premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is wise is both funny and not quiet and vice versa.
Everyone who is old or kind is humble or generous and vice versa.
Everyone who is either not wise or not patient is both not happy and wise and vice versa.
Everyone who is both rich and creative is either not humble or brave and vice versa.
Everyone who is not creative or quiet is not humble or not wise.
Everyone who is both quiet and old is rich or curious.
Everyone who is either strong or not quiet is either not generous or quiet and vice versa.
Everyone who is either not kind or curious is not calm or generous.
Everyone who is wise or calm is brave or not old.
Everyone who is either humble or curious is either kind or not wise and vice versa.
If john is both humble and not humble then someone is brave and vice versa.
Everyone who is not humble or not old is either calm or tall.
Everyone who is either not strong or not tall is funny or not rich and vice versa.
Everyone who is either generous or patient is patient and vice versa.
Everyone who is either tall or not generous is both old and wise.
Everyone who is brave or not calm is either funny or quiet and vice versa.
Someone is happy or rich.
Someone is curious or not wise.
Someone is curious or happy.
Fred is either happy or not strong. | Fred is tall. | entailment | (![X]:(wise(X)<=>(funny(X)&~quiet(X))))&
(![X]:((old(X)|kind(X))<=>(humble(X)|generous(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~happy(X)&wise(X))))&
(![X]:((rich(X)&creative(X))<=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)|quiet(X))=>(~humble(X)|~wise(X))))&
(![X]:((quiet(X)&old(X))=>(rich(X)|curious(X))))&
(![X]:((strong(X)<~>~quiet(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:((~kind(X)<~>curious(X))=>(~calm(X)|generous(X))))&
(![X]:((wise(X)|calm(X))=>(brave(X)|~old(X))))&
(![X]:((humble(X)<~>curious(X))<=>(kind(X)<~>~wise(X))))&
(((humble(john)&~humble(john)))<=>(?[X]:(brave(X))))&
(![X]:((~humble(X)|~old(X))=>(calm(X)<~>tall(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>(funny(X)|~rich(X))))&
(![X]:((generous(X)<~>patient(X))<=>patient(X)))&
(![X]:((tall(X)<~>~generous(X))=>(old(X)&wise(X))))&
(![X]:((brave(X)|~calm(X))<=>(funny(X)<~>quiet(X))))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:((curious(X)|~wise(X))))&
(?[X]:((curious(X)|happy(X))))&
((happy(fred)<~>~strong(fred))) | tall(fred) | [
"p8",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3792010774469640342830048
% SZS output start Proof for 3792010774469640342830048
9. ! [X0] : ((calm(X0) | wise(X0)) => (~old(X0) | brave(X0))) [input p8]
11. (~humble(john) & humble(john)) <=> ? [X0] : brave(X0) [input p10]
14. ! [X0] : ((generous(X0) <~> patient(X0)) <=> patient(X0)) [input p13]
15. ! [X0] : ((tall(X0) <~> ~generous(X0)) => (wise(X0) & old(X0))) [input p14]
21. ~tall(fred) [input hypothesis]
28. ! [X0] : ((~old(X0) | brave(X0)) | (~calm(X0) & ~wise(X0))) [ennf transformation 9]
29. ! [X0] : (~old(X0) | brave(X0) | (~calm(X0) & ~wise(X0))) [flattening 28]
31. ! [X0] : ((wise(X0) & old(X0)) | (tall(X0) <=> ~generous(X0))) [ennf transformation 15]
43. ((~humble(john) & humble(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (humble(john) | ~humble(john))) [nnf transformation 11]
44. ((~humble(john) & humble(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | humble(john) | ~humble(john)) [flattening 43]
45. ((~humble(john) & humble(john)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | humble(john) | ~humble(john)) [rectify 44]
46. ? [X1] : brave(X1) => brave(sK0) [choice axiom]
47. ((~humble(john) & humble(john)) | ! [X0] : ~brave(X0)) & (brave(sK0) | humble(john) | ~humble(john)) [skolemisation 45,46]
51. ! [X0] : ((((~patient(X0) | ~generous(X0)) & (patient(X0) | generous(X0))) | ~patient(X0)) & (patient(X0) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0))))) [nnf transformation 14]
52. ! [X0] : ((wise(X0) & old(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) [nnf transformation 31]
94. ~old(X0) | brave(X0) | ~wise(X0) [cnf transformation 29]
105. humble(john) | ~brave(X0) [cnf transformation 47]
106. ~humble(john) | ~brave(X0) [cnf transformation 47]
117. patient(X0) | patient(X0) | ~generous(X0) [cnf transformation 51]
120. ~patient(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 51]
122. old(X0) | tall(X0) | generous(X0) [cnf transformation 52]
124. wise(X0) | tall(X0) | generous(X0) [cnf transformation 52]
136. ~tall(fred) [cnf transformation 21]
137. patient(X0) | ~generous(X0) [duplicate literal removal 117]
138. ~patient(X0) | ~generous(X0) [duplicate literal removal 120]
148. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
149. ~brave(X0) <- (1) [avatar component clause 148]
151. 2 <=> humble(john) [avatar definition]
154. 1 | ~2 [avatar split clause 106,151,148]
155. 1 | 2 [avatar split clause 105,151,148]
156. ~generous(X0) [subsumption resolution 137,138]
157. tall(X0) | wise(X0) [subsumption resolution 124,156]
158. tall(X0) | old(X0) [subsumption resolution 122,156]
196. wise(fred) [resolution 157,136]
197. old(fred) [resolution 158,136]
223. brave(fred) | ~wise(fred) [resolution 94,197]
224. ~wise(fred) <- (1) [subsumption resolution 223,149]
225. $false <- (1) [subsumption resolution 224,196]
226. ~1 [avatar contradiction clause 225]
227. $false [avatar sat refutation 154,155,226]
% SZS output end Proof for 3792010774469640342830048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and patient is either not patient or not kind and vice versa.
If someone is not strong then someone is quiet.
Everyone who is either kind or not brave is not patient or not quiet.
Everyone who is generous is both tall and happy and vice versa.
Everyone who is not quiet or brave is both not curious and not funny.
Everyone who is not funny or wise is not strong or not old and vice versa.
Everyone who is either not happy or old is not humble.
If someone is not kind or happy then someone is not patient or not happy.
If someone is either kind or funny then someone is either funny or curious and vice versa.
If lucy is not tall or not wise then someone is not old and vice versa.
If susan is both not funny and not patient then someone is both not tall and not creative.
If susan is curious or not quiet then fred is either not brave or brave.
Everyone who is both not curious and quiet is both kind and not generous.
Everyone who is both curious and not quiet is both not wise and funny and vice versa.
If susan is either old or not curious then john is not funny or not kind and vice versa.
Everyone who is either old or not rich is not creative.
Fred is either rich or not happy.
Someone is not funny.
Alice is rich or funny.
Someone is not humble.
Mary is not strong.
Mary is brave.
Someone is both creative and wise.
Someone is not happy or quiet. | Mary is brave. | entailment | (![X]:((~strong(X)&patient(X))<=>(~patient(X)<~>~kind(X))))&
((?[X]:(~strong(X)))=>(?[X]:(quiet(X))))&
(![X]:((kind(X)<~>~brave(X))=>(~patient(X)|~quiet(X))))&
(![X]:(generous(X)<=>(tall(X)&happy(X))))&
(![X]:((~quiet(X)|brave(X))=>(~curious(X)&~funny(X))))&
(![X]:((~funny(X)|wise(X))<=>(~strong(X)|~old(X))))&
(![X]:((~happy(X)<~>old(X))=>~humble(X)))&
((?[X]:((~kind(X)|happy(X))))=>(?[X]:((~patient(X)|~happy(X)))))&
((?[X]:((kind(X)<~>funny(X))))<=>(?[X]:((funny(X)<~>curious(X)))))&
(((~tall(lucy)|~wise(lucy)))<=>(?[X]:(~old(X))))&
(((~funny(susan)&~patient(susan)))=>(?[X]:((~tall(X)&~creative(X)))))&
(((curious(susan)|~quiet(susan)))=>((~brave(fred)<~>brave(fred))))&
(![X]:((~curious(X)&quiet(X))=>(kind(X)&~generous(X))))&
(![X]:((curious(X)&~quiet(X))<=>(~wise(X)&funny(X))))&
(((old(susan)<~>~curious(susan)))<=>((~funny(john)|~kind(john))))&
(![X]:((old(X)<~>~rich(X))=>~creative(X)))&
((rich(fred)<~>~happy(fred)))&
(?[X]:(~funny(X)))&
((rich(alice)|funny(alice)))&
(?[X]:(~humble(X)))&
(~strong(mary))&
(brave(mary))&
(?[X]:((creative(X)&wise(X))))&
(?[X]:((~happy(X)|quiet(X)))) | brave(mary) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2971776306253114984894921
% SZS output start Proof for 2971776306253114984894921
22. brave(mary) [input p21]
25. ~brave(mary) [input hypothesis]
137. brave(mary) [cnf transformation 22]
141. ~brave(mary) [cnf transformation 25]
293. $false [subsumption resolution 141,137]
% SZS output end Proof for 2971776306253114984894921
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then someone is tall or not rich.
Everyone who is both not curious and patient is both patient and curious and vice versa.
If paul is not happy or not curious then someone is either not funny or strong.
Everyone who is either not creative or not generous is not strong or generous.
Everyone who is either brave or not wise is not kind or funny.
Everyone who is strong or funny is either not curious or not happy and vice versa.
If someone is wise then susan is funny or generous and vice versa.
Everyone who is either not creative or humble is not strong or curious.
If paul is both not calm and not patient then someone is not rich and vice versa.
If someone is either brave or not happy then fred is not funny or not happy and vice versa.
Everyone who is not generous or not strong is either not calm or curious.
If alice is not generous or quiet then susan is either not rich or not brave and vice versa.
If alice is both not patient and kind then someone is both not happy and not quiet and vice versa.
Everyone who is both not generous and funny is either not quiet or not humble.
If john is both not wise and curious then someone is both not quiet and not happy and vice versa.
Everyone who is not generous is either not generous or patient.
Fred is not creative.
Someone is either not quiet or patient.
John is creative.
Mary is both not curious and quiet.
Alice is either tall or not rich.
Alice is both calm and humble.
Someone is not humble or curious. | Susan is not tall. | neutral | ((?[X]:(~brave(X)))=>(?[X]:((tall(X)|~rich(X)))))&
(![X]:((~curious(X)&patient(X))<=>(patient(X)&curious(X))))&
(((~happy(paul)|~curious(paul)))=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:((~creative(X)<~>~generous(X))=>(~strong(X)|generous(X))))&
(![X]:((brave(X)<~>~wise(X))=>(~kind(X)|funny(X))))&
(![X]:((strong(X)|funny(X))<=>(~curious(X)<~>~happy(X))))&
((?[X]:(wise(X)))<=>((funny(susan)|generous(susan))))&
(![X]:((~creative(X)<~>humble(X))=>(~strong(X)|curious(X))))&
(((~calm(paul)&~patient(paul)))<=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)<~>~happy(X))))<=>((~funny(fred)|~happy(fred))))&
(![X]:((~generous(X)|~strong(X))=>(~calm(X)<~>curious(X))))&
(((~generous(alice)|quiet(alice)))<=>((~rich(susan)<~>~brave(susan))))&
(((~patient(alice)&kind(alice)))<=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:((~generous(X)&funny(X))=>(~quiet(X)<~>~humble(X))))&
(((~wise(john)&curious(john)))<=>(?[X]:((~quiet(X)&~happy(X)))))&
(![X]:(~generous(X)=>(~generous(X)<~>patient(X))))&
(~creative(fred))&
(?[X]:((~quiet(X)<~>patient(X))))&
(creative(john))&
((~curious(mary)&quiet(mary)))&
((tall(alice)<~>~rich(alice)))&
((calm(alice)&humble(alice)))&
(?[X]:((~humble(X)|curious(X)))) | ~tall(susan) | [] | null | 0 |
If someone is either humble or not strong then someone is both creative and not calm.
If alice is not generous or curious then lucy is not brave.
Everyone who is old or not quiet is either not patient or not tall and vice versa.
If alice is both not curious and creative then mary is either not kind or strong and vice versa.
If someone is curious then mary is both happy and strong.
Everyone who is not happy is both not brave and brave.
Everyone who is both not patient and old is both not happy and not rich and vice versa.
If someone is either happy or brave then fred is either not generous or generous and vice versa.
Everyone who is both not tall and curious is either not generous or not humble and vice versa.
Everyone who is curious or funny is both happy and not funny.
Everyone who is both not happy and tall is kind and vice versa.
If fred is both not curious and strong then someone is either humble or not funny and vice versa.
Everyone who is not old or not curious is either not kind or brave and vice versa.
Everyone who is not kind or rich is quiet or wise.
Everyone who is either old or not old is happy and vice versa.
If alice is both brave and curious then someone is not happy and vice versa.
Someone is not humble or not patient.
Mary is both not kind and wise.
Someone is not tall or creative.
Someone is not strong or not generous.
Alice is both not brave and curious.
Someone is either humble or not kind. | Alice is old. | contradiction | ((?[X]:((humble(X)<~>~strong(X))))=>(?[X]:((creative(X)&~calm(X)))))&
(((~generous(alice)|curious(alice)))=>(~brave(lucy)))&
(![X]:((old(X)|~quiet(X))<=>(~patient(X)<~>~tall(X))))&
(((~curious(alice)&creative(alice)))<=>((~kind(mary)<~>strong(mary))))&
((?[X]:(curious(X)))=>((happy(mary)&strong(mary))))&
(![X]:(~happy(X)=>(~brave(X)&brave(X))))&
(![X]:((~patient(X)&old(X))<=>(~happy(X)&~rich(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>((~generous(fred)<~>generous(fred))))&
(![X]:((~tall(X)&curious(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((curious(X)|funny(X))=>(happy(X)&~funny(X))))&
(![X]:((~happy(X)&tall(X))<=>kind(X)))&
(((~curious(fred)&strong(fred)))<=>(?[X]:((humble(X)<~>~funny(X)))))&
(![X]:((~old(X)|~curious(X))<=>(~kind(X)<~>brave(X))))&
(![X]:((~kind(X)|rich(X))=>(quiet(X)|wise(X))))&
(![X]:((old(X)<~>~old(X))<=>happy(X)))&
(((brave(alice)&curious(alice)))<=>(?[X]:(~happy(X))))&
(?[X]:((~humble(X)|~patient(X))))&
((~kind(mary)&wise(mary)))&
(?[X]:((~tall(X)|creative(X))))&
(?[X]:((~strong(X)|~generous(X))))&
((~brave(alice)&curious(alice)))&
(?[X]:((humble(X)<~>~kind(X)))) | old(alice) | [
"p5",
"p10",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 782171029877962843348962
% SZS output start Proof for 782171029877962843348962
6. ! [X0] : (~happy(X0) => (brave(X0) & ~brave(X0))) [input p5]
11. ! [X0] : ((tall(X0) & ~happy(X0)) <=> kind(X0)) [input p10]
13. ! [X0] : ((~curious(X0) | ~old(X0)) <=> (~kind(X0) <~> brave(X0))) [input p12]
16. (curious(alice) & brave(alice)) <=> ? [X0] : ~happy(X0) [input p15]
21. curious(alice) & ~brave(alice) [input p20]
23. old(alice) [input hypothesis]
31. ! [X0] : ((brave(X0) & ~brave(X0)) | happy(X0)) [ennf transformation 6]
49. ! [X0] : (((tall(X0) & ~happy(X0)) | ~kind(X0)) & (kind(X0) | (~tall(X0) | happy(X0)))) [nnf transformation 11]
50. ! [X0] : (((tall(X0) & ~happy(X0)) | ~kind(X0)) & (kind(X0) | ~tall(X0) | happy(X0))) [flattening 49]
56. ! [X0] : (((~curious(X0) | ~old(X0)) | ((~kind(X0) | ~brave(X0)) & (brave(X0) | kind(X0)))) & (((~brave(X0) | kind(X0)) & (brave(X0) | ~kind(X0))) | (curious(X0) & old(X0)))) [nnf transformation 13]
57. ! [X0] : ((~curious(X0) | ~old(X0) | ((~kind(X0) | ~brave(X0)) & (brave(X0) | kind(X0)))) & (((~brave(X0) | kind(X0)) & (brave(X0) | ~kind(X0))) | (curious(X0) & old(X0)))) [flattening 56]
59. ((curious(alice) & brave(alice)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (~curious(alice) | ~brave(alice))) [nnf transformation 16]
60. ((curious(alice) & brave(alice)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | ~curious(alice) | ~brave(alice)) [flattening 59]
61. ((curious(alice) & brave(alice)) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | ~curious(alice) | ~brave(alice)) [rectify 60]
62. ? [X1] : ~happy(X1) => ~happy(sK3) [choice axiom]
63. ((curious(alice) & brave(alice)) | ! [X0] : happy(X0)) & (~happy(sK3) | ~curious(alice) | ~brave(alice)) [skolemisation 61,62]
91. ~brave(X0) | happy(X0) [cnf transformation 31]
92. happy(X0) | brave(X0) [cnf transformation 31]
116. ~happy(X0) | ~kind(X0) [cnf transformation 50]
127. ~brave(X0) | kind(X0) | curious(X0) [cnf transformation 57]
128. ~curious(X0) | ~old(X0) | brave(X0) | kind(X0) [cnf transformation 57]
134. ~happy(sK3) | ~curious(alice) | ~brave(alice) [cnf transformation 63]
142. curious(alice) [cnf transformation 21]
145. old(alice) [cnf transformation 23]
166. 4 <=> curious(alice) [avatar definition]
167. curious(alice) <- (4) [avatar component clause 166]
206. happy(X0) [subsumption resolution 91,92]
220. ~kind(X0) [subsumption resolution 116,206]
242. ~old(X0) | ~curious(X0) | brave(X0) [subsumption resolution 128,220]
243. ~brave(X0) | curious(X0) [subsumption resolution 127,220]
245. ~curious(alice) | ~brave(alice) [subsumption resolution 134,206]
246. ~brave(alice) [subsumption resolution 245,243]
274. 4 [avatar split clause 142,166]
314. ~curious(alice) | brave(alice) [resolution 242,145]
315. brave(alice) <- (4) [subsumption resolution 314,167]
316. $false <- (4) [subsumption resolution 315,246]
317. ~4 [avatar contradiction clause 316]
318. $false [avatar sat refutation 274,317]
% SZS output end Proof for 782171029877962843348962
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not calm and kind then mary is happy and vice versa.
Everyone who is both brave and strong is both curious and not humble and vice versa.
If mary is both not patient and not generous then paul is not funny or not kind.
If someone is funny or not generous then alice is both not humble and not happy and vice versa.
If alice is not funny then susan is not old.
If paul is tall then someone is not strong or not brave and vice versa.
Everyone who is strong is both not generous and funny and vice versa.
Everyone who is either not kind or kind is either not curious or not happy and vice versa.
Everyone who is curious or creative is either not wise or wise.
Everyone who is both wise and old is generous and vice versa.
Everyone who is either wise or not generous is both funny and rich and vice versa.
Everyone who is generous is not old.
Everyone who is both not brave and calm is both strong and tall.
Everyone who is old is either not patient or not strong.
Everyone who is not funny is either not kind or not quiet and vice versa.
Susan is either not calm or generous.
John is either not tall or not patient.
Someone is not funny or not creative.
Someone is rich.
Someone is quiet or calm.
John is both not strong and not curious. | John is not old. | entailment | (((~calm(susan)&kind(susan)))<=>(happy(mary)))&
(![X]:((brave(X)&strong(X))<=>(curious(X)&~humble(X))))&
(((~patient(mary)&~generous(mary)))=>((~funny(paul)|~kind(paul))))&
((?[X]:((funny(X)|~generous(X))))<=>((~humble(alice)&~happy(alice))))&
((~funny(alice))=>(~old(susan)))&
((tall(paul))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:(strong(X)<=>(~generous(X)&funny(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(~curious(X)<~>~happy(X))))&
(![X]:((curious(X)|creative(X))=>(~wise(X)<~>wise(X))))&
(![X]:((wise(X)&old(X))<=>generous(X)))&
(![X]:((wise(X)<~>~generous(X))<=>(funny(X)&rich(X))))&
(![X]:(generous(X)=>~old(X)))&
(![X]:((~brave(X)&calm(X))=>(strong(X)&tall(X))))&
(![X]:(old(X)=>(~patient(X)<~>~strong(X))))&
(![X]:(~funny(X)<=>(~kind(X)<~>~quiet(X))))&
((~calm(susan)<~>generous(susan)))&
((~tall(john)<~>~patient(john)))&
(?[X]:((~funny(X)|~creative(X))))&
(?[X]:(rich(X)))&
(?[X]:((quiet(X)|calm(X))))&
((~strong(john)&~curious(john))) | ~old(john) | [
"p6",
"p9",
"p10",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4698750721956998285232549
% SZS output start Proof for 4698750721956998285232549
7. ! [X0] : (strong(X0) <=> (funny(X0) & ~generous(X0))) [input p6]
10. ! [X0] : ((old(X0) & wise(X0)) <=> generous(X0)) [input p9]
11. ! [X0] : ((wise(X0) <~> ~generous(X0)) <=> (rich(X0) & funny(X0))) [input p10]
12. ! [X0] : (generous(X0) => ~old(X0)) [input p11]
21. ~curious(john) & ~strong(john) [input p20]
22. old(john) [input hypothesis]
29. ! [X0] : (~old(X0) | ~generous(X0)) [ennf transformation 12]
46. ! [X0] : ((strong(X0) | (~funny(X0) | generous(X0))) & ((funny(X0) & ~generous(X0)) | ~strong(X0))) [nnf transformation 7]
47. ! [X0] : ((strong(X0) | ~funny(X0) | generous(X0)) & ((funny(X0) & ~generous(X0)) | ~strong(X0))) [flattening 46]
50. ! [X0] : (((old(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | (~old(X0) | ~wise(X0)))) [nnf transformation 10]
51. ! [X0] : (((old(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | ~old(X0) | ~wise(X0))) [flattening 50]
52. ! [X0] : ((((generous(X0) | ~wise(X0)) & (~generous(X0) | wise(X0))) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | ((wise(X0) | generous(X0)) & (~generous(X0) | ~wise(X0))))) [nnf transformation 11]
53. ! [X0] : ((((generous(X0) | ~wise(X0)) & (~generous(X0) | wise(X0))) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | ((wise(X0) | generous(X0)) & (~generous(X0) | ~wise(X0))))) [flattening 52]
81. ~funny(X0) | strong(X0) | generous(X0) [cnf transformation 47]
92. ~wise(X0) | ~old(X0) | generous(X0) [cnf transformation 51]
93. ~generous(X0) | wise(X0) [cnf transformation 51]
94. ~generous(X0) | old(X0) [cnf transformation 51]
96. funny(X0) | wise(X0) | generous(X0) [cnf transformation 53]
101. ~old(X0) | ~generous(X0) [cnf transformation 29]
116. ~strong(john) [cnf transformation 21]
118. old(john) [cnf transformation 22]
216. wise(X0) | funny(X0) [subsumption resolution 96,93]
218. ~generous(X0) [subsumption resolution 101,94]
244. ~old(X0) | generous(X0) | funny(X0) [resolution 92,216]
245. ~old(X0) | funny(X0) [subsumption resolution 244,218]
246. funny(john) [resolution 245,118]
247. strong(john) | generous(john) [resolution 246,81]
248. generous(john) [subsumption resolution 247,116]
249. $false [subsumption resolution 248,218]
% SZS output end Proof for 4698750721956998285232549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then someone is not happy. If someone is happy then someone is not brave or funny. If someone is not rich then susan is kind. Everyone who is either not rich or not humble is both creative and not quiet. If lucy is creative or not strong then paul is either not strong or not tall and vice versa. If someone is patient or not generous then lucy is both quiet and not generous. If someone is either not creative or not strong then someone is either not strong or funny. If alice is both not creative and old then lucy is both kind and rich and vice versa. Everyone who is both not happy and tall is not brave or not wise. If paul is either not old or not happy then mary is either not happy or not brave. Everyone who is both brave and quiet is not patient and vice versa. If someone is not strong or patient then someone is happy. Everyone who is either old or not curious is both not strong and strong. If someone is not rich then susan is both not brave and not humble. If someone is brave or not creative then paul is either not strong or not patient and vice versa. Everyone who is both not strong and not quiet is not old. Someone is both funny and not happy. Mary is both not quiet and not curious. Someone is quiet. Mary is generous. Someone is brave or old. Susan is strong. Paul is both not funny and quiet. Fred is funny or not old. | Lucy is not quiet. | contradiction | ((?[X]:(happy(X)))=>(?[X]:(~happy(X))))&
((?[X]:(happy(X)))=>(?[X]:((~brave(X)|funny(X)))))&
((?[X]:(~rich(X)))=>(kind(susan)))&
(![X]:((~rich(X)<~>~humble(X))=>(creative(X)&~quiet(X))))&
(((creative(lucy)|~strong(lucy)))<=>((~strong(paul)<~>~tall(paul))))&
((?[X]:((patient(X)|~generous(X))))=>((quiet(lucy)&~generous(lucy))))&
((?[X]:((~creative(X)<~>~strong(X))))=>(?[X]:((~strong(X)<~>funny(X)))))&
(((~creative(alice)&old(alice)))<=>((kind(lucy)&rich(lucy))))&
(![X]:((~happy(X)&tall(X))=>(~brave(X)|~wise(X))))&
(((~old(paul)<~>~happy(paul)))=>((~happy(mary)<~>~brave(mary))))&
(![X]:((brave(X)&quiet(X))<=>~patient(X)))&
((?[X]:((~strong(X)|patient(X))))=>(?[X]:(happy(X))))&
(![X]:((old(X)<~>~curious(X))=>(~strong(X)&strong(X))))&
((?[X]:(~rich(X)))=>((~brave(susan)&~humble(susan))))&
((?[X]:((brave(X)|~creative(X))))<=>((~strong(paul)<~>~patient(paul))))&
(![X]:((~strong(X)&~quiet(X))=>~old(X)))&
(?[X]:((funny(X)&~happy(X))))&
((~quiet(mary)&~curious(mary)))&
(?[X]:(quiet(X)))&
(generous(mary))&
(?[X]:((brave(X)|old(X))))&
(strong(susan))&
((~funny(paul)&quiet(paul)))&
((funny(fred)|~old(fred))) | ~quiet(lucy) | [
"p5",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5733265116012503350472221
% SZS output start Proof for 5733265116012503350472221
6. ? [X0] : (~generous(X0) | patient(X0)) => (~generous(lucy) & quiet(lucy)) [input p5]
11. ! [X0] : ((quiet(X0) & brave(X0)) <=> ~patient(X0)) [input p10]
18. ~curious(mary) & ~quiet(mary) [input p17]
25. ~quiet(lucy) [input hypothesis]
35. (~generous(lucy) & quiet(lucy)) | ! [X0] : (generous(X0) & ~patient(X0)) [ennf transformation 6]
59. ! [X0] : (((quiet(X0) & brave(X0)) | patient(X0)) & (~patient(X0) | (~quiet(X0) | ~brave(X0)))) [nnf transformation 11]
60. ! [X0] : (((quiet(X0) & brave(X0)) | patient(X0)) & (~patient(X0) | ~quiet(X0) | ~brave(X0))) [flattening 59]
88. quiet(lucy) | ~patient(X0) [cnf transformation 35]
106. patient(X0) | quiet(X0) [cnf transformation 60]
124. ~quiet(mary) [cnf transformation 18]
133. ~quiet(lucy) [cnf transformation 25]
190. 13 <=> ! [X0] : ~patient(X0) [avatar definition]
191. ~patient(X0) <- (13) [avatar component clause 190]
194. 14 <=> quiet(lucy) [avatar definition]
198. 13 | 14 [avatar split clause 88,194,190]
320. ~14 [avatar split clause 133,194]
323. quiet(X0) <- (13) [resolution 106,191]
327. $false <- (13) [resolution 323,124]
330. ~13 [avatar contradiction clause 327]
331. $false [avatar sat refutation 198,320,330]
% SZS output end Proof for 5733265116012503350472221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and calm is both not kind and not tall.
If someone is either not brave or humble then john is both not tall and patient.
If mary is not wise or quiet then someone is not wise and vice versa.
Everyone who is not happy is both not quiet and old.
Everyone who is both curious and strong is either patient or quiet and vice versa.
Everyone who is wise is both wise and not calm and vice versa.
Everyone who is either happy or humble is either brave or generous and vice versa.
Everyone who is not humble is either not happy or creative.
If someone is old then someone is both not calm and tall.
Everyone who is either strong or funny is either not curious or happy.
Everyone who is not calm is both funny and not funny and vice versa.
Everyone who is both not creative and not strong is both not generous and curious.
If susan is generous then someone is happy or not quiet.
Everyone who is not calm is strong or patient and vice versa.
If someone is either humble or not strong then someone is both strong and happy.
Everyone who is both not strong and not generous is either not generous or strong and vice versa.
Someone is funny or not strong.
Someone is either wise or not funny.
Susan is rich or not brave.
John is not happy or not generous. | Mary is not quiet. | entailment | (![X]:((generous(X)&calm(X))=>(~kind(X)&~tall(X))))&
((?[X]:((~brave(X)<~>humble(X))))=>((~tall(john)&patient(john))))&
(((~wise(mary)|quiet(mary)))<=>(?[X]:(~wise(X))))&
(![X]:(~happy(X)=>(~quiet(X)&old(X))))&
(![X]:((curious(X)&strong(X))<=>(patient(X)<~>quiet(X))))&
(![X]:(wise(X)<=>(wise(X)&~calm(X))))&
(![X]:((happy(X)<~>humble(X))<=>(brave(X)<~>generous(X))))&
(![X]:(~humble(X)=>(~happy(X)<~>creative(X))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((strong(X)<~>funny(X))=>(~curious(X)<~>happy(X))))&
(![X]:(~calm(X)<=>(funny(X)&~funny(X))))&
(![X]:((~creative(X)&~strong(X))=>(~generous(X)&curious(X))))&
((generous(susan))=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:(~calm(X)<=>(strong(X)|patient(X))))&
((?[X]:((humble(X)<~>~strong(X))))=>(?[X]:((strong(X)&happy(X)))))&
(![X]:((~strong(X)&~generous(X))<=>(~generous(X)<~>strong(X))))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((wise(X)<~>~funny(X))))&
((rich(susan)|~brave(susan)))&
((~happy(john)|~generous(john))) | ~quiet(mary) | [
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2861188974551627874356685
% SZS output start Proof for 2861188974551627874356685
5. ! [X0] : ((strong(X0) & curious(X0)) <=> (patient(X0) <~> quiet(X0))) [input p4]
11. ! [X0] : (~calm(X0) <=> (~funny(X0) & funny(X0))) [input p10]
14. ! [X0] : (~calm(X0) <=> (patient(X0) | strong(X0))) [input p13]
21. quiet(mary) [input hypothesis]
43. ! [X0] : (((strong(X0) & curious(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~strong(X0) | ~curious(X0)))) [nnf transformation 5]
44. ! [X0] : (((strong(X0) & curious(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | ~strong(X0) | ~curious(X0))) [flattening 43]
53. ! [X0] : ((~calm(X0) | (funny(X0) | ~funny(X0))) & ((~funny(X0) & funny(X0)) | calm(X0))) [nnf transformation 11]
54. ! [X0] : ((~calm(X0) | funny(X0) | ~funny(X0)) & ((~funny(X0) & funny(X0)) | calm(X0))) [flattening 53]
57. ! [X0] : ((~calm(X0) | (~patient(X0) & ~strong(X0))) & ((patient(X0) | strong(X0)) | calm(X0))) [nnf transformation 14]
58. ! [X0] : ((~calm(X0) | (~patient(X0) & ~strong(X0))) & (patient(X0) | strong(X0) | calm(X0))) [flattening 57]
85. ~quiet(X0) | patient(X0) | strong(X0) [cnf transformation 44]
105. funny(X0) | calm(X0) [cnf transformation 54]
106. ~funny(X0) | calm(X0) [cnf transformation 54]
112. ~calm(X0) | ~strong(X0) [cnf transformation 58]
113. ~calm(X0) | ~patient(X0) [cnf transformation 58]
128. quiet(mary) [cnf transformation 21]
159. 7 <=> quiet(mary) [avatar definition]
161. quiet(mary) <- (7) [avatar component clause 159]
182. calm(X0) [subsumption resolution 105,106]
183. ~patient(X0) [subsumption resolution 113,182]
184. ~strong(X0) [subsumption resolution 112,182]
216. 7 [avatar split clause 128,159]
224. patient(mary) | strong(mary) <- (7) [resolution 85,161]
225. strong(mary) <- (7) [subsumption resolution 224,183]
226. $false <- (7) [subsumption resolution 225,184]
227. ~7 [avatar contradiction clause 226]
228. $false [avatar sat refutation 216,227]
% SZS output end Proof for 2861188974551627874356685
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or kind is either calm or not patient. If someone is quiet or not curious then lucy is either not kind or wise. If someone is either strong or funny then someone is brave and vice versa. If paul is both not calm and quiet then someone is both humble and not generous and vice versa. If someone is both kind and wise then paul is either not quiet or not creative. If john is both kind and not humble then someone is curious or calm and vice versa. Everyone who is both humble and not rich is either not rich or not curious and vice versa. Everyone who is not generous or funny is old. If alice is both not calm and not happy then someone is not humble. If paul is both creative and patient then someone is not generous or not wise. If someone is both not strong and quiet then mary is either not happy or generous and vice versa. Everyone who is both quiet and generous is either not calm or calm and vice versa. If john is not wise then lucy is old or funny and vice versa. If mary is both not humble and rich then someone is not tall. If someone is tall or generous then lucy is both curious and kind and vice versa. Someone is both not calm and not wise. Someone is not wise. Mary is both rich and not funny. Someone is both kind and funny. Someone is both humble and not tall. John is kind or old. Someone is both not calm and not brave. | John is generous. | entailment | (![X]:((~humble(X)|kind(X))=>(calm(X)<~>~patient(X))))&
((?[X]:((quiet(X)|~curious(X))))=>((~kind(lucy)<~>wise(lucy))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:(brave(X))))&
(((~calm(paul)&quiet(paul)))<=>(?[X]:((humble(X)&~generous(X)))))&
((?[X]:((kind(X)&wise(X))))=>((~quiet(paul)<~>~creative(paul))))&
(((kind(john)&~humble(john)))<=>(?[X]:((curious(X)|calm(X)))))&
(![X]:((humble(X)&~rich(X))<=>(~rich(X)<~>~curious(X))))&
(![X]:((~generous(X)|funny(X))=>old(X)))&
(((~calm(alice)&~happy(alice)))=>(?[X]:(~humble(X))))&
(((creative(paul)&patient(paul)))=>(?[X]:((~generous(X)|~wise(X)))))&
((?[X]:((~strong(X)&quiet(X))))<=>((~happy(mary)<~>generous(mary))))&
(![X]:((quiet(X)&generous(X))<=>(~calm(X)<~>calm(X))))&
((~wise(john))<=>((old(lucy)|funny(lucy))))&
(((~humble(mary)&rich(mary)))=>(?[X]:(~tall(X))))&
((?[X]:((tall(X)|generous(X))))<=>((curious(lucy)&kind(lucy))))&
(?[X]:((~calm(X)&~wise(X))))&
(?[X]:(~wise(X)))&
((rich(mary)&~funny(mary)))&
(?[X]:((kind(X)&funny(X))))&
(?[X]:((humble(X)&~tall(X))))&
((kind(john)|old(john)))&
(?[X]:((~calm(X)&~brave(X)))) | generous(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8535645044892958679674249
% SZS output start Proof for 8535645044892958679674249
12. ! [X0] : ((generous(X0) & quiet(X0)) <=> (~calm(X0) <~> calm(X0))) [input p11]
23. ~generous(john) [input hypothesis]
63. ! [X0] : (((generous(X0) & quiet(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~generous(X0) | ~quiet(X0)))) [nnf transformation 12]
64. ! [X0] : (((generous(X0) & quiet(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~generous(X0) | ~quiet(X0))) [flattening 63]
127. generous(X0) | calm(X0) | calm(X0) [cnf transformation 64]
128. generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 64]
150. ~generous(john) [cnf transformation 23]
153. generous(X0) | calm(X0) [duplicate literal removal 127]
154. generous(X0) | ~calm(X0) [duplicate literal removal 128]
311. generous(X0) [subsumption resolution 153,154]
355. $false [subsumption resolution 150,311]
% SZS output end Proof for 8535645044892958679674249
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then alice is both not wise and not funny and vice versa.
If paul is not happy or not patient then john is not wise.
If susan is not kind or not tall then mary is brave and vice versa.
Everyone who is either not old or happy is not kind and vice versa.
If someone is either not wise or generous then someone is not patient.
Everyone who is tall is not rich and vice versa.
Everyone who is humble is not wise or not creative and vice versa.
Everyone who is both not wise and strong is either tall or happy and vice versa.
Everyone who is either not tall or rich is not brave or not creative.
Everyone who is either not old or not patient is both old and patient and vice versa.
Everyone who is happy is not patient and vice versa.
If paul is either generous or not happy then alice is both not patient and not brave.
If john is either not happy or curious then someone is quiet.
If someone is both calm and not creative then someone is both not patient and brave.
If someone is not patient then someone is quiet and vice versa.
Everyone who is either not tall or not patient is both not calm and tall.
Someone is either patient or quiet.
Alice is not happy or creative.
Susan is not rich.
Someone is curious or not happy.
Someone is either not happy or not strong.
Someone is quiet. | Susan is quiet. | neutral | ((?[X]:(happy(X)))<=>((~wise(alice)&~funny(alice))))&
(((~happy(paul)|~patient(paul)))=>(~wise(john)))&
(((~kind(susan)|~tall(susan)))<=>(brave(mary)))&
(![X]:((~old(X)<~>happy(X))<=>~kind(X)))&
((?[X]:((~wise(X)<~>generous(X))))=>(?[X]:(~patient(X))))&
(![X]:(tall(X)<=>~rich(X)))&
(![X]:(humble(X)<=>(~wise(X)|~creative(X))))&
(![X]:((~wise(X)&strong(X))<=>(tall(X)<~>happy(X))))&
(![X]:((~tall(X)<~>rich(X))=>(~brave(X)|~creative(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(old(X)&patient(X))))&
(![X]:(happy(X)<=>~patient(X)))&
(((generous(paul)<~>~happy(paul)))=>((~patient(alice)&~brave(alice))))&
(((~happy(john)<~>curious(john)))=>(?[X]:(quiet(X))))&
((?[X]:((calm(X)&~creative(X))))=>(?[X]:((~patient(X)&brave(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:(quiet(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(~calm(X)&tall(X))))&
(?[X]:((patient(X)<~>quiet(X))))&
((~happy(alice)|creative(alice)))&
(~rich(susan))&
(?[X]:((curious(X)|~happy(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:(quiet(X))) | quiet(susan) | [] | null | 0 |
If someone is either not tall or not strong then someone is calm and vice versa.
Everyone who is not kind is both not brave and not rich.
Everyone who is both generous and humble is not calm or creative.
If mary is both calm and not patient then mary is both brave and creative.
Everyone who is not creative or not curious is both curious and not quiet.
If someone is tall then someone is not curious or not tall.
Everyone who is not creative or happy is both patient and not calm.
If someone is not funny then alice is not old.
Everyone who is either not humble or not calm is generous.
Everyone who is not patient or generous is not happy.
If someone is not creative then mary is either quiet or not calm and vice versa.
If someone is either not wise or not tall then someone is both quiet and creative and vice versa.
If alice is happy then alice is not tall or tall and vice versa.
If alice is either not kind or brave then someone is humble or brave.
Everyone who is either quiet or not old is creative or not tall.
If paul is either rich or not funny then someone is either not quiet or rich.
Someone is not quiet.
Alice is not quiet.
Someone is both not patient and brave.
Someone is not funny or not generous.
Mary is either not old or kind.
Someone is quiet or not wise. | Alice is not patient. | contradiction | ((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:(calm(X))))&
(![X]:(~kind(X)=>(~brave(X)&~rich(X))))&
(![X]:((generous(X)&humble(X))=>(~calm(X)|creative(X))))&
(((calm(mary)&~patient(mary)))=>((brave(mary)&creative(mary))))&
(![X]:((~creative(X)|~curious(X))=>(curious(X)&~quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:((~curious(X)|~tall(X)))))&
(![X]:((~creative(X)|happy(X))=>(patient(X)&~calm(X))))&
((?[X]:(~funny(X)))=>(~old(alice)))&
(![X]:((~humble(X)<~>~calm(X))=>generous(X)))&
(![X]:((~patient(X)|generous(X))=>~happy(X)))&
((?[X]:(~creative(X)))<=>((quiet(mary)<~>~calm(mary))))&
((?[X]:((~wise(X)<~>~tall(X))))<=>(?[X]:((quiet(X)&creative(X)))))&
((happy(alice))<=>((~tall(alice)|tall(alice))))&
(((~kind(alice)<~>brave(alice)))=>(?[X]:((humble(X)|brave(X)))))&
(![X]:((quiet(X)<~>~old(X))=>(creative(X)|~tall(X))))&
(((rich(paul)<~>~funny(paul)))=>(?[X]:((~quiet(X)<~>rich(X)))))&
(?[X]:(~quiet(X)))&
(~quiet(alice))&
(?[X]:((~patient(X)&brave(X))))&
(?[X]:((~funny(X)|~generous(X))))&
((~old(mary)<~>kind(mary)))&
(?[X]:((quiet(X)|~wise(X)))) | ~patient(alice) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8300903854719491718558986
% SZS output start Proof for 8300903854719491718558986
7. ! [X0] : ((happy(X0) | ~creative(X0)) => (~calm(X0) & patient(X0))) [input p6]
13. happy(alice) <=> (tall(alice) | ~tall(alice)) [input p12]
23. ~patient(alice) [input hypothesis]
34. ! [X0] : ((~calm(X0) & patient(X0)) | (~happy(X0) & creative(X0))) [ennf transformation 7]
60. (happy(alice) | (~tall(alice) & tall(alice))) & ((tall(alice) | ~tall(alice)) | ~happy(alice)) [nnf transformation 13]
61. (happy(alice) | (~tall(alice) & tall(alice))) & (tall(alice) | ~tall(alice) | ~happy(alice)) [flattening 60]
93. ~happy(X0) | patient(X0) [cnf transformation 34]
112. happy(alice) | tall(alice) [cnf transformation 61]
113. happy(alice) | ~tall(alice) [cnf transformation 61]
130. ~patient(alice) [cnf transformation 23]
241. 25 <=> tall(alice) [avatar definition]
245. 26 <=> happy(alice) [avatar definition]
247. happy(alice) <- (26) [avatar component clause 245]
248. ~25 | 26 [avatar split clause 113,245,241]
249. 25 | 26 [avatar split clause 112,245,241]
322. patient(alice) <- (26) [resolution 93,247]
323. $false <- (26) [subsumption resolution 322,130]
324. ~26 [avatar contradiction clause 323]
325. $false [avatar sat refutation 248,249,324]
% SZS output end Proof for 8300903854719491718558986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not happy is both not old and not happy and vice versa.
Everyone who is both generous and creative is either not curious or curious.
Everyone who is humble or wise is either not strong or creative and vice versa.
Everyone who is either not brave or quiet is not kind.
If someone is not funny then alice is kind.
Everyone who is both humble and happy is either brave or not creative.
Everyone who is not quiet or patient is brave and vice versa.
If someone is either not calm or wise then john is not generous or rich and vice versa.
Everyone who is not funny or generous is not funny or kind and vice versa.
Everyone who is not curious is happy or not humble.
If someone is both not funny and not creative then john is both not generous and not old.
Everyone who is either strong or not happy is calm and vice versa.
If someone is both curious and not kind then fred is creative.
Everyone who is calm is kind and vice versa.
Everyone who is not quiet is both calm and not calm.
Everyone who is not patient is creative or brave and vice versa.
Lucy is not curious.
Susan is quiet or not rich.
Susan is not curious or not calm.
Someone is wise.
John is either happy or not creative.
John is either wise or generous. | John is strong. | neutral | (![X]:((tall(X)&~happy(X))<=>(~old(X)&~happy(X))))&
(![X]:((generous(X)&creative(X))=>(~curious(X)<~>curious(X))))&
(![X]:((humble(X)|wise(X))<=>(~strong(X)<~>creative(X))))&
(![X]:((~brave(X)<~>quiet(X))=>~kind(X)))&
((?[X]:(~funny(X)))=>(kind(alice)))&
(![X]:((humble(X)&happy(X))=>(brave(X)<~>~creative(X))))&
(![X]:((~quiet(X)|patient(X))<=>brave(X)))&
((?[X]:((~calm(X)<~>wise(X))))<=>((~generous(john)|rich(john))))&
(![X]:((~funny(X)|generous(X))<=>(~funny(X)|kind(X))))&
(![X]:(~curious(X)=>(happy(X)|~humble(X))))&
((?[X]:((~funny(X)&~creative(X))))=>((~generous(john)&~old(john))))&
(![X]:((strong(X)<~>~happy(X))<=>calm(X)))&
((?[X]:((curious(X)&~kind(X))))=>(creative(fred)))&
(![X]:(calm(X)<=>kind(X)))&
(![X]:(~quiet(X)=>(calm(X)&~calm(X))))&
(![X]:(~patient(X)<=>(creative(X)|brave(X))))&
(~curious(lucy))&
((quiet(susan)|~rich(susan)))&
((~curious(susan)|~calm(susan)))&
(?[X]:(wise(X)))&
((happy(john)<~>~creative(john)))&
((wise(john)<~>generous(john))) | strong(john) | [] | null | 0 |
Everyone who is either humble or brave is either happy or not old and vice versa.
If someone is calm or old then someone is either curious or not brave and vice versa.
Everyone who is not old is not happy or happy and vice versa.
If susan is tall or not strong then alice is both not tall and wise.
If someone is either not humble or quiet then john is wise or patient and vice versa.
If fred is not wise or brave then someone is not brave and vice versa.
If susan is calm or not calm then john is not wise or old.
Everyone who is both not patient and rich is not happy or not rich.
If someone is happy then lucy is both not strong and rich and vice versa.
If someone is not happy or calm then someone is not tall or not curious and vice versa.
If mary is not creative then someone is not strong and vice versa.
If fred is both old and not humble then alice is generous.
If lucy is both rich and not patient then someone is happy or kind and vice versa.
If someone is not humble or patient then lucy is not kind or humble and vice versa.
If susan is both not kind and wise then someone is both quiet and kind.
Everyone who is happy or not curious is strong or not curious.
Lucy is not rich.
Someone is curious.
Someone is generous.
Someone is either not rich or patient.
Someone is not calm or not old.
Someone is both strong and not rich. | Susan is not old. | entailment | (![X]:((humble(X)<~>brave(X))<=>(happy(X)<~>~old(X))))&
((?[X]:((calm(X)|old(X))))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:(~old(X)<=>(~happy(X)|happy(X))))&
(((tall(susan)|~strong(susan)))=>((~tall(alice)&wise(alice))))&
((?[X]:((~humble(X)<~>quiet(X))))<=>((wise(john)|patient(john))))&
(((~wise(fred)|brave(fred)))<=>(?[X]:(~brave(X))))&
(((calm(susan)|~calm(susan)))=>((~wise(john)|old(john))))&
(![X]:((~patient(X)&rich(X))=>(~happy(X)|~rich(X))))&
((?[X]:(happy(X)))<=>((~strong(lucy)&rich(lucy))))&
((?[X]:((~happy(X)|calm(X))))<=>(?[X]:((~tall(X)|~curious(X)))))&
((~creative(mary))<=>(?[X]:(~strong(X))))&
(((old(fred)&~humble(fred)))=>(generous(alice)))&
(((rich(lucy)&~patient(lucy)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((~humble(X)|patient(X))))<=>((~kind(lucy)|humble(lucy))))&
(((~kind(susan)&wise(susan)))=>(?[X]:((quiet(X)&kind(X)))))&
(![X]:((happy(X)|~curious(X))=>(strong(X)|~curious(X))))&
(~rich(lucy))&
(?[X]:(curious(X)))&
(?[X]:(generous(X)))&
(?[X]:((~rich(X)<~>patient(X))))&
(?[X]:((~calm(X)|~old(X))))&
(?[X]:((strong(X)&~rich(X)))) | ~old(susan) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 6715411576360403530749830
% SZS output start Proof for 6715411576360403530749830
3. ! [X0] : (~old(X0) <=> (happy(X0) | ~happy(X0))) [input p2]
23. old(susan) [input hypothesis]
43. ! [X0] : ((~old(X0) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | old(X0))) [nnf transformation 3]
44. ! [X0] : ((~old(X0) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | old(X0))) [flattening 43]
105. ~old(X0) | happy(X0) [cnf transformation 44]
106. ~old(X0) | ~happy(X0) [cnf transformation 44]
152. old(susan) [cnf transformation 23]
171. 5 <=> ! [X3] : ~old(X3) [avatar definition]
172. ~old(X3) <- (5) [avatar component clause 171]
188. ~old(X0) [subsumption resolution 105,106]
189. 5 [avatar split clause 188,171]
410. $false <- (5) [resolution 172,152]
411. ~5 [avatar contradiction clause 410]
412. $false [avatar sat refutation 189,411]
% SZS output end Proof for 6715411576360403530749830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and not wise then someone is both not humble and old and vice versa. Everyone who is either funny or creative is both patient and not creative. If john is creative then susan is not creative or not funny and vice versa. Everyone who is both not wise and not humble is not humble or not patient and vice versa. If lucy is both not tall and not wise then someone is not creative or not patient and vice versa. Everyone who is both calm and not creative is both not curious and not strong. Everyone who is not kind is both tall and not funny and vice versa. Everyone who is both quiet and old is both humble and not quiet. Everyone who is kind or not curious is brave or tall and vice versa. If someone is both not kind and strong then paul is generous or calm and vice versa. If john is either humble or creative then mary is either wise or not calm and vice versa. If someone is brave or creative then someone is either not happy or wise. Everyone who is either not generous or not kind is both patient and wise and vice versa. If someone is happy then paul is generous or not generous. If fred is tall or strong then someone is both tall and rich and vice versa. John is not curious or not creative. Mary is not happy or funny. Susan is generous. Lucy is either not funny or not old. | Paul is not strong. | neutral | ((?[X]:((~patient(X)&~wise(X))))<=>(?[X]:((~humble(X)&old(X)))))&
(![X]:((funny(X)<~>creative(X))=>(patient(X)&~creative(X))))&
((creative(john))<=>((~creative(susan)|~funny(susan))))&
(![X]:((~wise(X)&~humble(X))<=>(~humble(X)|~patient(X))))&
(((~tall(lucy)&~wise(lucy)))<=>(?[X]:((~creative(X)|~patient(X)))))&
(![X]:((calm(X)&~creative(X))=>(~curious(X)&~strong(X))))&
(![X]:(~kind(X)<=>(tall(X)&~funny(X))))&
(![X]:((quiet(X)&old(X))=>(humble(X)&~quiet(X))))&
(![X]:((kind(X)|~curious(X))<=>(brave(X)|tall(X))))&
((?[X]:((~kind(X)&strong(X))))<=>((generous(paul)|calm(paul))))&
(((humble(john)<~>creative(john)))<=>((wise(mary)<~>~calm(mary))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:((~happy(X)<~>wise(X)))))&
(![X]:((~generous(X)<~>~kind(X))<=>(patient(X)&wise(X))))&
((?[X]:(happy(X)))=>((generous(paul)|~generous(paul))))&
(((tall(fred)|strong(fred)))<=>(?[X]:((tall(X)&rich(X)))))&
((~curious(john)|~creative(john)))&
((~happy(mary)|funny(mary)))&
(generous(susan))&
((~funny(lucy)<~>~old(lucy))) | ~strong(paul) | [] | null | 0 |
Everyone who is either old or not curious is not old or calm and vice versa.
Everyone who is either not humble or brave is not curious and vice versa.
If mary is either rich or not brave then someone is either quiet or not rich and vice versa.
Everyone who is either curious or funny is calm.
If someone is either curious or not funny then john is calm.
If alice is not strong then alice is not creative or creative and vice versa.
Everyone who is both not tall and rich is either not happy or brave and vice versa.
If john is not funny then fred is either not humble or wise and vice versa.
If john is either not calm or not wise then lucy is calm and vice versa.
Everyone who is both humble and not creative is curious or happy.
Everyone who is funny or not humble is either not generous or not rich and vice versa.
Everyone who is not calm or old is not wise or patient.
Everyone who is not funny is either not patient or not quiet and vice versa.
If alice is curious then mary is strong and vice versa.
If someone is both not happy and not humble then someone is not creative or kind.
Everyone who is either humble or happy is kind and vice versa.
Someone is curious or not happy.
Mary is both brave and not wise.
Susan is happy.
Someone is not creative or not happy.
Alice is not patient.
Paul is either not funny or not patient.
Someone is not old. | John is not generous. | neutral | (![X]:((old(X)<~>~curious(X))<=>(~old(X)|calm(X))))&
(![X]:((~humble(X)<~>brave(X))<=>~curious(X)))&
(((rich(mary)<~>~brave(mary)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(![X]:((curious(X)<~>funny(X))=>calm(X)))&
((?[X]:((curious(X)<~>~funny(X))))=>(calm(john)))&
((~strong(alice))<=>((~creative(alice)|creative(alice))))&
(![X]:((~tall(X)&rich(X))<=>(~happy(X)<~>brave(X))))&
((~funny(john))<=>((~humble(fred)<~>wise(fred))))&
(((~calm(john)<~>~wise(john)))<=>(calm(lucy)))&
(![X]:((humble(X)&~creative(X))=>(curious(X)|happy(X))))&
(![X]:((funny(X)|~humble(X))<=>(~generous(X)<~>~rich(X))))&
(![X]:((~calm(X)|old(X))=>(~wise(X)|patient(X))))&
(![X]:(~funny(X)<=>(~patient(X)<~>~quiet(X))))&
((curious(alice))<=>(strong(mary)))&
((?[X]:((~happy(X)&~humble(X))))=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((humble(X)<~>happy(X))<=>kind(X)))&
(?[X]:((curious(X)|~happy(X))))&
((brave(mary)&~wise(mary)))&
(happy(susan))&
(?[X]:((~creative(X)|~happy(X))))&
(~patient(alice))&
((~funny(paul)<~>~patient(paul)))&
(?[X]:(~old(X))) | ~generous(john) | [] | null | 0 |
Everyone who is rich is not happy or not curious.
Everyone who is both brave and not old is either not kind or not generous.
If someone is either generous or not quiet then lucy is not calm and vice versa.
If john is calm then someone is not tall and vice versa.
If alice is both not happy and not patient then someone is not brave.
Everyone who is either wise or creative is either not calm or patient.
If someone is funny then someone is strong or kind and vice versa.
Everyone who is either quiet or calm is either rich or not generous.
If someone is not tall then john is brave.
If someone is wise then someone is funny.
Everyone who is both curious and not tall is rich and vice versa.
If someone is not old or generous then someone is either patient or old and vice versa.
If fred is both not brave and happy then someone is brave and vice versa.
Everyone who is both not wise and strong is wise or rich and vice versa.
Everyone who is either curious or not rich is not happy.
Everyone who is not kind is both rich and not brave.
John is generous or not brave.
Someone is either curious or not strong.
Someone is kind.
Susan is both not funny and curious.
Someone is not strong.
John is both calm and not humble.
Someone is either not calm or not tall.
Someone is not brave or wise. | Fred is curious. | entailment | (![X]:(rich(X)=>(~happy(X)|~curious(X))))&
(![X]:((brave(X)&~old(X))=>(~kind(X)<~>~generous(X))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>(~calm(lucy)))&
((calm(john))<=>(?[X]:(~tall(X))))&
(((~happy(alice)&~patient(alice)))=>(?[X]:(~brave(X))))&
(![X]:((wise(X)<~>creative(X))=>(~calm(X)<~>patient(X))))&
((?[X]:(funny(X)))<=>(?[X]:((strong(X)|kind(X)))))&
(![X]:((quiet(X)<~>calm(X))=>(rich(X)<~>~generous(X))))&
((?[X]:(~tall(X)))=>(brave(john)))&
((?[X]:(wise(X)))=>(?[X]:(funny(X))))&
(![X]:((curious(X)&~tall(X))<=>rich(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((patient(X)<~>old(X)))))&
(((~brave(fred)&happy(fred)))<=>(?[X]:(brave(X))))&
(![X]:((~wise(X)&strong(X))<=>(wise(X)|rich(X))))&
(![X]:((curious(X)<~>~rich(X))=>~happy(X)))&
(![X]:(~kind(X)=>(rich(X)&~brave(X))))&
((generous(john)|~brave(john)))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:(kind(X)))&
((~funny(susan)&curious(susan)))&
(?[X]:(~strong(X)))&
((calm(john)&~humble(john)))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((~brave(X)|wise(X)))) | curious(fred) | [
"p3",
"p8",
"p10",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 504464416451719071867073
% SZS output start Proof for 504464416451719071867073
4. calm(john) <=> ? [X0] : ~tall(X0) [input p3]
9. ? [X0] : ~tall(X0) => brave(john) [input p8]
11. ! [X0] : ((~tall(X0) & curious(X0)) <=> rich(X0)) [input p10]
13. (happy(fred) & ~brave(fred)) <=> ? [X0] : brave(X0) [input p12]
15. ! [X0] : ((curious(X0) <~> ~rich(X0)) => ~happy(X0)) [input p14]
22. ~humble(john) & calm(john) [input p21]
25. ~curious(fred) [input hypothesis]
29. calm(john) [pure predicate removal 22]
38. brave(john) | ! [X0] : tall(X0) [ennf transformation 9]
40. ! [X0] : (~happy(X0) | (curious(X0) <=> ~rich(X0))) [ennf transformation 15]
47. (calm(john) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | ~calm(john)) [nnf transformation 4]
48. (calm(john) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | ~calm(john)) [rectify 47]
49. ? [X1] : ~tall(X1) => ~tall(sK1) [choice axiom]
50. (calm(john) | ! [X0] : tall(X0)) & (~tall(sK1) | ~calm(john)) [skolemisation 48,49]
63. ! [X0] : (((~tall(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | (tall(X0) | ~curious(X0)))) [nnf transformation 11]
64. ! [X0] : (((~tall(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | tall(X0) | ~curious(X0))) [flattening 63]
70. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~happy(fred) | brave(fred))) [nnf transformation 13]
71. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~happy(fred) | brave(fred)) [flattening 70]
72. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~happy(fred) | brave(fred)) [rectify 71]
73. ? [X1] : brave(X1) => brave(sK8) [choice axiom]
74. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (brave(sK8) | ~happy(fred) | brave(fred)) [skolemisation 72,73]
77. ! [X0] : (~happy(X0) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) [nnf transformation 40]
97. ~tall(sK1) | ~calm(john) [cnf transformation 50]
111. brave(john) | tall(X0) [cnf transformation 38]
114. ~rich(X0) | curious(X0) [cnf transformation 64]
124. happy(fred) | ~brave(X0) [cnf transformation 74]
131. ~happy(X0) | curious(X0) | rich(X0) [cnf transformation 77]
141. calm(john) [cnf transformation 29]
145. ~curious(fred) [cnf transformation 25]
171. 6 <=> ! [X0] : tall(X0) [avatar definition]
172. tall(X0) <- (6) [avatar component clause 171]
174. 7 <=> calm(john) [avatar definition]
179. 8 <=> tall(sK1) [avatar definition]
181. ~tall(sK1) <- (~8) [avatar component clause 179]
182. ~7 | ~8 [avatar split clause 97,179,174]
221. 18 <=> brave(john) [avatar definition]
223. brave(john) <- (18) [avatar component clause 221]
224. 6 | 18 [avatar split clause 111,221,171]
268. 29 <=> ! [X0] : ~brave(X0) [avatar definition]
269. ~brave(X0) <- (29) [avatar component clause 268]
271. 30 <=> happy(fred) [avatar definition]
273. happy(fred) <- (30) [avatar component clause 271]
274. 29 | 30 [avatar split clause 124,271,268]
286. ~happy(X0) | curious(X0) [subsumption resolution 131,114]
302. 7 [avatar split clause 141,174]
324. $false <- (6, ~8) [resolution 181,172]
325. ~6 | 8 [avatar contradiction clause 324]
326. $false <- (18, 29) [subsumption resolution 223,269]
327. ~18 | ~29 [avatar contradiction clause 326]
334. curious(fred) <- (30) [resolution 286,273]
335. $false <- (30) [subsumption resolution 334,145]
336. ~30 [avatar contradiction clause 335]
337. $false [avatar sat refutation 182,224,274,302,325,327,336]
% SZS output end Proof for 504464416451719071867073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not happy is either wise or quiet.
If someone is either quiet or creative then someone is both not creative and rich and vice versa.
If john is rich or not old then someone is wise or not happy and vice versa.
Everyone who is not creative or not strong is either quiet or patient and vice versa.
If someone is not kind then alice is both generous and not quiet and vice versa.
Everyone who is calm is either not happy or curious.
If mary is not brave or creative then someone is both humble and quiet.
If fred is either not quiet or not patient then mary is kind or old.
If susan is either brave or not creative then mary is not rich and vice versa.
Everyone who is not kind or not tall is both not wise and rich.
Everyone who is happy or funny is either not patient or not quiet.
If john is not kind or not old then mary is either kind or not strong and vice versa.
If susan is both brave and calm then someone is both not strong and calm.
Everyone who is funny or not patient is either quiet or not curious.
Everyone who is calm or patient is not generous.
If someone is both patient and kind then someone is both tall and not creative.
John is both not tall and rich.
Someone is both not kind and humble.
Someone is either wise or happy.
Someone is generous or curious.
Mary is either not quiet or curious.
Fred is kind or not creative.
Someone is kind.
Lucy is both not kind and not generous. | Alice is wise. | entailment | (![X]:((brave(X)|~happy(X))=>(wise(X)<~>quiet(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(?[X]:((~creative(X)&rich(X)))))&
(((rich(john)|~old(john)))<=>(?[X]:((wise(X)|~happy(X)))))&
(![X]:((~creative(X)|~strong(X))<=>(quiet(X)<~>patient(X))))&
((?[X]:(~kind(X)))<=>((generous(alice)&~quiet(alice))))&
(![X]:(calm(X)=>(~happy(X)<~>curious(X))))&
(((~brave(mary)|creative(mary)))=>(?[X]:((humble(X)&quiet(X)))))&
(((~quiet(fred)<~>~patient(fred)))=>((kind(mary)|old(mary))))&
(((brave(susan)<~>~creative(susan)))<=>(~rich(mary)))&
(![X]:((~kind(X)|~tall(X))=>(~wise(X)&rich(X))))&
(![X]:((happy(X)|funny(X))=>(~patient(X)<~>~quiet(X))))&
(((~kind(john)|~old(john)))<=>((kind(mary)<~>~strong(mary))))&
(((brave(susan)&calm(susan)))=>(?[X]:((~strong(X)&calm(X)))))&
(![X]:((funny(X)|~patient(X))=>(quiet(X)<~>~curious(X))))&
(![X]:((calm(X)|patient(X))=>~generous(X)))&
((?[X]:((patient(X)&kind(X))))=>(?[X]:((tall(X)&~creative(X)))))&
((~tall(john)&rich(john)))&
(?[X]:((~kind(X)&humble(X))))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:((generous(X)|curious(X))))&
((~quiet(mary)<~>curious(mary)))&
((kind(fred)|~creative(fred)))&
(?[X]:(kind(X)))&
((~kind(lucy)&~generous(lucy))) | wise(alice) | [
"p0",
"p4",
"p10",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 329637303072868742943117
% SZS output start Proof for 329637303072868742943117
1. ! [X0] : ((~happy(X0) | brave(X0)) => (wise(X0) <~> quiet(X0))) [input p0]
5. ? [X0] : ~kind(X0) <=> (~quiet(alice) & generous(alice)) [input p4]
11. ! [X0] : ((funny(X0) | happy(X0)) => (~patient(X0) <~> ~quiet(X0))) [input p10]
15. ! [X0] : ((patient(X0) | calm(X0)) => ~generous(X0)) [input p14]
24. ~generous(lucy) & ~kind(lucy) [input p23]
25. ~wise(alice) [input hypothesis]
28. ! [X0] : (happy(X0) => (~patient(X0) <~> ~quiet(X0))) [pure predicate removal 11]
32. ! [X0] : ((wise(X0) <~> quiet(X0)) | (happy(X0) & ~brave(X0))) [ennf transformation 1]
38. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) | ~happy(X0)) [ennf transformation 28]
42. ! [X0] : (~generous(X0) | (~patient(X0) & ~calm(X0))) [ennf transformation 15]
44. ! [X0] : (((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | (happy(X0) & ~brave(X0))) [nnf transformation 32]
57. (? [X0] : ~kind(X0) | (quiet(alice) | ~generous(alice))) & ((~quiet(alice) & generous(alice)) | ! [X0] : kind(X0)) [nnf transformation 5]
58. (? [X0] : ~kind(X0) | quiet(alice) | ~generous(alice)) & ((~quiet(alice) & generous(alice)) | ! [X0] : kind(X0)) [flattening 57]
59. (? [X0] : ~kind(X0) | quiet(alice) | ~generous(alice)) & ((~quiet(alice) & generous(alice)) | ! [X1] : kind(X1)) [rectify 58]
60. ? [X0] : ~kind(X0) => ~kind(sK3) [choice axiom]
61. (~kind(sK3) | quiet(alice) | ~generous(alice)) & ((~quiet(alice) & generous(alice)) | ! [X1] : kind(X1)) [skolemisation 59,60]
67. ! [X0] : (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ~happy(X0)) [nnf transformation 38]
87. quiet(X0) | wise(X0) | happy(X0) [cnf transformation 44]
106. generous(alice) | kind(X1) [cnf transformation 61]
107. ~quiet(alice) | kind(X1) [cnf transformation 61]
124. ~happy(X0) | patient(X0) | quiet(X0) [cnf transformation 67]
136. ~generous(X0) | ~patient(X0) [cnf transformation 42]
149. ~kind(lucy) [cnf transformation 24]
151. ~wise(alice) [cnf transformation 25]
210. 14 <=> generous(alice) [avatar definition]
211. generous(alice) <- (14) [avatar component clause 210]
214. 15 <=> quiet(alice) [avatar definition]
215. ~quiet(alice) <- (~15) [avatar component clause 214]
223. 17 <=> ! [X1] : kind(X1) [avatar definition]
224. kind(X1) <- (17) [avatar component clause 223]
225. 17 | ~15 [avatar split clause 107,214,223]
226. 17 | 14 [avatar split clause 106,210,223]
365. ~patient(alice) <- (14) [resolution 136,211]
380. wise(alice) | happy(alice) <- (~15) [resolution 87,215]
383. happy(alice) <- (~15) [subsumption resolution 380,151]
497. patient(alice) | quiet(alice) <- (~15) [resolution 124,383]
498. quiet(alice) <- (14, ~15) [subsumption resolution 497,365]
499. $false <- (14, ~15) [subsumption resolution 498,215]
500. ~14 | 15 [avatar contradiction clause 499]
503. $false <- (17) [resolution 224,149]
508. ~17 [avatar contradiction clause 503]
510. $false [avatar sat refutation 225,226,500,508]
% SZS output end Proof for 329637303072868742943117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not rich is either not funny or patient. Everyone who is not tall is either not calm or not old. If someone is not old or kind then someone is calm or not rich and vice versa. If someone is both creative and not curious then someone is either rich or not creative and vice versa. Everyone who is happy is curious or brave. If john is kind then someone is either generous or not curious and vice versa. If alice is not curious then someone is both not tall and not kind. If susan is curious then someone is not rich or not funny. Everyone who is not kind or tall is happy or not wise and vice versa. Everyone who is either strong or happy is patient or curious. Everyone who is not curious is patient. If paul is both humble and not calm then fred is either not funny or wise and vice versa. Everyone who is both not kind and rich is rich or not calm and vice versa. If someone is either patient or not curious then paul is either kind or humble and vice versa. Everyone who is both strong and not rich is not old and vice versa. If someone is both generous and curious then john is tall and vice versa. Mary is not creative or tall. Alice is both not generous and curious. John is rich or old. Someone is not patient or not tall. John is either not curious or not patient. Fred is not patient or happy. Paul is both quiet and calm. Someone is not brave or humble. | John is kind. | neutral | (![X]:((~funny(X)|~rich(X))=>(~funny(X)<~>patient(X))))&
(![X]:(~tall(X)=>(~calm(X)<~>~old(X))))&
((?[X]:((~old(X)|kind(X))))<=>(?[X]:((calm(X)|~rich(X)))))&
((?[X]:((creative(X)&~curious(X))))<=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:(happy(X)=>(curious(X)|brave(X))))&
((kind(john))<=>(?[X]:((generous(X)<~>~curious(X)))))&
((~curious(alice))=>(?[X]:((~tall(X)&~kind(X)))))&
((curious(susan))=>(?[X]:((~rich(X)|~funny(X)))))&
(![X]:((~kind(X)|tall(X))<=>(happy(X)|~wise(X))))&
(![X]:((strong(X)<~>happy(X))=>(patient(X)|curious(X))))&
(![X]:(~curious(X)=>patient(X)))&
(((humble(paul)&~calm(paul)))<=>((~funny(fred)<~>wise(fred))))&
(![X]:((~kind(X)&rich(X))<=>(rich(X)|~calm(X))))&
((?[X]:((patient(X)<~>~curious(X))))<=>((kind(paul)<~>humble(paul))))&
(![X]:((strong(X)&~rich(X))<=>~old(X)))&
((?[X]:((generous(X)&curious(X))))<=>(tall(john)))&
((~creative(mary)|tall(mary)))&
((~generous(alice)&curious(alice)))&
((rich(john)|old(john)))&
(?[X]:((~patient(X)|~tall(X))))&
((~curious(john)<~>~patient(john)))&
((~patient(fred)|happy(fred)))&
((quiet(paul)&calm(paul)))&
(?[X]:((~brave(X)|humble(X)))) | kind(john) | [] | null | 0 |
Everyone who is either patient or brave is both strong and not strong.
If alice is not generous or patient then someone is old or brave and vice versa.
Everyone who is not happy or not creative is both kind and generous and vice versa.
If someone is either not tall or calm then someone is both rich and creative.
If alice is either not brave or not rich then alice is either curious or not rich and vice versa.
If lucy is both not quiet and not strong then lucy is old.
Everyone who is both not old and patient is tall and vice versa.
If someone is either strong or rich then alice is patient.
If someone is either not strong or patient then alice is calm and vice versa.
Everyone who is not curious is both not curious and old and vice versa.
Everyone who is wise is creative or rich and vice versa.
Everyone who is either tall or not kind is not funny or tall and vice versa.
Everyone who is either not creative or not calm is old.
If paul is not quiet then someone is not curious or brave and vice versa.
Everyone who is not quiet or not brave is quiet.
If someone is not calm then fred is generous and vice versa.
Someone is both not happy and not creative.
Someone is kind.
Fred is not strong or curious.
Someone is wise or brave.
Someone is both not wise and curious.
Someone is generous. | Lucy is happy. | neutral | (![X]:((patient(X)<~>brave(X))=>(strong(X)&~strong(X))))&
(((~generous(alice)|patient(alice)))<=>(?[X]:((old(X)|brave(X)))))&
(![X]:((~happy(X)|~creative(X))<=>(kind(X)&generous(X))))&
((?[X]:((~tall(X)<~>calm(X))))=>(?[X]:((rich(X)&creative(X)))))&
(((~brave(alice)<~>~rich(alice)))<=>((curious(alice)<~>~rich(alice))))&
(((~quiet(lucy)&~strong(lucy)))=>(old(lucy)))&
(![X]:((~old(X)&patient(X))<=>tall(X)))&
((?[X]:((strong(X)<~>rich(X))))=>(patient(alice)))&
((?[X]:((~strong(X)<~>patient(X))))<=>(calm(alice)))&
(![X]:(~curious(X)<=>(~curious(X)&old(X))))&
(![X]:(wise(X)<=>(creative(X)|rich(X))))&
(![X]:((tall(X)<~>~kind(X))<=>(~funny(X)|tall(X))))&
(![X]:((~creative(X)<~>~calm(X))=>old(X)))&
((~quiet(paul))<=>(?[X]:((~curious(X)|brave(X)))))&
(![X]:((~quiet(X)|~brave(X))=>quiet(X)))&
((?[X]:(~calm(X)))<=>(generous(fred)))&
(?[X]:((~happy(X)&~creative(X))))&
(?[X]:(kind(X)))&
((~strong(fred)|curious(fred)))&
(?[X]:((wise(X)|brave(X))))&
(?[X]:((~wise(X)&curious(X))))&
(?[X]:(generous(X))) | happy(lucy) | [] | null | 0 |
Everyone who is either wise or calm is wise and vice versa.
If alice is not rich or not generous then susan is either old or not creative and vice versa.
Everyone who is both funny and humble is creative or funny and vice versa.
Everyone who is strong or not humble is either rich or not strong.
Everyone who is both calm and quiet is not brave and vice versa.
If alice is both happy and strong then fred is both not quiet and quiet.
Everyone who is not kind or not creative is not rich.
Everyone who is both curious and not generous is either strong or not quiet and vice versa.
If fred is either not happy or not kind then someone is both humble and not generous and vice versa.
Everyone who is curious is wise.
Everyone who is both not quiet and not kind is not tall or not strong and vice versa.
Everyone who is both not patient and generous is either not patient or generous.
If someone is either tall or old then alice is strong.
Everyone who is generous or kind is not humble or not quiet and vice versa.
Everyone who is both kind and not brave is both rich and not funny and vice versa.
Everyone who is either not rich or curious is calm.
Paul is not creative or not patient.
Someone is not creative or funny.
Someone is either rich or old.
Someone is funny or not generous.
Alice is not rich or not wise.
Someone is old.
Someone is not quiet or creative. | Alice is kind. | entailment | (![X]:((wise(X)<~>calm(X))<=>wise(X)))&
(((~rich(alice)|~generous(alice)))<=>((old(susan)<~>~creative(susan))))&
(![X]:((funny(X)&humble(X))<=>(creative(X)|funny(X))))&
(![X]:((strong(X)|~humble(X))=>(rich(X)<~>~strong(X))))&
(![X]:((calm(X)&quiet(X))<=>~brave(X)))&
(((happy(alice)&strong(alice)))=>((~quiet(fred)&quiet(fred))))&
(![X]:((~kind(X)|~creative(X))=>~rich(X)))&
(![X]:((curious(X)&~generous(X))<=>(strong(X)<~>~quiet(X))))&
(((~happy(fred)<~>~kind(fred)))<=>(?[X]:((humble(X)&~generous(X)))))&
(![X]:(curious(X)=>wise(X)))&
(![X]:((~quiet(X)&~kind(X))<=>(~tall(X)|~strong(X))))&
(![X]:((~patient(X)&generous(X))=>(~patient(X)<~>generous(X))))&
((?[X]:((tall(X)<~>old(X))))=>(strong(alice)))&
(![X]:((generous(X)|kind(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((kind(X)&~brave(X))<=>(rich(X)&~funny(X))))&
(![X]:((~rich(X)<~>curious(X))=>calm(X)))&
((~creative(paul)|~patient(paul)))&
(?[X]:((~creative(X)|funny(X))))&
(?[X]:((rich(X)<~>old(X))))&
(?[X]:((funny(X)|~generous(X))))&
((~rich(alice)|~wise(alice)))&
(?[X]:(old(X)))&
(?[X]:((~quiet(X)|creative(X)))) | kind(alice) | [
"p3",
"p6",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 258544038719385625320298
% SZS output start Proof for 258544038719385625320298
4. ! [X0] : ((~humble(X0) | strong(X0)) => (rich(X0) <~> ~strong(X0))) [input p3]
7. ! [X0] : ((~creative(X0) | ~kind(X0)) => ~rich(X0)) [input p6]
8. ! [X0] : ((~generous(X0) & curious(X0)) <=> (strong(X0) <~> ~quiet(X0))) [input p7]
11. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> (~strong(X0) | ~tall(X0))) [input p10]
14. ! [X0] : ((kind(X0) | generous(X0)) <=> (~quiet(X0) | ~humble(X0))) [input p13]
24. ~kind(alice) [input hypothesis]
25. ! [X0] : ((rich(X0) <~> ~strong(X0)) | (humble(X0) & ~strong(X0))) [ennf transformation 4]
28. ! [X0] : (~rich(X0) | (creative(X0) & kind(X0))) [ennf transformation 7]
39. ! [X0] : (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (humble(X0) & ~strong(X0))) [nnf transformation 25]
42. ! [X0] : (((~generous(X0) & curious(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (generous(X0) | ~curious(X0)))) [nnf transformation 8]
43. ! [X0] : (((~generous(X0) & curious(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | generous(X0) | ~curious(X0))) [flattening 42]
48. ! [X0] : (((~kind(X0) & ~quiet(X0)) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | (kind(X0) | quiet(X0)))) [nnf transformation 11]
49. ! [X0] : (((~kind(X0) & ~quiet(X0)) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | kind(X0) | quiet(X0))) [flattening 48]
52. ! [X0] : (((kind(X0) | generous(X0)) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | (~kind(X0) & ~generous(X0)))) [nnf transformation 14]
53. ! [X0] : ((kind(X0) | generous(X0) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | (~kind(X0) & ~generous(X0)))) [flattening 52]
83. ~strong(X0) | rich(X0) | ~strong(X0) [cnf transformation 39]
92. ~rich(X0) | kind(X0) [cnf transformation 28]
99. ~generous(X0) | strong(X0) | quiet(X0) [cnf transformation 43]
109. ~quiet(X0) | strong(X0) [cnf transformation 49]
111. ~kind(X0) | strong(X0) [cnf transformation 49]
119. kind(X0) | generous(X0) | quiet(X0) [cnf transformation 53]
134. ~kind(alice) [cnf transformation 24]
136. ~strong(X0) | rich(X0) [duplicate literal removal 83]
149. 3 <=> rich(alice) [avatar definition]
150. rich(alice) <- (3) [avatar component clause 149]
151. ~rich(alice) <- (~3) [avatar component clause 149]
168. 6 <=> strong(alice) [avatar definition]
169. strong(alice) <- (6) [avatar component clause 168]
170. ~strong(alice) <- (~6) [avatar component clause 168]
262. rich(alice) <- (6) [resolution 136,169]
264. $false <- (~3, 6) [subsumption resolution 262,151]
265. 3 | ~6 [avatar contradiction clause 264]
285. kind(alice) <- (3) [resolution 150,92]
286. $false <- (3) [subsumption resolution 285,134]
287. ~3 [avatar contradiction clause 286]
333. generous(X1) | quiet(X1) | strong(X1) [resolution 119,111]
337. quiet(X1) | strong(X1) [subsumption resolution 333,99]
338. strong(X1) [subsumption resolution 337,109]
355. $false <- (~6) [resolution 338,170]
356. 6 [avatar contradiction clause 355]
357. $false [avatar sat refutation 265,287,356]
% SZS output end Proof for 258544038719385625320298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both patient and not tall then someone is either old or brave.
Everyone who is calm is both tall and not brave.
Everyone who is not wise is both humble and rich and vice versa.
If someone is old or not generous then someone is not calm.
Everyone who is funny or not happy is both patient and not happy and vice versa.
If someone is brave then fred is either creative or patient and vice versa.
Everyone who is both patient and creative is generous or not brave.
Everyone who is curious is strong or not funny and vice versa.
Everyone who is both not happy and strong is either not patient or not kind.
If someone is funny or not generous then paul is either not kind or not calm and vice versa.
Everyone who is happy is both not creative and not calm and vice versa.
If mary is either patient or strong then someone is both rich and brave and vice versa.
If mary is either generous or funny then lucy is kind and vice versa.
Everyone who is not old or not curious is quiet and vice versa.
If someone is tall or not brave then someone is not humble and vice versa.
Everyone who is kind or not humble is either creative or not generous.
Fred is tall or not wise.
Someone is either not kind or not humble.
John is not curious.
Someone is not rich or kind.
Someone is not quiet.
Paul is not calm.
Someone is not curious.
Fred is not old or not happy. | Fred is not happy. | neutral | ((?[X]:((patient(X)&~tall(X))))=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:(calm(X)=>(tall(X)&~brave(X))))&
(![X]:(~wise(X)<=>(humble(X)&rich(X))))&
((?[X]:((old(X)|~generous(X))))=>(?[X]:(~calm(X))))&
(![X]:((funny(X)|~happy(X))<=>(patient(X)&~happy(X))))&
((?[X]:(brave(X)))<=>((creative(fred)<~>patient(fred))))&
(![X]:((patient(X)&creative(X))=>(generous(X)|~brave(X))))&
(![X]:(curious(X)<=>(strong(X)|~funny(X))))&
(![X]:((~happy(X)&strong(X))=>(~patient(X)<~>~kind(X))))&
((?[X]:((funny(X)|~generous(X))))<=>((~kind(paul)<~>~calm(paul))))&
(![X]:(happy(X)<=>(~creative(X)&~calm(X))))&
(((patient(mary)<~>strong(mary)))<=>(?[X]:((rich(X)&brave(X)))))&
(((generous(mary)<~>funny(mary)))<=>(kind(lucy)))&
(![X]:((~old(X)|~curious(X))<=>quiet(X)))&
((?[X]:((tall(X)|~brave(X))))<=>(?[X]:(~humble(X))))&
(![X]:((kind(X)|~humble(X))=>(creative(X)<~>~generous(X))))&
((tall(fred)|~wise(fred)))&
(?[X]:((~kind(X)<~>~humble(X))))&
(~curious(john))&
(?[X]:((~rich(X)|kind(X))))&
(?[X]:(~quiet(X)))&
(~calm(paul))&
(?[X]:(~curious(X)))&
((~old(fred)|~happy(fred))) | ~happy(fred) | [] | null | 0 |
Everyone who is both brave and not curious is not humble or not creative.
If lucy is both creative and patient then someone is patient or not tall and vice versa.
If someone is both not funny and creative then someone is brave.
If someone is both not kind and not strong then fred is not generous and vice versa.
If john is either wise or creative then john is either wise or funny.
Everyone who is not wise or not old is not brave and vice versa.
Everyone who is either not kind or wise is not calm or old and vice versa.
Everyone who is both not creative and not curious is not happy or kind and vice versa.
If john is both curious and not funny then alice is wise and vice versa.
If someone is humble then someone is not quiet.
If someone is either not creative or not curious then alice is not quiet or calm.
Everyone who is not creative or generous is creative.
If someone is either not calm or not brave then fred is either not patient or not humble and vice versa.
Everyone who is generous is not funny or generous.
If someone is either quiet or not patient then someone is not happy and vice versa.
Everyone who is wise or not funny is generous or happy.
Someone is patient or kind.
Mary is not strong.
Someone is not strong.
Someone is either funny or not wise.
Someone is either not tall or not creative.
Someone is not curious. | Lucy is funny. | entailment | (![X]:((brave(X)&~curious(X))=>(~humble(X)|~creative(X))))&
(((creative(lucy)&patient(lucy)))<=>(?[X]:((patient(X)|~tall(X)))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:(brave(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(~generous(fred)))&
(((wise(john)<~>creative(john)))=>((wise(john)<~>funny(john))))&
(![X]:((~wise(X)|~old(X))<=>~brave(X)))&
(![X]:((~kind(X)<~>wise(X))<=>(~calm(X)|old(X))))&
(![X]:((~creative(X)&~curious(X))<=>(~happy(X)|kind(X))))&
(((curious(john)&~funny(john)))<=>(wise(alice)))&
((?[X]:(humble(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((~creative(X)<~>~curious(X))))=>((~quiet(alice)|calm(alice))))&
(![X]:((~creative(X)|generous(X))=>creative(X)))&
((?[X]:((~calm(X)<~>~brave(X))))<=>((~patient(fred)<~>~humble(fred))))&
(![X]:(generous(X)=>(~funny(X)|generous(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))=>(generous(X)|happy(X))))&
(?[X]:((patient(X)|kind(X))))&
(~strong(mary))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:(~curious(X))) | funny(lucy) | [
"p2",
"p5",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3243303060916938686324908
% SZS output start Proof for 3243303060916938686324908
3. ? [X0] : (creative(X0) & ~funny(X0)) => ? [X0] : brave(X0) [input p2]
6. ! [X0] : ((~old(X0) | ~wise(X0)) <=> ~brave(X0)) [input p5]
7. ! [X0] : ((~kind(X0) <~> wise(X0)) <=> (old(X0) | ~calm(X0))) [input p6]
8. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (kind(X0) | ~happy(X0))) [input p7]
12. ! [X0] : ((generous(X0) | ~creative(X0)) => creative(X0)) [input p11]
23. ~funny(lucy) [input hypothesis]
24. ? [X0] : (creative(X0) & ~funny(X0)) => ? [X1] : brave(X1) [rectify 3]
29. ? [X1] : brave(X1) | ! [X0] : (~creative(X0) | funny(X0)) [ennf transformation 24]
34. ! [X0] : (creative(X0) | (~generous(X0) & creative(X0))) [ennf transformation 12]
44. ? [X0] : brave(X0) | ! [X1] : (~creative(X1) | funny(X1)) [rectify 29]
45. ? [X0] : brave(X0) => brave(sK1) [choice axiom]
46. brave(sK1) | ! [X1] : (~creative(X1) | funny(X1)) [skolemisation 44,45]
52. ! [X0] : (((~old(X0) | ~wise(X0)) | brave(X0)) & (~brave(X0) | (old(X0) & wise(X0)))) [nnf transformation 6]
53. ! [X0] : ((~old(X0) | ~wise(X0) | brave(X0)) & (~brave(X0) | (old(X0) & wise(X0)))) [flattening 52]
54. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [nnf transformation 7]
55. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [flattening 54]
56. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~kind(X0) & happy(X0))) & ((kind(X0) | ~happy(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 8]
57. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~kind(X0) & happy(X0))) & (kind(X0) | ~happy(X0) | curious(X0) | creative(X0))) [flattening 56]
91. brave(sK1) | ~creative(X1) | funny(X1) [cnf transformation 46]
99. ~brave(X0) | wise(X0) [cnf transformation 53]
100. ~brave(X0) | old(X0) [cnf transformation 53]
107. ~old(X0) | kind(X0) | ~wise(X0) [cnf transformation 55]
110. ~kind(X0) | ~creative(X0) [cnf transformation 57]
119. creative(X0) | creative(X0) [cnf transformation 34]
144. ~funny(lucy) [cnf transformation 23]
145. creative(X0) [duplicate literal removal 119]
176. 7 <=> ! [X1] : (~creative(X1) | funny(X1)) [avatar definition]
177. ~creative(X1) | funny(X1) <- (7) [avatar component clause 176]
179. 8 <=> brave(sK1) [avatar definition]
181. brave(sK1) <- (8) [avatar component clause 179]
182. 7 | 8 [avatar split clause 91,179,176]
327. funny(X1) <- (7) [subsumption resolution 177,145]
328. $false <- (7) [resolution 327,144]
333. ~7 [avatar contradiction clause 328]
334. wise(sK1) <- (8) [resolution 99,181]
335. old(sK1) <- (8) [resolution 100,181]
365. 43 <=> kind(sK1) [avatar definition]
367. kind(sK1) <- (43) [avatar component clause 365]
369. kind(sK1) | ~wise(sK1) <- (8) [resolution 107,335]
370. kind(sK1) <- (8) [subsumption resolution 369,334]
371. 43 | ~8 [avatar split clause 370,179,365]
376. ~creative(sK1) <- (43) [resolution 367,110]
377. $false <- (43) [subsumption resolution 376,145]
378. ~43 [avatar contradiction clause 377]
379. $false [avatar sat refutation 182,333,371,378]
% SZS output end Proof for 3243303060916938686324908
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both humble and not rich then paul is both strong and patient and vice versa.
If alice is kind or generous then john is strong or not curious.
Everyone who is funny is both not happy and patient.
Everyone who is not humble or calm is both rich and not curious.
Everyone who is not old is both not tall and not old.
Everyone who is either creative or patient is either not funny or funny and vice versa.
If someone is both brave and generous then alice is either brave or kind.
Everyone who is both not funny and strong is creative or not tall.
If john is not wise then someone is both rich and strong.
If paul is wise or kind then someone is not wise or rich.
Everyone who is not rich is either not brave or not tall and vice versa.
Everyone who is not happy or not brave is not old and vice versa.
If fred is not old then alice is both not happy and not calm and vice versa.
Everyone who is strong is both not funny and not humble.
If someone is both not funny and not kind then someone is either old or not calm and vice versa.
Everyone who is either not old or not rich is either not creative or not old and vice versa.
Mary is brave or not happy.
Alice is generous or not wise.
Alice is not generous or creative.
Someone is wise.
Someone is strong.
Someone is not wise or not rich. | Alice is not brave. | neutral | ((?[X]:((humble(X)&~rich(X))))<=>((strong(paul)&patient(paul))))&
(((kind(alice)|generous(alice)))=>((strong(john)|~curious(john))))&
(![X]:(funny(X)=>(~happy(X)&patient(X))))&
(![X]:((~humble(X)|calm(X))=>(rich(X)&~curious(X))))&
(![X]:(~old(X)=>(~tall(X)&~old(X))))&
(![X]:((creative(X)<~>patient(X))<=>(~funny(X)<~>funny(X))))&
((?[X]:((brave(X)&generous(X))))=>((brave(alice)<~>kind(alice))))&
(![X]:((~funny(X)&strong(X))=>(creative(X)|~tall(X))))&
((~wise(john))=>(?[X]:((rich(X)&strong(X)))))&
(((wise(paul)|kind(paul)))=>(?[X]:((~wise(X)|rich(X)))))&
(![X]:(~rich(X)<=>(~brave(X)<~>~tall(X))))&
(![X]:((~happy(X)|~brave(X))<=>~old(X)))&
((~old(fred))<=>((~happy(alice)&~calm(alice))))&
(![X]:(strong(X)=>(~funny(X)&~humble(X))))&
((?[X]:((~funny(X)&~kind(X))))<=>(?[X]:((old(X)<~>~calm(X)))))&
(![X]:((~old(X)<~>~rich(X))<=>(~creative(X)<~>~old(X))))&
((brave(mary)|~happy(mary)))&
((generous(alice)|~wise(alice)))&
((~generous(alice)|creative(alice)))&
(?[X]:(wise(X)))&
(?[X]:(strong(X)))&
(?[X]:((~wise(X)|~rich(X)))) | ~brave(alice) | [] | null | 0 |
Everyone who is both curious and not happy is both not wise and quiet and vice versa. Everyone who is both creative and not humble is both funny and curious and vice versa. If alice is happy then lucy is either not old or generous. If lucy is either not happy or not generous then susan is not old or patient and vice versa. Everyone who is both brave and not patient is creative. Everyone who is both not kind and humble is either strong or not patient. Everyone who is either strong or not calm is strong. Everyone who is either not humble or calm is not curious or calm. If susan is either not quiet or not humble then susan is either not strong or not generous and vice versa. Everyone who is not kind or not old is both not funny and old and vice versa. Everyone who is not quiet is not rich and vice versa. Everyone who is not strong is not funny and vice versa. Everyone who is either generous or rich is both funny and old and vice versa. If fred is not patient or not happy then paul is either kind or humble and vice versa. If someone is either not creative or happy then someone is either kind or not brave. Everyone who is not generous or kind is kind and vice versa. Someone is either strong or tall. Fred is both not patient and calm. Someone is either not kind or not creative. Paul is both not curious and happy. Susan is either generous or not funny. Mary is both curious and quiet. Someone is humble or generous. Mary is patient or not strong. | Susan is not kind. | contradiction | (![X]:((curious(X)&~happy(X))<=>(~wise(X)&quiet(X))))&
(![X]:((creative(X)&~humble(X))<=>(funny(X)&curious(X))))&
((happy(alice))=>((~old(lucy)<~>generous(lucy))))&
(((~happy(lucy)<~>~generous(lucy)))<=>((~old(susan)|patient(susan))))&
(![X]:((brave(X)&~patient(X))=>creative(X)))&
(![X]:((~kind(X)&humble(X))=>(strong(X)<~>~patient(X))))&
(![X]:((strong(X)<~>~calm(X))=>strong(X)))&
(![X]:((~humble(X)<~>calm(X))=>(~curious(X)|calm(X))))&
(((~quiet(susan)<~>~humble(susan)))<=>((~strong(susan)<~>~generous(susan))))&
(![X]:((~kind(X)|~old(X))<=>(~funny(X)&old(X))))&
(![X]:(~quiet(X)<=>~rich(X)))&
(![X]:(~strong(X)<=>~funny(X)))&
(![X]:((generous(X)<~>rich(X))<=>(funny(X)&old(X))))&
(((~patient(fred)|~happy(fred)))<=>((kind(paul)<~>humble(paul))))&
((?[X]:((~creative(X)<~>happy(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((~generous(X)|kind(X))<=>kind(X)))&
(?[X]:((strong(X)<~>tall(X))))&
((~patient(fred)&calm(fred)))&
(?[X]:((~kind(X)<~>~creative(X))))&
((~curious(paul)&happy(paul)))&
((generous(susan)<~>~funny(susan)))&
((curious(mary)&quiet(mary)))&
(?[X]:((humble(X)|generous(X))))&
((patient(mary)|~strong(mary))) | ~kind(susan) | [
"p9",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2426007979867567486768000
% SZS output start Proof for 2426007979867567486768000
10. ! [X0] : ((~old(X0) | ~kind(X0)) <=> (old(X0) & ~funny(X0))) [input p9]
16. ! [X0] : ((kind(X0) | ~generous(X0)) <=> kind(X0)) [input p15]
21. generous(susan) <~> ~funny(susan) [input p20]
25. ~kind(susan) [input hypothesis]
47. ! [X0] : (((~old(X0) | ~kind(X0)) | (~old(X0) | funny(X0))) & ((old(X0) & ~funny(X0)) | (old(X0) & kind(X0)))) [nnf transformation 10]
48. ! [X0] : ((~old(X0) | ~kind(X0) | ~old(X0) | funny(X0)) & ((old(X0) & ~funny(X0)) | (old(X0) & kind(X0)))) [flattening 47]
59. ! [X0] : (((kind(X0) | ~generous(X0)) | ~kind(X0)) & (kind(X0) | (~kind(X0) & generous(X0)))) [nnf transformation 16]
60. ! [X0] : ((kind(X0) | ~generous(X0) | ~kind(X0)) & (kind(X0) | (~kind(X0) & generous(X0)))) [flattening 59]
67. (funny(susan) | ~generous(susan)) & (~funny(susan) | generous(susan)) [nnf transformation 21]
101. ~funny(X0) | kind(X0) [cnf transformation 48]
126. kind(X0) | generous(X0) [cnf transformation 60]
138. funny(susan) | ~generous(susan) [cnf transformation 67]
143. ~kind(susan) [cnf transformation 25]
181. 7 <=> generous(susan) [avatar definition]
268. 23 <=> funny(susan) [avatar definition]
270. funny(susan) <- (23) [avatar component clause 268]
271. ~7 | 23 [avatar split clause 138,268,181]
296. generous(susan) [resolution 126,143]
301. 7 [avatar split clause 296,181]
304. kind(susan) <- (23) [resolution 270,101]
305. $false <- (23) [subsumption resolution 304,143]
306. ~23 [avatar contradiction clause 305]
307. $false [avatar sat refutation 271,301,306]
% SZS output end Proof for 2426007979867567486768000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is kind.
Everyone who is not creative or not strong is both strong and curious and vice versa.
Everyone who is both not rich and wise is both not strong and creative.
If someone is wise or calm then someone is not humble or humble.
Everyone who is old or wise is not funny and vice versa.
Everyone who is both not kind and not wise is wise.
If lucy is generous then fred is generous and vice versa.
If lucy is either not happy or old then someone is both not wise and quiet and vice versa.
Everyone who is not creative is either not funny or not curious and vice versa.
Everyone who is kind is generous or not curious.
If mary is either wise or generous then someone is old.
Everyone who is either not strong or not patient is both brave and not quiet.
Everyone who is both brave and not creative is not wise and vice versa.
Everyone who is both creative and funny is not old and vice versa.
Everyone who is not quiet is both happy and not calm.
If someone is not generous or humble then alice is either not humble or not curious and vice versa.
Someone is both not quiet and not creative.
Someone is either kind or not quiet.
John is kind.
Susan is not old or creative.
Someone is either patient or not funny.
John is either generous or not wise.
Lucy is not funny or strong.
Someone is not creative. | Susan is not curious. | entailment | (![X]:(tall(X)=>kind(X)))&
(![X]:((~creative(X)|~strong(X))<=>(strong(X)&curious(X))))&
(![X]:((~rich(X)&wise(X))=>(~strong(X)&creative(X))))&
((?[X]:((wise(X)|calm(X))))=>(?[X]:((~humble(X)|humble(X)))))&
(![X]:((old(X)|wise(X))<=>~funny(X)))&
(![X]:((~kind(X)&~wise(X))=>wise(X)))&
((generous(lucy))<=>(generous(fred)))&
(((~happy(lucy)<~>old(lucy)))<=>(?[X]:((~wise(X)&quiet(X)))))&
(![X]:(~creative(X)<=>(~funny(X)<~>~curious(X))))&
(![X]:(kind(X)=>(generous(X)|~curious(X))))&
(((wise(mary)<~>generous(mary)))=>(?[X]:(old(X))))&
(![X]:((~strong(X)<~>~patient(X))=>(brave(X)&~quiet(X))))&
(![X]:((brave(X)&~creative(X))<=>~wise(X)))&
(![X]:((creative(X)&funny(X))<=>~old(X)))&
(![X]:(~quiet(X)=>(happy(X)&~calm(X))))&
((?[X]:((~generous(X)|humble(X))))<=>((~humble(alice)<~>~curious(alice))))&
(?[X]:((~quiet(X)&~creative(X))))&
(?[X]:((kind(X)<~>~quiet(X))))&
(kind(john))&
((~old(susan)|creative(susan)))&
(?[X]:((patient(X)<~>~funny(X))))&
((generous(john)<~>~wise(john)))&
((~funny(lucy)|strong(lucy)))&
(?[X]:(~creative(X))) | ~curious(susan) | [
"p4",
"p8",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7983059004702598040669672
% SZS output start Proof for 7983059004702598040669672
5. ! [X0] : ((wise(X0) | old(X0)) <=> ~funny(X0)) [input p4]
9. ! [X0] : (~creative(X0) <=> (~funny(X0) <~> ~curious(X0))) [input p8]
13. ! [X0] : ((~creative(X0) & brave(X0)) <=> ~wise(X0)) [input p12]
14. ! [X0] : ((funny(X0) & creative(X0)) <=> ~old(X0)) [input p13]
20. creative(susan) | ~old(susan) [input p19]
25. curious(susan) [input hypothesis]
44. ! [X0] : (((wise(X0) | old(X0)) | funny(X0)) & (~funny(X0) | (~wise(X0) & ~old(X0)))) [nnf transformation 5]
45. ! [X0] : ((wise(X0) | old(X0) | funny(X0)) & (~funny(X0) | (~wise(X0) & ~old(X0)))) [flattening 44]
51. ! [X0] : ((~creative(X0) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0)))) & (((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | creative(X0))) [nnf transformation 9]
56. ! [X0] : (((~creative(X0) & brave(X0)) | wise(X0)) & (~wise(X0) | (creative(X0) | ~brave(X0)))) [nnf transformation 13]
57. ! [X0] : (((~creative(X0) & brave(X0)) | wise(X0)) & (~wise(X0) | creative(X0) | ~brave(X0))) [flattening 56]
58. ! [X0] : (((funny(X0) & creative(X0)) | old(X0)) & (~old(X0) | (~funny(X0) | ~creative(X0)))) [nnf transformation 14]
59. ! [X0] : (((funny(X0) & creative(X0)) | old(X0)) & (~old(X0) | ~funny(X0) | ~creative(X0))) [flattening 58]
82. ~funny(X0) | ~wise(X0) [cnf transformation 45]
95. ~curious(X0) | ~creative(X0) | funny(X0) [cnf transformation 51]
106. ~creative(X0) | wise(X0) [cnf transformation 57]
108. old(X0) | creative(X0) [cnf transformation 59]
122. creative(susan) | ~old(susan) [cnf transformation 20]
129. curious(susan) [cnf transformation 25]
224. creative(susan) [subsumption resolution 122,108]
245. wise(susan) [resolution 106,224]
269. ~creative(susan) | funny(susan) [resolution 95,129]
273. funny(susan) [subsumption resolution 269,224]
285. ~wise(susan) [resolution 273,82]
287. $false [subsumption resolution 285,245]
% SZS output end Proof for 7983059004702598040669672
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious then someone is humble or not strong.
If someone is both patient and not creative then someone is not old and vice versa.
Everyone who is both not humble and not quiet is not funny or not brave and vice versa.
Everyone who is both not wise and not humble is wise.
Everyone who is happy or not old is both not happy and not funny and vice versa.
If someone is both rich and not patient then paul is not tall and vice versa.
Everyone who is either generous or not quiet is both patient and not quiet and vice versa.
If lucy is old or tall then someone is either humble or not humble and vice versa.
If someone is either not kind or not wise then paul is not strong and vice versa.
Everyone who is either not brave or not old is both not funny and not old and vice versa.
Everyone who is not creative or not brave is either not calm or calm and vice versa.
Everyone who is brave or creative is both not calm and old.
If someone is either not calm or tall then susan is either not wise or humble and vice versa.
If someone is either not funny or not curious then fred is not funny or generous and vice versa.
If paul is quiet or curious then someone is not creative or not generous and vice versa.
If paul is strong or not creative then someone is strong or not funny.
John is either creative or not patient.
John is not kind.
Someone is either not curious or not humble.
Someone is not happy.
Someone is either not old or not strong.
Someone is happy or kind. | Lucy is funny. | entailment | ((?[X]:(curious(X)))=>(?[X]:((humble(X)|~strong(X)))))&
((?[X]:((patient(X)&~creative(X))))<=>(?[X]:(~old(X))))&
(![X]:((~humble(X)&~quiet(X))<=>(~funny(X)|~brave(X))))&
(![X]:((~wise(X)&~humble(X))=>wise(X)))&
(![X]:((happy(X)|~old(X))<=>(~happy(X)&~funny(X))))&
((?[X]:((rich(X)&~patient(X))))<=>(~tall(paul)))&
(![X]:((generous(X)<~>~quiet(X))<=>(patient(X)&~quiet(X))))&
(((old(lucy)|tall(lucy)))<=>(?[X]:((humble(X)<~>~humble(X)))))&
((?[X]:((~kind(X)<~>~wise(X))))<=>(~strong(paul)))&
(![X]:((~brave(X)<~>~old(X))<=>(~funny(X)&~old(X))))&
(![X]:((~creative(X)|~brave(X))<=>(~calm(X)<~>calm(X))))&
(![X]:((brave(X)|creative(X))=>(~calm(X)&old(X))))&
((?[X]:((~calm(X)<~>tall(X))))<=>((~wise(susan)<~>humble(susan))))&
((?[X]:((~funny(X)<~>~curious(X))))<=>((~funny(fred)|generous(fred))))&
(((quiet(paul)|curious(paul)))<=>(?[X]:((~creative(X)|~generous(X)))))&
(((strong(paul)|~creative(paul)))=>(?[X]:((strong(X)|~funny(X)))))&
((creative(john)<~>~patient(john)))&
(~kind(john))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~old(X)<~>~strong(X))))&
(?[X]:((happy(X)|kind(X)))) | funny(lucy) | [
"p4",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3707340293911048448267275
% SZS output start Proof for 3707340293911048448267275
5. ! [X0] : ((~old(X0) | happy(X0)) <=> (~funny(X0) & ~happy(X0))) [input p4]
10. ! [X0] : ((~brave(X0) <~> ~old(X0)) <=> (~old(X0) & ~funny(X0))) [input p9]
12. ! [X0] : ((creative(X0) | brave(X0)) => (old(X0) & ~calm(X0))) [input p11]
23. ~funny(lucy) [input hypothesis]
29. ! [X0] : ((old(X0) & ~calm(X0)) | (~creative(X0) & ~brave(X0))) [ennf transformation 12]
41. ! [X0] : (((~old(X0) | happy(X0)) | (funny(X0) | happy(X0))) & ((~funny(X0) & ~happy(X0)) | (old(X0) & ~happy(X0)))) [nnf transformation 5]
42. ! [X0] : ((~old(X0) | happy(X0) | funny(X0) | happy(X0)) & ((~funny(X0) & ~happy(X0)) | (old(X0) & ~happy(X0)))) [flattening 41]
58. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (old(X0) | funny(X0))) & ((~old(X0) & ~funny(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [nnf transformation 10]
59. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | old(X0) | funny(X0)) & ((~old(X0) & ~funny(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [flattening 58]
99. ~happy(X0) | ~happy(X0) [cnf transformation 42]
102. ~funny(X0) | old(X0) [cnf transformation 42]
103. ~old(X0) | happy(X0) | funny(X0) | happy(X0) [cnf transformation 42]
125. ~old(X0) | ~old(X0) | brave(X0) [cnf transformation 59]
128. old(X0) | brave(X0) | old(X0) | funny(X0) [cnf transformation 59]
137. old(X0) | ~brave(X0) [cnf transformation 29]
168. ~funny(lucy) [cnf transformation 23]
171. ~old(X0) | brave(X0) [duplicate literal removal 125]
172. old(X0) | brave(X0) | funny(X0) [duplicate literal removal 128]
177. ~happy(X0) [duplicate literal removal 99]
178. ~old(X0) | happy(X0) | funny(X0) [duplicate literal removal 103]
193. 4 <=> ! [X1] : old(X1) [avatar definition]
194. old(X1) <- (4) [avatar component clause 193]
269. brave(X0) | old(X0) [subsumption resolution 172,102]
270. brave(X0) [subsumption resolution 171,269]
274. old(X0) [subsumption resolution 137,270]
275. 4 [avatar split clause 274,193]
400. happy(X0) | funny(X0) <- (4) [resolution 178,194]
403. funny(X0) <- (4) [subsumption resolution 400,177]
408. $false <- (4) [resolution 403,168]
413. ~4 [avatar contradiction clause 408]
414. $false [avatar sat refutation 275,413]
% SZS output end Proof for 3707340293911048448267275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or happy then someone is not kind. Everyone who is not calm or rich is either not rich or not happy and vice versa. If someone is not patient then paul is both not kind and not old. If paul is not humble then someone is either not rich or happy. Everyone who is both funny and wise is not wise and vice versa. If someone is patient or generous then paul is either patient or old. Everyone who is either rich or calm is either not old or not creative. Everyone who is either not brave or funny is both wise and not curious. If paul is either not generous or not funny then someone is both not tall and patient. Everyone who is either kind or not humble is both not quiet and not tall. Everyone who is both happy and not strong is both creative and not calm and vice versa. Everyone who is either not creative or creative is generous or creative and vice versa. Everyone who is old is not tall and vice versa. If someone is humble then paul is either tall or wise. If paul is both not quiet and not old then someone is both not quiet and calm. Everyone who is not tall or tall is both brave and not happy. Paul is rich. Susan is strong. Someone is both not kind and not strong. Paul is not rich or not humble. Someone is generous. Someone is curious or wise. Someone is not rich or not wise. | Paul is calm. | entailment | ((?[X]:((~generous(X)<~>happy(X))))=>(?[X]:(~kind(X))))&
(![X]:((~calm(X)|rich(X))<=>(~rich(X)<~>~happy(X))))&
((?[X]:(~patient(X)))=>((~kind(paul)&~old(paul))))&
((~humble(paul))=>(?[X]:((~rich(X)<~>happy(X)))))&
(![X]:((funny(X)&wise(X))<=>~wise(X)))&
((?[X]:((patient(X)|generous(X))))=>((patient(paul)<~>old(paul))))&
(![X]:((rich(X)<~>calm(X))=>(~old(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>funny(X))=>(wise(X)&~curious(X))))&
(((~generous(paul)<~>~funny(paul)))=>(?[X]:((~tall(X)&patient(X)))))&
(![X]:((kind(X)<~>~humble(X))=>(~quiet(X)&~tall(X))))&
(![X]:((happy(X)&~strong(X))<=>(creative(X)&~calm(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(generous(X)|creative(X))))&
(![X]:(old(X)<=>~tall(X)))&
((?[X]:(humble(X)))=>((tall(paul)<~>wise(paul))))&
(((~quiet(paul)&~old(paul)))=>(?[X]:((~quiet(X)&calm(X)))))&
(![X]:((~tall(X)|tall(X))=>(brave(X)&~happy(X))))&
(rich(paul))&
(strong(susan))&
(?[X]:((~kind(X)&~strong(X))))&
((~rich(paul)|~humble(paul)))&
(?[X]:(generous(X)))&
(?[X]:((curious(X)|wise(X))))&
(?[X]:((~rich(X)|~wise(X)))) | calm(paul) | [
"p2",
"p5",
"p6",
"p10",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 319089355326941392654904
% SZS output start Proof for 319089355326941392654904
3. ? [X0] : ~patient(X0) => (~old(paul) & ~kind(paul)) [input p2]
6. ? [X0] : (generous(X0) | patient(X0)) => (patient(paul) <~> old(paul)) [input p5]
7. ! [X0] : ((rich(X0) <~> calm(X0)) => (~old(X0) <~> ~creative(X0))) [input p6]
11. ! [X0] : ((~strong(X0) & happy(X0)) <=> (~calm(X0) & creative(X0))) [input p10]
16. ! [X0] : ((tall(X0) | ~tall(X0)) => (~happy(X0) & brave(X0))) [input p15]
17. rich(paul) [input p16]
21. ? [X0] : generous(X0) [input p20]
24. ~calm(paul) [input hypothesis]
27. (~old(paul) & ~kind(paul)) | ! [X0] : patient(X0) [ennf transformation 3]
29. (patient(paul) <~> old(paul)) | ! [X0] : (~generous(X0) & ~patient(X0)) [ennf transformation 6]
30. ! [X0] : ((~old(X0) <~> ~creative(X0)) | (rich(X0) <=> calm(X0))) [ennf transformation 7]
37. ! [X0] : ((~happy(X0) & brave(X0)) | (~tall(X0) & tall(X0))) [ennf transformation 16]
49. ((~old(paul) | ~patient(paul)) & (old(paul) | patient(paul))) | ! [X0] : (~generous(X0) & ~patient(X0)) [nnf transformation 29]
50. ! [X0] : (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) [nnf transformation 30]
56. ! [X0] : (((~strong(X0) & happy(X0)) | (calm(X0) | ~creative(X0))) & ((~calm(X0) & creative(X0)) | (strong(X0) | ~happy(X0)))) [nnf transformation 11]
57. ! [X0] : (((~strong(X0) & happy(X0)) | calm(X0) | ~creative(X0)) & ((~calm(X0) & creative(X0)) | strong(X0) | ~happy(X0))) [flattening 56]
66. ? [X0] : generous(X0) => generous(sK5) [choice axiom]
67. generous(sK5) [skolemisation 21,66]
81. ~old(paul) | patient(X0) [cnf transformation 27]
90. ~old(paul) | ~patient(paul) | ~generous(X0) [cnf transformation 49]
93. ~rich(X0) | old(X0) | calm(X0) | creative(X0) [cnf transformation 50]
109. ~creative(X0) | calm(X0) | happy(X0) [cnf transformation 57]
125. ~happy(X0) | tall(X0) [cnf transformation 37]
126. ~tall(X0) | ~happy(X0) [cnf transformation 37]
127. rich(paul) [cnf transformation 17]
132. generous(sK5) [cnf transformation 67]
135. ~calm(paul) [cnf transformation 24]
157. 4 <=> ! [X0] : patient(X0) [avatar definition]
158. patient(X0) <- (4) [avatar component clause 157]
160. 5 <=> old(paul) [avatar definition]
162. ~old(paul) <- (~5) [avatar component clause 160]
163. 4 | ~5 [avatar split clause 81,160,157]
187. 10 <=> ! [X0] : ~generous(X0) [avatar definition]
188. ~generous(X0) <- (10) [avatar component clause 187]
190. 11 <=> patient(paul) [avatar definition]
192. ~patient(paul) <- (~11) [avatar component clause 190]
193. 10 | ~11 | ~5 [avatar split clause 90,160,190,187]
240. ~happy(X0) [subsumption resolution 125,126]
245. $false <- (4, ~11) [resolution 192,158]
246. ~4 | 11 [avatar contradiction clause 245]
249. $false <- (10) [resolution 188,132]
250. ~10 [avatar contradiction clause 249]
314. old(paul) | calm(paul) | creative(paul) [resolution 93,127]
317. calm(paul) | creative(paul) <- (~5) [subsumption resolution 314,162]
318. creative(paul) <- (~5) [subsumption resolution 317,135]
322. calm(paul) | happy(paul) <- (~5) [resolution 318,109]
323. happy(paul) <- (~5) [subsumption resolution 322,135]
324. $false <- (~5) [subsumption resolution 323,240]
325. 5 [avatar contradiction clause 324]
326. $false [avatar sat refutation 163,193,246,250,325]
% SZS output end Proof for 319089355326941392654904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or old is rich or not calm.
Everyone who is both not tall and not calm is not brave or not creative and vice versa.
If john is both not brave and not wise then john is either happy or not calm.
Everyone who is tall is patient and vice versa.
If someone is either tall or strong then someone is both happy and funny and vice versa.
Everyone who is both not funny and not strong is strong.
If susan is tall then john is both old and calm and vice versa.
Everyone who is not brave or not humble is funny and vice versa.
If fred is not patient then someone is both kind and not creative.
Everyone who is either not creative or not calm is not old or not curious and vice versa.
If alice is calm or kind then mary is both rich and not kind and vice versa.
Everyone who is strong or not humble is not calm.
If john is not generous then alice is not wise.
If alice is not calm or humble then john is both not wise and curious and vice versa.
Everyone who is generous or not creative is generous or tall and vice versa.
Everyone who is wise is either calm or not old and vice versa.
Someone is kind or not kind.
Someone is wise or not funny.
Someone is not funny.
Someone is either humble or curious.
Someone is rich or generous.
Someone is both not humble and generous.
Susan is both not tall and not calm. | John is happy. | neutral | (![X]:((calm(X)<~>old(X))=>(rich(X)|~calm(X))))&
(![X]:((~tall(X)&~calm(X))<=>(~brave(X)|~creative(X))))&
(((~brave(john)&~wise(john)))=>((happy(john)<~>~calm(john))))&
(![X]:(tall(X)<=>patient(X)))&
((?[X]:((tall(X)<~>strong(X))))<=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((~funny(X)&~strong(X))=>strong(X)))&
((tall(susan))<=>((old(john)&calm(john))))&
(![X]:((~brave(X)|~humble(X))<=>funny(X)))&
((~patient(fred))=>(?[X]:((kind(X)&~creative(X)))))&
(![X]:((~creative(X)<~>~calm(X))<=>(~old(X)|~curious(X))))&
(((calm(alice)|kind(alice)))<=>((rich(mary)&~kind(mary))))&
(![X]:((strong(X)|~humble(X))=>~calm(X)))&
((~generous(john))=>(~wise(alice)))&
(((~calm(alice)|humble(alice)))<=>((~wise(john)&curious(john))))&
(![X]:((generous(X)|~creative(X))<=>(generous(X)|tall(X))))&
(![X]:(wise(X)<=>(calm(X)<~>~old(X))))&
(?[X]:((kind(X)|~kind(X))))&
(?[X]:((wise(X)|~funny(X))))&
(?[X]:(~funny(X)))&
(?[X]:((humble(X)<~>curious(X))))&
(?[X]:((rich(X)|generous(X))))&
(?[X]:((~humble(X)&generous(X))))&
((~tall(susan)&~calm(susan))) | happy(john) | [] | null | 0 |
Everyone who is funny or not calm is either brave or not brave and vice versa.
If john is old then john is curious or funny and vice versa.
If someone is not brave or not creative then alice is not strong and vice versa.
If john is either curious or generous then john is either calm or curious.
If someone is not old then someone is not patient or creative and vice versa.
If susan is either generous or old then someone is creative.
Everyone who is calm is either wise or not curious and vice versa.
Everyone who is curious or not happy is humble.
If fred is not tall then alice is not funny or not humble.
If susan is not quiet then paul is brave and vice versa.
Everyone who is either not calm or not curious is not patient.
Everyone who is either brave or not tall is quiet.
Everyone who is both calm and not humble is either not old or humble and vice versa.
Everyone who is not kind is tall or not old.
Everyone who is not tall or not generous is both quiet and not creative and vice versa.
If someone is not kind then someone is old.
Susan is rich.
Alice is not quiet or humble.
Susan is either not creative or not strong.
Someone is not generous or quiet.
Someone is not kind.
Fred is not old.
Someone is both not tall and curious.
Mary is not creative. | John is creative. | contradiction | (![X]:((funny(X)|~calm(X))<=>(brave(X)<~>~brave(X))))&
((old(john))<=>((curious(john)|funny(john))))&
((?[X]:((~brave(X)|~creative(X))))<=>(~strong(alice)))&
(((curious(john)<~>generous(john)))=>((calm(john)<~>curious(john))))&
((?[X]:(~old(X)))<=>(?[X]:((~patient(X)|creative(X)))))&
(((generous(susan)<~>old(susan)))=>(?[X]:(creative(X))))&
(![X]:(calm(X)<=>(wise(X)<~>~curious(X))))&
(![X]:((curious(X)|~happy(X))=>humble(X)))&
((~tall(fred))=>((~funny(alice)|~humble(alice))))&
((~quiet(susan))<=>(brave(paul)))&
(![X]:((~calm(X)<~>~curious(X))=>~patient(X)))&
(![X]:((brave(X)<~>~tall(X))=>quiet(X)))&
(![X]:((calm(X)&~humble(X))<=>(~old(X)<~>humble(X))))&
(![X]:(~kind(X)=>(tall(X)|~old(X))))&
(![X]:((~tall(X)|~generous(X))<=>(quiet(X)&~creative(X))))&
((?[X]:(~kind(X)))=>(?[X]:(old(X))))&
(rich(susan))&
((~quiet(alice)|humble(alice)))&
((~creative(susan)<~>~strong(susan)))&
(?[X]:((~generous(X)|quiet(X))))&
(?[X]:(~kind(X)))&
(~old(fred))&
(?[X]:((~tall(X)&curious(X))))&
(~creative(mary)) | creative(john) | [
"p0",
"p1",
"p3",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3846832442809031936425705
% SZS output start Proof for 3846832442809031936425705
1. ! [X0] : ((~calm(X0) | funny(X0)) <=> (brave(X0) <~> ~brave(X0))) [input p0]
2. old(john) <=> (funny(john) | curious(john)) [input p1]
4. (curious(john) <~> generous(john)) => (calm(john) <~> curious(john)) [input p3]
8. ! [X0] : ((~happy(X0) | curious(X0)) => humble(X0)) [input p7]
13. ! [X0] : ((~humble(X0) & calm(X0)) <=> (~old(X0) <~> humble(X0))) [input p12]
15. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~creative(X0) & quiet(X0))) [input p14]
25. creative(john) [input hypothesis]
29. ! [X0] : (curious(X0) => humble(X0)) [pure predicate removal 8]
30. (calm(john) <~> curious(john)) | (curious(john) <=> generous(john)) [ennf transformation 4]
32. ! [X0] : (humble(X0) | ~curious(X0)) [ennf transformation 29]
40. ! [X0] : (((~calm(X0) | funny(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (calm(X0) & ~funny(X0)))) [nnf transformation 1]
41. ! [X0] : ((~calm(X0) | funny(X0) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (calm(X0) & ~funny(X0)))) [flattening 40]
42. (old(john) | (~funny(john) & ~curious(john))) & ((funny(john) | curious(john)) | ~old(john)) [nnf transformation 2]
43. (old(john) | (~funny(john) & ~curious(john))) & (funny(john) | curious(john) | ~old(john)) [flattening 42]
48. ((~curious(john) | ~calm(john)) & (curious(john) | calm(john))) | ((curious(john) | ~generous(john)) & (generous(john) | ~curious(john))) [nnf transformation 30]
61. ! [X0] : (((~humble(X0) & calm(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) & (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | (humble(X0) | ~calm(X0)))) [nnf transformation 13]
62. ! [X0] : (((~humble(X0) & calm(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) & (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | humble(X0) | ~calm(X0))) [flattening 61]
63. ! [X0] : (((~generous(X0) | ~tall(X0)) | (creative(X0) | ~quiet(X0))) & ((~creative(X0) & quiet(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 15]
64. ! [X0] : ((~generous(X0) | ~tall(X0) | creative(X0) | ~quiet(X0)) & ((~creative(X0) & quiet(X0)) | (generous(X0) & tall(X0)))) [flattening 63]
79. ~calm(X0) | funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 41]
80. ~calm(X0) | funny(X0) | brave(X0) | brave(X0) [cnf transformation 41]
82. old(john) | ~curious(john) [cnf transformation 43]
83. old(john) | ~funny(john) [cnf transformation 43]
88. curious(john) | calm(john) | curious(john) | ~generous(john) [cnf transformation 48]
100. ~curious(X0) | humble(X0) [cnf transformation 32]
108. humble(X0) | ~old(X0) | humble(X0) | ~calm(X0) [cnf transformation 62]
113. ~humble(X0) | ~old(X0) | ~humble(X0) [cnf transformation 62]
118. ~creative(X0) | generous(X0) [cnf transformation 64]
130. creative(john) [cnf transformation 25]
131. humble(X0) | ~old(X0) | ~calm(X0) [duplicate literal removal 108]
132. ~humble(X0) | ~old(X0) [duplicate literal removal 113]
133. curious(john) | calm(john) | ~generous(john) [duplicate literal removal 88]
135. ~calm(X0) | funny(X0) | ~brave(X0) [duplicate literal removal 79]
136. ~calm(X0) | funny(X0) | brave(X0) [duplicate literal removal 80]
137. ~calm(X0) | funny(X0) [subsumption resolution 135,136]
139. 1 <=> funny(john) [avatar definition]
143. 2 <=> old(john) [avatar definition]
145. old(john) <- (2) [avatar component clause 143]
146. ~1 | 2 [avatar split clause 83,143,139]
148. 3 <=> curious(john) [avatar definition]
149. curious(john) <- (3) [avatar component clause 148]
151. ~3 | 2 [avatar split clause 82,143,148]
175. 9 <=> generous(john) [avatar definition]
179. 10 <=> calm(john) [avatar definition]
180. calm(john) <- (10) [avatar component clause 179]
183. ~9 | 10 | 3 [avatar split clause 133,148,179,175]
245. ~old(X0) | ~calm(X0) [subsumption resolution 131,132]
282. generous(john) [resolution 118,130]
286. 9 [avatar split clause 282,175]
287. humble(john) <- (3) [resolution 149,100]
289. ~old(john) <- (3) [resolution 287,132]
290. $false <- (2, 3) [subsumption resolution 289,145]
291. ~2 | ~3 [avatar contradiction clause 290]
292. funny(john) <- (10) [resolution 180,137]
295. ~calm(john) <- (2) [resolution 245,145]
296. $false <- (2, 10) [subsumption resolution 295,180]
297. ~2 | ~10 [avatar contradiction clause 296]
298. 1 | ~10 [avatar split clause 292,179,139]
299. $false [avatar sat refutation 146,151,183,286,291,297,298]
% SZS output end Proof for 3846832442809031936425705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and kind is both not calm and kind. If someone is both not quiet and kind then someone is kind and vice versa. Everyone who is old or kind is not kind. Everyone who is either wise or not quiet is both not old and funny and vice versa. If mary is quiet or not humble then someone is either kind or old and vice versa. If lucy is not brave then someone is strong or old and vice versa. Everyone who is not kind is either kind or not generous and vice versa. If someone is rich then someone is both not rich and wise. If someone is kind then alice is happy or not tall and vice versa. If someone is either not humble or not wise then someone is happy. If someone is not creative or strong then mary is not calm or creative and vice versa. Everyone who is both tall and not kind is either not creative or quiet and vice versa. If someone is both not humble and not rich then fred is kind or creative. Everyone who is not strong or humble is not wise and vice versa. If alice is either patient or not generous then paul is not humble. Everyone who is either calm or kind is not rich or not creative. John is not creative or brave. Someone is curious. Someone is either not curious or funny. John is not creative or not happy. Paul is both not quiet and patient. Paul is brave. Mary is either kind or humble. | Alice is not tall. | contradiction | (![X]:((~patient(X)&kind(X))=>(~calm(X)&kind(X))))&
((?[X]:((~quiet(X)&kind(X))))<=>(?[X]:(kind(X))))&
(![X]:((old(X)|kind(X))=>~kind(X)))&
(![X]:((wise(X)<~>~quiet(X))<=>(~old(X)&funny(X))))&
(((quiet(mary)|~humble(mary)))<=>(?[X]:((kind(X)<~>old(X)))))&
((~brave(lucy))<=>(?[X]:((strong(X)|old(X)))))&
(![X]:(~kind(X)<=>(kind(X)<~>~generous(X))))&
((?[X]:(rich(X)))=>(?[X]:((~rich(X)&wise(X)))))&
((?[X]:(kind(X)))<=>((happy(alice)|~tall(alice))))&
((?[X]:((~humble(X)<~>~wise(X))))=>(?[X]:(happy(X))))&
((?[X]:((~creative(X)|strong(X))))<=>((~calm(mary)|creative(mary))))&
(![X]:((tall(X)&~kind(X))<=>(~creative(X)<~>quiet(X))))&
((?[X]:((~humble(X)&~rich(X))))=>((kind(fred)|creative(fred))))&
(![X]:((~strong(X)|humble(X))<=>~wise(X)))&
(((patient(alice)<~>~generous(alice)))=>(~humble(paul)))&
(![X]:((calm(X)<~>kind(X))=>(~rich(X)|~creative(X))))&
((~creative(john)|brave(john)))&
(?[X]:(curious(X)))&
(?[X]:((~curious(X)<~>funny(X))))&
((~creative(john)|~happy(john)))&
((~quiet(paul)&patient(paul)))&
(brave(paul))&
((kind(mary)<~>humble(mary))) | ~tall(alice) | [
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4581723743070587099237193
% SZS output start Proof for 4581723743070587099237193
3. ! [X0] : ((kind(X0) | old(X0)) => ~kind(X0)) [input p2]
9. ? [X0] : kind(X0) <=> (~tall(alice) | happy(alice)) [input p8]
24. ~tall(alice) [input hypothesis]
30. ! [X0] : (~kind(X0) | (~kind(X0) & ~old(X0))) [ennf transformation 3]
58. (? [X0] : kind(X0) | (tall(alice) & ~happy(alice))) & ((~tall(alice) | happy(alice)) | ! [X0] : ~kind(X0)) [nnf transformation 9]
59. (? [X0] : kind(X0) | (tall(alice) & ~happy(alice))) & (~tall(alice) | happy(alice) | ! [X0] : ~kind(X0)) [flattening 58]
60. (? [X0] : kind(X0) | (tall(alice) & ~happy(alice))) & (~tall(alice) | happy(alice) | ! [X1] : ~kind(X1)) [rectify 59]
61. ? [X0] : kind(X0) => kind(sK5) [choice axiom]
62. (kind(sK5) | (tall(alice) & ~happy(alice))) & (~tall(alice) | happy(alice) | ! [X1] : ~kind(X1)) [skolemisation 60,61]
90. ~kind(X0) | ~kind(X0) [cnf transformation 30]
114. kind(sK5) | tall(alice) [cnf transformation 62]
145. ~tall(alice) [cnf transformation 24]
148. ~kind(X0) [duplicate literal removal 90]
150. 1 <=> ! [X1] : ~kind(X1) [avatar definition]
151. ~kind(X1) <- (1) [avatar component clause 150]
170. 1 [avatar split clause 148,150]
229. 18 <=> tall(alice) [avatar definition]
233. 19 <=> kind(sK5) [avatar definition]
235. kind(sK5) <- (19) [avatar component clause 233]
236. 18 | 19 [avatar split clause 114,233,229]
330. ~18 [avatar split clause 145,229]
331. $false <- (1, 19) [resolution 235,151]
332. ~1 | ~19 [avatar contradiction clause 331]
333. $false [avatar sat refutation 170,236,330,332]
% SZS output end Proof for 4581723743070587099237193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or not tall then susan is not curious or rich. Everyone who is rich is creative and vice versa. If someone is either not patient or funny then someone is both not humble and old and vice versa. Everyone who is both tall and not humble is either old or not strong and vice versa. Everyone who is both not happy and not brave is not wise or generous. If someone is not happy then someone is both wise and not old and vice versa. Everyone who is either creative or old is not creative. Everyone who is wise is calm or not old and vice versa. Everyone who is not humble is not old or not patient. Everyone who is not funny or rich is both not wise and not rich. If susan is either wise or not curious then someone is not quiet or creative and vice versa. If someone is brave or generous then someone is not patient or strong. If someone is either not tall or old then lucy is either humble or not strong. If someone is brave or not patient then lucy is tall or brave and vice versa. Everyone who is both not curious and not calm is wise or kind. If someone is either not kind or patient then someone is not funny or curious. Someone is either not creative or not funny. Susan is either not generous or calm. Mary is generous. Susan is tall or not tall. Someone is not calm or not tall. John is both not wise and happy. | Lucy is calm. | neutral | ((?[X]:((calm(X)<~>~tall(X))))=>((~curious(susan)|rich(susan))))&
(![X]:(rich(X)<=>creative(X)))&
((?[X]:((~patient(X)<~>funny(X))))<=>(?[X]:((~humble(X)&old(X)))))&
(![X]:((tall(X)&~humble(X))<=>(old(X)<~>~strong(X))))&
(![X]:((~happy(X)&~brave(X))=>(~wise(X)|generous(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((wise(X)&~old(X)))))&
(![X]:((creative(X)<~>old(X))=>~creative(X)))&
(![X]:(wise(X)<=>(calm(X)|~old(X))))&
(![X]:(~humble(X)=>(~old(X)|~patient(X))))&
(![X]:((~funny(X)|rich(X))=>(~wise(X)&~rich(X))))&
(((wise(susan)<~>~curious(susan)))<=>(?[X]:((~quiet(X)|creative(X)))))&
((?[X]:((brave(X)|generous(X))))=>(?[X]:((~patient(X)|strong(X)))))&
((?[X]:((~tall(X)<~>old(X))))=>((humble(lucy)<~>~strong(lucy))))&
((?[X]:((brave(X)|~patient(X))))<=>((tall(lucy)|brave(lucy))))&
(![X]:((~curious(X)&~calm(X))=>(wise(X)|kind(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>(?[X]:((~funny(X)|curious(X)))))&
(?[X]:((~creative(X)<~>~funny(X))))&
((~generous(susan)<~>calm(susan)))&
(generous(mary))&
((tall(susan)|~tall(susan)))&
(?[X]:((~calm(X)|~tall(X))))&
((~wise(john)&happy(john))) | calm(lucy) | [] | null | 0 |
Everyone who is not strong is not creative and vice versa. Everyone who is patient is either brave or not creative and vice versa. If fred is either not old or strong then someone is both not calm and calm. Everyone who is either not brave or not kind is both not old and not rich and vice versa. Everyone who is both not quiet and not kind is tall and vice versa. Everyone who is either not curious or not tall is both not quiet and curious and vice versa. If someone is either happy or not calm then someone is both not brave and tall and vice versa. If alice is both not wise and brave then someone is not kind. If paul is either not calm or not rich then someone is not rich or not old. If mary is either not quiet or not strong then susan is both not happy and funny. If paul is both not wise and not curious then someone is curious. Everyone who is both kind and not kind is either not funny or brave. Everyone who is either happy or not quiet is either wise or happy and vice versa. If susan is both not humble and not rich then fred is not brave and vice versa. If mary is not rich or not wise then someone is brave or happy. Everyone who is either tall or humble is either strong or not creative and vice versa. Someone is either not tall or tall. Someone is not generous or not kind. Fred is both not calm and not kind. Someone is both not strong and not kind. Paul is calm or not strong. Paul is either strong or not happy. Susan is not happy. Someone is either not curious or wise. | Fred is not old. | entailment | (![X]:(~strong(X)<=>~creative(X)))&
(![X]:(patient(X)<=>(brave(X)<~>~creative(X))))&
(((~old(fred)<~>strong(fred)))=>(?[X]:((~calm(X)&calm(X)))))&
(![X]:((~brave(X)<~>~kind(X))<=>(~old(X)&~rich(X))))&
(![X]:((~quiet(X)&~kind(X))<=>tall(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(((~wise(alice)&brave(alice)))=>(?[X]:(~kind(X))))&
(((~calm(paul)<~>~rich(paul)))=>(?[X]:((~rich(X)|~old(X)))))&
(((~quiet(mary)<~>~strong(mary)))=>((~happy(susan)&funny(susan))))&
(((~wise(paul)&~curious(paul)))=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))=>(~funny(X)<~>brave(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(wise(X)<~>happy(X))))&
(((~humble(susan)&~rich(susan)))<=>(~brave(fred)))&
(((~rich(mary)|~wise(mary)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((tall(X)<~>humble(X))<=>(strong(X)<~>~creative(X))))&
(?[X]:((~tall(X)<~>tall(X))))&
(?[X]:((~generous(X)|~kind(X))))&
((~calm(fred)&~kind(fred)))&
(?[X]:((~strong(X)&~kind(X))))&
((calm(paul)|~strong(paul)))&
((strong(paul)<~>~happy(paul)))&
(~happy(susan))&
(?[X]:((~curious(X)<~>wise(X)))) | ~old(fred) | [
"p0",
"p3",
"p4",
"p5",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 319893733445168866466449
% SZS output start Proof for 319893733445168866466449
1. ! [X0] : (~strong(X0) <=> ~creative(X0)) [input p0]
4. ! [X0] : ((~brave(X0) <~> ~kind(X0)) <=> (~rich(X0) & ~old(X0))) [input p3]
5. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> tall(X0)) [input p4]
6. ! [X0] : ((~curious(X0) <~> ~tall(X0)) <=> (curious(X0) & ~quiet(X0))) [input p5]
14. (~rich(susan) & ~humble(susan)) <=> ~brave(fred) [input p13]
16. ! [X0] : ((tall(X0) <~> humble(X0)) <=> (strong(X0) <~> ~creative(X0))) [input p15]
19. ~kind(fred) & ~calm(fred) [input p18]
25. old(fred) [input hypothesis]
38. ! [X0] : ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))) [nnf transformation 1]
42. ! [X0] : ((((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | (rich(X0) | old(X0))) & ((~rich(X0) & ~old(X0)) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0))))) [nnf transformation 4]
43. ! [X0] : ((((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | rich(X0) | old(X0)) & ((~rich(X0) & ~old(X0)) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0))))) [flattening 42]
44. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | (kind(X0) | quiet(X0)))) [nnf transformation 5]
45. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | kind(X0) | quiet(X0))) [flattening 44]
46. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~curious(X0) | quiet(X0))) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [nnf transformation 6]
47. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | ~curious(X0) | quiet(X0)) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [flattening 46]
63. ((~rich(susan) & ~humble(susan)) | brave(fred)) & (~brave(fred) | (rich(susan) | humble(susan))) [nnf transformation 14]
64. ((~rich(susan) & ~humble(susan)) | brave(fred)) & (~brave(fred) | rich(susan) | humble(susan)) [flattening 63]
67. ! [X0] : ((((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ((strong(X0) | creative(X0)) & (~creative(X0) | ~strong(X0)))) & (((creative(X0) | ~strong(X0)) & (~creative(X0) | strong(X0))) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))))) [nnf transformation 16]
77. ~creative(X0) | strong(X0) [cnf transformation 38]
78. ~strong(X0) | creative(X0) [cnf transformation 38]
84. ~old(X0) | ~brave(X0) | kind(X0) [cnf transformation 43]
90. ~tall(X0) | ~quiet(X0) [cnf transformation 45]
94. curious(X0) | ~tall(X0) | curious(X0) [cnf transformation 47]
96. ~tall(X0) | ~curious(X0) | ~curious(X0) | quiet(X0) [cnf transformation 47]
123. ~humble(susan) | brave(fred) [cnf transformation 64]
131. humble(X0) | tall(X0) | ~creative(X0) | ~strong(X0) [cnf transformation 67]
132. humble(X0) | tall(X0) | strong(X0) | creative(X0) [cnf transformation 67]
138. ~kind(fred) [cnf transformation 19]
147. old(fred) [cnf transformation 25]
152. curious(X0) | ~tall(X0) [duplicate literal removal 94]
153. ~tall(X0) | ~curious(X0) | quiet(X0) [duplicate literal removal 96]
159. 2 <=> old(fred) [avatar definition]
160. old(fred) <- (2) [avatar component clause 159]
170. ~curious(X0) | ~tall(X0) [subsumption resolution 153,90]
171. ~tall(X0) [subsumption resolution 152,170]
242. 18 <=> brave(fred) [avatar definition]
244. brave(fred) <- (18) [avatar component clause 242]
251. 20 <=> humble(susan) [avatar definition]
253. ~humble(susan) <- (~20) [avatar component clause 251]
254. 18 | ~20 [avatar split clause 123,251,242]
274. humble(X0) | strong(X0) | creative(X0) [subsumption resolution 132,171]
275. humble(X0) | creative(X0) [subsumption resolution 274,78]
276. humble(X0) | ~creative(X0) | ~strong(X0) [subsumption resolution 131,171]
277. humble(X0) | ~creative(X0) [subsumption resolution 276,77]
278. humble(X0) [subsumption resolution 277,275]
301. 2 [avatar split clause 147,159]
302. $false <- (~20) [subsumption resolution 253,278]
303. 20 [avatar contradiction clause 302]
311. ~brave(fred) | kind(fred) <- (2) [resolution 84,160]
312. kind(fred) <- (2, 18) [subsumption resolution 311,244]
313. $false <- (2, 18) [subsumption resolution 312,138]
314. ~2 | ~18 [avatar contradiction clause 313]
315. $false [avatar sat refutation 254,301,303,314]
% SZS output end Proof for 319893733445168866466449
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not old or generous then john is both not humble and generous.
Everyone who is curious or humble is not tall or humble.
If someone is both strong and not strong then mary is both not brave and tall and vice versa.
Everyone who is both curious and strong is strong and vice versa.
Everyone who is both old and not calm is either humble or kind and vice versa.
Everyone who is not tall or not humble is either rich or brave.
If fred is both not brave and humble then someone is tall or not funny and vice versa.
If alice is not calm then john is not patient or tall.
If someone is not funny or generous then someone is not curious or tall and vice versa.
Everyone who is kind or not creative is both not funny and not tall.
If someone is generous or wise then someone is both not patient and wise.
If paul is not humble or not patient then fred is both patient and wise.
Everyone who is not rich or not brave is both kind and creative.
If someone is both not quiet and tall then someone is both brave and not strong and vice versa.
If someone is creative or not brave then john is both generous and not strong and vice versa.
If someone is not humble then someone is both not creative and calm.
Mary is generous or not generous.
Paul is either funny or not funny.
Someone is patient or not creative.
Someone is both not tall and creative.
Someone is either tall or wise.
John is either kind or rich.
John is patient or kind.
Lucy is creative or calm. | Lucy is not old. | contradiction | (((~old(lucy)|generous(lucy)))=>((~humble(john)&generous(john))))&
(![X]:((curious(X)|humble(X))=>(~tall(X)|humble(X))))&
((?[X]:((strong(X)&~strong(X))))<=>((~brave(mary)&tall(mary))))&
(![X]:((curious(X)&strong(X))<=>strong(X)))&
(![X]:((old(X)&~calm(X))<=>(humble(X)<~>kind(X))))&
(![X]:((~tall(X)|~humble(X))=>(rich(X)<~>brave(X))))&
(((~brave(fred)&humble(fred)))<=>(?[X]:((tall(X)|~funny(X)))))&
((~calm(alice))=>((~patient(john)|tall(john))))&
((?[X]:((~funny(X)|generous(X))))<=>(?[X]:((~curious(X)|tall(X)))))&
(![X]:((kind(X)|~creative(X))=>(~funny(X)&~tall(X))))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:((~patient(X)&wise(X)))))&
(((~humble(paul)|~patient(paul)))=>((patient(fred)&wise(fred))))&
(![X]:((~rich(X)|~brave(X))=>(kind(X)&creative(X))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:((brave(X)&~strong(X)))))&
((?[X]:((creative(X)|~brave(X))))<=>((generous(john)&~strong(john))))&
((?[X]:(~humble(X)))=>(?[X]:((~creative(X)&calm(X)))))&
((generous(mary)|~generous(mary)))&
((funny(paul)<~>~funny(paul)))&
(?[X]:((patient(X)|~creative(X))))&
(?[X]:((~tall(X)&creative(X))))&
(?[X]:((tall(X)<~>wise(X))))&
((kind(john)<~>rich(john)))&
((patient(john)|kind(john)))&
((creative(lucy)|calm(lucy))) | ~old(lucy) | [
"p0",
"p5",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3104352669027209887730056
% SZS output start Proof for 3104352669027209887730056
1. (generous(lucy) | ~old(lucy)) => (generous(john) & ~humble(john)) [input p0]
6. ! [X0] : ((~humble(X0) | ~tall(X0)) => (rich(X0) <~> brave(X0))) [input p5]
10. ! [X0] : ((~creative(X0) | kind(X0)) => (~tall(X0) & ~funny(X0))) [input p9]
13. ! [X0] : ((~brave(X0) | ~rich(X0)) => (creative(X0) & kind(X0))) [input p12]
16. ? [X0] : ~humble(X0) => ? [X0] : (calm(X0) & ~creative(X0)) [input p15]
25. ~old(lucy) [input hypothesis]
29. ? [X0] : ~humble(X0) => ? [X1] : (calm(X1) & ~creative(X1)) [rectify 16]
30. (generous(john) & ~humble(john)) | (~generous(lucy) & old(lucy)) [ennf transformation 1]
33. ! [X0] : ((rich(X0) <~> brave(X0)) | (humble(X0) & tall(X0))) [ennf transformation 6]
36. ! [X0] : ((~tall(X0) & ~funny(X0)) | (creative(X0) & ~kind(X0))) [ennf transformation 10]
39. ! [X0] : ((creative(X0) & kind(X0)) | (brave(X0) & rich(X0))) [ennf transformation 13]
40. ? [X1] : (calm(X1) & ~creative(X1)) | ! [X0] : humble(X0) [ennf transformation 29]
50. ! [X0] : (((~brave(X0) | ~rich(X0)) & (brave(X0) | rich(X0))) | (humble(X0) & tall(X0))) [nnf transformation 33]
74. ? [X0] : (calm(X0) & ~creative(X0)) | ! [X1] : humble(X1) [rectify 40]
75. ? [X0] : (calm(X0) & ~creative(X0)) => (calm(sK8) & ~creative(sK8)) [choice axiom]
76. (calm(sK8) & ~creative(sK8)) | ! [X1] : humble(X1) [skolemisation 74,75]
86. ~humble(john) | old(lucy) [cnf transformation 30]
107. ~rich(X0) | ~brave(X0) | tall(X0) [cnf transformation 50]
122. ~tall(X0) | creative(X0) [cnf transformation 36]
133. creative(X0) | rich(X0) [cnf transformation 39]
134. creative(X0) | brave(X0) [cnf transformation 39]
144. ~creative(sK8) | humble(X1) [cnf transformation 76]
158. ~old(lucy) [cnf transformation 25]
169. 3 <=> old(lucy) [avatar definition]
174. 4 <=> humble(john) [avatar definition]
176. ~humble(john) <- (~4) [avatar component clause 174]
178. 3 | ~4 [avatar split clause 86,174,169]
341. 40 <=> ! [X1] : humble(X1) [avatar definition]
342. humble(X1) <- (40) [avatar component clause 341]
349. 42 <=> creative(sK8) [avatar definition]
351. ~creative(sK8) <- (~42) [avatar component clause 349]
352. 40 | ~42 [avatar split clause 144,349,341]
391. ~3 [avatar split clause 158,169]
392. $false <- (~4, 40) [subsumption resolution 176,342]
393. 4 | ~40 [avatar contradiction clause 392]
401. rich(sK8) <- (~42) [resolution 133,351]
403. brave(sK8) <- (~42) [resolution 134,351]
478. ~brave(sK8) | tall(sK8) <- (~42) [resolution 107,401]
482. tall(sK8) <- (~42) [subsumption resolution 478,403]
485. creative(sK8) <- (~42) [resolution 482,122]
487. $false <- (~42) [subsumption resolution 485,351]
488. 42 [avatar contradiction clause 487]
489. $false [avatar sat refutation 178,352,391,393,488]
% SZS output end Proof for 3104352669027209887730056
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and not quiet then someone is not happy or not tall.
Everyone who is either not patient or not kind is patient and vice versa.
If paul is not strong then someone is either wise or not happy.
Everyone who is both tall and not happy is generous or kind and vice versa.
Everyone who is either rich or not rich is both not happy and not old.
If someone is quiet then someone is old or not calm and vice versa.
If someone is both funny and not patient then someone is quiet.
If alice is both happy and tall then paul is both curious and not calm and vice versa.
If someone is not happy then fred is brave or not kind and vice versa.
Everyone who is brave or wise is rich or strong.
If susan is creative then someone is strong and vice versa.
If someone is strong then someone is not funny.
If someone is not patient then john is both brave and old and vice versa.
If someone is not happy or strong then mary is generous or not funny.
Everyone who is generous or calm is both happy and not wise.
Everyone who is not patient or curious is tall or not humble and vice versa.
Someone is not patient or curious.
Fred is not quiet.
Alice is not patient or not happy.
John is not curious.
John is both not curious and not funny. | Fred is tall. | contradiction | ((?[X]:((happy(X)&~quiet(X))))=>(?[X]:((~happy(X)|~tall(X)))))&
(![X]:((~patient(X)<~>~kind(X))<=>patient(X)))&
((~strong(paul))=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:((tall(X)&~happy(X))<=>(generous(X)|kind(X))))&
(![X]:((rich(X)<~>~rich(X))=>(~happy(X)&~old(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((old(X)|~calm(X)))))&
((?[X]:((funny(X)&~patient(X))))=>(?[X]:(quiet(X))))&
(((happy(alice)&tall(alice)))<=>((curious(paul)&~calm(paul))))&
((?[X]:(~happy(X)))<=>((brave(fred)|~kind(fred))))&
(![X]:((brave(X)|wise(X))=>(rich(X)|strong(X))))&
((creative(susan))<=>(?[X]:(strong(X))))&
((?[X]:(strong(X)))=>(?[X]:(~funny(X))))&
((?[X]:(~patient(X)))<=>((brave(john)&old(john))))&
((?[X]:((~happy(X)|strong(X))))=>((generous(mary)|~funny(mary))))&
(![X]:((generous(X)|calm(X))=>(happy(X)&~wise(X))))&
(![X]:((~patient(X)|curious(X))<=>(tall(X)|~humble(X))))&
(?[X]:((~patient(X)|curious(X))))&
(~quiet(fred))&
((~patient(alice)|~happy(alice)))&
(~curious(john))&
((~curious(john)&~funny(john))) | tall(fred) | [
"p1",
"p3",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2994801911360189255636351
% SZS output start Proof for 2994801911360189255636351
2. ! [X0] : ((~patient(X0) <~> ~kind(X0)) <=> patient(X0)) [input p1]
4. ! [X0] : ((~happy(X0) & tall(X0)) <=> (kind(X0) | generous(X0))) [input p3]
5. ! [X0] : ((rich(X0) <~> ~rich(X0)) => (~old(X0) & ~happy(X0))) [input p4]
15. ! [X0] : ((calm(X0) | generous(X0)) => (~wise(X0) & happy(X0))) [input p14]
22. tall(fred) [input hypothesis]
33. ! [X0] : ((~old(X0) & ~happy(X0)) | (rich(X0) <=> ~rich(X0))) [ennf transformation 5]
36. ! [X0] : ((~wise(X0) & happy(X0)) | (~calm(X0) & ~generous(X0))) [ennf transformation 15]
40. ! [X0] : ((((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0))))) [nnf transformation 2]
44. ! [X0] : (((~happy(X0) & tall(X0)) | (~kind(X0) & ~generous(X0))) & ((kind(X0) | generous(X0)) | (happy(X0) | ~tall(X0)))) [nnf transformation 4]
45. ! [X0] : (((~happy(X0) & tall(X0)) | (~kind(X0) & ~generous(X0))) & (kind(X0) | generous(X0) | happy(X0) | ~tall(X0))) [flattening 44]
46. ! [X0] : ((~old(X0) & ~happy(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) [nnf transformation 33]
73. patient(X0) | ~kind(X0) | patient(X0) [cnf transformation 40]
75. ~kind(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 40]
79. kind(X0) | generous(X0) | happy(X0) | ~tall(X0) [cnf transformation 45]
84. ~happy(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 46]
85. ~happy(X0) | rich(X0) | rich(X0) [cnf transformation 46]
105. happy(X0) | ~generous(X0) [cnf transformation 36]
118. tall(fred) [cnf transformation 22]
119. ~happy(X0) | ~rich(X0) [duplicate literal removal 84]
120. ~happy(X0) | rich(X0) [duplicate literal removal 85]
123. patient(X0) | ~kind(X0) [duplicate literal removal 73]
124. ~kind(X0) | ~patient(X0) [duplicate literal removal 75]
137. ~kind(X0) [subsumption resolution 123,124]
152. ~tall(X0) | happy(X0) | generous(X0) [subsumption resolution 79,137]
154. ~happy(X0) [subsumption resolution 119,120]
202. ~generous(X0) [subsumption resolution 105,154]
210. happy(fred) | generous(fred) [resolution 152,118]
211. generous(fred) [subsumption resolution 210,154]
212. $false [subsumption resolution 211,202]
% SZS output end Proof for 2994801911360189255636351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both curious and humble.
If paul is both not wise and humble then someone is kind.
Everyone who is both humble and brave is not tall and vice versa.
If mary is either not rich or wise then susan is happy and vice versa.
If lucy is both not strong and strong then someone is both not brave and calm and vice versa.
Everyone who is not strong or calm is either not happy or calm.
If someone is not rich or strong then paul is quiet and vice versa.
Everyone who is not wise is both not quiet and not rich and vice versa.
If susan is either not calm or not patient then someone is humble or not quiet.
Everyone who is creative is both not brave and not quiet and vice versa.
Everyone who is either wise or not old is either humble or brave.
If someone is not generous then susan is not calm or rich and vice versa.
Everyone who is not tall or not brave is either creative or funny and vice versa.
If someone is funny then paul is patient.
If lucy is not strong then mary is not rich and vice versa.
Everyone who is either not curious or not humble is not wise and vice versa.
Susan is both not curious and not brave.
Someone is creative.
Someone is not strong.
Fred is not patient.
Someone is funny or curious.
Someone is not quiet or old.
Someone is not tall or tall.
Someone is both not funny and not humble. | Paul is wise. | entailment | (![X]:(~kind(X)=>(curious(X)&humble(X))))&
(((~wise(paul)&humble(paul)))=>(?[X]:(kind(X))))&
(![X]:((humble(X)&brave(X))<=>~tall(X)))&
(((~rich(mary)<~>wise(mary)))<=>(happy(susan)))&
(((~strong(lucy)&strong(lucy)))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~strong(X)|calm(X))=>(~happy(X)<~>calm(X))))&
((?[X]:((~rich(X)|strong(X))))<=>(quiet(paul)))&
(![X]:(~wise(X)<=>(~quiet(X)&~rich(X))))&
(((~calm(susan)<~>~patient(susan)))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:(creative(X)<=>(~brave(X)&~quiet(X))))&
(![X]:((wise(X)<~>~old(X))=>(humble(X)<~>brave(X))))&
((?[X]:(~generous(X)))<=>((~calm(susan)|rich(susan))))&
(![X]:((~tall(X)|~brave(X))<=>(creative(X)<~>funny(X))))&
((?[X]:(funny(X)))=>(patient(paul)))&
((~strong(lucy))<=>(~rich(mary)))&
(![X]:((~curious(X)<~>~humble(X))<=>~wise(X)))&
((~curious(susan)&~brave(susan)))&
(?[X]:(creative(X)))&
(?[X]:(~strong(X)))&
(~patient(fred))&
(?[X]:((funny(X)|curious(X))))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:((~tall(X)|tall(X))))&
(?[X]:((~funny(X)&~humble(X)))) | wise(paul) | [
"p6",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1214215041722539043647500
% SZS output start Proof for 1214215041722539043647500
7. ? [X0] : (strong(X0) | ~rich(X0)) <=> quiet(paul) [input p6]
8. ! [X0] : (~wise(X0) <=> (~rich(X0) & ~quiet(X0))) [input p7]
15. ~strong(lucy) <=> ~rich(mary) [input p14]
25. ~wise(paul) [input hypothesis]
41. (? [X0] : (strong(X0) | ~rich(X0)) | ~quiet(paul)) & (quiet(paul) | ! [X0] : (~strong(X0) & rich(X0))) [nnf transformation 7]
42. (? [X0] : (strong(X0) | ~rich(X0)) | ~quiet(paul)) & (quiet(paul) | ! [X1] : (~strong(X1) & rich(X1))) [rectify 41]
43. ? [X0] : (strong(X0) | ~rich(X0)) => (strong(sK1) | ~rich(sK1)) [choice axiom]
44. ((strong(sK1) | ~rich(sK1)) | ~quiet(paul)) & (quiet(paul) | ! [X1] : (~strong(X1) & rich(X1))) [skolemisation 42,43]
45. ! [X0] : ((~wise(X0) | (rich(X0) | quiet(X0))) & ((~rich(X0) & ~quiet(X0)) | wise(X0))) [nnf transformation 8]
46. ! [X0] : ((~wise(X0) | rich(X0) | quiet(X0)) & ((~rich(X0) & ~quiet(X0)) | wise(X0))) [flattening 45]
60. (~strong(lucy) | rich(mary)) & (~rich(mary) | strong(lucy)) [nnf transformation 15]
89. quiet(paul) | rich(X1) [cnf transformation 44]
90. quiet(paul) | ~strong(X1) [cnf transformation 44]
92. ~quiet(X0) | wise(X0) [cnf transformation 46]
114. ~rich(mary) | strong(lucy) [cnf transformation 60]
130. ~wise(paul) [cnf transformation 25]
137. 2 <=> rich(mary) [avatar definition]
138. ~rich(mary) <- (~2) [avatar component clause 137]
152. 5 <=> strong(lucy) [avatar definition]
154. strong(lucy) <- (5) [avatar component clause 152]
158. 6 <=> quiet(paul) [avatar definition]
159. quiet(paul) <- (6) [avatar component clause 158]
171. 9 <=> ! [X1] : ~strong(X1) [avatar definition]
172. ~strong(X1) <- (9) [avatar component clause 171]
173. 9 | 6 [avatar split clause 90,158,171]
175. 10 <=> ! [X1] : rich(X1) [avatar definition]
176. rich(X1) <- (10) [avatar component clause 175]
177. 10 | 6 [avatar split clause 89,158,175]
221. 5 | ~2 [avatar split clause 114,137,152]
242. wise(paul) <- (6) [resolution 92,159]
243. $false <- (6) [subsumption resolution 242,130]
244. ~6 [avatar contradiction clause 243]
245. $false <- (~2, 10) [resolution 176,138]
248. 2 | ~10 [avatar contradiction clause 245]
249. $false <- (5, 9) [subsumption resolution 154,172]
250. ~5 | ~9 [avatar contradiction clause 249]
251. $false [avatar sat refutation 173,177,221,244,248,250]
% SZS output end Proof for 1214215041722539043647500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not creative and happy then susan is both not rich and not brave and vice versa. Everyone who is either not creative or humble is either not rich or quiet. Everyone who is both rich and not rich is tall or kind and vice versa. If alice is both not kind and not patient then someone is kind. If someone is both not wise and curious then fred is not happy or not strong and vice versa. If mary is either brave or not patient then lucy is not wise. If someone is wise or funny then paul is either generous or not quiet and vice versa. Everyone who is both generous and wise is both brave and not kind and vice versa. Everyone who is rich is both old and rich. Everyone who is not rich or happy is both tall and strong. If fred is not wise or not generous then someone is either not humble or not quiet and vice versa. Everyone who is either creative or not humble is both not generous and not patient. If paul is both patient and funny then someone is humble or patient and vice versa. If someone is brave or not quiet then alice is not creative. If susan is not patient or not humble then fred is either generous or curious and vice versa. If susan is wise then susan is both happy and quiet and vice versa. Lucy is both not patient and not quiet. Susan is both creative and old. Lucy is calm or not funny. Fred is either old or calm. Someone is not kind. | Lucy is rich. | entailment | (((~creative(susan)&happy(susan)))<=>((~rich(susan)&~brave(susan))))&
(![X]:((~creative(X)<~>humble(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((rich(X)&~rich(X))<=>(tall(X)|kind(X))))&
(((~kind(alice)&~patient(alice)))=>(?[X]:(kind(X))))&
((?[X]:((~wise(X)&curious(X))))<=>((~happy(fred)|~strong(fred))))&
(((brave(mary)<~>~patient(mary)))=>(~wise(lucy)))&
((?[X]:((wise(X)|funny(X))))<=>((generous(paul)<~>~quiet(paul))))&
(![X]:((generous(X)&wise(X))<=>(brave(X)&~kind(X))))&
(![X]:(rich(X)=>(old(X)&rich(X))))&
(![X]:((~rich(X)|happy(X))=>(tall(X)&strong(X))))&
(((~wise(fred)|~generous(fred)))<=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(![X]:((creative(X)<~>~humble(X))=>(~generous(X)&~patient(X))))&
(((patient(paul)&funny(paul)))<=>(?[X]:((humble(X)|patient(X)))))&
((?[X]:((brave(X)|~quiet(X))))=>(~creative(alice)))&
(((~patient(susan)|~humble(susan)))<=>((generous(fred)<~>curious(fred))))&
((wise(susan))<=>((happy(susan)&quiet(susan))))&
((~patient(lucy)&~quiet(lucy)))&
((creative(susan)&old(susan)))&
((calm(lucy)|~funny(lucy)))&
((old(fred)<~>calm(fred)))&
(?[X]:(~kind(X))) | rich(lucy) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3203178694091733547424804
% SZS output start Proof for 3203178694091733547424804
3. ! [X0] : ((~rich(X0) & rich(X0)) <=> (kind(X0) | tall(X0))) [input p2]
10. ! [X0] : ((happy(X0) | ~rich(X0)) => (strong(X0) & tall(X0))) [input p9]
22. ~rich(lucy) [input hypothesis]
28. ! [X0] : ((strong(X0) & tall(X0)) | (~happy(X0) & rich(X0))) [ennf transformation 10]
34. ! [X0] : (((~rich(X0) & rich(X0)) | (~kind(X0) & ~tall(X0))) & ((kind(X0) | tall(X0)) | (rich(X0) | ~rich(X0)))) [nnf transformation 3]
35. ! [X0] : (((~rich(X0) & rich(X0)) | (~kind(X0) & ~tall(X0))) & (kind(X0) | tall(X0) | rich(X0) | ~rich(X0))) [flattening 34]
77. rich(X0) | ~tall(X0) [cnf transformation 35]
79. ~rich(X0) | ~tall(X0) [cnf transformation 35]
101. tall(X0) | rich(X0) [cnf transformation 28]
139. ~rich(lucy) [cnf transformation 22]
161. ~tall(X0) [subsumption resolution 77,79]
233. rich(X0) [subsumption resolution 101,161]
350. $false [subsumption resolution 139,233]
% SZS output end Proof for 3203178694091733547424804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or kind is not old. If someone is not kind then someone is not brave or creative. If someone is either not funny or wise then lucy is both not patient and wise and vice versa. Everyone who is either brave or not curious is calm or not wise. Everyone who is creative is calm or not strong and vice versa. Everyone who is not creative or not funny is brave and vice versa. If fred is brave then someone is funny and vice versa. Everyone who is both not calm and patient is either not curious or not calm and vice versa. Everyone who is both old and not curious is rich. If susan is both rich and not quiet then alice is either not patient or not happy and vice versa. If fred is not funny then someone is creative or not old and vice versa. Everyone who is both tall and not humble is either brave or curious and vice versa. If john is either rich or not tall then mary is either generous or creative. If paul is rich then someone is both not tall and wise and vice versa. Everyone who is either not curious or generous is either funny or not curious. Everyone who is either old or not generous is old or kind and vice versa. Mary is old or not patient. Someone is not tall. John is either not old or curious. Fred is generous. Someone is strong. Someone is not strong. | Paul is generous. | neutral | (![X]:((generous(X)|kind(X))=>~old(X)))&
((?[X]:(~kind(X)))=>(?[X]:((~brave(X)|creative(X)))))&
((?[X]:((~funny(X)<~>wise(X))))<=>((~patient(lucy)&wise(lucy))))&
(![X]:((brave(X)<~>~curious(X))=>(calm(X)|~wise(X))))&
(![X]:(creative(X)<=>(calm(X)|~strong(X))))&
(![X]:((~creative(X)|~funny(X))<=>brave(X)))&
((brave(fred))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)&patient(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((old(X)&~curious(X))=>rich(X)))&
(((rich(susan)&~quiet(susan)))<=>((~patient(alice)<~>~happy(alice))))&
((~funny(fred))<=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((tall(X)&~humble(X))<=>(brave(X)<~>curious(X))))&
(((rich(john)<~>~tall(john)))=>((generous(mary)<~>creative(mary))))&
((rich(paul))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((~curious(X)<~>generous(X))=>(funny(X)<~>~curious(X))))&
(![X]:((old(X)<~>~generous(X))<=>(old(X)|kind(X))))&
((old(mary)|~patient(mary)))&
(?[X]:(~tall(X)))&
((~old(john)<~>curious(john)))&
(generous(fred))&
(?[X]:(strong(X)))&
(?[X]:(~strong(X))) | generous(paul) | [] | null | 0 |
Everyone who is either patient or old is both not curious and not humble.
If susan is either strong or not happy then someone is either happy or generous and vice versa.
Everyone who is both not rich and generous is both not tall and patient.
Everyone who is not tall is both funny and not calm.
Everyone who is both not funny and not humble is not brave or creative and vice versa.
If susan is both not humble and not happy then fred is either brave or not brave.
If susan is not funny then alice is not kind or happy.
If someone is not calm then susan is either generous or tall.
Everyone who is calm or not generous is both not creative and patient and vice versa.
Everyone who is both not old and kind is tall or not old and vice versa.
Everyone who is both rich and not old is old or not quiet.
Everyone who is happy or funny is both creative and kind.
If lucy is both not funny and not tall then someone is either not curious or not wise.
Everyone who is both not curious and creative is both not quiet and not generous.
Everyone who is either not tall or old is humble.
If alice is quiet or strong then someone is either calm or not tall.
Someone is happy or rich.
Susan is either humble or rich.
Someone is not rich or patient.
Someone is wise or not strong. | Alice is humble. | contradiction | (![X]:((patient(X)<~>old(X))=>(~curious(X)&~humble(X))))&
(((strong(susan)<~>~happy(susan)))<=>(?[X]:((happy(X)<~>generous(X)))))&
(![X]:((~rich(X)&generous(X))=>(~tall(X)&patient(X))))&
(![X]:(~tall(X)=>(funny(X)&~calm(X))))&
(![X]:((~funny(X)&~humble(X))<=>(~brave(X)|creative(X))))&
(((~humble(susan)&~happy(susan)))=>((brave(fred)<~>~brave(fred))))&
((~funny(susan))=>((~kind(alice)|happy(alice))))&
((?[X]:(~calm(X)))=>((generous(susan)<~>tall(susan))))&
(![X]:((calm(X)|~generous(X))<=>(~creative(X)&patient(X))))&
(![X]:((~old(X)&kind(X))<=>(tall(X)|~old(X))))&
(![X]:((rich(X)&~old(X))=>(old(X)|~quiet(X))))&
(![X]:((happy(X)|funny(X))=>(creative(X)&kind(X))))&
(((~funny(lucy)&~tall(lucy)))=>(?[X]:((~curious(X)<~>~wise(X)))))&
(![X]:((~curious(X)&creative(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~tall(X)<~>old(X))=>humble(X)))&
(((quiet(alice)|strong(alice)))=>(?[X]:((calm(X)<~>~tall(X)))))&
(?[X]:((happy(X)|rich(X))))&
((humble(susan)<~>rich(susan)))&
(?[X]:((~rich(X)|patient(X))))&
(?[X]:((wise(X)|~strong(X)))) | humble(alice) | [
"p3",
"p4",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8885155252844605057704744
% SZS output start Proof for 8885155252844605057704744
4. ! [X0] : (~tall(X0) => (~calm(X0) & funny(X0))) [input p3]
5. ! [X0] : ((~humble(X0) & ~funny(X0)) <=> (creative(X0) | ~brave(X0))) [input p4]
7. ~funny(susan) => (happy(alice) | ~kind(alice)) [input p6]
10. ! [X0] : ((kind(X0) & ~old(X0)) <=> (~old(X0) | tall(X0))) [input p9]
12. ! [X0] : ((funny(X0) | happy(X0)) => (kind(X0) & creative(X0))) [input p11]
21. humble(alice) [input hypothesis]
28. ! [X0] : ((~calm(X0) & funny(X0)) | tall(X0)) [ennf transformation 4]
31. (happy(alice) | ~kind(alice)) | funny(susan) [ennf transformation 7]
32. happy(alice) | ~kind(alice) | funny(susan) [flattening 31]
34. ! [X0] : ((kind(X0) & creative(X0)) | (~funny(X0) & ~happy(X0))) [ennf transformation 12]
46. ! [X0] : (((~humble(X0) & ~funny(X0)) | (~creative(X0) & brave(X0))) & ((creative(X0) | ~brave(X0)) | (humble(X0) | funny(X0)))) [nnf transformation 5]
47. ! [X0] : (((~humble(X0) & ~funny(X0)) | (~creative(X0) & brave(X0))) & (creative(X0) | ~brave(X0) | humble(X0) | funny(X0))) [flattening 46]
52. ! [X0] : (((kind(X0) & ~old(X0)) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | (~kind(X0) | old(X0)))) [nnf transformation 10]
53. ! [X0] : (((kind(X0) & ~old(X0)) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | ~kind(X0) | old(X0))) [flattening 52]
82. funny(X0) | tall(X0) [cnf transformation 28]
86. ~creative(X0) | ~funny(X0) [cnf transformation 47]
88. ~creative(X0) | ~humble(X0) [cnf transformation 47]
91. happy(alice) | ~kind(alice) | funny(susan) [cnf transformation 32]
102. ~tall(X0) | kind(X0) [cnf transformation 53]
104. ~happy(X0) | creative(X0) [cnf transformation 34]
105. creative(X0) | ~funny(X0) [cnf transformation 34]
120. humble(alice) [cnf transformation 21]
152. 7 <=> funny(susan) [avatar definition]
154. funny(susan) <- (7) [avatar component clause 152]
156. 8 <=> kind(alice) [avatar definition]
158. ~kind(alice) <- (~8) [avatar component clause 156]
160. 9 <=> happy(alice) [avatar definition]
162. happy(alice) <- (9) [avatar component clause 160]
163. 7 | ~8 | 9 [avatar split clause 91,160,156,152]
177. ~funny(X0) [subsumption resolution 105,86]
229. tall(X0) [resolution 82,177]
239. kind(X0) [resolution 102,229]
240. $false <- (~8) [resolution 239,158]
241. 8 [avatar contradiction clause 240]
242. $false <- (7) [subsumption resolution 154,177]
243. ~7 [avatar contradiction clause 242]
246. creative(alice) <- (9) [resolution 104,162]
268. ~humble(alice) <- (9) [resolution 246,88]
270. $false <- (9) [subsumption resolution 268,120]
271. ~9 [avatar contradiction clause 270]
272. $false [avatar sat refutation 163,241,243,271]
% SZS output end Proof for 8885155252844605057704744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not tall is generous. If fred is either not generous or quiet then lucy is not strong. Everyone who is either not creative or humble is either quiet or not patient and vice versa. If someone is either strong or not curious then john is not strong and vice versa. If someone is not kind or not patient then lucy is both not rich and tall. If someone is either not tall or not creative then someone is not curious. Everyone who is both kind and not calm is not funny or brave and vice versa. Everyone who is not happy is not rich. If susan is not wise then paul is brave and vice versa. Everyone who is both wise and brave is either not funny or happy. Everyone who is happy is both creative and not tall and vice versa. Everyone who is both not creative and wise is either brave or calm and vice versa. If mary is both not old and not wise then someone is tall and vice versa. Everyone who is patient is either not creative or old and vice versa. Everyone who is not strong or not quiet is rich or patient and vice versa. Everyone who is humble or quiet is both generous and old. Someone is not brave. Someone is either not creative or not tall. Someone is not humble or kind. Lucy is not funny. Paul is not rich or not generous. Someone is humble. Susan is not humble. Someone is generous or curious. | John is old. | entailment | (![X]:((strong(X)&~tall(X))=>generous(X)))&
(((~generous(fred)<~>quiet(fred)))=>(~strong(lucy)))&
(![X]:((~creative(X)<~>humble(X))<=>(quiet(X)<~>~patient(X))))&
((?[X]:((strong(X)<~>~curious(X))))<=>(~strong(john)))&
((?[X]:((~kind(X)|~patient(X))))=>((~rich(lucy)&tall(lucy))))&
((?[X]:((~tall(X)<~>~creative(X))))=>(?[X]:(~curious(X))))&
(![X]:((kind(X)&~calm(X))<=>(~funny(X)|brave(X))))&
(![X]:(~happy(X)=>~rich(X)))&
((~wise(susan))<=>(brave(paul)))&
(![X]:((wise(X)&brave(X))=>(~funny(X)<~>happy(X))))&
(![X]:(happy(X)<=>(creative(X)&~tall(X))))&
(![X]:((~creative(X)&wise(X))<=>(brave(X)<~>calm(X))))&
(((~old(mary)&~wise(mary)))<=>(?[X]:(tall(X))))&
(![X]:(patient(X)<=>(~creative(X)<~>old(X))))&
(![X]:((~strong(X)|~quiet(X))<=>(rich(X)|patient(X))))&
(![X]:((humble(X)|quiet(X))=>(generous(X)&old(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~creative(X)<~>~tall(X))))&
(?[X]:((~humble(X)|kind(X))))&
(~funny(lucy))&
((~rich(paul)|~generous(paul)))&
(?[X]:(humble(X)))&
(~humble(susan))&
(?[X]:((generous(X)|curious(X)))) | old(john) | [
"p2",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 421596030532897613221526
% SZS output start Proof for 421596030532897613221526
3. ! [X0] : ((~creative(X0) <~> humble(X0)) <=> (quiet(X0) <~> ~patient(X0))) [input p2]
14. ! [X0] : (patient(X0) <=> (~creative(X0) <~> old(X0))) [input p13]
16. ! [X0] : ((quiet(X0) | humble(X0)) => (old(X0) & generous(X0))) [input p15]
25. ~old(john) [input hypothesis]
35. ! [X0] : ((old(X0) & generous(X0)) | (~quiet(X0) & ~humble(X0))) [ennf transformation 16]
37. ! [X0] : ((((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) & (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))))) [nnf transformation 3]
59. ! [X0] : ((patient(X0) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) & (((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | ~patient(X0))) [nnf transformation 14]
76. ~patient(X0) | quiet(X0) | humble(X0) | creative(X0) [cnf transformation 37]
81. ~creative(X0) | humble(X0) | quiet(X0) | patient(X0) [cnf transformation 37]
116. ~patient(X0) | ~creative(X0) | old(X0) [cnf transformation 59]
118. old(X0) | patient(X0) | creative(X0) [cnf transformation 59]
126. ~humble(X0) | old(X0) [cnf transformation 35]
127. ~quiet(X0) | old(X0) [cnf transformation 35]
137. ~old(john) [cnf transformation 25]
291. patient(john) | creative(john) [resolution 118,137]
358. 38 <=> creative(john) [avatar definition]
360. creative(john) <- (38) [avatar component clause 358]
362. 39 <=> patient(john) [avatar definition]
363. ~patient(john) <- (~39) [avatar component clause 362]
364. patient(john) <- (39) [avatar component clause 362]
365. 38 | 39 [avatar split clause 291,362,358]
555. quiet(john) | humble(john) | creative(john) <- (39) [resolution 364,76]
557. ~creative(john) | old(john) <- (39) [resolution 364,116]
560. 62 <=> quiet(john) [avatar definition]
561. quiet(john) <- (62) [avatar component clause 560]
564. 63 <=> humble(john) [avatar definition]
565. humble(john) <- (63) [avatar component clause 564]
570. ~creative(john) <- (39) [subsumption resolution 557,137]
571. ~38 | ~39 [avatar split clause 570,362,358]
572. 38 | 63 | 62 | ~39 [avatar split clause 555,362,560,564,358]
576. humble(john) | quiet(john) | patient(john) <- (38) [resolution 360,81]
578. humble(john) | quiet(john) <- (38, ~39) [subsumption resolution 576,363]
579. 62 | 63 | ~38 | 39 [avatar split clause 578,362,358,564,560]
685. old(john) <- (62) [resolution 561,127]
687. $false <- (62) [subsumption resolution 685,137]
688. ~62 [avatar contradiction clause 687]
697. old(john) <- (63) [resolution 565,126]
699. $false <- (63) [subsumption resolution 697,137]
700. ~63 [avatar contradiction clause 699]
701. $false [avatar sat refutation 365,571,572,579,688,700]
% SZS output end Proof for 421596030532897613221526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or calm is brave or not funny and vice versa. Everyone who is not creative is rich or patient. If someone is both generous and not brave then someone is both creative and quiet. If fred is not strong or not funny then paul is old and vice versa. Everyone who is not happy is both wise and not old and vice versa. Everyone who is rich is strong and vice versa. Everyone who is either not brave or wise is either not creative or brave and vice versa. If someone is not happy then someone is both kind and not happy. If susan is both not creative and patient then someone is not strong or quiet and vice versa. If susan is either strong or kind then alice is both humble and not creative and vice versa. Everyone who is either not generous or not rich is either not happy or not calm and vice versa. Everyone who is not tall or happy is brave and vice versa. Everyone who is strong is humble or not rich and vice versa. If someone is either brave or strong then someone is both not wise and old. If fred is either not generous or not old then someone is not old. Everyone who is not kind or not creative is not happy or creative. Someone is both old and patient. Susan is either quiet or brave. Someone is either quiet or funny. Susan is either patient or not calm. Paul is wise. Someone is old or not generous. | Fred is calm. | entailment | (![X]:((~brave(X)|calm(X))<=>(brave(X)|~funny(X))))&
(![X]:(~creative(X)=>(rich(X)|patient(X))))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:((creative(X)&quiet(X)))))&
(((~strong(fred)|~funny(fred)))<=>(old(paul)))&
(![X]:(~happy(X)<=>(wise(X)&~old(X))))&
(![X]:(rich(X)<=>strong(X)))&
(![X]:((~brave(X)<~>wise(X))<=>(~creative(X)<~>brave(X))))&
((?[X]:(~happy(X)))=>(?[X]:((kind(X)&~happy(X)))))&
(((~creative(susan)&patient(susan)))<=>(?[X]:((~strong(X)|quiet(X)))))&
(((strong(susan)<~>kind(susan)))<=>((humble(alice)&~creative(alice))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~happy(X)<~>~calm(X))))&
(![X]:((~tall(X)|happy(X))<=>brave(X)))&
(![X]:(strong(X)<=>(humble(X)|~rich(X))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((~wise(X)&old(X)))))&
(((~generous(fred)<~>~old(fred)))=>(?[X]:(~old(X))))&
(![X]:((~kind(X)|~creative(X))=>(~happy(X)|creative(X))))&
(?[X]:((old(X)&patient(X))))&
((quiet(susan)<~>brave(susan)))&
(?[X]:((quiet(X)<~>funny(X))))&
((patient(susan)<~>~calm(susan)))&
(wise(paul))&
(?[X]:((old(X)|~generous(X)))) | calm(fred) | [
"p0",
"p4",
"p5",
"p6",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3761361111312310537264722
% SZS output start Proof for 3761361111312310537264722
1. ! [X0] : ((calm(X0) | ~brave(X0)) <=> (~funny(X0) | brave(X0))) [input p0]
5. ! [X0] : (~happy(X0) <=> (~old(X0) & wise(X0))) [input p4]
6. ! [X0] : (rich(X0) <=> strong(X0)) [input p5]
7. ! [X0] : ((~brave(X0) <~> wise(X0)) <=> (~creative(X0) <~> brave(X0))) [input p6]
13. ! [X0] : (strong(X0) <=> (~rich(X0) | humble(X0))) [input p12]
14. ? [X0] : (brave(X0) <~> strong(X0)) => ? [X0] : (old(X0) & ~wise(X0)) [input p13]
16. ! [X0] : ((~creative(X0) | ~kind(X0)) => (creative(X0) | ~happy(X0))) [input p15]
23. ~calm(fred) [input hypothesis]
26. ? [X0] : (brave(X0) <~> strong(X0)) => ? [X1] : (old(X1) & ~wise(X1)) [rectify 14]
31. ? [X1] : (old(X1) & ~wise(X1)) | ! [X0] : (brave(X0) <=> strong(X0)) [ennf transformation 26]
33. ! [X0] : ((creative(X0) | ~happy(X0)) | (creative(X0) & kind(X0))) [ennf transformation 16]
34. ! [X0] : (creative(X0) | ~happy(X0) | (creative(X0) & kind(X0))) [flattening 33]
35. ! [X0] : (((calm(X0) | ~brave(X0)) | (funny(X0) & ~brave(X0))) & ((~funny(X0) | brave(X0)) | (~calm(X0) & brave(X0)))) [nnf transformation 1]
36. ! [X0] : ((calm(X0) | ~brave(X0) | (funny(X0) & ~brave(X0))) & (~funny(X0) | brave(X0) | (~calm(X0) & brave(X0)))) [flattening 35]
42. ! [X0] : ((~happy(X0) | (old(X0) | ~wise(X0))) & ((~old(X0) & wise(X0)) | happy(X0))) [nnf transformation 5]
43. ! [X0] : ((~happy(X0) | old(X0) | ~wise(X0)) & ((~old(X0) & wise(X0)) | happy(X0))) [flattening 42]
44. ! [X0] : ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))) [nnf transformation 6]
45. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [nnf transformation 7]
59. ! [X0] : ((strong(X0) | (rich(X0) & ~humble(X0))) & ((~rich(X0) | humble(X0)) | ~strong(X0))) [nnf transformation 13]
60. ! [X0] : ((strong(X0) | (rich(X0) & ~humble(X0))) & (~rich(X0) | humble(X0) | ~strong(X0))) [flattening 59]
61. ? [X1] : (old(X1) & ~wise(X1)) | ! [X0] : ((brave(X0) | ~strong(X0)) & (strong(X0) | ~brave(X0))) [nnf transformation 31]
62. ? [X0] : (old(X0) & ~wise(X0)) | ! [X1] : ((brave(X1) | ~strong(X1)) & (strong(X1) | ~brave(X1))) [rectify 61]
63. ? [X0] : (old(X0) & ~wise(X0)) => (old(sK3) & ~wise(sK3)) [choice axiom]
64. (old(sK3) & ~wise(sK3)) | ! [X1] : ((brave(X1) | ~strong(X1)) & (strong(X1) | ~brave(X1))) [skolemisation 62,63]
79. calm(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 36]
87. wise(X0) | happy(X0) [cnf transformation 43]
90. ~rich(X0) | strong(X0) [cnf transformation 44]
91. ~strong(X0) | rich(X0) [cnf transformation 44]
92. brave(X0) | ~creative(X0) | wise(X0) | brave(X0) [cnf transformation 45]
95. ~brave(X0) | creative(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 45]
97. wise(X0) | ~brave(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 45]
98. ~wise(X0) | brave(X0) | brave(X0) | creative(X0) [cnf transformation 45]
126. strong(X0) | rich(X0) [cnf transformation 60]
128. ~wise(sK3) | brave(X1) | ~strong(X1) [cnf transformation 64]
134. creative(X0) | ~happy(X0) | creative(X0) [cnf transformation 34]
145. ~calm(fred) [cnf transformation 23]
146. ~happy(X0) | creative(X0) [duplicate literal removal 134]
147. brave(X0) | ~creative(X0) | wise(X0) [duplicate literal removal 92]
148. ~brave(X0) | creative(X0) | ~wise(X0) [duplicate literal removal 95]
149. ~creative(X0) | ~brave(X0) | wise(X0) [duplicate literal removal 97]
150. ~wise(X0) | brave(X0) | creative(X0) [duplicate literal removal 98]
152. ~brave(X0) | calm(X0) [duplicate literal removal 79]
181. ~wise(X0) | creative(X0) [subsumption resolution 148,150]
182. ~creative(X0) | wise(X0) [subsumption resolution 147,149]
205. 12 <=> ! [X0] : strong(X0) [avatar definition]
206. strong(X0) <- (12) [avatar component clause 205]
245. rich(X0) [subsumption resolution 126,91]
248. 20 <=> ! [X1] : (brave(X1) | ~strong(X1)) [avatar definition]
249. brave(X1) | ~strong(X1) <- (20) [avatar component clause 248]
260. 23 <=> wise(sK3) [avatar definition]
262. ~wise(sK3) <- (~23) [avatar component clause 260]
263. 20 | ~23 [avatar split clause 128,260,248]
322. strong(X0) [resolution 90,245]
323. 12 [avatar split clause 322,205]
341. creative(X0) | happy(X0) [resolution 181,87]
342. creative(X0) [subsumption resolution 341,146]
357. wise(X0) [resolution 182,342]
428. brave(X1) <- (12, 20) [subsumption resolution 249,206]
430. calm(X1) <- (12, 20) [resolution 428,152]
445. $false <- (12, 20) [resolution 430,145]
446. ~12 | ~20 [avatar contradiction clause 445]
455. $false <- (~23) [resolution 357,262]
459. 23 [avatar contradiction clause 455]
460. $false [avatar sat refutation 263,323,446,459]
% SZS output end Proof for 3761361111312310537264722
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not tall then paul is not happy or humble and vice versa. If susan is both creative and not patient then alice is not kind or generous and vice versa. Everyone who is either not happy or not strong is both not rich and brave and vice versa. Everyone who is wise or not rich is old and vice versa. If paul is both strong and not patient then lucy is either creative or old and vice versa. If someone is not humble then fred is not kind or kind. If someone is not patient then susan is both not tall and not old. Everyone who is both not patient and rich is wise and vice versa. If someone is both wise and not old then paul is both generous and kind. Everyone who is both not rich and not calm is both patient and not calm and vice versa. If someone is brave then mary is either not old or not strong and vice versa. If lucy is creative then paul is either not brave or not funny. Everyone who is both tall and strong is not old or not curious and vice versa. If john is brave then someone is both wise and brave. Everyone who is either not generous or quiet is both not funny and not strong. If john is both not curious and strong then paul is not humble. Someone is both old and tall. Someone is humble. Someone is either old or not wise. Fred is not happy or not tall. Someone is not patient or not curious. Alice is either kind or not humble. Someone is old or not funny. Someone is both not tall and humble. | Mary is not patient. | contradiction | ((~tall(paul))<=>((~happy(paul)|humble(paul))))&
(((creative(susan)&~patient(susan)))<=>((~kind(alice)|generous(alice))))&
(![X]:((~happy(X)<~>~strong(X))<=>(~rich(X)&brave(X))))&
(![X]:((wise(X)|~rich(X))<=>old(X)))&
(((strong(paul)&~patient(paul)))<=>((creative(lucy)<~>old(lucy))))&
((?[X]:(~humble(X)))=>((~kind(fred)|kind(fred))))&
((?[X]:(~patient(X)))=>((~tall(susan)&~old(susan))))&
(![X]:((~patient(X)&rich(X))<=>wise(X)))&
((?[X]:((wise(X)&~old(X))))=>((generous(paul)&kind(paul))))&
(![X]:((~rich(X)&~calm(X))<=>(patient(X)&~calm(X))))&
((?[X]:(brave(X)))<=>((~old(mary)<~>~strong(mary))))&
((creative(lucy))=>((~brave(paul)<~>~funny(paul))))&
(![X]:((tall(X)&strong(X))<=>(~old(X)|~curious(X))))&
((brave(john))=>(?[X]:((wise(X)&brave(X)))))&
(![X]:((~generous(X)<~>quiet(X))=>(~funny(X)&~strong(X))))&
(((~curious(john)&strong(john)))=>(~humble(paul)))&
(?[X]:((old(X)&tall(X))))&
(?[X]:(humble(X)))&
(?[X]:((old(X)<~>~wise(X))))&
((~happy(fred)|~tall(fred)))&
(?[X]:((~patient(X)|~curious(X))))&
((kind(alice)<~>~humble(alice)))&
(?[X]:((old(X)|~funny(X))))&
(?[X]:((~tall(X)&humble(X)))) | ~patient(mary) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5499292800687694580350517
% SZS output start Proof for 5499292800687694580350517
7. ? [X0] : ~patient(X0) => (~old(susan) & ~tall(susan)) [input p6]
13. ! [X0] : ((strong(X0) & tall(X0)) <=> (~curious(X0) | ~old(X0))) [input p12]
25. ~patient(mary) [input hypothesis]
28. (~old(susan) & ~tall(susan)) | ! [X0] : patient(X0) [ennf transformation 7]
54. ! [X0] : (((strong(X0) & tall(X0)) | (curious(X0) & old(X0))) & ((~curious(X0) | ~old(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 13]
55. ! [X0] : (((strong(X0) & tall(X0)) | (curious(X0) & old(X0))) & (~curious(X0) | ~old(X0) | ~strong(X0) | ~tall(X0))) [flattening 54]
97. ~tall(susan) | patient(X0) [cnf transformation 28]
98. ~old(susan) | patient(X0) [cnf transformation 28]
115. old(X0) | tall(X0) [cnf transformation 55]
138. ~patient(mary) [cnf transformation 25]
198. 12 <=> ! [X0] : patient(X0) [avatar definition]
199. patient(X0) <- (12) [avatar component clause 198]
201. 13 <=> old(susan) [avatar definition]
203. ~old(susan) <- (~13) [avatar component clause 201]
204. 12 | ~13 [avatar split clause 98,201,198]
206. 14 <=> tall(susan) [avatar definition]
208. ~tall(susan) <- (~14) [avatar component clause 206]
209. 12 | ~14 [avatar split clause 97,206,198]
305. tall(susan) <- (~13) [resolution 115,203]
309. $false <- (~13, ~14) [subsumption resolution 305,208]
310. 13 | 14 [avatar contradiction clause 309]
311. $false <- (12) [resolution 199,138]
314. ~12 [avatar contradiction clause 311]
315. $false [avatar sat refutation 204,209,310,314]
% SZS output end Proof for 5499292800687694580350517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is patient or quiet.
Everyone who is not creative or kind is patient and vice versa.
If fred is creative or not generous then john is not creative.
Everyone who is calm or curious is both not curious and not happy and vice versa.
If fred is either calm or not calm then someone is not kind or patient and vice versa.
Everyone who is rich is not brave and vice versa.
If someone is not rich or not curious then someone is not quiet and vice versa.
Everyone who is both funny and generous is happy.
If susan is wise then lucy is both kind and not patient.
Everyone who is both generous and not humble is both not happy and calm.
If lucy is creative or not rich then someone is both brave and not funny.
Everyone who is either creative or not wise is not old and vice versa.
If paul is both not kind and funny then someone is not old or not quiet and vice versa.
Everyone who is brave is creative or patient.
If susan is old then someone is both not kind and happy and vice versa.
If someone is tall then paul is not rich or not old.
Someone is either not patient or funny.
Someone is both not creative and brave.
Someone is not humble or not generous.
Someone is either not wise or humble.
Someone is not kind.
Someone is old or humble.
Lucy is old.
John is happy or kind. | Susan is not wise. | entailment | (![X]:((~humble(X)&quiet(X))=>(patient(X)|quiet(X))))&
(![X]:((~creative(X)|kind(X))<=>patient(X)))&
(((creative(fred)|~generous(fred)))=>(~creative(john)))&
(![X]:((calm(X)|curious(X))<=>(~curious(X)&~happy(X))))&
(((calm(fred)<~>~calm(fred)))<=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:(rich(X)<=>~brave(X)))&
((?[X]:((~rich(X)|~curious(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)&generous(X))=>happy(X)))&
((wise(susan))=>((kind(lucy)&~patient(lucy))))&
(![X]:((generous(X)&~humble(X))=>(~happy(X)&calm(X))))&
(((creative(lucy)|~rich(lucy)))=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:((creative(X)<~>~wise(X))<=>~old(X)))&
(((~kind(paul)&funny(paul)))<=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:(brave(X)=>(creative(X)|patient(X))))&
((old(susan))<=>(?[X]:((~kind(X)&happy(X)))))&
((?[X]:(tall(X)))=>((~rich(paul)|~old(paul))))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((~creative(X)&brave(X))))&
(?[X]:((~humble(X)|~generous(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)|humble(X))))&
(old(lucy))&
((happy(john)|kind(john))) | ~wise(susan) | [
"p1",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4347846288733951221513368
% SZS output start Proof for 4347846288733951221513368
2. ! [X0] : ((kind(X0) | ~creative(X0)) <=> patient(X0)) [input p1]
9. wise(susan) => (~patient(lucy) & kind(lucy)) [input p8]
25. wise(susan) [input hypothesis]
33. (~patient(lucy) & kind(lucy)) | ~wise(susan) [ennf transformation 9]
39. ! [X0] : (((kind(X0) | ~creative(X0)) | ~patient(X0)) & (patient(X0) | (~kind(X0) & creative(X0)))) [nnf transformation 2]
40. ! [X0] : ((kind(X0) | ~creative(X0) | ~patient(X0)) & (patient(X0) | (~kind(X0) & creative(X0)))) [flattening 39]
81. ~kind(X0) | patient(X0) [cnf transformation 40]
102. kind(lucy) | ~wise(susan) [cnf transformation 33]
103. ~patient(lucy) | ~wise(susan) [cnf transformation 33]
134. wise(susan) [cnf transformation 25]
155. 4 <=> wise(susan) [avatar definition]
159. 5 <=> patient(lucy) [avatar definition]
161. ~patient(lucy) <- (~5) [avatar component clause 159]
162. ~4 | ~5 [avatar split clause 103,159,155]
164. 6 <=> kind(lucy) [avatar definition]
166. kind(lucy) <- (6) [avatar component clause 164]
167. ~4 | 6 [avatar split clause 102,164,155]
280. 4 [avatar split clause 134,155]
286. patient(lucy) <- (6) [resolution 81,166]
287. $false <- (~5, 6) [subsumption resolution 286,161]
288. 5 | ~6 [avatar contradiction clause 287]
289. $false [avatar sat refutation 162,167,280,288]
% SZS output end Proof for 4347846288733951221513368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is creative or not brave then someone is tall.
If someone is not humble or not funny then john is not generous or not quiet and vice versa.
Everyone who is old or humble is both tall and generous and vice versa.
Everyone who is not patient or not rich is either not quiet or not old.
Everyone who is brave is kind or curious.
If someone is generous then someone is not funny.
Everyone who is not humble or creative is both old and not generous.
If fred is not curious or old then mary is both not happy and brave.
If mary is either wise or generous then someone is tall and vice versa.
Everyone who is happy or not creative is both brave and patient.
Everyone who is both funny and curious is both creative and not brave and vice versa.
Everyone who is generous is strong or calm and vice versa.
Everyone who is not wise is both not creative and not strong.
If someone is both not kind and rich then someone is generous.
Everyone who is both wise and not quiet is quiet.
If alice is not generous then mary is either old or not rich.
Someone is both not kind and calm.
Fred is not rich or not old.
Mary is tall or not kind.
Someone is happy or generous.
Lucy is not calm or not kind.
John is both kind and rich. | John is strong. | contradiction | (((creative(alice)|~brave(alice)))=>(?[X]:(tall(X))))&
((?[X]:((~humble(X)|~funny(X))))<=>((~generous(john)|~quiet(john))))&
(![X]:((old(X)|humble(X))<=>(tall(X)&generous(X))))&
(![X]:((~patient(X)|~rich(X))=>(~quiet(X)<~>~old(X))))&
(![X]:(brave(X)=>(kind(X)|curious(X))))&
((?[X]:(generous(X)))=>(?[X]:(~funny(X))))&
(![X]:((~humble(X)|creative(X))=>(old(X)&~generous(X))))&
(((~curious(fred)|old(fred)))=>((~happy(mary)&brave(mary))))&
(((wise(mary)<~>generous(mary)))<=>(?[X]:(tall(X))))&
(![X]:((happy(X)|~creative(X))=>(brave(X)&patient(X))))&
(![X]:((funny(X)&curious(X))<=>(creative(X)&~brave(X))))&
(![X]:(generous(X)<=>(strong(X)|calm(X))))&
(![X]:(~wise(X)=>(~creative(X)&~strong(X))))&
((?[X]:((~kind(X)&rich(X))))=>(?[X]:(generous(X))))&
(![X]:((wise(X)&~quiet(X))=>quiet(X)))&
((~generous(alice))=>((old(mary)<~>~rich(mary))))&
(?[X]:((~kind(X)&calm(X))))&
((~rich(fred)|~old(fred)))&
((tall(mary)|~kind(mary)))&
(?[X]:((happy(X)|generous(X))))&
((~calm(lucy)|~kind(lucy)))&
((kind(john)&rich(john))) | strong(john) | [
"p1",
"p2",
"p5",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8074277493595432704504910
% SZS output start Proof for 8074277493595432704504910
2. ? [X0] : (~funny(X0) | ~humble(X0)) <=> (~quiet(john) | ~generous(john)) [input p1]
3. ! [X0] : ((humble(X0) | old(X0)) <=> (generous(X0) & tall(X0))) [input p2]
6. ? [X0] : generous(X0) => ? [X0] : ~funny(X0) [input p5]
7. ! [X0] : ((creative(X0) | ~humble(X0)) => (~generous(X0) & old(X0))) [input p6]
13. ! [X0] : (~wise(X0) => (~strong(X0) & ~creative(X0))) [input p12]
15. ! [X0] : ((~quiet(X0) & wise(X0)) => quiet(X0)) [input p14]
23. strong(john) [input hypothesis]
24. ? [X0] : generous(X0) => ? [X1] : ~funny(X1) [rectify 6]
32. ? [X1] : ~funny(X1) | ! [X0] : ~generous(X0) [ennf transformation 24]
33. ! [X0] : ((~generous(X0) & old(X0)) | (~creative(X0) & humble(X0))) [ennf transformation 7]
36. ! [X0] : ((~strong(X0) & ~creative(X0)) | wise(X0)) [ennf transformation 13]
38. ! [X0] : (quiet(X0) | (quiet(X0) | ~wise(X0))) [ennf transformation 15]
39. ! [X0] : (quiet(X0) | quiet(X0) | ~wise(X0)) [flattening 38]
43. (? [X0] : (~funny(X0) | ~humble(X0)) | (quiet(john) & generous(john))) & ((~quiet(john) | ~generous(john)) | ! [X0] : (funny(X0) & humble(X0))) [nnf transformation 2]
44. (? [X0] : (~funny(X0) | ~humble(X0)) | (quiet(john) & generous(john))) & (~quiet(john) | ~generous(john) | ! [X0] : (funny(X0) & humble(X0))) [flattening 43]
45. (? [X0] : (~funny(X0) | ~humble(X0)) | (quiet(john) & generous(john))) & (~quiet(john) | ~generous(john) | ! [X1] : (funny(X1) & humble(X1))) [rectify 44]
46. ? [X0] : (~funny(X0) | ~humble(X0)) => (~funny(sK1) | ~humble(sK1)) [choice axiom]
47. ((~funny(sK1) | ~humble(sK1)) | (quiet(john) & generous(john))) & (~quiet(john) | ~generous(john) | ! [X1] : (funny(X1) & humble(X1))) [skolemisation 45,46]
48. ! [X0] : (((humble(X0) | old(X0)) | (~generous(X0) | ~tall(X0))) & ((generous(X0) & tall(X0)) | (~humble(X0) & ~old(X0)))) [nnf transformation 3]
49. ! [X0] : ((humble(X0) | old(X0) | ~generous(X0) | ~tall(X0)) & ((generous(X0) & tall(X0)) | (~humble(X0) & ~old(X0)))) [flattening 48]
51. ? [X0] : ~funny(X0) | ! [X1] : ~generous(X1) [rectify 32]
52. ? [X0] : ~funny(X0) => ~funny(sK2) [choice axiom]
53. ~funny(sK2) | ! [X1] : ~generous(X1) [skolemisation 51,52]
73. ~quiet(john) | ~generous(john) | funny(X1) [cnf transformation 47]
78. ~old(X0) | generous(X0) [cnf transformation 49]
79. ~humble(X0) | generous(X0) [cnf transformation 49]
84. ~funny(sK2) | ~generous(X1) [cnf transformation 53]
85. old(X0) | humble(X0) [cnf transformation 33]
107. ~strong(X0) | wise(X0) [cnf transformation 36]
109. quiet(X0) | quiet(X0) | ~wise(X0) [cnf transformation 39]
120. strong(john) [cnf transformation 23]
121. ~wise(X0) | quiet(X0) [duplicate literal removal 109]
137. 4 <=> quiet(john) [avatar definition]
150. 7 <=> generous(john) [avatar definition]
151. ~generous(john) <- (~7) [avatar component clause 150]
155. 8 <=> ! [X1] : funny(X1) [avatar definition]
156. funny(X1) <- (8) [avatar component clause 155]
157. 8 | ~7 | ~4 [avatar split clause 73,137,150,155]
163. 10 <=> ! [X1] : ~generous(X1) [avatar definition]
164. ~generous(X1) <- (10) [avatar component clause 163]
166. 11 <=> funny(sK2) [avatar definition]
168. ~funny(sK2) <- (~11) [avatar component clause 166]
169. 10 | ~11 [avatar split clause 84,166,163]
269. humble(X0) | generous(X0) [resolution 85,78]
271. generous(X0) [subsumption resolution 269,79]
293. wise(john) [resolution 107,120]
294. quiet(john) [resolution 121,293]
297. 4 [avatar split clause 294,137]
298. $false <- (~7) [subsumption resolution 151,271]
299. 7 [avatar contradiction clause 298]
300. $false <- (8, ~11) [resolution 156,168]
303. ~8 | 11 [avatar contradiction clause 300]
304. $false <- (10) [subsumption resolution 164,271]
305. ~10 [avatar contradiction clause 304]
306. $false [avatar sat refutation 157,169,297,299,303,305]
% SZS output end Proof for 8074277493595432704504910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both generous and happy and vice versa. Everyone who is not old or not patient is wise. If someone is both brave and wise then someone is both not calm and not brave and vice versa. If lucy is both humble and quiet then someone is both kind and calm and vice versa. Everyone who is not funny or not generous is both humble and not calm and vice versa. Everyone who is tall or not humble is not patient. Everyone who is creative is funny and vice versa. Everyone who is strong or calm is either not quiet or not calm. If paul is either generous or creative then someone is generous or funny. Everyone who is not strong or rich is both humble and rich. Everyone who is quiet or happy is creative or not calm. If someone is either rich or not creative then lucy is either not happy or old and vice versa. Everyone who is either not patient or not old is both not generous and not happy. Everyone who is not curious is funny or not curious. If fred is either funny or curious then mary is both curious and not creative and vice versa. Everyone who is kind or humble is both not generous and not tall and vice versa. Someone is both not quiet and not old. Someone is not rich. Someone is both not tall and not funny. Fred is either patient or not happy. Paul is either not tall or old. John is not brave. Fred is either not brave or tall. Paul is calm. | John is not humble. | neutral | (![X]:((~old(X)&generous(X))<=>(generous(X)&happy(X))))&
(![X]:((~old(X)|~patient(X))=>wise(X)))&
((?[X]:((brave(X)&wise(X))))<=>(?[X]:((~calm(X)&~brave(X)))))&
(((humble(lucy)&quiet(lucy)))<=>(?[X]:((kind(X)&calm(X)))))&
(![X]:((~funny(X)|~generous(X))<=>(humble(X)&~calm(X))))&
(![X]:((tall(X)|~humble(X))=>~patient(X)))&
(![X]:(creative(X)<=>funny(X)))&
(![X]:((strong(X)|calm(X))=>(~quiet(X)<~>~calm(X))))&
(((generous(paul)<~>creative(paul)))=>(?[X]:((generous(X)|funny(X)))))&
(![X]:((~strong(X)|rich(X))=>(humble(X)&rich(X))))&
(![X]:((quiet(X)|happy(X))=>(creative(X)|~calm(X))))&
((?[X]:((rich(X)<~>~creative(X))))<=>((~happy(lucy)<~>old(lucy))))&
(![X]:((~patient(X)<~>~old(X))=>(~generous(X)&~happy(X))))&
(![X]:(~curious(X)=>(funny(X)|~curious(X))))&
(((funny(fred)<~>curious(fred)))<=>((curious(mary)&~creative(mary))))&
(![X]:((kind(X)|humble(X))<=>(~generous(X)&~tall(X))))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~tall(X)&~funny(X))))&
((patient(fred)<~>~happy(fred)))&
((~tall(paul)<~>old(paul)))&
(~brave(john))&
((~brave(fred)<~>tall(fred)))&
(calm(paul)) | ~humble(john) | [] | null | 0 |
If john is wise then someone is both creative and not creative.
Everyone who is both brave and happy is not calm and vice versa.
If alice is either funny or patient then someone is both not strong and creative.
Everyone who is both not patient and patient is rich or funny.
Everyone who is not calm or old is not funny or not rich and vice versa.
Everyone who is either not humble or not tall is both funny and not humble.
Everyone who is not happy or not funny is both not calm and creative and vice versa.
Everyone who is either humble or brave is either happy or creative.
If someone is patient then someone is both humble and tall.
Everyone who is happy is both tall and not calm.
If someone is both not patient and not funny then mary is not patient.
Everyone who is old or happy is not funny.
Everyone who is both not happy and not curious is not curious or generous.
If mary is not creative or rich then alice is funny or not calm and vice versa.
Everyone who is not humble or humble is not calm or not funny and vice versa.
Someone is humble.
Someone is not patient.
Someone is patient.
Someone is either not kind or kind.
Alice is not old.
Mary is generous or old.
Someone is curious. | John is not wise. | entailment | ((wise(john))=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((brave(X)&happy(X))<=>~calm(X)))&
(((funny(alice)<~>patient(alice)))=>(?[X]:((~strong(X)&creative(X)))))&
(![X]:((~patient(X)&patient(X))=>(rich(X)|funny(X))))&
(![X]:((~calm(X)|old(X))<=>(~funny(X)|~rich(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(funny(X)&~humble(X))))&
(![X]:((~happy(X)|~funny(X))<=>(~calm(X)&creative(X))))&
(![X]:((humble(X)<~>brave(X))=>(happy(X)<~>creative(X))))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)&tall(X)))))&
(![X]:(happy(X)=>(tall(X)&~calm(X))))&
((?[X]:((~patient(X)&~funny(X))))=>(~patient(mary)))&
(![X]:((old(X)|happy(X))=>~funny(X)))&
(![X]:((~happy(X)&~curious(X))=>(~curious(X)|generous(X))))&
(((~creative(mary)|rich(mary)))<=>((funny(alice)|~calm(alice))))&
(![X]:((~humble(X)|humble(X))<=>(~calm(X)|~funny(X))))&
(?[X]:(humble(X)))&
(?[X]:(~patient(X)))&
(?[X]:(patient(X)))&
(?[X]:((~kind(X)<~>kind(X))))&
(~old(alice))&
((generous(mary)|old(mary)))&
(?[X]:(curious(X))) | ~wise(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 2699262573106170751216712
% SZS output start Proof for 2699262573106170751216712
1. wise(john) => ? [X0] : (~creative(X0) & creative(X0)) [input p0]
23. wise(john) [input hypothesis]
29. ? [X0] : (~creative(X0) & creative(X0)) | ~wise(john) [ennf transformation 1]
39. ? [X0] : (~creative(X0) & creative(X0)) => (~creative(sK0) & creative(sK0)) [choice axiom]
40. (~creative(sK0) & creative(sK0)) | ~wise(john) [skolemisation 29,39]
68. creative(sK0) | ~wise(john) [cnf transformation 40]
69. ~creative(sK0) | ~wise(john) [cnf transformation 40]
114. wise(john) [cnf transformation 23]
117. 1 <=> wise(john) [avatar definition]
121. 2 <=> creative(sK0) [avatar definition]
124. ~1 | ~2 [avatar split clause 69,121,117]
125. ~1 | 2 [avatar split clause 68,121,117]
178. 1 [avatar split clause 114,117]
179. $false [avatar sat refutation 124,125,178]
% SZS output end Proof for 2699262573106170751216712
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not curious is rich and vice versa.
Everyone who is curious is both old and not brave and vice versa.
If fred is either not brave or wise then someone is either not brave or not old.
If someone is either not calm or not patient then alice is both not old and calm and vice versa.
If someone is curious or not humble then someone is calm.
Everyone who is not patient is either not quiet or not generous and vice versa.
Everyone who is not calm is either strong or funny and vice versa.
If someone is quiet or not brave then paul is humble.
If john is both rich and tall then someone is patient and vice versa.
Everyone who is either not creative or humble is not 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.
If someone is curious or not wise then someone is not rich.
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 wise. | contradiction | (![X]:((tall(X)&~curious(X))<=>rich(X)))&
(![X]:(curious(X)<=>(old(X)&~brave(X))))&
(((~brave(fred)<~>wise(fred)))=>(?[X]:((~brave(X)<~>~old(X)))))&
((?[X]:((~calm(X)<~>~patient(X))))<=>((~old(alice)&calm(alice))))&
((?[X]:((curious(X)|~humble(X))))=>(?[X]:(calm(X))))&
(![X]:(~patient(X)<=>(~quiet(X)<~>~generous(X))))&
(![X]:(~calm(X)<=>(strong(X)<~>funny(X))))&
((?[X]:((quiet(X)|~brave(X))))=>(humble(paul)))&
(((rich(john)&tall(john)))<=>(?[X]:(patient(X))))&
(![X]:((~creative(X)<~>humble(X))<=>(~strong(X)|~patient(X))))&
(![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)|~wise(X))))=>(?[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))) | ~wise(susan) | [
"p1",
"p12",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9147619723771017981208677
% SZS output start Proof for 9147619723771017981208677
2. ! [X0] : (curious(X0) <=> (~brave(X0) & old(X0))) [input p1]
13. ? [X0] : (kind(X0) | ~rich(X0)) <=> curious(lucy) [input p12]
15. ? [X0] : (~wise(X0) | curious(X0)) => ? [X0] : ~rich(X0) [input p14]
21. ~curious(lucy) <~> brave(lucy) [input p20]
25. ~wise(susan) [input hypothesis]
27. ? [X0] : (~wise(X0) | curious(X0)) => ? [X1] : ~rich(X1) [rectify 15]
33. ? [X1] : ~rich(X1) | ! [X0] : (wise(X0) & ~curious(X0)) [ennf transformation 27]
36. ! [X0] : ((curious(X0) | (brave(X0) | ~old(X0))) & ((~brave(X0) & old(X0)) | ~curious(X0))) [nnf transformation 2]
37. ! [X0] : ((curious(X0) | brave(X0) | ~old(X0)) & ((~brave(X0) & old(X0)) | ~curious(X0))) [flattening 36]
60. (? [X0] : (kind(X0) | ~rich(X0)) | ~curious(lucy)) & (curious(lucy) | ! [X0] : (~kind(X0) & rich(X0))) [nnf transformation 13]
61. (? [X0] : (kind(X0) | ~rich(X0)) | ~curious(lucy)) & (curious(lucy) | ! [X1] : (~kind(X1) & rich(X1))) [rectify 60]
62. ? [X0] : (kind(X0) | ~rich(X0)) => (kind(sK4) | ~rich(sK4)) [choice axiom]
63. ((kind(sK4) | ~rich(sK4)) | ~curious(lucy)) & (curious(lucy) | ! [X1] : (~kind(X1) & rich(X1))) [skolemisation 61,62]
65. ? [X0] : ~rich(X0) | ! [X1] : (wise(X1) & ~curious(X1)) [rectify 33]
66. ? [X0] : ~rich(X0) => ~rich(sK5) [choice axiom]
67. ~rich(sK5) | ! [X1] : (wise(X1) & ~curious(X1)) [skolemisation 65,66]
76. (~brave(lucy) | curious(lucy)) & (brave(lucy) | ~curious(lucy)) [nnf transformation 21]
82. ~brave(X0) | ~curious(X0) [cnf transformation 37]
121. curious(lucy) | rich(X1) [cnf transformation 63]
129. ~rich(sK5) | wise(X1) [cnf transformation 67]
139. brave(lucy) | ~curious(lucy) [cnf transformation 76]
140. ~brave(lucy) | curious(lucy) [cnf transformation 76]
145. ~wise(susan) [cnf transformation 25]
239. 21 <=> curious(lucy) [avatar definition]
256. 25 <=> ! [X1] : rich(X1) [avatar definition]
257. rich(X1) <- (25) [avatar component clause 256]
258. 25 | 21 [avatar split clause 121,239,256]
260. 26 <=> ! [X1] : wise(X1) [avatar definition]
261. wise(X1) <- (26) [avatar component clause 260]
263. 27 <=> rich(sK5) [avatar definition]
265. ~rich(sK5) <- (~27) [avatar component clause 263]
266. 26 | ~27 [avatar split clause 129,263,260]
302. ~brave(lucy) [subsumption resolution 140,82]
303. ~curious(lucy) [subsumption resolution 139,302]
304. ~21 [avatar split clause 303,239]
329. $false <- (25, ~27) [resolution 265,257]
330. ~25 | 27 [avatar contradiction clause 329]
331. $false <- (26) [resolution 261,145]
334. ~26 [avatar contradiction clause 331]
335. $false [avatar sat refutation 258,266,304,330,334]
% SZS output end Proof for 9147619723771017981208677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or strong is not humble and vice versa.
Everyone who is either not old or not curious is patient.
If alice is kind then susan is either wise or not tall and vice versa.
Everyone who is either tall or not patient is either wise or not wise and vice versa.
Everyone who is either not rich or curious is either not strong or not humble and vice versa.
If fred is wise then someone is wise or humble and vice versa.
Everyone who is both not creative and not wise is either quiet or tall and vice versa.
If someone is rich then someone is old and vice versa.
Everyone who is either funny or generous is generous or not wise and vice versa.
Everyone who is either not happy or funny is both quiet and happy and vice versa.
If someone is both not kind and not creative then someone is either not quiet or not humble and vice versa.
Everyone who is both strong and not quiet is either quiet or not calm.
Everyone who is either humble or not calm is tall or not strong.
Everyone who is tall or calm is both not calm and creative and vice versa.
If john is not kind or not patient then lucy is both humble and creative and vice versa.
Someone is strong.
Someone is either not funny or curious.
Susan is strong.
Fred is either not creative or not brave.
Someone is not happy. | Fred is strong. | neutral | (![X]:((~creative(X)|strong(X))<=>~humble(X)))&
(![X]:((~old(X)<~>~curious(X))=>patient(X)))&
((kind(alice))<=>((wise(susan)<~>~tall(susan))))&
(![X]:((tall(X)<~>~patient(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~strong(X)<~>~humble(X))))&
((wise(fred))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((~creative(X)&~wise(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:(rich(X)))<=>(?[X]:(old(X))))&
(![X]:((funny(X)<~>generous(X))<=>(generous(X)|~wise(X))))&
(![X]:((~happy(X)<~>funny(X))<=>(quiet(X)&happy(X))))&
((?[X]:((~kind(X)&~creative(X))))<=>(?[X]:((~quiet(X)<~>~humble(X)))))&
(![X]:((strong(X)&~quiet(X))=>(quiet(X)<~>~calm(X))))&
(![X]:((humble(X)<~>~calm(X))=>(tall(X)|~strong(X))))&
(![X]:((tall(X)|calm(X))<=>(~calm(X)&creative(X))))&
(((~kind(john)|~patient(john)))<=>((humble(lucy)&creative(lucy))))&
(?[X]:(strong(X)))&
(?[X]:((~funny(X)<~>curious(X))))&
(strong(susan))&
((~creative(fred)<~>~brave(fred)))&
(?[X]:(~happy(X))) | strong(fred) | [] | null | 0 |
Everyone who is either kind or not calm is not brave and vice versa.
If someone is tall then someone is wise and vice versa.
Everyone who is not curious or curious is either not funny or brave.
Everyone who is both brave and kind is not strong or happy and vice versa.
If john is not happy or patient then someone is kind.
Everyone who is strong is both not tall and funny and vice versa.
If paul is either not wise or old then someone is not funny or not rich.
Everyone who is quiet or not humble is both not kind and not humble and vice versa.
If someone is tall or not tall then someone is not happy and vice versa.
If alice is not generous or not quiet then someone is both not brave and not strong and vice versa.
If someone is both not happy and not kind then john is wise.
Everyone who is either not strong or not generous is patient.
Everyone who is rich is not calm or not brave.
Everyone who is both not patient and curious is either rich or curious.
Everyone who is not brave is not generous or not patient.
Someone is either creative or strong.
Alice is brave.
Lucy is either not curious or patient.
Someone is either not patient or not brave.
Fred is not calm.
Alice is brave or funny.
Someone is both wise and not kind. | John is calm. | neutral | (![X]:((kind(X)<~>~calm(X))<=>~brave(X)))&
((?[X]:(tall(X)))<=>(?[X]:(wise(X))))&
(![X]:((~curious(X)|curious(X))=>(~funny(X)<~>brave(X))))&
(![X]:((brave(X)&kind(X))<=>(~strong(X)|happy(X))))&
(((~happy(john)|patient(john)))=>(?[X]:(kind(X))))&
(![X]:(strong(X)<=>(~tall(X)&funny(X))))&
(((~wise(paul)<~>old(paul)))=>(?[X]:((~funny(X)|~rich(X)))))&
(![X]:((quiet(X)|~humble(X))<=>(~kind(X)&~humble(X))))&
((?[X]:((tall(X)|~tall(X))))<=>(?[X]:(~happy(X))))&
(((~generous(alice)|~quiet(alice)))<=>(?[X]:((~brave(X)&~strong(X)))))&
((?[X]:((~happy(X)&~kind(X))))=>(wise(john)))&
(![X]:((~strong(X)<~>~generous(X))=>patient(X)))&
(![X]:(rich(X)=>(~calm(X)|~brave(X))))&
(![X]:((~patient(X)&curious(X))=>(rich(X)<~>curious(X))))&
(![X]:(~brave(X)=>(~generous(X)|~patient(X))))&
(?[X]:((creative(X)<~>strong(X))))&
(brave(alice))&
((~curious(lucy)<~>patient(lucy)))&
(?[X]:((~patient(X)<~>~brave(X))))&
(~calm(fred))&
((brave(alice)|funny(alice)))&
(?[X]:((wise(X)&~kind(X)))) | calm(john) | [] | null | 0 |
Everyone who is not rich or not creative is either quiet or rich and vice versa.
If alice is both not old and brave then someone is wise or not old and vice versa.
Everyone who is either not curious or curious is not strong and vice versa.
If mary is not tall or not creative then paul is wise or not funny and vice versa.
Everyone who is either curious or humble is both rich and not rich.
Everyone who is both wise and not calm is either not patient or not old and vice versa.
If someone is not curious then someone is kind.
If someone is either not calm or not tall then mary is quiet.
Everyone who is creative is both patient and not strong and vice versa.
Everyone who is either not quiet or not humble is both not curious and creative and vice versa.
Everyone who is not humble is both happy and not quiet.
Everyone who is either not kind or strong is either calm or not creative and vice versa.
Everyone who is wise is both not creative and generous.
Everyone who is not quiet or not wise is either not curious or curious and vice versa.
If someone is both generous and not strong then fred is quiet.
Everyone who is not old or not patient is both not old and not calm and vice versa.
Paul is either not generous or not calm.
Someone is either funny or not generous.
Mary is both not humble and not calm.
Paul is not happy or quiet.
Fred is either not old or not brave.
Someone is both rich and not curious.
Fred is not humble or not creative.
Someone is both not happy and not rich. | Mary is tall. | contradiction | (![X]:((~rich(X)|~creative(X))<=>(quiet(X)<~>rich(X))))&
(((~old(alice)&brave(alice)))<=>(?[X]:((wise(X)|~old(X)))))&
(![X]:((~curious(X)<~>curious(X))<=>~strong(X)))&
(((~tall(mary)|~creative(mary)))<=>((wise(paul)|~funny(paul))))&
(![X]:((curious(X)<~>humble(X))=>(rich(X)&~rich(X))))&
(![X]:((wise(X)&~calm(X))<=>(~patient(X)<~>~old(X))))&
((?[X]:(~curious(X)))=>(?[X]:(kind(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(quiet(mary)))&
(![X]:(creative(X)<=>(patient(X)&~strong(X))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(~curious(X)&creative(X))))&
(![X]:(~humble(X)=>(happy(X)&~quiet(X))))&
(![X]:((~kind(X)<~>strong(X))<=>(calm(X)<~>~creative(X))))&
(![X]:(wise(X)=>(~creative(X)&generous(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~curious(X)<~>curious(X))))&
((?[X]:((generous(X)&~strong(X))))=>(quiet(fred)))&
(![X]:((~old(X)|~patient(X))<=>(~old(X)&~calm(X))))&
((~generous(paul)<~>~calm(paul)))&
(?[X]:((funny(X)<~>~generous(X))))&
((~humble(mary)&~calm(mary)))&
((~happy(paul)|quiet(paul)))&
((~old(fred)<~>~brave(fred)))&
(?[X]:((rich(X)&~curious(X))))&
((~humble(fred)|~creative(fred)))&
(?[X]:((~happy(X)&~rich(X)))) | tall(mary) | [
"p7",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3018397965926103890427032
% SZS output start Proof for 3018397965926103890427032
8. ? [X0] : (~calm(X0) <~> ~tall(X0)) => quiet(mary) [input p7]
11. ! [X0] : (~humble(X0) => (~quiet(X0) & happy(X0))) [input p10]
19. ~calm(mary) & ~humble(mary) [input p18]
25. tall(mary) [input hypothesis]
29. quiet(mary) | ! [X0] : (~calm(X0) <=> ~tall(X0)) [ennf transformation 8]
30. ! [X0] : ((~quiet(X0) & happy(X0)) | humble(X0)) [ennf transformation 11]
49. quiet(mary) | ! [X0] : ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0))) [nnf transformation 29]
98. quiet(mary) | ~tall(X0) | calm(X0) [cnf transformation 49]
110. ~quiet(X0) | humble(X0) [cnf transformation 30]
137. ~humble(mary) [cnf transformation 19]
138. ~calm(mary) [cnf transformation 19]
147. tall(mary) [cnf transformation 25]
187. 8 <=> tall(mary) [avatar definition]
188. tall(mary) <- (8) [avatar component clause 187]
216. 14 <=> quiet(mary) [avatar definition]
218. quiet(mary) <- (14) [avatar component clause 216]
221. 15 <=> ! [X0] : (~tall(X0) | calm(X0)) [avatar definition]
222. ~tall(X0) | calm(X0) <- (15) [avatar component clause 221]
223. 15 | 14 [avatar split clause 98,216,221]
289. 8 [avatar split clause 147,187]
296. humble(mary) <- (14) [resolution 110,218]
298. $false <- (14) [subsumption resolution 296,137]
299. ~14 [avatar contradiction clause 298]
312. calm(mary) <- (8, 15) [resolution 222,188]
314. $false <- (8, 15) [subsumption resolution 312,138]
315. ~8 | ~15 [avatar contradiction clause 314]
316. $false [avatar sat refutation 223,289,299,315]
% SZS output end Proof for 3018397965926103890427032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both tall and rich.
If someone is either patient or funny then fred is both not old and not quiet.
Everyone who is either old or curious is either strong or not funny.
Everyone who is not rich or old is not strong.
Everyone who is either not creative or funny is either generous or funny and vice versa.
Everyone who is not patient is not creative and vice versa.
If someone is either not funny or not calm then fred is wise or generous and vice versa.
If someone is both not generous and not patient then someone is both not wise and brave and vice versa.
If john is wise then alice is either not creative or humble.
Everyone who is calm or not funny is kind or not humble and vice versa.
If alice is both not generous and brave then fred is not brave.
Everyone who is not curious or funny is either not patient or not humble.
Everyone who is both not curious and not funny is not tall and vice versa.
If someone is not rich or not kind then john is either not patient or not old and vice versa.
If alice is either not brave or tall then someone is strong and vice versa.
Everyone who is rich is brave or happy and vice versa.
Susan is both humble and not old.
Alice is either creative or funny.
Mary is both not strong and not old.
Lucy is not tall.
Mary is either not tall or strong.
John is not tall.
Paul is not brave or brave.
Someone is both not patient and wise. | Mary is strong. | contradiction | (![X]:(~humble(X)=>(tall(X)&rich(X))))&
((?[X]:((patient(X)<~>funny(X))))=>((~old(fred)&~quiet(fred))))&
(![X]:((old(X)<~>curious(X))=>(strong(X)<~>~funny(X))))&
(![X]:((~rich(X)|old(X))=>~strong(X)))&
(![X]:((~creative(X)<~>funny(X))<=>(generous(X)<~>funny(X))))&
(![X]:(~patient(X)<=>~creative(X)))&
((?[X]:((~funny(X)<~>~calm(X))))<=>((wise(fred)|generous(fred))))&
((?[X]:((~generous(X)&~patient(X))))<=>(?[X]:((~wise(X)&brave(X)))))&
((wise(john))=>((~creative(alice)<~>humble(alice))))&
(![X]:((calm(X)|~funny(X))<=>(kind(X)|~humble(X))))&
(((~generous(alice)&brave(alice)))=>(~brave(fred)))&
(![X]:((~curious(X)|funny(X))=>(~patient(X)<~>~humble(X))))&
(![X]:((~curious(X)&~funny(X))<=>~tall(X)))&
((?[X]:((~rich(X)|~kind(X))))<=>((~patient(john)<~>~old(john))))&
(((~brave(alice)<~>tall(alice)))<=>(?[X]:(strong(X))))&
(![X]:(rich(X)<=>(brave(X)|happy(X))))&
((humble(susan)&~old(susan)))&
((creative(alice)<~>funny(alice)))&
((~strong(mary)&~old(mary)))&
(~tall(lucy))&
((~tall(mary)<~>strong(mary)))&
(~tall(john))&
((~brave(paul)|brave(paul)))&
(?[X]:((~patient(X)&wise(X)))) | strong(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6938611122983626025913864
% SZS output start Proof for 6938611122983626025913864
19. ~old(mary) & ~strong(mary) [input p18]
25. strong(mary) [input hypothesis]
131. ~strong(mary) [cnf transformation 19]
140. strong(mary) [cnf transformation 25]
290. $false [subsumption resolution 140,131]
% SZS output end Proof for 6938611122983626025913864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative and not happy then someone is either quiet or not funny and vice versa. If fred is generous then paul is calm. Everyone who is either humble or wise is both funny and not brave and vice versa. Everyone who is either not wise or generous is either quiet or not calm and vice versa. If alice is calm then someone is either humble or brave and vice versa. If mary is not wise then someone is not old and vice versa. Everyone who is either wise or not strong is not curious or curious and vice versa. If someone is not humble or old then someone is tall or not old and vice versa. Everyone who is either not curious or not quiet is patient. Everyone who is either not wise or generous is both not wise and not funny and vice versa. Everyone who is both tall and not wise is not generous or tall and vice versa. Everyone who is either patient or happy is either happy or wise. Everyone who is either patient or humble is not funny or quiet and vice versa. If susan is either not quiet or calm then someone is not kind and vice versa. If someone is kind then mary is not calm and vice versa. Everyone who is funny is curious or not curious and vice versa. Someone is either not wise or not creative. Someone is either happy or old. Someone is either wise or old. Someone is not old or generous. Lucy is kind. Alice is both patient and not strong. Someone is not happy or kind. | Lucy is funny. | entailment | ((?[X]:((~creative(X)&~happy(X))))<=>(?[X]:((quiet(X)<~>~funny(X)))))&
((generous(fred))=>(calm(paul)))&
(![X]:((humble(X)<~>wise(X))<=>(funny(X)&~brave(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(quiet(X)<~>~calm(X))))&
((calm(alice))<=>(?[X]:((humble(X)<~>brave(X)))))&
((~wise(mary))<=>(?[X]:(~old(X))))&
(![X]:((wise(X)<~>~strong(X))<=>(~curious(X)|curious(X))))&
((?[X]:((~humble(X)|old(X))))<=>(?[X]:((tall(X)|~old(X)))))&
(![X]:((~curious(X)<~>~quiet(X))=>patient(X)))&
(![X]:((~wise(X)<~>generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:((tall(X)&~wise(X))<=>(~generous(X)|tall(X))))&
(![X]:((patient(X)<~>happy(X))=>(happy(X)<~>wise(X))))&
(![X]:((patient(X)<~>humble(X))<=>(~funny(X)|quiet(X))))&
(((~quiet(susan)<~>calm(susan)))<=>(?[X]:(~kind(X))))&
((?[X]:(kind(X)))<=>(~calm(mary)))&
(![X]:(funny(X)<=>(curious(X)|~curious(X))))&
(?[X]:((~wise(X)<~>~creative(X))))&
(?[X]:((happy(X)<~>old(X))))&
(?[X]:((wise(X)<~>old(X))))&
(?[X]:((~old(X)|generous(X))))&
(kind(lucy))&
((patient(alice)&~strong(alice)))&
(?[X]:((~happy(X)|kind(X)))) | funny(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7664329974985927348672104
% SZS output start Proof for 7664329974985927348672104
16. ! [X0] : (funny(X0) <=> (~curious(X0) | curious(X0))) [input p15]
24. ~funny(lucy) [input hypothesis]
69. ! [X0] : ((funny(X0) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | ~funny(X0))) [nnf transformation 16]
70. ! [X0] : ((funny(X0) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | ~funny(X0))) [flattening 69]
151. funny(X0) | ~curious(X0) [cnf transformation 70]
152. funny(X0) | curious(X0) [cnf transformation 70]
164. ~funny(lucy) [cnf transformation 24]
309. funny(X0) [subsumption resolution 151,152]
340. $false [subsumption resolution 164,309]
% SZS output end Proof for 7664329974985927348672104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not patient is not brave or generous and vice versa.
Everyone who is not funny is not generous.
If someone is either humble or not brave then someone is wise or not patient and vice versa.
If someone is not kind then fred is tall or not kind.
Everyone who is not strong is not tall or not wise.
If lucy is both not calm and not tall then someone is not rich or not strong.
If someone is both patient and strong then someone is either quiet or not kind and vice versa.
If mary is not humble then lucy is both kind and not old.
If someone is not old or not brave then someone is humble.
Everyone who is not strong is wise and vice versa.
If susan is either quiet or brave then someone is either not generous or humble.
Everyone who is not quiet is either not quiet or not kind and vice versa.
Everyone who is both funny and patient is strong or kind.
If someone is either not quiet or old then susan is either not patient or strong.
Everyone who is happy or creative is not funny or not tall and vice versa.
Fred is both not calm and creative.
Someone is either curious or not generous.
Someone is not strong or patient.
Someone is not old.
Paul is funny.
Alice is either not humble or not rich. | Susan is not calm. | neutral | (![X]:((curious(X)|~patient(X))<=>(~brave(X)|generous(X))))&
(![X]:(~funny(X)=>~generous(X)))&
((?[X]:((humble(X)<~>~brave(X))))<=>(?[X]:((wise(X)|~patient(X)))))&
((?[X]:(~kind(X)))=>((tall(fred)|~kind(fred))))&
(![X]:(~strong(X)=>(~tall(X)|~wise(X))))&
(((~calm(lucy)&~tall(lucy)))=>(?[X]:((~rich(X)|~strong(X)))))&
((?[X]:((patient(X)&strong(X))))<=>(?[X]:((quiet(X)<~>~kind(X)))))&
((~humble(mary))=>((kind(lucy)&~old(lucy))))&
((?[X]:((~old(X)|~brave(X))))=>(?[X]:(humble(X))))&
(![X]:(~strong(X)<=>wise(X)))&
(((quiet(susan)<~>brave(susan)))=>(?[X]:((~generous(X)<~>humble(X)))))&
(![X]:(~quiet(X)<=>(~quiet(X)<~>~kind(X))))&
(![X]:((funny(X)&patient(X))=>(strong(X)|kind(X))))&
((?[X]:((~quiet(X)<~>old(X))))=>((~patient(susan)<~>strong(susan))))&
(![X]:((happy(X)|creative(X))<=>(~funny(X)|~tall(X))))&
((~calm(fred)&creative(fred)))&
(?[X]:((curious(X)<~>~generous(X))))&
(?[X]:((~strong(X)|patient(X))))&
(?[X]:(~old(X)))&
(funny(paul))&
((~humble(alice)<~>~rich(alice))) | ~calm(susan) | [] | null | 0 |
Everyone who is both not patient and kind is both not calm and kind. If someone is both not quiet and kind then someone is kind and vice versa. Everyone who is old or kind is not kind. Everyone who is either wise or not quiet is both not old and funny and vice versa. If mary is quiet or not humble then someone is either kind or old and vice versa. If lucy is not brave then someone is strong or old and vice versa. Everyone who is not kind is either kind or not generous and vice versa. If someone is rich then someone is both not rich and wise. If someone is kind then alice is happy or not tall and vice versa. If someone is either not humble or not wise then someone is happy. If someone is not creative or strong then mary is not calm or creative and vice versa. Everyone who is both tall and not kind is either not creative or quiet and vice versa. If someone is both not humble and not rich then fred is kind or creative. Everyone who is not strong or humble is not wise and vice versa. If alice is either patient or not generous then paul is not humble. Everyone who is either calm or kind is not rich or not creative. John is not creative or brave. Someone is curious. Someone is either not curious or funny. John is not creative or not happy. Paul is both not quiet and patient. Paul is brave. Mary is either kind or humble. | Alice is not tall. | contradiction | (![X]:((~patient(X)&kind(X))=>(~calm(X)&kind(X))))&
((?[X]:((~quiet(X)&kind(X))))<=>(?[X]:(kind(X))))&
(![X]:((old(X)|kind(X))=>~kind(X)))&
(![X]:((wise(X)<~>~quiet(X))<=>(~old(X)&funny(X))))&
(((quiet(mary)|~humble(mary)))<=>(?[X]:((kind(X)<~>old(X)))))&
((~brave(lucy))<=>(?[X]:((strong(X)|old(X)))))&
(![X]:(~kind(X)<=>(kind(X)<~>~generous(X))))&
((?[X]:(rich(X)))=>(?[X]:((~rich(X)&wise(X)))))&
((?[X]:(kind(X)))<=>((happy(alice)|~tall(alice))))&
((?[X]:((~humble(X)<~>~wise(X))))=>(?[X]:(happy(X))))&
((?[X]:((~creative(X)|strong(X))))<=>((~calm(mary)|creative(mary))))&
(![X]:((tall(X)&~kind(X))<=>(~creative(X)<~>quiet(X))))&
((?[X]:((~humble(X)&~rich(X))))=>((kind(fred)|creative(fred))))&
(![X]:((~strong(X)|humble(X))<=>~wise(X)))&
(((patient(alice)<~>~generous(alice)))=>(~humble(paul)))&
(![X]:((calm(X)<~>kind(X))=>(~rich(X)|~creative(X))))&
((~creative(john)|brave(john)))&
(?[X]:(curious(X)))&
(?[X]:((~curious(X)<~>funny(X))))&
((~creative(john)|~happy(john)))&
((~quiet(paul)&patient(paul)))&
(brave(paul))&
((kind(mary)<~>humble(mary))) | ~tall(alice) | [
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4581723743070587099797555
% SZS output start Proof for 4581723743070587099797555
3. ! [X0] : ((kind(X0) | old(X0)) => ~kind(X0)) [input p2]
9. ? [X0] : kind(X0) <=> (~tall(alice) | happy(alice)) [input p8]
24. ~tall(alice) [input hypothesis]
30. ! [X0] : (~kind(X0) | (~kind(X0) & ~old(X0))) [ennf transformation 3]
58. (? [X0] : kind(X0) | (tall(alice) & ~happy(alice))) & ((~tall(alice) | happy(alice)) | ! [X0] : ~kind(X0)) [nnf transformation 9]
59. (? [X0] : kind(X0) | (tall(alice) & ~happy(alice))) & (~tall(alice) | happy(alice) | ! [X0] : ~kind(X0)) [flattening 58]
60. (? [X0] : kind(X0) | (tall(alice) & ~happy(alice))) & (~tall(alice) | happy(alice) | ! [X1] : ~kind(X1)) [rectify 59]
61. ? [X0] : kind(X0) => kind(sK5) [choice axiom]
62. (kind(sK5) | (tall(alice) & ~happy(alice))) & (~tall(alice) | happy(alice) | ! [X1] : ~kind(X1)) [skolemisation 60,61]
90. ~kind(X0) | ~kind(X0) [cnf transformation 30]
114. kind(sK5) | tall(alice) [cnf transformation 62]
145. ~tall(alice) [cnf transformation 24]
148. ~kind(X0) [duplicate literal removal 90]
150. 1 <=> ! [X1] : ~kind(X1) [avatar definition]
151. ~kind(X1) <- (1) [avatar component clause 150]
170. 1 [avatar split clause 148,150]
229. 18 <=> tall(alice) [avatar definition]
233. 19 <=> kind(sK5) [avatar definition]
235. kind(sK5) <- (19) [avatar component clause 233]
236. 18 | 19 [avatar split clause 114,233,229]
330. ~18 [avatar split clause 145,229]
331. $false <- (1, 19) [resolution 235,151]
332. ~1 | ~19 [avatar contradiction clause 331]
333. $false [avatar sat refutation 170,236,330,332]
% SZS output end Proof for 4581723743070587099797555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not curious or not kind then john is humble.
Everyone who is not humble or not tall is not calm or humble and vice versa.
If susan is both not generous and kind then fred is either not brave or not kind.
Everyone who is both not old and tall is creative or old and vice versa.
Everyone who is both not humble and not patient is not brave or patient and vice versa.
Everyone who is not creative or wise is not curious or humble.
Everyone who is tall or not tall is either not brave or old.
If mary is either quiet or humble then john is not tall.
If susan is both curious and strong then someone is either kind or not creative and vice versa.
If susan is patient then mary is both not wise and not funny.
If someone is either brave or not patient then someone is not wise or humble.
If mary is either calm or funny then someone is either brave or not humble and vice versa.
Everyone who is both patient and not quiet is both funny and calm.
Everyone who is either old or curious is either not quiet or calm.
Someone is not curious or brave.
Mary is both not tall and not wise.
John is not funny or happy.
John is either patient or tall.
Mary is not tall or not rich. | John is not patient. | entailment | (((~curious(susan)|~kind(susan)))=>(humble(john)))&
(![X]:((~humble(X)|~tall(X))<=>(~calm(X)|humble(X))))&
(((~generous(susan)&kind(susan)))=>((~brave(fred)<~>~kind(fred))))&
(![X]:((~old(X)&tall(X))<=>(creative(X)|old(X))))&
(![X]:((~humble(X)&~patient(X))<=>(~brave(X)|patient(X))))&
(![X]:((~creative(X)|wise(X))=>(~curious(X)|humble(X))))&
(![X]:((tall(X)|~tall(X))=>(~brave(X)<~>old(X))))&
(((quiet(mary)<~>humble(mary)))=>(~tall(john)))&
(((curious(susan)&strong(susan)))<=>(?[X]:((kind(X)<~>~creative(X)))))&
((patient(susan))=>((~wise(mary)&~funny(mary))))&
((?[X]:((brave(X)<~>~patient(X))))=>(?[X]:((~wise(X)|humble(X)))))&
(((calm(mary)<~>funny(mary)))<=>(?[X]:((brave(X)<~>~humble(X)))))&
(![X]:((patient(X)&~quiet(X))=>(funny(X)&calm(X))))&
(![X]:((old(X)<~>curious(X))=>(~quiet(X)<~>calm(X))))&
(?[X]:((~curious(X)|brave(X))))&
((~tall(mary)&~wise(mary)))&
((~funny(john)|happy(john)))&
((patient(john)<~>tall(john)))&
((~tall(mary)|~rich(mary))) | ~patient(john) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1136508816056452236598892
% SZS output start Proof for 1136508816056452236598892
5. ! [X0] : ((~patient(X0) & ~humble(X0)) <=> (patient(X0) | ~brave(X0))) [input p4]
20. patient(john) [input hypothesis]
42. ! [X0] : (((~patient(X0) & ~humble(X0)) | (~patient(X0) & brave(X0))) & ((patient(X0) | ~brave(X0)) | (patient(X0) | humble(X0)))) [nnf transformation 5]
43. ! [X0] : (((~patient(X0) & ~humble(X0)) | (~patient(X0) & brave(X0))) & (patient(X0) | ~brave(X0) | patient(X0) | humble(X0))) [flattening 42]
74. ~patient(X0) | ~patient(X0) [cnf transformation 43]
107. patient(john) [cnf transformation 20]
109. ~patient(X0) [duplicate literal removal 74]
191. $false [subsumption resolution 107,109]
% SZS output end Proof for 1136508816056452236598892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and strong is funny and vice versa.
Everyone who is both curious and kind is not quiet or happy and vice versa.
Everyone who is not patient is not curious.
Everyone who is not patient or strong is either not quiet or humble.
Everyone who is not tall or not creative is humble and vice versa.
Everyone who is quiet is both not generous and rich and vice versa.
Everyone who is both not humble and creative is patient.
Everyone who is either not patient or not kind is generous and vice versa.
If fred is not tall then mary is not curious.
If someone is strong then mary is either humble or happy.
Everyone who is both not kind and wise is not funny and vice versa.
Everyone who is not old or not patient is both kind and rich.
If someone is both not patient and humble then paul is not curious.
If someone is either not rich or strong then someone is not curious and vice versa.
If someone is not calm or quiet then susan is not humble or not curious.
Everyone who is not calm or not patient is both generous and strong and vice versa.
Mary is quiet or not brave.
Susan is both not brave and not old.
Someone is either generous or funny.
Lucy is not wise.
Someone is both not wise and strong. | Lucy is not calm. | contradiction | (![X]:((~tall(X)&strong(X))<=>funny(X)))&
(![X]:((curious(X)&kind(X))<=>(~quiet(X)|happy(X))))&
(![X]:(~patient(X)=>~curious(X)))&
(![X]:((~patient(X)|strong(X))=>(~quiet(X)<~>humble(X))))&
(![X]:((~tall(X)|~creative(X))<=>humble(X)))&
(![X]:(quiet(X)<=>(~generous(X)&rich(X))))&
(![X]:((~humble(X)&creative(X))=>patient(X)))&
(![X]:((~patient(X)<~>~kind(X))<=>generous(X)))&
((~tall(fred))=>(~curious(mary)))&
((?[X]:(strong(X)))=>((humble(mary)<~>happy(mary))))&
(![X]:((~kind(X)&wise(X))<=>~funny(X)))&
(![X]:((~old(X)|~patient(X))=>(kind(X)&rich(X))))&
((?[X]:((~patient(X)&humble(X))))=>(~curious(paul)))&
((?[X]:((~rich(X)<~>strong(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((~calm(X)|quiet(X))))=>((~humble(susan)|~curious(susan))))&
(![X]:((~calm(X)|~patient(X))<=>(generous(X)&strong(X))))&
((quiet(mary)|~brave(mary)))&
((~brave(susan)&~old(susan)))&
(?[X]:((generous(X)<~>funny(X))))&
(~wise(lucy))&
(?[X]:((~wise(X)&strong(X)))) | ~calm(lucy) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7501163777503587061185996
% SZS output start Proof for 7501163777503587061185996
2. ! [X0] : ((kind(X0) & curious(X0)) <=> (happy(X0) | ~quiet(X0))) [input p1]
4. ! [X0] : ((strong(X0) | ~patient(X0)) => (~quiet(X0) <~> humble(X0))) [input p3]
5. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> humble(X0)) [input p4]
6. ! [X0] : (quiet(X0) <=> (rich(X0) & ~generous(X0))) [input p5]
7. ! [X0] : ((creative(X0) & ~humble(X0)) => patient(X0)) [input p6]
8. ! [X0] : ((~patient(X0) <~> ~kind(X0)) <=> generous(X0)) [input p7]
16. ! [X0] : ((~patient(X0) | ~calm(X0)) <=> (strong(X0) & generous(X0))) [input p15]
22. ~calm(lucy) [input hypothesis]
27. ! [X0] : ((~quiet(X0) <~> humble(X0)) | (~strong(X0) & patient(X0))) [ennf transformation 4]
28. ! [X0] : (patient(X0) | (~creative(X0) | humble(X0))) [ennf transformation 7]
29. ! [X0] : (patient(X0) | ~creative(X0) | humble(X0)) [flattening 28]
38. ! [X0] : (((kind(X0) & curious(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~kind(X0) | ~curious(X0)))) [nnf transformation 2]
39. ! [X0] : (((kind(X0) & curious(X0)) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~kind(X0) | ~curious(X0))) [flattening 38]
40. ! [X0] : (((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~strong(X0) & patient(X0))) [nnf transformation 27]
41. ! [X0] : (((~creative(X0) | ~tall(X0)) | ~humble(X0)) & (humble(X0) | (creative(X0) & tall(X0)))) [nnf transformation 5]
42. ! [X0] : ((~creative(X0) | ~tall(X0) | ~humble(X0)) & (humble(X0) | (creative(X0) & tall(X0)))) [flattening 41]
43. ! [X0] : ((quiet(X0) | (~rich(X0) | generous(X0))) & ((rich(X0) & ~generous(X0)) | ~quiet(X0))) [nnf transformation 6]
44. ! [X0] : ((quiet(X0) | ~rich(X0) | generous(X0)) & ((rich(X0) & ~generous(X0)) | ~quiet(X0))) [flattening 43]
45. ! [X0] : ((((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | ~generous(X0)) & (generous(X0) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0))))) [nnf transformation 8]
54. ! [X0] : (((~patient(X0) | ~calm(X0)) | (~strong(X0) | ~generous(X0))) & ((strong(X0) & generous(X0)) | (patient(X0) & calm(X0)))) [nnf transformation 16]
55. ! [X0] : ((~patient(X0) | ~calm(X0) | ~strong(X0) | ~generous(X0)) & ((strong(X0) & generous(X0)) | (patient(X0) & calm(X0)))) [flattening 54]
67. quiet(X0) | kind(X0) [cnf transformation 39]
72. ~humble(X0) | quiet(X0) | patient(X0) [cnf transformation 40]
75. creative(X0) | humble(X0) [cnf transformation 42]
77. ~generous(X0) | ~quiet(X0) [cnf transformation 44]
80. patient(X0) | ~creative(X0) | humble(X0) [cnf transformation 29]
83. ~generous(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 45]
102. calm(X0) | generous(X0) [cnf transformation 55]
103. generous(X0) | patient(X0) [cnf transformation 55]
113. ~calm(lucy) [cnf transformation 22]
114. humble(X0) | patient(X0) [subsumption resolution 80,75]
139. 6 <=> ! [X0] : patient(X0) [avatar definition]
140. patient(X0) <- (6) [avatar component clause 139]
220. generous(lucy) [resolution 102,113]
221. patient(X0) | ~quiet(X0) [resolution 103,77]
224. ~quiet(lucy) [resolution 220,77]
234. quiet(X0) | patient(X0) | patient(X0) [resolution 72,114]
236. quiet(X0) | patient(X0) [duplicate literal removal 234]
238. patient(X0) [subsumption resolution 236,221]
239. 6 [avatar split clause 238,139]
274. kind(lucy) [resolution 224,67]
287. ~patient(lucy) | ~kind(lucy) [resolution 83,220]
288. ~kind(lucy) <- (6) [subsumption resolution 287,140]
289. $false <- (6) [subsumption resolution 288,274]
290. ~6 [avatar contradiction clause 289]
291. $false [avatar sat refutation 239,290]
% SZS output end Proof for 7501163777503587061185996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both tall and generous is funny or rich and vice versa.
If someone is both kind and not happy then susan is not generous and vice versa.
If someone is either generous or old then someone is both not patient and not rich and vice versa.
If john is not patient or not happy then someone is not quiet.
Everyone who is not calm or not funny is kind.
Everyone who is not humble is either not quiet or old and vice versa.
Everyone who is not kind is happy or tall.
If someone is not quiet then someone is either patient or not quiet.
If someone is kind or not quiet then paul is quiet or not quiet and vice versa.
Everyone who is either not strong or not tall is not rich or quiet and vice versa.
If someone is both not rich and tall then someone is either not creative or not generous and vice versa.
Everyone who is kind or patient is either rich or patient.
If paul is not tall or kind then alice is not old.
If someone is not patient then john is not quiet and vice versa.
If someone is not happy then someone is both not curious and funny and vice versa.
Everyone who is not curious or not happy is both not rich and wise and vice versa.
Alice is patient or humble.
Someone is both calm and not quiet.
Someone is either not rich or tall.
Lucy is rich or not creative.
Fred is old.
Someone is both wise and generous.
Mary is both not happy and not quiet.
Someone is both not tall and curious. | Mary is not wise. | contradiction | (![X]:((tall(X)&generous(X))<=>(funny(X)|rich(X))))&
((?[X]:((kind(X)&~happy(X))))<=>(~generous(susan)))&
((?[X]:((generous(X)<~>old(X))))<=>(?[X]:((~patient(X)&~rich(X)))))&
(((~patient(john)|~happy(john)))=>(?[X]:(~quiet(X))))&
(![X]:((~calm(X)|~funny(X))=>kind(X)))&
(![X]:(~humble(X)<=>(~quiet(X)<~>old(X))))&
(![X]:(~kind(X)=>(happy(X)|tall(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((patient(X)<~>~quiet(X)))))&
((?[X]:((kind(X)|~quiet(X))))<=>((quiet(paul)|~quiet(paul))))&
(![X]:((~strong(X)<~>~tall(X))<=>(~rich(X)|quiet(X))))&
((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((~creative(X)<~>~generous(X)))))&
(![X]:((kind(X)|patient(X))=>(rich(X)<~>patient(X))))&
(((~tall(paul)|kind(paul)))=>(~old(alice)))&
((?[X]:(~patient(X)))<=>(~quiet(john)))&
((?[X]:(~happy(X)))<=>(?[X]:((~curious(X)&funny(X)))))&
(![X]:((~curious(X)|~happy(X))<=>(~rich(X)&wise(X))))&
((patient(alice)|humble(alice)))&
(?[X]:((calm(X)&~quiet(X))))&
(?[X]:((~rich(X)<~>tall(X))))&
((rich(lucy)|~creative(lucy)))&
(old(fred))&
(?[X]:((wise(X)&generous(X))))&
((~happy(mary)&~quiet(mary)))&
(?[X]:((~tall(X)&curious(X)))) | ~wise(mary) | [
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3063402142320568376586685
% SZS output start Proof for 3063402142320568376586685
16. ! [X0] : ((~happy(X0) | ~curious(X0)) <=> (wise(X0) & ~rich(X0))) [input p15]
23. ~quiet(mary) & ~happy(mary) [input p22]
25. ~wise(mary) [input hypothesis]
81. ! [X0] : (((~happy(X0) | ~curious(X0)) | (~wise(X0) | rich(X0))) & ((wise(X0) & ~rich(X0)) | (happy(X0) & curious(X0)))) [nnf transformation 16]
82. ! [X0] : ((~happy(X0) | ~curious(X0) | ~wise(X0) | rich(X0)) & ((wise(X0) & ~rich(X0)) | (happy(X0) & curious(X0)))) [flattening 81]
144. wise(X0) | happy(X0) [cnf transformation 82]
154. ~happy(mary) [cnf transformation 23]
158. ~wise(mary) [cnf transformation 25]
365. happy(mary) [resolution 144,158]
366. $false [subsumption resolution 365,154]
% SZS output end Proof for 3063402142320568376586685
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then someone is wise and vice versa.
Everyone who is both quiet and funny is either not old or curious and vice versa.
Everyone who is either funny or wise is not kind and vice versa.
If someone is humble or quiet then mary is not humble and vice versa.
Everyone who is both tall and not generous is both not creative and old and vice versa.
Everyone who is tall or not humble is either not strong or not kind.
If someone is either not old or not kind then someone is patient and vice versa.
If someone is not rich or not creative then someone is happy and vice versa.
Everyone who is either rich or old is either not quiet or tall.
Everyone who is not humble is both curious and wise.
If mary is both not calm and not happy then lucy is rich and vice versa.
If someone is tall or not rich then fred is rich and vice versa.
Everyone who is brave is both not rich and patient and vice versa.
Everyone who is not happy or not patient is both wise and not quiet.
Everyone who is funny is funny or not wise and vice versa.
If someone is wise or not curious then someone is either creative or not brave.
Someone is either wise or not creative.
Mary is either brave or funny.
Susan is rich or patient.
Someone is both not creative and not funny.
Someone is tall or not kind.
Someone is both patient and not tall.
Someone is not strong or not patient. | Lucy is kind. | contradiction | ((~funny(lucy))<=>(?[X]:(wise(X))))&
(![X]:((quiet(X)&funny(X))<=>(~old(X)<~>curious(X))))&
(![X]:((funny(X)<~>wise(X))<=>~kind(X)))&
((?[X]:((humble(X)|quiet(X))))<=>(~humble(mary)))&
(![X]:((tall(X)&~generous(X))<=>(~creative(X)&old(X))))&
(![X]:((tall(X)|~humble(X))=>(~strong(X)<~>~kind(X))))&
((?[X]:((~old(X)<~>~kind(X))))<=>(?[X]:(patient(X))))&
((?[X]:((~rich(X)|~creative(X))))<=>(?[X]:(happy(X))))&
(![X]:((rich(X)<~>old(X))=>(~quiet(X)<~>tall(X))))&
(![X]:(~humble(X)=>(curious(X)&wise(X))))&
(((~calm(mary)&~happy(mary)))<=>(rich(lucy)))&
((?[X]:((tall(X)|~rich(X))))<=>(rich(fred)))&
(![X]:(brave(X)<=>(~rich(X)&patient(X))))&
(![X]:((~happy(X)|~patient(X))=>(wise(X)&~quiet(X))))&
(![X]:(funny(X)<=>(funny(X)|~wise(X))))&
((?[X]:((wise(X)|~curious(X))))=>(?[X]:((creative(X)<~>~brave(X)))))&
(?[X]:((wise(X)<~>~creative(X))))&
((brave(mary)<~>funny(mary)))&
((rich(susan)|patient(susan)))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((patient(X)&~tall(X))))&
(?[X]:((~strong(X)|~patient(X)))) | kind(lucy) | [
"p0",
"p2",
"p3",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2245082946236308926646070
% SZS output start Proof for 2245082946236308926646070
1. ~funny(lucy) <=> ? [X0] : wise(X0) [input p0]
3. ! [X0] : ((funny(X0) <~> wise(X0)) <=> ~kind(X0)) [input p2]
4. ? [X0] : (quiet(X0) | humble(X0)) <=> ~humble(mary) [input p3]
10. ! [X0] : (~humble(X0) => (wise(X0) & curious(X0))) [input p9]
15. ! [X0] : (funny(X0) <=> (~wise(X0) | funny(X0))) [input p14]
24. kind(lucy) [input hypothesis]
30. ! [X0] : ((wise(X0) & curious(X0)) | humble(X0)) [ennf transformation 10]
33. (~funny(lucy) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | funny(lucy)) [nnf transformation 1]
34. (~funny(lucy) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | funny(lucy)) [rectify 33]
35. ? [X1] : wise(X1) => wise(sK0) [choice axiom]
36. (~funny(lucy) | ! [X0] : ~wise(X0)) & (wise(sK0) | funny(lucy)) [skolemisation 34,35]
39. ! [X0] : ((((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | kind(X0)) & (~kind(X0) | ((funny(X0) | ~wise(X0)) & (wise(X0) | ~funny(X0))))) [nnf transformation 3]
40. (? [X0] : (quiet(X0) | humble(X0)) | humble(mary)) & (~humble(mary) | ! [X0] : (~quiet(X0) & ~humble(X0))) [nnf transformation 4]
41. (? [X0] : (quiet(X0) | humble(X0)) | humble(mary)) & (~humble(mary) | ! [X1] : (~quiet(X1) & ~humble(X1))) [rectify 40]
42. ? [X0] : (quiet(X0) | humble(X0)) => (quiet(sK1) | humble(sK1)) [choice axiom]
43. ((quiet(sK1) | humble(sK1)) | humble(mary)) & (~humble(mary) | ! [X1] : (~quiet(X1) & ~humble(X1))) [skolemisation 41,42]
66. ! [X0] : ((funny(X0) | (wise(X0) & ~funny(X0))) & ((~wise(X0) | funny(X0)) | ~funny(X0))) [nnf transformation 15]
67. ! [X0] : ((funny(X0) | (wise(X0) & ~funny(X0))) & (~wise(X0) | funny(X0) | ~funny(X0))) [flattening 66]
85. ~funny(lucy) | ~wise(X0) [cnf transformation 36]
93. ~kind(X0) | funny(X0) | ~wise(X0) [cnf transformation 39]
96. ~humble(mary) | ~humble(X1) [cnf transformation 43]
119. humble(X0) | wise(X0) [cnf transformation 30]
135. wise(X0) | funny(X0) [cnf transformation 67]
151. kind(lucy) [cnf transformation 24]
153. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
154. ~wise(X0) <- (1) [avatar component clause 153]
156. 2 <=> funny(lucy) [avatar definition]
159. 1 | ~2 [avatar split clause 85,156,153]
166. 4 <=> humble(mary) [avatar definition]
167. ~humble(mary) <- (~4) [avatar component clause 166]
168. humble(mary) <- (4) [avatar component clause 166]
183. 8 <=> ! [X1] : ~humble(X1) [avatar definition]
184. ~humble(X1) <- (8) [avatar component clause 183]
185. 8 | ~4 [avatar split clause 96,166,183]
333. wise(mary) <- (~4) [resolution 119,167]
357. funny(lucy) | ~wise(lucy) [resolution 93,151]
368. funny(lucy) [subsumption resolution 357,135]
369. 2 [avatar split clause 368,156]
372. $false <- (1, ~4) [resolution 154,333]
377. ~1 | 4 [avatar contradiction clause 372]
380. $false <- (4, 8) [subsumption resolution 168,184]
381. ~4 | ~8 [avatar contradiction clause 380]
382. $false [avatar sat refutation 159,185,369,377,381]
% SZS output end Proof for 2245082946236308926646070
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is not strong or not curious and vice versa. If someone is creative or not humble then john is not brave or not calm and vice versa. If paul is not tall or rich then mary is both wise and not curious and vice versa. If someone is both kind and strong then john is not patient or happy. Everyone who is not brave is not quiet or not humble. Everyone who is either not old or humble is either creative or calm. Everyone who is either not wise or not creative is tall and vice versa. If john is tall then mary is either not curious or not old. If lucy is not happy then mary is not generous and vice versa. Everyone who is both not kind and not happy is not quiet and vice versa. Everyone who is both not curious and wise is both not old and not happy and vice versa. If someone is both not strong and quiet then someone is not calm or not happy. If susan is rich or funny then paul is old or patient and vice versa. Everyone who is both not generous and not wise is not brave. Everyone who is either not quiet or not kind is both creative and rich and vice versa. Everyone who is either not humble or not creative is funny or quiet and vice versa. Someone is either wise or old. Someone is either generous or old. Someone is both patient and wise. Fred is not wise or curious. Fred is not strong. Fred is either not humble or creative. Lucy is both happy and not kind. Someone is not funny or not brave. | Lucy is happy. | entailment | (![X]:(patient(X)<=>(~strong(X)|~curious(X))))&
((?[X]:((creative(X)|~humble(X))))<=>((~brave(john)|~calm(john))))&
(((~tall(paul)|rich(paul)))<=>((wise(mary)&~curious(mary))))&
((?[X]:((kind(X)&strong(X))))=>((~patient(john)|happy(john))))&
(![X]:(~brave(X)=>(~quiet(X)|~humble(X))))&
(![X]:((~old(X)<~>humble(X))=>(creative(X)<~>calm(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>tall(X)))&
((tall(john))=>((~curious(mary)<~>~old(mary))))&
((~happy(lucy))<=>(~generous(mary)))&
(![X]:((~kind(X)&~happy(X))<=>~quiet(X)))&
(![X]:((~curious(X)&wise(X))<=>(~old(X)&~happy(X))))&
((?[X]:((~strong(X)&quiet(X))))=>(?[X]:((~calm(X)|~happy(X)))))&
(((rich(susan)|funny(susan)))<=>((old(paul)|patient(paul))))&
(![X]:((~generous(X)&~wise(X))=>~brave(X)))&
(![X]:((~quiet(X)<~>~kind(X))<=>(creative(X)&rich(X))))&
(![X]:((~humble(X)<~>~creative(X))<=>(funny(X)|quiet(X))))&
(?[X]:((wise(X)<~>old(X))))&
(?[X]:((generous(X)<~>old(X))))&
(?[X]:((patient(X)&wise(X))))&
((~wise(fred)|curious(fred)))&
(~strong(fred))&
((~humble(fred)<~>creative(fred)))&
((happy(lucy)&~kind(lucy)))&
(?[X]:((~funny(X)|~brave(X)))) | happy(lucy) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 557240532441674692863039
% SZS output start Proof for 557240532441674692863039
23. ~kind(lucy) & happy(lucy) [input p22]
25. ~happy(lucy) [input hypothesis]
134. happy(lucy) [cnf transformation 23]
137. ~happy(lucy) [cnf transformation 25]
212. 17 <=> happy(lucy) [avatar definition]
290. 17 [avatar split clause 134,212]
300. ~17 [avatar split clause 137,212]
301. $false [avatar sat refutation 290,300]
% SZS output end Proof for 557240532441674692863039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or brave is not brave.
Everyone who is not wise or not happy is not kind or not funny.
Everyone who is either generous or not wise is either humble or not tall and vice versa.
If susan is both not strong and not brave then lucy is both not kind and brave and vice versa.
If mary is not rich or kind then someone is not funny or wise.
If someone is not humble or patient then lucy is tall or happy.
Everyone who is both creative and not old is creative and vice versa.
Everyone who is both funny and not generous is calm and vice versa.
If alice is funny then someone is rich and vice versa.
Everyone who is generous or happy is both generous and kind.
Everyone who is either not kind or generous is both quiet and not strong and vice versa.
Everyone who is not humble or funny is either creative or funny.
If susan is not rich or not creative then john is either not calm or not brave and vice versa.
Everyone who is both not kind and not rich is happy or not patient and vice versa.
Someone is both tall and patient.
Alice is patient or not creative.
Alice is either not patient or tall.
Someone is not funny or not tall.
Someone is both creative and not brave.
Susan is not quiet. | Mary is not rich. | neutral | (![X]:((~tall(X)|brave(X))=>~brave(X)))&
(![X]:((~wise(X)|~happy(X))=>(~kind(X)|~funny(X))))&
(![X]:((generous(X)<~>~wise(X))<=>(humble(X)<~>~tall(X))))&
(((~strong(susan)&~brave(susan)))<=>((~kind(lucy)&brave(lucy))))&
(((~rich(mary)|kind(mary)))=>(?[X]:((~funny(X)|wise(X)))))&
((?[X]:((~humble(X)|patient(X))))=>((tall(lucy)|happy(lucy))))&
(![X]:((creative(X)&~old(X))<=>creative(X)))&
(![X]:((funny(X)&~generous(X))<=>calm(X)))&
((funny(alice))<=>(?[X]:(rich(X))))&
(![X]:((generous(X)|happy(X))=>(generous(X)&kind(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(quiet(X)&~strong(X))))&
(![X]:((~humble(X)|funny(X))=>(creative(X)<~>funny(X))))&
(((~rich(susan)|~creative(susan)))<=>((~calm(john)<~>~brave(john))))&
(![X]:((~kind(X)&~rich(X))<=>(happy(X)|~patient(X))))&
(?[X]:((tall(X)&patient(X))))&
((patient(alice)|~creative(alice)))&
((~patient(alice)<~>tall(alice)))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((creative(X)&~brave(X))))&
(~quiet(susan)) | ~rich(mary) | [] | null | 0 |
If paul is quiet or kind then someone is not humble or not patient and vice versa.
If alice is brave then someone is not generous and vice versa.
Everyone who is humble or tall is either not creative or curious and vice versa.
If lucy is either tall or generous then someone is quiet.
Everyone who is either generous or not old is not humble or not quiet and vice versa.
Everyone who is both not wise and not generous is not old or not rich.
Everyone who is not rich is generous.
If someone is both brave and old then someone is not generous and vice versa.
If john is both brave and kind then someone is humble or not brave and vice versa.
If mary is not tall or not calm then paul is both not kind and wise.
Everyone who is either not tall or generous is either not funny or creative and vice versa.
Everyone who is both not quiet and not calm is not generous and vice versa.
If someone is old or not happy then someone is wise and vice versa.
If someone is both tall and not kind then someone is both not wise and not humble.
If someone is both not calm and humble then fred is not quiet or not generous.
Everyone who is both kind and brave is kind or not generous.
Lucy is either not humble or not old.
Mary is not generous.
Alice is tall or quiet.
Someone is not curious or not funny.
Mary is both not tall and kind.
Someone is either strong or not funny.
Someone is old or quiet.
Someone is not kind or not old. | Paul is not kind. | entailment | (((quiet(paul)|kind(paul)))<=>(?[X]:((~humble(X)|~patient(X)))))&
((brave(alice))<=>(?[X]:(~generous(X))))&
(![X]:((humble(X)|tall(X))<=>(~creative(X)<~>curious(X))))&
(((tall(lucy)<~>generous(lucy)))=>(?[X]:(quiet(X))))&
(![X]:((generous(X)<~>~old(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((~wise(X)&~generous(X))=>(~old(X)|~rich(X))))&
(![X]:(~rich(X)=>generous(X)))&
((?[X]:((brave(X)&old(X))))<=>(?[X]:(~generous(X))))&
(((brave(john)&kind(john)))<=>(?[X]:((humble(X)|~brave(X)))))&
(((~tall(mary)|~calm(mary)))=>((~kind(paul)&wise(paul))))&
(![X]:((~tall(X)<~>generous(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((~quiet(X)&~calm(X))<=>~generous(X)))&
((?[X]:((old(X)|~happy(X))))<=>(?[X]:(wise(X))))&
((?[X]:((tall(X)&~kind(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
((?[X]:((~calm(X)&humble(X))))=>((~quiet(fred)|~generous(fred))))&
(![X]:((kind(X)&brave(X))=>(kind(X)|~generous(X))))&
((~humble(lucy)<~>~old(lucy)))&
(~generous(mary))&
((tall(alice)|quiet(alice)))&
(?[X]:((~curious(X)|~funny(X))))&
((~tall(mary)&kind(mary)))&
(?[X]:((strong(X)<~>~funny(X))))&
(?[X]:((old(X)|quiet(X))))&
(?[X]:((~kind(X)|~old(X)))) | ~kind(paul) | [
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8653744948147753765290247
% SZS output start Proof for 8653744948147753765290247
10. (~calm(mary) | ~tall(mary)) => (wise(paul) & ~kind(paul)) [input p9]
21. kind(mary) & ~tall(mary) [input p20]
25. kind(paul) [input hypothesis]
33. (wise(paul) & ~kind(paul)) | (calm(mary) & tall(mary)) [ennf transformation 10]
116. ~kind(paul) | tall(mary) [cnf transformation 33]
143. ~tall(mary) [cnf transformation 21]
149. kind(paul) [cnf transformation 25]
158. 3 <=> kind(paul) [avatar definition]
258. 25 <=> tall(mary) [avatar definition]
263. 25 | ~3 [avatar split clause 116,158,258]
338. ~25 [avatar split clause 143,258]
367. 3 [avatar split clause 149,158]
368. $false [avatar sat refutation 263,338,367]
% SZS output end Proof for 8653744948147753765290247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is kind then lucy is either not curious or not rich and vice versa.
If fred is either generous or not patient then someone is curious and vice versa.
If someone is generous then john is not tall.
Everyone who is not curious is either happy or brave and vice versa.
If susan is not brave then someone is happy.
If someone is both not quiet and wise then someone is both not rich and old and vice versa.
Everyone who is either generous or not brave is not kind and vice versa.
If john is either brave or tall then someone is funny or happy.
If someone is either not funny or patient then fred is not curious and vice versa.
If john is either happy or tall then someone is both not humble and not strong and vice versa.
Everyone who is both not tall and not creative is either rich or strong.
Everyone who is both curious and not old is either not old or strong.
If someone is not humble then someone is not creative.
If someone is either not wise or old then lucy is both not kind and not funny.
Everyone who is either not tall or wise is not generous and vice versa.
Everyone who is either not patient or not tall is either not kind or not quiet.
Someone is either old or quiet.
Someone is not tall or not rich.
Someone is curious or patient.
Paul is rich.
Mary is both funny and brave.
Mary is either not wise or happy.
Lucy is generous or not happy. | Mary is happy. | neutral | ((kind(lucy))<=>((~curious(lucy)<~>~rich(lucy))))&
(((generous(fred)<~>~patient(fred)))<=>(?[X]:(curious(X))))&
((?[X]:(generous(X)))=>(~tall(john)))&
(![X]:(~curious(X)<=>(happy(X)<~>brave(X))))&
((~brave(susan))=>(?[X]:(happy(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>(?[X]:((~rich(X)&old(X)))))&
(![X]:((generous(X)<~>~brave(X))<=>~kind(X)))&
(((brave(john)<~>tall(john)))=>(?[X]:((funny(X)|happy(X)))))&
((?[X]:((~funny(X)<~>patient(X))))<=>(~curious(fred)))&
(((happy(john)<~>tall(john)))<=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((~tall(X)&~creative(X))=>(rich(X)<~>strong(X))))&
(![X]:((curious(X)&~old(X))=>(~old(X)<~>strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~creative(X))))&
((?[X]:((~wise(X)<~>old(X))))=>((~kind(lucy)&~funny(lucy))))&
(![X]:((~tall(X)<~>wise(X))<=>~generous(X)))&
(![X]:((~patient(X)<~>~tall(X))=>(~kind(X)<~>~quiet(X))))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul))&
((funny(mary)&brave(mary)))&
((~wise(mary)<~>happy(mary)))&
((generous(lucy)|~happy(lucy))) | happy(mary) | [] | null | 0 |
If someone is either not old or not patient then lucy is creative or not happy. Everyone who is both funny and curious is rich or brave and vice versa. If paul is either tall or curious then alice is both not old and generous and vice versa. Everyone who is not brave or not tall is humble and vice versa. Everyone who is not curious is calm and vice versa. Everyone who is either wise or not generous is not generous. If someone is not funny then someone is either not strong or not generous. Everyone who is rich or not curious is either not humble or strong and vice versa. Everyone who is not quiet is not curious or not calm and vice versa. Everyone who is not generous or brave is both happy and kind and vice versa. Everyone who is either wise or curious is not happy and vice versa. If mary is both not wise and not creative then john is both funny and humble and vice versa. If fred is not old then susan is not humble. If someone is brave then someone is either generous or curious. If mary is not humble or not old then someone is both happy and not quiet and vice versa. If alice is rich or not quiet then someone is generous and vice versa. Someone is either wise or not old. Susan is patient. Mary is wise or not quiet. Alice is both funny and kind. Paul is happy or not funny. Someone is either quiet or not rich. Someone is both not wise and tall. Someone is either brave or not humble. | Paul is humble. | neutral | ((?[X]:((~old(X)<~>~patient(X))))=>((creative(lucy)|~happy(lucy))))&
(![X]:((funny(X)&curious(X))<=>(rich(X)|brave(X))))&
(((tall(paul)<~>curious(paul)))<=>((~old(alice)&generous(alice))))&
(![X]:((~brave(X)|~tall(X))<=>humble(X)))&
(![X]:(~curious(X)<=>calm(X)))&
(![X]:((wise(X)<~>~generous(X))=>~generous(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((rich(X)|~curious(X))<=>(~humble(X)<~>strong(X))))&
(![X]:(~quiet(X)<=>(~curious(X)|~calm(X))))&
(![X]:((~generous(X)|brave(X))<=>(happy(X)&kind(X))))&
(![X]:((wise(X)<~>curious(X))<=>~happy(X)))&
(((~wise(mary)&~creative(mary)))<=>((funny(john)&humble(john))))&
((~old(fred))=>(~humble(susan)))&
((?[X]:(brave(X)))=>(?[X]:((generous(X)<~>curious(X)))))&
(((~humble(mary)|~old(mary)))<=>(?[X]:((happy(X)&~quiet(X)))))&
(((rich(alice)|~quiet(alice)))<=>(?[X]:(generous(X))))&
(?[X]:((wise(X)<~>~old(X))))&
(patient(susan))&
((wise(mary)|~quiet(mary)))&
((funny(alice)&kind(alice)))&
((happy(paul)|~funny(paul)))&
(?[X]:((quiet(X)<~>~rich(X))))&
(?[X]:((~wise(X)&tall(X))))&
(?[X]:((brave(X)<~>~humble(X)))) | humble(paul) | [] | null | 0 |
If fred is not calm then someone is not calm.
Everyone who is not kind is not quiet and vice versa.
If alice is rich or not old then fred is both not humble and wise.
If someone is both calm and funny then john is generous or not happy and vice versa.
If paul is either not tall or old then someone is both generous and quiet and vice versa.
Everyone who is not strong or rich is either tall or creative.
Everyone who is not curious or happy is either old or not patient.
Everyone who is not wise is either funny or not patient.
If someone is either old or not wise then someone is curious or patient.
If paul is rich or not humble then someone is both not quiet and tall.
Everyone who is both not funny and not wise is old and vice versa.
If someone is both creative and not brave then fred is either not creative or humble.
Everyone who is not tall or wise is both kind and happy and vice versa.
Everyone who is old or not funny is both patient and not generous and vice versa.
If alice is quiet or not old then someone is both humble and happy.
If fred is both happy and not humble then someone is not happy or tall.
Lucy is not wise or wise.
Someone is not quiet or happy.
Lucy is both funny and happy.
Someone is both not patient and not brave.
Someone is not quiet or not old.
Paul is both rich and quiet. | Fred is old. | contradiction | ((~calm(fred))=>(?[X]:(~calm(X))))&
(![X]:(~kind(X)<=>~quiet(X)))&
(((rich(alice)|~old(alice)))=>((~humble(fred)&wise(fred))))&
((?[X]:((calm(X)&funny(X))))<=>((generous(john)|~happy(john))))&
(((~tall(paul)<~>old(paul)))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:((~strong(X)|rich(X))=>(tall(X)<~>creative(X))))&
(![X]:((~curious(X)|happy(X))=>(old(X)<~>~patient(X))))&
(![X]:(~wise(X)=>(funny(X)<~>~patient(X))))&
((?[X]:((old(X)<~>~wise(X))))=>(?[X]:((curious(X)|patient(X)))))&
(((rich(paul)|~humble(paul)))=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((~funny(X)&~wise(X))<=>old(X)))&
((?[X]:((creative(X)&~brave(X))))=>((~creative(fred)<~>humble(fred))))&
(![X]:((~tall(X)|wise(X))<=>(kind(X)&happy(X))))&
(![X]:((old(X)|~funny(X))<=>(patient(X)&~generous(X))))&
(((quiet(alice)|~old(alice)))=>(?[X]:((humble(X)&happy(X)))))&
(((happy(fred)&~humble(fred)))=>(?[X]:((~happy(X)|tall(X)))))&
((~wise(lucy)|wise(lucy)))&
(?[X]:((~quiet(X)|happy(X))))&
((funny(lucy)&happy(lucy)))&
(?[X]:((~patient(X)&~brave(X))))&
(?[X]:((~quiet(X)|~old(X))))&
((rich(paul)&quiet(paul))) | old(fred) | [
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3708190575284821422287444
% SZS output start Proof for 3708190575284821422287444
8. ! [X0] : (~wise(X0) => (funny(X0) <~> ~patient(X0))) [input p7]
11. ! [X0] : ((~wise(X0) & ~funny(X0)) <=> old(X0)) [input p10]
14. ! [X0] : ((~funny(X0) | old(X0)) <=> (~generous(X0) & patient(X0))) [input p13]
23. old(fred) [input hypothesis]
32. ! [X0] : ((funny(X0) <~> ~patient(X0)) | wise(X0)) [ennf transformation 8]
52. ! [X0] : (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | wise(X0)) [nnf transformation 32]
55. ! [X0] : (((~wise(X0) & ~funny(X0)) | ~old(X0)) & (old(X0) | (wise(X0) | funny(X0)))) [nnf transformation 11]
56. ! [X0] : (((~wise(X0) & ~funny(X0)) | ~old(X0)) & (old(X0) | wise(X0) | funny(X0))) [flattening 55]
60. ! [X0] : (((~funny(X0) | old(X0)) | (generous(X0) | ~patient(X0))) & ((~generous(X0) & patient(X0)) | (funny(X0) & ~old(X0)))) [nnf transformation 14]
61. ! [X0] : ((~funny(X0) | old(X0) | generous(X0) | ~patient(X0)) & ((~generous(X0) & patient(X0)) | (funny(X0) & ~old(X0)))) [flattening 60]
94. ~patient(X0) | funny(X0) | wise(X0) [cnf transformation 52]
101. ~funny(X0) | ~old(X0) [cnf transformation 56]
102. ~wise(X0) | ~old(X0) [cnf transformation 56]
111. patient(X0) | funny(X0) [cnf transformation 61]
129. old(fred) [cnf transformation 23]
296. funny(X0) | wise(X0) | funny(X0) [resolution 94,111]
299. funny(X0) | wise(X0) [duplicate literal removal 296]
300. wise(X0) | ~old(X0) [resolution 299,101]
301. ~old(X0) [subsumption resolution 300,102]
307. $false [resolution 301,129]
% SZS output end Proof for 3708190575284821422287444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is kind.
If someone is quiet then alice is both creative and not old and vice versa.
Everyone who is either brave or not patient is old or wise.
Everyone who is patient is not strong or not brave and vice versa.
Everyone who is both wise and happy is not old or kind and vice versa.
Everyone who is either not old or not curious is not wise or not funny and vice versa.
If someone is either not strong or not funny then alice is not kind or humble and vice versa.
Everyone who is either not funny or not generous is both funny and brave.
If lucy is not curious or old then someone is brave or not brave and vice versa.
Everyone who is either not happy or tall is both kind and not funny and vice versa.
If mary is not calm then someone is either not patient or curious and vice versa.
Everyone who is rich or funny is not quiet or old and vice versa.
Everyone who is either wise or quiet is both humble and rich and vice versa.
If alice is calm or rich then fred is not humble or curious and vice versa.
Everyone who is generous or not happy is both tall and wise and vice versa.
Everyone who is both not rich and creative is creative or funny.
Someone is both not patient and happy.
Someone is both not humble and not tall.
Susan is happy.
Lucy is both not tall and not brave.
Someone is either humble or not quiet.
Alice is both humble and not generous.
Alice is rich.
Someone is not calm or not curious. | Alice is not wise. | contradiction | (![X]:(wise(X)=>kind(X)))&
((?[X]:(quiet(X)))<=>((creative(alice)&~old(alice))))&
(![X]:((brave(X)<~>~patient(X))=>(old(X)|wise(X))))&
(![X]:(patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((wise(X)&happy(X))<=>(~old(X)|kind(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(humble(X)&rich(X))))&
(((calm(alice)|rich(alice)))<=>((~humble(fred)|curious(fred))))&
(![X]:((generous(X)|~happy(X))<=>(tall(X)&wise(X))))&
(![X]:((~rich(X)&creative(X))=>(creative(X)|funny(X))))&
(?[X]:((~patient(X)&happy(X))))&
(?[X]:((~humble(X)&~tall(X))))&
(happy(susan))&
((~tall(lucy)&~brave(lucy)))&
(?[X]:((humble(X)<~>~quiet(X))))&
((humble(alice)&~generous(alice)))&
(rich(alice))&
(?[X]:((~calm(X)|~curious(X)))) | ~wise(alice) | [
"p1",
"p11",
"p12",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6418780487144357708790721
% SZS output start Proof for 6418780487144357708790721
2. ? [X0] : quiet(X0) <=> (~old(alice) & creative(alice)) [input p1]
12. ! [X0] : ((funny(X0) | rich(X0)) <=> (old(X0) | ~quiet(X0))) [input p11]
13. ! [X0] : ((wise(X0) <~> quiet(X0)) <=> (rich(X0) & humble(X0))) [input p12]
22. ~generous(alice) & humble(alice) [input p21]
23. rich(alice) [input p22]
25. ~wise(alice) [input hypothesis]
32. (? [X0] : quiet(X0) | (old(alice) | ~creative(alice))) & ((~old(alice) & creative(alice)) | ! [X0] : ~quiet(X0)) [nnf transformation 2]
33. (? [X0] : quiet(X0) | old(alice) | ~creative(alice)) & ((~old(alice) & creative(alice)) | ! [X0] : ~quiet(X0)) [flattening 32]
34. (? [X0] : quiet(X0) | old(alice) | ~creative(alice)) & ((~old(alice) & creative(alice)) | ! [X1] : ~quiet(X1)) [rectify 33]
35. ? [X0] : quiet(X0) => quiet(sK0) [choice axiom]
36. (quiet(sK0) | old(alice) | ~creative(alice)) & ((~old(alice) & creative(alice)) | ! [X1] : ~quiet(X1)) [skolemisation 34,35]
61. ! [X0] : (((funny(X0) | rich(X0)) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | (~funny(X0) & ~rich(X0)))) [nnf transformation 12]
62. ! [X0] : ((funny(X0) | rich(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | (~funny(X0) & ~rich(X0)))) [flattening 61]
63. ! [X0] : ((((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0))))) [nnf transformation 13]
64. ! [X0] : ((((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0))))) [flattening 63]
80. ~old(alice) | ~quiet(X1) [cnf transformation 36]
122. ~rich(X0) | ~quiet(X0) | old(X0) [cnf transformation 62]
130. ~rich(X0) | wise(X0) | quiet(X0) | ~humble(X0) [cnf transformation 64]
151. humble(alice) [cnf transformation 22]
153. rich(alice) [cnf transformation 23]
155. ~wise(alice) [cnf transformation 25]
162. 2 <=> old(alice) [avatar definition]
171. 4 <=> ! [X1] : ~quiet(X1) [avatar definition]
172. ~quiet(X1) <- (4) [avatar component clause 171]
173. 4 | ~2 [avatar split clause 80,162,171]
178. 5 <=> humble(alice) [avatar definition]
179. humble(alice) <- (5) [avatar component clause 178]
254. 22 <=> rich(alice) [avatar definition]
256. rich(alice) <- (22) [avatar component clause 254]
275. 5 [avatar split clause 151,178]
276. 22 [avatar split clause 153,254]
325. ~quiet(alice) | old(alice) <- (22) [resolution 122,256]
350. wise(alice) | quiet(alice) | ~humble(alice) <- (22) [resolution 130,256]
356. quiet(alice) | ~humble(alice) <- (22) [subsumption resolution 350,155]
357. ~humble(alice) <- (4, 22) [subsumption resolution 356,172]
358. $false <- (4, 5, 22) [subsumption resolution 357,179]
359. ~4 | ~5 | ~22 [avatar contradiction clause 358]
361. quiet(alice) <- (5, 22) [subsumption resolution 356,179]
376. old(alice) <- (5, 22) [subsumption resolution 325,361]
377. 2 | ~5 | ~22 [avatar split clause 376,254,178,162]
378. $false [avatar sat refutation 173,275,276,359,377]
% SZS output end Proof for 6418780487144357708790721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is old. If someone is humble then lucy is not quiet or not old and vice versa. If someone is not tall then lucy is both wise and not tall. If lucy is either not old or not strong then paul is not happy. If susan is wise then someone is happy or wise. Everyone who is both not old and old is kind or wise and vice versa. Everyone who is either not curious or strong is either patient or not generous and vice versa. Everyone who is either calm or generous is not calm or kind and vice versa. If someone is happy or not tall then someone is wise or not generous. Everyone who is not tall or not strong is not rich or not calm and vice versa. Everyone who is either not quiet or not tall is either funny or not brave. If lucy is patient or rich then paul is not patient. If someone is not patient or patient then john is both not funny and not wise. Everyone who is either not generous or not funny is not rich and vice versa. If someone is strong then someone is both not tall and happy and vice versa. Fred is calm or not generous. Someone is funny. Alice is humble or quiet. Someone is either funny or not quiet. Someone is either brave or funny. John is curious. Someone is either quiet or creative. | Alice is not tall. | contradiction | (![X]:(kind(X)=>old(X)))&
((?[X]:(humble(X)))<=>((~quiet(lucy)|~old(lucy))))&
((?[X]:(~tall(X)))=>((wise(lucy)&~tall(lucy))))&
(((~old(lucy)<~>~strong(lucy)))=>(~happy(paul)))&
((wise(susan))=>(?[X]:((happy(X)|wise(X)))))&
(![X]:((~old(X)&old(X))<=>(kind(X)|wise(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~calm(X)|kind(X))))&
((?[X]:((happy(X)|~tall(X))))=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:((~tall(X)|~strong(X))<=>(~rich(X)|~calm(X))))&
(![X]:((~quiet(X)<~>~tall(X))=>(funny(X)<~>~brave(X))))&
(((patient(lucy)|rich(lucy)))=>(~patient(paul)))&
((?[X]:((~patient(X)|patient(X))))=>((~funny(john)&~wise(john))))&
(![X]:((~generous(X)<~>~funny(X))<=>~rich(X)))&
((?[X]:(strong(X)))<=>(?[X]:((~tall(X)&happy(X)))))&
((calm(fred)|~generous(fred)))&
(?[X]:(funny(X)))&
((humble(alice)|quiet(alice)))&
(?[X]:((funny(X)<~>~quiet(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(curious(john))&
(?[X]:((quiet(X)<~>creative(X)))) | ~tall(alice) | [
"p0",
"p5",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1131387808222788850469602
% SZS output start Proof for 1131387808222788850469602
1. ! [X0] : (kind(X0) => old(X0)) [input p0]
6. ! [X0] : ((old(X0) & ~old(X0)) <=> (wise(X0) | kind(X0))) [input p5]
8. ! [X0] : ((calm(X0) <~> generous(X0)) <=> (kind(X0) | ~calm(X0))) [input p7]
9. ? [X0] : (~tall(X0) | happy(X0)) => ? [X0] : (~generous(X0) | wise(X0)) [input p8]
23. ~tall(alice) [input hypothesis]
24. ? [X0] : (~tall(X0) | happy(X0)) => ? [X1] : (~generous(X1) | wise(X1)) [rectify 9]
26. ! [X0] : (old(X0) | ~kind(X0)) [ennf transformation 1]
30. ? [X1] : (~generous(X1) | wise(X1)) | ! [X0] : (tall(X0) & ~happy(X0)) [ennf transformation 24]
42. ! [X0] : (((old(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & ((wise(X0) | kind(X0)) | (~old(X0) | old(X0)))) [nnf transformation 6]
43. ! [X0] : (((old(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & (wise(X0) | kind(X0) | ~old(X0) | old(X0))) [flattening 42]
45. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (~kind(X0) & calm(X0))) & ((kind(X0) | ~calm(X0)) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (~kind(X0) & calm(X0))) & (kind(X0) | ~calm(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [flattening 45]
47. ? [X0] : (~generous(X0) | wise(X0)) | ! [X1] : (tall(X1) & ~happy(X1)) [rectify 30]
48. ? [X0] : (~generous(X0) | wise(X0)) => (~generous(sK2) | wise(sK2)) [choice axiom]
49. (~generous(sK2) | wise(sK2)) | ! [X1] : (tall(X1) & ~happy(X1)) [skolemisation 47,48]
70. old(X0) | ~kind(X0) [cnf transformation 26]
80. ~old(X0) | ~kind(X0) [cnf transformation 43]
81. ~old(X0) | ~wise(X0) [cnf transformation 43]
83. old(X0) | ~wise(X0) [cnf transformation 43]
92. kind(X0) | ~calm(X0) | generous(X0) | ~calm(X0) [cnf transformation 46]
94. generous(X0) | calm(X0) | calm(X0) [cnf transformation 46]
99. ~generous(sK2) | wise(sK2) | tall(X1) [cnf transformation 49]
131. ~tall(alice) [cnf transformation 23]
132. kind(X0) | ~calm(X0) | generous(X0) [duplicate literal removal 92]
133. generous(X0) | calm(X0) [duplicate literal removal 94]
153. 5 <=> ! [X0] : tall(X0) [avatar definition]
154. tall(X0) <- (5) [avatar component clause 153]
188. ~wise(X0) [subsumption resolution 81,83]
189. ~kind(X0) [subsumption resolution 80,70]
190. ~calm(X0) | generous(X0) [subsumption resolution 132,189]
191. generous(X0) [subsumption resolution 190,133]
192. wise(sK2) | tall(X1) [subsumption resolution 99,191]
193. tall(X1) [subsumption resolution 192,188]
194. 5 [avatar split clause 193,153]
266. $false <- (5) [resolution 154,131]
267. ~5 [avatar contradiction clause 266]
268. $false [avatar sat refutation 194,267]
% SZS output end Proof for 1131387808222788850469602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or curious is both quiet and not quiet. Everyone who is either happy or not curious is either kind or old and vice versa. If someone is not creative or strong then someone is both patient and tall and vice versa. If paul is both funny and not rich then someone is not curious and vice versa. Everyone who is brave or not curious is both patient and curious and vice versa. If susan is not strong or not rich then someone is not humble and vice versa. Everyone who is not brave or strong is not patient or not strong and vice versa. Everyone who is both not humble and generous is rich and vice versa. If someone is either not happy or tall then someone is not patient or not curious and vice versa. Everyone who is either not calm or calm is curious or creative and vice versa. Everyone who is both not rich and not calm is creative or calm. Everyone who is both not humble and not strong is either not wise or not calm. Everyone who is either creative or quiet is either not rich or humble and vice versa. Everyone who is either curious or not funny is curious or not wise and vice versa. Mary is both not humble and old. Alice is not strong. Mary is funny. Someone is happy or patient. Someone is both kind and tall. Someone is both calm and not strong. Susan is not humble or old. | Mary is not brave. | entailment | (![X]:((wise(X)<~>curious(X))=>(quiet(X)&~quiet(X))))&
(![X]:((happy(X)<~>~curious(X))<=>(kind(X)<~>old(X))))&
((?[X]:((~creative(X)|strong(X))))<=>(?[X]:((patient(X)&tall(X)))))&
(((funny(paul)&~rich(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((brave(X)|~curious(X))<=>(patient(X)&curious(X))))&
(((~strong(susan)|~rich(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)|strong(X))<=>(~patient(X)|~strong(X))))&
(![X]:((~humble(X)&generous(X))<=>rich(X)))&
((?[X]:((~happy(X)<~>tall(X))))<=>(?[X]:((~patient(X)|~curious(X)))))&
(![X]:((~calm(X)<~>calm(X))<=>(curious(X)|creative(X))))&
(![X]:((~rich(X)&~calm(X))=>(creative(X)|calm(X))))&
(![X]:((~humble(X)&~strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(curious(X)|~wise(X))))&
((~humble(mary)&old(mary)))&
(~strong(alice))&
(funny(mary))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:((kind(X)&tall(X))))&
(?[X]:((calm(X)&~strong(X))))&
((~humble(susan)|old(susan))) | ~brave(mary) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2397846652813164692167060
% SZS output start Proof for 2397846652813164692167060
5. ! [X0] : ((~curious(X0) | brave(X0)) <=> (curious(X0) & patient(X0))) [input p4]
7. ! [X0] : ((strong(X0) | ~brave(X0)) <=> (~strong(X0) | ~patient(X0))) [input p6]
22. brave(mary) [input hypothesis]
42. ! [X0] : (((~curious(X0) | brave(X0)) | (~curious(X0) | ~patient(X0))) & ((curious(X0) & patient(X0)) | (curious(X0) & ~brave(X0)))) [nnf transformation 5]
43. ! [X0] : ((~curious(X0) | brave(X0) | ~curious(X0) | ~patient(X0)) & ((curious(X0) & patient(X0)) | (curious(X0) & ~brave(X0)))) [flattening 42]
49. ! [X0] : (((strong(X0) | ~brave(X0)) | (strong(X0) & patient(X0))) & ((~strong(X0) | ~patient(X0)) | (~strong(X0) & brave(X0)))) [nnf transformation 7]
50. ! [X0] : ((strong(X0) | ~brave(X0) | (strong(X0) & patient(X0))) & (~strong(X0) | ~patient(X0) | (~strong(X0) & brave(X0)))) [flattening 49]
90. ~brave(X0) | patient(X0) [cnf transformation 43]
99. ~strong(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 50]
101. strong(X0) | ~brave(X0) | strong(X0) [cnf transformation 50]
144. brave(mary) [cnf transformation 22]
150. ~patient(X0) | ~strong(X0) [duplicate literal removal 99]
151. ~brave(X0) | strong(X0) [duplicate literal removal 101]
282. patient(mary) [resolution 90,144]
290. ~strong(mary) [resolution 150,282]
292. strong(mary) [resolution 151,144]
295. $false [subsumption resolution 290,292]
% SZS output end Proof for 2397846652813164692167060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not funny is strong or quiet and vice versa.
If someone is either generous or funny then someone is curious.
Everyone who is either happy or rich is tall.
Everyone who is either not curious or not old is not happy and vice versa.
If fred is both not kind and not generous then someone is both not generous and funny.
If someone is not old or strong then alice is both not humble and tall and vice versa.
Everyone who is both rich and curious is old or kind.
If someone is either strong or brave then someone is humble.
If someone is either patient or not tall then someone is either quiet or not curious and vice versa.
If someone is generous or not happy then mary is both not brave and wise and vice versa.
Everyone who is not creative is not wise and vice versa.
Everyone who is brave or strong is both not curious and not brave.
If fred is both not curious and not creative then alice is both generous and not wise.
If someone is both patient and not old then john is generous.
Everyone who is either not kind or not happy is not calm or quiet.
If john is either brave or not kind then someone is not wise and vice versa.
Mary is both funny and not old.
Someone is both calm and generous.
Alice is both not creative and not wise.
Alice is both calm and rich.
Alice is rich.
Someone is not creative.
Someone is humble.
Someone is funny. | Mary is strong. | contradiction | (![X]:((~quiet(X)&~funny(X))<=>(strong(X)|quiet(X))))&
((?[X]:((generous(X)<~>funny(X))))=>(?[X]:(curious(X))))&
(![X]:((happy(X)<~>rich(X))=>tall(X)))&
(![X]:((~curious(X)<~>~old(X))<=>~happy(X)))&
(((~kind(fred)&~generous(fred)))=>(?[X]:((~generous(X)&funny(X)))))&
((?[X]:((~old(X)|strong(X))))<=>((~humble(alice)&tall(alice))))&
(![X]:((rich(X)&curious(X))=>(old(X)|kind(X))))&
((?[X]:((strong(X)<~>brave(X))))=>(?[X]:(humble(X))))&
((?[X]:((patient(X)<~>~tall(X))))<=>(?[X]:((quiet(X)<~>~curious(X)))))&
((?[X]:((generous(X)|~happy(X))))<=>((~brave(mary)&wise(mary))))&
(![X]:(~creative(X)<=>~wise(X)))&
(![X]:((brave(X)|strong(X))=>(~curious(X)&~brave(X))))&
(((~curious(fred)&~creative(fred)))=>((generous(alice)&~wise(alice))))&
((?[X]:((patient(X)&~old(X))))=>(generous(john)))&
(![X]:((~kind(X)<~>~happy(X))=>(~calm(X)|quiet(X))))&
(((brave(john)<~>~kind(john)))<=>(?[X]:(~wise(X))))&
((funny(mary)&~old(mary)))&
(?[X]:((calm(X)&generous(X))))&
((~creative(alice)&~wise(alice)))&
((calm(alice)&rich(alice)))&
(rich(alice))&
(?[X]:(~creative(X)))&
(?[X]:(humble(X)))&
(?[X]:(funny(X))) | strong(mary) | [
"p0",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1781958678760556627340687
% SZS output start Proof for 1781958678760556627340687
1. ! [X0] : ((~funny(X0) & ~quiet(X0)) <=> (quiet(X0) | strong(X0))) [input p0]
17. ~old(mary) & funny(mary) [input p16]
25. strong(mary) [input hypothesis]
42. ! [X0] : (((~funny(X0) & ~quiet(X0)) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | (funny(X0) | quiet(X0)))) [nnf transformation 1]
43. ! [X0] : (((~funny(X0) & ~quiet(X0)) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | funny(X0) | quiet(X0))) [flattening 42]
88. ~strong(X0) | ~funny(X0) [cnf transformation 43]
136. funny(mary) [cnf transformation 17]
148. strong(mary) [cnf transformation 25]
322. ~funny(mary) [resolution 88,148]
323. $false [subsumption resolution 322,136]
% SZS output end Proof for 1781958678760556627340687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is either humble or not quiet and vice versa. Everyone who is not quiet is either not wise or not humble and vice versa. If mary is not curious then someone is not kind or happy. If susan is both not old and not generous then paul is patient or not patient and vice versa. If someone is either wise or not generous then someone is both not rich and creative and vice versa. Everyone who is generous is both not calm and not brave and vice versa. If someone is both creative and not creative then paul is not creative or calm. Everyone who is both calm and not calm is not funny or quiet and vice versa. Everyone who is both calm and tall is either curious or not wise and vice versa. If john is not kind then mary is either funny or strong. If someone is either not funny or old then someone is rich or not creative. If someone is either generous or old then fred is not brave and vice versa. If someone is either calm or not funny then someone is both generous and patient and vice versa. Everyone who is both funny and happy is curious. If someone is both strong and calm then mary is not patient or brave. If someone is happy or not calm then someone is either not humble or not generous and vice versa. Fred is not creative. Lucy is both kind and happy. John is curious or patient. Someone is both happy and brave. Someone is both strong and happy. Alice is happy. Someone is tall. | Lucy is kind. | entailment | (![X]:(creative(X)<=>(humble(X)<~>~quiet(X))))&
(![X]:(~quiet(X)<=>(~wise(X)<~>~humble(X))))&
((~curious(mary))=>(?[X]:((~kind(X)|happy(X)))))&
(((~old(susan)&~generous(susan)))<=>((patient(paul)|~patient(paul))))&
((?[X]:((wise(X)<~>~generous(X))))<=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:(generous(X)<=>(~calm(X)&~brave(X))))&
((?[X]:((creative(X)&~creative(X))))=>((~creative(paul)|calm(paul))))&
(![X]:((calm(X)&~calm(X))<=>(~funny(X)|quiet(X))))&
(![X]:((calm(X)&tall(X))<=>(curious(X)<~>~wise(X))))&
((~kind(john))=>((funny(mary)<~>strong(mary))))&
((?[X]:((~funny(X)<~>old(X))))=>(?[X]:((rich(X)|~creative(X)))))&
((?[X]:((generous(X)<~>old(X))))<=>(~brave(fred)))&
((?[X]:((calm(X)<~>~funny(X))))<=>(?[X]:((generous(X)&patient(X)))))&
(![X]:((funny(X)&happy(X))=>curious(X)))&
((?[X]:((strong(X)&calm(X))))=>((~patient(mary)|brave(mary))))&
((?[X]:((happy(X)|~calm(X))))<=>(?[X]:((~humble(X)<~>~generous(X)))))&
(~creative(fred))&
((kind(lucy)&happy(lucy)))&
((curious(john)|patient(john)))&
(?[X]:((happy(X)&brave(X))))&
(?[X]:((strong(X)&happy(X))))&
(happy(alice))&
(?[X]:(tall(X))) | kind(lucy) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6565792400206582595909233
% SZS output start Proof for 6565792400206582595909233
18. happy(lucy) & kind(lucy) [input p17]
24. ~kind(lucy) [input hypothesis]
138. kind(lucy) [cnf transformation 18]
147. ~kind(lucy) [cnf transformation 24]
335. $false [subsumption resolution 147,138]
% SZS output end Proof for 6565792400206582595909233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and happy then lucy is both not quiet and generous and vice versa.
Everyone who is not humble is either not tall or old and vice versa.
Everyone who is either generous or humble is both humble and not calm and vice versa.
Everyone who is brave is both not rich and not tall and vice versa.
Everyone who is both patient and old is tall or rich.
Everyone who is not wise or not tall is curious or humble.
If mary is kind then paul is not quiet and vice versa.
If someone is either generous or not curious then fred is not humble and vice versa.
Everyone who is wise or strong is either not old or not tall.
If someone is curious then someone is not humble and vice versa.
If alice is not quiet then alice is not old or rich and vice versa.
Everyone who is rich is not creative or not tall and vice versa.
Everyone who is both not creative and not tall is rich and vice versa.
If someone is either funny or not humble then susan is creative or not wise.
Everyone who is both brave and creative is either brave or tall and vice versa.
If fred is kind then someone is either calm or not humble.
John is both calm and old.
Someone is both rich and not creative.
Someone is both not kind and wise.
Susan is not quiet or generous.
Susan is either not funny or brave.
Someone is either not wise or tall.
Someone is funny.
John is either calm or not old. | Mary is creative. | contradiction | ((?[X]:((~calm(X)&happy(X))))<=>((~quiet(lucy)&generous(lucy))))&
(![X]:(~humble(X)<=>(~tall(X)<~>old(X))))&
(![X]:((generous(X)<~>humble(X))<=>(humble(X)&~calm(X))))&
(![X]:(brave(X)<=>(~rich(X)&~tall(X))))&
(![X]:((patient(X)&old(X))=>(tall(X)|rich(X))))&
(![X]:((~wise(X)|~tall(X))=>(curious(X)|humble(X))))&
((kind(mary))<=>(~quiet(paul)))&
((?[X]:((generous(X)<~>~curious(X))))<=>(~humble(fred)))&
(![X]:((wise(X)|strong(X))=>(~old(X)<~>~tall(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~humble(X))))&
((~quiet(alice))<=>((~old(alice)|rich(alice))))&
(![X]:(rich(X)<=>(~creative(X)|~tall(X))))&
(![X]:((~creative(X)&~tall(X))<=>rich(X)))&
((?[X]:((funny(X)<~>~humble(X))))=>((creative(susan)|~wise(susan))))&
(![X]:((brave(X)&creative(X))<=>(brave(X)<~>tall(X))))&
((kind(fred))=>(?[X]:((calm(X)<~>~humble(X)))))&
((calm(john)&old(john)))&
(?[X]:((rich(X)&~creative(X))))&
(?[X]:((~kind(X)&wise(X))))&
((~quiet(susan)|generous(susan)))&
((~funny(susan)<~>brave(susan)))&
(?[X]:((~wise(X)<~>tall(X))))&
(?[X]:(funny(X)))&
((calm(john)<~>~old(john))) | creative(mary) | [
"p3",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4712185550521695582302016
% SZS output start Proof for 4712185550521695582302016
4. ! [X0] : (brave(X0) <=> (~tall(X0) & ~rich(X0))) [input p3]
12. ! [X0] : (rich(X0) <=> (~tall(X0) | ~creative(X0))) [input p11]
13. ! [X0] : ((~tall(X0) & ~creative(X0)) <=> rich(X0)) [input p12]
15. ! [X0] : ((creative(X0) & brave(X0)) <=> (brave(X0) <~> tall(X0))) [input p14]
25. creative(mary) [input hypothesis]
43. ! [X0] : ((brave(X0) | (tall(X0) | rich(X0))) & ((~tall(X0) & ~rich(X0)) | ~brave(X0))) [nnf transformation 4]
44. ! [X0] : ((brave(X0) | tall(X0) | rich(X0)) & ((~tall(X0) & ~rich(X0)) | ~brave(X0))) [flattening 43]
58. ! [X0] : ((rich(X0) | (tall(X0) & creative(X0))) & ((~tall(X0) | ~creative(X0)) | ~rich(X0))) [nnf transformation 12]
59. ! [X0] : ((rich(X0) | (tall(X0) & creative(X0))) & (~tall(X0) | ~creative(X0) | ~rich(X0))) [flattening 58]
60. ! [X0] : (((~tall(X0) & ~creative(X0)) | ~rich(X0)) & (rich(X0) | (tall(X0) | creative(X0)))) [nnf transformation 13]
61. ! [X0] : (((~tall(X0) & ~creative(X0)) | ~rich(X0)) & (rich(X0) | tall(X0) | creative(X0))) [flattening 60]
63. ! [X0] : (((creative(X0) & brave(X0)) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0)))) & (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | (~creative(X0) | ~brave(X0)))) [nnf transformation 15]
64. ! [X0] : (((creative(X0) & brave(X0)) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0)))) & (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | ~creative(X0) | ~brave(X0))) [flattening 63]
94. ~brave(X0) | ~tall(X0) [cnf transformation 44]
113. rich(X0) | tall(X0) [cnf transformation 59]
115. ~creative(X0) | ~rich(X0) [cnf transformation 61]
122. brave(X0) | brave(X0) | ~tall(X0) [cnf transformation 64]
141. creative(mary) [cnf transformation 25]
143. brave(X0) | ~tall(X0) [duplicate literal removal 122]
250. ~tall(X0) [subsumption resolution 143,94]
293. ~rich(mary) [resolution 115,141]
295. tall(mary) [resolution 293,113]
296. $false [subsumption resolution 295,250]
% SZS output end Proof for 4712185550521695582302016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is not brave then susan is not kind or not wise.
Everyone who is happy or not humble is patient or humble.
Everyone who is not brave or tall is both not patient and not humble and vice versa.
Everyone who is both not old and tall is both not calm and not tall and vice versa.
If john is not kind or not strong then fred is either not kind or wise and vice versa.
Everyone who is either not funny or patient is either not humble or not quiet.
Everyone who is either happy or calm is tall.
If someone is not tall or not brave then susan is either rich or funny and vice versa.
If fred is both not patient and not wise then someone is both not rich and not generous and vice versa.
Everyone who is not happy or generous is kind or generous.
Everyone who is not wise is humble and vice versa.
Everyone who is old is both curious and quiet and vice versa.
If fred is both kind and strong then lucy is calm and vice versa.
Everyone who is patient or generous is curious or kind.
If someone is both not quiet and not rich then someone is not humble or not brave and vice versa.
If mary is patient or funny then someone is both not curious and not happy and vice versa.
Lucy is either not happy or not funny.
Fred is rich or not curious.
Someone is strong or kind.
Someone is either generous or rich.
Lucy is either brave or not strong.
Fred is both humble and rich. | Fred is not strong. | contradiction | ((~brave(john))=>((~kind(susan)|~wise(susan))))&
(![X]:((happy(X)|~humble(X))=>(patient(X)|humble(X))))&
(![X]:((~brave(X)|tall(X))<=>(~patient(X)&~humble(X))))&
(![X]:((~old(X)&tall(X))<=>(~calm(X)&~tall(X))))&
(((~kind(john)|~strong(john)))<=>((~kind(fred)<~>wise(fred))))&
(![X]:((~funny(X)<~>patient(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((happy(X)<~>calm(X))=>tall(X)))&
((?[X]:((~tall(X)|~brave(X))))<=>((rich(susan)<~>funny(susan))))&
(((~patient(fred)&~wise(fred)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((~happy(X)|generous(X))=>(kind(X)|generous(X))))&
(![X]:(~wise(X)<=>humble(X)))&
(![X]:(old(X)<=>(curious(X)&quiet(X))))&
(((kind(fred)&strong(fred)))<=>(calm(lucy)))&
(![X]:((patient(X)|generous(X))=>(curious(X)|kind(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>(?[X]:((~humble(X)|~brave(X)))))&
(((patient(mary)|funny(mary)))<=>(?[X]:((~curious(X)&~happy(X)))))&
((~happy(lucy)<~>~funny(lucy)))&
((rich(fred)|~curious(fred)))&
(?[X]:((strong(X)|kind(X))))&
(?[X]:((generous(X)<~>rich(X))))&
((brave(lucy)<~>~strong(lucy)))&
((humble(fred)&rich(fred))) | ~strong(fred) | [
"p1",
"p2",
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6057182794996950349422087
% SZS output start Proof for 6057182794996950349422087
2. ! [X0] : ((~humble(X0) | happy(X0)) => (humble(X0) | patient(X0))) [input p1]
3. ! [X0] : ((tall(X0) | ~brave(X0)) <=> (~humble(X0) & ~patient(X0))) [input p2]
4. ! [X0] : ((tall(X0) & ~old(X0)) <=> (~tall(X0) & ~calm(X0))) [input p3]
13. (strong(fred) & kind(fred)) <=> calm(lucy) [input p12]
23. ~strong(fred) [input hypothesis]
27. ! [X0] : ((humble(X0) | patient(X0)) | (humble(X0) & ~happy(X0))) [ennf transformation 2]
28. ! [X0] : (humble(X0) | patient(X0) | (humble(X0) & ~happy(X0))) [flattening 27]
35. ! [X0] : (((tall(X0) | ~brave(X0)) | (humble(X0) | patient(X0))) & ((~humble(X0) & ~patient(X0)) | (~tall(X0) & brave(X0)))) [nnf transformation 3]
36. ! [X0] : ((tall(X0) | ~brave(X0) | humble(X0) | patient(X0)) & ((~humble(X0) & ~patient(X0)) | (~tall(X0) & brave(X0)))) [flattening 35]
37. ! [X0] : (((tall(X0) & ~old(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~tall(X0) | old(X0)))) [nnf transformation 4]
38. ! [X0] : (((tall(X0) & ~old(X0)) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | ~tall(X0) | old(X0))) [flattening 37]
55. ((strong(fred) & kind(fred)) | ~calm(lucy)) & (calm(lucy) | (~strong(fred) | ~kind(fred))) [nnf transformation 13]
56. ((strong(fred) & kind(fred)) | ~calm(lucy)) & (calm(lucy) | ~strong(fred) | ~kind(fred)) [flattening 55]
76. humble(X0) | patient(X0) | humble(X0) [cnf transformation 28]
78. ~tall(X0) | ~patient(X0) [cnf transformation 36]
80. ~tall(X0) | ~humble(X0) [cnf transformation 36]
85. tall(X0) | tall(X0) | calm(X0) [cnf transformation 38]
117. strong(fred) | ~calm(lucy) [cnf transformation 56]
140. ~strong(fred) [cnf transformation 23]
142. calm(X0) | tall(X0) [duplicate literal removal 85]
143. patient(X0) | humble(X0) [duplicate literal removal 76]
230. 18 <=> calm(lucy) [avatar definition]
232. ~calm(lucy) <- (~18) [avatar component clause 230]
234. 19 <=> strong(fred) [avatar definition]
237. ~18 | 19 [avatar split clause 117,234,230]
337. ~19 [avatar split clause 140,234]
343. tall(lucy) <- (~18) [resolution 142,232]
345. ~humble(lucy) <- (~18) [resolution 343,80]
346. ~patient(lucy) <- (~18) [resolution 343,78]
378. humble(lucy) <- (~18) [resolution 346,143]
379. $false <- (~18) [subsumption resolution 378,345]
380. 18 [avatar contradiction clause 379]
381. $false [avatar sat refutation 237,337,380]
% SZS output end Proof for 6057182794996950349422087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or funny is not funny or creative and vice versa. Everyone who is funny is both not funny and funny. If mary is quiet or curious then susan is brave and vice versa. Everyone who is both funny and not wise is wise or not creative and vice versa. Everyone who is either not wise or strong is patient. If someone is humble or not curious then susan is both not patient and not kind and vice versa. If someone is both not quiet and not generous then fred is not curious or not kind and vice versa. If alice is brave then someone is both not humble and not rich. Everyone who is both creative and brave is not curious and vice versa. Everyone who is both tall and happy is both not funny and not patient. If john is not kind or happy then john is either humble or quiet. If someone is both creative and not wise then someone is rich and vice versa. Everyone who is quiet or not humble is happy. Everyone who is not kind or not quiet is both not old and not kind. If paul is either generous or curious then someone is calm or tall and vice versa. Someone is funny or happy. Mary is patient. John is either tall or patient. Someone is not old or happy. Lucy is either not strong or not kind. Someone is not funny. | Lucy is calm. | neutral | (![X]:((~humble(X)|funny(X))<=>(~funny(X)|creative(X))))&
(![X]:(funny(X)=>(~funny(X)&funny(X))))&
(((quiet(mary)|curious(mary)))<=>(brave(susan)))&
(![X]:((funny(X)&~wise(X))<=>(wise(X)|~creative(X))))&
(![X]:((~wise(X)<~>strong(X))=>patient(X)))&
((?[X]:((humble(X)|~curious(X))))<=>((~patient(susan)&~kind(susan))))&
((?[X]:((~quiet(X)&~generous(X))))<=>((~curious(fred)|~kind(fred))))&
((brave(alice))=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((creative(X)&brave(X))<=>~curious(X)))&
(![X]:((tall(X)&happy(X))=>(~funny(X)&~patient(X))))&
(((~kind(john)|happy(john)))=>((humble(john)<~>quiet(john))))&
((?[X]:((creative(X)&~wise(X))))<=>(?[X]:(rich(X))))&
(![X]:((quiet(X)|~humble(X))=>happy(X)))&
(![X]:((~kind(X)|~quiet(X))=>(~old(X)&~kind(X))))&
(((generous(paul)<~>curious(paul)))<=>(?[X]:((calm(X)|tall(X)))))&
(?[X]:((funny(X)|happy(X))))&
(patient(mary))&
((tall(john)<~>patient(john)))&
(?[X]:((~old(X)|happy(X))))&
((~strong(lucy)<~>~kind(lucy)))&
(?[X]:(~funny(X))) | calm(lucy) | [] | null | 0 |
If john is both not generous and not happy then someone is either brave or not wise.
Everyone who is either patient or not wise is rich.
Everyone who is not generous is not patient.
Everyone who is both not old and strong is either not kind or tall.
Everyone who is both generous and creative is not tall or not generous and vice versa.
If susan is not rich or not curious then mary is both not quiet and not kind and vice versa.
Everyone who is either not tall or funny is either not curious or humble.
Everyone who is both calm and not funny is not quiet or not wise.
If someone is either not humble or not tall then mary is not strong or not tall and vice versa.
If lucy is both wise and rich then someone is wise.
If fred is not wise then mary is not curious or not tall and vice versa.
If mary is funny or not funny then someone is tall or not curious.
If fred is both kind and strong then mary is quiet or calm and vice versa.
Everyone who is not calm or old is not patient.
If someone is brave or not generous then someone is not curious or patient.
Everyone who is not strong is not curious or humble.
Lucy is either happy or not kind.
Susan is not kind or creative.
Lucy is not rich or wise.
Mary is both strong and wise.
John is not tall.
Lucy is both not happy and not calm.
Someone is humble. | Mary is curious. | neutral | (((~generous(john)&~happy(john)))=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
(![X]:(~generous(X)=>~patient(X)))&
(![X]:((~old(X)&strong(X))=>(~kind(X)<~>tall(X))))&
(![X]:((generous(X)&creative(X))<=>(~tall(X)|~generous(X))))&
(((~rich(susan)|~curious(susan)))<=>((~quiet(mary)&~kind(mary))))&
(![X]:((~tall(X)<~>funny(X))=>(~curious(X)<~>humble(X))))&
(![X]:((calm(X)&~funny(X))=>(~quiet(X)|~wise(X))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>((~strong(mary)|~tall(mary))))&
(((wise(lucy)&rich(lucy)))=>(?[X]:(wise(X))))&
((~wise(fred))<=>((~curious(mary)|~tall(mary))))&
(((funny(mary)|~funny(mary)))=>(?[X]:((tall(X)|~curious(X)))))&
(((kind(fred)&strong(fred)))<=>((quiet(mary)|calm(mary))))&
(![X]:((~calm(X)|old(X))=>~patient(X)))&
((?[X]:((brave(X)|~generous(X))))=>(?[X]:((~curious(X)|patient(X)))))&
(![X]:(~strong(X)=>(~curious(X)|humble(X))))&
((happy(lucy)<~>~kind(lucy)))&
((~kind(susan)|creative(susan)))&
((~rich(lucy)|wise(lucy)))&
((strong(mary)&wise(mary)))&
(~tall(john))&
((~happy(lucy)&~calm(lucy)))&
(?[X]:(humble(X))) | curious(mary) | [] | null | 0 |
If lucy is either not strong or generous then someone is either patient or wise. Everyone who is not tall or strong is not curious or quiet. If john is not tall then someone is quiet and vice versa. If lucy is not wise then mary is either not rich or not generous. Everyone who is not kind or not rich is both happy and not old and vice versa. Everyone who is happy or not rich is both happy and not happy and vice versa. Everyone who is both generous and not funny is both brave and happy. Everyone who is not rich is either not quiet or not happy and vice versa. Everyone who is either not happy or not quiet is both not rich and not curious. If someone is funny then someone is both strong and curious. If john is either tall or creative then someone is not strong or rich and vice versa. Everyone who is generous is either rich or not generous and vice versa. Everyone who is both happy and not happy is both kind and not wise. If mary is not curious then alice is either kind or not old and vice versa. If paul is both not curious and old then susan is both not creative and not humble and vice versa. Someone is either not tall or not quiet. Someone is not patient or not quiet. Someone is not brave or not calm. Lucy is not wise or not quiet. Mary is both curious and not brave. Someone is not curious. | Susan is not quiet. | entailment | (((~strong(lucy)<~>generous(lucy)))=>(?[X]:((patient(X)<~>wise(X)))))&
(![X]:((~tall(X)|strong(X))=>(~curious(X)|quiet(X))))&
((~tall(john))<=>(?[X]:(quiet(X))))&
((~wise(lucy))=>((~rich(mary)<~>~generous(mary))))&
(![X]:((~kind(X)|~rich(X))<=>(happy(X)&~old(X))))&
(![X]:((happy(X)|~rich(X))<=>(happy(X)&~happy(X))))&
(![X]:((generous(X)&~funny(X))=>(brave(X)&happy(X))))&
(![X]:(~rich(X)<=>(~quiet(X)<~>~happy(X))))&
(![X]:((~happy(X)<~>~quiet(X))=>(~rich(X)&~curious(X))))&
((?[X]:(funny(X)))=>(?[X]:((strong(X)&curious(X)))))&
(((tall(john)<~>creative(john)))<=>(?[X]:((~strong(X)|rich(X)))))&
(![X]:(generous(X)<=>(rich(X)<~>~generous(X))))&
(![X]:((happy(X)&~happy(X))=>(kind(X)&~wise(X))))&
((~curious(mary))<=>((kind(alice)<~>~old(alice))))&
(((~curious(paul)&old(paul)))<=>((~creative(susan)&~humble(susan))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~brave(X)|~calm(X))))&
((~wise(lucy)|~quiet(lucy)))&
((curious(mary)&~brave(mary)))&
(?[X]:(~curious(X))) | ~quiet(susan) | [
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8850142003502728894271373
% SZS output start Proof for 8850142003502728894271373
5. ! [X0] : ((~rich(X0) | ~kind(X0)) <=> (~old(X0) & happy(X0))) [input p4]
6. ! [X0] : ((~rich(X0) | happy(X0)) <=> (~happy(X0) & happy(X0))) [input p5]
9. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) => (~curious(X0) & ~rich(X0))) [input p8]
22. quiet(susan) [input hypothesis]
31. ! [X0] : ((~curious(X0) & ~rich(X0)) | (~happy(X0) <=> ~quiet(X0))) [ennf transformation 9]
43. ! [X0] : (((~rich(X0) | ~kind(X0)) | (old(X0) | ~happy(X0))) & ((~old(X0) & happy(X0)) | (rich(X0) & kind(X0)))) [nnf transformation 5]
44. ! [X0] : ((~rich(X0) | ~kind(X0) | old(X0) | ~happy(X0)) & ((~old(X0) & happy(X0)) | (rich(X0) & kind(X0)))) [flattening 43]
45. ! [X0] : (((~rich(X0) | happy(X0)) | (happy(X0) | ~happy(X0))) & ((~happy(X0) & happy(X0)) | (rich(X0) & ~happy(X0)))) [nnf transformation 6]
46. ! [X0] : ((~rich(X0) | happy(X0) | happy(X0) | ~happy(X0)) & ((~happy(X0) & happy(X0)) | (rich(X0) & ~happy(X0)))) [flattening 45]
48. ! [X0] : ((~curious(X0) & ~rich(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0)))) [nnf transformation 31]
78. happy(X0) | rich(X0) [cnf transformation 44]
84. ~happy(X0) | ~happy(X0) [cnf transformation 46]
85. ~happy(X0) | rich(X0) [cnf transformation 46]
93. ~rich(X0) | ~quiet(X0) | happy(X0) [cnf transformation 48]
126. quiet(susan) [cnf transformation 22]
129. ~happy(X0) [duplicate literal removal 84]
152. 5 <=> ! [X0] : ~quiet(X0) [avatar definition]
153. ~quiet(X0) <- (5) [avatar component clause 152]
178. rich(X0) [subsumption resolution 85,78]
184. ~quiet(X0) | happy(X0) [subsumption resolution 93,178]
185. ~quiet(X0) [subsumption resolution 184,129]
186. 5 [avatar split clause 185,152]
275. $false <- (5) [resolution 153,126]
276. ~5 [avatar contradiction clause 275]
277. $false [avatar sat refutation 186,276]
% SZS output end Proof for 8850142003502728894271373
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.015 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or quiet is tall or not patient.
Everyone who is not calm is not patient.
Everyone who is not generous or not kind is not rich and vice versa.
If someone is either patient or not wise then john is not creative.
If paul is brave or wise then someone is kind and vice versa.
Everyone who is either tall or old is both not brave and happy.
Everyone who is both wise and not quiet is humble or not brave.
If someone is not kind then someone is both not tall and curious and vice versa.
Everyone who is not kind or not tall is either strong or not calm and vice versa.
Everyone who is not calm or not generous is both not patient and not creative and vice versa.
If someone is old then someone is happy or not generous and vice versa.
If someone is curious or brave then susan is not generous and vice versa.
If fred is quiet then john is either not calm or not brave and vice versa.
Everyone who is generous or not old is quiet or humble and vice versa.
Everyone who is wise or calm is both kind and not wise.
Everyone who is both not old and not calm is either not tall or rich and vice versa.
Someone is both not funny and not patient.
Someone is not wise or not funny.
Someone is both not kind and not creative.
Fred is either not wise or not tall.
Someone is both kind and not happy.
John is not wise.
Paul is both kind and not strong.
Lucy is patient. | Susan is not wise. | entailment | (![X]:((~wise(X)<~>quiet(X))=>(tall(X)|~patient(X))))&
(![X]:(~calm(X)=>~patient(X)))&
(![X]:((~generous(X)|~kind(X))<=>~rich(X)))&
((?[X]:((patient(X)<~>~wise(X))))=>(~creative(john)))&
(((brave(paul)|wise(paul)))<=>(?[X]:(kind(X))))&
(![X]:((tall(X)<~>old(X))=>(~brave(X)&happy(X))))&
(![X]:((wise(X)&~quiet(X))=>(humble(X)|~brave(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~tall(X)&curious(X)))))&
(![X]:((~kind(X)|~tall(X))<=>(strong(X)<~>~calm(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~patient(X)&~creative(X))))&
((?[X]:(old(X)))<=>(?[X]:((happy(X)|~generous(X)))))&
((?[X]:((curious(X)|brave(X))))<=>(~generous(susan)))&
((quiet(fred))<=>((~calm(john)<~>~brave(john))))&
(![X]:((generous(X)|~old(X))<=>(quiet(X)|humble(X))))&
(![X]:((wise(X)|calm(X))=>(kind(X)&~wise(X))))&
(![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>rich(X))))&
(?[X]:((~funny(X)&~patient(X))))&
(?[X]:((~wise(X)|~funny(X))))&
(?[X]:((~kind(X)&~creative(X))))&
((~wise(fred)<~>~tall(fred)))&
(?[X]:((kind(X)&~happy(X))))&
(~wise(john))&
((kind(paul)&~strong(paul)))&
(patient(lucy)) | ~wise(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4970649042284514759769141
% SZS output start Proof for 4970649042284514759769141
15. ! [X0] : ((calm(X0) | wise(X0)) => (~wise(X0) & kind(X0))) [input p14]
25. wise(susan) [input hypothesis]
37. ! [X0] : ((~wise(X0) & kind(X0)) | (~calm(X0) & ~wise(X0))) [ennf transformation 15]
124. ~wise(X0) | ~wise(X0) [cnf transformation 37]
143. wise(susan) [cnf transformation 25]
144. ~wise(X0) [duplicate literal removal 124]
258. $false [subsumption resolution 143,144]
% SZS output end Proof for 4970649042284514759769141
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not curious then someone is not wise and vice versa.
If john is either humble or not tall then susan is funny or not rich and vice versa.
Everyone who is both funny and not funny is curious or funny.
If susan is not funny or not humble then someone is either not patient or patient.
If someone is patient or funny then lucy is not curious.
Everyone who is both not tall and not calm is both strong and curious.
If paul is not kind or brave then fred is not quiet or kind and vice versa.
If alice is either strong or funny then someone is both not rich and tall.
Everyone who is either happy or not calm is either rich or not calm.
Everyone who is not quiet or humble is calm and vice versa.
If someone is both not tall and creative then someone is either funny or calm and vice versa.
Everyone who is both not brave and quiet is either patient or not creative and vice versa.
If someone is not happy then susan is either not curious or not kind and vice versa.
Everyone who is strong is not calm or not strong and vice versa.
Everyone who is brave is not quiet and vice versa.
If someone is either not tall or not creative then susan is both not quiet and strong.
Lucy is not humble.
Someone is both kind and not generous.
Paul is not curious.
Fred is rich.
Susan is funny or kind.
Alice is not patient or funny. | John is not happy. | neutral | ((?[X]:((strong(X)<~>~curious(X))))<=>(?[X]:(~wise(X))))&
(((humble(john)<~>~tall(john)))<=>((funny(susan)|~rich(susan))))&
(![X]:((funny(X)&~funny(X))=>(curious(X)|funny(X))))&
(((~funny(susan)|~humble(susan)))=>(?[X]:((~patient(X)<~>patient(X)))))&
((?[X]:((patient(X)|funny(X))))=>(~curious(lucy)))&
(![X]:((~tall(X)&~calm(X))=>(strong(X)&curious(X))))&
(((~kind(paul)|brave(paul)))<=>((~quiet(fred)|kind(fred))))&
(((strong(alice)<~>funny(alice)))=>(?[X]:((~rich(X)&tall(X)))))&
(![X]:((happy(X)<~>~calm(X))=>(rich(X)<~>~calm(X))))&
(![X]:((~quiet(X)|humble(X))<=>calm(X)))&
((?[X]:((~tall(X)&creative(X))))<=>(?[X]:((funny(X)<~>calm(X)))))&
(![X]:((~brave(X)&quiet(X))<=>(patient(X)<~>~creative(X))))&
((?[X]:(~happy(X)))<=>((~curious(susan)<~>~kind(susan))))&
(![X]:(strong(X)<=>(~calm(X)|~strong(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
((?[X]:((~tall(X)<~>~creative(X))))=>((~quiet(susan)&strong(susan))))&
(~humble(lucy))&
(?[X]:((kind(X)&~generous(X))))&
(~curious(paul))&
(rich(fred))&
((funny(susan)|kind(susan)))&
((~patient(alice)|funny(alice))) | ~happy(john) | [] | null | 0 |
Everyone who is both not creative and happy is both not curious and not kind. If john is not brave or brave then someone is not curious or old and vice versa. If john is either not tall or not old then someone is not wise or brave and vice versa. If someone is both not quiet and not calm then someone is not tall and vice versa. Everyone who is either not rich or not calm is rich or wise. If john is not brave or brave then someone is kind or happy. Everyone who is both old and not quiet is either curious or quiet and vice versa. If someone is not kind then lucy is kind or generous. If someone is generous then fred is both quiet and curious and vice versa. Everyone who is not patient is not kind or not strong and vice versa. If someone is both not strong and creative then someone is not quiet or old. Everyone who is not strong or old is either not wise or not humble and vice versa. If alice is curious or calm then someone is either patient or not wise and vice versa. Everyone who is quiet or not tall is not curious and vice versa. If paul is old or not creative then john is either not creative or kind. If lucy is both creative and not old then fred is not funny and vice versa. Someone is both not creative and patient. Lucy is either happy or not funny. Susan is both not funny and not happy. Fred is not patient or funny. | Fred is old. | neutral | (![X]:((~creative(X)&happy(X))=>(~curious(X)&~kind(X))))&
(((~brave(john)|brave(john)))<=>(?[X]:((~curious(X)|old(X)))))&
(((~tall(john)<~>~old(john)))<=>(?[X]:((~wise(X)|brave(X)))))&
((?[X]:((~quiet(X)&~calm(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~rich(X)<~>~calm(X))=>(rich(X)|wise(X))))&
(((~brave(john)|brave(john)))=>(?[X]:((kind(X)|happy(X)))))&
(![X]:((old(X)&~quiet(X))<=>(curious(X)<~>quiet(X))))&
((?[X]:(~kind(X)))=>((kind(lucy)|generous(lucy))))&
((?[X]:(generous(X)))<=>((quiet(fred)&curious(fred))))&
(![X]:(~patient(X)<=>(~kind(X)|~strong(X))))&
((?[X]:((~strong(X)&creative(X))))=>(?[X]:((~quiet(X)|old(X)))))&
(![X]:((~strong(X)|old(X))<=>(~wise(X)<~>~humble(X))))&
(((curious(alice)|calm(alice)))<=>(?[X]:((patient(X)<~>~wise(X)))))&
(![X]:((quiet(X)|~tall(X))<=>~curious(X)))&
(((old(paul)|~creative(paul)))=>((~creative(john)<~>kind(john))))&
(((creative(lucy)&~old(lucy)))<=>(~funny(fred)))&
(?[X]:((~creative(X)&patient(X))))&
((happy(lucy)<~>~funny(lucy)))&
((~funny(susan)&~happy(susan)))&
((~patient(fred)|funny(fred))) | old(fred) | [] | null | 0 |
Everyone who is not curious is curious or brave. If someone is strong then mary is not old. Everyone who is creative is old and vice versa. If mary is either happy or patient then someone is either not patient or old. Everyone who is not generous or not curious is either not quiet or tall. If alice is either quiet or not patient then someone is either brave or not brave and vice versa. Everyone who is either quiet or happy is both brave and not kind. If someone is both not wise and happy then someone is not brave or generous and vice versa. If lucy is either not curious or creative then someone is both not calm and old and vice versa. Everyone who is kind is both not kind and not funny and vice versa. If someone is not kind or not generous then someone is not patient or not funny. If someone is both not tall and not strong then someone is either not happy or strong. If alice is not humble then susan is either strong or generous and vice versa. Everyone who is both not quiet and strong is quiet and vice versa. Everyone who is both not rich and not quiet is both not generous and old and vice versa. Everyone who is both not patient and not humble is both not creative and humble and vice versa. Lucy is not generous. Someone is brave or curious. Someone is both not generous and wise. Someone is both not tall and not strong. Fred is either brave or curious. Someone is creative or not humble. Alice is strong or old. | Mary is patient. | neutral | (![X]:(~curious(X)=>(curious(X)|brave(X))))&
((?[X]:(strong(X)))=>(~old(mary)))&
(![X]:(creative(X)<=>old(X)))&
(((happy(mary)<~>patient(mary)))=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:((~generous(X)|~curious(X))=>(~quiet(X)<~>tall(X))))&
(((quiet(alice)<~>~patient(alice)))<=>(?[X]:((brave(X)<~>~brave(X)))))&
(![X]:((quiet(X)<~>happy(X))=>(brave(X)&~kind(X))))&
((?[X]:((~wise(X)&happy(X))))<=>(?[X]:((~brave(X)|generous(X)))))&
(((~curious(lucy)<~>creative(lucy)))<=>(?[X]:((~calm(X)&old(X)))))&
(![X]:(kind(X)<=>(~kind(X)&~funny(X))))&
((?[X]:((~kind(X)|~generous(X))))=>(?[X]:((~patient(X)|~funny(X)))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:((~happy(X)<~>strong(X)))))&
((~humble(alice))<=>((strong(susan)<~>generous(susan))))&
(![X]:((~quiet(X)&strong(X))<=>quiet(X)))&
(![X]:((~rich(X)&~quiet(X))<=>(~generous(X)&old(X))))&
(![X]:((~patient(X)&~humble(X))<=>(~creative(X)&humble(X))))&
(~generous(lucy))&
(?[X]:((brave(X)|curious(X))))&
(?[X]:((~generous(X)&wise(X))))&
(?[X]:((~tall(X)&~strong(X))))&
((brave(fred)<~>curious(fred)))&
(?[X]:((creative(X)|~humble(X))))&
((strong(alice)|old(alice))) | patient(mary) | [] | null | 0 |
Everyone who is both creative and brave is either not brave or happy.
If mary is not kind then john is either not wise or humble.
Everyone who is not wise or not patient is both not old and old and vice versa.
Everyone who is either generous or curious is either not funny or rich and vice versa.
Everyone who is brave or not brave is not funny or humble.
Everyone who is either curious or kind is either not kind or not patient and vice versa.
Everyone who is both not old and not kind is not strong and vice versa.
Everyone who is not tall is both not old and calm and vice versa.
Everyone who is not curious or not humble is rich.
Everyone who is both not quiet and wise is curious and vice versa.
If john is not generous then someone is either tall or curious.
Everyone who is not generous is both not rich and brave.
Everyone who is not patient or not brave is tall and vice versa.
If susan is both brave and wise then someone is not humble or calm and vice versa.
Everyone who is either generous or old is either not patient or creative and vice versa.
Everyone who is not funny or not curious is either wise or not calm.
Someone is both calm and wise.
Fred is both not humble and kind.
Someone is not brave or not calm.
Someone is either kind or wise.
Someone is not brave.
Alice is either humble or funny.
Lucy is either happy or not patient. | Lucy is not calm. | neutral | (![X]:((creative(X)&brave(X))=>(~brave(X)<~>happy(X))))&
((~kind(mary))=>((~wise(john)<~>humble(john))))&
(![X]:((~wise(X)|~patient(X))<=>(~old(X)&old(X))))&
(![X]:((generous(X)<~>curious(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|humble(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)&~kind(X))<=>~strong(X)))&
(![X]:(~tall(X)<=>(~old(X)&calm(X))))&
(![X]:((~curious(X)|~humble(X))=>rich(X)))&
(![X]:((~quiet(X)&wise(X))<=>curious(X)))&
((~generous(john))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:(~generous(X)=>(~rich(X)&brave(X))))&
(![X]:((~patient(X)|~brave(X))<=>tall(X)))&
(((brave(susan)&wise(susan)))<=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((generous(X)<~>old(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((~funny(X)|~curious(X))=>(wise(X)<~>~calm(X))))&
(?[X]:((calm(X)&wise(X))))&
((~humble(fred)&kind(fred)))&
(?[X]:((~brave(X)|~calm(X))))&
(?[X]:((kind(X)<~>wise(X))))&
(?[X]:(~brave(X)))&
((humble(alice)<~>funny(alice)))&
((happy(lucy)<~>~patient(lucy))) | ~calm(lucy) | [] | null | 0 |
Everyone who is either not creative or not generous is rich and vice versa.
Everyone who is not brave or not strong is both not old and not wise and vice versa.
If someone is creative or patient then paul is brave and vice versa.
Everyone who is humble is both funny and not quiet.
Everyone who is funny is both happy and not tall and vice versa.
Everyone who is either not calm or not generous is either not wise or not rich and vice versa.
Everyone who is either not brave or curious is happy.
Everyone who is both not creative and quiet is not creative.
Everyone who is funny is not funny or curious and vice versa.
Everyone who is both curious and happy is both brave and kind and vice versa.
Everyone who is either not patient or not rich is either not brave or strong.
If mary is both not brave and calm then someone is either quiet or wise.
If someone is both not brave and humble then alice is both not strong and wise.
If paul is not strong then someone is not generous or rich.
If someone is not wise or patient then someone is either rich or creative and vice versa.
If someone is either rich or old then alice is both not rich and creative.
Someone is not calm or brave.
Alice is patient.
Someone is not patient.
Alice is not creative.
Someone is both not wise and funny. | Paul is kind. | entailment | (![X]:((~creative(X)<~>~generous(X))<=>rich(X)))&
(![X]:((~brave(X)|~strong(X))<=>(~old(X)&~wise(X))))&
((?[X]:((creative(X)|patient(X))))<=>(brave(paul)))&
(![X]:(humble(X)=>(funny(X)&~quiet(X))))&
(![X]:(funny(X)<=>(happy(X)&~tall(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:((~brave(X)<~>curious(X))=>happy(X)))&
(![X]:((~creative(X)&quiet(X))=>~creative(X)))&
(![X]:(funny(X)<=>(~funny(X)|curious(X))))&
(![X]:((curious(X)&happy(X))<=>(brave(X)&kind(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(~brave(X)<~>strong(X))))&
(((~brave(mary)&calm(mary)))=>(?[X]:((quiet(X)<~>wise(X)))))&
((?[X]:((~brave(X)&humble(X))))=>((~strong(alice)&wise(alice))))&
((~strong(paul))=>(?[X]:((~generous(X)|rich(X)))))&
((?[X]:((~wise(X)|patient(X))))<=>(?[X]:((rich(X)<~>creative(X)))))&
((?[X]:((rich(X)<~>old(X))))=>((~rich(alice)&creative(alice))))&
(?[X]:((~calm(X)|brave(X))))&
(patient(alice))&
(?[X]:(~patient(X)))&
(~creative(alice))&
(?[X]:((~wise(X)&funny(X)))) | kind(paul) | [
"p4",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 985895313486682038537977
% SZS output start Proof for 985895313486682038537977
5. ! [X0] : (funny(X0) <=> (~tall(X0) & happy(X0))) [input p4]
9. ! [X0] : (funny(X0) <=> (curious(X0) | ~funny(X0))) [input p8]
10. ! [X0] : ((happy(X0) & curious(X0)) <=> (kind(X0) & brave(X0))) [input p9]
22. ~kind(paul) [input hypothesis]
41. ! [X0] : ((funny(X0) | (tall(X0) | ~happy(X0))) & ((~tall(X0) & happy(X0)) | ~funny(X0))) [nnf transformation 5]
42. ! [X0] : ((funny(X0) | tall(X0) | ~happy(X0)) & ((~tall(X0) & happy(X0)) | ~funny(X0))) [flattening 41]
45. ! [X0] : ((funny(X0) | (~curious(X0) & funny(X0))) & ((curious(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 9]
46. ! [X0] : ((funny(X0) | (~curious(X0) & funny(X0))) & (curious(X0) | ~funny(X0) | ~funny(X0))) [flattening 45]
47. ! [X0] : (((happy(X0) & curious(X0)) | (~kind(X0) | ~brave(X0))) & ((kind(X0) & brave(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 10]
48. ! [X0] : (((happy(X0) & curious(X0)) | ~kind(X0) | ~brave(X0)) & ((kind(X0) & brave(X0)) | ~happy(X0) | ~curious(X0))) [flattening 47]
79. ~funny(X0) | happy(X0) [cnf transformation 42]
93. curious(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 46]
94. funny(X0) | funny(X0) [cnf transformation 46]
97. kind(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 48]
123. ~kind(paul) [cnf transformation 22]
124. curious(X0) | ~funny(X0) [duplicate literal removal 93]
125. funny(X0) [duplicate literal removal 94]
147. curious(X0) [subsumption resolution 124,125]
148. ~happy(X0) | kind(X0) [subsumption resolution 97,147]
242. happy(X0) [resolution 79,125]
244. kind(X0) [resolution 148,242]
246. $false [resolution 244,123]
% SZS output end Proof for 985895313486682038537977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is not generous or not humble and vice versa. Everyone who is not humble is kind or calm. Everyone who is kind or not calm is both wise and funny. Everyone who is not kind is generous. Everyone who is either brave or happy is not old or funny and vice versa. If lucy is either not creative or calm then susan is not creative or not generous. If john is generous or not happy then fred is not quiet and vice versa. If someone is both not kind and not tall then alice is not calm or not humble and vice versa. Everyone who is either tall or generous is either wise or kind and vice versa. Everyone who is not kind or creative is not patient or funny. If someone is generous or curious then mary is wise. If lucy is not tall then someone is either not happy or not curious. If someone is not calm or not funny then someone is either not quiet or creative and vice versa. If alice is both brave and humble then someone is not happy or not patient and vice versa. Everyone who is both not calm and kind is wise. Paul is not brave. Someone is not calm or not funny. Someone is both not calm and quiet. Someone is both creative and brave. Lucy is both not strong and not creative. Someone is curious or funny. Susan is either funny or not strong. Paul is rich or tall. | John is wise. | entailment | (![X]:(humble(X)<=>(~generous(X)|~humble(X))))&
(![X]:(~humble(X)=>(kind(X)|calm(X))))&
(![X]:((kind(X)|~calm(X))=>(wise(X)&funny(X))))&
(![X]:(~kind(X)=>generous(X)))&
(![X]:((brave(X)<~>happy(X))<=>(~old(X)|funny(X))))&
(((~creative(lucy)<~>calm(lucy)))=>((~creative(susan)|~generous(susan))))&
(((generous(john)|~happy(john)))<=>(~quiet(fred)))&
((?[X]:((~kind(X)&~tall(X))))<=>((~calm(alice)|~humble(alice))))&
(![X]:((tall(X)<~>generous(X))<=>(wise(X)<~>kind(X))))&
(![X]:((~kind(X)|creative(X))=>(~patient(X)|funny(X))))&
((?[X]:((generous(X)|curious(X))))=>(wise(mary)))&
((~tall(lucy))=>(?[X]:((~happy(X)<~>~curious(X)))))&
((?[X]:((~calm(X)|~funny(X))))<=>(?[X]:((~quiet(X)<~>creative(X)))))&
(((brave(alice)&humble(alice)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((~calm(X)&kind(X))=>wise(X)))&
(~brave(paul))&
(?[X]:((~calm(X)|~funny(X))))&
(?[X]:((~calm(X)&quiet(X))))&
(?[X]:((creative(X)&brave(X))))&
((~strong(lucy)&~creative(lucy)))&
(?[X]:((curious(X)|funny(X))))&
((funny(susan)<~>~strong(susan)))&
((rich(paul)|tall(paul))) | wise(john) | [
"p0",
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2683169286472499797900039
% SZS output start Proof for 2683169286472499797900039
1. ! [X0] : (humble(X0) <=> (~humble(X0) | ~generous(X0))) [input p0]
3. ! [X0] : ((~calm(X0) | kind(X0)) => (funny(X0) & wise(X0))) [input p2]
4. ! [X0] : (~kind(X0) => generous(X0)) [input p3]
24. ~wise(john) [input hypothesis]
29. ! [X0] : ((funny(X0) & wise(X0)) | (calm(X0) & ~kind(X0))) [ennf transformation 3]
30. ! [X0] : (generous(X0) | kind(X0)) [ennf transformation 4]
39. ! [X0] : ((humble(X0) | (humble(X0) & generous(X0))) & ((~humble(X0) | ~generous(X0)) | ~humble(X0))) [nnf transformation 1]
40. ! [X0] : ((humble(X0) | (humble(X0) & generous(X0))) & (~humble(X0) | ~generous(X0) | ~humble(X0))) [flattening 39]
74. ~humble(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 40]
76. humble(X0) | humble(X0) [cnf transformation 40]
78. ~kind(X0) | wise(X0) [cnf transformation 29]
82. generous(X0) | kind(X0) [cnf transformation 30]
136. ~wise(john) [cnf transformation 24]
137. ~humble(X0) | ~generous(X0) [duplicate literal removal 74]
138. humble(X0) [duplicate literal removal 76]
139. ~generous(X0) [subsumption resolution 137,138]
140. kind(X0) [subsumption resolution 82,139]
273. wise(X0) [resolution 78,140]
275. $false [resolution 273,136]
% SZS output end Proof for 2683169286472499797900039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not kind is funny or brave and vice versa.
If john is quiet then john is either humble or curious and vice versa.
Everyone who is generous is either tall or quiet.
If someone is either not wise or kind then john is both brave and not strong.
Everyone who is not brave is both brave and not brave.
Everyone who is both calm and not quiet is not brave.
If someone is not old or curious then mary is both calm and humble.
Everyone who is either patient or not old is both happy and curious and vice versa.
Everyone who is both not curious and not happy is not happy and vice versa.
Everyone who is either quiet or not kind is not kind and vice versa.
Everyone who is not quiet or not brave is either humble or happy and vice versa.
Everyone who is not happy or not curious is either not calm or humble.
If someone is curious or not wise then someone is not strong or not generous and vice versa.
Everyone who is not generous or not funny is not generous.
Someone is not funny or happy.
Lucy is not old or brave.
Paul is not quiet or rich. | John is humble. | contradiction | (![X]:((~tall(X)&~kind(X))<=>(funny(X)|brave(X))))&
((quiet(john))<=>((humble(john)<~>curious(john))))&
(![X]:(generous(X)=>(tall(X)<~>quiet(X))))&
((?[X]:((~wise(X)<~>kind(X))))=>((brave(john)&~strong(john))))&
(![X]:(~brave(X)=>(brave(X)&~brave(X))))&
(![X]:((calm(X)&~quiet(X))=>~brave(X)))&
((?[X]:((~old(X)|curious(X))))=>((calm(mary)&humble(mary))))&
(![X]:((patient(X)<~>~old(X))<=>(happy(X)&curious(X))))&
(![X]:((~curious(X)&~happy(X))<=>~happy(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~kind(X)))&
(![X]:((~quiet(X)|~brave(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
(![X]:((~generous(X)|~funny(X))=>~generous(X)))&
(?[X]:((~funny(X)|happy(X))))&
((~old(lucy)|brave(lucy)))&
((~quiet(paul)|rich(paul))) | humble(john) | [
"p1",
"p4",
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 9103238703966619318582519
% SZS output start Proof for 9103238703966619318582519
2. quiet(john) <=> (humble(john) <~> curious(john)) [input p1]
5. ! [X0] : (~brave(X0) => (~brave(X0) & brave(X0))) [input p4]
6. ! [X0] : ((~quiet(X0) & calm(X0)) => ~brave(X0)) [input p5]
7. ? [X0] : (curious(X0) | ~old(X0)) => (humble(mary) & calm(mary)) [input p6]
10. ! [X0] : ((quiet(X0) <~> ~kind(X0)) <=> ~kind(X0)) [input p9]
18. humble(john) [input hypothesis]
23. ! [X0] : ((~brave(X0) & brave(X0)) | brave(X0)) [ennf transformation 5]
24. ! [X0] : (~brave(X0) | (quiet(X0) | ~calm(X0))) [ennf transformation 6]
25. ! [X0] : (~brave(X0) | quiet(X0) | ~calm(X0)) [flattening 24]
26. (humble(mary) & calm(mary)) | ! [X0] : (~curious(X0) & old(X0)) [ennf transformation 7]
31. (quiet(john) | ((humble(john) | ~curious(john)) & (curious(john) | ~humble(john)))) & (((~curious(john) | ~humble(john)) & (curious(john) | humble(john))) | ~quiet(john)) [nnf transformation 2]
38. ! [X0] : ((((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | kind(X0)) & (~kind(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0))))) [nnf transformation 10]
56. quiet(john) | curious(john) | ~humble(john) [cnf transformation 31]
64. brave(X0) | brave(X0) [cnf transformation 23]
66. ~brave(X0) | quiet(X0) | ~calm(X0) [cnf transformation 25]
68. calm(mary) | ~curious(X0) [cnf transformation 26]
80. ~kind(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 38]
83. kind(X0) | ~quiet(X0) | kind(X0) [cnf transformation 38]
102. humble(john) [cnf transformation 18]
103. ~kind(X0) | ~quiet(X0) [duplicate literal removal 80]
104. ~quiet(X0) | kind(X0) [duplicate literal removal 83]
105. brave(X0) [duplicate literal removal 64]
107. 1 <=> curious(john) [avatar definition]
108. curious(john) <- (1) [avatar component clause 107]
111. 2 <=> humble(john) [avatar definition]
115. 3 <=> quiet(john) [avatar definition]
117. quiet(john) <- (3) [avatar component clause 115]
119. ~2 | 1 | 3 [avatar split clause 56,115,107,111]
140. ~calm(X0) | quiet(X0) [subsumption resolution 66,105]
142. 8 <=> ! [X0] : ~curious(X0) [avatar definition]
143. ~curious(X0) <- (8) [avatar component clause 142]
154. 11 <=> calm(mary) [avatar definition]
156. calm(mary) <- (11) [avatar component clause 154]
157. 8 | 11 [avatar split clause 68,154,142]
159. ~quiet(X0) [subsumption resolution 103,104]
201. 2 [avatar split clause 102,111]
202. $false <- (3) [subsumption resolution 117,159]
203. ~3 [avatar contradiction clause 202]
204. $false <- (1, 8) [subsumption resolution 108,143]
205. ~1 | ~8 [avatar contradiction clause 204]
213. quiet(mary) <- (11) [resolution 140,156]
214. $false <- (11) [subsumption resolution 213,159]
215. ~11 [avatar contradiction clause 214]
216. $false [avatar sat refutation 119,157,201,203,205,215]
% SZS output end Proof for 9103238703966619318582519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and patient then someone is calm and vice versa.
If mary is not generous or not quiet then paul is both creative and brave.
Everyone who is both generous and not wise is old or creative and vice versa.
Everyone who is either not patient or quiet is tall or not curious and vice versa.
If someone is both strong and wise then alice is both not old and humble.
Everyone who is humble or strong is not patient.
Everyone who is not quiet is not humble and vice versa.
Everyone who is both not quiet and calm is not funny or tall.
If fred is not quiet then someone is not humble and vice versa.
Everyone who is rich or not generous is either quiet or not humble and vice versa.
Everyone who is either not happy or kind is not curious or strong.
Everyone who is either not patient or not curious is both not wise and kind and vice versa.
If susan is not quiet or not brave then john is both kind and not strong and vice versa.
If mary is either patient or creative then mary is either not generous or not wise and vice versa.
Everyone who is both not quiet and not rich is both not wise and not generous and vice versa.
Everyone who is kind or curious is either kind or old.
Susan is either not generous or happy.
Fred is either not calm or not strong.
Paul is both not funny and not strong.
Someone is either not humble or not strong.
Fred is not rich.
Fred is not quiet.
Mary is not funny or not old.
Someone is not creative. | Fred is patient. | contradiction | ((?[X]:((creative(X)&patient(X))))<=>(?[X]:(calm(X))))&
(((~generous(mary)|~quiet(mary)))=>((creative(paul)&brave(paul))))&
(![X]:((generous(X)&~wise(X))<=>(old(X)|creative(X))))&
(![X]:((~patient(X)<~>quiet(X))<=>(tall(X)|~curious(X))))&
((?[X]:((strong(X)&wise(X))))=>((~old(alice)&humble(alice))))&
(![X]:((humble(X)|strong(X))=>~patient(X)))&
(![X]:(~quiet(X)<=>~humble(X)))&
(![X]:((~quiet(X)&calm(X))=>(~funny(X)|tall(X))))&
((~quiet(fred))<=>(?[X]:(~humble(X))))&
(![X]:((rich(X)|~generous(X))<=>(quiet(X)<~>~humble(X))))&
(![X]:((~happy(X)<~>kind(X))=>(~curious(X)|strong(X))))&
(![X]:((~patient(X)<~>~curious(X))<=>(~wise(X)&kind(X))))&
(((~quiet(susan)|~brave(susan)))<=>((kind(john)&~strong(john))))&
(((patient(mary)<~>creative(mary)))<=>((~generous(mary)<~>~wise(mary))))&
(![X]:((~quiet(X)&~rich(X))<=>(~wise(X)&~generous(X))))&
(![X]:((kind(X)|curious(X))=>(kind(X)<~>old(X))))&
((~generous(susan)<~>happy(susan)))&
((~calm(fred)<~>~strong(fred)))&
((~funny(paul)&~strong(paul)))&
(?[X]:((~humble(X)<~>~strong(X))))&
(~rich(fred))&
(~quiet(fred))&
((~funny(mary)|~old(mary)))&
(?[X]:(~creative(X))) | patient(fred) | [
"p2",
"p3",
"p6",
"p9",
"p11",
"p14",
"p15",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3990767769567809513252324
% SZS output start Proof for 3990767769567809513252324
3. ! [X0] : ((~wise(X0) & generous(X0)) <=> (creative(X0) | old(X0))) [input p2]
4. ! [X0] : ((~patient(X0) <~> quiet(X0)) <=> (~curious(X0) | tall(X0))) [input p3]
7. ! [X0] : (~quiet(X0) <=> ~humble(X0)) [input p6]
10. ! [X0] : ((~generous(X0) | rich(X0)) <=> (quiet(X0) <~> ~humble(X0))) [input p9]
12. ! [X0] : ((~patient(X0) <~> ~curious(X0)) <=> (kind(X0) & ~wise(X0))) [input p11]
15. ! [X0] : ((~rich(X0) & ~quiet(X0)) <=> (~generous(X0) & ~wise(X0))) [input p14]
16. ! [X0] : ((curious(X0) | kind(X0)) => (kind(X0) <~> old(X0))) [input p15]
21. ~rich(fred) [input p20]
22. ~quiet(fred) [input p21]
25. patient(fred) [input hypothesis]
35. ! [X0] : ((kind(X0) <~> old(X0)) | (~curious(X0) & ~kind(X0))) [ennf transformation 16]
41. ! [X0] : (((~wise(X0) & generous(X0)) | (~creative(X0) & ~old(X0))) & ((creative(X0) | old(X0)) | (wise(X0) | ~generous(X0)))) [nnf transformation 3]
42. ! [X0] : (((~wise(X0) & generous(X0)) | (~creative(X0) & ~old(X0))) & (creative(X0) | old(X0) | wise(X0) | ~generous(X0))) [flattening 41]
43. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (curious(X0) & ~tall(X0))) & ((~curious(X0) | tall(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (curious(X0) & ~tall(X0))) & (~curious(X0) | tall(X0) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [flattening 43]
45. ! [X0] : ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0))) [nnf transformation 7]
50. ! [X0] : (((~generous(X0) | rich(X0)) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0)))) & (((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | (generous(X0) & ~rich(X0)))) [nnf transformation 10]
51. ! [X0] : ((~generous(X0) | rich(X0) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0)))) & (((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | (generous(X0) & ~rich(X0)))) [flattening 50]
53. ! [X0] : ((((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | (~kind(X0) | wise(X0))) & ((kind(X0) & ~wise(X0)) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0))))) [nnf transformation 12]
54. ! [X0] : ((((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | ~kind(X0) | wise(X0)) & ((kind(X0) & ~wise(X0)) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0))))) [flattening 53]
58. ! [X0] : (((~rich(X0) & ~quiet(X0)) | (generous(X0) | wise(X0))) & ((~generous(X0) & ~wise(X0)) | (rich(X0) | quiet(X0)))) [nnf transformation 15]
59. ! [X0] : (((~rich(X0) & ~quiet(X0)) | generous(X0) | wise(X0)) & ((~generous(X0) & ~wise(X0)) | rich(X0) | quiet(X0))) [flattening 58]
60. ! [X0] : (((~old(X0) | ~kind(X0)) & (old(X0) | kind(X0))) | (~curious(X0) & ~kind(X0))) [nnf transformation 35]
76. ~old(X0) | generous(X0) [cnf transformation 42]
83. ~patient(X0) | quiet(X0) | curious(X0) [cnf transformation 44]
91. ~quiet(X0) | humble(X0) [cnf transformation 45]
98. ~generous(X0) | rich(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 51]
106. ~kind(X0) | ~patient(X0) | ~curious(X0) | wise(X0) [cnf transformation 54]
121. ~wise(X0) | rich(X0) | quiet(X0) [cnf transformation 59]
122. ~generous(X0) | rich(X0) | quiet(X0) [cnf transformation 59]
126. ~curious(X0) | kind(X0) | old(X0) [cnf transformation 60]
136. ~rich(fred) [cnf transformation 21]
137. ~quiet(fred) [cnf transformation 22]
139. patient(fred) [cnf transformation 25]
199. 14 <=> quiet(fred) [avatar definition]
201. ~quiet(fred) <- (~14) [avatar component clause 199]
209. ~quiet(X0) | rich(X0) | ~generous(X0) [subsumption resolution 98,91]
253. ~generous(X0) | rich(X0) [subsumption resolution 122,209]
284. ~14 [avatar split clause 137,199]
302. quiet(fred) | curious(fred) [resolution 83,139]
304. curious(fred) <- (~14) [subsumption resolution 302,201]
333. kind(fred) | old(fred) <- (~14) [resolution 126,304]
337. 31 <=> old(fred) [avatar definition]
339. old(fred) <- (31) [avatar component clause 337]
341. 32 <=> kind(fred) [avatar definition]
343. kind(fred) <- (32) [avatar component clause 341]
344. 31 | 32 | 14 [avatar split clause 333,199,341,337]
435. ~patient(fred) | ~curious(fred) | wise(fred) <- (32) [resolution 106,343]
436. ~curious(fred) | wise(fred) <- (32) [subsumption resolution 435,139]
437. wise(fred) <- (~14, 32) [subsumption resolution 436,304]
508. rich(fred) | quiet(fred) <- (~14, 32) [resolution 437,121]
511. quiet(fred) <- (~14, 32) [subsumption resolution 508,136]
512. $false <- (~14, 32) [subsumption resolution 511,201]
513. 14 | ~32 [avatar contradiction clause 512]
515. generous(fred) <- (31) [resolution 339,76]
607. rich(fred) <- (31) [resolution 515,253]
609. $false <- (31) [subsumption resolution 607,136]
610. ~31 [avatar contradiction clause 609]
611. $false [avatar sat refutation 284,344,513,610]
% SZS output end Proof for 3990767769567809513252324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or patient is both not generous and old and vice versa.
Everyone who is not quiet or not wise is both not kind and quiet and vice versa.
Everyone who is either rich or happy is not strong and vice versa.
If mary is wise or creative then fred is both curious and not curious and vice versa.
Everyone who is not happy or kind is not creative or not happy and vice versa.
If someone is not rich or happy then john is both not old and patient and vice versa.
Everyone who is both humble and not happy is either not creative or brave and vice versa.
Everyone who is both brave and tall is either not strong or kind.
Everyone who is both curious and brave is not patient and vice versa.
If someone is both calm and not old then john is rich or not brave.
Everyone who is either curious or brave is not happy and vice versa.
Everyone who is both wise and not old is either generous or not quiet and vice versa.
Everyone who is strong is both patient and not generous.
Everyone who is happy is either not creative or not curious.
Everyone who is not calm is both old and brave.
Everyone who is either humble or calm is both happy and quiet.
John is rich or not happy.
Someone is both not calm and not funny.
Lucy is not brave.
Someone is either brave or not tall.
Someone is not wise. | Lucy is humble. | entailment | (![X]:((~old(X)|patient(X))<=>(~generous(X)&old(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~kind(X)&quiet(X))))&
(![X]:((rich(X)<~>happy(X))<=>~strong(X)))&
(((wise(mary)|creative(mary)))<=>((curious(fred)&~curious(fred))))&
(![X]:((~happy(X)|kind(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((~old(john)&patient(john))))&
(![X]:((humble(X)&~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((brave(X)&tall(X))=>(~strong(X)<~>kind(X))))&
(![X]:((curious(X)&brave(X))<=>~patient(X)))&
((?[X]:((calm(X)&~old(X))))=>((rich(john)|~brave(john))))&
(![X]:((curious(X)<~>brave(X))<=>~happy(X)))&
(![X]:((wise(X)&~old(X))<=>(generous(X)<~>~quiet(X))))&
(![X]:(strong(X)=>(patient(X)&~generous(X))))&
(![X]:(happy(X)=>(~creative(X)<~>~curious(X))))&
(![X]:(~calm(X)=>(old(X)&brave(X))))&
(![X]:((humble(X)<~>calm(X))=>(happy(X)&quiet(X))))&
((rich(john)|~happy(john)))&
(?[X]:((~calm(X)&~funny(X))))&
(~brave(lucy))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:(~wise(X))) | humble(lucy) | [
"p0",
"p5",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3424540013876249259862917
% SZS output start Proof for 3424540013876249259862917
1. ! [X0] : ((patient(X0) | ~old(X0)) <=> (old(X0) & ~generous(X0))) [input p0]
6. ? [X0] : (happy(X0) | ~rich(X0)) <=> (patient(john) & ~old(john)) [input p5]
15. ! [X0] : (~calm(X0) => (brave(X0) & old(X0))) [input p14]
16. ! [X0] : ((humble(X0) <~> calm(X0)) => (quiet(X0) & happy(X0))) [input p15]
19. ~brave(lucy) [input p18]
22. ~humble(lucy) [input hypothesis]
30. ! [X0] : ((brave(X0) & old(X0)) | calm(X0)) [ennf transformation 15]
31. ! [X0] : ((quiet(X0) & happy(X0)) | (humble(X0) <=> calm(X0))) [ennf transformation 16]
32. ! [X0] : (((patient(X0) | ~old(X0)) | (~old(X0) | generous(X0))) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [nnf transformation 1]
33. ! [X0] : ((patient(X0) | ~old(X0) | ~old(X0) | generous(X0)) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [flattening 32]
41. (? [X0] : (happy(X0) | ~rich(X0)) | (~patient(john) | old(john))) & ((patient(john) & ~old(john)) | ! [X0] : (~happy(X0) & rich(X0))) [nnf transformation 6]
42. (? [X0] : (happy(X0) | ~rich(X0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X0] : (~happy(X0) & rich(X0))) [flattening 41]
43. (? [X0] : (happy(X0) | ~rich(X0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X1] : (~happy(X1) & rich(X1))) [rectify 42]
44. ? [X0] : (happy(X0) | ~rich(X0)) => (happy(sK0) | ~rich(sK0)) [choice axiom]
45. ((happy(sK0) | ~rich(sK0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X1] : (~happy(X1) & rich(X1))) [skolemisation 43,44]
55. ! [X0] : ((quiet(X0) & happy(X0)) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) [nnf transformation 31]
65. old(X0) | old(X0) [cnf transformation 33]
87. ~old(john) | ~happy(X1) [cnf transformation 45]
118. calm(X0) | brave(X0) [cnf transformation 30]
120. ~calm(X0) | humble(X0) | happy(X0) [cnf transformation 55]
125. ~brave(lucy) [cnf transformation 19]
129. ~humble(lucy) [cnf transformation 22]
132. old(X0) [duplicate literal removal 65]
151. 4 <=> ! [X1] : ~happy(X1) [avatar definition]
152. ~happy(X1) <- (4) [avatar component clause 151]
162. ~happy(X1) [subsumption resolution 87,132]
163. 4 [avatar split clause 162,151]
292. humble(X0) | happy(X0) | brave(X0) [resolution 120,118]
293. brave(X0) | humble(X0) <- (4) [subsumption resolution 292,152]
295. humble(lucy) <- (4) [resolution 293,125]
302. $false <- (4) [subsumption resolution 295,129]
303. ~4 [avatar contradiction clause 302]
305. $false [avatar sat refutation 163,303]
% SZS output end Proof for 3424540013876249259862917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or creative is not old and vice versa.
Everyone who is not creative is brave.
Everyone who is not humble or not creative is both not kind and humble and vice versa.
Everyone who is either not tall or happy is both happy and rich and vice versa.
Everyone who is both not happy and generous is either not strong or not calm and vice versa.
If mary is either generous or not old then mary is both humble and not quiet and vice versa.
If john is not creative then lucy is brave or not rich and vice versa.
If someone is not brave or not humble then paul is rich or not old and vice versa.
Everyone who is either not humble or wise is not rich or tall and vice versa.
Everyone who is creative is either not kind or tall and vice versa.
Everyone who is both quiet and not calm is strong or not wise and vice versa.
If susan is not rich or not humble then someone is either not funny or not kind.
Everyone who is not strong is either not kind or curious and vice versa.
Everyone who is either not patient or patient is creative or strong.
If fred is both not tall and strong then someone is both brave and not tall.
Everyone who is generous or not happy is not humble.
Someone is humble or not curious.
Someone is not funny.
Someone is not humble or tall.
Someone is either quiet or not patient. | Susan is not wise. | contradiction | (![X]:((humble(X)|creative(X))<=>~old(X)))&
(![X]:(~creative(X)=>brave(X)))&
(![X]:((~humble(X)|~creative(X))<=>(~kind(X)&humble(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(happy(X)&rich(X))))&
(![X]:((~happy(X)&generous(X))<=>(~strong(X)<~>~calm(X))))&
(((generous(mary)<~>~old(mary)))<=>((humble(mary)&~quiet(mary))))&
((~creative(john))<=>((brave(lucy)|~rich(lucy))))&
((?[X]:((~brave(X)|~humble(X))))<=>((rich(paul)|~old(paul))))&
(![X]:((~humble(X)<~>wise(X))<=>(~rich(X)|tall(X))))&
(![X]:(creative(X)<=>(~kind(X)<~>tall(X))))&
(![X]:((quiet(X)&~calm(X))<=>(strong(X)|~wise(X))))&
(((~rich(susan)|~humble(susan)))=>(?[X]:((~funny(X)<~>~kind(X)))))&
(![X]:(~strong(X)<=>(~kind(X)<~>curious(X))))&
(![X]:((~patient(X)<~>patient(X))=>(creative(X)|strong(X))))&
(((~tall(fred)&strong(fred)))=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((generous(X)|~happy(X))=>~humble(X)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:((quiet(X)<~>~patient(X)))) | ~wise(susan) | [
"p2",
"p3",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1450224485275447045244502
% SZS output start Proof for 1450224485275447045244502
3. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (humble(X0) & ~kind(X0))) [input p2]
4. ! [X0] : ((~tall(X0) <~> happy(X0)) <=> (rich(X0) & happy(X0))) [input p3]
9. ! [X0] : ((~humble(X0) <~> wise(X0)) <=> (tall(X0) | ~rich(X0))) [input p8]
16. ! [X0] : ((~happy(X0) | generous(X0)) => ~humble(X0)) [input p15]
21. ~wise(susan) [input hypothesis]
28. ! [X0] : (~humble(X0) | (happy(X0) & ~generous(X0))) [ennf transformation 16]
31. ! [X0] : (((~creative(X0) | ~humble(X0)) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | (creative(X0) & humble(X0)))) [nnf transformation 3]
32. ! [X0] : ((~creative(X0) | ~humble(X0) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | (creative(X0) & humble(X0)))) [flattening 31]
33. ! [X0] : ((((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0))))) [nnf transformation 4]
34. ! [X0] : ((((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0))))) [flattening 33]
46. ! [X0] : ((((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | (~tall(X0) & rich(X0))) & ((tall(X0) | ~rich(X0)) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | (~tall(X0) & rich(X0))) & (tall(X0) | ~rich(X0) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))))) [flattening 46]
73. humble(X0) | humble(X0) [cnf transformation 32]
81. ~happy(X0) | tall(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 34]
103. wise(X0) | ~humble(X0) | rich(X0) [cnf transformation 47]
104. wise(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 47]
129. ~humble(X0) | happy(X0) [cnf transformation 28]
135. ~wise(susan) [cnf transformation 21]
139. ~rich(X0) | tall(X0) | ~happy(X0) [duplicate literal removal 81]
140. humble(X0) [duplicate literal removal 73]
193. ~tall(X0) | wise(X0) [subsumption resolution 104,140]
194. wise(X0) | rich(X0) [subsumption resolution 103,140]
199. 11 <=> rich(susan) [avatar definition]
201. rich(susan) <- (11) [avatar component clause 199]
231. happy(X0) [subsumption resolution 129,140]
248. rich(susan) [resolution 194,135]
308. tall(susan) | ~happy(susan) <- (11) [resolution 139,201]
312. tall(susan) <- (11) [subsumption resolution 308,231]
327. wise(susan) <- (11) [resolution 312,193]
328. $false <- (11) [subsumption resolution 327,135]
329. ~11 [avatar contradiction clause 328]
330. 11 [avatar split clause 248,199]
333. $false [avatar sat refutation 329,330]
% SZS output end Proof for 1450224485275447045244502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not old is either humble or kind and vice versa.
Everyone who is not kind is both brave and creative and vice versa.
Everyone who is both strong and not strong is both not kind and not strong and vice versa.
Everyone who is either not funny or not curious is either strong or quiet and vice versa.
If someone is not old then lucy is humble.
If someone is funny then someone is either patient or kind and vice versa.
Everyone who is both brave and creative is not quiet or generous and vice versa.
Everyone who is both quiet and not brave is not creative and vice versa.
Everyone who is both happy and strong is patient.
Everyone who is calm or not rich is not humble and vice versa.
Everyone who is both not quiet and old is both not creative and not wise and vice versa.
If susan is either quiet or creative then susan is either not patient or rich and vice versa.
Everyone who is not happy is either not patient or patient.
Everyone who is old is either not strong or not old and vice versa.
Everyone who is not curious is either not generous or not creative.
Someone is not generous or humble.
Someone is not tall.
Someone is both not humble and not happy.
Lucy is not rich or not patient.
Alice is wise or not kind.
Lucy is not wise or wise. | Alice is not wise. | contradiction | (![X]:((old(X)<~>~old(X))<=>(humble(X)<~>kind(X))))&
(![X]:(~kind(X)<=>(brave(X)&creative(X))))&
(![X]:((strong(X)&~strong(X))<=>(~kind(X)&~strong(X))))&
(![X]:((~funny(X)<~>~curious(X))<=>(strong(X)<~>quiet(X))))&
((?[X]:(~old(X)))=>(humble(lucy)))&
((?[X]:(funny(X)))<=>(?[X]:((patient(X)<~>kind(X)))))&
(![X]:((brave(X)&creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:((quiet(X)&~brave(X))<=>~creative(X)))&
(![X]:((happy(X)&strong(X))=>patient(X)))&
(![X]:((calm(X)|~rich(X))<=>~humble(X)))&
(![X]:((~quiet(X)&old(X))<=>(~creative(X)&~wise(X))))&
(((quiet(susan)<~>creative(susan)))<=>((~patient(susan)<~>rich(susan))))&
(![X]:(~happy(X)=>(~patient(X)<~>patient(X))))&
(![X]:(old(X)<=>(~strong(X)<~>~old(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~creative(X))))&
(?[X]:((~generous(X)|humble(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~humble(X)&~happy(X))))&
((~rich(lucy)|~patient(lucy)))&
((wise(alice)|~kind(alice)))&
((~wise(lucy)|wise(lucy))) | ~wise(alice) | [
"p2",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 138471460199365515777049
% SZS output start Proof for 138471460199365515777049
3. ! [X0] : ((~strong(X0) & strong(X0)) <=> (~strong(X0) & ~kind(X0))) [input p2]
14. ! [X0] : (old(X0) <=> (~strong(X0) <~> ~old(X0))) [input p13]
20. ~kind(alice) | wise(alice) [input p19]
22. ~wise(alice) [input hypothesis]
33. ! [X0] : (((~strong(X0) & strong(X0)) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | (strong(X0) | ~strong(X0)))) [nnf transformation 3]
34. ! [X0] : (((~strong(X0) & strong(X0)) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | strong(X0) | ~strong(X0))) [flattening 33]
51. ! [X0] : ((old(X0) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | ~old(X0))) [nnf transformation 14]
70. strong(X0) | strong(X0) | kind(X0) [cnf transformation 34]
111. ~old(X0) | ~strong(X0) | ~old(X0) [cnf transformation 51]
114. old(X0) | ~strong(X0) | old(X0) [cnf transformation 51]
121. ~kind(alice) | wise(alice) [cnf transformation 20]
123. ~wise(alice) [cnf transformation 22]
124. ~old(X0) | ~strong(X0) [duplicate literal removal 111]
125. ~strong(X0) | old(X0) [duplicate literal removal 114]
127. strong(X0) | kind(X0) [duplicate literal removal 70]
196. ~strong(X0) [subsumption resolution 124,125]
218. 17 <=> wise(alice) [avatar definition]
222. 18 <=> kind(alice) [avatar definition]
224. ~kind(alice) <- (~18) [avatar component clause 222]
225. 17 | ~18 [avatar split clause 121,222,218]
226. ~17 [avatar split clause 123,218]
236. kind(X1) [resolution 127,196]
238. $false <- (~18) [resolution 236,224]
239. 18 [avatar contradiction clause 238]
241. $false [avatar sat refutation 225,226,239]
% SZS output end Proof for 138471460199365515777049
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and quiet is patient or quiet.
Everyone who is not creative or kind is patient and vice versa.
If fred is creative or not generous then john is not creative.
Everyone who is calm or curious is both not curious and not happy and vice versa.
If fred is either calm or not calm then someone is not kind or patient and vice versa.
Everyone who is rich is not brave and vice versa.
If someone is not rich or not curious then someone is not quiet and vice versa.
Everyone who is both funny and generous is happy.
If susan is wise then lucy is both kind and not patient.
Everyone who is both generous and not humble is both not happy and calm.
If lucy is creative or not rich then someone is both brave and not funny.
Everyone who is either creative or not wise is not old and vice versa.
If paul is both not kind and funny then someone is not old or not quiet and vice versa.
Everyone who is brave is creative or patient.
If susan is old then someone is both not kind and happy and vice versa.
If someone is tall then paul is not rich or not old.
Someone is either not patient or funny.
Someone is both not creative and brave.
Someone is not humble or not generous.
Someone is either not wise or humble.
Someone is not kind.
Someone is old or humble.
Lucy is old.
John is happy or kind. | Fred is not brave. | neutral | (![X]:((~humble(X)&quiet(X))=>(patient(X)|quiet(X))))&
(![X]:((~creative(X)|kind(X))<=>patient(X)))&
(((creative(fred)|~generous(fred)))=>(~creative(john)))&
(![X]:((calm(X)|curious(X))<=>(~curious(X)&~happy(X))))&
(((calm(fred)<~>~calm(fred)))<=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:(rich(X)<=>~brave(X)))&
((?[X]:((~rich(X)|~curious(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)&generous(X))=>happy(X)))&
((wise(susan))=>((kind(lucy)&~patient(lucy))))&
(![X]:((generous(X)&~humble(X))=>(~happy(X)&calm(X))))&
(((creative(lucy)|~rich(lucy)))=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:((creative(X)<~>~wise(X))<=>~old(X)))&
(((~kind(paul)&funny(paul)))<=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:(brave(X)=>(creative(X)|patient(X))))&
((old(susan))<=>(?[X]:((~kind(X)&happy(X)))))&
((?[X]:(tall(X)))=>((~rich(paul)|~old(paul))))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((~creative(X)&brave(X))))&
(?[X]:((~humble(X)|~generous(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)|humble(X))))&
(old(lucy))&
((happy(john)|kind(john))) | ~brave(fred) | [] | null | 0 |
Everyone who is both wise and humble is creative and vice versa.
If someone is not wise then someone is not happy.
If someone is not generous or not tall then someone is both funny and calm.
Everyone who is not creative is either not creative or not rich.
Everyone who is both not rich and brave is wise and vice versa.
Everyone who is not creative or wise is both not patient and generous.
If someone is either not kind or funny then someone is not strong or curious.
If someone is both calm and not brave then someone is rich and vice versa.
Everyone who is both not quiet and happy is funny or generous.
If someone is creative then someone is either brave or not generous.
Everyone who is either not old or wise is tall or happy and vice versa.
If john is not happy then someone is both quiet and curious.
Everyone who is either brave or humble is either rich or calm and vice versa.
Everyone who is not wise is both rich and old and vice versa.
Everyone who is either not happy or not calm is creative and vice versa.
Everyone who is not tall or patient is either not happy or not curious.
Someone is kind.
Someone is rich or old.
Mary is humble or quiet.
Someone is either not happy or humble. | John is humble. | entailment | (![X]:((wise(X)&humble(X))<=>creative(X)))&
((?[X]:(~wise(X)))=>(?[X]:(~happy(X))))&
((?[X]:((~generous(X)|~tall(X))))=>(?[X]:((funny(X)&calm(X)))))&
(![X]:(~creative(X)=>(~creative(X)<~>~rich(X))))&
(![X]:((~rich(X)&brave(X))<=>wise(X)))&
(![X]:((~creative(X)|wise(X))=>(~patient(X)&generous(X))))&
((?[X]:((~kind(X)<~>funny(X))))=>(?[X]:((~strong(X)|curious(X)))))&
((?[X]:((calm(X)&~brave(X))))<=>(?[X]:(rich(X))))&
(![X]:((~quiet(X)&happy(X))=>(funny(X)|generous(X))))&
((?[X]:(creative(X)))=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~old(X)<~>wise(X))<=>(tall(X)|happy(X))))&
((~happy(john))=>(?[X]:((quiet(X)&curious(X)))))&
(![X]:((brave(X)<~>humble(X))<=>(rich(X)<~>calm(X))))&
(![X]:(~wise(X)<=>(rich(X)&old(X))))&
(![X]:((~happy(X)<~>~calm(X))<=>creative(X)))&
(![X]:((~tall(X)|patient(X))=>(~happy(X)<~>~curious(X))))&
(?[X]:(kind(X)))&
(?[X]:((rich(X)|old(X))))&
((humble(mary)|quiet(mary)))&
(?[X]:((~happy(X)<~>humble(X)))) | humble(john) | [
"p0",
"p3",
"p4",
"p7",
"p10",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 693489895576285729535196
% SZS output start Proof for 693489895576285729535196
1. ! [X0] : ((humble(X0) & wise(X0)) <=> creative(X0)) [input p0]
4. ! [X0] : (~creative(X0) => (~creative(X0) <~> ~rich(X0))) [input p3]
5. ! [X0] : ((brave(X0) & ~rich(X0)) <=> wise(X0)) [input p4]
8. ? [X0] : (~brave(X0) & calm(X0)) <=> ? [X0] : rich(X0) [input p7]
11. ! [X0] : ((~old(X0) <~> wise(X0)) <=> (happy(X0) | tall(X0))) [input p10]
13. ! [X0] : ((brave(X0) <~> humble(X0)) <=> (rich(X0) <~> calm(X0))) [input p12]
14. ! [X0] : (~wise(X0) <=> (old(X0) & rich(X0))) [input p13]
15. ! [X0] : ((~happy(X0) <~> ~calm(X0)) <=> creative(X0)) [input p14]
21. ~humble(john) [input hypothesis]
25. ? [X0] : (~brave(X0) & calm(X0)) <=> ? [X1] : rich(X1) [rectify 8]
37. ! [X0] : ((~creative(X0) <~> ~rich(X0)) | creative(X0)) [ennf transformation 4]
42. ! [X0] : (((humble(X0) & wise(X0)) | ~creative(X0)) & (creative(X0) | (~humble(X0) | ~wise(X0)))) [nnf transformation 1]
43. ! [X0] : (((humble(X0) & wise(X0)) | ~creative(X0)) & (creative(X0) | ~humble(X0) | ~wise(X0))) [flattening 42]
50. ! [X0] : (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | creative(X0)) [nnf transformation 37]
51. ! [X0] : (((brave(X0) & ~rich(X0)) | ~wise(X0)) & (wise(X0) | (~brave(X0) | rich(X0)))) [nnf transformation 5]
52. ! [X0] : (((brave(X0) & ~rich(X0)) | ~wise(X0)) & (wise(X0) | ~brave(X0) | rich(X0))) [flattening 51]
53. (? [X0] : (~brave(X0) & calm(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (brave(X0) | ~calm(X0))) [nnf transformation 25]
54. (? [X0] : (~brave(X0) & calm(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (brave(X3) | ~calm(X3))) [rectify 53]
55. ? [X0] : (~brave(X0) & calm(X0)) => (~brave(sK2) & calm(sK2)) [choice axiom]
56. ? [X2] : rich(X2) => rich(sK3) [choice axiom]
57. ((~brave(sK2) & calm(sK2)) | ! [X1] : ~rich(X1)) & (rich(sK3) | ! [X3] : (brave(X3) | ~calm(X3))) [skolemisation 54,56,55]
62. ! [X0] : ((((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (~happy(X0) & ~tall(X0))) & ((happy(X0) | tall(X0)) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))))) [nnf transformation 11]
63. ! [X0] : ((((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (~happy(X0) & ~tall(X0))) & (happy(X0) | tall(X0) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))))) [flattening 62]
66. ! [X0] : ((((~humble(X0) | ~brave(X0)) & (humble(X0) | brave(X0))) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) & (((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0))))) [nnf transformation 13]
67. ! [X0] : ((~wise(X0) | (~old(X0) | ~rich(X0))) & ((old(X0) & rich(X0)) | wise(X0))) [nnf transformation 14]
68. ! [X0] : ((~wise(X0) | ~old(X0) | ~rich(X0)) & ((old(X0) & rich(X0)) | wise(X0))) [flattening 67]
69. ! [X0] : ((((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | ~creative(X0)) & (creative(X0) | ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))))) [nnf transformation 15]
78. ~creative(X0) | humble(X0) [cnf transformation 43]
83. rich(X0) | creative(X0) | creative(X0) [cnf transformation 50]
85. ~rich(X0) | ~wise(X0) [cnf transformation 52]
86. ~wise(X0) | brave(X0) [cnf transformation 52]
90. calm(sK2) | ~rich(X1) [cnf transformation 57]
91. ~brave(sK2) | ~rich(X1) [cnf transformation 57]
97. ~old(X0) | wise(X0) | ~happy(X0) [cnf transformation 63]
104. ~rich(X0) | ~calm(X0) | brave(X0) | ~humble(X0) [cnf transformation 66]
106. ~calm(X0) | brave(X0) | rich(X0) | humble(X0) [cnf transformation 66]
109. rich(X0) | wise(X0) [cnf transformation 68]
110. old(X0) | wise(X0) [cnf transformation 68]
112. ~calm(X0) | creative(X0) | happy(X0) [cnf transformation 69]
121. ~humble(john) [cnf transformation 21]
122. rich(X0) | creative(X0) [duplicate literal removal 83]
144. 6 <=> ! [X1] : ~rich(X1) [avatar definition]
145. ~rich(X1) <- (6) [avatar component clause 144]
147. 7 <=> brave(sK2) [avatar definition]
149. ~brave(sK2) <- (~7) [avatar component clause 147]
150. 6 | ~7 [avatar split clause 91,147,144]
152. 8 <=> calm(sK2) [avatar definition]
154. calm(sK2) <- (8) [avatar component clause 152]
155. 6 | 8 [avatar split clause 90,152,144]
228. wise(X0) | ~happy(X0) | wise(X0) [resolution 97,110]
229. ~happy(X0) | wise(X0) [duplicate literal removal 228]
250. 22 <=> happy(sK2) [avatar definition]
252. happy(sK2) <- (22) [avatar component clause 250]
254. 23 <=> creative(sK2) [avatar definition]
256. creative(sK2) <- (23) [avatar component clause 254]
261. creative(X0) <- (6) [resolution 145,122]
273. humble(X0) <- (6) [resolution 261,78]
279. $false <- (6) [resolution 273,121]
283. ~6 [avatar contradiction clause 279]
294. creative(sK2) | happy(sK2) <- (8) [resolution 154,112]
349. ~calm(X1) | brave(X1) | ~humble(X1) | wise(X1) [resolution 104,109]
358. brave(sK2) | rich(sK2) | humble(sK2) <- (8) [resolution 106,154]
359. rich(sK2) | humble(sK2) <- (~7, 8) [subsumption resolution 358,149]
361. 31 <=> humble(sK2) [avatar definition]
362. ~humble(sK2) <- (~31) [avatar component clause 361]
365. 32 <=> rich(sK2) [avatar definition]
367. rich(sK2) <- (32) [avatar component clause 365]
368. 31 | 32 | 7 | ~8 [avatar split clause 359,152,147,365,361]
407. wise(sK2) <- (22) [resolution 229,252]
446. ~calm(X1) | brave(X1) | ~humble(X1) [subsumption resolution 349,86]
514. brave(sK2) | ~humble(sK2) <- (8) [resolution 446,154]
516. ~humble(sK2) <- (~7, 8) [subsumption resolution 514,149]
521. ~31 | 7 | ~8 [avatar split clause 516,152,147,361]
525. ~wise(sK2) <- (32) [resolution 367,85]
526. $false <- (22, 32) [subsumption resolution 525,407]
527. ~22 | ~32 [avatar contradiction clause 526]
528. 22 | 23 | ~8 [avatar split clause 294,152,254,250]
531. humble(sK2) <- (23) [resolution 256,78]
533. $false <- (23, ~31) [subsumption resolution 531,362]
534. ~23 | 31 [avatar contradiction clause 533]
537. $false [avatar sat refutation 150,155,283,368,521,527,528,534]
% SZS output end Proof for 693489895576285729535196
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not generous or not tall and vice versa. If someone is either patient or humble then lucy is happy or not brave and vice versa. Everyone who is either not humble or kind is rich and vice versa. Everyone who is both not generous and tall is old or curious and vice versa. Everyone who is both not quiet and not old is wise and vice versa. If lucy is brave or happy then someone is either creative or not quiet and vice versa. If paul is not quiet then someone is generous. If alice is both not old and not patient then fred is not strong or humble. Everyone who is patient or old is both creative and wise and vice versa. If someone is quiet or funny then someone is quiet and vice versa. Everyone who is either not old or not strong is quiet and vice versa. Everyone who is happy or strong is funny. If someone is strong then someone is not generous. If fred is both not quiet and not curious then paul is either not patient or not kind. If paul is either tall or not generous then fred is both kind and not generous. Everyone who is not calm is not funny or generous and vice versa. Mary is not creative. Someone is both not creative and not curious. Someone is not funny. Lucy is either brave or not rich. Paul is calm. John is either generous or quiet. Someone is brave. | Alice is generous. | neutral | (![X]:(~brave(X)<=>(~generous(X)<~>~tall(X))))&
((?[X]:((patient(X)<~>humble(X))))<=>((happy(lucy)|~brave(lucy))))&
(![X]:((~humble(X)<~>kind(X))<=>rich(X)))&
(![X]:((~generous(X)&tall(X))<=>(old(X)|curious(X))))&
(![X]:((~quiet(X)&~old(X))<=>wise(X)))&
(((brave(lucy)|happy(lucy)))<=>(?[X]:((creative(X)<~>~quiet(X)))))&
((~quiet(paul))=>(?[X]:(generous(X))))&
(((~old(alice)&~patient(alice)))=>((~strong(fred)|humble(fred))))&
(![X]:((patient(X)|old(X))<=>(creative(X)&wise(X))))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~old(X)<~>~strong(X))<=>quiet(X)))&
(![X]:((happy(X)|strong(X))=>funny(X)))&
((?[X]:(strong(X)))=>(?[X]:(~generous(X))))&
(((~quiet(fred)&~curious(fred)))=>((~patient(paul)<~>~kind(paul))))&
(((tall(paul)<~>~generous(paul)))=>((kind(fred)&~generous(fred))))&
(![X]:(~calm(X)<=>(~funny(X)|generous(X))))&
(~creative(mary))&
(?[X]:((~creative(X)&~curious(X))))&
(?[X]:(~funny(X)))&
((brave(lucy)<~>~rich(lucy)))&
(calm(paul))&
((generous(john)<~>quiet(john)))&
(?[X]:(brave(X))) | generous(alice) | [] | null | 0 |
Everyone who is happy or not patient is either not funny or creative and vice versa. Everyone who is not creative or not happy is wise and vice versa. Everyone who is generous or not creative is both calm and quiet and vice versa. Everyone who is either kind or creative is not brave or calm and vice versa. Everyone who is humble is either not humble or humble and vice versa. Everyone who is either old or strong is both not rich and not happy. Everyone who is not calm or not funny is either not happy or 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. Paul is not old. Susan is brave or strong. Someone is old or generous. Someone is either rich or not generous. Someone is quiet. Alice is not happy. | Alice is not creative. | contradiction | (![X]:((happy(X)|~patient(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((~creative(X)|~happy(X))<=>wise(X)))&
(![X]:((generous(X)|~creative(X))<=>(calm(X)&quiet(X))))&
(![X]:((kind(X)<~>creative(X))<=>(~brave(X)|calm(X))))&
(![X]:(humble(X)<=>(~humble(X)<~>humble(X))))&
(![X]:((old(X)<~>strong(X))=>(~rich(X)&~happy(X))))&
(![X]:((~calm(X)|~funny(X))=>(~happy(X)<~>wise(X))))&
((?[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))))&
(~old(paul))&
((brave(susan)|strong(susan)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:(quiet(X)))&
(~happy(alice)) | ~creative(alice) | [
"p1",
"p6",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8772915275582876577476941
% SZS output start Proof for 8772915275582876577476941
2. ! [X0] : ((~happy(X0) | ~creative(X0)) <=> wise(X0)) [input p1]
7. ! [X0] : ((~funny(X0) | ~calm(X0)) => (~happy(X0) <~> wise(X0))) [input p6]
10. ? [X0] : ~creative(X0) <=> ? [X0] : (brave(X0) & ~funny(X0)) [input p9]
11. ! [X0] : (~funny(X0) => (~calm(X0) & tall(X0))) [input p10]
16. ! [X0] : ((brave(X0) | ~calm(X0)) <=> (~funny(X0) <~> happy(X0))) [input p15]
23. ~creative(alice) [input hypothesis]
25. ? [X0] : ~creative(X0) <=> ? [X1] : (brave(X1) & ~funny(X1)) [rectify 10]
27. ! [X0] : ((~happy(X0) <~> wise(X0)) | (funny(X0) & calm(X0))) [ennf transformation 7]
30. ! [X0] : ((~calm(X0) & tall(X0)) | funny(X0)) [ennf transformation 11]
36. ! [X0] : (((~happy(X0) | ~creative(X0)) | ~wise(X0)) & (wise(X0) | (happy(X0) & creative(X0)))) [nnf transformation 2]
37. ! [X0] : ((~happy(X0) | ~creative(X0) | ~wise(X0)) & (wise(X0) | (happy(X0) & creative(X0)))) [flattening 36]
44. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (funny(X0) & calm(X0))) [nnf transformation 27]
50. (? [X0] : ~creative(X0) | ! [X1] : (~brave(X1) | funny(X1))) & (? [X1] : (brave(X1) & ~funny(X1)) | ! [X0] : creative(X0)) [nnf transformation 25]
51. (? [X0] : ~creative(X0) | ! [X1] : (~brave(X1) | funny(X1))) & (? [X2] : (brave(X2) & ~funny(X2)) | ! [X3] : creative(X3)) [rectify 50]
52. ? [X0] : ~creative(X0) => ~creative(sK1) [choice axiom]
53. ? [X2] : (brave(X2) & ~funny(X2)) => (brave(sK2) & ~funny(sK2)) [choice axiom]
54. (~creative(sK1) | ! [X1] : (~brave(X1) | funny(X1))) & ((brave(sK2) & ~funny(sK2)) | ! [X3] : creative(X3)) [skolemisation 51,53,52]
63. ! [X0] : (((brave(X0) | ~calm(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~brave(X0) & calm(X0)))) [nnf transformation 16]
64. ! [X0] : ((brave(X0) | ~calm(X0) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~brave(X0) & calm(X0)))) [flattening 63]
79. wise(X0) | happy(X0) [cnf transformation 37]
102. ~wise(X0) | happy(X0) | calm(X0) [cnf transformation 44]
110. ~funny(sK2) | creative(X3) [cnf transformation 54]
114. ~calm(X0) | funny(X0) [cnf transformation 30]
127. ~happy(X0) | funny(X0) | calm(X0) [cnf transformation 64]
138. ~creative(alice) [cnf transformation 23]
146. happy(X0) | calm(X0) [subsumption resolution 102,79]
194. 11 <=> ! [X3] : creative(X3) [avatar definition]
195. creative(X3) <- (11) [avatar component clause 194]
202. 13 <=> funny(sK2) [avatar definition]
204. ~funny(sK2) <- (~13) [avatar component clause 202]
205. 11 | ~13 [avatar split clause 110,202,194]
252. funny(X0) | calm(X0) [subsumption resolution 127,146]
253. funny(X0) [subsumption resolution 252,114]
283. $false <- (11) [resolution 195,138]
284. ~11 [avatar contradiction clause 283]
285. $false <- (~13) [subsumption resolution 204,253]
286. 13 [avatar contradiction clause 285]
287. $false [avatar sat refutation 205,284,286]
% SZS output end Proof for 8772915275582876577476941
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is not calm or not creative then someone is curious and vice versa.
Everyone who is both not generous and kind is both not quiet and not creative.
Everyone who is tall is not strong or not tall and vice versa.
If someone is humble then someone is both not creative and not humble and vice versa.
If lucy is both calm and not funny then someone is both not kind and not happy.
Everyone who is curious or old is patient and vice versa.
If someone is either happy or not old then john is not strong or not calm.
If susan is both rich and not strong then someone is either not calm or kind.
Everyone who is both curious and not creative is not old and vice versa.
Everyone who is both brave and creative is both not curious and humble and vice versa.
If mary is either tall or curious then alice is generous or not strong and vice versa.
If mary is not funny or not curious then mary is not strong or not curious.
Everyone who is strong is both creative and generous and vice versa.
If someone is either not humble or not funny then susan is not humble or not brave and vice versa.
If paul is either quiet or patient then someone is either not creative or not curious.
Everyone who is not creative is both creative and quiet.
Someone is either patient or brave.
Lucy is calm or not quiet.
Someone is not quiet.
Lucy is not patient or tall.
Paul is not calm or not tall.
Mary is both not kind and not humble.
Someone is not wise or not happy. | Paul is calm. | contradiction | (((~calm(john)|~creative(john)))<=>(?[X]:(curious(X))))&
(![X]:((~generous(X)&kind(X))=>(~quiet(X)&~creative(X))))&
(![X]:(tall(X)<=>(~strong(X)|~tall(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~creative(X)&~humble(X)))))&
(((calm(lucy)&~funny(lucy)))=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:((curious(X)|old(X))<=>patient(X)))&
((?[X]:((happy(X)<~>~old(X))))=>((~strong(john)|~calm(john))))&
(((rich(susan)&~strong(susan)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((curious(X)&~creative(X))<=>~old(X)))&
(![X]:((brave(X)&creative(X))<=>(~curious(X)&humble(X))))&
(((tall(mary)<~>curious(mary)))<=>((generous(alice)|~strong(alice))))&
(((~funny(mary)|~curious(mary)))=>((~strong(mary)|~curious(mary))))&
(![X]:(strong(X)<=>(creative(X)&generous(X))))&
((?[X]:((~humble(X)<~>~funny(X))))<=>((~humble(susan)|~brave(susan))))&
(((quiet(paul)<~>patient(paul)))=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:(~creative(X)=>(creative(X)&quiet(X))))&
(?[X]:((patient(X)<~>brave(X))))&
((calm(lucy)|~quiet(lucy)))&
(?[X]:(~quiet(X)))&
((~patient(lucy)|tall(lucy)))&
((~calm(paul)|~tall(paul)))&
((~kind(mary)&~humble(mary)))&
(?[X]:((~wise(X)|~happy(X)))) | calm(paul) | [
"p2",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3927742268563030192807607
% SZS output start Proof for 3927742268563030192807607
3. ! [X0] : (tall(X0) <=> (~tall(X0) | ~strong(X0))) [input p2]
21. ~tall(paul) | ~calm(paul) [input p20]
24. calm(paul) [input hypothesis]
44. ! [X0] : ((tall(X0) | (tall(X0) & strong(X0))) & ((~tall(X0) | ~strong(X0)) | ~tall(X0))) [nnf transformation 3]
45. ! [X0] : ((tall(X0) | (tall(X0) & strong(X0))) & (~tall(X0) | ~strong(X0) | ~tall(X0))) [flattening 44]
82. tall(X0) | tall(X0) [cnf transformation 45]
127. ~tall(paul) | ~calm(paul) [cnf transformation 21]
129. calm(paul) [cnf transformation 24]
132. tall(X0) [duplicate literal removal 82]
252. ~calm(paul) [subsumption resolution 127,132]
253. $false [subsumption resolution 129,252]
% SZS output end Proof for 3927742268563030192807607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not happy or curious then alice is either kind or tall and vice versa.
Everyone who is both not tall and happy is either happy or not happy and vice versa.
If someone is generous or not old then susan is tall or not strong.
Everyone who is either quiet or not humble is both not kind and generous and vice versa.
If susan is brave then mary is both wise and not happy.
If alice is either not curious or brave then susan is curious and vice versa.
Everyone who is both curious and old is either brave or tall.
Everyone who is quiet is either patient or not funny.
Everyone who is both old and funny is both calm and creative and vice versa.
If paul is funny or not curious then someone is not strong and vice versa.
If someone is humble or not kind then alice is both quiet and not tall.
Everyone who is not kind or funny is not strong or tall.
Everyone who is tall or strong is either calm or quiet.
Everyone who is both wise and kind is old or humble.
If someone is tall then susan is not patient or funny.
Everyone who is both brave and strong is tall.
Paul is either not curious or quiet.
Someone is both not quiet and not calm.
Someone is curious.
Paul is wise or strong.
Someone is strong.
Paul is creative or not humble.
Lucy is brave.
Alice is both not patient and not wise. | Paul is not strong. | entailment | (((~happy(fred)<~>curious(fred)))<=>((kind(alice)<~>tall(alice))))&
(![X]:((~tall(X)&happy(X))<=>(happy(X)<~>~happy(X))))&
((?[X]:((generous(X)|~old(X))))=>((tall(susan)|~strong(susan))))&
(![X]:((quiet(X)<~>~humble(X))<=>(~kind(X)&generous(X))))&
((brave(susan))=>((wise(mary)&~happy(mary))))&
(((~curious(alice)<~>brave(alice)))<=>(curious(susan)))&
(![X]:((curious(X)&old(X))=>(brave(X)<~>tall(X))))&
(![X]:(quiet(X)=>(patient(X)<~>~funny(X))))&
(![X]:((old(X)&funny(X))<=>(calm(X)&creative(X))))&
(((funny(paul)|~curious(paul)))<=>(?[X]:(~strong(X))))&
((?[X]:((humble(X)|~kind(X))))=>((quiet(alice)&~tall(alice))))&
(![X]:((~kind(X)|funny(X))=>(~strong(X)|tall(X))))&
(![X]:((tall(X)|strong(X))=>(calm(X)<~>quiet(X))))&
(![X]:((wise(X)&kind(X))=>(old(X)|humble(X))))&
((?[X]:(tall(X)))=>((~patient(susan)|funny(susan))))&
(![X]:((brave(X)&strong(X))=>tall(X)))&
((~curious(paul)<~>quiet(paul)))&
(?[X]:((~quiet(X)&~calm(X))))&
(?[X]:(curious(X)))&
((wise(paul)|strong(paul)))&
(?[X]:(strong(X)))&
((creative(paul)|~humble(paul)))&
(brave(lucy))&
((~patient(alice)&~wise(alice))) | ~strong(paul) | [
"p1",
"p3",
"p8",
"p9",
"p11",
"p12",
"p15",
"p16",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5341860084700618479926622
% SZS output start Proof for 5341860084700618479926622
2. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (happy(X0) <~> ~happy(X0))) [input p1]
4. ! [X0] : ((quiet(X0) <~> ~humble(X0)) <=> (generous(X0) & ~kind(X0))) [input p3]
9. ! [X0] : ((funny(X0) & old(X0)) <=> (creative(X0) & calm(X0))) [input p8]
10. (~curious(paul) | funny(paul)) <=> ? [X0] : ~strong(X0) [input p9]
12. ! [X0] : ((funny(X0) | ~kind(X0)) => (tall(X0) | ~strong(X0))) [input p11]
13. ! [X0] : ((strong(X0) | tall(X0)) => (calm(X0) <~> quiet(X0))) [input p12]
16. ! [X0] : ((strong(X0) & brave(X0)) => tall(X0)) [input p15]
17. ~curious(paul) <~> quiet(paul) [input p16]
22. ~humble(paul) | creative(paul) [input p21]
23. brave(lucy) [input p22]
25. strong(paul) [input hypothesis]
33. ! [X0] : ((tall(X0) | ~strong(X0)) | (~funny(X0) & kind(X0))) [ennf transformation 12]
34. ! [X0] : (tall(X0) | ~strong(X0) | (~funny(X0) & kind(X0))) [flattening 33]
35. ! [X0] : ((calm(X0) <~> quiet(X0)) | (~strong(X0) & ~tall(X0))) [ennf transformation 13]
40. ! [X0] : (tall(X0) | (~strong(X0) | ~brave(X0))) [ennf transformation 16]
41. ! [X0] : (tall(X0) | ~strong(X0) | ~brave(X0)) [flattening 40]
43. ! [X0] : (((happy(X0) & ~tall(X0)) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | (~happy(X0) | tall(X0)))) [nnf transformation 2]
44. ! [X0] : (((happy(X0) & ~tall(X0)) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | ~happy(X0) | tall(X0))) [flattening 43]
45. ! [X0] : ((((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | (~generous(X0) | kind(X0))) & ((generous(X0) & ~kind(X0)) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0))))) [nnf transformation 4]
46. ! [X0] : ((((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | ~generous(X0) | kind(X0)) & ((generous(X0) & ~kind(X0)) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0))))) [flattening 45]
50. ! [X0] : (((funny(X0) & old(X0)) | (~creative(X0) | ~calm(X0))) & ((creative(X0) & calm(X0)) | (~funny(X0) | ~old(X0)))) [nnf transformation 9]
51. ! [X0] : (((funny(X0) & old(X0)) | ~creative(X0) | ~calm(X0)) & ((creative(X0) & calm(X0)) | ~funny(X0) | ~old(X0))) [flattening 50]
52. ((~curious(paul) | funny(paul)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | (curious(paul) & ~funny(paul))) [nnf transformation 10]
53. (~curious(paul) | funny(paul) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | (curious(paul) & ~funny(paul))) [flattening 52]
54. (~curious(paul) | funny(paul) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | (curious(paul) & ~funny(paul))) [rectify 53]
55. ? [X1] : ~strong(X1) => ~strong(sK0) [choice axiom]
56. (~curious(paul) | funny(paul) | ! [X0] : strong(X0)) & (~strong(sK0) | (curious(paul) & ~funny(paul))) [skolemisation 54,55]
57. ! [X0] : (((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | (~strong(X0) & ~tall(X0))) [nnf transformation 35]
58. (~quiet(paul) | curious(paul)) & (quiet(paul) | ~curious(paul)) [nnf transformation 17]
75. ~tall(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 44]
78. happy(X0) | happy(X0) | happy(X0) [cnf transformation 44]
82. ~kind(X0) | quiet(X0) | humble(X0) [cnf transformation 46]
100. ~creative(X0) | funny(X0) | ~calm(X0) [cnf transformation 51]
103. ~curious(paul) | funny(paul) | strong(X0) [cnf transformation 56]
108. tall(X0) | ~strong(X0) | kind(X0) [cnf transformation 34]
109. tall(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 34]
111. ~strong(X0) | calm(X0) | quiet(X0) [cnf transformation 57]
116. tall(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 41]
118. ~quiet(paul) | curious(paul) [cnf transformation 58]
124. ~humble(paul) | creative(paul) [cnf transformation 22]
125. brave(lucy) [cnf transformation 23]
128. strong(paul) [cnf transformation 25]
131. ~tall(X0) | ~happy(X0) [duplicate literal removal 75]
134. happy(X0) [duplicate literal removal 78]
159. ~tall(X0) [subsumption resolution 131,134]
193. 11 <=> ! [X0] : strong(X0) [avatar definition]
194. strong(X0) <- (11) [avatar component clause 193]
196. 12 <=> funny(paul) [avatar definition]
197. ~funny(paul) <- (~12) [avatar component clause 196]
198. funny(paul) <- (12) [avatar component clause 196]
200. 13 <=> curious(paul) [avatar definition]
203. 11 | 12 | ~13 [avatar split clause 103,200,196,193]
222. ~funny(X0) | ~strong(X0) [subsumption resolution 109,159]
223. ~strong(X0) | kind(X0) [subsumption resolution 108,159]
224. ~brave(X0) | ~strong(X0) [subsumption resolution 116,159]
226. 18 <=> quiet(paul) [avatar definition]
228. ~quiet(paul) <- (~18) [avatar component clause 226]
229. 13 | ~18 [avatar split clause 118,226,200]
236. 20 <=> strong(paul) [avatar definition]
238. strong(paul) <- (20) [avatar component clause 236]
241. 21 <=> creative(paul) [avatar definition]
243. creative(paul) <- (21) [avatar component clause 241]
245. 22 <=> humble(paul) [avatar definition]
248. 21 | ~22 [avatar split clause 124,245,241]
249. 20 [avatar split clause 128,236]
253. kind(paul) <- (20) [resolution 223,238]
254. ~strong(lucy) [resolution 224,125]
257. quiet(paul) | humble(paul) <- (20) [resolution 82,253]
274. $false <- (11) [resolution 194,254]
277. ~11 [avatar contradiction clause 274]
280. ~strong(paul) <- (12) [resolution 198,222]
281. $false <- (12, 20) [subsumption resolution 280,238]
282. ~12 | ~20 [avatar contradiction clause 281]
283. 22 | 18 | ~20 [avatar split clause 257,236,226,245]
300. 26 <=> calm(paul) [avatar definition]
308. funny(paul) | ~calm(paul) <- (21) [resolution 100,243]
310. calm(paul) | quiet(paul) <- (20) [resolution 111,238]
315. calm(paul) <- (~18, 20) [subsumption resolution 310,228]
316. 26 | 18 | ~20 [avatar split clause 315,236,226,300]
317. ~calm(paul) <- (~12, 21) [subsumption resolution 308,197]
318. ~26 | 12 | ~21 [avatar split clause 317,241,196,300]
319. $false [avatar sat refutation 203,229,248,249,277,282,283,316,318]
% SZS output end Proof for 5341860084700618479926622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not funny and vice versa. Everyone who is both not creative and not calm is not brave. Everyone who is not generous or not rich is either tall or funny and vice versa. If alice is both not brave and not happy then someone is quiet or not old. If john is both calm and happy then someone is creative or not brave. If someone is either not creative or rich then fred is either old or not humble and vice versa. If someone is both not humble and not old then alice is both not rich and old and vice versa. Everyone who is not funny is not happy and vice versa. If someone is both not funny and quiet then someone is either not tall or not wise. Everyone who is both not curious and not brave is not quiet. If someone is not happy then someone is strong or not generous. Everyone who is generous is either not curious or not tall. If someone is either not funny or not wise then alice is both rich and old and vice versa. Everyone who is both not rich and brave is either not calm or not quiet and vice versa. Everyone who is brave is tall or not curious. Susan is funny. Someone is not humble or happy. Someone is not quiet. Alice is patient or not curious. Alice is not funny. Someone is either not old or not calm. Lucy is not patient or generous. Mary is quiet or curious. | Susan is tall. | contradiction | (![X]:(generous(X)<=>~funny(X)))&
(![X]:((~creative(X)&~calm(X))=>~brave(X)))&
(![X]:((~generous(X)|~rich(X))<=>(tall(X)<~>funny(X))))&
(((~brave(alice)&~happy(alice)))=>(?[X]:((quiet(X)|~old(X)))))&
(((calm(john)&happy(john)))=>(?[X]:((creative(X)|~brave(X)))))&
((?[X]:((~creative(X)<~>rich(X))))<=>((old(fred)<~>~humble(fred))))&
((?[X]:((~humble(X)&~old(X))))<=>((~rich(alice)&old(alice))))&
(![X]:(~funny(X)<=>~happy(X)))&
((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((~tall(X)<~>~wise(X)))))&
(![X]:((~curious(X)&~brave(X))=>~quiet(X)))&
((?[X]:(~happy(X)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:(generous(X)=>(~curious(X)<~>~tall(X))))&
((?[X]:((~funny(X)<~>~wise(X))))<=>((rich(alice)&old(alice))))&
(![X]:((~rich(X)&brave(X))<=>(~calm(X)<~>~quiet(X))))&
(![X]:(brave(X)=>(tall(X)|~curious(X))))&
(funny(susan))&
(?[X]:((~humble(X)|happy(X))))&
(?[X]:(~quiet(X)))&
((patient(alice)|~curious(alice)))&
(~funny(alice))&
(?[X]:((~old(X)<~>~calm(X))))&
((~patient(lucy)|generous(lucy)))&
((quiet(mary)|curious(mary))) | tall(susan) | [
"p0",
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6339023015609135340802084
% SZS output start Proof for 6339023015609135340802084
1. ! [X0] : (generous(X0) <=> ~funny(X0)) [input p0]
3. ! [X0] : ((~rich(X0) | ~generous(X0)) <=> (tall(X0) <~> funny(X0))) [input p2]
16. funny(susan) [input p15]
24. tall(susan) [input hypothesis]
40. ! [X0] : ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))) [nnf transformation 1]
41. ! [X0] : (((~rich(X0) | ~generous(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (rich(X0) & generous(X0)))) [nnf transformation 3]
42. ! [X0] : ((~rich(X0) | ~generous(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (rich(X0) & generous(X0)))) [flattening 41]
76. ~funny(X0) | ~generous(X0) [cnf transformation 40]
77. funny(X0) | generous(X0) [cnf transformation 40]
81. ~funny(X0) | ~tall(X0) | generous(X0) [cnf transformation 42]
119. funny(susan) [cnf transformation 16]
128. tall(susan) [cnf transformation 24]
130. ~tall(X0) | generous(X0) [subsumption resolution 81,77]
299. ~generous(susan) [resolution 76,119]
306. generous(susan) [resolution 130,128]
307. $false [subsumption resolution 306,299]
% SZS output end Proof for 6339023015609135340802084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or wise is either funny or brave.
Everyone who is either not quiet or patient is either rich or not tall and vice versa.
If someone is either not quiet or not tall then someone is either not funny or brave and vice versa.
Everyone who is calm or not funny is not happy.
Everyone who is humble is both old and kind and vice versa.
Everyone who is either old or not curious is tall.
If someone is either not generous or patient then someone is kind or not creative.
Everyone who is wise or not old is not funny.
Everyone who is either kind or tall is brave.
If fred is both not generous and humble then susan is not happy and vice versa.
If someone is generous or not strong then someone is not old.
Everyone who is quiet or patient is wise.
Everyone who is brave or tall is both rich and happy and vice versa.
If someone is strong then alice is not kind or not wise.
Everyone who is not happy is not rich or curious.
Susan is creative or tall.
Alice is either not wise or wise.
Someone is tall or patient.
Susan is either not calm or patient.
Someone is not quiet or quiet. | Susan is not quiet. | entailment | (![X]:((curious(X)|wise(X))=>(funny(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>patient(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:((calm(X)|~funny(X))=>~happy(X)))&
(![X]:(humble(X)<=>(old(X)&kind(X))))&
(![X]:((old(X)<~>~curious(X))=>tall(X)))&
((?[X]:((~generous(X)<~>patient(X))))=>(?[X]:((kind(X)|~creative(X)))))&
(![X]:((wise(X)|~old(X))=>~funny(X)))&
(![X]:((kind(X)<~>tall(X))=>brave(X)))&
(((~generous(fred)&humble(fred)))<=>(~happy(susan)))&
((?[X]:((generous(X)|~strong(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|patient(X))=>wise(X)))&
(![X]:((brave(X)|tall(X))<=>(rich(X)&happy(X))))&
((?[X]:(strong(X)))=>((~kind(alice)|~wise(alice))))&
(![X]:(~happy(X)=>(~rich(X)|curious(X))))&
((creative(susan)|tall(susan)))&
((~wise(alice)<~>wise(alice)))&
(?[X]:((tall(X)|patient(X))))&
((~calm(susan)<~>patient(susan)))&
(?[X]:((~quiet(X)|quiet(X)))) | ~quiet(susan) | [
"p0",
"p3",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 24100821725658282987552
% SZS output start Proof for 24100821725658282987552
1. ! [X0] : ((wise(X0) | curious(X0)) => (funny(X0) <~> brave(X0))) [input p0]
4. ! [X0] : ((~funny(X0) | calm(X0)) => ~happy(X0)) [input p3]
8. ! [X0] : ((~old(X0) | wise(X0)) => ~funny(X0)) [input p7]
12. ! [X0] : ((patient(X0) | quiet(X0)) => wise(X0)) [input p11]
13. ! [X0] : ((tall(X0) | brave(X0)) <=> (happy(X0) & rich(X0))) [input p12]
21. quiet(susan) [input hypothesis]
25. ! [X0] : ((funny(X0) <~> brave(X0)) | (~wise(X0) & ~curious(X0))) [ennf transformation 1]
26. ! [X0] : (~happy(X0) | (funny(X0) & ~calm(X0))) [ennf transformation 4]
29. ! [X0] : (~funny(X0) | (old(X0) & ~wise(X0))) [ennf transformation 8]
32. ! [X0] : (wise(X0) | (~patient(X0) & ~quiet(X0))) [ennf transformation 12]
37. ! [X0] : (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~wise(X0) & ~curious(X0))) [nnf transformation 25]
57. ! [X0] : (((tall(X0) | brave(X0)) | (~happy(X0) | ~rich(X0))) & ((happy(X0) & rich(X0)) | (~tall(X0) & ~brave(X0)))) [nnf transformation 13]
58. ! [X0] : ((tall(X0) | brave(X0) | ~happy(X0) | ~rich(X0)) & ((happy(X0) & rich(X0)) | (~tall(X0) & ~brave(X0)))) [flattening 57]
66. ~wise(X0) | funny(X0) | brave(X0) [cnf transformation 37]
86. ~happy(X0) | funny(X0) [cnf transformation 26]
94. ~funny(X0) | ~wise(X0) [cnf transformation 29]
103. ~quiet(X0) | wise(X0) [cnf transformation 32]
107. ~brave(X0) | happy(X0) [cnf transformation 58]
119. quiet(susan) [cnf transformation 21]
173. 13 <=> happy(susan) [avatar definition]
174. ~happy(susan) <- (~13) [avatar component clause 173]
175. happy(susan) <- (13) [avatar component clause 173]
240. funny(susan) <- (13) [resolution 86,175]
241. ~wise(susan) <- (13) [resolution 94,240]
243. wise(susan) [resolution 103,119]
245. $false <- (13) [subsumption resolution 243,241]
246. ~13 [avatar contradiction clause 245]
253. funny(susan) | brave(susan) [resolution 66,243]
256. 28 <=> brave(susan) [avatar definition]
258. brave(susan) <- (28) [avatar component clause 256]
260. 29 <=> funny(susan) [avatar definition]
262. funny(susan) <- (29) [avatar component clause 260]
263. 28 | 29 [avatar split clause 253,260,256]
295. happy(susan) <- (28) [resolution 258,107]
302. $false <- (~13, 28) [subsumption resolution 295,174]
303. 13 | ~28 [avatar contradiction clause 302]
363. ~wise(susan) <- (29) [resolution 262,94]
364. $false <- (29) [subsumption resolution 363,243]
365. ~29 [avatar contradiction clause 364]
366. $false [avatar sat refutation 246,263,303,365]
% SZS output end Proof for 24100821725658282987552
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If 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 8020400976492034970865502
% SZS output start Proof for 8020400976492034970865502
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 8020400976492034970865502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or strong is either rich or creative and vice versa. Everyone who is old is curious. If someone is either brave or wise then someone is not quiet and vice versa. If john is both not funny and quiet then alice is generous. Everyone who is happy is both wise and not generous. Everyone who is not creative is not quiet and vice versa. Everyone who is not curious or kind is both old and tall. If someone is either not patient or wise then lucy is not strong. Everyone who is wise or rich is not calm. Everyone who is happy is not humble. If john is not old or not calm then someone is creative. If mary is both patient and wise then lucy is either not kind or not humble and vice versa. Everyone who is both wise and patient is both calm and brave. Everyone who is both old and not tall is both tall and curious and vice versa. Everyone who is both brave and not wise is both old and patient. If someone is both not creative and not quiet then someone is not happy. Paul is either not curious or not funny. Mary is not funny or wise. Paul is both not humble and not happy. Someone is not humble. Someone is not funny or calm. Alice is humble. | Mary is happy. | neutral | (![X]:((~kind(X)<~>strong(X))<=>(rich(X)<~>creative(X))))&
(![X]:(old(X)=>curious(X)))&
((?[X]:((brave(X)<~>wise(X))))<=>(?[X]:(~quiet(X))))&
(((~funny(john)&quiet(john)))=>(generous(alice)))&
(![X]:(happy(X)=>(wise(X)&~generous(X))))&
(![X]:(~creative(X)<=>~quiet(X)))&
(![X]:((~curious(X)|kind(X))=>(old(X)&tall(X))))&
((?[X]:((~patient(X)<~>wise(X))))=>(~strong(lucy)))&
(![X]:((wise(X)|rich(X))=>~calm(X)))&
(![X]:(happy(X)=>~humble(X)))&
(((~old(john)|~calm(john)))=>(?[X]:(creative(X))))&
(((patient(mary)&wise(mary)))<=>((~kind(lucy)<~>~humble(lucy))))&
(![X]:((wise(X)&patient(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)&~tall(X))<=>(tall(X)&curious(X))))&
(![X]:((brave(X)&~wise(X))=>(old(X)&patient(X))))&
((?[X]:((~creative(X)&~quiet(X))))=>(?[X]:(~happy(X))))&
((~curious(paul)<~>~funny(paul)))&
((~funny(mary)|wise(mary)))&
((~humble(paul)&~happy(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((~funny(X)|calm(X))))&
(humble(alice)) | happy(mary) | [] | null | 0 |
If paul is both humble and not old then someone is not creative or not curious and vice versa.
If someone is old or rich then john is either creative or curious.
If susan is both not curious and not calm then someone is tall or not quiet and vice versa.
Everyone who is either not patient or not rich is not rich or not strong and vice versa.
Everyone who is either not generous or not old is both brave and generous and vice versa.
Everyone who is not wise or not brave is both not patient and not humble and vice versa.
If someone is both not humble and not kind then fred is not quiet or old and vice versa.
If someone is rich or not calm then fred is either not humble or old and vice versa.
Everyone who is generous or humble is either not funny or patient and vice versa.
If someone is old then someone is both brave and not old.
If someone is both happy and wise then someone is both not generous and funny.
If alice is either humble or funny then alice is quiet or kind.
Everyone who is not curious or not quiet is not strong and vice versa.
Everyone who is not creative is both not patient and happy and vice versa.
Everyone who is rich or happy is not creative or kind and vice versa.
Everyone who is both not curious and creative is patient and vice versa.
Someone is curious.
Fred is tall.
Fred is kind.
Alice is not strong.
Alice is not rich or not old.
Alice is not old or humble.
Someone is both generous and not old. | Paul is brave. | entailment | (((humble(paul)&~old(paul)))<=>(?[X]:((~creative(X)|~curious(X)))))&
((?[X]:((old(X)|rich(X))))=>((creative(john)<~>curious(john))))&
(((~curious(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~quiet(X)))))&
(![X]:((~patient(X)<~>~rich(X))<=>(~rich(X)|~strong(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(brave(X)&generous(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~patient(X)&~humble(X))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~quiet(fred)|old(fred))))&
((?[X]:((rich(X)|~calm(X))))<=>((~humble(fred)<~>old(fred))))&
(![X]:((generous(X)|humble(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:(old(X)))=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((happy(X)&wise(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((humble(alice)<~>funny(alice)))=>((quiet(alice)|kind(alice))))&
(![X]:((~curious(X)|~quiet(X))<=>~strong(X)))&
(![X]:(~creative(X)<=>(~patient(X)&happy(X))))&
(![X]:((rich(X)|happy(X))<=>(~creative(X)|kind(X))))&
(![X]:((~curious(X)&creative(X))<=>patient(X)))&
(?[X]:(curious(X)))&
(tall(fred))&
(kind(fred))&
(~strong(alice))&
((~rich(alice)|~old(alice)))&
((~old(alice)|humble(alice)))&
(?[X]:((generous(X)&~old(X)))) | brave(paul) | [
"p0",
"p2",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2972160371609496292461235
% SZS output start Proof for 2972160371609496292461235
1. (~old(paul) & humble(paul)) <=> ? [X0] : (~curious(X0) | ~creative(X0)) [input p0]
3. (~calm(susan) & ~curious(susan)) <=> ? [X0] : (~quiet(X0) | tall(X0)) [input p2]
6. ! [X0] : ((~brave(X0) | ~wise(X0)) <=> (~humble(X0) & ~patient(X0))) [input p5]
18. tall(fred) [input p17]
24. ~brave(paul) [input hypothesis]
32. ((~old(paul) & humble(paul)) | ! [X0] : (curious(X0) & creative(X0))) & (? [X0] : (~curious(X0) | ~creative(X0)) | (old(paul) | ~humble(paul))) [nnf transformation 1]
33. ((~old(paul) & humble(paul)) | ! [X0] : (curious(X0) & creative(X0))) & (? [X0] : (~curious(X0) | ~creative(X0)) | old(paul) | ~humble(paul)) [flattening 32]
34. ((~old(paul) & humble(paul)) | ! [X0] : (curious(X0) & creative(X0))) & (? [X1] : (~curious(X1) | ~creative(X1)) | old(paul) | ~humble(paul)) [rectify 33]
35. ? [X1] : (~curious(X1) | ~creative(X1)) => (~curious(sK0) | ~creative(sK0)) [choice axiom]
36. ((~old(paul) & humble(paul)) | ! [X0] : (curious(X0) & creative(X0))) & ((~curious(sK0) | ~creative(sK0)) | old(paul) | ~humble(paul)) [skolemisation 34,35]
38. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & (? [X0] : (~quiet(X0) | tall(X0)) | (calm(susan) | curious(susan))) [nnf transformation 3]
39. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & (? [X0] : (~quiet(X0) | tall(X0)) | calm(susan) | curious(susan)) [flattening 38]
40. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & (? [X1] : (~quiet(X1) | tall(X1)) | calm(susan) | curious(susan)) [rectify 39]
41. ? [X1] : (~quiet(X1) | tall(X1)) => (~quiet(sK1) | tall(sK1)) [choice axiom]
42. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & ((~quiet(sK1) | tall(sK1)) | calm(susan) | curious(susan)) [skolemisation 40,41]
47. ! [X0] : (((~brave(X0) | ~wise(X0)) | (humble(X0) | patient(X0))) & ((~humble(X0) & ~patient(X0)) | (brave(X0) & wise(X0)))) [nnf transformation 6]
48. ! [X0] : ((~brave(X0) | ~wise(X0) | humble(X0) | patient(X0)) & ((~humble(X0) & ~patient(X0)) | (brave(X0) & wise(X0)))) [flattening 47]
81. humble(paul) | curious(X0) [cnf transformation 36]
89. ~curious(susan) | ~tall(X0) [cnf transformation 42]
108. ~humble(X0) | brave(X0) [cnf transformation 48]
147. tall(fred) [cnf transformation 18]
154. ~brave(paul) [cnf transformation 24]
160. 1 <=> ! [X0] : curious(X0) [avatar definition]
161. curious(X0) <- (1) [avatar component clause 160]
172. 4 <=> humble(paul) [avatar definition]
174. humble(paul) <- (4) [avatar component clause 172]
175. 1 | 4 [avatar split clause 81,172,160]
213. 13 <=> ! [X0] : ~tall(X0) [avatar definition]
214. ~tall(X0) <- (13) [avatar component clause 213]
217. 14 <=> curious(susan) [avatar definition]
219. ~curious(susan) <- (~14) [avatar component clause 217]
221. 13 | ~14 [avatar split clause 89,217,213]
329. brave(paul) <- (4) [resolution 108,174]
330. $false <- (4) [subsumption resolution 329,154]
331. ~4 [avatar contradiction clause 330]
333. $false <- (1, ~14) [resolution 161,219]
334. ~1 | 14 [avatar contradiction clause 333]
340. $false <- (13) [resolution 214,147]
341. ~13 [avatar contradiction clause 340]
342. $false [avatar sat refutation 175,221,331,334,341]
% SZS output end Proof for 2972160371609496292461235
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is both not old and not kind. Everyone who is happy or creative is happy or not patient and vice versa. If someone is not generous or strong then lucy is not brave or quiet. Everyone who is both humble and rich is either funny or brave and vice versa. Everyone who is both strong and not rich is wise. Everyone who is either not quiet or humble is calm or rich and vice versa. Everyone who is both not happy and not wise is either strong or not funny. Everyone who is either not rich or not wise is patient and vice versa. Everyone who is both humble and rich is not creative or quiet and vice versa. Everyone who is both not happy and not tall is not rich or quiet and vice versa. Everyone who is both not rich and patient is rich or calm. If alice is both not wise and not brave then susan is either patient or not tall and vice versa. Everyone who is both old and patient is either generous or not happy. If someone is patient then someone is happy or not happy. If someone is either brave or tall then someone is curious or not kind. If fred is not calm or quiet then someone is rich or not happy and vice versa. Paul is either not patient or not creative. Someone is either not curious or not funny. John is both humble and not strong. Someone is not generous. Mary is kind. Mary is either not rich or not humble. Fred is not rich or kind. Someone is both kind and calm. | John is not happy. | entailment | (![X]:(~happy(X)=>(~old(X)&~kind(X))))&
(![X]:((happy(X)|creative(X))<=>(happy(X)|~patient(X))))&
((?[X]:((~generous(X)|strong(X))))=>((~brave(lucy)|quiet(lucy))))&
(![X]:((humble(X)&rich(X))<=>(funny(X)<~>brave(X))))&
(![X]:((strong(X)&~rich(X))=>wise(X)))&
(![X]:((~quiet(X)<~>humble(X))<=>(calm(X)|rich(X))))&
(![X]:((~happy(X)&~wise(X))=>(strong(X)<~>~funny(X))))&
(![X]:((~rich(X)<~>~wise(X))<=>patient(X)))&
(![X]:((humble(X)&rich(X))<=>(~creative(X)|quiet(X))))&
(![X]:((~happy(X)&~tall(X))<=>(~rich(X)|quiet(X))))&
(![X]:((~rich(X)&patient(X))=>(rich(X)|calm(X))))&
(((~wise(alice)&~brave(alice)))<=>((patient(susan)<~>~tall(susan))))&
(![X]:((old(X)&patient(X))=>(generous(X)<~>~happy(X))))&
((?[X]:(patient(X)))=>(?[X]:((happy(X)|~happy(X)))))&
((?[X]:((brave(X)<~>tall(X))))=>(?[X]:((curious(X)|~kind(X)))))&
(((~calm(fred)|quiet(fred)))<=>(?[X]:((rich(X)|~happy(X)))))&
((~patient(paul)<~>~creative(paul)))&
(?[X]:((~curious(X)<~>~funny(X))))&
((humble(john)&~strong(john)))&
(?[X]:(~generous(X)))&
(kind(mary))&
((~rich(mary)<~>~humble(mary)))&
((~rich(fred)|kind(fred)))&
(?[X]:((kind(X)&calm(X)))) | ~happy(john) | [
"p5",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 302884956786233272154747
% SZS output start Proof for 302884956786233272154747
6. ! [X0] : ((~quiet(X0) <~> humble(X0)) <=> (rich(X0) | calm(X0))) [input p5]
10. ! [X0] : ((~tall(X0) & ~happy(X0)) <=> (quiet(X0) | ~rich(X0))) [input p9]
19. ~strong(john) & humble(john) [input p18]
25. happy(john) [input hypothesis]
45. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~rich(X0) & ~calm(X0))) & ((rich(X0) | calm(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [nnf transformation 6]
46. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~rich(X0) & ~calm(X0))) & (rich(X0) | calm(X0) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [flattening 45]
51. ! [X0] : (((~tall(X0) & ~happy(X0)) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | (tall(X0) | happy(X0)))) [nnf transformation 10]
52. ! [X0] : (((~tall(X0) & ~happy(X0)) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | tall(X0) | happy(X0))) [flattening 51]
95. ~rich(X0) | quiet(X0) | ~humble(X0) [cnf transformation 46]
108. ~happy(X0) | rich(X0) [cnf transformation 52]
109. ~quiet(X0) | ~happy(X0) [cnf transformation 52]
130. humble(john) [cnf transformation 19]
139. happy(john) [cnf transformation 25]
254. rich(john) [resolution 108,139]
292. quiet(john) | ~humble(john) [resolution 95,254]
297. quiet(john) [subsumption resolution 292,130]
395. ~happy(john) [resolution 297,109]
398. $false [subsumption resolution 395,139]
% SZS output end Proof for 302884956786233272154747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or wise is not happy.
If mary is either quiet or not funny then someone is either not humble or not quiet.
If someone is curious or kind then someone is either strong or not brave.
If someone is both not wise and not patient then someone is not strong or not funny and vice versa.
Everyone who is either not quiet or strong is old and vice versa.
Everyone who is both funny and not happy is not creative.
Everyone who is patient or tall is not rich or kind.
If lucy is both tall and not old then fred is both not creative and brave.
Everyone who is calm or not generous is both generous and happy.
Everyone who is both calm and old is not patient.
Everyone who is either happy or brave is both happy and not calm and vice versa.
If john is quiet or rich then susan is both brave and not patient.
Everyone who is either funny or not wise is either strong or quiet and vice versa.
If alice is both not happy and quiet then someone is either not quiet or funny.
If mary is either not strong or not wise then someone is patient.
If someone is both not patient and wise then someone is either quiet or strong and vice versa.
Someone is not wise.
Someone is not wise or creative.
Someone is both tall and not brave.
Mary is both happy and rich.
Fred is happy or old.
John is both not tall and brave. | Alice is generous. | entailment | (![X]:((~happy(X)|wise(X))=>~happy(X)))&
(((quiet(mary)<~>~funny(mary)))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
((?[X]:((curious(X)|kind(X))))=>(?[X]:((strong(X)<~>~brave(X)))))&
((?[X]:((~wise(X)&~patient(X))))<=>(?[X]:((~strong(X)|~funny(X)))))&
(![X]:((~quiet(X)<~>strong(X))<=>old(X)))&
(![X]:((funny(X)&~happy(X))=>~creative(X)))&
(![X]:((patient(X)|tall(X))=>(~rich(X)|kind(X))))&
(((tall(lucy)&~old(lucy)))=>((~creative(fred)&brave(fred))))&
(![X]:((calm(X)|~generous(X))=>(generous(X)&happy(X))))&
(![X]:((calm(X)&old(X))=>~patient(X)))&
(![X]:((happy(X)<~>brave(X))<=>(happy(X)&~calm(X))))&
(((quiet(john)|rich(john)))=>((brave(susan)&~patient(susan))))&
(![X]:((funny(X)<~>~wise(X))<=>(strong(X)<~>quiet(X))))&
(((~happy(alice)&quiet(alice)))=>(?[X]:((~quiet(X)<~>funny(X)))))&
(((~strong(mary)<~>~wise(mary)))=>(?[X]:(patient(X))))&
((?[X]:((~patient(X)&wise(X))))<=>(?[X]:((quiet(X)<~>strong(X)))))&
(?[X]:(~wise(X)))&
(?[X]:((~wise(X)|creative(X))))&
(?[X]:((tall(X)&~brave(X))))&
((happy(mary)&rich(mary)))&
((happy(fred)|old(fred)))&
((~tall(john)&brave(john))) | generous(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7348327462149438051425329
% SZS output start Proof for 7348327462149438051425329
9. ! [X0] : ((~generous(X0) | calm(X0)) => (happy(X0) & generous(X0))) [input p8]
23. ~generous(alice) [input hypothesis]
37. ! [X0] : ((happy(X0) & generous(X0)) | (generous(X0) & ~calm(X0))) [ennf transformation 9]
100. generous(X0) | generous(X0) [cnf transformation 37]
141. ~generous(alice) [cnf transformation 23]
144. generous(X0) [duplicate literal removal 100]
328. $false [subsumption resolution 141,144]
% SZS output end Proof for 7348327462149438051425329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either funny or not strong then lucy is not brave or brave. If fred is not strong or creative then john is either not quiet or kind. Everyone who is brave or tall is tall. Everyone who is both not tall and not patient is either tall or happy. Everyone who is not brave is either old or rich and vice versa. If john is both generous and humble then someone is either not tall or kind. Everyone who is both tall and not generous is not old or not rich and vice versa. Everyone who is not funny or not tall is not patient or not curious. Everyone who is happy is rich or not rich and vice versa. If someone is not rich then alice is not brave or strong and vice versa. Everyone who is not brave is both not funny and not quiet. Everyone who is kind or not humble is either happy or not creative and vice versa. If lucy is not strong then fred is either not curious or not creative and vice versa. If mary is quiet or funny then someone is kind and vice versa. If john is tall then lucy is both not calm and tall. If someone is either humble or not funny then john is both not tall and rich. Someone is either not humble or not curious. Alice is both not creative and not brave. Someone is quiet or brave. John is either not rich or not patient. Someone is not strong or patient. Someone is happy. Someone is both not humble and tall. Someone is not curious. | Fred is kind. | neutral | (((funny(alice)<~>~strong(alice)))=>((~brave(lucy)|brave(lucy))))&
(((~strong(fred)|creative(fred)))=>((~quiet(john)<~>kind(john))))&
(![X]:((brave(X)|tall(X))=>tall(X)))&
(![X]:((~tall(X)&~patient(X))=>(tall(X)<~>happy(X))))&
(![X]:(~brave(X)<=>(old(X)<~>rich(X))))&
(((generous(john)&humble(john)))=>(?[X]:((~tall(X)<~>kind(X)))))&
(![X]:((tall(X)&~generous(X))<=>(~old(X)|~rich(X))))&
(![X]:((~funny(X)|~tall(X))=>(~patient(X)|~curious(X))))&
(![X]:(happy(X)<=>(rich(X)|~rich(X))))&
((?[X]:(~rich(X)))<=>((~brave(alice)|strong(alice))))&
(![X]:(~brave(X)=>(~funny(X)&~quiet(X))))&
(![X]:((kind(X)|~humble(X))<=>(happy(X)<~>~creative(X))))&
((~strong(lucy))<=>((~curious(fred)<~>~creative(fred))))&
(((quiet(mary)|funny(mary)))<=>(?[X]:(kind(X))))&
((tall(john))=>((~calm(lucy)&tall(lucy))))&
((?[X]:((humble(X)<~>~funny(X))))=>((~tall(john)&rich(john))))&
(?[X]:((~humble(X)<~>~curious(X))))&
((~creative(alice)&~brave(alice)))&
(?[X]:((quiet(X)|brave(X))))&
((~rich(john)<~>~patient(john)))&
(?[X]:((~strong(X)|patient(X))))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)&tall(X))))&
(?[X]:(~curious(X))) | kind(fred) | [] | null | 0 |
Everyone who is not humble or not tall is not calm or humble and vice versa. If susan is both not generous and kind then fred is either not brave or not kind. Everyone who is both not old and tall is creative or old and vice versa. Everyone who is both not humble and not patient is not brave or patient and vice versa. Everyone who is not creative or wise is not curious or humble. Everyone who is tall or not tall is either not brave or old. If mary is either quiet or humble then john is not tall. If susan is both curious and strong then someone is either kind or not creative and vice versa. If susan is patient then mary is both not wise and not funny. If someone is either brave or not patient then someone is not wise or humble. Everyone who is both patient and wise is strong and vice versa. If mary is either calm or funny then someone is either brave or not humble and vice versa. Everyone who is both patient and not quiet is both funny and calm. Everyone who is either old or curious is either not quiet or calm. Everyone who is quiet is either brave or creative and vice versa. John is not kind or curious. Someone is happy or not old. Fred is either generous or not creative. Mary is not tall or not rich. | Fred is creative. | neutral | (![X]:((~humble(X)|~tall(X))<=>(~calm(X)|humble(X))))&
(((~generous(susan)&kind(susan)))=>((~brave(fred)<~>~kind(fred))))&
(![X]:((~old(X)&tall(X))<=>(creative(X)|old(X))))&
(![X]:((~humble(X)&~patient(X))<=>(~brave(X)|patient(X))))&
(![X]:((~creative(X)|wise(X))=>(~curious(X)|humble(X))))&
(![X]:((tall(X)|~tall(X))=>(~brave(X)<~>old(X))))&
(((quiet(mary)<~>humble(mary)))=>(~tall(john)))&
(((curious(susan)&strong(susan)))<=>(?[X]:((kind(X)<~>~creative(X)))))&
((patient(susan))=>((~wise(mary)&~funny(mary))))&
((?[X]:((brave(X)<~>~patient(X))))=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:((patient(X)&wise(X))<=>strong(X)))&
(((calm(mary)<~>funny(mary)))<=>(?[X]:((brave(X)<~>~humble(X)))))&
(![X]:((patient(X)&~quiet(X))=>(funny(X)&calm(X))))&
(![X]:((old(X)<~>curious(X))=>(~quiet(X)<~>calm(X))))&
(![X]:(quiet(X)<=>(brave(X)<~>creative(X))))&
((~kind(john)|curious(john)))&
(?[X]:((happy(X)|~old(X))))&
((generous(fred)<~>~creative(fred)))&
((~tall(mary)|~rich(mary))) | creative(fred) | [] | null | 0 |
If someone is not kind then someone is both rich and not happy. If someone is both generous and curious then someone is rich and vice versa. Everyone who is not kind or not wise is not old or not patient. Everyone who is both kind and humble is generous or happy and vice versa. Everyone who is both rich and funny is not old or wise and vice versa. Everyone who is either wise or not curious is both curious and not brave. Everyone who is both tall and funny is both not patient and not wise. Everyone who is either happy or curious is both brave and not humble and vice versa. Everyone who is old is funny or not kind. If someone is not wise or brave then someone is both not tall and curious. Everyone who is either curious or not curious is wise and vice versa. Everyone who is either creative or strong is quiet or not wise and vice versa. If mary is not humble or patient then lucy is funny or generous. If alice is quiet then someone is kind. If alice is either not kind or patient then mary is not tall. Everyone who is both old and quiet is either brave or rich and vice versa. Someone is both not brave and calm. Someone is not curious or not old. Someone is brave or creative. John is rich or not happy. Alice is not humble or not kind. Alice is either not brave or old. Alice is both creative and not happy. | Alice is not tall. | entailment | ((?[X]:(~kind(X)))=>(?[X]:((rich(X)&~happy(X)))))&
((?[X]:((generous(X)&curious(X))))<=>(?[X]:(rich(X))))&
(![X]:((~kind(X)|~wise(X))=>(~old(X)|~patient(X))))&
(![X]:((kind(X)&humble(X))<=>(generous(X)|happy(X))))&
(![X]:((rich(X)&funny(X))<=>(~old(X)|wise(X))))&
(![X]:((wise(X)<~>~curious(X))=>(curious(X)&~brave(X))))&
(![X]:((tall(X)&funny(X))=>(~patient(X)&~wise(X))))&
(![X]:((happy(X)<~>curious(X))<=>(brave(X)&~humble(X))))&
(![X]:(old(X)=>(funny(X)|~kind(X))))&
((?[X]:((~wise(X)|brave(X))))=>(?[X]:((~tall(X)&curious(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>wise(X)))&
(![X]:((creative(X)<~>strong(X))<=>(quiet(X)|~wise(X))))&
(((~humble(mary)|patient(mary)))=>((funny(lucy)|generous(lucy))))&
((quiet(alice))=>(?[X]:(kind(X))))&
(((~kind(alice)<~>patient(alice)))=>(~tall(mary)))&
(![X]:((old(X)&quiet(X))<=>(brave(X)<~>rich(X))))&
(?[X]:((~brave(X)&calm(X))))&
(?[X]:((~curious(X)|~old(X))))&
(?[X]:((brave(X)|creative(X))))&
((rich(john)|~happy(john)))&
((~humble(alice)|~kind(alice)))&
((~brave(alice)<~>old(alice)))&
((creative(alice)&~happy(alice))) | ~tall(alice) | [
"p4",
"p5",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2844051144803325072840355
% SZS output start Proof for 2844051144803325072840355
5. ! [X0] : ((funny(X0) & rich(X0)) <=> (wise(X0) | ~old(X0))) [input p4]
6. ! [X0] : ((wise(X0) <~> ~curious(X0)) => (~brave(X0) & curious(X0))) [input p5]
7. ! [X0] : ((funny(X0) & tall(X0)) => (~wise(X0) & ~patient(X0))) [input p6]
11. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> wise(X0)) [input p10]
24. tall(alice) [input hypothesis]
32. ! [X0] : ((~brave(X0) & curious(X0)) | (wise(X0) <=> ~curious(X0))) [ennf transformation 6]
33. ! [X0] : ((~wise(X0) & ~patient(X0)) | (~funny(X0) | ~tall(X0))) [ennf transformation 7]
34. ! [X0] : ((~wise(X0) & ~patient(X0)) | ~funny(X0) | ~tall(X0)) [flattening 33]
52. ! [X0] : (((funny(X0) & rich(X0)) | (~wise(X0) & old(X0))) & ((wise(X0) | ~old(X0)) | (~funny(X0) | ~rich(X0)))) [nnf transformation 5]
53. ! [X0] : (((funny(X0) & rich(X0)) | (~wise(X0) & old(X0))) & (wise(X0) | ~old(X0) | ~funny(X0) | ~rich(X0))) [flattening 52]
54. ! [X0] : ((~brave(X0) & curious(X0)) | ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0)))) [nnf transformation 32]
60. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ~wise(X0)) & (wise(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 11]
91. ~wise(X0) | funny(X0) [cnf transformation 53]
93. curious(X0) | wise(X0) | curious(X0) [cnf transformation 54]
97. ~wise(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 34]
109. wise(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 60]
139. tall(alice) [cnf transformation 24]
140. wise(X0) | ~curious(X0) [duplicate literal removal 109]
142. wise(X0) | curious(X0) [duplicate literal removal 93]
177. ~tall(X0) | ~wise(X0) [subsumption resolution 97,91]
190. 11 <=> ! [X1] : wise(X1) [avatar definition]
191. wise(X1) <- (11) [avatar component clause 190]
199. wise(X0) [subsumption resolution 140,142]
200. 11 [avatar split clause 199,190]
298. ~wise(alice) [resolution 177,139]
299. $false <- (11) [subsumption resolution 298,191]
300. ~11 [avatar contradiction clause 299]
301. $false [avatar sat refutation 200,300]
% SZS output end Proof for 2844051144803325072840355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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