premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If mary is not humble or not creative then lucy is either not generous or kind and vice versa.
If someone is rich or not happy then someone is not wise and vice versa.
Everyone who is both rich and calm is either curious or strong.
If mary is curious or kind then paul is not patient.
Everyone who is not strong or patient is not generous and vice versa.
If lucy is wise or funny then someone is both happy and old and vice versa.
Everyone who is either not humble or not funny is not tall.
Everyone who is generous or old is both not curious and tall.
If someone is both not creative and not humble then susan is either not kind or generous and vice versa.
Everyone who is either creative or not wise is not calm or not brave and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Everyone who is not strong is both not brave and funny and vice versa.
Everyone who is calm or quiet is both not funny and wise and vice versa.
Everyone who is not generous is both humble and curious and vice versa.
If someone is not curious or not generous then fred is both creative and old and vice versa.
Someone is either funny or not calm.
Lucy is not wise or calm.
Susan is rich.
Susan is not calm.
Someone is both humble and rich.
Someone is generous or wise.
Paul is not strong or not generous.
Alice is not generous. | Alice is not old. | entailment | (((~humble(mary)|~creative(mary)))<=>((~generous(lucy)<~>kind(lucy))))&
((?[X]:((rich(X)|~happy(X))))<=>(?[X]:(~wise(X))))&
(![X]:((rich(X)&calm(X))=>(curious(X)<~>strong(X))))&
(((curious(mary)|kind(mary)))=>(~patient(paul)))&
(![X]:((~strong(X)|patient(X))<=>~generous(X)))&
(((wise(lucy)|funny(lucy)))<=>(?[X]:((happy(X)&old(X)))))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((creative(fred)&old(fred))))&
(?[X]:((funny(X)<~>~calm(X))))&
((~wise(lucy)|calm(lucy)))&
(rich(susan))&
(~calm(susan))&
(?[X]:((humble(X)&rich(X))))&
(?[X]:((generous(X)|wise(X))))&
((~strong(paul)|~generous(paul)))&
(~generous(alice)) | ~old(alice) | [
"p7",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7911729117087459220390969
% SZS output start Proof for 7911729117087459220390969
8. ! [X0] : ((old(X0) | generous(X0)) => (tall(X0) & ~curious(X0))) [input p7]
15. ! [X0] : (~generous(X0) <=> (curious(X0) & humble(X0))) [input p14]
24. ~generous(alice) [input p23]
25. old(alice) [input hypothesis]
31. ! [X0] : ((tall(X0) & ~curious(X0)) | (~old(X0) & ~generous(X0))) [ennf transformation 8]
62. ! [X0] : ((~generous(X0) | (~curious(X0) | ~humble(X0))) & ((curious(X0) & humble(X0)) | generous(X0))) [nnf transformation 15]
63. ! [X0] : ((~generous(X0) | ~curious(X0) | ~humble(X0)) & ((curious(X0) & humble(X0)) | generous(X0))) [flattening 62]
100. ~old(X0) | ~curious(X0) [cnf transformation 31]
129. curious(X0) | generous(X0) [cnf transformation 63]
145. ~generous(alice) [cnf transformation 24]
146. old(alice) [cnf transformation 25]
325. ~curious(alice) [resolution 100,146]
340. generous(alice) [resolution 129,325]
342. $false [subsumption resolution 340,145]
% SZS output end Proof for 7911729117087459220390969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and humble then john is both not wise and not old.
If lucy is old then someone is either curious or not quiet.
Everyone who is not generous is either strong or generous.
If lucy is not brave then someone is not humble and vice versa.
Everyone who is either brave or not calm is not kind or calm and vice versa.
Everyone who is humble or curious is humble or wise and vice versa.
If fred is both quiet and not rich then someone is wise or not humble.
Everyone who is either not patient or not creative is either rich or patient and vice versa.
If someone is either generous or brave then someone is funny or not generous and vice versa.
If paul is either patient or humble then someone is both kind and not patient and vice versa.
If susan is not curious or wise then someone is both wise and not curious and vice versa.
Everyone who is either rich or brave is not happy.
Everyone who is tall or not humble is not generous or quiet and vice versa.
Everyone who is rich or brave is either not wise or not old.
Everyone who is not quiet is curious and vice versa.
If paul is either not happy or strong then someone is either not kind or not patient.
Someone is both tall and curious.
John is both happy and wise.
Fred is not creative or wise.
Someone is creative.
Someone is not old.
Someone is either not funny or not generous.
Someone is creative or not strong.
Paul is funny or not quiet. | Lucy is kind. | contradiction | ((?[X]:((~generous(X)&humble(X))))=>((~wise(john)&~old(john))))&
((old(lucy))=>(?[X]:((curious(X)<~>~quiet(X)))))&
(![X]:(~generous(X)=>(strong(X)<~>generous(X))))&
((~brave(lucy))<=>(?[X]:(~humble(X))))&
(![X]:((brave(X)<~>~calm(X))<=>(~kind(X)|calm(X))))&
(![X]:((humble(X)|curious(X))<=>(humble(X)|wise(X))))&
(((quiet(fred)&~rich(fred)))=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:((~patient(X)<~>~creative(X))<=>(rich(X)<~>patient(X))))&
((?[X]:((generous(X)<~>brave(X))))<=>(?[X]:((funny(X)|~generous(X)))))&
(((patient(paul)<~>humble(paul)))<=>(?[X]:((kind(X)&~patient(X)))))&
(((~curious(susan)|wise(susan)))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:((rich(X)<~>brave(X))=>~happy(X)))&
(![X]:((tall(X)|~humble(X))<=>(~generous(X)|quiet(X))))&
(![X]:((rich(X)|brave(X))=>(~wise(X)<~>~old(X))))&
(![X]:(~quiet(X)<=>curious(X)))&
(((~happy(paul)<~>strong(paul)))=>(?[X]:((~kind(X)<~>~patient(X)))))&
(?[X]:((tall(X)&curious(X))))&
((happy(john)&wise(john)))&
((~creative(fred)|wise(fred)))&
(?[X]:(creative(X)))&
(?[X]:(~old(X)))&
(?[X]:((~funny(X)<~>~generous(X))))&
(?[X]:((creative(X)|~strong(X))))&
((funny(paul)|~quiet(paul))) | kind(lucy) | [
"p0",
"p3",
"p4",
"p12",
"p14",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7727402524774357469476720
% SZS output start Proof for 7727402524774357469476720
1. ? [X0] : (humble(X0) & ~generous(X0)) => (~old(john) & ~wise(john)) [input p0]
4. ~brave(lucy) <=> ? [X0] : ~humble(X0) [input p3]
5. ! [X0] : ((brave(X0) <~> ~calm(X0)) <=> (calm(X0) | ~kind(X0))) [input p4]
13. ! [X0] : ((~humble(X0) | tall(X0)) <=> (quiet(X0) | ~generous(X0))) [input p12]
15. ! [X0] : (~quiet(X0) <=> curious(X0)) [input p14]
17. ? [X0] : (curious(X0) & tall(X0)) [input p16]
18. wise(john) & happy(john) [input p17]
25. kind(lucy) [input hypothesis]
27. (~old(john) & ~wise(john)) | ! [X0] : (~humble(X0) | generous(X0)) [ennf transformation 1]
39. (~brave(lucy) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | brave(lucy)) [nnf transformation 4]
40. (~brave(lucy) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | brave(lucy)) [rectify 39]
41. ? [X1] : ~humble(X1) => ~humble(sK1) [choice axiom]
42. (~brave(lucy) | ! [X0] : humble(X0)) & (~humble(sK1) | brave(lucy)) [skolemisation 40,41]
43. ! [X0] : ((((calm(X0) | ~brave(X0)) & (~calm(X0) | brave(X0))) | (~calm(X0) & kind(X0))) & ((calm(X0) | ~kind(X0)) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0))))) [nnf transformation 5]
44. ! [X0] : ((((calm(X0) | ~brave(X0)) & (~calm(X0) | brave(X0))) | (~calm(X0) & kind(X0))) & (calm(X0) | ~kind(X0) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0))))) [flattening 43]
65. ! [X0] : (((~humble(X0) | tall(X0)) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | (humble(X0) & ~tall(X0)))) [nnf transformation 13]
66. ! [X0] : ((~humble(X0) | tall(X0) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | (humble(X0) & ~tall(X0)))) [flattening 65]
68. ! [X0] : ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))) [nnf transformation 15]
72. ? [X0] : (curious(X0) & tall(X0)) => (curious(sK8) & tall(sK8)) [choice axiom]
73. curious(sK8) & tall(sK8) [skolemisation 17,72]
83. ~wise(john) | ~humble(X0) | generous(X0) [cnf transformation 27]
90. ~brave(lucy) | humble(X0) [cnf transformation 42]
92. calm(X0) | ~kind(X0) | brave(X0) | calm(X0) [cnf transformation 44]
94. ~calm(X0) | brave(X0) | ~calm(X0) [cnf transformation 44]
129. ~tall(X0) | ~generous(X0) | quiet(X0) [cnf transformation 66]
138. ~quiet(X0) | ~curious(X0) [cnf transformation 68]
143. tall(sK8) [cnf transformation 73]
144. curious(sK8) [cnf transformation 73]
146. wise(john) [cnf transformation 18]
154. kind(lucy) [cnf transformation 25]
159. calm(X0) | ~kind(X0) | brave(X0) [duplicate literal removal 92]
160. ~calm(X0) | brave(X0) [duplicate literal removal 94]
163. 1 <=> ! [X0] : (~humble(X0) | generous(X0)) [avatar definition]
164. ~humble(X0) | generous(X0) <- (1) [avatar component clause 163]
171. 3 <=> wise(john) [avatar definition]
174. 1 | ~3 [avatar split clause 83,171,163]
190. 7 <=> ! [X0] : humble(X0) [avatar definition]
191. humble(X0) <- (7) [avatar component clause 190]
193. 8 <=> brave(lucy) [avatar definition]
196. 7 | ~8 [avatar split clause 90,193,190]
202. ~kind(X0) | brave(X0) [subsumption resolution 159,160]
223. 14 <=> ! [X1] : generous(X1) [avatar definition]
224. generous(X1) <- (14) [avatar component clause 223]
325. 3 [avatar split clause 146,171]
367. brave(lucy) [resolution 202,154]
370. 8 [avatar split clause 367,193]
373. generous(X0) <- (1, 7) [resolution 191,164]
376. 14 | ~1 | ~7 [avatar split clause 373,190,163,223]
405. ~generous(sK8) | quiet(sK8) [resolution 129,143]
406. quiet(sK8) <- (14) [subsumption resolution 405,224]
410. ~curious(sK8) <- (14) [resolution 406,138]
411. $false <- (14) [subsumption resolution 410,144]
412. ~14 [avatar contradiction clause 411]
413. $false [avatar sat refutation 174,196,325,370,376,412]
% SZS output end Proof for 7727402524774357469476720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious then mary is not generous and vice versa.
Everyone who is not rich or not patient is generous.
If someone is creative or not happy then someone is either not wise or curious and vice versa.
If someone is not calm or not curious then someone is not tall or wise and vice versa.
If susan is old then alice is tall or not humble and vice versa.
If someone is either strong or not happy then someone is both not strong and not old.
Everyone who is tall is not humble and vice versa.
If john is either patient or not tall then someone is both kind and strong.
Everyone who is either not brave or generous is not funny and vice versa.
If someone is both not rich and humble then someone is both not wise and not humble.
Everyone who is not wise or curious is quiet.
If john is both happy and calm then someone is kind or not rich and vice versa.
Everyone who is patient is either strong or humble.
If someone is either creative or not old then someone is happy.
Everyone who is quiet or not curious is both not calm and not brave.
Everyone who is both not brave and not calm is not kind or wise and vice versa.
Someone is not generous.
Alice is tall or wise.
Someone is not generous or old.
Someone is not happy.
Someone is either humble or not curious.
Lucy is strong or not calm. | John is calm. | contradiction | ((?[X]:(~curious(X)))<=>(~generous(mary)))&
(![X]:((~rich(X)|~patient(X))=>generous(X)))&
((?[X]:((creative(X)|~happy(X))))<=>(?[X]:((~wise(X)<~>curious(X)))))&
((?[X]:((~calm(X)|~curious(X))))<=>(?[X]:((~tall(X)|wise(X)))))&
((old(susan))<=>((tall(alice)|~humble(alice))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:(tall(X)<=>~humble(X)))&
(((patient(john)<~>~tall(john)))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:((~brave(X)<~>generous(X))<=>~funny(X)))&
((?[X]:((~rich(X)&humble(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~wise(X)|curious(X))=>quiet(X)))&
(((happy(john)&calm(john)))<=>(?[X]:((kind(X)|~rich(X)))))&
(![X]:(patient(X)=>(strong(X)<~>humble(X))))&
((?[X]:((creative(X)<~>~old(X))))=>(?[X]:(happy(X))))&
(![X]:((quiet(X)|~curious(X))=>(~calm(X)&~brave(X))))&
(![X]:((~brave(X)&~calm(X))<=>(~kind(X)|wise(X))))&
(?[X]:(~generous(X)))&
((tall(alice)|wise(alice)))&
(?[X]:((~generous(X)|old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)<~>~curious(X))))&
((strong(lucy)|~calm(lucy))) | calm(john) | [
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8629456656865050153915229
% SZS output start Proof for 8629456656865050153915229
11. ! [X0] : ((curious(X0) | ~wise(X0)) => quiet(X0)) [input p10]
15. ! [X0] : ((~curious(X0) | quiet(X0)) => (~brave(X0) & ~calm(X0))) [input p14]
16. ! [X0] : ((~calm(X0) & ~brave(X0)) <=> (wise(X0) | ~kind(X0))) [input p15]
23. calm(john) [input hypothesis]
33. ! [X0] : (quiet(X0) | (~curious(X0) & wise(X0))) [ennf transformation 11]
36. ! [X0] : ((~brave(X0) & ~calm(X0)) | (curious(X0) & ~quiet(X0))) [ennf transformation 15]
74. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~wise(X0) & kind(X0))) & ((wise(X0) | ~kind(X0)) | (calm(X0) | brave(X0)))) [nnf transformation 16]
75. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~wise(X0) & kind(X0))) & (wise(X0) | ~kind(X0) | calm(X0) | brave(X0))) [flattening 74]
114. quiet(X0) | wise(X0) [cnf transformation 33]
125. ~quiet(X0) | ~calm(X0) [cnf transformation 36]
133. ~calm(X0) | ~wise(X0) [cnf transformation 75]
141. calm(john) [cnf transformation 23]
288. 34 <=> calm(john) [avatar definition]
290. calm(john) <- (34) [avatar component clause 288]
356. 34 [avatar split clause 141,288]
361. ~calm(X0) | wise(X0) [resolution 125,114]
362. ~calm(X0) [subsumption resolution 361,133]
363. $false <- (34) [resolution 362,290]
364. ~34 [avatar contradiction clause 363]
365. $false [avatar sat refutation 356,364]
% SZS output end Proof for 8629456656865050153915229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not wise and wise is both not old and brave and vice versa.
If someone is not wise then lucy is either wise or not kind and vice versa.
Everyone who is generous is not patient.
If someone is both humble and tall then mary is either not quiet or wise.
If paul is both not curious and not patient then lucy is old or not humble and vice versa.
Everyone who is both not humble and humble is either strong or not quiet and vice versa.
Everyone who is either calm or not quiet is both wise and curious and vice versa.
Everyone who is not old or happy is both generous and not quiet and vice versa.
If mary is strong or curious then someone is not rich or kind.
If someone is both generous and strong then fred is calm or brave and vice versa.
If someone is either tall or not happy then someone is both strong and brave and vice versa.
If someone is not strong or tall then someone is old.
Everyone who is both not rich and not strong is either happy or wise.
Everyone who is strong or not wise is both not generous and tall and vice versa.
Everyone who is not calm is either not calm or not rich and vice versa.
Everyone who is both quiet and not brave is happy.
Lucy is wise.
Someone is wise.
Someone is either funny or not humble.
Fred is not curious or not brave.
Someone is kind.
Someone is not funny or brave.
Someone is both not creative and wise.
Someone is either not calm or kind. | Fred is strong. | entailment | (![X]:((~wise(X)&wise(X))<=>(~old(X)&brave(X))))&
((?[X]:(~wise(X)))<=>((wise(lucy)<~>~kind(lucy))))&
(![X]:(generous(X)=>~patient(X)))&
((?[X]:((humble(X)&tall(X))))=>((~quiet(mary)<~>wise(mary))))&
(((~curious(paul)&~patient(paul)))<=>((old(lucy)|~humble(lucy))))&
(![X]:((~humble(X)&humble(X))<=>(strong(X)<~>~quiet(X))))&
(![X]:((calm(X)<~>~quiet(X))<=>(wise(X)&curious(X))))&
(![X]:((~old(X)|happy(X))<=>(generous(X)&~quiet(X))))&
(((strong(mary)|curious(mary)))=>(?[X]:((~rich(X)|kind(X)))))&
((?[X]:((generous(X)&strong(X))))<=>((calm(fred)|brave(fred))))&
((?[X]:((tall(X)<~>~happy(X))))<=>(?[X]:((strong(X)&brave(X)))))&
((?[X]:((~strong(X)|tall(X))))=>(?[X]:(old(X))))&
(![X]:((~rich(X)&~strong(X))=>(happy(X)<~>wise(X))))&
(![X]:((strong(X)|~wise(X))<=>(~generous(X)&tall(X))))&
(![X]:(~calm(X)<=>(~calm(X)<~>~rich(X))))&
(![X]:((quiet(X)&~brave(X))=>happy(X)))&
(wise(lucy))&
(?[X]:(wise(X)))&
(?[X]:((funny(X)<~>~humble(X))))&
((~curious(fred)|~brave(fred)))&
(?[X]:(kind(X)))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((~creative(X)&wise(X))))&
(?[X]:((~calm(X)<~>kind(X)))) | strong(fred) | [
"p5",
"p7",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7647090829932013294974787
% SZS output start Proof for 7647090829932013294974787
6. ! [X0] : ((humble(X0) & ~humble(X0)) <=> (strong(X0) <~> ~quiet(X0))) [input p5]
8. ! [X0] : ((happy(X0) | ~old(X0)) <=> (~quiet(X0) & generous(X0))) [input p7]
10. ? [X0] : (strong(X0) & generous(X0)) <=> (brave(fred) | calm(fred)) [input p9]
14. ! [X0] : ((~wise(X0) | strong(X0)) <=> (tall(X0) & ~generous(X0))) [input p13]
16. ! [X0] : ((~brave(X0) & quiet(X0)) => happy(X0)) [input p15]
25. ~strong(fred) [input hypothesis]
35. ! [X0] : (happy(X0) | (brave(X0) | ~quiet(X0))) [ennf transformation 16]
36. ! [X0] : (happy(X0) | brave(X0) | ~quiet(X0)) [flattening 35]
46. ! [X0] : (((humble(X0) & ~humble(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (~humble(X0) | humble(X0)))) [nnf transformation 6]
47. ! [X0] : (((humble(X0) & ~humble(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | ~humble(X0) | humble(X0))) [flattening 46]
50. ! [X0] : (((happy(X0) | ~old(X0)) | (quiet(X0) | ~generous(X0))) & ((~quiet(X0) & generous(X0)) | (~happy(X0) & old(X0)))) [nnf transformation 8]
51. ! [X0] : ((happy(X0) | ~old(X0) | quiet(X0) | ~generous(X0)) & ((~quiet(X0) & generous(X0)) | (~happy(X0) & old(X0)))) [flattening 50]
54. (? [X0] : (strong(X0) & generous(X0)) | (~brave(fred) & ~calm(fred))) & ((brave(fred) | calm(fred)) | ! [X0] : (~strong(X0) | ~generous(X0))) [nnf transformation 10]
55. (? [X0] : (strong(X0) & generous(X0)) | (~brave(fred) & ~calm(fred))) & (brave(fred) | calm(fred) | ! [X0] : (~strong(X0) | ~generous(X0))) [flattening 54]
56. (? [X0] : (strong(X0) & generous(X0)) | (~brave(fred) & ~calm(fred))) & (brave(fred) | calm(fred) | ! [X1] : (~strong(X1) | ~generous(X1))) [rectify 55]
57. ? [X0] : (strong(X0) & generous(X0)) => (strong(sK2) & generous(sK2)) [choice axiom]
58. ((strong(sK2) & generous(sK2)) | (~brave(fred) & ~calm(fred))) & (brave(fred) | calm(fred) | ! [X1] : (~strong(X1) | ~generous(X1))) [skolemisation 56,57]
68. ! [X0] : (((~wise(X0) | strong(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (wise(X0) & ~strong(X0)))) [nnf transformation 14]
69. ! [X0] : ((~wise(X0) | strong(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (wise(X0) & ~strong(X0)))) [flattening 68]
104. ~humble(X0) | strong(X0) | quiet(X0) [cnf transformation 47]
106. humble(X0) | strong(X0) | quiet(X0) [cnf transformation 47]
116. ~happy(X0) | ~quiet(X0) [cnf transformation 51]
122. generous(sK2) | ~brave(fred) [cnf transformation 58]
124. strong(sK2) | ~brave(fred) [cnf transformation 58]
135. ~generous(X0) | ~strong(X0) [cnf transformation 69]
144. happy(X0) | brave(X0) | ~quiet(X0) [cnf transformation 36]
155. ~strong(fred) [cnf transformation 25]
212. strong(X0) | quiet(X0) [subsumption resolution 104,106]
233. 16 <=> brave(fred) [avatar definition]
237. 17 <=> strong(sK2) [avatar definition]
239. strong(sK2) <- (17) [avatar component clause 237]
240. ~16 | 17 [avatar split clause 124,237,233]
247. 19 <=> generous(sK2) [avatar definition]
249. generous(sK2) <- (19) [avatar component clause 247]
250. ~16 | 19 [avatar split clause 122,247,233]
253. 20 <=> ! [X1] : (~strong(X1) | ~generous(X1)) [avatar definition]
254. ~strong(X1) | ~generous(X1) <- (20) [avatar component clause 253]
299. 20 [avatar split clause 135,253]
301. ~quiet(X0) | brave(X0) [subsumption resolution 144,116]
344. quiet(fred) [resolution 212,155]
364. brave(fred) [resolution 301,344]
367. 16 [avatar split clause 364,233]
370. ~generous(sK2) <- (17, 20) [resolution 239,254]
373. $false <- (17, 19, 20) [subsumption resolution 370,249]
374. ~17 | ~19 | ~20 [avatar contradiction clause 373]
375. $false [avatar sat refutation 240,250,299,367,374]
% SZS output end Proof for 7647090829932013294974787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or rich is either strong or tall.
If someone is both patient and not kind then someone is both not generous and not creative and vice versa.
Everyone who is quiet is both not calm and not humble.
Everyone who is funny or not happy is generous or brave and vice versa.
If someone is both patient and generous then alice is either patient or not rich and vice versa.
Everyone who is not generous or generous is either curious or not quiet and vice versa.
Everyone who is tall or not generous is either not generous or not wise and vice versa.
Everyone who is either not funny or not calm is either rich or not old and vice versa.
If someone is old or not funny then someone is kind or not happy.
Everyone who is patient is rich.
If susan is creative or humble then someone is tall and vice versa.
Everyone who is tall or funny is not tall.
If john is either humble or quiet then alice is strong and vice versa.
If someone is not strong or not patient then susan is old and vice versa.
Everyone who is either humble or curious is tall.
If someone is tall then someone is both calm and brave and vice versa.
Lucy is either tall or rich.
Someone is either kind or not generous.
Paul is strong or not kind.
Mary is both not brave and strong.
Susan is not happy or tall.
Fred is not creative.
Mary is either not tall or tall. | Paul is quiet. | contradiction | (![X]:((~funny(X)|rich(X))=>(strong(X)<~>tall(X))))&
((?[X]:((patient(X)&~kind(X))))<=>(?[X]:((~generous(X)&~creative(X)))))&
(![X]:(quiet(X)=>(~calm(X)&~humble(X))))&
(![X]:((funny(X)|~happy(X))<=>(generous(X)|brave(X))))&
((?[X]:((patient(X)&generous(X))))<=>((patient(alice)<~>~rich(alice))))&
(![X]:((~generous(X)|generous(X))<=>(curious(X)<~>~quiet(X))))&
(![X]:((tall(X)|~generous(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((~funny(X)<~>~calm(X))<=>(rich(X)<~>~old(X))))&
((?[X]:((old(X)|~funny(X))))=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:(patient(X)=>rich(X)))&
(((creative(susan)|humble(susan)))<=>(?[X]:(tall(X))))&
(![X]:((tall(X)|funny(X))=>~tall(X)))&
(((humble(john)<~>quiet(john)))<=>(strong(alice)))&
((?[X]:((~strong(X)|~patient(X))))<=>(old(susan)))&
(![X]:((humble(X)<~>curious(X))=>tall(X)))&
((?[X]:(tall(X)))<=>(?[X]:((calm(X)&brave(X)))))&
((tall(lucy)<~>rich(lucy)))&
(?[X]:((kind(X)<~>~generous(X))))&
((strong(paul)|~kind(paul)))&
((~brave(mary)&strong(mary)))&
((~happy(susan)|tall(susan)))&
(~creative(fred))&
((~tall(mary)<~>tall(mary))) | quiet(paul) | [
"p2",
"p5",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7546767851475573598424956
% SZS output start Proof for 7546767851475573598424956
3. ! [X0] : (quiet(X0) => (~humble(X0) & ~calm(X0))) [input p2]
6. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (curious(X0) <~> ~quiet(X0))) [input p5]
12. ! [X0] : ((funny(X0) | tall(X0)) => ~tall(X0)) [input p11]
15. ! [X0] : ((humble(X0) <~> curious(X0)) => tall(X0)) [input p14]
24. quiet(paul) [input hypothesis]
29. ! [X0] : ((~humble(X0) & ~calm(X0)) | ~quiet(X0)) [ennf transformation 3]
32. ! [X0] : (~tall(X0) | (~funny(X0) & ~tall(X0))) [ennf transformation 12]
33. ! [X0] : (tall(X0) | (humble(X0) <=> curious(X0))) [ennf transformation 15]
46. ! [X0] : (((generous(X0) | ~generous(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (~generous(X0) & generous(X0)))) [nnf transformation 6]
47. ! [X0] : ((generous(X0) | ~generous(X0) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (~generous(X0) & generous(X0)))) [flattening 46]
64. ! [X0] : (tall(X0) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0)))) [nnf transformation 33]
84. ~humble(X0) | ~quiet(X0) [cnf transformation 29]
95. ~quiet(X0) | curious(X0) | generous(X0) [cnf transformation 47]
96. ~quiet(X0) | curious(X0) | ~generous(X0) [cnf transformation 47]
121. ~tall(X0) | ~tall(X0) [cnf transformation 32]
131. ~curious(X0) | humble(X0) | tall(X0) [cnf transformation 64]
146. quiet(paul) [cnf transformation 24]
147. ~tall(X0) [duplicate literal removal 121]
202. ~quiet(X0) | curious(X0) [subsumption resolution 95,96]
220. 16 <=> ! [X0] : ~tall(X0) [avatar definition]
221. ~tall(X0) <- (16) [avatar component clause 220]
237. 16 [avatar split clause 147,220]
336. curious(paul) [resolution 202,146]
383. humble(paul) | tall(paul) [resolution 131,336]
384. humble(paul) <- (16) [subsumption resolution 383,221]
386. ~quiet(paul) <- (16) [resolution 384,84]
387. $false <- (16) [subsumption resolution 386,146]
388. ~16 [avatar contradiction clause 387]
389. $false [avatar sat refutation 237,388]
% SZS output end Proof for 7546767851475573598424956
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and old is strong.
If mary is either tall or calm then someone is either strong or happy.
Everyone who is humble is either wise or rich and vice versa.
If someone is calm or creative then alice is not generous or strong and vice versa.
If lucy is funny then alice is both humble and happy and vice versa.
Everyone who is not tall is calm and vice versa.
If alice is both creative and not generous then someone is both funny and kind and vice versa.
Everyone who is not strong or patient is curious or not happy and vice versa.
Everyone who is both not brave and humble is not quiet.
If lucy is either not rich or old then someone is generous.
Everyone who is not brave or not calm is both not humble and curious and vice versa.
If someone is both tall and curious then fred is both strong and not happy and vice versa.
Everyone who is both calm and not patient is happy or rich and vice versa.
If mary is not humble or humble then lucy is either rich or kind.
If lucy is both patient and old then mary is tall or not rich and vice versa.
Everyone who is both old and generous is kind.
Someone is not funny or strong.
Alice is old or not kind.
Susan is wise.
Paul is not tall or humble.
Susan is not brave.
Mary is both not generous and not brave.
Lucy is patient.
Someone is kind. | Susan is not tall. | entailment | (![X]:((~happy(X)&old(X))=>strong(X)))&
(((tall(mary)<~>calm(mary)))=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:(humble(X)<=>(wise(X)<~>rich(X))))&
((?[X]:((calm(X)|creative(X))))<=>((~generous(alice)|strong(alice))))&
((funny(lucy))<=>((humble(alice)&happy(alice))))&
(![X]:(~tall(X)<=>calm(X)))&
(((creative(alice)&~generous(alice)))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:((~strong(X)|patient(X))<=>(curious(X)|~happy(X))))&
(![X]:((~brave(X)&humble(X))=>~quiet(X)))&
(((~rich(lucy)<~>old(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~humble(X)&curious(X))))&
((?[X]:((tall(X)&curious(X))))<=>((strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~patient(X))<=>(happy(X)|rich(X))))&
(((~humble(mary)|humble(mary)))=>((rich(lucy)<~>kind(lucy))))&
(((patient(lucy)&old(lucy)))<=>((tall(mary)|~rich(mary))))&
(![X]:((old(X)&generous(X))=>kind(X)))&
(?[X]:((~funny(X)|strong(X))))&
((old(alice)|~kind(alice)))&
(wise(susan))&
((~tall(paul)|humble(paul)))&
(~brave(susan))&
((~generous(mary)&~brave(mary)))&
(patient(lucy))&
(?[X]:(kind(X))) | ~tall(susan) | [
"p2",
"p5",
"p10",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8466361812236253379169843
% SZS output start Proof for 8466361812236253379169843
3. ! [X0] : (humble(X0) <=> (wise(X0) <~> rich(X0))) [input p2]
6. ! [X0] : (~tall(X0) <=> calm(X0)) [input p5]
11. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> (curious(X0) & ~humble(X0))) [input p10]
13. ! [X0] : ((~patient(X0) & calm(X0)) <=> (rich(X0) | happy(X0))) [input p12]
19. wise(susan) [input p18]
21. ~brave(susan) [input p20]
25. tall(susan) [input hypothesis]
37. ! [X0] : ((humble(X0) | ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0)))) & (((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | ~humble(X0))) [nnf transformation 3]
45. ! [X0] : ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))) [nnf transformation 6]
56. ! [X0] : (((~calm(X0) | ~brave(X0)) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [nnf transformation 11]
57. ! [X0] : ((~calm(X0) | ~brave(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [flattening 56]
63. ! [X0] : (((~patient(X0) & calm(X0)) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | (patient(X0) | ~calm(X0)))) [nnf transformation 13]
64. ! [X0] : (((~patient(X0) & calm(X0)) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | patient(X0) | ~calm(X0))) [flattening 63]
79. ~wise(X0) | rich(X0) | humble(X0) [cnf transformation 37]
89. ~calm(X0) | ~tall(X0) [cnf transformation 45]
100. ~humble(X0) | brave(X0) [cnf transformation 57]
111. ~rich(X0) | calm(X0) [cnf transformation 64]
126. wise(susan) [cnf transformation 19]
128. ~brave(susan) [cnf transformation 21]
133. tall(susan) [cnf transformation 25]
323. rich(susan) | humble(susan) [resolution 79,126]
325. 36 <=> humble(susan) [avatar definition]
327. humble(susan) <- (36) [avatar component clause 325]
329. 37 <=> rich(susan) [avatar definition]
331. rich(susan) <- (37) [avatar component clause 329]
332. 36 | 37 [avatar split clause 323,329,325]
335. brave(susan) <- (36) [resolution 327,100]
336. $false <- (36) [subsumption resolution 335,128]
337. ~36 [avatar contradiction clause 336]
341. calm(susan) <- (37) [resolution 331,111]
435. ~tall(susan) <- (37) [resolution 341,89]
436. $false <- (37) [subsumption resolution 435,133]
437. ~37 [avatar contradiction clause 436]
438. $false [avatar sat refutation 332,337,437]
% SZS output end Proof for 8466361812236253379169843
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not funny or rich.
Everyone who is not humble or not wise is either patient or not calm.
Everyone who is either not wise or not humble is either not tall or brave and vice versa.
Everyone who is either not kind or not old is not old or not wise.
Everyone who is brave or not strong is tall.
Everyone who is either patient or wise is either not quiet or not curious and vice versa.
If someone is either not brave or not humble then someone is either brave or generous and vice versa.
If alice is not generous then someone is either strong or calm.
Everyone who is both not rich and not happy is not patient or not generous and vice versa.
Everyone who is wise or happy is either not quiet or not brave.
Everyone who is quiet or tall is not calm or not tall and vice versa.
Everyone who is either old or not happy is either humble or wise and vice versa.
Everyone who is both kind and calm is creative or not generous.
Everyone who is strong is not patient and vice versa.
If someone is creative then lucy is either kind or not rich.
Everyone who is both patient and rich is not strong or not humble.
Mary is either not creative or not patient.
Someone is not curious.
Fred is both kind and not curious.
Lucy is either humble or wise.
Someone is not calm.
Someone is humble or not rich.
Lucy is either quiet or patient.
Mary is both curious and brave. | Fred is not rich. | entailment | (![X]:(funny(X)=>(~funny(X)|rich(X))))&
(![X]:((~humble(X)|~wise(X))=>(patient(X)<~>~calm(X))))&
(![X]:((~wise(X)<~>~humble(X))<=>(~tall(X)<~>brave(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~old(X)|~wise(X))))&
(![X]:((brave(X)|~strong(X))=>tall(X)))&
(![X]:((patient(X)<~>wise(X))<=>(~quiet(X)<~>~curious(X))))&
((?[X]:((~brave(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>generous(X)))))&
((~generous(alice))=>(?[X]:((strong(X)<~>calm(X)))))&
(![X]:((~rich(X)&~happy(X))<=>(~patient(X)|~generous(X))))&
(![X]:((wise(X)|happy(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((quiet(X)|tall(X))<=>(~calm(X)|~tall(X))))&
(![X]:((old(X)<~>~happy(X))<=>(humble(X)<~>wise(X))))&
(![X]:((kind(X)&calm(X))=>(creative(X)|~generous(X))))&
(![X]:(strong(X)<=>~patient(X)))&
((?[X]:(creative(X)))=>((kind(lucy)<~>~rich(lucy))))&
(![X]:((patient(X)&rich(X))=>(~strong(X)|~humble(X))))&
((~creative(mary)<~>~patient(mary)))&
(?[X]:(~curious(X)))&
((kind(fred)&~curious(fred)))&
((humble(lucy)<~>wise(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((humble(X)|~rich(X))))&
((quiet(lucy)<~>patient(lucy)))&
((curious(mary)&brave(mary))) | ~rich(fred) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p9",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8088175728428651241988208
% SZS output start Proof for 8088175728428651241988208
2. ! [X0] : ((~wise(X0) | ~humble(X0)) => (patient(X0) <~> ~calm(X0))) [input p1]
3. ! [X0] : ((~wise(X0) <~> ~humble(X0)) <=> (~tall(X0) <~> brave(X0))) [input p2]
5. ! [X0] : ((~strong(X0) | brave(X0)) => tall(X0)) [input p4]
6. ! [X0] : ((patient(X0) <~> wise(X0)) <=> (~quiet(X0) <~> ~curious(X0))) [input p5]
9. ! [X0] : ((~happy(X0) & ~rich(X0)) <=> (~generous(X0) | ~patient(X0))) [input p8]
10. ! [X0] : ((happy(X0) | wise(X0)) => (~quiet(X0) <~> ~brave(X0))) [input p9]
11. ! [X0] : ((tall(X0) | quiet(X0)) <=> (~tall(X0) | ~calm(X0))) [input p10]
14. ! [X0] : (strong(X0) <=> ~patient(X0)) [input p13]
19. ~curious(fred) & kind(fred) [input p18]
25. rich(fred) [input hypothesis]
28. ! [X0] : ((patient(X0) <~> ~calm(X0)) | (wise(X0) & humble(X0))) [ennf transformation 2]
31. ! [X0] : (tall(X0) | (strong(X0) & ~brave(X0))) [ennf transformation 5]
33. ! [X0] : ((~quiet(X0) <~> ~brave(X0)) | (~happy(X0) & ~wise(X0))) [ennf transformation 10]
39. ! [X0] : (((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | (wise(X0) & humble(X0))) [nnf transformation 28]
40. ! [X0] : ((((humble(X0) | wise(X0)) & (~humble(X0) | ~wise(X0))) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ((~wise(X0) | humble(X0)) & (~humble(X0) | wise(X0))))) [nnf transformation 3]
42. ! [X0] : ((((~wise(X0) | ~patient(X0)) & (wise(X0) | patient(X0))) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) & (((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0))))) [nnf transformation 6]
51. ! [X0] : (((~happy(X0) & ~rich(X0)) | (generous(X0) & patient(X0))) & ((~generous(X0) | ~patient(X0)) | (happy(X0) | rich(X0)))) [nnf transformation 9]
52. ! [X0] : (((~happy(X0) & ~rich(X0)) | (generous(X0) & patient(X0))) & (~generous(X0) | ~patient(X0) | happy(X0) | rich(X0))) [flattening 51]
53. ! [X0] : (((brave(X0) | quiet(X0)) & (~brave(X0) | ~quiet(X0))) | (~happy(X0) & ~wise(X0))) [nnf transformation 33]
54. ! [X0] : (((tall(X0) | quiet(X0)) | (tall(X0) & calm(X0))) & ((~tall(X0) | ~calm(X0)) | (~tall(X0) & ~quiet(X0)))) [nnf transformation 11]
55. ! [X0] : ((tall(X0) | quiet(X0) | (tall(X0) & calm(X0))) & (~tall(X0) | ~calm(X0) | (~tall(X0) & ~quiet(X0)))) [flattening 54]
57. ! [X0] : ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0))) [nnf transformation 14]
70. ~patient(X0) | calm(X0) | humble(X0) [cnf transformation 39]
71. ~patient(X0) | calm(X0) | wise(X0) [cnf transformation 39]
77. ~brave(X0) | ~wise(X0) | ~tall(X0) | ~humble(X0) [cnf transformation 40]
83. strong(X0) | tall(X0) [cnf transformation 31]
91. ~quiet(X0) | ~patient(X0) | ~wise(X0) | curious(X0) [cnf transformation 42]
103. ~rich(X0) | patient(X0) [cnf transformation 52]
109. ~wise(X0) | quiet(X0) | brave(X0) [cnf transformation 53]
112. ~tall(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 55]
124. ~strong(X0) | ~patient(X0) [cnf transformation 57]
133. ~curious(fred) [cnf transformation 19]
142. rich(fred) [cnf transformation 25]
143. ~tall(X0) | ~calm(X0) [duplicate literal removal 112]
251. patient(fred) [resolution 103,142]
253. ~patient(X0) | tall(X0) [resolution 124,83]
258. calm(fred) | humble(fred) [resolution 70,251]
260. 23 <=> humble(fred) [avatar definition]
262. humble(fred) <- (23) [avatar component clause 260]
264. 24 <=> calm(fred) [avatar definition]
267. 23 | 24 [avatar split clause 258,264,260]
268. calm(fred) | wise(fred) [resolution 71,251]
270. 25 <=> wise(fred) [avatar definition]
272. wise(fred) <- (25) [avatar component clause 270]
273. 25 | 24 [avatar split clause 268,264,270]
278. tall(fred) [resolution 253,251]
279. ~calm(fred) [resolution 278,143]
282. ~24 [avatar split clause 279,264]
283. quiet(fred) | brave(fred) <- (25) [resolution 272,109]
285. 26 <=> brave(fred) [avatar definition]
287. brave(fred) <- (26) [avatar component clause 285]
289. 27 <=> quiet(fred) [avatar definition]
291. quiet(fred) <- (27) [avatar component clause 289]
292. 26 | 27 | ~25 [avatar split clause 283,270,289,285]
312. ~wise(fred) | ~tall(fred) | ~humble(fred) <- (26) [resolution 77,287]
325. ~tall(fred) | ~humble(fred) <- (25, 26) [subsumption resolution 312,272]
326. ~humble(fred) <- (25, 26) [subsumption resolution 325,278]
327. $false <- (23, 25, 26) [subsumption resolution 326,262]
328. ~23 | ~25 | ~26 [avatar contradiction clause 327]
403. ~patient(fred) | ~wise(fred) | curious(fred) <- (27) [resolution 91,291]
404. ~wise(fred) | curious(fred) <- (27) [subsumption resolution 403,251]
405. curious(fred) <- (25, 27) [subsumption resolution 404,272]
406. $false <- (25, 27) [subsumption resolution 405,133]
407. ~25 | ~27 [avatar contradiction clause 406]
408. $false [avatar sat refutation 267,273,282,292,328,407]
% SZS output end Proof for 8088175728428651241988208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and old is both wise and kind and vice versa.
Everyone who is not curious is both not kind and not tall and vice versa.
If someone is not kind or not funny then someone is not wise or humble.
If someone is both calm and generous then susan is either not quiet or not happy.
If fred is not old or humble then someone is generous or not calm.
If someone is curious or humble then someone is either quiet or not rich and vice versa.
If someone is either tall or not strong then someone is happy or generous and vice versa.
Everyone who is either wise or not old is tall and vice versa.
If someone is both not rich and not strong then someone is wise or old and vice versa.
If john is either curious or not quiet then someone is tall or not happy and vice versa.
Everyone who is either tall or not generous is tall or rich and vice versa.
Everyone who is curious is both not creative and not funny and vice versa.
Everyone who is not brave is both tall and calm and vice versa.
Everyone who is both not creative and kind is both not strong and happy and vice versa.
Everyone who is both not creative and curious is both not tall and happy.
Everyone who is either tall or not generous is both wise and tall.
Fred is humble.
Paul is brave.
Fred is both happy and not quiet.
Someone is either not funny or quiet.
Mary is either not curious or not calm.
Someone is both brave and not curious.
John is both not kind and strong. | Fred is not humble. | contradiction | (![X]:((~quiet(X)&old(X))<=>(wise(X)&kind(X))))&
(![X]:(~curious(X)<=>(~kind(X)&~tall(X))))&
((?[X]:((~kind(X)|~funny(X))))=>(?[X]:((~wise(X)|humble(X)))))&
((?[X]:((calm(X)&generous(X))))=>((~quiet(susan)<~>~happy(susan))))&
(((~old(fred)|humble(fred)))=>(?[X]:((generous(X)|~calm(X)))))&
((?[X]:((curious(X)|humble(X))))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
((?[X]:((tall(X)<~>~strong(X))))<=>(?[X]:((happy(X)|generous(X)))))&
(![X]:((wise(X)<~>~old(X))<=>tall(X)))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:((wise(X)|old(X)))))&
(((curious(john)<~>~quiet(john)))<=>(?[X]:((tall(X)|~happy(X)))))&
(![X]:((tall(X)<~>~generous(X))<=>(tall(X)|rich(X))))&
(![X]:(curious(X)<=>(~creative(X)&~funny(X))))&
(![X]:(~brave(X)<=>(tall(X)&calm(X))))&
(![X]:((~creative(X)&kind(X))<=>(~strong(X)&happy(X))))&
(![X]:((~creative(X)&curious(X))=>(~tall(X)&happy(X))))&
(![X]:((tall(X)<~>~generous(X))=>(wise(X)&tall(X))))&
(humble(fred))&
(brave(paul))&
((happy(fred)&~quiet(fred)))&
(?[X]:((~funny(X)<~>quiet(X))))&
((~curious(mary)<~>~calm(mary)))&
(?[X]:((brave(X)&~curious(X))))&
((~kind(john)&strong(john))) | ~humble(fred) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8856011106434928383728402
% SZS output start Proof for 8856011106434928383728402
17. humble(fred) [input p16]
24. ~humble(fred) [input hypothesis]
141. humble(fred) [cnf transformation 17]
153. ~humble(fred) [cnf transformation 24]
187. 8 <=> humble(fred) [avatar definition]
335. 8 [avatar split clause 141,187]
356. ~8 [avatar split clause 153,187]
357. $false [avatar sat refutation 335,356]
% SZS output end Proof for 8856011106434928383728402
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is either not calm or happy.
Everyone who is strong is both rich and tall and vice versa.
If someone is either not curious or kind then someone is wise or strong.
Everyone who is rich is tall or not quiet.
Everyone who is tall or not calm is either calm or generous and vice versa.
Everyone who is both tall and creative is strong.
Everyone who is both not curious and happy is tall or wise.
Everyone who is strong or not generous is either tall or not curious and vice versa.
Everyone who is either not kind or not old is both not happy and not patient.
Everyone who is both brave and not funny is both rich and not happy and vice versa.
Everyone who is not strong or not calm is both curious and creative.
If fred is not quiet then susan is both calm and not funny and vice versa.
If someone is not strong or not brave then fred is both not curious and not wise and vice versa.
If lucy is both rich and not strong then paul is not curious or curious.
If someone is tall or humble then alice is either not humble or patient.
Lucy is not generous.
Susan is not patient.
Alice is either happy or not old.
Susan is either curious or creative.
Mary is not calm or not curious. | Mary is calm. | contradiction | (![X]:(~brave(X)=>(~calm(X)<~>happy(X))))&
(![X]:(strong(X)<=>(rich(X)&tall(X))))&
((?[X]:((~curious(X)<~>kind(X))))=>(?[X]:((wise(X)|strong(X)))))&
(![X]:(rich(X)=>(tall(X)|~quiet(X))))&
(![X]:((tall(X)|~calm(X))<=>(calm(X)<~>generous(X))))&
(![X]:((tall(X)&creative(X))=>strong(X)))&
(![X]:((~curious(X)&happy(X))=>(tall(X)|wise(X))))&
(![X]:((strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~happy(X)&~patient(X))))&
(![X]:((brave(X)&~funny(X))<=>(rich(X)&~happy(X))))&
(![X]:((~strong(X)|~calm(X))=>(curious(X)&creative(X))))&
((~quiet(fred))<=>((calm(susan)&~funny(susan))))&
((?[X]:((~strong(X)|~brave(X))))<=>((~curious(fred)&~wise(fred))))&
(((rich(lucy)&~strong(lucy)))=>((~curious(paul)|curious(paul))))&
((?[X]:((tall(X)|humble(X))))=>((~humble(alice)<~>patient(alice))))&
(~generous(lucy))&
(~patient(susan))&
((happy(alice)<~>~old(alice)))&
((curious(susan)<~>creative(susan)))&
((~calm(mary)|~curious(mary))) | calm(mary) | [
"p1",
"p7",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 46900173271097389276589
% SZS output start Proof for 46900173271097389276589
2. ! [X0] : (strong(X0) <=> (tall(X0) & rich(X0))) [input p1]
8. ! [X0] : ((~generous(X0) | strong(X0)) <=> (tall(X0) <~> ~curious(X0))) [input p7]
11. ! [X0] : ((~calm(X0) | ~strong(X0)) => (creative(X0) & curious(X0))) [input p10]
20. ~curious(mary) | ~calm(mary) [input p19]
21. calm(mary) [input hypothesis]
32. ! [X0] : ((creative(X0) & curious(X0)) | (calm(X0) & strong(X0))) [ennf transformation 11]
37. ! [X0] : ((strong(X0) | (~tall(X0) | ~rich(X0))) & ((tall(X0) & rich(X0)) | ~strong(X0))) [nnf transformation 2]
38. ! [X0] : ((strong(X0) | ~tall(X0) | ~rich(X0)) & ((tall(X0) & rich(X0)) | ~strong(X0))) [flattening 37]
45. ! [X0] : (((~generous(X0) | strong(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (generous(X0) & ~strong(X0)))) [nnf transformation 8]
46. ! [X0] : ((~generous(X0) | strong(X0) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (generous(X0) & ~strong(X0)))) [flattening 45]
63. tall(X0) | ~strong(X0) [cnf transformation 38]
78. curious(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 46]
90. curious(X0) | strong(X0) [cnf transformation 32]
113. ~curious(mary) | ~calm(mary) [cnf transformation 20]
114. calm(mary) [cnf transformation 21]
134. curious(X0) | ~strong(X0) [subsumption resolution 78,63]
135. curious(X0) [subsumption resolution 90,134]
196. ~calm(mary) [subsumption resolution 113,135]
197. $false [subsumption resolution 114,196]
% SZS output end Proof for 46900173271097389276589
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not curious is both not old and not generous and vice versa. Everyone who is both calm and not patient is both not patient and not wise. Everyone who is either old or humble is either not creative or happy. If someone is generous or not calm then paul is calm. Everyone who is either not brave or not rich is not funny and vice versa. Everyone who is funny is tall and vice versa. If alice is not wise or strong then paul is both not patient and quiet. If lucy is both tall and funny then lucy is both patient and curious. Everyone who is old or funny is both not creative and brave and vice versa. Everyone who is generous or quiet is both quiet and calm. If mary is not curious or not happy then someone is both not old and happy and vice versa. Everyone who is not rich or not tall is either not kind or not happy and vice versa. Everyone who is both not patient and not humble is either curious or strong and vice versa. If someone is both not old and creative then someone is not curious and vice versa. If someone is both generous and kind then fred is not wise. Everyone who is not kind is either not tall or calm and vice versa. Alice is not strong. Lucy is either quiet or not patient. Susan is not kind. Someone is both funny and happy. Susan is either not funny or not quiet. Someone is either not generous or humble. John is either not calm or not rich. Someone is either not old or humble. | Alice is rich. | neutral | (![X]:((creative(X)|~curious(X))<=>(~old(X)&~generous(X))))&
(![X]:((calm(X)&~patient(X))=>(~patient(X)&~wise(X))))&
(![X]:((old(X)<~>humble(X))=>(~creative(X)<~>happy(X))))&
((?[X]:((generous(X)|~calm(X))))=>(calm(paul)))&
(![X]:((~brave(X)<~>~rich(X))<=>~funny(X)))&
(![X]:(funny(X)<=>tall(X)))&
(((~wise(alice)|strong(alice)))=>((~patient(paul)&quiet(paul))))&
(((tall(lucy)&funny(lucy)))=>((patient(lucy)&curious(lucy))))&
(![X]:((old(X)|funny(X))<=>(~creative(X)&brave(X))))&
(![X]:((generous(X)|quiet(X))=>(quiet(X)&calm(X))))&
(((~curious(mary)|~happy(mary)))<=>(?[X]:((~old(X)&happy(X)))))&
(![X]:((~rich(X)|~tall(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:((~patient(X)&~humble(X))<=>(curious(X)<~>strong(X))))&
((?[X]:((~old(X)&creative(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((generous(X)&kind(X))))=>(~wise(fred)))&
(![X]:(~kind(X)<=>(~tall(X)<~>calm(X))))&
(~strong(alice))&
((quiet(lucy)<~>~patient(lucy)))&
(~kind(susan))&
(?[X]:((funny(X)&happy(X))))&
((~funny(susan)<~>~quiet(susan)))&
(?[X]:((~generous(X)<~>humble(X))))&
((~calm(john)<~>~rich(john)))&
(?[X]:((~old(X)<~>humble(X)))) | rich(alice) | [] | null | 0 |
Everyone who is creative is not humble or not funny and vice versa.
Everyone who is not curious or quiet is both not curious and quiet and vice versa.
If someone is either humble or not old then someone is not happy or happy.
Everyone who is not funny is generous or funny.
Everyone who is either quiet or not quiet is both kind and rich.
If john is not happy then someone is not humble or brave and vice versa.
If john is not strong then fred is not creative and vice versa.
If alice is not humble then fred is old or not tall.
If susan is either quiet or not rich then someone is either creative or wise and vice versa.
Everyone who is not old or not brave is either creative or not humble and vice versa.
Everyone who is not funny or creative is calm or creative.
Everyone who is not curious is not strong or quiet.
Everyone who is not happy or kind is not brave or not rich.
Everyone who is either patient or kind is creative.
If someone is either quiet or not strong then lucy is either not generous or not kind.
Lucy is tall or curious.
Susan is brave or not funny.
Paul is generous.
Someone is not strong or kind.
Paul is not old or not quiet.
Fred is either not wise or not generous.
John is humble or not wise. | Susan is quiet. | entailment | (![X]:(creative(X)<=>(~humble(X)|~funny(X))))&
(![X]:((~curious(X)|quiet(X))<=>(~curious(X)&quiet(X))))&
((?[X]:((humble(X)<~>~old(X))))=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:(~funny(X)=>(generous(X)|funny(X))))&
(![X]:((quiet(X)<~>~quiet(X))=>(kind(X)&rich(X))))&
((~happy(john))<=>(?[X]:((~humble(X)|brave(X)))))&
((~strong(john))<=>(~creative(fred)))&
((~humble(alice))=>((old(fred)|~tall(fred))))&
(((quiet(susan)<~>~rich(susan)))<=>(?[X]:((creative(X)<~>wise(X)))))&
(![X]:((~old(X)|~brave(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((~funny(X)|creative(X))=>(calm(X)|creative(X))))&
(![X]:(~curious(X)=>(~strong(X)|quiet(X))))&
(![X]:((~happy(X)|kind(X))=>(~brave(X)|~rich(X))))&
(![X]:((patient(X)<~>kind(X))=>creative(X)))&
((?[X]:((quiet(X)<~>~strong(X))))=>((~generous(lucy)<~>~kind(lucy))))&
((tall(lucy)|curious(lucy)))&
((brave(susan)|~funny(susan)))&
(generous(paul))&
(?[X]:((~strong(X)|kind(X))))&
((~old(paul)|~quiet(paul)))&
((~wise(fred)<~>~generous(fred)))&
((humble(john)|~wise(john))) | quiet(susan) | [
"p0",
"p3",
"p4",
"p8",
"p9",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 633396751512026246465737
% SZS output start Proof for 633396751512026246465737
1. ! [X0] : (creative(X0) <=> (~funny(X0) | ~humble(X0))) [input p0]
4. ! [X0] : (~funny(X0) => (funny(X0) | generous(X0))) [input p3]
5. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) => (rich(X0) & kind(X0))) [input p4]
9. (quiet(susan) <~> ~rich(susan)) <=> ? [X0] : (creative(X0) <~> wise(X0)) [input p8]
10. ! [X0] : ((~brave(X0) | ~old(X0)) <=> (creative(X0) <~> ~humble(X0))) [input p9]
13. ! [X0] : ((kind(X0) | ~happy(X0)) => (~rich(X0) | ~brave(X0))) [input p12]
21. ~wise(fred) <~> ~generous(fred) [input p20]
23. ~quiet(susan) [input hypothesis]
27. ! [X0] : ((funny(X0) | generous(X0)) | funny(X0)) [ennf transformation 4]
28. ! [X0] : (funny(X0) | generous(X0) | funny(X0)) [flattening 27]
29. ! [X0] : ((rich(X0) & kind(X0)) | (quiet(X0) <=> ~quiet(X0))) [ennf transformation 5]
34. ! [X0] : ((~rich(X0) | ~brave(X0)) | (~kind(X0) & happy(X0))) [ennf transformation 13]
35. ! [X0] : (~rich(X0) | ~brave(X0) | (~kind(X0) & happy(X0))) [flattening 34]
38. ! [X0] : ((creative(X0) | (funny(X0) & humble(X0))) & ((~funny(X0) | ~humble(X0)) | ~creative(X0))) [nnf transformation 1]
39. ! [X0] : ((creative(X0) | (funny(X0) & humble(X0))) & (~funny(X0) | ~humble(X0) | ~creative(X0))) [flattening 38]
46. ! [X0] : ((rich(X0) & kind(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) [nnf transformation 29]
52. (((rich(susan) | ~quiet(susan)) & (~rich(susan) | quiet(susan))) | ! [X0] : ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (? [X0] : ((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | ((quiet(susan) | rich(susan)) & (~rich(susan) | ~quiet(susan)))) [nnf transformation 9]
53. (((rich(susan) | ~quiet(susan)) & (~rich(susan) | quiet(susan))) | ! [X0] : ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (? [X1] : ((~wise(X1) | ~creative(X1)) & (wise(X1) | creative(X1))) | ((quiet(susan) | rich(susan)) & (~rich(susan) | ~quiet(susan)))) [rectify 52]
54. ? [X1] : ((~wise(X1) | ~creative(X1)) & (wise(X1) | creative(X1))) => ((~wise(sK2) | ~creative(sK2)) & (wise(sK2) | creative(sK2))) [choice axiom]
55. (((rich(susan) | ~quiet(susan)) & (~rich(susan) | quiet(susan))) | ! [X0] : ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (((~wise(sK2) | ~creative(sK2)) & (wise(sK2) | creative(sK2))) | ((quiet(susan) | rich(susan)) & (~rich(susan) | ~quiet(susan)))) [skolemisation 53,54]
56. ! [X0] : (((~brave(X0) | ~old(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | (brave(X0) & old(X0)))) [nnf transformation 10]
57. ! [X0] : ((~brave(X0) | ~old(X0) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | (brave(X0) & old(X0)))) [flattening 56]
62. (generous(fred) | wise(fred)) & (~generous(fred) | ~wise(fred)) [nnf transformation 21]
63. ~funny(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 39]
64. humble(X0) | creative(X0) [cnf transformation 39]
73. funny(X0) | generous(X0) | funny(X0) [cnf transformation 28]
74. kind(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 46]
75. kind(X0) | quiet(X0) | quiet(X0) [cnf transformation 46]
76. rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 46]
77. rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 46]
88. ~rich(susan) | quiet(susan) | wise(X0) | ~creative(X0) [cnf transformation 55]
89. ~rich(susan) | quiet(susan) | creative(X0) | ~wise(X0) [cnf transformation 55]
93. ~humble(X0) | creative(X0) | brave(X0) [cnf transformation 57]
95. humble(X0) | ~creative(X0) | brave(X0) [cnf transformation 57]
100. ~rich(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 35]
112. ~generous(fred) | ~wise(fred) [cnf transformation 62]
115. ~quiet(susan) [cnf transformation 23]
116. kind(X0) | ~quiet(X0) [duplicate literal removal 74]
117. kind(X0) | quiet(X0) [duplicate literal removal 75]
118. rich(X0) | ~quiet(X0) [duplicate literal removal 76]
119. rich(X0) | quiet(X0) [duplicate literal removal 77]
120. generous(X0) | funny(X0) [duplicate literal removal 73]
121. rich(X0) [subsumption resolution 118,119]
122. kind(X0) [subsumption resolution 116,117]
124. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
125. ~brave(X0) <- (1) [avatar component clause 124]
132. 3 <=> ! [X0] : humble(X0) [avatar definition]
133. humble(X0) <- (3) [avatar component clause 132]
145. 6 <=> creative(fred) [avatar definition]
147. creative(fred) <- (6) [avatar component clause 145]
167. quiet(susan) | creative(X0) | ~wise(X0) [subsumption resolution 89,121]
169. 11 <=> ! [X0] : (creative(X0) | ~wise(X0)) [avatar definition]
170. ~wise(X0) | creative(X0) <- (11) [avatar component clause 169]
172. 12 <=> quiet(susan) [avatar definition]
175. 11 | 12 [avatar split clause 167,172,169]
176. quiet(susan) | wise(X0) | ~creative(X0) [subsumption resolution 88,121]
178. 13 <=> ! [X0] : (wise(X0) | ~creative(X0)) [avatar definition]
179. ~creative(X0) | wise(X0) <- (13) [avatar component clause 178]
180. 13 | 12 [avatar split clause 176,172,178]
193. brave(X0) | humble(X0) [subsumption resolution 95,64]
195. brave(X0) | creative(X0) [subsumption resolution 93,193]
197. ~brave(X0) | ~kind(X0) [subsumption resolution 100,121]
198. ~brave(X0) [subsumption resolution 197,122]
199. 1 [avatar split clause 198,124]
244. 25 <=> wise(fred) [avatar definition]
245. ~wise(fred) <- (~25) [avatar component clause 244]
246. wise(fred) <- (25) [avatar component clause 244]
248. 26 <=> generous(fred) [avatar definition]
249. ~generous(fred) <- (~26) [avatar component clause 248]
252. ~25 | ~26 [avatar split clause 112,248,244]
262. ~12 [avatar split clause 115,172]
269. funny(fred) <- (~26) [resolution 120,249]
270. creative(fred) <- (11, 25) [resolution 170,246]
273. 6 | ~11 | ~25 [avatar split clause 270,244,169,145]
278. humble(X0) <- (1) [resolution 193,125]
279. 3 | ~1 [avatar split clause 278,124,132]
285. creative(X0) <- (1) [resolution 195,125]
286. wise(X0) <- (1, 13) [resolution 285,179]
294. ~humble(fred) | ~creative(fred) <- (~26) [resolution 63,269]
298. ~creative(fred) <- (3, ~26) [subsumption resolution 294,133]
299. $false <- (3, 6, ~26) [subsumption resolution 298,147]
300. ~3 | ~6 | 26 [avatar contradiction clause 299]
301. $false <- (1, 13, ~25) [subsumption resolution 245,286]
302. ~1 | ~13 | 25 [avatar contradiction clause 301]
303. $false [avatar sat refutation 175,180,199,252,262,273,279,300,302]
% SZS output end Proof for 633396751512026246465737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both not patient and wise then someone is both not creative and humble.
If someone is both not generous and brave then alice is old.
If fred is kind or generous then paul is quiet or curious and vice versa.
Everyone who is either kind or curious is both funny and not curious.
If susan is both not strong and not brave then susan is not rich.
Everyone who is either curious or not curious is both not old and not generous and vice versa.
Everyone who is both calm and not patient is both not patient and not wise.
Everyone who is either old or humble is either not creative or happy.
If someone is generous or not calm then paul is calm.
Everyone who is either not brave or not rich is not funny and vice versa.
Everyone who is funny is tall and vice versa.
If alice is not wise or strong then paul is both not patient and quiet.
If lucy is both tall and funny then lucy is both patient and curious.
Everyone who is old or funny is both not creative and brave and vice versa.
Everyone who is generous or quiet is both quiet and calm.
If mary is not curious or not happy then someone is both not old and happy and vice versa.
Someone is old or not tall.
Fred is either not quiet or not curious.
John is curious or not calm.
Someone is either not quiet or not strong.
Someone is either not rich or rich.
Someone is either tall or kind. | Mary is old. | contradiction | ((?[X]:((~patient(X)&wise(X))))=>(?[X]:((~creative(X)&humble(X)))))&
((?[X]:((~generous(X)&brave(X))))=>(old(alice)))&
(((kind(fred)|generous(fred)))<=>((quiet(paul)|curious(paul))))&
(![X]:((kind(X)<~>curious(X))=>(funny(X)&~curious(X))))&
(((~strong(susan)&~brave(susan)))=>(~rich(susan)))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)&~generous(X))))&
(![X]:((calm(X)&~patient(X))=>(~patient(X)&~wise(X))))&
(![X]:((old(X)<~>humble(X))=>(~creative(X)<~>happy(X))))&
((?[X]:((generous(X)|~calm(X))))=>(calm(paul)))&
(![X]:((~brave(X)<~>~rich(X))<=>~funny(X)))&
(![X]:(funny(X)<=>tall(X)))&
(((~wise(alice)|strong(alice)))=>((~patient(paul)&quiet(paul))))&
(((tall(lucy)&funny(lucy)))=>((patient(lucy)&curious(lucy))))&
(![X]:((old(X)|funny(X))<=>(~creative(X)&brave(X))))&
(![X]:((generous(X)|quiet(X))=>(quiet(X)&calm(X))))&
(((~curious(mary)|~happy(mary)))<=>(?[X]:((~old(X)&happy(X)))))&
(?[X]:((old(X)|~tall(X))))&
((~quiet(fred)<~>~curious(fred)))&
((curious(john)|~calm(john)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~rich(X)<~>rich(X))))&
(?[X]:((tall(X)<~>kind(X)))) | old(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2696621575331279633296240
% SZS output start Proof for 2696621575331279633296240
6. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (~generous(X0) & ~old(X0))) [input p5]
23. old(mary) [input hypothesis]
44. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (generous(X0) | old(X0))) & ((~generous(X0) & ~old(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 6]
45. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | generous(X0) | old(X0)) & ((~generous(X0) & ~old(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 44]
80. ~old(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 45]
81. ~old(X0) | curious(X0) | curious(X0) [cnf transformation 45]
130. old(mary) [cnf transformation 23]
131. ~old(X0) | ~curious(X0) [duplicate literal removal 80]
132. ~old(X0) | curious(X0) [duplicate literal removal 81]
191. ~old(X0) [subsumption resolution 131,132]
294. $false [subsumption resolution 130,191]
% SZS output end Proof for 2696621575331279633296240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not wise is either generous or not creative. Everyone who is either not brave or not generous is both rich and strong. If lucy is curious or wise then someone is not kind or generous and vice versa. If someone is generous or rich then mary is both wise and creative and vice versa. Everyone who is either not creative or not strong is both strong and not brave and vice versa. Everyone who is curious is creative and vice versa. If someone is not funny or not curious then someone is not strong or not brave and vice versa. If alice is both not humble and quiet then susan is either wise or happy and vice versa. Everyone who is either brave or not tall is both calm and rich. If mary is both not rich and rich then susan is both wise and funny and vice versa. Everyone who is both generous and not strong is humble. If alice is both not patient and wise then john is either not rich or humble and vice versa. Everyone who is either wise or funny is not calm and vice versa. If someone is not calm or not wise then someone is both funny and rich. If someone is not old then alice is old or happy and vice versa. Everyone who is creative or not kind is not kind or brave and vice versa. Someone is not tall or funny. John is both not tall and patient. Someone is both not kind and humble. John is either not strong or kind. Someone is both not generous and kind. Someone is patient or not curious. Someone is wise. | Lucy is old. | neutral | (![X]:((generous(X)&~wise(X))=>(generous(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>~generous(X))=>(rich(X)&strong(X))))&
(((curious(lucy)|wise(lucy)))<=>(?[X]:((~kind(X)|generous(X)))))&
((?[X]:((generous(X)|rich(X))))<=>((wise(mary)&creative(mary))))&
(![X]:((~creative(X)<~>~strong(X))<=>(strong(X)&~brave(X))))&
(![X]:(curious(X)<=>creative(X)))&
((?[X]:((~funny(X)|~curious(X))))<=>(?[X]:((~strong(X)|~brave(X)))))&
(((~humble(alice)&quiet(alice)))<=>((wise(susan)<~>happy(susan))))&
(![X]:((brave(X)<~>~tall(X))=>(calm(X)&rich(X))))&
(((~rich(mary)&rich(mary)))<=>((wise(susan)&funny(susan))))&
(![X]:((generous(X)&~strong(X))=>humble(X)))&
(((~patient(alice)&wise(alice)))<=>((~rich(john)<~>humble(john))))&
(![X]:((wise(X)<~>funny(X))<=>~calm(X)))&
((?[X]:((~calm(X)|~wise(X))))=>(?[X]:((funny(X)&rich(X)))))&
((?[X]:(~old(X)))<=>((old(alice)|happy(alice))))&
(![X]:((creative(X)|~kind(X))<=>(~kind(X)|brave(X))))&
(?[X]:((~tall(X)|funny(X))))&
((~tall(john)&patient(john)))&
(?[X]:((~kind(X)&humble(X))))&
((~strong(john)<~>kind(john)))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:((patient(X)|~curious(X))))&
(?[X]:(wise(X))) | old(lucy) | [] | null | 0 |
Everyone who is either quiet or funny is quiet or not patient and vice versa. Everyone who is not happy is not wise and vice versa. Everyone who is either generous or tall is not patient and vice versa. Everyone who is both not brave and humble is either not curious or old. Everyone who is not patient or not generous is both generous and not quiet and vice versa. If susan is tall then someone is either calm or kind. If susan is not generous or not tall then someone is not humble. Everyone who is both strong and not generous is wise and vice versa. Everyone who is generous is either not strong or wise and vice versa. If someone is tall or humble then alice is not calm or not wise and vice versa. If someone is either not quiet or not funny then fred is not humble. If someone is either happy or not humble then john is not tall or creative. Everyone who is patient is not humble and vice versa. Everyone who is both rich and quiet is both creative and calm. Everyone who is either quiet or not humble is both not curious and not happy. If someone is not rich or not humble then someone is both generous and not curious and vice versa. Someone is not curious or happy. Someone is not happy or kind. Someone is either not brave or not happy. Fred is either curious or not kind. Someone is not patient or happy. Paul is both not rich and not tall. Paul is either brave or kind. Someone is either not quiet or strong. | Alice is wise. | contradiction | (![X]:((quiet(X)<~>funny(X))<=>(quiet(X)|~patient(X))))&
(![X]:(~happy(X)<=>~wise(X)))&
(![X]:((generous(X)<~>tall(X))<=>~patient(X)))&
(![X]:((~brave(X)&humble(X))=>(~curious(X)<~>old(X))))&
(![X]:((~patient(X)|~generous(X))<=>(generous(X)&~quiet(X))))&
((tall(susan))=>(?[X]:((calm(X)<~>kind(X)))))&
(((~generous(susan)|~tall(susan)))=>(?[X]:(~humble(X))))&
(![X]:((strong(X)&~generous(X))<=>wise(X)))&
(![X]:(generous(X)<=>(~strong(X)<~>wise(X))))&
((?[X]:((tall(X)|humble(X))))<=>((~calm(alice)|~wise(alice))))&
((?[X]:((~quiet(X)<~>~funny(X))))=>(~humble(fred)))&
((?[X]:((happy(X)<~>~humble(X))))=>((~tall(john)|creative(john))))&
(![X]:(patient(X)<=>~humble(X)))&
(![X]:((rich(X)&quiet(X))=>(creative(X)&calm(X))))&
(![X]:((quiet(X)<~>~humble(X))=>(~curious(X)&~happy(X))))&
((?[X]:((~rich(X)|~humble(X))))<=>(?[X]:((generous(X)&~curious(X)))))&
(?[X]:((~curious(X)|happy(X))))&
(?[X]:((~happy(X)|kind(X))))&
(?[X]:((~brave(X)<~>~happy(X))))&
((curious(fred)<~>~kind(fred)))&
(?[X]:((~patient(X)|happy(X))))&
((~rich(paul)&~tall(paul)))&
((brave(paul)<~>kind(paul)))&
(?[X]:((~quiet(X)<~>strong(X)))) | wise(alice) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5599345992833444796243525
% SZS output start Proof for 5599345992833444796243525
5. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> (~quiet(X0) & generous(X0))) [input p4]
8. ! [X0] : ((~generous(X0) & strong(X0)) <=> wise(X0)) [input p7]
25. wise(alice) [input hypothesis]
42. ! [X0] : (((~generous(X0) | ~patient(X0)) | (quiet(X0) | ~generous(X0))) & ((~quiet(X0) & generous(X0)) | (generous(X0) & patient(X0)))) [nnf transformation 5]
43. ! [X0] : ((~generous(X0) | ~patient(X0) | quiet(X0) | ~generous(X0)) & ((~quiet(X0) & generous(X0)) | (generous(X0) & patient(X0)))) [flattening 42]
49. ! [X0] : (((~generous(X0) & strong(X0)) | ~wise(X0)) & (wise(X0) | (generous(X0) | ~strong(X0)))) [nnf transformation 8]
50. ! [X0] : (((~generous(X0) & strong(X0)) | ~wise(X0)) & (wise(X0) | generous(X0) | ~strong(X0))) [flattening 49]
94. generous(X0) | generous(X0) [cnf transformation 43]
104. ~generous(X0) | ~wise(X0) [cnf transformation 50]
140. wise(alice) [cnf transformation 25]
141. generous(X0) [duplicate literal removal 94]
165. ~wise(X0) [subsumption resolution 104,141]
280. $false [subsumption resolution 140,165]
% SZS output end Proof for 5599345992833444796243525
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not strong is either not wise or not strong and vice versa.
Everyone who is either wise or not patient is curious or not calm.
If someone is both wise and not curious then someone is either curious or humble.
Everyone who is either patient or not kind is both not brave and not creative.
If susan is both humble and happy then someone is calm or not curious and vice versa.
Everyone who is not rich or humble is wise.
If someone is not patient then lucy is not calm.
If someone is brave or not funny then john is both not strong and old.
Everyone who is both quiet and rich is both generous and not wise.
Everyone who is either not strong or brave is both wise and not tall.
Everyone who is tall is wise and vice versa.
If fred is generous then lucy is both not generous and funny and vice versa.
If someone is curious or not patient then someone is either tall or not tall and vice versa.
Everyone who is not happy or happy is not old.
If mary is generous then susan is creative and vice versa.
Everyone who is either old or not funny is patient or quiet and vice versa.
John is not happy or generous.
Mary is both not quiet and not brave.
Susan is not calm.
Someone is not happy or wise.
Someone is either happy or not humble.
Someone is either not creative or not curious.
Someone is both creative and strong.
Someone is not brave or not generous. | Lucy is not tall. | contradiction | (![X]:((patient(X)&~strong(X))<=>(~wise(X)<~>~strong(X))))&
(![X]:((wise(X)<~>~patient(X))=>(curious(X)|~calm(X))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((patient(X)<~>~kind(X))=>(~brave(X)&~creative(X))))&
(((humble(susan)&happy(susan)))<=>(?[X]:((calm(X)|~curious(X)))))&
(![X]:((~rich(X)|humble(X))=>wise(X)))&
((?[X]:(~patient(X)))=>(~calm(lucy)))&
((?[X]:((brave(X)|~funny(X))))=>((~strong(john)&old(john))))&
(![X]:((quiet(X)&rich(X))=>(generous(X)&~wise(X))))&
(![X]:((~strong(X)<~>brave(X))=>(wise(X)&~tall(X))))&
(![X]:(tall(X)<=>wise(X)))&
((generous(fred))<=>((~generous(lucy)&funny(lucy))))&
((?[X]:((curious(X)|~patient(X))))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:((~happy(X)|happy(X))=>~old(X)))&
((generous(mary))<=>(creative(susan)))&
(![X]:((old(X)<~>~funny(X))<=>(patient(X)|quiet(X))))&
((~happy(john)|generous(john)))&
((~quiet(mary)&~brave(mary)))&
(~calm(susan))&
(?[X]:((~happy(X)|wise(X))))&
(?[X]:((happy(X)<~>~humble(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((creative(X)&strong(X))))&
(?[X]:((~brave(X)|~generous(X)))) | ~tall(lucy) | [
"p0",
"p7",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 605563949723476227914886
% SZS output start Proof for 605563949723476227914886
1. ! [X0] : ((~strong(X0) & patient(X0)) <=> (~wise(X0) <~> ~strong(X0))) [input p0]
8. ? [X0] : (~funny(X0) | brave(X0)) => (old(john) & ~strong(john)) [input p7]
10. ! [X0] : ((~strong(X0) <~> brave(X0)) => (~tall(X0) & wise(X0))) [input p9]
11. ! [X0] : (tall(X0) <=> wise(X0)) [input p10]
14. ! [X0] : ((happy(X0) | ~happy(X0)) => ~old(X0)) [input p13]
25. ~tall(lucy) [input hypothesis]
34. (old(john) & ~strong(john)) | ! [X0] : (funny(X0) & ~brave(X0)) [ennf transformation 8]
37. ! [X0] : ((~tall(X0) & wise(X0)) | (~strong(X0) <=> brave(X0))) [ennf transformation 10]
38. ! [X0] : (~old(X0) | (~happy(X0) & happy(X0))) [ennf transformation 14]
39. ! [X0] : (((~strong(X0) & patient(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (strong(X0) | ~patient(X0)))) [nnf transformation 1]
40. ! [X0] : (((~strong(X0) & patient(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | strong(X0) | ~patient(X0))) [flattening 39]
52. ! [X0] : ((~tall(X0) & wise(X0)) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) [nnf transformation 37]
53. ! [X0] : ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0))) [nnf transformation 11]
80. ~strong(X0) | ~strong(X0) | wise(X0) [cnf transformation 40]
100. old(john) | ~brave(X0) [cnf transformation 34]
104. wise(X0) | brave(X0) | strong(X0) [cnf transformation 52]
109. ~wise(X0) | tall(X0) [cnf transformation 53]
119. ~old(X0) | happy(X0) [cnf transformation 38]
120. ~old(X0) | ~happy(X0) [cnf transformation 38]
141. ~tall(lucy) [cnf transformation 25]
145. ~strong(X0) | wise(X0) [duplicate literal removal 80]
201. 13 <=> old(john) [avatar definition]
203. old(john) <- (13) [avatar component clause 201]
206. 14 <=> ! [X0] : ~brave(X0) [avatar definition]
207. ~brave(X0) <- (14) [avatar component clause 206]
208. 14 | 13 [avatar split clause 100,201,206]
215. brave(X0) | wise(X0) [subsumption resolution 104,145]
232. 19 <=> ! [X1] : tall(X1) [avatar definition]
233. tall(X1) <- (19) [avatar component clause 232]
247. ~old(X0) [subsumption resolution 119,120]
308. $false <- (13) [subsumption resolution 203,247]
309. ~13 [avatar contradiction clause 308]
320. wise(X0) <- (14) [resolution 215,207]
323. tall(X0) <- (14) [resolution 320,109]
324. 19 | ~14 [avatar split clause 323,206,232]
325. $false <- (19) [resolution 233,141]
327. ~19 [avatar contradiction clause 325]
328. $false [avatar sat refutation 208,309,324,327]
% SZS output end Proof for 605563949723476227914886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not brave is not quiet and vice versa.
Everyone who is either not funny or not curious is not funny or rich.
Everyone who is both not tall and not old is strong and vice versa.
If someone is humble then someone is humble or happy and vice versa.
Everyone who is not curious is either calm or not calm and vice versa.
If paul is either not quiet or quiet then paul is both not rich and humble.
Everyone who is funny is curious and vice versa.
Everyone who is not curious or not rich is either humble or not humble and vice versa.
Everyone who is both old and wise is both old and rich and vice versa.
Everyone who is tall is not calm or not tall and vice versa.
If lucy is either wise or calm then someone is not rich or calm and vice versa.
If someone is either not happy or not wise then someone is both creative and not creative and vice versa.
Everyone who is not funny or creative is either brave or not patient.
Everyone who is not old or not humble is either strong or patient and vice versa.
If fred is not calm or tall then susan is patient or not strong.
Fred is both humble and patient.
Someone is either not tall or not patient.
Someone is both not rich and old.
Someone is generous.
Someone is either not calm or curious. | Paul is not tall. | contradiction | (![X]:((kind(X)&~brave(X))<=>~quiet(X)))&
(![X]:((~funny(X)<~>~curious(X))=>(~funny(X)|rich(X))))&
(![X]:((~tall(X)&~old(X))<=>strong(X)))&
((?[X]:(humble(X)))<=>(?[X]:((humble(X)|happy(X)))))&
(![X]:(~curious(X)<=>(calm(X)<~>~calm(X))))&
(((~quiet(paul)<~>quiet(paul)))=>((~rich(paul)&humble(paul))))&
(![X]:(funny(X)<=>curious(X)))&
(![X]:((~curious(X)|~rich(X))<=>(humble(X)<~>~humble(X))))&
(![X]:((old(X)&wise(X))<=>(old(X)&rich(X))))&
(![X]:(tall(X)<=>(~calm(X)|~tall(X))))&
(((wise(lucy)<~>calm(lucy)))<=>(?[X]:((~rich(X)|calm(X)))))&
((?[X]:((~happy(X)<~>~wise(X))))<=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((~funny(X)|creative(X))=>(brave(X)<~>~patient(X))))&
(![X]:((~old(X)|~humble(X))<=>(strong(X)<~>patient(X))))&
(((~calm(fred)|tall(fred)))=>((patient(susan)|~strong(susan))))&
((humble(fred)&patient(fred)))&
(?[X]:((~tall(X)<~>~patient(X))))&
(?[X]:((~rich(X)&old(X))))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)<~>curious(X)))) | ~tall(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6268013075016182997319904
% SZS output start Proof for 6268013075016182997319904
10. ! [X0] : (tall(X0) <=> (~tall(X0) | ~calm(X0))) [input p9]
21. ~tall(paul) [input hypothesis]
48. ! [X0] : ((tall(X0) | (tall(X0) & calm(X0))) & ((~tall(X0) | ~calm(X0)) | ~tall(X0))) [nnf transformation 10]
49. ! [X0] : ((tall(X0) | (tall(X0) & calm(X0))) & (~tall(X0) | ~calm(X0) | ~tall(X0))) [flattening 48]
103. tall(X0) | tall(X0) [cnf transformation 49]
136. ~tall(paul) [cnf transformation 21]
138. tall(X0) [duplicate literal removal 103]
225. $false [subsumption resolution 136,138]
% SZS output end Proof for 6268013075016182997319904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either kind or rich then fred is happy or brave.
If paul is brave then someone is both calm and patient and vice versa.
Everyone who is not tall is not kind and vice versa.
If someone is either not curious or not strong then john is either not happy or wise.
Everyone who is not happy or kind is both not rich and happy and vice versa.
If susan is not tall or not old then someone is not creative or old.
If someone is either brave or not tall then someone is curious and vice versa.
Everyone who is creative or old is either not wise or calm.
Everyone who is both quiet and not creative is either not quiet or strong.
If fred is not funny then someone is both not creative and not calm.
Everyone who is brave or not creative is either quiet or not patient and vice versa.
Everyone who is brave or rich is funny or old and vice versa.
Everyone who is not patient or humble is not brave or not wise.
If someone is not brave or kind then someone is both rich and not old.
Everyone who is not strong is patient or not happy and vice versa.
Everyone who is generous is both kind and not generous and vice versa.
Susan is either happy or wise.
Someone is not quiet.
Paul is not generous.
Paul is either not strong or wise.
Someone is both brave and patient. | John is not old. | neutral | (((kind(lucy)<~>rich(lucy)))=>((happy(fred)|brave(fred))))&
((brave(paul))<=>(?[X]:((calm(X)&patient(X)))))&
(![X]:(~tall(X)<=>~kind(X)))&
((?[X]:((~curious(X)<~>~strong(X))))=>((~happy(john)<~>wise(john))))&
(![X]:((~happy(X)|kind(X))<=>(~rich(X)&happy(X))))&
(((~tall(susan)|~old(susan)))=>(?[X]:((~creative(X)|old(X)))))&
((?[X]:((brave(X)<~>~tall(X))))<=>(?[X]:(curious(X))))&
(![X]:((creative(X)|old(X))=>(~wise(X)<~>calm(X))))&
(![X]:((quiet(X)&~creative(X))=>(~quiet(X)<~>strong(X))))&
((~funny(fred))=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((brave(X)|~creative(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:((brave(X)|rich(X))<=>(funny(X)|old(X))))&
(![X]:((~patient(X)|humble(X))=>(~brave(X)|~wise(X))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((rich(X)&~old(X)))))&
(![X]:(~strong(X)<=>(patient(X)|~happy(X))))&
(![X]:(generous(X)<=>(kind(X)&~generous(X))))&
((happy(susan)<~>wise(susan)))&
(?[X]:(~quiet(X)))&
(~generous(paul))&
((~strong(paul)<~>wise(paul)))&
(?[X]:((brave(X)&patient(X)))) | ~old(john) | [] | null | 0 |
Everyone who is not generous or not calm is both not old and humble. Everyone who is both tall and brave is humble and vice versa. Everyone who is either not happy or funny is both rich and patient and vice versa. If lucy is not calm or wise then lucy is either not quiet or strong. Everyone who is wise is old and vice versa. Everyone who is either rich or kind is either not generous or old and vice versa. Everyone who is either kind or not tall is either not funny or creative and vice versa. Everyone who is both humble and strong is both rich and not old. If alice is not generous then alice is not rich and vice versa. If paul is both funny and old then someone is both strong and not calm and vice versa. If someone is either not strong or strong then someone is not wise and vice versa. Everyone who is both not happy and creative is either not curious or wise. Everyone who is both patient and not calm is rich and vice versa. Everyone who is not quiet is strong or calm and vice versa. Everyone who is not patient or not humble is not humble. If someone is either brave or not strong then someone is old or happy. Someone is not kind or not calm. Mary is both brave and not strong. Someone is generous. Someone is either not humble or not happy. Fred is either not funny or tall. Someone is either curious or rich. Lucy is tall. Alice is either happy or not rich. | Alice is patient. | entailment | (![X]:((~generous(X)|~calm(X))=>(~old(X)&humble(X))))&
(![X]:((tall(X)&brave(X))<=>humble(X)))&
(![X]:((~happy(X)<~>funny(X))<=>(rich(X)&patient(X))))&
(((~calm(lucy)|wise(lucy)))=>((~quiet(lucy)<~>strong(lucy))))&
(![X]:(wise(X)<=>old(X)))&
(![X]:((rich(X)<~>kind(X))<=>(~generous(X)<~>old(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((humble(X)&strong(X))=>(rich(X)&~old(X))))&
((~generous(alice))<=>(~rich(alice)))&
(((funny(paul)&old(paul)))<=>(?[X]:((strong(X)&~calm(X)))))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:(~wise(X))))&
(![X]:((~happy(X)&creative(X))=>(~curious(X)<~>wise(X))))&
(![X]:((patient(X)&~calm(X))<=>rich(X)))&
(![X]:(~quiet(X)<=>(strong(X)|calm(X))))&
(![X]:((~patient(X)|~humble(X))=>~humble(X)))&
((?[X]:((brave(X)<~>~strong(X))))=>(?[X]:((old(X)|happy(X)))))&
(?[X]:((~kind(X)|~calm(X))))&
((brave(mary)&~strong(mary)))&
(?[X]:(generous(X)))&
(?[X]:((~humble(X)<~>~happy(X))))&
((~funny(fred)<~>tall(fred)))&
(?[X]:((curious(X)<~>rich(X))))&
(tall(lucy))&
((happy(alice)<~>~rich(alice))) | patient(alice) | [
"p0",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5962209759866180799816309
% SZS output start Proof for 5962209759866180799816309
1. ! [X0] : ((~calm(X0) | ~generous(X0)) => (humble(X0) & ~old(X0))) [input p0]
9. ~generous(alice) <=> ~rich(alice) [input p8]
13. ! [X0] : ((~calm(X0) & patient(X0)) <=> rich(X0)) [input p12]
15. ! [X0] : ((~humble(X0) | ~patient(X0)) => ~humble(X0)) [input p14]
25. ~patient(alice) [input hypothesis]
28. ! [X0] : ((humble(X0) & ~old(X0)) | (calm(X0) & generous(X0))) [ennf transformation 1]
34. ! [X0] : (~humble(X0) | (humble(X0) & patient(X0))) [ennf transformation 15]
44. (~generous(alice) | rich(alice)) & (~rich(alice) | generous(alice)) [nnf transformation 9]
56. ! [X0] : (((~calm(X0) & patient(X0)) | ~rich(X0)) & (rich(X0) | (calm(X0) | ~patient(X0)))) [nnf transformation 13]
57. ! [X0] : (((~calm(X0) & patient(X0)) | ~rich(X0)) & (rich(X0) | calm(X0) | ~patient(X0))) [flattening 56]
78. humble(X0) | generous(X0) [cnf transformation 28]
114. ~generous(alice) | rich(alice) [cnf transformation 44]
126. ~rich(X0) | patient(X0) [cnf transformation 57]
131. ~humble(X0) | patient(X0) [cnf transformation 34]
148. ~patient(alice) [cnf transformation 25]
176. 5 <=> rich(alice) [avatar definition]
178. rich(alice) <- (5) [avatar component clause 176]
180. 6 <=> generous(alice) [avatar definition]
182. ~generous(alice) <- (~6) [avatar component clause 180]
183. 5 | ~6 [avatar split clause 114,180,176]
293. patient(X1) | generous(X1) [resolution 131,78]
580. patient(alice) <- (5) [resolution 178,126]
583. $false <- (5) [subsumption resolution 580,148]
584. ~5 [avatar contradiction clause 583]
594. generous(alice) [resolution 293,148]
598. $false <- (~6) [subsumption resolution 594,182]
599. 6 [avatar contradiction clause 598]
600. $false [avatar sat refutation 183,584,599]
% SZS output end Proof for 5962209759866180799816309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is quiet then john is not brave or humble and vice versa.
Everyone who is both not wise and quiet is not calm.
Everyone who is not patient or not brave is not curious or not kind and vice versa.
If paul is not quiet then someone is curious and vice versa.
Everyone who is either not kind or curious is old or rich.
If susan is either not quiet or brave then someone is both not rich and not kind.
If alice is wise then someone is not humble.
Everyone who is old or not calm is either not creative or not patient and vice versa.
Everyone who is not calm or curious is generous or brave and vice versa.
If susan is both not curious and not generous then someone is not brave or not generous and vice versa.
If someone is both generous and calm then someone is not kind.
Everyone who is both not creative and not humble is either happy or not kind and vice versa.
Everyone who is not creative is either not curious or not happy and vice versa.
Everyone who is patient or brave is not creative or not curious and vice versa.
Everyone who is either not brave or kind is not kind and vice versa.
Everyone who is not patient or wise is not generous.
Mary is strong.
Someone is either creative or not generous.
Someone is old or not quiet.
Mary is both generous and quiet.
Paul is not brave.
Alice is not kind.
Alice is either not old or calm.
Someone is either not strong or strong. | John is not quiet. | neutral | ((quiet(alice))<=>((~brave(john)|humble(john))))&
(![X]:((~wise(X)&quiet(X))=>~calm(X)))&
(![X]:((~patient(X)|~brave(X))<=>(~curious(X)|~kind(X))))&
((~quiet(paul))<=>(?[X]:(curious(X))))&
(![X]:((~kind(X)<~>curious(X))=>(old(X)|rich(X))))&
(((~quiet(susan)<~>brave(susan)))=>(?[X]:((~rich(X)&~kind(X)))))&
((wise(alice))=>(?[X]:(~humble(X))))&
(![X]:((old(X)|~calm(X))<=>(~creative(X)<~>~patient(X))))&
(![X]:((~calm(X)|curious(X))<=>(generous(X)|brave(X))))&
(((~curious(susan)&~generous(susan)))<=>(?[X]:((~brave(X)|~generous(X)))))&
((?[X]:((generous(X)&calm(X))))=>(?[X]:(~kind(X))))&
(![X]:((~creative(X)&~humble(X))<=>(happy(X)<~>~kind(X))))&
(![X]:(~creative(X)<=>(~curious(X)<~>~happy(X))))&
(![X]:((patient(X)|brave(X))<=>(~creative(X)|~curious(X))))&
(![X]:((~brave(X)<~>kind(X))<=>~kind(X)))&
(![X]:((~patient(X)|wise(X))=>~generous(X)))&
(strong(mary))&
(?[X]:((creative(X)<~>~generous(X))))&
(?[X]:((old(X)|~quiet(X))))&
((generous(mary)&quiet(mary)))&
(~brave(paul))&
(~kind(alice))&
((~old(alice)<~>calm(alice)))&
(?[X]:((~strong(X)<~>strong(X)))) | ~quiet(john) | [] | null | 0 |
If someone is curious then someone is either not funny or not quiet and vice versa.
Everyone who is not quiet or not rich is either wise or not happy.
If paul is both tall and not old then someone is brave or creative.
Everyone who is both not strong and not creative is not strong or not tall and vice versa.
Everyone who is calm is not creative or old.
If someone is either not quiet or calm then fred is old or not brave.
Everyone who is either not tall or humble is either not funny or kind.
Everyone who is either not brave or not generous is either quiet or not funny.
If mary is either not kind or tall then john is both not generous and not brave and vice versa.
If paul is not strong or not brave then someone is not calm.
If mary is both funny and patient then someone is either not happy or wise.
Everyone who is either old or rich is either not brave or rich and vice versa.
If someone is either tall or not curious then someone is strong and vice versa.
If mary is not funny then someone is not quiet or creative and vice versa.
If lucy is either not kind or not strong then alice is not creative or rich.
Everyone who is brave is either patient or not generous.
Susan is not strong or humble.
Fred is not creative or brave.
John is creative.
Someone is either creative or not quiet.
Susan is tall.
Someone is either kind or not quiet.
Someone is not brave or not curious. | Lucy is kind. | neutral | ((?[X]:(curious(X)))<=>(?[X]:((~funny(X)<~>~quiet(X)))))&
(![X]:((~quiet(X)|~rich(X))=>(wise(X)<~>~happy(X))))&
(((tall(paul)&~old(paul)))=>(?[X]:((brave(X)|creative(X)))))&
(![X]:((~strong(X)&~creative(X))<=>(~strong(X)|~tall(X))))&
(![X]:(calm(X)=>(~creative(X)|old(X))))&
((?[X]:((~quiet(X)<~>calm(X))))=>((old(fred)|~brave(fred))))&
(![X]:((~tall(X)<~>humble(X))=>(~funny(X)<~>kind(X))))&
(![X]:((~brave(X)<~>~generous(X))=>(quiet(X)<~>~funny(X))))&
(((~kind(mary)<~>tall(mary)))<=>((~generous(john)&~brave(john))))&
(((~strong(paul)|~brave(paul)))=>(?[X]:(~calm(X))))&
(((funny(mary)&patient(mary)))=>(?[X]:((~happy(X)<~>wise(X)))))&
(![X]:((old(X)<~>rich(X))<=>(~brave(X)<~>rich(X))))&
((?[X]:((tall(X)<~>~curious(X))))<=>(?[X]:(strong(X))))&
((~funny(mary))<=>(?[X]:((~quiet(X)|creative(X)))))&
(((~kind(lucy)<~>~strong(lucy)))=>((~creative(alice)|rich(alice))))&
(![X]:(brave(X)=>(patient(X)<~>~generous(X))))&
((~strong(susan)|humble(susan)))&
((~creative(fred)|brave(fred)))&
(creative(john))&
(?[X]:((creative(X)<~>~quiet(X))))&
(tall(susan))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:((~brave(X)|~curious(X)))) | kind(lucy) | [] | null | 0 |
Everyone who is either not brave or happy is both calm and not calm and vice versa.
If someone is strong or not generous then alice is brave or generous.
If someone is not old or creative then paul is kind or not tall and vice versa.
Everyone who is calm is either quiet or not kind.
If lucy is both not creative and not strong then someone is rich or humble.
Everyone who is either not funny or funny is not patient or not old.
Everyone who is tall is either happy or not creative.
Everyone who is both quiet and not calm is either funny or not happy and vice versa.
If john is not rich or not patient then john is both not quiet and not brave.
Everyone who is both not patient and happy is not old and vice versa.
If john is both calm and kind then someone is old and vice versa.
Everyone who is both humble and patient is both not generous and quiet and vice versa.
Everyone who is either happy or not curious is either brave or humble.
If someone is either funny or wise then paul is either not creative or generous and vice versa.
If fred is humble then fred is both not tall and not happy.
Lucy is not kind.
Someone is both not old and tall.
Someone is not strong or not happy.
Mary is both strong and not generous.
Someone is not tall.
Susan is either creative or not creative. | Susan is not happy. | contradiction | (![X]:((~brave(X)<~>happy(X))<=>(calm(X)&~calm(X))))&
((?[X]:((strong(X)|~generous(X))))=>((brave(alice)|generous(alice))))&
((?[X]:((~old(X)|creative(X))))<=>((kind(paul)|~tall(paul))))&
(![X]:(calm(X)=>(quiet(X)<~>~kind(X))))&
(((~creative(lucy)&~strong(lucy)))=>(?[X]:((rich(X)|humble(X)))))&
(![X]:((~funny(X)<~>funny(X))=>(~patient(X)|~old(X))))&
(![X]:(tall(X)=>(happy(X)<~>~creative(X))))&
(![X]:((quiet(X)&~calm(X))<=>(funny(X)<~>~happy(X))))&
(((~rich(john)|~patient(john)))=>((~quiet(john)&~brave(john))))&
(![X]:((~patient(X)&happy(X))<=>~old(X)))&
(((calm(john)&kind(john)))<=>(?[X]:(old(X))))&
(![X]:((humble(X)&patient(X))<=>(~generous(X)&quiet(X))))&
(![X]:((happy(X)<~>~curious(X))=>(brave(X)<~>humble(X))))&
((?[X]:((funny(X)<~>wise(X))))<=>((~creative(paul)<~>generous(paul))))&
((humble(fred))=>((~tall(fred)&~happy(fred))))&
(~kind(lucy))&
(?[X]:((~old(X)&tall(X))))&
(?[X]:((~strong(X)|~happy(X))))&
((strong(mary)&~generous(mary)))&
(?[X]:(~tall(X)))&
((creative(susan)<~>~creative(susan))) | ~happy(susan) | [
"p3",
"p5",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2499134336506270042404946
% SZS output start Proof for 2499134336506270042404946
4. ! [X0] : (calm(X0) => (quiet(X0) <~> ~kind(X0))) [input p3]
6. ! [X0] : ((~funny(X0) <~> funny(X0)) => (~old(X0) | ~patient(X0))) [input p5]
9. (~patient(john) | ~rich(john)) => (~brave(john) & ~quiet(john)) [input p8]
10. ! [X0] : ((happy(X0) & ~patient(X0)) <=> ~old(X0)) [input p9]
11. (kind(john) & calm(john)) <=> ? [X0] : old(X0) [input p10]
22. ~happy(susan) [input hypothesis]
23. ~patient(john) => (~brave(john) & ~quiet(john)) [pure predicate removal 9]
27. ! [X0] : ((quiet(X0) <~> ~kind(X0)) | ~calm(X0)) [ennf transformation 4]
28. ! [X0] : ((~old(X0) | ~patient(X0)) | (~funny(X0) <=> funny(X0))) [ennf transformation 6]
29. ! [X0] : (~old(X0) | ~patient(X0) | (~funny(X0) <=> funny(X0))) [flattening 28]
31. (~brave(john) & ~quiet(john)) | patient(john) [ennf transformation 23]
41. ! [X0] : (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | ~calm(X0)) [nnf transformation 27]
42. ! [X0] : (~old(X0) | ~patient(X0) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) [nnf transformation 29]
46. ! [X0] : (((happy(X0) & ~patient(X0)) | old(X0)) & (~old(X0) | (~happy(X0) | patient(X0)))) [nnf transformation 10]
47. ! [X0] : (((happy(X0) & ~patient(X0)) | old(X0)) & (~old(X0) | ~happy(X0) | patient(X0))) [flattening 46]
48. ((kind(john) & calm(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (~kind(john) | ~calm(john))) [nnf transformation 11]
49. ((kind(john) & calm(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | ~kind(john) | ~calm(john)) [flattening 48]
50. ((kind(john) & calm(john)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | ~kind(john) | ~calm(john)) [rectify 49]
51. ? [X1] : old(X1) => old(sK1) [choice axiom]
52. ((kind(john) & calm(john)) | ! [X0] : ~old(X0)) & (old(sK1) | ~kind(john) | ~calm(john)) [skolemisation 50,51]
79. ~kind(X0) | quiet(X0) | ~calm(X0) [cnf transformation 41]
81. ~old(X0) | ~patient(X0) | funny(X0) | funny(X0) [cnf transformation 42]
82. ~old(X0) | ~patient(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 42]
91. ~quiet(john) | patient(john) [cnf transformation 31]
94. ~patient(X0) | old(X0) [cnf transformation 47]
95. old(X0) | happy(X0) [cnf transformation 47]
97. calm(john) | ~old(X0) [cnf transformation 52]
98. kind(john) | ~old(X0) [cnf transformation 52]
126. ~happy(susan) [cnf transformation 22]
127. ~old(X0) | ~patient(X0) | funny(X0) [duplicate literal removal 81]
128. ~old(X0) | ~patient(X0) | ~funny(X0) [duplicate literal removal 82]
173. ~patient(X0) | ~old(X0) [subsumption resolution 127,128]
175. 11 <=> patient(john) [avatar definition]
177. patient(john) <- (11) [avatar component clause 175]
184. 13 <=> quiet(john) [avatar definition]
187. 11 | ~13 [avatar split clause 91,184,175]
188. ~patient(X0) [subsumption resolution 94,173]
191. 14 <=> ! [X0] : ~old(X0) [avatar definition]
192. ~old(X0) <- (14) [avatar component clause 191]
194. 15 <=> kind(john) [avatar definition]
196. kind(john) <- (15) [avatar component clause 194]
197. 14 | 15 [avatar split clause 98,194,191]
199. 16 <=> calm(john) [avatar definition]
201. calm(john) <- (16) [avatar component clause 199]
202. 14 | 16 [avatar split clause 97,199,191]
265. happy(X0) <- (14) [resolution 95,192]
270. $false <- (14) [resolution 265,126]
274. ~14 [avatar contradiction clause 270]
282. quiet(john) | ~calm(john) <- (15) [resolution 79,196]
286. quiet(john) <- (15, 16) [subsumption resolution 282,201]
287. 13 | ~15 | ~16 [avatar split clause 286,199,194,184]
288. $false <- (11) [subsumption resolution 177,188]
289. ~11 [avatar contradiction clause 288]
290. $false [avatar sat refutation 187,197,202,274,287,289]
% SZS output end Proof for 2499134336506270042404946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative and not happy then alice is both kind and humble.
If mary is not kind then lucy is both not patient and not tall and vice versa.
Everyone who is not strong is not curious and vice versa.
Everyone who is not happy or not brave is both patient and not strong and vice versa.
If someone is either funny or wise then lucy is not tall or quiet.
Everyone who is not happy is both not calm and calm.
If john is not old or calm then john is both quiet and curious.
Everyone who is either not calm or not funny is not kind or not patient and vice versa.
Everyone who is both not kind and patient is both tall and rich.
If mary is not rich or not happy then someone is curious or not strong.
If mary is either not old or wise then someone is not quiet.
If lucy is not humble then john is not patient or old and vice versa.
Everyone who is not quiet or strong is not patient or not tall.
If mary is not old or wise then someone is funny.
If lucy is both not creative and not wise then alice is both quiet and curious and vice versa.
Everyone who is either not calm or not rich is strong and vice versa.
John is calm.
Alice is not brave or not curious.
Lucy is both humble and not wise.
Alice is wise.
Fred is both strong and rich.
Someone is not curious or strong.
Someone is either not curious or rich.
Someone is not old or patient. | Mary is brave. | neutral | ((?[X]:((~creative(X)&~happy(X))))=>((kind(alice)&humble(alice))))&
((~kind(mary))<=>((~patient(lucy)&~tall(lucy))))&
(![X]:(~strong(X)<=>~curious(X)))&
(![X]:((~happy(X)|~brave(X))<=>(patient(X)&~strong(X))))&
((?[X]:((funny(X)<~>wise(X))))=>((~tall(lucy)|quiet(lucy))))&
(![X]:(~happy(X)=>(~calm(X)&calm(X))))&
(((~old(john)|calm(john)))=>((quiet(john)&curious(john))))&
(![X]:((~calm(X)<~>~funny(X))<=>(~kind(X)|~patient(X))))&
(![X]:((~kind(X)&patient(X))=>(tall(X)&rich(X))))&
(((~rich(mary)|~happy(mary)))=>(?[X]:((curious(X)|~strong(X)))))&
(((~old(mary)<~>wise(mary)))=>(?[X]:(~quiet(X))))&
((~humble(lucy))<=>((~patient(john)|old(john))))&
(![X]:((~quiet(X)|strong(X))=>(~patient(X)|~tall(X))))&
(((~old(mary)|wise(mary)))=>(?[X]:(funny(X))))&
(((~creative(lucy)&~wise(lucy)))<=>((quiet(alice)&curious(alice))))&
(![X]:((~calm(X)<~>~rich(X))<=>strong(X)))&
(calm(john))&
((~brave(alice)|~curious(alice)))&
((humble(lucy)&~wise(lucy)))&
(wise(alice))&
((strong(fred)&rich(fred)))&
(?[X]:((~curious(X)|strong(X))))&
(?[X]:((~curious(X)<~>rich(X))))&
(?[X]:((~old(X)|patient(X)))) | brave(mary) | [] | null | 0 |
Everyone who is generous or happy is both rich and curious.
Everyone who is either funny or not kind is strong.
If someone is wise then lucy is calm or not wise and vice versa.
If alice is kind or quiet then susan is happy.
Everyone who is not wise is both generous and funny and vice versa.
Everyone who is not generous is both not happy and not patient.
If someone is both humble and quiet then fred is both not tall and happy.
If susan is curious or not generous then alice is both not kind and calm and vice versa.
If john is old then someone is not kind and vice versa.
Everyone who is humble or not tall is both curious and happy.
If someone is calm then mary is calm or patient and vice versa.
Everyone who is both not creative and calm is not strong or tall.
If alice is strong or not humble then someone is both wise and not wise.
Everyone who is both funny and not strong is quiet or creative.
If alice is either not quiet or not creative then someone is both not tall and strong.
Everyone who is both not kind and not creative is either not patient or not funny and vice versa.
Mary is either calm or not generous.
John is not brave or wise.
Mary is funny or quiet.
Someone is strong or rich.
Someone is either not old or quiet.
Someone is not rich.
John is either not old or not funny.
Someone is either not old or not creative. | Alice is not rich. | contradiction | (![X]:((generous(X)|happy(X))=>(rich(X)&curious(X))))&
(![X]:((funny(X)<~>~kind(X))=>strong(X)))&
((?[X]:(wise(X)))<=>((calm(lucy)|~wise(lucy))))&
(((kind(alice)|quiet(alice)))=>(happy(susan)))&
(![X]:(~wise(X)<=>(generous(X)&funny(X))))&
(![X]:(~generous(X)=>(~happy(X)&~patient(X))))&
((?[X]:((humble(X)&quiet(X))))=>((~tall(fred)&happy(fred))))&
(((curious(susan)|~generous(susan)))<=>((~kind(alice)&calm(alice))))&
((old(john))<=>(?[X]:(~kind(X))))&
(![X]:((humble(X)|~tall(X))=>(curious(X)&happy(X))))&
((?[X]:(calm(X)))<=>((calm(mary)|patient(mary))))&
(![X]:((~creative(X)&calm(X))=>(~strong(X)|tall(X))))&
(((strong(alice)|~humble(alice)))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((funny(X)&~strong(X))=>(quiet(X)|creative(X))))&
(((~quiet(alice)<~>~creative(alice)))=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((~kind(X)&~creative(X))<=>(~patient(X)<~>~funny(X))))&
((calm(mary)<~>~generous(mary)))&
((~brave(john)|wise(john)))&
((funny(mary)|quiet(mary)))&
(?[X]:((strong(X)|rich(X))))&
(?[X]:((~old(X)<~>quiet(X))))&
(?[X]:(~rich(X)))&
((~old(john)<~>~funny(john)))&
(?[X]:((~old(X)<~>~creative(X)))) | ~rich(alice) | [
"p0",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 115655233502430710659546
% SZS output start Proof for 115655233502430710659546
1. ! [X0] : ((happy(X0) | generous(X0)) => (curious(X0) & rich(X0))) [input p0]
10. ! [X0] : ((~tall(X0) | humble(X0)) => (happy(X0) & curious(X0))) [input p9]
13. (~humble(alice) | strong(alice)) => ? [X0] : (~wise(X0) & wise(X0)) [input p12]
25. ~rich(alice) [input hypothesis]
27. ! [X0] : ((curious(X0) & rich(X0)) | (~happy(X0) & ~generous(X0))) [ennf transformation 1]
32. ! [X0] : ((happy(X0) & curious(X0)) | (tall(X0) & ~humble(X0))) [ennf transformation 10]
35. ? [X0] : (~wise(X0) & wise(X0)) | (humble(alice) & ~strong(alice)) [ennf transformation 13]
58. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK3) & wise(sK3)) [choice axiom]
59. (~wise(sK3) & wise(sK3)) | (humble(alice) & ~strong(alice)) [skolemisation 35,58]
78. ~happy(X0) | rich(X0) [cnf transformation 27]
104. ~humble(X0) | happy(X0) [cnf transformation 32]
111. wise(sK3) | humble(alice) [cnf transformation 59]
113. ~wise(sK3) | humble(alice) [cnf transformation 59]
136. ~rich(alice) [cnf transformation 25]
230. 21 <=> humble(alice) [avatar definition]
232. humble(alice) <- (21) [avatar component clause 230]
234. 22 <=> wise(sK3) [avatar definition]
237. 21 | ~22 [avatar split clause 113,234,230]
243. 21 | 22 [avatar split clause 111,234,230]
333. happy(alice) <- (21) [resolution 104,232]
337. rich(alice) <- (21) [resolution 333,78]
338. $false <- (21) [subsumption resolution 337,136]
339. ~21 [avatar contradiction clause 338]
340. $false [avatar sat refutation 237,243,339]
% SZS output end Proof for 115655233502430710659546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not tall and not kind then someone is happy or old. If someone is either not rich or not calm then mary is not humble or calm. Everyone who is not generous is both tall and happy. Everyone who is quiet is either not humble or curious and vice versa. Everyone who is curious or not happy is both generous and tall and vice versa. Everyone who is either not humble or generous is old or generous and vice versa. Everyone who is happy is curious and vice versa. Everyone who is rich or happy is either brave or not humble. Everyone who is either not strong or not old is not humble and vice versa. Everyone who is either brave or quiet is curious and vice versa. If alice is quiet or kind then someone is either not quiet or wise and vice versa. If someone is both not patient and wise then susan is both brave and not brave. If paul is not quiet then fred is quiet or not wise and vice versa. If someone is either not quiet or not curious then mary is not creative and vice versa. Everyone who is brave or not humble is not kind or not strong. Everyone who is both not creative and strong is both not funny and funny. Alice is both creative and not wise. Fred is either not old or generous. Someone is both old and not brave. Fred is humble. Someone is curious or not calm. Someone is old. | Susan is tall. | entailment | (((~tall(mary)&~kind(mary)))=>(?[X]:((happy(X)|old(X)))))&
((?[X]:((~rich(X)<~>~calm(X))))=>((~humble(mary)|calm(mary))))&
(![X]:(~generous(X)=>(tall(X)&happy(X))))&
(![X]:(quiet(X)<=>(~humble(X)<~>curious(X))))&
(![X]:((curious(X)|~happy(X))<=>(generous(X)&tall(X))))&
(![X]:((~humble(X)<~>generous(X))<=>(old(X)|generous(X))))&
(![X]:(happy(X)<=>curious(X)))&
(![X]:((rich(X)|happy(X))=>(brave(X)<~>~humble(X))))&
(![X]:((~strong(X)<~>~old(X))<=>~humble(X)))&
(![X]:((brave(X)<~>quiet(X))<=>curious(X)))&
(((quiet(alice)|kind(alice)))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:((~patient(X)&wise(X))))=>((brave(susan)&~brave(susan))))&
((~quiet(paul))<=>((quiet(fred)|~wise(fred))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(~creative(mary)))&
(![X]:((brave(X)|~humble(X))=>(~kind(X)|~strong(X))))&
(![X]:((~creative(X)&strong(X))=>(~funny(X)&funny(X))))&
((creative(alice)&~wise(alice)))&
((~old(fred)<~>generous(fred)))&
(?[X]:((old(X)&~brave(X))))&
(humble(fred))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:(old(X))) | tall(susan) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 493945529453879410673847
% SZS output start Proof for 493945529453879410673847
5. ! [X0] : ((~happy(X0) | curious(X0)) <=> (tall(X0) & generous(X0))) [input p4]
7. ! [X0] : (happy(X0) <=> curious(X0)) [input p6]
23. ~tall(susan) [input hypothesis]
39. ! [X0] : (((~happy(X0) | curious(X0)) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | (happy(X0) & ~curious(X0)))) [nnf transformation 5]
40. ! [X0] : ((~happy(X0) | curious(X0) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | (happy(X0) & ~curious(X0)))) [flattening 39]
43. ! [X0] : ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0))) [nnf transformation 7]
76. ~curious(X0) | tall(X0) [cnf transformation 40]
77. happy(X0) | tall(X0) [cnf transformation 40]
85. ~happy(X0) | curious(X0) [cnf transformation 43]
125. ~tall(susan) [cnf transformation 23]
252. curious(X0) | tall(X0) [resolution 85,77]
253. tall(X0) [subsumption resolution 252,76]
254. $false [resolution 253,125]
% SZS output end Proof for 493945529453879410673847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is not happy.
If mary is either not strong or not patient then john is both humble and brave.
If someone is wise or not tall then someone is both not patient and not happy and vice versa.
If someone is either not strong or not calm then lucy is generous or rich.
If someone is not humble or tall then someone is both not quiet and not creative and vice versa.
If someone is both not creative and not funny then fred is either humble or curious.
If john is both brave and not rich then mary is both not generous and calm and vice versa.
Everyone who is either kind or generous is both generous and strong.
Everyone who is either not funny or humble is curious or not happy and vice versa.
Everyone who is both curious and funny is not old or not humble and vice versa.
Everyone who is brave or not curious is not tall and vice versa.
Everyone who is either wise or not happy is either not wise or not rich and vice versa.
Everyone who is not kind is calm or happy.
If someone is not humble then fred is either not curious or not funny.
Everyone who is both not quiet and not curious is either kind or not tall.
Everyone who is both not rich and generous is both quiet and not strong and vice versa.
Someone is either not wise or patient.
John is tall.
Fred is strong or rich.
John is not creative.
John is both not calm and not brave.
Lucy is either brave or old.
Someone is either curious or not kind.
Someone is not strong or funny. | Lucy is happy. | contradiction | (![X]:(~tall(X)=>~happy(X)))&
(((~strong(mary)<~>~patient(mary)))=>((humble(john)&brave(john))))&
((?[X]:((wise(X)|~tall(X))))<=>(?[X]:((~patient(X)&~happy(X)))))&
((?[X]:((~strong(X)<~>~calm(X))))=>((generous(lucy)|rich(lucy))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((~quiet(X)&~creative(X)))))&
((?[X]:((~creative(X)&~funny(X))))=>((humble(fred)<~>curious(fred))))&
(((brave(john)&~rich(john)))<=>((~generous(mary)&calm(mary))))&
(![X]:((kind(X)<~>generous(X))=>(generous(X)&strong(X))))&
(![X]:((~funny(X)<~>humble(X))<=>(curious(X)|~happy(X))))&
(![X]:((curious(X)&funny(X))<=>(~old(X)|~humble(X))))&
(![X]:((brave(X)|~curious(X))<=>~tall(X)))&
(![X]:((wise(X)<~>~happy(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:(~kind(X)=>(calm(X)|happy(X))))&
((?[X]:(~humble(X)))=>((~curious(fred)<~>~funny(fred))))&
(![X]:((~quiet(X)&~curious(X))=>(kind(X)<~>~tall(X))))&
(![X]:((~rich(X)&generous(X))<=>(quiet(X)&~strong(X))))&
(?[X]:((~wise(X)<~>patient(X))))&
(tall(john))&
((strong(fred)|rich(fred)))&
(~creative(john))&
((~calm(john)&~brave(john)))&
((brave(lucy)<~>old(lucy)))&
(?[X]:((curious(X)<~>~kind(X))))&
(?[X]:((~strong(X)|funny(X)))) | happy(lucy) | [
"p0",
"p8",
"p9",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7938676148068219517105587
% SZS output start Proof for 7938676148068219517105587
1. ! [X0] : (~tall(X0) => ~happy(X0)) [input p0]
9. ! [X0] : ((~funny(X0) <~> humble(X0)) <=> (~happy(X0) | curious(X0))) [input p8]
10. ! [X0] : ((funny(X0) & curious(X0)) <=> (~humble(X0) | ~old(X0))) [input p9]
11. ! [X0] : ((~curious(X0) | brave(X0)) <=> ~tall(X0)) [input p10]
22. brave(lucy) <~> old(lucy) [input p21]
25. happy(lucy) [input hypothesis]
28. ! [X0] : (~happy(X0) | tall(X0)) [ennf transformation 1]
55. ! [X0] : ((((~humble(X0) | funny(X0)) & (humble(X0) | ~funny(X0))) | (happy(X0) & ~curious(X0))) & ((~happy(X0) | curious(X0)) | ((~funny(X0) | ~humble(X0)) & (humble(X0) | funny(X0))))) [nnf transformation 9]
56. ! [X0] : ((((~humble(X0) | funny(X0)) & (humble(X0) | ~funny(X0))) | (happy(X0) & ~curious(X0))) & (~happy(X0) | curious(X0) | ((~funny(X0) | ~humble(X0)) & (humble(X0) | funny(X0))))) [flattening 55]
57. ! [X0] : (((funny(X0) & curious(X0)) | (humble(X0) & old(X0))) & ((~humble(X0) | ~old(X0)) | (~funny(X0) | ~curious(X0)))) [nnf transformation 10]
58. ! [X0] : (((funny(X0) & curious(X0)) | (humble(X0) & old(X0))) & (~humble(X0) | ~old(X0) | ~funny(X0) | ~curious(X0))) [flattening 57]
59. ! [X0] : (((~curious(X0) | brave(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) & ~brave(X0)))) [nnf transformation 11]
60. ! [X0] : ((~curious(X0) | brave(X0) | tall(X0)) & (~tall(X0) | (curious(X0) & ~brave(X0)))) [flattening 59]
69. (~old(lucy) | ~brave(lucy)) & (old(lucy) | brave(lucy)) [nnf transformation 22]
75. ~happy(X0) | tall(X0) [cnf transformation 28]
104. ~curious(X0) | ~funny(X0) | humble(X0) [cnf transformation 56]
106. ~curious(X0) | funny(X0) | ~humble(X0) [cnf transformation 56]
108. ~humble(X0) | ~old(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 58]
110. curious(X0) | humble(X0) [cnf transformation 58]
112. funny(X0) | humble(X0) [cnf transformation 58]
113. ~brave(X0) | ~tall(X0) [cnf transformation 60]
114. ~tall(X0) | curious(X0) [cnf transformation 60]
140. old(lucy) | brave(lucy) [cnf transformation 69]
145. happy(lucy) [cnf transformation 25]
238. 21 <=> ! [X3] : humble(X3) [avatar definition]
239. humble(X3) <- (21) [avatar component clause 238]
276. ~old(X0) | ~humble(X0) | ~curious(X0) [subsumption resolution 108,106]
307. 34 <=> brave(lucy) [avatar definition]
308. brave(lucy) <- (34) [avatar component clause 307]
311. 35 <=> old(lucy) [avatar definition]
312. old(lucy) <- (35) [avatar component clause 311]
315. 34 | 35 [avatar split clause 140,311,307]
337. tall(lucy) [resolution 75,145]
341. ~tall(lucy) <- (34) [resolution 113,308]
342. $false <- (34) [subsumption resolution 341,337]
343. ~34 [avatar contradiction clause 342]
345. curious(lucy) [resolution 114,337]
368. ~funny(X0) | humble(X0) | humble(X0) [resolution 104,110]
372. ~funny(X0) | humble(X0) [duplicate literal removal 368]
429. ~humble(lucy) | ~curious(lucy) <- (35) [resolution 276,312]
430. ~curious(lucy) <- (21, 35) [subsumption resolution 429,239]
431. $false <- (21, 35) [subsumption resolution 430,345]
432. ~21 | ~35 [avatar contradiction clause 431]
441. humble(X0) [subsumption resolution 372,112]
442. 21 [avatar split clause 441,238]
443. $false [avatar sat refutation 315,343,432,442]
% SZS output end Proof for 7938676148068219517105587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or curious then someone is not rich or old.
Everyone who is brave or happy is both not quiet and not humble and vice versa.
Everyone who is not rich is either tall or rich and vice versa.
Everyone who is either humble or not rich is not old and vice versa.
Everyone who is either rich or not wise is happy.
Everyone who is happy is either rich or not quiet.
Everyone who is patient is not quiet.
If someone is not rich then paul is patient or brave and vice versa.
Everyone who is either not quiet or not generous is both strong and patient and vice versa.
Everyone who is rich or not humble is both not brave and happy.
If someone is kind or quiet then someone is not brave and vice versa.
Everyone who is calm is either not tall or calm.
If someone is not humble then someone is strong or not quiet and vice versa.
Everyone who is not humble or curious is either not calm or curious and vice versa.
If lucy is either calm or not kind then someone is both not generous and humble.
Everyone who is both not creative and strong is not brave and vice versa.
Someone is patient or happy.
Someone is calm or not kind.
Paul is creative or strong.
Paul is either old or funny.
Someone is both not calm and not rich.
Someone is humble or not kind. | Lucy is not happy. | neutral | ((?[X]:((happy(X)|curious(X))))=>(?[X]:((~rich(X)|old(X)))))&
(![X]:((brave(X)|happy(X))<=>(~quiet(X)&~humble(X))))&
(![X]:(~rich(X)<=>(tall(X)<~>rich(X))))&
(![X]:((humble(X)<~>~rich(X))<=>~old(X)))&
(![X]:((rich(X)<~>~wise(X))=>happy(X)))&
(![X]:(happy(X)=>(rich(X)<~>~quiet(X))))&
(![X]:(patient(X)=>~quiet(X)))&
((?[X]:(~rich(X)))<=>((patient(paul)|brave(paul))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(strong(X)&patient(X))))&
(![X]:((rich(X)|~humble(X))=>(~brave(X)&happy(X))))&
((?[X]:((kind(X)|quiet(X))))<=>(?[X]:(~brave(X))))&
(![X]:(calm(X)=>(~tall(X)<~>calm(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((~humble(X)|curious(X))<=>(~calm(X)<~>curious(X))))&
(((calm(lucy)<~>~kind(lucy)))=>(?[X]:((~generous(X)&humble(X)))))&
(![X]:((~creative(X)&strong(X))<=>~brave(X)))&
(?[X]:((patient(X)|happy(X))))&
(?[X]:((calm(X)|~kind(X))))&
((creative(paul)|strong(paul)))&
((old(paul)<~>funny(paul)))&
(?[X]:((~calm(X)&~rich(X))))&
(?[X]:((humble(X)|~kind(X)))) | ~happy(lucy) | [] | null | 0 |
Everyone who is not patient or not kind is either kind or not patient and vice versa.
If someone is not kind or quiet then lucy is either old or not generous.
Everyone who is both not creative and not generous is creative and vice versa.
If someone is not rich then someone is either curious or not calm.
Everyone who is patient is not quiet and vice versa.
If someone is either not kind or not tall then john is either not funny or not quiet and vice versa.
Everyone who is either patient or curious is both kind and humble and vice versa.
Everyone who is either not tall or curious is creative or brave.
If someone is either not humble or not calm then fred is strong and vice versa.
If lucy is tall or not creative then someone is both not calm and generous.
If someone is either funny or not happy then someone is both tall and happy.
Everyone who is either brave or not strong is wise and vice versa.
Everyone who is not wise is old and vice versa.
Everyone who is not funny or brave is both generous and tall and vice versa.
Someone is both generous and strong.
Susan is either old or not creative.
Someone is not strong or not creative.
Someone is not humble or not happy.
Lucy is humble.
Paul is either not wise or quiet. | Susan is not tall. | contradiction | (![X]:((~patient(X)|~kind(X))<=>(kind(X)<~>~patient(X))))&
((?[X]:((~kind(X)|quiet(X))))=>((old(lucy)<~>~generous(lucy))))&
(![X]:((~creative(X)&~generous(X))<=>creative(X)))&
((?[X]:(~rich(X)))=>(?[X]:((curious(X)<~>~calm(X)))))&
(![X]:(patient(X)<=>~quiet(X)))&
((?[X]:((~kind(X)<~>~tall(X))))<=>((~funny(john)<~>~quiet(john))))&
(![X]:((patient(X)<~>curious(X))<=>(kind(X)&humble(X))))&
(![X]:((~tall(X)<~>curious(X))=>(creative(X)|brave(X))))&
((?[X]:((~humble(X)<~>~calm(X))))<=>(strong(fred)))&
(((tall(lucy)|~creative(lucy)))=>(?[X]:((~calm(X)&generous(X)))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((tall(X)&happy(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>wise(X)))&
(![X]:(~wise(X)<=>old(X)))&
(![X]:((~funny(X)|brave(X))<=>(generous(X)&tall(X))))&
(?[X]:((generous(X)&strong(X))))&
((old(susan)<~>~creative(susan)))&
(?[X]:((~strong(X)|~creative(X))))&
(?[X]:((~humble(X)|~happy(X))))&
(humble(lucy))&
((~wise(paul)<~>quiet(paul))) | ~tall(susan) | [
"p0",
"p2",
"p6",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 461602963258628453464616
% SZS output start Proof for 461602963258628453464616
1. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (kind(X0) <~> ~patient(X0))) [input p0]
3. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> creative(X0)) [input p2]
7. ! [X0] : ((patient(X0) <~> curious(X0)) <=> (humble(X0) & kind(X0))) [input p6]
8. ! [X0] : ((~tall(X0) <~> curious(X0)) => (brave(X0) | creative(X0))) [input p7]
14. ! [X0] : ((brave(X0) | ~funny(X0)) <=> (tall(X0) & generous(X0))) [input p13]
21. ~tall(susan) [input hypothesis]
26. ! [X0] : ((brave(X0) | creative(X0)) | (~tall(X0) <=> curious(X0))) [ennf transformation 8]
27. ! [X0] : (brave(X0) | creative(X0) | (~tall(X0) <=> curious(X0))) [flattening 26]
30. ! [X0] : (((~kind(X0) | ~patient(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0)))) & (((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (kind(X0) & patient(X0)))) [nnf transformation 1]
31. ! [X0] : ((~kind(X0) | ~patient(X0) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0)))) & (((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (kind(X0) & patient(X0)))) [flattening 30]
33. ! [X0] : (((~generous(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | (generous(X0) | creative(X0)))) [nnf transformation 3]
34. ! [X0] : (((~generous(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | generous(X0) | creative(X0))) [flattening 33]
40. ! [X0] : ((((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | (~humble(X0) | ~kind(X0))) & ((humble(X0) & kind(X0)) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0))))) [nnf transformation 7]
41. ! [X0] : ((((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | ~humble(X0) | ~kind(X0)) & ((humble(X0) & kind(X0)) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0))))) [flattening 40]
42. ! [X0] : (brave(X0) | creative(X0) | ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0)))) [nnf transformation 27]
55. ! [X0] : (((brave(X0) | ~funny(X0)) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | (~brave(X0) & funny(X0)))) [nnf transformation 14]
56. ! [X0] : ((brave(X0) | ~funny(X0) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | (~brave(X0) & funny(X0)))) [flattening 55]
66. ~patient(X0) | kind(X0) | kind(X0) [cnf transformation 31]
67. patient(X0) | ~kind(X0) | patient(X0) [cnf transformation 31]
69. ~kind(X0) | ~patient(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 31]
76. ~creative(X0) | ~creative(X0) [cnf transformation 34]
89. kind(X0) | patient(X0) | ~curious(X0) [cnf transformation 41]
94. brave(X0) | creative(X0) | curious(X0) | tall(X0) [cnf transformation 42]
117. tall(X0) | ~brave(X0) [cnf transformation 56]
128. ~tall(susan) [cnf transformation 21]
130. ~creative(X0) [duplicate literal removal 76]
131. ~patient(X0) | kind(X0) [duplicate literal removal 66]
132. patient(X0) | ~kind(X0) [duplicate literal removal 67]
133. ~kind(X0) | ~patient(X0) [duplicate literal removal 69]
134. ~kind(X0) [subsumption resolution 132,133]
135. ~patient(X0) [subsumption resolution 131,134]
173. patient(X0) | ~curious(X0) [subsumption resolution 89,134]
174. ~curious(X0) [subsumption resolution 173,135]
175. brave(X0) | curious(X0) | tall(X0) [subsumption resolution 94,130]
176. brave(X0) | tall(X0) [subsumption resolution 175,174]
220. tall(X0) [subsumption resolution 117,176]
232. $false [subsumption resolution 128,220]
% SZS output end Proof for 461602963258628453464616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not kind is old or tall. Everyone who is creative is either patient or wise and vice versa. Everyone who is both not quiet and not old is creative or not happy and vice versa. Everyone who is not happy is not brave and vice versa. If someone is both not old and kind then someone is not brave or not wise. If someone is both not kind and brave then someone is both calm and not rich. If someone is both humble and not calm then fred is both not quiet and not calm. If someone is not humble or brave then someone is both wise and strong and vice versa. Everyone who is not curious is both humble and calm and vice versa. Everyone who is either old or creative is both not kind and not curious and vice versa. Everyone who is strong is humble and vice versa. Everyone who is both curious and tall is curious and vice versa. Everyone who is either strong or quiet is either patient or not brave. If someone is both not quiet and not kind then susan is funny or not patient. If lucy is either patient or not happy then paul is either brave or not brave and vice versa. Everyone who is both brave and not old is kind and vice versa. Someone is either not generous or strong. Fred is not calm or old. Someone is both quiet and not humble. Someone is old or not creative. Lucy is not tall. Alice is either rich or not patient. Someone is both not wise and not kind. Someone is not wise or not generous. | Paul is wise. | neutral | (![X]:((quiet(X)|~kind(X))=>(old(X)|tall(X))))&
(![X]:(creative(X)<=>(patient(X)<~>wise(X))))&
(![X]:((~quiet(X)&~old(X))<=>(creative(X)|~happy(X))))&
(![X]:(~happy(X)<=>~brave(X)))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~brave(X)|~wise(X)))))&
((?[X]:((~kind(X)&brave(X))))=>(?[X]:((calm(X)&~rich(X)))))&
((?[X]:((humble(X)&~calm(X))))=>((~quiet(fred)&~calm(fred))))&
((?[X]:((~humble(X)|brave(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:(~curious(X)<=>(humble(X)&calm(X))))&
(![X]:((old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(![X]:(strong(X)<=>humble(X)))&
(![X]:((curious(X)&tall(X))<=>curious(X)))&
(![X]:((strong(X)<~>quiet(X))=>(patient(X)<~>~brave(X))))&
((?[X]:((~quiet(X)&~kind(X))))=>((funny(susan)|~patient(susan))))&
(((patient(lucy)<~>~happy(lucy)))<=>((brave(paul)<~>~brave(paul))))&
(![X]:((brave(X)&~old(X))<=>kind(X)))&
(?[X]:((~generous(X)<~>strong(X))))&
((~calm(fred)|old(fred)))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((old(X)|~creative(X))))&
(~tall(lucy))&
((rich(alice)<~>~patient(alice)))&
(?[X]:((~wise(X)&~kind(X))))&
(?[X]:((~wise(X)|~generous(X)))) | wise(paul) | [] | null | 0 |
Everyone who is either not quiet or not funny is either patient or not funny.
If someone is rich or humble then susan is patient and vice versa.
If someone is either brave or rich then susan is strong and vice versa.
Everyone who is not calm or not kind is old.
Everyone who is not strong or not patient is not old and vice versa.
Everyone who is brave is patient or strong.
Everyone who is not brave is curious or not funny and vice versa.
If someone is both not funny and rich then susan is patient and vice versa.
Everyone who is old is either kind or not wise and vice versa.
Everyone who is either not funny or strong is not patient.
If someone is generous or not humble then fred is either strong or old and vice versa.
Everyone who is both not happy and rich is either calm or not brave.
If john is either old or not old then someone is either kind or not curious.
If someone is not strong or not humble then someone is both not curious and rich.
If someone is either creative or kind then someone is old or not wise and vice versa.
Everyone who is either tall or happy is both patient and calm.
John is not old.
Susan is both creative and not tall.
Fred is either strong or not happy.
Someone is not brave or brave.
Alice is not brave or old.
John is either generous or funny.
Fred is either brave or not calm. | Alice is quiet. | neutral | (![X]:((~quiet(X)<~>~funny(X))=>(patient(X)<~>~funny(X))))&
((?[X]:((rich(X)|humble(X))))<=>(patient(susan)))&
((?[X]:((brave(X)<~>rich(X))))<=>(strong(susan)))&
(![X]:((~calm(X)|~kind(X))=>old(X)))&
(![X]:((~strong(X)|~patient(X))<=>~old(X)))&
(![X]:(brave(X)=>(patient(X)|strong(X))))&
(![X]:(~brave(X)<=>(curious(X)|~funny(X))))&
((?[X]:((~funny(X)&rich(X))))<=>(patient(susan)))&
(![X]:(old(X)<=>(kind(X)<~>~wise(X))))&
(![X]:((~funny(X)<~>strong(X))=>~patient(X)))&
((?[X]:((generous(X)|~humble(X))))<=>((strong(fred)<~>old(fred))))&
(![X]:((~happy(X)&rich(X))=>(calm(X)<~>~brave(X))))&
(((old(john)<~>~old(john)))=>(?[X]:((kind(X)<~>~curious(X)))))&
((?[X]:((~strong(X)|~humble(X))))=>(?[X]:((~curious(X)&rich(X)))))&
((?[X]:((creative(X)<~>kind(X))))<=>(?[X]:((old(X)|~wise(X)))))&
(![X]:((tall(X)<~>happy(X))=>(patient(X)&calm(X))))&
(~old(john))&
((creative(susan)&~tall(susan)))&
((strong(fred)<~>~happy(fred)))&
(?[X]:((~brave(X)|brave(X))))&
((~brave(alice)|old(alice)))&
((generous(john)<~>funny(john)))&
((brave(fred)<~>~calm(fred))) | quiet(alice) | [] | null | 0 |
If someone is either wise or not rich then someone is creative or not rich. If john is brave or not old then lucy is not quiet. If paul is both curious and not funny then paul is both creative and wise and vice versa. Everyone who is both not rich and not kind is humble. If susan is quiet then someone is not patient or not strong. Everyone who is not rich or generous is either happy or creative. If susan is not calm or generous then someone is not creative or not funny and vice versa. If alice is either patient or not strong then paul is not quiet and vice versa. Everyone who is either not brave or not funny is not funny or tall and vice versa. Everyone who is either humble or calm is happy or humble and vice versa. Everyone who is either curious or not rich is both quiet and kind and vice versa. Everyone who is not wise or wise is not curious or not creative. Everyone who is either not kind or kind is both not wise and tall. If someone is funny or not calm then alice is wise and vice versa. If someone is funny then paul is either humble or not humble. If susan is either not wise or not calm then susan is strong or not creative. Someone is either not quiet or happy. Someone is not calm or kind. Lucy is both generous and not humble. Mary is not curious or not funny. Someone is happy or kind. Someone is brave or not kind. | Mary is strong. | neutral | ((?[X]:((wise(X)<~>~rich(X))))=>(?[X]:((creative(X)|~rich(X)))))&
(((brave(john)|~old(john)))=>(~quiet(lucy)))&
(((curious(paul)&~funny(paul)))<=>((creative(paul)&wise(paul))))&
(![X]:((~rich(X)&~kind(X))=>humble(X)))&
((quiet(susan))=>(?[X]:((~patient(X)|~strong(X)))))&
(![X]:((~rich(X)|generous(X))=>(happy(X)<~>creative(X))))&
(((~calm(susan)|generous(susan)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(((patient(alice)<~>~strong(alice)))<=>(~quiet(paul)))&
(![X]:((~brave(X)<~>~funny(X))<=>(~funny(X)|tall(X))))&
(![X]:((humble(X)<~>calm(X))<=>(happy(X)|humble(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(quiet(X)&kind(X))))&
(![X]:((~wise(X)|wise(X))=>(~curious(X)|~creative(X))))&
(![X]:((~kind(X)<~>kind(X))=>(~wise(X)&tall(X))))&
((?[X]:((funny(X)|~calm(X))))<=>(wise(alice)))&
((?[X]:(funny(X)))=>((humble(paul)<~>~humble(paul))))&
(((~wise(susan)<~>~calm(susan)))=>((strong(susan)|~creative(susan))))&
(?[X]:((~quiet(X)<~>happy(X))))&
(?[X]:((~calm(X)|kind(X))))&
((generous(lucy)&~humble(lucy)))&
((~curious(mary)|~funny(mary)))&
(?[X]:((happy(X)|kind(X))))&
(?[X]:((brave(X)|~kind(X)))) | strong(mary) | [] | null | 0 |
Everyone who is rich or patient is both not tall and strong. If fred is not humble then someone is both happy and patient. Everyone who is both not funny and not patient is both not kind and old and vice versa. Everyone who is not humble is both funny and curious. Everyone who is not generous or funny is both not creative and not quiet. Everyone who is brave or curious is not humble or not tall and vice versa. Everyone who is not patient is old or happy. If john is strong or not brave then someone is either not happy or not strong. Everyone who is not quiet is patient. If someone is curious then alice is both creative and generous. Everyone who is not funny is both not wise and patient and vice versa. If someone is either calm or quiet then mary is curious or not creative. Everyone who is both not patient and not rich is both tall and creative. If john is not happy then someone is happy and vice versa. Alice is either not calm or brave. Someone is wise or not strong. Lucy is not wise or calm. Lucy is wise. Paul is either rich or not brave. Someone is calm. | John is tall. | contradiction | (![X]:((rich(X)|patient(X))=>(~tall(X)&strong(X))))&
((~humble(fred))=>(?[X]:((happy(X)&patient(X)))))&
(![X]:((~funny(X)&~patient(X))<=>(~kind(X)&old(X))))&
(![X]:(~humble(X)=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
((~calm(alice)<~>brave(alice)))&
(?[X]:((wise(X)|~strong(X))))&
((~wise(lucy)|calm(lucy)))&
(wise(lucy))&
((rich(paul)<~>~brave(paul)))&
(?[X]:(calm(X))) | tall(john) | [
"p0",
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7042737902982244522136155
% SZS output start Proof for 7042737902982244522136155
1. ! [X0] : ((patient(X0) | rich(X0)) => (strong(X0) & ~tall(X0))) [input p0]
5. ! [X0] : ((funny(X0) | ~generous(X0)) => (~quiet(X0) & ~creative(X0))) [input p4]
9. ! [X0] : (~quiet(X0) => patient(X0)) [input p8]
11. ! [X0] : (~funny(X0) <=> (patient(X0) & ~wise(X0))) [input p10]
21. tall(john) [input hypothesis]
23. ! [X0] : (funny(X0) => (~quiet(X0) & ~creative(X0))) [pure predicate removal 5]
24. ! [X0] : ((strong(X0) & ~tall(X0)) | (~patient(X0) & ~rich(X0))) [ennf transformation 1]
27. ! [X0] : ((~quiet(X0) & ~creative(X0)) | ~funny(X0)) [ennf transformation 23]
31. ! [X0] : (patient(X0) | quiet(X0)) [ennf transformation 9]
46. ! [X0] : ((~funny(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | funny(X0))) [nnf transformation 11]
47. ! [X0] : ((~funny(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | funny(X0))) [flattening 46]
60. ~tall(X0) | ~patient(X0) [cnf transformation 24]
72. ~quiet(X0) | ~funny(X0) [cnf transformation 27]
82. quiet(X0) | patient(X0) [cnf transformation 31]
85. patient(X0) | funny(X0) [cnf transformation 47]
101. tall(john) [cnf transformation 21]
215. ~patient(john) [resolution 60,101]
218. patient(X0) | ~funny(X0) [resolution 82,72]
219. patient(X0) [subsumption resolution 218,85]
221. $false [resolution 219,215]
% SZS output end Proof for 7042737902982244522136155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not quiet or not calm is tall or not rich and vice versa.
If mary is humble then susan is generous or creative.
If someone is either patient or quiet then john is not tall or not curious.
If paul is brave then paul is both not wise and not calm and vice versa.
Everyone who is wise is both not wise and not calm and vice versa.
If someone is not strong then someone is either wise or rich.
Everyone who is both not strong and not patient is both not calm and old.
If someone is both curious and old then john is not kind and vice versa.
Everyone who is not strong is patient and vice versa.
If someone is patient then someone is not kind or happy.
Everyone who is both kind and generous is both calm and not brave and vice versa.
If mary is either strong or brave then someone is either not humble or creative.
If someone is curious or not quiet then lucy is not calm and vice versa.
If john is brave then alice is both not kind and not brave and vice versa.
Everyone who is quiet is both not happy and not creative.
John is funny or not strong.
Mary is either not happy or curious.
Paul is not creative.
Someone is both not brave and patient.
Lucy is either calm or not brave. | John is not kind. | contradiction | (![X]:((~quiet(X)<~>~calm(X))<=>(tall(X)|~rich(X))))&
((humble(mary))=>((generous(susan)|creative(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>((~tall(john)|~curious(john))))&
((brave(paul))<=>((~wise(paul)&~calm(paul))))&
(![X]:(wise(X)<=>(~wise(X)&~calm(X))))&
((?[X]:(~strong(X)))=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((~strong(X)&~patient(X))=>(~calm(X)&old(X))))&
((?[X]:((curious(X)&old(X))))<=>(~kind(john)))&
(![X]:(~strong(X)<=>patient(X)))&
((?[X]:(patient(X)))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((kind(X)&generous(X))<=>(calm(X)&~brave(X))))&
(((strong(mary)<~>brave(mary)))=>(?[X]:((~humble(X)<~>creative(X)))))&
((?[X]:((curious(X)|~quiet(X))))<=>(~calm(lucy)))&
((brave(john))<=>((~kind(alice)&~brave(alice))))&
(![X]:(quiet(X)=>(~happy(X)&~creative(X))))&
((funny(john)|~strong(john)))&
((~happy(mary)<~>curious(mary)))&
(~creative(paul))&
(?[X]:((~brave(X)&patient(X))))&
((calm(lucy)<~>~brave(lucy))) | ~kind(john) | [
"p4",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 450450096145061703604396
% SZS output start Proof for 450450096145061703604396
5. ! [X0] : (wise(X0) <=> (~calm(X0) & ~wise(X0))) [input p4]
8. ? [X0] : (old(X0) & curious(X0)) <=> ~kind(john) [input p7]
13. ? [X0] : (~quiet(X0) | curious(X0)) <=> ~calm(lucy) [input p12]
21. ~kind(john) [input hypothesis]
40. ! [X0] : ((wise(X0) | (calm(X0) | wise(X0))) & ((~calm(X0) & ~wise(X0)) | ~wise(X0))) [nnf transformation 5]
41. ! [X0] : ((wise(X0) | calm(X0) | wise(X0)) & ((~calm(X0) & ~wise(X0)) | ~wise(X0))) [flattening 40]
46. (? [X0] : (old(X0) & curious(X0)) | kind(john)) & (~kind(john) | ! [X0] : (~old(X0) | ~curious(X0))) [nnf transformation 8]
47. (? [X0] : (old(X0) & curious(X0)) | kind(john)) & (~kind(john) | ! [X1] : (~old(X1) | ~curious(X1))) [rectify 46]
48. ? [X0] : (old(X0) & curious(X0)) => (old(sK1) & curious(sK1)) [choice axiom]
49. ((old(sK1) & curious(sK1)) | kind(john)) & (~kind(john) | ! [X1] : (~old(X1) | ~curious(X1))) [skolemisation 47,48]
59. (? [X0] : (~quiet(X0) | curious(X0)) | calm(lucy)) & (~calm(lucy) | ! [X0] : (quiet(X0) & ~curious(X0))) [nnf transformation 13]
60. (? [X0] : (~quiet(X0) | curious(X0)) | calm(lucy)) & (~calm(lucy) | ! [X1] : (quiet(X1) & ~curious(X1))) [rectify 59]
61. ? [X0] : (~quiet(X0) | curious(X0)) => (~quiet(sK4) | curious(sK4)) [choice axiom]
62. ((~quiet(sK4) | curious(sK4)) | calm(lucy)) & (~calm(lucy) | ! [X1] : (quiet(X1) & ~curious(X1))) [skolemisation 60,61]
81. ~wise(X0) | ~wise(X0) [cnf transformation 41]
83. wise(X0) | calm(X0) | wise(X0) [cnf transformation 41]
89. curious(sK1) | kind(john) [cnf transformation 49]
102. ~calm(lucy) | ~curious(X1) [cnf transformation 62]
117. ~kind(john) [cnf transformation 21]
118. ~wise(X0) [duplicate literal removal 81]
119. wise(X0) | calm(X0) [duplicate literal removal 83]
174. 13 <=> kind(john) [avatar definition]
183. 15 <=> curious(sK1) [avatar definition]
185. curious(sK1) <- (15) [avatar component clause 183]
186. 13 | 15 [avatar split clause 89,183,174]
224. 24 <=> calm(lucy) [avatar definition]
225. ~calm(lucy) <- (~24) [avatar component clause 224]
241. 28 <=> ! [X1] : ~curious(X1) [avatar definition]
242. ~curious(X1) <- (28) [avatar component clause 241]
243. 28 | ~24 [avatar split clause 102,224,241]
275. ~13 [avatar split clause 117,174]
283. calm(X1) [resolution 119,118]
284. $false <- (~24) [resolution 283,225]
285. 24 [avatar contradiction clause 284]
288. $false <- (15, 28) [resolution 242,185]
289. ~15 | ~28 [avatar contradiction clause 288]
290. $false [avatar sat refutation 186,243,275,285,289]
% SZS output end Proof for 450450096145061703604396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or strong then someone is both brave and rich and vice versa.
Everyone who is either not wise or brave is either funny or patient and vice versa.
Everyone who is humble is not patient and vice versa.
If someone is either not creative or calm then someone is both old and happy.
If someone is either happy or not calm then someone is either strong or generous.
Everyone who is either funny or brave is funny.
Everyone who is not strong is both not generous and strong.
Everyone who is generous is either funny or not strong and vice versa.
Everyone who is curious or funny is not happy or quiet and vice versa.
Everyone who is either not creative or calm is not calm and vice versa.
Everyone who is both wise and tall is curious or not patient and vice versa.
Everyone who is quiet or creative is humble or curious and vice versa.
Everyone who is both happy and curious is rich and vice versa.
If alice is either not creative or patient then someone is either not brave or calm.
Everyone who is generous is creative.
If someone is not brave then someone is either old or brave.
Someone is both old and quiet.
Someone is quiet or not happy.
Someone is either wise or not tall.
Someone is wise.
Alice is both not humble and strong.
Someone is not kind.
Alice is generous or calm. | Alice is not quiet. | entailment | ((?[X]:((happy(X)<~>strong(X))))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:((~wise(X)<~>brave(X))<=>(funny(X)<~>patient(X))))&
(![X]:(humble(X)<=>~patient(X)))&
((?[X]:((~creative(X)<~>calm(X))))=>(?[X]:((old(X)&happy(X)))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((strong(X)<~>generous(X)))))&
(![X]:((funny(X)<~>brave(X))=>funny(X)))&
(![X]:(~strong(X)=>(~generous(X)&strong(X))))&
(![X]:(generous(X)<=>(funny(X)<~>~strong(X))))&
(![X]:((curious(X)|funny(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~creative(X)<~>calm(X))<=>~calm(X)))&
(![X]:((wise(X)&tall(X))<=>(curious(X)|~patient(X))))&
(![X]:((quiet(X)|creative(X))<=>(humble(X)|curious(X))))&
(![X]:((happy(X)&curious(X))<=>rich(X)))&
(((~creative(alice)<~>patient(alice)))=>(?[X]:((~brave(X)<~>calm(X)))))&
(![X]:(generous(X)=>creative(X)))&
((?[X]:(~brave(X)))=>(?[X]:((old(X)<~>brave(X)))))&
(?[X]:((old(X)&quiet(X))))&
(?[X]:((quiet(X)|~happy(X))))&
(?[X]:((wise(X)<~>~tall(X))))&
(?[X]:(wise(X)))&
((~humble(alice)&strong(alice)))&
(?[X]:(~kind(X)))&
((generous(alice)|calm(alice))) | ~quiet(alice) | [
"p1",
"p2",
"p5",
"p6",
"p7",
"p8",
"p9",
"p10",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6154639429800561901986748
% SZS output start Proof for 6154639429800561901986748
2. ! [X0] : ((~wise(X0) <~> brave(X0)) <=> (funny(X0) <~> patient(X0))) [input p1]
3. ! [X0] : (humble(X0) <=> ~patient(X0)) [input p2]
6. ! [X0] : ((funny(X0) <~> brave(X0)) => funny(X0)) [input p5]
7. ! [X0] : (~strong(X0) => (strong(X0) & ~generous(X0))) [input p6]
8. ! [X0] : (generous(X0) <=> (funny(X0) <~> ~strong(X0))) [input p7]
9. ! [X0] : ((funny(X0) | curious(X0)) <=> (quiet(X0) | ~happy(X0))) [input p8]
10. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> ~calm(X0)) [input p9]
11. ! [X0] : ((tall(X0) & wise(X0)) <=> (~patient(X0) | curious(X0))) [input p10]
15. ! [X0] : (generous(X0) => creative(X0)) [input p14]
21. strong(alice) & ~humble(alice) [input p20]
24. quiet(alice) [input hypothesis]
32. ! [X0] : (funny(X0) | (funny(X0) <=> brave(X0))) [ennf transformation 6]
33. ! [X0] : ((strong(X0) & ~generous(X0)) | strong(X0)) [ennf transformation 7]
35. ! [X0] : (creative(X0) | ~generous(X0)) [ennf transformation 15]
42. ! [X0] : ((((~brave(X0) | wise(X0)) & (brave(X0) | ~wise(X0))) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0))))) [nnf transformation 2]
43. ! [X0] : ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0))) [nnf transformation 3]
52. ! [X0] : (funny(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) [nnf transformation 32]
53. ! [X0] : ((generous(X0) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0)))) & (((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | ~generous(X0))) [nnf transformation 8]
54. ! [X0] : (((funny(X0) | curious(X0)) | (~quiet(X0) & happy(X0))) & ((quiet(X0) | ~happy(X0)) | (~funny(X0) & ~curious(X0)))) [nnf transformation 9]
55. ! [X0] : ((funny(X0) | curious(X0) | (~quiet(X0) & happy(X0))) & (quiet(X0) | ~happy(X0) | (~funny(X0) & ~curious(X0)))) [flattening 54]
56. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | calm(X0)) & (~calm(X0) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 10]
57. ! [X0] : (((tall(X0) & wise(X0)) | (patient(X0) & ~curious(X0))) & ((~patient(X0) | curious(X0)) | (~tall(X0) | ~wise(X0)))) [nnf transformation 11]
58. ! [X0] : (((tall(X0) & wise(X0)) | (patient(X0) & ~curious(X0))) & (~patient(X0) | curious(X0) | ~tall(X0) | ~wise(X0))) [flattening 57]
90. ~patient(X0) | ~wise(X0) | funny(X0) | brave(X0) [cnf transformation 42]
94. humble(X0) | patient(X0) [cnf transformation 43]
104. funny(X0) | funny(X0) | ~brave(X0) [cnf transformation 52]
106. strong(X0) | strong(X0) [cnf transformation 33]
109. generous(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 53]
114. ~quiet(X0) | curious(X0) | funny(X0) [cnf transformation 55]
116. ~calm(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 56]
117. calm(X0) | ~creative(X0) | calm(X0) [cnf transformation 56]
120. ~curious(X0) | wise(X0) [cnf transformation 58]
135. creative(X0) | ~generous(X0) [cnf transformation 35]
144. ~humble(alice) [cnf transformation 21]
147. quiet(alice) [cnf transformation 24]
148. ~calm(X0) | ~creative(X0) [duplicate literal removal 116]
149. ~creative(X0) | calm(X0) [duplicate literal removal 117]
150. strong(X0) [duplicate literal removal 106]
151. ~brave(X0) | funny(X0) [duplicate literal removal 104]
219. ~funny(X0) | generous(X0) [subsumption resolution 109,150]
221. ~creative(X0) [subsumption resolution 148,149]
226. 16 <=> patient(alice) [avatar definition]
228. patient(alice) <- (16) [avatar component clause 226]
240. ~generous(X0) [subsumption resolution 135,221]
287. patient(alice) [resolution 94,144]
312. curious(alice) | funny(alice) [resolution 114,147]
316. 26 <=> funny(alice) [avatar definition]
317. ~funny(alice) <- (~26) [avatar component clause 316]
318. funny(alice) <- (26) [avatar component clause 316]
320. 27 <=> curious(alice) [avatar definition]
322. curious(alice) <- (27) [avatar component clause 320]
323. 26 | 27 [avatar split clause 312,320,316]
343. generous(alice) <- (26) [resolution 318,219]
344. $false <- (26) [subsumption resolution 343,240]
345. ~26 [avatar contradiction clause 344]
360. wise(alice) <- (27) [resolution 322,120]
391. ~wise(alice) | funny(alice) | brave(alice) <- (16) [resolution 90,228]
396. funny(alice) | brave(alice) <- (16, 27) [subsumption resolution 391,360]
397. brave(alice) <- (16, ~26, 27) [subsumption resolution 396,317]
398. funny(alice) <- (16, ~26, 27) [resolution 397,151]
399. $false <- (16, ~26, 27) [subsumption resolution 398,317]
400. ~16 | 26 | ~27 [avatar contradiction clause 399]
401. 16 [avatar split clause 287,226]
402. $false [avatar sat refutation 323,345,400,401]
% SZS output end Proof for 6154639429800561901986748
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not curious or curious then someone is both tall and not rich.
If susan is not rich then mary is generous or curious.
If john is both not happy and not curious then alice is not humble.
Everyone who is not humble is both patient and tall and vice versa.
Everyone who is either curious or generous is both not strong and brave and vice versa.
Everyone who is generous is either not old or curious.
Everyone who is either creative or not wise is humble and vice versa.
If someone is both quiet and kind then someone is not happy or not calm.
If mary is not kind or not rich then lucy is either kind or not brave.
Everyone who is both not rich and old is strong and vice versa.
If someone is either not humble or not quiet then someone is both old and not humble and vice versa.
Everyone who is both not curious and not humble is wise or not brave and vice versa.
Everyone who is not kind is either old or not wise and vice versa.
Everyone who is either wise or old is not calm or not generous and vice versa.
If someone is tall then paul is either not patient or not generous.
Everyone who is funny or humble is curious.
Someone is quiet or not patient.
Mary is not humble or happy.
Lucy is either creative or not generous.
Susan is either not calm or not quiet.
Someone is not humble.
Someone is not calm.
Mary is not creative. | Susan is quiet. | neutral | (((~curious(susan)|curious(susan)))=>(?[X]:((tall(X)&~rich(X)))))&
((~rich(susan))=>((generous(mary)|curious(mary))))&
(((~happy(john)&~curious(john)))=>(~humble(alice)))&
(![X]:(~humble(X)<=>(patient(X)&tall(X))))&
(![X]:((curious(X)<~>generous(X))<=>(~strong(X)&brave(X))))&
(![X]:(generous(X)=>(~old(X)<~>curious(X))))&
(![X]:((creative(X)<~>~wise(X))<=>humble(X)))&
((?[X]:((quiet(X)&kind(X))))=>(?[X]:((~happy(X)|~calm(X)))))&
(((~kind(mary)|~rich(mary)))=>((kind(lucy)<~>~brave(lucy))))&
(![X]:((~rich(X)&old(X))<=>strong(X)))&
((?[X]:((~humble(X)<~>~quiet(X))))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:((~curious(X)&~humble(X))<=>(wise(X)|~brave(X))))&
(![X]:(~kind(X)<=>(old(X)<~>~wise(X))))&
(![X]:((wise(X)<~>old(X))<=>(~calm(X)|~generous(X))))&
((?[X]:(tall(X)))=>((~patient(paul)<~>~generous(paul))))&
(![X]:((funny(X)|humble(X))=>curious(X)))&
(?[X]:((quiet(X)|~patient(X))))&
((~humble(mary)|happy(mary)))&
((creative(lucy)<~>~generous(lucy)))&
((~calm(susan)<~>~quiet(susan)))&
(?[X]:(~humble(X)))&
(?[X]:(~calm(X)))&
(~creative(mary)) | quiet(susan) | [] | null | 0 |
Everyone who is brave or wise is both not humble and humble.
If someone is humble then someone is rich or happy.
If someone is kind or quiet then fred is not kind or not funny and vice versa.
If mary is strong or not curious then someone is both curious and not old and vice versa.
If someone is either not humble or calm then mary is creative or brave and vice versa.
If someone is old or not brave then susan is either not wise or tall.
If someone is funny or not strong then someone is not wise and vice versa.
Everyone who is strong or not funny is not happy.
Everyone who is both not strong and not happy is humble or not tall and vice versa.
If paul is either not kind or brave then someone is either rich or patient.
If mary is either not patient or not creative then someone is either kind or happy and vice versa.
If alice is not happy then someone is either happy or strong and vice versa.
Everyone who is strong or old is quiet and vice versa.
Everyone who is both strong and not rich is not generous.
If someone is both not creative and not old then paul is strong and vice versa.
Everyone who is kind is strong or humble and vice versa.
John is creative.
Fred is not old or generous.
John is not quiet.
Someone is funny or not creative.
Susan is either patient or not creative.
Susan is kind.
Someone is not rich or quiet. | John is not funny. | neutral | (![X]:((brave(X)|wise(X))=>(~humble(X)&humble(X))))&
((?[X]:(humble(X)))=>(?[X]:((rich(X)|happy(X)))))&
((?[X]:((kind(X)|quiet(X))))<=>((~kind(fred)|~funny(fred))))&
(((strong(mary)|~curious(mary)))<=>(?[X]:((curious(X)&~old(X)))))&
((?[X]:((~humble(X)<~>calm(X))))<=>((creative(mary)|brave(mary))))&
((?[X]:((old(X)|~brave(X))))=>((~wise(susan)<~>tall(susan))))&
((?[X]:((funny(X)|~strong(X))))<=>(?[X]:(~wise(X))))&
(![X]:((strong(X)|~funny(X))=>~happy(X)))&
(![X]:((~strong(X)&~happy(X))<=>(humble(X)|~tall(X))))&
(((~kind(paul)<~>brave(paul)))=>(?[X]:((rich(X)<~>patient(X)))))&
(((~patient(mary)<~>~creative(mary)))<=>(?[X]:((kind(X)<~>happy(X)))))&
((~happy(alice))<=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:((strong(X)|old(X))<=>quiet(X)))&
(![X]:((strong(X)&~rich(X))=>~generous(X)))&
((?[X]:((~creative(X)&~old(X))))<=>(strong(paul)))&
(![X]:(kind(X)<=>(strong(X)|humble(X))))&
(creative(john))&
((~old(fred)|generous(fred)))&
(~quiet(john))&
(?[X]:((funny(X)|~creative(X))))&
((patient(susan)<~>~creative(susan)))&
(kind(susan))&
(?[X]:((~rich(X)|quiet(X)))) | ~funny(john) | [] | null | 0 |
Everyone who is either old or calm is quiet or not tall and vice versa.
If lucy is strong then susan is both curious and patient and vice versa.
Everyone who is either curious or not strong is either not funny or not calm and vice versa.
Everyone who is creative or wise is both brave and not generous and vice versa.
If mary is both curious and not quiet then someone is old or not strong.
If lucy is either not tall or tall then mary is either calm or strong and vice versa.
Everyone who is not old is kind.
If paul is both happy and not kind then someone is both creative and wise and vice versa.
Everyone who is quiet is not creative and vice versa.
Everyone who is strong is calm or not old and vice versa.
If someone is not kind then someone is patient and vice versa.
If someone is either calm or not kind then lucy is strong or not funny.
Everyone who is happy or not rich is either not kind or not patient and vice versa.
Everyone who is both funny and not calm is either kind or not old.
Everyone who is happy or rich is happy or tall.
Someone is not generous or not strong.
Someone is either brave or tall.
Someone is wise or not brave.
Someone is not patient or patient.
Fred is both not humble and not brave.
Susan is not old.
Someone is not strong. | Lucy is not curious. | neutral | (![X]:((old(X)<~>calm(X))<=>(quiet(X)|~tall(X))))&
((strong(lucy))<=>((curious(susan)&patient(susan))))&
(![X]:((curious(X)<~>~strong(X))<=>(~funny(X)<~>~calm(X))))&
(![X]:((creative(X)|wise(X))<=>(brave(X)&~generous(X))))&
(((curious(mary)&~quiet(mary)))=>(?[X]:((old(X)|~strong(X)))))&
(((~tall(lucy)<~>tall(lucy)))<=>((calm(mary)<~>strong(mary))))&
(![X]:(~old(X)=>kind(X)))&
(((happy(paul)&~kind(paul)))<=>(?[X]:((creative(X)&wise(X)))))&
(![X]:(quiet(X)<=>~creative(X)))&
(![X]:(strong(X)<=>(calm(X)|~old(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(patient(X))))&
((?[X]:((calm(X)<~>~kind(X))))=>((strong(lucy)|~funny(lucy))))&
(![X]:((happy(X)|~rich(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((funny(X)&~calm(X))=>(kind(X)<~>~old(X))))&
(![X]:((happy(X)|rich(X))=>(happy(X)|tall(X))))&
(?[X]:((~generous(X)|~strong(X))))&
(?[X]:((brave(X)<~>tall(X))))&
(?[X]:((wise(X)|~brave(X))))&
(?[X]:((~patient(X)|patient(X))))&
((~humble(fred)&~brave(fred)))&
(~old(susan))&
(?[X]:(~strong(X))) | ~curious(lucy) | [] | null | 0 |
If alice is both creative and not funny then someone is not patient or generous and vice versa.
Everyone who is both patient and brave is not tall or generous and vice versa.
Everyone who is not curious or patient is not wise or brave and vice versa.
Everyone who is both quiet and funny is both patient and wise and vice versa.
Everyone who is creative or wise is brave.
If alice is either tall or not generous then fred is not old or not kind.
Everyone who is both brave and quiet is either not wise or wise and vice versa.
Everyone who is brave or not rich is not calm.
Everyone who is humble or not kind is either wise or not rich.
If alice is either quiet or wise then lucy is both patient and not wise.
Everyone who is not calm or wise is not patient or tall.
If someone is either rich or not funny then mary is happy or not quiet and vice versa.
If fred is not strong or patient then someone is kind or not funny and vice versa.
If someone is creative then someone is either not wise or not humble and vice versa.
Everyone who is both patient and brave is not wise and vice versa.
If someone is tall or not old then someone is not calm.
Mary is both quiet and creative.
Someone is not funny.
Someone is both patient and curious.
Someone is funny or old.
Susan is both tall and not happy.
Paul is not rich or not funny.
Someone is kind. | Fred is not brave. | contradiction | (((creative(alice)&~funny(alice)))<=>(?[X]:((~patient(X)|generous(X)))))&
(![X]:((patient(X)&brave(X))<=>(~tall(X)|generous(X))))&
(![X]:((~curious(X)|patient(X))<=>(~wise(X)|brave(X))))&
(![X]:((quiet(X)&funny(X))<=>(patient(X)&wise(X))))&
(![X]:((creative(X)|wise(X))=>brave(X)))&
(((tall(alice)<~>~generous(alice)))=>((~old(fred)|~kind(fred))))&
(![X]:((brave(X)&quiet(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((brave(X)|~rich(X))=>~calm(X)))&
(![X]:((humble(X)|~kind(X))=>(wise(X)<~>~rich(X))))&
(((quiet(alice)<~>wise(alice)))=>((patient(lucy)&~wise(lucy))))&
(![X]:((~calm(X)|wise(X))=>(~patient(X)|tall(X))))&
((?[X]:((rich(X)<~>~funny(X))))<=>((happy(mary)|~quiet(mary))))&
(((~strong(fred)|patient(fred)))<=>(?[X]:((kind(X)|~funny(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((patient(X)&brave(X))<=>~wise(X)))&
((?[X]:((tall(X)|~old(X))))=>(?[X]:(~calm(X))))&
((quiet(mary)&creative(mary)))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)&curious(X))))&
(?[X]:((funny(X)|old(X))))&
((tall(susan)&~happy(susan)))&
((~rich(paul)|~funny(paul)))&
(?[X]:(kind(X))) | ~brave(fred) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4831729176547068315775134
% SZS output start Proof for 4831729176547068315775134
5. ! [X0] : ((wise(X0) | creative(X0)) => brave(X0)) [input p4]
7. ! [X0] : ((quiet(X0) & brave(X0)) <=> (~wise(X0) <~> wise(X0))) [input p6]
24. ~brave(fred) [input hypothesis]
27. ! [X0] : (brave(X0) | (~wise(X0) & ~creative(X0))) [ennf transformation 5]
48. ! [X0] : (((quiet(X0) & brave(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~quiet(X0) | ~brave(X0)))) [nnf transformation 7]
49. ! [X0] : (((quiet(X0) & brave(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~quiet(X0) | ~brave(X0))) [flattening 48]
99. brave(X0) | ~wise(X0) [cnf transformation 27]
104. brave(X0) | wise(X0) | wise(X0) [cnf transformation 49]
149. ~brave(fred) [cnf transformation 24]
150. brave(X0) | wise(X0) [duplicate literal removal 104]
200. brave(X0) [subsumption resolution 150,99]
315. $false [subsumption resolution 149,200]
% SZS output end Proof for 4831729176547068315775134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or not patient then someone is calm and vice versa.
If someone is either not strong or not patient then paul is both generous and rich and vice versa.
Everyone who is both not kind and tall is not calm or rich.
If someone is not humble then someone is kind or not tall.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
If paul is patient or not curious then susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Susan is not kind or curious.
Someone is old. | Lucy is not creative. | entailment | ((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:(calm(X))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>((generous(paul)&rich(paul))))&
(![X]:((~kind(X)&tall(X))=>(~calm(X)|rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
(((patient(paul)|~curious(paul)))=>((~happy(susan)|happy(susan))))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
((~kind(susan)|curious(susan)))&
(?[X]:(old(X))) | ~creative(lucy) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 410560466285005589258783
% SZS output start Proof for 410560466285005589258783
1. ? [X0] : (~humble(X0) <~> ~patient(X0)) <=> ? [X0] : calm(X0) [input p0]
2. ? [X0] : (~strong(X0) <~> ~patient(X0)) <=> (rich(paul) & generous(paul)) [input p1]
5. ! [X0] : (brave(X0) <=> (~generous(X0) <~> humble(X0))) [input p4]
6. ! [X0] : ((~calm(X0) <~> ~curious(X0)) <=> (~strong(X0) | generous(X0))) [input p5]
8. ! [X0] : ((~wise(X0) | creative(X0)) => brave(X0)) [input p7]
9. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> strong(X0)) [input p8]
12. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X0] : curious(X0) [input p11]
21. creative(lucy) [input hypothesis]
22. ? [X0] : (~humble(X0) <~> ~patient(X0)) <=> ? [X1] : calm(X1) [rectify 1]
24. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X1] : curious(X1) [rectify 12]
25. ! [X0] : (brave(X0) => (~generous(X0) <~> humble(X0))) [unused predicate definition removal 5]
28. ! [X0] : ((~generous(X0) <~> humble(X0)) | ~brave(X0)) [ennf transformation 25]
29. ! [X0] : (brave(X0) | (wise(X0) & ~creative(X0))) [ennf transformation 8]
37. (? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) [nnf transformation 22]
38. (? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : ((~humble(X3) | patient(X3)) & (~patient(X3) | humble(X3)))) [rectify 37]
39. ? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) => ((patient(sK0) | humble(sK0)) & (~patient(sK0) | ~humble(sK0))) [choice axiom]
40. ? [X2] : calm(X2) => calm(sK1) [choice axiom]
41. (((patient(sK0) | humble(sK0)) & (~patient(sK0) | ~humble(sK0))) | ! [X1] : ~calm(X1)) & (calm(sK1) | ! [X3] : ((~humble(X3) | patient(X3)) & (~patient(X3) | humble(X3)))) [skolemisation 38,40,39]
42. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (~rich(paul) | ~generous(paul))) & ((rich(paul) & generous(paul)) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 2]
43. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [flattening 42]
44. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X1] : ((~strong(X1) | patient(X1)) & (~patient(X1) | strong(X1)))) [rectify 43]
45. ? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) => ((patient(sK2) | strong(sK2)) & (~patient(sK2) | ~strong(sK2))) [choice axiom]
46. (((patient(sK2) | strong(sK2)) & (~patient(sK2) | ~strong(sK2))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X1] : ((~strong(X1) | patient(X1)) & (~patient(X1) | strong(X1)))) [skolemisation 44,45]
47. ! [X0] : (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | ~brave(X0)) [nnf transformation 28]
48. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [nnf transformation 6]
49. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [flattening 48]
52. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [nnf transformation 9]
53. ! [X0] : ((~generous(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [flattening 52]
58. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (funny(X0) | ~generous(X0))) [nnf transformation 24]
59. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (funny(X3) | ~generous(X3))) [rectify 58]
60. ? [X0] : (~funny(X0) & generous(X0)) => (~funny(sK4) & generous(sK4)) [choice axiom]
61. ? [X2] : curious(X2) => curious(sK5) [choice axiom]
62. ((~funny(sK4) & generous(sK4)) | ! [X1] : ~curious(X1)) & (curious(sK5) | ! [X3] : (funny(X3) | ~generous(X3))) [skolemisation 59,61,60]
69. calm(sK1) | ~patient(X3) | humble(X3) [cnf transformation 41]
74. generous(paul) | ~strong(X1) | patient(X1) [cnf transformation 46]
80. ~brave(X0) | generous(X0) | ~humble(X0) [cnf transformation 47]
82. ~strong(X0) | generous(X0) | ~calm(X0) | curious(X0) [cnf transformation 49]
93. ~creative(X0) | brave(X0) [cnf transformation 29]
95. strong(X0) | strong(X0) [cnf transformation 53]
97. ~generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 53]
106. generous(sK4) | ~curious(X1) [cnf transformation 62]
125. creative(lucy) [cnf transformation 21]
126. strong(X0) [duplicate literal removal 95]
127. ~generous(X0) | ~strong(X0) [duplicate literal removal 97]
147. 5 <=> calm(sK1) [avatar definition]
149. calm(sK1) <- (5) [avatar component clause 147]
152. 6 <=> ! [X3] : (~patient(X3) | humble(X3)) [avatar definition]
153. ~patient(X3) | humble(X3) <- (6) [avatar component clause 152]
154. 6 | 5 [avatar split clause 69,147,152]
156. 7 <=> generous(paul) [avatar definition]
157. generous(paul) <- (7) [avatar component clause 156]
174. 11 <=> ! [X1] : (~strong(X1) | patient(X1)) [avatar definition]
175. ~strong(X1) | patient(X1) <- (11) [avatar component clause 174]
181. 11 | 7 [avatar split clause 74,156,174]
209. 18 <=> ! [X1] : ~curious(X1) [avatar definition]
210. ~curious(X1) <- (18) [avatar component clause 209]
217. 20 <=> generous(sK4) [avatar definition]
219. generous(sK4) <- (20) [avatar component clause 217]
220. 18 | 20 [avatar split clause 106,217,209]
274. brave(lucy) [resolution 93,125]
278. ~strong(paul) <- (7) [resolution 127,157]
280. $false <- (7) [subsumption resolution 278,126]
281. ~7 [avatar contradiction clause 280]
282. patient(X1) <- (11) [subsumption resolution 175,126]
296. 34 <=> generous(lucy) [avatar definition]
297. generous(lucy) <- (34) [avatar component clause 296]
300. generous(lucy) | ~humble(lucy) [resolution 80,274]
318. generous(X0) | ~calm(X0) | curious(X0) [resolution 82,126]
319. ~calm(X0) | generous(X0) <- (18) [subsumption resolution 318,210]
320. generous(sK1) <- (5, 18) [resolution 319,149]
343. ~strong(sK1) <- (5, 18) [resolution 320,127]
344. $false <- (5, 18) [subsumption resolution 343,126]
345. ~5 | ~18 [avatar contradiction clause 344]
349. ~strong(sK4) <- (20) [resolution 219,127]
361. $false <- (20) [subsumption resolution 349,126]
362. ~20 [avatar contradiction clause 361]
363. humble(X3) <- (6, 11) [subsumption resolution 153,282]
376. generous(lucy) <- (6, 11) [subsumption resolution 300,363]
377. 34 | ~6 | ~11 [avatar split clause 376,174,152,296]
404. ~strong(lucy) <- (34) [resolution 297,127]
418. $false <- (34) [subsumption resolution 404,126]
419. ~34 [avatar contradiction clause 418]
420. $false [avatar sat refutation 154,181,220,281,345,362,377,419]
% SZS output end Proof for 410560466285005589258783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is patient and vice versa.
Everyone who is either not tall or not kind is not funny or humble.
Everyone who is rich is both wise and not curious and vice versa.
If someone is rich or tall then someone is either not creative or not tall and vice versa.
Everyone who is either happy or not patient is not happy or creative and vice versa.
If john is funny then someone is either not rich or rich and vice versa.
If fred is not brave then john is calm or wise and vice versa.
If lucy is patient or calm then paul is either quiet or calm.
If someone is not quiet or creative then alice is not humble.
Everyone who is either humble or kind is either not calm or not rich.
Everyone who is either not strong or curious is not creative and vice versa.
Everyone who is rich is either old or tall and vice versa.
Everyone who is either not happy or not quiet is not humble or funny and vice versa.
Everyone who is not curious or generous is generous or wise.
Everyone who is either creative or not quiet is not tall.
Everyone who is not quiet is either not creative or brave.
Lucy is old or not humble.
Someone is either not brave or patient.
Someone is either not humble or wise.
Someone is both not happy and not tall.
Someone is happy.
Someone is calm.
Susan is either humble or not patient.
Someone is humble. | John is not tall. | neutral | (![X]:(humble(X)<=>patient(X)))&
(![X]:((~tall(X)<~>~kind(X))=>(~funny(X)|humble(X))))&
(![X]:(rich(X)<=>(wise(X)&~curious(X))))&
((?[X]:((rich(X)|tall(X))))<=>(?[X]:((~creative(X)<~>~tall(X)))))&
(![X]:((happy(X)<~>~patient(X))<=>(~happy(X)|creative(X))))&
((funny(john))<=>(?[X]:((~rich(X)<~>rich(X)))))&
((~brave(fred))<=>((calm(john)|wise(john))))&
(((patient(lucy)|calm(lucy)))=>((quiet(paul)<~>calm(paul))))&
((?[X]:((~quiet(X)|creative(X))))=>(~humble(alice)))&
(![X]:((humble(X)<~>kind(X))=>(~calm(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>curious(X))<=>~creative(X)))&
(![X]:(rich(X)<=>(old(X)<~>tall(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(~humble(X)|funny(X))))&
(![X]:((~curious(X)|generous(X))=>(generous(X)|wise(X))))&
(![X]:((creative(X)<~>~quiet(X))=>~tall(X)))&
(![X]:(~quiet(X)=>(~creative(X)<~>brave(X))))&
((old(lucy)|~humble(lucy)))&
(?[X]:((~brave(X)<~>patient(X))))&
(?[X]:((~humble(X)<~>wise(X))))&
(?[X]:((~happy(X)&~tall(X))))&
(?[X]:(happy(X)))&
(?[X]:(calm(X)))&
((humble(susan)<~>~patient(susan)))&
(?[X]:(humble(X))) | ~tall(john) | [] | null | 0 |
If alice is not tall or funny then mary is not funny and vice versa. If someone is either not wise or not rich then susan is quiet. If someone is not quiet or tall then someone is kind or wise and vice versa. Everyone who is curious or generous is both not rich and not humble and vice versa. If someone is both not happy and happy then john is not curious or funny. Everyone who is not creative or not patient is happy or humble. Everyone who is both not curious and strong is either not humble or not quiet. If lucy is either tall or not patient then susan is strong or brave and vice versa. If someone is not tall then someone is brave or not quiet. Everyone who is generous is either humble or old. Everyone who is not rich or not generous is either curious or strong. If mary is not kind then fred is generous or not wise and vice versa. Everyone who is either not brave or calm is not calm and vice versa. If someone is patient or not creative then mary is creative. Everyone who is not creative is either curious or creative and vice versa. If someone is humble then susan is either not old or not rich and vice versa. Someone is not happy. Someone is not funny. Susan is either not creative or not generous. Someone is not old or old. Someone is both funny and not quiet. Someone is rich or not old. Someone is either funny or not funny. | Alice is not generous. | neutral | (((~tall(alice)|funny(alice)))<=>(~funny(mary)))&
((?[X]:((~wise(X)<~>~rich(X))))=>(quiet(susan)))&
((?[X]:((~quiet(X)|tall(X))))<=>(?[X]:((kind(X)|wise(X)))))&
(![X]:((curious(X)|generous(X))<=>(~rich(X)&~humble(X))))&
((?[X]:((~happy(X)&happy(X))))=>((~curious(john)|funny(john))))&
(![X]:((~creative(X)|~patient(X))=>(happy(X)|humble(X))))&
(![X]:((~curious(X)&strong(X))=>(~humble(X)<~>~quiet(X))))&
(((tall(lucy)<~>~patient(lucy)))<=>((strong(susan)|brave(susan))))&
((?[X]:(~tall(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:(generous(X)=>(humble(X)<~>old(X))))&
(![X]:((~rich(X)|~generous(X))=>(curious(X)<~>strong(X))))&
((~kind(mary))<=>((generous(fred)|~wise(fred))))&
(![X]:((~brave(X)<~>calm(X))<=>~calm(X)))&
((?[X]:((patient(X)|~creative(X))))=>(creative(mary)))&
(![X]:(~creative(X)<=>(curious(X)<~>creative(X))))&
((?[X]:(humble(X)))<=>((~old(susan)<~>~rich(susan))))&
(?[X]:(~happy(X)))&
(?[X]:(~funny(X)))&
((~creative(susan)<~>~generous(susan)))&
(?[X]:((~old(X)|old(X))))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((funny(X)<~>~funny(X)))) | ~generous(alice) | [] | null | 0 |
Everyone who is not humble is either not generous or old.
If someone is not curious then mary is both tall and not curious.
Everyone who is brave is not calm.
Everyone who is either not calm or creative is not patient or tall and vice versa.
If someone is brave then paul is either not patient or funny.
Everyone who is funny is patient or not patient and vice versa.
Everyone who is either not happy or old is either patient or not humble and vice versa.
Everyone who is old is not happy or not calm.
If someone is happy or tall then mary is both not patient and not tall.
Everyone who is curious is both not creative and rich and vice versa.
If alice is not curious then alice is both strong and creative and vice versa.
If someone is tall then lucy is kind or not creative.
Everyone who is funny or creative is either not tall or happy.
If someone is both quiet and humble then mary is either not rich or not creative.
Everyone who is not creative or not brave is either not patient or not rich and vice versa.
If susan is kind then fred is either funny or not brave and vice versa.
Someone is both not creative and not tall.
Someone is not quiet.
Someone is either not generous or brave.
John is not strong or not rich. | John is rich. | entailment | (![X]:(~humble(X)=>(~generous(X)<~>old(X))))&
((?[X]:(~curious(X)))=>((tall(mary)&~curious(mary))))&
(![X]:(brave(X)=>~calm(X)))&
(![X]:((~calm(X)<~>creative(X))<=>(~patient(X)|tall(X))))&
((?[X]:(brave(X)))=>((~patient(paul)<~>funny(paul))))&
(![X]:(funny(X)<=>(patient(X)|~patient(X))))&
(![X]:((~happy(X)<~>old(X))<=>(patient(X)<~>~humble(X))))&
(![X]:(old(X)=>(~happy(X)|~calm(X))))&
((?[X]:((happy(X)|tall(X))))=>((~patient(mary)&~tall(mary))))&
(![X]:(curious(X)<=>(~creative(X)&rich(X))))&
((~curious(alice))<=>((strong(alice)&creative(alice))))&
((?[X]:(tall(X)))=>((kind(lucy)|~creative(lucy))))&
(![X]:((funny(X)|creative(X))=>(~tall(X)<~>happy(X))))&
((?[X]:((quiet(X)&humble(X))))=>((~rich(mary)<~>~creative(mary))))&
(![X]:((~creative(X)|~brave(X))<=>(~patient(X)<~>~rich(X))))&
((kind(susan))<=>((funny(fred)<~>~brave(fred))))&
(?[X]:((~creative(X)&~tall(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)<~>brave(X))))&
((~strong(john)|~rich(john))) | rich(john) | [
"p1",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 458526702605596383344244
% SZS output start Proof for 458526702605596383344244
2. ? [X0] : ~curious(X0) => (~curious(mary) & tall(mary)) [input p1]
9. ? [X0] : (tall(X0) | happy(X0)) => (~tall(mary) & ~patient(mary)) [input p8]
10. ! [X0] : (curious(X0) <=> (rich(X0) & ~creative(X0))) [input p9]
21. ~rich(john) [input hypothesis]
25. (~curious(mary) & tall(mary)) | ! [X0] : curious(X0) [ennf transformation 2]
30. (~tall(mary) & ~patient(mary)) | ! [X0] : (~tall(X0) & ~happy(X0)) [ennf transformation 9]
41. ! [X0] : ((curious(X0) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | ~curious(X0))) [nnf transformation 10]
42. ! [X0] : ((curious(X0) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | ~curious(X0))) [flattening 41]
56. tall(mary) | curious(X0) [cnf transformation 25]
82. ~tall(mary) | ~tall(X0) [cnf transformation 30]
84. ~curious(X0) | rich(X0) [cnf transformation 42]
109. ~rich(john) [cnf transformation 21]
111. 1 <=> ! [X0] : curious(X0) [avatar definition]
112. curious(X0) <- (1) [avatar component clause 111]
119. 3 <=> tall(mary) [avatar definition]
121. tall(mary) <- (3) [avatar component clause 119]
122. 1 | 3 [avatar split clause 56,119,111]
138. 7 <=> ! [X0] : ~tall(X0) [avatar definition]
139. ~tall(X0) <- (7) [avatar component clause 138]
140. 7 | ~3 [avatar split clause 82,119,138]
203. 20 <=> rich(john) [avatar definition]
205. ~rich(john) <- (~20) [avatar component clause 203]
207. ~20 [avatar split clause 109,203]
210. $false <- (3, 7) [subsumption resolution 121,139]
211. ~3 | ~7 [avatar contradiction clause 210]
214. rich(X0) <- (1) [resolution 84,112]
216. $false <- (1, ~20) [resolution 214,205]
217. ~1 | 20 [avatar contradiction clause 216]
218. $false [avatar sat refutation 122,140,207,211,217]
% SZS output end Proof for 458526702605596383344244
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or patient then lucy is both not strong and not generous.
If someone is not patient then lucy is either wise or not patient and vice versa.
Everyone who is both not generous and humble is either not curious or quiet and vice versa.
Everyone who is both not strong and not happy is creative and vice versa.
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.
If someone is not happy or funny then someone is both not creative and brave and vice versa.
Everyone who is either tall or not tall is generous or old.
If someone is either not calm or old then john is happy or kind.
Everyone who is old or not funny is both not curious and patient.
Everyone who is not wise or brave is not funny or not brave.
John is both not rich and humble.
Someone is tall or not generous.
Susan is not tall or not generous.
Someone is quiet or not old.
Someone is both not generous and old.
Paul is either creative or not kind.
Someone is either funny or patient. | John is not rich. | entailment | ((?[X]:((wise(X)<~>patient(X))))=>((~strong(lucy)&~generous(lucy))))&
((?[X]:(~patient(X)))<=>((wise(lucy)<~>~patient(lucy))))&
(![X]:((~generous(X)&humble(X))<=>(~curious(X)<~>quiet(X))))&
(![X]:((~strong(X)&~happy(X))<=>creative(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]:((~happy(X)|funny(X))))<=>(?[X]:((~creative(X)&brave(X)))))&
(![X]:((tall(X)<~>~tall(X))=>(generous(X)|old(X))))&
((?[X]:((~calm(X)<~>old(X))))=>((happy(john)|kind(john))))&
(![X]:((old(X)|~funny(X))=>(~curious(X)&patient(X))))&
(![X]:((~wise(X)|brave(X))=>(~funny(X)|~brave(X))))&
((~rich(john)&humble(john)))&
(?[X]:((tall(X)|~generous(X))))&
((~tall(susan)|~generous(susan)))&
(?[X]:((quiet(X)|~old(X))))&
(?[X]:((~generous(X)&old(X))))&
((creative(paul)<~>~kind(paul)))&
(?[X]:((funny(X)<~>patient(X)))) | ~rich(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8986785839258379028350957
% SZS output start Proof for 8986785839258379028350957
16. humble(john) & ~rich(john) [input p15]
23. rich(john) [input hypothesis]
126. ~rich(john) [cnf transformation 16]
137. rich(john) [cnf transformation 23]
344. $false [subsumption resolution 137,126]
% SZS output end Proof for 8986785839258379028350957
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative then someone is either tall or quiet.
Everyone who is happy is either funny or patient and vice versa.
Everyone who is tall is rich.
If john is either not patient or kind then someone is not creative and vice versa.
Everyone who is patient is both not curious and strong and vice versa.
Everyone who is strong is happy and vice versa.
If paul is curious then someone is not happy.
If someone is both funny and not tall then mary is either not happy or wise and vice versa.
If john is both not funny and not calm then someone is either not rich or quiet and vice versa.
Everyone who is both old and humble is either wise or calm and vice versa.
If fred is either not strong or not humble then fred is tall or not calm and vice versa.
Everyone who is either not brave or rich is not rich or not old and vice versa.
Everyone who is humble is both rich and not creative.
Everyone who is patient is either not curious or not creative and vice versa.
If someone is either curious or not brave then someone is either not happy or not strong.
Someone is not rich.
Paul is generous or curious.
John is either tall or humble.
Fred is not brave.
Someone is tall or not tall.
Alice is not calm or funny. | John is calm. | neutral | ((?[X]:(creative(X)))=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:(happy(X)<=>(funny(X)<~>patient(X))))&
(![X]:(tall(X)=>rich(X)))&
(((~patient(john)<~>kind(john)))<=>(?[X]:(~creative(X))))&
(![X]:(patient(X)<=>(~curious(X)&strong(X))))&
(![X]:(strong(X)<=>happy(X)))&
((curious(paul))=>(?[X]:(~happy(X))))&
((?[X]:((funny(X)&~tall(X))))<=>((~happy(mary)<~>wise(mary))))&
(((~funny(john)&~calm(john)))<=>(?[X]:((~rich(X)<~>quiet(X)))))&
(![X]:((old(X)&humble(X))<=>(wise(X)<~>calm(X))))&
(((~strong(fred)<~>~humble(fred)))<=>((tall(fred)|~calm(fred))))&
(![X]:((~brave(X)<~>rich(X))<=>(~rich(X)|~old(X))))&
(![X]:(humble(X)=>(rich(X)&~creative(X))))&
(![X]:(patient(X)<=>(~curious(X)<~>~creative(X))))&
((?[X]:((curious(X)<~>~brave(X))))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(?[X]:(~rich(X)))&
((generous(paul)|curious(paul)))&
((tall(john)<~>humble(john)))&
(~brave(fred))&
(?[X]:((tall(X)|~tall(X))))&
((~calm(alice)|funny(alice))) | calm(john) | [] | null | 0 |
Everyone who is either creative or calm is either not curious or old and vice versa. Everyone who is not creative is either not happy or not wise. Everyone who is not happy or not curious is kind or humble. Everyone who is kind or not tall is not wise or patient. If paul is either not tall or tall then paul is not tall or not patient. Everyone who is both not kind and not old is either curious or not quiet and vice versa. Everyone who is both not old and not strong is either humble or strong. If someone is not tall or not funny then someone is not creative or rich and vice versa. Everyone who is not old is not patient. Everyone who is both not happy and not calm is not patient or funny. Everyone who is either not old or curious is not curious and vice versa. Everyone who is either humble or happy is strong or not calm. If someone is either generous or not patient then someone is strong. If someone is not funny or funny then mary is not tall or funny and vice versa. If john is both calm and patient then someone is curious or not rich and vice versa. Everyone who is either quiet or not tall is not wise or not strong. Alice is not quiet or old. Someone is either calm or not calm. John is humble or rich. Someone is either funny or not tall. Lucy is funny. Someone is not calm. | Alice is happy. | neutral | (![X]:((creative(X)<~>calm(X))<=>(~curious(X)<~>old(X))))&
(![X]:(~creative(X)=>(~happy(X)<~>~wise(X))))&
(![X]:((~happy(X)|~curious(X))=>(kind(X)|humble(X))))&
(![X]:((kind(X)|~tall(X))=>(~wise(X)|patient(X))))&
(((~tall(paul)<~>tall(paul)))=>((~tall(paul)|~patient(paul))))&
(![X]:((~kind(X)&~old(X))<=>(curious(X)<~>~quiet(X))))&
(![X]:((~old(X)&~strong(X))=>(humble(X)<~>strong(X))))&
((?[X]:((~tall(X)|~funny(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:(~old(X)=>~patient(X)))&
(![X]:((~happy(X)&~calm(X))=>(~patient(X)|funny(X))))&
(![X]:((~old(X)<~>curious(X))<=>~curious(X)))&
(![X]:((humble(X)<~>happy(X))=>(strong(X)|~calm(X))))&
((?[X]:((generous(X)<~>~patient(X))))=>(?[X]:(strong(X))))&
((?[X]:((~funny(X)|funny(X))))<=>((~tall(mary)|funny(mary))))&
(((calm(john)&patient(john)))<=>(?[X]:((curious(X)|~rich(X)))))&
(![X]:((quiet(X)<~>~tall(X))=>(~wise(X)|~strong(X))))&
((~quiet(alice)|old(alice)))&
(?[X]:((calm(X)<~>~calm(X))))&
((humble(john)|rich(john)))&
(?[X]:((funny(X)<~>~tall(X))))&
(funny(lucy))&
(?[X]:(~calm(X))) | happy(alice) | [] | null | 0 |
Everyone who is happy or generous is either wise or brave and vice versa.
If someone is either not happy or rich then mary is old and vice versa.
If john is both not humble and humble then someone is either not wise or curious.
Everyone who is either creative or patient is either creative or not creative.
Everyone who is both quiet and not old is both tall and wise.
If paul is rich then someone is either calm or not generous.
If mary is both not rich and generous then paul is either not kind or brave.
Everyone who is funny is both kind and rich and vice versa.
If someone is patient or creative then someone is not funny or not curious.
Everyone who is both funny and strong is either happy or not happy and vice versa.
Everyone who is patient is not curious or rich and vice versa.
If someone is either quiet or wise then someone is either brave or kind.
Everyone who is not humble or funny is either not patient or not humble and vice versa.
Everyone who is not generous is either not kind or calm.
Everyone who is both quiet and not patient is not strong or not kind and vice versa.
If alice is wise or brave then someone is tall or not generous.
Someone is either funny or wise.
Someone is not tall.
Someone is both old and curious.
Alice is old or tall.
Someone is both rich and not brave.
Lucy is kind or tall. | Alice is kind. | entailment | (![X]:((happy(X)|generous(X))<=>(wise(X)<~>brave(X))))&
((?[X]:((~happy(X)<~>rich(X))))<=>(old(mary)))&
(((~humble(john)&humble(john)))=>(?[X]:((~wise(X)<~>curious(X)))))&
(![X]:((creative(X)<~>patient(X))=>(creative(X)<~>~creative(X))))&
(![X]:((quiet(X)&~old(X))=>(tall(X)&wise(X))))&
((rich(paul))=>(?[X]:((calm(X)<~>~generous(X)))))&
(((~rich(mary)&generous(mary)))=>((~kind(paul)<~>brave(paul))))&
(![X]:(funny(X)<=>(kind(X)&rich(X))))&
((?[X]:((patient(X)|creative(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((funny(X)&strong(X))<=>(happy(X)<~>~happy(X))))&
(![X]:(patient(X)<=>(~curious(X)|rich(X))))&
((?[X]:((quiet(X)<~>wise(X))))=>(?[X]:((brave(X)<~>kind(X)))))&
(![X]:((~humble(X)|funny(X))<=>(~patient(X)<~>~humble(X))))&
(![X]:(~generous(X)=>(~kind(X)<~>calm(X))))&
(![X]:((quiet(X)&~patient(X))<=>(~strong(X)|~kind(X))))&
(((wise(alice)|brave(alice)))=>(?[X]:((tall(X)|~generous(X)))))&
(?[X]:((funny(X)<~>wise(X))))&
(?[X]:(~tall(X)))&
(?[X]:((old(X)&curious(X))))&
((old(alice)|tall(alice)))&
(?[X]:((rich(X)&~brave(X))))&
((kind(lucy)|tall(lucy))) | kind(alice) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5659882495983477615489573
% SZS output start Proof for 5659882495983477615489573
8. ! [X0] : (funny(X0) <=> (rich(X0) & kind(X0))) [input p7]
10. ! [X0] : ((strong(X0) & funny(X0)) <=> (happy(X0) <~> ~happy(X0))) [input p9]
23. ~kind(alice) [input hypothesis]
52. ! [X0] : ((funny(X0) | (~rich(X0) | ~kind(X0))) & ((rich(X0) & kind(X0)) | ~funny(X0))) [nnf transformation 8]
53. ! [X0] : ((funny(X0) | ~rich(X0) | ~kind(X0)) & ((rich(X0) & kind(X0)) | ~funny(X0))) [flattening 52]
57. ! [X0] : (((strong(X0) & funny(X0)) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | (~strong(X0) | ~funny(X0)))) [nnf transformation 10]
58. ! [X0] : (((strong(X0) & funny(X0)) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | ~strong(X0) | ~funny(X0))) [flattening 57]
103. ~funny(X0) | kind(X0) [cnf transformation 53]
110. funny(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 58]
111. funny(X0) | happy(X0) | happy(X0) [cnf transformation 58]
145. ~kind(alice) [cnf transformation 23]
148. funny(X0) | ~happy(X0) [duplicate literal removal 110]
149. funny(X0) | happy(X0) [duplicate literal removal 111]
227. funny(X0) [subsumption resolution 148,149]
288. kind(X0) [resolution 103,227]
290. $false [resolution 288,145]
% SZS output end Proof for 5659882495983477615489573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is not quiet or not generous and vice versa. If someone is either not generous or calm then susan is either generous or not tall and vice versa. If someone is not creative then paul is both curious and humble and vice versa. Everyone who is both not wise and not tall is either not rich or quiet. Everyone who is both funny and rich is either humble or tall and vice versa. Everyone who is old is both not generous and happy. Everyone who is both tall and not kind is both old and not tall and vice versa. Everyone who is either not humble or not calm is both brave and not rich and vice versa. If someone is not funny then someone is either not quiet or happy. Everyone who is not happy or not calm is strong. If someone is not old or humble then someone is both rich and not generous and vice versa. If mary is not old or not happy then fred is not brave or funny. Everyone who is curious or not patient is both old and not calm and vice versa. If alice is not happy or not old then someone is either not patient or not happy and vice versa. If someone is not generous or wise then alice is both not wise and generous and vice versa. Someone is either kind or not tall. Someone is not generous. Paul is funny or not kind. Fred is old. John is not patient. Paul is either patient or rich. | Paul is not patient. | contradiction | (![X]:(humble(X)<=>(~quiet(X)|~generous(X))))&
((?[X]:((~generous(X)<~>calm(X))))<=>((generous(susan)<~>~tall(susan))))&
((?[X]:(~creative(X)))<=>((curious(paul)&humble(paul))))&
(![X]:((~wise(X)&~tall(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((funny(X)&rich(X))<=>(humble(X)<~>tall(X))))&
(![X]:(old(X)=>(~generous(X)&happy(X))))&
(![X]:((tall(X)&~kind(X))<=>(old(X)&~tall(X))))&
(![X]:((~humble(X)<~>~calm(X))<=>(brave(X)&~rich(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((~happy(X)|~calm(X))=>strong(X)))&
((?[X]:((~old(X)|humble(X))))<=>(?[X]:((rich(X)&~generous(X)))))&
(((~old(mary)|~happy(mary)))=>((~brave(fred)|funny(fred))))&
(![X]:((curious(X)|~patient(X))<=>(old(X)&~calm(X))))&
(((~happy(alice)|~old(alice)))<=>(?[X]:((~patient(X)<~>~happy(X)))))&
((?[X]:((~generous(X)|wise(X))))<=>((~wise(alice)&generous(alice))))&
(?[X]:((kind(X)<~>~tall(X))))&
(?[X]:(~generous(X)))&
((funny(paul)|~kind(paul)))&
(old(fred))&
(~patient(john))&
((patient(paul)<~>rich(paul))) | ~patient(paul) | [
"p0",
"p4",
"p5",
"p6",
"p12",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5386017940825475768345977
% SZS output start Proof for 5386017940825475768345977
1. ! [X0] : (humble(X0) <=> (~generous(X0) | ~quiet(X0))) [input p0]
5. ! [X0] : ((rich(X0) & funny(X0)) <=> (humble(X0) <~> tall(X0))) [input p4]
6. ! [X0] : (old(X0) => (happy(X0) & ~generous(X0))) [input p5]
7. ! [X0] : ((~kind(X0) & tall(X0)) <=> (~tall(X0) & old(X0))) [input p6]
13. ! [X0] : ((~patient(X0) | curious(X0)) <=> (~calm(X0) & old(X0))) [input p12]
18. ~kind(paul) | funny(paul) [input p17]
21. patient(paul) <~> rich(paul) [input p20]
22. ~patient(paul) [input hypothesis]
28. ! [X0] : ((happy(X0) & ~generous(X0)) | ~old(X0)) [ennf transformation 6]
32. ! [X0] : ((humble(X0) | (generous(X0) & quiet(X0))) & ((~generous(X0) | ~quiet(X0)) | ~humble(X0))) [nnf transformation 1]
33. ! [X0] : ((humble(X0) | (generous(X0) & quiet(X0))) & (~generous(X0) | ~quiet(X0) | ~humble(X0))) [flattening 32]
44. ! [X0] : (((rich(X0) & funny(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (~rich(X0) | ~funny(X0)))) [nnf transformation 5]
45. ! [X0] : (((rich(X0) & funny(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ~rich(X0) | ~funny(X0))) [flattening 44]
46. ! [X0] : (((~kind(X0) & tall(X0)) | (tall(X0) | ~old(X0))) & ((~tall(X0) & old(X0)) | (kind(X0) | ~tall(X0)))) [nnf transformation 7]
47. ! [X0] : (((~kind(X0) & tall(X0)) | tall(X0) | ~old(X0)) & ((~tall(X0) & old(X0)) | kind(X0) | ~tall(X0))) [flattening 46]
59. ! [X0] : (((~patient(X0) | curious(X0)) | (calm(X0) | ~old(X0))) & ((~calm(X0) & old(X0)) | (patient(X0) & ~curious(X0)))) [nnf transformation 13]
60. ! [X0] : ((~patient(X0) | curious(X0) | calm(X0) | ~old(X0)) & ((~calm(X0) & old(X0)) | (patient(X0) & ~curious(X0)))) [flattening 59]
76. (~rich(paul) | ~patient(paul)) & (rich(paul) | patient(paul)) [nnf transformation 21]
79. generous(X0) | humble(X0) [cnf transformation 33]
94. ~funny(X0) | ~humble(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 45]
99. ~old(X0) | ~generous(X0) [cnf transformation 28]
102. ~tall(X0) | kind(X0) | ~tall(X0) [cnf transformation 47]
103. tall(X0) | tall(X0) | ~old(X0) [cnf transformation 47]
121. patient(X0) | old(X0) [cnf transformation 60]
139. ~kind(paul) | funny(paul) [cnf transformation 18]
142. rich(paul) | patient(paul) [cnf transformation 76]
144. ~patient(paul) [cnf transformation 22]
145. ~tall(X0) | kind(X0) [duplicate literal removal 102]
146. ~old(X0) | tall(X0) [duplicate literal removal 103]
182. 8 <=> humble(paul) [avatar definition]
323. 39 <=> funny(paul) [avatar definition]
325. funny(paul) <- (39) [avatar component clause 323]
327. 40 <=> kind(paul) [avatar definition]
330. 39 | ~40 [avatar split clause 139,327,323]
332. 41 <=> patient(paul) [avatar definition]
334. ~patient(paul) <- (~41) [avatar component clause 332]
336. 42 <=> rich(paul) [avatar definition]
337. rich(paul) <- (42) [avatar component clause 336]
340. 41 | 42 [avatar split clause 142,336,332]
341. ~41 [avatar split clause 144,332]
374. old(paul) <- (~41) [resolution 121,334]
461. tall(paul) <- (~41) [resolution 374,146]
463. ~generous(paul) <- (~41) [resolution 374,99]
706. kind(paul) <- (~41) [resolution 461,145]
711. 40 | 41 [avatar split clause 706,332,327]
712. ~humble(paul) | ~rich(paul) | ~tall(paul) <- (39) [resolution 325,94]
715. humble(paul) <- (~41) [resolution 463,79]
718. 8 | 41 [avatar split clause 715,332,182]
719. ~humble(paul) | ~tall(paul) <- (39, 42) [subsumption resolution 712,337]
720. ~humble(paul) <- (39, ~41, 42) [subsumption resolution 719,461]
721. ~8 | ~39 | 41 | ~42 [avatar split clause 720,336,332,323,182]
722. $false [avatar sat refutation 330,340,341,711,718,721]
% SZS output end Proof for 5386017940825475768345977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is either brave or not brave and vice versa.
Everyone who is not wise is not old or not humble and vice versa.
If someone is either not funny or not calm then someone is not tall or not kind.
Everyone who is not generous is both not kind and not funny and vice versa.
If alice is not kind or not old then someone is brave and vice versa.
Everyone who is curious is not humble or wise.
Everyone who is generous or not strong is not quiet and vice versa.
If john is either not old or old then someone is either not rich or strong.
Everyone who is not patient is both quiet and wise.
If mary is brave or wise then someone is both old and patient.
Everyone who is either not funny or kind is rich or not tall and vice versa.
If someone is either not happy or not kind then someone is either not tall or not strong and vice versa.
Everyone who is old or not tall is not old.
Everyone who is either not humble or curious is not creative or happy and vice versa.
If someone is not funny or not quiet then paul is generous and vice versa.
If someone is not kind or quiet then paul is both not brave and not tall.
Paul is both not happy and not calm.
Susan is not happy.
Paul is either not brave or kind.
Susan is either brave or rich.
Paul is generous or not rich.
John is both generous and rich.
Someone is both not humble and not strong.
Someone is either not calm or quiet. | Mary is generous. | entailment | (![X]:(~creative(X)<=>(brave(X)<~>~brave(X))))&
(![X]:(~wise(X)<=>(~old(X)|~humble(X))))&
((?[X]:((~funny(X)<~>~calm(X))))=>(?[X]:((~tall(X)|~kind(X)))))&
(![X]:(~generous(X)<=>(~kind(X)&~funny(X))))&
(((~kind(alice)|~old(alice)))<=>(?[X]:(brave(X))))&
(![X]:(curious(X)=>(~humble(X)|wise(X))))&
(![X]:((generous(X)|~strong(X))<=>~quiet(X)))&
(((~old(john)<~>old(john)))=>(?[X]:((~rich(X)<~>strong(X)))))&
(![X]:(~patient(X)=>(quiet(X)&wise(X))))&
(((brave(mary)|wise(mary)))=>(?[X]:((old(X)&patient(X)))))&
(![X]:((~funny(X)<~>kind(X))<=>(rich(X)|~tall(X))))&
((?[X]:((~happy(X)<~>~kind(X))))<=>(?[X]:((~tall(X)<~>~strong(X)))))&
(![X]:((old(X)|~tall(X))=>~old(X)))&
(![X]:((~humble(X)<~>curious(X))<=>(~creative(X)|happy(X))))&
((?[X]:((~funny(X)|~quiet(X))))<=>(generous(paul)))&
((?[X]:((~kind(X)|quiet(X))))=>((~brave(paul)&~tall(paul))))&
((~happy(paul)&~calm(paul)))&
(~happy(susan))&
((~brave(paul)<~>kind(paul)))&
((brave(susan)<~>rich(susan)))&
((generous(paul)|~rich(paul)))&
((generous(john)&rich(john)))&
(?[X]:((~humble(X)&~strong(X))))&
(?[X]:((~calm(X)<~>quiet(X)))) | generous(mary) | [
"p3",
"p10",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3986843297099412670955737
% SZS output start Proof for 3986843297099412670955737
4. ! [X0] : (~generous(X0) <=> (~funny(X0) & ~kind(X0))) [input p3]
11. ! [X0] : ((~funny(X0) <~> kind(X0)) <=> (~tall(X0) | rich(X0))) [input p10]
15. ? [X0] : (~quiet(X0) | ~funny(X0)) <=> generous(paul) [input p14]
16. ? [X0] : (quiet(X0) | ~kind(X0)) => (~tall(paul) & ~brave(paul)) [input p15]
19. ~brave(paul) <~> kind(paul) [input p18]
25. ~generous(mary) [input hypothesis]
36. (~tall(paul) & ~brave(paul)) | ! [X0] : (~quiet(X0) & kind(X0)) [ennf transformation 16]
44. ! [X0] : ((~generous(X0) | (funny(X0) | kind(X0))) & ((~funny(X0) & ~kind(X0)) | generous(X0))) [nnf transformation 4]
45. ! [X0] : ((~generous(X0) | funny(X0) | kind(X0)) & ((~funny(X0) & ~kind(X0)) | generous(X0))) [flattening 44]
58. ! [X0] : ((((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))))) [nnf transformation 11]
59. ! [X0] : ((((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))))) [flattening 58]
67. (? [X0] : (~quiet(X0) | ~funny(X0)) | ~generous(paul)) & (generous(paul) | ! [X0] : (quiet(X0) & funny(X0))) [nnf transformation 15]
68. (? [X0] : (~quiet(X0) | ~funny(X0)) | ~generous(paul)) & (generous(paul) | ! [X1] : (quiet(X1) & funny(X1))) [rectify 67]
69. ? [X0] : (~quiet(X0) | ~funny(X0)) => (~quiet(sK6) | ~funny(sK6)) [choice axiom]
70. ((~quiet(sK6) | ~funny(sK6)) | ~generous(paul)) & (generous(paul) | ! [X1] : (quiet(X1) & funny(X1))) [skolemisation 68,69]
71. (~kind(paul) | brave(paul)) & (kind(paul) | ~brave(paul)) [nnf transformation 19]
87. ~kind(X0) | generous(X0) [cnf transformation 45]
88. ~funny(X0) | generous(X0) [cnf transformation 45]
89. ~generous(X0) | funny(X0) | kind(X0) [cnf transformation 45]
106. ~funny(X0) | kind(X0) | tall(X0) [cnf transformation 59]
125. generous(paul) | funny(X1) [cnf transformation 70]
128. ~brave(paul) | kind(X0) [cnf transformation 36]
130. ~tall(paul) | kind(X0) [cnf transformation 36]
136. ~kind(paul) | brave(paul) [cnf transformation 71]
146. ~generous(mary) [cnf transformation 25]
258. 23 <=> generous(paul) [avatar definition]
259. generous(paul) <- (23) [avatar component clause 258]
275. 27 <=> ! [X1] : funny(X1) [avatar definition]
276. funny(X1) <- (27) [avatar component clause 275]
277. 27 | 23 [avatar split clause 125,258,275]
282. 29 <=> tall(paul) [avatar definition]
284. ~tall(paul) <- (~29) [avatar component clause 282]
287. 30 <=> ! [X0] : kind(X0) [avatar definition]
288. kind(X0) <- (30) [avatar component clause 287]
289. 30 | ~29 [avatar split clause 130,282,287]
291. 31 <=> brave(paul) [avatar definition]
295. 30 | ~31 [avatar split clause 128,291,287]
297. 32 <=> kind(paul) [avatar definition]
299. ~kind(paul) <- (~32) [avatar component clause 297]
300. 31 | ~32 [avatar split clause 136,297,291]
333. funny(paul) | kind(paul) <- (23) [resolution 89,259]
344. funny(paul) <- (23, ~32) [subsumption resolution 333,299]
348. kind(paul) | tall(paul) <- (23, ~32) [resolution 106,344]
349. tall(paul) <- (23, ~32) [subsumption resolution 348,299]
350. $false <- (23, ~29, ~32) [subsumption resolution 349,284]
351. ~23 | 29 | 32 [avatar contradiction clause 350]
359. generous(X1) <- (27) [resolution 276,88]
363. generous(X0) <- (30) [resolution 288,87]
367. $false <- (27) [resolution 359,146]
369. ~27 [avatar contradiction clause 367]
388. $false <- (30) [resolution 363,146]
390. ~30 [avatar contradiction clause 388]
391. $false [avatar sat refutation 277,289,295,300,351,369,390]
% SZS output end Proof for 3986843297099412670955737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
Everyone who is old or not quiet is both curious and not brave.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
If alice is curious then someone is either not humble or not creative and vice versa.
Everyone who is both creative and not creative is both not strong and strong.
Everyone who is both not strong and generous is quiet and vice versa.
Everyone who is both kind and not old is either not strong or not funny and vice versa.
If john is either kind or quiet then paul is either kind or tall.
Everyone who is both not brave and happy is both tall and wise.
Everyone who is either old or tall is old and vice versa.
Everyone who is not humble or tall is not wise.
Someone is kind or not happy.
Someone is not kind.
Lucy is either calm or happy.
Paul is not funny or generous.
Someone is generous. | Lucy is brave. | contradiction | ((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((curious(alice))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:((creative(X)&~creative(X))=>(~strong(X)&strong(X))))&
(![X]:((~strong(X)&generous(X))<=>quiet(X)))&
(![X]:((kind(X)&~old(X))<=>(~strong(X)<~>~funny(X))))&
(((kind(john)<~>quiet(john)))=>((kind(paul)<~>tall(paul))))&
(![X]:((~brave(X)&happy(X))=>(tall(X)&wise(X))))&
(![X]:((old(X)<~>tall(X))<=>old(X)))&
(![X]:((~humble(X)|tall(X))=>~wise(X)))&
(?[X]:((kind(X)|~happy(X))))&
(?[X]:(~kind(X)))&
((calm(lucy)<~>happy(lucy)))&
((~funny(paul)|generous(paul)))&
(?[X]:(generous(X))) | brave(lucy) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 849216766282562661835907
% SZS output start Proof for 849216766282562661835907
2. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p1]
4. ! [X0] : ((~quiet(X0) | old(X0)) => (~brave(X0) & curious(X0))) [input p3]
22. brave(lucy) [input hypothesis]
26. ! [X0] : ((~brave(X0) & curious(X0)) | (quiet(X0) & ~old(X0))) [ennf transformation 4]
41. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 2]
42. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 41]
70. ~patient(X0) | ~patient(X0) [cnf transformation 42]
72. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 42]
77. ~brave(X0) | quiet(X0) [cnf transformation 26]
123. brave(lucy) [cnf transformation 22]
126. ~patient(X0) [duplicate literal removal 70]
127. ~quiet(X0) | patient(X0) [duplicate literal removal 72]
251. quiet(lucy) [resolution 77,123]
253. patient(lucy) [resolution 127,251]
256. $false [subsumption resolution 253,126]
% SZS output end Proof for 849216766282562661835907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is old or creative. If mary is both generous and not rich then fred is both not curious and not generous and vice versa. Everyone who is not tall is either not strong or rich and vice versa. Everyone who is both not curious and quiet is either not calm or happy. Everyone who is funny or not kind is either strong or humble. If lucy is not creative then someone is not humble or not brave and vice versa. If lucy is wise then someone is rich or patient and vice versa. Everyone who is kind is both strong and tall. Everyone who is strong or not humble is not quiet or not generous and vice versa. If susan is both happy and not generous then someone is not humble or patient and vice versa. Everyone who is not tall is both happy and not wise. If lucy is quiet then alice is not happy. If someone is kind then fred is both not calm and brave and vice versa. If paul is both not funny and tall then susan is both not patient and not funny and vice versa. If someone is both curious and calm then someone is not creative or not curious and vice versa. Everyone who is either quiet or not calm is curious or not creative. John is both calm and brave. Paul is both kind and not wise. Someone is both not creative and not curious. John is both wise and quiet. Someone is not kind or not tall. Someone is both not strong and not tall. Paul is either quiet or not quiet. Mary is both not tall and funny. | Lucy is not kind. | neutral | (![X]:(strong(X)=>(old(X)|creative(X))))&
(((generous(mary)&~rich(mary)))<=>((~curious(fred)&~generous(fred))))&
(![X]:(~tall(X)<=>(~strong(X)<~>rich(X))))&
(![X]:((~curious(X)&quiet(X))=>(~calm(X)<~>happy(X))))&
(![X]:((funny(X)|~kind(X))=>(strong(X)<~>humble(X))))&
((~creative(lucy))<=>(?[X]:((~humble(X)|~brave(X)))))&
((wise(lucy))<=>(?[X]:((rich(X)|patient(X)))))&
(![X]:(kind(X)=>(strong(X)&tall(X))))&
(![X]:((strong(X)|~humble(X))<=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~generous(susan)))<=>(?[X]:((~humble(X)|patient(X)))))&
(![X]:(~tall(X)=>(happy(X)&~wise(X))))&
((quiet(lucy))=>(~happy(alice)))&
((?[X]:(kind(X)))<=>((~calm(fred)&brave(fred))))&
(((~funny(paul)&tall(paul)))<=>((~patient(susan)&~funny(susan))))&
((?[X]:((curious(X)&calm(X))))<=>(?[X]:((~creative(X)|~curious(X)))))&
(![X]:((quiet(X)<~>~calm(X))=>(curious(X)|~creative(X))))&
((calm(john)&brave(john)))&
((kind(paul)&~wise(paul)))&
(?[X]:((~creative(X)&~curious(X))))&
((wise(john)&quiet(john)))&
(?[X]:((~kind(X)|~tall(X))))&
(?[X]:((~strong(X)&~tall(X))))&
((quiet(paul)<~>~quiet(paul)))&
((~tall(mary)&funny(mary))) | ~kind(lucy) | [] | null | 0 |
Everyone who is either not happy or not tall is quiet or not patient and vice versa.
If alice is happy or strong then someone is both not rich and not humble.
If someone is either wise or tall then someone is either old or not happy.
Everyone who is either not happy or not quiet is both curious and calm and vice versa.
If someone is strong or not old then someone is not creative or not brave and vice versa.
If someone is generous then lucy is either curious or creative.
Everyone who is both not kind and not tall is not calm or old and vice versa.
If lucy is both generous and not rich then someone is both generous and happy and vice versa.
Everyone who is both not kind and not wise is not generous.
Everyone who is both not tall and calm is either not patient or not calm and vice versa.
Everyone who is either kind or not old is either curious or tall.
Everyone who is either rich or curious is not kind or not patient and vice versa.
Everyone who is not kind or not brave is not kind or funny and vice versa.
If alice is generous then someone is tall.
If susan is either not quiet or not brave then susan is both not kind and calm and vice versa.
Everyone who is kind is both patient and not rich.
Susan is either calm or not calm.
Paul is both not old and not tall.
John is both not funny and not generous.
Susan is funny.
Someone is both old and not tall.
Someone is either not strong or not tall.
Someone is both old and funny. | Susan is patient. | contradiction | (![X]:((~happy(X)<~>~tall(X))<=>(quiet(X)|~patient(X))))&
(((happy(alice)|strong(alice)))=>(?[X]:((~rich(X)&~humble(X)))))&
((?[X]:((wise(X)<~>tall(X))))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(curious(X)&calm(X))))&
((?[X]:((strong(X)|~old(X))))<=>(?[X]:((~creative(X)|~brave(X)))))&
((?[X]:(generous(X)))=>((curious(lucy)<~>creative(lucy))))&
(![X]:((~kind(X)&~tall(X))<=>(~calm(X)|old(X))))&
(((generous(lucy)&~rich(lucy)))<=>(?[X]:((generous(X)&happy(X)))))&
(![X]:((~kind(X)&~wise(X))=>~generous(X)))&
(![X]:((~tall(X)&calm(X))<=>(~patient(X)<~>~calm(X))))&
(![X]:((kind(X)<~>~old(X))=>(curious(X)<~>tall(X))))&
(![X]:((rich(X)<~>curious(X))<=>(~kind(X)|~patient(X))))&
(![X]:((~kind(X)|~brave(X))<=>(~kind(X)|funny(X))))&
((generous(alice))=>(?[X]:(tall(X))))&
(((~quiet(susan)<~>~brave(susan)))<=>((~kind(susan)&calm(susan))))&
(![X]:(kind(X)=>(patient(X)&~rich(X))))&
((calm(susan)<~>~calm(susan)))&
((~old(paul)&~tall(paul)))&
((~funny(john)&~generous(john)))&
(funny(susan))&
(?[X]:((old(X)&~tall(X))))&
(?[X]:((~strong(X)<~>~tall(X))))&
(?[X]:((old(X)&funny(X)))) | patient(susan) | [
"p0",
"p3",
"p6",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1949424874795949851526970
% SZS output start Proof for 1949424874795949851526970
1. ! [X0] : ((~happy(X0) <~> ~tall(X0)) <=> (~patient(X0) | quiet(X0))) [input p0]
4. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) <=> (calm(X0) & curious(X0))) [input p3]
7. ! [X0] : ((~tall(X0) & ~kind(X0)) <=> (old(X0) | ~calm(X0))) [input p6]
10. ! [X0] : ((calm(X0) & ~tall(X0)) <=> (~patient(X0) <~> ~calm(X0))) [input p9]
11. ! [X0] : ((kind(X0) <~> ~old(X0)) => (curious(X0) <~> tall(X0))) [input p10]
12. ! [X0] : ((rich(X0) <~> curious(X0)) <=> (~patient(X0) | ~kind(X0))) [input p11]
16. ! [X0] : (kind(X0) => (~rich(X0) & patient(X0))) [input p15]
24. patient(susan) [input hypothesis]
33. ! [X0] : ((curious(X0) <~> tall(X0)) | (kind(X0) <=> ~old(X0))) [ennf transformation 11]
35. ! [X0] : ((~rich(X0) & patient(X0)) | ~kind(X0)) [ennf transformation 16]
36. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (patient(X0) & ~quiet(X0))) & ((~patient(X0) | quiet(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [nnf transformation 1]
37. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (patient(X0) & ~quiet(X0))) & (~patient(X0) | quiet(X0) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [flattening 36]
44. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (~calm(X0) | ~curious(X0))) & ((calm(X0) & curious(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [nnf transformation 4]
45. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | ~calm(X0) | ~curious(X0)) & ((calm(X0) & curious(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [flattening 44]
52. ! [X0] : (((~tall(X0) & ~kind(X0)) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | (tall(X0) | kind(X0)))) [nnf transformation 7]
53. ! [X0] : (((~tall(X0) & ~kind(X0)) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | tall(X0) | kind(X0))) [flattening 52]
59. ! [X0] : (((calm(X0) & ~tall(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~calm(X0) | tall(X0)))) [nnf transformation 10]
60. ! [X0] : (((calm(X0) & ~tall(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ~calm(X0) | tall(X0))) [flattening 59]
61. ! [X0] : (((~tall(X0) | ~curious(X0)) & (tall(X0) | curious(X0))) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) [nnf transformation 33]
62. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (patient(X0) & kind(X0))) & ((~patient(X0) | ~kind(X0)) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [nnf transformation 12]
63. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (patient(X0) & kind(X0))) & (~patient(X0) | ~kind(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [flattening 62]
78. ~patient(X0) | quiet(X0) | ~tall(X0) | happy(X0) [cnf transformation 37]
80. ~quiet(X0) | ~happy(X0) | ~tall(X0) [cnf transformation 37]
83. patient(X0) | happy(X0) | tall(X0) [cnf transformation 37]
90. ~quiet(X0) | curious(X0) | happy(X0) [cnf transformation 45]
91. ~happy(X0) | curious(X0) | quiet(X0) [cnf transformation 45]
105. ~tall(X0) | calm(X0) [cnf transformation 53]
106. ~old(X0) | ~tall(X0) [cnf transformation 53]
112. ~calm(X0) | ~patient(X0) | ~calm(X0) | tall(X0) [cnf transformation 60]
114. ~tall(X0) | ~calm(X0) | patient(X0) [cnf transformation 60]
117. calm(X0) | ~patient(X0) | calm(X0) [cnf transformation 60]
121. ~tall(X0) | ~curious(X0) | kind(X0) | old(X0) [cnf transformation 61]
123. ~kind(X0) | ~patient(X0) | rich(X0) | ~curious(X0) [cnf transformation 63]
140. ~kind(X0) | ~rich(X0) [cnf transformation 35]
154. patient(susan) [cnf transformation 24]
155. ~calm(X0) | ~patient(X0) | tall(X0) [duplicate literal removal 112]
156. ~patient(X0) | calm(X0) [duplicate literal removal 117]
257. ~tall(X0) | patient(X0) [subsumption resolution 114,105]
258. ~patient(X0) | tall(X0) [subsumption resolution 155,156]
259. ~curious(X0) | ~tall(X0) | kind(X0) [subsumption resolution 121,106]
270. 26 <=> kind(susan) [avatar definition]
271. ~kind(susan) <- (~26) [avatar component clause 270]
272. kind(susan) <- (26) [avatar component clause 270]
278. 28 <=> quiet(susan) [avatar definition]
279. ~quiet(susan) <- (~28) [avatar component clause 278]
280. quiet(susan) <- (28) [avatar component clause 278]
307. ~rich(susan) <- (26) [resolution 272,140]
311. tall(susan) [resolution 258,154]
315. happy(X0) | tall(X0) | tall(X0) [resolution 83,258]
317. tall(X0) | happy(X0) [duplicate literal removal 315]
319. patient(X1) | happy(X1) [resolution 317,257]
426. quiet(susan) | ~tall(susan) | happy(susan) [resolution 78,154]
427. quiet(X0) | ~tall(X0) | happy(X0) | happy(X0) [resolution 78,319]
430. quiet(X0) | ~tall(X0) | happy(X0) [duplicate literal removal 427]
431. ~tall(susan) | happy(susan) <- (~28) [subsumption resolution 426,279]
432. happy(susan) <- (~28) [subsumption resolution 431,311]
433. quiet(X0) | happy(X0) [subsumption resolution 430,317]
435. curious(susan) | quiet(susan) <- (~28) [resolution 432,91]
436. curious(susan) <- (~28) [subsumption resolution 435,279]
451. happy(X1) | curious(X1) | happy(X1) [resolution 433,90]
455. curious(X1) | happy(X1) [duplicate literal removal 451]
459. happy(X0) | ~tall(X0) | kind(X0) [resolution 455,259]
462. kind(X0) | happy(X0) [subsumption resolution 459,317]
471. ~rich(X1) | happy(X1) [resolution 462,140]
481. ~patient(susan) | rich(susan) | ~curious(susan) <- (26) [resolution 123,272]
482. ~patient(X0) | rich(X0) | ~curious(X0) | happy(X0) [resolution 123,462]
486. rich(susan) | ~curious(susan) <- (26) [subsumption resolution 481,154]
487. ~curious(susan) <- (26) [subsumption resolution 486,307]
488. $false <- (26, ~28) [subsumption resolution 487,436]
489. ~26 | 28 [avatar contradiction clause 488]
490. rich(X0) | ~curious(X0) | happy(X0) [subsumption resolution 482,319]
491. ~curious(X0) | happy(X0) [subsumption resolution 490,471]
492. happy(X0) [subsumption resolution 491,455]
495. 44 <=> curious(susan) [avatar definition]
496. curious(susan) <- (44) [avatar component clause 495]
497. ~curious(susan) <- (~44) [avatar component clause 495]
506. ~happy(susan) | ~tall(susan) <- (28) [resolution 280,80]
507. ~tall(susan) <- (28) [subsumption resolution 506,492]
508. $false <- (28) [subsumption resolution 507,311]
509. ~28 [avatar contradiction clause 508]
516. curious(X1) | quiet(X1) [resolution 492,91]
627. quiet(susan) <- (~44) [resolution 516,497]
629. $false <- (~28, ~44) [subsumption resolution 627,279]
630. 28 | 44 [avatar contradiction clause 629]
636. ~tall(susan) | kind(susan) <- (44) [resolution 496,259]
639. kind(susan) <- (44) [subsumption resolution 636,311]
640. $false <- (~26, 44) [subsumption resolution 639,271]
641. 26 | ~44 [avatar contradiction clause 640]
644. $false [avatar sat refutation 489,509,630,641]
% SZS output end Proof for 1949424874795949851526970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both generous and happy then mary is not curious.
If lucy is creative or not old then alice is patient.
If susan is wise then mary is both wise and brave.
If someone is both not wise and creative then mary is kind and vice versa.
Everyone who is not rich is not patient.
Everyone who is not happy or not curious is both tall and not curious and vice versa.
Everyone who is rich or not quiet is both happy and not happy and vice versa.
Everyone who is both not tall and not curious is either not generous or patient.
If susan is not old or not patient then someone is both brave and funny and vice versa.
Everyone who is strong is both calm and quiet.
Everyone who is not patient or not strong is not happy or happy.
If paul is both patient and old then paul is either not funny or quiet and vice versa.
Everyone who is not curious is rich or funny.
If lucy is patient then someone is both rich and funny.
Everyone who is either curious or brave is both not rich and not happy and vice versa.
Everyone who is curious is not humble.
Lucy is either kind or patient.
Someone is both happy and not rich.
Fred is kind.
Someone is kind or not wise.
Someone is either patient or brave.
Lucy is not tall or happy. | Susan is not rich. | entailment | ((?[X]:((generous(X)&happy(X))))=>(~curious(mary)))&
(((creative(lucy)|~old(lucy)))=>(patient(alice)))&
((wise(susan))=>((wise(mary)&brave(mary))))&
((?[X]:((~wise(X)&creative(X))))<=>(kind(mary)))&
(![X]:(~rich(X)=>~patient(X)))&
(![X]:((~happy(X)|~curious(X))<=>(tall(X)&~curious(X))))&
(![X]:((rich(X)|~quiet(X))<=>(happy(X)&~happy(X))))&
(![X]:((~tall(X)&~curious(X))=>(~generous(X)<~>patient(X))))&
(((~old(susan)|~patient(susan)))<=>(?[X]:((brave(X)&funny(X)))))&
(![X]:(strong(X)=>(calm(X)&quiet(X))))&
(![X]:((~patient(X)|~strong(X))=>(~happy(X)|happy(X))))&
(((patient(paul)&old(paul)))<=>((~funny(paul)<~>quiet(paul))))&
(![X]:(~curious(X)=>(rich(X)|funny(X))))&
((patient(lucy))=>(?[X]:((rich(X)&funny(X)))))&
(![X]:((curious(X)<~>brave(X))<=>(~rich(X)&~happy(X))))&
(![X]:(curious(X)=>~humble(X)))&
((kind(lucy)<~>patient(lucy)))&
(?[X]:((happy(X)&~rich(X))))&
(kind(fred))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((patient(X)<~>brave(X))))&
((~tall(lucy)|happy(lucy))) | ~rich(susan) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 9167489571117146135825138
% SZS output start Proof for 9167489571117146135825138
7. ! [X0] : ((~quiet(X0) | rich(X0)) <=> (~happy(X0) & happy(X0))) [input p6]
23. rich(susan) [input hypothesis]
44. ! [X0] : (((~quiet(X0) | rich(X0)) | (happy(X0) | ~happy(X0))) & ((~happy(X0) & happy(X0)) | (quiet(X0) & ~rich(X0)))) [nnf transformation 7]
45. ! [X0] : ((~quiet(X0) | rich(X0) | happy(X0) | ~happy(X0)) & ((~happy(X0) & happy(X0)) | (quiet(X0) & ~rich(X0)))) [flattening 44]
80. happy(X0) | ~rich(X0) [cnf transformation 45]
82. ~happy(X0) | ~rich(X0) [cnf transformation 45]
119. rich(susan) [cnf transformation 23]
175. ~rich(X0) [subsumption resolution 80,82]
259. $false [subsumption resolution 119,175]
% SZS output end Proof for 9167489571117146135825138
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not generous is not calm or patient. Everyone who is funny is kind and vice versa. If john is not tall then john is either not quiet or wise. If susan is tall or not happy then someone is both not curious and not old. If someone is tall or not calm then someone is not quiet and vice versa. Everyone who is either strong or not strong is both wise and happy and vice versa. Everyone who is humble or generous is strong. Everyone who is either happy or not creative is tall or brave. If someone is either not wise or quiet then john is old and vice versa. Everyone who is strong is curious and vice versa. Everyone who is either not humble or not funny is not kind and vice versa. If someone is both not creative and calm then fred is either tall or curious and vice versa. If someone is not tall then fred is either rich or not calm and vice versa. If someone is rich or not strong then someone is both not funny and not wise. Everyone who is both not strong and not tall is calm or old and vice versa. Alice is not generous or happy. Someone is wise. Susan is curious. Lucy is either not kind or patient. John is either not wise or not brave. Someone is not quiet. John is either not tall or not generous. Someone is curious. | Lucy is not humble. | contradiction | (![X]:((~calm(X)|~generous(X))=>(~calm(X)|patient(X))))&
(![X]:(funny(X)<=>kind(X)))&
((~tall(john))=>((~quiet(john)<~>wise(john))))&
(((tall(susan)|~happy(susan)))=>(?[X]:((~curious(X)&~old(X)))))&
((?[X]:((tall(X)|~calm(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((strong(X)<~>~strong(X))<=>(wise(X)&happy(X))))&
(![X]:((humble(X)|generous(X))=>strong(X)))&
(![X]:((happy(X)<~>~creative(X))=>(tall(X)|brave(X))))&
((?[X]:((~wise(X)<~>quiet(X))))<=>(old(john)))&
(![X]:(strong(X)<=>curious(X)))&
(![X]:((~humble(X)<~>~funny(X))<=>~kind(X)))&
((?[X]:((~creative(X)&calm(X))))<=>((tall(fred)<~>curious(fred))))&
((?[X]:(~tall(X)))<=>((rich(fred)<~>~calm(fred))))&
((?[X]:((rich(X)|~strong(X))))=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:((~strong(X)&~tall(X))<=>(calm(X)|old(X))))&
((~generous(alice)|happy(alice)))&
(?[X]:(wise(X)))&
(curious(susan))&
((~kind(lucy)<~>patient(lucy)))&
((~wise(john)<~>~brave(john)))&
(?[X]:(~quiet(X)))&
((~tall(john)<~>~generous(john)))&
(?[X]:(curious(X))) | ~humble(lucy) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6548577280807015389386
% SZS output start Proof for 6548577280807015389386
2. ! [X0] : (funny(X0) <=> kind(X0)) [input p1]
11. ! [X0] : ((~humble(X0) <~> ~funny(X0)) <=> ~kind(X0)) [input p10]
24. ~humble(lucy) [input hypothesis]
35. ! [X0] : ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))) [nnf transformation 2]
52. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | kind(X0)) & (~kind(X0) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [nnf transformation 11]
77. ~funny(X0) | kind(X0) [cnf transformation 35]
78. ~kind(X0) | funny(X0) [cnf transformation 35]
104. ~kind(X0) | ~funny(X0) | humble(X0) [cnf transformation 52]
107. funny(X0) | humble(X0) | kind(X0) [cnf transformation 52]
138. ~humble(lucy) [cnf transformation 24]
219. humble(X0) | kind(X0) [subsumption resolution 107,77]
220. ~funny(X0) | humble(X0) [subsumption resolution 104,219]
270. 26 <=> kind(lucy) [avatar definition]
272. kind(lucy) <- (26) [avatar component clause 270]
306. kind(lucy) [resolution 219,138]
310. 26 [avatar split clause 306,270]
311. funny(lucy) <- (26) [resolution 272,78]
313. humble(lucy) <- (26) [resolution 220,311]
314. $false <- (26) [subsumption resolution 313,138]
315. ~26 [avatar contradiction clause 314]
316. $false [avatar sat refutation 310,315]
% SZS output end Proof for 6548577280807015389386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not happy is either wise or not old. Everyone who is either not calm or humble is either funny or not creative and vice versa. If someone is either not brave or calm then paul is not funny. Everyone who is both not generous and curious is either not generous or rich. Everyone who is happy is creative or not humble. If paul is both not patient and not calm then someone is strong. If lucy is both not curious and brave then someone is not calm or not patient. Everyone who is both not humble and funny is both not quiet and calm. Everyone who is both not quiet and not calm is patient and vice versa. If someone is not patient then someone is old and vice versa. If someone is generous then someone is either not curious or not happy and vice versa. If mary is wise or not strong then mary is not rich or generous and vice versa. If someone is not happy then paul is happy. Everyone who is not curious or not happy is either generous or strong and vice versa. Everyone who is not patient is both not humble and old. Everyone who is both creative and funny is both not kind and not strong and vice versa. Mary is both creative and tall. Paul is either not funny or not strong. Lucy is strong or patient. Someone is either not kind or tall. Someone is not kind. John is either funny or not rich. Someone is either quiet or not kind. Someone is not creative. | Mary is not rich. | neutral | (![X]:((rich(X)|~happy(X))=>(wise(X)<~>~old(X))))&
(![X]:((~calm(X)<~>humble(X))<=>(funny(X)<~>~creative(X))))&
((?[X]:((~brave(X)<~>calm(X))))=>(~funny(paul)))&
(![X]:((~generous(X)&curious(X))=>(~generous(X)<~>rich(X))))&
(![X]:(happy(X)=>(creative(X)|~humble(X))))&
(((~patient(paul)&~calm(paul)))=>(?[X]:(strong(X))))&
(((~curious(lucy)&brave(lucy)))=>(?[X]:((~calm(X)|~patient(X)))))&
(![X]:((~humble(X)&funny(X))=>(~quiet(X)&calm(X))))&
(![X]:((~quiet(X)&~calm(X))<=>patient(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(old(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~curious(X)<~>~happy(X)))))&
(((wise(mary)|~strong(mary)))<=>((~rich(mary)|generous(mary))))&
((?[X]:(~happy(X)))=>(happy(paul)))&
(![X]:((~curious(X)|~happy(X))<=>(generous(X)<~>strong(X))))&
(![X]:(~patient(X)=>(~humble(X)&old(X))))&
(![X]:((creative(X)&funny(X))<=>(~kind(X)&~strong(X))))&
((creative(mary)&tall(mary)))&
((~funny(paul)<~>~strong(paul)))&
((strong(lucy)|patient(lucy)))&
(?[X]:((~kind(X)<~>tall(X))))&
(?[X]:(~kind(X)))&
((funny(john)<~>~rich(john)))&
(?[X]:((quiet(X)<~>~kind(X))))&
(?[X]:(~creative(X))) | ~rich(mary) | [] | null | 0 |
Everyone who is not humble is both not quiet and calm. If someone is both not curious and not brave then someone is both rich and kind and vice versa. Everyone who is both quiet and not old is both not rich and rich and vice versa. If someone is calm or rich then fred is either quiet or not tall and vice versa. If susan is both not rich and not happy then susan is calm and vice versa. If susan is curious or quiet then someone is either not happy or not old and vice versa. If someone is either strong or not quiet then someone is kind. Everyone who is both rich and brave is both not calm and tall. Everyone who is strong is either generous or brave and vice versa. Everyone who is generous is both not old and not strong and vice versa. Everyone who is strong is either curious or rich and vice versa. Everyone who is old or not old is not tall. Everyone who is both not funny and funny is both old and strong. If paul is calm then someone is either not funny or not creative and vice versa. If someone is either not curious or not brave then fred is not brave or generous. If someone is either creative or not calm then alice is creative. Alice is either humble or not rich. Someone is curious. Someone is not brave. Mary is either not creative or quiet. Someone is either rich or quiet. Someone is either creative or tall. John is both not strong and quiet. | Susan is not creative. | neutral | (![X]:(~humble(X)=>(~quiet(X)&calm(X))))&
((?[X]:((~curious(X)&~brave(X))))<=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((quiet(X)&~old(X))<=>(~rich(X)&rich(X))))&
((?[X]:((calm(X)|rich(X))))<=>((quiet(fred)<~>~tall(fred))))&
(((~rich(susan)&~happy(susan)))<=>(calm(susan)))&
(((curious(susan)|quiet(susan)))<=>(?[X]:((~happy(X)<~>~old(X)))))&
((?[X]:((strong(X)<~>~quiet(X))))=>(?[X]:(kind(X))))&
(![X]:((rich(X)&brave(X))=>(~calm(X)&tall(X))))&
(![X]:(strong(X)<=>(generous(X)<~>brave(X))))&
(![X]:(generous(X)<=>(~old(X)&~strong(X))))&
(![X]:(strong(X)<=>(curious(X)<~>rich(X))))&
(![X]:((old(X)|~old(X))=>~tall(X)))&
(![X]:((~funny(X)&funny(X))=>(old(X)&strong(X))))&
((calm(paul))<=>(?[X]:((~funny(X)<~>~creative(X)))))&
((?[X]:((~curious(X)<~>~brave(X))))=>((~brave(fred)|generous(fred))))&
((?[X]:((creative(X)<~>~calm(X))))=>(creative(alice)))&
((humble(alice)<~>~rich(alice)))&
(?[X]:(curious(X)))&
(?[X]:(~brave(X)))&
((~creative(mary)<~>quiet(mary)))&
(?[X]:((rich(X)<~>quiet(X))))&
(?[X]:((creative(X)<~>tall(X))))&
((~strong(john)&quiet(john))) | ~creative(susan) | [] | null | 0 |
Everyone who is both rich and kind is generous.
If someone is both happy and humble then someone is generous or not old and vice versa.
Everyone who is calm is curious.
If john is not funny or not wise then mary is either not brave or not happy and vice versa.
Everyone who is either wise or strong is both creative and not wise and vice versa.
Everyone who is not brave is not creative or not patient and vice versa.
If someone is either not generous or brave then susan is either not humble or strong and vice versa.
Everyone who is both not patient and strong is both creative and not generous and vice versa.
Everyone who is rich or not humble is either not generous or not quiet and vice versa.
If someone is either funny or happy then someone is either wise or old and vice versa.
Everyone who is both calm and not kind is both not rich and strong.
If someone is creative then mary is both calm and happy.
Everyone who is brave or not quiet is both not patient and not rich.
Everyone who is either patient or tall is wise or humble.
Everyone who is both not quiet and not generous is creative or curious and vice versa.
If john is either generous or kind then someone is kind and vice versa.
Susan is either funny or quiet.
Alice is either not calm or not quiet.
Alice is both creative and old.
Someone is tall.
John is not happy or humble.
Someone is not brave or not wise. | Susan is generous. | neutral | (![X]:((rich(X)&kind(X))=>generous(X)))&
((?[X]:((happy(X)&humble(X))))<=>(?[X]:((generous(X)|~old(X)))))&
(![X]:(calm(X)=>curious(X)))&
(((~funny(john)|~wise(john)))<=>((~brave(mary)<~>~happy(mary))))&
(![X]:((wise(X)<~>strong(X))<=>(creative(X)&~wise(X))))&
(![X]:(~brave(X)<=>(~creative(X)|~patient(X))))&
((?[X]:((~generous(X)<~>brave(X))))<=>((~humble(susan)<~>strong(susan))))&
(![X]:((~patient(X)&strong(X))<=>(creative(X)&~generous(X))))&
(![X]:((rich(X)|~humble(X))<=>(~generous(X)<~>~quiet(X))))&
((?[X]:((funny(X)<~>happy(X))))<=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((calm(X)&~kind(X))=>(~rich(X)&strong(X))))&
((?[X]:(creative(X)))=>((calm(mary)&happy(mary))))&
(![X]:((brave(X)|~quiet(X))=>(~patient(X)&~rich(X))))&
(![X]:((patient(X)<~>tall(X))=>(wise(X)|humble(X))))&
(![X]:((~quiet(X)&~generous(X))<=>(creative(X)|curious(X))))&
(((generous(john)<~>kind(john)))<=>(?[X]:(kind(X))))&
((funny(susan)<~>quiet(susan)))&
((~calm(alice)<~>~quiet(alice)))&
((creative(alice)&old(alice)))&
(?[X]:(tall(X)))&
((~happy(john)|humble(john)))&
(?[X]:((~brave(X)|~wise(X)))) | generous(susan) | [] | null | 0 |
Everyone who is wise or tall is either not kind or calm.
If someone is creative or strong then alice is both old and not curious and vice versa.
Everyone who is both not brave and kind is either not brave or not quiet.
If fred is either rich or kind then someone is calm.
If someone is not curious or not creative then someone is quiet and vice versa.
Everyone who is both generous and not rich is both curious and not rich and vice versa.
If fred is either tall or not happy then paul is not funny and vice versa.
If john is brave then someone is both not strong and creative.
If someone is both not strong and not old then paul is not tall.
Everyone who is either brave or not creative is not tall or wise and vice versa.
Everyone who is both not tall and kind is generous or not curious and vice versa.
If someone is not rich or wise then alice is old or happy.
Everyone who is generous or old is curious and vice versa.
Everyone who is both happy and calm is not quiet and vice versa.
Everyone who is either not tall or brave is both not tall and rich.
Someone is kind.
Someone is not humble or quiet.
Someone is not calm.
Someone is not funny.
Mary is either not patient or curious.
John is not quiet or not old.
Someone is humble or generous.
Mary is strong or not strong. | Paul is rich. | entailment | (![X]:((wise(X)|tall(X))=>(~kind(X)<~>calm(X))))&
((?[X]:((creative(X)|strong(X))))<=>((old(alice)&~curious(alice))))&
(![X]:((~brave(X)&kind(X))=>(~brave(X)<~>~quiet(X))))&
(((rich(fred)<~>kind(fred)))=>(?[X]:(calm(X))))&
((?[X]:((~curious(X)|~creative(X))))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)&~rich(X))<=>(curious(X)&~rich(X))))&
(((tall(fred)<~>~happy(fred)))<=>(~funny(paul)))&
((brave(john))=>(?[X]:((~strong(X)&creative(X)))))&
((?[X]:((~strong(X)&~old(X))))=>(~tall(paul)))&
(![X]:((brave(X)<~>~creative(X))<=>(~tall(X)|wise(X))))&
(![X]:((~tall(X)&kind(X))<=>(generous(X)|~curious(X))))&
((?[X]:((~rich(X)|wise(X))))=>((old(alice)|happy(alice))))&
(![X]:((generous(X)|old(X))<=>curious(X)))&
(![X]:((happy(X)&calm(X))<=>~quiet(X)))&
(![X]:((~tall(X)<~>brave(X))=>(~tall(X)&rich(X))))&
(?[X]:(kind(X)))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:(~calm(X)))&
(?[X]:(~funny(X)))&
((~patient(mary)<~>curious(mary)))&
((~quiet(john)|~old(john)))&
(?[X]:((humble(X)|generous(X))))&
((strong(mary)|~strong(mary))) | rich(paul) | [
"p1",
"p5",
"p8",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8096046724738670970644683
% SZS output start Proof for 8096046724738670970644683
2. ? [X0] : (strong(X0) | creative(X0)) <=> (~curious(alice) & old(alice)) [input p1]
6. ! [X0] : ((~rich(X0) & generous(X0)) <=> (~rich(X0) & curious(X0))) [input p5]
9. ? [X0] : (~old(X0) & ~strong(X0)) => ~tall(paul) [input p8]
10. ! [X0] : ((brave(X0) <~> ~creative(X0)) <=> (wise(X0) | ~tall(X0))) [input p9]
11. ! [X0] : ((kind(X0) & ~tall(X0)) <=> (~curious(X0) | generous(X0))) [input p10]
13. ! [X0] : ((old(X0) | generous(X0)) <=> curious(X0)) [input p12]
15. ! [X0] : ((~tall(X0) <~> brave(X0)) => (rich(X0) & ~tall(X0))) [input p14]
24. ~rich(paul) [input hypothesis]
31. ~tall(paul) | ! [X0] : (old(X0) | strong(X0)) [ennf transformation 9]
34. ! [X0] : ((rich(X0) & ~tall(X0)) | (~tall(X0) <=> brave(X0))) [ennf transformation 15]
36. (? [X0] : (strong(X0) | creative(X0)) | (curious(alice) | ~old(alice))) & ((~curious(alice) & old(alice)) | ! [X0] : (~strong(X0) & ~creative(X0))) [nnf transformation 2]
37. (? [X0] : (strong(X0) | creative(X0)) | curious(alice) | ~old(alice)) & ((~curious(alice) & old(alice)) | ! [X0] : (~strong(X0) & ~creative(X0))) [flattening 36]
38. (? [X0] : (strong(X0) | creative(X0)) | curious(alice) | ~old(alice)) & ((~curious(alice) & old(alice)) | ! [X1] : (~strong(X1) & ~creative(X1))) [rectify 37]
39. ? [X0] : (strong(X0) | creative(X0)) => (strong(sK0) | creative(sK0)) [choice axiom]
40. ((strong(sK0) | creative(sK0)) | curious(alice) | ~old(alice)) & ((~curious(alice) & old(alice)) | ! [X1] : (~strong(X1) & ~creative(X1))) [skolemisation 38,39]
50. ! [X0] : (((~rich(X0) & generous(X0)) | (rich(X0) | ~curious(X0))) & ((~rich(X0) & curious(X0)) | (rich(X0) | ~generous(X0)))) [nnf transformation 6]
51. ! [X0] : (((~rich(X0) & generous(X0)) | rich(X0) | ~curious(X0)) & ((~rich(X0) & curious(X0)) | rich(X0) | ~generous(X0))) [flattening 50]
55. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | (~wise(X0) & tall(X0))) & ((wise(X0) | ~tall(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [nnf transformation 10]
56. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | (~wise(X0) & tall(X0))) & (wise(X0) | ~tall(X0) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [flattening 55]
57. ! [X0] : (((kind(X0) & ~tall(X0)) | (curious(X0) & ~generous(X0))) & ((~curious(X0) | generous(X0)) | (~kind(X0) | tall(X0)))) [nnf transformation 11]
58. ! [X0] : (((kind(X0) & ~tall(X0)) | (curious(X0) & ~generous(X0))) & (~curious(X0) | generous(X0) | ~kind(X0) | tall(X0))) [flattening 57]
59. ! [X0] : (((old(X0) | generous(X0)) | ~curious(X0)) & (curious(X0) | (~old(X0) & ~generous(X0)))) [nnf transformation 13]
60. ! [X0] : ((old(X0) | generous(X0) | ~curious(X0)) & (curious(X0) | (~old(X0) & ~generous(X0)))) [flattening 59]
63. ! [X0] : ((rich(X0) & ~tall(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) [nnf transformation 34]
79. old(alice) | ~creative(X1) [cnf transformation 40]
80. old(alice) | ~strong(X1) [cnf transformation 40]
81. ~curious(alice) | ~creative(X1) [cnf transformation 40]
82. ~curious(alice) | ~strong(X1) [cnf transformation 40]
93. ~curious(X0) | rich(X0) | generous(X0) [cnf transformation 51]
101. ~tall(paul) | old(X0) | strong(X0) [cnf transformation 31]
106. ~brave(X0) | creative(X0) | tall(X0) [cnf transformation 56]
109. ~generous(X0) | ~tall(X0) [cnf transformation 58]
116. ~old(X0) | curious(X0) [cnf transformation 60]
123. rich(X0) | brave(X0) | tall(X0) [cnf transformation 63]
134. ~rich(paul) [cnf transformation 24]
138. 1 <=> old(alice) [avatar definition]
139. old(alice) <- (1) [avatar component clause 138]
142. 2 <=> curious(alice) [avatar definition]
155. 5 <=> ! [X1] : ~strong(X1) [avatar definition]
156. ~strong(X1) <- (5) [avatar component clause 155]
157. 5 | ~2 [avatar split clause 82,142,155]
159. 6 <=> ! [X1] : ~creative(X1) [avatar definition]
160. ~creative(X1) <- (6) [avatar component clause 159]
161. 6 | ~2 [avatar split clause 81,142,159]
162. 5 | 1 [avatar split clause 80,138,155]
163. 6 | 1 [avatar split clause 79,138,159]
199. 15 <=> ! [X3] : curious(X3) [avatar definition]
200. curious(X3) <- (15) [avatar component clause 199]
233. 22 <=> ! [X0] : (old(X0) | strong(X0)) [avatar definition]
234. old(X0) | strong(X0) <- (22) [avatar component clause 233]
236. 23 <=> tall(paul) [avatar definition]
237. tall(paul) <- (23) [avatar component clause 236]
238. ~tall(paul) <- (~23) [avatar component clause 236]
239. 22 | ~23 [avatar split clause 101,236,233]
380. brave(paul) | tall(paul) [resolution 123,134]
381. brave(paul) <- (~23) [subsumption resolution 380,238]
383. creative(paul) | tall(paul) <- (~23) [resolution 381,106]
385. tall(paul) <- (6, ~23) [subsumption resolution 383,160]
386. $false <- (6, ~23) [subsumption resolution 385,238]
387. ~6 | 23 [avatar contradiction clause 386]
394. old(X0) <- (5, 22) [subsumption resolution 234,156]
398. curious(X0) <- (5, 22) [resolution 394,116]
401. 15 | ~5 | ~22 [avatar split clause 398,233,155,199]
404. curious(alice) <- (1) [resolution 139,116]
407. 2 | ~1 [avatar split clause 404,138,142]
411. generous(X1) | rich(X1) <- (15) [resolution 200,93]
470. ~tall(X3) | rich(X3) <- (15) [resolution 411,109]
487. rich(paul) <- (15, 23) [resolution 470,237]
488. $false <- (15, 23) [subsumption resolution 487,134]
489. ~15 | ~23 [avatar contradiction clause 488]
490. $false [avatar sat refutation 157,161,162,163,239,387,401,407,489]
% SZS output end Proof for 8096046724738670970644683
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and not strong then paul is either funny or not creative. If someone is either not calm or brave then someone is tall and vice versa. Everyone who is calm or not quiet is either not brave or not generous. If someone is rich then someone is both kind and patient and vice versa. If alice is both not tall and brave then fred is not kind. Everyone who is both creative and brave is funny or not humble and vice versa. Everyone who is either happy or curious is not quiet and vice versa. If someone is not quiet then someone is either not curious or happy. If lucy is either not happy or not creative then susan is both creative and not humble and vice versa. Everyone who is either calm or not curious is not creative. If paul is either not brave or not rich then lucy is wise and vice versa. If someone is not brave then someone is not tall or not strong and vice versa. If someone is not quiet or creative then lucy is both old and not old and vice versa. If someone is either funny or not tall then paul is not rich. Everyone who is brave is brave or not patient and vice versa. Everyone who is both rich and not brave is either not kind or not tall and vice versa. Alice is not curious or not kind. Alice is either rich or funny. Someone is either patient or not kind. Fred is both not calm and humble. Someone is wise or not humble. Susan is patient or not happy. Someone is patient. | Lucy is curious. | contradiction | ((?[X]:((~calm(X)&~strong(X))))=>((funny(paul)<~>~creative(paul))))&
((?[X]:((~calm(X)<~>brave(X))))<=>(?[X]:(tall(X))))&
(![X]:((calm(X)|~quiet(X))=>(~brave(X)<~>~generous(X))))&
((?[X]:(rich(X)))<=>(?[X]:((kind(X)&patient(X)))))&
(((~tall(alice)&brave(alice)))=>(~kind(fred)))&
(![X]:((creative(X)&brave(X))<=>(funny(X)|~humble(X))))&
(![X]:((happy(X)<~>curious(X))<=>~quiet(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((~curious(X)<~>happy(X)))))&
(((~happy(lucy)<~>~creative(lucy)))<=>((creative(susan)&~humble(susan))))&
(![X]:((calm(X)<~>~curious(X))=>~creative(X)))&
(((~brave(paul)<~>~rich(paul)))<=>(wise(lucy)))&
((?[X]:(~brave(X)))<=>(?[X]:((~tall(X)|~strong(X)))))&
((?[X]:((~quiet(X)|creative(X))))<=>((old(lucy)&~old(lucy))))&
((?[X]:((funny(X)<~>~tall(X))))=>(~rich(paul)))&
(![X]:(brave(X)<=>(brave(X)|~patient(X))))&
(![X]:((rich(X)&~brave(X))<=>(~kind(X)<~>~tall(X))))&
((~curious(alice)|~kind(alice)))&
((rich(alice)<~>funny(alice)))&
(?[X]:((patient(X)<~>~kind(X))))&
((~calm(fred)&humble(fred)))&
(?[X]:((wise(X)|~humble(X))))&
((patient(susan)|~happy(susan)))&
(?[X]:(patient(X))) | curious(lucy) | [
"p6",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4958374163026598435477230
% SZS output start Proof for 4958374163026598435477230
7. ! [X0] : ((happy(X0) <~> curious(X0)) <=> ~quiet(X0)) [input p6]
9. (~happy(lucy) <~> ~creative(lucy)) <=> (~humble(susan) & creative(susan)) [input p8]
13. ? [X0] : (creative(X0) | ~quiet(X0)) <=> (~old(lucy) & old(lucy)) [input p12]
24. curious(lucy) [input hypothesis]
50. ! [X0] : ((((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | quiet(X0)) & (~quiet(X0) | ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0))))) [nnf transformation 7]
55. (((creative(lucy) | happy(lucy)) & (~creative(lucy) | ~happy(lucy))) | (humble(susan) | ~creative(susan))) & ((~humble(susan) & creative(susan)) | ((~happy(lucy) | creative(lucy)) & (~creative(lucy) | happy(lucy)))) [nnf transformation 9]
56. (((creative(lucy) | happy(lucy)) & (~creative(lucy) | ~happy(lucy))) | humble(susan) | ~creative(susan)) & ((~humble(susan) & creative(susan)) | ((~happy(lucy) | creative(lucy)) & (~creative(lucy) | happy(lucy)))) [flattening 55]
64. (? [X0] : (creative(X0) | ~quiet(X0)) | (old(lucy) | ~old(lucy))) & ((~old(lucy) & old(lucy)) | ! [X0] : (~creative(X0) & quiet(X0))) [nnf transformation 13]
65. (? [X0] : (creative(X0) | ~quiet(X0)) | old(lucy) | ~old(lucy)) & ((~old(lucy) & old(lucy)) | ! [X0] : (~creative(X0) & quiet(X0))) [flattening 64]
66. (? [X0] : (creative(X0) | ~quiet(X0)) | old(lucy) | ~old(lucy)) & ((~old(lucy) & old(lucy)) | ! [X1] : (~creative(X1) & quiet(X1))) [rectify 65]
67. ? [X0] : (creative(X0) | ~quiet(X0)) => (creative(sK7) | ~quiet(sK7)) [choice axiom]
68. ((creative(sK7) | ~quiet(sK7)) | old(lucy) | ~old(lucy)) & ((~old(lucy) & old(lucy)) | ! [X1] : (~creative(X1) & quiet(X1))) [skolemisation 66,67]
102. ~curious(X0) | happy(X0) | ~quiet(X0) [cnf transformation 50]
108. creative(susan) | ~happy(lucy) | creative(lucy) [cnf transformation 56]
122. old(lucy) | quiet(X1) [cnf transformation 68]
123. old(lucy) | ~creative(X1) [cnf transformation 68]
124. ~old(lucy) | quiet(X1) [cnf transformation 68]
125. ~old(lucy) | ~creative(X1) [cnf transformation 68]
148. curious(lucy) [cnf transformation 24]
222. 18 <=> ! [X1] : quiet(X1) [avatar definition]
223. quiet(X1) <- (18) [avatar component clause 222]
240. 22 <=> happy(lucy) [avatar definition]
244. 23 <=> creative(lucy) [avatar definition]
246. creative(lucy) <- (23) [avatar component clause 244]
253. 24 <=> creative(susan) [avatar definition]
255. creative(susan) <- (24) [avatar component clause 253]
256. 23 | ~22 | 24 [avatar split clause 108,253,240,244]
299. 34 <=> ! [X1] : ~creative(X1) [avatar definition]
300. ~creative(X1) <- (34) [avatar component clause 299]
302. 35 <=> old(lucy) [avatar definition]
305. 34 | ~35 [avatar split clause 125,302,299]
306. 18 | ~35 [avatar split clause 124,302,222]
307. 34 | 35 [avatar split clause 123,302,299]
308. 18 | 35 [avatar split clause 122,302,222]
378. happy(lucy) | ~quiet(lucy) [resolution 102,148]
382. happy(lucy) <- (18) [subsumption resolution 378,223]
383. 22 | ~18 [avatar split clause 382,222,240]
384. $false <- (23, 34) [subsumption resolution 246,300]
385. ~23 | ~34 [avatar contradiction clause 384]
386. $false <- (24, 34) [subsumption resolution 255,300]
387. ~24 | ~34 [avatar contradiction clause 386]
388. $false [avatar sat refutation 256,305,306,307,308,383,385,387]
% SZS output end Proof for 4958374163026598435477230
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both old and not kind then fred is generous. If paul is generous then fred is both not quiet and not wise. If susan is humble or strong then mary is either rich or old and vice versa. If someone is patient or generous then mary is either not creative or curious and vice versa. Everyone who is both calm and not brave is either quiet or not brave and vice versa. If alice is not old then someone is both tall and old. If paul is both funny and not creative then someone is not creative or curious and vice versa. If lucy is not wise then paul is both not funny and wise and vice versa. If someone is tall or generous then fred is not curious and vice versa. Everyone who is both generous and wise is either wise or kind. If someone is not wise then someone is not rich or wise. Everyone who is both not funny and happy is funny and vice versa. If someone is both not kind and humble then someone is not curious or quiet and vice versa. If someone is either rich or creative then john is not generous. Everyone who is either not patient or not happy is not brave. If someone is not patient or quiet then john is either not calm or happy. Someone is not kind. Someone is creative. Mary is both wise and not curious. Susan is curious or rich. Fred is curious or not happy. Someone is both kind and tall. | Susan is patient. | contradiction | (((old(susan)&~kind(susan)))=>(generous(fred)))&
((generous(paul))=>((~quiet(fred)&~wise(fred))))&
(((humble(susan)|strong(susan)))<=>((rich(mary)<~>old(mary))))&
((?[X]:((patient(X)|generous(X))))<=>((~creative(mary)<~>curious(mary))))&
(![X]:((calm(X)&~brave(X))<=>(quiet(X)<~>~brave(X))))&
((~old(alice))=>(?[X]:((tall(X)&old(X)))))&
(((funny(paul)&~creative(paul)))<=>(?[X]:((~creative(X)|curious(X)))))&
((~wise(lucy))<=>((~funny(paul)&wise(paul))))&
((?[X]:((tall(X)|generous(X))))<=>(~curious(fred)))&
(![X]:((generous(X)&wise(X))=>(wise(X)<~>kind(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~rich(X)|wise(X)))))&
(![X]:((~funny(X)&happy(X))<=>funny(X)))&
((?[X]:((~kind(X)&humble(X))))<=>(?[X]:((~curious(X)|quiet(X)))))&
((?[X]:((rich(X)<~>creative(X))))=>(~generous(john)))&
(![X]:((~patient(X)<~>~happy(X))=>~brave(X)))&
((?[X]:((~patient(X)|quiet(X))))=>((~calm(john)<~>happy(john))))&
(?[X]:(~kind(X)))&
(?[X]:(creative(X)))&
((wise(mary)&~curious(mary)))&
((curious(susan)|rich(susan)))&
((curious(fred)|~happy(fred)))&
(?[X]:((kind(X)&tall(X)))) | patient(susan) | [
"p3",
"p6",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8468878993642137957117238
% SZS output start Proof for 8468878993642137957117238
4. ? [X0] : (generous(X0) | patient(X0)) <=> (~creative(mary) <~> curious(mary)) [input p3]
7. (~creative(paul) & funny(paul)) <=> ? [X0] : (curious(X0) | ~creative(X0)) [input p6]
12. ! [X0] : ((happy(X0) & ~funny(X0)) <=> funny(X0)) [input p11]
19. ~curious(mary) & wise(mary) [input p18]
23. patient(susan) [input hypothesis]
38. (? [X0] : (generous(X0) | patient(X0)) | ((~creative(mary) | ~curious(mary)) & (curious(mary) | creative(mary)))) & (((~curious(mary) | creative(mary)) & (curious(mary) | ~creative(mary))) | ! [X0] : (~generous(X0) & ~patient(X0))) [nnf transformation 4]
39. (? [X0] : (generous(X0) | patient(X0)) | ((~creative(mary) | ~curious(mary)) & (curious(mary) | creative(mary)))) & (((~curious(mary) | creative(mary)) & (curious(mary) | ~creative(mary))) | ! [X1] : (~generous(X1) & ~patient(X1))) [rectify 38]
40. ? [X0] : (generous(X0) | patient(X0)) => (generous(sK0) | patient(sK0)) [choice axiom]
41. ((generous(sK0) | patient(sK0)) | ((~creative(mary) | ~curious(mary)) & (curious(mary) | creative(mary)))) & (((~curious(mary) | creative(mary)) & (curious(mary) | ~creative(mary))) | ! [X1] : (~generous(X1) & ~patient(X1))) [skolemisation 39,40]
46. ((~creative(paul) & funny(paul)) | ! [X0] : (~curious(X0) & creative(X0))) & (? [X0] : (curious(X0) | ~creative(X0)) | (creative(paul) | ~funny(paul))) [nnf transformation 7]
47. ((~creative(paul) & funny(paul)) | ! [X0] : (~curious(X0) & creative(X0))) & (? [X0] : (curious(X0) | ~creative(X0)) | creative(paul) | ~funny(paul)) [flattening 46]
48. ((~creative(paul) & funny(paul)) | ! [X0] : (~curious(X0) & creative(X0))) & (? [X1] : (curious(X1) | ~creative(X1)) | creative(paul) | ~funny(paul)) [rectify 47]
49. ? [X1] : (curious(X1) | ~creative(X1)) => (curious(sK2) | ~creative(sK2)) [choice axiom]
50. ((~creative(paul) & funny(paul)) | ! [X0] : (~curious(X0) & creative(X0))) & ((curious(sK2) | ~creative(sK2)) | creative(paul) | ~funny(paul)) [skolemisation 48,49]
61. ! [X0] : (((happy(X0) & ~funny(X0)) | ~funny(X0)) & (funny(X0) | (~happy(X0) | funny(X0)))) [nnf transformation 12]
62. ! [X0] : (((happy(X0) & ~funny(X0)) | ~funny(X0)) & (funny(X0) | ~happy(X0) | funny(X0))) [flattening 61]
86. curious(mary) | ~creative(mary) | ~patient(X1) [cnf transformation 41]
101. funny(paul) | creative(X0) [cnf transformation 50]
115. ~funny(X0) | ~funny(X0) [cnf transformation 62]
133. ~curious(mary) [cnf transformation 19]
138. patient(susan) [cnf transformation 23]
140. ~funny(X0) [duplicate literal removal 115]
194. 11 <=> curious(mary) [avatar definition]
198. 12 <=> creative(mary) [avatar definition]
200. ~creative(mary) <- (~12) [avatar component clause 198]
216. 16 <=> ! [X1] : ~patient(X1) [avatar definition]
217. ~patient(X1) <- (16) [avatar component clause 216]
220. 16 | ~12 | 11 [avatar split clause 86,194,198,216]
245. 22 <=> ! [X0] : creative(X0) [avatar definition]
246. creative(X0) <- (22) [avatar component clause 245]
249. 23 <=> funny(paul) [avatar definition]
251. funny(paul) <- (23) [avatar component clause 249]
253. 22 | 23 [avatar split clause 101,249,245]
359. ~11 [avatar split clause 133,194]
369. $false <- (~12, 22) [subsumption resolution 200,246]
370. 12 | ~22 [avatar contradiction clause 369]
371. $false <- (16) [resolution 217,138]
374. ~16 [avatar contradiction clause 371]
375. $false <- (23) [subsumption resolution 251,140]
376. ~23 [avatar contradiction clause 375]
377. $false [avatar sat refutation 220,253,359,370,374,376]
% SZS output end Proof for 8468878993642137957117238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If paul is either wise or not generous then someone is either not rich or rich and vice versa. If lucy is brave or patient then someone is not old or rich. If someone is either calm or not rich then fred is not quiet or strong and vice versa. Everyone who is either not curious or wise is both not happy and calm and vice versa. Everyone who is either old or not old is not quiet or not humble and vice versa. Everyone who is either patient or not tall is either not rich or brave. If susan is not humble or not tall then paul is not creative. If someone is both generous and not quiet then john is both curious and brave and vice versa. If someone is not quiet or not rich then alice is happy or calm. If someone is not generous or not curious then someone is creative or old. If someone is tall or not happy then someone is either not generous or wise. If someone is not happy then someone is not funny and vice versa. If paul is both not brave and brave then someone is both kind and happy and vice versa. Everyone who is not generous is both generous and humble. Everyone who is not wise is either generous or not curious. If susan is tall then someone is brave or strong. John is both not brave and not calm. Someone is old or not rich. Lucy is both not funny and not patient. Paul is not tall. Alice is either not tall or not quiet. Someone is either not calm or humble. Someone is either not curious or wise. Someone is tall or patient. | John is humble. | contradiction | (((wise(paul)<~>~generous(paul)))<=>(?[X]:((~rich(X)<~>rich(X)))))&
(((brave(lucy)|patient(lucy)))=>(?[X]:((~old(X)|rich(X)))))&
((?[X]:((calm(X)<~>~rich(X))))<=>((~quiet(fred)|strong(fred))))&
(![X]:((~curious(X)<~>wise(X))<=>(~happy(X)&calm(X))))&
(![X]:((old(X)<~>~old(X))<=>(~quiet(X)|~humble(X))))&
(![X]:((patient(X)<~>~tall(X))=>(~rich(X)<~>brave(X))))&
(((~humble(susan)|~tall(susan)))=>(~creative(paul)))&
((?[X]:((generous(X)&~quiet(X))))<=>((curious(john)&brave(john))))&
((?[X]:((~quiet(X)|~rich(X))))=>((happy(alice)|calm(alice))))&
((?[X]:((~generous(X)|~curious(X))))=>(?[X]:((creative(X)|old(X)))))&
((?[X]:((tall(X)|~happy(X))))=>(?[X]:((~generous(X)<~>wise(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:(~funny(X))))&
(((~brave(paul)&brave(paul)))<=>(?[X]:((kind(X)&happy(X)))))&
(![X]:(~generous(X)=>(generous(X)&humble(X))))&
(![X]:(~wise(X)=>(generous(X)<~>~curious(X))))&
((tall(susan))=>(?[X]:((brave(X)|strong(X)))))&
((~brave(john)&~calm(john)))&
(?[X]:((old(X)|~rich(X))))&
((~funny(lucy)&~patient(lucy)))&
(~tall(paul))&
((~tall(alice)<~>~quiet(alice)))&
(?[X]:((~calm(X)<~>humble(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
(?[X]:((tall(X)|patient(X)))) | humble(john) | [
"p4",
"p7",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 72928011077448512671835
% SZS output start Proof for 72928011077448512671835
5. ! [X0] : ((old(X0) <~> ~old(X0)) <=> (~humble(X0) | ~quiet(X0))) [input p4]
8. ? [X0] : (~quiet(X0) & generous(X0)) <=> (brave(john) & curious(john)) [input p7]
14. ! [X0] : (~generous(X0) => (humble(X0) & generous(X0))) [input p13]
17. ~calm(john) & ~brave(john) [input p16]
25. humble(john) [input hypothesis]
36. ! [X0] : ((humble(X0) & generous(X0)) | generous(X0)) [ennf transformation 14]
52. ! [X0] : ((((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0))))) [nnf transformation 5]
53. ! [X0] : ((((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0))))) [flattening 52]
55. (? [X0] : (~quiet(X0) & generous(X0)) | (~brave(john) | ~curious(john))) & ((brave(john) & curious(john)) | ! [X0] : (quiet(X0) | ~generous(X0))) [nnf transformation 8]
56. (? [X0] : (~quiet(X0) & generous(X0)) | ~brave(john) | ~curious(john)) & ((brave(john) & curious(john)) | ! [X0] : (quiet(X0) | ~generous(X0))) [flattening 55]
57. (? [X0] : (~quiet(X0) & generous(X0)) | ~brave(john) | ~curious(john)) & ((brave(john) & curious(john)) | ! [X1] : (quiet(X1) | ~generous(X1))) [rectify 56]
58. ? [X0] : (~quiet(X0) & generous(X0)) => (~quiet(sK3) & generous(sK3)) [choice axiom]
59. ((~quiet(sK3) & generous(sK3)) | ~brave(john) | ~curious(john)) & ((brave(john) & curious(john)) | ! [X1] : (quiet(X1) | ~generous(X1))) [skolemisation 57,58]
113. ~humble(X0) | ~quiet(X0) | ~old(X0) | ~old(X0) [cnf transformation 53]
114. ~humble(X0) | ~quiet(X0) | old(X0) | old(X0) [cnf transformation 53]
126. brave(john) | quiet(X1) | ~generous(X1) [cnf transformation 59]
143. generous(X0) | generous(X0) [cnf transformation 36]
148. ~brave(john) [cnf transformation 17]
161. humble(john) [cnf transformation 25]
162. generous(X0) [duplicate literal removal 143]
163. ~humble(X0) | ~quiet(X0) | ~old(X0) [duplicate literal removal 113]
164. ~humble(X0) | ~quiet(X0) | old(X0) [duplicate literal removal 114]
233. ~humble(X0) | ~quiet(X0) [subsumption resolution 163,164]
253. 19 <=> brave(john) [avatar definition]
267. 22 <=> ! [X1] : (quiet(X1) | ~generous(X1)) [avatar definition]
268. quiet(X1) | ~generous(X1) <- (22) [avatar component clause 267]
269. 22 | 19 [avatar split clause 126,253,267]
281. 25 <=> ! [X0] : quiet(X0) [avatar definition]
282. quiet(X0) <- (25) [avatar component clause 281]
297. 29 <=> ! [X1] : generous(X1) [avatar definition]
298. generous(X1) <- (29) [avatar component clause 297]
340. 29 [avatar split clause 162,297]
350. ~19 [avatar split clause 148,253]
400. quiet(X1) <- (22, 29) [subsumption resolution 268,298]
401. 25 | ~22 | ~29 [avatar split clause 400,297,267,281]
415. ~quiet(john) [resolution 233,161]
417. $false <- (25) [subsumption resolution 415,282]
418. ~25 [avatar contradiction clause 417]
419. $false [avatar sat refutation 269,340,350,401,418]
% SZS output end Proof for 72928011077448512671835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or not tall is either not calm or not generous. Everyone who is either humble or old is rich or kind and vice versa. Everyone who is rich or not wise is generous. Everyone who is not strong is not tall or patient. Everyone who is both not creative and not generous is not calm and vice versa. If mary is both kind and happy then susan is either not kind or quiet and vice versa. Everyone who is not tall or not quiet is funny or rich and vice versa. Everyone who is not creative is old or tall and vice versa. If mary is either wise or not patient then john is either old or not old and vice versa. Everyone who is not funny or not wise is curious or not wise and vice versa. If paul is either tall or not kind then someone is wise and vice versa. If someone is calm or not quiet then someone is both strong and quiet. If someone is either patient or kind then john is either not funny or happy and vice versa. Everyone who is old is both not quiet and kind and vice versa. If someone is not brave or patient then mary is kind or not humble. If mary is curious or patient then someone is either humble or not humble. Paul is either not brave or creative. John is not happy or not calm. John is either curious or not patient. John is not brave. Susan is not kind or humble. Someone is either not patient or not generous. | Paul is not creative. | contradiction | (![X]:((tall(X)|~tall(X))=>(~calm(X)<~>~generous(X))))&
(![X]:((humble(X)<~>old(X))<=>(rich(X)|kind(X))))&
(![X]:((rich(X)|~wise(X))=>generous(X)))&
(![X]:(~strong(X)=>(~tall(X)|patient(X))))&
(![X]:((~creative(X)&~generous(X))<=>~calm(X)))&
(((kind(mary)&happy(mary)))<=>((~kind(susan)<~>quiet(susan))))&
(![X]:((~tall(X)|~quiet(X))<=>(funny(X)|rich(X))))&
(![X]:(~creative(X)<=>(old(X)|tall(X))))&
(((wise(mary)<~>~patient(mary)))<=>((old(john)<~>~old(john))))&
(![X]:((~funny(X)|~wise(X))<=>(curious(X)|~wise(X))))&
(((tall(paul)<~>~kind(paul)))<=>(?[X]:(wise(X))))&
((?[X]:((calm(X)|~quiet(X))))=>(?[X]:((strong(X)&quiet(X)))))&
((?[X]:((patient(X)<~>kind(X))))<=>((~funny(john)<~>happy(john))))&
(![X]:(old(X)<=>(~quiet(X)&kind(X))))&
((?[X]:((~brave(X)|patient(X))))=>((kind(mary)|~humble(mary))))&
(((curious(mary)|patient(mary)))=>(?[X]:((humble(X)<~>~humble(X)))))&
((~brave(paul)<~>creative(paul)))&
((~happy(john)|~calm(john)))&
((curious(john)<~>~patient(john)))&
(~brave(john))&
((~kind(susan)|humble(susan)))&
(?[X]:((~patient(X)<~>~generous(X)))) | ~creative(paul) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4116190305507744542495381
% SZS output start Proof for 4116190305507744542495381
1. ! [X0] : ((~tall(X0) | tall(X0)) => (~calm(X0) <~> ~generous(X0))) [input p0]
5. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> ~calm(X0)) [input p4]
23. ~creative(paul) [input hypothesis]
27. ! [X0] : ((~calm(X0) <~> ~generous(X0)) | (tall(X0) & ~tall(X0))) [ennf transformation 1]
33. ! [X0] : (((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | (tall(X0) & ~tall(X0))) [nnf transformation 27]
36. ! [X0] : (((~generous(X0) & ~creative(X0)) | calm(X0)) & (~calm(X0) | (generous(X0) | creative(X0)))) [nnf transformation 5]
37. ! [X0] : (((~generous(X0) & ~creative(X0)) | calm(X0)) & (~calm(X0) | generous(X0) | creative(X0))) [flattening 36]
68. ~generous(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 33]
69. ~generous(X0) | ~calm(X0) | tall(X0) [cnf transformation 33]
70. generous(X0) | calm(X0) | ~tall(X0) [cnf transformation 33]
71. generous(X0) | calm(X0) | tall(X0) [cnf transformation 33]
80. ~calm(X0) | generous(X0) | creative(X0) [cnf transformation 37]
82. ~generous(X0) | calm(X0) [cnf transformation 37]
140. ~creative(paul) [cnf transformation 23]
145. generous(X0) | calm(X0) [subsumption resolution 70,71]
146. ~generous(X0) | ~calm(X0) [subsumption resolution 68,69]
147. ~generous(X0) [subsumption resolution 82,146]
148. ~calm(X0) | creative(X0) [subsumption resolution 80,147]
265. 25 <=> creative(paul) [avatar definition]
267. ~creative(paul) <- (~25) [avatar component clause 265]
291. ~25 [avatar split clause 140,265]
299. calm(X0) [resolution 145,147]
301. creative(X0) [resolution 148,299]
302. $false <- (~25) [resolution 301,267]
306. 25 [avatar contradiction clause 302]
307. $false [avatar sat refutation 291,306]
% SZS output end Proof for 4116190305507744542495381
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not funny is both not patient and not funny and vice versa.
Everyone who is either calm or curious is both not kind and not happy.
If someone is not kind or calm then mary is not wise or not funny and vice versa.
Everyone who is either not curious or wise is both not kind and not tall.
Everyone who is both not rich and happy is either not rich or not brave and vice versa.
Everyone who is either patient or not funny is not calm and vice versa.
Everyone who is not calm is both creative and not happy.
Everyone who is both happy and calm is both not quiet and strong.
Everyone who is both quiet and not creative is not kind or funny and vice versa.
If someone is either funny or creative then someone is both not kind and patient and vice versa.
Everyone who is both generous and humble is brave.
If someone is both not curious and old then mary is tall.
Everyone who is not happy is not patient and vice versa.
Everyone who is calm or curious is both calm and kind.
Everyone who is both not creative and not humble is old or tall.
Everyone who is both not kind and brave is creative or tall.
Alice is either funny or not humble.
Someone is not curious or strong.
Mary is not humble or kind.
Someone is generous.
Someone is both not wise and not generous.
John is old or quiet. | Mary is happy. | entailment | (![X]:((tall(X)<~>~funny(X))<=>(~patient(X)&~funny(X))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)&~happy(X))))&
((?[X]:((~kind(X)|calm(X))))<=>((~wise(mary)|~funny(mary))))&
(![X]:((~curious(X)<~>wise(X))=>(~kind(X)&~tall(X))))&
(![X]:((~rich(X)&happy(X))<=>(~rich(X)<~>~brave(X))))&
(![X]:((patient(X)<~>~funny(X))<=>~calm(X)))&
(![X]:(~calm(X)=>(creative(X)&~happy(X))))&
(![X]:((happy(X)&calm(X))=>(~quiet(X)&strong(X))))&
(![X]:((quiet(X)&~creative(X))<=>(~kind(X)|funny(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((generous(X)&humble(X))=>brave(X)))&
((?[X]:((~curious(X)&old(X))))=>(tall(mary)))&
(![X]:(~happy(X)<=>~patient(X)))&
(![X]:((calm(X)|curious(X))=>(calm(X)&kind(X))))&
(![X]:((~creative(X)&~humble(X))=>(old(X)|tall(X))))&
(![X]:((~kind(X)&brave(X))=>(creative(X)|tall(X))))&
((funny(alice)<~>~humble(alice)))&
(?[X]:((~curious(X)|strong(X))))&
((~humble(mary)|kind(mary)))&
(?[X]:(generous(X)))&
(?[X]:((~wise(X)&~generous(X))))&
((old(john)|quiet(john))) | happy(mary) | [
"p5",
"p6",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7142408626817580502350183
% SZS output start Proof for 7142408626817580502350183
6. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> ~calm(X0)) [input p5]
7. ! [X0] : (~calm(X0) => (~happy(X0) & creative(X0))) [input p6]
9. ! [X0] : ((~creative(X0) & quiet(X0)) <=> (funny(X0) | ~kind(X0))) [input p8]
10. ? [X0] : (funny(X0) <~> creative(X0)) <=> ? [X0] : (patient(X0) & ~kind(X0)) [input p9]
13. ! [X0] : (~happy(X0) <=> ~patient(X0)) [input p12]
14. ! [X0] : ((curious(X0) | calm(X0)) => (kind(X0) & calm(X0))) [input p13]
23. ~happy(mary) [input hypothesis]
24. ? [X0] : (funny(X0) <~> creative(X0)) <=> ? [X1] : (patient(X1) & ~kind(X1)) [rectify 10]
29. ! [X0] : ((~happy(X0) & creative(X0)) | calm(X0)) [ennf transformation 7]
35. ! [X0] : ((kind(X0) & calm(X0)) | (~curious(X0) & ~calm(X0))) [ennf transformation 14]
51. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | calm(X0)) & (~calm(X0) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 6]
52. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | (creative(X0) | ~quiet(X0)))) [nnf transformation 9]
53. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | creative(X0) | ~quiet(X0))) [flattening 52]
54. (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ! [X1] : (~patient(X1) | kind(X1))) & (? [X1] : (patient(X1) & ~kind(X1)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) [nnf transformation 24]
55. (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ! [X1] : (~patient(X1) | kind(X1))) & (? [X2] : (patient(X2) & ~kind(X2)) | ! [X3] : ((funny(X3) | ~creative(X3)) & (creative(X3) | ~funny(X3)))) [rectify 54]
56. ? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) => ((~creative(sK1) | ~funny(sK1)) & (creative(sK1) | funny(sK1))) [choice axiom]
57. ? [X2] : (patient(X2) & ~kind(X2)) => (patient(sK2) & ~kind(sK2)) [choice axiom]
58. (((~creative(sK1) | ~funny(sK1)) & (creative(sK1) | funny(sK1))) | ! [X1] : (~patient(X1) | kind(X1))) & ((patient(sK2) & ~kind(sK2)) | ! [X3] : ((funny(X3) | ~creative(X3)) & (creative(X3) | ~funny(X3)))) [skolemisation 55,57,56]
59. ! [X0] : ((~happy(X0) | patient(X0)) & (~patient(X0) | happy(X0))) [nnf transformation 13]
90. ~calm(X0) | patient(X0) | funny(X0) [cnf transformation 51]
93. creative(X0) | calm(X0) [cnf transformation 29]
99. ~creative(X0) | kind(X0) [cnf transformation 53]
100. ~creative(X0) | ~funny(X0) [cnf transformation 53]
101. ~kind(sK2) | creative(X3) | ~funny(X3) [cnf transformation 58]
102. ~kind(sK2) | funny(X3) | ~creative(X3) [cnf transformation 58]
109. ~patient(X0) | happy(X0) [cnf transformation 59]
113. ~calm(X0) | kind(X0) [cnf transformation 35]
124. ~happy(mary) [cnf transformation 23]
152. 6 <=> ! [X1] : kind(X1) [avatar definition]
153. kind(X1) <- (6) [avatar component clause 152]
171. 10 <=> ! [X3] : ~creative(X3) [avatar definition]
172. ~creative(X3) <- (10) [avatar component clause 171]
180. 12 <=> ! [X3] : ~funny(X3) [avatar definition]
181. ~funny(X3) <- (12) [avatar component clause 180]
183. ~kind(sK2) | ~creative(X3) [subsumption resolution 102,100]
185. 13 <=> kind(sK2) [avatar definition]
187. ~kind(sK2) <- (~13) [avatar component clause 185]
188. 10 | ~13 [avatar split clause 183,185,171]
189. ~kind(sK2) | ~funny(X3) [subsumption resolution 101,100]
190. 12 | ~13 [avatar split clause 189,185,180]
228. kind(X0) | calm(X0) [resolution 99,93]
229. kind(X0) [subsumption resolution 228,113]
230. 6 [avatar split clause 229,152]
232. $false <- (6, ~13) [resolution 153,187]
233. ~6 | 13 [avatar contradiction clause 232]
235. calm(X0) <- (10) [resolution 172,93]
263. patient(X0) | funny(X0) <- (10) [resolution 90,235]
265. patient(X0) <- (10, 12) [subsumption resolution 263,181]
272. happy(X2) <- (10, 12) [resolution 265,109]
285. $false <- (10, 12) [resolution 272,124]
291. ~10 | ~12 [avatar contradiction clause 285]
292. $false [avatar sat refutation 188,190,230,233,291]
% SZS output end Proof for 7142408626817580502350183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or tall is both patient and not creative.
Everyone who is funny or old is both not funny and not rich and vice versa.
Everyone who is not humble or humble is either kind or funny and vice versa.
If alice is both not humble and rich then alice is both curious and not generous and vice versa.
If someone is either not generous or calm then mary is both curious and not wise and vice versa.
If alice is both wise and not funny then someone is not funny or not happy.
Everyone who is patient or not generous is either rich or not creative.
Everyone who is wise or not strong is both not old and generous.
Everyone who is not strong is not patient.
If fred is not curious then susan is either not patient or creative.
If someone is both kind and not generous then someone is either wise or curious and vice versa.
If someone is not tall then someone is either not old or humble and vice versa.
If someone is not strong or not quiet then someone is both old and humble and vice versa.
Everyone who is calm is either calm or creative and vice versa.
Everyone who is generous is not old or not humble.
If mary is not generous then susan is both creative and not kind and vice versa.
Susan is not tall or humble.
Alice is both not curious and humble.
Someone is not humble.
John is brave or not rich.
Alice is not curious.
Someone is both not creative and old.
John is not curious or rich. | Mary is wise. | contradiction | (![X]:((generous(X)|tall(X))=>(patient(X)&~creative(X))))&
(![X]:((funny(X)|old(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~humble(X)|humble(X))<=>(kind(X)<~>funny(X))))&
(((~humble(alice)&rich(alice)))<=>((curious(alice)&~generous(alice))))&
((?[X]:((~generous(X)<~>calm(X))))<=>((curious(mary)&~wise(mary))))&
(((wise(alice)&~funny(alice)))=>(?[X]:((~funny(X)|~happy(X)))))&
(![X]:((patient(X)|~generous(X))=>(rich(X)<~>~creative(X))))&
(![X]:((wise(X)|~strong(X))=>(~old(X)&generous(X))))&
(![X]:(~strong(X)=>~patient(X)))&
((~curious(fred))=>((~patient(susan)<~>creative(susan))))&
((?[X]:((kind(X)&~generous(X))))<=>(?[X]:((wise(X)<~>curious(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((~old(X)<~>humble(X)))))&
((?[X]:((~strong(X)|~quiet(X))))<=>(?[X]:((old(X)&humble(X)))))&
(![X]:(calm(X)<=>(calm(X)<~>creative(X))))&
(![X]:(generous(X)=>(~old(X)|~humble(X))))&
((~generous(mary))<=>((creative(susan)&~kind(susan))))&
((~tall(susan)|humble(susan)))&
((~curious(alice)&humble(alice)))&
(?[X]:(~humble(X)))&
((brave(john)|~rich(john)))&
(~curious(alice))&
(?[X]:((~creative(X)&old(X))))&
((~curious(john)|rich(john))) | wise(mary) | [
"p0",
"p1",
"p2",
"p6",
"p7",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8457050381063239033322778
% SZS output start Proof for 8457050381063239033322778
1. ! [X0] : ((tall(X0) | generous(X0)) => (~creative(X0) & patient(X0))) [input p0]
2. ! [X0] : ((old(X0) | funny(X0)) <=> (~rich(X0) & ~funny(X0))) [input p1]
3. ! [X0] : ((humble(X0) | ~humble(X0)) <=> (kind(X0) <~> funny(X0))) [input p2]
7. ! [X0] : ((~generous(X0) | patient(X0)) => (rich(X0) <~> ~creative(X0))) [input p6]
8. ! [X0] : ((~strong(X0) | wise(X0)) => (generous(X0) & ~old(X0))) [input p7]
14. ! [X0] : (calm(X0) <=> (calm(X0) <~> creative(X0))) [input p13]
16. ~generous(mary) <=> (~kind(susan) & creative(susan)) [input p15]
24. wise(mary) [input hypothesis]
30. ! [X0] : ((~creative(X0) & patient(X0)) | (~tall(X0) & ~generous(X0))) [ennf transformation 1]
31. ! [X0] : ((rich(X0) <~> ~creative(X0)) | (generous(X0) & ~patient(X0))) [ennf transformation 7]
32. ! [X0] : ((generous(X0) & ~old(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 8]
37. ! [X0] : (((old(X0) | funny(X0)) | (rich(X0) | funny(X0))) & ((~rich(X0) & ~funny(X0)) | (~old(X0) & ~funny(X0)))) [nnf transformation 2]
38. ! [X0] : ((old(X0) | funny(X0) | rich(X0) | funny(X0)) & ((~rich(X0) & ~funny(X0)) | (~old(X0) & ~funny(X0)))) [flattening 37]
39. ! [X0] : (((humble(X0) | ~humble(X0)) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) & (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | (~humble(X0) & humble(X0)))) [nnf transformation 3]
40. ! [X0] : ((humble(X0) | ~humble(X0) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) & (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | (~humble(X0) & humble(X0)))) [flattening 39]
48. ! [X0] : (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (generous(X0) & ~patient(X0))) [nnf transformation 31]
65. ! [X0] : ((calm(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ~calm(X0))) [nnf transformation 14]
66. (~generous(mary) | (kind(susan) | ~creative(susan))) & ((~kind(susan) & creative(susan)) | generous(mary)) [nnf transformation 16]
67. (~generous(mary) | kind(susan) | ~creative(susan)) & ((~kind(susan) & creative(susan)) | generous(mary)) [flattening 66]
72. ~generous(X0) | patient(X0) [cnf transformation 30]
76. ~funny(X0) | ~funny(X0) [cnf transformation 38]
80. old(X0) | funny(X0) | rich(X0) | funny(X0) [cnf transformation 38]
81. funny(X0) | kind(X0) | humble(X0) [cnf transformation 40]
82. funny(X0) | kind(X0) | ~humble(X0) [cnf transformation 40]
99. ~rich(X0) | creative(X0) | ~patient(X0) [cnf transformation 48]
101. ~wise(X0) | ~old(X0) [cnf transformation 32]
124. ~creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 65]
126. calm(X0) | calm(X0) | ~creative(X0) [cnf transformation 65]
129. ~kind(susan) | generous(mary) [cnf transformation 67]
139. wise(mary) [cnf transformation 24]
140. ~creative(X0) | ~calm(X0) [duplicate literal removal 124]
141. ~creative(X0) | calm(X0) [duplicate literal removal 126]
142. ~funny(X0) [duplicate literal removal 76]
143. rich(X0) | funny(X0) | old(X0) [duplicate literal removal 80]
144. ~humble(X0) | kind(X0) [subsumption resolution 82,142]
145. kind(X0) | humble(X0) [subsumption resolution 81,142]
146. kind(X0) [subsumption resolution 145,144]
172. 6 <=> wise(mary) [avatar definition]
174. wise(mary) <- (6) [avatar component clause 172]
289. ~creative(X0) [subsumption resolution 140,141]
290. generous(mary) [subsumption resolution 129,146]
312. 6 [avatar split clause 139,172]
321. patient(mary) [resolution 72,290]
325. ~old(mary) <- (6) [resolution 101,174]
347. funny(X1) | old(X1) | creative(X1) | ~patient(X1) [resolution 143,99]
352. old(X1) | creative(X1) | ~patient(X1) [subsumption resolution 347,142]
353. ~patient(X1) | old(X1) [subsumption resolution 352,289]
373. old(mary) [resolution 353,321]
377. $false <- (6) [subsumption resolution 373,325]
378. ~6 [avatar contradiction clause 377]
383. $false [avatar sat refutation 312,378]
% SZS output end Proof for 8457050381063239033322778
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and patient is old or brave and vice versa.
If fred is not curious or creative then mary is both brave and not wise and vice versa.
If someone is either creative or calm then someone is both humble and calm.
Everyone who is creative or not tall is not funny or not brave.
If someone is strong or funny then someone is either wise or not funny and vice versa.
Everyone who is both not humble and not curious is not wise.
If someone is not calm then mary is both not happy and not strong.
Everyone who is either not rich or generous is curious.
If mary is patient then susan is not patient and vice versa.
If lucy is either strong or curious then lucy is both not old and happy.
If someone is not wise then someone is not humble or patient and vice versa.
Everyone who is not wise is not quiet or kind.
Everyone who is either not tall or brave is both creative and not calm.
Everyone who is either not calm or not humble is not kind or kind and vice versa.
Everyone who is either rich or brave is not kind or not happy and vice versa.
Everyone who is quiet or not funny is not curious and vice versa.
Someone is either not brave or quiet.
Someone is both not funny and strong.
Lucy is both not generous and curious.
Fred is wise or not rich.
Fred is both rich and not curious.
Paul is humble or not quiet.
Someone is not patient or funny.
John is both quiet and strong. | Lucy is not brave. | entailment | (![X]:((~old(X)&patient(X))<=>(old(X)|brave(X))))&
(((~curious(fred)|creative(fred)))<=>((brave(mary)&~wise(mary))))&
((?[X]:((creative(X)<~>calm(X))))=>(?[X]:((humble(X)&calm(X)))))&
(![X]:((creative(X)|~tall(X))=>(~funny(X)|~brave(X))))&
((?[X]:((strong(X)|funny(X))))<=>(?[X]:((wise(X)<~>~funny(X)))))&
(![X]:((~humble(X)&~curious(X))=>~wise(X)))&
((?[X]:(~calm(X)))=>((~happy(mary)&~strong(mary))))&
(![X]:((~rich(X)<~>generous(X))=>curious(X)))&
((patient(mary))<=>(~patient(susan)))&
(((strong(lucy)<~>curious(lucy)))=>((~old(lucy)&happy(lucy))))&
((?[X]:(~wise(X)))<=>(?[X]:((~humble(X)|patient(X)))))&
(![X]:(~wise(X)=>(~quiet(X)|kind(X))))&
(![X]:((~tall(X)<~>brave(X))=>(creative(X)&~calm(X))))&
(![X]:((~calm(X)<~>~humble(X))<=>(~kind(X)|kind(X))))&
(![X]:((rich(X)<~>brave(X))<=>(~kind(X)|~happy(X))))&
(![X]:((quiet(X)|~funny(X))<=>~curious(X)))&
(?[X]:((~brave(X)<~>quiet(X))))&
(?[X]:((~funny(X)&strong(X))))&
((~generous(lucy)&curious(lucy)))&
((wise(fred)|~rich(fred)))&
((rich(fred)&~curious(fred)))&
((humble(paul)|~quiet(paul)))&
(?[X]:((~patient(X)|funny(X))))&
((quiet(john)&strong(john))) | ~brave(lucy) | [
"p3",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2090604058611120844584689
% SZS output start Proof for 2090604058611120844584689
4. ! [X0] : ((~tall(X0) | creative(X0)) => (~brave(X0) | ~funny(X0))) [input p3]
13. ! [X0] : ((~tall(X0) <~> brave(X0)) => (~calm(X0) & creative(X0))) [input p12]
16. ! [X0] : ((~funny(X0) | quiet(X0)) <=> ~curious(X0)) [input p15]
19. curious(lucy) & ~generous(lucy) [input p18]
25. brave(lucy) [input hypothesis]
30. ! [X0] : ((~brave(X0) | ~funny(X0)) | (tall(X0) & ~creative(X0))) [ennf transformation 4]
31. ! [X0] : (~brave(X0) | ~funny(X0) | (tall(X0) & ~creative(X0))) [flattening 30]
39. ! [X0] : ((~calm(X0) & creative(X0)) | (~tall(X0) <=> brave(X0))) [ennf transformation 13]
61. ! [X0] : ((~calm(X0) & creative(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) [nnf transformation 39]
66. ! [X0] : (((~funny(X0) | quiet(X0)) | curious(X0)) & (~curious(X0) | (funny(X0) & ~quiet(X0)))) [nnf transformation 16]
67. ! [X0] : ((~funny(X0) | quiet(X0) | curious(X0)) & (~curious(X0) | (funny(X0) & ~quiet(X0)))) [flattening 66]
89. ~funny(X0) | ~brave(X0) | ~creative(X0) [cnf transformation 31]
90. ~funny(X0) | ~brave(X0) | tall(X0) [cnf transformation 31]
113. ~tall(X0) | creative(X0) | ~brave(X0) [cnf transformation 61]
129. ~curious(X0) | funny(X0) [cnf transformation 67]
136. curious(lucy) [cnf transformation 19]
144. brave(lucy) [cnf transformation 25]
245. 22 <=> curious(lucy) [avatar definition]
246. curious(lucy) <- (22) [avatar component clause 245]
294. 22 [avatar split clause 136,245]
332. funny(lucy) <- (22) [resolution 129,246]
338. ~brave(lucy) | ~creative(lucy) <- (22) [resolution 89,332]
339. ~creative(lucy) <- (22) [subsumption resolution 338,144]
341. ~brave(lucy) | tall(lucy) <- (22) [resolution 90,332]
342. tall(lucy) <- (22) [subsumption resolution 341,144]
362. creative(lucy) | ~brave(lucy) <- (22) [resolution 113,342]
365. ~brave(lucy) <- (22) [subsumption resolution 362,339]
366. $false <- (22) [subsumption resolution 365,144]
367. ~22 [avatar contradiction clause 366]
368. $false [avatar sat refutation 294,367]
% SZS output end Proof for 2090604058611120844584689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not curious then someone is either tall or not generous and vice versa. If john is brave then someone is either brave or not tall and vice versa. If someone is either patient or not humble then someone is humble or brave. If someone is either old or curious then someone is calm. Everyone who is happy is generous and vice versa. Everyone who is either not curious or patient is not old or rich and vice versa. If someone is generous then someone is both old and not strong. If someone is not quiet then lucy is either not old or not brave and vice versa. Everyone who is curious is not strong and vice versa. If mary is both curious and not calm then someone is not tall and vice versa. Everyone who is both rich and not funny is either tall or not brave and vice versa. Everyone who is not old or not tall is both generous and rich and vice versa. Everyone who is curious or not old is either not kind or not patient and vice versa. If someone is not generous or kind then susan is both curious and strong. If someone is both not old and wise then john is not calm or not curious and vice versa. If mary is both generous and not creative then someone is either not rich or not patient. Someone is either humble or not strong. Someone is curious or not quiet. Someone is both not tall and not quiet. Someone is both not calm and patient. Someone is not wise or creative. John is not brave. | Lucy is brave. | entailment | ((?[X]:((curious(X)|~curious(X))))<=>(?[X]:((tall(X)<~>~generous(X)))))&
((brave(john))<=>(?[X]:((brave(X)<~>~tall(X)))))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((humble(X)|brave(X)))))&
((?[X]:((old(X)<~>curious(X))))=>(?[X]:(calm(X))))&
(![X]:(happy(X)<=>generous(X)))&
(![X]:((~curious(X)<~>patient(X))<=>(~old(X)|rich(X))))&
((?[X]:(generous(X)))=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:(~quiet(X)))<=>((~old(lucy)<~>~brave(lucy))))&
(![X]:(curious(X)<=>~strong(X)))&
(((curious(mary)&~calm(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((rich(X)&~funny(X))<=>(tall(X)<~>~brave(X))))&
(![X]:((~old(X)|~tall(X))<=>(generous(X)&rich(X))))&
(![X]:((curious(X)|~old(X))<=>(~kind(X)<~>~patient(X))))&
((?[X]:((~generous(X)|kind(X))))=>((curious(susan)&strong(susan))))&
((?[X]:((~old(X)&wise(X))))<=>((~calm(john)|~curious(john))))&
(((generous(mary)&~creative(mary)))=>(?[X]:((~rich(X)<~>~patient(X)))))&
(?[X]:((humble(X)<~>~strong(X))))&
(?[X]:((curious(X)|~quiet(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
(?[X]:((~calm(X)&patient(X))))&
(?[X]:((~wise(X)|creative(X))))&
(~brave(john)) | brave(lucy) | [
"p1",
"p5",
"p7",
"p8",
"p11",
"p12",
"p13",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6161533309775369798481113
% SZS output start Proof for 6161533309775369798481113
2. brave(john) <=> ? [X0] : (brave(X0) <~> ~tall(X0)) [input p1]
6. ! [X0] : ((~curious(X0) <~> patient(X0)) <=> (rich(X0) | ~old(X0))) [input p5]
8. ? [X0] : ~quiet(X0) <=> (~old(lucy) <~> ~brave(lucy)) [input p7]
9. ! [X0] : (curious(X0) <=> ~strong(X0)) [input p8]
12. ! [X0] : ((~tall(X0) | ~old(X0)) <=> (rich(X0) & generous(X0))) [input p11]
13. ! [X0] : ((~old(X0) | curious(X0)) <=> (~kind(X0) <~> ~patient(X0))) [input p12]
14. ? [X0] : (kind(X0) | ~generous(X0)) => (strong(susan) & curious(susan)) [input p13]
19. ? [X0] : (~quiet(X0) & ~tall(X0)) [input p18]
22. ~brave(john) [input p21]
23. ~brave(lucy) [input hypothesis]
33. (strong(susan) & curious(susan)) | ! [X0] : (~kind(X0) & generous(X0)) [ennf transformation 14]
39. (brave(john) | ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (? [X0] : ((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | ~brave(john)) [nnf transformation 2]
40. (brave(john) | ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (? [X1] : ((tall(X1) | ~brave(X1)) & (~tall(X1) | brave(X1))) | ~brave(john)) [rectify 39]
41. ? [X1] : ((tall(X1) | ~brave(X1)) & (~tall(X1) | brave(X1))) => ((tall(sK2) | ~brave(sK2)) & (~tall(sK2) | brave(sK2))) [choice axiom]
42. (brave(john) | ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (((tall(sK2) | ~brave(sK2)) & (~tall(sK2) | brave(sK2))) | ~brave(john)) [skolemisation 40,41]
51. ! [X0] : ((((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))))) [nnf transformation 6]
52. ! [X0] : ((((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))))) [flattening 51]
56. (? [X0] : ~quiet(X0) | ((~old(lucy) | brave(lucy)) & (~brave(lucy) | old(lucy)))) & (((brave(lucy) | old(lucy)) & (~brave(lucy) | ~old(lucy))) | ! [X0] : quiet(X0)) [nnf transformation 8]
57. (? [X0] : ~quiet(X0) | ((~old(lucy) | brave(lucy)) & (~brave(lucy) | old(lucy)))) & (((brave(lucy) | old(lucy)) & (~brave(lucy) | ~old(lucy))) | ! [X1] : quiet(X1)) [rectify 56]
58. ? [X0] : ~quiet(X0) => ~quiet(sK6) [choice axiom]
59. (~quiet(sK6) | ((~old(lucy) | brave(lucy)) & (~brave(lucy) | old(lucy)))) & (((brave(lucy) | old(lucy)) & (~brave(lucy) | ~old(lucy))) | ! [X1] : quiet(X1)) [skolemisation 57,58]
60. ! [X0] : ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0))) [nnf transformation 9]
68. ! [X0] : (((~tall(X0) | ~old(X0)) | (~rich(X0) | ~generous(X0))) & ((rich(X0) & generous(X0)) | (tall(X0) & old(X0)))) [nnf transformation 12]
69. ! [X0] : ((~tall(X0) | ~old(X0) | ~rich(X0) | ~generous(X0)) & ((rich(X0) & generous(X0)) | (tall(X0) & old(X0)))) [flattening 68]
70. ! [X0] : (((~old(X0) | curious(X0)) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (old(X0) & ~curious(X0)))) [nnf transformation 13]
71. ! [X0] : ((~old(X0) | curious(X0) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (old(X0) & ~curious(X0)))) [flattening 70]
82. ? [X0] : (~quiet(X0) & ~tall(X0)) => (~quiet(sK11) & ~tall(sK11)) [choice axiom]
83. ~quiet(sK11) & ~tall(sK11) [skolemisation 19,82]
95. brave(john) | brave(X0) | tall(X0) [cnf transformation 42]
100. ~old(X0) | rich(X0) | patient(X0) | curious(X0) [cnf transformation 52]
101. ~old(X0) | rich(X0) | ~curious(X0) | ~patient(X0) [cnf transformation 52]
104. ~patient(X0) | curious(X0) | old(X0) [cnf transformation 52]
109. brave(lucy) | old(lucy) | quiet(X1) [cnf transformation 59]
112. ~strong(X0) | ~curious(X0) [cnf transformation 60]
127. ~rich(X0) | ~old(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 69]
130. ~curious(X0) | kind(X0) | patient(X0) [cnf transformation 71]
132. ~old(X0) | curious(X0) | ~patient(X0) | kind(X0) [cnf transformation 71]
134. curious(susan) | generous(X0) [cnf transformation 33]
135. curious(susan) | ~kind(X0) [cnf transformation 33]
136. strong(susan) | generous(X0) [cnf transformation 33]
137. strong(susan) | ~kind(X0) [cnf transformation 33]
147. ~quiet(sK11) [cnf transformation 83]
150. ~brave(john) [cnf transformation 22]
151. ~brave(lucy) [cnf transformation 23]
171. 5 <=> ! [X0] : (brave(X0) | tall(X0)) [avatar definition]
172. brave(X0) | tall(X0) <- (5) [avatar component clause 171]
174. 6 <=> brave(john) [avatar definition]
177. 5 | 6 [avatar split clause 95,174,171]
234. 20 <=> brave(lucy) [avatar definition]
235. ~brave(lucy) <- (~20) [avatar component clause 234]
238. 21 <=> old(lucy) [avatar definition]
239. old(lucy) <- (21) [avatar component clause 238]
248. 23 <=> ! [X1] : quiet(X1) [avatar definition]
249. quiet(X1) <- (23) [avatar component clause 248]
250. 23 | 21 | 20 [avatar split clause 109,234,238,248]
270. ~patient(X0) | curious(X0) | kind(X0) [subsumption resolution 132,104]
272. 28 <=> ! [X0] : ~kind(X0) [avatar definition]
273. ~kind(X0) <- (28) [avatar component clause 272]
275. 29 <=> strong(susan) [avatar definition]
277. strong(susan) <- (29) [avatar component clause 275]
278. 28 | 29 [avatar split clause 137,275,272]
280. 30 <=> ! [X0] : generous(X0) [avatar definition]
281. generous(X0) <- (30) [avatar component clause 280]
282. 30 | 29 [avatar split clause 136,275,280]
284. 31 <=> curious(susan) [avatar definition]
287. 28 | 31 [avatar split clause 135,284,272]
288. 30 | 31 [avatar split clause 134,284,280]
332. ~6 [avatar split clause 150,174]
333. ~20 [avatar split clause 151,234]
341. ~curious(susan) <- (29) [resolution 112,277]
344. ~31 | ~29 [avatar split clause 341,275,284]
355. tall(lucy) <- (5, ~20) [resolution 172,235]
454. $false <- (23) [resolution 249,147]
459. ~23 [avatar contradiction clause 454]
483. rich(lucy) | ~curious(lucy) | ~patient(lucy) <- (21) [resolution 239,101]
484. rich(lucy) | patient(lucy) | curious(lucy) <- (21) [resolution 239,100]
486. 47 <=> patient(lucy) [avatar definition]
487. patient(lucy) <- (47) [avatar component clause 486]
490. 48 <=> curious(lucy) [avatar definition]
491. curious(lucy) <- (48) [avatar component clause 490]
494. 49 <=> rich(lucy) [avatar definition]
496. rich(lucy) <- (49) [avatar component clause 494]
497. ~47 | ~48 | 49 | ~21 [avatar split clause 483,238,494,490,486]
498. 48 | 47 | 49 | ~21 [avatar split clause 484,238,494,486,490]
528. kind(lucy) | patient(lucy) <- (48) [resolution 491,130]
530. patient(lucy) <- (28, 48) [subsumption resolution 528,273]
533. 47 | ~28 | ~48 [avatar split clause 530,490,272,486]
534. curious(lucy) | kind(lucy) <- (47) [resolution 487,270]
536. ~old(lucy) | ~tall(lucy) | ~generous(lucy) <- (49) [resolution 496,127]
541. ~tall(lucy) | ~generous(lucy) <- (21, 49) [subsumption resolution 536,239]
542. ~generous(lucy) <- (5, ~20, 21, 49) [subsumption resolution 541,355]
543. $false <- (5, ~20, 21, 30, 49) [subsumption resolution 542,281]
544. ~5 | 20 | ~21 | ~30 | ~49 [avatar contradiction clause 543]
547. curious(lucy) <- (28, 47) [subsumption resolution 534,273]
548. 48 | ~28 | ~47 [avatar split clause 547,486,272,490]
549. $false [avatar sat refutation 177,250,278,282,287,288,332,333,344,459,497,498,533,544,548]
% SZS output end Proof for 6161533309775369798481113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both not curious and curious.
Everyone who is strong or not patient is either not creative or humble and vice versa.
Everyone who is not generous is either not calm or not brave and vice versa.
Everyone who is either not rich or not old is not funny.
Everyone who is not happy or not curious is both quiet and not kind and vice versa.
If someone is both not kind and humble then someone is both not strong and not patient and vice versa.
Everyone who is not strong or tall is either tall or not kind and vice versa.
Everyone who is either kind or quiet is not humble and vice versa.
If someone is either funny or brave then someone is both strong and brave.
If john is either patient or not happy then john is both strong and creative.
If someone is either not old or not patient then someone is not brave or not patient and vice versa.
If someone is not quiet or tall then paul is not kind or not brave.
If someone is either brave or not generous then someone is either creative or not brave and vice versa.
If john is not rich then someone is not old or not creative and vice versa.
Everyone who is both kind and calm is both curious and not wise.
Everyone who is both not humble and not generous is not calm.
Paul is both calm and kind.
Someone is brave.
Someone is not calm or tall.
Someone is brave or not patient.
Paul is tall or not generous.
Lucy is both rich and not curious.
Someone is not patient.
Someone is not old. | John is not old. | neutral | (![X]:(~calm(X)=>(~curious(X)&curious(X))))&
(![X]:((strong(X)|~patient(X))<=>(~creative(X)<~>humble(X))))&
(![X]:(~generous(X)<=>(~calm(X)<~>~brave(X))))&
(![X]:((~rich(X)<~>~old(X))=>~funny(X)))&
(![X]:((~happy(X)|~curious(X))<=>(quiet(X)&~kind(X))))&
((?[X]:((~kind(X)&humble(X))))<=>(?[X]:((~strong(X)&~patient(X)))))&
(![X]:((~strong(X)|tall(X))<=>(tall(X)<~>~kind(X))))&
(![X]:((kind(X)<~>quiet(X))<=>~humble(X)))&
((?[X]:((funny(X)<~>brave(X))))=>(?[X]:((strong(X)&brave(X)))))&
(((patient(john)<~>~happy(john)))=>((strong(john)&creative(john))))&
((?[X]:((~old(X)<~>~patient(X))))<=>(?[X]:((~brave(X)|~patient(X)))))&
((?[X]:((~quiet(X)|tall(X))))=>((~kind(paul)|~brave(paul))))&
((?[X]:((brave(X)<~>~generous(X))))<=>(?[X]:((creative(X)<~>~brave(X)))))&
((~rich(john))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((kind(X)&calm(X))=>(curious(X)&~wise(X))))&
(![X]:((~humble(X)&~generous(X))=>~calm(X)))&
((calm(paul)&kind(paul)))&
(?[X]:(brave(X)))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:((brave(X)|~patient(X))))&
((tall(paul)|~generous(paul)))&
((rich(lucy)&~curious(lucy)))&
(?[X]:(~patient(X)))&
(?[X]:(~old(X))) | ~old(john) | [] | null | 0 |
Everyone who is both not strong and not rich is tall and vice versa.
Everyone who is both kind and not patient is either not funny or quiet and vice versa.
Everyone who is quiet is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
Everyone who is generous is generous or not kind and vice versa.
If someone is both kind and quiet then someone is strong or not old.
Everyone who is both old and not calm is not rich or not funny and vice versa.
Everyone who is both rich and not wise is both curious and quiet.
If john is both curious and old then susan is rich and vice versa.
Everyone who is either patient or happy is funny or not curious and vice versa.
If someone is rich or calm then alice is rich or not old and vice versa.
Everyone who is either tall or not funny is both strong and funny and vice versa.
Someone is both brave and not strong.
Lucy is either generous or not brave.
Someone is not strong or not quiet.
Someone is rich.
Someone is either quiet or not curious.
Someone is either humble or not wise. | Lucy is patient. | contradiction | (![X]:((~strong(X)&~rich(X))<=>tall(X)))&
(![X]:((kind(X)&~patient(X))<=>(~funny(X)<~>quiet(X))))&
(![X]:(quiet(X)<=>(happy(X)|generous(X))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)&~calm(X))<=>(~rich(X)|~funny(X))))&
(![X]:((rich(X)&~wise(X))=>(curious(X)&quiet(X))))&
(((curious(john)&old(john)))<=>(rich(susan)))&
(![X]:((patient(X)<~>happy(X))<=>(funny(X)|~curious(X))))&
((?[X]:((rich(X)|calm(X))))<=>((rich(alice)|~old(alice))))&
(![X]:((tall(X)<~>~funny(X))<=>(strong(X)&funny(X))))&
(?[X]:((brave(X)&~strong(X))))&
((generous(lucy)<~>~brave(lucy)))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~wise(X)))) | patient(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p6",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3546469542293323342897974
% SZS output start Proof for 3546469542293323342897974
1. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> tall(X0)) [input p0]
2. ! [X0] : ((~patient(X0) & kind(X0)) <=> (~funny(X0) <~> quiet(X0))) [input p1]
3. ! [X0] : (quiet(X0) <=> (generous(X0) | happy(X0))) [input p2]
4. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p3]
5. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (funny(X0) | curious(X0))) [input p4]
7. ! [X0] : ((rich(X0) <~> curious(X0)) <=> (~quiet(X0) | brave(X0))) [input p6]
16. ! [X0] : ((tall(X0) <~> ~funny(X0)) <=> (funny(X0) & strong(X0))) [input p15]
18. generous(lucy) <~> ~brave(lucy) [input p17]
23. patient(lucy) [input hypothesis]
25. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 4]
29. ! [X0] : (((~rich(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | (rich(X0) | strong(X0)))) [nnf transformation 1]
30. ! [X0] : (((~rich(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | rich(X0) | strong(X0))) [flattening 29]
31. ! [X0] : (((~patient(X0) & kind(X0)) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0)))) & (((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | (patient(X0) | ~kind(X0)))) [nnf transformation 2]
32. ! [X0] : (((~patient(X0) & kind(X0)) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0)))) & (((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | patient(X0) | ~kind(X0))) [flattening 31]
33. ! [X0] : ((quiet(X0) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | ~quiet(X0))) [nnf transformation 3]
34. ! [X0] : ((quiet(X0) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | ~quiet(X0))) [flattening 33]
35. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 5]
36. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 35]
39. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (quiet(X0) & ~brave(X0))) & ((~quiet(X0) | brave(X0)) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [nnf transformation 7]
40. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (quiet(X0) & ~brave(X0))) & (~quiet(X0) | brave(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [flattening 39]
62. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [nnf transformation 16]
63. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [flattening 62]
66. (brave(lucy) | ~generous(lucy)) & (~brave(lucy) | generous(lucy)) [nnf transformation 18]
77. tall(X0) | rich(X0) | strong(X0) [cnf transformation 30]
78. ~tall(X0) | ~strong(X0) [cnf transformation 30]
79. ~tall(X0) | ~rich(X0) [cnf transformation 30]
84. ~patient(X0) | quiet(X0) | funny(X0) [cnf transformation 32]
85. ~quiet(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 32]
86. ~quiet(X0) | happy(X0) | generous(X0) [cnf transformation 34]
88. ~generous(X0) | quiet(X0) [cnf transformation 34]
90. ~happy(X0) | rich(X0) [cnf transformation 25]
92. ~brave(X0) | rich(X0) [cnf transformation 25]
98. ~funny(X0) | curious(X0) | brave(X0) [cnf transformation 36]
107. ~curious(X0) | ~rich(X0) | quiet(X0) [cnf transformation 40]
137. strong(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 63]
140. funny(X0) | tall(X0) | funny(X0) [cnf transformation 63]
141. ~funny(X0) | tall(X0) | ~funny(X0) | ~strong(X0) [cnf transformation 63]
145. ~brave(lucy) | generous(lucy) [cnf transformation 66]
146. brave(lucy) | ~generous(lucy) [cnf transformation 66]
153. patient(lucy) [cnf transformation 23]
154. funny(X0) | tall(X0) [duplicate literal removal 140]
155. ~funny(X0) | tall(X0) | ~strong(X0) [duplicate literal removal 141]
233. ~funny(X0) | ~strong(X0) [subsumption resolution 155,78]
234. ~funny(X0) | ~tall(X0) [subsumption resolution 137,78]
236. 16 <=> generous(lucy) [avatar definition]
237. generous(lucy) <- (16) [avatar component clause 236]
238. ~generous(lucy) <- (~16) [avatar component clause 236]
240. 17 <=> brave(lucy) [avatar definition]
241. ~brave(lucy) <- (~17) [avatar component clause 240]
242. brave(lucy) <- (17) [avatar component clause 240]
243. ~16 | 17 [avatar split clause 146,240,236]
244. 16 | ~17 [avatar split clause 145,240,236]
282. ~strong(X0) | tall(X0) [resolution 233,154]
285. ~strong(X0) [subsumption resolution 282,78]
321. quiet(lucy) | funny(lucy) [resolution 84,153]
323. 28 <=> funny(lucy) [avatar definition]
324. ~funny(lucy) <- (~28) [avatar component clause 323]
325. funny(lucy) <- (28) [avatar component clause 323]
327. 29 <=> quiet(lucy) [avatar definition]
329. quiet(lucy) <- (29) [avatar component clause 327]
330. 28 | 29 [avatar split clause 321,327,323]
481. curious(lucy) | brave(lucy) <- (28) [resolution 325,98]
482. ~tall(lucy) <- (28) [resolution 325,234]
484. curious(lucy) <- (~17, 28) [subsumption resolution 481,241]
827. rich(lucy) | strong(lucy) <- (28) [resolution 482,77]
828. rich(lucy) <- (28) [subsumption resolution 827,285]
860. ~rich(lucy) | quiet(lucy) <- (~17, 28) [resolution 484,107]
863. quiet(lucy) <- (~17, 28) [subsumption resolution 860,828]
864. 29 | 17 | ~28 [avatar split clause 863,323,240,327]
868. happy(lucy) | generous(lucy) <- (29) [resolution 329,86]
869. ~funny(lucy) | ~patient(lucy) <- (29) [resolution 329,85]
873. happy(lucy) <- (~16, 29) [subsumption resolution 868,238]
878. ~funny(lucy) <- (29) [subsumption resolution 869,153]
879. ~28 | ~29 [avatar split clause 878,327,323]
882. 84 <=> rich(lucy) [avatar definition]
898. tall(lucy) <- (~28) [resolution 324,154]
1208. rich(lucy) <- (~16, 29) [resolution 873,90]
1215. 84 | 16 | ~29 [avatar split clause 1208,327,236,882]
1226. ~rich(lucy) <- (~28) [resolution 898,79]
1233. ~84 | 28 [avatar split clause 1226,323,882]
1236. quiet(lucy) <- (16) [resolution 237,88]
1239. rich(lucy) <- (17) [resolution 242,92]
1246. 29 | ~16 [avatar split clause 1236,236,327]
1247. 84 | ~17 [avatar split clause 1239,240,882]
1248. $false [avatar sat refutation 243,244,330,864,879,1215,1233,1246,1247]
% SZS output end Proof for 3546469542293323342897974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5628
% Time elapsed: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is both not kind and funny.
If someone is not creative then someone is not rich and vice versa.
Everyone who is not quiet is not tall and vice versa.
If someone is both not quiet and not rich then fred is both humble and not patient and vice versa.
Everyone who is not generous or strong is brave.
Everyone who is either old or kind is old.
Everyone who is not wise or not generous is happy.
If susan is either funny or happy then susan is not quiet and vice versa.
Everyone who is either curious or not tall is both humble and not kind and vice versa.
Everyone who is either humble or old is not quiet and vice versa.
Everyone who is either not old or tall is not tall and vice versa.
Everyone who is both happy and not happy is patient or happy and vice versa.
If susan is not happy then fred is curious or calm.
Everyone who is not quiet is both curious and not brave and vice versa.
If alice is either old or not creative then someone is either strong or not curious.
Everyone who is either wise or creative is both creative and not quiet.
John is not creative or not brave.
Someone is not strong.
Someone is rich.
Someone is either not kind or humble.
Someone is calm or not creative.
Fred is either not strong or calm.
Alice is both quiet and not happy. | Susan is humble. | contradiction | (![X]:(~brave(X)=>(~kind(X)&funny(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~rich(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
((?[X]:((~quiet(X)&~rich(X))))<=>((humble(fred)&~patient(fred))))&
(![X]:((~generous(X)|strong(X))=>brave(X)))&
(![X]:((old(X)<~>kind(X))=>old(X)))&
(![X]:((~wise(X)|~generous(X))=>happy(X)))&
(((funny(susan)<~>happy(susan)))<=>(~quiet(susan)))&
(![X]:((curious(X)<~>~tall(X))<=>(humble(X)&~kind(X))))&
(![X]:((humble(X)<~>old(X))<=>~quiet(X)))&
(![X]:((~old(X)<~>tall(X))<=>~tall(X)))&
(![X]:((happy(X)&~happy(X))<=>(patient(X)|happy(X))))&
((~happy(susan))=>((curious(fred)|calm(fred))))&
(![X]:(~quiet(X)<=>(curious(X)&~brave(X))))&
(((old(alice)<~>~creative(alice)))=>(?[X]:((strong(X)<~>~curious(X)))))&
(![X]:((wise(X)<~>creative(X))=>(creative(X)&~quiet(X))))&
((~creative(john)|~brave(john)))&
(?[X]:(~strong(X)))&
(?[X]:(rich(X)))&
(?[X]:((~kind(X)<~>humble(X))))&
(?[X]:((calm(X)|~creative(X))))&
((~strong(fred)<~>calm(fred)))&
((quiet(alice)&~happy(alice))) | humble(susan) | [
"p2",
"p5",
"p8",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 479650324982355642410533
% SZS output start Proof for 479650324982355642410533
3. ! [X0] : (~quiet(X0) <=> ~tall(X0)) [input p2]
6. ! [X0] : ((old(X0) <~> kind(X0)) => old(X0)) [input p5]
9. ! [X0] : ((curious(X0) <~> ~tall(X0)) <=> (~kind(X0) & humble(X0))) [input p8]
10. ! [X0] : ((humble(X0) <~> old(X0)) <=> ~quiet(X0)) [input p9]
11. ! [X0] : ((~old(X0) <~> tall(X0)) <=> ~tall(X0)) [input p10]
14. ! [X0] : (~quiet(X0) <=> (~brave(X0) & curious(X0))) [input p13]
24. humble(susan) [input hypothesis]
30. ! [X0] : (old(X0) | (old(X0) <=> kind(X0))) [ennf transformation 6]
41. ! [X0] : ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))) [nnf transformation 3]
47. ! [X0] : (old(X0) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0)))) [nnf transformation 30]
49. ! [X0] : ((((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (kind(X0) | ~humble(X0))) & ((~kind(X0) & humble(X0)) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0))))) [nnf transformation 9]
50. ! [X0] : ((((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | kind(X0) | ~humble(X0)) & ((~kind(X0) & humble(X0)) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0))))) [flattening 49]
51. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | quiet(X0)) & (~quiet(X0) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 10]
52. ! [X0] : ((((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | tall(X0)) & (~tall(X0) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))))) [nnf transformation 11]
55. ! [X0] : ((~quiet(X0) | (brave(X0) | ~curious(X0))) & ((~brave(X0) & curious(X0)) | quiet(X0))) [nnf transformation 14]
56. ! [X0] : ((~quiet(X0) | brave(X0) | ~curious(X0)) & ((~brave(X0) & curious(X0)) | quiet(X0))) [flattening 55]
75. ~tall(X0) | quiet(X0) [cnf transformation 41]
76. ~quiet(X0) | tall(X0) [cnf transformation 41]
83. old(X0) | old(X0) | ~kind(X0) [cnf transformation 47]
94. ~curious(X0) | tall(X0) | kind(X0) | ~humble(X0) [cnf transformation 50]
95. ~humble(X0) | old(X0) | ~quiet(X0) [cnf transformation 51]
97. old(X0) | humble(X0) | quiet(X0) [cnf transformation 51]
100. ~tall(X0) | ~old(X0) | ~tall(X0) [cnf transformation 52]
101. tall(X0) | ~old(X0) | tall(X0) [cnf transformation 52]
109. curious(X0) | quiet(X0) [cnf transformation 56]
130. humble(susan) [cnf transformation 24]
134. ~tall(X0) | ~old(X0) [duplicate literal removal 100]
135. ~old(X0) | tall(X0) [duplicate literal removal 101]
136. ~kind(X0) | old(X0) [duplicate literal removal 83]
177. 10 <=> quiet(susan) [avatar definition]
178. ~quiet(susan) <- (~10) [avatar component clause 177]
192. ~old(X0) [subsumption resolution 134,135]
285. old(susan) | ~quiet(susan) [resolution 95,130]
286. ~quiet(susan) [subsumption resolution 285,192]
289. ~10 [avatar split clause 286,177]
292. humble(X2) | quiet(X2) [resolution 97,192]
322. 25 <=> tall(susan) [avatar definition]
323. tall(susan) <- (25) [avatar component clause 322]
324. ~tall(susan) <- (~25) [avatar component clause 322]
326. 26 <=> kind(susan) [avatar definition]
328. kind(susan) <- (26) [avatar component clause 326]
335. tall(X1) | kind(X1) | ~humble(X1) | quiet(X1) [resolution 94,109]
337. tall(X1) | kind(X1) | quiet(X1) [subsumption resolution 335,292]
338. tall(X1) | kind(X1) [subsumption resolution 337,76]
345. kind(susan) <- (~25) [resolution 338,324]
346. 26 | 25 [avatar split clause 345,322,326]
348. old(susan) <- (26) [resolution 328,136]
352. $false <- (26) [subsumption resolution 348,192]
353. ~26 [avatar contradiction clause 352]
354. quiet(susan) <- (25) [resolution 323,75]
355. $false <- (~10, 25) [subsumption resolution 354,178]
356. 10 | ~25 [avatar contradiction clause 355]
357. $false [avatar sat refutation 289,346,353,356]
% SZS output end Proof for 479650324982355642410533
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either not wise or quiet and vice versa. Everyone who is either not funny or creative is rich. If susan is strong then fred is strong or not calm. If alice is either not patient or funny then someone is wise or tall. Everyone who is not humble or not patient is either wise or not patient. If someone is either not strong or rich then susan is not rich or not curious and vice versa. Everyone who is not generous is old or quiet and vice versa. Everyone who is both curious and not kind is both not generous and old. If someone is either patient or not brave then lucy is kind or brave and vice versa. Everyone who is both not kind and not generous is both creative and not generous. If someone is happy then someone is wise and vice versa. Everyone who is not funny or not patient is not happy or wise and vice versa. Everyone who is either patient or generous is not quiet and vice versa. If someone is not quiet then lucy is either not tall or brave. If someone is not kind or not tall then lucy is wise and vice versa. If someone is not brave then someone is either not calm or kind and vice versa. Paul is both generous and not humble. Someone is either not humble or curious. Someone is either not humble or humble. Someone is either not old or not kind. Lucy is not generous or tall. | Paul is not kind. | contradiction | (![X]:((~happy(X)|patient(X))<=>(~wise(X)<~>quiet(X))))&
(![X]:((~funny(X)<~>creative(X))=>rich(X)))&
((strong(susan))=>((strong(fred)|~calm(fred))))&
(((~patient(alice)<~>funny(alice)))=>(?[X]:((wise(X)|tall(X)))))&
(![X]:((~humble(X)|~patient(X))=>(wise(X)<~>~patient(X))))&
((?[X]:((~strong(X)<~>rich(X))))<=>((~rich(susan)|~curious(susan))))&
(![X]:(~generous(X)<=>(old(X)|quiet(X))))&
(![X]:((curious(X)&~kind(X))=>(~generous(X)&old(X))))&
((?[X]:((patient(X)<~>~brave(X))))<=>((kind(lucy)|brave(lucy))))&
(![X]:((~kind(X)&~generous(X))=>(creative(X)&~generous(X))))&
((?[X]:(happy(X)))<=>(?[X]:(wise(X))))&
(![X]:((~funny(X)|~patient(X))<=>(~happy(X)|wise(X))))&
(![X]:((patient(X)<~>generous(X))<=>~quiet(X)))&
((?[X]:(~quiet(X)))=>((~tall(lucy)<~>brave(lucy))))&
((?[X]:((~kind(X)|~tall(X))))<=>(wise(lucy)))&
((?[X]:(~brave(X)))<=>(?[X]:((~calm(X)<~>kind(X)))))&
((generous(paul)&~humble(paul)))&
(?[X]:((~humble(X)<~>curious(X))))&
(?[X]:((~humble(X)<~>humble(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
((~generous(lucy)|tall(lucy))) | ~kind(paul) | [
"p0",
"p4",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1025358859021046816450919
% SZS output start Proof for 1025358859021046816450919
1. ! [X0] : ((patient(X0) | ~happy(X0)) <=> (~wise(X0) <~> quiet(X0))) [input p0]
5. ! [X0] : ((~patient(X0) | ~humble(X0)) => (wise(X0) <~> ~patient(X0))) [input p4]
7. ! [X0] : (~generous(X0) <=> (quiet(X0) | old(X0))) [input p6]
13. ! [X0] : ((patient(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p12]
15. ? [X0] : (~tall(X0) | ~kind(X0)) <=> wise(lucy) [input p14]
22. ~kind(paul) [input hypothesis]
29. ! [X0] : ((wise(X0) <~> ~patient(X0)) | (patient(X0) & humble(X0))) [ennf transformation 5]
35. ! [X0] : (((patient(X0) | ~happy(X0)) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | (~patient(X0) & happy(X0)))) [nnf transformation 1]
36. ! [X0] : ((patient(X0) | ~happy(X0) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | (~patient(X0) & happy(X0)))) [flattening 35]
41. ! [X0] : (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (patient(X0) & humble(X0))) [nnf transformation 29]
47. ! [X0] : ((~generous(X0) | (~quiet(X0) & ~old(X0))) & ((quiet(X0) | old(X0)) | generous(X0))) [nnf transformation 7]
48. ! [X0] : ((~generous(X0) | (~quiet(X0) & ~old(X0))) & (quiet(X0) | old(X0) | generous(X0))) [flattening 47]
61. ! [X0] : ((((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | quiet(X0)) & (~quiet(X0) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0))))) [nnf transformation 13]
63. (? [X0] : (~tall(X0) | ~kind(X0)) | ~wise(lucy)) & (wise(lucy) | ! [X0] : (tall(X0) & kind(X0))) [nnf transformation 15]
64. (? [X0] : (~tall(X0) | ~kind(X0)) | ~wise(lucy)) & (wise(lucy) | ! [X1] : (tall(X1) & kind(X1))) [rectify 63]
65. ? [X0] : (~tall(X0) | ~kind(X0)) => (~tall(sK5) | ~kind(sK5)) [choice axiom]
66. ((~tall(sK5) | ~kind(sK5)) | ~wise(lucy)) & (wise(lucy) | ! [X1] : (tall(X1) & kind(X1))) [skolemisation 64,65]
82. ~wise(X0) | quiet(X0) | ~patient(X0) [cnf transformation 36]
95. patient(X0) | ~wise(X0) | patient(X0) [cnf transformation 41]
104. ~generous(X0) | ~quiet(X0) [cnf transformation 48]
121. ~quiet(X0) | generous(X0) | ~patient(X0) [cnf transformation 61]
127. wise(lucy) | kind(X1) [cnf transformation 66]
143. ~kind(paul) [cnf transformation 22]
144. ~wise(X0) | patient(X0) [duplicate literal removal 95]
251. ~quiet(X0) | ~patient(X0) [subsumption resolution 121,104]
262. 26 <=> wise(lucy) [avatar definition]
263. wise(lucy) <- (26) [avatar component clause 262]
279. 30 <=> ! [X1] : kind(X1) [avatar definition]
280. kind(X1) <- (30) [avatar component clause 279]
281. 30 | 26 [avatar split clause 127,262,279]
350. 43 <=> quiet(lucy) [avatar definition]
352. quiet(lucy) <- (43) [avatar component clause 350]
367. $false <- (30) [resolution 280,143]
372. ~30 [avatar contradiction clause 367]
377. patient(lucy) <- (26) [resolution 263,144]
379. quiet(lucy) | ~patient(lucy) <- (26) [resolution 82,263]
382. quiet(lucy) <- (26) [subsumption resolution 379,377]
383. 43 | ~26 [avatar split clause 382,262,350]
387. ~patient(lucy) <- (43) [resolution 352,251]
388. $false <- (26, 43) [subsumption resolution 387,377]
389. ~26 | ~43 [avatar contradiction clause 388]
390. $false [avatar sat refutation 281,372,383,389]
% SZS output end Proof for 1025358859021046816450919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or tall then paul is not patient and vice versa.
If mary is either not kind or not curious then fred is not rich or not creative.
Everyone who is old or not strong is both wise and generous.
If someone is both not quiet and not funny then someone is creative or not rich and vice versa.
If john is not creative or not rich then alice is either not quiet or not curious.
If someone is either not brave or not happy then lucy is both not humble and humble.
Everyone who is happy is humble or happy and vice versa.
Everyone who is rich is both not happy and generous.
If fred is not strong or happy then someone is not patient.
Everyone who is not creative is both humble and rich and vice versa.
If lucy is not happy or not creative then someone is either not brave or not old.
Everyone who is not generous or not brave is not happy or quiet.
If someone is not quiet then someone is both quiet and not wise and vice versa.
Everyone who is both quiet and not tall is either not patient or creative.
Everyone who is funny or creative is both kind and not brave.
If susan is both not creative and not humble then someone is either not quiet or wise and vice versa.
John is patient.
John is both tall and curious.
Someone is not funny.
Someone is patient or tall.
Paul is wise.
Someone is either humble or not tall.
Paul is both curious and not calm. | Mary is not brave. | entailment | ((?[X]:((~calm(X)<~>tall(X))))<=>(~patient(paul)))&
(((~kind(mary)<~>~curious(mary)))=>((~rich(fred)|~creative(fred))))&
(![X]:((old(X)|~strong(X))=>(wise(X)&generous(X))))&
((?[X]:((~quiet(X)&~funny(X))))<=>(?[X]:((creative(X)|~rich(X)))))&
(((~creative(john)|~rich(john)))=>((~quiet(alice)<~>~curious(alice))))&
((?[X]:((~brave(X)<~>~happy(X))))=>((~humble(lucy)&humble(lucy))))&
(![X]:(happy(X)<=>(humble(X)|happy(X))))&
(![X]:(rich(X)=>(~happy(X)&generous(X))))&
(((~strong(fred)|happy(fred)))=>(?[X]:(~patient(X))))&
(![X]:(~creative(X)<=>(humble(X)&rich(X))))&
(((~happy(lucy)|~creative(lucy)))=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)|quiet(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((quiet(X)&~wise(X)))))&
(![X]:((quiet(X)&~tall(X))=>(~patient(X)<~>creative(X))))&
(![X]:((funny(X)|creative(X))=>(kind(X)&~brave(X))))&
(((~creative(susan)&~humble(susan)))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
(patient(john))&
((tall(john)&curious(john)))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)|tall(X))))&
(wise(paul))&
(?[X]:((humble(X)<~>~tall(X))))&
((curious(paul)&~calm(paul))) | ~brave(mary) | [
"p5",
"p7",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4085178666664465700630902
% SZS output start Proof for 4085178666664465700630902
6. ? [X0] : (~brave(X0) <~> ~happy(X0)) => (humble(lucy) & ~humble(lucy)) [input p5]
8. ! [X0] : (rich(X0) => (generous(X0) & ~happy(X0))) [input p7]
10. ! [X0] : (~creative(X0) <=> (rich(X0) & humble(X0))) [input p9]
15. ! [X0] : ((creative(X0) | funny(X0)) => (~brave(X0) & kind(X0))) [input p14]
24. brave(mary) [input hypothesis]
28. ! [X0] : (rich(X0) => ~happy(X0)) [pure predicate removal 8]
36. (humble(lucy) & ~humble(lucy)) | ! [X0] : (~brave(X0) <=> ~happy(X0)) [ennf transformation 6]
37. ! [X0] : (~happy(X0) | ~rich(X0)) [ennf transformation 28]
44. ! [X0] : ((~brave(X0) & kind(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 15]
56. (humble(lucy) & ~humble(lucy)) | ! [X0] : ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0))) [nnf transformation 36]
61. ! [X0] : ((~creative(X0) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | creative(X0))) [nnf transformation 10]
62. ! [X0] : ((~creative(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | creative(X0))) [flattening 61]
101. ~humble(lucy) | ~brave(X0) | happy(X0) [cnf transformation 56]
103. humble(lucy) | ~brave(X0) | happy(X0) [cnf transformation 56]
107. ~happy(X0) | ~rich(X0) [cnf transformation 37]
110. creative(X0) | rich(X0) [cnf transformation 62]
125. ~brave(X0) | ~creative(X0) [cnf transformation 44]
142. brave(mary) [cnf transformation 24]
234. 21 <=> ! [X0] : (~brave(X0) | happy(X0)) [avatar definition]
235. ~brave(X0) | happy(X0) <- (21) [avatar component clause 234]
237. 22 <=> humble(lucy) [avatar definition]
240. 21 | 22 [avatar split clause 103,237,234]
245. 21 | ~22 [avatar split clause 101,237,234]
369. ~creative(mary) [resolution 125,142]
378. happy(mary) <- (21) [resolution 235,142]
380. rich(mary) [resolution 369,110]
389. ~rich(mary) <- (21) [resolution 378,107]
392. $false <- (21) [subsumption resolution 380,389]
393. ~21 [avatar contradiction clause 392]
395. $false [avatar sat refutation 240,245,393]
% SZS output end Proof for 4085178666664465700630902
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not old is both generous and calm.
If someone is both not happy and not funny then lucy is brave and vice versa.
Everyone who is either rich or tall is both not quiet and curious and vice versa.
Everyone who is either not patient or not funny is either not patient or curious and vice versa.
Everyone who is not kind or strong is both funny and not quiet and vice versa.
Everyone who is either humble or not brave is either old or humble.
Everyone who is not calm is both quiet and not rich.
If susan is either not wise or not humble then alice is creative or kind and vice versa.
If mary is wise or not quiet then someone is both not humble and patient and vice versa.
Everyone who is quiet is either not wise or not curious and vice versa.
If lucy is both brave and not calm then someone is patient and vice versa.
If fred is either kind or not wise then susan is not happy and vice versa.
If fred is either tall or strong then someone is either curious or tall.
If someone is not rich or old then mary is not kind or not tall.
Everyone who is not rich or wise is both not strong and creative and vice versa.
If someone is both old and creative then someone is both strong and rich.
Someone is either brave or strong.
Someone is both old and not funny.
Fred is either creative or brave.
Alice is not curious.
Alice is both not humble and not calm.
Someone is either not creative or not patient.
John is not humble or brave.
Susan is humble. | Susan is wise. | contradiction | (![X]:((~patient(X)<~>~old(X))=>(generous(X)&calm(X))))&
((?[X]:((~happy(X)&~funny(X))))<=>(brave(lucy)))&
(![X]:((rich(X)<~>tall(X))<=>(~quiet(X)&curious(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(~patient(X)<~>curious(X))))&
(![X]:((~kind(X)|strong(X))<=>(funny(X)&~quiet(X))))&
(![X]:((humble(X)<~>~brave(X))=>(old(X)<~>humble(X))))&
(![X]:(~calm(X)=>(quiet(X)&~rich(X))))&
(((~wise(susan)<~>~humble(susan)))<=>((creative(alice)|kind(alice))))&
(((wise(mary)|~quiet(mary)))<=>(?[X]:((~humble(X)&patient(X)))))&
(![X]:(quiet(X)<=>(~wise(X)<~>~curious(X))))&
(((brave(lucy)&~calm(lucy)))<=>(?[X]:(patient(X))))&
(((kind(fred)<~>~wise(fred)))<=>(~happy(susan)))&
(((tall(fred)<~>strong(fred)))=>(?[X]:((curious(X)<~>tall(X)))))&
((?[X]:((~rich(X)|old(X))))=>((~kind(mary)|~tall(mary))))&
(![X]:((~rich(X)|wise(X))<=>(~strong(X)&creative(X))))&
((?[X]:((old(X)&creative(X))))=>(?[X]:((strong(X)&rich(X)))))&
(?[X]:((brave(X)<~>strong(X))))&
(?[X]:((old(X)&~funny(X))))&
((creative(fred)<~>brave(fred)))&
(~curious(alice))&
((~humble(alice)&~calm(alice)))&
(?[X]:((~creative(X)<~>~patient(X))))&
((~humble(john)|brave(john)))&
(humble(susan)) | wise(susan) | [
"p6",
"p7",
"p14",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5681714749256302406912507
% SZS output start Proof for 5681714749256302406912507
7. ! [X0] : (~calm(X0) => (~rich(X0) & quiet(X0))) [input p6]
8. (~wise(susan) <~> ~humble(susan)) <=> (kind(alice) | creative(alice)) [input p7]
15. ! [X0] : ((wise(X0) | ~rich(X0)) <=> (creative(X0) & ~strong(X0))) [input p14]
21. ~calm(alice) & ~humble(alice) [input p20]
24. humble(susan) [input p23]
25. wise(susan) [input hypothesis]
30. ! [X0] : ((~rich(X0) & quiet(X0)) | calm(X0)) [ennf transformation 7]
46. (((humble(susan) | wise(susan)) & (~humble(susan) | ~wise(susan))) | (~kind(alice) & ~creative(alice))) & ((kind(alice) | creative(alice)) | ((~wise(susan) | humble(susan)) & (~humble(susan) | wise(susan)))) [nnf transformation 8]
47. (((humble(susan) | wise(susan)) & (~humble(susan) | ~wise(susan))) | (~kind(alice) & ~creative(alice))) & (kind(alice) | creative(alice) | ((~wise(susan) | humble(susan)) & (~humble(susan) | wise(susan)))) [flattening 46]
63. ! [X0] : (((wise(X0) | ~rich(X0)) | (~creative(X0) | strong(X0))) & ((creative(X0) & ~strong(X0)) | (~wise(X0) & rich(X0)))) [nnf transformation 15]
64. ! [X0] : ((wise(X0) | ~rich(X0) | ~creative(X0) | strong(X0)) & ((creative(X0) & ~strong(X0)) | (~wise(X0) & rich(X0)))) [flattening 63]
106. ~rich(X0) | calm(X0) [cnf transformation 30]
109. ~humble(susan) | ~wise(susan) | ~creative(alice) [cnf transformation 47]
137. creative(X0) | rich(X0) [cnf transformation 64]
150. ~calm(alice) [cnf transformation 21]
154. humble(susan) [cnf transformation 24]
155. wise(susan) [cnf transformation 25]
187. 6 <=> wise(susan) [avatar definition]
191. 7 <=> humble(susan) [avatar definition]
196. 8 <=> creative(alice) [avatar definition]
198. ~creative(alice) <- (~8) [avatar component clause 196]
201. ~8 | ~6 | ~7 [avatar split clause 109,191,187,196]
346. 7 [avatar split clause 154,191]
347. 6 [avatar split clause 155,187]
359. rich(alice) <- (~8) [resolution 137,198]
361. calm(alice) <- (~8) [resolution 359,106]
362. $false <- (~8) [subsumption resolution 361,150]
363. 8 [avatar contradiction clause 362]
364. $false [avatar sat refutation 201,346,347,363]
% SZS output end Proof for 5681714749256302406912507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not tall or not rich then susan is kind and vice versa.
If someone is not humble then someone is not tall or curious and vice versa.
Everyone who is both not generous and brave is either not happy or quiet.
Everyone who is both not rich and strong is tall and vice versa.
If john is either funny or not curious then paul is not kind or not calm.
If paul is strong then someone is old.
Everyone who is happy or not old is patient or not strong and vice versa.
Everyone who is both tall and not tall is rich or not strong and vice versa.
If paul is both not calm and not humble then mary is either brave or creative.
Everyone who is tall or rich is either not wise or brave.
Everyone who is both not humble and funny is either not quiet or not generous and vice versa.
Everyone who is not generous is funny or creative and vice versa.
If alice is either not wise or patient then mary is not quiet or happy and vice versa.
Everyone who is both curious and happy is curious or old and vice versa.
If someone is either not old or not strong then someone is either funny or not happy.
Everyone who is not wise or not rich is both strong and not creative.
Someone is brave or not tall.
Someone is not old or not brave.
Someone is either not generous or not wise.
Fred is quiet or not curious.
Someone is either brave or not quiet.
Fred is not wise. | Alice is generous. | neutral | ((?[X]:((~tall(X)<~>~rich(X))))<=>(kind(susan)))&
((?[X]:(~humble(X)))<=>(?[X]:((~tall(X)|curious(X)))))&
(![X]:((~generous(X)&brave(X))=>(~happy(X)<~>quiet(X))))&
(![X]:((~rich(X)&strong(X))<=>tall(X)))&
(((funny(john)<~>~curious(john)))=>((~kind(paul)|~calm(paul))))&
((strong(paul))=>(?[X]:(old(X))))&
(![X]:((happy(X)|~old(X))<=>(patient(X)|~strong(X))))&
(![X]:((tall(X)&~tall(X))<=>(rich(X)|~strong(X))))&
(((~calm(paul)&~humble(paul)))=>((brave(mary)<~>creative(mary))))&
(![X]:((tall(X)|rich(X))=>(~wise(X)<~>brave(X))))&
(![X]:((~humble(X)&funny(X))<=>(~quiet(X)<~>~generous(X))))&
(![X]:(~generous(X)<=>(funny(X)|creative(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~quiet(mary)|happy(mary))))&
(![X]:((curious(X)&happy(X))<=>(curious(X)|old(X))))&
((?[X]:((~old(X)<~>~strong(X))))=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:((~wise(X)|~rich(X))=>(strong(X)&~creative(X))))&
(?[X]:((brave(X)|~tall(X))))&
(?[X]:((~old(X)|~brave(X))))&
(?[X]:((~generous(X)<~>~wise(X))))&
((quiet(fred)|~curious(fred)))&
(?[X]:((brave(X)<~>~quiet(X))))&
(~wise(fred)) | generous(alice) | [] | null | 0 |
Everyone who is either not kind or not tall is either quiet or not generous and vice versa. Everyone who is either wise or not tall is not creative and vice versa. Everyone who is not generous or curious is not brave or not strong and vice versa. If john is both not funny and not wise then someone is humble and vice versa. Everyone who is both not funny and kind is calm. Everyone who is not rich or not tall is not brave or creative and vice versa. Everyone who is either not brave or humble is strong or not quiet and vice versa. If someone is not wise then someone is either not kind or rich and vice versa. Everyone who is not strong is creative. Everyone who is happy is rich. If someone is not rich or happy then lucy is both not funny and not wise and vice versa. Everyone who is happy is either strong or not old and vice versa. If paul is brave or creative then paul is not brave or kind and vice versa. If someone is either old or generous then susan is either calm or patient and vice versa. Everyone who is not rich or not old is old or kind. Everyone who is not generous is happy or generous and vice versa. Someone is not creative or not generous. Someone is either not strong or not quiet. Someone is not old or old. Someone is tall or funny. Susan is kind. John is either quiet or not patient. Fred is not humble. Someone is creative or tall. | Susan is creative. | neutral | (![X]:((~kind(X)<~>~tall(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:((wise(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((~generous(X)|curious(X))<=>(~brave(X)|~strong(X))))&
(((~funny(john)&~wise(john)))<=>(?[X]:(humble(X))))&
(![X]:((~funny(X)&kind(X))=>calm(X)))&
(![X]:((~rich(X)|~tall(X))<=>(~brave(X)|creative(X))))&
(![X]:((~brave(X)<~>humble(X))<=>(strong(X)|~quiet(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~kind(X)<~>rich(X)))))&
(![X]:(~strong(X)=>creative(X)))&
(![X]:(happy(X)=>rich(X)))&
((?[X]:((~rich(X)|happy(X))))<=>((~funny(lucy)&~wise(lucy))))&
(![X]:(happy(X)<=>(strong(X)<~>~old(X))))&
(((brave(paul)|creative(paul)))<=>((~brave(paul)|kind(paul))))&
((?[X]:((old(X)<~>generous(X))))<=>((calm(susan)<~>patient(susan))))&
(![X]:((~rich(X)|~old(X))=>(old(X)|kind(X))))&
(![X]:(~generous(X)<=>(happy(X)|generous(X))))&
(?[X]:((~creative(X)|~generous(X))))&
(?[X]:((~strong(X)<~>~quiet(X))))&
(?[X]:((~old(X)|old(X))))&
(?[X]:((tall(X)|funny(X))))&
(kind(susan))&
((quiet(john)<~>~patient(john)))&
(~humble(fred))&
(?[X]:((creative(X)|tall(X)))) | creative(susan) | [] | null | 0 |
Everyone who is not curious or tall is not quiet or not brave. Everyone who is either not strong or not old is both not brave and calm and vice versa. Everyone who is not brave or not humble is not tall and vice versa. If paul is not quiet then someone is either kind or strong. If alice is rich or funny then mary is either not strong or calm. If lucy is both funny and not humble then someone is either humble or generous. If lucy is generous then someone is both calm and funny. Everyone who is not strong is strong. If someone is tall or not calm then susan is not patient or old and vice versa. Everyone who is not kind is rich and vice versa. If lucy is both not old and not strong then someone is both calm and strong. If fred is not wise then paul is not old and vice versa. If mary is not patient then someone is either creative or not strong. Everyone who is either not kind or strong is funny or not curious. Everyone who is both funny and quiet is rich or not kind and vice versa. If someone is kind then someone is not strong. John is both not brave and wise. Paul is generous. Someone is either not curious or strong. Someone is rich. Someone is patient or not funny. Susan is generous or not wise. Fred is quiet. Someone is either generous or not calm. | Lucy is not tall. | entailment | (![X]:((~curious(X)|tall(X))=>(~quiet(X)|~brave(X))))&
(![X]:((~strong(X)<~>~old(X))<=>(~brave(X)&calm(X))))&
(![X]:((~brave(X)|~humble(X))<=>~tall(X)))&
((~quiet(paul))=>(?[X]:((kind(X)<~>strong(X)))))&
(((rich(alice)|funny(alice)))=>((~strong(mary)<~>calm(mary))))&
(((funny(lucy)&~humble(lucy)))=>(?[X]:((humble(X)<~>generous(X)))))&
((generous(lucy))=>(?[X]:((calm(X)&funny(X)))))&
(![X]:(~strong(X)=>strong(X)))&
((?[X]:((tall(X)|~calm(X))))<=>((~patient(susan)|old(susan))))&
(![X]:(~kind(X)<=>rich(X)))&
(((~old(lucy)&~strong(lucy)))=>(?[X]:((calm(X)&strong(X)))))&
((~wise(fred))<=>(~old(paul)))&
((~patient(mary))=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((~kind(X)<~>strong(X))=>(funny(X)|~curious(X))))&
(![X]:((funny(X)&quiet(X))<=>(rich(X)|~kind(X))))&
((?[X]:(kind(X)))=>(?[X]:(~strong(X))))&
((~brave(john)&wise(john)))&
(generous(paul))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)|~funny(X))))&
((generous(susan)|~wise(susan)))&
(quiet(fred))&
(?[X]:((generous(X)<~>~calm(X)))) | ~tall(lucy) | [
"p0",
"p2",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1338320559151090684219714
% SZS output start Proof for 1338320559151090684219714
1. ! [X0] : ((tall(X0) | ~curious(X0)) => (~brave(X0) | ~quiet(X0))) [input p0]
3. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> ~tall(X0)) [input p2]
8. ! [X0] : (~strong(X0) => strong(X0)) [input p7]
15. ! [X0] : ((quiet(X0) & funny(X0)) <=> (~kind(X0) | rich(X0))) [input p14]
16. ? [X0] : kind(X0) => ? [X0] : ~strong(X0) [input p15]
25. tall(lucy) [input hypothesis]
26. ? [X0] : kind(X0) => ? [X1] : ~strong(X1) [rectify 16]
27. ! [X0] : ((~brave(X0) | ~quiet(X0)) | (~tall(X0) & curious(X0))) [ennf transformation 1]
28. ! [X0] : (~brave(X0) | ~quiet(X0) | (~tall(X0) & curious(X0))) [flattening 27]
34. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 8]
40. ? [X1] : ~strong(X1) | ! [X0] : ~kind(X0) [ennf transformation 26]
43. ! [X0] : (((~humble(X0) | ~brave(X0)) | tall(X0)) & (~tall(X0) | (humble(X0) & brave(X0)))) [nnf transformation 3]
44. ! [X0] : ((~humble(X0) | ~brave(X0) | tall(X0)) & (~tall(X0) | (humble(X0) & brave(X0)))) [flattening 43]
67. ! [X0] : (((quiet(X0) & funny(X0)) | (kind(X0) & ~rich(X0))) & ((~kind(X0) | rich(X0)) | (~quiet(X0) | ~funny(X0)))) [nnf transformation 15]
68. ! [X0] : (((quiet(X0) & funny(X0)) | (kind(X0) & ~rich(X0))) & (~kind(X0) | rich(X0) | ~quiet(X0) | ~funny(X0))) [flattening 67]
69. ? [X0] : ~strong(X0) | ! [X1] : ~kind(X1) [rectify 40]
70. ? [X0] : ~strong(X0) => ~strong(sK6) [choice axiom]
71. ~strong(sK6) | ! [X1] : ~kind(X1) [skolemisation 69,70]
83. ~brave(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 28]
90. ~tall(X0) | brave(X0) [cnf transformation 44]
103. strong(X0) | strong(X0) [cnf transformation 34]
122. kind(X0) | quiet(X0) [cnf transformation 68]
123. ~strong(sK6) | ~kind(X1) [cnf transformation 71]
135. tall(lucy) [cnf transformation 25]
136. strong(X0) [duplicate literal removal 103]
251. ~kind(X1) [subsumption resolution 123,136]
287. brave(lucy) [resolution 90,135]
311. quiet(X0) [resolution 122,251]
314. ~quiet(lucy) | ~tall(lucy) [resolution 83,287]
315. ~tall(lucy) [subsumption resolution 314,311]
316. $false [subsumption resolution 315,135]
% SZS output end Proof for 1338320559151090684219714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is curious.
If susan is not happy or old then someone is not humble and vice versa.
Everyone who is both tall and kind is both generous and rich and vice versa.
If john is rich then lucy is both not funny and not rich and vice versa.
Everyone who is calm or humble is both creative and tall and vice versa.
If alice is either creative or not calm then paul is not tall or generous.
Everyone who is strong is either not patient or not kind and vice versa.
Everyone who is both patient and brave is not strong or patient and vice versa.
Everyone who is not calm or old is brave.
Everyone who is either old or not rich is rich and vice versa.
Everyone who is both not quiet and not patient is both quiet and not kind.
Everyone who is both not kind and not generous is not brave.
If lucy is happy then someone is creative.
Everyone who is either curious or not humble is creative.
Everyone who is creative or brave is both not happy and generous.
If mary is brave or not rich then fred is calm or not generous and vice versa.
Susan is either not kind or kind.
Someone is wise or not patient.
Paul is either tall or not creative.
Alice is not quiet.
Someone is both not kind and calm.
Someone is either strong or old.
Someone is either not quiet or not old. | Fred is not creative. | contradiction | (![X]:(~generous(X)=>curious(X)))&
(((~happy(susan)|old(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((tall(X)&kind(X))<=>(generous(X)&rich(X))))&
((rich(john))<=>((~funny(lucy)&~rich(lucy))))&
(![X]:((calm(X)|humble(X))<=>(creative(X)&tall(X))))&
(((creative(alice)<~>~calm(alice)))=>((~tall(paul)|generous(paul))))&
(![X]:(strong(X)<=>(~patient(X)<~>~kind(X))))&
(![X]:((patient(X)&brave(X))<=>(~strong(X)|patient(X))))&
(![X]:((~calm(X)|old(X))=>brave(X)))&
(![X]:((old(X)<~>~rich(X))<=>rich(X)))&
(![X]:((~quiet(X)&~patient(X))=>(quiet(X)&~kind(X))))&
(![X]:((~kind(X)&~generous(X))=>~brave(X)))&
((happy(lucy))=>(?[X]:(creative(X))))&
(![X]:((curious(X)<~>~humble(X))=>creative(X)))&
(![X]:((creative(X)|brave(X))=>(~happy(X)&generous(X))))&
(((brave(mary)|~rich(mary)))<=>((calm(fred)|~generous(fred))))&
((~kind(susan)<~>kind(susan)))&
(?[X]:((wise(X)|~patient(X))))&
((tall(paul)<~>~creative(paul)))&
(~quiet(alice))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((~quiet(X)<~>~old(X)))) | ~creative(fred) | [
"p4",
"p8",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6458760719399957326169387
% SZS output start Proof for 6458760719399957326169387
5. ! [X0] : ((humble(X0) | calm(X0)) <=> (tall(X0) & creative(X0))) [input p4]
9. ! [X0] : ((old(X0) | ~calm(X0)) => brave(X0)) [input p8]
10. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> rich(X0)) [input p9]
15. ! [X0] : ((brave(X0) | creative(X0)) => (generous(X0) & ~happy(X0))) [input p14]
16. (~rich(mary) | brave(mary)) <=> (~generous(fred) | calm(fred)) [input p15]
24. ~creative(fred) [input hypothesis]
29. ! [X0] : (brave(X0) | (~old(X0) & calm(X0))) [ennf transformation 9]
36. ! [X0] : ((generous(X0) & ~happy(X0)) | (~brave(X0) & ~creative(X0))) [ennf transformation 15]
46. ! [X0] : (((humble(X0) | calm(X0)) | (~tall(X0) | ~creative(X0))) & ((tall(X0) & creative(X0)) | (~humble(X0) & ~calm(X0)))) [nnf transformation 5]
47. ! [X0] : ((humble(X0) | calm(X0) | ~tall(X0) | ~creative(X0)) & ((tall(X0) & creative(X0)) | (~humble(X0) & ~calm(X0)))) [flattening 46]
52. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~rich(X0)) & (rich(X0) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 10]
56. ((~rich(mary) | brave(mary)) | (generous(fred) & ~calm(fred))) & ((~generous(fred) | calm(fred)) | (rich(mary) & ~brave(mary))) [nnf transformation 16]
57. (~rich(mary) | brave(mary) | (generous(fred) & ~calm(fred))) & (~generous(fred) | calm(fred) | (rich(mary) & ~brave(mary))) [flattening 56]
79. ~calm(X0) | creative(X0) [cnf transformation 47]
96. ~old(X0) | brave(X0) [cnf transformation 29]
98. rich(X0) | old(X0) | rich(X0) [cnf transformation 52]
99. ~rich(X0) | old(X0) | ~rich(X0) [cnf transformation 52]
110. ~brave(X0) | generous(X0) [cnf transformation 36]
111. ~generous(fred) | calm(fred) | ~brave(mary) [cnf transformation 57]
126. ~creative(fred) [cnf transformation 24]
128. rich(X0) | old(X0) [duplicate literal removal 98]
129. ~rich(X0) | old(X0) [duplicate literal removal 99]
183. old(X0) [subsumption resolution 128,129]
195. 14 <=> generous(fred) [avatar definition]
196. ~generous(fred) <- (~14) [avatar component clause 195]
199. 15 <=> brave(mary) [avatar definition]
200. ~brave(mary) <- (~15) [avatar component clause 199]
208. 17 <=> calm(fred) [avatar definition]
209. calm(fred) <- (17) [avatar component clause 208]
213. ~15 | 17 | ~14 [avatar split clause 111,195,208,199]
225. brave(X0) [resolution 96,183]
231. generous(X0) [resolution 110,225]
234. $false <- (~14) [resolution 231,196]
235. 14 [avatar contradiction clause 234]
236. $false <- (~15) [subsumption resolution 200,225]
237. 15 [avatar contradiction clause 236]
239. creative(fred) <- (17) [resolution 209,79]
240. $false <- (17) [subsumption resolution 239,126]
241. ~17 [avatar contradiction clause 240]
242. $false [avatar sat refutation 213,235,237,241]
% SZS output end Proof for 6458760719399957326169387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and not creative then someone is either brave or tall and vice versa.
Everyone who is either not humble or humble is both brave and not old.
Everyone who is wise is not creative.
If someone is not funny then someone is not tall and vice versa.
Everyone who is curious is both kind and patient and vice versa.
Everyone who is not kind is rich and vice versa.
If someone is both not rich and not creative then someone is either not curious or funny and vice versa.
If someone is not wise then someone is both wise and not curious and vice versa.
Everyone who is not kind or strong is both curious and rich and vice versa.
Everyone who is either not calm or patient is either curious or not generous and vice versa.
Everyone who is either not calm or not patient is not tall and vice versa.
Everyone who is not generous or wise is not patient.
If lucy is either kind or old then someone is creative or humble.
Susan is tall.
Someone is not rich or not quiet.
Fred is either not rich or curious.
Mary is not rich or funny.
Susan is both kind and generous.
Someone is quiet or curious. | Lucy is not quiet. | neutral | ((?[X]:((creative(X)&~creative(X))))<=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((~humble(X)<~>humble(X))=>(brave(X)&~old(X))))&
(![X]:(wise(X)=>~creative(X)))&
((?[X]:(~funny(X)))<=>(?[X]:(~tall(X))))&
(![X]:(curious(X)<=>(kind(X)&patient(X))))&
(![X]:(~kind(X)<=>rich(X)))&
((?[X]:((~rich(X)&~creative(X))))<=>(?[X]:((~curious(X)<~>funny(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:((~kind(X)|strong(X))<=>(curious(X)&rich(X))))&
(![X]:((~calm(X)<~>patient(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>~patient(X))<=>~tall(X)))&
(![X]:((~generous(X)|wise(X))=>~patient(X)))&
(((kind(lucy)<~>old(lucy)))=>(?[X]:((creative(X)|humble(X)))))&
(tall(susan))&
(?[X]:((~rich(X)|~quiet(X))))&
((~rich(fred)<~>curious(fred)))&
((~rich(mary)|funny(mary)))&
((kind(susan)&generous(susan)))&
(?[X]:((quiet(X)|curious(X)))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is happy or not patient is curious and vice versa.
Everyone who is creative is both strong and generous.
Everyone who is not creative or funny is kind or not funny.
Everyone who is either not quiet or old is not quiet or creative and vice versa.
If someone is either kind or not brave then someone is both happy and not rich and vice versa.
Everyone who is either not funny or rich is either not creative or humble and vice versa.
If someone is either not humble or generous then someone is both not brave and calm and vice versa.
Everyone who is either not funny or funny is not creative or strong and vice versa.
Everyone who is both calm and funny is both kind and not kind.
Everyone who is either not old or not kind is both not patient and not wise.
Everyone who is both patient and funny is not creative or not kind and vice versa.
If someone is both creative and happy then someone is either not kind or old.
If mary is both not generous and not funny then lucy is not funny or not tall.
If john is generous or not tall then someone is either not kind or not tall.
Everyone who is either humble or not funny is both not calm and not strong and vice versa.
Everyone who is either calm or wise is brave or strong and vice versa.
Paul is either not wise or old.
Someone is not creative or not rich.
Someone is both not old and not happy.
Fred is kind or not happy.
Fred is patient.
Fred is not calm. | Paul is not strong. | contradiction | (![X]:((happy(X)|~patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(strong(X)&generous(X))))&
(![X]:((~creative(X)|funny(X))=>(kind(X)|~funny(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(~quiet(X)|creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((~funny(X)<~>rich(X))<=>(~creative(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~creative(X)|strong(X))))&
(![X]:((calm(X)&funny(X))=>(kind(X)&~kind(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~patient(X)&~wise(X))))&
(![X]:((patient(X)&funny(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((creative(X)&happy(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(((~generous(mary)&~funny(mary)))=>((~funny(lucy)|~tall(lucy))))&
(((generous(john)|~tall(john)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
(![X]:((humble(X)<~>~funny(X))<=>(~calm(X)&~strong(X))))&
(![X]:((calm(X)<~>wise(X))<=>(brave(X)|strong(X))))&
((~wise(paul)<~>old(paul)))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:((~old(X)&~happy(X))))&
((kind(fred)|~happy(fred)))&
(patient(fred))&
(~calm(fred)) | ~strong(paul) | [
"p1",
"p2",
"p3",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5284868073279797617399083
% SZS output start Proof for 5284868073279797617399083
2. ! [X0] : (creative(X0) => (generous(X0) & strong(X0))) [input p1]
3. ! [X0] : ((funny(X0) | ~creative(X0)) => (~funny(X0) | kind(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) <~> old(X0)) <=> (creative(X0) | ~quiet(X0))) [input p3]
10. ! [X0] : ((~old(X0) <~> ~kind(X0)) => (~wise(X0) & ~patient(X0))) [input p9]
11. ! [X0] : ((funny(X0) & patient(X0)) <=> (~kind(X0) | ~creative(X0))) [input p10]
23. ~strong(paul) [input hypothesis]
27. ! [X0] : ((generous(X0) & strong(X0)) | ~creative(X0)) [ennf transformation 2]
28. ! [X0] : ((~funny(X0) | kind(X0)) | (~funny(X0) & creative(X0))) [ennf transformation 3]
29. ! [X0] : (~funny(X0) | kind(X0) | (~funny(X0) & creative(X0))) [flattening 28]
32. ! [X0] : ((~wise(X0) & ~patient(X0)) | (~old(X0) <=> ~kind(X0))) [ennf transformation 10]
37. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [nnf transformation 4]
38. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [flattening 37]
52. ! [X0] : ((~wise(X0) & ~patient(X0)) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 32]
53. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | (~funny(X0) | ~patient(X0)))) [nnf transformation 11]
54. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ~funny(X0) | ~patient(X0))) [flattening 53]
71. ~creative(X0) | strong(X0) [cnf transformation 27]
74. ~funny(X0) | kind(X0) | ~funny(X0) [cnf transformation 29]
76. creative(X0) | ~quiet(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 38]
79. ~old(X0) | quiet(X0) | quiet(X0) [cnf transformation 38]
109. ~kind(X0) | ~patient(X0) | old(X0) [cnf transformation 52]
114. creative(X0) | patient(X0) [cnf transformation 54]
117. funny(X0) | kind(X0) [cnf transformation 54]
145. ~strong(paul) [cnf transformation 23]
148. creative(X0) | ~quiet(X0) | ~old(X0) [duplicate literal removal 76]
149. ~old(X0) | quiet(X0) [duplicate literal removal 79]
150. ~funny(X0) | kind(X0) [duplicate literal removal 74]
151. ~old(X0) | creative(X0) [subsumption resolution 148,149]
215. kind(X0) [subsumption resolution 117,150]
266. 25 <=> old(paul) [avatar definition]
267. old(paul) <- (25) [avatar component clause 266]
287. strong(X1) | patient(X1) [resolution 114,71]
296. ~patient(X0) | old(X0) [resolution 109,215]
299. patient(paul) [resolution 287,145]
320. old(paul) [resolution 296,299]
327. 25 [avatar split clause 320,266]
333. creative(paul) <- (25) [resolution 267,151]
336. 30 <=> creative(paul) [avatar definition]
337. creative(paul) <- (30) [avatar component clause 336]
344. 30 | ~25 [avatar split clause 333,266,336]
349. strong(paul) <- (30) [resolution 337,71]
350. $false <- (30) [subsumption resolution 349,145]
351. ~30 [avatar contradiction clause 350]
352. $false [avatar sat refutation 327,344,351]
% SZS output end Proof for 5284868073279797617399083
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not brave is both calm and generous.
Everyone who is wise or patient is either not strong or happy and vice versa.
If someone is creative or not kind then alice is both not tall and not quiet.
Everyone who is humble is quiet or patient.
If susan is both humble and not brave then susan is wise or patient.
If someone is either creative or not brave then fred is not rich and vice versa.
If paul is either not humble or funny then lucy is either patient or strong and vice versa.
Everyone who is not curious or not kind is not strong or curious.
Everyone who is both not tall and creative is both calm and not calm.
Everyone who is either not wise or not quiet is both rich and generous.
If someone is both brave and not calm then fred is not creative or rich and vice versa.
If someone is humble or not tall then someone is generous and vice versa.
Everyone who is generous or kind is not tall.
Everyone who is both patient and not quiet is not patient and vice versa.
If john is both tall and curious then someone is not happy.
Everyone who is not creative or rich is both not old and not humble and vice versa.
Someone is not kind or brave.
Someone is both not tall and not creative.
Someone is calm or not wise.
Lucy is brave.
Someone is kind or not tall.
Someone is both not calm and generous. | Susan is not patient. | contradiction | (![X]:((~quiet(X)&~brave(X))=>(calm(X)&generous(X))))&
(![X]:((wise(X)|patient(X))<=>(~strong(X)<~>happy(X))))&
((?[X]:((creative(X)|~kind(X))))=>((~tall(alice)&~quiet(alice))))&
(![X]:(humble(X)=>(quiet(X)|patient(X))))&
(((humble(susan)&~brave(susan)))=>((wise(susan)|patient(susan))))&
((?[X]:((creative(X)<~>~brave(X))))<=>(~rich(fred)))&
(((~humble(paul)<~>funny(paul)))<=>((patient(lucy)<~>strong(lucy))))&
(![X]:((~curious(X)|~kind(X))=>(~strong(X)|curious(X))))&
(![X]:((~tall(X)&creative(X))=>(calm(X)&~calm(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>(rich(X)&generous(X))))&
((?[X]:((brave(X)&~calm(X))))<=>((~creative(fred)|rich(fred))))&
((?[X]:((humble(X)|~tall(X))))<=>(?[X]:(generous(X))))&
(![X]:((generous(X)|kind(X))=>~tall(X)))&
(![X]:((patient(X)&~quiet(X))<=>~patient(X)))&
(((tall(john)&curious(john)))=>(?[X]:(~happy(X))))&
(![X]:((~creative(X)|rich(X))<=>(~old(X)&~humble(X))))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((~tall(X)&~creative(X))))&
(?[X]:((calm(X)|~wise(X))))&
(brave(lucy))&
(?[X]:((kind(X)|~tall(X))))&
(?[X]:((~calm(X)&generous(X)))) | ~patient(susan) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2381343004790620860377544
% SZS output start Proof for 2381343004790620860377544
14. ! [X0] : ((~quiet(X0) & patient(X0)) <=> ~patient(X0)) [input p13]
23. ~patient(susan) [input hypothesis]
58. ! [X0] : (((~quiet(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | (quiet(X0) | ~patient(X0)))) [nnf transformation 14]
59. ! [X0] : (((~quiet(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | quiet(X0) | ~patient(X0))) [flattening 58]
119. patient(X0) | patient(X0) [cnf transformation 59]
135. ~patient(susan) [cnf transformation 23]
137. patient(X0) [duplicate literal removal 119]
298. $false [subsumption resolution 135,137]
% SZS output end Proof for 2381343004790620860377544
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not patient is both happy and rich and vice versa.
If someone is happy or quiet then fred is both not creative and not tall and vice versa.
Everyone who is both not calm and old is both not curious and not funny.
If someone is either not wise or kind then lucy is both quiet and not calm and vice versa.
Everyone who is both not strong and not quiet is either not tall or tall and vice versa.
Everyone who is humble or not kind is not rich and vice versa.
If someone is either rich or not funny then someone is not creative or not generous and vice versa.
Everyone who is not quiet or creative is both not generous and not patient and vice versa.
If someone is either quiet or creative then john is not brave and vice versa.
Everyone who is either not rich or not happy is either brave or curious and vice versa.
If someone is either patient or wise then alice is not curious or not old and vice versa.
Everyone who is curious or not quiet is both brave and not humble.
Everyone who is both not wise and creative is not kind.
Everyone who is happy or not strong is curious or not rich.
Someone is not quiet.
Someone is not rich or not creative.
Paul is either not humble or old.
Mary is not humble. | Lucy is not quiet. | entailment | (![X]:((~rich(X)|~patient(X))<=>(happy(X)&rich(X))))&
((?[X]:((happy(X)|quiet(X))))<=>((~creative(fred)&~tall(fred))))&
(![X]:((~calm(X)&old(X))=>(~curious(X)&~funny(X))))&
((?[X]:((~wise(X)<~>kind(X))))<=>((quiet(lucy)&~calm(lucy))))&
(![X]:((~strong(X)&~quiet(X))<=>(~tall(X)<~>tall(X))))&
(![X]:((humble(X)|~kind(X))<=>~rich(X)))&
((?[X]:((rich(X)<~>~funny(X))))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((~quiet(X)|creative(X))<=>(~generous(X)&~patient(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(~brave(john)))&
(![X]:((~rich(X)<~>~happy(X))<=>(brave(X)<~>curious(X))))&
((?[X]:((patient(X)<~>wise(X))))<=>((~curious(alice)|~old(alice))))&
(![X]:((curious(X)|~quiet(X))=>(brave(X)&~humble(X))))&
(![X]:((~wise(X)&creative(X))=>~kind(X)))&
(![X]:((happy(X)|~strong(X))=>(curious(X)|~rich(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~rich(X)|~creative(X))))&
((~humble(paul)<~>old(paul)))&
(~humble(mary)) | ~quiet(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 9161459310089470387188147
% SZS output start Proof for 9161459310089470387188147
5. ! [X0] : ((~quiet(X0) & ~strong(X0)) <=> (~tall(X0) <~> tall(X0))) [input p4]
19. quiet(lucy) [input hypothesis]
40. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | (quiet(X0) | strong(X0)))) [nnf transformation 5]
41. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | quiet(X0) | strong(X0))) [flattening 40]
88. ~quiet(X0) | tall(X0) | tall(X0) [cnf transformation 41]
89. ~quiet(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 41]
134. quiet(lucy) [cnf transformation 19]
137. ~quiet(X0) | tall(X0) [duplicate literal removal 88]
138. ~quiet(X0) | ~tall(X0) [duplicate literal removal 89]
159. 5 <=> ! [X1] : ~quiet(X1) [avatar definition]
160. ~quiet(X1) <- (5) [avatar component clause 159]
169. 7 <=> quiet(lucy) [avatar definition]
170. quiet(lucy) <- (7) [avatar component clause 169]
196. ~quiet(X0) [subsumption resolution 137,138]
197. 5 [avatar split clause 196,159]
287. 7 [avatar split clause 134,169]
292. $false <- (5, 7) [resolution 170,160]
293. ~5 | ~7 [avatar contradiction clause 292]
294. $false [avatar sat refutation 197,287,293]
% SZS output end Proof for 9161459310089470387188147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is both not patient and creative. If paul is not old or brave then alice is both not kind and not tall. If someone is both not creative and not brave then john is either not funny or creative and vice versa. If lucy is both not funny and funny then someone is calm and vice versa. Everyone who is kind or not funny is old and vice versa. Everyone who is not quiet is both not brave and tall. If john is old then paul is not happy or quiet. Everyone who is not happy or not funny is either calm or brave and vice versa. Everyone who is both not creative and not calm is either creative or wise and vice versa. If someone is happy then lucy is either calm or brave and vice versa. Everyone who is curious or old is either creative or brave and vice versa. If alice is both strong and not tall then someone is wise and vice versa. If lucy is either patient or not creative then susan is not brave or not strong and vice versa. If someone is either not curious or not happy then someone is not generous or not old and vice versa. If someone is either not humble or not curious then fred is both not generous and not wise. If mary is both funny and calm then someone is rich. Mary is either not curious or not generous. Someone is tall. John is either not funny or patient. Someone is either not calm or strong. Someone is kind or not old. Alice is rich or generous. Someone is either brave or not creative. Alice is both not patient and creative. | Susan is not wise. | contradiction | (![X]:(~quiet(X)=>(~patient(X)&creative(X))))&
(((~old(paul)|brave(paul)))=>((~kind(alice)&~tall(alice))))&
((?[X]:((~creative(X)&~brave(X))))<=>((~funny(john)<~>creative(john))))&
(((~funny(lucy)&funny(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((kind(X)|~funny(X))<=>old(X)))&
(![X]:(~quiet(X)=>(~brave(X)&tall(X))))&
((old(john))=>((~happy(paul)|quiet(paul))))&
(![X]:((~happy(X)|~funny(X))<=>(calm(X)<~>brave(X))))&
(![X]:((~creative(X)&~calm(X))<=>(creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>((calm(lucy)<~>brave(lucy))))&
(![X]:((curious(X)|old(X))<=>(creative(X)<~>brave(X))))&
(((strong(alice)&~tall(alice)))<=>(?[X]:(wise(X))))&
(((patient(lucy)<~>~creative(lucy)))<=>((~brave(susan)|~strong(susan))))&
((?[X]:((~curious(X)<~>~happy(X))))<=>(?[X]:((~generous(X)|~old(X)))))&
((?[X]:((~humble(X)<~>~curious(X))))=>((~generous(fred)&~wise(fred))))&
(((funny(mary)&calm(mary)))=>(?[X]:(rich(X))))&
((~curious(mary)<~>~generous(mary)))&
(?[X]:(tall(X)))&
((~funny(john)<~>patient(john)))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:((kind(X)|~old(X))))&
((rich(alice)|generous(alice)))&
(?[X]:((brave(X)<~>~creative(X))))&
((~patient(alice)&creative(alice))) | ~wise(susan) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3867298292820281697304553
% SZS output start Proof for 3867298292820281697304553
4. (funny(lucy) & ~funny(lucy)) <=> ? [X0] : calm(X0) [input p3]
9. ! [X0] : ((~calm(X0) & ~creative(X0)) <=> (creative(X0) <~> wise(X0))) [input p8]
25. ~wise(susan) [input hypothesis]
38. ((funny(lucy) & ~funny(lucy)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (~funny(lucy) | funny(lucy))) [nnf transformation 4]
39. ((funny(lucy) & ~funny(lucy)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ~funny(lucy) | funny(lucy)) [flattening 38]
40. ((funny(lucy) & ~funny(lucy)) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ~funny(lucy) | funny(lucy)) [rectify 39]
41. ? [X1] : calm(X1) => calm(sK1) [choice axiom]
42. ((funny(lucy) & ~funny(lucy)) | ! [X0] : ~calm(X0)) & (calm(sK1) | ~funny(lucy) | funny(lucy)) [skolemisation 40,41]
47. ! [X0] : (((~calm(X0) & ~creative(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (calm(X0) | creative(X0)))) [nnf transformation 9]
48. ! [X0] : (((~calm(X0) & ~creative(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | calm(X0) | creative(X0))) [flattening 47]
91. ~funny(lucy) | ~calm(X0) [cnf transformation 42]
92. funny(lucy) | ~calm(X0) [cnf transformation 42]
102. wise(X0) | creative(X0) | calm(X0) | creative(X0) [cnf transformation 48]
104. ~creative(X0) | wise(X0) | ~creative(X0) [cnf transformation 48]
149. ~wise(susan) [cnf transformation 25]
150. wise(X0) | creative(X0) | calm(X0) [duplicate literal removal 102]
151. ~creative(X0) | wise(X0) [duplicate literal removal 104]
198. 10 <=> ! [X0] : ~calm(X0) [avatar definition]
199. ~calm(X0) <- (10) [avatar component clause 198]
201. 11 <=> funny(lucy) [avatar definition]
204. 10 | 11 [avatar split clause 92,201,198]
205. 10 | ~11 [avatar split clause 91,201,198]
206. wise(X0) | calm(X0) [subsumption resolution 150,151]
363. calm(susan) [resolution 206,149]
365. $false <- (10) [subsumption resolution 363,199]
366. ~10 [avatar contradiction clause 365]
369. $false [avatar sat refutation 204,205,366]
% SZS output end Proof for 3867298292820281697304553
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not strong is both not tall and not rich.
If someone is not calm or humble then someone is both old and not rich and vice versa.
If someone is either tall or old then someone is either brave or rich and vice versa.
If someone is not happy then someone is both not calm and not rich and vice versa.
If alice is either not rich or tall then someone is either creative or not humble.
Everyone who is strong or calm is not tall or not kind.
Everyone who is either not wise or not happy is not generous.
If someone is both curious and not kind then someone is either rich or not curious.
Everyone who is calm is either not generous or not creative and vice versa.
If someone is both brave and not kind then someone is curious.
If someone is not wise then someone is not happy and vice versa.
If paul is either quiet or not strong then someone is both not wise and strong.
Everyone who is both not brave and not strong is either not quiet or humble.
Everyone who is not happy is either humble or tall.
Everyone who is either not patient or funny is either rich or not generous and vice versa.
If someone is either patient or happy then someone is humble and vice versa.
Susan is not patient.
Someone is either not quiet or creative.
Fred is both humble and not creative.
Fred is both not funny and curious.
Fred is either not wise or not quiet.
Someone is both not kind and tall.
Mary is both calm and not curious.
Someone is either not kind or quiet. | Fred is not quiet. | neutral | (![X]:((~rich(X)<~>~strong(X))=>(~tall(X)&~rich(X))))&
((?[X]:((~calm(X)|humble(X))))<=>(?[X]:((old(X)&~rich(X)))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((brave(X)<~>rich(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((~calm(X)&~rich(X)))))&
(((~rich(alice)<~>tall(alice)))=>(?[X]:((creative(X)<~>~humble(X)))))&
(![X]:((strong(X)|calm(X))=>(~tall(X)|~kind(X))))&
(![X]:((~wise(X)<~>~happy(X))=>~generous(X)))&
((?[X]:((curious(X)&~kind(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:(calm(X)<=>(~generous(X)<~>~creative(X))))&
((?[X]:((brave(X)&~kind(X))))=>(?[X]:(curious(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(~happy(X))))&
(((quiet(paul)<~>~strong(paul)))=>(?[X]:((~wise(X)&strong(X)))))&
(![X]:((~brave(X)&~strong(X))=>(~quiet(X)<~>humble(X))))&
(![X]:(~happy(X)=>(humble(X)<~>tall(X))))&
(![X]:((~patient(X)<~>funny(X))<=>(rich(X)<~>~generous(X))))&
((?[X]:((patient(X)<~>happy(X))))<=>(?[X]:(humble(X))))&
(~patient(susan))&
(?[X]:((~quiet(X)<~>creative(X))))&
((humble(fred)&~creative(fred)))&
((~funny(fred)&curious(fred)))&
((~wise(fred)<~>~quiet(fred)))&
(?[X]:((~kind(X)&tall(X))))&
((calm(mary)&~curious(mary)))&
(?[X]:((~kind(X)<~>quiet(X)))) | ~quiet(fred) | [] | null | 0 |
If someone is not quiet or brave then lucy is both not rich and brave and vice versa.
Everyone who is curious is either brave or strong.
Everyone who is either patient or creative is both curious and not rich.
If lucy is not old or not happy then someone is both not wise and not happy.
Everyone who is brave or curious is not quiet and vice versa.
Everyone who is old is not funny.
If someone is either calm or not kind then someone is not wise.
If someone is not brave or not quiet then someone is curious or not rich and vice versa.
Everyone who is both not brave and quiet is both not curious and funny.
Everyone who is humble or kind is either not quiet or not tall.
If someone is both generous and kind then john is not kind and vice versa.
If someone is both creative and not quiet then alice is happy or calm.
If john is either humble or patient then paul is calm and vice versa.
If someone is both not humble and old then lucy is either brave or not wise.
Everyone who is not rich is either rich or patient and vice versa.
If someone is wise or calm then fred is generous and vice versa.
John is both not happy and old.
Someone is wise.
Someone is both strong and not curious.
Fred is both not happy and not creative.
John is both not curious and not generous.
Someone is both not rich and old. | John is creative. | entailment | ((?[X]:((~quiet(X)|brave(X))))<=>((~rich(lucy)&brave(lucy))))&
(![X]:(curious(X)=>(brave(X)<~>strong(X))))&
(![X]:((patient(X)<~>creative(X))=>(curious(X)&~rich(X))))&
(((~old(lucy)|~happy(lucy)))=>(?[X]:((~wise(X)&~happy(X)))))&
(![X]:((brave(X)|curious(X))<=>~quiet(X)))&
(![X]:(old(X)=>~funny(X)))&
((?[X]:((calm(X)<~>~kind(X))))=>(?[X]:(~wise(X))))&
((?[X]:((~brave(X)|~quiet(X))))<=>(?[X]:((curious(X)|~rich(X)))))&
(![X]:((~brave(X)&quiet(X))=>(~curious(X)&funny(X))))&
(![X]:((humble(X)|kind(X))=>(~quiet(X)<~>~tall(X))))&
((?[X]:((generous(X)&kind(X))))<=>(~kind(john)))&
((?[X]:((creative(X)&~quiet(X))))=>((happy(alice)|calm(alice))))&
(((humble(john)<~>patient(john)))<=>(calm(paul)))&
((?[X]:((~humble(X)&old(X))))=>((brave(lucy)<~>~wise(lucy))))&
(![X]:(~rich(X)<=>(rich(X)<~>patient(X))))&
((?[X]:((wise(X)|calm(X))))<=>(generous(fred)))&
((~happy(john)&old(john)))&
(?[X]:(wise(X)))&
(?[X]:((strong(X)&~curious(X))))&
((~happy(fred)&~creative(fred)))&
((~curious(john)&~generous(john)))&
(?[X]:((~rich(X)&old(X)))) | creative(john) | [
"p2",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4708472858115314727697453
% SZS output start Proof for 4708472858115314727697453
3. ! [X0] : ((patient(X0) <~> creative(X0)) => (~rich(X0) & curious(X0))) [input p2]
15. ! [X0] : (~rich(X0) <=> (rich(X0) <~> patient(X0))) [input p14]
21. ~generous(john) & ~curious(john) [input p20]
23. ~creative(john) [input hypothesis]
27. ! [X0] : ((~rich(X0) & curious(X0)) | (patient(X0) <=> creative(X0))) [ennf transformation 3]
43. ! [X0] : ((~rich(X0) & curious(X0)) | ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0)))) [nnf transformation 27]
64. ! [X0] : ((~rich(X0) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | rich(X0))) [nnf transformation 15]
82. ~patient(X0) | creative(X0) | curious(X0) [cnf transformation 43]
116. patient(X0) | rich(X0) | rich(X0) [cnf transformation 64]
118. ~rich(X0) | patient(X0) | ~rich(X0) [cnf transformation 64]
130. ~curious(john) [cnf transformation 21]
134. ~creative(john) [cnf transformation 23]
135. patient(X0) | rich(X0) [duplicate literal removal 116]
136. ~rich(X0) | patient(X0) [duplicate literal removal 118]
265. patient(X0) [subsumption resolution 135,136]
304. creative(X0) | curious(X0) [resolution 82,265]
306. curious(john) [resolution 304,134]
308. $false [subsumption resolution 306,130]
% SZS output end Proof for 4708472858115314727697453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is wise or not brave. If someone is either not calm or not curious then someone is either not creative or brave. If john is old or not old then susan is not quiet and vice versa. If susan is brave or not old then someone is both not strong and not quiet and vice versa. If john is both not wise and not old then paul is not brave and vice versa. If someone is not old or not wise then someone is either kind or strong and vice versa. If fred is both not generous and funny then someone is either strong or creative. Everyone who is humble or old is patient and vice versa. Everyone who is humble or generous is both generous and strong. If alice is rich or not rich then mary is rich and vice versa. Everyone who is both tall and not rich is not rich. If susan is either quiet or funny then someone is either kind or not generous and vice versa. Everyone who is either not wise or not happy is either brave or happy and vice versa. If someone is generous or not wise then someone is not rich or creative and vice versa. If susan is not old then fred is rich or quiet. If lucy is both patient and not strong then fred is both quiet and not quiet and vice versa. Someone is not curious. Someone is either wise or not creative. Someone is either old or not kind. Someone is not kind. Lucy is not tall or not kind. Susan is both old and not rich. Fred is either not humble or strong. Someone is patient or not creative. | Mary is rich. | entailment | (![X]:(~patient(X)=>(wise(X)|~brave(X))))&
((?[X]:((~calm(X)<~>~curious(X))))=>(?[X]:((~creative(X)<~>brave(X)))))&
(((old(john)|~old(john)))<=>(~quiet(susan)))&
(((brave(susan)|~old(susan)))<=>(?[X]:((~strong(X)&~quiet(X)))))&
(((~wise(john)&~old(john)))<=>(~brave(paul)))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:((kind(X)<~>strong(X)))))&
(((~generous(fred)&funny(fred)))=>(?[X]:((strong(X)<~>creative(X)))))&
(![X]:((humble(X)|old(X))<=>patient(X)))&
(![X]:((humble(X)|generous(X))=>(generous(X)&strong(X))))&
(((rich(alice)|~rich(alice)))<=>(rich(mary)))&
(![X]:((tall(X)&~rich(X))=>~rich(X)))&
(((quiet(susan)<~>funny(susan)))<=>(?[X]:((kind(X)<~>~generous(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(brave(X)<~>happy(X))))&
((?[X]:((generous(X)|~wise(X))))<=>(?[X]:((~rich(X)|creative(X)))))&
((~old(susan))=>((rich(fred)|quiet(fred))))&
(((patient(lucy)&~strong(lucy)))<=>((quiet(fred)&~quiet(fred))))&
(?[X]:(~curious(X)))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:((old(X)<~>~kind(X))))&
(?[X]:(~kind(X)))&
((~tall(lucy)|~kind(lucy)))&
((old(susan)&~rich(susan)))&
((~humble(fred)<~>strong(fred)))&
(?[X]:((patient(X)|~creative(X)))) | rich(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2032481545207818248633271
% SZS output start Proof for 2032481545207818248633271
10. (~rich(alice) | rich(alice)) <=> rich(mary) [input p9]
25. ~rich(mary) [input hypothesis]
62. ((~rich(alice) | rich(alice)) | ~rich(mary)) & (rich(mary) | (rich(alice) & ~rich(alice))) [nnf transformation 10]
63. (~rich(alice) | rich(alice) | ~rich(mary)) & (rich(mary) | (rich(alice) & ~rich(alice))) [flattening 62]
120. rich(mary) | ~rich(alice) [cnf transformation 63]
121. rich(mary) | rich(alice) [cnf transformation 63]
159. ~rich(mary) [cnf transformation 25]
280. 26 <=> rich(alice) [avatar definition]
284. 27 <=> rich(mary) [avatar definition]
287. 26 | 27 [avatar split clause 121,284,280]
288. ~26 | 27 [avatar split clause 120,284,280]
404. ~27 [avatar split clause 159,284]
405. $false [avatar sat refutation 287,288,404]
% SZS output end Proof for 2032481545207818248633271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or old is either not happy or generous and vice versa.
If someone is either strong or not calm then fred is not creative.
If paul is calm then mary is both not humble and not rich.
If susan is not creative then someone is both not creative and patient and vice versa.
Everyone who is not curious is not wise or not old.
If someone is either brave or not funny then lucy is rich.
If someone is generous or creative then someone is both not tall and not kind and vice versa.
Everyone who is both not old and old is generous.
Everyone who is generous is not wise and vice versa.
Everyone who is old is not tall or not humble.
If john is both not kind and wise then someone is not rich.
Everyone who is not happy or not brave is not rich.
Everyone who is either humble or not generous is either not generous or not old.
If paul is either old or curious then susan is both quiet and not old.
Everyone who is not tall or not creative is both humble and wise.
Everyone who is tall is humble or wise and vice versa.
John is both patient and wise.
Someone is either not brave or creative.
Paul is both not strong and patient.
Someone is not patient or not generous.
Someone is either patient or humble.
Someone is not patient or not calm.
Paul is either patient or not happy.
John is not humble or not kind. | Fred is generous. | contradiction | (![X]:((~curious(X)|old(X))<=>(~happy(X)<~>generous(X))))&
((?[X]:((strong(X)<~>~calm(X))))=>(~creative(fred)))&
((calm(paul))=>((~humble(mary)&~rich(mary))))&
((~creative(susan))<=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:(~curious(X)=>(~wise(X)|~old(X))))&
((?[X]:((brave(X)<~>~funny(X))))=>(rich(lucy)))&
((?[X]:((generous(X)|creative(X))))<=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:((~old(X)&old(X))=>generous(X)))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:(old(X)=>(~tall(X)|~humble(X))))&
(((~kind(john)&wise(john)))=>(?[X]:(~rich(X))))&
(![X]:((~happy(X)|~brave(X))=>~rich(X)))&
(![X]:((humble(X)<~>~generous(X))=>(~generous(X)<~>~old(X))))&
(((old(paul)<~>curious(paul)))=>((quiet(susan)&~old(susan))))&
(![X]:((~tall(X)|~creative(X))=>(humble(X)&wise(X))))&
(![X]:(tall(X)<=>(humble(X)|wise(X))))&
((patient(john)&wise(john)))&
(?[X]:((~brave(X)<~>creative(X))))&
((~strong(paul)&patient(paul)))&
(?[X]:((~patient(X)|~generous(X))))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:((~patient(X)|~calm(X))))&
((patient(paul)<~>~happy(paul)))&
((~humble(john)|~kind(john))) | generous(fred) | [
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3510931063541512762636705
% SZS output start Proof for 3510931063541512762636705
7. ? [X0] : (creative(X0) | generous(X0)) <=> ? [X0] : (~kind(X0) & ~tall(X0)) [input p6]
15. ! [X0] : ((~creative(X0) | ~tall(X0)) => (wise(X0) & humble(X0))) [input p14]
16. ! [X0] : (tall(X0) <=> (wise(X0) | humble(X0))) [input p15]
25. generous(fred) [input hypothesis]
26. ? [X0] : (creative(X0) | generous(X0)) <=> ? [X1] : (~kind(X1) & ~tall(X1)) [rectify 7]
42. ! [X0] : ((wise(X0) & humble(X0)) | (creative(X0) & tall(X0))) [ennf transformation 15]
51. (? [X0] : (creative(X0) | generous(X0)) | ! [X1] : (kind(X1) | tall(X1))) & (? [X1] : (~kind(X1) & ~tall(X1)) | ! [X0] : (~creative(X0) & ~generous(X0))) [nnf transformation 26]
52. (? [X0] : (creative(X0) | generous(X0)) | ! [X1] : (kind(X1) | tall(X1))) & (? [X2] : (~kind(X2) & ~tall(X2)) | ! [X3] : (~creative(X3) & ~generous(X3))) [rectify 51]
53. ? [X0] : (creative(X0) | generous(X0)) => (creative(sK1) | generous(sK1)) [choice axiom]
54. ? [X2] : (~kind(X2) & ~tall(X2)) => (~kind(sK2) & ~tall(sK2)) [choice axiom]
55. ((creative(sK1) | generous(sK1)) | ! [X1] : (kind(X1) | tall(X1))) & ((~kind(sK2) & ~tall(sK2)) | ! [X3] : (~creative(X3) & ~generous(X3))) [skolemisation 52,54,53]
61. ! [X0] : ((tall(X0) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | ~tall(X0))) [nnf transformation 16]
62. ! [X0] : ((tall(X0) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ~tall(X0))) [flattening 61]
90. ~tall(sK2) | ~generous(X3) [cnf transformation 55]
110. wise(X0) | tall(X0) [cnf transformation 42]
114. tall(X0) | ~wise(X0) [cnf transformation 62]
128. generous(fred) [cnf transformation 25]
208. 19 <=> ! [X3] : ~generous(X3) [avatar definition]
209. ~generous(X3) <- (19) [avatar component clause 208]
212. 20 <=> tall(sK2) [avatar definition]
214. ~tall(sK2) <- (~20) [avatar component clause 212]
216. 19 | ~20 [avatar split clause 90,212,208]
244. tall(X0) [subsumption resolution 114,110]
291. $false <- (~20) [subsumption resolution 214,244]
292. 20 [avatar contradiction clause 291]
295. $false <- (19) [resolution 209,128]
296. ~19 [avatar contradiction clause 295]
297. $false [avatar sat refutation 216,292,296]
% SZS output end Proof for 3510931063541512762636705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is rich then john is both curious and not kind and vice versa. If someone is both not brave and kind then fred is either not rich or happy and vice versa. Everyone who is both not old and kind is both tall and quiet and vice versa. If someone is not strong then paul is both not creative and not happy and vice versa. Everyone who is both strong and not rich is either not funny or happy and vice versa. If someone is patient then someone is either old or not curious and vice versa. If someone is both not old and funny then john is not humble or creative. If john is both not creative and not humble then someone is not brave and vice versa. If someone is patient or tall then alice is patient and vice versa. If fred is both not kind and not happy then someone is either not happy or strong and vice versa. If mary is both not calm and not creative then someone is both kind and not old and vice versa. If susan is both brave and not quiet then paul is both generous and tall. Everyone who is happy or funny is not rich. Everyone who is either not tall or tall is either humble or rich and vice versa. If john is not tall or not wise then someone is both calm and not generous and vice versa. Everyone who is either not calm or not wise is either humble or not curious. John is not kind or kind. Someone is not brave or not wise. Someone is either not old or not wise. Susan is not curious. Lucy is not patient. Someone is creative or not patient. | Fred is not funny. | entailment | ((rich(alice))<=>((curious(john)&~kind(john))))&
((?[X]:((~brave(X)&kind(X))))<=>((~rich(fred)<~>happy(fred))))&
(![X]:((~old(X)&kind(X))<=>(tall(X)&quiet(X))))&
((?[X]:(~strong(X)))<=>((~creative(paul)&~happy(paul))))&
(![X]:((strong(X)&~rich(X))<=>(~funny(X)<~>happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((old(X)<~>~curious(X)))))&
((?[X]:((~old(X)&funny(X))))=>((~humble(john)|creative(john))))&
(((~creative(john)&~humble(john)))<=>(?[X]:(~brave(X))))&
((?[X]:((patient(X)|tall(X))))<=>(patient(alice)))&
(((~kind(fred)&~happy(fred)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(((~calm(mary)&~creative(mary)))<=>(?[X]:((kind(X)&~old(X)))))&
(((brave(susan)&~quiet(susan)))=>((generous(paul)&tall(paul))))&
(![X]:((happy(X)|funny(X))=>~rich(X)))&
(![X]:((~tall(X)<~>tall(X))<=>(humble(X)<~>rich(X))))&
(((~tall(john)|~wise(john)))<=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((~calm(X)<~>~wise(X))=>(humble(X)<~>~curious(X))))&
((~kind(john)|kind(john)))&
(?[X]:((~brave(X)|~wise(X))))&
(?[X]:((~old(X)<~>~wise(X))))&
(~curious(susan))&
(~patient(lucy))&
(?[X]:((creative(X)|~patient(X)))) | ~funny(fred) | [
"p1",
"p4",
"p7",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 555478312933256325886357
% SZS output start Proof for 555478312933256325886357
2. ? [X0] : (kind(X0) & ~brave(X0)) <=> (~rich(fred) <~> happy(fred)) [input p1]
5. ! [X0] : ((~rich(X0) & strong(X0)) <=> (~funny(X0) <~> happy(X0))) [input p4]
8. (~humble(john) & ~creative(john)) <=> ? [X0] : ~brave(X0) [input p7]
10. (~happy(fred) & ~kind(fred)) <=> ? [X0] : (~happy(X0) <~> strong(X0)) [input p9]
13. ! [X0] : ((funny(X0) | happy(X0)) => ~rich(X0)) [input p12]
14. ! [X0] : ((~tall(X0) <~> tall(X0)) <=> (humble(X0) <~> rich(X0))) [input p13]
23. funny(fred) [input hypothesis]
29. ! [X0] : (~rich(X0) | (~funny(X0) & ~happy(X0))) [ennf transformation 13]
33. (? [X0] : (kind(X0) & ~brave(X0)) | ((~rich(fred) | ~happy(fred)) & (happy(fred) | rich(fred)))) & (((~happy(fred) | rich(fred)) & (happy(fred) | ~rich(fred))) | ! [X0] : (~kind(X0) | brave(X0))) [nnf transformation 2]
34. (? [X0] : (kind(X0) & ~brave(X0)) | ((~rich(fred) | ~happy(fred)) & (happy(fred) | rich(fred)))) & (((~happy(fred) | rich(fred)) & (happy(fred) | ~rich(fred))) | ! [X1] : (~kind(X1) | brave(X1))) [rectify 33]
35. ? [X0] : (kind(X0) & ~brave(X0)) => (kind(sK0) & ~brave(sK0)) [choice axiom]
36. ((kind(sK0) & ~brave(sK0)) | ((~rich(fred) | ~happy(fred)) & (happy(fred) | rich(fred)))) & (((~happy(fred) | rich(fred)) & (happy(fred) | ~rich(fred))) | ! [X1] : (~kind(X1) | brave(X1))) [skolemisation 34,35]
44. ! [X0] : (((~rich(X0) & strong(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (rich(X0) | ~strong(X0)))) [nnf transformation 5]
45. ! [X0] : (((~rich(X0) & strong(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | rich(X0) | ~strong(X0))) [flattening 44]
51. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (humble(john) | creative(john))) [nnf transformation 8]
52. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | humble(john) | creative(john)) [flattening 51]
53. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | humble(john) | creative(john)) [rectify 52]
54. ? [X1] : ~brave(X1) => ~brave(sK4) [choice axiom]
55. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (~brave(sK4) | humble(john) | creative(john)) [skolemisation 53,54]
60. ((~happy(fred) & ~kind(fred)) | ! [X0] : ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) & (? [X0] : ((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | (happy(fred) | kind(fred))) [nnf transformation 10]
61. ((~happy(fred) & ~kind(fred)) | ! [X0] : ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) & (? [X0] : ((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | happy(fred) | kind(fred)) [flattening 60]
62. ((~happy(fred) & ~kind(fred)) | ! [X0] : ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) & (? [X1] : ((~strong(X1) | happy(X1)) & (strong(X1) | ~happy(X1))) | happy(fred) | kind(fred)) [rectify 61]
63. ? [X1] : ((~strong(X1) | happy(X1)) & (strong(X1) | ~happy(X1))) => ((~strong(sK6) | happy(sK6)) & (strong(sK6) | ~happy(sK6))) [choice axiom]
64. ((~happy(fred) & ~kind(fred)) | ! [X0] : ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) & (((~strong(sK6) | happy(sK6)) & (strong(sK6) | ~happy(sK6))) | happy(fred) | kind(fred)) [skolemisation 62,63]
70. ! [X0] : ((((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))))) [nnf transformation 14]
89. ~brave(sK0) | happy(fred) | rich(fred) [cnf transformation 36]
103. ~funny(X0) | strong(X0) | ~happy(X0) [cnf transformation 45]
104. ~rich(X0) | happy(X0) | funny(X0) [cnf transformation 45]
113. ~humble(john) | brave(X0) [cnf transformation 55]
122. ~happy(fred) | ~happy(X0) | ~strong(X0) [cnf transformation 64]
129. ~happy(X0) | ~rich(X0) [cnf transformation 29]
130. ~funny(X0) | ~rich(X0) [cnf transformation 29]
131. rich(X0) | humble(X0) | tall(X0) | tall(X0) [cnf transformation 70]
132. rich(X0) | humble(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 70]
155. funny(fred) [cnf transformation 23]
156. rich(X0) | humble(X0) | tall(X0) [duplicate literal removal 131]
157. ~tall(X0) | humble(X0) | rich(X0) [duplicate literal removal 132]
176. 4 <=> happy(fred) [avatar definition]
177. happy(fred) <- (4) [avatar component clause 176]
180. 5 <=> rich(fred) [avatar definition]
190. 7 <=> brave(sK0) [avatar definition]
192. ~brave(sK0) <- (~7) [avatar component clause 190]
194. 5 | 4 | ~7 [avatar split clause 89,190,176,180]
247. 20 <=> humble(john) [avatar definition]
249. ~humble(john) <- (~20) [avatar component clause 247]
256. 22 <=> ! [X0] : brave(X0) [avatar definition]
257. brave(X0) <- (22) [avatar component clause 256]
258. 22 | ~20 [avatar split clause 113,247,256]
284. 28 <=> ! [X0] : (~happy(X0) | ~strong(X0)) [avatar definition]
285. ~strong(X0) | ~happy(X0) <- (28) [avatar component clause 284]
286. 28 | ~4 [avatar split clause 122,176,284]
349. humble(X0) | rich(X0) [subsumption resolution 156,157]
402. ~rich(fred) [resolution 130,155]
411. strong(fred) | ~happy(fred) [resolution 103,155]
416. 53 <=> funny(john) [avatar definition]
418. funny(john) <- (53) [avatar component clause 416]
420. 54 <=> happy(john) [avatar definition]
422. happy(john) <- (54) [avatar component clause 420]
426. $false <- (~7, 22) [resolution 257,192]
431. 7 | ~22 [avatar contradiction clause 426]
433. rich(john) <- (~20) [resolution 249,349]
436. happy(john) | funny(john) <- (~20) [resolution 433,104]
444. ~rich(john) <- (53) [resolution 418,130]
445. $false <- (~20, 53) [subsumption resolution 444,433]
446. 20 | ~53 [avatar contradiction clause 445]
447. 53 | 54 | 20 [avatar split clause 436,247,420,416]
455. ~rich(john) <- (54) [resolution 422,129]
456. $false <- (~20, 54) [subsumption resolution 455,433]
457. 20 | ~54 [avatar contradiction clause 456]
459. 55 <=> strong(fred) [avatar definition]
460. strong(fred) <- (55) [avatar component clause 459]
463. ~5 [avatar split clause 402,180]
470. ~4 | 55 [avatar split clause 411,459,176]
492. ~happy(fred) <- (28, 55) [resolution 285,460]
493. $false <- (4, 28, 55) [subsumption resolution 492,177]
494. ~4 | ~28 | ~55 [avatar contradiction clause 493]
495. $false [avatar sat refutation 194,258,286,431,446,447,457,463,470,494]
% SZS output end Proof for 555478312933256325886357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or humble is either rich or curious.
Everyone who is old or wise is either brave or not curious and vice versa.
Everyone who is either not quiet or not humble is either funny or not creative and vice versa.
If someone is either humble or not old then lucy is both brave and generous and vice versa.
Everyone who is both not strong and quiet is not patient.
Everyone who is either not old or not humble is not generous or not wise and vice versa.
Everyone who is creative or not curious is creative.
Everyone who is either not tall or calm is brave or happy and vice versa.
If paul is not rich or not calm then someone is either kind or not rich and vice versa.
Everyone who is both creative and not calm is either old or not old and vice versa.
If someone is either calm or not curious then someone is not funny or not generous and vice versa.
If someone is not tall or calm then susan is both not quiet and strong.
Everyone who is either creative or not humble is both not kind and not strong and vice versa.
Everyone who is not rich or patient is both humble and rich and vice versa.
If someone is not creative or not humble then someone is not kind and vice versa.
Someone is either not brave or kind.
Alice is not tall or not rich.
Paul is not kind or calm.
John is either generous or not calm.
John is either funny or curious.
Fred is brave or not curious.
Paul is both old and patient.
Lucy is either not kind or tall. | Susan is humble. | contradiction | (![X]:((~old(X)|humble(X))=>(rich(X)<~>curious(X))))&
(![X]:((old(X)|wise(X))<=>(brave(X)<~>~curious(X))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(funny(X)<~>~creative(X))))&
((?[X]:((humble(X)<~>~old(X))))<=>((brave(lucy)&generous(lucy))))&
(![X]:((~strong(X)&quiet(X))=>~patient(X)))&
(![X]:((~old(X)<~>~humble(X))<=>(~generous(X)|~wise(X))))&
(![X]:((creative(X)|~curious(X))=>creative(X)))&
(![X]:((~tall(X)<~>calm(X))<=>(brave(X)|happy(X))))&
(((~rich(paul)|~calm(paul)))<=>(?[X]:((kind(X)<~>~rich(X)))))&
(![X]:((creative(X)&~calm(X))<=>(old(X)<~>~old(X))))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
((?[X]:((~tall(X)|calm(X))))=>((~quiet(susan)&strong(susan))))&
(![X]:((creative(X)<~>~humble(X))<=>(~kind(X)&~strong(X))))&
(![X]:((~rich(X)|patient(X))<=>(humble(X)&rich(X))))&
((?[X]:((~creative(X)|~humble(X))))<=>(?[X]:(~kind(X))))&
(?[X]:((~brave(X)<~>kind(X))))&
((~tall(alice)|~rich(alice)))&
((~kind(paul)|calm(paul)))&
((generous(john)<~>~calm(john)))&
((funny(john)<~>curious(john)))&
((brave(fred)|~curious(fred)))&
((old(paul)&patient(paul)))&
((~kind(lucy)<~>tall(lucy))) | humble(susan) | [
"p9",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9188784871968822264595595
% SZS output start Proof for 9188784871968822264595595
10. ! [X0] : ((~calm(X0) & creative(X0)) <=> (old(X0) <~> ~old(X0))) [input p9]
12. ? [X0] : (calm(X0) | ~tall(X0)) => (strong(susan) & ~quiet(susan)) [input p11]
13. ! [X0] : ((creative(X0) <~> ~humble(X0)) <=> (~strong(X0) & ~kind(X0))) [input p12]
14. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (rich(X0) & humble(X0))) [input p13]
17. ~rich(alice) | ~tall(alice) [input p16]
24. humble(susan) [input hypothesis]
31. (strong(susan) & ~quiet(susan)) | ! [X0] : (~calm(X0) & tall(X0)) [ennf transformation 12]
50. ! [X0] : (((~calm(X0) & creative(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) & (((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | (calm(X0) | ~creative(X0)))) [nnf transformation 10]
51. ! [X0] : (((~calm(X0) & creative(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) & (((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | calm(X0) | ~creative(X0))) [flattening 50]
57. ! [X0] : ((((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))))) [nnf transformation 13]
58. ! [X0] : ((((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))))) [flattening 57]
59. ! [X0] : (((patient(X0) | ~rich(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 14]
60. ! [X0] : ((patient(X0) | ~rich(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [flattening 59]
119. creative(X0) | ~old(X0) | ~old(X0) [cnf transformation 51]
120. creative(X0) | old(X0) | old(X0) [cnf transformation 51]
131. strong(susan) | tall(X0) [cnf transformation 31]
135. ~strong(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 58]
141. rich(X0) | rich(X0) [cnf transformation 60]
149. ~rich(alice) | ~tall(alice) [cnf transformation 17]
160. humble(susan) [cnf transformation 24]
161. rich(X0) [duplicate literal removal 141]
163. creative(X0) | ~old(X0) [duplicate literal removal 119]
164. creative(X0) | old(X0) [duplicate literal removal 120]
224. creative(X0) [subsumption resolution 163,164]
253. 19 <=> ! [X0] : tall(X0) [avatar definition]
254. tall(X0) <- (19) [avatar component clause 253]
256. 20 <=> strong(susan) [avatar definition]
258. strong(susan) <- (20) [avatar component clause 256]
259. 19 | 20 [avatar split clause 131,256,253]
266. ~strong(X0) | ~humble(X0) [subsumption resolution 135,224]
295. ~tall(alice) [subsumption resolution 149,161]
334. $false <- (19) [resolution 295,254]
335. ~19 [avatar contradiction clause 334]
347. ~humble(susan) <- (20) [resolution 266,258]
348. $false <- (20) [subsumption resolution 347,160]
349. ~20 [avatar contradiction clause 348]
350. $false [avatar sat refutation 259,335,349]
% SZS output end Proof for 9188784871968822264595595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or patient then susan is not patient and vice versa.
Everyone who is either not strong or not patient is both rich and curious and vice versa.
Everyone who is both strong and not kind is funny and vice versa.
Everyone who is not curious is either not brave or not rich and vice versa.
Everyone who is both humble and brave is both generous and kind.
Everyone who is both not funny and generous is either wise or not curious.
If someone is calm then someone is not happy or tall.
If lucy is both happy and brave then fred is curious.
Everyone who is both quiet and kind is curious.
If fred is either kind or not curious then someone is either not kind or not humble.
If susan is not happy or not curious then someone is both not funny and not creative and vice versa.
If someone is either not brave or strong then someone is either generous or curious and vice versa.
Everyone who is not wise or not tall is tall and vice versa.
Everyone who is strong is either tall or generous and vice versa.
Everyone who is funny or not generous is not wise or quiet.
Everyone who is both kind and generous is not curious and vice versa.
Mary is not kind.
Someone is either humble or not wise.
Someone is not funny.
Alice is not kind.
Alice is quiet.
Susan is old. | Mary is not tall. | contradiction | ((?[X]:((brave(X)<~>patient(X))))<=>(~patient(susan)))&
(![X]:((~strong(X)<~>~patient(X))<=>(rich(X)&curious(X))))&
(![X]:((strong(X)&~kind(X))<=>funny(X)))&
(![X]:(~curious(X)<=>(~brave(X)<~>~rich(X))))&
(![X]:((humble(X)&brave(X))=>(generous(X)&kind(X))))&
(![X]:((~funny(X)&generous(X))=>(wise(X)<~>~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~happy(X)|tall(X)))))&
(((happy(lucy)&brave(lucy)))=>(curious(fred)))&
(![X]:((quiet(X)&kind(X))=>curious(X)))&
(((kind(fred)<~>~curious(fred)))=>(?[X]:((~kind(X)<~>~humble(X)))))&
(((~happy(susan)|~curious(susan)))<=>(?[X]:((~funny(X)&~creative(X)))))&
((?[X]:((~brave(X)<~>strong(X))))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((~wise(X)|~tall(X))<=>tall(X)))&
(![X]:(strong(X)<=>(tall(X)<~>generous(X))))&
(![X]:((funny(X)|~generous(X))=>(~wise(X)|quiet(X))))&
(![X]:((kind(X)&generous(X))<=>~curious(X)))&
(~kind(mary))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:(~funny(X)))&
(~kind(alice))&
(quiet(alice))&
(old(susan)) | ~tall(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3159451049659474593433568
% SZS output start Proof for 3159451049659474593433568
13. ! [X0] : ((~tall(X0) | ~wise(X0)) <=> tall(X0)) [input p12]
23. ~tall(mary) [input hypothesis]
62. ! [X0] : (((~tall(X0) | ~wise(X0)) | ~tall(X0)) & (tall(X0) | (tall(X0) & wise(X0)))) [nnf transformation 13]
63. ! [X0] : ((~tall(X0) | ~wise(X0) | ~tall(X0)) & (tall(X0) | (tall(X0) & wise(X0)))) [flattening 62]
113. tall(X0) | tall(X0) [cnf transformation 63]
130. ~tall(mary) [cnf transformation 23]
131. tall(X0) [duplicate literal removal 113]
256. $false [subsumption resolution 130,131]
% SZS output end Proof for 3159451049659474593433568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not brave is both not strong and strong and vice versa. Everyone who is creative is not strong and vice versa. If someone is either humble or not calm then lucy is both not creative and not rich. If someone is not old or not happy then susan is not calm or happy. Everyone who is brave is not creative. Everyone who is either not brave or not tall is humble. Everyone who is quiet is not happy or not creative and vice versa. Everyone who is both happy and brave is not tall or quiet and vice versa. Everyone who is brave is calm or humble. Everyone who is either funny or not calm is humble or curious. Everyone who is not calm or not tall is rich and vice versa. If someone is not wise or happy then alice is both brave and wise and vice versa. If someone is either wise or patient then someone is not patient or not kind. If someone is generous or not generous then john is quiet. If john is not strong then someone is either quiet or humble and vice versa. Paul is either humble or generous. John is either curious or rich. Someone is not humble or tall. Someone is funny. Someone is strong. Susan is both humble and calm. Someone is not old or not curious. | Paul is not tall. | neutral | (![X]:((~calm(X)|~brave(X))<=>(~strong(X)&strong(X))))&
(![X]:(creative(X)<=>~strong(X)))&
((?[X]:((humble(X)<~>~calm(X))))=>((~creative(lucy)&~rich(lucy))))&
((?[X]:((~old(X)|~happy(X))))=>((~calm(susan)|happy(susan))))&
(![X]:(brave(X)=>~creative(X)))&
(![X]:((~brave(X)<~>~tall(X))=>humble(X)))&
(![X]:(quiet(X)<=>(~happy(X)|~creative(X))))&
(![X]:((happy(X)&brave(X))<=>(~tall(X)|quiet(X))))&
(![X]:(brave(X)=>(calm(X)|humble(X))))&
(![X]:((funny(X)<~>~calm(X))=>(humble(X)|curious(X))))&
(![X]:((~calm(X)|~tall(X))<=>rich(X)))&
((?[X]:((~wise(X)|happy(X))))<=>((brave(alice)&wise(alice))))&
((?[X]:((wise(X)<~>patient(X))))=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((generous(X)|~generous(X))))=>(quiet(john)))&
((~strong(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
((humble(paul)<~>generous(paul)))&
((curious(john)<~>rich(john)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:(funny(X)))&
(?[X]:(strong(X)))&
((humble(susan)&calm(susan)))&
(?[X]:((~old(X)|~curious(X)))) | ~tall(paul) | [] | null | 0 |
Everyone who is not tall is both not calm and not creative and vice versa. Everyone who is generous is happy or not strong. If paul is not humble then someone is not quiet. If someone is both kind and brave then someone is both brave and not kind. Everyone who is both not generous and not strong is either not patient or happy. Everyone who is not wise or not rich is brave or not patient and vice versa. If alice is not calm or not patient then paul is either happy or not brave. If paul is both wise and not quiet then fred is strong. Everyone who is patient or not generous is either rich or patient and vice versa. If someone is not humble or not rich then fred is either not curious or funny and vice versa. Everyone who is not tall or not generous is not quiet. Everyone who is not humble is not curious and vice versa. Everyone who is either not happy or not patient is both not curious and funny. Everyone who is not strong is curious or happy. Everyone who is both strong and calm is not strong or not generous and vice versa. Everyone who is either not rich or not calm is both not humble and strong. Susan is both not funny and creative. Mary is both tall and not happy. Alice is humble. Paul is both quiet and strong. John is not humble. Fred is not humble. Alice is not generous. Someone is not old. | Mary is strong. | entailment | (![X]:(~tall(X)<=>(~calm(X)&~creative(X))))&
(![X]:(generous(X)=>(happy(X)|~strong(X))))&
((~humble(paul))=>(?[X]:(~quiet(X))))&
((?[X]:((kind(X)&brave(X))))=>(?[X]:((brave(X)&~kind(X)))))&
(![X]:((~generous(X)&~strong(X))=>(~patient(X)<~>happy(X))))&
(![X]:((~wise(X)|~rich(X))<=>(brave(X)|~patient(X))))&
(((~calm(alice)|~patient(alice)))=>((happy(paul)<~>~brave(paul))))&
(((wise(paul)&~quiet(paul)))=>(strong(fred)))&
(![X]:((patient(X)|~generous(X))<=>(rich(X)<~>patient(X))))&
((?[X]:((~humble(X)|~rich(X))))<=>((~curious(fred)<~>funny(fred))))&
(![X]:((~tall(X)|~generous(X))=>~quiet(X)))&
(![X]:(~humble(X)<=>~curious(X)))&
(![X]:((~happy(X)<~>~patient(X))=>(~curious(X)&funny(X))))&
(![X]:(~strong(X)=>(curious(X)|happy(X))))&
(![X]:((strong(X)&calm(X))<=>(~strong(X)|~generous(X))))&
(![X]:((~rich(X)<~>~calm(X))=>(~humble(X)&strong(X))))&
((~funny(susan)&creative(susan)))&
((tall(mary)&~happy(mary)))&
(humble(alice))&
((quiet(paul)&strong(paul)))&
(~humble(john))&
(~humble(fred))&
(~generous(alice))&
(?[X]:(~old(X))) | strong(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4643609303275202612929040
% SZS output start Proof for 4643609303275202612929040
15. ! [X0] : ((calm(X0) & strong(X0)) <=> (~generous(X0) | ~strong(X0))) [input p14]
25. ~strong(mary) [input hypothesis]
61. ! [X0] : (((calm(X0) & strong(X0)) | (generous(X0) & strong(X0))) & ((~generous(X0) | ~strong(X0)) | (~calm(X0) | ~strong(X0)))) [nnf transformation 15]
62. ! [X0] : (((calm(X0) & strong(X0)) | (generous(X0) & strong(X0))) & (~generous(X0) | ~strong(X0) | ~calm(X0) | ~strong(X0))) [flattening 61]
98. strong(X0) | strong(X0) [cnf transformation 62]
114. ~strong(mary) [cnf transformation 25]
116. strong(X0) [duplicate literal removal 98]
191. $false [subsumption resolution 114,116]
% SZS output end Proof for 4643609303275202612929040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both kind and not brave then lucy is happy. Everyone who is not old is old. If mary is not tall or not rich then paul is both creative and generous and vice versa. If someone is humble then someone is both not brave and kind and vice versa. Everyone who is both not creative and not strong is not tall or wise. If someone is wise then john is both curious and not humble. Everyone who is not brave is calm or creative and vice versa. If someone is either humble or quiet then fred is tall or not wise. Everyone who is not wise is both old and strong and vice versa. Everyone who is not creative or not humble is either humble or not quiet. If susan is humble or rich then paul is not curious or happy. Everyone who is creative is not brave and vice versa. Everyone who is either not humble or not wise is not happy or happy. Everyone who is funny or not tall is both kind and tall and vice versa. If fred is either tall or not old then susan is not kind and vice versa. Everyone who is not tall is both not patient and humble and vice versa. Alice is either calm or humble. Fred is generous or not generous. Mary is either rich or not curious. Someone is either not curious or wise. Susan is not rich. Fred is either tall or strong. Someone is not calm. Someone is wise. | Susan is kind. | contradiction | (((kind(fred)&~brave(fred)))=>(happy(lucy)))&
(![X]:(~old(X)=>old(X)))&
(((~tall(mary)|~rich(mary)))<=>((creative(paul)&generous(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((~brave(X)&kind(X)))))&
(![X]:((~creative(X)&~strong(X))=>(~tall(X)|wise(X))))&
((?[X]:(wise(X)))=>((curious(john)&~humble(john))))&
(![X]:(~brave(X)<=>(calm(X)|creative(X))))&
((?[X]:((humble(X)<~>quiet(X))))=>((tall(fred)|~wise(fred))))&
(![X]:(~wise(X)<=>(old(X)&strong(X))))&
(![X]:((~creative(X)|~humble(X))=>(humble(X)<~>~quiet(X))))&
(((humble(susan)|rich(susan)))=>((~curious(paul)|happy(paul))))&
(![X]:(creative(X)<=>~brave(X)))&
(![X]:((~humble(X)<~>~wise(X))=>(~happy(X)|happy(X))))&
(![X]:((funny(X)|~tall(X))<=>(kind(X)&tall(X))))&
(((tall(fred)<~>~old(fred)))<=>(~kind(susan)))&
(![X]:(~tall(X)<=>(~patient(X)&humble(X))))&
((calm(alice)<~>humble(alice)))&
((generous(fred)|~generous(fred)))&
((rich(mary)<~>~curious(mary)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~rich(susan))&
((tall(fred)<~>strong(fred)))&
(?[X]:(~calm(X)))&
(?[X]:(wise(X))) | kind(susan) | [
"p1",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9029248210879432203337151
% SZS output start Proof for 9029248210879432203337151
2. ! [X0] : (~old(X0) => old(X0)) [input p1]
14. ! [X0] : ((~tall(X0) | funny(X0)) <=> (tall(X0) & kind(X0))) [input p13]
15. (tall(fred) <~> ~old(fred)) <=> ~kind(susan) [input p14]
25. kind(susan) [input hypothesis]
29. ! [X0] : (old(X0) | old(X0)) [ennf transformation 2]
55. ! [X0] : (((~tall(X0) | funny(X0)) | (~tall(X0) | ~kind(X0))) & ((tall(X0) & kind(X0)) | (tall(X0) & ~funny(X0)))) [nnf transformation 14]
56. ! [X0] : ((~tall(X0) | funny(X0) | ~tall(X0) | ~kind(X0)) & ((tall(X0) & kind(X0)) | (tall(X0) & ~funny(X0)))) [flattening 55]
57. (((old(fred) | ~tall(fred)) & (~old(fred) | tall(fred))) | kind(susan)) & (~kind(susan) | ((tall(fred) | old(fred)) & (~old(fred) | ~tall(fred)))) [nnf transformation 15]
71. old(X0) | old(X0) [cnf transformation 29]
104. tall(X0) | tall(X0) [cnf transformation 56]
106. ~kind(susan) | ~old(fred) | ~tall(fred) [cnf transformation 57]
125. kind(susan) [cnf transformation 25]
126. tall(X0) [duplicate literal removal 104]
129. old(X0) [duplicate literal removal 71]
234. ~kind(susan) | ~tall(fred) [subsumption resolution 106,129]
235. ~kind(susan) [subsumption resolution 234,126]
265. $false [subsumption resolution 125,235]
% SZS output end Proof for 9029248210879432203337151
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is either not curious or old and vice versa.
Everyone who is both not wise and not patient is wise.
If susan is either not old or not patient then paul is either humble or not kind and vice versa.
Everyone who is either not wise or not creative is either not calm or happy.
If fred is humble or brave then someone is both not old and not generous and vice versa.
If john is calm then someone is both not funny and not calm and vice versa.
Everyone who is both not old and creative is not quiet or calm and vice versa.
Everyone who is either not funny or not quiet is strong or humble and vice versa.
If someone is both creative and not brave then someone is both not strong and not generous and vice versa.
If someone is not happy then someone is either old or creative and vice versa.
Everyone who is rich or not curious is both not kind and tall and vice versa.
If mary is old or happy then mary is either creative or strong.
Everyone who is not quiet or not kind is not curious and vice versa.
Everyone who is not generous or brave is not patient or not rich and vice versa.
If john is either not creative or not generous then someone is not patient.
Everyone who is either not curious or old is either not tall or strong and vice versa.
Someone is not creative.
Someone is either not funny or not happy.
Someone is either strong or not patient.
Lucy is either not rich or tall.
Paul is not curious or not humble.
John is either not creative or not generous.
Alice is not patient. | Fred is not curious. | entailment | (![X]:(~old(X)<=>(~curious(X)<~>old(X))))&
(![X]:((~wise(X)&~patient(X))=>wise(X)))&
(((~old(susan)<~>~patient(susan)))<=>((humble(paul)<~>~kind(paul))))&
(![X]:((~wise(X)<~>~creative(X))=>(~calm(X)<~>happy(X))))&
(((humble(fred)|brave(fred)))<=>(?[X]:((~old(X)&~generous(X)))))&
((calm(john))<=>(?[X]:((~funny(X)&~calm(X)))))&
(![X]:((~old(X)&creative(X))<=>(~quiet(X)|calm(X))))&
(![X]:((~funny(X)<~>~quiet(X))<=>(strong(X)|humble(X))))&
((?[X]:((creative(X)&~brave(X))))<=>(?[X]:((~strong(X)&~generous(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:((rich(X)|~curious(X))<=>(~kind(X)&tall(X))))&
(((old(mary)|happy(mary)))=>((creative(mary)<~>strong(mary))))&
(![X]:((~quiet(X)|~kind(X))<=>~curious(X)))&
(![X]:((~generous(X)|brave(X))<=>(~patient(X)|~rich(X))))&
(((~creative(john)<~>~generous(john)))=>(?[X]:(~patient(X))))&
(![X]:((~curious(X)<~>old(X))<=>(~tall(X)<~>strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)<~>~happy(X))))&
(?[X]:((strong(X)<~>~patient(X))))&
((~rich(lucy)<~>tall(lucy)))&
((~curious(paul)|~humble(paul)))&
((~creative(john)<~>~generous(john)))&
(~patient(alice)) | ~curious(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 7512793061146326450751218
% SZS output start Proof for 7512793061146326450751218
1. ! [X0] : (~old(X0) <=> (~curious(X0) <~> old(X0))) [input p0]
24. curious(fred) [input hypothesis]
32. ! [X0] : ((~old(X0) | ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | old(X0))) [nnf transformation 1]
79. old(X0) | ~curious(X0) | old(X0) [cnf transformation 32]
82. ~old(X0) | ~curious(X0) | ~old(X0) [cnf transformation 32]
160. curious(fred) [cnf transformation 24]
162. old(X0) | ~curious(X0) [duplicate literal removal 79]
163. ~old(X0) | ~curious(X0) [duplicate literal removal 82]
164. ~curious(X0) [subsumption resolution 162,163]
345. $false [subsumption resolution 160,164]
% SZS output end Proof for 7512793061146326450751218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not kind is wise. If alice is either calm or humble then susan is both not wise and not quiet and vice versa. Everyone who is both not brave and not curious is both not patient and not tall and vice versa. If susan is either quiet or curious then someone is either not wise or not old and vice versa. Everyone who is both not rich and not calm is either tall or not wise and vice versa. Everyone who is wise is both not wise and not tall. Everyone who is not humble or generous is both not curious and quiet. Everyone who is either not brave or happy is creative or patient and vice versa. Everyone who is both not brave and generous is funny or wise. Everyone who is both not kind and humble is both not creative and patient and vice versa. Everyone who is not funny or not curious is both not curious and not brave. If someone is not humble then alice is both generous and kind and vice versa. If john is both quiet and not humble then paul is tall or not rich. If fred is not brave then john is either not humble or not tall and vice versa. Everyone who is not humble is strong or not creative. If john is either not creative or strong then susan is both not strong and not kind and vice versa. Someone is not humble or not creative. Someone is either not calm or strong. Someone is either strong or not strong. Someone is humble or strong. Fred is both not calm and kind. Someone is both not quiet and calm. Susan is not wise or happy. | Fred is old. | neutral | (![X]:((~generous(X)<~>~kind(X))=>wise(X)))&
(((calm(alice)<~>humble(alice)))<=>((~wise(susan)&~quiet(susan))))&
(![X]:((~brave(X)&~curious(X))<=>(~patient(X)&~tall(X))))&
(((quiet(susan)<~>curious(susan)))<=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((~rich(X)&~calm(X))<=>(tall(X)<~>~wise(X))))&
(![X]:(wise(X)=>(~wise(X)&~tall(X))))&
(![X]:((~humble(X)|generous(X))=>(~curious(X)&quiet(X))))&
(![X]:((~brave(X)<~>happy(X))<=>(creative(X)|patient(X))))&
(![X]:((~brave(X)&generous(X))=>(funny(X)|wise(X))))&
(![X]:((~kind(X)&humble(X))<=>(~creative(X)&patient(X))))&
(![X]:((~funny(X)|~curious(X))=>(~curious(X)&~brave(X))))&
((?[X]:(~humble(X)))<=>((generous(alice)&kind(alice))))&
(((quiet(john)&~humble(john)))=>((tall(paul)|~rich(paul))))&
((~brave(fred))<=>((~humble(john)<~>~tall(john))))&
(![X]:(~humble(X)=>(strong(X)|~creative(X))))&
(((~creative(john)<~>strong(john)))<=>((~strong(susan)&~kind(susan))))&
(?[X]:((~humble(X)|~creative(X))))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:((strong(X)<~>~strong(X))))&
(?[X]:((humble(X)|strong(X))))&
((~calm(fred)&kind(fred)))&
(?[X]:((~quiet(X)&calm(X))))&
((~wise(susan)|happy(susan))) | old(fred) | [] | null | 0 |
Everyone who is either strong or not brave is curious or kind and vice versa.
If someone is both humble and not funny then someone is either not funny or patient and vice versa.
If someone is either kind or rich then someone is either wise or patient and vice versa.
Everyone who is either happy or not humble is either wise or not rich.
If someone is either funny or old then someone is not strong and vice versa.
Everyone who is funny or not kind is wise or not happy.
Everyone who is either not curious or not strong is either not creative or not patient and vice versa.
Everyone who is not rich is not humble and vice versa.
If someone is not happy or not kind then someone is generous or not kind.
If john is curious or not generous then lucy is either not strong or not creative and vice versa.
Everyone who is not kind or not generous is both not generous and not wise and vice versa.
Everyone who is either not curious or patient is old or not quiet.
If someone is either humble or not tall then paul is either not patient or not creative and vice versa.
If john is generous or not tall then someone is both generous and curious.
Everyone who is curious or not humble is either not happy or not curious and vice versa.
Everyone who is either not happy or not rich is both happy and quiet and vice versa.
Someone is generous or not patient.
Susan is wise or happy.
Someone is not generous or not rich.
John is not rich or quiet.
Someone is either not happy or not quiet.
Someone is both funny and old.
John is either rich or not kind. | Paul is not generous. | neutral | (![X]:((strong(X)<~>~brave(X))<=>(curious(X)|kind(X))))&
((?[X]:((humble(X)&~funny(X))))<=>(?[X]:((~funny(X)<~>patient(X)))))&
((?[X]:((kind(X)<~>rich(X))))<=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:((happy(X)<~>~humble(X))=>(wise(X)<~>~rich(X))))&
((?[X]:((funny(X)<~>old(X))))<=>(?[X]:(~strong(X))))&
(![X]:((funny(X)|~kind(X))=>(wise(X)|~happy(X))))&
(![X]:((~curious(X)<~>~strong(X))<=>(~creative(X)<~>~patient(X))))&
(![X]:(~rich(X)<=>~humble(X)))&
((?[X]:((~happy(X)|~kind(X))))=>(?[X]:((generous(X)|~kind(X)))))&
(((curious(john)|~generous(john)))<=>((~strong(lucy)<~>~creative(lucy))))&
(![X]:((~kind(X)|~generous(X))<=>(~generous(X)&~wise(X))))&
(![X]:((~curious(X)<~>patient(X))=>(old(X)|~quiet(X))))&
((?[X]:((humble(X)<~>~tall(X))))<=>((~patient(paul)<~>~creative(paul))))&
(((generous(john)|~tall(john)))=>(?[X]:((generous(X)&curious(X)))))&
(![X]:((curious(X)|~humble(X))<=>(~happy(X)<~>~curious(X))))&
(![X]:((~happy(X)<~>~rich(X))<=>(happy(X)&quiet(X))))&
(?[X]:((generous(X)|~patient(X))))&
((wise(susan)|happy(susan)))&
(?[X]:((~generous(X)|~rich(X))))&
((~rich(john)|quiet(john)))&
(?[X]:((~happy(X)<~>~quiet(X))))&
(?[X]:((funny(X)&old(X))))&
((rich(john)<~>~kind(john))) | ~generous(paul) | [] | null | 0 |
If someone is not curious or patient then john is funny. If john is both humble and not brave then john is not brave or not curious and vice versa. If susan is not creative or not tall then mary is either patient or funny. If someone is not brave or tall then someone is either not funny or not tall and vice versa. If fred is either strong or curious then someone is brave. Everyone who is kind is funny and vice versa. Everyone who is not quiet or not humble is both not strong and not tall. Everyone who is creative or wise is curious or not generous. Everyone who is kind is patient. Everyone who is either not brave or humble is not creative and vice versa. Everyone who is not kind is either brave or patient and vice versa. Everyone who is either calm or not quiet is both curious and happy. Everyone who is wise is strong or creative. If paul is both kind and not curious then john is not quiet. Everyone who is both wise and kind is not old. Someone is either wise or not strong. John is not calm. John is quiet. Lucy is both not generous and not old. Someone is both not humble and funny. Alice is not creative. | Susan is quiet. | neutral | ((?[X]:((~curious(X)|patient(X))))=>(funny(john)))&
(((humble(john)&~brave(john)))<=>((~brave(john)|~curious(john))))&
(((~creative(susan)|~tall(susan)))=>((patient(mary)<~>funny(mary))))&
((?[X]:((~brave(X)|tall(X))))<=>(?[X]:((~funny(X)<~>~tall(X)))))&
(((strong(fred)<~>curious(fred)))=>(?[X]:(brave(X))))&
(![X]:(kind(X)<=>funny(X)))&
(![X]:((~quiet(X)|~humble(X))=>(~strong(X)&~tall(X))))&
(![X]:((creative(X)|wise(X))=>(curious(X)|~generous(X))))&
(![X]:(kind(X)=>patient(X)))&
(![X]:((~brave(X)<~>humble(X))<=>~creative(X)))&
(![X]:(~kind(X)<=>(brave(X)<~>patient(X))))&
(![X]:((calm(X)<~>~quiet(X))=>(curious(X)&happy(X))))&
(![X]:(wise(X)=>(strong(X)|creative(X))))&
(((kind(paul)&~curious(paul)))=>(~quiet(john)))&
(![X]:((wise(X)&kind(X))=>~old(X)))&
(?[X]:((wise(X)<~>~strong(X))))&
(~calm(john))&
(quiet(john))&
((~generous(lucy)&~old(lucy)))&
(?[X]:((~humble(X)&funny(X))))&
(~creative(alice)) | quiet(susan) | [] | null | 0 |
If someone is brave then mary is not funny or not rich and vice versa.
Everyone who is brave or rich is happy or quiet and vice versa.
If someone is both not humble and not generous then someone is either not creative or kind.
If someone is not wise or generous then someone is not generous or not curious and vice versa.
Everyone who is tall is tall or not tall and vice versa.
If susan is happy or not tall then john is either not happy or not creative and vice versa.
If fred is both not calm and not brave then someone is either tall or old and vice versa.
If someone is either not wise or not brave then fred is old or not funny and vice versa.
Everyone who is either not calm or curious is tall.
Everyone who is both not old and not quiet is not strong or brave.
Everyone who is not kind or tall is either kind or patient.
Everyone who is creative or wise is funny or not humble.
If someone is either wise or creative then lucy is not humble or not funny and vice versa.
If someone is not brave then susan is not patient or old and vice versa.
Everyone who is funny or old is not brave and vice versa.
Everyone who is not strong or not funny is calm and vice versa.
Lucy is creative or not calm.
Someone is both quiet and rich.
Susan is either not humble or kind.
Alice is both not old and humble.
Lucy is not calm or not wise.
Fred is either quiet or not tall.
Someone is either happy or old. | Susan is wise. | neutral | ((?[X]:(brave(X)))<=>((~funny(mary)|~rich(mary))))&
(![X]:((brave(X)|rich(X))<=>(happy(X)|quiet(X))))&
((?[X]:((~humble(X)&~generous(X))))=>(?[X]:((~creative(X)<~>kind(X)))))&
((?[X]:((~wise(X)|generous(X))))<=>(?[X]:((~generous(X)|~curious(X)))))&
(![X]:(tall(X)<=>(tall(X)|~tall(X))))&
(((happy(susan)|~tall(susan)))<=>((~happy(john)<~>~creative(john))))&
(((~calm(fred)&~brave(fred)))<=>(?[X]:((tall(X)<~>old(X)))))&
((?[X]:((~wise(X)<~>~brave(X))))<=>((old(fred)|~funny(fred))))&
(![X]:((~calm(X)<~>curious(X))=>tall(X)))&
(![X]:((~old(X)&~quiet(X))=>(~strong(X)|brave(X))))&
(![X]:((~kind(X)|tall(X))=>(kind(X)<~>patient(X))))&
(![X]:((creative(X)|wise(X))=>(funny(X)|~humble(X))))&
((?[X]:((wise(X)<~>creative(X))))<=>((~humble(lucy)|~funny(lucy))))&
((?[X]:(~brave(X)))<=>((~patient(susan)|old(susan))))&
(![X]:((funny(X)|old(X))<=>~brave(X)))&
(![X]:((~strong(X)|~funny(X))<=>calm(X)))&
((creative(lucy)|~calm(lucy)))&
(?[X]:((quiet(X)&rich(X))))&
((~humble(susan)<~>kind(susan)))&
((~old(alice)&humble(alice)))&
((~calm(lucy)|~wise(lucy)))&
((quiet(fred)<~>~tall(fred)))&
(?[X]:((happy(X)<~>old(X)))) | wise(susan) | [] | null | 0 |
If someone is either not wise or patient then fred is either not curious or strong and vice versa. Everyone who is not kind or not happy is not creative. Everyone who is both not rich and happy is kind or funny and vice versa. If someone is not brave then alice is generous or not funny and vice versa. Everyone who is both not curious and not creative is not brave or tall. Everyone who is old or creative is not happy and vice versa. Everyone who is not curious is both funny and not generous. If someone is either strong or kind then someone is either not strong or rich and vice versa. If paul is either not funny or quiet then fred is not generous or not brave and vice versa. If someone is not generous then someone is either wise or old. If someone is not kind or patient then lucy is both old and not calm and vice versa. Everyone who is not generous is both not quiet and kind. Everyone who is wise or not patient is not brave. Everyone who is not wise or humble is not humble. Everyone who is not happy or funny is not curious. If john is creative then someone is not wise. Someone is not rich. Someone is not strong or not happy. Someone is either quiet or not generous. John is not calm. Paul is strong. Someone is both happy and not humble. Lucy is either old or strong. Someone is both generous and not calm. | Lucy is not patient. | entailment | ((?[X]:((~wise(X)<~>patient(X))))<=>((~curious(fred)<~>strong(fred))))&
(![X]:((~kind(X)|~happy(X))=>~creative(X)))&
(![X]:((~rich(X)&happy(X))<=>(kind(X)|funny(X))))&
((?[X]:(~brave(X)))<=>((generous(alice)|~funny(alice))))&
(![X]:((~curious(X)&~creative(X))=>(~brave(X)|tall(X))))&
(![X]:((old(X)|creative(X))<=>~happy(X)))&
(![X]:(~curious(X)=>(funny(X)&~generous(X))))&
((?[X]:((strong(X)<~>kind(X))))<=>(?[X]:((~strong(X)<~>rich(X)))))&
(((~funny(paul)<~>quiet(paul)))<=>((~generous(fred)|~brave(fred))))&
((?[X]:(~generous(X)))=>(?[X]:((wise(X)<~>old(X)))))&
((?[X]:((~kind(X)|patient(X))))<=>((old(lucy)&~calm(lucy))))&
(![X]:(~generous(X)=>(~quiet(X)&kind(X))))&
(![X]:((wise(X)|~patient(X))=>~brave(X)))&
(![X]:((~wise(X)|humble(X))=>~humble(X)))&
(![X]:((~happy(X)|funny(X))=>~curious(X)))&
((creative(john))=>(?[X]:(~wise(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~strong(X)|~happy(X))))&
(?[X]:((quiet(X)<~>~generous(X))))&
(~calm(john))&
(strong(paul))&
(?[X]:((happy(X)&~humble(X))))&
((old(lucy)<~>strong(lucy)))&
(?[X]:((generous(X)&~calm(X)))) | ~patient(lucy) | [
"p2",
"p5",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8089897180514821361505779
% SZS output start Proof for 8089897180514821361505779
3. ! [X0] : ((happy(X0) & ~rich(X0)) <=> (funny(X0) | kind(X0))) [input p2]
6. ! [X0] : ((creative(X0) | old(X0)) <=> ~happy(X0)) [input p5]
7. ! [X0] : (~curious(X0) => (~generous(X0) & funny(X0))) [input p6]
11. ? [X0] : (patient(X0) | ~kind(X0)) <=> (~calm(lucy) & old(lucy)) [input p10]
15. ! [X0] : ((funny(X0) | ~happy(X0)) => ~curious(X0)) [input p14]
25. patient(lucy) [input hypothesis]
32. ! [X0] : ((~generous(X0) & funny(X0)) | curious(X0)) [ennf transformation 7]
36. ! [X0] : (~curious(X0) | (~funny(X0) & happy(X0))) [ennf transformation 15]
42. ! [X0] : (((happy(X0) & ~rich(X0)) | (~funny(X0) & ~kind(X0))) & ((funny(X0) | kind(X0)) | (~happy(X0) | rich(X0)))) [nnf transformation 3]
43. ! [X0] : (((happy(X0) & ~rich(X0)) | (~funny(X0) & ~kind(X0))) & (funny(X0) | kind(X0) | ~happy(X0) | rich(X0))) [flattening 42]
49. ! [X0] : (((creative(X0) | old(X0)) | happy(X0)) & (~happy(X0) | (~creative(X0) & ~old(X0)))) [nnf transformation 6]
50. ! [X0] : ((creative(X0) | old(X0) | happy(X0)) & (~happy(X0) | (~creative(X0) & ~old(X0)))) [flattening 49]
62. (? [X0] : (patient(X0) | ~kind(X0)) | (calm(lucy) | ~old(lucy))) & ((~calm(lucy) & old(lucy)) | ! [X0] : (~patient(X0) & kind(X0))) [nnf transformation 11]
63. (? [X0] : (patient(X0) | ~kind(X0)) | calm(lucy) | ~old(lucy)) & ((~calm(lucy) & old(lucy)) | ! [X0] : (~patient(X0) & kind(X0))) [flattening 62]
64. (? [X0] : (patient(X0) | ~kind(X0)) | calm(lucy) | ~old(lucy)) & ((~calm(lucy) & old(lucy)) | ! [X1] : (~patient(X1) & kind(X1))) [rectify 63]
65. ? [X0] : (patient(X0) | ~kind(X0)) => (patient(sK5) | ~kind(sK5)) [choice axiom]
66. ((patient(sK5) | ~kind(sK5)) | calm(lucy) | ~old(lucy)) & ((~calm(lucy) & old(lucy)) | ! [X1] : (~patient(X1) & kind(X1))) [skolemisation 64,65]
95. ~funny(X0) | happy(X0) [cnf transformation 43]
99. ~old(X0) | ~happy(X0) [cnf transformation 50]
102. funny(X0) | curious(X0) [cnf transformation 32]
121. old(lucy) | ~patient(X1) [cnf transformation 66]
129. ~curious(X0) | happy(X0) [cnf transformation 36]
143. patient(lucy) [cnf transformation 25]
266. 26 <=> old(lucy) [avatar definition]
267. old(lucy) <- (26) [avatar component clause 266]
283. 30 <=> ! [X1] : ~patient(X1) [avatar definition]
284. ~patient(X1) <- (30) [avatar component clause 283]
290. 30 | 26 [avatar split clause 121,266,283]
320. ~happy(lucy) <- (26) [resolution 99,267]
323. curious(X0) | happy(X0) [resolution 102,95]
325. happy(X0) [subsumption resolution 323,129]
334. $false <- (26) [resolution 325,320]
335. ~26 [avatar contradiction clause 334]
337. $false <- (30) [resolution 284,143]
338. ~30 [avatar contradiction clause 337]
339. $false [avatar sat refutation 290,335,338]
% SZS output end Proof for 8089897180514821361505779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not strong is not old or strong.
Everyone who is not wise or generous is either calm or old and vice versa.
If fred is humble then lucy is not curious or old.
Everyone who is both creative and kind is not tall or not rich and vice versa.
If someone is both not quiet and quiet then someone is not funny.
Everyone who is either not curious or not quiet is tall or brave and vice versa.
If someone is creative then susan is either not quiet or strong.
If someone is both happy and curious then lucy is either rich or curious and vice versa.
If someone is either humble or not curious then john is strong or wise and vice versa.
Everyone who is both old and not generous is both not quiet and strong and vice versa.
If someone is not generous or not patient then someone is kind.
Everyone who is either curious or not strong is both not creative and kind.
Everyone who is both tall and not funny is happy and vice versa.
Everyone who is either generous or curious is both tall and not funny.
If someone is both not curious and kind then fred is both creative and humble and vice versa.
Everyone who is either kind or strong is not strong or not humble and vice versa.
Someone is not patient.
Mary is not patient or not funny.
Lucy is not wise.
Someone is generous.
Someone is not quiet.
Mary is not old or happy.
Someone is brave or not happy. | Fred is not old. | neutral | (![X]:((creative(X)&~strong(X))=>(~old(X)|strong(X))))&
(![X]:((~wise(X)|generous(X))<=>(calm(X)<~>old(X))))&
((humble(fred))=>((~curious(lucy)|old(lucy))))&
(![X]:((creative(X)&kind(X))<=>(~tall(X)|~rich(X))))&
((?[X]:((~quiet(X)&quiet(X))))=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(tall(X)|brave(X))))&
((?[X]:(creative(X)))=>((~quiet(susan)<~>strong(susan))))&
((?[X]:((happy(X)&curious(X))))<=>((rich(lucy)<~>curious(lucy))))&
((?[X]:((humble(X)<~>~curious(X))))<=>((strong(john)|wise(john))))&
(![X]:((old(X)&~generous(X))<=>(~quiet(X)&strong(X))))&
((?[X]:((~generous(X)|~patient(X))))=>(?[X]:(kind(X))))&
(![X]:((curious(X)<~>~strong(X))=>(~creative(X)&kind(X))))&
(![X]:((tall(X)&~funny(X))<=>happy(X)))&
(![X]:((generous(X)<~>curious(X))=>(tall(X)&~funny(X))))&
((?[X]:((~curious(X)&kind(X))))<=>((creative(fred)&humble(fred))))&
(![X]:((kind(X)<~>strong(X))<=>(~strong(X)|~humble(X))))&
(?[X]:(~patient(X)))&
((~patient(mary)|~funny(mary)))&
(~wise(lucy))&
(?[X]:(generous(X)))&
(?[X]:(~quiet(X)))&
((~old(mary)|happy(mary)))&
(?[X]:((brave(X)|~happy(X)))) | ~old(fred) | [] | null | 0 |
Everyone who is both wise and happy is curious or not brave.
If fred is both generous and not patient then someone is both humble and generous.
Everyone who is not generous or not strong is both wise and not funny and vice versa.
Everyone who is not curious or not creative is either rich or curious and vice versa.
Everyone who is both not old and not generous is either generous or not creative and vice versa.
If paul is both tall and quiet then someone is both strong and not curious.
If someone is humble or not funny then someone is curious and vice versa.
Everyone who is quiet is both kind and tall.
Everyone who is either not funny or not humble is both not creative and strong.
Everyone who is both not happy and calm is either quiet or not funny and vice versa.
Everyone who is tall is humble or strong and vice versa.
If someone is not generous then paul is funny and vice versa.
Everyone who is either strong or kind is not calm or not rich.
If mary is both rich and patient then susan is creative or old.
Everyone who is not brave or not strong is both quiet and tall.
If someone is not calm then someone is either quiet or not calm.
Someone is not quiet or happy.
Mary is both not humble and not kind.
Someone is both not brave and happy.
Someone is either not curious or quiet.
Mary is either calm or not strong.
Someone is not rich or humble.
Paul is either not funny or wise. | Fred is brave. | neutral | (![X]:((wise(X)&happy(X))=>(curious(X)|~brave(X))))&
(((generous(fred)&~patient(fred)))=>(?[X]:((humble(X)&generous(X)))))&
(![X]:((~generous(X)|~strong(X))<=>(wise(X)&~funny(X))))&
(![X]:((~curious(X)|~creative(X))<=>(rich(X)<~>curious(X))))&
(![X]:((~old(X)&~generous(X))<=>(generous(X)<~>~creative(X))))&
(((tall(paul)&quiet(paul)))=>(?[X]:((strong(X)&~curious(X)))))&
((?[X]:((humble(X)|~funny(X))))<=>(?[X]:(curious(X))))&
(![X]:(quiet(X)=>(kind(X)&tall(X))))&
(![X]:((~funny(X)<~>~humble(X))=>(~creative(X)&strong(X))))&
(![X]:((~happy(X)&calm(X))<=>(quiet(X)<~>~funny(X))))&
(![X]:(tall(X)<=>(humble(X)|strong(X))))&
((?[X]:(~generous(X)))<=>(funny(paul)))&
(![X]:((strong(X)<~>kind(X))=>(~calm(X)|~rich(X))))&
(((rich(mary)&patient(mary)))=>((creative(susan)|old(susan))))&
(![X]:((~brave(X)|~strong(X))=>(quiet(X)&tall(X))))&
((?[X]:(~calm(X)))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(?[X]:((~quiet(X)|happy(X))))&
((~humble(mary)&~kind(mary)))&
(?[X]:((~brave(X)&happy(X))))&
(?[X]:((~curious(X)<~>quiet(X))))&
((calm(mary)<~>~strong(mary)))&
(?[X]:((~rich(X)|humble(X))))&
((~funny(paul)<~>wise(paul))) | brave(fred) | [] | null | 0 |
Everyone who is either old or happy is either not kind or not calm and vice versa.
Everyone who is both not tall and curious is either not brave or old and vice versa.
If someone is not calm then someone is not tall or wise and vice versa.
If john is rich then john is either brave or not quiet.
Everyone who is either not kind or not wise is either wise or not quiet and vice versa.
Everyone who is both not patient and not wise is not funny or rich.
Everyone who is both not curious and not calm is not creative and vice versa.
Everyone who is either not calm or not happy is not patient.
If paul is not kind or curious then someone is brave or not kind and vice versa.
If alice is not tall then someone is brave.
Everyone who is rich or calm is both not funny and not tall.
Everyone who is not quiet is patient.
If susan is both not wise and brave then fred is strong or wise.
If susan is both not generous and quiet then someone is not funny.
Everyone who is both not happy and brave is curious and vice versa.
Fred is either not old or tall.
Someone is not quiet.
Someone is not generous.
Mary is patient.
Someone is both brave and kind.
Someone is both humble and not patient.
Someone is happy. | Alice is humble. | neutral | (![X]:((old(X)<~>happy(X))<=>(~kind(X)<~>~calm(X))))&
(![X]:((~tall(X)&curious(X))<=>(~brave(X)<~>old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)|wise(X)))))&
((rich(john))=>((brave(john)<~>~quiet(john))))&
(![X]:((~kind(X)<~>~wise(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~patient(X)&~wise(X))=>(~funny(X)|rich(X))))&
(![X]:((~curious(X)&~calm(X))<=>~creative(X)))&
(![X]:((~calm(X)<~>~happy(X))=>~patient(X)))&
(((~kind(paul)|curious(paul)))<=>(?[X]:((brave(X)|~kind(X)))))&
((~tall(alice))=>(?[X]:(brave(X))))&
(![X]:((rich(X)|calm(X))=>(~funny(X)&~tall(X))))&
(![X]:(~quiet(X)=>patient(X)))&
(((~wise(susan)&brave(susan)))=>((strong(fred)|wise(fred))))&
(((~generous(susan)&quiet(susan)))=>(?[X]:(~funny(X))))&
(![X]:((~happy(X)&brave(X))<=>curious(X)))&
((~old(fred)<~>tall(fred)))&
(?[X]:(~quiet(X)))&
(?[X]:(~generous(X)))&
(patient(mary))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:(happy(X))) | humble(alice) | [] | null | 0 |
Everyone who is strong or not curious is either happy or not curious and vice versa. If paul is not old or generous then someone is brave. Everyone who is either kind or not kind is both old and not wise. If someone is either quiet or not patient then someone is both generous and not brave and vice versa. If someone is calm or curious then paul is kind or rich. If someone is not quiet or wise then someone is both strong and brave. If mary is both happy and curious then susan is not curious. Everyone who is not patient or not old is either generous or rich and vice versa. If mary is either creative or humble then someone is patient or not funny. Everyone who is wise or not humble is either old or not brave and vice versa. Everyone who is old or not old is both not generous and not curious. Everyone who is humble or generous is either not generous or not strong. If someone is either not patient or rich then mary is both not quiet and not strong. Everyone who is both not curious and not old is not quiet and vice versa. Everyone who is old is kind. If mary is not patient or old then paul is not happy or strong. Someone is not strong or not tall. Mary is both rich and not humble. Fred is not strong or creative. Someone is either quiet or generous. Mary is not wise or calm. Someone is either humble or strong. Lucy is kind or not rich. | Paul is patient. | contradiction | (![X]:((strong(X)|~curious(X))<=>(happy(X)<~>~curious(X))))&
(((~old(paul)|generous(paul)))=>(?[X]:(brave(X))))&
(![X]:((kind(X)<~>~kind(X))=>(old(X)&~wise(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((calm(X)|curious(X))))=>((kind(paul)|rich(paul))))&
((?[X]:((~quiet(X)|wise(X))))=>(?[X]:((strong(X)&brave(X)))))&
(((happy(mary)&curious(mary)))=>(~curious(susan)))&
(![X]:((~patient(X)|~old(X))<=>(generous(X)<~>rich(X))))&
(((creative(mary)<~>humble(mary)))=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((wise(X)|~humble(X))<=>(old(X)<~>~brave(X))))&
(![X]:((old(X)|~old(X))=>(~generous(X)&~curious(X))))&
(![X]:((humble(X)|generous(X))=>(~generous(X)<~>~strong(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~quiet(mary)&~strong(mary))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
(![X]:(old(X)=>kind(X)))&
(((~patient(mary)|old(mary)))=>((~happy(paul)|strong(paul))))&
(?[X]:((~strong(X)|~tall(X))))&
((rich(mary)&~humble(mary)))&
((~strong(fred)|creative(fred)))&
(?[X]:((quiet(X)<~>generous(X))))&
((~wise(mary)|calm(mary)))&
(?[X]:((humble(X)<~>strong(X))))&
((kind(lucy)|~rich(lucy))) | patient(paul) | [
"p2",
"p3",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 366064522674878886793216
% SZS output start Proof for 366064522674878886793216
3. ! [X0] : ((kind(X0) <~> ~kind(X0)) => (~wise(X0) & old(X0))) [input p2]
4. ? [X0] : (quiet(X0) <~> ~patient(X0)) <=> ? [X0] : (~brave(X0) & generous(X0)) [input p3]
11. ! [X0] : ((~old(X0) | old(X0)) => (~curious(X0) & ~generous(X0))) [input p10]
14. ! [X0] : ((~old(X0) & ~curious(X0)) <=> ~quiet(X0)) [input p13]
24. patient(paul) [input hypothesis]
25. ? [X0] : (quiet(X0) <~> ~patient(X0)) <=> ? [X1] : (~brave(X1) & generous(X1)) [rectify 4]
31. ! [X0] : ((~wise(X0) & old(X0)) | (kind(X0) <=> ~kind(X0))) [ennf transformation 3]
37. ! [X0] : ((~curious(X0) & ~generous(X0)) | (old(X0) & ~old(X0))) [ennf transformation 11]
47. ! [X0] : ((~wise(X0) & old(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 31]
48. (? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | ! [X1] : (brave(X1) | ~generous(X1))) & (? [X1] : (~brave(X1) & generous(X1)) | ! [X0] : ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) [nnf transformation 25]
49. (? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | ! [X1] : (brave(X1) | ~generous(X1))) & (? [X2] : (~brave(X2) & generous(X2)) | ! [X3] : ((quiet(X3) | patient(X3)) & (~patient(X3) | ~quiet(X3)))) [rectify 48]
50. ? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) => ((patient(sK1) | ~quiet(sK1)) & (~patient(sK1) | quiet(sK1))) [choice axiom]
51. ? [X2] : (~brave(X2) & generous(X2)) => (~brave(sK2) & generous(sK2)) [choice axiom]
52. (((patient(sK1) | ~quiet(sK1)) & (~patient(sK1) | quiet(sK1))) | ! [X1] : (brave(X1) | ~generous(X1))) & ((~brave(sK2) & generous(sK2)) | ! [X3] : ((quiet(X3) | patient(X3)) & (~patient(X3) | ~quiet(X3)))) [skolemisation 49,51,50]
62. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | (old(X0) | curious(X0)))) [nnf transformation 14]
63. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | old(X0) | curious(X0))) [flattening 62]
78. old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 47]
79. old(X0) | kind(X0) | kind(X0) [cnf transformation 47]
82. generous(sK2) | ~patient(X3) | ~quiet(X3) [cnf transformation 52]
107. ~generous(X0) | ~old(X0) [cnf transformation 37]
121. ~old(X0) | quiet(X0) [cnf transformation 63]
133. patient(paul) [cnf transformation 24]
135. old(X0) | ~kind(X0) [duplicate literal removal 78]
136. old(X0) | kind(X0) [duplicate literal removal 79]
156. old(X0) [subsumption resolution 135,136]
179. 9 <=> ! [X3] : (~patient(X3) | ~quiet(X3)) [avatar definition]
180. ~patient(X3) | ~quiet(X3) <- (9) [avatar component clause 179]
183. 10 <=> generous(sK2) [avatar definition]
185. generous(sK2) <- (10) [avatar component clause 183]
187. 9 | 10 [avatar split clause 82,183,179]
205. 15 <=> ! [X1] : quiet(X1) [avatar definition]
206. quiet(X1) <- (15) [avatar component clause 205]
234. ~generous(X0) [subsumption resolution 107,156]
254. quiet(X0) [subsumption resolution 121,156]
255. 15 [avatar split clause 254,205]
275. ~patient(X3) <- (9, 15) [subsumption resolution 180,206]
281. $false <- (9, 15) [resolution 275,133]
282. ~9 | ~15 [avatar contradiction clause 281]
283. $false <- (10) [subsumption resolution 185,234]
284. ~10 [avatar contradiction clause 283]
285. $false [avatar sat refutation 187,255,282,284]
% SZS output end Proof for 366064522674878886793216
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or patient then fred is wise or not rich.
Everyone who is both tall and patient is both not generous and humble and vice versa.
Everyone who is tall is both not happy and creative and vice versa.
Everyone who is quiet is curious and vice versa.
Everyone who is both funny and quiet is either tall or patient and vice versa.
If someone is wise or not generous then someone is either happy or tall and vice versa.
Everyone who is brave is not calm.
If someone is either tall or not patient then paul is tall or curious and vice versa.
If lucy is not brave or not rich then alice is not strong or quiet.
If someone is creative then paul is happy or not brave.
Everyone who is either kind or not creative is patient or strong and vice versa.
Everyone who is both creative and not brave is both not patient and not wise and vice versa.
Everyone who is either tall or not creative is tall or creative and vice versa.
Everyone who is humble or funny is old.
If alice is not curious then someone is tall or wise.
Someone is not old or not humble.
Someone is not kind or funny.
Someone is funny.
Alice is creative.
Someone is both not funny and not curious.
Mary is tall or creative.
Lucy is not old or old. | Fred is not tall. | contradiction | ((?[X]:((~old(X)|patient(X))))=>((wise(fred)|~rich(fred))))&
(![X]:((tall(X)&patient(X))<=>(~generous(X)&humble(X))))&
(![X]:(tall(X)<=>(~happy(X)&creative(X))))&
(![X]:(quiet(X)<=>curious(X)))&
(![X]:((funny(X)&quiet(X))<=>(tall(X)<~>patient(X))))&
((?[X]:((wise(X)|~generous(X))))<=>(?[X]:((happy(X)<~>tall(X)))))&
(![X]:(brave(X)=>~calm(X)))&
((?[X]:((tall(X)<~>~patient(X))))<=>((tall(paul)|curious(paul))))&
(((~brave(lucy)|~rich(lucy)))=>((~strong(alice)|quiet(alice))))&
((?[X]:(creative(X)))=>((happy(paul)|~brave(paul))))&
(![X]:((kind(X)<~>~creative(X))<=>(patient(X)|strong(X))))&
(![X]:((creative(X)&~brave(X))<=>(~patient(X)&~wise(X))))&
(![X]:((tall(X)<~>~creative(X))<=>(tall(X)|creative(X))))&
(![X]:((humble(X)|funny(X))=>old(X)))&
((~curious(alice))=>(?[X]:((tall(X)|wise(X)))))&
(?[X]:((~old(X)|~humble(X))))&
(?[X]:((~kind(X)|funny(X))))&
(?[X]:(funny(X)))&
(creative(alice))&
(?[X]:((~funny(X)&~curious(X))))&
((tall(mary)|creative(mary)))&
((~old(lucy)|old(lucy))) | ~tall(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2579197911368185260623660
% SZS output start Proof for 2579197911368185260623660
13. ! [X0] : ((tall(X0) <~> ~creative(X0)) <=> (creative(X0) | tall(X0))) [input p12]
23. ~tall(fred) [input hypothesis]
55. ! [X0] : ((((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (~creative(X0) & ~tall(X0))) & ((creative(X0) | tall(X0)) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))))) [nnf transformation 13]
56. ! [X0] : ((((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (~creative(X0) & ~tall(X0))) & (creative(X0) | tall(X0) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))))) [flattening 55]
110. creative(X0) | tall(X0) | tall(X0) | creative(X0) [cnf transformation 56]
112. ~creative(X0) | tall(X0) | ~creative(X0) [cnf transformation 56]
126. ~tall(fred) [cnf transformation 23]
127. creative(X0) | tall(X0) [duplicate literal removal 110]
128. ~creative(X0) | tall(X0) [duplicate literal removal 112]
238. tall(X0) [subsumption resolution 127,128]
249. $false [subsumption resolution 126,238]
% SZS output end Proof for 2579197911368185260623660
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
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