premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is either brave or not funny then paul is not kind and vice versa. If lucy is either not creative or tall then someone is either not old or generous. If someone is either not strong or not calm then someone is curious or calm and vice versa. Everyone who is either not patient or kind is both kind and not kind and vice versa. If someone is not tall or not curious then susan is not funny or humble and vice versa. Everyone who is not humble is either not quiet or tall and vice versa. Everyone who is not generous or funny is not creative or not funny and vice versa. Everyone who is both funny and humble is both funny and creative and vice versa. Everyone who is both patient and quiet is not curious or not quiet. If someone is both calm and tall then someone is both tall and funny and vice versa. If fred is funny then mary is not calm or not wise and vice versa. Everyone who is not creative is both not funny and rich. If someone is not kind then fred is not humble or not tall and vice versa. Everyone who is both humble and curious is both wise and not humble and vice versa. Everyone who is not kind or happy is both happy and not generous. If someone is wise then someone is curious. Paul is humble or not funny. Someone is not strong or not generous. Alice is not strong or old. Susan is not tall. Someone is both creative and rich. Someone is either not creative or tall. | Mary is not quiet. | contradiction | ((?[X]:((brave(X)<~>~funny(X))))<=>(~kind(paul)))&
(((~creative(lucy)<~>tall(lucy)))=>(?[X]:((~old(X)<~>generous(X)))))&
((?[X]:((~strong(X)<~>~calm(X))))<=>(?[X]:((curious(X)|calm(X)))))&
(![X]:((~patient(X)<~>kind(X))<=>(kind(X)&~kind(X))))&
((?[X]:((~tall(X)|~curious(X))))<=>((~funny(susan)|humble(susan))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>tall(X))))&
(![X]:((~generous(X)|funny(X))<=>(~creative(X)|~funny(X))))&
(![X]:((funny(X)&humble(X))<=>(funny(X)&creative(X))))&
(![X]:((patient(X)&quiet(X))=>(~curious(X)|~quiet(X))))&
((?[X]:((calm(X)&tall(X))))<=>(?[X]:((tall(X)&funny(X)))))&
((funny(fred))<=>((~calm(mary)|~wise(mary))))&
(![X]:(~creative(X)=>(~funny(X)&rich(X))))&
((?[X]:(~kind(X)))<=>((~humble(fred)|~tall(fred))))&
(![X]:((humble(X)&curious(X))<=>(wise(X)&~humble(X))))&
(![X]:((~kind(X)|happy(X))=>(happy(X)&~generous(X))))&
((?[X]:(wise(X)))=>(?[X]:(curious(X))))&
((humble(paul)|~funny(paul)))&
(?[X]:((~strong(X)|~generous(X))))&
((~strong(alice)|old(alice)))&
(~tall(susan))&
(?[X]:((creative(X)&rich(X))))&
(?[X]:((~creative(X)<~>tall(X)))) | ~quiet(mary) | [
"p5",
"p6",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3423724652558183974946622
% SZS output start Proof for 3423724652558183974946622
6. ! [X0] : (~humble(X0) <=> (~quiet(X0) <~> tall(X0))) [input p5]
7. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (~funny(X0) | ~creative(X0))) [input p6]
10. ? [X0] : (tall(X0) & calm(X0)) <=> ? [X0] : (funny(X0) & tall(X0)) [input p9]
11. funny(fred) <=> (~wise(mary) | ~calm(mary)) [input p10]
12. ! [X0] : (~creative(X0) => (rich(X0) & ~funny(X0))) [input p11]
14. ! [X0] : ((curious(X0) & humble(X0)) <=> (~humble(X0) & wise(X0))) [input p13]
23. ~quiet(mary) [input hypothesis]
25. ? [X0] : (tall(X0) & calm(X0)) <=> ? [X1] : (funny(X1) & tall(X1)) [rectify 10]
28. ! [X0] : (~creative(X0) => ~funny(X0)) [pure predicate removal 12]
32. ! [X0] : (~funny(X0) | creative(X0)) [ennf transformation 28]
54. ! [X0] : ((~humble(X0) | ((~quiet(X0) | ~tall(X0)) & (tall(X0) | quiet(X0)))) & (((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | humble(X0))) [nnf transformation 6]
55. ! [X0] : (((funny(X0) | ~generous(X0)) | (funny(X0) & creative(X0))) & ((~funny(X0) | ~creative(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 7]
56. ! [X0] : ((funny(X0) | ~generous(X0) | (funny(X0) & creative(X0))) & (~funny(X0) | ~creative(X0) | (~funny(X0) & generous(X0)))) [flattening 55]
59. (? [X0] : (tall(X0) & calm(X0)) | ! [X1] : (~funny(X1) | ~tall(X1))) & (? [X1] : (funny(X1) & tall(X1)) | ! [X0] : (~tall(X0) | ~calm(X0))) [nnf transformation 25]
60. (? [X0] : (tall(X0) & calm(X0)) | ! [X1] : (~funny(X1) | ~tall(X1))) & (? [X2] : (funny(X2) & tall(X2)) | ! [X3] : (~tall(X3) | ~calm(X3))) [rectify 59]
61. ? [X0] : (tall(X0) & calm(X0)) => (tall(sK5) & calm(sK5)) [choice axiom]
62. ? [X2] : (funny(X2) & tall(X2)) => (funny(sK6) & tall(sK6)) [choice axiom]
63. ((tall(sK5) & calm(sK5)) | ! [X1] : (~funny(X1) | ~tall(X1))) & ((funny(sK6) & tall(sK6)) | ! [X3] : (~tall(X3) | ~calm(X3))) [skolemisation 60,62,61]
64. (funny(fred) | (wise(mary) & calm(mary))) & ((~wise(mary) | ~calm(mary)) | ~funny(fred)) [nnf transformation 11]
65. (funny(fred) | (wise(mary) & calm(mary))) & (~wise(mary) | ~calm(mary) | ~funny(fred)) [flattening 64]
71. ! [X0] : (((curious(X0) & humble(X0)) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | (~curious(X0) | ~humble(X0)))) [nnf transformation 14]
72. ! [X0] : (((curious(X0) & humble(X0)) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | ~curious(X0) | ~humble(X0))) [flattening 71]
109. ~humble(X0) | tall(X0) | quiet(X0) [cnf transformation 54]
112. ~funny(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 56]
121. funny(sK6) | ~tall(X3) | ~calm(X3) [cnf transformation 63]
125. funny(fred) | calm(mary) [cnf transformation 65]
126. funny(fred) | wise(mary) [cnf transformation 65]
127. ~funny(X0) | creative(X0) [cnf transformation 32]
133. humble(X0) | humble(X0) | ~wise(X0) [cnf transformation 72]
147. ~quiet(mary) [cnf transformation 23]
149. ~wise(X0) | humble(X0) [duplicate literal removal 133]
151. ~creative(X0) | ~funny(X0) [duplicate literal removal 112]
274. 27 <=> ! [X3] : (~tall(X3) | ~calm(X3)) [avatar definition]
275. ~calm(X3) | ~tall(X3) <- (27) [avatar component clause 274]
277. 28 <=> funny(sK6) [avatar definition]
279. funny(sK6) <- (28) [avatar component clause 277]
280. 27 | 28 [avatar split clause 121,277,274]
287. 30 <=> wise(mary) [avatar definition]
289. wise(mary) <- (30) [avatar component clause 287]
291. 31 <=> funny(fred) [avatar definition]
293. funny(fred) <- (31) [avatar component clause 291]
294. 30 | 31 [avatar split clause 126,291,287]
296. 32 <=> calm(mary) [avatar definition]
298. calm(mary) <- (32) [avatar component clause 296]
299. 32 | 31 [avatar split clause 125,291,296]
301. ~funny(X0) [subsumption resolution 127,151]
356. $false <- (31) [subsumption resolution 293,301]
357. ~31 [avatar contradiction clause 356]
361. humble(mary) <- (30) [resolution 149,289]
366. ~tall(mary) <- (27, 32) [resolution 275,298]
367. tall(mary) | quiet(mary) <- (30) [resolution 109,361]
368. quiet(mary) <- (27, 30, 32) [subsumption resolution 367,366]
369. $false <- (27, 30, 32) [subsumption resolution 368,147]
370. ~27 | ~30 | ~32 [avatar contradiction clause 369]
372. $false <- (28) [subsumption resolution 279,301]
373. ~28 [avatar contradiction clause 372]
374. $false [avatar sat refutation 280,294,299,357,370,373]
% SZS output end Proof for 3423724652558183974946622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient is not creative or kind and vice versa.
Everyone who is not funny or not creative is curious and vice versa.
Everyone who is not rich or not happy is creative or not patient.
Everyone who is either not quiet or not calm is either not patient or calm and vice versa.
Everyone who is not happy or not curious is both not brave and generous.
Everyone who is both not creative and not happy is both not kind and funny and vice versa.
Everyone who is both funny and not brave is either not old or not strong.
If someone is not curious then someone is both quiet and patient.
If alice is both happy and funny then someone is patient.
Everyone who is either kind or not tall is rich and vice versa.
Everyone who is either not funny or brave is both not curious and not generous.
If someone is both happy and calm then alice is either not brave or curious and vice versa.
If someone is either not brave or generous then fred is quiet and vice versa.
If someone is both curious and not funny then someone is wise.
If someone is both not tall and not patient then someone is both quiet and not creative.
If someone is not brave or not curious then paul is old and vice versa.
Lucy is wise or not humble.
Alice is not brave.
Susan is both not humble and quiet.
Someone is not kind.
Susan is both tall and not kind.
John is both kind and wise.
Someone is either kind or not quiet.
John is both brave and not patient. | Susan is curious. | entailment | (![X]:(~patient(X)<=>(~creative(X)|kind(X))))&
(![X]:((~funny(X)|~creative(X))<=>curious(X)))&
(![X]:((~rich(X)|~happy(X))=>(creative(X)|~patient(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~happy(X))<=>(~kind(X)&funny(X))))&
(![X]:((funny(X)&~brave(X))=>(~old(X)<~>~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(((happy(alice)&funny(alice)))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~generous(X))))&
((?[X]:((happy(X)&calm(X))))<=>((~brave(alice)<~>curious(alice))))&
((?[X]:((~brave(X)<~>generous(X))))<=>(quiet(fred)))&
((?[X]:((curious(X)&~funny(X))))=>(?[X]:(wise(X))))&
((?[X]:((~tall(X)&~patient(X))))=>(?[X]:((quiet(X)&~creative(X)))))&
((?[X]:((~brave(X)|~curious(X))))<=>(old(paul)))&
((wise(lucy)|~humble(lucy)))&
(~brave(alice))&
((~humble(susan)&quiet(susan)))&
(?[X]:(~kind(X)))&
((tall(susan)&~kind(susan)))&
((kind(john)&wise(john)))&
(?[X]:((kind(X)<~>~quiet(X))))&
((brave(john)&~patient(john))) | curious(susan) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1582693285288750167509737
% SZS output start Proof for 1582693285288750167509737
4. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~patient(X0) <~> calm(X0))) [input p3]
8. ? [X0] : ~curious(X0) => ? [X0] : (patient(X0) & quiet(X0)) [input p7]
25. ~curious(susan) [input hypothesis]
26. ? [X0] : ~curious(X0) => ? [X1] : (patient(X1) & quiet(X1)) [rectify 8]
39. ? [X1] : (patient(X1) & quiet(X1)) | ! [X0] : curious(X0) [ennf transformation 26]
49. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) & (((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 4]
53. ? [X0] : (patient(X0) & quiet(X0)) | ! [X1] : curious(X1) [rectify 39]
54. ? [X0] : (patient(X0) & quiet(X0)) => (patient(sK0) & quiet(sK0)) [choice axiom]
55. (patient(sK0) & quiet(sK0)) | ! [X1] : curious(X1) [skolemisation 53,54]
89. calm(X0) | ~patient(X0) | ~quiet(X0) | calm(X0) [cnf transformation 49]
93. ~calm(X0) | ~quiet(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 49]
106. quiet(sK0) | curious(X1) [cnf transformation 55]
107. patient(sK0) | curious(X1) [cnf transformation 55]
140. ~curious(susan) [cnf transformation 25]
141. calm(X0) | ~patient(X0) | ~quiet(X0) [duplicate literal removal 89]
143. ~calm(X0) | ~quiet(X0) | ~patient(X0) [duplicate literal removal 93]
146. ~quiet(X0) | ~patient(X0) [subsumption resolution 141,143]
148. 1 <=> ! [X1] : curious(X1) [avatar definition]
149. curious(X1) <- (1) [avatar component clause 148]
151. 2 <=> patient(sK0) [avatar definition]
153. patient(sK0) <- (2) [avatar component clause 151]
154. 1 | 2 [avatar split clause 107,151,148]
156. 3 <=> quiet(sK0) [avatar definition]
158. quiet(sK0) <- (3) [avatar component clause 156]
159. 1 | 3 [avatar split clause 106,156,148]
279. ~patient(sK0) <- (3) [resolution 146,158]
280. $false <- (2, 3) [subsumption resolution 279,153]
281. ~2 | ~3 [avatar contradiction clause 280]
282. $false <- (1) [resolution 149,140]
285. ~1 [avatar contradiction clause 282]
286. $false [avatar sat refutation 154,159,281,285]
% SZS output end Proof for 1582693285288750167509737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then paul is not tall or not funny. Everyone who is both brave and strong is not brave or patient. Everyone who is calm or patient is humble and vice versa. Everyone who is both not curious and not generous is kind and vice versa. If alice is either not happy or not brave then someone is not rich or tall and vice versa. Everyone who is funny is not kind and vice versa. Everyone who is either wise or not brave is either creative or not funny and vice versa. Everyone who is both happy and not quiet is either brave or not funny and vice versa. Everyone who is not rich is not wise and vice versa. Everyone who is either tall or happy is calm and vice versa. If someone is not quiet or wise then someone is both not tall and not humble. If someone is either tall or not patient then someone is both not funny and not strong and vice versa. Everyone who is either calm or kind is either strong or rich. If paul is humble then someone is not brave and vice versa. If someone is quiet or not creative then someone is tall or not calm. If someone is not creative or not humble then someone is both humble and creative. Mary is both strong and not humble. Someone is old or patient. Someone is strong or kind. Someone is either brave or not humble. Alice is both not quiet and not calm. Mary is wise or tall. Paul is both patient and calm. John is strong or not creative. | Paul is not patient. | contradiction | ((?[X]:(~quiet(X)))=>((~tall(paul)|~funny(paul))))&
(![X]:((brave(X)&strong(X))=>(~brave(X)|patient(X))))&
(![X]:((calm(X)|patient(X))<=>humble(X)))&
(![X]:((~curious(X)&~generous(X))<=>kind(X)))&
(((~happy(alice)<~>~brave(alice)))<=>(?[X]:((~rich(X)|tall(X)))))&
(![X]:(funny(X)<=>~kind(X)))&
(![X]:((wise(X)<~>~brave(X))<=>(creative(X)<~>~funny(X))))&
(![X]:((happy(X)&~quiet(X))<=>(brave(X)<~>~funny(X))))&
(![X]:(~rich(X)<=>~wise(X)))&
(![X]:((tall(X)<~>happy(X))<=>calm(X)))&
((?[X]:((~quiet(X)|wise(X))))=>(?[X]:((~tall(X)&~humble(X)))))&
((?[X]:((tall(X)<~>~patient(X))))<=>(?[X]:((~funny(X)&~strong(X)))))&
(![X]:((calm(X)<~>kind(X))=>(strong(X)<~>rich(X))))&
((humble(paul))<=>(?[X]:(~brave(X))))&
((?[X]:((quiet(X)|~creative(X))))=>(?[X]:((tall(X)|~calm(X)))))&
((?[X]:((~creative(X)|~humble(X))))=>(?[X]:((humble(X)&creative(X)))))&
((strong(mary)&~humble(mary)))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((strong(X)|kind(X))))&
(?[X]:((brave(X)<~>~humble(X))))&
((~quiet(alice)&~calm(alice)))&
((wise(mary)|tall(mary)))&
((patient(paul)&calm(paul)))&
((strong(john)|~creative(john))) | ~patient(paul) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9220013060495943230803807
% SZS output start Proof for 9220013060495943230803807
23. calm(paul) & patient(paul) [input p22]
25. ~patient(paul) [input hypothesis]
143. patient(paul) [cnf transformation 23]
146. ~patient(paul) [cnf transformation 25]
315. $false [subsumption resolution 146,143]
% SZS output end Proof for 9220013060495943230803807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If paul is creative then someone is not curious and vice versa.
If someone is either not kind or tall then someone is wise or not tall and vice versa.
Everyone who is rich is either not strong or not generous.
If mary is both not happy and not wise then someone is either rich or quiet and vice versa.
Everyone who is not old is either not humble or not happy.
If paul is either generous or not quiet then mary is happy or kind and vice versa.
If alice is both humble and happy then susan is both not strong and happy and vice versa.
If someone is not funny or patient then someone is not kind and vice versa.
If someone is not generous then someone is either not brave or not old.
Everyone who is humble or kind is either wise or not humble and vice versa.
Everyone who is patient or rich is both not strong and kind and vice versa.
Everyone who is not brave is both tall and old.
Everyone who is not quiet is both wise and not creative.
If someone is brave then alice is not quiet or old.
Everyone who is kind is both not kind and not happy.
Everyone who is either calm or humble is both rich and not happy and vice versa.
Someone is either tall or old.
Someone is not kind.
Paul is patient or old.
Alice is old.
Mary is creative or not patient.
Someone is tall or funny.
Fred is not patient. | Fred is not happy. | neutral | ((creative(paul))<=>(?[X]:(~curious(X))))&
((?[X]:((~kind(X)<~>tall(X))))<=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(rich(X)=>(~strong(X)<~>~generous(X))))&
(((~happy(mary)&~wise(mary)))<=>(?[X]:((rich(X)<~>quiet(X)))))&
(![X]:(~old(X)=>(~humble(X)<~>~happy(X))))&
(((generous(paul)<~>~quiet(paul)))<=>((happy(mary)|kind(mary))))&
(((humble(alice)&happy(alice)))<=>((~strong(susan)&happy(susan))))&
((?[X]:((~funny(X)|patient(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((humble(X)|kind(X))<=>(wise(X)<~>~humble(X))))&
(![X]:((patient(X)|rich(X))<=>(~strong(X)&kind(X))))&
(![X]:(~brave(X)=>(tall(X)&old(X))))&
(![X]:(~quiet(X)=>(wise(X)&~creative(X))))&
((?[X]:(brave(X)))=>((~quiet(alice)|old(alice))))&
(![X]:(kind(X)=>(~kind(X)&~happy(X))))&
(![X]:((calm(X)<~>humble(X))<=>(rich(X)&~happy(X))))&
(?[X]:((tall(X)<~>old(X))))&
(?[X]:(~kind(X)))&
((patient(paul)|old(paul)))&
(old(alice))&
((creative(mary)|~patient(mary)))&
(?[X]:((tall(X)|funny(X))))&
(~patient(fred)) | ~happy(fred) | [] | null | 0 |
If someone is not kind then someone is not calm or funny and vice versa.
Everyone who is not funny or not rich is not patient or not quiet and vice versa.
If someone is not old then someone is not creative.
Everyone who is either not kind or not calm is both old and not calm and vice versa.
Everyone who is not funny is not happy or not quiet.
If lucy is both tall and wise then someone is not tall or not calm.
If john is tall then someone is either not patient or not funny and vice versa.
If someone is not kind then lucy is curious and vice versa.
Everyone who is both happy and not brave is strong and vice versa.
Everyone who is not creative is both creative and not brave.
If someone is not happy then someone is brave and vice versa.
Everyone who is both curious and not strong is patient or not patient.
If someone is not curious or not quiet then someone is either not generous or not brave and vice versa.
If someone is humble or creative then someone is either calm or rich and vice versa.
If john is both not quiet and quiet then someone is either brave or tall.
If someone is curious or patient then alice is either rich or not creative and vice versa.
Susan is both not humble and brave.
Alice is not creative or not strong.
Someone is brave or tall.
Alice is not rich or patient.
John is either not rich or not happy.
Someone is both happy and generous. | Lucy is not quiet. | neutral | ((?[X]:(~kind(X)))<=>(?[X]:((~calm(X)|funny(X)))))&
(![X]:((~funny(X)|~rich(X))<=>(~patient(X)|~quiet(X))))&
((?[X]:(~old(X)))=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)<~>~calm(X))<=>(old(X)&~calm(X))))&
(![X]:(~funny(X)=>(~happy(X)|~quiet(X))))&
(((tall(lucy)&wise(lucy)))=>(?[X]:((~tall(X)|~calm(X)))))&
((tall(john))<=>(?[X]:((~patient(X)<~>~funny(X)))))&
((?[X]:(~kind(X)))<=>(curious(lucy)))&
(![X]:((happy(X)&~brave(X))<=>strong(X)))&
(![X]:(~creative(X)=>(creative(X)&~brave(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(brave(X))))&
(![X]:((curious(X)&~strong(X))=>(patient(X)|~patient(X))))&
((?[X]:((~curious(X)|~quiet(X))))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
((?[X]:((humble(X)|creative(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(((~quiet(john)&quiet(john)))=>(?[X]:((brave(X)<~>tall(X)))))&
((?[X]:((curious(X)|patient(X))))<=>((rich(alice)<~>~creative(alice))))&
((~humble(susan)&brave(susan)))&
((~creative(alice)|~strong(alice)))&
(?[X]:((brave(X)|tall(X))))&
((~rich(alice)|patient(alice)))&
((~rich(john)<~>~happy(john)))&
(?[X]:((happy(X)&generous(X)))) | ~quiet(lucy) | [] | null | 0 |
If someone is either not wise or quiet then fred is not funny or not quiet.
If mary is either not rich or funny then mary is either funny or strong.
If susan is either patient or curious then someone is both curious and old and vice versa.
Everyone who is either kind or curious is either not creative or old and vice versa.
Everyone who is humble or not kind is both strong and old and vice versa.
If alice is both not curious and wise then someone is not strong and vice versa.
If mary is not kind then someone is tall and vice versa.
If susan is tall then susan is wise or not kind and vice versa.
If someone is either quiet or patient then mary is not generous.
If john is quiet or not rich then someone is either old or happy and vice versa.
Everyone who is wise is either not humble or calm.
Everyone who is humble or not funny is tall.
Everyone who is strong or not generous is old or tall.
If lucy is generous or brave then paul is not quiet or curious and vice versa.
If paul is either curious or not quiet then someone is either kind or calm and vice versa.
If someone is either strong or not funny then someone is both not humble and not quiet.
Paul is not tall or brave.
Lucy is both not wise and not rich.
Susan is not happy or kind.
Someone is both rich and generous.
Alice is generous.
Alice is both brave and calm.
Fred is not calm.
Someone is not humble. | Mary is kind. | contradiction | ((?[X]:((~wise(X)<~>quiet(X))))=>((~funny(fred)|~quiet(fred))))&
(((~rich(mary)<~>funny(mary)))=>((funny(mary)<~>strong(mary))))&
(((patient(susan)<~>curious(susan)))<=>(?[X]:((curious(X)&old(X)))))&
(![X]:((kind(X)<~>curious(X))<=>(~creative(X)<~>old(X))))&
(![X]:((humble(X)|~kind(X))<=>(strong(X)&old(X))))&
(((~curious(alice)&wise(alice)))<=>(?[X]:(~strong(X))))&
((~kind(mary))<=>(?[X]:(tall(X))))&
((tall(susan))<=>((wise(susan)|~kind(susan))))&
((?[X]:((quiet(X)<~>patient(X))))=>(~generous(mary)))&
(((quiet(john)|~rich(john)))<=>(?[X]:((old(X)<~>happy(X)))))&
(![X]:(wise(X)=>(~humble(X)<~>calm(X))))&
(![X]:((humble(X)|~funny(X))=>tall(X)))&
(![X]:((strong(X)|~generous(X))=>(old(X)|tall(X))))&
(((generous(lucy)|brave(lucy)))<=>((~quiet(paul)|curious(paul))))&
(((curious(paul)<~>~quiet(paul)))<=>(?[X]:((kind(X)<~>calm(X)))))&
((?[X]:((strong(X)<~>~funny(X))))=>(?[X]:((~humble(X)&~quiet(X)))))&
((~tall(paul)|brave(paul)))&
((~wise(lucy)&~rich(lucy)))&
((~happy(susan)|kind(susan)))&
(?[X]:((rich(X)&generous(X))))&
(generous(alice))&
((brave(alice)&calm(alice)))&
(~calm(fred))&
(?[X]:(~humble(X))) | kind(mary) | [
"p4",
"p5",
"p6",
"p7",
"p10",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7482853887046729086176784
% SZS output start Proof for 7482853887046729086176784
5. ! [X0] : ((~kind(X0) | humble(X0)) <=> (old(X0) & strong(X0))) [input p4]
6. (wise(alice) & ~curious(alice)) <=> ? [X0] : ~strong(X0) [input p5]
7. ~kind(mary) <=> ? [X0] : tall(X0) [input p6]
8. tall(susan) <=> (~kind(susan) | wise(susan)) [input p7]
11. ! [X0] : (wise(X0) => (~humble(X0) <~> calm(X0))) [input p10]
12. ! [X0] : ((~funny(X0) | humble(X0)) => tall(X0)) [input p11]
13. ! [X0] : ((~generous(X0) | strong(X0)) => (tall(X0) | old(X0))) [input p12]
22. calm(alice) & brave(alice) [input p21]
25. kind(mary) [input hypothesis]
31. ! [X0] : ((~humble(X0) <~> calm(X0)) | ~wise(X0)) [ennf transformation 11]
32. ! [X0] : (tall(X0) | (funny(X0) & ~humble(X0))) [ennf transformation 12]
33. ! [X0] : ((tall(X0) | old(X0)) | (generous(X0) & ~strong(X0))) [ennf transformation 13]
34. ! [X0] : (tall(X0) | old(X0) | (generous(X0) & ~strong(X0))) [flattening 33]
43. ! [X0] : (((~kind(X0) | humble(X0)) | (~old(X0) | ~strong(X0))) & ((old(X0) & strong(X0)) | (kind(X0) & ~humble(X0)))) [nnf transformation 5]
44. ! [X0] : ((~kind(X0) | humble(X0) | ~old(X0) | ~strong(X0)) & ((old(X0) & strong(X0)) | (kind(X0) & ~humble(X0)))) [flattening 43]
45. ((wise(alice) & ~curious(alice)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | (~wise(alice) | curious(alice))) [nnf transformation 6]
46. ((wise(alice) & ~curious(alice)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | ~wise(alice) | curious(alice)) [flattening 45]
47. ((wise(alice) & ~curious(alice)) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | ~wise(alice) | curious(alice)) [rectify 46]
48. ? [X1] : ~strong(X1) => ~strong(sK1) [choice axiom]
49. ((wise(alice) & ~curious(alice)) | ! [X0] : strong(X0)) & (~strong(sK1) | ~wise(alice) | curious(alice)) [skolemisation 47,48]
50. (~kind(mary) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | kind(mary)) [nnf transformation 7]
51. (~kind(mary) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | kind(mary)) [rectify 50]
52. ? [X1] : tall(X1) => tall(sK2) [choice axiom]
53. (~kind(mary) | ! [X0] : ~tall(X0)) & (tall(sK2) | kind(mary)) [skolemisation 51,52]
54. (tall(susan) | (kind(susan) & ~wise(susan))) & ((~kind(susan) | wise(susan)) | ~tall(susan)) [nnf transformation 8]
55. (tall(susan) | (kind(susan) & ~wise(susan))) & (~kind(susan) | wise(susan) | ~tall(susan)) [flattening 54]
62. ! [X0] : (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | ~wise(X0)) [nnf transformation 31]
101. ~kind(X0) | humble(X0) | ~old(X0) | ~strong(X0) [cnf transformation 44]
104. wise(alice) | strong(X0) [cnf transformation 49]
106. ~kind(mary) | ~tall(X0) [cnf transformation 53]
109. tall(susan) | kind(susan) [cnf transformation 55]
119. ~calm(X0) | humble(X0) | ~wise(X0) [cnf transformation 62]
120. ~humble(X0) | tall(X0) [cnf transformation 32]
122. ~strong(X0) | old(X0) | tall(X0) [cnf transformation 34]
148. calm(alice) [cnf transformation 22]
151. kind(mary) [cnf transformation 25]
210. 13 <=> ! [X0] : strong(X0) [avatar definition]
211. strong(X0) <- (13) [avatar component clause 210]
213. 14 <=> wise(alice) [avatar definition]
215. wise(alice) <- (14) [avatar component clause 213]
216. 13 | 14 [avatar split clause 104,213,210]
228. 17 <=> ! [X0] : ~tall(X0) [avatar definition]
229. ~tall(X0) <- (17) [avatar component clause 228]
231. 18 <=> kind(mary) [avatar definition]
234. 17 | ~18 [avatar split clause 106,231,228]
241. 20 <=> kind(susan) [avatar definition]
243. kind(susan) <- (20) [avatar component clause 241]
245. 21 <=> tall(susan) [avatar definition]
246. ~tall(susan) <- (~21) [avatar component clause 245]
247. tall(susan) <- (21) [avatar component clause 245]
248. 20 | 21 [avatar split clause 109,245,241]
369. 18 [avatar split clause 151,231]
384. humble(alice) | ~wise(alice) [resolution 119,148]
386. humble(alice) <- (14) [subsumption resolution 384,215]
399. tall(alice) <- (14) [resolution 386,120]
402. $false <- (14, 17) [subsumption resolution 399,229]
403. ~14 | ~17 [avatar contradiction clause 402]
411. old(X0) | tall(X0) <- (13) [resolution 211,122]
414. old(X0) <- (13, 17) [subsumption resolution 411,229]
492. humble(susan) | ~old(susan) | ~strong(susan) <- (20) [resolution 101,243]
497. humble(susan) | ~strong(susan) <- (13, 17, 20) [subsumption resolution 492,414]
498. humble(susan) <- (13, 17, 20) [subsumption resolution 497,211]
527. tall(susan) <- (13, 17, 20) [resolution 498,120]
530. $false <- (13, 17, 20, ~21) [subsumption resolution 527,246]
531. ~13 | ~17 | ~20 | 21 [avatar contradiction clause 530]
534. $false <- (17, 21) [subsumption resolution 247,229]
535. ~17 | ~21 [avatar contradiction clause 534]
536. $false [avatar sat refutation 216,234,248,369,403,531,535]
% SZS output end Proof for 7482853887046729086176784
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall then someone is either calm or generous and vice versa. If someone is both not quiet and funny then someone is calm and vice versa. If someone is creative or not happy then fred is not calm and vice versa. If someone is not wise then mary is either not kind or funny and vice versa. If john is either humble or not funny then someone is not patient or patient. Everyone who is curious or quiet is not old or not brave and vice versa. Everyone who is not brave or patient is not quiet. If someone is not old then fred is both creative and not happy. If mary is funny or calm then mary is both not calm and not humble. If someone is either generous or curious then mary is not generous or not old and vice versa. If someone is not tall then john is curious or rich. If fred is quiet or not curious then someone is both brave and not calm and vice versa. Everyone who is either not strong or not funny is either not creative or funny and vice versa. Everyone who is not generous is quiet. If john is either not generous or quiet then fred is not humble and vice versa. If mary is not humble then alice is both old and not funny. Someone is both not tall and not curious. Someone is patient. Fred is either rich or not kind. Someone is either kind or creative. Someone is either not rich or not wise. Someone is not funny. Alice is not calm or not kind. Someone is wise or not rich. | Fred is strong. | contradiction | ((?[X]:(~tall(X)))<=>(?[X]:((calm(X)<~>generous(X)))))&
((?[X]:((~quiet(X)&funny(X))))<=>(?[X]:(calm(X))))&
((?[X]:((creative(X)|~happy(X))))<=>(~calm(fred)))&
((?[X]:(~wise(X)))<=>((~kind(mary)<~>funny(mary))))&
(((humble(john)<~>~funny(john)))=>(?[X]:((~patient(X)|patient(X)))))&
(![X]:((curious(X)|quiet(X))<=>(~old(X)|~brave(X))))&
(![X]:((~brave(X)|patient(X))=>~quiet(X)))&
((?[X]:(~old(X)))=>((creative(fred)&~happy(fred))))&
(((funny(mary)|calm(mary)))=>((~calm(mary)&~humble(mary))))&
((?[X]:((generous(X)<~>curious(X))))<=>((~generous(mary)|~old(mary))))&
((?[X]:(~tall(X)))=>((curious(john)|rich(john))))&
(((quiet(fred)|~curious(fred)))<=>(?[X]:((brave(X)&~calm(X)))))&
(![X]:((~strong(X)<~>~funny(X))<=>(~creative(X)<~>funny(X))))&
(![X]:(~generous(X)=>quiet(X)))&
(((~generous(john)<~>quiet(john)))<=>(~humble(fred)))&
((~humble(mary))=>((old(alice)&~funny(alice))))&
(?[X]:((~tall(X)&~curious(X))))&
(?[X]:(patient(X)))&
((rich(fred)<~>~kind(fred)))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:(~funny(X)))&
((~calm(alice)|~kind(alice)))&
(?[X]:((wise(X)|~rich(X)))) | strong(fred) | [
"p5",
"p6",
"p7",
"p9",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 521824908787676748217490
% SZS output start Proof for 521824908787676748217490
6. ! [X0] : ((quiet(X0) | curious(X0)) <=> (~brave(X0) | ~old(X0))) [input p5]
7. ! [X0] : ((patient(X0) | ~brave(X0)) => ~quiet(X0)) [input p6]
8. ? [X0] : ~old(X0) => (~happy(fred) & creative(fred)) [input p7]
10. ? [X0] : (generous(X0) <~> curious(X0)) <=> (~old(mary) | ~generous(mary)) [input p9]
13. ! [X0] : ((~strong(X0) <~> ~funny(X0)) <=> (~creative(X0) <~> funny(X0))) [input p12]
14. ! [X0] : (~generous(X0) => quiet(X0)) [input p13]
17. ? [X0] : (~curious(X0) & ~tall(X0)) [input p16]
25. strong(fred) [input hypothesis]
29. ! [X0] : (~quiet(X0) | (~patient(X0) & brave(X0))) [ennf transformation 7]
30. (~happy(fred) & creative(fred)) | ! [X0] : old(X0) [ennf transformation 8]
34. ! [X0] : (quiet(X0) | generous(X0)) [ennf transformation 14]
57. ! [X0] : (((quiet(X0) | curious(X0)) | (brave(X0) & old(X0))) & ((~brave(X0) | ~old(X0)) | (~quiet(X0) & ~curious(X0)))) [nnf transformation 6]
58. ! [X0] : ((quiet(X0) | curious(X0) | (brave(X0) & old(X0))) & (~brave(X0) | ~old(X0) | (~quiet(X0) & ~curious(X0)))) [flattening 57]
59. (? [X0] : ((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (old(mary) & generous(mary))) & ((~old(mary) | ~generous(mary)) | ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) [nnf transformation 10]
60. (? [X0] : ((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (old(mary) & generous(mary))) & (~old(mary) | ~generous(mary) | ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) [flattening 59]
61. (? [X0] : ((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (old(mary) & generous(mary))) & (~old(mary) | ~generous(mary) | ! [X1] : ((generous(X1) | ~curious(X1)) & (curious(X1) | ~generous(X1)))) [rectify 60]
62. ? [X0] : ((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) => ((~curious(sK7) | ~generous(sK7)) & (curious(sK7) | generous(sK7))) [choice axiom]
63. (((~curious(sK7) | ~generous(sK7)) & (curious(sK7) | generous(sK7))) | (old(mary) & generous(mary))) & (~old(mary) | ~generous(mary) | ! [X1] : ((generous(X1) | ~curious(X1)) & (curious(X1) | ~generous(X1)))) [skolemisation 61,62]
69. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [nnf transformation 13]
71. ? [X0] : (~curious(X0) & ~tall(X0)) => (~curious(sK9) & ~tall(sK9)) [choice axiom]
72. ~curious(sK9) & ~tall(sK9) [skolemisation 17,71]
103. ~brave(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 58]
106. ~quiet(X0) | brave(X0) [cnf transformation 29]
108. creative(fred) | old(X0) [cnf transformation 30]
114. ~old(mary) | ~generous(mary) | curious(X1) | ~generous(X1) [cnf transformation 63]
127. funny(X0) | ~creative(X0) | ~strong(X0) | funny(X0) [cnf transformation 69]
131. ~funny(X0) | ~strong(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 69]
134. quiet(X0) | generous(X0) [cnf transformation 34]
142. ~curious(sK9) [cnf transformation 72]
153. strong(fred) [cnf transformation 25]
154. funny(X0) | ~creative(X0) | ~strong(X0) [duplicate literal removal 127]
156. ~funny(X0) | ~strong(X0) | ~creative(X0) [duplicate literal removal 131]
246. 21 <=> ! [X0] : old(X0) [avatar definition]
247. old(X0) <- (21) [avatar component clause 246]
254. 23 <=> creative(fred) [avatar definition]
257. 21 | 23 [avatar split clause 108,254,246]
271. 26 <=> old(mary) [avatar definition]
272. ~old(mary) <- (~26) [avatar component clause 271]
284. 29 <=> generous(mary) [avatar definition]
285. ~generous(mary) <- (~29) [avatar component clause 284]
295. 31 <=> ! [X1] : (curious(X1) | ~generous(X1)) [avatar definition]
296. curious(X1) | ~generous(X1) <- (31) [avatar component clause 295]
297. 31 | ~29 | ~26 [avatar split clause 114,271,284,295]
332. ~strong(X0) | ~creative(X0) [subsumption resolution 154,156]
412. $false <- (21, ~26) [resolution 272,247]
413. ~21 | 26 [avatar contradiction clause 412]
415. brave(X0) | generous(X0) [resolution 134,106]
422. ~creative(fred) [resolution 332,153]
426. ~23 [avatar split clause 422,254]
448. ~old(X0) | ~quiet(X0) | generous(X0) [resolution 103,415]
450. ~quiet(X0) | generous(X0) <- (21) [subsumption resolution 448,247]
451. generous(X0) <- (21) [subsumption resolution 450,134]
456. $false <- (21, ~29) [resolution 451,285]
457. ~21 | 29 [avatar contradiction clause 456]
458. curious(X1) <- (21, 31) [subsumption resolution 296,451]
463. $false <- (21, 31) [resolution 458,142]
464. ~21 | ~31 [avatar contradiction clause 463]
468. $false [avatar sat refutation 257,297,413,426,457,464]
% SZS output end Proof for 521824908787676748217490
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is not humble.
Everyone who is either strong or not strong is calm.
If someone is either not generous or patient then mary is patient or not curious and vice versa.
If mary is not funny then mary is either not wise or humble and vice versa.
If susan is old then someone is either not curious or not brave.
If susan is not happy then someone is both not curious and not calm and vice versa.
If lucy is patient or not old then susan is either creative or not strong.
If someone is both not funny and not humble then lucy is both patient and strong and vice versa.
If paul is patient or tall then someone is both rich and funny.
Everyone who is both rich and not strong is both not strong and funny.
Everyone who is either not old or not kind is both not old and brave.
Everyone who is not humble or not wise is tall or not old.
Everyone who is wise is either not creative or not tall.
Everyone who is not old or brave is both not funny and not old.
Everyone who is both not curious and not generous is not curious and vice versa.
Everyone who is not brave is not curious or not old and vice versa.
Someone is not humble or wise.
Susan is both not curious and happy.
Paul is not brave or not rich.
Paul is both creative and not rich.
Paul is not old or not wise.
Someone is not generous.
Someone is either not creative or not tall.
Someone is not old. | Lucy is not humble. | neutral | (![X]:(~quiet(X)=>~humble(X)))&
(![X]:((strong(X)<~>~strong(X))=>calm(X)))&
((?[X]:((~generous(X)<~>patient(X))))<=>((patient(mary)|~curious(mary))))&
((~funny(mary))<=>((~wise(mary)<~>humble(mary))))&
((old(susan))=>(?[X]:((~curious(X)<~>~brave(X)))))&
((~happy(susan))<=>(?[X]:((~curious(X)&~calm(X)))))&
(((patient(lucy)|~old(lucy)))=>((creative(susan)<~>~strong(susan))))&
((?[X]:((~funny(X)&~humble(X))))<=>((patient(lucy)&strong(lucy))))&
(((patient(paul)|tall(paul)))=>(?[X]:((rich(X)&funny(X)))))&
(![X]:((rich(X)&~strong(X))=>(~strong(X)&funny(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~old(X)&brave(X))))&
(![X]:((~humble(X)|~wise(X))=>(tall(X)|~old(X))))&
(![X]:(wise(X)=>(~creative(X)<~>~tall(X))))&
(![X]:((~old(X)|brave(X))=>(~funny(X)&~old(X))))&
(![X]:((~curious(X)&~generous(X))<=>~curious(X)))&
(![X]:(~brave(X)<=>(~curious(X)|~old(X))))&
(?[X]:((~humble(X)|wise(X))))&
((~curious(susan)&happy(susan)))&
((~brave(paul)|~rich(paul)))&
((creative(paul)&~rich(paul)))&
((~old(paul)|~wise(paul)))&
(?[X]:(~generous(X)))&
(?[X]:((~creative(X)<~>~tall(X))))&
(?[X]:(~old(X))) | ~humble(lucy) | [] | null | 0 |
If paul is both not generous and not curious then lucy is both not funny and not creative and vice versa.
If someone is curious or not tall then someone is both not quiet and not kind and vice versa.
If paul is not generous then fred is both not humble and old.
If alice is both not old and happy then mary is both generous and not funny and vice versa.
Everyone who is either not kind or old is not creative or calm.
Everyone who is both not happy and strong is either not curious or kind.
Everyone who is not humble is not rich or rich.
Everyone who is both not patient and wise is either old or not quiet.
Everyone who is not patient or not brave is not happy and vice versa.
Everyone who is patient is either funny or strong.
If susan is not rich then john is not kind and vice versa.
If someone is both not rich and not happy then someone is both wise and not creative.
If lucy is either generous or old then someone is generous or not rich.
Everyone who is both generous and brave is either rich or humble and vice versa.
Everyone who is not generous is not humble.
If someone is both not funny and creative then fred is both not quiet and patient.
Paul is either happy or not happy.
Someone is either generous or not strong.
Someone is either kind or tall.
Paul is curious.
Mary is both strong and not calm.
Someone is not funny.
Paul is both brave and not strong.
Someone is humble. | Fred is creative. | neutral | (((~generous(paul)&~curious(paul)))<=>((~funny(lucy)&~creative(lucy))))&
((?[X]:((curious(X)|~tall(X))))<=>(?[X]:((~quiet(X)&~kind(X)))))&
((~generous(paul))=>((~humble(fred)&old(fred))))&
(((~old(alice)&happy(alice)))<=>((generous(mary)&~funny(mary))))&
(![X]:((~kind(X)<~>old(X))=>(~creative(X)|calm(X))))&
(![X]:((~happy(X)&strong(X))=>(~curious(X)<~>kind(X))))&
(![X]:(~humble(X)=>(~rich(X)|rich(X))))&
(![X]:((~patient(X)&wise(X))=>(old(X)<~>~quiet(X))))&
(![X]:((~patient(X)|~brave(X))<=>~happy(X)))&
(![X]:(patient(X)=>(funny(X)<~>strong(X))))&
((~rich(susan))<=>(~kind(john)))&
((?[X]:((~rich(X)&~happy(X))))=>(?[X]:((wise(X)&~creative(X)))))&
(((generous(lucy)<~>old(lucy)))=>(?[X]:((generous(X)|~rich(X)))))&
(![X]:((generous(X)&brave(X))<=>(rich(X)<~>humble(X))))&
(![X]:(~generous(X)=>~humble(X)))&
((?[X]:((~funny(X)&creative(X))))=>((~quiet(fred)&patient(fred))))&
((happy(paul)<~>~happy(paul)))&
(?[X]:((generous(X)<~>~strong(X))))&
(?[X]:((kind(X)<~>tall(X))))&
(curious(paul))&
((strong(mary)&~calm(mary)))&
(?[X]:(~funny(X)))&
((brave(paul)&~strong(paul)))&
(?[X]:(humble(X))) | creative(fred) | [] | null | 0 |
Everyone who is not brave or not calm is not kind and vice versa.
Everyone who is either funny or not quiet is happy or not wise and vice versa.
Everyone who is old or brave is both tall and not humble and vice versa.
Everyone who is either not happy or happy is both not curious and quiet.
Everyone who is not calm is both curious and not strong and vice versa.
Everyone who is not kind or not brave is either creative or not wise and vice versa.
Everyone who is both calm and wise is not old or not generous and vice versa.
Everyone who is old is not humble.
Everyone who is not funny or not brave is either not rich or brave.
Everyone who is calm or not curious is not kind and vice versa.
Everyone who is not funny or not quiet is quiet or not funny.
Everyone who is not brave is either rich or not generous and vice versa.
Everyone who is both calm and not creative is wise.
Everyone who is not tall or rich is tall or creative and vice versa.
If mary is both not humble and not happy then paul is both happy and not generous.
Someone is either patient or calm.
Someone is not brave or not funny.
Lucy is humble or calm.
Fred is either humble or brave.
Paul is not happy or not curious. | Paul is old. | contradiction | (![X]:((~brave(X)|~calm(X))<=>~kind(X)))&
(![X]:((funny(X)<~>~quiet(X))<=>(happy(X)|~wise(X))))&
(![X]:((old(X)|brave(X))<=>(tall(X)&~humble(X))))&
(![X]:((~happy(X)<~>happy(X))=>(~curious(X)&quiet(X))))&
(![X]:(~calm(X)<=>(curious(X)&~strong(X))))&
(![X]:((~kind(X)|~brave(X))<=>(creative(X)<~>~wise(X))))&
(![X]:((calm(X)&wise(X))<=>(~old(X)|~generous(X))))&
(![X]:(old(X)=>~humble(X)))&
(![X]:((~funny(X)|~brave(X))=>(~rich(X)<~>brave(X))))&
(![X]:((calm(X)|~curious(X))<=>~kind(X)))&
(![X]:((~funny(X)|~quiet(X))=>(quiet(X)|~funny(X))))&
(![X]:(~brave(X)<=>(rich(X)<~>~generous(X))))&
(![X]:((calm(X)&~creative(X))=>wise(X)))&
(![X]:((~tall(X)|rich(X))<=>(tall(X)|creative(X))))&
(((~humble(mary)&~happy(mary)))=>((happy(paul)&~generous(paul))))&
(?[X]:((patient(X)<~>calm(X))))&
(?[X]:((~brave(X)|~funny(X))))&
((humble(lucy)|calm(lucy)))&
((humble(fred)<~>brave(fred)))&
((~happy(paul)|~curious(paul))) | old(paul) | [
"p0",
"p2",
"p3",
"p4",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2368075289636194857750770
% SZS output start Proof for 2368075289636194857750770
1. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> ~kind(X0)) [input p0]
3. ! [X0] : ((brave(X0) | old(X0)) <=> (~humble(X0) & tall(X0))) [input p2]
4. ! [X0] : ((~happy(X0) <~> happy(X0)) => (quiet(X0) & ~curious(X0))) [input p3]
5. ! [X0] : (~calm(X0) <=> (~strong(X0) & curious(X0))) [input p4]
9. ! [X0] : ((~brave(X0) | ~funny(X0)) => (~rich(X0) <~> brave(X0))) [input p8]
10. ! [X0] : ((~curious(X0) | calm(X0)) <=> ~kind(X0)) [input p9]
14. ! [X0] : ((rich(X0) | ~tall(X0)) <=> (creative(X0) | tall(X0))) [input p13]
21. old(paul) [input hypothesis]
22. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~happy(X0) <=> happy(X0))) [ennf transformation 4]
24. ! [X0] : ((~rich(X0) <~> brave(X0)) | (brave(X0) & funny(X0))) [ennf transformation 9]
31. ! [X0] : (((~calm(X0) | ~brave(X0)) | kind(X0)) & (~kind(X0) | (calm(X0) & brave(X0)))) [nnf transformation 1]
32. ! [X0] : ((~calm(X0) | ~brave(X0) | kind(X0)) & (~kind(X0) | (calm(X0) & brave(X0)))) [flattening 31]
35. ! [X0] : (((brave(X0) | old(X0)) | (humble(X0) | ~tall(X0))) & ((~humble(X0) & tall(X0)) | (~brave(X0) & ~old(X0)))) [nnf transformation 3]
36. ! [X0] : ((brave(X0) | old(X0) | humble(X0) | ~tall(X0)) & ((~humble(X0) & tall(X0)) | (~brave(X0) & ~old(X0)))) [flattening 35]
37. ! [X0] : ((quiet(X0) & ~curious(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 22]
38. ! [X0] : ((~calm(X0) | (strong(X0) | ~curious(X0))) & ((~strong(X0) & curious(X0)) | calm(X0))) [nnf transformation 5]
39. ! [X0] : ((~calm(X0) | strong(X0) | ~curious(X0)) & ((~strong(X0) & curious(X0)) | calm(X0))) [flattening 38]
44. ! [X0] : (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (brave(X0) & funny(X0))) [nnf transformation 24]
45. ! [X0] : (((~curious(X0) | calm(X0)) | kind(X0)) & (~kind(X0) | (curious(X0) & ~calm(X0)))) [nnf transformation 10]
46. ! [X0] : ((~curious(X0) | calm(X0) | kind(X0)) & (~kind(X0) | (curious(X0) & ~calm(X0)))) [flattening 45]
48. ! [X0] : (((rich(X0) | ~tall(X0)) | (~creative(X0) & ~tall(X0))) & ((creative(X0) | tall(X0)) | (~rich(X0) & tall(X0)))) [nnf transformation 14]
49. ! [X0] : ((rich(X0) | ~tall(X0) | (~creative(X0) & ~tall(X0))) & (creative(X0) | tall(X0) | (~rich(X0) & tall(X0)))) [flattening 48]
58. ~calm(X0) | ~brave(X0) | kind(X0) [cnf transformation 32]
65. ~old(X0) | tall(X0) [cnf transformation 36]
70. ~curious(X0) | happy(X0) | happy(X0) [cnf transformation 37]
71. ~curious(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 37]
74. curious(X0) | calm(X0) [cnf transformation 39]
90. brave(X0) | ~rich(X0) | brave(X0) [cnf transformation 44]
94. ~kind(X0) | curious(X0) [cnf transformation 46]
105. rich(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 49]
116. old(paul) [cnf transformation 21]
118. ~tall(X0) | rich(X0) [duplicate literal removal 105]
120. ~rich(X0) | brave(X0) [duplicate literal removal 90]
121. ~curious(X0) | happy(X0) [duplicate literal removal 70]
122. ~curious(X0) | ~happy(X0) [duplicate literal removal 71]
126. ~curious(X0) [subsumption resolution 121,122]
127. calm(X0) [subsumption resolution 74,126]
131. ~kind(X0) [subsumption resolution 94,126]
172. tall(paul) [resolution 65,116]
178. rich(paul) [resolution 118,172]
179. brave(paul) [resolution 120,178]
187. ~brave(X0) | kind(X0) [resolution 58,127]
188. ~brave(X0) [subsumption resolution 187,131]
189. $false [resolution 188,179]
% SZS output end Proof for 2368075289636194857750770
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or not tall then fred is both not kind and tall.
If paul is both not creative and not strong then john is not generous and vice versa.
Everyone who is both humble and not tall is both humble and kind and vice versa.
Everyone who is both happy and not calm is not humble.
Everyone who is both not kind and quiet is either patient or not quiet.
Everyone who is quiet is not strong or humble.
If someone is funny then alice is either funny or not rich and vice versa.
Everyone who is brave is both not happy and generous.
Everyone who is creative or not patient is wise or kind.
If someone is not quiet or strong then john is not creative or not calm.
If someone is both quiet and calm then susan is funny or not kind.
Everyone who is happy or not wise is both strong and not generous.
If someone is both funny and not brave then susan is quiet and vice versa.
If someone is not creative or tall then someone is both not tall and not calm and vice versa.
Everyone who is not curious is not kind or rich and vice versa.
If someone is wise then someone is tall and vice versa.
Someone is either funny or not kind.
Someone is kind or not wise.
Someone is either not kind or happy.
Someone is both not patient and humble.
Lucy is tall.
Susan is quiet.
John is both happy and kind.
Someone is not rich. | Paul is not happy. | entailment | ((?[X]:((~curious(X)|~tall(X))))=>((~kind(fred)&tall(fred))))&
(((~creative(paul)&~strong(paul)))<=>(~generous(john)))&
(![X]:((humble(X)&~tall(X))<=>(humble(X)&kind(X))))&
(![X]:((happy(X)&~calm(X))=>~humble(X)))&
(![X]:((~kind(X)&quiet(X))=>(patient(X)<~>~quiet(X))))&
(![X]:(quiet(X)=>(~strong(X)|humble(X))))&
((?[X]:(funny(X)))<=>((funny(alice)<~>~rich(alice))))&
(![X]:(brave(X)=>(~happy(X)&generous(X))))&
(![X]:((creative(X)|~patient(X))=>(wise(X)|kind(X))))&
((?[X]:((~quiet(X)|strong(X))))=>((~creative(john)|~calm(john))))&
((?[X]:((quiet(X)&calm(X))))=>((funny(susan)|~kind(susan))))&
(![X]:((happy(X)|~wise(X))=>(strong(X)&~generous(X))))&
((?[X]:((funny(X)&~brave(X))))<=>(quiet(susan)))&
((?[X]:((~creative(X)|tall(X))))<=>(?[X]:((~tall(X)&~calm(X)))))&
(![X]:(~curious(X)<=>(~kind(X)|rich(X))))&
((?[X]:(wise(X)))<=>(?[X]:(tall(X))))&
(?[X]:((funny(X)<~>~kind(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:((~patient(X)&humble(X))))&
(tall(lucy))&
(quiet(susan))&
((happy(john)&kind(john)))&
(?[X]:(~rich(X))) | ~happy(paul) | [
"p1",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1631124508243573985406860
% SZS output start Proof for 1631124508243573985406860
2. (~strong(paul) & ~creative(paul)) <=> ~generous(john) [input p1]
12. ! [X0] : ((~wise(X0) | happy(X0)) => (~generous(X0) & strong(X0))) [input p11]
23. kind(john) & happy(john) [input p22]
25. happy(paul) [input hypothesis]
43. ! [X0] : ((~generous(X0) & strong(X0)) | (wise(X0) & ~happy(X0))) [ennf transformation 12]
45. ((~strong(paul) & ~creative(paul)) | generous(john)) & (~generous(john) | (strong(paul) | creative(paul))) [nnf transformation 2]
46. ((~strong(paul) & ~creative(paul)) | generous(john)) & (~generous(john) | strong(paul) | creative(paul)) [flattening 45]
86. ~strong(paul) | generous(john) [cnf transformation 46]
106. ~happy(X0) | strong(X0) [cnf transformation 43]
108. ~happy(X0) | ~generous(X0) [cnf transformation 43]
131. happy(john) [cnf transformation 23]
134. happy(paul) [cnf transformation 25]
155. 5 <=> generous(john) [avatar definition]
157. generous(john) <- (5) [avatar component clause 155]
159. 6 <=> strong(paul) [avatar definition]
162. 5 | ~6 [avatar split clause 86,159,155]
314. strong(paul) [resolution 106,134]
317. 6 [avatar split clause 314,159]
319. ~generous(john) [resolution 108,131]
321. $false <- (5) [subsumption resolution 319,157]
322. ~5 [avatar contradiction clause 321]
323. $false [avatar sat refutation 162,317,322]
% SZS output end Proof for 1631124508243573985406860
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or brave is tall or humble.
If john is both not generous and not patient then alice is not rich.
Everyone who is both not happy and not tall is both humble and old.
Everyone who is both not generous and calm is either not kind or old and vice versa.
Everyone who is not generous is both kind and not quiet and vice versa.
Everyone who is humble or generous is not wise or not happy and vice versa.
If alice is not creative or not kind then someone is not funny or old and vice versa.
If paul is not calm or not generous then lucy is not old or not tall and vice versa.
If someone is not calm then fred is not curious or strong and vice versa.
If john is both old and rich then someone is both not wise and not kind.
Everyone who is not brave is both funny and not wise and vice versa.
Everyone who is happy or not quiet is quiet and vice versa.
Everyone who is kind or not rich is brave or not wise.
Everyone who is quiet or not happy is both kind and not tall.
Everyone who is brave or not wise is rich or brave.
Everyone who is both not quiet and curious is either curious or funny.
Someone is both generous and not creative.
Alice is rich or creative.
Fred is either old or funny.
Susan is not funny.
Alice is not wise. | Lucy is not patient. | neutral | (![X]:((curious(X)<~>brave(X))=>(tall(X)|humble(X))))&
(((~generous(john)&~patient(john)))=>(~rich(alice)))&
(![X]:((~happy(X)&~tall(X))=>(humble(X)&old(X))))&
(![X]:((~generous(X)&calm(X))<=>(~kind(X)<~>old(X))))&
(![X]:(~generous(X)<=>(kind(X)&~quiet(X))))&
(![X]:((humble(X)|generous(X))<=>(~wise(X)|~happy(X))))&
(((~creative(alice)|~kind(alice)))<=>(?[X]:((~funny(X)|old(X)))))&
(((~calm(paul)|~generous(paul)))<=>((~old(lucy)|~tall(lucy))))&
((?[X]:(~calm(X)))<=>((~curious(fred)|strong(fred))))&
(((old(john)&rich(john)))=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(~brave(X)<=>(funny(X)&~wise(X))))&
(![X]:((happy(X)|~quiet(X))<=>quiet(X)))&
(![X]:((kind(X)|~rich(X))=>(brave(X)|~wise(X))))&
(![X]:((quiet(X)|~happy(X))=>(kind(X)&~tall(X))))&
(![X]:((brave(X)|~wise(X))=>(rich(X)|brave(X))))&
(![X]:((~quiet(X)&curious(X))=>(curious(X)<~>funny(X))))&
(?[X]:((generous(X)&~creative(X))))&
((rich(alice)|creative(alice)))&
((old(fred)<~>funny(fred)))&
(~funny(susan))&
(~wise(alice)) | ~patient(lucy) | [] | null | 0 |
If someone is patient then susan is either humble or not generous. If someone is not generous then someone is both not creative and not funny. Everyone who is both not patient and not rich is either not quiet or generous. Everyone who is either wise or quiet is not strong or not wise. If someone is both creative and not generous then alice is creative. If alice is either not generous or generous then lucy is both not curious and not rich. If someone is both tall and old then mary is not funny and vice versa. Everyone who is either rich or not tall is rich or creative. Everyone who is old or quiet is either old or not kind and vice versa. If someone is both not tall and kind then susan is either humble or not happy and vice versa. Everyone who is strong or curious is not kind or not tall. If fred is wise or not curious then paul is not funny and vice versa. Everyone who is either curious or patient is strong or not humble and vice versa. Everyone who is calm or not old is both brave and rich. Everyone who is happy or generous is both not wise and calm. If fred is both not wise and funny then lucy is both not curious and strong. Fred is curious. Someone is not wise. Paul is either not happy or generous. John is happy or kind. Someone is both kind and tall. John is both not rich and not quiet. Mary is both curious and funny. Someone is both tall and patient. | Lucy is tall. | contradiction | ((?[X]:(patient(X)))=>((humble(susan)<~>~generous(susan))))&
((?[X]:(~generous(X)))=>(?[X]:((~creative(X)&~funny(X)))))&
(![X]:((~patient(X)&~rich(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((wise(X)<~>quiet(X))=>(~strong(X)|~wise(X))))&
((?[X]:((creative(X)&~generous(X))))=>(creative(alice)))&
(((~generous(alice)<~>generous(alice)))=>((~curious(lucy)&~rich(lucy))))&
((?[X]:((tall(X)&old(X))))<=>(~funny(mary)))&
(![X]:((rich(X)<~>~tall(X))=>(rich(X)|creative(X))))&
(![X]:((old(X)|quiet(X))<=>(old(X)<~>~kind(X))))&
((?[X]:((~tall(X)&kind(X))))<=>((humble(susan)<~>~happy(susan))))&
(![X]:((strong(X)|curious(X))=>(~kind(X)|~tall(X))))&
(((wise(fred)|~curious(fred)))<=>(~funny(paul)))&
(![X]:((curious(X)<~>patient(X))<=>(strong(X)|~humble(X))))&
(![X]:((calm(X)|~old(X))=>(brave(X)&rich(X))))&
(![X]:((happy(X)|generous(X))=>(~wise(X)&calm(X))))&
(((~wise(fred)&funny(fred)))=>((~curious(lucy)&strong(lucy))))&
(curious(fred))&
(?[X]:(~wise(X)))&
((~happy(paul)<~>generous(paul)))&
((happy(john)|kind(john)))&
(?[X]:((kind(X)&tall(X))))&
((~rich(john)&~quiet(john)))&
((curious(mary)&funny(mary)))&
(?[X]:((tall(X)&patient(X)))) | tall(lucy) | [
"p5",
"p6",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9111733214586459656521397
% SZS output start Proof for 9111733214586459656521397
6. (~generous(alice) <~> generous(alice)) => (~rich(lucy) & ~curious(lucy)) [input p5]
7. ? [X0] : (old(X0) & tall(X0)) <=> ~funny(mary) [input p6]
14. ! [X0] : ((~old(X0) | calm(X0)) => (rich(X0) & brave(X0))) [input p13]
23. funny(mary) & curious(mary) [input p22]
25. tall(lucy) [input hypothesis]
27. ! [X0] : ((~old(X0) | calm(X0)) => rich(X0)) [pure predicate removal 14]
35. (~rich(lucy) & ~curious(lucy)) | (~generous(alice) <=> generous(alice)) [ennf transformation 6]
40. ! [X0] : (rich(X0) | (old(X0) & ~calm(X0))) [ennf transformation 27]
50. (~rich(lucy) & ~curious(lucy)) | ((~generous(alice) | ~generous(alice)) & (generous(alice) | generous(alice))) [nnf transformation 35]
51. (? [X0] : (old(X0) & tall(X0)) | funny(mary)) & (~funny(mary) | ! [X0] : (~old(X0) | ~tall(X0))) [nnf transformation 7]
52. (? [X0] : (old(X0) & tall(X0)) | funny(mary)) & (~funny(mary) | ! [X1] : (~old(X1) | ~tall(X1))) [rectify 51]
53. ? [X0] : (old(X0) & tall(X0)) => (old(sK1) & tall(sK1)) [choice axiom]
54. ((old(sK1) & tall(sK1)) | funny(mary)) & (~funny(mary) | ! [X1] : (~old(X1) | ~tall(X1))) [skolemisation 52,53]
84. ~rich(lucy) | generous(alice) | generous(alice) [cnf transformation 50]
85. ~rich(lucy) | ~generous(alice) | ~generous(alice) [cnf transformation 50]
86. ~funny(mary) | ~old(X1) | ~tall(X1) [cnf transformation 54]
115. old(X0) | rich(X0) [cnf transformation 40]
132. funny(mary) [cnf transformation 23]
135. tall(lucy) [cnf transformation 25]
141. ~rich(lucy) | generous(alice) [duplicate literal removal 84]
142. ~rich(lucy) | ~generous(alice) [duplicate literal removal 85]
179. 9 <=> generous(alice) [avatar definition]
183. 10 <=> rich(lucy) [avatar definition]
185. ~rich(lucy) <- (~10) [avatar component clause 183]
186. ~9 | ~10 [avatar split clause 142,183,179]
187. 9 | ~10 [avatar split clause 141,183,179]
195. 12 <=> funny(mary) [avatar definition]
209. 15 <=> ! [X1] : (~old(X1) | ~tall(X1)) [avatar definition]
210. ~old(X1) | ~tall(X1) <- (15) [avatar component clause 209]
211. 15 | ~12 [avatar split clause 86,195,209]
278. 12 [avatar split clause 132,195]
285. ~tall(X0) | rich(X0) <- (15) [resolution 210,115]
433. rich(lucy) <- (15) [resolution 285,135]
437. $false <- (~10, 15) [subsumption resolution 433,185]
438. 10 | ~15 [avatar contradiction clause 437]
439. $false [avatar sat refutation 186,187,211,278,438]
% SZS output end Proof for 9111733214586459656521397
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or curious is both funny and not humble and vice versa.
Everyone who is both not strong and old is not creative or not brave and vice versa.
If john is kind or humble then susan is either tall or patient.
Everyone who is either not patient or humble is not generous or not brave and vice versa.
If someone is not kind then someone is curious or humble.
If someone is either funny or not generous then someone is both not curious and not brave and vice versa.
Everyone who is not old or not generous is funny or calm and vice versa.
Everyone who is quiet or not creative is curious.
Everyone who is either funny or not generous is either wise or not creative and vice versa.
Everyone who is strong or wise is wise or curious.
Everyone who is both not kind and funny is not curious or funny and vice versa.
Everyone who is not quiet is tall.
If susan is happy or not tall then someone is either generous or not curious.
If john is either humble or not calm then someone is not curious or not patient.
Everyone who is not creative or not happy is both old and wise.
If paul is not happy or strong then john is patient or not tall and vice versa.
Paul is not generous or not creative.
Susan is not generous.
Paul is not humble.
Fred is patient or not funny.
Someone is either old or strong.
Lucy is either creative or patient. | Lucy is generous. | neutral | (![X]:((~strong(X)|curious(X))<=>(funny(X)&~humble(X))))&
(![X]:((~strong(X)&old(X))<=>(~creative(X)|~brave(X))))&
(((kind(john)|humble(john)))=>((tall(susan)<~>patient(susan))))&
(![X]:((~patient(X)<~>humble(X))<=>(~generous(X)|~brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((curious(X)|humble(X)))))&
((?[X]:((funny(X)<~>~generous(X))))<=>(?[X]:((~curious(X)&~brave(X)))))&
(![X]:((~old(X)|~generous(X))<=>(funny(X)|calm(X))))&
(![X]:((quiet(X)|~creative(X))=>curious(X)))&
(![X]:((funny(X)<~>~generous(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((strong(X)|wise(X))=>(wise(X)|curious(X))))&
(![X]:((~kind(X)&funny(X))<=>(~curious(X)|funny(X))))&
(![X]:(~quiet(X)=>tall(X)))&
(((happy(susan)|~tall(susan)))=>(?[X]:((generous(X)<~>~curious(X)))))&
(((humble(john)<~>~calm(john)))=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:((~creative(X)|~happy(X))=>(old(X)&wise(X))))&
(((~happy(paul)|strong(paul)))<=>((patient(john)|~tall(john))))&
((~generous(paul)|~creative(paul)))&
(~generous(susan))&
(~humble(paul))&
((patient(fred)|~funny(fred)))&
(?[X]:((old(X)<~>strong(X))))&
((creative(lucy)<~>patient(lucy))) | generous(lucy) | [] | null | 0 |
If someone is either funny or patient then someone is not kind or strong and vice versa.
Everyone who is both not generous and brave is not humble or not brave.
Everyone who is calm or not calm is both rich and strong and vice versa.
Everyone who is both patient and not kind is both not curious and not old and vice versa.
Everyone who is not curious or not calm is not wise or not humble.
If john is not calm or not old then someone is patient or generous and vice versa.
Everyone who is either not wise or not tall is tall or strong and vice versa.
If someone is either tall or brave then susan is kind or not brave and vice versa.
Everyone who is not tall is either calm or not funny and vice versa.
If someone is calm then john is rich or not quiet.
Everyone who is not curious is old.
Everyone who is kind is not brave or not funny and vice versa.
If fred is not kind then someone is not humble and vice versa.
If someone is not tall or curious then someone is either strong or not kind and vice versa.
Everyone who is either calm or not kind is either wise or humble and vice versa.
If someone is not old then someone is not happy.
Alice is either rich or brave.
Someone is both not humble and happy.
Someone is either kind or not kind.
Someone is either strong or tall.
John is not generous.
Paul is not creative or not old.
Someone is either not curious or calm.
Someone is patient or not strong. | Alice is rich. | entailment | ((?[X]:((funny(X)<~>patient(X))))<=>(?[X]:((~kind(X)|strong(X)))))&
(![X]:((~generous(X)&brave(X))=>(~humble(X)|~brave(X))))&
(![X]:((calm(X)|~calm(X))<=>(rich(X)&strong(X))))&
(![X]:((patient(X)&~kind(X))<=>(~curious(X)&~old(X))))&
(![X]:((~curious(X)|~calm(X))=>(~wise(X)|~humble(X))))&
(((~calm(john)|~old(john)))<=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~wise(X)<~>~tall(X))<=>(tall(X)|strong(X))))&
((?[X]:((tall(X)<~>brave(X))))<=>((kind(susan)|~brave(susan))))&
(![X]:(~tall(X)<=>(calm(X)<~>~funny(X))))&
((?[X]:(calm(X)))=>((rich(john)|~quiet(john))))&
(![X]:(~curious(X)=>old(X)))&
(![X]:(kind(X)<=>(~brave(X)|~funny(X))))&
((~kind(fred))<=>(?[X]:(~humble(X))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:((strong(X)<~>~kind(X)))))&
(![X]:((calm(X)<~>~kind(X))<=>(wise(X)<~>humble(X))))&
((?[X]:(~old(X)))=>(?[X]:(~happy(X))))&
((rich(alice)<~>brave(alice)))&
(?[X]:((~humble(X)&happy(X))))&
(?[X]:((kind(X)<~>~kind(X))))&
(?[X]:((strong(X)<~>tall(X))))&
(~generous(john))&
((~creative(paul)|~old(paul)))&
(?[X]:((~curious(X)<~>calm(X))))&
(?[X]:((patient(X)|~strong(X)))) | rich(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 3125706317317262364960984
% SZS output start Proof for 3125706317317262364960984
3. ! [X0] : ((~calm(X0) | calm(X0)) <=> (strong(X0) & rich(X0))) [input p2]
25. ~rich(alice) [input hypothesis]
42. ! [X0] : (((~calm(X0) | calm(X0)) | (~strong(X0) | ~rich(X0))) & ((strong(X0) & rich(X0)) | (calm(X0) & ~calm(X0)))) [nnf transformation 3]
43. ! [X0] : ((~calm(X0) | calm(X0) | ~strong(X0) | ~rich(X0)) & ((strong(X0) & rich(X0)) | (calm(X0) & ~calm(X0)))) [flattening 42]
95. rich(X0) | ~calm(X0) [cnf transformation 43]
96. rich(X0) | calm(X0) [cnf transformation 43]
159. ~rich(alice) [cnf transformation 25]
198. rich(X0) [subsumption resolution 95,96]
319. $false [subsumption resolution 159,198]
% SZS output end Proof for 3125706317317262364960984
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or creative is both not humble and not brave and vice versa.
Everyone who is creative is either not strong or strong and vice versa.
Everyone who is both wise and tall is both old and not brave.
If someone is old then someone is not strong or not generous and vice versa.
Everyone who is not quiet or not patient is brave or kind.
Everyone who is not wise or brave is generous and vice versa.
Everyone who is rich or wise is both not kind and patient.
Everyone who is not kind is both not rich and not kind and vice versa.
If someone is both not happy and creative then someone is not curious and vice versa.
Everyone who is calm is either kind or not rich.
Everyone who is both rich and generous is not funny and vice versa.
Everyone who is brave or tall is either not curious or not kind.
If lucy is not patient then someone is not happy.
Everyone who is not patient is not calm or wise.
If fred is either quiet or strong then susan is both not funny and calm.
If someone is both curious and brave then someone is either not calm or not humble.
Someone is not wise or strong.
Someone is either strong or kind.
Someone is creative.
Someone is both not tall and not quiet.
John is happy or patient.
Fred is not calm or quiet.
Someone is not generous or strong. | Fred is not brave. | entailment | (![X]:((kind(X)|creative(X))<=>(~humble(X)&~brave(X))))&
(![X]:(creative(X)<=>(~strong(X)<~>strong(X))))&
(![X]:((wise(X)&tall(X))=>(old(X)&~brave(X))))&
((?[X]:(old(X)))<=>(?[X]:((~strong(X)|~generous(X)))))&
(![X]:((~quiet(X)|~patient(X))=>(brave(X)|kind(X))))&
(![X]:((~wise(X)|brave(X))<=>generous(X)))&
(![X]:((rich(X)|wise(X))=>(~kind(X)&patient(X))))&
(![X]:(~kind(X)<=>(~rich(X)&~kind(X))))&
((?[X]:((~happy(X)&creative(X))))<=>(?[X]:(~curious(X))))&
(![X]:(calm(X)=>(kind(X)<~>~rich(X))))&
(![X]:((rich(X)&generous(X))<=>~funny(X)))&
(![X]:((brave(X)|tall(X))=>(~curious(X)<~>~kind(X))))&
((~patient(lucy))=>(?[X]:(~happy(X))))&
(![X]:(~patient(X)=>(~calm(X)|wise(X))))&
(((quiet(fred)<~>strong(fred)))=>((~funny(susan)&calm(susan))))&
((?[X]:((curious(X)&brave(X))))=>(?[X]:((~calm(X)<~>~humble(X)))))&
(?[X]:((~wise(X)|strong(X))))&
(?[X]:((strong(X)<~>kind(X))))&
(?[X]:(creative(X)))&
(?[X]:((~tall(X)&~quiet(X))))&
((happy(john)|patient(john)))&
((~calm(fred)|quiet(fred)))&
(?[X]:((~generous(X)|strong(X)))) | ~brave(fred) | [
"p0",
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6601610405372104515569105
% SZS output start Proof for 6601610405372104515569105
1. ! [X0] : ((creative(X0) | kind(X0)) <=> (~brave(X0) & ~humble(X0))) [input p0]
2. ! [X0] : (creative(X0) <=> (~strong(X0) <~> strong(X0))) [input p1]
24. brave(fred) [input hypothesis]
45. ! [X0] : (((creative(X0) | kind(X0)) | (brave(X0) | humble(X0))) & ((~brave(X0) & ~humble(X0)) | (~creative(X0) & ~kind(X0)))) [nnf transformation 1]
46. ! [X0] : ((creative(X0) | kind(X0) | brave(X0) | humble(X0)) & ((~brave(X0) & ~humble(X0)) | (~creative(X0) & ~kind(X0)))) [flattening 45]
47. ! [X0] : ((creative(X0) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ~creative(X0))) [nnf transformation 2]
83. ~brave(X0) | ~creative(X0) [cnf transformation 46]
87. creative(X0) | strong(X0) | strong(X0) [cnf transformation 47]
88. creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 47]
123. brave(fred) [cnf transformation 24]
124. creative(X0) | strong(X0) [duplicate literal removal 87]
125. creative(X0) | ~strong(X0) [duplicate literal removal 88]
126. creative(X0) [subsumption resolution 124,125]
241. ~creative(fred) [resolution 83,123]
242. $false [subsumption resolution 241,126]
% SZS output end Proof for 6601610405372104515569105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not generous or kind then alice is patient or curious and vice versa. Everyone who is either not rich or not patient is generous. If someone is creative or not happy then someone is either not wise or curious and vice versa. If someone is not calm or not curious then someone is not tall or wise and vice versa. If susan is old then alice is tall or not humble and vice versa. If someone is either strong or not happy then someone is both not strong and not old. Everyone who is tall is not humble and vice versa. If john is either patient or not tall then someone is both kind and strong. Everyone who is either not brave or generous is not funny and vice versa. If someone is both not rich and humble then someone is both not wise and not humble. Everyone who is not wise or curious is quiet. If john is both happy and calm then someone is kind or not rich and vice versa. Everyone who is patient is either strong or humble. If someone is either creative or not old then someone is happy. Everyone who is quiet or not curious is both not calm and not brave. Everyone who is both not brave and not calm is not kind or wise and vice versa. Someone is not generous. Alice is tall or wise. Someone is not generous or old. Someone is not happy. Someone is either humble or not curious. Lucy is strong or not calm. | Lucy is not brave. | entailment | (((~generous(susan)|kind(susan)))<=>((patient(alice)|curious(alice))))&
(![X]:((~rich(X)<~>~patient(X))=>generous(X)))&
((?[X]:((creative(X)|~happy(X))))<=>(?[X]:((~wise(X)<~>curious(X)))))&
((?[X]:((~calm(X)|~curious(X))))<=>(?[X]:((~tall(X)|wise(X)))))&
((old(susan))<=>((tall(alice)|~humble(alice))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:(tall(X)<=>~humble(X)))&
(((patient(john)<~>~tall(john)))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:((~brave(X)<~>generous(X))<=>~funny(X)))&
((?[X]:((~rich(X)&humble(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~wise(X)|curious(X))=>quiet(X)))&
(((happy(john)&calm(john)))<=>(?[X]:((kind(X)|~rich(X)))))&
(![X]:(patient(X)=>(strong(X)<~>humble(X))))&
((?[X]:((creative(X)<~>~old(X))))=>(?[X]:(happy(X))))&
(![X]:((quiet(X)|~curious(X))=>(~calm(X)&~brave(X))))&
(![X]:((~brave(X)&~calm(X))<=>(~kind(X)|wise(X))))&
(?[X]:(~generous(X)))&
((tall(alice)|wise(alice)))&
(?[X]:((~generous(X)|old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)<~>~curious(X))))&
((strong(lucy)|~calm(lucy))) | ~brave(lucy) | [
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8275468878567295626957330
% SZS output start Proof for 8275468878567295626957330
11. ! [X0] : ((curious(X0) | ~wise(X0)) => quiet(X0)) [input p10]
15. ! [X0] : ((~curious(X0) | quiet(X0)) => (~brave(X0) & ~calm(X0))) [input p14]
16. ! [X0] : ((~calm(X0) & ~brave(X0)) <=> (wise(X0) | ~kind(X0))) [input p15]
23. brave(lucy) [input hypothesis]
33. ! [X0] : (quiet(X0) | (~curious(X0) & wise(X0))) [ennf transformation 11]
36. ! [X0] : ((~brave(X0) & ~calm(X0)) | (curious(X0) & ~quiet(X0))) [ennf transformation 15]
73. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~wise(X0) & kind(X0))) & ((wise(X0) | ~kind(X0)) | (calm(X0) | brave(X0)))) [nnf transformation 16]
74. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~wise(X0) & kind(X0))) & (wise(X0) | ~kind(X0) | calm(X0) | brave(X0))) [flattening 73]
115. quiet(X0) | wise(X0) [cnf transformation 33]
128. ~quiet(X0) | ~brave(X0) [cnf transformation 36]
132. ~brave(X0) | ~wise(X0) [cnf transformation 74]
142. brave(lucy) [cnf transformation 23]
376. ~brave(X0) | wise(X0) [resolution 128,115]
377. ~brave(X0) [subsumption resolution 376,132]
379. $false [resolution 377,142]
% SZS output end Proof for 8275468878567295626957330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is calm or not rich and vice versa.
Everyone who is either not strong or brave is quiet or creative.
Everyone who is not tall or funny is both tall and kind and vice versa.
Everyone who is humble is both generous and funny and vice versa.
If susan is both not creative and not curious then alice is curious or not tall and vice versa.
If alice is either rich or not curious then paul is either not calm or not rich and vice versa.
If paul is either not generous or kind then someone is either calm or creative and vice versa.
Everyone who is rich is both generous and strong.
Everyone who is either not kind or not wise is either not kind or brave.
Everyone who is not calm is either not funny or not curious.
If someone is both not funny and not tall then someone is not wise.
Everyone who is either tall or not kind is happy or brave and vice versa.
Everyone who is either wise or not generous is both curious and kind and vice versa.
Everyone who is not rich is not creative and vice versa.
Everyone who is not funny or wise is both not calm and not tall and vice versa.
If susan is not creative or patient then someone is both not rich and not quiet.
Alice is not creative or funny.
Someone is both kind and brave.
Someone is not funny or not patient.
Lucy is both not strong and quiet.
Fred is either quiet or not kind.
Fred is creative or generous.
Mary is not old or happy.
Someone is strong or quiet. | Fred is not generous. | contradiction | (![X]:(funny(X)<=>(calm(X)|~rich(X))))&
(![X]:((~strong(X)<~>brave(X))=>(quiet(X)|creative(X))))&
(![X]:((~tall(X)|funny(X))<=>(tall(X)&kind(X))))&
(![X]:(humble(X)<=>(generous(X)&funny(X))))&
(((~creative(susan)&~curious(susan)))<=>((curious(alice)|~tall(alice))))&
(((rich(alice)<~>~curious(alice)))<=>((~calm(paul)<~>~rich(paul))))&
(((~generous(paul)<~>kind(paul)))<=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:(rich(X)=>(generous(X)&strong(X))))&
(![X]:((~kind(X)<~>~wise(X))=>(~kind(X)<~>brave(X))))&
(![X]:(~calm(X)=>(~funny(X)<~>~curious(X))))&
((?[X]:((~funny(X)&~tall(X))))=>(?[X]:(~wise(X))))&
(![X]:((tall(X)<~>~kind(X))<=>(happy(X)|brave(X))))&
(![X]:((wise(X)<~>~generous(X))<=>(curious(X)&kind(X))))&
(![X]:(~rich(X)<=>~creative(X)))&
(![X]:((~funny(X)|wise(X))<=>(~calm(X)&~tall(X))))&
(((~creative(susan)|patient(susan)))=>(?[X]:((~rich(X)&~quiet(X)))))&
((~creative(alice)|funny(alice)))&
(?[X]:((kind(X)&brave(X))))&
(?[X]:((~funny(X)|~patient(X))))&
((~strong(lucy)&quiet(lucy)))&
((quiet(fred)<~>~kind(fred)))&
((creative(fred)|generous(fred)))&
((~old(mary)|happy(mary)))&
(?[X]:((strong(X)|quiet(X)))) | ~generous(fred) | [
"p7",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6593327546527785074726340
% SZS output start Proof for 6593327546527785074726340
8. ! [X0] : (rich(X0) => (strong(X0) & generous(X0))) [input p7]
14. ! [X0] : (~rich(X0) <=> ~creative(X0)) [input p13]
22. generous(fred) | creative(fred) [input p21]
25. ~generous(fred) [input hypothesis]
32. ! [X0] : ((strong(X0) & generous(X0)) | ~rich(X0)) [ennf transformation 8]
58. ! [X0] : ((~rich(X0) | creative(X0)) & (~creative(X0) | rich(X0))) [nnf transformation 14]
99. ~rich(X0) | generous(X0) [cnf transformation 32]
120. ~creative(X0) | rich(X0) [cnf transformation 58]
136. generous(fred) | creative(fred) [cnf transformation 22]
138. ~generous(fred) [cnf transformation 25]
236. 17 <=> creative(fred) [avatar definition]
238. creative(fred) <- (17) [avatar component clause 236]
240. 18 <=> generous(fred) [avatar definition]
241. ~generous(fred) <- (~18) [avatar component clause 240]
243. 17 | 18 [avatar split clause 136,240,236]
253. ~18 [avatar split clause 138,240]
268. rich(fred) <- (17) [resolution 120,238]
277. generous(fred) <- (17) [resolution 268,99]
278. $false <- (17, ~18) [subsumption resolution 277,241]
279. ~17 | 18 [avatar contradiction clause 278]
280. $false [avatar sat refutation 243,253,279]
% SZS output end Proof for 6593327546527785074726340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or funny is either not curious or not creative and vice versa.
Everyone who is not tall is patient and vice versa.
Everyone who is old or creative is both funny and brave.
Everyone who is either not patient or old is either quiet or kind and vice versa.
If alice is old then susan is both old and not wise and vice versa.
If paul is either rich or brave then someone is tall and vice versa.
If someone is either not strong or strong then someone is old or not strong and vice versa.
Everyone who is not calm or wise is either not curious or old.
Everyone who is generous is not funny and vice versa.
Everyone who is not curious is either not brave or not old.
If alice is either not brave or wise then lucy is patient and vice versa.
Everyone who is not rich is either not rich or not funny and vice versa.
If paul is either not strong or not humble then lucy is quiet or not humble.
If lucy is both brave and strong then someone is not humble or not old.
Everyone who is either not happy or not strong is brave and vice versa.
Everyone who is old or creative is either not wise or generous and vice versa.
Paul is not patient or not happy.
Mary is both curious and not quiet.
Susan is both not curious and funny.
Someone is both calm and not tall.
Someone is old or not old.
Someone is both old and calm.
Paul is either not happy or brave. | Alice is not old. | entailment | (![X]:((~generous(X)|funny(X))<=>(~curious(X)<~>~creative(X))))&
(![X]:(~tall(X)<=>patient(X)))&
(![X]:((old(X)|creative(X))=>(funny(X)&brave(X))))&
(![X]:((~patient(X)<~>old(X))<=>(quiet(X)<~>kind(X))))&
((old(alice))<=>((old(susan)&~wise(susan))))&
(((rich(paul)<~>brave(paul)))<=>(?[X]:(tall(X))))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~calm(X)|wise(X))=>(~curious(X)<~>old(X))))&
(![X]:(generous(X)<=>~funny(X)))&
(![X]:(~curious(X)=>(~brave(X)<~>~old(X))))&
(((~brave(alice)<~>wise(alice)))<=>(patient(lucy)))&
(![X]:(~rich(X)<=>(~rich(X)<~>~funny(X))))&
(((~strong(paul)<~>~humble(paul)))=>((quiet(lucy)|~humble(lucy))))&
(((brave(lucy)&strong(lucy)))=>(?[X]:((~humble(X)|~old(X)))))&
(![X]:((~happy(X)<~>~strong(X))<=>brave(X)))&
(![X]:((old(X)|creative(X))<=>(~wise(X)<~>generous(X))))&
((~patient(paul)|~happy(paul)))&
((curious(mary)&~quiet(mary)))&
((~curious(susan)&funny(susan)))&
(?[X]:((calm(X)&~tall(X))))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((old(X)&calm(X))))&
((~happy(paul)<~>brave(paul))) | ~old(alice) | [
"p2",
"p4",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 718604238730593117186277
% SZS output start Proof for 718604238730593117186277
3. ! [X0] : ((creative(X0) | old(X0)) => (brave(X0) & funny(X0))) [input p2]
5. old(alice) <=> (~wise(susan) & old(susan)) [input p4]
10. ! [X0] : (~curious(X0) => (~brave(X0) <~> ~old(X0))) [input p9]
19. funny(susan) & ~curious(susan) [input p18]
24. old(alice) [input hypothesis]
29. ! [X0] : ((brave(X0) & funny(X0)) | (~creative(X0) & ~old(X0))) [ennf transformation 3]
31. ! [X0] : ((~brave(X0) <~> ~old(X0)) | curious(X0)) [ennf transformation 10]
40. (old(alice) | (wise(susan) | ~old(susan))) & ((~wise(susan) & old(susan)) | ~old(alice)) [nnf transformation 5]
41. (old(alice) | wise(susan) | ~old(susan)) & ((~wise(susan) & old(susan)) | ~old(alice)) [flattening 40]
53. ! [X0] : (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | curious(X0)) [nnf transformation 31]
79. ~old(X0) | brave(X0) [cnf transformation 29]
89. old(susan) | ~old(alice) [cnf transformation 41]
106. ~old(X0) | ~brave(X0) | curious(X0) [cnf transformation 53]
132. ~curious(susan) [cnf transformation 19]
139. old(alice) [cnf transformation 24]
145. 1 <=> old(susan) [avatar definition]
146. old(susan) <- (1) [avatar component clause 145]
153. 3 <=> old(alice) [avatar definition]
158. ~3 | 1 [avatar split clause 89,145,153]
195. ~old(X0) | curious(X0) [subsumption resolution 106,79]
259. 3 [avatar split clause 139,153]
277. curious(susan) <- (1) [resolution 195,146]
279. $false <- (1) [subsumption resolution 277,132]
280. ~1 [avatar contradiction clause 279]
281. $false [avatar sat refutation 158,259,280]
% SZS output end Proof for 718604238730593117186277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or wise then fred is either creative or happy and vice versa.
Everyone who is happy or not wise is strong.
Everyone who is both wise and calm is not generous.
Everyone who is both not quiet and brave is either creative or funny.
If someone is either tall or not tall then someone is either rich or not kind.
Everyone who is calm or quiet is both creative and not tall.
If mary is not wise or brave then lucy is either kind or funny and vice versa.
If someone is quiet then lucy is both not tall and not patient and vice versa.
Everyone who is both rich and patient is not tall.
If someone is not funny or patient then someone is generous or not funny.
If susan is both not funny and not patient then alice is brave.
Everyone who is not curious or not happy is either calm or rich.
Everyone who is funny or old is either generous or not calm and vice versa.
Everyone who is both quiet and old is kind or calm and vice versa.
Everyone who is not calm or not old is humble.
Everyone who is not kind or wise is creative.
Mary is both rich and not quiet.
Mary is curious.
John is both not brave and not quiet.
Susan is rich.
Someone is brave.
Someone is either kind or curious.
Someone is both kind and not tall.
Susan is creative. | Fred is not creative. | contradiction | ((?[X]:((kind(X)<~>wise(X))))<=>((creative(fred)<~>happy(fred))))&
(![X]:((happy(X)|~wise(X))=>strong(X)))&
(![X]:((wise(X)&calm(X))=>~generous(X)))&
(![X]:((~quiet(X)&brave(X))=>(creative(X)<~>funny(X))))&
((?[X]:((tall(X)<~>~tall(X))))=>(?[X]:((rich(X)<~>~kind(X)))))&
(![X]:((calm(X)|quiet(X))=>(creative(X)&~tall(X))))&
(((~wise(mary)|brave(mary)))<=>((kind(lucy)<~>funny(lucy))))&
((?[X]:(quiet(X)))<=>((~tall(lucy)&~patient(lucy))))&
(![X]:((rich(X)&patient(X))=>~tall(X)))&
((?[X]:((~funny(X)|patient(X))))=>(?[X]:((generous(X)|~funny(X)))))&
(((~funny(susan)&~patient(susan)))=>(brave(alice)))&
(![X]:((~curious(X)|~happy(X))=>(calm(X)<~>rich(X))))&
(![X]:((funny(X)|old(X))<=>(generous(X)<~>~calm(X))))&
(![X]:((quiet(X)&old(X))<=>(kind(X)|calm(X))))&
(![X]:((~calm(X)|~old(X))=>humble(X)))&
(![X]:((~kind(X)|wise(X))=>creative(X)))&
((rich(mary)&~quiet(mary)))&
(curious(mary))&
((~brave(john)&~quiet(john)))&
(rich(susan))&
(?[X]:(brave(X)))&
(?[X]:((kind(X)<~>curious(X))))&
(?[X]:((kind(X)&~tall(X))))&
(creative(susan)) | ~creative(fred) | [
"p5",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4210764410011959288380519
% SZS output start Proof for 4210764410011959288380519
6. ! [X0] : ((quiet(X0) | calm(X0)) => (~tall(X0) & creative(X0))) [input p5]
14. ! [X0] : ((old(X0) & quiet(X0)) <=> (calm(X0) | kind(X0))) [input p13]
16. ! [X0] : ((wise(X0) | ~kind(X0)) => creative(X0)) [input p15]
25. ~creative(fred) [input hypothesis]
35. ! [X0] : ((~tall(X0) & creative(X0)) | (~quiet(X0) & ~calm(X0))) [ennf transformation 6]
42. ! [X0] : (creative(X0) | (~wise(X0) & kind(X0))) [ennf transformation 16]
65. ! [X0] : (((old(X0) & quiet(X0)) | (~calm(X0) & ~kind(X0))) & ((calm(X0) | kind(X0)) | (~old(X0) | ~quiet(X0)))) [nnf transformation 14]
66. ! [X0] : (((old(X0) & quiet(X0)) | (~calm(X0) & ~kind(X0))) & (calm(X0) | kind(X0) | ~old(X0) | ~quiet(X0))) [flattening 65]
90. ~quiet(X0) | creative(X0) [cnf transformation 35]
117. ~kind(X0) | quiet(X0) [cnf transformation 66]
121. creative(X0) | kind(X0) [cnf transformation 42]
135. ~creative(fred) [cnf transformation 25]
145. 2 <=> creative(fred) [avatar definition]
146. ~creative(fred) <- (~2) [avatar component clause 145]
267. ~2 [avatar split clause 135,145]
275. kind(fred) <- (~2) [resolution 121,146]
277. quiet(fred) <- (~2) [resolution 275,117]
295. creative(fred) <- (~2) [resolution 277,90]
296. $false <- (~2) [subsumption resolution 295,146]
297. 2 [avatar contradiction clause 296]
298. $false [avatar sat refutation 267,297]
% SZS output end Proof for 4210764410011959288380519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or rich is both generous and old.
Everyone who is both not strong and not happy is funny or generous and vice versa.
If someone is old then someone is both patient and rich and vice versa.
If someone is either not strong or not generous then someone is both not creative and creative.
If someone is not tall then fred is both patient and not quiet and vice versa.
If someone is not wise or not tall then lucy is not curious or old and vice versa.
Everyone who is either not funny or not quiet is both rich and not creative.
Everyone who is both wise and curious is both strong and not kind and vice versa.
Everyone who is either quiet or not kind is kind.
If paul is creative then someone is both calm and creative.
Everyone who is not strong or not tall is quiet or funny and vice versa.
If susan is either not creative or quiet then susan is not tall or old and vice versa.
If someone is creative then paul is both not tall and not kind.
Someone is patient or strong.
Paul is both not rich and funny.
Lucy is either not quiet or not kind.
Paul is strong or not happy.
Someone is both not old and not creative. | Fred is old. | contradiction | (![X]:((~brave(X)|rich(X))=>(generous(X)&old(X))))&
(![X]:((~strong(X)&~happy(X))<=>(funny(X)|generous(X))))&
((?[X]:(old(X)))<=>(?[X]:((patient(X)&rich(X)))))&
((?[X]:((~strong(X)<~>~generous(X))))=>(?[X]:((~creative(X)&creative(X)))))&
((?[X]:(~tall(X)))<=>((patient(fred)&~quiet(fred))))&
((?[X]:((~wise(X)|~tall(X))))<=>((~curious(lucy)|old(lucy))))&
(![X]:((~funny(X)<~>~quiet(X))=>(rich(X)&~creative(X))))&
(![X]:((wise(X)&curious(X))<=>(strong(X)&~kind(X))))&
(![X]:((quiet(X)<~>~kind(X))=>kind(X)))&
((creative(paul))=>(?[X]:((calm(X)&creative(X)))))&
(![X]:((~strong(X)|~tall(X))<=>(quiet(X)|funny(X))))&
(((~creative(susan)<~>quiet(susan)))<=>((~tall(susan)|old(susan))))&
((?[X]:(creative(X)))=>((~tall(paul)&~kind(paul))))&
(?[X]:((patient(X)|strong(X))))&
((~rich(paul)&funny(paul)))&
((~quiet(lucy)<~>~kind(lucy)))&
((strong(paul)|~happy(paul)))&
(?[X]:((~old(X)&~creative(X)))) | old(fred) | [
"p0",
"p1",
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3521992022770357956921177
% SZS output start Proof for 3521992022770357956921177
1. ! [X0] : ((rich(X0) | ~brave(X0)) => (old(X0) & generous(X0))) [input p0]
2. ! [X0] : ((~happy(X0) & ~strong(X0)) <=> (generous(X0) | funny(X0))) [input p1]
3. ? [X0] : old(X0) <=> ? [X0] : (rich(X0) & patient(X0)) [input p2]
4. ? [X0] : (~strong(X0) <~> ~generous(X0)) => ? [X0] : (creative(X0) & ~creative(X0)) [input p3]
19. old(fred) [input hypothesis]
20. ? [X0] : old(X0) <=> ? [X1] : (rich(X1) & patient(X1)) [rectify 3]
21. ? [X0] : (~strong(X0) <~> ~generous(X0)) => ? [X1] : (creative(X1) & ~creative(X1)) [rectify 4]
23. ! [X0] : (rich(X0) => (old(X0) & generous(X0))) [pure predicate removal 1]
24. ! [X0] : ((old(X0) & generous(X0)) | ~rich(X0)) [ennf transformation 23]
25. ? [X1] : (creative(X1) & ~creative(X1)) | ! [X0] : (~strong(X0) <=> ~generous(X0)) [ennf transformation 21]
30. ! [X0] : (((~happy(X0) & ~strong(X0)) | (~generous(X0) & ~funny(X0))) & ((generous(X0) | funny(X0)) | (happy(X0) | strong(X0)))) [nnf transformation 2]
31. ! [X0] : (((~happy(X0) & ~strong(X0)) | (~generous(X0) & ~funny(X0))) & (generous(X0) | funny(X0) | happy(X0) | strong(X0))) [flattening 30]
32. (? [X0] : old(X0) | ! [X1] : (~rich(X1) | ~patient(X1))) & (? [X1] : (rich(X1) & patient(X1)) | ! [X0] : ~old(X0)) [nnf transformation 20]
33. (? [X0] : old(X0) | ! [X1] : (~rich(X1) | ~patient(X1))) & (? [X2] : (rich(X2) & patient(X2)) | ! [X3] : ~old(X3)) [rectify 32]
34. ? [X0] : old(X0) => old(sK0) [choice axiom]
35. ? [X2] : (rich(X2) & patient(X2)) => (rich(sK1) & patient(sK1)) [choice axiom]
36. (old(sK0) | ! [X1] : (~rich(X1) | ~patient(X1))) & ((rich(sK1) & patient(sK1)) | ! [X3] : ~old(X3)) [skolemisation 33,35,34]
37. ? [X1] : (creative(X1) & ~creative(X1)) | ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0))) [nnf transformation 25]
38. ? [X0] : (creative(X0) & ~creative(X0)) | ! [X1] : ((~strong(X1) | generous(X1)) & (~generous(X1) | strong(X1))) [rectify 37]
39. ? [X0] : (creative(X0) & ~creative(X0)) => (creative(sK2) & ~creative(sK2)) [choice axiom]
40. (creative(sK2) & ~creative(sK2)) | ! [X1] : ((~strong(X1) | generous(X1)) & (~generous(X1) | strong(X1))) [skolemisation 38,39]
66. ~rich(X0) | generous(X0) [cnf transformation 24]
70. ~strong(X0) | ~generous(X0) [cnf transformation 31]
74. rich(sK1) | ~old(X3) [cnf transformation 36]
76. ~creative(sK2) | ~generous(X1) | strong(X1) [cnf transformation 40]
78. creative(sK2) | ~generous(X1) | strong(X1) [cnf transformation 40]
118. old(fred) [cnf transformation 19]
129. 3 <=> ! [X3] : ~old(X3) [avatar definition]
130. ~old(X3) <- (3) [avatar component clause 129]
132. 4 <=> rich(sK1) [avatar definition]
134. rich(sK1) <- (4) [avatar component clause 132]
135. 3 | 4 [avatar split clause 74,132,129]
146. 7 <=> creative(sK2) [avatar definition]
150. creative(sK2) | ~generous(X1) [subsumption resolution 78,70]
152. 8 <=> ! [X1] : ~generous(X1) [avatar definition]
153. ~generous(X1) <- (8) [avatar component clause 152]
154. 8 | 7 [avatar split clause 150,146,152]
157. ~creative(sK2) | ~generous(X1) [subsumption resolution 76,70]
158. 8 | ~7 [avatar split clause 157,146,152]
271. generous(sK1) <- (4) [resolution 66,134]
272. $false <- (4, 8) [subsumption resolution 271,153]
273. ~4 | ~8 [avatar contradiction clause 272]
274. $false <- (3) [resolution 130,118]
277. ~3 [avatar contradiction clause 274]
278. $false [avatar sat refutation 135,154,158,273,277]
% SZS output end Proof for 3521992022770357956921177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not quiet then someone is funny.
Everyone who is patient is not generous.
Everyone who is either curious or not happy is calm and vice versa.
Everyone who is humble is either not funny or not strong and vice versa.
Everyone who is not brave is both generous and wise and vice versa.
If susan is not old or not calm then fred is both brave and strong and vice versa.
If alice is patient then someone is not creative or kind and vice versa.
If mary is not strong then alice is both brave and wise.
Everyone who is both not wise and not kind is not creative or not brave.
If someone is not strong or not old then paul is not quiet.
If someone is not quiet or humble then mary is humble or not wise.
If mary is brave or not strong then paul is both happy and curious.
Everyone who is either not quiet or old is either not happy or not calm and vice versa.
If susan is either calm or not tall then alice is not wise or not rich and vice versa.
If fred is humble then alice is either generous or not wise and vice versa.
If someone is not kind or curious then someone is happy or old.
Paul is humble.
Alice is either not quiet or not tall.
Someone is both not old and tall.
Mary is not humble.
Lucy is both not brave and not strong.
Someone is either not humble or not kind.
Lucy is not curious.
Someone is not tall or quiet. | Paul is calm. | entailment | ((~quiet(paul))=>(?[X]:(funny(X))))&
(![X]:(patient(X)=>~generous(X)))&
(![X]:((curious(X)<~>~happy(X))<=>calm(X)))&
(![X]:(humble(X)<=>(~funny(X)<~>~strong(X))))&
(![X]:(~brave(X)<=>(generous(X)&wise(X))))&
(((~old(susan)|~calm(susan)))<=>((brave(fred)&strong(fred))))&
((patient(alice))<=>(?[X]:((~creative(X)|kind(X)))))&
((~strong(mary))=>((brave(alice)&wise(alice))))&
(![X]:((~wise(X)&~kind(X))=>(~creative(X)|~brave(X))))&
((?[X]:((~strong(X)|~old(X))))=>(~quiet(paul)))&
((?[X]:((~quiet(X)|humble(X))))=>((humble(mary)|~wise(mary))))&
(((brave(mary)|~strong(mary)))=>((happy(paul)&curious(paul))))&
(![X]:((~quiet(X)<~>old(X))<=>(~happy(X)<~>~calm(X))))&
(((calm(susan)<~>~tall(susan)))<=>((~wise(alice)|~rich(alice))))&
((humble(fred))<=>((generous(alice)<~>~wise(alice))))&
((?[X]:((~kind(X)|curious(X))))=>(?[X]:((happy(X)|old(X)))))&
(humble(paul))&
((~quiet(alice)<~>~tall(alice)))&
(?[X]:((~old(X)&tall(X))))&
(~humble(mary))&
((~brave(lucy)&~strong(lucy)))&
(?[X]:((~humble(X)<~>~kind(X))))&
(~curious(lucy))&
(?[X]:((~tall(X)|quiet(X)))) | calm(paul) | [
"p2",
"p4",
"p10",
"p11",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5806603741114149535619148
% SZS output start Proof for 5806603741114149535619148
3. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> calm(X0)) [input p2]
5. ! [X0] : (~brave(X0) <=> (wise(X0) & generous(X0))) [input p4]
11. ? [X0] : (humble(X0) | ~quiet(X0)) => (~wise(mary) | humble(mary)) [input p10]
12. (~strong(mary) | brave(mary)) => (curious(paul) & happy(paul)) [input p11]
17. humble(paul) [input p16]
20. ~humble(mary) [input p19]
25. ~calm(paul) [input hypothesis]
33. (~wise(mary) | humble(mary)) | ! [X0] : (~humble(X0) & quiet(X0)) [ennf transformation 11]
34. ~wise(mary) | humble(mary) | ! [X0] : (~humble(X0) & quiet(X0)) [flattening 33]
35. (curious(paul) & happy(paul)) | (strong(mary) & ~brave(mary)) [ennf transformation 12]
39. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~calm(X0)) & (calm(X0) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 3]
41. ! [X0] : ((~brave(X0) | (~wise(X0) | ~generous(X0))) & ((wise(X0) & generous(X0)) | brave(X0))) [nnf transformation 5]
42. ! [X0] : ((~brave(X0) | ~wise(X0) | ~generous(X0)) & ((wise(X0) & generous(X0)) | brave(X0))) [flattening 41]
66. ~happy(X0) | calm(X0) | ~curious(X0) [cnf transformation 39]
75. wise(X0) | brave(X0) [cnf transformation 42]
91. ~wise(mary) | humble(mary) | ~humble(X0) [cnf transformation 34]
92. happy(paul) | ~brave(mary) [cnf transformation 35]
94. curious(paul) | ~brave(mary) [cnf transformation 35]
116. humble(paul) [cnf transformation 17]
121. ~humble(mary) [cnf transformation 20]
128. ~calm(paul) [cnf transformation 25]
204. 17 <=> ! [X0] : ~humble(X0) [avatar definition]
205. ~humble(X0) <- (17) [avatar component clause 204]
207. 18 <=> humble(mary) [avatar definition]
211. 19 <=> wise(mary) [avatar definition]
213. ~wise(mary) <- (~19) [avatar component clause 211]
214. 17 | 18 | ~19 [avatar split clause 91,211,207,204]
220. 21 <=> curious(paul) [avatar definition]
222. curious(paul) <- (21) [avatar component clause 220]
225. 22 <=> brave(mary) [avatar definition]
227. ~brave(mary) <- (~22) [avatar component clause 225]
228. ~22 | 21 [avatar split clause 94,220,225]
230. 23 <=> happy(paul) [avatar definition]
232. happy(paul) <- (23) [avatar component clause 230]
234. ~22 | 23 [avatar split clause 92,230,225]
287. ~18 [avatar split clause 121,207]
309. brave(mary) <- (~19) [resolution 75,213]
310. $false <- (~19, ~22) [subsumption resolution 309,227]
311. 19 | 22 [avatar contradiction clause 310]
312. $false <- (17) [resolution 205,116]
315. ~17 [avatar contradiction clause 312]
321. calm(paul) | ~curious(paul) <- (23) [resolution 66,232]
331. ~curious(paul) <- (23) [subsumption resolution 321,128]
332. $false <- (21, 23) [subsumption resolution 331,222]
333. ~21 | ~23 [avatar contradiction clause 332]
334. $false [avatar sat refutation 214,228,234,287,311,315,333]
% SZS output end Proof for 5806603741114149535619148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then someone is not kind or not old. If someone is both not brave and funny then mary is brave. If alice is not rich or generous then alice is both strong and creative and vice versa. Everyone who is not strong is generous or not calm. Everyone who is both kind and happy is either generous or humble and vice versa. Everyone who is both not tall and not generous is both not wise and kind. Everyone who is both not curious and not rich is either not rich or not funny and vice versa. Everyone who is both not wise and happy is creative or not patient and vice versa. If mary is humble then someone is rich. Everyone who is not calm or tall is not calm. If someone is both rich and not kind then someone is both not kind and not funny and vice versa. Everyone who is both not humble and tall is either rich or not quiet and vice versa. Everyone who is rich is curious and vice versa. If someone is either not old or not curious then someone is both wise and funny and vice versa. Everyone who is both not kind and not humble is not calm and vice versa. Everyone who is either humble or generous is not patient or not humble. Someone is both calm and funny. Lucy is either not kind or curious. Lucy is either not tall or not brave. Someone is not quiet. Someone is not strong. John is both not quiet and not kind. Lucy is happy. John is either funny or kind. | John is calm. | contradiction | ((?[X]:(funny(X)))=>(?[X]:((~kind(X)|~old(X)))))&
((?[X]:((~brave(X)&funny(X))))=>(brave(mary)))&
(((~rich(alice)|generous(alice)))<=>((strong(alice)&creative(alice))))&
(![X]:(~strong(X)=>(generous(X)|~calm(X))))&
(![X]:((kind(X)&happy(X))<=>(generous(X)<~>humble(X))))&
(![X]:((~tall(X)&~generous(X))=>(~wise(X)&kind(X))))&
(![X]:((~curious(X)&~rich(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:((~wise(X)&happy(X))<=>(creative(X)|~patient(X))))&
((humble(mary))=>(?[X]:(rich(X))))&
(![X]:((~calm(X)|tall(X))=>~calm(X)))&
((?[X]:((rich(X)&~kind(X))))<=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:((~humble(X)&tall(X))<=>(rich(X)<~>~quiet(X))))&
(![X]:(rich(X)<=>curious(X)))&
((?[X]:((~old(X)<~>~curious(X))))<=>(?[X]:((wise(X)&funny(X)))))&
(![X]:((~kind(X)&~humble(X))<=>~calm(X)))&
(![X]:((humble(X)<~>generous(X))=>(~patient(X)|~humble(X))))&
(?[X]:((calm(X)&funny(X))))&
((~kind(lucy)<~>curious(lucy)))&
((~tall(lucy)<~>~brave(lucy)))&
(?[X]:(~quiet(X)))&
(?[X]:(~strong(X)))&
((~quiet(john)&~kind(john)))&
(happy(lucy))&
((funny(john)<~>kind(john))) | calm(john) | [
"p6",
"p9",
"p10",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9211269261676643421777692
% SZS output start Proof for 9211269261676643421777692
7. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (~rich(X0) <~> ~funny(X0))) [input p6]
10. ! [X0] : ((tall(X0) | ~calm(X0)) => ~calm(X0)) [input p9]
11. ? [X0] : (~kind(X0) & rich(X0)) <=> ? [X0] : (~funny(X0) & ~kind(X0)) [input p10]
12. ! [X0] : ((tall(X0) & ~humble(X0)) <=> (rich(X0) <~> ~quiet(X0))) [input p11]
13. ! [X0] : (rich(X0) <=> curious(X0)) [input p12]
22. ~kind(john) & ~quiet(john) [input p21]
25. calm(john) [input hypothesis]
27. ? [X0] : (~kind(X0) & rich(X0)) <=> ? [X1] : (~funny(X1) & ~kind(X1)) [rectify 11]
36. ! [X0] : (~calm(X0) | (~tall(X0) & calm(X0))) [ennf transformation 10]
46. ! [X0] : (((~rich(X0) & ~curious(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (rich(X0) | curious(X0)))) [nnf transformation 7]
47. ! [X0] : (((~rich(X0) & ~curious(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | rich(X0) | curious(X0))) [flattening 46]
52. (? [X0] : (~kind(X0) & rich(X0)) | ! [X1] : (funny(X1) | kind(X1))) & (? [X1] : (~funny(X1) & ~kind(X1)) | ! [X0] : (kind(X0) | ~rich(X0))) [nnf transformation 27]
53. (? [X0] : (~kind(X0) & rich(X0)) | ! [X1] : (funny(X1) | kind(X1))) & (? [X2] : (~funny(X2) & ~kind(X2)) | ! [X3] : (kind(X3) | ~rich(X3))) [rectify 52]
54. ? [X0] : (~kind(X0) & rich(X0)) => (~kind(sK2) & rich(sK2)) [choice axiom]
55. ? [X2] : (~funny(X2) & ~kind(X2)) => (~funny(sK3) & ~kind(sK3)) [choice axiom]
56. ((~kind(sK2) & rich(sK2)) | ! [X1] : (funny(X1) | kind(X1))) & ((~funny(sK3) & ~kind(sK3)) | ! [X3] : (kind(X3) | ~rich(X3))) [skolemisation 53,55,54]
57. ! [X0] : (((tall(X0) & ~humble(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0)))) & (((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (~tall(X0) | humble(X0)))) [nnf transformation 12]
58. ! [X0] : (((tall(X0) & ~humble(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0)))) & (((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | ~tall(X0) | humble(X0))) [flattening 57]
59. ! [X0] : ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))) [nnf transformation 13]
94. funny(X0) | rich(X0) | rich(X0) | curious(X0) [cnf transformation 47]
98. ~rich(X0) | ~rich(X0) | funny(X0) [cnf transformation 47]
106. ~tall(X0) | ~calm(X0) [cnf transformation 36]
108. ~funny(sK3) | kind(X3) | ~rich(X3) [cnf transformation 56]
116. quiet(X0) | rich(X0) | tall(X0) [cnf transformation 58]
118. ~curious(X0) | rich(X0) [cnf transformation 59]
138. ~quiet(john) [cnf transformation 22]
139. ~kind(john) [cnf transformation 22]
143. calm(john) [cnf transformation 25]
145. funny(X0) | rich(X0) | curious(X0) [duplicate literal removal 94]
146. ~rich(X0) | funny(X0) [duplicate literal removal 98]
188. curious(X0) | funny(X0) [subsumption resolution 145,146]
212. 15 <=> ! [X3] : (kind(X3) | ~rich(X3)) [avatar definition]
213. ~rich(X3) | kind(X3) <- (15) [avatar component clause 212]
215. 16 <=> funny(sK3) [avatar definition]
217. ~funny(sK3) <- (~16) [avatar component clause 215]
218. 15 | ~16 [avatar split clause 108,215,212]
281. funny(X0) | rich(X0) [resolution 188,118]
282. funny(X0) [subsumption resolution 281,146]
291. $false <- (~16) [resolution 282,217]
292. 16 [avatar contradiction clause 291]
317. rich(john) | tall(john) [resolution 116,138]
331. 35 <=> tall(john) [avatar definition]
333. tall(john) <- (35) [avatar component clause 331]
335. 36 <=> rich(john) [avatar definition]
337. rich(john) <- (36) [avatar component clause 335]
338. 35 | 36 [avatar split clause 317,335,331]
352. ~calm(john) <- (35) [resolution 333,106]
353. $false <- (35) [subsumption resolution 352,143]
354. ~35 [avatar contradiction clause 353]
372. kind(john) <- (15, 36) [resolution 337,213]
375. $false <- (15, 36) [subsumption resolution 372,139]
376. ~15 | ~36 [avatar contradiction clause 375]
377. $false [avatar sat refutation 218,292,338,354,376]
% SZS output end Proof for 9211269261676643421777692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not creative is creative.
If mary is either strong or not quiet then lucy is either wise or curious and vice versa.
Everyone who is either wise or brave is not wise or not strong and vice versa.
If someone is either quiet or creative then john is either rich or not curious and vice versa.
Everyone who is not rich or brave is both calm and not calm.
If lucy is either not brave or not creative then someone is old or happy.
If lucy is both brave and not curious then someone is not happy and vice versa.
Everyone who is either not strong or patient is not rich and vice versa.
Everyone who is either not humble or not creative is either not generous or not happy and vice versa.
If paul is brave then someone is not strong.
Everyone who is either not brave or rich is not happy or happy.
Everyone who is kind or not brave is not creative and vice versa.
Everyone who is not kind or curious is not humble.
Everyone who is both not curious and funny is either not happy or brave and vice versa.
Everyone who is either curious or creative is either brave or kind.
If someone is either not happy or not calm then paul is both funny and kind and vice versa.
Someone is funny or happy.
Paul is either happy or not rich.
Someone is both not brave and generous.
Someone is happy.
Paul is kind. | John is not curious. | neutral | (![X]:((~tall(X)<~>~creative(X))=>creative(X)))&
(((strong(mary)<~>~quiet(mary)))<=>((wise(lucy)<~>curious(lucy))))&
(![X]:((wise(X)<~>brave(X))<=>(~wise(X)|~strong(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>((rich(john)<~>~curious(john))))&
(![X]:((~rich(X)|brave(X))=>(calm(X)&~calm(X))))&
(((~brave(lucy)<~>~creative(lucy)))=>(?[X]:((old(X)|happy(X)))))&
(((brave(lucy)&~curious(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)<~>patient(X))<=>~rich(X)))&
(![X]:((~humble(X)<~>~creative(X))<=>(~generous(X)<~>~happy(X))))&
((brave(paul))=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~happy(X)|happy(X))))&
(![X]:((kind(X)|~brave(X))<=>~creative(X)))&
(![X]:((~kind(X)|curious(X))=>~humble(X)))&
(![X]:((~curious(X)&funny(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((curious(X)<~>creative(X))=>(brave(X)<~>kind(X))))&
((?[X]:((~happy(X)<~>~calm(X))))<=>((funny(paul)&kind(paul))))&
(?[X]:((funny(X)|happy(X))))&
((happy(paul)<~>~rich(paul)))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:(happy(X)))&
(kind(paul)) | ~curious(john) | [] | null | 0 |
If someone is not humble or not kind then lucy is both not humble and not funny.
Everyone who is not kind or strong is humble or quiet and vice versa.
If mary is old or generous then someone is tall and vice versa.
Everyone who is quiet or kind is brave and vice versa.
If paul is both humble and not strong then someone is old or kind and vice versa.
Everyone who is humble is either humble or not wise.
Everyone who is either not wise or quiet is not kind.
If susan is either tall or wise then paul is both quiet and old.
Everyone who is both rich and old is either not rich or not patient and vice versa.
Everyone who is not strong is tall and vice versa.
Everyone who is both curious and not patient is either patient or strong.
If someone is not strong then someone is either funny or not humble and vice versa.
Everyone who is not kind or calm is both not quiet and rich.
Everyone who is not brave is not quiet or old and vice versa.
Everyone who is either not patient or humble is not happy or not kind and vice versa.
If fred is either not wise or not calm then john is not generous or wise and vice versa.
Someone is not creative or not happy.
Paul is wise or not funny.
Someone is not patient.
Someone is both generous and calm.
John is not quiet.
Someone is either kind or funny.
Susan is either curious or rich.
Someone is not patient or not creative. | John is patient. | entailment | ((?[X]:((~humble(X)|~kind(X))))=>((~humble(lucy)&~funny(lucy))))&
(![X]:((~kind(X)|strong(X))<=>(humble(X)|quiet(X))))&
(((old(mary)|generous(mary)))<=>(?[X]:(tall(X))))&
(![X]:((quiet(X)|kind(X))<=>brave(X)))&
(((humble(paul)&~strong(paul)))<=>(?[X]:((old(X)|kind(X)))))&
(![X]:(humble(X)=>(humble(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>quiet(X))=>~kind(X)))&
(((tall(susan)<~>wise(susan)))=>((quiet(paul)&old(paul))))&
(![X]:((rich(X)&old(X))<=>(~rich(X)<~>~patient(X))))&
(![X]:(~strong(X)<=>tall(X)))&
(![X]:((curious(X)&~patient(X))=>(patient(X)<~>strong(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((funny(X)<~>~humble(X)))))&
(![X]:((~kind(X)|calm(X))=>(~quiet(X)&rich(X))))&
(![X]:(~brave(X)<=>(~quiet(X)|old(X))))&
(![X]:((~patient(X)<~>humble(X))<=>(~happy(X)|~kind(X))))&
(((~wise(fred)<~>~calm(fred)))<=>((~generous(john)|wise(john))))&
(?[X]:((~creative(X)|~happy(X))))&
((wise(paul)|~funny(paul)))&
(?[X]:(~patient(X)))&
(?[X]:((generous(X)&calm(X))))&
(~quiet(john))&
(?[X]:((kind(X)<~>funny(X))))&
((curious(susan)<~>rich(susan)))&
(?[X]:((~patient(X)|~creative(X)))) | patient(john) | [
"p1",
"p3",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 434968709082977779311496
% SZS output start Proof for 434968709082977779311496
2. ! [X0] : ((strong(X0) | ~kind(X0)) <=> (quiet(X0) | humble(X0))) [input p1]
4. ! [X0] : ((kind(X0) | quiet(X0)) <=> brave(X0)) [input p3]
14. ! [X0] : (~brave(X0) <=> (old(X0) | ~quiet(X0))) [input p13]
15. ! [X0] : ((~patient(X0) <~> humble(X0)) <=> (~kind(X0) | ~happy(X0))) [input p14]
21. ~quiet(john) [input p20]
25. ~patient(john) [input hypothesis]
36. ! [X0] : (((strong(X0) | ~kind(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (~strong(X0) & kind(X0)))) [nnf transformation 2]
37. ! [X0] : ((strong(X0) | ~kind(X0) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | (~strong(X0) & kind(X0)))) [flattening 36]
43. ! [X0] : (((kind(X0) | quiet(X0)) | ~brave(X0)) & (brave(X0) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 4]
44. ! [X0] : ((kind(X0) | quiet(X0) | ~brave(X0)) & (brave(X0) | (~kind(X0) & ~quiet(X0)))) [flattening 43]
62. ! [X0] : ((~brave(X0) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | brave(X0))) [nnf transformation 14]
63. ! [X0] : ((~brave(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | brave(X0))) [flattening 62]
64. ! [X0] : ((((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0))))) [nnf transformation 15]
65. ! [X0] : ((((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0))))) [flattening 64]
80. quiet(X0) | humble(X0) | kind(X0) [cnf transformation 37]
88. ~kind(X0) | brave(X0) [cnf transformation 44]
122. ~brave(X0) | quiet(X0) [cnf transformation 63]
129. ~humble(X0) | patient(X0) | kind(X0) [cnf transformation 65]
140. ~quiet(john) [cnf transformation 21]
145. ~patient(john) [cnf transformation 25]
359. humble(john) | kind(john) [resolution 80,140]
382. 35 <=> kind(john) [avatar definition]
383. ~kind(john) <- (~35) [avatar component clause 382]
384. kind(john) <- (35) [avatar component clause 382]
386. 36 <=> humble(john) [avatar definition]
388. humble(john) <- (36) [avatar component clause 386]
389. 35 | 36 [avatar split clause 359,386,382]
413. brave(john) <- (35) [resolution 384,88]
606. quiet(john) <- (35) [resolution 413,122]
607. $false <- (35) [subsumption resolution 606,140]
608. ~35 [avatar contradiction clause 607]
615. patient(john) | kind(john) <- (36) [resolution 388,129]
618. kind(john) <- (36) [subsumption resolution 615,145]
619. $false <- (~35, 36) [subsumption resolution 618,383]
620. 35 | ~36 [avatar contradiction clause 619]
622. $false [avatar sat refutation 389,608,620]
% SZS output end Proof for 434968709082977779311496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or funny is quiet or old and vice versa.
If someone is both creative and not calm then someone is not strong.
If alice is either not humble or not happy then lucy is strong and vice versa.
Everyone who is kind or happy is brave or not happy.
If someone is both not curious and not generous then fred is humble.
Everyone who is happy is both not quiet and old.
If lucy is funny then fred is either not quiet or not old.
If someone is patient or strong then someone is not old or tall.
If someone is not patient then fred is both not strong and not patient and vice versa.
If mary is humble or not curious then alice is both humble and calm.
Everyone who is either funny or curious is both generous and tall and vice versa.
If someone is both happy and wise then someone is kind or tall and vice versa.
If someone is not tall then someone is brave and vice versa.
Everyone who is kind or patient is either tall or not creative and vice versa.
Everyone who is not tall is creative and vice versa.
If someone is both not wise and not humble then someone is not generous or not funny.
Someone is both tall and curious.
Someone is either calm or not patient.
Someone is not creative or not quiet.
Someone is either old or not funny.
Someone is quiet.
Lucy is both creative and not kind.
John is wise. | Fred is not kind. | entailment | (![X]:((strong(X)<~>funny(X))<=>(quiet(X)|old(X))))&
((?[X]:((creative(X)&~calm(X))))=>(?[X]:(~strong(X))))&
(((~humble(alice)<~>~happy(alice)))<=>(strong(lucy)))&
(![X]:((kind(X)|happy(X))=>(brave(X)|~happy(X))))&
((?[X]:((~curious(X)&~generous(X))))=>(humble(fred)))&
(![X]:(happy(X)=>(~quiet(X)&old(X))))&
((funny(lucy))=>((~quiet(fred)<~>~old(fred))))&
((?[X]:((patient(X)|strong(X))))=>(?[X]:((~old(X)|tall(X)))))&
((?[X]:(~patient(X)))<=>((~strong(fred)&~patient(fred))))&
(((humble(mary)|~curious(mary)))=>((humble(alice)&calm(alice))))&
(![X]:((funny(X)<~>curious(X))<=>(generous(X)&tall(X))))&
((?[X]:((happy(X)&wise(X))))<=>(?[X]:((kind(X)|tall(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:(brave(X))))&
(![X]:((kind(X)|patient(X))<=>(tall(X)<~>~creative(X))))&
(![X]:(~tall(X)<=>creative(X)))&
((?[X]:((~wise(X)&~humble(X))))=>(?[X]:((~generous(X)|~funny(X)))))&
(?[X]:((tall(X)&curious(X))))&
(?[X]:((calm(X)<~>~patient(X))))&
(?[X]:((~creative(X)|~quiet(X))))&
(?[X]:((old(X)<~>~funny(X))))&
(?[X]:(quiet(X)))&
((creative(lucy)&~kind(lucy)))&
(wise(john)) | ~kind(fred) | [
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6996902546246924381729638
% SZS output start Proof for 6996902546246924381729638
14. ! [X0] : ((patient(X0) | kind(X0)) <=> (tall(X0) <~> ~creative(X0))) [input p13]
15. ! [X0] : (~tall(X0) <=> creative(X0)) [input p14]
24. kind(fred) [input hypothesis]
66. ! [X0] : (((patient(X0) | kind(X0)) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (~patient(X0) & ~kind(X0)))) [nnf transformation 14]
67. ! [X0] : ((patient(X0) | kind(X0) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (~patient(X0) & ~kind(X0)))) [flattening 66]
68. ! [X0] : ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0))) [nnf transformation 15]
124. ~kind(X0) | tall(X0) | ~creative(X0) [cnf transformation 67]
126. ~tall(X0) | creative(X0) | ~kind(X0) [cnf transformation 67]
130. tall(X0) | creative(X0) [cnf transformation 68]
131. ~tall(X0) | ~creative(X0) [cnf transformation 68]
144. kind(fred) [cnf transformation 24]
422. tall(fred) | ~creative(fred) [resolution 124,144]
424. ~creative(fred) [subsumption resolution 422,131]
439. creative(X0) | ~kind(X0) | creative(X0) [resolution 126,130]
440. ~kind(X0) | creative(X0) [duplicate literal removal 439]
534. creative(fred) [resolution 440,144]
536. $false [subsumption resolution 534,424]
% SZS output end Proof for 6996902546246924381729638
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not calm or wise then mary is strong or wise.
Everyone who is both funny and not creative is not happy or wise and vice versa.
If mary is both tall and not quiet then someone is either curious or not happy.
If john is not tall or tall then someone is kind and vice versa.
If lucy is generous or quiet then someone is both humble and not calm and vice versa.
If alice is both calm and not quiet then someone is kind.
Everyone who is generous or quiet is both not calm and humble and vice versa.
Everyone who is either funny or not tall is not calm or not rich and vice versa.
Everyone who is not rich or tall is both humble and creative and vice versa.
If mary is both not curious and not brave then paul is not strong or rich and vice versa.
Everyone who is not wise or kind is not humble or generous and vice versa.
Everyone who is both humble and wise is both calm and not old.
If mary is not quiet then someone is curious and vice versa.
If john is not funny then someone is both not funny and creative.
If alice is curious or not quiet then lucy is not humble or old and vice versa.
Everyone who is humble is both tall and not patient.
Someone is both not quiet and not brave.
Someone is rich or not calm.
Alice is humble or quiet.
Someone is not rich.
Alice is either quiet or not wise.
Someone is both not happy and not old.
Fred is either not happy or calm. | Fred is humble. | contradiction | (((~calm(lucy)<~>wise(lucy)))=>((strong(mary)|wise(mary))))&
(![X]:((funny(X)&~creative(X))<=>(~happy(X)|wise(X))))&
(((tall(mary)&~quiet(mary)))=>(?[X]:((curious(X)<~>~happy(X)))))&
(((~tall(john)|tall(john)))<=>(?[X]:(kind(X))))&
(((generous(lucy)|quiet(lucy)))<=>(?[X]:((humble(X)&~calm(X)))))&
(((calm(alice)&~quiet(alice)))=>(?[X]:(kind(X))))&
(![X]:((generous(X)|quiet(X))<=>(~calm(X)&humble(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(~calm(X)|~rich(X))))&
(![X]:((~rich(X)|tall(X))<=>(humble(X)&creative(X))))&
(((~curious(mary)&~brave(mary)))<=>((~strong(paul)|rich(paul))))&
(![X]:((~wise(X)|kind(X))<=>(~humble(X)|generous(X))))&
(![X]:((humble(X)&wise(X))=>(calm(X)&~old(X))))&
((~quiet(mary))<=>(?[X]:(curious(X))))&
((~funny(john))=>(?[X]:((~funny(X)&creative(X)))))&
(((curious(alice)|~quiet(alice)))<=>((~humble(lucy)|old(lucy))))&
(![X]:(humble(X)=>(tall(X)&~patient(X))))&
(?[X]:((~quiet(X)&~brave(X))))&
(?[X]:((rich(X)|~calm(X))))&
((humble(alice)|quiet(alice)))&
(?[X]:(~rich(X)))&
((quiet(alice)<~>~wise(alice)))&
(?[X]:((~happy(X)&~old(X))))&
((~happy(fred)<~>calm(fred))) | humble(fred) | [
"p1",
"p6",
"p8",
"p10",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 948637970792008117495335
% SZS output start Proof for 948637970792008117495335
2. ! [X0] : ((~creative(X0) & funny(X0)) <=> (wise(X0) | ~happy(X0))) [input p1]
7. ! [X0] : ((quiet(X0) | generous(X0)) <=> (humble(X0) & ~calm(X0))) [input p6]
9. ! [X0] : ((tall(X0) | ~rich(X0)) <=> (creative(X0) & humble(X0))) [input p8]
11. ! [X0] : ((kind(X0) | ~wise(X0)) <=> (generous(X0) | ~humble(X0))) [input p10]
16. ! [X0] : (humble(X0) => (~patient(X0) & tall(X0))) [input p15]
23. ~happy(fred) <~> calm(fred) [input p22]
24. humble(fred) [input hypothesis]
25. ! [X0] : (humble(X0) => tall(X0)) [pure predicate removal 16]
35. ! [X0] : (tall(X0) | ~humble(X0)) [ennf transformation 25]
37. ! [X0] : (((~creative(X0) & funny(X0)) | (~wise(X0) & happy(X0))) & ((wise(X0) | ~happy(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 2]
38. ! [X0] : (((~creative(X0) & funny(X0)) | (~wise(X0) & happy(X0))) & (wise(X0) | ~happy(X0) | creative(X0) | ~funny(X0))) [flattening 37]
54. ! [X0] : (((quiet(X0) | generous(X0)) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | (~quiet(X0) & ~generous(X0)))) [nnf transformation 7]
55. ! [X0] : ((quiet(X0) | generous(X0) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | (~quiet(X0) & ~generous(X0)))) [flattening 54]
58. ! [X0] : (((tall(X0) | ~rich(X0)) | (~creative(X0) | ~humble(X0))) & ((creative(X0) & humble(X0)) | (~tall(X0) & rich(X0)))) [nnf transformation 9]
59. ! [X0] : ((tall(X0) | ~rich(X0) | ~creative(X0) | ~humble(X0)) & ((creative(X0) & humble(X0)) | (~tall(X0) & rich(X0)))) [flattening 58]
62. ! [X0] : (((kind(X0) | ~wise(X0)) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | (~kind(X0) & wise(X0)))) [nnf transformation 11]
63. ! [X0] : ((kind(X0) | ~wise(X0) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | (~kind(X0) & wise(X0)))) [flattening 62]
81. (~calm(fred) | happy(fred)) & (calm(fred) | ~happy(fred)) [nnf transformation 23]
87. ~creative(X0) | happy(X0) [cnf transformation 38]
88. ~creative(X0) | ~wise(X0) [cnf transformation 38]
100. ~generous(X0) | ~calm(X0) [cnf transformation 55]
114. ~tall(X0) | creative(X0) [cnf transformation 59]
121. ~humble(X0) | generous(X0) | wise(X0) [cnf transformation 63]
135. ~humble(X0) | tall(X0) [cnf transformation 35]
145. calm(fred) | ~happy(fred) [cnf transformation 81]
147. humble(fred) [cnf transformation 24]
308. 34 <=> happy(fred) [avatar definition]
312. 35 <=> calm(fred) [avatar definition]
316. ~34 | 35 [avatar split clause 145,312,308]
328. tall(fred) [resolution 135,147]
360. creative(fred) [resolution 328,114]
419. generous(fred) | wise(fred) [resolution 121,147]
425. 43 <=> wise(fred) [avatar definition]
429. 44 <=> generous(fred) [avatar definition]
431. generous(fred) <- (44) [avatar component clause 429]
432. 43 | 44 [avatar split clause 419,429,425]
592. ~calm(fred) <- (44) [resolution 431,100]
595. ~35 | ~44 [avatar split clause 592,429,312]
690. ~wise(fred) [resolution 360,88]
691. happy(fred) [resolution 360,87]
694. 34 [avatar split clause 691,308]
695. ~43 [avatar split clause 690,425]
702. $false [avatar sat refutation 316,432,595,694,695]
% SZS output end Proof for 948637970792008117495335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or kind then lucy is tall and vice versa.
If someone is either not brave or strong then someone is either not funny or old.
If someone is curious then someone is not wise or not brave.
If someone is either patient or humble then someone is curious and vice versa.
Everyone who is either not creative or rich is both not patient and not curious and vice versa.
If john is not curious then someone is rich and vice versa.
If fred is either not humble or quiet then susan is both rich and wise and vice versa.
If susan is not happy or old then someone is both creative and rich and vice versa.
Everyone who is creative is either not kind or kind and vice versa.
If someone is both not brave and not tall then lucy is rich or not curious.
If alice is not generous then paul is both not rich and not tall.
If someone is both quiet and not funny then mary is not happy or strong.
If someone is rich or patient then someone is not curious or tall and vice versa.
Everyone who is both not kind and not funny is not funny.
If john is curious or not creative then someone is calm or curious and vice versa.
Everyone who is not tall or curious is either not curious or not creative and vice versa.
Someone is funny.
Someone is old or kind.
Paul is either not humble or calm.
Lucy is kind or not tall.
Alice is both not curious and not wise.
Mary is not patient or not quiet. | Paul is not patient. | entailment | ((?[X]:((strong(X)|kind(X))))<=>(tall(lucy)))&
((?[X]:((~brave(X)<~>strong(X))))=>(?[X]:((~funny(X)<~>old(X)))))&
((?[X]:(curious(X)))=>(?[X]:((~wise(X)|~brave(X)))))&
((?[X]:((patient(X)<~>humble(X))))<=>(?[X]:(curious(X))))&
(![X]:((~creative(X)<~>rich(X))<=>(~patient(X)&~curious(X))))&
((~curious(john))<=>(?[X]:(rich(X))))&
(((~humble(fred)<~>quiet(fred)))<=>((rich(susan)&wise(susan))))&
(((~happy(susan)|old(susan)))<=>(?[X]:((creative(X)&rich(X)))))&
(![X]:(creative(X)<=>(~kind(X)<~>kind(X))))&
((?[X]:((~brave(X)&~tall(X))))=>((rich(lucy)|~curious(lucy))))&
((~generous(alice))=>((~rich(paul)&~tall(paul))))&
((?[X]:((quiet(X)&~funny(X))))=>((~happy(mary)|strong(mary))))&
((?[X]:((rich(X)|patient(X))))<=>(?[X]:((~curious(X)|tall(X)))))&
(![X]:((~kind(X)&~funny(X))=>~funny(X)))&
(((curious(john)|~creative(john)))<=>(?[X]:((calm(X)|curious(X)))))&
(![X]:((~tall(X)|curious(X))<=>(~curious(X)<~>~creative(X))))&
(?[X]:(funny(X)))&
(?[X]:((old(X)|kind(X))))&
((~humble(paul)<~>calm(paul)))&
((kind(lucy)|~tall(lucy)))&
((~curious(alice)&~wise(alice)))&
((~patient(mary)|~quiet(mary))) | ~patient(paul) | [
"p3",
"p8",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3745711345256500858837698
% SZS output start Proof for 3745711345256500858837698
4. ? [X0] : (patient(X0) <~> humble(X0)) <=> ? [X0] : curious(X0) [input p3]
9. ! [X0] : (creative(X0) <=> (~kind(X0) <~> kind(X0))) [input p8]
15. (~creative(john) | curious(john)) <=> ? [X0] : (curious(X0) | calm(X0)) [input p14]
16. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (~curious(X0) <~> ~creative(X0))) [input p15]
19. ~humble(paul) <~> calm(paul) [input p18]
23. patient(paul) [input hypothesis]
26. ? [X0] : (patient(X0) <~> humble(X0)) <=> ? [X1] : curious(X1) [rectify 4]
48. (? [X0] : ((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0)))) [nnf transformation 26]
49. (? [X0] : ((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : ((patient(X3) | ~humble(X3)) & (humble(X3) | ~patient(X3)))) [rectify 48]
50. ? [X0] : ((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) => ((~humble(sK3) | ~patient(sK3)) & (humble(sK3) | patient(sK3))) [choice axiom]
51. ? [X2] : curious(X2) => curious(sK4) [choice axiom]
52. (((~humble(sK3) | ~patient(sK3)) & (humble(sK3) | patient(sK3))) | ! [X1] : ~curious(X1)) & (curious(sK4) | ! [X3] : ((patient(X3) | ~humble(X3)) & (humble(X3) | ~patient(X3)))) [skolemisation 49,51,50]
66. ! [X0] : ((creative(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~creative(X0))) [nnf transformation 9]
72. ((~creative(john) | curious(john)) | ! [X0] : (~curious(X0) & ~calm(X0))) & (? [X0] : (curious(X0) | calm(X0)) | (creative(john) & ~curious(john))) [nnf transformation 15]
73. (~creative(john) | curious(john) | ! [X0] : (~curious(X0) & ~calm(X0))) & (? [X0] : (curious(X0) | calm(X0)) | (creative(john) & ~curious(john))) [flattening 72]
74. (~creative(john) | curious(john) | ! [X0] : (~curious(X0) & ~calm(X0))) & (? [X1] : (curious(X1) | calm(X1)) | (creative(john) & ~curious(john))) [rectify 73]
75. ? [X1] : (curious(X1) | calm(X1)) => (curious(sK9) | calm(sK9)) [choice axiom]
76. (~creative(john) | curious(john) | ! [X0] : (~curious(X0) & ~calm(X0))) & ((curious(sK9) | calm(sK9)) | (creative(john) & ~curious(john))) [skolemisation 74,75]
77. ! [X0] : (((curious(X0) | ~tall(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | (~curious(X0) & tall(X0)))) [nnf transformation 16]
78. ! [X0] : ((curious(X0) | ~tall(X0) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | (~curious(X0) & tall(X0)))) [flattening 77]
83. (~calm(paul) | humble(paul)) & (calm(paul) | ~humble(paul)) [nnf transformation 19]
92. curious(sK4) | humble(X3) | ~patient(X3) [cnf transformation 52]
117. creative(X0) | kind(X0) | kind(X0) [cnf transformation 66]
118. creative(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 66]
128. ~creative(john) | curious(john) | ~calm(X0) [cnf transformation 76]
131. ~creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 78]
138. calm(paul) | ~humble(paul) [cnf transformation 83]
144. patient(paul) [cnf transformation 23]
145. ~creative(X0) | ~curious(X0) [duplicate literal removal 131]
147. creative(X0) | kind(X0) [duplicate literal removal 117]
148. ~kind(X0) | creative(X0) [duplicate literal removal 118]
189. 10 <=> ! [X1] : ~curious(X1) [avatar definition]
190. ~curious(X1) <- (10) [avatar component clause 189]
214. 16 <=> curious(sK4) [avatar definition]
216. curious(sK4) <- (16) [avatar component clause 214]
219. 17 <=> ! [X3] : (humble(X3) | ~patient(X3)) [avatar definition]
220. ~patient(X3) | humble(X3) <- (17) [avatar component clause 219]
221. 17 | 16 [avatar split clause 92,214,219]
226. 19 <=> curious(john) [avatar definition]
227. curious(john) <- (19) [avatar component clause 226]
281. creative(X0) [subsumption resolution 147,148]
337. curious(john) | ~calm(X0) [subsumption resolution 128,281]
339. 43 <=> ! [X0] : ~calm(X0) [avatar definition]
340. ~calm(X0) <- (43) [avatar component clause 339]
341. 43 | 19 [avatar split clause 337,226,339]
352. ~curious(X0) [subsumption resolution 145,281]
353. 10 [avatar split clause 352,189]
365. 48 <=> humble(paul) [avatar definition]
369. 49 <=> calm(paul) [avatar definition]
370. calm(paul) <- (49) [avatar component clause 369]
373. ~48 | 49 [avatar split clause 138,369,365]
390. $false <- (10, 16) [resolution 216,190]
391. ~10 | ~16 [avatar contradiction clause 390]
394. humble(paul) <- (17) [resolution 220,144]
397. 48 | ~17 [avatar split clause 394,219,365]
398. $false <- (43, 49) [subsumption resolution 370,340]
399. ~43 | ~49 [avatar contradiction clause 398]
400. $false <- (10, 19) [subsumption resolution 227,190]
401. ~10 | ~19 [avatar contradiction clause 400]
402. $false [avatar sat refutation 221,341,353,373,391,397,399,401]
% SZS output end Proof for 3745711345256500858837698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not curious or patient then fred is either humble or not happy. Everyone who is not curious is either not strong or happy. If someone is both not calm and creative then paul is either not funny or not curious. Everyone who is both not tall and old is not funny or not curious. Everyone who is both not brave and not quiet is not wise and vice versa. If someone is both wise and not funny then fred is not funny or not old. Everyone who is either not funny or not generous is brave and vice versa. Everyone who is not calm or old is not old. Everyone who is wise is not curious. Everyone who is both not strong and not happy is both not quiet and strong and vice versa. If someone is not patient or funny then fred is tall and vice versa. If john is both not tall and not kind then someone is either rich or kind and vice versa. Everyone who is both not funny and old is curious. If lucy is either humble or not wise then paul is either brave or not generous and vice versa. Everyone who is not old is both patient and not creative. If someone is not kind or not calm then alice is not quiet. Someone is either kind or not creative. Susan is not wise or not calm. Lucy is not funny. Alice is both tall and generous. Alice is generous. Someone is funny. Someone is both strong and tall. | Susan is not old. | entailment | (((~curious(paul)<~>patient(paul)))=>((humble(fred)<~>~happy(fred))))&
(![X]:(~curious(X)=>(~strong(X)<~>happy(X))))&
((?[X]:((~calm(X)&creative(X))))=>((~funny(paul)<~>~curious(paul))))&
(![X]:((~tall(X)&old(X))=>(~funny(X)|~curious(X))))&
(![X]:((~brave(X)&~quiet(X))<=>~wise(X)))&
((?[X]:((wise(X)&~funny(X))))=>((~funny(fred)|~old(fred))))&
(![X]:((~funny(X)<~>~generous(X))<=>brave(X)))&
(![X]:((~calm(X)|old(X))=>~old(X)))&
(![X]:(wise(X)=>~curious(X)))&
(![X]:((~strong(X)&~happy(X))<=>(~quiet(X)&strong(X))))&
((?[X]:((~patient(X)|funny(X))))<=>(tall(fred)))&
(((~tall(john)&~kind(john)))<=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((~funny(X)&old(X))=>curious(X)))&
(((humble(lucy)<~>~wise(lucy)))<=>((brave(paul)<~>~generous(paul))))&
(![X]:(~old(X)=>(patient(X)&~creative(X))))&
((?[X]:((~kind(X)|~calm(X))))=>(~quiet(alice)))&
(?[X]:((kind(X)<~>~creative(X))))&
((~wise(susan)|~calm(susan)))&
(~funny(lucy))&
((tall(alice)&generous(alice)))&
(generous(alice))&
(?[X]:(funny(X)))&
(?[X]:((strong(X)&tall(X)))) | ~old(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2050661325844510675954020
% SZS output start Proof for 2050661325844510675954020
8. ! [X0] : ((old(X0) | ~calm(X0)) => ~old(X0)) [input p7]
24. old(susan) [input hypothesis]
32. ! [X0] : (~old(X0) | (~old(X0) & calm(X0))) [ennf transformation 8]
81. ~old(X0) | ~old(X0) [cnf transformation 32]
119. old(susan) [cnf transformation 24]
122. ~old(X0) [duplicate literal removal 81]
262. $false [subsumption resolution 119,122]
% SZS output end Proof for 2050661325844510675954020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either kind or not funny then mary is both creative and calm and vice versa.
If alice is not creative then someone is both wise and happy and vice versa.
Everyone who is humble or brave is not happy and vice versa.
If someone is either not strong or not kind then someone is either old or not kind.
Everyone who is not kind or not strong is not brave or not wise.
Everyone who is either wise or patient is not generous and vice versa.
If john is not humble then fred is both not strong and not kind.
Everyone who is not curious or not tall is not humble or strong and vice versa.
Everyone who is both not tall and not curious is humble or rich.
Everyone who is either not strong or curious is not old and vice versa.
If lucy is both not old and old then someone is not curious or brave and vice versa.
Everyone who is happy or funny is generous.
Everyone who is both not creative and not kind is quiet and vice versa.
If someone is not curious or not old then alice is patient.
If someone is generous then someone is creative or tall and vice versa.
Everyone who is not strong or not rich is not kind or wise and vice versa.
Mary is humble.
Someone is brave or calm.
John is either not humble or old.
Someone is either quiet or kind.
John is both strong and curious.
Someone is either not strong or not quiet.
Lucy is either not wise or kind.
Someone is old or not old. | Mary is not brave. | entailment | (((kind(paul)<~>~funny(paul)))<=>((creative(mary)&calm(mary))))&
((~creative(alice))<=>(?[X]:((wise(X)&happy(X)))))&
(![X]:((humble(X)|brave(X))<=>~happy(X)))&
((?[X]:((~strong(X)<~>~kind(X))))=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:((~kind(X)|~strong(X))=>(~brave(X)|~wise(X))))&
(![X]:((wise(X)<~>patient(X))<=>~generous(X)))&
((~humble(john))=>((~strong(fred)&~kind(fred))))&
(![X]:((~curious(X)|~tall(X))<=>(~humble(X)|strong(X))))&
(![X]:((~tall(X)&~curious(X))=>(humble(X)|rich(X))))&
(![X]:((~strong(X)<~>curious(X))<=>~old(X)))&
(((~old(lucy)&old(lucy)))<=>(?[X]:((~curious(X)|brave(X)))))&
(![X]:((happy(X)|funny(X))=>generous(X)))&
(![X]:((~creative(X)&~kind(X))<=>quiet(X)))&
((?[X]:((~curious(X)|~old(X))))=>(patient(alice)))&
((?[X]:(generous(X)))<=>(?[X]:((creative(X)|tall(X)))))&
(![X]:((~strong(X)|~rich(X))<=>(~kind(X)|wise(X))))&
(humble(mary))&
(?[X]:((brave(X)|calm(X))))&
((~humble(john)<~>old(john)))&
(?[X]:((quiet(X)<~>kind(X))))&
((strong(john)&curious(john)))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((~wise(lucy)<~>kind(lucy)))&
(?[X]:((old(X)|~old(X)))) | ~brave(mary) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8174808839336615091507801
% SZS output start Proof for 8174808839336615091507801
11. (old(lucy) & ~old(lucy)) <=> ? [X0] : (brave(X0) | ~curious(X0)) [input p10]
25. brave(mary) [input hypothesis]
52. ((old(lucy) & ~old(lucy)) | ! [X0] : (~brave(X0) & curious(X0))) & (? [X0] : (brave(X0) | ~curious(X0)) | (~old(lucy) | old(lucy))) [nnf transformation 11]
53. ((old(lucy) & ~old(lucy)) | ! [X0] : (~brave(X0) & curious(X0))) & (? [X0] : (brave(X0) | ~curious(X0)) | ~old(lucy) | old(lucy)) [flattening 52]
54. ((old(lucy) & ~old(lucy)) | ! [X0] : (~brave(X0) & curious(X0))) & (? [X1] : (brave(X1) | ~curious(X1)) | ~old(lucy) | old(lucy)) [rectify 53]
55. ? [X1] : (brave(X1) | ~curious(X1)) => (brave(sK2) | ~curious(sK2)) [choice axiom]
56. ((old(lucy) & ~old(lucy)) | ! [X0] : (~brave(X0) & curious(X0))) & ((brave(sK2) | ~curious(sK2)) | ~old(lucy) | old(lucy)) [skolemisation 54,55]
113. ~old(lucy) | ~brave(X0) [cnf transformation 56]
115. old(lucy) | ~brave(X0) [cnf transformation 56]
143. brave(mary) [cnf transformation 25]
217. 16 <=> ! [X0] : ~brave(X0) [avatar definition]
218. ~brave(X0) <- (16) [avatar component clause 217]
220. 17 <=> old(lucy) [avatar definition]
223. 16 | 17 [avatar split clause 115,220,217]
228. 16 | ~17 [avatar split clause 113,220,217]
311. $false <- (16) [resolution 218,143]
312. ~16 [avatar contradiction clause 311]
313. $false [avatar sat refutation 223,228,312]
% SZS output end Proof for 8174808839336615091507801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not tall is not strong or wise.
Everyone who is not quiet or calm is either humble or happy.
If fred is both brave and not old then someone is both curious and not rich.
Everyone who is not brave is not kind or kind and vice versa.
If someone is creative then susan is old and vice versa.
Everyone who is both not happy and kind is either not tall or quiet and vice versa.
Everyone who is not curious or generous is happy.
Everyone who is not happy or generous is quiet and vice versa.
If someone is either quiet or funny then someone is humble or not funny and vice versa.
Everyone who is generous or creative is kind or quiet.
Everyone who is both not happy and not calm is either not rich or not humble and vice versa.
If someone is both curious and not generous then someone is not old or not calm.
If someone is both not curious and humble then someone is not funny or patient and vice versa.
If someone is humble or not humble then someone is either calm or patient and vice versa.
If someone is either not funny or strong then alice is not tall.
Everyone who is both not kind and not generous is not quiet and vice versa.
Mary is both kind and humble.
Someone is either not funny or not tall.
Fred is both creative and patient.
Someone is not tall.
Someone is both not curious and old.
Someone is funny or generous.
Someone is both not brave and not wise.
Fred is tall or wise. | Fred is brave. | contradiction | (![X]:((happy(X)<~>~tall(X))=>(~strong(X)|wise(X))))&
(![X]:((~quiet(X)|calm(X))=>(humble(X)<~>happy(X))))&
(((brave(fred)&~old(fred)))=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:(~brave(X)<=>(~kind(X)|kind(X))))&
((?[X]:(creative(X)))<=>(old(susan)))&
(![X]:((~happy(X)&kind(X))<=>(~tall(X)<~>quiet(X))))&
(![X]:((~curious(X)|generous(X))=>happy(X)))&
(![X]:((~happy(X)|generous(X))<=>quiet(X)))&
((?[X]:((quiet(X)<~>funny(X))))<=>(?[X]:((humble(X)|~funny(X)))))&
(![X]:((generous(X)|creative(X))=>(kind(X)|quiet(X))))&
(![X]:((~happy(X)&~calm(X))<=>(~rich(X)<~>~humble(X))))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:((~old(X)|~calm(X)))))&
((?[X]:((~curious(X)&humble(X))))<=>(?[X]:((~funny(X)|patient(X)))))&
((?[X]:((humble(X)|~humble(X))))<=>(?[X]:((calm(X)<~>patient(X)))))&
((?[X]:((~funny(X)<~>strong(X))))=>(~tall(alice)))&
(![X]:((~kind(X)&~generous(X))<=>~quiet(X)))&
((kind(mary)&humble(mary)))&
(?[X]:((~funny(X)<~>~tall(X))))&
((creative(fred)&patient(fred)))&
(?[X]:(~tall(X)))&
(?[X]:((~curious(X)&old(X))))&
(?[X]:((funny(X)|generous(X))))&
(?[X]:((~brave(X)&~wise(X))))&
((tall(fred)|wise(fred))) | brave(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8626503355702378984783048
% SZS output start Proof for 8626503355702378984783048
4. ! [X0] : (~brave(X0) <=> (kind(X0) | ~kind(X0))) [input p3]
25. brave(fred) [input hypothesis]
44. ! [X0] : ((~brave(X0) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | brave(X0))) [nnf transformation 4]
45. ! [X0] : ((~brave(X0) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | brave(X0))) [flattening 44]
97. ~brave(X0) | kind(X0) [cnf transformation 45]
98. ~brave(X0) | ~kind(X0) [cnf transformation 45]
156. brave(fred) [cnf transformation 25]
175. ~brave(X0) [subsumption resolution 97,98]
318. $false [subsumption resolution 156,175]
% SZS output end Proof for 8626503355702378984783048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not curious is generous or not creative. Everyone who is creative is not curious and vice versa. Everyone who is curious or not calm is both not calm and not patient. If alice is not tall then john is not quiet or quiet and vice versa. If lucy is either not rich or rich then someone is either funny or curious and vice versa. If someone is not rich or not quiet then paul is either strong or happy. Everyone who is both tall and funny is both not brave and not tall and vice versa. If alice is both kind and funny then someone is both not creative and calm. Everyone who is either rich or curious is both kind and not kind. If someone is not quiet then someone is brave or not brave. Everyone who is both not generous and happy is both not humble and wise and vice versa. Everyone who is both not old and rich is not quiet and vice versa. If alice is either generous or calm then someone is strong and vice versa. Everyone who is tall or not kind is not generous or not quiet and vice versa. Everyone who is brave is both not wise and generous and vice versa. If fred is both rich and calm then someone is either not wise or curious and vice versa. Someone is humble or not humble. Lucy is either not patient or not generous. Someone is not creative. Someone is either curious or old. Paul is not humble. Someone is either old or calm. Mary is both creative and not generous. Paul is not rich. | Mary is wise. | entailment | (![X]:((rich(X)&~curious(X))=>(generous(X)|~creative(X))))&
(![X]:(creative(X)<=>~curious(X)))&
(![X]:((curious(X)|~calm(X))=>(~calm(X)&~patient(X))))&
((~tall(alice))<=>((~quiet(john)|quiet(john))))&
(((~rich(lucy)<~>rich(lucy)))<=>(?[X]:((funny(X)<~>curious(X)))))&
((?[X]:((~rich(X)|~quiet(X))))=>((strong(paul)<~>happy(paul))))&
(![X]:((tall(X)&funny(X))<=>(~brave(X)&~tall(X))))&
(((kind(alice)&funny(alice)))=>(?[X]:((~creative(X)&calm(X)))))&
(![X]:((rich(X)<~>curious(X))=>(kind(X)&~kind(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~generous(X)&happy(X))<=>(~humble(X)&wise(X))))&
(![X]:((~old(X)&rich(X))<=>~quiet(X)))&
(((generous(alice)<~>calm(alice)))<=>(?[X]:(strong(X))))&
(![X]:((tall(X)|~kind(X))<=>(~generous(X)|~quiet(X))))&
(![X]:(brave(X)<=>(~wise(X)&generous(X))))&
(((rich(fred)&calm(fred)))<=>(?[X]:((~wise(X)<~>curious(X)))))&
(?[X]:((humble(X)|~humble(X))))&
((~patient(lucy)<~>~generous(lucy)))&
(?[X]:(~creative(X)))&
(?[X]:((curious(X)<~>old(X))))&
(~humble(paul))&
(?[X]:((old(X)<~>calm(X))))&
((creative(mary)&~generous(mary)))&
(~rich(paul)) | wise(mary) | [
"p1",
"p2",
"p8",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 171487403744870523757126
% SZS output start Proof for 171487403744870523757126
2. ! [X0] : (creative(X0) <=> ~curious(X0)) [input p1]
3. ! [X0] : ((~calm(X0) | curious(X0)) => (~patient(X0) & ~calm(X0))) [input p2]
9. ! [X0] : ((rich(X0) <~> curious(X0)) => (~kind(X0) & kind(X0))) [input p8]
16. (calm(fred) & rich(fred)) <=> ? [X0] : (~wise(X0) <~> curious(X0)) [input p15]
23. ~generous(mary) & creative(mary) [input p22]
25. ~wise(mary) [input hypothesis]
29. ! [X0] : ((~patient(X0) & ~calm(X0)) | (calm(X0) & ~curious(X0))) [ennf transformation 3]
33. ! [X0] : ((~kind(X0) & kind(X0)) | (rich(X0) <=> curious(X0))) [ennf transformation 9]
35. ! [X0] : ((creative(X0) | curious(X0)) & (~curious(X0) | ~creative(X0))) [nnf transformation 2]
47. ! [X0] : ((~kind(X0) & kind(X0)) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0)))) [nnf transformation 33]
63. ((calm(fred) & rich(fred)) | ! [X0] : ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0)))) & (? [X0] : ((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (~calm(fred) | ~rich(fred))) [nnf transformation 16]
64. ((calm(fred) & rich(fred)) | ! [X0] : ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0)))) & (? [X0] : ((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | ~calm(fred) | ~rich(fred)) [flattening 63]
65. ((calm(fred) & rich(fred)) | ! [X0] : ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0)))) & (? [X1] : ((~curious(X1) | wise(X1)) & (curious(X1) | ~wise(X1))) | ~calm(fred) | ~rich(fred)) [rectify 64]
66. ? [X1] : ((~curious(X1) | wise(X1)) & (curious(X1) | ~wise(X1))) => ((~curious(sK4) | wise(sK4)) & (curious(sK4) | ~wise(sK4))) [choice axiom]
67. ((calm(fred) & rich(fred)) | ! [X0] : ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0)))) & (((~curious(sK4) | wise(sK4)) & (curious(sK4) | ~wise(sK4))) | ~calm(fred) | ~rich(fred)) [skolemisation 65,66]
80. ~creative(X0) | ~curious(X0) [cnf transformation 35]
82. ~calm(X0) | ~curious(X0) [cnf transformation 29]
107. kind(X0) | curious(X0) | ~rich(X0) [cnf transformation 47]
109. ~kind(X0) | curious(X0) | ~rich(X0) [cnf transformation 47]
132. rich(fred) | curious(X0) | wise(X0) [cnf transformation 67]
134. calm(fred) | curious(X0) | wise(X0) [cnf transformation 67]
145. creative(mary) [cnf transformation 23]
148. ~wise(mary) [cnf transformation 25]
218. ~rich(X0) | curious(X0) [subsumption resolution 107,109]
242. 19 <=> calm(fred) [avatar definition]
244. calm(fred) <- (19) [avatar component clause 242]
247. 20 <=> ! [X0] : (curious(X0) | wise(X0)) [avatar definition]
248. wise(X0) | curious(X0) <- (20) [avatar component clause 247]
249. 20 | 19 [avatar split clause 134,242,247]
251. 21 <=> rich(fred) [avatar definition]
253. rich(fred) <- (21) [avatar component clause 251]
255. 20 | 21 [avatar split clause 132,251,247]
298. ~curious(mary) [resolution 80,145]
311. curious(mary) <- (20) [resolution 248,148]
314. $false <- (20) [subsumption resolution 311,298]
315. ~20 [avatar contradiction clause 314]
316. ~curious(fred) <- (19) [resolution 244,82]
317. curious(fred) <- (21) [resolution 253,218]
318. $false <- (19, 21) [subsumption resolution 317,316]
319. ~19 | ~21 [avatar contradiction clause 318]
320. $false [avatar sat refutation 249,255,315,319]
% SZS output end Proof for 171487403744870523757126
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or not tall then fred is either patient or not calm and vice versa.
Everyone who is wise is both old and not brave and vice versa.
Everyone who is either old or creative is both tall and not quiet.
If fred is wise or not tall then susan is both not kind and humble and vice versa.
Everyone who is both calm and not calm is either rich or not calm.
Everyone who is both generous and creative is either quiet or not patient.
If someone is not strong or happy then lucy is not brave and vice versa.
Everyone who is calm or not quiet is either old or wise and vice versa.
Everyone who is not happy or quiet is either not calm or generous and vice versa.
If someone is both kind and not wise then lucy is both not old and not patient.
Everyone who is both not old and not tall is both old and not quiet and vice versa.
Everyone who is both not generous and old is quiet.
Everyone who is both humble and not happy is not patient.
If someone is not calm or patient then mary is happy.
If susan is both not strong and quiet then someone is old or not generous and vice versa.
If lucy is not patient then someone is both kind and not funny and vice versa.
Alice is not tall.
Paul is curious.
Mary is old or patient.
Someone is old.
Susan is both not funny and humble.
Mary is either not old or rich.
Someone is both not calm and curious.
Susan is strong or happy. | Mary is not happy. | contradiction | ((?[X]:((~wise(X)|~tall(X))))<=>((patient(fred)<~>~calm(fred))))&
(![X]:(wise(X)<=>(old(X)&~brave(X))))&
(![X]:((old(X)<~>creative(X))=>(tall(X)&~quiet(X))))&
(((wise(fred)|~tall(fred)))<=>((~kind(susan)&humble(susan))))&
(![X]:((calm(X)&~calm(X))=>(rich(X)<~>~calm(X))))&
(![X]:((generous(X)&creative(X))=>(quiet(X)<~>~patient(X))))&
((?[X]:((~strong(X)|happy(X))))<=>(~brave(lucy)))&
(![X]:((calm(X)|~quiet(X))<=>(old(X)<~>wise(X))))&
(![X]:((~happy(X)|quiet(X))<=>(~calm(X)<~>generous(X))))&
((?[X]:((kind(X)&~wise(X))))=>((~old(lucy)&~patient(lucy))))&
(![X]:((~old(X)&~tall(X))<=>(old(X)&~quiet(X))))&
(![X]:((~generous(X)&old(X))=>quiet(X)))&
(![X]:((humble(X)&~happy(X))=>~patient(X)))&
((?[X]:((~calm(X)|patient(X))))=>(happy(mary)))&
(((~strong(susan)&quiet(susan)))<=>(?[X]:((old(X)|~generous(X)))))&
((~patient(lucy))<=>(?[X]:((kind(X)&~funny(X)))))&
(~tall(alice))&
(curious(paul))&
((old(mary)|patient(mary)))&
(?[X]:(old(X)))&
((~funny(susan)&humble(susan)))&
((~old(mary)<~>rich(mary)))&
(?[X]:((~calm(X)&curious(X))))&
((strong(susan)|happy(susan))) | ~happy(mary) | [
"p0",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5603825387302923048741298
% SZS output start Proof for 5603825387302923048741298
1. ? [X0] : (~tall(X0) | ~wise(X0)) <=> (patient(fred) <~> ~calm(fred)) [input p0]
14. ? [X0] : (patient(X0) | ~calm(X0)) => happy(mary) [input p13]
17. ~tall(alice) [input p16]
25. ~happy(mary) [input hypothesis]
38. happy(mary) | ! [X0] : (~patient(X0) & calm(X0)) [ennf transformation 14]
39. (? [X0] : (~tall(X0) | ~wise(X0)) | ((patient(fred) | calm(fred)) & (~calm(fred) | ~patient(fred)))) & (((calm(fred) | ~patient(fred)) & (~calm(fred) | patient(fred))) | ! [X0] : (tall(X0) & wise(X0))) [nnf transformation 1]
40. (? [X0] : (~tall(X0) | ~wise(X0)) | ((patient(fred) | calm(fred)) & (~calm(fred) | ~patient(fred)))) & (((calm(fred) | ~patient(fred)) & (~calm(fred) | patient(fred))) | ! [X1] : (tall(X1) & wise(X1))) [rectify 39]
41. ? [X0] : (~tall(X0) | ~wise(X0)) => (~tall(sK0) | ~wise(sK0)) [choice axiom]
42. ((~tall(sK0) | ~wise(sK0)) | ((patient(fred) | calm(fred)) & (~calm(fred) | ~patient(fred)))) & (((calm(fred) | ~patient(fred)) & (~calm(fred) | patient(fred))) | ! [X1] : (tall(X1) & wise(X1))) [skolemisation 40,41]
75. ~calm(fred) | patient(fred) | tall(X1) [cnf transformation 42]
119. happy(mary) | calm(X0) [cnf transformation 38]
120. happy(mary) | ~patient(X0) [cnf transformation 38]
129. ~tall(alice) [cnf transformation 17]
138. ~happy(mary) [cnf transformation 25]
144. 1 <=> calm(fred) [avatar definition]
145. ~calm(fred) <- (~1) [avatar component clause 144]
148. 2 <=> patient(fred) [avatar definition]
150. patient(fred) <- (2) [avatar component clause 148]
162. 5 <=> ! [X1] : tall(X1) [avatar definition]
163. tall(X1) <- (5) [avatar component clause 162]
169. 5 | 2 | ~1 [avatar split clause 75,144,148,162]
234. 19 <=> ! [X0] : ~patient(X0) [avatar definition]
235. ~patient(X0) <- (19) [avatar component clause 234]
237. 20 <=> happy(mary) [avatar definition]
240. 19 | 20 [avatar split clause 120,237,234]
242. 21 <=> ! [X0] : calm(X0) [avatar definition]
243. calm(X0) <- (21) [avatar component clause 242]
244. 21 | 20 [avatar split clause 119,237,242]
302. ~20 [avatar split clause 138,237]
305. $false <- (~1, 21) [subsumption resolution 145,243]
306. 1 | ~21 [avatar contradiction clause 305]
307. $false <- (2, 19) [subsumption resolution 150,235]
308. ~2 | ~19 [avatar contradiction clause 307]
309. $false <- (5) [resolution 163,129]
312. ~5 [avatar contradiction clause 309]
313. $false [avatar sat refutation 169,240,244,302,306,308,312]
% SZS output end Proof for 5603825387302923048741298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not rich or creative then paul is either kind or not quiet.
Everyone who is not brave or not quiet is humble or curious and vice versa.
Everyone who is not brave or brave is not creative.
If someone is creative then susan is curious and vice versa.
Everyone who is calm is not calm or strong and vice versa.
Everyone who is both quiet and not tall is not calm.
If paul is both not happy and curious then someone is patient.
Everyone who is quiet or not calm is both patient and not funny and vice versa.
Everyone who is either calm or patient is not strong or calm and vice versa.
Everyone who is either not tall or not humble is both old and not wise.
Everyone who is either old or not humble is not calm and vice versa.
If someone is happy or not brave then someone is both old and not patient.
If john is not funny then someone is both not calm and not creative.
If someone is brave then john is brave and vice versa.
Someone is humble or curious.
Mary is both not happy and not rich.
Someone is both not humble and not funny.
Someone is kind.
Someone is not wise.
Mary is either happy or not generous. | Paul is not quiet. | entailment | (((~rich(fred)|creative(fred)))=>((kind(paul)<~>~quiet(paul))))&
(![X]:((~brave(X)|~quiet(X))<=>(humble(X)|curious(X))))&
(![X]:((~brave(X)|brave(X))=>~creative(X)))&
((?[X]:(creative(X)))<=>(curious(susan)))&
(![X]:(calm(X)<=>(~calm(X)|strong(X))))&
(![X]:((quiet(X)&~tall(X))=>~calm(X)))&
(((~happy(paul)&curious(paul)))=>(?[X]:(patient(X))))&
(![X]:((quiet(X)|~calm(X))<=>(patient(X)&~funny(X))))&
(![X]:((calm(X)<~>patient(X))<=>(~strong(X)|calm(X))))&
(![X]:((~tall(X)<~>~humble(X))=>(old(X)&~wise(X))))&
(![X]:((old(X)<~>~humble(X))<=>~calm(X)))&
((?[X]:((happy(X)|~brave(X))))=>(?[X]:((old(X)&~patient(X)))))&
((~funny(john))=>(?[X]:((~calm(X)&~creative(X)))))&
((?[X]:(brave(X)))<=>(brave(john)))&
(?[X]:((humble(X)|curious(X))))&
((~happy(mary)&~rich(mary)))&
(?[X]:((~humble(X)&~funny(X))))&
(?[X]:(kind(X)))&
(?[X]:(~wise(X)))&
((happy(mary)<~>~generous(mary))) | ~quiet(paul) | [
"p4",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2658302267314976872186791
% SZS output start Proof for 2658302267314976872186791
5. ! [X0] : (calm(X0) <=> (strong(X0) | ~calm(X0))) [input p4]
8. ! [X0] : ((~calm(X0) | quiet(X0)) <=> (~funny(X0) & patient(X0))) [input p7]
9. ! [X0] : ((calm(X0) <~> patient(X0)) <=> (calm(X0) | ~strong(X0))) [input p8]
21. quiet(paul) [input hypothesis]
41. ! [X0] : ((calm(X0) | (~strong(X0) & calm(X0))) & ((strong(X0) | ~calm(X0)) | ~calm(X0))) [nnf transformation 5]
42. ! [X0] : ((calm(X0) | (~strong(X0) & calm(X0))) & (strong(X0) | ~calm(X0) | ~calm(X0))) [flattening 41]
45. ! [X0] : (((~calm(X0) | quiet(X0)) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | (calm(X0) & ~quiet(X0)))) [nnf transformation 8]
46. ! [X0] : ((~calm(X0) | quiet(X0) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | (calm(X0) & ~quiet(X0)))) [flattening 45]
47. ! [X0] : ((((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0))))) [nnf transformation 9]
48. ! [X0] : ((((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0))))) [flattening 47]
80. calm(X0) | calm(X0) [cnf transformation 42]
84. ~quiet(X0) | patient(X0) [cnf transformation 46]
94. ~patient(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 48]
117. quiet(paul) [cnf transformation 21]
119. ~patient(X0) | ~calm(X0) [duplicate literal removal 94]
121. calm(X0) [duplicate literal removal 80]
131. 3 <=> quiet(paul) [avatar definition]
133. quiet(paul) <- (3) [avatar component clause 131]
160. ~patient(X0) [subsumption resolution 119,121]
199. 3 [avatar split clause 117,131]
203. patient(paul) <- (3) [resolution 84,133]
204. $false <- (3) [subsumption resolution 203,160]
205. ~3 [avatar contradiction clause 204]
206. $false [avatar sat refutation 199,205]
% SZS output end Proof for 2658302267314976872186791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or patient then someone is not calm or not kind and vice versa. Everyone who is both not happy and not old is not tall or humble and vice versa. Everyone who is brave is not rich and vice versa. Everyone who is not humble or not old is either happy or not wise and vice versa. If mary is both creative and not curious then someone is either not rich or not brave. Everyone who is not patient or not quiet is quiet or calm and vice versa. If someone is rich or not kind then someone is old. Everyone who is wise is not humble and vice versa. Everyone who is not strong or not wise is both funny and patient. Everyone who is both funny and not creative is not wise or not old and vice versa. If mary is creative then someone is not brave and vice versa. Everyone who is tall is both not happy and happy and vice versa. Everyone who is quiet is either not creative or patient. Everyone who is not old is either not strong or not happy. Everyone who is not old is either happy or humble. Someone is quiet or not creative. Someone is either strong or happy. Someone is not rich or not kind. Someone is calm or not old. Lucy is either kind or not kind. | Mary is not old. | entailment | ((?[X]:((~rich(X)<~>patient(X))))<=>(?[X]:((~calm(X)|~kind(X)))))&
(![X]:((~happy(X)&~old(X))<=>(~tall(X)|humble(X))))&
(![X]:(brave(X)<=>~rich(X)))&
(![X]:((~humble(X)|~old(X))<=>(happy(X)<~>~wise(X))))&
(((creative(mary)&~curious(mary)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>(quiet(X)|calm(X))))&
((?[X]:((rich(X)|~kind(X))))=>(?[X]:(old(X))))&
(![X]:(wise(X)<=>~humble(X)))&
(![X]:((~strong(X)|~wise(X))=>(funny(X)&patient(X))))&
(![X]:((funny(X)&~creative(X))<=>(~wise(X)|~old(X))))&
((creative(mary))<=>(?[X]:(~brave(X))))&
(![X]:(tall(X)<=>(~happy(X)&happy(X))))&
(![X]:(quiet(X)=>(~creative(X)<~>patient(X))))&
(![X]:(~old(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~old(X)=>(happy(X)<~>humble(X))))&
(?[X]:((quiet(X)|~creative(X))))&
(?[X]:((strong(X)<~>happy(X))))&
(?[X]:((~rich(X)|~kind(X))))&
(?[X]:((calm(X)|~old(X))))&
((kind(lucy)<~>~kind(lucy))) | ~old(mary) | [
"p1",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8532092385021386197919347
% SZS output start Proof for 8532092385021386197919347
2. ! [X0] : ((~old(X0) & ~happy(X0)) <=> (humble(X0) | ~tall(X0))) [input p1]
12. ! [X0] : (tall(X0) <=> (happy(X0) & ~happy(X0))) [input p11]
21. old(mary) [input hypothesis]
35. ! [X0] : (((~old(X0) & ~happy(X0)) | (~humble(X0) & tall(X0))) & ((humble(X0) | ~tall(X0)) | (old(X0) | happy(X0)))) [nnf transformation 2]
36. ! [X0] : (((~old(X0) & ~happy(X0)) | (~humble(X0) & tall(X0))) & (humble(X0) | ~tall(X0) | old(X0) | happy(X0))) [flattening 35]
52. ! [X0] : ((tall(X0) | (~happy(X0) | happy(X0))) & ((happy(X0) & ~happy(X0)) | ~tall(X0))) [nnf transformation 12]
53. ! [X0] : ((tall(X0) | ~happy(X0) | happy(X0)) & ((happy(X0) & ~happy(X0)) | ~tall(X0))) [flattening 52]
76. ~old(X0) | tall(X0) [cnf transformation 36]
105. ~happy(X0) | ~tall(X0) [cnf transformation 53]
106. happy(X0) | ~tall(X0) [cnf transformation 53]
121. old(mary) [cnf transformation 21]
181. ~tall(X0) [subsumption resolution 105,106]
214. tall(mary) [resolution 76,121]
216. $false [subsumption resolution 214,181]
% SZS output end Proof for 8532092385021386197919347
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or quiet is both wise and not brave. Everyone who is not happy or patient is not curious or not generous and vice versa. Everyone who is not patient or curious is not creative and vice versa. Everyone who is patient or not calm is tall. 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. Someone is wise. Someone is both patient and happy. Someone is both not old and quiet. Fred is not calm or not humble. Paul is both strong and rich. Lucy is either not calm or not rich. | Paul is calm. | contradiction | (![X]:((curious(X)<~>quiet(X))=>(wise(X)&~brave(X))))&
(![X]:((~happy(X)|patient(X))<=>(~curious(X)|~generous(X))))&
(![X]:((~patient(X)|curious(X))<=>~creative(X)))&
(![X]:((patient(X)|~calm(X))=>tall(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]:(wise(X)))&
(?[X]:((patient(X)&happy(X))))&
(?[X]:((~old(X)&quiet(X))))&
((~calm(fred)|~humble(fred)))&
((strong(paul)&rich(paul)))&
((~calm(lucy)<~>~rich(lucy))) | calm(paul) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7628416398902355106975272
% SZS output start Proof for 7628416398902355106975272
14. ! [X0] : ((~calm(X0) & quiet(X0)) <=> (happy(X0) | ~happy(X0))) [input p13]
22. calm(paul) [input hypothesis]
63. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | (calm(X0) | ~quiet(X0)))) [nnf transformation 14]
64. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | calm(X0) | ~quiet(X0))) [flattening 63]
120. ~calm(X0) | happy(X0) [cnf transformation 64]
121. ~calm(X0) | ~happy(X0) [cnf transformation 64]
136. calm(paul) [cnf transformation 22]
255. ~calm(X0) [subsumption resolution 120,121]
260. $false [subsumption resolution 136,255]
% SZS output end Proof for 7628416398902355106975272
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or creative then someone is funny and vice versa.
Everyone who is not rich is old or not brave.
If susan is rich or not quiet then someone is either old or not patient.
If lucy is not curious or calm then someone is not old or not tall and vice versa.
Everyone who is not wise is either curious or not wise and vice versa.
Everyone who is not tall or brave is both not kind and curious and vice versa.
Everyone who is not happy or generous is funny.
Everyone who is quiet is happy and vice versa.
If mary is both humble and generous then someone is both tall and kind and vice versa.
Everyone who is strong or not patient is not brave or generous and vice versa.
Everyone who is both calm and not wise is not brave or calm.
If someone is not quiet then paul is brave or strong and vice versa.
If john is happy or kind then someone is both tall and old and vice versa.
Everyone who is both humble and not strong is quiet.
If someone is not quiet then paul is generous or not curious.
Paul is either not brave or not rich.
Alice is generous or strong.
Someone is either not brave or not wise.
Someone is both not happy and not quiet.
Alice is both not strong and not curious.
Someone is not creative.
Someone is not funny or happy. | John is not generous. | neutral | ((?[X]:((quiet(X)|creative(X))))<=>(?[X]:(funny(X))))&
(![X]:(~rich(X)=>(old(X)|~brave(X))))&
(((rich(susan)|~quiet(susan)))=>(?[X]:((old(X)<~>~patient(X)))))&
(((~curious(lucy)|calm(lucy)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:(~wise(X)<=>(curious(X)<~>~wise(X))))&
(![X]:((~tall(X)|brave(X))<=>(~kind(X)&curious(X))))&
(![X]:((~happy(X)|generous(X))=>funny(X)))&
(![X]:(quiet(X)<=>happy(X)))&
(((humble(mary)&generous(mary)))<=>(?[X]:((tall(X)&kind(X)))))&
(![X]:((strong(X)|~patient(X))<=>(~brave(X)|generous(X))))&
(![X]:((calm(X)&~wise(X))=>(~brave(X)|calm(X))))&
((?[X]:(~quiet(X)))<=>((brave(paul)|strong(paul))))&
(((happy(john)|kind(john)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:((humble(X)&~strong(X))=>quiet(X)))&
((?[X]:(~quiet(X)))=>((generous(paul)|~curious(paul))))&
((~brave(paul)<~>~rich(paul)))&
((generous(alice)|strong(alice)))&
(?[X]:((~brave(X)<~>~wise(X))))&
(?[X]:((~happy(X)&~quiet(X))))&
((~strong(alice)&~curious(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)|happy(X)))) | ~generous(john) | [] | null | 0 |
If someone is patient then someone is not creative.
Everyone who is either not old or tall is both not quiet and not humble and vice versa.
If susan is either not strong or not calm then susan is either strong or brave and vice versa.
If someone is both patient and not quiet then someone is either not quiet or brave and vice versa.
Everyone who is not old is either not rich or not creative.
If john is either not wise or patient then john is both not calm and generous and vice versa.
If fred is both not creative and not generous then someone is both not strong and not humble and vice versa.
Everyone who is not wise is tall or not creative and vice versa.
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
Alice is either quiet or not happy.
Susan is either strong or not generous.
Someone is happy.
Lucy is generous or not brave.
Susan is not creative. | John is tall. | contradiction | ((?[X]:(patient(X)))=>(?[X]:(~creative(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~quiet(X)&~humble(X))))&
(((~strong(susan)<~>~calm(susan)))<=>((strong(susan)<~>brave(susan))))&
((?[X]:((patient(X)&~quiet(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
(![X]:(~old(X)=>(~rich(X)<~>~creative(X))))&
(((~wise(john)<~>patient(john)))<=>((~calm(john)&generous(john))))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((quiet(alice)<~>~happy(alice)))&
((strong(susan)<~>~generous(susan)))&
(?[X]:(happy(X)))&
((generous(lucy)|~brave(lucy)))&
(~creative(susan)) | tall(john) | [
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1641532718791442090955495
% SZS output start Proof for 1641532718791442090955495
10. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p9]
13. ! [X0] : ((~patient(X0) & ~quiet(X0)) => (old(X0) & ~tall(X0))) [input p12]
21. tall(john) [input hypothesis]
30. ! [X0] : ((old(X0) & ~tall(X0)) | (patient(X0) | quiet(X0))) [ennf transformation 13]
31. ! [X0] : ((old(X0) & ~tall(X0)) | patient(X0) | quiet(X0)) [flattening 30]
58. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 10]
59. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 58]
110. ~patient(X0) | ~patient(X0) [cnf transformation 59]
112. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 59]
116. ~tall(X0) | patient(X0) | quiet(X0) [cnf transformation 31]
133. tall(john) [cnf transformation 21]
134. ~patient(X0) [duplicate literal removal 110]
135. ~quiet(X0) | patient(X0) [duplicate literal removal 112]
141. 1 <=> ! [X1] : ~patient(X1) [avatar definition]
142. ~patient(X1) <- (1) [avatar component clause 141]
259. 1 [avatar split clause 134,141]
284. ~tall(X0) | patient(X0) [subsumption resolution 116,135]
349. patient(john) [resolution 284,133]
352. $false <- (1) [subsumption resolution 349,142]
353. ~1 [avatar contradiction clause 352]
356. $false [avatar sat refutation 259,353]
% SZS output end Proof for 1641532718791442090955495
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or not curious then mary is both not old and not calm. If lucy is either not brave or not wise then someone is funny or curious and vice versa. Everyone who is tall is humble. If someone is both tall and happy then someone is quiet or generous. Everyone who is not patient is either wise or not generous and vice versa. Everyone who is either not kind or not rich is wise or not patient and vice versa. Everyone who is not creative is generous. Everyone who is either happy or rich is both not funny and not rich and vice versa. Everyone who is either curious or not humble is either humble or not kind. Everyone who is humble is not creative and vice versa. Everyone who is not rich is both brave and humble. If fred is not wise or not generous then someone is both rich and not creative and vice versa. Everyone who is creative or not kind is quiet or curious and vice versa. Everyone who is both not quiet and not strong is not happy or not humble and vice versa. If someone is not old or not creative then someone is both old and calm and vice versa. If someone is both humble and not quiet then paul is both rich and old. Lucy is not strong. Alice is either not brave or curious. Mary is both not brave and funny. Mary is both tall and kind. Someone is both not kind and not generous. Paul is both not tall and not curious. Alice is generous. | Alice is not rich. | contradiction | ((?[X]:((~brave(X)|~curious(X))))=>((~old(mary)&~calm(mary))))&
(((~brave(lucy)<~>~wise(lucy)))<=>(?[X]:((funny(X)|curious(X)))))&
(![X]:(tall(X)=>humble(X)))&
((?[X]:((tall(X)&happy(X))))=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:(~patient(X)<=>(wise(X)<~>~generous(X))))&
(![X]:((~kind(X)<~>~rich(X))<=>(wise(X)|~patient(X))))&
(![X]:(~creative(X)=>generous(X)))&
(![X]:((happy(X)<~>rich(X))<=>(~funny(X)&~rich(X))))&
(![X]:((curious(X)<~>~humble(X))=>(humble(X)<~>~kind(X))))&
(![X]:(humble(X)<=>~creative(X)))&
(![X]:(~rich(X)=>(brave(X)&humble(X))))&
(((~wise(fred)|~generous(fred)))<=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:((creative(X)|~kind(X))<=>(quiet(X)|curious(X))))&
(![X]:((~quiet(X)&~strong(X))<=>(~happy(X)|~humble(X))))&
((?[X]:((~old(X)|~creative(X))))<=>(?[X]:((old(X)&calm(X)))))&
((?[X]:((humble(X)&~quiet(X))))=>((rich(paul)&old(paul))))&
(~strong(lucy))&
((~brave(alice)<~>curious(alice)))&
((~brave(mary)&funny(mary)))&
((tall(mary)&kind(mary)))&
(?[X]:((~kind(X)&~generous(X))))&
((~tall(paul)&~curious(paul)))&
(generous(alice)) | ~rich(alice) | [
"p8",
"p9",
"p10",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5829755501105475819942720
% SZS output start Proof for 5829755501105475819942720
9. ! [X0] : ((curious(X0) <~> ~humble(X0)) => (humble(X0) <~> ~kind(X0))) [input p8]
10. ! [X0] : (humble(X0) <=> ~creative(X0)) [input p9]
11. ! [X0] : (~rich(X0) => (humble(X0) & brave(X0))) [input p10]
13. ! [X0] : ((~kind(X0) | creative(X0)) <=> (curious(X0) | quiet(X0))) [input p12]
18. ~brave(alice) <~> curious(alice) [input p17]
24. ~rich(alice) [input hypothesis]
31. ! [X0] : ((humble(X0) <~> ~kind(X0)) | (curious(X0) <=> ~humble(X0))) [ennf transformation 9]
32. ! [X0] : ((humble(X0) & brave(X0)) | rich(X0)) [ennf transformation 11]
46. ! [X0] : (((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0)))) [nnf transformation 31]
47. ! [X0] : ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0))) [nnf transformation 10]
53. ! [X0] : (((~kind(X0) | creative(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (kind(X0) & ~creative(X0)))) [nnf transformation 13]
54. ! [X0] : ((~kind(X0) | creative(X0) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | (kind(X0) & ~creative(X0)))) [flattening 53]
62. (~curious(alice) | brave(alice)) & (curious(alice) | ~brave(alice)) [nnf transformation 18]
96. kind(X0) | ~humble(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 46]
98. ~creative(X0) | ~humble(X0) [cnf transformation 47]
100. rich(X0) | brave(X0) [cnf transformation 32]
101. rich(X0) | humble(X0) [cnf transformation 32]
110. ~kind(X0) | creative(X0) | ~curious(X0) [cnf transformation 54]
124. curious(alice) | ~brave(alice) [cnf transformation 62]
135. ~rich(alice) [cnf transformation 24]
137. ~humble(X0) | kind(X0) | ~curious(X0) [duplicate literal removal 96]
266. 29 <=> brave(alice) [avatar definition]
270. 30 <=> curious(alice) [avatar definition]
271. curious(alice) <- (30) [avatar component clause 270]
274. ~29 | 30 [avatar split clause 124,270,266]
294. brave(alice) [resolution 100,135]
297. 29 [avatar split clause 294,266]
300. humble(alice) [resolution 101,135]
491. kind(alice) | ~curious(alice) [resolution 137,300]
493. kind(alice) <- (30) [subsumption resolution 491,271]
731. creative(alice) | ~curious(alice) <- (30) [resolution 493,110]
746. 77 <=> creative(alice) [avatar definition]
748. creative(alice) <- (77) [avatar component clause 746]
750. creative(alice) <- (30) [subsumption resolution 731,271]
751. 77 | ~30 [avatar split clause 750,270,746]
937. ~humble(alice) <- (77) [resolution 748,98]
938. $false <- (77) [subsumption resolution 937,300]
939. ~77 [avatar contradiction clause 938]
940. $false [avatar sat refutation 274,297,751,939]
% SZS output end Proof for 5829755501105475819942720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is either patient or old and vice versa. Everyone who is tall is either strong or old and vice versa. Everyone who is both rich and old is either strong or humble and vice versa. Everyone who is strong or not creative is either not calm or generous and vice versa. Everyone who is both not generous and old is either not wise or quiet and vice versa. Everyone who is either funny or generous is either wise or not strong and vice versa. If someone is both not old and old then lucy is both not generous and not rich and vice versa. Everyone who is curious or not kind is not funny and vice versa. If someone is not happy then someone is not creative or not old. If paul is both creative and wise then john is calm and vice versa. If john is either not happy or not brave then someone is both strong and quiet and vice versa. If someone is either not wise or creative then mary is not quiet or kind. Everyone who is strong is both quiet and not curious. Everyone who is not patient is either not patient or wise. Everyone who is wise or not wise is both old and not funny. If john is not patient then someone is not kind or not happy and vice versa. Someone is curious. Alice is both not rich and not strong. | Paul is not tall. | contradiction | (![X]:(kind(X)<=>(patient(X)<~>old(X))))&
(![X]:(tall(X)<=>(strong(X)<~>old(X))))&
(![X]:((rich(X)&old(X))<=>(strong(X)<~>humble(X))))&
(![X]:((strong(X)|~creative(X))<=>(~calm(X)<~>generous(X))))&
(![X]:((~generous(X)&old(X))<=>(~wise(X)<~>quiet(X))))&
(![X]:((funny(X)<~>generous(X))<=>(wise(X)<~>~strong(X))))&
((?[X]:((~old(X)&old(X))))<=>((~generous(lucy)&~rich(lucy))))&
(![X]:((curious(X)|~kind(X))<=>~funny(X)))&
((?[X]:(~happy(X)))=>(?[X]:((~creative(X)|~old(X)))))&
(((creative(paul)&wise(paul)))<=>(calm(john)))&
(((~happy(john)<~>~brave(john)))<=>(?[X]:((strong(X)&quiet(X)))))&
((?[X]:((~wise(X)<~>creative(X))))=>((~quiet(mary)|kind(mary))))&
(![X]:(strong(X)=>(quiet(X)&~curious(X))))&
(![X]:(~patient(X)=>(~patient(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(old(X)&~funny(X))))&
((~patient(john))<=>(?[X]:((~kind(X)|~happy(X)))))&
(?[X]:(curious(X)))&
((~rich(alice)&~strong(alice))) | ~tall(paul) | [
"p1",
"p4",
"p5",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2762963820904538936957692
% SZS output start Proof for 2762963820904538936957692
2. ! [X0] : (tall(X0) <=> (strong(X0) <~> old(X0))) [input p1]
5. ! [X0] : ((old(X0) & ~generous(X0)) <=> (~wise(X0) <~> quiet(X0))) [input p4]
6. ! [X0] : ((funny(X0) <~> generous(X0)) <=> (wise(X0) <~> ~strong(X0))) [input p5]
11. (~happy(john) <~> ~brave(john)) <=> ? [X0] : (quiet(X0) & strong(X0)) [input p10]
13. ! [X0] : (strong(X0) => (~curious(X0) & quiet(X0))) [input p12]
15. ! [X0] : ((~wise(X0) | wise(X0)) => (~funny(X0) & old(X0))) [input p14]
19. ~tall(paul) [input hypothesis]
21. ! [X0] : ((strong(X0) <~> old(X0)) => tall(X0)) [unused predicate definition removal 2]
22. ! [X0] : (tall(X0) | (strong(X0) <=> old(X0))) [ennf transformation 21]
26. ! [X0] : ((~curious(X0) & quiet(X0)) | ~strong(X0)) [ennf transformation 13]
28. ! [X0] : ((~funny(X0) & old(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 15]
30. ! [X0] : (tall(X0) | ((strong(X0) | ~old(X0)) & (old(X0) | ~strong(X0)))) [nnf transformation 22]
35. ! [X0] : (((old(X0) & ~generous(X0)) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | (~old(X0) | generous(X0)))) [nnf transformation 5]
36. ! [X0] : (((old(X0) & ~generous(X0)) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | ~old(X0) | generous(X0))) [flattening 35]
37. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [nnf transformation 6]
50. (((brave(john) | happy(john)) & (~brave(john) | ~happy(john))) | ! [X0] : (~quiet(X0) | ~strong(X0))) & (? [X0] : (quiet(X0) & strong(X0)) | ((~happy(john) | brave(john)) & (~brave(john) | happy(john)))) [nnf transformation 11]
51. (((brave(john) | happy(john)) & (~brave(john) | ~happy(john))) | ! [X0] : (~quiet(X0) | ~strong(X0))) & (? [X1] : (quiet(X1) & strong(X1)) | ((~happy(john) | brave(john)) & (~brave(john) | happy(john)))) [rectify 50]
52. ? [X1] : (quiet(X1) & strong(X1)) => (quiet(sK2) & strong(sK2)) [choice axiom]
53. (((brave(john) | happy(john)) & (~brave(john) | ~happy(john))) | ! [X0] : (~quiet(X0) | ~strong(X0))) & ((quiet(sK2) & strong(sK2)) | ((~happy(john) | brave(john)) & (~brave(john) | happy(john)))) [skolemisation 51,52]
67. ~old(X0) | strong(X0) | tall(X0) [cnf transformation 30]
81. ~quiet(X0) | wise(X0) | ~old(X0) | generous(X0) [cnf transformation 36]
83. ~quiet(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 36]
87. ~generous(X0) | wise(X0) | funny(X0) | ~strong(X0) [cnf transformation 37]
90. ~wise(X0) | funny(X0) | ~strong(X0) | generous(X0) [cnf transformation 37]
105. strong(sK2) | ~brave(john) | happy(john) [cnf transformation 53]
106. strong(sK2) | ~happy(john) | brave(john) [cnf transformation 53]
107. quiet(sK2) | ~brave(john) | happy(john) [cnf transformation 53]
108. quiet(sK2) | ~happy(john) | brave(john) [cnf transformation 53]
109. ~brave(john) | ~happy(john) | ~quiet(X0) | ~strong(X0) [cnf transformation 53]
110. brave(john) | happy(john) | ~quiet(X0) | ~strong(X0) [cnf transformation 53]
113. ~strong(X0) | quiet(X0) [cnf transformation 26]
117. old(X0) | ~wise(X0) [cnf transformation 28]
118. wise(X0) | old(X0) [cnf transformation 28]
119. ~funny(X0) | ~wise(X0) [cnf transformation 28]
120. ~funny(X0) | wise(X0) [cnf transformation 28]
127. ~tall(paul) [cnf transformation 19]
171. 10 <=> ! [X0] : (~quiet(X0) | ~strong(X0)) [avatar definition]
172. ~quiet(X0) | ~strong(X0) <- (10) [avatar component clause 171]
174. 11 <=> happy(john) [avatar definition]
178. 12 <=> brave(john) [avatar definition]
181. 10 | 11 | 12 [avatar split clause 110,178,174,171]
182. 10 | ~11 | ~12 [avatar split clause 109,178,174,171]
184. 13 <=> quiet(sK2) [avatar definition]
186. quiet(sK2) <- (13) [avatar component clause 184]
187. 12 | ~11 | 13 [avatar split clause 108,184,174,178]
188. 11 | ~12 | 13 [avatar split clause 107,184,178,174]
190. 14 <=> strong(sK2) [avatar definition]
192. strong(sK2) <- (14) [avatar component clause 190]
193. 12 | ~11 | 14 [avatar split clause 106,190,174,178]
194. 11 | ~12 | 14 [avatar split clause 105,190,178,174]
211. ~funny(X0) [subsumption resolution 119,120]
212. old(X0) [subsumption resolution 117,118]
231. ~strong(X0) <- (10) [subsumption resolution 172,113]
244. strong(X0) | tall(X0) [resolution 67,212]
245. tall(X0) <- (10) [subsumption resolution 244,231]
246. $false <- (10) [resolution 245,127]
247. ~10 [avatar contradiction clause 246]
271. ~wise(sK2) | ~generous(sK2) <- (13) [resolution 83,186]
274. 25 <=> generous(sK2) [avatar definition]
275. generous(sK2) <- (25) [avatar component clause 274]
276. ~generous(sK2) <- (~25) [avatar component clause 274]
278. 26 <=> wise(sK2) [avatar definition]
279. wise(sK2) <- (26) [avatar component clause 278]
280. ~wise(sK2) <- (~26) [avatar component clause 278]
281. ~25 | ~26 | ~13 [avatar split clause 271,184,278,274]
320. wise(sK2) | ~old(sK2) | generous(sK2) <- (13) [resolution 81,186]
325. wise(sK2) | generous(sK2) <- (13) [subsumption resolution 320,212]
332. 25 | 26 | ~13 [avatar split clause 325,184,278,274]
349. wise(sK2) | funny(sK2) | ~strong(sK2) <- (25) [resolution 87,275]
350. funny(sK2) | ~strong(sK2) <- (25, ~26) [subsumption resolution 349,280]
351. ~strong(sK2) <- (25, ~26) [subsumption resolution 350,211]
352. $false <- (14, 25, ~26) [subsumption resolution 351,192]
353. ~14 | ~25 | 26 [avatar contradiction clause 352]
366. funny(sK2) | ~strong(sK2) | generous(sK2) <- (26) [resolution 90,279]
367. ~strong(sK2) | generous(sK2) <- (26) [subsumption resolution 366,211]
368. generous(sK2) <- (14, 26) [subsumption resolution 367,192]
369. $false <- (14, ~25, 26) [subsumption resolution 368,276]
370. ~14 | 25 | ~26 [avatar contradiction clause 369]
371. $false [avatar sat refutation 181,182,187,188,193,194,247,281,332,353,370]
% SZS output end Proof for 2762963820904538936957692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not rich then someone is both not tall and humble and vice versa. If mary is not quiet or kind then susan is not humble or humble and vice versa. Everyone who is either not wise or not old is both patient and rich and vice versa. Everyone who is generous or not creative is either not curious or not brave and vice versa. Everyone who is wise is not calm or funny and vice versa. If someone is both not strong and brave then mary is not strong or quiet. Everyone who is either old or rich is either rich or calm and vice versa. If someone is not happy or brave then someone is not tall or not quiet. If paul is brave or wise then paul is either generous or strong. Everyone who is not brave is both not funny and brave. If someone is both not funny and not patient then someone is either generous or not tall. Everyone who is both not creative and generous is either curious or calm. If lucy is both not tall and not generous then someone is kind or creative and vice versa. If someone is not happy then someone is patient or not humble and vice versa. If mary is strong then susan is both calm and not generous and vice versa. Everyone who is both funny and not wise is not creative or generous and vice versa. Someone is not brave or happy. Susan is either humble or not kind. Alice is funny. Susan is both not quiet and not funny. Someone is both not funny and patient. Someone is either not patient or not old. | Paul is not quiet. | neutral | ((?[X]:((creative(X)|~rich(X))))<=>(?[X]:((~tall(X)&humble(X)))))&
(((~quiet(mary)|kind(mary)))<=>((~humble(susan)|humble(susan))))&
(![X]:((~wise(X)<~>~old(X))<=>(patient(X)&rich(X))))&
(![X]:((generous(X)|~creative(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:(wise(X)<=>(~calm(X)|funny(X))))&
((?[X]:((~strong(X)&brave(X))))=>((~strong(mary)|quiet(mary))))&
(![X]:((old(X)<~>rich(X))<=>(rich(X)<~>calm(X))))&
((?[X]:((~happy(X)|brave(X))))=>(?[X]:((~tall(X)|~quiet(X)))))&
(((brave(paul)|wise(paul)))=>((generous(paul)<~>strong(paul))))&
(![X]:(~brave(X)=>(~funny(X)&brave(X))))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:((generous(X)<~>~tall(X)))))&
(![X]:((~creative(X)&generous(X))=>(curious(X)<~>calm(X))))&
(((~tall(lucy)&~generous(lucy)))<=>(?[X]:((kind(X)|creative(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((patient(X)|~humble(X)))))&
((strong(mary))<=>((calm(susan)&~generous(susan))))&
(![X]:((funny(X)&~wise(X))<=>(~creative(X)|generous(X))))&
(?[X]:((~brave(X)|happy(X))))&
((humble(susan)<~>~kind(susan)))&
(funny(alice))&
((~quiet(susan)&~funny(susan)))&
(?[X]:((~funny(X)&patient(X))))&
(?[X]:((~patient(X)<~>~old(X)))) | ~quiet(paul) | [] | null | 0 |
Everyone who is not rich or kind is both not funny and quiet and vice versa. If someone is not calm or not rich then john is both humble and not quiet. If alice is both happy and not funny then susan is not old and vice versa. If someone is both not wise and strong then someone is not funny or generous. If mary is either not generous or curious then someone is either not curious or rich. Everyone who is either not wise or humble is either humble or not happy. Everyone who is both wise and not quiet is both not quiet and brave and vice versa. Everyone who is both brave and kind is rich or not quiet and vice versa. Everyone who is both generous and brave is strong or not calm. If lucy is either not humble or generous then someone is either strong or not rich. If alice is tall then someone is either not generous or curious and vice versa. If someone is both calm and tall then someone is wise or not funny and vice versa. If mary is either not strong or generous then someone is either strong or happy and vice versa. If fred is strong then susan is both not generous and not creative and vice versa. If alice is not creative or not tall then someone is calm or not rich and vice versa. If someone is both not calm and strong then john is either creative or not happy and vice versa. Lucy is not happy or generous. Lucy is both not funny and not wise. Paul is not funny. Someone is old or quiet. Someone is either humble or creative. Alice is both not patient and not creative. Susan is both patient and wise. John is both not generous and not old. | Mary is brave. | entailment | (![X]:((~rich(X)|kind(X))<=>(~funny(X)&quiet(X))))&
((?[X]:((~calm(X)|~rich(X))))=>((humble(john)&~quiet(john))))&
(((happy(alice)&~funny(alice)))<=>(~old(susan)))&
((?[X]:((~wise(X)&strong(X))))=>(?[X]:((~funny(X)|generous(X)))))&
(((~generous(mary)<~>curious(mary)))=>(?[X]:((~curious(X)<~>rich(X)))))&
(![X]:((~wise(X)<~>humble(X))=>(humble(X)<~>~happy(X))))&
(![X]:((wise(X)&~quiet(X))<=>(~quiet(X)&brave(X))))&
(![X]:((brave(X)&kind(X))<=>(rich(X)|~quiet(X))))&
(![X]:((generous(X)&brave(X))=>(strong(X)|~calm(X))))&
(((~humble(lucy)<~>generous(lucy)))=>(?[X]:((strong(X)<~>~rich(X)))))&
((tall(alice))<=>(?[X]:((~generous(X)<~>curious(X)))))&
((?[X]:((calm(X)&tall(X))))<=>(?[X]:((wise(X)|~funny(X)))))&
(((~strong(mary)<~>generous(mary)))<=>(?[X]:((strong(X)<~>happy(X)))))&
((strong(fred))<=>((~generous(susan)&~creative(susan))))&
(((~creative(alice)|~tall(alice)))<=>(?[X]:((calm(X)|~rich(X)))))&
((?[X]:((~calm(X)&strong(X))))<=>((creative(john)<~>~happy(john))))&
((~happy(lucy)|generous(lucy)))&
((~funny(lucy)&~wise(lucy)))&
(~funny(paul))&
(?[X]:((old(X)|quiet(X))))&
(?[X]:((humble(X)<~>creative(X))))&
((~patient(alice)&~creative(alice)))&
((patient(susan)&wise(susan)))&
((~generous(john)&~old(john))) | brave(mary) | [
"p0",
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8449176424625452198456987
% SZS output start Proof for 8449176424625452198456987
1. ! [X0] : ((kind(X0) | ~rich(X0)) <=> (quiet(X0) & ~funny(X0))) [input p0]
2. ? [X0] : (~rich(X0) | ~calm(X0)) => (~quiet(john) & humble(john)) [input p1]
8. ! [X0] : ((kind(X0) & brave(X0)) <=> (~quiet(X0) | rich(X0))) [input p7]
25. ~brave(mary) [input hypothesis]
28. (~quiet(john) & humble(john)) | ! [X0] : (rich(X0) & calm(X0)) [ennf transformation 2]
35. ! [X0] : (((kind(X0) | ~rich(X0)) | (~quiet(X0) | funny(X0))) & ((quiet(X0) & ~funny(X0)) | (~kind(X0) & rich(X0)))) [nnf transformation 1]
36. ! [X0] : ((kind(X0) | ~rich(X0) | ~quiet(X0) | funny(X0)) & ((quiet(X0) & ~funny(X0)) | (~kind(X0) & rich(X0)))) [flattening 35]
48. ! [X0] : (((kind(X0) & brave(X0)) | (quiet(X0) & ~rich(X0))) & ((~quiet(X0) | rich(X0)) | (~kind(X0) | ~brave(X0)))) [nnf transformation 8]
49. ! [X0] : (((kind(X0) & brave(X0)) | (quiet(X0) & ~rich(X0))) & (~quiet(X0) | rich(X0) | ~kind(X0) | ~brave(X0))) [flattening 48]
85. ~kind(X0) | quiet(X0) [cnf transformation 36]
90. ~quiet(john) | rich(X0) [cnf transformation 28]
108. ~rich(X0) | brave(X0) [cnf transformation 49]
111. kind(X0) | quiet(X0) [cnf transformation 49]
160. ~brave(mary) [cnf transformation 25]
164. 1 <=> ! [X0] : rich(X0) [avatar definition]
165. rich(X0) <- (1) [avatar component clause 164]
167. 2 <=> quiet(john) [avatar definition]
169. ~quiet(john) <- (~2) [avatar component clause 167]
170. 1 | ~2 [avatar split clause 90,167,164]
228. quiet(X0) [subsumption resolution 111,85]
407. $false <- (~2) [subsumption resolution 169,228]
408. 2 [avatar contradiction clause 407]
426. brave(X0) <- (1) [resolution 108,165]
427. $false <- (1) [resolution 426,160]
428. ~1 [avatar contradiction clause 427]
429. $false [avatar sat refutation 170,408,428]
% SZS output end Proof for 8449176424625452198456987
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not happy is either not quiet or generous.
Everyone who is generous or not kind is calm and vice versa.
If someone is not old or rich then someone is kind or not happy and vice versa.
If someone is either old or humble then someone is either not funny or patient and vice versa.
Everyone who is curious or not humble is both creative and kind and vice versa.
Everyone who is both not patient and not calm is kind.
If john is not kind then john is generous and vice versa.
If someone is curious or brave then mary is not creative.
Everyone who is both not generous and not kind is both curious and old.
Everyone who is either not happy or not wise is brave or generous.
Everyone who is both happy and brave is either not quiet or not kind.
Everyone who is both happy and curious is either quiet or humble.
Everyone who is both not quiet and generous is not happy.
If lucy is both not quiet and quiet then fred is humble.
Everyone who is either not old or not wise is both funny and generous.
Everyone who is not brave or kind is both not happy and tall and vice versa.
Susan is not old.
Lucy is quiet.
Someone is both strong and not funny.
Susan is either not curious or funny.
Paul is both not brave and not humble.
Alice is not generous or not happy.
Lucy is both not curious and not creative.
Someone is both rich and patient. | Lucy is generous. | entailment | (![X]:((~humble(X)<~>~happy(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((generous(X)|~kind(X))<=>calm(X)))&
((?[X]:((~old(X)|rich(X))))<=>(?[X]:((kind(X)|~happy(X)))))&
((?[X]:((old(X)<~>humble(X))))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((curious(X)|~humble(X))<=>(creative(X)&kind(X))))&
(![X]:((~patient(X)&~calm(X))=>kind(X)))&
((~kind(john))<=>(generous(john)))&
((?[X]:((curious(X)|brave(X))))=>(~creative(mary)))&
(![X]:((~generous(X)&~kind(X))=>(curious(X)&old(X))))&
(![X]:((~happy(X)<~>~wise(X))=>(brave(X)|generous(X))))&
(![X]:((happy(X)&brave(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:((happy(X)&curious(X))=>(quiet(X)<~>humble(X))))&
(![X]:((~quiet(X)&generous(X))=>~happy(X)))&
(((~quiet(lucy)&quiet(lucy)))=>(humble(fred)))&
(![X]:((~old(X)<~>~wise(X))=>(funny(X)&generous(X))))&
(![X]:((~brave(X)|kind(X))<=>(~happy(X)&tall(X))))&
(~old(susan))&
(quiet(lucy))&
(?[X]:((strong(X)&~funny(X))))&
((~curious(susan)<~>funny(susan)))&
((~brave(paul)&~humble(paul)))&
((~generous(alice)|~happy(alice)))&
((~curious(lucy)&~creative(lucy)))&
(?[X]:((rich(X)&patient(X)))) | generous(lucy) | [
"p0",
"p4",
"p8",
"p15",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6563122605681116036171196
% SZS output start Proof for 6563122605681116036171196
1. ! [X0] : ((~humble(X0) <~> ~happy(X0)) => (~quiet(X0) <~> generous(X0))) [input p0]
5. ! [X0] : ((~humble(X0) | curious(X0)) <=> (kind(X0) & creative(X0))) [input p4]
9. ! [X0] : ((~kind(X0) & ~generous(X0)) => (old(X0) & curious(X0))) [input p8]
16. ! [X0] : ((kind(X0) | ~brave(X0)) <=> (tall(X0) & ~happy(X0))) [input p15]
18. quiet(lucy) [input p17]
23. ~creative(lucy) & ~curious(lucy) [input p22]
25. ~generous(lucy) [input hypothesis]
30. ! [X0] : ((~quiet(X0) <~> generous(X0)) | (~humble(X0) <=> ~happy(X0))) [ennf transformation 1]
36. ! [X0] : ((old(X0) & curious(X0)) | (kind(X0) | generous(X0))) [ennf transformation 9]
37. ! [X0] : ((old(X0) & curious(X0)) | kind(X0) | generous(X0)) [flattening 36]
49. ! [X0] : (((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) [nnf transformation 30]
60. ! [X0] : (((~humble(X0) | curious(X0)) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | (humble(X0) & ~curious(X0)))) [nnf transformation 5]
61. ! [X0] : ((~humble(X0) | curious(X0) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | (humble(X0) & ~curious(X0)))) [flattening 60]
67. ! [X0] : (((kind(X0) | ~brave(X0)) | (~tall(X0) | happy(X0))) & ((tall(X0) & ~happy(X0)) | (~kind(X0) & brave(X0)))) [nnf transformation 16]
68. ! [X0] : ((kind(X0) | ~brave(X0) | ~tall(X0) | happy(X0)) & ((tall(X0) & ~happy(X0)) | (~kind(X0) & brave(X0)))) [flattening 67]
75. ~quiet(X0) | generous(X0) | ~humble(X0) | happy(X0) [cnf transformation 49]
92. creative(X0) | humble(X0) [cnf transformation 61]
93. ~curious(X0) | kind(X0) [cnf transformation 61]
101. curious(X0) | kind(X0) | generous(X0) [cnf transformation 37]
116. ~kind(X0) | ~happy(X0) [cnf transformation 68]
121. quiet(lucy) [cnf transformation 18]
129. ~creative(lucy) [cnf transformation 23]
132. ~generous(lucy) [cnf transformation 25]
223. kind(X0) | generous(X0) [subsumption resolution 101,93]
243. humble(lucy) [resolution 92,129]
250. ~happy(X1) | generous(X1) [resolution 223,116]
288. generous(lucy) | ~humble(lucy) | happy(lucy) [resolution 75,121]
289. ~humble(lucy) | happy(lucy) [subsumption resolution 288,132]
290. happy(lucy) [subsumption resolution 289,243]
292. generous(lucy) [resolution 290,250]
295. $false [subsumption resolution 292,132]
% SZS output end Proof for 6563122605681116036171196
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or not humble then someone is both old and calm and vice versa.
If alice is either not generous or not humble then someone is either not old or not creative and vice versa.
Everyone who is generous or tall is tall.
If someone is not creative then someone is both tall and happy and vice versa.
Everyone who is either tall or calm is either not funny or strong.
Everyone who is generous or patient is either not wise or brave and vice versa.
If someone is not generous then paul is both not humble and humble.
Everyone who is either calm or kind is not creative.
If paul is either not quiet or not calm then alice is not brave.
If someone is either not quiet or wise then someone is either not calm or not curious.
Everyone who is not brave is either not patient or wise and vice versa.
Everyone who is not tall or funny is both not rich and not calm.
Everyone who is either old or strong is not tall or wise.
If someone is not quiet then someone is not happy and vice versa.
If someone is either brave or creative then someone is both not old and not rich and vice versa.
Everyone who is either creative or tall is curious or not strong and vice versa.
Someone is both not wise and not quiet.
Someone is not happy or funny.
Lucy is calm or not tall.
Mary is both brave and not quiet.
Someone is not happy or generous.
Alice is either not tall or not strong.
Paul is kind.
Mary is not kind. | Alice is creative. | contradiction | ((?[X]:((calm(X)<~>~humble(X))))<=>(?[X]:((old(X)&calm(X)))))&
(((~generous(alice)<~>~humble(alice)))<=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:((generous(X)|tall(X))=>tall(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((tall(X)&happy(X)))))&
(![X]:((tall(X)<~>calm(X))=>(~funny(X)<~>strong(X))))&
(![X]:((generous(X)|patient(X))<=>(~wise(X)<~>brave(X))))&
((?[X]:(~generous(X)))=>((~humble(paul)&humble(paul))))&
(![X]:((calm(X)<~>kind(X))=>~creative(X)))&
(((~quiet(paul)<~>~calm(paul)))=>(~brave(alice)))&
((?[X]:((~quiet(X)<~>wise(X))))=>(?[X]:((~calm(X)<~>~curious(X)))))&
(![X]:(~brave(X)<=>(~patient(X)<~>wise(X))))&
(![X]:((~tall(X)|funny(X))=>(~rich(X)&~calm(X))))&
(![X]:((old(X)<~>strong(X))=>(~tall(X)|wise(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(~happy(X))))&
((?[X]:((brave(X)<~>creative(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((creative(X)<~>tall(X))<=>(curious(X)|~strong(X))))&
(?[X]:((~wise(X)&~quiet(X))))&
(?[X]:((~happy(X)|funny(X))))&
((calm(lucy)|~tall(lucy)))&
((brave(mary)&~quiet(mary)))&
(?[X]:((~happy(X)|generous(X))))&
((~tall(alice)<~>~strong(alice)))&
(kind(paul))&
(~kind(mary)) | creative(alice) | [
"p2",
"p6",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8219851370646858494244194
% SZS output start Proof for 8219851370646858494244194
3. ! [X0] : ((tall(X0) | generous(X0)) => tall(X0)) [input p2]
7. ? [X0] : ~generous(X0) => (humble(paul) & ~humble(paul)) [input p6]
16. ! [X0] : ((creative(X0) <~> tall(X0)) <=> (~strong(X0) | curious(X0))) [input p15]
22. ~tall(alice) <~> ~strong(alice) [input p21]
25. creative(alice) [input hypothesis]
31. ! [X0] : (tall(X0) | (~tall(X0) & ~generous(X0))) [ennf transformation 3]
33. (humble(paul) & ~humble(paul)) | ! [X0] : generous(X0) [ennf transformation 7]
75. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (strong(X0) & ~curious(X0))) & ((~strong(X0) | curious(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [nnf transformation 16]
76. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (strong(X0) & ~curious(X0))) & (~strong(X0) | curious(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [flattening 75]
83. (strong(alice) | tall(alice)) & (~strong(alice) | ~tall(alice)) [nnf transformation 22]
98. ~generous(X0) | tall(X0) [cnf transformation 31]
113. ~humble(paul) | generous(X0) [cnf transformation 33]
114. humble(paul) | generous(X0) [cnf transformation 33]
146. ~tall(X0) | ~creative(X0) | strong(X0) [cnf transformation 76]
154. ~strong(alice) | ~tall(alice) [cnf transformation 83]
155. strong(alice) | tall(alice) [cnf transformation 83]
158. creative(alice) [cnf transformation 25]
242. 19 <=> ! [X0] : generous(X0) [avatar definition]
243. generous(X0) <- (19) [avatar component clause 242]
245. 20 <=> humble(paul) [avatar definition]
248. 19 | 20 [avatar split clause 114,245,242]
249. 19 | ~20 [avatar split clause 113,245,242]
362. 45 <=> tall(alice) [avatar definition]
363. ~tall(alice) <- (~45) [avatar component clause 362]
364. tall(alice) <- (45) [avatar component clause 362]
366. 46 <=> strong(alice) [avatar definition]
367. ~strong(alice) <- (~46) [avatar component clause 366]
369. 45 | 46 [avatar split clause 155,366,362]
370. ~45 | ~46 [avatar split clause 154,366,362]
378. tall(X0) <- (19) [resolution 98,243]
448. ~creative(alice) | strong(alice) <- (45) [resolution 146,364]
459. strong(alice) <- (45) [subsumption resolution 448,158]
460. $false <- (45, ~46) [subsumption resolution 459,367]
461. ~45 | 46 [avatar contradiction clause 460]
462. $false <- (19, ~45) [subsumption resolution 363,378]
463. ~19 | 45 [avatar contradiction clause 462]
464. $false [avatar sat refutation 248,249,369,370,461,463]
% SZS output end Proof for 8219851370646858494244194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then mary is not calm.
Everyone who is either not curious or patient is either happy or not old.
If mary is not old then mary is humble and vice versa.
Everyone who is either not tall or creative is tall or not generous.
If alice is wise or humble then lucy is either tall or patient.
Everyone who is either old or happy is both rich and kind and vice versa.
If fred is not quiet then someone is both not brave and not patient and vice versa.
Everyone who is both not patient and not creative is curious or patient.
Everyone who is either not rich or not old is calm or not humble and vice versa.
Everyone who is either not quiet or quiet is both patient and not humble.
Everyone who is either not quiet or not happy is not patient.
Everyone who is both generous and wise is either brave or not strong.
If someone is both creative and not rich then john is not old or not creative.
If someone is either funny or not rich then paul is either quiet or humble.
If someone is both strong and old then someone is either not humble or calm.
If someone is either calm or not patient then someone is either generous or creative.
Alice is both happy and tall.
Lucy is either calm or happy.
Lucy is either old or happy.
Susan is not generous.
Alice is both not generous and not rich.
Someone is not happy.
Someone is either kind or not quiet. | Alice is not quiet. | contradiction | ((?[X]:(~creative(X)))=>(~calm(mary)))&
(![X]:((~curious(X)<~>patient(X))=>(happy(X)<~>~old(X))))&
((~old(mary))<=>(humble(mary)))&
(![X]:((~tall(X)<~>creative(X))=>(tall(X)|~generous(X))))&
(((wise(alice)|humble(alice)))=>((tall(lucy)<~>patient(lucy))))&
(![X]:((old(X)<~>happy(X))<=>(rich(X)&kind(X))))&
((~quiet(fred))<=>(?[X]:((~brave(X)&~patient(X)))))&
(![X]:((~patient(X)&~creative(X))=>(curious(X)|patient(X))))&
(![X]:((~rich(X)<~>~old(X))<=>(calm(X)|~humble(X))))&
(![X]:((~quiet(X)<~>quiet(X))=>(patient(X)&~humble(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>~patient(X)))&
(![X]:((generous(X)&wise(X))=>(brave(X)<~>~strong(X))))&
((?[X]:((creative(X)&~rich(X))))=>((~old(john)|~creative(john))))&
((?[X]:((funny(X)<~>~rich(X))))=>((quiet(paul)<~>humble(paul))))&
((?[X]:((strong(X)&old(X))))=>(?[X]:((~humble(X)<~>calm(X)))))&
((?[X]:((calm(X)<~>~patient(X))))=>(?[X]:((generous(X)<~>creative(X)))))&
((happy(alice)&tall(alice)))&
((calm(lucy)<~>happy(lucy)))&
((old(lucy)<~>happy(lucy)))&
(~generous(susan))&
((~generous(alice)&~rich(alice)))&
(?[X]:(~happy(X)))&
(?[X]:((kind(X)<~>~quiet(X)))) | ~quiet(alice) | [
"p9",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8572085155627281521604591
% SZS output start Proof for 8572085155627281521604591
10. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => (~humble(X0) & patient(X0))) [input p9]
11. ! [X0] : ((~quiet(X0) <~> ~happy(X0)) => ~patient(X0)) [input p10]
17. tall(alice) & happy(alice) [input p16]
24. ~quiet(alice) [input hypothesis]
37. ! [X0] : ((~humble(X0) & patient(X0)) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 10]
38. ! [X0] : (~patient(X0) | (~quiet(X0) <=> ~happy(X0))) [ennf transformation 11]
55. ! [X0] : ((~humble(X0) & patient(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 37]
56. ! [X0] : (~patient(X0) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0)))) [nnf transformation 38]
96. patient(X0) | quiet(X0) | quiet(X0) [cnf transformation 55]
97. patient(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 55]
100. ~patient(X0) | ~happy(X0) | quiet(X0) [cnf transformation 56]
111. happy(alice) [cnf transformation 17]
123. ~quiet(alice) [cnf transformation 24]
124. patient(X0) | quiet(X0) [duplicate literal removal 96]
125. ~quiet(X0) | patient(X0) [duplicate literal removal 97]
181. patient(X0) [subsumption resolution 124,125]
183. ~happy(X0) | quiet(X0) [subsumption resolution 100,181]
261. quiet(alice) [resolution 183,111]
263. $false [subsumption resolution 261,123]
% SZS output end Proof for 8572085155627281521604591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not generous is either not happy or old. Everyone who is either not creative or curious is not humble and vice versa. Everyone who is both not humble and not quiet is both not generous and not brave and vice versa. Everyone who is either kind or not rich is both not strong and not kind. If john is humble then someone is creative. Everyone who is either not patient or wise is creative or generous. Everyone who is both quiet and not calm is both patient and not generous. If someone is brave then john is either not patient or happy. Everyone who is both not wise and rich is wise. If fred is both not generous and funny then susan is either generous or not quiet. If alice is both kind and not patient then someone is not generous or not rich. Everyone who is both not happy and brave is either not humble or rich and vice versa. Everyone who is both not curious and not rich is curious or not generous and vice versa. If susan is not calm then john is both not curious and wise and vice versa. Everyone who is not tall or not happy is either patient or not generous and vice versa. Everyone who is both not tall and not calm is not quiet or funny. Someone is both not funny and not wise. Alice is not patient or strong. Someone is not generous or patient. Susan is either quiet or not strong. Lucy is wise. Someone is either tall or old. John is patient or not quiet. Someone is not wise or quiet. | Susan is curious. | contradiction | (![X]:((creative(X)|~generous(X))=>(~happy(X)<~>old(X))))&
(![X]:((~creative(X)<~>curious(X))<=>~humble(X)))&
(![X]:((~humble(X)&~quiet(X))<=>(~generous(X)&~brave(X))))&
(![X]:((kind(X)<~>~rich(X))=>(~strong(X)&~kind(X))))&
((humble(john))=>(?[X]:(creative(X))))&
(![X]:((~patient(X)<~>wise(X))=>(creative(X)|generous(X))))&
(![X]:((quiet(X)&~calm(X))=>(patient(X)&~generous(X))))&
((?[X]:(brave(X)))=>((~patient(john)<~>happy(john))))&
(![X]:((~wise(X)&rich(X))=>wise(X)))&
(((~generous(fred)&funny(fred)))=>((generous(susan)<~>~quiet(susan))))&
(((kind(alice)&~patient(alice)))=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~happy(X)&brave(X))<=>(~humble(X)<~>rich(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)|~generous(X))))&
((~calm(susan))<=>((~curious(john)&wise(john))))&
(![X]:((~tall(X)|~happy(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((~tall(X)&~calm(X))=>(~quiet(X)|funny(X))))&
(?[X]:((~funny(X)&~wise(X))))&
((~patient(alice)|strong(alice)))&
(?[X]:((~generous(X)|patient(X))))&
((quiet(susan)<~>~strong(susan)))&
(wise(lucy))&
(?[X]:((tall(X)<~>old(X))))&
((patient(john)|~quiet(john)))&
(?[X]:((~wise(X)|quiet(X)))) | curious(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4467046745751320353612903
% SZS output start Proof for 4467046745751320353612903
13. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (~generous(X0) | curious(X0))) [input p12]
25. curious(susan) [input hypothesis]
56. ! [X0] : (((~rich(X0) & ~curious(X0)) | (generous(X0) & ~curious(X0))) & ((~generous(X0) | curious(X0)) | (rich(X0) | curious(X0)))) [nnf transformation 13]
57. ! [X0] : (((~rich(X0) & ~curious(X0)) | (generous(X0) & ~curious(X0))) & (~generous(X0) | curious(X0) | rich(X0) | curious(X0))) [flattening 56]
106. ~curious(X0) | ~curious(X0) [cnf transformation 57]
131. curious(susan) [cnf transformation 25]
133. ~curious(X0) [duplicate literal removal 106]
249. $false [subsumption resolution 131,133]
% SZS output end Proof for 4467046745751320353612903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not tall or not happy then paul is either old or not calm.
Everyone who is not patient is wise and vice versa.
If lucy is strong or humble then someone is either tall or not curious and vice versa.
Everyone who is either patient or tall is funny and vice versa.
If alice is wise or not humble then susan is both not kind and not curious.
If lucy is rich or patient then susan is not rich and vice versa.
If someone is both generous and not wise then john is not old and vice versa.
If alice is funny or not rich then someone is humble.
If lucy is both not creative and not tall then someone is wise or not happy and vice versa.
Everyone who is funny or not tall is either not tall or funny.
Everyone who is both not tall and not curious is patient.
If alice is not funny then someone is both creative and brave.
Everyone who is not quiet or not wise is both not creative and not brave.
Everyone who is creative or not generous is both not brave and not kind and vice versa.
Everyone who is old is both not funny and not humble.
Everyone who is not old is both quiet and brave and vice versa.
Someone is not calm or not happy.
Someone is calm.
Paul is both not quiet and patient.
John is calm.
Someone is both generous and happy.
Someone is either not curious or not wise.
Someone is either quiet or not generous.
Someone is both strong and calm. | Lucy is not creative. | entailment | (((~tall(lucy)|~happy(lucy)))=>((old(paul)<~>~calm(paul))))&
(![X]:(~patient(X)<=>wise(X)))&
(((strong(lucy)|humble(lucy)))<=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:((patient(X)<~>tall(X))<=>funny(X)))&
(((wise(alice)|~humble(alice)))=>((~kind(susan)&~curious(susan))))&
(((rich(lucy)|patient(lucy)))<=>(~rich(susan)))&
((?[X]:((generous(X)&~wise(X))))<=>(~old(john)))&
(((funny(alice)|~rich(alice)))=>(?[X]:(humble(X))))&
(((~creative(lucy)&~tall(lucy)))<=>(?[X]:((wise(X)|~happy(X)))))&
(![X]:((funny(X)|~tall(X))=>(~tall(X)<~>funny(X))))&
(![X]:((~tall(X)&~curious(X))=>patient(X)))&
((~funny(alice))=>(?[X]:((creative(X)&brave(X)))))&
(![X]:((~quiet(X)|~wise(X))=>(~creative(X)&~brave(X))))&
(![X]:((creative(X)|~generous(X))<=>(~brave(X)&~kind(X))))&
(![X]:(old(X)=>(~funny(X)&~humble(X))))&
(![X]:(~old(X)<=>(quiet(X)&brave(X))))&
(?[X]:((~calm(X)|~happy(X))))&
(?[X]:(calm(X)))&
((~quiet(paul)&patient(paul)))&
(calm(john))&
(?[X]:((generous(X)&happy(X))))&
(?[X]:((~curious(X)<~>~wise(X))))&
(?[X]:((quiet(X)<~>~generous(X))))&
(?[X]:((strong(X)&calm(X)))) | ~creative(lucy) | [
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3298452278742488610792746
% SZS output start Proof for 3298452278742488610792746
9. (~tall(lucy) & ~creative(lucy)) <=> ? [X0] : (~happy(X0) | wise(X0)) [input p8]
13. ! [X0] : ((~wise(X0) | ~quiet(X0)) => (~brave(X0) & ~creative(X0))) [input p12]
25. creative(lucy) [input hypothesis]
33. ! [X0] : ((~brave(X0) & ~creative(X0)) | (wise(X0) & quiet(X0))) [ennf transformation 13]
51. ((~tall(lucy) & ~creative(lucy)) | ! [X0] : (happy(X0) & ~wise(X0))) & (? [X0] : (~happy(X0) | wise(X0)) | (tall(lucy) | creative(lucy))) [nnf transformation 9]
52. ((~tall(lucy) & ~creative(lucy)) | ! [X0] : (happy(X0) & ~wise(X0))) & (? [X0] : (~happy(X0) | wise(X0)) | tall(lucy) | creative(lucy)) [flattening 51]
53. ((~tall(lucy) & ~creative(lucy)) | ! [X0] : (happy(X0) & ~wise(X0))) & (? [X1] : (~happy(X1) | wise(X1)) | tall(lucy) | creative(lucy)) [rectify 52]
54. ? [X1] : (~happy(X1) | wise(X1)) => (~happy(sK3) | wise(sK3)) [choice axiom]
55. ((~tall(lucy) & ~creative(lucy)) | ! [X0] : (happy(X0) & ~wise(X0))) & ((~happy(sK3) | wise(sK3)) | tall(lucy) | creative(lucy)) [skolemisation 53,54]
106. ~creative(lucy) | ~wise(X0) [cnf transformation 55]
118. ~creative(X0) | wise(X0) [cnf transformation 33]
144. creative(lucy) [cnf transformation 25]
267. 26 <=> ! [X0] : ~wise(X0) [avatar definition]
268. ~wise(X0) <- (26) [avatar component clause 267]
271. 27 <=> creative(lucy) [avatar definition]
272. creative(lucy) <- (27) [avatar component clause 271]
275. 26 | ~27 [avatar split clause 106,271,267]
325. 27 [avatar split clause 144,271]
332. wise(lucy) <- (27) [resolution 118,272]
333. $false <- (26, 27) [subsumption resolution 332,268]
334. ~26 | ~27 [avatar contradiction clause 333]
335. $false [avatar sat refutation 275,325,334]
% SZS output end Proof for 3298452278742488610792746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not quiet then someone is not kind. If someone is either not generous or kind then someone is both creative and not happy. Everyone who is both not funny and patient is either rich or not happy and vice versa. If fred is either not rich or calm then someone is either not kind or not brave. Everyone who is both quiet and not wise is either not calm or generous and vice versa. If someone is both not happy and not generous then susan is either not rich or not patient and vice versa. Everyone who is either not tall or not brave is creative. If susan is wise then someone is either brave or tall. Everyone who is tall is both curious and quiet and vice versa. If john is not kind or rich then mary is either not creative or not humble. Everyone who is wise is either not happy or not tall. If someone is rich or not old then someone is both not humble and tall and vice versa. Everyone who is creative or not wise is kind. Everyone who is not happy is not quiet or funny and vice versa. Everyone who is funny or not quiet is kind. If someone is rich then fred is either curious or not old and vice versa. Someone is either curious or not tall. Someone is both not tall and not patient. John is not quiet. Alice is either curious or not happy. Susan is not tall or not patient. Someone is either humble or kind. Someone is not generous. Mary is not creative. | John is kind. | entailment | ((~quiet(lucy))=>(?[X]:(~kind(X))))&
((?[X]:((~generous(X)<~>kind(X))))=>(?[X]:((creative(X)&~happy(X)))))&
(![X]:((~funny(X)&patient(X))<=>(rich(X)<~>~happy(X))))&
(((~rich(fred)<~>calm(fred)))=>(?[X]:((~kind(X)<~>~brave(X)))))&
(![X]:((quiet(X)&~wise(X))<=>(~calm(X)<~>generous(X))))&
((?[X]:((~happy(X)&~generous(X))))<=>((~rich(susan)<~>~patient(susan))))&
(![X]:((~tall(X)<~>~brave(X))=>creative(X)))&
((wise(susan))=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:(tall(X)<=>(curious(X)&quiet(X))))&
(((~kind(john)|rich(john)))=>((~creative(mary)<~>~humble(mary))))&
(![X]:(wise(X)=>(~happy(X)<~>~tall(X))))&
((?[X]:((rich(X)|~old(X))))<=>(?[X]:((~humble(X)&tall(X)))))&
(![X]:((creative(X)|~wise(X))=>kind(X)))&
(![X]:(~happy(X)<=>(~quiet(X)|funny(X))))&
(![X]:((funny(X)|~quiet(X))=>kind(X)))&
((?[X]:(rich(X)))<=>((curious(fred)<~>~old(fred))))&
(?[X]:((curious(X)<~>~tall(X))))&
(?[X]:((~tall(X)&~patient(X))))&
(~quiet(john))&
((curious(alice)<~>~happy(alice)))&
((~tall(susan)|~patient(susan)))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:(~generous(X)))&
(~creative(mary)) | kind(john) | [
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7654781638468492765845693
% SZS output start Proof for 7654781638468492765845693
15. ! [X0] : ((~quiet(X0) | funny(X0)) => kind(X0)) [input p14]
19. ~quiet(john) [input p18]
25. ~kind(john) [input hypothesis]
36. ! [X0] : (kind(X0) | (quiet(X0) & ~funny(X0))) [ennf transformation 15]
135. kind(X0) | quiet(X0) [cnf transformation 36]
144. ~quiet(john) [cnf transformation 19]
152. ~kind(john) [cnf transformation 25]
253. 22 <=> kind(john) [avatar definition]
254. ~kind(john) <- (~22) [avatar component clause 253]
340. ~22 [avatar split clause 152,253]
345. quiet(john) <- (~22) [resolution 135,254]
347. $false <- (~22) [subsumption resolution 345,144]
348. 22 [avatar contradiction clause 347]
349. $false [avatar sat refutation 340,348]
% SZS output end Proof for 7654781638468492765845693
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or strong is not quiet and vice versa.
Everyone who is both funny and not funny is not rich or not generous and vice versa.
If fred is strong then alice is not patient and vice versa.
If paul is both brave and not curious then john is brave and vice versa.
If mary is either not curious or patient then someone is both not quiet and not old and vice versa.
Everyone who is not happy is kind or not funny.
If mary is either patient or not patient then someone is either not brave or not curious.
If someone is either generous or brave then someone is funny.
If fred is not quiet then someone is not quiet or not calm.
Everyone who is both patient and creative is either generous or brave.
If someone is quiet then john is either not old or brave and vice versa.
Everyone who is either happy or brave is both not wise and calm.
If fred is not creative or not kind then someone is not humble and vice versa.
Everyone who is either calm or not calm is either kind or happy and vice versa.
Everyone who is patient is not rich and vice versa.
Everyone who is patient or not quiet is either patient or not kind.
Alice is old.
Someone is both not quiet and creative.
Someone is either not patient or not brave.
Paul is quiet.
Fred is not curious or not brave.
Alice is calm.
Someone is generous or strong. | John is not rich. | contradiction | (![X]:((humble(X)|strong(X))<=>~quiet(X)))&
(![X]:((funny(X)&~funny(X))<=>(~rich(X)|~generous(X))))&
((strong(fred))<=>(~patient(alice)))&
(((brave(paul)&~curious(paul)))<=>(brave(john)))&
(((~curious(mary)<~>patient(mary)))<=>(?[X]:((~quiet(X)&~old(X)))))&
(![X]:(~happy(X)=>(kind(X)|~funny(X))))&
(((patient(mary)<~>~patient(mary)))=>(?[X]:((~brave(X)<~>~curious(X)))))&
((?[X]:((generous(X)<~>brave(X))))=>(?[X]:(funny(X))))&
((~quiet(fred))=>(?[X]:((~quiet(X)|~calm(X)))))&
(![X]:((patient(X)&creative(X))=>(generous(X)<~>brave(X))))&
((?[X]:(quiet(X)))<=>((~old(john)<~>brave(john))))&
(![X]:((happy(X)<~>brave(X))=>(~wise(X)&calm(X))))&
(((~creative(fred)|~kind(fred)))<=>(?[X]:(~humble(X))))&
(![X]:((calm(X)<~>~calm(X))<=>(kind(X)<~>happy(X))))&
(![X]:(patient(X)<=>~rich(X)))&
(![X]:((patient(X)|~quiet(X))=>(patient(X)<~>~kind(X))))&
(old(alice))&
(?[X]:((~quiet(X)&creative(X))))&
(?[X]:((~patient(X)<~>~brave(X))))&
(quiet(paul))&
((~curious(fred)|~brave(fred)))&
(calm(alice))&
(?[X]:((generous(X)|strong(X)))) | ~rich(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 3781303985803538014844051
% SZS output start Proof for 3781303985803538014844051
2. ! [X0] : ((~funny(X0) & funny(X0)) <=> (~generous(X0) | ~rich(X0))) [input p1]
24. ~rich(john) [input hypothesis]
38. ! [X0] : (((~funny(X0) & funny(X0)) | (generous(X0) & rich(X0))) & ((~generous(X0) | ~rich(X0)) | (funny(X0) | ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : (((~funny(X0) & funny(X0)) | (generous(X0) & rich(X0))) & (~generous(X0) | ~rich(X0) | funny(X0) | ~funny(X0))) [flattening 38]
81. funny(X0) | rich(X0) [cnf transformation 39]
83. ~funny(X0) | rich(X0) [cnf transformation 39]
138. ~rich(john) [cnf transformation 24]
149. rich(X0) [subsumption resolution 81,83]
282. $false [subsumption resolution 138,149]
% SZS output end Proof for 3781303985803538014844051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not curious or kind then lucy is both brave and not wise and vice versa. Everyone who is not strong or not kind is both tall and brave. Everyone who is happy or not patient is not humble or not patient. If someone is not patient or not creative then john is either not tall or wise. Everyone who is kind or brave is either funny or generous. Everyone who is calm or not patient is either not kind or old and vice versa. Everyone who is not happy or not generous is not quiet or not calm. If fred is both quiet and not humble then someone is both tall and happy and vice versa. Everyone who is both wise and not rich is wise. If fred is either not wise or not rich then paul is both not patient and humble. If someone is either not old or not rich then someone is not rich and vice versa. If paul is either not old or rich then mary is not patient or not generous. If someone is either not funny or kind then someone is brave. If mary is not happy or funny then someone is both happy and quiet. Everyone who is kind or not generous is not old. Everyone who is not happy is not kind. Someone is not rich or not quiet. Lucy is kind. Someone is not brave or not patient. Someone is both not curious and calm. Someone is not calm or wise. Someone is curious. | Paul is not old. | neutral | (((~curious(paul)<~>kind(paul)))<=>((brave(lucy)&~wise(lucy))))&
(![X]:((~strong(X)|~kind(X))=>(tall(X)&brave(X))))&
(![X]:((happy(X)|~patient(X))=>(~humble(X)|~patient(X))))&
((?[X]:((~patient(X)|~creative(X))))=>((~tall(john)<~>wise(john))))&
(![X]:((kind(X)|brave(X))=>(funny(X)<~>generous(X))))&
(![X]:((calm(X)|~patient(X))<=>(~kind(X)<~>old(X))))&
(![X]:((~happy(X)|~generous(X))=>(~quiet(X)|~calm(X))))&
(((quiet(fred)&~humble(fred)))<=>(?[X]:((tall(X)&happy(X)))))&
(![X]:((wise(X)&~rich(X))=>wise(X)))&
(((~wise(fred)<~>~rich(fred)))=>((~patient(paul)&humble(paul))))&
((?[X]:((~old(X)<~>~rich(X))))<=>(?[X]:(~rich(X))))&
(((~old(paul)<~>rich(paul)))=>((~patient(mary)|~generous(mary))))&
((?[X]:((~funny(X)<~>kind(X))))=>(?[X]:(brave(X))))&
(((~happy(mary)|funny(mary)))=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:((kind(X)|~generous(X))=>~old(X)))&
(![X]:(~happy(X)=>~kind(X)))&
(?[X]:((~rich(X)|~quiet(X))))&
(kind(lucy))&
(?[X]:((~brave(X)|~patient(X))))&
(?[X]:((~curious(X)&calm(X))))&
(?[X]:((~calm(X)|wise(X))))&
(?[X]:(curious(X))) | ~old(paul) | [] | null | 0 |
If fred is not generous then someone is either tall or not calm and vice versa. If fred is both kind and strong then mary is tall. If fred is either funny or not creative then someone is brave. Everyone who is kind is either generous or kind. Everyone who is both patient and not curious is both strong and calm. Everyone who is patient or not brave is rich or not tall. If someone is not strong or not curious then john is not rich and vice versa. If someone is either kind or not funny then someone is either wise or kind and vice versa. Everyone who is creative is not happy or not strong and vice versa. Everyone who is not rich is either not brave or tall. Everyone who is either not calm or strong is patient and vice versa. Everyone who is patient or strong is not quiet. If someone is both not calm and tall then paul is both kind and curious. If john is not creative then someone is either strong or not quiet. If someone is both happy and not quiet then someone is not creative or not happy. Everyone who is either not funny or humble is either not creative or not brave. Susan is calm or strong. Mary is creative or not creative. Someone is not humble or not happy. John is both wise and strong. John is funny. Someone is not calm. Susan is either not tall or not wise. | Fred is kind. | neutral | ((~generous(fred))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(((kind(fred)&strong(fred)))=>(tall(mary)))&
(((funny(fred)<~>~creative(fred)))=>(?[X]:(brave(X))))&
(![X]:(kind(X)=>(generous(X)<~>kind(X))))&
(![X]:((patient(X)&~curious(X))=>(strong(X)&calm(X))))&
(![X]:((patient(X)|~brave(X))=>(rich(X)|~tall(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>(~rich(john)))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
(![X]:(creative(X)<=>(~happy(X)|~strong(X))))&
(![X]:(~rich(X)=>(~brave(X)<~>tall(X))))&
(![X]:((~calm(X)<~>strong(X))<=>patient(X)))&
(![X]:((patient(X)|strong(X))=>~quiet(X)))&
((?[X]:((~calm(X)&tall(X))))=>((kind(paul)&curious(paul))))&
((~creative(john))=>(?[X]:((strong(X)<~>~quiet(X)))))&
((?[X]:((happy(X)&~quiet(X))))=>(?[X]:((~creative(X)|~happy(X)))))&
(![X]:((~funny(X)<~>humble(X))=>(~creative(X)<~>~brave(X))))&
((calm(susan)|strong(susan)))&
((creative(mary)|~creative(mary)))&
(?[X]:((~humble(X)|~happy(X))))&
((wise(john)&strong(john)))&
(funny(john))&
(?[X]:(~calm(X)))&
((~tall(susan)<~>~wise(susan))) | kind(fred) | [] | null | 0 |
Everyone who is not patient is strong and vice versa.
Everyone who is not strong or strong is both not patient and not wise.
Everyone who is old or not tall is not rich or patient and vice versa.
Everyone who is either rich or not rich is not humble or patient.
If mary is not funny or brave then john is both not kind and happy.
If lucy is kind then someone is not calm or not old.
If susan is both not wise and not calm then lucy is either brave or wise.
Everyone who is generous is not patient.
If someone is funny then susan is tall.
Everyone who is not strong is not humble.
If someone is both old and kind then john is both not creative and not quiet and vice versa.
If someone is either not generous or calm then someone is either patient or generous and vice versa.
Everyone who is not generous or not curious is not strong.
If someone is both happy and not wise then paul is curious and vice versa.
If lucy is curious then alice is both not creative and not patient and vice versa.
Someone is both creative and not calm.
Someone is not tall.
Fred is not strong or not calm.
Someone is not calm.
Lucy is either not humble or not curious.
Someone is calm or kind.
John is old or calm. | Paul is strong. | entailment | (![X]:(~patient(X)<=>strong(X)))&
(![X]:((~strong(X)|strong(X))=>(~patient(X)&~wise(X))))&
(![X]:((old(X)|~tall(X))<=>(~rich(X)|patient(X))))&
(![X]:((rich(X)<~>~rich(X))=>(~humble(X)|patient(X))))&
(((~funny(mary)|brave(mary)))=>((~kind(john)&happy(john))))&
((kind(lucy))=>(?[X]:((~calm(X)|~old(X)))))&
(((~wise(susan)&~calm(susan)))=>((brave(lucy)<~>wise(lucy))))&
(![X]:(generous(X)=>~patient(X)))&
((?[X]:(funny(X)))=>(tall(susan)))&
(![X]:(~strong(X)=>~humble(X)))&
((?[X]:((old(X)&kind(X))))<=>((~creative(john)&~quiet(john))))&
((?[X]:((~generous(X)<~>calm(X))))<=>(?[X]:((patient(X)<~>generous(X)))))&
(![X]:((~generous(X)|~curious(X))=>~strong(X)))&
((?[X]:((happy(X)&~wise(X))))<=>(curious(paul)))&
((curious(lucy))<=>((~creative(alice)&~patient(alice))))&
(?[X]:((creative(X)&~calm(X))))&
(?[X]:(~tall(X)))&
((~strong(fred)|~calm(fred)))&
(?[X]:(~calm(X)))&
((~humble(lucy)<~>~curious(lucy)))&
(?[X]:((calm(X)|kind(X))))&
((old(john)|calm(john))) | strong(paul) | [
"p0",
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6608522263061689136559433
% SZS output start Proof for 6608522263061689136559433
1. ! [X0] : (~patient(X0) <=> strong(X0)) [input p0]
2. ! [X0] : ((strong(X0) | ~strong(X0)) => (~wise(X0) & ~patient(X0))) [input p1]
23. ~strong(paul) [input hypothesis]
25. ! [X0] : ((~wise(X0) & ~patient(X0)) | (~strong(X0) & strong(X0))) [ennf transformation 2]
36. ! [X0] : ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))) [nnf transformation 1]
68. strong(X0) | patient(X0) [cnf transformation 36]
70. ~patient(X0) | strong(X0) [cnf transformation 25]
119. ~strong(paul) [cnf transformation 23]
123. strong(X0) [subsumption resolution 70,68]
263. $false [subsumption resolution 119,123]
% SZS output end Proof for 6608522263061689136559433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient then someone is both kind and not calm and vice versa. If someone is brave or not curious then mary is not rich. If mary is both not kind and humble then someone is curious or not quiet and vice versa. If mary is both old and not generous then someone is kind. Everyone who is happy is both happy and patient. Everyone who is both old and rich is both not happy and quiet. Everyone who is both patient and not strong is not rich or kind and vice versa. If someone is calm then someone is quiet or happy. If someone is quiet then fred is either not wise or old and vice versa. If susan is either calm or patient then lucy is not generous or creative. Everyone who is both calm and not patient is either curious or wise and vice versa. Everyone who is either patient or not kind is not quiet and vice versa. Everyone who is not generous or not funny is not rich or brave. Everyone who is both not kind and not humble is both not quiet and tall and vice versa. Everyone who is either tall or humble is not tall and vice versa. Everyone who is both generous and not quiet is either humble or not generous. Someone is wise. John is both not curious and wise. Susan is not calm. Susan is not creative or not generous. Someone is both curious and not tall. Lucy is both rich and humble. Lucy is both tall and wise. | Lucy is not quiet. | contradiction | ((?[X]:(~patient(X)))<=>(?[X]:((kind(X)&~calm(X)))))&
((?[X]:((brave(X)|~curious(X))))=>(~rich(mary)))&
(((~kind(mary)&humble(mary)))<=>(?[X]:((curious(X)|~quiet(X)))))&
(((old(mary)&~generous(mary)))=>(?[X]:(kind(X))))&
(![X]:(happy(X)=>(happy(X)&patient(X))))&
(![X]:((old(X)&rich(X))=>(~happy(X)&quiet(X))))&
(![X]:((patient(X)&~strong(X))<=>(~rich(X)|kind(X))))&
((?[X]:(calm(X)))=>(?[X]:((quiet(X)|happy(X)))))&
((?[X]:(quiet(X)))<=>((~wise(fred)<~>old(fred))))&
(((calm(susan)<~>patient(susan)))=>((~generous(lucy)|creative(lucy))))&
(![X]:((calm(X)&~patient(X))<=>(curious(X)<~>wise(X))))&
(![X]:((patient(X)<~>~kind(X))<=>~quiet(X)))&
(![X]:((~generous(X)|~funny(X))=>(~rich(X)|brave(X))))&
(![X]:((~kind(X)&~humble(X))<=>(~quiet(X)&tall(X))))&
(![X]:((tall(X)<~>humble(X))<=>~tall(X)))&
(![X]:((generous(X)&~quiet(X))=>(humble(X)<~>~generous(X))))&
(?[X]:(wise(X)))&
((~curious(john)&wise(john)))&
(~calm(susan))&
((~creative(susan)|~generous(susan)))&
(?[X]:((curious(X)&~tall(X))))&
((rich(lucy)&humble(lucy)))&
((tall(lucy)&wise(lucy))) | ~quiet(lucy) | [
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6126209213745067918548826
% SZS output start Proof for 6126209213745067918548826
14. ! [X0] : ((~humble(X0) & ~kind(X0)) <=> (tall(X0) & ~quiet(X0))) [input p13]
15. ! [X0] : ((tall(X0) <~> humble(X0)) <=> ~tall(X0)) [input p14]
23. wise(lucy) & tall(lucy) [input p22]
24. ~quiet(lucy) [input hypothesis]
66. ! [X0] : (((~humble(X0) & ~kind(X0)) | (~tall(X0) | quiet(X0))) & ((tall(X0) & ~quiet(X0)) | (humble(X0) | kind(X0)))) [nnf transformation 14]
67. ! [X0] : (((~humble(X0) & ~kind(X0)) | ~tall(X0) | quiet(X0)) & ((tall(X0) & ~quiet(X0)) | humble(X0) | kind(X0))) [flattening 66]
68. ! [X0] : ((((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | tall(X0)) & (~tall(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))))) [nnf transformation 15]
115. ~tall(X0) | ~humble(X0) | quiet(X0) [cnf transformation 67]
116. ~tall(X0) | humble(X0) | ~tall(X0) [cnf transformation 68]
118. humble(X0) | tall(X0) | tall(X0) [cnf transformation 68]
131. tall(lucy) [cnf transformation 23]
133. ~quiet(lucy) [cnf transformation 24]
135. ~tall(X0) | humble(X0) [duplicate literal removal 116]
136. tall(X0) | humble(X0) [duplicate literal removal 118]
263. humble(X0) [subsumption resolution 135,136]
373. ~humble(lucy) | quiet(lucy) [resolution 115,131]
376. quiet(lucy) [subsumption resolution 373,263]
377. $false [subsumption resolution 376,133]
% SZS output end Proof for 6126209213745067918548826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not patient is kind.
If someone is either not brave or not funny then someone is either not kind or quiet and vice versa.
Everyone who is either not creative or curious is not humble and vice versa.
Everyone who is quiet or not quiet is both quiet and strong.
If paul is either patient or curious then paul is either not generous or not brave and vice versa.
Everyone who is generous or not generous is both not curious and not tall.
If someone is funny or creative then someone is either old or not patient and vice versa.
Everyone who is both not creative and not rich is not tall or calm.
Everyone who is not patient or not brave is strong or not funny and vice versa.
Everyone who is wise is kind and vice versa.
Everyone who is either patient or not wise is both creative and not calm and vice versa.
Everyone who is either strong or not patient is both not patient and generous and vice versa.
If paul is either rich or kind then someone is curious and vice versa.
Everyone who is kind is either not humble or not creative and vice versa.
If someone is both funny and not wise then alice is either not old or strong and vice versa.
Mary is not brave.
Lucy is either not wise or wise.
Fred is either not curious or not funny.
Mary is wise or not curious.
Someone is either patient or not patient.
Susan is old or not old. | Alice is not wise. | entailment | (![X]:((patient(X)&~patient(X))=>kind(X)))&
((?[X]:((~brave(X)<~>~funny(X))))<=>(?[X]:((~kind(X)<~>quiet(X)))))&
(![X]:((~creative(X)<~>curious(X))<=>~humble(X)))&
(![X]:((quiet(X)|~quiet(X))=>(quiet(X)&strong(X))))&
(((patient(paul)<~>curious(paul)))<=>((~generous(paul)<~>~brave(paul))))&
(![X]:((generous(X)|~generous(X))=>(~curious(X)&~tall(X))))&
((?[X]:((funny(X)|creative(X))))<=>(?[X]:((old(X)<~>~patient(X)))))&
(![X]:((~creative(X)&~rich(X))=>(~tall(X)|calm(X))))&
(![X]:((~patient(X)|~brave(X))<=>(strong(X)|~funny(X))))&
(![X]:(wise(X)<=>kind(X)))&
(![X]:((patient(X)<~>~wise(X))<=>(creative(X)&~calm(X))))&
(![X]:((strong(X)<~>~patient(X))<=>(~patient(X)&generous(X))))&
(((rich(paul)<~>kind(paul)))<=>(?[X]:(curious(X))))&
(![X]:(kind(X)<=>(~humble(X)<~>~creative(X))))&
((?[X]:((funny(X)&~wise(X))))<=>((~old(alice)<~>strong(alice))))&
(~brave(mary))&
((~wise(lucy)<~>wise(lucy)))&
((~curious(fred)<~>~funny(fred)))&
((wise(mary)|~curious(mary)))&
(?[X]:((patient(X)<~>~patient(X))))&
((old(susan)|~old(susan))) | ~wise(alice) | [
"p1",
"p2",
"p3",
"p5",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 75634546659439988209903
% SZS output start Proof for 75634546659439988209903
2. ? [X0] : (~brave(X0) <~> ~funny(X0)) <=> ? [X0] : (~kind(X0) <~> quiet(X0)) [input p1]
3. ! [X0] : ((~creative(X0) <~> curious(X0)) <=> ~humble(X0)) [input p2]
4. ! [X0] : ((~quiet(X0) | quiet(X0)) => (strong(X0) & quiet(X0))) [input p3]
6. ! [X0] : ((~generous(X0) | generous(X0)) => (~tall(X0) & ~curious(X0))) [input p5]
10. ! [X0] : (wise(X0) <=> kind(X0)) [input p9]
14. ! [X0] : (kind(X0) <=> (~humble(X0) <~> ~creative(X0))) [input p13]
22. wise(alice) [input hypothesis]
23. ? [X0] : (~brave(X0) <~> ~funny(X0)) <=> ? [X1] : (~kind(X1) <~> quiet(X1)) [rectify 2]
26. ! [X0] : ((~generous(X0) | generous(X0)) => ~curious(X0)) [pure predicate removal 6]
29. ! [X0] : ((strong(X0) & quiet(X0)) | (quiet(X0) & ~quiet(X0))) [ennf transformation 4]
30. ! [X0] : (~curious(X0) | (generous(X0) & ~generous(X0))) [ennf transformation 26]
31. (? [X0] : ((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | ! [X1] : ((~kind(X1) | ~quiet(X1)) & (quiet(X1) | kind(X1)))) & (? [X1] : ((~quiet(X1) | kind(X1)) & (quiet(X1) | ~kind(X1))) | ! [X0] : ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) [nnf transformation 23]
32. (? [X0] : ((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | ! [X1] : ((~kind(X1) | ~quiet(X1)) & (quiet(X1) | kind(X1)))) & (? [X2] : ((~quiet(X2) | kind(X2)) & (quiet(X2) | ~kind(X2))) | ! [X3] : ((~brave(X3) | funny(X3)) & (~funny(X3) | brave(X3)))) [rectify 31]
33. ? [X0] : ((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) => ((funny(sK0) | brave(sK0)) & (~funny(sK0) | ~brave(sK0))) [choice axiom]
34. ? [X2] : ((~quiet(X2) | kind(X2)) & (quiet(X2) | ~kind(X2))) => ((~quiet(sK1) | kind(sK1)) & (quiet(sK1) | ~kind(sK1))) [choice axiom]
35. (((funny(sK0) | brave(sK0)) & (~funny(sK0) | ~brave(sK0))) | ! [X1] : ((~kind(X1) | ~quiet(X1)) & (quiet(X1) | kind(X1)))) & (((~quiet(sK1) | kind(sK1)) & (quiet(sK1) | ~kind(sK1))) | ! [X3] : ((~brave(X3) | funny(X3)) & (~funny(X3) | brave(X3)))) [skolemisation 32,34,33]
36. ! [X0] : ((((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | humble(X0)) & (~humble(X0) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0))))) [nnf transformation 3]
45. ! [X0] : ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0))) [nnf transformation 10]
54. ! [X0] : ((kind(X0) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0)))) & (((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | ~kind(X0))) [nnf transformation 14]
67. ~quiet(sK1) | kind(sK1) | ~funny(X3) | brave(X3) [cnf transformation 35]
68. ~quiet(sK1) | kind(sK1) | ~brave(X3) | funny(X3) [cnf transformation 35]
70. ~funny(sK0) | ~brave(sK0) | ~kind(X1) | ~quiet(X1) [cnf transformation 35]
72. funny(sK0) | brave(sK0) | ~kind(X1) | ~quiet(X1) [cnf transformation 35]
73. ~humble(X0) | curious(X0) | creative(X0) [cnf transformation 36]
75. ~creative(X0) | curious(X0) | humble(X0) [cnf transformation 36]
78. quiet(X0) | quiet(X0) [cnf transformation 29]
89. ~curious(X0) | ~generous(X0) [cnf transformation 30]
90. ~curious(X0) | generous(X0) [cnf transformation 30]
101. ~wise(X0) | kind(X0) [cnf transformation 45]
119. ~humble(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 54]
120. ~kind(X0) | humble(X0) | creative(X0) [cnf transformation 54]
138. wise(alice) [cnf transformation 22]
141. quiet(X0) [duplicate literal removal 78]
143. 1 <=> ! [X1] : (~kind(X1) | ~quiet(X1)) [avatar definition]
144. ~kind(X1) | ~quiet(X1) <- (1) [avatar component clause 143]
146. 2 <=> brave(sK0) [avatar definition]
147. ~brave(sK0) <- (~2) [avatar component clause 146]
148. brave(sK0) <- (2) [avatar component clause 146]
150. 3 <=> funny(sK0) [avatar definition]
151. ~funny(sK0) <- (~3) [avatar component clause 150]
152. funny(sK0) <- (3) [avatar component clause 150]
153. 1 | 2 | 3 [avatar split clause 72,150,146,143]
158. 1 | ~2 | ~3 [avatar split clause 70,150,146,143]
161. 5 <=> ! [X3] : (~brave(X3) | funny(X3)) [avatar definition]
162. ~brave(X3) | funny(X3) <- (5) [avatar component clause 161]
164. 6 <=> kind(sK1) [avatar definition]
166. kind(sK1) <- (6) [avatar component clause 164]
168. 7 <=> quiet(sK1) [avatar definition]
170. ~quiet(sK1) <- (~7) [avatar component clause 168]
171. 5 | 6 | ~7 [avatar split clause 68,168,164,161]
173. 8 <=> ! [X3] : (~funny(X3) | brave(X3)) [avatar definition]
174. ~funny(X3) | brave(X3) <- (8) [avatar component clause 173]
175. 8 | 6 | ~7 [avatar split clause 67,168,164,173]
203. ~curious(X0) [subsumption resolution 89,90]
276. $false <- (~7) [subsumption resolution 170,141]
277. 7 [avatar contradiction clause 276]
278. kind(alice) [resolution 101,138]
301. humble(sK1) | creative(sK1) <- (6) [resolution 120,166]
304. 27 <=> creative(sK1) [avatar definition]
306. creative(sK1) <- (27) [avatar component clause 304]
308. 28 <=> humble(sK1) [avatar definition]
310. humble(sK1) <- (28) [avatar component clause 308]
311. 27 | 28 | ~6 [avatar split clause 301,164,308,304]
321. funny(sK0) <- (2, 5) [resolution 162,148]
322. $false <- (2, ~3, 5) [subsumption resolution 321,151]
323. ~2 | 3 | ~5 [avatar contradiction clause 322]
328. brave(sK0) <- (3, 8) [resolution 174,152]
331. $false <- (~2, 3, 8) [subsumption resolution 328,147]
332. 2 | ~3 | ~8 [avatar contradiction clause 331]
338. curious(sK1) | humble(sK1) <- (27) [resolution 306,75]
339. humble(sK1) <- (27) [subsumption resolution 338,203]
340. 28 | ~27 [avatar split clause 339,304,308]
343. ~creative(sK1) | ~kind(sK1) <- (28) [resolution 310,119]
345. curious(sK1) | creative(sK1) <- (28) [resolution 310,73]
349. creative(sK1) <- (28) [subsumption resolution 345,203]
350. 27 | ~28 [avatar split clause 349,308,304]
351. ~creative(sK1) <- (6, 28) [subsumption resolution 343,166]
352. ~27 | ~6 | ~28 [avatar split clause 351,308,164,304]
353. ~kind(X1) <- (1) [subsumption resolution 144,141]
357. $false <- (1) [resolution 353,278]
358. ~1 [avatar contradiction clause 357]
359. $false [avatar sat refutation 153,158,171,175,277,311,323,332,340,350,352,358]
% SZS output end Proof for 75634546659439988209903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not curious is not generous. If paul is both not patient and not rich then someone is not curious. Everyone who is wise is not funny or not old. If someone is humble or not quiet then someone is both rich and old and vice versa. If susan is either not funny or not generous then fred is both not calm and not happy. Everyone who is creative or not strong is not creative. Everyone who is creative is tall. Everyone who is both patient and not kind is kind or not generous and vice versa. Everyone who is both not kind and not creative is either curious or not humble and vice versa. If someone is quiet or not kind then someone is either not humble or not patient and vice versa. Everyone who is both brave and not rich is either curious or not wise and vice versa. Everyone who is both wise and not rich is both not happy and not kind. Everyone who is either curious or kind is not old and vice versa. If mary is both not happy and not humble then fred is both calm and not strong. If lucy is both not happy and not strong then someone is both not wise and not kind and vice versa. Everyone who is strong is either not rich or not brave and vice versa. Paul is both not old and not quiet. Alice is humble or not tall. Fred is not patient. Lucy is not curious or patient. Lucy is not creative or humble. John is not tall or not patient. Mary is not old or not kind. John is both not wise and not creative. | John is creative. | contradiction | (![X]:((old(X)&~curious(X))=>~generous(X)))&
(((~patient(paul)&~rich(paul)))=>(?[X]:(~curious(X))))&
(![X]:(wise(X)=>(~funny(X)|~old(X))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
(![X]:((curious(X)<~>kind(X))<=>~old(X)))&
(((~happy(mary)&~humble(mary)))=>((calm(fred)&~strong(fred))))&
(((~happy(lucy)&~strong(lucy)))<=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(strong(X)<=>(~rich(X)<~>~brave(X))))&
((~old(paul)&~quiet(paul)))&
((humble(alice)|~tall(alice)))&
(~patient(fred))&
((~curious(lucy)|patient(lucy)))&
((~creative(lucy)|humble(lucy)))&
((~tall(john)|~patient(john)))&
((~old(mary)|~kind(mary)))&
((~wise(john)&~creative(john))) | creative(john) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3981525136724530166381730
% SZS output start Proof for 3981525136724530166381730
6. ! [X0] : ((~strong(X0) | creative(X0)) => ~creative(X0)) [input p5]
25. creative(john) [input hypothesis]
35. ! [X0] : (~creative(X0) | (strong(X0) & ~creative(X0))) [ennf transformation 6]
79. ~creative(X0) | ~creative(X0) [cnf transformation 35]
131. creative(john) [cnf transformation 25]
134. ~creative(X0) [duplicate literal removal 79]
283. $false [subsumption resolution 131,134]
% SZS output end Proof for 3981525136724530166381730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not funny is not generous and vice versa.
Everyone who is both not brave and not quiet is both happy and not quiet.
Everyone who is either not quiet or rich is strong.
Everyone who is old or not old is old or strong.
Everyone who is brave is not patient or not humble.
Everyone who is both not brave and not generous is not calm or not wise.
If someone is not humble then someone is not kind or not patient and vice versa.
Everyone who is both not brave and not creative is happy.
If someone is not curious or patient then paul is tall or not humble and vice versa.
If someone is either quiet or not generous then someone is not patient.
Everyone who is either old or not curious is both funny and not strong and vice versa.
If paul is rich then someone is not tall and vice versa.
Everyone who is either not happy or not strong is both rich and wise.
Everyone who is rich is not strong or happy.
Everyone who is either rich or tall is either calm or not happy and vice versa.
If someone is not humble or rich then mary is both wise and brave and vice versa.
Alice is old or quiet.
Someone is both not strong and not rich.
John is either not tall or not kind.
Someone is quiet.
John is both happy and not tall.
Someone is not tall.
Someone is either not curious or not creative.
Fred is not calm or brave. | John is not tall. | entailment | (![X]:((~quiet(X)|~funny(X))<=>~generous(X)))&
(![X]:((~brave(X)&~quiet(X))=>(happy(X)&~quiet(X))))&
(![X]:((~quiet(X)<~>rich(X))=>strong(X)))&
(![X]:((old(X)|~old(X))=>(old(X)|strong(X))))&
(![X]:(brave(X)=>(~patient(X)|~humble(X))))&
(![X]:((~brave(X)&~generous(X))=>(~calm(X)|~wise(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~kind(X)|~patient(X)))))&
(![X]:((~brave(X)&~creative(X))=>happy(X)))&
((?[X]:((~curious(X)|patient(X))))<=>((tall(paul)|~humble(paul))))&
((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:(~patient(X))))&
(![X]:((old(X)<~>~curious(X))<=>(funny(X)&~strong(X))))&
((rich(paul))<=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)<~>~strong(X))=>(rich(X)&wise(X))))&
(![X]:(rich(X)=>(~strong(X)|happy(X))))&
(![X]:((rich(X)<~>tall(X))<=>(calm(X)<~>~happy(X))))&
((?[X]:((~humble(X)|rich(X))))<=>((wise(mary)&brave(mary))))&
((old(alice)|quiet(alice)))&
(?[X]:((~strong(X)&~rich(X))))&
((~tall(john)<~>~kind(john)))&
(?[X]:(quiet(X)))&
((happy(john)&~tall(john)))&
(?[X]:(~tall(X)))&
(?[X]:((~curious(X)<~>~creative(X))))&
((~calm(fred)|brave(fred))) | ~tall(john) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8234471661629360102266143
% SZS output start Proof for 8234471661629360102266143
21. ~tall(john) & happy(john) [input p20]
25. tall(john) [input hypothesis]
137. ~tall(john) [cnf transformation 21]
142. tall(john) [cnf transformation 25]
258. 26 <=> tall(john) [avatar definition]
267. ~26 [avatar split clause 137,258]
287. 26 [avatar split clause 142,258]
288. $false [avatar sat refutation 267,287]
% SZS output end Proof for 8234471661629360102266143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or brave then someone is both not creative and wise and vice versa.
Everyone who is either not humble or not old is funny or not funny and vice versa.
Everyone who is either not brave or humble is not happy or not quiet.
If fred is both patient and creative then paul is either old or brave.
Everyone who is generous is not quiet and vice versa.
Everyone who is not wise or generous is not old and vice versa.
If susan is either not old or happy then someone is both not strong and not brave and vice versa.
If someone is old then fred is not calm.
Everyone who is not kind or rich is calm or not brave and vice versa.
If alice is both not strong and funny then susan is either brave or tall and vice versa.
If someone is both humble and not wise then john is both brave and not funny and vice versa.
If fred is both not happy and quiet then paul is either not creative or generous and vice versa.
Everyone who is happy or not rich is not wise.
If lucy is funny or not wise then paul is both not quiet and brave and vice versa.
Everyone who is either not funny or tall is strong or not patient.
Everyone who is both happy and not tall is not brave or tall and vice versa.
Lucy is not wise.
Someone is either not humble or quiet.
Someone is not humble or tall.
Someone is both not patient and not quiet. | Lucy is tall. | contradiction | ((?[X]:((~curious(X)<~>brave(X))))<=>(?[X]:((~creative(X)&wise(X)))))&
(![X]:((~humble(X)<~>~old(X))<=>(funny(X)|~funny(X))))&
(![X]:((~brave(X)<~>humble(X))=>(~happy(X)|~quiet(X))))&
(((patient(fred)&creative(fred)))=>((old(paul)<~>brave(paul))))&
(![X]:(generous(X)<=>~quiet(X)))&
(![X]:((~wise(X)|generous(X))<=>~old(X)))&
(((~old(susan)<~>happy(susan)))<=>(?[X]:((~strong(X)&~brave(X)))))&
((?[X]:(old(X)))=>(~calm(fred)))&
(![X]:((~kind(X)|rich(X))<=>(calm(X)|~brave(X))))&
(((~strong(alice)&funny(alice)))<=>((brave(susan)<~>tall(susan))))&
((?[X]:((humble(X)&~wise(X))))<=>((brave(john)&~funny(john))))&
(((~happy(fred)&quiet(fred)))<=>((~creative(paul)<~>generous(paul))))&
(![X]:((happy(X)|~rich(X))=>~wise(X)))&
(((funny(lucy)|~wise(lucy)))<=>((~quiet(paul)&brave(paul))))&
(![X]:((~funny(X)<~>tall(X))=>(strong(X)|~patient(X))))&
(![X]:((happy(X)&~tall(X))<=>(~brave(X)|tall(X))))&
(~wise(lucy))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:((~patient(X)&~quiet(X)))) | tall(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2545677118155814127167939
% SZS output start Proof for 2545677118155814127167939
16. ! [X0] : ((~tall(X0) & happy(X0)) <=> (tall(X0) | ~brave(X0))) [input p15]
21. tall(lucy) [input hypothesis]
58. ! [X0] : (((~tall(X0) & happy(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (tall(X0) | ~happy(X0)))) [nnf transformation 16]
59. ! [X0] : (((~tall(X0) & happy(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | tall(X0) | ~happy(X0))) [flattening 58]
124. ~tall(X0) | ~tall(X0) [cnf transformation 59]
130. tall(lucy) [cnf transformation 21]
132. ~tall(X0) [duplicate literal removal 124]
300. $false [subsumption resolution 130,132]
% SZS output end Proof for 2545677118155814127167939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not quiet is both not happy and not calm and vice versa.
If someone is both strong and funny then susan is tall or not wise and vice versa.
If someone is not funny then someone is both not tall and not humble.
If alice is both strong and not strong then someone is not curious or not calm and vice versa.
Everyone who is both not creative and tall is not tall.
If susan is both humble and generous then mary is not happy.
If someone is both calm and humble then fred is both not old and quiet.
Everyone who is not curious or not rich is both humble and brave.
Everyone who is either not funny or not wise is either rich or not funny.
Everyone who is not humble is either not calm or happy and vice versa.
If john is both strong and brave then paul is both not humble and not strong and vice versa.
If someone is either calm or not wise then alice is not curious or funny.
Everyone who is not kind is wise or generous and vice versa.
If fred is either not curious or not rich then someone is generous or not wise.
Everyone who is either calm or quiet is both not funny and happy and vice versa.
Everyone who is either not humble or humble is not humble.
Someone is not strong or happy.
Someone is either not old or brave.
Susan is not tall.
Someone is not kind.
Someone is either tall or old.
Susan is both not humble and not wise.
Paul is either curious or not wise. | Fred is not happy. | contradiction | (![X]:((~calm(X)<~>~quiet(X))<=>(~happy(X)&~calm(X))))&
((?[X]:((strong(X)&funny(X))))<=>((tall(susan)|~wise(susan))))&
((?[X]:(~funny(X)))=>(?[X]:((~tall(X)&~humble(X)))))&
(((strong(alice)&~strong(alice)))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:((~creative(X)&tall(X))=>~tall(X)))&
(((humble(susan)&generous(susan)))=>(~happy(mary)))&
((?[X]:((calm(X)&humble(X))))=>((~old(fred)&quiet(fred))))&
(![X]:((~curious(X)|~rich(X))=>(humble(X)&brave(X))))&
(![X]:((~funny(X)<~>~wise(X))=>(rich(X)<~>~funny(X))))&
(![X]:(~humble(X)<=>(~calm(X)<~>happy(X))))&
(((strong(john)&brave(john)))<=>((~humble(paul)&~strong(paul))))&
((?[X]:((calm(X)<~>~wise(X))))=>((~curious(alice)|funny(alice))))&
(![X]:(~kind(X)<=>(wise(X)|generous(X))))&
(((~curious(fred)<~>~rich(fred)))=>(?[X]:((generous(X)|~wise(X)))))&
(![X]:((calm(X)<~>quiet(X))<=>(~funny(X)&happy(X))))&
(![X]:((~humble(X)<~>humble(X))=>~humble(X)))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((~old(X)<~>brave(X))))&
(~tall(susan))&
(?[X]:(~kind(X)))&
(?[X]:((tall(X)<~>old(X))))&
((~humble(susan)&~wise(susan)))&
((curious(paul)<~>~wise(paul))) | ~happy(fred) | [
"p3",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7989290634935664592437997
% SZS output start Proof for 7989290634935664592437997
4. (~strong(alice) & strong(alice)) <=> ? [X0] : (~calm(X0) | ~curious(X0)) [input p3]
10. ! [X0] : (~humble(X0) <=> (~calm(X0) <~> happy(X0))) [input p9]
16. ! [X0] : ((~humble(X0) <~> humble(X0)) => ~humble(X0)) [input p15]
24. ~happy(fred) [input hypothesis]
39. ! [X0] : (~humble(X0) | (~humble(X0) <=> humble(X0))) [ennf transformation 16]
50. ((~strong(alice) & strong(alice)) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (strong(alice) | ~strong(alice))) [nnf transformation 4]
51. ((~strong(alice) & strong(alice)) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | strong(alice) | ~strong(alice)) [flattening 50]
52. ((~strong(alice) & strong(alice)) | ! [X0] : (calm(X0) & curious(X0))) & (? [X1] : (~calm(X1) | ~curious(X1)) | strong(alice) | ~strong(alice)) [rectify 51]
53. ? [X1] : (~calm(X1) | ~curious(X1)) => (~calm(sK2) | ~curious(sK2)) [choice axiom]
54. ((~strong(alice) & strong(alice)) | ! [X0] : (calm(X0) & curious(X0))) & ((~calm(sK2) | ~curious(sK2)) | strong(alice) | ~strong(alice)) [skolemisation 52,53]
56. ! [X0] : ((~humble(X0) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) & (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | humble(X0))) [nnf transformation 10]
65. ! [X0] : (~humble(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 39]
92. strong(alice) | calm(X0) [cnf transformation 54]
94. ~strong(alice) | calm(X0) [cnf transformation 54]
106. ~calm(X0) | happy(X0) | humble(X0) [cnf transformation 56]
126. ~humble(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 65]
138. ~happy(fred) [cnf transformation 24]
140. ~humble(X0) [duplicate literal removal 126]
183. 9 <=> ! [X0] : calm(X0) [avatar definition]
184. calm(X0) <- (9) [avatar component clause 183]
186. 10 <=> strong(alice) [avatar definition]
189. 9 | ~10 [avatar split clause 94,186,183]
194. 9 | 10 [avatar split clause 92,186,183]
335. happy(X0) | humble(X0) <- (9) [resolution 106,184]
336. happy(X0) <- (9) [subsumption resolution 335,140]
337. $false <- (9) [resolution 336,138]
341. ~9 [avatar contradiction clause 337]
342. $false [avatar sat refutation 189,194,341]
% SZS output end Proof for 7989290634935664592437997
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is both not funny and not kind and vice versa.
If lucy is both not tall and generous then lucy is both wise and not creative and vice versa.
Everyone who is not tall or funny is both not happy and not rich and vice versa.
If mary is not old then john is calm and vice versa.
Everyone who is not brave is rich or not patient.
Everyone who is not wise is either not brave or not wise and vice versa.
Everyone who is both funny and strong is quiet and vice versa.
Everyone who is not wise or not generous is both not strong and quiet.
If lucy is funny or wise then someone is rich or not curious and vice versa.
If someone is creative then someone is both not patient and strong and vice versa.
If someone is either not calm or funny then someone is funny or curious.
Everyone who is both rich and strong is both not funny and not quiet.
If paul is both creative and not patient then paul is both rich and funny.
Everyone who is either tall or wise is both not generous and rich and vice versa.
Everyone who is not patient or brave is either not creative or not kind and vice versa.
If someone is wise or strong then someone is either not rich or not generous.
Someone is humble or not old.
Susan is both happy and not old.
Susan is not old.
Alice is not old.
Someone is patient.
Paul is generous or curious.
Someone is both creative and not old. | Alice is not quiet. | neutral | (![X]:(calm(X)<=>(~funny(X)&~kind(X))))&
(((~tall(lucy)&generous(lucy)))<=>((wise(lucy)&~creative(lucy))))&
(![X]:((~tall(X)|funny(X))<=>(~happy(X)&~rich(X))))&
((~old(mary))<=>(calm(john)))&
(![X]:(~brave(X)=>(rich(X)|~patient(X))))&
(![X]:(~wise(X)<=>(~brave(X)<~>~wise(X))))&
(![X]:((funny(X)&strong(X))<=>quiet(X)))&
(![X]:((~wise(X)|~generous(X))=>(~strong(X)&quiet(X))))&
(((funny(lucy)|wise(lucy)))<=>(?[X]:((rich(X)|~curious(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((~patient(X)&strong(X)))))&
((?[X]:((~calm(X)<~>funny(X))))=>(?[X]:((funny(X)|curious(X)))))&
(![X]:((rich(X)&strong(X))=>(~funny(X)&~quiet(X))))&
(((creative(paul)&~patient(paul)))=>((rich(paul)&funny(paul))))&
(![X]:((tall(X)<~>wise(X))<=>(~generous(X)&rich(X))))&
(![X]:((~patient(X)|brave(X))<=>(~creative(X)<~>~kind(X))))&
((?[X]:((wise(X)|strong(X))))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(?[X]:((humble(X)|~old(X))))&
((happy(susan)&~old(susan)))&
(~old(susan))&
(~old(alice))&
(?[X]:(patient(X)))&
((generous(paul)|curious(paul)))&
(?[X]:((creative(X)&~old(X)))) | ~quiet(alice) | [] | null | 0 |
Everyone who is quiet is not happy.
Everyone who is not brave or brave is old and vice versa.
If lucy is not strong then someone is either patient or brave and vice versa.
Everyone who is not kind or old is either funny or generous and vice versa.
If john is old then paul is not humble or not calm.
Everyone who is both kind and rich is either not generous or happy.
If someone is both not kind and not tall then someone is either generous or not funny and vice versa.
Everyone who is both brave and not patient is patient and vice versa.
If someone is either not curious or not brave then someone is either generous or happy and vice versa.
Everyone who is patient is not patient or brave.
Everyone who is both not generous and humble is both not funny and not calm and vice versa.
If john is strong or not generous then fred is not happy and vice versa.
Everyone who is not old or calm is not wise.
If someone is not creative or not curious then paul is patient and vice versa.
If susan is either patient or not happy then someone is not funny or creative and vice versa.
Everyone who is funny is calm or tall and vice versa.
Someone is both kind and not rich.
Fred is both creative and calm.
Mary is both not patient and not rich.
Someone is brave or strong.
Someone is wise or not tall.
Someone is brave or wise. | Susan is not generous. | entailment | (![X]:(quiet(X)=>~happy(X)))&
(![X]:((~brave(X)|brave(X))<=>old(X)))&
((~strong(lucy))<=>(?[X]:((patient(X)<~>brave(X)))))&
(![X]:((~kind(X)|old(X))<=>(funny(X)<~>generous(X))))&
((old(john))=>((~humble(paul)|~calm(paul))))&
(![X]:((kind(X)&rich(X))=>(~generous(X)<~>happy(X))))&
((?[X]:((~kind(X)&~tall(X))))<=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:((brave(X)&~patient(X))<=>patient(X)))&
((?[X]:((~curious(X)<~>~brave(X))))<=>(?[X]:((generous(X)<~>happy(X)))))&
(![X]:(patient(X)=>(~patient(X)|brave(X))))&
(![X]:((~generous(X)&humble(X))<=>(~funny(X)&~calm(X))))&
(((strong(john)|~generous(john)))<=>(~happy(fred)))&
(![X]:((~old(X)|calm(X))=>~wise(X)))&
((?[X]:((~creative(X)|~curious(X))))<=>(patient(paul)))&
(((patient(susan)<~>~happy(susan)))<=>(?[X]:((~funny(X)|creative(X)))))&
(![X]:(funny(X)<=>(calm(X)|tall(X))))&
(?[X]:((kind(X)&~rich(X))))&
((creative(fred)&calm(fred)))&
((~patient(mary)&~rich(mary)))&
(?[X]:((brave(X)|strong(X))))&
(?[X]:((wise(X)|~tall(X))))&
(?[X]:((brave(X)|wise(X)))) | ~generous(susan) | [
"p1",
"p3",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1637845460384963769813905
% SZS output start Proof for 1637845460384963769813905
2. ! [X0] : ((brave(X0) | ~brave(X0)) <=> old(X0)) [input p1]
4. ! [X0] : ((old(X0) | ~kind(X0)) <=> (funny(X0) <~> generous(X0))) [input p3]
11. ! [X0] : ((humble(X0) & ~generous(X0)) <=> (~calm(X0) & ~funny(X0))) [input p10]
16. ! [X0] : (funny(X0) <=> (tall(X0) | calm(X0))) [input p15]
23. generous(susan) [input hypothesis]
35. ! [X0] : (((brave(X0) | ~brave(X0)) | ~old(X0)) & (old(X0) | (~brave(X0) & brave(X0)))) [nnf transformation 2]
36. ! [X0] : ((brave(X0) | ~brave(X0) | ~old(X0)) & (old(X0) | (~brave(X0) & brave(X0)))) [flattening 35]
41. ! [X0] : (((old(X0) | ~kind(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~old(X0) & kind(X0)))) [nnf transformation 4]
42. ! [X0] : ((old(X0) | ~kind(X0) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~old(X0) & kind(X0)))) [flattening 41]
55. ! [X0] : (((humble(X0) & ~generous(X0)) | (calm(X0) | funny(X0))) & ((~calm(X0) & ~funny(X0)) | (~humble(X0) | generous(X0)))) [nnf transformation 11]
56. ! [X0] : (((humble(X0) & ~generous(X0)) | calm(X0) | funny(X0)) & ((~calm(X0) & ~funny(X0)) | ~humble(X0) | generous(X0))) [flattening 55]
67. ! [X0] : ((funny(X0) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | ~funny(X0))) [nnf transformation 16]
68. ! [X0] : ((funny(X0) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | ~funny(X0))) [flattening 67]
77. old(X0) | brave(X0) [cnf transformation 36]
78. ~brave(X0) | old(X0) [cnf transformation 36]
85. generous(X0) | funny(X0) | ~old(X0) [cnf transformation 42]
87. ~generous(X0) | ~funny(X0) | ~old(X0) [cnf transformation 42]
111. ~generous(X0) | calm(X0) | funny(X0) [cnf transformation 56]
128. funny(X0) | ~calm(X0) [cnf transformation 68]
137. generous(susan) [cnf transformation 23]
141. old(X0) [subsumption resolution 77,78]
164. ~generous(X0) | ~funny(X0) [subsumption resolution 87,141]
165. generous(X0) | funny(X0) [subsumption resolution 85,141]
217. calm(X0) | funny(X0) [subsumption resolution 111,165]
238. funny(X0) [subsumption resolution 128,217]
258. ~funny(susan) [resolution 164,137]
260. $false [subsumption resolution 258,238]
% SZS output end Proof for 1637845460384963769813905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or calm is either not tall or not quiet.
Everyone who is funny or not patient is curious or not generous.
Everyone who is tall is funny and vice versa.
Everyone who is either not tall or funny is humble.
If someone is either strong or not calm then john is either not brave or not old and vice versa.
If paul is tall then someone is either not brave or curious and vice versa.
If someone is tall or calm then someone is both happy and not wise.
If someone is either not patient or not curious then someone is either not calm or creative and vice versa.
Everyone who is not strong or not curious is brave.
If someone is both not happy and curious then paul is either strong or wise and vice versa.
Everyone who is not patient is both wise and not old.
Everyone who is either humble or not generous is both not patient and not happy and vice versa.
If alice is both not creative and not old then someone is either quiet or not tall and vice versa.
Everyone who is either not wise or not generous is not wise or creative and vice versa.
If someone is wise then lucy is not calm and vice versa.
Everyone who is generous or not rich is not tall or generous.
Fred is not strong or not humble.
Someone is both not old and wise.
Someone is either not generous or happy.
John is both not brave and strong.
Paul is not generous or creative. | Lucy is funny. | contradiction | (![X]:((wise(X)<~>calm(X))=>(~tall(X)<~>~quiet(X))))&
(![X]:((funny(X)|~patient(X))=>(curious(X)|~generous(X))))&
(![X]:(tall(X)<=>funny(X)))&
(![X]:((~tall(X)<~>funny(X))=>humble(X)))&
((?[X]:((strong(X)<~>~calm(X))))<=>((~brave(john)<~>~old(john))))&
((tall(paul))<=>(?[X]:((~brave(X)<~>curious(X)))))&
((?[X]:((tall(X)|calm(X))))=>(?[X]:((happy(X)&~wise(X)))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~strong(X)|~curious(X))=>brave(X)))&
((?[X]:((~happy(X)&curious(X))))<=>((strong(paul)<~>wise(paul))))&
(![X]:(~patient(X)=>(wise(X)&~old(X))))&
(![X]:((humble(X)<~>~generous(X))<=>(~patient(X)&~happy(X))))&
(((~creative(alice)&~old(alice)))<=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:((~wise(X)<~>~generous(X))<=>(~wise(X)|creative(X))))&
((?[X]:(wise(X)))<=>(~calm(lucy)))&
(![X]:((generous(X)|~rich(X))=>(~tall(X)|generous(X))))&
((~strong(fred)|~humble(fred)))&
(?[X]:((~old(X)&wise(X))))&
(?[X]:((~generous(X)<~>happy(X))))&
((~brave(john)&strong(john)))&
((~generous(paul)|creative(paul))) | funny(lucy) | [
"p2",
"p3",
"p6",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2244080631201740744172485
% SZS output start Proof for 2244080631201740744172485
3. ! [X0] : (tall(X0) <=> funny(X0)) [input p2]
4. ! [X0] : ((~tall(X0) <~> funny(X0)) => humble(X0)) [input p3]
7. ? [X0] : (calm(X0) | tall(X0)) => ? [X0] : (~wise(X0) & happy(X0)) [input p6]
11. ! [X0] : (~patient(X0) => (~old(X0) & wise(X0))) [input p10]
12. ! [X0] : ((humble(X0) <~> ~generous(X0)) <=> (~happy(X0) & ~patient(X0))) [input p11]
14. ! [X0] : ((~wise(X0) <~> ~generous(X0)) <=> (creative(X0) | ~wise(X0))) [input p13]
22. funny(lucy) [input hypothesis]
23. ? [X0] : (calm(X0) | tall(X0)) => ? [X1] : (~wise(X1) & happy(X1)) [rectify 7]
29. ! [X0] : (humble(X0) | (~tall(X0) <=> funny(X0))) [ennf transformation 4]
30. ? [X1] : (~wise(X1) & happy(X1)) | ! [X0] : (~calm(X0) & ~tall(X0)) [ennf transformation 23]
32. ! [X0] : ((~old(X0) & wise(X0)) | patient(X0)) [ennf transformation 11]
36. ! [X0] : ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))) [nnf transformation 3]
37. ! [X0] : (humble(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) [nnf transformation 29]
46. ? [X0] : (~wise(X0) & happy(X0)) | ! [X1] : (~calm(X1) & ~tall(X1)) [rectify 30]
47. ? [X0] : (~wise(X0) & happy(X0)) => (~wise(sK2) & happy(sK2)) [choice axiom]
48. (~wise(sK2) & happy(sK2)) | ! [X1] : (~calm(X1) & ~tall(X1)) [skolemisation 46,47]
58. ! [X0] : ((((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | (happy(X0) | patient(X0))) & ((~happy(X0) & ~patient(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))))) [nnf transformation 12]
59. ! [X0] : ((((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | happy(X0) | patient(X0)) & ((~happy(X0) & ~patient(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))))) [flattening 58]
65. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (~creative(X0) & wise(X0))) & ((creative(X0) | ~wise(X0)) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [nnf transformation 14]
66. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (~creative(X0) & wise(X0))) & (creative(X0) | ~wise(X0) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [flattening 65]
82. ~tall(X0) | funny(X0) [cnf transformation 36]
83. ~funny(X0) | tall(X0) [cnf transformation 36]
84. humble(X0) | funny(X0) | tall(X0) [cnf transformation 37]
85. humble(X0) | ~tall(X0) | ~funny(X0) [cnf transformation 37]
100. ~wise(sK2) | ~tall(X1) [cnf transformation 48]
118. patient(X0) | wise(X0) [cnf transformation 32]
120. ~patient(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 59]
136. generous(X0) | wise(X0) | wise(X0) [cnf transformation 66]
149. funny(lucy) [cnf transformation 22]
151. generous(X0) | wise(X0) [duplicate literal removal 136]
152. ~funny(X0) | humble(X0) [subsumption resolution 85,83]
153. humble(X0) | funny(X0) [subsumption resolution 84,82]
154. humble(X0) [subsumption resolution 153,152]
211. 13 <=> wise(sK2) [avatar definition]
213. ~wise(sK2) <- (~13) [avatar component clause 211]
216. 14 <=> ! [X1] : ~tall(X1) [avatar definition]
217. ~tall(X1) <- (14) [avatar component clause 216]
218. 14 | ~13 [avatar split clause 100,211,216]
289. ~generous(X0) | ~patient(X0) [subsumption resolution 120,154]
342. tall(lucy) [resolution 83,149]
343. $false <- (14) [subsumption resolution 342,217]
344. ~14 [avatar contradiction clause 343]
357. ~patient(X0) | wise(X0) [resolution 289,151]
358. wise(X0) [subsumption resolution 357,118]
362. $false <- (~13) [resolution 358,213]
363. 13 [avatar contradiction clause 362]
364. $false [avatar sat refutation 218,344,363]
% SZS output end Proof for 2244080631201740744172485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or humble is quiet. Everyone who is not calm is not humble. If paul is both humble and not strong then someone is either not curious or wise. If someone is either happy or not kind then someone is patient or strong and vice versa. Everyone who is either humble or old is both not funny and humble and vice versa. Everyone who is not quiet is funny and vice versa. Everyone who is not kind is brave and vice versa. Everyone who is either not generous or calm is quiet or rich. Everyone who is not rich or not kind is calm or not rich and vice versa. If someone is either creative or calm then mary is either not funny or generous. If john is not happy or kind then someone is both patient and quiet and vice versa. If someone is either creative or wise then mary is either not humble or not tall. Everyone who is both funny and not strong is both not generous and creative and vice versa. Everyone who is not humble or not old is humble. If someone is not old or brave then someone is not old or patient and vice versa. Everyone who is both rich and not old is generous or creative and vice versa. Lucy is either rich or calm. Someone is both kind and not generous. Mary is not wise. Someone is either not strong or not generous. John is both brave and tall. Someone is both rich and not kind. | John is not humble. | contradiction | (![X]:((calm(X)|humble(X))=>quiet(X)))&
(![X]:(~calm(X)=>~humble(X)))&
(((humble(paul)&~strong(paul)))=>(?[X]:((~curious(X)<~>wise(X)))))&
((?[X]:((happy(X)<~>~kind(X))))<=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((humble(X)<~>old(X))<=>(~funny(X)&humble(X))))&
(![X]:(~quiet(X)<=>funny(X)))&
(![X]:(~kind(X)<=>brave(X)))&
(![X]:((~generous(X)<~>calm(X))=>(quiet(X)|rich(X))))&
(![X]:((~rich(X)|~kind(X))<=>(calm(X)|~rich(X))))&
((?[X]:((creative(X)<~>calm(X))))=>((~funny(mary)<~>generous(mary))))&
(((~happy(john)|kind(john)))<=>(?[X]:((patient(X)&quiet(X)))))&
((?[X]:((creative(X)<~>wise(X))))=>((~humble(mary)<~>~tall(mary))))&
(![X]:((funny(X)&~strong(X))<=>(~generous(X)&creative(X))))&
(![X]:((~humble(X)|~old(X))=>humble(X)))&
((?[X]:((~old(X)|brave(X))))<=>(?[X]:((~old(X)|patient(X)))))&
(![X]:((rich(X)&~old(X))<=>(generous(X)|creative(X))))&
((rich(lucy)<~>calm(lucy)))&
(?[X]:((kind(X)&~generous(X))))&
(~wise(mary))&
(?[X]:((~strong(X)<~>~generous(X))))&
((brave(john)&tall(john)))&
(?[X]:((rich(X)&~kind(X)))) | ~humble(john) | [
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7076992654409237587128783
% SZS output start Proof for 7076992654409237587128783
5. ! [X0] : ((humble(X0) <~> old(X0)) <=> (humble(X0) & ~funny(X0))) [input p4]
14. ! [X0] : ((~old(X0) | ~humble(X0)) => humble(X0)) [input p13]
23. ~humble(john) [input hypothesis]
34. ! [X0] : (humble(X0) | (old(X0) & humble(X0))) [ennf transformation 14]
43. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~humble(X0) | funny(X0))) & ((humble(X0) & ~funny(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 5]
44. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | ~humble(X0) | funny(X0)) & ((humble(X0) & ~funny(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 43]
88. humble(X0) | humble(X0) | ~old(X0) [cnf transformation 44]
119. humble(X0) | old(X0) [cnf transformation 34]
140. ~humble(john) [cnf transformation 23]
142. humble(X0) | ~old(X0) [duplicate literal removal 88]
257. humble(X0) [subsumption resolution 119,142]
304. $false [subsumption resolution 140,257]
% SZS output end Proof for 7076992654409237587128783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not creative then alice is not humble.
Everyone who is both not kind and humble is not funny or not generous.
If someone is not tall or generous then someone is both kind and not old and vice versa.
Everyone who is both brave and kind is not humble or strong and vice versa.
Everyone who is both rich and not kind is either not happy or not calm and vice versa.
Everyone who is tall is curious and vice versa.
If someone is both wise and not funny then someone is humble or rich.
If john is either quiet or old then someone is rich and vice versa.
Everyone who is both rich and not tall is both not generous and patient.
If mary is both not old and wise then someone is happy and vice versa.
Everyone who is both not old and not generous is either not rich or not kind and vice versa.
If fred is funny then alice is both not rich and not generous.
Everyone who is humble or not creative is both happy and rich.
Everyone who is both not strong and funny is either not calm or patient.
If someone is either not funny or not curious then someone is quiet or not curious.
Everyone who is strong or rich is both generous and not wise and vice versa.
Someone is wise or patient.
Someone is quiet.
Someone is either happy or rich.
Lucy is curious or wise.
Alice is both quiet and not rich.
Mary is both brave and curious.
Fred is not wise.
Someone is either not humble or not curious. | Alice is old. | contradiction | (((~wise(mary)&~creative(mary)))=>(~humble(alice)))&
(![X]:((~kind(X)&humble(X))=>(~funny(X)|~generous(X))))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((brave(X)&kind(X))<=>(~humble(X)|strong(X))))&
(![X]:((rich(X)&~kind(X))<=>(~happy(X)<~>~calm(X))))&
(![X]:(tall(X)<=>curious(X)))&
((?[X]:((wise(X)&~funny(X))))=>(?[X]:((humble(X)|rich(X)))))&
(((quiet(john)<~>old(john)))<=>(?[X]:(rich(X))))&
(![X]:((rich(X)&~tall(X))=>(~generous(X)&patient(X))))&
(((~old(mary)&wise(mary)))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)&~generous(X))<=>(~rich(X)<~>~kind(X))))&
((funny(fred))=>((~rich(alice)&~generous(alice))))&
(![X]:((humble(X)|~creative(X))=>(happy(X)&rich(X))))&
(![X]:((~strong(X)&funny(X))=>(~calm(X)<~>patient(X))))&
((?[X]:((~funny(X)<~>~curious(X))))=>(?[X]:((quiet(X)|~curious(X)))))&
(![X]:((strong(X)|rich(X))<=>(generous(X)&~wise(X))))&
(?[X]:((wise(X)|patient(X))))&
(?[X]:(quiet(X)))&
(?[X]:((happy(X)<~>rich(X))))&
((curious(lucy)|wise(lucy)))&
((quiet(alice)&~rich(alice)))&
((brave(mary)&curious(mary)))&
(~wise(fred))&
(?[X]:((~humble(X)<~>~curious(X)))) | old(alice) | [
"p3",
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 620382944058196565535238
% SZS output start Proof for 620382944058196565535238
4. ! [X0] : ((kind(X0) & brave(X0)) <=> (strong(X0) | ~humble(X0))) [input p3]
11. ! [X0] : ((~generous(X0) & ~old(X0)) <=> (~rich(X0) <~> ~kind(X0))) [input p10]
13. ! [X0] : ((~creative(X0) | humble(X0)) => (rich(X0) & happy(X0))) [input p12]
21. ~rich(alice) & quiet(alice) [input p20]
25. old(alice) [input hypothesis]
30. ! [X0] : (humble(X0) => (rich(X0) & happy(X0))) [pure predicate removal 13]
37. ! [X0] : ((rich(X0) & happy(X0)) | ~humble(X0)) [ennf transformation 30]
46. ! [X0] : (((kind(X0) & brave(X0)) | (~strong(X0) & humble(X0))) & ((strong(X0) | ~humble(X0)) | (~kind(X0) | ~brave(X0)))) [nnf transformation 4]
47. ! [X0] : (((kind(X0) & brave(X0)) | (~strong(X0) & humble(X0))) & (strong(X0) | ~humble(X0) | ~kind(X0) | ~brave(X0))) [flattening 46]
63. ! [X0] : (((~generous(X0) & ~old(X0)) | ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0)))) & (((kind(X0) | rich(X0)) & (~kind(X0) | ~rich(X0))) | (generous(X0) | old(X0)))) [nnf transformation 11]
64. ! [X0] : (((~generous(X0) & ~old(X0)) | ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0)))) & (((kind(X0) | rich(X0)) & (~kind(X0) | ~rich(X0))) | generous(X0) | old(X0))) [flattening 63]
91. kind(X0) | humble(X0) [cnf transformation 47]
113. ~old(X0) | ~kind(X0) | rich(X0) [cnf transformation 64]
120. ~humble(X0) | rich(X0) [cnf transformation 37]
136. ~rich(alice) [cnf transformation 21]
142. old(alice) [cnf transformation 25]
232. 21 <=> rich(alice) [avatar definition]
234. ~rich(alice) <- (~21) [avatar component clause 232]
280. ~21 [avatar split clause 136,232]
356. ~kind(alice) | rich(alice) [resolution 113,142]
357. ~kind(alice) <- (~21) [subsumption resolution 356,234]
358. humble(alice) <- (~21) [resolution 357,91]
524. rich(alice) <- (~21) [resolution 358,120]
526. $false <- (~21) [subsumption resolution 524,234]
527. 21 [avatar contradiction clause 526]
530. $false [avatar sat refutation 280,527]
% SZS output end Proof for 620382944058196565535238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or curious then mary is both not creative and creative. Everyone who is not humble or not tall is both generous and strong and vice versa. Everyone who is either not calm or not generous is either not kind or brave. Everyone who is either happy or not rich is both not brave and not strong. Everyone who is both not rich and not quiet is curious and vice versa. Everyone who is either happy or humble is brave. If fred is both not rich and tall then someone is quiet or not patient and vice versa. If someone is both not curious and not strong then someone is happy or not quiet. Everyone who is not funny or generous is not kind and vice versa. Everyone who is both not brave and wise is happy and vice versa. If lucy is curious then john is patient or not old. Everyone who is creative is either strong or not happy. If lucy is creative or not funny then fred is either creative or not generous and vice versa. Everyone who is not creative is rich and vice versa. Everyone who is not rich is both not strong and not patient and vice versa. If paul is quiet then someone is both not generous and quiet. Paul is rich. John is kind. Someone is not funny or funny. | Lucy is happy. | entailment | ((?[X]:((~happy(X)<~>curious(X))))=>((~creative(mary)&creative(mary))))&
(![X]:((~humble(X)|~tall(X))<=>(generous(X)&strong(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~kind(X)<~>brave(X))))&
(![X]:((happy(X)<~>~rich(X))=>(~brave(X)&~strong(X))))&
(![X]:((~rich(X)&~quiet(X))<=>curious(X)))&
(![X]:((happy(X)<~>humble(X))=>brave(X)))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)|~patient(X)))))&
((?[X]:((~curious(X)&~strong(X))))=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:((~funny(X)|generous(X))<=>~kind(X)))&
(![X]:((~brave(X)&wise(X))<=>happy(X)))&
((curious(lucy))=>((patient(john)|~old(john))))&
(![X]:(creative(X)=>(strong(X)<~>~happy(X))))&
(((creative(lucy)|~funny(lucy)))<=>((creative(fred)<~>~generous(fred))))&
(![X]:(~creative(X)<=>rich(X)))&
(![X]:(~rich(X)<=>(~strong(X)&~patient(X))))&
((quiet(paul))=>(?[X]:((~generous(X)&quiet(X)))))&
(rich(paul))&
(kind(john))&
(?[X]:((~funny(X)|funny(X)))) | happy(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8320627545426244381615545
% SZS output start Proof for 8320627545426244381615545
1. ? [X0] : (~happy(X0) <~> curious(X0)) => (creative(mary) & ~creative(mary)) [input p0]
2. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (strong(X0) & generous(X0))) [input p1]
4. ! [X0] : ((happy(X0) <~> ~rich(X0)) => (~strong(X0) & ~brave(X0))) [input p3]
5. ! [X0] : ((~quiet(X0) & ~rich(X0)) <=> curious(X0)) [input p4]
6. ! [X0] : ((happy(X0) <~> humble(X0)) => brave(X0)) [input p5]
7. (tall(fred) & ~rich(fred)) <=> ? [X0] : (~patient(X0) | quiet(X0)) [input p6]
12. ! [X0] : (creative(X0) => (strong(X0) <~> ~happy(X0))) [input p11]
14. ! [X0] : (~creative(X0) <=> rich(X0)) [input p13]
15. ! [X0] : (~rich(X0) <=> (~patient(X0) & ~strong(X0))) [input p14]
20. ~happy(lucy) [input hypothesis]
23. (creative(mary) & ~creative(mary)) | ! [X0] : (~happy(X0) <=> curious(X0)) [ennf transformation 1]
25. ! [X0] : ((~strong(X0) & ~brave(X0)) | (happy(X0) <=> ~rich(X0))) [ennf transformation 4]
26. ! [X0] : (brave(X0) | (happy(X0) <=> humble(X0))) [ennf transformation 6]
28. ! [X0] : ((strong(X0) <~> ~happy(X0)) | ~creative(X0)) [ennf transformation 12]
30. (creative(mary) & ~creative(mary)) | ! [X0] : ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))) [nnf transformation 23]
31. ! [X0] : (((~tall(X0) | ~humble(X0)) | (~strong(X0) | ~generous(X0))) & ((strong(X0) & generous(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 2]
32. ! [X0] : ((~tall(X0) | ~humble(X0) | ~strong(X0) | ~generous(X0)) & ((strong(X0) & generous(X0)) | (tall(X0) & humble(X0)))) [flattening 31]
34. ! [X0] : ((~strong(X0) & ~brave(X0)) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) [nnf transformation 25]
35. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | (quiet(X0) | rich(X0)))) [nnf transformation 5]
36. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | quiet(X0) | rich(X0))) [flattening 35]
37. ! [X0] : (brave(X0) | ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0)))) [nnf transformation 26]
38. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X0] : (~patient(X0) | quiet(X0)) | (~tall(fred) | rich(fred))) [nnf transformation 7]
39. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X0] : (~patient(X0) | quiet(X0)) | ~tall(fred) | rich(fred)) [flattening 38]
40. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X1] : (~patient(X1) | quiet(X1)) | ~tall(fred) | rich(fred)) [rectify 39]
41. ? [X1] : (~patient(X1) | quiet(X1)) => (~patient(sK0) | quiet(sK0)) [choice axiom]
42. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & ((~patient(sK0) | quiet(sK0)) | ~tall(fred) | rich(fred)) [skolemisation 40,41]
50. ! [X0] : (((happy(X0) | ~strong(X0)) & (~happy(X0) | strong(X0))) | ~creative(X0)) [nnf transformation 28]
53. ! [X0] : ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0))) [nnf transformation 14]
54. ! [X0] : ((~rich(X0) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | rich(X0))) [nnf transformation 15]
55. ! [X0] : ((~rich(X0) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | rich(X0))) [flattening 54]
60. ~creative(mary) | curious(X0) | happy(X0) [cnf transformation 30]
62. creative(mary) | curious(X0) | happy(X0) [cnf transformation 30]
66. strong(X0) | humble(X0) [cnf transformation 32]
74. ~brave(X0) | happy(X0) | rich(X0) [cnf transformation 34]
78. ~rich(X0) | ~curious(X0) [cnf transformation 36]
81. ~humble(X0) | happy(X0) | brave(X0) [cnf transformation 37]
84. ~rich(fred) | patient(X0) [cnf transformation 42]
94. ~creative(X0) | strong(X0) | ~happy(X0) [cnf transformation 50]
102. rich(X0) | creative(X0) [cnf transformation 53]
104. ~strong(X0) | rich(X0) [cnf transformation 55]
105. ~patient(X0) | rich(X0) [cnf transformation 55]
112. ~happy(lucy) [cnf transformation 20]
117. 2 <=> creative(mary) [avatar definition]
122. 3 <=> ! [X0] : (curious(X0) | happy(X0)) [avatar definition]
123. curious(X0) | happy(X0) <- (3) [avatar component clause 122]
124. 3 | 2 [avatar split clause 62,117,122]
126. 3 | ~2 [avatar split clause 60,117,122]
128. 4 <=> ! [X0] : patient(X0) [avatar definition]
129. patient(X0) <- (4) [avatar component clause 128]
140. 7 <=> rich(fred) [avatar definition]
142. ~rich(fred) <- (~7) [avatar component clause 140]
143. 4 | ~7 [avatar split clause 84,140,128]
171. 14 <=> creative(fred) [avatar definition]
172. ~creative(fred) <- (~14) [avatar component clause 171]
173. creative(fred) <- (14) [avatar component clause 171]
209. creative(fred) <- (~7) [resolution 102,142]
211. $false <- (~7, ~14) [subsumption resolution 209,172]
212. 7 | 14 [avatar contradiction clause 211]
220. rich(X1) | humble(X1) [resolution 104,66]
221. rich(X0) <- (4) [resolution 105,129]
223. ~curious(X1) <- (4) [resolution 221,78]
227. happy(X0) <- (3, 4) [resolution 223,123]
255. $false <- (3, 4) [resolution 227,112]
258. ~3 | ~4 [avatar contradiction clause 255]
305. strong(fred) | ~happy(fred) <- (14) [resolution 94,173]
307. 26 <=> happy(fred) [avatar definition]
309. ~happy(fred) <- (~26) [avatar component clause 307]
311. 27 <=> strong(fred) [avatar definition]
313. strong(fred) <- (27) [avatar component clause 311]
314. ~26 | 27 | ~14 [avatar split clause 305,171,311,307]
378. humble(fred) <- (~7) [resolution 220,142]
380. happy(fred) | brave(fred) <- (~7) [resolution 378,81]
381. brave(fred) <- (~7, ~26) [subsumption resolution 380,309]
482. happy(fred) | rich(fred) <- (~7, ~26) [resolution 381,74]
494. rich(fred) <- (~7, ~26) [subsumption resolution 482,309]
495. $false <- (~7, ~26) [subsumption resolution 494,142]
496. 7 | 26 [avatar contradiction clause 495]
508. rich(fred) <- (27) [resolution 313,104]
513. $false <- (~7, 27) [subsumption resolution 508,142]
514. 7 | ~27 [avatar contradiction clause 513]
515. $false [avatar sat refutation 124,126,143,212,258,314,496,514]
% SZS output end Proof for 8320627545426244381615545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or tall is both kind and old and vice versa.
If paul is either not old or humble then someone is not strong.
Everyone who is not patient or not tall is either not kind or calm and vice versa.
If someone is either not old or kind then someone is both wise and not wise.
Everyone who is either not strong or not creative is either not curious or rich.
If someone is both patient and tall then paul is not humble or not curious.
If john is either wise or not generous then someone is kind or curious.
If someone is both not wise and not happy then someone is tall and vice versa.
Everyone who is both happy and not creative is either not happy or rich.
Everyone who is either rich or humble is both happy and rich and vice versa.
Everyone who is old or creative is both not calm and not strong.
Everyone who is either strong or not generous is either not old or kind and vice versa.
Everyone who is funny is both not wise and happy and vice versa.
If john is either not quiet or not kind then lucy is either wise or not humble and vice versa.
If someone is happy then fred is humble and vice versa.
Someone is creative or strong.
Someone is either wise or happy.
Someone is both not brave and not curious. | Fred is quiet. | neutral | (![X]:((~strong(X)|tall(X))<=>(kind(X)&old(X))))&
(((~old(paul)<~>humble(paul)))=>(?[X]:(~strong(X))))&
(![X]:((~patient(X)|~tall(X))<=>(~kind(X)<~>calm(X))))&
((?[X]:((~old(X)<~>kind(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~strong(X)<~>~creative(X))=>(~curious(X)<~>rich(X))))&
((?[X]:((patient(X)&tall(X))))=>((~humble(paul)|~curious(paul))))&
(((wise(john)<~>~generous(john)))=>(?[X]:((kind(X)|curious(X)))))&
((?[X]:((~wise(X)&~happy(X))))<=>(?[X]:(tall(X))))&
(![X]:((happy(X)&~creative(X))=>(~happy(X)<~>rich(X))))&
(![X]:((rich(X)<~>humble(X))<=>(happy(X)&rich(X))))&
(![X]:((old(X)|creative(X))=>(~calm(X)&~strong(X))))&
(![X]:((strong(X)<~>~generous(X))<=>(~old(X)<~>kind(X))))&
(![X]:(funny(X)<=>(~wise(X)&happy(X))))&
(((~quiet(john)<~>~kind(john)))<=>((wise(lucy)<~>~humble(lucy))))&
((?[X]:(happy(X)))<=>(humble(fred)))&
(?[X]:((creative(X)|strong(X))))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:((~brave(X)&~curious(X)))) | quiet(fred) | [] | null | 0 |
Everyone who is not strong is generous. Everyone who is calm or patient is either not creative or not strong. Everyone who is not humble is not calm or old. If someone is generous or not quiet then someone is both tall and happy. If someone is either not brave or calm then lucy is humble or curious. If john is not strong then john is rich or old and vice versa. Everyone who is both not funny and old is not creative and vice versa. If someone is either quiet or not strong then john is either not kind or kind. Everyone who is both not calm and not curious is both not creative and patient. Everyone who is not happy is both curious and not generous and vice versa. If lucy is creative or curious then alice is both patient and not old and vice versa. Everyone who is either not curious or creative is patient or not funny and vice versa. Everyone who is both curious and happy is not old or rich and vice versa. Everyone who is creative is not strong and vice versa. If alice is either tall or not funny then someone is either not strong or patient and vice versa. If someone is kind or not happy then someone is either not humble or not rich. Someone is either kind or not patient. Someone is brave. Someone is both not strong and not funny. Someone is both brave and not strong. Someone is happy. Fred is either curious or not patient. Mary is either happy or not creative. | Alice is tall. | neutral | (![X]:(~strong(X)=>generous(X)))&
(![X]:((calm(X)|patient(X))=>(~creative(X)<~>~strong(X))))&
(![X]:(~humble(X)=>(~calm(X)|old(X))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((tall(X)&happy(X)))))&
((?[X]:((~brave(X)<~>calm(X))))=>((humble(lucy)|curious(lucy))))&
((~strong(john))<=>((rich(john)|old(john))))&
(![X]:((~funny(X)&old(X))<=>~creative(X)))&
((?[X]:((quiet(X)<~>~strong(X))))=>((~kind(john)<~>kind(john))))&
(![X]:((~calm(X)&~curious(X))=>(~creative(X)&patient(X))))&
(![X]:(~happy(X)<=>(curious(X)&~generous(X))))&
(((creative(lucy)|curious(lucy)))<=>((patient(alice)&~old(alice))))&
(![X]:((~curious(X)<~>creative(X))<=>(patient(X)|~funny(X))))&
(![X]:((curious(X)&happy(X))<=>(~old(X)|rich(X))))&
(![X]:(creative(X)<=>~strong(X)))&
(((tall(alice)<~>~funny(alice)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
((?[X]:((kind(X)|~happy(X))))=>(?[X]:((~humble(X)<~>~rich(X)))))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:(brave(X)))&
(?[X]:((~strong(X)&~funny(X))))&
(?[X]:((brave(X)&~strong(X))))&
(?[X]:(happy(X)))&
((curious(fred)<~>~patient(fred)))&
((happy(mary)<~>~creative(mary))) | tall(alice) | [] | null | 0 |
Everyone who is either kind or not brave is both not kind and kind and vice versa.
If someone is either calm or tall then someone is funny and vice versa.
Everyone who is not calm or quiet is both not wise and not generous.
If susan is not calm then someone is both not humble and not rich.
Everyone who is both not patient and not humble is not old or curious.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
Everyone who is generous is generous or not kind and vice versa.
If someone is both kind and quiet then someone is strong or not old.
Someone is not rich or not funny.
Lucy is either rich or happy.
Mary is not quiet.
Fred is either rich or curious.
Mary is both tall and not humble.
Someone is either not quiet or not creative. | Susan is rich. | neutral | (![X]:((kind(X)<~>~brave(X))<=>(~kind(X)&kind(X))))&
((?[X]:((calm(X)<~>tall(X))))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)|quiet(X))=>(~wise(X)&~generous(X))))&
((~calm(susan))=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((~patient(X)&~humble(X))=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(?[X]:((~rich(X)|~funny(X))))&
((rich(lucy)<~>happy(lucy)))&
(~quiet(mary))&
((rich(fred)<~>curious(fred)))&
((tall(mary)&~humble(mary)))&
(?[X]:((~quiet(X)<~>~creative(X)))) | rich(susan) | [] | null | 0 |
Everyone who is either kind or not calm is not funny or not kind and vice versa.
Everyone who is both calm and not patient is rich or wise and vice versa.
Everyone who is funny or generous is happy and vice versa.
If someone is not curious or curious then someone is not quiet.
Everyone who is not wise is either tall or wise.
Everyone who is quiet is not patient or rich.
Everyone who is both not kind and kind is both calm and curious.
Everyone who is not humble is brave.
Everyone who is both strong and humble is both not patient and curious.
Everyone who is not funny is both not quiet and not curious.
If lucy is both not brave and old then someone is not humble or not old.
Everyone who is either not patient or not rich is both funny and not brave.
If alice is not strong or not funny then someone is not strong.
Everyone who is not tall or quiet is both brave and happy.
If paul is not patient then alice is either not kind or not tall.
If alice is brave or funny then someone is both not wise and rich and vice versa.
Someone is brave or not calm.
Susan is tall.
Someone is not old or not kind.
Mary is both not quiet and kind.
Someone is either not funny or rich.
Someone is not tall or old.
Paul is curious.
Someone is both not old and not wise. | Susan is strong. | neutral | (![X]:((kind(X)<~>~calm(X))<=>(~funny(X)|~kind(X))))&
(![X]:((calm(X)&~patient(X))<=>(rich(X)|wise(X))))&
(![X]:((funny(X)|generous(X))<=>happy(X)))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:(~quiet(X))))&
(![X]:(~wise(X)=>(tall(X)<~>wise(X))))&
(![X]:(quiet(X)=>(~patient(X)|rich(X))))&
(![X]:((~kind(X)&kind(X))=>(calm(X)&curious(X))))&
(![X]:(~humble(X)=>brave(X)))&
(![X]:((strong(X)&humble(X))=>(~patient(X)&curious(X))))&
(![X]:(~funny(X)=>(~quiet(X)&~curious(X))))&
(((~brave(lucy)&old(lucy)))=>(?[X]:((~humble(X)|~old(X)))))&
(![X]:((~patient(X)<~>~rich(X))=>(funny(X)&~brave(X))))&
(((~strong(alice)|~funny(alice)))=>(?[X]:(~strong(X))))&
(![X]:((~tall(X)|quiet(X))=>(brave(X)&happy(X))))&
((~patient(paul))=>((~kind(alice)<~>~tall(alice))))&
(((brave(alice)|funny(alice)))<=>(?[X]:((~wise(X)&rich(X)))))&
(?[X]:((brave(X)|~calm(X))))&
(tall(susan))&
(?[X]:((~old(X)|~kind(X))))&
((~quiet(mary)&kind(mary)))&
(?[X]:((~funny(X)<~>rich(X))))&
(?[X]:((~tall(X)|old(X))))&
(curious(paul))&
(?[X]:((~old(X)&~wise(X)))) | strong(susan) | [] | null | 0 |
Everyone who is either tall or happy is not wise or rich and vice versa.
If susan is either quiet or generous then someone is both not generous and not strong and vice versa.
Everyone who is quiet or rich is not creative.
If alice is either tall or not happy then alice is both not patient and strong.
Everyone who is not happy is both patient and not kind.
Everyone who is not generous or not curious is not brave or wise.
Everyone who is not happy or not curious is both happy and not strong.
If alice is either calm or quiet then paul is both rich and not creative.
If someone is both happy and kind then someone is both not funny and not creative.
Everyone who is either wise or patient is both generous and funny.
Everyone who is not old is both not quiet and brave and vice versa.
Everyone who is both creative and funny is not humble or not rich.
Everyone who is not humble or kind is both generous and not brave and vice versa.
Everyone who is creative is not wise.
Everyone who is both not quiet and rich is both not tall and rich and vice versa.
If someone is both tall and not kind then john is brave.
Fred is both happy and strong.
Someone is not old or humble.
Someone is both not patient and tall.
Alice is both not rich and generous.
Someone is both curious and not funny.
Someone is happy or not old.
John is both patient and funny. | Alice is not humble. | neutral | (![X]:((tall(X)<~>happy(X))<=>(~wise(X)|rich(X))))&
(((quiet(susan)<~>generous(susan)))<=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:((quiet(X)|rich(X))=>~creative(X)))&
(((tall(alice)<~>~happy(alice)))=>((~patient(alice)&strong(alice))))&
(![X]:(~happy(X)=>(patient(X)&~kind(X))))&
(![X]:((~generous(X)|~curious(X))=>(~brave(X)|wise(X))))&
(![X]:((~happy(X)|~curious(X))=>(happy(X)&~strong(X))))&
(((calm(alice)<~>quiet(alice)))=>((rich(paul)&~creative(paul))))&
((?[X]:((happy(X)&kind(X))))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:((wise(X)<~>patient(X))=>(generous(X)&funny(X))))&
(![X]:(~old(X)<=>(~quiet(X)&brave(X))))&
(![X]:((creative(X)&funny(X))=>(~humble(X)|~rich(X))))&
(![X]:((~humble(X)|kind(X))<=>(generous(X)&~brave(X))))&
(![X]:(creative(X)=>~wise(X)))&
(![X]:((~quiet(X)&rich(X))<=>(~tall(X)&rich(X))))&
((?[X]:((tall(X)&~kind(X))))=>(brave(john)))&
((happy(fred)&strong(fred)))&
(?[X]:((~old(X)|humble(X))))&
(?[X]:((~patient(X)&tall(X))))&
((~rich(alice)&generous(alice)))&
(?[X]:((curious(X)&~funny(X))))&
(?[X]:((happy(X)|~old(X))))&
((patient(john)&funny(john))) | ~humble(alice) | [] | null | 0 |
If fred is either creative or wise then someone is kind.
Everyone who is strong is not creative or creative and vice versa.
Everyone who is not kind is both quiet and strong.
If susan is funny then alice is humble or curious.
If mary is old or humble then susan is both not humble and not creative and vice versa.
If john is both happy and patient then mary is either not patient or not tall.
If someone is either not curious or funny then alice is both not patient and creative.
If someone is not funny or generous then someone is both happy and not generous.
If someone is not generous or not brave then someone is not curious.
If john is either humble or strong then john is either curious or tall and vice versa.
If someone is not creative or not calm then someone is either wise or not quiet.
Everyone who is not quiet or rich is both happy and kind.
If fred is both not tall and tall then someone is both not happy and generous.
Everyone who is not brave is both not patient and not happy.
Everyone who is both not strong and quiet is not calm and vice versa.
If someone is brave then someone is both not tall and tall.
Someone is not generous.
Fred is not curious.
John is curious.
Someone is not generous or curious.
Mary is both tall and not humble.
Someone is either creative or strong. | Mary is not patient. | entailment | (((creative(fred)<~>wise(fred)))=>(?[X]:(kind(X))))&
(![X]:(strong(X)<=>(~creative(X)|creative(X))))&
(![X]:(~kind(X)=>(quiet(X)&strong(X))))&
((funny(susan))=>((humble(alice)|curious(alice))))&
(((old(mary)|humble(mary)))<=>((~humble(susan)&~creative(susan))))&
(((happy(john)&patient(john)))=>((~patient(mary)<~>~tall(mary))))&
((?[X]:((~curious(X)<~>funny(X))))=>((~patient(alice)&creative(alice))))&
((?[X]:((~funny(X)|generous(X))))=>(?[X]:((happy(X)&~generous(X)))))&
((?[X]:((~generous(X)|~brave(X))))=>(?[X]:(~curious(X))))&
(((humble(john)<~>strong(john)))<=>((curious(john)<~>tall(john))))&
((?[X]:((~creative(X)|~calm(X))))=>(?[X]:((wise(X)<~>~quiet(X)))))&
(![X]:((~quiet(X)|rich(X))=>(happy(X)&kind(X))))&
(((~tall(fred)&tall(fred)))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:(~brave(X)=>(~patient(X)&~happy(X))))&
(![X]:((~strong(X)&quiet(X))<=>~calm(X)))&
((?[X]:(brave(X)))=>(?[X]:((~tall(X)&tall(X)))))&
(?[X]:(~generous(X)))&
(~curious(fred))&
(curious(john))&
(?[X]:((~generous(X)|curious(X))))&
((tall(mary)&~humble(mary)))&
(?[X]:((creative(X)<~>strong(X)))) | ~patient(mary) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5835532576304947879297108
% SZS output start Proof for 5835532576304947879297108
14. ! [X0] : (~brave(X0) => (~happy(X0) & ~patient(X0))) [input p13]
16. ? [X0] : brave(X0) => ? [X0] : (tall(X0) & ~tall(X0)) [input p15]
23. patient(mary) [input hypothesis]
27. ? [X0] : brave(X0) => ? [X1] : (tall(X1) & ~tall(X1)) [rectify 16]
44. ! [X0] : ((~happy(X0) & ~patient(X0)) | brave(X0)) [ennf transformation 14]
47. ? [X1] : (tall(X1) & ~tall(X1)) | ! [X0] : ~brave(X0) [ennf transformation 27]
67. ? [X0] : (tall(X0) & ~tall(X0)) | ! [X1] : ~brave(X1) [rectify 47]
68. ? [X0] : (tall(X0) & ~tall(X0)) => (tall(sK4) & ~tall(sK4)) [choice axiom]
69. (tall(sK4) & ~tall(sK4)) | ! [X1] : ~brave(X1) [skolemisation 67,68]
113. ~patient(X0) | brave(X0) [cnf transformation 44]
116. ~tall(sK4) | ~brave(X1) [cnf transformation 69]
117. tall(sK4) | ~brave(X1) [cnf transformation 69]
126. patient(mary) [cnf transformation 23]
171. 10 <=> patient(mary) [avatar definition]
173. patient(mary) <- (10) [avatar component clause 171]
267. 30 <=> ! [X1] : ~brave(X1) [avatar definition]
268. ~brave(X1) <- (30) [avatar component clause 267]
270. 31 <=> tall(sK4) [avatar definition]
273. 30 | 31 [avatar split clause 117,270,267]
274. 30 | ~31 [avatar split clause 116,270,267]
288. 10 [avatar split clause 126,171]
293. brave(mary) <- (10) [resolution 113,173]
294. $false <- (10, 30) [subsumption resolution 293,268]
295. ~10 | ~30 [avatar contradiction clause 294]
296. $false [avatar sat refutation 273,274,288,295]
% SZS output end Proof for 5835532576304947879297108
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not wise then susan is not rich. If fred is either tall or wise then john is not humble. Everyone who is not happy or happy is patient and vice versa. Everyone who is either creative or funny is either not happy or not creative and vice versa. Everyone who is creative is either creative or not quiet. Everyone who is not creative is not funny. Everyone who is calm is both not patient and not happy and vice versa. Everyone who is either creative or old is either not humble or not quiet and vice versa. Everyone who is both not wise and quiet is either not calm or tall. Everyone who is both curious and not quiet is both not creative and not brave and vice versa. Everyone who is both not brave and not funny is not humble. If someone is either not patient or old then john is either wise or not rich and vice versa. If someone is either brave or not kind then alice is both generous and patient and vice versa. If someone is either not patient or happy then someone is generous or strong and vice versa. Everyone who is curious or not creative is not humble or not rich and vice versa. If alice is both wise and not kind then mary is either not strong or not curious. Alice is either not creative or old. Mary is creative. Paul is either curious or rich. John is creative or not creative. Susan is either not calm or not happy. Someone is both not calm and creative. Susan is both not tall and not wise. Fred is either funny or humble. | Susan is calm. | contradiction | ((?[X]:((brave(X)<~>~wise(X))))=>(~rich(susan)))&
(((tall(fred)<~>wise(fred)))=>(~humble(john)))&
(![X]:((~happy(X)|happy(X))<=>patient(X)))&
(![X]:((creative(X)<~>funny(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:(creative(X)=>(creative(X)<~>~quiet(X))))&
(![X]:(~creative(X)=>~funny(X)))&
(![X]:(calm(X)<=>(~patient(X)&~happy(X))))&
(![X]:((creative(X)<~>old(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((~wise(X)&quiet(X))=>(~calm(X)<~>tall(X))))&
(![X]:((curious(X)&~quiet(X))<=>(~creative(X)&~brave(X))))&
(![X]:((~brave(X)&~funny(X))=>~humble(X)))&
((?[X]:((~patient(X)<~>old(X))))<=>((wise(john)<~>~rich(john))))&
((?[X]:((brave(X)<~>~kind(X))))<=>((generous(alice)&patient(alice))))&
((?[X]:((~patient(X)<~>happy(X))))<=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((curious(X)|~creative(X))<=>(~humble(X)|~rich(X))))&
(((wise(alice)&~kind(alice)))=>((~strong(mary)<~>~curious(mary))))&
((~creative(alice)<~>old(alice)))&
(creative(mary))&
((curious(paul)<~>rich(paul)))&
((creative(john)|~creative(john)))&
((~calm(susan)<~>~happy(susan)))&
(?[X]:((~calm(X)&creative(X))))&
((~tall(susan)&~wise(susan)))&
((funny(fred)<~>humble(fred))) | calm(susan) | [
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 420432915407724450482245
% SZS output start Proof for 420432915407724450482245
3. ! [X0] : ((happy(X0) | ~happy(X0)) <=> patient(X0)) [input p2]
7. ! [X0] : (calm(X0) <=> (~happy(X0) & ~patient(X0))) [input p6]
25. calm(susan) [input hypothesis]
39. ! [X0] : (((happy(X0) | ~happy(X0)) | ~patient(X0)) & (patient(X0) | (~happy(X0) & happy(X0)))) [nnf transformation 3]
40. ! [X0] : ((happy(X0) | ~happy(X0) | ~patient(X0)) & (patient(X0) | (~happy(X0) & happy(X0)))) [flattening 39]
43. ! [X0] : ((calm(X0) | (happy(X0) | patient(X0))) & ((~happy(X0) & ~patient(X0)) | ~calm(X0))) [nnf transformation 7]
44. ! [X0] : ((calm(X0) | happy(X0) | patient(X0)) & ((~happy(X0) & ~patient(X0)) | ~calm(X0))) [flattening 43]
76. patient(X0) | happy(X0) [cnf transformation 40]
77. patient(X0) | ~happy(X0) [cnf transformation 40]
90. ~patient(X0) | ~calm(X0) [cnf transformation 44]
148. calm(susan) [cnf transformation 25]
180. patient(X0) [subsumption resolution 76,77]
183. ~calm(X0) [subsumption resolution 90,180]
312. $false [subsumption resolution 148,183]
% SZS output end Proof for 420432915407724450482245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either quiet or rich then someone is both creative and not calm.
Everyone who is either not brave or not strong is either not generous or not rich and vice versa.
Everyone who is either quiet or not wise is not curious or not quiet and vice versa.
Everyone who is calm or patient is both old and not creative.
Everyone who is not quiet or patient is not patient.
Everyone who is funny is wise.
If someone is either not patient or wise then someone is both not quiet and not old.
If mary is both not curious and tall then someone is old or wise and vice versa.
Everyone who is not curious is funny and vice versa.
If someone is both not tall and wise then lucy is either patient or not curious and vice versa.
If someone is both wise and not curious then someone is both not humble and patient.
If someone is generous or wise then someone is either not quiet or wise and vice versa.
If someone is either not creative or patient then mary is both strong and not strong and vice versa.
If someone is not rich then someone is both generous and not wise and vice versa.
Everyone who is not strong or creative is strong and vice versa.
Susan is either brave or tall.
Someone is generous.
Mary is strong.
Someone is either not patient or brave.
Mary is generous or not tall.
Someone is either not tall or calm. | Lucy is not funny. | entailment | ((?[X]:((quiet(X)<~>rich(X))))=>(?[X]:((creative(X)&~calm(X)))))&
(![X]:((~brave(X)<~>~strong(X))<=>(~generous(X)<~>~rich(X))))&
(![X]:((quiet(X)<~>~wise(X))<=>(~curious(X)|~quiet(X))))&
(![X]:((calm(X)|patient(X))=>(old(X)&~creative(X))))&
(![X]:((~quiet(X)|patient(X))=>~patient(X)))&
(![X]:(funny(X)=>wise(X)))&
((?[X]:((~patient(X)<~>wise(X))))=>(?[X]:((~quiet(X)&~old(X)))))&
(((~curious(mary)&tall(mary)))<=>(?[X]:((old(X)|wise(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
((?[X]:((~tall(X)&wise(X))))<=>((patient(lucy)<~>~curious(lucy))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:((~creative(X)<~>patient(X))))<=>((strong(mary)&~strong(mary))))&
((?[X]:(~rich(X)))<=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~strong(X)|creative(X))<=>strong(X)))&
((brave(susan)<~>tall(susan)))&
(?[X]:(generous(X)))&
(strong(mary))&
(?[X]:((~patient(X)<~>brave(X))))&
((generous(mary)|~tall(mary)))&
(?[X]:((~tall(X)<~>calm(X)))) | ~funny(lucy) | [
"p2",
"p4",
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7945644127930848159929500
% SZS output start Proof for 7945644127930848159929500
3. ! [X0] : ((quiet(X0) <~> ~wise(X0)) <=> (~quiet(X0) | ~curious(X0))) [input p2]
5. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~patient(X0)) [input p4]
6. ! [X0] : (funny(X0) => wise(X0)) [input p5]
11. ? [X0] : (~curious(X0) & wise(X0)) => ? [X0] : (patient(X0) & ~humble(X0)) [input p10]
22. funny(lucy) [input hypothesis]
25. ? [X0] : (~curious(X0) & wise(X0)) => ? [X1] : (patient(X1) & ~humble(X1)) [rectify 11]
28. ? [X0] : (~curious(X0) & wise(X0)) => ? [X1] : patient(X1) [pure predicate removal 25]
31. ! [X0] : (~patient(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 5]
32. ! [X0] : (wise(X0) | ~funny(X0)) [ennf transformation 6]
34. ? [X1] : patient(X1) | ! [X0] : (curious(X0) | ~wise(X0)) [ennf transformation 28]
40. ! [X0] : ((((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | (quiet(X0) & curious(X0))) & ((~quiet(X0) | ~curious(X0)) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0))))) [nnf transformation 3]
41. ! [X0] : ((((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | (quiet(X0) & curious(X0))) & (~quiet(X0) | ~curious(X0) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0))))) [flattening 40]
56. ? [X0] : patient(X0) | ! [X1] : (curious(X1) | ~wise(X1)) [rectify 34]
57. ? [X0] : patient(X0) => patient(sK4) [choice axiom]
58. patient(sK4) | ! [X1] : (curious(X1) | ~wise(X1)) [skolemisation 56,57]
97. ~quiet(X0) | ~curious(X0) | ~wise(X0) | ~quiet(X0) [cnf transformation 41]
100. ~wise(X0) | quiet(X0) | quiet(X0) [cnf transformation 41]
108. ~patient(X0) | ~patient(X0) [cnf transformation 31]
109. ~funny(X0) | wise(X0) [cnf transformation 32]
127. patient(sK4) | curious(X1) | ~wise(X1) [cnf transformation 58]
155. funny(lucy) [cnf transformation 22]
158. ~patient(X0) [duplicate literal removal 108]
159. ~quiet(X0) | ~curious(X0) | ~wise(X0) [duplicate literal removal 97]
160. ~wise(X0) | quiet(X0) [duplicate literal removal 100]
179. ~curious(X0) | ~wise(X0) [subsumption resolution 159,160]
196. 8 <=> ! [X0] : ~wise(X0) [avatar definition]
197. ~wise(X0) <- (8) [avatar component clause 196]
243. curious(X1) | ~wise(X1) [subsumption resolution 127,158]
244. ~wise(X1) [subsumption resolution 243,179]
245. 8 [avatar split clause 244,196]
342. wise(lucy) [resolution 109,155]
343. $false <- (8) [subsumption resolution 342,197]
344. ~8 [avatar contradiction clause 343]
345. $false [avatar sat refutation 245,344]
% SZS output end Proof for 7945644127930848159929500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not rich or not generous.
Everyone who is either not rich or not funny is both creative and not happy and vice versa.
If someone is either humble or curious then someone is humble.
If susan is both not curious and brave then alice is either strong or humble and vice versa.
Everyone who is either humble or patient is funny.
If someone is both strong and not strong then someone is either not patient or strong.
Everyone who is both creative and not old is generous or calm and vice versa.
Everyone who is creative is both not calm and generous and vice versa.
If someone is both generous and not brave then someone is brave or humble and vice versa.
If lucy is both rich and tall then john is either not funny or strong.
Everyone who is calm or strong is kind and vice versa.
If paul is kind then fred is not wise.
If john is either strong or not calm then fred is both patient and not happy.
Everyone who is not calm or creative is both not old and wise and vice versa.
Everyone who is not tall or not brave is not creative or patient and vice versa.
Everyone who is both rich and strong is either not humble or old.
Alice is either creative or not patient.
Someone is either not brave or humble.
Someone is not happy.
Alice is both not quiet and not generous.
Mary is both creative and not calm.
Susan is either not happy or not generous.
Someone is either not calm or not quiet.
Someone is either kind or curious. | Paul is kind. | contradiction | (![X]:(brave(X)=>(~rich(X)|~generous(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(creative(X)&~happy(X))))&
((?[X]:((humble(X)<~>curious(X))))=>(?[X]:(humble(X))))&
(((~curious(susan)&brave(susan)))<=>((strong(alice)<~>humble(alice))))&
(![X]:((humble(X)<~>patient(X))=>funny(X)))&
((?[X]:((strong(X)&~strong(X))))=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((creative(X)&~old(X))<=>(generous(X)|calm(X))))&
(![X]:(creative(X)<=>(~calm(X)&generous(X))))&
((?[X]:((generous(X)&~brave(X))))<=>(?[X]:((brave(X)|humble(X)))))&
(((rich(lucy)&tall(lucy)))=>((~funny(john)<~>strong(john))))&
(![X]:((calm(X)|strong(X))<=>kind(X)))&
((kind(paul))=>(~wise(fred)))&
(((strong(john)<~>~calm(john)))=>((patient(fred)&~happy(fred))))&
(![X]:((~calm(X)|creative(X))<=>(~old(X)&wise(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~creative(X)|patient(X))))&
(![X]:((rich(X)&strong(X))=>(~humble(X)<~>old(X))))&
((creative(alice)<~>~patient(alice)))&
(?[X]:((~brave(X)<~>humble(X))))&
(?[X]:(~happy(X)))&
((~quiet(alice)&~generous(alice)))&
((creative(mary)&~calm(mary)))&
((~happy(susan)<~>~generous(susan)))&
(?[X]:((~calm(X)<~>~quiet(X))))&
(?[X]:((kind(X)<~>curious(X)))) | kind(paul) | [
"p6",
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5352248571577509009470813
% SZS output start Proof for 5352248571577509009470813
7. ! [X0] : ((~old(X0) & creative(X0)) <=> (calm(X0) | generous(X0))) [input p6]
8. ! [X0] : (creative(X0) <=> (generous(X0) & ~calm(X0))) [input p7]
12. kind(paul) => ~wise(fred) [input p11]
14. ! [X0] : ((creative(X0) | ~calm(X0)) <=> (wise(X0) & ~old(X0))) [input p13]
25. kind(paul) [input hypothesis]
36. ~wise(fred) | ~kind(paul) [ennf transformation 12]
53. ! [X0] : (((~old(X0) & creative(X0)) | (~calm(X0) & ~generous(X0))) & ((calm(X0) | generous(X0)) | (old(X0) | ~creative(X0)))) [nnf transformation 7]
54. ! [X0] : (((~old(X0) & creative(X0)) | (~calm(X0) & ~generous(X0))) & (calm(X0) | generous(X0) | old(X0) | ~creative(X0))) [flattening 53]
55. ! [X0] : ((creative(X0) | (~generous(X0) | calm(X0))) & ((generous(X0) & ~calm(X0)) | ~creative(X0))) [nnf transformation 8]
56. ! [X0] : ((creative(X0) | ~generous(X0) | calm(X0)) & ((generous(X0) & ~calm(X0)) | ~creative(X0))) [flattening 55]
66. ! [X0] : (((creative(X0) | ~calm(X0)) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | (~creative(X0) & calm(X0)))) [nnf transformation 14]
67. ! [X0] : ((creative(X0) | ~calm(X0) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | (~creative(X0) & calm(X0)))) [flattening 66]
105. creative(X0) | ~calm(X0) [cnf transformation 54]
108. ~calm(X0) | ~creative(X0) [cnf transformation 56]
121. ~wise(fred) | ~kind(paul) [cnf transformation 36]
128. wise(X0) | calm(X0) [cnf transformation 67]
152. kind(paul) [cnf transformation 25]
187. ~calm(X0) [subsumption resolution 108,105]
238. 19 <=> kind(paul) [avatar definition]
242. 20 <=> wise(fred) [avatar definition]
244. ~wise(fred) <- (~20) [avatar component clause 242]
245. ~19 | ~20 [avatar split clause 121,242,238]
258. wise(X0) [subsumption resolution 128,187]
302. 19 [avatar split clause 152,238]
303. $false <- (~20) [subsumption resolution 244,258]
304. 20 [avatar contradiction clause 303]
307. $false [avatar sat refutation 245,302,304]
% SZS output end Proof for 5352248571577509009470813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then lucy is both not creative and not calm.
If someone is both curious and not funny then someone is either not generous or tall and vice versa.
Everyone who is not old or brave is brave and vice versa.
Everyone who is not patient is both not funny and not patient.
If fred is both not wise and rich then someone is both kind and not creative and vice versa.
If john is not creative or strong then someone is patient and vice versa.
If alice is both tall and wise then someone is either not strong or not calm and vice versa.
Everyone who is both not rich and not humble is both not calm and strong.
Everyone who is strong or creative is wise and vice versa.
If someone is either not tall or calm then mary is quiet and vice versa.
If someone is either not strong or brave then fred is either not humble or not brave and vice versa.
Everyone who is not quiet or old is happy or calm.
If susan is not patient or generous then someone is either kind or not curious.
Everyone who is both calm and humble is not funny or wise and vice versa.
Everyone who is either creative or kind is curious and vice versa.
Everyone who is both old and not humble is either brave or not wise.
Someone is both patient and calm.
Susan is both not strong and creative.
Paul is both funny and not old.
Someone is curious or not calm.
Someone is either curious or not strong.
Someone is not tall or patient.
Someone is either funny or not wise. | Susan is not strong. | entailment | ((?[X]:(patient(X)))=>((~creative(lucy)&~calm(lucy))))&
((?[X]:((curious(X)&~funny(X))))<=>(?[X]:((~generous(X)<~>tall(X)))))&
(![X]:((~old(X)|brave(X))<=>brave(X)))&
(![X]:(~patient(X)=>(~funny(X)&~patient(X))))&
(((~wise(fred)&rich(fred)))<=>(?[X]:((kind(X)&~creative(X)))))&
(((~creative(john)|strong(john)))<=>(?[X]:(patient(X))))&
(((tall(alice)&wise(alice)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((~rich(X)&~humble(X))=>(~calm(X)&strong(X))))&
(![X]:((strong(X)|creative(X))<=>wise(X)))&
((?[X]:((~tall(X)<~>calm(X))))<=>(quiet(mary)))&
((?[X]:((~strong(X)<~>brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~quiet(X)|old(X))=>(happy(X)|calm(X))))&
(((~patient(susan)|generous(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((calm(X)&humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>curious(X)))&
(![X]:((old(X)&~humble(X))=>(brave(X)<~>~wise(X))))&
(?[X]:((patient(X)&calm(X))))&
((~strong(susan)&creative(susan)))&
((funny(paul)&~old(paul)))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X)))) | ~strong(susan) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8869067801027911309626705
% SZS output start Proof for 8869067801027911309626705
18. creative(susan) & ~strong(susan) [input p17]
24. strong(susan) [input hypothesis]
145. ~strong(susan) [cnf transformation 18]
155. strong(susan) [cnf transformation 24]
377. $false [subsumption resolution 155,145]
% SZS output end Proof for 8869067801027911309626705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is rich and vice versa. Everyone who is not strong is either old or strong and vice versa. If someone is old then someone is not rich or not happy. Everyone who is strong or not rich is either generous or creative. Everyone who is patient or kind is not generous or not brave and vice versa. Everyone who is curious is both creative and funny and vice versa. Everyone who is either not funny or not wise is not curious and vice versa. Everyone who is both quiet and not curious is either not humble or not curious and vice versa. Everyone who is funny is not patient. Everyone who is either not wise or tall is quiet or not happy. If someone is not wise or not brave then someone is both kind and creative. Everyone who is patient is creative or not wise. Everyone who is either not creative or not calm is humble or funny and vice versa. If someone is not tall then john is not happy. Everyone who is not happy is not brave. Lucy is humble. Susan is patient or not happy. Someone is not wise. Someone is both kind and not rich. Someone is either quiet or wise. Someone is either calm or not generous. Someone is either patient or not happy. Fred is either not generous or not calm. | Lucy is kind. | neutral | (![X]:(~generous(X)<=>rich(X)))&
(![X]:(~strong(X)<=>(old(X)<~>strong(X))))&
((?[X]:(old(X)))=>(?[X]:((~rich(X)|~happy(X)))))&
(![X]:((strong(X)|~rich(X))=>(generous(X)<~>creative(X))))&
(![X]:((patient(X)|kind(X))<=>(~generous(X)|~brave(X))))&
(![X]:(curious(X)<=>(creative(X)&funny(X))))&
(![X]:((~funny(X)<~>~wise(X))<=>~curious(X)))&
(![X]:((quiet(X)&~curious(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:(funny(X)=>~patient(X)))&
(![X]:((~wise(X)<~>tall(X))=>(quiet(X)|~happy(X))))&
((?[X]:((~wise(X)|~brave(X))))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:(patient(X)=>(creative(X)|~wise(X))))&
(![X]:((~creative(X)<~>~calm(X))<=>(humble(X)|funny(X))))&
((?[X]:(~tall(X)))=>(~happy(john)))&
(![X]:(~happy(X)=>~brave(X)))&
(humble(lucy))&
((patient(susan)|~happy(susan)))&
(?[X]:(~wise(X)))&
(?[X]:((kind(X)&~rich(X))))&
(?[X]:((quiet(X)<~>wise(X))))&
(?[X]:((calm(X)<~>~generous(X))))&
(?[X]:((patient(X)<~>~happy(X))))&
((~generous(fred)<~>~calm(fred))) | kind(lucy) | [] | null | 0 |
Everyone who is not patient or not kind is either kind or not patient and vice versa.
If someone is not kind or quiet then lucy is either old or not generous.
Everyone who is both not creative and not generous is creative and vice versa.
If someone is not rich then someone is either curious or not calm.
Everyone who is patient is not quiet and vice versa.
If someone is either not kind or not tall then john is either not funny or not quiet and vice versa.
Everyone who is either patient or curious is both kind and humble and vice versa.
Everyone who is either not tall or curious is creative or brave.
If someone is either not humble or not calm then fred is strong and vice versa.
If lucy is tall or not creative then someone is both not calm and generous.
If someone is either funny or not happy then someone is both tall and happy.
Everyone who is either brave or not strong is wise and vice versa.
Everyone who is not wise is old and vice versa.
Everyone who is not funny or brave is both generous and tall and vice versa.
Someone is both generous and strong.
Susan is either old or not creative.
Someone is not strong or not creative.
Someone is not humble or not happy.
Lucy is humble.
Paul is either not wise or quiet. | Susan is not tall. | contradiction | (![X]:((~patient(X)|~kind(X))<=>(kind(X)<~>~patient(X))))&
((?[X]:((~kind(X)|quiet(X))))=>((old(lucy)<~>~generous(lucy))))&
(![X]:((~creative(X)&~generous(X))<=>creative(X)))&
((?[X]:(~rich(X)))=>(?[X]:((curious(X)<~>~calm(X)))))&
(![X]:(patient(X)<=>~quiet(X)))&
((?[X]:((~kind(X)<~>~tall(X))))<=>((~funny(john)<~>~quiet(john))))&
(![X]:((patient(X)<~>curious(X))<=>(kind(X)&humble(X))))&
(![X]:((~tall(X)<~>curious(X))=>(creative(X)|brave(X))))&
((?[X]:((~humble(X)<~>~calm(X))))<=>(strong(fred)))&
(((tall(lucy)|~creative(lucy)))=>(?[X]:((~calm(X)&generous(X)))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((tall(X)&happy(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>wise(X)))&
(![X]:(~wise(X)<=>old(X)))&
(![X]:((~funny(X)|brave(X))<=>(generous(X)&tall(X))))&
(?[X]:((generous(X)&strong(X))))&
((old(susan)<~>~creative(susan)))&
(?[X]:((~strong(X)|~creative(X))))&
(?[X]:((~humble(X)|~happy(X))))&
(humble(lucy))&
((~wise(paul)<~>quiet(paul))) | ~tall(susan) | [
"p0",
"p2",
"p6",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 461602963258628453423765
% SZS output start Proof for 461602963258628453423765
1. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (kind(X0) <~> ~patient(X0))) [input p0]
3. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> creative(X0)) [input p2]
7. ! [X0] : ((patient(X0) <~> curious(X0)) <=> (humble(X0) & kind(X0))) [input p6]
8. ! [X0] : ((~tall(X0) <~> curious(X0)) => (brave(X0) | creative(X0))) [input p7]
14. ! [X0] : ((brave(X0) | ~funny(X0)) <=> (tall(X0) & generous(X0))) [input p13]
21. ~tall(susan) [input hypothesis]
26. ! [X0] : ((brave(X0) | creative(X0)) | (~tall(X0) <=> curious(X0))) [ennf transformation 8]
27. ! [X0] : (brave(X0) | creative(X0) | (~tall(X0) <=> curious(X0))) [flattening 26]
30. ! [X0] : (((~kind(X0) | ~patient(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0)))) & (((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (kind(X0) & patient(X0)))) [nnf transformation 1]
31. ! [X0] : ((~kind(X0) | ~patient(X0) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0)))) & (((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (kind(X0) & patient(X0)))) [flattening 30]
33. ! [X0] : (((~generous(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | (generous(X0) | creative(X0)))) [nnf transformation 3]
34. ! [X0] : (((~generous(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | generous(X0) | creative(X0))) [flattening 33]
40. ! [X0] : ((((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | (~humble(X0) | ~kind(X0))) & ((humble(X0) & kind(X0)) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0))))) [nnf transformation 7]
41. ! [X0] : ((((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | ~humble(X0) | ~kind(X0)) & ((humble(X0) & kind(X0)) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0))))) [flattening 40]
42. ! [X0] : (brave(X0) | creative(X0) | ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0)))) [nnf transformation 27]
55. ! [X0] : (((brave(X0) | ~funny(X0)) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | (~brave(X0) & funny(X0)))) [nnf transformation 14]
56. ! [X0] : ((brave(X0) | ~funny(X0) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | (~brave(X0) & funny(X0)))) [flattening 55]
66. ~patient(X0) | kind(X0) | kind(X0) [cnf transformation 31]
67. patient(X0) | ~kind(X0) | patient(X0) [cnf transformation 31]
69. ~kind(X0) | ~patient(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 31]
76. ~creative(X0) | ~creative(X0) [cnf transformation 34]
89. kind(X0) | patient(X0) | ~curious(X0) [cnf transformation 41]
94. brave(X0) | creative(X0) | curious(X0) | tall(X0) [cnf transformation 42]
117. tall(X0) | ~brave(X0) [cnf transformation 56]
128. ~tall(susan) [cnf transformation 21]
130. ~creative(X0) [duplicate literal removal 76]
131. ~patient(X0) | kind(X0) [duplicate literal removal 66]
132. patient(X0) | ~kind(X0) [duplicate literal removal 67]
133. ~kind(X0) | ~patient(X0) [duplicate literal removal 69]
134. ~kind(X0) [subsumption resolution 132,133]
135. ~patient(X0) [subsumption resolution 131,134]
173. patient(X0) | ~curious(X0) [subsumption resolution 89,134]
174. ~curious(X0) [subsumption resolution 173,135]
175. brave(X0) | curious(X0) | tall(X0) [subsumption resolution 94,130]
176. brave(X0) | tall(X0) [subsumption resolution 175,174]
220. tall(X0) [subsumption resolution 117,176]
232. $false [subsumption resolution 128,220]
% SZS output end Proof for 461602963258628453423765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either not quiet or kind. Everyone who is not calm or not patient is not generous. If fred is both patient and kind then someone is not wise and vice versa. Everyone who is either not tall or not calm is brave. Everyone who is not brave is not curious or humble and vice versa. If someone is both strong and creative then someone is not creative and vice versa. If john is not humble then someone is either not humble or not patient and vice versa. If someone is both not patient and patient then alice is both curious and tall. If paul is not tall or not rich then lucy is not kind and vice versa. Everyone who is not strong is either quiet or tall. If someone is wise or not creative then someone is both brave and not curious. If lucy is either old or happy then someone is not wise. Everyone who is tall is patient and vice versa. Everyone who is quiet or not humble is not old or not rich and vice versa. Everyone who is either rich or not wise is both curious and not humble and vice versa. Lucy is both not humble and rich. Paul is either quiet or wise. Someone is brave. Someone is not brave. Someone is either tall or kind. Someone is either not tall or not quiet. Someone is both not wise and rich. | Lucy is creative. | entailment | (![X]:(~happy(X)=>(~quiet(X)<~>kind(X))))&
(![X]:((~calm(X)|~patient(X))=>~generous(X)))&
(((patient(fred)&kind(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)<~>~calm(X))=>brave(X)))&
(![X]:(~brave(X)<=>(~curious(X)|humble(X))))&
((?[X]:((strong(X)&creative(X))))<=>(?[X]:(~creative(X))))&
((~humble(john))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
((?[X]:((~patient(X)&patient(X))))=>((curious(alice)&tall(alice))))&
(((~tall(paul)|~rich(paul)))<=>(~kind(lucy)))&
(![X]:(~strong(X)=>(quiet(X)<~>tall(X))))&
((?[X]:((wise(X)|~creative(X))))=>(?[X]:((brave(X)&~curious(X)))))&
(((old(lucy)<~>happy(lucy)))=>(?[X]:(~wise(X))))&
(![X]:(tall(X)<=>patient(X)))&
(![X]:((quiet(X)|~humble(X))<=>(~old(X)|~rich(X))))&
(![X]:((rich(X)<~>~wise(X))<=>(curious(X)&~humble(X))))&
((~humble(lucy)&rich(lucy)))&
((quiet(paul)<~>wise(paul)))&
(?[X]:(brave(X)))&
(?[X]:(~brave(X)))&
(?[X]:((tall(X)<~>kind(X))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~wise(X)&rich(X)))) | creative(lucy) | [
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3929569396651249008341823
% SZS output start Proof for 3929569396651249008341823
5. ! [X0] : (~brave(X0) <=> (humble(X0) | ~curious(X0))) [input p4]
11. ? [X0] : (~creative(X0) | wise(X0)) => ? [X0] : (~curious(X0) & brave(X0)) [input p10]
23. ~creative(lucy) [input hypothesis]
25. ? [X0] : (~creative(X0) | wise(X0)) => ? [X1] : (~curious(X1) & brave(X1)) [rectify 11]
31. ? [X1] : (~curious(X1) & brave(X1)) | ! [X0] : (creative(X0) & ~wise(X0)) [ennf transformation 25]
40. ! [X0] : ((~brave(X0) | (~humble(X0) & curious(X0))) & ((humble(X0) | ~curious(X0)) | brave(X0))) [nnf transformation 5]
41. ! [X0] : ((~brave(X0) | (~humble(X0) & curious(X0))) & (humble(X0) | ~curious(X0) | brave(X0))) [flattening 40]
54. ? [X0] : (~curious(X0) & brave(X0)) | ! [X1] : (creative(X1) & ~wise(X1)) [rectify 31]
55. ? [X0] : (~curious(X0) & brave(X0)) => (~curious(sK4) & brave(sK4)) [choice axiom]
56. (~curious(sK4) & brave(sK4)) | ! [X1] : (creative(X1) & ~wise(X1)) [skolemisation 54,55]
86. ~brave(X0) | curious(X0) [cnf transformation 41]
103. brave(sK4) | creative(X1) [cnf transformation 56]
105. ~curious(sK4) | creative(X1) [cnf transformation 56]
132. ~creative(lucy) [cnf transformation 23]
152. 5 <=> ! [X1] : creative(X1) [avatar definition]
153. creative(X1) <- (5) [avatar component clause 152]
210. 18 <=> curious(sK4) [avatar definition]
212. ~curious(sK4) <- (~18) [avatar component clause 210]
213. 5 | ~18 [avatar split clause 105,210,152]
219. 20 <=> brave(sK4) [avatar definition]
221. brave(sK4) <- (20) [avatar component clause 219]
222. 5 | 20 [avatar split clause 103,219,152]
268. $false <- (5) [resolution 153,132]
269. ~5 [avatar contradiction clause 268]
271. curious(sK4) <- (20) [resolution 86,221]
272. $false <- (~18, 20) [subsumption resolution 271,212]
273. 18 | ~20 [avatar contradiction clause 272]
274. $false [avatar sat refutation 213,222,269,273]
% SZS output end Proof for 3929569396651249008341823
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or old then john is either brave or calm and vice versa.
Everyone who is not humble is humble.
If lucy is both curious and tall then someone is strong or not patient and vice versa.
Everyone who is happy is both rich and not kind and vice versa.
Everyone who is not strong or not happy is not funny or calm and vice versa.
If fred is rich or wise then mary is both not tall and not calm and vice versa.
Everyone who is not generous is calm or brave and vice versa.
If fred is not creative then lucy is quiet and vice versa.
Everyone who is either not quiet or not calm is tall or not patient and vice versa.
If someone is both brave and not tall then someone is both curious and strong and vice versa.
If mary is either happy or not kind then lucy is either funny or brave and vice versa.
If someone is kind or not generous then someone is quiet.
If fred is both not funny and tall then lucy is funny.
If lucy is curious then someone is both not quiet and kind.
If someone is creative or kind then someone is not humble and vice versa.
Everyone who is calm or not happy is either not humble or not old.
Someone is either old or not brave.
Someone is not curious or not strong.
Mary is not old.
John is either patient or quiet.
Mary is either rich or not wise.
Mary is not curious.
Someone is either rich or calm.
John is not tall or not strong. | Fred is not strong. | entailment | ((?[X]:((kind(X)<~>old(X))))<=>((brave(john)<~>calm(john))))&
(![X]:(~humble(X)=>humble(X)))&
(((curious(lucy)&tall(lucy)))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:(happy(X)<=>(rich(X)&~kind(X))))&
(![X]:((~strong(X)|~happy(X))<=>(~funny(X)|calm(X))))&
(((rich(fred)|wise(fred)))<=>((~tall(mary)&~calm(mary))))&
(![X]:(~generous(X)<=>(calm(X)|brave(X))))&
((~creative(fred))<=>(quiet(lucy)))&
(![X]:((~quiet(X)<~>~calm(X))<=>(tall(X)|~patient(X))))&
((?[X]:((brave(X)&~tall(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(((happy(mary)<~>~kind(mary)))<=>((funny(lucy)<~>brave(lucy))))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:(quiet(X))))&
(((~funny(fred)&tall(fred)))=>(funny(lucy)))&
((curious(lucy))=>(?[X]:((~quiet(X)&kind(X)))))&
((?[X]:((creative(X)|kind(X))))<=>(?[X]:(~humble(X))))&
(![X]:((calm(X)|~happy(X))=>(~humble(X)<~>~old(X))))&
(?[X]:((old(X)<~>~brave(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(~old(mary))&
((patient(john)<~>quiet(john)))&
((rich(mary)<~>~wise(mary)))&
(~curious(mary))&
(?[X]:((rich(X)<~>calm(X))))&
((~tall(john)|~strong(john))) | ~strong(fred) | [
"p1",
"p2",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7819758853584582018709491
% SZS output start Proof for 7819758853584582018709491
2. ! [X0] : (~humble(X0) => humble(X0)) [input p1]
3. (tall(lucy) & curious(lucy)) <=> ? [X0] : (~patient(X0) | strong(X0)) [input p2]
14. curious(lucy) => ? [X0] : (kind(X0) & ~quiet(X0)) [input p13]
15. ? [X0] : (kind(X0) | creative(X0)) <=> ? [X0] : ~humble(X0) [input p14]
25. strong(fred) [input hypothesis]
28. ? [X0] : (kind(X0) | creative(X0)) <=> ? [X1] : ~humble(X1) [rectify 15]
30. ! [X0] : (humble(X0) | humble(X0)) [ennf transformation 2]
35. ? [X0] : (kind(X0) & ~quiet(X0)) | ~curious(lucy) [ennf transformation 14]
41. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | (~tall(lucy) | ~curious(lucy))) [nnf transformation 3]
42. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | ~tall(lucy) | ~curious(lucy)) [flattening 41]
43. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X1] : (~patient(X1) | strong(X1)) | ~tall(lucy) | ~curious(lucy)) [rectify 42]
44. ? [X1] : (~patient(X1) | strong(X1)) => (~patient(sK1) | strong(sK1)) [choice axiom]
45. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & ((~patient(sK1) | strong(sK1)) | ~tall(lucy) | ~curious(lucy)) [skolemisation 43,44]
64. ? [X0] : (kind(X0) & ~quiet(X0)) => (kind(sK5) & ~quiet(sK5)) [choice axiom]
65. (kind(sK5) & ~quiet(sK5)) | ~curious(lucy) [skolemisation 35,64]
66. (? [X0] : (kind(X0) | creative(X0)) | ! [X1] : humble(X1)) & (? [X1] : ~humble(X1) | ! [X0] : (~kind(X0) & ~creative(X0))) [nnf transformation 28]
67. (? [X0] : (kind(X0) | creative(X0)) | ! [X1] : humble(X1)) & (? [X2] : ~humble(X2) | ! [X3] : (~kind(X3) & ~creative(X3))) [rectify 66]
68. ? [X0] : (kind(X0) | creative(X0)) => (kind(sK6) | creative(sK6)) [choice axiom]
69. ? [X2] : ~humble(X2) => ~humble(sK7) [choice axiom]
70. ((kind(sK6) | creative(sK6)) | ! [X1] : humble(X1)) & (~humble(sK7) | ! [X3] : (~kind(X3) & ~creative(X3))) [skolemisation 67,69,68]
90. humble(X0) | humble(X0) [cnf transformation 30]
92. curious(lucy) | ~strong(X0) [cnf transformation 45]
134. kind(sK5) | ~curious(lucy) [cnf transformation 65]
136. ~humble(sK7) | ~kind(X3) [cnf transformation 70]
154. strong(fred) [cnf transformation 25]
155. humble(X0) [duplicate literal removal 90]
195. 9 <=> ! [X0] : ~strong(X0) [avatar definition]
196. ~strong(X0) <- (9) [avatar component clause 195]
199. 10 <=> curious(lucy) [avatar definition]
203. 9 | 10 [avatar split clause 92,199,195]
305. 31 <=> ! [X1] : ~kind(X1) [avatar definition]
306. ~kind(X1) <- (31) [avatar component clause 305]
318. 34 <=> kind(sK5) [avatar definition]
320. kind(sK5) <- (34) [avatar component clause 318]
321. ~10 | 34 [avatar split clause 134,318,199]
327. ~kind(X3) [subsumption resolution 136,155]
328. 31 [avatar split clause 327,305]
392. $false <- (9) [resolution 196,154]
393. ~9 [avatar contradiction clause 392]
394. $false <- (31, 34) [subsumption resolution 320,306]
395. ~31 | ~34 [avatar contradiction clause 394]
398. $false [avatar sat refutation 203,321,328,393,395]
% SZS output end Proof for 7819758853584582018709491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and patient is calm and vice versa. Everyone who is not calm is either not wise or generous. If susan is patient then someone is both kind and creative and vice versa. Everyone who is both not strong and tall is either generous or wise. Everyone who is both humble and curious is both not kind and funny. Everyone who is either creative or patient is both patient and not funny and vice versa. If mary is both not strong and wise then someone is wise or not calm and vice versa. If someone is creative then paul is not generous or not funny and vice versa. If john is either not curious or strong then susan is both not happy and not humble and vice versa. If someone is either happy or not quiet then lucy is both humble and calm and vice versa. Everyone who is either not wise or kind is both curious and old and vice versa. Everyone who is both generous and not curious is not rich and vice versa. Everyone who is tall or happy is not rich or quiet and vice versa. Everyone who is either not generous or funny is either curious or not tall and vice versa. Everyone who is both not brave and not kind is kind. Everyone who is either curious or not patient is either not quiet or not old. Someone is wise or not curious. Someone is not generous or not strong. Mary is either generous or not strong. Someone is either not rich or not wise. Lucy is both quiet and creative. Alice is not kind. Alice is strong or not calm. Lucy is not strong. | Susan is not happy. | neutral | (![X]:((brave(X)&patient(X))<=>calm(X)))&
(![X]:(~calm(X)=>(~wise(X)<~>generous(X))))&
((patient(susan))<=>(?[X]:((kind(X)&creative(X)))))&
(![X]:((~strong(X)&tall(X))=>(generous(X)<~>wise(X))))&
(![X]:((humble(X)&curious(X))=>(~kind(X)&funny(X))))&
(![X]:((creative(X)<~>patient(X))<=>(patient(X)&~funny(X))))&
(((~strong(mary)&wise(mary)))<=>(?[X]:((wise(X)|~calm(X)))))&
((?[X]:(creative(X)))<=>((~generous(paul)|~funny(paul))))&
(((~curious(john)<~>strong(john)))<=>((~happy(susan)&~humble(susan))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>((humble(lucy)&calm(lucy))))&
(![X]:((~wise(X)<~>kind(X))<=>(curious(X)&old(X))))&
(![X]:((generous(X)&~curious(X))<=>~rich(X)))&
(![X]:((tall(X)|happy(X))<=>(~rich(X)|quiet(X))))&
(![X]:((~generous(X)<~>funny(X))<=>(curious(X)<~>~tall(X))))&
(![X]:((~brave(X)&~kind(X))=>kind(X)))&
(![X]:((curious(X)<~>~patient(X))=>(~quiet(X)<~>~old(X))))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:((~generous(X)|~strong(X))))&
((generous(mary)<~>~strong(mary)))&
(?[X]:((~rich(X)<~>~wise(X))))&
((quiet(lucy)&creative(lucy)))&
(~kind(alice))&
((strong(alice)|~calm(alice)))&
(~strong(lucy)) | ~happy(susan) | [] | null | 0 |
If someone is both humble and not curious then fred is both generous and not kind and vice versa.
Everyone who is not quiet or not generous is either happy or not curious.
If someone is calm then someone is either kind or not rich and vice versa.
Everyone who is both creative and not calm is either old or not old and vice versa.
If someone is either calm or not curious then someone is not funny or not generous and vice versa.
If someone is not tall or calm then susan is both not quiet and strong.
Everyone who is either creative or not humble is both not kind and not strong and vice versa.
Everyone who is not rich or patient is both humble and rich and vice versa.
If someone is not creative or not humble then someone is not kind and vice versa.
If someone is not wise then mary is not creative and vice versa.
Everyone who is tall is either not rich or not patient.
Everyone who is rich or humble is not patient and vice versa.
If fred is either funny or not old then john is either creative or patient and vice versa.
Everyone who is wise is both not patient and not kind and vice versa.
If lucy is not happy or old then someone is either creative or kind and vice versa.
Someone is not old or kind.
Someone is either tall or not quiet.
Alice is both not humble and not generous.
Alice is happy.
Paul is calm or quiet.
Someone is not happy or humble. | Paul is rich. | entailment | ((?[X]:((humble(X)&~curious(X))))<=>((generous(fred)&~kind(fred))))&
(![X]:((~quiet(X)|~generous(X))=>(happy(X)<~>~curious(X))))&
((?[X]:(calm(X)))<=>(?[X]:((kind(X)<~>~rich(X)))))&
(![X]:((creative(X)&~calm(X))<=>(old(X)<~>~old(X))))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
((?[X]:((~tall(X)|calm(X))))=>((~quiet(susan)&strong(susan))))&
(![X]:((creative(X)<~>~humble(X))<=>(~kind(X)&~strong(X))))&
(![X]:((~rich(X)|patient(X))<=>(humble(X)&rich(X))))&
((?[X]:((~creative(X)|~humble(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(~wise(X)))<=>(~creative(mary)))&
(![X]:(tall(X)=>(~rich(X)<~>~patient(X))))&
(![X]:((rich(X)|humble(X))<=>~patient(X)))&
(((funny(fred)<~>~old(fred)))<=>((creative(john)<~>patient(john))))&
(![X]:(wise(X)<=>(~patient(X)&~kind(X))))&
(((~happy(lucy)|old(lucy)))<=>(?[X]:((creative(X)<~>kind(X)))))&
(?[X]:((~old(X)|kind(X))))&
(?[X]:((tall(X)<~>~quiet(X))))&
((~humble(alice)&~generous(alice)))&
(happy(alice))&
((calm(paul)|quiet(paul)))&
(?[X]:((~happy(X)|humble(X)))) | rich(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2750839469942742192725702
% SZS output start Proof for 2750839469942742192725702
8. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (rich(X0) & humble(X0))) [input p7]
22. ~rich(paul) [input hypothesis]
49. ! [X0] : (((patient(X0) | ~rich(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 8]
50. ! [X0] : ((patient(X0) | ~rich(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [flattening 49]
114. rich(X0) | rich(X0) [cnf transformation 50]
152. ~rich(paul) [cnf transformation 22]
153. rich(X0) [duplicate literal removal 114]
337. $false [subsumption resolution 152,153]
% SZS output end Proof for 2750839469942742192725702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not funny is patient and vice versa. Everyone who is brave or not kind is either wise or not brave and vice versa. Everyone who is either not happy or patient is both tall and funny. If paul is strong or curious then john is both strong and happy. If lucy is tall then someone is not humble or old and vice versa. Everyone who is both not quiet and brave is either not wise or funny. Everyone who is both calm and not creative is not curious. Everyone who is both not patient and not strong is generous and vice versa. Everyone who is not old or wise is both patient and not kind and vice versa. Everyone who is not old is patient or generous and vice versa. Everyone who is both tall and not quiet is curious or not humble. Everyone who is curious or strong is either strong or generous. If someone is quiet or funny then lucy is either humble or not humble. Everyone who is generous is brave and vice versa. Everyone who is either calm or creative is brave or not brave. Everyone who is both not funny and not humble is generous or curious and vice versa. Mary is both funny and not patient. Lucy is happy or not wise. Someone is not calm. John is not quiet or old. Someone is not happy. Someone is either generous or patient. John is either not humble or creative. | Paul is old. | neutral | (![X]:((humble(X)<~>~funny(X))<=>patient(X)))&
(![X]:((brave(X)|~kind(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>patient(X))=>(tall(X)&funny(X))))&
(((strong(paul)|curious(paul)))=>((strong(john)&happy(john))))&
((tall(lucy))<=>(?[X]:((~humble(X)|old(X)))))&
(![X]:((~quiet(X)&brave(X))=>(~wise(X)<~>funny(X))))&
(![X]:((calm(X)&~creative(X))=>~curious(X)))&
(![X]:((~patient(X)&~strong(X))<=>generous(X)))&
(![X]:((~old(X)|wise(X))<=>(patient(X)&~kind(X))))&
(![X]:(~old(X)<=>(patient(X)|generous(X))))&
(![X]:((tall(X)&~quiet(X))=>(curious(X)|~humble(X))))&
(![X]:((curious(X)|strong(X))=>(strong(X)<~>generous(X))))&
((?[X]:((quiet(X)|funny(X))))=>((humble(lucy)<~>~humble(lucy))))&
(![X]:(generous(X)<=>brave(X)))&
(![X]:((calm(X)<~>creative(X))=>(brave(X)|~brave(X))))&
(![X]:((~funny(X)&~humble(X))<=>(generous(X)|curious(X))))&
((funny(mary)&~patient(mary)))&
((happy(lucy)|~wise(lucy)))&
(?[X]:(~calm(X)))&
((~quiet(john)|old(john)))&
(?[X]:(~happy(X)))&
(?[X]:((generous(X)<~>patient(X))))&
((~humble(john)<~>creative(john))) | old(paul) | [] | null | 0 |
Everyone who is not kind is either tall or not funny.
If someone is both creative and patient then someone is either funny or strong.
Everyone who is rich or not calm is either wise or brave and vice versa.
If paul is not tall or not strong then lucy is rich and vice versa.
Everyone who is either not strong or rich is not patient or not generous.
If lucy is both not old and generous then someone is both tall and not happy and vice versa.
Everyone who is not funny or wise is either not generous or not old and vice versa.
Everyone who is both not happy and happy is tall or funny and vice versa.
If alice is both rich and happy then mary is creative and vice versa.
Everyone who is both happy and calm is not curious or quiet.
If alice is both not calm and wise then someone is kind.
Everyone who is both not funny and not patient is kind or happy.
If someone is both generous and not calm then someone is either not patient or not tall and vice versa.
Everyone who is either not calm or not humble is either happy or not wise and vice versa.
If someone is both tall and calm then paul is strong.
Alice is not generous.
John is strong or not wise.
Susan is creative or rich.
Paul is curious.
Someone is curious. | Susan is generous. | neutral | (![X]:(~kind(X)=>(tall(X)<~>~funny(X))))&
((?[X]:((creative(X)&patient(X))))=>(?[X]:((funny(X)<~>strong(X)))))&
(![X]:((rich(X)|~calm(X))<=>(wise(X)<~>brave(X))))&
(((~tall(paul)|~strong(paul)))<=>(rich(lucy)))&
(![X]:((~strong(X)<~>rich(X))=>(~patient(X)|~generous(X))))&
(((~old(lucy)&generous(lucy)))<=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~funny(X)|wise(X))<=>(~generous(X)<~>~old(X))))&
(![X]:((~happy(X)&happy(X))<=>(tall(X)|funny(X))))&
(((rich(alice)&happy(alice)))<=>(creative(mary)))&
(![X]:((happy(X)&calm(X))=>(~curious(X)|quiet(X))))&
(((~calm(alice)&wise(alice)))=>(?[X]:(kind(X))))&
(![X]:((~funny(X)&~patient(X))=>(kind(X)|happy(X))))&
((?[X]:((generous(X)&~calm(X))))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:((~calm(X)<~>~humble(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:((tall(X)&calm(X))))=>(strong(paul)))&
(~generous(alice))&
((strong(john)|~wise(john)))&
((creative(susan)|rich(susan)))&
(curious(paul))&
(?[X]:(curious(X))) | generous(susan) | [] | null | 0 |
Everyone who is either humble or not strong is either not quiet or not rich.
Everyone who is not old is both old and calm.
Everyone who is patient is either not patient or not strong and vice versa.
Everyone who is both not generous and curious is not funny or old.
Everyone who is creative is both happy and not old.
If someone is both humble and creative then paul is both not funny and quiet and vice versa.
Everyone who is not generous is kind.
If someone is old or rich then john is not creative.
If someone is either not creative or not old then paul is either old or not quiet and vice versa.
If someone is not curious or not wise then someone is either not generous or not humble.
Everyone who is either calm or not quiet is both wise and not happy and vice versa.
If someone is either humble or not tall then someone is both not generous and not kind.
If someone is both not calm and wise then mary is not tall and vice versa.
Everyone who is not quiet or happy is either kind or wise.
Everyone who is either brave or not creative is not brave and vice versa.
Someone is either not tall or not quiet.
Someone is either humble or generous.
Someone is not rich.
John is both not wise and generous.
Lucy is not brave.
Someone is both quiet and humble.
Someone is rich or not wise. | Paul is quiet. | entailment | (![X]:((humble(X)<~>~strong(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:(~old(X)=>(old(X)&calm(X))))&
(![X]:(patient(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:((~generous(X)&curious(X))=>(~funny(X)|old(X))))&
(![X]:(creative(X)=>(happy(X)&~old(X))))&
((?[X]:((humble(X)&creative(X))))<=>((~funny(paul)&quiet(paul))))&
(![X]:(~generous(X)=>kind(X)))&
((?[X]:((old(X)|rich(X))))=>(~creative(john)))&
((?[X]:((~creative(X)<~>~old(X))))<=>((old(paul)<~>~quiet(paul))))&
((?[X]:((~curious(X)|~wise(X))))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:((calm(X)<~>~quiet(X))<=>(wise(X)&~happy(X))))&
((?[X]:((humble(X)<~>~tall(X))))=>(?[X]:((~generous(X)&~kind(X)))))&
((?[X]:((~calm(X)&wise(X))))<=>(~tall(mary)))&
(![X]:((~quiet(X)|happy(X))=>(kind(X)<~>wise(X))))&
(![X]:((brave(X)<~>~creative(X))<=>~brave(X)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((humble(X)<~>generous(X))))&
(?[X]:(~rich(X)))&
((~wise(john)&generous(john)))&
(~brave(lucy))&
(?[X]:((quiet(X)&humble(X))))&
(?[X]:((rich(X)|~wise(X)))) | quiet(paul) | [
"p1",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3435870739386747696804836
% SZS output start Proof for 3435870739386747696804836
2. ! [X0] : (~old(X0) => (calm(X0) & old(X0))) [input p1]
5. ! [X0] : (creative(X0) => (~old(X0) & happy(X0))) [input p4]
9. ? [X0] : (~creative(X0) <~> ~old(X0)) <=> (old(paul) <~> ~quiet(paul)) [input p8]
23. ~quiet(paul) [input hypothesis]
27. ! [X0] : ((calm(X0) & old(X0)) | old(X0)) [ennf transformation 2]
30. ! [X0] : ((~old(X0) & happy(X0)) | ~creative(X0)) [ennf transformation 5]
43. (? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | ((old(paul) | quiet(paul)) & (~quiet(paul) | ~old(paul)))) & (((quiet(paul) | ~old(paul)) & (~quiet(paul) | old(paul))) | ! [X0] : ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [nnf transformation 9]
44. (? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | ((old(paul) | quiet(paul)) & (~quiet(paul) | ~old(paul)))) & (((quiet(paul) | ~old(paul)) & (~quiet(paul) | old(paul))) | ! [X1] : ((~creative(X1) | old(X1)) & (~old(X1) | creative(X1)))) [rectify 43]
45. ? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) => ((old(sK1) | creative(sK1)) & (~old(sK1) | ~creative(sK1))) [choice axiom]
46. (((old(sK1) | creative(sK1)) & (~old(sK1) | ~creative(sK1))) | ((old(paul) | quiet(paul)) & (~quiet(paul) | ~old(paul)))) & (((quiet(paul) | ~old(paul)) & (~quiet(paul) | old(paul))) | ! [X1] : ((~creative(X1) | old(X1)) & (~old(X1) | creative(X1)))) [skolemisation 44,45]
79. old(X0) | old(X0) [cnf transformation 27]
87. ~old(X0) | ~creative(X0) [cnf transformation 30]
97. quiet(paul) | ~old(paul) | ~old(X1) | creative(X1) [cnf transformation 46]
139. ~quiet(paul) [cnf transformation 23]
144. old(X0) [duplicate literal removal 79]
146. ~creative(X0) [subsumption resolution 87,144]
153. 2 <=> quiet(paul) [avatar definition]
162. quiet(paul) | ~old(X1) | creative(X1) [subsumption resolution 97,144]
163. quiet(paul) | creative(X1) [subsumption resolution 162,144]
164. quiet(paul) [subsumption resolution 163,146]
165. 2 [avatar split clause 164,153]
249. ~2 [avatar split clause 139,153]
250. $false [avatar sat refutation 165,249]
% SZS output end Proof for 3435870739386747696804836
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is strong or happy then lucy is both not calm and funny and vice versa.
If john is both rich and not happy then john is both happy and tall and vice versa.
Everyone who is not funny is both not quiet and not old.
Everyone who is humble or brave is not strong.
If someone is either not rich or happy then someone is either not tall or not wise and vice versa.
Everyone who is both humble and quiet is happy or quiet and vice versa.
If mary is humble or strong then someone is both not wise and not patient and vice versa.
Everyone who is not wise or generous is both patient and not humble and vice versa.
If someone is not brave then someone is old.
Everyone who is either curious or patient is either not wise or kind.
Everyone who is not creative or not tall is not strong or not patient and vice versa.
If someone is either wise or not old then susan is either generous or not happy and vice versa.
If someone is wise or kind then fred is either not kind or wise.
If paul is generous or old then alice is either not tall or not wise and vice versa.
If john is either creative or happy then someone is quiet and vice versa.
Paul is not kind or brave.
Mary is quiet or wise.
John is either not patient or not strong.
Someone is brave or rich.
Mary is both not patient and creative.
Someone is either not tall or strong.
Paul is strong or not generous.
Someone is creative or not curious. | John is not old. | neutral | (((strong(fred)|happy(fred)))<=>((~calm(lucy)&funny(lucy))))&
(((rich(john)&~happy(john)))<=>((happy(john)&tall(john))))&
(![X]:(~funny(X)=>(~quiet(X)&~old(X))))&
(![X]:((humble(X)|brave(X))=>~strong(X)))&
((?[X]:((~rich(X)<~>happy(X))))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
(![X]:((humble(X)&quiet(X))<=>(happy(X)|quiet(X))))&
(((humble(mary)|strong(mary)))<=>(?[X]:((~wise(X)&~patient(X)))))&
(![X]:((~wise(X)|generous(X))<=>(patient(X)&~humble(X))))&
((?[X]:(~brave(X)))=>(?[X]:(old(X))))&
(![X]:((curious(X)<~>patient(X))=>(~wise(X)<~>kind(X))))&
(![X]:((~creative(X)|~tall(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((wise(X)<~>~old(X))))<=>((generous(susan)<~>~happy(susan))))&
((?[X]:((wise(X)|kind(X))))=>((~kind(fred)<~>wise(fred))))&
(((generous(paul)|old(paul)))<=>((~tall(alice)<~>~wise(alice))))&
(((creative(john)<~>happy(john)))<=>(?[X]:(quiet(X))))&
((~kind(paul)|brave(paul)))&
((quiet(mary)|wise(mary)))&
((~patient(john)<~>~strong(john)))&
(?[X]:((brave(X)|rich(X))))&
((~patient(mary)&creative(mary)))&
(?[X]:((~tall(X)<~>strong(X))))&
((strong(paul)|~generous(paul)))&
(?[X]:((creative(X)|~curious(X)))) | ~old(john) | [] | null | 0 |
If someone is kind or not brave then someone is humble or not calm.
Everyone who is not generous is not funny.
If someone is funny then mary is either not kind or creative and vice versa.
Everyone who is creative or kind is both not curious and quiet.
Everyone who is strong or not curious is kind and vice versa.
Everyone who is not brave or not creative is not old or quiet and vice versa.
Everyone who is old or brave is both tall and creative.
Everyone who is either not wise or quiet is not rich.
Everyone who is not brave or patient is not quiet or not kind.
Everyone who is not kind or not humble is either not happy or strong.
If someone is generous or not brave then alice is not curious or not creative.
If mary is either not old or not happy then someone is not rich or not curious.
Everyone who is brave or rich is calm or not tall.
If someone is either not quiet or curious then someone is patient and vice versa.
Everyone who is calm or wise is humble or not kind.
Susan is either happy or funny.
Someone is either brave or not calm.
Mary is patient.
Someone is either kind or patient.
Someone is rich. | Susan is not funny. | contradiction | ((?[X]:((kind(X)|~brave(X))))=>(?[X]:((humble(X)|~calm(X)))))&
(![X]:(~generous(X)=>~funny(X)))&
((?[X]:(funny(X)))<=>((~kind(mary)<~>creative(mary))))&
(![X]:((creative(X)|kind(X))=>(~curious(X)&quiet(X))))&
(![X]:((strong(X)|~curious(X))<=>kind(X)))&
(![X]:((~brave(X)|~creative(X))<=>(~old(X)|quiet(X))))&
(![X]:((old(X)|brave(X))=>(tall(X)&creative(X))))&
(![X]:((~wise(X)<~>quiet(X))=>~rich(X)))&
(![X]:((~brave(X)|patient(X))=>(~quiet(X)|~kind(X))))&
(![X]:((~kind(X)|~humble(X))=>(~happy(X)<~>strong(X))))&
((?[X]:((generous(X)|~brave(X))))=>((~curious(alice)|~creative(alice))))&
(((~old(mary)<~>~happy(mary)))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((brave(X)|rich(X))=>(calm(X)|~tall(X))))&
((?[X]:((~quiet(X)<~>curious(X))))<=>(?[X]:(patient(X))))&
(![X]:((calm(X)|wise(X))=>(humble(X)|~kind(X))))&
((happy(susan)<~>funny(susan)))&
(?[X]:((brave(X)<~>~calm(X))))&
(patient(mary))&
(?[X]:((kind(X)<~>patient(X))))&
(?[X]:(rich(X))) | ~funny(susan) | [
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 355945335600463847385262
% SZS output start Proof for 355945335600463847385262
4. ! [X0] : ((kind(X0) | creative(X0)) => (quiet(X0) & ~curious(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | strong(X0)) <=> kind(X0)) [input p4]
6. ! [X0] : ((~creative(X0) | ~brave(X0)) <=> (quiet(X0) | ~old(X0))) [input p5]
7. ! [X0] : ((brave(X0) | old(X0)) => (creative(X0) & tall(X0))) [input p6]
9. ! [X0] : ((patient(X0) | ~brave(X0)) => (~kind(X0) | ~quiet(X0))) [input p8]
10. ! [X0] : ((~humble(X0) | ~kind(X0)) => (~happy(X0) <~> strong(X0))) [input p9]
16. happy(susan) <~> funny(susan) [input p15]
21. ~funny(susan) [input hypothesis]
24. ! [X0] : (~kind(X0) => (~happy(X0) <~> strong(X0))) [pure predicate removal 10]
28. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~kind(X0) & ~creative(X0))) [ennf transformation 4]
29. ! [X0] : ((creative(X0) & tall(X0)) | (~brave(X0) & ~old(X0))) [ennf transformation 7]
31. ! [X0] : ((~kind(X0) | ~quiet(X0)) | (~patient(X0) & brave(X0))) [ennf transformation 9]
32. ! [X0] : (~kind(X0) | ~quiet(X0) | (~patient(X0) & brave(X0))) [flattening 31]
33. ! [X0] : ((~happy(X0) <~> strong(X0)) | kind(X0)) [ennf transformation 24]
43. ! [X0] : (((~curious(X0) | strong(X0)) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [nnf transformation 5]
44. ! [X0] : ((~curious(X0) | strong(X0) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [flattening 43]
45. ! [X0] : (((~creative(X0) | ~brave(X0)) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | (creative(X0) & brave(X0)))) [nnf transformation 6]
46. ! [X0] : ((~creative(X0) | ~brave(X0) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | (creative(X0) & brave(X0)))) [flattening 45]
48. ! [X0] : (((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | kind(X0)) [nnf transformation 33]
57. (~funny(susan) | ~happy(susan)) & (funny(susan) | happy(susan)) [nnf transformation 16]
73. ~creative(X0) | quiet(X0) [cnf transformation 28]
74. ~kind(X0) | quiet(X0) [cnf transformation 28]
75. ~strong(X0) | kind(X0) [cnf transformation 44]
81. ~creative(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 46]
85. creative(X0) | ~brave(X0) [cnf transformation 29]
88. ~kind(X0) | ~quiet(X0) | brave(X0) [cnf transformation 32]
90. strong(X0) | ~happy(X0) | kind(X0) [cnf transformation 48]
102. funny(susan) | happy(susan) [cnf transformation 57]
110. ~funny(susan) [cnf transformation 21]
130. ~creative(X0) | ~brave(X0) [subsumption resolution 81,73]
132. ~brave(X0) [subsumption resolution 85,130]
134. ~kind(X0) | ~quiet(X0) [subsumption resolution 88,132]
135. ~kind(X0) [subsumption resolution 134,74]
136. ~happy(X0) | strong(X0) [subsumption resolution 90,135]
181. 15 <=> happy(susan) [avatar definition]
182. happy(susan) <- (15) [avatar component clause 181]
185. 16 <=> funny(susan) [avatar definition]
189. 15 | 16 [avatar split clause 102,185,181]
192. ~16 [avatar split clause 110,185]
211. strong(susan) <- (15) [resolution 136,182]
212. kind(susan) <- (15) [resolution 211,75]
213. $false <- (15) [subsumption resolution 212,135]
214. ~15 [avatar contradiction clause 213]
215. $false [avatar sat refutation 189,192,214]
% SZS output end Proof for 355945335600463847385262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or kind is not funny.
If someone is not humble or humble then alice is not patient or not old.
If susan is either not tall or happy then someone is tall and vice versa.
Everyone who is both calm and funny is both happy and not curious and vice versa.
Everyone who is not funny is either humble or not wise and vice versa.
If fred is not kind then someone is curious or not patient and vice versa.
Everyone who is not strong is not creative or rich and vice versa.
Everyone who is both not creative and rich is both not creative and not strong.
If lucy is either not humble or generous then someone is either kind or generous and vice versa.
If someone is patient or not quiet then someone is wise and vice versa.
Everyone who is kind or not strong is either generous or not kind.
Everyone who is not quiet or not rich is both not happy and not patient.
Everyone who is not old or not wise is either rich or not tall and vice versa.
If someone is both brave and tall then someone is both not wise and not creative and vice versa.
Everyone who is curious is not happy and vice versa.
Everyone who is both not generous and quiet is not generous or not kind.
Fred is humble.
Fred is not generous.
Someone is not creative or not funny.
Someone is both not brave and not kind.
Someone is not humble.
Fred is either calm or creative.
Alice is not patient.
Someone is either funny or not happy. | Lucy is rich. | neutral | (![X]:((curious(X)<~>kind(X))=>~funny(X)))&
((?[X]:((~humble(X)|humble(X))))=>((~patient(alice)|~old(alice))))&
(((~tall(susan)<~>happy(susan)))<=>(?[X]:(tall(X))))&
(![X]:((calm(X)&funny(X))<=>(happy(X)&~curious(X))))&
(![X]:(~funny(X)<=>(humble(X)<~>~wise(X))))&
((~kind(fred))<=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:(~strong(X)<=>(~creative(X)|rich(X))))&
(![X]:((~creative(X)&rich(X))=>(~creative(X)&~strong(X))))&
(((~humble(lucy)<~>generous(lucy)))<=>(?[X]:((kind(X)<~>generous(X)))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~strong(X))=>(generous(X)<~>~kind(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~happy(X)&~patient(X))))&
(![X]:((~old(X)|~wise(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:(curious(X)<=>~happy(X)))&
(![X]:((~generous(X)&quiet(X))=>(~generous(X)|~kind(X))))&
(humble(fred))&
(~generous(fred))&
(?[X]:((~creative(X)|~funny(X))))&
(?[X]:((~brave(X)&~kind(X))))&
(?[X]:(~humble(X)))&
((calm(fred)<~>creative(fred)))&
(~patient(alice))&
(?[X]:((funny(X)<~>~happy(X)))) | rich(lucy) | [] | null | 0 |
If someone is not funny then someone is creative or not kind and vice versa.
If john is not brave then lucy is either tall or not tall and vice versa.
Everyone who is either humble or not creative is either patient or not happy and vice versa.
If alice is either humble or not quiet then someone is rich and vice versa.
If someone is not humble or humble then someone is not kind.
Everyone who is not old is humble or not wise and vice versa.
If lucy is either not generous or not brave then alice is wise and vice versa.
Everyone who is both wise and strong is not humble or old and vice versa.
Everyone who is not funny or not calm is both happy and not creative and vice versa.
Everyone who is either curious or kind is not funny or not strong.
Everyone who is either old or wise is either not strong or not humble and vice versa.
Everyone who is not humble is tall and vice versa.
Everyone who is not calm is either not happy or not creative.
If someone is both curious and wise then susan is either kind or humble.
If someone is wise then john is either not old or creative and vice versa.
Someone is not quiet or not old.
Paul is not quiet.
Someone is not wise.
Someone is not happy or calm.
Someone is brave or not generous.
Fred is both calm and not brave.
Someone is either not happy or quiet. | Fred is happy. | neutral | ((?[X]:(~funny(X)))<=>(?[X]:((creative(X)|~kind(X)))))&
((~brave(john))<=>((tall(lucy)<~>~tall(lucy))))&
(![X]:((humble(X)<~>~creative(X))<=>(patient(X)<~>~happy(X))))&
(((humble(alice)<~>~quiet(alice)))<=>(?[X]:(rich(X))))&
((?[X]:((~humble(X)|humble(X))))=>(?[X]:(~kind(X))))&
(![X]:(~old(X)<=>(humble(X)|~wise(X))))&
(((~generous(lucy)<~>~brave(lucy)))<=>(wise(alice)))&
(![X]:((wise(X)&strong(X))<=>(~humble(X)|old(X))))&
(![X]:((~funny(X)|~calm(X))<=>(happy(X)&~creative(X))))&
(![X]:((curious(X)<~>kind(X))=>(~funny(X)|~strong(X))))&
(![X]:((old(X)<~>wise(X))<=>(~strong(X)<~>~humble(X))))&
(![X]:(~humble(X)<=>tall(X)))&
(![X]:(~calm(X)=>(~happy(X)<~>~creative(X))))&
((?[X]:((curious(X)&wise(X))))=>((kind(susan)<~>humble(susan))))&
((?[X]:(wise(X)))<=>((~old(john)<~>creative(john))))&
(?[X]:((~quiet(X)|~old(X))))&
(~quiet(paul))&
(?[X]:(~wise(X)))&
(?[X]:((~happy(X)|calm(X))))&
(?[X]:((brave(X)|~generous(X))))&
((calm(fred)&~brave(fred)))&
(?[X]:((~happy(X)<~>quiet(X)))) | happy(fred) | [] | null | 0 |
Everyone who is either not old or not rich is not curious or not rich and vice versa. If alice is humble then john is both rich and not creative. If someone is quiet then john is either creative or kind. If someone is curious then someone is humble or funny. Everyone who is creative or curious is rich or not calm and vice versa. If alice is not generous then someone is both not tall and humble. Everyone who is either not happy or kind is happy or wise. Everyone who is creative is both not kind and kind. If john is brave or funny then susan is strong or not strong and vice versa. If alice is either old or patient then someone is strong. Everyone who is either not quiet or calm is both not quiet and not funny. Everyone who is either not wise or humble is funny and vice versa. Everyone who is either not curious or not strong is either not wise or not brave and vice versa. Everyone who is tall is happy. Everyone who is both not kind and not quiet is either rich or tall. Everyone who is not wise is not generous. Someone is both not brave and not generous. Lucy is kind. Mary is tall. Susan is not curious. Fred is rich or creative. John is not patient or not funny. | Susan is not generous. | neutral | (![X]:((~old(X)<~>~rich(X))<=>(~curious(X)|~rich(X))))&
((humble(alice))=>((rich(john)&~creative(john))))&
((?[X]:(quiet(X)))=>((creative(john)<~>kind(john))))&
((?[X]:(curious(X)))=>(?[X]:((humble(X)|funny(X)))))&
(![X]:((creative(X)|curious(X))<=>(rich(X)|~calm(X))))&
((~generous(alice))=>(?[X]:((~tall(X)&humble(X)))))&
(![X]:((~happy(X)<~>kind(X))=>(happy(X)|wise(X))))&
(![X]:(creative(X)=>(~kind(X)&kind(X))))&
(((brave(john)|funny(john)))<=>((strong(susan)|~strong(susan))))&
(((old(alice)<~>patient(alice)))=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)<~>calm(X))=>(~quiet(X)&~funny(X))))&
(![X]:((~wise(X)<~>humble(X))<=>funny(X)))&
(![X]:((~curious(X)<~>~strong(X))<=>(~wise(X)<~>~brave(X))))&
(![X]:(tall(X)=>happy(X)))&
(![X]:((~kind(X)&~quiet(X))=>(rich(X)<~>tall(X))))&
(![X]:(~wise(X)=>~generous(X)))&
(?[X]:((~brave(X)&~generous(X))))&
(kind(lucy))&
(tall(mary))&
(~curious(susan))&
((rich(fred)|creative(fred)))&
((~patient(john)|~funny(john))) | ~generous(susan) | [] | null | 0 |
If mary is both not strong and not rich then john is not quiet. If alice is not calm or not humble then susan is either brave or humble and vice versa. Everyone who is not quiet or generous is kind or not kind. Everyone who is not happy is not wise and vice versa. If mary is not tall then someone is either strong or curious. Everyone who is either brave or strong is kind. Everyone who is both not wise and not old is either not tall or brave and vice versa. If someone is not generous or not patient then someone is both not generous and not happy. Everyone who is funny or creative is not generous or wise. Everyone who is quiet or not calm is brave. If someone is not old or not calm then someone is tall or not humble and vice versa. Everyone who is both not happy and wise is both old and not old and vice versa. Everyone who is not wise is either not calm or rich. Everyone who is strong or not patient is not curious or rich and vice versa. If someone is not rich or not wise then someone is either happy or not wise and vice versa. Everyone who is either not humble or not funny is not humble. Lucy is either happy or brave. Alice is both not brave and not rich. Someone is not curious. Susan is either not tall or quiet. Fred is rich. Someone is both not funny and not humble. John is patient. | Mary is not happy. | neutral | (((~strong(mary)&~rich(mary)))=>(~quiet(john)))&
(((~calm(alice)|~humble(alice)))<=>((brave(susan)<~>humble(susan))))&
(![X]:((~quiet(X)|generous(X))=>(kind(X)|~kind(X))))&
(![X]:(~happy(X)<=>~wise(X)))&
((~tall(mary))=>(?[X]:((strong(X)<~>curious(X)))))&
(![X]:((brave(X)<~>strong(X))=>kind(X)))&
(![X]:((~wise(X)&~old(X))<=>(~tall(X)<~>brave(X))))&
((?[X]:((~generous(X)|~patient(X))))=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:((funny(X)|creative(X))=>(~generous(X)|wise(X))))&
(![X]:((quiet(X)|~calm(X))=>brave(X)))&
((?[X]:((~old(X)|~calm(X))))<=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~happy(X)&wise(X))<=>(old(X)&~old(X))))&
(![X]:(~wise(X)=>(~calm(X)<~>rich(X))))&
(![X]:((strong(X)|~patient(X))<=>(~curious(X)|rich(X))))&
((?[X]:((~rich(X)|~wise(X))))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((~humble(X)<~>~funny(X))=>~humble(X)))&
((happy(lucy)<~>brave(lucy)))&
((~brave(alice)&~rich(alice)))&
(?[X]:(~curious(X)))&
((~tall(susan)<~>quiet(susan)))&
(rich(fred))&
(?[X]:((~funny(X)&~humble(X))))&
(patient(john)) | ~happy(mary) | [] | null | 0 |
If someone is either not funny or wise then someone is both brave and rich and vice versa.
If paul is creative then lucy is not tall.
If paul is curious then someone is either creative or not patient and vice versa.
If susan is funny then someone is either not curious or not generous and vice versa.
If someone is creative or curious then someone is generous or not quiet.
Everyone who is not happy is either old or not patient.
Everyone who is either not tall or not old is old and vice versa.
If someone is either not calm or wise then someone is calm or not brave and vice versa.
Everyone who is both not tall and not wise is patient and vice versa.
If fred is not quiet or not old then alice is not old.
Everyone who is creative is either wise or not tall and vice versa.
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.
Lucy is not old or tall.
Susan is either kind or not happy.
Someone is not creative.
Paul is either not kind or quiet.
John is old.
John is not brave.
Alice is either kind or brave.
Alice is quiet or creative. | Paul is not curious. | contradiction | ((?[X]:((~funny(X)<~>wise(X))))<=>(?[X]:((brave(X)&rich(X)))))&
((creative(paul))=>(~tall(lucy)))&
((curious(paul))<=>(?[X]:((creative(X)<~>~patient(X)))))&
((funny(susan))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
((?[X]:((creative(X)|curious(X))))=>(?[X]:((generous(X)|~quiet(X)))))&
(![X]:(~happy(X)=>(old(X)<~>~patient(X))))&
(![X]:((~tall(X)<~>~old(X))<=>old(X)))&
((?[X]:((~calm(X)<~>wise(X))))<=>(?[X]:((calm(X)|~brave(X)))))&
(![X]:((~tall(X)&~wise(X))<=>patient(X)))&
(((~quiet(fred)|~old(fred)))=>(~old(alice)))&
(![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))))&
((~old(lucy)|tall(lucy)))&
((kind(susan)<~>~happy(susan)))&
(?[X]:(~creative(X)))&
((~kind(paul)<~>quiet(paul)))&
(old(john))&
(~brave(john))&
((kind(alice)<~>brave(alice)))&
((quiet(alice)|creative(alice))) | ~curious(paul) | [
"p2",
"p6",
"p8",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2171917294633825568293867
% SZS output start Proof for 2171917294633825568293867
3. curious(paul) <=> ? [X0] : (creative(X0) <~> ~patient(X0)) [input p2]
7. ! [X0] : ((~tall(X0) <~> ~old(X0)) <=> old(X0)) [input p6]
9. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> patient(X0)) [input p8]
11. ! [X0] : (creative(X0) <=> (wise(X0) <~> ~tall(X0))) [input p10]
19. ? [X0] : ~creative(X0) [input p18]
25. ~curious(paul) [input hypothesis]
44. (curious(paul) | ! [X0] : ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (? [X0] : ((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | ~curious(paul)) [nnf transformation 3]
45. (curious(paul) | ! [X0] : ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (? [X1] : ((patient(X1) | ~creative(X1)) & (~patient(X1) | creative(X1))) | ~curious(paul)) [rectify 44]
46. ? [X1] : ((patient(X1) | ~creative(X1)) & (~patient(X1) | creative(X1))) => ((patient(sK2) | ~creative(sK2)) & (~patient(sK2) | creative(sK2))) [choice axiom]
47. (curious(paul) | ! [X0] : ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(sK2) | ~creative(sK2)) & (~patient(sK2) | creative(sK2))) | ~curious(paul)) [skolemisation 45,46]
56. ! [X0] : ((((old(X0) | tall(X0)) & (~old(X0) | ~tall(X0))) | ~old(X0)) & (old(X0) | ((~tall(X0) | old(X0)) & (~old(X0) | tall(X0))))) [nnf transformation 7]
62. ! [X0] : (((~wise(X0) & ~tall(X0)) | ~patient(X0)) & (patient(X0) | (wise(X0) | tall(X0)))) [nnf transformation 9]
63. ! [X0] : (((~wise(X0) & ~tall(X0)) | ~patient(X0)) & (patient(X0) | wise(X0) | tall(X0))) [flattening 62]
64. ! [X0] : ((creative(X0) | ((wise(X0) | tall(X0)) & (~tall(X0) | ~wise(X0)))) & (((tall(X0) | ~wise(X0)) & (~tall(X0) | wise(X0))) | ~creative(X0))) [nnf transformation 11]
73. ? [X0] : ~creative(X0) => ~creative(sK8) [choice axiom]
74. ~creative(sK8) [skolemisation 19,73]
87. curious(paul) | creative(X0) | patient(X0) [cnf transformation 47]
97. old(X0) | ~tall(X0) | old(X0) [cnf transformation 56]
98. ~old(X0) | ~tall(X0) | ~old(X0) [cnf transformation 56]
108. ~patient(X0) | ~wise(X0) [cnf transformation 63]
114. creative(X0) | wise(X0) | tall(X0) [cnf transformation 64]
131. ~creative(sK8) [cnf transformation 74]
139. ~curious(paul) [cnf transformation 25]
140. old(X0) | ~tall(X0) [duplicate literal removal 97]
141. ~old(X0) | ~tall(X0) [duplicate literal removal 98]
183. 10 <=> ! [X0] : (creative(X0) | patient(X0)) [avatar definition]
184. patient(X0) | creative(X0) <- (10) [avatar component clause 183]
186. 11 <=> curious(paul) [avatar definition]
189. 10 | 11 [avatar split clause 87,186,183]
242. ~tall(X0) [subsumption resolution 140,141]
292. creative(X0) | wise(X0) [subsumption resolution 114,242]
371. ~11 [avatar split clause 139,186]
378. creative(X0) | ~wise(X0) <- (10) [resolution 184,108]
379. creative(X0) <- (10) [subsumption resolution 378,292]
380. $false <- (10) [resolution 379,131]
383. ~10 [avatar contradiction clause 380]
384. $false [avatar sat refutation 189,371,383]
% SZS output end Proof for 2171917294633825568293867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or curious is both not rich and not kind. Everyone who is generous is not rich and vice versa. If john is not creative then someone is either not generous or not patient and vice versa. Everyone who is both not strong and not wise is not rich and vice versa. Everyone who is either quiet or not kind is not strong or funny. Everyone who is either quiet or humble is either calm or generous and vice versa. If someone is both humble and quiet then fred is both not tall and not generous. Everyone who is kind or brave is either not curious or not funny. If mary is either not creative or strong then susan is both creative and not funny and vice versa. If lucy is not rich or not patient then john is quiet or not curious and vice versa. If lucy is not rich or creative then mary is either patient or not happy. Everyone who is not quiet is both not brave and not calm and vice versa. If lucy is not quiet then mary is not quiet. Everyone who is kind is either creative or not brave. If someone is not tall or quiet then john is either not creative or not curious and vice versa. Everyone who is not patient or generous is both wise and not quiet. Someone is not wise or not rich. Susan is both calm and not creative. Someone is creative or funny. Alice is calm. Alice is either creative or happy. Fred is either not humble or not patient. Someone is not patient or not strong. | Lucy is not rich. | contradiction | (![X]:((calm(X)<~>curious(X))=>(~rich(X)&~kind(X))))&
(![X]:(generous(X)<=>~rich(X)))&
((~creative(john))<=>(?[X]:((~generous(X)<~>~patient(X)))))&
(![X]:((~strong(X)&~wise(X))<=>~rich(X)))&
(![X]:((quiet(X)<~>~kind(X))=>(~strong(X)|funny(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(calm(X)<~>generous(X))))&
((?[X]:((humble(X)&quiet(X))))=>((~tall(fred)&~generous(fred))))&
(![X]:((kind(X)|brave(X))=>(~curious(X)<~>~funny(X))))&
(((~creative(mary)<~>strong(mary)))<=>((creative(susan)&~funny(susan))))&
(((~rich(lucy)|~patient(lucy)))<=>((quiet(john)|~curious(john))))&
(((~rich(lucy)|creative(lucy)))=>((patient(mary)<~>~happy(mary))))&
(![X]:(~quiet(X)<=>(~brave(X)&~calm(X))))&
((~quiet(lucy))=>(~quiet(mary)))&
(![X]:(kind(X)=>(creative(X)<~>~brave(X))))&
((?[X]:((~tall(X)|quiet(X))))<=>((~creative(john)<~>~curious(john))))&
(![X]:((~patient(X)|generous(X))=>(wise(X)&~quiet(X))))&
(?[X]:((~wise(X)|~rich(X))))&
((calm(susan)&~creative(susan)))&
(?[X]:((creative(X)|funny(X))))&
(calm(alice))&
((creative(alice)<~>happy(alice)))&
((~humble(fred)<~>~patient(fred)))&
(?[X]:((~patient(X)|~strong(X)))) | ~rich(lucy) | [
"p1",
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6662513716136392408531372
% SZS output start Proof for 6662513716136392408531372
2. ! [X0] : (generous(X0) <=> ~rich(X0)) [input p1]
4. ! [X0] : ((~wise(X0) & ~strong(X0)) <=> ~rich(X0)) [input p3]
16. ! [X0] : ((generous(X0) | ~patient(X0)) => (~quiet(X0) & wise(X0))) [input p15]
24. ~rich(lucy) [input hypothesis]
33. ! [X0] : ((~quiet(X0) & wise(X0)) | (~generous(X0) & patient(X0))) [ennf transformation 16]
35. ! [X0] : ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))) [nnf transformation 2]
40. ! [X0] : (((~wise(X0) & ~strong(X0)) | rich(X0)) & (~rich(X0) | (wise(X0) | strong(X0)))) [nnf transformation 4]
41. ! [X0] : (((~wise(X0) & ~strong(X0)) | rich(X0)) & (~rich(X0) | wise(X0) | strong(X0))) [flattening 40]
70. generous(X0) | rich(X0) [cnf transformation 35]
77. ~wise(X0) | rich(X0) [cnf transformation 41]
121. ~generous(X0) | wise(X0) [cnf transformation 33]
134. ~rich(lucy) [cnf transformation 24]
197. 14 <=> rich(lucy) [avatar definition]
199. ~rich(lucy) <- (~14) [avatar component clause 197]
297. ~14 [avatar split clause 134,197]
306. wise(X0) | rich(X0) [resolution 121,70]
307. rich(X0) [subsumption resolution 306,77]
325. $false <- (~14) [resolution 307,199]
329. 14 [avatar contradiction clause 325]
330. $false [avatar sat refutation 297,329]
% SZS output end Proof for 6662513716136392408531372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and quiet then john is rich.
Everyone who is either not brave or not humble is not curious.
If fred is both humble and not rich then lucy is either not calm or quiet.
If lucy is brave or wise then alice is both generous and not happy.
If mary is either not generous or not old then alice is both not patient and not quiet and vice versa.
If alice is not strong then someone is creative.
Everyone who is not tall or not kind is not creative and vice versa.
If john is both wise and not brave then mary is both calm and humble.
Everyone who is humble or quiet is wise or happy.
If someone is both not humble and not wise then someone is not old or not tall and vice versa.
Everyone who is not strong or not creative is both not generous and creative and vice versa.
Everyone who is not quiet is both calm and not curious.
If john is both not happy and calm then mary is both happy and wise.
Everyone who is both generous and not rich is not kind or patient.
Everyone who is either wise or generous is kind.
Everyone who is either brave or patient is both not funny and funny and vice versa.
Someone is both not strong and old.
Someone is either not tall or not old.
Someone is both generous and quiet.
Someone is tall.
Mary is wise or not quiet.
John is both not funny and tall.
Someone is not strong. | Alice is not strong. | neutral | ((?[X]:((brave(X)&quiet(X))))=>(rich(john)))&
(![X]:((~brave(X)<~>~humble(X))=>~curious(X)))&
(((humble(fred)&~rich(fred)))=>((~calm(lucy)<~>quiet(lucy))))&
(((brave(lucy)|wise(lucy)))=>((generous(alice)&~happy(alice))))&
(((~generous(mary)<~>~old(mary)))<=>((~patient(alice)&~quiet(alice))))&
((~strong(alice))=>(?[X]:(creative(X))))&
(![X]:((~tall(X)|~kind(X))<=>~creative(X)))&
(((wise(john)&~brave(john)))=>((calm(mary)&humble(mary))))&
(![X]:((humble(X)|quiet(X))=>(wise(X)|happy(X))))&
((?[X]:((~humble(X)&~wise(X))))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~strong(X)|~creative(X))<=>(~generous(X)&creative(X))))&
(![X]:(~quiet(X)=>(calm(X)&~curious(X))))&
(((~happy(john)&calm(john)))=>((happy(mary)&wise(mary))))&
(![X]:((generous(X)&~rich(X))=>(~kind(X)|patient(X))))&
(![X]:((wise(X)<~>generous(X))=>kind(X)))&
(![X]:((brave(X)<~>patient(X))<=>(~funny(X)&funny(X))))&
(?[X]:((~strong(X)&old(X))))&
(?[X]:((~tall(X)<~>~old(X))))&
(?[X]:((generous(X)&quiet(X))))&
(?[X]:(tall(X)))&
((wise(mary)|~quiet(mary)))&
((~funny(john)&tall(john)))&
(?[X]:(~strong(X))) | ~strong(alice) | [] | null | 0 |
Everyone who is both tall and strong is not wise or not happy and vice versa.
If susan is not curious then someone is either not kind or not wise.
Everyone who is not humble is both not humble and not creative.
If someone is either not happy or not patient then alice is both strong and not creative.
If someone is not rich or rich then paul is either not kind or not calm.
Everyone who is curious or tall is both brave and generous and vice versa.
If lucy is both not quiet and not rich then someone is calm.
Everyone who is either not patient or not kind is not creative or not patient.
If mary is not old then someone is generous.
Everyone who is either creative or generous is either not kind or strong and vice versa.
Everyone who is either not calm or not old is not curious.
Everyone who is either tall or not calm is both not old and not humble.
If someone is generous or patient then lucy is either not patient or funny and vice versa.
Everyone who is kind or patient is both not kind and creative and vice versa.
Everyone who is humble is either not kind or patient.
Someone is rich.
Fred is funny.
Someone is not old or not rich.
Someone is curious.
Mary is either not generous or not funny.
Someone is brave or strong. | Lucy is not strong. | neutral | (![X]:((tall(X)&strong(X))<=>(~wise(X)|~happy(X))))&
((~curious(susan))=>(?[X]:((~kind(X)<~>~wise(X)))))&
(![X]:(~humble(X)=>(~humble(X)&~creative(X))))&
((?[X]:((~happy(X)<~>~patient(X))))=>((strong(alice)&~creative(alice))))&
((?[X]:((~rich(X)|rich(X))))=>((~kind(paul)<~>~calm(paul))))&
(![X]:((curious(X)|tall(X))<=>(brave(X)&generous(X))))&
(((~quiet(lucy)&~rich(lucy)))=>(?[X]:(calm(X))))&
(![X]:((~patient(X)<~>~kind(X))=>(~creative(X)|~patient(X))))&
((~old(mary))=>(?[X]:(generous(X))))&
(![X]:((creative(X)<~>generous(X))<=>(~kind(X)<~>strong(X))))&
(![X]:((~calm(X)<~>~old(X))=>~curious(X)))&
(![X]:((tall(X)<~>~calm(X))=>(~old(X)&~humble(X))))&
((?[X]:((generous(X)|patient(X))))<=>((~patient(lucy)<~>funny(lucy))))&
(![X]:((kind(X)|patient(X))<=>(~kind(X)&creative(X))))&
(![X]:(humble(X)=>(~kind(X)<~>patient(X))))&
(?[X]:(rich(X)))&
(funny(fred))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:(curious(X)))&
((~generous(mary)<~>~funny(mary)))&
(?[X]:((brave(X)|strong(X)))) | ~strong(lucy) | [] | null | 0 |
If someone is humble then someone is either not patient or not rich and vice versa. If alice is brave or funny then someone is either not quiet or not funny and vice versa. Everyone who is both funny and brave is not curious or calm and vice versa. Everyone who is either strong or not happy is both tall and generous. Everyone who is either wise or tall is not brave or calm and vice versa. If alice is calm then someone is both not curious and brave and vice versa. Everyone who is calm is either rich or calm. Everyone who is both brave and curious is either old or not patient and vice versa. Everyone who is calm is old or not happy. If john is both quiet and funny then john is both creative and happy and vice versa. Everyone who is either tall or happy is curious and vice versa. If someone is both not funny and generous then someone is not quiet or curious. If someone is old then someone is either not humble or not funny and vice versa. Everyone who is humble is not patient or not kind. If fred is both happy and not calm then john is not wise or quiet and vice versa. Everyone who is happy or calm is not calm. Mary is both quiet and not humble. Lucy is either not generous or strong. Someone is tall or not strong. Someone is not humble. Someone is not happy or not funny. Someone is both humble and not funny. Someone is both happy and not patient. | Lucy is not humble. | neutral | ((?[X]:(humble(X)))<=>(?[X]:((~patient(X)<~>~rich(X)))))&
(((brave(alice)|funny(alice)))<=>(?[X]:((~quiet(X)<~>~funny(X)))))&
(![X]:((funny(X)&brave(X))<=>(~curious(X)|calm(X))))&
(![X]:((strong(X)<~>~happy(X))=>(tall(X)&generous(X))))&
(![X]:((wise(X)<~>tall(X))<=>(~brave(X)|calm(X))))&
((calm(alice))<=>(?[X]:((~curious(X)&brave(X)))))&
(![X]:(calm(X)=>(rich(X)<~>calm(X))))&
(![X]:((brave(X)&curious(X))<=>(old(X)<~>~patient(X))))&
(![X]:(calm(X)=>(old(X)|~happy(X))))&
(((quiet(john)&funny(john)))<=>((creative(john)&happy(john))))&
(![X]:((tall(X)<~>happy(X))<=>curious(X)))&
((?[X]:((~funny(X)&generous(X))))=>(?[X]:((~quiet(X)|curious(X)))))&
((?[X]:(old(X)))<=>(?[X]:((~humble(X)<~>~funny(X)))))&
(![X]:(humble(X)=>(~patient(X)|~kind(X))))&
(((happy(fred)&~calm(fred)))<=>((~wise(john)|quiet(john))))&
(![X]:((happy(X)|calm(X))=>~calm(X)))&
((quiet(mary)&~humble(mary)))&
((~generous(lucy)<~>strong(lucy)))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)|~funny(X))))&
(?[X]:((humble(X)&~funny(X))))&
(?[X]:((happy(X)&~patient(X)))) | ~humble(lucy) | [] | null | 0 |
Everyone who is not patient is both happy and curious. Everyone who is quiet or generous is calm or not kind. Everyone who is not wise is tall or not old. Everyone who is wise or not quiet is not generous or brave and vice versa. If mary is not humble or old then someone is not happy or not old and vice versa. If someone is curious or wise then someone is not kind or not wise and vice versa. Everyone who is not old is both not wise and humble. If susan is tall then mary is both quiet and brave and vice versa. If someone is brave or creative then susan is not patient and vice versa. Everyone who is not curious is not happy. Everyone who is quiet is funny. If someone is kind then someone is both not rich and not patient. Everyone who is both brave and tall is both generous and happy and vice versa. Everyone who is either generous or creative is either quiet or not tall and vice versa. Everyone who is calm is curious. If someone is either patient or not old then susan is both not happy and not funny and vice versa. Someone is not rich or generous. Alice is not brave or not curious. Someone is either rich or not quiet. Paul is either not old or calm. Paul is both quiet and creative. Someone is either quiet or strong. Mary is kind or not patient. Someone is either not humble or not old. | Mary is not curious. | contradiction | (![X]:(~patient(X)=>(happy(X)&curious(X))))&
(![X]:((quiet(X)|generous(X))=>(calm(X)|~kind(X))))&
(![X]:(~wise(X)=>(tall(X)|~old(X))))&
(![X]:((wise(X)|~quiet(X))<=>(~generous(X)|brave(X))))&
(((~humble(mary)|old(mary)))<=>(?[X]:((~happy(X)|~old(X)))))&
((?[X]:((curious(X)|wise(X))))<=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:(~old(X)=>(~wise(X)&humble(X))))&
((tall(susan))<=>((quiet(mary)&brave(mary))))&
((?[X]:((brave(X)|creative(X))))<=>(~patient(susan)))&
(![X]:(~curious(X)=>~happy(X)))&
(![X]:(quiet(X)=>funny(X)))&
((?[X]:(kind(X)))=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:((brave(X)&tall(X))<=>(generous(X)&happy(X))))&
(![X]:((generous(X)<~>creative(X))<=>(quiet(X)<~>~tall(X))))&
(![X]:(calm(X)=>curious(X)))&
((?[X]:((patient(X)<~>~old(X))))<=>((~happy(susan)&~funny(susan))))&
(?[X]:((~rich(X)|generous(X))))&
((~brave(alice)|~curious(alice)))&
(?[X]:((rich(X)<~>~quiet(X))))&
((~old(paul)<~>calm(paul)))&
((quiet(paul)&creative(paul)))&
(?[X]:((quiet(X)<~>strong(X))))&
((kind(mary)|~patient(mary)))&
(?[X]:((~humble(X)<~>~old(X)))) | ~curious(mary) | [
"p0",
"p4",
"p6",
"p8",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6419925990632162366452782
% SZS output start Proof for 6419925990632162366452782
1. ! [X0] : (~patient(X0) => (curious(X0) & happy(X0))) [input p0]
5. (old(mary) | ~humble(mary)) <=> ? [X0] : (~old(X0) | ~happy(X0)) [input p4]
7. ! [X0] : (~old(X0) => (humble(X0) & ~wise(X0))) [input p6]
9. ? [X0] : (creative(X0) | brave(X0)) <=> ~patient(susan) [input p8]
16. ? [X0] : (patient(X0) <~> ~old(X0)) <=> (~funny(susan) & ~happy(susan)) [input p15]
21. creative(paul) & quiet(paul) [input p20]
25. ~curious(mary) [input hypothesis]
28. ! [X0] : ((curious(X0) & happy(X0)) | patient(X0)) [ennf transformation 1]
33. ! [X0] : ((humble(X0) & ~wise(X0)) | old(X0)) [ennf transformation 7]
40. ((old(mary) | ~humble(mary)) | ! [X0] : (old(X0) & happy(X0))) & (? [X0] : (~old(X0) | ~happy(X0)) | (~old(mary) & humble(mary))) [nnf transformation 5]
41. (old(mary) | ~humble(mary) | ! [X0] : (old(X0) & happy(X0))) & (? [X0] : (~old(X0) | ~happy(X0)) | (~old(mary) & humble(mary))) [flattening 40]
42. (old(mary) | ~humble(mary) | ! [X0] : (old(X0) & happy(X0))) & (? [X1] : (~old(X1) | ~happy(X1)) | (~old(mary) & humble(mary))) [rectify 41]
43. ? [X1] : (~old(X1) | ~happy(X1)) => (~old(sK0) | ~happy(sK0)) [choice axiom]
44. (old(mary) | ~humble(mary) | ! [X0] : (old(X0) & happy(X0))) & ((~old(sK0) | ~happy(sK0)) | (~old(mary) & humble(mary))) [skolemisation 42,43]
52. (? [X0] : (creative(X0) | brave(X0)) | patient(susan)) & (~patient(susan) | ! [X0] : (~creative(X0) & ~brave(X0))) [nnf transformation 9]
53. (? [X0] : (creative(X0) | brave(X0)) | patient(susan)) & (~patient(susan) | ! [X1] : (~creative(X1) & ~brave(X1))) [rectify 52]
54. ? [X0] : (creative(X0) | brave(X0)) => (creative(sK3) | brave(sK3)) [choice axiom]
55. ((creative(sK3) | brave(sK3)) | patient(susan)) & (~patient(susan) | ! [X1] : (~creative(X1) & ~brave(X1))) [skolemisation 53,54]
62. (? [X0] : ((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (funny(susan) | happy(susan))) & ((~funny(susan) & ~happy(susan)) | ! [X0] : ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) [nnf transformation 16]
63. (? [X0] : ((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | funny(susan) | happy(susan)) & ((~funny(susan) & ~happy(susan)) | ! [X0] : ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) [flattening 62]
64. (? [X0] : ((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | funny(susan) | happy(susan)) & ((~funny(susan) & ~happy(susan)) | ! [X1] : ((patient(X1) | old(X1)) & (~old(X1) | ~patient(X1)))) [rectify 63]
65. ? [X0] : ((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) => ((old(sK5) | ~patient(sK5)) & (~old(sK5) | patient(sK5))) [choice axiom]
66. (((old(sK5) | ~patient(sK5)) & (~old(sK5) | patient(sK5))) | funny(susan) | happy(susan)) & ((~funny(susan) & ~happy(susan)) | ! [X1] : ((patient(X1) | old(X1)) & (~old(X1) | ~patient(X1)))) [skolemisation 64,65]
79. happy(X0) | patient(X0) [cnf transformation 28]
80. curious(X0) | patient(X0) [cnf transformation 28]
91. old(mary) | ~humble(mary) | old(X0) [cnf transformation 44]
97. humble(X0) | old(X0) [cnf transformation 33]
102. ~patient(susan) | ~creative(X1) [cnf transformation 55]
121. ~happy(susan) | ~old(X1) | ~patient(X1) [cnf transformation 66]
134. creative(paul) [cnf transformation 21]
140. ~curious(mary) [cnf transformation 25]
142. 1 <=> ! [X0] : old(X0) [avatar definition]
143. old(X0) <- (1) [avatar component clause 142]
145. 2 <=> humble(mary) [avatar definition]
147. ~humble(mary) <- (~2) [avatar component clause 145]
149. 3 <=> old(mary) [avatar definition]
151. old(mary) <- (3) [avatar component clause 149]
152. 1 | ~2 | 3 [avatar split clause 91,149,145,142]
215. 18 <=> patient(susan) [avatar definition]
228. 21 <=> ! [X1] : ~creative(X1) [avatar definition]
229. ~creative(X1) <- (21) [avatar component clause 228]
230. 21 | ~18 [avatar split clause 102,215,228]
249. 26 <=> happy(susan) [avatar definition]
250. ~happy(susan) <- (~26) [avatar component clause 249]
271. 31 <=> ! [X1] : (~old(X1) | ~patient(X1)) [avatar definition]
272. ~old(X1) | ~patient(X1) <- (31) [avatar component clause 271]
275. 31 | ~26 [avatar split clause 121,249,271]
329. 43 <=> patient(mary) [avatar definition]
330. patient(mary) <- (43) [avatar component clause 329]
342. patient(susan) <- (~26) [resolution 79,250]
345. 18 | 26 [avatar split clause 342,249,215]
346. $false <- (21) [resolution 229,134]
347. ~21 [avatar contradiction clause 346]
350. patient(mary) [resolution 80,140]
354. 43 [avatar split clause 350,329]
355. old(mary) <- (~2) [resolution 97,147]
356. 3 | 2 [avatar split clause 355,145,149]
375. ~patient(X1) <- (1, 31) [resolution 272,143]
377. $false <- (1, 31, 43) [resolution 375,330]
382. ~1 | ~31 | ~43 [avatar contradiction clause 377]
384. ~patient(mary) <- (3, 31) [resolution 151,272]
385. $false <- (3, 31, 43) [subsumption resolution 384,330]
386. ~3 | ~31 | ~43 [avatar contradiction clause 385]
387. $false [avatar sat refutation 152,230,275,345,347,354,356,382,386]
% SZS output end Proof for 6419925990632162366452782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not humble or not strong then fred is not creative and vice versa.
If someone is either strong or kind then someone is either wise or happy.
Everyone who is either kind or not strong is tall and vice versa.
Everyone who is kind or rich is not strong or calm.
If fred is creative then someone is not funny and vice versa.
Everyone who is both not brave and patient is brave and vice versa.
If someone is both patient and brave then fred is not quiet.
Everyone who is funny or not calm is patient and vice versa.
Everyone who is either not humble or not funny is not tall.
Everyone who is generous or old is both not curious and tall.
If someone is both not creative and not humble then susan is either not kind or generous and vice versa.
Everyone who is either creative or not wise is not calm or not brave and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Everyone who is not strong is both not brave and funny and vice versa.
Everyone who is calm or quiet is both not funny and wise and vice versa.
Fred is old or not generous.
Someone is not kind.
Someone is both rich and curious.
John is not humble.
John is not generous or kind.
John is either patient or not rich.
Mary is either not old or curious. | Mary is happy. | neutral | (((~humble(mary)|~strong(mary)))<=>(~creative(fred)))&
((?[X]:((strong(X)<~>kind(X))))=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((kind(X)<~>~strong(X))<=>tall(X)))&
(![X]:((kind(X)|rich(X))=>(~strong(X)|calm(X))))&
((creative(fred))<=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)&patient(X))<=>brave(X)))&
((?[X]:((patient(X)&brave(X))))=>(~quiet(fred)))&
(![X]:((funny(X)|~calm(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
((old(fred)|~generous(fred)))&
(?[X]:(~kind(X)))&
(?[X]:((rich(X)&curious(X))))&
(~humble(john))&
((~generous(john)|kind(john)))&
((patient(john)<~>~rich(john)))&
((~old(mary)<~>curious(mary))) | happy(mary) | [] | null | 0 |
Everyone who is not curious or tall is both curious and wise. If alice is not wise or wise then someone is happy and vice versa. Everyone who is not old or not humble is not brave or rich. Everyone who is both happy and not tall is both old and curious. If someone is both patient and humble then someone is calm or strong and vice versa. Everyone who is both not curious and happy is both humble and creative and vice versa. Everyone who is not rich or not humble is both not humble and not calm and vice versa. Everyone who is not calm or creative is not patient. If someone is either not happy or creative then john is both rich and not calm and vice versa. Everyone who is either not tall or old is not tall or generous. If susan is either tall or humble then paul is either rich or not patient and vice versa. If someone is humble or not wise then someone is both not happy and not tall and vice versa. Everyone who is either calm or not rich is both not brave and generous and vice versa. If john is not brave or not curious then someone is either humble or not wise. Everyone who is either not calm or rich is both kind and not strong and vice versa. Someone is not tall. Someone is both not creative and not generous. Someone is either strong or not kind. Paul is generous or not generous. Someone is not humble or wise. Paul is generous. Someone is both kind and old. | Alice is kind. | neutral | (![X]:((~curious(X)|tall(X))=>(curious(X)&wise(X))))&
(((~wise(alice)|wise(alice)))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)|~humble(X))=>(~brave(X)|rich(X))))&
(![X]:((happy(X)&~tall(X))=>(old(X)&curious(X))))&
((?[X]:((patient(X)&humble(X))))<=>(?[X]:((calm(X)|strong(X)))))&
(![X]:((~curious(X)&happy(X))<=>(humble(X)&creative(X))))&
(![X]:((~rich(X)|~humble(X))<=>(~humble(X)&~calm(X))))&
(![X]:((~calm(X)|creative(X))=>~patient(X)))&
((?[X]:((~happy(X)<~>creative(X))))<=>((rich(john)&~calm(john))))&
(![X]:((~tall(X)<~>old(X))=>(~tall(X)|generous(X))))&
(((tall(susan)<~>humble(susan)))<=>((rich(paul)<~>~patient(paul))))&
((?[X]:((humble(X)|~wise(X))))<=>(?[X]:((~happy(X)&~tall(X)))))&
(![X]:((calm(X)<~>~rich(X))<=>(~brave(X)&generous(X))))&
(((~brave(john)|~curious(john)))=>(?[X]:((humble(X)<~>~wise(X)))))&
(![X]:((~calm(X)<~>rich(X))<=>(kind(X)&~strong(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~creative(X)&~generous(X))))&
(?[X]:((strong(X)<~>~kind(X))))&
((generous(paul)|~generous(paul)))&
(?[X]:((~humble(X)|wise(X))))&
(generous(paul))&
(?[X]:((kind(X)&old(X)))) | kind(alice) | [] | null | 0 |
Everyone who is patient is either calm or not strong.
Everyone who is not calm is either not strong or not brave.
Everyone who is both happy and funny is generous or creative and vice versa.
Everyone who is both happy and not strong is old or not calm and vice versa.
Everyone who is generous is not rich or not happy and vice versa.
Everyone who is both curious and old is both humble and wise.
Everyone who is not quiet or strong is both generous and not generous.
If someone is funny or not kind then lucy is not brave or quiet.
If someone is either funny or brave then alice is kind or rich.
If someone is wise or not curious then alice is kind or generous.
If someone is rich or not calm then susan is either not creative or patient.
Everyone who is not curious is tall or kind.
If paul is not brave then someone is patient or wise and vice versa.
If john is both old and not happy then someone is old and vice versa.
Everyone who is not rich or calm is generous or not humble and vice versa.
Everyone who is both not funny and happy is both not generous and humble and vice versa.
Someone is not calm.
Fred is kind.
Lucy is rich.
Someone is not old or not curious.
Someone is not patient. | Susan is strong. | contradiction | (![X]:(patient(X)=>(calm(X)<~>~strong(X))))&
(![X]:(~calm(X)=>(~strong(X)<~>~brave(X))))&
(![X]:((happy(X)&funny(X))<=>(generous(X)|creative(X))))&
(![X]:((happy(X)&~strong(X))<=>(old(X)|~calm(X))))&
(![X]:(generous(X)<=>(~rich(X)|~happy(X))))&
(![X]:((curious(X)&old(X))=>(humble(X)&wise(X))))&
(![X]:((~quiet(X)|strong(X))=>(generous(X)&~generous(X))))&
((?[X]:((funny(X)|~kind(X))))=>((~brave(lucy)|quiet(lucy))))&
((?[X]:((funny(X)<~>brave(X))))=>((kind(alice)|rich(alice))))&
((?[X]:((wise(X)|~curious(X))))=>((kind(alice)|generous(alice))))&
((?[X]:((rich(X)|~calm(X))))=>((~creative(susan)<~>patient(susan))))&
(![X]:(~curious(X)=>(tall(X)|kind(X))))&
((~brave(paul))<=>(?[X]:((patient(X)|wise(X)))))&
(((old(john)&~happy(john)))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)|calm(X))<=>(generous(X)|~humble(X))))&
(![X]:((~funny(X)&happy(X))<=>(~generous(X)&humble(X))))&
(?[X]:(~calm(X)))&
(kind(fred))&
(rich(lucy))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:(~patient(X))) | strong(susan) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 9172695556658505732906244
% SZS output start Proof for 9172695556658505732906244
7. ! [X0] : ((strong(X0) | ~quiet(X0)) => (~generous(X0) & generous(X0))) [input p6]
22. strong(susan) [input hypothesis]
31. ! [X0] : (strong(X0) => (~generous(X0) & generous(X0))) [pure predicate removal 7]
34. ! [X0] : ((~generous(X0) & generous(X0)) | ~strong(X0)) [ennf transformation 31]
79. generous(X0) | ~strong(X0) [cnf transformation 34]
80. ~generous(X0) | ~strong(X0) [cnf transformation 34]
102. strong(susan) [cnf transformation 22]
105. ~strong(X0) [subsumption resolution 79,80]
147. $false [subsumption resolution 102,105]
% SZS output end Proof for 9172695556658505732906244
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is both old and not kind and vice versa.
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.
If mary is either quiet or patient then someone is strong or wise.
Everyone who is humble or curious is strong or not funny and vice versa.
Everyone who is old or not brave is both funny and not kind and vice versa.
Mary is not old or not patient.
Susan is not patient.
Someone is both not calm and happy.
Mary is wise.
Someone is strong or not strong.
Susan is funny.
John is both creative and curious.
Someone is not wise or not old. | John is not strong. | contradiction | (![X]:(~patient(X)<=>(old(X)&~kind(X))))&
((?[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))))&
(((quiet(mary)<~>patient(mary)))=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((humble(X)|curious(X))<=>(strong(X)|~funny(X))))&
(![X]:((old(X)|~brave(X))<=>(funny(X)&~kind(X))))&
((~old(mary)|~patient(mary)))&
(~patient(susan))&
(?[X]:((~calm(X)&happy(X))))&
(wise(mary))&
(?[X]:((strong(X)|~strong(X))))&
(funny(susan))&
((creative(john)&curious(john)))&
(?[X]:((~wise(X)|~old(X)))) | ~strong(john) | [
"p4",
"p5",
"p8",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8811207384255739434986039
% SZS output start Proof for 8811207384255739434986039
5. ! [X0] : (old(X0) <=> (~rich(X0) | ~kind(X0))) [input p4]
6. ! [X0] : ((humble(X0) | rich(X0)) <=> calm(X0)) [input p5]
9. ! [X0] : ((calm(X0) | creative(X0)) <=> (~rich(X0) | funny(X0))) [input p8]
15. ! [X0] : ((curious(X0) | humble(X0)) <=> (~funny(X0) | strong(X0))) [input p14]
16. ! [X0] : ((~brave(X0) | old(X0)) <=> (~kind(X0) & funny(X0))) [input p15]
23. curious(john) & creative(john) [input p22]
25. ~strong(john) [input hypothesis]
43. ! [X0] : ((old(X0) | (rich(X0) & kind(X0))) & ((~rich(X0) | ~kind(X0)) | ~old(X0))) [nnf transformation 5]
44. ! [X0] : ((old(X0) | (rich(X0) & kind(X0))) & (~rich(X0) | ~kind(X0) | ~old(X0))) [flattening 43]
45. ! [X0] : (((humble(X0) | rich(X0)) | ~calm(X0)) & (calm(X0) | (~humble(X0) & ~rich(X0)))) [nnf transformation 6]
46. ! [X0] : ((humble(X0) | rich(X0) | ~calm(X0)) & (calm(X0) | (~humble(X0) & ~rich(X0)))) [flattening 45]
57. ! [X0] : (((calm(X0) | creative(X0)) | (rich(X0) & ~funny(X0))) & ((~rich(X0) | funny(X0)) | (~calm(X0) & ~creative(X0)))) [nnf transformation 9]
58. ! [X0] : ((calm(X0) | creative(X0) | (rich(X0) & ~funny(X0))) & (~rich(X0) | funny(X0) | (~calm(X0) & ~creative(X0)))) [flattening 57]
64. ! [X0] : (((curious(X0) | humble(X0)) | (funny(X0) & ~strong(X0))) & ((~funny(X0) | strong(X0)) | (~curious(X0) & ~humble(X0)))) [nnf transformation 15]
65. ! [X0] : ((curious(X0) | humble(X0) | (funny(X0) & ~strong(X0))) & (~funny(X0) | strong(X0) | (~curious(X0) & ~humble(X0)))) [flattening 64]
66. ! [X0] : (((~brave(X0) | old(X0)) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | (brave(X0) & ~old(X0)))) [nnf transformation 16]
67. ! [X0] : ((~brave(X0) | old(X0) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | (brave(X0) & ~old(X0)))) [flattening 66]
92. rich(X0) | old(X0) [cnf transformation 44]
93. ~rich(X0) | calm(X0) [cnf transformation 46]
105. ~rich(X0) | funny(X0) | ~calm(X0) [cnf transformation 58]
119. ~curious(X0) | strong(X0) | ~funny(X0) [cnf transformation 65]
122. ~old(X0) | funny(X0) [cnf transformation 67]
135. curious(john) [cnf transformation 23]
137. ~strong(john) [cnf transformation 25]
220. ~rich(X0) | funny(X0) [subsumption resolution 105,93]
267. funny(X0) | old(X0) [resolution 220,92]
268. funny(X0) [subsumption resolution 267,122]
320. strong(john) | ~funny(john) [resolution 119,135]
323. ~funny(john) [subsumption resolution 320,137]
324. $false [subsumption resolution 323,268]
% SZS output end Proof for 8811207384255739434986039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not humble or not old.
Everyone who is not brave is both not patient and not wise and vice versa.
Everyone who is both not generous and patient is both funny and wise.
Everyone who is not curious is either not wise or calm.
If someone is not happy or not generous then someone is both brave and not brave.
If paul is not old then mary is not wise and vice versa.
If someone is not strong or calm then alice is not old or not brave and vice versa.
Everyone who is not happy or not quiet is kind and vice versa.
If susan is generous then john is both not wise and not calm.
If someone is brave or not rich then someone is either not calm or not quiet.
If someone is quiet then someone is not creative and vice versa.
Everyone who is both not old and not strong is either creative or not old and vice versa.
Everyone who is not strong or generous is either creative or humble.
Everyone who is not calm is funny or quiet.
Lucy is either quiet or humble.
Mary is not rich or not strong.
Paul is not creative.
Someone is both funny and not kind.
Someone is either not tall or not humble.
Mary is both calm and not tall.
Lucy is old or patient. | John is not humble. | neutral | (![X]:(quiet(X)=>(~humble(X)|~old(X))))&
(![X]:(~brave(X)<=>(~patient(X)&~wise(X))))&
(![X]:((~generous(X)&patient(X))=>(funny(X)&wise(X))))&
(![X]:(~curious(X)=>(~wise(X)<~>calm(X))))&
((?[X]:((~happy(X)|~generous(X))))=>(?[X]:((brave(X)&~brave(X)))))&
((~old(paul))<=>(~wise(mary)))&
((?[X]:((~strong(X)|calm(X))))<=>((~old(alice)|~brave(alice))))&
(![X]:((~happy(X)|~quiet(X))<=>kind(X)))&
((generous(susan))=>((~wise(john)&~calm(john))))&
((?[X]:((brave(X)|~rich(X))))=>(?[X]:((~calm(X)<~>~quiet(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:(~creative(X))))&
(![X]:((~old(X)&~strong(X))<=>(creative(X)<~>~old(X))))&
(![X]:((~strong(X)|generous(X))=>(creative(X)<~>humble(X))))&
(![X]:(~calm(X)=>(funny(X)|quiet(X))))&
((quiet(lucy)<~>humble(lucy)))&
((~rich(mary)|~strong(mary)))&
(~creative(paul))&
(?[X]:((funny(X)&~kind(X))))&
(?[X]:((~tall(X)<~>~humble(X))))&
((calm(mary)&~tall(mary)))&
((old(lucy)|patient(lucy))) | ~humble(john) | [] | null | 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.