premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
Everyone who is humble is both happy and not wise.
Everyone who is either not happy or brave is either happy or not wise and vice versa.
If someone is tall then mary is both strong and not calm and vice versa.
Everyone who is old is strong or quiet.
Everyone who is either not curious or not happy is not kind and vice versa.
Everyone who is both not humble and not kind is both funny and not brave.
If mary is rich or brave then paul is quiet or not funny and vice versa.
If someone is quiet or not generous then lucy is either curious or not happy and vice versa.
If someone is creative then paul is either humble or not humble and vice versa.
Susan is creative or not wise.
Someone is brave or happy.
Alice is creative or funny.
Susan is curious or not brave.
Paul is either brave or not rich.
Alice is not funny or kind. | Susan is not rich. | entailment | ((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
(![X]:(humble(X)=>(happy(X)&~wise(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:(tall(X)))<=>((strong(mary)&~calm(mary))))&
(![X]:(old(X)=>(strong(X)|quiet(X))))&
(![X]:((~curious(X)<~>~happy(X))<=>~kind(X)))&
(![X]:((~humble(X)&~kind(X))=>(funny(X)&~brave(X))))&
(((rich(mary)|brave(mary)))<=>((quiet(paul)|~funny(paul))))&
((?[X]:((quiet(X)|~generous(X))))<=>((curious(lucy)<~>~happy(lucy))))&
((?[X]:(creative(X)))<=>((humble(paul)<~>~humble(paul))))&
((creative(susan)|~wise(susan)))&
(?[X]:((brave(X)|happy(X))))&
((creative(alice)|funny(alice)))&
((curious(susan)|~brave(susan)))&
((brave(paul)<~>~rich(paul)))&
((~funny(alice)|kind(alice))) | ~rich(susan) | [
"p0",
"p5",
"p6",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 4856323950340304527307271
% SZS output start Proof for 4856323950340304527307271
1. ? [X0] : (rich(X0) | brave(X0)) => (~happy(john) & ~funny(john)) [input p0]
6. ! [X0] : (~curious(X0) <=> (~kind(X0) & old(X0))) [input p5]
7. ! [X0] : (humble(X0) => (~wise(X0) & happy(X0))) [input p6]
11. ! [X0] : ((~curious(X0) <~> ~happy(X0)) <=> ~kind(X0)) [input p10]
12. ! [X0] : ((~kind(X0) & ~humble(X0)) => (~brave(X0) & funny(X0))) [input p11]
22. rich(susan) [input hypothesis]
23. (~happy(john) & ~funny(john)) | ! [X0] : (~rich(X0) & ~brave(X0)) [ennf transformation 1]
24. ! [X0] : ((~wise(X0) & happy(X0)) | ~humble(X0)) [ennf transformation 7]
27. ! [X0] : ((~brave(X0) & funny(X0)) | (kind(X0) | humble(X0))) [ennf transformation 12]
28. ! [X0] : ((~brave(X0) & funny(X0)) | kind(X0) | humble(X0)) [flattening 27]
35. ! [X0] : ((~curious(X0) | (kind(X0) | ~old(X0))) & ((~kind(X0) & old(X0)) | curious(X0))) [nnf transformation 6]
36. ! [X0] : ((~curious(X0) | kind(X0) | ~old(X0)) & ((~kind(X0) & old(X0)) | curious(X0))) [flattening 35]
43. ! [X0] : ((((happy(X0) | curious(X0)) & (~happy(X0) | ~curious(X0))) | kind(X0)) & (~kind(X0) | ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0))))) [nnf transformation 11]
58. ~funny(john) | ~rich(X0) [cnf transformation 23]
60. ~happy(john) | ~rich(X0) [cnf transformation 23]
78. ~kind(X0) | curious(X0) [cnf transformation 36]
80. ~humble(X0) | happy(X0) [cnf transformation 24]
95. ~kind(X0) | ~curious(X0) | happy(X0) [cnf transformation 43]
98. kind(X0) | funny(X0) | humble(X0) [cnf transformation 28]
121. rich(susan) [cnf transformation 22]
129. 1 <=> ! [X0] : ~rich(X0) [avatar definition]
130. ~rich(X0) <- (1) [avatar component clause 129]
132. 2 <=> happy(john) [avatar definition]
134. ~happy(john) <- (~2) [avatar component clause 132]
135. 1 | ~2 [avatar split clause 60,132,129]
141. 4 <=> funny(john) [avatar definition]
143. ~funny(john) <- (~4) [avatar component clause 141]
144. 1 | ~4 [avatar split clause 58,141,129]
189. ~kind(X0) | happy(X0) [subsumption resolution 95,78]
353. funny(X0) | humble(X0) | happy(X0) [resolution 98,189]
391. happy(X0) | funny(X0) [subsumption resolution 353,80]
414. $false <- (1) [resolution 130,121]
415. ~1 [avatar contradiction clause 414]
444. funny(john) <- (~2) [resolution 391,134]
445. $false <- (~2, ~4) [subsumption resolution 444,143]
446. 2 | 4 [avatar contradiction clause 445]
447. $false [avatar sat refutation 135,144,415,446]
% SZS output end Proof for 4856323950340304527307271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise then susan is either strong or wise and vice versa.
Everyone who is not wise is humble and vice versa.
If lucy is both humble and not patient then someone is generous or not curious.
Everyone who is both not happy and not calm is both not wise and rich.
Everyone who is brave is creative or patient and vice versa.
If lucy is either not brave or generous then lucy is both curious and calm and vice versa.
Everyone who is not old or not generous is either funny or curious and vice versa.
If someone is either not tall or not wise then susan is tall or rich.
Everyone who is brave is tall and vice versa.
Everyone who is old is both tall and not old and vice versa.
If alice is either not calm or wise then someone is either not kind or kind.
Everyone who is quiet is kind.
Everyone who is not funny or generous is not happy or not strong and vice versa.
Everyone who is generous or curious is creative or not happy.
Everyone who is either kind or not kind is not curious and vice versa.
Lucy is either not humble or not strong.
Someone is either rich or strong.
Someone is either not strong or not creative.
Someone is either happy or not funny.
Mary is happy.
Mary is funny.
Mary is not calm. | Lucy is humble. | neutral | ((?[X]:(wise(X)))<=>((strong(susan)<~>wise(susan))))&
(![X]:(~wise(X)<=>humble(X)))&
(((humble(lucy)&~patient(lucy)))=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((~happy(X)&~calm(X))=>(~wise(X)&rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
(((~brave(lucy)<~>generous(lucy)))<=>((curious(lucy)&calm(lucy))))&
(![X]:((~old(X)|~generous(X))<=>(funny(X)<~>curious(X))))&
((?[X]:((~tall(X)<~>~wise(X))))=>((tall(susan)|rich(susan))))&
(![X]:(brave(X)<=>tall(X)))&
(![X]:(old(X)<=>(tall(X)&~old(X))))&
(((~calm(alice)<~>wise(alice)))=>(?[X]:((~kind(X)<~>kind(X)))))&
(![X]:(quiet(X)=>kind(X)))&
(![X]:((~funny(X)|generous(X))<=>(~happy(X)|~strong(X))))&
(![X]:((generous(X)|curious(X))=>(creative(X)|~happy(X))))&
(![X]:((kind(X)<~>~kind(X))<=>~curious(X)))&
((~humble(lucy)<~>~strong(lucy)))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((~strong(X)<~>~creative(X))))&
(?[X]:((happy(X)<~>~funny(X))))&
(happy(mary))&
(funny(mary))&
(~calm(mary)) | humble(lucy) | []
| null | 0 |
If someone is not brave then mary is both happy and creative and vice versa.
Everyone who is either not old or not funny is funny or not generous and vice versa.
If fred is humble or kind then someone is kind and vice versa.
If someone is not quiet or not generous then someone is quiet and vice versa.
If alice is both not funny and quiet then someone is either brave or happy and vice versa.
Everyone who is both happy and quiet is both happy and not rich and vice versa.
Everyone who is not rich is not wise or not strong and vice versa.
If alice is both not patient and not quiet then someone is brave or funny.
Everyone who is either not happy or not old is either not generous or not tall.
If susan is both not brave and not quiet then someone is either not generous or funny and vice versa.
If fred is both curious and brave then someone is wise or calm and vice versa.
Everyone who is calm or not calm is calm or brave.
Everyone who is patient is tall.
Everyone who is both not calm and not strong is patient.
Everyone who is not strong or not happy is not wise.
If someone is both old and generous then someone is happy or tall and vice versa.
John is brave or old.
Paul is calm or tall.
Fred is both not tall and not creative.
Someone is both not creative and not calm.
Someone is not rich or not creative.
Someone is either not curious or not creative.
Lucy is either wise or calm.
Someone is tall or curious. | Fred is not tall. | entailment | ((?[X]:(~brave(X)))<=>((happy(mary)&creative(mary))))&
(![X]:((~old(X)<~>~funny(X))<=>(funny(X)|~generous(X))))&
(((humble(fred)|kind(fred)))<=>(?[X]:(kind(X))))&
((?[X]:((~quiet(X)|~generous(X))))<=>(?[X]:(quiet(X))))&
(((~funny(alice)&quiet(alice)))<=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:((happy(X)&quiet(X))<=>(happy(X)&~rich(X))))&
(![X]:(~rich(X)<=>(~wise(X)|~strong(X))))&
(((~patient(alice)&~quiet(alice)))=>(?[X]:((brave(X)|funny(X)))))&
(![X]:((~happy(X)<~>~old(X))=>(~generous(X)<~>~tall(X))))&
(((~brave(susan)&~quiet(susan)))<=>(?[X]:((~generous(X)<~>funny(X)))))&
(((curious(fred)&brave(fred)))<=>(?[X]:((wise(X)|calm(X)))))&
(![X]:((calm(X)|~calm(X))=>(calm(X)|brave(X))))&
(![X]:(patient(X)=>tall(X)))&
(![X]:((~calm(X)&~strong(X))=>patient(X)))&
(![X]:((~strong(X)|~happy(X))=>~wise(X)))&
((?[X]:((old(X)&generous(X))))<=>(?[X]:((happy(X)|tall(X)))))&
((brave(john)|old(john)))&
((calm(paul)|tall(paul)))&
((~tall(fred)&~creative(fred)))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((~curious(X)<~>~creative(X))))&
((wise(lucy)<~>calm(lucy)))&
(?[X]:((tall(X)|curious(X)))) | ~tall(fred) | [
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 4511354595058200281518117
% SZS output start Proof for 4511354595058200281518117
19. ~creative(fred) & ~tall(fred) [input p18]
25. tall(fred) [input hypothesis]
148. ~tall(fred) [cnf transformation 19]
158. tall(fred) [cnf transformation 25]
395. $false [subsumption resolution 158,148]
% SZS output end Proof for 4511354595058200281518117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not 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 curious or rich is either not wise or not generous.
Everyone who is not calm or not patient is both not generous and wise.
If someone is old then susan is wise or not brave.
If someone is both funny and not rich then fred is either generous or kind and vice versa.
Everyone who is not rich is either not humble or not generous.
If john is either not humble or rich then mary is generous.
Everyone who is not curious or funny is kind or not curious and vice versa.
Everyone who is either not creative or not funny is not kind or tall and vice versa.
If lucy is either brave or not generous then someone is creative or calm and vice versa.
If paul is either not tall or not generous then someone is curious or brave and vice versa.
If susan is quiet then someone is not tall.
Everyone who is both kind and old is either not patient or not tall and vice versa.
If someone is wise or rich then someone is not wise or not tall and vice versa.
If someone is either not creative or not kind then john is brave or calm and vice versa.
Alice is either not quiet or not generous.
Someone is not creative.
Someone is either humble or kind.
Lucy is both happy and not calm.
Susan is kind.
Alice is wise or kind.
Someone is both not old and humble. | Lucy is brave. | contradiction | (![X]:((~calm(X)|~tall(X))=>(calm(X)|~funny(X))))&
(![X]:((funny(X)|brave(X))<=>(~kind(X)|~happy(X))))&
(![X]:((curious(X)<~>rich(X))=>(~wise(X)<~>~generous(X))))&
(![X]:((~calm(X)|~patient(X))=>(~generous(X)&wise(X))))&
((?[X]:(old(X)))=>((wise(susan)|~brave(susan))))&
((?[X]:((funny(X)&~rich(X))))<=>((generous(fred)<~>kind(fred))))&
(![X]:(~rich(X)=>(~humble(X)<~>~generous(X))))&
(((~humble(john)<~>rich(john)))=>(generous(mary)))&
(![X]:((~curious(X)|funny(X))<=>(kind(X)|~curious(X))))&
(![X]:((~creative(X)<~>~funny(X))<=>(~kind(X)|tall(X))))&
(((brave(lucy)<~>~generous(lucy)))<=>(?[X]:((creative(X)|calm(X)))))&
(((~tall(paul)<~>~generous(paul)))<=>(?[X]:((curious(X)|brave(X)))))&
((quiet(susan))=>(?[X]:(~tall(X))))&
(![X]:((kind(X)&old(X))<=>(~patient(X)<~>~tall(X))))&
((?[X]:((wise(X)|rich(X))))<=>(?[X]:((~wise(X)|~tall(X)))))&
((?[X]:((~creative(X)<~>~kind(X))))<=>((brave(john)|calm(john))))&
((~quiet(alice)<~>~generous(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((humble(X)<~>kind(X))))&
((happy(lucy)&~calm(lucy)))&
(kind(susan))&
((wise(alice)|kind(alice)))&
(?[X]:((~old(X)&humble(X)))) | brave(lucy) | [
"p0",
"p3",
"p9",
"p10",
"p11",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 4091356068768256558118726
% SZS output start Proof for 4091356068768256558118726
1. ! [X0] : ((~tall(X0) | ~calm(X0)) => (~funny(X0) | calm(X0))) [input p0]
4. ! [X0] : ((~patient(X0) | ~calm(X0)) => (wise(X0) & ~generous(X0))) [input p3]
10. ! [X0] : ((~creative(X0) <~> ~funny(X0)) <=> (tall(X0) | ~kind(X0))) [input p9]
11. (brave(lucy) <~> ~generous(lucy)) <=> ? [X0] : (calm(X0) | creative(X0)) [input p10]
12. (~tall(paul) <~> ~generous(paul)) <=> ? [X0] : (brave(X0) | curious(X0)) [input p11]
20. ~calm(lucy) & happy(lucy) [input p19]
24. brave(lucy) [input hypothesis]
26. ! [X0] : ((~funny(X0) | calm(X0)) | (tall(X0) & calm(X0))) [ennf transformation 1]
27. ! [X0] : (~funny(X0) | calm(X0) | (tall(X0) & calm(X0))) [flattening 26]
29. ! [X0] : ((wise(X0) & ~generous(X0)) | (patient(X0) & calm(X0))) [ennf transformation 4]
46. ! [X0] : ((((funny(X0) | creative(X0)) & (~funny(X0) | ~creative(X0))) | (~tall(X0) & kind(X0))) & ((tall(X0) | ~kind(X0)) | ((~creative(X0) | funny(X0)) & (~funny(X0) | creative(X0))))) [nnf transformation 10]
47. ! [X0] : ((((funny(X0) | creative(X0)) & (~funny(X0) | ~creative(X0))) | (~tall(X0) & kind(X0))) & (tall(X0) | ~kind(X0) | ((~creative(X0) | funny(X0)) & (~funny(X0) | creative(X0))))) [flattening 46]
48. (((generous(lucy) | ~brave(lucy)) & (~generous(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~creative(X0))) & (? [X0] : (calm(X0) | creative(X0)) | ((brave(lucy) | generous(lucy)) & (~generous(lucy) | ~brave(lucy)))) [nnf transformation 11]
49. (((generous(lucy) | ~brave(lucy)) & (~generous(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~creative(X0))) & (? [X1] : (calm(X1) | creative(X1)) | ((brave(lucy) | generous(lucy)) & (~generous(lucy) | ~brave(lucy)))) [rectify 48]
50. ? [X1] : (calm(X1) | creative(X1)) => (calm(sK1) | creative(sK1)) [choice axiom]
51. (((generous(lucy) | ~brave(lucy)) & (~generous(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~creative(X0))) & ((calm(sK1) | creative(sK1)) | ((brave(lucy) | generous(lucy)) & (~generous(lucy) | ~brave(lucy)))) [skolemisation 49,50]
52. (((generous(paul) | tall(paul)) & (~generous(paul) | ~tall(paul))) | ! [X0] : (~brave(X0) & ~curious(X0))) & (? [X0] : (brave(X0) | curious(X0)) | ((~tall(paul) | generous(paul)) & (~generous(paul) | tall(paul)))) [nnf transformation 12]
53. (((generous(paul) | tall(paul)) & (~generous(paul) | ~tall(paul))) | ! [X0] : (~brave(X0) & ~curious(X0))) & (? [X1] : (brave(X1) | curious(X1)) | ((~tall(paul) | generous(paul)) & (~generous(paul) | tall(paul)))) [rectify 52]
54. ? [X1] : (brave(X1) | curious(X1)) => (brave(sK2) | curious(sK2)) [choice axiom]
55. (((generous(paul) | tall(paul)) & (~generous(paul) | ~tall(paul))) | ! [X0] : (~brave(X0) & ~curious(X0))) & ((brave(sK2) | curious(sK2)) | ((~tall(paul) | generous(paul)) & (~generous(paul) | tall(paul)))) [skolemisation 53,54]
78. ~funny(X0) | calm(X0) | calm(X0) [cnf transformation 27]
88. ~generous(X0) | calm(X0) [cnf transformation 29]
112. ~tall(X0) | creative(X0) | funny(X0) [cnf transformation 47]
117. generous(lucy) | ~brave(lucy) | ~creative(X0) [cnf transformation 51]
118. generous(lucy) | ~brave(lucy) | ~calm(X0) [cnf transformation 51]
124. generous(paul) | tall(paul) | ~brave(X0) [cnf transformation 55]
148. ~calm(lucy) [cnf transformation 20]
153. brave(lucy) [cnf transformation 24]
154. ~funny(X0) | calm(X0) [duplicate literal removal 78]
207. 12 <=> ! [X0] : ~calm(X0) [avatar definition]
208. ~calm(X0) <- (12) [avatar component clause 207]
210. 13 <=> brave(lucy) [avatar definition]
211. brave(lucy) <- (13) [avatar component clause 210]
214. 14 <=> generous(lucy) [avatar definition]
216. generous(lucy) <- (14) [avatar component clause 214]
217. 12 | ~13 | 14 [avatar split clause 118,214,210,207]
219. 15 <=> ! [X0] : ~creative(X0) [avatar definition]
220. ~creative(X0) <- (15) [avatar component clause 219]
221. 15 | ~13 | 14 [avatar split clause 117,214,210,219]
235. 18 <=> ! [X0] : ~brave(X0) [avatar definition]
236. ~brave(X0) <- (18) [avatar component clause 235]
238. 19 <=> tall(paul) [avatar definition]
240. tall(paul) <- (19) [avatar component clause 238]
242. 20 <=> generous(paul) [avatar definition]
244. generous(paul) <- (20) [avatar component clause 242]
245. 18 | 19 | 20 [avatar split clause 124,242,238,235]
360. 13 [avatar split clause 153,210]
361. $false <- (13, 18) [subsumption resolution 211,236]
362. ~13 | ~18 [avatar contradiction clause 361]
367. calm(lucy) <- (14) [resolution 88,216]
368. $false <- (14) [subsumption resolution 367,148]
369. ~14 [avatar contradiction clause 368]
452. creative(paul) | funny(paul) <- (19) [resolution 112,240]
453. funny(paul) <- (15, 19) [subsumption resolution 452,220]
479. calm(paul) <- (15, 19) [resolution 453,154]
480. $false <- (12, 15, 19) [subsumption resolution 479,208]
481. ~12 | ~15 | ~19 [avatar contradiction clause 480]
483. calm(paul) <- (20) [resolution 244,88]
485. $false <- (12, 20) [subsumption resolution 483,208]
486. ~12 | ~20 [avatar contradiction clause 485]
487. $false [avatar sat refutation 217,221,245,360,362,369,481,486]
% SZS output end Proof for 4091356068768256558118726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and happy is both not wise and funny and vice versa.
Everyone who is tall is generous or not rich and vice versa.
Everyone who is calm or not generous is either not patient or not funny.
Everyone who is both happy and not kind is not creative or quiet.
Everyone who is either funny or not humble is creative or brave.
Everyone who is tall or brave is either not calm or quiet.
If mary is both not generous and calm then fred is strong or not old.
Everyone who is both quiet and wise is happy or not happy and vice versa.
Everyone who is both patient and strong is both not tall and not humble and vice versa.
Everyone who is both not brave and not calm is either not humble or not happy and vice versa.
Everyone who is not kind is both not humble and wise.
If mary is both not rich and kind then someone is either not tall or not humble.
Everyone who is old is either not tall or strong and vice versa.
If lucy is calm then someone is either tall or brave and vice versa.
Everyone who is happy is quiet or curious and vice versa.
Lucy is not patient.
Someone is strong or not rich.
Someone is quiet. | Fred is not tall. | contradiction | (![X]:((~tall(X)&happy(X))<=>(~wise(X)&funny(X))))&
(![X]:(tall(X)<=>(generous(X)|~rich(X))))&
(![X]:((calm(X)|~generous(X))=>(~patient(X)<~>~funny(X))))&
(![X]:((happy(X)&~kind(X))=>(~creative(X)|quiet(X))))&
(![X]:((funny(X)<~>~humble(X))=>(creative(X)|brave(X))))&
(![X]:((tall(X)|brave(X))=>(~calm(X)<~>quiet(X))))&
(((~generous(mary)&calm(mary)))=>((strong(fred)|~old(fred))))&
(![X]:((quiet(X)&wise(X))<=>(happy(X)|~happy(X))))&
(![X]:((patient(X)&strong(X))<=>(~tall(X)&~humble(X))))&
(![X]:((~brave(X)&~calm(X))<=>(~humble(X)<~>~happy(X))))&
(![X]:(~kind(X)=>(~humble(X)&wise(X))))&
(((~rich(mary)&kind(mary)))=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:(old(X)<=>(~tall(X)<~>strong(X))))&
((calm(lucy))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:(happy(X)<=>(quiet(X)|curious(X))))&
(~patient(lucy))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:(quiet(X))) | ~tall(fred) | [
"p0",
"p7",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 43651008624614967434610
% SZS output start Proof for 43651008624614967434610
1. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (funny(X0) & ~wise(X0))) [input p0]
8. ! [X0] : ((wise(X0) & quiet(X0)) <=> (~happy(X0) | happy(X0))) [input p7]
15. ! [X0] : (happy(X0) <=> (curious(X0) | quiet(X0))) [input p14]
19. ~tall(fred) [input hypothesis]
33. ! [X0] : (((happy(X0) & ~tall(X0)) | (~funny(X0) | wise(X0))) & ((funny(X0) & ~wise(X0)) | (~happy(X0) | tall(X0)))) [nnf transformation 1]
34. ! [X0] : (((happy(X0) & ~tall(X0)) | ~funny(X0) | wise(X0)) & ((funny(X0) & ~wise(X0)) | ~happy(X0) | tall(X0))) [flattening 33]
40. ! [X0] : (((wise(X0) & quiet(X0)) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | (~wise(X0) | ~quiet(X0)))) [nnf transformation 8]
41. ! [X0] : (((wise(X0) & quiet(X0)) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | ~wise(X0) | ~quiet(X0))) [flattening 40]
54. ! [X0] : ((happy(X0) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | ~happy(X0))) [nnf transformation 15]
55. ! [X0] : ((happy(X0) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | ~happy(X0))) [flattening 54]
60. ~wise(X0) | ~happy(X0) | tall(X0) [cnf transformation 34]
80. quiet(X0) | ~happy(X0) [cnf transformation 41]
81. quiet(X0) | happy(X0) [cnf transformation 41]
82. wise(X0) | ~happy(X0) [cnf transformation 41]
83. wise(X0) | happy(X0) [cnf transformation 41]
105. happy(X0) | ~quiet(X0) [cnf transformation 55]
110. ~tall(fred) [cnf transformation 19]
128. wise(X0) [subsumption resolution 82,83]
129. quiet(X0) [subsumption resolution 80,81]
170. happy(X0) [subsumption resolution 105,129]
184. ~happy(X1) | tall(X1) [resolution 60,128]
185. tall(X1) [subsumption resolution 184,170]
186. $false [resolution 185,110]
% SZS output end Proof for 43651008624614967434610
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not rich is generous or not patient. Everyone who is not old is either not calm or kind and vice versa. Everyone who is not strong is either not humble or brave and vice versa. Everyone who is not quiet or not funny is both quiet and not creative and vice versa. If mary is not tall then fred is not calm and vice versa. Everyone who is not generous is quiet or happy and vice versa. If susan is both not happy and not humble then susan is either happy or wise. If lucy is not rich or not wise then alice is both generous and not happy. Everyone who is not funny is not humble. If alice is brave then someone is rich. If someone is both not rich and curious then someone is both patient and not old and vice versa. If john is not creative or not strong then paul is not brave or not old. Everyone who is old is kind and vice versa. Everyone who is either not old or wise is both not curious and kind and vice versa. Everyone who is both not quiet and curious is both funny and strong and vice versa. Susan is not patient or not humble. Someone is both not strong and kind. Susan is generous or humble. Fred is not patient or quiet. Lucy is either strong or quiet. Someone is patient. Someone is brave or not tall. | Susan is not kind. | neutral | (![X]:((strong(X)<~>~rich(X))=>(generous(X)|~patient(X))))&
(![X]:(~old(X)<=>(~calm(X)<~>kind(X))))&
(![X]:(~strong(X)<=>(~humble(X)<~>brave(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(quiet(X)&~creative(X))))&
((~tall(mary))<=>(~calm(fred)))&
(![X]:(~generous(X)<=>(quiet(X)|happy(X))))&
(((~happy(susan)&~humble(susan)))=>((happy(susan)<~>wise(susan))))&
(((~rich(lucy)|~wise(lucy)))=>((generous(alice)&~happy(alice))))&
(![X]:(~funny(X)=>~humble(X)))&
((brave(alice))=>(?[X]:(rich(X))))&
((?[X]:((~rich(X)&curious(X))))<=>(?[X]:((patient(X)&~old(X)))))&
(((~creative(john)|~strong(john)))=>((~brave(paul)|~old(paul))))&
(![X]:(old(X)<=>kind(X)))&
(![X]:((~old(X)<~>wise(X))<=>(~curious(X)&kind(X))))&
(![X]:((~quiet(X)&curious(X))<=>(funny(X)&strong(X))))&
((~patient(susan)|~humble(susan)))&
(?[X]:((~strong(X)&kind(X))))&
((generous(susan)|humble(susan)))&
((~patient(fred)|quiet(fred)))&
((strong(lucy)<~>quiet(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((brave(X)|~tall(X)))) | ~kind(susan) | []
| null | 0 |
Everyone who is not wise or patient is either not old or not curious and vice versa. Everyone who is generous is either strong or not tall. If lucy is humble then susan is both not funny and not generous and vice versa. Everyone who is both quiet and not funny is patient or tall and vice versa. Everyone who is not wise is either not rich or old. If lucy is either wise or not brave then john is either creative or not creative and vice versa. Everyone who is either not strong or wise is both humble and creative and vice versa. Everyone who is not kind or patient is either brave or calm. If paul is either not brave or wise then someone is both not curious and not old and vice versa. Everyone who is not humble is either not wise or not curious and vice versa. Everyone who is funny is both not kind and not happy. Everyone who is wise is both not curious and patient. Everyone who is either calm or not patient is not kind or humble and vice versa. If john is old then someone is both not wise and not tall. If someone is not rich then mary is strong or funny and vice versa. Everyone who is rich is both not tall and old. Someone is either not rich or not generous. Someone is old or generous. Alice is either funny or rich. John is not happy. Alice is either not rich or quiet. Mary is either not curious or not humble. | Lucy is funny. | contradiction | (![X]:((~wise(X)|patient(X))<=>(~old(X)<~>~curious(X))))&
(![X]:(generous(X)=>(strong(X)<~>~tall(X))))&
((humble(lucy))<=>((~funny(susan)&~generous(susan))))&
(![X]:((quiet(X)&~funny(X))<=>(patient(X)|tall(X))))&
(![X]:(~wise(X)=>(~rich(X)<~>old(X))))&
(((wise(lucy)<~>~brave(lucy)))<=>((creative(john)<~>~creative(john))))&
(![X]:((~strong(X)<~>wise(X))<=>(humble(X)&creative(X))))&
(![X]:((~kind(X)|patient(X))=>(brave(X)<~>calm(X))))&
(((~brave(paul)<~>wise(paul)))<=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:(~humble(X)<=>(~wise(X)<~>~curious(X))))&
(![X]:(funny(X)=>(~kind(X)&~happy(X))))&
(![X]:(wise(X)=>(~curious(X)&patient(X))))&
(![X]:((calm(X)<~>~patient(X))<=>(~kind(X)|humble(X))))&
((old(john))=>(?[X]:((~wise(X)&~tall(X)))))&
((?[X]:(~rich(X)))<=>((strong(mary)|funny(mary))))&
(![X]:(rich(X)=>(~tall(X)&old(X))))&
(?[X]:((~rich(X)<~>~generous(X))))&
(?[X]:((old(X)|generous(X))))&
((funny(alice)<~>rich(alice)))&
(~happy(john))&
((~rich(alice)<~>quiet(alice)))&
((~curious(mary)<~>~humble(mary))) | funny(lucy) | [
"p3",
"p5",
"p7",
"p10",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 7992962106861173692682125
% SZS output start Proof for 7992962106861173692682125
4. ! [X0] : ((~funny(X0) & quiet(X0)) <=> (tall(X0) | patient(X0))) [input p3]
6. (wise(lucy) <~> ~brave(lucy)) <=> (creative(john) <~> ~creative(john)) [input p5]
8. ! [X0] : ((patient(X0) | ~kind(X0)) => (brave(X0) <~> calm(X0))) [input p7]
11. ! [X0] : (funny(X0) => (~happy(X0) & ~kind(X0))) [input p10]
12. ! [X0] : (wise(X0) => (patient(X0) & ~curious(X0))) [input p11]
13. ! [X0] : ((calm(X0) <~> ~patient(X0)) <=> (humble(X0) | ~kind(X0))) [input p12]
23. funny(lucy) [input hypothesis]
24. ! [X0] : (funny(X0) => ~kind(X0)) [pure predicate removal 11]
28. ! [X0] : ((brave(X0) <~> calm(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 8]
29. ! [X0] : (~kind(X0) | ~funny(X0)) [ennf transformation 24]
30. ! [X0] : ((patient(X0) & ~curious(X0)) | ~wise(X0)) [ennf transformation 12]
38. ! [X0] : (((~funny(X0) & quiet(X0)) | (~tall(X0) & ~patient(X0))) & ((tall(X0) | patient(X0)) | (funny(X0) | ~quiet(X0)))) [nnf transformation 4]
39. ! [X0] : (((~funny(X0) & quiet(X0)) | (~tall(X0) & ~patient(X0))) & (tall(X0) | patient(X0) | funny(X0) | ~quiet(X0))) [flattening 38]
41. (((brave(lucy) | ~wise(lucy)) & (~brave(lucy) | wise(lucy))) | ((creative(john) | creative(john)) & (~creative(john) | ~creative(john)))) & (((creative(john) | ~creative(john)) & (~creative(john) | creative(john))) | ((wise(lucy) | brave(lucy)) & (~brave(lucy) | ~wise(lucy)))) [nnf transformation 6]
44. ! [X0] : (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (~patient(X0) & kind(X0))) [nnf transformation 28]
50. ! [X0] : ((((patient(X0) | ~calm(X0)) & (~patient(X0) | calm(X0))) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0))))) [nnf transformation 13]
51. ! [X0] : ((((patient(X0) | ~calm(X0)) & (~patient(X0) | calm(X0))) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0))))) [flattening 50]
81. ~funny(X0) | ~patient(X0) [cnf transformation 39]
89. ~brave(lucy) | wise(lucy) | ~creative(john) | ~creative(john) [cnf transformation 41]
90. ~brave(lucy) | wise(lucy) | creative(john) | creative(john) [cnf transformation 41]
99. calm(X0) | brave(X0) | kind(X0) [cnf transformation 44]
113. ~kind(X0) | ~funny(X0) [cnf transformation 29]
115. ~wise(X0) | patient(X0) [cnf transformation 30]
120. ~calm(X0) | patient(X0) | kind(X0) [cnf transformation 51]
138. funny(lucy) [cnf transformation 23]
139. ~brave(lucy) | wise(lucy) | ~creative(john) [duplicate literal removal 89]
140. ~brave(lucy) | wise(lucy) | creative(john) [duplicate literal removal 90]
159. 4 <=> creative(john) [avatar definition]
163. 5 <=> wise(lucy) [avatar definition]
164. wise(lucy) <- (5) [avatar component clause 163]
167. 6 <=> brave(lucy) [avatar definition]
172. 4 | 5 | ~6 [avatar split clause 140,167,163,159]
173. ~4 | 5 | ~6 [avatar split clause 139,167,163,159]
276. ~patient(lucy) [resolution 81,138]
396. patient(X0) | kind(X0) | brave(X0) | kind(X0) [resolution 120,99]
397. kind(X0) | patient(X0) | brave(X0) [duplicate literal removal 396]
402. patient(X0) | brave(X0) | ~funny(X0) [resolution 397,113]
403. ~funny(X0) | brave(X0) [subsumption resolution 402,81]
411. brave(lucy) [resolution 403,138]
426. 6 [avatar split clause 411,167]
428. patient(lucy) <- (5) [resolution 164,115]
429. $false <- (5) [subsumption resolution 428,276]
430. ~5 [avatar contradiction clause 429]
431. $false [avatar sat refutation 172,173,426,430]
% SZS output end Proof for 7992962106861173692682125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not brave is both curious and happy.
Everyone who is not wise is not tall or not funny and vice versa.
If someone is both quiet and not happy then someone is not old or not wise.
If lucy is not quiet or curious then someone is either not kind or calm and vice versa.
Everyone who is not tall is not rich or quiet and vice versa.
Everyone who is both wise and not brave is either wise or funny and vice versa.
Everyone who is not wise is both rich and tall and vice versa.
If paul is humble or happy then someone is either quiet or not rich and vice versa.
If john is kind or brave then someone is either not creative or not funny.
Everyone who is either not funny or not kind is either humble or brave and vice versa.
If someone is funny then fred is kind or not curious.
If someone is both not brave and not calm then someone is happy or not humble and vice versa.
Everyone who is both brave and quiet is either not generous or not brave.
If alice is kind then someone is both strong and creative.
If someone is not generous or not old then someone is humble or old and vice versa.
Everyone who is either not brave or happy is either tall or not generous and vice versa.
Fred is calm.
Paul is either quiet or calm.
Someone is both not strong and curious.
Someone is either not kind or generous.
Mary is both not quiet and not funny.
Someone is not calm or quiet.
John is either old or not humble. | Alice is not wise. | entailment | (![X]:((~kind(X)&~brave(X))=>(curious(X)&happy(X))))&
(![X]:(~wise(X)<=>(~tall(X)|~funny(X))))&
((?[X]:((quiet(X)&~happy(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(((~quiet(lucy)|curious(lucy)))<=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:(~tall(X)<=>(~rich(X)|quiet(X))))&
(![X]:((wise(X)&~brave(X))<=>(wise(X)<~>funny(X))))&
(![X]:(~wise(X)<=>(rich(X)&tall(X))))&
(((humble(paul)|happy(paul)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(((kind(john)|brave(john)))=>(?[X]:((~creative(X)<~>~funny(X)))))&
(![X]:((~funny(X)<~>~kind(X))<=>(humble(X)<~>brave(X))))&
((?[X]:(funny(X)))=>((kind(fred)|~curious(fred))))&
((?[X]:((~brave(X)&~calm(X))))<=>(?[X]:((happy(X)|~humble(X)))))&
(![X]:((brave(X)&quiet(X))=>(~generous(X)<~>~brave(X))))&
((kind(alice))=>(?[X]:((strong(X)&creative(X)))))&
((?[X]:((~generous(X)|~old(X))))<=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~brave(X)<~>happy(X))<=>(tall(X)<~>~generous(X))))&
(calm(fred))&
((quiet(paul)<~>calm(paul)))&
(?[X]:((~strong(X)&curious(X))))&
(?[X]:((~kind(X)<~>generous(X))))&
((~quiet(mary)&~funny(mary)))&
(?[X]:((~calm(X)|quiet(X))))&
((old(john)<~>~humble(john))) | ~wise(alice) | [
"p1",
"p4",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 3585527109444299837931788
% SZS output start Proof for 3585527109444299837931788
2. ! [X0] : (~wise(X0) <=> (~funny(X0) | ~tall(X0))) [input p1]
5. ! [X0] : (~tall(X0) <=> (quiet(X0) | ~rich(X0))) [input p4]
7. ! [X0] : (~wise(X0) <=> (tall(X0) & rich(X0))) [input p6]
24. wise(alice) [input hypothesis]
37. ! [X0] : ((~wise(X0) | (funny(X0) & tall(X0))) & ((~funny(X0) | ~tall(X0)) | wise(X0))) [nnf transformation 2]
38. ! [X0] : ((~wise(X0) | (funny(X0) & tall(X0))) & (~funny(X0) | ~tall(X0) | wise(X0))) [flattening 37]
47. ! [X0] : ((~tall(X0) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | tall(X0))) [nnf transformation 5]
48. ! [X0] : ((~tall(X0) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | tall(X0))) [flattening 47]
51. ! [X0] : ((~wise(X0) | (~tall(X0) | ~rich(X0))) & ((tall(X0) & rich(X0)) | wise(X0))) [nnf transformation 7]
52. ! [X0] : ((~wise(X0) | ~tall(X0) | ~rich(X0)) & ((tall(X0) & rich(X0)) | wise(X0))) [flattening 51]
88. ~wise(X0) | tall(X0) [cnf transformation 38]
98. ~tall(X0) | rich(X0) [cnf transformation 48]
107. tall(X0) | wise(X0) [cnf transformation 52]
108. ~wise(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 52]
161. wise(alice) [cnf transformation 24]
206. ~rich(X0) | ~wise(X0) [subsumption resolution 108,88]
207. tall(X0) [subsumption resolution 107,88]
393. rich(X0) [resolution 98,207]
409. ~wise(X1) [resolution 206,393]
410. $false [resolution 409,161]
% SZS output end Proof for 3585527109444299837931788
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not calm is both strong and not quiet. Everyone who is both not old and not happy is both not strong and generous and vice versa. Everyone who is old is not old. Everyone who is both quiet and brave is either rich or creative. Everyone who is either kind or funny is both kind and not strong. If john is strong then mary is tall. Everyone who is either not calm or strong is either funny or not tall. Everyone who is not tall is both funny and humble. Everyone who is both happy and not strong is both strong and curious and vice versa. Everyone who is not curious or not strong is both not kind and strong. Everyone who is old or not kind is humble or calm and vice versa. If lucy is either not humble or not generous then mary is both not humble and humble and vice versa. If paul is either not quiet or patient then fred is both not rich and not wise and vice versa. Someone is kind or strong. Susan is both brave and not quiet. Paul is either patient or not wise. Fred is kind or not calm. Fred is either not quiet or not tall. Mary is not wise or not strong. Someone is either not calm or creative. Fred is both not kind and not generous. | Mary is not rich. | neutral | (![X]:((patient(X)|~calm(X))=>(strong(X)&~quiet(X))))&
(![X]:((~old(X)&~happy(X))<=>(~strong(X)&generous(X))))&
(![X]:(old(X)=>~old(X)))&
(![X]:((quiet(X)&brave(X))=>(rich(X)<~>creative(X))))&
(![X]:((kind(X)<~>funny(X))=>(kind(X)&~strong(X))))&
((strong(john))=>(tall(mary)))&
(![X]:((~calm(X)<~>strong(X))=>(funny(X)<~>~tall(X))))&
(![X]:(~tall(X)=>(funny(X)&humble(X))))&
(![X]:((happy(X)&~strong(X))<=>(strong(X)&curious(X))))&
(![X]:((~curious(X)|~strong(X))=>(~kind(X)&strong(X))))&
(![X]:((old(X)|~kind(X))<=>(humble(X)|calm(X))))&
(((~humble(lucy)<~>~generous(lucy)))<=>((~humble(mary)&humble(mary))))&
(((~quiet(paul)<~>patient(paul)))<=>((~rich(fred)&~wise(fred))))&
(?[X]:((kind(X)|strong(X))))&
((brave(susan)&~quiet(susan)))&
((patient(paul)<~>~wise(paul)))&
((kind(fred)|~calm(fred)))&
((~quiet(fred)<~>~tall(fred)))&
((~wise(mary)|~strong(mary)))&
(?[X]:((~calm(X)<~>creative(X))))&
((~kind(fred)&~generous(fred))) | ~rich(mary) | []
| null | 0 |
If john is both not rich and not happy then john is both creative and not creative and vice versa.
Everyone who is curious or not tall is rich or not humble and vice versa.
If someone is either not generous or not brave then someone is both tall and kind.
If paul is not curious then lucy is not strong.
If someone is either not curious or not happy then paul is both not tall and tall and vice versa.
If alice is not funny or not quiet then mary is either happy or brave and vice versa.
If someone is creative then paul is both not old and kind and vice versa.
Everyone who is brave is either not creative or brave and vice versa.
Everyone who is both not brave and not kind is not funny.
Everyone who is either not tall or not brave is strong or not creative.
If alice is quiet or funny then someone is either not quiet or quiet and vice versa.
Everyone who is both creative and funny is calm.
Everyone who is humble or quiet is both not creative and not rich.
If someone is either old or not creative then someone is either strong or not tall and vice versa.
Everyone who is either tall or not quiet is either humble or generous and vice versa.
Fred is not curious.
Someone is not calm or not generous.
Someone is not generous.
Someone is old.
Lucy is not patient. | Paul is not generous. | neutral | (((~rich(john)&~happy(john)))<=>((creative(john)&~creative(john))))&
(![X]:((curious(X)|~tall(X))<=>(rich(X)|~humble(X))))&
((?[X]:((~generous(X)<~>~brave(X))))=>(?[X]:((tall(X)&kind(X)))))&
((~curious(paul))=>(~strong(lucy)))&
((?[X]:((~curious(X)<~>~happy(X))))<=>((~tall(paul)&tall(paul))))&
(((~funny(alice)|~quiet(alice)))<=>((happy(mary)<~>brave(mary))))&
((?[X]:(creative(X)))<=>((~old(paul)&kind(paul))))&
(![X]:(brave(X)<=>(~creative(X)<~>brave(X))))&
(![X]:((~brave(X)&~kind(X))=>~funny(X)))&
(![X]:((~tall(X)<~>~brave(X))=>(strong(X)|~creative(X))))&
(((quiet(alice)|funny(alice)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((creative(X)&funny(X))=>calm(X)))&
(![X]:((humble(X)|quiet(X))=>(~creative(X)&~rich(X))))&
((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((tall(X)<~>~quiet(X))<=>(humble(X)<~>generous(X))))&
(~curious(fred))&
(?[X]:((~calm(X)|~generous(X))))&
(?[X]:(~generous(X)))&
(?[X]:(old(X)))&
(~patient(lucy)) | ~generous(paul) | []
| null | 0 |
Everyone who is not strong is quiet. Everyone who is either not patient or calm is not patient and vice versa. If someone is not kind then paul is both funny and curious. If someone is strong or not brave then alice is not funny or not humble. Everyone who is both old and not old is not creative or not wise and vice versa. If alice is generous then paul is both strong and old and vice versa. Everyone who is not funny is not old and vice versa. Everyone who is both not strong and not patient is strong or not patient and vice versa. Everyone who is both not kind and brave is either curious or not old and vice versa. Everyone who is either not rich or not patient is either strong or not humble and vice versa. Everyone who is both strong and not kind is old or brave and vice versa. If lucy is not wise then mary is both not curious and not funny. Everyone who is not curious is humble and vice versa. If someone is not brave or calm then fred is either tall or calm and vice versa. Everyone who is either not wise or not curious is either not wise or rich. Someone is either brave or not old. Someone is not quiet or not old. | Paul is generous. | neutral | (![X]:(~strong(X)=>quiet(X)))&
(![X]:((~patient(X)<~>calm(X))<=>~patient(X)))&
((?[X]:(~kind(X)))=>((funny(paul)&curious(paul))))&
((?[X]:((strong(X)|~brave(X))))=>((~funny(alice)|~humble(alice))))&
(![X]:((old(X)&~old(X))<=>(~creative(X)|~wise(X))))&
((generous(alice))<=>((strong(paul)&old(paul))))&
(![X]:(~funny(X)<=>~old(X)))&
(![X]:((~strong(X)&~patient(X))<=>(strong(X)|~patient(X))))&
(![X]:((~kind(X)&brave(X))<=>(curious(X)<~>~old(X))))&
(![X]:((~rich(X)<~>~patient(X))<=>(strong(X)<~>~humble(X))))&
(![X]:((strong(X)&~kind(X))<=>(old(X)|brave(X))))&
((~wise(lucy))=>((~curious(mary)&~funny(mary))))&
(![X]:(~curious(X)<=>humble(X)))&
((?[X]:((~brave(X)|calm(X))))<=>((tall(fred)<~>calm(fred))))&
(![X]:((~wise(X)<~>~curious(X))=>(~wise(X)<~>rich(X))))&
(?[X]:((brave(X)<~>~old(X))))&
(?[X]:((~quiet(X)|~old(X)))) | generous(paul) | []
| null | 0 |
Everyone who is both curious and wise is happy.
If john is either quiet or not rich then mary is old or happy and vice versa.
If susan is both not generous and not kind then paul is not wise and vice versa.
Everyone who is either not old or wise is both old and not funny and vice versa.
Everyone who is both not old and not wise is both generous and brave.
If alice is either not patient or kind then someone is either not brave or not happy and vice versa.
If someone is either not quiet or quiet then fred is both not patient and not funny.
Everyone who is kind or rich is quiet.
If lucy is quiet or not creative then john is wise or happy and vice versa.
If john is both not generous and not rich then someone is both not old and patient.
Everyone who is either rich or not strong is not generous.
Everyone who is not calm or rich is not brave.
If alice is both funny and happy then mary is not tall or not strong and vice versa.
If mary is creative then someone is either not funny or patient.
Everyone who is kind is either not creative or funny and vice versa.
Everyone who is generous or not humble is not generous or generous and vice versa.
Lucy is both not funny and rich.
Someone is not patient or happy.
Mary is not strong or brave.
Someone is not tall or not generous.
Susan is not wise or humble.
Susan is both rich and strong. | Paul is wise. | neutral | (![X]:((curious(X)&wise(X))=>happy(X)))&
(((quiet(john)<~>~rich(john)))<=>((old(mary)|happy(mary))))&
(((~generous(susan)&~kind(susan)))<=>(~wise(paul)))&
(![X]:((~old(X)<~>wise(X))<=>(old(X)&~funny(X))))&
(![X]:((~old(X)&~wise(X))=>(generous(X)&brave(X))))&
(((~patient(alice)<~>kind(alice)))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
((?[X]:((~quiet(X)<~>quiet(X))))=>((~patient(fred)&~funny(fred))))&
(![X]:((kind(X)|rich(X))=>quiet(X)))&
(((quiet(lucy)|~creative(lucy)))<=>((wise(john)|happy(john))))&
(((~generous(john)&~rich(john)))=>(?[X]:((~old(X)&patient(X)))))&
(![X]:((rich(X)<~>~strong(X))=>~generous(X)))&
(![X]:((~calm(X)|rich(X))=>~brave(X)))&
(((funny(alice)&happy(alice)))<=>((~tall(mary)|~strong(mary))))&
((creative(mary))=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:(kind(X)<=>(~creative(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))<=>(~generous(X)|generous(X))))&
((~funny(lucy)&rich(lucy)))&
(?[X]:((~patient(X)|happy(X))))&
((~strong(mary)|brave(mary)))&
(?[X]:((~tall(X)|~generous(X))))&
((~wise(susan)|humble(susan)))&
((rich(susan)&strong(susan))) | wise(paul) | []
| null | 0 |
Everyone who is both funny and generous is not creative and vice versa.
If someone is rich then susan is either not humble or not generous.
Everyone who is both strong and brave is strong or not brave.
If mary is rich then someone is patient.
If someone is both rich and not tall then john is either not strong or not creative.
Everyone who is not happy is not tall or not rich.
Everyone who is not quiet or happy is both tall and old.
If someone is generous or not quiet then someone is rich or creative and vice versa.
Everyone who is not quiet or not brave is not generous and vice versa.
If someone is not humble then alice is happy or not patient and vice versa.
Everyone who is either creative or not old is not happy or rich and vice versa.
Everyone who is quiet or wise is not quiet.
Everyone who is either kind or not happy is either not calm or strong.
Everyone who is both not curious and not brave is both humble and not quiet and vice versa.
If paul is not generous then someone is not happy and vice versa.
Someone is curious.
Someone is both not funny and rich.
John is not happy.
Someone is both strong and happy.
Fred is either rich or brave.
Someone is both not generous and strong.
Susan is patient. | Alice is quiet. | contradiction | (![X]:((funny(X)&generous(X))<=>~creative(X)))&
((?[X]:(rich(X)))=>((~humble(susan)<~>~generous(susan))))&
(![X]:((strong(X)&brave(X))=>(strong(X)|~brave(X))))&
((rich(mary))=>(?[X]:(patient(X))))&
((?[X]:((rich(X)&~tall(X))))=>((~strong(john)<~>~creative(john))))&
(![X]:(~happy(X)=>(~tall(X)|~rich(X))))&
(![X]:((~quiet(X)|happy(X))=>(tall(X)&old(X))))&
((?[X]:((generous(X)|~quiet(X))))<=>(?[X]:((rich(X)|creative(X)))))&
(![X]:((~quiet(X)|~brave(X))<=>~generous(X)))&
((?[X]:(~humble(X)))<=>((happy(alice)|~patient(alice))))&
(![X]:((creative(X)<~>~old(X))<=>(~happy(X)|rich(X))))&
(![X]:((quiet(X)|wise(X))=>~quiet(X)))&
(![X]:((kind(X)<~>~happy(X))=>(~calm(X)<~>strong(X))))&
(![X]:((~curious(X)&~brave(X))<=>(humble(X)&~quiet(X))))&
((~generous(paul))<=>(?[X]:(~happy(X))))&
(?[X]:(curious(X)))&
(?[X]:((~funny(X)&rich(X))))&
(~happy(john))&
(?[X]:((strong(X)&happy(X))))&
((rich(fred)<~>brave(fred)))&
(?[X]:((~generous(X)&strong(X))))&
(patient(susan)) | quiet(alice) | [
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 5446304148291776129963080
% SZS output start Proof for 5446304148291776129963080
12. ! [X0] : ((wise(X0) | quiet(X0)) => ~quiet(X0)) [input p11]
23. quiet(alice) [input hypothesis]
25. ! [X0] : (quiet(X0) => ~quiet(X0)) [pure predicate removal 12]
34. ! [X0] : (~quiet(X0) | ~quiet(X0)) [ennf transformation 25]
102. ~quiet(X0) | ~quiet(X0) [cnf transformation 34]
124. quiet(alice) [cnf transformation 23]
125. ~quiet(X0) [duplicate literal removal 102]
236. $false [subsumption resolution 124,125]
% SZS output end Proof for 5446304148291776129963080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not generous then mary is quiet or not quiet. Everyone who is not creative or old is either not brave or humble and vice versa. If mary is old then someone is calm or rich and vice versa. If paul is both not funny and generous then someone is either not curious or not brave and vice versa. If someone is not happy then fred is brave or not generous and vice versa. Everyone who is both old and creative is both generous and brave and vice versa. Everyone who is generous is not quiet or not generous. If someone is either brave or not humble then someone is either curious or funny and vice versa. Everyone who is both humble and kind is both rich and creative. Everyone who is curious is not funny and vice versa. If alice is both not generous and strong then john is both not tall and not quiet. If someone is brave or quiet then alice is either not strong or wise. If someone is both not happy and not quiet then someone is patient or not kind. If someone is both not strong and not wise then paul is either not calm or not happy and vice versa. If mary is both not strong and rich then lucy is both kind and brave and vice versa. Everyone who is both not creative and generous is not quiet or not generous and vice versa. Someone is patient or wise. Alice is both strong and not quiet. Mary is either not brave or calm. Mary is strong. Mary is both happy and not tall. Someone is patient or not kind. Fred is not kind or not old. | John is not curious. | neutral | ((?[X]:((creative(X)<~>~generous(X))))=>((quiet(mary)|~quiet(mary))))&
(![X]:((~creative(X)|old(X))<=>(~brave(X)<~>humble(X))))&
((old(mary))<=>(?[X]:((calm(X)|rich(X)))))&
(((~funny(paul)&generous(paul)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
((?[X]:(~happy(X)))<=>((brave(fred)|~generous(fred))))&
(![X]:((old(X)&creative(X))<=>(generous(X)&brave(X))))&
(![X]:(generous(X)=>(~quiet(X)|~generous(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)&kind(X))=>(rich(X)&creative(X))))&
(![X]:(curious(X)<=>~funny(X)))&
(((~generous(alice)&strong(alice)))=>((~tall(john)&~quiet(john))))&
((?[X]:((brave(X)|quiet(X))))=>((~strong(alice)<~>wise(alice))))&
((?[X]:((~happy(X)&~quiet(X))))=>(?[X]:((patient(X)|~kind(X)))))&
((?[X]:((~strong(X)&~wise(X))))<=>((~calm(paul)<~>~happy(paul))))&
(((~strong(mary)&rich(mary)))<=>((kind(lucy)&brave(lucy))))&
(![X]:((~creative(X)&generous(X))<=>(~quiet(X)|~generous(X))))&
(?[X]:((patient(X)|wise(X))))&
((strong(alice)&~quiet(alice)))&
((~brave(mary)<~>calm(mary)))&
(strong(mary))&
((happy(mary)&~tall(mary)))&
(?[X]:((patient(X)|~kind(X))))&
((~kind(fred)|~old(fred))) | ~curious(john) | []
| null | 0 |
Everyone who is both not old and not calm is either not tall or not happy and vice versa.
Everyone who is not kind or not funny is either wise or not funny and vice versa.
Everyone who is either happy or not calm is either not happy or not calm.
Everyone who is either quiet or not kind is quiet or kind.
If alice is not patient then mary is either creative or not brave.
Everyone who is both tall and strong is both brave and generous and vice versa.
Everyone who is funny or not wise is both tall and rich and vice versa.
Everyone who is happy or not patient is patient.
Everyone who is tall is both strong and humble and vice versa.
If someone is either happy or brave then someone is not patient and vice versa.
If someone is not kind then someone is brave or not creative.
If lucy is brave or old then someone is either not strong or patient and vice versa.
If alice is both not brave and humble then alice is either quiet or calm.
If someone is either happy or not creative then someone is either not humble or patient.
If paul is curious then susan is either not humble or old and vice versa.
Everyone who is both rich and not creative is either not happy or curious.
Paul is both rich and not creative.
Paul is either curious or funny.
Someone is either not old or brave.
Someone is not creative. | Mary is not humble. | contradiction | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~calm(X))=>(~happy(X)<~>~calm(X))))&
(![X]:((quiet(X)<~>~kind(X))=>(quiet(X)|kind(X))))&
((~patient(alice))=>((creative(mary)<~>~brave(mary))))&
(![X]:((tall(X)&strong(X))<=>(brave(X)&generous(X))))&
(![X]:((funny(X)|~wise(X))<=>(tall(X)&rich(X))))&
(![X]:((happy(X)|~patient(X))=>patient(X)))&
(![X]:(tall(X)<=>(strong(X)&humble(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)|~creative(X)))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~brave(alice)&humble(alice)))=>((quiet(alice)<~>calm(alice))))&
((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
((curious(paul))<=>((~humble(susan)<~>old(susan))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)<~>curious(X))))&
((rich(paul)&~creative(paul)))&
((curious(paul)<~>funny(paul)))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:(~creative(X))) | ~humble(mary) | [
"p1",
"p6",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 424034875935366798553182
% SZS output start Proof for 424034875935366798553182
2. ! [X0] : ((~funny(X0) | ~kind(X0)) <=> (wise(X0) <~> ~funny(X0))) [input p1]
7. ! [X0] : ((~wise(X0) | funny(X0)) <=> (rich(X0) & tall(X0))) [input p6]
9. ! [X0] : (tall(X0) <=> (humble(X0) & strong(X0))) [input p8]
21. ~humble(mary) [input hypothesis]
38. ! [X0] : (((~funny(X0) | ~kind(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (funny(X0) & kind(X0)))) [nnf transformation 2]
39. ! [X0] : ((~funny(X0) | ~kind(X0) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (funny(X0) & kind(X0)))) [flattening 38]
45. ! [X0] : (((~wise(X0) | funny(X0)) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [nnf transformation 7]
46. ! [X0] : ((~wise(X0) | funny(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [flattening 45]
47. ! [X0] : ((tall(X0) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | ~tall(X0))) [nnf transformation 9]
48. ! [X0] : ((tall(X0) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | ~tall(X0))) [flattening 47]
84. funny(X0) | ~wise(X0) | funny(X0) [cnf transformation 39]
99. ~funny(X0) | tall(X0) [cnf transformation 46]
100. wise(X0) | tall(X0) [cnf transformation 46]
107. ~tall(X0) | humble(X0) [cnf transformation 48]
139. ~humble(mary) [cnf transformation 21]
144. ~wise(X0) | funny(X0) [duplicate literal removal 84]
260. funny(X0) | tall(X0) [resolution 144,100]
261. tall(X0) [subsumption resolution 260,99]
262. humble(X0) [resolution 261,107]
266. $false [resolution 262,139]
% SZS output end Proof for 424034875935366798553182
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not kind and funny then paul is both not calm and old.
Everyone who is not rich is not strong or creative.
Everyone who is not creative is both rich and not creative and vice versa.
Everyone who is either not generous or kind is generous or not kind.
Everyone who is both not tall and strong is not calm and vice versa.
If someone is both not patient and quiet then paul is quiet or creative and vice versa.
Everyone who is wise or happy is either patient or not calm and vice versa.
If susan is both not patient and not generous then paul is either not happy or curious.
If someone is either funny or not creative then someone is not brave and vice versa.
Everyone who is not tall or brave is both not strong and not calm and vice versa.
If susan is either quiet or not humble then paul is not strong or wise.
If someone is rich then someone is humble or not creative and vice versa.
Everyone who is either not humble or not funny is either wise or not calm and vice versa.
Everyone who is either not creative or not curious is creative.
Everyone who is either not wise or humble is kind.
Everyone who is both calm and not tall is both not humble and curious.
Someone is both not rich and not wise.
Someone is not strong.
Someone is both kind and not creative.
Someone is not brave.
Someone is not quiet or brave.
John is both patient and not rich. | Paul is not kind. | contradiction | ((?[X]:((~kind(X)&funny(X))))=>((~calm(paul)&old(paul))))&
(![X]:(~rich(X)=>(~strong(X)|creative(X))))&
(![X]:(~creative(X)<=>(rich(X)&~creative(X))))&
(![X]:((~generous(X)<~>kind(X))=>(generous(X)|~kind(X))))&
(![X]:((~tall(X)&strong(X))<=>~calm(X)))&
((?[X]:((~patient(X)&quiet(X))))<=>((quiet(paul)|creative(paul))))&
(![X]:((wise(X)|happy(X))<=>(patient(X)<~>~calm(X))))&
(((~patient(susan)&~generous(susan)))=>((~happy(paul)<~>curious(paul))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~tall(X)|brave(X))<=>(~strong(X)&~calm(X))))&
(((quiet(susan)<~>~humble(susan)))=>((~strong(paul)|wise(paul))))&
((?[X]:(rich(X)))<=>(?[X]:((humble(X)|~creative(X)))))&
(![X]:((~humble(X)<~>~funny(X))<=>(wise(X)<~>~calm(X))))&
(![X]:((~creative(X)<~>~curious(X))=>creative(X)))&
(![X]:((~wise(X)<~>humble(X))=>kind(X)))&
(![X]:((calm(X)&~tall(X))=>(~humble(X)&curious(X))))&
(?[X]:((~rich(X)&~wise(X))))&
(?[X]:(~strong(X)))&
(?[X]:((kind(X)&~creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~quiet(X)|brave(X))))&
((patient(john)&~rich(john))) | ~kind(paul) | [
"p0",
"p4",
"p9",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2298471193566674233973110
% SZS output start Proof for 2298471193566674233973110
1. ? [X0] : (funny(X0) & ~kind(X0)) => (old(paul) & ~calm(paul)) [input p0]
5. ! [X0] : ((strong(X0) & ~tall(X0)) <=> ~calm(X0)) [input p4]
10. ! [X0] : ((brave(X0) | ~tall(X0)) <=> (~calm(X0) & ~strong(X0))) [input p9]
13. ! [X0] : ((~humble(X0) <~> ~funny(X0)) <=> (wise(X0) <~> ~calm(X0))) [input p12]
15. ! [X0] : ((~wise(X0) <~> humble(X0)) => kind(X0)) [input p14]
23. ~kind(paul) [input hypothesis]
26. ? [X0] : (funny(X0) & ~kind(X0)) => ~calm(paul) [pure predicate removal 1]
27. ~calm(paul) | ! [X0] : (~funny(X0) | kind(X0)) [ennf transformation 26]
37. ! [X0] : (kind(X0) | (~wise(X0) <=> humble(X0))) [ennf transformation 15]
43. ! [X0] : (((strong(X0) & ~tall(X0)) | calm(X0)) & (~calm(X0) | (~strong(X0) | tall(X0)))) [nnf transformation 5]
44. ! [X0] : (((strong(X0) & ~tall(X0)) | calm(X0)) & (~calm(X0) | ~strong(X0) | tall(X0))) [flattening 43]
58. ! [X0] : (((brave(X0) | ~tall(X0)) | (calm(X0) | strong(X0))) & ((~calm(X0) & ~strong(X0)) | (~brave(X0) & tall(X0)))) [nnf transformation 10]
59. ! [X0] : ((brave(X0) | ~tall(X0) | calm(X0) | strong(X0)) & ((~calm(X0) & ~strong(X0)) | (~brave(X0) & tall(X0)))) [flattening 58]
66. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0)))) & (((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [nnf transformation 13]
68. ! [X0] : (kind(X0) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0)))) [nnf transformation 37]
79. ~calm(paul) | ~funny(X0) | kind(X0) [cnf transformation 27]
87. ~tall(X0) | calm(X0) [cnf transformation 44]
88. strong(X0) | calm(X0) [cnf transformation 44]
106. ~strong(X0) | tall(X0) [cnf transformation 59]
117. ~humble(X0) | wise(X0) | ~calm(X0) | funny(X0) [cnf transformation 66]
122. ~wise(X0) | humble(X0) | ~calm(X0) | funny(X0) [cnf transformation 66]
126. humble(X0) | kind(X0) | wise(X0) [cnf transformation 68]
127. ~humble(X0) | ~wise(X0) | kind(X0) [cnf transformation 68]
139. ~kind(paul) [cnf transformation 23]
144. 1 <=> ! [X0] : (~funny(X0) | kind(X0)) [avatar definition]
145. ~funny(X0) | kind(X0) <- (1) [avatar component clause 144]
147. 2 <=> calm(paul) [avatar definition]
149. ~calm(paul) <- (~2) [avatar component clause 147]
150. 1 | ~2 [avatar split clause 79,147,144]
276. tall(X0) | calm(X0) [resolution 106,88]
278. calm(X0) [subsumption resolution 276,87]
281. $false <- (~2) [resolution 278,149]
283. 2 [avatar contradiction clause 281]
336. wise(X0) | ~calm(X0) | funny(X0) | kind(X0) | wise(X0) [resolution 117,126]
337. wise(X0) | ~calm(X0) | funny(X0) | kind(X0) [duplicate literal removal 336]
340. wise(X0) | funny(X0) | kind(X0) [subsumption resolution 337,278]
341. wise(X0) | kind(X0) <- (1) [subsumption resolution 340,145]
358. humble(X0) | ~calm(X0) | funny(X0) | kind(X0) <- (1) [resolution 122,341]
359. humble(X0) | funny(X0) | kind(X0) <- (1) [subsumption resolution 358,278]
360. humble(X0) | kind(X0) <- (1) [subsumption resolution 359,145]
374. kind(X4) | ~wise(X4) | kind(X4) <- (1) [resolution 360,127]
376. kind(X4) | ~wise(X4) <- (1) [duplicate literal removal 374]
377. kind(X4) <- (1) [subsumption resolution 376,341]
378. $false <- (1) [resolution 377,139]
379. ~1 [avatar contradiction clause 378]
380. $false [avatar sat refutation 150,283,379]
% SZS output end Proof for 2298471193566674233973110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not calm is either not humble or curious and vice versa.
If someone is not creative or not curious then someone is either kind or not old and vice versa.
If someone is both not calm and not wise then susan is old or not generous and vice versa.
If mary is both calm and not funny then mary is either creative or not calm.
Everyone who is both wise and curious is not calm or strong.
If someone is wise then paul is not curious and vice versa.
If someone is both not creative and not old then lucy is either humble or not humble.
Everyone who is kind or rich is tall.
If john is either old or patient then lucy is not humble or not strong.
Everyone who is tall or not curious is both not humble and humble and vice versa.
If mary is creative then someone is not tall.
Everyone who is either not tall or not funny is not creative.
Everyone who is either not kind or generous is rich.
Everyone who is curious is either not generous or brave.
If someone is both quiet and curious then someone is both creative and brave and vice versa.
Everyone who is not rich is either humble or not old.
Someone is either happy or generous.
Someone is both not rich and curious.
Alice is not old.
Fred is humble.
Someone is not kind.
John is not tall.
Someone is both not rich and funny. | John is patient. | neutral | (![X]:((humble(X)|~calm(X))<=>(~humble(X)<~>curious(X))))&
((?[X]:((~creative(X)|~curious(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:((~calm(X)&~wise(X))))<=>((old(susan)|~generous(susan))))&
(((calm(mary)&~funny(mary)))=>((creative(mary)<~>~calm(mary))))&
(![X]:((wise(X)&curious(X))=>(~calm(X)|strong(X))))&
((?[X]:(wise(X)))<=>(~curious(paul)))&
((?[X]:((~creative(X)&~old(X))))=>((humble(lucy)<~>~humble(lucy))))&
(![X]:((kind(X)|rich(X))=>tall(X)))&
(((old(john)<~>patient(john)))=>((~humble(lucy)|~strong(lucy))))&
(![X]:((tall(X)|~curious(X))<=>(~humble(X)&humble(X))))&
((creative(mary))=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)<~>~funny(X))=>~creative(X)))&
(![X]:((~kind(X)<~>generous(X))=>rich(X)))&
(![X]:(curious(X)=>(~generous(X)<~>brave(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((creative(X)&brave(X)))))&
(![X]:(~rich(X)=>(humble(X)<~>~old(X))))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:((~rich(X)&curious(X))))&
(~old(alice))&
(humble(fred))&
(?[X]:(~kind(X)))&
(~tall(john))&
(?[X]:((~rich(X)&funny(X)))) | patient(john) | []
| null | 0 |
Everyone who is both wise and not creative is humble or generous and vice versa.
If someone is both not humble and not curious then paul is both not quiet and not brave.
Everyone who is either not wise or not old is strong and vice versa.
Everyone who is not curious or not old is wise and vice versa.
Everyone who is quiet is strong or not humble and vice versa.
If susan is either not brave or not tall then mary is not creative.
If someone is not happy or not funny then alice is not humble and vice versa.
If mary is both wise and curious then someone is brave.
If someone is brave then someone is not calm.
Everyone who is both not curious and not funny is not rich and vice versa.
Everyone who is either calm or humble is either not quiet or not brave.
Everyone who is both wise and humble is either wise or not brave and vice versa.
Everyone who is generous or strong is brave and vice versa.
Everyone who is old or rich is not generous or not curious and vice versa.
Everyone who is either kind or curious is both not old and not rich and vice versa.
Everyone who is patient is both creative and humble and vice versa.
Someone is both not funny and not creative.
Someone is both old and strong.
Mary is kind or not old.
Alice is wise or not calm.
Someone is both not kind and not calm.
Fred is not funny. | Susan is not brave. | contradiction | (![X]:((wise(X)&~creative(X))<=>(humble(X)|generous(X))))&
((?[X]:((~humble(X)&~curious(X))))=>((~quiet(paul)&~brave(paul))))&
(![X]:((~wise(X)<~>~old(X))<=>strong(X)))&
(![X]:((~curious(X)|~old(X))<=>wise(X)))&
(![X]:(quiet(X)<=>(strong(X)|~humble(X))))&
(((~brave(susan)<~>~tall(susan)))=>(~creative(mary)))&
((?[X]:((~happy(X)|~funny(X))))<=>(~humble(alice)))&
(((wise(mary)&curious(mary)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:(~calm(X))))&
(![X]:((~curious(X)&~funny(X))<=>~rich(X)))&
(![X]:((calm(X)<~>humble(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((wise(X)&humble(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((generous(X)|strong(X))<=>brave(X)))&
(![X]:((old(X)|rich(X))<=>(~generous(X)|~curious(X))))&
(![X]:((kind(X)<~>curious(X))<=>(~old(X)&~rich(X))))&
(![X]:(patient(X)<=>(creative(X)&humble(X))))&
(?[X]:((~funny(X)&~creative(X))))&
(?[X]:((old(X)&strong(X))))&
((kind(mary)|~old(mary)))&
((wise(alice)|~calm(alice)))&
(?[X]:((~kind(X)&~calm(X))))&
(~funny(fred)) | ~brave(susan) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 864340602273405946291772
% SZS output start Proof for 864340602273405946291772
1. ! [X0] : ((~creative(X0) & wise(X0)) <=> (generous(X0) | humble(X0))) [input p0]
2. ? [X0] : (~curious(X0) & ~humble(X0)) => (~brave(paul) & ~quiet(paul)) [input p1]
3. ! [X0] : ((~wise(X0) <~> ~old(X0)) <=> strong(X0)) [input p2]
4. ! [X0] : ((~old(X0) | ~curious(X0)) <=> wise(X0)) [input p3]
5. ! [X0] : (quiet(X0) <=> (~humble(X0) | strong(X0))) [input p4]
12. ! [X0] : ((humble(X0) & wise(X0)) <=> (wise(X0) <~> ~brave(X0))) [input p11]
13. ! [X0] : ((strong(X0) | generous(X0)) <=> brave(X0)) [input p12]
23. ~brave(susan) [input hypothesis]
25. (~brave(paul) & ~quiet(paul)) | ! [X0] : (curious(X0) | humble(X0)) [ennf transformation 2]
31. ! [X0] : (((~creative(X0) & wise(X0)) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | (creative(X0) | ~wise(X0)))) [nnf transformation 1]
32. ! [X0] : (((~creative(X0) & wise(X0)) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | creative(X0) | ~wise(X0))) [flattening 31]
33. ! [X0] : ((((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | ~strong(X0)) & (strong(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0))))) [nnf transformation 3]
34. ! [X0] : (((~old(X0) | ~curious(X0)) | ~wise(X0)) & (wise(X0) | (old(X0) & curious(X0)))) [nnf transformation 4]
35. ! [X0] : ((~old(X0) | ~curious(X0) | ~wise(X0)) & (wise(X0) | (old(X0) & curious(X0)))) [flattening 34]
36. ! [X0] : ((quiet(X0) | (humble(X0) & ~strong(X0))) & ((~humble(X0) | strong(X0)) | ~quiet(X0))) [nnf transformation 5]
37. ! [X0] : ((quiet(X0) | (humble(X0) & ~strong(X0))) & (~humble(X0) | strong(X0) | ~quiet(X0))) [flattening 36]
51. ! [X0] : (((humble(X0) & wise(X0)) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (~humble(X0) | ~wise(X0)))) [nnf transformation 12]
52. ! [X0] : (((humble(X0) & wise(X0)) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ~humble(X0) | ~wise(X0))) [flattening 51]
53. ! [X0] : (((strong(X0) | generous(X0)) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [nnf transformation 13]
54. ! [X0] : ((strong(X0) | generous(X0) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [flattening 53]
66. ~humble(X0) | wise(X0) [cnf transformation 32]
70. ~quiet(paul) | curious(X0) | humble(X0) [cnf transformation 25]
71. ~brave(paul) | curious(X0) | humble(X0) [cnf transformation 25]
73. ~wise(X0) | strong(X0) | old(X0) [cnf transformation 33]
78. ~old(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 35]
81. quiet(X0) | humble(X0) [cnf transformation 37]
97. brave(X0) | ~wise(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 52]
101. humble(X0) | wise(X0) | brave(X0) [cnf transformation 52]
103. ~strong(X0) | brave(X0) [cnf transformation 54]
124. ~brave(susan) [cnf transformation 23]
125. brave(X0) | ~wise(X0) | ~humble(X0) [duplicate literal removal 97]
128. 1 <=> ! [X0] : (curious(X0) | humble(X0)) [avatar definition]
129. curious(X0) | humble(X0) <- (1) [avatar component clause 128]
131. 2 <=> brave(paul) [avatar definition]
133. ~brave(paul) <- (~2) [avatar component clause 131]
134. 1 | ~2 [avatar split clause 71,131,128]
136. 3 <=> quiet(paul) [avatar definition]
138. ~quiet(paul) <- (~3) [avatar component clause 136]
139. 1 | ~3 [avatar split clause 70,136,128]
145. 5 <=> brave(susan) [avatar definition]
147. ~brave(susan) <- (~5) [avatar component clause 145]
198. brave(X0) | wise(X0) [subsumption resolution 101,66]
199. ~humble(X0) | brave(X0) [subsumption resolution 125,66]
221. ~5 [avatar split clause 124,145]
226. humble(paul) <- (~3) [resolution 81,138]
232. wise(susan) <- (~5) [resolution 198,147]
233. brave(paul) <- (~3) [resolution 199,226]
234. $false <- (~2, ~3) [subsumption resolution 233,133]
235. 2 | 3 [avatar contradiction clause 234]
249. strong(susan) | old(susan) <- (~5) [resolution 73,232]
253. 21 <=> old(susan) [avatar definition]
255. old(susan) <- (21) [avatar component clause 253]
257. 22 <=> strong(susan) [avatar definition]
259. strong(susan) <- (22) [avatar component clause 257]
260. 21 | 22 | 5 [avatar split clause 249,145,257,253]
280. ~curious(susan) | ~wise(susan) <- (21) [resolution 78,255]
281. ~curious(susan) <- (~5, 21) [subsumption resolution 280,232]
307. humble(susan) <- (1, ~5, 21) [resolution 281,129]
613. brave(susan) <- (1, ~5, 21) [resolution 307,199]
616. $false <- (1, ~5, 21) [subsumption resolution 613,147]
617. ~1 | 5 | ~21 [avatar contradiction clause 616]
631. brave(susan) <- (22) [resolution 259,103]
633. $false <- (~5, 22) [subsumption resolution 631,147]
634. 5 | ~22 [avatar contradiction clause 633]
635. $false [avatar sat refutation 134,139,221,235,260,617,634]
% SZS output end Proof for 864340602273405946291772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or wise is not patient.
If someone is strong then mary is not wise or strong.
If paul is either kind or not humble then someone is humble or old.
If someone is both humble and not calm then fred is strong or not funny.
If someone is not quiet or not happy then someone is both not strong and not quiet.
If someone is happy or not tall then alice is wise or old and vice versa.
Everyone who is not curious or curious is not humble and vice versa.
If someone is either wise or not wise then alice is not humble and vice versa.
Everyone who is creative or not generous is curious and vice versa.
If paul is both humble and not funny then someone is not kind or calm and vice versa.
Everyone who is either not creative or old is either not funny or not humble and vice versa.
If someone is not rich then john is curious or not brave.
If someone is either kind or not calm then someone is either quiet or not funny and vice versa.
If someone is wise or not kind then fred is either not creative or funny.
Everyone who is both generous and not calm is not tall or not kind.
Everyone who is either kind or not tall is generous.
Paul is not curious.
Someone is both not brave and not generous.
Someone is rich.
Alice is both not brave and funny.
Lucy is not rich or not funny.
Mary is curious.
John is creative. | Paul is kind. | entailment | (![X]:((~calm(X)|wise(X))=>~patient(X)))&
((?[X]:(strong(X)))=>((~wise(mary)|strong(mary))))&
(((kind(paul)<~>~humble(paul)))=>(?[X]:((humble(X)|old(X)))))&
((?[X]:((humble(X)&~calm(X))))=>((strong(fred)|~funny(fred))))&
((?[X]:((~quiet(X)|~happy(X))))=>(?[X]:((~strong(X)&~quiet(X)))))&
((?[X]:((happy(X)|~tall(X))))<=>((wise(alice)|old(alice))))&
(![X]:((~curious(X)|curious(X))<=>~humble(X)))&
((?[X]:((wise(X)<~>~wise(X))))<=>(~humble(alice)))&
(![X]:((creative(X)|~generous(X))<=>curious(X)))&
(((humble(paul)&~funny(paul)))<=>(?[X]:((~kind(X)|calm(X)))))&
(![X]:((~creative(X)<~>old(X))<=>(~funny(X)<~>~humble(X))))&
((?[X]:(~rich(X)))=>((curious(john)|~brave(john))))&
((?[X]:((kind(X)<~>~calm(X))))<=>(?[X]:((quiet(X)<~>~funny(X)))))&
((?[X]:((wise(X)|~kind(X))))=>((~creative(fred)<~>funny(fred))))&
(![X]:((generous(X)&~calm(X))=>(~tall(X)|~kind(X))))&
(![X]:((kind(X)<~>~tall(X))=>generous(X)))&
(~curious(paul))&
(?[X]:((~brave(X)&~generous(X))))&
(?[X]:(rich(X)))&
((~brave(alice)&funny(alice)))&
((~rich(lucy)|~funny(lucy)))&
(curious(mary))&
(creative(john)) | kind(paul) | [
"p6",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 792404704711071051184380
% SZS output start Proof for 792404704711071051184380
7. ! [X0] : ((curious(X0) | ~curious(X0)) <=> ~humble(X0)) [input p6]
10. (~funny(paul) & humble(paul)) <=> ? [X0] : (calm(X0) | ~kind(X0)) [input p9]
24. ~kind(paul) [input hypothesis]
52. ! [X0] : (((curious(X0) | ~curious(X0)) | humble(X0)) & (~humble(X0) | (~curious(X0) & curious(X0)))) [nnf transformation 7]
53. ! [X0] : ((curious(X0) | ~curious(X0) | humble(X0)) & (~humble(X0) | (~curious(X0) & curious(X0)))) [flattening 52]
60. ((~funny(paul) & humble(paul)) | ! [X0] : (~calm(X0) & kind(X0))) & (? [X0] : (calm(X0) | ~kind(X0)) | (funny(paul) | ~humble(paul))) [nnf transformation 10]
61. ((~funny(paul) & humble(paul)) | ! [X0] : (~calm(X0) & kind(X0))) & (? [X0] : (calm(X0) | ~kind(X0)) | funny(paul) | ~humble(paul)) [flattening 60]
62. ((~funny(paul) & humble(paul)) | ! [X0] : (~calm(X0) & kind(X0))) & (? [X1] : (calm(X1) | ~kind(X1)) | funny(paul) | ~humble(paul)) [rectify 61]
63. ? [X1] : (calm(X1) | ~kind(X1)) => (calm(sK4) | ~kind(sK4)) [choice axiom]
64. ((~funny(paul) & humble(paul)) | ! [X0] : (~calm(X0) & kind(X0))) & ((calm(sK4) | ~kind(sK4)) | funny(paul) | ~humble(paul)) [skolemisation 62,63]
89. ~humble(X0) | curious(X0) [cnf transformation 53]
90. ~humble(X0) | ~curious(X0) [cnf transformation 53]
100. humble(paul) | kind(X0) [cnf transformation 64]
134. ~kind(paul) [cnf transformation 24]
154. 5 <=> kind(paul) [avatar definition]
155. ~kind(paul) <- (~5) [avatar component clause 154]
223. ~humble(X0) [subsumption resolution 89,90]
233. 23 <=> ! [X0] : kind(X0) [avatar definition]
234. kind(X0) <- (23) [avatar component clause 233]
238. kind(X0) [subsumption resolution 100,223]
239. 23 [avatar split clause 238,233]
300. ~5 [avatar split clause 134,154]
301. $false <- (~5, 23) [subsumption resolution 155,234]
302. 5 | ~23 [avatar contradiction clause 301]
305. $false [avatar sat refutation 239,300,302]
% SZS output end Proof for 792404704711071051184380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and wise is quiet or happy and vice versa.
If someone is kind then someone is not brave.
If john is not happy or tall then someone is not calm or not kind and vice versa.
If someone is either generous or not rich then lucy is both not creative and not patient and vice versa.
Everyone who is both strong and funny is either not funny or not strong and vice versa.
Everyone who is not humble is not happy.
If susan is both brave and rich then someone is happy and vice versa.
Everyone who is not patient is not strong.
If alice is both old and kind then someone is wise or not quiet.
Everyone who is old or not brave is happy.
Everyone who is both funny and not humble is not strong or not brave.
If someone is both brave and not brave then someone is either not wise or old and vice versa.
Everyone who is wise is both calm and brave and vice versa.
Everyone who is funny or brave is not happy and vice versa.
Everyone who is either not curious or not creative is either not calm or old.
Everyone who is either not creative or not generous is calm or not kind.
Fred is calm or quiet.
Someone is either wise or happy.
John is not kind.
Someone is either not wise or not patient.
Someone is calm or not curious. | Lucy is not wise. | contradiction | (![X]:((~patient(X)&wise(X))<=>(quiet(X)|happy(X))))&
((?[X]:(kind(X)))=>(?[X]:(~brave(X))))&
(((~happy(john)|tall(john)))<=>(?[X]:((~calm(X)|~kind(X)))))&
((?[X]:((generous(X)<~>~rich(X))))<=>((~creative(lucy)&~patient(lucy))))&
(![X]:((strong(X)&funny(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:(~humble(X)=>~happy(X)))&
(((brave(susan)&rich(susan)))<=>(?[X]:(happy(X))))&
(![X]:(~patient(X)=>~strong(X)))&
(((old(alice)&kind(alice)))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((old(X)|~brave(X))=>happy(X)))&
(![X]:((funny(X)&~humble(X))=>(~strong(X)|~brave(X))))&
((?[X]:((brave(X)&~brave(X))))<=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:(wise(X)<=>(calm(X)&brave(X))))&
(![X]:((funny(X)|brave(X))<=>~happy(X)))&
(![X]:((~curious(X)<~>~creative(X))=>(~calm(X)<~>old(X))))&
(![X]:((~creative(X)<~>~generous(X))=>(calm(X)|~kind(X))))&
((calm(fred)|quiet(fred)))&
(?[X]:((wise(X)<~>happy(X))))&
(~kind(john))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((calm(X)|~curious(X)))) | ~wise(lucy) | [
"p0",
"p9",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 311253970525977923347253
% SZS output start Proof for 311253970525977923347253
1. ! [X0] : ((wise(X0) & ~patient(X0)) <=> (happy(X0) | quiet(X0))) [input p0]
10. ! [X0] : ((~brave(X0) | old(X0)) => happy(X0)) [input p9]
12. ? [X0] : (~brave(X0) & brave(X0)) <=> ? [X0] : (~wise(X0) <~> old(X0)) [input p11]
22. ~wise(lucy) [input hypothesis]
24. ? [X0] : (~brave(X0) & brave(X0)) <=> ? [X1] : (~wise(X1) <~> old(X1)) [rectify 12]
31. ! [X0] : (happy(X0) | (brave(X0) & ~old(X0))) [ennf transformation 10]
35. ! [X0] : (((wise(X0) & ~patient(X0)) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | (~wise(X0) | patient(X0)))) [nnf transformation 1]
36. ! [X0] : (((wise(X0) & ~patient(X0)) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~wise(X0) | patient(X0))) [flattening 35]
59. (? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : ((~wise(X1) | ~old(X1)) & (old(X1) | wise(X1)))) & (? [X1] : ((~old(X1) | wise(X1)) & (old(X1) | ~wise(X1))) | ! [X0] : (brave(X0) | ~brave(X0))) [nnf transformation 24]
60. (? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : ((~wise(X1) | ~old(X1)) & (old(X1) | wise(X1)))) & (? [X2] : ((~old(X2) | wise(X2)) & (old(X2) | ~wise(X2))) | ! [X3] : (brave(X3) | ~brave(X3))) [rectify 59]
61. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK5) & brave(sK5)) [choice axiom]
62. ? [X2] : ((~old(X2) | wise(X2)) & (old(X2) | ~wise(X2))) => ((~old(sK6) | wise(sK6)) & (old(sK6) | ~wise(sK6))) [choice axiom]
63. ((~brave(sK5) & brave(sK5)) | ! [X1] : ((~wise(X1) | ~old(X1)) & (old(X1) | wise(X1)))) & (((~old(sK6) | wise(sK6)) & (old(sK6) | ~wise(sK6))) | ! [X3] : (brave(X3) | ~brave(X3))) [skolemisation 60,62,61]
82. ~happy(X0) | wise(X0) [cnf transformation 36]
105. ~old(X0) | happy(X0) [cnf transformation 31]
109. brave(sK5) | old(X1) | wise(X1) [cnf transformation 63]
111. ~brave(sK5) | old(X1) | wise(X1) [cnf transformation 63]
132. ~wise(lucy) [cnf transformation 22]
221. 20 <=> brave(sK5) [avatar definition]
226. 21 <=> ! [X1] : (old(X1) | wise(X1)) [avatar definition]
227. old(X1) | wise(X1) <- (21) [avatar component clause 226]
228. 21 | ~20 [avatar split clause 111,221,226]
230. 21 | 20 [avatar split clause 109,221,226]
273. wise(X1) | happy(X1) <- (21) [resolution 227,105]
292. wise(X1) <- (21) [subsumption resolution 273,82]
311. $false <- (21) [resolution 292,132]
315. ~21 [avatar contradiction clause 311]
317. $false [avatar sat refutation 228,230,315]
% SZS output end Proof for 311253970525977923347253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is kind or not wise and vice versa.
Everyone who is both not generous and not strong is not patient and vice versa.
Everyone who is either not curious or happy is either not humble or not rich.
Everyone who is creative or old is wise or quiet.
If mary is both curious and kind then someone is wise and vice versa.
Everyone who is generous is brave and vice versa.
If lucy is funny then paul is wise or not curious.
If someone is not wise then john is not wise and vice versa.
Everyone who is both not funny and not patient is either rich or wise.
Everyone who is not patient or not creative is not creative.
If mary is either not calm or wise then someone is either strong or not wise and vice versa.
If fred is either creative or not calm then paul is old.
Everyone who is wise or not happy is brave and vice versa.
Everyone who is quiet or not calm is either quiet or calm and vice versa.
Everyone who is not happy is both tall and kind.
If john is humble then someone is not rich and vice versa.
Lucy is either not patient or not funny.
Someone is old.
Someone is either patient or not old.
Susan is not wise or not tall.
Someone is both brave and not curious.
Someone is tall.
Someone is both old and not kind.
Someone is either not humble or not creative. | Paul is not tall. | neutral | (![X]:(~calm(X)<=>(kind(X)|~wise(X))))&
(![X]:((~generous(X)&~strong(X))<=>~patient(X)))&
(![X]:((~curious(X)<~>happy(X))=>(~humble(X)<~>~rich(X))))&
(![X]:((creative(X)|old(X))=>(wise(X)|quiet(X))))&
(((curious(mary)&kind(mary)))<=>(?[X]:(wise(X))))&
(![X]:(generous(X)<=>brave(X)))&
((funny(lucy))=>((wise(paul)|~curious(paul))))&
((?[X]:(~wise(X)))<=>(~wise(john)))&
(![X]:((~funny(X)&~patient(X))=>(rich(X)<~>wise(X))))&
(![X]:((~patient(X)|~creative(X))=>~creative(X)))&
(((~calm(mary)<~>wise(mary)))<=>(?[X]:((strong(X)<~>~wise(X)))))&
(((creative(fred)<~>~calm(fred)))=>(old(paul)))&
(![X]:((wise(X)|~happy(X))<=>brave(X)))&
(![X]:((quiet(X)|~calm(X))<=>(quiet(X)<~>calm(X))))&
(![X]:(~happy(X)=>(tall(X)&kind(X))))&
((humble(john))<=>(?[X]:(~rich(X))))&
((~patient(lucy)<~>~funny(lucy)))&
(?[X]:(old(X)))&
(?[X]:((patient(X)<~>~old(X))))&
((~wise(susan)|~tall(susan)))&
(?[X]:((brave(X)&~curious(X))))&
(?[X]:(tall(X)))&
(?[X]:((old(X)&~kind(X))))&
(?[X]:((~humble(X)<~>~creative(X)))) | ~tall(paul) | []
| null | 0 |
If fred is both curious and not strong then someone is curious and vice versa.
If someone is tall or not curious then alice is both quiet and not humble and vice versa.
Everyone who is both not calm and happy is either calm or not humble.
If someone is both kind and quiet then someone is both funny and tall.
Everyone who is either not brave or not quiet is both not wise and not funny and vice versa.
If someone is both not kind and kind then someone is either generous or creative.
Everyone who is not patient is both patient and generous.
If alice is both not curious and not quiet then john is either brave or not generous.
If fred is either not tall or old then lucy is not tall and vice versa.
If someone is either generous or curious then lucy is curious and vice versa.
If someone is either old or not funny then someone is either not curious or not kind and vice versa.
Everyone who is either generous or not funny is old or not curious and vice versa.
Everyone who is either tall or not curious is both not old and funny.
Everyone who is patient or not happy is brave and vice versa.
Everyone who is both not generous and not patient is both not patient and rich and vice versa.
Everyone who is calm or not creative is tall and vice versa.
Someone is patient.
Someone is either humble or generous.
Mary is funny.
Susan is old.
Someone is not curious.
Someone is either not wise or happy. | Lucy is not tall. | neutral | (((curious(fred)&~strong(fred)))<=>(?[X]:(curious(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((quiet(alice)&~humble(alice))))&
(![X]:((~calm(X)&happy(X))=>(calm(X)<~>~humble(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((funny(X)&tall(X)))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(~wise(X)&~funny(X))))&
((?[X]:((~kind(X)&kind(X))))=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:(~patient(X)=>(patient(X)&generous(X))))&
(((~curious(alice)&~quiet(alice)))=>((brave(john)<~>~generous(john))))&
(((~tall(fred)<~>old(fred)))<=>(~tall(lucy)))&
((?[X]:((generous(X)<~>curious(X))))<=>(curious(lucy)))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~kind(X)))))&
(![X]:((generous(X)<~>~funny(X))<=>(old(X)|~curious(X))))&
(![X]:((tall(X)<~>~curious(X))=>(~old(X)&funny(X))))&
(![X]:((patient(X)|~happy(X))<=>brave(X)))&
(![X]:((~generous(X)&~patient(X))<=>(~patient(X)&rich(X))))&
(![X]:((calm(X)|~creative(X))<=>tall(X)))&
(?[X]:(patient(X)))&
(?[X]:((humble(X)<~>generous(X))))&
(funny(mary))&
(old(susan))&
(?[X]:(~curious(X)))&
(?[X]:((~wise(X)<~>happy(X)))) | ~tall(lucy) | []
| null | 0 |
If someone is patient then someone is both happy and not patient.
If fred is curious or brave then someone is both quiet and rich.
Everyone who is strong or not patient is both not rich and not funny and vice versa.
If someone is either not wise or curious then someone is calm.
Everyone who is both not generous and tall is either not humble or funny.
If someone is happy or funny then mary is both strong and generous.
If someone is either brave or calm then someone is both wise and not creative and vice versa.
Everyone who is both tall and not funny is both not happy and generous and vice versa.
If someone is either quiet or creative then someone is patient or not calm and vice versa.
Everyone who is patient is both not wise and not calm and vice versa.
If someone is either not creative or not kind then someone is either happy or not kind.
Everyone who is not calm or not generous is either not generous or not tall and vice versa.
If someone is either not kind or wise then someone is both patient and brave.
Everyone who is either not wise or curious is not humble.
Everyone who is kind is quiet or kind and vice versa.
Lucy is both not humble and curious.
Someone is either patient or not quiet.
Lucy is both not happy and curious.
Someone is humble.
Someone is strong.
Paul is patient or not happy.
Alice is not patient. | Lucy is not funny. | entailment | ((?[X]:(patient(X)))=>(?[X]:((happy(X)&~patient(X)))))&
(((curious(fred)|brave(fred)))=>(?[X]:((quiet(X)&rich(X)))))&
(![X]:((strong(X)|~patient(X))<=>(~rich(X)&~funny(X))))&
((?[X]:((~wise(X)<~>curious(X))))=>(?[X]:(calm(X))))&
(![X]:((~generous(X)&tall(X))=>(~humble(X)<~>funny(X))))&
((?[X]:((happy(X)|funny(X))))=>((strong(mary)&generous(mary))))&
((?[X]:((brave(X)<~>calm(X))))<=>(?[X]:((wise(X)&~creative(X)))))&
(![X]:((tall(X)&~funny(X))<=>(~happy(X)&generous(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:(patient(X)<=>(~wise(X)&~calm(X))))&
((?[X]:((~creative(X)<~>~kind(X))))=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((~calm(X)|~generous(X))<=>(~generous(X)<~>~tall(X))))&
((?[X]:((~kind(X)<~>wise(X))))=>(?[X]:((patient(X)&brave(X)))))&
(![X]:((~wise(X)<~>curious(X))=>~humble(X)))&
(![X]:(kind(X)<=>(quiet(X)|kind(X))))&
((~humble(lucy)&curious(lucy)))&
(?[X]:((patient(X)<~>~quiet(X))))&
((~happy(lucy)&curious(lucy)))&
(?[X]:(humble(X)))&
(?[X]:(strong(X)))&
((patient(paul)|~happy(paul)))&
(~patient(alice)) | ~funny(lucy) | [
"p4",
"p7",
"p11",
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 4358138767111423228500106
% SZS output start Proof for 4358138767111423228500106
5. ! [X0] : ((tall(X0) & ~generous(X0)) => (~humble(X0) <~> funny(X0))) [input p4]
8. ! [X0] : ((~funny(X0) & tall(X0)) <=> (generous(X0) & ~happy(X0))) [input p7]
12. ! [X0] : ((~generous(X0) | ~calm(X0)) <=> (~generous(X0) <~> ~tall(X0))) [input p11]
16. curious(lucy) & ~humble(lucy) [input p15]
18. curious(lucy) & ~happy(lucy) [input p17]
23. funny(lucy) [input hypothesis]
33. ! [X0] : ((~humble(X0) <~> funny(X0)) | (~tall(X0) | generous(X0))) [ennf transformation 5]
34. ! [X0] : ((~humble(X0) <~> funny(X0)) | ~tall(X0) | generous(X0)) [flattening 33]
50. ! [X0] : (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | ~tall(X0) | generous(X0)) [nnf transformation 34]
56. ! [X0] : (((~funny(X0) & tall(X0)) | (~generous(X0) | happy(X0))) & ((generous(X0) & ~happy(X0)) | (funny(X0) | ~tall(X0)))) [nnf transformation 8]
57. ! [X0] : (((~funny(X0) & tall(X0)) | ~generous(X0) | happy(X0)) & ((generous(X0) & ~happy(X0)) | funny(X0) | ~tall(X0))) [flattening 56]
69. ! [X0] : (((~generous(X0) | ~calm(X0)) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0)))) & (((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (generous(X0) & calm(X0)))) [nnf transformation 12]
70. ! [X0] : ((~generous(X0) | ~calm(X0) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0)))) & (((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (generous(X0) & calm(X0)))) [flattening 69]
99. ~tall(X0) | humble(X0) | ~funny(X0) | generous(X0) [cnf transformation 50]
111. ~tall(X0) | funny(X0) | generous(X0) [cnf transformation 57]
113. ~generous(X0) | ~funny(X0) | happy(X0) [cnf transformation 57]
130. tall(X0) | generous(X0) | generous(X0) [cnf transformation 70]
142. ~humble(lucy) [cnf transformation 16]
146. ~happy(lucy) [cnf transformation 18]
152. funny(lucy) [cnf transformation 23]
153. tall(X0) | generous(X0) [duplicate literal removal 130]
353. funny(X0) | generous(X0) | generous(X0) [resolution 111,153]
354. generous(X0) | funny(X0) [duplicate literal removal 353]
441. humble(X0) | ~funny(X0) | generous(X0) | generous(X0) [resolution 99,153]
443. humble(X0) | ~funny(X0) | generous(X0) [duplicate literal removal 441]
444. humble(X0) | generous(X0) [subsumption resolution 443,354]
448. generous(lucy) [resolution 444,142]
471. ~funny(lucy) | happy(lucy) [resolution 448,113]
482. happy(lucy) [subsumption resolution 471,152]
483. $false [subsumption resolution 482,146]
% SZS output end Proof for 4358138767111423228500106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either strong or not patient then someone is both happy and funny and vice versa. If someone is rich then john is not strong and vice versa. If someone is both not old and calm then fred is either strong or happy and vice versa. Everyone who is both not kind and generous is either not kind or patient. Everyone who is strong or curious is either strong or brave and vice versa. Everyone who is both not generous and calm is tall or rich and vice versa. If paul is calm then alice is both not creative and creative. Everyone who is tall is not strong or old. Everyone who is either not patient or not old is humble and vice versa. If someone is kind then someone is not generous and vice versa. Everyone who is not funny is either not patient or not tall. Everyone who is either not patient or funny is not happy and vice versa. If fred is tall or not tall then someone is kind. If someone is either not patient or not wise then someone is either not calm or not old and vice versa. If john is tall then someone is old or brave. Everyone who is not strong or not brave is not humble and vice versa. Lucy is both wise and happy. Someone is not old. Fred is both not brave and not old. Mary is both patient and curious. John is both not happy and not brave. Someone is either not brave or not humble. Lucy is not rich or not generous. | Lucy is tall. | neutral | (((strong(paul)<~>~patient(paul)))<=>(?[X]:((happy(X)&funny(X)))))&
((?[X]:(rich(X)))<=>(~strong(john)))&
((?[X]:((~old(X)&calm(X))))<=>((strong(fred)<~>happy(fred))))&
(![X]:((~kind(X)&generous(X))=>(~kind(X)<~>patient(X))))&
(![X]:((strong(X)|curious(X))<=>(strong(X)<~>brave(X))))&
(![X]:((~generous(X)&calm(X))<=>(tall(X)|rich(X))))&
((calm(paul))=>((~creative(alice)&creative(alice))))&
(![X]:(tall(X)=>(~strong(X)|old(X))))&
(![X]:((~patient(X)<~>~old(X))<=>humble(X)))&
((?[X]:(kind(X)))<=>(?[X]:(~generous(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>~tall(X))))&
(![X]:((~patient(X)<~>funny(X))<=>~happy(X)))&
(((tall(fred)|~tall(fred)))=>(?[X]:(kind(X))))&
((?[X]:((~patient(X)<~>~wise(X))))<=>(?[X]:((~calm(X)<~>~old(X)))))&
((tall(john))=>(?[X]:((old(X)|brave(X)))))&
(![X]:((~strong(X)|~brave(X))<=>~humble(X)))&
((wise(lucy)&happy(lucy)))&
(?[X]:(~old(X)))&
((~brave(fred)&~old(fred)))&
((patient(mary)&curious(mary)))&
((~happy(john)&~brave(john)))&
(?[X]:((~brave(X)<~>~humble(X))))&
((~rich(lucy)|~generous(lucy))) | tall(lucy) | []
| null | 0 |
Everyone who is either old or not patient is tall or patient and vice versa.
If susan is both tall and calm then susan is both strong and not strong.
Everyone who is either not tall or not old is strong and vice versa.
Everyone who is not humble is either not kind or funny and vice versa.
If mary is either kind or strong then someone is not funny.
If someone is funny then someone is either tall or not wise and vice versa.
If someone is creative or funny then mary is humble or patient and vice versa.
Everyone who is both tall and curious is generous.
If mary is both not old and not funny then someone is funny and vice versa.
If someone is not creative or strong then fred is happy and vice versa.
Everyone who is strong is patient.
Everyone who is patient is both not rich and brave and vice versa.
If lucy is rich or not funny then someone is curious.
If lucy is brave then someone is quiet or not humble and vice versa.
Everyone who is either not old or not brave is either old or not strong.
Mary is both brave and old.
Paul is either not curious or generous.
Someone is either rich or not creative.
Someone is not brave or generous.
Alice is calm.
Fred is happy or not brave.
Fred is not wise or not funny. | Mary is not rich. | entailment | (![X]:((old(X)<~>~patient(X))<=>(tall(X)|patient(X))))&
(((tall(susan)&calm(susan)))=>((strong(susan)&~strong(susan))))&
(![X]:((~tall(X)<~>~old(X))<=>strong(X)))&
(![X]:(~humble(X)<=>(~kind(X)<~>funny(X))))&
(((kind(mary)<~>strong(mary)))=>(?[X]:(~funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((tall(X)<~>~wise(X)))))&
((?[X]:((creative(X)|funny(X))))<=>((humble(mary)|patient(mary))))&
(![X]:((tall(X)&curious(X))=>generous(X)))&
(((~old(mary)&~funny(mary)))<=>(?[X]:(funny(X))))&
((?[X]:((~creative(X)|strong(X))))<=>(happy(fred)))&
(![X]:(strong(X)=>patient(X)))&
(![X]:(patient(X)<=>(~rich(X)&brave(X))))&
(((rich(lucy)|~funny(lucy)))=>(?[X]:(curious(X))))&
((brave(lucy))<=>(?[X]:((quiet(X)|~humble(X)))))&
(![X]:((~old(X)<~>~brave(X))=>(old(X)<~>~strong(X))))&
((brave(mary)&old(mary)))&
((~curious(paul)<~>generous(paul)))&
(?[X]:((rich(X)<~>~creative(X))))&
(?[X]:((~brave(X)|generous(X))))&
(calm(alice))&
((happy(fred)|~brave(fred)))&
((~wise(fred)|~funny(fred))) | ~rich(mary) | [
"p0",
"p2",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 6154455636713478367692394
% SZS output start Proof for 6154455636713478367692394
1. ! [X0] : ((old(X0) <~> ~patient(X0)) <=> (patient(X0) | tall(X0))) [input p0]
3. ! [X0] : ((~tall(X0) <~> ~old(X0)) <=> strong(X0)) [input p2]
11. ! [X0] : (strong(X0) => patient(X0)) [input p10]
12. ! [X0] : (patient(X0) <=> (brave(X0) & ~rich(X0))) [input p11]
23. rich(mary) [input hypothesis]
30. ! [X0] : (patient(X0) | ~strong(X0)) [ennf transformation 11]
33. ! [X0] : ((((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | (~patient(X0) & ~tall(X0))) & ((patient(X0) | tall(X0)) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0))))) [nnf transformation 1]
34. ! [X0] : ((((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | (~patient(X0) & ~tall(X0))) & (patient(X0) | tall(X0) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0))))) [flattening 33]
35. ! [X0] : ((((old(X0) | tall(X0)) & (~old(X0) | ~tall(X0))) | ~strong(X0)) & (strong(X0) | ((~tall(X0) | old(X0)) & (~old(X0) | tall(X0))))) [nnf transformation 3]
59. ! [X0] : ((patient(X0) | (~brave(X0) | rich(X0))) & ((brave(X0) & ~rich(X0)) | ~patient(X0))) [nnf transformation 12]
60. ! [X0] : ((patient(X0) | ~brave(X0) | rich(X0)) & ((brave(X0) & ~rich(X0)) | ~patient(X0))) [flattening 59]
75. patient(X0) | tall(X0) | old(X0) | patient(X0) [cnf transformation 34]
77. ~patient(X0) | old(X0) | ~patient(X0) [cnf transformation 34]
78. ~tall(X0) | ~old(X0) | patient(X0) [cnf transformation 34]
82. strong(X0) | ~old(X0) | tall(X0) [cnf transformation 35]
83. strong(X0) | ~tall(X0) | old(X0) [cnf transformation 35]
107. ~strong(X0) | patient(X0) [cnf transformation 30]
108. ~rich(X0) | ~patient(X0) [cnf transformation 60]
130. rich(mary) [cnf transformation 23]
133. patient(X0) | tall(X0) | old(X0) [duplicate literal removal 75]
134. ~patient(X0) | old(X0) [duplicate literal removal 77]
135. tall(X0) | old(X0) [subsumption resolution 133,134]
150. strong(X0) | old(X0) [subsumption resolution 83,135]
151. strong(X0) | tall(X0) [subsumption resolution 82,135]
192. 13 <=> patient(mary) [avatar definition]
194. ~patient(mary) <- (~13) [avatar component clause 192]
335. ~patient(mary) [resolution 108,130]
338. ~13 [avatar split clause 335,192]
340. old(X0) | patient(X0) [resolution 150,107]
341. old(X0) [subsumption resolution 340,134]
342. tall(X0) | patient(X0) [resolution 151,107]
358. patient(X0) | ~old(X0) | patient(X0) [resolution 342,78]
359. patient(X0) | ~old(X0) [duplicate literal removal 358]
360. patient(X0) [subsumption resolution 359,341]
363. $false <- (~13) [resolution 360,194]
366. 13 [avatar contradiction clause 363]
367. $false [avatar sat refutation 338,366]
% SZS output end Proof for 6154455636713478367692394
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or rich then alice is both calm and not calm and vice versa.
If susan is kind then alice is creative or funny and vice versa.
Everyone who is both not rich and not funny is humble or patient and vice versa.
Everyone who is not kind is either strong or wise and vice versa.
Everyone who is calm is either rich or not humble and vice versa.
Everyone who is brave or humble is strong or generous.
If someone is old or kind then john is both not wise and funny.
Everyone who is both funny and not rich is not kind or quiet.
Everyone who is both curious and brave is both tall and not calm.
Everyone who is either calm or rich is not wise or not funny.
Everyone who is either not happy or calm is either not brave or not quiet.
Everyone who is both rich and not quiet is not humble and vice versa.
If someone is not humble then alice is not wise.
Everyone who is both not brave and calm is both creative and brave and vice versa.
If susan is generous or kind then john is both tall and funny.
If someone is both brave and not quiet then alice is funny or calm and vice versa.
Someone is not funny or calm.
Someone is either not curious or patient.
Someone is either tall or quiet.
Fred is not funny or happy.
Someone is calm or not calm.
Fred is either not humble or not tall. | John is not humble. | contradiction | ((?[X]:((~happy(X)|rich(X))))<=>((calm(alice)&~calm(alice))))&
((kind(susan))<=>((creative(alice)|funny(alice))))&
(![X]:((~rich(X)&~funny(X))<=>(humble(X)|patient(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>wise(X))))&
(![X]:(calm(X)<=>(rich(X)<~>~humble(X))))&
(![X]:((brave(X)|humble(X))=>(strong(X)|generous(X))))&
((?[X]:((old(X)|kind(X))))=>((~wise(john)&funny(john))))&
(![X]:((funny(X)&~rich(X))=>(~kind(X)|quiet(X))))&
(![X]:((curious(X)&brave(X))=>(tall(X)&~calm(X))))&
(![X]:((calm(X)<~>rich(X))=>(~wise(X)|~funny(X))))&
(![X]:((~happy(X)<~>calm(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((rich(X)&~quiet(X))<=>~humble(X)))&
((?[X]:(~humble(X)))=>(~wise(alice)))&
(![X]:((~brave(X)&calm(X))<=>(creative(X)&brave(X))))&
(((generous(susan)|kind(susan)))=>((tall(john)&funny(john))))&
((?[X]:((brave(X)&~quiet(X))))<=>((funny(alice)|calm(alice))))&
(?[X]:((~funny(X)|calm(X))))&
(?[X]:((~curious(X)<~>patient(X))))&
(?[X]:((tall(X)<~>quiet(X))))&
((~funny(fred)|happy(fred)))&
(?[X]:((calm(X)|~calm(X))))&
((~humble(fred)<~>~tall(fred))) | ~humble(john) | [
"p0",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 2156249307301589114346481
% SZS output start Proof for 2156249307301589114346481
1. ? [X0] : (rich(X0) | ~happy(X0)) <=> (~calm(alice) & calm(alice)) [input p0]
12. ! [X0] : ((~quiet(X0) & rich(X0)) <=> ~humble(X0)) [input p11]
23. ~humble(john) [input hypothesis]
37. (? [X0] : (rich(X0) | ~happy(X0)) | (calm(alice) | ~calm(alice))) & ((~calm(alice) & calm(alice)) | ! [X0] : (~rich(X0) & happy(X0))) [nnf transformation 1]
38. (? [X0] : (rich(X0) | ~happy(X0)) | calm(alice) | ~calm(alice)) & ((~calm(alice) & calm(alice)) | ! [X0] : (~rich(X0) & happy(X0))) [flattening 37]
39. (? [X0] : (rich(X0) | ~happy(X0)) | calm(alice) | ~calm(alice)) & ((~calm(alice) & calm(alice)) | ! [X1] : (~rich(X1) & happy(X1))) [rectify 38]
40. ? [X0] : (rich(X0) | ~happy(X0)) => (rich(sK0) | ~happy(sK0)) [choice axiom]
41. ((rich(sK0) | ~happy(sK0)) | calm(alice) | ~calm(alice)) & ((~calm(alice) & calm(alice)) | ! [X1] : (~rich(X1) & happy(X1))) [skolemisation 39,40]
50. ! [X0] : (((~quiet(X0) & rich(X0)) | humble(X0)) & (~humble(X0) | (quiet(X0) | ~rich(X0)))) [nnf transformation 12]
51. ! [X0] : (((~quiet(X0) & rich(X0)) | humble(X0)) & (~humble(X0) | quiet(X0) | ~rich(X0))) [flattening 50]
71. calm(alice) | ~rich(X1) [cnf transformation 41]
73. ~calm(alice) | ~rich(X1) [cnf transformation 41]
105. humble(X0) | rich(X0) [cnf transformation 51]
130. ~humble(john) [cnf transformation 23]
134. 1 <=> ! [X1] : ~rich(X1) [avatar definition]
135. ~rich(X1) <- (1) [avatar component clause 134]
137. 2 <=> calm(alice) [avatar definition]
140. 1 | ~2 [avatar split clause 73,137,134]
145. 1 | 2 [avatar split clause 71,137,134]
263. rich(john) [resolution 105,130]
267. $false <- (1) [subsumption resolution 263,135]
268. ~1 [avatar contradiction clause 267]
272. $false [avatar sat refutation 140,145,268]
% SZS output end Proof for 2156249307301589114346481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is either not kind or tall and vice versa. Everyone who is curious is both not rich and not creative. If someone is not brave or quiet then someone is kind and vice versa. Everyone who is funny or strong is both humble and not calm. If susan is rich then alice is rich and vice versa. Everyone who is not creative or generous is not patient or not generous and vice versa. Everyone who is not brave or patient is brave and vice versa. If someone is strong then someone is quiet or not rich. If someone is strong or quiet then someone is both funny and not creative and vice versa. Everyone who is not generous or quiet is not curious and vice versa. If susan is patient or not strong then someone is both not rich and wise. Everyone who is both not kind and wise is either not brave or not funny and vice versa. If lucy is both happy and kind then alice is both funny and creative. If paul is quiet then someone is not happy or happy. Everyone who is either calm or funny is both quiet and not old and vice versa. If someone is either not happy or not humble then someone is wise or not patient. Someone is not rich. Someone is calm or tall. Someone is not patient or not creative. Paul is either not strong or not humble. Someone is either kind or brave. Someone is either tall or not patient. Mary is brave. Someone is either not curious or quiet. | Mary is generous. | contradiction | (![X]:(patient(X)<=>(~kind(X)<~>tall(X))))&
(![X]:(curious(X)=>(~rich(X)&~creative(X))))&
((?[X]:((~brave(X)|quiet(X))))<=>(?[X]:(kind(X))))&
(![X]:((funny(X)|strong(X))=>(humble(X)&~calm(X))))&
((rich(susan))<=>(rich(alice)))&
(![X]:((~creative(X)|generous(X))<=>(~patient(X)|~generous(X))))&
(![X]:((~brave(X)|patient(X))<=>brave(X)))&
((?[X]:(strong(X)))=>(?[X]:((quiet(X)|~rich(X)))))&
((?[X]:((strong(X)|quiet(X))))<=>(?[X]:((funny(X)&~creative(X)))))&
(![X]:((~generous(X)|quiet(X))<=>~curious(X)))&
(((patient(susan)|~strong(susan)))=>(?[X]:((~rich(X)&wise(X)))))&
(![X]:((~kind(X)&wise(X))<=>(~brave(X)<~>~funny(X))))&
(((happy(lucy)&kind(lucy)))=>((funny(alice)&creative(alice))))&
((quiet(paul))=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((calm(X)<~>funny(X))<=>(quiet(X)&~old(X))))&
((?[X]:((~happy(X)<~>~humble(X))))=>(?[X]:((wise(X)|~patient(X)))))&
(?[X]:(~rich(X)))&
(?[X]:((calm(X)|tall(X))))&
(?[X]:((~patient(X)|~creative(X))))&
((~strong(paul)<~>~humble(paul)))&
(?[X]:((kind(X)<~>brave(X))))&
(?[X]:((tall(X)<~>~patient(X))))&
(brave(mary))&
(?[X]:((~curious(X)<~>quiet(X)))) | generous(mary) | [
"p5",
"p6",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 2552181636098462396561897
% SZS output start Proof for 2552181636098462396561897
6. ! [X0] : ((generous(X0) | ~creative(X0)) <=> (~generous(X0) | ~patient(X0))) [input p5]
7. ! [X0] : ((patient(X0) | ~brave(X0)) <=> brave(X0)) [input p6]
23. brave(mary) [input p22]
25. generous(mary) [input hypothesis]
45. ! [X0] : (((generous(X0) | ~creative(X0)) | (generous(X0) & patient(X0))) & ((~generous(X0) | ~patient(X0)) | (~generous(X0) & creative(X0)))) [nnf transformation 6]
46. ! [X0] : ((generous(X0) | ~creative(X0) | (generous(X0) & patient(X0))) & (~generous(X0) | ~patient(X0) | (~generous(X0) & creative(X0)))) [flattening 45]
47. ! [X0] : (((patient(X0) | ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~patient(X0) & brave(X0)))) [nnf transformation 7]
48. ! [X0] : ((patient(X0) | ~brave(X0) | ~brave(X0)) & (brave(X0) | (~patient(X0) & brave(X0)))) [flattening 47]
103. ~generous(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 46]
108. patient(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 48]
148. brave(mary) [cnf transformation 23]
151. generous(mary) [cnf transformation 25]
153. ~brave(X0) | patient(X0) [duplicate literal removal 108]
154. ~generous(X0) | ~patient(X0) [duplicate literal removal 103]
340. patient(mary) [resolution 153,148]
343. ~patient(mary) [resolution 154,151]
344. $false [subsumption resolution 343,340]
% SZS output end Proof for 2552181636098462396561897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not humble then paul is not funny or not calm and vice versa.
Everyone who is not funny or creative is both not humble and happy.
Everyone who is either not tall or strong is both happy and humble and vice versa.
Everyone who is not strong is either not patient or not calm.
If alice is old or curious then someone is humble or funny and vice versa.
If someone is not patient or quiet then someone is both calm and not humble and vice versa.
If someone is not generous or patient then susan is not tall and vice versa.
If someone is both tall and kind then someone is either curious or not curious and vice versa.
If someone is both strong and not creative then someone is not happy or not funny.
Everyone who is either not rich or not patient is wise or not strong and vice versa.
Everyone who is both calm and not humble is quiet or not old and vice versa.
Everyone who is both not old and curious is rich.
Everyone who is tall is generous or strong.
Everyone who is either not brave or not humble is happy or not wise.
Someone is both funny and rich.
Mary is either not patient or humble.
Someone is funny or not quiet.
Lucy is either not kind or patient.
Someone is either creative or not strong.
Paul is not creative.
Someone is both not humble and not creative. | Susan is not quiet. | neutral | ((~humble(alice))<=>((~funny(paul)|~calm(paul))))&
(![X]:((~funny(X)|creative(X))=>(~humble(X)&happy(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(happy(X)&humble(X))))&
(![X]:(~strong(X)=>(~patient(X)<~>~calm(X))))&
(((old(alice)|curious(alice)))<=>(?[X]:((humble(X)|funny(X)))))&
((?[X]:((~patient(X)|quiet(X))))<=>(?[X]:((calm(X)&~humble(X)))))&
((?[X]:((~generous(X)|patient(X))))<=>(~tall(susan)))&
((?[X]:((tall(X)&kind(X))))<=>(?[X]:((curious(X)<~>~curious(X)))))&
((?[X]:((strong(X)&~creative(X))))=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~rich(X)<~>~patient(X))<=>(wise(X)|~strong(X))))&
(![X]:((calm(X)&~humble(X))<=>(quiet(X)|~old(X))))&
(![X]:((~old(X)&curious(X))=>rich(X)))&
(![X]:(tall(X)=>(generous(X)|strong(X))))&
(![X]:((~brave(X)<~>~humble(X))=>(happy(X)|~wise(X))))&
(?[X]:((funny(X)&rich(X))))&
((~patient(mary)<~>humble(mary)))&
(?[X]:((funny(X)|~quiet(X))))&
((~kind(lucy)<~>patient(lucy)))&
(?[X]:((creative(X)<~>~strong(X))))&
(~creative(paul))&
(?[X]:((~humble(X)&~creative(X)))) | ~quiet(susan) | []
| null | 0 |
Everyone who is both quiet and not calm is funny or not humble and vice versa.
If someone is not funny then someone is either not patient or rich and vice versa.
Everyone who is not funny or wise is either tall or not happy.
If someone is both funny and kind then someone is both not happy and not rich.
If fred is either funny or not kind then alice is quiet or humble.
If someone is both funny and not calm then alice is both kind and not old.
If someone is both not quiet and rich then someone is both not quiet and wise and vice versa.
If paul is not calm then someone is not brave or old.
Everyone who is both not brave and creative is wise or not creative.
If someone is not generous then someone is not patient and vice versa.
If paul is both not strong and not happy then someone is both not kind and brave and vice versa.
Everyone who is not creative or happy is brave or wise.
Everyone who is creative is either generous or creative.
If fred is either curious or not old then someone is either not curious or not strong.
Everyone who is both rich and not tall is either kind or not wise and vice versa.
Everyone who is either not strong or not quiet is humble or strong and vice versa.
Alice is not happy.
Fred is both rich and not quiet.
Someone is old or patient.
John is either not brave or strong.
Someone is both old and not calm.
Someone is not generous or kind.
Someone is either not happy or not strong.
Someone is wise or not wise. | Fred is not rich. | contradiction | (![X]:((quiet(X)&~calm(X))<=>(funny(X)|~humble(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~patient(X)<~>rich(X)))))&
(![X]:((~funny(X)|wise(X))=>(tall(X)<~>~happy(X))))&
((?[X]:((funny(X)&kind(X))))=>(?[X]:((~happy(X)&~rich(X)))))&
(((funny(fred)<~>~kind(fred)))=>((quiet(alice)|humble(alice))))&
((?[X]:((funny(X)&~calm(X))))=>((kind(alice)&~old(alice))))&
((?[X]:((~quiet(X)&rich(X))))<=>(?[X]:((~quiet(X)&wise(X)))))&
((~calm(paul))=>(?[X]:((~brave(X)|old(X)))))&
(![X]:((~brave(X)&creative(X))=>(wise(X)|~creative(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~patient(X))))&
(((~strong(paul)&~happy(paul)))<=>(?[X]:((~kind(X)&brave(X)))))&
(![X]:((~creative(X)|happy(X))=>(brave(X)|wise(X))))&
(![X]:(creative(X)=>(generous(X)<~>creative(X))))&
(((curious(fred)<~>~old(fred)))=>(?[X]:((~curious(X)<~>~strong(X)))))&
(![X]:((rich(X)&~tall(X))<=>(kind(X)<~>~wise(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(humble(X)|strong(X))))&
(~happy(alice))&
((rich(fred)&~quiet(fred)))&
(?[X]:((old(X)|patient(X))))&
((~brave(john)<~>strong(john)))&
(?[X]:((old(X)&~calm(X))))&
(?[X]:((~generous(X)|kind(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((wise(X)|~wise(X)))) | ~rich(fred) | [
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 8605359907206662238651967
% SZS output start Proof for 8605359907206662238651967
18. ~quiet(fred) & rich(fred) [input p17]
25. ~rich(fred) [input hypothesis]
143. rich(fred) [cnf transformation 18]
154. ~rich(fred) [cnf transformation 25]
351. $false [subsumption resolution 154,143]
% SZS output end Proof for 8605359907206662238651967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is old then someone is rich or not old and vice versa.
If someone is quiet or wise then someone is not brave and vice versa.
If susan is not happy or not wise then lucy is either kind or not old.
If someone is curious then someone is both happy and not happy.
Everyone who is old is humble and vice versa.
If someone is not strong or strong then someone is either not generous or not humble.
Everyone who is either humble or happy is both not tall and brave and vice versa.
Everyone who is not tall is not humble and vice versa.
Everyone who is creative or quiet is both not wise and generous.
If mary is either generous or not rich then someone is patient and vice versa.
Everyone who is both patient and not generous is both not tall and not curious.
Everyone who is not quiet or not old is not patient or tall.
Everyone who is either not rich or not quiet is not brave or humble and vice versa.
Everyone who is either strong or generous is rich or not happy and vice versa.
Someone is not generous.
Someone is not quiet.
Someone is either patient or humble.
Paul is not happy.
Mary is either creative or not rich.
Lucy is either quiet or not curious.
Mary is either not wise or not strong. | Paul is not patient. | entailment | ((old(lucy))<=>(?[X]:((rich(X)|~old(X)))))&
((?[X]:((quiet(X)|wise(X))))<=>(?[X]:(~brave(X))))&
(((~happy(susan)|~wise(susan)))=>((kind(lucy)<~>~old(lucy))))&
((?[X]:(curious(X)))=>(?[X]:((happy(X)&~happy(X)))))&
(![X]:(old(X)<=>humble(X)))&
((?[X]:((~strong(X)|strong(X))))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:((humble(X)<~>happy(X))<=>(~tall(X)&brave(X))))&
(![X]:(~tall(X)<=>~humble(X)))&
(![X]:((creative(X)|quiet(X))=>(~wise(X)&generous(X))))&
(((generous(mary)<~>~rich(mary)))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~generous(X))=>(~tall(X)&~curious(X))))&
(![X]:((~quiet(X)|~old(X))=>(~patient(X)|tall(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(~brave(X)|humble(X))))&
(![X]:((strong(X)<~>generous(X))<=>(rich(X)|~happy(X))))&
(?[X]:(~generous(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((patient(X)<~>humble(X))))&
(~happy(paul))&
((creative(mary)<~>~rich(mary)))&
((quiet(lucy)<~>~curious(lucy)))&
((~wise(mary)<~>~strong(mary))) | ~patient(paul) | [
"p4",
"p6",
"p7",
"p11",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 895616137499517542310477
% SZS output start Proof for 895616137499517542310477
5. ! [X0] : (old(X0) <=> humble(X0)) [input p4]
7. ! [X0] : ((humble(X0) <~> happy(X0)) <=> (brave(X0) & ~tall(X0))) [input p6]
8. ! [X0] : (~tall(X0) <=> ~humble(X0)) [input p7]
12. ! [X0] : ((~old(X0) | ~quiet(X0)) => (tall(X0) | ~patient(X0))) [input p11]
18. ~happy(paul) [input p17]
22. patient(paul) [input hypothesis]
32. ! [X0] : ((tall(X0) | ~patient(X0)) | (old(X0) & quiet(X0))) [ennf transformation 12]
33. ! [X0] : (tall(X0) | ~patient(X0) | (old(X0) & quiet(X0))) [flattening 32]
47. ! [X0] : ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))) [nnf transformation 5]
52. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (~brave(X0) | tall(X0))) & ((brave(X0) & ~tall(X0)) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [nnf transformation 7]
53. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ~brave(X0) | tall(X0)) & ((brave(X0) & ~tall(X0)) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [flattening 52]
54. ! [X0] : ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))) [nnf transformation 8]
85. ~old(X0) | humble(X0) [cnf transformation 47]
91. ~tall(X0) | happy(X0) | ~humble(X0) [cnf transformation 53]
97. ~humble(X0) | tall(X0) [cnf transformation 54]
98. ~tall(X0) | humble(X0) [cnf transformation 54]
110. ~patient(X0) | tall(X0) | old(X0) [cnf transformation 33]
127. ~happy(paul) [cnf transformation 18]
134. patient(paul) [cnf transformation 22]
297. 32 <=> tall(paul) [avatar definition]
298. tall(paul) <- (32) [avatar component clause 297]
299. ~tall(paul) <- (~32) [avatar component clause 297]
332. tall(paul) | old(paul) [resolution 110,134]
335. old(paul) <- (~32) [subsumption resolution 332,299]
431. humble(paul) <- (~32) [resolution 335,85]
559. tall(paul) <- (~32) [resolution 431,97]
563. $false <- (~32) [subsumption resolution 559,299]
564. 32 [avatar contradiction clause 563]
576. happy(paul) | ~humble(paul) <- (32) [resolution 298,91]
577. humble(paul) <- (32) [resolution 298,98]
578. ~humble(paul) <- (32) [subsumption resolution 576,127]
579. $false <- (32) [subsumption resolution 577,578]
580. ~32 [avatar contradiction clause 579]
581. $false [avatar sat refutation 564,580]
% SZS output end Proof for 895616137499517542310477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and patient is not curious or not happy and vice versa. Everyone who is strong or wise is not happy or calm. If alice is either not calm or wise then mary is both funny and not happy and vice versa. If someone is both not generous and funny then lucy is generous and vice versa. If someone is not curious or not old then john is generous or not funny and vice versa. If someone is either old or not wise then someone is not curious. If someone is either not curious or not tall then someone is either not rich or curious and vice versa. Everyone who is either calm or brave is tall or creative. If someone is not curious then fred is not patient or curious and vice versa. If someone is not calm or generous then john is both not curious and not kind and vice versa. If john is brave then someone is either not patient or not old. If someone is either kind or not brave then someone is not funny or not generous and vice versa. If someone is both not strong and not tall then someone is curious. If someone is either not rich or not creative then someone is not funny. If fred is either rich or not rich then someone is generous or wise and vice versa. Everyone who is either rich or not curious is either strong or not kind. Someone is not rich or not wise. Mary is both not strong and patient. Someone is not creative or not tall. Susan is not wise. Someone is both generous and not strong. Lucy is not patient or funny. Someone is not strong. | Alice is not calm. | neutral | (![X]:((brave(X)&patient(X))<=>(~curious(X)|~happy(X))))&
(![X]:((strong(X)|wise(X))=>(~happy(X)|calm(X))))&
(((~calm(alice)<~>wise(alice)))<=>((funny(mary)&~happy(mary))))&
((?[X]:((~generous(X)&funny(X))))<=>(generous(lucy)))&
((?[X]:((~curious(X)|~old(X))))<=>((generous(john)|~funny(john))))&
((?[X]:((old(X)<~>~wise(X))))=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:((calm(X)<~>brave(X))=>(tall(X)|creative(X))))&
((?[X]:(~curious(X)))<=>((~patient(fred)|curious(fred))))&
((?[X]:((~calm(X)|generous(X))))<=>((~curious(john)&~kind(john))))&
((brave(john))=>(?[X]:((~patient(X)<~>~old(X)))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
((?[X]:((~strong(X)&~tall(X))))=>(?[X]:(curious(X))))&
((?[X]:((~rich(X)<~>~creative(X))))=>(?[X]:(~funny(X))))&
(((rich(fred)<~>~rich(fred)))<=>(?[X]:((generous(X)|wise(X)))))&
(![X]:((rich(X)<~>~curious(X))=>(strong(X)<~>~kind(X))))&
(?[X]:((~rich(X)|~wise(X))))&
((~strong(mary)&patient(mary)))&
(?[X]:((~creative(X)|~tall(X))))&
(~wise(susan))&
(?[X]:((generous(X)&~strong(X))))&
((~patient(lucy)|funny(lucy)))&
(?[X]:(~strong(X))) | ~calm(alice) | []
| null | 0 |
Everyone who is rich or strong is calm.
Everyone who is both not brave and patient is either not strong or not creative and vice versa.
If susan is both strong and brave then someone is either creative or not calm and vice versa.
If someone is kind then alice is both happy and not funny and vice versa.
Everyone who is not curious is both old and calm and vice versa.
Everyone who is brave is not quiet and vice versa.
Everyone who is wise is either patient or rich.
If someone is funny then lucy is not tall or curious.
Everyone who is either old or happy is not funny or generous and vice versa.
If someone is not kind then lucy is both not strong and not brave.
Everyone who is both calm and curious is both not curious and brave and vice versa.
If someone is both funny and not old then mary is both not funny and not kind.
Everyone who is brave or not tall is either old or brave and vice versa.
If someone is both not creative and not funny then someone is either not strong or not funny.
If alice is either not old or not brave then someone is both tall and old and vice versa.
Everyone who is strong or not funny is not wise or generous.
Lucy is not kind or creative.
Someone is both not generous and funny.
Mary is either not strong or not patient.
John is kind.
Someone is either happy or not brave.
Paul is strong.
Someone is not wise or generous.
Susan is not wise or brave. | Alice is strong. | contradiction | (![X]:((rich(X)|strong(X))=>calm(X)))&
(![X]:((~brave(X)&patient(X))<=>(~strong(X)<~>~creative(X))))&
(((strong(susan)&brave(susan)))<=>(?[X]:((creative(X)<~>~calm(X)))))&
((?[X]:(kind(X)))<=>((happy(alice)&~funny(alice))))&
(![X]:(~curious(X)<=>(old(X)&calm(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
(![X]:(wise(X)=>(patient(X)<~>rich(X))))&
((?[X]:(funny(X)))=>((~tall(lucy)|curious(lucy))))&
(![X]:((old(X)<~>happy(X))<=>(~funny(X)|generous(X))))&
((?[X]:(~kind(X)))=>((~strong(lucy)&~brave(lucy))))&
(![X]:((calm(X)&curious(X))<=>(~curious(X)&brave(X))))&
((?[X]:((funny(X)&~old(X))))=>((~funny(mary)&~kind(mary))))&
(![X]:((brave(X)|~tall(X))<=>(old(X)<~>brave(X))))&
((?[X]:((~creative(X)&~funny(X))))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~old(alice)<~>~brave(alice)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:((strong(X)|~funny(X))=>(~wise(X)|generous(X))))&
((~kind(lucy)|creative(lucy)))&
(?[X]:((~generous(X)&funny(X))))&
((~strong(mary)<~>~patient(mary)))&
(kind(john))&
(?[X]:((happy(X)<~>~brave(X))))&
(strong(paul))&
(?[X]:((~wise(X)|generous(X))))&
((~wise(susan)|brave(susan))) | strong(alice) | [
"p0",
"p3",
"p4",
"p8",
"p10",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 8091705760306862774272963
% SZS output start Proof for 8091705760306862774272963
1. ! [X0] : ((strong(X0) | rich(X0)) => calm(X0)) [input p0]
4. ? [X0] : kind(X0) <=> (~funny(alice) & happy(alice)) [input p3]
5. ! [X0] : (~curious(X0) <=> (calm(X0) & old(X0))) [input p4]
9. ! [X0] : ((old(X0) <~> happy(X0)) <=> (generous(X0) | ~funny(X0))) [input p8]
11. ! [X0] : ((curious(X0) & calm(X0)) <=> (brave(X0) & ~curious(X0))) [input p10]
20. kind(john) [input p19]
25. strong(alice) [input hypothesis]
31. ! [X0] : (strong(X0) => calm(X0)) [pure predicate removal 1]
32. ! [X0] : (calm(X0) | ~strong(X0)) [ennf transformation 31]
45. (? [X0] : kind(X0) | (funny(alice) | ~happy(alice))) & ((~funny(alice) & happy(alice)) | ! [X0] : ~kind(X0)) [nnf transformation 4]
46. (? [X0] : kind(X0) | funny(alice) | ~happy(alice)) & ((~funny(alice) & happy(alice)) | ! [X0] : ~kind(X0)) [flattening 45]
47. (? [X0] : kind(X0) | funny(alice) | ~happy(alice)) & ((~funny(alice) & happy(alice)) | ! [X1] : ~kind(X1)) [rectify 46]
48. ? [X0] : kind(X0) => kind(sK1) [choice axiom]
49. (kind(sK1) | funny(alice) | ~happy(alice)) & ((~funny(alice) & happy(alice)) | ! [X1] : ~kind(X1)) [skolemisation 47,48]
50. ! [X0] : ((~curious(X0) | (~calm(X0) | ~old(X0))) & ((calm(X0) & old(X0)) | curious(X0))) [nnf transformation 5]
51. ! [X0] : ((~curious(X0) | ~calm(X0) | ~old(X0)) & ((calm(X0) & old(X0)) | curious(X0))) [flattening 50]
53. ! [X0] : ((((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (~generous(X0) & funny(X0))) & ((generous(X0) | ~funny(X0)) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))))) [nnf transformation 9]
54. ! [X0] : ((((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (~generous(X0) & funny(X0))) & (generous(X0) | ~funny(X0) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))))) [flattening 53]
55. ! [X0] : (((curious(X0) & calm(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (~curious(X0) | ~calm(X0)))) [nnf transformation 11]
56. ! [X0] : (((curious(X0) & calm(X0)) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | ~curious(X0) | ~calm(X0))) [flattening 55]
73. ~strong(X0) | calm(X0) [cnf transformation 32]
86. happy(alice) | ~kind(X1) [cnf transformation 49]
87. ~funny(alice) | ~kind(X1) [cnf transformation 49]
89. old(X0) | curious(X0) [cnf transformation 51]
99. ~old(X0) | ~happy(X0) | funny(X0) [cnf transformation 54]
103. ~curious(X0) | ~curious(X0) | ~calm(X0) [cnf transformation 56]
128. kind(john) [cnf transformation 20]
132. strong(alice) [cnf transformation 25]
135. ~curious(X0) | ~calm(X0) [duplicate literal removal 103]
166. 7 <=> happy(alice) [avatar definition]
167. happy(alice) <- (7) [avatar component clause 166]
170. 8 <=> funny(alice) [avatar definition]
171. ~funny(alice) <- (~8) [avatar component clause 170]
179. 10 <=> ! [X1] : ~kind(X1) [avatar definition]
180. ~kind(X1) <- (10) [avatar component clause 179]
181. 10 | ~8 [avatar split clause 87,170,179]
182. 10 | 7 [avatar split clause 86,166,179]
238. 24 <=> old(alice) [avatar definition]
239. ~old(alice) <- (~24) [avatar component clause 238]
240. old(alice) <- (24) [avatar component clause 238]
292. calm(alice) [resolution 73,132]
295. curious(alice) <- (~24) [resolution 89,239]
299. ~calm(alice) <- (~24) [resolution 135,295]
300. $false <- (~24) [subsumption resolution 299,292]
301. 24 [avatar contradiction clause 300]
318. $false <- (10) [resolution 180,128]
321. ~10 [avatar contradiction clause 318]
390. ~happy(alice) | funny(alice) <- (24) [resolution 99,240]
393. funny(alice) <- (7, 24) [subsumption resolution 390,167]
394. $false <- (7, ~8, 24) [subsumption resolution 393,171]
395. ~7 | 8 | ~24 [avatar contradiction clause 394]
405. $false [avatar sat refutation 181,182,301,321,395]
% SZS output end Proof for 8091705760306862774272963
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or quiet then someone is either wise or not rich.
Everyone who is both not brave and not happy is wise or not humble and vice versa.
Everyone who is either not generous or not rich is both not patient and not wise and vice versa.
Everyone who is both not generous and happy is not funny or not happy and vice versa.
Everyone who is either humble or happy is either funny or not creative.
If someone is generous or funny then mary is quiet or not strong and vice versa.
If someone is funny then fred is either brave or quiet.
If someone is either not strong or generous then someone is either old or not tall and vice versa.
Everyone who is both not curious and patient is either not tall or not calm.
If mary is both quiet and humble then someone is either not rich or brave and vice versa.
Everyone who is not humble or not kind is both quiet and not funny.
Everyone who is either wise or old is both not funny and old and vice versa.
Everyone who is not brave or creative is either not calm or not strong.
If lucy is either creative or not old then alice is both not old and not tall.
If john is both quiet and creative then someone is either curious or patient and vice versa.
If paul is not brave then paul is both not calm and not happy.
Someone is either funny or not wise.
Alice is not calm or old.
Someone is not patient or curious.
Alice is both old and not funny.
Alice is both not tall and rich.
John is funny or not quiet. | Lucy is not generous. | neutral | ((?[X]:((strong(X)|quiet(X))))=>(?[X]:((wise(X)<~>~rich(X)))))&
(![X]:((~brave(X)&~happy(X))<=>(wise(X)|~humble(X))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~patient(X)&~wise(X))))&
(![X]:((~generous(X)&happy(X))<=>(~funny(X)|~happy(X))))&
(![X]:((humble(X)<~>happy(X))=>(funny(X)<~>~creative(X))))&
((?[X]:((generous(X)|funny(X))))<=>((quiet(mary)|~strong(mary))))&
((?[X]:(funny(X)))=>((brave(fred)<~>quiet(fred))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((~curious(X)&patient(X))=>(~tall(X)<~>~calm(X))))&
(((quiet(mary)&humble(mary)))<=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((~humble(X)|~kind(X))=>(quiet(X)&~funny(X))))&
(![X]:((wise(X)<~>old(X))<=>(~funny(X)&old(X))))&
(![X]:((~brave(X)|creative(X))=>(~calm(X)<~>~strong(X))))&
(((creative(lucy)<~>~old(lucy)))=>((~old(alice)&~tall(alice))))&
(((quiet(john)&creative(john)))<=>(?[X]:((curious(X)<~>patient(X)))))&
((~brave(paul))=>((~calm(paul)&~happy(paul))))&
(?[X]:((funny(X)<~>~wise(X))))&
((~calm(alice)|old(alice)))&
(?[X]:((~patient(X)|curious(X))))&
((old(alice)&~funny(alice)))&
((~tall(alice)&rich(alice)))&
((funny(john)|~quiet(john))) | ~generous(lucy) | []
| null | 0 |
Everyone who is not rich is both not kind and not quiet. Everyone who is both humble and not quiet is either not humble or not strong and vice versa. If alice is either humble or not kind then alice is not patient. If someone is either curious or happy then mary is both not strong and kind. Everyone who is either funny or wise is not rich. Everyone who is tall is either wise or not funny and vice versa. Everyone who is both brave and kind is both not curious and wise. If someone is either rich or not wise then someone is wise and vice versa. If john is not creative or not generous then someone is either wise or old and vice versa. If someone is either kind or curious then lucy is either wise or not rich and vice versa. Everyone who is not happy or humble is both not strong and not wise and vice versa. Everyone who is either brave or creative is either not rich or rich and vice versa. Everyone who is humble is either not wise or not curious and vice versa. If someone is both not brave and kind then someone is humble. If alice is either not humble or not generous then someone is either creative or generous and vice versa. Everyone who is generous is both not strong and not brave. Someone is creative. Someone is humble. Someone is both quiet and curious. Fred is either not patient or not generous. Mary is creative or patient. Alice is either not wise or not funny. Susan is either not quiet or not old. | John is curious. | neutral | (![X]:(~rich(X)=>(~kind(X)&~quiet(X))))&
(![X]:((humble(X)&~quiet(X))<=>(~humble(X)<~>~strong(X))))&
(((humble(alice)<~>~kind(alice)))=>(~patient(alice)))&
((?[X]:((curious(X)<~>happy(X))))=>((~strong(mary)&kind(mary))))&
(![X]:((funny(X)<~>wise(X))=>~rich(X)))&
(![X]:(tall(X)<=>(wise(X)<~>~funny(X))))&
(![X]:((brave(X)&kind(X))=>(~curious(X)&wise(X))))&
((?[X]:((rich(X)<~>~wise(X))))<=>(?[X]:(wise(X))))&
(((~creative(john)|~generous(john)))<=>(?[X]:((wise(X)<~>old(X)))))&
((?[X]:((kind(X)<~>curious(X))))<=>((wise(lucy)<~>~rich(lucy))))&
(![X]:((~happy(X)|humble(X))<=>(~strong(X)&~wise(X))))&
(![X]:((brave(X)<~>creative(X))<=>(~rich(X)<~>rich(X))))&
(![X]:(humble(X)<=>(~wise(X)<~>~curious(X))))&
((?[X]:((~brave(X)&kind(X))))=>(?[X]:(humble(X))))&
(((~humble(alice)<~>~generous(alice)))<=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:(generous(X)=>(~strong(X)&~brave(X))))&
(?[X]:(creative(X)))&
(?[X]:(humble(X)))&
(?[X]:((quiet(X)&curious(X))))&
((~patient(fred)<~>~generous(fred)))&
((creative(mary)|patient(mary)))&
((~wise(alice)<~>~funny(alice)))&
((~quiet(susan)<~>~old(susan))) | curious(john) | []
| null | 0 |
Everyone who is both quiet and not funny is either curious or not generous and vice versa.
Everyone who is both tall and not generous is creative or not happy and vice versa.
Everyone who is not curious or wise is not generous and vice versa.
Everyone who is not generous or not funny is funny.
Everyone who is old is not creative and vice versa.
If someone is either not creative or creative then alice is either rich or kind and vice versa.
Everyone who is both not rich and not happy is strong.
If fred is kind or patient then susan is both wise and not generous.
Everyone who is tall is both not rich and not humble.
Everyone who is both not humble and strong is not wise or creative.
If lucy is both kind and not tall then john is curious and vice versa.
If fred is quiet then someone is either curious or wise.
Everyone who is both not brave and not happy is creative or quiet.
If someone is both not tall and not wise then someone is not humble or creative and vice versa.
Everyone who is both kind and not curious is not old or rich and vice versa.
Everyone who is both strong and not tall is not calm.
John is either creative or old.
Someone is not old or brave.
Fred is kind or not creative.
Someone is both wise and strong.
Lucy is either not wise or calm.
Someone is either tall or not patient. | Susan is funny. | entailment | (![X]:((quiet(X)&~funny(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((tall(X)&~generous(X))<=>(creative(X)|~happy(X))))&
(![X]:((~curious(X)|wise(X))<=>~generous(X)))&
(![X]:((~generous(X)|~funny(X))=>funny(X)))&
(![X]:(old(X)<=>~creative(X)))&
((?[X]:((~creative(X)<~>creative(X))))<=>((rich(alice)<~>kind(alice))))&
(![X]:((~rich(X)&~happy(X))=>strong(X)))&
(((kind(fred)|patient(fred)))=>((wise(susan)&~generous(susan))))&
(![X]:(tall(X)=>(~rich(X)&~humble(X))))&
(![X]:((~humble(X)&strong(X))=>(~wise(X)|creative(X))))&
(((kind(lucy)&~tall(lucy)))<=>(curious(john)))&
((quiet(fred))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~brave(X)&~happy(X))=>(creative(X)|quiet(X))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~old(X)|rich(X))))&
(![X]:((strong(X)&~tall(X))=>~calm(X)))&
((creative(john)<~>old(john)))&
(?[X]:((~old(X)|brave(X))))&
((kind(fred)|~creative(fred)))&
(?[X]:((wise(X)&strong(X))))&
((~wise(lucy)<~>calm(lucy)))&
(?[X]:((tall(X)<~>~patient(X)))) | funny(susan) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 6595426287741811372836657
% SZS output start Proof for 6595426287741811372836657
4. ! [X0] : ((~funny(X0) | ~generous(X0)) => funny(X0)) [input p3]
23. ~funny(susan) [input hypothesis]
27. ! [X0] : (funny(X0) | (funny(X0) & generous(X0))) [ennf transformation 4]
82. funny(X0) | funny(X0) [cnf transformation 27]
126. ~funny(susan) [cnf transformation 23]
131. funny(X0) [duplicate literal removal 82]
251. $false [subsumption resolution 126,131]
% SZS output end Proof for 6595426287741811372836657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not brave is both curious and not rich.
If paul is not patient then paul is both not strong and tall and vice versa.
If susan is not rich or calm then alice is either old or quiet and vice versa.
If someone is funny or not generous then john is not creative.
If someone is generous then someone is either not quiet or not funny and vice versa.
If someone is not calm then susan is both not tall and strong.
Everyone who is tall is both calm and quiet and vice versa.
Everyone who is both not brave and happy is happy and vice versa.
If lucy is both not brave and not happy then paul is not curious or not generous.
If susan is rich then lucy is calm.
Everyone who is not funny is either not generous or wise.
If someone is both quiet and curious then someone is rich.
Everyone who is curious is either not tall or not creative and vice versa.
If john is creative then someone is not patient.
Everyone who is both not strong and quiet is not calm or patient and vice versa.
Everyone who is either curious or strong is wise or brave.
John is both not brave and not old.
John is either not generous or happy.
John is patient or not funny.
Mary is not happy or not brave.
Fred is not wise.
Someone is not creative or not humble.
Someone is either not curious or not funny. | Susan is quiet. | contradiction | (![X]:((~tall(X)|~brave(X))=>(curious(X)&~rich(X))))&
((~patient(paul))<=>((~strong(paul)&tall(paul))))&
(((~rich(susan)|calm(susan)))<=>((old(alice)<~>quiet(alice))))&
((?[X]:((funny(X)|~generous(X))))=>(~creative(john)))&
((?[X]:(generous(X)))<=>(?[X]:((~quiet(X)<~>~funny(X)))))&
((?[X]:(~calm(X)))=>((~tall(susan)&strong(susan))))&
(![X]:(tall(X)<=>(calm(X)&quiet(X))))&
(![X]:((~brave(X)&happy(X))<=>happy(X)))&
(((~brave(lucy)&~happy(lucy)))=>((~curious(paul)|~generous(paul))))&
((rich(susan))=>(calm(lucy)))&
(![X]:(~funny(X)=>(~generous(X)<~>wise(X))))&
((?[X]:((quiet(X)&curious(X))))=>(?[X]:(rich(X))))&
(![X]:(curious(X)<=>(~tall(X)<~>~creative(X))))&
((creative(john))=>(?[X]:(~patient(X))))&
(![X]:((~strong(X)&quiet(X))<=>(~calm(X)|patient(X))))&
(![X]:((curious(X)<~>strong(X))=>(wise(X)|brave(X))))&
((~brave(john)&~old(john)))&
((~generous(john)<~>happy(john)))&
((patient(john)|~funny(john)))&
((~happy(mary)|~brave(mary)))&
(~wise(fred))&
(?[X]:((~creative(X)|~humble(X))))&
(?[X]:((~curious(X)<~>~funny(X)))) | quiet(susan) | [
"p1",
"p5",
"p6",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 5328142786862115666108925
% SZS output start Proof for 5328142786862115666108925
2. ~patient(paul) <=> (tall(paul) & ~strong(paul)) [input p1]
6. ? [X0] : ~calm(X0) => (strong(susan) & ~tall(susan)) [input p5]
7. ! [X0] : (tall(X0) <=> (quiet(X0) & calm(X0))) [input p6]
15. ! [X0] : ((quiet(X0) & ~strong(X0)) <=> (patient(X0) | ~calm(X0))) [input p14]
24. quiet(susan) [input hypothesis]
30. (strong(susan) & ~tall(susan)) | ! [X0] : calm(X0) [ennf transformation 6]
39. (~patient(paul) | (~tall(paul) | strong(paul))) & ((tall(paul) & ~strong(paul)) | patient(paul)) [nnf transformation 2]
40. (~patient(paul) | ~tall(paul) | strong(paul)) & ((tall(paul) & ~strong(paul)) | patient(paul)) [flattening 39]
48. ! [X0] : ((tall(X0) | (~quiet(X0) | ~calm(X0))) & ((quiet(X0) & calm(X0)) | ~tall(X0))) [nnf transformation 7]
49. ! [X0] : ((tall(X0) | ~quiet(X0) | ~calm(X0)) & ((quiet(X0) & calm(X0)) | ~tall(X0))) [flattening 48]
59. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | (~quiet(X0) | strong(X0)))) [nnf transformation 15]
60. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | ~quiet(X0) | strong(X0))) [flattening 59]
70. ~strong(paul) | patient(paul) [cnf transformation 40]
71. tall(paul) | patient(paul) [cnf transformation 40]
72. ~patient(paul) | ~tall(paul) | strong(paul) [cnf transformation 40]
85. ~tall(susan) | calm(X0) [cnf transformation 30]
86. strong(susan) | calm(X0) [cnf transformation 30]
87. ~tall(X0) | calm(X0) [cnf transformation 49]
88. ~tall(X0) | quiet(X0) [cnf transformation 49]
89. ~quiet(X0) | tall(X0) | ~calm(X0) [cnf transformation 49]
103. ~quiet(X0) | ~calm(X0) | patient(X0) | strong(X0) [cnf transformation 60]
104. ~strong(X0) | calm(X0) [cnf transformation 60]
105. ~strong(X0) | ~patient(X0) [cnf transformation 60]
107. ~patient(X0) | quiet(X0) [cnf transformation 60]
119. quiet(susan) [cnf transformation 24]
121. 1 <=> strong(paul) [avatar definition]
123. strong(paul) <- (1) [avatar component clause 121]
125. 2 <=> tall(paul) [avatar definition]
126. tall(paul) <- (2) [avatar component clause 125]
127. ~tall(paul) <- (~2) [avatar component clause 125]
129. 3 <=> patient(paul) [avatar definition]
130. patient(paul) <- (3) [avatar component clause 129]
132. 1 | ~2 | ~3 [avatar split clause 72,129,125,121]
133. 3 | 2 [avatar split clause 71,125,129]
134. 3 | ~1 [avatar split clause 70,121,129]
148. 7 <=> calm(susan) [avatar definition]
195. 17 <=> ! [X0] : calm(X0) [avatar definition]
196. calm(X0) <- (17) [avatar component clause 195]
198. 18 <=> strong(susan) [avatar definition]
200. strong(susan) <- (18) [avatar component clause 198]
201. 17 | 18 [avatar split clause 86,198,195]
203. 19 <=> tall(susan) [avatar definition]
206. 17 | ~19 [avatar split clause 85,203,195]
276. calm(paul) <- (2) [resolution 87,126]
277. quiet(paul) <- (2) [resolution 88,126]
302. tall(susan) | ~calm(susan) [resolution 89,119]
324. ~calm(paul) | patient(paul) | strong(paul) <- (2) [resolution 103,277]
357. ~7 | 19 [avatar split clause 302,203,148]
363. patient(paul) | strong(paul) <- (2) [subsumption resolution 324,276]
364. 1 | 3 | ~2 [avatar split clause 363,125,129,121]
365. ~patient(paul) <- (1) [resolution 123,105]
367. $false <- (1, 3) [subsumption resolution 365,130]
368. ~1 | ~3 [avatar contradiction clause 367]
370. quiet(paul) <- (3) [resolution 130,107]
372. calm(susan) <- (18) [resolution 200,104]
376. 7 | ~18 [avatar split clause 372,198,148]
385. tall(paul) | ~calm(paul) <- (3) [resolution 370,89]
387. ~calm(paul) <- (~2, 3) [subsumption resolution 385,127]
388. $false <- (~2, 3, 17) [subsumption resolution 387,196]
389. 2 | ~3 | ~17 [avatar contradiction clause 388]
390. $false [avatar sat refutation 132,133,134,201,206,357,364,368,376,389]
% SZS output end Proof for 5328142786862115666108925
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not wise or not humble is both rich and not generous. If susan is not old then someone is brave or not strong. Everyone who is not rich is wise and vice versa. Everyone who is not patient or not wise is not funny. Everyone who is either quiet or happy is happy. If someone is both patient and not tall then alice is both wise and not wise and vice versa. If john is either not wise or brave then susan is not happy. If someone is patient or old then fred is either not generous or not tall and vice versa. Everyone who is both not quiet and strong is tall or calm and vice versa. If susan is either not humble or not generous then someone is not brave and vice versa. If mary is both not tall and not rich then john is both happy and not kind. Everyone who is not happy is rich or not humble. If someone is curious then someone is either wise or patient. If someone is either rich or not wise then someone is both wise and not patient. Everyone who is both not kind and not happy is either happy or not funny and vice versa. Everyone who is rich or not wise is both humble and creative and vice versa. Fred is old. Someone is generous or not kind. John is calm or not strong. Someone is either brave or not old. Fred is happy. Susan is either strong or quiet. Someone is tall or not brave. | John is wise. | neutral | (![X]:((~wise(X)<~>~humble(X))=>(rich(X)&~generous(X))))&
((~old(susan))=>(?[X]:((brave(X)|~strong(X)))))&
(![X]:(~rich(X)<=>wise(X)))&
(![X]:((~patient(X)|~wise(X))=>~funny(X)))&
(![X]:((quiet(X)<~>happy(X))=>happy(X)))&
((?[X]:((patient(X)&~tall(X))))<=>((wise(alice)&~wise(alice))))&
(((~wise(john)<~>brave(john)))=>(~happy(susan)))&
((?[X]:((patient(X)|old(X))))<=>((~generous(fred)<~>~tall(fred))))&
(![X]:((~quiet(X)&strong(X))<=>(tall(X)|calm(X))))&
(((~humble(susan)<~>~generous(susan)))<=>(?[X]:(~brave(X))))&
(((~tall(mary)&~rich(mary)))=>((happy(john)&~kind(john))))&
(![X]:(~happy(X)=>(rich(X)|~humble(X))))&
((?[X]:(curious(X)))=>(?[X]:((wise(X)<~>patient(X)))))&
((?[X]:((rich(X)<~>~wise(X))))=>(?[X]:((wise(X)&~patient(X)))))&
(![X]:((~kind(X)&~happy(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((rich(X)|~wise(X))<=>(humble(X)&creative(X))))&
(old(fred))&
(?[X]:((generous(X)|~kind(X))))&
((calm(john)|~strong(john)))&
(?[X]:((brave(X)<~>~old(X))))&
(happy(fred))&
((strong(susan)<~>quiet(susan)))&
(?[X]:((tall(X)|~brave(X)))) | wise(john) | []
| null | 0 |
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.
Everyone who is not patient is both not strong and creative and vice versa.
Everyone who is both quiet and not calm is not happy or happy and vice versa.
Everyone who is either curious or strong is not quiet or not brave and vice versa.
If someone is creative then paul is not patient and vice versa.
If someone is not old then someone is both not brave and not tall.
Everyone who is either humble or strong is strong or patient and vice versa.
Paul is both strong and rich.
Lucy is either not calm or not rich.
Fred is curious.
John is both not funny and not wise.
Someone is not brave or patient. | Susan is kind. | contradiction | (![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]:(~patient(X)<=>(~strong(X)&creative(X))))&
(![X]:((quiet(X)&~calm(X))<=>(~happy(X)|happy(X))))&
(![X]:((curious(X)<~>strong(X))<=>(~quiet(X)|~brave(X))))&
((?[X]:(creative(X)))<=>(~patient(paul)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((humble(X)<~>strong(X))<=>(strong(X)|patient(X))))&
((strong(paul)&rich(paul)))&
((~calm(lucy)<~>~rich(lucy)))&
(curious(fred))&
((~funny(john)&~wise(john)))&
(?[X]:((~brave(X)|patient(X)))) | kind(susan) | [
"p1",
"p5",
"p8",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 2526163922925403822346780
% SZS output start Proof for 2526163922925403822346780
2. (~patient(susan) | ~kind(susan)) <=> ? [X0] : (~quiet(X0) <~> happy(X0)) [input p1]
6. (~quiet(john) & patient(john)) <=> ? [X0] : (quiet(X0) & ~brave(X0)) [input p5]
9. ? [X0] : ~happy(X0) <=> ? [X0] : (wise(X0) & ~brave(X0)) [input p8]
10. ! [X0] : (~patient(X0) <=> (creative(X0) & ~strong(X0))) [input p9]
11. ! [X0] : ((~calm(X0) & quiet(X0)) <=> (happy(X0) | ~happy(X0))) [input p10]
13. ? [X0] : creative(X0) <=> ~patient(paul) [input p12]
16. rich(paul) & strong(paul) [input p15]
21. kind(susan) [input hypothesis]
23. ? [X0] : ~happy(X0) <=> ? [X1] : (wise(X1) & ~brave(X1)) [rectify 9]
33. ((~patient(susan) | ~kind(susan)) | ! [X0] : ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) & (? [X0] : ((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (patient(susan) & kind(susan))) [nnf transformation 2]
34. (~patient(susan) | ~kind(susan) | ! [X0] : ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) & (? [X0] : ((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (patient(susan) & kind(susan))) [flattening 33]
35. (~patient(susan) | ~kind(susan) | ! [X0] : ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) & (? [X1] : ((~happy(X1) | quiet(X1)) & (happy(X1) | ~quiet(X1))) | (patient(susan) & kind(susan))) [rectify 34]
36. ? [X1] : ((~happy(X1) | quiet(X1)) & (happy(X1) | ~quiet(X1))) => ((~happy(sK0) | quiet(sK0)) & (happy(sK0) | ~quiet(sK0))) [choice axiom]
37. (~patient(susan) | ~kind(susan) | ! [X0] : ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) & (((~happy(sK0) | quiet(sK0)) & (happy(sK0) | ~quiet(sK0))) | (patient(susan) & kind(susan))) [skolemisation 35,36]
43. ((~quiet(john) & patient(john)) | ! [X0] : (~quiet(X0) | brave(X0))) & (? [X0] : (quiet(X0) & ~brave(X0)) | (quiet(john) | ~patient(john))) [nnf transformation 6]
44. ((~quiet(john) & patient(john)) | ! [X0] : (~quiet(X0) | brave(X0))) & (? [X0] : (quiet(X0) & ~brave(X0)) | quiet(john) | ~patient(john)) [flattening 43]
45. ((~quiet(john) & patient(john)) | ! [X0] : (~quiet(X0) | brave(X0))) & (? [X1] : (quiet(X1) & ~brave(X1)) | quiet(john) | ~patient(john)) [rectify 44]
46. ? [X1] : (quiet(X1) & ~brave(X1)) => (quiet(sK2) & ~brave(sK2)) [choice axiom]
47. ((~quiet(john) & patient(john)) | ! [X0] : (~quiet(X0) | brave(X0))) & ((quiet(sK2) & ~brave(sK2)) | quiet(john) | ~patient(john)) [skolemisation 45,46]
48. (? [X0] : ~happy(X0) | ! [X1] : (~wise(X1) | brave(X1))) & (? [X1] : (wise(X1) & ~brave(X1)) | ! [X0] : happy(X0)) [nnf transformation 23]
49. (? [X0] : ~happy(X0) | ! [X1] : (~wise(X1) | brave(X1))) & (? [X2] : (wise(X2) & ~brave(X2)) | ! [X3] : happy(X3)) [rectify 48]
50. ? [X0] : ~happy(X0) => ~happy(sK3) [choice axiom]
51. ? [X2] : (wise(X2) & ~brave(X2)) => (wise(sK4) & ~brave(sK4)) [choice axiom]
52. (~happy(sK3) | ! [X1] : (~wise(X1) | brave(X1))) & ((wise(sK4) & ~brave(sK4)) | ! [X3] : happy(X3)) [skolemisation 49,51,50]
53. ! [X0] : ((~patient(X0) | (~creative(X0) | strong(X0))) & ((creative(X0) & ~strong(X0)) | patient(X0))) [nnf transformation 10]
54. ! [X0] : ((~patient(X0) | ~creative(X0) | strong(X0)) & ((creative(X0) & ~strong(X0)) | patient(X0))) [flattening 53]
55. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | (calm(X0) | ~quiet(X0)))) [nnf transformation 11]
56. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | calm(X0) | ~quiet(X0))) [flattening 55]
59. (? [X0] : creative(X0) | patient(paul)) & (~patient(paul) | ! [X0] : ~creative(X0)) [nnf transformation 13]
60. (? [X0] : creative(X0) | patient(paul)) & (~patient(paul) | ! [X1] : ~creative(X1)) [rectify 59]
61. ? [X0] : creative(X0) => creative(sK5) [choice axiom]
62. (creative(sK5) | patient(paul)) & (~patient(paul) | ! [X1] : ~creative(X1)) [skolemisation 60,61]
77. ~patient(susan) | ~kind(susan) | ~quiet(X0) | ~happy(X0) [cnf transformation 37]
89. ~quiet(john) | ~quiet(X0) | brave(X0) [cnf transformation 47]
95. ~brave(sK4) | happy(X3) [cnf transformation 52]
98. ~strong(X0) | patient(X0) [cnf transformation 54]
99. patient(X0) | creative(X0) [cnf transformation 54]
102. quiet(X0) | happy(X0) [cnf transformation 56]
103. quiet(X0) | ~happy(X0) [cnf transformation 56]
112. ~patient(paul) | ~creative(X1) [cnf transformation 62]
120. strong(paul) [cnf transformation 16]
128. kind(susan) [cnf transformation 21]
132. 1 <=> ! [X0] : (~quiet(X0) | ~happy(X0)) [avatar definition]
133. ~quiet(X0) | ~happy(X0) <- (1) [avatar component clause 132]
135. 2 <=> kind(susan) [avatar definition]
139. 3 <=> patient(susan) [avatar definition]
141. ~patient(susan) <- (~3) [avatar component clause 139]
142. 1 | ~2 | ~3 [avatar split clause 77,139,135,132]
178. 11 <=> ! [X0] : (~quiet(X0) | brave(X0)) [avatar definition]
179. ~quiet(X0) | brave(X0) <- (11) [avatar component clause 178]
181. 12 <=> quiet(john) [avatar definition]
183. ~quiet(john) <- (~12) [avatar component clause 181]
184. 11 | ~12 [avatar split clause 89,181,178]
222. 21 <=> ! [X3] : happy(X3) [avatar definition]
223. happy(X3) <- (21) [avatar component clause 222]
230. 23 <=> brave(sK4) [avatar definition]
232. ~brave(sK4) <- (~23) [avatar component clause 230]
233. 21 | ~23 [avatar split clause 95,230,222]
235. quiet(X0) [subsumption resolution 102,103]
241. 24 <=> patient(paul) [avatar definition]
250. 26 <=> ! [X1] : ~creative(X1) [avatar definition]
251. ~creative(X1) <- (26) [avatar component clause 250]
252. 26 | ~24 [avatar split clause 112,241,250]
265. 2 [avatar split clause 128,135]
275. $false <- (~12) [subsumption resolution 183,235]
276. 12 [avatar contradiction clause 275]
277. brave(X0) <- (11) [subsumption resolution 179,235]
284. patient(paul) [resolution 98,120]
287. 24 [avatar split clause 284,241]
290. creative(susan) <- (~3) [resolution 99,141]
291. $false <- (~3, 26) [subsumption resolution 290,251]
292. 3 | ~26 [avatar contradiction clause 291]
293. ~happy(X0) <- (1) [subsumption resolution 133,235]
294. $false <- (1, 21) [subsumption resolution 293,223]
295. ~1 | ~21 [avatar contradiction clause 294]
300. $false <- (11, ~23) [subsumption resolution 232,277]
301. ~11 | 23 [avatar contradiction clause 300]
302. $false [avatar sat refutation 142,184,233,252,265,276,287,292,295,301]
% SZS output end Proof for 2526163922925403822346780
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not creative is both generous and not wise and vice versa. If mary is both calm and not funny then someone is not tall. If paul is not rich then someone is both not humble and quiet. Everyone who is either old or not quiet is either strong or brave and vice versa. Everyone who is not tall is both wise and humble and vice versa. Everyone who is humble is either not calm or not brave and vice versa. Everyone who is not strong is not patient or not strong and vice versa. Everyone who is both humble and not brave is either calm or not wise and vice versa. If alice is both generous and old then someone is patient or curious. Everyone who is both happy and not tall is calm. If paul is calm or not kind then mary is patient. Everyone who is humble is not kind or not tall and vice versa. Everyone who is tall is either not humble or not old and vice versa. If someone is either not old or not calm then someone is generous and vice versa. Everyone who is both not old and not kind is humble and vice versa. Fred is both curious and quiet. Mary is not humble or not happy. Susan is tall. Someone is not happy. Paul is not quiet. Someone is calm. Someone is both quiet and curious. | Paul is not rich. | neutral | (![X]:((~brave(X)|~creative(X))<=>(generous(X)&~wise(X))))&
(((calm(mary)&~funny(mary)))=>(?[X]:(~tall(X))))&
((~rich(paul))=>(?[X]:((~humble(X)&quiet(X)))))&
(![X]:((old(X)<~>~quiet(X))<=>(strong(X)<~>brave(X))))&
(![X]:(~tall(X)<=>(wise(X)&humble(X))))&
(![X]:(humble(X)<=>(~calm(X)<~>~brave(X))))&
(![X]:(~strong(X)<=>(~patient(X)|~strong(X))))&
(![X]:((humble(X)&~brave(X))<=>(calm(X)<~>~wise(X))))&
(((generous(alice)&old(alice)))=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((happy(X)&~tall(X))=>calm(X)))&
(((calm(paul)|~kind(paul)))=>(patient(mary)))&
(![X]:(humble(X)<=>(~kind(X)|~tall(X))))&
(![X]:(tall(X)<=>(~humble(X)<~>~old(X))))&
((?[X]:((~old(X)<~>~calm(X))))<=>(?[X]:(generous(X))))&
(![X]:((~old(X)&~kind(X))<=>humble(X)))&
((curious(fred)&quiet(fred)))&
((~humble(mary)|~happy(mary)))&
(tall(susan))&
(?[X]:(~happy(X)))&
(~quiet(paul))&
(?[X]:(calm(X)))&
(?[X]:((quiet(X)&curious(X)))) | ~rich(paul) | []
| null | 0 |
If someone is either not humble or generous then john is not creative and vice versa.
Everyone who is old or not tall is not generous.
Everyone who is kind is patient or not happy and vice versa.
Everyone who is either patient or not kind is both not creative and brave.
Everyone who is either brave or not humble is both not quiet and not brave and vice versa.
Everyone who is calm is either funny or not funny and vice versa.
If lucy is tall then susan is either humble or not funny and vice versa.
If susan is both kind and rich then john is calm or kind.
Everyone who is old or kind is both old and creative and vice versa.
Everyone who is not generous is brave or not rich and vice versa.
Everyone who is either funny or not creative is either calm or wise and vice versa.
Everyone who is either quiet or not old is both not strong and not quiet.
Everyone who is happy is either happy or strong.
If someone is either creative or patient then someone is creative.
If someone is either not generous or not wise then someone is either humble or not happy and vice versa.
Everyone who is creative or not calm is both creative and generous.
Fred is not tall or not patient.
Someone is not humble or not funny.
Lucy is not funny or not wise.
Lucy is either not brave or not humble.
Someone is calm.
Mary is not strong or not curious. | Lucy is generous. | contradiction | ((?[X]:((~humble(X)<~>generous(X))))<=>(~creative(john)))&
(![X]:((old(X)|~tall(X))=>~generous(X)))&
(![X]:(kind(X)<=>(patient(X)|~happy(X))))&
(![X]:((patient(X)<~>~kind(X))=>(~creative(X)&brave(X))))&
(![X]:((brave(X)<~>~humble(X))<=>(~quiet(X)&~brave(X))))&
(![X]:(calm(X)<=>(funny(X)<~>~funny(X))))&
((tall(lucy))<=>((humble(susan)<~>~funny(susan))))&
(((kind(susan)&rich(susan)))=>((calm(john)|kind(john))))&
(![X]:((old(X)|kind(X))<=>(old(X)&creative(X))))&
(![X]:(~generous(X)<=>(brave(X)|~rich(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(calm(X)<~>wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~strong(X)&~quiet(X))))&
(![X]:(happy(X)=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:(creative(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((creative(X)|~calm(X))=>(creative(X)&generous(X))))&
((~tall(fred)|~patient(fred)))&
(?[X]:((~humble(X)|~funny(X))))&
((~funny(lucy)|~wise(lucy)))&
((~brave(lucy)<~>~humble(lucy)))&
(?[X]:(calm(X)))&
((~strong(mary)|~curious(mary))) | generous(lucy) | [
"p1",
"p2",
"p3",
"p8",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 4492470195284572978865458
% SZS output start Proof for 4492470195284572978865458
2. ! [X0] : ((~tall(X0) | old(X0)) => ~generous(X0)) [input p1]
3. ! [X0] : (kind(X0) <=> (~happy(X0) | patient(X0))) [input p2]
4. ! [X0] : ((patient(X0) <~> ~kind(X0)) => (brave(X0) & ~creative(X0))) [input p3]
9. ! [X0] : ((kind(X0) | old(X0)) <=> (creative(X0) & old(X0))) [input p8]
10. ! [X0] : (~generous(X0) <=> (~rich(X0) | brave(X0))) [input p9]
23. generous(lucy) [input hypothesis]
27. ! [X0] : (~generous(X0) | (tall(X0) & ~old(X0))) [ennf transformation 2]
28. ! [X0] : ((brave(X0) & ~creative(X0)) | (patient(X0) <=> ~kind(X0))) [ennf transformation 4]
39. ! [X0] : ((kind(X0) | (happy(X0) & ~patient(X0))) & ((~happy(X0) | patient(X0)) | ~kind(X0))) [nnf transformation 3]
40. ! [X0] : ((kind(X0) | (happy(X0) & ~patient(X0))) & (~happy(X0) | patient(X0) | ~kind(X0))) [flattening 39]
41. ! [X0] : ((brave(X0) & ~creative(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) [nnf transformation 28]
46. ! [X0] : (((kind(X0) | old(X0)) | (~creative(X0) | ~old(X0))) & ((creative(X0) & old(X0)) | (~kind(X0) & ~old(X0)))) [nnf transformation 9]
47. ! [X0] : ((kind(X0) | old(X0) | ~creative(X0) | ~old(X0)) & ((creative(X0) & old(X0)) | (~kind(X0) & ~old(X0)))) [flattening 46]
48. ! [X0] : ((~generous(X0) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | generous(X0))) [nnf transformation 10]
49. ! [X0] : ((~generous(X0) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | generous(X0))) [flattening 48]
71. ~old(X0) | ~generous(X0) [cnf transformation 27]
74. ~patient(X0) | kind(X0) [cnf transformation 40]
79. brave(X0) | patient(X0) | kind(X0) [cnf transformation 41]
96. ~kind(X0) | old(X0) [cnf transformation 47]
101. ~brave(X0) | ~generous(X0) [cnf transformation 49]
137. generous(lucy) [cnf transformation 23]
166. brave(X0) | kind(X0) [subsumption resolution 79,74]
269. 26 <=> brave(lucy) [avatar definition]
270. ~brave(lucy) <- (~26) [avatar component clause 269]
271. brave(lucy) <- (26) [avatar component clause 269]
287. ~generous(lucy) <- (26) [resolution 101,271]
288. $false <- (26) [subsumption resolution 287,137]
289. ~26 [avatar contradiction clause 288]
302. kind(lucy) <- (~26) [resolution 166,270]
304. old(lucy) <- (~26) [resolution 302,96]
311. ~generous(lucy) <- (~26) [resolution 304,71]
312. $false <- (~26) [subsumption resolution 311,137]
313. 26 [avatar contradiction clause 312]
314. $false [avatar sat refutation 289,313]
% SZS output end Proof for 4492470195284572978865458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and tall then someone is both generous and not old.
Everyone who is not brave is both not humble and kind.
If someone is either brave or not quiet then mary is either calm or tall.
If fred is both not strong and old then someone is not brave or brave and vice versa.
Everyone who is not humble or not strong is either brave or generous and vice versa.
If someone is not generous or quiet then john is either brave or funny.
Everyone who is not calm is generous or not quiet.
Everyone who is both not humble and not generous is both generous and not kind and vice versa.
Everyone who is humble is either brave or not kind.
Everyone who is both not calm and happy is either wise or humble.
Everyone who is both curious and not kind is rich and vice versa.
If john is either curious or not wise then someone is creative and vice versa.
Everyone who is not creative is both old and kind.
Everyone who is generous or not brave is funny and vice versa.
If lucy is either not brave or not quiet then someone is either not funny or tall.
If someone is both not strong and not rich then someone is not quiet or not happy.
Someone is not rich.
Paul is kind or not creative.
Someone is either not brave or funny.
Someone is both not tall and funny.
Someone is not patient or humble.
Alice is strong.
Mary is not old or not rich. | John is not rich. | entailment | ((?[X]:((~quiet(X)&tall(X))))=>(?[X]:((generous(X)&~old(X)))))&
(![X]:(~brave(X)=>(~humble(X)&kind(X))))&
((?[X]:((brave(X)<~>~quiet(X))))=>((calm(mary)<~>tall(mary))))&
(((~strong(fred)&old(fred)))<=>(?[X]:((~brave(X)|brave(X)))))&
(![X]:((~humble(X)|~strong(X))<=>(brave(X)<~>generous(X))))&
((?[X]:((~generous(X)|quiet(X))))=>((brave(john)<~>funny(john))))&
(![X]:(~calm(X)=>(generous(X)|~quiet(X))))&
(![X]:((~humble(X)&~generous(X))<=>(generous(X)&~kind(X))))&
(![X]:(humble(X)=>(brave(X)<~>~kind(X))))&
(![X]:((~calm(X)&happy(X))=>(wise(X)<~>humble(X))))&
(![X]:((curious(X)&~kind(X))<=>rich(X)))&
(((curious(john)<~>~wise(john)))<=>(?[X]:(creative(X))))&
(![X]:(~creative(X)=>(old(X)&kind(X))))&
(![X]:((generous(X)|~brave(X))<=>funny(X)))&
(((~brave(lucy)<~>~quiet(lucy)))=>(?[X]:((~funny(X)<~>tall(X)))))&
((?[X]:((~strong(X)&~rich(X))))=>(?[X]:((~quiet(X)|~happy(X)))))&
(?[X]:(~rich(X)))&
((kind(paul)|~creative(paul)))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:((~tall(X)&funny(X))))&
(?[X]:((~patient(X)|humble(X))))&
(strong(alice))&
((~old(mary)|~rich(mary))) | ~rich(john) | [
"p1",
"p7",
"p8",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 296486961628907438834670
% SZS output start Proof for 296486961628907438834670
2. ! [X0] : (~brave(X0) => (kind(X0) & ~humble(X0))) [input p1]
8. ! [X0] : ((~generous(X0) & ~humble(X0)) <=> (~kind(X0) & generous(X0))) [input p7]
9. ! [X0] : (humble(X0) => (brave(X0) <~> ~kind(X0))) [input p8]
11. ! [X0] : ((~kind(X0) & curious(X0)) <=> rich(X0)) [input p10]
24. rich(john) [input hypothesis]
31. ! [X0] : ((kind(X0) & ~humble(X0)) | brave(X0)) [ennf transformation 2]
36. ! [X0] : ((brave(X0) <~> ~kind(X0)) | ~humble(X0)) [ennf transformation 9]
51. ! [X0] : (((~generous(X0) & ~humble(X0)) | (kind(X0) | ~generous(X0))) & ((~kind(X0) & generous(X0)) | (generous(X0) | humble(X0)))) [nnf transformation 8]
52. ! [X0] : (((~generous(X0) & ~humble(X0)) | kind(X0) | ~generous(X0)) & ((~kind(X0) & generous(X0)) | generous(X0) | humble(X0))) [flattening 51]
53. ! [X0] : (((kind(X0) | ~brave(X0)) & (~kind(X0) | brave(X0))) | ~humble(X0)) [nnf transformation 36]
54. ! [X0] : (((~kind(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | (kind(X0) | ~curious(X0)))) [nnf transformation 11]
55. ! [X0] : (((~kind(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | kind(X0) | ~curious(X0))) [flattening 54]
74. ~humble(X0) | brave(X0) [cnf transformation 31]
96. generous(X0) | generous(X0) | humble(X0) [cnf transformation 52]
99. ~generous(X0) | kind(X0) | ~generous(X0) [cnf transformation 52]
101. kind(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 53]
104. ~rich(X0) | ~kind(X0) [cnf transformation 55]
126. rich(john) [cnf transformation 24]
127. humble(X0) | generous(X0) [duplicate literal removal 96]
128. ~generous(X0) | kind(X0) [duplicate literal removal 99]
198. ~humble(X0) | kind(X0) [subsumption resolution 101,74]
252. ~kind(john) [resolution 104,126]
269. kind(X0) | generous(X0) [resolution 198,127]
270. kind(X0) [subsumption resolution 269,128]
271. $false [resolution 270,252]
% SZS output end Proof for 296486961628907438834670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise is both not rich and happy and vice versa.
If mary is both not humble and rich then someone is not humble or strong.
Everyone who is not brave is either not kind or wise and vice versa.
If someone is both happy and not funny then susan is happy.
Everyone who is not brave or not generous is patient and vice versa.
Everyone who is not rich or curious is not rich.
Everyone who is either not creative or not funny is not calm or kind.
If paul is strong or not brave then fred is both not tall and tall and vice versa.
If someone is both calm and not humble then mary is quiet or calm and vice versa.
If someone is not generous or calm then someone is either tall or rich and vice versa.
Everyone who is both not creative and not old is not creative.
Everyone who is not humble is not brave and vice versa.
Everyone who is not patient or patient is kind.
Everyone who is not strong or not patient is humble or not rich and vice versa.
Everyone who is either curious or calm is not curious or funny.
Susan is both not tall and not patient.
Someone is both kind and quiet.
Someone is funny or strong.
Someone is funny.
Someone is wise. | Mary is not tall. | neutral | (![X]:((~patient(X)|~wise(X))<=>(~rich(X)&happy(X))))&
(((~humble(mary)&rich(mary)))=>(?[X]:((~humble(X)|strong(X)))))&
(![X]:(~brave(X)<=>(~kind(X)<~>wise(X))))&
((?[X]:((happy(X)&~funny(X))))=>(happy(susan)))&
(![X]:((~brave(X)|~generous(X))<=>patient(X)))&
(![X]:((~rich(X)|curious(X))=>~rich(X)))&
(![X]:((~creative(X)<~>~funny(X))=>(~calm(X)|kind(X))))&
(((strong(paul)|~brave(paul)))<=>((~tall(fred)&tall(fred))))&
((?[X]:((calm(X)&~humble(X))))<=>((quiet(mary)|calm(mary))))&
((?[X]:((~generous(X)|calm(X))))<=>(?[X]:((tall(X)<~>rich(X)))))&
(![X]:((~creative(X)&~old(X))=>~creative(X)))&
(![X]:(~humble(X)<=>~brave(X)))&
(![X]:((~patient(X)|patient(X))=>kind(X)))&
(![X]:((~strong(X)|~patient(X))<=>(humble(X)|~rich(X))))&
(![X]:((curious(X)<~>calm(X))=>(~curious(X)|funny(X))))&
((~tall(susan)&~patient(susan)))&
(?[X]:((kind(X)&quiet(X))))&
(?[X]:((funny(X)|strong(X))))&
(?[X]:(funny(X)))&
(?[X]:(wise(X))) | ~tall(mary) | []
| null | 0 |
If someone is either creative or not wise then someone is either not rich or funny and vice versa. If someone is not humble then someone is creative or not patient. Everyone who is not wise or quiet is both strong and funny. If john is both generous and quiet then someone is not happy or not creative and vice versa. If mary is not wise then mary is both tall and strong. Everyone who is both quiet and kind is either not strong or not funny. If fred is both not happy and not wise then someone is both not wise and not creative and vice versa. If lucy is not calm then lucy is not curious or patient. Everyone who is calm is not strong or tall and vice versa. Everyone who is either wise or not strong is not creative. Everyone who is either not quiet or kind is generous or brave and vice versa. If someone is not rich then someone is not generous or quiet. Everyone who is both not strong and not quiet is not creative and vice versa. If mary is either not generous or quiet then fred is both not brave and kind. Everyone who is either quiet or humble is both not wise and creative and vice versa. Everyone who is either not strong or generous is tall or humble and vice versa. Someone is either kind or quiet. Lucy is either not happy or not kind. Paul is not kind or not generous. Someone is both humble and not brave. Paul is both old and generous. Fred is not brave or tall. Someone is not tall. | Mary is funny. | entailment | ((?[X]:((creative(X)<~>~wise(X))))<=>(?[X]:((~rich(X)<~>funny(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((creative(X)|~patient(X)))))&
(![X]:((~wise(X)|quiet(X))=>(strong(X)&funny(X))))&
(((generous(john)&quiet(john)))<=>(?[X]:((~happy(X)|~creative(X)))))&
((~wise(mary))=>((tall(mary)&strong(mary))))&
(![X]:((quiet(X)&kind(X))=>(~strong(X)<~>~funny(X))))&
(((~happy(fred)&~wise(fred)))<=>(?[X]:((~wise(X)&~creative(X)))))&
((~calm(lucy))=>((~curious(lucy)|patient(lucy))))&
(![X]:(calm(X)<=>(~strong(X)|tall(X))))&
(![X]:((wise(X)<~>~strong(X))=>~creative(X)))&
(![X]:((~quiet(X)<~>kind(X))<=>(generous(X)|brave(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~generous(X)|quiet(X)))))&
(![X]:((~strong(X)&~quiet(X))<=>~creative(X)))&
(((~generous(mary)<~>quiet(mary)))=>((~brave(fred)&kind(fred))))&
(![X]:((quiet(X)<~>humble(X))<=>(~wise(X)&creative(X))))&
(![X]:((~strong(X)<~>generous(X))<=>(tall(X)|humble(X))))&
(?[X]:((kind(X)<~>quiet(X))))&
((~happy(lucy)<~>~kind(lucy)))&
((~kind(paul)|~generous(paul)))&
(?[X]:((humble(X)&~brave(X))))&
((old(paul)&generous(paul)))&
((~brave(fred)|tall(fred)))&
(?[X]:(~tall(X))) | funny(mary) | [
"p2",
"p3",
"p5",
"p9",
"p10",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 5551360450869758443866765
% SZS output start Proof for 5551360450869758443866765
3. ! [X0] : ((quiet(X0) | ~wise(X0)) => (funny(X0) & strong(X0))) [input p2]
4. (quiet(john) & generous(john)) <=> ? [X0] : (~creative(X0) | ~happy(X0)) [input p3]
6. ! [X0] : ((kind(X0) & quiet(X0)) => (~strong(X0) <~> ~funny(X0))) [input p5]
10. ! [X0] : ((wise(X0) <~> ~strong(X0)) => ~creative(X0)) [input p9]
11. ! [X0] : ((~quiet(X0) <~> kind(X0)) <=> (brave(X0) | generous(X0))) [input p10]
13. ! [X0] : ((~quiet(X0) & ~strong(X0)) <=> ~creative(X0)) [input p12]
24. ~funny(mary) [input hypothesis]
33. ! [X0] : ((funny(X0) & strong(X0)) | (~quiet(X0) & wise(X0))) [ennf transformation 3]
35. ! [X0] : ((~strong(X0) <~> ~funny(X0)) | (~kind(X0) | ~quiet(X0))) [ennf transformation 6]
36. ! [X0] : ((~strong(X0) <~> ~funny(X0)) | ~kind(X0) | ~quiet(X0)) [flattening 35]
37. ! [X0] : (~creative(X0) | (wise(X0) <=> ~strong(X0))) [ennf transformation 10]
45. ((quiet(john) & generous(john)) | ! [X0] : (creative(X0) & happy(X0))) & (? [X0] : (~creative(X0) | ~happy(X0)) | (~quiet(john) | ~generous(john))) [nnf transformation 4]
46. ((quiet(john) & generous(john)) | ! [X0] : (creative(X0) & happy(X0))) & (? [X0] : (~creative(X0) | ~happy(X0)) | ~quiet(john) | ~generous(john)) [flattening 45]
47. ((quiet(john) & generous(john)) | ! [X0] : (creative(X0) & happy(X0))) & (? [X1] : (~creative(X1) | ~happy(X1)) | ~quiet(john) | ~generous(john)) [rectify 46]
48. ? [X1] : (~creative(X1) | ~happy(X1)) => (~creative(sK2) | ~happy(sK2)) [choice axiom]
49. ((quiet(john) & generous(john)) | ! [X0] : (creative(X0) & happy(X0))) & ((~creative(sK2) | ~happy(sK2)) | ~quiet(john) | ~generous(john)) [skolemisation 47,48]
50. ! [X0] : (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ~kind(X0) | ~quiet(X0)) [nnf transformation 36]
56. ! [X0] : (~creative(X0) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) [nnf transformation 37]
57. ! [X0] : ((((~kind(X0) | quiet(X0)) & (kind(X0) | ~quiet(X0))) | (~brave(X0) & ~generous(X0))) & ((brave(X0) | generous(X0)) | ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0))))) [nnf transformation 11]
58. ! [X0] : ((((~kind(X0) | quiet(X0)) & (kind(X0) | ~quiet(X0))) | (~brave(X0) & ~generous(X0))) & (brave(X0) | generous(X0) | ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0))))) [flattening 57]
62. ! [X0] : (((~quiet(X0) & ~strong(X0)) | creative(X0)) & (~creative(X0) | (quiet(X0) | strong(X0)))) [nnf transformation 13]
63. ! [X0] : (((~quiet(X0) & ~strong(X0)) | creative(X0)) & (~creative(X0) | quiet(X0) | strong(X0))) [flattening 62]
86. ~quiet(X0) | strong(X0) [cnf transformation 33]
87. funny(X0) | wise(X0) [cnf transformation 33]
88. ~quiet(X0) | funny(X0) [cnf transformation 33]
91. generous(john) | creative(X0) [cnf transformation 49]
93. quiet(john) | creative(X0) [cnf transformation 49]
96. ~funny(X0) | ~strong(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 50]
102. ~strong(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 56]
106. kind(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 58]
108. ~kind(X0) | quiet(X0) | ~generous(X0) [cnf transformation 58]
111. ~creative(X0) | quiet(X0) | strong(X0) [cnf transformation 63]
140. ~funny(mary) [cnf transformation 24]
178. 9 <=> ! [X0] : creative(X0) [avatar definition]
179. creative(X0) <- (9) [avatar component clause 178]
181. 10 <=> quiet(john) [avatar definition]
183. quiet(john) <- (10) [avatar component clause 181]
184. 9 | 10 [avatar split clause 93,181,178]
190. 12 <=> generous(john) [avatar definition]
192. generous(john) <- (12) [avatar component clause 190]
193. 9 | 12 [avatar split clause 91,190,178]
213. ~strong(X0) | ~kind(X0) | ~quiet(X0) [subsumption resolution 96,88]
214. ~kind(X0) | ~quiet(X0) [subsumption resolution 213,86]
236. ~kind(X0) | ~generous(X0) [subsumption resolution 108,214]
238. ~generous(X0) | ~quiet(X0) [subsumption resolution 106,236]
248. ~creative(X0) | strong(X0) [subsumption resolution 111,86]
298. wise(mary) [resolution 87,140]
324. ~quiet(john) <- (12) [resolution 238,192]
326. $false <- (10, 12) [subsumption resolution 324,183]
327. ~10 | ~12 [avatar contradiction clause 326]
331. strong(X0) <- (9) [resolution 248,179]
337. ~creative(X0) | ~wise(X0) <- (9) [resolution 102,331]
340. ~wise(X0) <- (9) [subsumption resolution 337,179]
350. $false <- (9) [subsumption resolution 298,340]
351. ~9 [avatar contradiction clause 350]
352. $false [avatar sat refutation 184,193,327,351]
% SZS output end Proof for 5551360450869758443866765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or happy is tall and vice versa. Everyone who is either not patient or not tall is old or happy. If someone is not old or kind then susan is both wise and tall and vice versa. Everyone who is both not kind and old is not creative. Everyone who is creative or not strong is both strong and curious. If lucy is either not strong or not creative then someone is both not happy and not patient and vice versa. If someone is either quiet or not wise then someone is kind and vice versa. Everyone who is either generous or old is not humble or not wise and vice versa. Everyone who is either patient or curious is either not generous or humble. If fred is not happy then someone is wise or not calm. Everyone who is not patient is not happy and vice versa. Everyone who is both tall and not creative is not generous or not humble and vice versa. If susan is both happy and not strong then someone is either not old or curious and vice versa. Everyone who is either not generous or humble is either not happy or not creative and vice versa. If fred is both not rich and not old then lucy is either not calm or not humble and vice versa. Everyone who is not wise is both calm and old and vice versa. Someone is not humble. Someone is quiet. Fred is either not happy or not quiet. Mary is either not curious or not strong. Susan is not funny. Someone is funny. Alice is both not curious and humble. Susan is brave. | Mary is not strong. | contradiction | (![X]:((~happy(X)<~>happy(X))<=>tall(X)))&
(![X]:((~patient(X)<~>~tall(X))=>(old(X)|happy(X))))&
((?[X]:((~old(X)|kind(X))))<=>((wise(susan)&tall(susan))))&
(![X]:((~kind(X)&old(X))=>~creative(X)))&
(![X]:((creative(X)|~strong(X))=>(strong(X)&curious(X))))&
(((~strong(lucy)<~>~creative(lucy)))<=>(?[X]:((~happy(X)&~patient(X)))))&
((?[X]:((quiet(X)<~>~wise(X))))<=>(?[X]:(kind(X))))&
(![X]:((generous(X)<~>old(X))<=>(~humble(X)|~wise(X))))&
(![X]:((patient(X)<~>curious(X))=>(~generous(X)<~>humble(X))))&
((~happy(fred))=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:(~patient(X)<=>~happy(X)))&
(![X]:((tall(X)&~creative(X))<=>(~generous(X)|~humble(X))))&
(((happy(susan)&~strong(susan)))<=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:((~generous(X)<~>humble(X))<=>(~happy(X)<~>~creative(X))))&
(((~rich(fred)&~old(fred)))<=>((~calm(lucy)<~>~humble(lucy))))&
(![X]:(~wise(X)<=>(calm(X)&old(X))))&
(?[X]:(~humble(X)))&
(?[X]:(quiet(X)))&
((~happy(fred)<~>~quiet(fred)))&
((~curious(mary)<~>~strong(mary)))&
(~funny(susan))&
(?[X]:(funny(X)))&
((~curious(alice)&humble(alice)))&
(brave(susan)) | ~strong(mary) | [
"p4",
"hypothesis"
]
| % SZS status Unsatisfiable for 4089059796094067208116737
% SZS output start Proof for 4089059796094067208116737
5. ! [X0] : ((~strong(X0) | creative(X0)) => (curious(X0) & strong(X0))) [input p4]
25. ~strong(mary) [input hypothesis]
32. ! [X0] : ((curious(X0) & strong(X0)) | (strong(X0) & ~creative(X0))) [ennf transformation 5]
90. strong(X0) | strong(X0) [cnf transformation 32]
154. ~strong(mary) [cnf transformation 25]
155. strong(X0) [duplicate literal removal 90]
275. $false [subsumption resolution 154,155]
% SZS output end Proof for 4089059796094067208116737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and not old then someone is not funny.
If someone is both not generous and not creative then mary is both funny and not wise and vice versa.
Everyone who is funny is either old or not calm and vice versa.
If someone is both calm and rich then fred is either not kind or funny and vice versa.
Everyone who is both strong and not quiet is either strong or funny.
If someone is not generous then someone is both not quiet and happy.
If someone is not creative then someone is curious and vice versa.
If someone is both not kind and not humble then lucy is either kind or not strong and vice versa.
If someone is not generous then someone is not patient or strong and vice versa.
Everyone who is both rich and patient is both strong and not patient.
Everyone who is both tall and not quiet is both not patient and patient and vice versa.
If mary is either not wise or old then mary is either not happy or rich.
If someone is humble or happy then mary is not brave.
Everyone who is not creative is both not kind and patient.
Everyone who is not rich is either not brave or creative and vice versa.
Everyone who is tall or quiet is creative or not humble and vice versa.
Paul is both happy and rich.
Someone is curious.
Fred is both tall and kind.
Someone is both quiet and not curious.
Someone is either not calm or not strong.
John is both rich and not tall.
Alice is either not generous or funny.
Susan is either not kind or not funny. | Susan is calm. | neutral | ((?[X]:((patient(X)&~old(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~generous(X)&~creative(X))))<=>((funny(mary)&~wise(mary))))&
(![X]:(funny(X)<=>(old(X)<~>~calm(X))))&
((?[X]:((calm(X)&rich(X))))<=>((~kind(fred)<~>funny(fred))))&
(![X]:((strong(X)&~quiet(X))=>(strong(X)<~>funny(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:(curious(X))))&
((?[X]:((~kind(X)&~humble(X))))<=>((kind(lucy)<~>~strong(lucy))))&
((?[X]:(~generous(X)))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((rich(X)&patient(X))=>(strong(X)&~patient(X))))&
(![X]:((tall(X)&~quiet(X))<=>(~patient(X)&patient(X))))&
(((~wise(mary)<~>old(mary)))=>((~happy(mary)<~>rich(mary))))&
((?[X]:((humble(X)|happy(X))))=>(~brave(mary)))&
(![X]:(~creative(X)=>(~kind(X)&patient(X))))&
(![X]:(~rich(X)<=>(~brave(X)<~>creative(X))))&
(![X]:((tall(X)|quiet(X))<=>(creative(X)|~humble(X))))&
((happy(paul)&rich(paul)))&
(?[X]:(curious(X)))&
((tall(fred)&kind(fred)))&
(?[X]:((quiet(X)&~curious(X))))&
(?[X]:((~calm(X)<~>~strong(X))))&
((rich(john)&~tall(john)))&
((~generous(alice)<~>funny(alice)))&
((~kind(susan)<~>~funny(susan))) | calm(susan) | []
| null | 0 |
Everyone who is not creative or patient is strong or not happy and vice versa.
Everyone who is not humble or not wise is both generous and old.
If someone is both wise and old then someone is either funny or not humble.
Everyone who is both not wise and not quiet is not calm or funny and vice versa.
Everyone who is either not happy or wise is wise or brave and vice versa.
If fred is either not curious or calm then someone is either not strong or not creative and vice versa.
Everyone who is calm is not funny or rich.
Everyone who is not tall or not calm is funny and vice versa.
Everyone who is tall or generous is not funny or kind.
Everyone who is not old is both tall and humble.
If john is tall or not old then someone is not creative or quiet and vice versa.
Everyone who is both not calm and not rich is both curious and not brave and vice versa.
If someone is both funny and rich then someone is not funny or generous and vice versa.
If someone is both not humble and not happy then someone is either not quiet or generous.
If someone is both creative and not creative then someone is either not humble or not brave and vice versa.
Everyone who is either happy or curious is both generous and tall.
Susan is either funny or not humble.
Someone is quiet or not strong.
Susan is either patient or not calm.
Someone is not happy or humble.
Someone is either generous or not wise.
Someone is brave.
Someone is either curious or patient.
Someone is not curious. | Susan is not old. | contradiction | (![X]:((~creative(X)|patient(X))<=>(strong(X)|~happy(X))))&
(![X]:((~humble(X)|~wise(X))=>(generous(X)&old(X))))&
((?[X]:((wise(X)&old(X))))=>(?[X]:((funny(X)<~>~humble(X)))))&
(![X]:((~wise(X)&~quiet(X))<=>(~calm(X)|funny(X))))&
(![X]:((~happy(X)<~>wise(X))<=>(wise(X)|brave(X))))&
(((~curious(fred)<~>calm(fred)))<=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:(calm(X)=>(~funny(X)|rich(X))))&
(![X]:((~tall(X)|~calm(X))<=>funny(X)))&
(![X]:((tall(X)|generous(X))=>(~funny(X)|kind(X))))&
(![X]:(~old(X)=>(tall(X)&humble(X))))&
(((tall(john)|~old(john)))<=>(?[X]:((~creative(X)|quiet(X)))))&
(![X]:((~calm(X)&~rich(X))<=>(curious(X)&~brave(X))))&
((?[X]:((funny(X)&rich(X))))<=>(?[X]:((~funny(X)|generous(X)))))&
((?[X]:((~humble(X)&~happy(X))))=>(?[X]:((~quiet(X)<~>generous(X)))))&
((?[X]:((creative(X)&~creative(X))))<=>(?[X]:((~humble(X)<~>~brave(X)))))&
(![X]:((happy(X)<~>curious(X))=>(generous(X)&tall(X))))&
((funny(susan)<~>~humble(susan)))&
(?[X]:((quiet(X)|~strong(X))))&
((patient(susan)<~>~calm(susan)))&
(?[X]:((~happy(X)|humble(X))))&
(?[X]:((generous(X)<~>~wise(X))))&
(?[X]:(brave(X)))&
(?[X]:((curious(X)<~>patient(X))))&
(?[X]:(~curious(X))) | ~old(susan) | [
"p1",
"p3",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8199820633279079219586090
% SZS output start Proof for 8199820633279079219586090
2. ! [X0] : ((~wise(X0) | ~humble(X0)) => (old(X0) & generous(X0))) [input p1]
4. ! [X0] : ((~quiet(X0) & ~wise(X0)) <=> (funny(X0) | ~calm(X0))) [input p3]
17. funny(susan) <~> ~humble(susan) [input p16]
25. ~old(susan) [input hypothesis]
31. ! [X0] : ((old(X0) & generous(X0)) | (wise(X0) & humble(X0))) [ennf transformation 2]
44. ! [X0] : (((~quiet(X0) & ~wise(X0)) | (~funny(X0) & calm(X0))) & ((funny(X0) | ~calm(X0)) | (quiet(X0) | wise(X0)))) [nnf transformation 4]
45. ! [X0] : (((~quiet(X0) & ~wise(X0)) | (~funny(X0) & calm(X0))) & (funny(X0) | ~calm(X0) | quiet(X0) | wise(X0))) [flattening 44]
76. (humble(susan) | ~funny(susan)) & (~humble(susan) | funny(susan)) [nnf transformation 17]
98. old(X0) | humble(X0) [cnf transformation 31]
99. old(X0) | wise(X0) [cnf transformation 31]
104. ~funny(X0) | ~wise(X0) [cnf transformation 45]
152. ~humble(susan) | funny(susan) [cnf transformation 76]
164. ~old(susan) [cnf transformation 25]
297. 29 <=> funny(susan) [avatar definition]
298. funny(susan) <- (29) [avatar component clause 297]
301. 30 <=> humble(susan) [avatar definition]
305. 29 | ~30 [avatar split clause 152,301,297]
354. humble(susan) [resolution 98,164]
357. 30 [avatar split clause 354,301]
358. wise(susan) [resolution 99,164]
367. ~wise(susan) <- (29) [resolution 104,298]
368. $false <- (29) [subsumption resolution 367,358]
369. ~29 [avatar contradiction clause 368]
370. $false [avatar sat refutation 305,357,369]
% SZS output end Proof for 8199820633279079219586090
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not happy is either not kind or not old. If someone is not curious or rich then susan is calm or strong. If someone is humble then someone is not generous and vice versa. If mary is both not tall and curious then someone is both wise and tall and vice versa. Everyone who is not happy or curious is either not creative or not funny and vice versa. Everyone who is both not quiet and not old is both not quiet and not wise and vice versa. Everyone who is strong is not humble or wise and vice versa. Everyone who is not brave is both quiet and wise. If someone is either creative or rich then someone is not brave or generous. Everyone who is both quiet and humble is either not wise or not strong and vice versa. If someone is both not brave and not wise then someone is strong or creative. Everyone who is either not creative or not curious is funny and vice versa. Everyone who is not happy is brave. If someone is curious then someone is either not brave or old and vice versa. Everyone who is both not wise and tall is either curious or not humble. If someone is not tall then someone is both not happy and not calm and vice versa. Mary is strong or not rich. Alice is not calm. Paul is not wise or rich. Someone is both rich and generous. Susan is rich or not rich. Alice is both creative and tall. Someone is brave or not curious. Someone is not quiet. | Paul is funny. | neutral | (![X]:((kind(X)|~happy(X))=>(~kind(X)<~>~old(X))))&
((?[X]:((~curious(X)|rich(X))))=>((calm(susan)|strong(susan))))&
((?[X]:(humble(X)))<=>(?[X]:(~generous(X))))&
(((~tall(mary)&curious(mary)))<=>(?[X]:((wise(X)&tall(X)))))&
(![X]:((~happy(X)|curious(X))<=>(~creative(X)<~>~funny(X))))&
(![X]:((~quiet(X)&~old(X))<=>(~quiet(X)&~wise(X))))&
(![X]:(strong(X)<=>(~humble(X)|wise(X))))&
(![X]:(~brave(X)=>(quiet(X)&wise(X))))&
((?[X]:((creative(X)<~>rich(X))))=>(?[X]:((~brave(X)|generous(X)))))&
(![X]:((quiet(X)&humble(X))<=>(~wise(X)<~>~strong(X))))&
((?[X]:((~brave(X)&~wise(X))))=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((~creative(X)<~>~curious(X))<=>funny(X)))&
(![X]:(~happy(X)=>brave(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:((~wise(X)&tall(X))=>(curious(X)<~>~humble(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~happy(X)&~calm(X)))))&
((strong(mary)|~rich(mary)))&
(~calm(alice))&
((~wise(paul)|rich(paul)))&
(?[X]:((rich(X)&generous(X))))&
((rich(susan)|~rich(susan)))&
((creative(alice)&tall(alice)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:(~quiet(X))) | funny(paul) | []
| null | 0 |
Everyone who is either tall or strong is not generous and vice versa.
If someone is either not curious or old then someone is both not old and generous and vice versa.
If someone is both generous and not curious then someone is not funny and vice versa.
If john is creative or rich then someone is not strong.
If someone is both tall and strong then someone is both not happy and rich.
Everyone who is either not patient or not brave is not quiet and vice versa.
Everyone who is both calm and kind is both wise and not curious and vice versa.
If paul is both strong and rich then someone is old or not creative and vice versa.
Everyone who is either not strong or quiet is both not kind and not rich.
If someone is not patient or not generous then someone is either kind or not happy.
Everyone who is both strong and kind is not calm or quiet and vice versa.
Everyone who is either not curious or calm is either not patient or not tall and vice versa.
Everyone who is either calm or old is not humble.
If someone is either not generous or creative then paul is tall.
Everyone who is not quiet or not generous is both not rich and happy.
Everyone who is happy is both not funny and not wise.
Someone is not patient.
Someone is happy.
Someone is creative.
Someone is not kind or not tall.
Paul is not curious. | Paul is not old. | entailment | (![X]:((tall(X)<~>strong(X))<=>~generous(X)))&
((?[X]:((~curious(X)<~>old(X))))<=>(?[X]:((~old(X)&generous(X)))))&
((?[X]:((generous(X)&~curious(X))))<=>(?[X]:(~funny(X))))&
(((creative(john)|rich(john)))=>(?[X]:(~strong(X))))&
((?[X]:((tall(X)&strong(X))))=>(?[X]:((~happy(X)&rich(X)))))&
(![X]:((~patient(X)<~>~brave(X))<=>~quiet(X)))&
(![X]:((calm(X)&kind(X))<=>(wise(X)&~curious(X))))&
(((strong(paul)&rich(paul)))<=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~strong(X)<~>quiet(X))=>(~kind(X)&~rich(X))))&
((?[X]:((~patient(X)|~generous(X))))=>(?[X]:((kind(X)<~>~happy(X)))))&
(![X]:((strong(X)&kind(X))<=>(~calm(X)|quiet(X))))&
(![X]:((~curious(X)<~>calm(X))<=>(~patient(X)<~>~tall(X))))&
(![X]:((calm(X)<~>old(X))=>~humble(X)))&
((?[X]:((~generous(X)<~>creative(X))))=>(tall(paul)))&
(![X]:((~quiet(X)|~generous(X))=>(~rich(X)&happy(X))))&
(![X]:(happy(X)=>(~funny(X)&~wise(X))))&
(?[X]:(~patient(X)))&
(?[X]:(happy(X)))&
(?[X]:(creative(X)))&
(?[X]:((~kind(X)|~tall(X))))&
(~curious(paul)) | ~old(paul) | [
"p7",
"p8",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 735341911123186191291460
% SZS output start Proof for 735341911123186191291460
8. (rich(paul) & strong(paul)) <=> ? [X0] : (~creative(X0) | old(X0)) [input p7]
9. ! [X0] : ((~strong(X0) <~> quiet(X0)) => (~rich(X0) & ~kind(X0))) [input p8]
11. ! [X0] : ((kind(X0) & strong(X0)) <=> (quiet(X0) | ~calm(X0))) [input p10]
15. ! [X0] : ((~generous(X0) | ~quiet(X0)) => (happy(X0) & ~rich(X0))) [input p14]
22. old(paul) [input hypothesis]
30. ! [X0] : ((~rich(X0) & ~kind(X0)) | (~strong(X0) <=> quiet(X0))) [ennf transformation 9]
33. ! [X0] : ((happy(X0) & ~rich(X0)) | (generous(X0) & quiet(X0))) [ennf transformation 15]
54. ((rich(paul) & strong(paul)) | ! [X0] : (creative(X0) & ~old(X0))) & (? [X0] : (~creative(X0) | old(X0)) | (~rich(paul) | ~strong(paul))) [nnf transformation 8]
55. ((rich(paul) & strong(paul)) | ! [X0] : (creative(X0) & ~old(X0))) & (? [X0] : (~creative(X0) | old(X0)) | ~rich(paul) | ~strong(paul)) [flattening 54]
56. ((rich(paul) & strong(paul)) | ! [X0] : (creative(X0) & ~old(X0))) & (? [X1] : (~creative(X1) | old(X1)) | ~rich(paul) | ~strong(paul)) [rectify 55]
57. ? [X1] : (~creative(X1) | old(X1)) => (~creative(sK6) | old(sK6)) [choice axiom]
58. ((rich(paul) & strong(paul)) | ! [X0] : (creative(X0) & ~old(X0))) & ((~creative(sK6) | old(sK6)) | ~rich(paul) | ~strong(paul)) [skolemisation 56,57]
59. ! [X0] : ((~rich(X0) & ~kind(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0)))) [nnf transformation 30]
64. ! [X0] : (((kind(X0) & strong(X0)) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | (~kind(X0) | ~strong(X0)))) [nnf transformation 11]
65. ! [X0] : (((kind(X0) & strong(X0)) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ~kind(X0) | ~strong(X0))) [flattening 64]
102. strong(paul) | ~old(X0) [cnf transformation 58]
104. rich(paul) | ~old(X0) [cnf transformation 58]
107. ~kind(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 59]
118. ~quiet(X0) | kind(X0) [cnf transformation 65]
129. ~rich(X0) | quiet(X0) [cnf transformation 33]
140. old(paul) [cnf transformation 22]
224. 20 <=> rich(paul) [avatar definition]
226. rich(paul) <- (20) [avatar component clause 224]
229. 21 <=> ! [X0] : ~old(X0) [avatar definition]
230. ~old(X0) <- (21) [avatar component clause 229]
231. 21 | 20 [avatar split clause 104,224,229]
233. 22 <=> strong(paul) [avatar definition]
235. strong(paul) <- (22) [avatar component clause 233]
237. 21 | 22 [avatar split clause 102,233,229]
289. $false <- (21) [resolution 230,140]
290. ~21 [avatar contradiction clause 289]
295. quiet(paul) <- (20) [resolution 129,226]
296. kind(paul) <- (20) [resolution 295,118]
456. ~strong(paul) | ~quiet(paul) <- (20) [resolution 107,296]
458. ~quiet(paul) <- (20, 22) [subsumption resolution 456,235]
459. $false <- (20, 22) [subsumption resolution 458,295]
460. ~20 | ~22 [avatar contradiction clause 459]
461. $false [avatar sat refutation 231,237,290,460]
% SZS output end Proof for 735341911123186191291460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or not old is either not strong or not generous and vice versa.
If someone is wise then lucy is tall.
If alice is both patient and happy then fred is not generous.
If john is both not kind and happy then someone is brave or calm and vice versa.
If lucy is not generous or humble then someone is not strong or not humble.
Everyone who is both generous and not creative is not generous.
Everyone who is tall or kind is both generous and not patient and vice versa.
If susan is either not funny or not calm then someone is either quiet or not old and vice versa.
If someone is both not tall and not kind then john is both humble and not happy.
If someone is both not generous and not creative then someone is both strong and brave.
Everyone who is both creative and kind is generous.
Everyone who is not creative or wise is either not calm or rich and vice versa.
Everyone who is not curious or tall is both not happy and old and vice versa.
If mary is both calm and not tall then someone is not tall.
Everyone who is either generous or not old is either kind or not curious.
Everyone who is not tall or not humble is both patient and strong.
Alice is not happy.
Someone is not funny or not kind.
Someone is not wise.
Mary is not humble or quiet.
Someone is not kind or tall.
Someone is either quiet or creative.
Someone is not happy. | Alice is generous. | entailment | (![X]:((calm(X)|~old(X))<=>(~strong(X)<~>~generous(X))))&
((?[X]:(wise(X)))=>(tall(lucy)))&
(((patient(alice)&happy(alice)))=>(~generous(fred)))&
(((~kind(john)&happy(john)))<=>(?[X]:((brave(X)|calm(X)))))&
(((~generous(lucy)|humble(lucy)))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((generous(X)&~creative(X))=>~generous(X)))&
(![X]:((tall(X)|kind(X))<=>(generous(X)&~patient(X))))&
(((~funny(susan)<~>~calm(susan)))<=>(?[X]:((quiet(X)<~>~old(X)))))&
((?[X]:((~tall(X)&~kind(X))))=>((humble(john)&~happy(john))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((creative(X)&kind(X))=>generous(X)))&
(![X]:((~creative(X)|wise(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((~curious(X)|tall(X))<=>(~happy(X)&old(X))))&
(((calm(mary)&~tall(mary)))=>(?[X]:(~tall(X))))&
(![X]:((generous(X)<~>~old(X))=>(kind(X)<~>~curious(X))))&
(![X]:((~tall(X)|~humble(X))=>(patient(X)&strong(X))))&
(~happy(alice))&
(?[X]:((~funny(X)|~kind(X))))&
(?[X]:(~wise(X)))&
((~humble(mary)|quiet(mary)))&
(?[X]:((~kind(X)|tall(X))))&
(?[X]:((quiet(X)<~>creative(X))))&
(?[X]:(~happy(X))) | generous(alice) | [
"p0",
"p3",
"p6",
"p8",
"p12",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 8674607708628976115207955
% SZS output start Proof for 8674607708628976115207955
1. ! [X0] : ((~old(X0) | calm(X0)) <=> (~strong(X0) <~> ~generous(X0))) [input p0]
4. (happy(john) & ~kind(john)) <=> ? [X0] : (calm(X0) | brave(X0)) [input p3]
7. ! [X0] : ((kind(X0) | tall(X0)) <=> (~patient(X0) & generous(X0))) [input p6]
9. ? [X0] : (~kind(X0) & ~tall(X0)) => (~happy(john) & humble(john)) [input p8]
13. ! [X0] : ((tall(X0) | ~curious(X0)) <=> (old(X0) & ~happy(X0))) [input p12]
15. ! [X0] : ((generous(X0) <~> ~old(X0)) => (kind(X0) <~> ~curious(X0))) [input p14]
16. ! [X0] : ((~humble(X0) | ~tall(X0)) => (strong(X0) & patient(X0))) [input p15]
24. ~generous(alice) [input hypothesis]
32. (~happy(john) & humble(john)) | ! [X0] : (kind(X0) | tall(X0)) [ennf transformation 9]
38. ! [X0] : ((kind(X0) <~> ~curious(X0)) | (generous(X0) <=> ~old(X0))) [ennf transformation 15]
39. ! [X0] : ((strong(X0) & patient(X0)) | (humble(X0) & tall(X0))) [ennf transformation 16]
40. ! [X0] : (((~old(X0) | calm(X0)) | ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0)))) & (((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) | (old(X0) & ~calm(X0)))) [nnf transformation 1]
41. ! [X0] : ((~old(X0) | calm(X0) | ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0)))) & (((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) | (old(X0) & ~calm(X0)))) [flattening 40]
42. ((happy(john) & ~kind(john)) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X0] : (calm(X0) | brave(X0)) | (~happy(john) | kind(john))) [nnf transformation 4]
43. ((happy(john) & ~kind(john)) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X0] : (calm(X0) | brave(X0)) | ~happy(john) | kind(john)) [flattening 42]
44. ((happy(john) & ~kind(john)) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X1] : (calm(X1) | brave(X1)) | ~happy(john) | kind(john)) [rectify 43]
45. ? [X1] : (calm(X1) | brave(X1)) => (calm(sK0) | brave(sK0)) [choice axiom]
46. ((happy(john) & ~kind(john)) | ! [X0] : (~calm(X0) & ~brave(X0))) & ((calm(sK0) | brave(sK0)) | ~happy(john) | kind(john)) [skolemisation 44,45]
49. ! [X0] : (((kind(X0) | tall(X0)) | (patient(X0) | ~generous(X0))) & ((~patient(X0) & generous(X0)) | (~kind(X0) & ~tall(X0)))) [nnf transformation 7]
50. ! [X0] : ((kind(X0) | tall(X0) | patient(X0) | ~generous(X0)) & ((~patient(X0) & generous(X0)) | (~kind(X0) & ~tall(X0)))) [flattening 49]
60. ! [X0] : (((tall(X0) | ~curious(X0)) | (~old(X0) | happy(X0))) & ((old(X0) & ~happy(X0)) | (~tall(X0) & curious(X0)))) [nnf transformation 13]
61. ! [X0] : ((tall(X0) | ~curious(X0) | ~old(X0) | happy(X0)) & ((old(X0) & ~happy(X0)) | (~tall(X0) & curious(X0)))) [flattening 60]
64. ! [X0] : (((curious(X0) | ~kind(X0)) & (~curious(X0) | kind(X0))) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) [nnf transformation 38]
81. ~strong(X0) | calm(X0) | ~old(X0) | generous(X0) [cnf transformation 41]
88. happy(john) | ~calm(X0) [cnf transformation 46]
92. ~tall(X0) | generous(X0) [cnf transformation 50]
93. ~kind(X0) | generous(X0) [cnf transformation 50]
106. ~happy(john) | kind(X0) | tall(X0) [cnf transformation 32]
118. curious(X0) | old(X0) [cnf transformation 61]
123. ~curious(X0) | kind(X0) | generous(X0) | old(X0) [cnf transformation 64]
128. tall(X0) | strong(X0) [cnf transformation 39]
138. ~generous(alice) [cnf transformation 24]
162. 6 <=> ! [X0] : ~calm(X0) [avatar definition]
163. ~calm(X0) <- (6) [avatar component clause 162]
165. 7 <=> happy(john) [avatar definition]
168. 6 | 7 [avatar split clause 88,165,162]
237. 22 <=> ! [X0] : (kind(X0) | tall(X0)) [avatar definition]
238. kind(X0) | tall(X0) <- (22) [avatar component clause 237]
239. 22 | ~7 [avatar split clause 106,165,237]
275. kind(X0) | generous(X0) | old(X0) [subsumption resolution 123,118]
276. generous(X0) | old(X0) [subsumption resolution 275,93]
329. generous(X1) | strong(X1) [resolution 128,92]
342. tall(X1) | generous(X1) <- (22) [resolution 238,93]
347. generous(X1) <- (22) [subsumption resolution 342,92]
356. old(alice) [resolution 276,138]
373. $false <- (22) [resolution 347,138]
377. ~22 [avatar contradiction clause 373]
449. strong(alice) [resolution 329,138]
467. calm(alice) | ~old(alice) | generous(alice) [resolution 449,81]
468. ~old(alice) | generous(alice) <- (6) [subsumption resolution 467,163]
469. generous(alice) <- (6) [subsumption resolution 468,356]
470. $false <- (6) [subsumption resolution 469,138]
471. ~6 [avatar contradiction clause 470]
472. $false [avatar sat refutation 168,239,377,471]
% SZS output end Proof for 8674607708628976115207955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or not quiet is not funny or not creative and vice versa. Everyone who is curious is either not patient or not creative and vice versa. Everyone who is both not generous and calm is wise or not patient. If someone is not strong then someone is not generous. If mary is either not strong or not humble then lucy is either calm or happy. Everyone who is not wise is either not tall or quiet and vice versa. Everyone who is calm or not happy is brave or funny. Everyone who is either generous or not calm is either not funny or not tall. Everyone who is either kind or wise is strong and vice versa. Everyone who is both not funny and calm is both humble and not humble and vice versa. Everyone who is either not brave or kind is both not wise and not strong and vice versa. If john is not wise or not quiet then someone is wise and vice versa. If someone is both not wise and generous then lucy is old. If john is either not old or strong then lucy is both wise and calm. If someone is not tall or tall then someone is happy or humble and vice versa. Everyone who is both not wise and creative is either curious or rich and vice versa. Someone is not wise. Someone is either quiet or not tall. Susan is both not brave and not curious. John is both not patient and wise. John is funny. Susan is either not tall or tall. Susan is happy or tall. Someone is both not strong and quiet. | Lucy is happy. | neutral | (![X]:((rich(X)|~quiet(X))<=>(~funny(X)|~creative(X))))&
(![X]:(curious(X)<=>(~patient(X)<~>~creative(X))))&
(![X]:((~generous(X)&calm(X))=>(wise(X)|~patient(X))))&
((?[X]:(~strong(X)))=>(?[X]:(~generous(X))))&
(((~strong(mary)<~>~humble(mary)))=>((calm(lucy)<~>happy(lucy))))&
(![X]:(~wise(X)<=>(~tall(X)<~>quiet(X))))&
(![X]:((calm(X)|~happy(X))=>(brave(X)|funny(X))))&
(![X]:((generous(X)<~>~calm(X))=>(~funny(X)<~>~tall(X))))&
(![X]:((kind(X)<~>wise(X))<=>strong(X)))&
(![X]:((~funny(X)&calm(X))<=>(humble(X)&~humble(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(~wise(X)&~strong(X))))&
(((~wise(john)|~quiet(john)))<=>(?[X]:(wise(X))))&
((?[X]:((~wise(X)&generous(X))))=>(old(lucy)))&
(((~old(john)<~>strong(john)))=>((wise(lucy)&calm(lucy))))&
((?[X]:((~tall(X)|tall(X))))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((~wise(X)&creative(X))<=>(curious(X)<~>rich(X))))&
(?[X]:(~wise(X)))&
(?[X]:((quiet(X)<~>~tall(X))))&
((~brave(susan)&~curious(susan)))&
((~patient(john)&wise(john)))&
(funny(john))&
((~tall(susan)<~>tall(susan)))&
((happy(susan)|tall(susan)))&
(?[X]:((~strong(X)&quiet(X)))) | happy(lucy) | []
| null | 0 |
If someone is either not old or not wise then someone is both strong and not funny.
If alice is patient then lucy is either strong or generous.
If susan is both not quiet and curious then paul is funny or strong.
If someone is not brave or not tall then paul is not wise.
Everyone who is both not calm and calm is both generous and not generous and vice versa.
If lucy is either not strong or strong then someone is not quiet or humble and vice versa.
If fred is both not happy and not tall then someone is both wise and strong and vice versa.
If someone is either humble or not rich then someone is humble or not curious.
If mary is not patient or rich then someone is both not wise and not patient.
Everyone who is not tall or not brave is quiet.
If someone is happy then someone is not humble or not creative.
Everyone who is creative is not generous or generous and vice versa.
Everyone who is either humble or patient is not curious or generous and vice versa.
Everyone who is both creative and quiet is either rich or not old and vice versa.
If john is both not brave and calm then someone is not rich or wise.
If fred is quiet or not rich then fred is creative and vice versa.
Someone is either strong or not brave.
Paul is either quiet or old.
Someone is funny or not tall.
John is either kind or not happy.
Mary is not quiet.
Someone is generous.
Mary is patient.
Paul is both tall and generous. | John is not creative. | contradiction | ((?[X]:((~old(X)<~>~wise(X))))=>(?[X]:((strong(X)&~funny(X)))))&
((patient(alice))=>((strong(lucy)<~>generous(lucy))))&
(((~quiet(susan)&curious(susan)))=>((funny(paul)|strong(paul))))&
((?[X]:((~brave(X)|~tall(X))))=>(~wise(paul)))&
(![X]:((~calm(X)&calm(X))<=>(generous(X)&~generous(X))))&
(((~strong(lucy)<~>strong(lucy)))<=>(?[X]:((~quiet(X)|humble(X)))))&
(((~happy(fred)&~tall(fred)))<=>(?[X]:((wise(X)&strong(X)))))&
((?[X]:((humble(X)<~>~rich(X))))=>(?[X]:((humble(X)|~curious(X)))))&
(((~patient(mary)|rich(mary)))=>(?[X]:((~wise(X)&~patient(X)))))&
(![X]:((~tall(X)|~brave(X))=>quiet(X)))&
((?[X]:(happy(X)))=>(?[X]:((~humble(X)|~creative(X)))))&
(![X]:(creative(X)<=>(~generous(X)|generous(X))))&
(![X]:((humble(X)<~>patient(X))<=>(~curious(X)|generous(X))))&
(![X]:((creative(X)&quiet(X))<=>(rich(X)<~>~old(X))))&
(((~brave(john)&calm(john)))=>(?[X]:((~rich(X)|wise(X)))))&
(((quiet(fred)|~rich(fred)))<=>(creative(fred)))&
(?[X]:((strong(X)<~>~brave(X))))&
((quiet(paul)<~>old(paul)))&
(?[X]:((funny(X)|~tall(X))))&
((kind(john)<~>~happy(john)))&
(~quiet(mary))&
(?[X]:(generous(X)))&
(patient(mary))&
((tall(paul)&generous(paul))) | ~creative(john) | [
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 4414667476764113947118170
% SZS output start Proof for 4414667476764113947118170
12. ! [X0] : (creative(X0) <=> (generous(X0) | ~generous(X0))) [input p11]
25. ~creative(john) [input hypothesis]
65. ! [X0] : ((creative(X0) | (~generous(X0) & generous(X0))) & ((generous(X0) | ~generous(X0)) | ~creative(X0))) [nnf transformation 12]
66. ! [X0] : ((creative(X0) | (~generous(X0) & generous(X0))) & (generous(X0) | ~generous(X0) | ~creative(X0))) [flattening 65]
117. creative(X0) | generous(X0) [cnf transformation 66]
118. creative(X0) | ~generous(X0) [cnf transformation 66]
147. ~creative(john) [cnf transformation 25]
292. creative(X0) [subsumption resolution 117,118]
362. $false [subsumption resolution 147,292]
% SZS output end Proof for 4414667476764113947118170
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If fred is either wise or not strong then someone is either not funny or not patient and vice versa. Everyone who is either not humble or not calm is both patient and not funny and vice versa. If someone is creative then lucy is either wise or not calm and vice versa. Everyone who is not generous is either not curious or curious. Everyone who is both humble and not strong is not generous. Everyone who is rich or not rich is either tall or not quiet and vice versa. Everyone who is both not generous and not humble is either strong or quiet. Everyone who is both not old and old is tall or not rich and vice versa. If alice is kind or creative then susan is generous or not strong. Everyone who is kind or curious is not patient or creative and vice versa. If someone is funny or creative then someone is not happy or quiet. If someone is either wise or rich then someone is not strong or brave and vice versa. Everyone who is funny is strong. Everyone who is not curious is either not happy or not quiet and vice versa. If alice is either not kind or curious then john is rich and vice versa. If someone is calm or not tall then john is either not humble or tall. Someone is both rich and kind. Someone is funny or happy. Alice is both not brave and not generous. Someone is both not kind and not strong. Someone is either not quiet or patient. Someone is both not funny and rich. Someone is happy. Paul is either happy or not old. | Lucy is not quiet. | entailment | (((wise(fred)<~>~strong(fred)))<=>(?[X]:((~funny(X)<~>~patient(X)))))&
(![X]:((~humble(X)<~>~calm(X))<=>(patient(X)&~funny(X))))&
((?[X]:(creative(X)))<=>((wise(lucy)<~>~calm(lucy))))&
(![X]:(~generous(X)=>(~curious(X)<~>curious(X))))&
(![X]:((humble(X)&~strong(X))=>~generous(X)))&
(![X]:((rich(X)|~rich(X))<=>(tall(X)<~>~quiet(X))))&
(![X]:((~generous(X)&~humble(X))=>(strong(X)<~>quiet(X))))&
(![X]:((~old(X)&old(X))<=>(tall(X)|~rich(X))))&
(((kind(alice)|creative(alice)))=>((generous(susan)|~strong(susan))))&
(![X]:((kind(X)|curious(X))<=>(~patient(X)|creative(X))))&
((?[X]:((funny(X)|creative(X))))=>(?[X]:((~happy(X)|quiet(X)))))&
((?[X]:((wise(X)<~>rich(X))))<=>(?[X]:((~strong(X)|brave(X)))))&
(![X]:(funny(X)=>strong(X)))&
(![X]:(~curious(X)<=>(~happy(X)<~>~quiet(X))))&
(((~kind(alice)<~>curious(alice)))<=>(rich(john)))&
((?[X]:((calm(X)|~tall(X))))=>((~humble(john)<~>tall(john))))&
(?[X]:((rich(X)&kind(X))))&
(?[X]:((funny(X)|happy(X))))&
((~brave(alice)&~generous(alice)))&
(?[X]:((~kind(X)&~strong(X))))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:((~funny(X)&rich(X))))&
(?[X]:(happy(X)))&
((happy(paul)<~>~old(paul))) | ~quiet(lucy) | [
"p5",
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 1550930913058953832249374
% SZS output start Proof for 1550930913058953832249374
6. ! [X0] : ((~rich(X0) | rich(X0)) <=> (tall(X0) <~> ~quiet(X0))) [input p5]
8. ! [X0] : ((old(X0) & ~old(X0)) <=> (~rich(X0) | tall(X0))) [input p7]
25. quiet(lucy) [input hypothesis]
49. ! [X0] : (((~rich(X0) | rich(X0)) | ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) & (((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | (rich(X0) & ~rich(X0)))) [nnf transformation 6]
50. ! [X0] : ((~rich(X0) | rich(X0) | ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) & (((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | (rich(X0) & ~rich(X0)))) [flattening 49]
52. ! [X0] : (((old(X0) & ~old(X0)) | (rich(X0) & ~tall(X0))) & ((~rich(X0) | tall(X0)) | (~old(X0) | old(X0)))) [nnf transformation 8]
53. ! [X0] : (((old(X0) & ~old(X0)) | (rich(X0) & ~tall(X0))) & (~rich(X0) | tall(X0) | ~old(X0) | old(X0))) [flattening 52]
102. ~quiet(X0) | tall(X0) | ~rich(X0) [cnf transformation 50]
103. ~quiet(X0) | tall(X0) | rich(X0) [cnf transformation 50]
111. ~old(X0) | ~tall(X0) [cnf transformation 53]
113. ~tall(X0) | old(X0) [cnf transformation 53]
156. quiet(lucy) [cnf transformation 25]
207. ~quiet(X0) | tall(X0) [subsumption resolution 102,103]
209. ~tall(X0) [subsumption resolution 111,113]
310. tall(lucy) [resolution 207,156]
311. $false [subsumption resolution 310,209]
% SZS output end Proof for 1550930913058953832249374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or not wise then fred is not patient or rich and vice versa.
If lucy is quiet or generous then someone is creative and vice versa.
Everyone who is either not happy or old is funny.
If alice is both kind and not patient then john is calm or quiet.
Everyone who is both not wise and quiet is either not strong or strong.
Everyone who is both creative and quiet is old or not strong and vice versa.
Everyone who is not creative or quiet is either not curious or not old and vice versa.
If mary is both not old and not brave then someone is not funny or happy.
Everyone who is both humble and not tall is either brave or patient.
If someone is creative then someone is strong.
Everyone who is not strong is kind and vice versa.
Everyone who is both not curious and kind is not old and vice versa.
Everyone who is either humble or not happy is calm or not kind.
Everyone who is both not old and not funny is patient and vice versa.
If someone is not happy then someone is not creative.
Everyone who is both strong and patient is not wise.
Alice is both not brave and wise.
Someone is calm or not brave.
Someone is either not funny or not patient.
Someone is tall or not happy.
Alice is not calm or kind.
John is either happy or not happy. | Alice is not old. | contradiction | ((?[X]:((~kind(X)|~wise(X))))<=>((~patient(fred)|rich(fred))))&
(((quiet(lucy)|generous(lucy)))<=>(?[X]:(creative(X))))&
(![X]:((~happy(X)<~>old(X))=>funny(X)))&
(((kind(alice)&~patient(alice)))=>((calm(john)|quiet(john))))&
(![X]:((~wise(X)&quiet(X))=>(~strong(X)<~>strong(X))))&
(![X]:((creative(X)&quiet(X))<=>(old(X)|~strong(X))))&
(![X]:((~creative(X)|quiet(X))<=>(~curious(X)<~>~old(X))))&
(((~old(mary)&~brave(mary)))=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((humble(X)&~tall(X))=>(brave(X)<~>patient(X))))&
((?[X]:(creative(X)))=>(?[X]:(strong(X))))&
(![X]:(~strong(X)<=>kind(X)))&
(![X]:((~curious(X)&kind(X))<=>~old(X)))&
(![X]:((humble(X)<~>~happy(X))=>(calm(X)|~kind(X))))&
(![X]:((~old(X)&~funny(X))<=>patient(X)))&
((?[X]:(~happy(X)))=>(?[X]:(~creative(X))))&
(![X]:((strong(X)&patient(X))=>~wise(X)))&
((~brave(alice)&wise(alice)))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:((~funny(X)<~>~patient(X))))&
(?[X]:((tall(X)|~happy(X))))&
((~calm(alice)|kind(alice)))&
((happy(john)<~>~happy(john))) | ~old(alice) | [
"p5",
"p6",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 672220026747049126958942
% SZS output start Proof for 672220026747049126958942
6. ! [X0] : ((quiet(X0) & creative(X0)) <=> (~strong(X0) | old(X0))) [input p5]
7. ! [X0] : ((quiet(X0) | ~creative(X0)) <=> (~curious(X0) <~> ~old(X0))) [input p6]
11. ! [X0] : (~strong(X0) <=> kind(X0)) [input p10]
12. ! [X0] : ((kind(X0) & ~curious(X0)) <=> ~old(X0)) [input p11]
23. ~old(alice) [input hypothesis]
53. ! [X0] : (((quiet(X0) & creative(X0)) | (strong(X0) & ~old(X0))) & ((~strong(X0) | old(X0)) | (~quiet(X0) | ~creative(X0)))) [nnf transformation 6]
54. ! [X0] : (((quiet(X0) & creative(X0)) | (strong(X0) & ~old(X0))) & (~strong(X0) | old(X0) | ~quiet(X0) | ~creative(X0))) [flattening 53]
55. ! [X0] : (((quiet(X0) | ~creative(X0)) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (~quiet(X0) & creative(X0)))) [nnf transformation 7]
56. ! [X0] : ((quiet(X0) | ~creative(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (~quiet(X0) & creative(X0)))) [flattening 55]
62. ! [X0] : ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))) [nnf transformation 11]
63. ! [X0] : (((kind(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | (~kind(X0) | curious(X0)))) [nnf transformation 12]
64. ! [X0] : (((kind(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | ~kind(X0) | curious(X0))) [flattening 63]
92. ~old(X0) | quiet(X0) [cnf transformation 54]
93. strong(X0) | quiet(X0) [cnf transformation 54]
95. ~old(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 56]
97. ~quiet(X0) | curious(X0) | old(X0) [cnf transformation 56]
103. ~strong(X0) | ~kind(X0) [cnf transformation 62]
105. ~curious(X0) | old(X0) [cnf transformation 64]
106. old(X0) | kind(X0) [cnf transformation 64]
122. ~old(alice) [cnf transformation 23]
186. ~curious(X0) | ~old(X0) [subsumption resolution 95,92]
209. ~curious(X0) [subsumption resolution 105,186]
243. ~kind(X1) | quiet(X1) [resolution 103,93]
247. kind(X0) | quiet(X0) [resolution 106,92]
255. quiet(X0) [subsumption resolution 247,243]
272. curious(X0) | old(X0) [resolution 97,255]
273. old(X0) [subsumption resolution 272,209]
274. $false [resolution 273,122]
% SZS output end Proof for 672220026747049126958942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is funny or not quiet then mary is both not generous and not wise.
Everyone who is not calm or not happy is creative or not patient.
If someone is not quiet then paul is kind.
Everyone who is both strong and wise is both kind and not strong and vice versa.
If john is not generous or not quiet then someone is not funny and vice versa.
Everyone who is either rich or not wise is patient or not creative and vice versa.
Everyone who is not curious is not quiet or tall and vice versa.
Everyone who is either not happy or creative is not happy or kind.
Everyone who is funny or creative is either not creative or patient.
If susan is both not creative and not old then someone is either kind or happy and vice versa.
Everyone who is both not funny and not tall is not generous and vice versa.
If someone is both rich and strong then someone is strong or kind and vice versa.
If mary is either not humble or not patient then someone is patient.
Everyone who is not quiet or wise is either patient or not quiet.
Everyone who is calm or not brave is not brave or curious.
If someone is both humble and not generous then fred is not happy.
Someone is quiet or not strong.
Fred is calm or not calm.
Someone is kind or calm.
Someone is either generous or rich.
Someone is calm.
Paul is not patient or happy.
Fred is either wise or humble. | John is quiet. | entailment | ((?[X]:((funny(X)|~quiet(X))))=>((~generous(mary)&~wise(mary))))&
(![X]:((~calm(X)|~happy(X))=>(creative(X)|~patient(X))))&
((?[X]:(~quiet(X)))=>(kind(paul)))&
(![X]:((strong(X)&wise(X))<=>(kind(X)&~strong(X))))&
(((~generous(john)|~quiet(john)))<=>(?[X]:(~funny(X))))&
(![X]:((rich(X)<~>~wise(X))<=>(patient(X)|~creative(X))))&
(![X]:(~curious(X)<=>(~quiet(X)|tall(X))))&
(![X]:((~happy(X)<~>creative(X))=>(~happy(X)|kind(X))))&
(![X]:((funny(X)|creative(X))=>(~creative(X)<~>patient(X))))&
(((~creative(susan)&~old(susan)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((~funny(X)&~tall(X))<=>~generous(X)))&
((?[X]:((rich(X)&strong(X))))<=>(?[X]:((strong(X)|kind(X)))))&
(((~humble(mary)<~>~patient(mary)))=>(?[X]:(patient(X))))&
(![X]:((~quiet(X)|wise(X))=>(patient(X)<~>~quiet(X))))&
(![X]:((calm(X)|~brave(X))=>(~brave(X)|curious(X))))&
((?[X]:((humble(X)&~generous(X))))=>(~happy(fred)))&
(?[X]:((quiet(X)|~strong(X))))&
((calm(fred)|~calm(fred)))&
(?[X]:((kind(X)|calm(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:(calm(X)))&
((~patient(paul)|happy(paul)))&
((wise(fred)<~>humble(fred))) | quiet(john) | [
"p2",
"p3",
"p5",
"p8",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 1370167974465401959199720
% SZS output start Proof for 1370167974465401959199720
3. ? [X0] : ~quiet(X0) => kind(paul) [input p2]
4. ! [X0] : ((wise(X0) & strong(X0)) <=> (~strong(X0) & kind(X0))) [input p3]
6. ! [X0] : ((rich(X0) <~> ~wise(X0)) <=> (~creative(X0) | patient(X0))) [input p5]
9. ! [X0] : ((creative(X0) | funny(X0)) => (~creative(X0) <~> patient(X0))) [input p8]
12. ? [X0] : (strong(X0) & rich(X0)) <=> ? [X0] : (kind(X0) | strong(X0)) [input p11]
24. ~quiet(john) [input hypothesis]
25. ? [X0] : (strong(X0) & rich(X0)) <=> ? [X1] : (kind(X1) | strong(X1)) [rectify 12]
30. kind(paul) | ! [X0] : quiet(X0) [ennf transformation 3]
34. ! [X0] : ((~creative(X0) <~> patient(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 9]
40. ! [X0] : (((wise(X0) & strong(X0)) | (strong(X0) | ~kind(X0))) & ((~strong(X0) & kind(X0)) | (~wise(X0) | ~strong(X0)))) [nnf transformation 4]
41. ! [X0] : (((wise(X0) & strong(X0)) | strong(X0) | ~kind(X0)) & ((~strong(X0) & kind(X0)) | ~wise(X0) | ~strong(X0))) [flattening 40]
47. ! [X0] : ((((wise(X0) | ~rich(X0)) & (~wise(X0) | rich(X0))) | (creative(X0) & ~patient(X0))) & ((~creative(X0) | patient(X0)) | ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))))) [nnf transformation 6]
48. ! [X0] : ((((wise(X0) | ~rich(X0)) & (~wise(X0) | rich(X0))) | (creative(X0) & ~patient(X0))) & (~creative(X0) | patient(X0) | ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))))) [flattening 47]
50. ! [X0] : (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | (~creative(X0) & ~funny(X0))) [nnf transformation 34]
58. (? [X0] : (strong(X0) & rich(X0)) | ! [X1] : (~kind(X1) & ~strong(X1))) & (? [X1] : (kind(X1) | strong(X1)) | ! [X0] : (~strong(X0) | ~rich(X0))) [nnf transformation 25]
59. (? [X0] : (strong(X0) & rich(X0)) | ! [X1] : (~kind(X1) & ~strong(X1))) & (? [X2] : (kind(X2) | strong(X2)) | ! [X3] : (~strong(X3) | ~rich(X3))) [rectify 58]
60. ? [X0] : (strong(X0) & rich(X0)) => (strong(sK2) & rich(sK2)) [choice axiom]
61. ? [X2] : (kind(X2) | strong(X2)) => (kind(sK3) | strong(sK3)) [choice axiom]
62. ((strong(sK2) & rich(sK2)) | ! [X1] : (~kind(X1) & ~strong(X1))) & ((kind(sK3) | strong(sK3)) | ! [X3] : (~strong(X3) | ~rich(X3))) [skolemisation 59,61,60]
83. kind(paul) | quiet(X0) [cnf transformation 30]
85. ~strong(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 41]
95. ~rich(X0) | wise(X0) | ~patient(X0) [cnf transformation 48]
96. ~rich(X0) | wise(X0) | creative(X0) [cnf transformation 48]
102. patient(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 50]
116. rich(sK2) | ~kind(X1) [cnf transformation 62]
118. strong(sK2) | ~kind(X1) [cnf transformation 62]
137. ~quiet(john) [cnf transformation 24]
139. ~creative(X0) | patient(X0) [duplicate literal removal 102]
141. ~strong(X0) | ~wise(X0) [duplicate literal removal 85]
144. 1 <=> ! [X0] : quiet(X0) [avatar definition]
145. quiet(X0) <- (1) [avatar component clause 144]
162. 5 <=> kind(paul) [avatar definition]
164. kind(paul) <- (5) [avatar component clause 162]
165. 1 | 5 [avatar split clause 83,162,144]
174. 8 <=> quiet(john) [avatar definition]
176. ~quiet(john) <- (~8) [avatar component clause 174]
213. 16 <=> ! [X1] : ~kind(X1) [avatar definition]
214. ~kind(X1) <- (16) [avatar component clause 213]
216. 17 <=> strong(sK2) [avatar definition]
218. strong(sK2) <- (17) [avatar component clause 216]
219. 16 | 17 [avatar split clause 118,216,213]
225. 19 <=> rich(sK2) [avatar definition]
227. rich(sK2) <- (19) [avatar component clause 225]
228. 16 | 19 [avatar split clause 116,225,213]
308. ~8 [avatar split clause 137,174]
310. $false <- (5, 16) [subsumption resolution 164,214]
311. ~5 | ~16 [avatar contradiction clause 310]
314. ~wise(sK2) <- (17) [resolution 141,218]
341. wise(sK2) | ~patient(sK2) <- (19) [resolution 95,227]
342. ~patient(sK2) <- (17, 19) [subsumption resolution 341,314]
343. wise(sK2) | creative(sK2) <- (19) [resolution 96,227]
344. creative(sK2) <- (17, 19) [subsumption resolution 343,314]
345. patient(sK2) <- (17, 19) [resolution 344,139]
346. $false <- (17, 19) [subsumption resolution 345,342]
347. ~17 | ~19 [avatar contradiction clause 346]
348. $false <- (1, ~8) [resolution 145,176]
349. ~1 | 8 [avatar contradiction clause 348]
350. $false [avatar sat refutation 165,219,228,308,311,347,349]
% SZS output end Proof for 1370167974465401959199720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both not kind and not calm then someone is not rich and vice versa.
Everyone who is either not wise or not creative is not calm and vice versa.
If someone is not rich or not happy then paul is both strong and rich and vice versa.
Everyone who is happy or not creative is both not wise and creative.
If someone is not tall then someone is not humble or kind and vice versa.
If john is kind or calm then paul is either not patient or curious.
Everyone who is not calm is either not strong or strong and vice versa.
Everyone who is happy or calm is either not kind or not calm and vice versa.
If someone is both not humble and not calm then someone is not humble and vice versa.
If john is either not wise or not rich then paul is either not happy or generous and vice versa.
If someone is not funny or strong then fred is both kind and funny and vice versa.
If mary is not rich or patient then someone is either humble or not strong.
Everyone who is not quiet is not generous or funny and vice versa.
If someone is either kind or not happy then someone is creative and vice versa.
Everyone who is either not calm or strong is both creative and calm.
Everyone who is either not patient or rich is not brave and vice versa.
Someone is not tall or strong.
Someone is curious or strong.
Someone is not rich or humble.
Someone is either not patient or not wise.
Someone is generous or not humble.
Someone is not tall. | Fred is not quiet. | entailment | ((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>~calm(X)))&
((?[X]:((~rich(X)|~happy(X))))<=>((strong(paul)&rich(paul))))&
(![X]:((happy(X)|~creative(X))=>(~wise(X)&creative(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~humble(X)|kind(X)))))&
(((kind(john)|calm(john)))=>((~patient(paul)<~>curious(paul))))&
(![X]:(~calm(X)<=>(~strong(X)<~>strong(X))))&
(![X]:((happy(X)|calm(X))<=>(~kind(X)<~>~calm(X))))&
((?[X]:((~humble(X)&~calm(X))))<=>(?[X]:(~humble(X))))&
(((~wise(john)<~>~rich(john)))<=>((~happy(paul)<~>generous(paul))))&
((?[X]:((~funny(X)|strong(X))))<=>((kind(fred)&funny(fred))))&
(((~rich(mary)|patient(mary)))=>(?[X]:((humble(X)<~>~strong(X)))))&
(![X]:(~quiet(X)<=>(~generous(X)|funny(X))))&
((?[X]:((kind(X)<~>~happy(X))))<=>(?[X]:(creative(X))))&
(![X]:((~calm(X)<~>strong(X))=>(creative(X)&calm(X))))&
(![X]:((~patient(X)<~>rich(X))<=>~brave(X)))&
(?[X]:((~tall(X)|strong(X))))&
(?[X]:((curious(X)|strong(X))))&
(?[X]:((~rich(X)|humble(X))))&
(?[X]:((~patient(X)<~>~wise(X))))&
(?[X]:((generous(X)|~humble(X))))&
(?[X]:(~tall(X))) | ~quiet(fred) | [
"p10",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 8562004935698484855971415
% SZS output start Proof for 8562004935698484855971415
11. ? [X0] : (strong(X0) | ~funny(X0)) <=> (funny(fred) & kind(fred)) [input p10]
13. ! [X0] : (~quiet(X0) <=> (funny(X0) | ~generous(X0))) [input p12]
23. quiet(fred) [input hypothesis]
28. ! [X0] : ((funny(X0) | ~generous(X0)) => ~quiet(X0)) [unused predicate definition removal 13]
32. ! [X0] : (~quiet(X0) | (~funny(X0) & generous(X0))) [ennf transformation 28]
60. (? [X0] : (strong(X0) | ~funny(X0)) | (~funny(fred) | ~kind(fred))) & ((funny(fred) & kind(fred)) | ! [X0] : (~strong(X0) & funny(X0))) [nnf transformation 11]
61. (? [X0] : (strong(X0) | ~funny(X0)) | ~funny(fred) | ~kind(fred)) & ((funny(fred) & kind(fred)) | ! [X0] : (~strong(X0) & funny(X0))) [flattening 60]
62. (? [X0] : (strong(X0) | ~funny(X0)) | ~funny(fred) | ~kind(fred)) & ((funny(fred) & kind(fred)) | ! [X1] : (~strong(X1) & funny(X1))) [rectify 61]
63. ? [X0] : (strong(X0) | ~funny(X0)) => (strong(sK7) | ~funny(sK7)) [choice axiom]
64. ((strong(sK7) | ~funny(sK7)) | ~funny(fred) | ~kind(fred)) & ((funny(fred) & kind(fred)) | ! [X1] : (~strong(X1) & funny(X1))) [skolemisation 62,63]
133. funny(fred) | funny(X1) [cnf transformation 64]
141. ~quiet(X0) | ~funny(X0) [cnf transformation 32]
157. quiet(fred) [cnf transformation 23]
296. 28 <=> funny(fred) [avatar definition]
298. ~funny(fred) <- (~28) [avatar component clause 296]
313. 32 <=> ! [X1] : funny(X1) [avatar definition]
314. funny(X1) <- (32) [avatar component clause 313]
315. 32 | 28 [avatar split clause 133,296,313]
370. ~funny(fred) [resolution 141,157]
373. ~28 [avatar split clause 370,296]
376. $false <- (~28, 32) [subsumption resolution 298,314]
377. 28 | ~32 [avatar contradiction clause 376]
378. $false [avatar sat refutation 315,373,377]
% SZS output end Proof for 8562004935698484855971415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and rich is calm or patient and vice versa.
If lucy is not old or strong then fred is not tall or creative and vice versa.
Everyone who is either calm or not creative is not old or generous.
Everyone who is brave or tall is patient and vice versa.
If mary is both not kind and kind then someone is both quiet and calm.
If susan is kind or calm then lucy is either not generous or generous.
If someone is both not funny and rich then alice is either not wise or not strong.
If alice is not kind or wise then lucy is both not old and generous.
If someone is either not funny or creative then susan is both not happy and not wise and vice versa.
If someone is not curious or not happy then someone is both not old and tall and vice versa.
If john is calm then someone is not tall.
Everyone who is creative is either not kind or brave.
If someone is quiet or not patient then susan is both not kind and not funny and vice versa.
If someone is both not creative and kind then john is either generous or not humble and vice versa.
If someone is either creative or not happy then alice is patient or not rich.
Mary is not creative.
Alice is either quiet or strong.
Someone is generous or strong.
Someone is quiet or not kind.
Mary is both not patient and strong.
John is not humble or not patient. | Alice is not happy. | contradiction | (![X]:((~patient(X)&rich(X))<=>(calm(X)|patient(X))))&
(((~old(lucy)|strong(lucy)))<=>((~tall(fred)|creative(fred))))&
(![X]:((calm(X)<~>~creative(X))=>(~old(X)|generous(X))))&
(![X]:((brave(X)|tall(X))<=>patient(X)))&
(((~kind(mary)&kind(mary)))=>(?[X]:((quiet(X)&calm(X)))))&
(((kind(susan)|calm(susan)))=>((~generous(lucy)<~>generous(lucy))))&
((?[X]:((~funny(X)&rich(X))))=>((~wise(alice)<~>~strong(alice))))&
(((~kind(alice)|wise(alice)))=>((~old(lucy)&generous(lucy))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~happy(susan)&~wise(susan))))&
((?[X]:((~curious(X)|~happy(X))))<=>(?[X]:((~old(X)&tall(X)))))&
((calm(john))=>(?[X]:(~tall(X))))&
(![X]:(creative(X)=>(~kind(X)<~>brave(X))))&
((?[X]:((quiet(X)|~patient(X))))<=>((~kind(susan)&~funny(susan))))&
((?[X]:((~creative(X)&kind(X))))<=>((generous(john)<~>~humble(john))))&
((?[X]:((creative(X)<~>~happy(X))))=>((patient(alice)|~rich(alice))))&
(~creative(mary))&
((quiet(alice)<~>strong(alice)))&
(?[X]:((generous(X)|strong(X))))&
(?[X]:((quiet(X)|~kind(X))))&
((~patient(mary)&strong(mary)))&
((~humble(john)|~patient(john))) | ~happy(alice) | [
"p0",
"p3",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 441231865892156373828496
% SZS output start Proof for 441231865892156373828496
1. ! [X0] : ((rich(X0) & ~patient(X0)) <=> (patient(X0) | calm(X0))) [input p0]
4. ! [X0] : ((tall(X0) | brave(X0)) <=> patient(X0)) [input p3]
10. ? [X0] : (~happy(X0) | ~curious(X0)) <=> ? [X0] : (tall(X0) & ~old(X0)) [input p9]
22. ~happy(alice) [input hypothesis]
23. ? [X0] : (~happy(X0) | ~curious(X0)) <=> ? [X1] : (tall(X1) & ~old(X1)) [rectify 10]
35. ! [X0] : (((rich(X0) & ~patient(X0)) | (~patient(X0) & ~calm(X0))) & ((patient(X0) | calm(X0)) | (~rich(X0) | patient(X0)))) [nnf transformation 1]
36. ! [X0] : (((rich(X0) & ~patient(X0)) | (~patient(X0) & ~calm(X0))) & (patient(X0) | calm(X0) | ~rich(X0) | patient(X0))) [flattening 35]
40. ! [X0] : (((tall(X0) | brave(X0)) | ~patient(X0)) & (patient(X0) | (~tall(X0) & ~brave(X0)))) [nnf transformation 4]
41. ! [X0] : ((tall(X0) | brave(X0) | ~patient(X0)) & (patient(X0) | (~tall(X0) & ~brave(X0)))) [flattening 40]
51. (? [X0] : (~happy(X0) | ~curious(X0)) | ! [X1] : (~tall(X1) | old(X1))) & (? [X1] : (tall(X1) & ~old(X1)) | ! [X0] : (happy(X0) & curious(X0))) [nnf transformation 23]
52. (? [X0] : (~happy(X0) | ~curious(X0)) | ! [X1] : (~tall(X1) | old(X1))) & (? [X2] : (tall(X2) & ~old(X2)) | ! [X3] : (happy(X3) & curious(X3))) [rectify 51]
53. ? [X0] : (~happy(X0) | ~curious(X0)) => (~happy(sK2) | ~curious(sK2)) [choice axiom]
54. ? [X2] : (tall(X2) & ~old(X2)) => (tall(sK3) & ~old(sK3)) [choice axiom]
55. ((~happy(sK2) | ~curious(sK2)) | ! [X1] : (~tall(X1) | old(X1))) & ((tall(sK3) & ~old(sK3)) | ! [X3] : (happy(X3) & curious(X3))) [skolemisation 52,54,53]
76. ~patient(X0) | ~patient(X0) [cnf transformation 36]
86. patient(X0) | ~tall(X0) [cnf transformation 41]
109. tall(sK3) | happy(X3) [cnf transformation 55]
135. ~happy(alice) [cnf transformation 22]
137. ~patient(X0) [duplicate literal removal 76]
159. ~tall(X0) [subsumption resolution 86,137]
214. happy(X3) [subsumption resolution 109,159]
280. $false [subsumption resolution 135,214]
% SZS output end Proof for 441231865892156373828496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or funny is either tall or not strong.
Everyone who is strong or not kind is both happy and brave and vice versa.
If someone is either humble or tall then lucy is brave.
If someone is either not patient or generous then someone is both brave and calm.
Everyone who is either generous or calm is either rich or kind and vice versa.
Everyone who is not calm or not tall is either not humble or not brave.
If someone is either not happy or old then someone is not wise.
If alice is both not curious and not calm then someone is either rich or strong.
Everyone who is not happy is tall and vice versa.
Everyone who is creative or not calm is not old or not strong and vice versa.
If john is not creative or not humble then someone is strong and vice versa.
Everyone who is not happy or calm is both kind and old.
Everyone who is calm is both rich and not brave.
Everyone who is rich is both not creative and not strong.
If fred is patient then susan is not quiet or calm.
If lucy is kind then someone is not kind or rich and vice versa.
Alice is tall or happy.
Paul is not strong or not old.
Lucy is both not calm and wise.
John is either old or not creative.
Someone is either generous or not calm.
Alice is creative or generous. | Fred is not calm. | entailment | (![X]:((humble(X)|funny(X))=>(tall(X)<~>~strong(X))))&
(![X]:((strong(X)|~kind(X))<=>(happy(X)&brave(X))))&
((?[X]:((humble(X)<~>tall(X))))=>(brave(lucy)))&
((?[X]:((~patient(X)<~>generous(X))))=>(?[X]:((brave(X)&calm(X)))))&
(![X]:((generous(X)<~>calm(X))<=>(rich(X)<~>kind(X))))&
(![X]:((~calm(X)|~tall(X))=>(~humble(X)<~>~brave(X))))&
((?[X]:((~happy(X)<~>old(X))))=>(?[X]:(~wise(X))))&
(((~curious(alice)&~calm(alice)))=>(?[X]:((rich(X)<~>strong(X)))))&
(![X]:(~happy(X)<=>tall(X)))&
(![X]:((creative(X)|~calm(X))<=>(~old(X)|~strong(X))))&
(((~creative(john)|~humble(john)))<=>(?[X]:(strong(X))))&
(![X]:((~happy(X)|calm(X))=>(kind(X)&old(X))))&
(![X]:(calm(X)=>(rich(X)&~brave(X))))&
(![X]:(rich(X)=>(~creative(X)&~strong(X))))&
((patient(fred))=>((~quiet(susan)|calm(susan))))&
((kind(lucy))<=>(?[X]:((~kind(X)|rich(X)))))&
((tall(alice)|happy(alice)))&
((~strong(paul)|~old(paul)))&
((~calm(lucy)&wise(lucy)))&
((old(john)<~>~creative(john)))&
(?[X]:((generous(X)<~>~calm(X))))&
((creative(alice)|generous(alice))) | ~calm(fred) | [
"p9",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 8038872912910900852221112
% SZS output start Proof for 8038872912910900852221112
10. ! [X0] : ((~calm(X0) | creative(X0)) <=> (~strong(X0) | ~old(X0))) [input p9]
13. ! [X0] : (calm(X0) => (~brave(X0) & rich(X0))) [input p12]
14. ! [X0] : (rich(X0) => (~strong(X0) & ~creative(X0))) [input p13]
23. calm(fred) [input hypothesis]
35. ! [X0] : ((~brave(X0) & rich(X0)) | ~calm(X0)) [ennf transformation 13]
36. ! [X0] : ((~strong(X0) & ~creative(X0)) | ~rich(X0)) [ennf transformation 14]
52. ! [X0] : (((~calm(X0) | creative(X0)) | (strong(X0) & old(X0))) & ((~strong(X0) | ~old(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 10]
53. ! [X0] : ((~calm(X0) | creative(X0) | (strong(X0) & old(X0))) & (~strong(X0) | ~old(X0) | (calm(X0) & ~creative(X0)))) [flattening 52]
99. ~calm(X0) | creative(X0) | strong(X0) [cnf transformation 53]
107. ~calm(X0) | rich(X0) [cnf transformation 35]
109. ~creative(X0) | ~rich(X0) [cnf transformation 36]
110. ~rich(X0) | ~strong(X0) [cnf transformation 36]
123. calm(fred) [cnf transformation 23]
247. rich(fred) [resolution 107,123]
251. ~strong(fred) [resolution 110,247]
328. creative(fred) | strong(fred) [resolution 99,123]
330. creative(fred) [subsumption resolution 328,251]
333. ~rich(fred) [resolution 330,109]
334. $false [subsumption resolution 333,247]
% SZS output end Proof for 8038872912910900852221112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is not quiet or happy and vice versa.
Everyone who is not tall or not happy is both rich and quiet.
Everyone who is either not curious or kind is humble or patient and vice versa.
Everyone who is not brave is generous or humble and vice versa.
If someone is not happy then someone is not tall and vice versa.
Everyone who is not calm or not generous is either not rich or humble and vice versa.
If lucy is either not strong or humble then lucy is either happy or creative.
If fred is not tall then someone is patient or not calm.
If someone is not generous then someone is both patient and rich and vice versa.
Everyone who is either rich or humble is not happy and vice versa.
If mary is patient then someone is either not patient or funny and vice versa.
If someone is funny or creative then john is either not curious or brave and vice versa.
Everyone who is kind or not humble is not brave or not patient.
Everyone who is not brave is not quiet.
Everyone who is both not calm and not patient is either not wise or not generous.
Everyone who is both not patient and not old is either generous or rich and vice versa.
Someone is either brave or not calm.
Susan is either strong or tall.
John is either not quiet or not happy.
Someone is not strong.
Alice is not wise or old. | Susan is not humble. | entailment | (![X]:(~humble(X)<=>(~quiet(X)|happy(X))))&
(![X]:((~tall(X)|~happy(X))=>(rich(X)&quiet(X))))&
(![X]:((~curious(X)<~>kind(X))<=>(humble(X)|patient(X))))&
(![X]:(~brave(X)<=>(generous(X)|humble(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~rich(X)<~>humble(X))))&
(((~strong(lucy)<~>humble(lucy)))=>((happy(lucy)<~>creative(lucy))))&
((~tall(fred))=>(?[X]:((patient(X)|~calm(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((patient(X)&rich(X)))))&
(![X]:((rich(X)<~>humble(X))<=>~happy(X)))&
((patient(mary))<=>(?[X]:((~patient(X)<~>funny(X)))))&
((?[X]:((funny(X)|creative(X))))<=>((~curious(john)<~>brave(john))))&
(![X]:((kind(X)|~humble(X))=>(~brave(X)|~patient(X))))&
(![X]:(~brave(X)=>~quiet(X)))&
(![X]:((~calm(X)&~patient(X))=>(~wise(X)<~>~generous(X))))&
(![X]:((~patient(X)&~old(X))<=>(generous(X)<~>rich(X))))&
(?[X]:((brave(X)<~>~calm(X))))&
((strong(susan)<~>tall(susan)))&
((~quiet(john)<~>~happy(john)))&
(?[X]:(~strong(X)))&
((~wise(alice)|old(alice))) | ~humble(susan) | [
"p0",
"p1",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 750005515046460823781058
% SZS output start Proof for 750005515046460823781058
1. ! [X0] : (~humble(X0) <=> (happy(X0) | ~quiet(X0))) [input p0]
2. ! [X0] : ((~happy(X0) | ~tall(X0)) => (quiet(X0) & rich(X0))) [input p1]
10. ! [X0] : ((rich(X0) <~> humble(X0)) <=> ~happy(X0)) [input p9]
22. humble(susan) [input hypothesis]
25. ! [X0] : ((quiet(X0) & rich(X0)) | (happy(X0) & tall(X0))) [ennf transformation 2]
33. ! [X0] : ((~humble(X0) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | humble(X0))) [nnf transformation 1]
34. ! [X0] : ((~humble(X0) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | humble(X0))) [flattening 33]
54. ! [X0] : ((((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | happy(X0)) & (~happy(X0) | ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0))))) [nnf transformation 10]
75. ~humble(X0) | ~happy(X0) [cnf transformation 34]
77. rich(X0) | happy(X0) [cnf transformation 25]
108. ~humble(X0) | ~rich(X0) | happy(X0) [cnf transformation 54]
138. humble(susan) [cnf transformation 22]
210. ~humble(X0) | happy(X0) [subsumption resolution 108,77]
211. ~humble(X0) [subsumption resolution 210,75]
302. $false [subsumption resolution 138,211]
% SZS output end Proof for 750005515046460823781058
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and strong is both not calm and not funny and vice versa.
Everyone who is not rich is either kind or not wise and vice versa.
If someone is generous or not quiet then someone is both happy and old.
Everyone who is not tall is not funny and vice versa.
Everyone who is both kind and old is creative or wise and vice versa.
Everyone who is humble or not brave is not patient or not wise and vice versa.
If paul is not patient or creative then alice is not tall or not curious and vice versa.
Everyone who is happy or creative is either wise or not tall.
If someone is brave or wise then fred is both not kind and strong and vice versa.
If alice is both strong and not rich then fred is strong.
Everyone who is both not strong and not calm is tall.
Everyone who is either not wise or not old is not humble and vice versa.
Everyone who is both curious and brave is either humble or rich.
Everyone who is either not curious or tall is both not creative and patient and vice versa.
Everyone who is either not kind or old is brave.
Everyone who is not strong is both not tall and quiet.
Someone is patient or old.
Alice is not generous or quiet.
Someone is either not funny or not happy.
Someone is not rich.
Someone is rich.
Someone is kind or not kind.
Paul is not tall.
Someone is kind or not patient. | Alice is not kind. | neutral | (![X]:((~generous(X)&strong(X))<=>(~calm(X)&~funny(X))))&
(![X]:(~rich(X)<=>(kind(X)<~>~wise(X))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((happy(X)&old(X)))))&
(![X]:(~tall(X)<=>~funny(X)))&
(![X]:((kind(X)&old(X))<=>(creative(X)|wise(X))))&
(![X]:((humble(X)|~brave(X))<=>(~patient(X)|~wise(X))))&
(((~patient(paul)|creative(paul)))<=>((~tall(alice)|~curious(alice))))&
(![X]:((happy(X)|creative(X))=>(wise(X)<~>~tall(X))))&
((?[X]:((brave(X)|wise(X))))<=>((~kind(fred)&strong(fred))))&
(((strong(alice)&~rich(alice)))=>(strong(fred)))&
(![X]:((~strong(X)&~calm(X))=>tall(X)))&
(![X]:((~wise(X)<~>~old(X))<=>~humble(X)))&
(![X]:((curious(X)&brave(X))=>(humble(X)<~>rich(X))))&
(![X]:((~curious(X)<~>tall(X))<=>(~creative(X)&patient(X))))&
(![X]:((~kind(X)<~>old(X))=>brave(X)))&
(![X]:(~strong(X)=>(~tall(X)&quiet(X))))&
(?[X]:((patient(X)|old(X))))&
((~generous(alice)|quiet(alice)))&
(?[X]:((~funny(X)<~>~happy(X))))&
(?[X]:(~rich(X)))&
(?[X]:(rich(X)))&
(?[X]:((kind(X)|~kind(X))))&
(~tall(paul))&
(?[X]:((kind(X)|~patient(X)))) | ~kind(alice) | []
| null | 0 |
Everyone who is either not curious or not patient is generous or not curious and vice versa. If someone is either calm or not brave then paul is both not curious and not patient. If someone is not quiet then mary is not curious. If paul is either not curious or humble then fred is patient or generous and vice versa. If someone is not patient then lucy is tall and vice versa. If someone is either tall or wise then susan is both not funny and not patient. If susan is not wise or not happy then susan is tall. Everyone who is either not kind or curious is both curious and not calm. Everyone who is both calm and happy is either not humble or old and vice versa. If someone is either not rich or calm then someone is both generous and not wise and vice versa. Everyone who is both creative and not wise is either tall or funny and vice versa. Everyone who is both funny and not creative is not brave or not humble. Everyone who is either not kind or not funny is either not quiet or not rich and vice versa. If paul is both not patient and funny then susan is curious. Everyone who is not old is not humble or not kind. If someone is old then fred is either old or strong. Someone is humble. Fred is not kind. Alice is tall or not creative. Alice is old. Alice is not happy. John is rich or patient. Susan is both funny and creative. Someone is either wise or calm. | Alice is humble. | contradiction | (![X]:((~curious(X)<~>~patient(X))<=>(generous(X)|~curious(X))))&
((?[X]:((calm(X)<~>~brave(X))))=>((~curious(paul)&~patient(paul))))&
((?[X]:(~quiet(X)))=>(~curious(mary)))&
(((~curious(paul)<~>humble(paul)))<=>((patient(fred)|generous(fred))))&
((?[X]:(~patient(X)))<=>(tall(lucy)))&
((?[X]:((tall(X)<~>wise(X))))=>((~funny(susan)&~patient(susan))))&
(((~wise(susan)|~happy(susan)))=>(tall(susan)))&
(![X]:((~kind(X)<~>curious(X))=>(curious(X)&~calm(X))))&
(![X]:((calm(X)&happy(X))<=>(~humble(X)<~>old(X))))&
((?[X]:((~rich(X)<~>calm(X))))<=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((creative(X)&~wise(X))<=>(tall(X)<~>funny(X))))&
(![X]:((funny(X)&~creative(X))=>(~brave(X)|~humble(X))))&
(![X]:((~kind(X)<~>~funny(X))<=>(~quiet(X)<~>~rich(X))))&
(((~patient(paul)&funny(paul)))=>(curious(susan)))&
(![X]:(~old(X)=>(~humble(X)|~kind(X))))&
((?[X]:(old(X)))=>((old(fred)<~>strong(fred))))&
(?[X]:(humble(X)))&
(~kind(fred))&
((tall(alice)|~creative(alice)))&
(old(alice))&
(~happy(alice))&
((rich(john)|patient(john)))&
((funny(susan)&creative(susan)))&
(?[X]:((wise(X)<~>calm(X)))) | humble(alice) | [
"p8",
"p19",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 3333790478592371044390498
% SZS output start Proof for 3333790478592371044390498
9. ! [X0] : ((happy(X0) & calm(X0)) <=> (~humble(X0) <~> old(X0))) [input p8]
20. old(alice) [input p19]
21. ~happy(alice) [input p20]
25. humble(alice) [input hypothesis]
50. ! [X0] : (((happy(X0) & calm(X0)) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0)))) & (((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~happy(X0) | ~calm(X0)))) [nnf transformation 9]
51. ! [X0] : (((happy(X0) & calm(X0)) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0)))) & (((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | ~happy(X0) | ~calm(X0))) [flattening 50]
100. ~old(X0) | ~humble(X0) | happy(X0) [cnf transformation 51]
129. old(alice) [cnf transformation 20]
130. ~happy(alice) [cnf transformation 21]
136. humble(alice) [cnf transformation 25]
352. ~humble(alice) | happy(alice) [resolution 100,129]
357. happy(alice) [subsumption resolution 352,136]
358. $false [subsumption resolution 357,130]
% SZS output end Proof for 3333790478592371044390498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not old is both rich and not quiet. Everyone who is strong is not patient and vice versa. Everyone who is either patient or rich is not strong or not happy. Everyone who is either not kind or kind is generous or not curious and vice versa. Everyone who is either not creative or not quiet is not funny. If john is quiet then someone is humble. Everyone who is either strong or curious is not humble. If someone is either calm or quiet then lucy is not patient. Everyone who is either funny or not kind is either not creative or not quiet and vice versa. Everyone who is either not tall or not funny is both old and brave and vice versa. If someone is either not humble or not generous then someone is not humble or tall. Everyone who is both generous and not quiet is both not calm and quiet. Everyone who is both strong and brave is either not calm or not creative. If someone is not wise then someone is not old or kind. If alice is either wise or not funny then someone is both not generous and strong and vice versa. Everyone who is calm or not rich is either not happy or creative and vice versa. Someone is kind or strong. Susan is happy or not wise. Someone is both not humble and not curious. Someone is rich or not kind. Someone is either not curious or not brave. Someone is brave or not brave. Someone is not generous or humble. Someone is not creative. | Lucy is happy. | neutral | (![X]:((curious(X)<~>~old(X))=>(rich(X)&~quiet(X))))&
(![X]:(strong(X)<=>~patient(X)))&
(![X]:((patient(X)<~>rich(X))=>(~strong(X)|~happy(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(generous(X)|~curious(X))))&
(![X]:((~creative(X)<~>~quiet(X))=>~funny(X)))&
((quiet(john))=>(?[X]:(humble(X))))&
(![X]:((strong(X)<~>curious(X))=>~humble(X)))&
((?[X]:((calm(X)<~>quiet(X))))=>(~patient(lucy)))&
(![X]:((funny(X)<~>~kind(X))<=>(~creative(X)<~>~quiet(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>(old(X)&brave(X))))&
((?[X]:((~humble(X)<~>~generous(X))))=>(?[X]:((~humble(X)|tall(X)))))&
(![X]:((generous(X)&~quiet(X))=>(~calm(X)&quiet(X))))&
(![X]:((strong(X)&brave(X))=>(~calm(X)<~>~creative(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~old(X)|kind(X)))))&
(((wise(alice)<~>~funny(alice)))<=>(?[X]:((~generous(X)&strong(X)))))&
(![X]:((calm(X)|~rich(X))<=>(~happy(X)<~>creative(X))))&
(?[X]:((kind(X)|strong(X))))&
((happy(susan)|~wise(susan)))&
(?[X]:((~humble(X)&~curious(X))))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:((~generous(X)|humble(X))))&
(?[X]:(~creative(X))) | happy(lucy) | []
| null | 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 not kind. | contradiction | (![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 7337444085670195911292318
% SZS output start Proof for 7337444085670195911292318
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 7337444085670195911292318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and tall is kind or strong. Everyone who is both tall and brave is both calm and not rich. Everyone who is both generous and curious is not brave or patient and vice versa. If someone is not old then lucy is not quiet or not calm and vice versa. Everyone who is either humble or not humble is not calm. If someone is not creative or wise then someone is either not calm or not wise. If someone is either funny or brave then someone is not generous and vice versa. Everyone who is both generous and not calm is not quiet or creative. If someone is both quiet and strong then mary is calm or rich. Everyone who is either brave or strong is kind or not brave. If alice is both not quiet and not creative then fred is either not tall or not patient and vice versa. Everyone who is creative is both not generous and not strong and vice versa. If mary is old then mary is generous or not brave and vice versa. If john is funny then mary is both not rich and not happy and vice versa. Everyone who is both not wise and old is not rich and vice versa. If fred is either not quiet or brave then susan is old or not generous and vice versa. Someone is strong or generous. Someone is quiet. Someone is humble or strong. Someone is either not humble or not generous. Mary is either not kind or not rich. Someone is not curious or not quiet. | Fred is quiet. | neutral | (![X]:((~calm(X)&tall(X))=>(kind(X)|strong(X))))&
(![X]:((tall(X)&brave(X))=>(calm(X)&~rich(X))))&
(![X]:((generous(X)&curious(X))<=>(~brave(X)|patient(X))))&
((?[X]:(~old(X)))<=>((~quiet(lucy)|~calm(lucy))))&
(![X]:((humble(X)<~>~humble(X))=>~calm(X)))&
((?[X]:((~creative(X)|wise(X))))=>(?[X]:((~calm(X)<~>~wise(X)))))&
((?[X]:((funny(X)<~>brave(X))))<=>(?[X]:(~generous(X))))&
(![X]:((generous(X)&~calm(X))=>(~quiet(X)|creative(X))))&
((?[X]:((quiet(X)&strong(X))))=>((calm(mary)|rich(mary))))&
(![X]:((brave(X)<~>strong(X))=>(kind(X)|~brave(X))))&
(((~quiet(alice)&~creative(alice)))<=>((~tall(fred)<~>~patient(fred))))&
(![X]:(creative(X)<=>(~generous(X)&~strong(X))))&
((old(mary))<=>((generous(mary)|~brave(mary))))&
((funny(john))<=>((~rich(mary)&~happy(mary))))&
(![X]:((~wise(X)&old(X))<=>~rich(X)))&
(((~quiet(fred)<~>brave(fred)))<=>((old(susan)|~generous(susan))))&
(?[X]:((strong(X)|generous(X))))&
(?[X]:(quiet(X)))&
(?[X]:((humble(X)|strong(X))))&
(?[X]:((~humble(X)<~>~generous(X))))&
((~kind(mary)<~>~rich(mary)))&
(?[X]:((~curious(X)|~quiet(X)))) | quiet(fred) | []
| null | 0 |
Everyone who is happy is either brave or calm.
If john is curious or strong then susan is not humble and vice versa.
If alice is either humble or wise then someone is not funny or curious.
Everyone who is not patient or strong is either not strong or not patient and vice versa.
If someone is either not tall or not rich then lucy is either not rich or generous.
Everyone who is either calm or wise is brave.
Everyone who is either creative or not old is not quiet.
Everyone who is both calm and not old is either not wise or tall and vice versa.
If someone is not humble then someone is both not wise and not quiet and vice versa.
Everyone who is not wise or calm is not tall.
Everyone who is not rich is both quiet and humble and vice versa.
Everyone who is either strong or not brave is not curious.
If someone is not tall then someone is not curious and vice versa.
If alice is old or quiet then paul is either not curious or not calm and vice versa.
If someone is not humble or not curious then mary is not wise or tall and vice versa.
Everyone who is either not rich or not humble is wise or rich and vice versa.
Lucy is not generous.
Someone is rich or calm.
Someone is not creative.
Someone is not curious or creative.
Susan is either not generous or old.
Lucy is not creative.
Someone is either not happy or rich.
Someone is not patient. | Lucy is wise. | entailment | (![X]:(happy(X)=>(brave(X)<~>calm(X))))&
(((curious(john)|strong(john)))<=>(~humble(susan)))&
(((humble(alice)<~>wise(alice)))=>(?[X]:((~funny(X)|curious(X)))))&
(![X]:((~patient(X)|strong(X))<=>(~strong(X)<~>~patient(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>((~rich(lucy)<~>generous(lucy))))&
(![X]:((calm(X)<~>wise(X))=>brave(X)))&
(![X]:((creative(X)<~>~old(X))=>~quiet(X)))&
(![X]:((calm(X)&~old(X))<=>(~wise(X)<~>tall(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:((~wise(X)|calm(X))=>~tall(X)))&
(![X]:(~rich(X)<=>(quiet(X)&humble(X))))&
(![X]:((strong(X)<~>~brave(X))=>~curious(X)))&
((?[X]:(~tall(X)))<=>(?[X]:(~curious(X))))&
(((old(alice)|quiet(alice)))<=>((~curious(paul)<~>~calm(paul))))&
((?[X]:((~humble(X)|~curious(X))))<=>((~wise(mary)|tall(mary))))&
(![X]:((~rich(X)<~>~humble(X))<=>(wise(X)|rich(X))))&
(~generous(lucy))&
(?[X]:((rich(X)|calm(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~curious(X)|creative(X))))&
((~generous(susan)<~>old(susan)))&
(~creative(lucy))&
(?[X]:((~happy(X)<~>rich(X))))&
(?[X]:(~patient(X))) | wise(lucy) | [
"p4",
"p9",
"p10",
"p15",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 5931857027511570817908301
% SZS output start Proof for 5931857027511570817908301
5. ? [X0] : (~tall(X0) <~> ~rich(X0)) => (~rich(lucy) <~> generous(lucy)) [input p4]
10. ! [X0] : ((calm(X0) | ~wise(X0)) => ~tall(X0)) [input p9]
11. ! [X0] : (~rich(X0) <=> (humble(X0) & quiet(X0))) [input p10]
16. ! [X0] : ((~rich(X0) <~> ~humble(X0)) <=> (rich(X0) | wise(X0))) [input p15]
17. ~generous(lucy) [input p16]
25. ~wise(lucy) [input hypothesis]
30. (~rich(lucy) <~> generous(lucy)) | ! [X0] : (~tall(X0) <=> ~rich(X0)) [ennf transformation 5]
33. ! [X0] : (~tall(X0) | (~calm(X0) & wise(X0))) [ennf transformation 10]
40. ((~generous(lucy) | rich(lucy)) & (generous(lucy) | ~rich(lucy))) | ! [X0] : ((~tall(X0) | rich(X0)) & (~rich(X0) | tall(X0))) [nnf transformation 30]
50. ! [X0] : ((~rich(X0) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | rich(X0))) [nnf transformation 11]
51. ! [X0] : ((~rich(X0) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | rich(X0))) [flattening 50]
65. ! [X0] : ((((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | (~rich(X0) & ~wise(X0))) & ((rich(X0) | wise(X0)) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))))) [nnf transformation 16]
66. ! [X0] : ((((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | (~rich(X0) & ~wise(X0))) & (rich(X0) | wise(X0) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))))) [flattening 65]
90. generous(lucy) | ~rich(lucy) | ~rich(X0) | tall(X0) [cnf transformation 40]
107. ~tall(X0) | wise(X0) [cnf transformation 33]
110. rich(X0) | humble(X0) [cnf transformation 51]
126. rich(X0) | wise(X0) | ~humble(X0) | rich(X0) [cnf transformation 66]
129. ~humble(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 66]
132. ~generous(lucy) [cnf transformation 17]
142. ~wise(lucy) [cnf transformation 25]
143. rich(X0) | wise(X0) | ~humble(X0) [duplicate literal removal 126]
144. ~rich(X0) | ~humble(X0) [duplicate literal removal 129]
169. 5 <=> rich(lucy) [avatar definition]
170. ~rich(lucy) <- (~5) [avatar component clause 169]
171. rich(lucy) <- (5) [avatar component clause 169]
173. 6 <=> generous(lucy) [avatar definition]
178. 7 <=> ! [X0] : (~rich(X0) | tall(X0)) [avatar definition]
179. ~rich(X0) | tall(X0) <- (7) [avatar component clause 178]
182. 7 | ~5 | 6 [avatar split clause 90,173,169,178]
263. ~humble(X0) | wise(X0) [subsumption resolution 143,144]
264. ~6 [avatar split clause 132,173]
305. humble(lucy) <- (~5) [resolution 110,170]
312. wise(lucy) <- (~5) [resolution 263,305]
314. $false <- (~5) [subsumption resolution 312,142]
315. 5 [avatar contradiction clause 314]
319. tall(lucy) <- (5, 7) [resolution 179,171]
324. wise(lucy) <- (5, 7) [resolution 319,107]
325. $false <- (5, 7) [subsumption resolution 324,142]
326. ~5 | ~7 [avatar contradiction clause 325]
327. $false [avatar sat refutation 182,264,315,326]
% SZS output end Proof for 5931857027511570817908301
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not calm is either not tall or not happy and vice versa. Everyone who is not kind or not funny is either wise or not funny and vice versa. Everyone who is either quiet or not kind is quiet or kind. If alice is not patient then mary is either creative or not brave. Everyone who is both tall and strong is both brave and generous and vice versa. Everyone who is funny or not wise is both tall and rich and vice versa. Everyone who is happy or not patient is patient. Everyone who is tall is both strong and humble and vice versa. If someone is either happy or brave then someone is not patient and vice versa. If someone is not kind then someone is brave or not creative. If lucy is brave or old then someone is either not strong or patient and vice versa. If alice is both not brave and humble then alice is either quiet or calm. If someone is either happy or not creative then someone is either not humble or patient. If paul is curious then susan is either not humble or old and vice versa. Everyone who is both rich and not creative is either not happy or curious. Everyone who is rich is not curious or creative. Someone is not rich or calm. Lucy is funny. Someone is either not old or brave. Alice is wise. Mary is not old. | Lucy is not rich. | contradiction | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((quiet(X)<~>~kind(X))=>(quiet(X)|kind(X))))&
((~patient(alice))=>((creative(mary)<~>~brave(mary))))&
(![X]:((tall(X)&strong(X))<=>(brave(X)&generous(X))))&
(![X]:((funny(X)|~wise(X))<=>(tall(X)&rich(X))))&
(![X]:((happy(X)|~patient(X))=>patient(X)))&
(![X]:(tall(X)<=>(strong(X)&humble(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)|~creative(X)))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~brave(alice)&humble(alice)))=>((quiet(alice)<~>calm(alice))))&
((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
((curious(paul))<=>((~humble(susan)<~>old(susan))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)<~>curious(X))))&
(![X]:(rich(X)=>(~curious(X)|creative(X))))&
(?[X]:((~rich(X)|calm(X))))&
(funny(lucy))&
(?[X]:((~old(X)<~>brave(X))))&
(wise(alice))&
(~old(mary)) | ~rich(lucy) | [
"p5",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 2171788761762728375236050
% SZS output start Proof for 2171788761762728375236050
6. ! [X0] : ((~wise(X0) | funny(X0)) <=> (rich(X0) & tall(X0))) [input p5]
18. funny(lucy) [input p17]
22. ~rich(lucy) [input hypothesis]
46. ! [X0] : (((~wise(X0) | funny(X0)) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [nnf transformation 6]
47. ! [X0] : ((~wise(X0) | funny(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [flattening 46]
97. ~funny(X0) | rich(X0) [cnf transformation 47]
130. funny(lucy) [cnf transformation 18]
135. ~rich(lucy) [cnf transformation 22]
257. rich(lucy) [resolution 97,130]
258. $false [subsumption resolution 257,135]
% SZS output end Proof for 2171788761762728375236050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not rich and funny then mary is either funny or not generous and vice versa.
Everyone who is tall is both not happy and creative.
Everyone who is both kind and not calm is wise or not patient and vice versa.
If susan is both not tall and happy then someone is not calm or generous and vice versa.
Everyone who is not quiet or brave is creative and vice versa.
Everyone who is both not funny and curious is calm.
Everyone who is not quiet or tall is not calm or generous.
Everyone who is either tall or curious is either not curious or humble and vice versa.
Everyone who is both not creative and not old is both not wise and creative and vice versa.
Everyone who is either generous or not curious is funny or not brave.
Everyone who is either not tall or not patient is both curious and not tall and vice versa.
If john is not rich or not calm then paul is patient or creative.
Everyone who is both curious and not old is both not old and not generous and vice versa.
Everyone who is quiet is either not rich or generous and vice versa.
Everyone who is not rich is not wise or calm.
Everyone who is both not creative and calm is not calm.
Someone is either strong or not quiet.
Susan is both not quiet and kind.
John is patient.
Someone is both not rich and old.
John is either kind or creative.
Someone is humble.
Susan is either funny or not wise.
Someone is both humble and patient. | Mary is not generous. | neutral | (((~rich(mary)&funny(mary)))<=>((funny(mary)<~>~generous(mary))))&
(![X]:(tall(X)=>(~happy(X)&creative(X))))&
(![X]:((kind(X)&~calm(X))<=>(wise(X)|~patient(X))))&
(((~tall(susan)&happy(susan)))<=>(?[X]:((~calm(X)|generous(X)))))&
(![X]:((~quiet(X)|brave(X))<=>creative(X)))&
(![X]:((~funny(X)&curious(X))=>calm(X)))&
(![X]:((~quiet(X)|tall(X))=>(~calm(X)|generous(X))))&
(![X]:((tall(X)<~>curious(X))<=>(~curious(X)<~>humble(X))))&
(![X]:((~creative(X)&~old(X))<=>(~wise(X)&creative(X))))&
(![X]:((generous(X)<~>~curious(X))=>(funny(X)|~brave(X))))&
(![X]:((~tall(X)<~>~patient(X))<=>(curious(X)&~tall(X))))&
(((~rich(john)|~calm(john)))=>((patient(paul)|creative(paul))))&
(![X]:((curious(X)&~old(X))<=>(~old(X)&~generous(X))))&
(![X]:(quiet(X)<=>(~rich(X)<~>generous(X))))&
(![X]:(~rich(X)=>(~wise(X)|calm(X))))&
(![X]:((~creative(X)&calm(X))=>~calm(X)))&
(?[X]:((strong(X)<~>~quiet(X))))&
((~quiet(susan)&kind(susan)))&
(patient(john))&
(?[X]:((~rich(X)&old(X))))&
((kind(john)<~>creative(john)))&
(?[X]:(humble(X)))&
((funny(susan)<~>~wise(susan)))&
(?[X]:((humble(X)&patient(X)))) | ~generous(mary) | []
| null | 0 |
Everyone who is happy or generous is curious or strong and vice versa.
If someone is strong then someone is both quiet and not generous and vice versa.
If someone is rich or not quiet then lucy is not generous and vice versa.
Everyone who is either not rich or not kind is both not tall and not quiet.
If someone is happy or funny then someone is both not tall and creative and vice versa.
Everyone who is humble is both not tall and strong and vice versa.
If john is not strong then susan is either not creative or not funny.
If alice is both not curious and happy then someone is either not generous or patient.
Everyone who is either not wise or happy is not curious and vice versa.
If someone is not quiet or kind then someone is creative or not wise and vice versa.
Everyone who is humble is not old and vice versa.
Everyone who is either wise or not generous is both quiet and brave and vice versa.
Everyone who is either curious or patient is both generous and rich and vice versa.
If someone is tall or old then susan is both not tall and not creative.
If someone is tall or not humble then someone is not creative or not tall.
Everyone who is curious is either brave or funny.
Someone is either not creative or not curious.
Someone is funny.
John is happy or curious.
Paul is generous.
Someone is funny or not funny.
Susan is either not calm or not kind.
Someone is creative or not wise.
Someone is either quiet or not patient. | Susan is tall. | contradiction | (![X]:((happy(X)|generous(X))<=>(curious(X)|strong(X))))&
((?[X]:(strong(X)))<=>(?[X]:((quiet(X)&~generous(X)))))&
((?[X]:((rich(X)|~quiet(X))))<=>(~generous(lucy)))&
(![X]:((~rich(X)<~>~kind(X))=>(~tall(X)&~quiet(X))))&
((?[X]:((happy(X)|funny(X))))<=>(?[X]:((~tall(X)&creative(X)))))&
(![X]:(humble(X)<=>(~tall(X)&strong(X))))&
((~strong(john))=>((~creative(susan)<~>~funny(susan))))&
(((~curious(alice)&happy(alice)))=>(?[X]:((~generous(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>happy(X))<=>~curious(X)))&
((?[X]:((~quiet(X)|kind(X))))<=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:(humble(X)<=>~old(X)))&
(![X]:((wise(X)<~>~generous(X))<=>(quiet(X)&brave(X))))&
(![X]:((curious(X)<~>patient(X))<=>(generous(X)&rich(X))))&
((?[X]:((tall(X)|old(X))))=>((~tall(susan)&~creative(susan))))&
((?[X]:((tall(X)|~humble(X))))=>(?[X]:((~creative(X)|~tall(X)))))&
(![X]:(curious(X)=>(brave(X)<~>funny(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:(funny(X)))&
((happy(john)|curious(john)))&
(generous(paul))&
(?[X]:((funny(X)|~funny(X))))&
((~calm(susan)<~>~kind(susan)))&
(?[X]:((creative(X)|~wise(X))))&
(?[X]:((quiet(X)<~>~patient(X)))) | tall(susan) | [
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5373125081310285972338373
% SZS output start Proof for 5373125081310285972338373
14. ? [X0] : (old(X0) | tall(X0)) => (~creative(susan) & ~tall(susan)) [input p13]
25. tall(susan) [input hypothesis]
34. (~creative(susan) & ~tall(susan)) | ! [X0] : (~old(X0) & ~tall(X0)) [ennf transformation 14]
136. ~tall(susan) | ~tall(X0) [cnf transformation 34]
155. tall(susan) [cnf transformation 25]
294. 33 <=> ! [X0] : ~tall(X0) [avatar definition]
295. ~tall(X0) <- (33) [avatar component clause 294]
298. 34 <=> tall(susan) [avatar definition]
299. tall(susan) <- (34) [avatar component clause 298]
302. 33 | ~34 [avatar split clause 136,298,294]
364. 34 [avatar split clause 155,298]
369. $false <- (33, 34) [resolution 299,295]
370. ~33 | ~34 [avatar contradiction clause 369]
371. $false [avatar sat refutation 302,364,370]
% SZS output end Proof for 5373125081310285972338373
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is rich and vice versa.
Everyone who is both funny and not generous is rich or not quiet.
Everyone who is both brave and not humble is old or not patient.
Everyone who is not humble is both not quiet and not calm.
Everyone who is either not strong or not generous is not happy or calm and vice versa.
Everyone who is both not humble and not funny is either rich or not creative and vice versa.
Everyone who is calm or not brave is either not quiet or old and vice versa.
Everyone who is not curious or not kind is not humble or not calm.
Everyone who is strong or curious is not strong and vice versa.
Everyone who is not wise is both brave and not patient.
If someone is brave or tall then fred is both brave and not wise.
Everyone who is curious is creative.
Everyone who is either not curious or not tall is either not kind or not generous and vice versa.
If mary is either tall or not humble then fred is wise.
If alice is either not old or curious then someone is either not curious or humble and vice versa.
If lucy is either not calm or old then someone is both curious and calm.
Mary is patient or calm.
Lucy is not patient or not curious.
Paul is either tall or quiet.
Someone is both not strong and patient.
Someone is not funny or not curious. | Mary is calm. | contradiction | (![X]:(creative(X)<=>rich(X)))&
(![X]:((funny(X)&~generous(X))=>(rich(X)|~quiet(X))))&
(![X]:((brave(X)&~humble(X))=>(old(X)|~patient(X))))&
(![X]:(~humble(X)=>(~quiet(X)&~calm(X))))&
(![X]:((~strong(X)<~>~generous(X))<=>(~happy(X)|calm(X))))&
(![X]:((~humble(X)&~funny(X))<=>(rich(X)<~>~creative(X))))&
(![X]:((calm(X)|~brave(X))<=>(~quiet(X)<~>old(X))))&
(![X]:((~curious(X)|~kind(X))=>(~humble(X)|~calm(X))))&
(![X]:((strong(X)|curious(X))<=>~strong(X)))&
(![X]:(~wise(X)=>(brave(X)&~patient(X))))&
((?[X]:((brave(X)|tall(X))))=>((brave(fred)&~wise(fred))))&
(![X]:(curious(X)=>creative(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~kind(X)<~>~generous(X))))&
(((tall(mary)<~>~humble(mary)))=>(wise(fred)))&
(((~old(alice)<~>curious(alice)))<=>(?[X]:((~curious(X)<~>humble(X)))))&
(((~calm(lucy)<~>old(lucy)))=>(?[X]:((curious(X)&calm(X)))))&
((patient(mary)|calm(mary)))&
((~patient(lucy)|~curious(lucy)))&
((tall(paul)<~>quiet(paul)))&
(?[X]:((~strong(X)&patient(X))))&
(?[X]:((~funny(X)|~curious(X)))) | calm(mary) | [
"p0",
"p3",
"p5",
"p8",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 7546707534703990716317431
% SZS output start Proof for 7546707534703990716317431
1. ! [X0] : (creative(X0) <=> rich(X0)) [input p0]
4. ! [X0] : (~humble(X0) => (~calm(X0) & ~quiet(X0))) [input p3]
6. ! [X0] : ((~funny(X0) & ~humble(X0)) <=> (rich(X0) <~> ~creative(X0))) [input p5]
9. ! [X0] : ((curious(X0) | strong(X0)) <=> ~strong(X0)) [input p8]
12. ! [X0] : (curious(X0) => creative(X0)) [input p11]
22. calm(mary) [input hypothesis]
27. ! [X0] : ((~calm(X0) & ~quiet(X0)) | humble(X0)) [ennf transformation 4]
32. ! [X0] : (creative(X0) | ~curious(X0)) [ennf transformation 12]
35. ! [X0] : ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))) [nnf transformation 1]
38. ! [X0] : (((~funny(X0) & ~humble(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (funny(X0) | humble(X0)))) [nnf transformation 6]
39. ! [X0] : (((~funny(X0) & ~humble(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | funny(X0) | humble(X0))) [flattening 38]
42. ! [X0] : (((curious(X0) | strong(X0)) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)))) [nnf transformation 9]
43. ! [X0] : ((curious(X0) | strong(X0) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)))) [flattening 42]
58. ~creative(X0) | rich(X0) [cnf transformation 35]
59. ~rich(X0) | creative(X0) [cnf transformation 35]
63. ~calm(X0) | humble(X0) [cnf transformation 27]
72. ~humble(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 39]
84. ~strong(X0) | ~strong(X0) [cnf transformation 43]
86. curious(X0) | strong(X0) | strong(X0) [cnf transformation 43]
93. ~curious(X0) | creative(X0) [cnf transformation 32]
123. calm(mary) [cnf transformation 22]
124. ~strong(X0) [duplicate literal removal 84]
125. curious(X0) | strong(X0) [duplicate literal removal 86]
129. ~humble(X0) | ~rich(X0) [subsumption resolution 72,59]
151. 5 <=> humble(mary) [avatar definition]
153. humble(mary) <- (5) [avatar component clause 151]
215. 18 <=> calm(mary) [avatar definition]
217. calm(mary) <- (18) [avatar component clause 215]
247. 18 [avatar split clause 123,215]
248. humble(mary) <- (18) [resolution 63,217]
253. strong(X0) | creative(X0) [resolution 125,93]
259. creative(X0) [subsumption resolution 253,124]
264. rich(X0) [resolution 259,58]
267. ~rich(mary) <- (5) [resolution 129,153]
268. $false <- (5) [subsumption resolution 267,264]
269. ~5 [avatar contradiction clause 268]
270. 5 | ~18 [avatar split clause 248,215,151]
271. $false [avatar sat refutation 247,269,270]
% SZS output end Proof for 7546707534703990716317431
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not calm.
If someone is not rich or rich then someone is both not happy and not kind.
If someone is both not generous and not calm then someone is brave.
If mary is either not strong or not quiet then someone is not wise.
If paul is not rich then alice is not curious or not strong and vice versa.
If mary is both not creative and not tall then someone is not happy and vice versa.
If john is both happy and not quiet then someone is not curious and vice versa.
Everyone who is funny is either not happy or humble and vice versa.
If someone is either quiet or not patient then john is brave and vice versa.
If lucy is either curious or not old then fred is not kind or funny and vice versa.
If someone is generous or not patient then lucy is generous and vice versa.
If someone is either strong or not funny then mary is rich or quiet.
Everyone who is generous or brave is not generous.
Everyone who is kind or not creative is not curious or not rich and vice versa.
Everyone who is not strong or not rich is not brave or tall and vice versa.
If someone is wise or kind then mary is not kind or kind and vice versa.
Someone is not creative or creative.
Fred is quiet.
John is not strong or not brave.
Lucy is not funny or not quiet.
Fred is both not funny and not generous.
Mary is either rich or not happy.
John is not creative or not humble.
Alice is wise. | John is patient. | entailment | (![X]:(~tall(X)=>~calm(X)))&
((?[X]:((~rich(X)|rich(X))))=>(?[X]:((~happy(X)&~kind(X)))))&
((?[X]:((~generous(X)&~calm(X))))=>(?[X]:(brave(X))))&
(((~strong(mary)<~>~quiet(mary)))=>(?[X]:(~wise(X))))&
((~rich(paul))<=>((~curious(alice)|~strong(alice))))&
(((~creative(mary)&~tall(mary)))<=>(?[X]:(~happy(X))))&
(((happy(john)&~quiet(john)))<=>(?[X]:(~curious(X))))&
(![X]:(funny(X)<=>(~happy(X)<~>humble(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(brave(john)))&
(((curious(lucy)<~>~old(lucy)))<=>((~kind(fred)|funny(fred))))&
((?[X]:((generous(X)|~patient(X))))<=>(generous(lucy)))&
((?[X]:((strong(X)<~>~funny(X))))=>((rich(mary)|quiet(mary))))&
(![X]:((generous(X)|brave(X))=>~generous(X)))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|~rich(X))))&
(![X]:((~strong(X)|~rich(X))<=>(~brave(X)|tall(X))))&
((?[X]:((wise(X)|kind(X))))<=>((~kind(mary)|kind(mary))))&
(?[X]:((~creative(X)|creative(X))))&
(quiet(fred))&
((~strong(john)|~brave(john)))&
((~funny(lucy)|~quiet(lucy)))&
((~funny(fred)&~generous(fred)))&
((rich(mary)<~>~happy(mary)))&
((~creative(john)|~humble(john)))&
(wise(alice)) | patient(john) | [
"p10",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 51223913560513115544401
% SZS output start Proof for 51223913560513115544401
11. ? [X0] : (~patient(X0) | generous(X0)) <=> generous(lucy) [input p10]
13. ! [X0] : ((brave(X0) | generous(X0)) => ~generous(X0)) [input p12]
25. ~patient(john) [input hypothesis]
34. ! [X0] : (~generous(X0) | (~brave(X0) & ~generous(X0))) [ennf transformation 13]
63. (? [X0] : (~patient(X0) | generous(X0)) | ~generous(lucy)) & (generous(lucy) | ! [X0] : (patient(X0) & ~generous(X0))) [nnf transformation 11]
64. (? [X0] : (~patient(X0) | generous(X0)) | ~generous(lucy)) & (generous(lucy) | ! [X1] : (patient(X1) & ~generous(X1))) [rectify 63]
65. ? [X0] : (~patient(X0) | generous(X0)) => (~patient(sK6) | generous(sK6)) [choice axiom]
66. ((~patient(sK6) | generous(sK6)) | ~generous(lucy)) & (generous(lucy) | ! [X1] : (patient(X1) & ~generous(X1))) [skolemisation 64,65]
112. generous(lucy) | patient(X1) [cnf transformation 66]
116. ~generous(X0) | ~generous(X0) [cnf transformation 34]
140. ~patient(john) [cnf transformation 25]
141. ~generous(X0) [duplicate literal removal 116]
278. 30 <=> generous(lucy) [avatar definition]
279. generous(lucy) <- (30) [avatar component clause 278]
291. 33 <=> ! [X1] : patient(X1) [avatar definition]
292. patient(X1) <- (33) [avatar component clause 291]
293. 33 | 30 [avatar split clause 112,278,291]
295. 34 <=> ! [X1] : ~generous(X1) [avatar definition]
296. ~generous(X1) <- (34) [avatar component clause 295]
310. 34 [avatar split clause 141,295]
355. $false <- (30, 34) [subsumption resolution 279,296]
356. ~30 | ~34 [avatar contradiction clause 355]
360. $false <- (33) [resolution 292,140]
365. ~33 [avatar contradiction clause 360]
366. $false [avatar sat refutation 293,310,356,365]
% SZS output end Proof for 51223913560513115544401
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not calm is not old. Everyone who is both old and rich is both not curious and rich and vice versa. If john is both not patient and strong then someone is not tall. If someone is not quiet then someone is not calm or not old and vice versa. Everyone who is not generous or not calm is either not humble or patient. If mary is happy or not calm then lucy is not kind or not happy. Everyone who is wise or not generous is both generous and not tall and vice versa. Everyone who is not patient is curious. Everyone who is not brave is not curious or not old and vice versa. Everyone who is happy or wise is not calm or kind and vice versa. If someone is not calm then someone is either calm or rich. Everyone who is either patient or not creative is not old and vice versa. Everyone who is either creative or happy is either brave or not kind and vice versa. If someone is both brave and creative then someone is both patient and not old and vice versa. Everyone who is both rich and not happy is rich. Everyone who is funny or not generous is kind and vice versa. Someone is humble. Fred is not kind. Someone is generous or curious. Someone is both strong and not creative. Someone is both funny and patient. Someone is quiet. | John is not rich. | neutral | (![X]:((curious(X)&~calm(X))=>~old(X)))&
(![X]:((old(X)&rich(X))<=>(~curious(X)&rich(X))))&
(((~patient(john)&strong(john)))=>(?[X]:(~tall(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~calm(X)|~old(X)))))&
(![X]:((~generous(X)|~calm(X))=>(~humble(X)<~>patient(X))))&
(((happy(mary)|~calm(mary)))=>((~kind(lucy)|~happy(lucy))))&
(![X]:((wise(X)|~generous(X))<=>(generous(X)&~tall(X))))&
(![X]:(~patient(X)=>curious(X)))&
(![X]:(~brave(X)<=>(~curious(X)|~old(X))))&
(![X]:((happy(X)|wise(X))<=>(~calm(X)|kind(X))))&
((?[X]:(~calm(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((patient(X)<~>~creative(X))<=>~old(X)))&
(![X]:((creative(X)<~>happy(X))<=>(brave(X)<~>~kind(X))))&
((?[X]:((brave(X)&creative(X))))<=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((rich(X)&~happy(X))=>rich(X)))&
(![X]:((funny(X)|~generous(X))<=>kind(X)))&
(?[X]:(humble(X)))&
(~kind(fred))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((funny(X)&patient(X))))&
(?[X]:(quiet(X))) | ~rich(john) | []
| null | 0 |
If someone is rich or not calm then someone is either not brave or not quiet and vice versa.
If alice is either tall or not funny then john is either wise or not rich.
Everyone who is not happy or not wise is funny and vice versa.
Everyone who is strong or tall is curious or not tall and vice versa.
If susan is either quiet or happy then paul is calm or happy and vice versa.
If someone is both not generous and not rich then someone is either not generous or strong.
Everyone who is both not kind and not creative is not wise or rich.
Everyone who is both not kind and humble is brave and vice versa.
Everyone who is patient is both funny and not funny.
If john is curious or not generous then alice is either not happy or not strong and vice versa.
Everyone who is both not strong and not calm is either strong or not creative.
If someone is either patient or not creative then someone is either not calm or not patient and vice versa.
Everyone who is both not tall and not patient is both not curious and rich and vice versa.
Everyone who is happy is both happy and not strong.
Everyone who is not strong is either wise or patient.
If lucy is not funny then someone is both patient and strong and vice versa.
Susan is not creative or brave.
John is both happy and calm.
Someone is funny.
Alice is funny.
Someone is both not brave and not rich.
Fred is not rich.
Lucy is happy or strong.
Susan is generous. | Alice is happy. | contradiction | ((?[X]:((rich(X)|~calm(X))))<=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(((tall(alice)<~>~funny(alice)))=>((wise(john)<~>~rich(john))))&
(![X]:((~happy(X)|~wise(X))<=>funny(X)))&
(![X]:((strong(X)|tall(X))<=>(curious(X)|~tall(X))))&
(((quiet(susan)<~>happy(susan)))<=>((calm(paul)|happy(paul))))&
((?[X]:((~generous(X)&~rich(X))))=>(?[X]:((~generous(X)<~>strong(X)))))&
(![X]:((~kind(X)&~creative(X))=>(~wise(X)|rich(X))))&
(![X]:((~kind(X)&humble(X))<=>brave(X)))&
(![X]:(patient(X)=>(funny(X)&~funny(X))))&
(((curious(john)|~generous(john)))<=>((~happy(alice)<~>~strong(alice))))&
(![X]:((~strong(X)&~calm(X))=>(strong(X)<~>~creative(X))))&
((?[X]:((patient(X)<~>~creative(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((~tall(X)&~patient(X))<=>(~curious(X)&rich(X))))&
(![X]:(happy(X)=>(happy(X)&~strong(X))))&
(![X]:(~strong(X)=>(wise(X)<~>patient(X))))&
((~funny(lucy))<=>(?[X]:((patient(X)&strong(X)))))&
((~creative(susan)|brave(susan)))&
((happy(john)&calm(john)))&
(?[X]:(funny(X)))&
(funny(alice))&
(?[X]:((~brave(X)&~rich(X))))&
(~rich(fred))&
((happy(lucy)|strong(lucy)))&
(generous(susan)) | happy(alice) | [
"p2",
"p8",
"p13",
"p14",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 7637968931644376631139125
% SZS output start Proof for 7637968931644376631139125
3. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> funny(X0)) [input p2]
9. ! [X0] : (patient(X0) => (~funny(X0) & funny(X0))) [input p8]
14. ! [X0] : (happy(X0) => (~strong(X0) & happy(X0))) [input p13]
15. ! [X0] : (~strong(X0) => (wise(X0) <~> patient(X0))) [input p14]
20. funny(alice) [input p19]
25. happy(alice) [input hypothesis]
33. ! [X0] : ((~funny(X0) & funny(X0)) | ~patient(X0)) [ennf transformation 9]
36. ! [X0] : ((~strong(X0) & happy(X0)) | ~happy(X0)) [ennf transformation 14]
37. ! [X0] : ((wise(X0) <~> patient(X0)) | strong(X0)) [ennf transformation 15]
44. ! [X0] : (((~wise(X0) | ~happy(X0)) | ~funny(X0)) & (funny(X0) | (wise(X0) & happy(X0)))) [nnf transformation 3]
45. ! [X0] : ((~wise(X0) | ~happy(X0) | ~funny(X0)) & (funny(X0) | (wise(X0) & happy(X0)))) [flattening 44]
66. ! [X0] : (((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | strong(X0)) [nnf transformation 37]
87. ~happy(X0) | ~wise(X0) | ~funny(X0) [cnf transformation 45]
104. funny(X0) | ~patient(X0) [cnf transformation 33]
105. ~patient(X0) | ~funny(X0) [cnf transformation 33]
127. ~strong(X0) | ~happy(X0) [cnf transformation 36]
128. patient(X0) | wise(X0) | strong(X0) [cnf transformation 66]
137. funny(alice) [cnf transformation 20]
143. happy(alice) [cnf transformation 25]
182. 9 <=> funny(alice) [avatar definition]
184. funny(alice) <- (9) [avatar component clause 182]
236. ~patient(X0) [subsumption resolution 104,105]
238. 20 <=> strong(alice) [avatar definition]
239. ~strong(alice) <- (~20) [avatar component clause 238]
240. strong(alice) <- (20) [avatar component clause 238]
242. 21 <=> happy(alice) [avatar definition]
243. happy(alice) <- (21) [avatar component clause 242]
281. strong(X0) | wise(X0) [subsumption resolution 128,236]
302. 9 [avatar split clause 137,182]
312. 21 [avatar split clause 143,242]
332. wise(alice) <- (~20) [resolution 281,239]
335. ~wise(alice) | ~funny(alice) <- (21) [resolution 87,243]
338. ~funny(alice) <- (~20, 21) [subsumption resolution 335,332]
339. $false <- (9, ~20, 21) [subsumption resolution 338,184]
340. ~9 | 20 | ~21 [avatar contradiction clause 339]
343. ~happy(alice) <- (20) [resolution 240,127]
344. $false <- (20, 21) [subsumption resolution 343,243]
345. ~20 | ~21 [avatar contradiction clause 344]
346. $false [avatar sat refutation 302,312,340,345]
% SZS output end Proof for 7637968931644376631139125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or curious is both not brave and not generous.
Everyone who is either curious or not happy is strong and vice versa.
If paul is not calm or patient then mary is not kind.
Everyone who is both not curious and tall is funny or not calm and vice versa.
If alice is tall then someone is creative and vice versa.
Everyone who is brave or not rich is both brave and calm.
If someone is humble then someone is not calm and vice versa.
If someone is not quiet then someone is either not generous or rich and vice versa.
If john is both brave and kind then paul is patient or not curious.
If someone is not tall or not strong then john is humble and vice versa.
Everyone who is either patient or creative is not calm or not generous and vice versa.
If someone is either not calm or not creative then someone is either not quiet or brave and vice versa.
If someone is quiet or not old then john is both not creative and not humble.
If alice is not patient then alice is tall or not wise and vice versa.
If someone is humble then john is not humble.
Lucy is wise.
Fred is strong or not quiet.
Someone is not humble. | Mary is strong. | entailment | (![X]:((~strong(X)<~>curious(X))=>(~brave(X)&~generous(X))))&
(![X]:((curious(X)<~>~happy(X))<=>strong(X)))&
(((~calm(paul)|patient(paul)))=>(~kind(mary)))&
(![X]:((~curious(X)&tall(X))<=>(funny(X)|~calm(X))))&
((tall(alice))<=>(?[X]:(creative(X))))&
(![X]:((brave(X)|~rich(X))=>(brave(X)&calm(X))))&
((?[X]:(humble(X)))<=>(?[X]:(~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(((brave(john)&kind(john)))=>((patient(paul)|~curious(paul))))&
((?[X]:((~tall(X)|~strong(X))))<=>(humble(john)))&
(![X]:((patient(X)<~>creative(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((quiet(X)|~old(X))))=>((~creative(john)&~humble(john))))&
((~patient(alice))<=>((tall(alice)|~wise(alice))))&
((?[X]:(humble(X)))=>(~humble(john)))&
(wise(lucy))&
((strong(fred)|~quiet(fred)))&
(?[X]:(~humble(X))) | strong(mary) | [
"p9",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2277415832979781963311913
% SZS output start Proof for 2277415832979781963311913
10. ? [X0] : (~strong(X0) | ~tall(X0)) <=> humble(john) [input p9]
15. ? [X0] : humble(X0) => ~humble(john) [input p14]
19. ~strong(mary) [input hypothesis]
29. ~humble(john) | ! [X0] : ~humble(X0) [ennf transformation 15]
48. (? [X0] : (~strong(X0) | ~tall(X0)) | ~humble(john)) & (humble(john) | ! [X0] : (strong(X0) & tall(X0))) [nnf transformation 10]
49. (? [X0] : (~strong(X0) | ~tall(X0)) | ~humble(john)) & (humble(john) | ! [X1] : (strong(X1) & tall(X1))) [rectify 48]
50. ? [X0] : (~strong(X0) | ~tall(X0)) => (~strong(sK5) | ~tall(sK5)) [choice axiom]
51. ((~strong(sK5) | ~tall(sK5)) | ~humble(john)) & (humble(john) | ! [X1] : (strong(X1) & tall(X1))) [skolemisation 49,50]
89. humble(john) | strong(X1) [cnf transformation 51]
110. ~humble(john) | ~humble(X0) [cnf transformation 29]
114. ~strong(mary) [cnf transformation 19]
137. 6 <=> ! [X3] : ~humble(X3) [avatar definition]
138. ~humble(X3) <- (6) [avatar component clause 137]
170. 14 <=> humble(john) [avatar definition]
171. humble(john) <- (14) [avatar component clause 170]
183. 17 <=> ! [X1] : strong(X1) [avatar definition]
184. strong(X1) <- (17) [avatar component clause 183]
185. 17 | 14 [avatar split clause 89,170,183]
246. 6 | ~14 [avatar split clause 110,170,137]
258. $false <- (17) [resolution 184,114]
259. ~17 [avatar contradiction clause 258]
262. $false <- (6, 14) [subsumption resolution 171,138]
263. ~6 | ~14 [avatar contradiction clause 262]
264. $false [avatar sat refutation 185,246,259,263]
% SZS output end Proof for 2277415832979781963311913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not calm is either not funny or humble.
If someone is either not funny or not quiet then someone is either tall or brave and vice versa.
Everyone who is humble is not old or not tall.
Everyone who is strong or patient is either humble or not kind and vice versa.
If mary is tall then someone is funny.
Everyone who is either humble or curious is both not old and not brave and vice versa.
Everyone who is not tall or old is kind or strong and vice versa.
Everyone who is both not tall and not wise is patient or not rich and vice versa.
Everyone who is both curious and not calm is both not brave and brave and vice versa.
If someone is either not generous or not wise then someone is either tall or brave and vice versa.
Everyone who is curious is both not strong and not funny.
If fred is not strong or happy then john is happy or not kind and vice versa.
Everyone who is funny or generous is curious or rich.
If someone is wise then mary is both kind and strong.
If fred is either not patient or happy then alice is either brave or quiet.
Everyone who is curious is funny.
Someone is old or not rich.
Mary is not humble.
Someone is either brave or patient.
Someone is tall.
Mary is not wise or strong.
Someone is either humble or brave. | Alice is not brave. | neutral | (![X]:((curious(X)&~calm(X))=>(~funny(X)<~>humble(X))))&
((?[X]:((~funny(X)<~>~quiet(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:(humble(X)=>(~old(X)|~tall(X))))&
(![X]:((strong(X)|patient(X))<=>(humble(X)<~>~kind(X))))&
((tall(mary))=>(?[X]:(funny(X))))&
(![X]:((humble(X)<~>curious(X))<=>(~old(X)&~brave(X))))&
(![X]:((~tall(X)|old(X))<=>(kind(X)|strong(X))))&
(![X]:((~tall(X)&~wise(X))<=>(patient(X)|~rich(X))))&
(![X]:((curious(X)&~calm(X))<=>(~brave(X)&brave(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:(curious(X)=>(~strong(X)&~funny(X))))&
(((~strong(fred)|happy(fred)))<=>((happy(john)|~kind(john))))&
(![X]:((funny(X)|generous(X))=>(curious(X)|rich(X))))&
((?[X]:(wise(X)))=>((kind(mary)&strong(mary))))&
(((~patient(fred)<~>happy(fred)))=>((brave(alice)<~>quiet(alice))))&
(![X]:(curious(X)=>funny(X)))&
(?[X]:((old(X)|~rich(X))))&
(~humble(mary))&
(?[X]:((brave(X)<~>patient(X))))&
(?[X]:(tall(X)))&
((~wise(mary)|strong(mary)))&
(?[X]:((humble(X)<~>brave(X)))) | ~brave(alice) | []
| null | 0 |
Everyone who is either tall or creative is old.
Everyone who is either kind or not quiet is either not wise or generous and vice versa.
Everyone who is both kind and not generous is not strong or rich and vice versa.
Everyone who is calm is both not curious and funny.
Everyone who is both not quiet and curious is both not happy and not patient.
Everyone who is both not brave and generous is both not kind and generous.
Everyone who is both creative and not wise is both strong and not quiet and vice versa.
Everyone who is not calm or not quiet is either curious or strong and vice versa.
If someone is either not rich or not humble then alice is either not quiet or funny and vice versa.
Everyone who is patient is both creative and not brave.
If paul is creative then someone is both funny and rich and vice versa.
Everyone who is both quiet and kind is generous or not generous and vice versa.
Everyone who is happy or strong is both not humble and curious.
If susan is both brave and strong then someone is both not kind and not strong.
Everyone who is patient or not funny is both strong and rich and vice versa.
If someone is not humble or not calm then alice is either not humble or old.
Someone is both not rich and not brave.
Someone is either not humble or not calm.
Someone is not curious.
Fred is either not generous or wise.
Someone is old.
Fred is both not brave and not rich.
Alice is not calm. | Alice is not generous. | entailment | (![X]:((tall(X)<~>creative(X))=>old(X)))&
(![X]:((kind(X)<~>~quiet(X))<=>(~wise(X)<~>generous(X))))&
(![X]:((kind(X)&~generous(X))<=>(~strong(X)|rich(X))))&
(![X]:(calm(X)=>(~curious(X)&funny(X))))&
(![X]:((~quiet(X)&curious(X))=>(~happy(X)&~patient(X))))&
(![X]:((~brave(X)&generous(X))=>(~kind(X)&generous(X))))&
(![X]:((creative(X)&~wise(X))<=>(strong(X)&~quiet(X))))&
(![X]:((~calm(X)|~quiet(X))<=>(curious(X)<~>strong(X))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>((~quiet(alice)<~>funny(alice))))&
(![X]:(patient(X)=>(creative(X)&~brave(X))))&
((creative(paul))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((quiet(X)&kind(X))<=>(generous(X)|~generous(X))))&
(![X]:((happy(X)|strong(X))=>(~humble(X)&curious(X))))&
(((brave(susan)&strong(susan)))=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:((patient(X)|~funny(X))<=>(strong(X)&rich(X))))&
((?[X]:((~humble(X)|~calm(X))))=>((~humble(alice)<~>old(alice))))&
(?[X]:((~rich(X)&~brave(X))))&
(?[X]:((~humble(X)<~>~calm(X))))&
(?[X]:(~curious(X)))&
((~generous(fred)<~>wise(fred)))&
(?[X]:(old(X)))&
((~brave(fred)&~rich(fred)))&
(~calm(alice)) | ~generous(alice) | [
"p2",
"p3",
"p7",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 6322219503414077072877510
% SZS output start Proof for 6322219503414077072877510
3. ! [X0] : ((~generous(X0) & kind(X0)) <=> (rich(X0) | ~strong(X0))) [input p2]
4. ! [X0] : (calm(X0) => (funny(X0) & ~curious(X0))) [input p3]
8. ! [X0] : ((~quiet(X0) | ~calm(X0)) <=> (curious(X0) <~> strong(X0))) [input p7]
13. ! [X0] : ((strong(X0) | happy(X0)) => (curious(X0) & ~humble(X0))) [input p12]
24. generous(alice) [input hypothesis]
26. ! [X0] : (strong(X0) => (curious(X0) & ~humble(X0))) [pure predicate removal 13]
28. ! [X0] : ((funny(X0) & ~curious(X0)) | ~calm(X0)) [ennf transformation 4]
34. ! [X0] : ((curious(X0) & ~humble(X0)) | ~strong(X0)) [ennf transformation 26]
40. ! [X0] : (((~generous(X0) & kind(X0)) | (~rich(X0) & strong(X0))) & ((rich(X0) | ~strong(X0)) | (generous(X0) | ~kind(X0)))) [nnf transformation 3]
41. ! [X0] : (((~generous(X0) & kind(X0)) | (~rich(X0) & strong(X0))) & (rich(X0) | ~strong(X0) | generous(X0) | ~kind(X0))) [flattening 40]
44. ! [X0] : (((~quiet(X0) | ~calm(X0)) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0)))) & (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (quiet(X0) & calm(X0)))) [nnf transformation 8]
45. ! [X0] : ((~quiet(X0) | ~calm(X0) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0)))) & (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (quiet(X0) & calm(X0)))) [flattening 44]
84. ~generous(X0) | strong(X0) [cnf transformation 41]
86. ~curious(X0) | ~calm(X0) [cnf transformation 28]
97. ~strong(X0) | ~curious(X0) | calm(X0) [cnf transformation 45]
120. curious(X0) | ~strong(X0) [cnf transformation 34]
143. generous(alice) [cnf transformation 24]
145. ~strong(X0) | ~curious(X0) [subsumption resolution 97,86]
196. ~strong(X0) [subsumption resolution 120,145]
247. strong(alice) [resolution 84,143]
248. $false [subsumption resolution 247,196]
% SZS output end Proof for 6322219503414077072877510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then someone is both patient and not patient. If someone is both happy and humble then mary is either curious or brave. If lucy is either calm or not strong then someone is either humble or generous and vice versa. Everyone who is both kind and not curious is not calm or generous. Everyone who is brave or wise is either calm or not generous. If mary is tall then mary is not generous. If alice is either generous or brave then lucy is funny or not brave and vice versa. Everyone who is either generous or not kind is not strong and vice versa. If paul is creative then lucy is either not old or not generous. Everyone who is humble is quiet and vice versa. If someone is both not creative and not humble then alice is kind. Everyone who is either calm or curious is either not rich or humble. Everyone who is either not curious or curious is brave. If paul is not brave or not wise then someone is quiet or strong and vice versa. If susan is not patient or tall then susan is both strong and not funny and vice versa. Everyone who is either wise or patient is either not tall or not old and vice versa. John is either strong or creative. Alice is not generous. Someone is curious. Susan is either not wise or curious. Mary is not humble. Someone is quiet. Fred is not wise or not curious. | Alice is rich. | entailment | ((?[X]:(~rich(X)))=>(?[X]:((patient(X)&~patient(X)))))&
((?[X]:((happy(X)&humble(X))))=>((curious(mary)<~>brave(mary))))&
(((calm(lucy)<~>~strong(lucy)))<=>(?[X]:((humble(X)<~>generous(X)))))&
(![X]:((kind(X)&~curious(X))=>(~calm(X)|generous(X))))&
(![X]:((brave(X)|wise(X))=>(calm(X)<~>~generous(X))))&
((tall(mary))=>(~generous(mary)))&
(((generous(alice)<~>brave(alice)))<=>((funny(lucy)|~brave(lucy))))&
(![X]:((generous(X)<~>~kind(X))<=>~strong(X)))&
((creative(paul))=>((~old(lucy)<~>~generous(lucy))))&
(![X]:(humble(X)<=>quiet(X)))&
((?[X]:((~creative(X)&~humble(X))))=>(kind(alice)))&
(![X]:((calm(X)<~>curious(X))=>(~rich(X)<~>humble(X))))&
(![X]:((~curious(X)<~>curious(X))=>brave(X)))&
(((~brave(paul)|~wise(paul)))<=>(?[X]:((quiet(X)|strong(X)))))&
(((~patient(susan)|tall(susan)))<=>((strong(susan)&~funny(susan))))&
(![X]:((wise(X)<~>patient(X))<=>(~tall(X)<~>~old(X))))&
((strong(john)<~>creative(john)))&
(~generous(alice))&
(?[X]:(curious(X)))&
((~wise(susan)<~>curious(susan)))&
(~humble(mary))&
(?[X]:(quiet(X)))&
((~wise(fred)|~curious(fred))) | rich(alice) | [
"p0",
"hypothesis"
]
| % SZS status Unsatisfiable for 3939291949817713862263080
% SZS output start Proof for 3939291949817713862263080
1. ? [X0] : ~rich(X0) => ? [X0] : (~patient(X0) & patient(X0)) [input p0]
24. ~rich(alice) [input hypothesis]
25. ? [X0] : ~rich(X0) => ? [X1] : (~patient(X1) & patient(X1)) [rectify 1]
27. ? [X1] : (~patient(X1) & patient(X1)) | ! [X0] : rich(X0) [ennf transformation 25]
36. ? [X0] : (~patient(X0) & patient(X0)) | ! [X1] : rich(X1) [rectify 27]
37. ? [X0] : (~patient(X0) & patient(X0)) => (~patient(sK0) & patient(sK0)) [choice axiom]
38. (~patient(sK0) & patient(sK0)) | ! [X1] : rich(X1) [skolemisation 36,37]
65. patient(sK0) | rich(X1) [cnf transformation 38]
66. ~patient(sK0) | rich(X1) [cnf transformation 38]
128. ~rich(alice) [cnf transformation 24]
132. 1 <=> ! [X1] : rich(X1) [avatar definition]
133. rich(X1) <- (1) [avatar component clause 132]
135. 2 <=> patient(sK0) [avatar definition]
138. 1 | ~2 [avatar split clause 66,135,132]
139. 1 | 2 [avatar split clause 65,135,132]
304. $false <- (1) [resolution 133,128]
305. ~1 [avatar contradiction clause 304]
306. $false [avatar sat refutation 138,139,305]
% SZS output end Proof for 3939291949817713862263080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is both not kind and not brave. If someone is either happy or not rich then someone is both generous and happy. Everyone who is not creative is either not generous or not curious. If fred is not creative then lucy is either generous or not patient and vice versa. If someone is either funny or not kind then someone is both kind and wise. Everyone who is both happy and not curious is brave. If susan is curious or patient then alice is both not brave and patient. Everyone who is both patient and not generous is curious and vice versa. Everyone who is funny or quiet is either not rich or wise. Everyone who is either not kind or happy is both not wise and not funny and vice versa. If someone is calm or strong then someone is both not calm and not brave. If someone is not tall then someone is both not old and not humble and vice versa. Everyone who is both not wise and happy is generous. Everyone who is either quiet or not generous is patient and vice versa. If alice is either not patient or wise then someone is humble and vice versa. Everyone who is not funny or not brave is both not curious and brave and vice versa. Susan is both brave and not generous. Alice is both old and not humble. Susan is not old. Susan is either patient or wise. Someone is either not old or not brave. Mary is both not humble and not strong. Someone is quiet or humble. | Fred is not kind. | neutral | (![X]:(funny(X)=>(~kind(X)&~brave(X))))&
((?[X]:((happy(X)<~>~rich(X))))=>(?[X]:((generous(X)&happy(X)))))&
(![X]:(~creative(X)=>(~generous(X)<~>~curious(X))))&
((~creative(fred))<=>((generous(lucy)<~>~patient(lucy))))&
((?[X]:((funny(X)<~>~kind(X))))=>(?[X]:((kind(X)&wise(X)))))&
(![X]:((happy(X)&~curious(X))=>brave(X)))&
(((curious(susan)|patient(susan)))=>((~brave(alice)&patient(alice))))&
(![X]:((patient(X)&~generous(X))<=>curious(X)))&
(![X]:((funny(X)|quiet(X))=>(~rich(X)<~>wise(X))))&
(![X]:((~kind(X)<~>happy(X))<=>(~wise(X)&~funny(X))))&
((?[X]:((calm(X)|strong(X))))=>(?[X]:((~calm(X)&~brave(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((~old(X)&~humble(X)))))&
(![X]:((~wise(X)&happy(X))=>generous(X)))&
(![X]:((quiet(X)<~>~generous(X))<=>patient(X)))&
(((~patient(alice)<~>wise(alice)))<=>(?[X]:(humble(X))))&
(![X]:((~funny(X)|~brave(X))<=>(~curious(X)&brave(X))))&
((brave(susan)&~generous(susan)))&
((old(alice)&~humble(alice)))&
(~old(susan))&
((patient(susan)<~>wise(susan)))&
(?[X]:((~old(X)<~>~brave(X))))&
((~humble(mary)&~strong(mary)))&
(?[X]:((quiet(X)|humble(X)))) | ~kind(fred) | []
| null | 0 |
If alice is strong or curious then fred is not creative and vice versa.
Everyone who is either kind or not patient is funny and vice versa.
If someone is either calm or old then paul is rich or brave and vice versa.
Everyone who is either not brave or happy is both brave and kind and vice versa.
Everyone who is both not generous and funny is calm or patient and vice versa.
If lucy is quiet or not rich then susan is happy.
If paul is not humble or not wise then someone is both rich and kind.
Everyone who is brave or not quiet is not happy and vice versa.
If someone is not quiet or not kind then alice is not humble or quiet.
If someone is either calm or happy then alice is not quiet or not rich and vice versa.
Everyone who is both happy and curious is wise or rich and vice versa.
Everyone who is not old is either old or generous and vice versa.
Everyone who is not funny is tall or not strong.
If someone is both not creative and not funny then someone is either strong or not rich.
If paul is not funny then fred is not curious or generous and vice versa.
Everyone who is curious is either not humble or humble.
Someone is tall or not creative.
Someone is either calm or strong.
Someone is both not humble and not wise.
Mary is either not old or generous.
Someone is either not old or strong.
Someone is not patient.
Fred is not strong. | Paul is not patient. | entailment | (((strong(alice)|curious(alice)))<=>(~creative(fred)))&
(![X]:((kind(X)<~>~patient(X))<=>funny(X)))&
((?[X]:((calm(X)<~>old(X))))<=>((rich(paul)|brave(paul))))&
(![X]:((~brave(X)<~>happy(X))<=>(brave(X)&kind(X))))&
(![X]:((~generous(X)&funny(X))<=>(calm(X)|patient(X))))&
(((quiet(lucy)|~rich(lucy)))=>(happy(susan)))&
(((~humble(paul)|~wise(paul)))=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((brave(X)|~quiet(X))<=>~happy(X)))&
((?[X]:((~quiet(X)|~kind(X))))=>((~humble(alice)|quiet(alice))))&
((?[X]:((calm(X)<~>happy(X))))<=>((~quiet(alice)|~rich(alice))))&
(![X]:((happy(X)&curious(X))<=>(wise(X)|rich(X))))&
(![X]:(~old(X)<=>(old(X)<~>generous(X))))&
(![X]:(~funny(X)=>(tall(X)|~strong(X))))&
((?[X]:((~creative(X)&~funny(X))))=>(?[X]:((strong(X)<~>~rich(X)))))&
((~funny(paul))<=>((~curious(fred)|generous(fred))))&
(![X]:(curious(X)=>(~humble(X)<~>humble(X))))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:((calm(X)<~>strong(X))))&
(?[X]:((~humble(X)&~wise(X))))&
((~old(mary)<~>generous(mary)))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:(~patient(X)))&
(~strong(fred)) | ~patient(paul) | [
"p4",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 7404364207245473129214104
% SZS output start Proof for 7404364207245473129214104
5. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (patient(X0) | calm(X0))) [input p4]
12. ! [X0] : (~old(X0) <=> (old(X0) <~> generous(X0))) [input p11]
24. patient(paul) [input hypothesis]
44. ! [X0] : (((funny(X0) & ~generous(X0)) | (~patient(X0) & ~calm(X0))) & ((patient(X0) | calm(X0)) | (~funny(X0) | generous(X0)))) [nnf transformation 5]
45. ! [X0] : (((funny(X0) & ~generous(X0)) | (~patient(X0) & ~calm(X0))) & (patient(X0) | calm(X0) | ~funny(X0) | generous(X0))) [flattening 44]
57. ! [X0] : ((~old(X0) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) & (((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | old(X0))) [nnf transformation 12]
97. ~generous(X0) | ~patient(X0) [cnf transformation 45]
122. generous(X0) | old(X0) | old(X0) [cnf transformation 57]
124. ~old(X0) | generous(X0) | ~old(X0) [cnf transformation 57]
143. patient(paul) [cnf transformation 24]
144. generous(X0) | old(X0) [duplicate literal removal 122]
145. ~old(X0) | generous(X0) [duplicate literal removal 124]
265. generous(X0) [subsumption resolution 144,145]
302. ~patient(X0) [resolution 97,265]
307. $false [resolution 302,143]
% SZS output end Proof for 7404364207245473129214104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or kind is either not patient or creative. If someone is not rich or humble then alice is funny or brave and vice versa. If fred is either not calm or happy then someone is both not tall and funny and vice versa. If fred is either tall or not strong then someone is not funny or not brave and vice versa. If someone is happy then someone is both not strong and generous and vice versa. Everyone who is either patient or not calm is both not quiet and not happy. Everyone who is not old is generous and vice versa. Everyone who is both not wise and rich is generous or not humble and vice versa. Everyone who is either quiet or generous is either happy or not quiet and vice versa. Everyone who is either not kind or kind is not humble or generous and vice versa. Everyone who is both patient and not funny is not patient or happy and vice versa. Everyone who is either brave or not rich is not creative and vice versa. If john is old or humble then someone is both quiet and not patient. Everyone who is either patient or kind is both brave and not funny and vice versa. If someone is generous or calm then someone is kind and vice versa. If someone is either tall or old then fred is humble. Lucy is humble or not quiet. Someone is kind. Someone is not happy or not quiet. Someone is both kind and strong. John is not creative or not funny. Someone is not rich or not tall. Someone is either kind or not happy. | John is not generous. | contradiction | (![X]:((~curious(X)<~>kind(X))=>(~patient(X)<~>creative(X))))&
((?[X]:((~rich(X)|humble(X))))<=>((funny(alice)|brave(alice))))&
(((~calm(fred)<~>happy(fred)))<=>(?[X]:((~tall(X)&funny(X)))))&
(((tall(fred)<~>~strong(fred)))<=>(?[X]:((~funny(X)|~brave(X)))))&
((?[X]:(happy(X)))<=>(?[X]:((~strong(X)&generous(X)))))&
(![X]:((patient(X)<~>~calm(X))=>(~quiet(X)&~happy(X))))&
(![X]:(~old(X)<=>generous(X)))&
(![X]:((~wise(X)&rich(X))<=>(generous(X)|~humble(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(happy(X)<~>~quiet(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(~humble(X)|generous(X))))&
(![X]:((patient(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((brave(X)<~>~rich(X))<=>~creative(X)))&
(((old(john)|humble(john)))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((patient(X)<~>kind(X))<=>(brave(X)&~funny(X))))&
((?[X]:((generous(X)|calm(X))))<=>(?[X]:(kind(X))))&
((?[X]:((tall(X)<~>old(X))))=>(humble(fred)))&
((humble(lucy)|~quiet(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((kind(X)&strong(X))))&
((~creative(john)|~funny(john)))&
(?[X]:((~rich(X)|~tall(X))))&
(?[X]:((kind(X)<~>~happy(X)))) | ~generous(john) | [
"p6",
"p10",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 431400269893233318526077
% SZS output start Proof for 431400269893233318526077
7. ! [X0] : (~old(X0) <=> generous(X0)) [input p6]
11. ! [X0] : ((~funny(X0) & patient(X0)) <=> (happy(X0) | ~patient(X0))) [input p10]
13. (humble(john) | old(john)) => ? [X0] : (~patient(X0) & quiet(X0)) [input p12]
24. ~generous(john) [input hypothesis]
29. ? [X0] : (~patient(X0) & quiet(X0)) | (~humble(john) & ~old(john)) [ennf transformation 13]
51. ! [X0] : ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))) [nnf transformation 7]
57. ! [X0] : (((~funny(X0) & patient(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | ~patient(X0)))) [nnf transformation 11]
58. ! [X0] : (((~funny(X0) & patient(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | ~patient(X0))) [flattening 57]
60. ? [X0] : (~patient(X0) & quiet(X0)) => (~patient(sK5) & quiet(sK5)) [choice axiom]
61. (~patient(sK5) & quiet(sK5)) | (~humble(john) & ~old(john)) [skolemisation 29,60]
108. old(X0) | generous(X0) [cnf transformation 51]
130. patient(X0) | patient(X0) [cnf transformation 58]
140. ~patient(sK5) | ~old(john) [cnf transformation 61]
162. ~generous(john) [cnf transformation 24]
164. patient(X0) [duplicate literal removal 130]
276. ~old(john) [subsumption resolution 140,164]
366. generous(john) [resolution 108,276]
367. $false [subsumption resolution 366,162]
% SZS output end Proof for 431400269893233318526077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is both calm and rich and vice versa. If someone is not strong then john is rich or generous and vice versa. If fred is not strong or quiet then someone is both not brave and not strong and vice versa. If lucy is either not calm or not tall then lucy is either old or not kind. If someone is happy or funny then someone is both humble and quiet. If lucy is either patient or curious then mary is either generous or brave and vice versa. Everyone who is both kind and brave is both generous and not tall. Everyone who is old is not kind or not rich and vice versa. Everyone who is rich or humble is calm and vice versa. If lucy is not strong or not quiet then someone is curious or generous and vice versa. If someone is curious or not curious then susan is quiet or generous and vice versa. Everyone who is creative or calm is funny or not rich and vice versa. Everyone who is both tall and brave is not curious. Everyone who is either brave or not quiet is humble or not funny and vice versa. Everyone who is not humble is quiet or curious. Everyone who is kind is quiet or not rich. Lucy is both not kind and not curious. Someone is both not creative and quiet. John is either brave or funny. Someone is either calm or not rich. Susan is both old and not humble. Susan is either not wise or not kind. Mary is not old or not patient. Susan is not patient. | John is brave. | contradiction | (![X]:(quiet(X)<=>(calm(X)&rich(X))))&
((?[X]:(~strong(X)))<=>((rich(john)|generous(john))))&
(((~strong(fred)|quiet(fred)))<=>(?[X]:((~brave(X)&~strong(X)))))&
(((~calm(lucy)<~>~tall(lucy)))=>((old(lucy)<~>~kind(lucy))))&
((?[X]:((happy(X)|funny(X))))=>(?[X]:((humble(X)&quiet(X)))))&
(((patient(lucy)<~>curious(lucy)))<=>((generous(mary)<~>brave(mary))))&
(![X]:((kind(X)&brave(X))=>(generous(X)&~tall(X))))&
(![X]:(old(X)<=>(~kind(X)|~rich(X))))&
(![X]:((rich(X)|humble(X))<=>calm(X)))&
(((~strong(lucy)|~quiet(lucy)))<=>(?[X]:((curious(X)|generous(X)))))&
((?[X]:((curious(X)|~curious(X))))<=>((quiet(susan)|generous(susan))))&
(![X]:((creative(X)|calm(X))<=>(funny(X)|~rich(X))))&
(![X]:((tall(X)&brave(X))=>~curious(X)))&
(![X]:((brave(X)<~>~quiet(X))<=>(humble(X)|~funny(X))))&
(![X]:(~humble(X)=>(quiet(X)|curious(X))))&
(![X]:(kind(X)=>(quiet(X)|~rich(X))))&
((~kind(lucy)&~curious(lucy)))&
(?[X]:((~creative(X)&quiet(X))))&
((brave(john)<~>funny(john)))&
(?[X]:((calm(X)<~>~rich(X))))&
((old(susan)&~humble(susan)))&
((~wise(susan)<~>~kind(susan)))&
((~old(mary)|~patient(mary)))&
(~patient(susan)) | brave(john) | [
"p0",
"p8",
"p11",
"p13",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 4085022253593966009682394
% SZS output start Proof for 4085022253593966009682394
1. ! [X0] : (quiet(X0) <=> (rich(X0) & calm(X0))) [input p0]
9. ! [X0] : ((humble(X0) | rich(X0)) <=> calm(X0)) [input p8]
12. ! [X0] : ((calm(X0) | creative(X0)) <=> (~rich(X0) | funny(X0))) [input p11]
14. ! [X0] : ((brave(X0) <~> ~quiet(X0)) <=> (~funny(X0) | humble(X0))) [input p13]
19. brave(john) <~> funny(john) [input p18]
25. brave(john) [input hypothesis]
38. ! [X0] : ((quiet(X0) | (~rich(X0) | ~calm(X0))) & ((rich(X0) & calm(X0)) | ~quiet(X0))) [nnf transformation 1]
39. ! [X0] : ((quiet(X0) | ~rich(X0) | ~calm(X0)) & ((rich(X0) & calm(X0)) | ~quiet(X0))) [flattening 38]
57. ! [X0] : (((humble(X0) | rich(X0)) | ~calm(X0)) & (calm(X0) | (~humble(X0) & ~rich(X0)))) [nnf transformation 9]
58. ! [X0] : ((humble(X0) | rich(X0) | ~calm(X0)) & (calm(X0) | (~humble(X0) & ~rich(X0)))) [flattening 57]
69. ! [X0] : (((calm(X0) | creative(X0)) | (rich(X0) & ~funny(X0))) & ((~rich(X0) | funny(X0)) | (~calm(X0) & ~creative(X0)))) [nnf transformation 12]
70. ! [X0] : ((calm(X0) | creative(X0) | (rich(X0) & ~funny(X0))) & (~rich(X0) | funny(X0) | (~calm(X0) & ~creative(X0)))) [flattening 69]
71. ! [X0] : ((((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | (funny(X0) & ~humble(X0))) & ((~funny(X0) | humble(X0)) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0))))) [nnf transformation 14]
72. ! [X0] : ((((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | (funny(X0) & ~humble(X0))) & (~funny(X0) | humble(X0) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0))))) [flattening 71]
75. (~funny(john) | ~brave(john)) & (funny(john) | brave(john)) [nnf transformation 19]
81. ~quiet(X0) | rich(X0) [cnf transformation 39]
110. ~rich(X0) | calm(X0) [cnf transformation 58]
122. ~rich(X0) | funny(X0) | ~calm(X0) [cnf transformation 70]
131. ~brave(X0) | quiet(X0) | funny(X0) [cnf transformation 72]
139. ~funny(john) | ~brave(john) [cnf transformation 75]
148. brave(john) [cnf transformation 25]
159. 3 <=> rich(john) [avatar definition]
160. rich(john) <- (3) [avatar component clause 159]
161. ~rich(john) <- (~3) [avatar component clause 159]
288. ~rich(X0) | funny(X0) [subsumption resolution 122,110]
292. 30 <=> brave(john) [avatar definition]
293. brave(john) <- (30) [avatar component clause 292]
296. 31 <=> funny(john) [avatar definition]
298. ~funny(john) <- (~31) [avatar component clause 296]
299. ~30 | ~31 [avatar split clause 139,296,292]
329. 30 [avatar split clause 148,292]
353. funny(john) <- (3) [resolution 288,160]
358. $false <- (3, ~31) [subsumption resolution 353,298]
359. ~3 | 31 [avatar contradiction clause 358]
404. quiet(john) | funny(john) <- (30) [resolution 131,293]
406. quiet(john) <- (30, ~31) [subsumption resolution 404,298]
408. rich(john) <- (30, ~31) [resolution 406,81]
410. $false <- (~3, 30, ~31) [subsumption resolution 408,161]
411. 3 | ~30 | 31 [avatar contradiction clause 410]
412. $false [avatar sat refutation 299,329,359,411]
% SZS output end Proof for 4085022253593966009682394
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not strong is either wise or patient and vice versa. If lucy is both brave and funny then someone is humble or not generous. If lucy is either wise or rich then someone is both not humble and not happy and vice versa. If alice is both kind and tall then lucy is not kind or not old and vice versa. Everyone who is either not brave or not old is not kind or not old. If lucy is both happy and not brave then someone is both not brave and not rich and vice versa. If someone is both calm and rich then someone is either creative or patient and vice versa. Everyone who is not quiet or not tall is not curious. Everyone who is brave is either not patient or not wise and vice versa. Everyone who is either generous or patient is either not quiet or not patient and vice versa. Everyone who is either kind or not creative is not funny or not wise. Everyone who is both not rich and curious is either not kind or quiet and vice versa. Everyone who is calm is both not rich and not old. Everyone who is strong is not rich or not funny and vice versa. Everyone who is both humble and not humble is funny or creative and vice versa. Everyone who is not quiet is either wise or tall. Someone is either not happy or not strong. Paul is both not creative and not quiet. Lucy is not rich or not calm. Mary is strong. Lucy is not calm or not kind. | Lucy is old. | neutral | (![X]:((funny(X)|~strong(X))<=>(wise(X)<~>patient(X))))&
(((brave(lucy)&funny(lucy)))=>(?[X]:((humble(X)|~generous(X)))))&
(((wise(lucy)<~>rich(lucy)))<=>(?[X]:((~humble(X)&~happy(X)))))&
(((kind(alice)&tall(alice)))<=>((~kind(lucy)|~old(lucy))))&
(![X]:((~brave(X)<~>~old(X))=>(~kind(X)|~old(X))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~brave(X)&~rich(X)))))&
((?[X]:((calm(X)&rich(X))))<=>(?[X]:((creative(X)<~>patient(X)))))&
(![X]:((~quiet(X)|~tall(X))=>~curious(X)))&
(![X]:(brave(X)<=>(~patient(X)<~>~wise(X))))&
(![X]:((generous(X)<~>patient(X))<=>(~quiet(X)<~>~patient(X))))&
(![X]:((kind(X)<~>~creative(X))=>(~funny(X)|~wise(X))))&
(![X]:((~rich(X)&curious(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:(calm(X)=>(~rich(X)&~old(X))))&
(![X]:(strong(X)<=>(~rich(X)|~funny(X))))&
(![X]:((humble(X)&~humble(X))<=>(funny(X)|creative(X))))&
(![X]:(~quiet(X)=>(wise(X)<~>tall(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
((~creative(paul)&~quiet(paul)))&
((~rich(lucy)|~calm(lucy)))&
(strong(mary))&
((~calm(lucy)|~kind(lucy))) | old(lucy) | []
| null | 0 |
If someone is both not generous and not tall then someone is either not strong or rich.
Everyone who is strong is both brave and not rich.
Everyone who is not rich or strong is not humble and vice versa.
Everyone who is patient is both not kind and generous.
Everyone who is both strong and not calm is either not wise or not humble.
Everyone who is either not brave or not wise is both not patient and not humble.
Everyone who is happy or quiet is not rich or not wise.
Everyone who is not patient or generous is both not quiet and curious.
If susan is either tall or strong then fred is either not rich or not kind.
Everyone who is not calm or not patient is generous or curious and vice versa.
If alice is either creative or generous then someone is not old.
Everyone who is strong or not kind is both not happy and not wise and vice versa.
Everyone who is not calm or not wise is both tall and not curious.
Everyone who is quiet is not generous or patient.
If someone is either humble or tall then someone is old.
Someone is curious.
Someone is patient or tall.
Fred is either strong or not brave.
Lucy is not happy. | Alice is not kind. | contradiction | ((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~strong(X)<~>rich(X)))))&
(![X]:(strong(X)=>(brave(X)&~rich(X))))&
(![X]:((~rich(X)|strong(X))<=>~humble(X)))&
(![X]:(patient(X)=>(~kind(X)&generous(X))))&
(![X]:((strong(X)&~calm(X))=>(~wise(X)<~>~humble(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~patient(X)&~humble(X))))&
(![X]:((happy(X)|quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((~patient(X)|generous(X))=>(~quiet(X)&curious(X))))&
(((tall(susan)<~>strong(susan)))=>((~rich(fred)<~>~kind(fred))))&
(![X]:((~calm(X)|~patient(X))<=>(generous(X)|curious(X))))&
(((creative(alice)<~>generous(alice)))=>(?[X]:(~old(X))))&
(![X]:((strong(X)|~kind(X))<=>(~happy(X)&~wise(X))))&
(![X]:((~calm(X)|~wise(X))=>(tall(X)&~curious(X))))&
(![X]:(quiet(X)=>(~generous(X)|patient(X))))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:(old(X))))&
(?[X]:(curious(X)))&
(?[X]:((patient(X)|tall(X))))&
((strong(fred)<~>~brave(fred)))&
(~happy(lucy)) | ~kind(alice) | [
"p3",
"p7",
"p9",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 5861249521973388434926066
% SZS output start Proof for 5861249521973388434926066
4. ! [X0] : (patient(X0) => (generous(X0) & ~kind(X0))) [input p3]
8. ! [X0] : ((generous(X0) | ~patient(X0)) => (curious(X0) & ~quiet(X0))) [input p7]
10. ! [X0] : ((~patient(X0) | ~calm(X0)) <=> (curious(X0) | generous(X0))) [input p9]
12. ! [X0] : ((~kind(X0) | strong(X0)) <=> (~wise(X0) & ~happy(X0))) [input p11]
13. ! [X0] : ((~wise(X0) | ~calm(X0)) => (~curious(X0) & tall(X0))) [input p12]
20. ~kind(alice) [input hypothesis]
23. ! [X0] : ((generous(X0) | ~patient(X0)) => curious(X0)) [pure predicate removal 8]
28. ! [X0] : ((generous(X0) & ~kind(X0)) | ~patient(X0)) [ennf transformation 4]
34. ! [X0] : (curious(X0) | (~generous(X0) & patient(X0))) [ennf transformation 23]
37. ! [X0] : ((~curious(X0) & tall(X0)) | (wise(X0) & calm(X0))) [ennf transformation 13]
48. ! [X0] : (((~patient(X0) | ~calm(X0)) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | (patient(X0) & calm(X0)))) [nnf transformation 10]
49. ! [X0] : ((~patient(X0) | ~calm(X0) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | (patient(X0) & calm(X0)))) [flattening 48]
53. ! [X0] : (((~kind(X0) | strong(X0)) | (wise(X0) | happy(X0))) & ((~wise(X0) & ~happy(X0)) | (kind(X0) & ~strong(X0)))) [nnf transformation 12]
54. ! [X0] : ((~kind(X0) | strong(X0) | wise(X0) | happy(X0)) & ((~wise(X0) & ~happy(X0)) | (kind(X0) & ~strong(X0)))) [flattening 53]
72. ~patient(X0) | generous(X0) [cnf transformation 28]
80. curious(X0) | patient(X0) [cnf transformation 34]
81. ~generous(X0) | curious(X0) [cnf transformation 34]
86. curious(X0) | generous(X0) | calm(X0) [cnf transformation 49]
88. ~patient(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 49]
95. ~wise(X0) | kind(X0) [cnf transformation 54]
99. ~curious(X0) | calm(X0) [cnf transformation 37]
100. ~curious(X0) | wise(X0) [cnf transformation 37]
108. ~kind(alice) [cnf transformation 20]
144. ~calm(X0) | ~patient(X0) [subsumption resolution 88,72]
145. curious(X0) | calm(X0) [subsumption resolution 86,81]
160. calm(X0) [subsumption resolution 99,145]
196. wise(X0) | patient(X0) [resolution 100,80]
201. ~patient(X0) [resolution 144,160]
222. patient(X2) | kind(X2) [resolution 196,95]
225. kind(X2) [subsumption resolution 222,201]
230. $false [resolution 225,108]
% SZS output end Proof for 5861249521973388434926066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is kind or not creative then fred is either not kind or not generous and vice versa.
Everyone who is not old is patient.
Everyone who is both generous and patient is strong or not quiet and vice versa.
If someone is both humble and patient then someone is both not patient and not brave and vice versa.
If john is both tall and rich then someone is creative.
If susan is not humble then someone is both not humble and not wise.
Everyone who is strong or generous is not happy.
Everyone who is not patient or not old is either not rich or not creative and vice versa.
If alice is strong then mary is brave.
If someone is humble then fred is both not old and not generous and vice versa.
Everyone who is either not quiet or tall is either not curious or kind.
Everyone who is either not humble or wise is funny and vice versa.
Everyone who is not wise or not rich is both not quiet and old and vice versa.
If mary is either not happy or not rich then someone is either funny or not happy.
Everyone who is quiet is both old and not humble.
Everyone who is both creative and funny is brave or calm and vice versa.
Someone is old or kind.
Fred is either not creative or not kind.
Someone is not strong.
Fred is not brave.
Someone is either rich or not tall.
Mary is not creative. | Fred is not tall. | neutral | (((kind(paul)|~creative(paul)))<=>((~kind(fred)<~>~generous(fred))))&
(![X]:(~old(X)=>patient(X)))&
(![X]:((generous(X)&patient(X))<=>(strong(X)|~quiet(X))))&
((?[X]:((humble(X)&patient(X))))<=>(?[X]:((~patient(X)&~brave(X)))))&
(((tall(john)&rich(john)))=>(?[X]:(creative(X))))&
((~humble(susan))=>(?[X]:((~humble(X)&~wise(X)))))&
(![X]:((strong(X)|generous(X))=>~happy(X)))&
(![X]:((~patient(X)|~old(X))<=>(~rich(X)<~>~creative(X))))&
((strong(alice))=>(brave(mary)))&
((?[X]:(humble(X)))<=>((~old(fred)&~generous(fred))))&
(![X]:((~quiet(X)<~>tall(X))=>(~curious(X)<~>kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>funny(X)))&
(![X]:((~wise(X)|~rich(X))<=>(~quiet(X)&old(X))))&
(((~happy(mary)<~>~rich(mary)))=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:(quiet(X)=>(old(X)&~humble(X))))&
(![X]:((creative(X)&funny(X))<=>(brave(X)|calm(X))))&
(?[X]:((old(X)|kind(X))))&
((~creative(fred)<~>~kind(fred)))&
(?[X]:(~strong(X)))&
(~brave(fred))&
(?[X]:((rich(X)<~>~tall(X))))&
(~creative(mary)) | ~tall(fred) | []
| null | 0 |
If someone is both happy and strong then fred is both not curious and not tall and vice versa.
Everyone who is quiet or rich is not calm and vice versa.
If someone is not happy or not creative then paul is both curious and not calm.
Everyone who is kind is patient.
Everyone who is both rich and not curious is not tall and vice versa.
If someone is both tall and not tall then paul is not patient and vice versa.
Everyone who is either patient or old is happy or funny and vice versa.
If alice is both not quiet and not calm then john is humble or tall and vice versa.
Everyone who is both generous and not wise is humble and vice versa.
If someone is brave then susan is both quiet and curious.
Everyone who is both not patient and funny is both not patient and curious and vice versa.
Everyone who is either not kind or not curious is not strong and vice versa.
If someone is humble then paul is both kind and not strong and vice versa.
Everyone who is rich is not kind or not quiet.
If someone is either not quiet or not creative then mary is either tall or wise.
If someone is both not old and not humble then fred is not patient or humble and vice versa.
Lucy is not strong.
Someone is both wise and happy.
Lucy is kind.
Mary is not humble.
Someone is both calm and happy.
Someone is either not rich or not humble.
Someone is both old and not strong.
Someone is strong. | Lucy is generous. | neutral | ((?[X]:((happy(X)&strong(X))))<=>((~curious(fred)&~tall(fred))))&
(![X]:((quiet(X)|rich(X))<=>~calm(X)))&
((?[X]:((~happy(X)|~creative(X))))=>((curious(paul)&~calm(paul))))&
(![X]:(kind(X)=>patient(X)))&
(![X]:((rich(X)&~curious(X))<=>~tall(X)))&
((?[X]:((tall(X)&~tall(X))))<=>(~patient(paul)))&
(![X]:((patient(X)<~>old(X))<=>(happy(X)|funny(X))))&
(((~quiet(alice)&~calm(alice)))<=>((humble(john)|tall(john))))&
(![X]:((generous(X)&~wise(X))<=>humble(X)))&
((?[X]:(brave(X)))=>((quiet(susan)&curious(susan))))&
(![X]:((~patient(X)&funny(X))<=>(~patient(X)&curious(X))))&
(![X]:((~kind(X)<~>~curious(X))<=>~strong(X)))&
((?[X]:(humble(X)))<=>((kind(paul)&~strong(paul))))&
(![X]:(rich(X)=>(~kind(X)|~quiet(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))=>((tall(mary)<~>wise(mary))))&
((?[X]:((~old(X)&~humble(X))))<=>((~patient(fred)|humble(fred))))&
(~strong(lucy))&
(?[X]:((wise(X)&happy(X))))&
(kind(lucy))&
(~humble(mary))&
(?[X]:((calm(X)&happy(X))))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:((old(X)&~strong(X))))&
(?[X]:(strong(X))) | generous(lucy) | []
| null | 0 |
Everyone who is both not funny and creative is either strong or not wise and vice versa. If someone is either not strong or calm then fred is not brave and vice versa. Everyone who is rich or not calm is either not humble or humble and vice versa. Everyone who is not rich or not happy is brave. Everyone who is both curious and brave is calm or not happy. If fred is either not patient or not kind then someone is tall and vice versa. Everyone who is calm is rich and vice versa. If lucy is both brave and not curious then mary is both not brave and patient. Everyone who is creative or not calm is old or rich and vice versa. If someone is not generous or not wise then someone is rich or not kind. If paul is curious or happy then someone is either not rich or not happy and vice versa. If someone is creative then alice is old or calm. Everyone who is either not patient or not old is patient and vice versa. If someone is either not old or calm then fred is both funny and not generous and vice versa. If paul is not curious then someone is either not quiet or not old. If alice is not kind then someone is both not kind and not creative and vice versa. Mary is not tall. Susan is not curious or curious. Paul is not wise or not strong. Lucy is creative or not happy. Someone is not rich or not kind. Someone is either happy or not quiet. Someone is both curious and humble. | Susan is not rich. | contradiction | (![X]:((~funny(X)&creative(X))<=>(strong(X)<~>~wise(X))))&
((?[X]:((~strong(X)<~>calm(X))))<=>(~brave(fred)))&
(![X]:((rich(X)|~calm(X))<=>(~humble(X)<~>humble(X))))&
(![X]:((~rich(X)|~happy(X))=>brave(X)))&
(![X]:((curious(X)&brave(X))=>(calm(X)|~happy(X))))&
(((~patient(fred)<~>~kind(fred)))<=>(?[X]:(tall(X))))&
(![X]:(calm(X)<=>rich(X)))&
(((brave(lucy)&~curious(lucy)))=>((~brave(mary)&patient(mary))))&
(![X]:((creative(X)|~calm(X))<=>(old(X)|rich(X))))&
((?[X]:((~generous(X)|~wise(X))))=>(?[X]:((rich(X)|~kind(X)))))&
(((curious(paul)|happy(paul)))<=>(?[X]:((~rich(X)<~>~happy(X)))))&
((?[X]:(creative(X)))=>((old(alice)|calm(alice))))&
(![X]:((~patient(X)<~>~old(X))<=>patient(X)))&
((?[X]:((~old(X)<~>calm(X))))<=>((funny(fred)&~generous(fred))))&
((~curious(paul))=>(?[X]:((~quiet(X)<~>~old(X)))))&
((~kind(alice))<=>(?[X]:((~kind(X)&~creative(X)))))&
(~tall(mary))&
((~curious(susan)|curious(susan)))&
((~wise(paul)|~strong(paul)))&
((creative(lucy)|~happy(lucy)))&
(?[X]:((~rich(X)|~kind(X))))&
(?[X]:((happy(X)<~>~quiet(X))))&
(?[X]:((curious(X)&humble(X)))) | ~rich(susan) | [
"p2",
"p6",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 4055114174141912845950464
% SZS output start Proof for 4055114174141912845950464
3. ! [X0] : ((~calm(X0) | rich(X0)) <=> (~humble(X0) <~> humble(X0))) [input p2]
7. ! [X0] : (calm(X0) <=> rich(X0)) [input p6]
9. ! [X0] : ((~calm(X0) | creative(X0)) <=> (rich(X0) | old(X0))) [input p8]
13. ! [X0] : ((~patient(X0) <~> ~old(X0)) <=> patient(X0)) [input p12]
24. ~rich(susan) [input hypothesis]
41. ! [X0] : (((~calm(X0) | rich(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (calm(X0) & ~rich(X0)))) [nnf transformation 3]
42. ! [X0] : ((~calm(X0) | rich(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (calm(X0) & ~rich(X0)))) [flattening 41]
47. ! [X0] : ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0))) [nnf transformation 7]
48. ! [X0] : (((~calm(X0) | creative(X0)) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 9]
49. ! [X0] : ((~calm(X0) | creative(X0) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | (calm(X0) & ~creative(X0)))) [flattening 48]
58. ! [X0] : ((((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0))))) [nnf transformation 13]
92. ~calm(X0) | rich(X0) | humble(X0) | humble(X0) [cnf transformation 42]
93. ~calm(X0) | rich(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 42]
102. ~rich(X0) | calm(X0) [cnf transformation 47]
106. rich(X0) | old(X0) | calm(X0) [cnf transformation 49]
118. patient(X0) | ~old(X0) | patient(X0) [cnf transformation 58]
120. ~old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 58]
142. ~rich(susan) [cnf transformation 24]
143. patient(X0) | ~old(X0) [duplicate literal removal 118]
144. ~old(X0) | ~patient(X0) [duplicate literal removal 120]
145. ~calm(X0) | rich(X0) | humble(X0) [duplicate literal removal 92]
146. ~calm(X0) | rich(X0) | ~humble(X0) [duplicate literal removal 93]
169. ~calm(X0) | rich(X0) [subsumption resolution 145,146]
208. old(X0) | calm(X0) [subsumption resolution 106,102]
253. ~old(X0) [subsumption resolution 143,144]
343. calm(X1) [resolution 208,253]
347. rich(X0) [resolution 343,169]
350. $false [resolution 347,142]
% SZS output end Proof for 4055114174141912845950464
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not old or not quiet then someone is both not wise and not humble and vice versa. Everyone who is rich or not kind is either calm or not quiet and vice versa. Everyone who is creative is either not humble or rich and vice versa. Everyone who is either not kind or not brave is both rich and not wise. If someone is old or kind then someone is either funny or creative and vice versa. If someone is not funny then someone is either creative or curious. Everyone who is not curious is either not rich or humble and vice versa. Everyone who is both calm and not quiet is both happy and not kind. Everyone who is both humble and happy is not quiet or tall and vice versa. If someone is both tall and not rich then someone is rich or quiet. If alice is kind then someone is both not wise and not creative and vice versa. Everyone who is calm is not kind or patient and vice versa. Everyone who is wise or not old is not kind or creative and vice versa. If alice is both calm and patient then someone is either brave or not calm. If paul is creative or not brave then someone is either not curious or not quiet. Everyone who is happy or funny is either not brave or rich. Fred is not patient. John is either not patient or rich. Someone is tall or wise. Alice is both not funny and not curious. Someone is creative or not curious. Alice is not strong. Susan is not wise or kind. John is both calm and tall. | Alice is not creative. | contradiction | (((~old(mary)|~quiet(mary)))<=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((rich(X)|~kind(X))<=>(calm(X)<~>~quiet(X))))&
(![X]:(creative(X)<=>(~humble(X)<~>rich(X))))&
(![X]:((~kind(X)<~>~brave(X))=>(rich(X)&~wise(X))))&
((?[X]:((old(X)|kind(X))))<=>(?[X]:((funny(X)<~>creative(X)))))&
((?[X]:(~funny(X)))=>(?[X]:((creative(X)<~>curious(X)))))&
(![X]:(~curious(X)<=>(~rich(X)<~>humble(X))))&
(![X]:((calm(X)&~quiet(X))=>(happy(X)&~kind(X))))&
(![X]:((humble(X)&happy(X))<=>(~quiet(X)|tall(X))))&
((?[X]:((tall(X)&~rich(X))))=>(?[X]:((rich(X)|quiet(X)))))&
((kind(alice))<=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:(calm(X)<=>(~kind(X)|patient(X))))&
(![X]:((wise(X)|~old(X))<=>(~kind(X)|creative(X))))&
(((calm(alice)&patient(alice)))=>(?[X]:((brave(X)<~>~calm(X)))))&
(((creative(paul)|~brave(paul)))=>(?[X]:((~curious(X)<~>~quiet(X)))))&
(![X]:((happy(X)|funny(X))=>(~brave(X)<~>rich(X))))&
(~patient(fred))&
((~patient(john)<~>rich(john)))&
(?[X]:((tall(X)|wise(X))))&
((~funny(alice)&~curious(alice)))&
(?[X]:((creative(X)|~curious(X))))&
(~strong(alice))&
((~wise(susan)|kind(susan)))&
((calm(john)&tall(john))) | ~creative(alice) | [
"p2",
"p6",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 441272570604315610347371
% SZS output start Proof for 441272570604315610347371
3. ! [X0] : (creative(X0) <=> (~humble(X0) <~> rich(X0))) [input p2]
7. ! [X0] : (~curious(X0) <=> (~rich(X0) <~> humble(X0))) [input p6]
20. ~curious(alice) & ~funny(alice) [input p19]
25. ~creative(alice) [input hypothesis]
46. ! [X0] : ((creative(X0) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | ~creative(X0))) [nnf transformation 3]
57. ! [X0] : ((~curious(X0) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) & (((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | curious(X0))) [nnf transformation 7]
96. creative(X0) | rich(X0) | humble(X0) [cnf transformation 46]
97. ~rich(X0) | ~humble(X0) | creative(X0) [cnf transformation 46]
110. ~rich(X0) | humble(X0) | curious(X0) [cnf transformation 57]
111. ~humble(X0) | rich(X0) | curious(X0) [cnf transformation 57]
147. ~curious(alice) [cnf transformation 20]
152. ~creative(alice) [cnf transformation 25]
376. rich(alice) | humble(alice) [resolution 96,152]
382. 42 <=> humble(alice) [avatar definition]
384. humble(alice) <- (42) [avatar component clause 382]
386. 43 <=> rich(alice) [avatar definition]
388. rich(alice) <- (43) [avatar component clause 386]
389. 42 | 43 [avatar split clause 376,386,382]
441. rich(alice) | curious(alice) <- (42) [resolution 111,384]
444. rich(alice) <- (42) [subsumption resolution 441,147]
445. 43 | ~42 [avatar split clause 444,382,386]
456. humble(alice) | curious(alice) <- (43) [resolution 388,110]
457. ~humble(alice) | creative(alice) <- (43) [resolution 388,97]
463. ~humble(alice) <- (43) [subsumption resolution 457,152]
464. ~42 | ~43 [avatar split clause 463,386,382]
465. humble(alice) <- (43) [subsumption resolution 456,147]
466. 42 | ~43 [avatar split clause 465,386,382]
467. $false [avatar sat refutation 389,445,464,466]
% SZS output end Proof for 441272570604315610347371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and not old then someone is patient.
Everyone who is both not kind and funny is rich and vice versa.
If mary is curious then paul is either not tall or brave.
Everyone who is either kind or not creative is either funny or curious and vice versa.
Everyone who is either not funny or not old is either quiet or happy.
Everyone who is not wise is rich or not strong.
Everyone who is not happy or strong is not happy or happy and vice versa.
Everyone who is quiet is patient.
If alice is not happy or not calm then alice is kind or wise and vice versa.
If someone is not funny or not happy then alice is not calm or humble and vice versa.
If someone is rich or creative then john is either not humble or not happy and vice versa.
Everyone who is both not wise and brave is rich and vice versa.
Everyone who is not funny or not curious is both old and funny.
Everyone who is not creative or kind is brave.
If fred is either generous or not patient then paul is not humble and vice versa.
If fred is either wise or creative then susan is both not curious and not funny.
Someone is quiet.
Fred is either not humble or humble.
Someone is both not quiet and generous.
Alice is not curious.
Alice is not kind.
Mary is both not quiet and not patient.
Someone is brave.
Paul is humble or not creative. | Fred is not curious. | entailment | ((?[X]:((~humble(X)&~old(X))))=>(?[X]:(patient(X))))&
(![X]:((~kind(X)&funny(X))<=>rich(X)))&
((curious(mary))=>((~tall(paul)<~>brave(paul))))&
(![X]:((kind(X)<~>~creative(X))<=>(funny(X)<~>curious(X))))&
(![X]:((~funny(X)<~>~old(X))=>(quiet(X)<~>happy(X))))&
(![X]:(~wise(X)=>(rich(X)|~strong(X))))&
(![X]:((~happy(X)|strong(X))<=>(~happy(X)|happy(X))))&
(![X]:(quiet(X)=>patient(X)))&
(((~happy(alice)|~calm(alice)))<=>((kind(alice)|wise(alice))))&
((?[X]:((~funny(X)|~happy(X))))<=>((~calm(alice)|humble(alice))))&
((?[X]:((rich(X)|creative(X))))<=>((~humble(john)<~>~happy(john))))&
(![X]:((~wise(X)&brave(X))<=>rich(X)))&
(![X]:((~funny(X)|~curious(X))=>(old(X)&funny(X))))&
(![X]:((~creative(X)|kind(X))=>brave(X)))&
(((generous(fred)<~>~patient(fred)))<=>(~humble(paul)))&
(((wise(fred)<~>creative(fred)))=>((~curious(susan)&~funny(susan))))&
(?[X]:(quiet(X)))&
((~humble(fred)<~>humble(fred)))&
(?[X]:((~quiet(X)&generous(X))))&
(~curious(alice))&
(~kind(alice))&
((~quiet(mary)&~patient(mary)))&
(?[X]:(brave(X)))&
((humble(paul)|~creative(paul))) | ~curious(fred) | [
"p1",
"p3",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 2317639773213097102336962
% SZS output start Proof for 2317639773213097102336962
2. ! [X0] : ((funny(X0) & ~kind(X0)) <=> rich(X0)) [input p1]
4. ! [X0] : ((kind(X0) <~> ~creative(X0)) <=> (funny(X0) <~> curious(X0))) [input p3]
12. ! [X0] : ((brave(X0) & ~wise(X0)) <=> rich(X0)) [input p11]
13. ! [X0] : ((~curious(X0) | ~funny(X0)) => (funny(X0) & old(X0))) [input p12]
14. ! [X0] : ((kind(X0) | ~creative(X0)) => brave(X0)) [input p13]
16. (wise(fred) <~> creative(fred)) => (~funny(susan) & ~curious(susan)) [input p15]
25. curious(fred) [input hypothesis]
33. ! [X0] : ((funny(X0) & old(X0)) | (curious(X0) & funny(X0))) [ennf transformation 13]
34. ! [X0] : (brave(X0) | (~kind(X0) & creative(X0))) [ennf transformation 14]
35. (~funny(susan) & ~curious(susan)) | (wise(fred) <=> creative(fred)) [ennf transformation 16]
39. ! [X0] : (((funny(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | (~funny(X0) | kind(X0)))) [nnf transformation 2]
40. ! [X0] : (((funny(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | ~funny(X0) | kind(X0))) [flattening 39]
42. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0)))) & (((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [nnf transformation 4]
57. ! [X0] : (((brave(X0) & ~wise(X0)) | ~rich(X0)) & (rich(X0) | (~brave(X0) | wise(X0)))) [nnf transformation 12]
58. ! [X0] : (((brave(X0) & ~wise(X0)) | ~rich(X0)) & (rich(X0) | ~brave(X0) | wise(X0))) [flattening 57]
60. (~funny(susan) & ~curious(susan)) | ((wise(fred) | ~creative(fred)) & (creative(fred) | ~wise(fred))) [nnf transformation 35]
69. ~funny(X0) | rich(X0) | kind(X0) [cnf transformation 40]
70. ~rich(X0) | ~kind(X0) [cnf transformation 40]
76. ~creative(X0) | ~funny(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 42]
77. ~curious(X0) | ~funny(X0) | kind(X0) | creative(X0) [cnf transformation 42]
106. ~brave(X0) | rich(X0) | wise(X0) [cnf transformation 58]
107. ~wise(X0) | ~rich(X0) [cnf transformation 58]
111. funny(X0) | funny(X0) [cnf transformation 33]
113. creative(X0) | brave(X0) [cnf transformation 34]
121. ~funny(susan) | creative(fred) | ~wise(fred) [cnf transformation 60]
122. ~funny(susan) | wise(fred) | ~creative(fred) [cnf transformation 60]
134. curious(fred) [cnf transformation 25]
135. funny(X0) [duplicate literal removal 111]
199. 14 <=> ! [X1] : funny(X1) [avatar definition]
200. funny(X1) <- (14) [avatar component clause 199]
230. 14 [avatar split clause 135,199]
248. 24 <=> creative(fred) [avatar definition]
249. creative(fred) <- (24) [avatar component clause 248]
250. ~creative(fred) <- (~24) [avatar component clause 248]
252. 25 <=> wise(fred) [avatar definition]
253. ~wise(fred) <- (~25) [avatar component clause 252]
254. wise(fred) <- (25) [avatar component clause 252]
256. 26 <=> funny(susan) [avatar definition]
258. ~funny(susan) <- (~26) [avatar component clause 256]
259. ~24 | 25 | ~26 [avatar split clause 122,256,252,248]
260. ~25 | 24 | ~26 [avatar split clause 121,256,248,252]
275. $false <- (14, ~26) [resolution 258,200]
276. ~14 | 26 [avatar contradiction clause 275]
288. brave(fred) <- (~24) [resolution 113,250]
293. rich(X1) | kind(X1) <- (14) [resolution 69,200]
305. rich(fred) | wise(fred) <- (~24) [resolution 106,288]
317. rich(fred) <- (~24, ~25) [subsumption resolution 305,253]
341. ~funny(fred) | kind(fred) | creative(fred) [resolution 77,134]
344. kind(fred) | creative(fred) <- (14) [subsumption resolution 341,200]
345. kind(fred) <- (14, ~24) [subsumption resolution 344,250]
358. ~kind(fred) <- (~24, ~25) [resolution 317,70]
359. $false <- (14, ~24, ~25) [subsumption resolution 358,345]
360. ~14 | 24 | 25 [avatar contradiction clause 359]
362. 35 <=> kind(fred) [avatar definition]
363. ~kind(fred) <- (~35) [avatar component clause 362]
365. 24 | 35 | ~14 [avatar split clause 344,199,362,248]
368. ~funny(fred) | ~curious(fred) | ~kind(fred) <- (24) [resolution 249,76]
370. ~curious(fred) | ~kind(fred) <- (14, 24) [subsumption resolution 368,200]
371. ~kind(fred) <- (14, 24) [subsumption resolution 370,134]
372. ~35 | ~14 | ~24 [avatar split clause 371,248,199,362]
373. ~rich(fred) <- (25) [resolution 254,107]
392. kind(fred) <- (14, 25) [resolution 293,373]
396. $false <- (14, 25, ~35) [subsumption resolution 392,363]
397. ~14 | ~25 | 35 [avatar contradiction clause 396]
398. $false [avatar sat refutation 230,259,260,276,360,365,372,397]
% SZS output end Proof for 2317639773213097102336962
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not curious is not humble or not creative.
If lucy is both creative and patient then someone is patient or not tall and vice versa.
If someone is both not funny and creative then someone is brave.
If someone is both not kind and not strong then fred is not generous and vice versa.
If john is either wise or creative then john is either wise or funny.
Everyone who is not wise or not old is not brave and vice versa.
Everyone who is either not kind or wise is not calm or old and vice versa.
Everyone who is both not creative and not curious is not happy or kind and vice versa.
If john is both curious and not funny then alice is wise and vice versa.
If someone is humble then someone is not quiet.
If someone is either not creative or not curious then alice is not quiet or calm.
Everyone who is not creative or generous is creative.
If someone is either not calm or not brave then fred is either not patient or not humble and vice versa.
Everyone who is generous is not funny or generous.
If someone is either quiet or not patient then someone is not happy and vice versa.
Everyone who is wise or not funny is generous or happy.
Someone is patient or kind.
Mary is not strong.
Someone is not strong.
Someone is either funny or not wise.
Someone is either not tall or not creative.
Someone is not curious. | Lucy is not curious. | neutral | (![X]:((brave(X)&~curious(X))=>(~humble(X)|~creative(X))))&
(((creative(lucy)&patient(lucy)))<=>(?[X]:((patient(X)|~tall(X)))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:(brave(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(~generous(fred)))&
(((wise(john)<~>creative(john)))=>((wise(john)<~>funny(john))))&
(![X]:((~wise(X)|~old(X))<=>~brave(X)))&
(![X]:((~kind(X)<~>wise(X))<=>(~calm(X)|old(X))))&
(![X]:((~creative(X)&~curious(X))<=>(~happy(X)|kind(X))))&
(((curious(john)&~funny(john)))<=>(wise(alice)))&
((?[X]:(humble(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((~creative(X)<~>~curious(X))))=>((~quiet(alice)|calm(alice))))&
(![X]:((~creative(X)|generous(X))=>creative(X)))&
((?[X]:((~calm(X)<~>~brave(X))))<=>((~patient(fred)<~>~humble(fred))))&
(![X]:(generous(X)=>(~funny(X)|generous(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))=>(generous(X)|happy(X))))&
(?[X]:((patient(X)|kind(X))))&
(~strong(mary))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:(~curious(X))) | ~curious(lucy) | []
| null | 0 |
If someone is either not curious or not old then paul is both not patient and not brave and vice versa.
If alice is not brave or curious then someone is not strong and vice versa.
Everyone who is not tall is both not kind and brave.
Everyone who is either strong or patient is not tall or not kind and vice versa.
If someone is not curious or funny then fred is old or quiet and vice versa.
Everyone who is creative is curious or not tall and vice versa.
If someone is either humble or patient then john is either calm or old and vice versa.
Everyone who is both not quiet and brave is either not quiet or not kind and vice versa.
Everyone who is both quiet and tall is happy.
Everyone who is either old or creative is both not happy and old.
If mary is both tall and not wise then alice is humble.
Everyone who is funny or curious is creative or not wise.
Everyone who is not generous or humble is not brave and vice versa.
Everyone who is both not funny and not rich is rich and vice versa.
If john is old then someone is both wise and not rich and vice versa.
Everyone who is both not tall and quiet is kind and vice versa.
Someone is both old and not rich.
John is not kind or calm.
John is both not humble and not happy.
Someone is both not wise and not old.
Mary is calm.
Someone is old or humble.
Fred is either not calm or funny. | Alice is brave. | contradiction | ((?[X]:((~curious(X)<~>~old(X))))<=>((~patient(paul)&~brave(paul))))&
(((~brave(alice)|curious(alice)))<=>(?[X]:(~strong(X))))&
(![X]:(~tall(X)=>(~kind(X)&brave(X))))&
(![X]:((strong(X)<~>patient(X))<=>(~tall(X)|~kind(X))))&
((?[X]:((~curious(X)|funny(X))))<=>((old(fred)|quiet(fred))))&
(![X]:(creative(X)<=>(curious(X)|~tall(X))))&
((?[X]:((humble(X)<~>patient(X))))<=>((calm(john)<~>old(john))))&
(![X]:((~quiet(X)&brave(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:((quiet(X)&tall(X))=>happy(X)))&
(![X]:((old(X)<~>creative(X))=>(~happy(X)&old(X))))&
(((tall(mary)&~wise(mary)))=>(humble(alice)))&
(![X]:((funny(X)|curious(X))=>(creative(X)|~wise(X))))&
(![X]:((~generous(X)|humble(X))<=>~brave(X)))&
(![X]:((~funny(X)&~rich(X))<=>rich(X)))&
((old(john))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~tall(X)&quiet(X))<=>kind(X)))&
(?[X]:((old(X)&~rich(X))))&
((~kind(john)|calm(john)))&
((~humble(john)&~happy(john)))&
(?[X]:((~wise(X)&~old(X))))&
(calm(mary))&
(?[X]:((old(X)|humble(X))))&
((~calm(fred)<~>funny(fred))) | brave(alice) | [
"p2",
"p7",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 606338412740814153980808
% SZS output start Proof for 606338412740814153980808
3. ! [X0] : (~tall(X0) => (brave(X0) & ~kind(X0))) [input p2]
8. ! [X0] : ((brave(X0) & ~quiet(X0)) <=> (~quiet(X0) <~> ~kind(X0))) [input p7]
16. ! [X0] : ((quiet(X0) & ~tall(X0)) <=> kind(X0)) [input p15]
24. brave(alice) [input hypothesis]
25. ! [X0] : ((brave(X0) & ~kind(X0)) | tall(X0)) [ennf transformation 3]
56. ! [X0] : (((brave(X0) & ~quiet(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) & (((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (~brave(X0) | quiet(X0)))) [nnf transformation 8]
57. ! [X0] : (((brave(X0) & ~quiet(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) & (((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | ~brave(X0) | quiet(X0))) [flattening 56]
67. ! [X0] : (((quiet(X0) & ~tall(X0)) | ~kind(X0)) & (kind(X0) | (~quiet(X0) | tall(X0)))) [nnf transformation 16]
68. ! [X0] : (((quiet(X0) & ~tall(X0)) | ~kind(X0)) & (kind(X0) | ~quiet(X0) | tall(X0))) [flattening 67]
85. ~kind(X0) | tall(X0) [cnf transformation 25]
109. kind(X0) | quiet(X0) | ~brave(X0) | quiet(X0) [cnf transformation 57]
111. ~quiet(X0) | ~quiet(X0) | kind(X0) [cnf transformation 57]
132. ~tall(X0) | ~kind(X0) [cnf transformation 68]
145. brave(alice) [cnf transformation 24]
149. kind(X0) | quiet(X0) | ~brave(X0) [duplicate literal removal 109]
150. ~quiet(X0) | kind(X0) [duplicate literal removal 111]
183. 8 <=> brave(alice) [avatar definition]
184. brave(alice) <- (8) [avatar component clause 183]
255. ~brave(X0) | kind(X0) [subsumption resolution 149,150]
280. ~kind(X0) [subsumption resolution 132,85]
291. 8 [avatar split clause 145,183]
311. kind(alice) <- (8) [resolution 255,184]
314. $false <- (8) [subsumption resolution 311,280]
315. ~8 [avatar contradiction clause 314]
320. $false [avatar sat refutation 291,315]
% SZS output end Proof for 606338412740814153980808
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either rich or calm then susan is brave or patient. Everyone who is not old or patient is both not generous and old and vice versa. Everyone who is not quiet or not wise is both not kind and quiet and vice versa. Everyone who is either rich or happy is not strong and vice versa. If mary is wise or creative then fred is both curious and not curious and vice versa. Everyone who is not happy or kind is not creative or not happy and vice versa. If someone is not rich or happy then john is both not old and patient and vice versa. Everyone who is both humble and not happy is either not creative or brave and vice versa. Everyone who is both brave and tall is either not strong or kind. Everyone who is both curious and brave is not patient and vice versa. If someone is both calm and not old then john is rich or not brave. Everyone who is either curious or brave is not happy and vice versa. Everyone who is both wise and not old is either generous or not quiet and vice versa. Everyone who is strong is both patient and not generous. Everyone who is happy is either not creative or not curious. Everyone who is not calm is both old and brave. Someone is either quiet or not patient. Susan is not happy or not rich. Someone is both not calm and not funny. Lucy is not brave. Someone is either brave or not tall. Someone is not wise. | Fred is patient. | entailment | ((?[X]:((rich(X)<~>calm(X))))=>((brave(susan)|patient(susan))))&
(![X]:((~old(X)|patient(X))<=>(~generous(X)&old(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~kind(X)&quiet(X))))&
(![X]:((rich(X)<~>happy(X))<=>~strong(X)))&
(((wise(mary)|creative(mary)))<=>((curious(fred)&~curious(fred))))&
(![X]:((~happy(X)|kind(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((~old(john)&patient(john))))&
(![X]:((humble(X)&~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((brave(X)&tall(X))=>(~strong(X)<~>kind(X))))&
(![X]:((curious(X)&brave(X))<=>~patient(X)))&
((?[X]:((calm(X)&~old(X))))=>((rich(john)|~brave(john))))&
(![X]:((curious(X)<~>brave(X))<=>~happy(X)))&
(![X]:((wise(X)&~old(X))<=>(generous(X)<~>~quiet(X))))&
(![X]:(strong(X)=>(patient(X)&~generous(X))))&
(![X]:(happy(X)=>(~creative(X)<~>~curious(X))))&
(![X]:(~calm(X)=>(old(X)&brave(X))))&
(?[X]:((quiet(X)<~>~patient(X))))&
((~happy(susan)|~rich(susan)))&
(?[X]:((~calm(X)&~funny(X))))&
(~brave(lucy))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:(~wise(X))) | patient(fred) | [
"p1",
"p6",
"p9",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 8678030143160239935388302
% SZS output start Proof for 8678030143160239935388302
2. ! [X0] : ((patient(X0) | ~old(X0)) <=> (old(X0) & ~generous(X0))) [input p1]
7. ? [X0] : (happy(X0) | ~rich(X0)) <=> (patient(john) & ~old(john)) [input p6]
10. ! [X0] : ((brave(X0) & curious(X0)) <=> ~patient(X0)) [input p9]
12. ! [X0] : ((curious(X0) <~> brave(X0)) <=> ~happy(X0)) [input p11]
23. ~patient(fred) [input hypothesis]
35. ! [X0] : (((patient(X0) | ~old(X0)) | (~old(X0) | generous(X0))) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [nnf transformation 2]
36. ! [X0] : ((patient(X0) | ~old(X0) | ~old(X0) | generous(X0)) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [flattening 35]
44. (? [X0] : (happy(X0) | ~rich(X0)) | (~patient(john) | old(john))) & ((patient(john) & ~old(john)) | ! [X0] : (~happy(X0) & rich(X0))) [nnf transformation 7]
45. (? [X0] : (happy(X0) | ~rich(X0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X0] : (~happy(X0) & rich(X0))) [flattening 44]
46. (? [X0] : (happy(X0) | ~rich(X0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X1] : (~happy(X1) & rich(X1))) [rectify 45]
47. ? [X0] : (happy(X0) | ~rich(X0)) => (happy(sK0) | ~rich(sK0)) [choice axiom]
48. ((happy(sK0) | ~rich(sK0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X1] : (~happy(X1) & rich(X1))) [skolemisation 46,47]
52. ! [X0] : (((brave(X0) & curious(X0)) | patient(X0)) & (~patient(X0) | (~brave(X0) | ~curious(X0)))) [nnf transformation 10]
53. ! [X0] : (((brave(X0) & curious(X0)) | patient(X0)) & (~patient(X0) | ~brave(X0) | ~curious(X0))) [flattening 52]
54. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | happy(X0)) & (~happy(X0) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [nnf transformation 12]
72. old(X0) | old(X0) [cnf transformation 36]
94. ~old(john) | ~happy(X1) [cnf transformation 48]
107. curious(X0) | patient(X0) [cnf transformation 53]
108. patient(X0) | brave(X0) [cnf transformation 53]
113. ~curious(X0) | ~brave(X0) | happy(X0) [cnf transformation 54]
134. ~patient(fred) [cnf transformation 23]
137. old(X0) [duplicate literal removal 72]
172. 8 <=> ! [X1] : ~happy(X1) [avatar definition]
173. ~happy(X1) <- (8) [avatar component clause 172]
183. ~happy(X1) [subsumption resolution 94,137]
184. 8 [avatar split clause 183,172]
229. ~brave(X1) | happy(X1) | patient(X1) [resolution 113,107]
231. ~brave(X1) | patient(X1) <- (8) [subsumption resolution 229,173]
232. patient(X1) <- (8) [subsumption resolution 231,108]
233. $false <- (8) [resolution 232,134]
235. ~8 [avatar contradiction clause 233]
236. $false [avatar sat refutation 184,235]
% SZS output end Proof for 8678030143160239935388302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is not calm. If alice is either not quiet or not rich then someone is either calm or not kind. Everyone who is either not kind or happy is happy or calm and vice versa. If fred is not humble or not creative then someone is either not calm or rich. Everyone who is either kind or happy is either happy or rich. Everyone who is both not wise and not brave is not generous or not tall and vice versa. Everyone who is either not old or not wise is both not curious and old and vice versa. If someone is both brave and kind then susan is either tall or not funny. Everyone who is creative or generous is brave. If paul is either old or wise then someone is either creative or calm and vice versa. If someone is both generous and not strong then john is both strong and quiet and vice versa. Everyone who is strong is not humble and vice versa. Everyone who is not patient is either not old or kind and vice versa. Everyone who is either patient or not kind is either creative or not funny and vice versa. If lucy is both not creative and brave then someone is either not tall or creative and vice versa. If someone is not generous then mary is not creative. Lucy is both kind and not creative. Lucy is rich. Someone is patient. Mary is both tall and patient. Someone is calm. Mary is either kind or rich. Someone is curious. Someone is not generous. | Alice is not wise. | neutral | (![X]:(~funny(X)=>~calm(X)))&
(((~quiet(alice)<~>~rich(alice)))=>(?[X]:((calm(X)<~>~kind(X)))))&
(![X]:((~kind(X)<~>happy(X))<=>(happy(X)|calm(X))))&
(((~humble(fred)|~creative(fred)))=>(?[X]:((~calm(X)<~>rich(X)))))&
(![X]:((kind(X)<~>happy(X))=>(happy(X)<~>rich(X))))&
(![X]:((~wise(X)&~brave(X))<=>(~generous(X)|~tall(X))))&
(![X]:((~old(X)<~>~wise(X))<=>(~curious(X)&old(X))))&
((?[X]:((brave(X)&kind(X))))=>((tall(susan)<~>~funny(susan))))&
(![X]:((creative(X)|generous(X))=>brave(X)))&
(((old(paul)<~>wise(paul)))<=>(?[X]:((creative(X)<~>calm(X)))))&
((?[X]:((generous(X)&~strong(X))))<=>((strong(john)&quiet(john))))&
(![X]:(strong(X)<=>~humble(X)))&
(![X]:(~patient(X)<=>(~old(X)<~>kind(X))))&
(![X]:((patient(X)<~>~kind(X))<=>(creative(X)<~>~funny(X))))&
(((~creative(lucy)&brave(lucy)))<=>(?[X]:((~tall(X)<~>creative(X)))))&
((?[X]:(~generous(X)))=>(~creative(mary)))&
((kind(lucy)&~creative(lucy)))&
(rich(lucy))&
(?[X]:(patient(X)))&
((tall(mary)&patient(mary)))&
(?[X]:(calm(X)))&
((kind(mary)<~>rich(mary)))&
(?[X]:(curious(X)))&
(?[X]:(~generous(X))) | ~wise(alice) | []
| null | 0 |
Everyone who is not happy or not old is both not humble and generous and vice versa. Everyone who is either not wise or wise is both funny and not creative. If someone is kind or not funny then someone is calm and vice versa. If someone is not curious then susan is either curious or old. Everyone who is strong is both not funny and not curious and vice versa. If mary is both not happy and not creative then lucy is not brave. Everyone who is both not old and patient is kind. Everyone who is either patient or not patient is tall. If paul is either not wise or not kind then fred is both not calm and patient. If susan is tall then mary is either not quiet or brave. Everyone who is not curious is not strong or quiet and vice versa. Everyone who is either not wise or wise is old. Everyone who is either not strong or not creative is not patient or not brave. If fred is both old and brave then fred is both kind and funny and vice versa. Everyone who is humble or wise is both not humble and curious. If someone is either calm or kind then susan is both happy and brave and vice versa. Fred is both generous and not quiet. Alice is not old or not kind. Someone is either not kind or not funny. Someone is not happy or not funny. Fred is tall. | Fred is not strong. | entailment | (![X]:((~happy(X)|~old(X))<=>(~humble(X)&generous(X))))&
(![X]:((~wise(X)<~>wise(X))=>(funny(X)&~creative(X))))&
((?[X]:((kind(X)|~funny(X))))<=>(?[X]:(calm(X))))&
((?[X]:(~curious(X)))=>((curious(susan)<~>old(susan))))&
(![X]:(strong(X)<=>(~funny(X)&~curious(X))))&
(((~happy(mary)&~creative(mary)))=>(~brave(lucy)))&
(![X]:((~old(X)&patient(X))=>kind(X)))&
(![X]:((patient(X)<~>~patient(X))=>tall(X)))&
(((~wise(paul)<~>~kind(paul)))=>((~calm(fred)&patient(fred))))&
((tall(susan))=>((~quiet(mary)<~>brave(mary))))&
(![X]:(~curious(X)<=>(~strong(X)|quiet(X))))&
(![X]:((~wise(X)<~>wise(X))=>old(X)))&
(![X]:((~strong(X)<~>~creative(X))=>(~patient(X)|~brave(X))))&
(((old(fred)&brave(fred)))<=>((kind(fred)&funny(fred))))&
(![X]:((humble(X)|wise(X))=>(~humble(X)&curious(X))))&
((?[X]:((calm(X)<~>kind(X))))<=>((happy(susan)&brave(susan))))&
((generous(fred)&~quiet(fred)))&
((~old(alice)|~kind(alice)))&
(?[X]:((~kind(X)<~>~funny(X))))&
(?[X]:((~happy(X)|~funny(X))))&
(tall(fred)) | ~strong(fred) | [
"p1",
"p4",
"hypothesis"
]
| % SZS status Unsatisfiable for 5278846625133432084166056
% SZS output start Proof for 5278846625133432084166056
2. ! [X0] : ((~wise(X0) <~> wise(X0)) => (~creative(X0) & funny(X0))) [input p1]
5. ! [X0] : (strong(X0) <=> (~curious(X0) & ~funny(X0))) [input p4]
22. strong(fred) [input hypothesis]
24. ! [X0] : ((~creative(X0) & funny(X0)) | (~wise(X0) <=> wise(X0))) [ennf transformation 2]
39. ! [X0] : ((~creative(X0) & funny(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 24]
46. ! [X0] : ((strong(X0) | (curious(X0) | funny(X0))) & ((~curious(X0) & ~funny(X0)) | ~strong(X0))) [nnf transformation 5]
47. ! [X0] : ((strong(X0) | curious(X0) | funny(X0)) & ((~curious(X0) & ~funny(X0)) | ~strong(X0))) [flattening 46]
72. funny(X0) | wise(X0) | wise(X0) [cnf transformation 39]
73. funny(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 39]
81. ~funny(X0) | ~strong(X0) [cnf transformation 47]
122. strong(fred) [cnf transformation 22]
128. funny(X0) | wise(X0) [duplicate literal removal 72]
129. funny(X0) | ~wise(X0) [duplicate literal removal 73]
133. funny(X0) [subsumption resolution 128,129]
164. ~strong(X0) [subsumption resolution 81,133]
255. $false [subsumption resolution 122,164]
% SZS output end Proof for 5278846625133432084166056
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or not patient then someone is wise. Everyone who is tall is both not old and not happy and vice versa. Everyone who is not strong is either not wise or creative and vice versa. If someone is both humble and generous then susan is not calm or not wise. If alice is happy then john is curious or brave. Everyone who is brave is calm. Everyone who is either not old or not quiet is either not funny or kind and vice versa. If paul is not brave or generous then someone is happy or not tall. Everyone who is both quiet and not kind is both funny and not quiet. Everyone who is wise is strong or not funny and vice versa. Everyone who is tall or not creative is generous and vice versa. If alice is both patient and not kind then someone is not happy or not rich and vice versa. If someone is not wise or not patient then someone is generous and vice versa. Everyone who is curious is not tall or not wise and vice versa. Everyone who is kind or calm is both humble and not funny and vice versa. If someone is either not tall or not creative then someone is both not creative and quiet and vice versa. Someone is humble. Lucy is either quiet or brave. Fred is old. Someone is either wise or not kind. Mary is not strong. Someone is not happy or happy. Someone is not quiet. | John is not old. | neutral | ((?[X]:((~curious(X)|~patient(X))))=>(?[X]:(wise(X))))&
(![X]:(tall(X)<=>(~old(X)&~happy(X))))&
(![X]:(~strong(X)<=>(~wise(X)<~>creative(X))))&
((?[X]:((humble(X)&generous(X))))=>((~calm(susan)|~wise(susan))))&
((happy(alice))=>((curious(john)|brave(john))))&
(![X]:(brave(X)=>calm(X)))&
(![X]:((~old(X)<~>~quiet(X))<=>(~funny(X)<~>kind(X))))&
(((~brave(paul)|generous(paul)))=>(?[X]:((happy(X)|~tall(X)))))&
(![X]:((quiet(X)&~kind(X))=>(funny(X)&~quiet(X))))&
(![X]:(wise(X)<=>(strong(X)|~funny(X))))&
(![X]:((tall(X)|~creative(X))<=>generous(X)))&
(((patient(alice)&~kind(alice)))<=>(?[X]:((~happy(X)|~rich(X)))))&
((?[X]:((~wise(X)|~patient(X))))<=>(?[X]:(generous(X))))&
(![X]:(curious(X)<=>(~tall(X)|~wise(X))))&
(![X]:((kind(X)|calm(X))<=>(humble(X)&~funny(X))))&
((?[X]:((~tall(X)<~>~creative(X))))<=>(?[X]:((~creative(X)&quiet(X)))))&
(?[X]:(humble(X)))&
((quiet(lucy)<~>brave(lucy)))&
(old(fred))&
(?[X]:((wise(X)<~>~kind(X))))&
(~strong(mary))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:(~quiet(X))) | ~old(john) | []
| null | 0 |
Everyone who is not rich or not strong is wise. If susan is calm or not strong then john is not generous or tall and vice versa. If someone is either brave or not strong then someone is old or not quiet. If mary is not strong then someone is old or not funny and vice versa. Everyone who is both wise and not curious is both brave and generous. Everyone who is not generous or creative is both not tall and humble. Everyone who is not rich is both not tall and not happy. Everyone who is both tall and old is not patient or brave and vice versa. If mary is both not kind and generous then someone is humble and vice versa. If mary is either humble or generous then someone is either tall or not happy and vice versa. Everyone who is not humble is not old or creative. Everyone who is tall is either tall or humble and vice versa. Everyone who is generous or rich is either not funny or not happy. Everyone who is not quiet is both happy and kind. If paul is happy then fred is patient and vice versa. If someone is calm then susan is funny. Someone is both calm and not wise. Someone is either not kind or tall. Someone is strong. Someone is quiet or strong. Susan is either rich or not strong. Someone is not rich. | Mary is kind. | entailment | (![X]:((~rich(X)|~strong(X))=>wise(X)))&
(((calm(susan)|~strong(susan)))<=>((~generous(john)|tall(john))))&
((?[X]:((brave(X)<~>~strong(X))))=>(?[X]:((old(X)|~quiet(X)))))&
((~strong(mary))<=>(?[X]:((old(X)|~funny(X)))))&
(![X]:((wise(X)&~curious(X))=>(brave(X)&generous(X))))&
(![X]:((~generous(X)|creative(X))=>(~tall(X)&humble(X))))&
(![X]:(~rich(X)=>(~tall(X)&~happy(X))))&
(![X]:((tall(X)&old(X))<=>(~patient(X)|brave(X))))&
(((~kind(mary)&generous(mary)))<=>(?[X]:(humble(X))))&
(((humble(mary)<~>generous(mary)))<=>(?[X]:((tall(X)<~>~happy(X)))))&
(![X]:(~humble(X)=>(~old(X)|creative(X))))&
(![X]:(tall(X)<=>(tall(X)<~>humble(X))))&
(![X]:((generous(X)|rich(X))=>(~funny(X)<~>~happy(X))))&
(![X]:(~quiet(X)=>(happy(X)&kind(X))))&
((happy(paul))<=>(patient(fred)))&
((?[X]:(calm(X)))=>(funny(susan)))&
(?[X]:((calm(X)&~wise(X))))&
(?[X]:((~kind(X)<~>tall(X))))&
(?[X]:(strong(X)))&
(?[X]:((quiet(X)|strong(X))))&
((rich(susan)<~>~strong(susan)))&
(?[X]:(~rich(X))) | kind(mary) | [
"p5",
"p8",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 1574599579162678382299308
% SZS output start Proof for 1574599579162678382299308
6. ! [X0] : ((creative(X0) | ~generous(X0)) => (humble(X0) & ~tall(X0))) [input p5]
9. (generous(mary) & ~kind(mary)) <=> ? [X0] : humble(X0) [input p8]
12. ! [X0] : (tall(X0) <=> (tall(X0) <~> humble(X0))) [input p11]
23. ~kind(mary) [input hypothesis]
28. ! [X0] : ((humble(X0) & ~tall(X0)) | (~creative(X0) & generous(X0))) [ennf transformation 6]
47. ((generous(mary) & ~kind(mary)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (~generous(mary) | kind(mary))) [nnf transformation 9]
48. ((generous(mary) & ~kind(mary)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | ~generous(mary) | kind(mary)) [flattening 47]
49. ((generous(mary) & ~kind(mary)) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | ~generous(mary) | kind(mary)) [rectify 48]
50. ? [X1] : humble(X1) => humble(sK2) [choice axiom]
51. ((generous(mary) & ~kind(mary)) | ! [X0] : ~humble(X0)) & (humble(sK2) | ~generous(mary) | kind(mary)) [skolemisation 49,50]
56. ! [X0] : ((tall(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ~tall(X0))) [nnf transformation 12]
84. humble(X0) | generous(X0) [cnf transformation 28]
93. humble(sK2) | ~generous(mary) | kind(mary) [cnf transformation 51]
106. ~humble(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 56]
108. tall(X0) | tall(X0) | ~humble(X0) [cnf transformation 56]
127. ~kind(mary) [cnf transformation 23]
128. ~humble(X0) | ~tall(X0) [duplicate literal removal 106]
129. tall(X0) | ~humble(X0) [duplicate literal removal 108]
188. 14 <=> ! [X0] : ~humble(X0) [avatar definition]
189. ~humble(X0) <- (14) [avatar component clause 188]
191. 15 <=> generous(mary) [avatar definition]
192. ~generous(mary) <- (~15) [avatar component clause 191]
196. 16 <=> kind(mary) [avatar definition]
201. 17 <=> humble(sK2) [avatar definition]
203. humble(sK2) <- (17) [avatar component clause 201]
204. 16 | ~15 | 17 [avatar split clause 93,201,191,196]
234. ~humble(X0) [subsumption resolution 128,129]
235. 14 [avatar split clause 234,188]
280. ~16 [avatar split clause 127,196]
285. generous(X0) <- (14) [resolution 84,189]
287. $false <- (14, ~15) [resolution 285,192]
288. ~14 | 15 [avatar contradiction clause 287]
290. $false <- (14, 17) [subsumption resolution 203,189]
291. ~14 | ~17 [avatar contradiction clause 290]
292. $false [avatar sat refutation 204,235,280,288,291]
% SZS output end Proof for 1574599579162678382299308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and not tall is either curious or tall and vice versa. If someone is not humble then someone is humble or not tall and vice versa. Everyone who is not strong or brave is generous or wise. If alice is calm then someone is both happy and not happy and vice versa. If lucy is rich or wise then someone is not rich or not patient. Everyone who is not generous or not humble is either not curious or humble. Everyone who is not strong is humble. If john is both old and humble then someone is quiet. If paul is not generous then mary is patient or kind and vice versa. Everyone who is both not wise and funny is not funny or generous and vice versa. If someone is either rich or not generous then someone is not kind. Everyone who is not calm is both not old and happy and vice versa. If someone is not patient or not strong then someone is happy and vice versa. Everyone who is either not old or not creative is either not funny or not happy and vice versa. Everyone who is humble is both not strong and curious and vice versa. Everyone who is not old or calm is not old and vice versa. Someone is either not creative or wise. John is patient. Lucy is either patient or not old. Someone is not old. Someone is calm or not curious. Mary is rich. Someone is either kind or not calm. | Paul is not creative. | neutral | (![X]:((~patient(X)&~tall(X))<=>(curious(X)<~>tall(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((~strong(X)|brave(X))=>(generous(X)|wise(X))))&
((calm(alice))<=>(?[X]:((happy(X)&~happy(X)))))&
(((rich(lucy)|wise(lucy)))=>(?[X]:((~rich(X)|~patient(X)))))&
(![X]:((~generous(X)|~humble(X))=>(~curious(X)<~>humble(X))))&
(![X]:(~strong(X)=>humble(X)))&
(((old(john)&humble(john)))=>(?[X]:(quiet(X))))&
((~generous(paul))<=>((patient(mary)|kind(mary))))&
(![X]:((~wise(X)&funny(X))<=>(~funny(X)|generous(X))))&
((?[X]:((rich(X)<~>~generous(X))))=>(?[X]:(~kind(X))))&
(![X]:(~calm(X)<=>(~old(X)&happy(X))))&
((?[X]:((~patient(X)|~strong(X))))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)<~>~creative(X))<=>(~funny(X)<~>~happy(X))))&
(![X]:(humble(X)<=>(~strong(X)&curious(X))))&
(![X]:((~old(X)|calm(X))<=>~old(X)))&
(?[X]:((~creative(X)<~>wise(X))))&
(patient(john))&
((patient(lucy)<~>~old(lucy)))&
(?[X]:(~old(X)))&
(?[X]:((calm(X)|~curious(X))))&
(rich(mary))&
(?[X]:((kind(X)<~>~calm(X)))) | ~creative(paul) | []
| null | 0 |
If someone is both quiet and not strong then paul is both not old and not patient. Everyone who is either not strong or not tall is either not calm or not strong. Everyone who is strong is either not old or humble. Everyone who is not creative or not humble is both not old and not tall. If someone is not brave or not strong then fred is patient or tall. Everyone who is either wise or strong is not calm and vice versa. Everyone who is either strong or not strong is both not creative and curious and vice versa. If paul is not generous or tall then paul is not happy or not quiet and vice versa. Everyone who is funny is not funny or not calm and vice versa. Everyone who is not brave is creative or tall and vice versa. Everyone who is funny is both happy and not quiet and vice versa. Everyone who is both not rich and creative is either humble or not funny and vice versa. If paul is not wise then someone is both not humble and not tall. Everyone who is both generous and brave is both not calm and rich and vice versa. If someone is rich then someone is both happy and funny and vice versa. Fred is either tall or not wise. Susan is not tall. Lucy is either rich or not humble. Someone is both not quiet and not wise. Someone is not wise or patient. | Paul is not old. | entailment | ((?[X]:((quiet(X)&~strong(X))))=>((~old(paul)&~patient(paul))))&
(![X]:((~strong(X)<~>~tall(X))=>(~calm(X)<~>~strong(X))))&
(![X]:(strong(X)=>(~old(X)<~>humble(X))))&
(![X]:((~creative(X)|~humble(X))=>(~old(X)&~tall(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((patient(fred)|tall(fred))))&
(![X]:((wise(X)<~>strong(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~creative(X)&curious(X))))&
(((~generous(paul)|tall(paul)))<=>((~happy(paul)|~quiet(paul))))&
(![X]:(funny(X)<=>(~funny(X)|~calm(X))))&
(![X]:(~brave(X)<=>(creative(X)|tall(X))))&
(![X]:(funny(X)<=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)&creative(X))<=>(humble(X)<~>~funny(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((generous(X)&brave(X))<=>(~calm(X)&rich(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&funny(X)))))&
((tall(fred)<~>~wise(fred)))&
(~tall(susan))&
((rich(lucy)<~>~humble(lucy)))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((~wise(X)|patient(X)))) | ~old(paul) | [
"p3",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 8782550599938873731835423
% SZS output start Proof for 8782550599938873731835423
4. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~tall(X0) & ~old(X0))) [input p3]
7. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (curious(X0) & ~creative(X0))) [input p6]
21. old(paul) [input hypothesis]
26. ! [X0] : ((~tall(X0) & ~old(X0)) | (humble(X0) & creative(X0))) [ennf transformation 4]
33. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 7]
34. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [flattening 33]
68. ~old(X0) | creative(X0) [cnf transformation 26]
78. ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 34]
79. ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 34]
120. old(paul) [cnf transformation 21]
123. ~creative(X0) | ~strong(X0) [duplicate literal removal 78]
124. ~creative(X0) | strong(X0) [duplicate literal removal 79]
138. 3 <=> old(paul) [avatar definition]
139. old(paul) <- (3) [avatar component clause 138]
159. ~creative(X0) [subsumption resolution 123,124]
215. 3 [avatar split clause 120,138]
216. creative(paul) <- (3) [resolution 68,139]
217. $false <- (3) [subsumption resolution 216,159]
218. ~3 [avatar contradiction clause 217]
219. $false [avatar sat refutation 215,218]
% SZS output end Proof for 8782550599938873731835423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not happy is not patient and vice versa. If mary is both not creative and not tall then fred is both not generous and not patient and vice versa. If someone is not patient then someone is tall or not calm and vice versa. If someone is both not calm and calm then fred is either quiet or humble. If susan is happy or not creative then someone is both not strong and not generous and vice versa. If alice is not funny then paul is either brave or not tall and vice versa. If someone is both wise and rich then susan is either not tall or not patient and vice versa. If someone is either not funny or rich then susan is kind and vice versa. If someone is calm then someone is not rich or kind. If someone is both creative and not calm then alice is rich or brave. If someone is both brave and not humble then susan is either not wise or not creative and vice versa. Everyone who is both generous and tall is either not brave or tall. Everyone who is not old is both old and not generous. If susan is not calm or not funny then alice is both not curious and rich and vice versa. Everyone who is rich or quiet is not old. Everyone who is not happy is happy. Someone is not quiet or not brave. John is both not tall and not funny. Lucy is not rich or not strong. John is either patient or humble. Fred is tall. Someone is not calm or not humble. Someone is either tall or patient. | Paul is not happy. | contradiction | (![X]:((happy(X)<~>~happy(X))<=>~patient(X)))&
(((~creative(mary)&~tall(mary)))<=>((~generous(fred)&~patient(fred))))&
((?[X]:(~patient(X)))<=>(?[X]:((tall(X)|~calm(X)))))&
((?[X]:((~calm(X)&calm(X))))=>((quiet(fred)<~>humble(fred))))&
(((happy(susan)|~creative(susan)))<=>(?[X]:((~strong(X)&~generous(X)))))&
((~funny(alice))<=>((brave(paul)<~>~tall(paul))))&
((?[X]:((wise(X)&rich(X))))<=>((~tall(susan)<~>~patient(susan))))&
((?[X]:((~funny(X)<~>rich(X))))<=>(kind(susan)))&
((?[X]:(calm(X)))=>(?[X]:((~rich(X)|kind(X)))))&
((?[X]:((creative(X)&~calm(X))))=>((rich(alice)|brave(alice))))&
((?[X]:((brave(X)&~humble(X))))<=>((~wise(susan)<~>~creative(susan))))&
(![X]:((generous(X)&tall(X))=>(~brave(X)<~>tall(X))))&
(![X]:(~old(X)=>(old(X)&~generous(X))))&
(((~calm(susan)|~funny(susan)))<=>((~curious(alice)&rich(alice))))&
(![X]:((rich(X)|quiet(X))=>~old(X)))&
(![X]:(~happy(X)=>happy(X)))&
(?[X]:((~quiet(X)|~brave(X))))&
((~tall(john)&~funny(john)))&
((~rich(lucy)|~strong(lucy)))&
((patient(john)<~>humble(john)))&
(tall(fred))&
(?[X]:((~calm(X)|~humble(X))))&
(?[X]:((tall(X)<~>patient(X)))) | ~happy(paul) | [
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 3455501919198796792500755
% SZS output start Proof for 3455501919198796792500755
16. ! [X0] : (~happy(X0) => happy(X0)) [input p15]
24. ~happy(paul) [input hypothesis]
35. ! [X0] : (happy(X0) | happy(X0)) [ennf transformation 16]
128. happy(X0) | happy(X0) [cnf transformation 35]
139. ~happy(paul) [cnf transformation 24]
140. happy(X0) [duplicate literal removal 128]
331. $false [subsumption resolution 139,140]
% SZS output end Proof for 3455501919198796792500755
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not calm is old or not calm.
Everyone who is not creative is either not happy or strong and vice versa.
If paul is patient or not patient then john is wise or creative.
Everyone who is either creative or not old is not patient and vice versa.
If lucy is generous or not calm then mary is either not rich or not strong.
If mary is both not calm and calm then someone is not funny or happy and vice versa.
If fred is tall then someone is both not brave and not rich.
Everyone who is not tall or humble is both calm and strong.
If someone is either not calm or not old then someone is either rich or not humble and vice versa.
Everyone who is not funny is not patient and vice versa.
Everyone who is either curious or happy is both not wise and not quiet.
If someone is either not quiet or tall then lucy is not curious.
Everyone who is strong or calm is not funny and vice versa.
Everyone who is not calm or not happy is not calm or kind.
Everyone who is both kind and not happy is curious.
Someone is not creative or not happy.
Someone is both not kind and not strong.
Paul is either not rich or curious.
Alice is not rich or funny.
Lucy is both not curious and not happy. | Paul is humble. | contradiction | (![X]:((calm(X)<~>~calm(X))=>(old(X)|~calm(X))))&
(![X]:(~creative(X)<=>(~happy(X)<~>strong(X))))&
(((patient(paul)|~patient(paul)))=>((wise(john)|creative(john))))&
(![X]:((creative(X)<~>~old(X))<=>~patient(X)))&
(((generous(lucy)|~calm(lucy)))=>((~rich(mary)<~>~strong(mary))))&
(((~calm(mary)&calm(mary)))<=>(?[X]:((~funny(X)|happy(X)))))&
((tall(fred))=>(?[X]:((~brave(X)&~rich(X)))))&
(![X]:((~tall(X)|humble(X))=>(calm(X)&strong(X))))&
((?[X]:((~calm(X)<~>~old(X))))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(![X]:(~funny(X)<=>~patient(X)))&
(![X]:((curious(X)<~>happy(X))=>(~wise(X)&~quiet(X))))&
((?[X]:((~quiet(X)<~>tall(X))))=>(~curious(lucy)))&
(![X]:((strong(X)|calm(X))<=>~funny(X)))&
(![X]:((~calm(X)|~happy(X))=>(~calm(X)|kind(X))))&
(![X]:((kind(X)&~happy(X))=>curious(X)))&
(?[X]:((~creative(X)|~happy(X))))&
(?[X]:((~kind(X)&~strong(X))))&
((~rich(paul)<~>curious(paul)))&
((~rich(alice)|funny(alice)))&
((~curious(lucy)&~happy(lucy))) | humble(paul) | [
"p5",
"p7",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 7353828478557463745263956
% SZS output start Proof for 7353828478557463745263956
6. (calm(mary) & ~calm(mary)) <=> ? [X0] : (happy(X0) | ~funny(X0)) [input p5]
8. ! [X0] : ((humble(X0) | ~tall(X0)) => (strong(X0) & calm(X0))) [input p7]
13. ! [X0] : ((calm(X0) | strong(X0)) <=> ~funny(X0)) [input p12]
21. humble(paul) [input hypothesis]
31. ! [X0] : ((strong(X0) & calm(X0)) | (~humble(X0) & tall(X0))) [ennf transformation 8]
42. ((calm(mary) & ~calm(mary)) | ! [X0] : (~happy(X0) & funny(X0))) & (? [X0] : (happy(X0) | ~funny(X0)) | (~calm(mary) | calm(mary))) [nnf transformation 6]
43. ((calm(mary) & ~calm(mary)) | ! [X0] : (~happy(X0) & funny(X0))) & (? [X0] : (happy(X0) | ~funny(X0)) | ~calm(mary) | calm(mary)) [flattening 42]
44. ((calm(mary) & ~calm(mary)) | ! [X0] : (~happy(X0) & funny(X0))) & (? [X1] : (happy(X1) | ~funny(X1)) | ~calm(mary) | calm(mary)) [rectify 43]
45. ? [X1] : (happy(X1) | ~funny(X1)) => (happy(sK0) | ~funny(sK0)) [choice axiom]
46. ((calm(mary) & ~calm(mary)) | ! [X0] : (~happy(X0) & funny(X0))) & ((happy(sK0) | ~funny(sK0)) | ~calm(mary) | calm(mary)) [skolemisation 44,45]
57. ! [X0] : (((calm(X0) | strong(X0)) | funny(X0)) & (~funny(X0) | (~calm(X0) & ~strong(X0)))) [nnf transformation 13]
58. ! [X0] : ((calm(X0) | strong(X0) | funny(X0)) & (~funny(X0) | (~calm(X0) & ~strong(X0)))) [flattening 57]
79. ~calm(mary) | funny(X0) [cnf transformation 46]
81. calm(mary) | funny(X0) [cnf transformation 46]
87. ~humble(X0) | strong(X0) [cnf transformation 31]
104. ~funny(X0) | ~strong(X0) [cnf transformation 58]
118. humble(paul) [cnf transformation 21]
153. 8 <=> calm(mary) [avatar definition]
158. 9 <=> ! [X0] : funny(X0) [avatar definition]
159. funny(X0) <- (9) [avatar component clause 158]
160. 9 | 8 [avatar split clause 81,153,158]
162. 9 | ~8 [avatar split clause 79,153,158]
249. strong(paul) [resolution 87,118]
251. ~strong(X0) <- (9) [resolution 104,159]
254. $false <- (9) [resolution 251,249]
255. ~9 [avatar contradiction clause 254]
256. $false [avatar sat refutation 160,162,255]
% SZS output end Proof for 7353828478557463745263956
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not generous or creative then someone is both rich and not curious and vice versa. If someone is not brave or not quiet then paul is both brave and not old and vice versa. Everyone who is either not wise or not quiet is both not curious and not strong and vice versa. If someone is tall then someone is quiet or not rich. If someone is both not humble and not quiet then mary is not kind and vice versa. Everyone who is wise is either rich or not curious. If someone is humble or not calm then fred is humble and vice versa. Everyone who is both calm and not generous is quiet. If paul is old or not humble then alice is either not funny or humble. Everyone who is strong or not brave is either not creative or kind. Everyone who is not happy is both happy and not curious. Everyone who is generous is not quiet and vice versa. Everyone who is either not funny or not rich is not creative. Everyone who is happy or old is funny. Everyone who is wise is both tall and kind and vice versa. Everyone who is old is not quiet or happy and vice versa. Susan is creative or not brave. Someone is old or wise. Fred is not patient. Someone is either not creative or patient. Mary is calm. Fred is either kind or calm. Paul is funny. | Paul is not old. | contradiction | (((~generous(paul)|creative(paul)))<=>(?[X]:((rich(X)&~curious(X)))))&
((?[X]:((~brave(X)|~quiet(X))))<=>((brave(paul)&~old(paul))))&
(![X]:((~wise(X)<~>~quiet(X))<=>(~curious(X)&~strong(X))))&
((?[X]:(tall(X)))=>(?[X]:((quiet(X)|~rich(X)))))&
((?[X]:((~humble(X)&~quiet(X))))<=>(~kind(mary)))&
(![X]:(wise(X)=>(rich(X)<~>~curious(X))))&
((?[X]:((humble(X)|~calm(X))))<=>(humble(fred)))&
(![X]:((calm(X)&~generous(X))=>quiet(X)))&
(((old(paul)|~humble(paul)))=>((~funny(alice)<~>humble(alice))))&
(![X]:((strong(X)|~brave(X))=>(~creative(X)<~>kind(X))))&
(![X]:(~happy(X)=>(happy(X)&~curious(X))))&
(![X]:(generous(X)<=>~quiet(X)))&
(![X]:((~funny(X)<~>~rich(X))=>~creative(X)))&
(![X]:((happy(X)|old(X))=>funny(X)))&
(![X]:(wise(X)<=>(tall(X)&kind(X))))&
(![X]:(old(X)<=>(~quiet(X)|happy(X))))&
((creative(susan)|~brave(susan)))&
(?[X]:((old(X)|wise(X))))&
(~patient(fred))&
(?[X]:((~creative(X)<~>patient(X))))&
(calm(mary))&
((kind(fred)<~>calm(fred)))&
(funny(paul)) | ~old(paul) | [
"p10",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 6476341030457215296946229
% SZS output start Proof for 6476341030457215296946229
11. ! [X0] : (~happy(X0) => (~curious(X0) & happy(X0))) [input p10]
16. ! [X0] : (old(X0) <=> (happy(X0) | ~quiet(X0))) [input p15]
24. ~old(paul) [input hypothesis]
32. ! [X0] : ((~curious(X0) & happy(X0)) | happy(X0)) [ennf transformation 11]
65. ! [X0] : ((old(X0) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | ~old(X0))) [nnf transformation 16]
66. ! [X0] : ((old(X0) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~old(X0))) [flattening 65]
107. happy(X0) | happy(X0) [cnf transformation 32]
120. old(X0) | ~happy(X0) [cnf transformation 66]
130. ~old(paul) [cnf transformation 24]
131. happy(X0) [duplicate literal removal 107]
251. old(X0) [subsumption resolution 120,131]
281. $false [subsumption resolution 130,251]
% SZS output end Proof for 6476341030457215296946229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either generous or not curious is either rich or not kind. Everyone who is both not humble and generous is both humble and wise and vice versa. Everyone who is patient or not calm is either curious or brave and vice versa. If susan is strong then susan is tall and vice versa. Everyone who is both brave and rich is not humble and vice versa. If someone is not patient or not funny then lucy is not tall or calm and vice versa. Everyone who is strong or quiet is old or not tall and vice versa. If someone is either not strong or strong then someone is either not kind or kind and vice versa. If someone is both not creative and not kind then lucy is not curious or not wise and vice versa. If someone is tall or brave then susan is both not calm and brave. Everyone who is either not curious or not creative is either not brave or not curious and vice versa. Everyone who is humble or brave is both tall and generous. If someone is wise then someone is both not humble and not kind. Everyone who is funny or not humble is either not brave or old and vice versa. Everyone who is either not kind or funny is strong or funny and vice versa. If alice is either not curious or not rich then lucy is not rich and vice versa. John is old. Mary is not funny or calm. Lucy is either not wise or not quiet. Someone is wise or humble. Lucy is either quiet or wise. Lucy is humble or kind. Alice is either curious or quiet. | Lucy is old. | entailment | (![X]:((generous(X)<~>~curious(X))=>(rich(X)<~>~kind(X))))&
(![X]:((~humble(X)&generous(X))<=>(humble(X)&wise(X))))&
(![X]:((patient(X)|~calm(X))<=>(curious(X)<~>brave(X))))&
((strong(susan))<=>(tall(susan)))&
(![X]:((brave(X)&rich(X))<=>~humble(X)))&
((?[X]:((~patient(X)|~funny(X))))<=>((~tall(lucy)|calm(lucy))))&
(![X]:((strong(X)|quiet(X))<=>(old(X)|~tall(X))))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((~kind(X)<~>kind(X)))))&
((?[X]:((~creative(X)&~kind(X))))<=>((~curious(lucy)|~wise(lucy))))&
((?[X]:((tall(X)|brave(X))))=>((~calm(susan)&brave(susan))))&
(![X]:((~curious(X)<~>~creative(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((humble(X)|brave(X))=>(tall(X)&generous(X))))&
((?[X]:(wise(X)))=>(?[X]:((~humble(X)&~kind(X)))))&
(![X]:((funny(X)|~humble(X))<=>(~brave(X)<~>old(X))))&
(![X]:((~kind(X)<~>funny(X))<=>(strong(X)|funny(X))))&
(((~curious(alice)<~>~rich(alice)))<=>(~rich(lucy)))&
(old(john))&
((~funny(mary)|calm(mary)))&
((~wise(lucy)<~>~quiet(lucy)))&
(?[X]:((wise(X)|humble(X))))&
((quiet(lucy)<~>wise(lucy)))&
((humble(lucy)|kind(lucy)))&
((curious(alice)<~>quiet(alice))) | old(lucy) | [
"p1",
"p4",
"p6",
"p11",
"p12",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 6320749710682026445797862
% SZS output start Proof for 6320749710682026445797862
2. ! [X0] : ((generous(X0) & ~humble(X0)) <=> (wise(X0) & humble(X0))) [input p1]
5. ! [X0] : ((rich(X0) & brave(X0)) <=> ~humble(X0)) [input p4]
7. ! [X0] : ((quiet(X0) | strong(X0)) <=> (~tall(X0) | old(X0))) [input p6]
12. ! [X0] : ((brave(X0) | humble(X0)) => (generous(X0) & tall(X0))) [input p11]
13. ? [X0] : wise(X0) => ? [X0] : (~kind(X0) & ~humble(X0)) [input p12]
21. quiet(lucy) <~> wise(lucy) [input p20]
24. ~old(lucy) [input hypothesis]
26. ? [X0] : wise(X0) => ? [X1] : (~kind(X1) & ~humble(X1)) [rectify 13]
29. ! [X0] : ((generous(X0) & tall(X0)) | (~brave(X0) & ~humble(X0))) [ennf transformation 12]
30. ? [X1] : (~kind(X1) & ~humble(X1)) | ! [X0] : ~wise(X0) [ennf transformation 26]
32. ! [X0] : (((generous(X0) & ~humble(X0)) | (~wise(X0) | ~humble(X0))) & ((wise(X0) & humble(X0)) | (~generous(X0) | humble(X0)))) [nnf transformation 2]
33. ! [X0] : (((generous(X0) & ~humble(X0)) | ~wise(X0) | ~humble(X0)) & ((wise(X0) & humble(X0)) | ~generous(X0) | humble(X0))) [flattening 32]
37. ! [X0] : (((rich(X0) & brave(X0)) | humble(X0)) & (~humble(X0) | (~rich(X0) | ~brave(X0)))) [nnf transformation 5]
38. ! [X0] : (((rich(X0) & brave(X0)) | humble(X0)) & (~humble(X0) | ~rich(X0) | ~brave(X0))) [flattening 37]
44. ! [X0] : (((quiet(X0) | strong(X0)) | (tall(X0) & ~old(X0))) & ((~tall(X0) | old(X0)) | (~quiet(X0) & ~strong(X0)))) [nnf transformation 7]
45. ! [X0] : ((quiet(X0) | strong(X0) | (tall(X0) & ~old(X0))) & (~tall(X0) | old(X0) | (~quiet(X0) & ~strong(X0)))) [flattening 44]
57. ? [X0] : (~kind(X0) & ~humble(X0)) | ! [X1] : ~wise(X1) [rectify 30]
58. ? [X0] : (~kind(X0) & ~humble(X0)) => (~kind(sK4) & ~humble(sK4)) [choice axiom]
59. (~kind(sK4) & ~humble(sK4)) | ! [X1] : ~wise(X1) [skolemisation 57,58]
68. (~wise(lucy) | ~quiet(lucy)) & (wise(lucy) | quiet(lucy)) [nnf transformation 21]
74. humble(X0) | ~generous(X0) | humble(X0) [cnf transformation 33]
87. brave(X0) | humble(X0) [cnf transformation 38]
94. ~quiet(X0) | old(X0) | ~tall(X0) [cnf transformation 45]
122. ~humble(X0) | tall(X0) [cnf transformation 29]
123. ~brave(X0) | tall(X0) [cnf transformation 29]
125. ~brave(X0) | generous(X0) [cnf transformation 29]
126. ~humble(sK4) | ~wise(X1) [cnf transformation 59]
149. wise(lucy) | quiet(lucy) [cnf transformation 68]
154. ~old(lucy) [cnf transformation 24]
169. ~generous(X0) | humble(X0) [duplicate literal removal 74]
208. 9 <=> wise(lucy) [avatar definition]
210. wise(lucy) <- (9) [avatar component clause 208]
252. 18 <=> ! [X1] : ~wise(X1) [avatar definition]
253. ~wise(X1) <- (18) [avatar component clause 252]
260. 20 <=> humble(sK4) [avatar definition]
262. ~humble(sK4) <- (~20) [avatar component clause 260]
263. 18 | ~20 [avatar split clause 126,260,252]
293. 26 <=> quiet(lucy) [avatar definition]
295. quiet(lucy) <- (26) [avatar component clause 293]
308. 26 | 9 [avatar split clause 149,208,293]
339. tall(X0) | humble(X0) [resolution 123,87]
342. tall(X0) [subsumption resolution 339,122]
351. generous(X0) | humble(X0) [resolution 125,87]
353. humble(X0) [subsumption resolution 351,169]
355. $false <- (~20) [resolution 353,262]
360. 20 [avatar contradiction clause 355]
361. $false <- (9, 18) [resolution 253,210]
364. ~9 | ~18 [avatar contradiction clause 361]
407. old(lucy) | ~tall(lucy) <- (26) [resolution 94,295]
408. ~tall(lucy) <- (26) [subsumption resolution 407,154]
409. $false <- (26) [subsumption resolution 408,342]
410. ~26 [avatar contradiction clause 409]
411. $false [avatar sat refutation 263,308,360,364,410]
% SZS output end Proof for 6320749710682026445797862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then someone is either not rich or brave.
Everyone who is tall is both creative and funny and vice versa.
If paul is both calm and not rich then paul is both not strong and not happy.
Everyone who is both happy and not brave is not humble or humble and vice versa.
Everyone who is old or not brave is not quiet or not strong.
Everyone who is not kind or not happy is curious or not wise.
Everyone who is both not funny and rich is not patient.
Everyone who is both kind and not patient is not kind or not generous.
If alice is funny or not curious then someone is humble or tall and vice versa.
Everyone who is wise or quiet is either not kind or not funny and vice versa.
If someone is both kind and not rich then someone is not curious.
Everyone who is rich or not tall is either tall or calm.
If someone is either not strong or not rich then paul is both not humble and not rich.
Everyone who is kind or funny is not rich or happy.
Everyone who is both funny and not old is not tall or not quiet and vice versa.
Everyone who is old is not quiet or not generous.
Someone is quiet or creative.
Lucy is wise.
Lucy is not kind.
Paul is not brave.
Lucy is both funny and not brave.
Fred is tall.
Someone is both tall and old.
Alice is strong. | Paul is tall. | neutral | ((?[X]:(~strong(X)))=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:(tall(X)<=>(creative(X)&funny(X))))&
(((calm(paul)&~rich(paul)))=>((~strong(paul)&~happy(paul))))&
(![X]:((happy(X)&~brave(X))<=>(~humble(X)|humble(X))))&
(![X]:((old(X)|~brave(X))=>(~quiet(X)|~strong(X))))&
(![X]:((~kind(X)|~happy(X))=>(curious(X)|~wise(X))))&
(![X]:((~funny(X)&rich(X))=>~patient(X)))&
(![X]:((kind(X)&~patient(X))=>(~kind(X)|~generous(X))))&
(((funny(alice)|~curious(alice)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)<~>~funny(X))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:(~curious(X))))&
(![X]:((rich(X)|~tall(X))=>(tall(X)<~>calm(X))))&
((?[X]:((~strong(X)<~>~rich(X))))=>((~humble(paul)&~rich(paul))))&
(![X]:((kind(X)|funny(X))=>(~rich(X)|happy(X))))&
(![X]:((funny(X)&~old(X))<=>(~tall(X)|~quiet(X))))&
(![X]:(old(X)=>(~quiet(X)|~generous(X))))&
(?[X]:((quiet(X)|creative(X))))&
(wise(lucy))&
(~kind(lucy))&
(~brave(paul))&
((funny(lucy)&~brave(lucy)))&
(tall(fred))&
(?[X]:((tall(X)&old(X))))&
(strong(alice)) | tall(paul) | []
| null | 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.