happy(X))<=>(~tall(X)|wise(X))))&
((~wise(susan))=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
(((~wise(fred)&patient(fred)))<=>((strong(alice)<~>~wise(alice))))&
(![X]:((quiet(X)&~kind(X))<=>(brave(X)|~happy(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
(old(paul))&
((~happy(john)|~calm(john)))&
((~tall(mary)<~>generous(mary)))&
(brave(mary))&
(?[X]:(~old(X)))&
(tall(john))&
((~old(alice)&humble(alice))) | ~kind(mary) | [
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 740907984264819051617385
% SZS output start Proof for 740907984264819051617385
15. ! [X0] : ((~kind(X0) & quiet(X0)) <=> (~happy(X0) | brave(X0))) [input p14]
20. brave(mary) [input p19]
24. kind(mary) [input hypothesis]
66. ! [X0] : (((~kind(X0) & quiet(X0)) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | (kind(X0) | ~quiet(X0)))) [nnf transformation 15]
67. ! [X0] : (((~kind(X0) & quiet(X0)) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | kind(X0) | ~quiet(X0))) [flattening 66]
126. ~brave(X0) | ~kind(X0) [cnf transformation 67]
133. brave(mary) [cnf transformation 20]
138. kind(mary) [cnf transformation 24]
315. ~kind(mary) [resolution 126,133]
316. $false [subsumption resolution 315,138]
% SZS output end Proof for 740907984264819051617385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or creative is either rich or not strong and vice versa.
Everyone who is funny or curious is creative or not quiet and vice versa.
Everyone who is both not curious and tall is either creative or not quiet and vice versa.
If fred is funny then john is not curious or rich and vice versa.
Everyone who is both not rich and not happy is not brave and vice versa.
If john is quiet then someone is not tall or not generous.
If paul is curious or patient then someone is both not humble and tall.
Everyone who is both not calm and brave is both not patient and not funny and vice versa.
Everyone who is both not happy and calm is both not quiet and patient.
If someone is brave then john is both funny and not rich and vice versa.
Everyone who is not funny is either not rich or strong.
Everyone who is not patient is both not strong and humble.
Everyone who is not humble or not kind is not old or generous.
If alice is both not quiet and not rich then someone is not creative and vice versa.
Everyone who is wise is old and vice versa.
If alice is either not quiet or curious then mary is either old or curious.
Someone is quiet.
Mary is either strong or rich.
Fred is not generous or patient.
Someone is either generous or old.
Someone is not patient.
Someone is creative.
Someone is either not old or funny.
Someone is both happy and not funny. | Mary is tall. | entailment | (![X]:((patient(X)|creative(X))<=>(rich(X)<~>~strong(X))))&
(![X]:((funny(X)|curious(X))<=>(creative(X)|~quiet(X))))&
(![X]:((~curious(X)&tall(X))<=>(creative(X)<~>~quiet(X))))&
((funny(fred))<=>((~curious(john)|rich(john))))&
(![X]:((~rich(X)&~happy(X))<=>~brave(X)))&
((quiet(john))=>(?[X]:((~tall(X)|~generous(X)))))&
(((curious(paul)|patient(paul)))=>(?[X]:((~humble(X)&tall(X)))))&
(![X]:((~calm(X)&brave(X))<=>(~patient(X)&~funny(X))))&
(![X]:((~happy(X)&calm(X))=>(~quiet(X)&patient(X))))&
((?[X]:(brave(X)))<=>((funny(john)&~rich(john))))&
(![X]:(~funny(X)=>(~rich(X)<~>strong(X))))&
(![X]:(~patient(X)=>(~strong(X)&humble(X))))&
(![X]:((~humble(X)|~kind(X))=>(~old(X)|generous(X))))&
(((~quiet(alice)&~rich(alice)))<=>(?[X]:(~creative(X))))&
(![X]:(wise(X)<=>old(X)))&
(((~quiet(alice)<~>curious(alice)))=>((old(mary)<~>curious(mary))))&
(?[X]:(quiet(X)))&
((strong(mary)<~>rich(mary)))&
((~generous(fred)|patient(fred)))&
(?[X]:((generous(X)<~>old(X))))&
(?[X]:(~patient(X)))&
(?[X]:(creative(X)))&
(?[X]:((~old(X)<~>funny(X))))&
(?[X]:((happy(X)&~funny(X)))) | tall(mary) | [
"p0",
"p1",
"p2",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8107844844800453604517288
% SZS output start Proof for 8107844844800453604517288
1. ! [X0] : ((creative(X0) | patient(X0)) <=> (rich(X0) <~> ~strong(X0))) [input p0]
2. ! [X0] : ((curious(X0) | funny(X0)) <=> (~quiet(X0) | creative(X0))) [input p1]
3. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (creative(X0) <~> ~quiet(X0))) [input p2]
11. ! [X0] : (~funny(X0) => (~rich(X0) <~> strong(X0))) [input p10]
12. ! [X0] : (~patient(X0) => (humble(X0) & ~strong(X0))) [input p11]
18. strong(mary) <~> rich(mary) [input p17]
25. ~tall(mary) [input hypothesis]
31. ! [X0] : ((~rich(X0) <~> strong(X0)) | funny(X0)) [ennf transformation 11]
32. ! [X0] : ((humble(X0) & ~strong(X0)) | patient(X0)) [ennf transformation 12]
36. ! [X0] : (((creative(X0) | patient(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (~creative(X0) & ~patient(X0)))) [nnf transformation 1]
37. ! [X0] : ((creative(X0) | patient(X0) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (~creative(X0) & ~patient(X0)))) [flattening 36]
38. ! [X0] : (((curious(X0) | funny(X0)) | (quiet(X0) & ~creative(X0))) & ((~quiet(X0) | creative(X0)) | (~curious(X0) & ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | funny(X0) | (quiet(X0) & ~creative(X0))) & (~quiet(X0) | creative(X0) | (~curious(X0) & ~funny(X0)))) [flattening 38]
40. ! [X0] : (((tall(X0) & ~curious(X0)) | ((creative(X0) | quiet(X0)) & (~quiet(X0) | ~creative(X0)))) & (((quiet(X0) | ~creative(X0)) & (~quiet(X0) | creative(X0))) | (~tall(X0) | curious(X0)))) [nnf transformation 3]
41. ! [X0] : (((tall(X0) & ~curious(X0)) | ((creative(X0) | quiet(X0)) & (~quiet(X0) | ~creative(X0)))) & (((quiet(X0) | ~creative(X0)) & (~quiet(X0) | creative(X0))) | ~tall(X0) | curious(X0))) [flattening 40]
57. ! [X0] : (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | funny(X0)) [nnf transformation 31]
66. (~rich(mary) | ~strong(mary)) & (rich(mary) | strong(mary)) [nnf transformation 18]
79. ~strong(X0) | rich(X0) | ~patient(X0) [cnf transformation 37]
82. ~rich(X0) | strong(X0) | ~creative(X0) [cnf transformation 37]
85. ~quiet(X0) | creative(X0) | ~funny(X0) [cnf transformation 39]
94. tall(X0) | creative(X0) | quiet(X0) [cnf transformation 41]
115. ~rich(X0) | strong(X0) | funny(X0) [cnf transformation 57]
117. ~strong(X0) | patient(X0) [cnf transformation 32]
128. rich(mary) | strong(mary) [cnf transformation 66]
129. ~rich(mary) | ~strong(mary) [cnf transformation 66]
139. ~tall(mary) [cnf transformation 25]
238. 21 <=> strong(mary) [avatar definition]
239. strong(mary) <- (21) [avatar component clause 238]
240. ~strong(mary) <- (~21) [avatar component clause 238]
242. 22 <=> rich(mary) [avatar definition]
243. rich(mary) <- (22) [avatar component clause 242]
244. ~rich(mary) <- (~22) [avatar component clause 242]
245. ~21 | ~22 [avatar split clause 129,242,238]
246. 21 | 22 [avatar split clause 128,242,238]
277. patient(mary) <- (21) [resolution 117,239]
281. rich(mary) | ~patient(mary) <- (21) [resolution 79,239]
282. ~patient(mary) <- (21, ~22) [subsumption resolution 281,244]
283. $false <- (21, ~22) [subsumption resolution 282,277]
284. ~21 | 22 [avatar contradiction clause 283]
288. strong(mary) | ~creative(mary) <- (22) [resolution 82,243]
289. ~creative(mary) <- (~21, 22) [subsumption resolution 288,240]
328. creative(mary) | quiet(mary) [resolution 94,139]
329. quiet(mary) <- (~21, 22) [subsumption resolution 328,289]
332. creative(mary) | ~funny(mary) <- (~21, 22) [resolution 329,85]
334. ~funny(mary) <- (~21, 22) [subsumption resolution 332,289]
423. strong(mary) | funny(mary) <- (22) [resolution 115,243]
425. funny(mary) <- (~21, 22) [subsumption resolution 423,240]
426. $false <- (~21, 22) [subsumption resolution 425,334]
427. 21 | ~22 [avatar contradiction clause 426]
430. $false [avatar sat refutation 245,246,284,427]
% SZS output end Proof for 8107844844800453604517288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or patient is either curious or not curious. If lucy is kind or not rich then someone is either tall or kind and vice versa. Everyone who is either not curious or humble is both funny and curious. Everyone who is not generous or funny is both not creative and not quiet. Everyone who is brave or curious is not humble or not tall and vice versa. Everyone who is not patient is old or happy. If john is strong or not brave then someone is either not happy or not strong. Everyone who is not quiet is patient. If someone is curious then alice is both creative and generous. Everyone who is not funny is both not wise and patient and vice versa. If someone is either calm or quiet then mary is curious or not creative. Everyone who is both not patient and not rich is both tall and creative. If john is not happy then someone is happy and vice versa. Everyone who is both creative and wise is not funny or strong and vice versa. Everyone who is either creative or brave is either rich or not happy and vice versa. Alice is either not patient or not old. John is not calm. Lucy is wise. Paul is either rich or not brave. Someone is calm. | Alice is not kind. | neutral | (![X]:((rich(X)|patient(X))=>(curious(X)<~>~curious(X))))&
(((kind(lucy)|~rich(lucy)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
((~patient(alice)<~>~old(alice)))&
(~calm(john))&
(wise(lucy))&
((rich(paul)<~>~brave(paul)))&
(?[X]:(calm(X))) | ~kind(alice) | [] | null | 0 |
If someone is not creative then someone is not tall.
If paul is either curious or patient then paul is both not happy and rich and vice versa.
If john is either patient or not brave then mary is either not generous or not calm and vice versa.
If lucy is both not kind and curious then someone is creative or not quiet.
Everyone who is either not strong or not patient is both not strong and not happy and vice versa.
If someone is both happy and not creative then mary is quiet and vice versa.
If paul is not happy or not tall then someone is happy or humble and vice versa.
Everyone who is either curious or not happy is both curious and kind and vice versa.
Everyone who is both not calm and tall is calm and vice versa.
Everyone who is both tall and funny is either funny or quiet.
If fred is either not strong or not kind then someone is funny or rich.
Everyone who is both not creative and not patient is either not old or not wise and vice versa.
If paul is tall then fred is happy and vice versa.
Everyone who is either not creative or quiet is either curious or not patient.
If someone is kind then paul is humble.
If someone is both humble and strong then paul is either tall or not strong and vice versa.
Someone is not kind or not generous.
Someone is quiet.
Someone is strong.
Mary is both not tall and humble.
Alice is wise.
Mary is brave. | Fred is not humble. | neutral | ((?[X]:(~creative(X)))=>(?[X]:(~tall(X))))&
(((curious(paul)<~>patient(paul)))<=>((~happy(paul)&rich(paul))))&
(((patient(john)<~>~brave(john)))<=>((~generous(mary)<~>~calm(mary))))&
(((~kind(lucy)&curious(lucy)))=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((~strong(X)<~>~patient(X))<=>(~strong(X)&~happy(X))))&
((?[X]:((happy(X)&~creative(X))))<=>(quiet(mary)))&
(((~happy(paul)|~tall(paul)))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((curious(X)<~>~happy(X))<=>(curious(X)&kind(X))))&
(![X]:((~calm(X)&tall(X))<=>calm(X)))&
(![X]:((tall(X)&funny(X))=>(funny(X)<~>quiet(X))))&
(((~strong(fred)<~>~kind(fred)))=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((~creative(X)&~patient(X))<=>(~old(X)<~>~wise(X))))&
((tall(paul))<=>(happy(fred)))&
(![X]:((~creative(X)<~>quiet(X))=>(curious(X)<~>~patient(X))))&
((?[X]:(kind(X)))=>(humble(paul)))&
((?[X]:((humble(X)&strong(X))))<=>((tall(paul)<~>~strong(paul))))&
(?[X]:((~kind(X)|~generous(X))))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X)))&
((~tall(mary)&humble(mary)))&
(wise(alice))&
(brave(mary)) | ~humble(fred) | [] | null | 0 |
If someone is both not rich and not patient then someone is either not rich or not kind. Everyone who is both humble and not funny is wise or not calm and vice versa. Everyone who is either not generous or not curious is patient and vice versa. Everyone who is either not generous or curious is not brave and vice versa. If someone is kind then paul is creative and vice versa. Everyone who is both wise and brave is either funny or not patient and vice versa. If someone is either not quiet or not generous then someone is either generous or quiet. Everyone who is both kind and not curious is humble or calm and vice versa. Everyone who is brave is kind or not generous. If someone is funny or not creative then susan is not generous and vice versa. Everyone who is both rich and patient is either not funny or kind. If susan is happy or not rich then someone is brave or humble. If alice is humble then john is not old. If lucy is rich or calm then someone is curious and vice versa. Everyone who is either not calm or old is either not creative or not calm and vice versa. If someone is not wise then someone is not patient and vice versa. Someone is brave. Someone is either generous or calm. Mary is strong. John is either creative or not funny. Mary is not calm. Susan is tall. Someone is not quiet or humble. Someone is tall. | Susan is not wise. | entailment | ((?[X]:((~rich(X)&~patient(X))))=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((humble(X)&~funny(X))<=>(wise(X)|~calm(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>patient(X)))&
(![X]:((~generous(X)<~>curious(X))<=>~brave(X)))&
((?[X]:(kind(X)))<=>(creative(paul)))&
(![X]:((wise(X)&brave(X))<=>(funny(X)<~>~patient(X))))&
((?[X]:((~quiet(X)<~>~generous(X))))=>(?[X]:((generous(X)<~>quiet(X)))))&
(![X]:((kind(X)&~curious(X))<=>(humble(X)|calm(X))))&
(![X]:(brave(X)=>(kind(X)|~generous(X))))&
((?[X]:((funny(X)|~creative(X))))<=>(~generous(susan)))&
(![X]:((rich(X)&patient(X))=>(~funny(X)<~>kind(X))))&
(((happy(susan)|~rich(susan)))=>(?[X]:((brave(X)|humble(X)))))&
((humble(alice))=>(~old(john)))&
(((rich(lucy)|calm(lucy)))<=>(?[X]:(curious(X))))&
(![X]:((~calm(X)<~>old(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(~patient(X))))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)<~>calm(X))))&
(strong(mary))&
((creative(john)<~>~funny(john)))&
(~calm(mary))&
(tall(susan))&
(?[X]:((~quiet(X)|humble(X))))&
(?[X]:(tall(X))) | ~wise(susan) | [
"p1",
"p2",
"p3",
"p5",
"p7",
"p9",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 223765784935093173235715
% SZS output start Proof for 223765784935093173235715
2. ! [X0] : ((~funny(X0) & humble(X0)) <=> (~calm(X0) | wise(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> ~curious(X0)) <=> patient(X0)) [input p2]
4. ! [X0] : ((~generous(X0) <~> curious(X0)) <=> ~brave(X0)) [input p3]
6. ! [X0] : ((brave(X0) & wise(X0)) <=> (funny(X0) <~> ~patient(X0))) [input p5]
8. ! [X0] : ((~curious(X0) & kind(X0)) <=> (calm(X0) | humble(X0))) [input p7]
10. ? [X0] : (~creative(X0) | funny(X0)) <=> ~generous(susan) [input p9]
14. (calm(lucy) | rich(lucy)) <=> ? [X0] : curious(X0) [input p13]
16. ? [X0] : ~wise(X0) <=> ? [X0] : ~patient(X0) [input p15]
17. ? [X0] : brave(X0) [input p16]
25. wise(susan) [input hypothesis]
28. ? [X0] : ~wise(X0) <=> ? [X1] : ~patient(X1) [rectify 16]
45. ! [X0] : (((~funny(X0) & humble(X0)) | (calm(X0) & ~wise(X0))) & ((~calm(X0) | wise(X0)) | (funny(X0) | ~humble(X0)))) [nnf transformation 2]
46. ! [X0] : (((~funny(X0) & humble(X0)) | (calm(X0) & ~wise(X0))) & (~calm(X0) | wise(X0) | funny(X0) | ~humble(X0))) [flattening 45]
47. ! [X0] : ((((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | ~patient(X0)) & (patient(X0) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))))) [nnf transformation 3]
48. ! [X0] : ((((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | brave(X0)) & (~brave(X0) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0))))) [nnf transformation 4]
53. ! [X0] : (((brave(X0) & wise(X0)) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (~brave(X0) | ~wise(X0)))) [nnf transformation 6]
54. ! [X0] : (((brave(X0) & wise(X0)) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | ~brave(X0) | ~wise(X0))) [flattening 53]
59. ! [X0] : (((~curious(X0) & kind(X0)) | (~calm(X0) & ~humble(X0))) & ((calm(X0) | humble(X0)) | (curious(X0) | ~kind(X0)))) [nnf transformation 8]
60. ! [X0] : (((~curious(X0) & kind(X0)) | (~calm(X0) & ~humble(X0))) & (calm(X0) | humble(X0) | curious(X0) | ~kind(X0))) [flattening 59]
61. (? [X0] : (~creative(X0) | funny(X0)) | generous(susan)) & (~generous(susan) | ! [X0] : (creative(X0) & ~funny(X0))) [nnf transformation 10]
62. (? [X0] : (~creative(X0) | funny(X0)) | generous(susan)) & (~generous(susan) | ! [X1] : (creative(X1) & ~funny(X1))) [rectify 61]
63. ? [X0] : (~creative(X0) | funny(X0)) => (~creative(sK3) | funny(sK3)) [choice axiom]
64. ((~creative(sK3) | funny(sK3)) | generous(susan)) & (~generous(susan) | ! [X1] : (creative(X1) & ~funny(X1))) [skolemisation 62,63]
68. ((calm(lucy) | rich(lucy)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~calm(lucy) & ~rich(lucy))) [nnf transformation 14]
69. (calm(lucy) | rich(lucy) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~calm(lucy) & ~rich(lucy))) [flattening 68]
70. (calm(lucy) | rich(lucy) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | (~calm(lucy) & ~rich(lucy))) [rectify 69]
71. ? [X1] : curious(X1) => curious(sK5) [choice axiom]
72. (calm(lucy) | rich(lucy) | ! [X0] : ~curious(X0)) & (curious(sK5) | (~calm(lucy) & ~rich(lucy))) [skolemisation 70,71]
74. (? [X0] : ~wise(X0) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : wise(X0)) [nnf transformation 28]
75. (? [X0] : ~wise(X0) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : wise(X3)) [rectify 74]
76. ? [X0] : ~wise(X0) => ~wise(sK6) [choice axiom]
77. ? [X2] : ~patient(X2) => ~patient(sK7) [choice axiom]
78. (~wise(sK6) | ! [X1] : patient(X1)) & (~patient(sK7) | ! [X3] : wise(X3)) [skolemisation 75,77,76]
79. ? [X0] : brave(X0) => brave(sK8) [choice axiom]
80. brave(sK8) [skolemisation 17,79]
91. calm(X0) | humble(X0) [cnf transformation 46]
92. ~wise(X0) | ~funny(X0) [cnf transformation 46]
95. ~generous(X0) | patient(X0) | curious(X0) [cnf transformation 47]
97. ~patient(X0) | generous(X0) | curious(X0) [cnf transformation 47]
98. ~brave(X0) | curious(X0) | generous(X0) [cnf transformation 48]
104. ~patient(X0) | funny(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 54]
109. brave(X0) | funny(X0) | patient(X0) [cnf transformation 54]
117. ~curious(X0) | ~humble(X0) [cnf transformation 60]
118. ~curious(X0) | ~calm(X0) [cnf transformation 60]
120. ~generous(susan) | ~funny(X1) [cnf transformation 64]
127. curious(sK5) | ~rich(lucy) [cnf transformation 72]
128. curious(sK5) | ~calm(lucy) [cnf transformation 72]
129. calm(lucy) | rich(lucy) | ~curious(X0) [cnf transformation 72]
138. ~patient(sK7) | wise(X3) [cnf transformation 78]
140. brave(sK8) [cnf transformation 80]
147. wise(susan) [cnf transformation 25]
179. ~brave(X0) | ~patient(X0) | ~wise(X0) [subsumption resolution 104,92]
199. 11 <=> generous(susan) [avatar definition]
216. 15 <=> ! [X1] : ~funny(X1) [avatar definition]
217. ~funny(X1) <- (15) [avatar component clause 216]
218. 15 | ~11 [avatar split clause 120,199,216]
243. 21 <=> ! [X0] : ~curious(X0) [avatar definition]
244. ~curious(X0) <- (21) [avatar component clause 243]
246. 22 <=> rich(lucy) [avatar definition]
250. 23 <=> calm(lucy) [avatar definition]
253. 21 | 22 | 23 [avatar split clause 129,250,246,243]
255. 24 <=> curious(sK5) [avatar definition]
257. curious(sK5) <- (24) [avatar component clause 255]
258. ~23 | 24 [avatar split clause 128,255,250]
259. ~22 | 24 [avatar split clause 127,255,246]
263. 25 <=> ! [X1] : patient(X1) [avatar definition]
264. patient(X1) <- (25) [avatar component clause 263]
271. 27 <=> ! [X3] : wise(X3) [avatar definition]
272. wise(X3) <- (27) [avatar component clause 271]
274. 28 <=> patient(sK7) [avatar definition]
276. ~patient(sK7) <- (~28) [avatar component clause 274]
277. 27 | ~28 [avatar split clause 138,274,271]
311. ~funny(susan) [resolution 92,147]
336. curious(sK8) | generous(sK8) [resolution 98,140]
365. $false <- (25, ~28) [resolution 264,276]
367. ~25 | 28 [avatar contradiction clause 365]
403. 41 <=> curious(sK8) [avatar definition]
404. curious(sK8) <- (41) [avatar component clause 403]
405. ~curious(sK8) <- (~41) [avatar component clause 403]
407. 42 <=> generous(sK8) [avatar definition]
408. generous(sK8) <- (42) [avatar component clause 407]
415. ~calm(sK5) <- (24) [resolution 257,118]
416. ~humble(sK5) <- (24) [resolution 257,117]
438. 42 | 41 [avatar split clause 336,403,407]
443. funny(X1) | patient(X1) | curious(X1) | generous(X1) [resolution 109,98]
446. patient(X1) | curious(X1) | generous(X1) <- (15) [subsumption resolution 443,217]
447. curious(X1) | generous(X1) <- (15) [subsumption resolution 446,97]
463. patient(sK8) | curious(sK8) <- (42) [resolution 408,95]
464. patient(sK8) <- (~41, 42) [subsumption resolution 463,405]
465. ~patient(sK8) | ~wise(sK8) [resolution 179,140]
467. ~wise(sK8) <- (~41, 42) [subsumption resolution 465,464]
468. humble(sK5) <- (24) [resolution 415,91]
469. $false <- (24) [subsumption resolution 468,416]
470. ~24 [avatar contradiction clause 469]
508. generous(X5) <- (15, 21) [resolution 447,244]
515. patient(X1) | curious(X1) <- (15, 21) [resolution 508,95]
525. patient(X1) <- (15, 21) [subsumption resolution 515,244]
526. 25 | ~15 | ~21 [avatar split clause 525,243,216,263]
531. generous(X1) | patient(X1) | funny(X1) <- (21) [subsumption resolution 443,244]
587. patient(X1) | funny(X1) | patient(X1) | curious(X1) <- (21) [resolution 531,95]
592. patient(X1) | funny(X1) | curious(X1) <- (21) [duplicate literal removal 587]
593. funny(X1) | patient(X1) <- (21) [subsumption resolution 592,244]
614. patient(susan) <- (21) [resolution 593,311]
635. generous(susan) | curious(susan) <- (21) [resolution 614,97]
641. generous(susan) <- (21) [subsumption resolution 635,244]
642. 11 | ~21 [avatar split clause 641,243,199]
670. $false <- (27, ~41, 42) [resolution 272,467]
671. ~27 | 41 | ~42 [avatar contradiction clause 670]
681. $false <- (21, 41) [subsumption resolution 404,244]
682. ~21 | ~41 [avatar contradiction clause 681]
683. $false [avatar sat refutation 218,253,258,259,277,367,438,470,526,642,671,682]
% SZS output end Proof for 223765784935093173235715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old or happy is not generous.
Everyone who is strong is brave or not kind and vice versa.
If someone is strong or quiet then someone is both not quiet and not patient and vice versa.
Everyone who is not kind or not humble is strong or creative.
If john is not kind then someone is both not curious and not quiet.
Everyone who is both quiet and not tall is both kind and generous.
Everyone who is not rich is not wise or not old and vice versa.
Everyone who is both not rich and brave is not happy or not funny.
Everyone who is curious or funny is not wise.
Everyone who is either not strong or kind is not funny or strong.
Everyone who is kind is not old.
Everyone who is either brave or happy is both wise and not generous.
If someone is both kind and not quiet then someone is both curious and humble and vice versa.
Everyone who is both funny and wise is not wise.
If someone is both tall and not curious then john is kind or creative.
Everyone who is either quiet or not old is both not wise and rich and vice versa.
Someone is both strong and rich.
Mary is patient.
Mary is not funny or not humble.
Someone is either curious or wise.
Someone is either not funny or not kind.
Fred is both not tall and funny.
Someone is not quiet.
Susan is not funny. | Fred is not happy. | entailment | (![X]:((~old(X)|happy(X))=>~generous(X)))&
(![X]:(strong(X)<=>(brave(X)|~kind(X))))&
((?[X]:((strong(X)|quiet(X))))<=>(?[X]:((~quiet(X)&~patient(X)))))&
(![X]:((~kind(X)|~humble(X))=>(strong(X)|creative(X))))&
((~kind(john))=>(?[X]:((~curious(X)&~quiet(X)))))&
(![X]:((quiet(X)&~tall(X))=>(kind(X)&generous(X))))&
(![X]:(~rich(X)<=>(~wise(X)|~old(X))))&
(![X]:((~rich(X)&brave(X))=>(~happy(X)|~funny(X))))&
(![X]:((curious(X)|funny(X))=>~wise(X)))&
(![X]:((~strong(X)<~>kind(X))=>(~funny(X)|strong(X))))&
(![X]:(kind(X)=>~old(X)))&
(![X]:((brave(X)<~>happy(X))=>(wise(X)&~generous(X))))&
((?[X]:((kind(X)&~quiet(X))))<=>(?[X]:((curious(X)&humble(X)))))&
(![X]:((funny(X)&wise(X))=>~wise(X)))&
((?[X]:((tall(X)&~curious(X))))=>((kind(john)|creative(john))))&
(![X]:((quiet(X)<~>~old(X))<=>(~wise(X)&rich(X))))&
(?[X]:((strong(X)&rich(X))))&
(patient(mary))&
((~funny(mary)|~humble(mary)))&
(?[X]:((curious(X)<~>wise(X))))&
(?[X]:((~funny(X)<~>~kind(X))))&
((~tall(fred)&funny(fred)))&
(?[X]:(~quiet(X)))&
(~funny(susan)) | ~happy(fred) | [
"p6",
"p7",
"p8",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7960658029002510587739712
% SZS output start Proof for 7960658029002510587739712
7. ! [X0] : (~rich(X0) <=> (~old(X0) | ~wise(X0))) [input p6]
8. ! [X0] : ((brave(X0) & ~rich(X0)) => (~funny(X0) | ~happy(X0))) [input p7]
9. ! [X0] : ((funny(X0) | curious(X0)) => ~wise(X0)) [input p8]
12. ! [X0] : ((brave(X0) <~> happy(X0)) => (~generous(X0) & wise(X0))) [input p11]
22. funny(fred) & ~tall(fred) [input p21]
25. happy(fred) [input hypothesis]
34. ! [X0] : ((~funny(X0) | ~happy(X0)) | (~brave(X0) | rich(X0))) [ennf transformation 8]
35. ! [X0] : (~funny(X0) | ~happy(X0) | ~brave(X0) | rich(X0)) [flattening 34]
36. ! [X0] : (~wise(X0) | (~funny(X0) & ~curious(X0))) [ennf transformation 9]
40. ! [X0] : ((~generous(X0) & wise(X0)) | (brave(X0) <=> happy(X0))) [ennf transformation 12]
52. ! [X0] : ((~rich(X0) | (old(X0) & wise(X0))) & ((~old(X0) | ~wise(X0)) | rich(X0))) [nnf transformation 7]
53. ! [X0] : ((~rich(X0) | (old(X0) & wise(X0))) & (~old(X0) | ~wise(X0) | rich(X0))) [flattening 52]
55. ! [X0] : ((~generous(X0) & wise(X0)) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0)))) [nnf transformation 40]
88. ~rich(X0) | wise(X0) [cnf transformation 53]
90. ~funny(X0) | ~happy(X0) | ~brave(X0) | rich(X0) [cnf transformation 35]
92. ~funny(X0) | ~wise(X0) [cnf transformation 36]
97. ~happy(X0) | brave(X0) | wise(X0) [cnf transformation 55]
120. funny(fred) [cnf transformation 22]
123. happy(fred) [cnf transformation 25]
230. ~wise(fred) [resolution 92,120]
247. brave(fred) | wise(fred) [resolution 97,123]
248. brave(fred) [subsumption resolution 247,230]
255. ~happy(fred) | ~brave(fred) | rich(fred) [resolution 90,120]
257. ~brave(fred) | rich(fred) [subsumption resolution 255,123]
258. rich(fred) [subsumption resolution 257,248]
273. wise(fred) [resolution 258,88]
274. $false [subsumption resolution 273,230]
% SZS output end Proof for 7960658029002510587739712
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not old and kind then fred is both humble and not quiet.
Everyone who is not kind or not generous is patient or not wise and vice versa.
If someone is either not funny or old then someone is not brave or quiet and vice versa.
If lucy is not humble or generous then john is happy or not funny.
Everyone who is kind or not wise is either generous or kind and vice versa.
If someone is rich or not creative then john is both not quiet and quiet and vice versa.
Everyone who is not generous or not wise is patient or funny and vice versa.
Everyone who is not humble is either calm or not tall.
Everyone who is not quiet or not creative is not rich or not kind.
Everyone who is humble is not funny and vice versa.
Everyone who is either happy or patient is not tall.
Everyone who is wise or curious is either not tall or wise.
If someone is both not generous and patient then susan is both wise and calm.
If fred is both not funny and not wise then someone is strong.
Everyone who is not happy or patient is not creative.
Everyone who is happy is not rich and vice versa.
Fred is rich or not quiet.
Fred is not wise.
Someone is creative or not wise.
Fred is funny or rich.
Someone is either strong or not wise.
Someone is either not brave or tall.
Mary is either not quiet or tall. | John is not calm. | entailment | (((~old(john)&kind(john)))=>((humble(fred)&~quiet(fred))))&
(![X]:((~kind(X)|~generous(X))<=>(patient(X)|~wise(X))))&
((?[X]:((~funny(X)<~>old(X))))<=>(?[X]:((~brave(X)|quiet(X)))))&
(((~humble(lucy)|generous(lucy)))=>((happy(john)|~funny(john))))&
(![X]:((kind(X)|~wise(X))<=>(generous(X)<~>kind(X))))&
((?[X]:((rich(X)|~creative(X))))<=>((~quiet(john)&quiet(john))))&
(![X]:((~generous(X)|~wise(X))<=>(patient(X)|funny(X))))&
(![X]:(~humble(X)=>(calm(X)<~>~tall(X))))&
(![X]:((~quiet(X)|~creative(X))=>(~rich(X)|~kind(X))))&
(![X]:(humble(X)<=>~funny(X)))&
(![X]:((happy(X)<~>patient(X))=>~tall(X)))&
(![X]:((wise(X)|curious(X))=>(~tall(X)<~>wise(X))))&
((?[X]:((~generous(X)&patient(X))))=>((wise(susan)&calm(susan))))&
(((~funny(fred)&~wise(fred)))=>(?[X]:(strong(X))))&
(![X]:((~happy(X)|patient(X))=>~creative(X)))&
(![X]:(happy(X)<=>~rich(X)))&
((rich(fred)|~quiet(fred)))&
(~wise(fred))&
(?[X]:((creative(X)|~wise(X))))&
((funny(fred)|rich(fred)))&
(?[X]:((strong(X)<~>~wise(X))))&
(?[X]:((~brave(X)<~>tall(X))))&
((~quiet(mary)<~>tall(mary))) | ~calm(john) | [
"p1",
"p4",
"p5",
"p6",
"p7",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6961087938773539090751856
% SZS output start Proof for 6961087938773539090751856
2. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (~wise(X0) | patient(X0))) [input p1]
5. ! [X0] : ((~wise(X0) | kind(X0)) <=> (generous(X0) <~> kind(X0))) [input p4]
6. ? [X0] : (~creative(X0) | rich(X0)) <=> (quiet(john) & ~quiet(john)) [input p5]
7. ! [X0] : ((~wise(X0) | ~generous(X0)) <=> (funny(X0) | patient(X0))) [input p6]
8. ! [X0] : (~humble(X0) => (calm(X0) <~> ~tall(X0))) [input p7]
10. ! [X0] : (humble(X0) <=> ~funny(X0)) [input p9]
11. ! [X0] : ((happy(X0) <~> patient(X0)) => ~tall(X0)) [input p10]
15. ! [X0] : ((patient(X0) | ~happy(X0)) => ~creative(X0)) [input p14]
24. calm(john) [input hypothesis]
26. ! [X0] : (humble(X0) => ~funny(X0)) [unused predicate definition removal 10]
32. ! [X0] : ((calm(X0) <~> ~tall(X0)) | humble(X0)) [ennf transformation 8]
35. ! [X0] : (~funny(X0) | ~humble(X0)) [ennf transformation 26]
36. ! [X0] : (~tall(X0) | (happy(X0) <=> patient(X0))) [ennf transformation 11]
41. ! [X0] : (~creative(X0) | (~patient(X0) & happy(X0))) [ennf transformation 15]
42. ! [X0] : (((~generous(X0) | ~kind(X0)) | (wise(X0) & ~patient(X0))) & ((~wise(X0) | patient(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 2]
43. ! [X0] : ((~generous(X0) | ~kind(X0) | (wise(X0) & ~patient(X0))) & (~wise(X0) | patient(X0) | (generous(X0) & kind(X0)))) [flattening 42]
49. ! [X0] : (((~wise(X0) | kind(X0)) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | (wise(X0) & ~kind(X0)))) [nnf transformation 5]
50. ! [X0] : ((~wise(X0) | kind(X0) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | (wise(X0) & ~kind(X0)))) [flattening 49]
51. (? [X0] : (~creative(X0) | rich(X0)) | (~quiet(john) | quiet(john))) & ((quiet(john) & ~quiet(john)) | ! [X0] : (creative(X0) & ~rich(X0))) [nnf transformation 6]
52. (? [X0] : (~creative(X0) | rich(X0)) | ~quiet(john) | quiet(john)) & ((quiet(john) & ~quiet(john)) | ! [X0] : (creative(X0) & ~rich(X0))) [flattening 51]
53. (? [X0] : (~creative(X0) | rich(X0)) | ~quiet(john) | quiet(john)) & ((quiet(john) & ~quiet(john)) | ! [X1] : (creative(X1) & ~rich(X1))) [rectify 52]
54. ? [X0] : (~creative(X0) | rich(X0)) => (~creative(sK2) | rich(sK2)) [choice axiom]
55. ((~creative(sK2) | rich(sK2)) | ~quiet(john) | quiet(john)) & ((quiet(john) & ~quiet(john)) | ! [X1] : (creative(X1) & ~rich(X1))) [skolemisation 53,54]
56. ! [X0] : (((~wise(X0) | ~generous(X0)) | (~funny(X0) & ~patient(X0))) & ((funny(X0) | patient(X0)) | (wise(X0) & generous(X0)))) [nnf transformation 7]
57. ! [X0] : ((~wise(X0) | ~generous(X0) | (~funny(X0) & ~patient(X0))) & (funny(X0) | patient(X0) | (wise(X0) & generous(X0)))) [flattening 56]
58. ! [X0] : (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | humble(X0)) [nnf transformation 32]
59. ! [X0] : (~tall(X0) | ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0)))) [nnf transformation 36]
75. ~wise(X0) | patient(X0) | kind(X0) [cnf transformation 43]
89. ~kind(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 50]
94. ~quiet(john) | creative(X1) [cnf transformation 55]
96. quiet(john) | creative(X1) [cnf transformation 55]
98. funny(X0) | patient(X0) | generous(X0) [cnf transformation 57]
99. funny(X0) | patient(X0) | wise(X0) [cnf transformation 57]
103. ~calm(X0) | tall(X0) | humble(X0) [cnf transformation 58]
106. ~funny(X0) | ~humble(X0) [cnf transformation 35]
107. ~tall(X0) | patient(X0) | ~happy(X0) [cnf transformation 59]
114. ~creative(X0) | happy(X0) [cnf transformation 41]
115. ~creative(X0) | ~patient(X0) [cnf transformation 41]
128. calm(john) [cnf transformation 24]
130. ~generous(X0) | ~kind(X0) [duplicate literal removal 89]
137. 2 <=> kind(john) [avatar definition]
193. 15 <=> funny(john) [avatar definition]
194. funny(john) <- (15) [avatar component clause 193]
195. ~funny(john) <- (~15) [avatar component clause 193]
203. 17 <=> ! [X1] : creative(X1) [avatar definition]
204. creative(X1) <- (17) [avatar component clause 203]
206. 18 <=> quiet(john) [avatar definition]
209. 17 | 18 [avatar split clause 96,206,203]
214. 17 | ~18 [avatar split clause 94,206,203]
290. happy(X0) <- (17) [resolution 114,204]
291. ~patient(X0) <- (17) [resolution 115,204]
306. patient(john) | generous(john) <- (~15) [resolution 98,195]
309. generous(john) <- (~15, 17) [subsumption resolution 306,291]
324. patient(john) | wise(john) <- (~15) [resolution 99,195]
328. wise(john) <- (~15, 17) [subsumption resolution 324,291]
332. ~kind(john) <- (~15, 17) [resolution 309,130]
336. patient(john) | kind(john) <- (~15, 17) [resolution 328,75]
338. kind(john) <- (~15, 17) [subsumption resolution 336,291]
341. 2 | 15 | ~17 [avatar split clause 338,203,193,137]
342. ~2 | 15 | ~17 [avatar split clause 332,203,193,137]
344. ~humble(john) <- (15) [resolution 194,106]
365. tall(john) | humble(john) [resolution 103,128]
366. tall(john) <- (15) [subsumption resolution 365,344]
371. patient(john) | ~happy(john) <- (15) [resolution 107,366]
372. ~happy(john) <- (15, 17) [subsumption resolution 371,291]
373. $false <- (15, 17) [subsumption resolution 372,290]
374. ~15 | ~17 [avatar contradiction clause 373]
375. $false [avatar sat refutation 209,214,341,342,374]
% SZS output end Proof for 6961087938773539090751856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is not calm or not quiet then lucy is tall or generous. Everyone who is either not humble or not old is both not quiet and rich. Everyone who is either not tall or not creative is not tall or brave and vice versa. If john is either patient or kind then john is not kind. If fred is calm then susan is both not funny and kind. Everyone who is both kind and wise is not calm and vice versa. Everyone who is patient is not patient. Everyone who is not curious is wise. If someone is patient then mary is brave or not funny and vice versa. If someone is either rich or not brave then alice is not humble or old. Everyone who is rich or curious is both brave and old and vice versa. Everyone who is not kind or calm is both humble and tall and vice versa. Everyone who is either not quiet or not patient is wise or not creative. Everyone who is wise or happy is either tall or creative and vice versa. If someone is both not creative and not kind then someone is both tall and funny. Everyone who is generous is either old or not humble and vice versa. Lucy is either wise or patient. Lucy is not patient or not wise. Lucy is both curious and wise. Susan is not brave. Someone is both not patient and not funny. Someone is creative. Alice is both quiet and not brave. | Mary is not calm. | entailment | (((~calm(john)|~quiet(john)))=>((tall(lucy)|generous(lucy))))&
(![X]:((~humble(X)<~>~old(X))=>(~quiet(X)&rich(X))))&
(![X]:((~tall(X)<~>~creative(X))<=>(~tall(X)|brave(X))))&
(((patient(john)<~>kind(john)))=>(~kind(john)))&
((calm(fred))=>((~funny(susan)&kind(susan))))&
(![X]:((kind(X)&wise(X))<=>~calm(X)))&
(![X]:(patient(X)=>~patient(X)))&
(![X]:(~curious(X)=>wise(X)))&
((?[X]:(patient(X)))<=>((brave(mary)|~funny(mary))))&
((?[X]:((rich(X)<~>~brave(X))))=>((~humble(alice)|old(alice))))&
(![X]:((rich(X)|curious(X))<=>(brave(X)&old(X))))&
(![X]:((~kind(X)|calm(X))<=>(humble(X)&tall(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(wise(X)|~creative(X))))&
(![X]:((wise(X)|happy(X))<=>(tall(X)<~>creative(X))))&
((?[X]:((~creative(X)&~kind(X))))=>(?[X]:((tall(X)&funny(X)))))&
(![X]:(generous(X)<=>(old(X)<~>~humble(X))))&
((wise(lucy)<~>patient(lucy)))&
((~patient(lucy)|~wise(lucy)))&
((curious(lucy)&wise(lucy)))&
(~brave(susan))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:(creative(X)))&
((quiet(alice)&~brave(alice))) | ~calm(mary) | [
"p2",
"p6",
"p7",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4913383551376933616140513
% SZS output start Proof for 4913383551376933616140513
3. ! [X0] : ((~tall(X0) <~> ~creative(X0)) <=> (brave(X0) | ~tall(X0))) [input p2]
7. ! [X0] : (patient(X0) => ~patient(X0)) [input p6]
8. ! [X0] : (~curious(X0) => wise(X0)) [input p7]
9. ? [X0] : patient(X0) <=> (~funny(mary) | brave(mary)) [input p8]
11. ! [X0] : ((curious(X0) | rich(X0)) <=> (old(X0) & brave(X0))) [input p10]
12. ! [X0] : ((calm(X0) | ~kind(X0)) <=> (tall(X0) & humble(X0))) [input p11]
14. ! [X0] : ((happy(X0) | wise(X0)) <=> (tall(X0) <~> creative(X0))) [input p13]
24. calm(mary) [input hypothesis]
32. ! [X0] : (~patient(X0) | ~patient(X0)) [ennf transformation 7]
33. ! [X0] : (wise(X0) | curious(X0)) [ennf transformation 8]
41. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~brave(X0) & tall(X0))) & ((brave(X0) | ~tall(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [nnf transformation 3]
42. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~brave(X0) & tall(X0))) & (brave(X0) | ~tall(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [flattening 41]
46. (? [X0] : patient(X0) | (funny(mary) & ~brave(mary))) & ((~funny(mary) | brave(mary)) | ! [X0] : ~patient(X0)) [nnf transformation 9]
47. (? [X0] : patient(X0) | (funny(mary) & ~brave(mary))) & (~funny(mary) | brave(mary) | ! [X0] : ~patient(X0)) [flattening 46]
48. (? [X0] : patient(X0) | (funny(mary) & ~brave(mary))) & (~funny(mary) | brave(mary) | ! [X1] : ~patient(X1)) [rectify 47]
49. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
50. (patient(sK0) | (funny(mary) & ~brave(mary))) & (~funny(mary) | brave(mary) | ! [X1] : ~patient(X1)) [skolemisation 48,49]
52. ! [X0] : (((curious(X0) | rich(X0)) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | (~curious(X0) & ~rich(X0)))) [nnf transformation 11]
53. ! [X0] : ((curious(X0) | rich(X0) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | (~curious(X0) & ~rich(X0)))) [flattening 52]
54. ! [X0] : (((calm(X0) | ~kind(X0)) | (~tall(X0) | ~humble(X0))) & ((tall(X0) & humble(X0)) | (~calm(X0) & kind(X0)))) [nnf transformation 12]
55. ! [X0] : ((calm(X0) | ~kind(X0) | ~tall(X0) | ~humble(X0)) & ((tall(X0) & humble(X0)) | (~calm(X0) & kind(X0)))) [flattening 54]
57. ! [X0] : (((happy(X0) | wise(X0)) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) & (((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | (~happy(X0) & ~wise(X0)))) [nnf transformation 14]
58. ! [X0] : ((happy(X0) | wise(X0) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) & (((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | (~happy(X0) & ~wise(X0)))) [flattening 57]
75. brave(X0) | ~tall(X0) | ~tall(X0) | creative(X0) [cnf transformation 42]
78. creative(X0) | tall(X0) | tall(X0) [cnf transformation 42]
87. ~patient(X0) | ~patient(X0) [cnf transformation 32]
88. curious(X0) | wise(X0) [cnf transformation 33]
90. patient(sK0) | ~brave(mary) [cnf transformation 50]
95. ~curious(X0) | brave(X0) [cnf transformation 53]
102. ~calm(X0) | tall(X0) [cnf transformation 55]
108. ~wise(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 58]
127. calm(mary) [cnf transformation 24]
128. ~patient(X0) [duplicate literal removal 87]
130. brave(X0) | ~tall(X0) | creative(X0) [duplicate literal removal 75]
131. creative(X0) | tall(X0) [duplicate literal removal 78]
150. brave(X0) | creative(X0) [subsumption resolution 130,131]
175. ~brave(mary) [subsumption resolution 90,128]
213. wise(X0) | brave(X0) [resolution 95,88]
220. tall(mary) [resolution 102,127]
343. brave(X0) | ~tall(X0) | ~creative(X0) [resolution 213,108]
345. ~tall(X0) | brave(X0) [subsumption resolution 343,150]
399. brave(mary) [resolution 345,220]
401. $false [subsumption resolution 399,175]
% SZS output end Proof for 4913383551376933616140513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or calm is either curious or wise and vice versa. Everyone who is curious is both not creative and brave and vice versa. If paul is both not patient and not calm then fred is either not wise or rich. If alice is either not rich or rich then fred is both not curious and not strong and vice versa. Everyone who is either not happy or funny is strong and vice versa. Everyone who is both not tall and not old is patient or not patient. Everyone who is either not brave or patient is either patient or not happy. Everyone who is either not calm or funny is either not tall or curious and vice versa. Everyone who is either curious or humble is quiet or not rich. If mary is not old then someone is either not creative or creative and vice versa. Everyone who is brave is either tall or not calm and vice versa. Everyone who is either not tall or rich is either wise or not tall and vice versa. Everyone who is either not happy or not creative is both generous and quiet and vice versa. Everyone who is both happy and not generous is not calm or funny and vice versa. Everyone who is either not old or not funny is not humble and vice versa. If someone is calm then someone is not brave and vice versa. Fred is either not kind or not tall. Someone is either not happy or wise. Mary is tall or not creative. Someone is not curious or kind. Someone is not kind or not strong. Fred is not quiet. | Fred is not tall. | neutral | (![X]:((old(X)<~>calm(X))<=>(curious(X)<~>wise(X))))&
(![X]:(curious(X)<=>(~creative(X)&brave(X))))&
(((~patient(paul)&~calm(paul)))=>((~wise(fred)<~>rich(fred))))&
(((~rich(alice)<~>rich(alice)))<=>((~curious(fred)&~strong(fred))))&
(![X]:((~happy(X)<~>funny(X))<=>strong(X)))&
(![X]:((~tall(X)&~old(X))=>(patient(X)|~patient(X))))&
(![X]:((~brave(X)<~>patient(X))=>(patient(X)<~>~happy(X))))&
(![X]:((~calm(X)<~>funny(X))<=>(~tall(X)<~>curious(X))))&
(![X]:((curious(X)<~>humble(X))=>(quiet(X)|~rich(X))))&
((~old(mary))<=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:(brave(X)<=>(tall(X)<~>~calm(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(wise(X)<~>~tall(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(generous(X)&quiet(X))))&
(![X]:((happy(X)&~generous(X))<=>(~calm(X)|funny(X))))&
(![X]:((~old(X)<~>~funny(X))<=>~humble(X)))&
((?[X]:(calm(X)))<=>(?[X]:(~brave(X))))&
((~kind(fred)<~>~tall(fred)))&
(?[X]:((~happy(X)<~>wise(X))))&
((tall(mary)|~creative(mary)))&
(?[X]:((~curious(X)|kind(X))))&
(?[X]:((~kind(X)|~strong(X))))&
(~quiet(fred)) | ~tall(fred) | [] | null | 0 |
Everyone who is patient is humble and vice versa.
Everyone who is quiet is either not rich or brave.
If mary is not creative or rich then someone is either rich or not happy.
Everyone who is both funny and not strong is strong or happy and vice versa.
If paul is wise or brave then someone is either not tall or not curious.
If someone is either not calm or creative then someone is both rich and not humble and vice versa.
If someone is both patient and generous then someone is not kind and vice versa.
Everyone who is either not calm or not humble is not brave.
Everyone who is wise or not strong is both creative and tall and vice versa.
Everyone who is not tall is not funny or wise and vice versa.
Everyone who is either happy or not generous is not funny or old and vice versa.
Everyone who is not creative is not generous or not curious.
Everyone who is not brave is brave or not generous and vice versa.
If someone is brave or patient then alice is either not humble or not funny and vice versa.
If someone is tall then someone is not humble.
If lucy is generous then someone is creative or funny.
Paul is funny.
Mary is not rich.
Susan is not wise.
Susan is both creative and rich.
Alice is either calm or creative. | Alice is not creative. | contradiction | (![X]:(patient(X)<=>humble(X)))&
(![X]:(quiet(X)=>(~rich(X)<~>brave(X))))&
(((~creative(mary)|rich(mary)))=>(?[X]:((rich(X)<~>~happy(X)))))&
(![X]:((funny(X)&~strong(X))<=>(strong(X)|happy(X))))&
(((wise(paul)|brave(paul)))=>(?[X]:((~tall(X)<~>~curious(X)))))&
((?[X]:((~calm(X)<~>creative(X))))<=>(?[X]:((rich(X)&~humble(X)))))&
((?[X]:((patient(X)&generous(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~calm(X)<~>~humble(X))=>~brave(X)))&
(![X]:((wise(X)|~strong(X))<=>(creative(X)&tall(X))))&
(![X]:(~tall(X)<=>(~funny(X)|wise(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(~funny(X)|old(X))))&
(![X]:(~creative(X)=>(~generous(X)|~curious(X))))&
(![X]:(~brave(X)<=>(brave(X)|~generous(X))))&
((?[X]:((brave(X)|patient(X))))<=>((~humble(alice)<~>~funny(alice))))&
((?[X]:(tall(X)))=>(?[X]:(~humble(X))))&
((generous(lucy))=>(?[X]:((creative(X)|funny(X)))))&
(funny(paul))&
(~rich(mary))&
(~wise(susan))&
((creative(susan)&rich(susan)))&
((calm(alice)<~>creative(alice))) | ~creative(alice) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3477578315676272891224374
% SZS output start Proof for 3477578315676272891224374
4. ! [X0] : ((~strong(X0) & funny(X0)) <=> (happy(X0) | strong(X0))) [input p3]
9. ! [X0] : ((~strong(X0) | wise(X0)) <=> (tall(X0) & creative(X0))) [input p8]
22. ~creative(alice) [input hypothesis]
38. ! [X0] : (((~strong(X0) & funny(X0)) | (~happy(X0) & ~strong(X0))) & ((happy(X0) | strong(X0)) | (strong(X0) | ~funny(X0)))) [nnf transformation 4]
39. ! [X0] : (((~strong(X0) & funny(X0)) | (~happy(X0) & ~strong(X0))) & (happy(X0) | strong(X0) | strong(X0) | ~funny(X0))) [flattening 38]
54. ! [X0] : (((~strong(X0) | wise(X0)) | (~tall(X0) | ~creative(X0))) & ((tall(X0) & creative(X0)) | (strong(X0) & ~wise(X0)))) [nnf transformation 9]
55. ! [X0] : ((~strong(X0) | wise(X0) | ~tall(X0) | ~creative(X0)) & ((tall(X0) & creative(X0)) | (strong(X0) & ~wise(X0)))) [flattening 54]
81. ~strong(X0) | ~strong(X0) [cnf transformation 39]
99. creative(X0) | strong(X0) [cnf transformation 55]
131. ~creative(alice) [cnf transformation 22]
135. ~strong(X0) [duplicate literal removal 81]
230. creative(X0) [subsumption resolution 99,135]
254. $false [subsumption resolution 131,230]
% SZS output end Proof for 3477578315676272891224374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not wise and not quiet then someone is both not funny and tall and vice versa. If john is either not rich or not calm then john is both not wise and not kind. Everyone who is both not strong and not generous is funny or curious and vice versa. Everyone who is both generous and not patient is not humble. If alice is both not old and old then paul is strong or wise and vice versa. If someone is either curious or generous then someone is either calm or happy. Everyone who is rich or not creative is both kind and not generous. If someone is funny then someone is not curious and vice versa. If someone is not rich or not creative then someone is funny or not quiet and vice versa. Everyone who is not rich is either not old or creative and vice versa. Everyone who is calm is generous. If someone is calm or rich then susan is either not quiet or creative and vice versa. Everyone who is brave or not brave is not brave and vice versa. If someone is both not quiet and not happy then john is not rich and vice versa. Everyone who is both not strong and not brave is both not funny and not brave. Everyone who is not funny or not humble is wise or not creative. Mary is either wise or kind. Someone is not humble. Alice is either curious or brave. Fred is either happy or not quiet. Someone is either kind or generous. | Fred is funny. | contradiction | (((~wise(fred)&~quiet(fred)))<=>(?[X]:((~funny(X)&tall(X)))))&
(((~rich(john)<~>~calm(john)))=>((~wise(john)&~kind(john))))&
(![X]:((~strong(X)&~generous(X))<=>(funny(X)|curious(X))))&
(![X]:((generous(X)&~patient(X))=>~humble(X)))&
(((~old(alice)&old(alice)))<=>((strong(paul)|wise(paul))))&
((?[X]:((curious(X)<~>generous(X))))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((rich(X)|~creative(X))=>(kind(X)&~generous(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((~rich(X)|~creative(X))))<=>(?[X]:((funny(X)|~quiet(X)))))&
(![X]:(~rich(X)<=>(~old(X)<~>creative(X))))&
(![X]:(calm(X)=>generous(X)))&
((?[X]:((calm(X)|rich(X))))<=>((~quiet(susan)<~>creative(susan))))&
(![X]:((brave(X)|~brave(X))<=>~brave(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>(~rich(john)))&
(![X]:((~strong(X)&~brave(X))=>(~funny(X)&~brave(X))))&
(![X]:((~funny(X)|~humble(X))=>(wise(X)|~creative(X))))&
((wise(mary)<~>kind(mary)))&
(?[X]:(~humble(X)))&
((curious(alice)<~>brave(alice)))&
((happy(fred)<~>~quiet(fred)))&
(?[X]:((kind(X)<~>generous(X)))) | funny(fred) | [
"p2",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2899663857808329401567534
% SZS output start Proof for 2899663857808329401567534
3. ! [X0] : ((~generous(X0) & ~strong(X0)) <=> (curious(X0) | funny(X0))) [input p2]
13. ! [X0] : ((~brave(X0) | brave(X0)) <=> ~brave(X0)) [input p12]
15. ! [X0] : ((~brave(X0) & ~strong(X0)) => (~brave(X0) & ~funny(X0))) [input p14]
22. funny(fred) [input hypothesis]
31. ! [X0] : ((~brave(X0) & ~funny(X0)) | (brave(X0) | strong(X0))) [ennf transformation 15]
32. ! [X0] : ((~brave(X0) & ~funny(X0)) | brave(X0) | strong(X0)) [flattening 31]
41. ! [X0] : (((~generous(X0) & ~strong(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (generous(X0) | strong(X0)))) [nnf transformation 3]
42. ! [X0] : (((~generous(X0) & ~strong(X0)) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | generous(X0) | strong(X0))) [flattening 41]
64. ! [X0] : (((~brave(X0) | brave(X0)) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [nnf transformation 13]
65. ! [X0] : ((~brave(X0) | brave(X0) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [flattening 64]
87. ~strong(X0) | ~funny(X0) [cnf transformation 42]
121. ~brave(X0) | ~brave(X0) [cnf transformation 65]
127. ~funny(X0) | brave(X0) | strong(X0) [cnf transformation 32]
140. funny(fred) [cnf transformation 22]
141. ~brave(X0) [duplicate literal removal 121]
233. 19 <=> ! [X3] : ~funny(X3) [avatar definition]
234. ~funny(X3) <- (19) [avatar component clause 233]
311. ~funny(X0) | strong(X0) [subsumption resolution 127,141]
312. ~funny(X0) [subsumption resolution 311,87]
313. 19 [avatar split clause 312,233]
341. $false <- (19) [resolution 234,140]
342. ~19 [avatar contradiction clause 341]
343. $false [avatar sat refutation 313,342]
% SZS output end Proof for 2899663857808329401567534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is humble or not patient then someone is both calm and patient and vice versa.
If someone is wise then someone is old or not strong and vice versa.
Everyone who is both not happy and brave is either not generous or not patient and vice versa.
Everyone who is brave or tall is both tall and creative and vice versa.
If susan is both not creative and not strong then someone is not brave or not tall.
If someone is not kind or wise then john is either not curious or brave and vice versa.
If someone is either patient or not patient then john is both not calm and not quiet and vice versa.
Everyone who is either kind or not curious is generous and vice versa.
Everyone who is either happy or not funny is both curious and happy and vice versa.
If susan is both not rich and quiet then lucy is funny or not humble and vice versa.
If someone is both not wise and curious then someone is either quiet or not tall.
Everyone who is both not happy and not brave is not curious or generous and vice versa.
If someone is not humble then someone is not happy or patient.
Everyone who is curious is both old and creative and vice versa.
If someone is not calm or calm then someone is quiet and vice versa.
If someone is both strong and creative then paul is either strong or rich.
Someone is both not curious and not rich.
Someone is not patient.
John is funny or not rich.
John is not generous.
John is both humble and not happy.
Susan is either not generous or not tall.
Paul is strong or tall. | Susan is rich. | contradiction | ((?[X]:((humble(X)|~patient(X))))<=>(?[X]:((calm(X)&patient(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~happy(X)&brave(X))<=>(~generous(X)<~>~patient(X))))&
(![X]:((brave(X)|tall(X))<=>(tall(X)&creative(X))))&
(((~creative(susan)&~strong(susan)))=>(?[X]:((~brave(X)|~tall(X)))))&
((?[X]:((~kind(X)|wise(X))))<=>((~curious(john)<~>brave(john))))&
((?[X]:((patient(X)<~>~patient(X))))<=>((~calm(john)&~quiet(john))))&
(![X]:((kind(X)<~>~curious(X))<=>generous(X)))&
(![X]:((happy(X)<~>~funny(X))<=>(curious(X)&happy(X))))&
(((~rich(susan)&quiet(susan)))<=>((funny(lucy)|~humble(lucy))))&
((?[X]:((~wise(X)&curious(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:((~happy(X)&~brave(X))<=>(~curious(X)|generous(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:(curious(X)<=>(old(X)&creative(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((strong(X)&creative(X))))=>((strong(paul)<~>rich(paul))))&
(?[X]:((~curious(X)&~rich(X))))&
(?[X]:(~patient(X)))&
((funny(john)|~rich(john)))&
(~generous(john))&
((humble(john)&~happy(john)))&
((~generous(susan)<~>~tall(susan)))&
((strong(paul)|tall(paul))) | rich(susan) | [
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 583915571536684293451662
% SZS output start Proof for 583915571536684293451662
9. ! [X0] : ((happy(X0) <~> ~funny(X0)) <=> (happy(X0) & curious(X0))) [input p8]
10. (quiet(susan) & ~rich(susan)) <=> (~humble(lucy) | funny(lucy)) [input p9]
12. ! [X0] : ((~brave(X0) & ~happy(X0)) <=> (generous(X0) | ~curious(X0))) [input p11]
24. rich(susan) [input hypothesis]
61. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [nnf transformation 9]
62. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [flattening 61]
63. ((quiet(susan) & ~rich(susan)) | (humble(lucy) & ~funny(lucy))) & ((~humble(lucy) | funny(lucy)) | (~quiet(susan) | rich(susan))) [nnf transformation 10]
64. ((quiet(susan) & ~rich(susan)) | (humble(lucy) & ~funny(lucy))) & (~humble(lucy) | funny(lucy) | ~quiet(susan) | rich(susan)) [flattening 63]
69. ! [X0] : (((~brave(X0) & ~happy(X0)) | (~generous(X0) & curious(X0))) & ((generous(X0) | ~curious(X0)) | (brave(X0) | happy(X0)))) [nnf transformation 12]
70. ! [X0] : (((~brave(X0) & ~happy(X0)) | (~generous(X0) & curious(X0))) & (generous(X0) | ~curious(X0) | brave(X0) | happy(X0))) [flattening 69]
126. happy(X0) | happy(X0) | funny(X0) [cnf transformation 62]
128. funny(X0) | ~happy(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 62]
130. ~rich(susan) | ~funny(lucy) [cnf transformation 64]
137. ~happy(X0) | curious(X0) [cnf transformation 70]
160. rich(susan) [cnf transformation 24]
161. funny(X0) | happy(X0) [duplicate literal removal 126]
162. ~curious(X0) | ~happy(X0) | funny(X0) [duplicate literal removal 128]
285. 27 <=> funny(lucy) [avatar definition]
287. ~funny(lucy) <- (~27) [avatar component clause 285]
290. 28 <=> rich(susan) [avatar definition]
294. ~27 | ~28 [avatar split clause 130,290,285]
370. 28 [avatar split clause 160,290]
377. happy(lucy) <- (~27) [resolution 161,287]
378. curious(lucy) <- (~27) [resolution 377,137]
460. ~happy(lucy) | funny(lucy) <- (~27) [resolution 162,378]
462. funny(lucy) <- (~27) [subsumption resolution 460,377]
463. $false <- (~27) [subsumption resolution 462,287]
464. 27 [avatar contradiction clause 463]
466. $false [avatar sat refutation 294,370,464]
% SZS output end Proof for 583915571536684293451662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or calm is curious and vice versa. Everyone who is both rich and calm is either calm or not quiet and vice versa. If someone is either not happy or not strong then paul is both brave and not humble. If someone is both quiet and not old then lucy is not tall or rich. Everyone who is patient or not funny is both rich and quiet and vice versa. Everyone who is not calm or not brave is both not tall and not humble. If someone is not tall then someone is humble and vice versa. If susan is not old then someone is not happy. Everyone who is not quiet or not old is not brave. If someone is humble then fred is both not calm and not strong. Everyone who is either humble or not kind is both not happy and not creative and vice versa. If someone is not funny then someone is both not humble and happy and vice versa. Everyone who is not quiet is not patient or quiet. If someone is humble then alice is not curious and vice versa. Everyone who is humble is not funny and vice versa. If someone is generous or calm then lucy is not happy and vice versa. Someone is not humble. Alice is either wise or not tall. Someone is both patient and not wise. Paul is not strong or kind. Someone is both curious and not funny. Fred is either not patient or not humble. John is both not humble and not curious. Someone is either not rich or not brave. | Alice is not funny. | contradiction | (![X]:((~rich(X)<~>calm(X))<=>curious(X)))&
(![X]:((rich(X)&calm(X))<=>(calm(X)<~>~quiet(X))))&
((?[X]:((~happy(X)<~>~strong(X))))=>((brave(paul)&~humble(paul))))&
((?[X]:((quiet(X)&~old(X))))=>((~tall(lucy)|rich(lucy))))&
(![X]:((patient(X)|~funny(X))<=>(rich(X)&quiet(X))))&
(![X]:((~calm(X)|~brave(X))=>(~tall(X)&~humble(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(humble(X))))&
((~old(susan))=>(?[X]:(~happy(X))))&
(![X]:((~quiet(X)|~old(X))=>~brave(X)))&
((?[X]:(humble(X)))=>((~calm(fred)&~strong(fred))))&
(![X]:((humble(X)<~>~kind(X))<=>(~happy(X)&~creative(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~humble(X)&happy(X)))))&
(![X]:(~quiet(X)=>(~patient(X)|quiet(X))))&
((?[X]:(humble(X)))<=>(~curious(alice)))&
(![X]:(humble(X)<=>~funny(X)))&
((?[X]:((generous(X)|calm(X))))<=>(~happy(lucy)))&
(?[X]:(~humble(X)))&
((wise(alice)<~>~tall(alice)))&
(?[X]:((patient(X)&~wise(X))))&
((~strong(paul)|kind(paul)))&
(?[X]:((curious(X)&~funny(X))))&
((~patient(fred)<~>~humble(fred)))&
((~humble(john)&~curious(john)))&
(?[X]:((~rich(X)<~>~brave(X)))) | ~funny(alice) | [
"p0",
"p4",
"p5",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2345017327946160147783820
% SZS output start Proof for 2345017327946160147783820
1. ! [X0] : ((~rich(X0) <~> calm(X0)) <=> curious(X0)) [input p0]
5. ! [X0] : ((~funny(X0) | patient(X0)) <=> (quiet(X0) & rich(X0))) [input p4]
6. ! [X0] : ((~brave(X0) | ~calm(X0)) => (~humble(X0) & ~tall(X0))) [input p5]
14. ? [X0] : humble(X0) <=> ~curious(alice) [input p13]
15. ! [X0] : (humble(X0) <=> ~funny(X0)) [input p14]
25. ~funny(alice) [input hypothesis]
32. ! [X0] : ((~humble(X0) & ~tall(X0)) | (brave(X0) & calm(X0))) [ennf transformation 6]
37. ! [X0] : ((((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | ~curious(X0)) & (curious(X0) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0))))) [nnf transformation 1]
41. ! [X0] : (((~funny(X0) | patient(X0)) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | (funny(X0) & ~patient(X0)))) [nnf transformation 5]
42. ! [X0] : ((~funny(X0) | patient(X0) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | (funny(X0) & ~patient(X0)))) [flattening 41]
55. (? [X0] : humble(X0) | curious(alice)) & (~curious(alice) | ! [X0] : ~humble(X0)) [nnf transformation 14]
56. (? [X0] : humble(X0) | curious(alice)) & (~curious(alice) | ! [X1] : ~humble(X1)) [rectify 55]
57. ? [X0] : humble(X0) => humble(sK4) [choice axiom]
58. (humble(sK4) | curious(alice)) & (~curious(alice) | ! [X1] : ~humble(X1)) [skolemisation 56,57]
59. ! [X0] : ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))) [nnf transformation 15]
76. ~calm(X0) | ~rich(X0) | curious(X0) [cnf transformation 37]
90. funny(X0) | rich(X0) [cnf transformation 42]
96. ~humble(X0) | calm(X0) [cnf transformation 32]
113. ~curious(alice) | ~humble(X1) [cnf transformation 58]
116. funny(X0) | humble(X0) [cnf transformation 59]
134. ~funny(alice) [cnf transformation 25]
159. 5 <=> ! [X1] : ~humble(X1) [avatar definition]
160. ~humble(X1) <- (5) [avatar component clause 159]
206. 16 <=> curious(alice) [avatar definition]
207. ~curious(alice) <- (~16) [avatar component clause 206]
214. 5 | ~16 [avatar split clause 113,206,159]
291. rich(alice) [resolution 90,134]
306. humble(alice) [resolution 116,134]
356. calm(alice) [resolution 306,96]
395. $false <- (5) [resolution 160,306]
402. ~5 [avatar contradiction clause 395]
549. ~rich(alice) | curious(alice) [resolution 356,76]
550. curious(alice) [subsumption resolution 549,291]
551. $false <- (~16) [subsumption resolution 550,207]
552. 16 [avatar contradiction clause 551]
553. $false [avatar sat refutation 214,402,552]
% SZS output end Proof for 2345017327946160147783820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is strong then alice is either not old or not calm.
If john is both not old and humble then someone is either not brave or creative.
Everyone who is not generous or generous is both creative and rich.
Everyone who is both not quiet and happy is either brave or calm and vice versa.
If alice is generous or calm then someone is tall.
Everyone who is funny or not rich is either creative or not patient.
Everyone who is both quiet and funny is calm or brave and vice versa.
Everyone who is not kind is not patient and vice versa.
Everyone who is strong or curious is calm or funny and vice versa.
If someone is not curious then someone is either tall or calm.
If mary is either quiet or calm then susan is either not calm or curious.
If susan is either calm or not funny then susan is either quiet or calm and vice versa.
If alice is both not wise and calm then paul is not calm or generous and vice versa.
Everyone who is not generous or tall is either happy or not old and vice versa.
If someone is either strong or calm then someone is both not patient and strong and vice versa.
If someone is not calm or quiet then fred is both happy and not strong and vice versa.
Lucy is both funny and not curious.
Someone is either not brave or humble.
Susan is humble.
Someone is not happy.
Lucy is funny.
John is either not curious or not brave. | John is not humble. | neutral | ((strong(lucy))=>((~old(alice)<~>~calm(alice))))&
(((~old(john)&humble(john)))=>(?[X]:((~brave(X)<~>creative(X)))))&
(![X]:((~generous(X)|generous(X))=>(creative(X)&rich(X))))&
(![X]:((~quiet(X)&happy(X))<=>(brave(X)<~>calm(X))))&
(((generous(alice)|calm(alice)))=>(?[X]:(tall(X))))&
(![X]:((funny(X)|~rich(X))=>(creative(X)<~>~patient(X))))&
(![X]:((quiet(X)&funny(X))<=>(calm(X)|brave(X))))&
(![X]:(~kind(X)<=>~patient(X)))&
(![X]:((strong(X)|curious(X))<=>(calm(X)|funny(X))))&
((?[X]:(~curious(X)))=>(?[X]:((tall(X)<~>calm(X)))))&
(((quiet(mary)<~>calm(mary)))=>((~calm(susan)<~>curious(susan))))&
(((calm(susan)<~>~funny(susan)))<=>((quiet(susan)<~>calm(susan))))&
(((~wise(alice)&calm(alice)))<=>((~calm(paul)|generous(paul))))&
(![X]:((~generous(X)|tall(X))<=>(happy(X)<~>~old(X))))&
((?[X]:((strong(X)<~>calm(X))))<=>(?[X]:((~patient(X)&strong(X)))))&
((?[X]:((~calm(X)|quiet(X))))<=>((happy(fred)&~strong(fred))))&
((funny(lucy)&~curious(lucy)))&
(?[X]:((~brave(X)<~>humble(X))))&
(humble(susan))&
(?[X]:(~happy(X)))&
(funny(lucy))&
((~curious(john)<~>~brave(john))) | ~humble(john) | [] | null | 0 |
Everyone who is humble or not humble is either rich or tall.
If john is quiet or not funny then john is not humble.
If someone is both old and not quiet then paul is either creative or humble.
If mary is both curious and kind then someone is brave.
If someone is not funny then alice is either curious or not wise and vice versa.
If someone is both not brave and not happy then someone is funny and vice versa.
If someone is not wise or not humble then paul is not strong or not happy and vice versa.
Everyone who is not brave is kind and vice versa.
Everyone who is rich or not calm is both not strong and humble.
Everyone who is either calm or generous is not calm and vice versa.
Everyone who is either kind or not happy is both tall and curious and vice versa.
If someone is both not patient and not strong then someone is both calm and rich and vice versa.
Everyone who is not humble is not old or rich and vice versa.
If someone is either old or generous then lucy is both humble and kind and vice versa.
Everyone who is both not happy and creative is brave and vice versa.
If mary is both not rich and not funny then someone is both rich and patient and vice versa.
Someone is either calm or kind.
Someone is kind or not strong.
Susan is happy.
Someone is either not kind or wise.
Lucy is either kind or tall.
John is either not kind or not old.
Lucy is either curious or not quiet. | John is not quiet. | entailment | (![X]:((humble(X)|~humble(X))=>(rich(X)<~>tall(X))))&
(((quiet(john)|~funny(john)))=>(~humble(john)))&
((?[X]:((old(X)&~quiet(X))))=>((creative(paul)<~>humble(paul))))&
(((curious(mary)&kind(mary)))=>(?[X]:(brave(X))))&
((?[X]:(~funny(X)))<=>((curious(alice)<~>~wise(alice))))&
((?[X]:((~brave(X)&~happy(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~wise(X)|~humble(X))))<=>((~strong(paul)|~happy(paul))))&
(![X]:(~brave(X)<=>kind(X)))&
(![X]:((rich(X)|~calm(X))=>(~strong(X)&humble(X))))&
(![X]:((calm(X)<~>generous(X))<=>~calm(X)))&
(![X]:((kind(X)<~>~happy(X))<=>(tall(X)&curious(X))))&
((?[X]:((~patient(X)&~strong(X))))<=>(?[X]:((calm(X)&rich(X)))))&
(![X]:(~humble(X)<=>(~old(X)|rich(X))))&
((?[X]:((old(X)<~>generous(X))))<=>((humble(lucy)&kind(lucy))))&
(![X]:((~happy(X)&creative(X))<=>brave(X)))&
(((~rich(mary)&~funny(mary)))<=>(?[X]:((rich(X)&patient(X)))))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((kind(X)|~strong(X))))&
(happy(susan))&
(?[X]:((~kind(X)<~>wise(X))))&
((kind(lucy)<~>tall(lucy)))&
((~kind(john)<~>~old(john)))&
((curious(lucy)<~>~quiet(lucy))) | ~quiet(john) | [
"p0",
"p1",
"p8",
"p9",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5201530450909119441600496
% SZS output start Proof for 5201530450909119441600496
1. ! [X0] : ((~humble(X0) | humble(X0)) => (rich(X0) <~> tall(X0))) [input p0]
2. (~funny(john) | quiet(john)) => ~humble(john) [input p1]
9. ! [X0] : ((~calm(X0) | rich(X0)) => (humble(X0) & ~strong(X0))) [input p8]
10. ! [X0] : ((calm(X0) <~> generous(X0)) <=> ~calm(X0)) [input p9]
13. ! [X0] : (~humble(X0) <=> (rich(X0) | ~old(X0))) [input p12]
14. ? [X0] : (old(X0) <~> generous(X0)) <=> (kind(lucy) & humble(lucy)) [input p13]
21. kind(lucy) <~> tall(lucy) [input p20]
24. quiet(john) [input hypothesis]
27. ! [X0] : ((rich(X0) <~> tall(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 1]
28. ~humble(john) | (funny(john) & ~quiet(john)) [ennf transformation 2]
32. ! [X0] : ((humble(X0) & ~strong(X0)) | (calm(X0) & ~rich(X0))) [ennf transformation 9]
33. ! [X0] : (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (humble(X0) & ~humble(X0))) [nnf transformation 27]
52. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | calm(X0)) & (~calm(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 10]
60. ! [X0] : ((~humble(X0) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | humble(X0))) [nnf transformation 13]
61. ! [X0] : ((~humble(X0) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | humble(X0))) [flattening 60]
62. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (~kind(lucy) | ~humble(lucy))) & ((kind(lucy) & humble(lucy)) | ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [nnf transformation 14]
63. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [flattening 62]
64. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X1] : ((old(X1) | ~generous(X1)) & (generous(X1) | ~old(X1)))) [rectify 63]
65. ? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) => ((~generous(sK7) | ~old(sK7)) & (generous(sK7) | old(sK7))) [choice axiom]
66. (((~generous(sK7) | ~old(sK7)) & (generous(sK7) | old(sK7))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X1] : ((old(X1) | ~generous(X1)) & (generous(X1) | ~old(X1)))) [skolemisation 64,65]
82. (~tall(lucy) | ~kind(lucy)) & (tall(lucy) | kind(lucy)) [nnf transformation 21]
85. tall(X0) | rich(X0) | ~humble(X0) [cnf transformation 33]
86. tall(X0) | rich(X0) | humble(X0) [cnf transformation 33]
89. ~humble(john) | ~quiet(john) [cnf transformation 28]
109. ~rich(X0) | humble(X0) [cnf transformation 32]
111. ~calm(X0) | generous(X0) | ~calm(X0) [cnf transformation 52]
113. generous(X0) | calm(X0) | calm(X0) [cnf transformation 52]
125. rich(X0) | ~old(X0) | humble(X0) [cnf transformation 61]
127. ~humble(X0) | ~rich(X0) [cnf transformation 61]
131. kind(lucy) | old(X1) | ~generous(X1) [cnf transformation 66]
148. ~tall(lucy) | ~kind(lucy) [cnf transformation 82]
153. quiet(john) [cnf transformation 24]
154. ~calm(X0) | generous(X0) [duplicate literal removal 111]
155. generous(X0) | calm(X0) [duplicate literal removal 113]
157. tall(X0) | rich(X0) [subsumption resolution 85,86]
163. 2 <=> humble(john) [avatar definition]
165. ~humble(john) <- (~2) [avatar component clause 163]
168. 3 <=> quiet(john) [avatar definition]
171. ~3 | ~2 [avatar split clause 89,163,168]
257. 23 <=> ! [X1] : humble(X1) [avatar definition]
258. humble(X1) <- (23) [avatar component clause 257]
264. generous(X0) [subsumption resolution 154,155]
291. ~rich(X0) [subsumption resolution 127,109]
292. ~old(X0) | humble(X0) [subsumption resolution 125,291]
299. 32 <=> kind(lucy) [avatar definition]
307. kind(lucy) | old(X1) [subsumption resolution 131,264]
309. 34 <=> ! [X1] : old(X1) [avatar definition]
310. old(X1) <- (34) [avatar component clause 309]
311. 34 | 32 [avatar split clause 307,299,309]
357. 43 <=> tall(lucy) [avatar definition]
359. ~tall(lucy) <- (~43) [avatar component clause 357]
360. ~32 | ~43 [avatar split clause 148,357,299]
382. 3 [avatar split clause 153,168]
389. rich(lucy) <- (~43) [resolution 157,359]
391. $false <- (~43) [subsumption resolution 389,291]
392. 43 [avatar contradiction clause 391]
415. humble(X0) <- (34) [resolution 292,310]
416. 23 | ~34 [avatar split clause 415,309,257]
417. $false <- (~2, 23) [resolution 258,165]
421. 2 | ~23 [avatar contradiction clause 417]
422. $false [avatar sat refutation 171,311,360,382,392,416,421]
% SZS output end Proof for 5201530450909119441600496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or humble then someone is either not happy or creative. If someone is both not brave and not happy then mary is old and vice versa. If susan is not creative or funny then susan is not kind or not old. Everyone who is both not kind and not old is not curious or not patient. Everyone who is either not brave or not wise is happy and vice versa. If someone is either not old or patient then someone is both funny and curious and vice versa. Everyone who is not old is funny or calm and vice versa. Everyone who is funny is not happy or happy and vice versa. If fred is not brave or not patient then fred is both not old and brave. If someone is both not strong and not rich then mary is both not patient and not wise and vice versa. If someone is not rich then mary is generous or brave. Everyone who is not kind is calm and vice versa. Everyone who is not creative is not rich or calm. Everyone who is either not kind or quiet is both not creative and not happy and vice versa. Everyone who is both calm and kind is either old or not tall and vice versa. If someone is quiet or wise then susan is both wise and not old. Someone is both not strong and brave. Fred is either not humble or not curious. Susan is quiet. Someone is both creative and brave. Someone is both not humble and not strong. Mary is not strong or not kind. | Fred is humble. | neutral | ((?[X]:((generous(X)|humble(X))))=>(?[X]:((~happy(X)<~>creative(X)))))&
((?[X]:((~brave(X)&~happy(X))))<=>(old(mary)))&
(((~creative(susan)|funny(susan)))=>((~kind(susan)|~old(susan))))&
(![X]:((~kind(X)&~old(X))=>(~curious(X)|~patient(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>happy(X)))&
((?[X]:((~old(X)<~>patient(X))))<=>(?[X]:((funny(X)&curious(X)))))&
(![X]:(~old(X)<=>(funny(X)|calm(X))))&
(![X]:(funny(X)<=>(~happy(X)|happy(X))))&
(((~brave(fred)|~patient(fred)))=>((~old(fred)&brave(fred))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~patient(mary)&~wise(mary))))&
((?[X]:(~rich(X)))=>((generous(mary)|brave(mary))))&
(![X]:(~kind(X)<=>calm(X)))&
(![X]:(~creative(X)=>(~rich(X)|calm(X))))&
(![X]:((~kind(X)<~>quiet(X))<=>(~creative(X)&~happy(X))))&
(![X]:((calm(X)&kind(X))<=>(old(X)<~>~tall(X))))&
((?[X]:((quiet(X)|wise(X))))=>((wise(susan)&~old(susan))))&
(?[X]:((~strong(X)&brave(X))))&
((~humble(fred)<~>~curious(fred)))&
(quiet(susan))&
(?[X]:((creative(X)&brave(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~strong(mary)|~kind(mary))) | humble(fred) | [] | null | 0 |
Everyone who is quiet or strong is both brave and not wise and vice versa.
If susan is tall or generous then someone is humble or not generous.
Everyone who is both not creative and not calm is both not quiet and not calm and vice versa.
Everyone who is not old or humble is quiet or strong.
If susan is both old and not tall then susan is either not creative or patient and vice versa.
If lucy is not funny or not wise then mary is happy or generous.
If someone is both not calm and not humble then someone is either not wise or funny and vice versa.
If fred is either quiet or not calm then susan is either quiet or not generous and vice versa.
Everyone who is both curious and not tall is both patient and rich.
If someone is calm then paul is not quiet or not brave and vice versa.
If lucy is not happy then paul is not generous and vice versa.
Everyone who is either not rich or not curious is either generous or funny and vice versa.
Everyone who is both not rich and not creative is both not tall and not rich and vice versa.
If alice is both not old and tall then someone is not strong and vice versa.
Everyone who is not old is tall or kind.
Everyone who is not creative is both curious and strong and vice versa.
Alice is not happy or not tall.
Someone is not curious.
Paul is both brave and creative.
John is both not strong and not funny.
Someone is brave or not kind.
Fred is not brave.
Mary is not wise.
Lucy is happy or rich. | John is not creative. | contradiction | (![X]:((quiet(X)|strong(X))<=>(brave(X)&~wise(X))))&
(((tall(susan)|generous(susan)))=>(?[X]:((humble(X)|~generous(X)))))&
(![X]:((~creative(X)&~calm(X))<=>(~quiet(X)&~calm(X))))&
(![X]:((~old(X)|humble(X))=>(quiet(X)|strong(X))))&
(((old(susan)&~tall(susan)))<=>((~creative(susan)<~>patient(susan))))&
(((~funny(lucy)|~wise(lucy)))=>((happy(mary)|generous(mary))))&
((?[X]:((~calm(X)&~humble(X))))<=>(?[X]:((~wise(X)<~>funny(X)))))&
(((quiet(fred)<~>~calm(fred)))<=>((quiet(susan)<~>~generous(susan))))&
(![X]:((curious(X)&~tall(X))=>(patient(X)&rich(X))))&
((?[X]:(calm(X)))<=>((~quiet(paul)|~brave(paul))))&
((~happy(lucy))<=>(~generous(paul)))&
(![X]:((~rich(X)<~>~curious(X))<=>(generous(X)<~>funny(X))))&
(![X]:((~rich(X)&~creative(X))<=>(~tall(X)&~rich(X))))&
(((~old(alice)&tall(alice)))<=>(?[X]:(~strong(X))))&
(![X]:(~old(X)=>(tall(X)|kind(X))))&
(![X]:(~creative(X)<=>(curious(X)&strong(X))))&
((~happy(alice)|~tall(alice)))&
(?[X]:(~curious(X)))&
((brave(paul)&creative(paul)))&
((~strong(john)&~funny(john)))&
(?[X]:((brave(X)|~kind(X))))&
(~brave(fred))&
(~wise(mary))&
((happy(lucy)|rich(lucy))) | ~creative(john) | [
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8720431931932952821103247
% SZS output start Proof for 8720431931932952821103247
16. ! [X0] : (~creative(X0) <=> (strong(X0) & curious(X0))) [input p15]
20. ~funny(john) & ~strong(john) [input p19]
25. ~creative(john) [input hypothesis]
64. ! [X0] : ((~creative(X0) | (~strong(X0) | ~curious(X0))) & ((strong(X0) & curious(X0)) | creative(X0))) [nnf transformation 16]
65. ! [X0] : ((~creative(X0) | ~strong(X0) | ~curious(X0)) & ((strong(X0) & curious(X0)) | creative(X0))) [flattening 64]
129. creative(X0) | strong(X0) [cnf transformation 65]
135. ~strong(john) [cnf transformation 20]
141. ~creative(john) [cnf transformation 25]
317. strong(john) [resolution 129,141]
319. $false [subsumption resolution 317,135]
% SZS output end Proof for 8720431931932952821103247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not happy is both not wise and not calm.
Everyone who is strong is both not kind and rich.
If someone is not patient then someone is either funny or humble and vice versa.
If susan is patient or quiet then mary is both curious and not strong.
If someone is humble then someone is strong or not curious and vice versa.
If someone is both quiet and not generous then someone is either not creative or not happy and vice versa.
If someone is both humble and strong then someone is brave or calm.
If someone is either happy or not patient then susan is both generous and not patient.
Everyone who is either happy or not brave is not quiet.
If john is both not rich and not humble then someone is not kind or happy.
If someone is not curious then someone is not kind or not tall and vice versa.
If paul is both patient and not strong then someone is not quiet or not generous.
If someone is quiet then fred is either not calm or tall and vice versa.
If lucy is either rich or not humble then fred is both not kind and not tall and vice versa.
If susan is generous then someone is both not funny and funny and vice versa.
If someone is quiet or not kind then paul is both funny and not funny.
Fred is not tall or not wise.
Fred is either not patient or rich.
Mary is curious.
Fred is either old or brave.
Someone is both calm and not brave.
Alice is kind. | Alice is quiet. | contradiction | (![X]:((quiet(X)<~>~happy(X))=>(~wise(X)&~calm(X))))&
(![X]:(strong(X)=>(~kind(X)&rich(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((funny(X)<~>humble(X)))))&
(((patient(susan)|quiet(susan)))=>((curious(mary)&~strong(mary))))&
((?[X]:(humble(X)))<=>(?[X]:((strong(X)|~curious(X)))))&
((?[X]:((quiet(X)&~generous(X))))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:((humble(X)&strong(X))))=>(?[X]:((brave(X)|calm(X)))))&
((?[X]:((happy(X)<~>~patient(X))))=>((generous(susan)&~patient(susan))))&
(![X]:((happy(X)<~>~brave(X))=>~quiet(X)))&
(((~rich(john)&~humble(john)))=>(?[X]:((~kind(X)|happy(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((~kind(X)|~tall(X)))))&
(((patient(paul)&~strong(paul)))=>(?[X]:((~quiet(X)|~generous(X)))))&
((?[X]:(quiet(X)))<=>((~calm(fred)<~>tall(fred))))&
(((rich(lucy)<~>~humble(lucy)))<=>((~kind(fred)&~tall(fred))))&
((generous(susan))<=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((quiet(X)|~kind(X))))=>((funny(paul)&~funny(paul))))&
((~tall(fred)|~wise(fred)))&
((~patient(fred)<~>rich(fred)))&
(curious(mary))&
((old(fred)<~>brave(fred)))&
(?[X]:((calm(X)&~brave(X))))&
(kind(alice)) | quiet(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4919365497481963089655253
% SZS output start Proof for 4919365497481963089655253
16. ? [X0] : (~kind(X0) | quiet(X0)) => (~funny(paul) & funny(paul)) [input p15]
23. quiet(alice) [input hypothesis]
41. (~funny(paul) & funny(paul)) | ! [X0] : (kind(X0) & ~quiet(X0)) [ennf transformation 16]
132. funny(paul) | ~quiet(X0) [cnf transformation 41]
134. ~funny(paul) | ~quiet(X0) [cnf transformation 41]
144. quiet(alice) [cnf transformation 23]
341. 46 <=> ! [X1] : ~quiet(X1) [avatar definition]
342. ~quiet(X1) <- (46) [avatar component clause 341]
370. 51 <=> funny(paul) [avatar definition]
374. 46 | ~51 [avatar split clause 134,370,341]
376. 46 | 51 [avatar split clause 132,370,341]
404. $false <- (46) [resolution 342,144]
405. ~46 [avatar contradiction clause 404]
406. $false [avatar sat refutation 374,376,405]
% SZS output end Proof for 4919365497481963089655253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not wise or funny is tall. Everyone who is not patient is humble or curious and vice versa. Everyone who is both strong and rich is both not funny and patient. If someone is either kind or brave then someone is not quiet or not kind. Everyone who is happy or kind is both generous and not generous and vice versa. Everyone who is generous or strong is not calm or not humble and vice versa. If john is both not creative and tall then someone is both generous and curious and vice versa. Everyone who is either not rich or not generous is either not wise or rich and vice versa. If someone is either not calm or not wise then lucy is both not kind and not strong and vice versa. Everyone who is both rich and not humble is both tall and rich and vice versa. If john is generous or humble then alice is both not generous and not brave and vice versa. Everyone who is either brave or rich is not generous or quiet. If someone is brave or not calm then someone is not patient or not old and vice versa. Everyone who is humble or not humble is either not happy or not funny and vice versa. Everyone who is not wise is not old or not creative and vice versa. Everyone who is either not strong or wise is either curious or not wise and vice versa. Susan is either not generous or rich. Someone is not humble. Lucy is strong. Mary is calm or not kind. Susan is not patient or not calm. John is either tall or not creative. Lucy is either old or not quiet. | Lucy is calm. | entailment | (![X]:((~wise(X)|funny(X))=>tall(X)))&
(![X]:(~patient(X)<=>(humble(X)|curious(X))))&
(![X]:((strong(X)&rich(X))=>(~funny(X)&patient(X))))&
((?[X]:((kind(X)<~>brave(X))))=>(?[X]:((~quiet(X)|~kind(X)))))&
(![X]:((happy(X)|kind(X))<=>(generous(X)&~generous(X))))&
(![X]:((generous(X)|strong(X))<=>(~calm(X)|~humble(X))))&
(((~creative(john)&tall(john)))<=>(?[X]:((generous(X)&curious(X)))))&
(![X]:((~rich(X)<~>~generous(X))<=>(~wise(X)<~>rich(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>((~kind(lucy)&~strong(lucy))))&
(![X]:((rich(X)&~humble(X))<=>(tall(X)&rich(X))))&
(((generous(john)|humble(john)))<=>((~generous(alice)&~brave(alice))))&
(![X]:((brave(X)<~>rich(X))=>(~generous(X)|quiet(X))))&
((?[X]:((brave(X)|~calm(X))))<=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:((humble(X)|~humble(X))<=>(~happy(X)<~>~funny(X))))&
(![X]:(~wise(X)<=>(~old(X)|~creative(X))))&
(![X]:((~strong(X)<~>wise(X))<=>(curious(X)<~>~wise(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:(~humble(X)))&
(strong(lucy))&
((calm(mary)|~kind(mary)))&
((~patient(susan)|~calm(susan)))&
((tall(john)<~>~creative(john)))&
((old(lucy)<~>~quiet(lucy))) | calm(lucy) | [
"p0",
"p4",
"p6",
"p7",
"p8",
"p13",
"p15",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3668102769125470603862685
% SZS output start Proof for 3668102769125470603862685
1. ! [X0] : ((funny(X0) | ~wise(X0)) => tall(X0)) [input p0]
5. ! [X0] : ((kind(X0) | happy(X0)) <=> (~generous(X0) & generous(X0))) [input p4]
7. (tall(john) & ~creative(john)) <=> ? [X0] : (curious(X0) & generous(X0)) [input p6]
8. ! [X0] : ((~rich(X0) <~> ~generous(X0)) <=> (~wise(X0) <~> rich(X0))) [input p7]
9. ? [X0] : (~calm(X0) <~> ~wise(X0)) <=> (~strong(lucy) & ~kind(lucy)) [input p8]
14. ! [X0] : ((~humble(X0) | humble(X0)) <=> (~happy(X0) <~> ~funny(X0))) [input p13]
16. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> (curious(X0) <~> ~wise(X0))) [input p15]
19. strong(lucy) [input p18]
22. tall(john) <~> ~creative(john) [input p21]
24. ~calm(lucy) [input hypothesis]
27. ! [X0] : (tall(X0) | (~funny(X0) & wise(X0))) [ennf transformation 1]
39. ! [X0] : (((kind(X0) | happy(X0)) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | (~kind(X0) & ~happy(X0)))) [nnf transformation 5]
40. ! [X0] : ((kind(X0) | happy(X0) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | (~kind(X0) & ~happy(X0)))) [flattening 39]
43. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & (? [X0] : (curious(X0) & generous(X0)) | (~tall(john) | creative(john))) [nnf transformation 7]
44. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & (? [X0] : (curious(X0) & generous(X0)) | ~tall(john) | creative(john)) [flattening 43]
45. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & (? [X1] : (curious(X1) & generous(X1)) | ~tall(john) | creative(john)) [rectify 44]
46. ? [X1] : (curious(X1) & generous(X1)) => (curious(sK1) & generous(sK1)) [choice axiom]
47. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & ((curious(sK1) & generous(sK1)) | ~tall(john) | creative(john)) [skolemisation 45,46]
48. ! [X0] : ((((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0)))) & (((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))))) [nnf transformation 8]
49. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (strong(lucy) | kind(lucy))) & ((~strong(lucy) & ~kind(lucy)) | ! [X0] : ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) [nnf transformation 9]
50. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | strong(lucy) | kind(lucy)) & ((~strong(lucy) & ~kind(lucy)) | ! [X0] : ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) [flattening 49]
51. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | strong(lucy) | kind(lucy)) & ((~strong(lucy) & ~kind(lucy)) | ! [X1] : ((~calm(X1) | wise(X1)) & (~wise(X1) | calm(X1)))) [rectify 50]
52. ? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) => ((wise(sK2) | calm(sK2)) & (~wise(sK2) | ~calm(sK2))) [choice axiom]
53. (((wise(sK2) | calm(sK2)) & (~wise(sK2) | ~calm(sK2))) | strong(lucy) | kind(lucy)) & ((~strong(lucy) & ~kind(lucy)) | ! [X1] : ((~calm(X1) | wise(X1)) & (~wise(X1) | calm(X1)))) [skolemisation 51,52]
64. ! [X0] : (((~humble(X0) | humble(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (humble(X0) & ~humble(X0)))) [nnf transformation 14]
65. ! [X0] : ((~humble(X0) | humble(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (humble(X0) & ~humble(X0)))) [flattening 64]
68. ! [X0] : ((((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))))) [nnf transformation 16]
72. (creative(john) | ~tall(john)) & (~creative(john) | tall(john)) [nnf transformation 22]
75. ~funny(X0) | tall(X0) [cnf transformation 27]
83. generous(X0) | ~happy(X0) [cnf transformation 40]
85. ~generous(X0) | ~happy(X0) [cnf transformation 40]
94. ~creative(john) | ~curious(X0) | ~generous(X0) [cnf transformation 47]
99. ~rich(X0) | wise(X0) | ~rich(X0) | generous(X0) [cnf transformation 48]
102. generous(X0) | rich(X0) | rich(X0) | wise(X0) [cnf transformation 48]
106. ~strong(lucy) | ~wise(X1) | calm(X1) [cnf transformation 53]
127. funny(X0) | happy(X0) | ~humble(X0) [cnf transformation 65]
128. funny(X0) | happy(X0) | humble(X0) [cnf transformation 65]
135. ~wise(X0) | curious(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 68]
139. wise(X0) | ~strong(X0) | curious(X0) | wise(X0) [cnf transformation 68]
145. strong(lucy) [cnf transformation 19]
149. creative(john) | ~tall(john) [cnf transformation 72]
152. ~calm(lucy) [cnf transformation 24]
153. ~wise(X0) | curious(X0) | ~strong(X0) [duplicate literal removal 135]
155. ~strong(X0) | wise(X0) | curious(X0) [duplicate literal removal 139]
158. ~rich(X0) | wise(X0) | generous(X0) [duplicate literal removal 99]
160. generous(X0) | rich(X0) | wise(X0) [duplicate literal removal 102]
178. ~happy(X0) [subsumption resolution 83,85]
180. 5 <=> ! [X0] : (~curious(X0) | ~generous(X0)) [avatar definition]
181. ~generous(X0) | ~curious(X0) <- (5) [avatar component clause 180]
183. 6 <=> tall(john) [avatar definition]
184. ~tall(john) <- (~6) [avatar component clause 183]
188. 7 <=> creative(john) [avatar definition]
191. 5 | ~7 [avatar split clause 94,188,180]
202. generous(X0) | wise(X0) [subsumption resolution 158,160]
206. 10 <=> strong(lucy) [avatar definition]
208. strong(lucy) <- (10) [avatar component clause 206]
225. 14 <=> ! [X1] : (~wise(X1) | calm(X1)) [avatar definition]
226. ~wise(X1) | calm(X1) <- (14) [avatar component clause 225]
227. 14 | ~10 [avatar split clause 106,206,225]
281. humble(X0) | funny(X0) [subsumption resolution 128,178]
282. funny(X0) | ~humble(X0) [subsumption resolution 127,178]
283. funny(X0) [subsumption resolution 282,281]
285. ~strong(X0) | curious(X0) [subsumption resolution 153,155]
296. 10 [avatar split clause 145,206]
306. ~6 | 7 [avatar split clause 149,188,183]
319. tall(X0) [resolution 75,283]
320. $false <- (~6) [resolution 319,184]
321. 6 [avatar contradiction clause 320]
327. ~curious(X0) | wise(X0) <- (5) [resolution 202,181]
347. curious(lucy) <- (10) [resolution 285,208]
491. wise(lucy) <- (5, 10) [resolution 327,347]
515. calm(lucy) <- (5, 10, 14) [resolution 491,226]
518. $false <- (5, 10, 14) [subsumption resolution 515,152]
519. ~5 | ~10 | ~14 [avatar contradiction clause 518]
522. $false [avatar sat refutation 191,227,296,306,321,519]
% SZS output end Proof for 3668102769125470603862685
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and brave is either not brave or happy.
If mary is not kind then john is either not wise or humble.
Everyone who is not wise or not patient is both not old and old and vice versa.
Everyone who is either generous or curious is either not funny or rich and vice versa.
Everyone who is brave or not brave is not funny or humble.
Everyone who is either curious or kind is either not kind or not patient and vice versa.
Everyone who is both not old and not kind is not strong and vice versa.
Everyone who is not tall is both not old and calm and vice versa.
Everyone who is not curious or not humble is rich.
Everyone who is both not quiet and wise is curious and vice versa.
If john is not generous then someone is either tall or curious.
Everyone who is not generous is both not rich and brave.
Everyone who is not patient or not brave is tall and vice versa.
If susan is both brave and wise then someone is not humble or calm and vice versa.
Everyone who is either generous or old is either not patient or creative and vice versa.
Everyone who is not funny or not curious is either wise or not calm.
Someone is both calm and wise.
Fred is both not humble and kind.
Someone is not brave or not calm.
Someone is either kind or wise.
Someone is not brave.
Alice is either humble or funny.
Lucy is either happy or not patient. | Susan is not kind. | neutral | (![X]:((creative(X)&brave(X))=>(~brave(X)<~>happy(X))))&
((~kind(mary))=>((~wise(john)<~>humble(john))))&
(![X]:((~wise(X)|~patient(X))<=>(~old(X)&old(X))))&
(![X]:((generous(X)<~>curious(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|humble(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)&~kind(X))<=>~strong(X)))&
(![X]:(~tall(X)<=>(~old(X)&calm(X))))&
(![X]:((~curious(X)|~humble(X))=>rich(X)))&
(![X]:((~quiet(X)&wise(X))<=>curious(X)))&
((~generous(john))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:(~generous(X)=>(~rich(X)&brave(X))))&
(![X]:((~patient(X)|~brave(X))<=>tall(X)))&
(((brave(susan)&wise(susan)))<=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((generous(X)<~>old(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((~funny(X)|~curious(X))=>(wise(X)<~>~calm(X))))&
(?[X]:((calm(X)&wise(X))))&
((~humble(fred)&kind(fred)))&
(?[X]:((~brave(X)|~calm(X))))&
(?[X]:((kind(X)<~>wise(X))))&
(?[X]:(~brave(X)))&
((humble(alice)<~>funny(alice)))&
((happy(lucy)<~>~patient(lucy))) | ~kind(susan) | [] | null | 0 |
Everyone who is old or not rich is either not kind or kind. If fred is both creative and not humble then someone is curious or patient and vice versa. Everyone who is both not funny and not strong is patient or curious and vice versa. If someone is both wise and calm then fred is both patient and not brave. If john is not humble or not quiet then someone is either not kind or old. Everyone who is both not humble and creative is either not funny or not patient and vice versa. If someone is both not happy and not calm then mary is quiet or patient and vice versa. If someone is not humble then fred is not kind or generous and vice versa. Everyone who is both not creative and not rich is curious or rich. Everyone who is not calm or not brave is either not rich or rich and vice versa. Everyone who is not humble is either brave or calm and vice versa. If fred is both not tall and calm then someone is both patient and not creative. Everyone who is either funny or not humble is strong or not patient and vice versa. Everyone who is either humble or not strong is humble and vice versa. Everyone who is both curious and not generous is either not quiet or rich and vice versa. If lucy is either not quiet or curious then mary is both not creative and not calm. Fred is quiet or not tall. Lucy is either not creative or not generous. Someone is not quiet. Someone is rich or not brave. Alice is not patient. | Mary is brave. | entailment | (![X]:((old(X)|~rich(X))=>(~kind(X)<~>kind(X))))&
(((creative(fred)&~humble(fred)))<=>(?[X]:((curious(X)|patient(X)))))&
(![X]:((~funny(X)&~strong(X))<=>(patient(X)|curious(X))))&
((?[X]:((wise(X)&calm(X))))=>((patient(fred)&~brave(fred))))&
(((~humble(john)|~quiet(john)))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((~humble(X)&creative(X))<=>(~funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>((quiet(mary)|patient(mary))))&
((?[X]:(~humble(X)))<=>((~kind(fred)|generous(fred))))&
(![X]:((~creative(X)&~rich(X))=>(curious(X)|rich(X))))&
(![X]:((~calm(X)|~brave(X))<=>(~rich(X)<~>rich(X))))&
(![X]:(~humble(X)<=>(brave(X)<~>calm(X))))&
(((~tall(fred)&calm(fred)))=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(strong(X)|~patient(X))))&
(![X]:((humble(X)<~>~strong(X))<=>humble(X)))&
(![X]:((curious(X)&~generous(X))<=>(~quiet(X)<~>rich(X))))&
(((~quiet(lucy)<~>curious(lucy)))=>((~creative(mary)&~calm(mary))))&
((quiet(fred)|~tall(fred)))&
((~creative(lucy)<~>~generous(lucy)))&
(?[X]:(~quiet(X)))&
(?[X]:((rich(X)|~brave(X))))&
(~patient(alice)) | brave(mary) | [
"p2",
"p5",
"p8",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4620076423687273309190447
% SZS output start Proof for 4620076423687273309190447
3. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (curious(X0) | patient(X0))) [input p2]
6. ! [X0] : ((creative(X0) & ~humble(X0)) <=> (~funny(X0) <~> ~patient(X0))) [input p5]
9. ! [X0] : ((~rich(X0) & ~creative(X0)) => (rich(X0) | curious(X0))) [input p8]
11. ! [X0] : (~humble(X0) <=> (brave(X0) <~> calm(X0))) [input p10]
13. ! [X0] : ((funny(X0) <~> ~humble(X0)) <=> (~patient(X0) | strong(X0))) [input p12]
14. ! [X0] : ((humble(X0) <~> ~strong(X0)) <=> humble(X0)) [input p13]
15. ! [X0] : ((~generous(X0) & curious(X0)) <=> (~quiet(X0) <~> rich(X0))) [input p14]
16. (~quiet(lucy) <~> curious(lucy)) => (~calm(mary) & ~creative(mary)) [input p15]
22. ~brave(mary) [input hypothesis]
26. ! [X0] : ((rich(X0) | curious(X0)) | (rich(X0) | creative(X0))) [ennf transformation 9]
27. ! [X0] : (rich(X0) | curious(X0) | rich(X0) | creative(X0)) [flattening 26]
30. (~calm(mary) & ~creative(mary)) | (~quiet(lucy) <=> curious(lucy)) [ennf transformation 16]
37. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | (strong(X0) | funny(X0)))) [nnf transformation 3]
38. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | strong(X0) | funny(X0))) [flattening 37]
42. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | (~creative(X0) | humble(X0)))) [nnf transformation 6]
43. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | ~creative(X0) | humble(X0))) [flattening 42]
56. ! [X0] : ((~humble(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | humble(X0))) [nnf transformation 11]
59. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & ((~patient(X0) | strong(X0)) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [nnf transformation 13]
60. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & (~patient(X0) | strong(X0) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [flattening 59]
61. ! [X0] : ((((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | ~humble(X0)) & (humble(X0) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0))))) [nnf transformation 14]
62. ! [X0] : (((~generous(X0) & curious(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (generous(X0) | ~curious(X0)))) [nnf transformation 15]
63. ! [X0] : (((~generous(X0) & curious(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | generous(X0) | ~curious(X0))) [flattening 62]
64. (~calm(mary) & ~creative(mary)) | ((~quiet(lucy) | ~curious(lucy)) & (curious(lucy) | quiet(lucy))) [nnf transformation 30]
80. ~funny(X0) | ~patient(X0) [cnf transformation 38]
82. ~strong(X0) | ~patient(X0) [cnf transformation 38]
83. ~strong(X0) | ~curious(X0) [cnf transformation 38]
89. ~creative(X0) | funny(X0) | patient(X0) | humble(X0) [cnf transformation 43]
90. ~humble(X0) | ~patient(X0) | funny(X0) [cnf transformation 43]
91. ~humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 43]
102. rich(X0) | curious(X0) | rich(X0) | creative(X0) [cnf transformation 27]
109. brave(X0) | calm(X0) | humble(X0) [cnf transformation 56]
116. ~patient(X0) | strong(X0) | funny(X0) | humble(X0) [cnf transformation 60]
118. ~humble(X0) | funny(X0) | patient(X0) [cnf transformation 60]
120. humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 60]
122. humble(X0) | humble(X0) | strong(X0) [cnf transformation 61]
128. ~quiet(X0) | curious(X0) | ~rich(X0) [cnf transformation 63]
133. ~calm(mary) | curious(lucy) | quiet(lucy) [cnf transformation 64]
141. ~brave(mary) [cnf transformation 22]
142. humble(X0) | strong(X0) [duplicate literal removal 122]
146. curious(X0) | rich(X0) | creative(X0) [duplicate literal removal 102]
148. 1 <=> ! [X0] : ~patient(X0) [avatar definition]
149. ~patient(X0) <- (1) [avatar component clause 148]
156. 3 <=> ! [X0] : ~curious(X0) [avatar definition]
157. ~curious(X0) <- (3) [avatar component clause 156]
196. ~funny(X0) | ~humble(X0) [subsumption resolution 91,80]
197. ~patient(X0) | ~humble(X0) [subsumption resolution 90,80]
261. ~funny(X0) | patient(X0) [subsumption resolution 120,196]
262. ~funny(X0) [subsumption resolution 261,80]
263. ~humble(X0) | patient(X0) [subsumption resolution 118,262]
264. ~humble(X0) [subsumption resolution 263,197]
265. ~patient(X0) | strong(X0) | humble(X0) [subsumption resolution 116,262]
266. ~patient(X0) | strong(X0) [subsumption resolution 265,264]
267. ~patient(X0) [subsumption resolution 266,82]
268. 1 [avatar split clause 267,148]
269. strong(X0) [subsumption resolution 142,264]
271. 24 <=> curious(lucy) [avatar definition]
272. curious(lucy) <- (24) [avatar component clause 271]
273. ~curious(lucy) <- (~24) [avatar component clause 271]
275. 25 <=> quiet(lucy) [avatar definition]
276. quiet(lucy) <- (25) [avatar component clause 275]
279. 26 <=> calm(mary) [avatar definition]
283. 25 | 24 | ~26 [avatar split clause 133,279,271,275]
317. ~curious(X0) [resolution 83,269]
318. calm(mary) | humble(mary) [resolution 109,141]
326. calm(mary) [subsumption resolution 318,264]
327. 26 [avatar split clause 326,279]
328. $false <- (3, 24) [subsumption resolution 272,157]
329. ~3 | ~24 [avatar contradiction clause 328]
330. 3 [avatar split clause 317,156]
338. curious(lucy) | ~rich(lucy) <- (25) [resolution 128,276]
342. ~rich(lucy) <- (~24, 25) [subsumption resolution 338,273]
344. creative(X0) | rich(X0) <- (3) [resolution 146,157]
359. funny(X0) | patient(X0) | humble(X0) | rich(X0) <- (3) [resolution 89,344]
364. patient(X0) | humble(X0) | rich(X0) <- (3) [subsumption resolution 359,262]
365. humble(X0) | rich(X0) <- (1, 3) [subsumption resolution 364,149]
366. rich(X0) <- (1, 3) [subsumption resolution 365,264]
373. $false <- (1, 3, ~24, 25) [resolution 366,342]
374. ~1 | ~3 | 24 | ~25 [avatar contradiction clause 373]
375. $false [avatar sat refutation 268,283,327,329,330,374]
% SZS output end Proof for 4620076423687273309190447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not wise is not funny or humble and vice versa. If paul is both not rich and not curious then someone is creative or kind. Everyone who is not kind is either not humble or not tall. If someone is not creative or not calm then someone is not patient or funny. If fred is both strong and funny then someone is either not brave or funny. Everyone who is either not generous or patient is patient and vice versa. If someone is both not humble and not strong then someone is both not creative and calm. Everyone who is either patient or brave is not curious and vice versa. If someone is either not wise or humble then someone is both not happy and rich and vice versa. Everyone who is funny is not strong. If someone is creative then paul is humble or happy and vice versa. If someone is either funny or not kind then paul is both not brave and not old and vice versa. If john is both patient and generous then lucy is generous or quiet and vice versa. If paul is both not tall and not generous then lucy is both brave and not creative. Everyone who is not strong is not patient or not tall. If paul is both not strong and brave then lucy is calm or not kind. Someone is both wise and happy. Someone is both strong and generous. Mary is either not happy or not calm. Someone is patient. Susan is both calm and kind. Someone is not kind or patient. John is either brave or not generous. Someone is old. | John is not patient. | contradiction | (![X]:((funny(X)<~>~wise(X))<=>(~funny(X)|humble(X))))&
(((~rich(paul)&~curious(paul)))=>(?[X]:((creative(X)|kind(X)))))&
(![X]:(~kind(X)=>(~humble(X)<~>~tall(X))))&
((?[X]:((~creative(X)|~calm(X))))=>(?[X]:((~patient(X)|funny(X)))))&
(((strong(fred)&funny(fred)))=>(?[X]:((~brave(X)<~>funny(X)))))&
(![X]:((~generous(X)<~>patient(X))<=>patient(X)))&
((?[X]:((~humble(X)&~strong(X))))=>(?[X]:((~creative(X)&calm(X)))))&
(![X]:((patient(X)<~>brave(X))<=>~curious(X)))&
((?[X]:((~wise(X)<~>humble(X))))<=>(?[X]:((~happy(X)&rich(X)))))&
(![X]:(funny(X)=>~strong(X)))&
((?[X]:(creative(X)))<=>((humble(paul)|happy(paul))))&
((?[X]:((funny(X)<~>~kind(X))))<=>((~brave(paul)&~old(paul))))&
(((patient(john)&generous(john)))<=>((generous(lucy)|quiet(lucy))))&
(((~tall(paul)&~generous(paul)))=>((brave(lucy)&~creative(lucy))))&
(![X]:(~strong(X)=>(~patient(X)|~tall(X))))&
(((~strong(paul)&brave(paul)))=>((calm(lucy)|~kind(lucy))))&
(?[X]:((wise(X)&happy(X))))&
(?[X]:((strong(X)&generous(X))))&
((~happy(mary)<~>~calm(mary)))&
(?[X]:(patient(X)))&
((calm(susan)&kind(susan)))&
(?[X]:((~kind(X)|patient(X))))&
((brave(john)<~>~generous(john)))&
(?[X]:(old(X))) | ~patient(john) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6265431898775180504736035
% SZS output start Proof for 6265431898775180504736035
6. ! [X0] : ((~generous(X0) <~> patient(X0)) <=> patient(X0)) [input p5]
13. (generous(john) & patient(john)) <=> (quiet(lucy) | generous(lucy)) [input p12]
25. ~patient(john) [input hypothesis]
56. ! [X0] : ((((~patient(X0) | generous(X0)) & (patient(X0) | ~generous(X0))) | ~patient(X0)) & (patient(X0) | ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))))) [nnf transformation 6]
76. ((generous(john) & patient(john)) | (~quiet(lucy) & ~generous(lucy))) & ((quiet(lucy) | generous(lucy)) | (~generous(john) | ~patient(john))) [nnf transformation 13]
77. ((generous(john) & patient(john)) | (~quiet(lucy) & ~generous(lucy))) & (quiet(lucy) | generous(lucy) | ~generous(john) | ~patient(john)) [flattening 76]
103. patient(X0) | patient(X0) | generous(X0) [cnf transformation 56]
106. ~patient(X0) | generous(X0) | ~patient(X0) [cnf transformation 56]
128. patient(john) | ~generous(lucy) [cnf transformation 77]
149. ~patient(john) [cnf transformation 25]
150. patient(X0) | generous(X0) [duplicate literal removal 103]
151. ~patient(X0) | generous(X0) [duplicate literal removal 106]
206. generous(X0) [subsumption resolution 150,151]
305. 34 <=> patient(john) [avatar definition]
309. patient(john) [subsumption resolution 128,206]
310. 34 [avatar split clause 309,305]
344. ~34 [avatar split clause 149,305]
345. $false [avatar sat refutation 310,344]
% SZS output end Proof for 6265431898775180504736035
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or not tall then someone is rich.
Everyone who is not kind or generous is generous and vice versa.
Everyone who is either old or kind is not wise or rich and vice versa.
If john is either humble or not strong then paul is both rich and not funny.
If mary is not generous then someone is either calm or humble.
If alice is either quiet or tall then someone is either wise or kind and vice versa.
If someone is not wise then someone is either not strong or patient and vice versa.
Everyone who is strong is generous and vice versa.
Everyone who is kind is both curious and humble and vice versa.
If someone is brave or not generous then someone is either strong or rich and vice versa.
If someone is both not happy and not generous then someone is not kind or old and vice versa.
Everyone who is both not generous and old is either generous or not wise and vice versa.
If someone is either not patient or not strong then someone is not calm.
Everyone who is tall or funny is old and vice versa.
Everyone who is funny or generous is both not happy and rich and vice versa.
If fred is either not humble or not patient then lucy is both creative and not old.
Alice is both brave and not patient.
Someone is generous or not patient.
Someone is both wise and not brave.
Someone is not strong.
Fred is brave or wise. | Mary is old. | contradiction | ((?[X]:((generous(X)|~tall(X))))=>(?[X]:(rich(X))))&
(![X]:((~kind(X)|generous(X))<=>generous(X)))&
(![X]:((old(X)<~>kind(X))<=>(~wise(X)|rich(X))))&
(((humble(john)<~>~strong(john)))=>((rich(paul)&~funny(paul))))&
((~generous(mary))=>(?[X]:((calm(X)<~>humble(X)))))&
(((quiet(alice)<~>tall(alice)))<=>(?[X]:((wise(X)<~>kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(![X]:(strong(X)<=>generous(X)))&
(![X]:(kind(X)<=>(curious(X)&humble(X))))&
((?[X]:((brave(X)|~generous(X))))<=>(?[X]:((strong(X)<~>rich(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((~kind(X)|old(X)))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)<~>~wise(X))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:(~calm(X))))&
(![X]:((tall(X)|funny(X))<=>old(X)))&
(![X]:((funny(X)|generous(X))<=>(~happy(X)&rich(X))))&
(((~humble(fred)<~>~patient(fred)))=>((creative(lucy)&~old(lucy))))&
((brave(alice)&~patient(alice)))&
(?[X]:((generous(X)|~patient(X))))&
(?[X]:((wise(X)&~brave(X))))&
(?[X]:(~strong(X)))&
((brave(fred)|wise(fred))) | old(mary) | [
"p1",
"p2",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4864316253254316743780754
% SZS output start Proof for 4864316253254316743780754
2. ! [X0] : ((generous(X0) | ~kind(X0)) <=> generous(X0)) [input p1]
3. ! [X0] : ((old(X0) <~> kind(X0)) <=> (rich(X0) | ~wise(X0))) [input p2]
11. ? [X0] : (~generous(X0) & ~happy(X0)) <=> ? [X0] : (old(X0) | ~kind(X0)) [input p10]
12. ! [X0] : ((old(X0) & ~generous(X0)) <=> (generous(X0) <~> ~wise(X0))) [input p11]
14. ! [X0] : ((funny(X0) | tall(X0)) <=> old(X0)) [input p13]
15. ! [X0] : ((generous(X0) | funny(X0)) <=> (rich(X0) & ~happy(X0))) [input p14]
22. old(mary) [input hypothesis]
26. ? [X0] : (~generous(X0) & ~happy(X0)) <=> ? [X1] : (old(X1) | ~kind(X1)) [rectify 11]
37. ! [X0] : (((generous(X0) | ~kind(X0)) | ~generous(X0)) & (generous(X0) | (~generous(X0) & kind(X0)))) [nnf transformation 2]
38. ! [X0] : ((generous(X0) | ~kind(X0) | ~generous(X0)) & (generous(X0) | (~generous(X0) & kind(X0)))) [flattening 37]
39. ! [X0] : ((((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | (~rich(X0) & wise(X0))) & ((rich(X0) | ~wise(X0)) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0))))) [nnf transformation 3]
40. ! [X0] : ((((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | (~rich(X0) & wise(X0))) & (rich(X0) | ~wise(X0) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0))))) [flattening 39]
62. (? [X0] : (~generous(X0) & ~happy(X0)) | ! [X1] : (~old(X1) & kind(X1))) & (? [X1] : (old(X1) | ~kind(X1)) | ! [X0] : (generous(X0) | happy(X0))) [nnf transformation 26]
63. (? [X0] : (~generous(X0) & ~happy(X0)) | ! [X1] : (~old(X1) & kind(X1))) & (? [X2] : (old(X2) | ~kind(X2)) | ! [X3] : (generous(X3) | happy(X3))) [rectify 62]
64. ? [X0] : (~generous(X0) & ~happy(X0)) => (~generous(sK7) & ~happy(sK7)) [choice axiom]
65. ? [X2] : (old(X2) | ~kind(X2)) => (old(sK8) | ~kind(sK8)) [choice axiom]
66. ((~generous(sK7) & ~happy(sK7)) | ! [X1] : (~old(X1) & kind(X1))) & ((old(sK8) | ~kind(sK8)) | ! [X3] : (generous(X3) | happy(X3))) [skolemisation 63,65,64]
67. ! [X0] : (((old(X0) & ~generous(X0)) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) & (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | (~old(X0) | generous(X0)))) [nnf transformation 12]
68. ! [X0] : (((old(X0) & ~generous(X0)) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) & (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | ~old(X0) | generous(X0))) [flattening 67]
73. ! [X0] : (((funny(X0) | tall(X0)) | ~old(X0)) & (old(X0) | (~funny(X0) & ~tall(X0)))) [nnf transformation 14]
74. ! [X0] : ((funny(X0) | tall(X0) | ~old(X0)) & (old(X0) | (~funny(X0) & ~tall(X0)))) [flattening 73]
75. ! [X0] : (((generous(X0) | funny(X0)) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | (~generous(X0) & ~funny(X0)))) [nnf transformation 15]
76. ! [X0] : ((generous(X0) | funny(X0) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | (~generous(X0) & ~funny(X0)))) [flattening 75]
86. kind(X0) | generous(X0) [cnf transformation 38]
90. ~wise(X0) | rich(X0) | old(X0) | ~kind(X0) [cnf transformation 40]
93. ~old(X0) | ~kind(X0) | wise(X0) [cnf transformation 40]
94. ~old(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 40]
126. ~happy(sK7) | ~old(X1) [cnf transformation 66]
128. ~generous(sK7) | ~old(X1) [cnf transformation 66]
129. ~wise(X0) | generous(X0) | ~old(X0) | generous(X0) [cnf transformation 68]
131. ~generous(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 68]
134. wise(X0) | generous(X0) | old(X0) [cnf transformation 68]
137. ~tall(X0) | old(X0) [cnf transformation 74]
138. ~funny(X0) | old(X0) [cnf transformation 74]
139. ~old(X0) | tall(X0) | funny(X0) [cnf transformation 74]
142. ~funny(X0) | rich(X0) [cnf transformation 76]
143. ~generous(X0) | rich(X0) [cnf transformation 76]
144. ~rich(X0) | funny(X0) | generous(X0) | happy(X0) [cnf transformation 76]
154. old(mary) [cnf transformation 22]
155. ~wise(X0) | generous(X0) | ~old(X0) [duplicate literal removal 129]
156. ~wise(X0) | ~generous(X0) [duplicate literal removal 131]
293. 31 <=> ! [X1] : ~old(X1) [avatar definition]
294. ~old(X1) <- (31) [avatar component clause 293]
296. 32 <=> generous(sK7) [avatar definition]
298. ~generous(sK7) <- (~32) [avatar component clause 296]
299. 31 | ~32 [avatar split clause 128,296,293]
305. 34 <=> happy(sK7) [avatar definition]
307. ~happy(sK7) <- (~34) [avatar component clause 305]
308. 31 | ~34 [avatar split clause 126,305,293]
322. ~wise(X0) | ~old(X0) [subsumption resolution 155,156]
462. rich(X0) | old(X0) | ~kind(X0) | generous(X0) | old(X0) [resolution 90,134]
465. rich(X0) | old(X0) | ~kind(X0) | generous(X0) [duplicate literal removal 462]
663. 71 <=> tall(sK7) [avatar definition]
665. tall(sK7) <- (71) [avatar component clause 663]
667. 72 <=> funny(sK7) [avatar definition]
668. ~funny(sK7) <- (~72) [avatar component clause 667]
669. funny(sK7) <- (72) [avatar component clause 667]
690. $false <- (31) [resolution 294,154]
693. ~31 [avatar contradiction clause 690]
836. old(sK7) <- (72) [resolution 669,138]
842. ~kind(sK7) | ~rich(sK7) <- (72) [resolution 836,94]
854. 82 <=> kind(sK7) [avatar definition]
855. kind(sK7) <- (82) [avatar component clause 854]
856. ~kind(sK7) <- (~82) [avatar component clause 854]
859. 83 <=> rich(sK7) [avatar definition]
861. ~rich(sK7) <- (~83) [avatar component clause 859]
862. ~83 | ~82 | ~72 [avatar split clause 842,667,854,859]
873. rich(X0) | old(X0) | generous(X0) [subsumption resolution 465,86]
874. old(X0) | rich(X0) [subsumption resolution 873,143]
892. rich(X0) | tall(X0) | funny(X0) [resolution 874,139]
894. ~kind(X2) | rich(X2) | wise(X2) [resolution 874,93]
897. rich(X0) | tall(X0) [subsumption resolution 892,142]
919. happy(X0) | funny(X0) | generous(X0) | tall(X0) [resolution 897,144]
922. rich(X0) | wise(X0) | generous(X0) [resolution 894,86]
927. wise(X0) | rich(X0) [subsumption resolution 922,143]
935. generous(sK7) <- (~82) [resolution 856,86]
936. $false <- (~32, ~82) [subsumption resolution 935,298]
937. 32 | 82 [avatar contradiction clause 936]
941. rich(X3) | ~old(X3) [resolution 927,322]
949. rich(X3) [subsumption resolution 941,874]
953. funny(sK7) | generous(sK7) | tall(sK7) <- (~34) [resolution 919,307]
955. generous(sK7) | tall(sK7) <- (~34, ~72) [subsumption resolution 953,668]
956. tall(sK7) <- (~32, ~34, ~72) [subsumption resolution 955,298]
959. 71 | 32 | 34 | 72 [avatar split clause 956,667,305,296,663]
960. old(sK7) <- (71) [resolution 665,137]
964. ~kind(sK7) | ~rich(sK7) <- (71) [resolution 960,94]
966. ~rich(sK7) <- (71, 82) [subsumption resolution 964,855]
971. $false <- (71, 82) [subsumption resolution 966,949]
972. ~71 | ~82 [avatar contradiction clause 971]
973. $false <- (~83) [subsumption resolution 861,949]
974. 83 [avatar contradiction clause 973]
975. $false [avatar sat refutation 299,308,693,862,937,959,972,974]
% SZS output end Proof for 4864316253254316743780754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both not funny and curious is either not quiet or generous.
Everyone who is not creative or not patient is either generous or kind and vice versa.
Everyone who is either not brave or brave is happy.
If someone is patient then alice is not generous.
Everyone who is not calm is either brave or not happy and vice versa.
Everyone who is not rich or not humble is both not generous and brave and vice versa.
If john is tall or quiet then mary is strong or curious and vice versa.
If someone is not curious or not generous then mary is both wise and curious and vice versa.
If lucy is rich or not creative then someone is not brave and vice versa.
If someone is either not wise or not brave then someone is creative or generous.
If mary is either humble or wise then someone is not tall or rich.
Everyone who is not wise or generous is both happy and not brave.
If someone is funny or not strong then someone is curious.
Everyone who is patient is either not funny or tall and vice versa.
Everyone who is either not brave or quiet is old.
If someone is both tall and quiet then someone is not tall or not happy and vice versa.
Lucy is both not quiet and not tall.
Susan is not humble.
Susan is happy or creative.
Someone is either not creative or not strong.
Mary is either not strong or creative.
Someone is either not patient or humble.
Alice is both kind and happy.
Paul is patient. | Alice is generous. | contradiction | (![X]:((~funny(X)&curious(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((~creative(X)|~patient(X))<=>(generous(X)<~>kind(X))))&
(![X]:((~brave(X)<~>brave(X))=>happy(X)))&
((?[X]:(patient(X)))=>(~generous(alice)))&
(![X]:(~calm(X)<=>(brave(X)<~>~happy(X))))&
(![X]:((~rich(X)|~humble(X))<=>(~generous(X)&brave(X))))&
(((tall(john)|quiet(john)))<=>((strong(mary)|curious(mary))))&
((?[X]:((~curious(X)|~generous(X))))<=>((wise(mary)&curious(mary))))&
(((rich(lucy)|~creative(lucy)))<=>(?[X]:(~brave(X))))&
((?[X]:((~wise(X)<~>~brave(X))))=>(?[X]:((creative(X)|generous(X)))))&
(((humble(mary)<~>wise(mary)))=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:((~wise(X)|generous(X))=>(happy(X)&~brave(X))))&
((?[X]:((funny(X)|~strong(X))))=>(?[X]:(curious(X))))&
(![X]:(patient(X)<=>(~funny(X)<~>tall(X))))&
(![X]:((~brave(X)<~>quiet(X))=>old(X)))&
((?[X]:((tall(X)&quiet(X))))<=>(?[X]:((~tall(X)|~happy(X)))))&
((~quiet(lucy)&~tall(lucy)))&
(~humble(susan))&
((happy(susan)|creative(susan)))&
(?[X]:((~creative(X)<~>~strong(X))))&
((~strong(mary)<~>creative(mary)))&
(?[X]:((~patient(X)<~>humble(X))))&
((kind(alice)&happy(alice)))&
(patient(paul)) | generous(alice) | [
"p3",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7512326316840422594724354
% SZS output start Proof for 7512326316840422594724354
4. ? [X0] : patient(X0) => ~generous(alice) [input p3]
24. patient(paul) [input p23]
25. generous(alice) [input hypothesis]
33. ~generous(alice) | ! [X0] : ~patient(X0) [ennf transformation 4]
89. ~generous(alice) | ~patient(X0) [cnf transformation 33]
138. patient(paul) [cnf transformation 24]
139. generous(alice) [cnf transformation 25]
144. 1 <=> ! [X0] : ~patient(X0) [avatar definition]
145. ~patient(X0) <- (1) [avatar component clause 144]
147. 2 <=> generous(alice) [avatar definition]
150. 1 | ~2 [avatar split clause 89,147,144]
303. 2 [avatar split clause 139,147]
310. $false <- (1) [resolution 145,138]
311. ~1 [avatar contradiction clause 310]
312. $false [avatar sat refutation 150,303,311]
% SZS output end Proof for 7512326316840422594724354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not rich and vice versa.
Everyone who is not generous is either not patient or not strong and vice versa.
If someone is both tall and not calm then alice is both strong and old.
If alice is both kind and not tall then john is both not rich and not generous and vice versa.
If someone is not strong or not calm then alice is rich and vice versa.
Everyone who is generous is rich or not generous.
If lucy is creative or rich then alice is either funny or wise and vice versa.
If alice is creative or not rich then someone is both rich and not old and vice versa.
Everyone who is either happy or generous is either creative or not rich and vice versa.
Everyone who is both funny and not calm is both not quiet and curious.
Everyone who is rich or not happy is brave.
If someone is wise then susan is both not generous and happy.
Everyone who is not strong is either happy or creative and vice versa.
If someone is both not funny and not wise then john is both not calm and not curious.
Everyone who is tall is either not curious or rich.
If someone is brave then someone is both tall and not funny and vice versa.
Someone is both kind and not wise.
John is both kind and rich.
Someone is tall or brave.
Mary is not brave or old.
Someone is happy or not patient.
Someone is both not quiet and creative.
Someone is not curious or not patient.
Mary is both not calm and not wise. | Alice is patient. | contradiction | (![X]:(funny(X)<=>~rich(X)))&
(![X]:(~generous(X)<=>(~patient(X)<~>~strong(X))))&
((?[X]:((tall(X)&~calm(X))))=>((strong(alice)&old(alice))))&
(((kind(alice)&~tall(alice)))<=>((~rich(john)&~generous(john))))&
((?[X]:((~strong(X)|~calm(X))))<=>(rich(alice)))&
(![X]:(generous(X)=>(rich(X)|~generous(X))))&
(((creative(lucy)|rich(lucy)))<=>((funny(alice)<~>wise(alice))))&
(((creative(alice)|~rich(alice)))<=>(?[X]:((rich(X)&~old(X)))))&
(![X]:((happy(X)<~>generous(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((funny(X)&~calm(X))=>(~quiet(X)&curious(X))))&
(![X]:((rich(X)|~happy(X))=>brave(X)))&
((?[X]:(wise(X)))=>((~generous(susan)&happy(susan))))&
(![X]:(~strong(X)<=>(happy(X)<~>creative(X))))&
((?[X]:((~funny(X)&~wise(X))))=>((~calm(john)&~curious(john))))&
(![X]:(tall(X)=>(~curious(X)<~>rich(X))))&
((?[X]:(brave(X)))<=>(?[X]:((tall(X)&~funny(X)))))&
(?[X]:((kind(X)&~wise(X))))&
((kind(john)&rich(john)))&
(?[X]:((tall(X)|brave(X))))&
((~brave(mary)|old(mary)))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((~quiet(X)&creative(X))))&
(?[X]:((~curious(X)|~patient(X))))&
((~calm(mary)&~wise(mary))) | patient(alice) | [
"p1",
"p4",
"p5",
"p8",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7693117229268164796599932
% SZS output start Proof for 7693117229268164796599932
2. ! [X0] : (~generous(X0) <=> (~patient(X0) <~> ~strong(X0))) [input p1]
5. ? [X0] : (~calm(X0) | ~strong(X0)) <=> rich(alice) [input p4]
6. ! [X0] : (generous(X0) => (~generous(X0) | rich(X0))) [input p5]
9. ! [X0] : ((happy(X0) <~> generous(X0)) <=> (creative(X0) <~> ~rich(X0))) [input p8]
13. ! [X0] : (~strong(X0) <=> (happy(X0) <~> creative(X0))) [input p12]
24. ~wise(mary) & ~calm(mary) [input p23]
25. patient(alice) [input hypothesis]
30. ! [X0] : ((~generous(X0) | rich(X0)) | ~generous(X0)) [ennf transformation 6]
31. ! [X0] : (~generous(X0) | rich(X0) | ~generous(X0)) [flattening 30]
39. ! [X0] : ((~generous(X0) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | generous(X0))) [nnf transformation 2]
42. (? [X0] : (~calm(X0) | ~strong(X0)) | ~rich(alice)) & (rich(alice) | ! [X0] : (calm(X0) & strong(X0))) [nnf transformation 5]
43. (? [X0] : (~calm(X0) | ~strong(X0)) | ~rich(alice)) & (rich(alice) | ! [X1] : (calm(X1) & strong(X1))) [rectify 42]
44. ? [X0] : (~calm(X0) | ~strong(X0)) => (~calm(sK0) | ~strong(sK0)) [choice axiom]
45. ((~calm(sK0) | ~strong(sK0)) | ~rich(alice)) & (rich(alice) | ! [X1] : (calm(X1) & strong(X1))) [skolemisation 43,44]
53. ! [X0] : ((((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) & (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0))))) [nnf transformation 9]
54. ! [X0] : ((~strong(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | strong(X0))) [nnf transformation 13]
73. ~strong(X0) | ~patient(X0) | generous(X0) [cnf transformation 39]
76. ~patient(X0) | ~generous(X0) | strong(X0) [cnf transformation 39]
84. rich(alice) | calm(X1) [cnf transformation 45]
86. ~generous(X0) | rich(X0) | ~generous(X0) [cnf transformation 31]
98. ~happy(X0) | creative(X0) | generous(X0) | ~rich(X0) [cnf transformation 53]
99. ~rich(X0) | creative(X0) | happy(X0) | ~generous(X0) [cnf transformation 53]
102. ~creative(X0) | happy(X0) | ~rich(X0) | generous(X0) [cnf transformation 53]
104. ~generous(X0) | ~happy(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 53]
111. happy(X0) | creative(X0) | strong(X0) [cnf transformation 54]
112. ~happy(X0) | ~creative(X0) | strong(X0) [cnf transformation 54]
113. ~happy(X0) | creative(X0) | ~strong(X0) [cnf transformation 54]
114. ~creative(X0) | happy(X0) | ~strong(X0) [cnf transformation 54]
131. ~calm(mary) [cnf transformation 24]
133. patient(alice) [cnf transformation 25]
134. ~generous(X0) | rich(X0) [duplicate literal removal 86]
144. 3 <=> strong(alice) [avatar definition]
145. ~strong(alice) <- (~3) [avatar component clause 144]
146. strong(alice) <- (3) [avatar component clause 144]
169. 8 <=> rich(alice) [avatar definition]
170. rich(alice) <- (8) [avatar component clause 169]
182. 11 <=> ! [X1] : calm(X1) [avatar definition]
183. calm(X1) <- (11) [avatar component clause 182]
184. 11 | 8 [avatar split clause 84,169,182]
215. 18 <=> creative(alice) [avatar definition]
216. ~creative(alice) <- (~18) [avatar component clause 215]
217. creative(alice) <- (18) [avatar component clause 215]
231. ~happy(X0) | ~generous(X0) | ~creative(X0) [subsumption resolution 104,134]
234. ~generous(X0) | happy(X0) | creative(X0) [subsumption resolution 99,134]
339. ~patient(alice) | generous(alice) <- (3) [resolution 73,146]
340. generous(alice) <- (3) [subsumption resolution 339,133]
348. ~generous(alice) | strong(alice) [resolution 76,133]
368. $false <- (11) [resolution 183,131]
373. ~11 [avatar contradiction clause 368]
398. happy(alice) | ~strong(alice) <- (18) [resolution 114,217]
400. happy(alice) <- (3, 18) [subsumption resolution 398,146]
435. ~generous(alice) | ~creative(alice) <- (3, 18) [resolution 400,231]
438. ~creative(alice) <- (3, 18) [subsumption resolution 435,340]
439. $false <- (3, 18) [subsumption resolution 438,217]
440. ~3 | ~18 [avatar contradiction clause 439]
459. happy(alice) | creative(alice) <- (3) [resolution 234,340]
460. happy(alice) <- (3, ~18) [subsumption resolution 459,216]
465. creative(X1) | generous(X1) | ~rich(X1) | creative(X1) | strong(X1) [resolution 98,111]
469. ~rich(X1) | generous(X1) | creative(X1) | strong(X1) [duplicate literal removal 465]
580. creative(alice) | ~strong(alice) <- (3, ~18) [resolution 460,113]
582. ~strong(alice) <- (3, ~18) [subsumption resolution 580,216]
583. $false <- (3, ~18) [subsumption resolution 582,146]
584. ~3 | 18 [avatar contradiction clause 583]
586. 59 <=> generous(alice) [avatar definition]
588. ~generous(alice) <- (~59) [avatar component clause 586]
589. 3 | ~59 [avatar split clause 348,586,144]
595. generous(alice) | creative(alice) | strong(alice) <- (8) [resolution 469,170]
602. creative(alice) | strong(alice) <- (8, ~59) [subsumption resolution 595,588]
665. creative(alice) <- (~3, 8, ~59) [subsumption resolution 602,145]
666. 18 | 3 | ~8 | 59 [avatar split clause 665,586,169,144,215]
685. happy(alice) | ~rich(alice) | generous(alice) <- (18) [resolution 217,102]
687. happy(alice) | generous(alice) <- (8, 18) [subsumption resolution 685,170]
688. happy(alice) <- (8, 18, ~59) [subsumption resolution 687,588]
696. ~creative(alice) | strong(alice) <- (8, 18, ~59) [resolution 688,112]
697. strong(alice) <- (8, 18, ~59) [subsumption resolution 696,217]
698. $false <- (~3, 8, 18, ~59) [subsumption resolution 697,145]
699. 3 | ~8 | ~18 | 59 [avatar contradiction clause 698]
700. $false [avatar sat refutation 184,373,440,584,589,666,699]
% SZS output end Proof for 7693117229268164796599932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or not kind is either kind or not tall. If susan is both funny and rich then someone is both not funny and brave. Everyone who is not creative or not calm is both not patient and creative. Everyone who is both creative and not curious is patient or humble. Everyone who is both not funny and quiet is either not old or not kind and vice versa. Everyone who is quiet is both not curious and not patient. Everyone who is kind is wise. Everyone who is quiet or old is either strong or not quiet and vice versa. Everyone who is either not patient or not strong is both happy and strong and vice versa. Everyone who is happy or not curious is both rich and curious. Everyone who is not curious is not happy. Everyone who is not rich is both tall and generous. If john is both not happy and not rich then susan is either not quiet or wise. Everyone who is both not calm and not kind is not creative and vice versa. Everyone who is patient or curious is not patient or wise and vice versa. If someone is both not wise and rich then susan is either brave or not kind and vice versa. Mary is either happy or wise. Mary is not rich. Mary is humble. Lucy is funny. Alice is both rich and old. John is not happy. | Alice is tall. | entailment | (![X]:((creative(X)<~>~kind(X))=>(kind(X)<~>~tall(X))))&
(((funny(susan)&rich(susan)))=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:((~creative(X)|~calm(X))=>(~patient(X)&creative(X))))&
(![X]:((creative(X)&~curious(X))=>(patient(X)|humble(X))))&
(![X]:((~funny(X)&quiet(X))<=>(~old(X)<~>~kind(X))))&
(![X]:(quiet(X)=>(~curious(X)&~patient(X))))&
(![X]:(kind(X)=>wise(X)))&
(![X]:((quiet(X)|old(X))<=>(strong(X)<~>~quiet(X))))&
(![X]:((~patient(X)<~>~strong(X))<=>(happy(X)&strong(X))))&
(![X]:((happy(X)|~curious(X))=>(rich(X)&curious(X))))&
(![X]:(~curious(X)=>~happy(X)))&
(![X]:(~rich(X)=>(tall(X)&generous(X))))&
(((~happy(john)&~rich(john)))=>((~quiet(susan)<~>wise(susan))))&
(![X]:((~calm(X)&~kind(X))<=>~creative(X)))&
(![X]:((patient(X)|curious(X))<=>(~patient(X)|wise(X))))&
((?[X]:((~wise(X)&rich(X))))<=>((brave(susan)<~>~kind(susan))))&
((happy(mary)<~>wise(mary)))&
(~rich(mary))&
(humble(mary))&
(funny(lucy))&
((rich(alice)&old(alice)))&
(~happy(john)) | tall(alice) | [
"p0",
"p2",
"p4",
"p5",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1738094415036279840645408
% SZS output start Proof for 1738094415036279840645408
1. ! [X0] : ((creative(X0) <~> ~kind(X0)) => (kind(X0) <~> ~tall(X0))) [input p0]
3. ! [X0] : ((~calm(X0) | ~creative(X0)) => (creative(X0) & ~patient(X0))) [input p2]
5. ! [X0] : ((quiet(X0) & ~funny(X0)) <=> (~old(X0) <~> ~kind(X0))) [input p4]
6. ! [X0] : (quiet(X0) => (~patient(X0) & ~curious(X0))) [input p5]
10. ! [X0] : ((~curious(X0) | happy(X0)) => (curious(X0) & rich(X0))) [input p9]
21. old(alice) & rich(alice) [input p20]
23. ~tall(alice) [input hypothesis]
27. ! [X0] : ((kind(X0) <~> ~tall(X0)) | (creative(X0) <=> ~kind(X0))) [ennf transformation 1]
30. ! [X0] : ((creative(X0) & ~patient(X0)) | (calm(X0) & creative(X0))) [ennf transformation 3]
31. ! [X0] : ((~patient(X0) & ~curious(X0)) | ~quiet(X0)) [ennf transformation 6]
33. ! [X0] : ((curious(X0) & rich(X0)) | (curious(X0) & ~happy(X0))) [ennf transformation 10]
38. ! [X0] : (((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) [nnf transformation 27]
41. ! [X0] : (((quiet(X0) & ~funny(X0)) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) & (((kind(X0) | old(X0)) & (~kind(X0) | ~old(X0))) | (~quiet(X0) | funny(X0)))) [nnf transformation 5]
42. ! [X0] : (((quiet(X0) & ~funny(X0)) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) & (((kind(X0) | old(X0)) & (~kind(X0) | ~old(X0))) | ~quiet(X0) | funny(X0))) [flattening 41]
59. tall(X0) | ~kind(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 38]
65. creative(X0) | creative(X0) [cnf transformation 30]
72. ~old(X0) | quiet(X0) | kind(X0) [cnf transformation 42]
73. ~quiet(X0) | ~curious(X0) [cnf transformation 31]
91. curious(X0) | curious(X0) [cnf transformation 33]
114. old(alice) [cnf transformation 21]
116. ~tall(alice) [cnf transformation 23]
119. curious(X0) [duplicate literal removal 91]
124. creative(X0) [duplicate literal removal 65]
126. ~kind(X0) | tall(X0) | ~creative(X0) [duplicate literal removal 59]
215. 17 <=> kind(alice) [avatar definition]
217. kind(alice) <- (17) [avatar component clause 215]
223. quiet(alice) | kind(alice) [resolution 72,114]
225. 19 <=> quiet(alice) [avatar definition]
227. quiet(alice) <- (19) [avatar component clause 225]
228. 17 | 19 [avatar split clause 223,225,215]
231. ~curious(alice) <- (19) [resolution 227,73]
232. $false <- (19) [subsumption resolution 231,119]
233. ~19 [avatar contradiction clause 232]
242. tall(alice) | ~creative(alice) <- (17) [resolution 126,217]
243. ~creative(alice) <- (17) [subsumption resolution 242,116]
244. $false <- (17) [subsumption resolution 243,124]
245. ~17 [avatar contradiction clause 244]
246. $false [avatar sat refutation 228,233,245]
% SZS output end Proof for 1738094415036279840645408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall is strong or wise and vice versa.
Everyone who is not creative or happy is humble.
If someone is both not curious and not calm then someone is not quiet or generous and vice versa.
If someone is funny or not tall then someone is either calm or brave and vice versa.
Everyone who is both calm and not kind is calm or not patient and vice versa.
If someone is not funny or humble then john is not brave or brave and vice versa.
Everyone who is not strong is both not generous and creative and vice versa.
Everyone who is not tall is not old or calm and vice versa.
If someone is either curious or not creative then paul is happy or curious.
Everyone who is happy or not wise is both not rich and not curious.
Everyone who is both not curious and not quiet is not creative or not quiet and vice versa.
Everyone who is both happy and humble is not wise or strong and vice versa.
Everyone who is not happy or humble is either kind or not brave and vice versa.
Everyone who is both calm and not calm is not curious and vice versa.
If susan is old or not wise then fred is not wise or rich.
Everyone who is calm or curious is either not creative or not rich and vice versa.
Paul is brave.
Fred is not generous.
Someone is either quiet or not curious.
Fred is either creative or not wise.
Lucy is not strong or not creative. | John is tall. | neutral | (![X]:((~happy(X)|~tall(X))<=>(strong(X)|wise(X))))&
(![X]:((~creative(X)|happy(X))=>humble(X)))&
((?[X]:((~curious(X)&~calm(X))))<=>(?[X]:((~quiet(X)|generous(X)))))&
((?[X]:((funny(X)|~tall(X))))<=>(?[X]:((calm(X)<~>brave(X)))))&
(![X]:((calm(X)&~kind(X))<=>(calm(X)|~patient(X))))&
((?[X]:((~funny(X)|humble(X))))<=>((~brave(john)|brave(john))))&
(![X]:(~strong(X)<=>(~generous(X)&creative(X))))&
(![X]:(~tall(X)<=>(~old(X)|calm(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>((happy(paul)|curious(paul))))&
(![X]:((happy(X)|~wise(X))=>(~rich(X)&~curious(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~creative(X)|~quiet(X))))&
(![X]:((happy(X)&humble(X))<=>(~wise(X)|strong(X))))&
(![X]:((~happy(X)|humble(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((calm(X)&~calm(X))<=>~curious(X)))&
(((old(susan)|~wise(susan)))=>((~wise(fred)|rich(fred))))&
(![X]:((calm(X)|curious(X))<=>(~creative(X)<~>~rich(X))))&
(brave(paul))&
(~generous(fred))&
(?[X]:((quiet(X)<~>~curious(X))))&
((creative(fred)<~>~wise(fred)))&
((~strong(lucy)|~creative(lucy))) | tall(john) | [] | null | 0 |
If someone is both tall and not patient then john is not strong.
If mary is not humble then someone is both brave and not patient and vice versa.
Everyone who is not calm or not humble is both old and funny.
If someone is humble or wise then someone is both tall and creative.
If susan is patient or not curious then someone is not happy or funny and vice versa.
Everyone who is rich or not calm is humble.
Everyone who is happy is humble.
Everyone who is both not quiet and not wise is creative.
If someone is not brave then someone is either tall or old.
Everyone who is either kind or curious is both generous and curious.
Everyone who is not creative or happy is either funny or not patient and vice versa.
If someone is both not happy and not tall then someone is either not generous or kind and vice versa.
If someone is both not creative and wise then john is not old.
If susan is either brave or not calm then john is both not tall and tall.
Everyone who is not tall or wise is both funny and not brave.
Everyone who is not creative or not rich is either quiet or happy and vice versa.
Alice is humble.
John is not old.
John is strong or tall.
Someone is not strong or not rich.
Someone is either patient or funny.
Someone is both not curious and calm.
Mary is either not curious or not calm. | John is not funny. | neutral | ((?[X]:((tall(X)&~patient(X))))=>(~strong(john)))&
((~humble(mary))<=>(?[X]:((brave(X)&~patient(X)))))&
(![X]:((~calm(X)|~humble(X))=>(old(X)&funny(X))))&
((?[X]:((humble(X)|wise(X))))=>(?[X]:((tall(X)&creative(X)))))&
(((patient(susan)|~curious(susan)))<=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:((rich(X)|~calm(X))=>humble(X)))&
(![X]:(happy(X)=>humble(X)))&
(![X]:((~quiet(X)&~wise(X))=>creative(X)))&
((?[X]:(~brave(X)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((kind(X)<~>curious(X))=>(generous(X)&curious(X))))&
(![X]:((~creative(X)|happy(X))<=>(funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~tall(X))))<=>(?[X]:((~generous(X)<~>kind(X)))))&
((?[X]:((~creative(X)&wise(X))))=>(~old(john)))&
(((brave(susan)<~>~calm(susan)))=>((~tall(john)&tall(john))))&
(![X]:((~tall(X)|wise(X))=>(funny(X)&~brave(X))))&
(![X]:((~creative(X)|~rich(X))<=>(quiet(X)<~>happy(X))))&
(humble(alice))&
(~old(john))&
((strong(john)|tall(john)))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((patient(X)<~>funny(X))))&
(?[X]:((~curious(X)&calm(X))))&
((~curious(mary)<~>~calm(mary))) | ~funny(john) | [] | null | 0 |
Everyone who is not wise is both tall and happy and vice versa.
Everyone who is either not happy or patient is not brave and vice versa.
Everyone who is not quiet is both patient and generous and vice versa.
Everyone who is kind or funny is generous and vice versa.
If someone is not brave or humble then someone is both not kind and wise and vice versa.
Everyone who is both not curious and not humble is either brave or not creative.
Everyone who is not wise is humble or not brave and vice versa.
Everyone who is brave or generous is not wise or old.
If paul is either not brave or not creative then someone is either not strong or curious.
Everyone who is either not generous or not wise is not patient and vice versa.
If fred is both not patient and not old then susan is either not tall or not generous and vice versa.
If mary is either not humble or not kind then someone is either wise or humble and vice versa.
If someone is both tall and not strong then someone is curious or calm and vice versa.
Everyone who is not curious is either not humble or not brave.
Everyone who is both not wise and generous is either old or not kind and vice versa.
Everyone who is not wise or not tall is either not happy or brave and vice versa.
Mary is either not kind or calm.
Someone is either not curious or quiet.
Someone is generous or not patient.
Paul is either kind or not rich.
Someone is both creative and kind.
Paul is not kind.
Someone is both not kind and happy.
Fred is calm or not funny. | Susan is not humble. | neutral | (![X]:(~wise(X)<=>(tall(X)&happy(X))))&
(![X]:((~happy(X)<~>patient(X))<=>~brave(X)))&
(![X]:(~quiet(X)<=>(patient(X)&generous(X))))&
(![X]:((kind(X)|funny(X))<=>generous(X)))&
((?[X]:((~brave(X)|humble(X))))<=>(?[X]:((~kind(X)&wise(X)))))&
(![X]:((~curious(X)&~humble(X))=>(brave(X)<~>~creative(X))))&
(![X]:(~wise(X)<=>(humble(X)|~brave(X))))&
(![X]:((brave(X)|generous(X))=>(~wise(X)|old(X))))&
(((~brave(paul)<~>~creative(paul)))=>(?[X]:((~strong(X)<~>curious(X)))))&
(![X]:((~generous(X)<~>~wise(X))<=>~patient(X)))&
(((~patient(fred)&~old(fred)))<=>((~tall(susan)<~>~generous(susan))))&
(((~humble(mary)<~>~kind(mary)))<=>(?[X]:((wise(X)<~>humble(X)))))&
((?[X]:((tall(X)&~strong(X))))<=>(?[X]:((curious(X)|calm(X)))))&
(![X]:(~curious(X)=>(~humble(X)<~>~brave(X))))&
(![X]:((~wise(X)&generous(X))<=>(old(X)<~>~kind(X))))&
(![X]:((~wise(X)|~tall(X))<=>(~happy(X)<~>brave(X))))&
((~kind(mary)<~>calm(mary)))&
(?[X]:((~curious(X)<~>quiet(X))))&
(?[X]:((generous(X)|~patient(X))))&
((kind(paul)<~>~rich(paul)))&
(?[X]:((creative(X)&kind(X))))&
(~kind(paul))&
(?[X]:((~kind(X)&happy(X))))&
((calm(fred)|~funny(fred))) | ~humble(susan) | [] | null | 0 |
Everyone who is either not curious or funny is both old and not creative.
Everyone who is old or not curious is both not old and not strong.
Everyone who is not strong or not happy is both not happy and kind.
Everyone who is not kind or generous is calm and vice versa.
If john is both not quiet and tall then someone is tall or humble and vice versa.
Everyone who is curious or quiet is both funny and rich.
Everyone who is not patient is both not old and funny and vice versa.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
Everyone who is quiet is kind.
Someone is brave or strong.
Alice is wise.
Someone is not strong or not rich.
Mary is rich. | Paul is generous. | neutral | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|~curious(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((brave(X)|strong(X))))&
(wise(alice))&
(?[X]:((~strong(X)|~rich(X))))&
(rich(mary)) | generous(paul) | [] | null | 0 |
Everyone who is old is happy or not kind and vice versa.
If someone is not calm or tall then someone is either not humble or not strong and vice versa.
Everyone who is not kind is both wise and not strong.
Everyone who is either old or not curious is either not strong or generous and vice versa.
If someone is either not funny or not creative then someone is either not brave or brave and vice versa.
If someone is either not rich or not wise then paul is either not curious or not brave and vice versa.
If someone is curious or not tall then someone is kind and vice versa.
Everyone who is either not patient or creative is either not patient or not curious and vice versa.
Everyone who is either not patient or quiet is wise or humble and vice versa.
Everyone who is not strong is not old.
Everyone who is either strong or tall is quiet or happy.
Everyone who is either not happy or not strong is both curious and not humble and vice versa.
Everyone who is generous or not brave is either not patient or funny and vice versa.
If fred is both not creative and old then fred is strong or quiet and vice versa.
Everyone who is generous is either not creative or patient.
Everyone who is both not wise and not creative is happy.
Someone is not rich.
Mary is either not strong or not humble.
Someone is not rich or not funny.
Someone is both old and not brave.
Mary is not tall or not kind.
Paul is not quiet.
Someone is not strong.
Someone is either not funny or not old. | Paul is not happy. | neutral | (![X]:(old(X)<=>(happy(X)|~kind(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:(~kind(X)=>(wise(X)&~strong(X))))&
(![X]:((old(X)<~>~curious(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>(?[X]:((~brave(X)<~>brave(X)))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>((~curious(paul)<~>~brave(paul))))&
((?[X]:((curious(X)|~tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((~patient(X)<~>creative(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((~patient(X)<~>quiet(X))<=>(wise(X)|humble(X))))&
(![X]:(~strong(X)=>~old(X)))&
(![X]:((strong(X)<~>tall(X))=>(quiet(X)|happy(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>(curious(X)&~humble(X))))&
(![X]:((generous(X)|~brave(X))<=>(~patient(X)<~>funny(X))))&
(((~creative(fred)&old(fred)))<=>((strong(fred)|quiet(fred))))&
(![X]:(generous(X)=>(~creative(X)<~>patient(X))))&
(![X]:((~wise(X)&~creative(X))=>happy(X)))&
(?[X]:(~rich(X)))&
((~strong(mary)<~>~humble(mary)))&
(?[X]:((~rich(X)|~funny(X))))&
(?[X]:((old(X)&~brave(X))))&
((~tall(mary)|~kind(mary)))&
(~quiet(paul))&
(?[X]:(~strong(X)))&
(?[X]:((~funny(X)<~>~old(X)))) | ~happy(paul) | [] | null | 0 |
If alice is either wise or creative then fred is both not strong and not happy and vice versa.
If alice is not quiet or rich then someone is both calm and not old and vice versa.
Everyone who is both patient and creative is both curious and not patient.
If someone is both tall and patient then someone is either not strong or not old and vice versa.
If someone is both not brave and brave then someone is both quiet and not generous.
Everyone who is not funny or rich is humble or happy.
Everyone who is not old or old is both not brave and calm.
If lucy is not wise then someone is not wise or curious.
Everyone who is either creative or not calm is rich and vice versa.
Everyone who is creative is either not rich or generous.
If lucy is either not quiet or not rich then susan is not happy or not wise.
Everyone who is both wise and not wise is either not generous or rich and vice versa.
If paul is either not curious or not strong then someone is either not strong or not wise and vice versa.
Everyone who is not tall is both strong and not calm.
Everyone who is either not brave or not humble is either patient or not tall.
If someone is curious or strong then someone is not brave and vice versa.
Someone is either not humble or happy.
Alice is either not generous or not old.
Someone is wise.
John is not rich or not tall.
Lucy is both not humble and not wise.
Someone is either not curious or happy.
Fred is not brave or rich. | John is rich. | contradiction | (((wise(alice)<~>creative(alice)))<=>((~strong(fred)&~happy(fred))))&
(((~quiet(alice)|rich(alice)))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((patient(X)&creative(X))=>(curious(X)&~patient(X))))&
((?[X]:((tall(X)&patient(X))))<=>(?[X]:((~strong(X)<~>~old(X)))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:((quiet(X)&~generous(X)))))&
(![X]:((~funny(X)|rich(X))=>(humble(X)|happy(X))))&
(![X]:((~old(X)|old(X))=>(~brave(X)&calm(X))))&
((~wise(lucy))=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((creative(X)<~>~calm(X))<=>rich(X)))&
(![X]:(creative(X)=>(~rich(X)<~>generous(X))))&
(((~quiet(lucy)<~>~rich(lucy)))=>((~happy(susan)|~wise(susan))))&
(![X]:((wise(X)&~wise(X))<=>(~generous(X)<~>rich(X))))&
(((~curious(paul)<~>~strong(paul)))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
(![X]:(~tall(X)=>(strong(X)&~calm(X))))&
(![X]:((~brave(X)<~>~humble(X))=>(patient(X)<~>~tall(X))))&
((?[X]:((curious(X)|strong(X))))<=>(?[X]:(~brave(X))))&
(?[X]:((~humble(X)<~>happy(X))))&
((~generous(alice)<~>~old(alice)))&
(?[X]:(wise(X)))&
((~rich(john)|~tall(john)))&
((~humble(lucy)&~wise(lucy)))&
(?[X]:((~curious(X)<~>happy(X))))&
((~brave(fred)|rich(fred))) | rich(john) | [
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2761734496561953056124985
% SZS output start Proof for 2761734496561953056124985
7. ! [X0] : ((old(X0) | ~old(X0)) => (calm(X0) & ~brave(X0))) [input p6]
14. ! [X0] : (~tall(X0) => (~calm(X0) & strong(X0))) [input p13]
20. ~tall(john) | ~rich(john) [input p19]
24. rich(john) [input hypothesis]
34. ! [X0] : ((calm(X0) & ~brave(X0)) | (~old(X0) & old(X0))) [ennf transformation 7]
39. ! [X0] : ((~calm(X0) & strong(X0)) | tall(X0)) [ennf transformation 14]
106. calm(X0) | old(X0) [cnf transformation 34]
107. calm(X0) | ~old(X0) [cnf transformation 34]
132. ~calm(X0) | tall(X0) [cnf transformation 39]
145. ~tall(john) | ~rich(john) [cnf transformation 20]
151. rich(john) [cnf transformation 24]
230. calm(X0) [subsumption resolution 106,107]
298. tall(X0) [subsumption resolution 132,230]
331. ~rich(john) [subsumption resolution 145,298]
343. $false [subsumption resolution 151,331]
% SZS output end Proof for 2761734496561953056124985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is either not funny or humble and vice versa.
Everyone who is not funny is not old or not kind and vice versa.
If someone is strong then mary is both not rich and not tall.
If someone is not generous or not funny then mary is not quiet or creative and vice versa.
If someone is not old then someone is either rich or old.
Everyone who is either wise or quiet is both not calm and wise and vice versa.
Everyone who is either not funny or not happy is not quiet or not happy.
Everyone who is generous or not patient is not patient or kind.
If someone is either wise or not strong then susan is either not old or not calm and vice versa.
Everyone who is not generous is either not strong or curious and vice versa.
Everyone who is not kind or not calm is calm and vice versa.
Everyone who is both old and not kind is either not generous or not calm and vice versa.
Everyone who is either not kind or quiet is not rich.
Everyone who is humble is either not happy or not kind.
If someone is strong or funny then someone is humble and vice versa.
John is not creative or creative.
Mary is not funny.
Mary is both creative and not strong.
Susan is happy.
Susan is both not brave and not funny.
John is either old or quiet.
Someone is either kind or not curious.
Someone is not wise or not humble. | Susan is quiet. | contradiction | (![X]:(brave(X)<=>(~funny(X)<~>humble(X))))&
(![X]:(~funny(X)<=>(~old(X)|~kind(X))))&
((?[X]:(strong(X)))=>((~rich(mary)&~tall(mary))))&
((?[X]:((~generous(X)|~funny(X))))<=>((~quiet(mary)|creative(mary))))&
((?[X]:(~old(X)))=>(?[X]:((rich(X)<~>old(X)))))&
(![X]:((wise(X)<~>quiet(X))<=>(~calm(X)&wise(X))))&
(![X]:((~funny(X)<~>~happy(X))=>(~quiet(X)|~happy(X))))&
(![X]:((generous(X)|~patient(X))=>(~patient(X)|kind(X))))&
((?[X]:((wise(X)<~>~strong(X))))<=>((~old(susan)<~>~calm(susan))))&
(![X]:(~generous(X)<=>(~strong(X)<~>curious(X))))&
(![X]:((~kind(X)|~calm(X))<=>calm(X)))&
(![X]:((old(X)&~kind(X))<=>(~generous(X)<~>~calm(X))))&
(![X]:((~kind(X)<~>quiet(X))=>~rich(X)))&
(![X]:(humble(X)=>(~happy(X)<~>~kind(X))))&
((?[X]:((strong(X)|funny(X))))<=>(?[X]:(humble(X))))&
((~creative(john)|creative(john)))&
(~funny(mary))&
((creative(mary)&~strong(mary)))&
(happy(susan))&
((~brave(susan)&~funny(susan)))&
((old(john)<~>quiet(john)))&
(?[X]:((kind(X)<~>~curious(X))))&
(?[X]:((~wise(X)|~humble(X)))) | quiet(susan) | [
"p6",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7753530239749764415180148
% SZS output start Proof for 7753530239749764415180148
7. ! [X0] : ((~funny(X0) <~> ~happy(X0)) => (~happy(X0) | ~quiet(X0))) [input p6]
19. happy(susan) [input p18]
20. ~funny(susan) & ~brave(susan) [input p19]
24. quiet(susan) [input hypothesis]
32. ! [X0] : ((~happy(X0) | ~quiet(X0)) | (~funny(X0) <=> ~happy(X0))) [ennf transformation 7]
33. ! [X0] : (~happy(X0) | ~quiet(X0) | (~funny(X0) <=> ~happy(X0))) [flattening 32]
52. ! [X0] : (~happy(X0) | ~quiet(X0) | ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0)))) [nnf transformation 33]
93. ~happy(X0) | ~quiet(X0) | ~happy(X0) | funny(X0) [cnf transformation 52]
129. happy(susan) [cnf transformation 19]
131. ~funny(susan) [cnf transformation 20]
137. quiet(susan) [cnf transformation 24]
140. ~happy(X0) | ~quiet(X0) | funny(X0) [duplicate literal removal 93]
323. ~quiet(susan) | funny(susan) [resolution 140,129]
325. funny(susan) [subsumption resolution 323,137]
326. $false [subsumption resolution 325,131]
% SZS output end Proof for 7753530239749764415180148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is either not brave or humble and vice versa.
Everyone who is not strong is quiet and vice versa.
Everyone who is not strong or old is both brave and not happy and vice versa.
Everyone who is both not patient and not humble is tall and vice versa.
If someone is both not brave and not tall then someone is not tall.
If mary is either not calm or creative then alice is not curious.
Everyone who is calm is not kind.
If paul is not wise or happy then someone is strong.
If someone is not quiet or wise then fred is generous or not generous and vice versa.
Everyone who is both not creative and not old is either not quiet or strong and vice versa.
Everyone who is not wise is not quiet or not curious and vice versa.
Everyone who is calm is both not strong and not kind and vice versa.
Everyone who is patient is not generous and vice versa.
If someone is both not wise and generous then lucy is either patient or not rich and vice versa.
If someone is either patient or not kind then someone is either wise or strong and vice versa.
Everyone who is both not calm and creative is not strong or tall and vice versa.
John is not tall or not rich.
Someone is either tall or not happy.
John is either funny or not humble.
Someone is generous.
Someone is both rich and not quiet.
Alice is either not tall or happy. | Fred is not creative. | contradiction | (![X]:(~humble(X)<=>(~brave(X)<~>humble(X))))&
(![X]:(~strong(X)<=>quiet(X)))&
(![X]:((~strong(X)|old(X))<=>(brave(X)&~happy(X))))&
(![X]:((~patient(X)&~humble(X))<=>tall(X)))&
((?[X]:((~brave(X)&~tall(X))))=>(?[X]:(~tall(X))))&
(((~calm(mary)<~>creative(mary)))=>(~curious(alice)))&
(![X]:(calm(X)=>~kind(X)))&
(((~wise(paul)|happy(paul)))=>(?[X]:(strong(X))))&
((?[X]:((~quiet(X)|wise(X))))<=>((generous(fred)|~generous(fred))))&
(![X]:((~creative(X)&~old(X))<=>(~quiet(X)<~>strong(X))))&
(![X]:(~wise(X)<=>(~quiet(X)|~curious(X))))&
(![X]:(calm(X)<=>(~strong(X)&~kind(X))))&
(![X]:(patient(X)<=>~generous(X)))&
((?[X]:((~wise(X)&generous(X))))<=>((patient(lucy)<~>~rich(lucy))))&
((?[X]:((patient(X)<~>~kind(X))))<=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:((~calm(X)&creative(X))<=>(~strong(X)|tall(X))))&
((~tall(john)|~rich(john)))&
(?[X]:((tall(X)<~>~happy(X))))&
((funny(john)<~>~humble(john)))&
(?[X]:(generous(X)))&
(?[X]:((rich(X)&~quiet(X))))&
((~tall(alice)<~>happy(alice))) | ~creative(fred) | [
"p0",
"p1",
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 922396028061384876868073
% SZS output start Proof for 922396028061384876868073
1. ! [X0] : (~humble(X0) <=> (~brave(X0) <~> humble(X0))) [input p0]
2. ! [X0] : (~strong(X0) <=> quiet(X0)) [input p1]
3. ! [X0] : ((old(X0) | ~strong(X0)) <=> (~happy(X0) & brave(X0))) [input p2]
10. ! [X0] : ((~old(X0) & ~creative(X0)) <=> (~quiet(X0) <~> strong(X0))) [input p9]
23. ~creative(fred) [input hypothesis]
30. ! [X0] : ((~humble(X0) | ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) & (((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | humble(X0))) [nnf transformation 1]
31. ! [X0] : ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))) [nnf transformation 2]
32. ! [X0] : (((old(X0) | ~strong(X0)) | (happy(X0) | ~brave(X0))) & ((~happy(X0) & brave(X0)) | (~old(X0) & strong(X0)))) [nnf transformation 3]
33. ! [X0] : ((old(X0) | ~strong(X0) | happy(X0) | ~brave(X0)) & ((~happy(X0) & brave(X0)) | (~old(X0) & strong(X0)))) [flattening 32]
47. ! [X0] : (((~old(X0) & ~creative(X0)) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) & (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | (old(X0) | creative(X0)))) [nnf transformation 10]
48. ! [X0] : (((~old(X0) & ~creative(X0)) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) & (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | old(X0) | creative(X0))) [flattening 47]
74. humble(X0) | ~brave(X0) | humble(X0) [cnf transformation 30]
77. ~humble(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 30]
79. ~quiet(X0) | ~strong(X0) [cnf transformation 31]
80. brave(X0) | strong(X0) [cnf transformation 33]
81. brave(X0) | ~old(X0) [cnf transformation 33]
99. ~strong(X0) | quiet(X0) | old(X0) | creative(X0) [cnf transformation 48]
141. ~creative(fred) [cnf transformation 23]
142. humble(X0) | ~brave(X0) [duplicate literal removal 74]
143. ~brave(X0) | ~humble(X0) [duplicate literal removal 77]
144. ~brave(X0) [subsumption resolution 142,143]
145. ~old(X0) [subsumption resolution 81,144]
146. strong(X0) [subsumption resolution 80,144]
184. quiet(X0) | old(X0) | creative(X0) [subsumption resolution 99,146]
185. creative(X0) | quiet(X0) [subsumption resolution 184,145]
288. quiet(fred) [resolution 185,141]
290. ~strong(fred) [resolution 288,79]
291. $false [subsumption resolution 290,146]
% SZS output end Proof for 922396028061384876868073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not brave is both not happy and happy and vice versa. If someone is wise or not creative then susan is either creative or brave. Everyone who is not happy or happy is not kind and vice versa. If someone is either kind or humble then mary is both not rich and not wise. Everyone who is not happy or not patient is happy or not calm and vice versa. If alice is either brave or happy then paul is not calm and vice versa. If someone is both kind and patient then someone is not funny or not quiet. If paul is either not kind or not curious then someone is both generous and not funny and vice versa. If someone is either not rich or not patient then lucy is either not humble or not wise. If lucy is rich or not rich then someone is not old or not patient and vice versa. Everyone who is both patient and calm is generous and vice versa. Everyone who is both not generous and not curious is quiet and vice versa. If lucy is not funny then someone is strong or not brave and vice versa. Everyone who is either strong or not strong is either not calm or not tall. If paul is either kind or not brave then someone is not curious and vice versa. Everyone who is both not patient and not tall is generous. Someone is either not strong or old. John is either not happy or curious. Someone is not funny. Someone is both patient and not humble. Fred is rich or not strong. Someone is both not generous and humble. Susan is tall. | Fred is creative. | neutral | (![X]:((rich(X)&~brave(X))<=>(~happy(X)&happy(X))))&
((?[X]:((wise(X)|~creative(X))))=>((creative(susan)<~>brave(susan))))&
(![X]:((~happy(X)|happy(X))<=>~kind(X)))&
((?[X]:((kind(X)<~>humble(X))))=>((~rich(mary)&~wise(mary))))&
(![X]:((~happy(X)|~patient(X))<=>(happy(X)|~calm(X))))&
(((brave(alice)<~>happy(alice)))<=>(~calm(paul)))&
((?[X]:((kind(X)&patient(X))))=>(?[X]:((~funny(X)|~quiet(X)))))&
(((~kind(paul)<~>~curious(paul)))<=>(?[X]:((generous(X)&~funny(X)))))&
((?[X]:((~rich(X)<~>~patient(X))))=>((~humble(lucy)<~>~wise(lucy))))&
(((rich(lucy)|~rich(lucy)))<=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((patient(X)&calm(X))<=>generous(X)))&
(![X]:((~generous(X)&~curious(X))<=>quiet(X)))&
((~funny(lucy))<=>(?[X]:((strong(X)|~brave(X)))))&
(![X]:((strong(X)<~>~strong(X))=>(~calm(X)<~>~tall(X))))&
(((kind(paul)<~>~brave(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((~patient(X)&~tall(X))=>generous(X)))&
(?[X]:((~strong(X)<~>old(X))))&
((~happy(john)<~>curious(john)))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)&~humble(X))))&
((rich(fred)|~strong(fred)))&
(?[X]:((~generous(X)&humble(X))))&
(tall(susan)) | creative(fred) | [] | null | 0 |
Everyone who is curious or patient is quiet or humble.
Everyone who is rich is both not calm and not generous and vice versa.
If john is not funny or tall then susan is both not humble and happy and vice versa.
Everyone who is both strong and creative is both quiet and not happy.
Everyone who is strong is brave.
Everyone who is tall is both not brave and old and vice versa.
Everyone who is either creative or not wise is not tall.
Everyone who is either rich or tall is both not generous and patient and vice versa.
Everyone who is either not tall or not happy is both not tall and not calm and vice versa.
Everyone who is generous is either brave or not generous and vice versa.
Everyone who is humble is brave or patient and vice versa.
If paul is either not happy or curious then someone is either not kind or kind.
Everyone who is both generous and not funny is both not funny and not happy and vice versa.
If paul is curious then someone is both not strong and quiet.
If someone is either not calm or not brave then someone is either not tall or not happy and vice versa.
Everyone who is not kind or old is both not tall and curious.
Someone is both not patient and not rich.
Fred is not old or not funny.
Fred is not rich or kind.
Alice is both wise and humble.
Alice is either quiet or funny.
Susan is not curious or happy.
Alice is either not calm or not old. | Paul is kind. | neutral | (![X]:((curious(X)|patient(X))=>(quiet(X)|humble(X))))&
(![X]:(rich(X)<=>(~calm(X)&~generous(X))))&
(((~funny(john)|tall(john)))<=>((~humble(susan)&happy(susan))))&
(![X]:((strong(X)&creative(X))=>(quiet(X)&~happy(X))))&
(![X]:(strong(X)=>brave(X)))&
(![X]:(tall(X)<=>(~brave(X)&old(X))))&
(![X]:((creative(X)<~>~wise(X))=>~tall(X)))&
(![X]:((rich(X)<~>tall(X))<=>(~generous(X)&patient(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(~tall(X)&~calm(X))))&
(![X]:(generous(X)<=>(brave(X)<~>~generous(X))))&
(![X]:(humble(X)<=>(brave(X)|patient(X))))&
(((~happy(paul)<~>curious(paul)))=>(?[X]:((~kind(X)<~>kind(X)))))&
(![X]:((generous(X)&~funny(X))<=>(~funny(X)&~happy(X))))&
((curious(paul))=>(?[X]:((~strong(X)&quiet(X)))))&
((?[X]:((~calm(X)<~>~brave(X))))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~kind(X)|old(X))=>(~tall(X)&curious(X))))&
(?[X]:((~patient(X)&~rich(X))))&
((~old(fred)|~funny(fred)))&
((~rich(fred)|kind(fred)))&
((wise(alice)&humble(alice)))&
((quiet(alice)<~>funny(alice)))&
((~curious(susan)|happy(susan)))&
((~calm(alice)<~>~old(alice))) | kind(paul) | [] | null | 0 |
Everyone who is not kind is both humble and strong and vice versa.
Everyone who is not curious or strong is wise and vice versa.
Everyone who is both not brave and not patient is brave or humble and vice versa.
If someone is strong or not funny then someone is not happy or not brave and vice versa.
Everyone who is either curious or not funny is either kind or not brave and vice versa.
Everyone who is both patient and not old is both not patient and funny and vice versa.
Everyone who is both not happy and not generous is either not creative or not funny.
If john is not brave or old then fred is rich and vice versa.
Everyone who is strong is either not patient or not strong and vice versa.
Everyone who is not rich is either not calm or not brave.
Everyone who is humble or rich is curious or not quiet.
If someone is both old and not funny then someone is quiet or not strong and vice versa.
If someone is strong or kind then fred is both old and not patient and vice versa.
If someone is kind or rich then someone is quiet.
If someone is not strong or brave then someone is generous or strong.
Lucy is creative.
Paul is rich or not generous.
Someone is calm.
Someone is either not happy or funny.
Someone is not patient or not funny.
Susan is both strong and generous.
Paul is not happy. | Susan is curious. | contradiction | (![X]:(~kind(X)<=>(humble(X)&strong(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:((curious(X)<~>~funny(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((patient(X)&~old(X))<=>(~patient(X)&funny(X))))&
(![X]:((~happy(X)&~generous(X))=>(~creative(X)<~>~funny(X))))&
(((~brave(john)|old(john)))<=>(rich(fred)))&
(![X]:(strong(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:(~rich(X)=>(~calm(X)<~>~brave(X))))&
(![X]:((humble(X)|rich(X))=>(curious(X)|~quiet(X))))&
((?[X]:((old(X)&~funny(X))))<=>(?[X]:((quiet(X)|~strong(X)))))&
((?[X]:((strong(X)|kind(X))))<=>((old(fred)&~patient(fred))))&
((?[X]:((kind(X)|rich(X))))=>(?[X]:(quiet(X))))&
((?[X]:((~strong(X)|brave(X))))=>(?[X]:((generous(X)|strong(X)))))&
(creative(lucy))&
((rich(paul)|~generous(paul)))&
(?[X]:(calm(X)))&
(?[X]:((~happy(X)<~>funny(X))))&
(?[X]:((~patient(X)|~funny(X))))&
((strong(susan)&generous(susan)))&
(~happy(paul)) | curious(susan) | [
"p0",
"p2",
"p4",
"p5",
"p8",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3680120631558987202153041
% SZS output start Proof for 3680120631558987202153041
1. ! [X0] : (~kind(X0) <=> (strong(X0) & humble(X0))) [input p0]
3. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p2]
5. ! [X0] : ((curious(X0) <~> ~funny(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p4]
6. ! [X0] : ((~old(X0) & patient(X0)) <=> (funny(X0) & ~patient(X0))) [input p5]
9. ! [X0] : (strong(X0) <=> (~patient(X0) <~> ~strong(X0))) [input p8]
21. generous(susan) & strong(susan) [input p20]
23. curious(susan) [input hypothesis]
35. ! [X0] : ((~kind(X0) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | kind(X0))) [nnf transformation 1]
36. ! [X0] : ((~kind(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | kind(X0))) [flattening 35]
37. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (patient(X0) | brave(X0)))) [nnf transformation 3]
38. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | patient(X0) | brave(X0))) [flattening 37]
44. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [nnf transformation 5]
45. ! [X0] : (((~old(X0) & patient(X0)) | (~funny(X0) | patient(X0))) & ((funny(X0) & ~patient(X0)) | (old(X0) | ~patient(X0)))) [nnf transformation 6]
46. ! [X0] : (((~old(X0) & patient(X0)) | ~funny(X0) | patient(X0)) & ((funny(X0) & ~patient(X0)) | old(X0) | ~patient(X0))) [flattening 45]
50. ! [X0] : ((strong(X0) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ~strong(X0))) [nnf transformation 9]
77. ~strong(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 36]
78. humble(X0) | brave(X0) | patient(X0) | brave(X0) [cnf transformation 38]
79. ~brave(X0) | ~brave(X0) [cnf transformation 38]
94. funny(X0) | ~curious(X0) | kind(X0) | brave(X0) [cnf transformation 44]
97. patient(X0) | ~funny(X0) | patient(X0) [cnf transformation 46]
104. ~strong(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 50]
107. strong(X0) | ~patient(X0) | strong(X0) [cnf transformation 50]
132. strong(susan) [cnf transformation 21]
135. curious(susan) [cnf transformation 23]
136. ~strong(X0) | ~patient(X0) [duplicate literal removal 104]
137. ~patient(X0) | strong(X0) [duplicate literal removal 107]
139. ~funny(X0) | patient(X0) [duplicate literal removal 97]
140. humble(X0) | brave(X0) | patient(X0) [duplicate literal removal 78]
141. ~brave(X0) [duplicate literal removal 79]
142. patient(X0) | humble(X0) [subsumption resolution 140,141]
157. ~curious(X0) | funny(X0) | kind(X0) [subsumption resolution 94,141]
172. ~patient(X0) [subsumption resolution 136,137]
263. humble(X4) [resolution 142,172]
268. ~kind(susan) | ~humble(susan) [resolution 77,132]
281. funny(susan) | kind(susan) [resolution 157,135]
309. 28 <=> kind(susan) [avatar definition]
313. 29 <=> funny(susan) [avatar definition]
315. funny(susan) <- (29) [avatar component clause 313]
316. 28 | 29 [avatar split clause 281,313,309]
319. ~kind(susan) [subsumption resolution 268,263]
320. ~28 [avatar split clause 319,309]
337. patient(susan) <- (29) [resolution 315,139]
338. $false <- (29) [subsumption resolution 337,172]
339. ~29 [avatar contradiction clause 338]
340. $false [avatar sat refutation 316,320,339]
% SZS output end Proof for 3680120631558987202153041
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not wise is not creative and vice versa. If mary is either strong or humble then john is either not quiet or not patient. If someone is humble then susan is not kind or not calm and vice versa. Everyone who is kind or not rich is both not patient and not happy. Everyone who is strong or not wise is both not humble and not calm. Everyone who is not rich or not funny is rich and vice versa. If someone is old or not generous then someone is creative and vice versa. If someone is quiet or old then someone is both curious and not curious. Everyone who is not generous or calm is both quiet and not generous and vice versa. Everyone who is both not funny and not quiet is both not old and brave. If someone is both not humble and brave then fred is not curious and vice versa. If fred is both not tall and not brave then someone is both old and calm. If mary is both funny and wise then fred is not funny or old. Everyone who is strong is either not happy or old and vice versa. If someone is generous then alice is either not quiet or patient. Alice is not curious. Someone is kind. John is not curious or not humble. Someone is curious. Fred is either not curious or not generous. | Fred is creative. | contradiction | (![X]:((~kind(X)|~wise(X))<=>~creative(X)))&
(((strong(mary)<~>humble(mary)))=>((~quiet(john)<~>~patient(john))))&
((?[X]:(humble(X)))<=>((~kind(susan)|~calm(susan))))&
(![X]:((kind(X)|~rich(X))=>(~patient(X)&~happy(X))))&
(![X]:((strong(X)|~wise(X))=>(~humble(X)&~calm(X))))&
(![X]:((~rich(X)|~funny(X))<=>rich(X)))&
((?[X]:((old(X)|~generous(X))))<=>(?[X]:(creative(X))))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:((curious(X)&~curious(X)))))&
(![X]:((~generous(X)|calm(X))<=>(quiet(X)&~generous(X))))&
(![X]:((~funny(X)&~quiet(X))=>(~old(X)&brave(X))))&
((?[X]:((~humble(X)&brave(X))))<=>(~curious(fred)))&
(((~tall(fred)&~brave(fred)))=>(?[X]:((old(X)&calm(X)))))&
(((funny(mary)&wise(mary)))=>((~funny(fred)|old(fred))))&
(![X]:(strong(X)<=>(~happy(X)<~>old(X))))&
((?[X]:(generous(X)))=>((~quiet(alice)<~>patient(alice))))&
(~curious(alice))&
(?[X]:(kind(X)))&
((~curious(john)|~humble(john)))&
(?[X]:(curious(X)))&
((~curious(fred)<~>~generous(fred))) | creative(fred) | [
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6824949881731296937387908
% SZS output start Proof for 6824949881731296937387908
7. ? [X0] : (~generous(X0) | old(X0)) <=> ? [X0] : creative(X0) [input p6]
8. ? [X0] : (old(X0) | quiet(X0)) => ? [X0] : (~curious(X0) & curious(X0)) [input p7]
9. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (~generous(X0) & quiet(X0))) [input p8]
21. creative(fred) [input hypothesis]
22. ? [X0] : (~generous(X0) | old(X0)) <=> ? [X1] : creative(X1) [rectify 7]
23. ? [X0] : (old(X0) | quiet(X0)) => ? [X1] : (~curious(X1) & curious(X1)) [rectify 8]
28. ? [X1] : (~curious(X1) & curious(X1)) | ! [X0] : (~old(X0) & ~quiet(X0)) [ennf transformation 23]
44. (? [X0] : (~generous(X0) | old(X0)) | ! [X1] : ~creative(X1)) & (? [X1] : creative(X1) | ! [X0] : (generous(X0) & ~old(X0))) [nnf transformation 22]
45. (? [X0] : (~generous(X0) | old(X0)) | ! [X1] : ~creative(X1)) & (? [X2] : creative(X2) | ! [X3] : (generous(X3) & ~old(X3))) [rectify 44]
46. ? [X0] : (~generous(X0) | old(X0)) => (~generous(sK1) | old(sK1)) [choice axiom]
47. ? [X2] : creative(X2) => creative(sK2) [choice axiom]
48. ((~generous(sK1) | old(sK1)) | ! [X1] : ~creative(X1)) & (creative(sK2) | ! [X3] : (generous(X3) & ~old(X3))) [skolemisation 45,47,46]
49. ? [X0] : (~curious(X0) & curious(X0)) | ! [X1] : (~old(X1) & ~quiet(X1)) [rectify 28]
50. ? [X0] : (~curious(X0) & curious(X0)) => (~curious(sK3) & curious(sK3)) [choice axiom]
51. (~curious(sK3) & curious(sK3)) | ! [X1] : (~old(X1) & ~quiet(X1)) [skolemisation 49,50]
52. ! [X0] : (((calm(X0) | ~generous(X0)) | (generous(X0) | ~quiet(X0))) & ((~generous(X0) & quiet(X0)) | (~calm(X0) & generous(X0)))) [nnf transformation 9]
53. ! [X0] : ((calm(X0) | ~generous(X0) | generous(X0) | ~quiet(X0)) & ((~generous(X0) & quiet(X0)) | (~calm(X0) & generous(X0)))) [flattening 52]
88. ~generous(sK1) | old(sK1) | ~creative(X1) [cnf transformation 48]
89. curious(sK3) | ~quiet(X1) [cnf transformation 51]
90. curious(sK3) | ~old(X1) [cnf transformation 51]
91. ~curious(sK3) | ~quiet(X1) [cnf transformation 51]
92. ~curious(sK3) | ~old(X1) [cnf transformation 51]
93. generous(X0) | quiet(X0) [cnf transformation 53]
116. creative(fred) [cnf transformation 21]
158. 9 <=> ! [X1] : ~creative(X1) [avatar definition]
159. ~creative(X1) <- (9) [avatar component clause 158]
161. 10 <=> old(sK1) [avatar definition]
163. old(sK1) <- (10) [avatar component clause 161]
165. 11 <=> generous(sK1) [avatar definition]
167. ~generous(sK1) <- (~11) [avatar component clause 165]
168. 9 | 10 | ~11 [avatar split clause 88,165,161,158]
178. 14 <=> ! [X3] : ~old(X3) [avatar definition]
179. ~old(X3) <- (14) [avatar component clause 178]
182. 15 <=> curious(sK3) [avatar definition]
185. 14 | ~15 [avatar split clause 92,182,178]
187. 16 <=> ! [X1] : ~quiet(X1) [avatar definition]
188. ~quiet(X1) <- (16) [avatar component clause 187]
189. 16 | ~15 [avatar split clause 91,182,187]
190. 14 | 15 [avatar split clause 90,182,178]
191. 16 | 15 [avatar split clause 89,182,187]
257. $false <- (10, 14) [subsumption resolution 163,179]
258. ~10 | ~14 [avatar contradiction clause 257]
259. $false <- (9) [resolution 159,116]
260. ~9 [avatar contradiction clause 259]
268. quiet(sK1) <- (~11) [resolution 93,167]
270. $false <- (~11, 16) [subsumption resolution 268,188]
271. 11 | ~16 [avatar contradiction clause 270]
274. $false [avatar sat refutation 168,185,189,190,191,258,260,271]
% SZS output end Proof for 6824949881731296937387908
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both humble and not kind is not creative and vice versa.
Everyone who is both humble and not calm is both happy and not brave.
Everyone who is both not creative and generous is both old and not creative and vice versa.
If someone is not kind then paul is either quiet or curious.
Everyone who is not strong or calm is both humble and not wise and vice versa.
If alice is not rich or strong then someone is not happy or patient and vice versa.
Everyone who is both not generous and old is either generous or strong and vice versa.
Everyone who is not wise is both kind and not kind.
Everyone who is happy or not curious is humble.
Everyone who is either not happy or brave is both not strong and not rich.
Everyone who is not calm or not quiet is either funny or wise.
Everyone who is not strong is either rich or strong and vice versa.
Everyone who is either rich or strong is either creative or not brave and vice versa.
If alice is either wise or tall then paul is not curious.
If someone is both not creative and not wise then susan is patient.
If someone is calm then someone is curious or not old.
Alice is patient.
John is either not patient or not kind.
Paul is both tall and not quiet.
Alice is either not kind or humble.
John is happy or humble.
Someone is either not patient or generous.
Lucy is not funny. | Alice is happy. | entailment | (![X]:((humble(X)&~kind(X))<=>~creative(X)))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&~brave(X))))&
(![X]:((~creative(X)&generous(X))<=>(old(X)&~creative(X))))&
((?[X]:(~kind(X)))=>((quiet(paul)<~>curious(paul))))&
(![X]:((~strong(X)|calm(X))<=>(humble(X)&~wise(X))))&
(((~rich(alice)|strong(alice)))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)<~>strong(X))))&
(![X]:(~wise(X)=>(kind(X)&~kind(X))))&
(![X]:((happy(X)|~curious(X))=>humble(X)))&
(![X]:((~happy(X)<~>brave(X))=>(~strong(X)&~rich(X))))&
(![X]:((~calm(X)|~quiet(X))=>(funny(X)<~>wise(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>strong(X))))&
(![X]:((rich(X)<~>strong(X))<=>(creative(X)<~>~brave(X))))&
(((wise(alice)<~>tall(alice)))=>(~curious(paul)))&
((?[X]:((~creative(X)&~wise(X))))=>(patient(susan)))&
((?[X]:(calm(X)))=>(?[X]:((curious(X)|~old(X)))))&
(patient(alice))&
((~patient(john)<~>~kind(john)))&
((tall(paul)&~quiet(paul)))&
((~kind(alice)<~>humble(alice)))&
((happy(john)|humble(john)))&
(?[X]:((~patient(X)<~>generous(X))))&
(~funny(lucy)) | happy(alice) | [
"p0",
"p1",
"p4",
"p7",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4853406307503854072770454
% SZS output start Proof for 4853406307503854072770454
1. ! [X0] : ((~kind(X0) & humble(X0)) <=> ~creative(X0)) [input p0]
2. ! [X0] : ((~calm(X0) & humble(X0)) => (~brave(X0) & happy(X0))) [input p1]
5. ! [X0] : ((calm(X0) | ~strong(X0)) <=> (~wise(X0) & humble(X0))) [input p4]
8. ! [X0] : (~wise(X0) => (~kind(X0) & kind(X0))) [input p7]
10. ! [X0] : ((~happy(X0) <~> brave(X0)) => (~rich(X0) & ~strong(X0))) [input p9]
12. ! [X0] : (~strong(X0) <=> (rich(X0) <~> strong(X0))) [input p11]
13. ! [X0] : ((rich(X0) <~> strong(X0)) <=> (creative(X0) <~> ~brave(X0))) [input p12]
24. ~happy(alice) [input hypothesis]
26. ! [X0] : ((~brave(X0) & happy(X0)) | (calm(X0) | ~humble(X0))) [ennf transformation 2]
27. ! [X0] : ((~brave(X0) & happy(X0)) | calm(X0) | ~humble(X0)) [flattening 26]
29. ! [X0] : ((~kind(X0) & kind(X0)) | wise(X0)) [ennf transformation 8]
31. ! [X0] : ((~rich(X0) & ~strong(X0)) | (~happy(X0) <=> brave(X0))) [ennf transformation 10]
36. ! [X0] : (((~kind(X0) & humble(X0)) | creative(X0)) & (~creative(X0) | (kind(X0) | ~humble(X0)))) [nnf transformation 1]
37. ! [X0] : (((~kind(X0) & humble(X0)) | creative(X0)) & (~creative(X0) | kind(X0) | ~humble(X0))) [flattening 36]
41. ! [X0] : (((calm(X0) | ~strong(X0)) | (wise(X0) | ~humble(X0))) & ((~wise(X0) & humble(X0)) | (~calm(X0) & strong(X0)))) [nnf transformation 5]
42. ! [X0] : ((calm(X0) | ~strong(X0) | wise(X0) | ~humble(X0)) & ((~wise(X0) & humble(X0)) | (~calm(X0) & strong(X0)))) [flattening 41]
50. ! [X0] : ((~rich(X0) & ~strong(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) [nnf transformation 31]
52. ! [X0] : ((~strong(X0) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) & (((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | strong(X0))) [nnf transformation 12]
53. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0)))) & (((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [nnf transformation 13]
64. creative(X0) | humble(X0) [cnf transformation 37]
67. ~brave(X0) | calm(X0) | ~humble(X0) [cnf transformation 27]
76. ~wise(X0) | strong(X0) [cnf transformation 42]
77. ~wise(X0) | ~calm(X0) [cnf transformation 42]
89. kind(X0) | wise(X0) [cnf transformation 29]
90. ~kind(X0) | wise(X0) [cnf transformation 29]
93. ~strong(X0) | brave(X0) | happy(X0) [cnf transformation 50]
101. strong(X0) | rich(X0) | strong(X0) [cnf transformation 52]
104. ~strong(X0) | rich(X0) | ~strong(X0) [cnf transformation 52]
111. ~strong(X0) | ~rich(X0) | ~brave(X0) | ~creative(X0) [cnf transformation 53]
128. ~happy(alice) [cnf transformation 24]
129. strong(X0) | rich(X0) [duplicate literal removal 101]
130. ~strong(X0) | rich(X0) [duplicate literal removal 104]
154. 6 <=> strong(alice) [avatar definition]
155. ~strong(alice) <- (~6) [avatar component clause 154]
156. strong(alice) <- (6) [avatar component clause 154]
173. wise(X0) [subsumption resolution 89,90]
176. rich(X0) [subsumption resolution 129,130]
178. ~strong(X0) | ~brave(X0) | ~creative(X0) [subsumption resolution 111,176]
188. 11 <=> ! [X1] : ~calm(X1) [avatar definition]
189. ~calm(X1) <- (11) [avatar component clause 188]
215. 17 <=> humble(alice) [avatar definition]
233. strong(X0) [resolution 76,173]
234. ~calm(X0) [resolution 77,173]
235. 11 [avatar split clause 234,188]
255. brave(alice) | happy(alice) <- (6) [resolution 93,156]
258. brave(alice) <- (6) [subsumption resolution 255,128]
262. 22 <=> creative(alice) [avatar definition]
263. ~creative(alice) <- (~22) [avatar component clause 262]
273. calm(alice) | ~humble(alice) <- (6) [resolution 258,67]
286. ~brave(alice) | ~creative(alice) <- (6) [resolution 178,156]
289. ~creative(alice) <- (6) [subsumption resolution 286,258]
290. ~22 | ~6 [avatar split clause 289,154,262]
291. humble(alice) <- (~22) [resolution 263,64]
294. 17 | 22 [avatar split clause 291,262,215]
295. ~humble(alice) <- (6, 11) [subsumption resolution 273,189]
296. ~17 | ~6 | ~11 [avatar split clause 295,188,154,215]
297. $false <- (~6) [subsumption resolution 155,233]
298. 6 [avatar contradiction clause 297]
299. $false [avatar sat refutation 235,290,294,296,298]
% SZS output end Proof for 4853406307503854072770454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is kind or not wise then alice is not curious and vice versa.
If someone is both not kind and creative then someone is either not wise or not creative.
Everyone who is generous is either wise or not old.
Everyone who is funny is both not tall and patient.
If someone is brave then someone is both creative and not brave and vice versa.
If lucy is not strong or patient then mary is not humble and vice versa.
Everyone who is not old or rich is either not curious or old and vice versa.
Everyone who is old or not funny is strong or patient.
If someone is either brave or not rich then mary is not humble or strong.
If mary is not curious or calm then paul is not wise and vice versa.
If someone is both creative and wise then mary is either wise or curious and vice versa.
Everyone who is not happy or not rich is kind and vice versa.
If fred is both happy and not patient then someone is wise.
Everyone who is generous is not generous or not happy and vice versa.
Everyone who is either not happy or quiet is not tall or brave and vice versa.
Everyone who is generous or not curious is both not curious and not calm and vice versa.
Lucy is either wise or tall.
Alice is patient or not humble.
Someone is not happy.
Paul is either strong or old.
John is either not funny or not tall.
Alice is both funny and patient.
Someone is both not funny and not wise. | Paul is curious. | contradiction | (((kind(lucy)|~wise(lucy)))<=>(~curious(alice)))&
((?[X]:((~kind(X)&creative(X))))=>(?[X]:((~wise(X)<~>~creative(X)))))&
(![X]:(generous(X)=>(wise(X)<~>~old(X))))&
(![X]:(funny(X)=>(~tall(X)&patient(X))))&
((?[X]:(brave(X)))<=>(?[X]:((creative(X)&~brave(X)))))&
(((~strong(lucy)|patient(lucy)))<=>(~humble(mary)))&
(![X]:((~old(X)|rich(X))<=>(~curious(X)<~>old(X))))&
(![X]:((old(X)|~funny(X))=>(strong(X)|patient(X))))&
((?[X]:((brave(X)<~>~rich(X))))=>((~humble(mary)|strong(mary))))&
(((~curious(mary)|calm(mary)))<=>(~wise(paul)))&
((?[X]:((creative(X)&wise(X))))<=>((wise(mary)<~>curious(mary))))&
(![X]:((~happy(X)|~rich(X))<=>kind(X)))&
(((happy(fred)&~patient(fred)))=>(?[X]:(wise(X))))&
(![X]:(generous(X)<=>(~generous(X)|~happy(X))))&
(![X]:((~happy(X)<~>quiet(X))<=>(~tall(X)|brave(X))))&
(![X]:((generous(X)|~curious(X))<=>(~curious(X)&~calm(X))))&
((wise(lucy)<~>tall(lucy)))&
((patient(alice)|~humble(alice)))&
(?[X]:(~happy(X)))&
((strong(paul)<~>old(paul)))&
((~funny(john)<~>~tall(john)))&
((funny(alice)&patient(alice)))&
(?[X]:((~funny(X)&~wise(X)))) | curious(paul) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8319095731713822881698292
% SZS output start Proof for 8319095731713822881698292
14. ! [X0] : (generous(X0) <=> (~happy(X0) | ~generous(X0))) [input p13]
16. ! [X0] : ((~curious(X0) | generous(X0)) <=> (~calm(X0) & ~curious(X0))) [input p15]
24. curious(paul) [input hypothesis]
63. ! [X0] : ((generous(X0) | (happy(X0) & generous(X0))) & ((~happy(X0) | ~generous(X0)) | ~generous(X0))) [nnf transformation 14]
64. ! [X0] : ((generous(X0) | (happy(X0) & generous(X0))) & (~happy(X0) | ~generous(X0) | ~generous(X0))) [flattening 63]
67. ! [X0] : (((~curious(X0) | generous(X0)) | (calm(X0) | curious(X0))) & ((~calm(X0) & ~curious(X0)) | (curious(X0) & ~generous(X0)))) [nnf transformation 16]
68. ! [X0] : ((~curious(X0) | generous(X0) | calm(X0) | curious(X0)) & ((~calm(X0) & ~curious(X0)) | (curious(X0) & ~generous(X0)))) [flattening 67]
115. generous(X0) | generous(X0) [cnf transformation 64]
123. ~curious(X0) | ~generous(X0) [cnf transformation 68]
140. curious(paul) [cnf transformation 24]
142. generous(X0) [duplicate literal removal 115]
276. ~curious(X0) [subsumption resolution 123,142]
312. $false [subsumption resolution 140,276]
% SZS output end Proof for 8319095731713822881698292
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not happy is either humble or quiet. If someone is both not wise and not creative then john is not rich and vice versa. If someone is kind then paul is either old or not curious. If john is not funny then lucy is not brave or not humble and vice versa. Everyone who is both wise and quiet is not wise and vice versa. Everyone who is curious or strong is old and vice versa. If someone is both strong and calm then someone is both happy and not creative. Everyone who is humble or calm is both brave and not humble. Everyone who is calm or wise is either not calm or not quiet and vice versa. Everyone who is not generous is rich or not creative. If john is not humble or not creative then someone is either not curious or brave. Everyone who is both not curious and generous is either not strong or not creative and vice versa. If alice is not calm then lucy is not brave or not quiet. Everyone who is not funny is not creative. Someone is both not humble and tall. Lucy is creative or not funny. Someone is either brave or not brave. Fred is tall. Alice is not strong or not quiet. | Lucy is strong. | contradiction | (![X]:((wise(X)<~>~happy(X))=>(humble(X)<~>quiet(X))))&
((?[X]:((~wise(X)&~creative(X))))<=>(~rich(john)))&
((?[X]:(kind(X)))=>((old(paul)<~>~curious(paul))))&
((~funny(john))<=>((~brave(lucy)|~humble(lucy))))&
(![X]:((wise(X)&quiet(X))<=>~wise(X)))&
(![X]:((curious(X)|strong(X))<=>old(X)))&
((?[X]:((strong(X)&calm(X))))=>(?[X]:((happy(X)&~creative(X)))))&
(![X]:((humble(X)|calm(X))=>(brave(X)&~humble(X))))&
(![X]:((calm(X)|wise(X))<=>(~calm(X)<~>~quiet(X))))&
(![X]:(~generous(X)=>(rich(X)|~creative(X))))&
(((~humble(john)|~creative(john)))=>(?[X]:((~curious(X)<~>brave(X)))))&
(![X]:((~curious(X)&generous(X))<=>(~strong(X)<~>~creative(X))))&
((~calm(alice))=>((~brave(lucy)|~quiet(lucy))))&
(![X]:(~funny(X)=>~creative(X)))&
(?[X]:((~humble(X)&tall(X))))&
((creative(lucy)|~funny(lucy)))&
(?[X]:((brave(X)<~>~brave(X))))&
(tall(fred))&
((~strong(alice)|~quiet(alice))) | strong(lucy) | [
"p0",
"p4",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6533251961203542553438797
% SZS output start Proof for 6533251961203542553438797
1. ! [X0] : ((wise(X0) <~> ~happy(X0)) => (humble(X0) <~> quiet(X0))) [input p0]
5. ! [X0] : ((quiet(X0) & wise(X0)) <=> ~wise(X0)) [input p4]
7. ? [X0] : (calm(X0) & strong(X0)) => ? [X0] : (~creative(X0) & happy(X0)) [input p6]
8. ! [X0] : ((calm(X0) | humble(X0)) => (~humble(X0) & brave(X0))) [input p7]
9. ! [X0] : ((wise(X0) | calm(X0)) <=> (~calm(X0) <~> ~quiet(X0))) [input p8]
20. strong(lucy) [input hypothesis]
21. ? [X0] : (calm(X0) & strong(X0)) => ? [X1] : (~creative(X1) & happy(X1)) [rectify 7]
25. ! [X0] : ((humble(X0) <~> quiet(X0)) | (wise(X0) <=> ~happy(X0))) [ennf transformation 1]
26. ? [X1] : (~creative(X1) & happy(X1)) | ! [X0] : (~calm(X0) | ~strong(X0)) [ennf transformation 21]
27. ! [X0] : ((~humble(X0) & brave(X0)) | (~calm(X0) & ~humble(X0))) [ennf transformation 8]
34. ! [X0] : (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0)))) [nnf transformation 25]
41. ! [X0] : (((quiet(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | (~quiet(X0) | ~wise(X0)))) [nnf transformation 5]
42. ! [X0] : (((quiet(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | ~quiet(X0) | ~wise(X0))) [flattening 41]
43. ? [X0] : (~creative(X0) & happy(X0)) | ! [X1] : (~calm(X1) | ~strong(X1)) [rectify 26]
44. ? [X0] : (~creative(X0) & happy(X0)) => (~creative(sK1) & happy(sK1)) [choice axiom]
45. (~creative(sK1) & happy(sK1)) | ! [X1] : (~calm(X1) | ~strong(X1)) [skolemisation 43,44]
46. ! [X0] : (((wise(X0) | calm(X0)) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0)))) & (((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | (~wise(X0) & ~calm(X0)))) [nnf transformation 9]
47. ! [X0] : ((wise(X0) | calm(X0) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0)))) & (((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | (~wise(X0) & ~calm(X0)))) [flattening 46]
58. ~happy(X0) | humble(X0) | quiet(X0) | ~wise(X0) [cnf transformation 34]
68. ~wise(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 42]
69. wise(X0) | wise(X0) [cnf transformation 42]
71. happy(sK1) | ~calm(X1) | ~strong(X1) [cnf transformation 45]
75. ~humble(X0) | ~humble(X0) [cnf transformation 27]
80. quiet(X0) | calm(X0) | ~wise(X0) [cnf transformation 47]
101. strong(lucy) [cnf transformation 20]
104. ~humble(X0) [duplicate literal removal 75]
105. ~wise(X0) | ~quiet(X0) [duplicate literal removal 68]
106. wise(X0) [duplicate literal removal 69]
140. ~quiet(X0) [subsumption resolution 105,106]
142. 8 <=> ! [X1] : (~calm(X1) | ~strong(X1)) [avatar definition]
143. ~calm(X1) | ~strong(X1) <- (8) [avatar component clause 142]
150. 10 <=> happy(sK1) [avatar definition]
152. happy(sK1) <- (10) [avatar component clause 150]
153. 8 | 10 [avatar split clause 71,150,142]
154. calm(X0) | ~wise(X0) [subsumption resolution 80,140]
155. calm(X0) [subsumption resolution 154,106]
183. ~strong(X1) <- (8) [subsumption resolution 143,155]
186. $false <- (8) [resolution 183,101]
187. ~8 [avatar contradiction clause 186]
228. humble(sK1) | quiet(sK1) | ~wise(sK1) <- (10) [resolution 58,152]
229. quiet(sK1) | ~wise(sK1) <- (10) [subsumption resolution 228,104]
230. ~wise(sK1) <- (10) [subsumption resolution 229,140]
231. $false <- (10) [subsumption resolution 230,106]
232. ~10 [avatar contradiction clause 231]
233. $false [avatar sat refutation 153,187,232]
% SZS output end Proof for 6533251961203542553438797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not patient is not happy and vice versa. Everyone who is not curious or not calm is not brave. Everyone who is either humble or not patient is both not rich and old. If someone is both not quiet and rich then someone is humble and vice versa. Everyone who is both not kind and not brave is rich. If someone is either brave or patient then someone is not curious. Everyone who is both funny and not kind is both tall and creative and vice versa. Everyone who is patient is brave or wise. Everyone who is kind is either kind or calm. Everyone who is not happy or funny is both not creative and not tall. If mary is both tall and calm then paul is either old or not wise. If john is generous then someone is both not creative and old and vice versa. If someone is both tall and not quiet then someone is brave or calm. Everyone who is both not tall and happy is both brave and rich and vice versa. Everyone who is both not brave and patient is not tall and vice versa. Everyone who is either brave or not humble is quiet or calm. Fred is both not quiet and kind. Someone is either not strong or not generous. Susan is brave or quiet. Alice is not old. Someone is both not calm and not funny. Someone is humble. John is kind or not old. Mary is not happy or happy. | Fred is old. | entailment | (![X]:((~quiet(X)|~patient(X))<=>~happy(X)))&
(![X]:((~curious(X)|~calm(X))=>~brave(X)))&
(![X]:((humble(X)<~>~patient(X))=>(~rich(X)&old(X))))&
((?[X]:((~quiet(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((~kind(X)&~brave(X))=>rich(X)))&
((?[X]:((brave(X)<~>patient(X))))=>(?[X]:(~curious(X))))&
(![X]:((funny(X)&~kind(X))<=>(tall(X)&creative(X))))&
(![X]:(patient(X)=>(brave(X)|wise(X))))&
(![X]:(kind(X)=>(kind(X)<~>calm(X))))&
(![X]:((~happy(X)|funny(X))=>(~creative(X)&~tall(X))))&
(((tall(mary)&calm(mary)))=>((old(paul)<~>~wise(paul))))&
((generous(john))<=>(?[X]:((~creative(X)&old(X)))))&
((?[X]:((tall(X)&~quiet(X))))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~tall(X)&happy(X))<=>(brave(X)&rich(X))))&
(![X]:((~brave(X)&patient(X))<=>~tall(X)))&
(![X]:((brave(X)<~>~humble(X))=>(quiet(X)|calm(X))))&
((~quiet(fred)&kind(fred)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((brave(susan)|quiet(susan)))&
(~old(alice))&
(?[X]:((~calm(X)&~funny(X))))&
(?[X]:(humble(X)))&
((kind(john)|~old(john)))&
((~happy(mary)|happy(mary))) | old(fred) | [
"p0",
"p1",
"p2",
"p8",
"p9",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6085963587691184217935972
% SZS output start Proof for 6085963587691184217935972
1. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> ~happy(X0)) [input p0]
2. ! [X0] : ((~calm(X0) | ~curious(X0)) => ~brave(X0)) [input p1]
3. ! [X0] : ((humble(X0) <~> ~patient(X0)) => (old(X0) & ~rich(X0))) [input p2]
9. ! [X0] : (kind(X0) => (kind(X0) <~> calm(X0))) [input p8]
10. ! [X0] : ((funny(X0) | ~happy(X0)) => (~tall(X0) & ~creative(X0))) [input p9]
15. ! [X0] : ((patient(X0) & ~brave(X0)) <=> ~tall(X0)) [input p14]
16. ! [X0] : ((brave(X0) <~> ~humble(X0)) => (calm(X0) | quiet(X0))) [input p15]
17. kind(fred) & ~quiet(fred) [input p16]
25. ~old(fred) [input hypothesis]
29. ! [X0] : (~brave(X0) | (calm(X0) & curious(X0))) [ennf transformation 2]
30. ! [X0] : ((old(X0) & ~rich(X0)) | (humble(X0) <=> ~patient(X0))) [ennf transformation 3]
36. ! [X0] : ((kind(X0) <~> calm(X0)) | ~kind(X0)) [ennf transformation 9]
37. ! [X0] : ((~tall(X0) & ~creative(X0)) | (~funny(X0) & happy(X0))) [ennf transformation 10]
41. ! [X0] : ((calm(X0) | quiet(X0)) | (brave(X0) <=> ~humble(X0))) [ennf transformation 16]
42. ! [X0] : (calm(X0) | quiet(X0) | (brave(X0) <=> ~humble(X0))) [flattening 41]
43. ! [X0] : (((~patient(X0) | ~quiet(X0)) | happy(X0)) & (~happy(X0) | (patient(X0) & quiet(X0)))) [nnf transformation 1]
44. ! [X0] : ((~patient(X0) | ~quiet(X0) | happy(X0)) & (~happy(X0) | (patient(X0) & quiet(X0)))) [flattening 43]
45. ! [X0] : ((old(X0) & ~rich(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) [nnf transformation 30]
57. ! [X0] : (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | ~kind(X0)) [nnf transformation 36]
68. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) | brave(X0)))) [nnf transformation 15]
69. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | ~patient(X0) | brave(X0))) [flattening 68]
70. ! [X0] : (calm(X0) | quiet(X0) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0)))) [nnf transformation 42]
79. ~happy(X0) | patient(X0) [cnf transformation 44]
82. ~brave(X0) | calm(X0) [cnf transformation 29]
85. ~humble(X0) | ~patient(X0) | old(X0) [cnf transformation 45]
99. ~calm(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 57]
102. ~tall(X0) | happy(X0) [cnf transformation 37]
116. tall(X0) | patient(X0) [cnf transformation 69]
118. calm(X0) | quiet(X0) | brave(X0) | humble(X0) [cnf transformation 70]
119. ~quiet(fred) [cnf transformation 17]
120. kind(fred) [cnf transformation 17]
130. ~old(fred) [cnf transformation 25]
131. ~kind(X0) | ~calm(X0) [duplicate literal removal 99]
210. humble(X0) | quiet(X0) | calm(X0) [subsumption resolution 118,82]
244. patient(X1) | happy(X1) [resolution 116,102]
245. patient(X1) [subsumption resolution 244,79]
248. ~calm(fred) [resolution 131,120]
351. quiet(X0) | calm(X0) | ~patient(X0) | old(X0) [resolution 210,85]
353. old(X0) | calm(X0) | quiet(X0) [subsumption resolution 351,245]
380. calm(fred) | quiet(fred) [resolution 353,130]
400. quiet(fred) [subsumption resolution 380,248]
401. $false [subsumption resolution 400,119]
% SZS output end Proof for 6085963587691184217935972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or tall is not generous and vice versa. Everyone who is not quiet or not happy is either not happy or tall. If someone is creative then someone is not humble or brave and vice versa. If john is creative then john is either not humble or not brave and vice versa. If alice is either not patient or not happy then someone is patient and vice versa. If lucy is either not strong or old then someone is not calm or not quiet. Everyone who is not patient is not tall or not calm and vice versa. Everyone who is both patient and kind is either not rich or brave and vice versa. Everyone who is both wise and not old is both quiet and not quiet. If alice is not funny or strong then paul is generous. Everyone who is either curious or not curious is not calm or curious and vice versa. Everyone who is not creative or wise is brave or not calm and vice versa. If lucy is either not curious or strong then someone is not strong and vice versa. If someone is humble or not old then someone is either not brave or not happy. Everyone who is kind or funny is either not rich or quiet. If alice is either happy or tall then fred is creative or strong and vice versa. Someone is both not brave and funny. Lucy is both not rich and funny. Someone is either tall or brave. Someone is not rich. Someone is both not old and calm. Alice is both calm and not old. | Alice is happy. | neutral | (![X]:((~patient(X)|tall(X))<=>~generous(X)))&
(![X]:((~quiet(X)|~happy(X))=>(~happy(X)<~>tall(X))))&
((?[X]:(creative(X)))<=>(?[X]:((~humble(X)|brave(X)))))&
((creative(john))<=>((~humble(john)<~>~brave(john))))&
(((~patient(alice)<~>~happy(alice)))<=>(?[X]:(patient(X))))&
(((~strong(lucy)<~>old(lucy)))=>(?[X]:((~calm(X)|~quiet(X)))))&
(![X]:(~patient(X)<=>(~tall(X)|~calm(X))))&
(![X]:((patient(X)&kind(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((wise(X)&~old(X))=>(quiet(X)&~quiet(X))))&
(((~funny(alice)|strong(alice)))=>(generous(paul)))&
(![X]:((curious(X)<~>~curious(X))<=>(~calm(X)|curious(X))))&
(![X]:((~creative(X)|wise(X))<=>(brave(X)|~calm(X))))&
(((~curious(lucy)<~>strong(lucy)))<=>(?[X]:(~strong(X))))&
((?[X]:((humble(X)|~old(X))))=>(?[X]:((~brave(X)<~>~happy(X)))))&
(![X]:((kind(X)|funny(X))=>(~rich(X)<~>quiet(X))))&
(((happy(alice)<~>tall(alice)))<=>((creative(fred)|strong(fred))))&
(?[X]:((~brave(X)&funny(X))))&
((~rich(lucy)&funny(lucy)))&
(?[X]:((tall(X)<~>brave(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~old(X)&calm(X))))&
((calm(alice)&~old(alice))) | happy(alice) | [] | null | 0 |
If fred is calm then someone is not curious or not happy.
Everyone who is not curious is calm.
If someone is either brave or kind then someone is patient or not kind and vice versa.
Everyone who is generous or not funny is both funny and kind and vice versa.
Everyone who is calm is either tall or not humble and vice versa.
If susan is both not quiet and not patient then someone is generous or humble and vice versa.
Everyone who is old or kind is either brave or not patient and vice versa.
Everyone who is both not calm and wise is wise or not patient and vice versa.
If someone is not brave then alice is not funny and vice versa.
Everyone who is both curious and not generous is not old and vice versa.
Everyone who is tall or not patient is both rich and not strong.
Everyone who is humble or kind is not funny or rich and vice versa.
Everyone who is not happy or quiet is both creative and not funny and vice versa.
Everyone who is not old is either brave or not generous.
Everyone who is either quiet or not curious is funny or kind.
Someone is happy.
Mary is not quiet.
Susan is either strong or not strong. | Mary is not generous. | entailment | ((calm(fred))=>(?[X]:((~curious(X)|~happy(X)))))&
(![X]:(~curious(X)=>calm(X)))&
((?[X]:((brave(X)<~>kind(X))))<=>(?[X]:((patient(X)|~kind(X)))))&
(![X]:((generous(X)|~funny(X))<=>(funny(X)&kind(X))))&
(![X]:(calm(X)<=>(tall(X)<~>~humble(X))))&
(((~quiet(susan)&~patient(susan)))<=>(?[X]:((generous(X)|humble(X)))))&
(![X]:((old(X)|kind(X))<=>(brave(X)<~>~patient(X))))&
(![X]:((~calm(X)&wise(X))<=>(wise(X)|~patient(X))))&
((?[X]:(~brave(X)))<=>(~funny(alice)))&
(![X]:((curious(X)&~generous(X))<=>~old(X)))&
(![X]:((tall(X)|~patient(X))=>(rich(X)&~strong(X))))&
(![X]:((humble(X)|kind(X))<=>(~funny(X)|rich(X))))&
(![X]:((~happy(X)|quiet(X))<=>(creative(X)&~funny(X))))&
(![X]:(~old(X)=>(brave(X)<~>~generous(X))))&
(![X]:((quiet(X)<~>~curious(X))=>(funny(X)|kind(X))))&
(?[X]:(happy(X)))&
(~quiet(mary))&
((strong(susan)<~>~strong(susan))) | ~generous(mary) | [
"p3",
"p5",
"p6",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4245156411905473874382223
% SZS output start Proof for 4245156411905473874382223
4. ! [X0] : ((~funny(X0) | generous(X0)) <=> (kind(X0) & funny(X0))) [input p3]
6. (~patient(susan) & ~quiet(susan)) <=> ? [X0] : (humble(X0) | generous(X0)) [input p5]
7. ! [X0] : ((kind(X0) | old(X0)) <=> (brave(X0) <~> ~patient(X0))) [input p6]
9. ? [X0] : ~brave(X0) <=> ~funny(alice) [input p8]
10. ! [X0] : ((~generous(X0) & curious(X0)) <=> ~old(X0)) [input p9]
14. ! [X0] : (~old(X0) => (brave(X0) <~> ~generous(X0))) [input p13]
19. generous(mary) [input hypothesis]
24. ! [X0] : ((brave(X0) <~> ~generous(X0)) | old(X0)) [ennf transformation 14]
34. ! [X0] : (((~funny(X0) | generous(X0)) | (~kind(X0) | ~funny(X0))) & ((kind(X0) & funny(X0)) | (funny(X0) & ~generous(X0)))) [nnf transformation 4]
35. ! [X0] : ((~funny(X0) | generous(X0) | ~kind(X0) | ~funny(X0)) & ((kind(X0) & funny(X0)) | (funny(X0) & ~generous(X0)))) [flattening 34]
37. ((~patient(susan) & ~quiet(susan)) | ! [X0] : (~humble(X0) & ~generous(X0))) & (? [X0] : (humble(X0) | generous(X0)) | (patient(susan) | quiet(susan))) [nnf transformation 6]
38. ((~patient(susan) & ~quiet(susan)) | ! [X0] : (~humble(X0) & ~generous(X0))) & (? [X0] : (humble(X0) | generous(X0)) | patient(susan) | quiet(susan)) [flattening 37]
39. ((~patient(susan) & ~quiet(susan)) | ! [X0] : (~humble(X0) & ~generous(X0))) & (? [X1] : (humble(X1) | generous(X1)) | patient(susan) | quiet(susan)) [rectify 38]
40. ? [X1] : (humble(X1) | generous(X1)) => (humble(sK3) | generous(sK3)) [choice axiom]
41. ((~patient(susan) & ~quiet(susan)) | ! [X0] : (~humble(X0) & ~generous(X0))) & ((humble(sK3) | generous(sK3)) | patient(susan) | quiet(susan)) [skolemisation 39,40]
42. ! [X0] : (((kind(X0) | old(X0)) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | (~kind(X0) & ~old(X0)))) [nnf transformation 7]
43. ! [X0] : ((kind(X0) | old(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | (~kind(X0) & ~old(X0)))) [flattening 42]
46. (? [X0] : ~brave(X0) | funny(alice)) & (~funny(alice) | ! [X0] : brave(X0)) [nnf transformation 9]
47. (? [X0] : ~brave(X0) | funny(alice)) & (~funny(alice) | ! [X1] : brave(X1)) [rectify 46]
48. ? [X0] : ~brave(X0) => ~brave(sK4) [choice axiom]
49. (~brave(sK4) | funny(alice)) & (~funny(alice) | ! [X1] : brave(X1)) [skolemisation 47,48]
50. ! [X0] : (((~generous(X0) & curious(X0)) | old(X0)) & (~old(X0) | (generous(X0) | ~curious(X0)))) [nnf transformation 10]
51. ! [X0] : (((~generous(X0) & curious(X0)) | old(X0)) & (~old(X0) | generous(X0) | ~curious(X0))) [flattening 50]
56. ! [X0] : (((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | old(X0)) [nnf transformation 24]
70. funny(X0) | funny(X0) [cnf transformation 35]
81. ~patient(susan) | ~generous(X0) [cnf transformation 41]
85. ~old(X0) | ~brave(X0) | patient(X0) [cnf transformation 43]
94. ~funny(alice) | brave(X1) [cnf transformation 49]
98. ~generous(X0) | old(X0) [cnf transformation 51]
113. generous(X0) | ~brave(X0) | old(X0) [cnf transformation 56]
120. generous(mary) [cnf transformation 19]
121. funny(X0) [duplicate literal removal 70]
174. 13 <=> patient(susan) [avatar definition]
176. ~patient(susan) <- (~13) [avatar component clause 174]
179. 14 <=> ! [X0] : ~generous(X0) [avatar definition]
180. ~generous(X0) <- (14) [avatar component clause 179]
181. 14 | ~13 [avatar split clause 81,174,179]
197. brave(X1) [subsumption resolution 94,121]
202. generous(X0) | old(X0) [subsumption resolution 113,197]
203. old(X0) [subsumption resolution 202,98]
206. $false <- (14) [resolution 180,120]
207. ~14 [avatar contradiction clause 206]
227. ~brave(X1) | patient(X1) [resolution 85,203]
229. patient(X1) [subsumption resolution 227,197]
232. $false <- (~13) [resolution 229,176]
234. 13 [avatar contradiction clause 232]
235. $false [avatar sat refutation 181,207,234]
% SZS output end Proof for 4245156411905473874382223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble 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.
If someone is kind then fred is both not happy and calm.
Everyone who is not calm is both not rich and creative.
If susan is strong or tall then someone is tall.
Everyone who is not curious or kind is either not kind or not wise.
Everyone who is either rich or not quiet is either kind or not old and vice versa.
If lucy is either wise or not quiet then lucy is not funny and vice versa.
If someone is both patient and rich then someone is both not quiet and not funny.
If someone is not humble or happy then someone is either not generous or not creative.
Everyone who is either not brave or humble is both curious and not rich.
Everyone who is curious or not funny is patient or not quiet.
Everyone who is either not humble or wise is both humble and not humble and vice versa.
Someone is calm.
Someone is both humble and not old.
Someone is humble or strong.
Paul is not patient or curious.
Someone is either not humble or not happy.
Mary is not rich. | Fred is not curious. | entailment | ((?[X]:(~humble(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)))&
((?[X]:(kind(X)))=>((~happy(fred)&calm(fred))))&
(![X]:(~calm(X)=>(~rich(X)&creative(X))))&
(((strong(susan)|tall(susan)))=>(?[X]:(tall(X))))&
(![X]:((~curious(X)|kind(X))=>(~kind(X)<~>~wise(X))))&
(![X]:((rich(X)<~>~quiet(X))<=>(kind(X)<~>~old(X))))&
(((wise(lucy)<~>~quiet(lucy)))<=>(~funny(lucy)))&
((?[X]:((patient(X)&rich(X))))=>(?[X]:((~quiet(X)&~funny(X)))))&
((?[X]:((~humble(X)|happy(X))))=>(?[X]:((~generous(X)<~>~creative(X)))))&
(![X]:((~brave(X)<~>humble(X))=>(curious(X)&~rich(X))))&
(![X]:((curious(X)|~funny(X))=>(patient(X)|~quiet(X))))&
(![X]:((~humble(X)<~>wise(X))<=>(humble(X)&~humble(X))))&
(?[X]:(calm(X)))&
(?[X]:((humble(X)&~old(X))))&
(?[X]:((humble(X)|strong(X))))&
((~patient(paul)|curious(paul)))&
(?[X]:((~humble(X)<~>~happy(X))))&
(~rich(mary)) | ~curious(fred) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"p12",
"p13",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1917964229633658750527361
% SZS output start Proof for 1917964229633658750527361
2. ! [X0] : (~curious(X0) <=> (patient(X0) | calm(X0))) [input p1]
3. ! [X0] : ((~brave(X0) & old(X0)) <=> (creative(X0) <~> ~old(X0))) [input p2]
4. ! [X0] : ((~generous(X0) & creative(X0)) <=> old(X0)) [input p3]
5. ! [X0] : ((old(X0) <~> ~happy(X0)) <=> ~creative(X0)) [input p4]
6. ? [X0] : kind(X0) => (calm(fred) & ~happy(fred)) [input p5]
7. ! [X0] : (~calm(X0) => (creative(X0) & ~rich(X0))) [input p6]
9. ! [X0] : ((kind(X0) | ~curious(X0)) => (~kind(X0) <~> ~wise(X0))) [input p8]
10. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> (kind(X0) <~> ~old(X0))) [input p9]
13. ? [X0] : (happy(X0) | ~humble(X0)) => ? [X0] : (~generous(X0) <~> ~creative(X0)) [input p12]
14. ! [X0] : ((~brave(X0) <~> humble(X0)) => (~rich(X0) & curious(X0))) [input p13]
15. ! [X0] : ((~funny(X0) | curious(X0)) => (~quiet(X0) | patient(X0))) [input p14]
16. ! [X0] : ((~humble(X0) <~> wise(X0)) <=> (~humble(X0) & humble(X0))) [input p15]
18. ? [X0] : (~old(X0) & humble(X0)) [input p17]
23. curious(fred) [input hypothesis]
26. ? [X0] : (happy(X0) | ~humble(X0)) => ? [X1] : (~generous(X1) <~> ~creative(X1)) [rectify 13]
28. (calm(fred) & ~happy(fred)) | ! [X0] : ~kind(X0) [ennf transformation 6]
29. ! [X0] : ((creative(X0) & ~rich(X0)) | calm(X0)) [ennf transformation 7]
31. ! [X0] : ((~kind(X0) <~> ~wise(X0)) | (~kind(X0) & curious(X0))) [ennf transformation 9]
33. ? [X1] : (~generous(X1) <~> ~creative(X1)) | ! [X0] : (~happy(X0) & humble(X0)) [ennf transformation 26]
34. ! [X0] : ((~rich(X0) & curious(X0)) | (~brave(X0) <=> humble(X0))) [ennf transformation 14]
35. ! [X0] : ((~quiet(X0) | patient(X0)) | (funny(X0) & ~curious(X0))) [ennf transformation 15]
36. ! [X0] : (~quiet(X0) | patient(X0) | (funny(X0) & ~curious(X0))) [flattening 35]
41. ! [X0] : ((~curious(X0) | (~patient(X0) & ~calm(X0))) & ((patient(X0) | calm(X0)) | curious(X0))) [nnf transformation 2]
42. ! [X0] : ((~curious(X0) | (~patient(X0) & ~calm(X0))) & (patient(X0) | calm(X0) | curious(X0))) [flattening 41]
43. ! [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 3]
44. ! [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 43]
45. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | (generous(X0) | ~creative(X0)))) [nnf transformation 4]
46. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | generous(X0) | ~creative(X0))) [flattening 45]
47. ! [X0] : ((((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | creative(X0)) & (~creative(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0))))) [nnf transformation 5]
50. ! [X0] : (((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (~kind(X0) & curious(X0))) [nnf transformation 31]
51. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 10]
56. ? [X1] : ((creative(X1) | generous(X1)) & (~creative(X1) | ~generous(X1))) | ! [X0] : (~happy(X0) & humble(X0)) [nnf transformation 33]
57. ? [X0] : ((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | ! [X1] : (~happy(X1) & humble(X1)) [rectify 56]
58. ? [X0] : ((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) => ((creative(sK3) | generous(sK3)) & (~creative(sK3) | ~generous(sK3))) [choice axiom]
59. ((creative(sK3) | generous(sK3)) & (~creative(sK3) | ~generous(sK3))) | ! [X1] : (~happy(X1) & humble(X1)) [skolemisation 57,58]
60. ! [X0] : ((~rich(X0) & curious(X0)) | ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) [nnf transformation 34]
61. ! [X0] : ((((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))))) [nnf transformation 16]
62. ! [X0] : ((((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))))) [flattening 61]
65. ? [X0] : (~old(X0) & humble(X0)) => (~old(sK5) & humble(sK5)) [choice axiom]
66. ~old(sK5) & humble(sK5) [skolemisation 18,65]
75. ~calm(X0) | ~curious(X0) [cnf transformation 42]
76. ~patient(X0) | ~curious(X0) [cnf transformation 42]
80. old(X0) | creative(X0) | old(X0) [cnf transformation 44]
81. ~creative(X0) | ~old(X0) | ~brave(X0) [cnf transformation 44]
83. old(X0) | generous(X0) | ~creative(X0) [cnf transformation 46]
84. creative(X0) | ~old(X0) [cnf transformation 46]
87. ~creative(X0) | old(X0) | happy(X0) [cnf transformation 47]
91. calm(fred) | ~kind(X0) [cnf transformation 28]
92. ~rich(X0) | calm(X0) [cnf transformation 29]
98. wise(X0) | kind(X0) | curious(X0) [cnf transformation 50]
101. ~old(X0) | kind(X0) | rich(X0) | quiet(X0) [cnf transformation 51]
115. ~creative(sK3) | ~generous(sK3) | ~happy(X1) [cnf transformation 59]
118. brave(X0) | humble(X0) | curious(X0) [cnf transformation 60]
122. ~quiet(X0) | patient(X0) | ~curious(X0) [cnf transformation 36]
127. ~humble(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 62]
132. ~old(sK5) [cnf transformation 66]
138. curious(fred) [cnf transformation 23]
140. ~wise(X0) | ~humble(X0) [duplicate literal removal 127]
145. creative(X0) | old(X0) [duplicate literal removal 80]
160. creative(X0) [subsumption resolution 84,145]
161. generous(X0) | old(X0) [subsumption resolution 83,160]
162. happy(X0) | old(X0) [subsumption resolution 87,160]
165. 4 <=> ! [X0] : ~kind(X0) [avatar definition]
166. ~kind(X0) <- (4) [avatar component clause 165]
168. 5 <=> calm(fred) [avatar definition]
170. calm(fred) <- (5) [avatar component clause 168]
171. 4 | 5 [avatar split clause 91,168,165]
220. ~generous(sK3) | ~happy(X1) [subsumption resolution 115,160]
222. 16 <=> ! [X1] : ~happy(X1) [avatar definition]
223. ~happy(X1) <- (16) [avatar component clause 222]
225. 17 <=> generous(sK3) [avatar definition]
227. ~generous(sK3) <- (~17) [avatar component clause 225]
228. 16 | ~17 [avatar split clause 220,225,222]
231. ~quiet(X0) | ~curious(X0) [subsumption resolution 122,76]
273. ~brave(X2) | ~old(X2) [resolution 81,160]
276. kind(X1) | curious(X1) | ~humble(X1) [resolution 98,140]
279. humble(X0) | curious(X0) | ~old(X0) [resolution 118,273]
294. 24 <=> quiet(sK3) [avatar definition]
296. quiet(sK3) <- (24) [avatar component clause 294]
298. 25 <=> rich(sK3) [avatar definition]
300. rich(sK3) <- (25) [avatar component clause 298]
315. old(X0) <- (16) [resolution 223,162]
320. ~curious(fred) <- (5) [resolution 170,75]
321. $false <- (5) [subsumption resolution 320,138]
322. ~5 [avatar contradiction clause 321]
323. old(sK3) <- (~17) [resolution 227,161]
327. ~humble(X1) | curious(X1) <- (4) [subsumption resolution 276,166]
335. $false <- (16) [resolution 315,132]
337. ~16 [avatar contradiction clause 335]
339. ~old(X0) | curious(X0) <- (4) [subsumption resolution 279,327]
342. kind(sK3) | rich(sK3) | quiet(sK3) <- (~17) [resolution 323,101]
374. rich(sK3) | quiet(sK3) <- (4, ~17) [subsumption resolution 342,166]
375. 24 | 25 | ~4 | 17 [avatar split clause 374,225,165,298,294]
400. ~curious(sK3) <- (24) [resolution 296,231]
422. curious(sK3) <- (4, ~17) [resolution 339,323]
423. $false <- (4, ~17, 24) [subsumption resolution 422,400]
424. ~4 | 17 | ~24 [avatar contradiction clause 423]
429. calm(sK3) <- (25) [resolution 300,92]
432. ~curious(sK3) <- (25) [resolution 429,75]
433. $false <- (4, ~17, 25) [subsumption resolution 432,422]
434. ~4 | 17 | ~25 [avatar contradiction clause 433]
435. $false [avatar sat refutation 171,228,322,337,375,424,434]
% SZS output end Proof for 1917964229633658750527361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave or not rich is both humble and old and vice versa.
If someone is generous then alice is both brave and not wise and vice versa.
Everyone who is both not generous and brave is not brave and vice versa.
If john is old then john is both happy and patient and vice versa.
If someone is either not brave or not creative then someone is both not quiet and not kind and vice versa.
If someone is either not funny or not happy then someone is both strong and not happy and vice versa.
Everyone who is not curious is not brave.
Everyone who is strong or old is both rich and not quiet and vice versa.
Everyone who is both funny and not humble is either patient or not rich.
If john is not brave or creative then someone is strong or not tall and vice versa.
Everyone who is either not generous or not patient is not wise.
If paul is either curious or tall then someone is both not quiet and strong.
Everyone who is both not creative and not happy is not wise.
If someone is either humble or patient then paul is strong and vice versa.
If someone is calm or strong then alice is both not generous and funny.
Everyone who is not quiet or not tall is kind.
Someone is either not kind or not curious.
Paul is creative or funny.
Someone is not old or tall.
Someone is both not kind and not humble.
Someone is creative or brave.
Someone is rich. | Paul is kind. | neutral | (![X]:((~brave(X)|~rich(X))<=>(humble(X)&old(X))))&
((?[X]:(generous(X)))<=>((brave(alice)&~wise(alice))))&
(![X]:((~generous(X)&brave(X))<=>~brave(X)))&
((old(john))<=>((happy(john)&patient(john))))&
((?[X]:((~brave(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)&~kind(X)))))&
((?[X]:((~funny(X)<~>~happy(X))))<=>(?[X]:((strong(X)&~happy(X)))))&
(![X]:(~curious(X)=>~brave(X)))&
(![X]:((strong(X)|old(X))<=>(rich(X)&~quiet(X))))&
(![X]:((funny(X)&~humble(X))=>(patient(X)<~>~rich(X))))&
(((~brave(john)|creative(john)))<=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((~generous(X)<~>~patient(X))=>~wise(X)))&
(((curious(paul)<~>tall(paul)))=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:((~creative(X)&~happy(X))=>~wise(X)))&
((?[X]:((humble(X)<~>patient(X))))<=>(strong(paul)))&
((?[X]:((calm(X)|strong(X))))=>((~generous(alice)&funny(alice))))&
(![X]:((~quiet(X)|~tall(X))=>kind(X)))&
(?[X]:((~kind(X)<~>~curious(X))))&
((creative(paul)|funny(paul)))&
(?[X]:((~old(X)|tall(X))))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((creative(X)|brave(X))))&
(?[X]:(rich(X))) | kind(paul) | [] | null | 0 |
If john is happy or curious then someone is either not tall or curious and vice versa.
Everyone who is both not tall and brave is either not strong or generous and vice versa.
Everyone who is both creative and funny is both not curious and generous and vice versa.
If john is either strong or not happy then susan is either calm or strong.
Everyone who is both not curious and wise is both not tall and calm.
Everyone who is wise or patient is both patient and funny.
Everyone who is rich is not happy.
Everyone who is humble is not generous and vice versa.
Everyone who is either calm or old is not creative and vice versa.
Everyone who is either not brave or not rich is either not funny or creative and vice versa.
Everyone who is both patient and old is both kind and not curious and vice versa.
Everyone who is both not old and not humble is both not brave and creative and vice versa.
Everyone who is both not creative and generous is not brave or not humble and vice versa.
Everyone who is brave is either patient or not calm and vice versa.
Everyone who is not rich is patient or curious.
If john is not patient or humble then fred is either not funny or old and vice versa.
Someone is not curious.
Susan is either not generous or not brave.
Someone is both not generous and not kind.
Someone is either strong or not tall.
Paul is both not strong and not kind.
Paul is tall.
Someone is both strong and humble.
Someone is not rich. | Paul is not calm. | entailment | (((happy(john)|curious(john)))<=>(?[X]:((~tall(X)<~>curious(X)))))&
(![X]:((~tall(X)&brave(X))<=>(~strong(X)<~>generous(X))))&
(![X]:((creative(X)&funny(X))<=>(~curious(X)&generous(X))))&
(((strong(john)<~>~happy(john)))=>((calm(susan)<~>strong(susan))))&
(![X]:((~curious(X)&wise(X))=>(~tall(X)&calm(X))))&
(![X]:((wise(X)|patient(X))=>(patient(X)&funny(X))))&
(![X]:(rich(X)=>~happy(X)))&
(![X]:(humble(X)<=>~generous(X)))&
(![X]:((calm(X)<~>old(X))<=>~creative(X)))&
(![X]:((~brave(X)<~>~rich(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((patient(X)&old(X))<=>(kind(X)&~curious(X))))&
(![X]:((~old(X)&~humble(X))<=>(~brave(X)&creative(X))))&
(![X]:((~creative(X)&generous(X))<=>(~brave(X)|~humble(X))))&
(![X]:(brave(X)<=>(patient(X)<~>~calm(X))))&
(![X]:(~rich(X)=>(patient(X)|curious(X))))&
(((~patient(john)|humble(john)))<=>((~funny(fred)<~>old(fred))))&
(?[X]:(~curious(X)))&
((~generous(susan)<~>~brave(susan)))&
(?[X]:((~generous(X)&~kind(X))))&
(?[X]:((strong(X)<~>~tall(X))))&
((~strong(paul)&~kind(paul)))&
(tall(paul))&
(?[X]:((strong(X)&humble(X))))&
(?[X]:(~rich(X))) | ~calm(paul) | [
"p1",
"p7",
"p8",
"p11",
"p12",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3781749306498326205590348
% SZS output start Proof for 3781749306498326205590348
2. ! [X0] : ((brave(X0) & ~tall(X0)) <=> (~strong(X0) <~> generous(X0))) [input p1]
8. ! [X0] : (humble(X0) <=> ~generous(X0)) [input p7]
9. ! [X0] : ((calm(X0) <~> old(X0)) <=> ~creative(X0)) [input p8]
12. ! [X0] : ((~humble(X0) & ~old(X0)) <=> (creative(X0) & ~brave(X0))) [input p11]
13. ! [X0] : ((generous(X0) & ~creative(X0)) <=> (~humble(X0) | ~brave(X0))) [input p12]
21. ~kind(paul) & ~strong(paul) [input p20]
22. tall(paul) [input p21]
25. calm(paul) [input hypothesis]
38. ! [X0] : (((brave(X0) & ~tall(X0)) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | (~brave(X0) | tall(X0)))) [nnf transformation 2]
39. ! [X0] : (((brave(X0) & ~tall(X0)) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ~brave(X0) | tall(X0))) [flattening 38]
43. ! [X0] : ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))) [nnf transformation 8]
44. ! [X0] : ((((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | creative(X0)) & (~creative(X0) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0))))) [nnf transformation 9]
48. ! [X0] : (((~humble(X0) & ~old(X0)) | (~creative(X0) | brave(X0))) & ((creative(X0) & ~brave(X0)) | (humble(X0) | old(X0)))) [nnf transformation 12]
49. ! [X0] : (((~humble(X0) & ~old(X0)) | ~creative(X0) | brave(X0)) & ((creative(X0) & ~brave(X0)) | humble(X0) | old(X0))) [flattening 48]
50. ! [X0] : (((generous(X0) & ~creative(X0)) | (humble(X0) & brave(X0))) & ((~humble(X0) | ~brave(X0)) | (~generous(X0) | creative(X0)))) [nnf transformation 13]
51. ! [X0] : (((generous(X0) & ~creative(X0)) | (humble(X0) & brave(X0))) & (~humble(X0) | ~brave(X0) | ~generous(X0) | creative(X0))) [flattening 50]
75. ~tall(X0) | generous(X0) | strong(X0) [cnf transformation 39]
90. ~humble(X0) | ~generous(X0) [cnf transformation 43]
95. ~old(X0) | ~calm(X0) | creative(X0) [cnf transformation 44]
109. old(X0) | humble(X0) | creative(X0) [cnf transformation 49]
114. ~creative(X0) | humble(X0) [cnf transformation 51]
135. ~strong(paul) [cnf transformation 21]
137. tall(paul) [cnf transformation 22]
141. calm(paul) [cnf transformation 25]
231. generous(paul) | strong(paul) [resolution 75,137]
232. generous(paul) [subsumption resolution 231,135]
341. humble(X2) | creative(X2) | ~calm(X2) | creative(X2) [resolution 109,95]
343. humble(X2) | creative(X2) | ~calm(X2) [duplicate literal removal 341]
346. ~calm(X2) | humble(X2) [subsumption resolution 343,114]
364. humble(paul) [resolution 346,141]
366. ~generous(paul) [resolution 364,90]
367. $false [subsumption resolution 366,232]
% SZS output end Proof for 3781749306498326205590348
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and old is both generous and not funny.
If mary is either not happy or not curious then alice is not patient and vice versa.
Everyone who is both rich and not kind is both not creative and not generous and vice versa.
If someone is both brave and kind then susan is both tall and not strong.
Everyone who is both not humble and not kind is both curious and rich and vice versa.
Everyone who is either not rich or not happy is either not patient or not curious.
Everyone who is either not humble or old is rich or humble.
If alice is both not generous and patient then someone is both not patient and happy.
If someone is either kind or rich then paul is not strong or not brave.
Everyone who is not rich is both not happy and happy.
If mary is not generous or creative then john is either not calm or not quiet and vice versa.
If someone is creative or quiet then alice is either not curious or rich.
Everyone who is both not tall and not funny is not strong or funny and vice versa.
Everyone who is not kind is both not patient and funny.
If susan is not humble or not generous then someone is both not curious and happy.
Someone is either kind or not rich.
Someone is not calm or quiet.
Mary is not tall or humble.
Paul is both tall and not patient.
Fred is both kind and patient.
Someone is funny or tall. | John is calm. | contradiction | (![X]:((~curious(X)&old(X))=>(generous(X)&~funny(X))))&
(((~happy(mary)<~>~curious(mary)))<=>(~patient(alice)))&
(![X]:((rich(X)&~kind(X))<=>(~creative(X)&~generous(X))))&
((?[X]:((brave(X)&kind(X))))=>((tall(susan)&~strong(susan))))&
(![X]:((~humble(X)&~kind(X))<=>(curious(X)&rich(X))))&
(![X]:((~rich(X)<~>~happy(X))=>(~patient(X)<~>~curious(X))))&
(![X]:((~humble(X)<~>old(X))=>(rich(X)|humble(X))))&
(((~generous(alice)&patient(alice)))=>(?[X]:((~patient(X)&happy(X)))))&
((?[X]:((kind(X)<~>rich(X))))=>((~strong(paul)|~brave(paul))))&
(![X]:(~rich(X)=>(~happy(X)&happy(X))))&
(((~generous(mary)|creative(mary)))<=>((~calm(john)<~>~quiet(john))))&
((?[X]:((creative(X)|quiet(X))))=>((~curious(alice)<~>rich(alice))))&
(![X]:((~tall(X)&~funny(X))<=>(~strong(X)|funny(X))))&
(![X]:(~kind(X)=>(~patient(X)&funny(X))))&
(((~humble(susan)|~generous(susan)))=>(?[X]:((~curious(X)&happy(X)))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((~calm(X)|quiet(X))))&
((~tall(mary)|humble(mary)))&
((tall(paul)&~patient(paul)))&
((kind(fred)&patient(fred)))&
(?[X]:((funny(X)|tall(X)))) | calm(john) | [
"p2",
"p4",
"p9",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2445974326016643057447565
% SZS output start Proof for 2445974326016643057447565
3. ! [X0] : ((~kind(X0) & rich(X0)) <=> (~generous(X0) & ~creative(X0))) [input p2]
5. ! [X0] : ((~kind(X0) & ~humble(X0)) <=> (rich(X0) & curious(X0))) [input p4]
10. ! [X0] : (~rich(X0) => (happy(X0) & ~happy(X0))) [input p9]
11. (creative(mary) | ~generous(mary)) <=> (~calm(john) <~> ~quiet(john)) [input p10]
12. ? [X0] : (quiet(X0) | creative(X0)) => (~curious(alice) <~> rich(alice)) [input p11]
13. ! [X0] : ((~funny(X0) & ~tall(X0)) <=> (funny(X0) | ~strong(X0))) [input p12]
14. ! [X0] : (~kind(X0) => (funny(X0) & ~patient(X0))) [input p13]
22. calm(john) [input hypothesis]
32. ! [X0] : ((happy(X0) & ~happy(X0)) | rich(X0)) [ennf transformation 10]
33. (~curious(alice) <~> rich(alice)) | ! [X0] : (~quiet(X0) & ~creative(X0)) [ennf transformation 12]
34. ! [X0] : ((funny(X0) & ~patient(X0)) | kind(X0)) [ennf transformation 14]
37. ! [X0] : (((~kind(X0) & rich(X0)) | (generous(X0) | creative(X0))) & ((~generous(X0) & ~creative(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 3]
38. ! [X0] : (((~kind(X0) & rich(X0)) | generous(X0) | creative(X0)) & ((~generous(X0) & ~creative(X0)) | kind(X0) | ~rich(X0))) [flattening 37]
39. ! [X0] : (((~kind(X0) & ~humble(X0)) | (~rich(X0) | ~curious(X0))) & ((rich(X0) & curious(X0)) | (kind(X0) | humble(X0)))) [nnf transformation 5]
40. ! [X0] : (((~kind(X0) & ~humble(X0)) | ~rich(X0) | ~curious(X0)) & ((rich(X0) & curious(X0)) | kind(X0) | humble(X0))) [flattening 39]
45. ((creative(mary) | ~generous(mary)) | ((~calm(john) | quiet(john)) & (~quiet(john) | calm(john)))) & (((quiet(john) | calm(john)) & (~quiet(john) | ~calm(john))) | (~creative(mary) & generous(mary))) [nnf transformation 11]
46. (creative(mary) | ~generous(mary) | ((~calm(john) | quiet(john)) & (~quiet(john) | calm(john)))) & (((quiet(john) | calm(john)) & (~quiet(john) | ~calm(john))) | (~creative(mary) & generous(mary))) [flattening 45]
47. ((~rich(alice) | curious(alice)) & (rich(alice) | ~curious(alice))) | ! [X0] : (~quiet(X0) & ~creative(X0)) [nnf transformation 33]
48. ! [X0] : (((~funny(X0) & ~tall(X0)) | (~funny(X0) & strong(X0))) & ((funny(X0) | ~strong(X0)) | (funny(X0) | tall(X0)))) [nnf transformation 13]
49. ! [X0] : (((~funny(X0) & ~tall(X0)) | (~funny(X0) & strong(X0))) & (funny(X0) | ~strong(X0) | funny(X0) | tall(X0))) [flattening 48]
68. ~kind(X0) | generous(X0) | creative(X0) [cnf transformation 38]
72. ~kind(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 40]
81. ~happy(X0) | rich(X0) [cnf transformation 32]
82. rich(X0) | happy(X0) [cnf transformation 32]
88. creative(mary) | ~generous(mary) | ~calm(john) | quiet(john) [cnf transformation 46]
91. ~rich(alice) | curious(alice) | ~creative(X0) [cnf transformation 47]
92. ~rich(alice) | curious(alice) | ~quiet(X0) [cnf transformation 47]
97. ~funny(X0) | ~funny(X0) [cnf transformation 49]
99. funny(X0) | kind(X0) [cnf transformation 34]
113. calm(john) [cnf transformation 22]
115. ~funny(X0) [duplicate literal removal 97]
147. rich(X0) [subsumption resolution 81,82]
149. 7 <=> quiet(john) [avatar definition]
151. quiet(john) <- (7) [avatar component clause 149]
153. 8 <=> calm(john) [avatar definition]
157. 9 <=> generous(mary) [avatar definition]
159. ~generous(mary) <- (~9) [avatar component clause 157]
161. 10 <=> creative(mary) [avatar definition]
163. creative(mary) <- (10) [avatar component clause 161]
164. 7 | ~8 | ~9 | 10 [avatar split clause 88,161,157,153,149]
170. curious(alice) | ~quiet(X0) [subsumption resolution 92,147]
172. 11 <=> ! [X0] : ~quiet(X0) [avatar definition]
173. ~quiet(X0) <- (11) [avatar component clause 172]
175. 12 <=> curious(alice) [avatar definition]
177. curious(alice) <- (12) [avatar component clause 175]
178. 11 | 12 [avatar split clause 170,175,172]
179. curious(alice) | ~creative(X0) [subsumption resolution 91,147]
181. 13 <=> ! [X0] : ~creative(X0) [avatar definition]
182. ~creative(X0) <- (13) [avatar component clause 181]
183. 13 | 12 [avatar split clause 179,175,181]
185. kind(X0) [subsumption resolution 99,115]
225. 8 [avatar split clause 113,153]
233. creative(X0) | generous(X0) [resolution 68,185]
237. ~rich(X0) | ~curious(X0) [resolution 72,185]
238. ~curious(X0) [subsumption resolution 237,147]
239. $false <- (12) [resolution 238,177]
240. ~12 [avatar contradiction clause 239]
241. generous(X0) <- (13) [resolution 182,233]
244. $false <- (~9, 13) [resolution 241,159]
245. 9 | ~13 [avatar contradiction clause 244]
246. $false <- (7, 11) [subsumption resolution 151,173]
247. ~7 | ~11 [avatar contradiction clause 246]
248. $false <- (10, 13) [subsumption resolution 163,182]
249. ~10 | ~13 [avatar contradiction clause 248]
250. $false [avatar sat refutation 164,178,183,225,240,245,247,249]
% SZS output end Proof for 2445974326016643057447565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is not kind or not tall. If someone is humble or not happy then john is both not strong and tall. If someone is not strong or brave then someone is happy or rich. If john is quiet or not brave then someone is either tall or not generous. Everyone who is happy or not generous is both calm and not old. Everyone who is either not curious or old is not kind. If someone is either funny or not humble then alice is both not old and rich and vice versa. If someone is both rich and old then someone is not funny and vice versa. Everyone who is either quiet or tall is both not rich and not strong and vice versa. If alice is not tall then paul is calm or not creative and vice versa. If alice is both not curious and not old then someone is not rich or calm and vice versa. If susan is curious or funny then someone is not brave or patient. If paul is strong then john is both happy and kind. Everyone who is kind or not rich is not curious or not wise. Everyone who is either old or not tall is either not kind or generous and vice versa. Everyone who is not funny or wise is humble or not happy and vice versa. Lucy is not creative or not generous. John is either rich or old. Someone is both old and generous. John is kind or calm. Someone is not rich. Someone is both funny and not happy. Paul is kind or not humble. Someone is either patient or kind. | Paul is creative. | neutral | (![X]:(~humble(X)=>(~kind(X)|~tall(X))))&
((?[X]:((humble(X)|~happy(X))))=>((~strong(john)&tall(john))))&
((?[X]:((~strong(X)|brave(X))))=>(?[X]:((happy(X)|rich(X)))))&
(((quiet(john)|~brave(john)))=>(?[X]:((tall(X)<~>~generous(X)))))&
(![X]:((happy(X)|~generous(X))=>(calm(X)&~old(X))))&
(![X]:((~curious(X)<~>old(X))=>~kind(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>((~old(alice)&rich(alice))))&
((?[X]:((rich(X)&old(X))))<=>(?[X]:(~funny(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~rich(X)&~strong(X))))&
((~tall(alice))<=>((calm(paul)|~creative(paul))))&
(((~curious(alice)&~old(alice)))<=>(?[X]:((~rich(X)|calm(X)))))&
(((curious(susan)|funny(susan)))=>(?[X]:((~brave(X)|patient(X)))))&
((strong(paul))=>((happy(john)&kind(john))))&
(![X]:((kind(X)|~rich(X))=>(~curious(X)|~wise(X))))&
(![X]:((old(X)<~>~tall(X))<=>(~kind(X)<~>generous(X))))&
(![X]:((~funny(X)|wise(X))<=>(humble(X)|~happy(X))))&
((~creative(lucy)|~generous(lucy)))&
((rich(john)<~>old(john)))&
(?[X]:((old(X)&generous(X))))&
((kind(john)|calm(john)))&
(?[X]:(~rich(X)))&
(?[X]:((funny(X)&~happy(X))))&
((kind(paul)|~humble(paul)))&
(?[X]:((patient(X)<~>kind(X)))) | creative(paul) | [] | null | 0 |
If someone is not humble or quiet then alice is tall or not generous.
Everyone who is not patient or not kind is old.
Everyone who is both not curious and not happy is curious or not rich.
Everyone who is tall is not funny.
If someone is either not quiet or happy then someone is not generous.
Everyone who is both humble and not wise is brave or wise.
Everyone who is calm or not rich is not curious or not wise.
Everyone who is not kind or rich is either not generous or quiet.
Everyone who is both not strong and not creative is calm.
If someone is not brave or patient then someone is both not brave and funny.
Everyone who is not humble or happy is either not tall or not humble and vice versa.
Everyone who is either not rich or not old is both strong and funny and vice versa.
If john is strong or creative then susan is not brave or not old and vice versa.
Everyone who is brave or calm is not kind.
Everyone who is quiet or not quiet is both wise and funny and vice versa.
Everyone who is not old is brave or not brave.
Lucy is not generous or not strong.
Someone is not creative or curious.
John is both not generous and brave.
Someone is either generous or not calm.
Someone is both not tall and not kind.
Mary is either not quiet or humble.
John is not patient or not curious. | John is creative. | neutral | ((?[X]:((~humble(X)|quiet(X))))=>((tall(alice)|~generous(alice))))&
(![X]:((~patient(X)|~kind(X))=>old(X)))&
(![X]:((~curious(X)&~happy(X))=>(curious(X)|~rich(X))))&
(![X]:(tall(X)=>~funny(X)))&
((?[X]:((~quiet(X)<~>happy(X))))=>(?[X]:(~generous(X))))&
(![X]:((humble(X)&~wise(X))=>(brave(X)|wise(X))))&
(![X]:((calm(X)|~rich(X))=>(~curious(X)|~wise(X))))&
(![X]:((~kind(X)|rich(X))=>(~generous(X)<~>quiet(X))))&
(![X]:((~strong(X)&~creative(X))=>calm(X)))&
((?[X]:((~brave(X)|patient(X))))=>(?[X]:((~brave(X)&funny(X)))))&
(![X]:((~humble(X)|happy(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>~old(X))<=>(strong(X)&funny(X))))&
(((strong(john)|creative(john)))<=>((~brave(susan)|~old(susan))))&
(![X]:((brave(X)|calm(X))=>~kind(X)))&
(![X]:((quiet(X)|~quiet(X))<=>(wise(X)&funny(X))))&
(![X]:(~old(X)=>(brave(X)|~brave(X))))&
((~generous(lucy)|~strong(lucy)))&
(?[X]:((~creative(X)|curious(X))))&
((~generous(john)&brave(john)))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((~tall(X)&~kind(X))))&
((~quiet(mary)<~>humble(mary)))&
((~patient(john)|~curious(john))) | creative(john) | [] | null | 0 |
If paul is not wise or not rich then someone is both not rich and not strong and vice versa. Everyone who is not funny or not wise is either not strong or quiet and vice versa. Everyone who is either brave or creative is either strong or happy and vice versa. If john is either not quiet or strong then susan is brave or rich and vice versa. Everyone who is both not calm and not rich is curious and vice versa. If john is wise or not humble then mary is either humble or not funny. If someone is not generous or funny then mary is not creative or generous. Everyone who is either not humble or calm is either not calm or not rich and vice versa. Everyone who is both tall and not kind is both funny and curious. Everyone who is not rich is either humble or creative. If fred is not wise or not curious then someone is both creative and happy. Everyone who is both quiet and not generous is both brave and calm. Everyone who is both funny and wise is strong or happy and vice versa. If someone is curious or not rich then someone is either not old or tall. Everyone who is not strong is not brave and vice versa. If someone is both kind and not tall then someone is wise and vice versa. Lucy is either not quiet or quiet. Alice is either not patient or not tall. Alice is not tall or not generous. Lucy is either rich or quiet. Lucy is either not generous or calm. John is both not quiet and kind. Someone is curious. | Lucy is not curious. | entailment | (((~wise(paul)|~rich(paul)))<=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:((~funny(X)|~wise(X))<=>(~strong(X)<~>quiet(X))))&
(![X]:((brave(X)<~>creative(X))<=>(strong(X)<~>happy(X))))&
(((~quiet(john)<~>strong(john)))<=>((brave(susan)|rich(susan))))&
(![X]:((~calm(X)&~rich(X))<=>curious(X)))&
(((wise(john)|~humble(john)))=>((humble(mary)<~>~funny(mary))))&
((?[X]:((~generous(X)|funny(X))))=>((~creative(mary)|generous(mary))))&
(![X]:((~humble(X)<~>calm(X))<=>(~calm(X)<~>~rich(X))))&
(![X]:((tall(X)&~kind(X))=>(funny(X)&curious(X))))&
(![X]:(~rich(X)=>(humble(X)<~>creative(X))))&
(((~wise(fred)|~curious(fred)))=>(?[X]:((creative(X)&happy(X)))))&
(![X]:((quiet(X)&~generous(X))=>(brave(X)&calm(X))))&
(![X]:((funny(X)&wise(X))<=>(strong(X)|happy(X))))&
((?[X]:((curious(X)|~rich(X))))=>(?[X]:((~old(X)<~>tall(X)))))&
(![X]:(~strong(X)<=>~brave(X)))&
((?[X]:((kind(X)&~tall(X))))<=>(?[X]:(wise(X))))&
((~quiet(lucy)<~>quiet(lucy)))&
((~patient(alice)<~>~tall(alice)))&
((~tall(alice)|~generous(alice)))&
((rich(lucy)<~>quiet(lucy)))&
((~generous(lucy)<~>calm(lucy)))&
((~quiet(john)&kind(john)))&
(?[X]:(curious(X))) | ~curious(lucy) | [
"p4",
"p11",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 851388032079356660738698
% SZS output start Proof for 851388032079356660738698
5. ! [X0] : ((~rich(X0) & ~calm(X0)) <=> curious(X0)) [input p4]
12. ! [X0] : ((~generous(X0) & quiet(X0)) => (calm(X0) & brave(X0))) [input p11]
20. rich(lucy) <~> quiet(lucy) [input p19]
21. ~generous(lucy) <~> calm(lucy) [input p20]
24. curious(lucy) [input hypothesis]
34. ! [X0] : ((calm(X0) & brave(X0)) | (generous(X0) | ~quiet(X0))) [ennf transformation 12]
35. ! [X0] : ((calm(X0) & brave(X0)) | generous(X0) | ~quiet(X0)) [flattening 34]
47. ! [X0] : (((~rich(X0) & ~calm(X0)) | ~curious(X0)) & (curious(X0) | (rich(X0) | calm(X0)))) [nnf transformation 5]
48. ! [X0] : (((~rich(X0) & ~calm(X0)) | ~curious(X0)) & (curious(X0) | rich(X0) | calm(X0))) [flattening 47]
68. (~quiet(lucy) | ~rich(lucy)) & (quiet(lucy) | rich(lucy)) [nnf transformation 20]
69. (~calm(lucy) | generous(lucy)) & (calm(lucy) | ~generous(lucy)) [nnf transformation 21]
98. ~curious(X0) | ~calm(X0) [cnf transformation 48]
99. ~curious(X0) | ~rich(X0) [cnf transformation 48]
123. ~quiet(X0) | generous(X0) | calm(X0) [cnf transformation 35]
143. quiet(lucy) | rich(lucy) [cnf transformation 68]
145. calm(lucy) | ~generous(lucy) [cnf transformation 69]
150. curious(lucy) [cnf transformation 24]
315. 34 <=> rich(lucy) [avatar definition]
319. 35 <=> quiet(lucy) [avatar definition]
320. quiet(lucy) <- (35) [avatar component clause 319]
323. 34 | 35 [avatar split clause 143,319,315]
325. 36 <=> generous(lucy) [avatar definition]
329. 37 <=> calm(lucy) [avatar definition]
333. ~36 | 37 [avatar split clause 145,329,325]
338. ~calm(lucy) [resolution 98,150]
341. ~rich(lucy) [resolution 99,150]
345. ~34 [avatar split clause 341,315]
367. generous(lucy) | calm(lucy) <- (35) [resolution 123,320]
371. 37 | 36 | ~35 [avatar split clause 367,319,325,329]
377. ~37 [avatar split clause 338,329]
378. $false [avatar sat refutation 323,333,345,371,377]
% SZS output end Proof for 851388032079356660738698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or wise is both patient and curious. Everyone who is not quiet is generous or happy and vice versa. Everyone who is either wise or calm is patient. Everyone who is not funny or quiet is both not wise and tall and vice versa. Everyone who is both creative and humble is not wise. Everyone who is brave is not quiet or not happy. If paul is not kind or not rich then someone is funny or quiet. If paul is both not humble and quiet then mary is not generous. Everyone who is both creative and not curious is not kind or not wise and vice versa. Everyone who is either not curious or patient is either not calm or not happy and vice versa. If susan is not kind or generous then someone is both not happy and not brave and vice versa. If alice is humble or not kind then someone is both not quiet and rich and vice versa. If someone is not calm then john is wise and vice versa. Everyone who is not quiet or generous is kind or not old. If fred is not brave or brave then fred is not curious or funny. If someone is either rich or not creative then mary is both not patient and not funny and vice versa. Lucy is not generous. Lucy is happy or not calm. Someone is both old and not rich. Someone is both not funny and rich. Someone is not old. John is either old or not generous. Paul is curious or generous. | Mary is curious. | contradiction | (![X]:((old(X)|wise(X))=>(patient(X)&curious(X))))&
(![X]:(~quiet(X)<=>(generous(X)|happy(X))))&
(![X]:((wise(X)<~>calm(X))=>patient(X)))&
(![X]:((~funny(X)|quiet(X))<=>(~wise(X)&tall(X))))&
(![X]:((creative(X)&humble(X))=>~wise(X)))&
(![X]:(brave(X)=>(~quiet(X)|~happy(X))))&
(((~kind(paul)|~rich(paul)))=>(?[X]:((funny(X)|quiet(X)))))&
(((~humble(paul)&quiet(paul)))=>(~generous(mary)))&
(![X]:((creative(X)&~curious(X))<=>(~kind(X)|~wise(X))))&
(![X]:((~curious(X)<~>patient(X))<=>(~calm(X)<~>~happy(X))))&
(((~kind(susan)|generous(susan)))<=>(?[X]:((~happy(X)&~brave(X)))))&
(((humble(alice)|~kind(alice)))<=>(?[X]:((~quiet(X)&rich(X)))))&
((?[X]:(~calm(X)))<=>(wise(john)))&
(![X]:((~quiet(X)|generous(X))=>(kind(X)|~old(X))))&
(((~brave(fred)|brave(fred)))=>((~curious(fred)|funny(fred))))&
((?[X]:((rich(X)<~>~creative(X))))<=>((~patient(mary)&~funny(mary))))&
(~generous(lucy))&
((happy(lucy)|~calm(lucy)))&
(?[X]:((old(X)&~rich(X))))&
(?[X]:((~funny(X)&rich(X))))&
(?[X]:(~old(X)))&
((old(john)<~>~generous(john)))&
((curious(paul)|generous(paul))) | curious(mary) | [
"p0",
"p3",
"p8",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8730320411255724656829059
% SZS output start Proof for 8730320411255724656829059
1. ! [X0] : ((wise(X0) | old(X0)) => (curious(X0) & patient(X0))) [input p0]
4. ! [X0] : ((quiet(X0) | ~funny(X0)) <=> (tall(X0) & ~wise(X0))) [input p3]
9. ! [X0] : ((~curious(X0) & creative(X0)) <=> (~wise(X0) | ~kind(X0))) [input p8]
16. ? [X0] : (rich(X0) <~> ~creative(X0)) <=> (~funny(mary) & ~patient(mary)) [input p15]
20. ? [X0] : (rich(X0) & ~funny(X0)) [input p19]
24. curious(mary) [input hypothesis]
25. ! [X0] : ((curious(X0) & patient(X0)) | (~wise(X0) & ~old(X0))) [ennf transformation 1]
41. ! [X0] : (((quiet(X0) | ~funny(X0)) | (~tall(X0) | wise(X0))) & ((tall(X0) & ~wise(X0)) | (~quiet(X0) & funny(X0)))) [nnf transformation 4]
42. ! [X0] : ((quiet(X0) | ~funny(X0) | ~tall(X0) | wise(X0)) & ((tall(X0) & ~wise(X0)) | (~quiet(X0) & funny(X0)))) [flattening 41]
45. ! [X0] : (((~curious(X0) & creative(X0)) | (wise(X0) & kind(X0))) & ((~wise(X0) | ~kind(X0)) | (curious(X0) | ~creative(X0)))) [nnf transformation 9]
46. ! [X0] : (((~curious(X0) & creative(X0)) | (wise(X0) & kind(X0))) & (~wise(X0) | ~kind(X0) | curious(X0) | ~creative(X0))) [flattening 45]
62. (? [X0] : ((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (funny(mary) | patient(mary))) & ((~funny(mary) & ~patient(mary)) | ! [X0] : ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) [nnf transformation 16]
63. (? [X0] : ((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | funny(mary) | patient(mary)) & ((~funny(mary) & ~patient(mary)) | ! [X0] : ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) [flattening 62]
64. (? [X0] : ((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | funny(mary) | patient(mary)) & ((~funny(mary) & ~patient(mary)) | ! [X1] : ((rich(X1) | creative(X1)) & (~creative(X1) | ~rich(X1)))) [rectify 63]
65. ? [X0] : ((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) => ((creative(sK4) | ~rich(sK4)) & (~creative(sK4) | rich(sK4))) [choice axiom]
66. (((creative(sK4) | ~rich(sK4)) & (~creative(sK4) | rich(sK4))) | funny(mary) | patient(mary)) & ((~funny(mary) & ~patient(mary)) | ! [X1] : ((rich(X1) | creative(X1)) & (~creative(X1) | ~rich(X1)))) [skolemisation 64,65]
69. ? [X0] : (rich(X0) & ~funny(X0)) => (rich(sK6) & ~funny(sK6)) [choice axiom]
70. rich(sK6) & ~funny(sK6) [skolemisation 20,69]
75. ~wise(X0) | patient(X0) [cnf transformation 25]
83. ~wise(X0) | funny(X0) [cnf transformation 42]
95. creative(X0) | wise(X0) [cnf transformation 46]
97. ~curious(X0) | wise(X0) [cnf transformation 46]
122. ~patient(mary) | ~creative(X1) | ~rich(X1) [cnf transformation 66]
132. ~funny(sK6) [cnf transformation 70]
133. rich(sK6) [cnf transformation 70]
138. curious(mary) [cnf transformation 24]
251. 24 <=> patient(mary) [avatar definition]
273. 29 <=> ! [X1] : (~creative(X1) | ~rich(X1)) [avatar definition]
274. ~rich(X1) | ~creative(X1) <- (29) [avatar component clause 273]
277. 29 | ~24 [avatar split clause 122,251,273]
322. wise(mary) [resolution 97,138]
331. patient(mary) [resolution 322,75]
336. 24 [avatar split clause 331,251]
344. ~creative(sK6) <- (29) [resolution 274,133]
369. wise(sK6) <- (29) [resolution 344,95]
489. funny(sK6) <- (29) [resolution 369,83]
492. $false <- (29) [subsumption resolution 489,132]
493. ~29 [avatar contradiction clause 492]
494. $false [avatar sat refutation 277,336,493]
% SZS output end Proof for 8730320411255724656829059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not wise and funny then someone is not tall or not curious and vice versa. Everyone who is both happy and not humble is both not kind and humble and vice versa. If someone is either generous or creative then alice is brave or rich. Everyone who is old is creative or kind and vice versa. If someone is not curious or wise then someone is old. Everyone who is not brave is not curious or strong. If someone is calm then someone is both humble and not old and vice versa. Everyone who is humble is both happy and not brave and vice versa. If someone is tall then alice is humble. If fred is not humble or creative then paul is not humble or not happy and vice versa. Everyone who is calm or rich is quiet or not brave. Everyone who is either calm or humble is happy or not happy and vice versa. Everyone who is either patient or not kind is not kind. If john is not old then someone is either brave or tall. Everyone who is either not generous or not humble is either strong or not generous and vice versa. Everyone who is both kind and rich is either humble or not tall and vice versa. Alice is both humble and quiet. Someone is either calm or happy. Paul is either not happy or not patient. Someone is wise. Susan is humble. Fred is funny. Mary is old or happy. Someone is old. | John is kind. | entailment | (((~wise(susan)&funny(susan)))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((happy(X)&~humble(X))<=>(~kind(X)&humble(X))))&
((?[X]:((generous(X)<~>creative(X))))=>((brave(alice)|rich(alice))))&
(![X]:(old(X)<=>(creative(X)|kind(X))))&
((?[X]:((~curious(X)|wise(X))))=>(?[X]:(old(X))))&
(![X]:(~brave(X)=>(~curious(X)|strong(X))))&
((?[X]:(calm(X)))<=>(?[X]:((humble(X)&~old(X)))))&
(![X]:(humble(X)<=>(happy(X)&~brave(X))))&
((?[X]:(tall(X)))=>(humble(alice)))&
(((~humble(fred)|creative(fred)))<=>((~humble(paul)|~happy(paul))))&
(![X]:((calm(X)|rich(X))=>(quiet(X)|~brave(X))))&
(![X]:((calm(X)<~>humble(X))<=>(happy(X)|~happy(X))))&
(![X]:((patient(X)<~>~kind(X))=>~kind(X)))&
((~old(john))=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((~generous(X)<~>~humble(X))<=>(strong(X)<~>~generous(X))))&
(![X]:((kind(X)&rich(X))<=>(humble(X)<~>~tall(X))))&
((humble(alice)&quiet(alice)))&
(?[X]:((calm(X)<~>happy(X))))&
((~happy(paul)<~>~patient(paul)))&
(?[X]:(wise(X)))&
(humble(susan))&
(funny(fred))&
((old(mary)|happy(mary)))&
(?[X]:(old(X))) | kind(john) | [
"p1",
"p3",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8582527123883105958544100
% SZS output start Proof for 8582527123883105958544100
2. ! [X0] : ((~humble(X0) & happy(X0)) <=> (humble(X0) & ~kind(X0))) [input p1]
4. ! [X0] : (old(X0) <=> (kind(X0) | creative(X0))) [input p3]
7. ? [X0] : calm(X0) <=> ? [X0] : (~old(X0) & humble(X0)) [input p6]
8. ! [X0] : (humble(X0) <=> (~brave(X0) & happy(X0))) [input p7]
12. ! [X0] : ((calm(X0) <~> humble(X0)) <=> (~happy(X0) | happy(X0))) [input p11]
25. ~kind(john) [input hypothesis]
27. ? [X0] : calm(X0) <=> ? [X1] : (~old(X1) & humble(X1)) [rectify 7]
43. ! [X0] : (((~humble(X0) & happy(X0)) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | (humble(X0) | ~happy(X0)))) [nnf transformation 2]
44. ! [X0] : (((~humble(X0) & happy(X0)) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | humble(X0) | ~happy(X0))) [flattening 43]
46. ! [X0] : ((old(X0) | (~kind(X0) & ~creative(X0))) & ((kind(X0) | creative(X0)) | ~old(X0))) [nnf transformation 4]
47. ! [X0] : ((old(X0) | (~kind(X0) & ~creative(X0))) & (kind(X0) | creative(X0) | ~old(X0))) [flattening 46]
51. (? [X0] : calm(X0) | ! [X1] : (old(X1) | ~humble(X1))) & (? [X1] : (~old(X1) & humble(X1)) | ! [X0] : ~calm(X0)) [nnf transformation 27]
52. (? [X0] : calm(X0) | ! [X1] : (old(X1) | ~humble(X1))) & (? [X2] : (~old(X2) & humble(X2)) | ! [X3] : ~calm(X3)) [rectify 51]
53. ? [X0] : calm(X0) => calm(sK2) [choice axiom]
54. ? [X2] : (~old(X2) & humble(X2)) => (~old(sK3) & humble(sK3)) [choice axiom]
55. (calm(sK2) | ! [X1] : (old(X1) | ~humble(X1))) & ((~old(sK3) & humble(sK3)) | ! [X3] : ~calm(X3)) [skolemisation 52,54,53]
56. ! [X0] : ((humble(X0) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | ~humble(X0))) [nnf transformation 8]
57. ! [X0] : ((humble(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | ~humble(X0))) [flattening 56]
60. ! [X0] : ((((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0))))) [nnf transformation 12]
61. ! [X0] : ((((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0))))) [flattening 60]
83. humble(X0) | humble(X0) | ~happy(X0) [cnf transformation 44]
85. ~humble(X0) | ~humble(X0) | kind(X0) [cnf transformation 44]
90. ~kind(X0) | old(X0) [cnf transformation 47]
94. humble(sK3) | ~calm(X3) [cnf transformation 55]
95. ~old(sK3) | ~calm(X3) [cnf transformation 55]
97. ~humble(X0) | happy(X0) [cnf transformation 57]
108. humble(X0) | calm(X0) | happy(X0) [cnf transformation 61]
139. ~kind(john) [cnf transformation 25]
145. ~happy(X0) | humble(X0) [duplicate literal removal 83]
146. ~humble(X0) | kind(X0) [duplicate literal removal 85]
208. 15 <=> ! [X3] : ~calm(X3) [avatar definition]
209. ~calm(X3) <- (15) [avatar component clause 208]
211. 16 <=> old(sK3) [avatar definition]
214. 15 | ~16 [avatar split clause 95,211,208]
216. 17 <=> humble(sK3) [avatar definition]
218. humble(sK3) <- (17) [avatar component clause 216]
219. 15 | 17 [avatar split clause 94,216,208]
251. calm(X0) | happy(X0) [subsumption resolution 108,97]
416. kind(sK3) <- (17) [resolution 218,146]
437. happy(X0) <- (15) [resolution 209,251]
441. old(sK3) <- (17) [resolution 416,90]
456. humble(X0) <- (15) [resolution 437,145]
463. kind(X2) <- (15) [resolution 456,146]
466. $false <- (15) [resolution 463,139]
468. ~15 [avatar contradiction clause 466]
469. 16 | ~17 [avatar split clause 441,216,211]
470. $false [avatar sat refutation 214,219,468,469]
% SZS output end Proof for 8582527123883105958544100
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or old is either tall or not rich. Everyone who is both wise and humble is wise. Everyone who is not tall or brave is brave and vice versa. If susan is either not curious or not wise then john is both patient and not calm and vice versa. If fred is not wise then someone is kind or not funny and vice versa. If someone is both wise and patient then someone is both not calm and not tall and vice versa. If someone is not happy then mary is either old or not rich and vice versa. Everyone who is either patient or tall is both old and calm. Everyone who is both happy and not tall is either not kind or not funny. Everyone who is either not humble or not kind is tall and vice versa. Everyone who is not old is quiet or calm. Everyone who is humble or not happy is both not old and kind and vice versa. Everyone who is not generous is either wise or curious. Everyone who is either not humble or not tall is both strong and not old. Everyone who is kind or not funny is rich or not strong and vice versa. Everyone who is either not brave or strong is tall or not patient and vice versa. Mary is either rich or not humble. Someone is not generous or tall. Fred is both wise and old. Someone is either not brave or happy. Alice is either wise or not tall. Someone is both not old and brave. Paul is either not quiet or not generous. Someone is either not quiet or not brave. | Mary is not humble. | entailment | (![X]:((funny(X)|old(X))=>(tall(X)<~>~rich(X))))&
(![X]:((wise(X)&humble(X))=>wise(X)))&
(![X]:((~tall(X)|brave(X))<=>brave(X)))&
(((~curious(susan)<~>~wise(susan)))<=>((patient(john)&~calm(john))))&
((~wise(fred))<=>(?[X]:((kind(X)|~funny(X)))))&
((?[X]:((wise(X)&patient(X))))<=>(?[X]:((~calm(X)&~tall(X)))))&
((?[X]:(~happy(X)))<=>((old(mary)<~>~rich(mary))))&
(![X]:((patient(X)<~>tall(X))=>(old(X)&calm(X))))&
(![X]:((happy(X)&~tall(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((~humble(X)<~>~kind(X))<=>tall(X)))&
(![X]:(~old(X)=>(quiet(X)|calm(X))))&
(![X]:((humble(X)|~happy(X))<=>(~old(X)&kind(X))))&
(![X]:(~generous(X)=>(wise(X)<~>curious(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(strong(X)&~old(X))))&
(![X]:((kind(X)|~funny(X))<=>(rich(X)|~strong(X))))&
(![X]:((~brave(X)<~>strong(X))<=>(tall(X)|~patient(X))))&
((rich(mary)<~>~humble(mary)))&
(?[X]:((~generous(X)|tall(X))))&
((wise(fred)&old(fred)))&
(?[X]:((~brave(X)<~>happy(X))))&
((wise(alice)<~>~tall(alice)))&
(?[X]:((~old(X)&brave(X))))&
((~quiet(paul)<~>~generous(paul)))&
(?[X]:((~quiet(X)<~>~brave(X)))) | ~humble(mary) | [
"p4",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3265859979488382420207628
% SZS output start Proof for 3265859979488382420207628
5. ~wise(fred) <=> ? [X0] : (~funny(X0) | kind(X0)) [input p4]
12. ! [X0] : ((~happy(X0) | humble(X0)) <=> (kind(X0) & ~old(X0))) [input p11]
19. old(fred) & wise(fred) [input p18]
25. humble(mary) [input hypothesis]
42. (~wise(fred) | ! [X0] : (funny(X0) & ~kind(X0))) & (? [X0] : (~funny(X0) | kind(X0)) | wise(fred)) [nnf transformation 5]
43. (~wise(fred) | ! [X0] : (funny(X0) & ~kind(X0))) & (? [X1] : (~funny(X1) | kind(X1)) | wise(fred)) [rectify 42]
44. ? [X1] : (~funny(X1) | kind(X1)) => (~funny(sK0) | kind(sK0)) [choice axiom]
45. (~wise(fred) | ! [X0] : (funny(X0) & ~kind(X0))) & ((~funny(sK0) | kind(sK0)) | wise(fred)) [skolemisation 43,44]
58. ! [X0] : (((~happy(X0) | humble(X0)) | (~kind(X0) | old(X0))) & ((kind(X0) & ~old(X0)) | (happy(X0) & ~humble(X0)))) [nnf transformation 12]
59. ! [X0] : ((~happy(X0) | humble(X0) | ~kind(X0) | old(X0)) & ((kind(X0) & ~old(X0)) | (happy(X0) & ~humble(X0)))) [flattening 58]
94. ~wise(fred) | ~kind(X0) [cnf transformation 45]
117. ~humble(X0) | kind(X0) [cnf transformation 59]
139. wise(fred) [cnf transformation 19]
151. humble(mary) [cnf transformation 25]
178. 6 <=> wise(fred) [avatar definition]
183. 7 <=> ! [X0] : ~kind(X0) [avatar definition]
184. ~kind(X0) <- (7) [avatar component clause 183]
185. 7 | ~6 [avatar split clause 94,178,183]
244. 20 <=> humble(mary) [avatar definition]
246. humble(mary) <- (20) [avatar component clause 244]
258. 6 [avatar split clause 139,178]
299. 20 [avatar split clause 151,244]
311. kind(mary) <- (20) [resolution 117,246]
312. $false <- (7, 20) [subsumption resolution 311,184]
313. ~7 | ~20 [avatar contradiction clause 312]
314. $false [avatar sat refutation 185,258,299,313]
% SZS output end Proof for 3265859979488382420207628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is humble or wise and vice versa.
Everyone who is happy or humble is either not happy or not strong and vice versa.
If susan is both not humble and old then someone is either curious or brave.
Everyone who is both kind and not curious is either not happy or not rich and vice versa.
Everyone who is kind or curious is humble and vice versa.
Everyone who is both not calm and quiet is either not rich or brave and vice versa.
Everyone who is happy or wise is either rich or not strong and vice versa.
Everyone who is not patient is either old or happy.
Everyone who is either quiet or not tall is not quiet or patient and vice versa.
Everyone who is either quiet or not humble is either not generous or not strong and vice versa.
If someone is patient then mary is brave or not tall and vice versa.
If alice is not old then someone is not rich or not wise.
If lucy is creative or old then someone is not patient and vice versa.
Everyone who is creative is both patient and happy and vice versa.
If someone is both wise and not generous then someone is both not wise and generous and vice versa.
If someone is creative then fred is both curious and calm.
Fred is either not old or happy.
Paul is both not happy and not tall.
John is either not creative or quiet.
Someone is either strong or not rich.
John is both generous and not quiet.
Lucy is either funny or not generous.
Someone is both humble and happy. | Fred is not kind. | entailment | (![X]:(~strong(X)<=>(humble(X)|wise(X))))&
(![X]:((happy(X)|humble(X))<=>(~happy(X)<~>~strong(X))))&
(((~humble(susan)&old(susan)))=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:((kind(X)|curious(X))<=>humble(X)))&
(![X]:((~calm(X)&quiet(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((happy(X)|wise(X))<=>(rich(X)<~>~strong(X))))&
(![X]:(~patient(X)=>(old(X)<~>happy(X))))&
(![X]:((quiet(X)<~>~tall(X))<=>(~quiet(X)|patient(X))))&
(![X]:((quiet(X)<~>~humble(X))<=>(~generous(X)<~>~strong(X))))&
((?[X]:(patient(X)))<=>((brave(mary)|~tall(mary))))&
((~old(alice))=>(?[X]:((~rich(X)|~wise(X)))))&
(((creative(lucy)|old(lucy)))<=>(?[X]:(~patient(X))))&
(![X]:(creative(X)<=>(patient(X)&happy(X))))&
((?[X]:((wise(X)&~generous(X))))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:(creative(X)))=>((curious(fred)&calm(fred))))&
((~old(fred)<~>happy(fred)))&
((~happy(paul)&~tall(paul)))&
((~creative(john)<~>quiet(john)))&
(?[X]:((strong(X)<~>~rich(X))))&
((generous(john)&~quiet(john)))&
((funny(lucy)<~>~generous(lucy)))&
(?[X]:((humble(X)&happy(X)))) | ~kind(fred) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p7",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3160700245540229710567818
% SZS output start Proof for 3160700245540229710567818
1. ! [X0] : (~strong(X0) <=> (wise(X0) | humble(X0))) [input p0]
2. ! [X0] : ((humble(X0) | happy(X0)) <=> (~happy(X0) <~> ~strong(X0))) [input p1]
4. ! [X0] : ((~curious(X0) & kind(X0)) <=> (~happy(X0) <~> ~rich(X0))) [input p3]
5. ! [X0] : ((curious(X0) | kind(X0)) <=> humble(X0)) [input p4]
7. ! [X0] : ((wise(X0) | happy(X0)) <=> (rich(X0) <~> ~strong(X0))) [input p6]
8. ! [X0] : (~patient(X0) => (old(X0) <~> happy(X0))) [input p7]
14. ! [X0] : (creative(X0) <=> (happy(X0) & patient(X0))) [input p13]
16. ? [X0] : creative(X0) => (calm(fred) & curious(fred)) [input p15]
17. ~old(fred) <~> happy(fred) [input p16]
24. kind(fred) [input hypothesis]
28. ! [X0] : ((old(X0) <~> happy(X0)) | patient(X0)) [ennf transformation 8]
30. (calm(fred) & curious(fred)) | ! [X0] : ~creative(X0) [ennf transformation 16]
31. ! [X0] : ((~strong(X0) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | strong(X0))) [nnf transformation 1]
32. ! [X0] : ((~strong(X0) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | strong(X0))) [flattening 31]
33. ! [X0] : (((humble(X0) | happy(X0)) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) & (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | (~humble(X0) & ~happy(X0)))) [nnf transformation 2]
34. ! [X0] : ((humble(X0) | happy(X0) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) & (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | (~humble(X0) & ~happy(X0)))) [flattening 33]
38. ! [X0] : (((~curious(X0) & kind(X0)) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | (curious(X0) | ~kind(X0)))) [nnf transformation 4]
39. ! [X0] : (((~curious(X0) & kind(X0)) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | curious(X0) | ~kind(X0))) [flattening 38]
40. ! [X0] : (((curious(X0) | kind(X0)) | ~humble(X0)) & (humble(X0) | (~curious(X0) & ~kind(X0)))) [nnf transformation 5]
41. ! [X0] : ((curious(X0) | kind(X0) | ~humble(X0)) & (humble(X0) | (~curious(X0) & ~kind(X0)))) [flattening 40]
44. ! [X0] : (((wise(X0) | happy(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (~wise(X0) & ~happy(X0)))) [nnf transformation 7]
45. ! [X0] : ((wise(X0) | happy(X0) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (~wise(X0) & ~happy(X0)))) [flattening 44]
46. ! [X0] : (((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | patient(X0)) [nnf transformation 28]
62. ! [X0] : ((creative(X0) | (~happy(X0) | ~patient(X0))) & ((happy(X0) & patient(X0)) | ~creative(X0))) [nnf transformation 14]
63. ! [X0] : ((creative(X0) | ~happy(X0) | ~patient(X0)) & ((happy(X0) & patient(X0)) | ~creative(X0))) [flattening 62]
69. (~happy(fred) | old(fred)) & (happy(fred) | ~old(fred)) [nnf transformation 17]
78. ~humble(X0) | ~strong(X0) [cnf transformation 32]
80. ~strong(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 34]
83. strong(X0) | happy(X0) | ~humble(X0) [cnf transformation 34]
84. humble(X0) | happy(X0) | ~strong(X0) | happy(X0) [cnf transformation 34]
93. ~curious(X0) | ~happy(X0) | rich(X0) [cnf transformation 39]
94. ~kind(X0) | humble(X0) [cnf transformation 41]
105. strong(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 45]
110. ~old(X0) | ~happy(X0) | patient(X0) [cnf transformation 46]
134. ~patient(X0) | ~happy(X0) | creative(X0) [cnf transformation 63]
139. curious(fred) | ~creative(X0) [cnf transformation 30]
142. ~happy(fred) | old(fred) [cnf transformation 69]
155. kind(fred) [cnf transformation 24]
158. ~strong(X0) | ~happy(X0) [duplicate literal removal 80]
159. humble(X0) | happy(X0) | ~strong(X0) [duplicate literal removal 84]
160. ~strong(X0) | happy(X0) [subsumption resolution 159,78]
161. ~humble(X0) | happy(X0) [subsumption resolution 83,78]
162. ~strong(X0) [subsumption resolution 158,160]
183. ~rich(X0) | ~happy(X0) [subsumption resolution 105,162]
252. 19 <=> ! [X0] : ~creative(X0) [avatar definition]
253. ~creative(X0) <- (19) [avatar component clause 252]
260. 21 <=> curious(fred) [avatar definition]
262. curious(fred) <- (21) [avatar component clause 260]
263. 19 | 21 [avatar split clause 139,260,252]
265. 22 <=> old(fred) [avatar definition]
267. old(fred) <- (22) [avatar component clause 265]
269. 23 <=> happy(fred) [avatar definition]
270. happy(fred) <- (23) [avatar component clause 269]
272. 22 | ~23 [avatar split clause 142,269,265]
301. humble(fred) [resolution 94,155]
304. happy(fred) [resolution 161,301]
307. 23 [avatar split clause 304,269]
423. ~happy(fred) | patient(fred) <- (22) [resolution 110,267]
433. patient(fred) <- (22, 23) [subsumption resolution 423,270]
451. ~happy(fred) | creative(fred) <- (22, 23) [resolution 433,134]
453. creative(fred) <- (22, 23) [subsumption resolution 451,270]
454. $false <- (19, 22, 23) [subsumption resolution 453,253]
455. ~19 | ~22 | ~23 [avatar contradiction clause 454]
481. 50 <=> rich(fred) [avatar definition]
482. rich(fred) <- (50) [avatar component clause 481]
486. ~happy(fred) | rich(fred) <- (21) [resolution 262,93]
488. rich(fred) <- (21, 23) [subsumption resolution 486,270]
491. 50 | ~21 | ~23 [avatar split clause 488,269,260,481]
566. ~happy(fred) <- (50) [resolution 482,183]
568. $false <- (23, 50) [subsumption resolution 566,270]
569. ~23 | ~50 [avatar contradiction clause 568]
570. $false [avatar sat refutation 263,272,307,455,491,569]
% SZS output end Proof for 3160700245540229710567818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is kind or not kind then fred is kind or brave and vice versa.
If alice is either humble or calm then susan is both calm and strong.
Everyone who is both kind and humble is both not calm and not wise and vice versa.
If fred is both wise and generous then fred is not happy and vice versa.
If mary is not happy or not old then fred is patient or kind.
If lucy is both not kind and not brave then someone is rich or wise and vice versa.
If someone is either not brave or not funny then mary is not old.
Everyone who is both strong and generous is either patient or not happy.
Everyone who is either not wise or not creative is not kind or not creative.
Everyone who is both not brave and not happy is either quiet or kind.
If john is either not creative or not tall then someone is curious.
Everyone who is not happy is both funny and kind.
If paul is not humble then alice is not funny or not strong.
Everyone who is not brave or not patient is not humble and vice versa.
Everyone who is both tall and generous is either old or not creative and vice versa.
Everyone who is either not generous or not kind is patient or happy.
Lucy is not kind or not humble.
Someone is generous or curious.
Someone is kind.
John is curious or not kind.
Paul is curious.
Someone is quiet or not happy.
Someone is both not curious and not calm.
Susan is not happy. | Susan is kind. | entailment | (((kind(paul)|~kind(paul)))<=>((kind(fred)|brave(fred))))&
(((humble(alice)<~>calm(alice)))=>((calm(susan)&strong(susan))))&
(![X]:((kind(X)&humble(X))<=>(~calm(X)&~wise(X))))&
(((wise(fred)&generous(fred)))<=>(~happy(fred)))&
(((~happy(mary)|~old(mary)))=>((patient(fred)|kind(fred))))&
(((~kind(lucy)&~brave(lucy)))<=>(?[X]:((rich(X)|wise(X)))))&
((?[X]:((~brave(X)<~>~funny(X))))=>(~old(mary)))&
(![X]:((strong(X)&generous(X))=>(patient(X)<~>~happy(X))))&
(![X]:((~wise(X)<~>~creative(X))=>(~kind(X)|~creative(X))))&
(![X]:((~brave(X)&~happy(X))=>(quiet(X)<~>kind(X))))&
(((~creative(john)<~>~tall(john)))=>(?[X]:(curious(X))))&
(![X]:(~happy(X)=>(funny(X)&kind(X))))&
((~humble(paul))=>((~funny(alice)|~strong(alice))))&
(![X]:((~brave(X)|~patient(X))<=>~humble(X)))&
(![X]:((tall(X)&generous(X))<=>(old(X)<~>~creative(X))))&
(![X]:((~generous(X)<~>~kind(X))=>(patient(X)|happy(X))))&
((~kind(lucy)|~humble(lucy)))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:(kind(X)))&
((curious(john)|~kind(john)))&
(curious(paul))&
(?[X]:((quiet(X)|~happy(X))))&
(?[X]:((~curious(X)&~calm(X))))&
(~happy(susan)) | kind(susan) | [
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3895043931161090900159836
% SZS output start Proof for 3895043931161090900159836
12. ! [X0] : (~happy(X0) => (kind(X0) & funny(X0))) [input p11]
24. ~happy(susan) [input p23]
25. ~kind(susan) [input hypothesis]
37. ! [X0] : ((kind(X0) & funny(X0)) | happy(X0)) [ennf transformation 12]
107. happy(X0) | kind(X0) [cnf transformation 37]
128. ~happy(susan) [cnf transformation 24]
129. ~kind(susan) [cnf transformation 25]
290. kind(susan) [resolution 107,128]
292. $false [subsumption resolution 290,129]
% SZS output end Proof for 3895043931161090900159836
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is kind or brave then someone is funny or not creative and vice versa. Everyone who is not patient or happy is not curious or not tall. Everyone who is creative or not patient is curious or not wise. Everyone who is both creative and quiet is not calm or wise and vice versa. If john is humble or not tall then someone is not humble or generous and vice versa. Everyone who is either strong or not creative is either not calm or strong and vice versa. Everyone who is not brave is not humble. Everyone who is happy or not humble is both brave and generous and vice versa. If susan is wise then someone is both brave and tall. If mary is either not patient or tall then fred is curious or tall. Everyone who is either creative or not patient is not wise. If fred is both not curious and not creative then alice is both generous and not wise. If someone is both patient and not old then john is generous. Everyone who is either not kind or not happy is not calm or quiet. If john is either brave or not kind then someone is not wise and vice versa. Mary is both funny and not old. Someone is both calm and generous. Alice is both calm and rich. Alice is rich. Someone is humble. Someone is funny. | Alice is not brave. | contradiction | (((kind(paul)|brave(paul)))<=>(?[X]:((funny(X)|~creative(X)))))&
(![X]:((~patient(X)|happy(X))=>(~curious(X)|~tall(X))))&
(![X]:((creative(X)|~patient(X))=>(curious(X)|~wise(X))))&
(![X]:((creative(X)&quiet(X))<=>(~calm(X)|wise(X))))&
(((humble(john)|~tall(john)))<=>(?[X]:((~humble(X)|generous(X)))))&
(![X]:((strong(X)<~>~creative(X))<=>(~calm(X)<~>strong(X))))&
(![X]:(~brave(X)=>~humble(X)))&
(![X]:((happy(X)|~humble(X))<=>(brave(X)&generous(X))))&
((wise(susan))=>(?[X]:((brave(X)&tall(X)))))&
(((~patient(mary)<~>tall(mary)))=>((curious(fred)|tall(fred))))&
(![X]:((creative(X)<~>~patient(X))=>~wise(X)))&
(((~curious(fred)&~creative(fred)))=>((generous(alice)&~wise(alice))))&
((?[X]:((patient(X)&~old(X))))=>(generous(john)))&
(![X]:((~kind(X)<~>~happy(X))=>(~calm(X)|quiet(X))))&
(((brave(john)<~>~kind(john)))<=>(?[X]:(~wise(X))))&
((funny(mary)&~old(mary)))&
(?[X]:((calm(X)&generous(X))))&
((calm(alice)&rich(alice)))&
(rich(alice))&
(?[X]:(humble(X)))&
(?[X]:(funny(X))) | ~brave(alice) | [
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5736264392038767104328067
% SZS output start Proof for 5736264392038767104328067
7. ! [X0] : (~brave(X0) => ~humble(X0)) [input p6]
8. ! [X0] : ((~humble(X0) | happy(X0)) <=> (generous(X0) & brave(X0))) [input p7]
22. ~brave(alice) [input hypothesis]
29. ! [X0] : (~humble(X0) | brave(X0)) [ennf transformation 7]
52. ! [X0] : (((~humble(X0) | happy(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (humble(X0) & ~happy(X0)))) [nnf transformation 8]
53. ! [X0] : ((~humble(X0) | happy(X0) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | (humble(X0) & ~happy(X0)))) [flattening 52]
94. ~humble(X0) | brave(X0) [cnf transformation 29]
96. brave(X0) | humble(X0) [cnf transformation 53]
122. ~brave(alice) [cnf transformation 22]
187. brave(X0) [subsumption resolution 96,94]
255. $false [subsumption resolution 122,187]
% SZS output end Proof for 5736264392038767104328067
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then mary is not quiet.
Everyone who is either happy or patient is either not wise or kind and vice versa.
Everyone who is funny or not curious is not wise.
If someone is both patient and brave then lucy is not brave or not curious and vice versa.
If someone is not old then fred is either wise or rich and vice versa.
If someone is either not tall or not happy then someone is both not humble and brave and vice versa.
Everyone who is not old or not strong is either not tall or wise and vice versa.
If fred is not kind or not happy then john is both not wise and not strong.
If mary is humble or not creative then paul is not tall.
Everyone who is both quiet and not humble is tall or not curious and vice versa.
Everyone who is either not patient or humble is not generous or not brave and vice versa.
If someone is not kind then someone is curious or humble.
If someone is either funny or not generous then someone is both not curious and not brave and vice versa.
Everyone who is not old or not generous is funny or calm and vice versa.
Everyone who is quiet or not creative is curious.
Everyone who is either funny or not generous is either wise or not creative and vice versa.
Someone is not creative.
Someone is either old or curious.
Someone is creative or not old.
Someone is either strong or not strong.
Someone is both not wise and not tall.
Someone is either funny or not old.
Someone is not tall or strong. | John is not curious. | contradiction | ((?[X]:(funny(X)))=>(~quiet(mary)))&
(![X]:((happy(X)<~>patient(X))<=>(~wise(X)<~>kind(X))))&
(![X]:((funny(X)|~curious(X))=>~wise(X)))&
((?[X]:((patient(X)&brave(X))))<=>((~brave(lucy)|~curious(lucy))))&
((?[X]:(~old(X)))<=>((wise(fred)<~>rich(fred))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((~old(X)|~strong(X))<=>(~tall(X)<~>wise(X))))&
(((~kind(fred)|~happy(fred)))=>((~wise(john)&~strong(john))))&
(((humble(mary)|~creative(mary)))=>(~tall(paul)))&
(![X]:((quiet(X)&~humble(X))<=>(tall(X)|~curious(X))))&
(![X]:((~patient(X)<~>humble(X))<=>(~generous(X)|~brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((curious(X)|humble(X)))))&
((?[X]:((funny(X)<~>~generous(X))))<=>(?[X]:((~curious(X)&~brave(X)))))&
(![X]:((~old(X)|~generous(X))<=>(funny(X)|calm(X))))&
(![X]:((quiet(X)|~creative(X))=>curious(X)))&
(![X]:((funny(X)<~>~generous(X))<=>(wise(X)<~>~creative(X))))&
(?[X]:(~creative(X)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((strong(X)<~>~strong(X))))&
(?[X]:((~wise(X)&~tall(X))))&
(?[X]:((funny(X)<~>~old(X))))&
(?[X]:((~tall(X)|strong(X)))) | ~curious(john) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2163866315395463907104036
% SZS output start Proof for 2163866315395463907104036
10. ! [X0] : ((~humble(X0) & quiet(X0)) <=> (~curious(X0) | tall(X0))) [input p9]
15. ! [X0] : ((~creative(X0) | quiet(X0)) => curious(X0)) [input p14]
24. ~curious(john) [input hypothesis]
33. ! [X0] : (curious(X0) | (creative(X0) & ~quiet(X0))) [ennf transformation 15]
51. ! [X0] : (((~humble(X0) & quiet(X0)) | (curious(X0) & ~tall(X0))) & ((~curious(X0) | tall(X0)) | (humble(X0) | ~quiet(X0)))) [nnf transformation 10]
52. ! [X0] : (((~humble(X0) & quiet(X0)) | (curious(X0) & ~tall(X0))) & (~curious(X0) | tall(X0) | humble(X0) | ~quiet(X0))) [flattening 51]
123. quiet(X0) | curious(X0) [cnf transformation 52]
143. curious(X0) | ~quiet(X0) [cnf transformation 33]
164. ~curious(john) [cnf transformation 24]
321. curious(X0) [subsumption resolution 143,123]
355. $false [subsumption resolution 164,321]
% SZS output end Proof for 2163866315395463907104036
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not kind is either not kind or not curious and vice versa.
Everyone who is creative is both happy and not humble and vice versa.
Everyone who is either not quiet or not funny is rich and vice versa.
Everyone who is not quiet or not humble is either rich or not calm and vice versa.
Everyone who is either happy or not brave is both not tall and not generous.
Everyone who is either quiet or not brave is not tall or patient and vice versa.
If john is not generous or not rich then someone is not patient or generous and vice versa.
If paul is both brave and not happy then someone is either not calm or not funny and vice versa.
If someone is either calm or not calm then someone is either generous or rich.
Everyone who is both not old and strong is humble.
Everyone who is not old or not tall is not tall or not funny.
Everyone who is either tall or creative is both strong and happy.
Everyone who is both curious and calm is curious or creative and vice versa.
If someone is both tall and funny then someone is either wise or happy.
Everyone who is kind or patient is both creative and calm and vice versa.
If someone is either old or not tall then fred is either rich or not rich and vice versa.
Someone is creative.
Someone is happy.
Someone is either strong or patient.
Someone is old.
Someone is not kind.
Lucy is quiet.
Someone is not humble. | Lucy is curious. | entailment | (![X]:((~strong(X)|~kind(X))<=>(~kind(X)<~>~curious(X))))&
(![X]:(creative(X)<=>(happy(X)&~humble(X))))&
(![X]:((~quiet(X)<~>~funny(X))<=>rich(X)))&
(![X]:((~quiet(X)|~humble(X))<=>(rich(X)<~>~calm(X))))&
(![X]:((happy(X)<~>~brave(X))=>(~tall(X)&~generous(X))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~tall(X)|patient(X))))&
(((~generous(john)|~rich(john)))<=>(?[X]:((~patient(X)|generous(X)))))&
(((brave(paul)&~happy(paul)))<=>(?[X]:((~calm(X)<~>~funny(X)))))&
((?[X]:((calm(X)<~>~calm(X))))=>(?[X]:((generous(X)<~>rich(X)))))&
(![X]:((~old(X)&strong(X))=>humble(X)))&
(![X]:((~old(X)|~tall(X))=>(~tall(X)|~funny(X))))&
(![X]:((tall(X)<~>creative(X))=>(strong(X)&happy(X))))&
(![X]:((curious(X)&calm(X))<=>(curious(X)|creative(X))))&
((?[X]:((tall(X)&funny(X))))=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((kind(X)|patient(X))<=>(creative(X)&calm(X))))&
((?[X]:((old(X)<~>~tall(X))))<=>((rich(fred)<~>~rich(fred))))&
(?[X]:(creative(X)))&
(?[X]:(happy(X)))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:(old(X)))&
(?[X]:(~kind(X)))&
(quiet(lucy))&
(?[X]:(~humble(X))) | curious(lucy) | [
"p0",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2463700481898463774482734
% SZS output start Proof for 2463700481898463774482734
1. ! [X0] : ((~kind(X0) | ~strong(X0)) <=> (~kind(X0) <~> ~curious(X0))) [input p0]
13. ! [X0] : ((calm(X0) & curious(X0)) <=> (creative(X0) | curious(X0))) [input p12]
15. ! [X0] : ((patient(X0) | kind(X0)) <=> (calm(X0) & creative(X0))) [input p14]
24. ~curious(lucy) [input hypothesis]
35. ! [X0] : (((~kind(X0) | ~strong(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | (kind(X0) & strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((~kind(X0) | ~strong(X0) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | (kind(X0) & strong(X0)))) [flattening 35]
60. ! [X0] : (((calm(X0) & curious(X0)) | (~creative(X0) & ~curious(X0))) & ((creative(X0) | curious(X0)) | (~calm(X0) | ~curious(X0)))) [nnf transformation 13]
61. ! [X0] : (((calm(X0) & curious(X0)) | (~creative(X0) & ~curious(X0))) & (creative(X0) | curious(X0) | ~calm(X0) | ~curious(X0))) [flattening 60]
66. ! [X0] : (((patient(X0) | kind(X0)) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | (~patient(X0) & ~kind(X0)))) [nnf transformation 15]
67. ! [X0] : ((patient(X0) | kind(X0) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | (~patient(X0) & ~kind(X0)))) [flattening 66]
88. curious(X0) | kind(X0) | kind(X0) [cnf transformation 36]
137. ~creative(X0) | curious(X0) [cnf transformation 61]
142. ~kind(X0) | creative(X0) [cnf transformation 67]
163. ~curious(lucy) [cnf transformation 24]
172. curious(X0) | kind(X0) [duplicate literal removal 88]
291. kind(lucy) [resolution 172,163]
296. creative(lucy) [resolution 291,142]
301. curious(lucy) [resolution 296,137]
303. $false [subsumption resolution 301,163]
% SZS output end Proof for 2463700481898463774482734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not tall or not humble then someone is either not tall or not calm and vice versa.
If mary is both not old and not patient then alice is both not brave and funny and vice versa.
If john is not creative or not patient then lucy is either not wise or humble and vice versa.
Everyone who is not rich is not brave and vice versa.
Everyone who is rich is both strong and old and vice versa.
Everyone who is brave or calm is wise or not humble and vice versa.
Everyone who is both quiet and not tall is curious or not patient.
Everyone who is happy or not brave is both not funny and funny.
If alice is not quiet then john is either quiet or not calm and vice versa.
Everyone who is either calm or generous is not humble.
If alice is both patient and not curious then someone is both not brave and strong.
Everyone who is generous or not quiet is both not kind and not calm.
If someone is quiet or strong then alice is happy or not generous and vice versa.
If john is not strong then someone is either not kind or happy and vice versa.
Everyone who is either quiet or not brave is either quiet or not creative and vice versa.
If mary is not calm then fred is either kind or not tall.
Fred is quiet or generous.
Someone is creative or strong.
Fred is not tall or happy.
Someone is not old or strong.
Someone is brave or not generous.
Someone is humble or creative.
Someone is brave or generous.
Someone is either not creative or wise. | Lucy is rich. | entailment | ((?[X]:((~tall(X)|~humble(X))))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
(((~old(mary)&~patient(mary)))<=>((~brave(alice)&funny(alice))))&
(((~creative(john)|~patient(john)))<=>((~wise(lucy)<~>humble(lucy))))&
(![X]:(~rich(X)<=>~brave(X)))&
(![X]:(rich(X)<=>(strong(X)&old(X))))&
(![X]:((brave(X)|calm(X))<=>(wise(X)|~humble(X))))&
(![X]:((quiet(X)&~tall(X))=>(curious(X)|~patient(X))))&
(![X]:((happy(X)|~brave(X))=>(~funny(X)&funny(X))))&
((~quiet(alice))<=>((quiet(john)<~>~calm(john))))&
(![X]:((calm(X)<~>generous(X))=>~humble(X)))&
(((patient(alice)&~curious(alice)))=>(?[X]:((~brave(X)&strong(X)))))&
(![X]:((generous(X)|~quiet(X))=>(~kind(X)&~calm(X))))&
((?[X]:((quiet(X)|strong(X))))<=>((happy(alice)|~generous(alice))))&
((~strong(john))<=>(?[X]:((~kind(X)<~>happy(X)))))&
(![X]:((quiet(X)<~>~brave(X))<=>(quiet(X)<~>~creative(X))))&
((~calm(mary))=>((kind(fred)<~>~tall(fred))))&
((quiet(fred)|generous(fred)))&
(?[X]:((creative(X)|strong(X))))&
((~tall(fred)|happy(fred)))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:((humble(X)|creative(X))))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:((~creative(X)<~>wise(X)))) | rich(lucy) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 374311800251001300749754
% SZS output start Proof for 374311800251001300749754
4. ! [X0] : (~rich(X0) <=> ~brave(X0)) [input p3]
8. ! [X0] : ((~brave(X0) | happy(X0)) => (funny(X0) & ~funny(X0))) [input p7]
25. ~rich(lucy) [input hypothesis]
29. ! [X0] : ((funny(X0) & ~funny(X0)) | (brave(X0) & ~happy(X0))) [ennf transformation 8]
42. ! [X0] : ((~rich(X0) | brave(X0)) & (~brave(X0) | rich(X0))) [nnf transformation 4]
89. ~brave(X0) | rich(X0) [cnf transformation 42]
99. ~funny(X0) | brave(X0) [cnf transformation 29]
101. funny(X0) | brave(X0) [cnf transformation 29]
139. ~rich(lucy) [cnf transformation 25]
220. brave(X0) [subsumption resolution 99,101]
316. rich(X0) [resolution 89,220]
317. $false [resolution 316,139]
% SZS output end Proof for 374311800251001300749754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both tall and not happy then mary is either not tall or not patient.
If someone is not patient or not happy then mary is both not happy and not funny.
Everyone who is either quiet or not tall is either not calm or funny.
If fred is not rich then someone is funny.
Everyone who is both quiet and wise is not brave.
Everyone who is either not creative or kind is either rich or tall.
Everyone who is humble or not quiet is not kind.
Everyone who is not patient or not creative is both not patient and not kind and vice versa.
Everyone who is generous or creative is both not patient and not wise.
If someone is not strong then lucy is strong or not tall.
Everyone who is not rich or funny is both not tall and not calm.
If john is not happy or not patient then mary is generous or creative and vice versa.
If alice is either not tall or funny then someone is either not funny or not patient.
If someone is either not patient or strong then someone is old or not generous.
Everyone who is not wise or brave is not tall or humble.
Someone is not brave.
Paul is not generous or wise.
John is patient or not creative.
Someone is old or kind.
Someone is funny or tall.
John is either old or not creative.
Someone is generous or not happy. | John is not rich. | contradiction | (((tall(fred)&~happy(fred)))=>((~tall(mary)<~>~patient(mary))))&
((?[X]:((~patient(X)|~happy(X))))=>((~happy(mary)&~funny(mary))))&
(![X]:((quiet(X)<~>~tall(X))=>(~calm(X)<~>funny(X))))&
((~rich(fred))=>(?[X]:(funny(X))))&
(![X]:((quiet(X)&wise(X))=>~brave(X)))&
(![X]:((~creative(X)<~>kind(X))=>(rich(X)<~>tall(X))))&
(![X]:((humble(X)|~quiet(X))=>~kind(X)))&
(![X]:((~patient(X)|~creative(X))<=>(~patient(X)&~kind(X))))&
(![X]:((generous(X)|creative(X))=>(~patient(X)&~wise(X))))&
((?[X]:(~strong(X)))=>((strong(lucy)|~tall(lucy))))&
(![X]:((~rich(X)|funny(X))=>(~tall(X)&~calm(X))))&
(((~happy(john)|~patient(john)))<=>((generous(mary)|creative(mary))))&
(((~tall(alice)<~>funny(alice)))=>(?[X]:((~funny(X)<~>~patient(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((~wise(X)|brave(X))=>(~tall(X)|humble(X))))&
(?[X]:(~brave(X)))&
((~generous(paul)|wise(paul)))&
((patient(john)|~creative(john)))&
(?[X]:((old(X)|kind(X))))&
(?[X]:((funny(X)|tall(X))))&
((old(john)<~>~creative(john)))&
(?[X]:((generous(X)|~happy(X)))) | ~rich(john) | [
"p5",
"p7",
"p8",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2788689791419854809779431
% SZS output start Proof for 2788689791419854809779431
6. ! [X0] : ((~creative(X0) <~> kind(X0)) => (rich(X0) <~> tall(X0))) [input p5]
8. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (~kind(X0) & ~patient(X0))) [input p7]
9. ! [X0] : ((creative(X0) | generous(X0)) => (~wise(X0) & ~patient(X0))) [input p8]
11. ! [X0] : ((funny(X0) | ~rich(X0)) => (~calm(X0) & ~tall(X0))) [input p10]
18. ~creative(john) | patient(john) [input p17]
23. ~rich(john) [input hypothesis]
33. ! [X0] : ((rich(X0) <~> tall(X0)) | (~creative(X0) <=> kind(X0))) [ennf transformation 6]
35. ! [X0] : ((~wise(X0) & ~patient(X0)) | (~creative(X0) & ~generous(X0))) [ennf transformation 9]
38. ! [X0] : ((~calm(X0) & ~tall(X0)) | (~funny(X0) & rich(X0))) [ennf transformation 11]
47. ! [X0] : (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) [nnf transformation 33]
48. ! [X0] : (((~creative(X0) | ~patient(X0)) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 8]
49. ! [X0] : ((~creative(X0) | ~patient(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | (creative(X0) & patient(X0)))) [flattening 48]
77. kind(X0) | rich(X0) | tall(X0) | creative(X0) [cnf transformation 47]
84. ~patient(X0) | creative(X0) [cnf transformation 49]
86. ~kind(X0) | creative(X0) [cnf transformation 49]
89. ~patient(X0) | ~creative(X0) [cnf transformation 35]
93. ~tall(X0) | rich(X0) [cnf transformation 38]
109. ~creative(john) | patient(john) [cnf transformation 18]
115. ~rich(john) [cnf transformation 23]
161. ~patient(X0) [subsumption resolution 89,84]
214. ~creative(john) [subsumption resolution 109,161]
307. rich(X0) | tall(X0) | creative(X0) | creative(X0) [resolution 77,86]
310. rich(X0) | tall(X0) | creative(X0) [duplicate literal removal 307]
311. creative(X0) | rich(X0) [subsumption resolution 310,93]
320. rich(john) [resolution 311,214]
322. $false [subsumption resolution 320,115]
% SZS output end Proof for 2788689791419854809779431
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or creative is either calm or patient and vice versa.
Everyone who is either not old or wise is both funny and quiet.
Everyone who is not old is both not creative and not happy.
Everyone who is either kind or not rich is calm.
If paul is not quiet then john is quiet.
If someone is both wise and patient then someone is both happy and funny.
Everyone who is both not creative and not kind is both patient and not humble and vice versa.
Everyone who is both old and wise is both brave and quiet.
Everyone who is not generous or quiet is both not happy and tall and vice versa.
If someone is not creative then someone is not humble or not wise.
Everyone who is not humble or not brave is not old or rich and vice versa.
Everyone who is not rich is not humble and vice versa.
Everyone who is patient is both not old and creative.
If someone is creative or patient then susan is not patient or generous.
Everyone who is calm is wise and vice versa.
Everyone who is tall or not funny is either funny or tall.
Lucy is generous.
Someone is old or not generous.
Mary is wise.
Someone is not humble.
Someone is both brave and kind.
Someone is happy or funny.
Someone is funny or not funny. | Lucy is not wise. | contradiction | (![X]:((~old(X)<~>creative(X))<=>(calm(X)<~>patient(X))))&
(![X]:((~old(X)<~>wise(X))=>(funny(X)&quiet(X))))&
(![X]:(~old(X)=>(~creative(X)&~happy(X))))&
(![X]:((kind(X)<~>~rich(X))=>calm(X)))&
((~quiet(paul))=>(quiet(john)))&
((?[X]:((wise(X)&patient(X))))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((~creative(X)&~kind(X))<=>(patient(X)&~humble(X))))&
(![X]:((old(X)&wise(X))=>(brave(X)&quiet(X))))&
(![X]:((~generous(X)|quiet(X))<=>(~happy(X)&tall(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:((~humble(X)|~brave(X))<=>(~old(X)|rich(X))))&
(![X]:(~rich(X)<=>~humble(X)))&
(![X]:(patient(X)=>(~old(X)&creative(X))))&
((?[X]:((creative(X)|patient(X))))=>((~patient(susan)|generous(susan))))&
(![X]:(calm(X)<=>wise(X)))&
(![X]:((tall(X)|~funny(X))=>(funny(X)<~>tall(X))))&
(generous(lucy))&
(?[X]:((old(X)|~generous(X))))&
(wise(mary))&
(?[X]:(~humble(X)))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((happy(X)|funny(X))))&
(?[X]:((funny(X)|~funny(X)))) | ~wise(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p6",
"p8",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5286720863722849616807913
% SZS output start Proof for 5286720863722849616807913
1. ! [X0] : ((~old(X0) <~> creative(X0)) <=> (calm(X0) <~> patient(X0))) [input p0]
2. ! [X0] : ((~old(X0) <~> wise(X0)) => (quiet(X0) & funny(X0))) [input p1]
3. ! [X0] : (~old(X0) => (~happy(X0) & ~creative(X0))) [input p2]
4. ! [X0] : ((kind(X0) <~> ~rich(X0)) => calm(X0)) [input p3]
6. ? [X0] : (patient(X0) & wise(X0)) => ? [X0] : (funny(X0) & happy(X0)) [input p5]
7. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> (~humble(X0) & patient(X0))) [input p6]
9. ! [X0] : ((quiet(X0) | ~generous(X0)) <=> (tall(X0) & ~happy(X0))) [input p8]
11. ! [X0] : ((~brave(X0) | ~humble(X0)) <=> (rich(X0) | ~old(X0))) [input p10]
12. ! [X0] : (~rich(X0) <=> ~humble(X0)) [input p11]
13. ! [X0] : (patient(X0) => (creative(X0) & ~old(X0))) [input p12]
15. ! [X0] : (calm(X0) <=> wise(X0)) [input p14]
24. ~wise(lucy) [input hypothesis]
25. ? [X0] : (patient(X0) & wise(X0)) => ? [X1] : (funny(X1) & happy(X1)) [rectify 6]
27. ! [X0] : ((quiet(X0) & funny(X0)) | (~old(X0) <=> wise(X0))) [ennf transformation 2]
28. ! [X0] : ((~happy(X0) & ~creative(X0)) | old(X0)) [ennf transformation 3]
29. ! [X0] : (calm(X0) | (kind(X0) <=> ~rich(X0))) [ennf transformation 4]
31. ? [X1] : (funny(X1) & happy(X1)) | ! [X0] : (~patient(X0) | ~wise(X0)) [ennf transformation 25]
35. ! [X0] : ((creative(X0) & ~old(X0)) | ~patient(X0)) [ennf transformation 13]
39. ! [X0] : ((((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0)))) & (((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0))))) [nnf transformation 1]
40. ! [X0] : ((quiet(X0) & funny(X0)) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0)))) [nnf transformation 27]
41. ! [X0] : (calm(X0) | ((kind(X0) | rich(X0)) & (~rich(X0) | ~kind(X0)))) [nnf transformation 29]
42. ? [X0] : (funny(X0) & happy(X0)) | ! [X1] : (~patient(X1) | ~wise(X1)) [rectify 31]
43. ? [X0] : (funny(X0) & happy(X0)) => (funny(sK0) & happy(sK0)) [choice axiom]
44. (funny(sK0) & happy(sK0)) | ! [X1] : (~patient(X1) | ~wise(X1)) [skolemisation 42,43]
45. ! [X0] : (((~kind(X0) & ~creative(X0)) | (humble(X0) | ~patient(X0))) & ((~humble(X0) & patient(X0)) | (kind(X0) | creative(X0)))) [nnf transformation 7]
46. ! [X0] : (((~kind(X0) & ~creative(X0)) | humble(X0) | ~patient(X0)) & ((~humble(X0) & patient(X0)) | kind(X0) | creative(X0))) [flattening 45]
47. ! [X0] : (((quiet(X0) | ~generous(X0)) | (~tall(X0) | happy(X0))) & ((tall(X0) & ~happy(X0)) | (~quiet(X0) & generous(X0)))) [nnf transformation 9]
48. ! [X0] : ((quiet(X0) | ~generous(X0) | ~tall(X0) | happy(X0)) & ((tall(X0) & ~happy(X0)) | (~quiet(X0) & generous(X0)))) [flattening 47]
52. ! [X0] : (((~brave(X0) | ~humble(X0)) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | (brave(X0) & humble(X0)))) [nnf transformation 11]
53. ! [X0] : ((~brave(X0) | ~humble(X0) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | (brave(X0) & humble(X0)))) [flattening 52]
54. ! [X0] : ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))) [nnf transformation 12]
55. ! [X0] : ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0))) [nnf transformation 15]
67. patient(X0) | calm(X0) | creative(X0) | old(X0) [cnf transformation 39]
68. ~creative(X0) | calm(X0) | ~old(X0) | patient(X0) [cnf transformation 39]
78. ~wise(X0) | ~old(X0) | quiet(X0) [cnf transformation 40]
79. ~creative(X0) | old(X0) [cnf transformation 28]
80. ~happy(X0) | old(X0) [cnf transformation 28]
81. ~rich(X0) | calm(X0) | ~kind(X0) [cnf transformation 41]
82. rich(X0) | kind(X0) | calm(X0) [cnf transformation 41]
84. happy(sK0) | ~patient(X1) | ~wise(X1) [cnf transformation 44]
87. ~humble(X0) | kind(X0) | creative(X0) [cnf transformation 46]
93. ~happy(X0) | ~quiet(X0) [cnf transformation 48]
98. ~old(X0) | rich(X0) | humble(X0) [cnf transformation 53]
102. ~humble(X0) | rich(X0) [cnf transformation 54]
103. ~rich(X0) | humble(X0) [cnf transformation 54]
104. ~patient(X0) | ~old(X0) [cnf transformation 35]
105. ~patient(X0) | creative(X0) [cnf transformation 35]
108. ~calm(X0) | wise(X0) [cnf transformation 55]
122. ~wise(lucy) [cnf transformation 24]
135. 3 <=> ! [X1] : (~patient(X1) | ~wise(X1)) [avatar definition]
136. ~wise(X1) | ~patient(X1) <- (3) [avatar component clause 135]
143. 5 <=> happy(sK0) [avatar definition]
145. happy(sK0) <- (5) [avatar component clause 143]
146. 3 | 5 [avatar split clause 84,143,135]
160. 9 <=> ! [X0] : ~patient(X0) [avatar definition]
161. ~patient(X0) <- (9) [avatar component clause 160]
241. humble(X1) | calm(X1) | kind(X1) [resolution 82,103]
306. calm(X1) | creative(X1) | old(X1) | creative(X1) [resolution 67,105]
311. calm(X1) | creative(X1) | old(X1) [duplicate literal removal 306]
312. calm(X1) | old(X1) [subsumption resolution 311,79]
381. wise(X2) | old(X2) [resolution 312,108]
396. calm(X0) | kind(X0) | kind(X0) | creative(X0) [resolution 241,87]
399. kind(X0) | calm(X0) | creative(X0) [duplicate literal removal 396]
432. old(lucy) [resolution 381,122]
437. old(X3) | ~patient(X3) <- (3) [resolution 381,136]
439. ~patient(X3) <- (3) [subsumption resolution 437,104]
440. 9 | ~3 [avatar split clause 439,135,160]
451. 45 <=> rich(lucy) [avatar definition]
452. ~rich(lucy) <- (~45) [avatar component clause 451]
453. rich(lucy) <- (45) [avatar component clause 451]
511. 53 <=> calm(lucy) [avatar definition]
512. ~calm(lucy) <- (~53) [avatar component clause 511]
513. calm(lucy) <- (53) [avatar component clause 511]
515. 54 <=> kind(lucy) [avatar definition]
516. ~kind(lucy) <- (~54) [avatar component clause 515]
522. 55 <=> creative(lucy) [avatar definition]
524. creative(lucy) <- (55) [avatar component clause 522]
529. calm(lucy) | ~kind(lucy) <- (45) [resolution 453,81]
614. wise(lucy) <- (53) [resolution 513,108]
618. $false <- (53) [subsumption resolution 614,122]
619. ~53 [avatar contradiction clause 618]
622. ~kind(lucy) <- (45, ~53) [subsumption resolution 529,512]
623. ~54 | ~45 | 53 [avatar split clause 622,511,451,515]
625. calm(lucy) | creative(lucy) <- (~54) [resolution 516,399]
627. calm(lucy) | ~old(lucy) | patient(lucy) <- (55) [resolution 524,68]
628. old(lucy) <- (55) [resolution 524,79]
629. ~old(lucy) | patient(lucy) <- (~53, 55) [subsumption resolution 627,512]
633. patient(lucy) <- (~53, 55) [subsumption resolution 629,628]
634. $false <- (9, ~53, 55) [subsumption resolution 633,161]
635. ~9 | 53 | ~55 [avatar contradiction clause 634]
638. creative(lucy) <- (~53, ~54) [subsumption resolution 625,512]
639. 55 | 53 | 54 [avatar split clause 638,515,511,522]
642. rich(lucy) | humble(lucy) [resolution 432,98]
646. humble(lucy) <- (~45) [subsumption resolution 642,452]
652. rich(lucy) <- (~45) [resolution 646,102]
653. $false <- (~45) [subsumption resolution 652,452]
654. 45 [avatar contradiction clause 653]
669. ~quiet(sK0) <- (5) [resolution 145,93]
671. old(sK0) <- (5) [resolution 145,80]
674. rich(sK0) | humble(sK0) <- (5) [resolution 671,98]
680. 61 <=> rich(sK0) [avatar definition]
682. rich(sK0) <- (61) [avatar component clause 680]
684. humble(sK0) <- (5) [subsumption resolution 674,103]
692. 62 <=> calm(sK0) [avatar definition]
694. calm(sK0) <- (62) [avatar component clause 692]
696. 63 <=> kind(sK0) [avatar definition]
697. ~kind(sK0) <- (~63) [avatar component clause 696]
700. calm(sK0) | ~kind(sK0) <- (61) [resolution 682,81]
702. ~63 | 62 | ~61 [avatar split clause 700,680,692,696]
703. kind(sK0) | creative(sK0) <- (5) [resolution 684,87]
704. rich(sK0) <- (5) [resolution 684,102]
705. creative(sK0) <- (5, ~63) [subsumption resolution 703,697]
709. calm(sK0) | ~old(sK0) | patient(sK0) <- (5, ~63) [resolution 705,68]
711. calm(sK0) | patient(sK0) <- (5, ~63) [subsumption resolution 709,671]
713. 64 <=> patient(sK0) [avatar definition]
715. patient(sK0) <- (64) [avatar component clause 713]
716. 64 | 62 | ~5 | 63 [avatar split clause 711,696,143,692,713]
719. wise(sK0) <- (62) [resolution 694,108]
726. ~old(sK0) | quiet(sK0) <- (62) [resolution 719,78]
732. quiet(sK0) <- (5, 62) [subsumption resolution 726,671]
733. $false <- (5, 62) [subsumption resolution 732,669]
734. ~5 | ~62 [avatar contradiction clause 733]
741. ~old(sK0) <- (64) [resolution 715,104]
743. $false <- (5, 64) [subsumption resolution 741,671]
744. ~5 | ~64 [avatar contradiction clause 743]
745. 61 | ~5 [avatar split clause 704,143,680]
751. $false [avatar sat refutation 146,440,619,623,635,639,654,702,716,734,744,745]
% SZS output end Proof for 5286720863722849616807913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is brave or not quiet then paul is not patient or happy and vice versa.
Everyone who is not creative is both not wise and not funny and vice versa.
Everyone who is either not funny or funny is either calm or kind.
If susan is either not curious or wise then someone is either funny or not humble and vice versa.
Everyone who is both brave and wise is either patient or not curious and vice versa.
If john is either tall or not strong then someone is both curious and not kind and vice versa.
Everyone who is either not humble or quiet is not creative or not strong and vice versa.
Everyone who is not wise is not curious.
If someone is happy or patient then someone is either not kind or not humble and vice versa.
Everyone who is both curious and old is not generous or not old and vice versa.
If someone is both not happy and not tall then someone is strong or patient.
If someone is both tall and creative then someone is either not curious or not old and vice versa.
If someone is not patient or tall then someone is rich or quiet.
Everyone who is both not generous and not calm is either not patient or calm.
If someone is not humble or tall then alice is both not quiet and quiet and vice versa.
If someone is both wise and kind then fred is either patient or kind and vice versa.
Someone is not kind or humble.
Lucy is quiet or kind.
Someone is both quiet and not funny.
Someone is brave.
Alice is either not humble or quiet.
Fred is either not old or old.
Paul is both funny and patient.
Someone is not calm. | John is quiet. | entailment | (((brave(paul)|~quiet(paul)))<=>((~patient(paul)|happy(paul))))&
(![X]:(~creative(X)<=>(~wise(X)&~funny(X))))&
(![X]:((~funny(X)<~>funny(X))=>(calm(X)<~>kind(X))))&
(((~curious(susan)<~>wise(susan)))<=>(?[X]:((funny(X)<~>~humble(X)))))&
(![X]:((brave(X)&wise(X))<=>(patient(X)<~>~curious(X))))&
(((tall(john)<~>~strong(john)))<=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~creative(X)|~strong(X))))&
(![X]:(~wise(X)=>~curious(X)))&
((?[X]:((happy(X)|patient(X))))<=>(?[X]:((~kind(X)<~>~humble(X)))))&
(![X]:((curious(X)&old(X))<=>(~generous(X)|~old(X))))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((strong(X)|patient(X)))))&
((?[X]:((tall(X)&creative(X))))<=>(?[X]:((~curious(X)<~>~old(X)))))&
((?[X]:((~patient(X)|tall(X))))=>(?[X]:((rich(X)|quiet(X)))))&
(![X]:((~generous(X)&~calm(X))=>(~patient(X)<~>calm(X))))&
((?[X]:((~humble(X)|tall(X))))<=>((~quiet(alice)&quiet(alice))))&
((?[X]:((wise(X)&kind(X))))<=>((patient(fred)<~>kind(fred))))&
(?[X]:((~kind(X)|humble(X))))&
((quiet(lucy)|kind(lucy)))&
(?[X]:((quiet(X)&~funny(X))))&
(?[X]:(brave(X)))&
((~humble(alice)<~>quiet(alice)))&
((~old(fred)<~>old(fred)))&
((funny(paul)&patient(paul)))&
(?[X]:(~calm(X))) | quiet(john) | [
"p5",
"p6",
"p8",
"p9",
"p11",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4126841014085180153789380
% SZS output start Proof for 4126841014085180153789380
6. (tall(john) <~> ~strong(john)) <=> ? [X0] : (~kind(X0) & curious(X0)) [input p5]
7. ! [X0] : ((~humble(X0) <~> quiet(X0)) <=> (~strong(X0) | ~creative(X0))) [input p6]
9. ? [X0] : (patient(X0) | happy(X0)) <=> ? [X0] : (~kind(X0) <~> ~humble(X0)) [input p8]
10. ! [X0] : ((old(X0) & curious(X0)) <=> (~old(X0) | ~generous(X0))) [input p9]
12. ? [X0] : (creative(X0) & tall(X0)) <=> ? [X0] : (~curious(X0) <~> ~old(X0)) [input p11]
15. ? [X0] : (tall(X0) | ~humble(X0)) <=> (quiet(alice) & ~quiet(alice)) [input p14]
23. patient(paul) & funny(paul) [input p22]
25. ~quiet(john) [input hypothesis]
26. ? [X0] : (patient(X0) | happy(X0)) <=> ? [X1] : (~kind(X1) <~> ~humble(X1)) [rectify 9]
28. ? [X0] : (creative(X0) & tall(X0)) <=> ? [X1] : (~curious(X1) <~> ~old(X1)) [rectify 12]
47. (((strong(john) | ~tall(john)) & (~strong(john) | tall(john))) | ! [X0] : (kind(X0) | ~curious(X0))) & (? [X0] : (~kind(X0) & curious(X0)) | ((tall(john) | strong(john)) & (~strong(john) | ~tall(john)))) [nnf transformation 6]
48. (((strong(john) | ~tall(john)) & (~strong(john) | tall(john))) | ! [X0] : (kind(X0) | ~curious(X0))) & (? [X1] : (~kind(X1) & curious(X1)) | ((tall(john) | strong(john)) & (~strong(john) | ~tall(john)))) [rectify 47]
49. ? [X1] : (~kind(X1) & curious(X1)) => (~kind(sK1) & curious(sK1)) [choice axiom]
50. (((strong(john) | ~tall(john)) & (~strong(john) | tall(john))) | ! [X0] : (kind(X0) | ~curious(X0))) & ((~kind(sK1) & curious(sK1)) | ((tall(john) | strong(john)) & (~strong(john) | ~tall(john)))) [skolemisation 48,49]
51. ! [X0] : ((((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (strong(X0) & creative(X0))) & ((~strong(X0) | ~creative(X0)) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))))) [nnf transformation 7]
52. ! [X0] : ((((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (strong(X0) & creative(X0))) & (~strong(X0) | ~creative(X0) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))))) [flattening 51]
53. (? [X0] : (patient(X0) | happy(X0)) | ! [X1] : ((~kind(X1) | humble(X1)) & (~humble(X1) | kind(X1)))) & (? [X1] : ((humble(X1) | kind(X1)) & (~humble(X1) | ~kind(X1))) | ! [X0] : (~patient(X0) & ~happy(X0))) [nnf transformation 26]
54. (? [X0] : (patient(X0) | happy(X0)) | ! [X1] : ((~kind(X1) | humble(X1)) & (~humble(X1) | kind(X1)))) & (? [X2] : ((humble(X2) | kind(X2)) & (~humble(X2) | ~kind(X2))) | ! [X3] : (~patient(X3) & ~happy(X3))) [rectify 53]
55. ? [X0] : (patient(X0) | happy(X0)) => (patient(sK2) | happy(sK2)) [choice axiom]
56. ? [X2] : ((humble(X2) | kind(X2)) & (~humble(X2) | ~kind(X2))) => ((humble(sK3) | kind(sK3)) & (~humble(sK3) | ~kind(sK3))) [choice axiom]
57. ((patient(sK2) | happy(sK2)) | ! [X1] : ((~kind(X1) | humble(X1)) & (~humble(X1) | kind(X1)))) & (((humble(sK3) | kind(sK3)) & (~humble(sK3) | ~kind(sK3))) | ! [X3] : (~patient(X3) & ~happy(X3))) [skolemisation 54,56,55]
58. ! [X0] : (((old(X0) & curious(X0)) | (old(X0) & generous(X0))) & ((~old(X0) | ~generous(X0)) | (~old(X0) | ~curious(X0)))) [nnf transformation 10]
59. ! [X0] : (((old(X0) & curious(X0)) | (old(X0) & generous(X0))) & (~old(X0) | ~generous(X0) | ~old(X0) | ~curious(X0))) [flattening 58]
63. (? [X0] : (creative(X0) & tall(X0)) | ! [X1] : ((~curious(X1) | old(X1)) & (~old(X1) | curious(X1)))) & (? [X1] : ((old(X1) | curious(X1)) & (~old(X1) | ~curious(X1))) | ! [X0] : (~creative(X0) | ~tall(X0))) [nnf transformation 28]
64. (? [X0] : (creative(X0) & tall(X0)) | ! [X1] : ((~curious(X1) | old(X1)) & (~old(X1) | curious(X1)))) & (? [X2] : ((old(X2) | curious(X2)) & (~old(X2) | ~curious(X2))) | ! [X3] : (~creative(X3) | ~tall(X3))) [rectify 63]
65. ? [X0] : (creative(X0) & tall(X0)) => (creative(sK5) & tall(sK5)) [choice axiom]
66. ? [X2] : ((old(X2) | curious(X2)) & (~old(X2) | ~curious(X2))) => ((old(sK6) | curious(sK6)) & (~old(sK6) | ~curious(sK6))) [choice axiom]
67. ((creative(sK5) & tall(sK5)) | ! [X1] : ((~curious(X1) | old(X1)) & (~old(X1) | curious(X1)))) & (((old(sK6) | curious(sK6)) & (~old(sK6) | ~curious(sK6))) | ! [X3] : (~creative(X3) | ~tall(X3))) [skolemisation 64,66,65]
69. (? [X0] : (tall(X0) | ~humble(X0)) | (~quiet(alice) | quiet(alice))) & ((quiet(alice) & ~quiet(alice)) | ! [X0] : (~tall(X0) & humble(X0))) [nnf transformation 15]
70. (? [X0] : (tall(X0) | ~humble(X0)) | ~quiet(alice) | quiet(alice)) & ((quiet(alice) & ~quiet(alice)) | ! [X0] : (~tall(X0) & humble(X0))) [flattening 69]
71. (? [X0] : (tall(X0) | ~humble(X0)) | ~quiet(alice) | quiet(alice)) & ((quiet(alice) & ~quiet(alice)) | ! [X1] : (~tall(X1) & humble(X1))) [rectify 70]
72. ? [X0] : (tall(X0) | ~humble(X0)) => (tall(sK7) | ~humble(sK7)) [choice axiom]
73. ((tall(sK7) | ~humble(sK7)) | ~quiet(alice) | quiet(alice)) & ((quiet(alice) & ~quiet(alice)) | ! [X1] : (~tall(X1) & humble(X1))) [skolemisation 71,72]
117. ~strong(john) | tall(john) | kind(X0) | ~curious(X0) [cnf transformation 50]
122. ~humble(X0) | quiet(X0) | strong(X0) [cnf transformation 52]
127. ~humble(sK3) | ~kind(sK3) | ~patient(X3) [cnf transformation 57]
136. old(X0) | old(X0) [cnf transformation 59]
140. tall(sK5) | ~old(X1) | curious(X1) [cnf transformation 67]
146. ~quiet(alice) | humble(X1) [cnf transformation 73]
147. ~quiet(alice) | ~tall(X1) [cnf transformation 73]
148. quiet(alice) | humble(X1) [cnf transformation 73]
149. quiet(alice) | ~tall(X1) [cnf transformation 73]
167. patient(paul) [cnf transformation 23]
169. ~quiet(john) [cnf transformation 25]
172. old(X0) [duplicate literal removal 136]
191. 4 <=> patient(paul) [avatar definition]
193. patient(paul) <- (4) [avatar component clause 191]
230. 11 <=> ! [X0] : (kind(X0) | ~curious(X0)) [avatar definition]
231. kind(X0) | ~curious(X0) <- (11) [avatar component clause 230]
233. 12 <=> tall(john) [avatar definition]
234. tall(john) <- (12) [avatar component clause 233]
237. 13 <=> strong(john) [avatar definition]
238. ~strong(john) <- (~13) [avatar component clause 237]
241. 11 | 12 | ~13 [avatar split clause 117,237,233,230]
271. 20 <=> ! [X3] : ~patient(X3) [avatar definition]
272. ~patient(X3) <- (20) [avatar component clause 271]
274. 21 <=> kind(sK3) [avatar definition]
275. ~kind(sK3) <- (~21) [avatar component clause 274]
278. 22 <=> humble(sK3) [avatar definition]
279. ~humble(sK3) <- (~22) [avatar component clause 278]
286. 20 | ~21 | ~22 [avatar split clause 127,278,274,271]
303. 27 <=> ! [X1] : curious(X1) [avatar definition]
304. curious(X1) <- (27) [avatar component clause 303]
310. tall(sK5) | curious(X1) [subsumption resolution 140,172]
312. 29 <=> tall(sK5) [avatar definition]
314. tall(sK5) <- (29) [avatar component clause 312]
315. 27 | 29 [avatar split clause 310,312,303]
326. 32 <=> ! [X1] : ~tall(X1) [avatar definition]
327. ~tall(X1) <- (32) [avatar component clause 326]
329. 33 <=> quiet(alice) [avatar definition]
332. 32 | 33 [avatar split clause 149,329,326]
334. 34 <=> ! [X1] : humble(X1) [avatar definition]
335. humble(X1) <- (34) [avatar component clause 334]
336. 34 | 33 [avatar split clause 148,329,334]
337. 32 | ~33 [avatar split clause 147,329,326]
338. 34 | ~33 [avatar split clause 146,329,334]
388. 4 [avatar split clause 167,191]
390. $false <- (~22, 34) [subsumption resolution 279,335]
391. 22 | ~34 [avatar contradiction clause 390]
392. $false <- (12, 32) [subsumption resolution 234,327]
393. ~12 | ~32 [avatar contradiction clause 392]
394. kind(X0) <- (11, 27) [subsumption resolution 231,304]
408. $false <- (4, 20) [resolution 272,193]
409. ~4 | ~20 [avatar contradiction clause 408]
410. $false <- (11, ~21, 27) [subsumption resolution 275,394]
411. ~11 | 21 | ~27 [avatar contradiction clause 410]
456. strong(X0) | quiet(X0) <- (34) [resolution 122,335]
457. quiet(john) <- (~13, 34) [resolution 456,238]
458. $false <- (~13, 34) [subsumption resolution 457,169]
459. 13 | ~34 [avatar contradiction clause 458]
460. $false <- (29, 32) [subsumption resolution 314,327]
461. ~29 | ~32 [avatar contradiction clause 460]
462. $false [avatar sat refutation 241,286,315,332,336,337,338,388,391,393,409,411,459,461]
% SZS output end Proof for 4126841014085180153789380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet is not kind or funny.
Everyone who is not quiet is either not kind or quiet.
If alice is both kind and wise then someone is not rich or old and vice versa.
Everyone who is not generous or tall is not wise or curious.
If someone is both not kind and wise then someone is wise or not generous and vice versa.
Everyone who is not kind is both not generous and strong.
If fred is both funny and not brave then someone is either not happy or creative.
Everyone who is both quiet and not curious is either humble or calm and vice versa.
If mary is not curious then alice is old or quiet and vice versa.
Everyone who is both kind and creative is kind and vice versa.
If fred is either not old or not happy then someone is either not calm or kind.
Everyone who is both quiet and strong is not happy or quiet and vice versa.
Everyone who is either not old or not funny is either strong or humble and vice versa.
If paul is both not humble and not old then lucy is patient or not tall and vice versa.
Everyone who is either kind or creative is either old or not tall and vice versa.
Everyone who is not creative is either not creative or creative and vice versa.
Alice is happy.
Someone is either not curious or brave.
Someone is either not generous or not calm.
Mary is wise.
Someone is not brave or wise.
Someone is brave or not quiet.
Alice is generous or patient. | Paul is not generous. | entailment | (![X]:(~quiet(X)=>(~kind(X)|funny(X))))&
(![X]:(~quiet(X)=>(~kind(X)<~>quiet(X))))&
(((kind(alice)&wise(alice)))<=>(?[X]:((~rich(X)|old(X)))))&
(![X]:((~generous(X)|tall(X))=>(~wise(X)|curious(X))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~generous(X)&strong(X))))&
(((funny(fred)&~brave(fred)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((quiet(X)&~curious(X))<=>(humble(X)<~>calm(X))))&
((~curious(mary))<=>((old(alice)|quiet(alice))))&
(![X]:((kind(X)&creative(X))<=>kind(X)))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))&
(((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>creative(X))))&
(happy(alice))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(wise(mary))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((generous(alice)|patient(alice))) | ~generous(paul) | [
"p5",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 191332187211496622636760
% SZS output start Proof for 191332187211496622636760
6. ! [X0] : (~kind(X0) => (strong(X0) & ~generous(X0))) [input p5]
10. ! [X0] : ((creative(X0) & kind(X0)) <=> kind(X0)) [input p9]
16. ! [X0] : (~creative(X0) <=> (~creative(X0) <~> creative(X0))) [input p15]
24. generous(paul) [input hypothesis]
31. ! [X0] : ((strong(X0) & ~generous(X0)) | kind(X0)) [ennf transformation 6]
53. ! [X0] : (((creative(X0) & kind(X0)) | ~kind(X0)) & (kind(X0) | (~creative(X0) | ~kind(X0)))) [nnf transformation 10]
54. ! [X0] : (((creative(X0) & kind(X0)) | ~kind(X0)) & (kind(X0) | ~creative(X0) | ~kind(X0))) [flattening 53]
64. ! [X0] : ((~creative(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | creative(X0))) [nnf transformation 16]
90. ~generous(X0) | kind(X0) [cnf transformation 31]
105. ~kind(X0) | creative(X0) [cnf transformation 54]
139. ~creative(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 64]
149. generous(paul) [cnf transformation 24]
153. ~creative(X0) [duplicate literal removal 139]
337. kind(paul) [resolution 90,149]
341. creative(paul) [resolution 105,337]
345. $false [subsumption resolution 341,153]
% SZS output end Proof for 191332187211496622636760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both curious and not happy then paul is not humble.
If someone is not tall or not humble then someone is both not kind and wise and vice versa.
Everyone who is both old and tall is not old and vice versa.
Everyone who is both patient and humble is both not strong and curious.
Everyone who is not calm is both not wise and not curious and vice versa.
Everyone who is either brave or not tall is funny and vice versa.
Everyone who is either kind or strong is not creative.
Everyone who is not wise or rich is either not calm or creative.
Everyone who is old or not calm is strong.
If susan is both patient and not happy then paul is happy or not strong.
If mary is both funny and not quiet then someone is both not humble and happy.
If lucy is patient or not creative then someone is generous and vice versa.
Everyone who is not quiet or not rich is brave or not curious and vice versa.
If someone is not wise or not old then fred is both quiet and not creative.
If someone is both not curious and not humble then someone is kind or not wise.
Everyone who is both not calm and not patient is not rich.
Fred is brave or tall.
John is humble or not creative.
Someone is either generous or not patient.
Someone is patient or not kind.
Someone is calm.
Lucy is either brave or not strong.
Mary is wise. | Susan is old. | entailment | (((curious(fred)&~happy(fred)))=>(~humble(paul)))&
((?[X]:((~tall(X)|~humble(X))))<=>(?[X]:((~kind(X)&wise(X)))))&
(![X]:((old(X)&tall(X))<=>~old(X)))&
(![X]:((patient(X)&humble(X))=>(~strong(X)&curious(X))))&
(![X]:(~calm(X)<=>(~wise(X)&~curious(X))))&
(![X]:((brave(X)<~>~tall(X))<=>funny(X)))&
(![X]:((kind(X)<~>strong(X))=>~creative(X)))&
(![X]:((~wise(X)|rich(X))=>(~calm(X)<~>creative(X))))&
(![X]:((old(X)|~calm(X))=>strong(X)))&
(((patient(susan)&~happy(susan)))=>((happy(paul)|~strong(paul))))&
(((funny(mary)&~quiet(mary)))=>(?[X]:((~humble(X)&happy(X)))))&
(((patient(lucy)|~creative(lucy)))<=>(?[X]:(generous(X))))&
(![X]:((~quiet(X)|~rich(X))<=>(brave(X)|~curious(X))))&
((?[X]:((~wise(X)|~old(X))))=>((quiet(fred)&~creative(fred))))&
((?[X]:((~curious(X)&~humble(X))))=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((~calm(X)&~patient(X))=>~rich(X)))&
((brave(fred)|tall(fred)))&
((humble(john)|~creative(john)))&
(?[X]:((generous(X)<~>~patient(X))))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:(calm(X)))&
((brave(lucy)<~>~strong(lucy)))&
(wise(mary)) | old(susan) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4945826558440522450725814
% SZS output start Proof for 4945826558440522450725814
3. ! [X0] : ((tall(X0) & old(X0)) <=> ~old(X0)) [input p2]
24. ~old(susan) [input hypothesis]
48. ! [X0] : (((tall(X0) & old(X0)) | old(X0)) & (~old(X0) | (~tall(X0) | ~old(X0)))) [nnf transformation 3]
49. ! [X0] : (((tall(X0) & old(X0)) | old(X0)) & (~old(X0) | ~tall(X0) | ~old(X0))) [flattening 48]
81. old(X0) | old(X0) [cnf transformation 49]
121. ~old(susan) [cnf transformation 24]
123. old(X0) [duplicate literal removal 81]
244. $false [subsumption resolution 121,123]
% SZS output end Proof for 4945826558440522450725814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or wise is not funny. If fred is either not funny or strong then someone is not happy or quiet. Everyone who is quiet is not calm or not kind and vice versa. If someone is either not brave or strong then someone is not old. If someone is not patient or patient then lucy is both wise and old and vice versa. If susan is both not creative and quiet then someone is patient and vice versa. Everyone who is not funny is not wise and vice versa. Everyone who is either not curious or not generous is not brave or brave. If someone is either not old or humble then alice is not funny and vice versa. If someone is patient then someone is not patient and vice versa. Everyone who is happy is either not brave or not patient. Everyone who is not old or old is either not quiet or patient. Everyone who is either kind or curious is kind and vice versa. Everyone who is both not funny and not patient is either not rich or calm and vice versa. Everyone who is either curious or humble is patient or not wise. If paul is funny or tall then someone is not kind. John is wise. Alice is not creative or not quiet. Someone is both quiet and happy. Someone is both funny and calm. Susan is either old or not brave. Fred is strong or happy. Paul is either tall or not humble. | Fred is funny. | neutral | (![X]:((creative(X)<~>wise(X))=>~funny(X)))&
(((~funny(fred)<~>strong(fred)))=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:(quiet(X)<=>(~calm(X)|~kind(X))))&
((?[X]:((~brave(X)<~>strong(X))))=>(?[X]:(~old(X))))&
((?[X]:((~patient(X)|patient(X))))<=>((wise(lucy)&old(lucy))))&
(((~creative(susan)&quiet(susan)))<=>(?[X]:(patient(X))))&
(![X]:(~funny(X)<=>~wise(X)))&
(![X]:((~curious(X)<~>~generous(X))=>(~brave(X)|brave(X))))&
((?[X]:((~old(X)<~>humble(X))))<=>(~funny(alice)))&
((?[X]:(patient(X)))<=>(?[X]:(~patient(X))))&
(![X]:(happy(X)=>(~brave(X)<~>~patient(X))))&
(![X]:((~old(X)|old(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((kind(X)<~>curious(X))<=>kind(X)))&
(![X]:((~funny(X)&~patient(X))<=>(~rich(X)<~>calm(X))))&
(![X]:((curious(X)<~>humble(X))=>(patient(X)|~wise(X))))&
(((funny(paul)|tall(paul)))=>(?[X]:(~kind(X))))&
(wise(john))&
((~creative(alice)|~quiet(alice)))&
(?[X]:((quiet(X)&happy(X))))&
(?[X]:((funny(X)&calm(X))))&
((old(susan)<~>~brave(susan)))&
((strong(fred)|happy(fred)))&
((tall(paul)<~>~humble(paul))) | funny(fred) | [] | null | 0 |
Everyone who is kind is both not tall and tall. If lucy is calm then paul is not generous. Everyone who is either not curious or rich is calm. Everyone who is rich is either not creative or not funny. If someone is either not brave or quiet then someone is curious. Everyone who is not wise or not patient is both funny and not funny and vice versa. If someone is kind then someone is rich or curious and vice versa. If fred is either not brave or rich then susan is both not kind and calm. If john is both strong and not calm then paul is either generous or not humble and vice versa. Everyone who is both not quiet and not happy is not curious and vice versa. Everyone who is both rich and not rich is either patient or not rich. If someone is both not rich and kind then someone is generous and vice versa. Everyone who is humble or not rich is creative or not rich and vice versa. Everyone who is patient is not calm or not generous and vice versa. If susan is both not kind and not quiet then susan is brave or strong and vice versa. Mary is not generous or humble. Mary is both funny and not kind. Someone is either tall or wise. Someone is not kind. Fred is brave or not happy. | Paul is humble. | entailment | (![X]:(kind(X)=>(~tall(X)&tall(X))))&
((calm(lucy))=>(~generous(paul)))&
(![X]:((~curious(X)<~>rich(X))=>calm(X)))&
(![X]:(rich(X)=>(~creative(X)<~>~funny(X))))&
((?[X]:((~brave(X)<~>quiet(X))))=>(?[X]:(curious(X))))&
(![X]:((~wise(X)|~patient(X))<=>(funny(X)&~funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((rich(X)|curious(X)))))&
(((~brave(fred)<~>rich(fred)))=>((~kind(susan)&calm(susan))))&
(((strong(john)&~calm(john)))<=>((generous(paul)<~>~humble(paul))))&
(![X]:((~quiet(X)&~happy(X))<=>~curious(X)))&
(![X]:((rich(X)&~rich(X))=>(patient(X)<~>~rich(X))))&
((?[X]:((~rich(X)&kind(X))))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|~rich(X))<=>(creative(X)|~rich(X))))&
(![X]:(patient(X)<=>(~calm(X)|~generous(X))))&
(((~kind(susan)&~quiet(susan)))<=>((brave(susan)|strong(susan))))&
((~generous(mary)|humble(mary)))&
((funny(mary)&~kind(mary)))&
(?[X]:((tall(X)<~>wise(X))))&
(?[X]:(~kind(X)))&
((brave(fred)|~happy(fred))) | humble(paul) | [
"p0",
"p2",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4888544785310250763416761
% SZS output start Proof for 4888544785310250763416761
1. ! [X0] : (kind(X0) => (tall(X0) & ~tall(X0))) [input p0]
3. ! [X0] : ((~curious(X0) <~> rich(X0)) => calm(X0)) [input p2]
7. ? [X0] : kind(X0) <=> ? [X0] : (curious(X0) | rich(X0)) [input p6]
9. (~calm(john) & strong(john)) <=> (generous(paul) <~> ~humble(paul)) [input p8]
12. ? [X0] : (kind(X0) & ~rich(X0)) <=> ? [X0] : generous(X0) [input p11]
21. ~humble(paul) [input hypothesis]
23. ? [X0] : kind(X0) <=> ? [X1] : (curious(X1) | rich(X1)) [rectify 7]
24. ? [X0] : (kind(X0) & ~rich(X0)) <=> ? [X1] : generous(X1) [rectify 12]
25. ! [X0] : ((tall(X0) & ~tall(X0)) | ~kind(X0)) [ennf transformation 1]
27. ! [X0] : (calm(X0) | (~curious(X0) <=> rich(X0))) [ennf transformation 3]
33. ! [X0] : (calm(X0) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) [nnf transformation 27]
41. (? [X0] : kind(X0) | ! [X1] : (~curious(X1) & ~rich(X1))) & (? [X1] : (curious(X1) | rich(X1)) | ! [X0] : ~kind(X0)) [nnf transformation 23]
42. (? [X0] : kind(X0) | ! [X1] : (~curious(X1) & ~rich(X1))) & (? [X2] : (curious(X2) | rich(X2)) | ! [X3] : ~kind(X3)) [rectify 41]
43. ? [X0] : kind(X0) => kind(sK1) [choice axiom]
44. ? [X2] : (curious(X2) | rich(X2)) => (curious(sK2) | rich(sK2)) [choice axiom]
45. (kind(sK1) | ! [X1] : (~curious(X1) & ~rich(X1))) & ((curious(sK2) | rich(sK2)) | ! [X3] : ~kind(X3)) [skolemisation 42,44,43]
47. ((~calm(john) & strong(john)) | ((generous(paul) | humble(paul)) & (~humble(paul) | ~generous(paul)))) & (((humble(paul) | ~generous(paul)) & (~humble(paul) | generous(paul))) | (calm(john) | ~strong(john))) [nnf transformation 9]
48. ((~calm(john) & strong(john)) | ((generous(paul) | humble(paul)) & (~humble(paul) | ~generous(paul)))) & (((humble(paul) | ~generous(paul)) & (~humble(paul) | generous(paul))) | calm(john) | ~strong(john)) [flattening 47]
52. (? [X0] : (kind(X0) & ~rich(X0)) | ! [X1] : ~generous(X1)) & (? [X1] : generous(X1) | ! [X0] : (~kind(X0) | rich(X0))) [nnf transformation 24]
53. (? [X0] : (kind(X0) & ~rich(X0)) | ! [X1] : ~generous(X1)) & (? [X2] : generous(X2) | ! [X3] : (~kind(X3) | rich(X3))) [rectify 52]
54. ? [X0] : (kind(X0) & ~rich(X0)) => (kind(sK3) & ~rich(sK3)) [choice axiom]
55. ? [X2] : generous(X2) => generous(sK4) [choice axiom]
56. ((kind(sK3) & ~rich(sK3)) | ! [X1] : ~generous(X1)) & (generous(sK4) | ! [X3] : (~kind(X3) | rich(X3))) [skolemisation 53,55,54]
68. ~tall(X0) | ~kind(X0) [cnf transformation 25]
69. ~kind(X0) | tall(X0) [cnf transformation 25]
71. rich(X0) | calm(X0) | curious(X0) [cnf transformation 33]
83. kind(sK1) | ~rich(X1) [cnf transformation 45]
84. kind(sK1) | ~curious(X1) [cnf transformation 45]
94. ~calm(john) | generous(paul) | humble(paul) [cnf transformation 48]
102. kind(sK3) | ~generous(X1) [cnf transformation 56]
122. ~humble(paul) [cnf transformation 21]
125. ~kind(X0) [subsumption resolution 68,69]
131. 2 <=> generous(paul) [avatar definition]
132. generous(paul) <- (2) [avatar component clause 131]
149. ~curious(X1) [subsumption resolution 84,125]
150. ~rich(X1) [subsumption resolution 83,125]
162. 8 <=> humble(paul) [avatar definition]
166. 9 <=> calm(john) [avatar definition]
168. ~calm(john) <- (~9) [avatar component clause 166]
169. 8 | 2 | ~9 [avatar split clause 94,166,131,162]
181. ~generous(X1) [subsumption resolution 102,125]
194. ~8 [avatar split clause 122,162]
197. $false <- (2) [subsumption resolution 132,181]
198. ~2 [avatar contradiction clause 197]
202. calm(X0) | curious(X0) [resolution 71,150]
203. calm(X0) [subsumption resolution 202,149]
207. $false <- (~9) [resolution 203,168]
208. 9 [avatar contradiction clause 207]
210. $false [avatar sat refutation 169,194,198,208]
% SZS output end Proof for 4888544785310250763416761
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or wise then someone is both not old and curious and vice versa.
Everyone who is either brave or not funny is not rich or curious and vice versa.
Everyone who is brave or calm is old or rich and vice versa.
Everyone who is both calm and not humble is not generous or creative.
Everyone who is generous or not strong is patient or humble.
If someone is either not humble or not patient then someone is brave or not funny.
Everyone who is either generous or not old is not old or brave.
Everyone who is not quiet or not patient is either not kind or generous and vice versa.
Everyone who is happy or not quiet is not kind and vice versa.
Everyone who is both not happy and creative is either not patient or not happy.
If someone is curious or quiet then mary is calm or funny and vice versa.
Everyone who is not brave is either brave or not happy and vice versa.
Everyone who is not old is either generous or not patient.
If lucy is both patient and not happy then paul is either quiet or not humble.
Everyone who is rich is patient and vice versa.
Everyone who is both not wise and not generous is both happy and generous.
Susan is either quiet or not quiet.
Someone is curious or not tall.
Someone is both creative and not quiet.
Someone is both wise and strong.
Fred is both not funny and quiet.
Paul is either strong or not calm.
Someone is both brave and calm. | Fred is old. | entailment | ((?[X]:((kind(X)<~>wise(X))))<=>(?[X]:((~old(X)&curious(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(~rich(X)|curious(X))))&
(![X]:((brave(X)|calm(X))<=>(old(X)|rich(X))))&
(![X]:((calm(X)&~humble(X))=>(~generous(X)|creative(X))))&
(![X]:((generous(X)|~strong(X))=>(patient(X)|humble(X))))&
((?[X]:((~humble(X)<~>~patient(X))))=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((generous(X)<~>~old(X))=>(~old(X)|brave(X))))&
(![X]:((~quiet(X)|~patient(X))<=>(~kind(X)<~>generous(X))))&
(![X]:((happy(X)|~quiet(X))<=>~kind(X)))&
(![X]:((~happy(X)&creative(X))=>(~patient(X)<~>~happy(X))))&
((?[X]:((curious(X)|quiet(X))))<=>((calm(mary)|funny(mary))))&
(![X]:(~brave(X)<=>(brave(X)<~>~happy(X))))&
(![X]:(~old(X)=>(generous(X)<~>~patient(X))))&
(((patient(lucy)&~happy(lucy)))=>((quiet(paul)<~>~humble(paul))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((~wise(X)&~generous(X))=>(happy(X)&generous(X))))&
((quiet(susan)<~>~quiet(susan)))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(?[X]:((wise(X)&strong(X))))&
((~funny(fred)&quiet(fred)))&
((strong(paul)<~>~calm(paul)))&
(?[X]:((brave(X)&calm(X)))) | old(fred) | [
"p7",
"p8",
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1823865893553530529353349
% SZS output start Proof for 1823865893553530529353349
8. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (~kind(X0) <~> generous(X0))) [input p7]
9. ! [X0] : ((~quiet(X0) | happy(X0)) <=> ~kind(X0)) [input p8]
12. ! [X0] : (~brave(X0) <=> (brave(X0) <~> ~happy(X0))) [input p11]
13. ! [X0] : (~old(X0) => (generous(X0) <~> ~patient(X0))) [input p12]
21. quiet(fred) & ~funny(fred) [input p20]
24. ~old(fred) [input hypothesis]
37. ! [X0] : ((generous(X0) <~> ~patient(X0)) | old(X0)) [ennf transformation 13]
56. ! [X0] : (((~patient(X0) | ~quiet(X0)) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (patient(X0) & quiet(X0)))) [nnf transformation 8]
57. ! [X0] : ((~patient(X0) | ~quiet(X0) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (patient(X0) & quiet(X0)))) [flattening 56]
58. ! [X0] : (((~quiet(X0) | happy(X0)) | kind(X0)) & (~kind(X0) | (quiet(X0) & ~happy(X0)))) [nnf transformation 9]
59. ! [X0] : ((~quiet(X0) | happy(X0) | kind(X0)) & (~kind(X0) | (quiet(X0) & ~happy(X0)))) [flattening 58]
66. ! [X0] : ((~brave(X0) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | brave(X0))) [nnf transformation 12]
67. ! [X0] : (((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | old(X0)) [nnf transformation 37]
102. ~kind(X0) | generous(X0) | patient(X0) [cnf transformation 57]
106. ~quiet(X0) | ~patient(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 57]
109. ~quiet(X0) | happy(X0) | kind(X0) [cnf transformation 59]
116. ~happy(X0) | brave(X0) | brave(X0) [cnf transformation 66]
118. ~brave(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 66]
120. ~patient(X0) | generous(X0) | old(X0) [cnf transformation 67]
121. ~generous(X0) | patient(X0) | old(X0) [cnf transformation 67]
135. quiet(fred) [cnf transformation 21]
140. ~old(fred) [cnf transformation 24]
142. ~happy(X0) | brave(X0) [duplicate literal removal 116]
143. ~happy(X0) | ~brave(X0) [duplicate literal removal 118]
219. ~happy(X0) [subsumption resolution 142,143]
341. happy(fred) | kind(fred) [resolution 109,135]
343. kind(fred) [subsumption resolution 341,219]
344. generous(fred) | patient(fred) [resolution 343,102]
348. 35 <=> patient(fred) [avatar definition]
350. patient(fred) <- (35) [avatar component clause 348]
352. 36 <=> generous(fred) [avatar definition]
354. generous(fred) <- (36) [avatar component clause 352]
355. 35 | 36 [avatar split clause 344,352,348]
373. generous(fred) | old(fred) <- (35) [resolution 350,120]
375. generous(fred) <- (35) [subsumption resolution 373,140]
376. 36 | ~35 [avatar split clause 375,348,352]
384. patient(fred) | old(fred) <- (36) [resolution 354,121]
470. ~patient(fred) | ~kind(fred) | ~generous(fred) [resolution 106,135]
479. ~patient(fred) | ~generous(fred) [subsumption resolution 470,343]
480. ~patient(fred) <- (36) [subsumption resolution 479,354]
481. ~35 | ~36 [avatar split clause 480,352,348]
483. patient(fred) <- (36) [subsumption resolution 384,140]
484. 35 | ~36 [avatar split clause 483,352,348]
485. $false [avatar sat refutation 355,376,481,484]
% SZS output end Proof for 1823865893553530529353349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not tall is calm or not funny.
Everyone who is funny or brave is not kind or not happy and vice versa.
Everyone who is either not funny or not rich is both not quiet and strong.
Everyone who is not patient is funny or rich and vice versa.
If alice is both humble and old then someone is strong.
If lucy is not kind then fred is generous and vice versa.
If fred is both strong and happy then lucy is either not wise or brave.
Everyone who is wise or patient is either wise or not tall.
If john is not quiet or not creative then fred is both not old and not strong.
Everyone who is both not quiet and not rich is creative and vice versa.
If someone is generous or not quiet then someone is both patient and not wise.
If alice is either patient or curious then someone is kind.
If susan is wise then mary is old or not funny and vice versa.
If someone is creative then someone is either humble or not generous and vice versa.
Everyone who is either not rich or not old is either not generous or happy and vice versa.
Everyone who is kind or not kind is either rich or not wise.
Alice is rich.
Someone is not creative.
Someone is either not strong or not creative.
Someone is old or not humble.
Someone is both humble and not rich.
Someone is either brave or not rich.
Someone is either generous or kind.
Mary is both brave and not calm. | Susan is not tall. | contradiction | (![X]:((~calm(X)|~tall(X))=>(calm(X)|~funny(X))))&
(![X]:((funny(X)|brave(X))<=>(~kind(X)|~happy(X))))&
(![X]:((~funny(X)<~>~rich(X))=>(~quiet(X)&strong(X))))&
(![X]:(~patient(X)<=>(funny(X)|rich(X))))&
(((humble(alice)&old(alice)))=>(?[X]:(strong(X))))&
((~kind(lucy))<=>(generous(fred)))&
(((strong(fred)&happy(fred)))=>((~wise(lucy)<~>brave(lucy))))&
(![X]:((wise(X)|patient(X))=>(wise(X)<~>~tall(X))))&
(((~quiet(john)|~creative(john)))=>((~old(fred)&~strong(fred))))&
(![X]:((~quiet(X)&~rich(X))<=>creative(X)))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((patient(X)&~wise(X)))))&
(((patient(alice)<~>curious(alice)))=>(?[X]:(kind(X))))&
((wise(susan))<=>((old(mary)|~funny(mary))))&
((?[X]:(creative(X)))<=>(?[X]:((humble(X)<~>~generous(X)))))&
(![X]:((~rich(X)<~>~old(X))<=>(~generous(X)<~>happy(X))))&
(![X]:((kind(X)|~kind(X))=>(rich(X)<~>~wise(X))))&
(rich(alice))&
(?[X]:(~creative(X)))&
(?[X]:((~strong(X)<~>~creative(X))))&
(?[X]:((old(X)|~humble(X))))&
(?[X]:((humble(X)&~rich(X))))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:((generous(X)<~>kind(X))))&
((brave(mary)&~calm(mary))) | ~tall(susan) | [
"p0",
"p7",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1310629930706213703127155
% SZS output start Proof for 1310629930706213703127155
1. ! [X0] : ((~tall(X0) | ~calm(X0)) => (~funny(X0) | calm(X0))) [input p0]
8. ! [X0] : ((patient(X0) | wise(X0)) => (wise(X0) <~> ~tall(X0))) [input p7]
13. wise(susan) <=> (~funny(mary) | old(mary)) [input p12]
24. ~calm(mary) & brave(mary) [input p23]
25. ~tall(susan) [input hypothesis]
28. ! [X0] : ((~funny(X0) | calm(X0)) | (tall(X0) & calm(X0))) [ennf transformation 1]
29. ! [X0] : (~funny(X0) | calm(X0) | (tall(X0) & calm(X0))) [flattening 28]
35. ! [X0] : ((wise(X0) <~> ~tall(X0)) | (~patient(X0) & ~wise(X0))) [ennf transformation 8]
49. ! [X0] : (((tall(X0) | ~wise(X0)) & (~tall(X0) | wise(X0))) | (~patient(X0) & ~wise(X0))) [nnf transformation 35]
58. (wise(susan) | (funny(mary) & ~old(mary))) & ((~funny(mary) | old(mary)) | ~wise(susan)) [nnf transformation 13]
59. (wise(susan) | (funny(mary) & ~old(mary))) & (~funny(mary) | old(mary) | ~wise(susan)) [flattening 58]
82. ~funny(X0) | calm(X0) | calm(X0) [cnf transformation 29]
102. tall(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 49]
119. wise(susan) | funny(mary) [cnf transformation 59]
148. ~calm(mary) [cnf transformation 24]
149. ~tall(susan) [cnf transformation 25]
150. ~wise(X0) | tall(X0) [duplicate literal removal 102]
151. ~funny(X0) | calm(X0) [duplicate literal removal 82]
242. 20 <=> funny(mary) [avatar definition]
244. funny(mary) <- (20) [avatar component clause 242]
246. 21 <=> wise(susan) [avatar definition]
248. wise(susan) <- (21) [avatar component clause 246]
249. 20 | 21 [avatar split clause 119,246,242]
332. calm(mary) <- (20) [resolution 151,244]
333. $false <- (20) [subsumption resolution 332,148]
334. ~20 [avatar contradiction clause 333]
335. tall(susan) <- (21) [resolution 248,150]
336. $false <- (21) [subsumption resolution 335,149]
337. ~21 [avatar contradiction clause 336]
338. $false [avatar sat refutation 249,334,337]
% SZS output end Proof for 1310629930706213703127155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
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