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
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| proof
stringlengths 684
15.9k
⌀ | rule_concentration
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|---|---|---|---|---|---|---|---|
Everyone who is patient or not patient is calm or tall.
Everyone who is both not rich and not humble is both generous and wise and vice versa.
Everyone who is not quiet or not old is calm and vice versa.
If john is not wise or curious then someone is not patient.
If paul is strong or old then paul is not tall and vice versa.
If someone is wise or kind then someone is both quiet and calm and vice versa.
If lucy is both happy and wise then susan is quiet and vice versa.
If alice is curious or brave then someone is tall or not humble.
Everyone who is not old or not humble is funny and vice versa.
If someone is either funny or not humble then someone is either brave or not calm and vice versa.
Everyone who is funny or not old is both wise and not strong and vice versa.
Everyone who is either strong or not funny is either not tall or tall and vice versa.
If fred is not tall or tall then someone is not curious and vice versa.
If someone is both not curious and happy then someone is both not humble and not wise.
If mary is not quiet or not strong then alice is kind or not tall.
If fred is either calm or not curious then lucy is not rich or brave.
Alice is both not tall and creative.
Someone is wise or not wise.
Someone is not funny.
Someone is both creative and happy.
Lucy is not old or not happy.
Lucy is wise or creative. | Paul is not brave. | entailment | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~rich(X)&~humble(X))<=>(generous(X)&wise(X))))&
(![X]:((~quiet(X)|~old(X))<=>calm(X)))&
(((~wise(john)|curious(john)))=>(?[X]:(~patient(X))))&
(((strong(paul)|old(paul)))<=>(~tall(paul)))&
((?[X]:((wise(X)|kind(X))))<=>(?[X]:((quiet(X)&calm(X)))))&
(((happy(lucy)&wise(lucy)))<=>(quiet(susan)))&
(((curious(alice)|brave(alice)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~old(X)|~humble(X))<=>funny(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((funny(X)|~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~tall(X)<~>tall(X))))&
(((~tall(fred)|tall(fred)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~humble(X)&~wise(X)))))&
(((~quiet(mary)|~strong(mary)))=>((kind(alice)|~tall(alice))))&
(((calm(fred)<~>~curious(fred)))=>((~rich(lucy)|brave(lucy))))&
((~tall(alice)&creative(alice)))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)&happy(X))))&
((~old(lucy)|~happy(lucy)))&
((wise(lucy)|creative(lucy))) | ~brave(paul) | [
"p0",
"p4",
"p8",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6417385777878051930743826
% SZS output start Proof for 6417385777878051930743826
1. ! [X0] : ((~patient(X0) | patient(X0)) => (tall(X0) | calm(X0))) [input p0]
5. (old(paul) | strong(paul)) <=> ~tall(paul) [input p4]
9. ! [X0] : ((~humble(X0) | ~old(X0)) <=> funny(X0)) [input p8]
10. ? [X0] : (funny(X0) <~> ~humble(X0)) <=> ? [X0] : (brave(X0) <~> ~calm(X0)) [input p9]
11. ! [X0] : ((~old(X0) | funny(X0)) <=> (~strong(X0) & wise(X0))) [input p10]
12. ! [X0] : ((strong(X0) <~> ~funny(X0)) <=> (~tall(X0) <~> tall(X0))) [input p11]
23. brave(paul) [input hypothesis]
25. ? [X0] : (funny(X0) <~> ~humble(X0)) <=> ? [X1] : (brave(X1) <~> ~calm(X1)) [rectify 10]
30. ! [X0] : ((tall(X0) | calm(X0)) | (patient(X0) & ~patient(X0))) [ennf transformation 1]
31. ! [X0] : (tall(X0) | calm(X0) | (patient(X0) & ~patient(X0))) [flattening 30]
45. ((old(paul) | strong(paul)) | tall(paul)) & (~tall(paul) | (~old(paul) & ~strong(paul))) [nnf transformation 5]
46. (old(paul) | strong(paul) | tall(paul)) & (~tall(paul) | (~old(paul) & ~strong(paul))) [flattening 45]
56. ! [X0] : (((~humble(X0) | ~old(X0)) | ~funny(X0)) & (funny(X0) | (humble(X0) & old(X0)))) [nnf transformation 9]
57. ! [X0] : ((~humble(X0) | ~old(X0) | ~funny(X0)) & (funny(X0) | (humble(X0) & old(X0)))) [flattening 56]
58. (? [X0] : ((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | ! [X1] : ((brave(X1) | calm(X1)) & (~calm(X1) | ~brave(X1)))) & (? [X1] : ((calm(X1) | ~brave(X1)) & (~calm(X1) | brave(X1))) | ! [X0] : ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0)))) [nnf transformation 25]
59. (? [X0] : ((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | ! [X1] : ((brave(X1) | calm(X1)) & (~calm(X1) | ~brave(X1)))) & (? [X2] : ((calm(X2) | ~brave(X2)) & (~calm(X2) | brave(X2))) | ! [X3] : ((funny(X3) | humble(X3)) & (~humble(X3) | ~funny(X3)))) [rectify 58]
60. ? [X0] : ((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) => ((humble(sK4) | ~funny(sK4)) & (~humble(sK4) | funny(sK4))) [choice axiom]
61. ? [X2] : ((calm(X2) | ~brave(X2)) & (~calm(X2) | brave(X2))) => ((calm(sK5) | ~brave(sK5)) & (~calm(sK5) | brave(sK5))) [choice axiom]
62. (((humble(sK4) | ~funny(sK4)) & (~humble(sK4) | funny(sK4))) | ! [X1] : ((brave(X1) | calm(X1)) & (~calm(X1) | ~brave(X1)))) & (((calm(sK5) | ~brave(sK5)) & (~calm(sK5) | brave(sK5))) | ! [X3] : ((funny(X3) | humble(X3)) & (~humble(X3) | ~funny(X3)))) [skolemisation 59,61,60]
63. ! [X0] : (((~old(X0) | funny(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (old(X0) & ~funny(X0)))) [nnf transformation 11]
64. ! [X0] : ((~old(X0) | funny(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (old(X0) & ~funny(X0)))) [flattening 63]
65. ! [X0] : ((((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0))))) [nnf transformation 12]
81. tall(X0) | calm(X0) | ~patient(X0) [cnf transformation 31]
82. tall(X0) | calm(X0) | patient(X0) [cnf transformation 31]
93. ~tall(paul) | ~old(paul) [cnf transformation 46]
105. funny(X0) | old(X0) [cnf transformation 57]
106. funny(X0) | humble(X0) [cnf transformation 57]
112. ~humble(sK4) | funny(sK4) | ~calm(X1) | ~brave(X1) [cnf transformation 62]
118. ~funny(X0) | ~strong(X0) [cnf transformation 64]
125. ~funny(X0) | strong(X0) | tall(X0) | tall(X0) [cnf transformation 65]
126. ~funny(X0) | strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 65]
127. funny(X0) | ~strong(X0) | tall(X0) | tall(X0) [cnf transformation 65]
128. funny(X0) | ~strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 65]
143. brave(paul) [cnf transformation 23]
144. ~funny(X0) | strong(X0) | tall(X0) [duplicate literal removal 125]
145. ~funny(X0) | strong(X0) | ~tall(X0) [duplicate literal removal 126]
146. funny(X0) | ~strong(X0) | tall(X0) [duplicate literal removal 127]
147. funny(X0) | ~strong(X0) | ~tall(X0) [duplicate literal removal 128]
148. tall(X0) | calm(X0) [subsumption resolution 81,82]
164. 4 <=> tall(paul) [avatar definition]
165. ~tall(paul) <- (~4) [avatar component clause 164]
172. 6 <=> old(paul) [avatar definition]
173. ~old(paul) <- (~6) [avatar component clause 172]
176. ~6 | ~4 [avatar split clause 93,164,172]
252. 23 <=> ! [X1] : (~calm(X1) | ~brave(X1)) [avatar definition]
253. ~brave(X1) | ~calm(X1) <- (23) [avatar component clause 252]
257. 24 <=> funny(sK4) [avatar definition]
259. funny(sK4) <- (24) [avatar component clause 257]
261. funny(sK4) | ~calm(X1) | ~brave(X1) [subsumption resolution 112,106]
262. 23 | 24 [avatar split clause 261,257,252]
277. ~strong(X0) | ~tall(X0) [subsumption resolution 147,118]
278. ~strong(X0) | tall(X0) [subsumption resolution 146,118]
279. ~strong(X0) [subsumption resolution 278,277]
280. ~funny(X0) | ~tall(X0) [subsumption resolution 145,279]
281. ~funny(X0) | tall(X0) [subsumption resolution 144,279]
282. ~funny(X0) [subsumption resolution 281,280]
347. old(X0) [resolution 105,282]
348. $false <- (~6) [resolution 347,173]
349. 6 [avatar contradiction clause 348]
360. calm(paul) <- (~4) [resolution 148,165]
366. $false <- (24) [subsumption resolution 259,282]
367. ~24 [avatar contradiction clause 366]
369. ~calm(paul) <- (23) [resolution 253,143]
372. $false <- (~4, 23) [subsumption resolution 369,360]
373. 4 | ~23 [avatar contradiction clause 372]
374. $false [avatar sat refutation 176,262,349,367,373]
% SZS output end Proof for 6417385777878051930743826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is either not curious or not creative.
If alice is not funny or quiet then someone is not happy and vice versa.
Everyone who is calm or wise is not rich and vice versa.
If someone is quiet then john is not strong and vice versa.
If someone is both brave and humble then susan is not wise or rich and vice versa.
Everyone who is both quiet and not tall is either not tall or quiet and vice versa.
If paul is either not brave or not wise then someone is generous.
If john is either happy or creative then alice is either humble or not tall.
Everyone who is either not humble or not old is either humble or not happy and vice versa.
Everyone who is not happy or not calm is quiet or old and vice versa.
Everyone who is either patient or not wise is both creative and strong and vice versa.
If fred is either not tall or strong then someone is generous or quiet and vice versa.
Everyone who is rich or happy is creative or wise.
Everyone who is both tall and not brave is either not curious or calm.
Everyone who is not old is not calm or rich and vice versa.
Everyone who is creative is not happy and vice versa.
Alice is either not rich or not tall.
Alice is either not tall or not funny.
Someone is either quiet or creative.
John is calm.
Someone is old.
John is rich or not humble.
Someone is both tall and wise.
Alice is wise. | John is not rich. | entailment | (![X]:(humble(X)=>(~curious(X)<~>~creative(X))))&
(((~funny(alice)|quiet(alice)))<=>(?[X]:(~happy(X))))&
(![X]:((calm(X)|wise(X))<=>~rich(X)))&
((?[X]:(quiet(X)))<=>(~strong(john)))&
((?[X]:((brave(X)&humble(X))))<=>((~wise(susan)|rich(susan))))&
(![X]:((quiet(X)&~tall(X))<=>(~tall(X)<~>quiet(X))))&
(((~brave(paul)<~>~wise(paul)))=>(?[X]:(generous(X))))&
(((happy(john)<~>creative(john)))=>((humble(alice)<~>~tall(alice))))&
(![X]:((~humble(X)<~>~old(X))<=>(humble(X)<~>~happy(X))))&
(![X]:((~happy(X)|~calm(X))<=>(quiet(X)|old(X))))&
(![X]:((patient(X)<~>~wise(X))<=>(creative(X)&strong(X))))&
(((~tall(fred)<~>strong(fred)))<=>(?[X]:((generous(X)|quiet(X)))))&
(![X]:((rich(X)|happy(X))=>(creative(X)|wise(X))))&
(![X]:((tall(X)&~brave(X))=>(~curious(X)<~>calm(X))))&
(![X]:(~old(X)<=>(~calm(X)|rich(X))))&
(![X]:(creative(X)<=>~happy(X)))&
((~rich(alice)<~>~tall(alice)))&
((~tall(alice)<~>~funny(alice)))&
(?[X]:((quiet(X)<~>creative(X))))&
(calm(john))&
(?[X]:(old(X)))&
((rich(john)|~humble(john)))&
(?[X]:((tall(X)&wise(X))))&
(wise(alice)) | ~rich(john) | [
"p2",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3768482218939802598115702
% SZS output start Proof for 3768482218939802598115702
3. ! [X0] : ((wise(X0) | calm(X0)) <=> ~rich(X0)) [input p2]
20. calm(john) [input p19]
25. rich(john) [input hypothesis]
39. ! [X0] : (((wise(X0) | calm(X0)) | rich(X0)) & (~rich(X0) | (~wise(X0) & ~calm(X0)))) [nnf transformation 3]
40. ! [X0] : ((wise(X0) | calm(X0) | rich(X0)) & (~rich(X0) | (~wise(X0) & ~calm(X0)))) [flattening 39]
83. ~rich(X0) | ~calm(X0) [cnf transformation 40]
144. calm(john) [cnf transformation 20]
150. rich(john) [cnf transformation 25]
286. 25 <=> rich(john) [avatar definition]
288. rich(john) <- (25) [avatar component clause 286]
294. 25 [avatar split clause 150,286]
299. ~calm(john) <- (25) [resolution 83,288]
300. $false <- (25) [subsumption resolution 299,144]
301. ~25 [avatar contradiction clause 300]
302. $false [avatar sat refutation 294,301]
% SZS output end Proof for 3768482218939802598115702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is creative or not generous and vice versa.
Everyone who is both not brave and not creative is not wise and vice versa.
Everyone who is humble or not tall is tall or not creative and vice versa.
Everyone who is both not humble and not rich is not wise and vice versa.
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.
If someone is not wise then lucy is both not generous and old.
If someone is either funny or not humble then mary is either generous or kind and vice versa.
If alice is kind then fred is either humble or tall.
If someone is not old then someone is both not patient and not quiet.
If someone is both old and strong then someone is patient or not brave and vice versa.
If someone is both not quiet and quiet then someone is either calm or happy and vice versa.
Everyone who is both not strong and happy is not tall.
If someone is both not quiet and quiet then john is funny and vice versa.
Everyone who is either not wise or patient is either not kind or curious.
Fred is both not rich and not tall.
Mary is not brave or old.
Someone is happy or not tall.
Lucy is either not patient or not quiet.
Susan is either not funny or not old.
Someone is both not patient and not wise.
Lucy is either not generous or humble.
Someone is either strong or kind. | Alice is creative. | contradiction | (![X]:(~patient(X)<=>(creative(X)|~generous(X))))&
(![X]:((~brave(X)&~creative(X))<=>~wise(X)))&
(![X]:((humble(X)|~tall(X))<=>(tall(X)|~creative(X))))&
(![X]:((~humble(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))))&
((?[X]:(~wise(X)))=>((~generous(lucy)&old(lucy))))&
((?[X]:((funny(X)<~>~humble(X))))<=>((generous(mary)<~>kind(mary))))&
((kind(alice))=>((humble(fred)<~>tall(fred))))&
((?[X]:(~old(X)))=>(?[X]:((~patient(X)&~quiet(X)))))&
((?[X]:((old(X)&strong(X))))<=>(?[X]:((patient(X)|~brave(X)))))&
((?[X]:((~quiet(X)&quiet(X))))<=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((~strong(X)&happy(X))=>~tall(X)))&
((?[X]:((~quiet(X)&quiet(X))))<=>(funny(john)))&
(![X]:((~wise(X)<~>patient(X))=>(~kind(X)<~>curious(X))))&
((~rich(fred)&~tall(fred)))&
((~brave(mary)|old(mary)))&
(?[X]:((happy(X)|~tall(X))))&
((~patient(lucy)<~>~quiet(lucy)))&
((~funny(susan)<~>~old(susan)))&
(?[X]:((~patient(X)&~wise(X))))&
((~generous(lucy)<~>humble(lucy)))&
(?[X]:((strong(X)<~>kind(X)))) | creative(alice) | [
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4331008773928650541168947
% SZS output start Proof for 4331008773928650541168947
3. ! [X0] : ((~tall(X0) | humble(X0)) <=> (~creative(X0) | tall(X0))) [input p2]
7. ! [X0] : ((~tall(X0) & happy(X0)) <=> (tall(X0) | ~brave(X0))) [input p6]
25. creative(alice) [input hypothesis]
41. ! [X0] : (((~tall(X0) | humble(X0)) | (creative(X0) & ~tall(X0))) & ((~creative(X0) | tall(X0)) | (tall(X0) & ~humble(X0)))) [nnf transformation 3]
42. ! [X0] : ((~tall(X0) | humble(X0) | (creative(X0) & ~tall(X0))) & (~creative(X0) | tall(X0) | (tall(X0) & ~humble(X0)))) [flattening 41]
48. ! [X0] : (((~tall(X0) & happy(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (tall(X0) | ~happy(X0)))) [nnf transformation 7]
49. ! [X0] : (((~tall(X0) & happy(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | tall(X0) | ~happy(X0))) [flattening 48]
90. ~creative(X0) | tall(X0) | tall(X0) [cnf transformation 42]
107. ~tall(X0) | ~tall(X0) [cnf transformation 49]
155. creative(alice) [cnf transformation 25]
157. ~tall(X0) [duplicate literal removal 107]
158. ~creative(X0) | tall(X0) [duplicate literal removal 90]
364. tall(alice) [resolution 158,155]
365. $false [subsumption resolution 364,157]
% SZS output end Proof for 4331008773928650541168947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is not creative and vice versa.
Everyone who is both not happy and quiet is not rich or old and vice versa.
Everyone who is either happy or quiet is both not old and generous and vice versa.
Everyone who is generous is both creative and quiet and vice versa.
Everyone who is either humble or quiet is funny.
Everyone who is both old and happy is humble or not strong and vice versa.
Everyone who is rich is either not humble or not tall.
If susan is strong then someone is calm.
If mary is calm or not generous then someone is both not rich and tall.
If john is both curious and not generous then someone is not happy or kind.
If fred is rich then someone is both not generous and not happy.
Everyone who is not strong is both not patient and not generous and vice versa.
If someone is not wise then alice is not happy and vice versa.
Everyone who is brave is not happy.
Everyone who is happy is either wise or rich.
Paul is both not kind and tall.
Someone is either not generous or quiet.
Someone is either old or not humble.
John is either not creative or happy.
Susan is either not rich or not kind. | John is not curious. | neutral | (![X]:(tall(X)<=>~creative(X)))&
(![X]:((~happy(X)&quiet(X))<=>(~rich(X)|old(X))))&
(![X]:((happy(X)<~>quiet(X))<=>(~old(X)&generous(X))))&
(![X]:(generous(X)<=>(creative(X)&quiet(X))))&
(![X]:((humble(X)<~>quiet(X))=>funny(X)))&
(![X]:((old(X)&happy(X))<=>(humble(X)|~strong(X))))&
(![X]:(rich(X)=>(~humble(X)<~>~tall(X))))&
((strong(susan))=>(?[X]:(calm(X))))&
(((calm(mary)|~generous(mary)))=>(?[X]:((~rich(X)&tall(X)))))&
(((curious(john)&~generous(john)))=>(?[X]:((~happy(X)|kind(X)))))&
((rich(fred))=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:(~strong(X)<=>(~patient(X)&~generous(X))))&
((?[X]:(~wise(X)))<=>(~happy(alice)))&
(![X]:(brave(X)=>~happy(X)))&
(![X]:(happy(X)=>(wise(X)<~>rich(X))))&
((~kind(paul)&tall(paul)))&
(?[X]:((~generous(X)<~>quiet(X))))&
(?[X]:((old(X)<~>~humble(X))))&
((~creative(john)<~>happy(john)))&
((~rich(susan)<~>~kind(susan))) | ~curious(john) | [] | null | 0 |
Everyone who is funny or patient is either kind or quiet. Everyone who is either happy or not strong is both not calm and not kind and vice versa. If mary is not rich then alice is either strong or not curious. Everyone who is both humble and not funny is happy or creative. If paul is not kind or old then someone is not calm or not wise. If john is both not generous and kind then alice is brave and vice versa. If alice is either not creative or patient then someone is wise or not humble and vice versa. Everyone who is either not curious or old is either tall or not brave and vice versa. Everyone who is both rich and not humble is both not funny and not happy. If lucy is not generous then lucy is either humble or not curious and vice versa. Everyone who is both not wise and rich is both not curious and patient and vice versa. Everyone who is not patient or not humble is not curious or not wise. If someone is both curious and strong then mary is humble. Everyone who is either not creative or wise is humble and vice versa. If someone is not funny then paul is curious or creative and vice versa. If fred is not quiet or kind then someone is kind and vice versa. Alice is not creative. Someone is either old or happy. Lucy is not curious or wise. Fred is calm or creative. Someone is calm or not strong. Susan is both not creative and old. Paul is not wise. John is both not funny and not curious. | Fred is kind. | neutral | (![X]:((funny(X)|patient(X))=>(kind(X)<~>quiet(X))))&
(![X]:((happy(X)<~>~strong(X))<=>(~calm(X)&~kind(X))))&
((~rich(mary))=>((strong(alice)<~>~curious(alice))))&
(![X]:((humble(X)&~funny(X))=>(happy(X)|creative(X))))&
(((~kind(paul)|old(paul)))=>(?[X]:((~calm(X)|~wise(X)))))&
(((~generous(john)&kind(john)))<=>(brave(alice)))&
(((~creative(alice)<~>patient(alice)))<=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:((~curious(X)<~>old(X))<=>(tall(X)<~>~brave(X))))&
(![X]:((rich(X)&~humble(X))=>(~funny(X)&~happy(X))))&
((~generous(lucy))<=>((humble(lucy)<~>~curious(lucy))))&
(![X]:((~wise(X)&rich(X))<=>(~curious(X)&patient(X))))&
(![X]:((~patient(X)|~humble(X))=>(~curious(X)|~wise(X))))&
((?[X]:((curious(X)&strong(X))))=>(humble(mary)))&
(![X]:((~creative(X)<~>wise(X))<=>humble(X)))&
((?[X]:(~funny(X)))<=>((curious(paul)|creative(paul))))&
(((~quiet(fred)|kind(fred)))<=>(?[X]:(kind(X))))&
(~creative(alice))&
(?[X]:((old(X)<~>happy(X))))&
((~curious(lucy)|wise(lucy)))&
((calm(fred)|creative(fred)))&
(?[X]:((calm(X)|~strong(X))))&
((~creative(susan)&old(susan)))&
(~wise(paul))&
((~funny(john)&~curious(john))) | kind(fred) | [] | null | 0 |
Everyone who is old or wise is both funny and not creative and vice versa.
If someone is both strong and wise then someone is either not quiet or quiet.
Everyone who is strong is happy or not rich.
If someone is humble or not old then fred is old and vice versa.
Everyone who is calm or not creative is either not humble or calm.
If someone is both not kind and not calm then someone is either not creative or not patient and vice versa.
If susan is rich then someone is brave or not creative and vice versa.
Everyone who is both happy and old is not strong or calm and vice versa.
Everyone who is creative or funny is calm or not strong.
If fred is both patient and not quiet then someone is either not quiet or not strong and vice versa.
Everyone who is not wise is both not tall and quiet.
If alice is not old or strong then someone is not generous or not funny.
If susan is not old then someone is both not generous and creative.
If lucy is happy then someone is not curious and vice versa.
Everyone who is both generous and old is either rich or not calm and vice versa.
If someone is quiet or not calm then paul is not old.
Someone is not generous.
Paul is wise.
Someone is either not calm or not curious.
Fred is either not kind or patient.
Fred is not tall.
Someone is either not brave or calm.
Fred is both not kind and old. | Alice is humble. | entailment | (![X]:((old(X)|wise(X))<=>(funny(X)&~creative(X))))&
((?[X]:((strong(X)&wise(X))))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:(strong(X)=>(happy(X)|~rich(X))))&
((?[X]:((humble(X)|~old(X))))<=>(old(fred)))&
(![X]:((calm(X)|~creative(X))=>(~humble(X)<~>calm(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((~creative(X)<~>~patient(X)))))&
((rich(susan))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((happy(X)&old(X))<=>(~strong(X)|calm(X))))&
(![X]:((creative(X)|funny(X))=>(calm(X)|~strong(X))))&
(((patient(fred)&~quiet(fred)))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(![X]:(~wise(X)=>(~tall(X)&quiet(X))))&
(((~old(alice)|strong(alice)))=>(?[X]:((~generous(X)|~funny(X)))))&
((~old(susan))=>(?[X]:((~generous(X)&creative(X)))))&
((happy(lucy))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&old(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(~old(paul)))&
(?[X]:(~generous(X)))&
(wise(paul))&
(?[X]:((~calm(X)<~>~curious(X))))&
((~kind(fred)<~>patient(fred)))&
(~tall(fred))&
(?[X]:((~brave(X)<~>calm(X))))&
((~kind(fred)&old(fred))) | humble(alice) | [
"p0",
"p4",
"p7",
"p8",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 65012060390655741254803
% SZS output start Proof for 65012060390655741254803
1. ! [X0] : ((wise(X0) | old(X0)) <=> (~creative(X0) & funny(X0))) [input p0]
5. ! [X0] : ((~creative(X0) | calm(X0)) => (~humble(X0) <~> calm(X0))) [input p4]
8. ! [X0] : ((old(X0) & happy(X0)) <=> (calm(X0) | ~strong(X0))) [input p7]
9. ! [X0] : ((funny(X0) | creative(X0)) => (~strong(X0) | calm(X0))) [input p8]
16. ? [X0] : (~calm(X0) | quiet(X0)) => ~old(paul) [input p15]
18. wise(paul) [input p17]
24. ~humble(alice) [input hypothesis]
32. ! [X0] : ((~humble(X0) <~> calm(X0)) | (creative(X0) & ~calm(X0))) [ennf transformation 5]
33. ! [X0] : ((~strong(X0) | calm(X0)) | (~funny(X0) & ~creative(X0))) [ennf transformation 9]
34. ! [X0] : (~strong(X0) | calm(X0) | (~funny(X0) & ~creative(X0))) [flattening 33]
38. ~old(paul) | ! [X0] : (calm(X0) & ~quiet(X0)) [ennf transformation 16]
39. ! [X0] : (((wise(X0) | old(X0)) | (creative(X0) | ~funny(X0))) & ((~creative(X0) & funny(X0)) | (~wise(X0) & ~old(X0)))) [nnf transformation 1]
40. ! [X0] : ((wise(X0) | old(X0) | creative(X0) | ~funny(X0)) & ((~creative(X0) & funny(X0)) | (~wise(X0) & ~old(X0)))) [flattening 39]
49. ! [X0] : (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (creative(X0) & ~calm(X0))) [nnf transformation 32]
59. ! [X0] : (((old(X0) & happy(X0)) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | (~old(X0) | ~happy(X0)))) [nnf transformation 8]
60. ! [X0] : (((old(X0) & happy(X0)) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | ~old(X0) | ~happy(X0))) [flattening 59]
86. ~wise(X0) | funny(X0) [cnf transformation 40]
87. ~creative(X0) | ~old(X0) [cnf transformation 40]
99. ~calm(X0) | humble(X0) | creative(X0) [cnf transformation 49]
112. strong(X0) | old(X0) [cnf transformation 60]
113. ~calm(X0) | old(X0) [cnf transformation 60]
114. ~strong(X0) | calm(X0) | ~creative(X0) [cnf transformation 34]
115. ~strong(X0) | calm(X0) | ~funny(X0) [cnf transformation 34]
136. ~old(paul) | calm(X0) [cnf transformation 38]
138. wise(paul) [cnf transformation 18]
147. ~humble(alice) [cnf transformation 24]
298. 34 <=> ! [X0] : calm(X0) [avatar definition]
299. calm(X0) <- (34) [avatar component clause 298]
301. 35 <=> old(paul) [avatar definition]
304. 34 | ~35 [avatar split clause 136,301,298]
341. funny(paul) [resolution 86,138]
370. calm(X0) | ~creative(X0) | old(X0) [resolution 114,112]
371. ~creative(X0) | old(X0) [subsumption resolution 370,113]
372. ~creative(X0) [subsumption resolution 371,87]
373. calm(X0) | ~funny(X0) | old(X0) [resolution 115,112]
374. ~funny(X0) | old(X0) [subsumption resolution 373,113]
500. old(paul) [resolution 374,341]
505. 35 [avatar split clause 500,301]
507. humble(X1) | creative(X1) <- (34) [resolution 299,99]
515. humble(X1) <- (34) [subsumption resolution 507,372]
526. $false <- (34) [resolution 515,147]
528. ~34 [avatar contradiction clause 526]
529. $false [avatar sat refutation 304,505,528]
% SZS output end Proof for 65012060390655741254803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not rich is generous or not patient. Everyone who is not old is either not calm or kind and vice versa. Everyone who is not strong is either not humble or brave and vice versa. Everyone who is not quiet or not funny is both quiet and not creative and vice versa. If mary is not tall then fred is not calm and vice versa. Everyone who is not generous is quiet or happy and vice versa. If susan is both not happy and not humble then susan is either happy or wise. If lucy is not rich or not wise then alice is both generous and not happy. Everyone who is not funny is not humble. If alice is brave then someone is rich. If someone is both not rich and curious then someone is both patient and not old and vice versa. If john is not creative or not strong then paul is not brave or not old. Everyone who is old is kind and vice versa. Everyone who is either not old or wise is both not curious and kind and vice versa. Everyone who is both not quiet and curious is both funny and strong and vice versa. Susan is not patient or not humble. Someone is both not strong and kind. Susan is generous or humble. Fred is not patient or quiet. Lucy is either strong or quiet. Someone is patient. Someone is brave or not tall. | Susan is strong. | contradiction | (![X]:((strong(X)<~>~rich(X))=>(generous(X)|~patient(X))))&
(![X]:(~old(X)<=>(~calm(X)<~>kind(X))))&
(![X]:(~strong(X)<=>(~humble(X)<~>brave(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(quiet(X)&~creative(X))))&
((~tall(mary))<=>(~calm(fred)))&
(![X]:(~generous(X)<=>(quiet(X)|happy(X))))&
(((~happy(susan)&~humble(susan)))=>((happy(susan)<~>wise(susan))))&
(((~rich(lucy)|~wise(lucy)))=>((generous(alice)&~happy(alice))))&
(![X]:(~funny(X)=>~humble(X)))&
((brave(alice))=>(?[X]:(rich(X))))&
((?[X]:((~rich(X)&curious(X))))<=>(?[X]:((patient(X)&~old(X)))))&
(((~creative(john)|~strong(john)))=>((~brave(paul)|~old(paul))))&
(![X]:(old(X)<=>kind(X)))&
(![X]:((~old(X)<~>wise(X))<=>(~curious(X)&kind(X))))&
(![X]:((~quiet(X)&curious(X))<=>(funny(X)&strong(X))))&
((~patient(susan)|~humble(susan)))&
(?[X]:((~strong(X)&kind(X))))&
((generous(susan)|humble(susan)))&
((~patient(fred)|quiet(fred)))&
((strong(lucy)<~>quiet(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((brave(X)|~tall(X)))) | strong(susan) | [
"p3",
"p5",
"p8",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4690272376077815668504280
% SZS output start Proof for 4690272376077815668504280
4. ! [X0] : ((~funny(X0) | ~quiet(X0)) <=> (~creative(X0) & quiet(X0))) [input p3]
6. ! [X0] : (~generous(X0) <=> (happy(X0) | quiet(X0))) [input p5]
9. ! [X0] : (~funny(X0) => ~humble(X0)) [input p8]
15. ! [X0] : ((curious(X0) & ~quiet(X0)) <=> (strong(X0) & funny(X0))) [input p14]
18. humble(susan) | generous(susan) [input p17]
23. strong(susan) [input hypothesis]
25. ! [X0] : ((happy(X0) | quiet(X0)) => ~generous(X0)) [unused predicate definition removal 6]
28. ! [X0] : (~generous(X0) | (~happy(X0) & ~quiet(X0))) [ennf transformation 25]
32. ! [X0] : (~humble(X0) | funny(X0)) [ennf transformation 9]
39. ! [X0] : (((~funny(X0) | ~quiet(X0)) | (creative(X0) | ~quiet(X0))) & ((~creative(X0) & quiet(X0)) | (funny(X0) & quiet(X0)))) [nnf transformation 4]
40. ! [X0] : ((~funny(X0) | ~quiet(X0) | creative(X0) | ~quiet(X0)) & ((~creative(X0) & quiet(X0)) | (funny(X0) & quiet(X0)))) [flattening 39]
53. ! [X0] : (((curious(X0) & ~quiet(X0)) | (~strong(X0) | ~funny(X0))) & ((strong(X0) & funny(X0)) | (~curious(X0) | quiet(X0)))) [nnf transformation 15]
54. ! [X0] : (((curious(X0) & ~quiet(X0)) | ~strong(X0) | ~funny(X0)) & ((strong(X0) & funny(X0)) | ~curious(X0) | quiet(X0))) [flattening 53]
72. quiet(X0) | quiet(X0) [cnf transformation 40]
79. ~generous(X0) | ~quiet(X0) [cnf transformation 28]
87. ~humble(X0) | funny(X0) [cnf transformation 32]
105. ~quiet(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 54]
110. humble(susan) | generous(susan) [cnf transformation 18]
116. strong(susan) [cnf transformation 23]
118. quiet(X0) [duplicate literal removal 72]
130. ~generous(X0) [subsumption resolution 79,118]
132. 3 <=> humble(susan) [avatar definition]
134. humble(susan) <- (3) [avatar component clause 132]
217. ~funny(X0) | ~strong(X0) [subsumption resolution 105,118]
223. humble(susan) [subsumption resolution 110,130]
224. 3 [avatar split clause 223,132]
235. funny(susan) <- (3) [resolution 87,134]
242. ~strong(susan) <- (3) [resolution 217,235]
243. $false <- (3) [subsumption resolution 242,116]
244. ~3 [avatar contradiction clause 243]
245. $false [avatar sat refutation 224,244]
% SZS output end Proof for 4690272376077815668504280
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and not curious then someone is kind or old. Everyone who is not old is calm and vice versa. Everyone who is not curious or creative is both not calm and quiet. If someone is quiet or kind then mary is not happy. If alice is either not curious or quiet then mary is not patient or not happy. If lucy is not strong then someone is happy or not funny. Everyone who is either happy or brave is not rich and vice versa. If someone is both not creative and not happy then lucy is not wise and vice versa. Everyone who is funny is either tall or not quiet and vice versa. Everyone who is both not humble and not strong is not old or not tall and vice versa. Everyone who is generous is either old or not funny and vice versa. Everyone who is either not happy or tall is wise or not calm and vice versa. If someone is both wise and calm then lucy is either not patient or not happy and vice versa. If paul is not generous then someone is either not curious or not rich. If alice is happy then someone is either curious or not creative and vice versa. If susan is both patient and not calm then someone is not quiet. Someone is either not brave or quiet. Someone is either not patient or not calm. Paul is strong or happy. Fred is quiet. Lucy is wise. Lucy is either not old or humble. Someone is old. | Paul is happy. | entailment | ((?[X]:((tall(X)&~curious(X))))=>(?[X]:((kind(X)|old(X)))))&
(![X]:(~old(X)<=>calm(X)))&
(![X]:((~curious(X)|creative(X))=>(~calm(X)&quiet(X))))&
((?[X]:((quiet(X)|kind(X))))=>(~happy(mary)))&
(((~curious(alice)<~>quiet(alice)))=>((~patient(mary)|~happy(mary))))&
((~strong(lucy))=>(?[X]:((happy(X)|~funny(X)))))&
(![X]:((happy(X)<~>brave(X))<=>~rich(X)))&
((?[X]:((~creative(X)&~happy(X))))<=>(~wise(lucy)))&
(![X]:(funny(X)<=>(tall(X)<~>~quiet(X))))&
(![X]:((~humble(X)&~strong(X))<=>(~old(X)|~tall(X))))&
(![X]:(generous(X)<=>(old(X)<~>~funny(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(wise(X)|~calm(X))))&
((?[X]:((wise(X)&calm(X))))<=>((~patient(lucy)<~>~happy(lucy))))&
((~generous(paul))=>(?[X]:((~curious(X)<~>~rich(X)))))&
((happy(alice))<=>(?[X]:((curious(X)<~>~creative(X)))))&
(((patient(susan)&~calm(susan)))=>(?[X]:(~quiet(X))))&
(?[X]:((~brave(X)<~>quiet(X))))&
(?[X]:((~patient(X)<~>~calm(X))))&
((strong(paul)|happy(paul)))&
(quiet(fred))&
(wise(lucy))&
((~old(lucy)<~>humble(lucy)))&
(?[X]:(old(X))) | happy(paul) | [
"p2",
"p7",
"p9",
"p11",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 377717334370956731166047
% SZS output start Proof for 377717334370956731166047
3. ! [X0] : ((creative(X0) | ~curious(X0)) => (quiet(X0) & ~calm(X0))) [input p2]
8. ? [X0] : (~happy(X0) & ~creative(X0)) <=> ~wise(lucy) [input p7]
10. ! [X0] : ((~strong(X0) & ~humble(X0)) <=> (~tall(X0) | ~old(X0))) [input p9]
12. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (~calm(X0) | wise(X0))) [input p11]
19. happy(paul) | strong(paul) [input p18]
21. wise(lucy) [input p20]
24. ~happy(paul) [input hypothesis]
28. ! [X0] : ((quiet(X0) & ~calm(X0)) | (~creative(X0) & curious(X0))) [ennf transformation 3]
45. (? [X0] : (~happy(X0) & ~creative(X0)) | wise(lucy)) & (~wise(lucy) | ! [X0] : (happy(X0) | creative(X0))) [nnf transformation 8]
46. (? [X0] : (~happy(X0) & ~creative(X0)) | wise(lucy)) & (~wise(lucy) | ! [X1] : (happy(X1) | creative(X1))) [rectify 45]
47. ? [X0] : (~happy(X0) & ~creative(X0)) => (~happy(sK2) & ~creative(sK2)) [choice axiom]
48. ((~happy(sK2) & ~creative(sK2)) | wise(lucy)) & (~wise(lucy) | ! [X1] : (happy(X1) | creative(X1))) [skolemisation 46,47]
50. ! [X0] : (((~strong(X0) & ~humble(X0)) | (tall(X0) & old(X0))) & ((~tall(X0) | ~old(X0)) | (strong(X0) | humble(X0)))) [nnf transformation 10]
51. ! [X0] : (((~strong(X0) & ~humble(X0)) | (tall(X0) & old(X0))) & (~tall(X0) | ~old(X0) | strong(X0) | humble(X0))) [flattening 50]
53. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (calm(X0) & ~wise(X0))) & ((~calm(X0) | wise(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 12]
54. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (calm(X0) & ~wise(X0))) & (~calm(X0) | wise(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [flattening 53]
81. ~creative(X0) | ~calm(X0) [cnf transformation 28]
93. ~wise(lucy) | happy(X1) | creative(X1) [cnf transformation 48]
104. ~strong(X0) | tall(X0) [cnf transformation 51]
112. ~tall(X0) | happy(X0) | calm(X0) [cnf transformation 54]
130. happy(paul) | strong(paul) [cnf transformation 19]
132. wise(lucy) [cnf transformation 21]
136. ~happy(paul) [cnf transformation 24]
188. 13 <=> wise(lucy) [avatar definition]
202. 16 <=> ! [X1] : (happy(X1) | creative(X1)) [avatar definition]
203. happy(X1) | creative(X1) <- (16) [avatar component clause 202]
204. 16 | ~13 [avatar split clause 93,188,202]
300. 37 <=> strong(paul) [avatar definition]
302. strong(paul) <- (37) [avatar component clause 300]
304. 38 <=> happy(paul) [avatar definition]
305. ~happy(paul) <- (~38) [avatar component clause 304]
307. 37 | 38 [avatar split clause 130,304,300]
308. 13 [avatar split clause 132,188]
318. ~38 [avatar split clause 136,304]
327. tall(paul) <- (37) [resolution 104,302]
329. creative(paul) <- (16, ~38) [resolution 203,305]
333. ~calm(paul) <- (16, ~38) [resolution 329,81]
410. happy(paul) | calm(paul) <- (37) [resolution 112,327]
413. calm(paul) <- (37, ~38) [subsumption resolution 410,305]
414. $false <- (16, 37, ~38) [subsumption resolution 413,333]
415. ~16 | ~37 | 38 [avatar contradiction clause 414]
421. $false [avatar sat refutation 204,307,308,318,415]
% SZS output end Proof for 377717334370956731166047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is both funny and not brave.
Everyone who is either curious or kind is humble.
If paul is quiet then someone is either rich or not strong.
Everyone who is wise or creative is both not quiet and not patient.
If someone is both happy and not happy then someone is either not tall or strong and vice versa.
Everyone who is either patient or humble is not wise and vice versa.
If someone is funny then someone is wise or generous.
If someone is not curious or old then fred is either not curious or tall.
If lucy is tall then someone is either not rich or not generous.
Everyone who is not humble or not calm is both old and not rich.
If someone is either not generous or not humble then someone is not funny or not rich.
If lucy is either not tall or not calm then paul is humble or not curious and vice versa.
If someone is both not creative and funny then someone is not rich or not curious.
If mary is patient then alice is both patient and not generous and vice versa.
Everyone who is both not rich and not strong is either not happy or kind and vice versa.
If someone is both not strong and quiet then lucy is either not strong or not tall.
Alice is both wise and not quiet.
Someone is either not kind or not calm.
Someone is not wise or kind.
Alice is either not creative or creative.
Someone is both not old and not patient.
John is either wise or not patient.
Fred is both not curious and creative.
Fred is tall or old. | Alice is old. | entailment | (![X]:(rich(X)=>(funny(X)&~brave(X))))&
(![X]:((curious(X)<~>kind(X))=>humble(X)))&
((quiet(paul))=>(?[X]:((rich(X)<~>~strong(X)))))&
(![X]:((wise(X)|creative(X))=>(~quiet(X)&~patient(X))))&
((?[X]:((happy(X)&~happy(X))))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((patient(X)<~>humble(X))<=>~wise(X)))&
((?[X]:(funny(X)))=>(?[X]:((wise(X)|generous(X)))))&
((?[X]:((~curious(X)|old(X))))=>((~curious(fred)<~>tall(fred))))&
((tall(lucy))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:((~humble(X)|~calm(X))=>(old(X)&~rich(X))))&
((?[X]:((~generous(X)<~>~humble(X))))=>(?[X]:((~funny(X)|~rich(X)))))&
(((~tall(lucy)<~>~calm(lucy)))<=>((humble(paul)|~curious(paul))))&
((?[X]:((~creative(X)&funny(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
((patient(mary))<=>((patient(alice)&~generous(alice))))&
(![X]:((~rich(X)&~strong(X))<=>(~happy(X)<~>kind(X))))&
((?[X]:((~strong(X)&quiet(X))))=>((~strong(lucy)<~>~tall(lucy))))&
((wise(alice)&~quiet(alice)))&
(?[X]:((~kind(X)<~>~calm(X))))&
(?[X]:((~wise(X)|kind(X))))&
((~creative(alice)<~>creative(alice)))&
(?[X]:((~old(X)&~patient(X))))&
((wise(john)<~>~patient(john)))&
((~curious(fred)&creative(fred)))&
((tall(fred)|old(fred))) | old(alice) | [
"p3",
"p5",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 375924915633307124135866
% SZS output start Proof for 375924915633307124135866
4. ! [X0] : ((creative(X0) | wise(X0)) => (~patient(X0) & ~quiet(X0))) [input p3]
6. ! [X0] : ((patient(X0) <~> humble(X0)) <=> ~wise(X0)) [input p5]
10. ! [X0] : ((~calm(X0) | ~humble(X0)) => (~rich(X0) & old(X0))) [input p9]
17. ~quiet(alice) & wise(alice) [input p16]
25. ~old(alice) [input hypothesis]
32. ! [X0] : ((creative(X0) | wise(X0)) => ~patient(X0)) [pure predicate removal 4]
33. wise(alice) [pure predicate removal 17]
37. ! [X0] : (~patient(X0) | (~creative(X0) & ~wise(X0))) [ennf transformation 32]
41. ! [X0] : ((~rich(X0) & old(X0)) | (calm(X0) & humble(X0))) [ennf transformation 10]
50. ! [X0] : ((((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | wise(X0)) & (~wise(X0) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0))))) [nnf transformation 6]
83. ~patient(X0) | ~wise(X0) [cnf transformation 37]
92. ~wise(X0) | patient(X0) | ~humble(X0) [cnf transformation 50]
94. ~humble(X0) | ~patient(X0) | wise(X0) [cnf transformation 50]
102. old(X0) | humble(X0) [cnf transformation 41]
124. wise(alice) [cnf transformation 33]
137. ~old(alice) [cnf transformation 25]
152. ~patient(X0) | ~humble(X0) [subsumption resolution 94,83]
153. ~wise(X0) | ~humble(X0) [subsumption resolution 92,152]
288. humble(alice) [resolution 102,137]
296. ~humble(alice) [resolution 153,124]
298. $false [subsumption resolution 296,288]
% SZS output end Proof for 375924915633307124135866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is not old and vice versa. Everyone who is rich or not generous is not funny or strong. Everyone who is not patient or strong is both not rich and rich and vice versa. If someone is both strong and kind then someone is not tall or kind. Everyone who is patient is both quiet and not kind. Everyone who is not patient is either quiet or wise and vice versa. Everyone who is both not humble and strong is brave and vice versa. If alice is both not curious and calm then someone is not kind or strong. Everyone who is not generous is not tall. If mary is either not curious or old then someone is both not brave and not quiet and vice versa. If someone is not creative then someone is either not creative or not happy and vice versa. If someone is both not patient and not quiet then paul is either not generous or not kind and vice versa. If lucy is both rich and not old then someone is either patient or not generous and vice versa. Everyone who is not happy or not rich is not funny or not curious. Someone is not rich. Someone is either strong or not tall. Someone is both humble and happy. Someone is either creative or not brave. Mary is humble. Mary is not wise or happy. Someone is either not old or not kind. | Alice is wise. | entailment | (![X]:(strong(X)<=>~old(X)))&
(![X]:((rich(X)|~generous(X))=>(~funny(X)|strong(X))))&
(![X]:((~patient(X)|strong(X))<=>(~rich(X)&rich(X))))&
((?[X]:((strong(X)&kind(X))))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:(patient(X)=>(quiet(X)&~kind(X))))&
(![X]:(~patient(X)<=>(quiet(X)<~>wise(X))))&
(![X]:((~humble(X)&strong(X))<=>brave(X)))&
(((~curious(alice)&calm(alice)))=>(?[X]:((~kind(X)|strong(X)))))&
(![X]:(~generous(X)=>~tall(X)))&
(((~curious(mary)<~>old(mary)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:((~patient(X)&~quiet(X))))<=>((~generous(paul)<~>~kind(paul))))&
(((rich(lucy)&~old(lucy)))<=>(?[X]:((patient(X)<~>~generous(X)))))&
(![X]:((~happy(X)|~rich(X))=>(~funny(X)|~curious(X))))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)<~>~tall(X))))&
(?[X]:((humble(X)&happy(X))))&
(?[X]:((creative(X)<~>~brave(X))))&
(humble(mary))&
((~wise(mary)|happy(mary)))&
(?[X]:((~old(X)<~>~kind(X)))) | wise(alice) | [
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1945150466988110422348811
% SZS output start Proof for 1945150466988110422348811
3. ! [X0] : ((strong(X0) | ~patient(X0)) <=> (rich(X0) & ~rich(X0))) [input p2]
5. ! [X0] : (patient(X0) => (~kind(X0) & quiet(X0))) [input p4]
6. ! [X0] : (~patient(X0) <=> (quiet(X0) <~> wise(X0))) [input p5]
22. ~wise(alice) [input hypothesis]
29. ! [X0] : ((~kind(X0) & quiet(X0)) | ~patient(X0)) [ennf transformation 5]
32. ! [X0] : (((strong(X0) | ~patient(X0)) | (~rich(X0) | rich(X0))) & ((rich(X0) & ~rich(X0)) | (~strong(X0) & patient(X0)))) [nnf transformation 3]
33. ! [X0] : ((strong(X0) | ~patient(X0) | ~rich(X0) | rich(X0)) & ((rich(X0) & ~rich(X0)) | (~strong(X0) & patient(X0)))) [flattening 32]
37. ! [X0] : ((~patient(X0) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | patient(X0))) [nnf transformation 6]
73. ~rich(X0) | patient(X0) [cnf transformation 33]
75. rich(X0) | patient(X0) [cnf transformation 33]
79. quiet(X0) | ~patient(X0) [cnf transformation 29]
83. ~patient(X0) | wise(X0) | ~quiet(X0) [cnf transformation 37]
122. ~wise(alice) [cnf transformation 22]
124. patient(X0) [subsumption resolution 73,75]
126. quiet(X0) [subsumption resolution 79,124]
127. wise(X0) | ~quiet(X0) [subsumption resolution 83,124]
128. wise(X0) [subsumption resolution 127,126]
194. $false [subsumption resolution 122,128]
% SZS output end Proof for 1945150466988110422348811
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous or kind then someone is either old or calm.
Everyone who is not generous is old.
Everyone who is not kind or kind is not happy and vice versa.
If paul is humble or happy then john is old or not patient and vice versa.
Everyone who is either not kind or not old is both not kind and tall and vice versa.
Everyone who is not happy is both not humble and quiet.
Everyone who is both not strong and rich is not rich.
If paul is either tall or not generous then alice is generous or not funny.
If someone is creative or tall then john is both not wise and not happy and vice versa.
If someone is both curious and quiet then fred is not old or not kind.
If someone is kind or not strong then someone is not brave.
If someone is not old then john is either not wise or not strong.
If someone is both patient and quiet then someone is either not creative or calm and vice versa.
Everyone who is not old is rich.
If someone is either humble or calm then someone is rich.
Paul is either creative or rich.
Someone is not funny or patient.
Someone is not quiet or curious.
Someone is funny.
Someone is either tall or generous. | Paul is calm. | neutral | ((?[X]:((~generous(X)<~>kind(X))))=>(?[X]:((old(X)<~>calm(X)))))&
(![X]:(~generous(X)=>old(X)))&
(![X]:((~kind(X)|kind(X))<=>~happy(X)))&
(((humble(paul)|happy(paul)))<=>((old(john)|~patient(john))))&
(![X]:((~kind(X)<~>~old(X))<=>(~kind(X)&tall(X))))&
(![X]:(~happy(X)=>(~humble(X)&quiet(X))))&
(![X]:((~strong(X)&rich(X))=>~rich(X)))&
(((tall(paul)<~>~generous(paul)))=>((generous(alice)|~funny(alice))))&
((?[X]:((creative(X)|tall(X))))<=>((~wise(john)&~happy(john))))&
((?[X]:((curious(X)&quiet(X))))=>((~old(fred)|~kind(fred))))&
((?[X]:((kind(X)|~strong(X))))=>(?[X]:(~brave(X))))&
((?[X]:(~old(X)))=>((~wise(john)<~>~strong(john))))&
((?[X]:((patient(X)&quiet(X))))<=>(?[X]:((~creative(X)<~>calm(X)))))&
(![X]:(~old(X)=>rich(X)))&
((?[X]:((humble(X)<~>calm(X))))=>(?[X]:(rich(X))))&
((creative(paul)<~>rich(paul)))&
(?[X]:((~funny(X)|patient(X))))&
(?[X]:((~quiet(X)|curious(X))))&
(?[X]:(funny(X)))&
(?[X]:((tall(X)<~>generous(X)))) | calm(paul) | [] | null | 0 |
Everyone who is curious is either not wise or not strong and vice versa. If someone is not curious or creative then susan is not generous and vice versa. Everyone who is not kind or strong is both not generous and not calm and vice versa. Everyone who is both funny and not strong is both not funny and not kind. If someone is either patient or not humble then alice is either creative or calm and vice versa. If fred is either not happy or strong then someone is both rich and not creative and vice versa. Everyone who is tall or not tall is old and vice versa. Everyone who is strong or brave is wise and vice versa. Everyone who is calm is old or generous and vice versa. If alice is kind then someone is either brave or not funny and vice versa. Everyone who is not happy or patient is either patient or tall. Everyone who is not generous or wise is not wise and vice versa. Everyone who is patient is generous or old. Everyone who is either funny or not curious is either not creative or generous and vice versa. Everyone who is both not brave and not kind is both not happy and wise and vice versa. Everyone who is rich is happy or not old. Someone is not curious or calm. Alice is not patient or not kind. Someone is not patient. John is happy. Lucy is either not strong or generous. Susan is tall. Paul is either humble or not happy. | John is rich. | neutral | (![X]:(curious(X)<=>(~wise(X)<~>~strong(X))))&
((?[X]:((~curious(X)|creative(X))))<=>(~generous(susan)))&
(![X]:((~kind(X)|strong(X))<=>(~generous(X)&~calm(X))))&
(![X]:((funny(X)&~strong(X))=>(~funny(X)&~kind(X))))&
((?[X]:((patient(X)<~>~humble(X))))<=>((creative(alice)<~>calm(alice))))&
(((~happy(fred)<~>strong(fred)))<=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:((tall(X)|~tall(X))<=>old(X)))&
(![X]:((strong(X)|brave(X))<=>wise(X)))&
(![X]:(calm(X)<=>(old(X)|generous(X))))&
((kind(alice))<=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:((~happy(X)|patient(X))=>(patient(X)<~>tall(X))))&
(![X]:((~generous(X)|wise(X))<=>~wise(X)))&
(![X]:(patient(X)=>(generous(X)|old(X))))&
(![X]:((funny(X)<~>~curious(X))<=>(~creative(X)<~>generous(X))))&
(![X]:((~brave(X)&~kind(X))<=>(~happy(X)&wise(X))))&
(![X]:(rich(X)=>(happy(X)|~old(X))))&
(?[X]:((~curious(X)|calm(X))))&
((~patient(alice)|~kind(alice)))&
(?[X]:(~patient(X)))&
(happy(john))&
((~strong(lucy)<~>generous(lucy)))&
(tall(susan))&
((humble(paul)<~>~happy(paul))) | rich(john) | [] | null | 0 |
Everyone who is both not happy and not strong is not funny or not brave and vice versa.
Everyone who is both humble and not patient is not kind and vice versa.
If someone is wise or not humble then someone is quiet.
If john is either brave or not rich then lucy is funny or happy.
If john is both humble and not curious then someone is calm or not tall.
If someone is patient or not quiet then someone is funny or not patient.
If someone is both curious and not humble then someone is both calm and not old.
Everyone who is funny or not humble is both not creative and strong.
Everyone who is either not funny or patient is patient or quiet and vice versa.
If someone is both not strong and not old then someone is brave or funny.
Everyone who is either not strong or funny is both kind and brave.
Everyone who is both quiet and not rich is both happy and tall.
If someone is either not tall or not generous then someone is old and vice versa.
If someone is not funny then fred is not kind or creative and vice versa.
If someone is both not happy and not curious then alice is either not tall or creative and vice versa.
If someone is both quiet and humble then someone is not kind.
Paul is not humble or funny.
Mary is both tall and happy.
Someone is either patient or calm.
Lucy is either not kind or happy.
Someone is not humble.
Someone is strong or brave. | Alice is strong. | entailment | (![X]:((~happy(X)&~strong(X))<=>(~funny(X)|~brave(X))))&
(![X]:((humble(X)&~patient(X))<=>~kind(X)))&
((?[X]:((wise(X)|~humble(X))))=>(?[X]:(quiet(X))))&
(((brave(john)<~>~rich(john)))=>((funny(lucy)|happy(lucy))))&
(((humble(john)&~curious(john)))=>(?[X]:((calm(X)|~tall(X)))))&
((?[X]:((patient(X)|~quiet(X))))=>(?[X]:((funny(X)|~patient(X)))))&
((?[X]:((curious(X)&~humble(X))))=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((funny(X)|~humble(X))=>(~creative(X)&strong(X))))&
(![X]:((~funny(X)<~>patient(X))<=>(patient(X)|quiet(X))))&
((?[X]:((~strong(X)&~old(X))))=>(?[X]:((brave(X)|funny(X)))))&
(![X]:((~strong(X)<~>funny(X))=>(kind(X)&brave(X))))&
(![X]:((quiet(X)&~rich(X))=>(happy(X)&tall(X))))&
((?[X]:((~tall(X)<~>~generous(X))))<=>(?[X]:(old(X))))&
((?[X]:(~funny(X)))<=>((~kind(fred)|creative(fred))))&
((?[X]:((~happy(X)&~curious(X))))<=>((~tall(alice)<~>creative(alice))))&
((?[X]:((quiet(X)&humble(X))))=>(?[X]:(~kind(X))))&
((~humble(paul)|funny(paul)))&
((tall(mary)&happy(mary)))&
(?[X]:((patient(X)<~>calm(X))))&
((~kind(lucy)<~>happy(lucy)))&
(?[X]:(~humble(X)))&
(?[X]:((strong(X)|brave(X)))) | strong(alice) | [
"p0",
"p7",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7323004793770810591183251
% SZS output start Proof for 7323004793770810591183251
1. ! [X0] : ((~strong(X0) & ~happy(X0)) <=> (~brave(X0) | ~funny(X0))) [input p0]
8. ! [X0] : ((~humble(X0) | funny(X0)) => (strong(X0) & ~creative(X0))) [input p7]
9. ! [X0] : ((~funny(X0) <~> patient(X0)) <=> (quiet(X0) | patient(X0))) [input p8]
11. ! [X0] : ((~strong(X0) <~> funny(X0)) => (brave(X0) & kind(X0))) [input p10]
16. ? [X0] : (humble(X0) & quiet(X0)) => ? [X0] : ~kind(X0) [input p15]
23. ~strong(alice) [input hypothesis]
29. ? [X0] : (humble(X0) & quiet(X0)) => ? [X1] : ~kind(X1) [rectify 16]
38. ! [X0] : ((strong(X0) & ~creative(X0)) | (humble(X0) & ~funny(X0))) [ennf transformation 8]
40. ! [X0] : ((brave(X0) & kind(X0)) | (~strong(X0) <=> funny(X0))) [ennf transformation 11]
43. ? [X1] : ~kind(X1) | ! [X0] : (~humble(X0) | ~quiet(X0)) [ennf transformation 29]
44. ! [X0] : (((~strong(X0) & ~happy(X0)) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | (strong(X0) | happy(X0)))) [nnf transformation 1]
45. ! [X0] : (((~strong(X0) & ~happy(X0)) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | strong(X0) | happy(X0))) [flattening 44]
60. ! [X0] : ((((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0))))) [nnf transformation 9]
61. ! [X0] : ((((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0))))) [flattening 60]
65. ! [X0] : ((brave(X0) & kind(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) [nnf transformation 40]
80. ? [X0] : ~kind(X0) | ! [X1] : (~humble(X1) | ~quiet(X1)) [rectify 43]
81. ? [X0] : ~kind(X0) => ~kind(sK9) [choice axiom]
82. ~kind(sK9) | ! [X1] : (~humble(X1) | ~quiet(X1)) [skolemisation 80,81]
94. ~strong(X0) | funny(X0) [cnf transformation 45]
109. ~funny(X0) | strong(X0) [cnf transformation 38]
110. humble(X0) | strong(X0) [cnf transformation 38]
111. quiet(X0) | patient(X0) | patient(X0) | funny(X0) [cnf transformation 61]
115. ~patient(X0) | funny(X0) | ~patient(X0) [cnf transformation 61]
118. kind(X0) | funny(X0) | strong(X0) [cnf transformation 65]
119. kind(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 65]
137. ~kind(sK9) | ~humble(X1) | ~quiet(X1) [cnf transformation 82]
147. ~strong(alice) [cnf transformation 23]
148. quiet(X0) | patient(X0) | funny(X0) [duplicate literal removal 111]
149. ~patient(X0) | funny(X0) [duplicate literal removal 115]
220. quiet(X0) | funny(X0) [subsumption resolution 148,149]
234. ~funny(X0) | kind(X0) [subsumption resolution 119,109]
235. kind(X0) | funny(X0) [subsumption resolution 118,94]
236. kind(X0) [subsumption resolution 235,234]
273. 28 <=> ! [X1] : funny(X1) [avatar definition]
274. funny(X1) <- (28) [avatar component clause 273]
301. ~quiet(X1) | ~humble(X1) [subsumption resolution 137,236]
365. ~humble(X0) | funny(X0) [resolution 301,220]
432. funny(X0) | strong(X0) [resolution 365,110]
435. funny(X0) [subsumption resolution 432,94]
436. 28 [avatar split clause 435,273]
438. strong(X1) <- (28) [resolution 274,109]
441. $false <- (28) [resolution 438,147]
444. ~28 [avatar contradiction clause 441]
445. $false [avatar sat refutation 436,444]
% SZS output end Proof for 7323004793770810591183251
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or wise is not calm and vice versa.
Everyone who is either funny or strong is humble or calm.
If alice is either quiet or not generous then someone is not brave and vice versa.
Everyone who is generous or not funny is either tall or not rich.
If susan is rich or strong then fred is both not strong and not happy and vice versa.
Everyone who is both calm and not rich is happy and vice versa.
If fred is both not funny and brave then susan is not humble or not old and vice versa.
Everyone who is creative or humble is kind or not patient.
Everyone who is not generous is wise or not rich and vice versa.
Everyone who is both old and not wise is not creative or not patient and vice versa.
If someone is patient or not old then alice is both wise and happy.
Everyone who is humble is either humble or not calm and vice versa.
Everyone who is either brave or not quiet is either creative or not kind and vice versa.
If fred is not calm then john is not patient or not quiet and vice versa.
If lucy is either not rich or not calm then someone is both creative and brave and vice versa.
If alice is funny or not generous then mary is calm or not humble and vice versa.
Mary is either not rich or kind.
Someone is rich or not quiet.
John is both humble and funny.
Susan is old or rich.
Someone is either not old or not tall.
Mary is not generous or not kind. | Alice is happy. | entailment | (![X]:((~humble(X)<~>wise(X))<=>~calm(X)))&
(![X]:((funny(X)<~>strong(X))=>(humble(X)|calm(X))))&
(((quiet(alice)<~>~generous(alice)))<=>(?[X]:(~brave(X))))&
(![X]:((generous(X)|~funny(X))=>(tall(X)<~>~rich(X))))&
(((rich(susan)|strong(susan)))<=>((~strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~rich(X))<=>happy(X)))&
(((~funny(fred)&brave(fred)))<=>((~humble(susan)|~old(susan))))&
(![X]:((creative(X)|humble(X))=>(kind(X)|~patient(X))))&
(![X]:(~generous(X)<=>(wise(X)|~rich(X))))&
(![X]:((old(X)&~wise(X))<=>(~creative(X)|~patient(X))))&
((?[X]:((patient(X)|~old(X))))=>((wise(alice)&happy(alice))))&
(![X]:(humble(X)<=>(humble(X)<~>~calm(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>(creative(X)<~>~kind(X))))&
((~calm(fred))<=>((~patient(john)|~quiet(john))))&
(((~rich(lucy)<~>~calm(lucy)))<=>(?[X]:((creative(X)&brave(X)))))&
(((funny(alice)|~generous(alice)))<=>((calm(mary)|~humble(mary))))&
((~rich(mary)<~>kind(mary)))&
(?[X]:((rich(X)|~quiet(X))))&
((humble(john)&funny(john)))&
((old(susan)|rich(susan)))&
(?[X]:((~old(X)<~>~tall(X))))&
((~generous(mary)|~kind(mary))) | happy(alice) | [
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 10745599339554462526709
% SZS output start Proof for 10745599339554462526709
11. ? [X0] : (~old(X0) | patient(X0)) => (happy(alice) & wise(alice)) [input p10]
12. ! [X0] : (humble(X0) <=> (humble(X0) <~> ~calm(X0))) [input p11]
14. ~calm(fred) <=> (~quiet(john) | ~patient(john)) [input p13]
23. ~happy(alice) [input hypothesis]
29. (happy(alice) & wise(alice)) | ! [X0] : (old(X0) & ~patient(X0)) [ennf transformation 11]
47. ! [X0] : ((humble(X0) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0)))) & (((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | ~humble(X0))) [nnf transformation 12]
49. (~calm(fred) | (quiet(john) & patient(john))) & ((~quiet(john) | ~patient(john)) | calm(fred)) [nnf transformation 14]
50. (~calm(fred) | (quiet(john) & patient(john))) & (~quiet(john) | ~patient(john) | calm(fred)) [flattening 49]
102. happy(alice) | ~patient(X0) [cnf transformation 29]
105. calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 47]
107. humble(X0) | humble(X0) | calm(X0) [cnf transformation 47]
117. ~calm(fred) | patient(john) [cnf transformation 50]
138. ~happy(alice) [cnf transformation 23]
139. calm(X0) | ~humble(X0) [duplicate literal removal 105]
140. humble(X0) | calm(X0) [duplicate literal removal 107]
206. 14 <=> happy(alice) [avatar definition]
211. 15 <=> ! [X0] : ~patient(X0) [avatar definition]
212. ~patient(X0) <- (15) [avatar component clause 211]
213. 15 | 14 [avatar split clause 102,206,211]
220. calm(X0) [subsumption resolution 139,140]
222. patient(john) [subsumption resolution 117,220]
290. ~14 [avatar split clause 138,206]
291. $false <- (15) [resolution 222,212]
292. ~15 [avatar contradiction clause 291]
293. $false [avatar sat refutation 213,290,292]
% SZS output end Proof for 10745599339554462526709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not creative is strong.
If someone is old then someone is not generous or calm.
Everyone who is not humble or not funny is old or rich and vice versa.
Everyone who is generous or quiet is both quiet and creative.
If paul is either not humble or not rich then someone is creative and vice versa.
If paul is not creative or funny then someone is not quiet.
If susan is both not tall and happy then someone is not wise.
Everyone who is either calm or brave is curious or humble and vice versa.
If someone is both not generous and brave then someone is both patient and not curious and vice versa.
Everyone who is not tall or not patient is rich.
Everyone who is either funny or not rich is both quiet and generous and vice versa.
Everyone who is not funny is either curious or patient.
If mary is both rich and old then someone is either strong or not brave.
Everyone who is either patient or not kind is both not curious and strong.
Everyone who is not happy is either not generous or not happy.
Everyone who is both not tall and funny is either tall or not humble and vice versa.
Someone is happy.
Someone is not happy.
Someone is both funny and wise.
Someone is either funny or not quiet.
John is either not wise or creative.
Lucy is not happy.
Mary is both patient and strong.
Someone is not kind or brave. | Lucy is not humble. | entailment | (![X]:((quiet(X)&~creative(X))=>strong(X)))&
((?[X]:(old(X)))=>(?[X]:((~generous(X)|calm(X)))))&
(![X]:((~humble(X)|~funny(X))<=>(old(X)|rich(X))))&
(![X]:((generous(X)|quiet(X))=>(quiet(X)&creative(X))))&
(((~humble(paul)<~>~rich(paul)))<=>(?[X]:(creative(X))))&
(((~creative(paul)|funny(paul)))=>(?[X]:(~quiet(X))))&
(((~tall(susan)&happy(susan)))=>(?[X]:(~wise(X))))&
(![X]:((calm(X)<~>brave(X))<=>(curious(X)|humble(X))))&
((?[X]:((~generous(X)&brave(X))))<=>(?[X]:((patient(X)&~curious(X)))))&
(![X]:((~tall(X)|~patient(X))=>rich(X)))&
(![X]:((funny(X)<~>~rich(X))<=>(quiet(X)&generous(X))))&
(![X]:(~funny(X)=>(curious(X)<~>patient(X))))&
(((rich(mary)&old(mary)))=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((patient(X)<~>~kind(X))=>(~curious(X)&strong(X))))&
(![X]:(~happy(X)=>(~generous(X)<~>~happy(X))))&
(![X]:((~tall(X)&funny(X))<=>(tall(X)<~>~humble(X))))&
(?[X]:(happy(X)))&
(?[X]:(~happy(X)))&
(?[X]:((funny(X)&wise(X))))&
(?[X]:((funny(X)<~>~quiet(X))))&
((~wise(john)<~>creative(john)))&
(~happy(lucy))&
((patient(mary)&strong(mary)))&
(?[X]:((~kind(X)|brave(X)))) | ~humble(lucy) | [
"p3",
"p9",
"p10",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5780219269547826819907245
% SZS output start Proof for 5780219269547826819907245
4. ! [X0] : ((quiet(X0) | generous(X0)) => (creative(X0) & quiet(X0))) [input p3]
10. ! [X0] : ((~patient(X0) | ~tall(X0)) => rich(X0)) [input p9]
11. ! [X0] : ((funny(X0) <~> ~rich(X0)) <=> (generous(X0) & quiet(X0))) [input p10]
15. ! [X0] : (~happy(X0) => (~generous(X0) <~> ~happy(X0))) [input p14]
16. ! [X0] : ((funny(X0) & ~tall(X0)) <=> (tall(X0) <~> ~humble(X0))) [input p15]
22. ~happy(lucy) [input p21]
25. humble(lucy) [input hypothesis]
31. ! [X0] : ((creative(X0) & quiet(X0)) | (~quiet(X0) & ~generous(X0))) [ennf transformation 4]
35. ! [X0] : (rich(X0) | (patient(X0) & tall(X0))) [ennf transformation 10]
40. ! [X0] : ((~generous(X0) <~> ~happy(X0)) | happy(X0)) [ennf transformation 15]
61. ! [X0] : ((((rich(X0) | ~funny(X0)) & (~rich(X0) | funny(X0))) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | ((funny(X0) | rich(X0)) & (~rich(X0) | ~funny(X0))))) [nnf transformation 11]
62. ! [X0] : ((((rich(X0) | ~funny(X0)) & (~rich(X0) | funny(X0))) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | ((funny(X0) | rich(X0)) & (~rich(X0) | ~funny(X0))))) [flattening 61]
68. ! [X0] : (((happy(X0) | generous(X0)) & (~happy(X0) | ~generous(X0))) | happy(X0)) [nnf transformation 40]
69. ! [X0] : (((funny(X0) & ~tall(X0)) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0)))) & (((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | (~funny(X0) | tall(X0)))) [nnf transformation 16]
70. ! [X0] : (((funny(X0) & ~tall(X0)) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0)))) & (((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | ~funny(X0) | tall(X0))) [flattening 69]
89. ~generous(X0) | quiet(X0) [cnf transformation 31]
110. tall(X0) | rich(X0) [cnf transformation 35]
116. ~rich(X0) | funny(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 62]
127. happy(X0) | generous(X0) | happy(X0) [cnf transformation 68]
128. ~humble(X0) | tall(X0) | ~funny(X0) | tall(X0) [cnf transformation 70]
130. ~tall(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 70]
142. ~happy(lucy) [cnf transformation 22]
146. humble(lucy) [cnf transformation 25]
147. ~humble(X0) | tall(X0) | ~funny(X0) [duplicate literal removal 128]
148. ~tall(X0) | ~humble(X0) [duplicate literal removal 130]
149. happy(X0) | generous(X0) [duplicate literal removal 127]
235. ~rich(X0) | funny(X0) | ~generous(X0) [subsumption resolution 116,89]
254. ~funny(X0) | ~humble(X0) [subsumption resolution 147,148]
284. ~humble(X0) | rich(X0) [resolution 148,110]
286. generous(lucy) [resolution 149,142]
471. rich(lucy) [resolution 284,146]
509. funny(lucy) | ~generous(lucy) [resolution 471,235]
513. funny(lucy) [subsumption resolution 509,286]
533. ~humble(lucy) [resolution 513,254]
535. $false [subsumption resolution 533,146]
% SZS output end Proof for 5780219269547826819907245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and quiet is not kind or strong and vice versa.
Everyone who is not wise or patient is happy.
If alice is old or not curious then someone is both not brave and not patient and vice versa.
If lucy is not humble then someone is both generous and wise.
If someone is creative then fred is both wise and not brave and vice versa.
If alice is calm or not quiet then lucy is both happy and curious and vice versa.
If someone is tall then someone is both patient and not generous.
Everyone who is either kind or not curious is either happy or not calm and vice versa.
Everyone who is both generous and not quiet is not strong and vice versa.
Everyone who is both not humble and calm is curious.
If lucy is both not rich and not wise then someone is both funny and quiet.
If lucy is both calm and strong then fred is both not patient and not funny.
If someone is quiet or happy then alice is either not calm or not generous.
Everyone who is humble is either not kind or tall and vice versa.
Everyone who is both not calm and not old is creative or happy and vice versa.
If alice is either not funny or old then someone is either not generous or old and vice versa.
Paul is patient.
Alice is both curious and not old.
Someone is rich.
Paul is generous.
Alice is brave or not happy.
Alice is both generous and curious.
Lucy is both happy and not strong.
Someone is not quiet or creative. | Lucy is generous. | entailment | (![X]:((~calm(X)&quiet(X))<=>(~kind(X)|strong(X))))&
(![X]:((~wise(X)|patient(X))=>happy(X)))&
(((old(alice)|~curious(alice)))<=>(?[X]:((~brave(X)&~patient(X)))))&
((~humble(lucy))=>(?[X]:((generous(X)&wise(X)))))&
((?[X]:(creative(X)))<=>((wise(fred)&~brave(fred))))&
(((calm(alice)|~quiet(alice)))<=>((happy(lucy)&curious(lucy))))&
((?[X]:(tall(X)))=>(?[X]:((patient(X)&~generous(X)))))&
(![X]:((kind(X)<~>~curious(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((generous(X)&~quiet(X))<=>~strong(X)))&
(![X]:((~humble(X)&calm(X))=>curious(X)))&
(((~rich(lucy)&~wise(lucy)))=>(?[X]:((funny(X)&quiet(X)))))&
(((calm(lucy)&strong(lucy)))=>((~patient(fred)&~funny(fred))))&
((?[X]:((quiet(X)|happy(X))))=>((~calm(alice)<~>~generous(alice))))&
(![X]:(humble(X)<=>(~kind(X)<~>tall(X))))&
(![X]:((~calm(X)&~old(X))<=>(creative(X)|happy(X))))&
(((~funny(alice)<~>old(alice)))<=>(?[X]:((~generous(X)<~>old(X)))))&
(patient(paul))&
((curious(alice)&~old(alice)))&
(?[X]:(rich(X)))&
(generous(paul))&
((brave(alice)|~happy(alice)))&
((generous(alice)&curious(alice)))&
((happy(lucy)&~strong(lucy)))&
(?[X]:((~quiet(X)|creative(X)))) | generous(lucy) | [
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1097870933527393613425082
% SZS output start Proof for 1097870933527393613425082
9. ! [X0] : ((~quiet(X0) & generous(X0)) <=> ~strong(X0)) [input p8]
23. ~strong(lucy) & happy(lucy) [input p22]
25. ~generous(lucy) [input hypothesis]
59. ! [X0] : (((~quiet(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (quiet(X0) | ~generous(X0)))) [nnf transformation 9]
60. ! [X0] : (((~quiet(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | quiet(X0) | ~generous(X0))) [flattening 59]
104. generous(X0) | strong(X0) [cnf transformation 60]
136. ~strong(lucy) [cnf transformation 23]
138. ~generous(lucy) [cnf transformation 25]
298. strong(lucy) [resolution 104,138]
300. $false [subsumption resolution 298,136]
% SZS output end Proof for 1097870933527393613425082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and tall is not old or not creative and vice versa.
If alice is both humble and not wise then someone is rich.
If someone is either not strong or kind then susan is either old or tall.
Everyone who is either not generous or brave is not patient or brave and vice versa.
If alice is generous then alice is rich or strong.
Everyone who is funny or not calm is both creative and not patient and vice versa.
If someone is both curious and not old then someone is both not quiet and wise and vice versa.
Everyone who is either not wise or not rich is either brave or rich and vice versa.
If someone is either calm or not old then fred is either creative or generous.
Everyone who is not humble is either funny or quiet.
If someone is wise then someone is both not generous and not brave.
Everyone who is both old and kind is strong or not rich and vice versa.
Everyone who is not curious is either funny or not kind and vice versa.
Everyone who is quiet or not tall is not patient and vice versa.
Everyone who is either not calm or not creative is not brave.
Everyone who is kind is either not generous or tall and vice versa.
John is either not tall or not wise.
Someone is either happy or curious.
John is wise or rich.
Someone is strong or not strong.
Someone is not tall or strong.
Someone is not generous.
Mary is not humble or funny.
Someone is not brave. | John is not rich. | contradiction | (![X]:((~old(X)&tall(X))<=>(~old(X)|~creative(X))))&
(((humble(alice)&~wise(alice)))=>(?[X]:(rich(X))))&
((?[X]:((~strong(X)<~>kind(X))))=>((old(susan)<~>tall(susan))))&
(![X]:((~generous(X)<~>brave(X))<=>(~patient(X)|brave(X))))&
((generous(alice))=>((rich(alice)|strong(alice))))&
(![X]:((funny(X)|~calm(X))<=>(creative(X)&~patient(X))))&
((?[X]:((curious(X)&~old(X))))<=>(?[X]:((~quiet(X)&wise(X)))))&
(![X]:((~wise(X)<~>~rich(X))<=>(brave(X)<~>rich(X))))&
((?[X]:((calm(X)<~>~old(X))))=>((creative(fred)<~>generous(fred))))&
(![X]:(~humble(X)=>(funny(X)<~>quiet(X))))&
((?[X]:(wise(X)))=>(?[X]:((~generous(X)&~brave(X)))))&
(![X]:((old(X)&kind(X))<=>(strong(X)|~rich(X))))&
(![X]:(~curious(X)<=>(funny(X)<~>~kind(X))))&
(![X]:((quiet(X)|~tall(X))<=>~patient(X)))&
(![X]:((~calm(X)<~>~creative(X))=>~brave(X)))&
(![X]:(kind(X)<=>(~generous(X)<~>tall(X))))&
((~tall(john)<~>~wise(john)))&
(?[X]:((happy(X)<~>curious(X))))&
((wise(john)|rich(john)))&
(?[X]:((strong(X)|~strong(X))))&
(?[X]:((~tall(X)|strong(X))))&
(?[X]:(~generous(X)))&
((~humble(mary)|funny(mary)))&
(?[X]:(~brave(X))) | ~rich(john) | [
"p3",
"p7",
"p11",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1282598920838865968932548
% SZS output start Proof for 1282598920838865968932548
4. ! [X0] : ((~generous(X0) <~> brave(X0)) <=> (brave(X0) | ~patient(X0))) [input p3]
8. ! [X0] : ((~wise(X0) <~> ~rich(X0)) <=> (brave(X0) <~> rich(X0))) [input p7]
12. ! [X0] : ((kind(X0) & old(X0)) <=> (~rich(X0) | strong(X0))) [input p11]
16. ! [X0] : (kind(X0) <=> (~generous(X0) <~> tall(X0))) [input p15]
17. ~tall(john) <~> ~wise(john) [input p16]
19. rich(john) | wise(john) [input p18]
25. ~rich(john) [input hypothesis]
42. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [nnf transformation 4]
43. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [flattening 42]
51. ! [X0] : ((((rich(X0) | wise(X0)) & (~rich(X0) | ~wise(X0))) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0)))) & (((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0))))) [nnf transformation 8]
57. ! [X0] : (((kind(X0) & old(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (~kind(X0) | ~old(X0)))) [nnf transformation 12]
58. ! [X0] : (((kind(X0) & old(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | ~kind(X0) | ~old(X0))) [flattening 57]
63. ! [X0] : ((kind(X0) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | ~kind(X0))) [nnf transformation 16]
64. (wise(john) | tall(john)) & (~wise(john) | ~tall(john)) [nnf transformation 17]
91. ~brave(X0) | generous(X0) | ~brave(X0) [cnf transformation 43]
103. rich(X0) | brave(X0) | ~wise(X0) | rich(X0) [cnf transformation 51]
107. ~rich(X0) | ~wise(X0) | brave(X0) | ~rich(X0) [cnf transformation 51]
122. kind(X0) | rich(X0) [cnf transformation 58]
132. ~generous(X0) | tall(X0) | ~kind(X0) [cnf transformation 63]
136. ~wise(john) | ~tall(john) [cnf transformation 64]
140. rich(john) | wise(john) [cnf transformation 19]
146. ~rich(john) [cnf transformation 25]
147. rich(X0) | brave(X0) | ~wise(X0) [duplicate literal removal 103]
149. ~rich(X0) | ~wise(X0) | brave(X0) [duplicate literal removal 107]
152. ~brave(X0) | generous(X0) [duplicate literal removal 91]
223. ~wise(X0) | brave(X0) [subsumption resolution 147,149]
258. 24 <=> tall(john) [avatar definition]
259. ~tall(john) <- (~24) [avatar component clause 258]
262. 25 <=> wise(john) [avatar definition]
264. wise(john) <- (25) [avatar component clause 262]
266. ~24 | ~25 [avatar split clause 136,262,258]
278. 28 <=> rich(john) [avatar definition]
279. ~rich(john) <- (~28) [avatar component clause 278]
281. 25 | 28 [avatar split clause 140,278,262]
300. ~28 [avatar split clause 146,278]
308. brave(john) <- (25) [resolution 223,264]
311. generous(john) <- (25) [resolution 308,152]
330. tall(john) | ~kind(john) <- (25) [resolution 132,311]
331. ~kind(john) <- (~24, 25) [subsumption resolution 330,259]
333. rich(john) <- (~24, 25) [resolution 331,122]
334. $false <- (~24, 25, ~28) [subsumption resolution 333,279]
335. 24 | ~25 | 28 [avatar contradiction clause 334]
336. $false [avatar sat refutation 266,281,300,335]
% SZS output end Proof for 1282598920838865968932548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or strong is both calm and rich and vice versa.
If someone is both not old and not rich then someone is either not kind or not brave and vice versa.
Everyone who is funny is either funny or calm.
If someone is both tall and not old then lucy is humble and vice versa.
If fred is quiet or creative then someone is either humble or tall and vice versa.
If fred is not generous then lucy is tall or not tall and vice versa.
Everyone who is generous is generous or not generous.
Everyone who is either rich or humble is creative or brave.
If alice is either not happy or not strong then paul is not quiet and vice versa.
If paul is both generous and quiet then paul is both not old and happy and vice versa.
Everyone who is happy is both creative and not humble and vice versa.
If lucy is both not rich and kind then fred is either tall or rich and vice versa.
Everyone who is either not rich or brave is both kind and not kind and vice versa.
Everyone who is not strong or not calm is not strong or strong and vice versa.
If fred is not calm or strong then someone is either funny or not curious.
If someone is not old or not kind then someone is both not kind and calm.
Someone is either calm or not kind.
Someone is not curious.
John is either not tall or creative.
Mary is either quiet or brave.
Someone is both calm and not wise.
Someone is either tall or not humble.
Someone is happy or calm.
Paul is both not strong and not wise. | Paul is strong. | contradiction | (![X]:((~kind(X)|strong(X))<=>(calm(X)&rich(X))))&
((?[X]:((~old(X)&~rich(X))))<=>(?[X]:((~kind(X)<~>~brave(X)))))&
(![X]:(funny(X)=>(funny(X)<~>calm(X))))&
((?[X]:((tall(X)&~old(X))))<=>(humble(lucy)))&
(((quiet(fred)|creative(fred)))<=>(?[X]:((humble(X)<~>tall(X)))))&
((~generous(fred))<=>((tall(lucy)|~tall(lucy))))&
(![X]:(generous(X)=>(generous(X)|~generous(X))))&
(![X]:((rich(X)<~>humble(X))=>(creative(X)|brave(X))))&
(((~happy(alice)<~>~strong(alice)))<=>(~quiet(paul)))&
(((generous(paul)&quiet(paul)))<=>((~old(paul)&happy(paul))))&
(![X]:(happy(X)<=>(creative(X)&~humble(X))))&
(((~rich(lucy)&kind(lucy)))<=>((tall(fred)<~>rich(fred))))&
(![X]:((~rich(X)<~>brave(X))<=>(kind(X)&~kind(X))))&
(![X]:((~strong(X)|~calm(X))<=>(~strong(X)|strong(X))))&
(((~calm(fred)|strong(fred)))=>(?[X]:((funny(X)<~>~curious(X)))))&
((?[X]:((~old(X)|~kind(X))))=>(?[X]:((~kind(X)&calm(X)))))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:(~curious(X)))&
((~tall(john)<~>creative(john)))&
((quiet(mary)<~>brave(mary)))&
(?[X]:((calm(X)&~wise(X))))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:((happy(X)|calm(X))))&
((~strong(paul)&~wise(paul))) | strong(paul) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2360341279312416657601609
% SZS output start Proof for 2360341279312416657601609
1. ! [X0] : ((strong(X0) | ~kind(X0)) <=> (rich(X0) & calm(X0))) [input p0]
14. ! [X0] : ((~calm(X0) | ~strong(X0)) <=> (strong(X0) | ~strong(X0))) [input p13]
25. strong(paul) [input hypothesis]
37. ! [X0] : (((strong(X0) | ~kind(X0)) | (~rich(X0) | ~calm(X0))) & ((rich(X0) & calm(X0)) | (~strong(X0) & kind(X0)))) [nnf transformation 1]
38. ! [X0] : ((strong(X0) | ~kind(X0) | ~rich(X0) | ~calm(X0)) & ((rich(X0) & calm(X0)) | (~strong(X0) & kind(X0)))) [flattening 37]
66. ! [X0] : (((~calm(X0) | ~strong(X0)) | (~strong(X0) & strong(X0))) & ((strong(X0) | ~strong(X0)) | (calm(X0) & strong(X0)))) [nnf transformation 14]
67. ! [X0] : ((~calm(X0) | ~strong(X0) | (~strong(X0) & strong(X0))) & (strong(X0) | ~strong(X0) | (calm(X0) & strong(X0)))) [flattening 66]
89. calm(X0) | ~strong(X0) [cnf transformation 38]
142. ~calm(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 67]
163. strong(paul) [cnf transformation 25]
165. ~calm(X0) | ~strong(X0) [duplicate literal removal 142]
313. ~strong(X0) [subsumption resolution 165,89]
387. $false [subsumption resolution 163,313]
% SZS output end Proof for 2360341279312416657601609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not wise or not quiet.
If someone is not happy then someone is either tall or strong and vice versa.
Everyone who is either calm or creative is brave or strong.
Everyone who is curious or quiet is not brave.
If someone is creative or rich then someone is tall and vice versa.
If someone is not wise then someone is tall or not brave.
If susan is quiet then john is either rich or funny and vice versa.
Everyone who is both not calm and not happy is generous or calm and vice versa.
Everyone who is curious is not patient.
Everyone who is not funny or tall is not strong or creative and vice versa.
Everyone who is strong or curious is either calm or not generous and vice versa.
If mary is not strong then fred is both not generous and calm and vice versa.
Everyone who is tall or not brave is not creative or strong.
If someone is either not old or old then someone is not curious and vice versa.
Everyone who is humble or curious is not old or rich and vice versa.
Everyone who is either generous or not generous is either quiet or not brave and vice versa.
Someone is not tall.
Someone is either not wise or not patient.
Someone is not quiet or not wise.
Someone is either strong or kind.
Someone is funny or not kind.
Fred is not calm or happy. | Susan is wise. | neutral | (![X]:(~calm(X)=>(~wise(X)|~quiet(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((tall(X)<~>strong(X)))))&
(![X]:((calm(X)<~>creative(X))=>(brave(X)|strong(X))))&
(![X]:((curious(X)|quiet(X))=>~brave(X)))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:(tall(X))))&
((?[X]:(~wise(X)))=>(?[X]:((tall(X)|~brave(X)))))&
((quiet(susan))<=>((rich(john)<~>funny(john))))&
(![X]:((~calm(X)&~happy(X))<=>(generous(X)|calm(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((~funny(X)|tall(X))<=>(~strong(X)|creative(X))))&
(![X]:((strong(X)|curious(X))<=>(calm(X)<~>~generous(X))))&
((~strong(mary))<=>((~generous(fred)&calm(fred))))&
(![X]:((tall(X)|~brave(X))=>(~creative(X)|strong(X))))&
((?[X]:((~old(X)<~>old(X))))<=>(?[X]:(~curious(X))))&
(![X]:((humble(X)|curious(X))<=>(~old(X)|rich(X))))&
(![X]:((generous(X)<~>~generous(X))<=>(quiet(X)<~>~brave(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((~quiet(X)|~wise(X))))&
(?[X]:((strong(X)<~>kind(X))))&
(?[X]:((funny(X)|~kind(X))))&
((~calm(fred)|happy(fred))) | wise(susan) | [] | null | 0 |
Everyone who is both not calm and patient is not rich or not tall and vice versa.
Everyone who is either not calm or not wise is either not strong or wise and vice versa.
Everyone who is both not curious and rich is not creative.
Everyone who is humble or creative is both not tall and not old and vice versa.
Everyone who is not generous is funny.
Everyone who is not patient or calm is not tall and vice versa.
If mary is either quiet or not curious then someone is both not kind and not strong.
If someone is either not patient or not strong then someone is creative or humble.
Everyone who is both quiet and not kind is both calm and happy and vice versa.
Everyone who is not happy or happy is both not wise and not brave and vice versa.
Everyone who is both not strong and kind is both not kind and rich.
Everyone who is either happy or not old is both quiet and not humble and vice versa.
Everyone who is either rich or quiet is both not rich and curious.
Everyone who is both not curious and kind is both not wise and not creative.
Everyone who is happy or curious is either kind or not brave.
Mary is strong.
Susan is not brave.
John is either creative or patient.
Fred is not wise or not curious.
Lucy is curious or not generous.
Susan is not old. | Susan is brave. | contradiction | (![X]:((~calm(X)&patient(X))<=>(~rich(X)|~tall(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>(~strong(X)<~>wise(X))))&
(![X]:((~curious(X)&rich(X))=>~creative(X)))&
(![X]:((humble(X)|creative(X))<=>(~tall(X)&~old(X))))&
(![X]:(~generous(X)=>funny(X)))&
(![X]:((~patient(X)|calm(X))<=>~tall(X)))&
(((quiet(mary)<~>~curious(mary)))=>(?[X]:((~kind(X)&~strong(X)))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:((creative(X)|humble(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(calm(X)&happy(X))))&
(![X]:((~happy(X)|happy(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~strong(X)&kind(X))=>(~kind(X)&rich(X))))&
(![X]:((happy(X)<~>~old(X))<=>(quiet(X)&~humble(X))))&
(![X]:((rich(X)<~>quiet(X))=>(~rich(X)&curious(X))))&
(![X]:((~curious(X)&kind(X))=>(~wise(X)&~creative(X))))&
(![X]:((happy(X)|curious(X))=>(kind(X)<~>~brave(X))))&
(strong(mary))&
(~brave(susan))&
((creative(john)<~>patient(john)))&
((~wise(fred)|~curious(fred)))&
((curious(lucy)|~generous(lucy)))&
(~old(susan)) | brave(susan) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 422308972909251228568152
% SZS output start Proof for 422308972909251228568152
10. ! [X0] : ((happy(X0) | ~happy(X0)) <=> (~brave(X0) & ~wise(X0))) [input p9]
22. brave(susan) [input hypothesis]
52. ! [X0] : (((happy(X0) | ~happy(X0)) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | (~happy(X0) & happy(X0)))) [nnf transformation 10]
53. ! [X0] : ((happy(X0) | ~happy(X0) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | (~happy(X0) & happy(X0)))) [flattening 52]
93. ~brave(X0) | happy(X0) [cnf transformation 53]
94. ~brave(X0) | ~happy(X0) [cnf transformation 53]
120. brave(susan) [cnf transformation 22]
167. ~brave(X0) [subsumption resolution 93,94]
174. $false [subsumption resolution 120,167]
% SZS output end Proof for 422308972909251228568152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not kind or creative.
Everyone who is either wise or not rich is strong or not calm and vice versa.
Everyone who is humble is both patient and not quiet.
Everyone who is both not happy and rich is both happy and not old.
If someone is either not brave or not generous then mary is not funny or brave.
Everyone who is creative or not tall is either old or calm and vice versa.
Everyone who is both not curious and wise is either funny or calm and vice versa.
If someone is not curious or curious then john is not quiet or not old.
If susan is either not old or not kind then john is both not quiet and creative and vice versa.
Everyone who is either tall or not tall is either not old or humble and vice versa.
If alice is not rich or happy then someone is not quiet or happy and vice versa.
Everyone who is not humble or wise is not strong or not rich and vice versa.
Everyone who is both not wise and quiet is patient and vice versa.
If someone is not old then someone is not calm.
If someone is both generous and calm then someone is kind or not curious.
Everyone who is tall or creative is either funny or not curious and vice versa.
Someone is calm.
Alice is either not kind or creative.
John is either humble or tall.
Someone is generous.
Someone is not humble.
Lucy is either humble or not creative.
John is strong.
Alice is funny or not rich. | Susan is old. | contradiction | (![X]:(brave(X)=>(~kind(X)<~>creative(X))))&
(![X]:((wise(X)<~>~rich(X))<=>(strong(X)|~calm(X))))&
(![X]:(humble(X)=>(patient(X)&~quiet(X))))&
(![X]:((~happy(X)&rich(X))=>(happy(X)&~old(X))))&
((?[X]:((~brave(X)<~>~generous(X))))=>((~funny(mary)|brave(mary))))&
(![X]:((creative(X)|~tall(X))<=>(old(X)<~>calm(X))))&
(![X]:((~curious(X)&wise(X))<=>(funny(X)<~>calm(X))))&
((?[X]:((~curious(X)|curious(X))))=>((~quiet(john)|~old(john))))&
(((~old(susan)<~>~kind(susan)))<=>((~quiet(john)&creative(john))))&
(![X]:((tall(X)<~>~tall(X))<=>(~old(X)<~>humble(X))))&
(((~rich(alice)|happy(alice)))<=>(?[X]:((~quiet(X)|happy(X)))))&
(![X]:((~humble(X)|wise(X))<=>(~strong(X)|~rich(X))))&
(![X]:((~wise(X)&quiet(X))<=>patient(X)))&
((?[X]:(~old(X)))=>(?[X]:(~calm(X))))&
((?[X]:((generous(X)&calm(X))))=>(?[X]:((kind(X)|~curious(X)))))&
(![X]:((tall(X)|creative(X))<=>(funny(X)<~>~curious(X))))&
(?[X]:(calm(X)))&
((~kind(alice)<~>creative(alice)))&
((humble(john)<~>tall(john)))&
(?[X]:(generous(X)))&
(?[X]:(~humble(X)))&
((humble(lucy)<~>~creative(lucy)))&
(strong(john))&
((funny(alice)|~rich(alice))) | old(susan) | [
"p2",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5921374247394847843670541
% SZS output start Proof for 5921374247394847843670541
3. ! [X0] : (humble(X0) => (~quiet(X0) & patient(X0))) [input p2]
10. ! [X0] : ((tall(X0) <~> ~tall(X0)) <=> (~old(X0) <~> humble(X0))) [input p9]
13. ! [X0] : ((quiet(X0) & ~wise(X0)) <=> patient(X0)) [input p12]
25. old(susan) [input hypothesis]
28. ! [X0] : (patient(X0) => (quiet(X0) & ~wise(X0))) [unused predicate definition removal 13]
30. ! [X0] : ((~quiet(X0) & patient(X0)) | ~humble(X0)) [ennf transformation 3]
37. ! [X0] : ((quiet(X0) & ~wise(X0)) | ~patient(X0)) [ennf transformation 28]
50. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) & (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [nnf transformation 10]
83. ~humble(X0) | patient(X0) [cnf transformation 30]
84. ~quiet(X0) | ~humble(X0) [cnf transformation 30]
109. humble(X0) | ~old(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 50]
110. humble(X0) | ~old(X0) | tall(X0) | tall(X0) [cnf transformation 50]
126. ~patient(X0) | quiet(X0) [cnf transformation 37]
146. old(susan) [cnf transformation 25]
147. humble(X0) | ~old(X0) | ~tall(X0) [duplicate literal removal 109]
148. humble(X0) | ~old(X0) | tall(X0) [duplicate literal removal 110]
189. 10 <=> old(susan) [avatar definition]
191. old(susan) <- (10) [avatar component clause 189]
203. ~old(X0) | humble(X0) [subsumption resolution 147,148]
278. 10 [avatar split clause 146,189]
289. humble(susan) <- (10) [resolution 203,191]
291. patient(susan) <- (10) [resolution 289,83]
315. quiet(susan) <- (10) [resolution 291,126]
318. ~humble(susan) <- (10) [resolution 315,84]
319. $false <- (10) [subsumption resolution 318,289]
320. ~10 [avatar contradiction clause 319]
321. $false [avatar sat refutation 278,320]
% SZS output end Proof for 5921374247394847843670541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is tall then someone is not wise or not creative.
If susan is not kind or kind then someone is either not rich or not happy and vice versa.
Everyone who is either curious or not funny is either not generous or not curious.
If fred is curious or rich then paul is not old or not tall.
If fred is not funny then someone is either not quiet or funny and vice versa.
If someone is both tall and not calm then mary is both not old and not strong.
Everyone who is not kind or not patient is old.
If alice is both creative and humble then someone is creative or not strong.
Everyone who is either not patient or kind is either curious or brave and vice versa.
If someone is both old and not old then someone is creative and vice versa.
Everyone who is brave is not humble or humble.
If someone is either not tall or not brave then fred is both kind and happy.
If someone is either not happy or kind then someone is either not wise or not kind and vice versa.
Everyone who is both old and calm is either patient or not happy.
Everyone who is either brave or quiet is happy or not calm and vice versa.
If alice is humble or tall then someone is not creative.
Someone is both patient and generous.
Someone is both not strong and generous.
Susan is not old.
Fred is old.
John is both old and not brave.
Lucy is not tall or not calm.
Lucy is not rich or not tall.
Someone is quiet or curious. | Lucy is creative. | contradiction | ((tall(paul))=>(?[X]:((~wise(X)|~creative(X)))))&
(((~kind(susan)|kind(susan)))<=>(?[X]:((~rich(X)<~>~happy(X)))))&
(![X]:((curious(X)<~>~funny(X))=>(~generous(X)<~>~curious(X))))&
(((curious(fred)|rich(fred)))=>((~old(paul)|~tall(paul))))&
((~funny(fred))<=>(?[X]:((~quiet(X)<~>funny(X)))))&
((?[X]:((tall(X)&~calm(X))))=>((~old(mary)&~strong(mary))))&
(![X]:((~kind(X)|~patient(X))=>old(X)))&
(((creative(alice)&humble(alice)))=>(?[X]:((creative(X)|~strong(X)))))&
(![X]:((~patient(X)<~>kind(X))<=>(curious(X)<~>brave(X))))&
((?[X]:((old(X)&~old(X))))<=>(?[X]:(creative(X))))&
(![X]:(brave(X)=>(~humble(X)|humble(X))))&
((?[X]:((~tall(X)<~>~brave(X))))=>((kind(fred)&happy(fred))))&
((?[X]:((~happy(X)<~>kind(X))))<=>(?[X]:((~wise(X)<~>~kind(X)))))&
(![X]:((old(X)&calm(X))=>(patient(X)<~>~happy(X))))&
(![X]:((brave(X)<~>quiet(X))<=>(happy(X)|~calm(X))))&
(((humble(alice)|tall(alice)))=>(?[X]:(~creative(X))))&
(?[X]:((patient(X)&generous(X))))&
(?[X]:((~strong(X)&generous(X))))&
(~old(susan))&
(old(fred))&
((old(john)&~brave(john)))&
((~tall(lucy)|~calm(lucy)))&
((~rich(lucy)|~tall(lucy)))&
(?[X]:((quiet(X)|curious(X)))) | creative(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2470427982109115681322128
% SZS output start Proof for 2470427982109115681322128
10. ? [X0] : (~old(X0) & old(X0)) <=> ? [X0] : creative(X0) [input p9]
25. creative(lucy) [input hypothesis]
26. ? [X0] : (~old(X0) & old(X0)) <=> ? [X1] : creative(X1) [rectify 10]
56. (? [X0] : (~old(X0) & old(X0)) | ! [X1] : ~creative(X1)) & (? [X1] : creative(X1) | ! [X0] : (old(X0) | ~old(X0))) [nnf transformation 26]
57. (? [X0] : (~old(X0) & old(X0)) | ! [X1] : ~creative(X1)) & (? [X2] : creative(X2) | ! [X3] : (old(X3) | ~old(X3))) [rectify 56]
58. ? [X0] : (~old(X0) & old(X0)) => (~old(sK3) & old(sK3)) [choice axiom]
59. ? [X2] : creative(X2) => creative(sK4) [choice axiom]
60. ((~old(sK3) & old(sK3)) | ! [X1] : ~creative(X1)) & (creative(sK4) | ! [X3] : (old(X3) | ~old(X3))) [skolemisation 57,59,58]
107. old(sK3) | ~creative(X1) [cnf transformation 60]
108. ~old(sK3) | ~creative(X1) [cnf transformation 60]
142. creative(lucy) [cnf transformation 25]
219. 17 <=> ! [X1] : ~creative(X1) [avatar definition]
220. ~creative(X1) <- (17) [avatar component clause 219]
222. 18 <=> old(sK3) [avatar definition]
225. 17 | ~18 [avatar split clause 108,222,219]
226. 17 | 18 [avatar split clause 107,222,219]
319. $false <- (17) [resolution 220,142]
320. ~17 [avatar contradiction clause 319]
321. $false [avatar sat refutation 225,226,320]
% SZS output end Proof for 2470427982109115681322128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not quiet is kind or not funny and vice versa.
If someone is generous then someone is either creative or not rich.
If someone is either happy or not humble then lucy is not brave or not generous and vice versa.
Everyone who is both brave and not calm is either patient or not brave.
Everyone who is not rich or kind is strong.
If someone is not brave then paul is creative or humble and vice versa.
If someone is either funny or tall then lucy is either happy or rich.
Everyone who is either brave or not rich is either funny or strong.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Someone is curious.
Someone is either not old or not kind.
Susan is not wise.
Someone is either funny or not funny.
Someone is both not calm and not curious.
Fred is not strong or not creative.
Someone is generous or not kind. | Paul is kind. | entailment | (![X]:((calm(X)|~quiet(X))<=>(kind(X)|~funny(X))))&
((?[X]:(generous(X)))=>(?[X]:((creative(X)<~>~rich(X)))))&
((?[X]:((happy(X)<~>~humble(X))))<=>((~brave(lucy)|~generous(lucy))))&
(![X]:((brave(X)&~calm(X))=>(patient(X)<~>~brave(X))))&
(![X]:((~rich(X)|kind(X))=>strong(X)))&
((?[X]:(~brave(X)))<=>((creative(paul)|humble(paul))))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(lucy)<~>rich(lucy))))&
(![X]:((brave(X)<~>~rich(X))=>(funny(X)<~>strong(X))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((~calm(X)&~curious(X))))&
((~strong(fred)|~creative(fred)))&
(?[X]:((generous(X)|~kind(X)))) | kind(paul) | [
"p4",
"p11",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8428918922405498990223061
% SZS output start Proof for 8428918922405498990223061
5. ! [X0] : ((kind(X0) | ~rich(X0)) => strong(X0)) [input p4]
12. ~happy(lucy) <=> (~creative(fred) <~> rich(fred)) [input p11]
15. ? [X0] : rich(X0) => kind(paul) [input p14]
16. ! [X0] : (~happy(X0) <=> rich(X0)) [input p15]
22. ~creative(fred) | ~strong(fred) [input p21]
24. ~kind(paul) [input hypothesis]
31. ! [X0] : (strong(X0) | (~kind(X0) & rich(X0))) [ennf transformation 5]
35. kind(paul) | ! [X0] : ~rich(X0) [ennf transformation 15]
59. (~happy(lucy) | ((~creative(fred) | ~rich(fred)) & (rich(fred) | creative(fred)))) & (((~rich(fred) | creative(fred)) & (rich(fred) | ~creative(fred))) | happy(lucy)) [nnf transformation 12]
62. ! [X0] : ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))) [nnf transformation 16]
89. strong(X0) | rich(X0) [cnf transformation 31]
112. ~happy(lucy) | rich(fred) | creative(fred) [cnf transformation 59]
117. kind(paul) | ~rich(X0) [cnf transformation 35]
118. happy(X0) | rich(X0) [cnf transformation 62]
127. ~creative(fred) | ~strong(fred) [cnf transformation 22]
129. ~kind(paul) [cnf transformation 24]
194. 15 <=> happy(lucy) [avatar definition]
196. ~happy(lucy) <- (~15) [avatar component clause 194]
212. 18 <=> rich(fred) [avatar definition]
213. rich(fred) <- (18) [avatar component clause 212]
216. 19 <=> creative(fred) [avatar definition]
220. 19 | 18 | ~15 [avatar split clause 112,194,212,216]
224. 20 <=> ! [X0] : ~rich(X0) [avatar definition]
225. ~rich(X0) <- (20) [avatar component clause 224]
227. 21 <=> kind(paul) [avatar definition]
230. 20 | 21 [avatar split clause 117,227,224]
242. 24 <=> strong(fred) [avatar definition]
244. ~strong(fred) <- (~24) [avatar component clause 242]
245. ~24 | ~19 [avatar split clause 127,216,242]
255. ~21 [avatar split clause 129,227]
260. rich(lucy) <- (~15) [resolution 118,196]
263. $false <- (~15, 20) [subsumption resolution 260,225]
264. 15 | ~20 [avatar contradiction clause 263]
265. $false <- (18, 20) [subsumption resolution 213,225]
266. ~18 | ~20 [avatar contradiction clause 265]
267. rich(fred) <- (~24) [resolution 244,89]
268. $false <- (20, ~24) [subsumption resolution 267,225]
269. ~20 | 24 [avatar contradiction clause 268]
270. $false [avatar sat refutation 220,230,245,255,264,266,269]
% SZS output end Proof for 8428918922405498990223061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either tall or not happy then someone is either happy or kind and vice versa.
Everyone who is kind or not happy is patient or not curious and vice versa.
If someone is happy then someone is either not happy or curious and vice versa.
Everyone who is not old or generous is both not happy and not wise and vice versa.
If mary is funny then someone is not patient or not funny.
Everyone who is either not happy or generous is either not happy or old and vice versa.
Everyone who is not quiet is not tall or happy and vice versa.
If someone is not rich then someone is both patient and kind.
Everyone who is both humble and not wise is both not rich and not funny.
If someone is either not generous or not strong then alice is either calm or old.
If someone is not calm then mary is either funny or tall and vice versa.
Everyone who is either not generous or not creative is not humble or creative and vice versa.
Everyone who is either not quiet or not happy is either not funny or not generous and vice versa.
If alice is not kind or not tall then someone is not patient and vice versa.
If someone is both not kind and calm then someone is not curious or not strong.
If someone is not quiet then susan is not strong.
Someone is kind or not creative.
Paul is calm or wise.
Lucy is not strong or not happy.
Someone is humble or generous.
Someone is both not creative and not rich.
Someone is not quiet or not humble. | Mary is not patient. | contradiction | (((tall(paul)<~>~happy(paul)))<=>(?[X]:((happy(X)<~>kind(X)))))&
(![X]:((kind(X)|~happy(X))<=>(patient(X)|~curious(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~happy(X)<~>curious(X)))))&
(![X]:((~old(X)|generous(X))<=>(~happy(X)&~wise(X))))&
((funny(mary))=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:((~happy(X)<~>generous(X))<=>(~happy(X)<~>old(X))))&
(![X]:(~quiet(X)<=>(~tall(X)|happy(X))))&
((?[X]:(~rich(X)))=>(?[X]:((patient(X)&kind(X)))))&
(![X]:((humble(X)&~wise(X))=>(~rich(X)&~funny(X))))&
((?[X]:((~generous(X)<~>~strong(X))))=>((calm(alice)<~>old(alice))))&
((?[X]:(~calm(X)))<=>((funny(mary)<~>tall(mary))))&
(![X]:((~generous(X)<~>~creative(X))<=>(~humble(X)|creative(X))))&
(![X]:((~quiet(X)<~>~happy(X))<=>(~funny(X)<~>~generous(X))))&
(((~kind(alice)|~tall(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:((~kind(X)&calm(X))))=>(?[X]:((~curious(X)|~strong(X)))))&
((?[X]:(~quiet(X)))=>(~strong(susan)))&
(?[X]:((kind(X)|~creative(X))))&
((calm(paul)|wise(paul)))&
((~strong(lucy)|~happy(lucy)))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((~creative(X)&~rich(X))))&
(?[X]:((~quiet(X)|~humble(X)))) | ~patient(mary) | [
"p1",
"p2",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8798608411805906531552497
% SZS output start Proof for 8798608411805906531552497
2. ! [X0] : ((~happy(X0) | kind(X0)) <=> (~curious(X0) | patient(X0))) [input p1]
3. ? [X0] : happy(X0) <=> ? [X0] : (~happy(X0) <~> curious(X0)) [input p2]
4. ! [X0] : ((generous(X0) | ~old(X0)) <=> (~wise(X0) & ~happy(X0))) [input p3]
6. ! [X0] : ((~happy(X0) <~> generous(X0)) <=> (~happy(X0) <~> old(X0))) [input p5]
23. ~patient(mary) [input hypothesis]
24. ? [X0] : happy(X0) <=> ? [X1] : (~happy(X1) <~> curious(X1)) [rectify 3]
38. ! [X0] : (((~happy(X0) | kind(X0)) | (curious(X0) & ~patient(X0))) & ((~curious(X0) | patient(X0)) | (happy(X0) & ~kind(X0)))) [nnf transformation 2]
39. ! [X0] : ((~happy(X0) | kind(X0) | (curious(X0) & ~patient(X0))) & (~curious(X0) | patient(X0) | (happy(X0) & ~kind(X0)))) [flattening 38]
40. (? [X0] : happy(X0) | ! [X1] : ((~happy(X1) | ~curious(X1)) & (curious(X1) | happy(X1)))) & (? [X1] : ((~curious(X1) | happy(X1)) & (curious(X1) | ~happy(X1))) | ! [X0] : ~happy(X0)) [nnf transformation 24]
41. (? [X0] : happy(X0) | ! [X1] : ((~happy(X1) | ~curious(X1)) & (curious(X1) | happy(X1)))) & (? [X2] : ((~curious(X2) | happy(X2)) & (curious(X2) | ~happy(X2))) | ! [X3] : ~happy(X3)) [rectify 40]
42. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
43. ? [X2] : ((~curious(X2) | happy(X2)) & (curious(X2) | ~happy(X2))) => ((~curious(sK2) | happy(sK2)) & (curious(sK2) | ~happy(sK2))) [choice axiom]
44. (happy(sK1) | ! [X1] : ((~happy(X1) | ~curious(X1)) & (curious(X1) | happy(X1)))) & (((~curious(sK2) | happy(sK2)) & (curious(sK2) | ~happy(sK2))) | ! [X3] : ~happy(X3)) [skolemisation 41,43,42]
45. ! [X0] : (((generous(X0) | ~old(X0)) | (wise(X0) | happy(X0))) & ((~wise(X0) & ~happy(X0)) | (~generous(X0) & old(X0)))) [nnf transformation 4]
46. ! [X0] : ((generous(X0) | ~old(X0) | wise(X0) | happy(X0)) & ((~wise(X0) & ~happy(X0)) | (~generous(X0) & old(X0)))) [flattening 45]
49. ! [X0] : ((((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((~happy(X0) | ~old(X0)) & (old(X0) | happy(X0)))) & (((~old(X0) | happy(X0)) & (old(X0) | ~happy(X0))) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0))))) [nnf transformation 6]
88. ~curious(X0) | patient(X0) | happy(X0) [cnf transformation 39]
93. happy(sK1) | curious(X1) | happy(X1) [cnf transformation 44]
95. ~happy(X0) | old(X0) [cnf transformation 46]
96. ~generous(X0) | ~happy(X0) [cnf transformation 46]
106. generous(X0) | ~happy(X0) | ~happy(X0) | ~old(X0) [cnf transformation 49]
150. ~patient(mary) [cnf transformation 23]
155. generous(X0) | ~happy(X0) | ~old(X0) [duplicate literal removal 106]
191. 8 <=> happy(sK1) [avatar definition]
193. happy(sK1) <- (8) [avatar component clause 191]
196. 9 <=> ! [X1] : (curious(X1) | happy(X1)) [avatar definition]
197. curious(X1) | happy(X1) <- (9) [avatar component clause 196]
198. 9 | 8 [avatar split clause 93,191,196]
200. 10 <=> ! [X3] : ~happy(X3) [avatar definition]
201. ~happy(X3) <- (10) [avatar component clause 200]
226. ~happy(X0) | ~old(X0) [subsumption resolution 155,96]
227. ~happy(X0) [subsumption resolution 226,95]
228. 10 [avatar split clause 227,200]
282. 26 <=> ! [X0] : patient(X0) [avatar definition]
283. patient(X0) <- (26) [avatar component clause 282]
364. $false <- (8, 10) [subsumption resolution 193,201]
365. ~8 | ~10 [avatar contradiction clause 364]
368. curious(X1) <- (9, 10) [subsumption resolution 197,201]
379. patient(X0) | happy(X0) <- (9, 10) [resolution 88,368]
380. patient(X0) <- (9, 10) [subsumption resolution 379,201]
381. 26 | ~9 | ~10 [avatar split clause 380,200,196,282]
382. $false <- (26) [resolution 283,150]
387. ~26 [avatar contradiction clause 382]
388. $false [avatar sat refutation 198,228,365,381,387]
% SZS output end Proof for 8798608411805906531552497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not happy or not strong then fred is either not funny or tall and vice versa.
Everyone who is tall or not quiet is both not calm and not funny and vice versa.
If john is curious or not wise then mary is either calm or happy.
Everyone who is either curious or creative is not funny or curious and vice versa.
If alice is not creative or not humble then someone is both happy and not old and vice versa.
If someone is either generous or not generous then someone is either calm or rich and vice versa.
Everyone who is both not creative and not wise is either curious or not tall.
Everyone who is both not curious and not generous is calm and vice versa.
Everyone who is curious or rich is either kind or brave.
Everyone who is both not kind and not generous is creative or rich and vice versa.
If someone is generous or not old then someone is not old and vice versa.
If john is not creative then lucy is either not generous or calm.
If mary is not strong or not wise then someone is either not creative or happy.
Everyone who is creative or old is either not creative or not calm.
If someone is either not creative or tall then paul is both creative and old.
Someone is not curious or quiet.
Someone is not kind.
Susan is either not generous or not wise.
Someone is funny or wise.
Susan is patient. | Susan is not calm. | entailment | (((~happy(lucy)<~>~strong(lucy)))<=>((~funny(fred)<~>tall(fred))))&
(![X]:((tall(X)|~quiet(X))<=>(~calm(X)&~funny(X))))&
(((curious(john)|~wise(john)))=>((calm(mary)<~>happy(mary))))&
(![X]:((curious(X)<~>creative(X))<=>(~funny(X)|curious(X))))&
(((~creative(alice)|~humble(alice)))<=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:((generous(X)<~>~generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~creative(X)&~wise(X))=>(curious(X)<~>~tall(X))))&
(![X]:((~curious(X)&~generous(X))<=>calm(X)))&
(![X]:((curious(X)|rich(X))=>(kind(X)<~>brave(X))))&
(![X]:((~kind(X)&~generous(X))<=>(creative(X)|rich(X))))&
((?[X]:((generous(X)|~old(X))))<=>(?[X]:(~old(X))))&
((~creative(john))=>((~generous(lucy)<~>calm(lucy))))&
(((~strong(mary)|~wise(mary)))=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:((creative(X)|old(X))=>(~creative(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>tall(X))))=>((creative(paul)&old(paul))))&
(?[X]:((~curious(X)|quiet(X))))&
(?[X]:(~kind(X)))&
((~generous(susan)<~>~wise(susan)))&
(?[X]:((funny(X)|wise(X))))&
(patient(susan)) | ~calm(susan) | [
"p1",
"p3",
"p7",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1816360636119735441802219
% SZS output start Proof for 1816360636119735441802219
2. ! [X0] : ((~quiet(X0) | tall(X0)) <=> (~funny(X0) & ~calm(X0))) [input p1]
4. ! [X0] : ((curious(X0) <~> creative(X0)) <=> (curious(X0) | ~funny(X0))) [input p3]
8. ! [X0] : ((~generous(X0) & ~curious(X0)) <=> calm(X0)) [input p7]
10. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> (rich(X0) | creative(X0))) [input p9]
14. ! [X0] : ((old(X0) | creative(X0)) => (~creative(X0) <~> ~calm(X0))) [input p13]
15. ? [X0] : (~creative(X0) <~> tall(X0)) => (old(paul) & creative(paul)) [input p14]
21. calm(susan) [input hypothesis]
31. ! [X0] : ((~creative(X0) <~> ~calm(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 14]
32. (old(paul) & creative(paul)) | ! [X0] : (~creative(X0) <=> tall(X0)) [ennf transformation 15]
34. ! [X0] : (((~quiet(X0) | tall(X0)) | (funny(X0) | calm(X0))) & ((~funny(X0) & ~calm(X0)) | (quiet(X0) & ~tall(X0)))) [nnf transformation 2]
35. ! [X0] : ((~quiet(X0) | tall(X0) | funny(X0) | calm(X0)) & ((~funny(X0) & ~calm(X0)) | (quiet(X0) & ~tall(X0)))) [flattening 34]
37. ! [X0] : ((((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~curious(X0) & funny(X0))) & ((curious(X0) | ~funny(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))))) [nnf transformation 4]
38. ! [X0] : ((((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~curious(X0) & funny(X0))) & (curious(X0) | ~funny(X0) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))))) [flattening 37]
50. ! [X0] : (((~generous(X0) & ~curious(X0)) | ~calm(X0)) & (calm(X0) | (generous(X0) | curious(X0)))) [nnf transformation 8]
51. ! [X0] : (((~generous(X0) & ~curious(X0)) | ~calm(X0)) & (calm(X0) | generous(X0) | curious(X0))) [flattening 50]
53. ! [X0] : (((~generous(X0) & ~kind(X0)) | (~rich(X0) & ~creative(X0))) & ((rich(X0) | creative(X0)) | (generous(X0) | kind(X0)))) [nnf transformation 10]
54. ! [X0] : (((~generous(X0) & ~kind(X0)) | (~rich(X0) & ~creative(X0))) & (rich(X0) | creative(X0) | generous(X0) | kind(X0))) [flattening 53]
64. ! [X0] : (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (~old(X0) & ~creative(X0))) [nnf transformation 31]
65. (old(paul) & creative(paul)) | ! [X0] : ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))) [nnf transformation 32]
81. ~calm(X0) | ~tall(X0) [cnf transformation 35]
95. ~creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 38]
111. generous(X0) | calm(X0) | curious(X0) [cnf transformation 51]
121. ~generous(X0) | ~creative(X0) [cnf transformation 54]
132. ~calm(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 64]
136. creative(paul) | tall(X0) | creative(X0) [cnf transformation 65]
145. calm(susan) [cnf transformation 21]
146. ~creative(X0) | ~calm(X0) [duplicate literal removal 132]
152. ~creative(X0) | ~curious(X0) [duplicate literal removal 95]
304. 31 <=> ! [X0] : (tall(X0) | creative(X0)) [avatar definition]
305. creative(X0) | tall(X0) <- (31) [avatar component clause 304]
308. 32 <=> creative(paul) [avatar definition]
310. creative(paul) <- (32) [avatar component clause 308]
312. 31 | 32 [avatar split clause 136,308,304]
341. ~tall(susan) [resolution 81,145]
396. calm(X0) | curious(X0) | ~creative(X0) [resolution 111,121]
400. curious(X0) | ~creative(X0) [subsumption resolution 396,146]
401. ~creative(X0) [subsumption resolution 400,152]
440. $false <- (32) [resolution 401,310]
443. ~32 [avatar contradiction clause 440]
446. tall(X0) <- (31) [subsumption resolution 305,401]
454. $false <- (31) [resolution 446,341]
457. ~31 [avatar contradiction clause 454]
460. $false [avatar sat refutation 312,443,457]
% SZS output end Proof for 1816360636119735441802219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not brave is either curious or not old and vice versa.
Everyone who is creative is humble.
If fred is kind or rich then someone is not generous.
If mary is either patient or brave then mary is both not creative and strong.
Everyone who is either rich or not quiet is either strong or not creative and vice versa.
Everyone who is not tall is both not brave and rich.
Everyone who is either tall or curious is not happy.
Everyone who is quiet or brave is either not rich or not strong and vice versa.
Everyone who is not wise is both not strong and not old and vice versa.
Everyone who is happy or quiet is not creative or tall and vice versa.
If someone is either generous or brave then john is both quiet and old.
Everyone who is tall is both generous and not generous and vice versa.
If john is either not generous or old then paul is happy and vice versa.
If someone is both creative and not humble then someone is both tall and creative and vice versa.
Everyone who is not creative or kind is funny or not generous and vice versa.
Everyone who is either not humble or not calm is either not happy or not old and vice versa.
Someone is not tall.
Fred is quiet or rich.
Someone is both not patient and not generous.
Someone is either old or not funny.
Someone is both rich and not happy. | Mary is not funny. | neutral | (![X]:((~tall(X)&~brave(X))<=>(curious(X)<~>~old(X))))&
(![X]:(creative(X)=>humble(X)))&
(((kind(fred)|rich(fred)))=>(?[X]:(~generous(X))))&
(((patient(mary)<~>brave(mary)))=>((~creative(mary)&strong(mary))))&
(![X]:((rich(X)<~>~quiet(X))<=>(strong(X)<~>~creative(X))))&
(![X]:(~tall(X)=>(~brave(X)&rich(X))))&
(![X]:((tall(X)<~>curious(X))=>~happy(X)))&
(![X]:((quiet(X)|brave(X))<=>(~rich(X)<~>~strong(X))))&
(![X]:(~wise(X)<=>(~strong(X)&~old(X))))&
(![X]:((happy(X)|quiet(X))<=>(~creative(X)|tall(X))))&
((?[X]:((generous(X)<~>brave(X))))=>((quiet(john)&old(john))))&
(![X]:(tall(X)<=>(generous(X)&~generous(X))))&
(((~generous(john)<~>old(john)))<=>(happy(paul)))&
((?[X]:((creative(X)&~humble(X))))<=>(?[X]:((tall(X)&creative(X)))))&
(![X]:((~creative(X)|kind(X))<=>(funny(X)|~generous(X))))&
(![X]:((~humble(X)<~>~calm(X))<=>(~happy(X)<~>~old(X))))&
(?[X]:(~tall(X)))&
((quiet(fred)|rich(fred)))&
(?[X]:((~patient(X)&~generous(X))))&
(?[X]:((old(X)<~>~funny(X))))&
(?[X]:((rich(X)&~happy(X)))) | ~funny(mary) | [] | null | 0 |
Everyone who is either wise or curious is either not brave or tall and vice versa.
If john is both quiet and not quiet then paul is not funny and vice versa.
If susan is either happy or rich then susan is humble.
If someone is humble or generous then someone is both brave and not generous and vice versa.
If someone is both patient and curious then paul is curious or funny and vice versa.
If someone is either not humble or wise then someone is not rich or not curious and vice versa.
If mary is not brave then someone is not kind.
Everyone who is happy is not curious.
Everyone who is not humble is kind or not tall and vice versa.
Everyone who is patient is not brave or not quiet.
Everyone who is not calm or not brave is not tall or strong and vice versa.
Everyone who is both not strong and funny is either wise or not creative and vice versa.
Everyone who is either not quiet or quiet is either rich or not curious and vice versa.
If someone is either humble or not tall then someone is not tall or happy.
Everyone who is both not creative and not old is both curious and happy and vice versa.
If mary is either not curious or not happy then someone is funny and vice versa.
Someone is both quiet and brave.
Someone is not patient or not humble.
Someone is both patient and kind.
Someone is both not curious and not kind.
Someone is either not strong or not humble.
Someone is not happy or tall.
Someone is either funny or not tall.
John is either rich or calm. | Mary is happy. | neutral | (![X]:((wise(X)<~>curious(X))<=>(~brave(X)<~>tall(X))))&
(((quiet(john)&~quiet(john)))<=>(~funny(paul)))&
(((happy(susan)<~>rich(susan)))=>(humble(susan)))&
((?[X]:((humble(X)|generous(X))))<=>(?[X]:((brave(X)&~generous(X)))))&
((?[X]:((patient(X)&curious(X))))<=>((curious(paul)|funny(paul))))&
((?[X]:((~humble(X)<~>wise(X))))<=>(?[X]:((~rich(X)|~curious(X)))))&
((~brave(mary))=>(?[X]:(~kind(X))))&
(![X]:(happy(X)=>~curious(X)))&
(![X]:(~humble(X)<=>(kind(X)|~tall(X))))&
(![X]:(patient(X)=>(~brave(X)|~quiet(X))))&
(![X]:((~calm(X)|~brave(X))<=>(~tall(X)|strong(X))))&
(![X]:((~strong(X)&funny(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(rich(X)<~>~curious(X))))&
((?[X]:((humble(X)<~>~tall(X))))=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:((~creative(X)&~old(X))<=>(curious(X)&happy(X))))&
(((~curious(mary)<~>~happy(mary)))<=>(?[X]:(funny(X))))&
(?[X]:((quiet(X)&brave(X))))&
(?[X]:((~patient(X)|~humble(X))))&
(?[X]:((patient(X)&kind(X))))&
(?[X]:((~curious(X)&~kind(X))))&
(?[X]:((~strong(X)<~>~humble(X))))&
(?[X]:((~happy(X)|tall(X))))&
(?[X]:((funny(X)<~>~tall(X))))&
((rich(john)<~>calm(john))) | happy(mary) | [] | null | 0 |
Everyone who is both not kind and rich is not funny and vice versa.
If someone is both brave and not patient then alice is both not humble and creative and vice versa.
Everyone who is curious is not tall or happy and vice versa.
If someone is generous then someone is rich or funny and vice versa.
Everyone who is not humble is both not calm and not strong.
Everyone who is rich is kind or not rich and vice versa.
Everyone who is generous is both not old and curious and vice versa.
Everyone who is not quiet or not curious is either not strong or rich.
If someone is not tall then susan is not quiet or strong and vice versa.
If someone is not funny then someone is either generous or happy.
If someone is happy then lucy is not old or rich and vice versa.
Everyone who is quiet or not brave is both not quiet and wise and vice versa.
Everyone who is both not kind and not generous is not quiet or wise.
Everyone who is both not kind and brave is generous.
Everyone who is either not patient or not wise is both rich and generous.
Mary is not creative.
Lucy is not calm.
Mary is calm or humble.
Someone is either humble or happy.
Paul is strong or rich.
John is not humble or not patient.
Alice is both not happy and not creative. | Mary is strong. | entailment | (![X]:((~kind(X)&rich(X))<=>~funny(X)))&
((?[X]:((brave(X)&~patient(X))))<=>((~humble(alice)&creative(alice))))&
(![X]:(curious(X)<=>(~tall(X)|happy(X))))&
((?[X]:(generous(X)))<=>(?[X]:((rich(X)|funny(X)))))&
(![X]:(~humble(X)=>(~calm(X)&~strong(X))))&
(![X]:(rich(X)<=>(kind(X)|~rich(X))))&
(![X]:(generous(X)<=>(~old(X)&curious(X))))&
(![X]:((~quiet(X)|~curious(X))=>(~strong(X)<~>rich(X))))&
((?[X]:(~tall(X)))<=>((~quiet(susan)|strong(susan))))&
((?[X]:(~funny(X)))=>(?[X]:((generous(X)<~>happy(X)))))&
((?[X]:(happy(X)))<=>((~old(lucy)|rich(lucy))))&
(![X]:((quiet(X)|~brave(X))<=>(~quiet(X)&wise(X))))&
(![X]:((~kind(X)&~generous(X))=>(~quiet(X)|wise(X))))&
(![X]:((~kind(X)&brave(X))=>generous(X)))&
(![X]:((~patient(X)<~>~wise(X))=>(rich(X)&generous(X))))&
(~creative(mary))&
(~calm(lucy))&
((calm(mary)|humble(mary)))&
(?[X]:((humble(X)<~>happy(X))))&
((strong(paul)|rich(paul)))&
((~humble(john)|~patient(john)))&
((~happy(alice)&~creative(alice))) | strong(mary) | [
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7709909424592134638850516
% SZS output start Proof for 7709909424592134638850516
6. ! [X0] : (rich(X0) <=> (~rich(X0) | kind(X0))) [input p5]
8. ! [X0] : ((~curious(X0) | ~quiet(X0)) => (~strong(X0) <~> rich(X0))) [input p7]
12. ! [X0] : ((~brave(X0) | quiet(X0)) <=> (wise(X0) & ~quiet(X0))) [input p11]
23. ~strong(mary) [input hypothesis]
27. ! [X0] : ((~strong(X0) <~> rich(X0)) | (curious(X0) & quiet(X0))) [ennf transformation 8]
48. ! [X0] : ((rich(X0) | (rich(X0) & ~kind(X0))) & ((~rich(X0) | kind(X0)) | ~rich(X0))) [nnf transformation 6]
49. ! [X0] : ((rich(X0) | (rich(X0) & ~kind(X0))) & (~rich(X0) | kind(X0) | ~rich(X0))) [flattening 48]
52. ! [X0] : (((~rich(X0) | strong(X0)) & (rich(X0) | ~strong(X0))) | (curious(X0) & quiet(X0))) [nnf transformation 27]
67. ! [X0] : (((~brave(X0) | quiet(X0)) | (~wise(X0) | quiet(X0))) & ((wise(X0) & ~quiet(X0)) | (brave(X0) & ~quiet(X0)))) [nnf transformation 12]
68. ! [X0] : ((~brave(X0) | quiet(X0) | ~wise(X0) | quiet(X0)) & ((wise(X0) & ~quiet(X0)) | (brave(X0) & ~quiet(X0)))) [flattening 67]
90. rich(X0) | rich(X0) [cnf transformation 49]
96. ~rich(X0) | strong(X0) | quiet(X0) [cnf transformation 52]
106. ~quiet(X0) | ~quiet(X0) [cnf transformation 68]
126. ~strong(mary) [cnf transformation 23]
127. ~quiet(X0) [duplicate literal removal 106]
130. rich(X0) [duplicate literal removal 90]
168. quiet(X0) | strong(X0) [subsumption resolution 96,130]
232. strong(X2) [resolution 168,127]
233. $false [resolution 232,126]
% SZS output end Proof for 7709909424592134638850516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then alice is both creative and tall and vice versa. Everyone who is both not patient and funny is either brave or funny. Everyone who is either tall or not generous is not calm or not happy. Everyone who is either not humble or strong is rich. Everyone who is quiet or not patient is creative. If john is not patient then someone is both wise and not kind and vice versa. If fred is not humble then someone is curious. If alice is not patient then fred is either not strong or not quiet and vice versa. Everyone who is strong or not rich is both creative and not patient. Everyone who is both not happy and quiet is either not old or not happy and vice versa. Everyone who is both funny and not creative is not quiet or not wise and vice versa. If someone is quiet or not wise then someone is both not old and not rich and vice versa. Everyone who is either strong or old is not kind or humble. Everyone who is quiet is old or not funny and vice versa. If someone is either not curious or kind then paul is both not calm and not creative and vice versa. Mary is not calm or not funny. Fred is either not old or humble. Someone is not happy. Someone is not creative or not patient. Fred is patient. | Paul is rich. | entailment | ((?[X]:(calm(X)))<=>((creative(alice)&tall(alice))))&
(![X]:((~patient(X)&funny(X))=>(brave(X)<~>funny(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~calm(X)|~happy(X))))&
(![X]:((~humble(X)<~>strong(X))=>rich(X)))&
(![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fred))=>(?[X]:(curious(X))))&
((~patient(alice))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:((strong(X)|~rich(X))=>(creative(X)&~patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~old(X)<~>~happy(X))))&
(![X]:((funny(X)&~creative(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|humble(X))))&
(![X]:(quiet(X)<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>kind(X))))<=>((~calm(paul)&~creative(paul))))&
((~calm(mary)|~funny(mary)))&
((~old(fred)<~>humble(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((~creative(X)|~patient(X))))&
(patient(fred)) | rich(paul) | [
"p8",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 695214193691630216182883
% SZS output start Proof for 695214193691630216182883
9. ! [X0] : ((~rich(X0) | strong(X0)) => (~patient(X0) & creative(X0))) [input p8]
10. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p9]
11. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p10]
12. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X0] : (~rich(X0) & ~old(X0)) [input p11]
21. ~rich(paul) [input hypothesis]
22. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X1] : (~rich(X1) & ~old(X1)) [rectify 12]
30. ! [X0] : ((~patient(X0) & creative(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 9]
48. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 10]
49. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ~quiet(X0) | happy(X0))) [flattening 48]
50. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 11]
51. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | creative(X0) | ~funny(X0))) [flattening 50]
52. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X1] : (~rich(X1) & ~old(X1)) | ! [X0] : (wise(X0) & ~quiet(X0))) [nnf transformation 22]
53. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X2] : (~rich(X2) & ~old(X2)) | ! [X3] : (wise(X3) & ~quiet(X3))) [rectify 52]
54. ? [X0] : (~wise(X0) | quiet(X0)) => (~wise(sK3) | quiet(sK3)) [choice axiom]
55. ? [X2] : (~rich(X2) & ~old(X2)) => (~rich(sK4) & ~old(sK4)) [choice axiom]
56. ((~wise(sK3) | quiet(sK3)) | ! [X1] : (rich(X1) | old(X1))) & ((~rich(sK4) & ~old(sK4)) | ! [X3] : (wise(X3) & ~quiet(X3))) [skolemisation 53,55,54]
90. rich(X0) | creative(X0) [cnf transformation 30]
94. happy(X0) | old(X0) | ~quiet(X0) | happy(X0) [cnf transformation 49]
95. ~happy(X0) | ~happy(X0) | old(X0) [cnf transformation 49]
102. ~creative(X0) | quiet(X0) [cnf transformation 51]
104. ~old(sK4) | ~quiet(X3) [cnf transformation 56]
106. ~rich(sK4) | ~quiet(X3) [cnf transformation 56]
126. ~rich(paul) [cnf transformation 21]
127. happy(X0) | old(X0) | ~quiet(X0) [duplicate literal removal 94]
128. ~happy(X0) | old(X0) [duplicate literal removal 95]
191. ~quiet(X0) | old(X0) [subsumption resolution 127,128]
208. 18 <=> rich(sK4) [avatar definition]
210. ~rich(sK4) <- (~18) [avatar component clause 208]
213. 19 <=> ! [X3] : ~quiet(X3) [avatar definition]
214. ~quiet(X3) <- (19) [avatar component clause 213]
215. 19 | ~18 [avatar split clause 106,208,213]
217. 20 <=> old(sK4) [avatar definition]
219. ~old(sK4) <- (~20) [avatar component clause 217]
221. 19 | ~20 [avatar split clause 104,217,213]
227. 22 <=> creative(paul) [avatar definition]
229. creative(paul) <- (22) [avatar component clause 227]
278. creative(paul) [resolution 90,126]
279. creative(sK4) <- (~18) [resolution 90,210]
282. 22 [avatar split clause 278,227]
290. quiet(paul) <- (22) [resolution 102,229]
291. quiet(sK4) <- (~18) [resolution 102,279]
300. old(sK4) <- (~18) [resolution 191,291]
301. $false <- (~18, ~20) [subsumption resolution 300,219]
302. 18 | 20 [avatar contradiction clause 301]
307. $false <- (19, 22) [resolution 214,290]
308. ~19 | ~22 [avatar contradiction clause 307]
309. $false [avatar sat refutation 215,221,282,302,308]
% SZS output end Proof for 695214193691630216182883
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or old is strong or calm and vice versa.
Everyone who is not strong or curious is both not tall and not brave and vice versa.
Everyone who is both not tall and creative is either not patient or not funny and vice versa.
Everyone who is both funny and not creative is either not old or quiet and vice versa.
If mary is not rich or humble then someone is both not old and tall and vice versa.
If someone is kind then paul is creative.
Everyone who is happy is patient or calm.
Everyone who is both not creative and not generous is both not humble and not wise and vice versa.
Everyone who is either curious or happy is both generous and not funny.
Everyone who is old or funny is not creative or curious.
Everyone who is not funny or not kind is either tall or funny and vice versa.
If someone is not brave then lucy is either not rich or not old and vice versa.
Everyone who is not kind is not old.
If lucy is not humble then paul is either rich or not curious and vice versa.
If someone is not humble or generous then someone is either not rich or not wise.
Everyone who is both not rich and wise is happy.
Someone is both not humble and not patient.
Someone is not rich or not curious.
Someone is not tall.
Someone is either happy or not curious.
John is funny.
Lucy is both rich and wise.
Lucy is both humble and not funny. | John is strong. | entailment | (![X]:((~humble(X)<~>old(X))<=>(strong(X)|calm(X))))&
(![X]:((~strong(X)|curious(X))<=>(~tall(X)&~brave(X))))&
(![X]:((~tall(X)&creative(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((funny(X)&~creative(X))<=>(~old(X)<~>quiet(X))))&
(((~rich(mary)|humble(mary)))<=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(kind(X)))=>(creative(paul)))&
(![X]:(happy(X)=>(patient(X)|calm(X))))&
(![X]:((~creative(X)&~generous(X))<=>(~humble(X)&~wise(X))))&
(![X]:((curious(X)<~>happy(X))=>(generous(X)&~funny(X))))&
(![X]:((old(X)|funny(X))=>(~creative(X)|curious(X))))&
(![X]:((~funny(X)|~kind(X))<=>(tall(X)<~>funny(X))))&
((?[X]:(~brave(X)))<=>((~rich(lucy)<~>~old(lucy))))&
(![X]:(~kind(X)=>~old(X)))&
((~humble(lucy))<=>((rich(paul)<~>~curious(paul))))&
((?[X]:((~humble(X)|generous(X))))=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:((~rich(X)&wise(X))=>happy(X)))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((happy(X)<~>~curious(X))))&
(funny(john))&
((rich(lucy)&wise(lucy)))&
((humble(lucy)&~funny(lucy))) | strong(john) | [
"p0",
"p1",
"p10",
"p11",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1410723407089880965525011
% SZS output start Proof for 1410723407089880965525011
1. ! [X0] : ((~humble(X0) <~> old(X0)) <=> (calm(X0) | strong(X0))) [input p0]
2. ! [X0] : ((curious(X0) | ~strong(X0)) <=> (~brave(X0) & ~tall(X0))) [input p1]
11. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (tall(X0) <~> funny(X0))) [input p10]
12. ? [X0] : ~brave(X0) <=> (~rich(lucy) <~> ~old(lucy)) [input p11]
22. wise(lucy) & rich(lucy) [input p21]
23. ~funny(lucy) & humble(lucy) [input p22]
24. ~strong(john) [input hypothesis]
36. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [flattening 36]
38. ! [X0] : (((curious(X0) | ~strong(X0)) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | ~strong(X0) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [flattening 38]
52. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 11]
53. ! [X0] : ((~kind(X0) | ~funny(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [flattening 52]
54. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X0] : brave(X0)) [nnf transformation 12]
55. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [rectify 54]
56. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
57. (~brave(sK1) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [skolemisation 55,56]
74. ~strong(X0) | ~humble(X0) | old(X0) [cnf transformation 37]
78. ~tall(X0) | strong(X0) [cnf transformation 39]
80. ~brave(X0) | strong(X0) [cnf transformation 39]
112. funny(X0) | tall(X0) | funny(X0) [cnf transformation 53]
118. ~old(lucy) | ~rich(lucy) | brave(X1) [cnf transformation 57]
139. rich(lucy) [cnf transformation 22]
141. humble(lucy) [cnf transformation 23]
142. ~funny(lucy) [cnf transformation 23]
143. ~strong(john) [cnf transformation 24]
144. funny(X0) | tall(X0) [duplicate literal removal 112]
179. 8 <=> old(lucy) [avatar definition]
183. 9 <=> rich(lucy) [avatar definition]
193. 11 <=> ! [X1] : brave(X1) [avatar definition]
194. brave(X1) <- (11) [avatar component clause 193]
196. 11 | ~9 | ~8 [avatar split clause 118,179,183,193]
206. 14 <=> humble(lucy) [avatar definition]
207. humble(lucy) <- (14) [avatar component clause 206]
250. 9 [avatar split clause 139,183]
251. 14 [avatar split clause 141,206]
254. tall(lucy) [resolution 144,142]
258. strong(lucy) [resolution 254,78]
261. ~humble(lucy) | old(lucy) [resolution 258,74]
262. old(lucy) <- (14) [subsumption resolution 261,207]
265. 8 | ~14 [avatar split clause 262,206,179]
271. strong(X1) <- (11) [resolution 194,80]
286. $false <- (11) [resolution 271,143]
289. ~11 [avatar contradiction clause 286]
290. $false [avatar sat refutation 196,250,251,265,289]
% SZS output end Proof for 1410723407089880965525011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or brave is either not tall or old and vice versa. If someone is either curious or not creative then someone is not funny. Everyone who is not quiet is not curious or not funny. Everyone who is both creative and humble is either not kind or not tall. If someone is not curious or creative then susan is both not creative and not quiet and vice versa. If fred is both not strong and patient then alice is not calm or not strong. If lucy is humble or not old then mary is both quiet and not calm and vice versa. Everyone who is both not creative and old is quiet or not humble and vice versa. Everyone who is kind or not wise is both wise and not strong and vice versa. If someone is kind or not creative then someone is both not happy and strong and vice versa. Everyone who is not tall is not strong or calm. If someone is both patient and curious then john is patient. Everyone who is both not strong and not funny is either not funny or brave. Everyone who is not brave is either not old or humble. Everyone who is either old or funny is either creative or wise. If someone is not humble or not generous then someone is happy and vice versa. Paul is funny. Someone is not old or not strong. Someone is either not strong or not wise. Paul is not rich or not generous. Someone is not patient or not quiet. Someone is either not generous or not patient. Paul is creative. | Paul is old. | entailment | (![X]:((creative(X)|brave(X))<=>(~tall(X)<~>old(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>(?[X]:(~funny(X))))&
(![X]:(~quiet(X)=>(~curious(X)|~funny(X))))&
(![X]:((creative(X)&humble(X))=>(~kind(X)<~>~tall(X))))&
((?[X]:((~curious(X)|creative(X))))<=>((~creative(susan)&~quiet(susan))))&
(((~strong(fred)&patient(fred)))=>((~calm(alice)|~strong(alice))))&
(((humble(lucy)|~old(lucy)))<=>((quiet(mary)&~calm(mary))))&
(![X]:((~creative(X)&old(X))<=>(quiet(X)|~humble(X))))&
(![X]:((kind(X)|~wise(X))<=>(wise(X)&~strong(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:(~tall(X)=>(~strong(X)|calm(X))))&
((?[X]:((patient(X)&curious(X))))=>(patient(john)))&
(![X]:((~strong(X)&~funny(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~brave(X)=>(~old(X)<~>humble(X))))&
(![X]:((old(X)<~>funny(X))=>(creative(X)<~>wise(X))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:(happy(X))))&
(funny(paul))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~strong(X)<~>~wise(X))))&
((~rich(paul)|~generous(paul)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~generous(X)<~>~patient(X))))&
(creative(paul)) | old(paul) | [
"p8",
"p14",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7275548598858324023133463
% SZS output start Proof for 7275548598858324023133463
9. ! [X0] : ((~wise(X0) | kind(X0)) <=> (~strong(X0) & wise(X0))) [input p8]
15. ! [X0] : ((old(X0) <~> funny(X0)) => (creative(X0) <~> wise(X0))) [input p14]
17. funny(paul) [input p16]
23. creative(paul) [input p22]
24. ~old(paul) [input hypothesis]
42. ! [X0] : ((creative(X0) <~> wise(X0)) | (old(X0) <=> funny(X0))) [ennf transformation 15]
59. ! [X0] : (((~wise(X0) | kind(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (wise(X0) & ~kind(X0)))) [nnf transformation 9]
60. ! [X0] : ((~wise(X0) | kind(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (wise(X0) & ~kind(X0)))) [flattening 59]
68. ! [X0] : (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0)))) [nnf transformation 42]
112. wise(X0) | wise(X0) [cnf transformation 60]
130. ~wise(X0) | ~creative(X0) | old(X0) | ~funny(X0) [cnf transformation 68]
134. funny(paul) [cnf transformation 17]
141. creative(paul) [cnf transformation 23]
142. ~old(paul) [cnf transformation 24]
144. wise(X0) [duplicate literal removal 112]
263. ~funny(X0) | old(X0) | ~creative(X0) [subsumption resolution 130,144]
401. old(paul) | ~creative(paul) [resolution 263,134]
402. ~creative(paul) [subsumption resolution 401,142]
403. $false [subsumption resolution 402,141]
% SZS output end Proof for 7275548598858324023133463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and patient then someone is old. Everyone who is either humble or not happy is not wise or curious and vice versa. If someone is not humble then someone is either rich or kind and vice versa. If john is either funny or patient then someone is either kind or not rich and vice versa. Everyone who is not humble is both not calm and tall and vice versa. Everyone who is either not calm or not funny is not patient or not kind. Everyone who is either not kind or funny is curious or not tall and vice versa. If susan is not happy then alice is kind or brave and vice versa. If paul is either rich or quiet then john is not rich or not calm and vice versa. Everyone who is not tall is either wise or not happy and vice versa. Everyone who is either not quiet or not calm is both not strong and happy. Everyone who is either brave or quiet is wise or not brave and vice versa. If someone is either brave or not tall then john is quiet or calm and vice versa. If someone is not curious then lucy is not funny and vice versa. Everyone who is not brave is both strong and not tall. Everyone who is tall or happy is not generous or not wise and vice versa. Someone is both tall and not kind. Lucy is old. Mary is not brave or not creative. Mary is not tall. John is quiet. Lucy is both not calm and not quiet. Alice is curious or creative. | Paul is rich. | neutral | ((?[X]:((old(X)&patient(X))))=>(?[X]:(old(X))))&
(![X]:((humble(X)<~>~happy(X))<=>(~wise(X)|curious(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((rich(X)<~>kind(X)))))&
(((funny(john)<~>patient(john)))<=>(?[X]:((kind(X)<~>~rich(X)))))&
(![X]:(~humble(X)<=>(~calm(X)&tall(X))))&
(![X]:((~calm(X)<~>~funny(X))=>(~patient(X)|~kind(X))))&
(![X]:((~kind(X)<~>funny(X))<=>(curious(X)|~tall(X))))&
((~happy(susan))<=>((kind(alice)|brave(alice))))&
(((rich(paul)<~>quiet(paul)))<=>((~rich(john)|~calm(john))))&
(![X]:(~tall(X)<=>(wise(X)<~>~happy(X))))&
(![X]:((~quiet(X)<~>~calm(X))=>(~strong(X)&happy(X))))&
(![X]:((brave(X)<~>quiet(X))<=>(wise(X)|~brave(X))))&
((?[X]:((brave(X)<~>~tall(X))))<=>((quiet(john)|calm(john))))&
((?[X]:(~curious(X)))<=>(~funny(lucy)))&
(![X]:(~brave(X)=>(strong(X)&~tall(X))))&
(![X]:((tall(X)|happy(X))<=>(~generous(X)|~wise(X))))&
(?[X]:((tall(X)&~kind(X))))&
(old(lucy))&
((~brave(mary)|~creative(mary)))&
(~tall(mary))&
(quiet(john))&
((~calm(lucy)&~quiet(lucy)))&
((curious(alice)|creative(alice))) | rich(paul) | [] | null | 0 |
Everyone who is not quiet is funny.
Everyone who is creative or strong is strong or patient and vice versa.
Everyone who is both not kind and kind is either patient or creative.
Everyone who is not kind is not rich.
Everyone who is both happy and not old is not calm and vice versa.
Everyone who is happy is both not creative and brave and vice versa.
If john is either not kind or calm then someone is rich and vice versa.
Everyone who is creative or not calm is funny or brave and vice versa.
Everyone who is not happy is either not calm or not humble.
Everyone who is brave or quiet is not quiet or curious and vice versa.
If fred is not wise then someone is both humble and not brave.
If someone is not creative or strong then mary is either kind or tall.
Everyone who is calm is both curious and humble.
If someone is brave then paul is not patient and vice versa.
If someone is funny or not quiet then someone is kind or brave.
Everyone who is both not calm and not happy is not brave and vice versa.
Paul is either not humble or quiet.
Someone is either creative or not tall.
Susan is calm or humble.
Fred is not humble.
Fred is both quiet and not patient.
Fred is both not patient and funny.
Someone is either not quiet or not kind. | John is not rich. | entailment | (![X]:(~quiet(X)=>funny(X)))&
(![X]:((creative(X)|strong(X))<=>(strong(X)|patient(X))))&
(![X]:((~kind(X)&kind(X))=>(patient(X)<~>creative(X))))&
(![X]:(~kind(X)=>~rich(X)))&
(![X]:((happy(X)&~old(X))<=>~calm(X)))&
(![X]:(happy(X)<=>(~creative(X)&brave(X))))&
(((~kind(john)<~>calm(john)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~calm(X))<=>(funny(X)|brave(X))))&
(![X]:(~happy(X)=>(~calm(X)<~>~humble(X))))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|curious(X))))&
((~wise(fred))=>(?[X]:((humble(X)&~brave(X)))))&
((?[X]:((~creative(X)|strong(X))))=>((kind(mary)<~>tall(mary))))&
(![X]:(calm(X)=>(curious(X)&humble(X))))&
((?[X]:(brave(X)))<=>(~patient(paul)))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((~calm(X)&~happy(X))<=>~brave(X)))&
((~humble(paul)<~>quiet(paul)))&
(?[X]:((creative(X)<~>~tall(X))))&
((calm(susan)|humble(susan)))&
(~humble(fred))&
((quiet(fred)&~patient(fred)))&
((~patient(fred)&funny(fred)))&
(?[X]:((~quiet(X)<~>~kind(X)))) | ~rich(john) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8132942912006723036249421
% SZS output start Proof for 8132942912006723036249421
4. ! [X0] : (~kind(X0) => ~rich(X0)) [input p3]
5. ! [X0] : ((~old(X0) & happy(X0)) <=> ~calm(X0)) [input p4]
6. ! [X0] : (happy(X0) <=> (brave(X0) & ~creative(X0))) [input p5]
7. (~kind(john) <~> calm(john)) <=> ? [X0] : rich(X0) [input p6]
8. ! [X0] : ((~calm(X0) | creative(X0)) <=> (brave(X0) | funny(X0))) [input p7]
9. ! [X0] : (~happy(X0) => (~calm(X0) <~> ~humble(X0))) [input p8]
13. ! [X0] : (calm(X0) => (humble(X0) & curious(X0))) [input p12]
24. rich(john) [input hypothesis]
30. ! [X0] : (~rich(X0) | kind(X0)) [ennf transformation 4]
31. ! [X0] : ((~calm(X0) <~> ~humble(X0)) | happy(X0)) [ennf transformation 9]
33. ! [X0] : ((humble(X0) & curious(X0)) | ~calm(X0)) [ennf transformation 13]
38. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 5]
39. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | old(X0) | ~happy(X0))) [flattening 38]
40. ! [X0] : ((happy(X0) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | ~happy(X0))) [nnf transformation 6]
41. ! [X0] : ((happy(X0) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | ~happy(X0))) [flattening 40]
42. (((~calm(john) | kind(john)) & (calm(john) | ~kind(john))) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | ((~kind(john) | ~calm(john)) & (calm(john) | kind(john)))) [nnf transformation 7]
43. (((~calm(john) | kind(john)) & (calm(john) | ~kind(john))) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | ((~kind(john) | ~calm(john)) & (calm(john) | kind(john)))) [rectify 42]
44. ? [X1] : rich(X1) => rich(sK0) [choice axiom]
45. (((~calm(john) | kind(john)) & (calm(john) | ~kind(john))) | ! [X0] : ~rich(X0)) & (rich(sK0) | ((~kind(john) | ~calm(john)) & (calm(john) | kind(john)))) [skolemisation 43,44]
46. ! [X0] : (((~calm(X0) | creative(X0)) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 8]
47. ! [X0] : ((~calm(X0) | creative(X0) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | (calm(X0) & ~creative(X0)))) [flattening 46]
48. ! [X0] : (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | happy(X0)) [nnf transformation 31]
75. ~rich(X0) | kind(X0) [cnf transformation 30]
77. calm(X0) | happy(X0) [cnf transformation 39]
79. ~happy(X0) | ~creative(X0) [cnf transformation 41]
80. ~happy(X0) | brave(X0) [cnf transformation 41]
84. calm(john) | ~kind(john) | ~rich(X0) [cnf transformation 45]
89. ~brave(X0) | creative(X0) | ~calm(X0) [cnf transformation 47]
90. ~humble(X0) | ~calm(X0) | happy(X0) [cnf transformation 48]
101. ~calm(X0) | humble(X0) [cnf transformation 33]
121. rich(john) [cnf transformation 24]
125. 1 <=> ! [X0] : ~rich(X0) [avatar definition]
126. ~rich(X0) <- (1) [avatar component clause 125]
128. 2 <=> kind(john) [avatar definition]
132. 3 <=> calm(john) [avatar definition]
133. calm(john) <- (3) [avatar component clause 132]
136. 1 | ~2 | 3 [avatar split clause 84,132,128,125]
143. ~humble(X0) | happy(X0) [subsumption resolution 90,77]
222. kind(john) [resolution 75,121]
226. 2 [avatar split clause 222,128]
227. $false <- (1) [resolution 126,121]
230. ~1 [avatar contradiction clause 227]
234. humble(X0) | happy(X0) [resolution 101,77]
235. happy(X0) [subsumption resolution 234,143]
240. brave(X0) [resolution 235,80]
241. ~creative(X1) [resolution 235,79]
258. creative(X1) | ~calm(X1) [resolution 89,240]
262. ~calm(X1) [subsumption resolution 258,241]
270. $false <- (3) [resolution 262,133]
272. ~3 [avatar contradiction clause 270]
273. $false [avatar sat refutation 136,226,230,272]
% SZS output end Proof for 8132942912006723036249421
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is either not calm or wise then someone is not generous or curious. Everyone who is tall is both not wise and kind. Everyone who is curious is not old or humble. If someone is either not wise or strong then alice is both not kind and not calm and vice versa. Everyone who is happy or not kind is either not generous or calm. Everyone who is kind is both patient and not kind. Everyone who is not strong or brave is not kind or not happy and vice versa. If alice is generous or quiet then someone is brave. If susan is either not happy or not strong then fred is either not wise or not old. If alice is happy then lucy is patient or strong and vice versa. Everyone who is not strong or old is both not kind and quiet. If mary is both quiet and not generous then someone is old or not strong. Everyone who is old or not calm is happy. Everyone who is patient or not calm is not wise and vice versa. Everyone who is either kind or humble is not wise or brave. If john is curious then someone is not creative or funny and vice versa. Susan is both curious and quiet. Alice is not old or humble. Someone is either happy or not patient. Lucy is tall or patient. Lucy is both not quiet and brave. Fred is old or tall. Someone is either humble or not generous. | Mary is calm. | neutral | (((~calm(mary)<~>wise(mary)))=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:(tall(X)=>(~wise(X)&kind(X))))&
(![X]:(curious(X)=>(~old(X)|humble(X))))&
((?[X]:((~wise(X)<~>strong(X))))<=>((~kind(alice)&~calm(alice))))&
(![X]:((happy(X)|~kind(X))=>(~generous(X)<~>calm(X))))&
(![X]:(kind(X)=>(patient(X)&~kind(X))))&
(![X]:((~strong(X)|brave(X))<=>(~kind(X)|~happy(X))))&
(((generous(alice)|quiet(alice)))=>(?[X]:(brave(X))))&
(((~happy(susan)<~>~strong(susan)))=>((~wise(fred)<~>~old(fred))))&
((happy(alice))<=>((patient(lucy)|strong(lucy))))&
(![X]:((~strong(X)|old(X))=>(~kind(X)&quiet(X))))&
(((quiet(mary)&~generous(mary)))=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((old(X)|~calm(X))=>happy(X)))&
(![X]:((patient(X)|~calm(X))<=>~wise(X)))&
(![X]:((kind(X)<~>humble(X))=>(~wise(X)|brave(X))))&
((curious(john))<=>(?[X]:((~creative(X)|funny(X)))))&
((curious(susan)&quiet(susan)))&
((~old(alice)|humble(alice)))&
(?[X]:((happy(X)<~>~patient(X))))&
((tall(lucy)|patient(lucy)))&
((~quiet(lucy)&brave(lucy)))&
((old(fred)|tall(fred)))&
(?[X]:((humble(X)<~>~generous(X)))) | calm(mary) | [] | null | 0 |
Everyone who is not calm or patient is old.
Everyone who is old or not kind is both calm and generous and vice versa.
Everyone who is either not rich or wise is both not humble and curious and vice versa.
If someone is not creative or not calm then susan is either not old or not strong and vice versa.
Everyone who is old is either quiet or not strong.
Everyone who is not strong is either kind or not calm.
If someone is not curious then someone is either not brave or quiet and vice versa.
Everyone who is either curious or funny is both brave and curious.
Everyone who is both not rich and brave is not generous.
If john is both not happy and kind then someone is either not funny or brave.
Everyone who is both funny and not brave is wise or not calm.
If fred is humble then lucy is both wise and not patient.
Everyone who is either not old or calm is both not curious and patient and vice versa.
Everyone who is wise is either not kind or happy.
If lucy is not patient or old then alice is brave and vice versa.
If someone is not humble then someone is not curious or not old.
Someone is wise.
Someone is both calm and wise.
Mary is not strong or not kind.
Someone is either not humble or kind.
Someone is creative.
John is both old and wise.
Someone is not curious.
Paul is either not strong or not funny. | John is not rich. | entailment | (![X]:((~calm(X)|patient(X))=>old(X)))&
(![X]:((old(X)|~kind(X))<=>(calm(X)&generous(X))))&
(![X]:((~rich(X)<~>wise(X))<=>(~humble(X)&curious(X))))&
((?[X]:((~creative(X)|~calm(X))))<=>((~old(susan)<~>~strong(susan))))&
(![X]:(old(X)=>(quiet(X)<~>~strong(X))))&
(![X]:(~strong(X)=>(kind(X)<~>~calm(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:((curious(X)<~>funny(X))=>(brave(X)&curious(X))))&
(![X]:((~rich(X)&brave(X))=>~generous(X)))&
(((~happy(john)&kind(john)))=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:((funny(X)&~brave(X))=>(wise(X)|~calm(X))))&
((humble(fred))=>((wise(lucy)&~patient(lucy))))&
(![X]:((~old(X)<~>calm(X))<=>(~curious(X)&patient(X))))&
(![X]:(wise(X)=>(~kind(X)<~>happy(X))))&
(((~patient(lucy)|old(lucy)))<=>(brave(alice)))&
((?[X]:(~humble(X)))=>(?[X]:((~curious(X)|~old(X)))))&
(?[X]:(wise(X)))&
(?[X]:((calm(X)&wise(X))))&
((~strong(mary)|~kind(mary)))&
(?[X]:((~humble(X)<~>kind(X))))&
(?[X]:(creative(X)))&
((old(john)&wise(john)))&
(?[X]:(~curious(X)))&
((~strong(paul)<~>~funny(paul))) | ~rich(john) | [
"p0",
"p1",
"p2",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5324028920070587348305191
% SZS output start Proof for 5324028920070587348305191
1. ! [X0] : ((patient(X0) | ~calm(X0)) => old(X0)) [input p0]
2. ! [X0] : ((~kind(X0) | old(X0)) <=> (generous(X0) & calm(X0))) [input p1]
3. ! [X0] : ((~rich(X0) <~> wise(X0)) <=> (curious(X0) & ~humble(X0))) [input p2]
13. ! [X0] : ((~old(X0) <~> calm(X0)) <=> (patient(X0) & ~curious(X0))) [input p12]
22. wise(john) & old(john) [input p21]
25. rich(john) [input hypothesis]
28. ! [X0] : (old(X0) | (~patient(X0) & calm(X0))) [ennf transformation 1]
41. ! [X0] : (((~kind(X0) | old(X0)) | (~generous(X0) | ~calm(X0))) & ((generous(X0) & calm(X0)) | (kind(X0) & ~old(X0)))) [nnf transformation 2]
42. ! [X0] : ((~kind(X0) | old(X0) | ~generous(X0) | ~calm(X0)) & ((generous(X0) & calm(X0)) | (kind(X0) & ~old(X0)))) [flattening 41]
43. ! [X0] : ((((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0))))) [nnf transformation 3]
44. ! [X0] : ((((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0))))) [flattening 43]
60. ! [X0] : ((((~calm(X0) | old(X0)) & (calm(X0) | ~old(X0))) | (~patient(X0) | curious(X0))) & ((patient(X0) & ~curious(X0)) | ((~old(X0) | ~calm(X0)) & (calm(X0) | old(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~calm(X0) | old(X0)) & (calm(X0) | ~old(X0))) | ~patient(X0) | curious(X0)) & ((patient(X0) & ~curious(X0)) | ((~old(X0) | ~calm(X0)) & (calm(X0) | old(X0))))) [flattening 60]
80. old(X0) | calm(X0) [cnf transformation 28]
82. calm(X0) | ~old(X0) [cnf transformation 42]
90. ~wise(X0) | ~rich(X0) | curious(X0) [cnf transformation 44]
118. ~curious(X0) | ~old(X0) | ~calm(X0) [cnf transformation 61]
136. old(john) [cnf transformation 22]
137. wise(john) [cnf transformation 22]
141. rich(john) [cnf transformation 25]
144. calm(X0) [subsumption resolution 82,80]
226. ~curious(X0) | ~old(X0) [subsumption resolution 118,144]
308. ~rich(john) | curious(john) [resolution 90,137]
327. curious(john) [subsumption resolution 308,141]
386. ~old(john) [resolution 327,226]
396. $false [subsumption resolution 386,136]
% SZS output end Proof for 5324028920070587348305191
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not humble is not strong and vice versa.
If mary is both humble and not rich then someone is both creative and kind and vice versa.
Everyone who is either not old or not rich is either old or quiet.
Everyone who is humble or not strong is creative and vice versa.
Everyone who is not wise is not happy.
Everyone who is either calm or not funny is either not calm or wise.
If someone is either not curious or happy then someone is not funny and vice versa.
If alice is both not curious and strong then someone is both happy and old and vice versa.
If someone is either tall or not wise then someone is generous or curious and vice versa.
If someone is not generous or not patient then john is kind or not creative and vice versa.
Everyone who is both not old and creative is either humble or kind.
If fred is not happy or not generous then john is either not patient or not tall.
Everyone who is not humble or not patient is both not quiet and brave.
Everyone who is both strong and patient is either not curious or old.
If someone is both tall and not calm then someone is not generous or strong and vice versa.
Everyone who is funny or not calm is both funny and not quiet and vice versa.
Alice is either not funny or tall.
Someone is humble.
John is calm.
Mary is not kind.
Fred is either not old or not humble.
Someone is humble or not humble.
Paul is not tall. | John is creative. | entailment | (![X]:((~generous(X)|~humble(X))<=>~strong(X)))&
(((humble(mary)&~rich(mary)))<=>(?[X]:((creative(X)&kind(X)))))&
(![X]:((~old(X)<~>~rich(X))=>(old(X)<~>quiet(X))))&
(![X]:((humble(X)|~strong(X))<=>creative(X)))&
(![X]:(~wise(X)=>~happy(X)))&
(![X]:((calm(X)<~>~funny(X))=>(~calm(X)<~>wise(X))))&
((?[X]:((~curious(X)<~>happy(X))))<=>(?[X]:(~funny(X))))&
(((~curious(alice)&strong(alice)))<=>(?[X]:((happy(X)&old(X)))))&
((?[X]:((tall(X)<~>~wise(X))))<=>(?[X]:((generous(X)|curious(X)))))&
((?[X]:((~generous(X)|~patient(X))))<=>((kind(john)|~creative(john))))&
(![X]:((~old(X)&creative(X))=>(humble(X)<~>kind(X))))&
(((~happy(fred)|~generous(fred)))=>((~patient(john)<~>~tall(john))))&
(![X]:((~humble(X)|~patient(X))=>(~quiet(X)&brave(X))))&
(![X]:((strong(X)&patient(X))=>(~curious(X)<~>old(X))))&
((?[X]:((tall(X)&~calm(X))))<=>(?[X]:((~generous(X)|strong(X)))))&
(![X]:((funny(X)|~calm(X))<=>(funny(X)&~quiet(X))))&
((~funny(alice)<~>tall(alice)))&
(?[X]:(humble(X)))&
(calm(john))&
(~kind(mary))&
((~old(fred)<~>~humble(fred)))&
(?[X]:((humble(X)|~humble(X))))&
(~tall(paul)) | creative(john) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2765753613167844852171990
% SZS output start Proof for 2765753613167844852171990
1. ! [X0] : ((~humble(X0) | ~generous(X0)) <=> ~strong(X0)) [input p0]
4. ! [X0] : ((~strong(X0) | humble(X0)) <=> creative(X0)) [input p3]
24. ~creative(john) [input hypothesis]
38. ! [X0] : (((~humble(X0) | ~generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) & generous(X0)))) [nnf transformation 1]
39. ! [X0] : ((~humble(X0) | ~generous(X0) | strong(X0)) & (~strong(X0) | (humble(X0) & generous(X0)))) [flattening 38]
46. ! [X0] : (((~strong(X0) | humble(X0)) | ~creative(X0)) & (creative(X0) | (strong(X0) & ~humble(X0)))) [nnf transformation 4]
47. ! [X0] : ((~strong(X0) | humble(X0) | ~creative(X0)) & (creative(X0) | (strong(X0) & ~humble(X0)))) [flattening 46]
86. ~strong(X0) | humble(X0) [cnf transformation 39]
96. ~humble(X0) | creative(X0) [cnf transformation 47]
97. creative(X0) | strong(X0) [cnf transformation 47]
151. ~creative(john) [cnf transformation 24]
262. 25 <=> creative(john) [avatar definition]
263. ~creative(john) <- (~25) [avatar component clause 262]
355. ~25 [avatar split clause 151,262]
362. strong(john) <- (~25) [resolution 97,263]
365. humble(john) <- (~25) [resolution 362,86]
370. creative(john) <- (~25) [resolution 365,96]
371. $false <- (~25) [subsumption resolution 370,263]
372. 25 [avatar contradiction clause 371]
373. $false [avatar sat refutation 355,372]
% SZS output end Proof for 2765753613167844852171990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and kind is creative and vice versa. If mary is calm then someone is either not brave or not humble and vice versa. Everyone who is not humble or brave is either not funny or not brave. Everyone who is old or kind is funny and vice versa. Everyone who is both rich and not tall is not funny or kind and vice versa. Everyone who is both not old and rich is both not rich and not curious. If mary is both not calm and creative then susan is brave or curious and vice versa. Everyone who is either not tall or generous is not generous or creative. Everyone who is either not humble or funny is strong. Everyone who is either brave or generous is both brave and quiet. Everyone who is funny is either humble or tall. If mary is either not kind or not creative then john is both not creative and not generous and vice versa. If someone is both not funny and curious then lucy is both not creative and not happy and vice versa. Everyone who is not curious or brave is not patient or not generous. Mary is either patient or funny. Someone is old or strong. Alice is calm or not creative. Mary is both not curious and not quiet. | John is old. | entailment | (![X]:((~kind(X)&kind(X))<=>creative(X)))&
((calm(mary))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(![X]:((~humble(X)|brave(X))=>(~funny(X)<~>~brave(X))))&
(![X]:((old(X)|kind(X))<=>funny(X)))&
(![X]:((rich(X)&~tall(X))<=>(~funny(X)|kind(X))))&
(![X]:((~old(X)&rich(X))=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(![X]:((~curious(X)|brave(X))=>(~patient(X)|~generous(X))))&
((patient(mary)<~>funny(mary)))&
(?[X]:((old(X)|strong(X))))&
((calm(alice)|~creative(alice)))&
((~curious(mary)&~quiet(mary))) | old(john) | [
"p3",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4317651837170478189656993
% SZS output start Proof for 4317651837170478189656993
4. ! [X0] : ((kind(X0) | old(X0)) <=> funny(X0)) [input p3]
5. ! [X0] : ((~tall(X0) & rich(X0)) <=> (kind(X0) | ~funny(X0))) [input p4]
6. ! [X0] : ((rich(X0) & ~old(X0)) => (~curious(X0) & ~rich(X0))) [input p5]
19. ~old(john) [input hypothesis]
23. ! [X0] : ((~curious(X0) & ~rich(X0)) | (~rich(X0) | old(X0))) [ennf transformation 6]
24. ! [X0] : ((~curious(X0) & ~rich(X0)) | ~rich(X0) | old(X0)) [flattening 23]
38. ! [X0] : (((kind(X0) | old(X0)) | ~funny(X0)) & (funny(X0) | (~kind(X0) & ~old(X0)))) [nnf transformation 4]
39. ! [X0] : ((kind(X0) | old(X0) | ~funny(X0)) & (funny(X0) | (~kind(X0) & ~old(X0)))) [flattening 38]
40. ! [X0] : (((~tall(X0) & rich(X0)) | (~kind(X0) & funny(X0))) & ((kind(X0) | ~funny(X0)) | (tall(X0) | ~rich(X0)))) [nnf transformation 5]
41. ! [X0] : (((~tall(X0) & rich(X0)) | (~kind(X0) & funny(X0))) & (kind(X0) | ~funny(X0) | tall(X0) | ~rich(X0))) [flattening 40]
66. ~old(X0) | funny(X0) [cnf transformation 39]
68. ~funny(X0) | old(X0) | kind(X0) [cnf transformation 39]
70. rich(X0) | funny(X0) [cnf transformation 41]
71. ~kind(X0) | rich(X0) [cnf transformation 41]
74. ~rich(X0) | ~rich(X0) | old(X0) [cnf transformation 24]
106. ~old(john) [cnf transformation 19]
109. ~rich(X0) | old(X0) [duplicate literal removal 74]
183. old(X0) | funny(X0) [resolution 109,70]
184. funny(X0) [subsumption resolution 183,66]
200. old(X1) | kind(X1) [resolution 68,184]
203. kind(john) [resolution 200,106]
205. rich(john) [resolution 203,71]
207. old(john) [resolution 205,109]
208. $false [subsumption resolution 207,106]
% SZS output end Proof for 4317651837170478189656993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not kind then someone is not generous. Everyone who is either not strong or creative is either not wise or funny. Everyone who is either not rich or generous is happy or not old. Everyone who is both tall and not brave is generous and vice versa. If mary is both curious and old then someone is not brave or kind. If someone is not calm then someone is creative and vice versa. Everyone who is not funny or not humble is both creative and strong and vice versa. Everyone who is calm or patient is not strong or funny and vice versa. Everyone who is not patient is kind. Everyone who is either strong or not strong is either not funny or patient and vice versa. If someone is either not creative or not funny then someone is not brave or not happy and vice versa. If someone is both not tall and not patient then someone is not calm and vice versa. If mary is not kind or not creative then mary is not funny or strong and vice versa. If john is not wise or not calm then someone is either curious or not funny and vice versa. Everyone who is not generous is wise. If paul is both creative and patient then someone is either not wise or old. Someone is both not old and not happy. Lucy is tall. Someone is either wise or not wise. John is not tall or rich. Someone is both curious and not kind. Fred is not strong. Someone is either strong or not happy. | John is not rich. | contradiction | ((?[X]:((~old(X)|~kind(X))))=>(?[X]:(~generous(X))))&
(![X]:((~strong(X)<~>creative(X))=>(~wise(X)<~>funny(X))))&
(![X]:((~rich(X)<~>generous(X))=>(happy(X)|~old(X))))&
(![X]:((tall(X)&~brave(X))<=>generous(X)))&
(((curious(mary)&old(mary)))=>(?[X]:((~brave(X)|kind(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:(creative(X))))&
(![X]:((~funny(X)|~humble(X))<=>(creative(X)&strong(X))))&
(![X]:((calm(X)|patient(X))<=>(~strong(X)|funny(X))))&
(![X]:(~patient(X)=>kind(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:((~creative(X)<~>~funny(X))))<=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:(~calm(X))))&
(((~kind(mary)|~creative(mary)))<=>((~funny(mary)|strong(mary))))&
(((~wise(john)|~calm(john)))<=>(?[X]:((curious(X)<~>~funny(X)))))&
(![X]:(~generous(X)=>wise(X)))&
(((creative(paul)&patient(paul)))=>(?[X]:((~wise(X)<~>old(X)))))&
(?[X]:((~old(X)&~happy(X))))&
(tall(lucy))&
(?[X]:((wise(X)<~>~wise(X))))&
((~tall(john)|rich(john)))&
(?[X]:((curious(X)&~kind(X))))&
(~strong(fred))&
(?[X]:((strong(X)<~>~happy(X)))) | ~rich(john) | [
"p1",
"p3",
"p6",
"p7",
"p9",
"p11",
"p13",
"p14",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1372563572589390002291074
% SZS output start Proof for 1372563572589390002291074
2. ! [X0] : ((~strong(X0) <~> creative(X0)) => (~wise(X0) <~> funny(X0))) [input p1]
4. ! [X0] : ((~brave(X0) & tall(X0)) <=> generous(X0)) [input p3]
7. ! [X0] : ((~humble(X0) | ~funny(X0)) <=> (strong(X0) & creative(X0))) [input p6]
8. ! [X0] : ((patient(X0) | calm(X0)) <=> (funny(X0) | ~strong(X0))) [input p7]
10. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (~funny(X0) <~> patient(X0))) [input p9]
12. ? [X0] : (~patient(X0) & ~tall(X0)) <=> ? [X0] : ~calm(X0) [input p11]
14. (~calm(john) | ~wise(john)) <=> ? [X0] : (curious(X0) <~> ~funny(X0)) [input p13]
15. ! [X0] : (~generous(X0) => wise(X0)) [input p14]
20. rich(john) | ~tall(john) [input p19]
21. ? [X0] : (~kind(X0) & curious(X0)) [input p20]
24. ~rich(john) [input hypothesis]
28. ? [X0] : (~patient(X0) & ~tall(X0)) <=> ? [X1] : ~calm(X1) [rectify 12]
30. ! [X0] : ((~wise(X0) <~> funny(X0)) | (~strong(X0) <=> creative(X0))) [ennf transformation 2]
36. ! [X0] : (wise(X0) | generous(X0)) [ennf transformation 15]
42. ! [X0] : (((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0)))) [nnf transformation 30]
44. ! [X0] : (((~brave(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | (brave(X0) | ~tall(X0)))) [nnf transformation 4]
45. ! [X0] : (((~brave(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | brave(X0) | ~tall(X0))) [flattening 44]
53. ! [X0] : (((~humble(X0) | ~funny(X0)) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | (humble(X0) & funny(X0)))) [nnf transformation 7]
54. ! [X0] : ((~humble(X0) | ~funny(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | (humble(X0) & funny(X0)))) [flattening 53]
55. ! [X0] : (((patient(X0) | calm(X0)) | (~funny(X0) & strong(X0))) & ((funny(X0) | ~strong(X0)) | (~patient(X0) & ~calm(X0)))) [nnf transformation 8]
56. ! [X0] : ((patient(X0) | calm(X0) | (~funny(X0) & strong(X0))) & (funny(X0) | ~strong(X0) | (~patient(X0) & ~calm(X0)))) [flattening 55]
57. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 10]
63. (? [X0] : (~patient(X0) & ~tall(X0)) | ! [X1] : calm(X1)) & (? [X1] : ~calm(X1) | ! [X0] : (patient(X0) | tall(X0))) [nnf transformation 28]
64. (? [X0] : (~patient(X0) & ~tall(X0)) | ! [X1] : calm(X1)) & (? [X2] : ~calm(X2) | ! [X3] : (patient(X3) | tall(X3))) [rectify 63]
65. ? [X0] : (~patient(X0) & ~tall(X0)) => (~patient(sK6) & ~tall(sK6)) [choice axiom]
66. ? [X2] : ~calm(X2) => ~calm(sK7) [choice axiom]
67. ((~patient(sK6) & ~tall(sK6)) | ! [X1] : calm(X1)) & (~calm(sK7) | ! [X3] : (patient(X3) | tall(X3))) [skolemisation 64,66,65]
70. ((~calm(john) | ~wise(john)) | ! [X0] : ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (? [X0] : ((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (calm(john) & wise(john))) [nnf transformation 14]
71. (~calm(john) | ~wise(john) | ! [X0] : ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (? [X0] : ((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (calm(john) & wise(john))) [flattening 70]
72. (~calm(john) | ~wise(john) | ! [X0] : ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (? [X1] : ((funny(X1) | ~curious(X1)) & (~funny(X1) | curious(X1))) | (calm(john) & wise(john))) [rectify 71]
73. ? [X1] : ((funny(X1) | ~curious(X1)) & (~funny(X1) | curious(X1))) => ((funny(sK8) | ~curious(sK8)) & (~funny(sK8) | curious(sK8))) [choice axiom]
74. (~calm(john) | ~wise(john) | ! [X0] : ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(sK8) | ~curious(sK8)) & (~funny(sK8) | curious(sK8))) | (calm(john) & wise(john))) [skolemisation 72,73]
83. ? [X0] : (~kind(X0) & curious(X0)) => (~kind(sK12) & curious(sK12)) [choice axiom]
84. ~kind(sK12) & curious(sK12) [skolemisation 21,83]
91. ~wise(X0) | funny(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 42]
97. ~generous(X0) | tall(X0) [cnf transformation 45]
102. funny(X0) | creative(X0) [cnf transformation 54]
104. funny(X0) | strong(X0) [cnf transformation 54]
107. funny(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 56]
112. patient(X0) | ~funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 57]
113. patient(X0) | ~funny(X0) | strong(X0) | strong(X0) [cnf transformation 57]
127. ~tall(sK6) | calm(X1) [cnf transformation 67]
128. ~patient(sK6) | calm(X1) [cnf transformation 67]
137. ~calm(john) | ~wise(john) | ~funny(X0) | ~curious(X0) [cnf transformation 74]
139. wise(X0) | generous(X0) [cnf transformation 36]
147. rich(john) | ~tall(john) [cnf transformation 20]
148. curious(sK12) [cnf transformation 84]
153. ~rich(john) [cnf transformation 24]
154. patient(X0) | ~funny(X0) | ~strong(X0) [duplicate literal removal 112]
155. patient(X0) | ~funny(X0) | strong(X0) [duplicate literal removal 113]
196. 10 <=> ! [X3] : calm(X3) [avatar definition]
197. calm(X3) <- (10) [avatar component clause 196]
204. ~calm(X0) | funny(X0) [subsumption resolution 107,104]
205. patient(X0) | strong(X0) [subsumption resolution 155,104]
206. ~funny(X0) | patient(X0) [subsumption resolution 154,205]
225. 16 <=> ! [X3] : funny(X3) [avatar definition]
226. funny(X3) <- (16) [avatar component clause 225]
242. 20 <=> patient(sK6) [avatar definition]
244. ~patient(sK6) <- (~20) [avatar component clause 242]
245. 10 | ~20 [avatar split clause 128,242,196]
247. 21 <=> tall(sK6) [avatar definition]
250. 10 | ~21 [avatar split clause 127,247,196]
286. 29 <=> wise(john) [avatar definition]
288. ~wise(john) <- (~29) [avatar component clause 286]
290. 30 <=> calm(john) [avatar definition]
292. ~calm(john) <- (~30) [avatar component clause 290]
295. 31 <=> ! [X0] : (~funny(X0) | ~curious(X0)) [avatar definition]
296. ~curious(X0) | ~funny(X0) <- (31) [avatar component clause 295]
297. 31 | ~29 | ~30 [avatar split clause 137,290,286,295]
329. 38 <=> tall(john) [avatar definition]
331. ~tall(john) <- (~38) [avatar component clause 329]
333. 39 <=> rich(john) [avatar definition]
336. ~38 | 39 [avatar split clause 147,333,329]
347. ~39 [avatar split clause 153,333]
360. generous(john) <- (~29) [resolution 139,288]
361. tall(john) <- (~29) [resolution 360,97]
362. $false <- (~29, ~38) [subsumption resolution 361,331]
363. 29 | 38 [avatar contradiction clause 362]
392. funny(X0) | ~strong(X0) | ~creative(X0) | generous(X0) [resolution 91,139]
394. funny(X0) | ~creative(X0) | generous(X0) [subsumption resolution 392,104]
395. funny(X0) | generous(X0) [subsumption resolution 394,102]
417. patient(X3) | generous(X3) [resolution 395,206]
426. generous(sK6) <- (~20) [resolution 417,244]
431. tall(sK6) <- (~20) [resolution 426,97]
434. 21 | 20 [avatar split clause 431,242,247]
441. funny(X0) <- (10) [resolution 197,204]
442. 16 | ~10 [avatar split clause 441,196,225]
473. ~funny(sK12) <- (31) [resolution 296,148]
475. $false <- (16, 31) [subsumption resolution 473,226]
476. ~16 | ~31 [avatar contradiction clause 475]
477. $false <- (10, ~30) [subsumption resolution 292,197]
478. ~10 | 30 [avatar contradiction clause 477]
479. $false [avatar sat refutation 245,250,297,336,347,363,434,442,476,478]
% SZS output end Proof for 1372563572589390002291074
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or curious is not tall or not strong and vice versa.
If someone is either not wise or not old then john is kind.
If someone is both not calm and funny then alice is not old.
Everyone who is either creative or patient is not tall and vice versa.
Everyone who is not kind is either not creative or patient and vice versa.
Everyone who is wise is not generous or tall and vice versa.
If someone is not humble or not rich then someone is patient or old.
If someone is either quiet or not happy then someone is happy and vice versa.
Everyone who is both quiet and not kind is both not quiet and not humble and vice versa.
Everyone who is either not happy or strong is both strong and not wise.
If susan is either not quiet or calm then someone is both not rich and not calm and vice versa.
Everyone who is not calm is brave or not patient.
Everyone who is not funny is either not kind or not brave.
Everyone who is quiet or not kind is both quiet and tall and vice versa.
If john is not humble then someone is curious or patient and vice versa.
If someone is not tall then alice is either not calm or not brave.
Someone is not curious or calm.
Mary is both not old and not calm.
Someone is both not strong and not patient.
Someone is creative or not old.
Lucy is not old or not wise.
Paul is not tall or generous. | Alice is calm. | entailment | (![X]:((~brave(X)|curious(X))<=>(~tall(X)|~strong(X))))&
((?[X]:((~wise(X)<~>~old(X))))=>(kind(john)))&
((?[X]:((~calm(X)&funny(X))))=>(~old(alice)))&
(![X]:((creative(X)<~>patient(X))<=>~tall(X)))&
(![X]:(~kind(X)<=>(~creative(X)<~>patient(X))))&
(![X]:(wise(X)<=>(~generous(X)|tall(X))))&
((?[X]:((~humble(X)|~rich(X))))=>(?[X]:((patient(X)|old(X)))))&
((?[X]:((quiet(X)<~>~happy(X))))<=>(?[X]:(happy(X))))&
(![X]:((quiet(X)&~kind(X))<=>(~quiet(X)&~humble(X))))&
(![X]:((~happy(X)<~>strong(X))=>(strong(X)&~wise(X))))&
(((~quiet(susan)<~>calm(susan)))<=>(?[X]:((~rich(X)&~calm(X)))))&
(![X]:(~calm(X)=>(brave(X)|~patient(X))))&
(![X]:(~funny(X)=>(~kind(X)<~>~brave(X))))&
(![X]:((quiet(X)|~kind(X))<=>(quiet(X)&tall(X))))&
((~humble(john))<=>(?[X]:((curious(X)|patient(X)))))&
((?[X]:(~tall(X)))=>((~calm(alice)<~>~brave(alice))))&
(?[X]:((~curious(X)|calm(X))))&
((~old(mary)&~calm(mary)))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:((creative(X)|~old(X))))&
((~old(lucy)|~wise(lucy)))&
((~tall(paul)|generous(paul))) | calm(alice) | [
"p0",
"p3",
"p4",
"p8",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7842672913541728479409656
% SZS output start Proof for 7842672913541728479409656
1. ! [X0] : ((curious(X0) | ~brave(X0)) <=> (~strong(X0) | ~tall(X0))) [input p0]
4. ! [X0] : ((creative(X0) <~> patient(X0)) <=> ~tall(X0)) [input p3]
5. ! [X0] : (~kind(X0) <=> (~creative(X0) <~> patient(X0))) [input p4]
9. ! [X0] : ((~kind(X0) & quiet(X0)) <=> (~humble(X0) & ~quiet(X0))) [input p8]
14. ! [X0] : ((~kind(X0) | quiet(X0)) <=> (tall(X0) & quiet(X0))) [input p13]
15. ~humble(john) <=> ? [X0] : (patient(X0) | curious(X0)) [input p14]
16. ? [X0] : ~tall(X0) => (~calm(alice) <~> ~brave(alice)) [input p15]
23. ~calm(alice) [input hypothesis]
33. (~calm(alice) <~> ~brave(alice)) | ! [X0] : tall(X0) [ennf transformation 16]
34. ! [X0] : (((curious(X0) | ~brave(X0)) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | (~curious(X0) & brave(X0)))) [nnf transformation 1]
35. ! [X0] : ((curious(X0) | ~brave(X0) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | (~curious(X0) & brave(X0)))) [flattening 34]
37. ! [X0] : ((((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | tall(X0)) & (~tall(X0) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0))))) [nnf transformation 4]
38. ! [X0] : ((~kind(X0) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | kind(X0))) [nnf transformation 5]
49. ! [X0] : (((~kind(X0) & quiet(X0)) | (humble(X0) | quiet(X0))) & ((~humble(X0) & ~quiet(X0)) | (kind(X0) | ~quiet(X0)))) [nnf transformation 9]
50. ! [X0] : (((~kind(X0) & quiet(X0)) | humble(X0) | quiet(X0)) & ((~humble(X0) & ~quiet(X0)) | kind(X0) | ~quiet(X0))) [flattening 49]
57. ! [X0] : (((~kind(X0) | quiet(X0)) | (~tall(X0) | ~quiet(X0))) & ((tall(X0) & quiet(X0)) | (kind(X0) & ~quiet(X0)))) [nnf transformation 14]
58. ! [X0] : ((~kind(X0) | quiet(X0) | ~tall(X0) | ~quiet(X0)) & ((tall(X0) & quiet(X0)) | (kind(X0) & ~quiet(X0)))) [flattening 57]
59. (~humble(john) | ! [X0] : (~patient(X0) & ~curious(X0))) & (? [X0] : (patient(X0) | curious(X0)) | humble(john)) [nnf transformation 15]
60. (~humble(john) | ! [X0] : (~patient(X0) & ~curious(X0))) & (? [X1] : (patient(X1) | curious(X1)) | humble(john)) [rectify 59]
61. ? [X1] : (patient(X1) | curious(X1)) => (patient(sK4) | curious(sK4)) [choice axiom]
62. (~humble(john) | ! [X0] : (~patient(X0) & ~curious(X0))) & ((patient(sK4) | curious(sK4)) | humble(john)) [skolemisation 60,61]
63. ((brave(alice) | calm(alice)) & (~brave(alice) | ~calm(alice))) | ! [X0] : tall(X0) [nnf transformation 33]
72. ~brave(X0) | curious(X0) | tall(X0) [cnf transformation 35]
77. ~creative(X0) | patient(X0) | ~tall(X0) [cnf transformation 37]
78. ~patient(X0) | creative(X0) | ~tall(X0) [cnf transformation 37]
83. ~kind(X0) | patient(X0) | creative(X0) [cnf transformation 38]
84. ~patient(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 38]
94. ~quiet(X0) | kind(X0) | ~quiet(X0) [cnf transformation 50]
96. quiet(X0) | humble(X0) | quiet(X0) [cnf transformation 50]
112. quiet(X0) | kind(X0) [cnf transformation 58]
113. ~quiet(X0) | tall(X0) [cnf transformation 58]
117. ~humble(john) | ~curious(X0) [cnf transformation 62]
118. ~humble(john) | ~patient(X0) [cnf transformation 62]
120. brave(alice) | calm(alice) | tall(X0) [cnf transformation 63]
129. ~calm(alice) [cnf transformation 23]
131. ~quiet(X0) | kind(X0) [duplicate literal removal 94]
132. quiet(X0) | humble(X0) [duplicate literal removal 96]
219. kind(X0) [subsumption resolution 112,131]
221. 21 <=> ! [X0] : ~patient(X0) [avatar definition]
222. ~patient(X0) <- (21) [avatar component clause 221]
224. 22 <=> humble(john) [avatar definition]
226. ~humble(john) <- (~22) [avatar component clause 224]
227. 21 | ~22 [avatar split clause 118,224,221]
229. 23 <=> ! [X0] : ~curious(X0) [avatar definition]
230. ~curious(X0) <- (23) [avatar component clause 229]
231. 23 | ~22 [avatar split clause 117,224,229]
242. 26 <=> ! [X0] : tall(X0) [avatar definition]
243. tall(X0) <- (26) [avatar component clause 242]
245. 27 <=> calm(alice) [avatar definition]
249. 28 <=> brave(alice) [avatar definition]
251. brave(alice) <- (28) [avatar component clause 249]
252. 26 | 27 | 28 [avatar split clause 120,249,245,242]
290. ~27 [avatar split clause 129,245]
299. humble(X1) | tall(X1) [resolution 132,113]
311. curious(alice) | tall(alice) <- (28) [resolution 72,251]
312. tall(alice) <- (23, 28) [subsumption resolution 311,230]
339. patient(X1) | creative(X1) [resolution 83,219]
340. creative(X1) <- (21) [subsumption resolution 339,222]
343. patient(X1) | ~tall(X1) <- (21) [resolution 340,77]
344. ~tall(X1) <- (21) [subsumption resolution 343,222]
346. $false <- (21, 23, 28) [resolution 344,312]
349. ~21 | ~23 | ~28 [avatar contradiction clause 346]
367. tall(john) <- (~22) [resolution 226,299]
385. creative(X3) | creative(X3) | ~tall(X3) [resolution 339,78]
387. ~tall(X3) | creative(X3) [duplicate literal removal 385]
390. creative(X3) <- (26) [subsumption resolution 387,243]
394. patient(X1) | ~tall(X1) <- (26) [resolution 390,77]
395. patient(X1) <- (26) [subsumption resolution 394,243]
403. ~creative(X1) | ~kind(X1) <- (26) [resolution 395,84]
410. ~kind(X1) <- (26) [subsumption resolution 403,390]
411. $false <- (26) [subsumption resolution 410,219]
412. ~26 [avatar contradiction clause 411]
454. creative(john) <- (~22) [resolution 387,367]
467. patient(john) | ~tall(john) <- (~22) [resolution 454,77]
468. patient(john) <- (~22) [subsumption resolution 467,367]
546. ~creative(john) | ~kind(john) <- (~22) [resolution 468,84]
550. ~kind(john) <- (~22) [subsumption resolution 546,454]
551. $false <- (~22) [subsumption resolution 550,219]
552. 22 [avatar contradiction clause 551]
553. $false [avatar sat refutation 227,231,252,290,349,412,552]
% SZS output end Proof for 7842672913541728479409656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and rich is not old or not funny and vice versa. If lucy is not curious or not generous then alice is not creative. Everyone who is not old or not calm is both kind and not calm and vice versa. If paul is both not happy and curious then alice is either old or funny and vice versa. If lucy is either wise or not patient then susan is both not rich and not tall and vice versa. Everyone who is humble or not tall is both calm and wise and vice versa. If mary is creative or not happy then someone is both quiet and kind. If someone is both kind and curious then someone is either not humble or not old and vice versa. If alice is both funny and quiet then lucy is patient or not happy and vice versa. If someone is not kind then john is both not creative and not curious and vice versa. Everyone who is either not creative or generous is both not calm and not tall. If mary is generous then someone is either not quiet or quiet and vice versa. Everyone who is both generous and humble is not brave or not kind and vice versa. Everyone who is not old or not happy is generous and vice versa. If someone is either brave or not rich then susan is either not creative or not generous and vice versa. Everyone who is not tall is either not generous or strong. Susan is both not strong and not wise. Someone is humble. John is not creative. Susan is both not creative and generous. Mary is either not wise or not curious. Someone is generous or not calm. | Mary is not old. | contradiction | (![X]:((calm(X)&rich(X))<=>(~old(X)|~funny(X))))&
(((~curious(lucy)|~generous(lucy)))=>(~creative(alice)))&
(![X]:((~old(X)|~calm(X))<=>(kind(X)&~calm(X))))&
(((~happy(paul)&curious(paul)))<=>((old(alice)<~>funny(alice))))&
(((wise(lucy)<~>~patient(lucy)))<=>((~rich(susan)&~tall(susan))))&
(![X]:((humble(X)|~tall(X))<=>(calm(X)&wise(X))))&
(((creative(mary)|~happy(mary)))=>(?[X]:((quiet(X)&kind(X)))))&
((?[X]:((kind(X)&curious(X))))<=>(?[X]:((~humble(X)<~>~old(X)))))&
(((funny(alice)&quiet(alice)))<=>((patient(lucy)|~happy(lucy))))&
((?[X]:(~kind(X)))<=>((~creative(john)&~curious(john))))&
(![X]:((~creative(X)<~>generous(X))=>(~calm(X)&~tall(X))))&
((generous(mary))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((generous(X)&humble(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~old(X)|~happy(X))<=>generous(X)))&
((?[X]:((brave(X)<~>~rich(X))))<=>((~creative(susan)<~>~generous(susan))))&
(![X]:(~tall(X)=>(~generous(X)<~>strong(X))))&
((~strong(susan)&~wise(susan)))&
(?[X]:(humble(X)))&
(~creative(john))&
((~creative(susan)&generous(susan)))&
((~wise(mary)<~>~curious(mary)))&
(?[X]:((generous(X)|~calm(X)))) | ~old(mary) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 2592584778268934286324300
% SZS output start Proof for 2592584778268934286324300
1. ! [X0] : ((rich(X0) & calm(X0)) <=> (~funny(X0) | ~old(X0))) [input p0]
3. ! [X0] : ((~calm(X0) | ~old(X0)) <=> (~calm(X0) & kind(X0))) [input p2]
23. ~old(mary) [input hypothesis]
29. ! [X0] : (((rich(X0) & calm(X0)) | (funny(X0) & old(X0))) & ((~funny(X0) | ~old(X0)) | (~rich(X0) | ~calm(X0)))) [nnf transformation 1]
30. ! [X0] : (((rich(X0) & calm(X0)) | (funny(X0) & old(X0))) & (~funny(X0) | ~old(X0) | ~rich(X0) | ~calm(X0))) [flattening 29]
31. ! [X0] : (((~calm(X0) | ~old(X0)) | (calm(X0) | ~kind(X0))) & ((~calm(X0) & kind(X0)) | (calm(X0) & old(X0)))) [nnf transformation 3]
32. ! [X0] : ((~calm(X0) | ~old(X0) | calm(X0) | ~kind(X0)) & ((~calm(X0) & kind(X0)) | (calm(X0) & old(X0)))) [flattening 31]
73. calm(X0) | old(X0) [cnf transformation 30]
81. ~calm(X0) | old(X0) [cnf transformation 32]
154. ~old(mary) [cnf transformation 23]
171. old(X0) [subsumption resolution 81,73]
352. $false [subsumption resolution 154,171]
% SZS output end Proof for 2592584778268934286324300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or creative then someone is both brave and not wise and vice versa.
Everyone who is both curious and brave is not curious or not patient and vice versa.
Everyone who is either not happy or not brave is either not generous or calm.
If someone is both generous and not curious then lucy is either not humble or calm.
Everyone who is not strong is not rich or not wise and vice versa.
If someone is not creative or not calm then alice is either kind or quiet and vice versa.
If paul is both not generous and wise then alice is either rich or not old.
Everyone who is not quiet or not tall is either kind or brave and vice versa.
Everyone who is either not brave or not calm is not tall and vice versa.
If someone is both not tall and kind then lucy is not happy or not strong and vice versa.
If someone is both kind and not kind then fred is either calm or not creative and vice versa.
Everyone who is both not tall and not calm is brave and vice versa.
If someone is both strong and not old then someone is old or not kind and vice versa.
If someone is both not patient and not old then someone is creative.
Everyone who is either brave or not brave is both not brave and not tall and vice versa.
If someone is not wise then fred is not tall and vice versa.
Alice is not calm or not funny.
Someone is kind or not brave.
Lucy is both happy and not humble.
John is not kind or not happy.
Someone is not generous.
Susan is curious. | John is not quiet. | neutral | ((?[X]:((~wise(X)<~>creative(X))))<=>(?[X]:((brave(X)&~wise(X)))))&
(![X]:((curious(X)&brave(X))<=>(~curious(X)|~patient(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~generous(X)<~>calm(X))))&
((?[X]:((generous(X)&~curious(X))))=>((~humble(lucy)<~>calm(lucy))))&
(![X]:(~strong(X)<=>(~rich(X)|~wise(X))))&
((?[X]:((~creative(X)|~calm(X))))<=>((kind(alice)<~>quiet(alice))))&
(((~generous(paul)&wise(paul)))=>((rich(alice)<~>~old(alice))))&
(![X]:((~quiet(X)|~tall(X))<=>(kind(X)<~>brave(X))))&
(![X]:((~brave(X)<~>~calm(X))<=>~tall(X)))&
((?[X]:((~tall(X)&kind(X))))<=>((~happy(lucy)|~strong(lucy))))&
((?[X]:((kind(X)&~kind(X))))<=>((calm(fred)<~>~creative(fred))))&
(![X]:((~tall(X)&~calm(X))<=>brave(X)))&
((?[X]:((strong(X)&~old(X))))<=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((~patient(X)&~old(X))))=>(?[X]:(creative(X))))&
(![X]:((brave(X)<~>~brave(X))<=>(~brave(X)&~tall(X))))&
((?[X]:(~wise(X)))<=>(~tall(fred)))&
((~calm(alice)|~funny(alice)))&
(?[X]:((kind(X)|~brave(X))))&
((happy(lucy)&~humble(lucy)))&
((~kind(john)|~happy(john)))&
(?[X]:(~generous(X)))&
(curious(susan)) | ~quiet(john) | [] | null | 0 |
If mary is not curious then someone is not old and vice versa.
Everyone who is funny or not patient is funny or curious and vice versa.
If someone is either not creative or tall then susan is not brave and vice versa.
Everyone who is both not humble and strong is calm or not generous and vice versa.
Everyone who is old is calm or not old and vice versa.
Everyone who is both not creative and not wise is not generous or tall.
If someone is both kind and wise then lucy is either not creative or not old.
Everyone who is either curious or brave is both not quiet and not kind and vice versa.
If fred is both calm and not happy then someone is not rich and vice versa.
If alice is tall then someone is brave or humble.
Everyone who is either not funny or not calm is either tall or not humble.
Everyone who is either not quiet or not generous is not rich.
Everyone who is both not calm and not funny is both not wise and generous and vice versa.
Everyone who is both rich and not creative is not creative or not patient and vice versa.
If someone is both patient and not strong then someone is both tall and patient.
If lucy is brave then mary is patient or not creative and vice versa.
Someone is both curious and not patient.
Susan is not humble or not old.
Someone is both tall and rich.
Susan is both not curious and not tall.
Fred is happy.
John is not quiet or brave.
Someone is either calm or not curious. | Mary is calm. | entailment | ((~curious(mary))<=>(?[X]:(~old(X))))&
(![X]:((funny(X)|~patient(X))<=>(funny(X)|curious(X))))&
((?[X]:((~creative(X)<~>tall(X))))<=>(~brave(susan)))&
(![X]:((~humble(X)&strong(X))<=>(calm(X)|~generous(X))))&
(![X]:(old(X)<=>(calm(X)|~old(X))))&
(![X]:((~creative(X)&~wise(X))=>(~generous(X)|tall(X))))&
((?[X]:((kind(X)&wise(X))))=>((~creative(lucy)<~>~old(lucy))))&
(![X]:((curious(X)<~>brave(X))<=>(~quiet(X)&~kind(X))))&
(((calm(fred)&~happy(fred)))<=>(?[X]:(~rich(X))))&
((tall(alice))=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~funny(X)<~>~calm(X))=>(tall(X)<~>~humble(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>~rich(X)))&
(![X]:((~calm(X)&~funny(X))<=>(~wise(X)&generous(X))))&
(![X]:((rich(X)&~creative(X))<=>(~creative(X)|~patient(X))))&
((?[X]:((patient(X)&~strong(X))))=>(?[X]:((tall(X)&patient(X)))))&
((brave(lucy))<=>((patient(mary)|~creative(mary))))&
(?[X]:((curious(X)&~patient(X))))&
((~humble(susan)|~old(susan)))&
(?[X]:((tall(X)&rich(X))))&
((~curious(susan)&~tall(susan)))&
(happy(fred))&
((~quiet(john)|brave(john)))&
(?[X]:((calm(X)<~>~curious(X)))) | calm(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8985630168497075423335623
% SZS output start Proof for 8985630168497075423335623
5. ! [X0] : (old(X0) <=> (~old(X0) | calm(X0))) [input p4]
24. ~calm(mary) [input hypothesis]
45. ! [X0] : ((old(X0) | (old(X0) & ~calm(X0))) & ((~old(X0) | calm(X0)) | ~old(X0))) [nnf transformation 5]
46. ! [X0] : ((old(X0) | (old(X0) & ~calm(X0))) & (~old(X0) | calm(X0) | ~old(X0))) [flattening 45]
90. ~old(X0) | calm(X0) | ~old(X0) [cnf transformation 46]
92. old(X0) | old(X0) [cnf transformation 46]
137. ~calm(mary) [cnf transformation 24]
138. ~old(X0) | calm(X0) [duplicate literal removal 90]
139. old(X0) [duplicate literal removal 92]
141. 1 <=> ! [X0] : old(X0) [avatar definition]
142. old(X0) <- (1) [avatar component clause 141]
175. 1 [avatar split clause 139,141]
285. calm(X0) <- (1) [resolution 138,142]
286. $false <- (1) [resolution 285,137]
292. ~1 [avatar contradiction clause 286]
293. $false [avatar sat refutation 175,292]
% SZS output end Proof for 8985630168497075423335623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not calm is both not wise and not brave and vice versa.
Everyone who is both quiet and not patient is either happy or not generous.
Everyone who is creative or funny is not tall.
Everyone who is not kind or calm is either not patient or not creative.
If fred is not quiet or generous then someone is old or not curious.
If someone is both strong and not patient then someone is rich or patient and vice versa.
Everyone who is both humble and old is both brave and not generous and vice versa.
If paul is both not generous and brave then someone is tall or happy and vice versa.
If alice is both patient and not brave then lucy is not rich or quiet and vice versa.
If someone is either not funny or strong then someone is both wise and not curious and vice versa.
Everyone who is not tall is both old and not patient.
Everyone who is humble or not humble is not calm and vice versa.
Everyone who is both not wise and not calm is not kind or not calm.
If paul is generous then someone is not curious.
If someone is not kind or funny then someone is both patient and happy and vice versa.
Fred is old or curious.
John is either not rich or brave.
Mary is old or not creative.
Susan is not strong or generous. | Lucy is rich. | entailment | (![X]:((~humble(X)|~calm(X))<=>(~wise(X)&~brave(X))))&
(![X]:((quiet(X)&~patient(X))=>(happy(X)<~>~generous(X))))&
(![X]:((creative(X)|funny(X))=>~tall(X)))&
(![X]:((~kind(X)|calm(X))=>(~patient(X)<~>~creative(X))))&
(((~quiet(fred)|generous(fred)))=>(?[X]:((old(X)|~curious(X)))))&
((?[X]:((strong(X)&~patient(X))))<=>(?[X]:((rich(X)|patient(X)))))&
(![X]:((humble(X)&old(X))<=>(brave(X)&~generous(X))))&
(((~generous(paul)&brave(paul)))<=>(?[X]:((tall(X)|happy(X)))))&
(((patient(alice)&~brave(alice)))<=>((~rich(lucy)|quiet(lucy))))&
((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:(~tall(X)=>(old(X)&~patient(X))))&
(![X]:((humble(X)|~humble(X))<=>~calm(X)))&
(![X]:((~wise(X)&~calm(X))=>(~kind(X)|~calm(X))))&
((generous(paul))=>(?[X]:(~curious(X))))&
((?[X]:((~kind(X)|funny(X))))<=>(?[X]:((patient(X)&happy(X)))))&
((old(fred)|curious(fred)))&
((~rich(john)<~>brave(john)))&
((old(mary)|~creative(mary)))&
((~strong(susan)|generous(susan))) | rich(lucy) | [
"p0",
"p7",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 998646053120571903966780
% SZS output start Proof for 998646053120571903966780
1. ! [X0] : ((~calm(X0) | ~humble(X0)) <=> (~brave(X0) & ~wise(X0))) [input p0]
8. (brave(paul) & ~generous(paul)) <=> ? [X0] : (happy(X0) | tall(X0)) [input p7]
9. (~brave(alice) & patient(alice)) <=> (quiet(lucy) | ~rich(lucy)) [input p8]
11. ! [X0] : (~tall(X0) => (~patient(X0) & old(X0))) [input p10]
12. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~calm(X0)) [input p11]
20. ~rich(lucy) [input hypothesis]
29. ! [X0] : ((~patient(X0) & old(X0)) | tall(X0)) [ennf transformation 11]
33. ! [X0] : (((~calm(X0) | ~humble(X0)) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | (calm(X0) & humble(X0)))) [nnf transformation 1]
34. ! [X0] : ((~calm(X0) | ~humble(X0) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | (calm(X0) & humble(X0)))) [flattening 33]
46. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X0] : (happy(X0) | tall(X0)) | (~brave(paul) | generous(paul))) [nnf transformation 8]
47. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X0] : (happy(X0) | tall(X0)) | ~brave(paul) | generous(paul)) [flattening 46]
48. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X1] : (happy(X1) | tall(X1)) | ~brave(paul) | generous(paul)) [rectify 47]
49. ? [X1] : (happy(X1) | tall(X1)) => (happy(sK3) | tall(sK3)) [choice axiom]
50. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & ((happy(sK3) | tall(sK3)) | ~brave(paul) | generous(paul)) [skolemisation 48,49]
51. ((~brave(alice) & patient(alice)) | (~quiet(lucy) & rich(lucy))) & ((quiet(lucy) | ~rich(lucy)) | (brave(alice) | ~patient(alice))) [nnf transformation 9]
52. ((~brave(alice) & patient(alice)) | (~quiet(lucy) & rich(lucy))) & (quiet(lucy) | ~rich(lucy) | brave(alice) | ~patient(alice)) [flattening 51]
58. ! [X0] : (((~humble(X0) | humble(X0)) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 12]
59. ! [X0] : ((~humble(X0) | humble(X0) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [flattening 58]
71. ~brave(X0) | calm(X0) [cnf transformation 34]
95. brave(paul) | ~tall(X0) [cnf transformation 50]
98. patient(alice) | rich(lucy) [cnf transformation 52]
109. ~patient(X0) | tall(X0) [cnf transformation 29]
110. ~calm(X0) | ~humble(X0) [cnf transformation 59]
111. ~calm(X0) | humble(X0) [cnf transformation 59]
125. ~rich(lucy) [cnf transformation 20]
178. 13 <=> brave(paul) [avatar definition]
180. brave(paul) <- (13) [avatar component clause 178]
183. 14 <=> ! [X0] : ~tall(X0) [avatar definition]
184. ~tall(X0) <- (14) [avatar component clause 183]
185. 14 | 13 [avatar split clause 95,178,183]
211. 20 <=> rich(lucy) [avatar definition]
216. 21 <=> patient(alice) [avatar definition]
218. patient(alice) <- (21) [avatar component clause 216]
220. 20 | 21 [avatar split clause 98,216,211]
253. ~calm(X0) [subsumption resolution 110,111]
326. ~20 [avatar split clause 125,211]
341. tall(alice) <- (21) [resolution 109,218]
342. $false <- (14, 21) [subsumption resolution 341,184]
343. ~14 | ~21 [avatar contradiction clause 342]
346. calm(paul) <- (13) [resolution 180,71]
348. $false <- (13) [subsumption resolution 346,253]
349. ~13 [avatar contradiction clause 348]
350. $false [avatar sat refutation 185,220,326,343,349]
% SZS output end Proof for 998646053120571903966780
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is wise or not strong.
Everyone who is humble is brave and vice versa.
If paul is either strong or wise then mary is either strong or tall.
Everyone who is either not funny or kind is either not curious or old.
Everyone who is either curious or not calm is both rich and curious and vice versa.
If someone is old or not happy then alice is either kind or not wise.
Everyone who is funny is either humble or not strong and vice versa.
Everyone who is not curious or generous is both rich and not generous and vice versa.
Everyone who is either not curious or not calm is either not kind or not funny.
If someone is both creative and not calm then fred is old.
Everyone who is generous is both not kind and rich and vice versa.
Everyone who is not quiet or not generous is both calm and not old.
If someone is not humble or not strong then someone is not happy and vice versa.
If alice is happy then someone is both not rich and not quiet.
Everyone who is creative or brave is wise or not brave.
If alice is not rich or not wise then someone is either not generous or not rich.
Susan is both creative and not old.
Someone is both brave and patient.
Someone is wise or not tall.
Alice is brave or calm.
Alice is both tall and rich.
Mary is not rich or happy.
Someone is not happy or kind. | Alice is wise. | entailment | (![X]:(~happy(X)=>(wise(X)|~strong(X))))&
(![X]:(humble(X)<=>brave(X)))&
(((strong(paul)<~>wise(paul)))=>((strong(mary)<~>tall(mary))))&
(![X]:((~funny(X)<~>kind(X))=>(~curious(X)<~>old(X))))&
(![X]:((curious(X)<~>~calm(X))<=>(rich(X)&curious(X))))&
((?[X]:((old(X)|~happy(X))))=>((kind(alice)<~>~wise(alice))))&
(![X]:(funny(X)<=>(humble(X)<~>~strong(X))))&
(![X]:((~curious(X)|generous(X))<=>(rich(X)&~generous(X))))&
(![X]:((~curious(X)<~>~calm(X))=>(~kind(X)<~>~funny(X))))&
((?[X]:((creative(X)&~calm(X))))=>(old(fred)))&
(![X]:(generous(X)<=>(~kind(X)&rich(X))))&
(![X]:((~quiet(X)|~generous(X))=>(calm(X)&~old(X))))&
((?[X]:((~humble(X)|~strong(X))))<=>(?[X]:(~happy(X))))&
((happy(alice))=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((creative(X)|brave(X))=>(wise(X)|~brave(X))))&
(((~rich(alice)|~wise(alice)))=>(?[X]:((~generous(X)<~>~rich(X)))))&
((creative(susan)&~old(susan)))&
(?[X]:((brave(X)&patient(X))))&
(?[X]:((wise(X)|~tall(X))))&
((brave(alice)|calm(alice)))&
((tall(alice)&rich(alice)))&
((~rich(mary)|happy(mary)))&
(?[X]:((~happy(X)|kind(X)))) | wise(alice) | [
"p4",
"p5",
"p7",
"p10",
"p11",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4518147145694488039217771
% SZS output start Proof for 4518147145694488039217771
5. ! [X0] : ((curious(X0) <~> ~calm(X0)) <=> (curious(X0) & rich(X0))) [input p4]
6. ? [X0] : (~happy(X0) | old(X0)) => (kind(alice) <~> ~wise(alice)) [input p5]
8. ! [X0] : ((generous(X0) | ~curious(X0)) <=> (~generous(X0) & rich(X0))) [input p7]
11. ! [X0] : (generous(X0) <=> (rich(X0) & ~kind(X0))) [input p10]
12. ! [X0] : ((~generous(X0) | ~quiet(X0)) => (~old(X0) & calm(X0))) [input p11]
14. happy(alice) => ? [X0] : (~quiet(X0) & ~rich(X0)) [input p13]
21. rich(alice) & tall(alice) [input p20]
24. ~wise(alice) [input hypothesis]
31. (kind(alice) <~> ~wise(alice)) | ! [X0] : (happy(X0) & ~old(X0)) [ennf transformation 6]
34. ! [X0] : ((~old(X0) & calm(X0)) | (generous(X0) & quiet(X0))) [ennf transformation 12]
35. ? [X0] : (~quiet(X0) & ~rich(X0)) | ~happy(alice) [ennf transformation 14]
42. ! [X0] : ((((calm(X0) | ~curious(X0)) & (~calm(X0) | curious(X0))) | (~curious(X0) | ~rich(X0))) & ((curious(X0) & rich(X0)) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))))) [nnf transformation 5]
43. ! [X0] : ((((calm(X0) | ~curious(X0)) & (~calm(X0) | curious(X0))) | ~curious(X0) | ~rich(X0)) & ((curious(X0) & rich(X0)) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))))) [flattening 42]
44. ((wise(alice) | ~kind(alice)) & (~wise(alice) | kind(alice))) | ! [X0] : (happy(X0) & ~old(X0)) [nnf transformation 31]
46. ! [X0] : (((generous(X0) | ~curious(X0)) | (generous(X0) | ~rich(X0))) & ((~generous(X0) & rich(X0)) | (~generous(X0) & curious(X0)))) [nnf transformation 8]
47. ! [X0] : ((generous(X0) | ~curious(X0) | generous(X0) | ~rich(X0)) & ((~generous(X0) & rich(X0)) | (~generous(X0) & curious(X0)))) [flattening 46]
49. ! [X0] : ((generous(X0) | (~rich(X0) | kind(X0))) & ((rich(X0) & ~kind(X0)) | ~generous(X0))) [nnf transformation 11]
50. ! [X0] : ((generous(X0) | ~rich(X0) | kind(X0)) & ((rich(X0) & ~kind(X0)) | ~generous(X0))) [flattening 49]
56. ? [X0] : (~quiet(X0) & ~rich(X0)) => (~quiet(sK2) & ~rich(sK2)) [choice axiom]
57. (~quiet(sK2) & ~rich(sK2)) | ~happy(alice) [skolemisation 35,56]
78. ~calm(X0) | rich(X0) | ~curious(X0) [cnf transformation 43]
87. wise(alice) | ~kind(alice) | happy(X0) [cnf transformation 44]
92. rich(X0) | curious(X0) [cnf transformation 47]
95. ~generous(X0) | ~generous(X0) [cnf transformation 47]
104. generous(X0) | ~rich(X0) | kind(X0) [cnf transformation 50]
106. calm(X0) | generous(X0) [cnf transformation 34]
112. ~rich(sK2) | ~happy(alice) [cnf transformation 57]
126. rich(alice) [cnf transformation 21]
129. ~wise(alice) [cnf transformation 24]
131. ~generous(X0) [duplicate literal removal 95]
156. 5 <=> ! [X0] : happy(X0) [avatar definition]
157. happy(X0) <- (5) [avatar component clause 156]
159. 6 <=> kind(alice) [avatar definition]
163. 7 <=> wise(alice) [avatar definition]
166. 5 | ~6 | 7 [avatar split clause 87,163,159,156]
185. ~rich(X0) | kind(X0) [subsumption resolution 104,131]
188. calm(X0) [subsumption resolution 106,131]
211. 16 <=> happy(alice) [avatar definition]
213. ~happy(alice) <- (~16) [avatar component clause 211]
220. 18 <=> rich(sK2) [avatar definition]
222. ~rich(sK2) <- (~18) [avatar component clause 220]
223. ~16 | ~18 [avatar split clause 112,220,211]
232. 20 <=> rich(alice) [avatar definition]
234. rich(alice) <- (20) [avatar component clause 232]
245. 20 [avatar split clause 126,232]
264. ~7 [avatar split clause 129,163]
270. kind(alice) <- (20) [resolution 185,234]
274. 6 | ~20 [avatar split clause 270,232,159]
276. $false <- (5, ~16) [resolution 157,213]
279. ~5 | 16 [avatar contradiction clause 276]
289. rich(X1) | ~curious(X1) [resolution 78,188]
290. rich(X1) [subsumption resolution 289,92]
295. $false <- (~18) [resolution 290,222]
296. 18 [avatar contradiction clause 295]
298. $false [avatar sat refutation 166,223,245,264,274,279,296]
% SZS output end Proof for 4518147145694488039217771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either rich or not kind is either tall or generous and vice versa. Everyone who is calm is old. Everyone who is not quiet or happy is both not strong and not humble and vice versa. Everyone who is humble or not patient is either not brave or not funny and vice versa. If susan is generous then someone is calm and vice versa. If alice is not brave then susan is not kind or not tall. Everyone who is both rich and creative is calm. Everyone who is either not brave or calm is either not patient or not strong and vice versa. If someone is strong then fred is not calm. Everyone who is strong is not curious or kind and vice versa. Everyone who is happy or curious is both old and not calm and vice versa. Everyone who is humble is not strong. Everyone who is both not happy and not humble is not tall and vice versa. If john is not brave or generous then someone is either tall or creative. Everyone who is not calm or wise is either not generous or kind. Everyone who is both brave and strong is not funny or tall and vice versa. Someone is either not brave or not happy. Someone is either calm or funny. Someone is not curious or not humble. Paul is wise. Fred is either creative or not generous. Mary is either quiet or not rich. | Susan is not quiet. | contradiction | (![X]:((rich(X)<~>~kind(X))<=>(tall(X)<~>generous(X))))&
(![X]:(calm(X)=>old(X)))&
(![X]:((~quiet(X)|happy(X))<=>(~strong(X)&~humble(X))))&
(![X]:((humble(X)|~patient(X))<=>(~brave(X)<~>~funny(X))))&
((generous(susan))<=>(?[X]:(calm(X))))&
((~brave(alice))=>((~kind(susan)|~tall(susan))))&
(![X]:((rich(X)&creative(X))=>calm(X)))&
(![X]:((~brave(X)<~>calm(X))<=>(~patient(X)<~>~strong(X))))&
((?[X]:(strong(X)))=>(~calm(fred)))&
(![X]:(strong(X)<=>(~curious(X)|kind(X))))&
(![X]:((happy(X)|curious(X))<=>(old(X)&~calm(X))))&
(![X]:(humble(X)=>~strong(X)))&
(![X]:((~happy(X)&~humble(X))<=>~tall(X)))&
(((~brave(john)|generous(john)))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((~calm(X)|wise(X))=>(~generous(X)<~>kind(X))))&
(![X]:((brave(X)&strong(X))<=>(~funny(X)|tall(X))))&
(?[X]:((~brave(X)<~>~happy(X))))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:((~curious(X)|~humble(X))))&
(wise(paul))&
((creative(fred)<~>~generous(fred)))&
((quiet(mary)<~>~rich(mary))) | ~quiet(susan) | [
"p2",
"p3",
"p4",
"p7",
"p9",
"p10",
"p11",
"p12",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7760408894249113108905083
% SZS output start Proof for 7760408894249113108905083
3. ! [X0] : ((happy(X0) | ~quiet(X0)) <=> (~humble(X0) & ~strong(X0))) [input p2]
4. ! [X0] : ((~patient(X0) | humble(X0)) <=> (~brave(X0) <~> ~funny(X0))) [input p3]
5. generous(susan) <=> ? [X0] : calm(X0) [input p4]
8. ! [X0] : ((~brave(X0) <~> calm(X0)) <=> (~patient(X0) <~> ~strong(X0))) [input p7]
10. ! [X0] : (strong(X0) <=> (kind(X0) | ~curious(X0))) [input p9]
11. ! [X0] : ((curious(X0) | happy(X0)) <=> (~calm(X0) & old(X0))) [input p10]
12. ! [X0] : (humble(X0) => ~strong(X0)) [input p11]
13. ! [X0] : ((~humble(X0) & ~happy(X0)) <=> ~tall(X0)) [input p12]
15. ! [X0] : ((wise(X0) | ~calm(X0)) => (~generous(X0) <~> kind(X0))) [input p14]
16. ! [X0] : ((strong(X0) & brave(X0)) <=> (tall(X0) | ~funny(X0))) [input p15]
17. ? [X0] : (~brave(X0) <~> ~happy(X0)) [input p16]
23. ~quiet(susan) [input hypothesis]
30. ! [X0] : (~strong(X0) | ~humble(X0)) [ennf transformation 12]
32. ! [X0] : ((~generous(X0) <~> kind(X0)) | (~wise(X0) & calm(X0))) [ennf transformation 15]
34. ! [X0] : (((happy(X0) | ~quiet(X0)) | (humble(X0) | strong(X0))) & ((~humble(X0) & ~strong(X0)) | (~happy(X0) & quiet(X0)))) [nnf transformation 3]
35. ! [X0] : ((happy(X0) | ~quiet(X0) | humble(X0) | strong(X0)) & ((~humble(X0) & ~strong(X0)) | (~happy(X0) & quiet(X0)))) [flattening 34]
36. ! [X0] : (((~patient(X0) | humble(X0)) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (patient(X0) & ~humble(X0)))) [nnf transformation 4]
37. ! [X0] : ((~patient(X0) | humble(X0) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (patient(X0) & ~humble(X0)))) [flattening 36]
38. (generous(susan) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ~generous(susan)) [nnf transformation 5]
39. (generous(susan) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ~generous(susan)) [rectify 38]
40. ? [X1] : calm(X1) => calm(sK0) [choice axiom]
41. (generous(susan) | ! [X0] : ~calm(X0)) & (calm(sK0) | ~generous(susan)) [skolemisation 39,40]
42. ! [X0] : ((((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0))))) [nnf transformation 8]
43. ! [X0] : ((strong(X0) | (~kind(X0) & curious(X0))) & ((kind(X0) | ~curious(X0)) | ~strong(X0))) [nnf transformation 10]
44. ! [X0] : ((strong(X0) | (~kind(X0) & curious(X0))) & (kind(X0) | ~curious(X0) | ~strong(X0))) [flattening 43]
45. ! [X0] : (((curious(X0) | happy(X0)) | (calm(X0) | ~old(X0))) & ((~calm(X0) & old(X0)) | (~curious(X0) & ~happy(X0)))) [nnf transformation 11]
46. ! [X0] : ((curious(X0) | happy(X0) | calm(X0) | ~old(X0)) & ((~calm(X0) & old(X0)) | (~curious(X0) & ~happy(X0)))) [flattening 45]
47. ! [X0] : (((~humble(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | (humble(X0) | happy(X0)))) [nnf transformation 13]
48. ! [X0] : (((~humble(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | humble(X0) | happy(X0))) [flattening 47]
52. ! [X0] : (((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (~wise(X0) & calm(X0))) [nnf transformation 32]
53. ! [X0] : (((strong(X0) & brave(X0)) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | (~strong(X0) | ~brave(X0)))) [nnf transformation 16]
54. ! [X0] : (((strong(X0) & brave(X0)) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~strong(X0) | ~brave(X0))) [flattening 53]
55. ? [X0] : ((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) [nnf transformation 17]
56. ? [X0] : ((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) => ((happy(sK2) | brave(sK2)) & (~happy(sK2) | ~brave(sK2))) [choice axiom]
57. (happy(sK2) | brave(sK2)) & (~happy(sK2) | ~brave(sK2)) [skolemisation 55,56]
74. ~strong(X0) | quiet(X0) [cnf transformation 35]
79. ~funny(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 37]
80. ~funny(X0) | ~brave(X0) | patient(X0) [cnf transformation 37]
84. ~brave(X0) | humble(X0) | ~patient(X0) | funny(X0) [cnf transformation 37]
86. generous(susan) | ~calm(X0) [cnf transformation 41]
93. ~brave(X0) | calm(X0) | ~strong(X0) | patient(X0) [cnf transformation 42]
94. ~brave(X0) | calm(X0) | ~patient(X0) | strong(X0) [cnf transformation 42]
99. curious(X0) | strong(X0) [cnf transformation 44]
100. ~kind(X0) | strong(X0) [cnf transformation 44]
104. ~curious(X0) | ~calm(X0) [cnf transformation 46]
106. ~humble(X0) | ~strong(X0) [cnf transformation 30]
107. ~tall(X0) | humble(X0) | happy(X0) [cnf transformation 48]
108. ~happy(X0) | tall(X0) [cnf transformation 48]
114. ~generous(X0) | kind(X0) | calm(X0) [cnf transformation 52]
118. ~funny(X0) | tall(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 54]
120. ~tall(X0) | brave(X0) [cnf transformation 54]
121. funny(X0) | strong(X0) [cnf transformation 54]
123. ~happy(sK2) | ~brave(sK2) [cnf transformation 57]
124. happy(sK2) | brave(sK2) [cnf transformation 57]
133. ~quiet(susan) [cnf transformation 23]
135. 1 <=> ! [X0] : ~calm(X0) [avatar definition]
136. ~calm(X0) <- (1) [avatar component clause 135]
138. 2 <=> generous(susan) [avatar definition]
140. generous(susan) <- (2) [avatar component clause 138]
141. 1 | 2 [avatar split clause 86,138,135]
152. 5 <=> kind(susan) [avatar definition]
153. kind(susan) <- (5) [avatar component clause 152]
189. 13 <=> brave(sK2) [avatar definition]
190. ~brave(sK2) <- (~13) [avatar component clause 189]
191. brave(sK2) <- (13) [avatar component clause 189]
193. 14 <=> happy(sK2) [avatar definition]
194. ~happy(sK2) <- (~14) [avatar component clause 193]
195. happy(sK2) <- (14) [avatar component clause 193]
196. 13 | 14 [avatar split clause 124,193,189]
197. ~13 | ~14 [avatar split clause 123,193,189]
240. ~calm(X0) | strong(X0) [resolution 104,99]
249. ~brave(X0) | ~humble(X0) | strong(X0) [resolution 79,121]
251. ~brave(X0) | ~humble(X0) [subsumption resolution 249,106]
252. ~brave(X0) | patient(X0) | strong(X0) [resolution 80,121]
282. kind(susan) | calm(susan) <- (2) [resolution 114,140]
284. 25 <=> calm(susan) [avatar definition]
286. calm(susan) <- (25) [avatar component clause 284]
287. 25 | 5 | ~2 [avatar split clause 282,138,152,284]
288. strong(susan) <- (5) [resolution 153,100]
301. quiet(susan) <- (5) [resolution 288,74]
302. $false <- (5) [subsumption resolution 301,133]
303. ~5 [avatar contradiction clause 302]
304. strong(susan) <- (25) [resolution 286,240]
397. quiet(susan) <- (25) [resolution 304,74]
398. $false <- (25) [subsumption resolution 397,133]
399. ~25 [avatar contradiction clause 398]
424. humble(sK2) | ~patient(sK2) | funny(sK2) <- (13) [resolution 84,191]
426. 37 <=> funny(sK2) [avatar definition]
428. funny(sK2) <- (37) [avatar component clause 426]
430. 38 <=> patient(sK2) [avatar definition]
431. patient(sK2) <- (38) [avatar component clause 430]
432. ~patient(sK2) <- (~38) [avatar component clause 430]
434. 39 <=> humble(sK2) [avatar definition]
435. ~humble(sK2) <- (~39) [avatar component clause 434]
437. 37 | ~38 | 39 | ~13 [avatar split clause 424,189,434,430,426]
453. calm(sK2) | ~strong(sK2) | patient(sK2) <- (13) [resolution 93,191]
456. ~strong(sK2) | patient(sK2) <- (1, 13) [subsumption resolution 453,136]
457. ~strong(sK2) <- (1, 13, ~38) [subsumption resolution 456,432]
494. ~humble(sK2) <- (13) [resolution 251,191]
496. ~39 | ~13 [avatar split clause 494,189,434]
499. patient(sK2) | strong(sK2) <- (13) [resolution 252,191]
502. strong(sK2) <- (13, ~38) [subsumption resolution 499,432]
503. $false <- (1, 13, ~38) [subsumption resolution 502,457]
504. ~1 | ~13 | 38 [avatar contradiction clause 503]
507. tall(sK2) <- (14) [resolution 195,108]
514. brave(sK2) <- (14) [resolution 507,120]
529. $false <- (~13, 14) [subsumption resolution 514,190]
530. 13 | ~14 [avatar contradiction clause 529]
535. calm(sK2) | ~patient(sK2) | strong(sK2) <- (13) [resolution 191,94]
538. ~patient(sK2) | strong(sK2) <- (1, 13) [subsumption resolution 535,136]
539. strong(sK2) <- (1, 13, 38) [subsumption resolution 538,431]
540. tall(sK2) | ~strong(sK2) | ~brave(sK2) <- (37) [resolution 428,118]
544. tall(sK2) | ~brave(sK2) <- (1, 13, 37, 38) [subsumption resolution 540,539]
545. tall(sK2) <- (1, 13, 37, 38) [subsumption resolution 544,191]
561. humble(sK2) | happy(sK2) <- (1, 13, 37, 38) [resolution 545,107]
566. happy(sK2) <- (1, 13, 37, 38, ~39) [subsumption resolution 561,435]
567. $false <- (1, 13, ~14, 37, 38, ~39) [subsumption resolution 566,194]
568. ~1 | ~13 | 14 | ~37 | ~38 | 39 [avatar contradiction clause 567]
569. $false [avatar sat refutation 141,196,197,287,303,399,437,496,504,530,568]
% SZS output end Proof for 7760408894249113108905083
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or not brave is quiet and vice versa. If john is both curious and not tall then someone is both not rich and not wise. Everyone who is wise is not old. Everyone who is either kind or not quiet is either calm or funny and vice versa. Everyone who is not strong is both quiet and calm and vice versa. Everyone who is not happy or not curious is either not strong or not happy. If lucy is either not funny or patient then paul is strong and vice versa. Everyone who is either not generous or not wise is patient and vice versa. Everyone who is not happy is either patient or not strong and vice versa. If someone is not old or tall then alice is not humble and vice versa. Everyone who is both not humble and brave is either rich or not tall and vice versa. Everyone who is both not strong and old is calm or quiet and vice versa. If someone is either not patient or old then someone is not brave. If someone is tall or rich then someone is calm and vice versa. Everyone who is both not calm and funny is patient or brave and vice versa. Everyone who is both rich and not humble is both old and not strong. Alice is not calm. Susan is either humble or not tall. Fred is not generous or not old. Someone is not wise. Alice is both not curious and not tall. John is strong. | Lucy is kind. | contradiction | (![X]:((old(X)<~>~brave(X))<=>quiet(X)))&
(((curious(john)&~tall(john)))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:(wise(X)=>~old(X)))&
(![X]:((kind(X)<~>~quiet(X))<=>(calm(X)<~>funny(X))))&
(![X]:(~strong(X)<=>(quiet(X)&calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~strong(X)<~>~happy(X))))&
(((~funny(lucy)<~>patient(lucy)))<=>(strong(paul)))&
(![X]:((~generous(X)<~>~wise(X))<=>patient(X)))&
(![X]:(~happy(X)<=>(patient(X)<~>~strong(X))))&
((?[X]:((~old(X)|tall(X))))<=>(~humble(alice)))&
(![X]:((~humble(X)&brave(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((~strong(X)&old(X))<=>(calm(X)|quiet(X))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:(~brave(X))))&
((?[X]:((tall(X)|rich(X))))<=>(?[X]:(calm(X))))&
(![X]:((~calm(X)&funny(X))<=>(patient(X)|brave(X))))&
(![X]:((rich(X)&~humble(X))=>(old(X)&~strong(X))))&
(~calm(alice))&
((humble(susan)<~>~tall(susan)))&
((~generous(fred)|~old(fred)))&
(?[X]:(~wise(X)))&
((~curious(alice)&~tall(alice)))&
(strong(john)) | kind(lucy) | [
"p3",
"p4",
"p5",
"p8",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7353699083041588538387480
% SZS output start Proof for 7353699083041588538387480
4. ! [X0] : ((kind(X0) <~> ~quiet(X0)) <=> (calm(X0) <~> funny(X0))) [input p3]
5. ! [X0] : (~strong(X0) <=> (calm(X0) & quiet(X0))) [input p4]
6. ! [X0] : ((~curious(X0) | ~happy(X0)) => (~strong(X0) <~> ~happy(X0))) [input p5]
9. ! [X0] : (~happy(X0) <=> (patient(X0) <~> ~strong(X0))) [input p8]
11. ! [X0] : ((brave(X0) & ~humble(X0)) <=> (rich(X0) <~> ~tall(X0))) [input p10]
12. ! [X0] : ((old(X0) & ~strong(X0)) <=> (quiet(X0) | calm(X0))) [input p11]
14. ? [X0] : (rich(X0) | tall(X0)) <=> ? [X0] : calm(X0) [input p13]
15. ! [X0] : ((funny(X0) & ~calm(X0)) <=> (brave(X0) | patient(X0))) [input p14]
23. kind(lucy) [input hypothesis]
25. ? [X0] : (rich(X0) | tall(X0)) <=> ? [X1] : calm(X1) [rectify 14]
29. ! [X0] : ((~strong(X0) <~> ~happy(X0)) | (curious(X0) & happy(X0))) [ennf transformation 6]
36. ! [X0] : ((((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0))))) [nnf transformation 4]
37. ! [X0] : ((~strong(X0) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | strong(X0))) [nnf transformation 5]
38. ! [X0] : ((~strong(X0) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | strong(X0))) [flattening 37]
39. ! [X0] : (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | (curious(X0) & happy(X0))) [nnf transformation 29]
42. ! [X0] : ((~happy(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0)))) & (((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | happy(X0))) [nnf transformation 9]
47. ! [X0] : (((brave(X0) & ~humble(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | (~brave(X0) | humble(X0)))) [nnf transformation 11]
48. ! [X0] : (((brave(X0) & ~humble(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | ~brave(X0) | humble(X0))) [flattening 47]
49. ! [X0] : (((old(X0) & ~strong(X0)) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | (~old(X0) | strong(X0)))) [nnf transformation 12]
50. ! [X0] : (((old(X0) & ~strong(X0)) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | ~old(X0) | strong(X0))) [flattening 49]
55. (? [X0] : (rich(X0) | tall(X0)) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : (~rich(X0) & ~tall(X0))) [nnf transformation 25]
56. (? [X0] : (rich(X0) | tall(X0)) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : (~rich(X3) & ~tall(X3))) [rectify 55]
57. ? [X0] : (rich(X0) | tall(X0)) => (rich(sK3) | tall(sK3)) [choice axiom]
58. ? [X2] : calm(X2) => calm(sK4) [choice axiom]
59. ((rich(sK3) | tall(sK3)) | ! [X1] : ~calm(X1)) & (calm(sK4) | ! [X3] : (~rich(X3) & ~tall(X3))) [skolemisation 56,58,57]
60. ! [X0] : (((funny(X0) & ~calm(X0)) | (~brave(X0) & ~patient(X0))) & ((brave(X0) | patient(X0)) | (~funny(X0) | calm(X0)))) [nnf transformation 15]
61. ! [X0] : (((funny(X0) & ~calm(X0)) | (~brave(X0) & ~patient(X0))) & (brave(X0) | patient(X0) | ~funny(X0) | calm(X0))) [flattening 60]
79. ~funny(X0) | ~kind(X0) | calm(X0) | quiet(X0) [cnf transformation 36]
81. strong(X0) | calm(X0) [cnf transformation 38]
85. happy(X0) | strong(X0) | happy(X0) [cnf transformation 39]
98. ~happy(X0) | patient(X0) | strong(X0) [cnf transformation 42]
107. rich(X0) | brave(X0) | tall(X0) [cnf transformation 48]
109. ~strong(X0) | ~calm(X0) [cnf transformation 50]
110. ~strong(X0) | ~quiet(X0) [cnf transformation 50]
115. calm(sK4) | ~tall(X3) [cnf transformation 59]
116. calm(sK4) | ~rich(X3) [cnf transformation 59]
119. ~patient(X0) | ~calm(X0) [cnf transformation 61]
122. ~brave(X0) | funny(X0) [cnf transformation 61]
133. kind(lucy) [cnf transformation 23]
134. happy(X0) | strong(X0) [duplicate literal removal 85]
158. 6 <=> funny(lucy) [avatar definition]
159. ~funny(lucy) <- (~6) [avatar component clause 158]
160. funny(lucy) <- (6) [avatar component clause 158]
169. patient(X0) | strong(X0) [subsumption resolution 98,134]
185. 11 <=> ! [X1] : ~tall(X1) [avatar definition]
186. ~tall(X1) <- (11) [avatar component clause 185]
205. 16 <=> ! [X1] : ~calm(X1) [avatar definition]
206. ~calm(X1) <- (16) [avatar component clause 205]
217. 19 <=> ! [X3] : ~rich(X3) [avatar definition]
218. ~rich(X3) <- (19) [avatar component clause 217]
220. 20 <=> calm(sK4) [avatar definition]
222. calm(sK4) <- (20) [avatar component clause 220]
223. 19 | 20 [avatar split clause 116,220,217]
224. 11 | 20 [avatar split clause 115,220,185]
255. strong(X1) | ~calm(X1) [resolution 169,119]
290. ~calm(X1) [subsumption resolution 255,109]
291. 16 [avatar split clause 290,205]
329. brave(X1) | tall(X1) <- (19) [resolution 107,218]
331. brave(X1) <- (11, 19) [subsumption resolution 329,186]
334. funny(X1) <- (11, 19) [resolution 331,122]
338. $false <- (~6, 11, 19) [resolution 334,159]
339. 6 | ~11 | ~19 [avatar contradiction clause 338]
340. $false <- (16, 20) [subsumption resolution 222,206]
341. ~16 | ~20 [avatar contradiction clause 340]
352. 30 <=> strong(lucy) [avatar definition]
353. strong(lucy) <- (30) [avatar component clause 352]
354. ~strong(lucy) <- (~30) [avatar component clause 352]
400. calm(lucy) <- (~30) [resolution 354,81]
402. $false <- (16, ~30) [subsumption resolution 400,206]
403. ~16 | 30 [avatar contradiction clause 402]
412. ~quiet(lucy) <- (30) [resolution 353,110]
433. ~kind(lucy) | calm(lucy) | quiet(lucy) <- (6) [resolution 79,160]
439. calm(lucy) | quiet(lucy) <- (6) [subsumption resolution 433,133]
440. quiet(lucy) <- (6, 16) [subsumption resolution 439,206]
441. $false <- (6, 16, 30) [subsumption resolution 440,412]
442. ~6 | ~16 | ~30 [avatar contradiction clause 441]
451. $false [avatar sat refutation 223,224,291,339,341,403,442]
% SZS output end Proof for 7353699083041588538387480
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not patient is not humble and vice versa.
If someone is creative then alice is strong and vice versa.
If lucy is not wise or generous then john is curious and vice versa.
If paul is not tall or tall then paul is not wise or happy.
If someone is not tall then susan is not old or not generous.
Everyone who is either humble or tall is both not generous and not strong and vice versa.
Everyone who is not humble is not brave and vice versa.
If someone is both not patient and not humble then someone is both not quiet and tall and vice versa.
Everyone who is rich is not generous.
Everyone who is both kind and not brave is not kind or not strong.
If john is not creative or not funny then someone is both not tall and kind.
Everyone who is not happy or brave is not patient and vice versa.
If mary is curious or not rich then fred is either not calm or humble and vice versa.
Everyone who is either not patient or generous is either tall or wise and vice versa.
If someone is both calm and not generous then fred is both patient and funny.
Everyone who is either not generous or happy is not tall and vice versa.
Fred is tall or not brave.
Someone is both patient and not brave.
Someone is funny or not calm.
Alice is not strong.
Mary is not happy or funny.
Mary is either not funny or humble.
Paul is either creative or not quiet. | Lucy is not creative. | entailment | (![X]:((happy(X)|~patient(X))<=>~humble(X)))&
((?[X]:(creative(X)))<=>(strong(alice)))&
(((~wise(lucy)|generous(lucy)))<=>(curious(john)))&
(((~tall(paul)|tall(paul)))=>((~wise(paul)|happy(paul))))&
((?[X]:(~tall(X)))=>((~old(susan)|~generous(susan))))&
(![X]:((humble(X)<~>tall(X))<=>(~generous(X)&~strong(X))))&
(![X]:(~humble(X)<=>~brave(X)))&
((?[X]:((~patient(X)&~humble(X))))<=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:(rich(X)=>~generous(X)))&
(![X]:((kind(X)&~brave(X))=>(~kind(X)|~strong(X))))&
(((~creative(john)|~funny(john)))=>(?[X]:((~tall(X)&kind(X)))))&
(![X]:((~happy(X)|brave(X))<=>~patient(X)))&
(((curious(mary)|~rich(mary)))<=>((~calm(fred)<~>humble(fred))))&
(![X]:((~patient(X)<~>generous(X))<=>(tall(X)<~>wise(X))))&
((?[X]:((calm(X)&~generous(X))))=>((patient(fred)&funny(fred))))&
(![X]:((~generous(X)<~>happy(X))<=>~tall(X)))&
((tall(fred)|~brave(fred)))&
(?[X]:((patient(X)&~brave(X))))&
(?[X]:((funny(X)|~calm(X))))&
(~strong(alice))&
((~happy(mary)|funny(mary)))&
((~funny(mary)<~>humble(mary)))&
((creative(paul)<~>~quiet(paul))) | ~creative(lucy) | [
"p1",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7301953917272281752310049
% SZS output start Proof for 7301953917272281752310049
2. ? [X0] : creative(X0) <=> strong(alice) [input p1]
20. ~strong(alice) [input p19]
24. creative(lucy) [input hypothesis]
36. (? [X0] : creative(X0) | ~strong(alice)) & (strong(alice) | ! [X0] : ~creative(X0)) [nnf transformation 2]
37. (? [X0] : creative(X0) | ~strong(alice)) & (strong(alice) | ! [X1] : ~creative(X1)) [rectify 36]
38. ? [X0] : creative(X0) => creative(sK0) [choice axiom]
39. (creative(sK0) | ~strong(alice)) & (strong(alice) | ! [X1] : ~creative(X1)) [skolemisation 37,38]
67. strong(alice) | ~creative(X1) [cnf transformation 39]
119. ~strong(alice) [cnf transformation 20]
125. creative(lucy) [cnf transformation 24]
128. 1 <=> strong(alice) [avatar definition]
137. 3 <=> ! [X1] : ~creative(X1) [avatar definition]
138. ~creative(X1) <- (3) [avatar component clause 137]
139. 3 | 1 [avatar split clause 67,128,137]
270. ~1 [avatar split clause 119,128]
298. $false <- (3) [resolution 138,125]
299. ~3 [avatar contradiction clause 298]
300. $false [avatar sat refutation 139,270,299]
% SZS output end Proof for 7301953917272281752310049
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is either not quiet or not rich and vice versa.
Everyone who is both not kind and not tall is either not generous or not old and vice versa.
Everyone who is either quiet or not wise is both not happy and quiet and vice versa.
If alice is either kind or not calm then someone is both not tall and not kind and vice versa.
If someone is not rich then someone is not curious and vice versa.
Everyone who is either not patient or strong is either calm or not rich.
If susan is not strong or not wise then someone is not old.
If someone is not humble or not old then mary is either not creative or wise and vice versa.
If lucy is either not creative or not old then susan is curious and vice versa.
Everyone who is either not patient or not quiet is either kind or not strong and vice versa.
Everyone who is both not funny and not generous is not patient and vice versa.
Everyone who is both kind and not generous is either calm or not kind and vice versa.
Everyone who is patient is not rich and vice versa.
Everyone who is not wise or not curious is brave or not kind and vice versa.
Everyone who is rich or humble is either humble or old and vice versa.
Everyone who is not rich or humble is funny or not curious and vice versa.
Someone is both rich and not curious.
Someone is funny.
Someone is patient or kind.
Someone is both funny and not strong.
Someone is either tall or not creative.
Mary is either rich or humble.
Someone is rich. | Lucy is tall. | entailment | (![X]:(strong(X)<=>(~quiet(X)<~>~rich(X))))&
(![X]:((~kind(X)&~tall(X))<=>(~generous(X)<~>~old(X))))&
(![X]:((quiet(X)<~>~wise(X))<=>(~happy(X)&quiet(X))))&
(((kind(alice)<~>~calm(alice)))<=>(?[X]:((~tall(X)&~kind(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:(~curious(X))))&
(![X]:((~patient(X)<~>strong(X))=>(calm(X)<~>~rich(X))))&
(((~strong(susan)|~wise(susan)))=>(?[X]:(~old(X))))&
((?[X]:((~humble(X)|~old(X))))<=>((~creative(mary)<~>wise(mary))))&
(((~creative(lucy)<~>~old(lucy)))<=>(curious(susan)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(kind(X)<~>~strong(X))))&
(![X]:((~funny(X)&~generous(X))<=>~patient(X)))&
(![X]:((kind(X)&~generous(X))<=>(calm(X)<~>~kind(X))))&
(![X]:(patient(X)<=>~rich(X)))&
(![X]:((~wise(X)|~curious(X))<=>(brave(X)|~kind(X))))&
(![X]:((rich(X)|humble(X))<=>(humble(X)<~>old(X))))&
(![X]:((~rich(X)|humble(X))<=>(funny(X)|~curious(X))))&
(?[X]:((rich(X)&~curious(X))))&
(?[X]:(funny(X)))&
(?[X]:((patient(X)|kind(X))))&
(?[X]:((funny(X)&~strong(X))))&
(?[X]:((tall(X)<~>~creative(X))))&
((rich(mary)<~>humble(mary)))&
(?[X]:(rich(X))) | tall(lucy) | [
"p0",
"p3",
"p5",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 491225349294108708192595
% SZS output start Proof for 491225349294108708192595
1. ! [X0] : (strong(X0) <=> (~quiet(X0) <~> ~rich(X0))) [input p0]
4. (kind(alice) <~> ~calm(alice)) <=> ? [X0] : (~kind(X0) & ~tall(X0)) [input p3]
6. ! [X0] : ((~patient(X0) <~> strong(X0)) => (calm(X0) <~> ~rich(X0))) [input p5]
10. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) <=> (kind(X0) <~> ~strong(X0))) [input p9]
12. ! [X0] : ((~generous(X0) & kind(X0)) <=> (calm(X0) <~> ~kind(X0))) [input p11]
13. ! [X0] : (patient(X0) <=> ~rich(X0)) [input p12]
24. ~tall(lucy) [input hypothesis]
26. ! [X0] : ((calm(X0) <~> ~rich(X0)) | (~patient(X0) <=> strong(X0))) [ennf transformation 6]
28. ! [X0] : ((strong(X0) | ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0)))) & (((rich(X0) | quiet(X0)) & (~rich(X0) | ~quiet(X0))) | ~strong(X0))) [nnf transformation 1]
33. (((calm(alice) | ~kind(alice)) & (~calm(alice) | kind(alice))) | ! [X0] : (kind(X0) | tall(X0))) & (? [X0] : (~kind(X0) & ~tall(X0)) | ((kind(alice) | calm(alice)) & (~calm(alice) | ~kind(alice)))) [nnf transformation 4]
34. (((calm(alice) | ~kind(alice)) & (~calm(alice) | kind(alice))) | ! [X0] : (kind(X0) | tall(X0))) & (? [X1] : (~kind(X1) & ~tall(X1)) | ((kind(alice) | calm(alice)) & (~calm(alice) | ~kind(alice)))) [rectify 33]
35. ? [X1] : (~kind(X1) & ~tall(X1)) => (~kind(sK0) & ~tall(sK0)) [choice axiom]
36. (((calm(alice) | ~kind(alice)) & (~calm(alice) | kind(alice))) | ! [X0] : (kind(X0) | tall(X0))) & ((~kind(sK0) & ~tall(sK0)) | ((kind(alice) | calm(alice)) & (~calm(alice) | ~kind(alice)))) [skolemisation 34,35]
42. ! [X0] : (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0)))) [nnf transformation 26]
50. ! [X0] : ((((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0)))) & (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0))))) [nnf transformation 10]
53. ! [X0] : (((~generous(X0) & kind(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (generous(X0) | ~kind(X0)))) [nnf transformation 12]
54. ! [X0] : (((~generous(X0) & kind(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | generous(X0) | ~kind(X0))) [flattening 53]
55. ! [X0] : ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))) [nnf transformation 13]
76. ~rich(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 28]
77. ~strong(X0) | quiet(X0) | rich(X0) [cnf transformation 28]
78. ~rich(X0) | strong(X0) | quiet(X0) [cnf transformation 28]
79. ~quiet(X0) | strong(X0) | rich(X0) [cnf transformation 28]
96. ~calm(alice) | kind(alice) | kind(X0) | tall(X0) [cnf transformation 36]
97. calm(alice) | ~kind(alice) | kind(X0) | tall(X0) [cnf transformation 36]
103. ~patient(X0) | ~calm(X0) | rich(X0) | ~strong(X0) [cnf transformation 42]
118. ~kind(X0) | strong(X0) | ~quiet(X0) | patient(X0) [cnf transformation 50]
119. ~patient(X0) | ~kind(X0) | strong(X0) | quiet(X0) [cnf transformation 50]
120. ~patient(X0) | ~quiet(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 50]
122. ~kind(X0) | patient(X0) | ~strong(X0) | quiet(X0) [cnf transformation 50]
130. kind(X0) | calm(X0) | kind(X0) [cnf transformation 54]
133. ~patient(X0) | ~rich(X0) [cnf transformation 55]
134. patient(X0) | rich(X0) [cnf transformation 55]
160. ~tall(lucy) [cnf transformation 24]
164. calm(X0) | kind(X0) [duplicate literal removal 130]
168. 1 <=> ! [X0] : (kind(X0) | tall(X0)) [avatar definition]
169. tall(X0) | kind(X0) <- (1) [avatar component clause 168]
171. 2 <=> kind(alice) [avatar definition]
172. kind(alice) <- (2) [avatar component clause 171]
173. ~kind(alice) <- (~2) [avatar component clause 171]
175. 3 <=> calm(alice) [avatar definition]
176. ~calm(alice) <- (~3) [avatar component clause 175]
177. calm(alice) <- (3) [avatar component clause 175]
178. 1 | ~2 | 3 [avatar split clause 97,175,171,168]
179. 1 | 2 | ~3 [avatar split clause 96,175,171,168]
302. kind(alice) <- (~3) [resolution 164,176]
303. $false <- (~2, ~3) [subsumption resolution 302,173]
304. 2 | 3 [avatar contradiction clause 303]
549. 60 <=> kind(lucy) [avatar definition]
551. kind(lucy) <- (60) [avatar component clause 549]
623. 73 <=> rich(lucy) [avatar definition]
624. ~rich(lucy) <- (~73) [avatar component clause 623]
625. rich(lucy) <- (73) [avatar component clause 623]
648. ~calm(X0) | rich(X0) | ~strong(X0) | rich(X0) [resolution 103,134]
652. ~calm(X0) | rich(X0) | ~strong(X0) [duplicate literal removal 648]
673. strong(alice) | ~quiet(alice) | patient(alice) <- (2) [resolution 118,172]
675. 79 <=> patient(alice) [avatar definition]
677. patient(alice) <- (79) [avatar component clause 675]
679. 80 <=> quiet(alice) [avatar definition]
680. quiet(alice) <- (80) [avatar component clause 679]
681. ~quiet(alice) <- (~80) [avatar component clause 679]
683. 81 <=> strong(alice) [avatar definition]
684. ~strong(alice) <- (~81) [avatar component clause 683]
686. 79 | ~80 | 81 | ~2 [avatar split clause 673,171,683,679,675]
719. ~kind(X0) | strong(X0) | quiet(X0) | rich(X0) [resolution 119,134]
723. ~kind(X0) | strong(X0) | rich(X0) [subsumption resolution 719,79]
744. ~quiet(X0) | ~strong(X0) | ~kind(X0) | rich(X0) [resolution 120,134]
748. ~kind(X0) | ~quiet(X0) | rich(X0) [subsumption resolution 744,79]
775. patient(alice) | ~strong(alice) | quiet(alice) <- (2) [resolution 122,172]
795. strong(lucy) | quiet(lucy) <- (73) [resolution 625,78]
796. ~quiet(lucy) | ~strong(lucy) <- (73) [resolution 625,76]
798. 91 <=> patient(lucy) [avatar definition]
800. patient(lucy) <- (91) [avatar component clause 798]
802. 92 <=> strong(lucy) [avatar definition]
804. strong(lucy) <- (92) [avatar component clause 802]
813. 94 <=> quiet(lucy) [avatar definition]
814. ~quiet(lucy) <- (~94) [avatar component clause 813]
816. 94 | 92 | ~73 [avatar split clause 795,623,802,813]
817. ~92 | ~94 | ~73 [avatar split clause 796,623,813,802]
841. rich(alice) | ~strong(alice) <- (3) [resolution 652,177]
843. strong(alice) | rich(alice) <- (2) [resolution 723,172]
845. rich(alice) <- (2, ~81) [subsumption resolution 843,684]
935. strong(alice) | quiet(alice) <- (2, ~81) [resolution 845,78]
938. quiet(alice) <- (2, ~81) [subsumption resolution 935,684]
939. $false <- (2, ~80, ~81) [subsumption resolution 938,681]
940. ~2 | 80 | 81 [avatar contradiction clause 939]
942. 99 <=> rich(alice) [avatar definition]
944. rich(alice) <- (99) [avatar component clause 942]
946. 80 | ~81 | 79 | ~2 [avatar split clause 775,171,675,683,679]
947. 99 | 81 | ~2 [avatar split clause 843,171,683,942]
948. ~81 | 99 | ~3 [avatar split clause 841,175,942,683]
959. ~quiet(alice) | ~strong(alice) <- (99) [resolution 944,76]
961. ~strong(alice) <- (80, 99) [subsumption resolution 959,680]
964. ~81 | ~80 | ~99 [avatar split clause 961,942,679,683]
972. ~rich(alice) <- (79) [resolution 677,133]
1001. ~99 | ~79 [avatar split clause 972,675,942]
1017. kind(lucy) <- (1) [resolution 169,160]
1066. ~quiet(lucy) | rich(lucy) <- (60) [resolution 551,748]
1067. strong(lucy) | rich(lucy) <- (60) [resolution 551,723]
1068. patient(lucy) | ~strong(lucy) | quiet(lucy) <- (60) [resolution 551,122]
1069. strong(lucy) | ~quiet(lucy) | patient(lucy) <- (60) [resolution 551,118]
1078. strong(lucy) <- (60, ~73) [subsumption resolution 1067,624]
1079. 92 | ~60 | 73 [avatar split clause 1078,623,549,802]
1084. ~quiet(lucy) <- (60, ~73) [subsumption resolution 1066,624]
1085. ~94 | ~60 | 73 [avatar split clause 1084,623,549,813]
1170. ~rich(lucy) <- (91) [resolution 800,133]
1175. quiet(lucy) | rich(lucy) <- (92) [resolution 804,77]
1176. rich(lucy) <- (92, ~94) [subsumption resolution 1175,814]
1179. 73 | ~92 | 94 [avatar split clause 1176,813,802,623]
1182. ~73 | ~91 [avatar split clause 1170,798,623]
1186. 91 | ~94 | 92 | ~60 [avatar split clause 1069,549,802,813,798]
1187. 94 | ~92 | 91 | ~60 [avatar split clause 1068,549,798,802,813]
1188. 60 | ~1 [avatar split clause 1017,168,549]
1189. $false [avatar sat refutation 178,179,304,686,816,817,940,946,947,948,964,1001,1079,1085,1179,1182,1186,1187,1188]
% SZS output end Proof for 491225349294108708192595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5628
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is strong.
If lucy is both creative and not brave then someone is either strong or not kind and vice versa.
Everyone who is either not patient or tall is not creative and vice versa.
Everyone who is strong or tall is either not tall or not creative.
If someone is funny then someone is old or quiet.
Everyone who is both not brave and not old is both not old and creative and vice versa.
Everyone who is both not old and not happy is humble and vice versa.
Everyone who is both not calm and creative is either creative or wise and vice versa.
If someone is old then someone is either not quiet or tall.
Everyone who is both calm and strong is not rich or wise.
Everyone who is not wise or happy is not patient.
Everyone who is not old is both not kind and not old.
If susan is both kind and not brave then someone is patient.
Everyone who is both not creative and patient is both not old and funny.
If someone is funny then john is either strong or happy and vice versa.
Fred is happy or not strong.
Paul is wise or not old.
Paul is either not rich or curious.
Alice is calm or funny.
Someone is both not creative and not generous. | Fred is not humble. | neutral | (![X]:(patient(X)=>strong(X)))&
(((creative(lucy)&~brave(lucy)))<=>(?[X]:((strong(X)<~>~kind(X)))))&
(![X]:((~patient(X)<~>tall(X))<=>~creative(X)))&
(![X]:((strong(X)|tall(X))=>(~tall(X)<~>~creative(X))))&
((?[X]:(funny(X)))=>(?[X]:((old(X)|quiet(X)))))&
(![X]:((~brave(X)&~old(X))<=>(~old(X)&creative(X))))&
(![X]:((~old(X)&~happy(X))<=>humble(X)))&
(![X]:((~calm(X)&creative(X))<=>(creative(X)<~>wise(X))))&
((?[X]:(old(X)))=>(?[X]:((~quiet(X)<~>tall(X)))))&
(![X]:((calm(X)&strong(X))=>(~rich(X)|wise(X))))&
(![X]:((~wise(X)|happy(X))=>~patient(X)))&
(![X]:(~old(X)=>(~kind(X)&~old(X))))&
(((kind(susan)&~brave(susan)))=>(?[X]:(patient(X))))&
(![X]:((~creative(X)&patient(X))=>(~old(X)&funny(X))))&
((?[X]:(funny(X)))<=>((strong(john)<~>happy(john))))&
((happy(fred)|~strong(fred)))&
((wise(paul)|~old(paul)))&
((~rich(paul)<~>curious(paul)))&
((calm(alice)|funny(alice)))&
(?[X]:((~creative(X)&~generous(X)))) | ~humble(fred) | [] | null | 0 |
Everyone who is not tall or rich is both not wise and generous and vice versa.
If someone is not wise or not strong then someone is both not creative and creative.
Everyone who is either not funny or not quiet is either not wise or curious and vice versa.
Everyone who is either not creative or not old is both happy and not wise and vice versa.
Everyone who is not creative is funny.
Everyone who is either not wise or creative is curious and vice versa.
If alice is not patient then someone is both generous and strong.
If paul is not kind then mary is both humble and funny and vice versa.
If someone is creative or not funny then fred is both patient and quiet and vice versa.
Everyone who is rich or not happy is either not calm or not tall and vice versa.
If someone is funny then someone is happy or wise.
Everyone who is kind is both not brave and not creative.
Everyone who is either not brave or happy is either not brave or creative.
Someone is either rich or old.
John is not strong or happy.
Someone is either kind or creative.
Paul is not brave or humble.
Someone is not brave. | Mary is not tall. | contradiction | (![X]:((~tall(X)|rich(X))<=>(~wise(X)&generous(X))))&
((?[X]:((~wise(X)|~strong(X))))=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:((~funny(X)<~>~quiet(X))<=>(~wise(X)<~>curious(X))))&
(![X]:((~creative(X)<~>~old(X))<=>(happy(X)&~wise(X))))&
(![X]:(~creative(X)=>funny(X)))&
(![X]:((~wise(X)<~>creative(X))<=>curious(X)))&
((~patient(alice))=>(?[X]:((generous(X)&strong(X)))))&
((~kind(paul))<=>((humble(mary)&funny(mary))))&
((?[X]:((creative(X)|~funny(X))))<=>((patient(fred)&quiet(fred))))&
(![X]:((rich(X)|~happy(X))<=>(~calm(X)<~>~tall(X))))&
((?[X]:(funny(X)))=>(?[X]:((happy(X)|wise(X)))))&
(![X]:(kind(X)=>(~brave(X)&~creative(X))))&
(![X]:((~brave(X)<~>happy(X))=>(~brave(X)<~>creative(X))))&
(?[X]:((rich(X)<~>old(X))))&
((~strong(john)|happy(john)))&
(?[X]:((kind(X)<~>creative(X))))&
((~brave(paul)|humble(paul)))&
(?[X]:(~brave(X))) | ~tall(mary) | [
"p0",
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6117562555241998683100876
% SZS output start Proof for 6117562555241998683100876
1. ! [X0] : ((rich(X0) | ~tall(X0)) <=> (generous(X0) & ~wise(X0))) [input p0]
2. ? [X0] : (~strong(X0) | ~wise(X0)) => ? [X0] : (creative(X0) & ~creative(X0)) [input p1]
19. ~tall(mary) [input hypothesis]
20. ? [X0] : (~strong(X0) | ~wise(X0)) => ? [X1] : (creative(X1) & ~creative(X1)) [rectify 2]
22. ? [X1] : (creative(X1) & ~creative(X1)) | ! [X0] : (strong(X0) & wise(X0)) [ennf transformation 20]
28. ! [X0] : (((rich(X0) | ~tall(X0)) | (~generous(X0) | wise(X0))) & ((generous(X0) & ~wise(X0)) | (~rich(X0) & tall(X0)))) [nnf transformation 1]
29. ! [X0] : ((rich(X0) | ~tall(X0) | ~generous(X0) | wise(X0)) & ((generous(X0) & ~wise(X0)) | (~rich(X0) & tall(X0)))) [flattening 28]
30. ? [X0] : (creative(X0) & ~creative(X0)) | ! [X1] : (strong(X1) & wise(X1)) [rectify 22]
31. ? [X0] : (creative(X0) & ~creative(X0)) => (creative(sK0) & ~creative(sK0)) [choice axiom]
32. (creative(sK0) & ~creative(sK0)) | ! [X1] : (strong(X1) & wise(X1)) [skolemisation 30,31]
60. ~wise(X0) | tall(X0) [cnf transformation 29]
65. ~creative(sK0) | wise(X1) [cnf transformation 32]
67. creative(sK0) | wise(X1) [cnf transformation 32]
118. ~tall(mary) [cnf transformation 19]
125. 2 <=> creative(sK0) [avatar definition]
130. 3 <=> ! [X1] : wise(X1) [avatar definition]
131. wise(X1) <- (3) [avatar component clause 130]
132. 3 | 2 [avatar split clause 67,125,130]
134. 3 | ~2 [avatar split clause 65,125,130]
241. tall(X0) <- (3) [resolution 60,131]
242. $false <- (3) [resolution 241,118]
243. ~3 [avatar contradiction clause 242]
244. $false [avatar sat refutation 132,134,243]
% SZS output end Proof for 6117562555241998683100876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not curious then someone is both curious and kind. Everyone who is quiet or not happy is rich and vice versa. If john is both not funny and not creative then someone is not curious or generous. If someone is quiet or not rich then someone is both not curious and not patient and vice versa. Everyone who is either not patient or not old is wise or not happy and vice versa. Everyone who is calm or quiet is both not kind and happy. If someone is both funny and humble then paul is not funny and vice versa. Everyone who is either not calm or funny is kind and vice versa. If susan is calm or old then alice is either not quiet or not creative and vice versa. Everyone who is quiet or not generous is calm or humble and vice versa. Everyone who is calm is both tall and not humble. If john is either tall or kind then someone is either not old or not calm and vice versa. Everyone who is happy is calm and vice versa. Everyone who is not patient or not calm is both not humble and old and vice versa. Everyone who is patient is not quiet. Someone is not wise or rich. Paul is both brave and not creative. John is not wise or brave. Someone is not old. Someone is either wise or happy. Mary is either not rich or old. Someone is happy. | Mary is not wise. | neutral | ((?[X]:((~rich(X)|~curious(X))))=>(?[X]:((curious(X)&kind(X)))))&
(![X]:((quiet(X)|~happy(X))<=>rich(X)))&
(((~funny(john)&~creative(john)))=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((quiet(X)|~rich(X))))<=>(?[X]:((~curious(X)&~patient(X)))))&
(![X]:((~patient(X)<~>~old(X))<=>(wise(X)|~happy(X))))&
(![X]:((calm(X)|quiet(X))=>(~kind(X)&happy(X))))&
((?[X]:((funny(X)&humble(X))))<=>(~funny(paul)))&
(![X]:((~calm(X)<~>funny(X))<=>kind(X)))&
(((calm(susan)|old(susan)))<=>((~quiet(alice)<~>~creative(alice))))&
(![X]:((quiet(X)|~generous(X))<=>(calm(X)|humble(X))))&
(![X]:(calm(X)=>(tall(X)&~humble(X))))&
(((tall(john)<~>kind(john)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:(happy(X)<=>calm(X)))&
(![X]:((~patient(X)|~calm(X))<=>(~humble(X)&old(X))))&
(![X]:(patient(X)=>~quiet(X)))&
(?[X]:((~wise(X)|rich(X))))&
((brave(paul)&~creative(paul)))&
((~wise(john)|brave(john)))&
(?[X]:(~old(X)))&
(?[X]:((wise(X)<~>happy(X))))&
((~rich(mary)<~>old(mary)))&
(?[X]:(happy(X))) | ~wise(mary) | [] | null | 0 |
If someone is either old or not creative then someone is both generous and not strong and vice versa. If mary is not curious then someone is not wise. Everyone who is both curious and not old is both not happy and 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. Everyone who is happy or wise is not calm or kind and vice versa. If someone is not calm then someone is either calm or rich. Everyone who is either patient or not creative is not old and vice versa. Everyone who is either creative or happy is either brave or not kind and vice versa. Someone is either not humble or creative. Someone is both patient and not old. Alice is either rich or not happy. Paul is wise. Someone is either quiet or brave. Alice is not patient. Someone is either funny or not kind. Someone is both old and wise. | Alice is not happy. | contradiction | ((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((generous(X)&~strong(X)))))&
((~curious(mary))=>(?[X]:(~wise(X))))&
(![X]:((curious(X)&~old(X))=>(~happy(X)&~strong(X))))&
((?[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]:((happy(X)|wise(X))<=>(~calm(X)|kind(X))))&
((?[X]:(~calm(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((patient(X)<~>~creative(X))<=>~old(X)))&
(![X]:((creative(X)<~>happy(X))<=>(brave(X)<~>~kind(X))))&
(?[X]:((~humble(X)<~>creative(X))))&
(?[X]:((patient(X)&~old(X))))&
((rich(alice)<~>~happy(alice)))&
(wise(paul))&
(?[X]:((quiet(X)<~>brave(X))))&
(~patient(alice))&
(?[X]:((funny(X)<~>~kind(X))))&
(?[X]:((old(X)&wise(X)))) | ~happy(alice) | [
"p6",
"p9",
"p11",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 228598418181089577888577
% SZS output start Proof for 228598418181089577888577
7. ! [X0] : ((~old(X0) <~> ~kind(X0)) => (brave(X0) & ~old(X0))) [input p6]
10. ! [X0] : ((brave(X0) | ~old(X0)) => (~old(X0) & ~funny(X0))) [input p9]
12. ! [X0] : (~brave(X0) <=> (~old(X0) | ~curious(X0))) [input p11]
15. ! [X0] : ((patient(X0) <~> ~creative(X0)) <=> ~old(X0)) [input p14]
16. ! [X0] : ((creative(X0) <~> happy(X0)) <=> (brave(X0) <~> ~kind(X0))) [input p15]
22. ~patient(alice) [input p21]
25. ~happy(alice) [input hypothesis]
34. ! [X0] : ((brave(X0) & ~old(X0)) | (~old(X0) <=> ~kind(X0))) [ennf transformation 7]
38. ! [X0] : ((~old(X0) & ~funny(X0)) | (~brave(X0) & old(X0))) [ennf transformation 10]
54. ! [X0] : ((brave(X0) & ~old(X0)) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 34]
58. ! [X0] : ((~brave(X0) | (old(X0) & curious(X0))) & ((~old(X0) | ~curious(X0)) | brave(X0))) [nnf transformation 12]
59. ! [X0] : ((~brave(X0) | (old(X0) & curious(X0))) & (~old(X0) | ~curious(X0) | brave(X0))) [flattening 58]
66. ! [X0] : ((((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | old(X0)) & (~old(X0) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0))))) [nnf transformation 15]
67. ! [X0] : ((((~happy(X0) | ~creative(X0)) & (happy(X0) | creative(X0))) | ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0)))) & (((kind(X0) | ~brave(X0)) & (~kind(X0) | brave(X0))) | ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0))))) [nnf transformation 16]
102. ~old(X0) | ~old(X0) | kind(X0) [cnf transformation 54]
103. ~kind(X0) | brave(X0) | old(X0) [cnf transformation 54]
112. ~brave(X0) | ~old(X0) [cnf transformation 38]
118. ~brave(X0) | old(X0) [cnf transformation 59]
126. ~old(X0) | patient(X0) | creative(X0) [cnf transformation 66]
127. ~creative(X0) | patient(X0) | old(X0) [cnf transformation 66]
129. ~kind(X0) | brave(X0) | happy(X0) | ~creative(X0) [cnf transformation 67]
134. happy(X0) | creative(X0) | brave(X0) | kind(X0) [cnf transformation 67]
146. ~patient(alice) [cnf transformation 22]
151. ~happy(alice) [cnf transformation 25]
152. ~old(X0) | kind(X0) [duplicate literal removal 102]
236. ~brave(X0) [subsumption resolution 118,112]
252. kind(X0) | creative(X0) | happy(X0) [subsumption resolution 134,236]
254. ~kind(X0) | happy(X0) | ~creative(X0) [subsumption resolution 129,236]
270. 25 <=> happy(alice) [avatar definition]
271. ~happy(alice) <- (~25) [avatar component clause 270]
286. ~25 [avatar split clause 151,270]
365. creative(X1) | happy(X1) | brave(X1) | old(X1) [resolution 252,103]
376. happy(X1) | creative(X1) | old(X1) [subsumption resolution 365,236]
478. 48 <=> creative(alice) [avatar definition]
480. creative(alice) <- (48) [avatar component clause 478]
484. creative(alice) | old(alice) <- (~25) [resolution 376,271]
491. 49 <=> old(alice) [avatar definition]
493. old(alice) <- (49) [avatar component clause 491]
494. 49 | 48 | 25 [avatar split clause 484,270,478,491]
551. patient(alice) | old(alice) <- (48) [resolution 480,127]
553. old(alice) <- (48) [subsumption resolution 551,146]
554. 49 | ~48 [avatar split clause 553,478,491]
556. patient(alice) | creative(alice) <- (49) [resolution 493,126]
560. kind(alice) <- (49) [resolution 493,152]
681. happy(alice) | ~creative(alice) <- (49) [resolution 560,254]
685. ~creative(alice) <- (~25, 49) [subsumption resolution 681,271]
688. ~48 | 25 | ~49 [avatar split clause 685,491,270,478]
689. creative(alice) <- (49) [subsumption resolution 556,146]
690. 48 | ~49 [avatar split clause 689,491,478]
692. $false [avatar sat refutation 286,494,554,688,690]
% SZS output end Proof for 228598418181089577888577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not calm is both rich and not patient. If someone is old then john is both generous and not creative. Everyone who is both strong and not generous is both tall and not funny. Everyone who is patient or not patient is not quiet and vice versa. Everyone who is either humble or not generous is both not funny and not brave. If john is both not tall and not happy then alice is both not creative and not happy. If someone is tall or not patient then someone is happy or not curious. Everyone who is both not strong and calm is both calm and not old and vice versa. If mary is either kind or not old then fred is either calm or strong and vice versa. If someone is not tall then paul is both not funny and not patient and vice versa. If someone is strong or brave then fred is not wise. Everyone who is patient or not strong is both curious and not calm and vice versa. If john is either generous or quiet then fred is not funny. Everyone who is either not brave or not calm is both curious and wise. Everyone who is not old or not rich is not humble and vice versa. Everyone who is both funny and not brave is both not strong and not generous. Mary is either not kind or not patient. Someone is either not humble or not wise. Someone is patient or creative. Someone is either brave or wise. Alice is both not rich and not wise. Someone is not tall. Susan is not strong. | John is not creative. | neutral | (![X]:((patient(X)<~>~calm(X))=>(rich(X)&~patient(X))))&
((?[X]:(old(X)))=>((generous(john)&~creative(john))))&
(![X]:((strong(X)&~generous(X))=>(tall(X)&~funny(X))))&
(![X]:((patient(X)|~patient(X))<=>~quiet(X)))&
(![X]:((humble(X)<~>~generous(X))=>(~funny(X)&~brave(X))))&
(((~tall(john)&~happy(john)))=>((~creative(alice)&~happy(alice))))&
((?[X]:((tall(X)|~patient(X))))=>(?[X]:((happy(X)|~curious(X)))))&
(![X]:((~strong(X)&calm(X))<=>(calm(X)&~old(X))))&
(((kind(mary)<~>~old(mary)))<=>((calm(fred)<~>strong(fred))))&
((?[X]:(~tall(X)))<=>((~funny(paul)&~patient(paul))))&
((?[X]:((strong(X)|brave(X))))=>(~wise(fred)))&
(![X]:((patient(X)|~strong(X))<=>(curious(X)&~calm(X))))&
(((generous(john)<~>quiet(john)))=>(~funny(fred)))&
(![X]:((~brave(X)<~>~calm(X))=>(curious(X)&wise(X))))&
(![X]:((~old(X)|~rich(X))<=>~humble(X)))&
(![X]:((funny(X)&~brave(X))=>(~strong(X)&~generous(X))))&
((~kind(mary)<~>~patient(mary)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(?[X]:((patient(X)|creative(X))))&
(?[X]:((brave(X)<~>wise(X))))&
((~rich(alice)&~wise(alice)))&
(?[X]:(~tall(X)))&
(~strong(susan)) | ~creative(john) | [] | null | 0 |
Everyone who is either funny or not humble is both humble and rich.
Everyone who is both rich and not tall is either not tall or kind.
Everyone who is both not calm and strong is both rich and not calm and vice versa.
If lucy is not strong or calm then fred is happy or not patient.
If lucy is both not tall and not curious then john is both not creative and curious and vice versa.
Everyone who is creative is both calm and curious.
Everyone who is either not creative or calm is both not happy and funny.
Everyone who is both generous and curious is both not old and patient.
Everyone who is curious is not old or patient.
If mary is not rich or not brave then susan is both calm and patient.
If someone is either not strong or patient then susan is patient or humble.
If john is not strong or not patient then someone is either funny or not quiet.
Everyone who is calm or not wise is happy and vice versa.
Everyone who is not kind or creative is not calm or strong.
Everyone who is not happy is not old and vice versa.
Everyone who is either strong or curious is both creative and not brave and vice versa.
Alice is either not rich or curious.
Susan is either not creative or tall.
Lucy is both not kind and not happy.
Alice is either funny or not quiet.
Someone is tall or not wise.
Someone is not brave.
Someone is both generous and wise. | Susan is creative. | contradiction | (![X]:((funny(X)<~>~humble(X))=>(humble(X)&rich(X))))&
(![X]:((rich(X)&~tall(X))=>(~tall(X)<~>kind(X))))&
(![X]:((~calm(X)&strong(X))<=>(rich(X)&~calm(X))))&
(((~strong(lucy)|calm(lucy)))=>((happy(fred)|~patient(fred))))&
(((~tall(lucy)&~curious(lucy)))<=>((~creative(john)&curious(john))))&
(![X]:(creative(X)=>(calm(X)&curious(X))))&
(![X]:((~creative(X)<~>calm(X))=>(~happy(X)&funny(X))))&
(![X]:((generous(X)&curious(X))=>(~old(X)&patient(X))))&
(![X]:(curious(X)=>(~old(X)|patient(X))))&
(((~rich(mary)|~brave(mary)))=>((calm(susan)&patient(susan))))&
((?[X]:((~strong(X)<~>patient(X))))=>((patient(susan)|humble(susan))))&
(((~strong(john)|~patient(john)))=>(?[X]:((funny(X)<~>~quiet(X)))))&
(![X]:((calm(X)|~wise(X))<=>happy(X)))&
(![X]:((~kind(X)|creative(X))=>(~calm(X)|strong(X))))&
(![X]:(~happy(X)<=>~old(X)))&
(![X]:((strong(X)<~>curious(X))<=>(creative(X)&~brave(X))))&
((~rich(alice)<~>curious(alice)))&
((~creative(susan)<~>tall(susan)))&
((~kind(lucy)&~happy(lucy)))&
((funny(alice)<~>~quiet(alice)))&
(?[X]:((tall(X)|~wise(X))))&
(?[X]:(~brave(X)))&
(?[X]:((generous(X)&wise(X)))) | creative(susan) | [
"p5",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 839959972194245931985686
% SZS output start Proof for 839959972194245931985686
6. ! [X0] : (creative(X0) => (curious(X0) & calm(X0))) [input p5]
7. ! [X0] : ((~creative(X0) <~> calm(X0)) => (funny(X0) & ~happy(X0))) [input p6]
13. ! [X0] : ((~wise(X0) | calm(X0)) <=> happy(X0)) [input p12]
24. creative(susan) [input hypothesis]
30. ! [X0] : ((curious(X0) & calm(X0)) | ~creative(X0)) [ennf transformation 6]
31. ! [X0] : ((funny(X0) & ~happy(X0)) | (~creative(X0) <=> calm(X0))) [ennf transformation 7]
48. ! [X0] : ((funny(X0) & ~happy(X0)) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0)))) [nnf transformation 31]
53. ! [X0] : (((~wise(X0) | calm(X0)) | ~happy(X0)) & (happy(X0) | (wise(X0) & ~calm(X0)))) [nnf transformation 13]
54. ! [X0] : ((~wise(X0) | calm(X0) | ~happy(X0)) & (happy(X0) | (wise(X0) & ~calm(X0)))) [flattening 53]
83. ~creative(X0) | calm(X0) [cnf transformation 30]
86. ~happy(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 48]
102. ~calm(X0) | happy(X0) [cnf transformation 54]
127. creative(susan) [cnf transformation 24]
170. ~creative(X0) | ~happy(X0) [subsumption resolution 86,83]
187. 12 <=> calm(susan) [avatar definition]
189. calm(susan) <- (12) [avatar component clause 187]
240. 22 <=> creative(susan) [avatar definition]
242. creative(susan) <- (22) [avatar component clause 240]
268. 22 [avatar split clause 127,240]
269. calm(susan) <- (22) [resolution 83,242]
270. 12 | ~22 [avatar split clause 269,240,187]
272. happy(susan) <- (12) [resolution 102,189]
280. ~happy(susan) <- (22) [resolution 170,242]
281. $false <- (12, 22) [subsumption resolution 280,272]
282. ~12 | ~22 [avatar contradiction clause 281]
283. $false [avatar sat refutation 268,270,282]
% SZS output end Proof for 839959972194245931985686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 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. | John is wise. | entailment | (![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))) | wise(john) | [
"p2",
"p3",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5404198144598260916219512
% SZS output start Proof for 5404198144598260916219512
3. ! [X0] : (tall(X0) <=> funny(X0)) [input p2]
4. ! [X0] : ((~tall(X0) <~> funny(X0)) => humble(X0)) [input p3]
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. ~wise(john) [input hypothesis]
29. ! [X0] : (humble(X0) | (~tall(X0) <=> funny(X0))) [ennf transformation 4]
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]
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]
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. ~wise(john) [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]
289. ~generous(X0) | ~patient(X0) [subsumption resolution 120,154]
352. ~patient(X0) | wise(X0) [resolution 289,151]
353. wise(X0) [subsumption resolution 352,118]
357. $false [resolution 353,149]
% SZS output end Proof for 5404198144598260916219512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 then mary is both happy and creative and vice versa. Everyone who is either not old or not funny is either not strong or not wise and vice versa. Everyone who is either calm or not strong is both old and creative. Everyone who is not strong or quiet is both quiet and old. If someone is not rich then lucy is both tall and not kind. Everyone who is not rich or not quiet is both not tall and kind and vice versa. Everyone who is both not wise and not curious is not happy and vice versa. Everyone who is either creative or kind is patient or creative. Everyone who is curious is not humble. Everyone who is not patient or not strong is old or not patient and vice versa. Everyone who is either not calm or calm is either not creative or generous. Everyone who is calm or not calm is calm or brave. Everyone who is patient is tall. Everyone who is both not calm and not strong is patient. Everyone who is not strong or not happy is not wise. If someone is both old and generous then someone is happy or tall and vice versa. John is brave or old. Paul is calm or tall. Fred is both not tall and not creative. Someone is both not creative and not calm. Someone is not rich or not creative. Someone is either not curious or not creative. Lucy is either wise or calm. Someone is tall or curious. | Fred is rich. | entailment | ((?[X]:(~brave(X)))<=>((happy(mary)&creative(mary))))&
(![X]:((~old(X)<~>~funny(X))<=>(~strong(X)<~>~wise(X))))&
(![X]:((calm(X)<~>~strong(X))=>(old(X)&creative(X))))&
(![X]:((~strong(X)|quiet(X))=>(quiet(X)&old(X))))&
((?[X]:(~rich(X)))=>((tall(lucy)&~kind(lucy))))&
(![X]:((~rich(X)|~quiet(X))<=>(~tall(X)&kind(X))))&
(![X]:((~wise(X)&~curious(X))<=>~happy(X)))&
(![X]:((creative(X)<~>kind(X))=>(patient(X)|creative(X))))&
(![X]:(curious(X)=>~humble(X)))&
(![X]:((~patient(X)|~strong(X))<=>(old(X)|~patient(X))))&
(![X]:((~calm(X)<~>calm(X))=>(~creative(X)<~>generous(X))))&
(![X]:((calm(X)|~calm(X))=>(calm(X)|brave(X))))&
(![X]:(patient(X)=>tall(X)))&
(![X]:((~calm(X)&~strong(X))=>patient(X)))&
(![X]:((~strong(X)|~happy(X))=>~wise(X)))&
((?[X]:((old(X)&generous(X))))<=>(?[X]:((happy(X)|tall(X)))))&
((brave(john)|old(john)))&
((calm(paul)|tall(paul)))&
((~tall(fred)&~creative(fred)))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((~curious(X)<~>~creative(X))))&
((wise(lucy)<~>calm(lucy)))&
(?[X]:((tall(X)|curious(X)))) | rich(fred) | [
"p5",
"p7",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1685079758606675358729624
% SZS output start Proof for 1685079758606675358729624
6. ! [X0] : ((~quiet(X0) | ~rich(X0)) <=> (kind(X0) & ~tall(X0))) [input p5]
8. ! [X0] : ((creative(X0) <~> kind(X0)) => (creative(X0) | patient(X0))) [input p7]
13. ! [X0] : (patient(X0) => tall(X0)) [input p12]
19. ~creative(fred) & ~tall(fred) [input p18]
25. ~rich(fred) [input hypothesis]
31. ! [X0] : ((creative(X0) | patient(X0)) | (creative(X0) <=> kind(X0))) [ennf transformation 8]
32. ! [X0] : (creative(X0) | patient(X0) | (creative(X0) <=> kind(X0))) [flattening 31]
36. ! [X0] : (tall(X0) | ~patient(X0)) [ennf transformation 13]
47. ! [X0] : (((~quiet(X0) | ~rich(X0)) | (~kind(X0) | tall(X0))) & ((kind(X0) & ~tall(X0)) | (quiet(X0) & rich(X0)))) [nnf transformation 6]
48. ! [X0] : ((~quiet(X0) | ~rich(X0) | ~kind(X0) | tall(X0)) & ((kind(X0) & ~tall(X0)) | (quiet(X0) & rich(X0)))) [flattening 47]
51. ! [X0] : (creative(X0) | patient(X0) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0)))) [nnf transformation 32]
91. ~tall(X0) | rich(X0) [cnf transformation 48]
93. kind(X0) | rich(X0) [cnf transformation 48]
100. creative(X0) | patient(X0) | creative(X0) | ~kind(X0) [cnf transformation 51]
111. ~patient(X0) | tall(X0) [cnf transformation 36]
123. ~creative(fred) [cnf transformation 19]
132. ~rich(fred) [cnf transformation 25]
138. ~kind(X0) | patient(X0) | creative(X0) [duplicate literal removal 100]
332. patient(X1) | creative(X1) | rich(X1) [resolution 138,93]
490. creative(X1) | rich(X1) | tall(X1) [resolution 332,111]
491. rich(X1) | creative(X1) [subsumption resolution 490,91]
510. creative(fred) [resolution 491,132]
511. $false [subsumption resolution 510,123]
% SZS output end Proof for 1685079758606675358729624
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is both curious and not quiet and vice versa. Everyone who is either old or not old is both not creative and happy and vice versa. Everyone who is creative is not brave and vice versa. If someone is either funny or not humble then john is either not brave or humble and vice versa. If someone is happy then fred is both tall and not creative and vice versa. Everyone who is both not brave and not tall is both funny and not funny. Everyone who is not kind is not quiet and vice versa. If someone is both funny and tall then someone is not kind and vice versa. If someone is wise or kind then mary is not kind or kind and vice versa. Everyone who is either not brave or generous is both not old and rich and vice versa. If john is not patient then lucy is not funny or not quiet. Everyone who is either creative or curious is wise. If alice is both not happy and old then someone is either old or curious and vice versa. If mary is either wise or not funny then someone is not patient and vice versa. If john is happy or tall then mary is both brave and not creative and vice versa. If fred is not generous then susan is both not brave and not curious and vice versa. Someone is happy or not quiet. Someone is not strong. Someone is not funny or creative. Someone is not humble. Alice is not calm or rich. Mary is not generous or not creative. | John is tall. | neutral | (![X]:(calm(X)<=>(curious(X)&~quiet(X))))&
(![X]:((old(X)<~>~old(X))<=>(~creative(X)&happy(X))))&
(![X]:(creative(X)<=>~brave(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>((~brave(john)<~>humble(john))))&
((?[X]:(happy(X)))<=>((tall(fred)&~creative(fred))))&
(![X]:((~brave(X)&~tall(X))=>(funny(X)&~funny(X))))&
(![X]:(~kind(X)<=>~quiet(X)))&
((?[X]:((funny(X)&tall(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((wise(X)|kind(X))))<=>((~kind(mary)|kind(mary))))&
(![X]:((~brave(X)<~>generous(X))<=>(~old(X)&rich(X))))&
((~patient(john))=>((~funny(lucy)|~quiet(lucy))))&
(![X]:((creative(X)<~>curious(X))=>wise(X)))&
(((~happy(alice)&old(alice)))<=>(?[X]:((old(X)<~>curious(X)))))&
(((wise(mary)<~>~funny(mary)))<=>(?[X]:(~patient(X))))&
(((happy(john)|tall(john)))<=>((brave(mary)&~creative(mary))))&
((~generous(fred))<=>((~brave(susan)&~curious(susan))))&
(?[X]:((happy(X)|~quiet(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~funny(X)|creative(X))))&
(?[X]:(~humble(X)))&
((~calm(alice)|rich(alice)))&
((~generous(mary)|~creative(mary))) | tall(john) | [] | null | 0 |
If lucy is either strong or funny then someone is creative or tall and vice versa.
If someone is either not generous or not funny then mary is not brave.
If someone is happy then alice is humble or happy and vice versa.
If fred is both calm and strong then fred is both wise and not calm.
Everyone who is either not calm or quiet is both old and not humble.
Everyone who is either not kind or tall is either old or not wise.
Everyone who is not strong or patient is either not old or kind.
Everyone who is not funny or not tall is both tall and not brave and vice versa.
If paul is brave or patient then someone is either strong or not happy and vice versa.
Everyone who is both tall and kind is either wise or old and vice versa.
If someone is old then someone is both not calm and not tall and vice versa.
If someone is both creative and not funny then paul is both generous and funny.
Everyone who is both calm and not kind is either not humble or not funny and vice versa.
Everyone who is both not humble and happy is not old or generous and vice versa.
If paul is both not quiet and happy then alice is not rich and vice versa.
If someone is not strong or calm then susan is curious.
Someone is either calm or not brave.
Someone is either calm or kind.
Someone is either strong or calm.
Paul is not strong.
Someone is both strong and happy.
Someone is both not generous and strong.
Fred is either not brave or not happy.
Someone is either not happy or curious. | Alice is old. | contradiction | (((strong(lucy)<~>funny(lucy)))<=>(?[X]:((creative(X)|tall(X)))))&
((?[X]:((~generous(X)<~>~funny(X))))=>(~brave(mary)))&
((?[X]:(happy(X)))<=>((humble(alice)|happy(alice))))&
(((calm(fred)&strong(fred)))=>((wise(fred)&~calm(fred))))&
(![X]:((~calm(X)<~>quiet(X))=>(old(X)&~humble(X))))&
(![X]:((~kind(X)<~>tall(X))=>(old(X)<~>~wise(X))))&
(![X]:((~strong(X)|patient(X))=>(~old(X)<~>kind(X))))&
(![X]:((~funny(X)|~tall(X))<=>(tall(X)&~brave(X))))&
(((brave(paul)|patient(paul)))<=>(?[X]:((strong(X)<~>~happy(X)))))&
(![X]:((tall(X)&kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:(old(X)))<=>(?[X]:((~calm(X)&~tall(X)))))&
((?[X]:((creative(X)&~funny(X))))=>((generous(paul)&funny(paul))))&
(![X]:((calm(X)&~kind(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((~humble(X)&happy(X))<=>(~old(X)|generous(X))))&
(((~quiet(paul)&happy(paul)))<=>(~rich(alice)))&
((?[X]:((~strong(X)|calm(X))))=>(curious(susan)))&
(?[X]:((calm(X)<~>~brave(X))))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((strong(X)<~>calm(X))))&
(~strong(paul))&
(?[X]:((strong(X)&happy(X))))&
(?[X]:((~generous(X)&strong(X))))&
((~brave(fred)<~>~happy(fred)))&
(?[X]:((~happy(X)<~>curious(X)))) | old(alice) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2909081563785224242867530
% SZS output start Proof for 2909081563785224242867530
8. ! [X0] : ((~tall(X0) | ~funny(X0)) <=> (~brave(X0) & tall(X0))) [input p7]
11. ? [X0] : old(X0) <=> ? [X0] : (~tall(X0) & ~calm(X0)) [input p10]
25. old(alice) [input hypothesis]
26. ? [X0] : old(X0) <=> ? [X1] : (~tall(X1) & ~calm(X1)) [rectify 11]
48. ! [X0] : (((~tall(X0) | ~funny(X0)) | (brave(X0) | ~tall(X0))) & ((~brave(X0) & tall(X0)) | (tall(X0) & funny(X0)))) [nnf transformation 8]
49. ! [X0] : ((~tall(X0) | ~funny(X0) | brave(X0) | ~tall(X0)) & ((~brave(X0) & tall(X0)) | (tall(X0) & funny(X0)))) [flattening 48]
57. (? [X0] : old(X0) | ! [X1] : (tall(X1) | calm(X1))) & (? [X1] : (~tall(X1) & ~calm(X1)) | ! [X0] : ~old(X0)) [nnf transformation 26]
58. (? [X0] : old(X0) | ! [X1] : (tall(X1) | calm(X1))) & (? [X2] : (~tall(X2) & ~calm(X2)) | ! [X3] : ~old(X3)) [rectify 57]
59. ? [X0] : old(X0) => old(sK3) [choice axiom]
60. ? [X2] : (~tall(X2) & ~calm(X2)) => (~tall(sK4) & ~calm(sK4)) [choice axiom]
61. (old(sK3) | ! [X1] : (tall(X1) | calm(X1))) & ((~tall(sK4) & ~calm(sK4)) | ! [X3] : ~old(X3)) [skolemisation 58,60,59]
111. tall(X0) | tall(X0) [cnf transformation 49]
128. ~tall(sK4) | ~old(X3) [cnf transformation 61]
163. old(alice) [cnf transformation 25]
164. tall(X0) [duplicate literal removal 111]
269. ~old(X3) [subsumption resolution 128,164]
340. $false [subsumption resolution 163,269]
% SZS output end Proof for 2909081563785224242867530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or rich then someone is both not rich and not old and vice versa. If someone is not brave then fred is not tall. Everyone who is either rich or not generous is not humble or not calm. If fred is either not creative or not happy then someone is not creative and vice versa. Everyone who is not strong is strong. Everyone who is not kind or humble is either not tall or funny. If fred is either not happy or not humble then susan is not wise or generous. If someone is either not patient or old then john is old. Everyone who is strong is not happy and vice versa. Everyone who is both happy and humble is both not wise and not old. If someone is not curious then someone is both strong and patient. If someone is not strong or not calm then fred is either not tall or curious and vice versa. Everyone who is old or not old is not wise. Everyone who is not rich or quiet is not funny. Everyone who is both not curious and curious is both kind and tall and vice versa. If someone is not creative then someone is not quiet or creative and vice versa. Someone is calm. Someone is both not kind and not wise. Someone is funny. Someone is generous or patient. Someone is humble or not creative. Mary is not rich or happy. Someone is not old. Someone is either curious or not creative. | Fred is not happy. | entailment | ((?[X]:((~calm(X)|rich(X))))<=>(?[X]:((~rich(X)&~old(X)))))&
((?[X]:(~brave(X)))=>(~tall(fred)))&
(![X]:((rich(X)<~>~generous(X))=>(~humble(X)|~calm(X))))&
(((~creative(fred)<~>~happy(fred)))<=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)=>strong(X)))&
(![X]:((~kind(X)|humble(X))=>(~tall(X)<~>funny(X))))&
(((~happy(fred)<~>~humble(fred)))=>((~wise(susan)|generous(susan))))&
((?[X]:((~patient(X)<~>old(X))))=>(old(john)))&
(![X]:(strong(X)<=>~happy(X)))&
(![X]:((happy(X)&humble(X))=>(~wise(X)&~old(X))))&
((?[X]:(~curious(X)))=>(?[X]:((strong(X)&patient(X)))))&
((?[X]:((~strong(X)|~calm(X))))<=>((~tall(fred)<~>curious(fred))))&
(![X]:((old(X)|~old(X))=>~wise(X)))&
(![X]:((~rich(X)|quiet(X))=>~funny(X)))&
(![X]:((~curious(X)&curious(X))<=>(kind(X)&tall(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~quiet(X)|creative(X)))))&
(?[X]:(calm(X)))&
(?[X]:((~kind(X)&~wise(X))))&
(?[X]:(funny(X)))&
(?[X]:((generous(X)|patient(X))))&
(?[X]:((humble(X)|~creative(X))))&
((~rich(mary)|happy(mary)))&
(?[X]:(~old(X)))&
(?[X]:((curious(X)<~>~creative(X)))) | ~happy(fred) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3458044149974083932111018
% SZS output start Proof for 3458044149974083932111018
5. ! [X0] : (~strong(X0) => strong(X0)) [input p4]
9. ! [X0] : (strong(X0) <=> ~happy(X0)) [input p8]
25. happy(fred) [input hypothesis]
36. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 5]
55. ! [X0] : ((strong(X0) | happy(X0)) & (~happy(X0) | ~strong(X0))) [nnf transformation 9]
96. strong(X0) | strong(X0) [cnf transformation 36]
103. ~happy(X0) | ~strong(X0) [cnf transformation 55]
132. happy(fred) [cnf transformation 25]
133. strong(X0) [duplicate literal removal 96]
195. ~happy(X0) [subsumption resolution 103,133]
273. $false [subsumption resolution 132,195]
% SZS output end Proof for 3458044149974083932111018
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either curious or kind then someone is curious and vice versa. If someone is not curious then mary is not patient. Everyone who is either not humble or not brave is both happy and not creative and vice versa. If someone is either not brave or wise then susan is both not wise and kind and vice versa. Everyone who is not creative is not quiet or humble and vice versa. Everyone who is both not old and not calm is old and vice versa. Everyone who is either not quiet or wise is calm. If alice is tall then someone is not old or calm and vice versa. Everyone who is not curious or not generous is not creative or not wise and vice versa. If someone is not humble then someone is both not old and strong. Everyone who is not patient is brave or not calm. If someone is tall then lucy is either not brave or not strong. Everyone who is not brave is old or quiet and vice versa. If someone is both not happy and not humble then someone is not old and vice versa. If someone is humble then someone is both humble and not humble and vice versa. If someone is both not rich and not patient then mary is not happy and vice versa. Fred is both not generous and not brave. Alice is not funny. Alice is kind. Someone is both curious and not kind. Alice is either calm or not brave. Someone is either not happy or not patient. | Fred is wise. | contradiction | (((curious(lucy)<~>kind(lucy)))<=>(?[X]:(curious(X))))&
((?[X]:(~curious(X)))=>(~patient(mary)))&
(![X]:((~humble(X)<~>~brave(X))<=>(happy(X)&~creative(X))))&
((?[X]:((~brave(X)<~>wise(X))))<=>((~wise(susan)&kind(susan))))&
(![X]:(~creative(X)<=>(~quiet(X)|humble(X))))&
(![X]:((~old(X)&~calm(X))<=>old(X)))&
(![X]:((~quiet(X)<~>wise(X))=>calm(X)))&
((tall(alice))<=>(?[X]:((~old(X)|calm(X)))))&
(![X]:((~curious(X)|~generous(X))<=>(~creative(X)|~wise(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(~patient(X)=>(brave(X)|~calm(X))))&
((?[X]:(tall(X)))=>((~brave(lucy)<~>~strong(lucy))))&
(![X]:(~brave(X)<=>(old(X)|quiet(X))))&
((?[X]:((~happy(X)&~humble(X))))<=>(?[X]:(~old(X))))&
((?[X]:(humble(X)))<=>(?[X]:((humble(X)&~humble(X)))))&
((?[X]:((~rich(X)&~patient(X))))<=>(~happy(mary)))&
((~generous(fred)&~brave(fred)))&
(~funny(alice))&
(kind(alice))&
(?[X]:((curious(X)&~kind(X))))&
((calm(alice)<~>~brave(alice)))&
(?[X]:((~happy(X)<~>~patient(X)))) | wise(fred) | [
"p4",
"p5",
"p8",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8750690781548052456135873
% SZS output start Proof for 8750690781548052456135873
5. ! [X0] : (~creative(X0) <=> (humble(X0) | ~quiet(X0))) [input p4]
6. ! [X0] : ((~calm(X0) & ~old(X0)) <=> old(X0)) [input p5]
9. ! [X0] : ((~generous(X0) | ~curious(X0)) <=> (~wise(X0) | ~creative(X0))) [input p8]
13. ! [X0] : (~brave(X0) <=> (quiet(X0) | old(X0))) [input p12]
15. ? [X0] : humble(X0) <=> ? [X0] : (~humble(X0) & humble(X0)) [input p14]
17. ~brave(fred) & ~generous(fred) [input p16]
23. wise(fred) [input hypothesis]
26. ? [X0] : humble(X0) <=> ? [X1] : (~humble(X1) & humble(X1)) [rectify 15]
45. ! [X0] : ((~creative(X0) | (~humble(X0) & quiet(X0))) & ((humble(X0) | ~quiet(X0)) | creative(X0))) [nnf transformation 5]
46. ! [X0] : ((~creative(X0) | (~humble(X0) & quiet(X0))) & (humble(X0) | ~quiet(X0) | creative(X0))) [flattening 45]
47. ! [X0] : (((~calm(X0) & ~old(X0)) | ~old(X0)) & (old(X0) | (calm(X0) | old(X0)))) [nnf transformation 6]
48. ! [X0] : (((~calm(X0) & ~old(X0)) | ~old(X0)) & (old(X0) | calm(X0) | old(X0))) [flattening 47]
54. ! [X0] : (((~generous(X0) | ~curious(X0)) | (wise(X0) & creative(X0))) & ((~wise(X0) | ~creative(X0)) | (generous(X0) & curious(X0)))) [nnf transformation 9]
55. ! [X0] : ((~generous(X0) | ~curious(X0) | (wise(X0) & creative(X0))) & (~wise(X0) | ~creative(X0) | (generous(X0) & curious(X0)))) [flattening 54]
60. ! [X0] : ((~brave(X0) | (~quiet(X0) & ~old(X0))) & ((quiet(X0) | old(X0)) | brave(X0))) [nnf transformation 13]
61. ! [X0] : ((~brave(X0) | (~quiet(X0) & ~old(X0))) & (quiet(X0) | old(X0) | brave(X0))) [flattening 60]
67. (? [X0] : humble(X0) | ! [X1] : (humble(X1) | ~humble(X1))) & (? [X1] : (~humble(X1) & humble(X1)) | ! [X0] : ~humble(X0)) [nnf transformation 26]
68. (? [X0] : humble(X0) | ! [X1] : (humble(X1) | ~humble(X1))) & (? [X2] : (~humble(X2) & humble(X2)) | ! [X3] : ~humble(X3)) [rectify 67]
69. ? [X0] : humble(X0) => humble(sK6) [choice axiom]
70. ? [X2] : (~humble(X2) & humble(X2)) => (~humble(sK7) & humble(sK7)) [choice axiom]
71. (humble(sK6) | ! [X1] : (humble(X1) | ~humble(X1))) & ((~humble(sK7) & humble(sK7)) | ! [X3] : ~humble(X3)) [skolemisation 68,70,69]
99. ~quiet(X0) | humble(X0) | creative(X0) [cnf transformation 46]
103. ~old(X0) | ~old(X0) [cnf transformation 48]
111. ~wise(X0) | ~creative(X0) | generous(X0) [cnf transformation 55]
119. quiet(X0) | old(X0) | brave(X0) [cnf transformation 61]
125. humble(sK7) | ~humble(X3) [cnf transformation 71]
126. ~humble(sK7) | ~humble(X3) [cnf transformation 71]
131. ~generous(fred) [cnf transformation 17]
132. ~brave(fred) [cnf transformation 17]
140. wise(fred) [cnf transformation 23]
142. ~old(X0) [duplicate literal removal 103]
222. quiet(X0) | brave(X0) [subsumption resolution 119,142]
226. 18 <=> ! [X3] : ~humble(X3) [avatar definition]
227. ~humble(X3) <- (18) [avatar component clause 226]
229. 19 <=> humble(sK7) [avatar definition]
232. 18 | ~19 [avatar split clause 126,229,226]
233. 18 | 19 [avatar split clause 125,229,226]
282. humble(X0) | creative(X0) | brave(X0) [resolution 99,222]
283. creative(X0) | brave(X0) <- (18) [subsumption resolution 282,227]
290. ~creative(fred) | generous(fred) [resolution 111,140]
291. ~creative(fred) [subsumption resolution 290,131]
292. brave(fred) <- (18) [resolution 291,283]
293. $false <- (18) [subsumption resolution 292,132]
294. ~18 [avatar contradiction clause 293]
295. $false [avatar sat refutation 232,233,294]
% SZS output end Proof for 8750690781548052456135873
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not creative is tall or patient and vice versa. Everyone who is either humble or old is either not strong or curious. Everyone who is both rich and not patient is both not old and brave and vice versa. Everyone who is rich is either not brave or brave. If someone is both not happy and rich then paul is humble and vice versa. If john is both not patient and not old then someone is both wise and not patient and vice versa. If someone is quiet or not brave then someone is not strong. Everyone who is kind or happy is both strong and quiet. Everyone who is either curious or kind is either humble or not creative and vice versa. If someone is not creative then someone is not calm and vice versa. If fred is either not wise or not humble then susan is brave and vice versa. If someone is both not creative and not rich then paul is either not wise or not calm. If someone is either not patient or not generous then susan is both creative and wise and vice versa. If fred is both funny and not creative then lucy is old and vice versa. Everyone who is both brave and not old is not funny or happy and vice versa. Everyone who is either happy or not wise is both rich and tall. Alice is either old or not generous. Someone is both calm and rich. Someone is kind or not old. Someone is not happy. Someone is either curious or funny. Someone is not generous. Someone is either happy or rich. Someone is not creative. | John is not wise. | neutral | (![X]:((~old(X)&~creative(X))<=>(tall(X)|patient(X))))&
(![X]:((humble(X)<~>old(X))=>(~strong(X)<~>curious(X))))&
(![X]:((rich(X)&~patient(X))<=>(~old(X)&brave(X))))&
(![X]:(rich(X)=>(~brave(X)<~>brave(X))))&
((?[X]:((~happy(X)&rich(X))))<=>(humble(paul)))&
(((~patient(john)&~old(john)))<=>(?[X]:((wise(X)&~patient(X)))))&
((?[X]:((quiet(X)|~brave(X))))=>(?[X]:(~strong(X))))&
(![X]:((kind(X)|happy(X))=>(strong(X)&quiet(X))))&
(![X]:((curious(X)<~>kind(X))<=>(humble(X)<~>~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~calm(X))))&
(((~wise(fred)<~>~humble(fred)))<=>(brave(susan)))&
((?[X]:((~creative(X)&~rich(X))))=>((~wise(paul)<~>~calm(paul))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>((creative(susan)&wise(susan))))&
(((funny(fred)&~creative(fred)))<=>(old(lucy)))&
(![X]:((brave(X)&~old(X))<=>(~funny(X)|happy(X))))&
(![X]:((happy(X)<~>~wise(X))=>(rich(X)&tall(X))))&
((old(alice)<~>~generous(alice)))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((kind(X)|~old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:(~generous(X)))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:(~creative(X))) | ~wise(john) | [] | null | 0 |
Everyone who is either not brave or not tall is both not tall and not funny.
If mary is kind then someone is rich or quiet and vice versa.
If paul is either creative or not old then someone is curious.
If john is either not curious or creative then fred is not patient and vice versa.
Everyone who is not strong is not calm and vice versa.
Everyone who is both happy and not happy is not calm or not tall.
If someone is happy or funny then someone is not tall or generous and vice versa.
Everyone who is humble is curious and vice versa.
Everyone who is either calm or not kind is both not happy and humble and vice versa.
Everyone who is either not calm or rich is not patient or not old and vice versa.
If fred is tall or quiet then susan is either calm or not brave and vice versa.
If someone is either wise or not generous then susan is either old or not old.
If susan is either not strong or not tall then paul is funny or not funny and vice versa.
If john is either not rich or wise then someone is both humble and brave and vice versa.
If fred is not old or not kind then someone is both creative and not quiet.
Everyone who is both not humble and not quiet is both patient and not old.
Someone is both not quiet and old.
Someone is either patient or generous.
Paul is both not old and calm.
Paul is both not curious and not kind.
Fred is quiet.
John is not strong.
Lucy is both generous and not calm.
Someone is either not quiet or not patient. | Susan is funny. | contradiction | (![X]:((~brave(X)<~>~tall(X))=>(~tall(X)&~funny(X))))&
((kind(mary))<=>(?[X]:((rich(X)|quiet(X)))))&
(((creative(paul)<~>~old(paul)))=>(?[X]:(curious(X))))&
(((~curious(john)<~>creative(john)))<=>(~patient(fred)))&
(![X]:(~strong(X)<=>~calm(X)))&
(![X]:((happy(X)&~happy(X))=>(~calm(X)|~tall(X))))&
((?[X]:((happy(X)|funny(X))))<=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:(humble(X)<=>curious(X)))&
(![X]:((calm(X)<~>~kind(X))<=>(~happy(X)&humble(X))))&
(![X]:((~calm(X)<~>rich(X))<=>(~patient(X)|~old(X))))&
(((tall(fred)|quiet(fred)))<=>((calm(susan)<~>~brave(susan))))&
((?[X]:((wise(X)<~>~generous(X))))=>((old(susan)<~>~old(susan))))&
(((~strong(susan)<~>~tall(susan)))<=>((funny(paul)|~funny(paul))))&
(((~rich(john)<~>wise(john)))<=>(?[X]:((humble(X)&brave(X)))))&
(((~old(fred)|~kind(fred)))=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:((~humble(X)&~quiet(X))=>(patient(X)&~old(X))))&
(?[X]:((~quiet(X)&old(X))))&
(?[X]:((patient(X)<~>generous(X))))&
((~old(paul)&calm(paul)))&
((~curious(paul)&~kind(paul)))&
(quiet(fred))&
(~strong(john))&
((generous(lucy)&~calm(lucy)))&
(?[X]:((~quiet(X)<~>~patient(X)))) | funny(susan) | [
"p0",
"p4",
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4879489657163145632873820
% SZS output start Proof for 4879489657163145632873820
1. ! [X0] : ((~brave(X0) <~> ~tall(X0)) => (~funny(X0) & ~tall(X0))) [input p0]
5. ! [X0] : (~strong(X0) <=> ~calm(X0)) [input p4]
11. (quiet(fred) | tall(fred)) <=> (calm(susan) <~> ~brave(susan)) [input p10]
13. (~strong(susan) <~> ~tall(susan)) <=> (~funny(paul) | funny(paul)) [input p12]
21. quiet(fred) [input p20]
25. funny(susan) [input hypothesis]
27. ! [X0] : ((~funny(X0) & ~tall(X0)) | (~brave(X0) <=> ~tall(X0))) [ennf transformation 1]
35. ! [X0] : ((~funny(X0) & ~tall(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0)))) [nnf transformation 27]
44. ! [X0] : ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0))) [nnf transformation 5]
55. ((quiet(fred) | tall(fred)) | ((calm(susan) | brave(susan)) & (~brave(susan) | ~calm(susan)))) & (((brave(susan) | ~calm(susan)) & (~brave(susan) | calm(susan))) | (~quiet(fred) & ~tall(fred))) [nnf transformation 11]
56. (quiet(fred) | tall(fred) | ((calm(susan) | brave(susan)) & (~brave(susan) | ~calm(susan)))) & (((brave(susan) | ~calm(susan)) & (~brave(susan) | calm(susan))) | (~quiet(fred) & ~tall(fred))) [flattening 55]
58. (((tall(susan) | strong(susan)) & (~tall(susan) | ~strong(susan))) | (funny(paul) & ~funny(paul))) & ((~funny(paul) | funny(paul)) | ((~strong(susan) | tall(susan)) & (~tall(susan) | strong(susan)))) [nnf transformation 13]
59. (((tall(susan) | strong(susan)) & (~tall(susan) | ~strong(susan))) | (funny(paul) & ~funny(paul))) & (~funny(paul) | funny(paul) | ((~strong(susan) | tall(susan)) & (~tall(susan) | strong(susan)))) [flattening 58]
74. ~tall(X0) | ~tall(X0) | brave(X0) [cnf transformation 35]
77. ~funny(X0) | ~brave(X0) | tall(X0) [cnf transformation 35]
87. ~calm(X0) | strong(X0) [cnf transformation 44]
88. ~strong(X0) | calm(X0) [cnf transformation 44]
109. ~brave(susan) | calm(susan) | ~quiet(fred) [cnf transformation 56]
111. brave(susan) | ~calm(susan) | ~quiet(fred) [cnf transformation 56]
120. ~tall(susan) | ~strong(susan) | ~funny(paul) [cnf transformation 59]
121. ~tall(susan) | ~strong(susan) | funny(paul) [cnf transformation 59]
122. tall(susan) | strong(susan) | ~funny(paul) [cnf transformation 59]
123. tall(susan) | strong(susan) | funny(paul) [cnf transformation 59]
144. quiet(fred) [cnf transformation 21]
150. funny(susan) [cnf transformation 25]
151. ~tall(X0) | brave(X0) [duplicate literal removal 74]
236. 20 <=> brave(susan) [avatar definition]
237. ~brave(susan) <- (~20) [avatar component clause 236]
238. brave(susan) <- (20) [avatar component clause 236]
240. 21 <=> calm(susan) [avatar definition]
242. calm(susan) <- (21) [avatar component clause 240]
248. 23 <=> quiet(fred) [avatar definition]
253. ~23 | ~21 | 20 [avatar split clause 111,236,240,248]
255. ~23 | 21 | ~20 [avatar split clause 109,236,240,248]
258. 24 <=> funny(paul) [avatar definition]
262. 25 <=> strong(susan) [avatar definition]
264. strong(susan) <- (25) [avatar component clause 262]
266. 26 <=> tall(susan) [avatar definition]
268. tall(susan) <- (26) [avatar component clause 266]
269. 24 | 25 | 26 [avatar split clause 123,266,262,258]
270. ~24 | 25 | 26 [avatar split clause 122,266,262,258]
271. 24 | ~25 | ~26 [avatar split clause 121,266,262,258]
272. ~24 | ~25 | ~26 [avatar split clause 120,266,262,258]
329. 23 [avatar split clause 144,248]
341. calm(susan) <- (25) [resolution 88,264]
344. 21 | ~25 [avatar split clause 341,262,240]
345. strong(susan) <- (21) [resolution 242,87]
349. ~brave(susan) | tall(susan) [resolution 77,150]
351. tall(susan) <- (20) [subsumption resolution 349,238]
363. 25 | ~21 [avatar split clause 345,240,262]
364. 26 | ~20 [avatar split clause 351,236,266]
365. brave(susan) <- (26) [resolution 268,151]
366. $false <- (~20, 26) [subsumption resolution 365,237]
367. 20 | ~26 [avatar contradiction clause 366]
368. $false [avatar sat refutation 253,255,269,270,271,272,329,344,363,364,367]
% SZS output end Proof for 4879489657163145632873820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is brave or not creative.
Everyone who is either strong or not rich is humble or not quiet and vice versa.
Everyone who is both patient and not funny is either not kind or brave.
If someone is either not wise or not humble then john is either old or creative and vice versa.
If someone is curious then fred is either happy or kind and vice versa.
If someone is either not patient or old then someone is not humble.
Everyone who is not strong or not kind is not curious.
If lucy is both not quiet and tall then someone is rich or creative.
Everyone who is either not brave or old is either not kind or old and vice versa.
Everyone who is both happy and curious is both funny and strong.
Everyone who is either strong or not humble is not rich.
Everyone who is brave is either not strong or calm.
Everyone who is both calm and brave is not calm or humble.
If someone is either humble or patient then alice is either not strong or not kind.
Everyone who is not creative is rich or calm and vice versa.
Everyone who is quiet or wise is either not tall or patient.
Someone is not rich.
Someone is not humble.
Fred is both humble and creative.
Someone is both humble and not quiet.
Someone is not creative or creative.
John is not calm.
Someone is either curious or brave.
John is either not brave or old. | Alice is curious. | contradiction | (![X]:(~creative(X)=>(brave(X)|~creative(X))))&
(![X]:((strong(X)<~>~rich(X))<=>(humble(X)|~quiet(X))))&
(![X]:((patient(X)&~funny(X))=>(~kind(X)<~>brave(X))))&
((?[X]:((~wise(X)<~>~humble(X))))<=>((old(john)<~>creative(john))))&
((?[X]:(curious(X)))<=>((happy(fred)<~>kind(fred))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:(~humble(X))))&
(![X]:((~strong(X)|~kind(X))=>~curious(X)))&
(((~quiet(lucy)&tall(lucy)))=>(?[X]:((rich(X)|creative(X)))))&
(![X]:((~brave(X)<~>old(X))<=>(~kind(X)<~>old(X))))&
(![X]:((happy(X)&curious(X))=>(funny(X)&strong(X))))&
(![X]:((strong(X)<~>~humble(X))=>~rich(X)))&
(![X]:(brave(X)=>(~strong(X)<~>calm(X))))&
(![X]:((calm(X)&brave(X))=>(~calm(X)|humble(X))))&
((?[X]:((humble(X)<~>patient(X))))=>((~strong(alice)<~>~kind(alice))))&
(![X]:(~creative(X)<=>(rich(X)|calm(X))))&
(![X]:((quiet(X)|wise(X))=>(~tall(X)<~>patient(X))))&
(?[X]:(~rich(X)))&
(?[X]:(~humble(X)))&
((humble(fred)&creative(fred)))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:((~creative(X)|creative(X))))&
(~calm(john))&
(?[X]:((curious(X)<~>brave(X))))&
((~brave(john)<~>old(john))) | curious(alice) | [
"p1",
"p6",
"p8",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3229673307321072095430756
% SZS output start Proof for 3229673307321072095430756
2. ! [X0] : ((strong(X0) <~> ~rich(X0)) <=> (~quiet(X0) | humble(X0))) [input p1]
7. ! [X0] : ((~kind(X0) | ~strong(X0)) => ~curious(X0)) [input p6]
9. ! [X0] : ((~brave(X0) <~> old(X0)) <=> (~kind(X0) <~> old(X0))) [input p8]
11. ! [X0] : ((strong(X0) <~> ~humble(X0)) => ~rich(X0)) [input p10]
12. ! [X0] : (brave(X0) => (~strong(X0) <~> calm(X0))) [input p11]
13. ! [X0] : ((brave(X0) & calm(X0)) => (humble(X0) | ~calm(X0))) [input p12]
25. curious(alice) [input hypothesis]
32. ! [X0] : (~curious(X0) | (kind(X0) & strong(X0))) [ennf transformation 7]
37. ! [X0] : (~rich(X0) | (strong(X0) <=> ~humble(X0))) [ennf transformation 11]
38. ! [X0] : ((~strong(X0) <~> calm(X0)) | ~brave(X0)) [ennf transformation 12]
39. ! [X0] : ((humble(X0) | ~calm(X0)) | (~brave(X0) | ~calm(X0))) [ennf transformation 13]
40. ! [X0] : (humble(X0) | ~calm(X0) | ~brave(X0) | ~calm(X0)) [flattening 39]
43. ! [X0] : ((((rich(X0) | ~strong(X0)) & (~rich(X0) | strong(X0))) | (quiet(X0) & ~humble(X0))) & ((~quiet(X0) | humble(X0)) | ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0))))) [nnf transformation 2]
44. ! [X0] : ((((rich(X0) | ~strong(X0)) & (~rich(X0) | strong(X0))) | (quiet(X0) & ~humble(X0))) & (~quiet(X0) | humble(X0) | ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0))))) [flattening 43]
59. ! [X0] : ((((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | ((~kind(X0) | ~old(X0)) & (old(X0) | kind(X0)))) & (((~old(X0) | kind(X0)) & (old(X0) | ~kind(X0))) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0))))) [nnf transformation 9]
60. ! [X0] : (~rich(X0) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) [nnf transformation 37]
61. ! [X0] : (((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | ~brave(X0)) [nnf transformation 38]
83. ~humble(X0) | ~strong(X0) | rich(X0) [cnf transformation 44]
99. ~curious(X0) | strong(X0) [cnf transformation 32]
100. ~curious(X0) | kind(X0) [cnf transformation 32]
102. old(X0) | ~kind(X0) | old(X0) | brave(X0) [cnf transformation 59]
109. ~old(X0) | brave(X0) | ~kind(X0) | ~old(X0) [cnf transformation 59]
111. ~rich(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 60]
113. ~strong(X0) | calm(X0) | ~brave(X0) [cnf transformation 61]
115. humble(X0) | ~calm(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 40]
139. curious(alice) [cnf transformation 25]
140. ~calm(X0) | humble(X0) | ~brave(X0) [duplicate literal removal 115]
141. old(X0) | ~kind(X0) | brave(X0) [duplicate literal removal 102]
144. ~old(X0) | brave(X0) | ~kind(X0) [duplicate literal removal 109]
224. ~kind(X0) | brave(X0) [subsumption resolution 141,144]
226. ~humble(X0) | ~strong(X0) [subsumption resolution 111,83]
231. 19 <=> strong(alice) [avatar definition]
233. strong(alice) <- (19) [avatar component clause 231]
235. 20 <=> kind(alice) [avatar definition]
237. kind(alice) <- (20) [avatar component clause 235]
261. strong(alice) [resolution 99,139]
264. kind(alice) [resolution 100,139]
269. 19 [avatar split clause 261,231]
270. 20 [avatar split clause 264,235]
276. brave(alice) <- (20) [resolution 224,237]
319. calm(alice) | ~brave(alice) <- (19) [resolution 113,233]
321. calm(alice) <- (19, 20) [subsumption resolution 319,276]
363. humble(alice) | ~brave(alice) <- (19, 20) [resolution 140,321]
366. humble(alice) <- (19, 20) [subsumption resolution 363,276]
379. ~strong(alice) <- (19, 20) [resolution 366,226]
381. $false <- (19, 20) [subsumption resolution 379,233]
382. ~19 | ~20 [avatar contradiction clause 381]
383. $false [avatar sat refutation 269,270,382]
% SZS output end Proof for 3229673307321072095430756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is generous or patient then susan is both tall and strong and vice versa.
Everyone who is not curious is calm or not brave and vice versa.
If someone is both not humble and not rich then alice is not curious.
If john is strong or rich then susan is creative and vice versa.
Everyone who is both not brave and old is either old or kind.
Everyone who is both not happy and not old is both quiet and kind and vice versa.
If mary is both brave and funny then someone is patient and vice versa.
Everyone who is not funny is both wise and curious and vice versa.
If someone is either not strong or calm then someone is not old and vice versa.
Everyone who is both not happy and not kind is generous or not humble and vice versa.
If someone is both not creative and not wise then mary is either not calm or creative and vice versa.
If lucy is both not quiet and patient then john is not kind or not old and vice versa.
Everyone who is not patient or brave is either not curious or not tall and vice versa.
Everyone who is either not strong or rich is generous.
Everyone who is not generous is both not old and old.
Everyone who is not wise or not humble is not generous and vice versa.
Paul is both not quiet and calm.
Lucy is not creative.
Susan is both not kind and wise.
Someone is not quiet or not old.
Someone is old. | Alice is happy. | contradiction | (((generous(paul)|patient(paul)))<=>((tall(susan)&strong(susan))))&
(![X]:(~curious(X)<=>(calm(X)|~brave(X))))&
((?[X]:((~humble(X)&~rich(X))))=>(~curious(alice)))&
(((strong(john)|rich(john)))<=>(creative(susan)))&
(![X]:((~brave(X)&old(X))=>(old(X)<~>kind(X))))&
(![X]:((~happy(X)&~old(X))<=>(quiet(X)&kind(X))))&
(((brave(mary)&funny(mary)))<=>(?[X]:(patient(X))))&
(![X]:(~funny(X)<=>(wise(X)&curious(X))))&
((?[X]:((~strong(X)<~>calm(X))))<=>(?[X]:(~old(X))))&
(![X]:((~happy(X)&~kind(X))<=>(generous(X)|~humble(X))))&
((?[X]:((~creative(X)&~wise(X))))<=>((~calm(mary)<~>creative(mary))))&
(((~quiet(lucy)&patient(lucy)))<=>((~kind(john)|~old(john))))&
(![X]:((~patient(X)|brave(X))<=>(~curious(X)<~>~tall(X))))&
(![X]:((~strong(X)<~>rich(X))=>generous(X)))&
(![X]:(~generous(X)=>(~old(X)&old(X))))&
(![X]:((~wise(X)|~humble(X))<=>~generous(X)))&
((~quiet(paul)&calm(paul)))&
(~creative(lucy))&
((~kind(susan)&wise(susan)))&
(?[X]:((~quiet(X)|~old(X))))&
(?[X]:(old(X))) | happy(alice) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1680641522371127427746716
% SZS output start Proof for 1680641522371127427746716
10. ! [X0] : ((~kind(X0) & ~happy(X0)) <=> (~humble(X0) | generous(X0))) [input p9]
15. ! [X0] : (~generous(X0) => (old(X0) & ~old(X0))) [input p14]
22. happy(alice) [input hypothesis]
28. ! [X0] : ((old(X0) & ~old(X0)) | generous(X0)) [ennf transformation 15]
50. ! [X0] : (((~kind(X0) & ~happy(X0)) | (humble(X0) & ~generous(X0))) & ((~humble(X0) | generous(X0)) | (kind(X0) | happy(X0)))) [nnf transformation 10]
51. ! [X0] : (((~kind(X0) & ~happy(X0)) | (humble(X0) & ~generous(X0))) & (~humble(X0) | generous(X0) | kind(X0) | happy(X0))) [flattening 50]
96. ~happy(X0) | ~generous(X0) [cnf transformation 51]
119. ~old(X0) | generous(X0) [cnf transformation 28]
120. old(X0) | generous(X0) [cnf transformation 28]
131. happy(alice) [cnf transformation 22]
268. generous(X0) [subsumption resolution 119,120]
288. ~generous(alice) [resolution 96,131]
289. $false [subsumption resolution 288,268]
% SZS output end Proof for 1680641522371127427746716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not strong is tall or brave.
If paul is not quiet then someone is either rich or not old and vice versa.
If someone is either tall or curious then mary is either patient or creative and vice versa.
If someone is both not curious and not creative then lucy is either old or not creative.
If someone is either not humble or not kind then paul is either not kind or humble and vice versa.
Everyone who is both calm and not kind is either not funny or calm and vice versa.
If paul is either happy or not patient then john is either not quiet or not patient and vice versa.
If someone is not patient or not calm then fred is both not rich and old and vice versa.
Everyone who is not patient is both not curious and not old.
If someone is not tall then someone is either not rich or not quiet and vice versa.
Everyone who is not funny is patient or not generous.
Everyone who is either humble or generous is both not humble and wise and vice versa.
Everyone who is patient is either wise or quiet and vice versa.
Everyone who is not rich or not quiet is not tall or not funny.
Everyone who is both not funny and not happy is patient or not tall and vice versa.
Everyone who is brave is not humble and vice versa.
Alice is not old.
Someone is not kind or not generous.
Fred is quiet or not creative.
Someone is both not quiet and calm.
Fred is rich or not tall.
Someone is not brave.
Paul is both not happy and wise.
Mary is both not calm and creative. | John is not quiet. | neutral | (![X]:((~creative(X)<~>~strong(X))=>(tall(X)|brave(X))))&
((~quiet(paul))<=>(?[X]:((rich(X)<~>~old(X)))))&
((?[X]:((tall(X)<~>curious(X))))<=>((patient(mary)<~>creative(mary))))&
((?[X]:((~curious(X)&~creative(X))))=>((old(lucy)<~>~creative(lucy))))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((~kind(paul)<~>humble(paul))))&
(![X]:((calm(X)&~kind(X))<=>(~funny(X)<~>calm(X))))&
(((happy(paul)<~>~patient(paul)))<=>((~quiet(john)<~>~patient(john))))&
((?[X]:((~patient(X)|~calm(X))))<=>((~rich(fred)&old(fred))))&
(![X]:(~patient(X)=>(~curious(X)&~old(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(![X]:(~funny(X)=>(patient(X)|~generous(X))))&
(![X]:((humble(X)<~>generous(X))<=>(~humble(X)&wise(X))))&
(![X]:(patient(X)<=>(wise(X)<~>quiet(X))))&
(![X]:((~rich(X)|~quiet(X))=>(~tall(X)|~funny(X))))&
(![X]:((~funny(X)&~happy(X))<=>(patient(X)|~tall(X))))&
(![X]:(brave(X)<=>~humble(X)))&
(~old(alice))&
(?[X]:((~kind(X)|~generous(X))))&
((quiet(fred)|~creative(fred)))&
(?[X]:((~quiet(X)&calm(X))))&
((rich(fred)|~tall(fred)))&
(?[X]:(~brave(X)))&
((~happy(paul)&wise(paul)))&
((~calm(mary)&creative(mary))) | ~quiet(john) | [] | null | 0 |
If someone is either old or humble then someone is both not funny and funny. Everyone who is either not happy or generous is either not rich or humble and vice versa. Everyone who is either humble or not kind is either humble or not old. Everyone who is both not old and kind is not generous. If lucy is humble or not creative then paul is patient. If someone is strong or not curious then alice is not rich or not creative and vice versa. Everyone who is not rich is not patient. If lucy is not strong then someone is both rich and not brave and vice versa. If alice is either funny or creative then paul is patient or not calm and vice versa. Everyone who is not kind is either not happy or funny. Everyone who is both not humble and not old is either not old or not humble and vice versa. If someone is both kind and not kind then lucy is both not creative and quiet. Everyone who is not brave is either old or quiet. If lucy is humble or not funny then john is both not curious and quiet. If fred is old then john is funny or happy. Someone is either patient or not humble. Fred is both not strong and not tall. Someone is both rich and generous. Susan is tall or strong. Alice is either happy or not old. | Alice is humble. | entailment | ((?[X]:((old(X)<~>humble(X))))=>(?[X]:((~funny(X)&funny(X)))))&
(![X]:((~happy(X)<~>generous(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((humble(X)<~>~kind(X))=>(humble(X)<~>~old(X))))&
(![X]:((~old(X)&kind(X))=>~generous(X)))&
(((humble(lucy)|~creative(lucy)))=>(patient(paul)))&
((?[X]:((strong(X)|~curious(X))))<=>((~rich(alice)|~creative(alice))))&
(![X]:(~rich(X)=>~patient(X)))&
((~strong(lucy))<=>(?[X]:((rich(X)&~brave(X)))))&
(((funny(alice)<~>creative(alice)))<=>((patient(paul)|~calm(paul))))&
(![X]:(~kind(X)=>(~happy(X)<~>funny(X))))&
(![X]:((~humble(X)&~old(X))<=>(~old(X)<~>~humble(X))))&
((?[X]:((kind(X)&~kind(X))))=>((~creative(lucy)&quiet(lucy))))&
(![X]:(~brave(X)=>(old(X)<~>quiet(X))))&
(((humble(lucy)|~funny(lucy)))=>((~curious(john)&quiet(john))))&
((old(fred))=>((funny(john)|happy(john))))&
(?[X]:((patient(X)<~>~humble(X))))&
((~strong(fred)&~tall(fred)))&
(?[X]:((rich(X)&generous(X))))&
((tall(susan)|strong(susan)))&
((happy(alice)<~>~old(alice))) | humble(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 335947820770005288638540
% SZS output start Proof for 335947820770005288638540
11. ! [X0] : ((~old(X0) & ~humble(X0)) <=> (~old(X0) <~> ~humble(X0))) [input p10]
21. ~humble(alice) [input hypothesis]
53. ! [X0] : (((~old(X0) & ~humble(X0)) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0)))) & (((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | (old(X0) | humble(X0)))) [nnf transformation 11]
54. ! [X0] : (((~old(X0) & ~humble(X0)) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0)))) & (((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | old(X0) | humble(X0))) [flattening 53]
98. humble(X0) | old(X0) | old(X0) | humble(X0) [cnf transformation 54]
102. ~old(X0) | ~old(X0) | humble(X0) [cnf transformation 54]
121. ~humble(alice) [cnf transformation 21]
122. humble(X0) | old(X0) [duplicate literal removal 98]
124. ~old(X0) | humble(X0) [duplicate literal removal 102]
136. 3 <=> ! [X1] : (humble(X1) | ~old(X1)) [avatar definition]
137. humble(X1) | ~old(X1) <- (3) [avatar component clause 136]
213. 3 [avatar split clause 124,136]
273. humble(X1) <- (3) [subsumption resolution 137,122]
275. $false <- (3) [resolution 273,121]
280. ~3 [avatar contradiction clause 275]
281. $false [avatar sat refutation 213,280]
% SZS output end Proof for 335947820770005288638540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or happy is not quiet and vice versa.
Everyone who is not quiet or not curious is not quiet.
If fred is old then alice is both not brave and funny.
Everyone who is not humble is both wise and not happy.
If someone is strong or not quiet then someone is both not funny and old and vice versa.
If john is not tall or calm then fred is either not funny or tall and vice versa.
Everyone who is either calm or not kind is calm and vice versa.
If someone is both strong and wise then fred is either wise or tall and vice versa.
Everyone who is either not quiet or not humble is humble or tall.
If john is not patient then mary is both brave and calm and vice versa.
If someone is either patient or wise then someone is both humble and wise.
Everyone who is wise or creative is both rich and strong.
If lucy is either patient or not quiet then mary is either not creative or not humble and vice versa.
Everyone who is both not wise and not humble is curious.
Everyone who is both curious and not strong is either humble or not brave and vice versa.
Everyone who is curious or not old is either not happy or tall and vice versa.
Someone is both kind and rich.
John is both not strong and humble.
Someone is either calm or not calm.
Lucy is not kind or not creative.
Fred is not humble or old.
Someone is either humble or not strong.
John is either not happy or not humble.
Susan is both rich and kind. | John is not wise. | entailment | (![X]:((humble(X)|happy(X))<=>~quiet(X)))&
(![X]:((~quiet(X)|~curious(X))=>~quiet(X)))&
((old(fred))=>((~brave(alice)&funny(alice))))&
(![X]:(~humble(X)=>(wise(X)&~happy(X))))&
((?[X]:((strong(X)|~quiet(X))))<=>(?[X]:((~funny(X)&old(X)))))&
(((~tall(john)|calm(john)))<=>((~funny(fred)<~>tall(fred))))&
(![X]:((calm(X)<~>~kind(X))<=>calm(X)))&
((?[X]:((strong(X)&wise(X))))<=>((wise(fred)<~>tall(fred))))&
(![X]:((~quiet(X)<~>~humble(X))=>(humble(X)|tall(X))))&
((~patient(john))<=>((brave(mary)&calm(mary))))&
((?[X]:((patient(X)<~>wise(X))))=>(?[X]:((humble(X)&wise(X)))))&
(![X]:((wise(X)|creative(X))=>(rich(X)&strong(X))))&
(((patient(lucy)<~>~quiet(lucy)))<=>((~creative(mary)<~>~humble(mary))))&
(![X]:((~wise(X)&~humble(X))=>curious(X)))&
(![X]:((curious(X)&~strong(X))<=>(humble(X)<~>~brave(X))))&
(![X]:((curious(X)|~old(X))<=>(~happy(X)<~>tall(X))))&
(?[X]:((kind(X)&rich(X))))&
((~strong(john)&humble(john)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~kind(lucy)|~creative(lucy)))&
((~humble(fred)|old(fred)))&
(?[X]:((humble(X)<~>~strong(X))))&
((~happy(john)<~>~humble(john)))&
((rich(susan)&kind(susan))) | ~wise(john) | [
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5523815556943099070367987
% SZS output start Proof for 5523815556943099070367987
12. ! [X0] : ((creative(X0) | wise(X0)) => (strong(X0) & rich(X0))) [input p11]
18. humble(john) & ~strong(john) [input p17]
25. wise(john) [input hypothesis]
30. ! [X0] : ((creative(X0) | wise(X0)) => strong(X0)) [pure predicate removal 12]
37. ! [X0] : (strong(X0) | (~creative(X0) & ~wise(X0))) [ennf transformation 30]
114. ~wise(X0) | strong(X0) [cnf transformation 37]
138. ~strong(john) [cnf transformation 18]
149. wise(john) [cnf transformation 25]
320. strong(john) [resolution 114,149]
323. $false [subsumption resolution 320,138]
% SZS output end Proof for 5523815556943099070367987
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is brave or kind then susan is funny or not funny.
Everyone who is old is happy and vice versa.
If susan is both not happy and not kind then someone is both not rich and rich.
If someone is wise or not happy then someone is both tall and not calm.
Everyone who is both old and not wise is generous or patient and vice versa.
If someone is either not curious or brave then someone is either brave or not wise and vice versa.
Everyone who is either not old or strong is both old and not curious and vice versa.
If susan is not humble then someone is either calm or curious.
Everyone who is either not tall or not brave is calm or patient.
If someone is either happy or generous then mary is strong.
If someone is wise or curious then someone is strong and vice versa.
Everyone who is creative or not wise is both rich and not wise and vice versa.
Everyone who is either not strong or not generous is either not tall or not generous.
If someone is not calm or not funny then alice is either tall or strong.
Everyone who is either calm or old is either patient or not humble and vice versa.
If someone is generous then someone is funny.
Someone is not funny.
Alice is both strong and not wise.
Someone is creative or brave.
Fred is patient.
Alice is not wise or tall.
Someone is tall or not wise.
Fred is not humble.
Alice is both not kind and not patient. | Fred is happy. | entailment | (((brave(paul)|kind(paul)))=>((funny(susan)|~funny(susan))))&
(![X]:(old(X)<=>happy(X)))&
(((~happy(susan)&~kind(susan)))=>(?[X]:((~rich(X)&rich(X)))))&
((?[X]:((wise(X)|~happy(X))))=>(?[X]:((tall(X)&~calm(X)))))&
(![X]:((old(X)&~wise(X))<=>(generous(X)|patient(X))))&
((?[X]:((~curious(X)<~>brave(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((~old(X)<~>strong(X))<=>(old(X)&~curious(X))))&
((~humble(susan))=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:((~tall(X)<~>~brave(X))=>(calm(X)|patient(X))))&
((?[X]:((happy(X)<~>generous(X))))=>(strong(mary)))&
((?[X]:((wise(X)|curious(X))))<=>(?[X]:(strong(X))))&
(![X]:((creative(X)|~wise(X))<=>(rich(X)&~wise(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(~tall(X)<~>~generous(X))))&
((?[X]:((~calm(X)|~funny(X))))=>((tall(alice)<~>strong(alice))))&
(![X]:((calm(X)<~>old(X))<=>(patient(X)<~>~humble(X))))&
((?[X]:(generous(X)))=>(?[X]:(funny(X))))&
(?[X]:(~funny(X)))&
((strong(alice)&~wise(alice)))&
(?[X]:((creative(X)|brave(X))))&
(patient(fred))&
((~wise(alice)|tall(alice)))&
(?[X]:((tall(X)|~wise(X))))&
(~humble(fred))&
((~kind(alice)&~patient(alice))) | happy(fred) | [
"p1",
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5106407044055562068500793
% SZS output start Proof for 5106407044055562068500793
2. ! [X0] : (old(X0) <=> happy(X0)) [input p1]
5. ! [X0] : ((~wise(X0) & old(X0)) <=> (patient(X0) | generous(X0))) [input p4]
20. patient(fred) [input p19]
25. ~happy(fred) [input hypothesis]
42. ! [X0] : ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))) [nnf transformation 2]
48. ! [X0] : (((~wise(X0) & old(X0)) | (~patient(X0) & ~generous(X0))) & ((patient(X0) | generous(X0)) | (wise(X0) | ~old(X0)))) [nnf transformation 5]
49. ! [X0] : (((~wise(X0) & old(X0)) | (~patient(X0) & ~generous(X0))) & (patient(X0) | generous(X0) | wise(X0) | ~old(X0))) [flattening 48]
83. ~old(X0) | happy(X0) [cnf transformation 42]
93. ~patient(X0) | old(X0) [cnf transformation 49]
145. patient(fred) [cnf transformation 20]
151. ~happy(fred) [cnf transformation 25]
331. old(fred) [resolution 93,145]
332. happy(fred) [resolution 331,83]
333. $false [subsumption resolution 332,151]
% SZS output end Proof for 5106407044055562068500793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or not generous then paul is either quiet or not quiet.
If fred is both curious and wise then alice is not generous or not funny and vice versa.
Everyone who is both calm and happy is not patient.
Everyone who is brave is humble and vice versa.
Everyone who is not strong or calm is either brave or generous and vice versa.
If someone is tall then fred is either curious or not old.
Everyone who is both not strong and not wise is not funny and vice versa.
Everyone who is happy is both not quiet and strong.
Everyone who is tall or humble is not creative and vice versa.
Everyone who is not happy is either patient or quiet and vice versa.
Everyone who is both not funny and not curious is both not happy and generous and vice versa.
If someone is not funny then john is kind and vice versa.
If mary is funny or not curious then fred is either not rich or quiet and vice versa.
Everyone who is either not creative or curious is not humble or patient and vice versa.
Everyone who is not curious is either wise or funny and vice versa.
If paul is quiet then someone is either not brave or not generous and vice versa.
Paul is either not funny or rich.
Alice is both humble and not quiet.
Susan is rich or not funny.
Fred is not old or not humble.
Susan is creative or not funny.
Susan is either not tall or kind.
John is generous.
Alice is not tall or strong. | John is funny. | entailment | ((?[X]:((~calm(X)<~>~generous(X))))=>((quiet(paul)<~>~quiet(paul))))&
(((curious(fred)&wise(fred)))<=>((~generous(alice)|~funny(alice))))&
(![X]:((calm(X)&happy(X))=>~patient(X)))&
(![X]:(brave(X)<=>humble(X)))&
(![X]:((~strong(X)|calm(X))<=>(brave(X)<~>generous(X))))&
((?[X]:(tall(X)))=>((curious(fred)<~>~old(fred))))&
(![X]:((~strong(X)&~wise(X))<=>~funny(X)))&
(![X]:(happy(X)=>(~quiet(X)&strong(X))))&
(![X]:((tall(X)|humble(X))<=>~creative(X)))&
(![X]:(~happy(X)<=>(patient(X)<~>quiet(X))))&
(![X]:((~funny(X)&~curious(X))<=>(~happy(X)&generous(X))))&
((?[X]:(~funny(X)))<=>(kind(john)))&
(((funny(mary)|~curious(mary)))<=>((~rich(fred)<~>quiet(fred))))&
(![X]:((~creative(X)<~>curious(X))<=>(~humble(X)|patient(X))))&
(![X]:(~curious(X)<=>(wise(X)<~>funny(X))))&
((quiet(paul))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((~funny(paul)<~>rich(paul)))&
((humble(alice)&~quiet(alice)))&
((rich(susan)|~funny(susan)))&
((~old(fred)|~humble(fred)))&
((creative(susan)|~funny(susan)))&
((~tall(susan)<~>kind(susan)))&
(generous(john))&
((~tall(alice)|strong(alice))) | funny(john) | [
"p6",
"p7",
"p10",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4280562019643067940305128
% SZS output start Proof for 4280562019643067940305128
7. ! [X0] : ((~wise(X0) & ~strong(X0)) <=> ~funny(X0)) [input p6]
8. ! [X0] : (happy(X0) => (strong(X0) & ~quiet(X0))) [input p7]
11. ! [X0] : ((~curious(X0) & ~funny(X0)) <=> (generous(X0) & ~happy(X0))) [input p10]
15. ! [X0] : (~curious(X0) <=> (wise(X0) <~> funny(X0))) [input p14]
23. generous(john) [input p22]
25. ~funny(john) [input hypothesis]
30. ! [X0] : ((strong(X0) & ~quiet(X0)) | ~happy(X0)) [ennf transformation 8]
38. ! [X0] : (((~wise(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | (wise(X0) | strong(X0)))) [nnf transformation 7]
39. ! [X0] : (((~wise(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | wise(X0) | strong(X0))) [flattening 38]
43. ! [X0] : (((~curious(X0) & ~funny(X0)) | (~generous(X0) | happy(X0))) & ((generous(X0) & ~happy(X0)) | (curious(X0) | funny(X0)))) [nnf transformation 11]
44. ! [X0] : (((~curious(X0) & ~funny(X0)) | ~generous(X0) | happy(X0)) & ((generous(X0) & ~happy(X0)) | curious(X0) | funny(X0))) [flattening 43]
53. ! [X0] : ((~curious(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | curious(X0))) [nnf transformation 15]
81. ~strong(X0) | funny(X0) [cnf transformation 39]
82. ~wise(X0) | funny(X0) [cnf transformation 39]
84. ~happy(X0) | strong(X0) [cnf transformation 30]
94. ~funny(X0) | ~generous(X0) | happy(X0) [cnf transformation 44]
95. ~curious(X0) | ~generous(X0) | happy(X0) [cnf transformation 44]
110. funny(X0) | wise(X0) | curious(X0) [cnf transformation 53]
111. ~funny(X0) | ~wise(X0) | curious(X0) [cnf transformation 53]
127. generous(john) [cnf transformation 23]
129. ~funny(john) [cnf transformation 25]
199. ~wise(X0) | curious(X0) [subsumption resolution 111,82]
200. funny(X0) | curious(X0) [subsumption resolution 110,199]
320. ~generous(X1) | happy(X1) | curious(X1) [resolution 94,200]
330. ~generous(X1) | happy(X1) [subsumption resolution 320,95]
340. happy(john) [resolution 330,127]
471. strong(john) [resolution 340,84]
578. funny(john) [resolution 471,81]
579. $false [subsumption resolution 578,129]
% SZS output end Proof for 4280562019643067940305128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not quiet is both tall and calm and vice versa.
Everyone who is either not generous or not humble is both generous and humble and vice versa.
If someone is either not patient or not tall then susan is either not creative or quiet.
Everyone who is not creative is either not quiet or not happy.
Everyone who is not calm or strong is either not humble or rich and vice versa.
If paul is both funny and not creative then susan is not patient or calm and vice versa.
If someone is not creative then mary is brave.
If someone is not curious or generous then fred is both old and not old and vice versa.
If someone is not creative or strong then someone is funny and vice versa.
If someone is either patient or strong then someone is patient or not old and vice versa.
Everyone who is humble is not patient and vice versa.
Everyone who is not wise or tall is either not rich or strong and vice versa.
If mary is both curious and not wise then someone is not happy and vice versa.
If lucy is both brave and not creative then paul is wise and vice versa.
If someone is both wise and not happy then fred is both not curious and not generous and vice versa.
Everyone who is either not brave or not funny is both not curious and not brave.
Someone is both not generous and not calm.
Someone is either quiet or not quiet.
Someone is both not rich and not strong.
Someone is calm or wise.
Someone is calm or old.
Someone is not humble.
Someone is both calm and old. | Fred is curious. | entailment | (![X]:((brave(X)|~quiet(X))<=>(tall(X)&calm(X))))&
(![X]:((~generous(X)<~>~humble(X))<=>(generous(X)&humble(X))))&
((?[X]:((~patient(X)<~>~tall(X))))=>((~creative(susan)<~>quiet(susan))))&
(![X]:(~creative(X)=>(~quiet(X)<~>~happy(X))))&
(![X]:((~calm(X)|strong(X))<=>(~humble(X)<~>rich(X))))&
(((funny(paul)&~creative(paul)))<=>((~patient(susan)|calm(susan))))&
((?[X]:(~creative(X)))=>(brave(mary)))&
((?[X]:((~curious(X)|generous(X))))<=>((old(fred)&~old(fred))))&
((?[X]:((~creative(X)|strong(X))))<=>(?[X]:(funny(X))))&
((?[X]:((patient(X)<~>strong(X))))<=>(?[X]:((patient(X)|~old(X)))))&
(![X]:(humble(X)<=>~patient(X)))&
(![X]:((~wise(X)|tall(X))<=>(~rich(X)<~>strong(X))))&
(((curious(mary)&~wise(mary)))<=>(?[X]:(~happy(X))))&
(((brave(lucy)&~creative(lucy)))<=>(wise(paul)))&
((?[X]:((wise(X)&~happy(X))))<=>((~curious(fred)&~generous(fred))))&
(![X]:((~brave(X)<~>~funny(X))=>(~curious(X)&~brave(X))))&
(?[X]:((~generous(X)&~calm(X))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
(?[X]:((~rich(X)&~strong(X))))&
(?[X]:((calm(X)|wise(X))))&
(?[X]:((calm(X)|old(X))))&
(?[X]:(~humble(X)))&
(?[X]:((calm(X)&old(X)))) | curious(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5432356149472873603123264
% SZS output start Proof for 5432356149472873603123264
8. ? [X0] : (generous(X0) | ~curious(X0)) <=> (~old(fred) & old(fred)) [input p7]
24. ~curious(fred) [input hypothesis]
41. (? [X0] : (generous(X0) | ~curious(X0)) | (old(fred) | ~old(fred))) & ((~old(fred) & old(fred)) | ! [X0] : (~generous(X0) & curious(X0))) [nnf transformation 8]
42. (? [X0] : (generous(X0) | ~curious(X0)) | old(fred) | ~old(fred)) & ((~old(fred) & old(fred)) | ! [X0] : (~generous(X0) & curious(X0))) [flattening 41]
43. (? [X0] : (generous(X0) | ~curious(X0)) | old(fred) | ~old(fred)) & ((~old(fred) & old(fred)) | ! [X1] : (~generous(X1) & curious(X1))) [rectify 42]
44. ? [X0] : (generous(X0) | ~curious(X0)) => (generous(sK0) | ~curious(sK0)) [choice axiom]
45. ((generous(sK0) | ~curious(sK0)) | old(fred) | ~old(fred)) & ((~old(fred) & old(fred)) | ! [X1] : (~generous(X1) & curious(X1))) [skolemisation 43,44]
116. old(fred) | curious(X1) [cnf transformation 45]
118. ~old(fred) | curious(X1) [cnf transformation 45]
163. ~curious(fred) [cnf transformation 24]
221. 11 <=> ! [X1] : curious(X1) [avatar definition]
222. curious(X1) <- (11) [avatar component clause 221]
224. 12 <=> old(fred) [avatar definition]
227. 11 | ~12 [avatar split clause 118,224,221]
228. 11 | 12 [avatar split clause 116,224,221]
324. 33 <=> curious(fred) [avatar definition]
325. ~curious(fred) <- (~33) [avatar component clause 324]
360. ~33 [avatar split clause 163,324]
367. $false <- (11, ~33) [resolution 325,222]
368. ~11 | 33 [avatar contradiction clause 367]
369. $false [avatar sat refutation 227,228,360,368]
% SZS output end Proof for 5432356149472873603123264
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not humble then fred is patient or calm and vice versa. If someone is both wise and funny then mary is both not tall and not humble and vice versa. Everyone who is patient or quiet is either not creative or quiet and vice versa. Everyone who is not strong is not kind. If susan is curious then someone is either tall or not quiet. If susan is brave or calm then someone is not wise. If john is not rich then someone is curious and vice versa. If paul is either not curious or not rich then someone is old or not tall and vice versa. If someone is either not brave or old then alice is tall. If mary is generous then someone is not happy. Everyone who is creative is both not calm and creative. Everyone who is either not kind or strong is not kind and vice versa. If someone is strong then someone is either rich or not strong and vice versa. Everyone who is funny or not wise is not happy or calm and vice versa. If someone is curious then someone is either humble or not funny and vice versa. Everyone who is curious or not wise is either not tall or generous and vice versa. Lucy is humble. Someone is both quiet and old. Lucy is not brave. Mary is calm. Someone is calm or not quiet. Fred is not tall. Mary is happy. | Fred is not kind. | entailment | ((?[X]:((~quiet(X)&~humble(X))))<=>((patient(fred)|calm(fred))))&
((?[X]:((wise(X)&funny(X))))<=>((~tall(mary)&~humble(mary))))&
(![X]:((patient(X)|quiet(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:(~strong(X)=>~kind(X)))&
((curious(susan))=>(?[X]:((tall(X)<~>~quiet(X)))))&
(((brave(susan)|calm(susan)))=>(?[X]:(~wise(X))))&
((~rich(john))<=>(?[X]:(curious(X))))&
(((~curious(paul)<~>~rich(paul)))<=>(?[X]:((old(X)|~tall(X)))))&
((?[X]:((~brave(X)<~>old(X))))=>(tall(alice)))&
((generous(mary))=>(?[X]:(~happy(X))))&
(![X]:(creative(X)=>(~calm(X)&creative(X))))&
(![X]:((~kind(X)<~>strong(X))<=>~kind(X)))&
((?[X]:(strong(X)))<=>(?[X]:((rich(X)<~>~strong(X)))))&
(![X]:((funny(X)|~wise(X))<=>(~happy(X)|calm(X))))&
((?[X]:(curious(X)))<=>(?[X]:((humble(X)<~>~funny(X)))))&
(![X]:((curious(X)|~wise(X))<=>(~tall(X)<~>generous(X))))&
(humble(lucy))&
(?[X]:((quiet(X)&old(X))))&
(~brave(lucy))&
(calm(mary))&
(?[X]:((calm(X)|~quiet(X))))&
(~tall(fred))&
(happy(mary)) | ~kind(fred) | [
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 575690766004625911958828
% SZS output start Proof for 575690766004625911958828
4. ! [X0] : (~strong(X0) => ~kind(X0)) [input p3]
12. ! [X0] : ((~kind(X0) <~> strong(X0)) <=> ~kind(X0)) [input p11]
24. kind(fred) [input hypothesis]
27. ! [X0] : (~kind(X0) | strong(X0)) [ennf transformation 4]
61. ! [X0] : ((((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | kind(X0)) & (~kind(X0) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0))))) [nnf transformation 12]
95. ~kind(X0) | strong(X0) [cnf transformation 27]
114. ~kind(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 61]
143. kind(fred) [cnf transformation 24]
144. ~kind(X0) | ~strong(X0) [duplicate literal removal 114]
285. ~kind(X0) [subsumption resolution 144,95]
342. $false [subsumption resolution 143,285]
% SZS output end Proof for 575690766004625911958828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is either not rich or not creative.
If alice is both brave and not tall then someone is not happy.
Everyone who is not rich or funny is not rich and vice versa.
Everyone who is not funny is both happy and not happy.
Everyone who is either wise or kind is either wise or not patient.
If paul is both old and not old then lucy is both not curious and calm.
Everyone who is both not wise and rich is not strong and vice versa.
If lucy is both not old and wise then mary is creative or not old.
If fred is either funny or not rich then someone is both humble and not curious and vice versa.
Everyone who is not patient is patient.
Everyone who is not wise or not strong is not quiet or strong and vice versa.
Everyone who is either tall or not creative is not humble or funny.
Everyone who is not brave is happy or generous.
If someone is not humble then someone is both not patient and not curious.
If someone is both not tall and not strong then someone is both strong and not curious.
If john is both not quiet and brave then someone is either creative or not brave and vice versa.
Someone is not calm.
Lucy is either quiet or not strong.
Mary is either creative or not strong.
Someone is quiet or not funny.
Someone is humble.
Someone is both quiet and brave. | John is not brave. | neutral | (![X]:(~calm(X)=>(~rich(X)<~>~creative(X))))&
(((brave(alice)&~tall(alice)))=>(?[X]:(~happy(X))))&
(![X]:((~rich(X)|funny(X))<=>~rich(X)))&
(![X]:(~funny(X)=>(happy(X)&~happy(X))))&
(![X]:((wise(X)<~>kind(X))=>(wise(X)<~>~patient(X))))&
(((old(paul)&~old(paul)))=>((~curious(lucy)&calm(lucy))))&
(![X]:((~wise(X)&rich(X))<=>~strong(X)))&
(((~old(lucy)&wise(lucy)))=>((creative(mary)|~old(mary))))&
(((funny(fred)<~>~rich(fred)))<=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:(~patient(X)=>patient(X)))&
(![X]:((~wise(X)|~strong(X))<=>(~quiet(X)|strong(X))))&
(![X]:((tall(X)<~>~creative(X))=>(~humble(X)|funny(X))))&
(![X]:(~brave(X)=>(happy(X)|generous(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~patient(X)&~curious(X)))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:((strong(X)&~curious(X)))))&
(((~quiet(john)&brave(john)))<=>(?[X]:((creative(X)<~>~brave(X)))))&
(?[X]:(~calm(X)))&
((quiet(lucy)<~>~strong(lucy)))&
((creative(mary)<~>~strong(mary)))&
(?[X]:((quiet(X)|~funny(X))))&
(?[X]:(humble(X)))&
(?[X]:((quiet(X)&brave(X)))) | ~brave(john) | [] | null | 0 |
If someone is patient then paul is strong.
If someone is calm or strong then alice is both not generous and funny.
Everyone who is not quiet or not tall is kind.
Everyone who is either not humble or curious is creative and vice versa.
Everyone who is not funny is not rich or tall.
Everyone who is both not old and not funny is not old and vice versa.
If paul is creative then susan is both humble and not generous and vice versa.
If someone is either not funny or calm then someone is either not strong or humble.
Everyone who is either tall or brave is tall or happy and vice versa.
If someone is happy or wise then mary is both not generous and humble and vice versa.
Everyone who is either not quiet or not creative is either creative or not tall and vice versa.
Everyone who is either calm or generous is not old and vice versa.
Everyone who is happy is not calm.
Everyone who is both not tall and not happy is not strong or humble.
If john is either not curious or wise then lucy is both not happy and not patient.
Everyone who is not calm is either not brave or rich and vice versa.
Susan is rich or strong.
John is either not tall or old.
Someone is either not quiet or not kind.
Someone is not rich.
John is wise.
Alice is either calm or funny.
Lucy is both patient and strong.
Lucy is either not generous or rich. | Lucy is patient. | entailment | ((?[X]:(patient(X)))=>(strong(paul)))&
((?[X]:((calm(X)|strong(X))))=>((~generous(alice)&funny(alice))))&
(![X]:((~quiet(X)|~tall(X))=>kind(X)))&
(![X]:((~humble(X)<~>curious(X))<=>creative(X)))&
(![X]:(~funny(X)=>(~rich(X)|tall(X))))&
(![X]:((~old(X)&~funny(X))<=>~old(X)))&
((creative(paul))<=>((humble(susan)&~generous(susan))))&
((?[X]:((~funny(X)<~>calm(X))))=>(?[X]:((~strong(X)<~>humble(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(tall(X)|happy(X))))&
((?[X]:((happy(X)|wise(X))))<=>((~generous(mary)&humble(mary))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(creative(X)<~>~tall(X))))&
(![X]:((calm(X)<~>generous(X))<=>~old(X)))&
(![X]:(happy(X)=>~calm(X)))&
(![X]:((~tall(X)&~happy(X))=>(~strong(X)|humble(X))))&
(((~curious(john)<~>wise(john)))=>((~happy(lucy)&~patient(lucy))))&
(![X]:(~calm(X)<=>(~brave(X)<~>rich(X))))&
((rich(susan)|strong(susan)))&
((~tall(john)<~>old(john)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:(~rich(X)))&
(wise(john))&
((calm(alice)<~>funny(alice)))&
((patient(lucy)&strong(lucy)))&
((~generous(lucy)<~>rich(lucy))) | patient(lucy) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 116175194989600405563165
% SZS output start Proof for 116175194989600405563165
23. strong(lucy) & patient(lucy) [input p22]
25. ~patient(lucy) [input hypothesis]
129. patient(lucy) [cnf transformation 23]
133. ~patient(lucy) [cnf transformation 25]
238. 22 <=> patient(lucy) [avatar definition]
284. 22 [avatar split clause 129,238]
295. ~22 [avatar split clause 133,238]
296. $false [avatar sat refutation 284,295]
% SZS output end Proof for 116175194989600405563165
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not wise is not rich.
Everyone who is old is not rich and vice versa.
If fred is patient then lucy is not curious or happy.
Everyone who is both not patient and rich is both creative and not humble and vice versa.
Everyone who is not old or rich is generous or not kind and vice versa.
Everyone who is either not brave or creative is not quiet or quiet and vice versa.
Everyone who is not happy is either generous or not generous.
If john is quiet then someone is either old or kind.
If alice is not kind then alice is either not happy or not generous.
Everyone who is funny is either not calm or not old and vice versa.
If mary is not calm or not brave then someone is both kind and creative and vice versa.
If someone is not generous or creative then john is happy or kind.
Everyone who is either not kind or not tall is either not kind or not generous.
Everyone who is either not rich or wise is calm.
If paul is either generous or kind then alice is either not calm or not tall.
Everyone who is both kind and wise is either generous or not funny and vice versa.
Someone is either not wise or humble.
Someone is funny.
Fred is either not calm or not brave.
Someone is either calm or rich.
Someone is rich.
Someone is not humble or not strong. | Paul is not wise. | contradiction | (![X]:((strong(X)|~wise(X))=>~rich(X)))&
(![X]:(old(X)<=>~rich(X)))&
((patient(fred))=>((~curious(lucy)|happy(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(creative(X)&~humble(X))))&
(![X]:((~old(X)|rich(X))<=>(generous(X)|~kind(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~happy(X)=>(generous(X)<~>~generous(X))))&
((quiet(john))=>(?[X]:((old(X)<~>kind(X)))))&
((~kind(alice))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(funny(X)<=>(~calm(X)<~>~old(X))))&
(((~calm(mary)|~brave(mary)))<=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:((~generous(X)|creative(X))))=>((happy(john)|kind(john))))&
(![X]:((~kind(X)<~>~tall(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>wise(X))=>calm(X)))&
(((generous(paul)<~>kind(paul)))=>((~calm(alice)<~>~tall(alice))))&
(![X]:((kind(X)&wise(X))<=>(generous(X)<~>~funny(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:(funny(X)))&
((~calm(fred)<~>~brave(fred)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((~humble(X)|~strong(X)))) | ~wise(paul) | [
"p0",
"p1",
"p4",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7565585589531630274237603
% SZS output start Proof for 7565585589531630274237603
1. ! [X0] : ((~wise(X0) | strong(X0)) => ~rich(X0)) [input p0]
2. ! [X0] : (old(X0) <=> ~rich(X0)) [input p1]
5. ! [X0] : ((rich(X0) | ~old(X0)) <=> (~kind(X0) | generous(X0))) [input p4]
10. ! [X0] : (funny(X0) <=> (~calm(X0) <~> ~old(X0))) [input p9]
14. ! [X0] : ((~rich(X0) <~> wise(X0)) => calm(X0)) [input p13]
16. ! [X0] : ((wise(X0) & kind(X0)) <=> (generous(X0) <~> ~funny(X0))) [input p15]
23. ~wise(paul) [input hypothesis]
25. ! [X0] : (~wise(X0) => ~rich(X0)) [pure predicate removal 1]
27. ! [X0] : (~rich(X0) | wise(X0)) [ennf transformation 25]
34. ! [X0] : (calm(X0) | (~rich(X0) <=> wise(X0))) [ennf transformation 14]
36. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 2]
39. ! [X0] : (((rich(X0) | ~old(X0)) | (kind(X0) & ~generous(X0))) & ((~kind(X0) | generous(X0)) | (~rich(X0) & old(X0)))) [nnf transformation 5]
40. ! [X0] : ((rich(X0) | ~old(X0) | (kind(X0) & ~generous(X0))) & (~kind(X0) | generous(X0) | (~rich(X0) & old(X0)))) [flattening 39]
48. ! [X0] : ((funny(X0) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | ~funny(X0))) [nnf transformation 10]
55. ! [X0] : (calm(X0) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0)))) [nnf transformation 34]
57. ! [X0] : (((wise(X0) & kind(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (~wise(X0) | ~kind(X0)))) [nnf transformation 16]
58. ! [X0] : (((wise(X0) & kind(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | ~wise(X0) | ~kind(X0))) [flattening 57]
70. ~rich(X0) | wise(X0) [cnf transformation 27]
71. ~old(X0) | ~rich(X0) [cnf transformation 36]
72. old(X0) | rich(X0) [cnf transformation 36]
79. rich(X0) | ~old(X0) | ~generous(X0) [cnf transformation 40]
93. ~calm(X0) | ~old(X0) | ~funny(X0) [cnf transformation 48]
108. calm(X0) | wise(X0) | rich(X0) [cnf transformation 55]
109. calm(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 55]
119. funny(X0) | generous(X0) | wise(X0) [cnf transformation 58]
128. ~wise(paul) [cnf transformation 23]
132. ~generous(X0) | ~old(X0) [subsumption resolution 79,71]
205. ~rich(X0) | calm(X0) [subsumption resolution 109,70]
206. calm(X0) | wise(X0) [subsumption resolution 108,205]
360. ~funny(X0) | ~old(X0) | wise(X0) [resolution 93,206]
594. ~old(X0) | wise(X0) | generous(X0) | wise(X0) [resolution 360,119]
599. ~old(X0) | wise(X0) | generous(X0) [duplicate literal removal 594]
600. ~old(X0) | wise(X0) [subsumption resolution 599,132]
802. wise(X0) | rich(X0) [resolution 600,72]
807. wise(X0) [subsumption resolution 802,70]
812. $false [resolution 807,128]
% SZS output end Proof for 7565585589531630274237603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or kind is old or rich. Everyone who is both not kind and old is creative or humble and vice versa. Everyone who is strong is either creative or old. Everyone who is both rich and not calm is both not brave and funny and vice versa. Everyone who is either not humble or old is either not brave or humble. If someone is not creative or quiet then someone is either wise or patient. If someone is both brave and not old then someone is both not rich and old. Everyone who is both not rich and not patient is not curious or not strong and vice versa. If someone is both tall and not calm then alice is both strong and old. If alice is both kind and not tall then john is both not rich and not generous and vice versa. If someone is not strong or not calm then alice is rich and vice versa. Everyone who is generous is rich or not generous. If lucy is creative or rich then alice is either funny or wise and vice versa. If alice is creative or not rich then someone is both rich and not old and vice versa. Everyone who is either happy or generous is either creative or not rich and vice versa. Everyone who is both funny and not calm is both not quiet and curious. Lucy is either not old or rich. John is either curious or old. Lucy is generous. Fred is both not brave and not wise. John is brave or not old. Someone is both not quiet and calm. | Alice is not brave. | neutral | (![X]:((happy(X)<~>kind(X))=>(old(X)|rich(X))))&
(![X]:((~kind(X)&old(X))<=>(creative(X)|humble(X))))&
(![X]:(strong(X)=>(creative(X)<~>old(X))))&
(![X]:((rich(X)&~calm(X))<=>(~brave(X)&funny(X))))&
(![X]:((~humble(X)<~>old(X))=>(~brave(X)<~>humble(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((wise(X)<~>patient(X)))))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((~rich(X)&old(X)))))&
(![X]:((~rich(X)&~patient(X))<=>(~curious(X)|~strong(X))))&
((?[X]:((tall(X)&~calm(X))))=>((strong(alice)&old(alice))))&
(((kind(alice)&~tall(alice)))<=>((~rich(john)&~generous(john))))&
((?[X]:((~strong(X)|~calm(X))))<=>(rich(alice)))&
(![X]:(generous(X)=>(rich(X)|~generous(X))))&
(((creative(lucy)|rich(lucy)))<=>((funny(alice)<~>wise(alice))))&
(((creative(alice)|~rich(alice)))<=>(?[X]:((rich(X)&~old(X)))))&
(![X]:((happy(X)<~>generous(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((funny(X)&~calm(X))=>(~quiet(X)&curious(X))))&
((~old(lucy)<~>rich(lucy)))&
((curious(john)<~>old(john)))&
(generous(lucy))&
((~brave(fred)&~wise(fred)))&
((brave(john)|~old(john)))&
(?[X]:((~quiet(X)&calm(X)))) | ~brave(alice) | [] | null | 0 |
Everyone who is either not patient or calm is generous or not funny.
If someone is either quiet or not calm then someone is kind or rich.
Everyone who is not funny or not wise is both old and kind.
Everyone who is both strong and tall is not happy and vice versa.
If alice is both funny and not calm then lucy is both not humble and wise.
If someone is either brave or calm then susan is both not quiet and not wise.
If someone is either quiet or not generous then someone is not tall or quiet.
If someone is not creative then someone is both not funny and brave and vice versa.
Everyone who is not funny is both tall and not calm.
If mary is not generous then susan is not curious.
Everyone who is rich or generous is quiet.
If mary is not old or quiet then someone is not tall and vice versa.
If mary is either rich or not curious then someone is either not humble or funny.
Everyone who is not calm or brave is either not funny or happy and vice versa.
Everyone who is not tall or not quiet is generous and vice versa.
Everyone who is not funny or not strong is wise and vice versa.
Mary is either not quiet or happy.
Paul is either not strong or wise.
John is both not humble and kind.
Someone is not calm.
Mary is not rich or rich.
Someone is either not rich or old.
Someone is not curious.
Mary is patient or wise. | Paul is old. | entailment | (![X]:((~patient(X)<~>calm(X))=>(generous(X)|~funny(X))))&
((?[X]:((quiet(X)<~>~calm(X))))=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((~funny(X)|~wise(X))=>(old(X)&kind(X))))&
(![X]:((strong(X)&tall(X))<=>~happy(X)))&
(((funny(alice)&~calm(alice)))=>((~humble(lucy)&wise(lucy))))&
((?[X]:((brave(X)<~>calm(X))))=>((~quiet(susan)&~wise(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:(~funny(X)=>(tall(X)&~calm(X))))&
((~generous(mary))=>(~curious(susan)))&
(![X]:((rich(X)|generous(X))=>quiet(X)))&
(((~old(mary)|quiet(mary)))<=>(?[X]:(~tall(X))))&
(((rich(mary)<~>~curious(mary)))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~calm(X)|brave(X))<=>(~funny(X)<~>happy(X))))&
(![X]:((~tall(X)|~quiet(X))<=>generous(X)))&
(![X]:((~funny(X)|~strong(X))<=>wise(X)))&
((~quiet(mary)<~>happy(mary)))&
((~strong(paul)<~>wise(paul)))&
((~humble(john)&kind(john)))&
(?[X]:(~calm(X)))&
((~rich(mary)|rich(mary)))&
(?[X]:((~rich(X)<~>old(X))))&
(?[X]:(~curious(X)))&
((patient(mary)|wise(mary))) | old(paul) | [
"p2",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5087629986019848055295584
% SZS output start Proof for 5087629986019848055295584
3. ! [X0] : ((~wise(X0) | ~funny(X0)) => (kind(X0) & old(X0))) [input p2]
16. ! [X0] : ((~strong(X0) | ~funny(X0)) <=> wise(X0)) [input p15]
18. ~strong(paul) <~> wise(paul) [input p17]
25. ~old(paul) [input hypothesis]
29. ! [X0] : ((~wise(X0) | ~funny(X0)) => old(X0)) [pure predicate removal 3]
34. ! [X0] : (old(X0) | (wise(X0) & funny(X0))) [ennf transformation 29]
68. ! [X0] : (((~strong(X0) | ~funny(X0)) | ~wise(X0)) & (wise(X0) | (strong(X0) & funny(X0)))) [nnf transformation 16]
69. ! [X0] : ((~strong(X0) | ~funny(X0) | ~wise(X0)) & (wise(X0) | (strong(X0) & funny(X0)))) [flattening 68]
71. (~wise(paul) | strong(paul)) & (wise(paul) | ~strong(paul)) [nnf transformation 18]
81. old(X0) | funny(X0) [cnf transformation 34]
119. strong(X0) | wise(X0) [cnf transformation 69]
120. ~strong(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 69]
123. wise(paul) | ~strong(paul) [cnf transformation 71]
124. ~wise(paul) | strong(paul) [cnf transformation 71]
132. ~old(paul) [cnf transformation 25]
258. strong(paul) [subsumption resolution 124,119]
259. wise(paul) [subsumption resolution 123,258]
283. funny(paul) [resolution 81,132]
380. ~funny(paul) | ~wise(paul) [resolution 120,258]
383. ~wise(paul) [subsumption resolution 380,283]
384. $false [subsumption resolution 383,259]
% SZS output end Proof for 5087629986019848055295584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not old is either rich or patient and vice versa.
If paul is tall or kind then someone is both not quiet and not patient and vice versa.
If john is both not calm and humble then someone is generous.
If someone is both not tall and not rich then someone is both old and happy and vice versa.
Everyone who is both kind and rich is not wise and vice versa.
Everyone who is both funny and not generous is both not wise and happy.
Everyone who is both not calm and strong is either old or not calm and vice versa.
Everyone who is tall is patient or not quiet and vice versa.
Everyone who is not rich is humble and vice versa.
Everyone who is either brave or rich is either curious or not quiet.
Everyone who is both not generous and not funny is not rich.
If someone is either patient or humble then fred is not wise or not curious.
Everyone who is not strong or not brave is either not patient or not strong.
Everyone who is not calm or creative is either rich or wise.
Everyone who is creative is either calm or not calm and vice versa.
If mary is both happy and brave then fred is either kind or not tall.
John is not funny.
Fred is either not generous or not tall.
Alice is kind.
Lucy is both not happy and calm.
John is not happy.
Lucy is not funny or curious.
Someone is both humble and not quiet.
Someone is either not curious or calm. | Lucy is strong. | entailment | (![X]:((~humble(X)&~old(X))<=>(rich(X)<~>patient(X))))&
(((tall(paul)|kind(paul)))<=>(?[X]:((~quiet(X)&~patient(X)))))&
(((~calm(john)&humble(john)))=>(?[X]:(generous(X))))&
((?[X]:((~tall(X)&~rich(X))))<=>(?[X]:((old(X)&happy(X)))))&
(![X]:((kind(X)&rich(X))<=>~wise(X)))&
(![X]:((funny(X)&~generous(X))=>(~wise(X)&happy(X))))&
(![X]:((~calm(X)&strong(X))<=>(old(X)<~>~calm(X))))&
(![X]:(tall(X)<=>(patient(X)|~quiet(X))))&
(![X]:(~rich(X)<=>humble(X)))&
(![X]:((brave(X)<~>rich(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((~generous(X)&~funny(X))=>~rich(X)))&
((?[X]:((patient(X)<~>humble(X))))=>((~wise(fred)|~curious(fred))))&
(![X]:((~strong(X)|~brave(X))=>(~patient(X)<~>~strong(X))))&
(![X]:((~calm(X)|creative(X))=>(rich(X)<~>wise(X))))&
(![X]:(creative(X)<=>(calm(X)<~>~calm(X))))&
(((happy(mary)&brave(mary)))=>((kind(fred)<~>~tall(fred))))&
(~funny(john))&
((~generous(fred)<~>~tall(fred)))&
(kind(alice))&
((~happy(lucy)&calm(lucy)))&
(~happy(john))&
((~funny(lucy)|curious(lucy)))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:((~curious(X)<~>calm(X)))) | strong(lucy) | [
"p0",
"p6",
"p8",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5368653277558786622408500
% SZS output start Proof for 5368653277558786622408500
1. ! [X0] : ((~old(X0) & ~humble(X0)) <=> (rich(X0) <~> patient(X0))) [input p0]
7. ! [X0] : ((strong(X0) & ~calm(X0)) <=> (old(X0) <~> ~calm(X0))) [input p6]
9. ! [X0] : (~rich(X0) <=> humble(X0)) [input p8]
13. ! [X0] : ((~brave(X0) | ~strong(X0)) => (~patient(X0) <~> ~strong(X0))) [input p12]
20. calm(lucy) & ~happy(lucy) [input p19]
25. ~strong(lucy) [input hypothesis]
37. ! [X0] : ((~patient(X0) <~> ~strong(X0)) | (brave(X0) & strong(X0))) [ennf transformation 13]
42. ! [X0] : (((~old(X0) & ~humble(X0)) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | (old(X0) | humble(X0)))) [nnf transformation 1]
43. ! [X0] : (((~old(X0) & ~humble(X0)) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | old(X0) | humble(X0))) [flattening 42]
58. ! [X0] : (((strong(X0) & ~calm(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0)))) & (((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | (~strong(X0) | calm(X0)))) [nnf transformation 7]
59. ! [X0] : (((strong(X0) & ~calm(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0)))) & (((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | ~strong(X0) | calm(X0))) [flattening 58]
62. ! [X0] : ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))) [nnf transformation 9]
65. ! [X0] : (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | (brave(X0) & strong(X0))) [nnf transformation 37]
76. ~patient(X0) | ~rich(X0) | old(X0) | humble(X0) [cnf transformation 43]
78. ~patient(X0) | rich(X0) | ~humble(X0) [cnf transformation 43]
98. ~calm(X0) | ~calm(X0) | ~old(X0) [cnf transformation 59]
105. rich(X0) | humble(X0) [cnf transformation 62]
106. ~rich(X0) | ~humble(X0) [cnf transformation 62]
116. strong(X0) | patient(X0) | strong(X0) [cnf transformation 65]
131. calm(lucy) [cnf transformation 20]
138. ~strong(lucy) [cnf transformation 25]
141. strong(X0) | patient(X0) [duplicate literal removal 116]
143. ~calm(X0) | ~old(X0) [duplicate literal removal 98]
274. patient(lucy) [resolution 141,138]
276. ~old(lucy) [resolution 143,131]
285. rich(lucy) | ~humble(lucy) [resolution 78,274]
286. rich(lucy) [subsumption resolution 285,105]
288. ~humble(lucy) [resolution 286,106]
338. ~rich(lucy) | old(lucy) | humble(lucy) [resolution 76,274]
341. old(lucy) | humble(lucy) [subsumption resolution 338,286]
342. humble(lucy) [subsumption resolution 341,276]
343. $false [subsumption resolution 342,288]
% SZS output end Proof for 5368653277558786622408500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is quiet or not old then someone is quiet and vice versa.
Everyone who is both happy and creative is not humble or not curious and vice versa.
Everyone who is curious or not strong is both creative and not old and vice versa.
Everyone who is wise is not creative or not calm and vice versa.
If mary is both funny and not quiet then someone is not creative or not brave and vice versa.
Everyone who is rich is both not wise and strong.
If fred is not brave then alice is strong or not quiet and vice versa.
If someone is not happy or not old then alice is both brave and tall.
Everyone who is patient or not happy is patient and vice versa.
If someone is either not tall or not strong then someone is both kind and calm.
Everyone who is both funny and kind is generous or creative.
Everyone who is both funny and not calm is either not happy or not patient.
Everyone who is not humble or calm is not strong and vice versa.
If someone is calm or curious then someone is not humble or not funny.
Everyone who is both not calm and not kind is either not humble or tall and vice versa.
If alice is quiet then someone is not curious or tall.
Alice is either not calm or creative.
Someone is either brave or not creative.
John is both not patient and not rich.
Alice is both funny and not quiet.
Someone is either not quiet or rich.
Alice is not strong or strong. | Fred is not calm. | neutral | (((quiet(john)|~old(john)))<=>(?[X]:(quiet(X))))&
(![X]:((happy(X)&creative(X))<=>(~humble(X)|~curious(X))))&
(![X]:((curious(X)|~strong(X))<=>(creative(X)&~old(X))))&
(![X]:(wise(X)<=>(~creative(X)|~calm(X))))&
(((funny(mary)&~quiet(mary)))<=>(?[X]:((~creative(X)|~brave(X)))))&
(![X]:(rich(X)=>(~wise(X)&strong(X))))&
((~brave(fred))<=>((strong(alice)|~quiet(alice))))&
((?[X]:((~happy(X)|~old(X))))=>((brave(alice)&tall(alice))))&
(![X]:((patient(X)|~happy(X))<=>patient(X)))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((kind(X)&calm(X)))))&
(![X]:((funny(X)&kind(X))=>(generous(X)|creative(X))))&
(![X]:((funny(X)&~calm(X))=>(~happy(X)<~>~patient(X))))&
(![X]:((~humble(X)|calm(X))<=>~strong(X)))&
((?[X]:((calm(X)|curious(X))))=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:((~calm(X)&~kind(X))<=>(~humble(X)<~>tall(X))))&
((quiet(alice))=>(?[X]:((~curious(X)|tall(X)))))&
((~calm(alice)<~>creative(alice)))&
(?[X]:((brave(X)<~>~creative(X))))&
((~patient(john)&~rich(john)))&
((funny(alice)&~quiet(alice)))&
(?[X]:((~quiet(X)<~>rich(X))))&
((~strong(alice)|strong(alice))) | ~calm(fred) | [] | null | 0 |
Everyone who is either not wise or brave is not tall or not patient. Everyone who is both happy and humble is not strong or creative. Everyone who is both not rich and happy is not tall. Everyone who is both not humble and not old is old and vice versa. Everyone who is not old or brave is either generous or not creative and vice versa. Everyone who is both generous and not brave is either funny or kind and vice versa. Everyone who is either curious or rich is strong. Everyone who is not funny or funny is curious or not humble. Everyone who is kind is both not humble and funny. If someone is both quiet and curious then someone is either happy or brave and vice versa. Everyone who is rich or not strong is strong or not humble. If someone is brave or curious then paul is either not curious or not generous. Everyone who is either humble or not funny is not wise. If alice is not funny then alice is either happy or not quiet. If susan is not generous or patient then someone is both kind and not funny. If someone is either rich or kind then someone is not wise. Someone is tall. Someone is both not generous and calm. Alice is not humble or brave. Susan is not strong or funny. Someone is humble. Mary is either happy or not creative. Alice is happy or wise. | Susan is not old. | entailment | (![X]:((~wise(X)<~>brave(X))=>(~tall(X)|~patient(X))))&
(![X]:((happy(X)&humble(X))=>(~strong(X)|creative(X))))&
(![X]:((~rich(X)&happy(X))=>~tall(X)))&
(![X]:((~humble(X)&~old(X))<=>old(X)))&
(![X]:((~old(X)|brave(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((generous(X)&~brave(X))<=>(funny(X)<~>kind(X))))&
(![X]:((curious(X)<~>rich(X))=>strong(X)))&
(![X]:((~funny(X)|funny(X))=>(curious(X)|~humble(X))))&
(![X]:(kind(X)=>(~humble(X)&funny(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((rich(X)|~strong(X))=>(strong(X)|~humble(X))))&
((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((humble(X)<~>~funny(X))=>~wise(X)))&
((~funny(alice))=>((happy(alice)<~>~quiet(alice))))&
(((~generous(susan)|patient(susan)))=>(?[X]:((kind(X)&~funny(X)))))&
((?[X]:((rich(X)<~>kind(X))))=>(?[X]:(~wise(X))))&
(?[X]:(tall(X)))&
(?[X]:((~generous(X)&calm(X))))&
((~humble(alice)|brave(alice)))&
((~strong(susan)|funny(susan)))&
(?[X]:(humble(X)))&
((happy(mary)<~>~creative(mary)))&
((happy(alice)|wise(alice))) | ~old(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 9006796498157631940398174
% SZS output start Proof for 9006796498157631940398174
4. ! [X0] : ((~old(X0) & ~humble(X0)) <=> old(X0)) [input p3]
24. old(susan) [input hypothesis]
45. ! [X0] : (((~old(X0) & ~humble(X0)) | ~old(X0)) & (old(X0) | (old(X0) | humble(X0)))) [nnf transformation 4]
46. ! [X0] : (((~old(X0) & ~humble(X0)) | ~old(X0)) & (old(X0) | old(X0) | humble(X0))) [flattening 45]
77. ~old(X0) | ~old(X0) [cnf transformation 46]
124. old(susan) [cnf transformation 24]
127. ~old(X0) [duplicate literal removal 77]
217. $false [subsumption resolution 124,127]
% SZS output end Proof for 9006796498157631940398174
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not generous or happy is brave or quiet.
If someone is not patient then john is both not rich and rich and vice versa.
If fred is not quiet or wise then john is not rich or funny and vice versa.
Everyone who is either rich or happy is strong or humble.
Everyone who is both curious and not quiet is not old or wise.
Everyone who is creative or not calm is brave or happy.
Everyone who is quiet or not wise is both funny and not humble and vice versa.
If someone is both not kind and wise then someone is not patient or not wise.
If someone is both tall and not creative then someone is either not strong or kind and vice versa.
Everyone who is brave or not strong is happy.
If someone is generous then susan is both kind and calm.
Everyone who is either old or not kind is generous.
If someone is both patient and not curious then alice is either not kind or not humble and vice versa.
Everyone who is either not strong or not patient is strong.
Everyone who is both strong and curious is brave or not old and vice versa.
Everyone who is both curious and not creative is tall or patient.
Susan is tall.
Someone is not funny or not strong.
Paul is strong.
Someone is brave.
Someone is both not humble and not happy.
Alice is both generous and rich. | Fred is not tall. | neutral | (![X]:((~generous(X)<~>happy(X))=>(brave(X)|quiet(X))))&
((?[X]:(~patient(X)))<=>((~rich(john)&rich(john))))&
(((~quiet(fred)|wise(fred)))<=>((~rich(john)|funny(john))))&
(![X]:((rich(X)<~>happy(X))=>(strong(X)|humble(X))))&
(![X]:((curious(X)&~quiet(X))=>(~old(X)|wise(X))))&
(![X]:((creative(X)|~calm(X))=>(brave(X)|happy(X))))&
(![X]:((quiet(X)|~wise(X))<=>(funny(X)&~humble(X))))&
((?[X]:((~kind(X)&wise(X))))=>(?[X]:((~patient(X)|~wise(X)))))&
((?[X]:((tall(X)&~creative(X))))<=>(?[X]:((~strong(X)<~>kind(X)))))&
(![X]:((brave(X)|~strong(X))=>happy(X)))&
((?[X]:(generous(X)))=>((kind(susan)&calm(susan))))&
(![X]:((old(X)<~>~kind(X))=>generous(X)))&
((?[X]:((patient(X)&~curious(X))))<=>((~kind(alice)<~>~humble(alice))))&
(![X]:((~strong(X)<~>~patient(X))=>strong(X)))&
(![X]:((strong(X)&curious(X))<=>(brave(X)|~old(X))))&
(![X]:((curious(X)&~creative(X))=>(tall(X)|patient(X))))&
(tall(susan))&
(?[X]:((~funny(X)|~strong(X))))&
(strong(paul))&
(?[X]:(brave(X)))&
(?[X]:((~humble(X)&~happy(X))))&
((generous(alice)&rich(alice))) | ~tall(fred) | [] | null | 0 |
If someone is both not curious and quiet then john is both not curious and happy. If someone is not humble or humble then lucy is calm. Everyone who is not wise or not patient is old. If someone is both not creative and brave then alice is both not old and not strong and vice versa. If lucy is either strong or not funny then fred is kind or patient and vice versa. If alice is both tall and not calm then someone is both happy and not quiet. Everyone who is not tall is both wise and tall. Everyone who is not generous is not wise or tall and vice versa. Everyone who is either not calm or not wise is happy or calm. Everyone who is old is not generous and vice versa. Everyone who is quiet or old is either rich or not brave and vice versa. Everyone who is not calm or patient is either not funny or not humble and vice versa. Everyone who is either not rich or not quiet is wise or patient and vice versa. Everyone who is curious is not wise and vice versa. Everyone who is both generous and patient is not quiet or not strong. Everyone who is calm or happy is either not tall or not happy and vice versa. Fred is not strong or not creative. Mary is humble. Alice is either not quiet or not rich. Paul is happy or not generous. Someone is both calm and kind. Someone is both not kind and not creative. | Paul is creative. | neutral | ((?[X]:((~curious(X)&quiet(X))))=>((~curious(john)&happy(john))))&
((?[X]:((~humble(X)|humble(X))))=>(calm(lucy)))&
(![X]:((~wise(X)|~patient(X))=>old(X)))&
((?[X]:((~creative(X)&brave(X))))<=>((~old(alice)&~strong(alice))))&
(((strong(lucy)<~>~funny(lucy)))<=>((kind(fred)|patient(fred))))&
(((tall(alice)&~calm(alice)))=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:(~tall(X)=>(wise(X)&tall(X))))&
(![X]:(~generous(X)<=>(~wise(X)|tall(X))))&
(![X]:((~calm(X)<~>~wise(X))=>(happy(X)|calm(X))))&
(![X]:(old(X)<=>~generous(X)))&
(![X]:((quiet(X)|old(X))<=>(rich(X)<~>~brave(X))))&
(![X]:((~calm(X)|patient(X))<=>(~funny(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(wise(X)|patient(X))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((generous(X)&patient(X))=>(~quiet(X)|~strong(X))))&
(![X]:((calm(X)|happy(X))<=>(~tall(X)<~>~happy(X))))&
((~strong(fred)|~creative(fred)))&
(humble(mary))&
((~quiet(alice)<~>~rich(alice)))&
((happy(paul)|~generous(paul)))&
(?[X]:((calm(X)&kind(X))))&
(?[X]:((~kind(X)&~creative(X)))) | creative(paul) | [] | null | 0 |
Everyone who is wise or quiet is both happy and patient and vice versa.
Everyone who is rich is either calm or not brave.
Everyone who is either not old or not kind is not wise.
Everyone who is not calm is both not wise and not kind.
Everyone who is both happy and not wise is both rich and not humble.
Everyone who is funny or brave is both not calm and calm.
If someone is either rich or curious then john is both funny and not humble and vice versa.
If john is creative or calm then fred is either kind or calm.
Everyone who is not generous is both strong and not old.
Everyone who is either quiet or generous is either funny or not humble and vice versa.
If paul is old then someone is either not happy or patient and vice versa.
Everyone who is creative is tall or humble and vice versa.
Everyone who is both not curious and not brave is either patient or brave.
If john is humble then someone is either strong or brave and vice versa.
If someone is not patient or kind then someone is both not rich and quiet.
If someone is creative then paul is kind.
Mary is either quiet or not wise.
Someone is strong or not curious.
Someone is wise.
Someone is either not rich or not calm.
Someone is either not strong or not brave.
Paul is both creative and happy. | Mary is not humble. | neutral | (![X]:((wise(X)|quiet(X))<=>(happy(X)&patient(X))))&
(![X]:(rich(X)=>(calm(X)<~>~brave(X))))&
(![X]:((~old(X)<~>~kind(X))=>~wise(X)))&
(![X]:(~calm(X)=>(~wise(X)&~kind(X))))&
(![X]:((happy(X)&~wise(X))=>(rich(X)&~humble(X))))&
(![X]:((funny(X)|brave(X))=>(~calm(X)&calm(X))))&
((?[X]:((rich(X)<~>curious(X))))<=>((funny(john)&~humble(john))))&
(((creative(john)|calm(john)))=>((kind(fred)<~>calm(fred))))&
(![X]:(~generous(X)=>(strong(X)&~old(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(funny(X)<~>~humble(X))))&
((old(paul))<=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:(creative(X)<=>(tall(X)|humble(X))))&
(![X]:((~curious(X)&~brave(X))=>(patient(X)<~>brave(X))))&
((humble(john))<=>(?[X]:((strong(X)<~>brave(X)))))&
((?[X]:((~patient(X)|kind(X))))=>(?[X]:((~rich(X)&quiet(X)))))&
((?[X]:(creative(X)))=>(kind(paul)))&
((quiet(mary)<~>~wise(mary)))&
(?[X]:((strong(X)|~curious(X))))&
(?[X]:(wise(X)))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~strong(X)<~>~brave(X))))&
((creative(paul)&happy(paul))) | ~humble(mary) | [] | null | 0 |
Everyone who is both patient and happy is not patient. Everyone who is both not wise and not old is old and vice versa. Everyone who is not happy is patient or wise. If someone is either generous or funny then mary is either not quiet or funny and vice versa. Everyone who is either not funny or not old is both kind and funny. If lucy is either not curious or not old then alice is creative and vice versa. Everyone who is not old is calm or kind. If john is both wise and not kind then someone is both not curious and not humble. If someone is either brave or quiet then mary is either old or creative and vice versa. Everyone who is not old is not wise or not happy. Everyone who is calm or not happy is not generous and vice versa. Everyone who is generous or tall is either wise or not quiet and vice versa. Everyone who is both quiet and patient is either calm or not generous. If someone is tall or not rich then someone is both not old and generous. If someone is either not old or not wise then someone is not old and vice versa. Someone is both curious and strong. Someone is curious or calm. Fred is either not wise or not strong. Someone is both not old and rich. Susan is both strong and creative. Someone is quiet or not strong. Fred is not generous. | Mary is tall. | contradiction | (![X]:((patient(X)&happy(X))=>~patient(X)))&
(![X]:((~wise(X)&~old(X))<=>old(X)))&
(![X]:(~happy(X)=>(patient(X)|wise(X))))&
((?[X]:((generous(X)<~>funny(X))))<=>((~quiet(mary)<~>funny(mary))))&
(![X]:((~funny(X)<~>~old(X))=>(kind(X)&funny(X))))&
(((~curious(lucy)<~>~old(lucy)))<=>(creative(alice)))&
(![X]:(~old(X)=>(calm(X)|kind(X))))&
(((wise(john)&~kind(john)))=>(?[X]:((~curious(X)&~humble(X)))))&
((?[X]:((brave(X)<~>quiet(X))))<=>((old(mary)<~>creative(mary))))&
(![X]:(~old(X)=>(~wise(X)|~happy(X))))&
(![X]:((calm(X)|~happy(X))<=>~generous(X)))&
(![X]:((generous(X)|tall(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((quiet(X)&patient(X))=>(calm(X)<~>~generous(X))))&
((?[X]:((tall(X)|~rich(X))))=>(?[X]:((~old(X)&generous(X)))))&
((?[X]:((~old(X)<~>~wise(X))))<=>(?[X]:(~old(X))))&
(?[X]:((curious(X)&strong(X))))&
(?[X]:((curious(X)|calm(X))))&
((~wise(fred)<~>~strong(fred)))&
(?[X]:((~old(X)&rich(X))))&
((strong(susan)&creative(susan)))&
(?[X]:((quiet(X)|~strong(X))))&
(~generous(fred)) | tall(mary) | [
"p1",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 429366445622551085714523
% SZS output start Proof for 429366445622551085714523
2. ! [X0] : ((~old(X0) & ~wise(X0)) <=> old(X0)) [input p1]
10. ! [X0] : (~old(X0) => (~happy(X0) | ~wise(X0))) [input p9]
11. ! [X0] : ((~happy(X0) | calm(X0)) <=> ~generous(X0)) [input p10]
14. ? [X0] : (~rich(X0) | tall(X0)) => ? [X0] : (generous(X0) & ~old(X0)) [input p13]
23. tall(mary) [input hypothesis]
24. ? [X0] : (~rich(X0) | tall(X0)) => ? [X1] : (generous(X1) & ~old(X1)) [rectify 14]
27. ? [X0] : tall(X0) => ? [X1] : (generous(X1) & ~old(X1)) [pure predicate removal 24]
37. ! [X0] : ((~happy(X0) | ~wise(X0)) | old(X0)) [ennf transformation 10]
38. ! [X0] : (~happy(X0) | ~wise(X0) | old(X0)) [flattening 37]
41. ? [X1] : (generous(X1) & ~old(X1)) | ! [X0] : ~tall(X0) [ennf transformation 27]
42. ! [X0] : (((~old(X0) & ~wise(X0)) | ~old(X0)) & (old(X0) | (old(X0) | wise(X0)))) [nnf transformation 2]
43. ! [X0] : (((~old(X0) & ~wise(X0)) | ~old(X0)) & (old(X0) | old(X0) | wise(X0))) [flattening 42]
54. ! [X0] : (((~happy(X0) | calm(X0)) | generous(X0)) & (~generous(X0) | (happy(X0) & ~calm(X0)))) [nnf transformation 11]
55. ! [X0] : ((~happy(X0) | calm(X0) | generous(X0)) & (~generous(X0) | (happy(X0) & ~calm(X0)))) [flattening 54]
59. ? [X0] : (generous(X0) & ~old(X0)) | ! [X1] : ~tall(X1) [rectify 41]
60. ? [X0] : (generous(X0) & ~old(X0)) => (generous(sK2) & ~old(sK2)) [choice axiom]
61. (generous(sK2) & ~old(sK2)) | ! [X1] : ~tall(X1) [skolemisation 59,60]
77. old(X0) | old(X0) | wise(X0) [cnf transformation 43]
79. ~old(X0) | ~old(X0) [cnf transformation 43]
103. ~happy(X0) | ~wise(X0) | old(X0) [cnf transformation 38]
105. ~generous(X0) | happy(X0) [cnf transformation 55]
116. generous(sK2) | ~tall(X1) [cnf transformation 61]
131. tall(mary) [cnf transformation 23]
133. old(X0) | wise(X0) [duplicate literal removal 77]
134. ~old(X0) [duplicate literal removal 79]
136. wise(X0) [subsumption resolution 133,134]
205. ~happy(X0) | old(X0) [subsumption resolution 103,136]
206. ~happy(X0) [subsumption resolution 205,134]
207. ~generous(X0) [subsumption resolution 105,206]
212. ~tall(X1) [subsumption resolution 116,207]
232. $false [subsumption resolution 131,212]
% SZS output end Proof for 429366445622551085714523
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or quiet is not strong.
If someone is curious or funny then fred is both kind and strong and vice versa.
Everyone who is both not happy and not generous is both not humble and not patient and vice versa.
If john is kind then john is either not brave or not patient and vice versa.
Everyone who is not rich is strong and vice versa.
Everyone who is either not funny or brave is either happy or curious.
If someone is not tall then fred is either patient or curious.
Everyone who is not quiet or not wise is either calm or not old and vice versa.
Everyone who is both not humble and not patient is calm and vice versa.
Everyone who is either wise or not calm is rich and vice versa.
Everyone who is either happy or not happy is not tall or not strong and vice versa.
Everyone who is both not humble and humble is both wise and not humble.
Everyone who is tall is not brave.
Everyone who is either not calm or not strong is happy or not old.
Everyone who is both not generous and wise is curious or not rich and vice versa.
If someone is both calm and not quiet then someone is both not calm and not old and vice versa.
John is not creative.
Someone is kind.
Someone is both old and brave.
Someone is either not old or strong.
Someone is calm.
Someone is either kind or not curious.
Susan is both not brave and strong. | Fred is not quiet. | contradiction | (![X]:((curious(X)<~>quiet(X))=>~strong(X)))&
((?[X]:((curious(X)|funny(X))))<=>((kind(fred)&strong(fred))))&
(![X]:((~happy(X)&~generous(X))<=>(~humble(X)&~patient(X))))&
((kind(john))<=>((~brave(john)<~>~patient(john))))&
(![X]:(~rich(X)<=>strong(X)))&
(![X]:((~funny(X)<~>brave(X))=>(happy(X)<~>curious(X))))&
((?[X]:(~tall(X)))=>((patient(fred)<~>curious(fred))))&
(![X]:((~quiet(X)|~wise(X))<=>(calm(X)<~>~old(X))))&
(![X]:((~humble(X)&~patient(X))<=>calm(X)))&
(![X]:((wise(X)<~>~calm(X))<=>rich(X)))&
(![X]:((happy(X)<~>~happy(X))<=>(~tall(X)|~strong(X))))&
(![X]:((~humble(X)&humble(X))=>(wise(X)&~humble(X))))&
(![X]:(tall(X)=>~brave(X)))&
(![X]:((~calm(X)<~>~strong(X))=>(happy(X)|~old(X))))&
(![X]:((~generous(X)&wise(X))<=>(curious(X)|~rich(X))))&
((?[X]:((calm(X)&~quiet(X))))<=>(?[X]:((~calm(X)&~old(X)))))&
(~creative(john))&
(?[X]:(kind(X)))&
(?[X]:((old(X)&brave(X))))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:(calm(X)))&
(?[X]:((kind(X)<~>~curious(X))))&
((~brave(susan)&strong(susan))) | ~quiet(fred) | [
"p2",
"p4",
"p7",
"p8",
"p9",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6119901647918049815420447
% SZS output start Proof for 6119901647918049815420447
3. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> (~patient(X0) & ~humble(X0))) [input p2]
5. ! [X0] : (~rich(X0) <=> strong(X0)) [input p4]
8. ! [X0] : ((~wise(X0) | ~quiet(X0)) <=> (calm(X0) <~> ~old(X0))) [input p7]
9. ! [X0] : ((~patient(X0) & ~humble(X0)) <=> calm(X0)) [input p8]
10. ! [X0] : ((wise(X0) <~> ~calm(X0)) <=> rich(X0)) [input p9]
14. ! [X0] : ((~calm(X0) <~> ~strong(X0)) => (~old(X0) | happy(X0))) [input p13]
15. ! [X0] : ((wise(X0) & ~generous(X0)) <=> (~rich(X0) | curious(X0))) [input p14]
16. ? [X0] : (~quiet(X0) & calm(X0)) <=> ? [X0] : (~old(X0) & ~calm(X0)) [input p15]
24. ~quiet(fred) [input hypothesis]
25. ? [X0] : (~quiet(X0) & calm(X0)) <=> ? [X1] : (~old(X1) & ~calm(X1)) [rectify 16]
33. ! [X0] : ((~old(X0) | happy(X0)) | (~calm(X0) <=> ~strong(X0))) [ennf transformation 14]
34. ! [X0] : (~old(X0) | happy(X0) | (~calm(X0) <=> ~strong(X0))) [flattening 33]
41. ! [X0] : (((~generous(X0) & ~happy(X0)) | (patient(X0) | humble(X0))) & ((~patient(X0) & ~humble(X0)) | (generous(X0) | happy(X0)))) [nnf transformation 3]
42. ! [X0] : (((~generous(X0) & ~happy(X0)) | patient(X0) | humble(X0)) & ((~patient(X0) & ~humble(X0)) | generous(X0) | happy(X0))) [flattening 41]
44. ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))) [nnf transformation 5]
47. ! [X0] : (((~wise(X0) | ~quiet(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | (wise(X0) & quiet(X0)))) [nnf transformation 8]
48. ! [X0] : ((~wise(X0) | ~quiet(X0) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | (wise(X0) & quiet(X0)))) [flattening 47]
49. ! [X0] : (((~patient(X0) & ~humble(X0)) | ~calm(X0)) & (calm(X0) | (patient(X0) | humble(X0)))) [nnf transformation 9]
50. ! [X0] : (((~patient(X0) & ~humble(X0)) | ~calm(X0)) & (calm(X0) | patient(X0) | humble(X0))) [flattening 49]
51. ! [X0] : ((((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | ~rich(X0)) & (rich(X0) | ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0))))) [nnf transformation 10]
54. ! [X0] : (~old(X0) | happy(X0) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) [nnf transformation 34]
55. ! [X0] : (((wise(X0) & ~generous(X0)) | (rich(X0) & ~curious(X0))) & ((~rich(X0) | curious(X0)) | (~wise(X0) | generous(X0)))) [nnf transformation 15]
56. ! [X0] : (((wise(X0) & ~generous(X0)) | (rich(X0) & ~curious(X0))) & (~rich(X0) | curious(X0) | ~wise(X0) | generous(X0))) [flattening 55]
57. (? [X0] : (~quiet(X0) & calm(X0)) | ! [X1] : (old(X1) | calm(X1))) & (? [X1] : (~old(X1) & ~calm(X1)) | ! [X0] : (quiet(X0) | ~calm(X0))) [nnf transformation 25]
58. (? [X0] : (~quiet(X0) & calm(X0)) | ! [X1] : (old(X1) | calm(X1))) & (? [X2] : (~old(X2) & ~calm(X2)) | ! [X3] : (quiet(X3) | ~calm(X3))) [rectify 57]
59. ? [X0] : (~quiet(X0) & calm(X0)) => (~quiet(sK1) & calm(sK1)) [choice axiom]
60. ? [X2] : (~old(X2) & ~calm(X2)) => (~old(sK2) & ~calm(sK2)) [choice axiom]
61. ((~quiet(sK1) & calm(sK1)) | ! [X1] : (old(X1) | calm(X1))) & ((~old(sK2) & ~calm(sK2)) | ! [X3] : (quiet(X3) | ~calm(X3))) [skolemisation 58,60,59]
83. ~happy(X0) | patient(X0) | humble(X0) [cnf transformation 42]
90. ~rich(X0) | ~strong(X0) [cnf transformation 44]
97. ~old(X0) | calm(X0) | quiet(X0) [cnf transformation 48]
99. ~calm(X0) | old(X0) | quiet(X0) [cnf transformation 48]
104. ~calm(X0) | ~humble(X0) [cnf transformation 50]
105. ~calm(X0) | ~patient(X0) [cnf transformation 50]
106. ~calm(X0) | rich(X0) | ~wise(X0) [cnf transformation 51]
120. ~old(X0) | happy(X0) | ~calm(X0) | strong(X0) [cnf transformation 54]
125. wise(X0) | rich(X0) [cnf transformation 56]
126. ~calm(sK2) | quiet(X3) | ~calm(X3) [cnf transformation 61]
127. ~old(sK2) | quiet(X3) | ~calm(X3) [cnf transformation 61]
128. calm(sK1) | old(X1) | calm(X1) [cnf transformation 61]
129. ~quiet(sK1) | old(X1) | calm(X1) [cnf transformation 61]
140. ~quiet(fred) [cnf transformation 24]
202. 13 <=> ! [X1] : (old(X1) | calm(X1)) [avatar definition]
203. old(X1) | calm(X1) <- (13) [avatar component clause 202]
205. 14 <=> quiet(sK1) [avatar definition]
208. 13 | ~14 [avatar split clause 129,205,202]
210. 15 <=> calm(sK1) [avatar definition]
212. calm(sK1) <- (15) [avatar component clause 210]
213. 13 | 15 [avatar split clause 128,210,202]
215. 16 <=> ! [X3] : (quiet(X3) | ~calm(X3)) [avatar definition]
216. ~calm(X3) | quiet(X3) <- (16) [avatar component clause 215]
218. 17 <=> old(sK2) [avatar definition]
220. ~old(sK2) <- (~17) [avatar component clause 218]
221. 16 | ~17 [avatar split clause 127,218,215]
223. 18 <=> calm(sK2) [avatar definition]
225. ~calm(sK2) <- (~18) [avatar component clause 223]
226. 16 | ~18 [avatar split clause 126,223,215]
253. calm(sK2) <- (13, ~17) [resolution 203,220]
255. $false <- (13, ~17, ~18) [subsumption resolution 253,225]
256. ~13 | 17 | 18 [avatar contradiction clause 255]
257. ~patient(sK1) <- (15) [resolution 212,105]
258. ~humble(sK1) <- (15) [resolution 212,104]
293. old(sK1) | quiet(sK1) <- (15) [resolution 99,212]
332. rich(sK1) | ~wise(sK1) <- (15) [resolution 106,212]
336. rich(sK1) <- (15) [subsumption resolution 332,125]
401. 35 <=> old(sK1) [avatar definition]
403. old(sK1) <- (35) [avatar component clause 401]
404. 14 | 35 | ~15 [avatar split clause 293,210,401,205]
408. calm(X1) | calm(X1) | quiet(X1) <- (13) [resolution 203,97]
409. calm(X1) | quiet(X1) <- (13) [duplicate literal removal 408]
411. quiet(X1) <- (13, 16) [subsumption resolution 409,216]
412. ~strong(sK1) <- (15) [resolution 336,90]
513. $false <- (13, 16) [resolution 411,140]
516. ~13 | ~16 [avatar contradiction clause 513]
520. happy(sK1) | ~calm(sK1) | strong(sK1) <- (35) [resolution 403,120]
525. happy(sK1) | strong(sK1) <- (15, 35) [subsumption resolution 520,212]
526. happy(sK1) <- (15, 35) [subsumption resolution 525,412]
717. patient(sK1) | humble(sK1) <- (15, 35) [resolution 526,83]
727. humble(sK1) <- (15, 35) [subsumption resolution 717,257]
728. $false <- (15, 35) [subsumption resolution 727,258]
729. ~15 | ~35 [avatar contradiction clause 728]
730. $false [avatar sat refutation 208,213,221,226,256,404,516,729]
% SZS output end Proof for 6119901647918049815420447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or curious is both curious and calm and vice versa.
Everyone who is humble is both generous and not old.
Everyone who is kind is calm and vice versa.
If someone is both creative and old then john is either calm or generous and vice versa.
If mary is kind then mary is generous and vice versa.
If someone is both tall and not patient then someone is patient or rich and vice versa.
Everyone who is funny is either not creative or old.
Everyone who is not patient is funny.
Everyone who is not funny is both brave and not brave and vice versa.
Everyone who is not tall is humble.
If alice is both curious and not wise then someone is both generous and strong.
Everyone who is strong is not creative and vice versa.
Everyone who is not brave is either not strong or not creative and vice versa.
If paul is quiet or funny then someone is strong and vice versa.
Everyone who is strong or not tall is both not kind and not generous.
Someone is either not old or happy.
Susan is not wise.
Susan is quiet.
Lucy is not wise or wise.
Someone is not creative. | Lucy is brave. | contradiction | (![X]:((happy(X)|curious(X))<=>(curious(X)&calm(X))))&
(![X]:(humble(X)=>(generous(X)&~old(X))))&
(![X]:(kind(X)<=>calm(X)))&
((?[X]:((creative(X)&old(X))))<=>((calm(john)<~>generous(john))))&
((kind(mary))<=>(generous(mary)))&
((?[X]:((tall(X)&~patient(X))))<=>(?[X]:((patient(X)|rich(X)))))&
(![X]:(funny(X)=>(~creative(X)<~>old(X))))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:(~funny(X)<=>(brave(X)&~brave(X))))&
(![X]:(~tall(X)=>humble(X)))&
(((curious(alice)&~wise(alice)))=>(?[X]:((generous(X)&strong(X)))))&
(![X]:(strong(X)<=>~creative(X)))&
(![X]:(~brave(X)<=>(~strong(X)<~>~creative(X))))&
(((quiet(paul)|funny(paul)))<=>(?[X]:(strong(X))))&
(![X]:((strong(X)|~tall(X))=>(~kind(X)&~generous(X))))&
(?[X]:((~old(X)<~>happy(X))))&
(~wise(susan))&
(quiet(susan))&
((~wise(lucy)|wise(lucy)))&
(?[X]:(~creative(X))) | brave(lucy) | [
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2461424113430124999374222
% SZS output start Proof for 2461424113430124999374222
12. ! [X0] : (strong(X0) <=> ~creative(X0)) [input p11]
13. ! [X0] : (~brave(X0) <=> (~strong(X0) <~> ~creative(X0))) [input p12]
21. brave(lucy) [input hypothesis]
48. ! [X0] : ((strong(X0) | creative(X0)) & (~creative(X0) | ~strong(X0))) [nnf transformation 12]
49. ! [X0] : ((~brave(X0) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0)))) & (((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | brave(X0))) [nnf transformation 13]
91. ~creative(X0) | ~strong(X0) [cnf transformation 48]
92. strong(X0) | creative(X0) [cnf transformation 48]
95. ~brave(X0) | ~creative(X0) | strong(X0) [cnf transformation 49]
96. ~brave(X0) | ~strong(X0) | creative(X0) [cnf transformation 49]
110. brave(lucy) [cnf transformation 21]
195. ~brave(X0) | ~strong(X0) [subsumption resolution 96,91]
196. ~brave(X0) | strong(X0) [subsumption resolution 95,92]
197. ~brave(X0) [subsumption resolution 196,195]
209. $false [subsumption resolution 110,197]
% SZS output end Proof for 2461424113430124999374222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not kind then someone is both happy and calm and vice versa. Everyone who is strong or rich is not kind or not rich. Everyone who is not rich or funny is either not curious or kind. If alice is both patient and not happy then someone is either not curious or not old. Everyone who is not wise or not old is both rich and not wise and vice versa. If john is not brave or not kind then alice is either not humble or not kind. Everyone who is humble or creative is either not humble or brave. Everyone who is not creative or creative is funny. If someone is patient then someone is both not curious and not generous and vice versa. If someone is both brave and not old then someone is kind or not strong. If someone is both old and not funny then someone is rich and vice versa. Everyone who is both not strong and not wise is both not wise and not calm. Everyone who is not calm is not quiet or old and vice versa. Everyone who is patient is either not old or not wise and vice versa. If lucy is both old and not tall then alice is either not curious or curious and vice versa. Everyone who is rich or quiet is not generous. Someone is rich or not happy. Someone is not happy. Alice is not wise or tall. Lucy is either not kind or not tall. Alice is both tall and not happy. | Alice is not wise. | contradiction | ((?[X]:((tall(X)<~>~kind(X))))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((strong(X)|rich(X))=>(~kind(X)|~rich(X))))&
(![X]:((~rich(X)|funny(X))=>(~curious(X)<~>kind(X))))&
(((patient(alice)&~happy(alice)))=>(?[X]:((~curious(X)<~>~old(X)))))&
(![X]:((~wise(X)|~old(X))<=>(rich(X)&~wise(X))))&
(((~brave(john)|~kind(john)))=>((~humble(alice)<~>~kind(alice))))&
(![X]:((humble(X)|creative(X))=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)|creative(X))=>funny(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~curious(X)&~generous(X)))))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((kind(X)|~strong(X)))))&
((?[X]:((old(X)&~funny(X))))<=>(?[X]:(rich(X))))&
(![X]:((~strong(X)&~wise(X))=>(~wise(X)&~calm(X))))&
(![X]:(~calm(X)<=>(~quiet(X)|old(X))))&
(![X]:(patient(X)<=>(~old(X)<~>~wise(X))))&
(((old(lucy)&~tall(lucy)))<=>((~curious(alice)<~>curious(alice))))&
(![X]:((rich(X)|quiet(X))=>~generous(X)))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:(~happy(X)))&
((~wise(alice)|tall(alice)))&
((~kind(lucy)<~>~tall(lucy)))&
((tall(alice)&~happy(alice))) | ~wise(alice) | [
"p4",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1675530675972123548178724
% SZS output start Proof for 1675530675972123548178724
5. ! [X0] : ((~old(X0) | ~wise(X0)) <=> (~wise(X0) & rich(X0))) [input p4]
8. ! [X0] : ((creative(X0) | ~creative(X0)) => funny(X0)) [input p7]
11. ? [X0] : (~funny(X0) & old(X0)) <=> ? [X0] : rich(X0) [input p10]
22. ~wise(alice) [input hypothesis]
26. ? [X0] : (~funny(X0) & old(X0)) <=> ? [X1] : rich(X1) [rectify 11]
34. ! [X0] : (funny(X0) | (~creative(X0) & creative(X0))) [ennf transformation 8]
48. ! [X0] : (((~old(X0) | ~wise(X0)) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | (old(X0) & wise(X0)))) [nnf transformation 5]
49. ! [X0] : ((~old(X0) | ~wise(X0) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | (old(X0) & wise(X0)))) [flattening 48]
60. (? [X0] : (~funny(X0) & old(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (funny(X0) | ~old(X0))) [nnf transformation 26]
61. (? [X0] : (~funny(X0) & old(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (funny(X3) | ~old(X3))) [rectify 60]
62. ? [X0] : (~funny(X0) & old(X0)) => (~funny(sK6) & old(sK6)) [choice axiom]
63. ? [X2] : rich(X2) => rich(sK7) [choice axiom]
64. ((~funny(sK6) & old(sK6)) | ! [X1] : ~rich(X1)) & (rich(sK7) | ! [X3] : (funny(X3) | ~old(X3))) [skolemisation 61,63,62]
89. wise(X0) | rich(X0) [cnf transformation 49]
102. funny(X0) | creative(X0) [cnf transformation 34]
103. funny(X0) | ~creative(X0) [cnf transformation 34]
110. ~funny(sK6) | ~rich(X1) [cnf transformation 64]
135. ~wise(alice) [cnf transformation 22]
212. funny(X0) [subsumption resolution 102,103]
246. ~rich(X1) [subsumption resolution 110,212]
267. 27 <=> wise(alice) [avatar definition]
269. ~wise(alice) <- (~27) [avatar component clause 267]
283. ~27 [avatar split clause 135,267]
284. rich(alice) <- (~27) [resolution 89,269]
285. $false <- (~27) [subsumption resolution 284,246]
286. 27 [avatar contradiction clause 285]
287. $false [avatar sat refutation 283,286]
% SZS output end Proof for 1675530675972123548178724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and old is both calm and patient and vice versa.
Everyone who is patient is both old and not creative.
If paul is either calm or old then someone is not kind or humble and vice versa.
Everyone who is both curious and strong is not creative and vice versa.
Everyone who is wise is both wise and kind and vice versa.
If someone is humble then someone is either not old or brave.
Everyone who is curious or not generous is not brave and vice versa.
If fred is both generous and old then john is both generous and patient.
If someone is not funny or not quiet then someone is happy or humble.
If lucy is curious then alice is happy.
If someone is either not strong or not generous then john is either creative or curious.
Everyone who is not brave is both humble and kind and vice versa.
Everyone who is humble is both not generous and not patient.
Everyone who is both not creative and curious is not patient or not rich and vice versa.
Everyone who is both curious and patient is either kind or curious and vice versa.
Everyone who is both rich and not quiet is either rich or tall and vice versa.
Susan is either not humble or not calm.
Someone is not happy.
Someone is either not happy or not funny.
Mary is either not brave or generous.
Susan is humble or old.
Someone is either rich or not wise. | Alice is not kind. | contradiction | (![X]:((kind(X)&old(X))<=>(calm(X)&patient(X))))&
(![X]:(patient(X)=>(old(X)&~creative(X))))&
(((calm(paul)<~>old(paul)))<=>(?[X]:((~kind(X)|humble(X)))))&
(![X]:((curious(X)&strong(X))<=>~creative(X)))&
(![X]:(wise(X)<=>(wise(X)&kind(X))))&
((?[X]:(humble(X)))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((curious(X)|~generous(X))<=>~brave(X)))&
(((generous(fred)&old(fred)))=>((generous(john)&patient(john))))&
((?[X]:((~funny(X)|~quiet(X))))=>(?[X]:((happy(X)|humble(X)))))&
((curious(lucy))=>(happy(alice)))&
((?[X]:((~strong(X)<~>~generous(X))))=>((creative(john)<~>curious(john))))&
(![X]:(~brave(X)<=>(humble(X)&kind(X))))&
(![X]:(humble(X)=>(~generous(X)&~patient(X))))&
(![X]:((~creative(X)&curious(X))<=>(~patient(X)|~rich(X))))&
(![X]:((curious(X)&patient(X))<=>(kind(X)<~>curious(X))))&
(![X]:((rich(X)&~quiet(X))<=>(rich(X)<~>tall(X))))&
((~humble(susan)<~>~calm(susan)))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)<~>~funny(X))))&
((~brave(mary)<~>generous(mary)))&
((humble(susan)|old(susan)))&
(?[X]:((rich(X)<~>~wise(X)))) | ~kind(alice) | [
"p1",
"p3",
"p6",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8680584092578566325797549
% SZS output start Proof for 8680584092578566325797549
2. ! [X0] : (patient(X0) => (~creative(X0) & old(X0))) [input p1]
4. ! [X0] : ((strong(X0) & curious(X0)) <=> ~creative(X0)) [input p3]
7. ! [X0] : ((~generous(X0) | curious(X0)) <=> ~brave(X0)) [input p6]
12. ! [X0] : (~brave(X0) <=> (kind(X0) & humble(X0))) [input p11]
13. ! [X0] : (humble(X0) => (~patient(X0) & ~generous(X0))) [input p12]
14. ! [X0] : ((curious(X0) & ~creative(X0)) <=> (~rich(X0) | ~patient(X0))) [input p13]
23. ~kind(alice) [input hypothesis]
26. ! [X0] : ((~creative(X0) & old(X0)) | ~patient(X0)) [ennf transformation 2]
33. ! [X0] : ((~patient(X0) & ~generous(X0)) | ~humble(X0)) [ennf transformation 13]
40. ! [X0] : (((strong(X0) & curious(X0)) | creative(X0)) & (~creative(X0) | (~strong(X0) | ~curious(X0)))) [nnf transformation 4]
41. ! [X0] : (((strong(X0) & curious(X0)) | creative(X0)) & (~creative(X0) | ~strong(X0) | ~curious(X0))) [flattening 40]
48. ! [X0] : (((~generous(X0) | curious(X0)) | brave(X0)) & (~brave(X0) | (generous(X0) & ~curious(X0)))) [nnf transformation 7]
49. ! [X0] : ((~generous(X0) | curious(X0) | brave(X0)) & (~brave(X0) | (generous(X0) & ~curious(X0)))) [flattening 48]
54. ! [X0] : ((~brave(X0) | (~kind(X0) | ~humble(X0))) & ((kind(X0) & humble(X0)) | brave(X0))) [nnf transformation 12]
55. ! [X0] : ((~brave(X0) | ~kind(X0) | ~humble(X0)) & ((kind(X0) & humble(X0)) | brave(X0))) [flattening 54]
56. ! [X0] : (((curious(X0) & ~creative(X0)) | (rich(X0) & patient(X0))) & ((~rich(X0) | ~patient(X0)) | (~curious(X0) | creative(X0)))) [nnf transformation 14]
57. ! [X0] : (((curious(X0) & ~creative(X0)) | (rich(X0) & patient(X0))) & (~rich(X0) | ~patient(X0) | ~curious(X0) | creative(X0))) [flattening 56]
77. ~creative(X0) | ~patient(X0) [cnf transformation 26]
85. curious(X0) | creative(X0) [cnf transformation 41]
92. ~brave(X0) | ~curious(X0) [cnf transformation 49]
93. ~brave(X0) | generous(X0) [cnf transformation 49]
104. brave(X0) | humble(X0) [cnf transformation 55]
105. brave(X0) | kind(X0) [cnf transformation 55]
107. ~generous(X0) | ~humble(X0) [cnf transformation 33]
110. ~creative(X0) | patient(X0) [cnf transformation 57]
136. ~kind(alice) [cnf transformation 23]
154. 4 <=> ! [X0] : kind(X0) [avatar definition]
155. kind(X0) <- (4) [avatar component clause 154]
238. ~creative(X0) [subsumption resolution 110,77]
292. ~curious(X1) | humble(X1) [resolution 104,92]
294. generous(X0) | kind(X0) [resolution 105,93]
324. humble(X1) | creative(X1) [resolution 292,85]
331. humble(X1) [subsumption resolution 324,238]
335. kind(X1) | ~humble(X1) [resolution 294,107]
336. kind(X1) [subsumption resolution 335,331]
337. 4 [avatar split clause 336,154]
338. $false <- (4) [resolution 155,136]
342. ~4 [avatar contradiction clause 338]
343. $false [avatar sat refutation 337,342]
% SZS output end Proof for 8680584092578566325797549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either humble or not kind then lucy is strong.
Everyone who is both humble and not calm is either not rich or calm.
If someone is quiet then paul is not tall or not old and vice versa.
Everyone who is not calm or not kind is creative or patient and vice versa.
Everyone who is calm is humble or not generous.
Everyone who is not happy or not old is both not kind and not happy.
Everyone who is brave or not creative is brave and vice versa.
If lucy is wise or funny then fred is not tall or humble.
Everyone who is not rich or tall is both wise and not curious and vice versa.
Everyone who is creative is not brave or happy and vice versa.
Everyone who is not strong or not creative is either rich or old.
Everyone who is not funny is both happy and not kind and vice versa.
Everyone who is not strong or not creative is not patient and vice versa.
Everyone who is both not old and quiet is not wise or not quiet and vice versa.
If john is either not quiet or brave then someone is generous.
Everyone who is not wise is happy.
Mary is either not kind or strong.
Someone is creative.
John is both not brave and creative.
Mary is both not happy and generous.
Someone is either funny or generous.
John is either creative or brave. | John is tall. | neutral | ((?[X]:((humble(X)<~>~kind(X))))=>(strong(lucy)))&
(![X]:((humble(X)&~calm(X))=>(~rich(X)<~>calm(X))))&
((?[X]:(quiet(X)))<=>((~tall(paul)|~old(paul))))&
(![X]:((~calm(X)|~kind(X))<=>(creative(X)|patient(X))))&
(![X]:(calm(X)=>(humble(X)|~generous(X))))&
(![X]:((~happy(X)|~old(X))=>(~kind(X)&~happy(X))))&
(![X]:((brave(X)|~creative(X))<=>brave(X)))&
(((wise(lucy)|funny(lucy)))=>((~tall(fred)|humble(fred))))&
(![X]:((~rich(X)|tall(X))<=>(wise(X)&~curious(X))))&
(![X]:(creative(X)<=>(~brave(X)|happy(X))))&
(![X]:((~strong(X)|~creative(X))=>(rich(X)<~>old(X))))&
(![X]:(~funny(X)<=>(happy(X)&~kind(X))))&
(![X]:((~strong(X)|~creative(X))<=>~patient(X)))&
(![X]:((~old(X)&quiet(X))<=>(~wise(X)|~quiet(X))))&
(((~quiet(john)<~>brave(john)))=>(?[X]:(generous(X))))&
(![X]:(~wise(X)=>happy(X)))&
((~kind(mary)<~>strong(mary)))&
(?[X]:(creative(X)))&
((~brave(john)&creative(john)))&
((~happy(mary)&generous(mary)))&
(?[X]:((funny(X)<~>generous(X))))&
((creative(john)<~>brave(john))) | tall(john) | [] | null | 0 |
Everyone who is both not wise and calm is either not curious or not happy and vice versa.
Everyone who is both not happy and not calm is not quiet.
If mary is not creative then someone is brave.
If someone is not tall then someone is either patient or happy and vice versa.
If someone is both not wise and brave then someone is either strong or not curious and vice versa.
If someone is either not brave or calm then someone is funny or strong and vice versa.
Everyone who is not kind is not happy and vice versa.
Everyone who is either not wise or not old is happy or kind.
Everyone who is creative is both not creative and not happy.
Everyone who is humble or not wise is not curious or strong and vice versa.
Everyone who is not kind or not tall is either not creative or not happy and vice versa.
Everyone who is not patient is either not curious or humble and vice versa.
Everyone who is both tall and not generous is either not brave or brave.
Everyone who is creative is not kind or not patient.
Everyone who is either not funny or creative is both not rich and wise and vice versa.
If someone is both not wise and not calm then someone is humble or not kind and vice versa.
Alice is not rich or not happy.
Susan is creative or not generous.
Someone is not curious.
Someone is either tall or rich.
Fred is rich.
Someone is both not creative and calm.
Alice is strong or quiet. | Susan is not brave. | neutral | (![X]:((~wise(X)&calm(X))<=>(~curious(X)<~>~happy(X))))&
(![X]:((~happy(X)&~calm(X))=>~quiet(X)))&
((~creative(mary))=>(?[X]:(brave(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((~wise(X)&brave(X))))<=>(?[X]:((strong(X)<~>~curious(X)))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((funny(X)|strong(X)))))&
(![X]:(~kind(X)<=>~happy(X)))&
(![X]:((~wise(X)<~>~old(X))=>(happy(X)|kind(X))))&
(![X]:(creative(X)=>(~creative(X)&~happy(X))))&
(![X]:((humble(X)|~wise(X))<=>(~curious(X)|strong(X))))&
(![X]:((~kind(X)|~tall(X))<=>(~creative(X)<~>~happy(X))))&
(![X]:(~patient(X)<=>(~curious(X)<~>humble(X))))&
(![X]:((tall(X)&~generous(X))=>(~brave(X)<~>brave(X))))&
(![X]:(creative(X)=>(~kind(X)|~patient(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(~rich(X)&wise(X))))&
((?[X]:((~wise(X)&~calm(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
((~rich(alice)|~happy(alice)))&
((creative(susan)|~generous(susan)))&
(?[X]:(~curious(X)))&
(?[X]:((tall(X)<~>rich(X))))&
(rich(fred))&
(?[X]:((~creative(X)&calm(X))))&
((strong(alice)|quiet(alice))) | ~brave(susan) | [] | null | 0 |
If alice is either not strong or not rich then paul is strong. If john is wise then fred is calm or strong. Everyone who is curious or not kind is quiet. If someone is quiet or calm then fred is both not curious and quiet and vice versa. If someone is not curious then someone is not funny or not brave. If someone is not brave or calm then someone is either generous or not calm. Everyone who is quiet or humble is both not happy and patient and vice versa. If alice is either not kind or not brave then someone is either not funny or not humble. If someone is tall then lucy is either not old or not strong. If someone is both creative and not kind then someone is both tall and funny. Everyone who is not old or not wise is rich and vice versa. Everyone who is rich is both not tall and wise. Everyone who is either not patient or patient is both strong and not curious and vice versa. If someone is calm or humble then someone is both wise and calm. If someone is not creative or not strong then lucy is both kind and brave. Everyone who is kind is both not kind and not strong. Fred is both wise and calm. Someone is not calm. Someone is wise or calm. John is not calm. | John is happy. | contradiction | (((~strong(alice)<~>~rich(alice)))=>(strong(paul)))&
((wise(john))=>((calm(fred)|strong(fred))))&
(![X]:((curious(X)|~kind(X))=>quiet(X)))&
((?[X]:((quiet(X)|calm(X))))<=>((~curious(fred)&quiet(fred))))&
((?[X]:(~curious(X)))=>(?[X]:((~funny(X)|~brave(X)))))&
((?[X]:((~brave(X)|calm(X))))=>(?[X]:((generous(X)<~>~calm(X)))))&
(![X]:((quiet(X)|humble(X))<=>(~happy(X)&patient(X))))&
(((~kind(alice)<~>~brave(alice)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
((?[X]:(tall(X)))=>((~old(lucy)<~>~strong(lucy))))&
((?[X]:((creative(X)&~kind(X))))=>(?[X]:((tall(X)&funny(X)))))&
(![X]:((~old(X)|~wise(X))<=>rich(X)))&
(![X]:(rich(X)=>(~tall(X)&wise(X))))&
(![X]:((~patient(X)<~>patient(X))<=>(strong(X)&~curious(X))))&
((?[X]:((calm(X)|humble(X))))=>(?[X]:((wise(X)&calm(X)))))&
((?[X]:((~creative(X)|~strong(X))))=>((kind(lucy)&brave(lucy))))&
(![X]:(kind(X)=>(~kind(X)&~strong(X))))&
((wise(fred)&calm(fred)))&
(?[X]:(~calm(X)))&
(?[X]:((wise(X)|calm(X))))&
(~calm(john)) | happy(john) | [
"p2",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7037761117773765013410792
% SZS output start Proof for 7037761117773765013410792
3. ! [X0] : ((~kind(X0) | curious(X0)) => quiet(X0)) [input p2]
7. ! [X0] : ((humble(X0) | quiet(X0)) <=> (patient(X0) & ~happy(X0))) [input p6]
13. ! [X0] : ((~patient(X0) <~> patient(X0)) <=> (~curious(X0) & strong(X0))) [input p12]
16. ! [X0] : (kind(X0) => (~strong(X0) & ~kind(X0))) [input p15]
21. happy(john) [input hypothesis]
29. ! [X0] : (quiet(X0) | (kind(X0) & ~curious(X0))) [ennf transformation 3]
38. ! [X0] : ((~strong(X0) & ~kind(X0)) | ~kind(X0)) [ennf transformation 16]
52. ! [X0] : (((humble(X0) | quiet(X0)) | (~patient(X0) | happy(X0))) & ((patient(X0) & ~happy(X0)) | (~humble(X0) & ~quiet(X0)))) [nnf transformation 7]
53. ! [X0] : ((humble(X0) | quiet(X0) | ~patient(X0) | happy(X0)) & ((patient(X0) & ~happy(X0)) | (~humble(X0) & ~quiet(X0)))) [flattening 52]
63. ! [X0] : ((((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | (curious(X0) | ~strong(X0))) & ((~curious(X0) & strong(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0))))) [nnf transformation 13]
64. ! [X0] : ((((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | curious(X0) | ~strong(X0)) & ((~curious(X0) & strong(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0))))) [flattening 63]
76. quiet(X0) | kind(X0) [cnf transformation 29]
87. ~happy(X0) | ~quiet(X0) [cnf transformation 53]
105. strong(X0) | patient(X0) | patient(X0) [cnf transformation 64]
106. strong(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 64]
120. ~strong(X0) | ~kind(X0) [cnf transformation 38]
126. happy(john) [cnf transformation 21]
128. strong(X0) | patient(X0) [duplicate literal removal 105]
129. strong(X0) | ~patient(X0) [duplicate literal removal 106]
261. strong(X0) [subsumption resolution 128,129]
284. ~kind(X0) [subsumption resolution 120,261]
297. ~quiet(john) [resolution 87,126]
298. kind(john) [resolution 297,76]
299. $false [subsumption resolution 298,284]
% SZS output end Proof for 7037761117773765013410792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or wise is both funny and not generous. Everyone who is either strong or humble is not patient or patient. If someone is both calm and not tall then susan is both not funny and not kind. Everyone who is either funny or old is both wise and calm and vice versa. Everyone who is either not kind or humble is both strong and tall and vice versa. Everyone who is both not strong and not patient is not funny and vice versa. If john is not curious then lucy is not creative and vice versa. Everyone who is either not tall or not rich is both strong and not kind. Everyone who is not humble or not quiet is not happy and vice versa. If someone is not tall or quiet then someone is not calm. If john is happy then fred is either calm or not kind. If lucy is not curious or not funny then someone is either not quiet or not strong. If susan is either happy or not old then susan is both not tall and not old and vice versa. Everyone who is not curious or not brave is not generous and vice versa. Everyone who is either not funny or not generous is either not tall or not wise. Everyone who is not curious is either not rich or not patient and vice versa. Someone is both happy and tall. Someone is not funny. Someone is either rich or tall. Someone is not humble or quiet. Susan is either not patient or not funny. Someone is creative. Susan is either not kind or not tall. Susan is either not creative or not funny. | Susan is patient. | contradiction | (![X]:((~funny(X)<~>wise(X))=>(funny(X)&~generous(X))))&
(![X]:((strong(X)<~>humble(X))=>(~patient(X)|patient(X))))&
((?[X]:((calm(X)&~tall(X))))=>((~funny(susan)&~kind(susan))))&
(![X]:((funny(X)<~>old(X))<=>(wise(X)&calm(X))))&
(![X]:((~kind(X)<~>humble(X))<=>(strong(X)&tall(X))))&
(![X]:((~strong(X)&~patient(X))<=>~funny(X)))&
((~curious(john))<=>(~creative(lucy)))&
(![X]:((~tall(X)<~>~rich(X))=>(strong(X)&~kind(X))))&
(![X]:((~humble(X)|~quiet(X))<=>~happy(X)))&
((?[X]:((~tall(X)|quiet(X))))=>(?[X]:(~calm(X))))&
((happy(john))=>((calm(fred)<~>~kind(fred))))&
(((~curious(lucy)|~funny(lucy)))=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(((happy(susan)<~>~old(susan)))<=>((~tall(susan)&~old(susan))))&
(![X]:((~curious(X)|~brave(X))<=>~generous(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~tall(X)<~>~wise(X))))&
(![X]:(~curious(X)<=>(~rich(X)<~>~patient(X))))&
(?[X]:((happy(X)&tall(X))))&
(?[X]:(~funny(X)))&
(?[X]:((rich(X)<~>tall(X))))&
(?[X]:((~humble(X)|quiet(X))))&
((~patient(susan)<~>~funny(susan)))&
(?[X]:(creative(X)))&
((~kind(susan)<~>~tall(susan)))&
((~creative(susan)<~>~funny(susan))) | patient(susan) | [
"p5",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1641098050009873307227913
% SZS output start Proof for 1641098050009873307227913
6. ! [X0] : ((~patient(X0) & ~strong(X0)) <=> ~funny(X0)) [input p5]
21. ~patient(susan) <~> ~funny(susan) [input p20]
25. patient(susan) [input hypothesis]
42. ! [X0] : (((~patient(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | (patient(X0) | strong(X0)))) [nnf transformation 6]
43. ! [X0] : (((~patient(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | patient(X0) | strong(X0))) [flattening 42]
70. (funny(susan) | patient(susan)) & (~funny(susan) | ~patient(susan)) [nnf transformation 21]
97. ~patient(X0) | funny(X0) [cnf transformation 43]
138. ~funny(susan) | ~patient(susan) [cnf transformation 70]
145. patient(susan) [cnf transformation 25]
260. ~patient(susan) [subsumption resolution 138,97]
269. $false [subsumption resolution 145,260]
% SZS output end Proof for 1641098050009873307227913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then mary is patient or happy.
Everyone who is not old or wise is quiet or not calm and vice versa.
If someone is both quiet and not strong then someone is rich or kind.
Everyone who is either not generous or not rich is happy and vice versa.
If susan is not calm then fred is humble and vice versa.
Everyone who is both not old and strong is both not calm and quiet and vice versa.
Everyone who is either not rich or strong is happy or rich.
Everyone who is curious or rich is not rich or not calm and vice versa.
Everyone who is both happy and not curious is wise or kind and vice versa.
If susan is not brave then fred is either curious or not humble.
Everyone who is either not kind or curious is either calm or not creative and vice versa.
If john is either not funny or not rich then lucy is not wise or patient and vice versa.
Everyone who is not happy or kind is old or not patient and vice versa.
If alice is calm then someone is either creative or not humble and vice versa.
If someone is strong or not brave then someone is both not calm and old and vice versa.
Everyone who is not strong is strong or curious and vice versa.
Lucy is either tall or not kind.
Mary is wise or quiet.
Paul is either tall or curious.
Fred is not funny.
Someone is either calm or funny.
Someone is both not tall and not quiet.
Someone is both not old and tall. | Mary is not generous. | contradiction | ((?[X]:(quiet(X)))=>((patient(mary)|happy(mary))))&
(![X]:((~old(X)|wise(X))<=>(quiet(X)|~calm(X))))&
((?[X]:((quiet(X)&~strong(X))))=>(?[X]:((rich(X)|kind(X)))))&
(![X]:((~generous(X)<~>~rich(X))<=>happy(X)))&
((~calm(susan))<=>(humble(fred)))&
(![X]:((~old(X)&strong(X))<=>(~calm(X)&quiet(X))))&
(![X]:((~rich(X)<~>strong(X))=>(happy(X)|rich(X))))&
(![X]:((curious(X)|rich(X))<=>(~rich(X)|~calm(X))))&
(![X]:((happy(X)&~curious(X))<=>(wise(X)|kind(X))))&
((~brave(susan))=>((curious(fred)<~>~humble(fred))))&
(![X]:((~kind(X)<~>curious(X))<=>(calm(X)<~>~creative(X))))&
(((~funny(john)<~>~rich(john)))<=>((~wise(lucy)|patient(lucy))))&
(![X]:((~happy(X)|kind(X))<=>(old(X)|~patient(X))))&
((calm(alice))<=>(?[X]:((creative(X)<~>~humble(X)))))&
((?[X]:((strong(X)|~brave(X))))<=>(?[X]:((~calm(X)&old(X)))))&
(![X]:(~strong(X)<=>(strong(X)|curious(X))))&
((tall(lucy)<~>~kind(lucy)))&
((wise(mary)|quiet(mary)))&
((tall(paul)<~>curious(paul)))&
(~funny(fred))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
(?[X]:((~old(X)&tall(X)))) | ~generous(mary) | [
"p0",
"p1",
"p3",
"p5",
"p7",
"p8",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8020400976492034970331106
% SZS output start Proof for 8020400976492034970331106
1. ? [X0] : quiet(X0) => (happy(mary) | patient(mary)) [input p0]
2. ! [X0] : ((wise(X0) | ~old(X0)) <=> (~calm(X0) | quiet(X0))) [input p1]
4. ! [X0] : ((~generous(X0) <~> ~rich(X0)) <=> happy(X0)) [input p3]
6. ! [X0] : ((strong(X0) & ~old(X0)) <=> (quiet(X0) & ~calm(X0))) [input p5]
8. ! [X0] : ((rich(X0) | curious(X0)) <=> (~calm(X0) | ~rich(X0))) [input p7]
9. ! [X0] : ((~curious(X0) & happy(X0)) <=> (kind(X0) | wise(X0))) [input p8]
13. ! [X0] : ((kind(X0) | ~happy(X0)) <=> (~patient(X0) | old(X0))) [input p12]
16. ! [X0] : (~strong(X0) <=> (curious(X0) | strong(X0))) [input p15]
18. quiet(mary) | wise(mary) [input p17]
24. ~generous(mary) [input hypothesis]
27. (happy(mary) | patient(mary)) | ! [X0] : ~quiet(X0) [ennf transformation 1]
28. happy(mary) | patient(mary) | ! [X0] : ~quiet(X0) [flattening 27]
33. ! [X0] : (((wise(X0) | ~old(X0)) | (calm(X0) & ~quiet(X0))) & ((~calm(X0) | quiet(X0)) | (~wise(X0) & old(X0)))) [nnf transformation 2]
34. ! [X0] : ((wise(X0) | ~old(X0) | (calm(X0) & ~quiet(X0))) & (~calm(X0) | quiet(X0) | (~wise(X0) & old(X0)))) [flattening 33]
38. ! [X0] : ((((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | ~happy(X0)) & (happy(X0) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))))) [nnf transformation 4]
40. ! [X0] : (((strong(X0) & ~old(X0)) | (~quiet(X0) | calm(X0))) & ((quiet(X0) & ~calm(X0)) | (~strong(X0) | old(X0)))) [nnf transformation 6]
41. ! [X0] : (((strong(X0) & ~old(X0)) | ~quiet(X0) | calm(X0)) & ((quiet(X0) & ~calm(X0)) | ~strong(X0) | old(X0))) [flattening 40]
43. ! [X0] : (((rich(X0) | curious(X0)) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | (~rich(X0) & ~curious(X0)))) [nnf transformation 8]
44. ! [X0] : ((rich(X0) | curious(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | (~rich(X0) & ~curious(X0)))) [flattening 43]
45. ! [X0] : (((~curious(X0) & happy(X0)) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | (curious(X0) | ~happy(X0)))) [nnf transformation 9]
46. ! [X0] : (((~curious(X0) & happy(X0)) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | curious(X0) | ~happy(X0))) [flattening 45]
51. ! [X0] : (((kind(X0) | ~happy(X0)) | (patient(X0) & ~old(X0))) & ((~patient(X0) | old(X0)) | (~kind(X0) & happy(X0)))) [nnf transformation 13]
52. ! [X0] : ((kind(X0) | ~happy(X0) | (patient(X0) & ~old(X0))) & (~patient(X0) | old(X0) | (~kind(X0) & happy(X0)))) [flattening 51]
62. ! [X0] : ((~strong(X0) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | strong(X0))) [nnf transformation 16]
63. ! [X0] : ((~strong(X0) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | strong(X0))) [flattening 62]
73. happy(mary) | patient(mary) | ~quiet(X0) [cnf transformation 28]
76. ~old(X0) | wise(X0) | ~quiet(X0) [cnf transformation 34]
82. ~happy(X0) | generous(X0) | rich(X0) [cnf transformation 38]
88. ~quiet(X0) | strong(X0) | calm(X0) [cnf transformation 41]
92. ~calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 44]
98. ~curious(X0) | ~wise(X0) [cnf transformation 46]
116. ~patient(X0) | old(X0) | happy(X0) [cnf transformation 52]
129. curious(X0) | strong(X0) | strong(X0) [cnf transformation 63]
130. ~strong(X0) | ~strong(X0) [cnf transformation 63]
134. quiet(mary) | wise(mary) [cnf transformation 18]
144. ~generous(mary) [cnf transformation 24]
145. curious(X0) | strong(X0) [duplicate literal removal 129]
146. ~strong(X0) [duplicate literal removal 130]
147. ~rich(X0) | ~calm(X0) [duplicate literal removal 92]
151. 1 <=> ! [X0] : ~quiet(X0) [avatar definition]
152. ~quiet(X0) <- (1) [avatar component clause 151]
154. 2 <=> patient(mary) [avatar definition]
156. patient(mary) <- (2) [avatar component clause 154]
158. 3 <=> happy(mary) [avatar definition]
160. happy(mary) <- (3) [avatar component clause 158]
161. 1 | 2 | 3 [avatar split clause 73,158,154,151]
263. 25 <=> ! [X3] : ~strong(X3) [avatar definition]
264. ~strong(X3) <- (25) [avatar component clause 263]
272. 25 [avatar split clause 146,263]
284. 29 <=> wise(mary) [avatar definition]
286. wise(mary) <- (29) [avatar component clause 284]
288. 30 <=> quiet(mary) [avatar definition]
290. quiet(mary) <- (30) [avatar component clause 288]
291. 29 | 30 [avatar split clause 134,288,284]
322. strong(X2) | ~wise(X2) [resolution 145,98]
328. ~wise(X2) <- (25) [subsumption resolution 322,264]
385. old(mary) | happy(mary) <- (2) [resolution 116,156]
387. 41 <=> old(mary) [avatar definition]
389. old(mary) <- (41) [avatar component clause 387]
390. 3 | 41 | ~2 [avatar split clause 385,154,387,158]
391. $false <- (1, 30) [resolution 152,290]
392. ~1 | ~30 [avatar contradiction clause 391]
393. $false <- (25, 29) [subsumption resolution 286,328]
394. ~25 | ~29 [avatar contradiction clause 393]
395. generous(mary) | rich(mary) <- (3) [resolution 160,82]
396. rich(mary) <- (3) [subsumption resolution 395,144]
397. strong(mary) | calm(mary) <- (30) [resolution 290,88]
398. calm(mary) <- (25, 30) [subsumption resolution 397,264]
400. ~calm(mary) <- (3) [resolution 396,147]
401. $false <- (3, 25, 30) [subsumption resolution 400,398]
402. ~3 | ~25 | ~30 [avatar contradiction clause 401]
406. wise(mary) | ~quiet(mary) <- (41) [resolution 389,76]
408. ~quiet(mary) <- (25, 41) [subsumption resolution 406,328]
409. $false <- (25, 30, 41) [subsumption resolution 408,290]
410. ~25 | ~30 | ~41 [avatar contradiction clause 409]
411. $false [avatar sat refutation 161,272,291,390,392,394,402,410]
% SZS output end Proof for 8020400976492034970331106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then paul is both not tall and not quiet and vice versa.
If lucy is curious then mary is either generous or patient.
Everyone who is not patient is old.
Everyone who is kind or strong is both not creative and calm and vice versa.
If alice is not happy or not tall then paul is both not patient and creative.
If mary is patient then fred is both creative and wise and vice versa.
Everyone who is brave is tall.
Everyone who is strong or tall is both generous and not old and vice versa.
Everyone who is either not generous or tall is not happy.
Everyone who is both not old and happy is not calm and vice versa.
Everyone who is either quiet or wise is both not generous and strong and vice versa.
If someone is creative then alice is both generous and strong.
If lucy is not curious or quiet then someone is either creative or old.
If someone is not generous then fred is not old.
Everyone who is happy or generous is strong or brave.
Everyone who is both not calm and quiet is both strong and old and vice versa.
Someone is either not generous or kind.
John is either humble or quiet.
John is not rich.
Alice is either not happy or not generous.
Someone is not tall or not curious. | Fred is calm. | entailment | ((?[X]:(old(X)))<=>((~tall(paul)&~quiet(paul))))&
((curious(lucy))=>((generous(mary)<~>patient(mary))))&
(![X]:(~patient(X)=>old(X)))&
(![X]:((kind(X)|strong(X))<=>(~creative(X)&calm(X))))&
(((~happy(alice)|~tall(alice)))=>((~patient(paul)&creative(paul))))&
((patient(mary))<=>((creative(fred)&wise(fred))))&
(![X]:(brave(X)=>tall(X)))&
(![X]:((strong(X)|tall(X))<=>(generous(X)&~old(X))))&
(![X]:((~generous(X)<~>tall(X))=>~happy(X)))&
(![X]:((~old(X)&happy(X))<=>~calm(X)))&
(![X]:((quiet(X)<~>wise(X))<=>(~generous(X)&strong(X))))&
((?[X]:(creative(X)))=>((generous(alice)&strong(alice))))&
(((~curious(lucy)|quiet(lucy)))=>(?[X]:((creative(X)<~>old(X)))))&
((?[X]:(~generous(X)))=>(~old(fred)))&
(![X]:((happy(X)|generous(X))=>(strong(X)|brave(X))))&
(![X]:((~calm(X)&quiet(X))<=>(strong(X)&old(X))))&
(?[X]:((~generous(X)<~>kind(X))))&
((humble(john)<~>quiet(john)))&
(~rich(john))&
((~happy(alice)<~>~generous(alice)))&
(?[X]:((~tall(X)|~curious(X)))) | calm(fred) | [
"p3",
"p6",
"p7",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4845188661702325520416562
% SZS output start Proof for 4845188661702325520416562
4. ! [X0] : ((strong(X0) | kind(X0)) <=> (calm(X0) & ~creative(X0))) [input p3]
7. ! [X0] : (brave(X0) => tall(X0)) [input p6]
8. ! [X0] : ((tall(X0) | strong(X0)) <=> (~old(X0) & generous(X0))) [input p7]
9. ! [X0] : ((~generous(X0) <~> tall(X0)) => ~happy(X0)) [input p8]
10. ! [X0] : ((happy(X0) & ~old(X0)) <=> ~calm(X0)) [input p9]
15. ! [X0] : ((generous(X0) | happy(X0)) => (brave(X0) | strong(X0))) [input p14]
22. ~calm(fred) [input hypothesis]
27. ! [X0] : (tall(X0) | ~brave(X0)) [ennf transformation 7]
28. ! [X0] : (~happy(X0) | (~generous(X0) <=> tall(X0))) [ennf transformation 9]
32. ! [X0] : ((brave(X0) | strong(X0)) | (~generous(X0) & ~happy(X0))) [ennf transformation 15]
33. ! [X0] : (brave(X0) | strong(X0) | (~generous(X0) & ~happy(X0))) [flattening 32]
40. ! [X0] : (((strong(X0) | kind(X0)) | (~calm(X0) | creative(X0))) & ((calm(X0) & ~creative(X0)) | (~strong(X0) & ~kind(X0)))) [nnf transformation 4]
41. ! [X0] : ((strong(X0) | kind(X0) | ~calm(X0) | creative(X0)) & ((calm(X0) & ~creative(X0)) | (~strong(X0) & ~kind(X0)))) [flattening 40]
44. ! [X0] : (((tall(X0) | strong(X0)) | (old(X0) | ~generous(X0))) & ((~old(X0) & generous(X0)) | (~tall(X0) & ~strong(X0)))) [nnf transformation 8]
45. ! [X0] : ((tall(X0) | strong(X0) | old(X0) | ~generous(X0)) & ((~old(X0) & generous(X0)) | (~tall(X0) & ~strong(X0)))) [flattening 44]
46. ! [X0] : (~happy(X0) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) [nnf transformation 28]
47. ! [X0] : (((happy(X0) & ~old(X0)) | calm(X0)) & (~calm(X0) | (~happy(X0) | old(X0)))) [nnf transformation 10]
48. ! [X0] : (((happy(X0) & ~old(X0)) | calm(X0)) & (~calm(X0) | ~happy(X0) | old(X0))) [flattening 47]
72. ~strong(X0) | calm(X0) [cnf transformation 41]
81. ~brave(X0) | tall(X0) [cnf transformation 27]
83. ~tall(X0) | generous(X0) [cnf transformation 45]
88. ~happy(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 46]
91. happy(X0) | calm(X0) [cnf transformation 48]
105. ~happy(X0) | strong(X0) | brave(X0) [cnf transformation 33]
118. ~calm(fred) [cnf transformation 22]
182. ~happy(X0) | ~tall(X0) [subsumption resolution 88,83]
268. ~tall(X0) | calm(X0) [resolution 182,91]
294. strong(X0) | brave(X0) | calm(X0) [resolution 105,91]
295. brave(X0) | calm(X0) [subsumption resolution 294,72]
296. calm(X0) | tall(X0) [resolution 295,81]
297. calm(X0) [subsumption resolution 296,268]
365. $false [resolution 297,118]
% SZS output end Proof for 4845188661702325520416562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not kind then someone is either old or patient and vice versa. Everyone who is tall is both funny and not tall and vice versa. Everyone who is not tall or not generous is not generous and vice versa. Everyone who is either calm or rich is both not funny and curious. If lucy is strong then someone is funny or not kind. If someone is not kind or old then someone is not strong or not old. If fred is either not tall or strong then someone is either not wise or generous and vice versa. If alice is both not creative and rich then someone is both tall and humble and vice versa. Everyone who is not strong is not generous and vice versa. If fred is creative or not kind then someone is not creative or creative and vice versa. Everyone who is patient is not calm or not strong and vice versa. If someone is strong then john is either generous or happy. If someone is either generous or not brave then mary is either calm or not quiet. Everyone who is either kind or wise is both not curious and calm and vice versa. Everyone who is either not strong or quiet is both wise and not patient. Everyone who is not happy or patient is not wise and vice versa. Someone is wise or not wise. Paul is not rich. Alice is both not funny and rich. Someone is not funny. Someone is either not curious or generous. Paul is humble or creative. Someone is generous or creative. Paul is both not old and humble. | Paul is quiet. | entailment | ((~kind(lucy))<=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:(tall(X)<=>(funny(X)&~tall(X))))&
(![X]:((~tall(X)|~generous(X))<=>~generous(X)))&
(![X]:((calm(X)<~>rich(X))=>(~funny(X)&curious(X))))&
((strong(lucy))=>(?[X]:((funny(X)|~kind(X)))))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:((~strong(X)|~old(X)))))&
(((~tall(fred)<~>strong(fred)))<=>(?[X]:((~wise(X)<~>generous(X)))))&
(((~creative(alice)&rich(alice)))<=>(?[X]:((tall(X)&humble(X)))))&
(![X]:(~strong(X)<=>~generous(X)))&
(((creative(fred)|~kind(fred)))<=>(?[X]:((~creative(X)|creative(X)))))&
(![X]:(patient(X)<=>(~calm(X)|~strong(X))))&
((?[X]:(strong(X)))=>((generous(john)<~>happy(john))))&
((?[X]:((generous(X)<~>~brave(X))))=>((calm(mary)<~>~quiet(mary))))&
(![X]:((kind(X)<~>wise(X))<=>(~curious(X)&calm(X))))&
(![X]:((~strong(X)<~>quiet(X))=>(wise(X)&~patient(X))))&
(![X]:((~happy(X)|patient(X))<=>~wise(X)))&
(?[X]:((wise(X)|~wise(X))))&
(~rich(paul))&
((~funny(alice)&rich(alice)))&
(?[X]:(~funny(X)))&
(?[X]:((~curious(X)<~>generous(X))))&
((humble(paul)|creative(paul)))&
(?[X]:((generous(X)|creative(X))))&
((~old(paul)&humble(paul))) | quiet(paul) | [
"p1",
"p2",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6036942926435118210939011
% SZS output start Proof for 6036942926435118210939011
2. ! [X0] : (tall(X0) <=> (~tall(X0) & funny(X0))) [input p1]
3. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> ~generous(X0)) [input p2]
9. ! [X0] : (~strong(X0) <=> ~generous(X0)) [input p8]
11. ! [X0] : (patient(X0) <=> (~strong(X0) | ~calm(X0))) [input p10]
15. ! [X0] : ((~strong(X0) <~> quiet(X0)) => (~patient(X0) & wise(X0))) [input p14]
25. ~quiet(paul) [input hypothesis]
32. ! [X0] : ((~patient(X0) & wise(X0)) | (~strong(X0) <=> quiet(X0))) [ennf transformation 15]
37. ! [X0] : ((tall(X0) | (tall(X0) | ~funny(X0))) & ((~tall(X0) & funny(X0)) | ~tall(X0))) [nnf transformation 2]
38. ! [X0] : ((tall(X0) | tall(X0) | ~funny(X0)) & ((~tall(X0) & funny(X0)) | ~tall(X0))) [flattening 37]
39. ! [X0] : (((~generous(X0) | ~tall(X0)) | generous(X0)) & (~generous(X0) | (generous(X0) & tall(X0)))) [nnf transformation 3]
40. ! [X0] : ((~generous(X0) | ~tall(X0) | generous(X0)) & (~generous(X0) | (generous(X0) & tall(X0)))) [flattening 39]
56. ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0))) [nnf transformation 9]
62. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | ~patient(X0))) [nnf transformation 11]
63. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | ~patient(X0))) [flattening 62]
68. ! [X0] : ((~patient(X0) & wise(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0)))) [nnf transformation 32]
85. ~tall(X0) | ~tall(X0) [cnf transformation 38]
87. ~generous(X0) | tall(X0) [cnf transformation 40]
110. ~strong(X0) | generous(X0) [cnf transformation 56]
117. patient(X0) | strong(X0) [cnf transformation 63]
132. ~patient(X0) | quiet(X0) | strong(X0) [cnf transformation 68]
148. ~quiet(paul) [cnf transformation 25]
149. ~tall(X0) [duplicate literal removal 85]
173. ~generous(X0) [subsumption resolution 87,149]
235. ~strong(X0) [subsumption resolution 110,173]
252. patient(X0) [subsumption resolution 117,235]
268. quiet(X0) | strong(X0) [subsumption resolution 132,252]
269. quiet(X0) [subsumption resolution 268,235]
284. $false [subsumption resolution 148,269]
% SZS output end Proof for 6036942926435118210939011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not brave or strong then susan is both not generous and wise and vice versa.
Everyone who is either not humble or strong is happy.
If someone is funny or curious then someone is not humble or not generous and vice versa.
Everyone who is either not wise or not brave is not quiet.
Everyone who is both happy and old is not happy or quiet.
If someone is both not kind and not tall then someone is either curious or not creative.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is either humble or old then paul is either patient or happy.
If someone is calm or generous then someone is not old.
Everyone who is quiet or funny is either not patient or not calm.
If someone is kind then paul is curious and vice versa.
If someone is both not curious and brave then someone is not old or not funny.
Everyone who is old or not humble is not humble or not patient and vice versa.
Everyone who is both humble and not calm is both happy and kind.
Everyone who is tall is either kind or not brave and vice versa.
Everyone who is either not old or not generous is not generous and vice versa.
John is either old or not rich.
Mary is both quiet and not strong.
Someone is old.
Fred is not happy.
Alice is not patient or not curious.
Fred is either not funny or not brave.
Paul is not brave or not humble. | Mary is old. | entailment | (((~brave(lucy)|strong(lucy)))<=>((~generous(susan)&wise(susan))))&
(![X]:((~humble(X)<~>strong(X))=>happy(X)))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>~quiet(X)))&
(![X]:((happy(X)&old(X))=>(~happy(X)|quiet(X))))&
((?[X]:((~kind(X)&~tall(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>((patient(paul)<~>happy(paul))))&
((?[X]:((calm(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|funny(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:(kind(X)))<=>(curious(paul)))&
((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((old(X)|~humble(X))<=>(~humble(X)|~patient(X))))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&kind(X))))&
(![X]:(tall(X)<=>(kind(X)<~>~brave(X))))&
(![X]:((~old(X)<~>~generous(X))<=>~generous(X)))&
((old(john)<~>~rich(john)))&
((quiet(mary)&~strong(mary)))&
(?[X]:(old(X)))&
(~happy(fred))&
((~patient(alice)|~curious(alice)))&
((~funny(fred)<~>~brave(fred)))&
((~brave(paul)|~humble(paul))) | old(mary) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7401221354047536566189539
% SZS output start Proof for 7401221354047536566189539
16. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> ~generous(X0)) [input p15]
24. ~old(mary) [input hypothesis]
72. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | generous(X0)) & (~generous(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 16]
119. ~generous(X0) | ~generous(X0) | old(X0) [cnf transformation 72]
122. generous(X0) | old(X0) | generous(X0) [cnf transformation 72]
133. ~old(mary) [cnf transformation 24]
134. ~generous(X0) | old(X0) [duplicate literal removal 119]
135. generous(X0) | old(X0) [duplicate literal removal 122]
258. old(X0) [subsumption resolution 134,135]
288. $false [subsumption resolution 133,258]
% SZS output end Proof for 7401221354047536566189539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is funny then someone is quiet or not kind.
If lucy is both not rich and quiet then someone is not humble and vice versa.
If fred is not quiet then susan is both tall and creative.
If someone is kind then someone is not generous.
If someone is either not funny or not wise then susan is not creative or funny.
Everyone who is either patient or wise is kind or funny and vice versa.
Everyone who is both creative and not kind is strong.
Everyone who is patient is not tall.
Everyone who is not tall or not generous is tall or not generous and vice versa.
Everyone who is not rich is either funny or happy and vice versa.
If someone is both humble and rich then john is both brave and generous.
Everyone who is not funny is either happy or strong and vice versa.
If someone is old or not old then someone is humble or funny.
Everyone who is either not creative or not generous is brave or rich.
Everyone who is not curious is both not happy and not brave and vice versa.
Everyone who is both strong and quiet is either not funny or calm and vice versa.
John is not funny.
Susan is either kind or not kind.
Fred is humble or not generous.
Someone is both not humble and kind.
Someone is not calm or brave.
Alice is both not strong and creative.
Someone is patient. | Lucy is generous. | contradiction | ((funny(lucy))=>(?[X]:((quiet(X)|~kind(X)))))&
(((~rich(lucy)&quiet(lucy)))<=>(?[X]:(~humble(X))))&
((~quiet(fred))=>((tall(susan)&creative(susan))))&
((?[X]:(kind(X)))=>(?[X]:(~generous(X))))&
((?[X]:((~funny(X)<~>~wise(X))))=>((~creative(susan)|funny(susan))))&
(![X]:((patient(X)<~>wise(X))<=>(kind(X)|funny(X))))&
(![X]:((creative(X)&~kind(X))=>strong(X)))&
(![X]:(patient(X)=>~tall(X)))&
(![X]:((~tall(X)|~generous(X))<=>(tall(X)|~generous(X))))&
(![X]:(~rich(X)<=>(funny(X)<~>happy(X))))&
((?[X]:((humble(X)&rich(X))))=>((brave(john)&generous(john))))&
(![X]:(~funny(X)<=>(happy(X)<~>strong(X))))&
((?[X]:((old(X)|~old(X))))=>(?[X]:((humble(X)|funny(X)))))&
(![X]:((~creative(X)<~>~generous(X))=>(brave(X)|rich(X))))&
(![X]:(~curious(X)<=>(~happy(X)&~brave(X))))&
(![X]:((strong(X)&quiet(X))<=>(~funny(X)<~>calm(X))))&
(~funny(john))&
((kind(susan)<~>~kind(susan)))&
((humble(fred)|~generous(fred)))&
(?[X]:((~humble(X)&kind(X))))&
(?[X]:((~calm(X)|brave(X))))&
((~strong(alice)&creative(alice)))&
(?[X]:(patient(X))) | generous(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5528272858947269568617687
% SZS output start Proof for 5528272858947269568617687
9. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~generous(X0) | tall(X0))) [input p8]
24. generous(lucy) [input hypothesis]
53. ! [X0] : (((~generous(X0) | ~tall(X0)) | (generous(X0) & ~tall(X0))) & ((~generous(X0) | tall(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 9]
54. ! [X0] : ((~generous(X0) | ~tall(X0) | (generous(X0) & ~tall(X0))) & (~generous(X0) | tall(X0) | (generous(X0) & tall(X0)))) [flattening 53]
84. ~generous(X0) | tall(X0) | tall(X0) [cnf transformation 54]
86. ~generous(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 54]
114. generous(lucy) [cnf transformation 24]
115. ~generous(X0) | tall(X0) [duplicate literal removal 84]
116. ~generous(X0) | ~tall(X0) [duplicate literal removal 86]
182. ~generous(X0) [subsumption resolution 115,116]
200. $false [subsumption resolution 114,182]
% SZS output end Proof for 5528272858947269568617687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or calm is either kind or old. Everyone who is both not funny and not quiet is both not funny and funny and vice versa. Everyone who is both curious and not generous is happy or not kind. If mary is calm or brave then someone is either kind or not tall. Everyone who is calm or kind is kind or humble and vice versa. If lucy is funny then someone is not creative or funny. If someone is curious then mary is either not happy or wise and vice versa. Everyone who is quiet or curious is not brave and vice versa. Everyone who is both not generous and generous is not strong and vice versa. Everyone who is not quiet is either curious or not old. Everyone who is not tall or not creative is rich or not old. If mary is both not creative and rich then john is generous. Everyone who is not strong or happy is not wise or not quiet. If someone is curious or humble then someone is either patient or not tall. If fred is either not kind or creative then mary is either not quiet or not kind. Everyone who is both not kind and strong is either quiet or patient. Someone is both not quiet and not patient. Someone is either humble or not patient. Fred is both not patient and not rich. Mary is not kind. Lucy is both generous and not quiet. Paul is not patient. Fred is both not quiet and wise. | Fred is curious. | neutral | (![X]:((generous(X)<~>calm(X))=>(kind(X)<~>old(X))))&
(![X]:((~funny(X)&~quiet(X))<=>(~funny(X)&funny(X))))&
(![X]:((curious(X)&~generous(X))=>(happy(X)|~kind(X))))&
(((calm(mary)|brave(mary)))=>(?[X]:((kind(X)<~>~tall(X)))))&
(![X]:((calm(X)|kind(X))<=>(kind(X)|humble(X))))&
((funny(lucy))=>(?[X]:((~creative(X)|funny(X)))))&
((?[X]:(curious(X)))<=>((~happy(mary)<~>wise(mary))))&
(![X]:((quiet(X)|curious(X))<=>~brave(X)))&
(![X]:((~generous(X)&generous(X))<=>~strong(X)))&
(![X]:(~quiet(X)=>(curious(X)<~>~old(X))))&
(![X]:((~tall(X)|~creative(X))=>(rich(X)|~old(X))))&
(((~creative(mary)&rich(mary)))=>(generous(john)))&
(![X]:((~strong(X)|happy(X))=>(~wise(X)|~quiet(X))))&
((?[X]:((curious(X)|humble(X))))=>(?[X]:((patient(X)<~>~tall(X)))))&
(((~kind(fred)<~>creative(fred)))=>((~quiet(mary)<~>~kind(mary))))&
(![X]:((~kind(X)&strong(X))=>(quiet(X)<~>patient(X))))&
(?[X]:((~quiet(X)&~patient(X))))&
(?[X]:((humble(X)<~>~patient(X))))&
((~patient(fred)&~rich(fred)))&
(~kind(mary))&
((generous(lucy)&~quiet(lucy)))&
(~patient(paul))&
((~quiet(fred)&wise(fred))) | curious(fred) | [] | null | 0 |
Everyone who is either rich or not generous is not funny or humble.
Everyone who is not patient or humble is either not curious or generous and vice versa.
Everyone who is either not creative or patient is both not kind and not creative.
Everyone who is either not calm or patient is creative or not wise and vice versa.
Everyone who is either not tall or generous is not funny or not quiet.
If alice is not wise or brave then someone is not tall or strong.
Everyone who is either patient or not brave is patient and vice versa.
Everyone who is not generous or calm is old.
Everyone who is not funny is both quiet and not patient and vice versa.
If someone is not quiet or kind then someone is both patient and funny.
If alice is both kind and tall then someone is humble and vice versa.
If someone is not generous then someone is either not old or not patient and vice versa.
If paul is both strong and calm then fred is both not humble and not old.
Everyone who is not wise is either humble or not quiet and vice versa.
If fred is either strong or not wise then lucy is not kind and vice versa.
Everyone who is both quiet and happy is either strong or brave and vice versa.
Fred is both rich and not humble.
Someone is both not old and not rich.
Paul is rich.
Fred is either not brave or not old.
Someone is not creative or patient. | Paul is patient. | neutral | (![X]:((rich(X)<~>~generous(X))=>(~funny(X)|humble(X))))&
(![X]:((~patient(X)|humble(X))<=>(~curious(X)<~>generous(X))))&
(![X]:((~creative(X)<~>patient(X))=>(~kind(X)&~creative(X))))&
(![X]:((~calm(X)<~>patient(X))<=>(creative(X)|~wise(X))))&
(![X]:((~tall(X)<~>generous(X))=>(~funny(X)|~quiet(X))))&
(((~wise(alice)|brave(alice)))=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((patient(X)<~>~brave(X))<=>patient(X)))&
(![X]:((~generous(X)|calm(X))=>old(X)))&
(![X]:(~funny(X)<=>(quiet(X)&~patient(X))))&
((?[X]:((~quiet(X)|kind(X))))=>(?[X]:((patient(X)&funny(X)))))&
(((kind(alice)&tall(alice)))<=>(?[X]:(humble(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~old(X)<~>~patient(X)))))&
(((strong(paul)&calm(paul)))=>((~humble(fred)&~old(fred))))&
(![X]:(~wise(X)<=>(humble(X)<~>~quiet(X))))&
(((strong(fred)<~>~wise(fred)))<=>(~kind(lucy)))&
(![X]:((quiet(X)&happy(X))<=>(strong(X)<~>brave(X))))&
((rich(fred)&~humble(fred)))&
(?[X]:((~old(X)&~rich(X))))&
(rich(paul))&
((~brave(fred)<~>~old(fred)))&
(?[X]:((~creative(X)|patient(X)))) | patient(paul) | [] | null | 0 |
Everyone who is both tall and not curious is rich and vice versa. Everyone who is curious is wise or brave and vice versa. Everyone who is calm is not generous. If susan is either creative or not humble then paul is not patient and vice versa. Everyone who is either wise or patient is either not generous or not humble. If susan is generous then susan is happy and vice versa. If someone is both kind and not humble then fred is either not funny or creative. Everyone who is curious or wise is not curious. Everyone who is both humble and rich is not brave and vice versa. If mary is not patient or funny then john is either strong or not patient and vice versa. Everyone who is either patient or kind is either strong or happy. Everyone who is either wise or happy is happy. If someone is not rich or kind then lucy is curious and vice versa. Everyone who is either not strong or not quiet is not rich and vice versa. Everyone who is not curious is creative or not patient and vice versa. Someone is not tall or old. John is either not humble or patient. Someone is either funny or not kind. Alice is funny or old. Lucy is either not curious or brave. Susan is either funny or not calm. Fred is not kind. Paul is tall or brave. | Susan is not happy. | neutral | (![X]:((tall(X)&~curious(X))<=>rich(X)))&
(![X]:(curious(X)<=>(wise(X)|brave(X))))&
(![X]:(calm(X)=>~generous(X)))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(?[X]:((~tall(X)|old(X))))&
((~humble(john)<~>patient(john)))&
(?[X]:((funny(X)<~>~kind(X))))&
((funny(alice)|old(alice)))&
((~curious(lucy)<~>brave(lucy)))&
((funny(susan)<~>~calm(susan)))&
(~kind(fred))&
((tall(paul)|brave(paul))) | ~happy(susan) | [] | null | 0 |
Everyone who is not rich or not strong is both humble and wise.
Everyone who is either brave or quiet is either not brave or not calm.
Everyone who is not creative or humble is rich or strong and vice versa.
Everyone who is both not humble and curious is either not funny or old.
If mary is generous or not generous then mary is not curious or not creative.
If mary is either humble or quiet then someone is kind and vice versa.
Everyone who is not old is both old and patient and vice versa.
Everyone who is both creative and not happy is quiet or not humble and vice versa.
If lucy is either kind or strong then someone is kind or not funny and vice versa.
Everyone who is quiet is not rich or funny and vice versa.
If fred is both not generous and not happy then someone is both wise and funny.
Everyone who is calm or strong is either old or tall and vice versa.
Everyone who is either not rich or rich is either funny or not curious and vice versa.
Everyone who is not calm or quiet is old.
If someone is either not wise or calm then someone is not generous or old.
Everyone who is both calm and not patient is both not quiet and strong.
Someone is either not humble or brave.
Someone is old.
John is either not happy or not generous.
Lucy is either funny or not strong.
John is both not wise and rich.
John is brave or not brave. | Lucy is not rich. | neutral | (![X]:((~rich(X)|~strong(X))=>(humble(X)&wise(X))))&
(![X]:((brave(X)<~>quiet(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((~creative(X)|humble(X))<=>(rich(X)|strong(X))))&
(![X]:((~humble(X)&curious(X))=>(~funny(X)<~>old(X))))&
(((generous(mary)|~generous(mary)))=>((~curious(mary)|~creative(mary))))&
(((humble(mary)<~>quiet(mary)))<=>(?[X]:(kind(X))))&
(![X]:(~old(X)<=>(old(X)&patient(X))))&
(![X]:((creative(X)&~happy(X))<=>(quiet(X)|~humble(X))))&
(((kind(lucy)<~>strong(lucy)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:(quiet(X)<=>(~rich(X)|funny(X))))&
(((~generous(fred)&~happy(fred)))=>(?[X]:((wise(X)&funny(X)))))&
(![X]:((calm(X)|strong(X))<=>(old(X)<~>tall(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(funny(X)<~>~curious(X))))&
(![X]:((~calm(X)|quiet(X))=>old(X)))&
((?[X]:((~wise(X)<~>calm(X))))=>(?[X]:((~generous(X)|old(X)))))&
(![X]:((calm(X)&~patient(X))=>(~quiet(X)&strong(X))))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:(old(X)))&
((~happy(john)<~>~generous(john)))&
((funny(lucy)<~>~strong(lucy)))&
((~wise(john)&rich(john)))&
((brave(john)|~brave(john))) | ~rich(lucy) | [] | null | 0 |
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