premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either humble or quiet is not strong or not happy and vice versa.
Everyone who is not brave is both happy and generous and vice versa.
Everyone who is either not generous or not creative is both humble and tall.
Everyone who is either not funny or brave is curious or not curious and vice versa.
Everyone who is not strong or generous is not humble or not curious.
Everyone who is either not quiet or calm is both old and calm and vice versa.
If someone is either humble or brave then mary is humble or not kind.
Everyone who is both not rich and calm is strong or not rich and vice versa.
If mary is not patient or not kind then mary is not generous.
Everyone who is both not humble and not old is both not calm and brave.
Everyone who is tall is not brave or happy.
If mary is both curious and not quiet then lucy is not wise or not creative.
Everyone who is either rich or not creative is generous and vice versa.
If john is generous then someone is both not calm and patient and vice versa.
Everyone who is not funny or tall is not calm or rich and vice versa.
If paul is not rich then someone is both not kind and not generous and vice versa.
Someone is brave.
Alice is creative.
Someone is happy or not calm.
Someone is not curious or not patient.
Someone is either not creative or rich.
Mary is both patient and not humble.
Someone is not quiet or not wise.
Fred is strong or not funny. | Fred is not quiet. | contradiction | (![X]:((humble(X)<~>quiet(X))<=>(~strong(X)|~happy(X))))&
(![X]:(~brave(X)<=>(happy(X)&generous(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(humble(X)&tall(X))))&
(![X]:((~funny(X)<~>brave(X))<=>(curious(X)|~curious(X))))&
(![X]:((~strong(X)|generous(X))=>(~humble(X)|~curious(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(old(X)&calm(X))))&
((?[X]:((humble(X)<~>brave(X))))=>((humble(mary)|~kind(mary))))&
(![X]:((~rich(X)&calm(X))<=>(strong(X)|~rich(X))))&
(((~patient(mary)|~kind(mary)))=>(~generous(mary)))&
(![X]:((~humble(X)&~old(X))=>(~calm(X)&brave(X))))&
(![X]:(tall(X)=>(~brave(X)|happy(X))))&
(((curious(mary)&~quiet(mary)))=>((~wise(lucy)|~creative(lucy))))&
(![X]:((rich(X)<~>~creative(X))<=>generous(X)))&
((generous(john))<=>(?[X]:((~calm(X)&patient(X)))))&
(![X]:((~funny(X)|tall(X))<=>(~calm(X)|rich(X))))&
((~rich(paul))<=>(?[X]:((~kind(X)&~generous(X)))))&
(?[X]:(brave(X)))&
(creative(alice))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:((~creative(X)<~>rich(X))))&
((patient(mary)&~humble(mary)))&
(?[X]:((~quiet(X)|~wise(X))))&
((strong(fred)|~funny(fred))) | ~quiet(fred) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p7",
"p8",
"p9",
"p10",
"p12",
"p14",
"p15",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3439186213677713577554308
% SZS output start Proof for 3439186213677713577554308
2. ! [X0] : (~brave(X0) <=> (generous(X0) & happy(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => (tall(X0) & humble(X0))) [input p2]
4. ! [X0] : ((~funny(X0) <~> brave(X0)) <=> (~curious(X0) | curious(X0))) [input p3]
6. ! [X0] : ((~quiet(X0) <~> calm(X0)) <=> (calm(X0) & old(X0))) [input p5]
7. ? [X0] : (humble(X0) <~> brave(X0)) => (~kind(mary) | humble(mary)) [input p6]
8. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (~rich(X0) | strong(X0))) [input p7]
9. (~kind(mary) | ~patient(mary)) => ~generous(mary) [input p8]
10. ! [X0] : ((~old(X0) & ~humble(X0)) => (brave(X0) & ~calm(X0))) [input p9]
11. ! [X0] : (tall(X0) => (happy(X0) | ~brave(X0))) [input p10]
13. ! [X0] : ((rich(X0) <~> ~creative(X0)) <=> generous(X0)) [input p12]
15. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (rich(X0) | ~calm(X0))) [input p14]
16. ~rich(paul) <=> ? [X0] : (~generous(X0) & ~kind(X0)) [input p15]
22. ~humble(mary) & patient(mary) [input p21]
24. ~funny(fred) | strong(fred) [input p23]
25. ~quiet(fred) [input hypothesis]
28. ! [X0] : ((tall(X0) & humble(X0)) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 3]
31. (~kind(mary) | humble(mary)) | ! [X0] : (humble(X0) <=> brave(X0)) [ennf transformation 7]
32. ~kind(mary) | humble(mary) | ! [X0] : (humble(X0) <=> brave(X0)) [flattening 31]
33. ~generous(mary) | (kind(mary) & patient(mary)) [ennf transformation 9]
34. ! [X0] : ((brave(X0) & ~calm(X0)) | (old(X0) | humble(X0))) [ennf transformation 10]
35. ! [X0] : ((brave(X0) & ~calm(X0)) | old(X0) | humble(X0)) [flattening 34]
36. ! [X0] : ((happy(X0) | ~brave(X0)) | ~tall(X0)) [ennf transformation 11]
37. ! [X0] : (happy(X0) | ~brave(X0) | ~tall(X0)) [flattening 36]
40. ! [X0] : ((~brave(X0) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | brave(X0))) [nnf transformation 2]
41. ! [X0] : ((~brave(X0) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | brave(X0))) [flattening 40]
42. ! [X0] : ((tall(X0) & humble(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 28]
43. ! [X0] : ((((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))))) [flattening 43]
45. ! [X0] : ((((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | (~calm(X0) | ~old(X0))) & ((calm(X0) & old(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))))) [nnf transformation 6]
46. ! [X0] : ((((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | ~calm(X0) | ~old(X0)) & ((calm(X0) & old(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))))) [flattening 45]
47. ~kind(mary) | humble(mary) | ! [X0] : ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0))) [nnf transformation 32]
48. ! [X0] : (((calm(X0) & ~rich(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 8]
49. ! [X0] : (((calm(X0) & ~rich(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | ~calm(X0) | rich(X0))) [flattening 48]
50. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | ~generous(X0)) & (generous(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [nnf transformation 13]
55. ! [X0] : (((tall(X0) | ~funny(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 15]
56. ! [X0] : ((tall(X0) | ~funny(X0) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | (~tall(X0) & funny(X0)))) [flattening 55]
57. (~rich(paul) | ! [X0] : (generous(X0) | kind(X0))) & (? [X0] : (~generous(X0) & ~kind(X0)) | rich(paul)) [nnf transformation 16]
58. (~rich(paul) | ! [X0] : (generous(X0) | kind(X0))) & (? [X1] : (~generous(X1) & ~kind(X1)) | rich(paul)) [rectify 57]
59. ? [X1] : (~generous(X1) & ~kind(X1)) => (~generous(sK1) & ~kind(sK1)) [choice axiom]
60. (~rich(paul) | ! [X0] : (generous(X0) | kind(X0))) & ((~generous(sK1) & ~kind(sK1)) | rich(paul)) [skolemisation 58,59]
76. brave(X0) | happy(X0) [cnf transformation 41]
77. generous(X0) | brave(X0) [cnf transformation 41]
78. ~generous(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 41]
81. ~creative(X0) | tall(X0) | generous(X0) [cnf transformation 42]
82. ~generous(X0) | tall(X0) | creative(X0) [cnf transformation 42]
87. ~brave(X0) | funny(X0) | ~curious(X0) [cnf transformation 44]
88. ~brave(X0) | funny(X0) | curious(X0) [cnf transformation 44]
93. calm(X0) | calm(X0) | quiet(X0) [cnf transformation 46]
96. ~calm(X0) | quiet(X0) | ~calm(X0) | ~old(X0) [cnf transformation 46]
97. ~kind(mary) | humble(mary) | brave(X0) | ~humble(X0) [cnf transformation 47]
98. ~kind(mary) | humble(mary) | humble(X0) | ~brave(X0) [cnf transformation 47]
100. ~rich(X0) | ~strong(X0) [cnf transformation 49]
103. rich(X0) | calm(X0) [cnf transformation 49]
105. ~generous(mary) | kind(mary) [cnf transformation 33]
107. old(X0) | brave(X0) | humble(X0) [cnf transformation 35]
108. happy(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 37]
109. ~rich(X0) | ~creative(X0) | generous(X0) [cnf transformation 50]
110. rich(X0) | generous(X0) | creative(X0) [cnf transformation 50]
111. ~creative(X0) | rich(X0) | ~generous(X0) [cnf transformation 50]
112. ~rich(X0) | creative(X0) | ~generous(X0) [cnf transformation 50]
116. rich(X0) | ~calm(X0) | funny(X0) [cnf transformation 56]
117. rich(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 56]
119. ~rich(X0) | ~funny(X0) | tall(X0) [cnf transformation 56]
122. ~rich(paul) | generous(X0) | kind(X0) [cnf transformation 60]
130. ~humble(mary) [cnf transformation 22]
131. ~funny(fred) | strong(fred) [cnf transformation 24]
132. ~quiet(fred) [cnf transformation 25]
133. calm(X0) | quiet(X0) [duplicate literal removal 93]
134. ~old(X0) | quiet(X0) | ~calm(X0) [duplicate literal removal 96]
135. ~brave(X0) | funny(X0) [subsumption resolution 87,88]
138. 1 <=> ! [X0] : (humble(X0) | ~brave(X0)) [avatar definition]
139. ~brave(X0) | humble(X0) <- (1) [avatar component clause 138]
141. 2 <=> humble(mary) [avatar definition]
145. 3 <=> kind(mary) [avatar definition]
147. ~kind(mary) <- (~3) [avatar component clause 145]
148. 1 | 2 | ~3 [avatar split clause 98,145,141,138]
150. 4 <=> ! [X0] : (brave(X0) | ~humble(X0)) [avatar definition]
151. ~humble(X0) | brave(X0) <- (4) [avatar component clause 150]
152. 4 | 2 | ~3 [avatar split clause 97,145,141,150]
154. 5 <=> generous(mary) [avatar definition]
156. ~generous(mary) <- (~5) [avatar component clause 154]
157. 3 | ~5 [avatar split clause 105,154,145]
163. ~tall(X0) | happy(X0) [subsumption resolution 108,76]
182. ~tall(X0) | rich(X0) [subsumption resolution 117,103]
183. rich(X0) | funny(X0) [subsumption resolution 116,103]
185. 11 <=> ! [X0] : (generous(X0) | kind(X0)) [avatar definition]
186. kind(X0) | generous(X0) <- (11) [avatar component clause 185]
188. 12 <=> rich(paul) [avatar definition]
190. ~rich(paul) <- (~12) [avatar component clause 188]
191. 11 | ~12 [avatar split clause 122,188,185]
230. ~2 [avatar split clause 130,141]
233. 21 <=> strong(fred) [avatar definition]
235. strong(fred) <- (21) [avatar component clause 233]
237. 22 <=> funny(fred) [avatar definition]
239. ~funny(fred) <- (~22) [avatar component clause 237]
240. 21 | ~22 [avatar split clause 131,237,233]
248. funny(X0) | happy(X0) [resolution 135,76]
427. ~creative(X0) | generous(X0) | funny(X0) [resolution 109,183]
447. ~strong(X1) | creative(X1) | generous(X1) [resolution 110,100]
451. 48 <=> creative(paul) [avatar definition]
453. creative(paul) <- (48) [avatar component clause 451]
455. 49 <=> generous(paul) [avatar definition]
464. generous(mary) <- (~3, 11) [resolution 186,147]
466. $false <- (~3, ~5, 11) [subsumption resolution 464,156]
467. 3 | 5 | ~11 [avatar contradiction clause 466]
533. ~generous(X1) | creative(X1) | funny(X1) [resolution 112,183]
563. ~funny(X0) | tall(X0) | generous(X0) | creative(X0) [resolution 119,110]
568. ~funny(X0) | tall(X0) | creative(X0) [subsumption resolution 563,82]
570. 60 <=> tall(paul) [avatar definition]
571. ~tall(paul) <- (~60) [avatar component clause 570]
572. tall(paul) <- (60) [avatar component clause 570]
603. quiet(X0) | ~calm(X0) | brave(X0) | humble(X0) [resolution 134,107]
604. quiet(X0) | brave(X0) | humble(X0) [subsumption resolution 603,133]
605. quiet(X0) | humble(X0) <- (1) [subsumption resolution 604,139]
616. 66 <=> humble(fred) [avatar definition]
617. humble(fred) <- (66) [avatar component clause 616]
688. humble(fred) <- (1) [resolution 605,132]
692. 66 | ~1 [avatar split clause 688,138,616]
731. creative(X0) | funny(X0) | brave(X0) [resolution 533,77]
737. funny(X0) | creative(X0) [subsumption resolution 731,135]
752. tall(X0) | creative(X0) | happy(X0) [resolution 568,248]
754. creative(X0) | happy(X0) [subsumption resolution 752,163]
795. rich(paul) <- (60) [resolution 572,182]
906. brave(fred) <- (4, 66) [resolution 617,151]
932. creative(X0) | tall(X0) | creative(X0) [resolution 737,568]
937. creative(fred) <- (~22) [resolution 737,239]
939. tall(X0) | creative(X0) [duplicate literal removal 932]
943. ~generous(X2) | rich(X2) | happy(X2) [resolution 754,111]
944. happy(X3) | tall(X3) | generous(X3) [resolution 754,81]
948. generous(X3) | happy(X3) [subsumption resolution 944,163]
991. generous(fred) | funny(fred) <- (~22) [resolution 937,427]
1000. 85 <=> generous(fred) [avatar definition]
1002. generous(fred) <- (85) [avatar component clause 1000]
1004. generous(fred) <- (~22) [subsumption resolution 991,239]
1005. 85 | 22 [avatar split clause 1004,237,1000]
1007. 86 <=> rich(fred) [avatar definition]
1009. rich(fred) <- (86) [avatar component clause 1007]
1012. 87 <=> tall(fred) [avatar definition]
1014. tall(fred) <- (87) [avatar component clause 1012]
1017. creative(fred) | generous(fred) <- (21) [resolution 235,447]
1021. 88 <=> creative(fred) [avatar definition]
1023. creative(fred) <- (88) [avatar component clause 1021]
1024. 85 | 88 | ~21 [avatar split clause 1017,233,1021,1000]
1046. rich(X0) | creative(X0) [resolution 939,182]
1062. ~brave(fred) | ~happy(fred) <- (85) [resolution 1002,78]
1063. ~happy(fred) <- (4, 66, 85) [subsumption resolution 1062,906]
1072. rich(X0) | happy(X0) | happy(X0) [resolution 943,948]
1079. rich(X0) | happy(X0) [duplicate literal removal 1072]
1085. happy(X0) | ~funny(X0) | tall(X0) [resolution 1079,119]
1089. happy(X0) | tall(X0) [subsumption resolution 1085,248]
1090. happy(X0) [subsumption resolution 1089,163]
1093. $false <- (4, 66, 85) [resolution 1090,1063]
1094. ~4 | ~66 | ~85 [avatar contradiction clause 1093]
1099. tall(fred) | generous(fred) <- (88) [resolution 1023,81]
1105. rich(fred) <- (87) [resolution 1014,182]
1107. 86 | ~87 [avatar split clause 1105,1012,1007]
1111. ~strong(fred) <- (86) [resolution 1009,100]
1115. $false <- (21, 86) [subsumption resolution 1111,235]
1116. ~21 | ~86 [avatar contradiction clause 1115]
1132. 12 | ~60 [avatar split clause 795,570,188]
1144. 85 | 87 | ~88 [avatar split clause 1099,1021,1012,1000]
1159. creative(paul) <- (~12) [resolution 190,1046]
1168. rich(paul) | ~generous(paul) <- (48) [resolution 453,111]
1169. tall(paul) | generous(paul) <- (48) [resolution 453,81]
1171. generous(paul) <- (48, ~60) [subsumption resolution 1169,571]
1174. 49 | ~48 | 60 [avatar split clause 1171,570,451,455]
1175. ~generous(paul) <- (~12, 48) [subsumption resolution 1168,190]
1176. ~49 | 12 | ~48 [avatar split clause 1175,451,188,455]
1177. 48 | 12 [avatar split clause 1159,188,451]
1178. $false [avatar sat refutation 148,152,157,191,230,240,467,692,1005,1024,1094,1107,1116,1132,1144,1174,1176,1177]
% SZS output end Proof for 3439186213677713577554308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is either not old or rich and vice versa. Everyone who is either patient or not old is not curious or old and vice versa. If someone is not strong then john is not rich and vice versa. Everyone who is not kind is either not quiet or not kind and vice versa. Everyone who is either generous or funny is both not brave and not rich. If alice is not rich then someone is either not tall or not humble. Everyone who is either funny or not curious is both happy and funny. If lucy is both strong and happy then lucy is not rich or not creative and vice versa. If someone is either curious or kind then someone is either not kind or happy and vice versa. Everyone who is either curious or calm is both not old and kind. If alice is either not humble or not strong then someone is patient. Everyone who is both not rich and not curious is not wise and vice versa. If someone is either creative or not patient then someone is not rich or not wise. If john is brave or not humble then mary is either not curious or not creative. If someone is both not curious and creative then someone is creative or not curious. Everyone who is both happy and not wise is quiet or not old and vice versa. Someone is either not tall or old. Mary is not old. Paul is not strong or not creative. John is not humble or generous. Alice is not funny or not tall. | Alice is not patient. | entailment | (![X]:(~rich(X)<=>(~old(X)<~>rich(X))))&
(![X]:((patient(X)<~>~old(X))<=>(~curious(X)|old(X))))&
((?[X]:(~strong(X)))<=>(~rich(john)))&
(![X]:(~kind(X)<=>(~quiet(X)<~>~kind(X))))&
(![X]:((generous(X)<~>funny(X))=>(~brave(X)&~rich(X))))&
((~rich(alice))=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((funny(X)<~>~curious(X))=>(happy(X)&funny(X))))&
(((strong(lucy)&happy(lucy)))<=>((~rich(lucy)|~creative(lucy))))&
((?[X]:((curious(X)<~>kind(X))))<=>(?[X]:((~kind(X)<~>happy(X)))))&
(![X]:((curious(X)<~>calm(X))=>(~old(X)&kind(X))))&
(((~humble(alice)<~>~strong(alice)))=>(?[X]:(patient(X))))&
(![X]:((~rich(X)&~curious(X))<=>~wise(X)))&
((?[X]:((creative(X)<~>~patient(X))))=>(?[X]:((~rich(X)|~wise(X)))))&
(((brave(john)|~humble(john)))=>((~curious(mary)<~>~creative(mary))))&
((?[X]:((~curious(X)&creative(X))))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((happy(X)&~wise(X))<=>(quiet(X)|~old(X))))&
(?[X]:((~tall(X)<~>old(X))))&
(~old(mary))&
((~strong(paul)|~creative(paul)))&
((~humble(john)|generous(john)))&
((~funny(alice)|~tall(alice))) | ~patient(alice) | [
"p0",
"p1",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6392673912941190276449738
% SZS output start Proof for 6392673912941190276449738
1. ! [X0] : (~rich(X0) <=> (~old(X0) <~> rich(X0))) [input p0]
2. ! [X0] : ((patient(X0) <~> ~old(X0)) <=> (old(X0) | ~curious(X0))) [input p1]
12. ! [X0] : ((~curious(X0) & ~rich(X0)) <=> ~wise(X0)) [input p11]
16. ! [X0] : ((~wise(X0) & happy(X0)) <=> (~old(X0) | quiet(X0))) [input p15]
22. patient(alice) [input hypothesis]
36. ! [X0] : ((~rich(X0) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0)))) & (((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | rich(X0))) [nnf transformation 1]
37. ! [X0] : ((((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (~old(X0) & curious(X0))) & ((old(X0) | ~curious(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))))) [nnf transformation 2]
38. ! [X0] : ((((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (~old(X0) & curious(X0))) & (old(X0) | ~curious(X0) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))))) [flattening 37]
60. ! [X0] : (((~curious(X0) & ~rich(X0)) | wise(X0)) & (~wise(X0) | (curious(X0) | rich(X0)))) [nnf transformation 12]
61. ! [X0] : (((~curious(X0) & ~rich(X0)) | wise(X0)) & (~wise(X0) | curious(X0) | rich(X0))) [flattening 60]
70. ! [X0] : (((~wise(X0) & happy(X0)) | (old(X0) & ~quiet(X0))) & ((~old(X0) | quiet(X0)) | (wise(X0) | ~happy(X0)))) [nnf transformation 16]
71. ! [X0] : (((~wise(X0) & happy(X0)) | (old(X0) & ~quiet(X0))) & (~old(X0) | quiet(X0) | wise(X0) | ~happy(X0))) [flattening 70]
75. rich(X0) | ~old(X0) | rich(X0) [cnf transformation 36]
78. ~rich(X0) | ~old(X0) | ~rich(X0) [cnf transformation 36]
83. old(X0) | ~patient(X0) | curious(X0) [cnf transformation 38]
120. ~curious(X0) | wise(X0) [cnf transformation 61]
130. ~wise(X0) | old(X0) [cnf transformation 71]
137. patient(alice) [cnf transformation 22]
143. rich(X0) | ~old(X0) [duplicate literal removal 75]
144. ~old(X0) | ~rich(X0) [duplicate literal removal 78]
145. ~old(X0) [subsumption resolution 143,144]
146. ~patient(X0) | curious(X0) [subsumption resolution 83,145]
287. ~wise(X0) [subsumption resolution 130,145]
329. curious(alice) [resolution 146,137]
331. wise(alice) [resolution 329,120]
332. $false [subsumption resolution 331,287]
% SZS output end Proof for 6392673912941190276449738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not creative is either rich or not strong. Everyone who is both not kind and patient is either not creative or creative and vice versa. Everyone who is not quiet is both not calm and old. Everyone who is brave is either not strong or not old. Everyone who is both calm and quiet is not brave. If susan is funny or wise then someone is not curious and vice versa. If someone is strong then alice is not kind or not brave and vice versa. If someone is not old or tall then susan is creative. Everyone who is quiet is either patient or not old and vice versa. If fred is either not curious or not calm then susan is either quiet or not curious. Everyone who is not quiet or not creative is curious and vice versa. Everyone who is both strong and not rich is curious. If fred is either wise or brave then someone is both not tall and not curious. If lucy is both curious and kind then lucy is either not wise or not creative. If someone is either not strong or not calm then mary is either humble or wise. Everyone who is both not calm and patient is both not funny and not generous and vice versa. Lucy is tall. Someone is not happy. Susan is not patient or happy. John is not tall. Someone is not strong. Someone is not calm or not old. | Fred is quiet. | entailment | (![X]:((tall(X)<~>~creative(X))=>(rich(X)<~>~strong(X))))&
(![X]:((~kind(X)&patient(X))<=>(~creative(X)<~>creative(X))))&
(![X]:(~quiet(X)=>(~calm(X)&old(X))))&
(![X]:(brave(X)=>(~strong(X)<~>~old(X))))&
(![X]:((calm(X)&quiet(X))=>~brave(X)))&
(((funny(susan)|wise(susan)))<=>(?[X]:(~curious(X))))&
((?[X]:(strong(X)))<=>((~kind(alice)|~brave(alice))))&
((?[X]:((~old(X)|tall(X))))=>(creative(susan)))&
(![X]:(quiet(X)<=>(patient(X)<~>~old(X))))&
(((~curious(fred)<~>~calm(fred)))=>((quiet(susan)<~>~curious(susan))))&
(![X]:((~quiet(X)|~creative(X))<=>curious(X)))&
(![X]:((strong(X)&~rich(X))=>curious(X)))&
(((wise(fred)<~>brave(fred)))=>(?[X]:((~tall(X)&~curious(X)))))&
(((curious(lucy)&kind(lucy)))=>((~wise(lucy)<~>~creative(lucy))))&
((?[X]:((~strong(X)<~>~calm(X))))=>((humble(mary)<~>wise(mary))))&
(![X]:((~calm(X)&patient(X))<=>(~funny(X)&~generous(X))))&
(tall(lucy))&
(?[X]:(~happy(X)))&
((~patient(susan)|happy(susan)))&
(~tall(john))&
(?[X]:(~strong(X)))&
(?[X]:((~calm(X)|~old(X)))) | quiet(fred) | [
"p1",
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5531330265213255736775035
% SZS output start Proof for 5531330265213255736775035
2. ! [X0] : ((patient(X0) & ~kind(X0)) <=> (~creative(X0) <~> creative(X0))) [input p1]
3. ! [X0] : (~quiet(X0) => (old(X0) & ~calm(X0))) [input p2]
9. ! [X0] : (quiet(X0) <=> (patient(X0) <~> ~old(X0))) [input p8]
23. ~quiet(fred) [input hypothesis]
25. ! [X0] : ((old(X0) & ~calm(X0)) | quiet(X0)) [ennf transformation 3]
38. ! [X0] : (((patient(X0) & ~kind(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~patient(X0) | kind(X0)))) [nnf transformation 2]
39. ! [X0] : (((patient(X0) & ~kind(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ~patient(X0) | kind(X0))) [flattening 38]
51. ! [X0] : ((quiet(X0) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | ~quiet(X0))) [nnf transformation 9]
76. patient(X0) | creative(X0) | creative(X0) [cnf transformation 39]
77. patient(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 39]
79. old(X0) | quiet(X0) [cnf transformation 25]
93. quiet(X0) | ~old(X0) | ~patient(X0) [cnf transformation 51]
123. ~quiet(fred) [cnf transformation 23]
126. patient(X0) | creative(X0) [duplicate literal removal 76]
127. patient(X0) | ~creative(X0) [duplicate literal removal 77]
128. patient(X0) [subsumption resolution 126,127]
172. quiet(X0) | ~old(X0) [subsumption resolution 93,128]
173. quiet(X0) [subsumption resolution 172,79]
244. $false [subsumption resolution 123,173]
% SZS output end Proof for 5531330265213255736775035
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and not kind then mary is rich or calm.
If someone is not creative or patient then susan is either not calm or not curious.
If someone is both rich and not happy then paul is not generous.
If someone is both not old and not rich then someone is curious or funny.
Everyone who is either creative or not generous is both happy and not rich and vice versa.
Everyone who is kind or not calm is both generous and kind.
If someone is either calm or not humble then mary is either not tall or funny and vice versa.
Everyone who is not calm is either not generous or rich and vice versa.
Everyone who is both brave and creative is both creative and old and vice versa.
If paul is calm then someone is curious or tall and vice versa.
Everyone who is both not patient and brave is either generous or not happy.
Everyone who is not rich or patient is creative or humble and vice versa.
If someone is humble or not funny then mary is not happy or not generous.
Everyone who is either not generous or not patient is wise.
If someone is either not brave or generous then someone is both not wise and generous.
If someone is old then someone is either not happy or not funny and vice versa.
Fred is either not calm or creative.
Someone is either creative or brave.
Alice is strong or not brave.
Someone is either not funny or not quiet.
Alice is tall or not generous.
Fred is either not rich or not generous.
Someone is either tall or not quiet.
Alice is both not humble and not wise. | Alice is patient. | entailment | ((?[X]:((~humble(X)&~kind(X))))=>((rich(mary)|calm(mary))))&
((?[X]:((~creative(X)|patient(X))))=>((~calm(susan)<~>~curious(susan))))&
((?[X]:((rich(X)&~happy(X))))=>(~generous(paul)))&
((?[X]:((~old(X)&~rich(X))))=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((creative(X)<~>~generous(X))<=>(happy(X)&~rich(X))))&
(![X]:((kind(X)|~calm(X))=>(generous(X)&kind(X))))&
((?[X]:((calm(X)<~>~humble(X))))<=>((~tall(mary)<~>funny(mary))))&
(![X]:(~calm(X)<=>(~generous(X)<~>rich(X))))&
(![X]:((brave(X)&creative(X))<=>(creative(X)&old(X))))&
((calm(paul))<=>(?[X]:((curious(X)|tall(X)))))&
(![X]:((~patient(X)&brave(X))=>(generous(X)<~>~happy(X))))&
(![X]:((~rich(X)|patient(X))<=>(creative(X)|humble(X))))&
((?[X]:((humble(X)|~funny(X))))=>((~happy(mary)|~generous(mary))))&
(![X]:((~generous(X)<~>~patient(X))=>wise(X)))&
((?[X]:((~brave(X)<~>generous(X))))=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:(old(X)))<=>(?[X]:((~happy(X)<~>~funny(X)))))&
((~calm(fred)<~>creative(fred)))&
(?[X]:((creative(X)<~>brave(X))))&
((strong(alice)|~brave(alice)))&
(?[X]:((~funny(X)<~>~quiet(X))))&
((tall(alice)|~generous(alice)))&
((~rich(fred)<~>~generous(fred)))&
(?[X]:((tall(X)<~>~quiet(X))))&
((~humble(alice)&~wise(alice))) | patient(alice) | [
"p4",
"p5",
"p7",
"p11",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8152618629270313423672694
% SZS output start Proof for 8152618629270313423672694
5. ! [X0] : ((creative(X0) <~> ~generous(X0)) <=> (~rich(X0) & happy(X0))) [input p4]
6. ! [X0] : ((~calm(X0) | kind(X0)) => (kind(X0) & generous(X0))) [input p5]
8. ! [X0] : (~calm(X0) <=> (~generous(X0) <~> rich(X0))) [input p7]
12. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (humble(X0) | creative(X0))) [input p11]
14. ! [X0] : ((~generous(X0) <~> ~patient(X0)) => wise(X0)) [input p13]
24. ~wise(alice) & ~humble(alice) [input p23]
25. ~patient(alice) [input hypothesis]
35. ! [X0] : ((kind(X0) & generous(X0)) | (calm(X0) & ~kind(X0))) [ennf transformation 6]
40. ! [X0] : (wise(X0) | (~generous(X0) <=> ~patient(X0))) [ennf transformation 14]
46. ! [X0] : ((((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | (rich(X0) | ~happy(X0))) & ((~rich(X0) & happy(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0))))) [nnf transformation 5]
47. ! [X0] : ((((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | rich(X0) | ~happy(X0)) & ((~rich(X0) & happy(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0))))) [flattening 46]
52. ! [X0] : ((~calm(X0) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | calm(X0))) [nnf transformation 8]
60. ! [X0] : (((patient(X0) | ~rich(X0)) | (~humble(X0) & ~creative(X0))) & ((humble(X0) | creative(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 12]
61. ! [X0] : ((patient(X0) | ~rich(X0) | (~humble(X0) & ~creative(X0))) & (humble(X0) | creative(X0) | (~patient(X0) & rich(X0)))) [flattening 60]
62. ! [X0] : (wise(X0) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) [nnf transformation 40]
93. ~rich(X0) | creative(X0) | generous(X0) [cnf transformation 47]
97. generous(X0) | calm(X0) [cnf transformation 35]
110. ~calm(X0) | rich(X0) | generous(X0) [cnf transformation 52]
123. ~creative(X0) | ~rich(X0) | patient(X0) [cnf transformation 61]
128. ~generous(X0) | wise(X0) | patient(X0) [cnf transformation 62]
149. ~wise(alice) [cnf transformation 24]
150. ~patient(alice) [cnf transformation 25]
231. generous(X0) | rich(X0) [subsumption resolution 110,97]
348. 45 <=> generous(alice) [avatar definition]
349. generous(alice) <- (45) [avatar component clause 348]
350. ~generous(alice) <- (~45) [avatar component clause 348]
422. 53 <=> creative(alice) [avatar definition]
423. ~creative(alice) <- (~53) [avatar component clause 422]
424. creative(alice) <- (53) [avatar component clause 422]
474. 56 <=> rich(alice) [avatar definition]
475. rich(alice) <- (56) [avatar component clause 474]
476. ~rich(alice) <- (~56) [avatar component clause 474]
528. rich(alice) <- (~45) [resolution 350,231]
530. $false <- (~45, ~56) [subsumption resolution 528,476]
531. 45 | 56 [avatar contradiction clause 530]
550. ~rich(alice) | patient(alice) <- (53) [resolution 424,123]
557. wise(alice) | patient(alice) <- (45) [resolution 128,349]
577. patient(alice) <- (45) [subsumption resolution 557,149]
578. $false <- (45) [subsumption resolution 577,150]
579. ~45 [avatar contradiction clause 578]
590. ~rich(alice) <- (53) [subsumption resolution 550,150]
591. ~56 | ~53 [avatar split clause 590,422,474]
669. creative(alice) | generous(alice) <- (56) [resolution 475,93]
671. generous(alice) <- (~53, 56) [subsumption resolution 669,423]
672. $false <- (~45, ~53, 56) [subsumption resolution 671,350]
673. 45 | 53 | ~56 [avatar contradiction clause 672]
674. $false [avatar sat refutation 531,579,591,673]
% SZS output end Proof for 8152618629270313423672694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not creative is tall and vice versa.
Everyone who is either rich or not humble is old.
If someone is not kind then someone is both not kind and happy and vice versa.
Everyone who is funny or not happy is either kind or patient.
Everyone who is not brave is patient and vice versa.
Everyone who is either not generous or creative is not strong and vice versa.
If alice is not brave then someone is either calm or not patient.
Everyone who is not creative or rich is not humble or quiet.
Everyone who is funny is either creative or patient and vice versa.
Everyone who is both not curious and not happy is not calm.
Everyone who is not generous or funny is not wise or not humble and vice versa.
Everyone who is either strong or not funny is both calm and not generous.
Everyone who is either not tall or not wise is either humble or not patient and vice versa.
Everyone who is not kind or happy is generous or not kind.
Everyone who is either not calm or not old is both not old and not tall and vice versa.
Everyone who is both not calm and not old is wise or brave and vice versa.
Someone is not generous or patient.
Mary is not quiet or strong.
Someone is not funny or generous.
Someone is either not old or not generous.
Alice is not brave or not wise.
Susan is not old.
Someone is tall or not calm.
John is either tall or calm. | Mary is not humble. | entailment | (![X]:((brave(X)<~>~creative(X))<=>tall(X)))&
(![X]:((rich(X)<~>~humble(X))=>old(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((funny(X)|~happy(X))=>(kind(X)<~>patient(X))))&
(![X]:(~brave(X)<=>patient(X)))&
(![X]:((~generous(X)<~>creative(X))<=>~strong(X)))&
((~brave(alice))=>(?[X]:((calm(X)<~>~patient(X)))))&
(![X]:((~creative(X)|rich(X))=>(~humble(X)|quiet(X))))&
(![X]:(funny(X)<=>(creative(X)<~>patient(X))))&
(![X]:((~curious(X)&~happy(X))=>~calm(X)))&
(![X]:((~generous(X)|funny(X))<=>(~wise(X)|~humble(X))))&
(![X]:((strong(X)<~>~funny(X))=>(calm(X)&~generous(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(humble(X)<~>~patient(X))))&
(![X]:((~kind(X)|happy(X))=>(generous(X)|~kind(X))))&
(![X]:((~calm(X)<~>~old(X))<=>(~old(X)&~tall(X))))&
(![X]:((~calm(X)&~old(X))<=>(wise(X)|brave(X))))&
(?[X]:((~generous(X)|patient(X))))&
((~quiet(mary)|strong(mary)))&
(?[X]:((~funny(X)|generous(X))))&
(?[X]:((~old(X)<~>~generous(X))))&
((~brave(alice)|~wise(alice)))&
(~old(susan))&
(?[X]:((tall(X)|~calm(X))))&
((tall(john)<~>calm(john))) | ~humble(mary) | [
"p0",
"p4",
"p5",
"p7",
"p8",
"p10",
"p11",
"p12",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 173005431842342818668114
% SZS output start Proof for 173005431842342818668114
1. ! [X0] : ((brave(X0) <~> ~creative(X0)) <=> tall(X0)) [input p0]
5. ! [X0] : (~brave(X0) <=> patient(X0)) [input p4]
6. ! [X0] : ((~generous(X0) <~> creative(X0)) <=> ~strong(X0)) [input p5]
8. ! [X0] : ((rich(X0) | ~creative(X0)) => (quiet(X0) | ~humble(X0))) [input p7]
9. ! [X0] : (funny(X0) <=> (creative(X0) <~> patient(X0))) [input p8]
11. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (~humble(X0) | ~wise(X0))) [input p10]
12. ! [X0] : ((strong(X0) <~> ~funny(X0)) => (~generous(X0) & calm(X0))) [input p11]
13. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (humble(X0) <~> ~patient(X0))) [input p12]
15. ! [X0] : ((~calm(X0) <~> ~old(X0)) <=> (~tall(X0) & ~old(X0))) [input p14]
16. ! [X0] : ((~old(X0) & ~calm(X0)) <=> (brave(X0) | wise(X0))) [input p15]
18. strong(mary) | ~quiet(mary) [input p17]
25. humble(mary) [input hypothesis]
31. ! [X0] : ((quiet(X0) | ~humble(X0)) | (~rich(X0) & creative(X0))) [ennf transformation 8]
32. ! [X0] : (quiet(X0) | ~humble(X0) | (~rich(X0) & creative(X0))) [flattening 31]
33. ! [X0] : ((~generous(X0) & calm(X0)) | (strong(X0) <=> ~funny(X0))) [ennf transformation 12]
36. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | ~tall(X0)) & (tall(X0) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [nnf transformation 1]
44. ! [X0] : ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))) [nnf transformation 5]
45. ! [X0] : ((((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | strong(X0)) & (~strong(X0) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0))))) [nnf transformation 6]
49. ! [X0] : ((funny(X0) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | ~funny(X0))) [nnf transformation 9]
50. ! [X0] : (((funny(X0) | ~generous(X0)) | (humble(X0) & wise(X0))) & ((~humble(X0) | ~wise(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 11]
51. ! [X0] : ((funny(X0) | ~generous(X0) | (humble(X0) & wise(X0))) & (~humble(X0) | ~wise(X0) | (~funny(X0) & generous(X0)))) [flattening 50]
52. ! [X0] : ((~generous(X0) & calm(X0)) | ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) [nnf transformation 33]
53. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 13]
54. ! [X0] : ((((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | (tall(X0) | old(X0))) & ((~tall(X0) & ~old(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))))) [nnf transformation 15]
55. ! [X0] : ((((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | tall(X0) | old(X0)) & ((~tall(X0) & ~old(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))))) [flattening 54]
56. ! [X0] : (((~old(X0) & ~calm(X0)) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | (old(X0) | calm(X0)))) [nnf transformation 16]
57. ! [X0] : (((~old(X0) & ~calm(X0)) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | old(X0) | calm(X0))) [flattening 56]
70. ~tall(X0) | brave(X0) | ~creative(X0) [cnf transformation 36]
71. ~tall(X0) | ~brave(X0) | creative(X0) [cnf transformation 36]
81. patient(X0) | brave(X0) [cnf transformation 44]
82. ~patient(X0) | ~brave(X0) [cnf transformation 44]
83. ~strong(X0) | creative(X0) | generous(X0) [cnf transformation 45]
84. ~strong(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 45]
89. ~humble(X0) | quiet(X0) | creative(X0) [cnf transformation 32]
94. ~patient(X0) | creative(X0) | funny(X0) [cnf transformation 49]
95. ~wise(X0) | ~humble(X0) | generous(X0) [cnf transformation 51]
96. ~wise(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 51]
100. calm(X0) | strong(X0) | funny(X0) [cnf transformation 52]
101. ~strong(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 52]
106. ~humble(X0) | patient(X0) | ~tall(X0) | wise(X0) [cnf transformation 53]
107. ~wise(X0) | ~tall(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 53]
109. ~patient(X0) | tall(X0) | wise(X0) | ~humble(X0) [cnf transformation 53]
113. ~old(X0) | ~old(X0) | calm(X0) [cnf transformation 55]
118. old(X0) | calm(X0) | tall(X0) | old(X0) [cnf transformation 55]
119. brave(X0) | wise(X0) | old(X0) | calm(X0) [cnf transformation 57]
120. ~wise(X0) | ~calm(X0) [cnf transformation 57]
121. ~calm(X0) | ~brave(X0) [cnf transformation 57]
122. ~wise(X0) | ~old(X0) [cnf transformation 57]
123. ~old(X0) | ~brave(X0) [cnf transformation 57]
125. strong(mary) | ~quiet(mary) [cnf transformation 18]
134. humble(mary) [cnf transformation 25]
135. ~old(X0) | calm(X0) [duplicate literal removal 113]
136. calm(X0) | old(X0) | tall(X0) [duplicate literal removal 118]
172. wise(X0) | brave(X0) | calm(X0) [subsumption resolution 119,135]
183. 11 <=> quiet(mary) [avatar definition]
187. 12 <=> strong(mary) [avatar definition]
189. strong(mary) <- (12) [avatar component clause 187]
190. ~11 | 12 [avatar split clause 125,187,183]
264. 25 <=> old(mary) [avatar definition]
265. ~old(mary) <- (~25) [avatar component clause 264]
292. quiet(mary) | creative(mary) [resolution 89,134]
308. 30 <=> generous(mary) [avatar definition]
309. ~generous(mary) <- (~30) [avatar component clause 308]
313. 31 <=> brave(mary) [avatar definition]
314. brave(mary) <- (31) [avatar component clause 313]
315. ~brave(mary) <- (~31) [avatar component clause 313]
317. 32 <=> tall(mary) [avatar definition]
319. tall(mary) <- (32) [avatar component clause 317]
321. ~generous(mary) | ~creative(mary) <- (12) [resolution 189,84]
322. creative(mary) | generous(mary) <- (12) [resolution 189,83]
329. 33 <=> funny(mary) [avatar definition]
330. ~funny(mary) <- (~33) [avatar component clause 329]
331. funny(mary) <- (33) [avatar component clause 329]
333. 34 <=> patient(mary) [avatar definition]
334. ~patient(mary) <- (~34) [avatar component clause 333]
335. patient(mary) <- (34) [avatar component clause 333]
339. funny(X1) | creative(X1) | brave(X1) [resolution 94,81]
346. 35 <=> creative(mary) [avatar definition]
347. creative(mary) <- (35) [avatar component clause 346]
349. ~35 | ~30 | ~12 [avatar split clause 321,187,308,346]
350. 30 | 35 | ~12 [avatar split clause 322,187,346,308]
354. 36 <=> wise(mary) [avatar definition]
356. wise(mary) <- (36) [avatar component clause 354]
424. ~funny(mary) | ~generous(mary) <- (12) [resolution 101,189]
426. ~generous(mary) <- (12, 33) [subsumption resolution 424,331]
429. ~30 | ~12 | ~33 [avatar split clause 426,329,187,308]
460. old(X1) | tall(X1) | ~brave(X1) [resolution 136,121]
465. ~brave(X1) | tall(X1) [subsumption resolution 460,123]
532. patient(mary) | ~tall(mary) | wise(mary) [resolution 106,134]
533. ~tall(X0) | ~patient(X0) | ~humble(X0) | brave(X0) | calm(X0) [resolution 107,172]
534. ~patient(X0) | ~tall(X0) | ~humble(X0) | calm(X0) [subsumption resolution 533,82]
559. tall(X1) | wise(X1) | ~humble(X1) | brave(X1) [resolution 109,81]
560. ~humble(X1) | wise(X1) | tall(X1) [subsumption resolution 559,465]
562. brave(mary) <- (~34) [resolution 334,81]
563. $false <- (~31, ~34) [subsumption resolution 562,315]
564. 31 | 34 [avatar contradiction clause 563]
567. 58 <=> calm(mary) [avatar definition]
568. ~calm(mary) <- (~58) [avatar component clause 567]
569. calm(mary) <- (58) [avatar component clause 567]
587. creative(mary) | funny(mary) <- (34) [resolution 335,94]
724. creative(mary) | brave(mary) <- (~33) [resolution 339,330]
808. wise(mary) | tall(mary) [resolution 560,134]
812. 32 | 36 [avatar split clause 808,354,317]
814. brave(mary) | ~creative(mary) <- (32) [resolution 319,70]
815. ~creative(mary) <- (~31, 32) [subsumption resolution 814,315]
816. $false <- (~31, 32, 35) [subsumption resolution 815,347]
817. 31 | ~32 | ~35 [avatar contradiction clause 816]
928. ~brave(mary) <- (58) [resolution 569,121]
943. ~tall(mary) | ~humble(mary) | calm(mary) <- (34) [resolution 534,335]
1190. ~humble(mary) | generous(mary) <- (36) [resolution 356,95]
1196. ~calm(mary) <- (36) [resolution 356,120]
1197. ~old(mary) <- (36) [resolution 356,122]
1198. generous(mary) <- (36) [subsumption resolution 1190,134]
1199. $false <- (~30, 36) [subsumption resolution 1198,309]
1200. 30 | ~36 [avatar contradiction clause 1199]
1201. $false <- (36, 58) [subsumption resolution 1196,569]
1202. ~36 | ~58 [avatar contradiction clause 1201]
1203. ~25 | ~36 [avatar split clause 1197,354,264]
1204. ~31 | ~58 [avatar split clause 928,567,313]
1211. 31 | 35 | 33 [avatar split clause 724,329,346,313]
1212. creative(mary) <- (~33, 34) [subsumption resolution 587,330]
1213. 35 | 33 | ~34 [avatar split clause 1212,333,329,346]
1214. ~tall(mary) | calm(mary) <- (34) [subsumption resolution 943,134]
1215. 58 | ~32 | ~34 [avatar split clause 1214,333,317,567]
1219. old(mary) | tall(mary) <- (~58) [resolution 568,136]
1220. strong(mary) | funny(mary) <- (~58) [resolution 568,100]
1221. tall(mary) <- (~25, ~58) [subsumption resolution 1219,265]
1222. 32 | 25 | 58 [avatar split clause 1221,567,264,317]
1234. ~brave(mary) | creative(mary) <- (32) [resolution 319,71]
1236. creative(mary) <- (31, 32) [subsumption resolution 1234,314]
1239. 35 | 11 [avatar split clause 292,183,346]
1245. 33 | 12 | 58 [avatar split clause 1220,567,187,329]
1246. 35 | ~31 | ~32 [avatar split clause 1236,317,313,346]
1248. ~tall(mary) | wise(mary) <- (~34) [subsumption resolution 532,334]
1249. wise(mary) <- (32, ~34) [subsumption resolution 1248,319]
1250. 36 | ~32 | 34 [avatar split clause 1249,333,317,354]
1263. ~humble(mary) | ~funny(mary) <- (36) [resolution 356,96]
1270. ~funny(mary) <- (36) [subsumption resolution 1263,134]
1271. $false <- (33, 36) [subsumption resolution 1270,331]
1272. ~33 | ~36 [avatar contradiction clause 1271]
1273. $false [avatar sat refutation 190,349,350,429,564,812,817,1200,1202,1203,1204,1211,1213,1215,1222,1239,1245,1246,1250,1272]
% SZS output end Proof for 173005431842342818668114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is funny or not quiet then lucy is rich.
If someone is both wise and not quiet then someone is rich and vice versa.
If lucy is humble then someone is quiet or tall and vice versa.
If someone is not curious or calm then lucy is both creative and not patient.
If john is not generous or not quiet then john is not calm or not generous and vice versa.
If lucy is not generous or curious then someone is either not funny or not curious and vice versa.
If someone is either not funny or curious then someone is either kind or not funny.
If someone is generous or creative then someone is either curious or not kind and vice versa.
If someone is tall then someone is either wise or not happy.
Everyone who is not old is not strong.
Everyone who is not generous or not tall is wise and vice versa.
If someone is both creative and not wise then someone is wise and vice versa.
If alice is both not wise and wise then someone is either kind or tall.
If alice is patient then lucy is not calm and vice versa.
If fred is either not brave or not funny then susan is both not quiet and happy.
If someone is both not humble and not calm then someone is both not generous and not happy.
Someone is happy or not calm.
Lucy is either not quiet or not funny.
Alice is both funny and not generous.
Someone is both curious and funny.
Susan is happy or brave.
Susan is not wise or rich.
Mary is both not funny and not curious.
Mary is wise or not funny. | Lucy is humble. | entailment | (((funny(alice)|~quiet(alice)))=>(rich(lucy)))&
((?[X]:((wise(X)&~quiet(X))))<=>(?[X]:(rich(X))))&
((humble(lucy))<=>(?[X]:((quiet(X)|tall(X)))))&
((?[X]:((~curious(X)|calm(X))))=>((creative(lucy)&~patient(lucy))))&
(((~generous(john)|~quiet(john)))<=>((~calm(john)|~generous(john))))&
(((~generous(lucy)|curious(lucy)))<=>(?[X]:((~funny(X)<~>~curious(X)))))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((kind(X)<~>~funny(X)))))&
((?[X]:((generous(X)|creative(X))))<=>(?[X]:((curious(X)<~>~kind(X)))))&
((?[X]:(tall(X)))=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:(~old(X)=>~strong(X)))&
(![X]:((~generous(X)|~tall(X))<=>wise(X)))&
((?[X]:((creative(X)&~wise(X))))<=>(?[X]:(wise(X))))&
(((~wise(alice)&wise(alice)))=>(?[X]:((kind(X)<~>tall(X)))))&
((patient(alice))<=>(~calm(lucy)))&
(((~brave(fred)<~>~funny(fred)))=>((~quiet(susan)&happy(susan))))&
((?[X]:((~humble(X)&~calm(X))))=>(?[X]:((~generous(X)&~happy(X)))))&
(?[X]:((happy(X)|~calm(X))))&
((~quiet(lucy)<~>~funny(lucy)))&
((funny(alice)&~generous(alice)))&
(?[X]:((curious(X)&funny(X))))&
((happy(susan)|brave(susan)))&
((~wise(susan)|rich(susan)))&
((~funny(mary)&~curious(mary)))&
((wise(mary)|~funny(mary))) | humble(lucy) | [
"p0",
"p1",
"p2",
"p10",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5376133826638175312128087
% SZS output start Proof for 5376133826638175312128087
1. (~quiet(alice) | funny(alice)) => rich(lucy) [input p0]
2. ? [X0] : (~quiet(X0) & wise(X0)) <=> ? [X0] : rich(X0) [input p1]
3. humble(lucy) <=> ? [X0] : (tall(X0) | quiet(X0)) [input p2]
11. ! [X0] : ((~tall(X0) | ~generous(X0)) <=> wise(X0)) [input p10]
12. ? [X0] : (~wise(X0) & creative(X0)) <=> ? [X0] : wise(X0) [input p11]
19. ~generous(alice) & funny(alice) [input p18]
25. ~humble(lucy) [input hypothesis]
26. ? [X0] : (~quiet(X0) & wise(X0)) <=> ? [X1] : rich(X1) [rectify 2]
30. ? [X0] : (~wise(X0) & creative(X0)) <=> ? [X1] : wise(X1) [rectify 12]
33. rich(lucy) | (quiet(alice) & ~funny(alice)) [ennf transformation 1]
41. (? [X0] : (~quiet(X0) & wise(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (quiet(X0) | ~wise(X0))) [nnf transformation 26]
42. (? [X0] : (~quiet(X0) & wise(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (quiet(X3) | ~wise(X3))) [rectify 41]
43. ? [X0] : (~quiet(X0) & wise(X0)) => (~quiet(sK0) & wise(sK0)) [choice axiom]
44. ? [X2] : rich(X2) => rich(sK1) [choice axiom]
45. ((~quiet(sK0) & wise(sK0)) | ! [X1] : ~rich(X1)) & (rich(sK1) | ! [X3] : (quiet(X3) | ~wise(X3))) [skolemisation 42,44,43]
46. (humble(lucy) | ! [X0] : (~tall(X0) & ~quiet(X0))) & (? [X0] : (tall(X0) | quiet(X0)) | ~humble(lucy)) [nnf transformation 3]
47. (humble(lucy) | ! [X0] : (~tall(X0) & ~quiet(X0))) & (? [X1] : (tall(X1) | quiet(X1)) | ~humble(lucy)) [rectify 46]
48. ? [X1] : (tall(X1) | quiet(X1)) => (tall(sK2) | quiet(sK2)) [choice axiom]
49. (humble(lucy) | ! [X0] : (~tall(X0) & ~quiet(X0))) & ((tall(sK2) | quiet(sK2)) | ~humble(lucy)) [skolemisation 47,48]
70. ! [X0] : (((~tall(X0) | ~generous(X0)) | ~wise(X0)) & (wise(X0) | (tall(X0) & generous(X0)))) [nnf transformation 11]
71. ! [X0] : ((~tall(X0) | ~generous(X0) | ~wise(X0)) & (wise(X0) | (tall(X0) & generous(X0)))) [flattening 70]
72. (? [X0] : (~wise(X0) & creative(X0)) | ! [X1] : ~wise(X1)) & (? [X1] : wise(X1) | ! [X0] : (wise(X0) | ~creative(X0))) [nnf transformation 30]
73. (? [X0] : (~wise(X0) & creative(X0)) | ! [X1] : ~wise(X1)) & (? [X2] : wise(X2) | ! [X3] : (wise(X3) | ~creative(X3))) [rectify 72]
74. ? [X0] : (~wise(X0) & creative(X0)) => (~wise(sK8) & creative(sK8)) [choice axiom]
75. ? [X2] : wise(X2) => wise(sK9) [choice axiom]
76. ((~wise(sK8) & creative(sK8)) | ! [X1] : ~wise(X1)) & (wise(sK9) | ! [X3] : (wise(X3) | ~creative(X3))) [skolemisation 73,75,74]
90. rich(lucy) | ~funny(alice) [cnf transformation 33]
93. wise(sK0) | ~rich(X1) [cnf transformation 45]
97. humble(lucy) | ~tall(X0) [cnf transformation 49]
125. tall(X0) | wise(X0) [cnf transformation 71]
129. ~wise(sK8) | ~wise(X1) [cnf transformation 76]
143. funny(alice) [cnf transformation 19]
152. ~humble(lucy) [cnf transformation 25]
158. 2 <=> rich(lucy) [avatar definition]
160. rich(lucy) <- (2) [avatar component clause 158]
163. 3 <=> funny(alice) [avatar definition]
166. ~3 | 2 [avatar split clause 90,158,163]
168. 4 <=> ! [X1] : ~rich(X1) [avatar definition]
169. ~rich(X1) <- (4) [avatar component clause 168]
176. 6 <=> wise(sK0) [avatar definition]
178. wise(sK0) <- (6) [avatar component clause 176]
179. 4 | 6 [avatar split clause 93,176,168]
189. 9 <=> ! [X0] : ~tall(X0) [avatar definition]
190. ~tall(X0) <- (9) [avatar component clause 189]
192. 10 <=> humble(lucy) [avatar definition]
195. 9 | 10 [avatar split clause 97,192,189]
332. 41 <=> ! [X1] : ~wise(X1) [avatar definition]
333. ~wise(X1) <- (41) [avatar component clause 332]
335. 42 <=> wise(sK8) [avatar definition]
337. ~wise(sK8) <- (~42) [avatar component clause 335]
338. 41 | ~42 [avatar split clause 129,335,332]
414. 3 [avatar split clause 143,163]
429. ~10 [avatar split clause 152,192]
430. $false <- (2, 4) [subsumption resolution 160,169]
431. ~2 | ~4 [avatar contradiction clause 430]
432. $false <- (6, 41) [subsumption resolution 178,333]
433. ~6 | ~41 [avatar contradiction clause 432]
445. wise(X0) <- (9) [resolution 125,190]
458. $false <- (9, ~42) [resolution 445,337]
461. ~9 | 42 [avatar contradiction clause 458]
462. $false [avatar sat refutation 166,179,195,338,414,429,431,433,461]
% SZS output end Proof for 5376133826638175312128087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not strong then lucy is either not tall or rich.
Everyone who is old or not calm is tall or quiet.
Everyone who is both not wise and old is either not rich or funny and vice versa.
Everyone who is either calm or not generous is not old or calm and vice versa.
Everyone who is brave is both kind and wise.
Everyone who is tall or patient is both old and not quiet.
If someone is either not tall or not generous then someone is happy or funny and vice versa.
If alice is tall then someone is both old and creative.
If someone is not kind then john is both not creative and not curious and vice versa.
Everyone who is either not creative or generous is both not calm and not tall.
If mary is generous then someone is either not quiet or quiet and vice versa.
Everyone who is both generous and humble is not brave or not kind and vice versa.
Everyone who is not old or not happy is generous and vice versa.
If someone is either brave or not rich then susan is either not creative or not generous and vice versa.
Everyone who is not tall is either not generous or strong.
If paul is not tall or not strong then someone is not curious and vice versa.
Someone is both strong and curious.
Mary is both calm and tall.
John is either not curious or not wise.
Fred is generous.
Someone is both not curious and patient.
Someone is either not old or wise.
Fred is wise or generous. | Mary is not curious. | neutral | ((?[X]:((brave(X)<~>~strong(X))))=>((~tall(lucy)<~>rich(lucy))))&
(![X]:((old(X)|~calm(X))=>(tall(X)|quiet(X))))&
(![X]:((~wise(X)&old(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(~old(X)|calm(X))))&
(![X]:(brave(X)=>(kind(X)&wise(X))))&
(![X]:((tall(X)|patient(X))=>(old(X)&~quiet(X))))&
((?[X]:((~tall(X)<~>~generous(X))))<=>(?[X]:((happy(X)|funny(X)))))&
((tall(alice))=>(?[X]:((old(X)&creative(X)))))&
((?[X]:(~kind(X)))<=>((~creative(john)&~curious(john))))&
(![X]:((~creative(X)<~>generous(X))=>(~calm(X)&~tall(X))))&
((generous(mary))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((generous(X)&humble(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~old(X)|~happy(X))<=>generous(X)))&
((?[X]:((brave(X)<~>~rich(X))))<=>((~creative(susan)<~>~generous(susan))))&
(![X]:(~tall(X)=>(~generous(X)<~>strong(X))))&
(((~tall(paul)|~strong(paul)))<=>(?[X]:(~curious(X))))&
(?[X]:((strong(X)&curious(X))))&
((calm(mary)&tall(mary)))&
((~curious(john)<~>~wise(john)))&
(generous(fred))&
(?[X]:((~curious(X)&patient(X))))&
(?[X]:((~old(X)<~>wise(X))))&
((wise(fred)|generous(fred))) | ~curious(mary) | [] | null | 0 |
If fred is both not funny and not patient then someone is either tall or humble and vice versa.
Everyone who is not strong or not happy is either quiet or not generous.
If susan is not rich then someone is either not strong or humble and vice versa.
Everyone who is either not brave or not funny is both brave and not tall and vice versa.
Everyone who is either not humble or strong is either not old or not quiet and vice versa.
If someone is humble or rich then someone is either wise or old and vice versa.
If lucy is not wise then someone is either not old or not tall and vice versa.
If someone is not rich then someone is both tall and patient.
Everyone who is not old or not wise is kind.
If someone is old then someone is both rich and strong and vice versa.
Everyone who is either not tall or not wise is strong.
Everyone who is curious or quiet is tall and vice versa.
If fred is either not strong or not tall then someone is either humble or strong.
Everyone who is wise is either not funny or not curious.
Everyone who is either not humble or not generous is wise and vice versa.
Everyone who is either quiet or happy is both humble and not patient and vice versa.
Someone is either old or not quiet.
Someone is not quiet.
John is both not generous and not old.
Susan is both not strong and humble.
Someone is either not tall or rich.
Someone is both generous and curious.
Mary is both happy and wise.
John is either not humble or wise. | Susan is not wise. | contradiction | (((~funny(fred)&~patient(fred)))<=>(?[X]:((tall(X)<~>humble(X)))))&
(![X]:((~strong(X)|~happy(X))=>(quiet(X)<~>~generous(X))))&
((~rich(susan))<=>(?[X]:((~strong(X)<~>humble(X)))))&
(![X]:((~brave(X)<~>~funny(X))<=>(brave(X)&~tall(X))))&
(![X]:((~humble(X)<~>strong(X))<=>(~old(X)<~>~quiet(X))))&
((?[X]:((humble(X)|rich(X))))<=>(?[X]:((wise(X)<~>old(X)))))&
((~wise(lucy))<=>(?[X]:((~old(X)<~>~tall(X)))))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)&patient(X)))))&
(![X]:((~old(X)|~wise(X))=>kind(X)))&
((?[X]:(old(X)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((~tall(X)<~>~wise(X))=>strong(X)))&
(![X]:((curious(X)|quiet(X))<=>tall(X)))&
(((~strong(fred)<~>~tall(fred)))=>(?[X]:((humble(X)<~>strong(X)))))&
(![X]:(wise(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>wise(X)))&
(![X]:((quiet(X)<~>happy(X))<=>(humble(X)&~patient(X))))&
(?[X]:((old(X)<~>~quiet(X))))&
(?[X]:(~quiet(X)))&
((~generous(john)&~old(john)))&
((~strong(susan)&humble(susan)))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:((generous(X)&curious(X))))&
((happy(mary)&wise(mary)))&
((~humble(john)<~>wise(john))) | ~wise(susan) | [
"p1",
"p10",
"p11",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1718670959788946583727656
% SZS output start Proof for 1718670959788946583727656
2. ! [X0] : ((~happy(X0) | ~strong(X0)) => (quiet(X0) <~> ~generous(X0))) [input p1]
11. ! [X0] : ((~tall(X0) <~> ~wise(X0)) => strong(X0)) [input p10]
12. ! [X0] : ((quiet(X0) | curious(X0)) <=> tall(X0)) [input p11]
15. ! [X0] : ((~humble(X0) <~> ~generous(X0)) <=> wise(X0)) [input p14]
20. humble(susan) & ~strong(susan) [input p19]
25. ~wise(susan) [input hypothesis]
30. ! [X0] : ((quiet(X0) <~> ~generous(X0)) | (happy(X0) & strong(X0))) [ennf transformation 2]
32. ! [X0] : (strong(X0) | (~tall(X0) <=> ~wise(X0))) [ennf transformation 11]
40. ! [X0] : (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | (happy(X0) & strong(X0))) [nnf transformation 30]
65. ! [X0] : (strong(X0) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0)))) [nnf transformation 32]
66. ! [X0] : (((quiet(X0) | curious(X0)) | ~tall(X0)) & (tall(X0) | (~quiet(X0) & ~curious(X0)))) [nnf transformation 12]
67. ! [X0] : ((quiet(X0) | curious(X0) | ~tall(X0)) & (tall(X0) | (~quiet(X0) & ~curious(X0)))) [flattening 66]
72. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | ~wise(X0)) & (wise(X0) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [nnf transformation 15]
92. ~generous(X0) | quiet(X0) | strong(X0) [cnf transformation 40]
130. ~tall(X0) | strong(X0) | wise(X0) [cnf transformation 65]
132. ~quiet(X0) | tall(X0) [cnf transformation 67]
141. ~humble(X0) | wise(X0) | generous(X0) [cnf transformation 72]
155. ~strong(susan) [cnf transformation 20]
156. humble(susan) [cnf transformation 20]
165. ~wise(susan) [cnf transformation 25]
545. wise(susan) | generous(susan) [resolution 141,156]
548. generous(susan) [subsumption resolution 545,165]
660. quiet(susan) | strong(susan) [resolution 548,92]
666. 85 <=> quiet(susan) [avatar definition]
668. quiet(susan) <- (85) [avatar component clause 666]
670. quiet(susan) [subsumption resolution 660,155]
671. 85 [avatar split clause 670,666]
888. tall(susan) <- (85) [resolution 668,132]
1507. strong(susan) | wise(susan) <- (85) [resolution 888,130]
1509. wise(susan) <- (85) [subsumption resolution 1507,155]
1510. $false <- (85) [subsumption resolution 1509,165]
1511. ~85 [avatar contradiction clause 1510]
1512. $false [avatar sat refutation 671,1511]
% SZS output end Proof for 1718670959788946583727656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5756
% Time elapsed: 0.044 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not happy or brave then mary is rich.
Everyone who is humble or kind is not calm.
Everyone who is not kind or wise is both curious and funny.
Everyone who is either funny or not funny is either not wise or brave.
Everyone who is humble or quiet is not humble or happy.
Everyone who is not generous is not rich or not old and vice versa.
Everyone who is either rich or brave is not humble or not rich.
Everyone who is creative or old is happy.
Everyone who is creative or not kind is either patient or not rich.
Everyone who is both calm and not curious is brave or not rich and vice versa.
If someone is both curious and happy then lucy is both not humble and rich and vice versa.
Everyone who is either not quiet or generous is not funny.
Everyone who is either old or funny is both not funny and funny.
If someone is either humble or quiet then mary is both not curious and not quiet.
If someone is kind then lucy is quiet and vice versa.
Everyone who is patient or humble is curious or not strong and vice versa.
John is either calm or not happy.
Someone is creative or not tall.
Mary is calm or tall.
Someone is either tall or not humble.
John is both not generous and tall.
Alice is brave or generous.
Someone is brave or funny. | John is happy. | contradiction | (((~happy(mary)|brave(mary)))=>(rich(mary)))&
(![X]:((humble(X)|kind(X))=>~calm(X)))&
(![X]:((~kind(X)|wise(X))=>(curious(X)&funny(X))))&
(![X]:((funny(X)<~>~funny(X))=>(~wise(X)<~>brave(X))))&
(![X]:((humble(X)|quiet(X))=>(~humble(X)|happy(X))))&
(![X]:(~generous(X)<=>(~rich(X)|~old(X))))&
(![X]:((rich(X)<~>brave(X))=>(~humble(X)|~rich(X))))&
(![X]:((creative(X)|old(X))=>happy(X)))&
(![X]:((creative(X)|~kind(X))=>(patient(X)<~>~rich(X))))&
(![X]:((calm(X)&~curious(X))<=>(brave(X)|~rich(X))))&
((?[X]:((curious(X)&happy(X))))<=>((~humble(lucy)&rich(lucy))))&
(![X]:((~quiet(X)<~>generous(X))=>~funny(X)))&
(![X]:((old(X)<~>funny(X))=>(~funny(X)&funny(X))))&
((?[X]:((humble(X)<~>quiet(X))))=>((~curious(mary)&~quiet(mary))))&
((?[X]:(kind(X)))<=>(quiet(lucy)))&
(![X]:((patient(X)|humble(X))<=>(curious(X)|~strong(X))))&
((calm(john)<~>~happy(john)))&
(?[X]:((creative(X)|~tall(X))))&
((calm(mary)|tall(mary)))&
(?[X]:((tall(X)<~>~humble(X))))&
((~generous(john)&tall(john)))&
((brave(alice)|generous(alice)))&
(?[X]:((brave(X)|funny(X)))) | happy(john) | [
"p1",
"p2",
"p5",
"p9",
"p12",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8081060248484333239810682
% SZS output start Proof for 8081060248484333239810682
2. ! [X0] : ((kind(X0) | humble(X0)) => ~calm(X0)) [input p1]
3. ! [X0] : ((wise(X0) | ~kind(X0)) => (funny(X0) & curious(X0))) [input p2]
6. ! [X0] : (~generous(X0) <=> (~old(X0) | ~rich(X0))) [input p5]
10. ! [X0] : ((~curious(X0) & calm(X0)) <=> (~rich(X0) | brave(X0))) [input p9]
13. ! [X0] : ((old(X0) <~> funny(X0)) => (funny(X0) & ~funny(X0))) [input p12]
17. calm(john) <~> ~happy(john) [input p16]
21. tall(john) & ~generous(john) [input p20]
24. happy(john) [input hypothesis]
26. ! [X0] : (~calm(X0) | (~kind(X0) & ~humble(X0))) [ennf transformation 2]
27. ! [X0] : ((funny(X0) & curious(X0)) | (~wise(X0) & kind(X0))) [ennf transformation 3]
36. ! [X0] : ((funny(X0) & ~funny(X0)) | (old(X0) <=> funny(X0))) [ennf transformation 13]
39. ! [X0] : ((~generous(X0) | (old(X0) & rich(X0))) & ((~old(X0) | ~rich(X0)) | generous(X0))) [nnf transformation 6]
40. ! [X0] : ((~generous(X0) | (old(X0) & rich(X0))) & (~old(X0) | ~rich(X0) | generous(X0))) [flattening 39]
43. ! [X0] : (((~curious(X0) & calm(X0)) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | (curious(X0) | ~calm(X0)))) [nnf transformation 10]
44. ! [X0] : (((~curious(X0) & calm(X0)) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | curious(X0) | ~calm(X0))) [flattening 43]
51. ! [X0] : ((funny(X0) & ~funny(X0)) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0)))) [nnf transformation 36]
59. (happy(john) | ~calm(john)) & (~happy(john) | calm(john)) [nnf transformation 17]
70. ~calm(X0) | ~kind(X0) [cnf transformation 26]
71. curious(X0) | kind(X0) [cnf transformation 27]
73. funny(X0) | kind(X0) [cnf transformation 27]
81. ~old(X0) | ~rich(X0) | generous(X0) [cnf transformation 40]
94. calm(X0) | rich(X0) [cnf transformation 44]
96. ~curious(X0) | rich(X0) [cnf transformation 44]
104. ~funny(X0) | old(X0) | ~funny(X0) [cnf transformation 51]
117. ~happy(john) | calm(john) [cnf transformation 59]
123. ~generous(john) [cnf transformation 21]
127. happy(john) [cnf transformation 24]
128. ~funny(X0) | old(X0) [duplicate literal removal 104]
208. 16 <=> calm(john) [avatar definition]
209. calm(john) <- (16) [avatar component clause 208]
212. 17 <=> happy(john) [avatar definition]
216. 16 | ~17 [avatar split clause 117,212,208]
255. 17 [avatar split clause 127,212]
258. ~kind(john) <- (16) [resolution 70,209]
264. ~kind(X0) | rich(X0) [resolution 94,70]
273. rich(X0) | kind(X0) [resolution 96,71]
275. rich(X0) [subsumption resolution 273,264]
277. old(X0) | kind(X0) [resolution 128,73]
338. kind(X0) | ~rich(X0) | generous(X0) [resolution 277,81]
349. generous(X0) | kind(X0) [subsumption resolution 338,275]
439. kind(john) [resolution 349,123]
443. $false <- (16) [subsumption resolution 439,258]
444. ~16 [avatar contradiction clause 443]
446. $false [avatar sat refutation 216,255,444]
% SZS output end Proof for 8081060248484333239810682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is not generous and vice versa.
Everyone who is either not quiet or not old is either quiet or happy.
Everyone who is either not brave or brave is either calm or humble and vice versa.
If paul is not curious or not brave then alice is quiet or rich and vice versa.
Everyone who is not calm is either brave or not old.
Everyone who is both not creative and not strong is both not creative and curious.
Everyone who is not humble or not generous is either not creative or not rich and vice versa.
If mary is both patient and old then paul is either generous or creative and vice versa.
If fred is tall then someone is curious or not funny.
If fred is both not rich and calm then someone is either not brave or not rich.
Everyone who is not rich or not happy is either not brave or strong and vice versa.
Everyone who is tall is wise.
If susan is tall then paul is not old or happy.
If susan is either not funny or rich then someone is rich or humble and vice versa.
If someone is not old then paul is not old and vice versa.
If someone is either rich or kind then someone is either tall or not strong.
Susan is calm or not patient.
Lucy is kind.
Someone is either not calm or calm.
John is both not wise and not rich.
Someone is strong or calm.
Paul is either generous or creative.
Someone is happy or quiet. | Susan is not funny. | neutral | (![X]:(strong(X)<=>~generous(X)))&
(![X]:((~quiet(X)<~>~old(X))=>(quiet(X)<~>happy(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(calm(X)<~>humble(X))))&
(((~curious(paul)|~brave(paul)))<=>((quiet(alice)|rich(alice))))&
(![X]:(~calm(X)=>(brave(X)<~>~old(X))))&
(![X]:((~creative(X)&~strong(X))=>(~creative(X)&curious(X))))&
(![X]:((~humble(X)|~generous(X))<=>(~creative(X)<~>~rich(X))))&
(((patient(mary)&old(mary)))<=>((generous(paul)<~>creative(paul))))&
((tall(fred))=>(?[X]:((curious(X)|~funny(X)))))&
(((~rich(fred)&calm(fred)))=>(?[X]:((~brave(X)<~>~rich(X)))))&
(![X]:((~rich(X)|~happy(X))<=>(~brave(X)<~>strong(X))))&
(![X]:(tall(X)=>wise(X)))&
((tall(susan))=>((~old(paul)|happy(paul))))&
(((~funny(susan)<~>rich(susan)))<=>(?[X]:((rich(X)|humble(X)))))&
((?[X]:(~old(X)))<=>(~old(paul)))&
((?[X]:((rich(X)<~>kind(X))))=>(?[X]:((tall(X)<~>~strong(X)))))&
((calm(susan)|~patient(susan)))&
(kind(lucy))&
(?[X]:((~calm(X)<~>calm(X))))&
((~wise(john)&~rich(john)))&
(?[X]:((strong(X)|calm(X))))&
((generous(paul)<~>creative(paul)))&
(?[X]:((happy(X)|quiet(X)))) | ~funny(susan) | [] | null | 0 |
Everyone who is wise or kind is either humble or not tall.
If someone is both not calm and not wise then john is either not rich or calm.
Everyone who is tall or not rich is not quiet or generous and vice versa.
If mary is either rich or curious then susan is not creative or rich and vice versa.
If john is kind then someone is both not wise and old and vice versa.
Everyone who is humble or rich is either tall or not tall and vice versa.
Everyone who is rich or not brave is not generous and vice versa.
Everyone who is both curious and not curious is either patient or rich.
Everyone who is not rich is not brave or rich and vice versa.
Everyone who is not generous is either not funny or quiet and vice versa.
If fred is quiet or not calm then john is not tall.
Everyone who is both not funny and not wise is strong.
If someone is strong then someone is funny or not creative and vice versa.
If someone is both not happy and funny then alice is both strong and kind and vice versa.
Everyone who is not happy or brave is happy.
If someone is both not generous and old then someone is both not wise and wise and vice versa.
Susan is either kind or not calm.
John is curious.
Someone is not humble or strong.
Someone is not wise.
Fred is both patient and not kind.
Someone is humble or not generous.
Alice is not humble or calm. | Susan is not curious. | neutral | (![X]:((wise(X)|kind(X))=>(humble(X)<~>~tall(X))))&
((?[X]:((~calm(X)&~wise(X))))=>((~rich(john)<~>calm(john))))&
(![X]:((tall(X)|~rich(X))<=>(~quiet(X)|generous(X))))&
(((rich(mary)<~>curious(mary)))<=>((~creative(susan)|rich(susan))))&
((kind(john))<=>(?[X]:((~wise(X)&old(X)))))&
(![X]:((humble(X)|rich(X))<=>(tall(X)<~>~tall(X))))&
(![X]:((rich(X)|~brave(X))<=>~generous(X)))&
(![X]:((curious(X)&~curious(X))=>(patient(X)<~>rich(X))))&
(![X]:(~rich(X)<=>(~brave(X)|rich(X))))&
(![X]:(~generous(X)<=>(~funny(X)<~>quiet(X))))&
(((quiet(fred)|~calm(fred)))=>(~tall(john)))&
(![X]:((~funny(X)&~wise(X))=>strong(X)))&
((?[X]:(strong(X)))<=>(?[X]:((funny(X)|~creative(X)))))&
((?[X]:((~happy(X)&funny(X))))<=>((strong(alice)&kind(alice))))&
(![X]:((~happy(X)|brave(X))=>happy(X)))&
((?[X]:((~generous(X)&old(X))))<=>(?[X]:((~wise(X)&wise(X)))))&
((kind(susan)<~>~calm(susan)))&
(curious(john))&
(?[X]:((~humble(X)|strong(X))))&
(?[X]:(~wise(X)))&
((patient(fred)&~kind(fred)))&
(?[X]:((humble(X)|~generous(X))))&
((~humble(alice)|calm(alice))) | ~curious(susan) | [] | null | 0 |
Everyone who is both strong and humble is either brave or not happy. Everyone who is either patient or curious is either creative or not curious. Everyone who is both patient and happy is not funny or not wise and vice versa. If lucy is kind then someone is either not wise or not calm. If someone is not generous or brave then someone is not tall or not calm. Everyone who is quiet or not generous is both calm and not old and vice versa. Everyone who is not brave is kind or not wise. Everyone who is happy or not rich is both not kind and not calm. Everyone who is brave or tall is both quiet and tall and vice versa. Everyone who is calm is both not humble and not wise. Everyone who is either happy or brave is curious and vice versa. If mary is rich then alice is either calm or curious. Everyone who is both not patient and strong is not strong. Everyone who is both not strong and funny is both not rich and old. Everyone who is either not quiet or old is both strong and not tall and vice versa. If john is either wise or not curious then paul is either calm or tall. Someone is either not generous or rich. Someone is rich. Someone is both patient and rich. Someone is either funny or not wise. Someone is both happy and not humble. John is strong or not quiet. Fred is either not tall or curious. | Fred is wise. | entailment | (![X]:((strong(X)&humble(X))=>(brave(X)<~>~happy(X))))&
(![X]:((patient(X)<~>curious(X))=>(creative(X)<~>~curious(X))))&
(![X]:((patient(X)&happy(X))<=>(~funny(X)|~wise(X))))&
((kind(lucy))=>(?[X]:((~wise(X)<~>~calm(X)))))&
((?[X]:((~generous(X)|brave(X))))=>(?[X]:((~tall(X)|~calm(X)))))&
(![X]:((quiet(X)|~generous(X))<=>(calm(X)&~old(X))))&
(![X]:(~brave(X)=>(kind(X)|~wise(X))))&
(![X]:((happy(X)|~rich(X))=>(~kind(X)&~calm(X))))&
(![X]:((brave(X)|tall(X))<=>(quiet(X)&tall(X))))&
(![X]:(calm(X)=>(~humble(X)&~wise(X))))&
(![X]:((happy(X)<~>brave(X))<=>curious(X)))&
((rich(mary))=>((calm(alice)<~>curious(alice))))&
(![X]:((~patient(X)&strong(X))=>~strong(X)))&
(![X]:((~strong(X)&funny(X))=>(~rich(X)&old(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(strong(X)&~tall(X))))&
(((wise(john)<~>~curious(john)))=>((calm(paul)<~>tall(paul))))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)&rich(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((happy(X)&~humble(X))))&
((strong(john)|~quiet(john)))&
((~tall(fred)<~>curious(fred))) | wise(fred) | [
"p2",
"p5",
"p7",
"p8",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8842996697098866724116492
% SZS output start Proof for 8842996697098866724116492
3. ! [X0] : ((happy(X0) & patient(X0)) <=> (~wise(X0) | ~funny(X0))) [input p2]
6. ! [X0] : ((~generous(X0) | quiet(X0)) <=> (~old(X0) & calm(X0))) [input p5]
8. ! [X0] : ((~rich(X0) | happy(X0)) => (~calm(X0) & ~kind(X0))) [input p7]
9. ! [X0] : ((tall(X0) | brave(X0)) <=> (tall(X0) & quiet(X0))) [input p8]
11. ! [X0] : ((happy(X0) <~> brave(X0)) <=> curious(X0)) [input p10]
23. ~tall(fred) <~> curious(fred) [input p22]
24. ~wise(fred) [input hypothesis]
34. ! [X0] : ((~calm(X0) & ~kind(X0)) | (rich(X0) & ~happy(X0))) [ennf transformation 8]
43. ! [X0] : (((happy(X0) & patient(X0)) | (wise(X0) & funny(X0))) & ((~wise(X0) | ~funny(X0)) | (~happy(X0) | ~patient(X0)))) [nnf transformation 3]
44. ! [X0] : (((happy(X0) & patient(X0)) | (wise(X0) & funny(X0))) & (~wise(X0) | ~funny(X0) | ~happy(X0) | ~patient(X0))) [flattening 43]
51. ! [X0] : (((~generous(X0) | quiet(X0)) | (old(X0) | ~calm(X0))) & ((~old(X0) & calm(X0)) | (generous(X0) & ~quiet(X0)))) [nnf transformation 6]
52. ! [X0] : ((~generous(X0) | quiet(X0) | old(X0) | ~calm(X0)) & ((~old(X0) & calm(X0)) | (generous(X0) & ~quiet(X0)))) [flattening 51]
53. ! [X0] : (((tall(X0) | brave(X0)) | (~tall(X0) | ~quiet(X0))) & ((tall(X0) & quiet(X0)) | (~tall(X0) & ~brave(X0)))) [nnf transformation 9]
54. ! [X0] : ((tall(X0) | brave(X0) | ~tall(X0) | ~quiet(X0)) & ((tall(X0) & quiet(X0)) | (~tall(X0) & ~brave(X0)))) [flattening 53]
55. ! [X0] : ((((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ~curious(X0)) & (curious(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0))))) [nnf transformation 11]
72. (~curious(fred) | tall(fred)) & (curious(fred) | ~tall(fred)) [nnf transformation 23]
81. wise(X0) | happy(X0) [cnf transformation 44]
86. ~quiet(X0) | calm(X0) [cnf transformation 52]
94. ~calm(X0) | ~happy(X0) [cnf transformation 34]
97. ~tall(X0) | quiet(X0) [cnf transformation 54]
98. ~brave(X0) | tall(X0) [cnf transformation 54]
102. ~happy(X0) | brave(X0) | curious(X0) [cnf transformation 55]
131. ~curious(fred) | tall(fred) [cnf transformation 72]
132. ~wise(fred) [cnf transformation 24]
233. 21 <=> tall(fred) [avatar definition]
234. ~tall(fred) <- (~21) [avatar component clause 233]
235. tall(fred) <- (21) [avatar component clause 233]
237. 22 <=> curious(fred) [avatar definition]
239. ~curious(fred) <- (~22) [avatar component clause 237]
240. 21 | ~22 [avatar split clause 131,237,233]
247. happy(fred) [resolution 81,132]
258. brave(fred) | curious(fred) [resolution 102,247]
261. brave(fred) <- (~22) [subsumption resolution 258,239]
357. tall(fred) <- (~22) [resolution 261,98]
359. $false <- (~21, ~22) [subsumption resolution 357,234]
360. 21 | 22 [avatar contradiction clause 359]
366. quiet(fred) <- (21) [resolution 235,97]
388. calm(fred) <- (21) [resolution 366,86]
514. ~happy(fred) <- (21) [resolution 388,94]
515. $false <- (21) [subsumption resolution 514,247]
516. ~21 [avatar contradiction clause 515]
517. $false [avatar sat refutation 240,360,516]
% SZS output end Proof for 8842996697098866724116492
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or tall then fred is not brave or not happy and vice versa.
Everyone who is not generous is not happy or strong.
Everyone who is both humble and not patient is not tall and vice versa.
Everyone who is not old is not rich and vice versa.
If someone is both strong and not calm then someone is strong and vice versa.
If susan is both not kind and not calm then someone is kind or funny and vice versa.
Everyone who is either not quiet or quiet is strong.
Everyone who is generous is old or not rich and vice versa.
If lucy is either quiet or kind then fred is not quiet or not brave and vice versa.
Everyone who is old is both humble and not happy and vice versa.
Everyone who is not calm or humble is both strong and not happy and vice versa.
If someone is either not old or not calm then paul is not strong or brave.
If someone is either not creative or tall then alice is not generous or not strong and vice versa.
If someone is not kind then someone is either not kind or quiet and vice versa.
Everyone who is brave or rich is both not brave and not patient.
Everyone who is either humble or creative is old or brave and vice versa.
Someone is creative or patient.
Someone is either not curious or old.
John is both not brave and not calm. | Lucy is creative. | contradiction | ((?[X]:((quiet(X)<~>tall(X))))<=>((~brave(fred)|~happy(fred))))&
(![X]:(~generous(X)=>(~happy(X)|strong(X))))&
(![X]:((humble(X)&~patient(X))<=>~tall(X)))&
(![X]:(~old(X)<=>~rich(X)))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:(strong(X))))&
(((~kind(susan)&~calm(susan)))<=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((~quiet(X)<~>quiet(X))=>strong(X)))&
(![X]:(generous(X)<=>(old(X)|~rich(X))))&
(((quiet(lucy)<~>kind(lucy)))<=>((~quiet(fred)|~brave(fred))))&
(![X]:(old(X)<=>(humble(X)&~happy(X))))&
(![X]:((~calm(X)|humble(X))<=>(strong(X)&~happy(X))))&
((?[X]:((~old(X)<~>~calm(X))))=>((~strong(paul)|brave(paul))))&
((?[X]:((~creative(X)<~>tall(X))))<=>((~generous(alice)|~strong(alice))))&
((?[X]:(~kind(X)))<=>(?[X]:((~kind(X)<~>quiet(X)))))&
(![X]:((brave(X)|rich(X))=>(~brave(X)&~patient(X))))&
(![X]:((humble(X)<~>creative(X))<=>(old(X)|brave(X))))&
(?[X]:((creative(X)|patient(X))))&
(?[X]:((~curious(X)<~>old(X))))&
((~brave(john)&~calm(john))) | creative(lucy) | [
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 590163445766255771993094
% SZS output start Proof for 590163445766255771993094
10. ! [X0] : (old(X0) <=> (~happy(X0) & humble(X0))) [input p9]
11. ! [X0] : ((humble(X0) | ~calm(X0)) <=> (~happy(X0) & strong(X0))) [input p10]
15. ! [X0] : ((rich(X0) | brave(X0)) => (~patient(X0) & ~brave(X0))) [input p14]
16. ! [X0] : ((humble(X0) <~> creative(X0)) <=> (brave(X0) | old(X0))) [input p15]
20. creative(lucy) [input hypothesis]
28. ! [X0] : ((~patient(X0) & ~brave(X0)) | (~rich(X0) & ~brave(X0))) [ennf transformation 15]
52. ! [X0] : ((old(X0) | (happy(X0) | ~humble(X0))) & ((~happy(X0) & humble(X0)) | ~old(X0))) [nnf transformation 10]
53. ! [X0] : ((old(X0) | happy(X0) | ~humble(X0)) & ((~happy(X0) & humble(X0)) | ~old(X0))) [flattening 52]
54. ! [X0] : (((humble(X0) | ~calm(X0)) | (happy(X0) | ~strong(X0))) & ((~happy(X0) & strong(X0)) | (~humble(X0) & calm(X0)))) [nnf transformation 11]
55. ! [X0] : ((humble(X0) | ~calm(X0) | happy(X0) | ~strong(X0)) & ((~happy(X0) & strong(X0)) | (~humble(X0) & calm(X0)))) [flattening 54]
67. ! [X0] : ((((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~brave(X0) & ~old(X0))) & ((brave(X0) | old(X0)) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))))) [nnf transformation 16]
68. ! [X0] : ((((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~brave(X0) & ~old(X0))) & (brave(X0) | old(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))))) [flattening 67]
105. ~old(X0) | humble(X0) [cnf transformation 53]
107. ~humble(X0) | happy(X0) | old(X0) [cnf transformation 53]
111. ~humble(X0) | ~happy(X0) [cnf transformation 55]
125. ~brave(X0) | ~brave(X0) [cnf transformation 28]
130. brave(X0) | old(X0) | humble(X0) | ~creative(X0) [cnf transformation 68]
133. ~creative(X0) | ~humble(X0) | ~old(X0) [cnf transformation 68]
140. creative(lucy) [cnf transformation 20]
141. ~brave(X0) [duplicate literal removal 125]
303. ~creative(X0) | ~old(X0) [subsumption resolution 133,105]
304. old(X0) | humble(X0) | ~creative(X0) [subsumption resolution 130,141]
305. ~creative(X0) | humble(X0) [subsumption resolution 304,303]
357. ~old(lucy) [resolution 303,140]
361. humble(lucy) [resolution 305,140]
368. happy(lucy) | old(lucy) [resolution 361,107]
370. ~happy(lucy) [resolution 361,111]
371. happy(lucy) [subsumption resolution 368,357]
372. $false [subsumption resolution 370,371]
% SZS output end Proof for 590163445766255771993094
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not wise then fred is either not generous or rich and vice versa.
Everyone who is wise is kind or not creative and vice versa.
If alice is both brave and curious then someone is either happy or not rich.
If someone is either not funny or not patient then someone is both generous and patient.
If john is patient or not calm then someone is not funny and vice versa.
Everyone who is either tall or not humble is either not funny or rich and vice versa.
If someone is curious or not brave then someone is either brave or not happy and vice versa.
If someone is either not funny or not brave then someone is both not quiet and strong.
Everyone who is brave is both not old and brave.
Everyone who is both humble and creative is not old.
Everyone who is both not happy and strong is both not humble and not quiet.
Everyone who is both not wise and tall is both quiet and not brave and vice versa.
If someone is either not rich or generous then someone is either brave or not quiet.
Everyone who is either not creative or creative is kind and vice versa.
If someone is old or patient then alice is wise or calm and vice versa.
Everyone who is not kind or quiet is both not creative and not kind.
Someone is either funny or not quiet.
Fred is both not quiet and not funny.
Someone is either happy or curious.
Alice is not funny.
Fred is either strong or brave. | John is not creative. | neutral | ((?[X]:((calm(X)|~wise(X))))<=>((~generous(fred)<~>rich(fred))))&
(![X]:(wise(X)<=>(kind(X)|~creative(X))))&
(((brave(alice)&curious(alice)))=>(?[X]:((happy(X)<~>~rich(X)))))&
((?[X]:((~funny(X)<~>~patient(X))))=>(?[X]:((generous(X)&patient(X)))))&
(((patient(john)|~calm(john)))<=>(?[X]:(~funny(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((curious(X)|~brave(X))))<=>(?[X]:((brave(X)<~>~happy(X)))))&
((?[X]:((~funny(X)<~>~brave(X))))=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:(brave(X)=>(~old(X)&brave(X))))&
(![X]:((humble(X)&creative(X))=>~old(X)))&
(![X]:((~happy(X)&strong(X))=>(~humble(X)&~quiet(X))))&
(![X]:((~wise(X)&tall(X))<=>(quiet(X)&~brave(X))))&
((?[X]:((~rich(X)<~>generous(X))))=>(?[X]:((brave(X)<~>~quiet(X)))))&
(![X]:((~creative(X)<~>creative(X))<=>kind(X)))&
((?[X]:((old(X)|patient(X))))<=>((wise(alice)|calm(alice))))&
(![X]:((~kind(X)|quiet(X))=>(~creative(X)&~kind(X))))&
(?[X]:((funny(X)<~>~quiet(X))))&
((~quiet(fred)&~funny(fred)))&
(?[X]:((happy(X)<~>curious(X))))&
(~funny(alice))&
((strong(fred)<~>brave(fred))) | ~creative(john) | [] | null | 0 |
Everyone who is tall is either kind or humble.
If paul is not wise or old then alice is both not creative and not patient and vice versa.
Everyone who is kind is both not old and not rich and vice versa.
Everyone who is either humble or not curious is either happy or not creative and vice versa.
If someone is either not creative or tall then john is tall.
Everyone who is not rich is not strong and vice versa.
Everyone who is humble or strong is either rich or quiet and vice versa.
If john is both not strong and not wise then john is not calm or tall.
If fred is both creative and funny then someone is either kind or generous and vice versa.
Everyone who is either brave or not quiet is happy.
Everyone who is brave is not calm and vice versa.
Everyone who is either old or strong is generous.
Everyone who is either not quiet or not kind is either old or not happy and vice versa.
If lucy is both kind and not strong then mary is not funny and vice versa.
If someone is not creative or funny then someone is either not patient or rich and vice versa.
Everyone who is brave is humble or strong and vice versa.
Someone is either patient or funny.
Someone is either happy or calm.
Paul is both not strong and humble.
John is not creative or not old.
Someone is not strong or not humble.
Someone is patient or old.
Someone is both old and not patient. | Lucy is not brave. | contradiction | (![X]:(tall(X)=>(kind(X)<~>humble(X))))&
(((~wise(paul)|old(paul)))<=>((~creative(alice)&~patient(alice))))&
(![X]:(kind(X)<=>(~old(X)&~rich(X))))&
(![X]:((humble(X)<~>~curious(X))<=>(happy(X)<~>~creative(X))))&
((?[X]:((~creative(X)<~>tall(X))))=>(tall(john)))&
(![X]:(~rich(X)<=>~strong(X)))&
(![X]:((humble(X)|strong(X))<=>(rich(X)<~>quiet(X))))&
(((~strong(john)&~wise(john)))=>((~calm(john)|tall(john))))&
(((creative(fred)&funny(fred)))<=>(?[X]:((kind(X)<~>generous(X)))))&
(![X]:((brave(X)<~>~quiet(X))=>happy(X)))&
(![X]:(brave(X)<=>~calm(X)))&
(![X]:((old(X)<~>strong(X))=>generous(X)))&
(![X]:((~quiet(X)<~>~kind(X))<=>(old(X)<~>~happy(X))))&
(((kind(lucy)&~strong(lucy)))<=>(~funny(mary)))&
((?[X]:((~creative(X)|funny(X))))<=>(?[X]:((~patient(X)<~>rich(X)))))&
(![X]:(brave(X)<=>(humble(X)|strong(X))))&
(?[X]:((patient(X)<~>funny(X))))&
(?[X]:((happy(X)<~>calm(X))))&
((~strong(paul)&humble(paul)))&
((~creative(john)|~old(john)))&
(?[X]:((~strong(X)|~humble(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((old(X)&~patient(X)))) | ~brave(lucy) | [
"p2",
"p5",
"p6",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6580349473408056268115804
% SZS output start Proof for 6580349473408056268115804
3. ! [X0] : (kind(X0) <=> (~rich(X0) & ~old(X0))) [input p2]
6. ! [X0] : (~rich(X0) <=> ~strong(X0)) [input p5]
7. ! [X0] : ((strong(X0) | humble(X0)) <=> (rich(X0) <~> quiet(X0))) [input p6]
10. ! [X0] : ((brave(X0) <~> ~quiet(X0)) => happy(X0)) [input p9]
13. ! [X0] : ((~quiet(X0) <~> ~kind(X0)) <=> (old(X0) <~> ~happy(X0))) [input p12]
16. ! [X0] : (brave(X0) <=> (strong(X0) | humble(X0))) [input p15]
24. ~brave(lucy) [input hypothesis]
30. ! [X0] : (happy(X0) | (brave(X0) <=> ~quiet(X0))) [ennf transformation 10]
35. ! [X0] : ((kind(X0) | (rich(X0) | old(X0))) & ((~rich(X0) & ~old(X0)) | ~kind(X0))) [nnf transformation 3]
36. ! [X0] : ((kind(X0) | rich(X0) | old(X0)) & ((~rich(X0) & ~old(X0)) | ~kind(X0))) [flattening 35]
39. ! [X0] : ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))) [nnf transformation 6]
40. ! [X0] : (((strong(X0) | humble(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) & (((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (~strong(X0) & ~humble(X0)))) [nnf transformation 7]
41. ! [X0] : ((strong(X0) | humble(X0) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) & (((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (~strong(X0) & ~humble(X0)))) [flattening 40]
47. ! [X0] : (happy(X0) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0)))) [nnf transformation 30]
50. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [nnf transformation 13]
58. ! [X0] : ((brave(X0) | (~strong(X0) & ~humble(X0))) & ((strong(X0) | humble(X0)) | ~brave(X0))) [nnf transformation 16]
59. ! [X0] : ((brave(X0) | (~strong(X0) & ~humble(X0))) & (strong(X0) | humble(X0) | ~brave(X0))) [flattening 58]
79. ~old(X0) | ~kind(X0) [cnf transformation 36]
81. rich(X0) | kind(X0) | old(X0) [cnf transformation 36]
93. ~rich(X0) | strong(X0) [cnf transformation 39]
99. strong(X0) | humble(X0) | rich(X0) | ~quiet(X0) [cnf transformation 41]
108. brave(X0) | happy(X0) | quiet(X0) [cnf transformation 47]
113. ~happy(X0) | old(X0) | ~kind(X0) | quiet(X0) [cnf transformation 50]
119. kind(X0) | quiet(X0) | ~happy(X0) | ~old(X0) [cnf transformation 50]
131. ~humble(X0) | brave(X0) [cnf transformation 59]
132. ~strong(X0) | brave(X0) [cnf transformation 59]
144. ~brave(lucy) [cnf transformation 24]
178. ~quiet(X0) | humble(X0) | strong(X0) [subsumption resolution 99,93]
221. ~happy(X0) | quiet(X0) | ~old(X0) [subsumption resolution 119,79]
224. ~happy(X0) | ~kind(X0) | quiet(X0) [subsumption resolution 113,79]
230. 18 <=> strong(lucy) [avatar definition]
231. strong(lucy) <- (18) [avatar component clause 230]
232. ~strong(lucy) <- (~18) [avatar component clause 230]
235. 19 <=> kind(lucy) [avatar definition]
370. strong(X0) | old(X0) | kind(X0) [resolution 81,93]
409. happy(lucy) | quiet(lucy) [resolution 108,144]
414. 50 <=> quiet(lucy) [avatar definition]
415. ~quiet(lucy) <- (~50) [avatar component clause 414]
416. quiet(lucy) <- (50) [avatar component clause 414]
418. 51 <=> happy(lucy) [avatar definition]
420. happy(lucy) <- (51) [avatar component clause 418]
421. 50 | 51 [avatar split clause 409,418,414]
466. humble(lucy) | strong(lucy) <- (50) [resolution 416,178]
470. 57 <=> humble(lucy) [avatar definition]
472. humble(lucy) <- (57) [avatar component clause 470]
473. 18 | 57 | ~50 [avatar split clause 466,414,470,230]
486. 59 <=> old(lucy) [avatar definition]
572. old(lucy) | kind(lucy) <- (~18) [resolution 370,232]
598. ~kind(lucy) | quiet(lucy) <- (51) [resolution 420,224]
599. quiet(lucy) | ~old(lucy) <- (51) [resolution 420,221]
634. brave(lucy) <- (57) [resolution 472,131]
636. $false <- (57) [subsumption resolution 634,144]
637. ~57 [avatar contradiction clause 636]
643. ~kind(lucy) <- (~50, 51) [subsumption resolution 598,415]
644. ~19 | 50 | ~51 [avatar split clause 643,418,414,235]
645. ~old(lucy) <- (~50, 51) [subsumption resolution 599,415]
646. ~59 | 50 | ~51 [avatar split clause 645,418,414,486]
647. 19 | 59 | 18 [avatar split clause 572,230,486,235]
652. brave(lucy) <- (18) [resolution 231,132]
654. $false <- (18) [subsumption resolution 652,144]
655. ~18 [avatar contradiction clause 654]
658. $false [avatar sat refutation 421,473,637,644,646,647,655]
% SZS output end Proof for 6580349473408056268115804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is patient and vice versa.
Everyone who is old is either not rich or quiet and vice versa.
Everyone who is calm is not tall.
Everyone who is brave is not patient or not happy and vice versa.
Everyone who is either not brave or curious is happy and vice versa.
If susan is either quiet or happy then someone is both not curious and not brave.
If fred is either not strong or quiet then someone is both calm and quiet and vice versa.
Everyone who is quiet is either happy or not curious and vice versa.
If someone is patient then someone is either creative or wise and vice versa.
If paul is happy or old then john is either creative or tall and vice versa.
If john is not tall or tall then lucy is either not creative or not generous and vice versa.
Everyone who is both not quiet and tall is not happy and vice versa.
Everyone who is either not brave or not wise is not curious or not funny and vice versa.
Everyone who is not calm or tall is either kind or not funny.
If someone is not tall then someone is either not calm or not tall.
Someone is either old or strong.
Someone is brave or funny.
Someone is either happy or not brave. | Susan is creative. | neutral | (![X]:(~kind(X)<=>patient(X)))&
(![X]:(old(X)<=>(~rich(X)<~>quiet(X))))&
(![X]:(calm(X)=>~tall(X)))&
(![X]:(brave(X)<=>(~patient(X)|~happy(X))))&
(![X]:((~brave(X)<~>curious(X))<=>happy(X)))&
(((quiet(susan)<~>happy(susan)))=>(?[X]:((~curious(X)&~brave(X)))))&
(((~strong(fred)<~>quiet(fred)))<=>(?[X]:((calm(X)&quiet(X)))))&
(![X]:(quiet(X)<=>(happy(X)<~>~curious(X))))&
((?[X]:(patient(X)))<=>(?[X]:((creative(X)<~>wise(X)))))&
(((happy(paul)|old(paul)))<=>((creative(john)<~>tall(john))))&
(((~tall(john)|tall(john)))<=>((~creative(lucy)<~>~generous(lucy))))&
(![X]:((~quiet(X)&tall(X))<=>~happy(X)))&
(![X]:((~brave(X)<~>~wise(X))<=>(~curious(X)|~funny(X))))&
(![X]:((~calm(X)|tall(X))=>(kind(X)<~>~funny(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~calm(X)<~>~tall(X)))))&
(?[X]:((old(X)<~>strong(X))))&
(?[X]:((brave(X)|funny(X))))&
(?[X]:((happy(X)<~>~brave(X)))) | creative(susan) | [] | null | 0 |
If john is either kind or not tall then alice is not wise or strong and vice versa.
If mary is not generous or creative then someone is not old.
If fred is curious or kind then someone is either not generous or not creative.
Everyone who is both kind and not wise is tall.
Everyone who is either calm or happy is both not wise and not curious and vice versa.
Everyone who is both tall and not old is either not kind or funny and vice versa.
If someone is either not patient or not funny then fred is both wise and strong.
Everyone who is wise or not humble is not happy and vice versa.
Everyone who is funny or not old is either generous or not patient and vice versa.
If someone is funny then paul is wise and vice versa.
If alice is both rich and tall then paul is either not calm or brave and vice versa.
Everyone who is brave or not calm is both funny and not funny.
If fred is both wise and not curious then someone is humble or not strong.
Everyone who is either patient or not happy is not creative or generous and vice versa.
If someone is not quiet then john is curious and vice versa.
Everyone who is humble or patient is calm or not patient.
Someone is not rich.
Someone is generous.
Someone is both happy and not kind. | Alice is not tall. | contradiction | (((kind(john)<~>~tall(john)))<=>((~wise(alice)|strong(alice))))&
(((~generous(mary)|creative(mary)))=>(?[X]:(~old(X))))&
(((curious(fred)|kind(fred)))=>(?[X]:((~generous(X)<~>~creative(X)))))&
(![X]:((kind(X)&~wise(X))=>tall(X)))&
(![X]:((calm(X)<~>happy(X))<=>(~wise(X)&~curious(X))))&
(![X]:((tall(X)&~old(X))<=>(~kind(X)<~>funny(X))))&
((?[X]:((~patient(X)<~>~funny(X))))=>((wise(fred)&strong(fred))))&
(![X]:((wise(X)|~humble(X))<=>~happy(X)))&
(![X]:((funny(X)|~old(X))<=>(generous(X)<~>~patient(X))))&
((?[X]:(funny(X)))<=>(wise(paul)))&
(((rich(alice)&tall(alice)))<=>((~calm(paul)<~>brave(paul))))&
(![X]:((brave(X)|~calm(X))=>(funny(X)&~funny(X))))&
(((wise(fred)&~curious(fred)))=>(?[X]:((humble(X)|~strong(X)))))&
(![X]:((patient(X)<~>~happy(X))<=>(~creative(X)|generous(X))))&
((?[X]:(~quiet(X)))<=>(curious(john)))&
(![X]:((humble(X)|patient(X))=>(calm(X)|~patient(X))))&
(?[X]:(~rich(X)))&
(?[X]:(generous(X)))&
(?[X]:((happy(X)&~kind(X)))) | ~tall(alice) | [
"p3",
"p4",
"p5",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 456943624583621381891340
% SZS output start Proof for 456943624583621381891340
4. ! [X0] : ((~wise(X0) & kind(X0)) => tall(X0)) [input p3]
5. ! [X0] : ((calm(X0) <~> happy(X0)) <=> (~curious(X0) & ~wise(X0))) [input p4]
6. ! [X0] : ((~old(X0) & tall(X0)) <=> (~kind(X0) <~> funny(X0))) [input p5]
8. ! [X0] : ((~humble(X0) | wise(X0)) <=> ~happy(X0)) [input p7]
10. ? [X0] : funny(X0) <=> wise(paul) [input p9]
12. ! [X0] : ((~calm(X0) | brave(X0)) => (~funny(X0) & funny(X0))) [input p11]
20. ~tall(alice) [input hypothesis]
23. ! [X0] : (tall(X0) | (wise(X0) | ~kind(X0))) [ennf transformation 4]
24. ! [X0] : (tall(X0) | wise(X0) | ~kind(X0)) [flattening 23]
26. ! [X0] : ((~funny(X0) & funny(X0)) | (calm(X0) & ~brave(X0))) [ennf transformation 12]
38. ! [X0] : ((((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))))) [flattening 38]
40. ! [X0] : (((~old(X0) & tall(X0)) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0)))) & (((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | (old(X0) | ~tall(X0)))) [nnf transformation 6]
41. ! [X0] : (((~old(X0) & tall(X0)) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0)))) & (((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | old(X0) | ~tall(X0))) [flattening 40]
43. ! [X0] : (((~humble(X0) | wise(X0)) | happy(X0)) & (~happy(X0) | (humble(X0) & ~wise(X0)))) [nnf transformation 8]
44. ! [X0] : ((~humble(X0) | wise(X0) | happy(X0)) & (~happy(X0) | (humble(X0) & ~wise(X0)))) [flattening 43]
47. (? [X0] : funny(X0) | ~wise(paul)) & (wise(paul) | ! [X0] : ~funny(X0)) [nnf transformation 10]
48. (? [X0] : funny(X0) | ~wise(paul)) & (wise(paul) | ! [X1] : ~funny(X1)) [rectify 47]
49. ? [X0] : funny(X0) => funny(sK2) [choice axiom]
50. (funny(sK2) | ~wise(paul)) & (wise(paul) | ! [X1] : ~funny(X1)) [skolemisation 48,49]
79. ~kind(X0) | wise(X0) | tall(X0) [cnf transformation 24]
80. ~calm(X0) | happy(X0) | ~wise(X0) [cnf transformation 39]
88. funny(X0) | tall(X0) | kind(X0) [cnf transformation 41]
96. ~happy(X0) | ~wise(X0) [cnf transformation 44]
105. wise(paul) | ~funny(X1) [cnf transformation 50]
114. funny(X0) | calm(X0) [cnf transformation 26]
116. ~funny(X0) | calm(X0) [cnf transformation 26]
132. ~tall(alice) [cnf transformation 20]
209. 16 <=> wise(paul) [avatar definition]
210. wise(paul) <- (16) [avatar component clause 209]
218. 18 <=> ! [X1] : ~funny(X1) [avatar definition]
219. ~funny(X1) <- (18) [avatar component clause 218]
220. 18 | 16 [avatar split clause 105,209,218]
230. 21 <=> tall(alice) [avatar definition]
231. ~tall(alice) <- (~21) [avatar component clause 230]
243. calm(X0) [subsumption resolution 114,116]
267. ~21 [avatar split clause 132,230]
277. happy(X0) | ~wise(X0) [resolution 80,243]
278. ~wise(X0) [subsumption resolution 277,96]
279. $false <- (16) [resolution 278,210]
280. ~16 [avatar contradiction clause 279]
291. tall(X0) | kind(X0) <- (18) [resolution 88,219]
297. kind(alice) <- (18, ~21) [resolution 291,231]
303. wise(alice) | tall(alice) <- (18, ~21) [resolution 297,79]
304. tall(alice) <- (18, ~21) [subsumption resolution 303,278]
305. $false <- (18, ~21) [subsumption resolution 304,231]
306. ~18 | 21 [avatar contradiction clause 305]
307. $false [avatar sat refutation 220,267,280,306]
% SZS output end Proof for 456943624583621381891340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or rich then lucy is either happy or patient.
If someone is not kind then paul is both not strong and kind and vice versa.
Everyone who is both not tall and brave is not old and vice versa.
Everyone who is both not funny and wise is patient or rich.
Everyone who is either not kind or not old is both not curious and patient and vice versa.
Everyone who is not curious or not generous is both curious and not creative and vice versa.
If mary is humble or not creative then someone is strong and vice versa.
If someone is either not calm or patient then someone is happy.
Everyone who is happy is not funny or funny.
If someone is not creative or quiet then mary is not humble or not happy and vice versa.
Everyone who is both not curious and humble is either not funny or patient and vice versa.
If someone is not funny then someone is not humble or not creative and vice versa.
Everyone who is not creative is either not old or not generous.
Everyone who is either humble or not strong is not tall.
Everyone who is both not strong and creative is not generous and vice versa.
If lucy is not calm then someone is happy or not rich and vice versa.
Alice is not tall.
Someone is curious or not generous.
Someone is not generous or not brave.
John is either quiet or not happy. | John is not tall. | neutral | ((?[X]:((old(X)<~>rich(X))))=>((happy(lucy)<~>patient(lucy))))&
((?[X]:(~kind(X)))<=>((~strong(paul)&kind(paul))))&
(![X]:((~tall(X)&brave(X))<=>~old(X)))&
(![X]:((~funny(X)&wise(X))=>(patient(X)|rich(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(~curious(X)&patient(X))))&
(![X]:((~curious(X)|~generous(X))<=>(curious(X)&~creative(X))))&
(((humble(mary)|~creative(mary)))<=>(?[X]:(strong(X))))&
((?[X]:((~calm(X)<~>patient(X))))=>(?[X]:(happy(X))))&
(![X]:(happy(X)=>(~funny(X)|funny(X))))&
((?[X]:((~creative(X)|quiet(X))))<=>((~humble(mary)|~happy(mary))))&
(![X]:((~curious(X)&humble(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~humble(X)|~creative(X)))))&
(![X]:(~creative(X)=>(~old(X)<~>~generous(X))))&
(![X]:((humble(X)<~>~strong(X))=>~tall(X)))&
(![X]:((~strong(X)&creative(X))<=>~generous(X)))&
((~calm(lucy))<=>(?[X]:((happy(X)|~rich(X)))))&
(~tall(alice))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((~generous(X)|~brave(X))))&
((quiet(john)<~>~happy(john))) | ~tall(john) | [] | null | 0 |
If someone is either not rich or not quiet then john is both not calm and strong.
Everyone who is both creative and quiet is happy and vice versa.
Everyone who is kind or creative is either not old or not curious.
Everyone who is patient or wise is creative or humble and vice versa.
If alice is creative or not funny then paul is calm or kind and vice versa.
Everyone who is strong is either not brave or calm and vice versa.
Everyone who is not old is both calm and not calm.
If someone is either humble or quiet then someone is not humble or not strong and vice versa.
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.
Everyone who is not strong or happy is either not kind or not happy and vice versa.
Everyone who is both calm and not calm is either not happy or not kind.
Everyone who is not rich or creative is either not rich or not quiet.
If susan is not generous then someone is not old or creative and vice versa.
Paul is either not patient or not quiet.
Someone is either generous or not humble.
Susan is humble.
Paul is not calm.
Alice is either not humble or not strong. | Paul is rich. | entailment | ((?[X]:((~rich(X)<~>~quiet(X))))=>((~calm(john)&strong(john))))&
(![X]:((creative(X)&quiet(X))<=>happy(X)))&
(![X]:((kind(X)|creative(X))=>(~old(X)<~>~curious(X))))&
(![X]:((patient(X)|wise(X))<=>(creative(X)|humble(X))))&
(((creative(alice)|~funny(alice)))<=>((calm(paul)|kind(paul))))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:(~old(X)=>(calm(X)&~calm(X))))&
((?[X]:((humble(X)<~>quiet(X))))<=>(?[X]:((~humble(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)|happy(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:((calm(X)&~calm(X))=>(~happy(X)<~>~kind(X))))&
(![X]:((~rich(X)|creative(X))=>(~rich(X)<~>~quiet(X))))&
((~generous(susan))<=>(?[X]:((~old(X)|creative(X)))))&
((~patient(paul)<~>~quiet(paul)))&
(?[X]:((generous(X)<~>~humble(X))))&
(humble(susan))&
(~calm(paul))&
((~humble(alice)<~>~strong(alice))) | rich(paul) | [
"p6",
"p8",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3873292775757152176718029
% SZS output start Proof for 3873292775757152176718029
7. ! [X0] : (~old(X0) => (~calm(X0) & calm(X0))) [input p6]
9. ? [X0] : (~patient(X0) <~> rich(X0)) => (~strong(mary) & ~quiet(mary)) [input p8]
10. ! [X0] : ((~old(X0) & ~curious(X0)) <=> ~quiet(X0)) [input p9]
17. ~patient(paul) <~> ~quiet(paul) [input p16]
22. ~rich(paul) [input hypothesis]
26. ! [X0] : ((~calm(X0) & calm(X0)) | old(X0)) [ennf transformation 7]
27. (~strong(mary) & ~quiet(mary)) | ! [X0] : (~patient(X0) <=> rich(X0)) [ennf transformation 9]
48. (~strong(mary) & ~quiet(mary)) | ! [X0] : ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0))) [nnf transformation 27]
49. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | (old(X0) | curious(X0)))) [nnf transformation 10]
50. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | old(X0) | curious(X0))) [flattening 49]
59. (quiet(paul) | patient(paul)) & (~quiet(paul) | ~patient(paul)) [nnf transformation 17]
87. calm(X0) | old(X0) [cnf transformation 26]
88. ~calm(X0) | old(X0) [cnf transformation 26]
95. ~quiet(mary) | rich(X0) | patient(X0) [cnf transformation 48]
101. ~old(X0) | quiet(X0) [cnf transformation 50]
120. ~quiet(paul) | ~patient(paul) [cnf transformation 59]
128. ~rich(paul) [cnf transformation 22]
170. old(X0) [subsumption resolution 87,88]
214. 19 <=> ! [X0] : (rich(X0) | patient(X0)) [avatar definition]
215. patient(X0) | rich(X0) <- (19) [avatar component clause 214]
218. 20 <=> quiet(mary) [avatar definition]
220. ~quiet(mary) <- (~20) [avatar component clause 218]
222. 19 | ~20 [avatar split clause 95,218,214]
223. quiet(X0) [subsumption resolution 101,170]
257. ~patient(paul) [subsumption resolution 120,223]
279. $false <- (~20) [subsumption resolution 220,223]
280. 20 [avatar contradiction clause 279]
283. rich(paul) <- (19) [resolution 215,257]
285. $false <- (19) [subsumption resolution 283,128]
286. ~19 [avatar contradiction clause 285]
287. $false [avatar sat refutation 222,280,286]
% SZS output end Proof for 3873292775757152176718029
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or wise is wise.
Everyone who is either not wise or calm is either not curious or not strong and vice versa.
Everyone who is both wise and not curious is both not curious and tall.
Everyone who is both kind and not wise is either patient or creative.
If someone is not creative then someone is creative or wise and vice versa.
Everyone who is either not happy or not wise is both humble and rich.
If paul is brave then someone is funny or not quiet.
Everyone who is happy is both not rich and not curious and vice versa.
Everyone who is humble or creative is both humble and patient and vice versa.
Everyone who is both not wise and kind is both happy and not wise and vice versa.
Everyone who is both not old and rich is either humble or happy.
Everyone who is not curious or not tall is either patient or not happy and vice versa.
Everyone who is not creative or not happy is either funny or creative.
If someone is calm then someone is both humble and patient and vice versa.
Everyone who is either not humble or generous is both humble and not creative.
Everyone who is not rich or not strong is both not funny and humble and vice versa.
Someone is either not quiet or kind.
Someone is not wise.
Mary is curious or patient.
Someone is curious.
Fred is both not kind and happy.
Someone is tall.
Mary is either quiet or not happy.
Someone is either not humble or humble. | Fred is creative. | entailment | (![X]:((generous(X)<~>wise(X))=>wise(X)))&
(![X]:((~wise(X)<~>calm(X))<=>(~curious(X)<~>~strong(X))))&
(![X]:((wise(X)&~curious(X))=>(~curious(X)&tall(X))))&
(![X]:((kind(X)&~wise(X))=>(patient(X)<~>creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((~happy(X)<~>~wise(X))=>(humble(X)&rich(X))))&
((brave(paul))=>(?[X]:((funny(X)|~quiet(X)))))&
(![X]:(happy(X)<=>(~rich(X)&~curious(X))))&
(![X]:((humble(X)|creative(X))<=>(humble(X)&patient(X))))&
(![X]:((~wise(X)&kind(X))<=>(happy(X)&~wise(X))))&
(![X]:((~old(X)&rich(X))=>(humble(X)<~>happy(X))))&
(![X]:((~curious(X)|~tall(X))<=>(patient(X)<~>~happy(X))))&
(![X]:((~creative(X)|~happy(X))=>(funny(X)<~>creative(X))))&
((?[X]:(calm(X)))<=>(?[X]:((humble(X)&patient(X)))))&
(![X]:((~humble(X)<~>generous(X))=>(humble(X)&~creative(X))))&
(![X]:((~rich(X)|~strong(X))<=>(~funny(X)&humble(X))))&
(?[X]:((~quiet(X)<~>kind(X))))&
(?[X]:(~wise(X)))&
((curious(mary)|patient(mary)))&
(?[X]:(curious(X)))&
((~kind(fred)&happy(fred)))&
(?[X]:(tall(X)))&
((quiet(mary)<~>~happy(mary)))&
(?[X]:((~humble(X)<~>humble(X)))) | creative(fred) | [
"p7",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8131350111264230820447101
% SZS output start Proof for 8131350111264230820447101
8. ! [X0] : (happy(X0) <=> (~curious(X0) & ~rich(X0))) [input p7]
13. ! [X0] : ((~happy(X0) | ~creative(X0)) => (funny(X0) <~> creative(X0))) [input p12]
16. ! [X0] : ((~strong(X0) | ~rich(X0)) <=> (humble(X0) & ~funny(X0))) [input p15]
21. happy(fred) & ~kind(fred) [input p20]
25. ~creative(fred) [input hypothesis]
36. ! [X0] : ((funny(X0) <~> creative(X0)) | (happy(X0) & creative(X0))) [ennf transformation 13]
47. ! [X0] : ((happy(X0) | (curious(X0) | rich(X0))) & ((~curious(X0) & ~rich(X0)) | ~happy(X0))) [nnf transformation 8]
48. ! [X0] : ((happy(X0) | curious(X0) | rich(X0)) & ((~curious(X0) & ~rich(X0)) | ~happy(X0))) [flattening 47]
55. ! [X0] : (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (happy(X0) & creative(X0))) [nnf transformation 36]
62. ! [X0] : (((~strong(X0) | ~rich(X0)) | (~humble(X0) | funny(X0))) & ((humble(X0) & ~funny(X0)) | (strong(X0) & rich(X0)))) [nnf transformation 16]
63. ! [X0] : ((~strong(X0) | ~rich(X0) | ~humble(X0) | funny(X0)) & ((humble(X0) & ~funny(X0)) | (strong(X0) & rich(X0)))) [flattening 62]
98. ~rich(X0) | ~happy(X0) [cnf transformation 48]
116. creative(X0) | funny(X0) | creative(X0) [cnf transformation 55]
127. ~funny(X0) | rich(X0) [cnf transformation 63]
138. happy(fred) [cnf transformation 21]
144. ~creative(fred) [cnf transformation 25]
146. funny(X0) | creative(X0) [duplicate literal removal 116]
241. rich(X1) | creative(X1) [resolution 146,127]
401. ~happy(X0) | creative(X0) [resolution 241,98]
490. creative(fred) [resolution 401,138]
493. $false [subsumption resolution 490,144]
% SZS output end Proof for 8131350111264230820447101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not funny is rich.
Everyone who is funny is not rich or not kind and vice versa.
If someone is both not creative and not generous then fred is either wise or not wise and vice versa.
Everyone who is kind is strong and vice versa.
Everyone who is both happy and old is both not kind and strong.
Everyone who is both not tall and brave is funny.
Everyone who is either not funny or wise is both not calm and kind and vice versa.
Everyone who is either patient or not curious is old.
If someone is not patient or rich then someone is both curious and brave.
If john is either not old or not quiet then mary is both not old and not creative and vice versa.
If alice is not wise or not kind then someone is not creative and vice versa.
Everyone who is both tall and generous is both not kind and not generous.
Everyone who is tall or happy is either patient or tall and vice versa.
Everyone who is both not happy and quiet is either not patient or kind and vice versa.
If susan is not wise or generous then someone is either wise or curious.
Everyone who is old is kind or not rich.
Fred is either humble or creative.
Someone is old or calm.
Someone is kind.
Someone is both calm and not funny.
Someone is not wise.
Someone is kind or not wise.
Someone is both not strong and not tall.
Someone is both not rich and not patient. | John is not old. | neutral | (![X]:((~kind(X)&~funny(X))=>rich(X)))&
(![X]:(funny(X)<=>(~rich(X)|~kind(X))))&
((?[X]:((~creative(X)&~generous(X))))<=>((wise(fred)<~>~wise(fred))))&
(![X]:(kind(X)<=>strong(X)))&
(![X]:((happy(X)&old(X))=>(~kind(X)&strong(X))))&
(![X]:((~tall(X)&brave(X))=>funny(X)))&
(![X]:((~funny(X)<~>wise(X))<=>(~calm(X)&kind(X))))&
(![X]:((patient(X)<~>~curious(X))=>old(X)))&
((?[X]:((~patient(X)|rich(X))))=>(?[X]:((curious(X)&brave(X)))))&
(((~old(john)<~>~quiet(john)))<=>((~old(mary)&~creative(mary))))&
(((~wise(alice)|~kind(alice)))<=>(?[X]:(~creative(X))))&
(![X]:((tall(X)&generous(X))=>(~kind(X)&~generous(X))))&
(![X]:((tall(X)|happy(X))<=>(patient(X)<~>tall(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~patient(X)<~>kind(X))))&
(((~wise(susan)|generous(susan)))=>(?[X]:((wise(X)<~>curious(X)))))&
(![X]:(old(X)=>(kind(X)|~rich(X))))&
((humble(fred)<~>creative(fred)))&
(?[X]:((old(X)|calm(X))))&
(?[X]:(kind(X)))&
(?[X]:((calm(X)&~funny(X))))&
(?[X]:(~wise(X)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~strong(X)&~tall(X))))&
(?[X]:((~rich(X)&~patient(X)))) | ~old(john) | [] | null | 0 |
If someone is old or not funny then someone is either creative or funny and vice versa.
If someone is either humble or not happy then someone is either curious or not tall and vice versa.
Everyone who is brave or not funny is not tall and vice versa.
If someone is not rich or not generous then susan is calm or not generous and vice versa.
Everyone who is either patient or brave is both quiet and not curious and vice versa.
Everyone who is not generous is both not patient and not happy.
Everyone who is patient or humble is either not happy or not creative.
If alice is not tall or humble then susan is curious and vice versa.
Everyone who is not old is either not old or not rich.
Everyone who is generous or strong is wise and vice versa.
If mary is not old then someone is not funny or old.
If lucy is both happy and curious then someone is not generous and vice versa.
If someone is wise or not old then someone is happy or quiet.
Everyone who is either not kind or not patient is both old and happy.
If someone is both old and rich then susan is not calm or happy and vice versa.
If alice is generous or old then mary is either not strong or not old and vice versa.
Someone is both not calm and not quiet.
Someone is both not curious and rich.
Fred is both generous and not kind.
Fred is not wise or creative.
Someone is not funny or old.
Susan is tall or quiet.
Lucy is either not funny or wise.
Someone is kind. | Susan is generous. | neutral | ((?[X]:((old(X)|~funny(X))))<=>(?[X]:((creative(X)<~>funny(X)))))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((brave(X)|~funny(X))<=>~tall(X)))&
((?[X]:((~rich(X)|~generous(X))))<=>((calm(susan)|~generous(susan))))&
(![X]:((patient(X)<~>brave(X))<=>(quiet(X)&~curious(X))))&
(![X]:(~generous(X)=>(~patient(X)&~happy(X))))&
(![X]:((patient(X)|humble(X))=>(~happy(X)<~>~creative(X))))&
(((~tall(alice)|humble(alice)))<=>(curious(susan)))&
(![X]:(~old(X)=>(~old(X)<~>~rich(X))))&
(![X]:((generous(X)|strong(X))<=>wise(X)))&
((~old(mary))=>(?[X]:((~funny(X)|old(X)))))&
(((happy(lucy)&curious(lucy)))<=>(?[X]:(~generous(X))))&
((?[X]:((wise(X)|~old(X))))=>(?[X]:((happy(X)|quiet(X)))))&
(![X]:((~kind(X)<~>~patient(X))=>(old(X)&happy(X))))&
((?[X]:((old(X)&rich(X))))<=>((~calm(susan)|happy(susan))))&
(((generous(alice)|old(alice)))<=>((~strong(mary)<~>~old(mary))))&
(?[X]:((~calm(X)&~quiet(X))))&
(?[X]:((~curious(X)&rich(X))))&
((generous(fred)&~kind(fred)))&
((~wise(fred)|creative(fred)))&
(?[X]:((~funny(X)|old(X))))&
((tall(susan)|quiet(susan)))&
((~funny(lucy)<~>wise(lucy)))&
(?[X]:(kind(X))) | generous(susan) | [] | null | 0 |
Everyone who is patient or not creative is kind or creative and vice versa.
If alice is not calm or curious then someone is not curious or not old and vice versa.
Everyone who is humble is either not tall or not old.
If someone is not old then someone is either not brave or quiet and vice versa.
Everyone who is old is both wise and not rich and vice versa.
Everyone who is patient or old is both quiet and not kind.
Everyone who is not patient or not wise is either quiet or old and vice versa.
Everyone who is both not calm and calm is either calm or humble.
Everyone who is calm is either not old or rich.
Everyone who is not curious or rich is either not rich or tall.
Everyone who is not wise or not patient is either kind or humble and vice versa.
Everyone who is happy is either not curious or not old and vice versa.
Everyone who is both not humble and happy is humble or curious and vice versa.
Everyone who is not wise is not curious.
If fred is either calm or not quiet then lucy is both not patient and wise.
Everyone who is not wise is either not kind or not creative and vice versa.
Someone is either creative or strong.
Fred is either not strong or creative.
Alice is not calm.
Fred is not creative.
Susan is either creative or not brave.
Paul is not brave or humble. | Lucy is creative. | contradiction | (![X]:((patient(X)|~creative(X))<=>(kind(X)|creative(X))))&
(((~calm(alice)|curious(alice)))<=>(?[X]:((~curious(X)|~old(X)))))&
(![X]:(humble(X)=>(~tall(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:(old(X)<=>(wise(X)&~rich(X))))&
(![X]:((patient(X)|old(X))=>(quiet(X)&~kind(X))))&
(![X]:((~patient(X)|~wise(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~calm(X)&calm(X))=>(calm(X)<~>humble(X))))&
(![X]:(calm(X)=>(~old(X)<~>rich(X))))&
(![X]:((~curious(X)|rich(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~wise(X)|~patient(X))<=>(kind(X)<~>humble(X))))&
(![X]:(happy(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((~humble(X)&happy(X))<=>(humble(X)|curious(X))))&
(![X]:(~wise(X)=>~curious(X)))&
(((calm(fred)<~>~quiet(fred)))=>((~patient(lucy)&wise(lucy))))&
(![X]:(~wise(X)<=>(~kind(X)<~>~creative(X))))&
(?[X]:((creative(X)<~>strong(X))))&
((~strong(fred)<~>creative(fred)))&
(~calm(alice))&
(~creative(fred))&
((creative(susan)<~>~brave(susan)))&
((~brave(paul)|humble(paul))) | creative(lucy) | [
"p0",
"p5",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3810525206297307647471840
% SZS output start Proof for 3810525206297307647471840
1. ! [X0] : ((~creative(X0) | patient(X0)) <=> (creative(X0) | kind(X0))) [input p0]
6. ! [X0] : ((old(X0) | patient(X0)) => (~kind(X0) & quiet(X0))) [input p5]
11. ! [X0] : ((~patient(X0) | ~wise(X0)) <=> (kind(X0) <~> humble(X0))) [input p10]
13. ! [X0] : ((happy(X0) & ~humble(X0)) <=> (curious(X0) | humble(X0))) [input p12]
16. ! [X0] : (~wise(X0) <=> (~kind(X0) <~> ~creative(X0))) [input p15]
23. creative(lucy) [input hypothesis]
26. ! [X0] : ((~kind(X0) & quiet(X0)) | (~old(X0) & ~patient(X0))) [ennf transformation 6]
33. ! [X0] : (((~creative(X0) | patient(X0)) | (~creative(X0) & ~kind(X0))) & ((creative(X0) | kind(X0)) | (creative(X0) & ~patient(X0)))) [nnf transformation 1]
34. ! [X0] : ((~creative(X0) | patient(X0) | (~creative(X0) & ~kind(X0))) & (creative(X0) | kind(X0) | (creative(X0) & ~patient(X0)))) [flattening 33]
53. ! [X0] : (((~patient(X0) | ~wise(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (patient(X0) & wise(X0)))) [nnf transformation 11]
54. ! [X0] : ((~patient(X0) | ~wise(X0) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (patient(X0) & wise(X0)))) [flattening 53]
56. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (~happy(X0) | humble(X0)))) [nnf transformation 13]
57. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | ~happy(X0) | humble(X0))) [flattening 56]
59. ! [X0] : ((~wise(X0) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0)))) & (((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | wise(X0))) [nnf transformation 16]
66. creative(X0) | kind(X0) | creative(X0) [cnf transformation 34]
68. ~creative(X0) | patient(X0) | ~creative(X0) [cnf transformation 34]
84. ~kind(X0) | ~patient(X0) [cnf transformation 26]
100. wise(X0) | kind(X0) | humble(X0) [cnf transformation 54]
111. ~humble(X0) | ~humble(X0) [cnf transformation 57]
122. ~wise(X0) | ~creative(X0) | kind(X0) [cnf transformation 59]
133. creative(lucy) [cnf transformation 23]
135. ~humble(X0) [duplicate literal removal 111]
139. kind(X0) | creative(X0) [duplicate literal removal 66]
140. ~creative(X0) | patient(X0) [duplicate literal removal 68]
211. 14 <=> patient(lucy) [avatar definition]
212. patient(lucy) <- (14) [avatar component clause 211]
216. ~wise(X0) | kind(X0) [subsumption resolution 122,139]
253. patient(lucy) [resolution 140,133]
255. 14 [avatar split clause 253,211]
264. kind(X1) | humble(X1) | kind(X1) [resolution 100,216]
266. kind(X1) | humble(X1) [duplicate literal removal 264]
268. kind(X1) [subsumption resolution 266,135]
269. ~patient(X0) [resolution 268,84]
275. $false <- (14) [resolution 269,212]
278. ~14 [avatar contradiction clause 275]
279. $false [avatar sat refutation 255,278]
% SZS output end Proof for 3810525206297307647471840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both creative and generous then someone is either funny or tall.
If paul is both not calm and not creative then lucy is either old or calm.
Everyone who is brave is not generous and vice versa.
If paul is not calm then someone is either not wise or kind.
If john is either brave or not funny then alice is not old or not humble.
Everyone who is either strong or not strong is both not kind and not happy and vice versa.
Everyone who is either tall or not generous is both not patient and funny.
If lucy is both not quiet and not tall then susan is both strong and not brave.
Everyone who is either humble or generous is both creative and not wise.
Everyone who is both not kind and not wise is both not creative and not humble and vice versa.
If lucy is both brave and not creative then john is strong.
Everyone who is both rich and patient is not tall.
If someone is not funny or patient then someone is generous or not funny.
If susan is both not funny and not patient then alice is brave.
Everyone who is not curious or not happy is either calm or rich.
Everyone who is funny or old is either generous or not calm and vice versa.
Someone is quiet or old.
Alice is both not tall and calm.
Someone is curious.
Lucy is not tall.
Fred is either not old or wise.
Paul is both funny and calm.
Mary is both wise and not humble.
Someone is calm. | Susan is not brave. | neutral | (((creative(paul)&generous(paul)))=>(?[X]:((funny(X)<~>tall(X)))))&
(((~calm(paul)&~creative(paul)))=>((old(lucy)<~>calm(lucy))))&
(![X]:(brave(X)<=>~generous(X)))&
((~calm(paul))=>(?[X]:((~wise(X)<~>kind(X)))))&
(((brave(john)<~>~funny(john)))=>((~old(alice)|~humble(alice))))&
(![X]:((strong(X)<~>~strong(X))<=>(~kind(X)&~happy(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~patient(X)&funny(X))))&
(((~quiet(lucy)&~tall(lucy)))=>((strong(susan)&~brave(susan))))&
(![X]:((humble(X)<~>generous(X))=>(creative(X)&~wise(X))))&
(![X]:((~kind(X)&~wise(X))<=>(~creative(X)&~humble(X))))&
(((brave(lucy)&~creative(lucy)))=>(strong(john)))&
(![X]:((rich(X)&patient(X))=>~tall(X)))&
((?[X]:((~funny(X)|patient(X))))=>(?[X]:((generous(X)|~funny(X)))))&
(((~funny(susan)&~patient(susan)))=>(brave(alice)))&
(![X]:((~curious(X)|~happy(X))=>(calm(X)<~>rich(X))))&
(![X]:((funny(X)|old(X))<=>(generous(X)<~>~calm(X))))&
(?[X]:((quiet(X)|old(X))))&
((~tall(alice)&calm(alice)))&
(?[X]:(curious(X)))&
(~tall(lucy))&
((~old(fred)<~>wise(fred)))&
((funny(paul)&calm(paul)))&
((wise(mary)&~humble(mary)))&
(?[X]:(calm(X))) | ~brave(susan) | [] | null | 0 |
If someone is not patient or quiet then someone is not humble or not generous and vice versa.
If someone is both not calm and not humble then susan is not tall or happy.
If someone is either not calm or not humble then mary is both brave and not happy and vice versa.
If someone is not generous or old then fred is either not patient or calm.
If fred is not patient then paul is either not rich or happy.
If someone is not old or not creative then someone is old or rich.
Everyone who is not funny is either not humble or kind and vice versa.
Everyone who is either not happy or funny is either not funny or not tall and vice versa.
Everyone who is either not tall or kind is either humble or not quiet.
If paul is both creative and humble then someone is not curious and vice versa.
If someone is not curious or not calm then someone is both quiet and not generous.
Everyone who is either generous or not funny is both generous and not curious and vice versa.
If someone is either rich or not brave then someone is both patient and tall.
If someone is patient or not wise then alice is strong.
Everyone who is not wise is both not funny and generous and vice versa.
If someone is old or not old then someone is both not old and wise.
Paul is humble or not generous.
Someone is not quiet or humble.
Susan is quiet or wise.
Mary is both brave and generous.
Fred is either not wise or humble.
Alice is not patient or not creative.
Paul is both happy and rich.
Someone is kind or happy. | Fred is not kind. | entailment | ((?[X]:((~patient(X)|quiet(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
((?[X]:((~calm(X)&~humble(X))))=>((~tall(susan)|happy(susan))))&
((?[X]:((~calm(X)<~>~humble(X))))<=>((brave(mary)&~happy(mary))))&
((?[X]:((~generous(X)|old(X))))=>((~patient(fred)<~>calm(fred))))&
((~patient(fred))=>((~rich(paul)<~>happy(paul))))&
((?[X]:((~old(X)|~creative(X))))=>(?[X]:((old(X)|rich(X)))))&
(![X]:(~funny(X)<=>(~humble(X)<~>kind(X))))&
(![X]:((~happy(X)<~>funny(X))<=>(~funny(X)<~>~tall(X))))&
(![X]:((~tall(X)<~>kind(X))=>(humble(X)<~>~quiet(X))))&
(((creative(paul)&humble(paul)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)|~calm(X))))=>(?[X]:((quiet(X)&~generous(X)))))&
(![X]:((generous(X)<~>~funny(X))<=>(generous(X)&~curious(X))))&
((?[X]:((rich(X)<~>~brave(X))))=>(?[X]:((patient(X)&tall(X)))))&
((?[X]:((patient(X)|~wise(X))))=>(strong(alice)))&
(![X]:(~wise(X)<=>(~funny(X)&generous(X))))&
((?[X]:((old(X)|~old(X))))=>(?[X]:((~old(X)&wise(X)))))&
((humble(paul)|~generous(paul)))&
(?[X]:((~quiet(X)|humble(X))))&
((quiet(susan)|wise(susan)))&
((brave(mary)&generous(mary)))&
((~wise(fred)<~>humble(fred)))&
((~patient(alice)|~creative(alice)))&
((happy(paul)&rich(paul)))&
(?[X]:((kind(X)|happy(X)))) | ~kind(fred) | [
"p6",
"p11",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1618708077151722382469995
% SZS output start Proof for 1618708077151722382469995
7. ! [X0] : (~funny(X0) <=> (~humble(X0) <~> kind(X0))) [input p6]
12. ! [X0] : ((generous(X0) <~> ~funny(X0)) <=> (~curious(X0) & generous(X0))) [input p11]
15. ! [X0] : (~wise(X0) <=> (generous(X0) & ~funny(X0))) [input p14]
21. ~wise(fred) <~> humble(fred) [input p20]
25. kind(fred) [input hypothesis]
56. ! [X0] : ((~funny(X0) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0)))) & (((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | funny(X0))) [nnf transformation 7]
67. ! [X0] : ((((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (curious(X0) | ~generous(X0))) & ((~curious(X0) & generous(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))))) [nnf transformation 12]
68. ! [X0] : ((((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | curious(X0) | ~generous(X0)) & ((~curious(X0) & generous(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))))) [flattening 67]
73. ! [X0] : ((~wise(X0) | (~generous(X0) | funny(X0))) & ((generous(X0) & ~funny(X0)) | wise(X0))) [nnf transformation 15]
74. ! [X0] : ((~wise(X0) | ~generous(X0) | funny(X0)) & ((generous(X0) & ~funny(X0)) | wise(X0))) [flattening 73]
80. (~humble(fred) | wise(fred)) & (humble(fred) | ~wise(fred)) [nnf transformation 21]
103. ~kind(X0) | humble(X0) | funny(X0) [cnf transformation 56]
105. ~kind(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 56]
126. generous(X0) | generous(X0) | funny(X0) [cnf transformation 68]
135. ~funny(X0) | wise(X0) [cnf transformation 74]
137. ~wise(X0) | ~generous(X0) | funny(X0) [cnf transformation 74]
147. humble(fred) | ~wise(fred) [cnf transformation 80]
148. ~humble(fred) | wise(fred) [cnf transformation 80]
153. kind(fred) [cnf transformation 25]
154. funny(X0) | generous(X0) [duplicate literal removal 126]
326. ~wise(X0) | funny(X0) [subsumption resolution 137,154]
364. 45 <=> wise(fred) [avatar definition]
365. ~wise(fred) <- (~45) [avatar component clause 364]
366. wise(fred) <- (45) [avatar component clause 364]
368. 46 <=> humble(fred) [avatar definition]
369. humble(fred) <- (46) [avatar component clause 368]
370. ~humble(fred) <- (~46) [avatar component clause 368]
371. 45 | ~46 [avatar split clause 148,368,364]
372. ~45 | 46 [avatar split clause 147,368,364]
424. humble(fred) | funny(fred) [resolution 103,153]
426. funny(fred) <- (~46) [subsumption resolution 424,370]
449. wise(fred) <- (~46) [resolution 426,135]
450. $false <- (~45, ~46) [subsumption resolution 449,365]
451. 45 | 46 [avatar contradiction clause 450]
453. 57 <=> funny(fred) [avatar definition]
455. funny(fred) <- (57) [avatar component clause 453]
456. 57 | 46 [avatar split clause 424,368,453]
457. funny(fred) <- (45) [resolution 366,326]
458. 57 | ~45 [avatar split clause 457,364,453]
460. ~humble(fred) | ~funny(fred) [resolution 105,153]
463. ~funny(fred) <- (46) [subsumption resolution 460,369]
464. $false <- (46, 57) [subsumption resolution 463,455]
465. ~46 | ~57 [avatar contradiction clause 464]
470. $false [avatar sat refutation 371,372,451,456,458,465]
% SZS output end Proof for 1618708077151722382469995
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or quiet is either not patient or strong and vice versa.
If someone is either not quiet or not creative then someone is creative or not rich and vice versa.
Everyone who is both brave and not happy is either not humble or calm and vice versa.
Everyone who is tall or not curious is not tall or generous and vice versa.
Everyone who is not creative or not kind is both patient and not kind.
Everyone who is not calm is happy or rich and vice versa.
Everyone who is curious is both not strong and quiet and vice versa.
Everyone who is not humble or calm is either creative or happy and vice versa.
Everyone who is both calm and not humble is not rich and vice versa.
Everyone who is happy is not rich or not calm and vice versa.
If someone is both not funny and creative then someone is both not calm and not old.
Everyone who is both kind and old is both funny and not wise.
Everyone who is kind is both not kind and not strong.
Everyone who is both not quiet and not patient is both humble and not strong and vice versa.
If someone is both patient and humble then someone is either not patient or not tall and vice versa.
Someone is not curious or humble.
Mary is brave or not funny.
Someone is not wise.
Someone is not kind.
Someone is old. | Mary is tall. | neutral | (![X]:((old(X)|quiet(X))<=>(~patient(X)<~>strong(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))<=>(?[X]:((creative(X)|~rich(X)))))&
(![X]:((brave(X)&~happy(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((tall(X)|~curious(X))<=>(~tall(X)|generous(X))))&
(![X]:((~creative(X)|~kind(X))=>(patient(X)&~kind(X))))&
(![X]:(~calm(X)<=>(happy(X)|rich(X))))&
(![X]:(curious(X)<=>(~strong(X)&quiet(X))))&
(![X]:((~humble(X)|calm(X))<=>(creative(X)<~>happy(X))))&
(![X]:((calm(X)&~humble(X))<=>~rich(X)))&
(![X]:(happy(X)<=>(~rich(X)|~calm(X))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((kind(X)&old(X))=>(funny(X)&~wise(X))))&
(![X]:(kind(X)=>(~kind(X)&~strong(X))))&
(![X]:((~quiet(X)&~patient(X))<=>(humble(X)&~strong(X))))&
((?[X]:((patient(X)&humble(X))))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
(?[X]:((~curious(X)|humble(X))))&
((brave(mary)|~funny(mary)))&
(?[X]:(~wise(X)))&
(?[X]:(~kind(X)))&
(?[X]:(old(X))) | tall(mary) | [] | null | 0 |
If someone is not humble or not happy then alice is both not generous and not rich. If fred is both happy and strong then susan is not curious. If paul is either tall or not old then mary is not tall. If someone is either not funny or funny then someone is either not kind or old. Everyone who is either happy or brave is either not patient or not kind and vice versa. If someone is either wise or tall then someone is both happy and tall and vice versa. Everyone who is both not rich and wise is either creative or not creative and vice versa. Everyone who is either rich or not curious is not brave and vice versa. Everyone who is kind or brave is both not quiet and patient. Everyone who is both not tall and not curious is strong. Everyone who is not happy or brave is not tall or not humble and vice versa. Everyone who is not curious or not funny is both not brave and not humble and vice versa. Everyone who is both not patient and not funny is not old or not curious and vice versa. Everyone who is patient is both tall and quiet and vice versa. If susan is both not calm and not generous then susan is old or brave. If someone is either patient or quiet then someone is not rich or brave. Someone is either not creative or not kind. Someone is strong. Mary is either not generous or not old. Someone is both not quiet and not funny. Someone is happy or wise. | Alice is not humble. | entailment | ((?[X]:((~humble(X)|~happy(X))))=>((~generous(alice)&~rich(alice))))&
(((happy(fred)&strong(fred)))=>(~curious(susan)))&
(((tall(paul)<~>~old(paul)))=>(~tall(mary)))&
((?[X]:((~funny(X)<~>funny(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(~patient(X)<~>~kind(X))))&
((?[X]:((wise(X)<~>tall(X))))<=>(?[X]:((happy(X)&tall(X)))))&
(![X]:((~rich(X)&wise(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((rich(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((kind(X)|brave(X))=>(~quiet(X)&patient(X))))&
(![X]:((~tall(X)&~curious(X))=>strong(X)))&
(![X]:((~happy(X)|brave(X))<=>(~tall(X)|~humble(X))))&
(![X]:((~curious(X)|~funny(X))<=>(~brave(X)&~humble(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~old(X)|~curious(X))))&
(![X]:(patient(X)<=>(tall(X)&quiet(X))))&
(((~calm(susan)&~generous(susan)))=>((old(susan)|brave(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>(?[X]:((~rich(X)|brave(X)))))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:(strong(X)))&
((~generous(mary)<~>~old(mary)))&
(?[X]:((~quiet(X)&~funny(X))))&
(?[X]:((happy(X)|wise(X)))) | ~humble(alice) | [
"p6",
"p7",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4458984036690486527427557
% SZS output start Proof for 4458984036690486527427557
7. ! [X0] : ((wise(X0) & ~rich(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p6]
8. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> ~brave(X0)) [input p7]
9. ! [X0] : ((brave(X0) | kind(X0)) => (patient(X0) & ~quiet(X0))) [input p8]
11. ! [X0] : ((brave(X0) | ~happy(X0)) <=> (~humble(X0) | ~tall(X0))) [input p10]
12. ! [X0] : ((~funny(X0) | ~curious(X0)) <=> (~humble(X0) & ~brave(X0))) [input p11]
14. ! [X0] : (patient(X0) <=> (quiet(X0) & tall(X0))) [input p13]
22. humble(alice) [input hypothesis]
32. ! [X0] : ((patient(X0) & ~quiet(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 9]
47. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~wise(X0) | rich(X0)))) [nnf transformation 7]
48. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~wise(X0) | rich(X0))) [flattening 47]
49. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | brave(X0)) & (~brave(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 8]
50. ! [X0] : (((brave(X0) | ~happy(X0)) | (humble(X0) & tall(X0))) & ((~humble(X0) | ~tall(X0)) | (~brave(X0) & happy(X0)))) [nnf transformation 11]
51. ! [X0] : ((brave(X0) | ~happy(X0) | (humble(X0) & tall(X0))) & (~humble(X0) | ~tall(X0) | (~brave(X0) & happy(X0)))) [flattening 50]
52. ! [X0] : (((~funny(X0) | ~curious(X0)) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | (funny(X0) & curious(X0)))) [nnf transformation 12]
53. ! [X0] : ((~funny(X0) | ~curious(X0) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | (funny(X0) & curious(X0)))) [flattening 52]
56. ! [X0] : ((patient(X0) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [nnf transformation 14]
57. ! [X0] : ((patient(X0) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [flattening 56]
99. ~rich(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
100. ~rich(X0) | creative(X0) | creative(X0) [cnf transformation 48]
105. ~curious(X0) | rich(X0) | brave(X0) [cnf transformation 49]
110. ~brave(X0) | patient(X0) [cnf transformation 32]
113. ~brave(X0) | ~tall(X0) | ~humble(X0) [cnf transformation 51]
118. ~humble(X0) | curious(X0) [cnf transformation 53]
126. ~patient(X0) | tall(X0) [cnf transformation 57]
139. humble(alice) [cnf transformation 22]
140. ~rich(X0) | ~creative(X0) [duplicate literal removal 99]
141. ~rich(X0) | creative(X0) [duplicate literal removal 100]
243. ~rich(X0) [subsumption resolution 140,141]
244. ~curious(X0) | brave(X0) [subsumption resolution 105,243]
272. curious(alice) [resolution 118,139]
276. brave(alice) [resolution 244,272]
279. patient(alice) [resolution 276,110]
281. tall(alice) [resolution 279,126]
344. ~tall(alice) | ~humble(alice) [resolution 113,276]
345. ~humble(alice) [subsumption resolution 344,281]
346. $false [subsumption resolution 345,139]
% SZS output end Proof for 4458984036690486527427557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is both not brave and not creative.
Everyone who is not curious or not brave is either tall or not happy.
Everyone who is not patient or not tall is curious.
Everyone who is both not wise and happy is not wise or funny and vice versa.
Everyone who is either not humble or not happy is strong or not patient.
If someone is patient or strong then susan is either generous or not kind and vice versa.
If mary is both not calm and not generous then lucy is not funny.
If someone is kind then lucy is happy and vice versa.
Everyone who is not wise is not humble.
Everyone who is not calm or rich is both wise and quiet and vice versa.
If someone is curious then someone is not generous and vice versa.
If john is brave or not patient then someone is not humble and vice versa.
If paul is brave then alice is both not generous and calm.
If someone is either curious or not funny then someone is both strong and funny.
Everyone who is both kind and not humble is either wise or not curious.
Everyone who is both curious and tall is both humble and not happy.
Someone is either old or not funny.
Someone is both not humble and curious.
Someone is not kind.
Susan is not generous or not tall.
Someone is both humble and strong.
Susan is tall or funny.
Fred is both not happy and not old.
Someone is humble. | Susan is not tall. | contradiction | (![X]:(curious(X)=>(~brave(X)&~creative(X))))&
(![X]:((~curious(X)|~brave(X))=>(tall(X)<~>~happy(X))))&
(![X]:((~patient(X)|~tall(X))=>curious(X)))&
(![X]:((~wise(X)&happy(X))<=>(~wise(X)|funny(X))))&
(![X]:((~humble(X)<~>~happy(X))=>(strong(X)|~patient(X))))&
((?[X]:((patient(X)|strong(X))))<=>((generous(susan)<~>~kind(susan))))&
(((~calm(mary)&~generous(mary)))=>(~funny(lucy)))&
((?[X]:(kind(X)))<=>(happy(lucy)))&
(![X]:(~wise(X)=>~humble(X)))&
(![X]:((~calm(X)|rich(X))<=>(wise(X)&quiet(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~generous(X))))&
(((brave(john)|~patient(john)))<=>(?[X]:(~humble(X))))&
((brave(paul))=>((~generous(alice)&calm(alice))))&
((?[X]:((curious(X)<~>~funny(X))))=>(?[X]:((strong(X)&funny(X)))))&
(![X]:((kind(X)&~humble(X))=>(wise(X)<~>~curious(X))))&
(![X]:((curious(X)&tall(X))=>(humble(X)&~happy(X))))&
(?[X]:((old(X)<~>~funny(X))))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:(~kind(X)))&
((~generous(susan)|~tall(susan)))&
(?[X]:((humble(X)&strong(X))))&
((tall(susan)|funny(susan)))&
((~happy(fred)&~old(fred)))&
(?[X]:(humble(X))) | ~tall(susan) | [
"p0",
"p1",
"p2",
"p3",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7467274607268136865512208
% SZS output start Proof for 7467274607268136865512208
1. ! [X0] : (curious(X0) => (~creative(X0) & ~brave(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | ~curious(X0)) => (tall(X0) <~> ~happy(X0))) [input p1]
3. ! [X0] : ((~tall(X0) | ~patient(X0)) => curious(X0)) [input p2]
4. ! [X0] : ((happy(X0) & ~wise(X0)) <=> (funny(X0) | ~wise(X0))) [input p3]
22. funny(susan) | tall(susan) [input p21]
25. ~tall(susan) [input hypothesis]
28. ! [X0] : (curious(X0) => ~brave(X0)) [pure predicate removal 1]
29. ! [X0] : (~brave(X0) | ~curious(X0)) [ennf transformation 28]
30. ! [X0] : ((tall(X0) <~> ~happy(X0)) | (brave(X0) & curious(X0))) [ennf transformation 2]
31. ! [X0] : (curious(X0) | (tall(X0) & patient(X0))) [ennf transformation 3]
43. ! [X0] : (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (brave(X0) & curious(X0))) [nnf transformation 30]
44. ! [X0] : (((happy(X0) & ~wise(X0)) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | (~happy(X0) | wise(X0)))) [nnf transformation 4]
45. ! [X0] : (((happy(X0) & ~wise(X0)) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | ~happy(X0) | wise(X0))) [flattening 44]
83. ~brave(X0) | ~curious(X0) [cnf transformation 29]
85. ~happy(X0) | tall(X0) | brave(X0) [cnf transformation 43]
89. tall(X0) | curious(X0) [cnf transformation 31]
92. ~funny(X0) | ~wise(X0) [cnf transformation 45]
93. wise(X0) | happy(X0) [cnf transformation 45]
135. funny(susan) | tall(susan) [cnf transformation 22]
139. ~tall(susan) [cnf transformation 25]
272. 30 <=> tall(susan) [avatar definition]
274. ~tall(susan) <- (~30) [avatar component clause 272]
277. 31 <=> funny(susan) [avatar definition]
279. funny(susan) <- (31) [avatar component clause 277]
280. 30 | 31 [avatar split clause 135,277,272]
281. ~30 [avatar split clause 139,272]
289. curious(susan) <- (~30) [resolution 89,274]
290. ~wise(susan) <- (31) [resolution 92,279]
291. happy(susan) <- (31) [resolution 290,93]
308. tall(susan) | brave(susan) <- (31) [resolution 85,291]
318. brave(susan) <- (~30, 31) [subsumption resolution 308,274]
338. ~curious(susan) <- (~30, 31) [resolution 318,83]
339. $false <- (~30, 31) [subsumption resolution 338,289]
340. 30 | ~31 [avatar contradiction clause 339]
341. $false [avatar sat refutation 280,281,340]
% SZS output end Proof for 7467274607268136865512208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or funny then alice is both happy and not brave and vice versa. If alice is not tall then mary is calm and vice versa. Everyone who is either not tall or not calm is either brave or not generous and vice versa. Everyone who is both not kind and old is not kind and vice versa. Everyone who is not calm is rich and vice versa. If mary is either tall or not tall then alice is quiet or not old and vice versa. Everyone who is happy is old and vice versa. If someone is both not old and generous then someone is both not creative and creative and vice versa. Everyone who is wise or calm is humble or rich. Everyone who is not happy is either not tall or not wise and vice versa. If someone is either not strong or wise then someone is funny and vice versa. If mary is tall or not patient then someone is quiet or old and vice versa. If alice is not old or happy then paul is tall and vice versa. If mary is not wise or not tall then alice is both happy and not happy. Everyone who is not curious or not rich is either happy or brave and vice versa. Someone is either curious or old. Someone is either not rich or not humble. Fred is not brave. Someone is creative. Someone is strong or not patient. Someone is not tall or not wise. Paul is either not brave or rich. | Paul is kind. | neutral | ((?[X]:((creative(X)<~>funny(X))))<=>((happy(alice)&~brave(alice))))&
((~tall(alice))<=>(calm(mary)))&
(![X]:((~tall(X)<~>~calm(X))<=>(brave(X)<~>~generous(X))))&
(![X]:((~kind(X)&old(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>rich(X)))&
(((tall(mary)<~>~tall(mary)))<=>((quiet(alice)|~old(alice))))&
(![X]:(happy(X)<=>old(X)))&
((?[X]:((~old(X)&generous(X))))<=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:((wise(X)|calm(X))=>(humble(X)|rich(X))))&
(![X]:(~happy(X)<=>(~tall(X)<~>~wise(X))))&
((?[X]:((~strong(X)<~>wise(X))))<=>(?[X]:(funny(X))))&
(((tall(mary)|~patient(mary)))<=>(?[X]:((quiet(X)|old(X)))))&
(((~old(alice)|happy(alice)))<=>(tall(paul)))&
(((~wise(mary)|~tall(mary)))=>((happy(alice)&~happy(alice))))&
(![X]:((~curious(X)|~rich(X))<=>(happy(X)<~>brave(X))))&
(?[X]:((curious(X)<~>old(X))))&
(?[X]:((~rich(X)<~>~humble(X))))&
(~brave(fred))&
(?[X]:(creative(X)))&
(?[X]:((strong(X)|~patient(X))))&
(?[X]:((~tall(X)|~wise(X))))&
((~brave(paul)<~>rich(paul))) | kind(paul) | [] | null | 0 |
Everyone who is both not curious and not rich is either not old or not calm.
Everyone who is either patient or not strong is both humble and tall and vice versa.
Everyone who is either not calm or not generous is not generous or not kind.
If someone is both not calm and generous then alice is rich or not curious.
Everyone who is both not generous and not old is both curious and creative and vice versa.
If someone is either not wise or generous then someone is humble and vice versa.
If lucy is creative then alice is not rich.
If someone is both not humble and rich then alice is generous or not humble and vice versa.
Everyone who is brave or funny is both not brave and humble and vice versa.
Everyone who is both not calm and not happy is wise or not funny and vice versa.
If alice is both not strong and not curious then susan is both not curious and not funny.
If lucy is not wise then someone is creative or old and vice versa.
Everyone who is strong or brave is both not strong and wise and vice versa.
Everyone who is not humble or not curious is both calm and not brave.
Everyone who is both tall and not brave is both old and not humble and vice versa.
Everyone who is calm or not rich is either not old or not brave and vice versa.
Someone is humble.
Mary is not tall or not creative.
Paul is either not funny or funny.
Someone is either tall or not kind.
Someone is either old or quiet.
Someone is both old and not quiet.
Someone is either not happy or wise. | Paul is not happy. | neutral | (![X]:((~curious(X)&~rich(X))=>(~old(X)<~>~calm(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(humble(X)&tall(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~generous(X)|~kind(X))))&
((?[X]:((~calm(X)&generous(X))))=>((rich(alice)|~curious(alice))))&
(![X]:((~generous(X)&~old(X))<=>(curious(X)&creative(X))))&
((?[X]:((~wise(X)<~>generous(X))))<=>(?[X]:(humble(X))))&
((creative(lucy))=>(~rich(alice)))&
((?[X]:((~humble(X)&rich(X))))<=>((generous(alice)|~humble(alice))))&
(![X]:((brave(X)|funny(X))<=>(~brave(X)&humble(X))))&
(![X]:((~calm(X)&~happy(X))<=>(wise(X)|~funny(X))))&
(((~strong(alice)&~curious(alice)))=>((~curious(susan)&~funny(susan))))&
((~wise(lucy))<=>(?[X]:((creative(X)|old(X)))))&
(![X]:((strong(X)|brave(X))<=>(~strong(X)&wise(X))))&
(![X]:((~humble(X)|~curious(X))=>(calm(X)&~brave(X))))&
(![X]:((tall(X)&~brave(X))<=>(old(X)&~humble(X))))&
(![X]:((calm(X)|~rich(X))<=>(~old(X)<~>~brave(X))))&
(?[X]:(humble(X)))&
((~tall(mary)|~creative(mary)))&
((~funny(paul)<~>funny(paul)))&
(?[X]:((tall(X)<~>~kind(X))))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((old(X)&~quiet(X))))&
(?[X]:((~happy(X)<~>wise(X)))) | ~happy(paul) | [] | null | 0 |
Everyone who is wise or kind is either not wise or creative and vice versa. If paul is humble then someone is wise and vice versa. If susan is kind then susan is either tall or funny and vice versa. If someone is not rich then someone is not brave or old. If paul is not patient or humble then mary is both not strong and not quiet and vice versa. Everyone who is either creative or kind is either wise or not patient and vice versa. If someone is not wise or kind then mary is curious. Everyone who is both not creative and generous is not humble or not wise and vice versa. If lucy is either calm or curious then lucy is both strong and old. If john is either strong or wise then susan is either kind or generous and vice versa. Everyone who is brave is not patient or not happy and vice versa. If someone is both not brave and tall then paul is either kind or not quiet and vice versa. Everyone who is not happy is both not strong and quiet and vice versa. Everyone who is both generous and not quiet is not old and vice versa. If lucy is not creative then paul is creative or strong. If paul is quiet or strong then someone is not old or not wise. Paul is not happy. Someone is either not curious or humble. Someone is old or not creative. Someone is rich or not wise. John is tall. John is either tall or not brave. Someone is not wise. Someone is either not humble or rich. | Paul is not quiet. | contradiction | (![X]:((wise(X)|kind(X))<=>(~wise(X)<~>creative(X))))&
((humble(paul))<=>(?[X]:(wise(X))))&
((kind(susan))<=>((tall(susan)<~>funny(susan))))&
((?[X]:(~rich(X)))=>(?[X]:((~brave(X)|old(X)))))&
(((~patient(paul)|humble(paul)))<=>((~strong(mary)&~quiet(mary))))&
(![X]:((creative(X)<~>kind(X))<=>(wise(X)<~>~patient(X))))&
((?[X]:((~wise(X)|kind(X))))=>(curious(mary)))&
(![X]:((~creative(X)&generous(X))<=>(~humble(X)|~wise(X))))&
(((calm(lucy)<~>curious(lucy)))=>((strong(lucy)&old(lucy))))&
(((strong(john)<~>wise(john)))<=>((kind(susan)<~>generous(susan))))&
(![X]:(brave(X)<=>(~patient(X)|~happy(X))))&
((?[X]:((~brave(X)&tall(X))))<=>((kind(paul)<~>~quiet(paul))))&
(![X]:(~happy(X)<=>(~strong(X)&quiet(X))))&
(![X]:((generous(X)&~quiet(X))<=>~old(X)))&
((~creative(lucy))=>((creative(paul)|strong(paul))))&
(((quiet(paul)|strong(paul)))=>(?[X]:((~old(X)|~wise(X)))))&
(~happy(paul))&
(?[X]:((~curious(X)<~>humble(X))))&
(?[X]:((old(X)|~creative(X))))&
(?[X]:((rich(X)|~wise(X))))&
(tall(john))&
((tall(john)<~>~brave(john)))&
(?[X]:(~wise(X)))&
(?[X]:((~humble(X)<~>rich(X)))) | ~quiet(paul) | [
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 382066661681299793190056
% SZS output start Proof for 382066661681299793190056
13. ! [X0] : (~happy(X0) <=> (quiet(X0) & ~strong(X0))) [input p12]
17. ~happy(paul) [input p16]
25. ~quiet(paul) [input hypothesis]
56. ! [X0] : ((~happy(X0) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | happy(X0))) [nnf transformation 13]
57. ! [X0] : ((~happy(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | happy(X0))) [flattening 56]
130. happy(X0) | quiet(X0) [cnf transformation 57]
138. ~happy(paul) [cnf transformation 17]
149. ~quiet(paul) [cnf transformation 25]
267. 23 <=> quiet(paul) [avatar definition]
268. ~quiet(paul) <- (~23) [avatar component clause 267]
353. ~23 [avatar split clause 149,267]
359. quiet(paul) [resolution 130,138]
360. $false <- (~23) [subsumption resolution 359,268]
361. 23 [avatar contradiction clause 360]
362. $false [avatar sat refutation 353,361]
% SZS output end Proof for 382066661681299793190056
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and wise is either curious or not old.
If mary is quiet then someone is quiet or old.
Everyone who is either not patient or not humble is both old and not brave.
Everyone who is funny or not quiet is wise or not rich and vice versa.
Everyone who is both not generous and rich is not creative or patient and vice versa.
Everyone who is calm is not funny or not rich and vice versa.
If mary is not quiet then alice is either not funny or not generous.
If mary is not kind or kind then someone is not quiet or not humble and vice versa.
If susan is not humble then someone is generous and vice versa.
If someone is either quiet or old then fred is both quiet and not rich.
If someone is not strong then someone is not funny or wise.
If alice is both not tall and old then someone is not humble or patient and vice versa.
If mary is either not strong or not brave then alice is not wise or old and vice versa.
If someone is not rich or not calm then someone is both not old and not quiet.
Everyone who is both not kind and creative is either generous or humble and vice versa.
Everyone who is not strong is either calm or not strong and vice versa.
Someone is old.
Susan is funny.
Someone is not kind or brave.
Paul is either not strong or curious.
Someone is not strong.
Someone is both strong and not generous.
Susan is both brave and old.
Someone is not quiet or creative. | Paul is curious. | neutral | (![X]:((~strong(X)&wise(X))=>(curious(X)<~>~old(X))))&
((quiet(mary))=>(?[X]:((quiet(X)|old(X)))))&
(![X]:((~patient(X)<~>~humble(X))=>(old(X)&~brave(X))))&
(![X]:((funny(X)|~quiet(X))<=>(wise(X)|~rich(X))))&
(![X]:((~generous(X)&rich(X))<=>(~creative(X)|patient(X))))&
(![X]:(calm(X)<=>(~funny(X)|~rich(X))))&
((~quiet(mary))=>((~funny(alice)<~>~generous(alice))))&
(((~kind(mary)|kind(mary)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
((~humble(susan))<=>(?[X]:(generous(X))))&
((?[X]:((quiet(X)<~>old(X))))=>((quiet(fred)&~rich(fred))))&
((?[X]:(~strong(X)))=>(?[X]:((~funny(X)|wise(X)))))&
(((~tall(alice)&old(alice)))<=>(?[X]:((~humble(X)|patient(X)))))&
(((~strong(mary)<~>~brave(mary)))<=>((~wise(alice)|old(alice))))&
((?[X]:((~rich(X)|~calm(X))))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((~kind(X)&creative(X))<=>(generous(X)<~>humble(X))))&
(![X]:(~strong(X)<=>(calm(X)<~>~strong(X))))&
(?[X]:(old(X)))&
(funny(susan))&
(?[X]:((~kind(X)|brave(X))))&
((~strong(paul)<~>curious(paul)))&
(?[X]:(~strong(X)))&
(?[X]:((strong(X)&~generous(X))))&
((brave(susan)&old(susan)))&
(?[X]:((~quiet(X)|creative(X)))) | curious(paul) | [] | null | 0 |
Everyone who is happy or not brave is both generous and not generous and vice versa. Everyone who is wise is not calm or humble. Everyone who is not happy is not wise or not creative and vice versa. If someone is both kind and not happy then someone is brave and vice versa. If lucy is both happy and humble then alice is either not strong or brave and vice versa. Everyone who is happy is patient or not old and vice versa. If paul is not wise then someone is both quiet and curious and vice versa. If lucy is either brave or not calm then alice is not creative or not calm. If someone is old then someone is not old or quiet and vice versa. If someone is either not generous or not tall then fred is not kind. If john is not kind or not patient then john is not kind or curious and vice versa. If fred is not funny or not happy then someone is humble or not humble. If someone is not wise then someone is both not happy and not brave. Everyone who is either not humble or generous is happy or calm and vice versa. Everyone who is curious is either happy or generous and vice versa. Someone is not funny. Lucy is not strong or quiet. Susan is either not rich or curious. Alice is not calm or rich. Someone is brave. John is either quiet or brave. Lucy is rich. | John is not brave. | contradiction | (![X]:((happy(X)|~brave(X))<=>(generous(X)&~generous(X))))&
(![X]:(wise(X)=>(~calm(X)|humble(X))))&
(![X]:(~happy(X)<=>(~wise(X)|~creative(X))))&
((?[X]:((kind(X)&~happy(X))))<=>(?[X]:(brave(X))))&
(((happy(lucy)&humble(lucy)))<=>((~strong(alice)<~>brave(alice))))&
(![X]:(happy(X)<=>(patient(X)|~old(X))))&
((~wise(paul))<=>(?[X]:((quiet(X)&curious(X)))))&
(((brave(lucy)<~>~calm(lucy)))=>((~creative(alice)|~calm(alice))))&
((?[X]:(old(X)))<=>(?[X]:((~old(X)|quiet(X)))))&
((?[X]:((~generous(X)<~>~tall(X))))=>(~kind(fred)))&
(((~kind(john)|~patient(john)))<=>((~kind(john)|curious(john))))&
(((~funny(fred)|~happy(fred)))=>(?[X]:((humble(X)|~humble(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:((~humble(X)<~>generous(X))<=>(happy(X)|calm(X))))&
(![X]:(curious(X)<=>(happy(X)<~>generous(X))))&
(?[X]:(~funny(X)))&
((~strong(lucy)|quiet(lucy)))&
((~rich(susan)<~>curious(susan)))&
((~calm(alice)|rich(alice)))&
(?[X]:(brave(X)))&
((quiet(john)<~>brave(john)))&
(rich(lucy)) | ~brave(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8577622546188561709810994
% SZS output start Proof for 8577622546188561709810994
1. ! [X0] : ((~brave(X0) | happy(X0)) <=> (~generous(X0) & generous(X0))) [input p0]
23. ~brave(john) [input hypothesis]
34. ! [X0] : (((~brave(X0) | happy(X0)) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | (brave(X0) & ~happy(X0)))) [nnf transformation 1]
35. ! [X0] : ((~brave(X0) | happy(X0) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | (brave(X0) & ~happy(X0)))) [flattening 34]
75. generous(X0) | brave(X0) [cnf transformation 35]
77. ~generous(X0) | brave(X0) [cnf transformation 35]
132. ~brave(john) [cnf transformation 23]
133. brave(X0) [subsumption resolution 75,77]
238. $false [subsumption resolution 132,133]
% SZS output end Proof for 8577622546188561709810994
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and patient is either not strong or rich and vice versa. Everyone who is both not curious and not calm is either creative or not humble and vice versa. If someone is wise or rich then alice is tall or creative and vice versa. If alice is not humble or not creative then someone is either quiet or not strong. Everyone who is happy is not humble or not old and vice versa. Everyone who is either curious or tall is calm or happy. If fred is not generous then alice is brave or not humble and vice versa. Everyone who is not humble is both not creative and not curious. If someone is both tall and brave then someone is generous or wise. Everyone who is either not humble or kind is both kind and not humble and vice versa. If someone is not curious or happy then someone is kind and vice versa. If someone is not calm then someone is not brave or kind and vice versa. Everyone who is rich or wise is either not rich or not tall. If john is not quiet or funny then someone is curious or not old. Everyone who is both not wise and happy is both tall and not rich and vice versa. Someone is either patient or happy. Paul is not quiet or strong. Lucy is both humble and not happy. Fred is both not strong and not creative. Someone is both strong and not happy. Someone is calm or creative. Someone is either quiet or not strong. | John is wise. | contradiction | (![X]:((~creative(X)&patient(X))<=>(~strong(X)<~>rich(X))))&
(![X]:((~curious(X)&~calm(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:((wise(X)|rich(X))))<=>((tall(alice)|creative(alice))))&
(((~humble(alice)|~creative(alice)))=>(?[X]:((quiet(X)<~>~strong(X)))))&
(![X]:(happy(X)<=>(~humble(X)|~old(X))))&
(![X]:((curious(X)<~>tall(X))=>(calm(X)|happy(X))))&
((~generous(fred))<=>((brave(alice)|~humble(alice))))&
(![X]:(~humble(X)=>(~creative(X)&~curious(X))))&
((?[X]:((tall(X)&brave(X))))=>(?[X]:((generous(X)|wise(X)))))&
(![X]:((~humble(X)<~>kind(X))<=>(kind(X)&~humble(X))))&
((?[X]:((~curious(X)|happy(X))))<=>(?[X]:(kind(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((rich(X)|wise(X))=>(~rich(X)<~>~tall(X))))&
(((~quiet(john)|funny(john)))=>(?[X]:((curious(X)|~old(X)))))&
(![X]:((~wise(X)&happy(X))<=>(tall(X)&~rich(X))))&
(?[X]:((patient(X)<~>happy(X))))&
((~quiet(paul)|strong(paul)))&
((humble(lucy)&~happy(lucy)))&
((~strong(fred)&~creative(fred)))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:((quiet(X)<~>~strong(X)))) | wise(john) | [
"p1",
"p2",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7262768529177240865222994
% SZS output start Proof for 7262768529177240865222994
2. ! [X0] : ((~calm(X0) & ~curious(X0)) <=> (creative(X0) <~> ~humble(X0))) [input p1]
3. ? [X0] : (rich(X0) | wise(X0)) <=> (creative(alice) | tall(alice)) [input p2]
10. ! [X0] : ((~humble(X0) <~> kind(X0)) <=> (~humble(X0) & kind(X0))) [input p9]
11. ? [X0] : (happy(X0) | ~curious(X0)) <=> ? [X0] : kind(X0) [input p10]
13. ! [X0] : ((wise(X0) | rich(X0)) => (~rich(X0) <~> ~tall(X0))) [input p12]
15. ! [X0] : ((happy(X0) & ~wise(X0)) <=> (~rich(X0) & tall(X0))) [input p14]
23. wise(john) [input hypothesis]
25. ? [X0] : (happy(X0) | ~curious(X0)) <=> ? [X1] : kind(X1) [rectify 11]
33. ! [X0] : ((~rich(X0) <~> ~tall(X0)) | (~wise(X0) & ~rich(X0))) [ennf transformation 13]
37. ! [X0] : (((~calm(X0) & ~curious(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | (calm(X0) | curious(X0)))) [nnf transformation 2]
38. ! [X0] : (((~calm(X0) & ~curious(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | calm(X0) | curious(X0))) [flattening 37]
39. (? [X0] : (rich(X0) | wise(X0)) | (~creative(alice) & ~tall(alice))) & ((creative(alice) | tall(alice)) | ! [X0] : (~rich(X0) & ~wise(X0))) [nnf transformation 3]
40. (? [X0] : (rich(X0) | wise(X0)) | (~creative(alice) & ~tall(alice))) & (creative(alice) | tall(alice) | ! [X0] : (~rich(X0) & ~wise(X0))) [flattening 39]
41. (? [X0] : (rich(X0) | wise(X0)) | (~creative(alice) & ~tall(alice))) & (creative(alice) | tall(alice) | ! [X1] : (~rich(X1) & ~wise(X1))) [rectify 40]
42. ? [X0] : (rich(X0) | wise(X0)) => (rich(sK0) | wise(sK0)) [choice axiom]
43. ((rich(sK0) | wise(sK0)) | (~creative(alice) & ~tall(alice))) & (creative(alice) | tall(alice) | ! [X1] : (~rich(X1) & ~wise(X1))) [skolemisation 41,42]
55. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (humble(X0) | ~kind(X0))) & ((~humble(X0) & kind(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [nnf transformation 10]
56. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | humble(X0) | ~kind(X0)) & ((~humble(X0) & kind(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [flattening 55]
57. (? [X0] : (happy(X0) | ~curious(X0)) | ! [X1] : ~kind(X1)) & (? [X1] : kind(X1) | ! [X0] : (~happy(X0) & curious(X0))) [nnf transformation 25]
58. (? [X0] : (happy(X0) | ~curious(X0)) | ! [X1] : ~kind(X1)) & (? [X2] : kind(X2) | ! [X3] : (~happy(X3) & curious(X3))) [rectify 57]
59. ? [X0] : (happy(X0) | ~curious(X0)) => (happy(sK3) | ~curious(sK3)) [choice axiom]
60. ? [X2] : kind(X2) => kind(sK4) [choice axiom]
61. ((happy(sK3) | ~curious(sK3)) | ! [X1] : ~kind(X1)) & (kind(sK4) | ! [X3] : (~happy(X3) & curious(X3))) [skolemisation 58,60,59]
67. ! [X0] : (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~wise(X0) & ~rich(X0))) [nnf transformation 33]
70. ! [X0] : (((happy(X0) & ~wise(X0)) | (rich(X0) | ~tall(X0))) & ((~rich(X0) & tall(X0)) | (~happy(X0) | wise(X0)))) [nnf transformation 15]
71. ! [X0] : (((happy(X0) & ~wise(X0)) | rich(X0) | ~tall(X0)) & ((~rich(X0) & tall(X0)) | ~happy(X0) | wise(X0))) [flattening 70]
90. ~humble(X0) | ~curious(X0) | ~creative(X0) [cnf transformation 38]
94. creative(alice) | tall(alice) | ~wise(X1) [cnf transformation 43]
113. kind(X0) | kind(X0) | humble(X0) [cnf transformation 56]
116. ~humble(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 56]
118. ~kind(X0) | humble(X0) | humble(X0) | ~kind(X0) [cnf transformation 56]
119. kind(sK4) | curious(X3) [cnf transformation 61]
120. kind(sK4) | ~happy(X3) [cnf transformation 61]
125. ~tall(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 67]
133. happy(X0) | rich(X0) | ~tall(X0) [cnf transformation 71]
146. wise(john) [cnf transformation 23]
147. ~tall(X0) | ~rich(X0) [duplicate literal removal 125]
148. kind(X0) | humble(X0) [duplicate literal removal 113]
149. ~humble(X0) | ~kind(X0) [duplicate literal removal 116]
150. ~kind(X0) | humble(X0) [duplicate literal removal 118]
152. 1 <=> creative(alice) [avatar definition]
153. creative(alice) <- (1) [avatar component clause 152]
165. 4 <=> tall(alice) [avatar definition]
166. tall(alice) <- (4) [avatar component clause 165]
174. 6 <=> ! [X1] : ~wise(X1) [avatar definition]
175. ~wise(X1) <- (6) [avatar component clause 174]
176. 6 | 4 | 1 [avatar split clause 94,152,165,174]
216. ~kind(X0) [subsumption resolution 149,150]
217. humble(X0) [subsumption resolution 148,216]
218. ~happy(X3) [subsumption resolution 120,216]
219. curious(X3) [subsumption resolution 119,216]
237. rich(X0) | ~tall(X0) [subsumption resolution 133,218]
238. ~tall(X0) [subsumption resolution 237,147]
270. $false <- (4) [subsumption resolution 166,238]
271. ~4 [avatar contradiction clause 270]
272. $false <- (6) [resolution 175,146]
275. ~6 [avatar contradiction clause 272]
288. ~curious(X0) | ~creative(X0) [resolution 90,217]
289. ~creative(X0) [subsumption resolution 288,219]
290. $false <- (1) [resolution 289,153]
291. ~1 [avatar contradiction clause 290]
292. $false [avatar sat refutation 176,271,275,291]
% SZS output end Proof for 7262768529177240865222994
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not tall is both kind and not generous.
Everyone who is not calm is humble or wise.
If someone is either not tall or brave then someone is either not strong or funny and vice versa.
Everyone who is either not happy or curious is either not generous or funny.
Everyone who is either creative or not quiet is wise or not old and vice versa.
Everyone who is either not tall or rich is patient and vice versa.
Everyone who is both not calm and not humble is not happy or brave.
Everyone who is both wise and not patient is humble or old and vice versa.
If alice is both not quiet and brave then alice is not brave or not tall.
Everyone who is not old or not generous is both humble and not humble.
Everyone who is funny or not brave is both rich and kind and vice versa.
Everyone who is curious is brave or not calm.
Everyone who is either happy or not curious is wise or not kind.
Everyone who is tall is creative or not wise and vice versa.
Everyone who is patient is either not kind or old and vice versa.
Everyone who is wise or old is either patient or strong.
Paul is both not kind and not patient.
Someone is old.
Someone is either wise or not generous.
Someone is either rich or not calm.
Someone is both brave and wise.
Paul is either not funny or not generous. | Alice is generous. | entailment | (![X]:((~creative(X)<~>~tall(X))=>(kind(X)&~generous(X))))&
(![X]:(~calm(X)=>(humble(X)|wise(X))))&
((?[X]:((~tall(X)<~>brave(X))))<=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((~happy(X)<~>curious(X))=>(~generous(X)<~>funny(X))))&
(![X]:((creative(X)<~>~quiet(X))<=>(wise(X)|~old(X))))&
(![X]:((~tall(X)<~>rich(X))<=>patient(X)))&
(![X]:((~calm(X)&~humble(X))=>(~happy(X)|brave(X))))&
(![X]:((wise(X)&~patient(X))<=>(humble(X)|old(X))))&
(((~quiet(alice)&brave(alice)))=>((~brave(alice)|~tall(alice))))&
(![X]:((~old(X)|~generous(X))=>(humble(X)&~humble(X))))&
(![X]:((funny(X)|~brave(X))<=>(rich(X)&kind(X))))&
(![X]:(curious(X)=>(brave(X)|~calm(X))))&
(![X]:((happy(X)<~>~curious(X))=>(wise(X)|~kind(X))))&
(![X]:(tall(X)<=>(creative(X)|~wise(X))))&
(![X]:(patient(X)<=>(~kind(X)<~>old(X))))&
(![X]:((wise(X)|old(X))=>(patient(X)<~>strong(X))))&
((~kind(paul)&~patient(paul)))&
(?[X]:(old(X)))&
(?[X]:((wise(X)<~>~generous(X))))&
(?[X]:((rich(X)<~>~calm(X))))&
(?[X]:((brave(X)&wise(X))))&
((~funny(paul)<~>~generous(paul))) | generous(alice) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 558374527737373849681868
% SZS output start Proof for 558374527737373849681868
10. ! [X0] : ((~generous(X0) | ~old(X0)) => (~humble(X0) & humble(X0))) [input p9]
23. ~generous(alice) [input hypothesis]
33. ! [X0] : ((~humble(X0) & humble(X0)) | (generous(X0) & old(X0))) [ennf transformation 10]
104. humble(X0) | generous(X0) [cnf transformation 33]
106. ~humble(X0) | generous(X0) [cnf transformation 33]
137. ~generous(alice) [cnf transformation 23]
188. generous(X0) [subsumption resolution 104,106]
204. $false [subsumption resolution 137,188]
% SZS output end Proof for 558374527737373849681868
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not generous is both calm and quiet.
If lucy is not creative or patient then paul is quiet or kind.
If someone is either not humble or not creative then someone is not strong and vice versa.
If someone is either not strong or quiet then someone is old and vice versa.
Everyone who is both not rich and not happy is not rich or brave.
If someone is either generous or calm then someone is not tall and vice versa.
Everyone who is humble or brave is both happy and not generous and vice versa.
Everyone who is funny is wise or not funny and vice versa.
Everyone who is both not patient and not kind is not wise.
Everyone who is wise is both curious and generous and vice versa.
If fred is either not kind or not happy then someone is kind or not strong and vice versa.
If paul is tall then susan is both not old and strong.
If someone is funny or happy then susan is not funny or not calm and vice versa.
Everyone who is both not quiet and patient is either not patient or not old and vice versa.
If susan is either not quiet or calm then fred is both patient and not funny and vice versa.
Everyone who is happy is either not strong or curious.
Someone is both not calm and happy.
Someone is both not rich and not old.
Someone is wise.
Someone is both creative and not rich.
Someone is not quiet or not tall.
Someone is both happy and strong. | Fred is not generous. | contradiction | (![X]:((~tall(X)&~generous(X))=>(calm(X)&quiet(X))))&
(((~creative(lucy)|patient(lucy)))=>((quiet(paul)|kind(paul))))&
((?[X]:((~humble(X)<~>~creative(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~strong(X)<~>quiet(X))))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)&~happy(X))=>(~rich(X)|brave(X))))&
((?[X]:((generous(X)<~>calm(X))))<=>(?[X]:(~tall(X))))&
(![X]:((humble(X)|brave(X))<=>(happy(X)&~generous(X))))&
(![X]:(funny(X)<=>(wise(X)|~funny(X))))&
(![X]:((~patient(X)&~kind(X))=>~wise(X)))&
(![X]:(wise(X)<=>(curious(X)&generous(X))))&
(((~kind(fred)<~>~happy(fred)))<=>(?[X]:((kind(X)|~strong(X)))))&
((tall(paul))=>((~old(susan)&strong(susan))))&
((?[X]:((funny(X)|happy(X))))<=>((~funny(susan)|~calm(susan))))&
(![X]:((~quiet(X)&patient(X))<=>(~patient(X)<~>~old(X))))&
(((~quiet(susan)<~>calm(susan)))<=>((patient(fred)&~funny(fred))))&
(![X]:(happy(X)=>(~strong(X)<~>curious(X))))&
(?[X]:((~calm(X)&happy(X))))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)&~rich(X))))&
(?[X]:((~quiet(X)|~tall(X))))&
(?[X]:((happy(X)&strong(X)))) | ~generous(fred) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7284368934218294696160708
% SZS output start Proof for 7284368934218294696160708
8. ! [X0] : (funny(X0) <=> (~funny(X0) | wise(X0))) [input p7]
10. ! [X0] : (wise(X0) <=> (generous(X0) & curious(X0))) [input p9]
23. ~generous(fred) [input hypothesis]
54. ! [X0] : ((funny(X0) | (funny(X0) & ~wise(X0))) & ((~funny(X0) | wise(X0)) | ~funny(X0))) [nnf transformation 8]
55. ! [X0] : ((funny(X0) | (funny(X0) & ~wise(X0))) & (~funny(X0) | wise(X0) | ~funny(X0))) [flattening 54]
56. ! [X0] : ((wise(X0) | (~generous(X0) | ~curious(X0))) & ((generous(X0) & curious(X0)) | ~wise(X0))) [nnf transformation 10]
57. ! [X0] : ((wise(X0) | ~generous(X0) | ~curious(X0)) & ((generous(X0) & curious(X0)) | ~wise(X0))) [flattening 56]
106. ~funny(X0) | wise(X0) | ~funny(X0) [cnf transformation 55]
108. funny(X0) | funny(X0) [cnf transformation 55]
111. generous(X0) | ~wise(X0) [cnf transformation 57]
149. ~generous(fred) [cnf transformation 23]
152. ~funny(X0) | wise(X0) [duplicate literal removal 106]
153. funny(X0) [duplicate literal removal 108]
247. wise(X0) [subsumption resolution 152,153]
249. generous(X0) [subsumption resolution 111,247]
327. $false [subsumption resolution 149,249]
% SZS output end Proof for 7284368934218294696160708
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not happy is either tall or humble and vice versa.
Everyone who is happy is strong.
If mary is humble then someone is either wise or generous.
Everyone who is both creative and rich is both creative and funny.
If john is both strong and funny then someone is not creative.
If someone is happy or curious then someone is either quiet or generous and vice versa.
If alice is wise or old then someone is either old or not tall.
Everyone who is both generous and patient is not happy and vice versa.
Everyone who is both quiet and not wise is not tall or not happy and vice versa.
If someone is either not generous or curious then john is both not brave and not quiet and vice versa.
Everyone who is brave or not rich is both curious and not brave and vice versa.
Everyone who is not wise or strong is both strong and tall.
Everyone who is both not calm and patient is not humble or not calm.
Everyone who is either not generous or calm is both not wise and generous and vice versa.
Susan is humble.
Someone is either rich or not quiet.
Mary is not happy or not old.
Susan is either not happy or not creative.
Susan is rich or curious.
Lucy is either brave or rich. | Lucy is happy. | neutral | (![X]:((curious(X)&~happy(X))<=>(tall(X)<~>humble(X))))&
(![X]:(happy(X)=>strong(X)))&
((humble(mary))=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((creative(X)&rich(X))=>(creative(X)&funny(X))))&
(((strong(john)&funny(john)))=>(?[X]:(~creative(X))))&
((?[X]:((happy(X)|curious(X))))<=>(?[X]:((quiet(X)<~>generous(X)))))&
(((wise(alice)|old(alice)))=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((generous(X)&patient(X))<=>~happy(X)))&
(![X]:((quiet(X)&~wise(X))<=>(~tall(X)|~happy(X))))&
((?[X]:((~generous(X)<~>curious(X))))<=>((~brave(john)&~quiet(john))))&
(![X]:((brave(X)|~rich(X))<=>(curious(X)&~brave(X))))&
(![X]:((~wise(X)|strong(X))=>(strong(X)&tall(X))))&
(![X]:((~calm(X)&patient(X))=>(~humble(X)|~calm(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(~wise(X)&generous(X))))&
(humble(susan))&
(?[X]:((rich(X)<~>~quiet(X))))&
((~happy(mary)|~old(mary)))&
((~happy(susan)<~>~creative(susan)))&
((rich(susan)|curious(susan)))&
((brave(lucy)<~>rich(lucy))) | happy(lucy) | [] | null | 0 |
If someone is either kind or not creative then susan is both generous and not rich. Everyone who is old or wise is not tall or happy. Everyone who is generous or not patient is both not brave and old. Everyone who is either not funny or not brave is not brave or wise and vice versa. Everyone who is funny is rich or not tall and vice versa. Everyone who is wise is not strong and vice versa. Everyone who is either strong or rich is both not rich and not curious and vice versa. If mary is both not calm and creative then susan is brave or curious and vice versa. Everyone who is either not tall or generous is not generous or creative. Everyone who is either not humble or funny is strong. Everyone who is either brave or generous is both brave and quiet. Everyone who is funny is either humble or tall. If mary is either not kind or not creative then john is both not creative and not generous and vice versa. Everyone who is both curious and happy is strong or not brave and vice versa. If someone is both not funny and curious then lucy is both not creative and not happy and vice versa. Fred is happy. Someone is rich or not old. Someone is either calm or rich. Someone is not patient or happy. Lucy is both brave and not generous. Someone is not calm. Someone is both kind and not old. | John is not patient. | neutral | ((?[X]:((kind(X)<~>~creative(X))))=>((generous(susan)&~rich(susan))))&
(![X]:((old(X)|wise(X))=>(~tall(X)|happy(X))))&
(![X]:((generous(X)|~patient(X))=>(~brave(X)&old(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~brave(X)|wise(X))))&
(![X]:(funny(X)<=>(rich(X)|~tall(X))))&
(![X]:(wise(X)<=>~strong(X)))&
(![X]:((strong(X)<~>rich(X))<=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
(![X]:((curious(X)&happy(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(happy(fred))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((~patient(X)|happy(X))))&
((brave(lucy)&~generous(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((kind(X)&~old(X)))) | ~patient(john) | [] | null | 0 |
If lucy is rich or not brave then paul is both rich and old and vice versa.
Everyone who is both rich and generous is either not patient or not generous.
If someone is tall or quiet then someone is patient and vice versa.
Everyone who is not curious or not old is both old and not creative and vice versa.
If john is either not generous or old then mary is both kind and not wise.
If mary is both not humble and rich then lucy is either wise or not kind.
If someone is generous or not creative then someone is either brave or wise.
If fred is either not wise or not curious then susan is either not funny or calm.
If someone is both rich and not humble then fred is both not rich and brave and vice versa.
Everyone who is not rich is tall or curious.
If john is both not brave and not creative then paul is either generous or calm.
Everyone who is both patient and not humble is not wise and vice versa.
If alice is not curious then john is either not strong or wise.
If someone is not creative then someone is not curious or wise.
Everyone who is both humble and not creative is either not calm or rich and vice versa.
Someone is not kind.
Alice is rich or not old.
Someone is either quiet or not tall.
Someone is kind or curious.
Someone is strong or not creative.
Fred is either humble or patient.
Someone is not generous or not rich.
Someone is quiet. | Susan is old. | entailment | (((rich(lucy)|~brave(lucy)))<=>((rich(paul)&old(paul))))&
(![X]:((rich(X)&generous(X))=>(~patient(X)<~>~generous(X))))&
((?[X]:((tall(X)|quiet(X))))<=>(?[X]:(patient(X))))&
(![X]:((~curious(X)|~old(X))<=>(old(X)&~creative(X))))&
(((~generous(john)<~>old(john)))=>((kind(mary)&~wise(mary))))&
(((~humble(mary)&rich(mary)))=>((wise(lucy)<~>~kind(lucy))))&
((?[X]:((generous(X)|~creative(X))))=>(?[X]:((brave(X)<~>wise(X)))))&
(((~wise(fred)<~>~curious(fred)))=>((~funny(susan)<~>calm(susan))))&
((?[X]:((rich(X)&~humble(X))))<=>((~rich(fred)&brave(fred))))&
(![X]:(~rich(X)=>(tall(X)|curious(X))))&
(((~brave(john)&~creative(john)))=>((generous(paul)<~>calm(paul))))&
(![X]:((patient(X)&~humble(X))<=>~wise(X)))&
((~curious(alice))=>((~strong(john)<~>wise(john))))&
((?[X]:(~creative(X)))=>(?[X]:((~curious(X)|wise(X)))))&
(![X]:((humble(X)&~creative(X))<=>(~calm(X)<~>rich(X))))&
(?[X]:(~kind(X)))&
((rich(alice)|~old(alice)))&
(?[X]:((quiet(X)<~>~tall(X))))&
(?[X]:((kind(X)|curious(X))))&
(?[X]:((strong(X)|~creative(X))))&
((humble(fred)<~>patient(fred)))&
(?[X]:((~generous(X)|~rich(X))))&
(?[X]:(quiet(X))) | old(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5786142763472321015539896
% SZS output start Proof for 5786142763472321015539896
4. ! [X0] : ((~old(X0) | ~curious(X0)) <=> (~creative(X0) & old(X0))) [input p3]
24. ~old(susan) [input hypothesis]
49. ! [X0] : (((~old(X0) | ~curious(X0)) | (creative(X0) | ~old(X0))) & ((~creative(X0) & old(X0)) | (old(X0) & curious(X0)))) [nnf transformation 4]
50. ! [X0] : ((~old(X0) | ~curious(X0) | creative(X0) | ~old(X0)) & ((~creative(X0) & old(X0)) | (old(X0) & curious(X0)))) [flattening 49]
97. old(X0) | old(X0) [cnf transformation 50]
144. ~old(susan) [cnf transformation 24]
145. old(X0) [duplicate literal removal 97]
377. $false [subsumption resolution 144,145]
% SZS output end Proof for 5786142763472321015539896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not wise is not rich and vice versa. If alice is not funny or not quiet then john is not generous and vice versa. If paul is not old or not patient then susan is both rich and wise and vice versa. If someone is either not generous or quiet then someone is both not humble and curious and vice versa. Everyone who is funny is not wise or creative and vice versa. If someone is either not kind or happy then someone is both old and funny and vice versa. If paul is not calm then someone is creative or not curious and vice versa. Everyone who is not curious is wise or not brave. If paul is both humble and curious then alice is wise. Everyone who is tall is both kind and curious. If lucy is generous or not tall then paul is both not generous and generous. Everyone who is either curious or not strong is both not rich and calm. Everyone who is quiet or humble is either not brave or creative and vice versa. Everyone who is rich or not kind is not wise or not humble and vice versa. If susan is both funny and happy then someone is both not patient and not generous. Everyone who is both not funny and not patient is rich or happy and vice versa. Susan is both not happy and calm. Fred is not creative or creative. John is humble or not happy. Someone is both not calm and not curious. Someone is either generous or not old. Fred is rich. Someone is either not tall or quiet. | Paul is curious. | neutral | (![X]:((brave(X)<~>~wise(X))<=>~rich(X)))&
(((~funny(alice)|~quiet(alice)))<=>(~generous(john)))&
(((~old(paul)|~patient(paul)))<=>((rich(susan)&wise(susan))))&
((?[X]:((~generous(X)<~>quiet(X))))<=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:(funny(X)<=>(~wise(X)|creative(X))))&
((?[X]:((~kind(X)<~>happy(X))))<=>(?[X]:((old(X)&funny(X)))))&
((~calm(paul))<=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:(~curious(X)=>(wise(X)|~brave(X))))&
(((humble(paul)&curious(paul)))=>(wise(alice)))&
(![X]:(tall(X)=>(kind(X)&curious(X))))&
(((generous(lucy)|~tall(lucy)))=>((~generous(paul)&generous(paul))))&
(![X]:((curious(X)<~>~strong(X))=>(~rich(X)&calm(X))))&
(![X]:((quiet(X)|humble(X))<=>(~brave(X)<~>creative(X))))&
(![X]:((rich(X)|~kind(X))<=>(~wise(X)|~humble(X))))&
(((funny(susan)&happy(susan)))=>(?[X]:((~patient(X)&~generous(X)))))&
(![X]:((~funny(X)&~patient(X))<=>(rich(X)|happy(X))))&
((~happy(susan)&calm(susan)))&
((~creative(fred)|creative(fred)))&
((humble(john)|~happy(john)))&
(?[X]:((~calm(X)&~curious(X))))&
(?[X]:((generous(X)<~>~old(X))))&
(rich(fred))&
(?[X]:((~tall(X)<~>quiet(X)))) | curious(paul) | [] | null | 0 |
If john is both not wise and rich then someone is either not creative or happy.
If someone is not curious then someone is not wise or not happy.
Everyone who is not curious is wise or happy and vice versa.
If someone is both calm and rich then someone is not creative or patient.
Everyone who is old is both not brave and brave.
If someone is not creative or creative then mary is either strong or not funny and vice versa.
Everyone who is not tall or not humble is calm.
Everyone who is both not happy and humble is not strong or happy.
Everyone who is calm or rich is both not calm and curious.
If someone is not strong or calm then fred is either not brave or not calm and vice versa.
Everyone who is quiet is not tall or brave and vice versa.
If john is not happy then paul is either brave or not creative.
If susan is patient or not wise then someone is not calm or generous.
Everyone who is not kind is not happy or strong and vice versa.
If john is not humble then alice is not quiet.
Everyone who is either not curious or creative is either rich or generous and vice versa.
Someone is both not rich and not patient.
Someone is either not creative or creative.
Someone is either creative or not patient.
Someone is either not brave or kind.
Someone is either not strong or kind.
Lucy is either not rich or not generous.
Alice is not calm or patient.
Lucy is not generous or not curious. | Paul is tall. | entailment | (((~wise(john)&rich(john)))=>(?[X]:((~creative(X)<~>happy(X)))))&
((?[X]:(~curious(X)))=>(?[X]:((~wise(X)|~happy(X)))))&
(![X]:(~curious(X)<=>(wise(X)|happy(X))))&
((?[X]:((calm(X)&rich(X))))=>(?[X]:((~creative(X)|patient(X)))))&
(![X]:(old(X)=>(~brave(X)&brave(X))))&
((?[X]:((~creative(X)|creative(X))))<=>((strong(mary)<~>~funny(mary))))&
(![X]:((~tall(X)|~humble(X))=>calm(X)))&
(![X]:((~happy(X)&humble(X))=>(~strong(X)|happy(X))))&
(![X]:((calm(X)|rich(X))=>(~calm(X)&curious(X))))&
((?[X]:((~strong(X)|calm(X))))<=>((~brave(fred)<~>~calm(fred))))&
(![X]:(quiet(X)<=>(~tall(X)|brave(X))))&
((~happy(john))=>((brave(paul)<~>~creative(paul))))&
(((patient(susan)|~wise(susan)))=>(?[X]:((~calm(X)|generous(X)))))&
(![X]:(~kind(X)<=>(~happy(X)|strong(X))))&
((~humble(john))=>(~quiet(alice)))&
(![X]:((~curious(X)<~>creative(X))<=>(rich(X)<~>generous(X))))&
(?[X]:((~rich(X)&~patient(X))))&
(?[X]:((~creative(X)<~>creative(X))))&
(?[X]:((creative(X)<~>~patient(X))))&
(?[X]:((~brave(X)<~>kind(X))))&
(?[X]:((~strong(X)<~>kind(X))))&
((~rich(lucy)<~>~generous(lucy)))&
((~calm(alice)|patient(alice)))&
((~generous(lucy)|~curious(lucy))) | tall(paul) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 612331060792531281193371
% SZS output start Proof for 612331060792531281193371
7. ! [X0] : ((~humble(X0) | ~tall(X0)) => calm(X0)) [input p6]
9. ! [X0] : ((rich(X0) | calm(X0)) => (curious(X0) & ~calm(X0))) [input p8]
25. ~tall(paul) [input hypothesis]
34. ! [X0] : (calm(X0) | (humble(X0) & tall(X0))) [ennf transformation 7]
37. ! [X0] : ((curious(X0) & ~calm(X0)) | (~rich(X0) & ~calm(X0))) [ennf transformation 9]
95. tall(X0) | calm(X0) [cnf transformation 34]
98. ~calm(X0) | ~calm(X0) [cnf transformation 37]
140. ~tall(paul) [cnf transformation 25]
141. ~calm(X0) [duplicate literal removal 98]
284. calm(paul) [resolution 95,140]
285. $false [subsumption resolution 284,141]
% SZS output end Proof for 612331060792531281193371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not kind is both happy and not brave. Everyone who is both humble and not rich is not calm or not humble. If lucy is either generous or not patient then susan is not strong and vice versa. If lucy is both curious and humble then john is both not strong and old and vice versa. Everyone who is both not curious and funny is calm. Everyone who is humble is both creative and strong and vice versa. Everyone who is not humble is both not calm and not rich. If someone is either not happy or not humble then fred is either kind or funny and vice versa. If someone is both not happy and wise then someone is both not strong and not calm and vice versa. If someone is either curious or not quiet then someone is not creative. Everyone who is strong or creative is both not rich and not humble. If mary is not quiet or calm then someone is both funny and old and vice versa. If lucy is not humble then someone is quiet. If someone is either not wise or creative then susan is either brave or not brave and vice versa. Everyone who is both tall and not quiet is either not creative or brave. If someone is not strong or not tall then someone is not happy or not patient and vice versa. Someone is not wise. Someone is either wise or generous. Someone is either not brave or humble. Someone is quiet. Paul is funny or humble. Alice is both kind and not brave. Someone is not strong. Alice is either tall or not tall. | Alice is not rich. | entailment | (![X]:((~generous(X)|~kind(X))=>(happy(X)&~brave(X))))&
(![X]:((humble(X)&~rich(X))=>(~calm(X)|~humble(X))))&
(((generous(lucy)<~>~patient(lucy)))<=>(~strong(susan)))&
(((curious(lucy)&humble(lucy)))<=>((~strong(john)&old(john))))&
(![X]:((~curious(X)&funny(X))=>calm(X)))&
(![X]:(humble(X)<=>(creative(X)&strong(X))))&
(![X]:(~humble(X)=>(~calm(X)&~rich(X))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>((kind(fred)<~>funny(fred))))&
((?[X]:((~happy(X)&wise(X))))<=>(?[X]:((~strong(X)&~calm(X)))))&
((?[X]:((curious(X)<~>~quiet(X))))=>(?[X]:(~creative(X))))&
(![X]:((strong(X)|creative(X))=>(~rich(X)&~humble(X))))&
(((~quiet(mary)|calm(mary)))<=>(?[X]:((funny(X)&old(X)))))&
((~humble(lucy))=>(?[X]:(quiet(X))))&
((?[X]:((~wise(X)<~>creative(X))))<=>((brave(susan)<~>~brave(susan))))&
(![X]:((tall(X)&~quiet(X))=>(~creative(X)<~>brave(X))))&
((?[X]:((~strong(X)|~tall(X))))<=>(?[X]:((~happy(X)|~patient(X)))))&
(?[X]:(~wise(X)))&
(?[X]:((wise(X)<~>generous(X))))&
(?[X]:((~brave(X)<~>humble(X))))&
(?[X]:(quiet(X)))&
((funny(paul)|humble(paul)))&
((kind(alice)&~brave(alice)))&
(?[X]:(~strong(X)))&
((tall(alice)<~>~tall(alice))) | ~rich(alice) | [
"p5",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4565137922937172346747645
% SZS output start Proof for 4565137922937172346747645
6. ! [X0] : (humble(X0) <=> (strong(X0) & creative(X0))) [input p5]
7. ! [X0] : (~humble(X0) => (~rich(X0) & ~calm(X0))) [input p6]
11. ! [X0] : ((creative(X0) | strong(X0)) => (~humble(X0) & ~rich(X0))) [input p10]
25. rich(alice) [input hypothesis]
34. ! [X0] : ((~rich(X0) & ~calm(X0)) | humble(X0)) [ennf transformation 7]
36. ! [X0] : ((~humble(X0) & ~rich(X0)) | (~creative(X0) & ~strong(X0))) [ennf transformation 11]
43. ! [X0] : ((humble(X0) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | ~humble(X0))) [nnf transformation 6]
44. ! [X0] : ((humble(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | ~humble(X0))) [flattening 43]
102. ~humble(X0) | creative(X0) [cnf transformation 44]
106. ~rich(X0) | humble(X0) [cnf transformation 34]
124. ~humble(X0) | ~creative(X0) [cnf transformation 36]
157. rich(alice) [cnf transformation 25]
267. ~humble(X0) [subsumption resolution 124,102]
355. humble(alice) [resolution 106,157]
356. $false [subsumption resolution 355,267]
% SZS output end Proof for 4565137922937172346747645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not creative is not strong or rich and vice versa.
If someone is either brave or humble then mary is either not rich or not patient.
If fred is not strong or tall then susan is curious or kind.
Everyone who is either not calm or not humble is creative or not humble and vice versa.
Everyone who is both not wise and generous is both not happy and happy and vice versa.
If lucy is either not strong or not wise then someone is either not funny or not brave.
If mary is both not happy and not calm then someone is both calm and tall.
Everyone who is either not strong or not calm is both not generous and not kind and vice versa.
Everyone who is kind is not kind or old and vice versa.
If susan is either creative or not happy then fred is both not brave and tall.
Everyone who is not wise or not patient is funny.
Everyone who is not calm is both funny and not patient and vice versa.
Everyone who is either generous or creative is old or not curious and vice versa.
If someone is either not creative or not strong then someone is not brave or not old.
If someone is not strong then someone is not creative or not kind.
If someone is either not wise or kind then fred is funny or not brave and vice versa.
Someone is old or not rich.
John is brave or not calm.
Paul is either rich or not tall.
Someone is both kind and rich.
Susan is not tall or not generous.
Someone is both not humble and creative.
Mary is funny or not funny. | Susan is happy. | neutral | (![X]:((calm(X)&~creative(X))<=>(~strong(X)|rich(X))))&
((?[X]:((brave(X)<~>humble(X))))=>((~rich(mary)<~>~patient(mary))))&
(((~strong(fred)|tall(fred)))=>((curious(susan)|kind(susan))))&
(![X]:((~calm(X)<~>~humble(X))<=>(creative(X)|~humble(X))))&
(![X]:((~wise(X)&generous(X))<=>(~happy(X)&happy(X))))&
(((~strong(lucy)<~>~wise(lucy)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(((~happy(mary)&~calm(mary)))=>(?[X]:((calm(X)&tall(X)))))&
(![X]:((~strong(X)<~>~calm(X))<=>(~generous(X)&~kind(X))))&
(![X]:(kind(X)<=>(~kind(X)|old(X))))&
(((creative(susan)<~>~happy(susan)))=>((~brave(fred)&tall(fred))))&
(![X]:((~wise(X)|~patient(X))=>funny(X)))&
(![X]:(~calm(X)<=>(funny(X)&~patient(X))))&
(![X]:((generous(X)<~>creative(X))<=>(old(X)|~curious(X))))&
((?[X]:((~creative(X)<~>~strong(X))))=>(?[X]:((~brave(X)|~old(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((~creative(X)|~kind(X)))))&
((?[X]:((~wise(X)<~>kind(X))))<=>((funny(fred)|~brave(fred))))&
(?[X]:((old(X)|~rich(X))))&
((brave(john)|~calm(john)))&
((rich(paul)<~>~tall(paul)))&
(?[X]:((kind(X)&rich(X))))&
((~tall(susan)|~generous(susan)))&
(?[X]:((~humble(X)&creative(X))))&
((funny(mary)|~funny(mary))) | happy(susan) | [] | null | 0 |
If mary is either not humble or not tall then someone is either happy or not humble.
If fred is not generous then someone is not old or strong.
Everyone who is not humble or not rich is kind and vice versa.
Everyone who is not rich or brave is not patient or humble.
If lucy is either wise or not quiet then someone is rich or not generous.
Everyone who is either not brave or not kind is either not strong or curious.
If alice is quiet or creative then susan is funny.
If mary is old then lucy is curious and vice versa.
Everyone who is calm is not old.
Everyone who is both happy and not happy is both not quiet and not funny.
If someone is either not humble or not happy then someone is both not humble and kind and vice versa.
If someone is not rich or not brave then fred is not calm.
Everyone who is kind or not strong is both not funny and creative.
Everyone who is either funny or strong is not humble or strong.
Everyone who is not happy or happy is old or not quiet.
If john is not wise or not strong then susan is either funny or not patient.
Someone is not strong or not generous.
Mary is funny.
Someone is both old and funny.
Someone is tall or not old.
Lucy is patient.
Someone is curious.
Someone is wise.
Susan is both rich and kind. | Mary is not rich. | contradiction | (((~humble(mary)<~>~tall(mary)))=>(?[X]:((happy(X)<~>~humble(X)))))&
((~generous(fred))=>(?[X]:((~old(X)|strong(X)))))&
(![X]:((~humble(X)|~rich(X))<=>kind(X)))&
(![X]:((~rich(X)|brave(X))=>(~patient(X)|humble(X))))&
(((wise(lucy)<~>~quiet(lucy)))=>(?[X]:((rich(X)|~generous(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(~strong(X)<~>curious(X))))&
(((quiet(alice)|creative(alice)))=>(funny(susan)))&
((old(mary))<=>(curious(lucy)))&
(![X]:(calm(X)=>~old(X)))&
(![X]:((happy(X)&~happy(X))=>(~quiet(X)&~funny(X))))&
((?[X]:((~humble(X)<~>~happy(X))))<=>(?[X]:((~humble(X)&kind(X)))))&
((?[X]:((~rich(X)|~brave(X))))=>(~calm(fred)))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)&creative(X))))&
(![X]:((funny(X)<~>strong(X))=>(~humble(X)|strong(X))))&
(![X]:((~happy(X)|happy(X))=>(old(X)|~quiet(X))))&
(((~wise(john)|~strong(john)))=>((funny(susan)<~>~patient(susan))))&
(?[X]:((~strong(X)|~generous(X))))&
(funny(mary))&
(?[X]:((old(X)&funny(X))))&
(?[X]:((tall(X)|~old(X))))&
(patient(lucy))&
(?[X]:(curious(X)))&
(?[X]:(wise(X)))&
((rich(susan)&kind(susan))) | ~rich(mary) | [
"p2",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8686020085789102437439180
% SZS output start Proof for 8686020085789102437439180
3. ! [X0] : ((~rich(X0) | ~humble(X0)) <=> kind(X0)) [input p2]
13. ! [X0] : ((~strong(X0) | kind(X0)) => (creative(X0) & ~funny(X0))) [input p12]
18. funny(mary) [input p17]
25. ~rich(mary) [input hypothesis]
38. ! [X0] : ((creative(X0) & ~funny(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 13]
49. ! [X0] : (((~rich(X0) | ~humble(X0)) | ~kind(X0)) & (kind(X0) | (rich(X0) & humble(X0)))) [nnf transformation 3]
50. ! [X0] : ((~rich(X0) | ~humble(X0) | ~kind(X0)) & (kind(X0) | (rich(X0) & humble(X0)))) [flattening 49]
79. kind(X0) | rich(X0) [cnf transformation 50]
101. ~funny(X0) | ~kind(X0) [cnf transformation 38]
114. funny(mary) [cnf transformation 18]
123. ~rich(mary) [cnf transformation 25]
270. ~kind(mary) [resolution 101,114]
272. rich(mary) [resolution 270,79]
274. $false [subsumption resolution 272,123]
% SZS output end Proof for 8686020085789102437439180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is both not generous and tall.
Everyone who is quiet or curious is either generous or brave.
Everyone who is both quiet and tall is both rich and tall and vice versa.
Everyone who is humble or not brave is old or not rich.
If john is quiet or not generous then paul is brave or funny and vice versa.
Everyone who is both not rich and not kind is not brave and vice versa.
If fred is not creative then alice is both rich and not funny and vice versa.
If lucy is both happy and rich then someone is either not generous or old and vice versa.
Everyone who is not kind is either not curious or not humble.
Everyone who is old or tall is not curious.
If someone is both happy and not patient then paul is not creative and vice versa.
If someone is either strong or wise then someone is not kind and vice versa.
If someone is either not patient or not kind then someone is both not curious and not kind.
If someone is curious then someone is not wise.
Susan is not funny.
Fred is either brave or not funny.
Someone is either not rich or kind.
Someone is either not wise or strong.
Someone is both not creative and strong.
Susan is happy or humble.
Fred is not rich or not tall.
Someone is not brave. | Fred is curious. | contradiction | (![X]:(~tall(X)=>(~generous(X)&tall(X))))&
(![X]:((quiet(X)|curious(X))=>(generous(X)<~>brave(X))))&
(![X]:((quiet(X)&tall(X))<=>(rich(X)&tall(X))))&
(![X]:((humble(X)|~brave(X))=>(old(X)|~rich(X))))&
(((quiet(john)|~generous(john)))<=>((brave(paul)|funny(paul))))&
(![X]:((~rich(X)&~kind(X))<=>~brave(X)))&
((~creative(fred))<=>((rich(alice)&~funny(alice))))&
(((happy(lucy)&rich(lucy)))<=>(?[X]:((~generous(X)<~>old(X)))))&
(![X]:(~kind(X)=>(~curious(X)<~>~humble(X))))&
(![X]:((old(X)|tall(X))=>~curious(X)))&
((?[X]:((happy(X)&~patient(X))))<=>(~creative(paul)))&
((?[X]:((strong(X)<~>wise(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((~patient(X)<~>~kind(X))))=>(?[X]:((~curious(X)&~kind(X)))))&
((?[X]:(curious(X)))=>(?[X]:(~wise(X))))&
(~funny(susan))&
((brave(fred)<~>~funny(fred)))&
(?[X]:((~rich(X)<~>kind(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((~creative(X)&strong(X))))&
((happy(susan)|humble(susan)))&
((~rich(fred)|~tall(fred)))&
(?[X]:(~brave(X))) | curious(fred) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3305296717216055985705322
% SZS output start Proof for 3305296717216055985705322
1. ! [X0] : (~tall(X0) => (tall(X0) & ~generous(X0))) [input p0]
10. ! [X0] : ((tall(X0) | old(X0)) => ~curious(X0)) [input p9]
23. curious(fred) [input hypothesis]
27. ! [X0] : ((tall(X0) & ~generous(X0)) | tall(X0)) [ennf transformation 1]
32. ! [X0] : (~curious(X0) | (~tall(X0) & ~old(X0))) [ennf transformation 10]
78. tall(X0) | tall(X0) [cnf transformation 27]
108. ~curious(X0) | ~tall(X0) [cnf transformation 32]
133. curious(fred) [cnf transformation 23]
134. tall(X0) [duplicate literal removal 78]
200. ~curious(X0) [subsumption resolution 108,134]
296. $false [subsumption resolution 133,200]
% SZS output end Proof for 3305296717216055985705322
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or humble then someone is rich and vice versa. If someone is not strong then someone is not brave or wise and vice versa. If fred is either funny or happy then lucy is either not happy or wise and vice versa. If someone is both not brave and not strong then mary is brave. If someone is not rich or not humble then alice is both not quiet and not patient. Everyone who is both not brave and not old is both not brave and creative and vice versa. Everyone who is not tall or not humble is both happy and patient. Everyone who is not quiet or not generous is not generous or not kind. If someone is tall or wise then susan is not funny and vice versa. If susan is not old then mary is either kind or calm and vice versa. Everyone who is either calm or not funny is not quiet and vice versa. If someone is not wise then someone is either not calm or rich and vice versa. If someone is not happy then paul is both not funny and rich and vice versa. Everyone who is either happy or not generous is not funny. If paul is not brave then someone is not patient and vice versa. If mary is either not happy or brave then mary is happy or not tall and vice versa. Fred is not generous or generous. Someone is either not happy or funny. Alice is both not strong and tall. Someone is not old. Alice is not wise. Lucy is either quiet or not quiet. Fred is either not patient or old. Susan is both generous and kind. | Susan is funny. | contradiction | ((?[X]:((creative(X)|humble(X))))<=>(?[X]:(rich(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~brave(X)|wise(X)))))&
(((funny(fred)<~>happy(fred)))<=>((~happy(lucy)<~>wise(lucy))))&
((?[X]:((~brave(X)&~strong(X))))=>(brave(mary)))&
((?[X]:((~rich(X)|~humble(X))))=>((~quiet(alice)&~patient(alice))))&
(![X]:((~brave(X)&~old(X))<=>(~brave(X)&creative(X))))&
(![X]:((~tall(X)|~humble(X))=>(happy(X)&patient(X))))&
(![X]:((~quiet(X)|~generous(X))=>(~generous(X)|~kind(X))))&
((?[X]:((tall(X)|wise(X))))<=>(~funny(susan)))&
((~old(susan))<=>((kind(mary)<~>calm(mary))))&
(![X]:((calm(X)<~>~funny(X))<=>~quiet(X)))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>rich(X)))))&
((?[X]:(~happy(X)))<=>((~funny(paul)&rich(paul))))&
(![X]:((happy(X)<~>~generous(X))=>~funny(X)))&
((~brave(paul))<=>(?[X]:(~patient(X))))&
(((~happy(mary)<~>brave(mary)))<=>((happy(mary)|~tall(mary))))&
((~generous(fred)|generous(fred)))&
(?[X]:((~happy(X)<~>funny(X))))&
((~strong(alice)&tall(alice)))&
(?[X]:(~old(X)))&
(~wise(alice))&
((quiet(lucy)<~>~quiet(lucy)))&
((~patient(fred)<~>old(fred)))&
((generous(susan)&kind(susan))) | funny(susan) | [
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2191289241869015852711756
% SZS output start Proof for 2191289241869015852711756
9. ? [X0] : (wise(X0) | tall(X0)) <=> ~funny(susan) [input p8]
19. tall(alice) & ~strong(alice) [input p18]
25. funny(susan) [input hypothesis]
48. (? [X0] : (wise(X0) | tall(X0)) | funny(susan)) & (~funny(susan) | ! [X0] : (~wise(X0) & ~tall(X0))) [nnf transformation 9]
49. (? [X0] : (wise(X0) | tall(X0)) | funny(susan)) & (~funny(susan) | ! [X1] : (~wise(X1) & ~tall(X1))) [rectify 48]
50. ? [X0] : (wise(X0) | tall(X0)) => (wise(sK4) | tall(sK4)) [choice axiom]
51. ((wise(sK4) | tall(sK4)) | funny(susan)) & (~funny(susan) | ! [X1] : (~wise(X1) & ~tall(X1))) [skolemisation 49,50]
107. ~funny(susan) | ~tall(X1) [cnf transformation 51]
139. tall(alice) [cnf transformation 19]
148. funny(susan) [cnf transformation 25]
250. 23 <=> funny(susan) [avatar definition]
264. 26 <=> ! [X1] : ~tall(X1) [avatar definition]
265. ~tall(X1) <- (26) [avatar component clause 264]
266. 26 | ~23 [avatar split clause 107,250,264]
372. 23 [avatar split clause 148,250]
375. $false <- (26) [resolution 265,139]
376. ~26 [avatar contradiction clause 375]
377. $false [avatar sat refutation 266,372,376]
% SZS output end Proof for 2191289241869015852711756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or not rich is quiet.
If someone is both old and tall then alice is either not creative or funny and vice versa.
If someone is either rich or not quiet then someone is not humble or not curious and vice versa.
Everyone who is not tall or patient is either not patient or old and vice versa.
Everyone who is kind or not strong is not tall or not kind.
Everyone who is not old or patient is not tall and vice versa.
Everyone who is both not wise and generous is not tall or curious and vice versa.
If john is not calm then someone is either not generous or not rich.
If fred is rich or generous then alice is both happy and quiet.
If someone is not creative or not kind then susan is both not rich and happy and vice versa.
Everyone who is either rich or brave is either kind or not generous and vice versa.
Everyone who is old or kind is either funny or patient.
If someone is rich or not calm then john is both happy and not creative and vice versa.
If mary is both brave and strong then alice is both calm and not humble.
Everyone who is not humble is either strong or calm and vice versa.
Everyone who is not wise is calm or not funny and vice versa.
Fred is rich.
Paul is calm.
Fred is either not old or curious.
Someone is not calm.
Someone is either curious or strong.
Mary is either not creative or old.
Fred is brave or curious.
Lucy is either humble or patient. | Susan is quiet. | entailment | (![X]:((tall(X)|~rich(X))=>quiet(X)))&
((?[X]:((old(X)&tall(X))))<=>((~creative(alice)<~>funny(alice))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>(?[X]:((~humble(X)|~curious(X)))))&
(![X]:((~tall(X)|patient(X))<=>(~patient(X)<~>old(X))))&
(![X]:((kind(X)|~strong(X))=>(~tall(X)|~kind(X))))&
(![X]:((~old(X)|patient(X))<=>~tall(X)))&
(![X]:((~wise(X)&generous(X))<=>(~tall(X)|curious(X))))&
((~calm(john))=>(?[X]:((~generous(X)<~>~rich(X)))))&
(((rich(fred)|generous(fred)))=>((happy(alice)&quiet(alice))))&
((?[X]:((~creative(X)|~kind(X))))<=>((~rich(susan)&happy(susan))))&
(![X]:((rich(X)<~>brave(X))<=>(kind(X)<~>~generous(X))))&
(![X]:((old(X)|kind(X))=>(funny(X)<~>patient(X))))&
((?[X]:((rich(X)|~calm(X))))<=>((happy(john)&~creative(john))))&
(((brave(mary)&strong(mary)))=>((calm(alice)&~humble(alice))))&
(![X]:(~humble(X)<=>(strong(X)<~>calm(X))))&
(![X]:(~wise(X)<=>(calm(X)|~funny(X))))&
(rich(fred))&
(calm(paul))&
((~old(fred)<~>curious(fred)))&
(?[X]:(~calm(X)))&
(?[X]:((curious(X)<~>strong(X))))&
((~creative(mary)<~>old(mary)))&
((brave(fred)|curious(fred)))&
((humble(lucy)<~>patient(lucy))) | quiet(susan) | [
"p0",
"p9",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7936357043906338661102476
% SZS output start Proof for 7936357043906338661102476
1. ! [X0] : ((~rich(X0) | tall(X0)) => quiet(X0)) [input p0]
10. ? [X0] : (~kind(X0) | ~creative(X0)) <=> (happy(susan) & ~rich(susan)) [input p9]
13. ? [X0] : (~calm(X0) | rich(X0)) <=> (~creative(john) & happy(john)) [input p12]
20. ? [X0] : ~calm(X0) [input p19]
25. ~quiet(susan) [input hypothesis]
27. ! [X0] : (quiet(X0) | (rich(X0) & ~tall(X0))) [ennf transformation 1]
53. (? [X0] : (~kind(X0) | ~creative(X0)) | (~happy(susan) | rich(susan))) & ((happy(susan) & ~rich(susan)) | ! [X0] : (kind(X0) & creative(X0))) [nnf transformation 10]
54. (? [X0] : (~kind(X0) | ~creative(X0)) | ~happy(susan) | rich(susan)) & ((happy(susan) & ~rich(susan)) | ! [X0] : (kind(X0) & creative(X0))) [flattening 53]
55. (? [X0] : (~kind(X0) | ~creative(X0)) | ~happy(susan) | rich(susan)) & ((happy(susan) & ~rich(susan)) | ! [X1] : (kind(X1) & creative(X1))) [rectify 54]
56. ? [X0] : (~kind(X0) | ~creative(X0)) => (~kind(sK4) | ~creative(sK4)) [choice axiom]
57. ((~kind(sK4) | ~creative(sK4)) | ~happy(susan) | rich(susan)) & ((happy(susan) & ~rich(susan)) | ! [X1] : (kind(X1) & creative(X1))) [skolemisation 55,56]
60. (? [X0] : (~calm(X0) | rich(X0)) | (creative(john) | ~happy(john))) & ((~creative(john) & happy(john)) | ! [X0] : (calm(X0) & ~rich(X0))) [nnf transformation 13]
61. (? [X0] : (~calm(X0) | rich(X0)) | creative(john) | ~happy(john)) & ((~creative(john) & happy(john)) | ! [X0] : (calm(X0) & ~rich(X0))) [flattening 60]
62. (? [X0] : (~calm(X0) | rich(X0)) | creative(john) | ~happy(john)) & ((~creative(john) & happy(john)) | ! [X1] : (calm(X1) & ~rich(X1))) [rectify 61]
63. ? [X0] : (~calm(X0) | rich(X0)) => (~calm(sK5) | rich(sK5)) [choice axiom]
64. ((~calm(sK5) | rich(sK5)) | creative(john) | ~happy(john)) & ((~creative(john) & happy(john)) | ! [X1] : (calm(X1) & ~rich(X1))) [skolemisation 62,63]
69. ? [X0] : ~calm(X0) => ~calm(sK6) [choice axiom]
70. ~calm(sK6) [skolemisation 20,69]
77. quiet(X0) | rich(X0) [cnf transformation 27]
112. ~rich(susan) | creative(X1) [cnf transformation 57]
132. ~creative(john) | calm(X1) [cnf transformation 64]
147. ~calm(sK6) [cnf transformation 70]
155. ~quiet(susan) [cnf transformation 25]
253. 20 <=> rich(susan) [avatar definition]
274. 25 <=> ! [X1] : creative(X1) [avatar definition]
275. creative(X1) <- (25) [avatar component clause 274]
278. 25 | ~20 [avatar split clause 112,253,274]
285. 27 <=> creative(john) [avatar definition]
286. ~creative(john) <- (~27) [avatar component clause 285]
298. 30 <=> ! [X1] : calm(X1) [avatar definition]
299. calm(X1) <- (30) [avatar component clause 298]
300. 30 | ~27 [avatar split clause 132,285,298]
374. rich(susan) [resolution 77,155]
377. 20 [avatar split clause 374,253]
381. $false <- (25, ~27) [resolution 275,286]
384. ~25 | 27 [avatar contradiction clause 381]
387. $false <- (30) [resolution 299,147]
390. ~30 [avatar contradiction clause 387]
391. $false [avatar sat refutation 278,300,377,384,390]
% SZS output end Proof for 7936357043906338661102476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is both wise and not tall and vice versa.
Everyone who is brave is wise or calm.
If paul is not creative or calm then someone is not strong and vice versa.
If someone is both tall and not creative then someone is both not curious and wise and vice versa.
If someone is both not kind and not wise then mary is either not tall or kind and vice versa.
Everyone who is both not patient and kind is curious and vice versa.
If susan is either not humble or calm then paul is both not rich and not brave.
Everyone who is both not patient and patient is not humble or funny and vice versa.
Everyone who is generous or happy is not strong or generous.
Everyone who is either not quiet or not kind is either not old or not generous.
Everyone who is kind is either not quiet or happy.
If someone is brave then someone is both not quiet and not humble.
Everyone who is not curious is either not curious or not wise and vice versa.
Everyone who is both brave and humble is humble or not rich.
Everyone who is not rich or quiet is both not happy and wise.
If susan is curious then mary is quiet or old.
Fred is curious or patient.
Fred is not patient or not calm.
Someone is both not old and not brave.
Mary is generous or not funny.
Someone is either not creative or tall.
Someone is rich. | Susan is tall. | neutral | (![X]:(~patient(X)<=>(wise(X)&~tall(X))))&
(![X]:(brave(X)=>(wise(X)|calm(X))))&
(((~creative(paul)|calm(paul)))<=>(?[X]:(~strong(X))))&
((?[X]:((tall(X)&~creative(X))))<=>(?[X]:((~curious(X)&wise(X)))))&
((?[X]:((~kind(X)&~wise(X))))<=>((~tall(mary)<~>kind(mary))))&
(![X]:((~patient(X)&kind(X))<=>curious(X)))&
(((~humble(susan)<~>calm(susan)))=>((~rich(paul)&~brave(paul))))&
(![X]:((~patient(X)&patient(X))<=>(~humble(X)|funny(X))))&
(![X]:((generous(X)|happy(X))=>(~strong(X)|generous(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~old(X)<~>~generous(X))))&
(![X]:(kind(X)=>(~quiet(X)<~>happy(X))))&
((?[X]:(brave(X)))=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:(~curious(X)<=>(~curious(X)<~>~wise(X))))&
(![X]:((brave(X)&humble(X))=>(humble(X)|~rich(X))))&
(![X]:((~rich(X)|quiet(X))=>(~happy(X)&wise(X))))&
((curious(susan))=>((quiet(mary)|old(mary))))&
((curious(fred)|patient(fred)))&
((~patient(fred)|~calm(fred)))&
(?[X]:((~old(X)&~brave(X))))&
((generous(mary)|~funny(mary)))&
(?[X]:((~creative(X)<~>tall(X))))&
(?[X]:(rich(X))) | tall(susan) | [] | null | 0 |
Everyone who is not patient or wise is both old and not rich. Everyone who is not humble or quiet is not humble. Everyone who is not kind is both old and funny and vice versa. If susan is not tall or tall then someone is funny or kind. If someone is rich or not wise then john is not funny or not humble and vice versa. Everyone who is both calm and not creative is either not funny or not strong and vice versa. If john is either rich or not funny then someone is not old or not humble and vice versa. Everyone who is not patient is both calm and generous and vice versa. Everyone who is both not curious and funny is either not humble or happy and vice versa. Everyone who is both not patient and not strong is either not tall or funny. If john is both not rich and curious then someone is both kind and not strong. Everyone who is brave or humble is not old and vice versa. If someone is wise then someone is both creative and old and vice versa. Everyone who is both rich and tall is either patient or not curious. If alice is either creative or generous then paul is calm or not calm and vice versa. Everyone who is calm is not humble or not brave and vice versa. Someone is funny or not calm. Someone is funny. Someone is kind or not brave. Someone is generous or quiet. Someone is both not funny and old. Susan is calm or wise. Alice is not calm. | Paul is funny. | neutral | (![X]:((~patient(X)|wise(X))=>(old(X)&~rich(X))))&
(![X]:((~humble(X)|quiet(X))=>~humble(X)))&
(![X]:(~kind(X)<=>(old(X)&funny(X))))&
(((~tall(susan)|tall(susan)))=>(?[X]:((funny(X)|kind(X)))))&
((?[X]:((rich(X)|~wise(X))))<=>((~funny(john)|~humble(john))))&
(![X]:((calm(X)&~creative(X))<=>(~funny(X)<~>~strong(X))))&
(((rich(john)<~>~funny(john)))<=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:(~patient(X)<=>(calm(X)&generous(X))))&
(![X]:((~curious(X)&funny(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((~patient(X)&~strong(X))=>(~tall(X)<~>funny(X))))&
(((~rich(john)&curious(john)))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((brave(X)|humble(X))<=>~old(X)))&
((?[X]:(wise(X)))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:((rich(X)&tall(X))=>(patient(X)<~>~curious(X))))&
(((creative(alice)<~>generous(alice)))<=>((calm(paul)|~calm(paul))))&
(![X]:(calm(X)<=>(~humble(X)|~brave(X))))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:((generous(X)|quiet(X))))&
(?[X]:((~funny(X)&old(X))))&
((calm(susan)|wise(susan)))&
(~calm(alice)) | funny(paul) | [] | null | 0 |
Everyone who is not quiet or kind is creative and vice versa.
If john is both wise and humble then susan is both wise and not quiet.
Everyone who is not patient or funny is funny or tall.
Everyone who is both calm and not creative is either curious or not quiet.
Everyone who is happy is not quiet or tall.
If someone is old or calm then lucy is both brave and not calm.
If someone is calm or quiet then mary is old or strong and vice versa.
Everyone who is both old and not happy is both quiet and not brave.
If someone is strong or not strong then alice is creative and vice versa.
If paul is both old and not patient then someone is either generous or creative.
Everyone who is not brave is both not calm and generous and vice versa.
Everyone who is either strong or patient is both not calm and not funny.
Everyone who is either funny or patient is happy and vice versa.
If fred is either curious or not kind then john is both quiet and not old.
If mary is both not tall and humble then someone is not strong.
Everyone who is both not curious and kind is brave.
Someone is not happy.
Lucy is both not calm and strong.
Someone is quiet or humble.
Mary is both curious and not quiet.
Someone is both quiet and not brave.
Alice is either not creative or generous.
Someone is both not rich and humble.
Someone is either not wise or strong. | Alice is not brave. | neutral | (![X]:((~quiet(X)|kind(X))<=>creative(X)))&
(((wise(john)&humble(john)))=>((wise(susan)&~quiet(susan))))&
(![X]:((~patient(X)|funny(X))=>(funny(X)|tall(X))))&
(![X]:((calm(X)&~creative(X))=>(curious(X)<~>~quiet(X))))&
(![X]:(happy(X)=>(~quiet(X)|tall(X))))&
((?[X]:((old(X)|calm(X))))=>((brave(lucy)&~calm(lucy))))&
((?[X]:((calm(X)|quiet(X))))<=>((old(mary)|strong(mary))))&
(![X]:((old(X)&~happy(X))=>(quiet(X)&~brave(X))))&
((?[X]:((strong(X)|~strong(X))))<=>(creative(alice)))&
(((old(paul)&~patient(paul)))=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:(~brave(X)<=>(~calm(X)&generous(X))))&
(![X]:((strong(X)<~>patient(X))=>(~calm(X)&~funny(X))))&
(![X]:((funny(X)<~>patient(X))<=>happy(X)))&
(((curious(fred)<~>~kind(fred)))=>((quiet(john)&~old(john))))&
(((~tall(mary)&humble(mary)))=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)&kind(X))=>brave(X)))&
(?[X]:(~happy(X)))&
((~calm(lucy)&strong(lucy)))&
(?[X]:((quiet(X)|humble(X))))&
((curious(mary)&~quiet(mary)))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(alice)<~>generous(alice)))&
(?[X]:((~rich(X)&humble(X))))&
(?[X]:((~wise(X)<~>strong(X)))) | ~brave(alice) | [] | null | 0 |
Everyone who is either not tall or not calm is both not creative and not old. If susan is funny then someone is rich and vice versa. Everyone who is not calm or patient is both creative and old and vice versa. If lucy is not kind then someone is either generous or not strong and vice versa. Everyone who is both not quiet and strong is both not humble and curious and vice versa. If someone is not calm or not strong then someone is both tall and not generous and vice versa. Everyone who is not strong is not wise or quiet and vice versa. If someone is not curious or not old then alice is wise or old and vice versa. Everyone who is generous or rich is either not patient or not brave. If someone is humble then susan is both not quiet and brave and vice versa. Everyone who is not patient or not creative is both humble and not generous and vice versa. Everyone who is either not quiet or not patient is both brave and not calm. If john is both not old and not rich then someone is not kind or happy. Everyone who is either not rich or patient is both not creative and not happy and vice versa. Everyone who is both funny and not kind is either humble or not old. Someone is quiet or not old. Someone is tall or rich. Mary is strong or generous. Alice is either kind or not brave. Someone is strong or happy. Someone is either quiet or not funny. Someone is humble or not creative. Susan is not brave or not funny. | John is quiet. | neutral | (![X]:((~tall(X)<~>~calm(X))=>(~creative(X)&~old(X))))&
((funny(susan))<=>(?[X]:(rich(X))))&
(![X]:((~calm(X)|patient(X))<=>(creative(X)&old(X))))&
((~kind(lucy))<=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((~quiet(X)&strong(X))<=>(~humble(X)&curious(X))))&
((?[X]:((~calm(X)|~strong(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
(![X]:(~strong(X)<=>(~wise(X)|quiet(X))))&
((?[X]:((~curious(X)|~old(X))))<=>((wise(alice)|old(alice))))&
(![X]:((generous(X)|rich(X))=>(~patient(X)<~>~brave(X))))&
((?[X]:(humble(X)))<=>((~quiet(susan)&brave(susan))))&
(![X]:((~patient(X)|~creative(X))<=>(humble(X)&~generous(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(brave(X)&~calm(X))))&
(((~old(john)&~rich(john)))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((~rich(X)<~>patient(X))<=>(~creative(X)&~happy(X))))&
(![X]:((funny(X)&~kind(X))=>(humble(X)<~>~old(X))))&
(?[X]:((quiet(X)|~old(X))))&
(?[X]:((tall(X)|rich(X))))&
((strong(mary)|generous(mary)))&
((kind(alice)<~>~brave(alice)))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((quiet(X)<~>~funny(X))))&
(?[X]:((humble(X)|~creative(X))))&
((~brave(susan)|~funny(susan))) | quiet(john) | [] | null | 0 |
If susan is strong then someone is not patient or wise and vice versa. If someone is not humble or strong then lucy is not strong and vice versa. Everyone who is not strong is either not patient or calm and vice versa. If someone is not generous then paul is not rich and vice versa. Everyone who is either not patient or brave is both not patient and creative and vice versa. Everyone who is both happy and not calm is both rich and not rich. If someone is both not brave and not funny then paul is both strong and not strong. If mary is creative or not quiet then someone is both not rich and humble. If someone is not rich then fred is not curious or not generous. Everyone who is both not happy and not calm is curious. Everyone who is not humble is curious. Everyone who is not wise or brave is rich or tall. If lucy is not humble or not quiet then someone is not happy or not brave. Everyone who is old or not funny is either not kind or strong and vice versa. Everyone who is calm is brave or funny and vice versa. If susan is old then mary is tall or not quiet and vice versa. Alice is not creative. Fred is either tall or not patient. Paul is happy or funny. Mary is both not old and not creative. John is both rich and happy. John is not funny or not tall. Lucy is not kind. | Fred is tall. | neutral | ((strong(susan))<=>(?[X]:((~patient(X)|wise(X)))))&
((?[X]:((~humble(X)|strong(X))))<=>(~strong(lucy)))&
(![X]:(~strong(X)<=>(~patient(X)<~>calm(X))))&
((?[X]:(~generous(X)))<=>(~rich(paul)))&
(![X]:((~patient(X)<~>brave(X))<=>(~patient(X)&creative(X))))&
(![X]:((happy(X)&~calm(X))=>(rich(X)&~rich(X))))&
((?[X]:((~brave(X)&~funny(X))))=>((strong(paul)&~strong(paul))))&
(((creative(mary)|~quiet(mary)))=>(?[X]:((~rich(X)&humble(X)))))&
((?[X]:(~rich(X)))=>((~curious(fred)|~generous(fred))))&
(![X]:((~happy(X)&~calm(X))=>curious(X)))&
(![X]:(~humble(X)=>curious(X)))&
(![X]:((~wise(X)|brave(X))=>(rich(X)|tall(X))))&
(((~humble(lucy)|~quiet(lucy)))=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:((old(X)|~funny(X))<=>(~kind(X)<~>strong(X))))&
(![X]:(calm(X)<=>(brave(X)|funny(X))))&
((old(susan))<=>((tall(mary)|~quiet(mary))))&
(~creative(alice))&
((tall(fred)<~>~patient(fred)))&
((happy(paul)|funny(paul)))&
((~old(mary)&~creative(mary)))&
((rich(john)&happy(john)))&
((~funny(john)|~tall(john)))&
(~kind(lucy)) | tall(fred) | [] | null | 0 |
If someone is not kind or humble then someone is both not wise and not quiet and vice versa.
Everyone who is quiet is not wise and vice versa.
Everyone who is quiet or creative is not strong and vice versa.
If someone is not funny then someone is either not patient or calm.
If someone is either not curious or patient then someone is not quiet.
If lucy is not funny then someone is quiet and vice versa.
If someone is not calm or rich then someone is both not patient and funny.
If someone is both humble and patient then alice is either not kind or generous.
If someone is both not old and funny then someone is both not kind and calm.
Everyone who is not humble is both calm and not creative.
Everyone who is either brave or humble is not wise or humble and vice versa.
Everyone who is either calm or not creative is either strong or funny and vice versa.
Everyone who is either calm or wise is both generous and funny and vice versa.
Everyone who is old is both strong and not rich and vice versa.
Everyone who is both not brave and kind is either not rich or creative and vice versa.
Everyone who is both not old and funny is not strong and vice versa.
Mary is not wise or happy.
Someone is both not creative and kind.
Someone is both not humble and not patient.
Someone is both not patient and strong.
Fred is quiet or not brave. | Fred is not generous. | entailment | ((?[X]:((~kind(X)|humble(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:(quiet(X)<=>~wise(X)))&
(![X]:((quiet(X)|creative(X))<=>~strong(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~patient(X)<~>calm(X)))))&
((?[X]:((~curious(X)<~>patient(X))))=>(?[X]:(~quiet(X))))&
((~funny(lucy))<=>(?[X]:(quiet(X))))&
((?[X]:((~calm(X)|rich(X))))=>(?[X]:((~patient(X)&funny(X)))))&
((?[X]:((humble(X)&patient(X))))=>((~kind(alice)<~>generous(alice))))&
((?[X]:((~old(X)&funny(X))))=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:(~humble(X)=>(calm(X)&~creative(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~wise(X)|humble(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(strong(X)<~>funny(X))))&
(![X]:((calm(X)<~>wise(X))<=>(generous(X)&funny(X))))&
(![X]:(old(X)<=>(strong(X)&~rich(X))))&
(![X]:((~brave(X)&kind(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((~old(X)&funny(X))<=>~strong(X)))&
((~wise(mary)|happy(mary)))&
(?[X]:((~creative(X)&kind(X))))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~patient(X)&strong(X))))&
((quiet(fred)|~brave(fred))) | ~generous(fred) | [
"p0",
"p1",
"p2",
"p8",
"p9",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7283484610740443471632758
% SZS output start Proof for 7283484610740443471632758
1. ? [X0] : (humble(X0) | ~kind(X0)) <=> ? [X0] : (~quiet(X0) & ~wise(X0)) [input p0]
2. ! [X0] : (quiet(X0) <=> ~wise(X0)) [input p1]
3. ! [X0] : ((creative(X0) | quiet(X0)) <=> ~strong(X0)) [input p2]
9. ? [X0] : (funny(X0) & ~old(X0)) => ? [X0] : (calm(X0) & ~kind(X0)) [input p8]
10. ! [X0] : (~humble(X0) => (~creative(X0) & calm(X0))) [input p9]
12. ! [X0] : ((calm(X0) <~> ~creative(X0)) <=> (strong(X0) <~> funny(X0))) [input p11]
13. ! [X0] : ((calm(X0) <~> wise(X0)) <=> (funny(X0) & generous(X0))) [input p12]
14. ! [X0] : (old(X0) <=> (~rich(X0) & strong(X0))) [input p13]
16. ! [X0] : ((funny(X0) & ~old(X0)) <=> ~strong(X0)) [input p15]
22. generous(fred) [input hypothesis]
23. ? [X0] : (humble(X0) | ~kind(X0)) <=> ? [X1] : (~quiet(X1) & ~wise(X1)) [rectify 1]
27. ? [X0] : (funny(X0) & ~old(X0)) => ? [X1] : (calm(X1) & ~kind(X1)) [rectify 9]
33. ? [X1] : (calm(X1) & ~kind(X1)) | ! [X0] : (~funny(X0) | old(X0)) [ennf transformation 27]
34. ! [X0] : ((~creative(X0) & calm(X0)) | humble(X0)) [ennf transformation 10]
35. (? [X0] : (humble(X0) | ~kind(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X1] : (~quiet(X1) & ~wise(X1)) | ! [X0] : (~humble(X0) & kind(X0))) [nnf transformation 23]
36. (? [X0] : (humble(X0) | ~kind(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X2] : (~quiet(X2) & ~wise(X2)) | ! [X3] : (~humble(X3) & kind(X3))) [rectify 35]
37. ? [X0] : (humble(X0) | ~kind(X0)) => (humble(sK0) | ~kind(sK0)) [choice axiom]
38. ? [X2] : (~quiet(X2) & ~wise(X2)) => (~quiet(sK1) & ~wise(sK1)) [choice axiom]
39. ((humble(sK0) | ~kind(sK0)) | ! [X1] : (quiet(X1) | wise(X1))) & ((~quiet(sK1) & ~wise(sK1)) | ! [X3] : (~humble(X3) & kind(X3))) [skolemisation 36,38,37]
40. ! [X0] : ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0))) [nnf transformation 2]
41. ! [X0] : (((creative(X0) | quiet(X0)) | strong(X0)) & (~strong(X0) | (~creative(X0) & ~quiet(X0)))) [nnf transformation 3]
42. ! [X0] : ((creative(X0) | quiet(X0) | strong(X0)) & (~strong(X0) | (~creative(X0) & ~quiet(X0)))) [flattening 41]
59. ? [X0] : (calm(X0) & ~kind(X0)) | ! [X1] : (~funny(X1) | old(X1)) [rectify 33]
60. ? [X0] : (calm(X0) & ~kind(X0)) => (calm(sK6) & ~kind(sK6)) [choice axiom]
61. (calm(sK6) & ~kind(sK6)) | ! [X1] : (~funny(X1) | old(X1)) [skolemisation 59,60]
64. ! [X0] : ((((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) & (((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0))))) [nnf transformation 12]
65. ! [X0] : ((((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | (~funny(X0) | ~generous(X0))) & ((funny(X0) & generous(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0))))) [nnf transformation 13]
66. ! [X0] : ((((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | ~funny(X0) | ~generous(X0)) & ((funny(X0) & generous(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0))))) [flattening 65]
67. ! [X0] : ((old(X0) | (rich(X0) | ~strong(X0))) & ((~rich(X0) & strong(X0)) | ~old(X0))) [nnf transformation 14]
68. ! [X0] : ((old(X0) | rich(X0) | ~strong(X0)) & ((~rich(X0) & strong(X0)) | ~old(X0))) [flattening 67]
71. ! [X0] : (((funny(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | (~funny(X0) | old(X0)))) [nnf transformation 16]
72. ! [X0] : (((funny(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | ~funny(X0) | old(X0))) [flattening 71]
79. ~wise(sK1) | kind(X3) [cnf transformation 39]
80. ~wise(sK1) | ~humble(X3) [cnf transformation 39]
81. ~quiet(sK1) | kind(X3) [cnf transformation 39]
85. quiet(X0) | wise(X0) [cnf transformation 40]
86. ~strong(X0) | ~quiet(X0) [cnf transformation 42]
87. ~strong(X0) | ~creative(X0) [cnf transformation 42]
101. ~kind(sK6) | ~funny(X1) | old(X1) [cnf transformation 61]
103. calm(X0) | humble(X0) [cnf transformation 34]
114. ~funny(X0) | ~strong(X0) | calm(X0) | creative(X0) [cnf transformation 64]
116. ~creative(X0) | calm(X0) | strong(X0) | ~funny(X0) [cnf transformation 64]
117. creative(X0) | ~calm(X0) | funny(X0) | ~strong(X0) [cnf transformation 64]
124. ~generous(X0) | ~calm(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 66]
125. ~old(X0) | strong(X0) [cnf transformation 68]
136. funny(X0) | strong(X0) [cnf transformation 72]
144. generous(fred) [cnf transformation 22]
148. 1 <=> ! [X1] : (quiet(X1) | wise(X1)) [avatar definition]
149. quiet(X1) | wise(X1) <- (1) [avatar component clause 148]
160. 4 <=> ! [X3] : ~humble(X3) [avatar definition]
161. ~humble(X3) <- (4) [avatar component clause 160]
163. 5 <=> quiet(sK1) [avatar definition]
165. ~quiet(sK1) <- (~5) [avatar component clause 163]
168. 6 <=> ! [X3] : kind(X3) [avatar definition]
169. kind(X3) <- (6) [avatar component clause 168]
170. 6 | ~5 [avatar split clause 81,163,168]
172. 7 <=> wise(sK1) [avatar definition]
174. ~wise(sK1) <- (~7) [avatar component clause 172]
175. 4 | ~7 [avatar split clause 80,172,160]
176. 6 | ~7 [avatar split clause 79,172,168]
177. 1 [avatar split clause 85,148]
179. 8 <=> ! [X1] : funny(X1) [avatar definition]
180. funny(X1) <- (8) [avatar component clause 179]
204. 14 <=> ! [X0] : ~quiet(X0) [avatar definition]
205. ~quiet(X0) <- (14) [avatar component clause 204]
225. 19 <=> ! [X1] : calm(X1) [avatar definition]
226. calm(X1) <- (19) [avatar component clause 225]
248. 24 <=> ! [X1] : (~funny(X1) | old(X1)) [avatar definition]
249. ~funny(X1) | old(X1) <- (24) [avatar component clause 248]
256. 26 <=> kind(sK6) [avatar definition]
258. ~kind(sK6) <- (~26) [avatar component clause 256]
259. 24 | ~26 [avatar split clause 101,256,248]
261. ~calm(X0) | funny(X0) | ~strong(X0) [subsumption resolution 117,87]
262. ~funny(X0) | calm(X0) | ~creative(X0) [subsumption resolution 116,87]
263. ~funny(X0) | ~strong(X0) | calm(X0) [subsumption resolution 114,262]
274. wise(X1) <- (1, 14) [subsumption resolution 149,205]
275. $false <- (1, ~7, 14) [resolution 274,174]
276. ~1 | 7 | ~14 [avatar contradiction clause 275]
289. wise(sK1) <- (1, ~5) [resolution 149,165]
294. 7 | ~1 | 5 [avatar split clause 289,163,148,172]
296. old(X0) | strong(X0) <- (24) [resolution 249,136]
297. strong(X0) <- (24) [subsumption resolution 296,125]
303. ~quiet(X1) <- (24) [resolution 297,86]
304. 14 | ~24 [avatar split clause 303,248,204]
348. $false <- (6, ~26) [subsumption resolution 258,169]
349. ~6 | 26 [avatar contradiction clause 348]
355. wise(X0) <- (1, 14) [resolution 205,149]
363. old(X0) | strong(X0) <- (24) [resolution 249,136]
365. strong(X0) <- (24) [subsumption resolution 363,125]
419. funny(X0) | ~strong(X0) | humble(X0) [resolution 261,103]
423. funny(X0) | humble(X0) <- (24) [subsumption resolution 419,365]
424. funny(X0) <- (4, 24) [subsumption resolution 423,161]
425. 8 | ~4 | ~24 [avatar split clause 424,248,160,179]
439. ~strong(X0) | calm(X0) <- (8) [resolution 263,180]
444. calm(X0) <- (8, 24) [subsumption resolution 439,365]
445. 19 | ~8 | ~24 [avatar split clause 444,248,179,225]
491. ~calm(fred) | ~funny(fred) | ~wise(fred) [resolution 124,144]
494. ~funny(fred) | ~wise(fred) <- (19) [subsumption resolution 491,226]
506. ~wise(fred) <- (8, 19) [subsumption resolution 494,180]
507. $false <- (1, 8, 14, 19) [subsumption resolution 506,355]
508. ~1 | ~8 | ~14 | ~19 [avatar contradiction clause 507]
511. $false [avatar sat refutation 170,175,176,177,259,276,294,304,349,425,445,508]
% SZS output end Proof for 7283484610740443471632758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either tall or not strong then someone is humble and vice versa.
If someone is both not kind and not wise then susan is either kind or generous.
Everyone who is not happy is both not funny and happy.
If someone is patient or not happy then fred is either not old or not curious and vice versa.
Everyone who is kind or humble is not humble.
If someone is either wise or curious then someone is either not brave or strong.
If someone is not wise or funny then mary is both old and tall and vice versa.
If someone is not old then paul is both not generous and tall.
If someone is rich or creative then paul is old and vice versa.
Everyone who is wise or strong is not old or not wise.
Everyone who is either funny or not patient is not kind or not old.
Everyone who is happy or old is both brave and wise.
Everyone who is generous or not kind is curious.
If someone is either not patient or kind then someone is wise or not happy.
If someone is both not happy and strong then someone is generous or not patient.
Someone is curious.
Susan is not generous.
Fred is either not rich or not happy.
Someone is patient.
Someone is both not creative and not old.
John is both wise and not quiet.
Someone is either quiet or happy. | Paul is not creative. | entailment | ((?[X]:((tall(X)<~>~strong(X))))<=>(?[X]:(humble(X))))&
((?[X]:((~kind(X)&~wise(X))))=>((kind(susan)<~>generous(susan))))&
(![X]:(~happy(X)=>(~funny(X)&happy(X))))&
((?[X]:((patient(X)|~happy(X))))<=>((~old(fred)<~>~curious(fred))))&
(![X]:((kind(X)|humble(X))=>~humble(X)))&
((?[X]:((wise(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>strong(X)))))&
((?[X]:((~wise(X)|funny(X))))<=>((old(mary)&tall(mary))))&
((?[X]:(~old(X)))=>((~generous(paul)&tall(paul))))&
((?[X]:((rich(X)|creative(X))))<=>(old(paul)))&
(![X]:((wise(X)|strong(X))=>(~old(X)|~wise(X))))&
(![X]:((funny(X)<~>~patient(X))=>(~kind(X)|~old(X))))&
(![X]:((happy(X)|old(X))=>(brave(X)&wise(X))))&
(![X]:((generous(X)|~kind(X))=>curious(X)))&
((?[X]:((~patient(X)<~>kind(X))))=>(?[X]:((wise(X)|~happy(X)))))&
((?[X]:((~happy(X)&strong(X))))=>(?[X]:((generous(X)|~patient(X)))))&
(?[X]:(curious(X)))&
(~generous(susan))&
((~rich(fred)<~>~happy(fred)))&
(?[X]:(patient(X)))&
(?[X]:((~creative(X)&~old(X))))&
((wise(john)&~quiet(john)))&
(?[X]:((quiet(X)<~>happy(X)))) | ~creative(paul) | [
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4499782490063729897106060
% SZS output start Proof for 4499782490063729897106060
9. ? [X0] : (creative(X0) | rich(X0)) <=> old(paul) [input p8]
10. ! [X0] : ((strong(X0) | wise(X0)) => (~wise(X0) | ~old(X0))) [input p9]
12. ! [X0] : ((old(X0) | happy(X0)) => (wise(X0) & brave(X0))) [input p11]
23. creative(paul) [input hypothesis]
33. ! [X0] : ((~wise(X0) | ~old(X0)) | (~strong(X0) & ~wise(X0))) [ennf transformation 10]
34. ! [X0] : (~wise(X0) | ~old(X0) | (~strong(X0) & ~wise(X0))) [flattening 33]
37. ! [X0] : ((wise(X0) & brave(X0)) | (~old(X0) & ~happy(X0))) [ennf transformation 12]
60. (? [X0] : (creative(X0) | rich(X0)) | ~old(paul)) & (old(paul) | ! [X0] : (~creative(X0) & ~rich(X0))) [nnf transformation 9]
61. (? [X0] : (creative(X0) | rich(X0)) | ~old(paul)) & (old(paul) | ! [X1] : (~creative(X1) & ~rich(X1))) [rectify 60]
62. ? [X0] : (creative(X0) | rich(X0)) => (creative(sK5) | rich(sK5)) [choice axiom]
63. ((creative(sK5) | rich(sK5)) | ~old(paul)) & (old(paul) | ! [X1] : (~creative(X1) & ~rich(X1))) [skolemisation 61,62]
110. old(paul) | ~creative(X1) [cnf transformation 63]
112. ~wise(X0) | ~old(X0) | ~wise(X0) [cnf transformation 34]
119. wise(X0) | ~old(X0) [cnf transformation 37]
136. creative(paul) [cnf transformation 23]
137. ~wise(X0) | ~old(X0) [duplicate literal removal 112]
259. 27 <=> old(paul) [avatar definition]
260. old(paul) <- (27) [avatar component clause 259]
272. 30 <=> ! [X1] : ~creative(X1) [avatar definition]
273. ~creative(X1) <- (30) [avatar component clause 272]
274. 30 | 27 [avatar split clause 110,259,272]
279. ~old(X0) [subsumption resolution 119,137]
300. $false <- (27) [subsumption resolution 260,279]
301. ~27 [avatar contradiction clause 300]
312. $false <- (30) [resolution 273,136]
313. ~30 [avatar contradiction clause 312]
314. $false [avatar sat refutation 274,301,313]
% SZS output end Proof for 4499782490063729897106060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or creative is both tall and not strong.
Everyone who is both generous and tall is both not old and humble and vice versa.
If paul is creative then someone is not happy and vice versa.
Everyone who is both not humble and not generous is happy and vice versa.
If someone is both not generous and calm then fred is either not strong or tall.
If lucy is both calm and not rich then someone is calm and vice versa.
Everyone who is curious or happy is either calm or kind.
If susan is not kind then alice is both patient and not humble and vice versa.
Everyone who is rich is both curious and not humble and vice versa.
If lucy is either not creative or humble then mary is either not brave or not humble.
If john is not curious then someone is calm or not humble.
Everyone who is either kind or not generous is rich.
Everyone who is either not patient or not old is not generous and vice versa.
If someone is patient or not wise then someone is both not curious and not funny.
Someone is not strong.
Paul is either humble or not brave.
Someone is either not rich or not calm.
Mary is both not curious and tall.
John is not brave. | Paul is curious. | neutral | (![X]:((~strong(X)|creative(X))=>(tall(X)&~strong(X))))&
(![X]:((generous(X)&tall(X))<=>(~old(X)&humble(X))))&
((creative(paul))<=>(?[X]:(~happy(X))))&
(![X]:((~humble(X)&~generous(X))<=>happy(X)))&
((?[X]:((~generous(X)&calm(X))))=>((~strong(fred)<~>tall(fred))))&
(((calm(lucy)&~rich(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((curious(X)|happy(X))=>(calm(X)<~>kind(X))))&
((~kind(susan))<=>((patient(alice)&~humble(alice))))&
(![X]:(rich(X)<=>(curious(X)&~humble(X))))&
(((~creative(lucy)<~>humble(lucy)))=>((~brave(mary)<~>~humble(mary))))&
((~curious(john))=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((kind(X)<~>~generous(X))=>rich(X)))&
(![X]:((~patient(X)<~>~old(X))<=>~generous(X)))&
((?[X]:((patient(X)|~wise(X))))=>(?[X]:((~curious(X)&~funny(X)))))&
(?[X]:(~strong(X)))&
((humble(paul)<~>~brave(paul)))&
(?[X]:((~rich(X)<~>~calm(X))))&
((~curious(mary)&tall(mary)))&
(~brave(john)) | curious(paul) | [] | null | 0 |
If someone is curious or old then lucy is both not old and rich and vice versa.
Everyone who is not rich or not brave is funny and vice versa.
If someone is not generous then mary is both curious and not happy and vice versa.
Everyone who is either not strong or strong is creative or calm.
Everyone who is both not quiet and funny is not brave or generous.
Everyone who is not tall or not generous is strong or not rich and vice versa.
If someone is not calm then someone is rich or kind.
If alice is either not humble or patient then someone is calm or not happy.
Everyone who is not humble or not tall is both old and not humble and vice versa.
Everyone who is either generous or not curious is not tall and vice versa.
If susan is not tall then alice is either not old or not curious and vice versa.
If john is tall then someone is happy or not strong and vice versa.
If paul is humble or kind then someone is both wise and not quiet.
If someone is either rich or quiet then susan is tall and vice versa.
Everyone who is either not patient or not old is either happy or kind and vice versa.
If someone is both generous and not humble then lucy is either kind or not generous.
Someone is tall.
Someone is either strong or not quiet.
Alice is both not generous and calm.
Alice is either funny or not calm.
Susan is both tall and not curious.
Susan is both old and quiet.
Someone is both happy and rich. | Paul is kind. | neutral | ((?[X]:((curious(X)|old(X))))<=>((~old(lucy)&rich(lucy))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)|calm(X))))&
(![X]:((~quiet(X)&funny(X))=>(~brave(X)|generous(X))))&
(![X]:((~tall(X)|~generous(X))<=>(strong(X)|~rich(X))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(((~humble(alice)<~>patient(alice)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((~humble(X)|~tall(X))<=>(old(X)&~humble(X))))&
(![X]:((generous(X)<~>~curious(X))<=>~tall(X)))&
((~tall(susan))<=>((~old(alice)<~>~curious(alice))))&
((tall(john))<=>(?[X]:((happy(X)|~strong(X)))))&
(((humble(paul)|kind(paul)))=>(?[X]:((wise(X)&~quiet(X)))))&
((?[X]:((rich(X)<~>quiet(X))))<=>(tall(susan)))&
(![X]:((~patient(X)<~>~old(X))<=>(happy(X)<~>kind(X))))&
((?[X]:((generous(X)&~humble(X))))=>((kind(lucy)<~>~generous(lucy))))&
(?[X]:(tall(X)))&
(?[X]:((strong(X)<~>~quiet(X))))&
((~generous(alice)&calm(alice)))&
((funny(alice)<~>~calm(alice)))&
((tall(susan)&~curious(susan)))&
((old(susan)&quiet(susan)))&
(?[X]:((happy(X)&rich(X)))) | kind(paul) | [] | null | 0 |
Everyone who is either quiet or not creative is either not quiet or not curious and vice versa. Everyone who is either wise or patient is not calm or creative. If someone is both tall and not brave then someone is creative. If someone is not calm or not happy then mary is generous. Everyone who is both generous and calm is tall and vice versa. If paul is funny then paul is not creative. Everyone who is either wise or quiet is kind or not brave and vice versa. Everyone who is not kind or kind is either calm or tall. Everyone who is both creative and strong is quiet or patient and vice versa. Everyone who is either quiet or humble is not rich or patient and vice versa. Everyone who is both not tall and funny is not old or curious and vice versa. Everyone who is either patient or not strong is both not calm and brave and vice versa. Everyone who is not strong is kind or not calm and vice versa. If susan is old or not tall then someone is quiet. If someone is both quiet and happy then fred is happy or generous and vice versa. Everyone who is not wise or not rich is both not happy and not brave. Fred is not funny or not brave. Someone is curious or funny. Someone is not quiet or humble. Someone is calm or kind. Someone is either calm or generous. Someone is both not kind and strong. | Susan is curious. | contradiction | (![X]:((quiet(X)<~>~creative(X))<=>(~quiet(X)<~>~curious(X))))&
(![X]:((wise(X)<~>patient(X))=>(~calm(X)|creative(X))))&
((?[X]:((tall(X)&~brave(X))))=>(?[X]:(creative(X))))&
((?[X]:((~calm(X)|~happy(X))))=>(generous(mary)))&
(![X]:((generous(X)&calm(X))<=>tall(X)))&
((funny(paul))=>(~creative(paul)))&
(![X]:((wise(X)<~>quiet(X))<=>(kind(X)|~brave(X))))&
(![X]:((~kind(X)|kind(X))=>(calm(X)<~>tall(X))))&
(![X]:((creative(X)&strong(X))<=>(quiet(X)|patient(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~rich(X)|patient(X))))&
(![X]:((~tall(X)&funny(X))<=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
((~funny(fred)|~brave(fred)))&
(?[X]:((curious(X)|funny(X))))&
(?[X]:((~quiet(X)|humble(X))))&
(?[X]:((calm(X)|kind(X))))&
(?[X]:((calm(X)<~>generous(X))))&
(?[X]:((~kind(X)&strong(X)))) | curious(susan) | [
"p0",
"p1",
"p3",
"p4",
"p7",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4354211223594868676199927
% SZS output start Proof for 4354211223594868676199927
1. ! [X0] : ((quiet(X0) <~> ~creative(X0)) <=> (~quiet(X0) <~> ~curious(X0))) [input p0]
2. ! [X0] : ((wise(X0) <~> patient(X0)) => (creative(X0) | ~calm(X0))) [input p1]
4. ? [X0] : (~happy(X0) | ~calm(X0)) => generous(mary) [input p3]
5. ! [X0] : ((calm(X0) & generous(X0)) <=> tall(X0)) [input p4]
8. ! [X0] : ((kind(X0) | ~kind(X0)) => (calm(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((strong(X0) & creative(X0)) <=> (patient(X0) | quiet(X0))) [input p8]
12. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p11]
16. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p15]
23. curious(susan) [input hypothesis]
25. ! [X0] : ((creative(X0) | ~calm(X0)) | (wise(X0) <=> patient(X0))) [ennf transformation 2]
26. ! [X0] : (creative(X0) | ~calm(X0) | (wise(X0) <=> patient(X0))) [flattening 25]
28. generous(mary) | ! [X0] : (happy(X0) & calm(X0)) [ennf transformation 4]
30. ! [X0] : ((calm(X0) <~> tall(X0)) | (~kind(X0) & kind(X0))) [ennf transformation 8]
32. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 16]
33. ! [X0] : ((((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) & (((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0))))) [nnf transformation 1]
34. ! [X0] : (creative(X0) | ~calm(X0) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0)))) [nnf transformation 26]
38. ! [X0] : (((calm(X0) & generous(X0)) | ~tall(X0)) & (tall(X0) | (~calm(X0) | ~generous(X0)))) [nnf transformation 5]
39. ! [X0] : (((calm(X0) & generous(X0)) | ~tall(X0)) & (tall(X0) | ~calm(X0) | ~generous(X0))) [flattening 38]
42. ! [X0] : (((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | (~kind(X0) & kind(X0))) [nnf transformation 30]
43. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 9]
44. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~strong(X0) | ~creative(X0))) [flattening 43]
49. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 12]
50. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 49]
71. ~curious(X0) | ~quiet(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 33]
75. ~creative(X0) | quiet(X0) | ~curious(X0) | quiet(X0) [cnf transformation 33]
79. ~calm(X0) | creative(X0) | patient(X0) | ~wise(X0) [cnf transformation 34]
83. generous(mary) | happy(X0) [cnf transformation 28]
84. ~generous(X0) | ~calm(X0) | tall(X0) [cnf transformation 39]
86. ~tall(X0) | calm(X0) [cnf transformation 39]
94. tall(X0) | calm(X0) | kind(X0) [cnf transformation 42]
95. tall(X0) | calm(X0) | ~kind(X0) [cnf transformation 42]
96. ~tall(X0) | ~calm(X0) | kind(X0) [cnf transformation 42]
97. ~tall(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 42]
102. ~patient(X0) | strong(X0) [cnf transformation 44]
114. ~calm(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 50]
130. ~happy(X0) | wise(X0) [cnf transformation 32]
142. curious(susan) [cnf transformation 23]
143. ~curious(X0) | ~quiet(X0) | ~creative(X0) [duplicate literal removal 71]
145. ~curious(X0) | quiet(X0) | ~creative(X0) [duplicate literal removal 75]
148. ~curious(X0) | ~creative(X0) [subsumption resolution 143,145]
158. 3 <=> ! [X0] : happy(X0) [avatar definition]
159. happy(X0) <- (3) [avatar component clause 158]
161. 4 <=> generous(mary) [avatar definition]
163. generous(mary) <- (4) [avatar component clause 161]
164. 3 | 4 [avatar split clause 83,161,158]
166. 5 <=> ! [X0] : calm(X0) [avatar definition]
167. calm(X0) <- (5) [avatar component clause 166]
178. ~kind(X0) | ~tall(X0) [subsumption resolution 97,86]
179. ~tall(X0) | kind(X0) [subsumption resolution 96,86]
180. ~tall(X0) [subsumption resolution 179,178]
181. ~kind(X0) | calm(X0) [subsumption resolution 95,180]
182. calm(X0) | kind(X0) [subsumption resolution 94,180]
183. calm(X0) [subsumption resolution 182,181]
184. 5 [avatar split clause 183,166]
189. ~calm(X0) | ~patient(X0) [subsumption resolution 114,102]
259. ~creative(susan) [resolution 148,142]
266. ~patient(X0) <- (5) [resolution 189,167]
271. ~calm(mary) | tall(mary) <- (4) [resolution 84,163]
273. tall(mary) <- (4, 5) [subsumption resolution 271,167]
274. $false <- (4, 5) [subsumption resolution 273,180]
275. ~4 | ~5 [avatar contradiction clause 274]
280. wise(X1) <- (3) [resolution 159,130]
301. creative(X0) | patient(X0) | ~wise(X0) <- (5) [resolution 79,167]
304. creative(X0) | ~wise(X0) <- (5) [subsumption resolution 301,266]
305. creative(X0) <- (3, 5) [subsumption resolution 304,280]
310. $false <- (3, 5) [resolution 305,259]
311. ~3 | ~5 [avatar contradiction clause 310]
313. $false [avatar sat refutation 164,184,275,311]
% SZS output end Proof for 4354211223594868676199927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both not rich and tall. If susan is strong or not humble then someone is both not calm and patient and vice versa. Everyone who is either not kind or rich is both not happy and brave. If someone is not rich then mary is either rich or humble and vice versa. If alice is either tall or not strong then someone is curious and vice versa. Everyone who is curious or calm is patient and vice versa. Everyone who is both rich and not kind is both happy and not tall and vice versa. Everyone who is quiet or patient is not curious or curious and vice versa. Everyone who is not happy is either not kind or wise and vice versa. If paul is both not patient and not kind then someone is both funny and not quiet and vice versa. If susan is both not kind and patient then someone is both strong and not tall and vice versa. Everyone who is either not kind or not quiet is creative or wise. If someone is both calm and not happy then lucy is either not generous or happy and vice versa. Everyone who is either not strong or not wise is wise and vice versa. If lucy is either not old or wise then fred is both not strong and not tall and vice versa. If someone is both patient and tall then susan is both not patient and calm. Someone is either generous or not brave. Someone is not kind. Someone is both calm and not brave. Someone is generous. Someone is kind or not old. Someone is either kind or not tall. Someone is not generous or wise. | Alice is not kind. | neutral | (![X]:(~wise(X)=>(~rich(X)&tall(X))))&
(((strong(susan)|~humble(susan)))<=>(?[X]:((~calm(X)&patient(X)))))&
(![X]:((~kind(X)<~>rich(X))=>(~happy(X)&brave(X))))&
((?[X]:(~rich(X)))<=>((rich(mary)<~>humble(mary))))&
(((tall(alice)<~>~strong(alice)))<=>(?[X]:(curious(X))))&
(![X]:((curious(X)|calm(X))<=>patient(X)))&
(![X]:((rich(X)&~kind(X))<=>(happy(X)&~tall(X))))&
(![X]:((quiet(X)|patient(X))<=>(~curious(X)|curious(X))))&
(![X]:(~happy(X)<=>(~kind(X)<~>wise(X))))&
(((~patient(paul)&~kind(paul)))<=>(?[X]:((funny(X)&~quiet(X)))))&
(((~kind(susan)&patient(susan)))<=>(?[X]:((strong(X)&~tall(X)))))&
(![X]:((~kind(X)<~>~quiet(X))=>(creative(X)|wise(X))))&
((?[X]:((calm(X)&~happy(X))))<=>((~generous(lucy)<~>happy(lucy))))&
(![X]:((~strong(X)<~>~wise(X))<=>wise(X)))&
(((~old(lucy)<~>wise(lucy)))<=>((~strong(fred)&~tall(fred))))&
((?[X]:((patient(X)&tall(X))))=>((~patient(susan)&calm(susan))))&
(?[X]:((generous(X)<~>~brave(X))))&
(?[X]:(~kind(X)))&
(?[X]:((calm(X)&~brave(X))))&
(?[X]:(generous(X)))&
(?[X]:((kind(X)|~old(X))))&
(?[X]:((kind(X)<~>~tall(X))))&
(?[X]:((~generous(X)|wise(X)))) | ~kind(alice) | [] | null | 0 |
Everyone who is either not funny or generous is either quiet or patient.
If lucy is both not rich and generous then lucy is both not quiet and old and vice versa.
If fred is not quiet or not strong then mary is not calm and vice versa.
If mary is either not curious or not quiet then someone is both not kind and curious and vice versa.
Everyone who is either old or brave is not tall and vice versa.
If someone is old then alice is both not happy and brave and vice versa.
Everyone who is humble or not generous is either quiet or tall and vice versa.
If someone is either not calm or not rich then paul is both not humble and rich.
Everyone who is generous or not tall is both not happy and not brave.
Everyone who is not quiet or rich is both quiet and not humble and vice versa.
Everyone who is brave or patient is either not funny or not creative.
If someone is old then lucy is happy or rich.
Everyone who is both happy and curious is strong.
If someone is rich then someone is both not brave and not kind.
Everyone who is not funny or not rich is not tall.
If lucy is not kind or strong then alice is old or not happy and vice versa.
Someone is curious or not brave.
Someone is humble or generous.
Fred is both not happy and rich.
Someone is kind or wise.
Someone is not calm or not generous. | Alice is not patient. | entailment | (![X]:((~funny(X)<~>generous(X))=>(quiet(X)<~>patient(X))))&
(((~rich(lucy)&generous(lucy)))<=>((~quiet(lucy)&old(lucy))))&
(((~quiet(fred)|~strong(fred)))<=>(~calm(mary)))&
(((~curious(mary)<~>~quiet(mary)))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((old(X)<~>brave(X))<=>~tall(X)))&
((?[X]:(old(X)))<=>((~happy(alice)&brave(alice))))&
(![X]:((humble(X)|~generous(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>((~humble(paul)&rich(paul))))&
(![X]:((generous(X)|~tall(X))=>(~happy(X)&~brave(X))))&
(![X]:((~quiet(X)|rich(X))<=>(quiet(X)&~humble(X))))&
(![X]:((brave(X)|patient(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:(old(X)))=>((happy(lucy)|rich(lucy))))&
(![X]:((happy(X)&curious(X))=>strong(X)))&
((?[X]:(rich(X)))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((~funny(X)|~rich(X))=>~tall(X)))&
(((~kind(lucy)|strong(lucy)))<=>((old(alice)|~happy(alice))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((humble(X)|generous(X))))&
((~happy(fred)&rich(fred)))&
(?[X]:((kind(X)|wise(X))))&
(?[X]:((~calm(X)|~generous(X)))) | ~patient(alice) | [
"p0",
"p4",
"p5",
"p6",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 547448604344809385935399
% SZS output start Proof for 547448604344809385935399
1. ! [X0] : ((~funny(X0) <~> generous(X0)) => (quiet(X0) <~> patient(X0))) [input p0]
5. ! [X0] : ((old(X0) <~> brave(X0)) <=> ~tall(X0)) [input p4]
6. ? [X0] : old(X0) <=> (brave(alice) & ~happy(alice)) [input p5]
7. ! [X0] : ((~generous(X0) | humble(X0)) <=> (quiet(X0) <~> tall(X0))) [input p6]
9. ! [X0] : ((~tall(X0) | generous(X0)) => (~brave(X0) & ~happy(X0))) [input p8]
10. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> (~humble(X0) & quiet(X0))) [input p9]
15. ! [X0] : ((~rich(X0) | ~funny(X0)) => ~tall(X0)) [input p14]
22. patient(alice) [input hypothesis]
25. ! [X0] : ((quiet(X0) <~> patient(X0)) | (~funny(X0) <=> generous(X0))) [ennf transformation 1]
27. ! [X0] : ((~brave(X0) & ~happy(X0)) | (tall(X0) & ~generous(X0))) [ennf transformation 9]
34. ! [X0] : (~tall(X0) | (rich(X0) & funny(X0))) [ennf transformation 15]
35. ! [X0] : (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | ((~funny(X0) | ~generous(X0)) & (generous(X0) | funny(X0)))) [nnf transformation 25]
44. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | tall(X0)) & (~tall(X0) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [nnf transformation 5]
45. (? [X0] : old(X0) | (~brave(alice) | happy(alice))) & ((brave(alice) & ~happy(alice)) | ! [X0] : ~old(X0)) [nnf transformation 6]
46. (? [X0] : old(X0) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X0] : ~old(X0)) [flattening 45]
47. (? [X0] : old(X0) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X1] : ~old(X1)) [rectify 46]
48. ? [X0] : old(X0) => old(sK1) [choice axiom]
49. (old(sK1) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X1] : ~old(X1)) [skolemisation 47,48]
50. ! [X0] : (((~generous(X0) | humble(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [nnf transformation 7]
51. ! [X0] : ((~generous(X0) | humble(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [flattening 50]
53. ! [X0] : (((rich(X0) | ~quiet(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [nnf transformation 10]
54. ! [X0] : ((rich(X0) | ~quiet(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [flattening 53]
70. ~patient(X0) | ~quiet(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 35]
85. ~tall(X0) | old(X0) | ~brave(X0) [cnf transformation 44]
86. tall(X0) | old(X0) | brave(X0) [cnf transformation 44]
87. ~brave(X0) | ~old(X0) | tall(X0) [cnf transformation 44]
89. brave(alice) | ~old(X1) [cnf transformation 49]
94. ~tall(X0) | ~quiet(X0) | generous(X0) [cnf transformation 51]
103. ~brave(X0) | ~generous(X0) [cnf transformation 27]
104. ~brave(X0) | tall(X0) [cnf transformation 27]
105. quiet(X0) | quiet(X0) [cnf transformation 54]
118. ~tall(X0) | funny(X0) [cnf transformation 34]
129. patient(alice) [cnf transformation 22]
130. quiet(X0) [duplicate literal removal 105]
197. 14 <=> brave(alice) [avatar definition]
198. brave(alice) <- (14) [avatar component clause 197]
199. ~brave(alice) <- (~14) [avatar component clause 197]
206. 16 <=> ! [X1] : ~old(X1) [avatar definition]
207. ~old(X1) <- (16) [avatar component clause 206]
208. 16 | 14 [avatar split clause 89,197,206]
256. 27 <=> old(alice) [avatar definition]
257. old(alice) <- (27) [avatar component clause 256]
292. tall(alice) <- (14) [resolution 104,198]
303. old(alice) | ~brave(alice) <- (14) [resolution 85,292]
304. old(alice) <- (14) [subsumption resolution 303,198]
305. 27 | ~14 [avatar split clause 304,197,256]
311. brave(X3) | old(X3) | funny(X3) [resolution 86,118]
327. ~old(alice) | tall(alice) <- (14) [resolution 198,87]
329. ~generous(alice) <- (14) [resolution 198,103]
330. tall(alice) <- (14, 27) [subsumption resolution 327,257]
353. ~quiet(X1) | generous(X1) | old(X1) | brave(X1) [resolution 94,86]
354. ~quiet(alice) | generous(alice) <- (14, 27) [resolution 94,330]
356. brave(X1) | old(X1) | generous(X1) [subsumption resolution 353,130]
357. generous(alice) <- (14, 27) [subsumption resolution 354,130]
358. $false <- (14, 27) [subsumption resolution 357,329]
359. ~14 | ~27 [avatar contradiction clause 358]
403. ~quiet(alice) | ~funny(alice) | ~generous(alice) [resolution 70,129]
409. old(X2) | funny(X2) | tall(X2) [resolution 311,104]
416. funny(X2) | tall(X2) <- (16) [subsumption resolution 409,207]
417. funny(X2) <- (16) [subsumption resolution 416,118]
423. ~funny(alice) | ~generous(alice) [subsumption resolution 403,130]
424. ~generous(alice) <- (16) [subsumption resolution 423,417]
429. old(alice) | generous(alice) <- (~14) [resolution 356,199]
433. generous(alice) <- (~14, 16) [subsumption resolution 429,207]
434. $false <- (~14, 16) [subsumption resolution 433,424]
435. 14 | ~16 [avatar contradiction clause 434]
438. $false [avatar sat refutation 208,305,359,435]
% SZS output end Proof for 547448604344809385935399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not quiet then someone is either creative or brave and vice versa.
If alice is either not strong or rich then someone is both not generous and patient.
Everyone who is either humble or patient is wise.
Everyone who is either not funny or not quiet is not quiet.
Everyone who is both not funny and tall is either not strong or strong and vice versa.
Everyone who is not quiet or patient is humble or not old.
Everyone who is both kind and not brave is humble and vice versa.
Everyone who is tall or happy is humble or not happy and vice versa.
Everyone who is both wise and curious is patient or humble.
Everyone who is both not patient and not wise is either not quiet or funny and vice versa.
If mary is patient then alice is both not patient and strong and vice versa.
If someone is not brave then paul is not old.
Everyone who is not brave or not calm is rich or not tall and vice versa.
If paul is both patient and humble then paul is patient or not funny.
Everyone who is generous is either not generous or not curious.
Mary is not quiet.
Lucy is happy or not humble.
John is both not strong and not kind.
Mary is not brave or not rich.
Someone is either not creative or not funny. | John is not rich. | neutral | ((?[X]:((strong(X)|~quiet(X))))<=>(?[X]:((creative(X)<~>brave(X)))))&
(((~strong(alice)<~>rich(alice)))=>(?[X]:((~generous(X)&patient(X)))))&
(![X]:((humble(X)<~>patient(X))=>wise(X)))&
(![X]:((~funny(X)<~>~quiet(X))=>~quiet(X)))&
(![X]:((~funny(X)&tall(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((~quiet(X)|patient(X))=>(humble(X)|~old(X))))&
(![X]:((kind(X)&~brave(X))<=>humble(X)))&
(![X]:((tall(X)|happy(X))<=>(humble(X)|~happy(X))))&
(![X]:((wise(X)&curious(X))=>(patient(X)|humble(X))))&
(![X]:((~patient(X)&~wise(X))<=>(~quiet(X)<~>funny(X))))&
((patient(mary))<=>((~patient(alice)&strong(alice))))&
((?[X]:(~brave(X)))=>(~old(paul)))&
(![X]:((~brave(X)|~calm(X))<=>(rich(X)|~tall(X))))&
(((patient(paul)&humble(paul)))=>((patient(paul)|~funny(paul))))&
(![X]:(generous(X)=>(~generous(X)<~>~curious(X))))&
(~quiet(mary))&
((happy(lucy)|~humble(lucy)))&
((~strong(john)&~kind(john)))&
((~brave(mary)|~rich(mary)))&
(?[X]:((~creative(X)<~>~funny(X)))) | ~rich(john) | [] | null | 0 |
Everyone who is both rich and not happy is not old or calm and vice versa.
Everyone who is happy or not humble is happy and vice versa.
Everyone who is both not brave and humble is both kind and not wise and vice versa.
Everyone who is both tall and old is humble or not strong and vice versa.
If fred is not calm then someone is either generous or calm and vice versa.
Everyone who is kind or old is quiet.
Everyone who is not happy or not tall is either not strong or tall and vice versa.
Everyone who is not creative is either not funny or funny.
If john is wise then someone is either old or creative and vice versa.
If mary is not happy or brave then someone is not strong or funny and vice versa.
Everyone who is either not patient or not calm is both not old and funny.
Everyone who is not patient is not kind.
Everyone who is both calm and not tall is rich.
Everyone who is strong is either not brave or humble and vice versa.
If someone is both rich and not quiet then fred is both curious and not brave.
If fred is brave or not kind then paul is wise and vice versa.
Someone is either not generous or old.
Someone is either humble or patient.
Someone is not humble.
Paul is quiet or not quiet.
Someone is either rich or not funny.
Paul is either not curious or kind. | Mary is not calm. | neutral | (![X]:((rich(X)&~happy(X))<=>(~old(X)|calm(X))))&
(![X]:((happy(X)|~humble(X))<=>happy(X)))&
(![X]:((~brave(X)&humble(X))<=>(kind(X)&~wise(X))))&
(![X]:((tall(X)&old(X))<=>(humble(X)|~strong(X))))&
((~calm(fred))<=>(?[X]:((generous(X)<~>calm(X)))))&
(![X]:((kind(X)|old(X))=>quiet(X)))&
(![X]:((~happy(X)|~tall(X))<=>(~strong(X)<~>tall(X))))&
(![X]:(~creative(X)=>(~funny(X)<~>funny(X))))&
((wise(john))<=>(?[X]:((old(X)<~>creative(X)))))&
(((~happy(mary)|brave(mary)))<=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~patient(X)<~>~calm(X))=>(~old(X)&funny(X))))&
(![X]:(~patient(X)=>~kind(X)))&
(![X]:((calm(X)&~tall(X))=>rich(X)))&
(![X]:(strong(X)<=>(~brave(X)<~>humble(X))))&
((?[X]:((rich(X)&~quiet(X))))=>((curious(fred)&~brave(fred))))&
(((brave(fred)|~kind(fred)))<=>(wise(paul)))&
(?[X]:((~generous(X)<~>old(X))))&
(?[X]:((humble(X)<~>patient(X))))&
(?[X]:(~humble(X)))&
((quiet(paul)|~quiet(paul)))&
(?[X]:((rich(X)<~>~funny(X))))&
((~curious(paul)<~>kind(paul))) | ~calm(mary) | [] | null | 0 |
If someone is brave or curious then paul is either not curious or not generous.
Everyone who is either humble or not funny is not wise.
If alice is not funny then alice is either happy or not quiet.
If susan is not patient or not quiet then someone is old.
If john is both not wise and not kind then alice is wise or strong.
If someone is quiet or funny then someone is both strong and not strong and vice versa.
Everyone who is not brave or not patient is not humble and vice versa.
Everyone who is both tall and generous is either old or not creative and vice versa.
Everyone who is either not generous or not kind is patient or happy.
If someone is strong or quiet then someone is not wise or not calm.
Everyone who is both not patient and wise is both not creative and not rich.
Everyone who is kind or patient is creative and vice versa.
If someone is both not humble and not brave then lucy is both funny and not happy.
Everyone who is either generous or curious is either not happy or funny and vice versa.
Everyone who is wise is either not humble or calm and vice versa.
If someone is both creative and patient then someone is old.
John is not old or strong.
Mary is rich.
Someone is not strong or generous.
Fred is not humble or not generous.
Someone is both not quiet and calm.
Paul is not quiet.
Someone is either not happy or rich.
Lucy is happy. | Alice is funny. | contradiction | ((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((humble(X)<~>~funny(X))=>~wise(X)))&
((~funny(alice))=>((happy(alice)<~>~quiet(alice))))&
(((~patient(susan)|~quiet(susan)))=>(?[X]:(old(X))))&
(((~wise(john)&~kind(john)))=>((wise(alice)|strong(alice))))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~brave(X)|~patient(X))<=>~humble(X)))&
(![X]:((tall(X)&generous(X))<=>(old(X)<~>~creative(X))))&
(![X]:((~generous(X)<~>~kind(X))=>(patient(X)|happy(X))))&
((?[X]:((strong(X)|quiet(X))))=>(?[X]:((~wise(X)|~calm(X)))))&
(![X]:((~patient(X)&wise(X))=>(~creative(X)&~rich(X))))&
(![X]:((kind(X)|patient(X))<=>creative(X)))&
((?[X]:((~humble(X)&~brave(X))))=>((funny(lucy)&~happy(lucy))))&
(![X]:((generous(X)<~>curious(X))<=>(~happy(X)<~>funny(X))))&
(![X]:(wise(X)<=>(~humble(X)<~>calm(X))))&
((?[X]:((creative(X)&patient(X))))=>(?[X]:(old(X))))&
((~old(john)|strong(john)))&
(rich(mary))&
(?[X]:((~strong(X)|generous(X))))&
((~humble(fred)|~generous(fred)))&
(?[X]:((~quiet(X)&calm(X))))&
(~quiet(paul))&
(?[X]:((~happy(X)<~>rich(X))))&
(happy(lucy)) | funny(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5449721817081755527584589
% SZS output start Proof for 5449721817081755527584589
6. ? [X0] : (funny(X0) | quiet(X0)) <=> ? [X0] : (~strong(X0) & strong(X0)) [input p5]
25. funny(alice) [input hypothesis]
26. ? [X0] : (funny(X0) | quiet(X0)) <=> ? [X1] : (~strong(X1) & strong(X1)) [rectify 6]
47. (? [X0] : (funny(X0) | quiet(X0)) | ! [X1] : (strong(X1) | ~strong(X1))) & (? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : (~funny(X0) & ~quiet(X0))) [nnf transformation 26]
48. (? [X0] : (funny(X0) | quiet(X0)) | ! [X1] : (strong(X1) | ~strong(X1))) & (? [X2] : (~strong(X2) & strong(X2)) | ! [X3] : (~funny(X3) & ~quiet(X3))) [rectify 47]
49. ? [X0] : (funny(X0) | quiet(X0)) => (funny(sK1) | quiet(sK1)) [choice axiom]
50. ? [X2] : (~strong(X2) & strong(X2)) => (~strong(sK2) & strong(sK2)) [choice axiom]
51. ((funny(sK1) | quiet(sK1)) | ! [X1] : (strong(X1) | ~strong(X1))) & ((~strong(sK2) & strong(sK2)) | ! [X3] : (~funny(X3) & ~quiet(X3))) [skolemisation 48,50,49]
86. strong(sK2) | ~funny(X3) [cnf transformation 51]
88. ~strong(sK2) | ~funny(X3) [cnf transformation 51]
133. funny(alice) [cnf transformation 25]
153. 5 <=> funny(alice) [avatar definition]
155. funny(alice) <- (5) [avatar component clause 153]
198. 15 <=> ! [X3] : ~funny(X3) [avatar definition]
199. ~funny(X3) <- (15) [avatar component clause 198]
201. 16 <=> strong(sK2) [avatar definition]
204. 15 | ~16 [avatar split clause 88,201,198]
209. 15 | 16 [avatar split clause 86,201,198]
286. 5 [avatar split clause 133,153]
287. $false <- (5, 15) [subsumption resolution 155,199]
288. ~5 | ~15 [avatar contradiction clause 287]
289. $false [avatar sat refutation 204,209,286,288]
% SZS output end Proof for 5449721817081755527584589
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not strong and funny then someone is creative or generous and vice versa. If someone is both not strong and not happy then lucy is both not quiet and not brave. If someone is both strong and not patient then alice is both not curious and funny. Everyone who is either not creative or not humble is patient or kind. Everyone who is either not quiet or creative is either patient or happy. Everyone who is not kind or not old is either not humble or not old. Everyone who is either kind or old is not humble or not calm. Everyone who is calm or not quiet is strong or patient and vice versa. If alice is curious or not humble then someone is strong or not patient and vice versa. Everyone who is both not patient and quiet is not rich or not wise and vice versa. Everyone who is either not rich or not funny is both calm and not funny and vice versa. If someone is either rich or calm then fred is happy and vice versa. Everyone who is both not generous and not rich is curious and vice versa. If fred is either not kind or quiet then someone is both rich and old and vice versa. Everyone who is not patient is either not humble or rich and vice versa. Everyone who is creative is both kind and not brave. Someone is not generous. Alice is both creative and happy. Someone is either rich or not kind. Paul is not creative or not calm. Someone is humble or funny. Someone is both calm and generous. Alice is not tall or not humble. | Lucy is creative. | neutral | (((~strong(alice)&funny(alice)))<=>(?[X]:((creative(X)|generous(X)))))&
((?[X]:((~strong(X)&~happy(X))))=>((~quiet(lucy)&~brave(lucy))))&
((?[X]:((strong(X)&~patient(X))))=>((~curious(alice)&funny(alice))))&
(![X]:((~creative(X)<~>~humble(X))=>(patient(X)|kind(X))))&
(![X]:((~quiet(X)<~>creative(X))=>(patient(X)<~>happy(X))))&
(![X]:((~kind(X)|~old(X))=>(~humble(X)<~>~old(X))))&
(![X]:((kind(X)<~>old(X))=>(~humble(X)|~calm(X))))&
(![X]:((calm(X)|~quiet(X))<=>(strong(X)|patient(X))))&
(((curious(alice)|~humble(alice)))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~patient(X)&quiet(X))<=>(~rich(X)|~wise(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(calm(X)&~funny(X))))&
((?[X]:((rich(X)<~>calm(X))))<=>(happy(fred)))&
(![X]:((~generous(X)&~rich(X))<=>curious(X)))&
(((~kind(fred)<~>quiet(fred)))<=>(?[X]:((rich(X)&old(X)))))&
(![X]:(~patient(X)<=>(~humble(X)<~>rich(X))))&
(![X]:(creative(X)=>(kind(X)&~brave(X))))&
(?[X]:(~generous(X)))&
((creative(alice)&happy(alice)))&
(?[X]:((rich(X)<~>~kind(X))))&
((~creative(paul)|~calm(paul)))&
(?[X]:((humble(X)|funny(X))))&
(?[X]:((calm(X)&generous(X))))&
((~tall(alice)|~humble(alice))) | creative(lucy) | [] | null | 0 |
Everyone who is both not calm and creative is either not quiet or not tall and vice versa. If someone is not curious or not generous then john is not tall or not quiet and vice versa. Everyone who is either not kind or not funny is curious or wise and vice versa. If someone is not creative then someone is both kind and wise and vice versa. If fred is both not kind and not rich then someone is not curious and vice versa. Everyone who is rich or not wise is not brave and vice versa. Everyone who is not creative or old is both wise and not kind. Everyone who is both not calm and creative is not quiet or generous and vice versa. Everyone who is both wise and patient is brave or not happy and vice versa. If fred is brave or not rich then someone is tall and vice versa. If someone is generous or happy then lucy is not creative or not generous. Everyone who is both not creative and humble is both not old and curious and vice versa. If someone is not happy or not kind then john is both generous and not quiet. Everyone who is not wise is not patient or happy. Everyone who is curious or not strong is either not old or wise. Everyone who is wise or not wise is both not curious and not wise. Mary is both not kind and calm. Someone is generous. Someone is old or rich. Alice is both not curious and not strong. John is creative or wise. Lucy is not quiet or not wise. John is either not kind or not humble. | Lucy is tall. | entailment | (![X]:((~calm(X)&creative(X))<=>(~quiet(X)<~>~tall(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((~tall(john)|~quiet(john))))&
(![X]:((~kind(X)<~>~funny(X))<=>(curious(X)|wise(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((kind(X)&wise(X)))))&
(((~kind(fred)&~rich(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((rich(X)|~wise(X))<=>~brave(X)))&
(![X]:((~creative(X)|old(X))=>(wise(X)&~kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:((wise(X)&patient(X))<=>(brave(X)|~happy(X))))&
(((brave(fred)|~rich(fred)))<=>(?[X]:(tall(X))))&
((?[X]:((generous(X)|happy(X))))=>((~creative(lucy)|~generous(lucy))))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
(![X]:(~wise(X)=>(~patient(X)|happy(X))))&
(![X]:((curious(X)|~strong(X))=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(~curious(X)&~wise(X))))&
((~kind(mary)&calm(mary)))&
(?[X]:(generous(X)))&
(?[X]:((old(X)|rich(X))))&
((~curious(alice)&~strong(alice)))&
((creative(john)|wise(john)))&
((~quiet(lucy)|~wise(lucy)))&
((~kind(john)<~>~humble(john))) | tall(lucy) | [
"p0",
"p6",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 383561954862480663610171
% SZS output start Proof for 383561954862480663610171
1. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (~quiet(X0) <~> ~tall(X0))) [input p0]
7. ! [X0] : ((old(X0) | ~creative(X0)) => (~kind(X0) & wise(X0))) [input p6]
8. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (generous(X0) | ~quiet(X0))) [input p7]
11. ? [X0] : (happy(X0) | generous(X0)) => (~generous(lucy) | ~creative(lucy)) [input p10]
16. ! [X0] : ((~wise(X0) | wise(X0)) => (~wise(X0) & ~curious(X0))) [input p15]
24. ~tall(lucy) [input hypothesis]
26. ! [X0] : ((~kind(X0) & wise(X0)) | (~old(X0) & creative(X0))) [ennf transformation 7]
27. (~generous(lucy) | ~creative(lucy)) | ! [X0] : (~happy(X0) & ~generous(X0)) [ennf transformation 11]
28. ~generous(lucy) | ~creative(lucy) | ! [X0] : (~happy(X0) & ~generous(X0)) [flattening 27]
33. ! [X0] : ((~wise(X0) & ~curious(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 16]
34. ! [X0] : (((creative(X0) & ~calm(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0)))) & (((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | (~creative(X0) | calm(X0)))) [nnf transformation 1]
35. ! [X0] : (((creative(X0) & ~calm(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0)))) & (((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | ~creative(X0) | calm(X0))) [flattening 34]
55. ! [X0] : (((creative(X0) & ~calm(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (~creative(X0) | calm(X0)))) [nnf transformation 8]
56. ! [X0] : (((creative(X0) & ~calm(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | ~creative(X0) | calm(X0))) [flattening 55]
73. ~creative(X0) | quiet(X0) | tall(X0) | calm(X0) [cnf transformation 35]
75. ~quiet(X0) | ~calm(X0) | tall(X0) [cnf transformation 35]
97. wise(X0) | creative(X0) [cnf transformation 26]
101. ~quiet(X0) | generous(X0) | ~creative(X0) | calm(X0) [cnf transformation 56]
102. ~calm(X0) | quiet(X0) [cnf transformation 56]
105. ~generous(X0) | creative(X0) [cnf transformation 56]
114. ~generous(lucy) | ~creative(lucy) | ~generous(X0) [cnf transformation 28]
131. ~wise(X0) | ~wise(X0) [cnf transformation 33]
143. ~tall(lucy) [cnf transformation 24]
144. ~wise(X0) [duplicate literal removal 131]
180. 9 <=> ! [X3] : creative(X3) [avatar definition]
181. creative(X3) <- (9) [avatar component clause 180]
227. 19 <=> generous(lucy) [avatar definition]
228. generous(lucy) <- (19) [avatar component clause 227]
229. ~generous(lucy) <- (~19) [avatar component clause 227]
231. ~generous(lucy) | ~generous(X0) [subsumption resolution 114,105]
233. 20 <=> ! [X0] : ~generous(X0) [avatar definition]
234. ~generous(X0) <- (20) [avatar component clause 233]
235. 20 | ~19 [avatar split clause 231,227,233]
278. creative(X0) [resolution 97,144]
317. quiet(X0) | tall(X0) | calm(X0) <- (9) [resolution 73,181]
318. tall(X0) | quiet(X0) <- (9) [subsumption resolution 317,102]
319. quiet(lucy) <- (9) [resolution 318,143]
326. ~calm(lucy) | tall(lucy) <- (9) [resolution 319,75]
327. ~calm(lucy) <- (9) [subsumption resolution 326,143]
335. generous(lucy) | ~creative(lucy) | calm(lucy) <- (9) [resolution 101,319]
336. ~creative(lucy) | calm(lucy) <- (9, ~19) [subsumption resolution 335,229]
337. calm(lucy) <- (9, ~19) [subsumption resolution 336,181]
338. $false <- (9, ~19) [subsumption resolution 337,327]
339. ~9 | 19 [avatar contradiction clause 338]
341. 9 [avatar split clause 278,180]
344. $false <- (19, 20) [subsumption resolution 228,234]
345. ~19 | ~20 [avatar contradiction clause 344]
348. $false [avatar sat refutation 235,339,341,345]
% SZS output end Proof for 383561954862480663610171
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not happy or not old then someone is either not brave or not generous and vice versa. If someone is happy or not creative then alice is not old. If someone is not tall or not generous then someone is both kind and curious. Everyone who is not happy or brave is not creative and vice versa. Everyone who is either not creative or funny is both kind and patient. If someone is not patient then someone is not calm. If mary is not kind or not patient then someone is old or patient and vice versa. If someone is both quiet and not funny then someone is both wise and not wise. Everyone who is not kind or old is both not quiet and not wise. If someone is both not calm and calm then someone is either not quiet or patient and vice versa. Everyone who is both humble and quiet is either not rich or humble. Everyone who is wise is either brave or rich. Everyone who is both not tall and old is either happy or not rich. If mary is both not curious and tall then fred is not old and vice versa. If someone is funny then someone is both rich and not generous. Everyone who is kind is both brave and creative. Someone is either not wise or kind. Susan is either old or not strong. Alice is either not brave or not happy. Someone is either not kind or not humble. Lucy is not calm or kind. Someone is not rich. | Lucy is generous. | entailment | (((~happy(fred)|~old(fred)))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((?[X]:((happy(X)|~creative(X))))=>(~old(alice)))&
((?[X]:((~tall(X)|~generous(X))))=>(?[X]:((kind(X)&curious(X)))))&
(![X]:((~happy(X)|brave(X))<=>~creative(X)))&
(![X]:((~creative(X)<~>funny(X))=>(kind(X)&patient(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~calm(X))))&
(((~kind(mary)|~patient(mary)))<=>(?[X]:((old(X)|patient(X)))))&
((?[X]:((quiet(X)&~funny(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~kind(X)|old(X))=>(~quiet(X)&~wise(X))))&
((?[X]:((~calm(X)&calm(X))))<=>(?[X]:((~quiet(X)<~>patient(X)))))&
(![X]:((humble(X)&quiet(X))=>(~rich(X)<~>humble(X))))&
(![X]:(wise(X)=>(brave(X)<~>rich(X))))&
(![X]:((~tall(X)&old(X))=>(happy(X)<~>~rich(X))))&
(((~curious(mary)&tall(mary)))<=>(~old(fred)))&
((?[X]:(funny(X)))=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:(kind(X)=>(brave(X)&creative(X))))&
(?[X]:((~wise(X)<~>kind(X))))&
((old(susan)<~>~strong(susan)))&
((~brave(alice)<~>~happy(alice)))&
(?[X]:((~kind(X)<~>~humble(X))))&
((~calm(lucy)|kind(lucy)))&
(?[X]:(~rich(X))) | generous(lucy) | [
"p2",
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4841968254397832076609818
% SZS output start Proof for 4841968254397832076609818
3. ? [X0] : (~generous(X0) | ~tall(X0)) => ? [X0] : (curious(X0) & kind(X0)) [input p2]
4. ! [X0] : ((brave(X0) | ~happy(X0)) <=> ~creative(X0)) [input p3]
16. ! [X0] : (kind(X0) => (creative(X0) & brave(X0))) [input p15]
23. ~generous(lucy) [input hypothesis]
24. ? [X0] : (~generous(X0) | ~tall(X0)) => ? [X1] : (curious(X1) & kind(X1)) [rectify 3]
30. ? [X1] : (curious(X1) & kind(X1)) | ! [X0] : (generous(X0) & tall(X0)) [ennf transformation 24]
41. ! [X0] : ((creative(X0) & brave(X0)) | ~kind(X0)) [ennf transformation 16]
47. ? [X0] : (curious(X0) & kind(X0)) | ! [X1] : (generous(X1) & tall(X1)) [rectify 30]
48. ? [X0] : (curious(X0) & kind(X0)) => (curious(sK1) & kind(sK1)) [choice axiom]
49. (curious(sK1) & kind(sK1)) | ! [X1] : (generous(X1) & tall(X1)) [skolemisation 47,48]
50. ! [X0] : (((brave(X0) | ~happy(X0)) | creative(X0)) & (~creative(X0) | (~brave(X0) & happy(X0)))) [nnf transformation 4]
51. ! [X0] : ((brave(X0) | ~happy(X0) | creative(X0)) & (~creative(X0) | (~brave(X0) & happy(X0)))) [flattening 50]
96. kind(sK1) | generous(X1) [cnf transformation 49]
100. ~creative(X0) | ~brave(X0) [cnf transformation 51]
134. ~kind(X0) | brave(X0) [cnf transformation 41]
135. ~kind(X0) | creative(X0) [cnf transformation 41]
146. ~generous(lucy) [cnf transformation 23]
189. 10 <=> ! [X1] : generous(X1) [avatar definition]
190. generous(X1) <- (10) [avatar component clause 189]
201. 13 <=> kind(sK1) [avatar definition]
203. kind(sK1) <- (13) [avatar component clause 201]
204. 10 | 13 [avatar split clause 96,201,189]
338. brave(sK1) <- (13) [resolution 134,203]
341. creative(sK1) <- (13) [resolution 135,203]
348. ~brave(sK1) <- (13) [resolution 341,100]
350. $false <- (13) [subsumption resolution 348,338]
351. ~13 [avatar contradiction clause 350]
352. $false <- (10) [resolution 190,146]
354. ~10 [avatar contradiction clause 352]
355. $false [avatar sat refutation 204,351,354]
% SZS output end Proof for 4841968254397832076609818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not tall then someone is either funny or not generous.
If someone is both not calm and wise then susan is not curious and vice versa.
If someone is either not kind or not creative then john is both creative and happy.
If someone is both not tall and not creative then fred is both not quiet and curious and vice versa.
If someone is strong or creative then john is old.
If someone is brave then fred is both not wise and strong.
If paul is not creative then susan is both funny and not funny and vice versa.
Everyone who is curious is humble.
Everyone who is not happy or funny is not patient and vice versa.
If mary is not quiet then someone is not brave.
If fred is both wise and not tall then someone is not quiet and vice versa.
Everyone who is not creative or not humble is not brave.
If someone is both tall and funny then john is both rich and wise.
If susan is quiet or not funny then someone is both kind and strong and vice versa.
If mary is not funny or quiet then lucy is not calm and vice versa.
Everyone who is either not wise or funny is both not funny and not old and vice versa.
Lucy is both not old and not patient.
Someone is kind or generous.
Alice is both not tall and happy.
Someone is not rich or not kind.
Mary is either not humble or not brave.
Paul is not old or tall.
Someone is both not kind and brave.
Someone is not kind or not rich. | Susan is quiet. | entailment | ((~tall(alice))=>(?[X]:((funny(X)<~>~generous(X)))))&
((?[X]:((~calm(X)&wise(X))))<=>(~curious(susan)))&
((?[X]:((~kind(X)<~>~creative(X))))=>((creative(john)&happy(john))))&
((?[X]:((~tall(X)&~creative(X))))<=>((~quiet(fred)&curious(fred))))&
((?[X]:((strong(X)|creative(X))))=>(old(john)))&
((?[X]:(brave(X)))=>((~wise(fred)&strong(fred))))&
((~creative(paul))<=>((funny(susan)&~funny(susan))))&
(![X]:(curious(X)=>humble(X)))&
(![X]:((~happy(X)|funny(X))<=>~patient(X)))&
((~quiet(mary))=>(?[X]:(~brave(X))))&
(((wise(fred)&~tall(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((~creative(X)|~humble(X))=>~brave(X)))&
((?[X]:((tall(X)&funny(X))))=>((rich(john)&wise(john))))&
(((quiet(susan)|~funny(susan)))<=>(?[X]:((kind(X)&strong(X)))))&
(((~funny(mary)|quiet(mary)))<=>(~calm(lucy)))&
(![X]:((~wise(X)<~>funny(X))<=>(~funny(X)&~old(X))))&
((~old(lucy)&~patient(lucy)))&
(?[X]:((kind(X)|generous(X))))&
((~tall(alice)&happy(alice)))&
(?[X]:((~rich(X)|~kind(X))))&
((~humble(mary)<~>~brave(mary)))&
((~old(paul)|tall(paul)))&
(?[X]:((~kind(X)&brave(X))))&
(?[X]:((~kind(X)|~rich(X)))) | quiet(susan) | [
"p5",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5556479666320022442963991
% SZS output start Proof for 5556479666320022442963991
6. ? [X0] : brave(X0) => (strong(fred) & ~wise(fred)) [input p5]
11. (~tall(fred) & wise(fred)) <=> ? [X0] : ~quiet(X0) [input p10]
23. ? [X0] : (brave(X0) & ~kind(X0)) [input p22]
25. ~quiet(susan) [input hypothesis]
30. (strong(fred) & ~wise(fred)) | ! [X0] : ~brave(X0) [ennf transformation 6]
54. ((~tall(fred) & wise(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (tall(fred) | ~wise(fred))) [nnf transformation 11]
55. ((~tall(fred) & wise(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | tall(fred) | ~wise(fred)) [flattening 54]
56. ((~tall(fred) & wise(fred)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | tall(fred) | ~wise(fred)) [rectify 55]
57. ? [X1] : ~quiet(X1) => ~quiet(sK4) [choice axiom]
58. ((~tall(fred) & wise(fred)) | ! [X0] : quiet(X0)) & (~quiet(sK4) | tall(fred) | ~wise(fred)) [skolemisation 56,57]
73. ? [X0] : (brave(X0) & ~kind(X0)) => (brave(sK8) & ~kind(sK8)) [choice axiom]
74. brave(sK8) & ~kind(sK8) [skolemisation 23,73]
92. ~wise(fred) | ~brave(X0) [cnf transformation 30]
101. wise(fred) | quiet(X0) [cnf transformation 58]
131. brave(sK8) [cnf transformation 74]
133. ~quiet(susan) [cnf transformation 25]
222. 20 <=> ! [X0] : ~brave(X0) [avatar definition]
223. ~brave(X0) <- (20) [avatar component clause 222]
230. 22 <=> wise(fred) [avatar definition]
233. 20 | ~22 [avatar split clause 92,230,222]
254. 27 <=> ! [X0] : quiet(X0) [avatar definition]
255. quiet(X0) <- (27) [avatar component clause 254]
261. 27 | 22 [avatar split clause 101,230,254]
284. 34 <=> quiet(susan) [avatar definition]
285. ~quiet(susan) <- (~34) [avatar component clause 284]
350. ~34 [avatar split clause 133,284]
351. $false <- (20) [resolution 223,131]
352. ~20 [avatar contradiction clause 351]
357. $false <- (27, ~34) [resolution 285,255]
358. ~27 | 34 [avatar contradiction clause 357]
359. $false [avatar sat refutation 233,261,350,352,358]
% SZS output end Proof for 5556479666320022442963991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or old is both funny and creative. Everyone who is curious or tall is happy and vice versa. Everyone who is both not old and patient is generous and vice versa. Everyone who is rich or patient is not patient or not strong and vice versa. Everyone who is either funny or happy is not patient. Everyone who is brave or not patient is not tall or funny and vice versa. Everyone who is either not strong or not wise is not funny. If paul is either humble or not creative then someone is brave. Everyone who is both not happy and happy is quiet or creative. Everyone who is not humble or rich is not tall. Everyone who is quiet or not happy is not generous. Everyone who is not generous or not funny is not rich or kind and vice versa. Everyone who is quiet is calm. Everyone who is either not happy or tall is either tall or not happy and vice versa. If someone is not humble or not strong then someone is either calm or quiet and vice versa. Everyone who is both not creative and not humble is not brave. Someone is calm or quiet. Alice is not old. Someone is rich or humble. John is either not tall or not generous. Alice is both not happy and brave. Someone is curious or old. Someone is either not wise or not rich. Someone is not tall or strong. | Alice is kind. | entailment | (![X]:((~old(X)|old(X))=>(funny(X)&creative(X))))&
(![X]:((curious(X)|tall(X))<=>happy(X)))&
(![X]:((~old(X)&patient(X))<=>generous(X)))&
(![X]:((rich(X)|patient(X))<=>(~patient(X)|~strong(X))))&
(![X]:((funny(X)<~>happy(X))=>~patient(X)))&
(![X]:((brave(X)|~patient(X))<=>(~tall(X)|funny(X))))&
(![X]:((~strong(X)<~>~wise(X))=>~funny(X)))&
(((humble(paul)<~>~creative(paul)))=>(?[X]:(brave(X))))&
(![X]:((~happy(X)&happy(X))=>(quiet(X)|creative(X))))&
(![X]:((~humble(X)|rich(X))=>~tall(X)))&
(![X]:((quiet(X)|~happy(X))=>~generous(X)))&
(![X]:((~generous(X)|~funny(X))<=>(~rich(X)|kind(X))))&
(![X]:(quiet(X)=>calm(X)))&
(![X]:((~happy(X)<~>tall(X))<=>(tall(X)<~>~happy(X))))&
((?[X]:((~humble(X)|~strong(X))))<=>(?[X]:((calm(X)<~>quiet(X)))))&
(![X]:((~creative(X)&~humble(X))=>~brave(X)))&
(?[X]:((calm(X)|quiet(X))))&
(~old(alice))&
(?[X]:((rich(X)|humble(X))))&
((~tall(john)<~>~generous(john)))&
((~happy(alice)&brave(alice)))&
(?[X]:((curious(X)|old(X))))&
(?[X]:((~wise(X)<~>~rich(X))))&
(?[X]:((~tall(X)|strong(X)))) | kind(alice) | [
"p0",
"p2",
"p3",
"p4",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2870123798136610088797740
% SZS output start Proof for 2870123798136610088797740
1. ! [X0] : ((old(X0) | ~old(X0)) => (creative(X0) & funny(X0))) [input p0]
3. ! [X0] : ((patient(X0) & ~old(X0)) <=> generous(X0)) [input p2]
4. ! [X0] : ((patient(X0) | rich(X0)) <=> (~strong(X0) | ~patient(X0))) [input p3]
5. ! [X0] : ((funny(X0) <~> happy(X0)) => ~patient(X0)) [input p4]
12. ! [X0] : ((~funny(X0) | ~generous(X0)) <=> (kind(X0) | ~rich(X0))) [input p11]
21. brave(alice) & ~happy(alice) [input p20]
25. ~kind(alice) [input hypothesis]
27. ! [X0] : ((creative(X0) & funny(X0)) | (~old(X0) & old(X0))) [ennf transformation 1]
28. ! [X0] : (~patient(X0) | (funny(X0) <=> happy(X0))) [ennf transformation 5]
40. ! [X0] : (((patient(X0) & ~old(X0)) | ~generous(X0)) & (generous(X0) | (~patient(X0) | old(X0)))) [nnf transformation 3]
41. ! [X0] : (((patient(X0) & ~old(X0)) | ~generous(X0)) & (generous(X0) | ~patient(X0) | old(X0))) [flattening 40]
42. ! [X0] : (((patient(X0) | rich(X0)) | (strong(X0) & patient(X0))) & ((~strong(X0) | ~patient(X0)) | (~patient(X0) & ~rich(X0)))) [nnf transformation 4]
43. ! [X0] : ((patient(X0) | rich(X0) | (strong(X0) & patient(X0))) & (~strong(X0) | ~patient(X0) | (~patient(X0) & ~rich(X0)))) [flattening 42]
44. ! [X0] : (~patient(X0) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) [nnf transformation 28]
51. ! [X0] : (((~funny(X0) | ~generous(X0)) | (~kind(X0) & rich(X0))) & ((kind(X0) | ~rich(X0)) | (funny(X0) & generous(X0)))) [nnf transformation 12]
52. ! [X0] : ((~funny(X0) | ~generous(X0) | (~kind(X0) & rich(X0))) & (kind(X0) | ~rich(X0) | (funny(X0) & generous(X0)))) [flattening 51]
71. funny(X0) | old(X0) [cnf transformation 27]
72. ~old(X0) | funny(X0) [cnf transformation 27]
80. ~generous(X0) | patient(X0) [cnf transformation 41]
83. patient(X0) | rich(X0) | patient(X0) [cnf transformation 43]
85. ~patient(X0) | happy(X0) | ~funny(X0) [cnf transformation 44]
100. ~rich(X0) | kind(X0) | generous(X0) [cnf transformation 52]
125. ~happy(alice) [cnf transformation 21]
131. ~kind(alice) [cnf transformation 25]
141. rich(X0) | patient(X0) [duplicate literal removal 83]
143. funny(X0) [subsumption resolution 71,72]
144. ~patient(X0) | happy(X0) [subsumption resolution 85,143]
274. kind(X0) | generous(X0) | patient(X0) [resolution 100,141]
285. kind(X0) | patient(X0) [subsumption resolution 274,80]
317. patient(alice) [resolution 285,131]
336. happy(alice) [resolution 317,144]
338. $false [subsumption resolution 336,125]
% SZS output end Proof for 2870123798136610088797740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not old or creative then someone is not curious and vice versa.
Everyone who is not brave is both creative and brave.
Everyone who is tall is not brave.
Everyone who is either not strong or rich is both generous and quiet.
If paul is old then susan is both funny and curious.
Everyone who is brave or funny is either not old or not brave and vice versa.
If someone is not curious or quiet then someone is either not happy or funny and vice versa.
If someone is both not old and brave then mary is brave or funny and vice versa.
Everyone who is not old is both not wise and not funny and vice versa.
Everyone who is either not old or kind is either generous or tall and vice versa.
Everyone who is both tall and humble is either not strong or kind.
If someone is not generous then lucy is not curious.
Everyone who is quiet or not creative is strong.
If someone is either not curious or tall then susan is wise or calm and vice versa.
Everyone who is either not strong or not brave is not rich.
Everyone who is kind or funny is either not strong or not curious and vice versa.
Alice is both not kind and not patient.
Lucy is calm.
Someone is either tall or generous.
Someone is either not brave or brave.
John is funny or curious.
Someone is not funny or not happy.
Paul is calm. | Susan is tall. | contradiction | (((~old(paul)<~>creative(paul)))<=>(?[X]:(~curious(X))))&
(![X]:(~brave(X)=>(creative(X)&brave(X))))&
(![X]:(tall(X)=>~brave(X)))&
(![X]:((~strong(X)<~>rich(X))=>(generous(X)&quiet(X))))&
((old(paul))=>((funny(susan)&curious(susan))))&
(![X]:((brave(X)|funny(X))<=>(~old(X)<~>~brave(X))))&
((?[X]:((~curious(X)|quiet(X))))<=>(?[X]:((~happy(X)<~>funny(X)))))&
((?[X]:((~old(X)&brave(X))))<=>((brave(mary)|funny(mary))))&
(![X]:(~old(X)<=>(~wise(X)&~funny(X))))&
(![X]:((~old(X)<~>kind(X))<=>(generous(X)<~>tall(X))))&
(![X]:((tall(X)&humble(X))=>(~strong(X)<~>kind(X))))&
((?[X]:(~generous(X)))=>(~curious(lucy)))&
(![X]:((quiet(X)|~creative(X))=>strong(X)))&
((?[X]:((~curious(X)<~>tall(X))))<=>((wise(susan)|calm(susan))))&
(![X]:((~strong(X)<~>~brave(X))=>~rich(X)))&
(![X]:((kind(X)|funny(X))<=>(~strong(X)<~>~curious(X))))&
((~kind(alice)&~patient(alice)))&
(calm(lucy))&
(?[X]:((tall(X)<~>generous(X))))&
(?[X]:((~brave(X)<~>brave(X))))&
((funny(john)|curious(john)))&
(?[X]:((~funny(X)|~happy(X))))&
(calm(paul)) | tall(susan) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 2383467247148325218594157
% SZS output start Proof for 2383467247148325218594157
2. ! [X0] : (~brave(X0) => (brave(X0) & creative(X0))) [input p1]
3. ! [X0] : (tall(X0) => ~brave(X0)) [input p2]
24. tall(susan) [input hypothesis]
28. ! [X0] : ((brave(X0) & creative(X0)) | brave(X0)) [ennf transformation 2]
29. ! [X0] : (~brave(X0) | ~tall(X0)) [ennf transformation 3]
76. brave(X0) | brave(X0) [cnf transformation 28]
77. ~brave(X0) | ~tall(X0) [cnf transformation 29]
138. tall(susan) [cnf transformation 24]
141. brave(X0) [duplicate literal removal 76]
161. ~tall(X0) [subsumption resolution 77,141]
237. $false [subsumption resolution 138,161]
% SZS output end Proof for 2383467247148325218594157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and wise is curious or brave and vice versa. If someone is both not curious and not calm then fred is old and vice versa. Everyone who is kind is both quiet and not happy and vice versa. Everyone who is curious or wise is wise or tall and vice versa. Everyone who is both generous and not kind is both not rich and quiet and vice versa. If someone is both happy and generous then fred is both wise and not rich. Everyone who is both not strong and not curious is either generous or not tall and vice versa. Everyone who is both old and calm is either not curious or rich and vice versa. Everyone who is either not strong or patient is kind and vice versa. If lucy is quiet or not wise then someone is either not calm or quiet. Everyone who is happy or not humble is both not rich and not generous. If paul is not rich then paul is curious. If someone is either not rich or calm then lucy is not calm or wise. Everyone who is rich or tall is either old or humble. If someone is funny or humble then alice is both humble and calm. If someone is not quiet then mary is both rich and patient and vice versa. Lucy is happy. Paul is not strong. Someone is strong or not wise. Lucy is either old or not old. Someone is both not calm and not humble. Fred is either not creative or not old. John is either not creative or strong. Someone is both not happy and not funny. | Mary is calm. | neutral | (![X]:((~kind(X)&wise(X))<=>(curious(X)|brave(X))))&
((?[X]:((~curious(X)&~calm(X))))<=>(old(fred)))&
(![X]:(kind(X)<=>(quiet(X)&~happy(X))))&
(![X]:((curious(X)|wise(X))<=>(wise(X)|tall(X))))&
(![X]:((generous(X)&~kind(X))<=>(~rich(X)&quiet(X))))&
((?[X]:((happy(X)&generous(X))))=>((wise(fred)&~rich(fred))))&
(![X]:((~strong(X)&~curious(X))<=>(generous(X)<~>~tall(X))))&
(![X]:((old(X)&calm(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((~strong(X)<~>patient(X))<=>kind(X)))&
(((quiet(lucy)|~wise(lucy)))=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:((happy(X)|~humble(X))=>(~rich(X)&~generous(X))))&
((~rich(paul))=>(curious(paul)))&
((?[X]:((~rich(X)<~>calm(X))))=>((~calm(lucy)|wise(lucy))))&
(![X]:((rich(X)|tall(X))=>(old(X)<~>humble(X))))&
((?[X]:((funny(X)|humble(X))))=>((humble(alice)&calm(alice))))&
((?[X]:(~quiet(X)))<=>((rich(mary)&patient(mary))))&
(happy(lucy))&
(~strong(paul))&
(?[X]:((strong(X)|~wise(X))))&
((old(lucy)<~>~old(lucy)))&
(?[X]:((~calm(X)&~humble(X))))&
((~creative(fred)<~>~old(fred)))&
((~creative(john)<~>strong(john)))&
(?[X]:((~happy(X)&~funny(X)))) | calm(mary) | [] | null | 0 |
If someone is either not calm or wise then lucy is quiet. Everyone who is both not calm and not brave is not quiet or quiet. If someone is rich then someone is either quiet or not wise and vice versa. Everyone who is rich or not quiet is both quiet and strong. If alice is not kind or rich then someone is either not quiet or not kind. Everyone who is old is both not humble and not brave. Everyone who is not generous or kind is brave or not tall and vice versa. Everyone who is either not rich or not curious is both tall and brave. Everyone who is both not calm and not humble is creative or not old. Everyone who is both calm and not kind is both not rich and not patient and vice versa. Everyone who is both strong and not rich is either wise or old and vice versa. If someone is kind then someone is both not patient and rich. Everyone who is curious or not wise is both not tall and not strong. Everyone who is both not calm and old is either not curious or not rich. Everyone who is either brave or not strong is either not patient or strong and vice versa. Someone is strong or not rich. Someone is not curious. Susan is funny. Mary is either not curious or not humble. Someone is not generous or brave. Fred is not brave or brave. Alice is both creative and quiet. | Lucy is not tall. | entailment | ((?[X]:((~calm(X)<~>wise(X))))=>(quiet(lucy)))&
(![X]:((~calm(X)&~brave(X))=>(~quiet(X)|quiet(X))))&
((?[X]:(rich(X)))<=>(?[X]:((quiet(X)<~>~wise(X)))))&
(![X]:((rich(X)|~quiet(X))=>(quiet(X)&strong(X))))&
(((~kind(alice)|rich(alice)))=>(?[X]:((~quiet(X)<~>~kind(X)))))&
(![X]:(old(X)=>(~humble(X)&~brave(X))))&
(![X]:((~generous(X)|kind(X))<=>(brave(X)|~tall(X))))&
(![X]:((~rich(X)<~>~curious(X))=>(tall(X)&brave(X))))&
(![X]:((~calm(X)&~humble(X))=>(creative(X)|~old(X))))&
(![X]:((calm(X)&~kind(X))<=>(~rich(X)&~patient(X))))&
(![X]:((strong(X)&~rich(X))<=>(wise(X)<~>old(X))))&
((?[X]:(kind(X)))=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:((curious(X)|~wise(X))=>(~tall(X)&~strong(X))))&
(![X]:((~calm(X)&old(X))=>(~curious(X)<~>~rich(X))))&
(![X]:((brave(X)<~>~strong(X))<=>(~patient(X)<~>strong(X))))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:(~curious(X)))&
(funny(susan))&
((~curious(mary)<~>~humble(mary)))&
(?[X]:((~generous(X)|brave(X))))&
((~brave(fred)|brave(fred)))&
((creative(alice)&quiet(alice))) | ~tall(lucy) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7004786625909767755942288
% SZS output start Proof for 7004786625909767755942288
3. ? [X0] : rich(X0) <=> ? [X0] : (quiet(X0) <~> ~wise(X0)) [input p2]
4. ! [X0] : ((~quiet(X0) | rich(X0)) => (strong(X0) & quiet(X0))) [input p3]
6. ! [X0] : (old(X0) => (~brave(X0) & ~humble(X0))) [input p5]
8. ! [X0] : ((~rich(X0) <~> ~curious(X0)) => (brave(X0) & tall(X0))) [input p7]
11. ! [X0] : ((~rich(X0) & strong(X0)) <=> (wise(X0) <~> old(X0))) [input p10]
13. ! [X0] : ((~wise(X0) | curious(X0)) => (~strong(X0) & ~tall(X0))) [input p12]
23. tall(lucy) [input hypothesis]
24. ? [X0] : rich(X0) <=> ? [X1] : (quiet(X1) <~> ~wise(X1)) [rectify 3]
32. ! [X0] : ((strong(X0) & quiet(X0)) | (quiet(X0) & ~rich(X0))) [ennf transformation 4]
34. ! [X0] : ((~brave(X0) & ~humble(X0)) | ~old(X0)) [ennf transformation 6]
35. ! [X0] : ((brave(X0) & tall(X0)) | (~rich(X0) <=> ~curious(X0))) [ennf transformation 8]
37. ! [X0] : ((~strong(X0) & ~tall(X0)) | (wise(X0) & ~curious(X0))) [ennf transformation 13]
41. (? [X0] : rich(X0) | ! [X1] : ((quiet(X1) | wise(X1)) & (~wise(X1) | ~quiet(X1)))) & (? [X1] : ((wise(X1) | ~quiet(X1)) & (~wise(X1) | quiet(X1))) | ! [X0] : ~rich(X0)) [nnf transformation 24]
42. (? [X0] : rich(X0) | ! [X1] : ((quiet(X1) | wise(X1)) & (~wise(X1) | ~quiet(X1)))) & (? [X2] : ((wise(X2) | ~quiet(X2)) & (~wise(X2) | quiet(X2))) | ! [X3] : ~rich(X3)) [rectify 41]
43. ? [X0] : rich(X0) => rich(sK0) [choice axiom]
44. ? [X2] : ((wise(X2) | ~quiet(X2)) & (~wise(X2) | quiet(X2))) => ((wise(sK1) | ~quiet(sK1)) & (~wise(sK1) | quiet(sK1))) [choice axiom]
45. (rich(sK0) | ! [X1] : ((quiet(X1) | wise(X1)) & (~wise(X1) | ~quiet(X1)))) & (((wise(sK1) | ~quiet(sK1)) & (~wise(sK1) | quiet(sK1))) | ! [X3] : ~rich(X3)) [skolemisation 42,44,43]
51. ! [X0] : ((brave(X0) & tall(X0)) | ((~rich(X0) | curious(X0)) & (~curious(X0) | rich(X0)))) [nnf transformation 35]
54. ! [X0] : (((~rich(X0) & strong(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | (rich(X0) | ~strong(X0)))) [nnf transformation 11]
55. ! [X0] : (((~rich(X0) & strong(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | rich(X0) | ~strong(X0))) [flattening 54]
73. rich(sK0) | ~wise(X1) | ~quiet(X1) [cnf transformation 45]
76. quiet(X0) | quiet(X0) [cnf transformation 32]
77. ~rich(X0) | strong(X0) [cnf transformation 32]
84. ~old(X0) | ~brave(X0) [cnf transformation 34]
92. ~rich(X0) | brave(X0) | curious(X0) [cnf transformation 51]
101. ~rich(X0) | old(X0) | ~wise(X0) [cnf transformation 55]
106. ~tall(X0) | wise(X0) [cnf transformation 37]
107. ~curious(X0) | ~strong(X0) [cnf transformation 37]
108. ~strong(X0) | wise(X0) [cnf transformation 37]
126. tall(lucy) [cnf transformation 23]
131. quiet(X0) [duplicate literal removal 76]
148. 5 <=> rich(sK0) [avatar definition]
150. rich(sK0) <- (5) [avatar component clause 148]
153. 6 <=> ! [X1] : (~wise(X1) | ~quiet(X1)) [avatar definition]
154. ~wise(X1) | ~quiet(X1) <- (6) [avatar component clause 153]
155. 6 | 5 [avatar split clause 73,148,153]
223. ~wise(X1) <- (6) [subsumption resolution 154,131]
225. wise(lucy) [resolution 106,126]
226. $false <- (6) [subsumption resolution 225,223]
227. ~6 [avatar contradiction clause 226]
228. strong(sK0) <- (5) [resolution 150,77]
231. wise(sK0) <- (5) [resolution 108,228]
252. 22 <=> curious(sK0) [avatar definition]
253. ~curious(sK0) <- (~22) [avatar component clause 252]
254. curious(sK0) <- (22) [avatar component clause 252]
267. ~strong(sK0) <- (22) [resolution 254,107]
269. $false <- (5, 22) [subsumption resolution 267,228]
270. ~5 | ~22 [avatar contradiction clause 269]
272. brave(sK0) | curious(sK0) <- (5) [resolution 92,150]
273. brave(sK0) <- (5, ~22) [subsumption resolution 272,253]
306. old(sK0) | ~wise(sK0) <- (5) [resolution 101,150]
307. old(sK0) <- (5) [subsumption resolution 306,231]
309. ~brave(sK0) <- (5) [resolution 307,84]
310. $false <- (5, ~22) [subsumption resolution 309,273]
311. ~5 | 22 [avatar contradiction clause 310]
312. $false [avatar sat refutation 155,227,270,311]
% SZS output end Proof for 7004786625909767755942288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or old is either not wise or wise.
Everyone who is both kind and not quiet is old or not quiet.
Everyone who is not creative or not kind is generous or creative.
If fred is either not curious or not calm then paul is not old or quiet.
If someone is either wise or humble then mary is tall or not happy.
Everyone who is either not quiet or creative is either funny or old and vice versa.
If someone is either not patient or quiet then alice is either not kind or not patient and vice versa.
Everyone who is old or patient is calm or not happy.
Everyone who is both patient and not wise is calm or humble and vice versa.
If paul is not brave or not tall then lucy is calm or old and vice versa.
If someone is either not generous or rich then someone is not strong and vice versa.
Everyone who is not quiet is happy.
Everyone who is not generous or tall is creative.
Everyone who is both not creative and not wise is both not happy and not curious.
If alice is either not rich or calm then someone is tall.
Everyone who is not curious is both not tall and rich.
Someone is not calm.
Someone is calm.
Someone is not rich.
Someone is strong or kind.
Lucy is tall or humble.
Mary is generous or not old.
Susan is both not kind and rich. | Fred is calm. | neutral | (![X]:((rich(X)<~>old(X))=>(~wise(X)<~>wise(X))))&
(![X]:((kind(X)&~quiet(X))=>(old(X)|~quiet(X))))&
(![X]:((~creative(X)|~kind(X))=>(generous(X)|creative(X))))&
(((~curious(fred)<~>~calm(fred)))=>((~old(paul)|quiet(paul))))&
((?[X]:((wise(X)<~>humble(X))))=>((tall(mary)|~happy(mary))))&
(![X]:((~quiet(X)<~>creative(X))<=>(funny(X)<~>old(X))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>((~kind(alice)<~>~patient(alice))))&
(![X]:((old(X)|patient(X))=>(calm(X)|~happy(X))))&
(![X]:((patient(X)&~wise(X))<=>(calm(X)|humble(X))))&
(((~brave(paul)|~tall(paul)))<=>((calm(lucy)|old(lucy))))&
((?[X]:((~generous(X)<~>rich(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~quiet(X)=>happy(X)))&
(![X]:((~generous(X)|tall(X))=>creative(X)))&
(![X]:((~creative(X)&~wise(X))=>(~happy(X)&~curious(X))))&
(((~rich(alice)<~>calm(alice)))=>(?[X]:(tall(X))))&
(![X]:(~curious(X)=>(~tall(X)&rich(X))))&
(?[X]:(~calm(X)))&
(?[X]:(calm(X)))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)|kind(X))))&
((tall(lucy)|humble(lucy)))&
((generous(mary)|~old(mary)))&
((~kind(susan)&rich(susan))) | calm(fred) | [] | null | 0 |
Everyone who is old is funny and vice versa.
Everyone who is either not humble or humble is either not patient or kind and vice versa.
Everyone who is tall or not tall is either not wise or curious and vice versa.
If paul is either generous or not rich then fred is patient and vice versa.
If alice is both not wise and not patient then someone is not happy or not curious.
Everyone who is either not generous or not strong is strong or not tall and vice versa.
If alice is not funny or not patient then fred is humble or patient.
Everyone who is not tall is not creative or patient.
Everyone who is not quiet or not calm is either not creative or rich.
If john is both not patient and not brave then john is not quiet or patient and vice versa.
Everyone who is either not generous or tall is either happy or rich and vice versa.
Everyone who is not strong or not kind is both not quiet and rich and vice versa.
Everyone who is both curious and not patient is not rich.
Everyone who is not patient or not funny is both old and not patient.
Everyone who is both patient and not generous is either not kind or not funny.
Paul is either quiet or not strong.
Someone is both wise and not humble.
Someone is either not funny or not brave.
Susan is both happy and generous.
Alice is calm or not curious. | Alice is not old. | contradiction | (![X]:(old(X)<=>funny(X)))&
(![X]:((~humble(X)<~>humble(X))<=>(~patient(X)<~>kind(X))))&
(![X]:((tall(X)|~tall(X))<=>(~wise(X)<~>curious(X))))&
(((generous(paul)<~>~rich(paul)))<=>(patient(fred)))&
(((~wise(alice)&~patient(alice)))=>(?[X]:((~happy(X)|~curious(X)))))&
(![X]:((~generous(X)<~>~strong(X))<=>(strong(X)|~tall(X))))&
(((~funny(alice)|~patient(alice)))=>((humble(fred)|patient(fred))))&
(![X]:(~tall(X)=>(~creative(X)|patient(X))))&
(![X]:((~quiet(X)|~calm(X))=>(~creative(X)<~>rich(X))))&
(((~patient(john)&~brave(john)))<=>((~quiet(john)|patient(john))))&
(![X]:((~generous(X)<~>tall(X))<=>(happy(X)<~>rich(X))))&
(![X]:((~strong(X)|~kind(X))<=>(~quiet(X)&rich(X))))&
(![X]:((curious(X)&~patient(X))=>~rich(X)))&
(![X]:((~patient(X)|~funny(X))=>(old(X)&~patient(X))))&
(![X]:((patient(X)&~generous(X))=>(~kind(X)<~>~funny(X))))&
((quiet(paul)<~>~strong(paul)))&
(?[X]:((wise(X)&~humble(X))))&
(?[X]:((~funny(X)<~>~brave(X))))&
((happy(susan)&generous(susan)))&
((calm(alice)|~curious(alice))) | ~old(alice) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8461923810047557161621965
% SZS output start Proof for 8461923810047557161621965
1. ! [X0] : (old(X0) <=> funny(X0)) [input p0]
14. ! [X0] : ((~funny(X0) | ~patient(X0)) => (~patient(X0) & old(X0))) [input p13]
21. ~old(alice) [input hypothesis]
33. ! [X0] : ((~patient(X0) & old(X0)) | (funny(X0) & patient(X0))) [ennf transformation 14]
36. ! [X0] : ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))) [nnf transformation 1]
58. ~old(X0) | funny(X0) [cnf transformation 36]
59. ~funny(X0) | old(X0) [cnf transformation 36]
110. old(X0) | funny(X0) [cnf transformation 33]
123. ~old(alice) [cnf transformation 21]
201. funny(X0) [subsumption resolution 110,58]
214. old(X0) [resolution 59,201]
215. $false [resolution 214,123]
% SZS output end Proof for 8461923810047557161621965
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not quiet is not patient or wise. Everyone who is both wise and funny is not generous and vice versa. Everyone who is both not calm and patient is both not creative and not old. Everyone who is both not creative and not wise is not quiet or creative. If someone is either happy or rich then paul is either generous or creative and vice versa. Everyone who is either not creative or not brave is both old and not calm. Everyone who is not generous or wise is either rich or not strong and vice versa. If someone is either not tall or not funny then someone is either creative or not kind. Everyone who is not humble or not generous is either not generous or not quiet and vice versa. Everyone who is not kind or not patient is humble. Everyone who is calm is either wise or tall and vice versa. Everyone who is rich is both wise and not strong and vice versa. Everyone who is either not old or not happy is not tall or wise. Everyone who is either curious or not rich is both humble and not patient and vice versa. Everyone who is humble is both not happy and not old. Everyone who is not creative is curious or kind. Fred is not old or not humble. Paul is either not generous or quiet. Someone is not wise or not kind. John is generous or calm. Alice is not happy or not generous. Someone is funny or quiet. Fred is creative or patient. | Paul is quiet. | entailment | (![X]:((brave(X)|~quiet(X))=>(~patient(X)|wise(X))))&
(![X]:((wise(X)&funny(X))<=>~generous(X)))&
(![X]:((~calm(X)&patient(X))=>(~creative(X)&~old(X))))&
(![X]:((~creative(X)&~wise(X))=>(~quiet(X)|creative(X))))&
((?[X]:((happy(X)<~>rich(X))))<=>((generous(paul)<~>creative(paul))))&
(![X]:((~creative(X)<~>~brave(X))=>(old(X)&~calm(X))))&
(![X]:((~generous(X)|wise(X))<=>(rich(X)<~>~strong(X))))&
((?[X]:((~tall(X)<~>~funny(X))))=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((~humble(X)|~generous(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((~kind(X)|~patient(X))=>humble(X)))&
(![X]:(calm(X)<=>(wise(X)<~>tall(X))))&
(![X]:(rich(X)<=>(wise(X)&~strong(X))))&
(![X]:((~old(X)<~>~happy(X))=>(~tall(X)|wise(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(humble(X)&~patient(X))))&
(![X]:(humble(X)=>(~happy(X)&~old(X))))&
(![X]:(~creative(X)=>(curious(X)|kind(X))))&
((~old(fred)|~humble(fred)))&
((~generous(paul)<~>quiet(paul)))&
(?[X]:((~wise(X)|~kind(X))))&
((generous(john)|calm(john)))&
((~happy(alice)|~generous(alice)))&
(?[X]:((funny(X)|quiet(X))))&
((creative(fred)|patient(fred))) | quiet(paul) | [
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7702160717971008884137174
% SZS output start Proof for 7702160717971008884137174
9. ! [X0] : ((~generous(X0) | ~humble(X0)) <=> (~generous(X0) <~> ~quiet(X0))) [input p8]
18. ~generous(paul) <~> quiet(paul) [input p17]
24. ~quiet(paul) [input hypothesis]
53. ! [X0] : (((~generous(X0) | ~humble(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (generous(X0) & humble(X0)))) [nnf transformation 9]
54. ! [X0] : ((~generous(X0) | ~humble(X0) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (generous(X0) & humble(X0)))) [flattening 53]
61. (~quiet(paul) | generous(paul)) & (quiet(paul) | ~generous(paul)) [nnf transformation 18]
99. quiet(X0) | generous(X0) | generous(X0) [cnf transformation 54]
123. quiet(paul) | ~generous(paul) [cnf transformation 61]
130. ~quiet(paul) [cnf transformation 24]
131. quiet(X0) | generous(X0) [duplicate literal removal 99]
189. quiet(paul) [subsumption resolution 123,131]
235. $false [subsumption resolution 130,189]
% SZS output end Proof for 7702160717971008884137174
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is not strong or curious.
If someone is either not curious or strong then fred is not quiet.
If someone is either wise or curious then john is either rich or not happy and vice versa.
Everyone who is not humble or kind is not kind.
Everyone who is either not funny or strong is either brave or not funny.
If mary is either wise or not kind then fred is both strong and curious and vice versa.
Everyone who is calm or not rich is creative and vice versa.
If paul is either strong or patient then paul is both not creative and funny and vice versa.
If paul is either strong or wise then mary is curious.
If fred is both not old and not strong then someone is not kind or not tall.
Everyone who is not funny is not old or happy.
If someone is either humble or not kind then paul is both curious and humble and vice versa.
Everyone who is both not old and curious is wise and vice versa.
If someone is not creative or kind then lucy is both creative and not patient.
If someone is quiet or creative then someone is either not kind or not curious and vice versa.
Everyone who is either not funny or not curious is both not brave and not patient.
Someone is both funny and creative.
Fred is rich or not funny.
Someone is both strong and not generous.
Lucy is not brave.
Mary is both not wise and old.
Someone is creative or not funny.
Someone is creative or brave.
Someone is wise or old. | Paul is humble. | entailment | (![X]:(~creative(X)=>(~strong(X)|curious(X))))&
((?[X]:((~curious(X)<~>strong(X))))=>(~quiet(fred)))&
((?[X]:((wise(X)<~>curious(X))))<=>((rich(john)<~>~happy(john))))&
(![X]:((~humble(X)|kind(X))=>~kind(X)))&
(![X]:((~funny(X)<~>strong(X))=>(brave(X)<~>~funny(X))))&
(((wise(mary)<~>~kind(mary)))<=>((strong(fred)&curious(fred))))&
(![X]:((calm(X)|~rich(X))<=>creative(X)))&
(((strong(paul)<~>patient(paul)))<=>((~creative(paul)&funny(paul))))&
(((strong(paul)<~>wise(paul)))=>(curious(mary)))&
(((~old(fred)&~strong(fred)))=>(?[X]:((~kind(X)|~tall(X)))))&
(![X]:(~funny(X)=>(~old(X)|happy(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>((curious(paul)&humble(paul))))&
(![X]:((~old(X)&curious(X))<=>wise(X)))&
((?[X]:((~creative(X)|kind(X))))=>((creative(lucy)&~patient(lucy))))&
((?[X]:((quiet(X)|creative(X))))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
(![X]:((~funny(X)<~>~curious(X))=>(~brave(X)&~patient(X))))&
(?[X]:((funny(X)&creative(X))))&
((rich(fred)|~funny(fred)))&
(?[X]:((strong(X)&~generous(X))))&
(~brave(lucy))&
((~wise(mary)&old(mary)))&
(?[X]:((creative(X)|~funny(X))))&
(?[X]:((creative(X)|brave(X))))&
(?[X]:((wise(X)|old(X)))) | humble(paul) | [
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3063845147457338330503662
% SZS output start Proof for 3063845147457338330503662
4. ! [X0] : ((kind(X0) | ~humble(X0)) => ~kind(X0)) [input p3]
12. ? [X0] : (humble(X0) <~> ~kind(X0)) <=> (humble(paul) & curious(paul)) [input p11]
25. ~humble(paul) [input hypothesis]
32. ! [X0] : (~kind(X0) | (~kind(X0) & humble(X0))) [ennf transformation 4]
52. (? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | (~humble(paul) | ~curious(paul))) & ((humble(paul) & curious(paul)) | ! [X0] : ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) [nnf transformation 12]
53. (? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | ~humble(paul) | ~curious(paul)) & ((humble(paul) & curious(paul)) | ! [X0] : ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) [flattening 52]
54. (? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | ~humble(paul) | ~curious(paul)) & ((humble(paul) & curious(paul)) | ! [X1] : ((humble(X1) | kind(X1)) & (~kind(X1) | ~humble(X1)))) [rectify 53]
55. ? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) => ((kind(sK1) | ~humble(sK1)) & (~kind(sK1) | humble(sK1))) [choice axiom]
56. (((kind(sK1) | ~humble(sK1)) & (~kind(sK1) | humble(sK1))) | ~humble(paul) | ~curious(paul)) & ((humble(paul) & curious(paul)) | ! [X1] : ((humble(X1) | kind(X1)) & (~kind(X1) | ~humble(X1)))) [skolemisation 54,55]
87. ~kind(X0) | ~kind(X0) [cnf transformation 32]
113. humble(paul) | humble(X1) | kind(X1) [cnf transformation 56]
143. ~humble(paul) [cnf transformation 25]
146. ~kind(X0) [duplicate literal removal 87]
245. 20 <=> humble(paul) [avatar definition]
247. ~humble(paul) <- (~20) [avatar component clause 245]
253. humble(paul) | humble(X1) [subsumption resolution 113,146]
255. 22 <=> ! [X1] : humble(X1) [avatar definition]
256. humble(X1) <- (22) [avatar component clause 255]
257. 22 | 20 [avatar split clause 253,245,255]
338. ~20 [avatar split clause 143,245]
339. $false <- (~20, 22) [subsumption resolution 247,256]
340. 20 | ~22 [avatar contradiction clause 339]
346. $false [avatar sat refutation 257,338,340]
% SZS output end Proof for 3063845147457338330503662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not quiet then someone is strong and vice versa. If someone is either not patient or calm then someone is either calm or funny. Everyone who is not curious or not creative is both not happy and curious. Everyone who is not rich is both not quiet and not calm and vice versa. Everyone who is tall or curious is either calm or not kind. Everyone who is strong or not calm is either curious or strong. If someone is not patient then someone is generous. If john is rich or patient then someone is calm or quiet and vice versa. Everyone who is either not humble or funny is both not wise and not brave and vice versa. Everyone who is not old or not quiet is kind or generous. If fred is both wise and rich then someone is rich and vice versa. If susan is both creative and not happy then john is both not tall and not humble and vice versa. Everyone who is not wise or not rich is not tall. Everyone who is either brave or calm is either not creative or not humble and vice versa. Everyone who is both creative and strong is both patient and rich and vice versa. John is both not patient and not generous. Mary is both humble and not happy. Someone is either kind or wise. Alice is both not creative and not old. Someone is either not strong or funny. Someone is not patient or not curious. Mary is both patient and not wise. Mary is either not rich or not creative. | Fred is not generous. | neutral | ((~quiet(susan))<=>(?[X]:(strong(X))))&
((?[X]:((~patient(X)<~>calm(X))))=>(?[X]:((calm(X)<~>funny(X)))))&
(![X]:((~curious(X)|~creative(X))=>(~happy(X)&curious(X))))&
(![X]:(~rich(X)<=>(~quiet(X)&~calm(X))))&
(![X]:((tall(X)|curious(X))=>(calm(X)<~>~kind(X))))&
(![X]:((strong(X)|~calm(X))=>(curious(X)<~>strong(X))))&
((?[X]:(~patient(X)))=>(?[X]:(generous(X))))&
(((rich(john)|patient(john)))<=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:((~humble(X)<~>funny(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~old(X)|~quiet(X))=>(kind(X)|generous(X))))&
(((wise(fred)&rich(fred)))<=>(?[X]:(rich(X))))&
(((creative(susan)&~happy(susan)))<=>((~tall(john)&~humble(john))))&
(![X]:((~wise(X)|~rich(X))=>~tall(X)))&
(![X]:((brave(X)<~>calm(X))<=>(~creative(X)<~>~humble(X))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)&rich(X))))&
((~patient(john)&~generous(john)))&
((humble(mary)&~happy(mary)))&
(?[X]:((kind(X)<~>wise(X))))&
((~creative(alice)&~old(alice)))&
(?[X]:((~strong(X)<~>funny(X))))&
(?[X]:((~patient(X)|~curious(X))))&
((patient(mary)&~wise(mary)))&
((~rich(mary)<~>~creative(mary))) | ~generous(fred) | [] | null | 0 |
Everyone who is patient is calm or not calm and vice versa.
Everyone who is both rich and not brave is not tall or brave and vice versa.
If someone is not wise then john is either not humble or brave and vice versa.
Everyone who is funny or not curious is either not funny or patient and vice versa.
If someone is both not quiet and happy then someone is not strong or generous.
Everyone who is creative is either not curious or curious and vice versa.
Everyone who is not wise is either happy or kind and vice versa.
If someone is old or not patient then someone is either not wise or rich and vice versa.
If susan is both not quiet and patient then susan is not old and vice versa.
If someone is either tall or not humble then susan is both not wise and humble and vice versa.
Everyone who is happy is not quiet or not generous.
If paul is both calm and not quiet then someone is not creative.
If alice is either patient or not calm then someone is curious.
If someone is both rich and not wise then mary is kind or not wise.
Everyone who is funny or not old is either calm or not humble and vice versa.
Everyone who is both humble and not humble is either not quiet or not strong and vice versa.
Someone is both tall and not quiet.
Fred is not humble.
Someone is kind.
Someone is not strong or wise.
Lucy is not generous or not humble.
John is either creative or funny.
Someone is strong. | Susan is not humble. | neutral | (![X]:(patient(X)<=>(calm(X)|~calm(X))))&
(![X]:((rich(X)&~brave(X))<=>(~tall(X)|brave(X))))&
((?[X]:(~wise(X)))<=>((~humble(john)<~>brave(john))))&
(![X]:((funny(X)|~curious(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:((~quiet(X)&happy(X))))=>(?[X]:((~strong(X)|generous(X)))))&
(![X]:(creative(X)<=>(~curious(X)<~>curious(X))))&
(![X]:(~wise(X)<=>(happy(X)<~>kind(X))))&
((?[X]:((old(X)|~patient(X))))<=>(?[X]:((~wise(X)<~>rich(X)))))&
(((~quiet(susan)&patient(susan)))<=>(~old(susan)))&
((?[X]:((tall(X)<~>~humble(X))))<=>((~wise(susan)&humble(susan))))&
(![X]:(happy(X)=>(~quiet(X)|~generous(X))))&
(((calm(paul)&~quiet(paul)))=>(?[X]:(~creative(X))))&
(((patient(alice)<~>~calm(alice)))=>(?[X]:(curious(X))))&
((?[X]:((rich(X)&~wise(X))))=>((kind(mary)|~wise(mary))))&
(![X]:((funny(X)|~old(X))<=>(calm(X)<~>~humble(X))))&
(![X]:((humble(X)&~humble(X))<=>(~quiet(X)<~>~strong(X))))&
(?[X]:((tall(X)&~quiet(X))))&
(~humble(fred))&
(?[X]:(kind(X)))&
(?[X]:((~strong(X)|wise(X))))&
((~generous(lucy)|~humble(lucy)))&
((creative(john)<~>funny(john)))&
(?[X]:(strong(X))) | ~humble(susan) | [] | null | 0 |
If someone is not rich or not strong then someone is both not funny and old.
If someone is both not strong and not brave then john is not wise or not kind.
Everyone who is old or rich is either not humble or not patient and vice versa.
Everyone who is not humble is either generous or not kind.
If someone is not creative or humble then fred is not wise and vice versa.
Everyone who is both rich and humble is not old or tall.
Everyone who is either kind or not happy is not brave.
If lucy is both patient and not old then alice is not kind and vice versa.
Everyone who is either funny or not kind is either not kind or not old and vice versa.
Everyone who is either quiet or not creative is either rich or old and vice versa.
If someone is either not quiet or quiet then fred is not tall or tall and vice versa.
If someone is humble or not funny then someone is not patient or quiet.
Everyone who is brave or curious is not brave.
Everyone who is curious or not old is either wise or not curious and vice versa.
Everyone who is wise or not funny is both brave and not curious.
Everyone who is either not strong or funny is either not wise or not funny and vice versa.
Someone is not generous.
Someone is either quiet or kind.
Paul is happy or not curious.
Fred is humble or not calm.
Paul is both funny and not old.
Someone is strong. | Lucy is funny. | entailment | ((?[X]:((~rich(X)|~strong(X))))=>(?[X]:((~funny(X)&old(X)))))&
((?[X]:((~strong(X)&~brave(X))))=>((~wise(john)|~kind(john))))&
(![X]:((old(X)|rich(X))<=>(~humble(X)<~>~patient(X))))&
(![X]:(~humble(X)=>(generous(X)<~>~kind(X))))&
((?[X]:((~creative(X)|humble(X))))<=>(~wise(fred)))&
(![X]:((rich(X)&humble(X))=>(~old(X)|tall(X))))&
(![X]:((kind(X)<~>~happy(X))=>~brave(X)))&
(((patient(lucy)&~old(lucy)))<=>(~kind(alice)))&
(![X]:((funny(X)<~>~kind(X))<=>(~kind(X)<~>~old(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(rich(X)<~>old(X))))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>((~tall(fred)|tall(fred))))&
((?[X]:((humble(X)|~funny(X))))=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((brave(X)|curious(X))=>~brave(X)))&
(![X]:((curious(X)|~old(X))<=>(wise(X)<~>~curious(X))))&
(![X]:((wise(X)|~funny(X))=>(brave(X)&~curious(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(~wise(X)<~>~funny(X))))&
(?[X]:(~generous(X)))&
(?[X]:((quiet(X)<~>kind(X))))&
((happy(paul)|~curious(paul)))&
((humble(fred)|~calm(fred)))&
((funny(paul)&~old(paul)))&
(?[X]:(strong(X))) | funny(lucy) | [
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2141841541809552710153258
% SZS output start Proof for 2141841541809552710153258
13. ! [X0] : ((curious(X0) | brave(X0)) => ~brave(X0)) [input p12]
15. ! [X0] : ((~funny(X0) | wise(X0)) => (~curious(X0) & brave(X0))) [input p14]
23. ~funny(lucy) [input hypothesis]
35. ! [X0] : (~brave(X0) | (~curious(X0) & ~brave(X0))) [ennf transformation 13]
36. ! [X0] : ((~curious(X0) & brave(X0)) | (funny(X0) & ~wise(X0))) [ennf transformation 15]
116. ~brave(X0) | ~brave(X0) [cnf transformation 35]
125. brave(X0) | funny(X0) [cnf transformation 36]
143. ~funny(lucy) [cnf transformation 23]
150. ~brave(X0) [duplicate literal removal 116]
226. 16 <=> ! [X1] : funny(X1) [avatar definition]
227. funny(X1) <- (16) [avatar component clause 226]
239. funny(X0) [subsumption resolution 125,150]
240. 16 [avatar split clause 239,226]
256. $false <- (16) [resolution 227,143]
257. ~16 [avatar contradiction clause 256]
258. $false [avatar sat refutation 240,257]
% SZS output end Proof for 2141841541809552710153258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is funny or not rich then paul is both creative and humble and vice versa. Everyone who is not funny is both curious and patient and vice versa. If susan is both kind and not rich then fred is either old or not happy. Everyone who is either not kind or not generous is both happy and not creative and vice versa. Everyone who is not quiet or not creative is not humble. If susan is both rich and generous then fred is wise and vice versa. If lucy is either not curious or funny then fred is either not rich or not generous. Everyone who is not tall or creative is either curious or not rich and vice versa. Everyone who is either not humble or not wise is not happy or generous. Everyone who is either not kind or quiet is funny and vice versa. Everyone who is not calm is patient. If someone is strong then someone is both not humble and not patient. If someone is either not curious or generous then susan is both generous and tall and vice versa. Everyone who is both not old and calm is tall and vice versa. Everyone who is either not rich or not funny is either not curious or happy and vice versa. Everyone who is funny or quiet is rich or not quiet and vice versa. Someone is not old or not rich. Someone is either brave or not strong. Someone is either quiet or funny. Lucy is funny or not patient. Someone is not patient. Mary is not calm. Someone is both quiet and not strong. | Susan is rich. | neutral | (((funny(paul)|~rich(paul)))<=>((creative(paul)&humble(paul))))&
(![X]:(~funny(X)<=>(curious(X)&patient(X))))&
(((kind(susan)&~rich(susan)))=>((old(fred)<~>~happy(fred))))&
(![X]:((~kind(X)<~>~generous(X))<=>(happy(X)&~creative(X))))&
(![X]:((~quiet(X)|~creative(X))=>~humble(X)))&
(((rich(susan)&generous(susan)))<=>(wise(fred)))&
(((~curious(lucy)<~>funny(lucy)))=>((~rich(fred)<~>~generous(fred))))&
(![X]:((~tall(X)|creative(X))<=>(curious(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>~wise(X))=>(~happy(X)|generous(X))))&
(![X]:((~kind(X)<~>quiet(X))<=>funny(X)))&
(![X]:(~calm(X)=>patient(X)))&
((?[X]:(strong(X)))=>(?[X]:((~humble(X)&~patient(X)))))&
((?[X]:((~curious(X)<~>generous(X))))<=>((generous(susan)&tall(susan))))&
(![X]:((~old(X)&calm(X))<=>tall(X)))&
(![X]:((~rich(X)<~>~funny(X))<=>(~curious(X)<~>happy(X))))&
(![X]:((funny(X)|quiet(X))<=>(rich(X)|~quiet(X))))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:((brave(X)<~>~strong(X))))&
(?[X]:((quiet(X)<~>funny(X))))&
((funny(lucy)|~patient(lucy)))&
(?[X]:(~patient(X)))&
(~calm(mary))&
(?[X]:((quiet(X)&~strong(X)))) | rich(susan) | [] | null | 0 |
Everyone who is old or curious is not old or not quiet.
If someone is either not patient or not generous then someone is rich.
If someone is creative then someone is tall and vice versa.
Everyone who is both tall and wise is strong or not happy.
Everyone who is both patient and not curious is both not strong and not creative and vice versa.
Everyone who is humble is either funny or brave.
Everyone who is either not curious or calm is happy.
Everyone who is quiet or not calm is either not tall or not wise.
Everyone who is old or humble is not funny and vice versa.
Everyone who is not happy or curious is either not curious or not calm.
If someone is not tall then alice is either not brave or not strong and vice versa.
Everyone who is both strong and creative is wise or not humble.
Everyone who is either not quiet or not kind is both rich and not wise and vice versa.
If susan is both not funny and calm then susan is humble or not strong.
If someone is either old or not humble then someone is both not calm and happy and vice versa.
Everyone who is not rich or wise is not rich and vice versa.
Someone is kind or not curious.
Lucy is funny or tall.
Fred is not generous.
Fred is both calm and rich.
Lucy is not old or humble.
Susan is both kind and not wise.
Someone is kind or not brave.
Someone is curious. | Fred is not wise. | entailment | (![X]:((old(X)|curious(X))=>(~old(X)|~quiet(X))))&
((?[X]:((~patient(X)<~>~generous(X))))=>(?[X]:(rich(X))))&
((?[X]:(creative(X)))<=>(?[X]:(tall(X))))&
(![X]:((tall(X)&wise(X))=>(strong(X)|~happy(X))))&
(![X]:((patient(X)&~curious(X))<=>(~strong(X)&~creative(X))))&
(![X]:(humble(X)=>(funny(X)<~>brave(X))))&
(![X]:((~curious(X)<~>calm(X))=>happy(X)))&
(![X]:((quiet(X)|~calm(X))=>(~tall(X)<~>~wise(X))))&
(![X]:((old(X)|humble(X))<=>~funny(X)))&
(![X]:((~happy(X)|curious(X))=>(~curious(X)<~>~calm(X))))&
((?[X]:(~tall(X)))<=>((~brave(alice)<~>~strong(alice))))&
(![X]:((strong(X)&creative(X))=>(wise(X)|~humble(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(rich(X)&~wise(X))))&
(((~funny(susan)&calm(susan)))=>((humble(susan)|~strong(susan))))&
((?[X]:((old(X)<~>~humble(X))))<=>(?[X]:((~calm(X)&happy(X)))))&
(![X]:((~rich(X)|wise(X))<=>~rich(X)))&
(?[X]:((kind(X)|~curious(X))))&
((funny(lucy)|tall(lucy)))&
(~generous(fred))&
((calm(fred)&rich(fred)))&
((~old(lucy)|humble(lucy)))&
((kind(susan)&~wise(susan)))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:(curious(X))) | ~wise(fred) | [
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4746679380450854042201783
% SZS output start Proof for 4746679380450854042201783
16. ! [X0] : ((wise(X0) | ~rich(X0)) <=> ~rich(X0)) [input p15]
20. rich(fred) & calm(fred) [input p19]
25. wise(fred) [input hypothesis]
70. ! [X0] : (((wise(X0) | ~rich(X0)) | rich(X0)) & (~rich(X0) | (~wise(X0) & rich(X0)))) [nnf transformation 16]
71. ! [X0] : ((wise(X0) | ~rich(X0) | rich(X0)) & (~rich(X0) | (~wise(X0) & rich(X0)))) [flattening 70]
123. ~wise(X0) | ~rich(X0) [cnf transformation 71]
129. rich(fred) [cnf transformation 20]
135. wise(fred) [cnf transformation 25]
272. ~rich(fred) [resolution 123,135]
273. $false [subsumption resolution 272,129]
% SZS output end Proof for 4746679380450854042201783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or curious is not creative and vice versa.
Everyone who is both not humble and not quiet is either curious or not rich.
Everyone who is both humble and not humble is not rich.
Everyone who is tall or not funny is not tall or patient and vice versa.
Everyone who is generous or not patient is both patient and calm.
If mary is both humble and not wise then susan is brave and vice versa.
Everyone who is both wise and calm is funny or not tall.
Everyone who is both curious and happy is either not kind or kind.
If fred is calm or quiet then susan is either not brave or not tall and vice versa.
Everyone who is both not happy and not quiet is either humble or curious.
Everyone who is either not rich or generous is both not brave and not curious and vice versa.
If someone is both not brave and brave then someone is either not rich or humble and vice versa.
If john is not funny or funny then susan is both not humble and not tall.
If alice is both happy and old then someone is not humble or happy.
If someone is tall then lucy is both wise and not tall and vice versa.
If someone is either not tall or happy then someone is humble or not rich and vice versa.
Lucy is either wise or not tall.
Someone is not strong.
Someone is either strong or creative.
Someone is not wise or not humble.
Someone is either creative or not tall.
Mary is both not tall and not humble.
Someone is either generous or funny. | Fred is generous. | contradiction | (![X]:((brave(X)|curious(X))<=>~creative(X)))&
(![X]:((~humble(X)&~quiet(X))=>(curious(X)<~>~rich(X))))&
(![X]:((humble(X)&~humble(X))=>~rich(X)))&
(![X]:((tall(X)|~funny(X))<=>(~tall(X)|patient(X))))&
(![X]:((generous(X)|~patient(X))=>(patient(X)&calm(X))))&
(((humble(mary)&~wise(mary)))<=>(brave(susan)))&
(![X]:((wise(X)&calm(X))=>(funny(X)|~tall(X))))&
(![X]:((curious(X)&happy(X))=>(~kind(X)<~>kind(X))))&
(((calm(fred)|quiet(fred)))<=>((~brave(susan)<~>~tall(susan))))&
(![X]:((~happy(X)&~quiet(X))=>(humble(X)<~>curious(X))))&
(![X]:((~rich(X)<~>generous(X))<=>(~brave(X)&~curious(X))))&
((?[X]:((~brave(X)&brave(X))))<=>(?[X]:((~rich(X)<~>humble(X)))))&
(((~funny(john)|funny(john)))=>((~humble(susan)&~tall(susan))))&
(((happy(alice)&old(alice)))=>(?[X]:((~humble(X)|happy(X)))))&
((?[X]:(tall(X)))<=>((wise(lucy)&~tall(lucy))))&
((?[X]:((~tall(X)<~>happy(X))))<=>(?[X]:((humble(X)|~rich(X)))))&
((wise(lucy)<~>~tall(lucy)))&
(?[X]:(~strong(X)))&
(?[X]:((strong(X)<~>creative(X))))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((creative(X)<~>~tall(X))))&
((~tall(mary)&~humble(mary)))&
(?[X]:((generous(X)<~>funny(X)))) | generous(fred) | [
"p4",
"p5",
"p8",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4327115180001576747273441
% SZS output start Proof for 4327115180001576747273441
5. ! [X0] : ((~patient(X0) | generous(X0)) => (calm(X0) & patient(X0))) [input p4]
6. (~wise(mary) & humble(mary)) <=> brave(susan) [input p5]
9. (quiet(fred) | calm(fred)) <=> (~brave(susan) <~> ~tall(susan)) [input p8]
13. (funny(john) | ~funny(john)) => (~tall(susan) & ~humble(susan)) [input p12]
22. ~humble(mary) & ~tall(mary) [input p21]
24. generous(fred) [input hypothesis]
32. ! [X0] : ((calm(X0) & patient(X0)) | (patient(X0) & ~generous(X0))) [ennf transformation 5]
39. (~tall(susan) & ~humble(susan)) | (~funny(john) & funny(john)) [ennf transformation 13]
45. ((~wise(mary) & humble(mary)) | ~brave(susan)) & (brave(susan) | (wise(mary) | ~humble(mary))) [nnf transformation 6]
46. ((~wise(mary) & humble(mary)) | ~brave(susan)) & (brave(susan) | wise(mary) | ~humble(mary)) [flattening 45]
48. ((quiet(fred) | calm(fred)) | ((~brave(susan) | tall(susan)) & (~tall(susan) | brave(susan)))) & (((tall(susan) | brave(susan)) & (~tall(susan) | ~brave(susan))) | (~quiet(fred) & ~calm(fred))) [nnf transformation 9]
49. (quiet(fred) | calm(fred) | ((~brave(susan) | tall(susan)) & (~tall(susan) | brave(susan)))) & (((tall(susan) | brave(susan)) & (~tall(susan) | ~brave(susan))) | (~quiet(fred) & ~calm(fred))) [flattening 48]
94. ~generous(X0) | calm(X0) [cnf transformation 32]
97. humble(mary) | ~brave(susan) [cnf transformation 46]
104. tall(susan) | brave(susan) | ~calm(fred) [cnf transformation 49]
124. ~tall(susan) | funny(john) [cnf transformation 39]
125. ~tall(susan) | ~funny(john) [cnf transformation 39]
144. ~humble(mary) [cnf transformation 22]
147. generous(fred) [cnf transformation 24]
152. 1 <=> brave(susan) [avatar definition]
161. 3 <=> humble(mary) [avatar definition]
164. ~1 | 3 [avatar split clause 97,161,152]
167. 4 <=> tall(susan) [avatar definition]
171. 5 <=> calm(fred) [avatar definition]
172. ~calm(fred) <- (~5) [avatar component clause 171]
181. ~5 | 1 | 4 [avatar split clause 104,167,152,171]
199. 10 <=> funny(john) [avatar definition]
202. ~10 | ~4 [avatar split clause 125,167,199]
203. 10 | ~4 [avatar split clause 124,167,199]
293. ~3 [avatar split clause 144,161]
306. calm(fred) [resolution 94,147]
308. $false <- (~5) [subsumption resolution 306,172]
309. 5 [avatar contradiction clause 308]
310. $false [avatar sat refutation 164,181,202,203,293,309]
% SZS output end Proof for 4327115180001576747273441
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and tall is either old or happy and vice versa.
If someone is humble then someone is either funny or kind.
If john is funny then john is not kind or not calm and vice versa.
Everyone who is either not happy or old is happy and vice versa.
If mary is generous then alice is both generous and not quiet.
Everyone who is either not funny or not brave is both not funny and humble and vice versa.
If john is not humble or strong then someone is both not rich and creative.
Everyone who is not calm or happy is both brave and rich and vice versa.
If alice is either not humble or humble then mary is curious or patient and vice versa.
Everyone who is either not tall or funny is either not old or not happy.
Everyone who is generous is either not strong or not generous and vice versa.
If someone is not funny or curious then susan is both not calm and patient and vice versa.
If someone is old then lucy is either curious or generous.
If someone is not generous or not happy then someone is both not tall and not quiet.
If lucy is either brave or not calm then someone is not funny or old.
If someone is either quiet or tall then fred is humble or funny.
Someone is rich.
Someone is humble.
Mary is not quiet or strong.
Mary is tall or patient.
Fred is generous or patient.
Mary is brave.
Someone is wise or patient.
Susan is quiet or not brave. | Alice is humble. | neutral | (![X]:((~humble(X)&tall(X))<=>(old(X)<~>happy(X))))&
((?[X]:(humble(X)))=>(?[X]:((funny(X)<~>kind(X)))))&
((funny(john))<=>((~kind(john)|~calm(john))))&
(![X]:((~happy(X)<~>old(X))<=>happy(X)))&
((generous(mary))=>((generous(alice)&~quiet(alice))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~funny(X)&humble(X))))&
(((~humble(john)|strong(john)))=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:((~calm(X)|happy(X))<=>(brave(X)&rich(X))))&
(((~humble(alice)<~>humble(alice)))<=>((curious(mary)|patient(mary))))&
(![X]:((~tall(X)<~>funny(X))=>(~old(X)<~>~happy(X))))&
(![X]:(generous(X)<=>(~strong(X)<~>~generous(X))))&
((?[X]:((~funny(X)|curious(X))))<=>((~calm(susan)&patient(susan))))&
((?[X]:(old(X)))=>((curious(lucy)<~>generous(lucy))))&
((?[X]:((~generous(X)|~happy(X))))=>(?[X]:((~tall(X)&~quiet(X)))))&
(((brave(lucy)<~>~calm(lucy)))=>(?[X]:((~funny(X)|old(X)))))&
((?[X]:((quiet(X)<~>tall(X))))=>((humble(fred)|funny(fred))))&
(?[X]:(rich(X)))&
(?[X]:(humble(X)))&
((~quiet(mary)|strong(mary)))&
((tall(mary)|patient(mary)))&
((generous(fred)|patient(fred)))&
(brave(mary))&
(?[X]:((wise(X)|patient(X))))&
((quiet(susan)|~brave(susan))) | humble(alice) | [] | null | 0 |
If fred is both humble and kind then someone is either not funny or not tall and vice versa. If john is either patient or not happy then someone is not brave. If someone is not brave or patient then mary is either kind or not strong and vice versa. If lucy is calm then someone is not happy. If paul is either kind or not curious then susan is kind and vice versa. If john is not old then someone is not funny. If someone is not rich then someone is both tall and patient. Everyone who is not old or not wise is kind. If someone is old then someone is both rich and strong and vice versa. Everyone who is either not tall or not wise is strong. Everyone who is curious or quiet is tall and vice versa. If fred is either not strong or not tall then someone is either humble or strong. Everyone who is wise is either not funny or not curious. Everyone who is either not humble or not generous is wise and vice versa. Everyone who is either quiet or happy is both humble and not patient and vice versa. If fred is patient then john is either patient or humble and vice versa. Someone is both funny and not old. Susan is both not strong and humble. Someone is either not tall or rich. Someone is both generous and curious. Mary is both happy and wise. John is either not humble or wise. Alice is funny or not wise. | Paul is not rich. | neutral | (((humble(fred)&kind(fred)))<=>(?[X]:((~funny(X)<~>~tall(X)))))&
(((patient(john)<~>~happy(john)))=>(?[X]:(~brave(X))))&
((?[X]:((~brave(X)|patient(X))))<=>((kind(mary)<~>~strong(mary))))&
((calm(lucy))=>(?[X]:(~happy(X))))&
(((kind(paul)<~>~curious(paul)))<=>(kind(susan)))&
((~old(john))=>(?[X]:(~funny(X))))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)&patient(X)))))&
(![X]:((~old(X)|~wise(X))=>kind(X)))&
((?[X]:(old(X)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((~tall(X)<~>~wise(X))=>strong(X)))&
(![X]:((curious(X)|quiet(X))<=>tall(X)))&
(((~strong(fred)<~>~tall(fred)))=>(?[X]:((humble(X)<~>strong(X)))))&
(![X]:(wise(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>wise(X)))&
(![X]:((quiet(X)<~>happy(X))<=>(humble(X)&~patient(X))))&
((patient(fred))<=>((patient(john)<~>humble(john))))&
(?[X]:((funny(X)&~old(X))))&
((~strong(susan)&humble(susan)))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:((generous(X)&curious(X))))&
((happy(mary)&wise(mary)))&
((~humble(john)<~>wise(john)))&
((funny(alice)|~wise(alice))) | ~rich(paul) | [] | null | 0 |
If susan is either quiet or not tall then someone is both calm and funny and vice versa.
Everyone who is both not generous and rich is both brave and not old and vice versa.
Everyone who is not curious is not humble or not funny.
Everyone who is not brave or not curious is either not rich or creative and vice versa.
Everyone who is either not brave or not quiet is not calm or not patient.
Everyone who is not brave is either not generous or not patient.
If someone is either tall or creative then someone is not quiet and vice versa.
Everyone who is both old and kind is not wise.
If someone is not brave or not wise then lucy is either old or patient.
Everyone who is not tall or kind is not quiet.
Everyone who is happy is both not kind and not humble and vice versa.
Everyone who is rich or not brave is not generous.
Everyone who is either not funny or humble is both not brave and not generous and vice versa.
If john is not old or tall then paul is happy or brave and vice versa.
Everyone who is both old and curious is quiet and vice versa.
Everyone who is both not old and not kind is not curious or curious and vice versa.
Alice is not creative or humble.
Fred is happy.
Someone is not tall.
John is happy.
Someone is either not tall or curious.
Someone is not humble or not wise.
John is both wise and not old. | Alice is not quiet. | entailment | (((quiet(susan)<~>~tall(susan)))<=>(?[X]:((calm(X)&funny(X)))))&
(![X]:((~generous(X)&rich(X))<=>(brave(X)&~old(X))))&
(![X]:(~curious(X)=>(~humble(X)|~funny(X))))&
(![X]:((~brave(X)|~curious(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((~brave(X)<~>~quiet(X))=>(~calm(X)|~patient(X))))&
(![X]:(~brave(X)=>(~generous(X)<~>~patient(X))))&
((?[X]:((tall(X)<~>creative(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((old(X)&kind(X))=>~wise(X)))&
((?[X]:((~brave(X)|~wise(X))))=>((old(lucy)<~>patient(lucy))))&
(![X]:((~tall(X)|kind(X))=>~quiet(X)))&
(![X]:(happy(X)<=>(~kind(X)&~humble(X))))&
(![X]:((rich(X)|~brave(X))=>~generous(X)))&
(![X]:((~funny(X)<~>humble(X))<=>(~brave(X)&~generous(X))))&
(((~old(john)|tall(john)))<=>((happy(paul)|brave(paul))))&
(![X]:((old(X)&curious(X))<=>quiet(X)))&
(![X]:((~old(X)&~kind(X))<=>(~curious(X)|curious(X))))&
((~creative(alice)|humble(alice)))&
(happy(fred))&
(?[X]:(~tall(X)))&
(happy(john))&
(?[X]:((~tall(X)<~>curious(X))))&
(?[X]:((~humble(X)|~wise(X))))&
((wise(john)&~old(john))) | ~quiet(alice) | [
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3794864890430048936992112
% SZS output start Proof for 3794864890430048936992112
15. ! [X0] : ((curious(X0) & old(X0)) <=> quiet(X0)) [input p14]
16. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (curious(X0) | ~curious(X0))) [input p15]
24. quiet(alice) [input hypothesis]
58. ! [X0] : (((curious(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | (~curious(X0) | ~old(X0)))) [nnf transformation 15]
59. ! [X0] : (((curious(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | ~curious(X0) | ~old(X0))) [flattening 58]
60. ! [X0] : (((~kind(X0) & ~old(X0)) | (~curious(X0) & curious(X0))) & ((curious(X0) | ~curious(X0)) | (kind(X0) | old(X0)))) [nnf transformation 16]
61. ! [X0] : (((~kind(X0) & ~old(X0)) | (~curious(X0) & curious(X0))) & (curious(X0) | ~curious(X0) | kind(X0) | old(X0))) [flattening 60]
117. ~quiet(X0) | old(X0) [cnf transformation 59]
120. ~old(X0) | curious(X0) [cnf transformation 61]
121. ~old(X0) | ~curious(X0) [cnf transformation 61]
133. quiet(alice) [cnf transformation 24]
225. ~old(X0) [subsumption resolution 120,121]
263. old(alice) [resolution 117,133]
264. $false [subsumption resolution 263,225]
% SZS output end Proof for 3794864890430048936992112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then someone is either old or not rich and vice versa. If someone is both not funny and strong then someone is both not humble and not funny. If someone is both not tall and tall then alice is not creative or not brave. Everyone who is not humble is both quiet and not curious and vice versa. Everyone who is not brave or curious is strong and vice versa. If someone is not rich or curious then someone is not happy. If paul is not old then someone is not patient. Everyone who is both quiet and not happy is not tall or not calm. Everyone who is either happy or quiet is quiet and vice versa. Everyone who is both not patient and not curious is either not old or humble and vice versa. Everyone who is either not rich or curious is patient and vice versa. If someone is not strong or wise then mary is either not patient or not quiet and vice versa. If someone is both humble and not rich then someone is both not brave and not old. Everyone who is either quiet or not quiet is both strong and patient. If someone is funny then someone is both kind and calm and vice versa. If someone is both not humble and not strong then someone is curious or not calm. Susan is old. Paul is tall. Lucy is not happy or strong. Someone is funny. Lucy is not patient or quiet. Mary is either not generous or funny. | Susan is curious. | contradiction | ((?[X]:(rich(X)))<=>(?[X]:((old(X)<~>~rich(X)))))&
((?[X]:((~funny(X)&strong(X))))=>(?[X]:((~humble(X)&~funny(X)))))&
((?[X]:((~tall(X)&tall(X))))=>((~creative(alice)|~brave(alice))))&
(![X]:(~humble(X)<=>(quiet(X)&~curious(X))))&
(![X]:((~brave(X)|curious(X))<=>strong(X)))&
((?[X]:((~rich(X)|curious(X))))=>(?[X]:(~happy(X))))&
((~old(paul))=>(?[X]:(~patient(X))))&
(![X]:((quiet(X)&~happy(X))=>(~tall(X)|~calm(X))))&
(![X]:((happy(X)<~>quiet(X))<=>quiet(X)))&
(![X]:((~patient(X)&~curious(X))<=>(~old(X)<~>humble(X))))&
(![X]:((~rich(X)<~>curious(X))<=>patient(X)))&
((?[X]:((~strong(X)|wise(X))))<=>((~patient(mary)<~>~quiet(mary))))&
((?[X]:((humble(X)&~rich(X))))=>(?[X]:((~brave(X)&~old(X)))))&
(![X]:((quiet(X)<~>~quiet(X))=>(strong(X)&patient(X))))&
((?[X]:(funny(X)))<=>(?[X]:((kind(X)&calm(X)))))&
((?[X]:((~humble(X)&~strong(X))))=>(?[X]:((curious(X)|~calm(X)))))&
(old(susan))&
(tall(paul))&
((~happy(lucy)|strong(lucy)))&
(?[X]:(funny(X)))&
((~patient(lucy)|quiet(lucy)))&
((~generous(mary)<~>funny(mary))) | curious(susan) | [
"p3",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6781087260400386963621818
% SZS output start Proof for 6781087260400386963621818
4. ! [X0] : (~humble(X0) <=> (~curious(X0) & quiet(X0))) [input p3]
10. ! [X0] : ((~curious(X0) & ~patient(X0)) <=> (~old(X0) <~> humble(X0))) [input p9]
17. old(susan) [input p16]
23. curious(susan) [input hypothesis]
47. ! [X0] : ((~humble(X0) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | humble(X0))) [nnf transformation 4]
48. ! [X0] : ((~humble(X0) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | humble(X0))) [flattening 47]
57. ! [X0] : (((~curious(X0) & ~patient(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) & (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | (curious(X0) | patient(X0)))) [nnf transformation 10]
58. ! [X0] : (((~curious(X0) & ~patient(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) & (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | curious(X0) | patient(X0))) [flattening 57]
86. ~curious(X0) | humble(X0) [cnf transformation 48]
104. ~curious(X0) | ~old(X0) | ~humble(X0) [cnf transformation 58]
125. old(susan) [cnf transformation 17]
132. curious(susan) [cnf transformation 23]
199. ~curious(X0) | ~old(X0) [subsumption resolution 104,86]
302. ~old(susan) [resolution 199,132]
303. $false [subsumption resolution 302,125]
% SZS output end Proof for 6781087260400386963621818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or strong then someone is not generous or not strong and vice versa. Everyone who is both humble and not creative is both not quiet and not generous and vice versa. Everyone who is either happy or strong is either not kind or not humble and vice versa. Everyone who is kind or not tall is either not wise or rich. If mary is not rich or wise then someone is either wise or not quiet and vice versa. Everyone who is quiet or creative is generous or wise and vice versa. If someone is quiet then someone is both not kind and creative. Everyone who is either not quiet or not brave is both humble and kind. Everyone who is not generous or brave is both tall and not quiet and vice versa. Everyone who is either old or quiet is either old or not curious. If lucy is not curious then someone is either kind or strong. If someone is both quiet and not strong then someone is quiet and vice versa. Everyone who is generous is brave and vice versa. If someone is either not humble or brave then someone is both old and patient. Everyone who is both creative and kind is humble or generous and vice versa. If paul is wise then mary is not creative. Susan is either strong or not brave. Lucy is either brave or not kind. Someone is calm. Alice is either not kind or funny. | Alice is quiet. | contradiction | ((?[X]:((~kind(X)<~>strong(X))))<=>(?[X]:((~generous(X)|~strong(X)))))&
(![X]:((humble(X)&~creative(X))<=>(~quiet(X)&~generous(X))))&
(![X]:((happy(X)<~>strong(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((kind(X)|~tall(X))=>(~wise(X)<~>rich(X))))&
(((~rich(mary)|wise(mary)))<=>(?[X]:((wise(X)<~>~quiet(X)))))&
(![X]:((quiet(X)|creative(X))<=>(generous(X)|wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((~quiet(X)<~>~brave(X))=>(humble(X)&kind(X))))&
(![X]:((~generous(X)|brave(X))<=>(tall(X)&~quiet(X))))&
(![X]:((old(X)<~>quiet(X))=>(old(X)<~>~curious(X))))&
((~curious(lucy))=>(?[X]:((kind(X)<~>strong(X)))))&
((?[X]:((quiet(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
(![X]:(generous(X)<=>brave(X)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((old(X)&patient(X)))))&
(![X]:((creative(X)&kind(X))<=>(humble(X)|generous(X))))&
((wise(paul))=>(~creative(mary)))&
((strong(susan)<~>~brave(susan)))&
((brave(lucy)<~>~kind(lucy)))&
(?[X]:(calm(X)))&
((~kind(alice)<~>funny(alice))) | quiet(alice) | [
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7952021668189884407738058
% SZS output start Proof for 7952021668189884407738058
9. ! [X0] : ((brave(X0) | ~generous(X0)) <=> (~quiet(X0) & tall(X0))) [input p8]
13. ! [X0] : (generous(X0) <=> brave(X0)) [input p12]
21. quiet(alice) [input hypothesis]
55. ! [X0] : (((brave(X0) | ~generous(X0)) | (quiet(X0) | ~tall(X0))) & ((~quiet(X0) & tall(X0)) | (~brave(X0) & generous(X0)))) [nnf transformation 9]
56. ! [X0] : ((brave(X0) | ~generous(X0) | quiet(X0) | ~tall(X0)) & ((~quiet(X0) & tall(X0)) | (~brave(X0) & generous(X0)))) [flattening 55]
66. ! [X0] : ((generous(X0) | ~brave(X0)) & (brave(X0) | ~generous(X0))) [nnf transformation 13]
116. ~quiet(X0) | generous(X0) [cnf transformation 56]
117. ~brave(X0) | ~quiet(X0) [cnf transformation 56]
128. ~generous(X0) | brave(X0) [cnf transformation 66]
144. quiet(alice) [cnf transformation 21]
307. generous(alice) [resolution 116,144]
309. brave(alice) [resolution 128,307]
311. ~quiet(alice) [resolution 309,117]
313. $false [subsumption resolution 311,144]
% SZS output end Proof for 7952021668189884407738058
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not brave is old. If alice is either creative or not brave then lucy is either quiet or not humble. Everyone who is not quiet or generous is either kind or curious and vice versa. If someone is curious then mary is both not humble and not wise. Everyone who is either strong or not curious is both not humble and wise and vice versa. Everyone who is both curious and patient is strong or happy and vice versa. If susan is either not quiet or not funny then someone is both kind and quiet. If john is not rich then fred is not old. Everyone who is not curious is both not quiet and wise and vice versa. If mary is both not funny and not happy then paul is not curious or brave. Everyone who is not happy or tall is either not generous or not funny and vice versa. If susan is not curious then mary is both not quiet and not creative and vice versa. Everyone who is humble is both quiet and generous and vice versa. Everyone who is both not wise and not quiet is either brave or patient and vice versa. Everyone who is wise is not humble or wise and vice versa. Everyone who is both not old and tall is both happy and generous and vice versa. Paul is not curious. Someone is funny. Someone is either not patient or not calm. Susan is both creative and rich. Someone is either not tall or not happy. | Alice is quiet. | contradiction | (![X]:((~wise(X)|~brave(X))=>old(X)))&
(((creative(alice)<~>~brave(alice)))=>((quiet(lucy)<~>~humble(lucy))))&
(![X]:((~quiet(X)|generous(X))<=>(kind(X)<~>curious(X))))&
((?[X]:(curious(X)))=>((~humble(mary)&~wise(mary))))&
(![X]:((strong(X)<~>~curious(X))<=>(~humble(X)&wise(X))))&
(![X]:((curious(X)&patient(X))<=>(strong(X)|happy(X))))&
(((~quiet(susan)<~>~funny(susan)))=>(?[X]:((kind(X)&quiet(X)))))&
((~rich(john))=>(~old(fred)))&
(![X]:(~curious(X)<=>(~quiet(X)&wise(X))))&
(((~funny(mary)&~happy(mary)))=>((~curious(paul)|brave(paul))))&
(![X]:((~happy(X)|tall(X))<=>(~generous(X)<~>~funny(X))))&
((~curious(susan))<=>((~quiet(mary)&~creative(mary))))&
(![X]:(humble(X)<=>(quiet(X)&generous(X))))&
(![X]:((~wise(X)&~quiet(X))<=>(brave(X)<~>patient(X))))&
(![X]:(wise(X)<=>(~humble(X)|wise(X))))&
(![X]:((~old(X)&tall(X))<=>(happy(X)&generous(X))))&
(~curious(paul))&
(?[X]:(funny(X)))&
(?[X]:((~patient(X)<~>~calm(X))))&
((creative(susan)&rich(susan)))&
(?[X]:((~tall(X)<~>~happy(X)))) | quiet(alice) | [
"p3",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 301473535387254687419669
% SZS output start Proof for 301473535387254687419669
4. ? [X0] : curious(X0) => (~wise(mary) & ~humble(mary)) [input p3]
9. ! [X0] : (~curious(X0) <=> (wise(X0) & ~quiet(X0))) [input p8]
15. ! [X0] : (wise(X0) <=> (wise(X0) | ~humble(X0))) [input p14]
22. quiet(alice) [input hypothesis]
27. (~wise(mary) & ~humble(mary)) | ! [X0] : ~curious(X0) [ennf transformation 4]
41. ! [X0] : ((~curious(X0) | (~wise(X0) | quiet(X0))) & ((wise(X0) & ~quiet(X0)) | curious(X0))) [nnf transformation 9]
42. ! [X0] : ((~curious(X0) | ~wise(X0) | quiet(X0)) & ((wise(X0) & ~quiet(X0)) | curious(X0))) [flattening 41]
51. ! [X0] : ((wise(X0) | (~wise(X0) & humble(X0))) & ((wise(X0) | ~humble(X0)) | ~wise(X0))) [nnf transformation 15]
52. ! [X0] : ((wise(X0) | (~wise(X0) & humble(X0))) & (wise(X0) | ~humble(X0) | ~wise(X0))) [flattening 51]
75. ~humble(mary) | ~curious(X0) [cnf transformation 27]
76. ~wise(mary) | ~curious(X0) [cnf transformation 27]
92. ~quiet(X0) | curious(X0) [cnf transformation 42]
115. humble(X0) | wise(X0) [cnf transformation 52]
128. quiet(alice) [cnf transformation 22]
150. 5 <=> ! [X0] : ~curious(X0) [avatar definition]
151. ~curious(X0) <- (5) [avatar component clause 150]
153. 6 <=> wise(mary) [avatar definition]
156. 5 | ~6 [avatar split clause 76,153,150]
158. 7 <=> humble(mary) [avatar definition]
160. ~humble(mary) <- (~7) [avatar component clause 158]
161. 5 | ~7 [avatar split clause 75,158,150]
235. curious(alice) [resolution 92,128]
239. wise(mary) <- (~7) [resolution 115,160]
244. 6 | 7 [avatar split clause 239,158,153]
246. $false <- (5) [resolution 151,235]
247. ~5 [avatar contradiction clause 246]
248. $false [avatar sat refutation 156,161,244,247]
% SZS output end Proof for 301473535387254687419669
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or funny then someone is patient.
If someone is either not wise or rich then paul is either not old or curious.
Everyone who is both not strong and rich is not rich or quiet.
If someone is patient or not funny then paul is both not generous and quiet and vice versa.
If paul is not generous then mary is old and vice versa.
If someone is either not generous or not funny then someone is either not wise or not generous.
If lucy is old or not happy then someone is patient or creative.
Everyone who is calm or quiet is both rich and patient.
Everyone who is not kind or not happy is both creative and old.
If someone is both funny and old then someone is generous and vice versa.
Everyone who is happy or quiet is both not patient and patient.
Everyone who is both kind and patient is not patient or not creative.
If someone is old then someone is not tall and vice versa.
Everyone who is not humble or creative is either kind or humble and vice versa.
Everyone who is rich or quiet is rich.
If someone is humble then someone is either not brave or not creative.
John is either rich or not old.
Someone is humble or generous.
Someone is funny or patient.
Susan is either not happy or not kind.
Someone is creative. | Paul is humble. | neutral | ((?[X]:((~brave(X)<~>funny(X))))=>(?[X]:(patient(X))))&
((?[X]:((~wise(X)<~>rich(X))))=>((~old(paul)<~>curious(paul))))&
(![X]:((~strong(X)&rich(X))=>(~rich(X)|quiet(X))))&
((?[X]:((patient(X)|~funny(X))))<=>((~generous(paul)&quiet(paul))))&
((~generous(paul))<=>(old(mary)))&
((?[X]:((~generous(X)<~>~funny(X))))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(((old(lucy)|~happy(lucy)))=>(?[X]:((patient(X)|creative(X)))))&
(![X]:((calm(X)|quiet(X))=>(rich(X)&patient(X))))&
(![X]:((~kind(X)|~happy(X))=>(creative(X)&old(X))))&
((?[X]:((funny(X)&old(X))))<=>(?[X]:(generous(X))))&
(![X]:((happy(X)|quiet(X))=>(~patient(X)&patient(X))))&
(![X]:((kind(X)&patient(X))=>(~patient(X)|~creative(X))))&
((?[X]:(old(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~humble(X)|creative(X))<=>(kind(X)<~>humble(X))))&
(![X]:((rich(X)|quiet(X))=>rich(X)))&
((?[X]:(humble(X)))=>(?[X]:((~brave(X)<~>~creative(X)))))&
((rich(john)<~>~old(john)))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((funny(X)|patient(X))))&
((~happy(susan)<~>~kind(susan)))&
(?[X]:(creative(X))) | humble(paul) | [] | null | 0 |
If fred is either not creative or not patient then lucy is either not brave or not old and vice versa.
Everyone who is either not creative or tall is either funny or not funny and vice versa.
If fred is not calm or not wise then someone is either generous or not curious.
Everyone who is not kind or not curious is happy and vice versa.
If mary is both not strong and generous then mary is not humble or quiet and vice versa.
Everyone who is either not humble or kind is not rich or old.
Everyone who is not tall is kind or humble.
If someone is old then someone is not brave.
Everyone who is rich is either calm or not old and vice versa.
Everyone who is either curious or not old is both not generous and not funny.
If alice is not humble or funny then someone is both not wise and old.
If alice is either curious or not brave then alice is either happy or not humble.
Everyone who is either quiet or not strong is both not generous and generous.
If someone is both not calm and not humble then fred is both strong and creative and vice versa.
Everyone who is quiet is brave or not creative.
Everyone who is both not tall and wise is either generous or not quiet.
Someone is either funny or not tall.
Alice is both happy and quiet.
Paul is not quiet or wise.
Someone is both kind and not old.
Someone is not rich.
Someone is both calm and not wise.
Mary is both creative and quiet.
Someone is old or kind. | Mary is tall. | entailment | (((~creative(fred)<~>~patient(fred)))<=>((~brave(lucy)<~>~old(lucy))))&
(![X]:((~creative(X)<~>tall(X))<=>(funny(X)<~>~funny(X))))&
(((~calm(fred)|~wise(fred)))=>(?[X]:((generous(X)<~>~curious(X)))))&
(![X]:((~kind(X)|~curious(X))<=>happy(X)))&
(((~strong(mary)&generous(mary)))<=>((~humble(mary)|quiet(mary))))&
(![X]:((~humble(X)<~>kind(X))=>(~rich(X)|old(X))))&
(![X]:(~tall(X)=>(kind(X)|humble(X))))&
((?[X]:(old(X)))=>(?[X]:(~brave(X))))&
(![X]:(rich(X)<=>(calm(X)<~>~old(X))))&
(![X]:((curious(X)<~>~old(X))=>(~generous(X)&~funny(X))))&
(((~humble(alice)|funny(alice)))=>(?[X]:((~wise(X)&old(X)))))&
(((curious(alice)<~>~brave(alice)))=>((happy(alice)<~>~humble(alice))))&
(![X]:((quiet(X)<~>~strong(X))=>(~generous(X)&generous(X))))&
((?[X]:((~calm(X)&~humble(X))))<=>((strong(fred)&creative(fred))))&
(![X]:(quiet(X)=>(brave(X)|~creative(X))))&
(![X]:((~tall(X)&wise(X))=>(generous(X)<~>~quiet(X))))&
(?[X]:((funny(X)<~>~tall(X))))&
((happy(alice)&quiet(alice)))&
((~quiet(paul)|wise(paul)))&
(?[X]:((kind(X)&~old(X))))&
(?[X]:(~rich(X)))&
(?[X]:((calm(X)&~wise(X))))&
((creative(mary)&quiet(mary)))&
(?[X]:((old(X)|kind(X)))) | tall(mary) | [
"p1",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 419869132599270964207282
% SZS output start Proof for 419869132599270964207282
2. ! [X0] : ((~creative(X0) <~> tall(X0)) <=> (funny(X0) <~> ~funny(X0))) [input p1]
23. quiet(mary) & creative(mary) [input p22]
25. ~tall(mary) [input hypothesis]
44. ! [X0] : ((((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0)))) & (((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))))) [nnf transformation 2]
91. tall(X0) | ~creative(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 44]
92. tall(X0) | ~creative(X0) | funny(X0) | funny(X0) [cnf transformation 44]
146. creative(mary) [cnf transformation 23]
149. ~tall(mary) [cnf transformation 25]
150. tall(X0) | ~creative(X0) | ~funny(X0) [duplicate literal removal 91]
151. tall(X0) | ~creative(X0) | funny(X0) [duplicate literal removal 92]
179. ~creative(X0) | tall(X0) [subsumption resolution 150,151]
317. tall(mary) [resolution 179,146]
319. $false [subsumption resolution 317,149]
% SZS output end Proof for 419869132599270964207282
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is wise then someone is not wise. If someone is either quiet or not brave then someone is not curious or patient and vice versa. Everyone who is either quiet or humble is curious or happy and vice versa. Everyone who is both brave and not strong is both calm and patient and vice versa. If lucy is either not happy or rich then john is either not wise or not patient and vice versa. Everyone who is not old is old. Everyone who is either generous or curious is either not funny or rich and vice versa. Everyone who is brave or not brave is not funny or humble. Everyone who is either curious or kind is either not kind or not patient and vice versa. Everyone who is both not old and not kind is not strong and vice versa. Everyone who is not tall is both not old and calm and vice versa. Everyone who is not curious or not humble is rich. Everyone who is both not quiet and wise is curious and vice versa. If john is not generous then someone is either tall or curious. Everyone who is not generous is both not rich and brave. Everyone who is not patient or not brave is tall and vice versa. Paul is either not humble or wise. Someone is not humble or calm. Someone is both not kind and calm. Someone is both wise and not funny. Someone is both not kind and not calm. Someone is not humble or tall. Someone is both wise and not happy. | Lucy is rich. | neutral | ((wise(john))=>(?[X]:(~wise(X))))&
((?[X]:((quiet(X)<~>~brave(X))))<=>(?[X]:((~curious(X)|patient(X)))))&
(![X]:((quiet(X)<~>humble(X))<=>(curious(X)|happy(X))))&
(![X]:((brave(X)&~strong(X))<=>(calm(X)&patient(X))))&
(((~happy(lucy)<~>rich(lucy)))<=>((~wise(john)<~>~patient(john))))&
(![X]:(~old(X)=>old(X)))&
(![X]:((generous(X)<~>curious(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|humble(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)&~kind(X))<=>~strong(X)))&
(![X]:(~tall(X)<=>(~old(X)&calm(X))))&
(![X]:((~curious(X)|~humble(X))=>rich(X)))&
(![X]:((~quiet(X)&wise(X))<=>curious(X)))&
((~generous(john))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:(~generous(X)=>(~rich(X)&brave(X))))&
(![X]:((~patient(X)|~brave(X))<=>tall(X)))&
((~humble(paul)<~>wise(paul)))&
(?[X]:((~humble(X)|calm(X))))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:((wise(X)&~funny(X))))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:((wise(X)&~happy(X)))) | rich(lucy) | [] | null | 0 |
Everyone who is both generous and not old is not funny or not patient and vice versa. Everyone who is either not tall or not patient is either calm or wise and vice versa. Everyone who is both curious and tall is tall or happy and vice versa. Everyone who is both tall and not brave is either not rich or not wise. If someone is not quiet then someone is both wise and not brave. If someone is either not curious or not rich then susan is not generous and vice versa. Everyone who is either old or funny is either brave or kind and vice versa. Everyone who is not creative is creative or not rich. If john is either not humble or old then someone is funny or not wise and vice versa. If lucy is not old then someone is not tall and vice versa. Everyone who is happy is not creative and vice versa. Everyone who is happy is not funny and vice versa. If someone is either old or patient then john is either generous or wise. Everyone who is calm is both not humble and quiet and vice versa. Everyone who is either happy or not curious is old or not patient. If someone is not generous then paul is not kind or not funny. Someone is not funny or not strong. Susan is both not curious and not generous. Someone is both generous and tall. Someone is both not humble and wise. Susan is not calm or calm. Alice is both strong and not curious. Someone is either generous or not funny. | Susan is not happy. | entailment | (![X]:((generous(X)&~old(X))<=>(~funny(X)|~patient(X))))&
(![X]:((~tall(X)<~>~patient(X))<=>(calm(X)<~>wise(X))))&
(![X]:((curious(X)&tall(X))<=>(tall(X)|happy(X))))&
(![X]:((tall(X)&~brave(X))=>(~rich(X)<~>~wise(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((wise(X)&~brave(X)))))&
((?[X]:((~curious(X)<~>~rich(X))))<=>(~generous(susan)))&
(![X]:((old(X)<~>funny(X))<=>(brave(X)<~>kind(X))))&
(![X]:(~creative(X)=>(creative(X)|~rich(X))))&
(((~humble(john)<~>old(john)))<=>(?[X]:((funny(X)|~wise(X)))))&
((~old(lucy))<=>(?[X]:(~tall(X))))&
(![X]:(happy(X)<=>~creative(X)))&
(![X]:(happy(X)<=>~funny(X)))&
((?[X]:((old(X)<~>patient(X))))=>((generous(john)<~>wise(john))))&
(![X]:(calm(X)<=>(~humble(X)&quiet(X))))&
(![X]:((happy(X)<~>~curious(X))=>(old(X)|~patient(X))))&
((?[X]:(~generous(X)))=>((~kind(paul)|~funny(paul))))&
(?[X]:((~funny(X)|~strong(X))))&
((~curious(susan)&~generous(susan)))&
(?[X]:((generous(X)&tall(X))))&
(?[X]:((~humble(X)&wise(X))))&
((~calm(susan)|calm(susan)))&
((strong(alice)&~curious(alice)))&
(?[X]:((generous(X)<~>~funny(X)))) | ~happy(susan) | [
"p2",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7464134719149620904183622
% SZS output start Proof for 7464134719149620904183622
3. ! [X0] : ((tall(X0) & curious(X0)) <=> (happy(X0) | tall(X0))) [input p2]
18. ~generous(susan) & ~curious(susan) [input p17]
24. happy(susan) [input hypothesis]
39. ! [X0] : (((tall(X0) & curious(X0)) | (~happy(X0) & ~tall(X0))) & ((happy(X0) | tall(X0)) | (~tall(X0) | ~curious(X0)))) [nnf transformation 3]
40. ! [X0] : (((tall(X0) & curious(X0)) | (~happy(X0) & ~tall(X0))) & (happy(X0) | tall(X0) | ~tall(X0) | ~curious(X0))) [flattening 39]
88. ~happy(X0) | curious(X0) [cnf transformation 40]
131. ~curious(susan) [cnf transformation 18]
142. happy(susan) [cnf transformation 24]
266. curious(susan) [resolution 88,142]
267. $false [subsumption resolution 266,131]
% SZS output end Proof for 7464134719149620904183622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both not funny and not patient is either funny or old and vice versa. Everyone who is both brave and not brave is either not humble or not old and vice versa. Everyone who is both creative and not curious is kind. If mary is either not humble or wise then susan is either not creative or not funny and vice versa. Everyone who is not creative or not curious is both not patient and patient. Everyone who is both not generous and not patient is not tall. Everyone who is both happy and rich is either not quiet or patient. If someone is either calm or not kind then paul is not strong and vice versa. If someone is not calm or curious then lucy is kind. Everyone who is not tall or not rich is both tall and not happy. Everyone who is both creative and not strong is old. Everyone who is either not strong or tall is not wise or not humble. Everyone who is not rich or creative is either not wise or not curious and vice versa. Everyone who is both quiet and creative is both not calm and not rich. If alice is not brave then someone is not rich. Everyone who is not calm is brave or not brave and vice versa. Paul is either not strong or not wise. Someone is not creative or not quiet. Lucy is rich. Someone is funny or not funny. Someone is funny. | Alice is old. | neutral | (![X]:((~funny(X)&~patient(X))<=>(funny(X)<~>old(X))))&
(![X]:((brave(X)&~brave(X))<=>(~humble(X)<~>~old(X))))&
(![X]:((creative(X)&~curious(X))=>kind(X)))&
(((~humble(mary)<~>wise(mary)))<=>((~creative(susan)<~>~funny(susan))))&
(![X]:((~creative(X)|~curious(X))=>(~patient(X)&patient(X))))&
(![X]:((~generous(X)&~patient(X))=>~tall(X)))&
(![X]:((happy(X)&rich(X))=>(~quiet(X)<~>patient(X))))&
((?[X]:((calm(X)<~>~kind(X))))<=>(~strong(paul)))&
((?[X]:((~calm(X)|curious(X))))=>(kind(lucy)))&
(![X]:((~tall(X)|~rich(X))=>(tall(X)&~happy(X))))&
(![X]:((creative(X)&~strong(X))=>old(X)))&
(![X]:((~strong(X)<~>tall(X))=>(~wise(X)|~humble(X))))&
(![X]:((~rich(X)|creative(X))<=>(~wise(X)<~>~curious(X))))&
(![X]:((quiet(X)&creative(X))=>(~calm(X)&~rich(X))))&
((~brave(alice))=>(?[X]:(~rich(X))))&
(![X]:(~calm(X)<=>(brave(X)|~brave(X))))&
((~strong(paul)<~>~wise(paul)))&
(?[X]:((~creative(X)|~quiet(X))))&
(rich(lucy))&
(?[X]:((funny(X)|~funny(X))))&
(?[X]:(funny(X))) | old(alice) | [] | null | 0 |
Everyone who is both happy and brave is both not generous and funny and vice versa. If susan is either creative or not humble then paul is not patient and vice versa. Everyone who is either wise or patient is either not generous or not humble. If susan is generous then susan is happy and vice versa. If someone is both kind and not humble then fred is either not funny or creative. Everyone who is curious or wise is not curious. Everyone who is both humble and rich is not brave and vice versa. If mary is not patient or funny then john is either strong or not patient and vice versa. Everyone who is either patient or kind is either strong or happy. Everyone who is either wise or happy is happy. If someone is not rich or kind then lucy is curious and vice versa. Everyone who is either not strong or not quiet is not rich and vice versa. If someone is curious or not wise then someone is not rich. Everyone who is not curious is creative or not patient and vice versa. Everyone who is old or not quiet is either not creative or not curious and vice versa. If someone is both not generous and not funny then someone is not quiet. Someone is not curious. Someone is either not kind or not old. Susan is not wise or rich. Someone is funny. Someone is not strong or kind. | Fred is not happy. | contradiction | (![X]:((happy(X)&brave(X))<=>(~generous(X)&funny(X))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(![X]:((old(X)|~quiet(X))<=>(~creative(X)<~>~curious(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:(~quiet(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~kind(X)<~>~old(X))))&
((~wise(susan)|rich(susan)))&
(?[X]:(funny(X)))&
(?[X]:((~strong(X)|kind(X)))) | ~happy(fred) | [
"p5",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6378055051706543559952035
% SZS output start Proof for 6378055051706543559952035
6. ! [X0] : ((wise(X0) | curious(X0)) => ~curious(X0)) [input p5]
10. ! [X0] : ((wise(X0) <~> happy(X0)) => happy(X0)) [input p9]
11. ? [X0] : (kind(X0) | ~rich(X0)) <=> curious(lucy) [input p10]
13. ? [X0] : (~wise(X0) | curious(X0)) => ? [X0] : ~rich(X0) [input p12]
22. ~happy(fred) [input hypothesis]
23. ? [X0] : (~wise(X0) | curious(X0)) => ? [X1] : ~rich(X1) [rectify 13]
27. ! [X0] : (~curious(X0) | (~wise(X0) & ~curious(X0))) [ennf transformation 6]
29. ! [X0] : (happy(X0) | (wise(X0) <=> happy(X0))) [ennf transformation 10]
30. ? [X1] : ~rich(X1) | ! [X0] : (wise(X0) & ~curious(X0)) [ennf transformation 23]
43. ! [X0] : (happy(X0) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0)))) [nnf transformation 29]
44. (? [X0] : (kind(X0) | ~rich(X0)) | ~curious(lucy)) & (curious(lucy) | ! [X0] : (~kind(X0) & rich(X0))) [nnf transformation 11]
45. (? [X0] : (kind(X0) | ~rich(X0)) | ~curious(lucy)) & (curious(lucy) | ! [X1] : (~kind(X1) & rich(X1))) [rectify 44]
46. ? [X0] : (kind(X0) | ~rich(X0)) => (kind(sK0) | ~rich(sK0)) [choice axiom]
47. ((kind(sK0) | ~rich(sK0)) | ~curious(lucy)) & (curious(lucy) | ! [X1] : (~kind(X1) & rich(X1))) [skolemisation 45,46]
49. ? [X0] : ~rich(X0) | ! [X1] : (wise(X1) & ~curious(X1)) [rectify 30]
50. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
51. ~rich(sK1) | ! [X1] : (wise(X1) & ~curious(X1)) [skolemisation 49,50]
84. ~curious(X0) | ~curious(X0) [cnf transformation 27]
99. happy(X0) | happy(X0) | ~wise(X0) [cnf transformation 43]
101. curious(lucy) | rich(X1) [cnf transformation 47]
109. ~rich(sK1) | wise(X1) [cnf transformation 51]
126. ~happy(fred) [cnf transformation 22]
127. ~wise(X0) | happy(X0) [duplicate literal removal 99]
128. ~curious(X0) [duplicate literal removal 84]
191. rich(X1) [subsumption resolution 101,128]
194. wise(X1) [subsumption resolution 109,191]
210. happy(X0) [resolution 127,194]
211. $false [resolution 210,126]
% SZS output end Proof for 6378055051706543559952035
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not calm is not kind or quiet and vice versa.
Everyone who is both wise and not happy is both quiet and not funny and vice versa.
Everyone who is kind is either strong or not wise.
Everyone who is not calm or humble is old or not tall and vice versa.
Everyone who is curious is not quiet or funny and vice versa.
Everyone who is either wise or quiet is either curious or calm and vice versa.
If alice is either happy or calm then someone is not creative or not kind.
Everyone who is either not funny or not humble is either creative or kind.
Everyone who is both patient and old is not generous or kind.
If someone is not strong or strong then someone is either tall or generous and vice versa.
If fred is either not generous or creative then someone is not quiet and vice versa.
Everyone who is quiet or not strong is both not creative and not rich and vice versa.
If someone is happy or not strong then susan is strong or not generous.
If someone is humble then someone is not old or wise and vice versa.
Everyone who is both quiet and not patient is either brave or not wise and vice versa.
Everyone who is either not curious or wise is either not rich or not wise and vice versa.
John is rich or patient.
Someone is either brave or old.
John is both funny and generous.
Paul is both tall and not kind.
Susan is not creative or curious.
Someone is not old.
John is not quiet or not strong. | Alice is not quiet. | entailment | (![X]:((wise(X)&~calm(X))<=>(~kind(X)|quiet(X))))&
(![X]:((wise(X)&~happy(X))<=>(quiet(X)&~funny(X))))&
(![X]:(kind(X)=>(strong(X)<~>~wise(X))))&
(![X]:((~calm(X)|humble(X))<=>(old(X)|~tall(X))))&
(![X]:(curious(X)<=>(~quiet(X)|funny(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(curious(X)<~>calm(X))))&
(((happy(alice)<~>calm(alice)))=>(?[X]:((~creative(X)|~kind(X)))))&
(![X]:((~funny(X)<~>~humble(X))=>(creative(X)<~>kind(X))))&
(![X]:((patient(X)&old(X))=>(~generous(X)|kind(X))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((tall(X)<~>generous(X)))))&
(((~generous(fred)<~>creative(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)|~strong(X))<=>(~creative(X)&~rich(X))))&
((?[X]:((happy(X)|~strong(X))))=>((strong(susan)|~generous(susan))))&
((?[X]:(humble(X)))<=>(?[X]:((~old(X)|wise(X)))))&
(![X]:((quiet(X)&~patient(X))<=>(brave(X)<~>~wise(X))))&
(![X]:((~curious(X)<~>wise(X))<=>(~rich(X)<~>~wise(X))))&
((rich(john)|patient(john)))&
(?[X]:((brave(X)<~>old(X))))&
((funny(john)&generous(john)))&
((tall(paul)&~kind(paul)))&
((~creative(susan)|curious(susan)))&
(?[X]:(~old(X)))&
((~quiet(john)|~strong(john))) | ~quiet(alice) | [
"p0",
"p4",
"p5",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7212883526976704076140597
% SZS output start Proof for 7212883526976704076140597
1. ! [X0] : ((~calm(X0) & wise(X0)) <=> (quiet(X0) | ~kind(X0))) [input p0]
5. ! [X0] : (curious(X0) <=> (funny(X0) | ~quiet(X0))) [input p4]
6. ! [X0] : ((wise(X0) <~> quiet(X0)) <=> (curious(X0) <~> calm(X0))) [input p5]
12. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (~rich(X0) & ~creative(X0))) [input p11]
16. ! [X0] : ((~curious(X0) <~> wise(X0)) <=> (~rich(X0) <~> ~wise(X0))) [input p15]
24. quiet(alice) [input hypothesis]
34. ! [X0] : (((~calm(X0) & wise(X0)) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | (calm(X0) | ~wise(X0)))) [nnf transformation 1]
35. ! [X0] : (((~calm(X0) & wise(X0)) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | calm(X0) | ~wise(X0))) [flattening 34]
41. ! [X0] : ((curious(X0) | (~funny(X0) & quiet(X0))) & ((funny(X0) | ~quiet(X0)) | ~curious(X0))) [nnf transformation 5]
42. ! [X0] : ((curious(X0) | (~funny(X0) & quiet(X0))) & (funny(X0) | ~quiet(X0) | ~curious(X0))) [flattening 41]
43. ! [X0] : ((((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) & (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0))))) [nnf transformation 6]
57. ! [X0] : (((~strong(X0) | quiet(X0)) | (rich(X0) | creative(X0))) & ((~rich(X0) & ~creative(X0)) | (strong(X0) & ~quiet(X0)))) [nnf transformation 12]
58. ! [X0] : ((~strong(X0) | quiet(X0) | rich(X0) | creative(X0)) & ((~rich(X0) & ~creative(X0)) | (strong(X0) & ~quiet(X0)))) [flattening 57]
66. ! [X0] : ((((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0))))) [nnf transformation 16]
74. ~quiet(X0) | wise(X0) [cnf transformation 35]
76. ~quiet(X0) | ~calm(X0) [cnf transformation 35]
88. curious(X0) | quiet(X0) [cnf transformation 42]
96. ~quiet(X0) | ~wise(X0) | calm(X0) | ~curious(X0) [cnf transformation 43]
117. ~rich(X0) | ~quiet(X0) [cnf transformation 58]
133. wise(X0) | rich(X0) | wise(X0) | curious(X0) [cnf transformation 66]
137. ~wise(X0) | curious(X0) | ~wise(X0) | rich(X0) [cnf transformation 66]
149. quiet(alice) [cnf transformation 24]
151. wise(X0) | rich(X0) | curious(X0) [duplicate literal removal 133]
153. ~wise(X0) | curious(X0) | rich(X0) [duplicate literal removal 137]
155. ~quiet(X0) | ~wise(X0) | ~curious(X0) [subsumption resolution 96,76]
156. ~curious(X0) | ~quiet(X0) [subsumption resolution 155,74]
253. rich(X0) | curious(X0) [subsumption resolution 151,153]
306. curious(X1) | ~quiet(X1) [resolution 253,117]
308. curious(X1) [subsumption resolution 306,88]
309. ~quiet(X0) [resolution 308,156]
311. $false [resolution 309,149]
% SZS output end Proof for 7212883526976704076140597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not kind is not rich or not strong and vice versa. Everyone who is either brave or not tall is either patient or not generous and vice versa. If fred is either brave or not patient then susan is not calm and vice versa. Everyone who is quiet or not curious is both quiet and rich. If mary is not old or not rich then someone is strong. If fred is both not rich and not funny then susan is both not funny and not curious and vice versa. Everyone who is either old or not calm is either old or tall. Everyone who is either creative or not wise is not kind or rich. If someone is either quiet or kind then susan is happy. If someone is either rich or not tall then someone is either kind or not creative and vice versa. If someone is both not strong and not humble then someone is either rich or not curious. Everyone who is both old and not patient is either not quiet or not kind and vice versa. Everyone who is either not calm or quiet is humble and vice versa. Everyone who is both not funny and not quiet is both not funny and not happy and vice versa. If someone is not old then fred is both quiet and not old and vice versa. Everyone who is happy is either not wise or not old. Paul is not quiet or not happy. Someone is generous. Someone is funny. Mary is both strong and not kind. Fred is both humble and not calm. Fred is both not rich and kind. Mary is not tall or not calm. | Fred is not old. | contradiction | (![X]:((generous(X)<~>~kind(X))<=>(~rich(X)|~strong(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(patient(X)<~>~generous(X))))&
(((brave(fred)<~>~patient(fred)))<=>(~calm(susan)))&
(![X]:((quiet(X)|~curious(X))=>(quiet(X)&rich(X))))&
(((~old(mary)|~rich(mary)))=>(?[X]:(strong(X))))&
(((~rich(fred)&~funny(fred)))<=>((~funny(susan)&~curious(susan))))&
(![X]:((old(X)<~>~calm(X))=>(old(X)<~>tall(X))))&
(![X]:((creative(X)<~>~wise(X))=>(~kind(X)|rich(X))))&
((?[X]:((quiet(X)<~>kind(X))))=>(happy(susan)))&
((?[X]:((rich(X)<~>~tall(X))))<=>(?[X]:((kind(X)<~>~creative(X)))))&
((?[X]:((~strong(X)&~humble(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:((old(X)&~patient(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>humble(X)))&
(![X]:((~funny(X)&~quiet(X))<=>(~funny(X)&~happy(X))))&
((?[X]:(~old(X)))<=>((quiet(fred)&~old(fred))))&
(![X]:(happy(X)=>(~wise(X)<~>~old(X))))&
((~quiet(paul)|~happy(paul)))&
(?[X]:(generous(X)))&
(?[X]:(funny(X)))&
((strong(mary)&~kind(mary)))&
((humble(fred)&~calm(fred)))&
((~rich(fred)&kind(fred)))&
((~tall(mary)|~calm(mary))) | ~old(fred) | [
"p3",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 820987085829128866354021
% SZS output start Proof for 820987085829128866354021
4. ! [X0] : ((~curious(X0) | quiet(X0)) => (rich(X0) & quiet(X0))) [input p3]
15. ? [X0] : ~old(X0) <=> (~old(fred) & quiet(fred)) [input p14]
22. kind(fred) & ~rich(fred) [input p21]
24. ~old(fred) [input hypothesis]
28. ! [X0] : ((rich(X0) & quiet(X0)) | (curious(X0) & ~quiet(X0))) [ennf transformation 4]
62. (? [X0] : ~old(X0) | (old(fred) | ~quiet(fred))) & ((~old(fred) & quiet(fred)) | ! [X0] : old(X0)) [nnf transformation 15]
63. (? [X0] : ~old(X0) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X0] : old(X0)) [flattening 62]
64. (? [X0] : ~old(X0) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X1] : old(X1)) [rectify 63]
65. ? [X0] : ~old(X0) => ~old(sK4) [choice axiom]
66. (~old(sK4) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X1] : old(X1)) [skolemisation 64,65]
92. ~quiet(X0) | rich(X0) [cnf transformation 28]
130. quiet(fred) | old(X1) [cnf transformation 66]
142. ~rich(fred) [cnf transformation 22]
145. ~old(fred) [cnf transformation 24]
192. 10 <=> rich(fred) [avatar definition]
194. ~rich(fred) <- (~10) [avatar component clause 192]
262. 25 <=> quiet(fred) [avatar definition]
263. quiet(fred) <- (25) [avatar component clause 262]
266. 26 <=> old(fred) [avatar definition]
267. ~old(fred) <- (~26) [avatar component clause 266]
275. 28 <=> ! [X1] : old(X1) [avatar definition]
276. old(X1) <- (28) [avatar component clause 275]
278. 28 | 25 [avatar split clause 130,262,275]
288. ~10 [avatar split clause 142,192]
298. ~26 [avatar split clause 145,266]
300. rich(fred) <- (25) [resolution 92,263]
302. $false <- (~10, 25) [subsumption resolution 300,194]
303. 10 | ~25 [avatar contradiction clause 302]
304. $false <- (~26, 28) [resolution 276,267]
307. 26 | ~28 [avatar contradiction clause 304]
308. $false [avatar sat refutation 278,288,298,303,307]
% SZS output end Proof for 820987085829128866354021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not curious or rich then someone is funny and vice versa.
If someone is either not happy or rich then alice is not strong or not funny and vice versa.
Everyone who is both not wise and not old is either not funny or not curious.
If someone is not curious or rich then alice is both creative and not brave.
If alice is not tall then someone is either not generous or curious.
If alice is either kind or calm then someone is both not tall and not generous.
If susan is both wise and creative then lucy is either old or not quiet.
If mary is both not happy and funny then lucy is not creative or not humble and vice versa.
If someone is both rich and not humble then john is both not brave and wise.
Everyone who is both patient and not creative is either not brave or not wise and vice versa.
Everyone who is both curious and not curious is patient or not humble and vice versa.
If paul is patient or not humble then susan is either patient or not calm and vice versa.
Everyone who is both generous and not curious is kind and vice versa.
If fred is brave then someone is either not old or not rich.
Everyone who is both curious and not creative is not strong or tall.
Everyone who is either happy or not quiet is humble or not generous.
Someone is either not funny or old.
Someone is curious or not kind.
Susan is not quiet or wise.
Someone is tall or not humble.
Fred is calm or not patient.
Someone is not quiet or not funny.
John is not kind or not calm.
Someone is either old or not brave. | Susan is not humble. | contradiction | (((~curious(fred)<~>rich(fred)))<=>(?[X]:(funny(X))))&
((?[X]:((~happy(X)<~>rich(X))))<=>((~strong(alice)|~funny(alice))))&
(![X]:((~wise(X)&~old(X))=>(~funny(X)<~>~curious(X))))&
((?[X]:((~curious(X)|rich(X))))=>((creative(alice)&~brave(alice))))&
((~tall(alice))=>(?[X]:((~generous(X)<~>curious(X)))))&
(((kind(alice)<~>calm(alice)))=>(?[X]:((~tall(X)&~generous(X)))))&
(((wise(susan)&creative(susan)))=>((old(lucy)<~>~quiet(lucy))))&
(((~happy(mary)&funny(mary)))<=>((~creative(lucy)|~humble(lucy))))&
((?[X]:((rich(X)&~humble(X))))=>((~brave(john)&wise(john))))&
(![X]:((patient(X)&~creative(X))<=>(~brave(X)<~>~wise(X))))&
(![X]:((curious(X)&~curious(X))<=>(patient(X)|~humble(X))))&
(((patient(paul)|~humble(paul)))<=>((patient(susan)<~>~calm(susan))))&
(![X]:((generous(X)&~curious(X))<=>kind(X)))&
((brave(fred))=>(?[X]:((~old(X)<~>~rich(X)))))&
(![X]:((curious(X)&~creative(X))=>(~strong(X)|tall(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(humble(X)|~generous(X))))&
(?[X]:((~funny(X)<~>old(X))))&
(?[X]:((curious(X)|~kind(X))))&
((~quiet(susan)|wise(susan)))&
(?[X]:((tall(X)|~humble(X))))&
((calm(fred)|~patient(fred)))&
(?[X]:((~quiet(X)|~funny(X))))&
((~kind(john)|~calm(john)))&
(?[X]:((old(X)<~>~brave(X)))) | ~humble(susan) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3569306249959624053403290
% SZS output start Proof for 3569306249959624053403290
11. ! [X0] : ((~curious(X0) & curious(X0)) <=> (~humble(X0) | patient(X0))) [input p10]
25. ~humble(susan) [input hypothesis]
60. ! [X0] : (((~curious(X0) & curious(X0)) | (humble(X0) & ~patient(X0))) & ((~humble(X0) | patient(X0)) | (curious(X0) | ~curious(X0)))) [nnf transformation 11]
61. ! [X0] : (((~curious(X0) & curious(X0)) | (humble(X0) & ~patient(X0))) & (~humble(X0) | patient(X0) | curious(X0) | ~curious(X0))) [flattening 60]
121. curious(X0) | humble(X0) [cnf transformation 61]
123. ~curious(X0) | humble(X0) [cnf transformation 61]
148. ~humble(susan) [cnf transformation 25]
300. humble(X0) [subsumption resolution 121,123]
364. $false [subsumption resolution 148,300]
% SZS output end Proof for 3569306249959624053403290
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not humble then paul is patient and vice versa. Everyone who is either happy or not old is both not happy and not quiet. Everyone who is old is either not kind or not quiet and vice versa. Everyone who is wise is both not strong and not calm. Everyone who is happy is not strong or patient and vice versa. If lucy is both quiet and kind then lucy is not calm or kind. Everyone who is either not quiet or not wise is either not funny or quiet and vice versa. If susan is both brave and not calm then paul is both tall and not creative and vice versa. Everyone who is both not funny and generous is not patient and vice versa. If someone is not calm or brave then someone is both not humble and rich and vice versa. Everyone who is rich is both not old and old and vice versa. Everyone who is both not humble and old is either not old or happy. If lucy is not generous then lucy is both not calm and tall and vice versa. Everyone who is happy or not kind is either creative or not kind and vice versa. If lucy is either not kind or quiet then alice is not rich. Susan is either curious or not generous. Someone is old or generous. Someone is patient or not calm. Someone is both humble and tall. Someone is happy. Lucy is not funny or quiet. | Susan is calm. | entailment | ((~humble(susan))<=>(patient(paul)))&
(![X]:((happy(X)<~>~old(X))=>(~happy(X)&~quiet(X))))&
(![X]:(old(X)<=>(~kind(X)<~>~quiet(X))))&
(![X]:(wise(X)=>(~strong(X)&~calm(X))))&
(![X]:(happy(X)<=>(~strong(X)|patient(X))))&
(((quiet(lucy)&kind(lucy)))=>((~calm(lucy)|kind(lucy))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~funny(X)<~>quiet(X))))&
(((brave(susan)&~calm(susan)))<=>((tall(paul)&~creative(paul))))&
(![X]:((~funny(X)&generous(X))<=>~patient(X)))&
((?[X]:((~calm(X)|brave(X))))<=>(?[X]:((~humble(X)&rich(X)))))&
(![X]:(rich(X)<=>(~old(X)&old(X))))&
(![X]:((~humble(X)&old(X))=>(~old(X)<~>happy(X))))&
((~generous(lucy))<=>((~calm(lucy)&tall(lucy))))&
(![X]:((happy(X)|~kind(X))<=>(creative(X)<~>~kind(X))))&
(((~kind(lucy)<~>quiet(lucy)))=>(~rich(alice)))&
((curious(susan)<~>~generous(susan)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((patient(X)|~calm(X))))&
(?[X]:((humble(X)&tall(X))))&
(?[X]:(happy(X)))&
((~funny(lucy)|quiet(lucy))) | calm(susan) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 643939127248856118899556
% SZS output start Proof for 643939127248856118899556
10. ? [X0] : (brave(X0) | ~calm(X0)) <=> ? [X0] : (rich(X0) & ~humble(X0)) [input p9]
11. ! [X0] : (rich(X0) <=> (old(X0) & ~old(X0))) [input p10]
22. ~calm(susan) [input hypothesis]
23. ? [X0] : (brave(X0) | ~calm(X0)) <=> ? [X1] : (rich(X1) & ~humble(X1)) [rectify 10]
41. (? [X0] : (brave(X0) | ~calm(X0)) | ! [X1] : (~rich(X1) | humble(X1))) & (? [X1] : (rich(X1) & ~humble(X1)) | ! [X0] : (~brave(X0) & calm(X0))) [nnf transformation 23]
42. (? [X0] : (brave(X0) | ~calm(X0)) | ! [X1] : (~rich(X1) | humble(X1))) & (? [X2] : (rich(X2) & ~humble(X2)) | ! [X3] : (~brave(X3) & calm(X3))) [rectify 41]
43. ? [X0] : (brave(X0) | ~calm(X0)) => (brave(sK0) | ~calm(sK0)) [choice axiom]
44. ? [X2] : (rich(X2) & ~humble(X2)) => (rich(sK1) & ~humble(sK1)) [choice axiom]
45. ((brave(sK0) | ~calm(sK0)) | ! [X1] : (~rich(X1) | humble(X1))) & ((rich(sK1) & ~humble(sK1)) | ! [X3] : (~brave(X3) & calm(X3))) [skolemisation 42,44,43]
46. ! [X0] : ((rich(X0) | (~old(X0) | old(X0))) & ((old(X0) & ~old(X0)) | ~rich(X0))) [nnf transformation 11]
47. ! [X0] : ((rich(X0) | ~old(X0) | old(X0)) & ((old(X0) & ~old(X0)) | ~rich(X0))) [flattening 46]
96. rich(sK1) | calm(X3) [cnf transformation 45]
99. ~old(X0) | ~rich(X0) [cnf transformation 47]
100. old(X0) | ~rich(X0) [cnf transformation 47]
123. ~calm(susan) [cnf transformation 22]
153. 5 <=> calm(susan) [avatar definition]
155. ~calm(susan) <- (~5) [avatar component clause 153]
180. 11 <=> rich(sK1) [avatar definition]
182. rich(sK1) <- (11) [avatar component clause 180]
185. 12 <=> ! [X3] : calm(X3) [avatar definition]
186. calm(X3) <- (12) [avatar component clause 185]
187. 12 | 11 [avatar split clause 96,180,185]
194. ~rich(X0) [subsumption resolution 99,100]
248. ~5 [avatar split clause 123,153]
249. $false <- (11) [subsumption resolution 182,194]
250. ~11 [avatar contradiction clause 249]
251. $false <- (~5, 12) [resolution 186,155]
254. 5 | ~12 [avatar contradiction clause 251]
255. $false [avatar sat refutation 187,248,250,254]
% SZS output end Proof for 643939127248856118899556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is either not humble or not patient.
If john is both funny and humble then susan is not brave and vice versa.
Everyone who is both not strong and not rich is either rich or patient and vice versa.
Everyone who is not humble or not happy is both not old and strong.
Everyone who is not old is not brave or not curious and vice versa.
Everyone who is both not kind and wise is both tall and not kind.
Everyone who is not old is both not humble and funny and vice versa.
Everyone who is both not curious and quiet is not creative and vice versa.
If someone is humble or not wise then someone is both not old and not funny.
If lucy is both wise and not humble then someone is happy and vice versa.
If someone is both curious and funny then someone is both not quiet and curious.
If fred is both not generous and not rich then lucy is both brave and humble.
If john is strong or not generous then mary is not patient and vice versa.
Everyone who is wise is either humble or funny and vice versa.
If someone is calm then fred is creative or quiet and vice versa.
Everyone who is both humble and old is rich.
Someone is rich or funny.
Lucy is not creative.
Someone is both kind and patient.
Someone is either wise or not funny.
Someone is wise.
Someone is not quiet or tall.
Someone is both calm and not creative. | Susan is not brave. | contradiction | (![X]:(~tall(X)=>(~humble(X)<~>~patient(X))))&
(((funny(john)&humble(john)))<=>(~brave(susan)))&
(![X]:((~strong(X)&~rich(X))<=>(rich(X)<~>patient(X))))&
(![X]:((~humble(X)|~happy(X))=>(~old(X)&strong(X))))&
(![X]:(~old(X)<=>(~brave(X)|~curious(X))))&
(![X]:((~kind(X)&wise(X))=>(tall(X)&~kind(X))))&
(![X]:(~old(X)<=>(~humble(X)&funny(X))))&
(![X]:((~curious(X)&quiet(X))<=>~creative(X)))&
((?[X]:((humble(X)|~wise(X))))=>(?[X]:((~old(X)&~funny(X)))))&
(((wise(lucy)&~humble(lucy)))<=>(?[X]:(happy(X))))&
((?[X]:((curious(X)&funny(X))))=>(?[X]:((~quiet(X)&curious(X)))))&
(((~generous(fred)&~rich(fred)))=>((brave(lucy)&humble(lucy))))&
(((strong(john)|~generous(john)))<=>(~patient(mary)))&
(![X]:(wise(X)<=>(humble(X)<~>funny(X))))&
((?[X]:(calm(X)))<=>((creative(fred)|quiet(fred))))&
(![X]:((humble(X)&old(X))=>rich(X)))&
(?[X]:((rich(X)|funny(X))))&
(~creative(lucy))&
(?[X]:((kind(X)&patient(X))))&
(?[X]:((wise(X)<~>~funny(X))))&
(?[X]:(wise(X)))&
(?[X]:((~quiet(X)|tall(X))))&
(?[X]:((calm(X)&~creative(X)))) | ~brave(susan) | [
"p1",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4053871731561756628986115
% SZS output start Proof for 4053871731561756628986115
2. (humble(john) & funny(john)) <=> ~brave(susan) [input p1]
7. ! [X0] : (~old(X0) <=> (funny(X0) & ~humble(X0))) [input p6]
9. ? [X0] : (~wise(X0) | humble(X0)) => ? [X0] : (~funny(X0) & ~old(X0)) [input p8]
24. ~brave(susan) [input hypothesis]
25. ? [X0] : (~wise(X0) | humble(X0)) => ? [X1] : (~funny(X1) & ~old(X1)) [rectify 9]
33. ? [X1] : (~funny(X1) & ~old(X1)) | ! [X0] : (wise(X0) & ~humble(X0)) [ennf transformation 25]
39. ((humble(john) & funny(john)) | brave(susan)) & (~brave(susan) | (~humble(john) | ~funny(john))) [nnf transformation 2]
40. ((humble(john) & funny(john)) | brave(susan)) & (~brave(susan) | ~humble(john) | ~funny(john)) [flattening 39]
45. ! [X0] : ((~old(X0) | (~funny(X0) | humble(X0))) & ((funny(X0) & ~humble(X0)) | old(X0))) [nnf transformation 7]
46. ! [X0] : ((~old(X0) | ~funny(X0) | humble(X0)) & ((funny(X0) & ~humble(X0)) | old(X0))) [flattening 45]
49. ? [X0] : (~funny(X0) & ~old(X0)) | ! [X1] : (wise(X1) & ~humble(X1)) [rectify 33]
50. ? [X0] : (~funny(X0) & ~old(X0)) => (~funny(sK0) & ~old(sK0)) [choice axiom]
51. (~funny(sK0) & ~old(sK0)) | ! [X1] : (wise(X1) & ~humble(X1)) [skolemisation 49,50]
81. humble(john) | brave(susan) [cnf transformation 40]
97. old(X0) | funny(X0) [cnf transformation 46]
102. ~old(sK0) | ~humble(X1) [cnf transformation 51]
104. ~funny(sK0) | ~humble(X1) [cnf transformation 51]
133. ~brave(susan) [cnf transformation 24]
137. 1 <=> brave(susan) [avatar definition]
141. 2 <=> humble(john) [avatar definition]
143. humble(john) <- (2) [avatar component clause 141]
144. 1 | 2 [avatar split clause 81,141,137]
156. 5 <=> funny(sK0) [avatar definition]
158. ~funny(sK0) <- (~5) [avatar component clause 156]
161. 6 <=> ! [X1] : ~humble(X1) [avatar definition]
162. ~humble(X1) <- (6) [avatar component clause 161]
163. 6 | ~5 [avatar split clause 104,156,161]
165. 7 <=> old(sK0) [avatar definition]
167. ~old(sK0) <- (~7) [avatar component clause 165]
169. 6 | ~7 [avatar split clause 102,165,161]
264. ~1 [avatar split clause 133,137]
267. funny(sK0) <- (~7) [resolution 97,167]
272. $false <- (~5, ~7) [subsumption resolution 267,158]
273. 5 | 7 [avatar contradiction clause 272]
284. $false <- (2, 6) [resolution 162,143]
285. ~2 | ~6 [avatar contradiction clause 284]
286. $false [avatar sat refutation 144,163,169,264,273,285]
% SZS output end Proof for 4053871731561756628986115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not quiet and not funny then someone is either not curious or calm and vice versa. Everyone who is quiet or not tall is either not curious or calm and vice versa. If someone is both funny and not patient then alice is not rich or not kind and vice versa. If someone is not brave or brave then fred is either old or not curious. If someone is wise then alice is both not curious and not wise. Everyone who is not tall or rich is both kind and not kind and vice versa. Everyone who is both quiet and not kind is tall or not rich. Everyone who is not patient is both not generous and not brave and vice versa. Everyone who is either not creative or rich is both not generous and wise. Everyone who is patient is either wise or calm. Everyone who is either generous or not kind is both not wise and not creative. If someone is both happy and brave then someone is both not kind and not rich and vice versa. Everyone who is creative is either not brave or patient and vice versa. Everyone who is either patient or not creative is either patient or not quiet. Everyone who is happy is not curious and vice versa. If someone is generous or not kind then alice is both creative and wise and vice versa. Someone is brave. Someone is both not old and calm. Fred is both curious and not happy. Lucy is either wise or creative. Someone is both not quiet and wise. John is not happy or not funny. John is not humble. | Alice is not kind. | contradiction | (((~quiet(john)&~funny(john)))<=>(?[X]:((~curious(X)<~>calm(X)))))&
(![X]:((quiet(X)|~tall(X))<=>(~curious(X)<~>calm(X))))&
((?[X]:((funny(X)&~patient(X))))<=>((~rich(alice)|~kind(alice))))&
((?[X]:((~brave(X)|brave(X))))=>((old(fred)<~>~curious(fred))))&
((?[X]:(wise(X)))=>((~curious(alice)&~wise(alice))))&
(![X]:((~tall(X)|rich(X))<=>(kind(X)&~kind(X))))&
(![X]:((quiet(X)&~kind(X))=>(tall(X)|~rich(X))))&
(![X]:(~patient(X)<=>(~generous(X)&~brave(X))))&
(![X]:((~creative(X)<~>rich(X))=>(~generous(X)&wise(X))))&
(![X]:(patient(X)=>(wise(X)<~>calm(X))))&
(![X]:((generous(X)<~>~kind(X))=>(~wise(X)&~creative(X))))&
((?[X]:((happy(X)&brave(X))))<=>(?[X]:((~kind(X)&~rich(X)))))&
(![X]:(creative(X)<=>(~brave(X)<~>patient(X))))&
(![X]:((patient(X)<~>~creative(X))=>(patient(X)<~>~quiet(X))))&
(![X]:(happy(X)<=>~curious(X)))&
((?[X]:((generous(X)|~kind(X))))<=>((creative(alice)&wise(alice))))&
(?[X]:(brave(X)))&
(?[X]:((~old(X)&calm(X))))&
((curious(fred)&~happy(fred)))&
((wise(lucy)<~>creative(lucy)))&
(?[X]:((~quiet(X)&wise(X))))&
((~happy(john)|~funny(john)))&
(~humble(john)) | ~kind(alice) | [
"p4",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1151247975415524666339926
% SZS output start Proof for 1151247975415524666339926
5. ? [X0] : wise(X0) => (~wise(alice) & ~curious(alice)) [input p4]
16. ? [X0] : (~kind(X0) | generous(X0)) <=> (wise(alice) & creative(alice)) [input p15]
21. ? [X0] : (wise(X0) & ~quiet(X0)) [input p20]
24. ~kind(alice) [input hypothesis]
28. (~wise(alice) & ~curious(alice)) | ! [X0] : ~wise(X0) [ennf transformation 5]
63. (? [X0] : (~kind(X0) | generous(X0)) | (~wise(alice) | ~creative(alice))) & ((wise(alice) & creative(alice)) | ! [X0] : (kind(X0) & ~generous(X0))) [nnf transformation 16]
64. (? [X0] : (~kind(X0) | generous(X0)) | ~wise(alice) | ~creative(alice)) & ((wise(alice) & creative(alice)) | ! [X0] : (kind(X0) & ~generous(X0))) [flattening 63]
65. (? [X0] : (~kind(X0) | generous(X0)) | ~wise(alice) | ~creative(alice)) & ((wise(alice) & creative(alice)) | ! [X1] : (kind(X1) & ~generous(X1))) [rectify 64]
66. ? [X0] : (~kind(X0) | generous(X0)) => (~kind(sK4) | generous(sK4)) [choice axiom]
67. ((~kind(sK4) | generous(sK4)) | ~wise(alice) | ~creative(alice)) & ((wise(alice) & creative(alice)) | ! [X1] : (kind(X1) & ~generous(X1))) [skolemisation 65,66]
73. ? [X0] : (wise(X0) & ~quiet(X0)) => (wise(sK7) & ~quiet(sK7)) [choice axiom]
74. wise(sK7) & ~quiet(sK7) [skolemisation 21,73]
97. ~wise(alice) | ~wise(X0) [cnf transformation 28]
134. wise(alice) | kind(X1) [cnf transformation 67]
144. wise(sK7) [cnf transformation 74]
146. ~kind(alice) [cnf transformation 24]
178. 7 <=> kind(alice) [avatar definition]
179. ~kind(alice) <- (~7) [avatar component clause 178]
220. 16 <=> ! [X0] : ~wise(X0) [avatar definition]
221. ~wise(X0) <- (16) [avatar component clause 220]
223. 17 <=> wise(alice) [avatar definition]
226. 16 | ~17 [avatar split clause 97,223,220]
239. 19 <=> ! [X1] : kind(X1) [avatar definition]
240. kind(X1) <- (19) [avatar component clause 239]
272. 19 | 17 [avatar split clause 134,223,239]
294. ~7 [avatar split clause 146,178]
295. $false <- (~7, 19) [subsumption resolution 179,240]
296. 7 | ~19 [avatar contradiction clause 295]
297. $false <- (16) [resolution 221,144]
298. ~16 [avatar contradiction clause 297]
299. $false [avatar sat refutation 226,272,294,296,298]
% SZS output end Proof for 1151247975415524666339926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not rich is both not generous and not humble and vice versa. Everyone who is kind or generous is not old or wise and vice versa. Everyone who is either curious or not generous is brave or not strong. Everyone who is patient or not happy is both wise and brave. If someone is not curious or not calm then someone is not calm or not quiet. Everyone who is both not funny and tall is either generous or kind and vice versa. Everyone who is not happy is both not funny and not wise. Everyone who is rich or not generous is not tall or brave. Everyone who is funny or not funny is either brave or not rich and vice versa. If mary is not creative or rich then susan is either not patient or not rich and vice versa. If someone is both funny and not creative then john is either not brave or kind and vice versa. Everyone who is either not humble or not creative is either generous or not generous and vice versa. If susan is tall then john is either not kind or not brave. Everyone who is not kind or not old is either not creative or not old. If someone is not kind or generous then someone is either creative or not patient. Everyone who is either tall or calm is strong or tall and vice versa. Mary is both not old and generous. John is not curious. Mary is brave. Lucy is old or not tall. Paul is not tall. Paul is old or not tall. Someone is brave. | Lucy is not calm. | entailment | (![X]:((strong(X)|~rich(X))<=>(~generous(X)&~humble(X))))&
(![X]:((kind(X)|generous(X))<=>(~old(X)|wise(X))))&
(![X]:((curious(X)<~>~generous(X))=>(brave(X)|~strong(X))))&
(![X]:((patient(X)|~happy(X))=>(wise(X)&brave(X))))&
((?[X]:((~curious(X)|~calm(X))))=>(?[X]:((~calm(X)|~quiet(X)))))&
(![X]:((~funny(X)&tall(X))<=>(generous(X)<~>kind(X))))&
(![X]:(~happy(X)=>(~funny(X)&~wise(X))))&
(![X]:((rich(X)|~generous(X))=>(~tall(X)|brave(X))))&
(![X]:((funny(X)|~funny(X))<=>(brave(X)<~>~rich(X))))&
(((~creative(mary)|rich(mary)))<=>((~patient(susan)<~>~rich(susan))))&
((?[X]:((funny(X)&~creative(X))))<=>((~brave(john)<~>kind(john))))&
(![X]:((~humble(X)<~>~creative(X))<=>(generous(X)<~>~generous(X))))&
((tall(susan))=>((~kind(john)<~>~brave(john))))&
(![X]:((~kind(X)|~old(X))=>(~creative(X)<~>~old(X))))&
((?[X]:((~kind(X)|generous(X))))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((tall(X)<~>calm(X))<=>(strong(X)|tall(X))))&
((~old(mary)&generous(mary)))&
(~curious(john))&
(brave(mary))&
((old(lucy)|~tall(lucy)))&
(~tall(paul))&
((old(paul)|~tall(paul)))&
(?[X]:(brave(X))) | ~calm(lucy) | [
"p0",
"p1",
"p5",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1696679132344284674571097
% SZS output start Proof for 1696679132344284674571097
1. ! [X0] : ((~rich(X0) | strong(X0)) <=> (~humble(X0) & ~generous(X0))) [input p0]
2. ! [X0] : ((generous(X0) | kind(X0)) <=> (wise(X0) | ~old(X0))) [input p1]
6. ! [X0] : ((tall(X0) & ~funny(X0)) <=> (generous(X0) <~> kind(X0))) [input p5]
12. ! [X0] : ((~humble(X0) <~> ~creative(X0)) <=> (generous(X0) <~> ~generous(X0))) [input p11]
14. ! [X0] : ((~old(X0) | ~kind(X0)) => (~creative(X0) <~> ~old(X0))) [input p13]
16. ! [X0] : ((tall(X0) <~> calm(X0)) <=> (tall(X0) | strong(X0))) [input p15]
24. calm(lucy) [input hypothesis]
36. ! [X0] : ((~creative(X0) <~> ~old(X0)) | (old(X0) & kind(X0))) [ennf transformation 14]
38. ! [X0] : (((~rich(X0) | strong(X0)) | (humble(X0) | generous(X0))) & ((~humble(X0) & ~generous(X0)) | (rich(X0) & ~strong(X0)))) [nnf transformation 1]
39. ! [X0] : ((~rich(X0) | strong(X0) | humble(X0) | generous(X0)) & ((~humble(X0) & ~generous(X0)) | (rich(X0) & ~strong(X0)))) [flattening 38]
40. ! [X0] : (((generous(X0) | kind(X0)) | (~wise(X0) & old(X0))) & ((wise(X0) | ~old(X0)) | (~generous(X0) & ~kind(X0)))) [nnf transformation 2]
41. ! [X0] : ((generous(X0) | kind(X0) | (~wise(X0) & old(X0))) & (wise(X0) | ~old(X0) | (~generous(X0) & ~kind(X0)))) [flattening 40]
43. ! [X0] : (((tall(X0) & ~funny(X0)) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | (~tall(X0) | funny(X0)))) [nnf transformation 6]
44. ! [X0] : (((tall(X0) & ~funny(X0)) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | ~tall(X0) | funny(X0))) [flattening 43]
53. ! [X0] : ((((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0))))) [nnf transformation 12]
55. ! [X0] : (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (old(X0) & kind(X0))) [nnf transformation 36]
60. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (~tall(X0) & ~strong(X0))) & ((tall(X0) | strong(X0)) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [nnf transformation 16]
61. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (~tall(X0) & ~strong(X0))) & (tall(X0) | strong(X0) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [flattening 60]
64. ~generous(X0) | ~strong(X0) [cnf transformation 39]
66. ~humble(X0) | ~strong(X0) [cnf transformation 39]
71. old(X0) | kind(X0) | generous(X0) [cnf transformation 41]
82. ~kind(X0) | generous(X0) | tall(X0) [cnf transformation 44]
109. creative(X0) | humble(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 53]
110. creative(X0) | humble(X0) | generous(X0) | generous(X0) [cnf transformation 53]
113. ~creative(X0) | ~old(X0) | kind(X0) [cnf transformation 55]
122. tall(X0) | strong(X0) | tall(X0) | ~calm(X0) [cnf transformation 61]
126. ~calm(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 61]
135. calm(lucy) [cnf transformation 24]
136. tall(X0) | strong(X0) | ~calm(X0) [duplicate literal removal 122]
137. ~tall(X0) | ~calm(X0) [duplicate literal removal 126]
141. creative(X0) | humble(X0) | ~generous(X0) [duplicate literal removal 109]
142. creative(X0) | humble(X0) | generous(X0) [duplicate literal removal 110]
193. creative(X0) | humble(X0) [subsumption resolution 141,142]
219. ~calm(X0) | strong(X0) [subsumption resolution 136,137]
225. 16 <=> tall(lucy) [avatar definition]
226. tall(lucy) <- (16) [avatar component clause 225]
227. ~tall(lucy) <- (~16) [avatar component clause 225]
249. strong(lucy) [resolution 219,135]
313. ~old(X0) | kind(X0) | humble(X0) [resolution 113,193]
409. kind(X0) | humble(X0) | kind(X0) | generous(X0) [resolution 313,71]
410. kind(X0) | humble(X0) | generous(X0) [duplicate literal removal 409]
423. humble(X0) | generous(X0) | generous(X0) | tall(X0) [resolution 410,82]
428. tall(X0) | generous(X0) | humble(X0) [duplicate literal removal 423]
458. generous(lucy) | humble(lucy) <- (~16) [resolution 428,227]
463. 40 <=> humble(lucy) [avatar definition]
465. humble(lucy) <- (40) [avatar component clause 463]
467. 41 <=> generous(lucy) [avatar definition]
469. generous(lucy) <- (41) [avatar component clause 467]
470. 40 | 41 | 16 [avatar split clause 458,225,467,463]
550. ~strong(lucy) <- (41) [resolution 469,64]
552. $false <- (41) [subsumption resolution 550,249]
553. ~41 [avatar contradiction clause 552]
571. ~calm(lucy) <- (16) [resolution 226,137]
576. $false <- (16) [subsumption resolution 571,135]
577. ~16 [avatar contradiction clause 576]
582. ~strong(lucy) <- (40) [resolution 465,66]
583. $false <- (40) [subsumption resolution 582,249]
584. ~40 [avatar contradiction clause 583]
585. $false [avatar sat refutation 470,553,577,584]
% SZS output end Proof for 1696679132344284674571097
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not patient is calm or not quiet.
If paul is tall then fred is both kind and not happy and vice versa.
Everyone who is both brave and old is not tall and vice versa.
If john is not rich or not tall then paul is both wise and generous.
Everyone who is funny or calm is both not tall and wise and vice versa.
Everyone who is tall is both funny and not happy.
If lucy is not humble or not calm then lucy is not patient or not calm and vice versa.
Everyone who is either happy or not calm is both not tall and not generous.
Everyone who is either not strong or not tall is either funny or not happy.
Everyone who is brave is not quiet or not patient and vice versa.
Everyone who is both not kind and not creative is either old or patient and vice versa.
Everyone who is both not calm and wise is not old or not calm.
Everyone who is either calm or not wise is either not patient or patient.
If someone is not brave then someone is both tall and not curious and vice versa.
If someone is both wise and quiet then lucy is curious and vice versa.
Everyone who is wise is both creative and wise and vice versa.
Someone is wise.
Susan is strong or kind.
John is either not kind or not generous.
Someone is not creative.
Fred is strong.
Alice is both wise and happy.
Lucy is strong. | Lucy is creative. | neutral | (![X]:((patient(X)|~patient(X))=>(calm(X)|~quiet(X))))&
((tall(paul))<=>((kind(fred)&~happy(fred))))&
(![X]:((brave(X)&old(X))<=>~tall(X)))&
(((~rich(john)|~tall(john)))=>((wise(paul)&generous(paul))))&
(![X]:((funny(X)|calm(X))<=>(~tall(X)&wise(X))))&
(![X]:(tall(X)=>(funny(X)&~happy(X))))&
(((~humble(lucy)|~calm(lucy)))<=>((~patient(lucy)|~calm(lucy))))&
(![X]:((happy(X)<~>~calm(X))=>(~tall(X)&~generous(X))))&
(![X]:((~strong(X)<~>~tall(X))=>(funny(X)<~>~happy(X))))&
(![X]:(brave(X)<=>(~quiet(X)|~patient(X))))&
(![X]:((~kind(X)&~creative(X))<=>(old(X)<~>patient(X))))&
(![X]:((~calm(X)&wise(X))=>(~old(X)|~calm(X))))&
(![X]:((calm(X)<~>~wise(X))=>(~patient(X)<~>patient(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((tall(X)&~curious(X)))))&
((?[X]:((wise(X)&quiet(X))))<=>(curious(lucy)))&
(![X]:(wise(X)<=>(creative(X)&wise(X))))&
(?[X]:(wise(X)))&
((strong(susan)|kind(susan)))&
((~kind(john)<~>~generous(john)))&
(?[X]:(~creative(X)))&
(strong(fred))&
((wise(alice)&happy(alice)))&
(strong(lucy)) | creative(lucy) | [] | null | 0 |
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