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Betty, Clarence, Chelsey, Bridget are the only persons in the room. Either Clarence neither plays the violin nor does not enjoy writing detailed reviews of new and classic board games or everyone in the room collects antique clocks or does not write a travel blog but not both. If everyone in the room writes a travel blog or does not play the violin then more than one person anywhere enjoys writing detailed reviews of new and classic board games. Clarence writes a travel blog if everyone in the room enjoys skydiving or does not play the violin. If Betty enjoys writing detailed reviews of new and classic board games then Chelsey does not play the violin. If Chelsey does not play the violin then if someone plays the violin then he/she enjoys writing detailed reviews of new and classic board games. If Betty enjoys writing detailed reviews of new and classic board games then no one in the room writes a travel blog if they collects antique clocks, plays the violin or enjoys writing detailed reviews of new and classic board games. Chelsey does not write a travel blog. Someone in the room writes a travel blog.

It is not the case that Clarence enjoys writing detailed reviews of new and classic board games.

neutral

room(betty)&room(clarence)&room(chelsey)&room(bridget)&(![X]:(room(X)=>(X='betty'|X='clarence'|X='chelsey'|X='bridget')))& ((~((plays_the_violin(clarence))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(clarence))))<~>(![X]:(room(X)=>(((does_not_write_a_travel_blog(X))|(collects_antique_clocks(X)))))))& ((![X]:(room(X)=>(((does_not_play_the_violin(X))|(writes_a_travel_blog(X))))))=>((?[X,Y]:(anywhere(X)&anywhere(Y)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)&enjoys_writing_detailed_reviews_of_new_and_classic_board_games(Y))&(X!=Y)))))& ((![X]:(room(X)=>(((does_not_play_the_violin(X))|(enjoys_skydiving(X))))))=>(writes_a_travel_blog(clarence)))& (((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(betty))=>(does_not_play_the_violin(chelsey)))& ((does_not_play_the_violin(chelsey))=>((![X]:((plays_the_violin(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))& ((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(betty))=>(~?[X]:(room(X)=>(((((collects_antique_clocks(X))|(plays_the_violin(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))=>(writes_a_travel_blog(X)))))))& (does_not_write_a_travel_blog(chelsey))& (?[X]:(room(X)&(writes_a_travel_blog(X))))& ((?[X,Y]:(room(X)&room(Y)&(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<~>(writes_a_travel_blog(X)))&((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(Y))<~>(writes_a_travel_blog(Y))))&(X!=Y))))& (((collects_antique_clocks(clarence))|(plays_the_violin(clarence))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(clarence))))& (collects_antique_clocks(chelsey))& ((![X]:((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(does_not_collect_antique_clocks(X)))))

room(betty)&room(clarence)&room(chelsey)&room(bridget)&(![X]:(room(X)=>(X='betty'|X='clarence'|X='chelsey'|X='bridget')))& ~(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(clarence))

There is a room. “At least one person in the room practices tai chi, owns an Android phone and is a creative person” unless “everyone in the room collects antique jewelry”. “Everyone in the room collects antique jewelry” unless “everyone in the room practices graffiti art”. If “everyone in the room does not collect antique jewelry” then “if someone owns an Android phone, does not practice graffiti art or does not collect antique jewelry then he/she does not practice graffiti art and vice versa” otherwise “at least one person in the room owns an Android phone”. If “everyone in the room practices graffiti art” then “everyone in the room does not own an Android phone” otherwise “everyone in the room does not practice tai chi”. If “everyone in the room is a creative person” then “everyone in the room collects antique jewelry” otherwise “if someone does not own an Android phone then he/she practices graffiti art”. If “everyone anywhere is not a funny person” then “if someone either collects antique jewelry or does not own an Android phone but not both then he/she either practices graffiti art or practices tai chi but not both” otherwise “if someone practices graffiti art then he/she is not tall”. “If someone practices tai chi then he/she does not collect antique jewelry and vice versa” unless “everyone anywhere does not practice graffiti art”. Not everyone in the room is a funny person. If someone owns an Android phone then he/she is a tall person. No tall person is funny.

Everyone in the room is a tall person.

entailment

(there_is_a_room)& (~(![X]:(room(X)=>(collects_antique_jewelry(X))))=>(((?[X]:(room(X)&((practices_tai_chi(X))&(owns_an_Android_phone(X))&(creative(X)&person(X))))))))& (~(![X]:(room(X)=>(practices_graffiti_art(X))))=>(![X]:(room(X)=>(collects_antique_jewelry(X)))))& (((![X]:(room(X)=>(does_not_collect_antique_jewelry(X))))=>((![X]:((((owns_an_Android_phone(X))|(does_not_practice_graffiti_art(X))|(does_not_collect_antique_jewelry(X))))<=>(does_not_practice_graffiti_art(X))))))&((~(![X]:(room(X)=>(does_not_collect_antique_jewelry(X)))))=>(((?[X]:(room(X)&owns_an_Android_phone(X)))))))& (((![X]:(room(X)=>(practices_graffiti_art(X))))=>(![X]:(room(X)=>(does_not_own_an_Android_phone(X)))))&((~(![X]:(room(X)=>(practices_graffiti_art(X)))))=>(![X]:(room(X)=>(does_not_practice_tai_chi(X))))))& (((![X]:(room(X)=>(creative(X)&person(X))))=>(![X]:(room(X)=>(collects_antique_jewelry(X)))))&((~(![X]:(room(X)=>(creative(X)&person(X)))))=>((![X]:((does_not_own_an_Android_phone(X))=>(practices_graffiti_art(X)))))))& (((![X]:(anywhere(X)=>(~(funny(X)&person(X)))))=>((![X]:((((collects_antique_jewelry(X))<~>(does_not_own_an_Android_phone(X))))=>(((practices_graffiti_art(X))<~>(practices_tai_chi(X))))))))&((~(![X]:(anywhere(X)=>(~(funny(X)&person(X))))))=>((![X]:((practices_graffiti_art(X))=>(~tall(X)))))))& (~(![X]:(anywhere(X)=>(does_not_practice_graffiti_art(X))))=>((![X]:((practices_tai_chi(X))<=>(does_not_collect_antique_jewelry(X))))))& (~![X]:(room(X)=>(funny(X)&person(X))))& ((![X]:((owns_an_Android_phone(X))=>(tall(X)&person(X)))))& (~?[X]:(tall(X)=>funny(X)))

(there_is_a_room)& ![X]:(room(X)=>(tall(X)&person(X)))

% SZS status Unsatisfiable for 2587944371284961253756290 % SZS output start Proof for 2587944371284961253756290 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 45. ~! [X0] : (room(X0) => predp(X0)) => ? [X0] : (person(X0) & creative(X0) & predl(X0) & predg(X0) & room(X0)) [input p1] 46. ~! [X0] : (room(X0) => predq(X0)) => ! [X0] : (room(X0) => predp(X0)) [input p2] 47. (~! [X0] : (room(X0) => ~predp(X0)) => ? [X0] : (predl(X0) & room(X0))) & (! [X0] : (room(X0) => ~predp(X0)) => ! [X0] : ((~predp(X0) | ~predq(X0) | predl(X0)) <=> ~predq(X0))) [input p3] 48. (~! [X0] : (room(X0) => predq(X0)) => ! [X0] : (room(X0) => ~predg(X0))) & (! [X0] : (room(X0) => predq(X0)) => ! [X0] : (room(X0) => ~predl(X0))) [input p4] 49. (~! [X0] : (room(X0) => (person(X0) & creative(X0))) => ! [X0] : (~predl(X0) => predq(X0))) & (! [X0] : (room(X0) => (person(X0) & creative(X0))) => ! [X0] : (room(X0) => predp(X0))) [input p5] 50. (~! [X0] : (anywhere(X0) => ~(person(X0) & funny(X0))) => ! [X0] : (predq(X0) => ~tall(X0))) & (! [X0] : (anywhere(X0) => ~(person(X0) & funny(X0))) => ! [X0] : ((predp(X0) <~> ~predl(X0)) => (predq(X0) <~> predg(X0)))) [input p6] 51. ~! [X0] : (anywhere(X0) => ~predq(X0)) => ! [X0] : (predg(X0) <=> ~predp(X0)) [input p7] 52. ~! [X0] : (room(X0) => (person(X0) & funny(X0))) [input p8] 54. ~? [X0] : (tall(X0) => funny(X0)) [input p10] 55. ~(! [X0] : (room(X0) => (person(X0) & tall(X0))) & there_is_a_room) [input hypothesis] 56. ~! [X0] : (room(X0) => predp(X0)) => ? [X1] : (person(X1) & creative(X1) & predl(X1) & predg(X1) & room(X1)) [rectify 45] 57. ~! [X0] : (room(X0) => predq(X0)) => ! [X1] : (room(X1) => predp(X1)) [rectify 46] 58. (~! [X0] : (room(X0) => ~predp(X0)) => ? [X1] : (predl(X1) & room(X1))) & (! [X2] : (room(X2) => ~predp(X2)) => ! [X3] : ((~predp(X3) | ~predq(X3) | predl(X3)) <=> ~predq(X3))) [rectify 47] 59. (~! [X0] : (room(X0) => predq(X0)) => ! [X1] : (room(X1) => ~predg(X1))) & (! [X2] : (room(X2) => predq(X2)) => ! [X3] : (room(X3) => ~predl(X3))) [rectify 48] 60. (~! [X0] : (room(X0) => (person(X0) & creative(X0))) => ! [X1] : (~predl(X1) => predq(X1))) & (! [X2] : (room(X2) => (person(X2) & creative(X2))) => ! [X3] : (room(X3) => predp(X3))) [rectify 49] 61. (~! [X0] : (anywhere(X0) => ~(person(X0) & funny(X0))) => ! [X1] : (predq(X1) => ~tall(X1))) & (! [X2] : (anywhere(X2) => ~(person(X2) & funny(X2))) => ! [X3] : ((predp(X3) <~> ~predl(X3)) => (predq(X3) <~> predg(X3)))) [rectify 50] 62. ~! [X0] : (anywhere(X0) => ~predq(X0)) => ! [X1] : (predg(X1) <=> ~predp(X1)) [rectify 51] 134. ? [X1] : (person(X1) & creative(X1) & predl(X1) & predg(X1) & room(X1)) | ! [X0] : (predp(X0) | ~room(X0)) [ennf transformation 56] 135. ! [X1] : (predp(X1) | ~room(X1)) | ! [X0] : (predq(X0) | ~room(X0)) [ennf transformation 57] 136. (? [X1] : (predl(X1) & room(X1)) | ! [X0] : (~predp(X0) | ~room(X0))) & (! [X3] : ((~predp(X3) | ~predq(X3) | predl(X3)) <=> ~predq(X3)) | ? [X2] : (predp(X2) & room(X2))) [ennf transformation 58] 137. (! [X1] : (~predg(X1) | ~room(X1)) | ! [X0] : (predq(X0) | ~room(X0))) & (! [X3] : (~predl(X3) | ~room(X3)) | ? [X2] : (~predq(X2) & room(X2))) [ennf transformation 59] 138. (! [X1] : (predq(X1) | predl(X1)) | ! [X0] : ((person(X0) & creative(X0)) | ~room(X0))) & (! [X3] : (predp(X3) | ~room(X3)) | ? [X2] : ((~person(X2) | ~creative(X2)) & room(X2))) [ennf transformation 60] 139. (! [X1] : (~tall(X1) | ~predq(X1)) | ! [X0] : ((~person(X0) | ~funny(X0)) | ~anywhere(X0))) & (! [X3] : ((predq(X3) <~> predg(X3)) | (predp(X3) <=> ~predl(X3))) | ? [X2] : ((person(X2) & funny(X2)) & anywhere(X2))) [ennf transformation 61] 140. (! [X1] : (~tall(X1) | ~predq(X1)) | ! [X0] : (~person(X0) | ~funny(X0) | ~anywhere(X0))) & (! [X3] : ((predq(X3) <~> predg(X3)) | (predp(X3) <=> ~predl(X3))) | ? [X2] : (person(X2) & funny(X2) & anywhere(X2))) [flattening 139] 141. ! [X1] : (predg(X1) <=> ~predp(X1)) | ! [X0] : (~predq(X0) | ~anywhere(X0)) [ennf transformation 62] 142. ? [X0] : ((~person(X0) | ~funny(X0)) & room(X0)) [ennf transformation 52] 144. ! [X0] : (~funny(X0) & tall(X0)) [ennf transformation 54] 145. ? [X0] : ((~person(X0) | ~tall(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 55] 146. ! [X3] : ((predq(X3) <~> predg(X3)) | (predp(X3) <=> ~predl(X3))) | ~sP0 [predicate definition introduction] 147. (! [X1] : (~tall(X1) | ~predq(X1)) | ! [X0] : (~person(X0) | ~funny(X0) | ~anywhere(X0))) & (sP0 | ? [X2] : (person(X2) & funny(X2) & anywhere(X2))) [definition folding 140,146] 149. ? [X0] : (person(X0) & creative(X0) & predl(X0) & predg(X0) & room(X0)) | ! [X1] : (predp(X1) | ~room(X1)) [rectify 134] 150. ? [X0] : (person(X0) & creative(X0) & predl(X0) & predg(X0) & room(X0)) => (person(sK1) & creative(sK1) & predl(sK1) & predg(sK1) & room(sK1)) [choice axiom] 151. (person(sK1) & creative(sK1) & predl(sK1) & predg(sK1) & room(sK1)) | ! [X1] : (predp(X1) | ~room(X1)) [skolemisation 149,150] 152. ! [X0] : (predp(X0) | ~room(X0)) | ! [X1] : (predq(X1) | ~room(X1)) [rectify 135] 153. (? [X1] : (predl(X1) & room(X1)) | ! [X0] : (~predp(X0) | ~room(X0))) & (! [X3] : (((~predp(X3) | ~predq(X3) | predl(X3)) | predq(X3)) & (~predq(X3) | (predp(X3) & predq(X3) & ~predl(X3)))) | ? [X2] : (predp(X2) & room(X2))) [nnf transformation 136] 154. (? [X1] : (predl(X1) & room(X1)) | ! [X0] : (~predp(X0) | ~room(X0))) & (! [X3] : ((~predp(X3) | ~predq(X3) | predl(X3) | predq(X3)) & (~predq(X3) | (predp(X3) & predq(X3) & ~predl(X3)))) | ? [X2] : (predp(X2) & room(X2))) [flattening 153] 155. (? [X0] : (predl(X0) & room(X0)) | ! [X1] : (~predp(X1) | ~room(X1))) & (! [X2] : ((~predp(X2) | ~predq(X2) | predl(X2) | predq(X2)) & (~predq(X2) | (predp(X2) & predq(X2) & ~predl(X2)))) | ? [X3] : (predp(X3) & room(X3))) [rectify 154] 156. ? [X0] : (predl(X0) & room(X0)) => (predl(sK2) & room(sK2)) [choice axiom] 157. ? [X3] : (predp(X3) & room(X3)) => (predp(sK3) & room(sK3)) [choice axiom] 158. ((predl(sK2) & room(sK2)) | ! [X1] : (~predp(X1) | ~room(X1))) & (! [X2] : ((~predp(X2) | ~predq(X2) | predl(X2) | predq(X2)) & (~predq(X2) | (predp(X2) & predq(X2) & ~predl(X2)))) | (predp(sK3) & room(sK3))) [skolemisation 155,157,156] 159. (! [X0] : (~predg(X0) | ~room(X0)) | ! [X1] : (predq(X1) | ~room(X1))) & (! [X2] : (~predl(X2) | ~room(X2)) | ? [X3] : (~predq(X3) & room(X3))) [rectify 137] 160. ? [X3] : (~predq(X3) & room(X3)) => (~predq(sK4) & room(sK4)) [choice axiom] 161. (! [X0] : (~predg(X0) | ~room(X0)) | ! [X1] : (predq(X1) | ~room(X1))) & (! [X2] : (~predl(X2) | ~room(X2)) | (~predq(sK4) & room(sK4))) [skolemisation 159,160] 162. (! [X0] : (predq(X0) | predl(X0)) | ! [X1] : ((person(X1) & creative(X1)) | ~room(X1))) & (! [X2] : (predp(X2) | ~room(X2)) | ? [X3] : ((~person(X3) | ~creative(X3)) & room(X3))) [rectify 138] 163. ? [X3] : ((~person(X3) | ~creative(X3)) & room(X3)) => ((~person(sK5) | ~creative(sK5)) & room(sK5)) [choice axiom] 164. (! [X0] : (predq(X0) | predl(X0)) | ! [X1] : ((person(X1) & creative(X1)) | ~room(X1))) & (! [X2] : (predp(X2) | ~room(X2)) | ((~person(sK5) | ~creative(sK5)) & room(sK5))) [skolemisation 162,163] 165. ! [X3] : (((~predg(X3) | ~predq(X3)) & (predg(X3) | predq(X3))) | ((predp(X3) | predl(X3)) & (~predl(X3) | ~predp(X3)))) | ~sP0 [nnf transformation 146] 166. ! [X0] : (((~predg(X0) | ~predq(X0)) & (predg(X0) | predq(X0))) | ((predp(X0) | predl(X0)) & (~predl(X0) | ~predp(X0)))) | ~sP0 [rectify 165] 167. (! [X0] : (~tall(X0) | ~predq(X0)) | ! [X1] : (~person(X1) | ~funny(X1) | ~anywhere(X1))) & (sP0 | ? [X2] : (person(X2) & funny(X2) & anywhere(X2))) [rectify 147] 168. ? [X2] : (person(X2) & funny(X2) & anywhere(X2)) => (person(sK6) & funny(sK6) & anywhere(sK6)) [choice axiom] 169. (! [X0] : (~tall(X0) | ~predq(X0)) | ! [X1] : (~person(X1) | ~funny(X1) | ~anywhere(X1))) & (sP0 | (person(sK6) & funny(sK6) & anywhere(sK6))) [skolemisation 167,168] 170. ! [X1] : ((predg(X1) | predp(X1)) & (~predp(X1) | ~predg(X1))) | ! [X0] : (~predq(X0) | ~anywhere(X0)) [nnf transformation 141] 171. ! [X0] : ((predg(X0) | predp(X0)) & (~predp(X0) | ~predg(X0))) | ! [X1] : (~predq(X1) | ~anywhere(X1)) [rectify 170] 172. ? [X0] : ((~person(X0) | ~funny(X0)) & room(X0)) => ((~person(sK7) | ~funny(sK7)) & room(sK7)) [choice axiom] 173. (~person(sK7) | ~funny(sK7)) & room(sK7) [skolemisation 142,172] 174. ? [X0] : ((~person(X0) | ~tall(X0)) & room(X0)) => ((~person(sK8) | ~tall(sK8)) & room(sK8)) [choice axiom] 175. ((~person(sK8) | ~tall(sK8)) & room(sK8)) | ~there_is_a_room [skolemisation 145,174] 176. anywhere(X0) [cnf transformation 5] 257. there_is_a_room [cnf transformation 44] 258. room(sK1) | predp(X1) | ~room(X1) [cnf transformation 151] 260. predl(sK1) | predp(X1) | ~room(X1) [cnf transformation 151] 263. predp(X0) | ~room(X0) | predq(X1) | ~room(X1) [cnf transformation 152] 264. ~predq(X2) | ~predl(X2) | room(sK3) [cnf transformation 158] 265. ~predq(X2) | ~predl(X2) | predp(sK3) [cnf transformation 158] 272. room(sK2) | ~predp(X1) | ~room(X1) [cnf transformation 158] 273. predl(sK2) | ~predp(X1) | ~room(X1) [cnf transformation 158] 274. ~predl(X2) | ~room(X2) | room(sK4) [cnf transformation 161] 275. ~predl(X2) | ~room(X2) | ~predq(sK4) [cnf transformation 161] 276. ~predg(X0) | ~room(X0) | predq(X1) | ~room(X1) [cnf transformation 161] 280. predq(X0) | predl(X0) | person(X1) | ~room(X1) [cnf transformation 164] 281. predg(X0) | predq(X0) | ~predl(X0) | ~predp(X0) | ~sP0 [cnf transformation 166] 286. sP0 | funny(sK6) [cnf transformation 169] 289. ~predp(X0) | ~predg(X0) | ~predq(X1) | ~anywhere(X1) [cnf transformation 171] 291. room(sK7) [cnf transformation 173] 295. tall(X0) [cnf transformation 144] 296. ~funny(X0) [cnf transformation 144] 297. room(sK8) | ~there_is_a_room [cnf transformation 175] 298. ~person(sK8) | ~tall(sK8) | ~there_is_a_room [cnf transformation 175] 300. 1 <=> ! [X1] : (predp(X1) | ~room(X1)) [avatar definition] 301. ~room(X1) | predp(X1) <- (1) [avatar component clause 300] 313. 4 <=> predl(sK1) [avatar definition] 315. predl(sK1) <- (4) [avatar component clause 313] 316. 1 | 4 [avatar split clause 260,313,300] 323. 6 <=> room(sK1) [avatar definition] 325. room(sK1) <- (6) [avatar component clause 323] 326. 1 | 6 [avatar split clause 258,323,300] 328. 7 <=> ! [X1] : (predq(X1) | ~room(X1)) [avatar definition] 329. ~room(X1) | predq(X1) <- (7) [avatar component clause 328] 330. 7 | 1 [avatar split clause 263,300,328] 332. 8 <=> ! [X1] : (~predp(X1) | ~room(X1)) [avatar definition] 333. ~predp(X1) | ~room(X1) <- (8) [avatar component clause 332] 335. 9 <=> predl(sK2) [avatar definition] 337. predl(sK2) <- (9) [avatar component clause 335] 338. 8 | 9 [avatar split clause 273,335,332] 340. 10 <=> room(sK2) [avatar definition] 342. room(sK2) <- (10) [avatar component clause 340] 343. 8 | 10 [avatar split clause 272,340,332] 345. 11 <=> predp(sK3) [avatar definition] 347. predp(sK3) <- (11) [avatar component clause 345] 353. 13 <=> room(sK3) [avatar definition] 358. 14 <=> ! [X2] : (~predq(X2) | ~predl(X2)) [avatar definition] 359. ~predq(X2) | ~predl(X2) <- (14) [avatar component clause 358] 360. 11 | 14 [avatar split clause 265,358,345] 361. 13 | 14 [avatar split clause 264,358,353] 363. 15 <=> ! [X0] : (~predg(X0) | ~room(X0)) [avatar definition] 364. ~predg(X0) | ~room(X0) <- (15) [avatar component clause 363] 365. 7 | 15 [avatar split clause 276,363,328] 367. 16 <=> predq(sK4) [avatar definition] 369. ~predq(sK4) <- (~16) [avatar component clause 367] 371. 17 <=> ! [X2] : (~predl(X2) | ~room(X2)) [avatar definition] 372. ~predl(X2) | ~room(X2) <- (17) [avatar component clause 371] 373. ~16 | 17 [avatar split clause 275,371,367] 375. 18 <=> room(sK4) [avatar definition] 377. room(sK4) <- (18) [avatar component clause 375] 378. 18 | 17 [avatar split clause 274,371,375] 380. 19 <=> ! [X1] : (person(X1) | ~room(X1)) [avatar definition] 381. ~room(X1) | person(X1) <- (19) [avatar component clause 380] 383. 20 <=> ! [X0] : (predq(X0) | predl(X0)) [avatar definition] 384. predq(X0) | predl(X0) <- (20) [avatar component clause 383] 385. 19 | 20 [avatar split clause 280,383,380] 405. 25 <=> sP0 [avatar definition] 421. 29 <=> ! [X0] : (predg(X0) | ~predp(X0) | ~predl(X0) | predq(X0)) [avatar definition] 422. predg(X0) | ~predp(X0) | ~predl(X0) | predq(X0) <- (29) [avatar component clause 421] 423. ~25 | 29 [avatar split clause 281,421,405] 438. 33 <=> funny(sK6) [avatar definition] 440. funny(sK6) <- (33) [avatar component clause 438] 441. 33 | 25 [avatar split clause 286,405,438] 444. 34 <=> ! [X1] : ~predq(X1) [avatar definition] 445. ~predq(X1) <- (34) [avatar component clause 444] 450. ~predp(X0) | ~predg(X0) | ~predq(X1) [subsumption resolution 289,176] 452. 36 <=> ! [X0] : (~predp(X0) | ~predg(X0)) [avatar definition] 453. ~predg(X0) | ~predp(X0) <- (36) [avatar component clause 452] 454. 34 | 36 [avatar split clause 450,452,444] 464. ~person(sK8) | ~there_is_a_room [subsumption resolution 298,295] 465. ~person(sK8) [subsumption resolution 464,257] 466. room(sK8) [subsumption resolution 297,257] 475. ~room(X1) <- (7, 34) [subsumption resolution 329,445] 482. $false <- (7, 34) [resolution 475,291] 485. ~7 | ~34 [avatar contradiction clause 482] 492. predq(sK1) <- (6, 7) [resolution 329,325] 496. ~room(sK3) <- (8, 11) [resolution 333,347] 499. ~predl(sK1) <- (6, 7, 14) [resolution 359,492] 501. $false <- (4, 6, 7, 14) [subsumption resolution 499,315] 502. ~4 | ~6 | ~7 | ~14 [avatar contradiction clause 501] 503. ~13 | ~8 | ~11 [avatar split clause 496,345,332,353] 505. ~room(X1) <- (1, 8) [subsumption resolution 301,333] 508. $false <- (1, 8) [resolution 505,291] 511. ~1 | ~8 [avatar contradiction clause 508] 518. predp(sK2) <- (1, 10) [resolution 301,342] 528. ~room(sK2) <- (9, 17) [resolution 372,337] 529. $false <- (9, 10, 17) [subsumption resolution 528,342] 530. ~9 | ~10 | ~17 [avatar contradiction clause 529] 531. predp(sK4) <- (1, 18) [resolution 377,301] 532. predq(sK4) <- (7, 18) [resolution 377,329] 533. $false <- (7, ~16, 18) [subsumption resolution 532,369] 534. ~7 | 16 | ~18 [avatar contradiction clause 533] 543. person(sK8) <- (19) [resolution 381,466] 548. $false <- (19) [subsumption resolution 543,465] 549. ~19 [avatar contradiction clause 548] 574. 40 <=> predg(sK2) [avatar definition] 575. ~predg(sK2) <- (~40) [avatar component clause 574] 576. predg(sK2) <- (40) [avatar component clause 574] 588. ~room(sK2) <- (15, 40) [resolution 576,364] 591. $false <- (10, 15, 40) [subsumption resolution 588,342] 592. ~10 | ~15 | ~40 [avatar contradiction clause 591] 593. predg(X0) | ~predp(X0) | predq(X0) <- (20, 29) [subsumption resolution 422,384] 594. ~predp(X0) | predq(X0) <- (20, 29, 36) [subsumption resolution 593,453] 599. predq(sK4) <- (1, 18, 20, 29, 36) [resolution 594,531] 609. $false <- (1, ~16, 18, 20, 29, 36) [subsumption resolution 599,369] 610. ~1 | 16 | ~18 | ~20 | ~29 | ~36 [avatar contradiction clause 609] 622. $false <- (33) [subsumption resolution 440,296] 623. ~33 [avatar contradiction clause 622] 624. ~predl(X0) | ~predp(X0) | predg(X0) <- (29, 34) [subsumption resolution 422,445] 630. ~predp(sK2) | predg(sK2) <- (9, 29, 34) [resolution 624,337] 636. predg(sK2) <- (1, 9, 10, 29, 34) [subsumption resolution 630,518] 637. $false <- (1, 9, 10, 29, 34, ~40) [subsumption resolution 636,575] 638. ~1 | ~9 | ~10 | ~29 | ~34 | 40 [avatar contradiction clause 637] 640. $false [avatar sat refutation 316,326,330,338,343,360,361,365,373,378,385,423,441,454,485,502,503,511,530,534,549,592,610,623,638] % SZS output end Proof for 2587944371284961253756290 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

Patrick, Ronald, Robert, Rose are the only persons in the room. Ronald is louder than Luz. Not everyone in the room who is louder than Amy cannot play the harmonica. Everyone in the room who is a sibling of Luz is louder than Luz. Everyone outside the room who is a client of Luz is older than Luz. Ronald is louder than Amy. Ronald who is quieter than Patricia is a sibling of Luz. Everyone in the room who is a sibling of Patricia is a sibling of Luz. Everyone in the room who either is louder than Patricia or is a sibling of Amy but not both is a sibling of Luz. Everyone in the room who cannot play the harmonica is a client of Luz. Everyone in the room who is a client of Luz is a sibling of Luz. Only one person in the room is louder than Amy. Everyone in the room who is richer than Patricia is a sibling of Amy. Everyone in the room who is not passionate about collecting and restoring classic cars is richer than Patricia and is a sibling of Patricia. Everyone in the room who is a sibling of Amy and does not build model airplanes is a sibling of Patricia and is a sibling of Amy. Robert who is a sibling of Luz does not collect action figures. Ronald is a sibling of Amy. Everyone in the room who is a client of Luz and is older than Amy either is a sibling of Amy or is quieter than Amy but not both. Everyone in the room who does not maintain a large, organic vegetable garden year-round either is a client of Patricia or is louder than Amy but not both. Luz is a sibling of Robert. Everyone in the room who is a sibling of Patricia is a sibling of Amy. Everyone in the room either is a sibling of Luz or is a sibling of Patricia but not both if they is a client of Amy and vice versa. Rose is older than Amy. Everyone in the room who is a client of Amy is louder than Patricia. Patricia is a client of Ronald.

Patricia is quieter than Patrick.

contradiction

room(patrick)&room(ronald)&room(robert)&room(rose)&(![X]:(room(X)=>(X='patrick'|X='ronald'|X='robert'|X='rose')))& (louder(luz,ronald))& (~![X]:(room(X)=>(((louder(amy,X))=>(cannot_play_the_harmonica(X))))))& (![X]:(room(X)=>(((sibling(luz,X))=>(louder(luz,X))))))& (![X]:(~room(X)=>(((client(luz,X))=>(older(luz,X))))))& (louder(amy,ronald))& ((quieter(patricia,ronald))&(sibling(luz,ronald)))& (![X]:(room(X)=>(((sibling(patricia,X))=>(sibling(luz,X))))))& (![X]:(room(X)=>(((((louder(patricia,X))<~>(sibling(amy,X))))=>(sibling(luz,X))))))& (![X]:(room(X)=>(((cannot_play_the_harmonica(X))=>(client(luz,X))))))& (![X]:(room(X)=>(((client(luz,X))=>(sibling(luz,X))))))& (((?[X]:(room(X)&louder(amy,X)))&(![X,Y]:((room(X)&room(Y)&(louder(amy,X))&(louder(amy,Y)))=>(X=Y)))))& (![X]:(room(X)=>(((richer(patricia,X))=>(sibling(amy,X))))))& (![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))=>(((richer(patricia,X))&(sibling(patricia,X))))))))& (![X]:(room(X)=>(((((sibling(amy,X))&(does_not_build_model_airplanes(X))))=>(((sibling(patricia,X))&(sibling(amy,X))))))))& ((sibling(luz,robert))&(does_not_collect_action_figures(robert)))& (sibling(amy,ronald))& (![X]:(room(X)=>(((((client(luz,X))&(older(amy,X))))=>(((sibling(amy,X))<~>(quieter(amy,X))))))))& (![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))=>(((client(patricia,X))<~>(louder(amy,X))))))))& (sibling(robert,luz))& (![X]:(room(X)=>(((sibling(patricia,X))=>(sibling(amy,X))))))& (![X]:(room(X)=>(((((sibling(luz,X))<~>(sibling(patricia,X))))<=>(client(amy,X))))))& (older(amy,rose))& (![X]:(room(X)=>(((client(amy,X))=>(louder(patricia,X))))))& (client(ronald,patricia))

room(patrick)&room(ronald)&room(robert)&room(rose)&(![X]:(room(X)=>(X='patrick'|X='ronald'|X='robert'|X='rose')))& quieter(patrick,patricia)

% SZS status Unsatisfiable for 8760120595375563898948366 % SZS output start Proof for 8760120595375563898948366 13. ! [X0,X1,X2] : ((X0 != X2 & X1 != X2 & X0 != X1) => ((quieter(X1,X2) & quieter(X0,X1)) => quieter(X0,X2))) [input b12] 17. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => louder(X1,X0))) [input b16] 35. ! [X0,X1] : (X0 != X1 => (louder(X0,X1) => quieter(X1,X0))) [input b34] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 49. louder(susan,paul) [input p5] 50. sibling(lucy,paul) & quieter(john,paul) [input p6] 55. ! [X0,X1] : ((louder(susan,X1) & louder(susan,X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (louder(susan,X0) & room(X0)) [input p11] 69. quieter(mary,john) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 70. ! [X0,X1] : ((louder(susan,X1) & louder(susan,X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (louder(susan,X2) & room(X2)) [rectify 55] 94. ! [X0,X1,X2] : ((quieter(X0,X2) | (~quieter(X1,X2) | ~quieter(X0,X1))) | (X0 = X2 | X1 = X2 | X0 = X1)) [ennf transformation 13] 95. ! [X0,X1,X2] : (quieter(X0,X2) | ~quieter(X1,X2) | ~quieter(X0,X1) | X0 = X2 | X1 = X2 | X0 = X1) [flattening 94] 102. ! [X0,X1] : ((louder(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 17] 103. ! [X0,X1] : (louder(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 102] 135. ! [X0,X1] : ((quieter(X1,X0) | ~louder(X0,X1)) | X0 = X1) [ennf transformation 35] 136. ! [X0,X1] : (quieter(X1,X0) | ~louder(X0,X1) | X0 = X1) [flattening 135] 149. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 150. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 149] 162. ! [X0,X1] : (X0 = X1 | (~louder(susan,X1) | ~louder(susan,X0) | ~room(X1) | ~room(X0))) & ? [X2] : (louder(susan,X2) & room(X2)) [ennf transformation 70] 163. ! [X0,X1] : (X0 = X1 | ~louder(susan,X1) | ~louder(susan,X0) | ~room(X1) | ~room(X0)) & ? [X2] : (louder(susan,X2) & room(X2)) [flattening 162] 173. quieter(mary,john) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 69] 174. quieter(mary,john) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 173] 179. ? [X2] : (louder(susan,X2) & room(X2)) => (louder(susan,sK1) & room(sK1)) [choice axiom] 180. ! [X0,X1] : (X0 = X1 | ~louder(susan,X1) | ~louder(susan,X0) | ~room(X1) | ~room(X0)) & (louder(susan,sK1) & room(sK1)) [skolemisation 163,179] 191. ~quieter(X1,X2) | quieter(X0,X2) | ~quieter(X0,X1) | X0 = X2 | X1 = X2 | X0 = X1 [cnf transformation 95] 195. ~quieter(X0,X1) | louder(X1,X0) | X0 = X1 [cnf transformation 103] 213. ~louder(X0,X1) | quieter(X1,X0) | X0 = X1 [cnf transformation 136] 227. mary != paul [cnf transformation 43] 245. mary != john [cnf transformation 43] 246. paul != john [cnf transformation 43] 251. mary != susan [cnf transformation 43] 252. paul != susan [cnf transformation 43] 263. room(mary) [cnf transformation 150] 264. room(paul) [cnf transformation 150] 273. louder(susan,paul) [cnf transformation 49] 274. quieter(john,paul) [cnf transformation 50] 282. ~louder(susan,X1) | X0 = X1 | ~louder(susan,X0) | ~room(X1) | ~room(X0) [cnf transformation 180] 302. quieter(mary,john) [cnf transformation 174] 361. quieter(paul,susan) | paul = susan [resolution 213,273] 370. quieter(paul,susan) [subsumption resolution 361,252] 589. paul = X1 | ~louder(susan,X1) | ~room(paul) | ~room(X1) [resolution 282,273] 593. ~louder(susan,X1) | paul = X1 | ~room(X1) [subsumption resolution 589,264] 688. quieter(X4,susan) | ~quieter(X4,paul) | susan = X4 | paul = susan | paul = X4 [resolution 191,370] 690. quieter(X6,paul) | ~quieter(X6,john) | paul = X6 | paul = john | john = X6 [resolution 191,274] 693. ~quieter(X4,paul) | quieter(X4,susan) | susan = X4 | paul = X4 [subsumption resolution 688,252] 695. ~quieter(X6,john) | quieter(X6,paul) | paul = X6 | john = X6 [subsumption resolution 690,246] 913. quieter(mary,paul) | mary = paul | mary = john [resolution 695,302] 917. quieter(mary,paul) | mary = john [subsumption resolution 913,227] 918. quieter(mary,paul) [subsumption resolution 917,245] 1418. quieter(mary,susan) | mary = susan | mary = paul [resolution 693,918] 1429. quieter(mary,susan) | mary = paul [subsumption resolution 1418,251] 1430. quieter(mary,susan) [subsumption resolution 1429,227] 1439. louder(susan,mary) | mary = susan [resolution 1430,195] 1444. louder(susan,mary) [subsumption resolution 1439,251] 1527. mary = paul | ~room(mary) [resolution 1444,593] 1535. ~room(mary) [subsumption resolution 1527,227] 1536. $false [subsumption resolution 1535,263] % SZS output end Proof for 8760120595375563898948366 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.049 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room is dedicated to sustainable living and zero-waste practices or is not a drone photographer only if everyone in the room enjoys making ceramics or does not enjoy virtual reality gaming. Everyone in the room who enjoys making ceramics neither hosts regular workshops on creative writing nor enjoys making ceramics. Everyone outside the room does not collect foreign coins or neither hosts regular workshops on creative writing nor enjoys making ceramics. Everyone in the room enjoys coding in Python or does not enjoy macrame. No one outside the room neither enjoys watercolor painting nor is dedicated to sustainable living and zero-waste practices if they collects foreign coins.

Everyone in the room writes a travel blog.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((is_not_a_drone_photographer(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(enjoys_making_ceramics(X)))))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(~((hosts_regular_workshops_on_creative_writing(X))|(enjoys_making_ceramics(X))))))))& (![X]:(~room(X)=>(((~((hosts_regular_workshops_on_creative_writing(X))|(enjoys_making_ceramics(X))))|(does_not_collect_foreign_coins(X))))))& (![X]:(room(X)=>(((does_not_enjoy_macrame(X))|(enjoys_coding_in_Python(X))))))& (![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(collects_foreign_coins(X))))))& (~?[X]:(~room(X)=>(((collects_foreign_coins(X))=>(~((enjoys_watercolor_painting(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))))& (![X]:(anywhere(X)=>(((~((enjoys_watercolor_painting(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))<=>(((enjoys_macrame(X))&(collects_foreign_coins(X))))))))& (![X]:(~room(X)=>(((((enjoys_macrame(X))&(collects_foreign_coins(X))))=>(((collects_modern_art(X))&(writes_a_travel_blog(X))))))))& (![X]:(room(X)=>(((((collects_modern_art(X))&(writes_a_travel_blog(X))))=>(enjoys_coding_in_Python(X))))))& ((![X]:((((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(writes_a_travel_blog(X))&(hosts_regular_workshops_on_creative_writing(X))))<=>(~((collects_foreign_coins(X))|(hosts_regular_workshops_on_creative_writing(X)))))))& (![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((cannot_play_the_guitar(X))|(enjoys_making_ceramics(X))))))

(there_is_a_room)& ![X]:(room(X)=>(writes_a_travel_blog(X)))

% SZS status Unsatisfiable for 5344399841879861983275947 % SZS output start Proof for 5344399841879861983275947 44. there_is_a_room [input p0] 51. ~? [X0] : (~room(X0) => (predf(X0) => ~(predb(X0) | predn(X0)))) [input p7] 58. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 144. ! [X0] : (((predb(X0) | predn(X0)) & predf(X0)) & ~room(X0)) [ennf transformation 51] 145. ! [X0] : ((predb(X0) | predn(X0)) & predf(X0) & ~room(X0)) [flattening 144] 150. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 58] 156. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK0) & room(sK0)) [choice axiom] 157. (~predc(sK0) & room(sK0)) | ~there_is_a_room [skolemisation 150,156] 239. there_is_a_room [cnf transformation 44] 242. ~room(X0) [cnf transformation 145] 255. room(sK0) | ~there_is_a_room [cnf transformation 157] 266. ~there_is_a_room [subsumption resolution 255,242] 267. $false [subsumption resolution 266,239] % SZS output end Proof for 5344399841879861983275947 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Douglas is the only person in the room. Douglas either is a chess master who participates in national tournaments or volunteers for local environmental conservation projects but not both. If someone hosts regular game nights featuring complex strategy games then he/she creates augmented reality experiences for mobile applications and vice versa. It is not the case that “Douglas enjoys wildlife photography”. Douglas is a chess master who participates in national tournaments. If someone is a chess master who participates in national tournaments then he/she creates augmented reality experiences for mobile applications.

Douglas hosts regular game nights featuring complex strategy games.

entailment

room(douglas)&(![X]:(room(X)=>(X='douglas')))& (((is_a_chess_master_who_participates_in_national_tournaments(douglas))<~>(volunteers_for_local_environmental_conservation_projects(douglas))))& ((![X]:((hosts_regular_game_nights_featuring_complex_strategy_games(X))<=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))& (~(enjoys_wildlife_photography(douglas)))& (~(~((enjoys_spelunking(douglas))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(douglas)))))& (~(has_a_saltwater_aquarium(douglas)))& (is_a_chess_master_who_participates_in_national_tournaments(douglas))& ((![X]:((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X)))))& (is_a_drone_photographer(douglas))& ((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))<=>(owns_a_smartwatch(X)))))& ((![X]:((is_a_chess_master_who_participates_in_national_tournaments(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))& (enjoys_bird_watching(douglas))& (~(((enjoys_spelunking(douglas))|(volunteers_for_local_environmental_conservation_projects(douglas)))))& ((![X]:((enjoys_salsa_dancing(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))

room(douglas)&(![X]:(room(X)=>(X='douglas')))& hosts_regular_game_nights_featuring_complex_strategy_games(douglas)

% SZS status Unsatisfiable for 7244859326576367911611241 % SZS output start Proof for 7244859326576367911611241 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (predv(X0) <=> preda(X0)) [input p2] 50. predb(mary) [input p6] 54. ! [X0] : (predb(X0) => preda(X0)) [input p10] 58. ~(predv(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 60. ! [X0] : (preda(X0) => predv(X0)) [unused predicate definition removal 46] 139. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 140. ! [X0] : (predv(X0) | ~preda(X0)) [ennf transformation 60] 142. ! [X0] : (preda(X0) | ~predb(X0)) [ennf transformation 54] 144. ~predv(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 58] 147. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom] 148. ~predv(mary) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 144,147] 229. room(mary) [cnf transformation 139] 230. ~room(X0) | mary = X0 [cnf transformation 139] 233. ~preda(X0) | predv(X0) [cnf transformation 140] 234. predb(mary) [cnf transformation 50] 236. ~predb(X0) | preda(X0) [cnf transformation 142] 238. ~predv(mary) | room(sK0) | ~room(mary) [cnf transformation 148] 239. ~predv(mary) | mary != sK0 | ~room(mary) [cnf transformation 148] 241. 1 <=> predb(mary) [avatar definition] 242. predb(mary) <- (1) [avatar component clause 241] 250. 1 [avatar split clause 234,241] 252. ~predv(mary) | mary != sK0 [subsumption resolution 239,229] 254. 3 <=> mary = sK0 [avatar definition] 256. mary != sK0 <- (~3) [avatar component clause 254] 258. 4 <=> predv(mary) [avatar definition] 261. ~3 | ~4 [avatar split clause 252,258,254] 262. ~predv(mary) | room(sK0) [subsumption resolution 238,229] 264. 5 <=> room(sK0) [avatar definition] 266. room(sK0) <- (5) [avatar component clause 264] 267. 5 | ~4 [avatar split clause 262,258,264] 268. preda(mary) <- (1) [resolution 236,242] 270. predv(mary) <- (1) [resolution 268,233] 273. 4 | ~1 [avatar split clause 270,241,258] 275. mary = sK0 <- (5) [resolution 266,230] 276. $false <- (~3, 5) [subsumption resolution 275,256] 277. 3 | ~5 [avatar contradiction clause 276] 278. $false [avatar sat refutation 250,261,267,273,277] % SZS output end Proof for 7244859326576367911611241 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Everyone in the room who enjoys logic puzzles practices calligraphy. If someone enjoys writing detailed reviews of new and classic board games then he/she enjoys logic puzzles. Someone in the room enjoys logic puzzles. Everyone in the room who enjoys writing detailed reviews of new and classic board games is not a wine connoisseur with a private cellar of vintage wines. More than one person in the room practices calligraphy. Everyone in the room is a wine connoisseur with a private cellar of vintage wines if they practices calligraphy. Everyone in the room who is a wine connoisseur with a private cellar of vintage wines is a wine connoisseur with a private cellar of vintage wines or enjoys logic puzzles or both. Everyone in the room who practices calligraphy, enjoys logic puzzles and volunteers for local environmental conservation projects enjoys logic puzzles.

Everyone in the room is a wine connoisseur with a private cellar of vintage wines.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(practices_calligraphy(X))))))& ((![X]:((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(enjoys_logic_puzzles(X)))))& (?[X]:(room(X)&(enjoys_logic_puzzles(X))))& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& ((?[X,Y]:(room(X)&room(Y)&(practices_calligraphy(X)&practices_calligraphy(Y))&(X!=Y))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(enjoys_logic_puzzles(X))))))))& (![X]:(room(X)=>(((((practices_calligraphy(X))&(enjoys_logic_puzzles(X))&(volunteers_for_local_environmental_conservation_projects(X))))=>(enjoys_logic_puzzles(X))))))

(there_is_a_room)& ![X]:(room(X)=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))

If “Mario enjoys logic puzzles” then “Mario enjoys snowboarding”. If “David collect rare sneakers” then “if someone enjoys snowboarding then he/she either can play the piano or is a skilled home brewer experimenting with craft beer recipes but not both”. Mario who has a tattoo can play the piano. David collect rare sneakers. Mario who is a skilled home brewer experimenting with craft beer recipes has a tattoo, owns a microscope or is an avid hiker.

Mario enjoys logic puzzles.

contradiction

room(mario)&room(david)&room(elizabeth)&(![X]:(room(X)=>(X='mario'|X='david'|X='elizabeth')))& ((enjoys_snowboarding(mario))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(david)))& ((((enjoys_logic_puzzles(david))|(has_a_vast_collection_of_first-edition_science_fiction_novels(david))|(is_an_avid_hiker(david))))=>(enjoys_logic_puzzles(david)))& ((enjoys_logic_puzzles(mario))=>(enjoys_snowboarding(mario)))& ((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(mario))=>(~(~((collect_rare_sneakers(mario))|(has_a_vast_collection_of_first-edition_science_fiction_novels(mario))))))& ((collect_rare_sneakers(david))=>((![X]:((enjoys_snowboarding(X))=>(((can_play_the_piano(X))<~>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))))& ((![X]:((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(collect_rare_sneakers(X)))))& (is_an_avid_hiker(mario))& (((collect_rare_sneakers(david))&(owns_a_microscope(david))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(david))))& ((has_a_tattoo(mario))&(can_play_the_piano(mario)))& ((![X]:((enjoys_logic_puzzles(X))=>(has_a_tattoo(X)))))& (~(((has_a_vast_collection_of_first-edition_science_fiction_novels(david))&(is_a_cybersecurity_expert(david))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(david)))))& (collect_rare_sneakers(david))& (enjoys_making_ceramics(david))& ((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(mario))&(((has_a_tattoo(mario))|(owns_a_microscope(mario))|(is_an_avid_hiker(mario)))))& (~(~((collect_rare_sneakers(mario))|(has_a_vast_collection_of_first-edition_science_fiction_novels(mario)))))

room(mario)&room(david)&room(elizabeth)&(![X]:(room(X)=>(X='mario'|X='david'|X='elizabeth')))& enjoys_logic_puzzles(mario)

% SZS status Unsatisfiable for 5166042569906807994603147 % SZS output start Proof for 5166042569906807994603147 47. predh(mary) => predd(mary) [input p3] 49. predc(paul) => ! [X0] : (predd(X0) => (predk(X0) <~> preda(X0))) [input p5] 53. predk(mary) & prede(mary) [input p9] 56. predc(paul) [input p12] 58. (predf(mary) | predi(mary) | prede(mary)) & preda(mary) [input p14] 60. predh(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 65. preda(mary) [pure predicate removal 58] 67. predk(mary) [pure predicate removal 53] 145. predd(mary) | ~predh(mary) [ennf transformation 47] 148. ! [X0] : ((predk(X0) <~> preda(X0)) | ~predd(X0)) | ~predc(paul) [ennf transformation 49] 150. predh(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 151. predh(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 150] 153. ! [X0] : (((~preda(X0) | ~predk(X0)) & (preda(X0) | predk(X0))) | ~predd(X0)) | ~predc(paul) [nnf transformation 148] 242. predd(mary) | ~predh(mary) [cnf transformation 145] 245. ~preda(X0) | ~predk(X0) | ~predd(X0) | ~predc(paul) [cnf transformation 153] 250. predk(mary) [cnf transformation 67] 251. predc(paul) [cnf transformation 56] 252. preda(mary) [cnf transformation 65] 258. predh(mary) [cnf transformation 151] 260. 1 <=> predd(mary) [avatar definition] 261. predd(mary) <- (1) [avatar component clause 260] 283. 6 <=> predh(mary) [avatar definition] 286. ~6 | 1 [avatar split clause 242,260,283] 288. 7 <=> preda(mary) [avatar definition] 289. preda(mary) <- (7) [avatar component clause 288] 301. 10 <=> predc(paul) [avatar definition] 305. 11 <=> ! [X0] : (~preda(X0) | ~predd(X0) | ~predk(X0)) [avatar definition] 306. ~predk(X0) | ~predd(X0) | ~preda(X0) <- (11) [avatar component clause 305] 307. ~10 | 11 [avatar split clause 245,305,301] 314. 10 [avatar split clause 251,301] 315. 7 [avatar split clause 252,288] 318. 6 [avatar split clause 258,283] 319. ~predd(mary) | ~preda(mary) <- (11) [resolution 306,250] 320. ~preda(mary) <- (1, 11) [subsumption resolution 319,261] 321. $false <- (1, 7, 11) [subsumption resolution 320,289] 322. ~1 | ~7 | ~11 [avatar contradiction clause 321] 323. $false [avatar sat refutation 286,307,314,315,318,322] % SZS output end Proof for 5166042569906807994603147 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jeffry, David, Beatriz are the only persons in the room. If 'Beatriz enjoys windsurfing' then 'Beatriz who is a professional photographer specializing in portrait photography enjoys windsurfing'. If 'Jeffry enjoys windsurfing' then 'Beatriz is a client of Costco'. If 'everyone in the room is a professional photographer specializing in portrait photography or does not work on fridays' then 'everyone in the room is not a professional photographer specializing in portrait photography or is a professional photographer specializing in portrait photography'. If 'David enjoys kayaking' then 'someone in the room enjoys windsurfing or is a professional photographer specializing in portrait photography or both'. If 'everyone anywhere enjoys windsurfing or is not a professional photographer specializing in portrait photography' then 'someone outside the room enjoys kayaking' otherwise 'everyone in the room who enjoys kayaking is a professional photographer specializing in portrait photography'. 'It is not the case that 'someone in the room enjoys windsurfing or is not a client of Costco or both'' if 'someone in the room is a client of Costco' and vice versa. 'More than one person anywhere is a professional photographer specializing in portrait photography' unless 'everyone in the room does not enjoy kayaking or is a professional photographer specializing in portrait photography'. 'Beatriz who does not enjoy kayaking enjoys windsurfing, is a professional photographer specializing in portrait photography or is not a professional photographer specializing in portrait photography' if 'everyone in the room does not enjoy windsurfing or enjoys kayaking'. If 'everyone outside the room enjoys kayaking or is not a client of Costco' then 'if someone enjoys windsurfing then he/she is a client of Costco and vice versa'. David is a client of Costco. David works on fridays. Everyone anywhere is a professional photographer specializing in portrait photography if they enjoys kayaking. Not everyone outside the room is a client of Costco. Everyone in the room does not enjoy windsurfing or is a professional photographer specializing in portrait photography.

Jeffry enjoys kayaking.

neutral

room(jeffry)&room(david)&room(beatriz)&(![X]:(room(X)=>(X='jeffry'|X='david'|X='beatriz')))& ((enjoys_windsurfing(beatriz))=>((is_a_professional_photographer_specializing_in_portrait_photography(beatriz))&(enjoys_windsurfing(beatriz))))& ((enjoys_windsurfing(jeffry))=>(is_a_client_of_Costco(beatriz)))& ((![X]:(room(X)=>(((does_not_work_on_fridays(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))))))=>(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))))& ((enjoys_kayaking(david))=>(?[X]:(room(X)&(((enjoys_windsurfing(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))& (((![X]:(anywhere(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(enjoys_windsurfing(X))))))=>(?[X]:(~room(X)&(enjoys_kayaking(X)))))&((~(![X]:(anywhere(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(enjoys_windsurfing(X)))))))=>(![X]:(room(X)=>(((enjoys_kayaking(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))))& ((?[X]:(room(X)&(is_a_client_of_Costco(X))))<=>(~(?[X]:(room(X)&(((enjoys_windsurfing(X))|(is_not_a_client_of_Costco(X))))))))& (~(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_enjoy_kayaking(X))))))=>((?[X,Y]:(anywhere(X)&anywhere(Y)&(is_a_professional_photographer_specializing_in_portrait_photography(X)&is_a_professional_photographer_specializing_in_portrait_photography(Y))&(X!=Y)))))& ((![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_enjoy_windsurfing(X))))))=>((does_not_enjoy_kayaking(beatriz))&(((enjoys_windsurfing(beatriz))|(is_a_professional_photographer_specializing_in_portrait_photography(beatriz))|(is_not_a_professional_photographer_specializing_in_portrait_photography(beatriz))))))& ((![X]:(~room(X)=>(((is_not_a_client_of_Costco(X))|(enjoys_kayaking(X))))))=>((![X]:((enjoys_windsurfing(X))<=>(is_a_client_of_Costco(X))))))& (is_a_client_of_Costco(david))& (works_on_fridays(david))& (![X]:(anywhere(X)=>(((enjoys_kayaking(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (~![X]:(~room(X)=>(is_a_client_of_Costco(X))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_enjoy_windsurfing(X))))))& (((?[X]:(room(X)&does_not_work_on_fridays(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_work_on_fridays(X))&(does_not_work_on_fridays(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((((does_not_enjoy_kayaking(X))<~>(is_not_a_client_of_Costco(X))))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))

room(jeffry)&room(david)&room(beatriz)&(![X]:(room(X)=>(X='jeffry'|X='david'|X='beatriz')))& enjoys_kayaking(jeffry)

Fritz is the only person in the room. If “Fritz practices calligraphy” then “if someone creates YouTube content then he/she is not a cybersecurity expert”. If “Fritz creates YouTube content” then “Fritz does enjoy mountain biking” otherwise “Fritz is a Linux enthusiast”. If “Fritz does practice yoga” then “Fritz plays video games”. “Fritz practices digital art” only if “Fritz practices calligraphy”. Fritz is a cybersecurity expert. Fritz collects foreign coins.

Fritz practices digital art.

neutral

room(fritz)&(![X]:(room(X)=>(X='fritz')))& ((practices_calligraphy(fritz))=>((![X]:((creates_YouTube_content(X))=>(is_not_a_cybersecurity_expert(X))))))& (((creates_YouTube_content(fritz))=>(does_enjoy_mountain_biking(fritz)))&((~(creates_YouTube_content(fritz)))=>(is_a_Linux_enthusiast(fritz))))& ((does_practice_yoga(fritz))=>(plays_video_games(fritz)))& ((practices_digital_art(fritz))=>(practices_calligraphy(fritz)))& (is_a_cybersecurity_expert(fritz))& (collects_foreign_coins(fritz))& (designs_and_sews_custom_cosplay_costumes_for_conventions(fritz))& (owns_a_3D_printer(fritz))& (works_on_fridays(fritz))

room(fritz)&(![X]:(room(X)=>(X='fritz')))& practices_digital_art(fritz)

Linda, Nancy, Yolanda, Myra, John are the only persons in the room. 'Linda is wise' only if 'Nancy and Myra are old persons, are strong and are tall'. If 'Myra is a quiet person' then 'someone anywhere is a kind person' otherwise 'if someone is a kind person then he/she is a strong person'. If 'Myra and Nancy are kind persons' then 'Yolanda is a wise person'. If 'Yolanda is a wise person' then 'someone in the room is not generous'. 'Yolanda is a creative person' if 'Myra is a quiet person' and vice versa. If 'Nancy is not creative and is a calm person' then 'Nancy is not tall' otherwise 'it is not the case that 'Yolanda is a funny person''. 'It is not the case that 'Linda is not generous'' only if 'Yolanda and Myra are respectively patient and kind'. If 'Nancy is a tall person and is not wise' then 'Yolanda is not wise' otherwise 'Myra is not old'. Linda is not creative. Linda is a humble person. Linda is calm. Nancy is wise. Linda and Nancy are humble persons. It is not the case that 'more than one person in the room is not humble'. Myra is not old. If someone is a patient person then he/she is tall or is not generous or both.

Not everyone in the room is not a old person, is quiet and is not quiet.

entailment

room(linda)&room(nancy)&room(yolanda)&room(myra)&room(john)&(![X]:(room(X)=>(X='linda'|X='nancy'|X='yolanda'|X='myra'|X='john')))& ((wise(linda))=>(((old(nancy)&person(nancy))&(strong(nancy))&(tall(nancy)))&((old(myra)&person(myra))&(strong(myra))&(tall(myra)))))& (((quiet(myra)&person(myra))=>(?[X]:(anywhere(X)&(kind(X)&person(X)))))&((~(quiet(myra)&person(myra)))=>((![X]:((kind(X)&person(X))=>(strong(X)&person(X)))))))& (((kind(myra)&person(myra)&kind(nancy)&person(nancy))=>(wise(yolanda)&person(yolanda)))& ((wise(yolanda)&person(yolanda))=>(?[X]:(room(X)&(~generous(X))))))& ((quiet(myra)&person(myra))<=>(creative(yolanda)&person(yolanda)))& (((((~creative(nancy))&(calm(nancy)&person(nancy))))=>(~tall(nancy)))&((~(((~creative(nancy))&(calm(nancy)&person(nancy)))))=>(~(funny(yolanda)&person(yolanda)))))& ((~(~generous(linda)))=>((patient(yolanda))&(kind(myra))))& (((((tall(nancy)&person(nancy))&(~wise(nancy))))=>(~wise(yolanda)))&((~(((tall(nancy)&person(nancy))&(~wise(nancy)))))=>(~old(myra))))& (~creative(linda))& (humble(linda)&person(linda))& (calm(linda))& (wise(nancy))& (humble(linda)&person(linda)&humble(nancy)&person(nancy))& (~((?[X,Y]:(room(X)&room(Y)&(~humble(X)&~humble(Y))&(X!=Y)))))& (~old(myra))& ((![X]:((patient(X)&person(X))=>(((tall(X))|(~generous(X)))))))

room(linda)&room(nancy)&room(yolanda)&room(myra)&room(john)&(![X]:(room(X)=>(X='linda'|X='nancy'|X='yolanda'|X='myra'|X='john')))& ~![X]:(room(X)=>(((~(old(X)&person(X)))&(quiet(X))&(~quiet(X)))))

% SZS status Unsatisfiable for 7363237648243208441555355 % SZS output start Proof for 7363237648243208441555355 44. ! [X0] : ((person(X0) & patient(X0)) => (~generous(X0) | tall(X0))) & ~old(alice) & ~? [X0,X1] : (X0 != X1 & ~humble(X1) & ~humble(X0) & room(X1) & room(X0)) & person(paul) & humble(paul) & person(mary) & humble(mary) & wise(paul) & calm(mary) & person(mary) & humble(mary) & ~creative(mary) & (~(~wise(paul) & person(paul) & tall(paul)) => ~old(alice)) & ((~wise(paul) & person(paul) & tall(paul)) => ~wise(fred)) & (generous(mary) => (kind(alice) & patient(fred))) & (~(person(paul) & calm(paul) & ~creative(paul)) => ~(person(fred) & funny(fred))) & ((person(paul) & calm(paul) & ~creative(paul)) => ~tall(paul)) & ((person(alice) & quiet(alice)) <=> (person(fred) & creative(fred))) & ((person(fred) & wise(fred)) => ? [X0] : (~generous(X0) & room(X0))) & ((person(paul) & kind(paul) & person(alice) & kind(alice)) => (person(fred) & wise(fred))) & (~(person(alice) & quiet(alice)) => ! [X0] : ((person(X0) & kind(X0)) => (person(X0) & strong(X0)))) & ((person(alice) & quiet(alice)) => ? [X0] : (person(X0) & kind(X0) & anywhere(X0))) & (wise(mary) => (tall(alice) & strong(alice) & person(alice) & old(alice) & tall(paul) & strong(paul) & person(paul) & old(paul))) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(~! [X0] : (room(X0) => (~quiet(X0) & quiet(X0) & ~(person(X0) & old(X0)))) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : ((person(X0) & patient(X0)) => (~generous(X0) | tall(X0))) & ~old(alice) & ~? [X1,X2] : (X1 != X2 & ~humble(X2) & ~humble(X1) & room(X2) & room(X1)) & person(paul) & humble(paul) & person(mary) & humble(mary) & wise(paul) & calm(mary) & person(mary) & humble(mary) & ~creative(mary) & (~(~wise(paul) & person(paul) & tall(paul)) => ~old(alice)) & ((~wise(paul) & person(paul) & tall(paul)) => ~wise(fred)) & (generous(mary) => (kind(alice) & patient(fred))) & (~(person(paul) & calm(paul) & ~creative(paul)) => ~(person(fred) & funny(fred))) & ((person(paul) & calm(paul) & ~creative(paul)) => ~tall(paul)) & ((person(alice) & quiet(alice)) <=> (person(fred) & creative(fred))) & ((person(fred) & wise(fred)) => ? [X3] : (~generous(X3) & room(X3))) & ((person(paul) & kind(paul) & person(alice) & kind(alice)) => (person(fred) & wise(fred))) & (~(person(alice) & quiet(alice)) => ! [X4] : ((person(X4) & kind(X4)) => (person(X4) & strong(X4)))) & ((person(alice) & quiet(alice)) => ? [X5] : (person(X5) & kind(X5) & anywhere(X5))) & (wise(mary) => (tall(alice) & strong(alice) & person(alice) & old(alice) & tall(paul) & strong(paul) & person(paul) & old(paul))) & ! [X6] : (room(X6) => (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ~(~! [X0] : (room(X0) => (~quiet(X0) & quiet(X0) & ~(person(X0) & old(X0)))) & ! [X1] : (room(X1) => (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 45] 48. ! [X0] : ((person(X0) & patient(X0)) => (~generous(X0) | tall(X0))) & ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~(~wise(paul) & person(paul) & tall(paul)) => ~old(alice)) & ((~wise(paul) & person(paul) & tall(paul)) => ~wise(fred)) & (generous(mary) => (kind(alice) & patient(fred))) & (~(person(paul) & calm(paul) & ~creative(paul)) => ~(person(fred) & funny(fred))) & ((person(paul) & calm(paul) & ~creative(paul)) => ~tall(paul)) & ((person(alice) & quiet(alice)) <=> (person(fred) & creative(fred))) & ((person(fred) & wise(fred)) => ? [X3] : (~generous(X3) & room(X3))) & ((person(paul) & kind(paul) & person(alice) & kind(alice)) => (person(fred) & wise(fred))) & (~(person(alice) & quiet(alice)) => ! [X4] : ((person(X4) & kind(X4)) => (person(X4) & strong(X4)))) & ((person(alice) & quiet(alice)) => ? [X5] : (person(X5) & kind(X5) & anywhere(X5))) & (wise(mary) => (tall(alice) & strong(alice) & person(alice) & old(alice) & tall(paul) & strong(paul) & person(paul) & old(paul))) & ! [X6] : (room(X6) => (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 49. ! [X0] : ((person(X0) & patient(X0)) => (~generous(X0) | tall(X0))) & ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~(~wise(paul) & person(paul) & tall(paul)) => ~old(alice)) & ((~wise(paul) & person(paul) & tall(paul)) => ~wise(fred)) & (generous(mary) => (kind(alice) & patient(fred))) & ((person(paul) & calm(paul) & ~creative(paul)) => ~tall(paul)) & ((person(alice) & quiet(alice)) <=> (person(fred) & creative(fred))) & ((person(fred) & wise(fred)) => ? [X3] : (~generous(X3) & room(X3))) & ((person(paul) & kind(paul) & person(alice) & kind(alice)) => (person(fred) & wise(fred))) & (~(person(alice) & quiet(alice)) => ! [X4] : ((person(X4) & kind(X4)) => (person(X4) & strong(X4)))) & ((person(alice) & quiet(alice)) => ? [X5] : (person(X5) & kind(X5) & anywhere(X5))) & (wise(mary) => (tall(alice) & strong(alice) & person(alice) & old(alice) & tall(paul) & strong(paul) & person(paul) & old(paul))) & ! [X6] : (room(X6) => (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~(~wise(paul) & person(paul) & tall(paul)) => ~old(alice)) & ((~wise(paul) & person(paul) & tall(paul)) => ~wise(fred)) & ((person(paul) & calm(paul) & ~creative(paul)) => ~tall(paul)) & ((person(alice) & quiet(alice)) <=> (person(fred) & creative(fred))) & ((person(fred) & wise(fred)) => ? [X3] : room(X3)) & ((person(paul) & kind(paul) & person(alice) & kind(alice)) => (person(fred) & wise(fred))) & (~(person(alice) & quiet(alice)) => ! [X4] : ((person(X4) & kind(X4)) => (person(X4) & strong(X4)))) & ((person(alice) & quiet(alice)) => ? [X5] : (person(X5) & kind(X5) & anywhere(X5))) & (wise(mary) => (tall(alice) & strong(alice) & person(alice) & old(alice) & tall(paul) & strong(paul) & person(paul) & old(paul))) & ! [X6] : (room(X6) => (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~(~wise(paul) & person(paul) & tall(paul)) => ~old(alice)) & ((~wise(paul) & person(paul) & tall(paul)) => ~wise(fred)) & ((person(paul) & calm(paul) & ~creative(paul)) => ~tall(paul)) & ((person(alice) & quiet(alice)) <=> (person(fred) & creative(fred))) & ((person(fred) & wise(fred)) => ? [X3] : room(X3)) & ((person(paul) & kind(paul) & person(alice) & kind(alice)) => (person(fred) & wise(fred))) & (~(person(alice) & quiet(alice)) => ! [X4] : ((person(X4) & kind(X4)) => person(X4))) & ((person(alice) & quiet(alice)) => ? [X5] : (person(X5) & kind(X5) & anywhere(X5))) & (wise(mary) => (tall(alice) & person(alice) & old(alice) & tall(paul) & person(paul) & old(paul))) & ! [X6] : (room(X6) => (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~(~wise(paul) & person(paul) & tall(paul)) => ~old(alice)) & ((~wise(paul) & person(paul) & tall(paul)) => ~wise(fred)) & ((person(paul) & calm(paul) & ~creative(paul)) => ~tall(paul)) & ((person(alice) & quiet(alice)) <=> (person(fred) & creative(fred))) & ((person(fred) & wise(fred)) => ? [X3] : room(X3)) & ((person(paul) & kind(paul) & person(alice) & kind(alice)) => (person(fred) & wise(fred))) & (~(person(alice) & quiet(alice)) => ! [X4] : ((person(X4) & kind(X4)) => person(X4))) & ((person(alice) & quiet(alice)) => ? [X5] : (person(X5) & kind(X5))) & (wise(mary) => (tall(alice) & person(alice) & old(alice) & tall(paul) & person(paul) & old(paul))) & ! [X6] : (room(X6) => (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 125. ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~old(alice) | (~wise(paul) & person(paul) & tall(paul))) & (~wise(fred) | (wise(paul) | ~person(paul) | ~tall(paul))) & (~tall(paul) | (~person(paul) | ~calm(paul) | creative(paul))) & ((person(alice) & quiet(alice)) <=> (person(fred) & creative(fred))) & (? [X3] : room(X3) | (~person(fred) | ~wise(fred))) & ((person(fred) & wise(fred)) | (~person(paul) | ~kind(paul) | ~person(alice) | ~kind(alice))) & (! [X4] : (person(X4) | (~person(X4) | ~kind(X4))) | (person(alice) & quiet(alice))) & (? [X5] : (person(X5) & kind(X5)) | (~person(alice) | ~quiet(alice))) & ((tall(alice) & person(alice) & old(alice) & tall(paul) & person(paul) & old(paul)) | ~wise(mary)) & ! [X6] : ((john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6) | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 52] 126. ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~old(alice) | (~wise(paul) & person(paul) & tall(paul))) & (~wise(fred) | wise(paul) | ~person(paul) | ~tall(paul)) & (~tall(paul) | ~person(paul) | ~calm(paul) | creative(paul)) & ((person(alice) & quiet(alice)) <=> (person(fred) & creative(fred))) & (? [X3] : room(X3) | ~person(fred) | ~wise(fred)) & ((person(fred) & wise(fred)) | ~person(paul) | ~kind(paul) | ~person(alice) | ~kind(alice)) & (! [X4] : (person(X4) | ~person(X4) | ~kind(X4)) | (person(alice) & quiet(alice))) & (? [X5] : (person(X5) & kind(X5)) | ~person(alice) | ~quiet(alice)) & ((tall(alice) & person(alice) & old(alice) & tall(paul) & person(paul) & old(paul)) | ~wise(mary)) & ! [X6] : (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 125] 127. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | ? [X1] : ((john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 47] 128. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 127] 129. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 130. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 128,129] 132. ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~old(alice) | (~wise(paul) & person(paul) & tall(paul))) & (~wise(fred) | wise(paul) | ~person(paul) | ~tall(paul)) & (~tall(paul) | ~person(paul) | ~calm(paul) | creative(paul)) & (((person(alice) & quiet(alice)) | (~person(fred) | ~creative(fred))) & ((person(fred) & creative(fred)) | (~person(alice) | ~quiet(alice)))) & (? [X3] : room(X3) | ~person(fred) | ~wise(fred)) & ((person(fred) & wise(fred)) | ~person(paul) | ~kind(paul) | ~person(alice) | ~kind(alice)) & (! [X4] : (person(X4) | ~person(X4) | ~kind(X4)) | (person(alice) & quiet(alice))) & (? [X5] : (person(X5) & kind(X5)) | ~person(alice) | ~quiet(alice)) & ((tall(alice) & person(alice) & old(alice) & tall(paul) & person(paul) & old(paul)) | ~wise(mary)) & ! [X6] : (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 126] 133. ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~old(alice) | (~wise(paul) & person(paul) & tall(paul))) & (~wise(fred) | wise(paul) | ~person(paul) | ~tall(paul)) & (~tall(paul) | ~person(paul) | ~calm(paul) | creative(paul)) & ((person(alice) & quiet(alice)) | ~person(fred) | ~creative(fred)) & ((person(fred) & creative(fred)) | ~person(alice) | ~quiet(alice)) & (? [X3] : room(X3) | ~person(fred) | ~wise(fred)) & ((person(fred) & wise(fred)) | ~person(paul) | ~kind(paul) | ~person(alice) | ~kind(alice)) & (! [X4] : (person(X4) | ~person(X4) | ~kind(X4)) | (person(alice) & quiet(alice))) & (? [X5] : (person(X5) & kind(X5)) | ~person(alice) | ~quiet(alice)) & ((tall(alice) & person(alice) & old(alice) & tall(paul) & person(paul) & old(paul)) | ~wise(mary)) & ! [X6] : (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132] 134. ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~old(alice) | (~wise(paul) & person(paul) & tall(paul))) & (~wise(fred) | wise(paul) | ~person(paul) | ~tall(paul)) & (~tall(paul) | ~person(paul) | ~calm(paul) | creative(paul)) & ((person(alice) & quiet(alice)) | ~person(fred) | ~creative(fred)) & ((person(fred) & creative(fred)) | ~person(alice) | ~quiet(alice)) & (? [X0] : room(X0) | ~person(fred) | ~wise(fred)) & ((person(fred) & wise(fred)) | ~person(paul) | ~kind(paul) | ~person(alice) | ~kind(alice)) & (! [X1] : (person(X1) | ~person(X1) | ~kind(X1)) | (person(alice) & quiet(alice))) & (? [X2] : (person(X2) & kind(X2)) | ~person(alice) | ~quiet(alice)) & ((tall(alice) & person(alice) & old(alice) & tall(paul) & person(paul) & old(paul)) | ~wise(mary)) & ! [X3] : (john = X3 | alice = X3 | fred = X3 | paul = X3 | mary = X3 | ~room(X3)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 133] 135. ? [X0] : room(X0) => room(sK1) [choice axiom] 136. ? [X2] : (person(X2) & kind(X2)) => (person(sK2) & kind(sK2)) [choice axiom] 137. ~old(alice) & person(paul) & person(mary) & wise(paul) & calm(mary) & person(mary) & ~creative(mary) & (~old(alice) | (~wise(paul) & person(paul) & tall(paul))) & (~wise(fred) | wise(paul) | ~person(paul) | ~tall(paul)) & (~tall(paul) | ~person(paul) | ~calm(paul) | creative(paul)) & ((person(alice) & quiet(alice)) | ~person(fred) | ~creative(fred)) & ((person(fred) & creative(fred)) | ~person(alice) | ~quiet(alice)) & (room(sK1) | ~person(fred) | ~wise(fred)) & ((person(fred) & wise(fred)) | ~person(paul) | ~kind(paul) | ~person(alice) | ~kind(alice)) & (! [X1] : (person(X1) | ~person(X1) | ~kind(X1)) | (person(alice) & quiet(alice))) & ((person(sK2) & kind(sK2)) | ~person(alice) | ~quiet(alice)) & ((tall(alice) & person(alice) & old(alice) & tall(paul) & person(paul) & old(paul)) | ~wise(mary)) & ! [X3] : (john = X3 | alice = X3 | fred = X3 | paul = X3 | mary = X3 | ~room(X3)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 134,136,135] 138. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 129] 139. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 138] 140. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 141. (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~sP0 [skolemisation 139,140] 222. room(mary) [cnf transformation 137] 223. room(paul) [cnf transformation 137] 224. room(fred) [cnf transformation 137] 225. room(alice) [cnf transformation 137] 226. room(john) [cnf transformation 137] 227. ~room(X3) | alice = X3 | fred = X3 | paul = X3 | mary = X3 | john = X3 [cnf transformation 137] 257. room(sK3) | ~sP0 [cnf transformation 141] 258. mary != sK3 | ~sP0 [cnf transformation 141] 259. paul != sK3 | ~sP0 [cnf transformation 141] 260. fred != sK3 | ~sP0 [cnf transformation 141] 261. alice != sK3 | ~sP0 [cnf transformation 141] 262. john != sK3 | ~sP0 [cnf transformation 141] 264. quiet(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 130] 265. ~quiet(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 130] 350. 17 <=> sP0 [avatar definition] 354. 18 <=> john = sK3 [avatar definition] 356. john != sK3 <- (~18) [avatar component clause 354] 357. ~17 | ~18 [avatar split clause 262,354,350] 359. 19 <=> alice = sK3 [avatar definition] 361. alice != sK3 <- (~19) [avatar component clause 359] 362. ~17 | ~19 [avatar split clause 261,359,350] 364. 20 <=> fred = sK3 [avatar definition] 367. ~17 | ~20 [avatar split clause 260,364,350] 369. 21 <=> paul = sK3 [avatar definition] 371. paul != sK3 <- (~21) [avatar component clause 369] 372. ~17 | ~21 [avatar split clause 259,369,350] 374. 22 <=> mary = sK3 [avatar definition] 376. mary != sK3 <- (~22) [avatar component clause 374] 377. ~17 | ~22 [avatar split clause 258,374,350] 379. 23 <=> room(sK3) [avatar definition] 381. room(sK3) <- (23) [avatar component clause 379] 382. ~17 | 23 [avatar split clause 257,379,350] 383. ~quiet(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,226] 384. ~quiet(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 383,225] 385. ~quiet(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 384,224] 386. ~quiet(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 385,223] 387. ~quiet(X0) | ~room(X0) | sP0 [subsumption resolution 386,222] 389. 24 <=> ! [X0] : (~quiet(X0) | ~room(X0)) [avatar definition] 390. ~quiet(X0) | ~room(X0) <- (24) [avatar component clause 389] 391. 17 | 24 [avatar split clause 387,389,350] 392. quiet(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 264,226] 393. quiet(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 392,225] 394. quiet(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 393,224] 395. quiet(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 394,223] 396. quiet(X0) | ~room(X0) | sP0 [subsumption resolution 395,222] 398. 25 <=> ! [X0] : (quiet(X0) | ~room(X0)) [avatar definition] 399. quiet(X0) | ~room(X0) <- (25) [avatar component clause 398] 400. 17 | 25 [avatar split clause 396,398,350] 451. alice = sK3 | fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (23) [resolution 227,381] 452. fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (~19, 23) [subsumption resolution 451,361] 458. fred = sK3 | mary = sK3 | john = sK3 <- (~19, ~21, 23) [subsumption resolution 452,371] 459. fred = sK3 | john = sK3 <- (~19, ~21, ~22, 23) [subsumption resolution 458,376] 460. fred = sK3 <- (~18, ~19, ~21, ~22, 23) [subsumption resolution 459,356] 461. 20 | 18 | 19 | 21 | 22 | ~23 [avatar split clause 460,379,374,369,359,354,364] 462. ~room(X0) <- (24, 25) [subsumption resolution 390,399] 466. $false <- (24, 25) [resolution 462,222] 475. ~24 | ~25 [avatar contradiction clause 466] 476. $false [avatar sat refutation 357,362,367,372,377,382,391,400,461,475] % SZS output end Proof for 7363237648243208441555355 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

Queen, Earl are the only persons in the room. Queen is a old quiet tall person. Earl is a kind person. If someone is not old then he/she is not tall. All kind persons are quiet. Queen is a kind person. Earl and Queen are respectively tall and quiet. If someone is a tall kind person then he/she is a quiet person. Queen is a tall person. Queen is the richest in the room. Someone anywhere is a old person. Someone anywhere is a kind person. Someone in the room is a kind person.

Earl is old.

entailment

room(queen)&room(earl)&(![X]:(room(X)=>(X='queen'|X='earl')))& (old(queen)&quiet(queen)&tall(queen)&person(queen))& (kind(earl)&person(earl))& ((![X]:((~old(X))=>(~tall(X)))))& (![X]:(kind(X)=>quiet(X)))& (kind(queen)&person(queen))& ((tall(earl))&(quiet(queen)))& ((![X]:((tall(X)&kind(X)&person(X))=>(quiet(X)&person(X)))))& (tall(queen)&person(queen))& (![X]:((room(X)&(X!=queen))=>richer(X,queen)))& (?[X]:(anywhere(X)&(old(X)&person(X))))& (?[X]:(anywhere(X)&(kind(X)&person(X))))& (?[X]:(room(X)&(kind(X)&person(X))))

room(queen)&room(earl)&(![X]:(room(X)=>(X='queen'|X='earl')))& old(earl)

% SZS status Unsatisfiable for 7785086404080495527641635 % SZS output start Proof for 7785086404080495527641635 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ! [X0] : (~old(X0) => ~tall(X0)) [input p3] 50. quiet(mary) & tall(paul) [input p6] 57. ~(old(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 132. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 133. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 132] 134. ! [X0] : (~tall(X0) | old(X0)) [ennf transformation 47] 140. ~old(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 57] 141. ~old(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 140] 149. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 150. ~old(paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 141,149] 231. room(mary) [cnf transformation 133] 232. room(paul) [cnf transformation 133] 233. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 133] 240. ~tall(X0) | old(X0) [cnf transformation 134] 244. tall(paul) [cnf transformation 50] 258. ~old(paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 150] 259. ~old(paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 150] 260. ~old(paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 150] 261. ~old(paul) | paul != sK3 | ~room(mary) [subsumption resolution 260,232] 262. ~old(paul) | paul != sK3 [subsumption resolution 261,231] 264. 1 <=> paul = sK3 [avatar definition] 266. paul != sK3 <- (~1) [avatar component clause 264] 268. 2 <=> old(paul) [avatar definition] 271. ~1 | ~2 [avatar split clause 262,268,264] 272. ~old(paul) | mary != sK3 | ~room(mary) [subsumption resolution 259,232] 273. ~old(paul) | mary != sK3 [subsumption resolution 272,231] 275. 3 <=> mary = sK3 [avatar definition] 277. mary != sK3 <- (~3) [avatar component clause 275] 278. ~3 | ~2 [avatar split clause 273,268,275] 279. ~old(paul) | room(sK3) | ~room(mary) [subsumption resolution 258,232] 280. ~old(paul) | room(sK3) [subsumption resolution 279,231] 282. 4 <=> room(sK3) [avatar definition] 284. room(sK3) <- (4) [avatar component clause 282] 285. 4 | ~2 [avatar split clause 280,268,282] 287. old(paul) [resolution 240,244] 290. 2 [avatar split clause 287,268] 298. mary = sK3 | paul = sK3 <- (4) [resolution 233,284] 308. paul = sK3 <- (~3, 4) [subsumption resolution 298,277] 309. $false <- (~1, ~3, 4) [subsumption resolution 308,266] 310. 1 | 3 | ~4 [avatar contradiction clause 309] 311. $false [avatar sat refutation 271,278,285,290,310] % SZS output end Proof for 7785086404080495527641635 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jerry is the only person in the room. If “it is not the case that “it is not the case that “Jerry and Elizabeth like each other””” then “someone in the room does not like Antonia”. If “it is not the case that “at least one person outside the room does not like Elizabeth, does not like Franklin and does not like Antonia”” then “if someone does not like Antonia then he/she does not like Antonia and does not like Franklin and vice versa”. Someone who does not like Elizabeth like someone who does not like Antonia. It is not the case that “at least one person outside the room does not like Elizabeth, does not like Franklin and does not like Antonia”. Jerry and Franklin like each other. Someone who does not like Antonia like someone who is liked by Elizabeth, does not like Elizabeth and is liked by Antonia. Someone outside the room does not like Franklin and does not like Antonia.

Jerry is liked by Antonia.

neutral

room(jerry)&(![X]:(room(X)=>(X='jerry')))& ((~(~((like(jerry,elizabeth) & like(elizabeth,jerry)))))=>(?[X]:(room(X)&(~like(antonia,X)))))& ((~(((?[X]:(~room(X)&((~like(elizabeth,X))&(~like(franklin,X))&(~like(antonia,X))))))))=>((![X]:((~like(antonia,X))<=>(((~like(antonia,X))&(~like(franklin,X))))))))& (?[X,Y]:((~like(elizabeth,X))&(~like(antonia,Y))&(like(X,Y))))& (~(((?[X]:(~room(X)&((~like(elizabeth,X))&(~like(franklin,X))&(~like(antonia,X))))))))& ((like(jerry,franklin) & like(franklin,jerry)))& (?[X,Y]:((~like(antonia,X))&(((like(Y,elizabeth))&(~like(elizabeth,Y))&(like(Y,antonia))))&(like(X,Y))))& (?[X]:(~room(X)&(((~like(franklin,X))&(~like(antonia,X))))))& (?[X,Y]:((((~like(antonia,X))&(~like(franklin,X))&(like(X,elizabeth))))&(like(Y,antonia))&(like(X,Y))))& (~((like(jerry,elizabeth) & like(elizabeth,jerry))))& ((![X]:((((~like(franklin,X))<~>(~like(elizabeth,X))))<=>(like(X,elizabeth)))))

room(jerry)&(![X]:(room(X)=>(X='jerry')))& like(jerry,antonia)

Erica, Lola, Melody are the only persons in the room. If “Lola and Melody are respectively kind and creative” then “if someone is a client of Lola then he/she hosts a YouTube channel dedicated to art tutorials”. Only one person anywhere is funny. If someone is not liked by Lola then he/she is not kind and vice versa. “All swans in one park are blue.” or “A pizza does not exist that tastes like ice cream.” or both. If someone is a client of Brian then he/she is not funny, not creative, not old and vice versa. Melody who owns a smart tv or is not liked by Lola or both is not tall, not wise. Someone outside the room is a sibling of Alicia. If someone either owns a 3D printer or is not a humble person but not both then he/she is liked by Alicia and vice versa. Someone anywhere regularly goes on multi-day backpacking trips in national parks. At least one person anywhere hosts a YouTube channel dedicated to art tutorials. If someone likes Lola then he/she owns a 3D printer or is a sibling of Alicia or both and vice versa. “Glass rain falls on a distant planet.” and “A pizza does not exist that tastes like ice cream.” and “Not all swans in one park are blue.”. More than one person in the room either does not host regular game nights featuring complex strategy games or does not write and illustrates their own graphic novels but not both. Only one person in the room plays video games. A shadow appears only at noon. If someone regularly goes on multi-day backpacking trips in national parks then he/she is creative.

A pizza exists that tastes like ice cream.

contradiction

room(erica)&room(lola)&room(melody)&(![X]:(room(X)=>(X='erica'|X='lola'|X='melody')))& (((kind(lola))&(creative(melody)))=>((![X]:((client(lola,X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (((?[X]:(anywhere(X)&funny(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(funny(X))&(funny(Y)))=>(X=Y)))))& ((![X]:((~like(X,lola))<=>(~kind(X)))))& (((All_swans_in_one_park_are_blue.)|(A_pizza_does_not_exist_that_tastes_like_ice_cream.)))& ((![X]:((client(brian,X))<=>(~funny(X)&~creative(X)&~old(X)))))& ((((owns_a_smart_tv(melody))|(~like(melody,lola))))&(~tall(melody)&~wise(melody)))& (?[X]:(~room(X)&(sibling(alicia,X))))& ((![X]:((((owns_a_3D_printer(X))<~>(~(humble(X)&person(X)))))<=>(like(X,alicia)))))& (?[X]:(anywhere(X)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))& (((?[X]:(anywhere(X)&hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& ((![X]:((like(lola,X))<=>(((owns_a_3D_printer(X))|(sibling(alicia,X)))))))& (((Glass_rain_falls_on_a_distant_planet.)&(A_pizza_does_not_exist_that_tastes_like_ice_cream.)&(Not_all_swans_in_one_park_are_blue.)))& ((?[X,Y]:(room(X)&room(Y)&(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))<~>(does_not_write_and_illustrates_their_own_graphic_novels(X)))&((does_not_host_regular_game_nights_featuring_complex_strategy_games(Y))<~>(does_not_write_and_illustrates_their_own_graphic_novels(Y))))&(X!=Y))))& (((?[X]:(room(X)&plays_video_games(X)))&(![X,Y]:((room(X)&room(Y)&(plays_video_games(X))&(plays_video_games(Y)))=>(X=Y)))))& (A_shadow_appears_only_at_noon.)& ((![X]:((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(creative(X)))))& (![X]:(quiet(X)=>curious(X)))& (![X]:(wise(X)=>strong(X)))& ((strong(melody))&(funny(erica)))

room(erica)&room(lola)&room(melody)&(![X]:(room(X)=>(X='erica'|X='lola'|X='melody')))& A_pizza_exists_that_tastes_like_ice_cream.

% SZS status Unsatisfiable for 3330711533909711615703687 % SZS output start Proof for 3330711533909711615703687 56. ~propositionb & ~propositionc & propositiona [input p12] 64. propositionc & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 72. ~propositionb & ~propositionc [pure predicate removal 56] 158. propositionc & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 64] 159. propositionc & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 158] 288. ~propositionc [cnf transformation 72] 306. propositionc [cnf transformation 159] 314. 2 <=> propositionc [avatar definition] 319. ~2 [avatar split clause 288,314] 340. 2 [avatar split clause 306,314] 341. $false [avatar sat refutation 319,340] % SZS output end Proof for 3330711533909711615703687 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jean, Josephina, Thelma are the only persons in the room. If "everyone in the room does not own a 3D printer or collects limited-edition art prints from contemporary artists" then "no one in the room practices and performs acrobatic dance routines if they practices graffiti art". Jean practices and performs acrobatic dance routines or does enjoy trail running or both. Josephina does not practice and performs acrobatic dance routines. Everyone in the room practices and performs acrobatic dance routines if they collects limited-edition art prints from contemporary artists. Jean practices and performs acrobatic dance routines. Everyone in the room who owns a 3D printer practices graffiti art. Someone in the room does enjoy trail running. Everyone in the room does not own a 3D printer if they collects limited-edition art prints from contemporary artists.

Everyone in the room practices graffiti art.

neutral

room(jean)&room(josephina)&room(thelma)&(![X]:(room(X)=>(X='jean'|X='josephina'|X='thelma')))& ((![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_own_a_3D_printer(X))))))=>(~?[X]:(room(X)=>(((practices_graffiti_art(X))=>(practices_and_performs_acrobatic_dance_routines(X)))))))& (((practices_and_performs_acrobatic_dance_routines(jean))|(does_enjoy_trail_running(jean))))& (does_not_practice_and_performs_acrobatic_dance_routines(josephina))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (practices_and_performs_acrobatic_dance_routines(jean))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(practices_graffiti_art(X))))))& (?[X]:(room(X)&(does_enjoy_trail_running(X))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(does_not_own_a_3D_printer(X))))))

room(jean)&room(josephina)&room(thelma)&(![X]:(room(X)=>(X='jean'|X='josephina'|X='thelma')))& ![X]:(room(X)=>(practices_graffiti_art(X)))

Sandra, Stephen, Frank, Anthony are the only persons in the room. Everyone outside the room is a client of Meta if they neither develops open-source software projects in their free time nor is a client of Meta. More than one person in the room uses a Windows laptop. Anthony knows morse code. Stephen does not host a YouTube channel dedicated to art tutorials. Sandra neither develops open-source software projects in their free time nor is a client of Meta. Anthony does not develop open-source software projects in their free time. Only one person in the room neither develops open-source software projects in their free time nor is a client of Meta. If someone neither develops open-source software projects in their free time nor owns a high-end gaming PC with custom-built components then he/she does not practice urban gardening and vice versa. Sandra either does not collect rare and antique scientific instruments or writes a travel blog but not both. Stephen does not collect comic books. Everyone outside the room who either does not create augmented reality experiences for mobile applications or collects rare and antique scientific instruments but not both collects luxury watches.

Anthony is a client of Meta.

entailment

room(sandra)&room(stephen)&room(frank)&room(anthony)&(![X]:(room(X)=>(X='sandra'|X='stephen'|X='frank'|X='anthony')))& (![X]:(~room(X)=>(((~((develops_open-source_software_projects_in_their_free_time(X))|(is_a_client_of_Meta(X))))=>(is_a_client_of_Meta(X))))))& ((?[X,Y]:(room(X)&room(Y)&(uses_a_Windows_laptop(X)&uses_a_Windows_laptop(Y))&(X!=Y))))& (knows_morse_code(anthony))& (does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(stephen))& (~((develops_open-source_software_projects_in_their_free_time(sandra))|(is_a_client_of_Meta(sandra))))& (does_not_develop_open-source_software_projects_in_their_free_time(anthony))& (((?[X]:(room(X)&~((develops_open-source_software_projects_in_their_free_time(X))|(is_a_client_of_Meta(X)))))&(![X,Y]:((room(X)&room(Y)&(~((develops_open-source_software_projects_in_their_free_time(X))|(is_a_client_of_Meta(X))))&(~((develops_open-source_software_projects_in_their_free_time(Y))|(is_a_client_of_Meta(Y)))))=>(X=Y)))))& ((![X]:((~((develops_open-source_software_projects_in_their_free_time(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))<=>(does_not_practice_urban_gardening(X)))))& (((does_not_collect_rare_and_antique_scientific_instruments(sandra))<~>(writes_a_travel_blog(sandra))))& (does_not_collect_comic_books(stephen))& (![X]:(~room(X)=>(((((does_not_create_augmented_reality_experiences_for_mobile_applications(X))<~>(collects_rare_and_antique_scientific_instruments(X))))=>(collects_luxury_watches(X))))))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(sandra))& (((is_an_expert_in_identifying_and_foraging_wild_edible_plants(frank))|(practices_urban_gardening(frank))))& ((![X]:((~((is_not_a_drone_photographer(X))|(does_not_practice_urban_gardening(X))))<=>(enjoys_bird_watching(X)))))& ((![X]:((practices_urban_gardening(X))<=>(does_not_own_a_3D_printer(X)))))& (?[X]:(room(X)&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))& (~((collects_luxury_watches(anthony))|(creates_augmented_reality_experiences_for_mobile_applications(anthony))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=(does_not_use_a_Windows_laptop(X))))))& (does_not_use_a_Windows_laptop(anthony))& (collects_rare_and_antique_scientific_instruments(sandra))& (((does_not_create_augmented_reality_experiences_for_mobile_applications(frank))<~>(collects_rare_and_antique_scientific_instruments(frank))))& (?[X]:(room(X)&(is_a_Linux_enthusiast(X))))& (![X]:(~room(X)=>(((uses_a_Windows_laptop(X))<~>(develops_open-source_software_projects_in_their_free_time(X))))))& (?[X]:(room(X)&(composes_and_performs_experimental_electronic_music(X))))& (is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(stephen))& (collects_comic_books(frank))& (~((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(anthony))|(collects_rare_and_antique_scientific_instruments(anthony))))& (~((is_not_a_certified_yoga_instructor_teaching_classes_weekly(frank))|(does_not_enjoy_skydiving(frank))))

room(sandra)&room(stephen)&room(frank)&room(anthony)&(![X]:(room(X)=>(X='sandra'|X='stephen'|X='frank'|X='anthony')))& is_a_client_of_Meta(anthony)

% SZS status Unsatisfiable for 4774623827315153897297361 % SZS output start Proof for 4774623827315153897297361 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (~room(X0) => (~(predv(X0) | predm(X0)) => predv(X0))) [input p1] 49. ~(predv(mary) | predm(mary)) [input p5] 50. ~predm(alice) [input p6] 51. ! [X0,X1] : ((~(predv(X1) | predm(X1)) & ~(predv(X0) | predm(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~(predv(X0) | predm(X0)) & room(X0)) [input p7] 73. ~(predv(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 74. ! [X0,X1] : ((~(predv(X1) | predm(X1)) & ~(predv(X0) | predm(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~(predv(X2) | predm(X2)) & room(X2)) [rectify 51] 152. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 153. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 152] 154. ! [X0] : ((predv(X0) | (predv(X0) | predm(X0))) | room(X0)) [ennf transformation 45] 155. ! [X0] : (predv(X0) | predv(X0) | predm(X0) | room(X0)) [flattening 154] 156. ~predv(mary) & ~predm(mary) [ennf transformation 49] 157. ! [X0,X1] : (X0 = X1 | ((predv(X1) | predm(X1)) | (predv(X0) | predm(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : ((~predv(X2) & ~predm(X2)) & room(X2)) [ennf transformation 74] 158. ! [X0,X1] : (X0 = X1 | predv(X1) | predm(X1) | predv(X0) | predm(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~predv(X2) & ~predm(X2) & room(X2)) [flattening 157] 167. ~predv(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 73] 168. ~predv(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 167] 172. ? [X2] : (~predv(X2) & ~predm(X2) & room(X2)) => (~predv(sK2) & ~predm(sK2) & room(sK2)) [choice axiom] 173. ! [X0,X1] : (X0 = X1 | predv(X1) | predm(X1) | predv(X0) | predm(X0) | ~room(X1) | ~room(X0)) & (~predv(sK2) & ~predm(sK2) & room(sK2)) [skolemisation 158,172] 187. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 188. ~predv(alice) | (alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 168,187] 245. mary != alice [cnf transformation 43] 269. room(mary) [cnf transformation 153] 270. room(paul) [cnf transformation 153] 271. room(fred) [cnf transformation 153] 272. room(alice) [cnf transformation 153] 273. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 153] 274. predv(X0) | predv(X0) | predm(X0) | room(X0) [cnf transformation 155] 281. ~predm(mary) [cnf transformation 156] 282. ~predv(mary) [cnf transformation 156] 283. ~predm(alice) [cnf transformation 50] 287. X0 = X1 | predv(X1) | predm(X1) | predv(X0) | predm(X0) | ~room(X1) | ~room(X0) [cnf transformation 173] 317. ~predv(alice) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 318. ~predv(alice) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 319. ~predv(alice) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 320. ~predv(alice) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 321. ~predv(alice) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 322. predv(X0) | predm(X0) | room(X0) [duplicate literal removal 274] 323. X0 = X1 | predv(X1) | predm(X1) | predv(X0) | predm(X0) | ~room(X0) [subsumption resolution 287,322] 324. predv(X1) | predv(X0) | predm(X1) | X0 = X1 | predm(X0) [subsumption resolution 323,322] 355. ~predv(alice) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,272] 356. ~predv(alice) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 355,271] 357. ~predv(alice) | alice != sK6 | ~room(mary) [subsumption resolution 356,270] 358. ~predv(alice) | alice != sK6 [subsumption resolution 357,269] 360. 7 <=> alice = sK6 [avatar definition] 362. alice != sK6 <- (~7) [avatar component clause 360] 364. 8 <=> predv(alice) [avatar definition] 366. ~predv(alice) <- (~8) [avatar component clause 364] 367. ~7 | ~8 [avatar split clause 358,364,360] 368. ~predv(alice) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,272] 369. ~predv(alice) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 368,271] 370. ~predv(alice) | fred != sK6 | ~room(mary) [subsumption resolution 369,270] 371. ~predv(alice) | fred != sK6 [subsumption resolution 370,269] 373. 9 <=> fred = sK6 [avatar definition] 375. fred != sK6 <- (~9) [avatar component clause 373] 376. ~9 | ~8 [avatar split clause 371,364,373] 377. ~predv(alice) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,272] 378. ~predv(alice) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 377,271] 379. ~predv(alice) | paul != sK6 | ~room(mary) [subsumption resolution 378,270] 380. ~predv(alice) | paul != sK6 [subsumption resolution 379,269] 382. 10 <=> paul = sK6 [avatar definition] 384. paul != sK6 <- (~10) [avatar component clause 382] 385. ~10 | ~8 [avatar split clause 380,364,382] 386. ~predv(alice) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,272] 387. ~predv(alice) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 386,271] 388. ~predv(alice) | mary != sK6 | ~room(mary) [subsumption resolution 387,270] 389. ~predv(alice) | mary != sK6 [subsumption resolution 388,269] 391. 11 <=> mary = sK6 [avatar definition] 393. mary != sK6 <- (~11) [avatar component clause 391] 394. ~11 | ~8 [avatar split clause 389,364,391] 395. ~predv(alice) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,272] 396. ~predv(alice) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 395,271] 397. ~predv(alice) | room(sK6) | ~room(mary) [subsumption resolution 396,270] 398. ~predv(alice) | room(sK6) [subsumption resolution 397,269] 400. 12 <=> room(sK6) [avatar definition] 402. room(sK6) <- (12) [avatar component clause 400] 403. 12 | ~8 [avatar split clause 398,364,400] 549. predv(X0) | predm(mary) | mary = X0 | predm(X0) [resolution 324,282] 557. predv(X0) | mary = X0 | predm(X0) [subsumption resolution 549,281] 562. mary = alice | predm(alice) <- (~8) [resolution 557,366] 570. predm(alice) <- (~8) [subsumption resolution 562,245] 571. $false <- (~8) [subsumption resolution 570,283] 572. 8 [avatar contradiction clause 571] 594. fred = sK6 | paul = sK6 | mary = sK6 | alice = sK6 <- (12) [resolution 273,402] 680. paul = sK6 | mary = sK6 | alice = sK6 <- (~9, 12) [subsumption resolution 594,375] 681. mary = sK6 | alice = sK6 <- (~9, ~10, 12) [subsumption resolution 680,384] 682. alice = sK6 <- (~9, ~10, ~11, 12) [subsumption resolution 681,393] 683. $false <- (~7, ~9, ~10, ~11, 12) [subsumption resolution 682,362] 684. 7 | 9 | 10 | 11 | ~12 [avatar contradiction clause 683] 685. $false [avatar sat refutation 367,376,385,394,403,572,684] % SZS output end Proof for 4774623827315153897297361 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s % ------------------------------ % ------------------------------

Charles, Joseph, Robert are the only persons in the room. 'At least one person outside the room is not a quiet creative person' if 'Robert is not wise, not creative' and vice versa. Joseph and Robert are respectively wise and patient. Charles is the least rich anywhere. Robert is not funny. Robert is not funny, not calm. Robert is not a strong quiet kind person. Charles is not strong, not happy, not creative or is not kind, not wise, not humble or both. Charles is not brave, not old. It is true that 'at least one person outside the room is not a curious person'. Only one person in the room is not a old tall person. Robert is not a quiet person.

Robert is not quiet.

entailment

room(charles)&room(joseph)&room(robert)&(![X]:(room(X)=>(X='charles'|X='joseph'|X='robert')))& ((~wise(robert)&~creative(robert))<=>(((?[X]:(~room(X)&~(quiet(X)&creative(X)&person(X)))))))& ((wise(joseph))&(patient(robert)))& (![X]:((anywhere(X)&(X!=charles))=>richer(charles,X)))& (~funny(robert))& (~funny(robert)&~calm(robert))& (~(strong(robert)&quiet(robert)&kind(robert)&person(robert)))& (((~strong(charles)&~happy(charles)&~creative(charles))|(~kind(charles)&~wise(charles)&~humble(charles))))& (~brave(charles)&~old(charles))& (((?[X]:(~room(X)&~(curious(X)&person(X))))))& ((patient(charles))&(old(robert)))& (((?[X]:(room(X)&~(old(X)&tall(X)&person(X))))&(![X,Y]:((room(X)&room(Y)&(~(old(X)&tall(X)&person(X)))&(~(old(Y)&tall(Y)&person(Y))))=>(X=Y)))))& (~(old(robert)&happy(robert)&person(robert)))& (~((~humble(robert))|(~patient(robert)&~quiet(robert)&~calm(robert)&~humble(robert)&~brave(robert)&~creative(robert))))& (![X]:((room(X)&(X!=charles))=>older(charles,X)))& (((~(calm(robert)&person(robert)))|(~(kind(robert)&person(robert)))))& (((~strong(charles))|(~(happy(charles)&person(charles)))))& (((~wise(charles)&~funny(charles)&~brave(charles)&~calm(charles))|(~(old(charles)&person(charles)))))& (~tall(charles))& (?[X,Y]:((~brave(X))&(~strong(Y)&~happy(Y)&~kind(Y)&~calm(Y)&~creative(Y))&(richer(X,Y))))& (~(quiet(robert)&person(robert)))& ((creative(robert))&(patient(joseph)))& (((~(creative(charles)&generous(charles)&person(charles)))|(~(strong(charles)&person(charles)))))& (?[X,Y]:((((~(strong(X)&tall(X)&person(X)))&(~brave(X)&~kind(X))))&(((~(funny(Y)&person(Y)))&(~humble(Y)&~happy(Y))))&(richer(X,Y))))& (~(generous(charles)&person(charles)))& (~(strong(charles)&calm(charles)&person(charles)))& (~(creative(charles)&strong(charles)&happy(charles)&person(charles)))& (((~(patient(charles)&old(charles)&person(charles)))&(~(funny(charles)&patient(charles)&person(charles)))))

room(charles)&room(joseph)&room(robert)&(![X]:(room(X)=>(X='charles'|X='joseph'|X='robert')))& ~quiet(robert)

% SZS status Unsatisfiable for 8433545172519975897868636 % SZS output start Proof for 8433545172519975897868636 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 52. ~old(mary) & ~brave(mary) [input p8] 55. ! [X0,X1] : ((~(person(X1) & tall(X1) & old(X1)) & ~(person(X0) & tall(X0) & old(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~(person(X0) & tall(X0) & old(X0)) & room(X0)) [input p11] 64. ~(person(fred) & quiet(fred)) [input p20] 72. ~(~quiet(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 73. ! [X0,X1] : ((~(person(X1) & tall(X1) & old(X1)) & ~(person(X0) & tall(X0) & old(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~(person(X2) & tall(X2) & old(X2)) & room(X2)) [rectify 55] 168. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 169. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 168] 173. ! [X0,X1] : (X0 = X1 | ((person(X1) & tall(X1) & old(X1)) | (person(X0) & tall(X0) & old(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : ((~person(X2) | ~tall(X2) | ~old(X2)) & room(X2)) [ennf transformation 73] 174. ! [X0,X1] : (X0 = X1 | (person(X1) & tall(X1) & old(X1)) | (person(X0) & tall(X0) & old(X0)) | ~room(X1) | ~room(X0)) & ? [X2] : ((~person(X2) | ~tall(X2) | ~old(X2)) & room(X2)) [flattening 173] 180. ~person(fred) | ~quiet(fred) [ennf transformation 64] 182. quiet(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 72] 183. quiet(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 182] 184. ! [X0] : ((person(X0) & tall(X0) & old(X0)) | ~sP0(X0)) [predicate definition introduction] 185. ! [X0,X1] : (X0 = X1 | (person(X1) & tall(X1) & old(X1)) | sP0(X0) | ~room(X1) | ~room(X0)) & ? [X2] : ((~person(X2) | ~tall(X2) | ~old(X2)) & room(X2)) [definition folding 174,184] 194. ! [X0] : ((person(X0) & tall(X0) & old(X0)) | ~sP0(X0)) [nnf transformation 184] 195. ? [X2] : ((~person(X2) | ~tall(X2) | ~old(X2)) & room(X2)) => ((~person(sK3) | ~tall(sK3) | ~old(sK3)) & room(sK3)) [choice axiom] 196. ! [X0,X1] : (X0 = X1 | (person(X1) & tall(X1) & old(X1)) | sP0(X0) | ~room(X1) | ~room(X0)) & ((~person(sK3) | ~tall(sK3) | ~old(sK3)) & room(sK3)) [skolemisation 185,195] 201. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 202. quiet(fred) | (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 183,201] 254. mary != fred [cnf transformation 43] 284. room(mary) [cnf transformation 169] 285. room(paul) [cnf transformation 169] 286. room(fred) [cnf transformation 169] 287. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 169] 303. ~old(mary) [cnf transformation 52] 309. ~sP0(X0) | person(X0) [cnf transformation 194] 312. ~room(X1) | old(X1) | sP0(X0) | X0 = X1 | ~room(X0) [cnf transformation 196] 326. ~person(fred) | ~quiet(fred) [cnf transformation 180] 333. quiet(fred) | room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 202] 334. quiet(fred) | mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 202] 335. quiet(fred) | paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 202] 336. quiet(fred) | fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 202] 407. 16 <=> quiet(fred) [avatar definition] 411. 17 <=> person(fred) [avatar definition] 414. ~16 | ~17 [avatar split clause 326,411,407] 416. quiet(fred) | fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 336,286] 417. quiet(fred) | fred != sK8 | ~room(mary) [subsumption resolution 416,285] 418. quiet(fred) | fred != sK8 [subsumption resolution 417,284] 420. 18 <=> fred = sK8 [avatar definition] 422. fred != sK8 <- (~18) [avatar component clause 420] 423. ~18 | 16 [avatar split clause 418,407,420] 424. quiet(fred) | paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 335,286] 425. quiet(fred) | paul != sK8 | ~room(mary) [subsumption resolution 424,285] 426. quiet(fred) | paul != sK8 [subsumption resolution 425,284] 428. 19 <=> paul = sK8 [avatar definition] 430. paul != sK8 <- (~19) [avatar component clause 428] 431. ~19 | 16 [avatar split clause 426,407,428] 432. quiet(fred) | mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 334,286] 433. quiet(fred) | mary != sK8 | ~room(mary) [subsumption resolution 432,285] 434. quiet(fred) | mary != sK8 [subsumption resolution 433,284] 436. 20 <=> mary = sK8 [avatar definition] 438. mary != sK8 <- (~20) [avatar component clause 436] 439. ~20 | 16 [avatar split clause 434,407,436] 440. quiet(fred) | room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 333,286] 441. quiet(fred) | room(sK8) | ~room(mary) [subsumption resolution 440,285] 442. quiet(fred) | room(sK8) [subsumption resolution 441,284] 444. 21 <=> room(sK8) [avatar definition] 446. room(sK8) <- (21) [avatar component clause 444] 447. 21 | 16 [avatar split clause 442,407,444] 709. old(mary) | sP0(X4) | mary = X4 | ~room(X4) [resolution 312,284] 712. ~room(X4) | mary = X4 | sP0(X4) [subsumption resolution 709,303] 756. mary = fred | sP0(fred) [resolution 712,286] 759. sP0(fred) [subsumption resolution 756,254] 776. person(fred) [resolution 759,309] 782. 17 [avatar split clause 776,411] 787. paul = sK8 | mary = sK8 | fred = sK8 <- (21) [resolution 446,287] 802. mary = sK8 | fred = sK8 <- (~19, 21) [subsumption resolution 787,430] 803. fred = sK8 <- (~19, ~20, 21) [subsumption resolution 802,438] 804. $false <- (~18, ~19, ~20, 21) [subsumption resolution 803,422] 805. 18 | 19 | 20 | ~21 [avatar contradiction clause 804] 806. $false [avatar sat refutation 414,423,431,439,447,782,805] % SZS output end Proof for 8433545172519975897868636 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s % ------------------------------ % ------------------------------

Either Patricia plays video games or Patricia collects rare and antique scientific instruments, collects vintage vinyl records or is a dedicated volunteer for local community service projects but not both. If Patricia bakes bread at home then Erica does not collect antique jewelry otherwise Erica plays video games. Patricia who bakes bread at home neither watches fantasy movies nor uses an ios phone. Patricia is a dedicated volunteer for local community service projects. Patrick has a saltwater aquarium. Patrick enjoys kayaking. Patricia collects vintage vinyl records. Patrick collect rare sneakers. Erica has a saltwater aquarium. It is not the case that Patricia is an expert in identifying and foraging wild edible plants.

Not everyone in the room collects antique jewelry.

entailment

room(erica)&room(patricia)&room(patrick)&room(brett)&room(john)&(![X]:(room(X)=>(X='erica'|X='patricia'|X='patrick'|X='brett'|X='john')))& ((plays_video_games(patricia))<~>(((collects_rare_and_antique_scientific_instruments(patricia))|(collects_vintage_vinyl_records(patricia))|(is_a_dedicated_volunteer_for_local_community_service_projects(patricia)))))& (((bakes_bread_at_home(patricia))=>(does_not_collect_antique_jewelry(erica)))&((~(bakes_bread_at_home(patricia)))=>(plays_video_games(erica))))& ((bakes_bread_at_home(patricia))&(~((watches_fantasy_movies(patricia))|(uses_an_ios_phone(patricia)))))& (is_a_dedicated_volunteer_for_local_community_service_projects(patricia))& (has_a_saltwater_aquarium(patrick))& (enjoys_kayaking(patrick))& (collects_vintage_vinyl_records(patricia))& (collect_rare_sneakers(patrick))& (has_a_saltwater_aquarium(erica))& (~(is_an_expert_in_identifying_and_foraging_wild_edible_plants(patricia)))

room(erica)&room(patricia)&room(patrick)&room(brett)&room(john)&(![X]:(room(X)=>(X='erica'|X='patricia'|X='patrick'|X='brett'|X='john')))& ~![X]:(room(X)=>(collects_antique_jewelry(X)))

% SZS status Unsatisfiable for 742911601365960035600626 % SZS output start Proof for 742911601365960035600626 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. (~predd(paul) => predp(mary)) & (predd(paul) => ~predj(mary)) [input p2] 47. ~(preda(paul) | predq(paul)) & predd(paul) [input p3] 55. ~(~! [X0] : (room(X0) => predj(X0)) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 56. ~(~! [X0] : (room(X0) => predj(X0)) & ! [X1] : (room(X1) => (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 55] 62. ~predq(paul) & predd(paul) [pure predicate removal 47] 63. predd(paul) [pure predicate removal 62] 136. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 136] 138. (predp(mary) | predd(paul)) & (~predj(mary) | ~predd(paul)) [ennf transformation 46] 139. ! [X0] : (predj(X0) | ~room(X0)) | ? [X1] : ((john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 56] 140. ! [X0] : (predj(X0) | ~room(X0)) | ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 139] 144. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) => (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 145. ! [X0] : (predj(X0) | ~room(X0)) | (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 140,144] 226. room(mary) [cnf transformation 137] 227. room(paul) [cnf transformation 137] 228. room(fred) [cnf transformation 137] 229. room(alice) [cnf transformation 137] 230. room(john) [cnf transformation 137] 231. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 137] 236. ~predj(mary) | ~predd(paul) [cnf transformation 138] 238. predd(paul) [cnf transformation 63] 241. predj(X0) | ~room(X0) | room(sK0) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145] 242. predj(X0) | ~room(X0) | mary != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145] 243. predj(X0) | ~room(X0) | paul != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145] 244. predj(X0) | ~room(X0) | fred != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145] 245. predj(X0) | ~room(X0) | alice != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145] 246. predj(X0) | ~room(X0) | john != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145] 268. 5 <=> predd(paul) [avatar definition] 277. 7 <=> predj(mary) [avatar definition] 279. ~predj(mary) <- (~7) [avatar component clause 277] 280. ~5 | ~7 [avatar split clause 236,277,268] 281. 5 [avatar split clause 238,268] 284. predj(X0) | ~room(X0) | john != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 246,230] 285. predj(X0) | ~room(X0) | john != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,229] 286. predj(X0) | ~room(X0) | john != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 285,228] 287. predj(X0) | ~room(X0) | john != sK0 | ~room(mary) [subsumption resolution 286,227] 288. predj(X0) | ~room(X0) | john != sK0 [subsumption resolution 287,226] 290. 8 <=> john = sK0 [avatar definition] 292. john != sK0 <- (~8) [avatar component clause 290] 294. 9 <=> ! [X0] : (predj(X0) | ~room(X0)) [avatar definition] 295. ~room(X0) | predj(X0) <- (9) [avatar component clause 294] 296. ~8 | 9 [avatar split clause 288,294,290] 297. predj(X0) | ~room(X0) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 245,230] 298. predj(X0) | ~room(X0) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 297,229] 299. predj(X0) | ~room(X0) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 298,228] 300. predj(X0) | ~room(X0) | alice != sK0 | ~room(mary) [subsumption resolution 299,227] 301. predj(X0) | ~room(X0) | alice != sK0 [subsumption resolution 300,226] 303. 10 <=> alice = sK0 [avatar definition] 305. alice != sK0 <- (~10) [avatar component clause 303] 306. ~10 | 9 [avatar split clause 301,294,303] 307. predj(X0) | ~room(X0) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 244,230] 308. predj(X0) | ~room(X0) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,229] 309. predj(X0) | ~room(X0) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 308,228] 310. predj(X0) | ~room(X0) | fred != sK0 | ~room(mary) [subsumption resolution 309,227] 311. predj(X0) | ~room(X0) | fred != sK0 [subsumption resolution 310,226] 313. 11 <=> fred = sK0 [avatar definition] 315. fred != sK0 <- (~11) [avatar component clause 313] 316. ~11 | 9 [avatar split clause 311,294,313] 317. predj(X0) | ~room(X0) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 243,230] 318. predj(X0) | ~room(X0) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,229] 319. predj(X0) | ~room(X0) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 318,228] 320. predj(X0) | ~room(X0) | paul != sK0 | ~room(mary) [subsumption resolution 319,227] 321. predj(X0) | ~room(X0) | paul != sK0 [subsumption resolution 320,226] 323. 12 <=> paul = sK0 [avatar definition] 325. paul != sK0 <- (~12) [avatar component clause 323] 326. ~12 | 9 [avatar split clause 321,294,323] 327. predj(X0) | ~room(X0) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 242,230] 328. predj(X0) | ~room(X0) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,229] 329. predj(X0) | ~room(X0) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 328,228] 330. predj(X0) | ~room(X0) | mary != sK0 | ~room(mary) [subsumption resolution 329,227] 331. predj(X0) | ~room(X0) | mary != sK0 [subsumption resolution 330,226] 333. 13 <=> mary = sK0 [avatar definition] 335. mary != sK0 <- (~13) [avatar component clause 333] 336. ~13 | 9 [avatar split clause 331,294,333] 337. predj(X0) | ~room(X0) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 241,230] 338. predj(X0) | ~room(X0) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 337,229] 339. predj(X0) | ~room(X0) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 338,228] 340. predj(X0) | ~room(X0) | room(sK0) | ~room(mary) [subsumption resolution 339,227] 341. predj(X0) | ~room(X0) | room(sK0) [subsumption resolution 340,226] 343. 14 <=> room(sK0) [avatar definition] 345. room(sK0) <- (14) [avatar component clause 343] 346. 14 | 9 [avatar split clause 341,294,343] 347. predj(mary) <- (9) [resolution 295,226] 352. $false <- (~7, 9) [subsumption resolution 347,279] 353. 7 | ~9 [avatar contradiction clause 352] 401. alice = sK0 | fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (14) [resolution 231,345] 402. fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (~10, 14) [subsumption resolution 401,305] 403. paul = sK0 | mary = sK0 | john = sK0 <- (~10, ~11, 14) [subsumption resolution 402,315] 404. mary = sK0 | john = sK0 <- (~10, ~11, ~12, 14) [subsumption resolution 403,325] 405. john = sK0 <- (~10, ~11, ~12, ~13, 14) [subsumption resolution 404,335] 406. $false <- (~8, ~10, ~11, ~12, ~13, 14) [subsumption resolution 405,292] 407. 8 | 10 | 11 | 12 | 13 | ~14 [avatar contradiction clause 406] 408. $false [avatar sat refutation 280,281,296,306,316,326,336,346,353,407] % SZS output end Proof for 742911601365960035600626 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Francis is the only person in the room. 'Brandon is richer than Francis' only if 'Francis who neither is richer than Martha nor is richer than Brandon is quiet'. If 'Francis is richer than Kate' then 'Francis is older than Brandon'. Francis is older than Kate. Everyone in the room is quieter than Elizabeth only if they is old. Francis who is quieter than Martha is richer than Brandon. Francis is old. Francis is richer than Brandon. Francis is older than Brandon. Everyone outside the room who is tall is older than Brandon. Francis is richer than Kate. Francis is richer than Martha. Francis is older than Elizabeth. Everyone in the room who is old either is richer than Martha or is kind but not both. Francis either is quieter than Martha or is quiet but not both. Not everyone anywhere who is richer than Martha is richer than Elizabeth.

Francis is older than Martha.

neutral

room(francis)&(![X]:(room(X)=>(X='francis')))& ((richer(francis,brandon))=>((~((richer(martha,francis))|(richer(brandon,francis))))&(quiet(francis))))& ((richer(kate,francis))=>(older(brandon,francis)))& (older(kate,francis))& (![X]:(room(X)=>(((old(X))<=(quieter(elizabeth,X))))))& ((quieter(martha,francis))&(richer(brandon,francis)))& (old(francis))& (richer(brandon,francis))& (older(brandon,francis))& (![X]:(~room(X)=>(((tall(X))=>(older(brandon,X))))))& (richer(kate,francis))& (richer(martha,francis))& (older(elizabeth,francis))& (![X]:(room(X)=>(((old(X))=>(((richer(martha,X))<~>(kind(X))))))))& (((quieter(martha,francis))<~>(quiet(francis))))& (~![X]:(anywhere(X)=>(((richer(martha,X))=>(richer(elizabeth,X))))))& (quieter(francis,kate))& (richer(elizabeth,francis))& ((tall(francis))&(quieter(martha,francis)))& (![X]:(kind(X)=>tall(X)))

room(francis)&(![X]:(room(X)=>(X='francis')))& older(martha,francis)

There is a room. If “at least one person outside the room is a cybersecurity expert” then “if someone either volunteers for local environmental conservation projects or enjoys fishing but not both then he/she is a certified scuba diver with advanced underwater photography skills and vice versa”. “Someone in the room owns a high-end gaming PC with custom-built components” unless “not everyone in the room does not write a travel blog or regularly goes on multi-day backpacking trips in national parks”. Everyone in the room who does not write a travel blog hosts a popular podcast about emerging technologies. Everyone in the room who enjoys coding in Python owns an Android phone. At least one person outside the room enjoys coding in Python. Everyone in the room who is a cybersecurity expert owns a high-end gaming PC with custom-built components. Only one person in the room owns an Android phone. Everyone in the room who either does practice yoga or enjoys kayaking but not both owns an Android phone. More than one person anywhere volunteers for local environmental conservation projects. Everyone in the room who writes a travel blog is a certified scuba diver with advanced underwater photography skills. At least one person outside the room enjoys fishing and enjoys coding in Python. Only one person in the room collects antique clocks, hosts a popular podcast about emerging technologies or enjoys logic puzzles. More than one person anywhere either does practice yoga or enjoys kayaking but not both. At least one person outside the room collects antique clocks. If someone owns a high-end gaming PC with custom-built components then he/she hosts regular game nights featuring complex strategy games and is a certified scuba diver with advanced underwater photography skills. Everyone in the room who hosts a popular podcast about emerging technologies enjoys coding in Python. More than one person in the room is a cybersecurity expert. If someone owns an Android phone then he/she enjoys kayaking and vice versa. At least one person outside the room hosts a popular podcast about emerging technologies. Everyone in the room who hosts regular game nights featuring complex strategy games regularly goes on multi-day backpacking trips in national parks.

Everyone in the room enjoys logic puzzles.

contradiction

(there_is_a_room)& ((((?[X]:(~room(X)&is_a_cybersecurity_expert(X)))))=>((![X]:((((volunteers_for_local_environmental_conservation_projects(X))<~>(enjoys_fishing(X))))<=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (~(~![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(does_not_write_a_travel_blog(X))))))=>(?[X]:(room(X)&(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))& (![X]:(room(X)=>(((does_not_write_a_travel_blog(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(owns_an_Android_phone(X))))))& (((?[X]:(~room(X)&enjoys_coding_in_Python(X)))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (((?[X]:(room(X)&owns_an_Android_phone(X)))&(![X,Y]:((room(X)&room(Y)&(owns_an_Android_phone(X))&(owns_an_Android_phone(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((((does_practice_yoga(X))<~>(enjoys_kayaking(X))))=>(owns_an_Android_phone(X))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(volunteers_for_local_environmental_conservation_projects(X)&volunteers_for_local_environmental_conservation_projects(Y))&(X!=Y))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (((?[X]:(~room(X)&((enjoys_fishing(X))&(enjoys_coding_in_Python(X)))))))& (((?[X]:(room(X)&((collects_antique_clocks(X))|(hosts_a_popular_podcast_about_emerging_technologies(X))|(enjoys_logic_puzzles(X)))))&(![X,Y]:((room(X)&room(Y)&(((collects_antique_clocks(X))|(hosts_a_popular_podcast_about_emerging_technologies(X))|(enjoys_logic_puzzles(X))))&(((collects_antique_clocks(Y))|(hosts_a_popular_podcast_about_emerging_technologies(Y))|(enjoys_logic_puzzles(Y)))))=>(X=Y)))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(((does_practice_yoga(X))<~>(enjoys_kayaking(X)))&((does_practice_yoga(Y))<~>(enjoys_kayaking(Y))))&(X!=Y))))& (((?[X]:(~room(X)&collects_antique_clocks(X)))))& ((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(enjoys_coding_in_Python(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_a_cybersecurity_expert(X)&is_a_cybersecurity_expert(Y))&(X!=Y))))& ((![X]:((owns_an_Android_phone(X))<=>(enjoys_kayaking(X)))))& (((?[X]:(~room(X)&hosts_a_popular_podcast_about_emerging_technologies(X)))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))

(there_is_a_room)& ![X]:(room(X)=>(enjoys_logic_puzzles(X)))

% SZS status Unsatisfiable for 1034340862576892325726294 % SZS output start Proof for 1034340862576892325726294 46. ~~! [X0] : (room(X0) => (~predp(X0) | predd(X0))) => ? [X0] : (preda(X0) & room(X0)) [input p2] 50. ! [X0] : (room(X0) => (predc(X0) => preda(X0))) [input p6] 56. ! [X0,X1] : (((predk(X1) | predf(X1) | predl(X1)) & (predk(X0) | predf(X0) | predl(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : ((predk(X0) | predf(X0) | predl(X0)) & room(X0)) [input p12] 59. ! [X0] : (preda(X0) => (predh(X0) & prede(X0))) [input p15] 61. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) [input p17] 64. ! [X0] : (room(X0) => (prede(X0) => predd(X0))) [input p20] 65. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 67. ~~! [X0] : (room(X0) => (~predp(X0) | predd(X0))) => ? [X1] : (preda(X1) & room(X1)) [rectify 46] 68. ! [X0] : (room(X0) => (~predp(X0) | predd(X0))) => ? [X1] : (preda(X1) & room(X1)) [flattening 67] 70. ! [X0,X1] : (((predk(X1) | predf(X1) | predl(X1)) & (predk(X0) | predf(X0) | predl(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : ((predk(X2) | predf(X2) | predl(X2)) & room(X2)) [rectify 56] 71. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 65] 148. ? [X1] : (preda(X1) & room(X1)) | ? [X0] : ((predp(X0) & ~predd(X0)) & room(X0)) [ennf transformation 68] 149. ? [X1] : (preda(X1) & room(X1)) | ? [X0] : (predp(X0) & ~predd(X0) & room(X0)) [flattening 148] 154. ! [X0] : ((preda(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 50] 155. ! [X0] : (preda(X0) | ~predc(X0) | ~room(X0)) [flattening 154] 162. ! [X0,X1] : (X0 = X1 | ((~predk(X1) & ~predf(X1) & ~predl(X1)) | (~predk(X0) & ~predf(X0) & ~predl(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : ((predk(X2) | predf(X2) | predl(X2)) & room(X2)) [ennf transformation 70] 163. ! [X0,X1] : (X0 = X1 | (~predk(X1) & ~predf(X1) & ~predl(X1)) | (~predk(X0) & ~predf(X0) & ~predl(X0)) | ~room(X1) | ~room(X0)) & ? [X2] : ((predk(X2) | predf(X2) | predl(X2)) & room(X2)) [flattening 162] 164. ! [X0] : ((predh(X0) & prede(X0)) | ~preda(X0)) [ennf transformation 59] 167. ! [X0] : ((predd(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 64] 168. ! [X0] : (predd(X0) | ~prede(X0) | ~room(X0)) [flattening 167] 169. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 71] 170. ! [X0] : ((~predk(X0) & ~predf(X0) & ~predl(X0)) | ~sP0(X0)) [predicate definition introduction] 171. ! [X0,X1] : (X0 = X1 | (~predk(X1) & ~predf(X1) & ~predl(X1)) | sP0(X0) | ~room(X1) | ~room(X0)) & ? [X2] : ((predk(X2) | predf(X2) | predl(X2)) & room(X2)) [definition folding 163,170] 175. ? [X0] : (preda(X0) & room(X0)) | ? [X1] : (predp(X1) & ~predd(X1) & room(X1)) [rectify 149] 176. ? [X0] : (preda(X0) & room(X0)) => (preda(sK1) & room(sK1)) [choice axiom] 177. ? [X1] : (predp(X1) & ~predd(X1) & room(X1)) => (predp(sK2) & ~predd(sK2) & room(sK2)) [choice axiom] 178. (preda(sK1) & room(sK1)) | (predp(sK2) & ~predd(sK2) & room(sK2)) [skolemisation 175,177,176] 188. ! [X0] : ((~predk(X0) & ~predf(X0) & ~predl(X0)) | ~sP0(X0)) [nnf transformation 170] 189. ? [X2] : ((predk(X2) | predf(X2) | predl(X2)) & room(X2)) => ((predk(sK8) | predf(sK8) | predl(sK8)) & room(sK8)) [choice axiom] 190. ! [X0,X1] : (X0 = X1 | (~predk(X1) & ~predf(X1) & ~predl(X1)) | sP0(X0) | ~room(X1) | ~room(X0)) & ((predk(sK8) | predf(sK8) | predl(sK8)) & room(sK8)) [skolemisation 171,189] 197. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) => (sK12 != sK13 & predc(sK13) & predc(sK12) & room(sK13) & room(sK12)) [choice axiom] 198. sK12 != sK13 & predc(sK13) & predc(sK12) & room(sK13) & room(sK12) [skolemisation 61,197] 286. room(sK1) | room(sK2) [cnf transformation 178] 287. room(sK1) | ~predd(sK2) [cnf transformation 178] 296. ~predc(X0) | preda(X0) | ~room(X0) [cnf transformation 155] 311. ~sP0(X0) | ~predk(X0) [cnf transformation 188] 316. ~predk(X1) | X0 = X1 | sP0(X0) | ~room(X1) | ~room(X0) [cnf transformation 190] 324. ~preda(X0) | prede(X0) [cnf transformation 164] 327. room(sK12) [cnf transformation 198] 328. room(sK13) [cnf transformation 198] 329. predc(sK12) [cnf transformation 198] 331. sK12 != sK13 [cnf transformation 198] 336. ~prede(X0) | predd(X0) | ~room(X0) [cnf transformation 168] 337. ~room(X0) | predk(X0) [cnf transformation 169] 367. 8 <=> predd(sK2) [avatar definition] 369. ~predd(sK2) <- (~8) [avatar component clause 367] 372. 9 <=> room(sK2) [avatar definition] 374. room(sK2) <- (9) [avatar component clause 372] 377. 10 <=> room(sK1) [avatar definition] 379. room(sK1) <- (10) [avatar component clause 377] 381. ~8 | 10 [avatar split clause 287,377,367] 382. 9 | 10 [avatar split clause 286,377,372] 421. predk(sK12) [resolution 337,327] 422. predk(sK13) [resolution 337,328] 463. preda(sK12) | ~room(sK12) [resolution 296,329] 465. preda(sK12) [subsumption resolution 463,327] 489. prede(sK12) [resolution 465,324] 566. predd(sK12) | ~room(sK12) [resolution 489,336] 567. predd(sK12) [subsumption resolution 566,327] 693. sK12 = X2 | sP0(X2) | ~room(sK12) | ~room(X2) [resolution 316,421] 695. ~room(X2) | sP0(X2) | sK12 = X2 [subsumption resolution 693,327] 724. 42 <=> sP0(sK2) [avatar definition] 726. sP0(sK2) <- (42) [avatar component clause 724] 744. 45 <=> sP0(sK1) [avatar definition] 745. ~sP0(sK1) <- (~45) [avatar component clause 744] 746. sP0(sK1) <- (45) [avatar component clause 744] 760. predk(sK2) <- (9) [resolution 374,337] 823. sP0(sK2) | sK2 = sK12 <- (9) [resolution 695,374] 827. 50 <=> sK2 = sK12 [avatar definition] 829. sK2 = sK12 <- (50) [avatar component clause 827] 830. 50 | 42 | ~9 [avatar split clause 823,372,724,827] 836. ~predk(sK2) <- (42) [resolution 726,311] 839. $false <- (9, 42) [subsumption resolution 836,760] 840. ~9 | ~42 [avatar contradiction clause 839] 846. sP0(sK1) | sK1 = sK12 <- (10) [resolution 379,695] 848. predk(sK1) <- (10) [resolution 379,337] 850. 52 <=> sK1 = sK12 [avatar definition] 852. sK1 = sK12 <- (52) [avatar component clause 850] 853. 52 | 45 | ~10 [avatar split clause 846,377,744,850] 893. ~predk(sK1) <- (45) [resolution 746,311] 896. $false <- (10, 45) [subsumption resolution 893,848] 897. ~10 | ~45 [avatar contradiction clause 896] 937. sK1 != sK13 <- (52) [forward demodulation 331,852] 942. sK13 = X0 | sP0(X0) | ~room(sK13) | ~room(X0) [resolution 422,316] 943. ~room(X0) | sP0(X0) | sK13 = X0 [subsumption resolution 942,328] 998. sP0(sK1) | sK1 = sK13 <- (10) [resolution 943,379] 1000. sK1 = sK13 <- (10, ~45) [subsumption resolution 998,745] 1001. $false <- (10, ~45, 52) [subsumption resolution 1000,937] 1002. ~10 | 45 | ~52 [avatar contradiction clause 1001] 1029. predd(sK2) <- (50) [forward demodulation 567,829] 1030. $false <- (~8, 50) [subsumption resolution 1029,369] 1031. 8 | ~50 [avatar contradiction clause 1030] 1041. $false [avatar sat refutation 381,382,830,840,853,897,1002,1031] % SZS output end Proof for 1034340862576892325726294 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s % ------------------------------ % ------------------------------

Bonnie, Misha, Shari are the only persons in the room. “Bonnie dreamt that “Misha collects antique clocks”” if “Shari collects modern art”. If “Shari hosts a YouTube channel dedicated to art tutorials” then “Misha practices zumba”. “Shari enjoys spelunking” if “Shari plays eSports competitively” and vice versa. Either “Bonnie either collects antique clocks or plays eSports competitively but not both” or “Shari collects classic novels” but not both. “It is not the case that “Shari enjoys spelunking”” if “Bonnie owns an extensive assortment of vintage comic book memorabilia”. Either “Misha plays eSports competitively” or “Bonnie enjoys spelunking” but not both. “Shari can play the harmonica” if “Bonnie regularly goes on multi-day backpacking trips in national parks and enjoys spelunking”. “Shari regularly goes on multi-day backpacking trips in national parks” if “Shari owns an extensive assortment of vintage comic book memorabilia” and vice versa. Bonnie plays eSports competitively. Bonnie collects modern art. Shari uses a Windows laptop. If someone uses a Windows laptop then he/she practices zumba and vice versa. Shari hosts a YouTube channel dedicated to art tutorials.

Misha uses a Windows laptop.

entailment

room(bonnie)&room(misha)&room(shari)&(![X]:(room(X)=>(X='bonnie'|X='misha'|X='shari')))& ((collects_modern_art(shari))=>((bonnie_dream=>(collects_antique_clocks(misha)))))& ((hosts_a_YouTube_channel_dedicated_to_art_tutorials(shari))=>(practices_zumba(misha)))& ((plays_eSports_competitively(shari))<=>(enjoys_spelunking(shari)))& ((((collects_antique_clocks(bonnie))<~>(plays_eSports_competitively(bonnie))))<~>(collects_classic_novels(shari)))& ((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(bonnie))=>(~(enjoys_spelunking(shari))))& ((plays_eSports_competitively(misha))<~>(enjoys_spelunking(bonnie)))& ((((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(bonnie))&(enjoys_spelunking(bonnie))))=>(can_play_the_harmonica(shari)))& ((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(shari))<=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(shari)))& (plays_eSports_competitively(bonnie))& (collects_modern_art(bonnie))& (uses_a_Windows_laptop(shari))& (enjoys_spelunking(bonnie))& ((![X]:((uses_a_Windows_laptop(X))<=>(practices_zumba(X)))))& (uses_a_Windows_laptop(bonnie))& (plays_eSports_competitively(shari))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(bonnie))& ((![X]:((((collects_antique_clocks(X))<~>(plays_eSports_competitively(X))))=>(can_play_the_harmonica(X)))))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(shari))& (collects_classic_novels(misha))& ((![X]:((((practices_zumba(X))&(collects_classic_novels(X))))<=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))& (practices_zumba(bonnie))& (((can_play_the_harmonica(shari))|(collects_modern_art(shari))))& ((?[X,Y]:(room(X)&room(Y)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)&regularly_goes_on_multi-day_backpacking_trips_in_national_parks(Y))&(X!=Y))))& (collects_classic_novels(shari))& ((![X]:((practices_zumba(X))<=>(enjoys_spelunking(X)))))

room(bonnie)&room(misha)&room(shari)&(![X]:(room(X)=>(X='bonnie'|X='misha'|X='shari')))& uses_a_Windows_laptop(misha)

% SZS status Unsatisfiable for 2048785695735418276414975 % SZS output start Proof for 2048785695735418276414975 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. predc(fred) => predh(paul) [input p2] 57. ! [X0] : (predi(X0) <=> predh(X0)) [input p13] 62. predc(fred) [input p18] 70. ~(predi(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 148. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 148] 150. predh(paul) | ~predc(fred) [ennf transformation 46] 152. ~predi(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 153. ~predi(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 152] 159. ! [X0] : ((predi(X0) | ~predh(X0)) & (predh(X0) | ~predi(X0))) [nnf transformation 57] 165. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 166. ~predi(paul) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 153,165] 247. room(mary) [cnf transformation 149] 248. room(paul) [cnf transformation 149] 249. room(fred) [cnf transformation 149] 250. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 149] 251. predh(paul) | ~predc(fred) [cnf transformation 150] 267. ~predh(X0) | predi(X0) [cnf transformation 159] 271. predc(fred) [cnf transformation 62] 285. ~predi(paul) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 286. ~predi(paul) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 287. ~predi(paul) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 288. ~predi(paul) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 290. 1 <=> predc(fred) [avatar definition] 294. 2 <=> predh(paul) [avatar definition] 296. predh(paul) <- (2) [avatar component clause 294] 297. ~1 | 2 [avatar split clause 251,294,290] 352. 1 [avatar split clause 271,290] 354. ~predi(paul) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 288,249] 355. ~predi(paul) | fred != sK2 | ~room(mary) [subsumption resolution 354,248] 356. ~predi(paul) | fred != sK2 [subsumption resolution 355,247] 358. 13 <=> fred = sK2 [avatar definition] 360. fred != sK2 <- (~13) [avatar component clause 358] 362. 14 <=> predi(paul) [avatar definition] 365. ~13 | ~14 [avatar split clause 356,362,358] 366. ~predi(paul) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 287,249] 367. ~predi(paul) | paul != sK2 | ~room(mary) [subsumption resolution 366,248] 368. ~predi(paul) | paul != sK2 [subsumption resolution 367,247] 370. 15 <=> paul = sK2 [avatar definition] 372. paul != sK2 <- (~15) [avatar component clause 370] 373. ~15 | ~14 [avatar split clause 368,362,370] 374. ~predi(paul) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 286,249] 375. ~predi(paul) | mary != sK2 | ~room(mary) [subsumption resolution 374,248] 376. ~predi(paul) | mary != sK2 [subsumption resolution 375,247] 378. 16 <=> mary = sK2 [avatar definition] 380. mary != sK2 <- (~16) [avatar component clause 378] 381. ~16 | ~14 [avatar split clause 376,362,378] 382. ~predi(paul) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 285,249] 383. ~predi(paul) | room(sK2) | ~room(mary) [subsumption resolution 382,248] 384. ~predi(paul) | room(sK2) [subsumption resolution 383,247] 386. 17 <=> room(sK2) [avatar definition] 388. room(sK2) <- (17) [avatar component clause 386] 389. 17 | ~14 [avatar split clause 384,362,386] 393. predi(paul) <- (2) [resolution 267,296] 396. 14 | ~2 [avatar split clause 393,294,362] 464. paul = sK2 | mary = sK2 | fred = sK2 <- (17) [resolution 250,388] 491. mary = sK2 | fred = sK2 <- (~15, 17) [subsumption resolution 464,372] 492. fred = sK2 <- (~15, ~16, 17) [subsumption resolution 491,380] 493. $false <- (~13, ~15, ~16, 17) [subsumption resolution 492,360] 494. 13 | 15 | 16 | ~17 [avatar contradiction clause 493] 495. $false [avatar sat refutation 297,352,365,373,381,389,396,494] % SZS output end Proof for 2048785695735418276414975 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara is the only person in the room. “If someone owns a smart tv then he/she is a culinary enthusiast who experiments with international cuisines and vice versa” unless “Barbara practices tai chi”. Barbara neither practices tai chi nor is a member of a local theater group specializing in improv. Barbara collects classic novels. If someone neither is not a member of a local theater group specializing in improv nor owns a 3D printer then he/she does not volunteer for local environmental conservation projects. If someone does not own a 3D printer then he/she neither enjoys coding in Python nor is a culinary enthusiast who experiments with international cuisines and vice versa.

It is not the case that “Barbara is a member of a local theater group specializing in improv”.

entailment

room(barbara)&(![X]:(room(X)=>(X='barbara')))& (~(practices_tai_chi(barbara))=>((![X]:((owns_a_smart_tv(X))<=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (~((practices_tai_chi(barbara))|(is_a_member_of_a_local_theater_group_specializing_in_improv(barbara))))& (collects_classic_novels(barbara))& ((![X]:((~((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(owns_a_3D_printer(X))))=>(does_not_volunteer_for_local_environmental_conservation_projects(X)))))& ((![X]:((does_not_own_a_3D_printer(X))<=>(~((enjoys_coding_in_Python(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(barbara))& (owns_a_smart_tv(barbara))& (![X]:(room(X)=>(((can_play_the_flute(X))|(does_not_own_a_smart_tv(X))))))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(barbara))& ((![X]:((practices_tai_chi(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))& (volunteers_for_local_environmental_conservation_projects(barbara))

room(barbara)&(![X]:(room(X)=>(X='barbara')))& ~(is_a_member_of_a_local_theater_group_specializing_in_improv(barbara))

% SZS status Unsatisfiable for 861820600519193889811380 % SZS output start Proof for 861820600519193889811380 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ~(preda(mary) | predh(mary)) [input p2] 56. ~(~preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 136. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 138. ~preda(mary) & ~predh(mary) [ennf transformation 46] 140. preda(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 56] 143. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom] 144. preda(mary) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 140,143] 225. room(mary) [cnf transformation 136] 226. ~room(X0) | mary = X0 [cnf transformation 136] 230. ~preda(mary) [cnf transformation 138] 234. preda(mary) | room(sK0) | ~room(mary) [cnf transformation 144] 235. preda(mary) | mary != sK0 | ~room(mary) [cnf transformation 144] 249. mary != sK0 | ~room(mary) [subsumption resolution 235,230] 250. mary != sK0 [subsumption resolution 249,225] 251. room(sK0) | ~room(mary) [subsumption resolution 234,230] 252. room(sK0) [subsumption resolution 251,225] 256. mary = sK0 [resolution 226,252] 257. $false [subsumption resolution 256,250] % SZS output end Proof for 861820600519193889811380 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Nora, Bryce, Victoria, Beth are the only persons in the room. Everyone outside the room who is an amateur astronomer who builds and uses custom telescopes creates bespoke furniture pieces from reclaimed wood, enjoys kayaking and is a member of a local theater group specializing in improv. Everyone in the room who creates bespoke furniture pieces from reclaimed wood, enjoys kayaking and is a member of a local theater group specializing in improv collects historical artifacts related to ancient civilizations. Bryce enjoys bird watching. If someone collects historical artifacts related to ancient civilizations, has a specialized collection of handmade artisan pottery or is an amateur astronomer who builds and uses custom telescopes then he/she is an amateur astronomer who builds and uses custom telescopes or practices digital art or both and vice versa. Everyone in the room who practices pilates enjoys bird watching. Everyone in the room who enjoys bird watching is an amateur astronomer who builds and uses custom telescopes. Everyone in the room is an amateur astronomer who builds and uses custom telescopes only if they collects rare minerals. Not everyone anywhere who collects rare minerals enjoys landscape photography. Everyone in the room who practices pilates has a vast collection of first-edition science fiction novels. Everyone in the room who has a vast collection of first-edition science fiction novels collects rare minerals. Everyone in the room who enjoys landscape photography enjoys kayaking and exploring remote waterways. Someone in the room reads mystery novels or creates bespoke furniture pieces from reclaimed wood or both. No one anywhere who enjoys windsurfing enjoys kayaking, has a specialized collection of handmade artisan pottery or reads mystery novels.

Victoria reads mystery novels.

contradiction

room(nora)&room(bryce)&room(victoria)&room(beth)&(![X]:(room(X)=>(X='nora'|X='bryce'|X='victoria'|X='beth')))& (![X]:(~room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(enjoys_kayaking(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))))& (![X]:(room(X)=>(((((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(enjoys_kayaking(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (enjoys_bird_watching(bryce))& ((![X]:((((collects_historical_artifacts_related_to_ancient_civilizations(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))<=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(practices_digital_art(X)))))))& (![X]:(room(X)=>(((practices_pilates(X))=>(enjoys_bird_watching(X))))))& (![X]:(room(X)=>(((enjoys_bird_watching(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((collects_rare_minerals(X))<=(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (~![X]:(anywhere(X)=>(((collects_rare_minerals(X))=>(enjoys_landscape_photography(X))))))& (![X]:(room(X)=>(((practices_pilates(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (?[X]:(room(X)&(((reads_mystery_novels(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (~?[X]:(anywhere(X)=>(((enjoys_windsurfing(X))=>(((enjoys_kayaking(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))|(reads_mystery_novels(X))))))))

room(nora)&room(bryce)&room(victoria)&room(beth)&(![X]:(room(X)=>(X='nora'|X='bryce'|X='victoria'|X='beth')))& reads_mystery_novels(victoria)

% SZS status Unsatisfiable for 8207837393737814276459204 % SZS output start Proof for 8207837393737814276459204 57. ~? [X0] : (anywhere(X0) => (predf(X0) => (predl(X0) | predw(X0) | predy(X0)))) [input p13] 58. predl(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 59. ~? [X0] : (anywhere(X0) => (predl(X0) | predw(X0) | predy(X0))) [pure predicate removal 57] 67. ~? [X0] : (predl(X0) | predw(X0) | predy(X0)) [pure predicate removal 59] 149. ! [X0] : (~predl(X0) & ~predw(X0) & ~predy(X0)) [ennf transformation 67] 150. predl(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 58] 151. predl(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 150] 257. ~predl(X0) [cnf transformation 149] 263. predl(fred) [cnf transformation 151] 273. $false [subsumption resolution 263,257] % SZS output end Proof for 8207837393737814276459204 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If “everyone in the room does not create bespoke furniture pieces from reclaimed wood and does not play eSports competitively” then “everyone in the room does not volunteer for local environmental conservation projects, does not enjoy bird watching or does not practice archery” otherwise “everyone in the room is not a Linux enthusiast or does not compose and performs experimental electronic music or both”. If “everyone outside the room does not play as a goalkeeper for a local amateur soccer team and does not compose and performs experimental electronic music” then “everyone in the room does not collect action figures, does not collect rare sneakers or is not a Linux enthusiast” otherwise “everyone in the room does not work as a freelance web developer specializing in e-commerce sites, does not collect action figures or does not collect antique jewelry”. “At least one person in the room does not practice archery, is not a craft beer aficionado or does not collect antique jewelry” only if “everyone in the room does not work as a freelance web developer specializing in e-commerce sites”. “Everyone in the room does not enjoy mountain biking” if “everyone outside the room does not collect action figures”. “Everyone in the room does not play eSports competitively” only if “everyone in the room does not mentor a youth basketball team on weekends and does not develop open-source software projects in their free time”. “If someone either does not collect rare sneakers or does not volunteer for local environmental conservation projects but not both then he/she does not play eSports competitively” if “everyone in the room does not enjoy writing detailed reviews of new and classic board games”. Everyone outside the room does not work as a freelance web developer specializing in e-commerce sites and does not collect antique jewelry. More than one person outside the room either does not collect antique jewelry or does not own a microscope but not both. Everyone in the room does not own a microscope.

Everyone outside the room does not own a microscope.

contradiction

(there_is_a_room)& (((![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))&(does_not_play_eSports_competitively(X))))))=>(![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_not_enjoy_bird_watching(X))|(does_not_practice_archery(X)))))))&((~(![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))&(does_not_play_eSports_competitively(X)))))))=>(![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(does_not_compose_and_performs_experimental_electronic_music(X))))))))& (((![X]:(~room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(does_not_compose_and_performs_experimental_electronic_music(X))))))=>(![X]:(room(X)=>(((does_not_collect_action_figures(X))|(does_not_collect_rare_sneakers(X))|(is_not_a_Linux_enthusiast(X)))))))&((~(![X]:(~room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(does_not_compose_and_performs_experimental_electronic_music(X)))))))=>(![X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(does_not_collect_action_figures(X))|(does_not_collect_antique_jewelry(X))))))))& ((((?[X]:(room(X)&((does_not_practice_archery(X))|(is_not_a_craft_beer_aficionado(X))|(does_not_collect_antique_jewelry(X)))))))=>(![X]:(room(X)=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))& ((![X]:(~room(X)=>(does_not_collect_action_figures(X))))=>(![X]:(room(X)=>(does_not_enjoy_mountain_biking(X)))))& ((![X]:(room(X)=>(does_not_play_eSports_competitively(X))))=>(![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))&(does_not_develop_open-source_software_projects_in_their_free_time(X)))))))& ((![X]:(room(X)=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))=>((![X]:((((does_not_collect_rare_sneakers(X))<~>(does_not_volunteer_for_local_environmental_conservation_projects(X))))=>(does_not_play_eSports_competitively(X))))))& (![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))|(does_not_collect_antique_jewelry(X))))))& ((![X]:((((does_not_collect_antique_jewelry(X))&(does_not_enjoy_bird_watching(X))))=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_not_collect_action_figures(X))|(is_not_a_scotch_connoisseur(X)))))))& (![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(~room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(does_not_collect_antique_jewelry(X))))))& (![X]:(room(X)=>(does_not_mentor_a_youth_basketball_team_on_weekends(X))))& (![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(does_not_collect_rare_sneakers(X))))))& (((?[X]:(room(X)&((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_collect_rare_sneakers(X))|(does_not_compose_and_performs_experimental_electronic_music(X)))))))& (((?[X]:(anywhere(X)&does_not_enjoy_mountain_biking(X)))))& (![X]:(room(X)=>(does_not_travel_domestically_frequently(X))))& (((?[X]:(room(X)&is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(does_not_travel_domestically_frequently(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& ((![X]:((((does_not_collect_rare_sneakers(X))<~>(does_not_volunteer_for_local_environmental_conservation_projects(X))))=>(does_not_play_eSports_competitively(X)))))& ((?[X,Y]:(~room(X)&~room(Y)&(((does_not_collect_antique_jewelry(X))<~>(does_not_own_a_microscope(X)))&((does_not_collect_antique_jewelry(Y))<~>(does_not_own_a_microscope(Y))))&(X!=Y))))& (![X]:(room(X)=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))& (![X]:(room(X)=>(does_not_volunteer_for_local_environmental_conservation_projects(X))))& (![X]:(room(X)=>(does_not_own_a_microscope(X))))& (![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))<~>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))

(there_is_a_room)& ![X]:(~room(X)=>(does_not_own_a_microscope(X)))

% SZS status Unsatisfiable for 7062937484199381650271484 % SZS output start Proof for 7062937484199381650271484 54. ! [X0] : (~room(X0) => (~predg(X0) & ~predu(X0))) [input p10] 63. ? [X0,X1] : (X0 != X1 & (~predg(X1) <~> ~preda(X1)) & (~predg(X0) <~> ~preda(X0)) & ~room(X1) & ~room(X0)) [input p19] 66. ! [X0] : (room(X0) => ~preda(X0)) [input p22] 68. ! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room [input hypothesis] 98. ! [X0] : (~room(X0) => ~predg(X0)) [pure predicate removal 54] 103. ! [X0] : (~room(X0) => ~preda(X0)) [pure predicate removal 68] 179. ! [X0] : (~predg(X0) | room(X0)) [ennf transformation 98] 180. ! [X0] : (~preda(X0) | ~room(X0)) [ennf transformation 66] 182. ! [X0] : (~preda(X0) | room(X0)) [ennf transformation 103] 193. ? [X0,X1] : (X0 != X1 & ((preda(X1) | predg(X1)) & (~preda(X1) | ~predg(X1))) & ((preda(X0) | predg(X0)) & (~preda(X0) | ~predg(X0))) & ~room(X1) & ~room(X0)) [nnf transformation 63] 194. ? [X0,X1] : (X0 != X1 & (preda(X1) | predg(X1)) & (~preda(X1) | ~predg(X1)) & (preda(X0) | predg(X0)) & (~preda(X0) | ~predg(X0)) & ~room(X1) & ~room(X0)) [flattening 193] 195. ? [X0,X1] : (X0 != X1 & (preda(X1) | predg(X1)) & (~preda(X1) | ~predg(X1)) & (preda(X0) | predg(X0)) & (~preda(X0) | ~predg(X0)) & ~room(X1) & ~room(X0)) => (sK4 != sK5 & (preda(sK5) | predg(sK5)) & (~preda(sK5) | ~predg(sK5)) & (preda(sK4) | predg(sK4)) & (~preda(sK4) | ~predg(sK4)) & ~room(sK5) & ~room(sK4)) [choice axiom] 196. sK4 != sK5 & (preda(sK5) | predg(sK5)) & (~preda(sK5) | ~predg(sK5)) & (preda(sK4) | predg(sK4)) & (~preda(sK4) | ~predg(sK4)) & ~room(sK5) & ~room(sK4) [skolemisation 194,195] 279. ~predg(X0) | room(X0) [cnf transformation 179] 283. ~room(sK4) [cnf transformation 196] 286. preda(sK4) | predg(sK4) [cnf transformation 196] 290. ~preda(X0) | ~room(X0) [cnf transformation 180] 293. ~preda(X0) | room(X0) [cnf transformation 182] 313. 5 <=> predg(sK4) [avatar definition] 315. predg(sK4) <- (5) [avatar component clause 313] 317. 6 <=> preda(sK4) [avatar definition] 319. preda(sK4) <- (6) [avatar component clause 317] 320. 5 | 6 [avatar split clause 286,317,313] 322. ~preda(X0) [subsumption resolution 293,290] 324. room(sK4) <- (5) [resolution 279,315] 327. $false <- (5) [subsumption resolution 324,283] 328. ~5 [avatar contradiction clause 327] 329. $false <- (6) [subsumption resolution 319,322] 330. ~6 [avatar contradiction clause 329] 333. $false [avatar sat refutation 320,328,330] % SZS output end Proof for 7062937484199381650271484 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Victor, Allan, Jacquetta, Jessie, Christian are the only persons in the room. Only one person in the room does not practice tai chi, is not a coffee connoisseur and does not host a popular podcast about emerging technologies. Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings. Everyone outside the room does not enjoy kayaking. Everyone in the room is not a coffee connoisseur, does not enjoy skydiving or does not practice tai chi. Allan does not practice tai chi. Allan is not an enthusiastic bird watcher who travels for rare sightings. Victor neither is not a coffee connoisseur nor does not practice kickboxing. Victor does not practice tai chi.

Everyone in the room does not practice tai chi.

neutral

room(victor)&room(allan)&room(jacquetta)&room(jessie)&room(christian)&(![X]:(room(X)=>(X='victor'|X='allan'|X='jacquetta'|X='jessie'|X='christian')))& (((?[X]:(room(X)&((does_not_practice_tai_chi(X))&(is_not_a_coffee_connoisseur(X))&(does_not_host_a_popular_podcast_about_emerging_technologies(X)))))&(![X,Y]:((room(X)&room(Y)&(((does_not_practice_tai_chi(X))&(is_not_a_coffee_connoisseur(X))&(does_not_host_a_popular_podcast_about_emerging_technologies(X))))&(((does_not_practice_tai_chi(Y))&(is_not_a_coffee_connoisseur(Y))&(does_not_host_a_popular_podcast_about_emerging_technologies(Y)))))=>(X=Y)))))& (![X]:(room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (![X]:(~room(X)=>(does_not_enjoy_kayaking(X))))& (![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))|(does_not_enjoy_skydiving(X))|(does_not_practice_tai_chi(X))))))& (does_not_practice_tai_chi(allan))& (is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(allan))& (~((is_not_a_coffee_connoisseur(victor))|(does_not_practice_kickboxing(victor))))& (does_not_practice_tai_chi(victor))& (((does_not_have_a_pet_dog(victor))<~>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(victor))))& (![X]:(room(X)=>(((does_not_have_a_pet_dog(X))|(does_not_enjoy_skydiving(X))))))

room(victor)&room(allan)&room(jacquetta)&room(jessie)&room(christian)&(![X]:(room(X)=>(X='victor'|X='allan'|X='jacquetta'|X='jessie'|X='christian')))& ![X]:(room(X)=>(does_not_practice_tai_chi(X)))

Bobby, Christina are the only persons in the room. If "everyone in the room has completed a triathlon or does not have completed a triathlon" then "Bobby enjoys rooftop gardening". Either "Bobby enjoys rooftop gardening" or "everyone in the room has completed a triathlon" but not both. Either "Bobby has completed a triathlon" or "Christina maintains a large, organic vegetable garden year-round" but not both. "Everyone in the room has completed a triathlon or is not a culinary enthusiast who experiments with international cuisines" if "it is true that "not everyone anywhere maintains a large, organic vegetable garden year-round or does not have completed a triathlon"" and vice versa. Everyone in the room has completed a triathlon or is not a culinary enthusiast who experiments with international cuisines. No wise person is patient. Bobby is not a patient person. Bobby maintains a large, organic vegetable garden year-round. Christina maintains a large, organic vegetable garden year-round. No curious person is patient. Everyone in the room enjoys rooftop gardening if they is a patient person. Everyone outside the room who is not a patient curious person is a culinary enthusiast who experiments with international cuisines. Everyone in the room is a wise curious person, has completed a triathlon and is a culinary enthusiast who experiments with international cuisines if they is not a wise person and vice versa. Everyone in the room maintains a large, organic vegetable garden year-round if they is a culinary enthusiast who experiments with international cuisines. Everyone anywhere enjoys rooftop gardening.

Christina is a culinary enthusiast who experiments with international cuisines.

contradiction

room(bobby)&room(christina)&(![X]:(room(X)=>(X='bobby'|X='christina')))& ((![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(has_completed_a_triathlon(X))))))=>(enjoys_rooftop_gardening(bobby)))& ((enjoys_rooftop_gardening(bobby))<~>(![X]:(room(X)=>(has_completed_a_triathlon(X)))))& ((has_completed_a_triathlon(bobby))<~>(maintains_a_large,_organic_vegetable_garden_year-round(christina)))& ((~![X]:(anywhere(X)=>(((does_not_have_completed_a_triathlon(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))<=>(![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(has_completed_a_triathlon(X)))))))& (![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(has_completed_a_triathlon(X))))))& (~?[X]:(wise(X)=>patient(X)))& (~(patient(bobby)&person(bobby)))& (maintains_a_large,_organic_vegetable_garden_year-round(bobby))& (maintains_a_large,_organic_vegetable_garden_year-round(christina))& (~?[X]:(curious(X)=>patient(X)))& (![X]:(room(X)=>(((patient(X)&person(X))=>(enjoys_rooftop_gardening(X))))))& (![X]:(~room(X)=>(((~(patient(X)&curious(X)&person(X)))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((((wise(X)&curious(X)&person(X))&(has_completed_a_triathlon(X))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))<=>(~(wise(X)&person(X)))))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(anywhere(X)=>(enjoys_rooftop_gardening(X))))

room(bobby)&room(christina)&(![X]:(room(X)=>(X='bobby'|X='christina')))& is_a_culinary_enthusiast_who_experiments_with_international_cuisines(christina)

% SZS status Unsatisfiable for 6050197163900841920812712 % SZS output start Proof for 6050197163900841920812712 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (predm(X0) | ~predd(X0))) [input p5] 50. ~? [X0] : (wise(X0) => patient(X0)) [input p6] 54. ~? [X0] : (curious(X0) => patient(X0)) [input p10] 57. ! [X0] : (room(X0) => ((predd(X0) & predm(X0) & person(X0) & curious(X0) & wise(X0)) <=> ~(person(X0) & wise(X0)))) [input p13] 60. predd(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 133. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 134. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 133] 140. ! [X0] : ((predm(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 49] 141. ! [X0] : (predm(X0) | ~predd(X0) | ~room(X0)) [flattening 140] 142. ! [X0] : (~patient(X0) & wise(X0)) [ennf transformation 50] 144. ! [X0] : (~patient(X0) & curious(X0)) [ennf transformation 54] 149. ! [X0] : (((predd(X0) & predm(X0) & person(X0) & curious(X0) & wise(X0)) <=> (~person(X0) | ~wise(X0))) | ~room(X0)) [ennf transformation 57] 153. predd(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 60] 154. predd(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 153] 157. ! [X0] : (sP1(X0) <=> (predd(X0) & predm(X0) & person(X0) & curious(X0) & wise(X0))) [predicate definition introduction] 158. ! [X0] : ((sP1(X0) <=> (~person(X0) | ~wise(X0))) | ~room(X0)) [definition folding 149,157] 175. ! [X0] : ((sP1(X0) | (~predd(X0) | ~predm(X0) | ~person(X0) | ~curious(X0) | ~wise(X0))) & ((predd(X0) & predm(X0) & person(X0) & curious(X0) & wise(X0)) | ~sP1(X0))) [nnf transformation 157] 176. ! [X0] : ((sP1(X0) | ~predd(X0) | ~predm(X0) | ~person(X0) | ~curious(X0) | ~wise(X0)) & ((predd(X0) & predm(X0) & person(X0) & curious(X0) & wise(X0)) | ~sP1(X0))) [flattening 175] 177. ! [X0] : (((sP1(X0) | (person(X0) & wise(X0))) & ((~person(X0) | ~wise(X0)) | ~sP1(X0))) | ~room(X0)) [nnf transformation 158] 178. ! [X0] : (((sP1(X0) | (person(X0) & wise(X0))) & (~person(X0) | ~wise(X0) | ~sP1(X0))) | ~room(X0)) [flattening 177] 261. room(paul) [cnf transformation 134] 279. predm(X0) | ~predd(X0) | ~room(X0) [cnf transformation 141] 280. wise(X0) [cnf transformation 142] 285. curious(X0) [cnf transformation 144] 293. ~sP1(X0) | person(X0) [cnf transformation 176] 296. sP1(X0) | ~predd(X0) | ~predm(X0) | ~person(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 176] 297. ~person(X0) | ~wise(X0) | ~sP1(X0) | ~room(X0) [cnf transformation 178] 299. sP1(X0) | person(X0) | ~room(X0) [cnf transformation 178] 305. predd(paul) [cnf transformation 154] 380. 16 <=> ! [X1] : (predm(X1) | ~room(X1) | ~predd(X1)) [avatar definition] 381. ~predd(X1) | ~room(X1) | predm(X1) <- (16) [avatar component clause 380] 383. 16 [avatar split clause 279,380] 386. sP1(X0) | ~predd(X0) | ~predm(X0) | ~person(X0) | ~wise(X0) [subsumption resolution 296,285] 387. ~predd(X0) | sP1(X0) | ~predm(X0) | ~person(X0) [subsumption resolution 386,280] 388. ~room(X0) | person(X0) [subsumption resolution 299,293] 389. ~person(X0) | ~sP1(X0) | ~room(X0) [subsumption resolution 297,280] 390. ~sP1(X0) | ~room(X0) [subsumption resolution 389,388] 393. person(paul) [resolution 388,261] 398. ~room(paul) | predm(paul) <- (16) [resolution 381,305] 401. predm(paul) <- (16) [subsumption resolution 398,261] 423. sP1(paul) | ~predm(paul) | ~person(paul) [resolution 387,305] 426. sP1(paul) | ~person(paul) <- (16) [subsumption resolution 423,401] 427. sP1(paul) <- (16) [subsumption resolution 426,393] 428. ~room(paul) <- (16) [resolution 427,390] 432. $false <- (16) [subsumption resolution 428,261] 433. ~16 [avatar contradiction clause 432] 434. $false [avatar sat refutation 383,433] % SZS output end Proof for 6050197163900841920812712 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

There is a room. “Everyone in the room does not use a Windows laptop or is not a generous person” only if “everyone in the room who does not use a Windows laptop is calm”. Everyone in the room either is not a generous person or is calm but not both if they is calm. All calm persons are generous. Everyone in the room has a specialized collection of handmade artisan pottery if they does not frequently participates in hackathons and coding competitions. Everyone anywhere does not collect rare sneakers if they does not play as a goalkeeper for a local amateur soccer team. Someone in the room uses a Windows laptop. Everyone anywhere is calm if they does not collect rare sneakers.

Everyone in the room uses a Windows laptop.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((~(generous(X)&person(X)))|(does_not_use_a_Windows_laptop(X))))))=>(![X]:(room(X)=>(((does_not_use_a_Windows_laptop(X))=>(calm(X)))))))& (![X]:(room(X)=>(((calm(X))=>(((~(generous(X)&person(X)))<~>(calm(X))))))))& (![X]:(calm(X)=>generous(X)))& (![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(anywhere(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(does_not_collect_rare_sneakers(X))))))& (?[X]:(room(X)&(uses_a_Windows_laptop(X))))& (![X]:(anywhere(X)=>(((does_not_collect_rare_sneakers(X))=>(calm(X))))))& (![X]:(generous(X)=>calm(X)))& (![X]:(room(X)=>(((((calm(X)&person(X))&(does_not_use_a_Windows_laptop(X))&(~(generous(X)&person(X)))))<=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))=>(((~(calm(X)&person(X)))|(~(calm(X)&generous(X)&person(X)))|(calm(X)&generous(X)&person(X))))))))

(there_is_a_room)& ![X]:(room(X)=>(uses_a_Windows_laptop(X)))

Mark, Beth, Ronald, Donna, Margaret are the only persons in the room. If “Mark uses a Windows laptop, collects foreign coins or does enjoy mountain biking” then “it is not the case that “Beth practices graffiti art and uses a Windows laptop””. “Everyone in the room enjoys landscape photography only if they collects foreign coins” if “everyone in the room enjoys landscape photography or does not own a smartwatch”. If “Beth is dedicated to sustainable living and zero-waste practices” then “everyone in the room who uses a Windows laptop practices graffiti art”. If “Ronald owns a smartwatch” then “if someone uses a Windows laptop then he/she neither enjoys landscape photography nor is a client of LVMH and vice versa” otherwise “not everyone in the room who is a client of LVMH does enjoy mountain biking”. “It is not the case that “Ronald is a client of LVMH”” only if “everyone in the room who is an avid hiker owns a smartwatch”. “Ronald does enjoy mountain biking” if “Beth is right-handed”.

Ronald is a client of LVMH.

neutral

room(mark)&room(beth)&room(ronald)&room(donna)&room(margaret)&(![X]:(room(X)=>(X='mark'|X='beth'|X='ronald'|X='donna'|X='margaret')))& ((((uses_a_Windows_laptop(mark))|(collects_foreign_coins(mark))|(does_enjoy_mountain_biking(mark))))=>(~(((practices_graffiti_art(beth))&(uses_a_Windows_laptop(beth))))))& ((![X]:(room(X)=>(((does_not_own_a_smartwatch(X))|(enjoys_landscape_photography(X))))))=>(![X]:(room(X)=>(((collects_foreign_coins(X))<=(enjoys_landscape_photography(X)))))))& ((is_dedicated_to_sustainable_living_and_zero-waste_practices(beth))=>(![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(practices_graffiti_art(X)))))))& (((owns_a_smartwatch(ronald))=>((![X]:((uses_a_Windows_laptop(X))<=>(~((enjoys_landscape_photography(X))|(is_a_client_of_LVMH(X))))))))&((~(owns_a_smartwatch(ronald)))=>(~![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(does_enjoy_mountain_biking(X))))))))& ((~(is_a_client_of_LVMH(ronald)))=>(![X]:(room(X)=>(((is_an_avid_hiker(X))=>(owns_a_smartwatch(X)))))))& ((is_right-handed(beth))=>(does_enjoy_mountain_biking(ronald)))& ((?[X]:(room(X)&(is_a_client_of_LVMH(X))))=>(![X]:(room(X)=>(((enjoys_landscape_photography(X))<=>(is_a_client_of_LVMH(X)))))))& ((?[X]:(room(X)&(is_an_avid_hiker(X))))=>(is_an_avid_hiker(beth)))& (is_right-handed(ronald))& (![X]:(room(X)=>(((does_not_write_a_travel_blog(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (is_an_avid_hiker(beth))& ((![X]:((enjoys_landscape_photography(X))=>(((does_enjoy_mountain_biking(X))<~>(practices_graffiti_art(X)))))))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(beth))& (![X]:(~room(X)=>(((((does_enjoy_mountain_biking(X))&(is_a_client_of_LVMH(X))))=>(((collects_foreign_coins(X))<~>(owns_a_smartwatch(X))))))))& (![X]:(room(X)=>(((((collects_foreign_coins(X))<~>(owns_a_smartwatch(X))))=>(collects_foreign_coins(X))))))

room(mark)&room(beth)&room(ronald)&room(donna)&room(margaret)&(![X]:(room(X)=>(X='mark'|X='beth'|X='ronald'|X='donna'|X='margaret')))& is_a_client_of_LVMH(ronald)

Either 'everyone in the room is not a wine connoisseur or enjoys kayaking' or 'everyone in the room cannot play the piano or is a scotch connoisseur' but not both. 'Everyone in the room does not enjoy kayaking or can play the piano' only if 'if someone is a scotch connoisseur then he/she can play the piano and vice versa'. No one in the room who writes poetry is a member of a local theater group specializing in improv. Everyone in the room is not a scotch connoisseur or enjoys kayaking.

Everyone in the room can play the piano.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_work_on_fridays(X))|(is_a_cybersecurity_expert(X))))))=>(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(((collects_rare_minerals(X))&(enjoys_kayaking(X)))))))))& ((![X]:(room(X)=>(((enjoys_kayaking(X))|(is_not_a_wine_connoisseur(X))))))<~>(![X]:(room(X)=>(((is_a_scotch_connoisseur(X))|(cannot_play_the_piano(X)))))))& ((![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_enjoy_kayaking(X))))))<=>(![X]:(~room(X)=>(((works_on_fridays(X))|(does_not_enjoy_logic_puzzles(X)))))))& ((~?[X]:(room(X)=>(((writes_poetry(X))|(is_not_a_scotch_connoisseur(X))))))=>(~?[X]:(anywhere(X)=>(((is_not_a_scotch_connoisseur(X))<=>(enjoys_logic_puzzles(X)))))))& ((![X]:(room(X)=>(((can_play_the_piano(X))|(does_not_enjoy_kayaking(X))))))=>((![X]:((is_a_scotch_connoisseur(X))<=>(can_play_the_piano(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))<=(does_not_enjoy_kayaking(X))))))& (![X]:(room(X)=>(((writes_poetry(X))<=(((is_a_scotch_connoisseur(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(works_on_fridays(X))))))))& (~?[X]:(room(X)=>(((writes_poetry(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(works_on_fridays(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((enjoys_kayaking(X))|(is_not_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((((enjoys_kayaking(X))<~>(writes_poetry(X))))=>(((enjoys_kayaking(X))|(enjoys_logic_puzzles(X))))))))& (![X]:(anywhere(X)=>(((is_a_cybersecurity_expert(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(((writes_poetry(X))<~>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=(((writes_poetry(X))<~>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))))& (~?[X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(((is_a_cybersecurity_expert(X))&(can_play_the_piano(X))&(works_on_fridays(X))))))))

(there_is_a_room)& ![X]:(room(X)=>(can_play_the_piano(X)))

% SZS status Unsatisfiable for 8865027769590731436440497 % SZS output start Proof for 8865027769590731436440497 46. ! [X0] : (room(X0) => (~predk(X0) | predd(X0))) <~> ! [X0] : (room(X0) => (~predc(X0) | predh(X0))) [input p2] 49. ! [X0] : (room(X0) => (~predd(X0) | predc(X0))) => ! [X0] : (predh(X0) <=> predc(X0)) [input p5] 52. ~? [X0] : (room(X0) => (predg(X0) => prede(X0))) [input p8] 55. ! [X0] : (room(X0) => (~predh(X0) | predd(X0))) [input p11] 61. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 63. ! [X0] : (room(X0) => (~predk(X0) | predd(X0))) <~> ! [X1] : (room(X1) => (~predc(X1) | predh(X1))) [rectify 46] 66. ! [X0] : (room(X0) => (~predd(X0) | predc(X0))) => ! [X1] : (predh(X1) <=> predc(X1)) [rectify 49] 72. ~? [X0] : (room(X0) => ~predg(X0)) [pure predicate removal 52] 77. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 61] 149. ! [X0] : ((~predk(X0) | predd(X0)) | ~room(X0)) <~> ! [X1] : ((~predc(X1) | predh(X1)) | ~room(X1)) [ennf transformation 63] 150. ! [X0] : (~predk(X0) | predd(X0) | ~room(X0)) <~> ! [X1] : (~predc(X1) | predh(X1) | ~room(X1)) [flattening 149] 155. ! [X1] : (predh(X1) <=> predc(X1)) | ? [X0] : ((predd(X0) & ~predc(X0)) & room(X0)) [ennf transformation 66] 156. ! [X1] : (predh(X1) <=> predc(X1)) | ? [X0] : (predd(X0) & ~predc(X0) & room(X0)) [flattening 155] 161. ! [X0] : (predg(X0) & room(X0)) [ennf transformation 72] 164. ! [X0] : ((~predh(X0) | predd(X0)) | ~room(X0)) [ennf transformation 55] 165. ! [X0] : (~predh(X0) | predd(X0) | ~room(X0)) [flattening 164] 171. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 77] 173. (? [X1] : (predc(X1) & ~predh(X1) & room(X1)) | ? [X0] : (predk(X0) & ~predd(X0) & room(X0))) & (! [X1] : (~predc(X1) | predh(X1) | ~room(X1)) | ! [X0] : (~predk(X0) | predd(X0) | ~room(X0))) [nnf transformation 150] 174. (? [X0] : (predc(X0) & ~predh(X0) & room(X0)) | ? [X1] : (predk(X1) & ~predd(X1) & room(X1))) & (! [X2] : (~predc(X2) | predh(X2) | ~room(X2)) | ! [X3] : (~predk(X3) | predd(X3) | ~room(X3))) [rectify 173] 175. ? [X0] : (predc(X0) & ~predh(X0) & room(X0)) => (predc(sK0) & ~predh(sK0) & room(sK0)) [choice axiom] 176. ? [X1] : (predk(X1) & ~predd(X1) & room(X1)) => (predk(sK1) & ~predd(sK1) & room(sK1)) [choice axiom] 177. ((predc(sK0) & ~predh(sK0) & room(sK0)) | (predk(sK1) & ~predd(sK1) & room(sK1))) & (! [X2] : (~predc(X2) | predh(X2) | ~room(X2)) | ! [X3] : (~predk(X3) | predd(X3) | ~room(X3))) [skolemisation 174,176,175] 187. ! [X1] : ((predh(X1) | ~predc(X1)) & (predc(X1) | ~predh(X1))) | ? [X0] : (predd(X0) & ~predc(X0) & room(X0)) [nnf transformation 156] 188. ! [X0] : ((predh(X0) | ~predc(X0)) & (predc(X0) | ~predh(X0))) | ? [X1] : (predd(X1) & ~predc(X1) & room(X1)) [rectify 187] 189. ? [X1] : (predd(X1) & ~predc(X1) & room(X1)) => (predd(sK5) & ~predc(sK5) & room(sK5)) [choice axiom] 190. ! [X0] : ((predh(X0) | ~predc(X0)) & (predc(X0) | ~predh(X0))) | (predd(sK5) & ~predc(sK5) & room(sK5)) [skolemisation 188,189] 278. ~predh(sK0) | ~predd(sK1) [cnf transformation 177] 295. predh(X0) | ~predc(X0) | ~predc(sK5) [cnf transformation 190] 299. room(X0) [cnf transformation 161] 302. ~predh(X0) | predd(X0) | ~room(X0) [cnf transformation 165] 309. predc(X0) | ~room(X0) [cnf transformation 171] 322. 3 <=> predd(sK1) [avatar definition] 324. ~predd(sK1) <- (~3) [avatar component clause 322] 332. 5 <=> predh(sK0) [avatar definition] 334. ~predh(sK0) <- (~5) [avatar component clause 332] 336. ~3 | ~5 [avatar split clause 278,332,322] 413. 23 <=> ! [X0] : (predh(X0) | ~predc(X0)) [avatar definition] 414. predh(X0) | ~predc(X0) <- (23) [avatar component clause 413] 417. 24 <=> predc(sK5) [avatar definition] 419. ~predc(sK5) <- (~24) [avatar component clause 417] 420. ~24 | 23 [avatar split clause 295,413,417] 433. ~predh(X0) | predd(X0) [subsumption resolution 302,299] 438. predc(X0) [subsumption resolution 309,299] 439. $false <- (~24) [subsumption resolution 419,438] 440. 24 [avatar contradiction clause 439] 446. predh(X0) <- (23) [subsumption resolution 414,438] 449. $false <- (~5, 23) [resolution 446,334] 450. 5 | ~23 [avatar contradiction clause 449] 451. predd(X0) <- (23) [resolution 433,446] 452. $false <- (~3, 23) [resolution 451,324] 453. 3 | ~23 [avatar contradiction clause 452] 454. $false [avatar sat refutation 336,420,440,450,453] % SZS output end Proof for 8865027769590731436440497 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Dennis, Marcelino, Evelyn, Dorothy are the only persons in the room. Dennis is richer than Pamela. All tall persons are kind. Marcelino is richer than Pamela. All kind persons are old. If someone is a tall person then he/she is richer than Pamela. More than one person in the room is not quiet. All tall persons are old. Dennis is kind. Marcelino is the least rich in the room. Dennis is the least quiet in the room. Marcelino is a quiet person. Pamela is quieter than Evelyn. Evelyn is old. Everyone in the room neither is not a old tall person nor is older than Pamela if and only if they is not a old person. Evelyn and Marcelino are respectively tall and old. Dennis is not a tall quiet person. Dorothy is quieter than Pamela. Dennis is old.

Evelyn is richer than Pamela.

entailment

room(dennis)&room(marcelino)&room(evelyn)&room(dorothy)&(![X]:(room(X)=>(X='dennis'|X='marcelino'|X='evelyn'|X='dorothy')))& (richer(pamela,dennis))& (![X]:(tall(X)=>kind(X)))& (richer(pamela,marcelino))& (![X]:(kind(X)=>old(X)))& ((![X]:((tall(X)&person(X))=>(richer(pamela,X)))))& ((?[X,Y]:(room(X)&room(Y)&(~quiet(X)&~quiet(Y))&(X!=Y))))& (![X]:(tall(X)=>old(X)))& (kind(dennis))& (![X]:((room(X)&(X!=marcelino))=>richer(marcelino,X)))& (![X]:((room(X)&(X!=dennis))=>quieter(dennis,X)))& (quiet(marcelino)&person(marcelino))& (quieter(evelyn,pamela))& (old(evelyn))& (![X]:(room(X)=>(((~((~(old(X)&tall(X)&person(X)))|(older(pamela,X))))<=>(~(old(X)&person(X)))))))& ((tall(evelyn))&(old(marcelino)))& (~(tall(dennis)&quiet(dennis)&person(dennis)))& (quieter(pamela,dorothy))& (old(dennis))

room(dennis)&room(marcelino)&room(evelyn)&room(dorothy)&(![X]:(room(X)=>(X='dennis'|X='marcelino'|X='evelyn'|X='dorothy')))& richer(pamela,evelyn)

% SZS status Unsatisfiable for 8110685078391944398705456 % SZS output start Proof for 8110685078391944398705456 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0] : ((person(X0) & tall(X0)) => richer(john,X0)) [input p5] 58. ! [X0] : (room(X0) => (~(older(john,X0) | ~(person(X0) & tall(X0) & old(X0))) <=> ~(person(X0) & old(X0)))) [input p14] 59. old(paul) & tall(fred) [input p15] 63. ~(richer(john,fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 136. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 136] 140. ! [X0] : (richer(john,X0) | (~person(X0) | ~tall(X0))) [ennf transformation 49] 141. ! [X0] : (richer(john,X0) | ~person(X0) | ~tall(X0)) [flattening 140] 147. ! [X0] : (((~older(john,X0) & (person(X0) & tall(X0) & old(X0))) <=> (~person(X0) | ~old(X0))) | ~room(X0)) [ennf transformation 58] 148. ! [X0] : (((~older(john,X0) & person(X0) & tall(X0) & old(X0)) <=> (~person(X0) | ~old(X0))) | ~room(X0)) [flattening 147] 150. ~richer(john,fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63] 151. ~richer(john,fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 150] 152. ! [X0] : (sP0(X0) <=> (~older(john,X0) & person(X0) & tall(X0) & old(X0))) [predicate definition introduction] 153. ! [X0] : ((sP0(X0) <=> (~person(X0) | ~old(X0))) | ~room(X0)) [definition folding 148,152] 157. ! [X0] : ((sP0(X0) | (older(john,X0) | ~person(X0) | ~tall(X0) | ~old(X0))) & ((~older(john,X0) & person(X0) & tall(X0) & old(X0)) | ~sP0(X0))) [nnf transformation 152] 158. ! [X0] : ((sP0(X0) | older(john,X0) | ~person(X0) | ~tall(X0) | ~old(X0)) & ((~older(john,X0) & person(X0) & tall(X0) & old(X0)) | ~sP0(X0))) [flattening 157] 159. ! [X0] : (((sP0(X0) | (person(X0) & old(X0))) & ((~person(X0) | ~old(X0)) | ~sP0(X0))) | ~room(X0)) [nnf transformation 153] 160. ! [X0] : (((sP0(X0) | (person(X0) & old(X0))) & (~person(X0) | ~old(X0) | ~sP0(X0))) | ~room(X0)) [flattening 159] 161. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 162. ~richer(john,fred) | (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 151,161] 243. room(mary) [cnf transformation 137] 244. room(paul) [cnf transformation 137] 245. room(fred) [cnf transformation 137] 246. room(alice) [cnf transformation 137] 247. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 137] 252. richer(john,X0) | ~person(X0) | ~tall(X0) [cnf transformation 141] 268. ~sP0(X0) | person(X0) [cnf transformation 158] 273. sP0(X0) | person(X0) | ~room(X0) [cnf transformation 160] 274. tall(fred) [cnf transformation 59] 279. ~richer(john,fred) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 280. ~richer(john,fred) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 281. ~richer(john,fred) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 282. ~richer(john,fred) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 283. ~richer(john,fred) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 285. ~room(X0) | person(X0) [subsumption resolution 273,268] 302. ~richer(john,fred) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,246] 303. ~richer(john,fred) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 302,245] 304. ~richer(john,fred) | alice != sK3 | ~room(mary) [subsumption resolution 303,244] 305. ~richer(john,fred) | alice != sK3 [subsumption resolution 304,243] 307. 4 <=> alice = sK3 [avatar definition] 309. alice != sK3 <- (~4) [avatar component clause 307] 311. 5 <=> richer(john,fred) [avatar definition] 313. ~richer(john,fred) <- (~5) [avatar component clause 311] 314. ~4 | ~5 [avatar split clause 305,311,307] 315. ~richer(john,fred) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,246] 316. ~richer(john,fred) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 315,245] 317. ~richer(john,fred) | fred != sK3 | ~room(mary) [subsumption resolution 316,244] 318. ~richer(john,fred) | fred != sK3 [subsumption resolution 317,243] 320. 6 <=> fred = sK3 [avatar definition] 322. fred != sK3 <- (~6) [avatar component clause 320] 323. ~6 | ~5 [avatar split clause 318,311,320] 324. ~richer(john,fred) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 281,246] 325. ~richer(john,fred) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 324,245] 326. ~richer(john,fred) | paul != sK3 | ~room(mary) [subsumption resolution 325,244] 327. ~richer(john,fred) | paul != sK3 [subsumption resolution 326,243] 329. 7 <=> paul = sK3 [avatar definition] 331. paul != sK3 <- (~7) [avatar component clause 329] 332. ~7 | ~5 [avatar split clause 327,311,329] 333. ~richer(john,fred) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,246] 334. ~richer(john,fred) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 333,245] 335. ~richer(john,fred) | mary != sK3 | ~room(mary) [subsumption resolution 334,244] 336. ~richer(john,fred) | mary != sK3 [subsumption resolution 335,243] 338. 8 <=> mary = sK3 [avatar definition] 340. mary != sK3 <- (~8) [avatar component clause 338] 341. ~8 | ~5 [avatar split clause 336,311,338] 342. ~richer(john,fred) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,246] 343. ~richer(john,fred) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 342,245] 344. ~richer(john,fred) | room(sK3) | ~room(mary) [subsumption resolution 343,244] 345. ~richer(john,fred) | room(sK3) [subsumption resolution 344,243] 347. 9 <=> room(sK3) [avatar definition] 349. room(sK3) <- (9) [avatar component clause 347] 350. 9 | ~5 [avatar split clause 345,311,347] 357. person(fred) [resolution 285,245] 368. ~person(fred) | ~tall(fred) <- (~5) [resolution 252,313] 369. ~tall(fred) <- (~5) [subsumption resolution 368,357] 370. $false <- (~5) [subsumption resolution 369,274] 371. 5 [avatar contradiction clause 370] 589. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (9) [resolution 247,349] 624. paul = sK3 | mary = sK3 | alice = sK3 <- (~6, 9) [subsumption resolution 589,322] 625. mary = sK3 | alice = sK3 <- (~6, ~7, 9) [subsumption resolution 624,331] 626. alice = sK3 <- (~6, ~7, ~8, 9) [subsumption resolution 625,340] 627. $false <- (~4, ~6, ~7, ~8, 9) [subsumption resolution 626,309] 628. 4 | 6 | 7 | 8 | ~9 [avatar contradiction clause 627] 629. $false [avatar sat refutation 314,323,332,341,350,371,628] % SZS output end Proof for 8110685078391944398705456 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

Mark, Donald, Kent are the only persons in the room. “Mark is not a quiet person” only if “Mark and Donald are not a kind old persons”. Mark is not a quiet person. Someone in the room is not a quiet person or is not a quiet kind person or both. Donald either is not a quiet person or is not a quiet kind person but not both. Donald is not not old or is not a kind person or both. Mark is not a tall old person or is quiet or both. Someone in the room is not a quiet kind person. Donald and Mark are respectively old and tall. Donald is quiet. At least one person in the room is tall. Mark is old. Mark is kind. Mark is the least old in the room.

Donald is old.

entailment

room(mark)&room(donald)&room(kent)&(![X]:(room(X)=>(X='mark'|X='donald'|X='kent')))& ((~(quiet(mark)&person(mark)))=>(~(kind(mark)&old(mark)&person(mark))&~(kind(donald)&old(donald)&person(donald))))& (~(quiet(mark)&person(mark)))& (?[X]:(room(X)&(((~(quiet(X)&person(X)))|(~(quiet(X)&kind(X)&person(X)))))))& (((~(quiet(donald)&person(donald)))<~>(~(quiet(donald)&kind(donald)&person(donald)))))& (((~~old(donald))|(~(kind(donald)&person(donald)))))& (((~(tall(mark)&old(mark)&person(mark)))|(quiet(mark))))& (?[X]:(room(X)&(~(quiet(X)&kind(X)&person(X)))))& ((old(donald))&(tall(mark)))& (quiet(donald))& (((?[X]:(room(X)&tall(X)))))& (old(mark))& (kind(mark))& (![X]:((room(X)&(X!=mark))=>older(mark,X)))& (((old(mark))<~>(~quiet(mark))))

room(mark)&room(donald)&room(kent)&(![X]:(room(X)=>(X='mark'|X='donald'|X='kent')))& old(donald)

% SZS status Unsatisfiable for 4209703505840179682803820 % SZS output start Proof for 4209703505840179682803820 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 52. tall(mary) & old(paul) [input p8] 59. ~(old(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 132. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 133. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 132] 146. ~old(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 147. ~old(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 146] 158. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 159. ~old(paul) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 147,158] 240. room(mary) [cnf transformation 133] 241. room(paul) [cnf transformation 133] 242. room(fred) [cnf transformation 133] 243. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 133] 262. old(paul) [cnf transformation 52] 272. ~old(paul) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 159] 273. ~old(paul) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 159] 274. ~old(paul) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 159] 275. ~old(paul) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 159] 289. 3 <=> old(paul) [avatar definition] 356. 3 [avatar split clause 262,289] 362. ~old(paul) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 275,242] 363. ~old(paul) | fred != sK3 | ~room(mary) [subsumption resolution 362,241] 364. ~old(paul) | fred != sK3 [subsumption resolution 363,240] 366. 16 <=> fred = sK3 [avatar definition] 368. fred != sK3 <- (~16) [avatar component clause 366] 369. ~16 | ~3 [avatar split clause 364,289,366] 370. ~old(paul) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 274,242] 371. ~old(paul) | paul != sK3 | ~room(mary) [subsumption resolution 370,241] 372. ~old(paul) | paul != sK3 [subsumption resolution 371,240] 374. 17 <=> paul = sK3 [avatar definition] 376. paul != sK3 <- (~17) [avatar component clause 374] 377. ~17 | ~3 [avatar split clause 372,289,374] 378. ~old(paul) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 273,242] 379. ~old(paul) | mary != sK3 | ~room(mary) [subsumption resolution 378,241] 380. ~old(paul) | mary != sK3 [subsumption resolution 379,240] 382. 18 <=> mary = sK3 [avatar definition] 384. mary != sK3 <- (~18) [avatar component clause 382] 385. ~18 | ~3 [avatar split clause 380,289,382] 386. ~old(paul) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 272,242] 387. ~old(paul) | room(sK3) | ~room(mary) [subsumption resolution 386,241] 388. ~old(paul) | room(sK3) [subsumption resolution 387,240] 390. 19 <=> room(sK3) [avatar definition] 392. room(sK3) <- (19) [avatar component clause 390] 393. 19 | ~3 [avatar split clause 388,289,390] 504. paul = sK3 | mary = sK3 | fred = sK3 <- (19) [resolution 243,392] 532. mary = sK3 | fred = sK3 <- (~17, 19) [subsumption resolution 504,376] 533. fred = sK3 <- (~17, ~18, 19) [subsumption resolution 532,384] 534. $false <- (~16, ~17, ~18, 19) [subsumption resolution 533,368] 535. 16 | 17 | 18 | ~19 [avatar contradiction clause 534] 536. $false [avatar sat refutation 356,369,377,385,393,535] % SZS output end Proof for 4209703505840179682803820 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.022 s % ------------------------------ % ------------------------------

Eric is the only person in the room. Eric streams on Twitch if Eric is a Linux enthusiast. Everyone in the room is a client of Meta if they enjoys kayaking and exploring remote waterways, enjoys windsurfing and practices calligraphy. Everyone in the room bakes bread at home if they is a client of Meta. Everyone in the room who regularly contributes to tech forums and online communities is a dedicated volunteer for local community service projects. Eric who enjoys kayaking and exploring remote waterways does not enjoy making ceramics. Everyone in the room is a dedicated volunteer for local community service projects. Eric enjoys kayaking. Eric enjoys writing detailed reviews of new and classic board games. Eric is a Linux enthusiast. Eric volunteers for local environmental conservation projects. Eric streams on Twitch. Eric enjoys writing detailed reviews of new and classic board games or practices archery or both. Everyone in the room collects vintage stamps or regularly contributes to tech forums and online communities or both if they either streams on Twitch or volunteers for local environmental conservation projects but not both. Everyone in the room volunteers for local environmental conservation projects, does not bake bread at home or owns an extensive assortment of vintage comic book memorabilia if they collects vintage stamps or regularly contributes to tech forums and online communities or both.

Eric enjoys making ceramics.

contradiction

room(eric)&(![X]:(room(X)=>(X='eric')))& ((is_a_Linux_enthusiast(eric))=>(streams_on_Twitch(eric)))& (![X]:(room(X)=>(((((enjoys_kayaking_and_exploring_remote_waterways(X))&(enjoys_windsurfing(X))&(practices_calligraphy(X))))=>(is_a_client_of_Meta(X))))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& ((enjoys_kayaking_and_exploring_remote_waterways(eric))&(does_not_enjoy_making_ceramics(eric)))& (![X]:(room(X)=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))& (enjoys_kayaking(eric))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(eric))& (is_a_Linux_enthusiast(eric))& (volunteers_for_local_environmental_conservation_projects(eric))& (streams_on_Twitch(eric))& (((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(eric))|(practices_archery(eric))))& (![X]:(room(X)=>(((((streams_on_Twitch(X))<~>(volunteers_for_local_environmental_conservation_projects(X))))=>(((collects_vintage_stamps(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))))& (![X]:(room(X)=>(((((collects_vintage_stamps(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(((volunteers_for_local_environmental_conservation_projects(X))|(does_not_bake_bread_at_home(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))))

room(eric)&(![X]:(room(X)=>(X='eric')))& enjoys_making_ceramics(eric)

% SZS status Unsatisfiable for 5773012966560391028840254 % SZS output start Proof for 5773012966560391028840254 49. ~predr(mary) & predf(mary) [input p5] 59. predr(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 63. ~predr(mary) [pure predicate removal 49] 147. predr(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 59] 231. ~predr(mary) [cnf transformation 63] 234. predr(mary) [cnf transformation 147] 235. $false [subsumption resolution 234,231] % SZS output end Proof for 5773012966560391028840254 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------

Abram, Janet, Kermit, Maria are the only persons in the room. “Abram is hated by Justin” unless “everyone in the room does not create large-scale murals for public art installations or is a happy person”. “Maria owns a significant collection of rare gemstones and minerals” only if “everyone outside the room who designs and sews custom cosplay costumes for conventions collects comic books”. If “everyone in the room does not own a smartwatch or creates YouTube content” then “Maria and Stacy hate each other”. If “not everyone in the room does not have a specialized collection of handmade artisan pottery or is not liked by Stacy” then “Maria is louder than Velma”. “All curious persons are quiet” unless “Abram has a curated collection of mid-century modern furniture”. “Abram is a happy generous kind person” unless “everyone anywhere is not liked by Justin”. “Abram is younger than Justin” only if “everyone in the room collects comic books if they is poorer than Velma and is brave”. If “Abram enjoys macrame” then “everyone in the room is not quiet, not generous, not strong if and only if they is a sibling of Stacy”. Justin and Abram like each other.

Everyone anywhere neither is a happy person nor is a kind happy person.

contradiction

room(abram)&room(janet)&room(kermit)&room(maria)&(![X]:(room(X)=>(X='abram'|X='janet'|X='kermit'|X='maria')))& (~(![X]:(room(X)=>(((happy(X)&person(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))=>(hate(abram,justin)))& ((owns_a_significant_collection_of_rare_gemstones_and_minerals(maria))=>(![X]:(~room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(collects_comic_books(X)))))))& ((![X]:(room(X)=>(((creates_YouTube_content(X))|(does_not_own_a_smartwatch(X))))))=>((hate(maria,stacy) & hate(stacy,maria))))& ((~![X]:(room(X)=>(((~like(X,stacy))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))=>(louder(velma,maria)))& (~(has_a_curated_collection_of_mid-century_modern_furniture(abram))=>(![X]:(curious(X)=>quiet(X))))& (~(![X]:(anywhere(X)=>(~like(X,justin))))=>(happy(abram)&generous(abram)&kind(abram)&person(abram)))& ((younger(justin,abram))=>(![X]:(room(X)=>(((((poorer(velma,X))&(brave(X))))=>(collects_comic_books(X)))))))& ((enjoys_macrame(abram))=>(![X]:(room(X)=>(((~quiet(X)&~generous(X)&~strong(X))<=>(sibling(stacy,X)))))))& (![X]:(room(X)=>(((younger(velma,X))=>(client(justin,X))))))& (~((like(justin,janet) & like(janet,justin))))& (has_a_specialized_collection_of_handmade_artisan_pottery(abram))& (~![X]:(room(X)=>(((~like(X,stacy))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (((makes_intricate_hand-cut_paper_art_for_exhibitions(janet))|(strong(janet)&humble(janet)&brave(janet)&european(janet))|(owns_a_smartwatch(janet))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(poorer(velma,X))))))& (![X]:(strong(X)=>tall(X)))& (((?[X]:(room(X)&designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))& ((client(stacy,abram))&(collects_comic_books(abram)))& (![X]:(tall(X)=>patient(X)))& ((like(justin,abram) & like(abram,justin)))& (has_a_curated_collection_of_mid-century_modern_furniture(abram))& (![X]:(room(X)=>(((client(stacy,X))=>(quieter(justin,X))))))& (![X]:(tall(X)=>strong(X)))& (frequently_participates_in_hackathons_and_coding_competitions(abram))& (sibling(kermit,velma))& ((![X]:((kind(X)&tall(X)&person(X))<=>(~like(X,velma)))))

room(abram)&room(janet)&room(kermit)&room(maria)&(![X]:(room(X)=>(X='abram'|X='janet'|X='kermit'|X='maria')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

% SZS status Unsatisfiable for 644183539003174668943065 % SZS output start Proof for 644183539003174668943065 5. ! [X0] : anywhere(X0) [input b4] 50. ~! [X0] : (anywhere(X0) => ~like(X0,lucy)) => (person(mary) & kind(mary) & generous(mary) & happy(mary)) [input p6] 63. like(mary,lucy) & like(lucy,mary) [input p19] 70. ! [X0] : (anywhere(X0) => ~((person(X0) & happy(X0) & kind(X0)) | (person(X0) & happy(X0)))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 71. ! [X0] : (anywhere(X0) => ~((person(X0) & happy(X0) & kind(X0)) | (person(X0) & happy(X0)))) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 70] 79. ~! [X0] : (anywhere(X0) => ~like(X0,lucy)) => (person(mary) & kind(mary) & happy(mary)) [pure predicate removal 50] 166. (person(mary) & kind(mary) & happy(mary)) | ! [X0] : (~like(X0,lucy) | ~anywhere(X0)) [ennf transformation 79] 176. ! [X0] : (((~person(X0) | ~happy(X0) | ~kind(X0)) & (~person(X0) | ~happy(X0))) | ~anywhere(X0)) & ! [X1] : ((alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 71] 177. ! [X0] : (((~person(X0) | ~happy(X0) | ~kind(X0)) & (~person(X0) | ~happy(X0))) | ~anywhere(X0)) & ! [X1] : (alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 176] 189. anywhere(X0) [cnf transformation 5] 278. happy(mary) | ~like(X0,lucy) | ~anywhere(X0) [cnf transformation 166] 280. person(mary) | ~like(X0,lucy) | ~anywhere(X0) [cnf transformation 166] 291. like(mary,lucy) [cnf transformation 63] 304. ~person(X0) | ~happy(X0) | ~anywhere(X0) [cnf transformation 177] 328. person(mary) | ~like(X0,lucy) [subsumption resolution 280,189] 330. 6 <=> ! [X0] : ~like(X0,lucy) [avatar definition] 331. ~like(X0,lucy) <- (6) [avatar component clause 330] 333. 7 <=> person(mary) [avatar definition] 335. person(mary) <- (7) [avatar component clause 333] 336. 6 | 7 [avatar split clause 328,333,330] 343. happy(mary) | ~like(X0,lucy) [subsumption resolution 278,189] 345. 9 <=> happy(mary) [avatar definition] 347. happy(mary) <- (9) [avatar component clause 345] 348. 6 | 9 [avatar split clause 343,345,330] 359. ~happy(X0) | ~person(X0) [subsumption resolution 304,189] 360. $false <- (6) [resolution 331,291] 361. ~6 [avatar contradiction clause 360] 362. ~person(mary) <- (9) [resolution 359,347] 363. $false <- (7, 9) [subsumption resolution 362,335] 364. ~7 | ~9 [avatar contradiction clause 363] 365. $false [avatar sat refutation 336,348,361,364] % SZS output end Proof for 644183539003174668943065 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Leslie, Richard, Timothy, Willie, Paul are the only persons in the room. “Richard does not hate Lee or frequently participates in hackathons and coding competitions or both” only if “Timothy frequently participates in hackathons and coding competitions”. Either “Richard frequently participates in hackathons and coding competitions” or “Paul frequently participates in hackathons and coding competitions” but not both.

Paul frequently participates in hackathons and coding competitions.

neutral

room(leslie)&room(richard)&room(timothy)&room(willie)&room(paul)&(![X]:(room(X)=>(X='leslie'|X='richard'|X='timothy'|X='willie'|X='paul')))& ((((~hate(lee,richard))|(frequently_participates_in_hackathons_and_coding_competitions(richard))))=>(frequently_participates_in_hackathons_and_coding_competitions(timothy)))& ((frequently_participates_in_hackathons_and_coding_competitions(richard))<~>(frequently_participates_in_hackathons_and_coding_competitions(paul)))& ((frequently_participates_in_hackathons_and_coding_competitions(willie))=>((hate(richard,lee) & hate(lee,richard))))& ((![X]:((frequently_participates_in_hackathons_and_coding_competitions(X))=>(does_not_collect_vintage_vinyl_records(X)))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(willie))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(paul))& (frequently_participates_in_hackathons_and_coding_competitions(timothy))& ((hate(timothy,lee) & hate(lee,timothy)))& (is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(leslie))& (collects_vintage_vinyl_records(willie))

room(leslie)&room(richard)&room(timothy)&room(willie)&room(paul)&(![X]:(room(X)=>(X='leslie'|X='richard'|X='timothy'|X='willie'|X='paul')))& frequently_participates_in_hackathons_and_coding_competitions(paul)

Laura, Jose are the only persons in the room. If “Laura practices kickboxing” then “no one in the room practices kickboxing or does not practice graffiti art”. If “Jose practices graffiti art” then “everyone outside the room who practices graffiti art uses a Windows laptop”. “Everyone in the room is a client of Meta” unless “not everyone outside the room is a client of Meta or does not practice kickboxing”. “Jose practices graffiti art” if “everyone in the room does not enjoy kayaking and exploring remote waterways or practices graffiti art” and vice versa. If “everyone in the room practices kickboxing or does not use a Windows laptop” then “Jose practices graffiti art, has a vast collection of first-edition science fiction novels and practices kickboxing”. Everyone in the room who practices graffiti art uses a Windows laptop. Everyone in the room does not use a Windows laptop if they neither practices kickboxing nor has a vast collection of first-edition science fiction novels and vice versa. Everyone in the room does not practice graffiti art if they neither practices kickboxing nor has a vast collection of first-edition science fiction novels. If someone practices graffiti art then he/she is a client of Meta. Jose does not practice graffiti art. Everyone outside the room has a vast collection of first-edition science fiction novels if they is a client of Meta or practices graffiti art or both. Jose has a vast collection of first-edition science fiction novels. Everyone in the room uses a Windows laptop if they enjoys kayaking and exploring remote waterways. Laura practices kickboxing or practices graffiti art or both. Jose uses a Windows laptop.

It is true that “Laura is a client of Meta”.

entailment

room(laura)&room(jose)&(![X]:(room(X)=>(X='laura'|X='jose')))& ((practices_kickboxing(laura))=>(~?[X]:(room(X)=>(((does_not_practice_graffiti_art(X))|(practices_kickboxing(X)))))))& ((practices_graffiti_art(jose))=>(![X]:(~room(X)=>(((practices_graffiti_art(X))=>(uses_a_Windows_laptop(X)))))))& (~(~![X]:(~room(X)=>(((does_not_practice_kickboxing(X))|(is_a_client_of_Meta(X))))))=>(![X]:(room(X)=>(is_a_client_of_Meta(X)))))& ((![X]:(room(X)=>(((practices_graffiti_art(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))<=>(practices_graffiti_art(jose)))& ((![X]:(room(X)=>(((does_not_use_a_Windows_laptop(X))|(practices_kickboxing(X))))))=>(((practices_graffiti_art(jose))&(has_a_vast_collection_of_first-edition_science_fiction_novels(jose))&(practices_kickboxing(jose)))))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(uses_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((does_not_use_a_Windows_laptop(X))<=>(~((practices_kickboxing(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))))& (![X]:(room(X)=>(((~((practices_kickboxing(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))=>(does_not_practice_graffiti_art(X))))))& ((![X]:((practices_graffiti_art(X))=>(is_a_client_of_Meta(X)))))& (does_not_practice_graffiti_art(jose))& (![X]:(~room(X)=>(((((is_a_client_of_Meta(X))|(practices_graffiti_art(X))))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (has_a_vast_collection_of_first-edition_science_fiction_novels(jose))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(uses_a_Windows_laptop(X))))))& (((practices_kickboxing(laura))|(practices_graffiti_art(laura))))& (uses_a_Windows_laptop(jose))

room(laura)&room(jose)&(![X]:(room(X)=>(X='laura'|X='jose')))& is_a_client_of_Meta(laura)

% SZS status Unsatisfiable for 6808394482217103296848345 % SZS output start Proof for 6808394482217103296848345 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. preda(mary) => ~? [X0] : (room(X0) => (preda(X0) | ~predc(X0))) [input p1] 53. ! [X0] : (predc(X0) => prede(X0)) [input p9] 58. predc(mary) | preda(mary) [input p14] 60. ~(prede(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 135. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 136. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 135] 137. ! [X0] : ((~preda(X0) & predc(X0)) & room(X0)) | ~preda(mary) [ennf transformation 45] 138. ! [X0] : (~preda(X0) & predc(X0) & room(X0)) | ~preda(mary) [flattening 137] 152. ! [X0] : (prede(X0) | ~predc(X0)) [ennf transformation 53] 157. ~prede(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 60] 158. ~prede(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 157] 174. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 175. ~prede(mary) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 158,174] 256. room(mary) [cnf transformation 136] 257. room(paul) [cnf transformation 136] 258. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 136] 261. ~preda(X0) | ~preda(mary) [cnf transformation 138] 281. ~predc(X0) | prede(X0) [cnf transformation 152] 287. predc(mary) | preda(mary) [cnf transformation 58] 289. ~prede(mary) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 175] 290. ~prede(mary) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 175] 291. ~prede(mary) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 175] 293. 1 <=> preda(mary) [avatar definition] 294. preda(mary) <- (1) [avatar component clause 293] 297. 2 <=> ! [X0] : ~preda(X0) [avatar definition] 298. ~preda(X0) <- (2) [avatar component clause 297] 299. ~1 | 2 [avatar split clause 261,297,293] 386. 21 <=> predc(mary) [avatar definition] 388. predc(mary) <- (21) [avatar component clause 386] 389. 1 | 21 [avatar split clause 287,386,293] 390. ~prede(mary) | paul != sK4 | ~room(mary) [subsumption resolution 291,257] 391. ~prede(mary) | paul != sK4 [subsumption resolution 390,256] 393. 22 <=> paul = sK4 [avatar definition] 395. paul != sK4 <- (~22) [avatar component clause 393] 397. 23 <=> prede(mary) [avatar definition] 400. ~22 | ~23 [avatar split clause 391,397,393] 401. ~prede(mary) | mary != sK4 | ~room(mary) [subsumption resolution 290,257] 402. ~prede(mary) | mary != sK4 [subsumption resolution 401,256] 404. 24 <=> mary = sK4 [avatar definition] 406. mary != sK4 <- (~24) [avatar component clause 404] 407. ~24 | ~23 [avatar split clause 402,397,404] 408. ~prede(mary) | room(sK4) | ~room(mary) [subsumption resolution 289,257] 409. ~prede(mary) | room(sK4) [subsumption resolution 408,256] 411. 25 <=> room(sK4) [avatar definition] 413. room(sK4) <- (25) [avatar component clause 411] 414. 25 | ~23 [avatar split clause 409,397,411] 415. prede(mary) <- (21) [resolution 281,388] 418. 23 | ~21 [avatar split clause 415,386,397] 439. mary = sK4 | paul = sK4 <- (25) [resolution 258,413] 458. paul = sK4 <- (~24, 25) [subsumption resolution 439,406] 459. $false <- (~22, ~24, 25) [subsumption resolution 458,395] 460. 22 | 24 | ~25 [avatar contradiction clause 459] 472. $false <- (1, 2) [subsumption resolution 294,298] 473. ~1 | ~2 [avatar contradiction clause 472] 474. $false [avatar sat refutation 299,389,400,407,414,418,460,473] % SZS output end Proof for 6808394482217103296848345 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.021 s % ------------------------------ % ------------------------------

Billie, Sarah, Seth, Deanna, Morton are the only persons in the room. 'Seth practices tai chi' unless 'it is not the case that 'Billie is an active member of a local robotics club or does not collect limited-edition art prints from contemporary artists or both''. Sarah collects limited-edition art prints from contemporary artists. Sarah is a chess master who participates in national tournaments. If someone is an active member of a local robotics club then he/she is a certified scuba diver with advanced underwater photography skills and vice versa. Sarah is an active member of a local robotics club. It is true that 'Seth is a professional photographer specializing in portrait photography, is a chess master who participates in national tournaments and practices tai chi'. It is not the case that 'Billie is an active member of a local robotics club or does not collect limited-edition art prints from contemporary artists or both'. Seth practices tai chi. Sarah practices tai chi. Deanna is a chess master who participates in national tournaments. Seth is an active member of a local robotics club.

Sarah is a certified scuba diver with advanced underwater photography skills.

entailment

room(billie)&room(sarah)&room(seth)&room(deanna)&room(morton)&(![X]:(room(X)=>(X='billie'|X='sarah'|X='seth'|X='deanna'|X='morton')))& (~(~(((is_an_active_member_of_a_local_robotics_club(billie))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(billie)))))=>(practices_tai_chi(seth)))& (collects_limited-edition_art_prints_from_contemporary_artists(sarah))& (is_a_chess_master_who_participates_in_national_tournaments(sarah))& ((![X]:((is_an_active_member_of_a_local_robotics_club(X))<=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& (is_an_active_member_of_a_local_robotics_club(sarah))& (((is_a_professional_photographer_specializing_in_portrait_photography(seth))&(is_a_chess_master_who_participates_in_national_tournaments(seth))&(practices_tai_chi(seth))))& (~(((is_an_active_member_of_a_local_robotics_club(billie))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(billie)))))& (practices_tai_chi(seth))& (practices_tai_chi(sarah))& (is_a_chess_master_who_participates_in_national_tournaments(deanna))& (is_an_active_member_of_a_local_robotics_club(seth))

room(billie)&room(sarah)&room(seth)&room(deanna)&room(morton)&(![X]:(room(X)=>(X='billie'|X='sarah'|X='seth'|X='deanna'|X='morton')))& is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(sarah)

% SZS status Unsatisfiable for 4970903398658220205278709 % SZS output start Proof for 4970903398658220205278709 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (predd(X0) <=> prede(X0)) [input p4] 49. predd(paul) [input p5] 56. ~(prede(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 140. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 141. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 140] 143. ~prede(paul) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 56] 144. ~prede(paul) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 143] 146. ! [X0] : ((predd(X0) | ~prede(X0)) & (prede(X0) | ~predd(X0))) [nnf transformation 48] 147. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 148. ~prede(paul) | (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 144,147] 229. room(mary) [cnf transformation 141] 230. room(paul) [cnf transformation 141] 231. room(fred) [cnf transformation 141] 232. room(alice) [cnf transformation 141] 233. room(john) [cnf transformation 141] 234. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 141] 235. ~predd(X0) | prede(X0) [cnf transformation 146] 237. predd(paul) [cnf transformation 49] 240. ~prede(paul) | room(sK0) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 241. ~prede(paul) | mary != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 242. ~prede(paul) | paul != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 243. ~prede(paul) | fred != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 244. ~prede(paul) | alice != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 245. ~prede(paul) | john != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 246. ~prede(paul) | john != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 245,233] 247. ~prede(paul) | john != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 246,232] 248. ~prede(paul) | john != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 247,231] 249. ~prede(paul) | john != sK0 | ~room(mary) [subsumption resolution 248,230] 250. ~prede(paul) | john != sK0 [subsumption resolution 249,229] 252. 1 <=> john = sK0 [avatar definition] 254. john != sK0 <- (~1) [avatar component clause 252] 256. 2 <=> prede(paul) [avatar definition] 259. ~1 | ~2 [avatar split clause 250,256,252] 260. ~prede(paul) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 244,233] 261. ~prede(paul) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,232] 262. ~prede(paul) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 261,231] 263. ~prede(paul) | alice != sK0 | ~room(mary) [subsumption resolution 262,230] 264. ~prede(paul) | alice != sK0 [subsumption resolution 263,229] 266. 3 <=> alice = sK0 [avatar definition] 268. alice != sK0 <- (~3) [avatar component clause 266] 269. ~3 | ~2 [avatar split clause 264,256,266] 270. ~prede(paul) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 243,233] 271. ~prede(paul) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,232] 272. ~prede(paul) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 271,231] 273. ~prede(paul) | fred != sK0 | ~room(mary) [subsumption resolution 272,230] 274. ~prede(paul) | fred != sK0 [subsumption resolution 273,229] 276. 4 <=> fred = sK0 [avatar definition] 278. fred != sK0 <- (~4) [avatar component clause 276] 279. ~4 | ~2 [avatar split clause 274,256,276] 280. ~prede(paul) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 242,233] 281. ~prede(paul) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,232] 282. ~prede(paul) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 281,231] 283. ~prede(paul) | paul != sK0 | ~room(mary) [subsumption resolution 282,230] 284. ~prede(paul) | paul != sK0 [subsumption resolution 283,229] 286. 5 <=> paul = sK0 [avatar definition] 288. paul != sK0 <- (~5) [avatar component clause 286] 289. ~5 | ~2 [avatar split clause 284,256,286] 290. ~prede(paul) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 241,233] 291. ~prede(paul) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,232] 292. ~prede(paul) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 291,231] 293. ~prede(paul) | mary != sK0 | ~room(mary) [subsumption resolution 292,230] 294. ~prede(paul) | mary != sK0 [subsumption resolution 293,229] 296. 6 <=> mary = sK0 [avatar definition] 298. mary != sK0 <- (~6) [avatar component clause 296] 299. ~6 | ~2 [avatar split clause 294,256,296] 300. ~prede(paul) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 240,233] 301. ~prede(paul) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 300,232] 302. ~prede(paul) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 301,231] 303. ~prede(paul) | room(sK0) | ~room(mary) [subsumption resolution 302,230] 304. ~prede(paul) | room(sK0) [subsumption resolution 303,229] 306. 7 <=> room(sK0) [avatar definition] 308. room(sK0) <- (7) [avatar component clause 306] 309. 7 | ~2 [avatar split clause 304,256,306] 310. prede(paul) [resolution 235,237] 314. 2 [avatar split clause 310,256] 364. alice = sK0 | fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (7) [resolution 234,308] 365. fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (~3, 7) [subsumption resolution 364,268] 366. paul = sK0 | mary = sK0 | john = sK0 <- (~3, ~4, 7) [subsumption resolution 365,278] 367. mary = sK0 | john = sK0 <- (~3, ~4, ~5, 7) [subsumption resolution 366,288] 368. john = sK0 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 367,298] 369. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 368,254] 370. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 369] 371. $false [avatar sat refutation 259,269,279,289,299,309,314,370] % SZS output end Proof for 4970903398658220205278709 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Henry is the only person in the room. Either “everyone outside the room does not enjoy macrame or competes in national level swimming championships” or “not everyone in the room competes in national level swimming championships or does not enjoy watercolor painting” but not both. “Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or is not dedicated to sustainable living and zero-waste practices” if “everyone in the room is a dedicated volunteer for local community service projects or is not a wine connoisseur” and vice versa. If “Henry is a dedicated volunteer for local community service projects” then “everyone in the room collects antique jewelry if they does not own an extensive assortment of vintage comic book memorabilia”. If “everyone in the room enjoys snowboarding or does not collect antique jewelry” then “no one in the room who enjoys snowboarding collects action figures” otherwise “Henry enjoys watercolor painting”. If “Henry hosts themed dinner parties featuring gourmet home-cooked meals” then “no one in the room does not host themed dinner parties featuring gourmet home-cooked meals or owns an extensive assortment of vintage comic book memorabilia”. If “no one in the room does not host themed dinner parties featuring gourmet home-cooked meals or owns an extensive assortment of vintage comic book memorabilia” then “everyone in the room who does not host themed dinner parties featuring gourmet home-cooked meals owns a high-end gaming PC with custom-built components and collects action figures”. If “it is not the case that “at least one person in the room does not collect antique jewelry”” then “everyone in the room does not own an extensive assortment of vintage comic book memorabilia or is a wine connoisseur” otherwise “Henry is a member of a local theater group specializing in improv”. “Someone anywhere hosts themed dinner parties featuring gourmet home-cooked meals” if “Henry owns a high-end gaming PC with custom-built components” and vice versa.

Everyone in the room does not collect action figures or collects action figures.

entailment

room(henry)&(![X]:(room(X)=>(X='henry')))& ((![X]:(~room(X)=>(((competes_in_national_level_swimming_championships(X))|(does_not_enjoy_macrame(X))))))<~>(~![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(competes_in_national_level_swimming_championships(X)))))))& ((![X]:(room(X)=>(((is_not_a_wine_connoisseur(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))<=>(![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))& ((is_a_dedicated_volunteer_for_local_community_service_projects(henry))=>(![X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(collects_antique_jewelry(X)))))))& (((![X]:(room(X)=>(((does_not_collect_antique_jewelry(X))|(enjoys_snowboarding(X))))))=>(~?[X]:(room(X)=>(((enjoys_snowboarding(X))=>(collects_action_figures(X)))))))&((~(![X]:(room(X)=>(((does_not_collect_antique_jewelry(X))|(enjoys_snowboarding(X)))))))=>(enjoys_watercolor_painting(henry))))& (((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(henry))=>(~?[X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))& ((~?[X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))=>(![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))&(collects_action_figures(X))))))))))& (((~(((?[X]:(room(X)&does_not_collect_antique_jewelry(X))))))=>(![X]:(room(X)=>(((is_a_wine_connoisseur(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))))&((~(~(((?[X]:(room(X)&does_not_collect_antique_jewelry(X)))))))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(henry))))& ((owns_a_high-end_gaming_PC_with_custom-built_components(henry))<=>(?[X]:(anywhere(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& (~(![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))=>(![X]:(room(X)=>(((((does_not_collect_action_figures(X))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(does_not_collect_antique_jewelry(X))))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))))& ((competes_in_national_level_swimming_championships(henry))=>(![X]:(~room(X)=>(((collects_action_figures(X))=>(enjoys_logic_puzzles(X)))))))& ((enjoys_watercolor_painting(henry))=>(((?[X]:(room(X)&plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (~(((?[X]:(room(X)&((is_not_a_wine_connoisseur(X))<~>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))=>(competes_in_national_level_swimming_championships(henry)))& ((~![X]:(~room(X)=>(((does_not_enjoy_macrame(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_a_wine_connoisseur(X)))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(enjoys_snowboarding(X))))))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (![X]:(room(X)=>(((((enjoys_watercolor_painting(X))|(does_not_collect_antique_jewelry(X))))<=(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_a_wine_connoisseur(X))))))& (((?[X]:(room(X)&enjoys_macrame(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_macrame(X))&(enjoys_macrame(Y)))=>(X=Y)))))& (competes_in_national_level_swimming_championships(henry))& (enjoys_logic_puzzles(henry))& (is_not_a_wine_connoisseur(henry))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))))& (![X]:(room(X)=>(((((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))=>(does_not_enjoy_watercolor_painting(X))))))& (![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))=>(enjoys_macrame(X))))))& (enjoys_watercolor_painting(henry))

room(henry)&(![X]:(room(X)=>(X='henry')))& ![X]:(room(X)=>(((collects_action_figures(X))|(does_not_collect_action_figures(X)))))

% SZS status Unsatisfiable for 4543761929244778984949486 % SZS output start Proof for 4543761929244778984949486 44. predc(mary) & ! [X0] : (room(X0) => (~predc(X0) => predg(X0))) & ! [X0] : (room(X0) => ((prede(X0) & predj(X0)) => ~predc(X0))) & ! [X0] : (room(X0) => (predo(X0) => (prede(X0) & predj(X0)))) & ~predd(mary) & predi(mary) & predn(mary) & ! [X0,X1] : ((predg(X1) & predg(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predg(X0) & room(X0)) & ! [X0] : (room(X0) => (predm(X0) => predd(X0))) & ! [X0] : (room(X0) => (predf(X0) => (~preda(X0) | predc(X0)))) & ! [X0] : (room(X0) => (predb(X0) => predo(X0))) & ! [X0] : (room(X0) => (prede(X0) <=> predb(X0))) & ! [X0] : (room(X0) => (predd(X0) => predk(X0))) & (~! [X0] : (~room(X0) => (predm(X0) | ~predg(X0))) => ! [X0] : (room(X0) => (predm(X0) => predd(X0)))) & (~? [X0] : ((~predd(X0) <~> predm(X0)) & room(X0)) => predn(mary)) & (predc(mary) => ? [X0] : (predl(X0) & room(X0))) & (predn(mary) => ! [X0] : (~room(X0) => (predb(X0) => predi(X0)))) & (~! [X0] : (room(X0) => (predj(X0) | ~predh(X0))) => ! [X0] : (room(X0) => ((~preda(X0) & ~predl(X0) & ~predb(X0)) => predo(X0)))) & (predm(mary) <=> ? [X0] : (prede(X0) & anywhere(X0))) & (~~? [X0] : (~preda(X0) & room(X0)) => predh(mary)) & (~? [X0] : (~preda(X0) & room(X0)) => ! [X0] : (room(X0) => (~predj(X0) | predd(X0)))) & (~? [X0] : (room(X0) => (~prede(X0) | predj(X0))) => ! [X0] : (room(X0) => (~prede(X0) => (predb(X0) & predm(X0))))) & (prede(mary) => ~? [X0] : (room(X0) => (~prede(X0) | predj(X0)))) & (~! [X0] : (room(X0) => (predk(X0) | ~preda(X0))) => predc(mary)) & (! [X0] : (room(X0) => (predk(X0) | ~preda(X0))) => ~? [X0] : (room(X0) => (predk(X0) => predb(X0)))) & (predo(mary) => ! [X0] : (room(X0) => (~predj(X0) => preda(X0)))) & (! [X0] : (room(X0) => (predo(X0) | ~predd(X0))) <=> ! [X0] : (room(X0) => (~prede(X0) | ~predp(X0)))) & (! [X0] : (~room(X0) => (~predg(X0) | predn(X0))) <~> ~! [X0] : (room(X0) => (predn(X0) | ~predc(X0)))) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ~(! [X0] : (room(X0) => (~predb(X0) | predb(X0))) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 46. predc(mary) & ! [X0] : (room(X0) => (~predc(X0) => predg(X0))) & ! [X1] : (room(X1) => ((prede(X1) & predj(X1)) => ~predc(X1))) & ! [X2] : (room(X2) => (predo(X2) => (prede(X2) & predj(X2)))) & ~predd(mary) & predi(mary) & predn(mary) & ! [X3,X4] : ((predg(X4) & predg(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (room(X6) => (predm(X6) => predd(X6))) & ! [X7] : (room(X7) => (predf(X7) => (~preda(X7) | predc(X7)))) & ! [X8] : (room(X8) => (predb(X8) => predo(X8))) & ! [X9] : (room(X9) => (prede(X9) <=> predb(X9))) & ! [X10] : (room(X10) => (predd(X10) => predk(X10))) & (~! [X11] : (~room(X11) => (predm(X11) | ~predg(X11))) => ! [X12] : (room(X12) => (predm(X12) => predd(X12)))) & (~? [X13] : ((~predd(X13) <~> predm(X13)) & room(X13)) => predn(mary)) & (predc(mary) => ? [X14] : (predl(X14) & room(X14))) & (predn(mary) => ! [X15] : (~room(X15) => (predb(X15) => predi(X15)))) & (~! [X16] : (room(X16) => (predj(X16) | ~predh(X16))) => ! [X17] : (room(X17) => ((~preda(X17) & ~predl(X17) & ~predb(X17)) => predo(X17)))) & (predm(mary) <=> ? [X18] : (prede(X18) & anywhere(X18))) & (~~? [X19] : (~preda(X19) & room(X19)) => predh(mary)) & (~? [X20] : (~preda(X20) & room(X20)) => ! [X21] : (room(X21) => (~predj(X21) | predd(X21)))) & (~? [X22] : (room(X22) => (~prede(X22) | predj(X22))) => ! [X23] : (room(X23) => (~prede(X23) => (predb(X23) & predm(X23))))) & (prede(mary) => ~? [X24] : (room(X24) => (~prede(X24) | predj(X24)))) & (~! [X25] : (room(X25) => (predk(X25) | ~preda(X25))) => predc(mary)) & (! [X26] : (room(X26) => (predk(X26) | ~preda(X26))) => ~? [X27] : (room(X27) => (predk(X27) => predb(X27)))) & (predo(mary) => ! [X28] : (room(X28) => (~predj(X28) => preda(X28)))) & (! [X29] : (room(X29) => (predo(X29) | ~predd(X29))) <=> ! [X30] : (room(X30) => (~prede(X30) | ~predp(X30)))) & (! [X31] : (~room(X31) => (~predg(X31) | predn(X31))) <~> ~! [X32] : (room(X32) => (predn(X32) | ~predc(X32)))) & ! [X33] : (room(X33) => mary = X33) & room(mary) [rectify 44] 47. predc(mary) & ! [X0] : (room(X0) => (~predc(X0) => predg(X0))) & ! [X1] : (room(X1) => ((prede(X1) & predj(X1)) => ~predc(X1))) & ! [X2] : (room(X2) => (predo(X2) => (prede(X2) & predj(X2)))) & ~predd(mary) & predi(mary) & predn(mary) & ! [X3,X4] : ((predg(X4) & predg(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (room(X6) => (predm(X6) => predd(X6))) & ! [X7] : (room(X7) => (predf(X7) => (~preda(X7) | predc(X7)))) & ! [X8] : (room(X8) => (predb(X8) => predo(X8))) & ! [X9] : (room(X9) => (prede(X9) <=> predb(X9))) & ! [X10] : (room(X10) => (predd(X10) => predk(X10))) & (~! [X11] : (~room(X11) => (predm(X11) | ~predg(X11))) => ! [X12] : (room(X12) => (predm(X12) => predd(X12)))) & (~? [X13] : ((~predd(X13) <~> predm(X13)) & room(X13)) => predn(mary)) & (predc(mary) => ? [X14] : (predl(X14) & room(X14))) & (predn(mary) => ! [X15] : (~room(X15) => (predb(X15) => predi(X15)))) & (~! [X16] : (room(X16) => (predj(X16) | ~predh(X16))) => ! [X17] : (room(X17) => ((~preda(X17) & ~predl(X17) & ~predb(X17)) => predo(X17)))) & (predm(mary) <=> ? [X18] : (prede(X18) & anywhere(X18))) & (? [X19] : (~preda(X19) & room(X19)) => predh(mary)) & (~? [X20] : (~preda(X20) & room(X20)) => ! [X21] : (room(X21) => (~predj(X21) | predd(X21)))) & (~? [X22] : (room(X22) => (~prede(X22) | predj(X22))) => ! [X23] : (room(X23) => (~prede(X23) => (predb(X23) & predm(X23))))) & (prede(mary) => ~? [X24] : (room(X24) => (~prede(X24) | predj(X24)))) & (~! [X25] : (room(X25) => (predk(X25) | ~preda(X25))) => predc(mary)) & (! [X26] : (room(X26) => (predk(X26) | ~preda(X26))) => ~? [X27] : (room(X27) => (predk(X27) => predb(X27)))) & (predo(mary) => ! [X28] : (room(X28) => (~predj(X28) => preda(X28)))) & (! [X29] : (room(X29) => (predo(X29) | ~predd(X29))) <=> ! [X30] : (room(X30) => (~prede(X30) | ~predp(X30)))) & (! [X31] : (~room(X31) => (~predg(X31) | predn(X31))) <~> ~! [X32] : (room(X32) => (predn(X32) | ~predc(X32)))) & ! [X33] : (room(X33) => mary = X33) & room(mary) [flattening 46] 48. ~(! [X0] : (room(X0) => (~predb(X0) | predb(X0))) & ! [X1] : (room(X1) => mary = X1) & room(mary)) [rectify 45] 49. predc(mary) & ! [X0] : (room(X0) => (~predc(X0) => predg(X0))) & ! [X1] : (room(X1) => ((prede(X1) & predj(X1)) => ~predc(X1))) & ! [X2] : (room(X2) => (predo(X2) => (prede(X2) & predj(X2)))) & ~predd(mary) & predi(mary) & predn(mary) & ! [X3,X4] : ((predg(X4) & predg(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (room(X6) => (predm(X6) => predd(X6))) & ! [X8] : (room(X8) => (predb(X8) => predo(X8))) & ! [X9] : (room(X9) => (prede(X9) <=> predb(X9))) & ! [X10] : (room(X10) => (predd(X10) => predk(X10))) & (~! [X11] : (~room(X11) => (predm(X11) | ~predg(X11))) => ! [X12] : (room(X12) => (predm(X12) => predd(X12)))) & (~? [X13] : ((~predd(X13) <~> predm(X13)) & room(X13)) => predn(mary)) & (predc(mary) => ? [X14] : (predl(X14) & room(X14))) & (predn(mary) => ! [X15] : (~room(X15) => (predb(X15) => predi(X15)))) & (~! [X16] : (room(X16) => (predj(X16) | ~predh(X16))) => ! [X17] : (room(X17) => ((~preda(X17) & ~predl(X17) & ~predb(X17)) => predo(X17)))) & (predm(mary) <=> ? [X18] : (prede(X18) & anywhere(X18))) & (? [X19] : (~preda(X19) & room(X19)) => predh(mary)) & (~? [X20] : (~preda(X20) & room(X20)) => ! [X21] : (room(X21) => (~predj(X21) | predd(X21)))) & (~? [X22] : (room(X22) => (~prede(X22) | predj(X22))) => ! [X23] : (room(X23) => (~prede(X23) => (predb(X23) & predm(X23))))) & (prede(mary) => ~? [X24] : (room(X24) => (~prede(X24) | predj(X24)))) & (~! [X25] : (room(X25) => (predk(X25) | ~preda(X25))) => predc(mary)) & (! [X26] : (room(X26) => (predk(X26) | ~preda(X26))) => ~? [X27] : (room(X27) => (predk(X27) => predb(X27)))) & (predo(mary) => ! [X28] : (room(X28) => (~predj(X28) => preda(X28)))) & (! [X29] : (room(X29) => (predo(X29) | ~predd(X29))) <=> ! [X30] : (room(X30) => (~prede(X30) | ~predp(X30)))) & (! [X31] : (~room(X31) => (~predg(X31) | predn(X31))) <~> ~! [X32] : (room(X32) => (predn(X32) | ~predc(X32)))) & ! [X33] : (room(X33) => mary = X33) & room(mary) [pure predicate removal 47] 50. predc(mary) & ! [X0] : (room(X0) => (~predc(X0) => predg(X0))) & ! [X1] : (room(X1) => ((prede(X1) & predj(X1)) => ~predc(X1))) & ! [X2] : (room(X2) => (predo(X2) => (prede(X2) & predj(X2)))) & ~predd(mary) & predn(mary) & ! [X3,X4] : ((predg(X4) & predg(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (room(X6) => (predm(X6) => predd(X6))) & ! [X8] : (room(X8) => (predb(X8) => predo(X8))) & ! [X9] : (room(X9) => (prede(X9) <=> predb(X9))) & ! [X10] : (room(X10) => (predd(X10) => predk(X10))) & (~! [X11] : (~room(X11) => (predm(X11) | ~predg(X11))) => ! [X12] : (room(X12) => (predm(X12) => predd(X12)))) & (~? [X13] : ((~predd(X13) <~> predm(X13)) & room(X13)) => predn(mary)) & (predc(mary) => ? [X14] : (predl(X14) & room(X14))) & (~! [X16] : (room(X16) => (predj(X16) | ~predh(X16))) => ! [X17] : (room(X17) => ((~preda(X17) & ~predl(X17) & ~predb(X17)) => predo(X17)))) & (predm(mary) <=> ? [X18] : (prede(X18) & anywhere(X18))) & (? [X19] : (~preda(X19) & room(X19)) => predh(mary)) & (~? [X20] : (~preda(X20) & room(X20)) => ! [X21] : (room(X21) => (~predj(X21) | predd(X21)))) & (~? [X22] : (room(X22) => (~prede(X22) | predj(X22))) => ! [X23] : (room(X23) => (~prede(X23) => (predb(X23) & predm(X23))))) & (prede(mary) => ~? [X24] : (room(X24) => (~prede(X24) | predj(X24)))) & (~! [X25] : (room(X25) => (predk(X25) | ~preda(X25))) => predc(mary)) & (! [X26] : (room(X26) => (predk(X26) | ~preda(X26))) => ~? [X27] : (room(X27) => (predk(X27) => predb(X27)))) & (predo(mary) => ! [X28] : (room(X28) => (~predj(X28) => preda(X28)))) & (! [X29] : (room(X29) => (predo(X29) | ~predd(X29))) <=> ! [X30] : (room(X30) => (~prede(X30) | ~predp(X30)))) & (! [X31] : (~room(X31) => (~predg(X31) | predn(X31))) <~> ~! [X32] : (room(X32) => (predn(X32) | ~predc(X32)))) & ! [X33] : (room(X33) => mary = X33) & room(mary) [pure predicate removal 49] 51. predc(mary) & ! [X0] : (room(X0) => (~predc(X0) => predg(X0))) & ! [X1] : (room(X1) => ((prede(X1) & predj(X1)) => ~predc(X1))) & ! [X2] : (room(X2) => (predo(X2) => (prede(X2) & predj(X2)))) & ~predd(mary) & predn(mary) & ! [X3,X4] : ((predg(X4) & predg(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (room(X6) => (predm(X6) => predd(X6))) & ! [X8] : (room(X8) => (predb(X8) => predo(X8))) & ! [X9] : (room(X9) => (prede(X9) <=> predb(X9))) & ! [X10] : (room(X10) => (predd(X10) => predk(X10))) & (~! [X11] : (~room(X11) => (predm(X11) | ~predg(X11))) => ! [X12] : (room(X12) => (predm(X12) => predd(X12)))) & (~? [X13] : ((~predd(X13) <~> predm(X13)) & room(X13)) => predn(mary)) & (predc(mary) => ? [X14] : room(X14)) & (predm(mary) <=> ? [X18] : (prede(X18) & anywhere(X18))) & (? [X19] : (~preda(X19) & room(X19)) => predh(mary)) & (~? [X20] : (~preda(X20) & room(X20)) => ! [X21] : (room(X21) => (~predj(X21) | predd(X21)))) & (~? [X22] : (room(X22) => (~prede(X22) | predj(X22))) => ! [X23] : (room(X23) => (~prede(X23) => (predb(X23) & predm(X23))))) & (prede(mary) => ~? [X24] : (room(X24) => (~prede(X24) | predj(X24)))) & (~! [X25] : (room(X25) => (predk(X25) | ~preda(X25))) => predc(mary)) & (! [X26] : (room(X26) => (predk(X26) | ~preda(X26))) => ~? [X27] : (room(X27) => (predk(X27) => predb(X27)))) & (predo(mary) => ! [X28] : (room(X28) => (~predj(X28) => preda(X28)))) & (! [X29] : (room(X29) => (predo(X29) | ~predd(X29))) <=> ! [X30] : (room(X30) => (~prede(X30) | ~predp(X30)))) & (! [X31] : (~room(X31) => (~predg(X31) | predn(X31))) <~> ~! [X32] : (room(X32) => (predn(X32) | ~predc(X32)))) & ! [X33] : (room(X33) => mary = X33) & room(mary) [pure predicate removal 50] 52. predc(mary) & ! [X0] : (room(X0) => (~predc(X0) => predg(X0))) & ! [X1] : (room(X1) => ((prede(X1) & predj(X1)) => ~predc(X1))) & ! [X2] : (room(X2) => (predo(X2) => (prede(X2) & predj(X2)))) & ~predd(mary) & predn(mary) & ! [X3,X4] : ((predg(X4) & predg(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (room(X6) => (predm(X6) => predd(X6))) & ! [X8] : (room(X8) => (predb(X8) => predo(X8))) & ! [X9] : (room(X9) => (prede(X9) <=> predb(X9))) & ! [X10] : (room(X10) => (predd(X10) => predk(X10))) & (~! [X11] : (~room(X11) => (predm(X11) | ~predg(X11))) => ! [X12] : (room(X12) => (predm(X12) => predd(X12)))) & (~? [X13] : ((~predd(X13) <~> predm(X13)) & room(X13)) => predn(mary)) & (predc(mary) => ? [X14] : room(X14)) & (predm(mary) <=> ? [X18] : (prede(X18) & anywhere(X18))) & (~? [X20] : (~preda(X20) & room(X20)) => ! [X21] : (room(X21) => (~predj(X21) | predd(X21)))) & (~? [X22] : (room(X22) => (~prede(X22) | predj(X22))) => ! [X23] : (room(X23) => (~prede(X23) => (predb(X23) & predm(X23))))) & (prede(mary) => ~? [X24] : (room(X24) => (~prede(X24) | predj(X24)))) & (~! [X25] : (room(X25) => (predk(X25) | ~preda(X25))) => predc(mary)) & (! [X26] : (room(X26) => (predk(X26) | ~preda(X26))) => ~? [X27] : (room(X27) => (predk(X27) => predb(X27)))) & (predo(mary) => ! [X28] : (room(X28) => (~predj(X28) => preda(X28)))) & (! [X29] : (room(X29) => (predo(X29) | ~predd(X29))) <=> ! [X30] : (room(X30) => (~prede(X30) | ~predp(X30)))) & (! [X31] : (~room(X31) => (~predg(X31) | predn(X31))) <~> ~! [X32] : (room(X32) => (predn(X32) | ~predc(X32)))) & ! [X33] : (room(X33) => mary = X33) & room(mary) [pure predicate removal 51] 124. predc(mary) & ! [X0] : ((predg(X0) | predc(X0)) | ~room(X0)) & ! [X1] : ((~predc(X1) | (~prede(X1) | ~predj(X1))) | ~room(X1)) & ! [X2] : (((prede(X2) & predj(X2)) | ~predo(X2)) | ~room(X2)) & ~predd(mary) & predn(mary) & ! [X3,X4] : (X3 = X4 | (~predg(X4) | ~predg(X3) | ~room(X4) | ~room(X3))) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : ((predd(X6) | ~predm(X6)) | ~room(X6)) & ! [X8] : ((predo(X8) | ~predb(X8)) | ~room(X8)) & ! [X9] : ((prede(X9) <=> predb(X9)) | ~room(X9)) & ! [X10] : ((predk(X10) | ~predd(X10)) | ~room(X10)) & (! [X12] : ((predd(X12) | ~predm(X12)) | ~room(X12)) | ! [X11] : ((predm(X11) | ~predg(X11)) | room(X11))) & (predn(mary) | ? [X13] : ((~predd(X13) <~> predm(X13)) & room(X13))) & (? [X14] : room(X14) | ~predc(mary)) & (predm(mary) <=> ? [X18] : (prede(X18) & anywhere(X18))) & (! [X21] : ((~predj(X21) | predd(X21)) | ~room(X21)) | ? [X20] : (~preda(X20) & room(X20))) & (! [X23] : (((predb(X23) & predm(X23)) | prede(X23)) | ~room(X23)) | ? [X22] : ((~prede(X22) | predj(X22)) | ~room(X22))) & (! [X24] : ((prede(X24) & ~predj(X24)) & room(X24)) | ~prede(mary)) & (predc(mary) | ! [X25] : ((predk(X25) | ~preda(X25)) | ~room(X25))) & (! [X27] : ((~predb(X27) & predk(X27)) & room(X27)) | ? [X26] : ((~predk(X26) & preda(X26)) & room(X26))) & (! [X28] : ((preda(X28) | predj(X28)) | ~room(X28)) | ~predo(mary)) & (! [X29] : ((predo(X29) | ~predd(X29)) | ~room(X29)) <=> ! [X30] : ((~prede(X30) | ~predp(X30)) | ~room(X30))) & (! [X31] : ((~predg(X31) | predn(X31)) | room(X31)) <~> ? [X32] : ((~predn(X32) & predc(X32)) & room(X32))) & ! [X33] : (mary = X33 | ~room(X33)) & room(mary) [ennf transformation 52] 125. predc(mary) & ! [X0] : (predg(X0) | predc(X0) | ~room(X0)) & ! [X1] : (~predc(X1) | ~prede(X1) | ~predj(X1) | ~room(X1)) & ! [X2] : ((prede(X2) & predj(X2)) | ~predo(X2) | ~room(X2)) & ~predd(mary) & predn(mary) & ! [X3,X4] : (X3 = X4 | ~predg(X4) | ~predg(X3) | ~room(X4) | ~room(X3)) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (predd(X6) | ~predm(X6) | ~room(X6)) & ! [X8] : (predo(X8) | ~predb(X8) | ~room(X8)) & ! [X9] : ((prede(X9) <=> predb(X9)) | ~room(X9)) & ! [X10] : (predk(X10) | ~predd(X10) | ~room(X10)) & (! [X12] : (predd(X12) | ~predm(X12) | ~room(X12)) | ! [X11] : (predm(X11) | ~predg(X11) | room(X11))) & (predn(mary) | ? [X13] : ((~predd(X13) <~> predm(X13)) & room(X13))) & (? [X14] : room(X14) | ~predc(mary)) & (predm(mary) <=> ? [X18] : (prede(X18) & anywhere(X18))) & (! [X21] : (~predj(X21) | predd(X21) | ~room(X21)) | ? [X20] : (~preda(X20) & room(X20))) & (! [X23] : ((predb(X23) & predm(X23)) | prede(X23) | ~room(X23)) | ? [X22] : (~prede(X22) | predj(X22) | ~room(X22))) & (! [X24] : (prede(X24) & ~predj(X24) & room(X24)) | ~prede(mary)) & (predc(mary) | ! [X25] : (predk(X25) | ~preda(X25) | ~room(X25))) & (! [X27] : (~predb(X27) & predk(X27) & room(X27)) | ? [X26] : (~predk(X26) & preda(X26) & room(X26))) & (! [X28] : (preda(X28) | predj(X28) | ~room(X28)) | ~predo(mary)) & (! [X29] : (predo(X29) | ~predd(X29) | ~room(X29)) <=> ! [X30] : (~prede(X30) | ~predp(X30) | ~room(X30))) & (! [X31] : (~predg(X31) | predn(X31) | room(X31)) <~> ? [X32] : (~predn(X32) & predc(X32) & room(X32))) & ! [X33] : (mary = X33 | ~room(X33)) & room(mary) [flattening 124] 126. ? [X0] : ((predb(X0) & ~predb(X0)) & room(X0)) | ? [X1] : (mary != X1 & room(X1)) | ~room(mary) [ennf transformation 48] 127. ? [X0] : (predb(X0) & ~predb(X0) & room(X0)) | ? [X1] : (mary != X1 & room(X1)) | ~room(mary) [flattening 126] 128. sP0 <=> ! [X31] : (~predg(X31) | predn(X31) | room(X31)) [predicate definition introduction] 129. ? [X26] : (~predk(X26) & preda(X26) & room(X26)) | ~sP1 [predicate definition introduction] 130. predc(mary) & ! [X0] : (predg(X0) | predc(X0) | ~room(X0)) & ! [X1] : (~predc(X1) | ~prede(X1) | ~predj(X1) | ~room(X1)) & ! [X2] : ((prede(X2) & predj(X2)) | ~predo(X2) | ~room(X2)) & ~predd(mary) & predn(mary) & ! [X3,X4] : (X3 = X4 | ~predg(X4) | ~predg(X3) | ~room(X4) | ~room(X3)) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (predd(X6) | ~predm(X6) | ~room(X6)) & ! [X8] : (predo(X8) | ~predb(X8) | ~room(X8)) & ! [X9] : ((prede(X9) <=> predb(X9)) | ~room(X9)) & ! [X10] : (predk(X10) | ~predd(X10) | ~room(X10)) & (! [X12] : (predd(X12) | ~predm(X12) | ~room(X12)) | ! [X11] : (predm(X11) | ~predg(X11) | room(X11))) & (predn(mary) | ? [X13] : ((~predd(X13) <~> predm(X13)) & room(X13))) & (? [X14] : room(X14) | ~predc(mary)) & (predm(mary) <=> ? [X18] : (prede(X18) & anywhere(X18))) & (! [X21] : (~predj(X21) | predd(X21) | ~room(X21)) | ? [X20] : (~preda(X20) & room(X20))) & (! [X23] : ((predb(X23) & predm(X23)) | prede(X23) | ~room(X23)) | ? [X22] : (~prede(X22) | predj(X22) | ~room(X22))) & (! [X24] : (prede(X24) & ~predj(X24) & room(X24)) | ~prede(mary)) & (predc(mary) | ! [X25] : (predk(X25) | ~preda(X25) | ~room(X25))) & (! [X27] : (~predb(X27) & predk(X27) & room(X27)) | sP1) & (! [X28] : (preda(X28) | predj(X28) | ~room(X28)) | ~predo(mary)) & (! [X29] : (predo(X29) | ~predd(X29) | ~room(X29)) <=> ! [X30] : (~prede(X30) | ~predp(X30) | ~room(X30))) & (sP0 <~> ? [X32] : (~predn(X32) & predc(X32) & room(X32))) & ! [X33] : (mary = X33 | ~room(X33)) & room(mary) [definition folding 125,129,128] 140. predc(mary) & ! [X0] : (predg(X0) | predc(X0) | ~room(X0)) & ! [X1] : (~predc(X1) | ~prede(X1) | ~predj(X1) | ~room(X1)) & ! [X2] : ((prede(X2) & predj(X2)) | ~predo(X2) | ~room(X2)) & ~predd(mary) & predn(mary) & ! [X3,X4] : (X3 = X4 | ~predg(X4) | ~predg(X3) | ~room(X4) | ~room(X3)) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (predd(X6) | ~predm(X6) | ~room(X6)) & ! [X8] : (predo(X8) | ~predb(X8) | ~room(X8)) & ! [X9] : (((prede(X9) | ~predb(X9)) & (predb(X9) | ~prede(X9))) | ~room(X9)) & ! [X10] : (predk(X10) | ~predd(X10) | ~room(X10)) & (! [X12] : (predd(X12) | ~predm(X12) | ~room(X12)) | ! [X11] : (predm(X11) | ~predg(X11) | room(X11))) & (predn(mary) | ? [X13] : (((~predm(X13) | predd(X13)) & (predm(X13) | ~predd(X13))) & room(X13))) & (? [X14] : room(X14) | ~predc(mary)) & ((predm(mary) | ! [X18] : (~prede(X18) | ~anywhere(X18))) & (? [X18] : (prede(X18) & anywhere(X18)) | ~predm(mary))) & (! [X21] : (~predj(X21) | predd(X21) | ~room(X21)) | ? [X20] : (~preda(X20) & room(X20))) & (! [X23] : ((predb(X23) & predm(X23)) | prede(X23) | ~room(X23)) | ? [X22] : (~prede(X22) | predj(X22) | ~room(X22))) & (! [X24] : (prede(X24) & ~predj(X24) & room(X24)) | ~prede(mary)) & (predc(mary) | ! [X25] : (predk(X25) | ~preda(X25) | ~room(X25))) & (! [X27] : (~predb(X27) & predk(X27) & room(X27)) | sP1) & (! [X28] : (preda(X28) | predj(X28) | ~room(X28)) | ~predo(mary)) & ((! [X29] : (predo(X29) | ~predd(X29) | ~room(X29)) | ? [X30] : (prede(X30) & predp(X30) & room(X30))) & (! [X30] : (~prede(X30) | ~predp(X30) | ~room(X30)) | ? [X29] : (~predo(X29) & predd(X29) & room(X29)))) & ((! [X32] : (predn(X32) | ~predc(X32) | ~room(X32)) | ~sP0) & (? [X32] : (~predn(X32) & predc(X32) & room(X32)) | sP0)) & ! [X33] : (mary = X33 | ~room(X33)) & room(mary) [nnf transformation 130] 141. predc(mary) & ! [X0] : (predg(X0) | predc(X0) | ~room(X0)) & ! [X1] : (~predc(X1) | ~prede(X1) | ~predj(X1) | ~room(X1)) & ! [X2] : ((prede(X2) & predj(X2)) | ~predo(X2) | ~room(X2)) & ~predd(mary) & predn(mary) & ! [X3,X4] : (X3 = X4 | ~predg(X4) | ~predg(X3) | ~room(X4) | ~room(X3)) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (predd(X6) | ~predm(X6) | ~room(X6)) & ! [X8] : (predo(X8) | ~predb(X8) | ~room(X8)) & ! [X9] : (((prede(X9) | ~predb(X9)) & (predb(X9) | ~prede(X9))) | ~room(X9)) & ! [X10] : (predk(X10) | ~predd(X10) | ~room(X10)) & (! [X12] : (predd(X12) | ~predm(X12) | ~room(X12)) | ! [X11] : (predm(X11) | ~predg(X11) | room(X11))) & (predn(mary) | ? [X13] : ((~predm(X13) | predd(X13)) & (predm(X13) | ~predd(X13)) & room(X13))) & (? [X14] : room(X14) | ~predc(mary)) & (predm(mary) | ! [X18] : (~prede(X18) | ~anywhere(X18))) & (? [X18] : (prede(X18) & anywhere(X18)) | ~predm(mary)) & (! [X21] : (~predj(X21) | predd(X21) | ~room(X21)) | ? [X20] : (~preda(X20) & room(X20))) & (! [X23] : ((predb(X23) & predm(X23)) | prede(X23) | ~room(X23)) | ? [X22] : (~prede(X22) | predj(X22) | ~room(X22))) & (! [X24] : (prede(X24) & ~predj(X24) & room(X24)) | ~prede(mary)) & (predc(mary) | ! [X25] : (predk(X25) | ~preda(X25) | ~room(X25))) & (! [X27] : (~predb(X27) & predk(X27) & room(X27)) | sP1) & (! [X28] : (preda(X28) | predj(X28) | ~room(X28)) | ~predo(mary)) & (! [X29] : (predo(X29) | ~predd(X29) | ~room(X29)) | ? [X30] : (prede(X30) & predp(X30) & room(X30))) & (! [X30] : (~prede(X30) | ~predp(X30) | ~room(X30)) | ? [X29] : (~predo(X29) & predd(X29) & room(X29))) & (! [X32] : (predn(X32) | ~predc(X32) | ~room(X32)) | ~sP0) & (? [X32] : (~predn(X32) & predc(X32) & room(X32)) | sP0) & ! [X33] : (mary = X33 | ~room(X33)) & room(mary) [flattening 140] 142. predc(mary) & ! [X0] : (predg(X0) | predc(X0) | ~room(X0)) & ! [X1] : (~predc(X1) | ~prede(X1) | ~predj(X1) | ~room(X1)) & ! [X2] : ((prede(X2) & predj(X2)) | ~predo(X2) | ~room(X2)) & ~predd(mary) & predn(mary) & ! [X3,X4] : (X3 = X4 | ~predg(X4) | ~predg(X3) | ~room(X4) | ~room(X3)) & ? [X5] : (predg(X5) & room(X5)) & ! [X6] : (predd(X6) | ~predm(X6) | ~room(X6)) & ! [X7] : (predo(X7) | ~predb(X7) | ~room(X7)) & ! [X8] : (((prede(X8) | ~predb(X8)) & (predb(X8) | ~prede(X8))) | ~room(X8)) & ! [X9] : (predk(X9) | ~predd(X9) | ~room(X9)) & (! [X10] : (predd(X10) | ~predm(X10) | ~room(X10)) | ! [X11] : (predm(X11) | ~predg(X11) | room(X11))) & (predn(mary) | ? [X12] : ((~predm(X12) | predd(X12)) & (predm(X12) | ~predd(X12)) & room(X12))) & (? [X13] : room(X13) | ~predc(mary)) & (predm(mary) | ! [X14] : (~prede(X14) | ~anywhere(X14))) & (? [X15] : (prede(X15) & anywhere(X15)) | ~predm(mary)) & (! [X16] : (~predj(X16) | predd(X16) | ~room(X16)) | ? [X17] : (~preda(X17) & room(X17))) & (! [X18] : ((predb(X18) & predm(X18)) | prede(X18) | ~room(X18)) | ? [X19] : (~prede(X19) | predj(X19) | ~room(X19))) & (! [X20] : (prede(X20) & ~predj(X20) & room(X20)) | ~prede(mary)) & (predc(mary) | ! [X21] : (predk(X21) | ~preda(X21) | ~room(X21))) & (! [X22] : (~predb(X22) & predk(X22) & room(X22)) | sP1) & (! [X23] : (preda(X23) | predj(X23) | ~room(X23)) | ~predo(mary)) & (! [X24] : (predo(X24) | ~predd(X24) | ~room(X24)) | ? [X25] : (prede(X25) & predp(X25) & room(X25))) & (! [X26] : (~prede(X26) | ~predp(X26) | ~room(X26)) | ? [X27] : (~predo(X27) & predd(X27) & room(X27))) & (! [X28] : (predn(X28) | ~predc(X28) | ~room(X28)) | ~sP0) & (? [X29] : (~predn(X29) & predc(X29) & room(X29)) | sP0) & ! [X30] : (mary = X30 | ~room(X30)) & room(mary) [rectify 141] 143. ? [X5] : (predg(X5) & room(X5)) => (predg(sK4) & room(sK4)) [choice axiom] 144. ? [X12] : ((~predm(X12) | predd(X12)) & (predm(X12) | ~predd(X12)) & room(X12)) => ((~predm(sK5) | predd(sK5)) & (predm(sK5) | ~predd(sK5)) & room(sK5)) [choice axiom] 145. ? [X13] : room(X13) => room(sK6) [choice axiom] 146. ? [X15] : (prede(X15) & anywhere(X15)) => (prede(sK7) & anywhere(sK7)) [choice axiom] 147. ? [X17] : (~preda(X17) & room(X17)) => (~preda(sK8) & room(sK8)) [choice axiom] 148. ? [X19] : (~prede(X19) | predj(X19) | ~room(X19)) => (~prede(sK9) | predj(sK9) | ~room(sK9)) [choice axiom] 149. ? [X25] : (prede(X25) & predp(X25) & room(X25)) => (prede(sK10) & predp(sK10) & room(sK10)) [choice axiom] 150. ? [X27] : (~predo(X27) & predd(X27) & room(X27)) => (~predo(sK11) & predd(sK11) & room(sK11)) [choice axiom] 151. ? [X29] : (~predn(X29) & predc(X29) & room(X29)) => (~predn(sK12) & predc(sK12) & room(sK12)) [choice axiom] 152. predc(mary) & ! [X0] : (predg(X0) | predc(X0) | ~room(X0)) & ! [X1] : (~predc(X1) | ~prede(X1) | ~predj(X1) | ~room(X1)) & ! [X2] : ((prede(X2) & predj(X2)) | ~predo(X2) | ~room(X2)) & ~predd(mary) & predn(mary) & ! [X3,X4] : (X3 = X4 | ~predg(X4) | ~predg(X3) | ~room(X4) | ~room(X3)) & (predg(sK4) & room(sK4)) & ! [X6] : (predd(X6) | ~predm(X6) | ~room(X6)) & ! [X7] : (predo(X7) | ~predb(X7) | ~room(X7)) & ! [X8] : (((prede(X8) | ~predb(X8)) & (predb(X8) | ~prede(X8))) | ~room(X8)) & ! [X9] : (predk(X9) | ~predd(X9) | ~room(X9)) & (! [X10] : (predd(X10) | ~predm(X10) | ~room(X10)) | ! [X11] : (predm(X11) | ~predg(X11) | room(X11))) & (predn(mary) | ((~predm(sK5) | predd(sK5)) & (predm(sK5) | ~predd(sK5)) & room(sK5))) & (room(sK6) | ~predc(mary)) & (predm(mary) | ! [X14] : (~prede(X14) | ~anywhere(X14))) & ((prede(sK7) & anywhere(sK7)) | ~predm(mary)) & (! [X16] : (~predj(X16) | predd(X16) | ~room(X16)) | (~preda(sK8) & room(sK8))) & (! [X18] : ((predb(X18) & predm(X18)) | prede(X18) | ~room(X18)) | (~prede(sK9) | predj(sK9) | ~room(sK9))) & (! [X20] : (prede(X20) & ~predj(X20) & room(X20)) | ~prede(mary)) & (predc(mary) | ! [X21] : (predk(X21) | ~preda(X21) | ~room(X21))) & (! [X22] : (~predb(X22) & predk(X22) & room(X22)) | sP1) & (! [X23] : (preda(X23) | predj(X23) | ~room(X23)) | ~predo(mary)) & (! [X24] : (predo(X24) | ~predd(X24) | ~room(X24)) | (prede(sK10) & predp(sK10) & room(sK10))) & (! [X26] : (~prede(X26) | ~predp(X26) | ~room(X26)) | (~predo(sK11) & predd(sK11) & room(sK11))) & (! [X28] : (predn(X28) | ~predc(X28) | ~room(X28)) | ~sP0) & ((~predn(sK12) & predc(sK12) & room(sK12)) | sP0) & ! [X30] : (mary = X30 | ~room(X30)) & room(mary) [skolemisation 142,151,150,149,148,147,146,145,144,143] 153. ? [X0] : (predb(X0) & ~predb(X0) & room(X0)) => (predb(sK13) & ~predb(sK13) & room(sK13)) [choice axiom] 154. ? [X1] : (mary != X1 & room(X1)) => (mary != sK14 & room(sK14)) [choice axiom] 155. (predb(sK13) & ~predb(sK13) & room(sK13)) | (mary != sK14 & room(sK14)) | ~room(mary) [skolemisation 127,154,153] 244. room(mary) [cnf transformation 152] 245. ~room(X30) | mary = X30 [cnf transformation 152] 293. ~predb(sK13) | room(sK14) | ~room(mary) [cnf transformation 155] 294. ~predb(sK13) | mary != sK14 | ~room(mary) [cnf transformation 155] 295. predb(sK13) | room(sK14) | ~room(mary) [cnf transformation 155] 296. predb(sK13) | mary != sK14 | ~room(mary) [cnf transformation 155] 476. predb(sK13) | mary != sK14 [subsumption resolution 296,244] 478. 41 <=> mary = sK14 [avatar definition] 480. mary != sK14 <- (~41) [avatar component clause 478] 482. 42 <=> predb(sK13) [avatar definition] 485. ~41 | 42 [avatar split clause 476,482,478] 486. predb(sK13) | room(sK14) [subsumption resolution 295,244] 488. 43 <=> room(sK14) [avatar definition] 490. room(sK14) <- (43) [avatar component clause 488] 491. 43 | 42 [avatar split clause 486,482,488] 492. ~predb(sK13) | mary != sK14 [subsumption resolution 294,244] 493. ~41 | ~42 [avatar split clause 492,482,478] 494. ~predb(sK13) | room(sK14) [subsumption resolution 293,244] 495. 43 | ~42 [avatar split clause 494,482,488] 511. mary = sK14 <- (43) [resolution 245,490] 561. $false <- (~41, 43) [subsumption resolution 511,480] 562. 41 | ~43 [avatar contradiction clause 561] 568. $false [avatar sat refutation 485,491,493,495,562] % SZS output end Proof for 4543761929244778984949486 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

Rene, David, Micheal are the only persons in the room. Everyone in the room who is a skilled home brewer experimenting with craft beer recipes practices pilates. If someone is a skilled home brewer experimenting with craft beer recipes then he/she bakes bread at home and vice versa. Everyone in the room does not practice digital art. Everyone in the room owns a telescope if they enjoys kayaking. Everyone in the room who enjoys making ceramics travels domestically frequently. No one anywhere who travels domestically frequently is a coffee connoisseur. Everyone in the room who is a coffee connoisseur can play the guitar. Everyone in the room either bakes bread at home or does not enjoy making ceramics but not both if they can play the guitar.

Rene is a coffee connoisseur.

contradiction

room(rene)&room(david)&room(micheal)&(![X]:(room(X)=>(X='rene'|X='david'|X='micheal')))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(practices_pilates(X))))))& ((![X]:((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=>(bakes_bread_at_home(X)))))& (![X]:(room(X)=>(does_not_practice_digital_art(X))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(owns_a_telescope(X))))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(travels_domestically_frequently(X))))))& (~?[X]:(anywhere(X)=>(((travels_domestically_frequently(X))=>(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(((bakes_bread_at_home(X))<~>(does_not_enjoy_making_ceramics(X))))))))

room(rene)&room(david)&room(micheal)&(![X]:(room(X)=>(X='rene'|X='david'|X='micheal')))& is_a_coffee_connoisseur(rene)

% SZS status Unsatisfiable for 4312256520963243815407784 % SZS output start Proof for 4312256520963243815407784 50. ~? [X0] : (anywhere(X0) => (predi(X0) => predc(X0))) [input p6] 53. predc(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 55. ~? [X0] : (anywhere(X0) => predc(X0)) [pure predicate removal 50] 61. ~? [X0] : predc(X0) [pure predicate removal 55] 136. ! [X0] : ~predc(X0) [ennf transformation 61] 141. predc(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 53] 142. predc(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 141] 229. ~predc(X0) [cnf transformation 136] 237. predc(mary) [cnf transformation 142] 238. $false [subsumption resolution 237,229] % SZS output end Proof for 4312256520963243815407784 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Leslie, Brandon, Dennis are the only persons in the room. Everyone in the room plays eSports competitively. Everyone in the room who practices kickboxing enjoys spelunking. If someone enjoys skydiving and plays the drums then he/she plays the drums and vice versa. Everyone in the room who writes poetry enjoys spelunking. Everyone in the room does not practice kickboxing if they plays eSports competitively and is a craft beer aficionado. Everyone in the room does not practice kickboxing if they can play the flute and vice versa. Everyone anywhere can play the flute only if they competes in national level swimming championships. Dennis writes poetry. Everyone in the room writes poetry if they can play the flute and vice versa. Everyone in the room enjoys skydiving only if they plays eSports competitively. Everyone in the room has completed a triathlon if they enjoys spelunking. If someone does not have completed a triathlon then he/she is a craft beer aficionado and vice versa.

Brandon is a craft beer aficionado.

contradiction

room(leslie)&room(brandon)&room(dennis)&(![X]:(room(X)=>(X='leslie'|X='brandon'|X='dennis')))& (![X]:(room(X)=>(plays_eSports_competitively(X))))& (![X]:(room(X)=>(((practices_kickboxing(X))=>(enjoys_spelunking(X))))))& ((![X]:((((enjoys_skydiving(X))&(plays_the_drums(X))))<=>(plays_the_drums(X)))))& (![X]:(room(X)=>(((writes_poetry(X))=>(enjoys_spelunking(X))))))& (![X]:(room(X)=>(((((plays_eSports_competitively(X))&(is_a_craft_beer_aficionado(X))))=>(does_not_practice_kickboxing(X))))))& (![X]:(room(X)=>(((does_not_practice_kickboxing(X))<=>(can_play_the_flute(X))))))& (![X]:(anywhere(X)=>(((competes_in_national_level_swimming_championships(X))<=(can_play_the_flute(X))))))& (writes_poetry(dennis))& (![X]:(room(X)=>(((writes_poetry(X))<=>(can_play_the_flute(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))<=(enjoys_skydiving(X))))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(has_completed_a_triathlon(X))))))& ((![X]:((does_not_have_completed_a_triathlon(X))<=>(is_a_craft_beer_aficionado(X)))))

room(leslie)&room(brandon)&room(dennis)&(![X]:(room(X)=>(X='leslie'|X='brandon'|X='dennis')))& is_a_craft_beer_aficionado(brandon)

% SZS status Unsatisfiable for 237637619035690930086858 % SZS output start Proof for 237637619035690930086858 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => predg(X0)) [input p1] 48. ! [X0] : (room(X0) => (predb(X0) => predf(X0))) [input p4] 49. ! [X0] : (room(X0) => ((predj(X0) & predg(X0)) => ~prede(X0))) [input p5] 50. ! [X0] : (room(X0) => (~prede(X0) <=> preda(X0))) [input p6] 53. ! [X0] : (room(X0) => (predb(X0) <=> preda(X0))) [input p9] 55. ! [X0] : (room(X0) => (predf(X0) => predh(X0))) [input p11] 56. ! [X0] : (~predh(X0) <=> predj(X0)) [input p12] 57. predj(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 58. ! [X0] : (predj(X0) => ~predh(X0)) [unused predicate definition removal 56] 132. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 133. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 132] 134. ! [X0] : (predg(X0) | ~room(X0)) [ennf transformation 45] 137. ! [X0] : ((predf(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 48] 138. ! [X0] : (predf(X0) | ~predb(X0) | ~room(X0)) [flattening 137] 139. ! [X0] : ((~prede(X0) | (~predj(X0) | ~predg(X0))) | ~room(X0)) [ennf transformation 49] 140. ! [X0] : (~prede(X0) | ~predj(X0) | ~predg(X0) | ~room(X0)) [flattening 139] 141. ! [X0] : ((~prede(X0) <=> preda(X0)) | ~room(X0)) [ennf transformation 50] 142. ! [X0] : ((predb(X0) <=> preda(X0)) | ~room(X0)) [ennf transformation 53] 145. ! [X0] : ((predh(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 55] 146. ! [X0] : (predh(X0) | ~predf(X0) | ~room(X0)) [flattening 145] 147. ! [X0] : (~predh(X0) | ~predj(X0)) [ennf transformation 58] 148. predj(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 149. predj(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 148] 153. ! [X0] : (((~prede(X0) | ~preda(X0)) & (preda(X0) | prede(X0))) | ~room(X0)) [nnf transformation 141] 154. ! [X0] : (((predb(X0) | ~preda(X0)) & (preda(X0) | ~predb(X0))) | ~room(X0)) [nnf transformation 142] 236. room(paul) [cnf transformation 133] 239. ~room(X0) | predg(X0) [cnf transformation 134] 244. ~predb(X0) | predf(X0) | ~room(X0) [cnf transformation 138] 245. ~prede(X0) | ~predj(X0) | ~predg(X0) | ~room(X0) [cnf transformation 140] 246. ~room(X0) | prede(X0) | preda(X0) [cnf transformation 153] 250. ~preda(X0) | predb(X0) | ~room(X0) [cnf transformation 154] 252. ~predf(X0) | predh(X0) | ~room(X0) [cnf transformation 146] 253. ~predh(X0) | ~predj(X0) [cnf transformation 147] 258. predj(paul) [cnf transformation 149] 259. ~predj(X0) | ~prede(X0) | ~room(X0) [subsumption resolution 245,239] 266. prede(paul) | preda(paul) [resolution 246,236] 278. 3 <=> preda(paul) [avatar definition] 280. preda(paul) <- (3) [avatar component clause 278] 282. 4 <=> prede(paul) [avatar definition] 285. 3 | 4 [avatar split clause 266,282,278] 301. predb(paul) | ~room(paul) <- (3) [resolution 250,280] 302. predb(paul) <- (3) [subsumption resolution 301,236] 309. ~prede(paul) | ~room(paul) [resolution 259,258] 313. predf(paul) | ~room(paul) <- (3) [resolution 302,244] 314. predf(paul) <- (3) [subsumption resolution 313,236] 317. predh(paul) | ~room(paul) <- (3) [resolution 314,252] 318. predh(paul) <- (3) [subsumption resolution 317,236] 319. ~predj(paul) <- (3) [resolution 318,253] 320. $false <- (3) [subsumption resolution 319,258] 321. ~3 [avatar contradiction clause 320] 322. ~prede(paul) [subsumption resolution 309,236] 323. ~4 [avatar split clause 322,282] 324. $false [avatar sat refutation 285,321,323] % SZS output end Proof for 237637619035690930086858 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If “everyone in the room is not a night owl or enjoys kayaking and exploring remote waterways” then “not everyone in the room does not use contact lenses if they is not a night owl”. “Everyone in the room does not collect comic books or enjoys kayaking” only if “if someone neither owns a telescope nor enjoys kayaking then he/she neither streams on Twitch nor is a client of Costco and vice versa”. Everyone in the room who does not collect comic books can play the guitar and practices zumba. No one in the room practices digital art or is not a craft beer aficionado. At least one person in the room does not collect comic books. Everyone in the room enjoys kayaking or cannot play the guitar. If someone enjoys camping and organizing outdoor survival workshops then he/she can play the guitar. Everyone anywhere who uses an ios phone enjoys coding in Python and practices digital art. Everyone in the room who enjoys coding in Python and practices digital art uses an ios phone. At least one person anywhere enjoys camping and organizing outdoor survival workshops. Everyone outside the room who is a client of Costco uses contact lenses. Everyone in the room can play the guitar if they uses contact lenses. Everyone in the room who has a curated collection of mid-century modern furniture can play the guitar. Everyone outside the room who has a curated collection of mid-century modern furniture, practices digital art and enjoys kayaking streams on Twitch. No one in the room who neither streams on Twitch nor enjoys kayaking and exploring remote waterways enjoys kayaking and exploring remote waterways and is a coffee connoisseur. Everyone outside the room who hosts regular workshops on creative writing enjoys kayaking, streams on Twitch and is a dedicated volunteer for local community service projects. Everyone in the room is not a night owl or enjoys kayaking, streams on Twitch and is a dedicated volunteer for local community service projects. Everyone in the room is not a night owl if and only if they is a craft beer aficionado. Everyone in the room who is a craft beer aficionado uses an ios phone, enjoys kayaking and exploring remote waterways or enjoys kayaking.

Everyone in the room does not enjoy cross-country skiing or enjoys kayaking.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(is_not_a_night_owl(X))))))=>(~![X]:(room(X)=>(((is_not_a_night_owl(X))=>(does_not_use_contact_lenses(X)))))))& ((![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_collect_comic_books(X))))))=>((![X]:((~((owns_a_telescope(X))|(enjoys_kayaking(X))))<=>(~((streams_on_Twitch(X))|(is_a_client_of_Costco(X))))))))& (![X]:(room(X)=>(((does_not_collect_comic_books(X))=>(((can_play_the_guitar(X))&(practices_zumba(X))))))))& (~?[X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(practices_digital_art(X))))))& (((?[X]:(room(X)&does_not_collect_comic_books(X)))))& (![X]:(room(X)=>(((cannot_play_the_guitar(X))|(enjoys_kayaking(X))))))& ((![X]:((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(can_play_the_guitar(X)))))& (![X]:(anywhere(X)=>(((uses_an_ios_phone(X))=>(((enjoys_coding_in_Python(X))&(practices_digital_art(X))))))))& (![X]:(room(X)=>(((((enjoys_coding_in_Python(X))&(practices_digital_art(X))))=>(uses_an_ios_phone(X))))))& (((?[X]:(anywhere(X)&enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (![X]:(~room(X)=>(((is_a_client_of_Costco(X))=>(uses_contact_lenses(X))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(can_play_the_guitar(X))))))& (![X]:(~room(X)=>(((((has_a_curated_collection_of_mid-century_modern_furniture(X))&(practices_digital_art(X))&(enjoys_kayaking(X))))=>(streams_on_Twitch(X))))))& (~?[X]:(room(X)=>(((~((streams_on_Twitch(X))|(enjoys_kayaking_and_exploring_remote_waterways(X))))=>(((enjoys_kayaking_and_exploring_remote_waterways(X))&(is_a_coffee_connoisseur(X))))))))& (![X]:(~room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(((enjoys_kayaking(X))&(streams_on_Twitch(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))))& (![X]:(room(X)=>(((((enjoys_kayaking(X))&(streams_on_Twitch(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))|(is_not_a_night_owl(X))))))& (![X]:(room(X)=>(((is_not_a_night_owl(X))<=>(is_a_craft_beer_aficionado(X))))))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(((uses_an_ios_phone(X))|(enjoys_kayaking_and_exploring_remote_waterways(X))|(enjoys_kayaking(X))))))))& (![X]:(room(X)=>(((((uses_an_ios_phone(X))|(enjoys_kayaking_and_exploring_remote_waterways(X))|(enjoys_kayaking(X))))=>(((enjoys_kayaking(X))&(is_a_craft_beer_aficionado(X))&(collects_vintage_vinyl_records(X))))))))& (![X]:(room(X)=>(((((enjoys_kayaking(X))&(is_a_craft_beer_aficionado(X))&(collects_vintage_vinyl_records(X))))|(does_not_enjoy_cross-country_skiing(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_cross-country_skiing(X))=>(is_a_client_of_Costco(X))))))& (![X]:(~room(X)=>(((is_a_client_of_Costco(X))<=>(can_play_the_guitar(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_enjoy_cross-country_skiing(X)))))

% SZS status Unsatisfiable for 6429393189098694529529983 % SZS output start Proof for 6429393189098694529529983 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 48. ~? [X0] : (room(X0) => (predl(X0) | ~predi(X0))) [input p4] 52. ! [X0] : (anywhere(X0) => (preda(X0) => (predl(X0) & preds(X0)))) [input p8] 59. ~? [X0] : (room(X0) => (~(predy(X0) | predh(X0)) => (predg(X0) & predy(X0)))) [input p15] 63. ! [X0] : (room(X0) => (predi(X0) => (predj(X0) | predy(X0) | preda(X0)))) [input p19] 68. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis] 76. ~? [X0] : (room(X0) => ~~(predy(X0) | predh(X0))) [pure predicate removal 59] 157. ! [X0] : ((~predl(X0) & predi(X0)) & room(X0)) [ennf transformation 48] 158. ! [X0] : (~predl(X0) & predi(X0) & room(X0)) [flattening 157] 162. ! [X0] : (((predl(X0) & preds(X0)) | ~preda(X0)) | ~anywhere(X0)) [ennf transformation 52] 163. ! [X0] : ((predl(X0) & preds(X0)) | ~preda(X0) | ~anywhere(X0)) [flattening 162] 170. ! [X0] : ((~predy(X0) & ~predh(X0)) & room(X0)) [ennf transformation 76] 171. ! [X0] : (~predy(X0) & ~predh(X0) & room(X0)) [flattening 170] 175. ! [X0] : (((predj(X0) | predy(X0) | preda(X0)) | ~predi(X0)) | ~room(X0)) [ennf transformation 63] 176. ! [X0] : (predj(X0) | predy(X0) | preda(X0) | ~predi(X0) | ~room(X0)) [flattening 175] 184. ? [X0] : ((predd(X0) & ~predj(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 68] 185. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ~there_is_a_room [flattening 184] 208. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK7) & ~predj(sK7) & room(sK7)) [choice axiom] 209. (predd(sK7) & ~predj(sK7) & room(sK7)) | ~there_is_a_room [skolemisation 185,208] 210. anywhere(X0) [cnf transformation 5] 291. there_is_a_room [cnf transformation 44] 306. room(X0) [cnf transformation 158] 307. predi(X0) [cnf transformation 158] 308. ~predl(X0) [cnf transformation 158] 314. predl(X0) | ~preda(X0) | ~anywhere(X0) [cnf transformation 163] 322. ~predy(X0) [cnf transformation 171] 327. predj(X0) | predy(X0) | preda(X0) | ~predi(X0) | ~room(X0) [cnf transformation 176] 340. ~predj(sK7) | ~there_is_a_room [cnf transformation 209] 412. ~preda(X0) | ~anywhere(X0) [subsumption resolution 314,308] 413. ~preda(X0) [subsumption resolution 412,210] 417. predj(X0) | preda(X0) | ~predi(X0) | ~room(X0) [subsumption resolution 327,322] 418. predj(X0) | ~predi(X0) | ~room(X0) [subsumption resolution 417,413] 419. predj(X0) | ~room(X0) [subsumption resolution 418,307] 420. predj(X0) [subsumption resolution 419,306] 422. ~there_is_a_room [subsumption resolution 340,420] 423. $false [subsumption resolution 422,291] % SZS output end Proof for 6429393189098694529529983 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Willie is the only person in the room. If “someone in the room is passionate about collecting and restoring classic cars” then “it is not the case that “someone in the room streams on Twitch””. If “someone in the room has a specialized collection of handmade artisan pottery” then “someone in the room collects action figures”. Someone outside the room enjoys skydiving. Someone in the room collects action figures. It is not the case that “someone in the room is passionate about collecting and restoring classic cars”. Someone in the room collects rare minerals or enjoys skydiving or both. Someone in the room practices and performs acrobatic dance routines. Someone in the room hosts regular workshops on creative writing. It is not the case that “someone in the room streams on Twitch”. Someone in the room enjoys making ceramics. It is not the case that “someone in the room plays video games”. It is not the case that “more than one person in the room collects rare and antique scientific instruments”.

Willie streams on Twitch.

contradiction

room(willie)&(![X]:(room(X)=>(X='willie')))& ((?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X))))=>(~(?[X]:(room(X)&(streams_on_Twitch(X))))))& ((?[X]:(room(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(?[X]:(room(X)&(collects_action_figures(X)))))& (?[X]:(~room(X)&(enjoys_skydiving(X))))& (?[X]:(room(X)&(collects_action_figures(X))))& (~(?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X)))))& (?[X]:(room(X)&(((collects_rare_minerals(X))|(enjoys_skydiving(X))))))& (?[X]:(room(X)&(practices_and_performs_acrobatic_dance_routines(X))))& (?[X]:(room(X)&(hosts_regular_workshops_on_creative_writing(X))))& (~(?[X]:(room(X)&(streams_on_Twitch(X)))))& (?[X]:(room(X)&(enjoys_making_ceramics(X))))& (~(?[X]:(room(X)&(plays_video_games(X)))))& (~((?[X,Y]:(room(X)&room(Y)&(collects_rare_and_antique_scientific_instruments(X)&collects_rare_and_antique_scientific_instruments(Y))&(X!=Y)))))

room(willie)&(![X]:(room(X)=>(X='willie')))& streams_on_Twitch(willie)

% SZS status Unsatisfiable for 5503180168122015712778947 % SZS output start Proof for 5503180168122015712778947 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 53. ~? [X0] : (predo(X0) & room(X0)) [input p9] 57. predo(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 144. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 145. ! [X0] : (~predo(X0) | ~room(X0)) [ennf transformation 53] 146. predo(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 57] 240. room(mary) [cnf transformation 144] 247. ~predo(X0) | ~room(X0) [cnf transformation 145] 251. predo(mary) [cnf transformation 146] 252. ~room(mary) [resolution 247,251] 253. $false [subsumption resolution 252,240] % SZS output end Proof for 5503180168122015712778947 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If 'everyone in the room does not write and illustrates their own graphic novels or is not a certified scuba diver with advanced underwater photography skills' then 'everyone in the room practices graffiti art if they does not write and illustrates their own graphic novels'. If 'everyone in the room collect rare sneakers' then 'everyone in the room who does enjoy mountain biking is a professional photographer specializing in portrait photography, is not an enthusiastic bird watcher who travels for rare sightings and is a certified scuba diver with advanced underwater photography skills'. Everyone in the room who is a professional photographer specializing in portrait photography, is not an enthusiastic bird watcher who travels for rare sightings and is a certified scuba diver with advanced underwater photography skills either is an enthusiastic bird watcher who travels for rare sightings or is a professional photographer specializing in portrait photography but not both. No one in the room who either is an enthusiastic bird watcher who travels for rare sightings or is a professional photographer specializing in portrait photography but not both is a drone photographer. Not everyone in the room who is a professional photographer specializing in portrait photography is a certified scuba diver with advanced underwater photography skills. At least one person anywhere practices graffiti art. Everyone in the room who does enjoy mountain biking collect rare sneakers. Everyone outside the room own a television if they practices graffiti art. Everyone outside the room practices graffiti art if they own a television. Everyone in the room who does enjoy mountain biking is a drone photographer. Everyone outside the room writes and illustrates their own graphic novels if they is a drone photographer. If someone is not a drone photographer then he/she is not a certified scuba diver with advanced underwater photography skills. Everyone in the room who practices graffiti art either own a television or enjoys spelunking but not both.

Everyone in the room is a drone photographer.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))))=>(![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))=>(practices_graffiti_art(X)))))))& ((![X]:(room(X)=>(collect_rare_sneakers(X))))=>(![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))))& (![X]:(room(X)=>(((((is_a_professional_photographer_specializing_in_portrait_photography(X))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))))& (~?[X]:(room(X)=>(((((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(is_a_professional_photographer_specializing_in_portrait_photography(X))))=>(is_a_drone_photographer(X))))))& (~![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (((?[X]:(anywhere(X)&practices_graffiti_art(X)))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(collect_rare_sneakers(X))))))& (![X]:(~room(X)=>(((practices_graffiti_art(X))=>(own_a_television(X))))))& (![X]:(~room(X)=>(((own_a_television(X))=>(practices_graffiti_art(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(is_a_drone_photographer(X))))))& (![X]:(~room(X)=>(((is_a_drone_photographer(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& ((![X]:((is_not_a_drone_photographer(X))=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(((own_a_television(X))<~>(enjoys_spelunking(X))))))))

(there_is_a_room)& ![X]:(room(X)=>(is_a_drone_photographer(X)))

% SZS status Unsatisfiable for 3081331049780731441117748 % SZS output start Proof for 3081331049780731441117748 48. ~? [X0] : (room(X0) => ((predh(X0) <~> predg(X0)) => predc(X0))) [input p4] 58. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 69. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 58] 144. ! [X0] : ((~predc(X0) & (predh(X0) <~> predg(X0))) & room(X0)) [ennf transformation 48] 145. ! [X0] : (~predc(X0) & (predh(X0) <~> predg(X0)) & room(X0)) [flattening 144] 153. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 69] 155. ! [X0] : (~predc(X0) & ((~predg(X0) | ~predh(X0)) & (predg(X0) | predh(X0))) & room(X0)) [nnf transformation 145] 156. ! [X0] : (~predc(X0) & (~predg(X0) | ~predh(X0)) & (predg(X0) | predh(X0)) & room(X0)) [flattening 155] 242. room(X0) [cnf transformation 156] 245. ~predc(X0) [cnf transformation 156] 253. predc(X0) | ~room(X0) [cnf transformation 153] 256. ~room(X0) [subsumption resolution 253,245] 257. $false [subsumption resolution 256,242] % SZS output end Proof for 3081331049780731441117748 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph is the only person in the room. "Everyone outside the room who practices tai chi enjoys writing detailed reviews of new and classic board games" if "Joseph own a television and is a client of Meta". "Only one person in the room uses an ios phone" if "it is not the case that "someone in the room plays the drums"". Either "everyone in the room enjoys kayaking or is not an active member of a local robotics club" or "Joseph practices tai chi" but not both. If "someone outside the room can play the harmonica and owns a smartwatch" then "only one person in the room practices tai chi". If "everyone in the room owns a smartwatch or is not a client of Costco" then "everyone in the room who can play the harmonica has lived in exactly three countries". If "everyone in the room is an active member of a local robotics club or does not work on fridays" then "Joseph is a client of Meta". "Joseph develops open-source software projects in their free time" only if "if someone can play the harmonica then he/she is a Linux enthusiast and vice versa". Joseph is not a client of Costco. If someone uses a Windows laptop then he/she is a wine connoisseur and vice versa. Someone in the room bakes bread at home. At least one person in the room is not a client of Costco. Only one person in the room own a television. Everyone in the room enjoys bird watching only if they watches fantasy movies. Someone in the room enjoys fishing. Someone in the room enjoys writing detailed reviews of new and classic board games. At least one person in the room is not an active member of a local robotics club. Someone in the room enjoys kayaking and collects vintage stamps. Everyone in the room who develops open-source software projects in their free time does enjoy mountain biking. Someone in the room is a wine connoisseur. Everyone in the room who enjoys kayaking enjoys fishing.

Joseph is a Linux enthusiast.

neutral

room(joseph)&(![X]:(room(X)=>(X='joseph')))& ((((own_a_television(joseph))&(is_a_client_of_Meta(joseph))))=>(![X]:(~room(X)=>(((practices_tai_chi(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))& ((~(?[X]:(room(X)&(plays_the_drums(X)))))=>(((?[X]:(room(X)&uses_an_ios_phone(X)))&(![X,Y]:((room(X)&room(Y)&(uses_an_ios_phone(X))&(uses_an_ios_phone(Y)))=>(X=Y))))))& ((![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))|(enjoys_kayaking(X))))))<~>(practices_tai_chi(joseph)))& ((?[X]:(~room(X)&(((can_play_the_harmonica(X))&(owns_a_smartwatch(X))))))=>(((?[X]:(room(X)&practices_tai_chi(X)))&(![X,Y]:((room(X)&room(Y)&(practices_tai_chi(X))&(practices_tai_chi(Y)))=>(X=Y))))))& ((![X]:(room(X)=>(((is_not_a_client_of_Costco(X))|(owns_a_smartwatch(X))))))=>(![X]:(room(X)=>(((can_play_the_harmonica(X))=>(has_lived_in_exactly_three_countries(X)))))))& ((![X]:(room(X)=>(((does_not_work_on_fridays(X))|(is_an_active_member_of_a_local_robotics_club(X))))))=>(is_a_client_of_Meta(joseph)))& ((develops_open-source_software_projects_in_their_free_time(joseph))=>((![X]:((can_play_the_harmonica(X))<=>(is_a_Linux_enthusiast(X))))))& (is_not_a_client_of_Costco(joseph))& ((![X]:((uses_a_Windows_laptop(X))<=>(is_a_wine_connoisseur(X)))))& (?[X]:(room(X)&(bakes_bread_at_home(X))))& (((?[X]:(room(X)&is_not_a_client_of_Costco(X)))))& (((?[X]:(room(X)&own_a_television(X)))&(![X,Y]:((room(X)&room(Y)&(own_a_television(X))&(own_a_television(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))<=(enjoys_bird_watching(X))))))& (?[X]:(room(X)&(enjoys_fishing(X))))& (?[X]:(room(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (((?[X]:(room(X)&is_not_an_active_member_of_a_local_robotics_club(X)))))& (?[X]:(room(X)&(((enjoys_kayaking(X))&(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(does_enjoy_mountain_biking(X))))))& (?[X]:(room(X)&(is_a_wine_connoisseur(X))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(enjoys_fishing(X))))))& (~(can_play_the_harmonica(joseph)))& (does_not_work_on_fridays(joseph))& ((![X]:((~((is_a_client_of_Costco(X))|(enjoys_kayaking(X))))=>(owns_a_smartwatch(X)))))

room(joseph)&(![X]:(room(X)=>(X='joseph')))& is_a_Linux_enthusiast(joseph)

Gerald is the only person in the room. If 'not everyone in the room does not play as a goalkeeper for a local amateur soccer team or collects antique clocks' then 'not everyone in the room who neither designs and sews custom cosplay costumes for conventions nor enjoys spelunking enjoys fishing' otherwise 'if someone hosts regular workshops on creative writing then he/she creates large-scale murals for public art installations and vice versa'. If 'it is not the case that 'Gerald is right-handed'' then 'everyone in the room who practices archery collects antique clocks'. If 'no one in the room collects rare minerals or does not develop open-source software projects in their free time' then 'no one in the room who collects rare minerals collects antique clocks'. 'Gerald practices zumba' if 'everyone in the room does not enjoy stand-up paddleboarding or competes in national level swimming championships' and vice versa. If 'everyone in the room collects rare and antique scientific instruments or does not collect antique clocks' then 'everyone in the room who collects rare and antique scientific instruments is right-handed'. Not everyone outside the room is right-handed if they owns a high-end gaming PC with custom-built components or competes in national level swimming championships or both and vice versa. Everyone anywhere owns a high-end gaming PC with custom-built components or does not own a high-end gaming PC with custom-built components. If someone enjoys spelunking then he/she collects rare minerals and vice versa. If someone is right-handed then he/she enjoys virtual reality gaming. Everyone in the room who creates large-scale murals for public art installations creates large-scale murals for public art installations, designs and sews custom cosplay costumes for conventions and hosts regular workshops on creative writing. Gerald practices archery. Everyone anywhere enjoys spelunking only if they enjoys making ceramics. Gerald enjoys spelunking. Everyone in the room who owns a smart tv collects rare and antique scientific instruments. If someone enjoys spelunking then he/she enjoys fishing. Only one person in the room competes in national level swimming championships. Everyone in the room who collects rare and antique scientific instruments is right-handed.

Gerald enjoys stand-up paddleboarding, is a certified yoga instructor teaching classes weekly and owns a high-end gaming PC with custom-built components.

neutral

room(gerald)&(![X]:(room(X)=>(X='gerald')))& (((~![X]:(room(X)=>(((collects_antique_clocks(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))=>(~![X]:(room(X)=>(((~((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(enjoys_spelunking(X))))=>(enjoys_fishing(X)))))))&((~(~![X]:(room(X)=>(((collects_antique_clocks(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))=>((![X]:((hosts_regular_workshops_on_creative_writing(X))<=>(creates_large-scale_murals_for_public_art_installations(X)))))))& ((~(is_right-handed(gerald)))=>(![X]:(room(X)=>(((practices_archery(X))=>(collects_antique_clocks(X)))))))& ((~?[X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(collects_rare_minerals(X))))))=>(~?[X]:(room(X)=>(((collects_rare_minerals(X))=>(collects_antique_clocks(X)))))))& ((![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))<=>(practices_zumba(gerald)))& ((![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(collects_rare_and_antique_scientific_instruments(X))))))=>(![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(is_right-handed(X)))))))& (~![X]:(~room(X)=>(((is_right-handed(X))<=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(competes_in_national_level_swimming_championships(X))))))))& (![X]:(anywhere(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& ((![X]:((enjoys_spelunking(X))<=>(collects_rare_minerals(X)))))& ((![X]:((is_right-handed(X))=>(enjoys_virtual_reality_gaming(X)))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(((creates_large-scale_murals_for_public_art_installations(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(hosts_regular_workshops_on_creative_writing(X))))))))& (practices_archery(gerald))& (![X]:(anywhere(X)=>(((enjoys_making_ceramics(X))<=(enjoys_spelunking(X))))))& (enjoys_spelunking(gerald))& (![X]:(room(X)=>(((owns_a_smart_tv(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& ((![X]:((enjoys_spelunking(X))=>(enjoys_fishing(X)))))& (((?[X]:(room(X)&competes_in_national_level_swimming_championships(X)))&(![X,Y]:((room(X)&room(Y)&(competes_in_national_level_swimming_championships(X))&(competes_in_national_level_swimming_championships(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(is_right-handed(X))))))& (is_right-handed(gerald))& ((![X]:((~((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(creates_large-scale_murals_for_public_art_installations(X))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))& (collects_antique_clocks(gerald))

room(gerald)&(![X]:(room(X)=>(X='gerald')))& ((enjoys_stand-up_paddleboarding(gerald))&(is_a_certified_yoga_instructor_teaching_classes_weekly(gerald))&(owns_a_high-end_gaming_PC_with_custom-built_components(gerald)))

Elisa, Kevin are the only persons in the room. Everyone outside the room who practices and performs acrobatic dance routines enjoys snowboarding. Everyone in the room who does not enjoy kayaking, owns a significant collection of rare gemstones and minerals or has a curated collection of mid-century modern furniture has a curated collection of mid-century modern furniture. Everyone in the room does not enjoy snowboarding if they has a curated collection of mid-century modern furniture. Everyone outside the room composes and performs experimental electronic music if they does not enjoy snowboarding. Everyone in the room who composes and performs experimental electronic music practices and performs acrobatic dance routines. Everyone outside the room participates in citizen science projects related to wildlife monitoring if they practices and performs acrobatic dance routines. Everyone in the room who participates in citizen science projects related to wildlife monitoring enjoys kayaking. Everyone in the room enjoys windsurfing if they enjoys kayaking. Everyone in the room who has a curated collection of mid-century modern furniture enjoys snowboarding. Everyone outside the room enjoys snowboarding only if they practices and performs acrobatic dance routines. Someone in the room enjoys snowboarding. If someone owns a high-end gaming PC with custom-built components then he/she writes and illustrates their own graphic novels and vice versa. Everyone in the room enjoys kayaking if they owns a high-end gaming PC with custom-built components. Everyone in the room practices and performs acrobatic dance routines if they has a curated collection of mid-century modern furniture. Everyone outside the room who enjoys snowboarding does not write and illustrates their own graphic novels. Everyone in the room practices and performs acrobatic dance routines if they uses a Windows laptop. Everyone in the room who practices and performs acrobatic dance routines practices and performs acrobatic dance routines, composes and performs experimental electronic music or does not participate in citizen science projects related to wildlife monitoring.

More than one person in the room uses a Windows laptop.

neutral

room(elisa)&room(kevin)&(![X]:(room(X)=>(X='elisa'|X='kevin')))& (![X]:(~room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(enjoys_snowboarding(X))))))& (![X]:(room(X)=>(((((does_not_enjoy_kayaking(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(does_not_enjoy_snowboarding(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_snowboarding(X))=>(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (![X]:(~room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(enjoys_snowboarding(X))))))& (![X]:(~room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))<=(enjoys_snowboarding(X))))))& (?[X]:(room(X)&(enjoys_snowboarding(X))))& ((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=>(writes_and_illustrates_their_own_graphic_novels(X)))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (![X]:(~room(X)=>(((enjoys_snowboarding(X))=>(does_not_write_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(((practices_and_performs_acrobatic_dance_routines(X))|(composes_and_performs_experimental_electronic_music(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))=>(((composes_and_performs_experimental_electronic_music(X))<~>(writes_and_illustrates_their_own_graphic_novels(X))))))))

room(elisa)&room(kevin)&(![X]:(room(X)=>(X='elisa'|X='kevin')))& (?[X,Y]:(room(X)&room(Y)&(uses_a_Windows_laptop(X)&uses_a_Windows_laptop(Y))&(X!=Y)))

Leslie, Marian, Thomas, Nellie are the only persons in the room. ''A pen does not exist that only writes secrets.' or 'A desert blooms with snowdrops every year.' or both' if 'Leslie is a client of Ben'. 'Marian and Mary hate each other' if 'neither 'All swans in one park are blue.' nor 'Not all swans in one park are blue.'' and vice versa. If 'someone in the room likes Ben' then 'Nellie and Thomas like each other' otherwise ''A car runs solely on saltwater.' or 'Not all swans in one park are blue.' but not both'. ''Mirrors fog permanently in one particular house.' and 'Not all swans in one park are blue.'' only if 'Ben is quieter than Leslie'. If 'Mary and Thomas hate each other' then 'Leslie and Marian are respectively creative and happy'. If 'Leslie is not a wise curious old european' then ''A desert blooms with snowdrops every year.' or 'Mirrors fog permanently in one particular house.' but not both' otherwise 'someone who is kind hate someone who is a wise person'. If 'Nellie does not like Ben' then 'Thomas and Nellie are respectively curious and kind'. Either 'someone in the room enjoys kayaking' or 'everyone in the room does not collect action figures or is calm' but not both. 'Nellie who is an avid hiker is not hated by Mary' unless 'everyone in the room collects action figures or does not enjoy trail running'. 'A car does not run solely on saltwater.' or 'Not all swans in one park are blue.' but not both. Everyone outside the room is a culinary enthusiast who experiments with international cuisines or is not a client of Costco. 'Mirrors do not fog permanently in one particular house.' and 'All swans in one park are blue.'. Everyone in the room is not liked by Mary if they is not a patient humble tourist. 'Mirrors do not fog permanently in one particular house.' and 'A desert does not bloom with snowdrops every year.'. Ben is quieter than Nellie. Everyone outside the room neither is hated by Nellie nor collects antique jewelry. Everyone in the room collects action figures only if they does not hate Nellie.

Thomas and Nellie are quieter than Ben.

contradiction

room(leslie)&room(marian)&room(thomas)&room(nellie)&(![X]:(room(X)=>(X='leslie'|X='marian'|X='thomas'|X='nellie')))& ((client(ben,leslie))=>(((A_pen_does_not_exist_that_only_writes_secrets.)|(A_desert_blooms_with_snowdrops_every_year.))))& ((~((All_swans_in_one_park_are_blue.)|(Not_all_swans_in_one_park_are_blue.)))<=>((hate(marian,mary) & hate(mary,marian))))& (((?[X]:(room(X)&(like(ben,X))))=>((like(nellie,thomas) & like(thomas,nellie))))&((~(?[X]:(room(X)&(like(ben,X)))))=>(((A_car_runs_solely_on_saltwater.)<~>(Not_all_swans_in_one_park_are_blue.)))))& ((((Mirrors_fog_permanently_in_one_particular_house.)&(Not_all_swans_in_one_park_are_blue.)))=>(quieter(leslie,ben)))& (((hate(mary,thomas) & hate(thomas,mary)))=>((creative(leslie))&(happy(marian))))& (((~(wise(leslie)&curious(leslie)&old(leslie)&european(leslie)))=>(((A_desert_blooms_with_snowdrops_every_year.)<~>(Mirrors_fog_permanently_in_one_particular_house.))))&((~(~(wise(leslie)&curious(leslie)&old(leslie)&european(leslie))))=>(?[X,Y]:((kind(X))&(wise(Y)&person(Y))&(hate(X,Y))))))& ((~like(ben,nellie))=>((curious(thomas))&(kind(nellie))))& ((?[X]:(room(X)&(enjoys_kayaking(X))))<~>(![X]:(room(X)=>(((calm(X))|(does_not_collect_action_figures(X)))))))& (~(![X]:(room(X)=>(((does_not_enjoy_trail_running(X))|(collects_action_figures(X))))))=>((is_an_avid_hiker(nellie))&(~hate(nellie,mary))))& (((A_car_does_not_run_solely_on_saltwater.)<~>(Not_all_swans_in_one_park_are_blue.)))& (![X]:(~room(X)=>(((is_not_a_client_of_Costco(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (((Mirrors_do_not_fog_permanently_in_one_particular_house.)&(All_swans_in_one_park_are_blue.)))& (![X]:(room(X)=>(((~(patient(X)&humble(X)&tourist(X)))=>(~like(X,mary))))))& (((Mirrors_do_not_fog_permanently_in_one_particular_house.)&(A_desert_does_not_bloom_with_snowdrops_every_year.)))& (quieter(nellie,ben))& (![X]:(~room(X)=>(~((hate(X,nellie))|(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((~hate(nellie,X))<=(collects_action_figures(X))))))& (![X]:(room(X)=>(((((is_a_professional_photographer_specializing_in_portrait_photography(X))&(has_lived_in_exactly_three_countries(X))))=>(can_play_the_flute(X))))))& (![X]:(room(X)=>(((can_play_the_flute(X))=>(patient(X)&tourist(X))))))& (?[X]:(room(X)&(~((creates_augmented_reality_experiences_for_mobile_applications(X))|(patient(X)&european(X))))))

room(leslie)&room(marian)&room(thomas)&room(nellie)&(![X]:(room(X)=>(X='leslie'|X='marian'|X='thomas'|X='nellie')))& quieter(ben,thomas)&quieter(ben,nellie)

% SZS status Unsatisfiable for 5697573474855214224396541 % SZS output start Proof for 5697573474855214224396541 14. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => ~quieter(X1,X0))) [input b13] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 59. quieter(alice,john) [input p15] 65. quieter(john,alice) & quieter(john,fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 105. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14] 106. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 105] 175. quieter(john,alice) & quieter(john,fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 65] 176. quieter(john,alice) & quieter(john,fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 175] 205. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 106] 261. alice != john [cnf transformation 43] 315. quieter(alice,john) [cnf transformation 59] 326. quieter(john,alice) [cnf transformation 176] 488. ~quieter(john,alice) | alice = john [resolution 205,315] 491. alice = john [subsumption resolution 488,326] 492. $false [subsumption resolution 491,261] % SZS output end Proof for 5697573474855214224396541 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Everyone in the room creates YouTube content if they is a scotch connoisseur. Everyone in the room does not have a pet dog, is a scotch connoisseur and creates YouTube content if they creates YouTube content. If someone is a drone photographer then he/she is an expert in identifying and foraging wild edible plants and vice versa. Everyone in the room who has a pet dog is a drone photographer. Everyone anywhere who is a drone photographer does not use a Windows laptop. If someone is a scotch connoisseur then he/she is a drone photographer. Everyone anywhere has a pet dog only if they is a scotch connoisseur.

Everyone outside the room is not an expert in identifying and foraging wild edible plants.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(creates_YouTube_content(X))))))& (![X]:(room(X)=>(((creates_YouTube_content(X))=>(((does_not_have_a_pet_dog(X))&(is_a_scotch_connoisseur(X))&(creates_YouTube_content(X))))))))& ((![X]:((is_a_drone_photographer(X))<=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))& (![X]:(room(X)=>(((has_a_pet_dog(X))=>(is_a_drone_photographer(X))))))& (![X]:(anywhere(X)=>(((is_a_drone_photographer(X))=>(does_not_use_a_Windows_laptop(X))))))& ((![X]:((is_a_scotch_connoisseur(X))=>(is_a_drone_photographer(X)))))& (![X]:(anywhere(X)=>(((is_a_scotch_connoisseur(X))<=(has_a_pet_dog(X))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(uses_a_Windows_laptop(X))))))& (![X]:(~room(X)=>(((uses_a_Windows_laptop(X))=>(does_not_create_YouTube_content(X))))))& (![X]:(room(X)=>(((((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<~>(has_a_pet_dog(X))))=>(uses_a_Windows_laptop(X))))))

(there_is_a_room)& ![X]:(~room(X)=>(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))

Guillermo, Jose, Grace, Willie are the only persons in the room. If "everyone in the room uses an ios phone or does not build model airplanes" then "Guillermo enjoys macrame". Guillermo uses an ios phone. Not everyone in the room who plays the drums is an avid collector of autographed memorabilia from famous musicians. Not everyone anywhere who is an avid collector of autographed memorabilia from famous musicians owns a smartwatch. Everyone anywhere who owns a smartwatch uses an ios phone. Everyone in the room who enjoys macrame hosts regular game nights featuring complex strategy games. Guillermo is a wine connoisseur with a private cellar of vintage wines. Guillermo practices kickboxing. Everyone in the room who collects action figures is a certified yoga instructor teaching classes weekly. Guillermo enjoys macrame. Everyone in the room who is a professional photographer specializing in portrait photography is an avid collector of autographed memorabilia from famous musicians. Everyone in the room is an avid collector of autographed memorabilia from famous musicians if they owns a smartwatch and vice versa. Everyone in the room plays the drums or does not own a smartwatch. Everyone in the room who hosts regular game nights featuring complex strategy games is a professional photographer specializing in portrait photography. Everyone in the room who is a professional photographer specializing in portrait photography enjoys macrame. Everyone in the room who enjoys macrame enjoys fishing. Everyone in the room who enjoys fishing is an avid collector of autographed memorabilia from famous musicians. Everyone outside the room who is an avid collector of autographed memorabilia from famous musicians practices pilates. Everyone in the room is an avid collector of autographed memorabilia from famous musicians or does not host regular game nights featuring complex strategy games. If someone practices pilates then he/she is a certified yoga instructor teaching classes weekly. Guillermo builds model airplanes. Everyone outside the room who plays eSports competitively is an avid collector of autographed memorabilia from famous musicians. Guillermo is a certified yoga instructor teaching classes weekly.

It is true that "Guillermo plays the drums".

entailment

room(guillermo)&room(jose)&room(grace)&room(willie)&(![X]:(room(X)=>(X='guillermo'|X='jose'|X='grace'|X='willie')))& ((![X]:(room(X)=>(((does_not_build_model_airplanes(X))|(uses_an_ios_phone(X))))))=>(enjoys_macrame(guillermo)))& (uses_an_ios_phone(guillermo))& (~![X]:(room(X)=>(((plays_the_drums(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (~![X]:(anywhere(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(owns_a_smartwatch(X))))))& (![X]:(anywhere(X)=>(((owns_a_smartwatch(X))=>(uses_an_ios_phone(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(guillermo))& (practices_kickboxing(guillermo))& (![X]:(room(X)=>(((collects_action_figures(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (enjoys_macrame(guillermo))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))<=>(owns_a_smartwatch(X))))))& (![X]:(room(X)=>(((does_not_own_a_smartwatch(X))|(plays_the_drums(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(enjoys_macrame(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(enjoys_fishing(X))))))& (![X]:(room(X)=>(((enjoys_fishing(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(~room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(practices_pilates(X))))))& (![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& ((![X]:((practices_pilates(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))& (builds_model_airplanes(guillermo))& (![X]:(~room(X)=>(((plays_eSports_competitively(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (is_a_certified_yoga_instructor_teaching_classes_weekly(guillermo))

room(guillermo)&room(jose)&room(grace)&room(willie)&(![X]:(room(X)=>(X='guillermo'|X='jose'|X='grace'|X='willie')))& plays_the_drums(guillermo)

% SZS status Unsatisfiable for 7996150030309436507675083 % SZS output start Proof for 7996150030309436507675083 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. ! [X0] : (room(X0) => (prede(X0) => predk(X0))) [input p6] 54. prede(mary) [input p10] 55. ! [X0] : (room(X0) => (predh(X0) => predg(X0))) [input p11] 56. ! [X0] : (room(X0) => (predg(X0) <=> predl(X0))) [input p12] 57. ! [X0] : (room(X0) => (predf(X0) | ~predl(X0))) [input p13] 58. ! [X0] : (room(X0) => (predk(X0) => predh(X0))) [input p14] 68. ~(predf(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 149. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 150. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 149] 158. ! [X0] : ((predk(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 50] 159. ! [X0] : (predk(X0) | ~prede(X0) | ~room(X0)) [flattening 158] 160. ! [X0] : ((predg(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 55] 161. ! [X0] : (predg(X0) | ~predh(X0) | ~room(X0)) [flattening 160] 162. ! [X0] : ((predg(X0) <=> predl(X0)) | ~room(X0)) [ennf transformation 56] 163. ! [X0] : ((predf(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 57] 164. ! [X0] : (predf(X0) | ~predl(X0) | ~room(X0)) [flattening 163] 165. ! [X0] : ((predh(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 58] 166. ! [X0] : (predh(X0) | ~predk(X0) | ~room(X0)) [flattening 165] 175. ~predf(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 68] 176. ~predf(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 175] 184. ! [X0] : (((predg(X0) | ~predl(X0)) & (predl(X0) | ~predg(X0))) | ~room(X0)) [nnf transformation 162] 185. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 186. ~predf(mary) | (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 176,185] 268. room(mary) [cnf transformation 150] 269. room(paul) [cnf transformation 150] 270. room(fred) [cnf transformation 150] 271. room(alice) [cnf transformation 150] 272. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 150] 283. ~prede(X0) | predk(X0) | ~room(X0) [cnf transformation 159] 284. prede(mary) [cnf transformation 54] 285. ~predh(X0) | predg(X0) | ~room(X0) [cnf transformation 161] 286. ~predg(X0) | predl(X0) | ~room(X0) [cnf transformation 184] 288. ~predl(X0) | predf(X0) | ~room(X0) [cnf transformation 164] 289. ~predk(X0) | predh(X0) | ~room(X0) [cnf transformation 166] 294. ~predf(mary) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186] 295. ~predf(mary) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186] 296. ~predf(mary) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186] 297. ~predf(mary) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186] 298. ~predf(mary) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186] 304. 2 <=> prede(mary) [avatar definition] 306. prede(mary) <- (2) [avatar component clause 304] 314. 2 [avatar split clause 284,304] 315. ~predf(mary) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 298,271] 316. ~predf(mary) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 315,270] 317. ~predf(mary) | alice != sK3 | ~room(mary) [subsumption resolution 316,269] 318. ~predf(mary) | alice != sK3 [subsumption resolution 317,268] 320. 4 <=> alice = sK3 [avatar definition] 322. alice != sK3 <- (~4) [avatar component clause 320] 324. 5 <=> predf(mary) [avatar definition] 327. ~4 | ~5 [avatar split clause 318,324,320] 328. ~predf(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 297,271] 329. ~predf(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 328,270] 330. ~predf(mary) | fred != sK3 | ~room(mary) [subsumption resolution 329,269] 331. ~predf(mary) | fred != sK3 [subsumption resolution 330,268] 333. 6 <=> fred = sK3 [avatar definition] 335. fred != sK3 <- (~6) [avatar component clause 333] 336. ~6 | ~5 [avatar split clause 331,324,333] 337. ~predf(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,271] 338. ~predf(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 337,270] 339. ~predf(mary) | paul != sK3 | ~room(mary) [subsumption resolution 338,269] 340. ~predf(mary) | paul != sK3 [subsumption resolution 339,268] 342. 7 <=> paul = sK3 [avatar definition] 344. paul != sK3 <- (~7) [avatar component clause 342] 345. ~7 | ~5 [avatar split clause 340,324,342] 346. ~predf(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,271] 347. ~predf(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 346,270] 348. ~predf(mary) | mary != sK3 | ~room(mary) [subsumption resolution 347,269] 349. ~predf(mary) | mary != sK3 [subsumption resolution 348,268] 351. 8 <=> mary = sK3 [avatar definition] 353. mary != sK3 <- (~8) [avatar component clause 351] 354. ~8 | ~5 [avatar split clause 349,324,351] 355. ~predf(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,271] 356. ~predf(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 355,270] 357. ~predf(mary) | room(sK3) | ~room(mary) [subsumption resolution 356,269] 358. ~predf(mary) | room(sK3) [subsumption resolution 357,268] 360. 9 <=> room(sK3) [avatar definition] 362. room(sK3) <- (9) [avatar component clause 360] 363. 9 | ~5 [avatar split clause 358,324,360] 364. predk(mary) | ~room(mary) <- (2) [resolution 283,306] 365. predk(mary) <- (2) [subsumption resolution 364,268] 368. predh(mary) | ~room(mary) <- (2) [resolution 289,365] 369. predh(mary) <- (2) [subsumption resolution 368,268] 370. predg(mary) | ~room(mary) <- (2) [resolution 369,285] 371. predg(mary) <- (2) [subsumption resolution 370,268] 373. predl(mary) | ~room(mary) <- (2) [resolution 371,286] 374. predl(mary) <- (2) [subsumption resolution 373,268] 378. predf(mary) | ~room(mary) <- (2) [resolution 374,288] 384. predf(mary) <- (2) [subsumption resolution 378,268] 385. 5 | ~2 [avatar split clause 384,304,324] 428. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (9) [resolution 272,362] 446. paul = sK3 | mary = sK3 | alice = sK3 <- (~6, 9) [subsumption resolution 428,335] 447. mary = sK3 | alice = sK3 <- (~6, ~7, 9) [subsumption resolution 446,344] 448. alice = sK3 <- (~6, ~7, ~8, 9) [subsumption resolution 447,353] 449. $false <- (~4, ~6, ~7, ~8, 9) [subsumption resolution 448,322] 450. 4 | 6 | 7 | 8 | ~9 [avatar contradiction clause 449] 451. $false [avatar sat refutation 314,327,336,345,354,363,385,450] % SZS output end Proof for 7996150030309436507675083 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Shawn, Gregory, Dena, Ben, Elmer are the only persons in the room. “At least one person in the room plays eSports competitively” if “Gregory plays eSports competitively” and vice versa. Only one person in the room can play the harmonica. Everyone in the room who does not play eSports competitively cannot play the harmonica. It is not the case that “Dena can play the harmonica”.

Gregory plays eSports competitively.

entailment

room(shawn)&room(gregory)&room(dena)&room(ben)&room(elmer)&(![X]:(room(X)=>(X='shawn'|X='gregory'|X='dena'|X='ben'|X='elmer')))& ((plays_eSports_competitively(gregory))<=>(((?[X]:(room(X)&plays_eSports_competitively(X))))))& ((~?[X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(enjoys_fishing(X))))))=>((?[X,Y]:(room(X)&room(Y)&(enjoys_fishing(X)&enjoys_fishing(Y))&(X!=Y)))))& ((~(cannot_play_the_harmonica(dena)))=>((is_allergic_to_anything(gregory))&(does_not_practice_digital_art(gregory))))& ((![X]:(room(X)=>(((does_not_enjoy_fishing(X))|(plays_eSports_competitively(X))))))=>(does_not_play_eSports_competitively(gregory)))& ((practices_digital_art(gregory))=>(![X]:(~room(X)=>(((enjoys_fishing(X))<=(is_allergic_to_anything(X)))))))& (enjoys_fishing(gregory))& (((?[X]:(room(X)&can_play_the_harmonica(X)))&(![X,Y]:((room(X)&room(Y)&(can_play_the_harmonica(X))&(can_play_the_harmonica(Y)))=>(X=Y)))))& (is_not_allergic_to_anything(gregory))& (![X]:(room(X)=>(((can_play_the_harmonica(X))|(cannot_play_the_harmonica(X))))))& (((practices_digital_art(gregory))|(is_allergic_to_anything(gregory))))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))=>(cannot_play_the_harmonica(X))))))& (~(can_play_the_harmonica(dena)))& (![X]:(~room(X)=>(((enjoys_fishing(X))<=(is_allergic_to_anything(X))))))

room(shawn)&room(gregory)&room(dena)&room(ben)&room(elmer)&(![X]:(room(X)=>(X='shawn'|X='gregory'|X='dena'|X='ben'|X='elmer')))& plays_eSports_competitively(gregory)

% SZS status Unsatisfiable for 5877143377896254910464756 % SZS output start Proof for 5877143377896254910464756 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. preda(paul) <=> ? [X0] : (preda(X0) & room(X0)) [input p1] 51. ! [X0,X1] : ((prede(X1) & prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (prede(X0) & room(X0)) [input p7] 55. ! [X0] : (room(X0) => (~preda(X0) => ~prede(X0))) [input p11] 56. ~prede(fred) [input p12] 58. ~(preda(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 60. ! [X0,X1] : ((prede(X1) & prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (prede(X2) & room(X2)) [rectify 51] 138. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 138] 142. ! [X0,X1] : (X0 = X1 | (~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (prede(X2) & room(X2)) [ennf transformation 60] 143. ! [X0,X1] : (X0 = X1 | ~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (prede(X2) & room(X2)) [flattening 142] 146. ! [X0] : ((~prede(X0) | preda(X0)) | ~room(X0)) [ennf transformation 55] 147. ! [X0] : (~prede(X0) | preda(X0) | ~room(X0)) [flattening 146] 148. ~preda(paul) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58] 149. ~preda(paul) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 148] 151. (preda(paul) | ! [X0] : (~preda(X0) | ~room(X0))) & (? [X0] : (preda(X0) & room(X0)) | ~preda(paul)) [nnf transformation 45] 152. (preda(paul) | ! [X0] : (~preda(X0) | ~room(X0))) & (? [X1] : (preda(X1) & room(X1)) | ~preda(paul)) [rectify 151] 153. ? [X1] : (preda(X1) & room(X1)) => (preda(sK0) & room(sK0)) [choice axiom] 154. (preda(paul) | ! [X0] : (~preda(X0) | ~room(X0))) & ((preda(sK0) & room(sK0)) | ~preda(paul)) [skolemisation 152,153] 157. ? [X2] : (prede(X2) & room(X2)) => (prede(sK2) & room(sK2)) [choice axiom] 158. ! [X0,X1] : (X0 = X1 | ~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0)) & (prede(sK2) & room(sK2)) [skolemisation 143,157] 159. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 160. ~preda(paul) | (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 149,159] 241. room(mary) [cnf transformation 139] 242. room(paul) [cnf transformation 139] 243. room(fred) [cnf transformation 139] 244. room(alice) [cnf transformation 139] 245. room(john) [cnf transformation 139] 246. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 139] 249. preda(paul) | ~preda(X0) | ~room(X0) [cnf transformation 154] 254. room(sK2) [cnf transformation 158] 255. prede(sK2) [cnf transformation 158] 260. ~prede(X0) | preda(X0) | ~room(X0) [cnf transformation 147] 261. ~prede(fred) [cnf transformation 56] 262. ~preda(paul) | room(sK3) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 263. ~preda(paul) | mary != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 264. ~preda(paul) | paul != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 265. ~preda(paul) | fred != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 266. ~preda(paul) | alice != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 267. ~preda(paul) | john != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 269. 1 <=> ! [X0] : (~preda(X0) | ~room(X0)) [avatar definition] 270. ~preda(X0) | ~room(X0) <- (1) [avatar component clause 269] 272. 2 <=> preda(paul) [avatar definition] 273. ~preda(paul) <- (~2) [avatar component clause 272] 275. 1 | 2 [avatar split clause 249,272,269] 287. 5 <=> prede(fred) [avatar definition] 289. ~prede(fred) <- (~5) [avatar component clause 287] 312. ~5 [avatar split clause 261,287] 313. ~preda(paul) | john != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 267,245] 314. ~preda(paul) | john != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,244] 315. ~preda(paul) | john != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 314,243] 316. ~preda(paul) | john != sK3 | ~room(mary) [subsumption resolution 315,242] 317. ~preda(paul) | john != sK3 [subsumption resolution 316,241] 319. 10 <=> john = sK3 [avatar definition] 321. john != sK3 <- (~10) [avatar component clause 319] 322. ~10 | ~2 [avatar split clause 317,272,319] 323. ~preda(paul) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 266,245] 324. ~preda(paul) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 323,244] 325. ~preda(paul) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 324,243] 326. ~preda(paul) | alice != sK3 | ~room(mary) [subsumption resolution 325,242] 327. ~preda(paul) | alice != sK3 [subsumption resolution 326,241] 329. 11 <=> alice = sK3 [avatar definition] 331. alice != sK3 <- (~11) [avatar component clause 329] 332. ~11 | ~2 [avatar split clause 327,272,329] 333. ~preda(paul) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,245] 334. ~preda(paul) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 333,244] 335. ~preda(paul) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 334,243] 336. ~preda(paul) | fred != sK3 | ~room(mary) [subsumption resolution 335,242] 337. ~preda(paul) | fred != sK3 [subsumption resolution 336,241] 339. 12 <=> fred = sK3 [avatar definition] 341. fred != sK3 <- (~12) [avatar component clause 339] 342. ~12 | ~2 [avatar split clause 337,272,339] 343. ~preda(paul) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 264,245] 344. ~preda(paul) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 343,244] 345. ~preda(paul) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 344,243] 346. ~preda(paul) | paul != sK3 | ~room(mary) [subsumption resolution 345,242] 347. ~preda(paul) | paul != sK3 [subsumption resolution 346,241] 349. 13 <=> paul = sK3 [avatar definition] 351. paul != sK3 <- (~13) [avatar component clause 349] 352. ~13 | ~2 [avatar split clause 347,272,349] 353. ~preda(paul) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 263,245] 354. ~preda(paul) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 353,244] 355. ~preda(paul) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 354,243] 356. ~preda(paul) | mary != sK3 | ~room(mary) [subsumption resolution 355,242] 357. ~preda(paul) | mary != sK3 [subsumption resolution 356,241] 359. 14 <=> mary = sK3 [avatar definition] 362. ~14 | ~2 [avatar split clause 357,272,359] 363. ~preda(paul) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,245] 364. ~preda(paul) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 363,244] 365. ~preda(paul) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 364,243] 366. ~preda(paul) | room(sK3) | ~room(mary) [subsumption resolution 365,242] 367. ~preda(paul) | room(sK3) [subsumption resolution 366,241] 369. 15 <=> room(sK3) [avatar definition] 371. room(sK3) <- (15) [avatar component clause 369] 372. 15 | ~2 [avatar split clause 367,272,369] 373. preda(sK2) | ~room(sK2) [resolution 260,255] 374. preda(sK2) [subsumption resolution 373,254] 427. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 [resolution 246,254] 428. alice = sK3 | fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (15) [resolution 246,371] 472. 26 <=> john = sK2 [avatar definition] 474. john = sK2 <- (26) [avatar component clause 472] 476. 27 <=> mary = sK2 [avatar definition] 478. mary = sK2 <- (27) [avatar component clause 476] 480. 28 <=> paul = sK2 [avatar definition] 482. paul = sK2 <- (28) [avatar component clause 480] 484. 29 <=> fred = sK2 [avatar definition] 486. fred = sK2 <- (29) [avatar component clause 484] 488. 30 <=> alice = sK2 [avatar definition] 490. alice = sK2 <- (30) [avatar component clause 488] 491. 26 | 27 | 28 | 29 | 30 [avatar split clause 427,488,484,480,476,472] 492. fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (~11, 15) [subsumption resolution 428,331] 493. paul = sK3 | mary = sK3 | john = sK3 <- (~11, ~12, 15) [subsumption resolution 492,341] 494. mary = sK3 | john = sK3 <- (~11, ~12, ~13, 15) [subsumption resolution 493,351] 498. mary = sK3 <- (~10, ~11, ~12, ~13, 15) [subsumption resolution 494,321] 499. 14 | 10 | 11 | 12 | 13 | ~15 [avatar split clause 498,369,349,339,329,319,359] 501. preda(john) <- (26) [backward demodulation 374,474] 512. ~room(john) <- (1, 26) [resolution 270,501] 513. $false <- (1, 26) [subsumption resolution 512,245] 514. ~1 | ~26 [avatar contradiction clause 513] 516. preda(mary) <- (27) [backward demodulation 374,478] 524. ~room(mary) <- (1, 27) [resolution 516,270] 525. $false <- (1, 27) [subsumption resolution 524,241] 526. ~1 | ~27 [avatar contradiction clause 525] 528. preda(paul) <- (28) [backward demodulation 374,482] 532. $false <- (~2, 28) [subsumption resolution 528,273] 533. 2 | ~28 [avatar contradiction clause 532] 537. prede(fred) <- (29) [backward demodulation 255,486] 539. $false <- (~5, 29) [subsumption resolution 537,289] 540. 5 | ~29 [avatar contradiction clause 539] 543. preda(alice) <- (30) [backward demodulation 374,490] 549. ~room(alice) <- (1, 30) [resolution 543,270] 550. $false <- (1, 30) [subsumption resolution 549,244] 551. ~1 | ~30 [avatar contradiction clause 550] 552. $false [avatar sat refutation 275,312,322,332,342,352,362,372,491,499,514,526,533,540,551] % SZS output end Proof for 5877143377896254910464756 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s % ------------------------------ % ------------------------------

There is a room. No one in the room is a dedicated volunteer for local community service projects, participates in long-distance cycling events across the country and owns an Android phone. If someone owns a significant collection of rare gemstones and minerals and maintains a personal blog focused on cybersecurity tips then he/she does not own a telescope and is a coffee connoisseur and vice versa. More than one person in the room is not a wine connoisseur. If someone maintains a large, organic vegetable garden year-round then he/she is a dedicated volunteer for local community service projects and vice versa. No one anywhere who neither collects modern art nor does enjoy mountain biking does enjoy mountain biking, is a cybersecurity expert and does not own a significant collection of rare gemstones and minerals. Everyone in the room who does enjoy mountain biking, is a cybersecurity expert and does not own a significant collection of rare gemstones and minerals does not own a significant collection of rare gemstones and minerals, is a coffee connoisseur and collects modern art. More than one person in the room does not own a significant collection of rare gemstones and minerals. Everyone in the room maintains a large, organic vegetable garden year-round if they is a dedicated volunteer for local community service projects and is a coffee connoisseur. Everyone outside the room is a coffee connoisseur. Everyone in the room who owns an Android phone, cannot play the harmonica or is not a wine connoisseur owns an Android phone.

Everyone in the room does not own a significant collection of rare gemstones and minerals.

neutral

(there_is_a_room)& (~?[X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(participates_in_long-distance_cycling_events_across_the_country(X))&(owns_an_Android_phone(X))))))& ((![X]:((((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))<=>(((does_not_own_a_telescope(X))&(is_a_coffee_connoisseur(X)))))))& ((?[X,Y]:(room(X)&room(Y)&(is_not_a_wine_connoisseur(X)&is_not_a_wine_connoisseur(Y))&(X!=Y))))& ((![X]:((maintains_a_large,_organic_vegetable_garden_year-round(X))<=>(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))& (~?[X]:(anywhere(X)=>(((~((collects_modern_art(X))|(does_enjoy_mountain_biking(X))))=>(((does_enjoy_mountain_biking(X))&(is_a_cybersecurity_expert(X))&(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))))& (![X]:(room(X)=>(((((does_enjoy_mountain_biking(X))&(is_a_cybersecurity_expert(X))&(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))&(is_a_coffee_connoisseur(X))&(collects_modern_art(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X)&does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(Y))&(X!=Y))))& (![X]:(room(X)=>(((((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(is_a_coffee_connoisseur(X))))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(~room(X)=>(is_a_coffee_connoisseur(X))))& (![X]:(room(X)=>(((((owns_an_Android_phone(X))|(cannot_play_the_harmonica(X))|(is_not_a_wine_connoisseur(X))))=>(owns_an_Android_phone(X))))))& (![X]:(room(X)=>(((owns_an_Android_phone(X))=>(is_a_coffee_connoisseur(X))))))& (![X]:(~room(X)=>(((can_play_the_harmonica(X))|(does_not_enjoy_mountain_biking(X))))))& ((?[X,Y]:(room(X)&room(Y)&(((is_a_wine_connoisseur(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))&((is_a_wine_connoisseur(Y))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(Y))))&(X!=Y))))& (~![X]:(anywhere(X)=>(((does_enjoy_mountain_biking(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(((maintains_a_large,_organic_vegetable_garden_year-round(X))&(is_a_coffee_connoisseur(X))&(can_play_the_harmonica(X)))&((maintains_a_large,_organic_vegetable_garden_year-round(Y))&(is_a_coffee_connoisseur(Y))&(can_play_the_harmonica(Y))))&(X!=Y))))& (![X]:(room(X)=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(is_a_wine_connoisseur(X))))))

(there_is_a_room)& ![X]:(room(X)=>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X)))

Maurice is the only person in the room. Either “Maurice is a generous humble person” or “no one in the room is a quiet european or does not collect antique clocks” but not both. Everyone in the room who is a quiet european is quiet. Everyone in the room who is quiet is quieter than Bud. Everyone in the room writes and illustrates their own graphic novels if they collects antique clocks and vice versa. Everyone in the room who does not collect antique clocks is quieter than Kenneth. All humble person is generous. Everyone in the room does not write and illustrates their own graphic novels, is humble or is quieter than Shirley if they is quieter than Shirley. Everyone in the room is quieter than Kenneth if they writes and illustrates their own graphic novels. Bud is quieter than Maurice. Everyone in the room who does not collect antique clocks, is quieter than Shirley and is a humble quiet generous european is quieter than Shirley. Maurice is humble. Maurice who is quieter than Katy is a humble generous person. Maurice is a humble person. Everyone in the room who collects antique clocks is generous.

Maurice collects antique clocks.

neutral

room(maurice)&(![X]:(room(X)=>(X='maurice')))& ((generous(maurice)&humble(maurice)&person(maurice))<~>(~?[X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(quiet(X)&european(X)))))))& (![X]:(room(X)=>(((quiet(X)&european(X))=>(quiet(X))))))& (![X]:(room(X)=>(((quiet(X))=>(quieter(bud,X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))<=>(collects_antique_clocks(X))))))& (![X]:(room(X)=>(((does_not_collect_antique_clocks(X))=>(quieter(kenneth,X))))))& (![X]:(humble(X)=>generous(X)))& (![X]:(room(X)=>(((quieter(shirley,X))=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(humble(X))|(quieter(shirley,X))))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(quieter(kenneth,X))))))& (quieter(maurice,bud))& (![X]:(room(X)=>(((((does_not_collect_antique_clocks(X))&(quieter(shirley,X))&(humble(X)&quiet(X)&generous(X)&european(X))))=>(quieter(shirley,X))))))& (humble(maurice))& ((quieter(katy,maurice))&(humble(maurice)&generous(maurice)&person(maurice)))& (humble(maurice)&person(maurice))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(generous(X))))))

room(maurice)&(![X]:(room(X)=>(X='maurice')))& collects_antique_clocks(maurice)

Brian, Sierra, Joann, Annie are the only persons in the room. If someone is not old then he/she is not quiet and vice versa. If someone is not quiet then he/she is not quiet, not old and vice versa. If someone is not old or is not quiet, not old or both then he/she is not old or is not quiet or both and vice versa. If someone is not old then he/she is not old, not quiet or is not old or both and vice versa. Sierra and Joann are respectively quiet and old. Someone in the room is not quiet. Someone in the room is not old. Someone in the room is not old, not quiet or is not old or both. Joann and Sierra are respectively old and quiet. Sierra and Brian are respectively quiet and old. Someone in the room is not old or is not quiet or both. Brian and Sierra are respectively quiet and old. Someone anywhere is not old.

Brian and Joann are respectively old and quiet.

entailment

room(brian)&room(sierra)&room(joann)&room(annie)&(![X]:(room(X)=>(X='brian'|X='sierra'|X='joann'|X='annie')))& ((![X]:((~old(X))<=>(~quiet(X)))))& ((![X]:((~quiet(X))<=>(~quiet(X)&~old(X)))))& ((![X]:((((~old(X))|(~quiet(X)&~old(X))))<=>(((~old(X))|(~quiet(X)))))))& ((![X]:((~old(X))<=>(((~old(X)&~quiet(X))|(~old(X)))))))& ((quiet(sierra))&(old(joann)))& (?[X]:(room(X)&(~quiet(X))))& (?[X]:(room(X)&(~old(X))))& (?[X]:(room(X)&(((~old(X)&~quiet(X))|(~old(X))))))& ((old(joann))&(quiet(sierra)))& ((quiet(sierra))&(old(brian)))& (?[X]:(room(X)&(((~old(X))|(~quiet(X))))))& ((quiet(brian))&(old(sierra)))& (?[X]:(anywhere(X)&(~old(X))))

room(brian)&room(sierra)&room(joann)&room(annie)&(![X]:(room(X)=>(X='brian'|X='sierra'|X='joann'|X='annie')))& (old(brian))&(quiet(joann))

% SZS status Unsatisfiable for 5379825521219958160380480 % SZS output start Proof for 5379825521219958160380480 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (~old(X0) <=> ~quiet(X0)) [input p1] 49. old(fred) & quiet(paul) [input p5] 54. old(mary) & quiet(paul) [input p10] 58. ~(quiet(fred) & old(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 132. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 133. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132] 134. ~quiet(fred) | ~old(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58] 135. ~quiet(fred) | ~old(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 134] 137. ! [X0] : ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0))) [nnf transformation 45] 154. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 155. ~quiet(fred) | ~old(mary) | (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 135,154] 236. room(mary) [cnf transformation 133] 237. room(paul) [cnf transformation 133] 238. room(fred) [cnf transformation 133] 239. room(alice) [cnf transformation 133] 240. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 133] 242. ~old(X0) | quiet(X0) [cnf transformation 137] 257. old(fred) [cnf transformation 49] 268. old(mary) [cnf transformation 54] 274. ~quiet(fred) | ~old(mary) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 275. ~quiet(fred) | ~old(mary) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 276. ~quiet(fred) | ~old(mary) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 277. ~quiet(fred) | ~old(mary) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 278. ~quiet(fred) | ~old(mary) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 285. ~quiet(fred) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,268] 286. ~quiet(fred) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,239] 287. ~quiet(fred) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 286,238] 288. ~quiet(fred) | alice != sK5 | ~room(mary) [subsumption resolution 287,237] 289. ~quiet(fred) | alice != sK5 [subsumption resolution 288,236] 291. 1 <=> alice = sK5 [avatar definition] 293. alice != sK5 <- (~1) [avatar component clause 291] 295. 2 <=> quiet(fred) [avatar definition] 298. ~1 | ~2 [avatar split clause 289,295,291] 299. ~quiet(fred) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,268] 300. ~quiet(fred) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 299,239] 301. ~quiet(fred) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 300,238] 302. ~quiet(fred) | fred != sK5 | ~room(mary) [subsumption resolution 301,237] 303. ~quiet(fred) | fred != sK5 [subsumption resolution 302,236] 305. 3 <=> fred = sK5 [avatar definition] 307. fred != sK5 <- (~3) [avatar component clause 305] 308. ~3 | ~2 [avatar split clause 303,295,305] 309. ~quiet(fred) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,268] 310. ~quiet(fred) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,239] 311. ~quiet(fred) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 310,238] 312. ~quiet(fred) | paul != sK5 | ~room(mary) [subsumption resolution 311,237] 313. ~quiet(fred) | paul != sK5 [subsumption resolution 312,236] 315. 4 <=> paul = sK5 [avatar definition] 317. paul != sK5 <- (~4) [avatar component clause 315] 318. ~4 | ~2 [avatar split clause 313,295,315] 319. ~quiet(fred) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,268] 320. ~quiet(fred) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,239] 321. ~quiet(fred) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 320,238] 322. ~quiet(fred) | mary != sK5 | ~room(mary) [subsumption resolution 321,237] 323. ~quiet(fred) | mary != sK5 [subsumption resolution 322,236] 325. 5 <=> mary = sK5 [avatar definition] 327. mary != sK5 <- (~5) [avatar component clause 325] 328. ~5 | ~2 [avatar split clause 323,295,325] 329. ~quiet(fred) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,268] 330. ~quiet(fred) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 329,239] 331. ~quiet(fred) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 330,238] 332. ~quiet(fred) | room(sK5) | ~room(mary) [subsumption resolution 331,237] 333. ~quiet(fred) | room(sK5) [subsumption resolution 332,236] 335. 6 <=> room(sK5) [avatar definition] 337. room(sK5) <- (6) [avatar component clause 335] 338. 6 | ~2 [avatar split clause 333,295,335] 341. quiet(fred) [resolution 242,257] 346. 2 [avatar split clause 341,295] 398. fred = sK5 | paul = sK5 | mary = sK5 | alice = sK5 <- (6) [resolution 240,337] 467. paul = sK5 | mary = sK5 | alice = sK5 <- (~3, 6) [subsumption resolution 398,307] 468. mary = sK5 | alice = sK5 <- (~3, ~4, 6) [subsumption resolution 467,317] 469. alice = sK5 <- (~3, ~4, ~5, 6) [subsumption resolution 468,327] 470. $false <- (~1, ~3, ~4, ~5, 6) [subsumption resolution 469,293] 471. 1 | 3 | 4 | 5 | ~6 [avatar contradiction clause 470] 472. $false [avatar sat refutation 298,308,318,328,338,346,471] % SZS output end Proof for 5379825521219958160380480 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Valerie is the only person in the room. “Valerie who is an avid collector of autographed memorabilia from famous musicians owns a smart tv” unless “everyone in the room does not have completed a triathlon or can play the harmonica”. It is not the case that “more than one person anywhere is a dedicated volunteer for local community service projects”. Everyone in the room cannot play the harmonica or mentors a youth basketball team on weekends. Everyone in the room owns a smart tv if they cannot play the harmonica. Valerie who owns a telescope makes intricate hand-cut paper art for exhibitions. Everyone outside the room has completed a triathlon if they is right-handed. Everyone in the room who has completed a triathlon is not right-handed. Everyone in the room does not have completed a triathlon or can play the harmonica. Everyone anywhere does not have a tattoo if they practices calligraphy and vice versa. Everyone in the room does not make intricate hand-cut paper art for exhibitions if they practices calligraphy. Everyone in the room who does not make intricate hand-cut paper art for exhibitions has a saltwater aquarium. Everyone in the room is a Linux enthusiast if they has a saltwater aquarium. Everyone in the room who is a Linux enthusiast practices calligraphy. Everyone in the room mentors a youth basketball team on weekends if they collects vintage stamps. Everyone in the room who mentors a youth basketball team on weekends has completed a triathlon.

Valerie is a Linux enthusiast.

contradiction

room(valerie)&(![X]:(room(X)=>(X='valerie')))& (~(![X]:(room(X)=>(((can_play_the_harmonica(X))|(does_not_have_completed_a_triathlon(X))))))=>((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(valerie))&(owns_a_smart_tv(valerie))))& (~((?[X,Y]:(anywhere(X)&anywhere(Y)&(is_a_dedicated_volunteer_for_local_community_service_projects(X)&is_a_dedicated_volunteer_for_local_community_service_projects(Y))&(X!=Y)))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(cannot_play_the_harmonica(X))))))& (![X]:(room(X)=>(((cannot_play_the_harmonica(X))=>(owns_a_smart_tv(X))))))& ((owns_a_telescope(valerie))&(makes_intricate_hand-cut_paper_art_for_exhibitions(valerie)))& (![X]:(~room(X)=>(((is_right-handed(X))=>(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(is_not_right-handed(X))))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))|(does_not_have_completed_a_triathlon(X))))))& (![X]:(anywhere(X)=>(((does_not_have_a_tattoo(X))<=>(practices_calligraphy(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))=>(has_a_saltwater_aquarium(X))))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(is_a_Linux_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(practices_calligraphy(X))))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(collects_modern_art(X))))))& ((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(valerie))&(owns_a_smart_tv(valerie)))& (![X]:(room(X)=>(((collects_modern_art(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))

room(valerie)&(![X]:(room(X)=>(X='valerie')))& is_a_Linux_enthusiast(valerie)

% SZS status Unsatisfiable for 6202818326388534331974457 % SZS output start Proof for 6202818326388534331974457 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. predu(mary) & predf(mary) [input p5] 54. ! [X0] : (room(X0) => (predt(X0) => ~predu(X0))) [input p10] 57. ! [X0] : (room(X0) => (predw(X0) => predt(X0))) [input p13] 63. predw(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 67. predu(mary) [pure predicate removal 49] 147. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 153. ! [X0] : ((~predu(X0) | ~predt(X0)) | ~room(X0)) [ennf transformation 54] 154. ! [X0] : (~predu(X0) | ~predt(X0) | ~room(X0)) [flattening 153] 159. ! [X0] : ((predt(X0) | ~predw(X0)) | ~room(X0)) [ennf transformation 57] 160. ! [X0] : (predt(X0) | ~predw(X0) | ~room(X0)) [flattening 159] 163. predw(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 63] 247. room(mary) [cnf transformation 147] 250. predu(mary) [cnf transformation 67] 254. ~predt(X0) | ~predu(X0) | ~room(X0) [cnf transformation 154] 257. ~predw(X0) | predt(X0) | ~room(X0) [cnf transformation 160] 261. predw(mary) [cnf transformation 163] 268. predt(mary) | ~room(mary) [resolution 257,261] 269. predt(mary) [subsumption resolution 268,247] 270. ~predu(mary) | ~room(mary) [resolution 269,254] 272. ~room(mary) [subsumption resolution 270,250] 273. $false [subsumption resolution 272,247] % SZS output end Proof for 6202818326388534331974457 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Allison is the only person in the room. If “not everyone in the room practices graffiti art” then “everyone in the room plays the drums or does not have a piercing”. “Allison makes intricate hand-cut paper art for exhibitions” unless “Allison practices graffiti art and practices calligraphy”. Either “everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations or practices graffiti art” or “Allison volunteers for local environmental conservation projects” but not both. If “everyone in the room is not right-handed or does not collect modern art” then “not everyone anywhere is not right-handed if they makes intricate hand-cut paper art for exhibitions and vice versa”. “Everyone in the room who is a certified scuba diver with advanced underwater photography skills is not dedicated to sustainable living and zero-waste practices” unless “everyone in the room is a certified scuba diver with advanced underwater photography skills or does not have a piercing”. Everyone anywhere who has a piercing collects modern art or volunteers for local environmental conservation projects or both. Not everyone anywhere is not right-handed if they makes intricate hand-cut paper art for exhibitions and vice versa. Everyone in the room does not volunteer for local environmental conservation projects only if they collects rare minerals. Allison is a client of Costco. Allison collects rare minerals, practices graffiti art or is right-handed. At least one person in the room does not have a piercing. Everyone in the room practices tai chi only if they is a client of Costco.

Allison is a night owl, practices tai chi and writes in-depth travel guides for off-the-beaten-path destinations.

neutral

room(allison)&(![X]:(room(X)=>(X='allison')))& ((~![X]:(room(X)=>(practices_graffiti_art(X))))=>(![X]:(room(X)=>(((does_not_have_a_piercing(X))|(plays_the_drums(X)))))))& (~(((practices_graffiti_art(allison))&(practices_calligraphy(allison))))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(allison)))& ((![X]:(room(X)=>(((practices_graffiti_art(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))<~>(volunteers_for_local_environmental_conservation_projects(allison)))& ((![X]:(room(X)=>(((does_not_collect_modern_art(X))|(is_not_right-handed(X))))))=>(~![X]:(anywhere(X)=>(((is_not_right-handed(X))<=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))))& (~(![X]:(room(X)=>(((does_not_have_a_piercing(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>(![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))& (![X]:(anywhere(X)=>(((has_a_piercing(X))=>(((collects_modern_art(X))|(volunteers_for_local_environmental_conservation_projects(X))))))))& (~![X]:(anywhere(X)=>(((is_not_right-handed(X))<=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((collects_rare_minerals(X))<=(does_not_volunteer_for_local_environmental_conservation_projects(X))))))& (is_a_client_of_Costco(allison))& (((collects_rare_minerals(allison))|(practices_graffiti_art(allison))|(is_right-handed(allison))))& (((?[X]:(room(X)&does_not_have_a_piercing(X)))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))<=(practices_tai_chi(X))))))& (![X]:(~room(X)=>(((is_a_client_of_Costco(X))=>(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(is_not_a_client_of_LVMH(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(collects_first_edition_books(X))))))& (is_a_night_owl(allison))& (does_not_have_a_piercing(allison))& (![X]:(room(X)=>(((collects_modern_art(X))=>(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (collects_rare_minerals(allison))& (![X]:(~room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=(enjoys_fishing(X))))))& (~((watches_fantasy_movies(allison))|(is_a_client_of_LVMH(allison))))& ((![X]:((is_a_client_of_LVMH(X))<=>(collects_vintage_stamps(X)))))

room(allison)&(![X]:(room(X)=>(X='allison')))& ((is_a_night_owl(allison))&(practices_tai_chi(allison))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(allison)))

Betty, Eduardo, Stephen are the only persons in the room. If “everyone in the room is older than Andrea or is generous or both” then “Betty is the least old in the room” otherwise “Eduardo is richer than Andrea”. Betty is the least old in the room. All patient persons are brave. Everyone in the room is older than Andrea or is generous or both. Everyone in the room is older than Andrea if they is not a funny humble strong generous person. All generous persons are brave. Everyone in the room who is funny is a tall curious calm quiet person. No brave person is old. Eduardo is a quiet strong person. Betty is not a tall person.

Eduardo is older than Andrea.

entailment

room(betty)&room(eduardo)&room(stephen)&(![X]:(room(X)=>(X='betty'|X='eduardo'|X='stephen')))& (((![X]:(room(X)=>(((older(andrea,X))|(generous(X))))))=>(![X]:((room(X)&(X!=betty))=>older(betty,X))))&((~(![X]:(room(X)=>(((older(andrea,X))|(generous(X)))))))=>(richer(andrea,eduardo))))& (![X]:((room(X)&(X!=betty))=>older(betty,X)))& (![X]:(patient(X)=>brave(X)))& (![X]:(room(X)=>(((older(andrea,X))|(generous(X))))))& (![X]:(room(X)=>(((~(funny(X)&humble(X)&strong(X)&generous(X)&person(X)))=>(older(andrea,X))))))& (![X]:(generous(X)=>brave(X)))& (![X]:(room(X)=>(((funny(X))=>(tall(X)&curious(X)&calm(X)&quiet(X)&person(X))))))& (~?[X]:(brave(X)=>old(X)))& (quiet(eduardo)&strong(eduardo)&person(eduardo))& (![X]:(~room(X)=>(((~(patient(X)&brave(X)&person(X)))=>(older(steven,X))))))& (~(tall(betty)&person(betty)))& (![X]:(room(X)=>(((older(steven,X))=>(quieter(andrea,X))))))& (generous(betty))& ((kind(stephen)&creative(stephen)&quiet(stephen)&person(stephen))&(~(funny(stephen)&humble(stephen)&strong(stephen)&generous(stephen)&person(stephen))))

room(betty)&room(eduardo)&room(stephen)&(![X]:(room(X)=>(X='betty'|X='eduardo'|X='stephen')))& older(andrea,eduardo)

% SZS status Unsatisfiable for 6938948438084075360542161 % SZS output start Proof for 6938948438084075360542161 19. ! [X0,X1,X2] : ((X0 != X2 & X1 != X2 & X0 != X1) => ((older(X1,X2) & older(X0,X1)) => older(X0,X2))) [input b18] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : ((mary != X0 & room(X0)) => older(mary,X0)) [input p2] 49. ! [X0] : (room(X0) => (~(person(X0) & generous(X0) & strong(X0) & humble(X0) & funny(X0)) => older(john,X0))) [input p5] 51. ! [X0] : (room(X0) => (funny(X0) => (person(X0) & quiet(X0) & calm(X0) & curious(X0) & tall(X0)))) [input p7] 55. ~(person(mary) & tall(mary)) [input p11] 59. ~(older(john,paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 63. ! [X0] : (room(X0) => (funny(X0) => (person(X0) & quiet(X0) & curious(X0) & tall(X0)))) [pure predicate removal 51] 64. ! [X0] : (room(X0) => (funny(X0) => (person(X0) & quiet(X0) & tall(X0)))) [pure predicate removal 63] 98. ! [X0,X1,X2] : ((older(X0,X2) | (~older(X1,X2) | ~older(X0,X1))) | (X0 = X2 | X1 = X2 | X0 = X1)) [ennf transformation 19] 99. ! [X0,X1,X2] : (older(X0,X2) | ~older(X1,X2) | ~older(X0,X1) | X0 = X2 | X1 = X2 | X0 = X1) [flattening 98] 142. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 142] 146. ! [X0] : (older(mary,X0) | (mary = X0 | ~room(X0))) [ennf transformation 46] 147. ! [X0] : (older(mary,X0) | mary = X0 | ~room(X0)) [flattening 146] 150. ! [X0] : ((older(john,X0) | (person(X0) & generous(X0) & strong(X0) & humble(X0) & funny(X0))) | ~room(X0)) [ennf transformation 49] 151. ! [X0] : (older(john,X0) | (person(X0) & generous(X0) & strong(X0) & humble(X0) & funny(X0)) | ~room(X0)) [flattening 150] 152. ! [X0] : (((person(X0) & quiet(X0) & tall(X0)) | ~funny(X0)) | ~room(X0)) [ennf transformation 64] 153. ! [X0] : ((person(X0) & quiet(X0) & tall(X0)) | ~funny(X0) | ~room(X0)) [flattening 152] 157. ~person(mary) | ~tall(mary) [ennf transformation 55] 161. ~older(john,paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 162. ~older(john,paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 161] 167. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 168. ~older(john,paul) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 162,167] 183. ~older(X1,X2) | older(X0,X2) | ~older(X0,X1) | X0 = X2 | X1 = X2 | X0 = X1 [cnf transformation 99] 213. mary != paul [cnf transformation 43] 231. mary != john [cnf transformation 43] 232. paul != john [cnf transformation 43] 249. room(mary) [cnf transformation 143] 250. room(paul) [cnf transformation 143] 251. room(fred) [cnf transformation 143] 252. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143] 257. older(mary,X0) | mary = X0 | ~room(X0) [cnf transformation 147] 259. older(john,X0) | funny(X0) | ~room(X0) [cnf transformation 151] 263. older(john,X0) | person(X0) | ~room(X0) [cnf transformation 151] 264. ~funny(X0) | tall(X0) | ~room(X0) [cnf transformation 153] 272. ~person(mary) | ~tall(mary) [cnf transformation 157] 278. ~older(john,paul) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 279. ~older(john,paul) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 280. ~older(john,paul) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 281. ~older(john,paul) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 295. 4 <=> ! [X1] : (older(mary,X1) | ~room(X1) | mary = X1) [avatar definition] 296. older(mary,X1) | ~room(X1) | mary = X1 <- (4) [avatar component clause 295] 308. 4 [avatar split clause 257,295] 312. 7 <=> tall(mary) [avatar definition] 316. 8 <=> person(mary) [avatar definition] 319. ~7 | ~8 [avatar split clause 272,316,312] 342. ~older(john,paul) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 281,251] 343. ~older(john,paul) | fred != sK1 | ~room(mary) [subsumption resolution 342,250] 344. ~older(john,paul) | fred != sK1 [subsumption resolution 343,249] 346. 14 <=> fred = sK1 [avatar definition] 348. fred != sK1 <- (~14) [avatar component clause 346] 350. 15 <=> older(john,paul) [avatar definition] 352. ~older(john,paul) <- (~15) [avatar component clause 350] 353. ~14 | ~15 [avatar split clause 344,350,346] 354. ~older(john,paul) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 280,251] 355. ~older(john,paul) | paul != sK1 | ~room(mary) [subsumption resolution 354,250] 356. ~older(john,paul) | paul != sK1 [subsumption resolution 355,249] 358. 16 <=> paul = sK1 [avatar definition] 360. paul != sK1 <- (~16) [avatar component clause 358] 361. ~16 | ~15 [avatar split clause 356,350,358] 362. ~older(john,paul) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 279,251] 363. ~older(john,paul) | mary != sK1 | ~room(mary) [subsumption resolution 362,250] 364. ~older(john,paul) | mary != sK1 [subsumption resolution 363,249] 366. 17 <=> mary = sK1 [avatar definition] 368. mary != sK1 <- (~17) [avatar component clause 366] 369. ~17 | ~15 [avatar split clause 364,350,366] 370. ~older(john,paul) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 278,251] 371. ~older(john,paul) | room(sK1) | ~room(mary) [subsumption resolution 370,250] 372. ~older(john,paul) | room(sK1) [subsumption resolution 371,249] 374. 18 <=> room(sK1) [avatar definition] 376. room(sK1) <- (18) [avatar component clause 374] 377. 18 | ~15 [avatar split clause 372,350,374] 431. 22 <=> funny(mary) [avatar definition] 433. funny(mary) <- (22) [avatar component clause 431] 583. older(X12,X13) | ~older(X12,mary) | X12 = X13 | mary = X13 | mary = X12 | ~room(X13) | mary = X13 <- (4) [resolution 183,296] 586. ~older(X12,mary) | older(X12,X13) | X12 = X13 | mary = X13 | mary = X12 | ~room(X13) <- (4) [duplicate literal removal 583] 774. older(john,X1) | john = X1 | mary = X1 | mary = john | ~room(X1) | person(mary) | ~room(mary) <- (4) [resolution 586,263] 777. older(john,X4) | john = X4 | mary = X4 | mary = john | ~room(X4) | funny(mary) | ~room(mary) <- (4) [resolution 586,259] 785. older(john,X1) | john = X1 | mary = X1 | ~room(X1) | person(mary) | ~room(mary) <- (4) [subsumption resolution 774,231] 786. older(john,X1) | john = X1 | mary = X1 | ~room(X1) | person(mary) <- (4) [subsumption resolution 785,249] 788. 32 <=> ! [X1] : (older(john,X1) | ~room(X1) | mary = X1 | john = X1) [avatar definition] 789. older(john,X1) | ~room(X1) | mary = X1 | john = X1 <- (32) [avatar component clause 788] 790. 8 | 32 | ~4 [avatar split clause 786,295,788,316] 797. older(john,X4) | john = X4 | mary = X4 | ~room(X4) | funny(mary) | ~room(mary) <- (4) [subsumption resolution 777,231] 798. older(john,X4) | john = X4 | mary = X4 | ~room(X4) | funny(mary) <- (4) [subsumption resolution 797,249] 799. 22 | 32 | ~4 [avatar split clause 798,295,788,431] 833. tall(mary) | ~room(mary) <- (22) [resolution 433,264] 838. tall(mary) <- (22) [subsumption resolution 833,249] 839. 7 | ~22 [avatar split clause 838,431,312] 1121. ~room(paul) | mary = paul | paul = john <- (~15, 32) [resolution 789,352] 1160. mary = paul | paul = john <- (~15, 32) [subsumption resolution 1121,250] 1161. paul = john <- (~15, 32) [subsumption resolution 1160,213] 1162. $false <- (~15, 32) [subsumption resolution 1161,232] 1163. 15 | ~32 [avatar contradiction clause 1162] 1164. paul = sK1 | mary = sK1 | fred = sK1 <- (18) [resolution 376,252] 1165. mary = sK1 | fred = sK1 <- (~16, 18) [subsumption resolution 1164,360] 1166. fred = sK1 <- (~16, ~17, 18) [subsumption resolution 1165,368] 1167. $false <- (~14, ~16, ~17, 18) [subsumption resolution 1166,348] 1168. 14 | 16 | 17 | ~18 [avatar contradiction clause 1167] 1169. $false [avatar sat refutation 308,319,353,361,369,377,790,799,839,1163,1168] % SZS output end Proof for 6938948438084075360542161 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Consuela, Melvin are the only persons in the room. If “not everyone in the room does not have a curated collection of mid-century modern furniture or does not train for and competes in international triathlons” then “everyone in the room trains for and competes in international triathlons if they does not have a curated collection of mid-century modern furniture”. Consuela either does not have a curated collection of mid-century modern furniture or regularly goes on multi-day backpacking trips in national parks but not both. Everyone in the room enjoys kayaking and exploring remote waterways if they collects rare minerals. Everyone anywhere who does not practice calligraphy, enjoys stand-up paddleboarding and practices pilates practices calligraphy, practices pilates or enjoys stand-up paddleboarding. Consuela practices pilates. Everyone anywhere does not collect rare minerals if they does not regularly goes on multi-day backpacking trips in national parks. Melvin who trains for and competes in international triathlons practices pilates. Everyone in the room does not maintain a personal blog focused on cybersecurity tips if they does not practice pilates and vice versa. Consuela who collects rare minerals or does not maintain a personal blog focused on cybersecurity tips or both has a tattoo.

Consuela regularly goes on multi-day backpacking trips in national parks.

entailment

room(consuela)&room(melvin)&(![X]:(room(X)=>(X='consuela'|X='melvin')))& ((~![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))=>(![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))=>(trains_for_and_competes_in_international_triathlons(X)))))))& (((does_not_have_a_curated_collection_of_mid-century_modern_furniture(consuela))<~>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(consuela))))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(anywhere(X)=>(((((does_not_practice_calligraphy(X))&(enjoys_stand-up_paddleboarding(X))&(practices_pilates(X))))=>(((practices_calligraphy(X))|(practices_pilates(X))|(enjoys_stand-up_paddleboarding(X))))))))& (practices_pilates(consuela))& (![X]:(anywhere(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(does_not_collect_rare_minerals(X))))))& ((trains_for_and_competes_in_international_triathlons(melvin))&(practices_pilates(melvin)))& (![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(collects_rare_minerals(X))))))& (?[X]:(room(X)&(practices_calligraphy(X))))& (((has_a_tattoo(consuela))|(enjoys_stand-up_paddleboarding(consuela))))& (![X]:(~room(X)=>(((enjoys_stand-up_paddleboarding(X))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))<=>(does_not_practice_pilates(X))))))& (![X]:(room(X)=>(((collects_rare_minerals(X))<=>(practices_pilates(X))))))& (![X]:(room(X)=>(((practices_pilates(X))=>(streams_on_Twitch(X))))))& (does_not_train_for_and_competes_in_international_triathlons(consuela))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& (~![X]:(anywhere(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(does_not_enjoy_stand-up_paddleboarding(X))))& ((consuela_dream=>(((streams_on_Twitch(melvin))&(collects_rare_minerals(melvin))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_collect_rare_minerals(X))))))& (((does_not_enjoy_kayaking_and_exploring_remote_waterways(consuela))|(has_a_curated_collection_of_mid-century_modern_furniture(consuela))))& (![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& ((((collects_rare_minerals(consuela))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(consuela))))&(has_a_tattoo(consuela)))

room(consuela)&room(melvin)&(![X]:(room(X)=>(X='consuela'|X='melvin')))& regularly_goes_on_multi-day_backpacking_trips_in_national_parks(consuela)

% SZS status Unsatisfiable for 2488676462970966561648980 % SZS output start Proof for 2488676462970966561648980 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. predj(mary) [input p5] 50. ! [X0] : (anywhere(X0) => (~predb(X0) => ~predh(X0))) [input p6] 56. ! [X0] : (room(X0) => (~predg(X0) <=> ~predj(X0))) [input p12] 68. predc(mary) & (~predg(mary) | predh(mary)) [input p24] 69. ~(predb(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 75. ~predg(mary) | predh(mary) [pure predicate removal 68] 147. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 148. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 147] 155. ! [X0] : ((~predh(X0) | predb(X0)) | ~anywhere(X0)) [ennf transformation 50] 156. ! [X0] : (~predh(X0) | predb(X0) | ~anywhere(X0)) [flattening 155] 161. ! [X0] : ((~predg(X0) <=> ~predj(X0)) | ~room(X0)) [ennf transformation 56] 172. ~predb(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 69] 173. ~predb(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 172] 179. ! [X0] : (((~predg(X0) | predj(X0)) & (~predj(X0) | predg(X0))) | ~room(X0)) [nnf transformation 161] 183. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 184. ~predb(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 173,183] 185. anywhere(X0) [cnf transformation 5] 266. room(mary) [cnf transformation 148] 267. room(paul) [cnf transformation 148] 268. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 148] 274. predj(mary) [cnf transformation 49] 275. ~predh(X0) | predb(X0) | ~anywhere(X0) [cnf transformation 156] 282. ~predj(X0) | predg(X0) | ~room(X0) [cnf transformation 179] 295. ~predg(mary) | predh(mary) [cnf transformation 75] 296. ~predb(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 184] 297. ~predb(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 184] 298. ~predb(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 184] 312. 4 <=> predb(mary) [avatar definition] 317. ~predh(X0) | predb(X0) [subsumption resolution 275,185] 324. 6 <=> predh(mary) [avatar definition] 326. predh(mary) <- (6) [avatar component clause 324] 328. 7 <=> predg(mary) [avatar definition] 331. 6 | ~7 [avatar split clause 295,328,324] 332. ~predb(mary) | paul != sK2 | ~room(mary) [subsumption resolution 298,267] 333. ~predb(mary) | paul != sK2 [subsumption resolution 332,266] 335. 8 <=> paul = sK2 [avatar definition] 337. paul != sK2 <- (~8) [avatar component clause 335] 338. ~8 | ~4 [avatar split clause 333,312,335] 339. ~predb(mary) | mary != sK2 | ~room(mary) [subsumption resolution 297,267] 340. ~predb(mary) | mary != sK2 [subsumption resolution 339,266] 342. 9 <=> mary = sK2 [avatar definition] 344. mary != sK2 <- (~9) [avatar component clause 342] 345. ~9 | ~4 [avatar split clause 340,312,342] 346. ~predb(mary) | room(sK2) | ~room(mary) [subsumption resolution 296,267] 347. ~predb(mary) | room(sK2) [subsumption resolution 346,266] 349. 10 <=> room(sK2) [avatar definition] 351. room(sK2) <- (10) [avatar component clause 349] 352. 10 | ~4 [avatar split clause 347,312,349] 358. predg(mary) | ~room(mary) [resolution 282,274] 364. predg(mary) [subsumption resolution 358,266] 365. 7 [avatar split clause 364,328] 367. predb(mary) <- (6) [resolution 326,317] 373. 4 | ~6 [avatar split clause 367,324,312] 440. mary = sK2 | paul = sK2 <- (10) [resolution 268,351] 459. paul = sK2 <- (~9, 10) [subsumption resolution 440,344] 460. $false <- (~8, ~9, 10) [subsumption resolution 459,337] 461. 8 | 9 | ~10 [avatar contradiction clause 460] 462. $false [avatar sat refutation 331,338,345,352,365,373,461] % SZS output end Proof for 2488676462970966561648980 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Charles is the only person in the room. Charles is older than David. Charles is tall. Everyone in the room is a strong person if they is a creative person. Charles is older than Lou. Everyone in the room who is tall is older than Lou. All tall person is kind. Charles is not a humble wise curious person. Everyone outside the room is old if they is richer than David. Charles is quieter than Lou. Everyone in the room who is older than David, is not a kind person and is richer than Lou is quieter than David. Everyone in the room is older than Lou if they is quieter than David. Everyone in the room who is older than Lou is richer than Lou. Everyone anywhere who is older than Lou and is happy is not funny. Charles is the least rich in the room. All funny person is calm. Everyone in the room who is quieter than David or is older than Lou or both is not a quiet person. Everyone outside the room is a curious person if they is older than David. Charles who is not a brave person is humble. No generous person is wise. Charles who is quieter than David is richer than David.

Charles is happy.

neutral

room(charles)&(![X]:(room(X)=>(X='charles')))& (older(david,charles))& (tall(charles))& (![X]:(room(X)=>(((creative(X)&person(X))=>(strong(X)&person(X))))))& (older(lou,charles))& (![X]:(room(X)=>(((tall(X))=>(older(lou,X))))))& (![X]:(tall(X)=>kind(X)))& (~(humble(charles)&wise(charles)&curious(charles)&person(charles)))& (![X]:(~room(X)=>(((richer(david,X))=>(old(X))))))& (quieter(lou,charles))& (![X]:(room(X)=>(((((older(david,X))&(~(kind(X)&person(X)))&(richer(lou,X))))=>(quieter(david,X))))))& (![X]:(room(X)=>(((quieter(david,X))=>(older(lou,X))))))& (![X]:(room(X)=>(((older(lou,X))=>(richer(lou,X))))))& (![X]:(anywhere(X)=>(((((older(lou,X))&(happy(X))))=>(~funny(X))))))& (![X]:((room(X)&(X!=charles))=>richer(charles,X)))& (![X]:(funny(X)=>calm(X)))& (![X]:(room(X)=>(((((quieter(david,X))|(older(lou,X))))=>(~(quiet(X)&person(X)))))))& (![X]:(~room(X)=>(((older(david,X))=>(curious(X)&person(X))))))& ((~(brave(charles)&person(charles)))&(humble(charles)))& (~?[X]:(generous(X)=>wise(X)))& ((quieter(david,charles))&(richer(david,charles)))

room(charles)&(![X]:(room(X)=>(X='charles')))& happy(charles)

“Everyone outside the room collects first edition books or does not bake bread at home” only if “more than one person in the room collects rare and antique scientific instruments”. If “everyone in the room collects comic books or does not host a YouTube channel dedicated to art tutorials” then “if someone does not collect first edition books then he/she hosts a popular podcast about emerging technologies and vice versa”. If someone reads mystery novels then he/she is an avid hiker and vice versa. If someone collects comic books then he/she does enjoy mountain biking and vice versa. It is not the case that “someone anywhere does not enjoy mountain biking”. If someone works on fridays then he/she hosts a popular podcast about emerging technologies and vice versa. Everyone outside the room reads mystery novels. No one anywhere who does enjoy mountain biking is an avid hiker. Everyone in the room who hosts a popular podcast about emerging technologies reads mystery novels.

Everyone in the room does not collect rare and antique scientific instruments or works on fridays.

contradiction

(there_is_a_room)& ((![X]:(~room(X)=>(((does_not_bake_bread_at_home(X))|(collects_first_edition_books(X))))))=>((?[X,Y]:(room(X)&room(Y)&(collects_rare_and_antique_scientific_instruments(X)&collects_rare_and_antique_scientific_instruments(Y))&(X!=Y)))))& ((![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(collects_comic_books(X))))))=>((![X]:((does_not_collect_first_edition_books(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& ((![X]:((reads_mystery_novels(X))<=>(is_an_avid_hiker(X)))))& ((![X]:((collects_comic_books(X))<=>(does_enjoy_mountain_biking(X)))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(~room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(reads_mystery_novels(X))))))& ((![X]:((practices_tai_chi(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))& ((![X]:((is_a_coffee_connoisseur(X))<=>(bakes_bread_at_home(X)))))& (~(?[X]:(anywhere(X)&(does_not_enjoy_mountain_biking(X)))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(((practices_digital_art(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))))))))& ((![X]:((works_on_fridays(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))& ((![X]:((composes_and_performs_experimental_electronic_music(X))<=>(practices_digital_art(X)))))& (![X]:(~room(X)=>(reads_mystery_novels(X))))& ((![X]:((collects_antique_jewelry(X))<=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))& ((![X]:((is_passionate_about_collecting_and_restoring_classic_cars(X))<=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& ((![X]:((composes_and_performs_experimental_electronic_music(X))<=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& (~?[X]:(anywhere(X)=>(((does_enjoy_mountain_biking(X))=>(is_an_avid_hiker(X))))))& (![X]:(~room(X)=>(((is_a_coffee_connoisseur(X))=>(enjoys_wildlife_photography(X))))))& (![X]:(~room(X)=>(((enjoys_wildlife_photography(X))=>(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(knows_morse_code(X))))))& (![X]:(~room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(practices_digital_art(X))))))& ((?[X,Y]:(room(X)&room(Y)&(practices_zumba(X)&practices_zumba(Y))&(X!=Y))))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(reads_mystery_novels(X))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(is_a_coffee_connoisseur(X))))))& ((![X]:((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<=>(composes_and_performs_experimental_electronic_music(X)))))& (?[X]:(room(X)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(does_enjoy_mountain_biking(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((works_on_fridays(X))|(does_not_collect_rare_and_antique_scientific_instruments(X)))))

% SZS status Unsatisfiable for 8682943168058331596416438 % SZS output start Proof for 8682943168058331596416438 5. ! [X0] : anywhere(X0) [input b4] 45. ! [X0] : (~room(X0) => (predp(X0) | ~predv(X0))) => ? [X0,X1] : (X0 != X1 & predd(X1) & predd(X0) & room(X1) & room(X0)) [input p1] 46. ! [X0] : (room(X0) => (predi(X0) | ~predq(X0))) => ! [X0] : (~predp(X0) <=> predy(X0)) [input p2] 47. ! [X0] : (predb(X0) <=> predz(X0)) [input p3] 48. ! [X0] : (predi(X0) <=> predn(X0)) [input p4] 53. ~? [X0] : (~predn(X0) & anywhere(X0)) [input p9] 55. ! [X0] : (predj(X0) <=> predy(X0)) [input p11] 57. ! [X0] : (~room(X0) => predb(X0)) [input p13] 61. ~? [X0] : (anywhere(X0) => (predn(X0) => predz(X0))) [input p17] 67. ! [X0] : (room(X0) => (predy(X0) => predb(X0))) [input p23] 72. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room [input hypothesis] 73. ! [X0] : (~room(X0) => (predp(X0) | ~predv(X0))) => ? [X1,X2] : (X1 != X2 & predd(X2) & predd(X1) & room(X2) & room(X1)) [rectify 45] 74. ! [X0] : (room(X0) => (predi(X0) | ~predq(X0))) => ! [X1] : (~predp(X1) <=> predy(X1)) [rectify 46] 75. ! [X0] : (predj(X0) => predy(X0)) [unused predicate definition removal 55] 76. ! [X0] : (predb(X0) => predz(X0)) [unused predicate definition removal 47] 77. ! [X0] : (predn(X0) => predi(X0)) [unused predicate definition removal 48] 81. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [pure predicate removal 72] 154. ? [X1,X2] : (X1 != X2 & predd(X2) & predd(X1) & room(X2) & room(X1)) | ? [X0] : ((~predp(X0) & predv(X0)) & ~room(X0)) [ennf transformation 73] 155. ? [X1,X2] : (X1 != X2 & predd(X2) & predd(X1) & room(X2) & room(X1)) | ? [X0] : (~predp(X0) & predv(X0) & ~room(X0)) [flattening 154] 156. ! [X1] : (~predp(X1) <=> predy(X1)) | ? [X0] : ((~predi(X0) & predq(X0)) & room(X0)) [ennf transformation 74] 157. ! [X1] : (~predp(X1) <=> predy(X1)) | ? [X0] : (~predi(X0) & predq(X0) & room(X0)) [flattening 156] 158. ! [X0] : (predz(X0) | ~predb(X0)) [ennf transformation 76] 159. ! [X0] : (predi(X0) | ~predn(X0)) [ennf transformation 77] 164. ! [X0] : (predn(X0) | ~anywhere(X0)) [ennf transformation 53] 167. ! [X0] : (predy(X0) | ~predj(X0)) [ennf transformation 75] 168. ! [X0] : (predb(X0) | room(X0)) [ennf transformation 57] 169. ! [X0] : ((~predz(X0) & predn(X0)) & anywhere(X0)) [ennf transformation 61] 170. ! [X0] : (~predz(X0) & predn(X0) & anywhere(X0)) [flattening 169] 177. ! [X0] : ((predb(X0) | ~predy(X0)) | ~room(X0)) [ennf transformation 67] 178. ! [X0] : (predb(X0) | ~predy(X0) | ~room(X0)) [flattening 177] 183. ! [X0] : ((~predd(X0) | predj(X0)) | ~room(X0)) [ennf transformation 81] 184. ! [X0] : (~predd(X0) | predj(X0) | ~room(X0)) [flattening 183] 185. ? [X1,X2] : (X1 != X2 & predd(X2) & predd(X1) & room(X2) & room(X1)) | ~sP0 [predicate definition introduction] 186. sP0 | ? [X0] : (~predp(X0) & predv(X0) & ~room(X0)) [definition folding 155,185] 188. ? [X1,X2] : (X1 != X2 & predd(X2) & predd(X1) & room(X2) & room(X1)) | ~sP0 [nnf transformation 185] 189. ? [X0,X1] : (X0 != X1 & predd(X1) & predd(X0) & room(X1) & room(X0)) | ~sP0 [rectify 188] 190. ? [X0,X1] : (X0 != X1 & predd(X1) & predd(X0) & room(X1) & room(X0)) => (sK1 != sK2 & predd(sK2) & predd(sK1) & room(sK2) & room(sK1)) [choice axiom] 191. (sK1 != sK2 & predd(sK2) & predd(sK1) & room(sK2) & room(sK1)) | ~sP0 [skolemisation 189,190] 192. ? [X0] : (~predp(X0) & predv(X0) & ~room(X0)) => (~predp(sK3) & predv(sK3) & ~room(sK3)) [choice axiom] 193. sP0 | (~predp(sK3) & predv(sK3) & ~room(sK3)) [skolemisation 186,192] 194. ! [X1] : ((~predp(X1) | ~predy(X1)) & (predy(X1) | predp(X1))) | ? [X0] : (~predi(X0) & predq(X0) & room(X0)) [nnf transformation 157] 195. ! [X0] : ((~predp(X0) | ~predy(X0)) & (predy(X0) | predp(X0))) | ? [X1] : (~predi(X1) & predq(X1) & room(X1)) [rectify 194] 196. ? [X1] : (~predi(X1) & predq(X1) & room(X1)) => (~predi(sK4) & predq(sK4) & room(sK4)) [choice axiom] 197. ! [X0] : ((~predp(X0) | ~predy(X0)) & (predy(X0) | predp(X0))) | (~predi(sK4) & predq(sK4) & room(sK4)) [skolemisation 195,196] 207. anywhere(X0) [cnf transformation 5] 291. predd(sK2) | ~sP0 [cnf transformation 191] 293. sP0 | ~room(sK3) [cnf transformation 193] 298. predy(X0) | predp(X0) | ~predi(sK4) [cnf transformation 197] 301. ~predp(X0) | ~predy(X0) | ~predi(sK4) [cnf transformation 197] 302. ~predb(X0) | predz(X0) [cnf transformation 158] 303. ~predn(X0) | predi(X0) [cnf transformation 159] 308. predn(X0) | ~anywhere(X0) [cnf transformation 164] 310. ~predj(X0) | predy(X0) [cnf transformation 167] 313. predb(X0) | room(X0) [cnf transformation 168] 322. ~predz(X0) [cnf transformation 170] 329. predb(X0) | ~predy(X0) | ~room(X0) [cnf transformation 178] 334. ~predd(X0) | predj(X0) | ~room(X0) [cnf transformation 184] 336. 1 <=> sP0 [avatar definition] 345. 3 <=> predd(sK2) [avatar definition] 347. predd(sK2) <- (3) [avatar component clause 345] 348. ~1 | 3 [avatar split clause 291,345,336] 375. 9 <=> room(sK3) [avatar definition] 377. ~room(sK3) <- (~9) [avatar component clause 375] 378. ~9 | 1 [avatar split clause 293,336,375] 380. 10 <=> predi(sK4) [avatar definition] 382. ~predi(sK4) <- (~10) [avatar component clause 380] 384. 11 <=> ! [X0] : (~predp(X0) | ~predy(X0)) [avatar definition] 385. ~predy(X0) | ~predp(X0) <- (11) [avatar component clause 384] 386. ~10 | 11 [avatar split clause 301,384,380] 398. 14 <=> ! [X0] : (predy(X0) | predp(X0)) [avatar definition] 399. predy(X0) | predp(X0) <- (14) [avatar component clause 398] 400. ~10 | 14 [avatar split clause 298,398,380] 403. predn(X0) [subsumption resolution 308,207] 404. ~predy(X0) | predb(X0) [subsumption resolution 329,313] 405. predi(X0) [resolution 303,403] 406. $false <- (~10) [resolution 405,382] 407. 10 [avatar contradiction clause 406] 410. room(X0) | predz(X0) [resolution 313,302] 411. room(X0) [subsumption resolution 410,322] 412. $false <- (~9) [resolution 411,377] 413. 9 [avatar contradiction clause 412] 423. predb(X0) | predp(X0) <- (14) [resolution 404,399] 435. predp(X0) | predz(X0) <- (14) [resolution 423,302] 436. predp(X0) <- (14) [subsumption resolution 435,322] 442. predj(sK2) | ~room(sK2) <- (3) [resolution 334,347] 444. predj(sK2) <- (3) [subsumption resolution 442,411] 446. predy(sK2) <- (3) [resolution 444,310] 449. ~predp(sK2) <- (3, 11) [resolution 446,385] 450. $false <- (3, 11, 14) [subsumption resolution 449,436] 451. ~3 | ~11 | ~14 [avatar contradiction clause 450] 452. $false [avatar sat refutation 348,378,386,400,407,413,451] % SZS output end Proof for 8682943168058331596416438 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Everyone in the room who can play the piano is a client of Meta. Everyone in the room who practices graffiti art enjoys macrame. Everyone anywhere either enjoys stand-up paddleboarding or is a scotch connoisseur but not both if they practices graffiti art. Everyone in the room can play the piano only if they does not enjoy macrame. Everyone in the room participates in citizen science projects related to wildlife monitoring only if they enjoys macrame. Everyone in the room who enjoys macrame can play the piano. Everyone in the room who is a scotch connoisseur participates in citizen science projects related to wildlife monitoring.

Everyone in the room is not a scotch connoisseur or enjoys stand-up paddleboarding.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((can_play_the_piano(X))=>(is_a_client_of_Meta(X))))))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(enjoys_macrame(X))))))& (![X]:(anywhere(X)=>(((practices_graffiti_art(X))=>(((enjoys_stand-up_paddleboarding(X))<~>(is_a_scotch_connoisseur(X))))))))& ((![X]:((reads_mystery_novels(X))=>(enjoys_stand-up_paddleboarding(X)))))& (![X]:(room(X)=>(((practices_archery(X))=>(enjoys_stand-up_paddleboarding(X))))))& ((![X]:((enjoys_snowboarding(X))<=>(reads_mystery_novels(X)))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))=>(can_play_the_piano(X))))))& (![X]:(~room(X)=>(((enjoys_snowboarding(X))=>(~((is_a_client_of_Meta(X))|(practices_graffiti_art(X))))))))& (![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(practices_graffiti_art(X))))))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(~((has_completed_a_triathlon(X))|(practices_archery(X))))))))& (?[X]:(~room(X)&(enjoys_snowboarding(X))))& ((![X]:((can_play_the_piano(X))=>(enjoys_snowboarding(X)))))& (![X]:(room(X)=>(((does_not_enjoy_macrame(X))<=(can_play_the_piano(X))))))& (![X]:(~room(X)=>(practices_archery(X))))& (![X]:(room(X)=>(((enjoys_macrame(X))<=(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(can_play_the_piano(X))))))& (?[X]:(room(X)&(~((is_a_scotch_connoisseur(X))|(enjoys_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))<=(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(~room(X)=>(((reads_mystery_novels(X))<=(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((((is_a_scotch_connoisseur(X))|(can_play_the_piano(X))|(does_not_have_completed_a_triathlon(X))))<=(reads_mystery_novels(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))|(is_not_a_scotch_connoisseur(X)))))

% SZS status Unsatisfiable for 8569654578882601624679863 % SZS output start Proof for 8569654578882601624679863 44. there_is_a_room [input p0] 57. ! [X0] : (room(X0) => (preda(X0) => ~prede(X0))) [input p13] 59. ! [X0] : (room(X0) => (predf(X0) => prede(X0))) [input p15] 60. ! [X0] : (room(X0) => (prede(X0) => preda(X0))) [input p16] 62. ! [X0] : (room(X0) => (predd(X0) => predf(X0))) [input p18] 66. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis] 158. ! [X0] : ((~prede(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 57] 159. ! [X0] : (~prede(X0) | ~preda(X0) | ~room(X0)) [flattening 158] 161. ! [X0] : ((prede(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 59] 162. ! [X0] : (prede(X0) | ~predf(X0) | ~room(X0)) [flattening 161] 163. ! [X0] : ((preda(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 60] 164. ! [X0] : (preda(X0) | ~prede(X0) | ~room(X0)) [flattening 163] 167. ! [X0] : ((predf(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 62] 168. ! [X0] : (predf(X0) | ~predd(X0) | ~room(X0)) [flattening 167] 173. ? [X0] : ((predd(X0) & ~predj(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 66] 174. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ~there_is_a_room [flattening 173] 182. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK2) & ~predj(sK2) & room(sK2)) [choice axiom] 183. (predd(sK2) & ~predj(sK2) & room(sK2)) | ~there_is_a_room [skolemisation 174,182] 265. there_is_a_room [cnf transformation 44] 282. ~prede(X0) | ~preda(X0) | ~room(X0) [cnf transformation 159] 284. ~predf(X0) | prede(X0) | ~room(X0) [cnf transformation 162] 285. preda(X0) | ~prede(X0) | ~room(X0) [cnf transformation 164] 289. ~predd(X0) | predf(X0) | ~room(X0) [cnf transformation 168] 292. room(sK2) | ~there_is_a_room [cnf transformation 183] 294. predd(sK2) | ~there_is_a_room [cnf transformation 183] 297. ~prede(X0) | ~room(X0) [subsumption resolution 285,282] 298. predd(sK2) [subsumption resolution 294,265] 300. room(sK2) [subsumption resolution 292,265] 311. predf(sK2) | ~room(sK2) [resolution 289,298] 312. predf(sK2) [subsumption resolution 311,300] 314. prede(sK2) | ~room(sK2) [resolution 312,284] 316. prede(sK2) [subsumption resolution 314,300] 320. ~room(sK2) [resolution 316,297] 322. $false [subsumption resolution 320,300] % SZS output end Proof for 8569654578882601624679863 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.031 s % ------------------------------ % ------------------------------

Carol, Olivia, William, Rose, Sabrina are the only persons in the room. If “everyone outside the room enjoys snowboarding or does not read mystery novels” then “not everyone in the room is a tea enthusiast if they enjoys snowboarding”. If “Carol enjoys landscape photography” then “everyone in the room is right-handed or is not a dedicated advocate for digital privacy and encryption”. If “everyone in the room is right-handed or is not a dedicated advocate for digital privacy and encryption” then “someone in the room is an avid mountain climber who has scaled several peaks”. “Not everyone in the room does not volunteer for local environmental conservation projects or does not know morse code” if “everyone in the room does not enjoy snowboarding or is a chess master who participates in national tournaments” and vice versa. If “everyone in the room is a tea enthusiast or does not use an ios phone” then “Olivia plays as a goalkeeper for a local amateur soccer team”. If “everyone in the room is a member of a local theater group specializing in improv or does not develop open-source software projects in their free time” then “it is not the case that “Olivia is a member of a local theater group specializing in improv””. Olivia either is not right-handed or uses an ios phone but not both. Carol who does not read mystery novels has a vast collection of first-edition science fiction novels. Olivia neither does not play as a goalkeeper for a local amateur soccer team nor is a tea enthusiast. Everyone in the room who does not know morse code, is a client of Costco or does not use an ios phone collects vintage stamps. Everyone in the room who enjoys watercolor painting is a tea enthusiast. Everyone in the room is a client of Costco if they is a tea enthusiast. Olivia does not know morse code. Olivia enjoys snowboarding, volunteers for local environmental conservation projects or is a member of a local theater group specializing in improv. If someone enjoys landscape photography then he/she is a chess master who participates in national tournaments. Olivia is an avid mountain climber who has scaled several peaks.

Olivia is a dedicated advocate for digital privacy and encryption.

contradiction

room(carol)&room(olivia)&room(william)&room(rose)&room(sabrina)&(![X]:(room(X)=>(X='carol'|X='olivia'|X='william'|X='rose'|X='sabrina')))& ((![X]:(~room(X)=>(((does_not_read_mystery_novels(X))|(enjoys_snowboarding(X))))))=>(~![X]:(room(X)=>(((enjoys_snowboarding(X))=>(is_a_tea_enthusiast(X)))))))& (((enjoys_landscape_photography(carol))=>(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_right-handed(X)))))))& ((![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_right-handed(X))))))=>(?[X]:(room(X)&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& ((![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_enjoy_snowboarding(X))))))<=>(~![X]:(room(X)=>(((does_not_know_morse_code(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X)))))))& ((![X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(is_a_tea_enthusiast(X))))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(olivia)))& ((![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(~(is_a_member_of_a_local_theater_group_specializing_in_improv(olivia))))& (((is_not_right-handed(olivia))<~>(uses_an_ios_phone(olivia))))& ((does_not_read_mystery_novels(carol))&(has_a_vast_collection_of_first-edition_science_fiction_novels(carol)))& (~((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(olivia))|(is_a_tea_enthusiast(olivia))))& (![X]:(room(X)=>(((((does_not_know_morse_code(X))|(is_a_client_of_Costco(X))|(does_not_use_an_ios_phone(X))))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(is_a_client_of_Costco(X))))))& (does_not_know_morse_code(olivia))& (((enjoys_snowboarding(olivia))|(volunteers_for_local_environmental_conservation_projects(olivia))|(is_a_member_of_a_local_theater_group_specializing_in_improv(olivia))))& ((![X]:((enjoys_landscape_photography(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X)))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(olivia))& (is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(olivia))& (![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(enjoys_watercolor_painting(X))))))& ((carol_dream=>(~(?[X]:(room(X)&(collects_vintage_stamps(X)))))))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(carol))&(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(carol)))& (![X]:(~room(X)=>(reads_mystery_novels(X))))& (~(is_a_member_of_a_local_theater_group_specializing_in_improv(olivia)))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))

room(carol)&room(olivia)&room(william)&room(rose)&room(sabrina)&(![X]:(room(X)=>(X='carol'|X='olivia'|X='william'|X='rose'|X='sabrina')))& is_a_dedicated_advocate_for_digital_privacy_and_encryption(olivia)

% SZS status Unsatisfiable for 1086457518201405351562543 % SZS output start Proof for 1086457518201405351562543 44. ! [X0] : (room(X0) => (~predp(X0) => predu(X0))) & ! [X0] : (room(X0) => (predv(X0) => ~predp(X0))) & ~predr(paul) & ! [X0] : (~room(X0) => prede(X0)) & ~predg(mary) & predd(mary) & (mary_dream => ~? [X0] : (predy(X0) & room(X0))) & ! [X0] : (room(X0) => (predm(X0) | ~predh(X0))) & ~predg(paul) & predu(paul) & ! [X0] : (predi(X0) => predn(X0)) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X0] : (room(X0) => (predf(X0) => predj(X0))) & ! [X0] : (room(X0) => (predm(X0) => predf(X0))) & ! [X0] : (room(X0) => ((~predo(X0) | predj(X0) | ~predt(X0)) => predy(X0))) & ~(predf(paul) | ~predd(paul)) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X0] : (room(X0) => (predr(X0) | ~predq(X0))) => ~predr(paul)) & (! [X0] : (room(X0) => (predf(X0) | ~predo(X0))) => predd(paul)) & (! [X0] : (room(X0) => (~predk(X0) | predn(X0))) <=> ~! [X0] : (room(X0) => (~predl(X0) | ~predt(X0)))) & (! [X0] : (room(X0) => (predb(X0) | ~predg(X0))) => ? [X0] : (predu(X0) & room(X0))) & (predi(mary) => ! [X0] : (room(X0) => (predb(X0) | ~predg(X0)))) & (! [X0] : (~room(X0) => (predk(X0) | ~prede(X0))) => ~! [X0] : (room(X0) => (predk(X0) => predf(X0)))) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. predg(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 46. ! [X0] : (room(X0) => (~predp(X0) => predu(X0))) & ! [X1] : (room(X1) => (predv(X1) => ~predp(X1))) & ~predr(paul) & ! [X2] : (~room(X2) => prede(X2)) & ~predg(mary) & predd(mary) & (mary_dream => ~? [X3] : (predy(X3) & room(X3))) & ! [X4] : (room(X4) => (predm(X4) | ~predh(X4))) & ~predg(paul) & predu(paul) & ! [X5] : (predi(X5) => predn(X5)) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X6] : (room(X6) => (predf(X6) => predj(X6))) & ! [X7] : (room(X7) => (predm(X7) => predf(X7))) & ! [X8] : (room(X8) => ((~predo(X8) | predj(X8) | ~predt(X8)) => predy(X8))) & ~(predf(paul) | ~predd(paul)) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X9] : (room(X9) => (predr(X9) | ~predq(X9))) => ~predr(paul)) & (! [X10] : (room(X10) => (predf(X10) | ~predo(X10))) => predd(paul)) & (! [X11] : (room(X11) => (~predk(X11) | predn(X11))) <=> ~! [X12] : (room(X12) => (~predl(X12) | ~predt(X12)))) & (! [X13] : (room(X13) => (predb(X13) | ~predg(X13))) => ? [X14] : (predu(X14) & room(X14))) & (predi(mary) => ! [X15] : (room(X15) => (predb(X15) | ~predg(X15)))) & (! [X16] : (~room(X16) => (predk(X16) | ~prede(X16))) => ~! [X17] : (room(X17) => (predk(X17) => predf(X17)))) & ! [X18] : (room(X18) => (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => (~predp(X0) => predu(X0))) & ~predr(paul) & ! [X2] : (~room(X2) => prede(X2)) & ~predg(mary) & predd(mary) & (mary_dream => ~? [X3] : (predy(X3) & room(X3))) & ! [X4] : (room(X4) => (predm(X4) | ~predh(X4))) & ~predg(paul) & predu(paul) & ! [X5] : (predi(X5) => predn(X5)) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X6] : (room(X6) => (predf(X6) => predj(X6))) & ! [X7] : (room(X7) => (predm(X7) => predf(X7))) & ! [X8] : (room(X8) => ((~predo(X8) | predj(X8) | ~predt(X8)) => predy(X8))) & ~(predf(paul) | ~predd(paul)) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X9] : (room(X9) => (predr(X9) | ~predq(X9))) => ~predr(paul)) & (! [X10] : (room(X10) => (predf(X10) | ~predo(X10))) => predd(paul)) & (! [X11] : (room(X11) => (~predk(X11) | predn(X11))) <=> ~! [X12] : (room(X12) => (~predl(X12) | ~predt(X12)))) & (! [X13] : (room(X13) => (predb(X13) | ~predg(X13))) => ? [X14] : (predu(X14) & room(X14))) & (predi(mary) => ! [X15] : (room(X15) => (predb(X15) | ~predg(X15)))) & (! [X16] : (~room(X16) => (predk(X16) | ~prede(X16))) => ~! [X17] : (room(X17) => (predk(X17) => predf(X17)))) & ! [X18] : (room(X18) => (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ~predr(paul) & ! [X2] : (~room(X2) => prede(X2)) & ~predg(mary) & predd(mary) & (mary_dream => ~? [X3] : (predy(X3) & room(X3))) & ! [X4] : (room(X4) => (predm(X4) | ~predh(X4))) & ~predg(paul) & predu(paul) & ! [X5] : (predi(X5) => predn(X5)) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X6] : (room(X6) => (predf(X6) => predj(X6))) & ! [X7] : (room(X7) => (predm(X7) => predf(X7))) & ! [X8] : (room(X8) => ((~predo(X8) | predj(X8) | ~predt(X8)) => predy(X8))) & ~(predf(paul) | ~predd(paul)) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X9] : (room(X9) => (predr(X9) | ~predq(X9))) => ~predr(paul)) & (! [X10] : (room(X10) => (predf(X10) | ~predo(X10))) => predd(paul)) & (! [X11] : (room(X11) => (~predk(X11) | predn(X11))) <=> ~! [X12] : (room(X12) => (~predl(X12) | ~predt(X12)))) & (! [X13] : (room(X13) => (predb(X13) | ~predg(X13))) => ? [X14] : (predu(X14) & room(X14))) & (predi(mary) => ! [X15] : (room(X15) => (predb(X15) | ~predg(X15)))) & (! [X16] : (~room(X16) => (predk(X16) | ~prede(X16))) => ~! [X17] : (room(X17) => (predk(X17) => predf(X17)))) & ! [X18] : (room(X18) => (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ~predr(paul) & ! [X2] : (~room(X2) => prede(X2)) & ~predg(mary) & predd(mary) & ! [X4] : (room(X4) => (predm(X4) | ~predh(X4))) & ~predg(paul) & predu(paul) & ! [X5] : (predi(X5) => predn(X5)) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X6] : (room(X6) => (predf(X6) => predj(X6))) & ! [X7] : (room(X7) => (predm(X7) => predf(X7))) & ! [X8] : (room(X8) => ((~predo(X8) | predj(X8) | ~predt(X8)) => predy(X8))) & ~(predf(paul) | ~predd(paul)) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X9] : (room(X9) => (predr(X9) | ~predq(X9))) => ~predr(paul)) & (! [X10] : (room(X10) => (predf(X10) | ~predo(X10))) => predd(paul)) & (! [X11] : (room(X11) => (~predk(X11) | predn(X11))) <=> ~! [X12] : (room(X12) => (~predl(X12) | ~predt(X12)))) & (! [X13] : (room(X13) => (predb(X13) | ~predg(X13))) => ? [X14] : (predu(X14) & room(X14))) & (predi(mary) => ! [X15] : (room(X15) => (predb(X15) | ~predg(X15)))) & (! [X16] : (~room(X16) => (predk(X16) | ~prede(X16))) => ~! [X17] : (room(X17) => (predk(X17) => predf(X17)))) & ! [X18] : (room(X18) => (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ~predr(paul) & ! [X2] : (~room(X2) => prede(X2)) & ~predg(mary) & predd(mary) & ! [X4] : (room(X4) => (predm(X4) | ~predh(X4))) & ~predg(paul) & predu(paul) & ! [X5] : (predi(X5) => predn(X5)) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X6] : (room(X6) => (predf(X6) => predj(X6))) & ! [X7] : (room(X7) => (predm(X7) => predf(X7))) & ~(predf(paul) | ~predd(paul)) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X9] : (room(X9) => (predr(X9) | ~predq(X9))) => ~predr(paul)) & (! [X10] : (room(X10) => (predf(X10) | ~predo(X10))) => predd(paul)) & (! [X11] : (room(X11) => (~predk(X11) | predn(X11))) <=> ~! [X12] : (room(X12) => (~predl(X12) | ~predt(X12)))) & (! [X13] : (room(X13) => (predb(X13) | ~predg(X13))) => ? [X14] : (predu(X14) & room(X14))) & (predi(mary) => ! [X15] : (room(X15) => (predb(X15) | ~predg(X15)))) & (! [X16] : (~room(X16) => (predk(X16) | ~prede(X16))) => ~! [X17] : (room(X17) => (predk(X17) => predf(X17)))) & ! [X18] : (room(X18) => (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ~predr(paul) & ! [X2] : (~room(X2) => prede(X2)) & ~predg(mary) & predd(mary) & ! [X4] : (room(X4) => (predm(X4) | ~predh(X4))) & ~predg(paul) & predu(paul) & ! [X5] : (predi(X5) => predn(X5)) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X7] : (room(X7) => (predm(X7) => predf(X7))) & ~(predf(paul) | ~predd(paul)) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X9] : (room(X9) => (predr(X9) | ~predq(X9))) => ~predr(paul)) & (! [X10] : (room(X10) => (predf(X10) | ~predo(X10))) => predd(paul)) & (! [X11] : (room(X11) => (~predk(X11) | predn(X11))) <=> ~! [X12] : (room(X12) => (~predl(X12) | ~predt(X12)))) & (! [X13] : (room(X13) => (predb(X13) | ~predg(X13))) => ? [X14] : (predu(X14) & room(X14))) & (predi(mary) => ! [X15] : (room(X15) => (predb(X15) | ~predg(X15)))) & (! [X16] : (~room(X16) => (predk(X16) | ~prede(X16))) => ~! [X17] : (room(X17) => (predk(X17) => predf(X17)))) & ! [X18] : (room(X18) => (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ~predr(paul) & ! [X2] : (~room(X2) => prede(X2)) & ~predg(mary) & predd(mary) & ! [X4] : (room(X4) => (predm(X4) | ~predh(X4))) & ~predg(paul) & predu(paul) & ! [X5] : (predi(X5) => predn(X5)) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X7] : (room(X7) => (predm(X7) => predf(X7))) & ~(predf(paul) | ~predd(paul)) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X9] : (room(X9) => predr(X9)) => ~predr(paul)) & (! [X10] : (room(X10) => (predf(X10) | ~predo(X10))) => predd(paul)) & (! [X11] : (room(X11) => (~predk(X11) | predn(X11))) <=> ~! [X12] : (room(X12) => (~predl(X12) | ~predt(X12)))) & (! [X13] : (room(X13) => (predb(X13) | ~predg(X13))) => ? [X14] : (predu(X14) & room(X14))) & (predi(mary) => ! [X15] : (room(X15) => (predb(X15) | ~predg(X15)))) & (! [X16] : (~room(X16) => (predk(X16) | ~prede(X16))) => ~! [X17] : (room(X17) => (predk(X17) => predf(X17)))) & ! [X18] : (room(X18) => (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ~predr(paul) & ! [X2] : (~room(X2) => prede(X2)) & ~predg(mary) & ! [X4] : (room(X4) => (predm(X4) | ~predh(X4))) & ~predg(paul) & predu(paul) & ! [X5] : (predi(X5) => predn(X5)) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X7] : (room(X7) => (predm(X7) => predf(X7))) & ~predf(paul) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X9] : (room(X9) => predr(X9)) => ~predr(paul)) & (! [X11] : (room(X11) => (~predk(X11) | predn(X11))) <=> ~! [X12] : (room(X12) => (~predl(X12) | ~predt(X12)))) & (! [X13] : (room(X13) => (predb(X13) | ~predg(X13))) => ? [X14] : (predu(X14) & room(X14))) & (predi(mary) => ! [X15] : (room(X15) => (predb(X15) | ~predg(X15)))) & (! [X16] : (~room(X16) => (predk(X16) | ~prede(X16))) => ~! [X17] : (room(X17) => (predk(X17) => predf(X17)))) & ! [X18] : (room(X18) => (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. ~predr(paul) & ! [X2] : (~room(X2) => prede(X2)) & ~predg(mary) & ! [X4] : (room(X4) => (predm(X4) | ~predh(X4))) & ~predg(paul) & ! [X5] : (predi(X5) => predn(X5)) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X7] : (room(X7) => (predm(X7) => predf(X7))) & ~predf(paul) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X9] : (room(X9) => predr(X9)) => ~predr(paul)) & (! [X11] : (room(X11) => (~predk(X11) | predn(X11))) <=> ~! [X12] : (room(X12) => (~predl(X12) | ~predt(X12)))) & (! [X13] : (room(X13) => (predb(X13) | ~predg(X13))) => ? [X14] : room(X14)) & (predi(mary) => ! [X15] : (room(X15) => (predb(X15) | ~predg(X15)))) & (! [X16] : (~room(X16) => (predk(X16) | ~prede(X16))) => ~! [X17] : (room(X17) => (predk(X17) => predf(X17)))) & ! [X18] : (room(X18) => (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. ~predr(paul) & ! [X2] : (~room(X2) => prede(X2)) & ~predg(mary) & ! [X4] : (room(X4) => (predm(X4) | ~predh(X4))) & ~predg(paul) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X7] : (room(X7) => (predm(X7) => predf(X7))) & ~predf(paul) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (! [X9] : (room(X9) => predr(X9)) => ~predr(paul)) & (! [X11] : (room(X11) => (~predk(X11) | predn(X11))) <=> ~! [X12] : (room(X12) => (~predl(X12) | ~predt(X12)))) & (! [X13] : (room(X13) => (predb(X13) | ~predg(X13))) => ? [X14] : room(X14)) & (! [X16] : (~room(X16) => (predk(X16) | ~prede(X16))) => ~! [X17] : (room(X17) => (predk(X17) => predf(X17)))) & ! [X18] : (room(X18) => (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 128. ~predr(paul) & ! [X2] : (prede(X2) | room(X2)) & ~predg(mary) & ! [X4] : ((predm(X4) | ~predh(X4)) | ~room(X4)) & ~predg(paul) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X7] : ((predf(X7) | ~predm(X7)) | ~room(X7)) & ~predf(paul) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (~predr(paul) | ? [X9] : (~predr(X9) & room(X9))) & (! [X11] : ((~predk(X11) | predn(X11)) | ~room(X11)) <=> ? [X12] : ((predl(X12) & predt(X12)) & room(X12))) & (? [X14] : room(X14) | ? [X13] : ((~predb(X13) & predg(X13)) & room(X13))) & (? [X17] : ((~predf(X17) & predk(X17)) & room(X17)) | ? [X16] : ((~predk(X16) & prede(X16)) & ~room(X16))) & ! [X18] : ((john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18) | ~room(X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 55] 129. ~predr(paul) & ! [X2] : (prede(X2) | room(X2)) & ~predg(mary) & ! [X4] : (predm(X4) | ~predh(X4) | ~room(X4)) & ~predg(paul) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X7] : (predf(X7) | ~predm(X7) | ~room(X7)) & ~predf(paul) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (~predr(paul) | ? [X9] : (~predr(X9) & room(X9))) & (! [X11] : (~predk(X11) | predn(X11) | ~room(X11)) <=> ? [X12] : (predl(X12) & predt(X12) & room(X12))) & (? [X14] : room(X14) | ? [X13] : (~predb(X13) & predg(X13) & room(X13))) & (? [X17] : (~predf(X17) & predk(X17) & room(X17)) | ? [X16] : (~predk(X16) & prede(X16) & ~room(X16))) & ! [X18] : (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 128] 130. predg(paul) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 45] 131. predg(paul) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 130] 132. ? [X16] : (~predk(X16) & prede(X16) & ~room(X16)) | ~sP0 [predicate definition introduction] 133. sP1 <=> ! [X11] : (~predk(X11) | predn(X11) | ~room(X11)) [predicate definition introduction] 134. ~predr(paul) & ! [X2] : (prede(X2) | room(X2)) & ~predg(mary) & ! [X4] : (predm(X4) | ~predh(X4) | ~room(X4)) & ~predg(paul) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X7] : (predf(X7) | ~predm(X7) | ~room(X7)) & ~predf(paul) & predh(mary) & ~prede(mary) & (~predb(paul) <~> predo(paul)) & (~predr(paul) | ? [X9] : (~predr(X9) & room(X9))) & (sP1 <=> ? [X12] : (predl(X12) & predt(X12) & room(X12))) & (? [X14] : room(X14) | ? [X13] : (~predb(X13) & predg(X13) & room(X13))) & (? [X17] : (~predf(X17) & predk(X17) & room(X17)) | sP0) & ! [X18] : (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [definition folding 129,133,132] 144. ~predr(paul) & ! [X2] : (prede(X2) | room(X2)) & ~predg(mary) & ! [X4] : (predm(X4) | ~predh(X4) | ~room(X4)) & ~predg(paul) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X7] : (predf(X7) | ~predm(X7) | ~room(X7)) & ~predf(paul) & predh(mary) & ~prede(mary) & ((~predo(paul) | predb(paul)) & (predo(paul) | ~predb(paul))) & (~predr(paul) | ? [X9] : (~predr(X9) & room(X9))) & ((sP1 | ! [X12] : (~predl(X12) | ~predt(X12) | ~room(X12))) & (? [X12] : (predl(X12) & predt(X12) & room(X12)) | ~sP1)) & (? [X14] : room(X14) | ? [X13] : (~predb(X13) & predg(X13) & room(X13))) & (? [X17] : (~predf(X17) & predk(X17) & room(X17)) | sP0) & ! [X18] : (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 134] 145. ~predr(paul) & ! [X2] : (prede(X2) | room(X2)) & ~predg(mary) & ! [X4] : (predm(X4) | ~predh(X4) | ~room(X4)) & ~predg(paul) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X7] : (predf(X7) | ~predm(X7) | ~room(X7)) & ~predf(paul) & predh(mary) & ~prede(mary) & (~predo(paul) | predb(paul)) & (predo(paul) | ~predb(paul)) & (~predr(paul) | ? [X9] : (~predr(X9) & room(X9))) & (sP1 | ! [X12] : (~predl(X12) | ~predt(X12) | ~room(X12))) & (? [X12] : (predl(X12) & predt(X12) & room(X12)) | ~sP1) & (? [X14] : room(X14) | ? [X13] : (~predb(X13) & predg(X13) & room(X13))) & (? [X17] : (~predf(X17) & predk(X17) & room(X17)) | sP0) & ! [X18] : (john = X18 | alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 146. ~predr(paul) & ! [X0] : (prede(X0) | room(X0)) & ~predg(mary) & ! [X1] : (predm(X1) | ~predh(X1) | ~room(X1)) & ~predg(paul) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X2] : (predf(X2) | ~predm(X2) | ~room(X2)) & ~predf(paul) & predh(mary) & ~prede(mary) & (~predo(paul) | predb(paul)) & (predo(paul) | ~predb(paul)) & (~predr(paul) | ? [X3] : (~predr(X3) & room(X3))) & (sP1 | ! [X4] : (~predl(X4) | ~predt(X4) | ~room(X4))) & (? [X5] : (predl(X5) & predt(X5) & room(X5)) | ~sP1) & (? [X6] : room(X6) | ? [X7] : (~predb(X7) & predg(X7) & room(X7))) & (? [X8] : (~predf(X8) & predk(X8) & room(X8)) | sP0) & ! [X9] : (john = X9 | alice = X9 | fred = X9 | paul = X9 | mary = X9 | ~room(X9)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 145] 147. ? [X3] : (~predr(X3) & room(X3)) => (~predr(sK4) & room(sK4)) [choice axiom] 148. ? [X5] : (predl(X5) & predt(X5) & room(X5)) => (predl(sK5) & predt(sK5) & room(sK5)) [choice axiom] 149. ? [X6] : room(X6) => room(sK6) [choice axiom] 150. ? [X7] : (~predb(X7) & predg(X7) & room(X7)) => (~predb(sK7) & predg(sK7) & room(sK7)) [choice axiom] 151. ? [X8] : (~predf(X8) & predk(X8) & room(X8)) => (~predf(sK8) & predk(sK8) & room(sK8)) [choice axiom] 152. ~predr(paul) & ! [X0] : (prede(X0) | room(X0)) & ~predg(mary) & ! [X1] : (predm(X1) | ~predh(X1) | ~room(X1)) & ~predg(paul) & (predr(paul) | predl(paul) | predk(paul)) & ~predt(paul) & ! [X2] : (predf(X2) | ~predm(X2) | ~room(X2)) & ~predf(paul) & predh(mary) & ~prede(mary) & (~predo(paul) | predb(paul)) & (predo(paul) | ~predb(paul)) & (~predr(paul) | (~predr(sK4) & room(sK4))) & (sP1 | ! [X4] : (~predl(X4) | ~predt(X4) | ~room(X4))) & ((predl(sK5) & predt(sK5) & room(sK5)) | ~sP1) & (room(sK6) | (~predb(sK7) & predg(sK7) & room(sK7))) & ((~predf(sK8) & predk(sK8) & room(sK8)) | sP0) & ! [X9] : (john = X9 | alice = X9 | fred = X9 | paul = X9 | mary = X9 | ~room(X9)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 146,151,150,149,148,147] 266. ~predg(paul) [cnf transformation 152] 277. predg(paul) [cnf transformation 131] 393. $false [subsumption resolution 277,266] % SZS output end Proof for 1086457518201405351562543 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Stanley, Melvin, Ned are the only persons in the room. It is true that “if someone writes poetry then he/she does not play eSports competitively and vice versa”. Melvin practices zumba. Someone in the room enjoys writing detailed reviews of new and classic board games. It is not the case that “Ned is a tea enthusiast”. Only one person in the room designs and sews custom cosplay costumes for conventions. Stanley is a scotch connoisseur. Ned plays eSports competitively. If someone practices zumba then he/she collects vintage stamps. Melvin designs and sews custom cosplay costumes for conventions. If someone trains for and competes in international triathlons then he/she is a tea enthusiast. Ned collects vintage stamps. Ned does not practice digital art. Melvin who is a tea enthusiast collects vintage stamps, maintains a personal blog focused on cybersecurity tips and enjoys writing detailed reviews of new and classic board games. Someone in the room does not practice digital art, is right-handed or has a saltwater aquarium. At least one person in the room drives a hybrid car. It is true that “it is true that “Stanley who has a saltwater aquarium collects vintage stamps””. Ned who enjoys writing detailed reviews of new and classic board games does not practice zumba, is a client of Meta or works on fridays. Someone in the room practices digital art.

Stanley designs and sews custom cosplay costumes for conventions.

contradiction

room(stanley)&room(melvin)&room(ned)&(![X]:(room(X)=>(X='stanley'|X='melvin'|X='ned')))& ((![X]:((writes_poetry(X))<=>(does_not_play_eSports_competitively(X)))))& (practices_zumba(melvin))& (?[X]:(room(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (~(is_a_tea_enthusiast(ned)))& (((?[X]:(room(X)&designs_and_sews_custom_cosplay_costumes_for_conventions(X)))&(![X,Y]:((room(X)&room(Y)&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(Y)))=>(X=Y)))))& (is_a_scotch_connoisseur(stanley))& (plays_eSports_competitively(ned))& ((![X]:((practices_zumba(X))=>(collects_vintage_stamps(X)))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(melvin))& ((![X]:((trains_for_and_competes_in_international_triathlons(X))=>(is_a_tea_enthusiast(X)))))& (collects_vintage_stamps(ned))& (does_not_practice_digital_art(ned))& ((is_a_tea_enthusiast(melvin))&(((collects_vintage_stamps(melvin))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(melvin))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(melvin)))))& (?[X]:(room(X)&(((does_not_practice_digital_art(X))|(is_right-handed(X))|(has_a_saltwater_aquarium(X))))))& (((?[X]:(room(X)&drives_a_hybrid_car(X)))))& ((has_a_saltwater_aquarium(stanley))&(collects_vintage_stamps(stanley)))& ((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(ned))&(((does_not_practice_zumba(ned))|(is_a_client_of_Meta(ned))|(works_on_fridays(ned)))))& (?[X]:(room(X)&(practices_digital_art(X))))

room(stanley)&room(melvin)&room(ned)&(![X]:(room(X)=>(X='stanley'|X='melvin'|X='ned')))& designs_and_sews_custom_cosplay_costumes_for_conventions(stanley)

% SZS status Unsatisfiable for 5559069185843279336636755 % SZS output start Proof for 5559069185843279336636755 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0,X1] : ((predp(X1) & predp(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predp(X0) & room(X0)) [input p5] 53. predp(paul) [input p9] 63. predp(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 64. ! [X0,X1] : ((predp(X1) & predp(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predp(X2) & room(X2)) [rectify 49] 153. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 154. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 153] 155. ! [X0,X1] : (X0 = X1 | (~predp(X1) | ~predp(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predp(X2) & room(X2)) [ennf transformation 64] 156. ! [X0,X1] : (X0 = X1 | ~predp(X1) | ~predp(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predp(X2) & room(X2)) [flattening 155] 157. predp(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 63] 158. predp(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 157] 162. ? [X2] : (predp(X2) & room(X2)) => (predp(sK1) & room(sK1)) [choice axiom] 163. ! [X0,X1] : (X0 = X1 | ~predp(X1) | ~predp(X0) | ~room(X1) | ~room(X0)) & (predp(sK1) & room(sK1)) [skolemisation 156,162] 214. mary != paul [cnf transformation 43] 250. room(mary) [cnf transformation 154] 251. room(paul) [cnf transformation 154] 258. ~predp(X1) | X0 = X1 | ~predp(X0) | ~room(X1) | ~room(X0) [cnf transformation 163] 259. predp(paul) [cnf transformation 53] 270. predp(mary) [cnf transformation 158] 398. mary = X0 | ~predp(X0) | ~room(mary) | ~room(X0) [resolution 258,270] 401. ~predp(X0) | mary = X0 | ~room(X0) [subsumption resolution 398,250] 415. mary = paul | ~room(paul) [resolution 401,259] 417. ~room(paul) [subsumption resolution 415,214] 418. $false [subsumption resolution 417,251] % SZS output end Proof for 5559069185843279336636755 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Joseph, Gary are the only persons in the room. Everyone in the room is a curious quiet person only if they is quieter than Jeannine. Joseph is quieter than Robert. Someone in the room is quiet. Joseph hosts regular game nights featuring complex strategy games. Someone in the room is a quiet person. All quiet persons are curious. Gary is a curious quiet person. If someone is a curious person then he/she is a curious quiet person and vice versa. Gary is quiet. More than one person in the room is quieter than Robert. It is not the case that “it is not the case that “someone in the room is a quiet person””. All curious persons are quiet. Joseph is a quiet curious person.

Jeannine is quieter than Joseph.

contradiction

room(joseph)&room(gary)&(![X]:(room(X)=>(X='joseph'|X='gary')))& (![X]:(room(X)=>(((quieter(jeannine,X))<=(curious(X)&quiet(X)&person(X))))))& (quieter(robert,joseph))& (?[X]:(room(X)&(quiet(X))))& (hosts_regular_game_nights_featuring_complex_strategy_games(joseph))& (?[X]:(room(X)&(quiet(X)&person(X))))& (![X]:(quiet(X)=>curious(X)))& (curious(gary)&quiet(gary)&person(gary))& ((![X]:((curious(X)&person(X))<=>(curious(X)&quiet(X)&person(X)))))& (quiet(gary))& ((?[X,Y]:(room(X)&room(Y)&(quieter(robert,X)&quieter(robert,Y))&(X!=Y))))& (~(~(?[X]:(room(X)&(quiet(X)&person(X))))))& (![X]:(curious(X)=>quiet(X)))& (quiet(joseph)&curious(joseph)&person(joseph))

room(joseph)&room(gary)&(![X]:(room(X)=>(X='joseph'|X='gary')))& quieter(joseph,jeannine)

% SZS status Unsatisfiable for 7407074679946998659919091 % SZS output start Proof for 7407074679946998659919091 14. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => ~quieter(X1,X0))) [input b13] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => ((person(X0) & quiet(X0) & curious(X0)) => quieter(fred,X0))) [input p1] 57. person(mary) & curious(mary) & quiet(mary) [input p13] 58. quieter(mary,fred) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 80. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14] 81. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 80] 133. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 134. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 133] 135. ! [X0] : ((quieter(fred,X0) | (~person(X0) | ~quiet(X0) | ~curious(X0))) | ~room(X0)) [ennf transformation 45] 136. ! [X0] : (quieter(fred,X0) | ~person(X0) | ~quiet(X0) | ~curious(X0) | ~room(X0)) [flattening 135] 139. quieter(mary,fred) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 58] 140. quieter(mary,fred) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 139] 161. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 81] 202. mary != fred [cnf transformation 43] 232. room(mary) [cnf transformation 134] 235. quieter(fred,X0) | ~person(X0) | ~quiet(X0) | ~curious(X0) | ~room(X0) [cnf transformation 136] 261. quiet(mary) [cnf transformation 57] 262. curious(mary) [cnf transformation 57] 263. person(mary) [cnf transformation 57] 267. quieter(mary,fred) [cnf transformation 140] 357. ~quieter(fred,mary) | mary = fred [resolution 161,267] 360. ~quieter(fred,mary) [subsumption resolution 357,202] 451. ~person(mary) | ~quiet(mary) | ~curious(mary) | ~room(mary) [resolution 235,360] 455. ~quiet(mary) | ~curious(mary) | ~room(mary) [subsumption resolution 451,263] 456. ~curious(mary) | ~room(mary) [subsumption resolution 455,261] 457. ~room(mary) [subsumption resolution 456,262] 458. $false [subsumption resolution 457,232] % SZS output end Proof for 7407074679946998659919091 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

Mildred is the only person in the room. “Mildred is a chess master who participates in national tournaments” if “everyone in the room enjoys virtual reality gaming or does not write and illustrates their own graphic novels” and vice versa. “Someone in the room is a certified scuba diver with advanced underwater photography skills” if “Mildred does not enjoy rooftop gardening”. Everyone in the room who enjoys virtual reality gaming is a wine connoisseur with a private cellar of vintage wines. Everyone in the room is a wine connoisseur with a private cellar of vintage wines if they enjoys bird watching, enjoys watercolor painting and writes and illustrates their own graphic novels and vice versa. It is not the case that “Mildred does not enjoy bird watching”. Everyone in the room enjoys watercolor painting if they enjoys wildlife photography, writes and illustrates their own graphic novels and collects comic books. Mildred enjoys virtual reality gaming. Mildred is an avid mountain climber who has scaled several peaks. Mildred enjoys macrame. Mildred enjoys bird watching. Mildred has a curated collection of mid-century modern furniture. Mildred enjoys watercolor painting. Mildred drives a hybrid car. Everyone in the room who collects first edition books composes and performs experimental electronic music. Mildred owns a smart tv.

Mildred writes and illustrates their own graphic novels.

entailment

room(mildred)&(![X]:(room(X)=>(X='mildred')))& ((![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(enjoys_virtual_reality_gaming(X))))))<=>(is_a_chess_master_who_participates_in_national_tournaments(mildred)))& ((does_not_enjoy_rooftop_gardening(mildred))=>(?[X]:(room(X)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(((enjoys_bird_watching(X))&(enjoys_watercolor_painting(X))&(writes_and_illustrates_their_own_graphic_novels(X))))))))& (~(does_not_enjoy_bird_watching(mildred)))& (![X]:(room(X)=>(((((enjoys_wildlife_photography(X))&(writes_and_illustrates_their_own_graphic_novels(X))&(collects_comic_books(X))))=>(enjoys_watercolor_painting(X))))))& (enjoys_virtual_reality_gaming(mildred))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(mildred))& (enjoys_macrame(mildred))& (enjoys_bird_watching(mildred))& (has_a_curated_collection_of_mid-century_modern_furniture(mildred))& (enjoys_watercolor_painting(mildred))& (drives_a_hybrid_car(mildred))& (![X]:(room(X)=>(((collects_first_edition_books(X))=>(composes_and_performs_experimental_electronic_music(X))))))& (owns_a_smart_tv(mildred))

room(mildred)&(![X]:(room(X)=>(X='mildred')))& writes_and_illustrates_their_own_graphic_novels(mildred)

% SZS status Unsatisfiable for 320392997129216332210162 % SZS output start Proof for 320392997129216332210162 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (predq(X0) => predj(X0))) [input p3] 48. ! [X0] : (room(X0) => (predj(X0) <=> (predv(X0) & predp(X0) & preda(X0)))) [input p4] 51. predq(mary) [input p7] 60. ~(predv(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 142. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 145. ! [X0] : ((predj(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 47] 146. ! [X0] : (predj(X0) | ~predq(X0) | ~room(X0)) [flattening 145] 147. ! [X0] : ((predj(X0) <=> (predv(X0) & predp(X0) & preda(X0))) | ~room(X0)) [ennf transformation 48] 148. ~predv(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 60] 154. ! [X0] : (((predj(X0) | (~predv(X0) | ~predp(X0) | ~preda(X0))) & ((predv(X0) & predp(X0) & preda(X0)) | ~predj(X0))) | ~room(X0)) [nnf transformation 147] 155. ! [X0] : (((predj(X0) | ~predv(X0) | ~predp(X0) | ~preda(X0)) & ((predv(X0) & predp(X0) & preda(X0)) | ~predj(X0))) | ~room(X0)) [flattening 154] 156. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 157. ~predv(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 148,156] 238. room(mary) [cnf transformation 142] 239. ~room(X0) | mary = X0 [cnf transformation 142] 244. ~predq(X0) | predj(X0) | ~room(X0) [cnf transformation 146] 247. ~predj(X0) | predv(X0) | ~room(X0) [cnf transformation 155] 250. predq(mary) [cnf transformation 51] 253. ~predv(mary) | room(sK1) | ~room(mary) [cnf transformation 157] 254. ~predv(mary) | mary != sK1 | ~room(mary) [cnf transformation 157] 278. ~predv(mary) | mary != sK1 [subsumption resolution 254,238] 280. 6 <=> mary = sK1 [avatar definition] 282. mary != sK1 <- (~6) [avatar component clause 280] 284. 7 <=> predv(mary) [avatar definition] 287. ~6 | ~7 [avatar split clause 278,284,280] 288. ~predv(mary) | room(sK1) [subsumption resolution 253,238] 290. 8 <=> room(sK1) [avatar definition] 292. room(sK1) <- (8) [avatar component clause 290] 293. 8 | ~7 [avatar split clause 288,284,290] 303. predj(mary) | ~room(mary) [resolution 244,250] 304. predj(mary) [subsumption resolution 303,238] 307. predv(mary) | ~room(mary) [resolution 247,304] 311. predv(mary) [subsumption resolution 307,238] 312. 7 [avatar split clause 311,284] 313. mary = sK1 <- (8) [resolution 292,239] 314. $false <- (~6, 8) [subsumption resolution 313,282] 315. 6 | ~8 [avatar contradiction clause 314] 316. $false [avatar sat refutation 287,293,312,315] % SZS output end Proof for 320392997129216332210162 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jean, Joshua are the only persons in the room. If 'Jean and Michael hate each other' then 'Jean is younger than Timothy'. If 'Jean is a happy european' then 'Jean is a old european'. If 'Jean is a old european' then 'Jean does not own a 3D printer'. If 'Jean collects vintage stamps' then 'Jean does not collect classic novels'. If 'Jean does not collect classic novels' then 'it is not the case that 'Jean and Timothy like each other''. If 'Joshua and Timothy hate each other' then 'at least one person in the room does not stream on Twitch'. 'Jean practices graffiti art' if 'Jean is a sibling of Matthew' and vice versa. If 'Jean likes Timothy' then 'Joshua likes Timothy'. If 'Joshua likes Timothy' then 'Joshua streams on Twitch'. If 'Joshua and Matthew like each other' then 'Joshua is a sibling of Michael'. If 'Joshua is a funny person' then 'Joshua is a sibling of Matthew'. If 'Jean writes a travel blog' then 'at least one person in the room is a funny patient tourist'. If 'Joshua can play the harmonica' then 'someone who does not own a television is a sibling of someone who hates Timothy'. If 'it is not the case that 'Joshua does not write a travel blog'' then 'Jean is a sibling of Elizabeth'. If 'everyone in the room is a old person or does not create YouTube content' then 'Jean practices graffiti art'. If 'Joshua and Matthew like each other' then 'all curious persons are patient'. Jean can play the harmonica. Jean writes a travel blog, is old and is a curious european. Joshua collects limited-edition art prints from contemporary artists. Someone who does not write a travel blog like someone who owns a 3D printer.

Jean is old.

entailment

room(jean)&room(joshua)&(![X]:(room(X)=>(X='jean'|X='joshua')))& (((hate(jean,michael) & hate(michael,jean)))=>(younger(timothy,jean)))& (((happy(jean)&european(jean))=>(old(jean)&european(jean)))& ((old(jean)&european(jean))=>(does_not_own_a_3D_printer(jean))))& (((collects_vintage_stamps(jean))=>(does_not_collect_classic_novels(jean)))& ((does_not_collect_classic_novels(jean))=>(~((like(jean,timothy) & like(timothy,jean))))))& (((hate(joshua,timothy) & hate(timothy,joshua)))=>(((?[X]:(room(X)&does_not_stream_on_Twitch(X))))))& ((sibling(matthew,jean))<=>(practices_graffiti_art(jean)))& (((like(timothy,jean))=>(like(timothy,joshua)))& ((like(timothy,joshua))=>(streams_on_Twitch(joshua))))& (((like(joshua,matthew) & like(matthew,joshua)))=>(sibling(michael,joshua)))& ((funny(joshua)&person(joshua))=>(sibling(matthew,joshua)))& ((writes_a_travel_blog(jean))=>(((?[X]:(room(X)&funny(X)&patient(X)&tourist(X))))))& ((can_play_the_harmonica(joshua))=>(?[X,Y]:((does_not_own_a_television(X))&(hate(timothy,Y))&(sibling(X,Y)))))& ((~(does_not_write_a_travel_blog(joshua)))=>(sibling(elizabeth,jean)))& ((![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(old(X)&person(X))))))=>(practices_graffiti_art(jean)))& (((like(joshua,matthew) & like(matthew,joshua)))=>(![X]:(curious(X)=>patient(X))))& (can_play_the_harmonica(jean))& (((writes_a_travel_blog(jean))&(old(jean))&(curious(jean)&european(jean))))& (collects_limited-edition_art_prints_from_contemporary_artists(joshua))& (?[X,Y]:((does_not_write_a_travel_blog(X))&(owns_a_3D_printer(Y))&(like(X,Y))))& (sibling(joshua,michael))& (((?[X]:(room(X)&hate(X,matthew)))))& (owns_a_smartwatch(jean))& (wise(jean)&person(jean))& (generous(joshua)&person(joshua))& (sibling(matthew,joshua))& ((hate(michael,jean) & hate(jean,michael)))& (builds_model_airplanes(joshua))& ((![X]:((client(michael,X))=>(humble(X)&person(X)))))& (quieter(elizabeth,joshua))& (does_not_own_a_3D_printer(joshua))& ((hate(matthew,joshua) & hate(joshua,matthew)))& ((hate(jean,robert) & hate(robert,jean)))

room(jean)&room(joshua)&(![X]:(room(X)=>(X='jean'|X='joshua')))& old(jean)

% SZS status Unsatisfiable for 903699914171350704618977 % SZS output start Proof for 903699914171350704618977 44. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & ! [X0] : (client(lucy,X0) => (person(X0) & humble(X0))) & predy(paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & generous(paul) & person(mary) & wise(mary) & predg(mary) & ? [X0] : (hate(X0,susan) & room(X0)) & sibling(paul,lucy) & ? [X0,X1] : (like(X0,X1) & predf(X1) & ~predt(X0)) & predu(paul) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X0] : (curious(X0) => patient(X0))) & (! [X0] : (room(X0) => ((person(X0) & old(X0)) | ~prede(X0))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X0,X1] : (sibling(X0,X1) & hate(alice,X1) & ~predh(X0))) & (predt(mary) => ? [X0] : (tourist(X0) & patient(X0) & funny(X0) & room(X0))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X0] : (~predk(X0) & room(X0))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~(old(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 46. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & ! [X0] : (client(lucy,X0) => (person(X0) & humble(X0))) & predy(paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & generous(paul) & person(mary) & wise(mary) & predg(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & predu(paul) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X4] : (curious(X4) => patient(X4))) & (! [X5] : (room(X5) => ((person(X5) & old(X5)) | ~prede(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7) & ~predh(X6))) & (predt(mary) => ? [X8] : (tourist(X8) & patient(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [rectify 44] 47. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & ! [X0] : (client(lucy,X0) => person(X0)) & predy(paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & generous(paul) & person(mary) & wise(mary) & predg(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & predu(paul) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X4] : (curious(X4) => patient(X4))) & (! [X5] : (room(X5) => ((person(X5) & old(X5)) | ~prede(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7) & ~predh(X6))) & (predt(mary) => ? [X8] : (tourist(X8) & patient(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 46] 48. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & predy(paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & generous(paul) & person(mary) & wise(mary) & predg(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & predu(paul) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X4] : (curious(X4) => patient(X4))) & (! [X5] : (room(X5) => ((person(X5) & old(X5)) | ~prede(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7) & ~predh(X6))) & (predt(mary) => ? [X8] : (tourist(X8) & patient(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 47] 49. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & generous(paul) & person(mary) & wise(mary) & predg(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & predu(paul) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X4] : (curious(X4) => patient(X4))) & (! [X5] : (room(X5) => ((person(X5) & old(X5)) | ~prede(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7) & ~predh(X6))) & (predt(mary) => ? [X8] : (tourist(X8) & patient(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 48] 50. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & wise(mary) & predg(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & predu(paul) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X4] : (curious(X4) => patient(X4))) & (! [X5] : (room(X5) => ((person(X5) & old(X5)) | ~prede(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7) & ~predh(X6))) & (predt(mary) => ? [X8] : (tourist(X8) & patient(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 49] 51. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & predg(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & predu(paul) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X4] : (curious(X4) => patient(X4))) & (! [X5] : (room(X5) => ((person(X5) & old(X5)) | ~prede(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7) & ~predh(X6))) & (predt(mary) => ? [X8] : (tourist(X8) & patient(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 50] 52. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & predu(paul) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X4] : (curious(X4) => patient(X4))) & (! [X5] : (room(X5) => ((person(X5) & old(X5)) | ~prede(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7) & ~predh(X6))) & (predt(mary) => ? [X8] : (tourist(X8) & patient(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 51] 53. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X4] : (curious(X4) => patient(X4))) & (! [X5] : (room(X5) => ((person(X5) & old(X5)) | ~prede(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7) & ~predh(X6))) & (predt(mary) => ? [X8] : (tourist(X8) & patient(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 52] 54. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X4] : (curious(X4) => patient(X4))) & (! [X5] : (room(X5) => (person(X5) & old(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7) & ~predh(X6))) & (predt(mary) => ? [X8] : (tourist(X8) & patient(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 53] 55. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & ((like(susan,paul) & like(paul,susan)) => ! [X4] : (curious(X4) => patient(X4))) & (! [X5] : (room(X5) => (person(X5) & old(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7))) & (predt(mary) => ? [X8] : (tourist(X8) & patient(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 54] 56. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & curious(mary) & old(mary) & predt(mary) & predw(mary) & (! [X5] : (room(X5) => (person(X5) & old(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7))) & (predt(mary) => ? [X8] : (tourist(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 55] 57. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & old(mary) & predt(mary) & predw(mary) & (! [X5] : (room(X5) => (person(X5) & old(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7))) & (predt(mary) => ? [X8] : (tourist(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & (preds(mary) => ~predc(mary)) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 56] 58. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & old(mary) & predt(mary) & predw(mary) & (! [X5] : (room(X5) => (person(X5) & old(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7))) & (predt(mary) => ? [X8] : (tourist(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & (~predc(mary) => ~(like(alice,mary) & like(mary,alice))) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 57] 59. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & old(mary) & predt(mary) & predw(mary) & (! [X5] : (room(X5) => (person(X5) & old(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7))) & (predt(mary) => ? [X8] : (tourist(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & ((european(mary) & old(mary)) => ~predf(mary)) & ((european(mary) & happy(mary)) => (european(mary) & old(mary))) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 58] 60. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & old(mary) & predt(mary) & predw(mary) & (! [X5] : (room(X5) => (person(X5) & old(X5))) => predv(mary)) & (predt(paul) => sibling(fred,mary)) & (predw(paul) => ? [X6,X7] : (sibling(X6,X7) & hate(alice,X7))) & (predt(mary) => ? [X8] : (tourist(X8) & funny(X8) & room(X8))) & ((person(paul) & funny(paul)) => sibling(susan,paul)) & ((like(susan,paul) & like(paul,susan)) => sibling(lucy,paul)) & (like(alice,paul) => predk(paul)) & (like(alice,mary) => like(alice,paul)) & (sibling(susan,mary) <=> predv(mary)) & ((hate(alice,paul) & hate(paul,alice)) => ? [X9] : (~predk(X9) & room(X9))) & ((european(mary) & old(mary)) => ~predf(mary)) & ((hate(lucy,mary) & hate(mary,lucy)) => younger(alice,mary)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 59] 135. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & old(mary) & predt(mary) & predw(mary) & (predv(mary) | ? [X5] : ((~person(X5) | ~old(X5)) & room(X5))) & (sibling(fred,mary) | ~predt(paul)) & (? [X6,X7] : (sibling(X6,X7) & hate(alice,X7)) | ~predw(paul)) & (? [X8] : (tourist(X8) & funny(X8) & room(X8)) | ~predt(mary)) & (sibling(susan,paul) | (~person(paul) | ~funny(paul))) & (sibling(lucy,paul) | (~like(susan,paul) | ~like(paul,susan))) & (predk(paul) | ~like(alice,paul)) & (like(alice,paul) | ~like(alice,mary)) & (sibling(susan,mary) <=> predv(mary)) & (? [X9] : (~predk(X9) & room(X9)) | (~hate(alice,paul) | ~hate(paul,alice))) & (~predf(mary) | (~european(mary) | ~old(mary))) & (younger(alice,mary) | (~hate(lucy,mary) | ~hate(mary,lucy))) & ! [X10] : ((paul = X10 | mary = X10) | ~room(X10)) & room(paul) & room(mary) [ennf transformation 60] 136. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & old(mary) & predt(mary) & predw(mary) & (predv(mary) | ? [X5] : ((~person(X5) | ~old(X5)) & room(X5))) & (sibling(fred,mary) | ~predt(paul)) & (? [X6,X7] : (sibling(X6,X7) & hate(alice,X7)) | ~predw(paul)) & (? [X8] : (tourist(X8) & funny(X8) & room(X8)) | ~predt(mary)) & (sibling(susan,paul) | ~person(paul) | ~funny(paul)) & (sibling(lucy,paul) | ~like(susan,paul) | ~like(paul,susan)) & (predk(paul) | ~like(alice,paul)) & (like(alice,paul) | ~like(alice,mary)) & (sibling(susan,mary) <=> predv(mary)) & (? [X9] : (~predk(X9) & room(X9)) | ~hate(alice,paul) | ~hate(paul,alice)) & (~predf(mary) | ~european(mary) | ~old(mary)) & (younger(alice,mary) | ~hate(lucy,mary) | ~hate(mary,lucy)) & ! [X10] : (paul = X10 | mary = X10 | ~room(X10)) & room(paul) & room(mary) [flattening 135] 137. ~old(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 45] 138. ~old(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 137] 140. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & old(mary) & predt(mary) & predw(mary) & (predv(mary) | ? [X5] : ((~person(X5) | ~old(X5)) & room(X5))) & (sibling(fred,mary) | ~predt(paul)) & (? [X6,X7] : (sibling(X6,X7) & hate(alice,X7)) | ~predw(paul)) & (? [X8] : (tourist(X8) & funny(X8) & room(X8)) | ~predt(mary)) & (sibling(susan,paul) | ~person(paul) | ~funny(paul)) & (sibling(lucy,paul) | ~like(susan,paul) | ~like(paul,susan)) & (predk(paul) | ~like(alice,paul)) & (like(alice,paul) | ~like(alice,mary)) & ((sibling(susan,mary) | ~predv(mary)) & (predv(mary) | ~sibling(susan,mary))) & (? [X9] : (~predk(X9) & room(X9)) | ~hate(alice,paul) | ~hate(paul,alice)) & (~predf(mary) | ~european(mary) | ~old(mary)) & (younger(alice,mary) | ~hate(lucy,mary) | ~hate(mary,lucy)) & ! [X10] : (paul = X10 | mary = X10 | ~room(X10)) & room(paul) & room(mary) [nnf transformation 136] 141. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X1] : (hate(X1,susan) & room(X1)) & sibling(paul,lucy) & ? [X2,X3] : (like(X2,X3) & predf(X3) & ~predt(X2)) & european(mary) & old(mary) & predt(mary) & predw(mary) & (predv(mary) | ? [X5] : ((~person(X5) | ~old(X5)) & room(X5))) & (sibling(fred,mary) | ~predt(paul)) & (? [X6,X7] : (sibling(X6,X7) & hate(alice,X7)) | ~predw(paul)) & (? [X8] : (tourist(X8) & funny(X8) & room(X8)) | ~predt(mary)) & (sibling(susan,paul) | ~person(paul) | ~funny(paul)) & (sibling(lucy,paul) | ~like(susan,paul) | ~like(paul,susan)) & (predk(paul) | ~like(alice,paul)) & (like(alice,paul) | ~like(alice,mary)) & (sibling(susan,mary) | ~predv(mary)) & (predv(mary) | ~sibling(susan,mary)) & (? [X9] : (~predk(X9) & room(X9)) | ~hate(alice,paul) | ~hate(paul,alice)) & (~predf(mary) | ~european(mary) | ~old(mary)) & (younger(alice,mary) | ~hate(lucy,mary) | ~hate(mary,lucy)) & ! [X10] : (paul = X10 | mary = X10 | ~room(X10)) & room(paul) & room(mary) [flattening 140] 142. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & ? [X0] : (hate(X0,susan) & room(X0)) & sibling(paul,lucy) & ? [X1,X2] : (like(X1,X2) & predf(X2) & ~predt(X1)) & european(mary) & old(mary) & predt(mary) & predw(mary) & (predv(mary) | ? [X3] : ((~person(X3) | ~old(X3)) & room(X3))) & (sibling(fred,mary) | ~predt(paul)) & (? [X4,X5] : (sibling(X4,X5) & hate(alice,X5)) | ~predw(paul)) & (? [X6] : (tourist(X6) & funny(X6) & room(X6)) | ~predt(mary)) & (sibling(susan,paul) | ~person(paul) | ~funny(paul)) & (sibling(lucy,paul) | ~like(susan,paul) | ~like(paul,susan)) & (predk(paul) | ~like(alice,paul)) & (like(alice,paul) | ~like(alice,mary)) & (sibling(susan,mary) | ~predv(mary)) & (predv(mary) | ~sibling(susan,mary)) & (? [X7] : (~predk(X7) & room(X7)) | ~hate(alice,paul) | ~hate(paul,alice)) & (~predf(mary) | ~european(mary) | ~old(mary)) & (younger(alice,mary) | ~hate(lucy,mary) | ~hate(mary,lucy)) & ! [X8] : (paul = X8 | mary = X8 | ~room(X8)) & room(paul) & room(mary) [rectify 141] 143. ? [X0] : (hate(X0,susan) & room(X0)) => (hate(sK0,susan) & room(sK0)) [choice axiom] 144. ? [X1,X2] : (like(X1,X2) & predf(X2) & ~predt(X1)) => (like(sK1,sK2) & predf(sK2) & ~predt(sK1)) [choice axiom] 145. ? [X3] : ((~person(X3) | ~old(X3)) & room(X3)) => ((~person(sK3) | ~old(sK3)) & room(sK3)) [choice axiom] 146. ? [X4,X5] : (sibling(X4,X5) & hate(alice,X5)) => (sibling(sK4,sK5) & hate(alice,sK5)) [choice axiom] 147. ? [X6] : (tourist(X6) & funny(X6) & room(X6)) => (tourist(sK6) & funny(sK6) & room(sK6)) [choice axiom] 148. ? [X7] : (~predk(X7) & room(X7)) => (~predk(sK7) & room(sK7)) [choice axiom] 149. hate(john,mary) & hate(mary,john) & hate(paul,susan) & hate(susan,paul) & ~predf(paul) & quieter(fred,paul) & hate(mary,lucy) & hate(lucy,mary) & sibling(susan,paul) & person(paul) & person(mary) & (hate(sK0,susan) & room(sK0)) & sibling(paul,lucy) & (like(sK1,sK2) & predf(sK2) & ~predt(sK1)) & european(mary) & old(mary) & predt(mary) & predw(mary) & (predv(mary) | ((~person(sK3) | ~old(sK3)) & room(sK3))) & (sibling(fred,mary) | ~predt(paul)) & ((sibling(sK4,sK5) & hate(alice,sK5)) | ~predw(paul)) & ((tourist(sK6) & funny(sK6) & room(sK6)) | ~predt(mary)) & (sibling(susan,paul) | ~person(paul) | ~funny(paul)) & (sibling(lucy,paul) | ~like(susan,paul) | ~like(paul,susan)) & (predk(paul) | ~like(alice,paul)) & (like(alice,paul) | ~like(alice,mary)) & (sibling(susan,mary) | ~predv(mary)) & (predv(mary) | ~sibling(susan,mary)) & ((~predk(sK7) & room(sK7)) | ~hate(alice,paul) | ~hate(paul,alice)) & (~predf(mary) | ~european(mary) | ~old(mary)) & (younger(alice,mary) | ~hate(lucy,mary) | ~hate(mary,lucy)) & ! [X8] : (paul = X8 | mary = X8 | ~room(X8)) & room(paul) & room(mary) [skolemisation 142,148,147,146,145,144,143] 150. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 151. ~old(mary) | (paul != sK8 & mary != sK8 & room(sK8)) | ~room(paul) | ~room(mary) [skolemisation 138,150] 236. room(mary) [cnf transformation 149] 237. room(paul) [cnf transformation 149] 238. ~room(X8) | mary = X8 | paul = X8 [cnf transformation 149] 259. old(mary) [cnf transformation 149] 278. ~old(mary) | room(sK8) | ~room(paul) | ~room(mary) [cnf transformation 151] 279. ~old(mary) | mary != sK8 | ~room(paul) | ~room(mary) [cnf transformation 151] 280. ~old(mary) | paul != sK8 | ~room(paul) | ~room(mary) [cnf transformation 151] 380. paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 280,259] 381. paul != sK8 | ~room(mary) [subsumption resolution 380,237] 382. paul != sK8 [subsumption resolution 381,236] 383. mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 279,259] 384. mary != sK8 | ~room(mary) [subsumption resolution 383,237] 385. mary != sK8 [subsumption resolution 384,236] 386. room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 278,259] 387. room(sK8) | ~room(mary) [subsumption resolution 386,237] 388. room(sK8) [subsumption resolution 387,236] 396. mary = sK8 | paul = sK8 [resolution 238,388] 424. paul = sK8 [subsumption resolution 396,385] 425. $false [subsumption resolution 424,382] % SZS output end Proof for 903699914171350704618977 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If “everyone in the room does not collect comic books or is an expert in identifying and foraging wild edible plants” then “only one person in the room is an expert in identifying and foraging wild edible plants”. If someone enjoys rooftop gardening then he/she does not enjoy spelunking or enjoys rooftop gardening or both and vice versa. Someone in the room does not enjoy making ceramics. No one in the room who does not enjoy writing detailed reviews of new and classic board games collects comic books. Everyone in the room does not play eSports competitively if they neither hosts regular workshops on creative writing nor enjoys writing detailed reviews of new and classic board games and vice versa. No one in the room who neither writes poetry nor does not enjoy rooftop gardening owns a microscope. Everyone in the room owns a microscope if they hosts regular workshops on creative writing.

Everyone in the room does not play eSports competitively.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_collect_comic_books(X))))))=>(((?[X]:(room(X)&is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))&(![X,Y]:((room(X)&room(Y)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(Y)))=>(X=Y))))))& ((![X]:((enjoys_rooftop_gardening(X))<=>(((does_not_enjoy_spelunking(X))|(enjoys_rooftop_gardening(X)))))))& (?[X]:(room(X)&(does_not_enjoy_making_ceramics(X))))& (((?[X]:(room(X)&is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))&(![X,Y]:((room(X)&room(Y)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((practices_urban_gardening(X))<=(owns_an_Android_phone(X))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(room(X)=>(((does_not_enjoy_spelunking(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (~?[X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((does_not_own_a_microscope(X))<=(writes_poetry(X))))))& (![X]:(room(X)=>(((((participates_in_long-distance_cycling_events_across_the_country(X))|(enjoys_windsurfing(X))|(writes_poetry(X))))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (((?[X]:(room(X)&is_a_professional_photographer_specializing_in_portrait_photography(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(is_a_professional_photographer_specializing_in_portrait_photography(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(hosts_regular_workshops_on_creative_writing(X))))))& (![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_play_eSports_competitively(X))))))& ((![X]:((is_a_chess_master_who_participates_in_national_tournaments(X))<=>(~((enjoys_windsurfing(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))<=>(~((hosts_regular_workshops_on_creative_writing(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))))& (((?[X]:(room(X)&is_a_professional_photographer_specializing_in_portrait_photography(X)))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(enjoys_making_ceramics(X))))))& ((![X]:((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<=>(collects_comic_books(X)))))& (~?[X]:(room(X)=>(((~((writes_poetry(X))|(does_not_enjoy_rooftop_gardening(X))))=>(owns_a_microscope(X))))))& (~?[X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_collect_comic_books(X))))))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(owns_a_microscope(X))))))

(there_is_a_room)& ![X]:(room(X)=>(does_not_play_eSports_competitively(X)))

% SZS status Unsatisfiable for 1859084211810365002614223 % SZS output start Proof for 1859084211810365002614223 44. there_is_a_room [input p0] 52. ~? [X0] : (room(X0) => (~predn(X0) => predb(X0))) [input p8] 59. ! [X0] : (room(X0) => (~predm(X0) <=> ~(predn(X0) | prede(X0)))) [input p15] 63. ~? [X0] : (room(X0) => (~(~predi(X0) | predd(X0)) => preds(X0))) [input p19] 66. ! [X0] : (room(X0) => (prede(X0) => preds(X0))) [input p22] 67. ~(! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room) [input hypothesis] 75. ~? [X0] : (room(X0) => (~~predi(X0) => preds(X0))) [pure predicate removal 63] 158. ! [X0] : ((~predb(X0) & ~predn(X0)) & room(X0)) [ennf transformation 52] 159. ! [X0] : (~predb(X0) & ~predn(X0) & room(X0)) [flattening 158] 166. ! [X0] : ((~predm(X0) <=> (~predn(X0) & ~prede(X0))) | ~room(X0)) [ennf transformation 59] 169. ! [X0] : ((~preds(X0) & predi(X0)) & room(X0)) [ennf transformation 75] 170. ! [X0] : (~preds(X0) & predi(X0) & room(X0)) [flattening 169] 174. ! [X0] : ((preds(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 66] 175. ! [X0] : (preds(X0) | ~prede(X0) | ~room(X0)) [flattening 174] 176. ? [X0] : (predm(X0) & room(X0)) | ~there_is_a_room [ennf transformation 67] 194. ! [X0] : (((~predm(X0) | (predn(X0) | prede(X0))) & ((~predn(X0) & ~prede(X0)) | predm(X0))) | ~room(X0)) [nnf transformation 166] 195. ! [X0] : (((~predm(X0) | predn(X0) | prede(X0)) & ((~predn(X0) & ~prede(X0)) | predm(X0))) | ~room(X0)) [flattening 194] 199. ? [X0] : (predm(X0) & room(X0)) => (predm(sK7) & room(sK7)) [choice axiom] 200. (predm(sK7) & room(sK7)) | ~there_is_a_room [skolemisation 176,199] 281. there_is_a_room [cnf transformation 44] 297. room(X0) [cnf transformation 159] 298. ~predn(X0) [cnf transformation 159] 307. ~predm(X0) | predn(X0) | prede(X0) | ~room(X0) [cnf transformation 195] 315. ~preds(X0) [cnf transformation 170] 318. preds(X0) | ~prede(X0) | ~room(X0) [cnf transformation 175] 320. predm(sK7) | ~there_is_a_room [cnf transformation 200] 358. ~predm(X0) | prede(X0) | ~room(X0) [subsumption resolution 307,298] 359. ~predm(X0) | prede(X0) [subsumption resolution 358,297] 362. ~prede(X0) | ~room(X0) [subsumption resolution 318,315] 363. ~prede(X0) [subsumption resolution 362,297] 364. predm(sK7) [subsumption resolution 320,281] 368. prede(sK7) [resolution 359,364] 369. $false [subsumption resolution 368,363] % SZS output end Proof for 1859084211810365002614223 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.022 s % ------------------------------ % ------------------------------

Linda, Nelson are the only persons in the room. If "Linda writes poetry" then "Nelson writes in-depth travel guides for off-the-beaten-path destinations". "Not everyone in the room enjoys kayaking or is not dedicated to sustainable living and zero-waste practices" if "everyone in the room writes poetry or does not write poetry" and vice versa. If "everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations or is not right-handed" then "Linda enjoys virtual reality gaming". "No one outside the room enjoys rooftop gardening" if "everyone in the room is not a dedicated advocate for digital privacy and encryption or enjoys skydiving". "Nelson collects vintage vinyl records, is dedicated to sustainable living and zero-waste practices and creates bespoke furniture pieces from reclaimed wood" if "Linda is a dedicated advocate for digital privacy and encryption and uses an ios phone" and vice versa. If "everyone in the room is not an amateur astronomer who builds and uses custom telescopes or practices and performs acrobatic dance routines" then "if someone either does not practice and performs acrobatic dance routines or collects vintage vinyl records but not both then he/she enjoys virtual reality gaming and vice versa". If "Nelson does not practice archery" then "it is true that "everyone in the room enjoys camping and organizing outdoor survival workshops if they collects luxury watches"". It is not the case that "Nelson collects luxury watches". Everyone in the room writes poetry or does not write poetry.

Nelson either does not practice archery or is not right-handed but not both.

neutral

room(linda)&room(nelson)&(![X]:(room(X)=>(X='linda'|X='nelson')))& ((writes_poetry(linda))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(nelson)))& ((![X]:(room(X)=>(((does_not_write_poetry(X))|(writes_poetry(X))))))<=>(~![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(enjoys_kayaking(X)))))))& ((![X]:(room(X)=>(((is_not_right-handed(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))=>(enjoys_virtual_reality_gaming(linda)))& ((![X]:(room(X)=>(((enjoys_skydiving(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(~?[X]:(~room(X)=>(enjoys_rooftop_gardening(X)))))& ((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(linda))&(uses_an_ios_phone(linda))))<=>(((collects_vintage_vinyl_records(nelson))&(is_dedicated_to_sustainable_living_and_zero-waste_practices(nelson))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(nelson)))))& ((![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))=>((![X]:((((does_not_practice_and_performs_acrobatic_dance_routines(X))<~>(collects_vintage_vinyl_records(X))))<=>(enjoys_virtual_reality_gaming(X))))))& ((does_not_practice_archery(nelson))=>(![X]:(room(X)=>(((collects_luxury_watches(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))& (~(collects_luxury_watches(nelson)))& (![X]:(room(X)=>(((does_not_write_poetry(X))|(writes_poetry(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& ((is_dedicated_to_sustainable_living_and_zero-waste_practices(nelson))&(uses_an_ios_phone(nelson)))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (~(enjoys_camping_and_organizing_outdoor_survival_workshops(nelson)))& (does_not_collect_luxury_watches(nelson))& (![X]:(room(X)=>(((is_right-handed(X))=>(uses_an_ios_phone(X))))))& (~![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(enjoys_kayaking(X))))))& (does_not_design_and_sews_custom_cosplay_costumes_for_conventions(nelson))& ((enjoys_rooftop_gardening(nelson))&(enjoys_skydiving(nelson)))& (![X]:(room(X)=>(((((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<~>(enjoys_kayaking(X))))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(nelson))& (is_not_right-handed(linda))& (![X]:(room(X)=>(((does_not_practice_archery(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))

room(linda)&room(nelson)&(![X]:(room(X)=>(X='linda'|X='nelson')))& ((does_not_practice_archery(nelson))<~>(is_not_right-handed(nelson)))

Linda, Melanie, Derek, Kathy are the only persons in the room. “Everyone in the room does not work as a freelance web developer specializing in e-commerce sites or is a client of LVMH” if “everyone anywhere does not play eSports competitively or uses an ios phone” and vice versa. If “everyone in the room does not host regular workshops on creative writing or plays eSports competitively” then “it is true that “everyone in the room uses an ios phone only if they practices calligraphy””. If “everyone in the room does not write poetry or creates augmented reality experiences for mobile applications” then “everyone in the room collects modern art and writes poetry only if they uses an ios phone”. If “no one outside the room does not write poetry or participates in citizen science projects related to wildlife monitoring” then “everyone in the room collects modern art”. Everyone anywhere who does not write poetry has completed a triathlon. Everyone in the room enjoys kayaking and exploring remote waterways only if they maintains a large, organic vegetable garden year-round. At least one person in the room is an expert in identifying and foraging wild edible plants. Everyone in the room collects modern art. Everyone in the room who practices calligraphy plays video games. Everyone in the room who collects modern art is not a professional photographer specializing in portrait photography. Not everyone outside the room who enjoys kayaking and exploring remote waterways plays video games. Everyone in the room is a professional photographer specializing in portrait photography if they plays video games.

It is true that “Linda practices calligraphy”.

contradiction

room(linda)&room(melanie)&room(derek)&room(kathy)&(![X]:(room(X)=>(X='linda'|X='melanie'|X='derek'|X='kathy')))& ((![X]:(anywhere(X)=>(((uses_an_ios_phone(X))|(does_not_play_eSports_competitively(X))))))<=>(![X]:(room(X)=>(((is_a_client_of_LVMH(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))& ((![X]:(room(X)=>(((plays_eSports_competitively(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))=>(![X]:(room(X)=>(((practices_calligraphy(X))<=(uses_an_ios_phone(X)))))))& ((![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_write_poetry(X))))))=>(![X]:(room(X)=>(((uses_an_ios_phone(X))<=(((collects_modern_art(X))&(writes_poetry(X)))))))))& ((~?[X]:(~room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_write_poetry(X))))))=>(![X]:(room(X)=>(collects_modern_art(X)))))& (![X]:(anywhere(X)=>(((does_not_write_poetry(X))=>(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))<=(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (((?[X]:(room(X)&is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))& (![X]:(room(X)=>(collects_modern_art(X))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((collects_modern_art(X))=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& (~![X]:(~room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(plays_video_games(X))))))& ((![X]:((((practices_urban_gardening(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))<=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))& ((![X]:((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=>(((enjoys_kayaking_and_exploring_remote_waterways(X))&(practices_urban_gardening(X))&(maintains_a_large,_organic_vegetable_garden_year-round(X)))))))& (plays_eSports_competitively(derek))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(((practices_urban_gardening(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))&(works_on_fridays(X))))))))& ((is_an_expert_in_identifying_and_foraging_wild_edible_plants(derek))&(practices_urban_gardening(derek)))& (![X]:(room(X)=>(((collects_modern_art(X))=>(uses_an_ios_phone(X))))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(collects_modern_art(X))))))& ((![X]:((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(((does_not_practice_calligraphy(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(writes_poetry(X))))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(practices_calligraphy(X))))))& (![X]:(room(X)=>(((((collects_modern_art(X))|(practices_calligraphy(X))))=>(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((writes_poetry(X))=>(collects_antique_jewelry(X))))))& ((writes_poetry(derek))&(practices_urban_gardening(derek)))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(uses_an_ios_phone(X))))))

room(linda)&room(melanie)&room(derek)&room(kathy)&(![X]:(room(X)=>(X='linda'|X='melanie'|X='derek'|X='kathy')))& practices_calligraphy(linda)

% SZS status Unsatisfiable for 694661499927832663281737 % SZS output start Proof for 694661499927832663281737 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 52. ! [X0] : (room(X0) => predb(X0)) [input p8] 53. ! [X0] : (room(X0) => (predf(X0) => predh(X0))) [input p9] 54. ! [X0] : (room(X0) => (predb(X0) => ~preda(X0))) [input p10] 60. ! [X0] : (room(X0) => (predh(X0) => preda(X0))) [input p16] 74. predf(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 154. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 155. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 154] 164. ! [X0] : (predb(X0) | ~room(X0)) [ennf transformation 52] 165. ! [X0] : ((predh(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 53] 166. ! [X0] : (predh(X0) | ~predf(X0) | ~room(X0)) [flattening 165] 167. ! [X0] : ((~preda(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 54] 168. ! [X0] : (~preda(X0) | ~predb(X0) | ~room(X0)) [flattening 167] 173. ! [X0] : ((preda(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 60] 174. ! [X0] : (preda(X0) | ~predh(X0) | ~room(X0)) [flattening 173] 195. predf(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 74] 196. predf(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 195] 298. room(mary) [cnf transformation 155] 317. ~room(X0) | predb(X0) [cnf transformation 164] 318. ~predf(X0) | predh(X0) | ~room(X0) [cnf transformation 166] 319. ~preda(X0) | ~predb(X0) | ~room(X0) [cnf transformation 168] 333. preda(X0) | ~predh(X0) | ~room(X0) [cnf transformation 174] 356. predf(mary) [cnf transformation 196] 422. ~preda(X0) | ~room(X0) [subsumption resolution 319,317] 424. ~predh(X0) | ~room(X0) [subsumption resolution 333,422] 462. predh(mary) | ~room(mary) [resolution 318,356] 463. predh(mary) [subsumption resolution 462,298] 498. ~room(mary) [resolution 463,424] 499. $false [subsumption resolution 498,298] % SZS output end Proof for 694661499927832663281737 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.028 s % ------------------------------ % ------------------------------

There is a room. If "it is true that "everyone in the room enjoys bird watching or does not stream on Twitch"" then "if someone is a chess master who participates in national tournaments then he/she is a dedicated advocate for digital privacy and encryption". If "everyone outside the room does not have a saltwater aquarium or collects first edition books" then "everyone in the room streams on Twitch if they is not a chess master who participates in national tournaments". If "no one in the room has a saltwater aquarium or does not enjoy bird watching" then "everyone in the room is a chess master who participates in national tournaments if they enjoys wildlife photography". Everyone in the room who writes in-depth travel guides for off-the-beaten-path destinations is a chess master who participates in national tournaments.

Everyone in the room is not a dedicated advocate for digital privacy and encryption or has a saltwater aquarium.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_stream_on_Twitch(X))|(enjoys_bird_watching(X))))))=>((![X]:((is_a_chess_master_who_participates_in_national_tournaments(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& ((![X]:(~room(X)=>(((collects_first_edition_books(X))|(does_not_have_a_saltwater_aquarium(X))))))=>(![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))=>(streams_on_Twitch(X)))))))& ((~?[X]:(room(X)=>(((does_not_enjoy_bird_watching(X))|(has_a_saltwater_aquarium(X))))))=>(![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X)))))))& (![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(anywhere(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(enjoys_wildlife_photography(X))))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (~?[X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(anywhere(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(collects_first_edition_books(X))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))=>(has_a_saltwater_aquarium(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((has_a_saltwater_aquarium(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))

Betty, Jessica, Travis are the only persons in the room. Everyone anywhere who can play the guitar does not have completed a triathlon. It is not the case that “Betty is a craft beer aficionado”. Only one person in the room can play the guitar. Betty is a dedicated advocate for digital privacy and encryption. It is not the case that “at least one person anywhere enjoys coding in Python”. Everyone in the room who enjoys deep-sea diving and exploring underwater caves collects action figures. Everyone in the room collects action figures if they can play the guitar. Everyone in the room who collects action figures is a dedicated advocate for digital privacy and encryption or can play the guitar or both.

Betty enjoys coding in Python.

contradiction

room(betty)&room(jessica)&room(travis)&(![X]:(room(X)=>(X='betty'|X='jessica'|X='travis')))& (![X]:(anywhere(X)=>(((can_play_the_guitar(X))=>(does_not_have_completed_a_triathlon(X))))))& (~(is_a_craft_beer_aficionado(betty)))& (((?[X]:(room(X)&can_play_the_guitar(X)))&(![X,Y]:((room(X)&room(Y)&(can_play_the_guitar(X))&(can_play_the_guitar(Y)))=>(X=Y)))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(betty))& (~(((?[X]:(anywhere(X)&enjoys_coding_in_Python(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(can_play_the_guitar(X))))))))

room(betty)&room(jessica)&room(travis)&(![X]:(room(X)=>(X='betty'|X='jessica'|X='travis')))& enjoys_coding_in_Python(betty)

% SZS status Unsatisfiable for 8402149190629444649754314 % SZS output start Proof for 8402149190629444649754314 5. ! [X0] : anywhere(X0) [input b4] 49. ~? [X0] : (predf(X0) & anywhere(X0)) [input p5] 53. predf(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 136. ! [X0] : (~predf(X0) | ~anywhere(X0)) [ennf transformation 49] 137. predf(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 53] 138. predf(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 137] 142. anywhere(X0) [cnf transformation 5] 230. ~predf(X0) | ~anywhere(X0) [cnf transformation 136] 235. predf(mary) [cnf transformation 138] 236. ~predf(X0) [subsumption resolution 230,142] 237. $false [subsumption resolution 235,236] % SZS output end Proof for 8402149190629444649754314 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.026 s % ------------------------------ % ------------------------------

There is a room. Not everyone in the room does not practice and performs acrobatic dance routines.

Everyone in the room does not practice and performs acrobatic dance routines.

contradiction

(there_is_a_room)& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<~>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (~![X]:(room(X)=>(does_not_practice_and_performs_acrobatic_dance_routines(X))))& (?[X]:(~room(X)&(enjoys_stand-up_paddleboarding(X))))& ((?[X,Y]:(room(X)&room(Y)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)&is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(Y))&(X!=Y))))& (~![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(does_not_practice_yoga(X))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(~room(X)=>(can_play_the_guitar(X))))

(there_is_a_room)& ![X]:(room(X)=>(does_not_practice_and_performs_acrobatic_dance_routines(X)))

% SZS status Unsatisfiable for 6233516495522136552137686 % SZS output start Proof for 6233516495522136552137686 48. ~! [X0] : (room(X0) => ~predm(X0)) [input p4] 54. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 63. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 54] 138. ? [X0] : (predm(X0) & room(X0)) [ennf transformation 48] 140. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 63] 143. ? [X0] : (predm(X0) & room(X0)) => (predm(sK0) & room(sK0)) [choice axiom] 144. predm(sK0) & room(sK0) [skolemisation 138,143] 233. room(sK0) [cnf transformation 144] 234. predm(sK0) [cnf transformation 144] 240. ~predm(X0) | ~room(X0) [cnf transformation 140] 241. ~room(sK0) [resolution 240,234] 242. $false [subsumption resolution 241,233] % SZS output end Proof for 6233516495522136552137686 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Isabel, Myrna are the only persons in the room. Isabel and Myrna either are funny persons or are kind persons but not both. Isabel either is not patient or is a kind person but not both. Myrna and Isabel are richer than Grace. Someone in the room is a humble person or is not funny, not humble or both. Isabel is a humble person, is a happy person or is a brave funny person. Everyone in the room is a strong person only if they is a calm person. Isabel is a funny person. Only one person in the room is a creative person. Myrna is a creative person. Isabel is richer than Amanda.

Grace is richer than Isabel.

contradiction

room(isabel)&room(myrna)&(![X]:(room(X)=>(X='isabel'|X='myrna')))& (((funny(isabel)&person(isabel))<~>(kind(isabel)&person(isabel)))&((funny(myrna)&person(myrna))<~>(kind(myrna)&person(myrna))))& (((~patient(isabel))<~>(kind(isabel)&person(isabel))))& (richer(grace,myrna)&richer(grace,isabel))& (?[X]:(room(X)&(((humble(X)&person(X))|(~funny(X)&~humble(X))))))& (((humble(isabel)&person(isabel))|(happy(isabel)&person(isabel))|(brave(isabel)&funny(isabel)&person(isabel))))& (![X]:(room(X)=>(((calm(X)&person(X))<=(strong(X)&person(X))))))& (funny(isabel)&person(isabel))& (((?[X]:(room(X)&creative(X)&person(X)))&(![X,Y]:((room(X)&room(Y)&(creative(X)&person(X))&(creative(Y)&person(Y)))=>(X=Y)))))& (creative(myrna)&person(myrna))& (richer(amanda,isabel))

room(isabel)&room(myrna)&(![X]:(room(X)=>(X='isabel'|X='myrna')))& richer(isabel,grace)

% SZS status Unsatisfiable for 1906809585763289910521019 % SZS output start Proof for 1906809585763289910521019 8. ! [X0,X1] : (X0 != X1 => (richer(X0,X1) => ~richer(X1,X0))) [input b7] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 47. richer(john,mary) & richer(john,paul) [input p3] 55. richer(mary,john) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 68. ! [X0,X1] : ((~richer(X1,X0) | ~richer(X0,X1)) | X0 = X1) [ennf transformation 8] 69. ! [X0,X1] : (~richer(X1,X0) | ~richer(X0,X1) | X0 = X1) [flattening 68] 136. richer(mary,john) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 55] 137. richer(mary,john) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 136] 150. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 69] 209. mary != john [cnf transformation 43] 244. richer(john,mary) [cnf transformation 47] 266. richer(mary,john) [cnf transformation 137] 370. ~richer(mary,john) | mary = john [resolution 150,244] 374. mary = john [subsumption resolution 370,266] 375. $false [subsumption resolution 374,209] % SZS output end Proof for 1906809585763289910521019 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Sean, Casey, Margaret, Martha are the only persons in the room. “Martha is an avid mountain climber who has scaled several peaks” if “everyone outside the room is a member of a local theater group specializing in improv or does not write in-depth travel guides for off-the-beaten-path destinations”. If someone practices zumba then he/she does not enjoy bird watching. Martha is an avid mountain climber who has scaled several peaks. Everyone anywhere who collects foreign coins collects antique jewelry and composes and performs experimental electronic music. It is not the case that “Margaret is a skilled home brewer experimenting with craft beer recipes”. If someone collects vintage vinyl records then he/she does not enjoy making ceramics and vice versa. Margaret enjoys bird watching. Everyone in the room is an avid mountain climber who has scaled several peaks. Not everyone in the room who collects antique jewelry plays the drums. Everyone in the room either writes in-depth travel guides for off-the-beaten-path destinations or is a wine connoisseur with a private cellar of vintage wines but not both if they plays the drums. Casey enjoys bird watching. If someone either enjoys bird watching or does not enjoy making ceramics but not both then he/she participates in citizen science projects related to wildlife monitoring and vice versa. Sean is a member of a local theater group specializing in improv. Everyone in the room who does not enjoy making ceramics owns a smart tv. Everyone in the room who collects vintage vinyl records participates in citizen science projects related to wildlife monitoring. Sean collects vintage vinyl records. Sean does not write in-depth travel guides for off-the-beaten-path destinations. Casey who is an avid mountain climber who has scaled several peaks is a certified scuba diver with advanced underwater photography skills.

Casey enjoys making ceramics.

entailment

room(sean)&room(casey)&room(margaret)&room(martha)&(![X]:(room(X)=>(X='sean'|X='casey'|X='margaret'|X='martha')))& ((![X]:(~room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(martha)))& ((![X]:((practices_zumba(X))=>(does_not_enjoy_bird_watching(X)))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(martha))& (![X]:(anywhere(X)=>(((collects_foreign_coins(X))=>(((collects_antique_jewelry(X))&(composes_and_performs_experimental_electronic_music(X))))))))& (~(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(margaret)))& ((![X]:((collects_vintage_vinyl_records(X))<=>(does_not_enjoy_making_ceramics(X)))))& (enjoys_bird_watching(margaret))& (![X]:(room(X)=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))& (~![X]:(room(X)=>(((collects_antique_jewelry(X))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<~>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))))& (enjoys_bird_watching(casey))& ((![X]:((((enjoys_bird_watching(X))<~>(does_not_enjoy_making_ceramics(X))))<=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))& (is_a_member_of_a_local_theater_group_specializing_in_improv(sean))& (![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))=>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (collects_vintage_vinyl_records(sean))& (does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(sean))& ((is_an_avid_mountain_climber_who_has_scaled_several_peaks(casey))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(casey)))

room(sean)&room(casey)&room(margaret)&room(martha)&(![X]:(room(X)=>(X='sean'|X='casey'|X='margaret'|X='martha')))& enjoys_making_ceramics(casey)

% SZS status Unsatisfiable for 5334817098876695983915608 % SZS output start Proof for 5334817098876695983915608 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. ! [X0] : (predp(X0) <=> ~predr(X0)) [input p6] 55. predw(paul) [input p11] 56. ! [X0] : ((predw(X0) <~> ~predr(X0)) <=> predc(X0)) [input p12] 59. ! [X0] : (room(X0) => (predp(X0) => predc(X0))) [input p15] 63. ~(predr(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 64. ! [X0] : (predc(X0) => (predw(X0) <~> ~predr(X0))) [unused predicate definition removal 56] 152. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 153. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 152] 155. ! [X0] : ((predw(X0) <~> ~predr(X0)) | ~predc(X0)) [ennf transformation 64] 156. ! [X0] : ((predc(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 59] 157. ! [X0] : (predc(X0) | ~predp(X0) | ~room(X0)) [flattening 156] 158. ~predr(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63] 159. ~predr(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 158] 161. ! [X0] : ((predp(X0) | predr(X0)) & (~predr(X0) | ~predp(X0))) [nnf transformation 50] 164. ! [X0] : (((predr(X0) | ~predw(X0)) & (~predr(X0) | predw(X0))) | ~predc(X0)) [nnf transformation 155] 165. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 166. ~predr(paul) | (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 159,165] 247. room(mary) [cnf transformation 153] 248. room(paul) [cnf transformation 153] 249. room(fred) [cnf transformation 153] 250. room(alice) [cnf transformation 153] 251. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 153] 253. predr(X0) | predp(X0) [cnf transformation 161] 256. predw(paul) [cnf transformation 55] 258. ~predc(X0) | ~predw(X0) | predr(X0) [cnf transformation 164] 259. ~predp(X0) | predc(X0) | ~room(X0) [cnf transformation 157] 261. ~predr(paul) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 262. ~predr(paul) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 263. ~predr(paul) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 264. ~predr(paul) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 265. ~predr(paul) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 266. ~predr(paul) | alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,250] 267. ~predr(paul) | alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 266,249] 268. ~predr(paul) | alice != sK1 | ~room(mary) [subsumption resolution 267,248] 269. ~predr(paul) | alice != sK1 [subsumption resolution 268,247] 271. 1 <=> alice = sK1 [avatar definition] 273. alice != sK1 <- (~1) [avatar component clause 271] 275. 2 <=> predr(paul) [avatar definition] 277. ~predr(paul) <- (~2) [avatar component clause 275] 278. ~1 | ~2 [avatar split clause 269,275,271] 279. ~predr(paul) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 264,250] 280. ~predr(paul) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 279,249] 281. ~predr(paul) | fred != sK1 | ~room(mary) [subsumption resolution 280,248] 282. ~predr(paul) | fred != sK1 [subsumption resolution 281,247] 284. 3 <=> fred = sK1 [avatar definition] 286. fred != sK1 <- (~3) [avatar component clause 284] 287. ~3 | ~2 [avatar split clause 282,275,284] 288. ~predr(paul) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 263,250] 289. ~predr(paul) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 288,249] 290. ~predr(paul) | paul != sK1 | ~room(mary) [subsumption resolution 289,248] 291. ~predr(paul) | paul != sK1 [subsumption resolution 290,247] 293. 4 <=> paul = sK1 [avatar definition] 295. paul != sK1 <- (~4) [avatar component clause 293] 296. ~4 | ~2 [avatar split clause 291,275,293] 297. ~predr(paul) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,250] 298. ~predr(paul) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 297,249] 299. ~predr(paul) | mary != sK1 | ~room(mary) [subsumption resolution 298,248] 300. ~predr(paul) | mary != sK1 [subsumption resolution 299,247] 302. 5 <=> mary = sK1 [avatar definition] 304. mary != sK1 <- (~5) [avatar component clause 302] 305. ~5 | ~2 [avatar split clause 300,275,302] 306. ~predr(paul) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,250] 307. ~predr(paul) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 306,249] 308. ~predr(paul) | room(sK1) | ~room(mary) [subsumption resolution 307,248] 309. ~predr(paul) | room(sK1) [subsumption resolution 308,247] 311. 6 <=> room(sK1) [avatar definition] 313. room(sK1) <- (6) [avatar component clause 311] 314. 6 | ~2 [avatar split clause 309,275,311] 315. predp(paul) <- (~2) [resolution 253,277] 318. predc(paul) | ~room(paul) <- (~2) [resolution 259,315] 320. predc(paul) <- (~2) [subsumption resolution 318,248] 333. ~predw(paul) | predr(paul) <- (~2) [resolution 320,258] 335. predr(paul) <- (~2) [subsumption resolution 333,256] 336. $false <- (~2) [subsumption resolution 335,277] 337. 2 [avatar contradiction clause 336] 381. fred = sK1 | paul = sK1 | mary = sK1 | alice = sK1 <- (6) [resolution 251,313] 399. paul = sK1 | mary = sK1 | alice = sK1 <- (~3, 6) [subsumption resolution 381,286] 400. mary = sK1 | alice = sK1 <- (~3, ~4, 6) [subsumption resolution 399,295] 401. alice = sK1 <- (~3, ~4, ~5, 6) [subsumption resolution 400,304] 402. $false <- (~1, ~3, ~4, ~5, 6) [subsumption resolution 401,273] 403. 1 | 3 | 4 | 5 | ~6 [avatar contradiction clause 402] 404. $false [avatar sat refutation 278,287,296,305,314,337,403] % SZS output end Proof for 5334817098876695983915608 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.028 s % ------------------------------ % ------------------------------

Hiram, Jodi are the only persons in the room. Everyone in the room is not wise if they is not a funny kind person. Everyone in the room who is not wise is a generous person. Everyone in the room who is a generous person is a wise person. Jodi is a brave patient person. Everyone outside the room is a wise person if they is a brave person. All tall persons are kind. Someone in the room is strong. If someone is not a kind patient person then he/she is a happy old tall person and vice versa. Jodi is a old calm person. More than one person in the room is a strong person.

It is not the case that “it is not the case that “it is not the case that “more than one person in the room is not tall, is a kind person and is a old person”””.

neutral

room(hiram)&room(jodi)&(![X]:(room(X)=>(X='hiram'|X='jodi')))& (![X]:(room(X)=>(((~(funny(X)&kind(X)&person(X)))=>(~wise(X))))))& (![X]:(room(X)=>(((~wise(X))=>(generous(X)&person(X))))))& (![X]:(room(X)=>(((generous(X)&person(X))=>(wise(X)&person(X))))))& (brave(jodi)&patient(jodi)&person(jodi))& (![X]:(~room(X)=>(((brave(X)&person(X))=>(wise(X)&person(X))))))& (![X]:(tall(X)=>kind(X)))& (?[X]:(room(X)&(strong(X))))& ((![X]:((~(kind(X)&patient(X)&person(X)))<=>(happy(X)&old(X)&tall(X)&person(X)))))& (old(jodi)&calm(jodi)&person(jodi))& ((?[X,Y]:(room(X)&room(Y)&(strong(X)&person(X)&strong(Y)&person(Y))&(X!=Y))))

room(hiram)&room(jodi)&(![X]:(room(X)=>(X='hiram'|X='jodi')))& ~(~(~((?[X,Y]:(room(X)&room(Y)&(((~tall(X))&(kind(X)&person(X))&(old(X)&person(X)))&((~tall(Y))&(kind(Y)&person(Y))&(old(Y)&person(Y))))&(X!=Y))))))

Larry, Thomas, Teresa, Jon are the only persons in the room. 'If someone enjoys stand-up paddleboarding then he/she has a saltwater aquarium' if 'someone anywhere enjoys watercolor painting'. If 'Thomas owns a telescope' then 'Larry collects foreign coins'. Either 'Thomas owns an extensive assortment of vintage comic book memorabilia' or 'Larry enjoys skydiving' but not both. If 'Larry practices digital art' then 'Teresa enjoys rooftop gardening or collects rare and antique scientific instruments or both'. Either 'everyone in the room practices graffiti art or is not a client of Meta' or 'everyone in the room does not own a microscope or is not a skilled home brewer experimenting with craft beer recipes' but not both. If 'Teresa collects action figures' then 'everyone in the room who is a craft beer aficionado is an enthusiastic bird watcher who travels for rare sightings'. 'Larry enjoys stand-up paddleboarding' if 'everyone in the room is a client of Costco or does not own a significant collection of rare gemstones and minerals' and vice versa. 'Teresa enjoys skydiving, enjoys spelunking or can play the piano' if 'everyone in the room is not a client of Meta or does enjoy mountain biking' and vice versa. If 'someone in the room collects action figures' then 'no one in the room who creates large-scale murals for public art installations enjoys fishing'. Either 'everyone in the room is an enthusiastic bird watcher who travels for rare sightings or does not own a telescope' or 'it is not the case that 'Teresa either enjoys stand-up paddleboarding or creates large-scale murals for public art installations but not both'' but not both. Not everyone in the room who is an enthusiastic bird watcher who travels for rare sightings is a client of Costco. Larry enjoys stand-up paddleboarding. Everyone in the room practices graffiti art if they collects action figures. Someone anywhere enjoys watercolor painting. Everyone in the room creates large-scale murals for public art installations. Everyone in the room enjoys fishing if they does not own a microscope, is not a drone photographer or enjoys stand-up paddleboarding and vice versa. Everyone in the room who enjoys stand-up paddleboarding does enjoy mountain biking. Everyone in the room who does enjoy mountain biking does not enjoy spelunking. If someone has a saltwater aquarium then he/she collects rare and antique scientific instruments and vice versa. It is not the case that 'Teresa practices graffiti art'.

Jon collects action figures.

contradiction

room(larry)&room(thomas)&room(teresa)&room(jon)&(![X]:(room(X)=>(X='larry'|X='thomas'|X='teresa'|X='jon')))& ((?[X]:(anywhere(X)&(enjoys_watercolor_painting(X))))=>((![X]:((enjoys_stand-up_paddleboarding(X))=>(has_a_saltwater_aquarium(X))))))& ((owns_a_telescope(thomas))=>(collects_foreign_coins(larry)))& ((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(thomas))<~>(enjoys_skydiving(larry)))& ((practices_digital_art(larry))=>(((enjoys_rooftop_gardening(teresa))|(collects_rare_and_antique_scientific_instruments(teresa)))))& ((![X]:(room(X)=>(((is_not_a_client_of_Meta(X))|(practices_graffiti_art(X))))))<~>(![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_own_a_microscope(X)))))))& ((collects_action_figures(teresa))=>(![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_a_client_of_Costco(X))))))<=>(enjoys_stand-up_paddleboarding(larry)))& ((![X]:(room(X)=>(((does_enjoy_mountain_biking(X))|(is_not_a_client_of_Meta(X))))))<=>(((enjoys_skydiving(teresa))|(enjoys_spelunking(teresa))|(can_play_the_piano(teresa)))))& ((?[X]:(room(X)&(collects_action_figures(X))))=>(~?[X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(enjoys_fishing(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_telescope(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))<~>(~(((enjoys_stand-up_paddleboarding(teresa))<~>(creates_large-scale_murals_for_public_art_installations(teresa))))))& (~![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(is_a_client_of_Costco(X))))))& (enjoys_stand-up_paddleboarding(larry))& (![X]:(room(X)=>(((collects_action_figures(X))=>(practices_graffiti_art(X))))))& (?[X]:(anywhere(X)&(enjoys_watercolor_painting(X))))& (![X]:(room(X)=>(creates_large-scale_murals_for_public_art_installations(X))))& (![X]:(room(X)=>(((enjoys_fishing(X))<=>(((does_not_own_a_microscope(X))|(is_not_a_drone_photographer(X))|(enjoys_stand-up_paddleboarding(X))))))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(does_not_enjoy_spelunking(X))))))& ((![X]:((has_a_saltwater_aquarium(X))<=>(collects_rare_and_antique_scientific_instruments(X)))))& (~(practices_graffiti_art(teresa)))

room(larry)&room(thomas)&room(teresa)&room(jon)&(![X]:(room(X)=>(X='larry'|X='thomas'|X='teresa'|X='jon')))& collects_action_figures(jon)

% SZS status Unsatisfiable for 3428719167462307732743374 % SZS output start Proof for 3428719167462307732743374 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 53. ? [X0] : (predz(X0) & room(X0)) => ~? [X0] : (room(X0) => (preda(X0) => predd(X0))) [input p9] 56. predj(mary) [input p12] 60. ! [X0] : (room(X0) => (predd(X0) <=> (predj(X0) | ~predx(X0) | ~predv(X0)))) [input p16] 65. predz(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 68. ? [X0] : (predz(X0) & room(X0)) => ~? [X1] : (room(X1) => (preda(X1) => predd(X1))) [rectify 53] 149. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 150. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 149] 157. ! [X1] : ((~predd(X1) & preda(X1)) & room(X1)) | ! [X0] : (~predz(X0) | ~room(X0)) [ennf transformation 68] 158. ! [X1] : (~predd(X1) & preda(X1) & room(X1)) | ! [X0] : (~predz(X0) | ~room(X0)) [flattening 157] 166. ! [X0] : ((predd(X0) <=> (predj(X0) | ~predx(X0) | ~predv(X0))) | ~room(X0)) [ennf transformation 60] 171. predz(alice) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 65] 172. predz(alice) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 171] 189. ! [X0] : (~predd(X0) & preda(X0) & room(X0)) | ! [X1] : (~predz(X1) | ~room(X1)) [rectify 158] 196. ! [X0] : (((predd(X0) | (~predj(X0) & predx(X0) & predv(X0))) & ((predj(X0) | ~predx(X0) | ~predv(X0)) | ~predd(X0))) | ~room(X0)) [nnf transformation 166] 197. ! [X0] : (((predd(X0) | (~predj(X0) & predx(X0) & predv(X0))) & (predj(X0) | ~predx(X0) | ~predv(X0) | ~predd(X0))) | ~room(X0)) [flattening 196] 278. room(mary) [cnf transformation 150] 281. room(alice) [cnf transformation 150] 307. ~predd(X0) | ~predz(X1) | ~room(X1) [cnf transformation 189] 319. predj(mary) [cnf transformation 56] 325. ~predj(X0) | predd(X0) | ~room(X0) [cnf transformation 197] 334. predz(alice) [cnf transformation 172] 386. 11 <=> predj(mary) [avatar definition] 387. predj(mary) <- (11) [avatar component clause 386] 442. 23 <=> ! [X1] : (~predz(X1) | ~room(X1)) [avatar definition] 443. ~predz(X1) | ~room(X1) <- (23) [avatar component clause 442] 445. 24 <=> ! [X0] : ~predd(X0) [avatar definition] 446. ~predd(X0) <- (24) [avatar component clause 445] 447. 23 | 24 [avatar split clause 307,445,442] 487. 11 [avatar split clause 319,386] 498. ~room(alice) <- (23) [resolution 443,334] 499. $false <- (23) [subsumption resolution 498,281] 500. ~23 [avatar contradiction clause 499] 522. predd(mary) | ~room(mary) <- (11) [resolution 325,387] 523. ~room(mary) <- (11, 24) [subsumption resolution 522,446] 524. $false <- (11, 24) [subsumption resolution 523,278] 525. ~11 | ~24 [avatar contradiction clause 524] 526. $false [avatar sat refutation 447,487,500,525] % SZS output end Proof for 3428719167462307732743374 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s % ------------------------------ % ------------------------------

There is a room. If everyone in the room plays video games then it is true that everyone in the room does not enjoy fishing or does not enjoy camping and organizing outdoor survival workshops. If it is true that everyone in the room does not enjoy fishing or does not enjoy camping and organizing outdoor survival workshops then everyone in the room neither collects vintage vinyl records nor is a cybersecurity expert if they does not enjoy fishing. Everyone in the room is a night owl if they mentors a youth basketball team on weekends. Everyone in the room either can play the piano or is a cybersecurity expert but not both if they is a night owl. It is true that everyone in the room does not enjoy fishing or does not enjoy camping and organizing outdoor survival workshops. Everyone in the room neither collects vintage vinyl records nor is a cybersecurity expert if they does not enjoy fishing. Everyone in the room who has lived in exactly three countries is not an amateur astronomer who builds and uses custom telescopes. No one outside the room who mentors a youth basketball team on weekends or has a piercing or both plays video games. Everyone in the room who plays video games collects vintage vinyl records.

Everyone in the room is a night owl or is not a night owl.

entailment

(there_is_a_room)& (((![X]:(room(X)=>(plays_video_games(X))))=>(![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_enjoy_fishing(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_enjoy_fishing(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_fishing(X))=>(~((collects_vintage_vinyl_records(X))|(is_a_cybersecurity_expert(X))))))))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(is_a_night_owl(X))))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(((can_play_the_piano(X))<~>(is_a_cybersecurity_expert(X))))))))& (![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_enjoy_fishing(X))))))& (![X]:(room(X)=>(((does_not_enjoy_fishing(X))=>(~((collects_vintage_vinyl_records(X))|(is_a_cybersecurity_expert(X))))))))& (![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (~?[X]:(~room(X)=>(((((mentors_a_youth_basketball_team_on_weekends(X))|(has_a_piercing(X))))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(collects_vintage_vinyl_records(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((is_not_a_night_owl(X))|(is_a_night_owl(X)))))

% SZS status Unsatisfiable for 2430407833598879498192039 % SZS output start Proof for 2430407833598879498192039 44. ! [X0] : (room(X0) => (preda(X0) => predl(X0))) & ~? [X0] : (~room(X0) => ((predi(X0) | predk(X0)) => preda(X0))) & ! [X0] : (room(X0) => (predn(X0) => ~predg(X0))) & ! [X0] : (room(X0) => (~predj(X0) => ~(predh(X0) | predl(X0)))) & ! [X0] : (room(X0) => (~predj(X0) | ~predf(X0))) & ! [X0] : (room(X0) => (predm(X0) => (predp(X0) <~> predh(X0)))) & ! [X0] : (room(X0) => (predk(X0) => predm(X0))) & (! [X0] : (room(X0) => (~predj(X0) | ~predf(X0))) => ! [X0] : (room(X0) => (~predj(X0) => ~(predh(X0) | predl(X0))))) & (! [X0] : (room(X0) => preda(X0)) => ! [X0] : (room(X0) => (~predj(X0) | ~predf(X0)))) & there_is_a_room [input p0] 45. ~(! [X0] : (room(X0) => (predm(X0) | ~predm(X0))) & there_is_a_room) [input hypothesis] 46. ! [X0] : (room(X0) => (preda(X0) => predl(X0))) & ~? [X1] : (~room(X1) => ((predi(X1) | predk(X1)) => preda(X1))) & ! [X2] : (room(X2) => (predn(X2) => ~predg(X2))) & ! [X3] : (room(X3) => (~predj(X3) => ~(predh(X3) | predl(X3)))) & ! [X4] : (room(X4) => (~predj(X4) | ~predf(X4))) & ! [X5] : (room(X5) => (predm(X5) => (predp(X5) <~> predh(X5)))) & ! [X6] : (room(X6) => (predk(X6) => predm(X6))) & (! [X7] : (room(X7) => (~predj(X7) | ~predf(X7))) => ! [X8] : (room(X8) => (~predj(X8) => ~(predh(X8) | predl(X8))))) & (! [X9] : (room(X9) => preda(X9)) => ! [X10] : (room(X10) => (~predj(X10) | ~predf(X10)))) & there_is_a_room [rectify 44] 47. ! [X0] : (room(X0) => (preda(X0) => predl(X0))) & ~? [X1] : (~room(X1) => preda(X1)) & ! [X2] : (room(X2) => (predn(X2) => ~predg(X2))) & ! [X3] : (room(X3) => (~predj(X3) => ~(predh(X3) | predl(X3)))) & ! [X4] : (room(X4) => (~predj(X4) | ~predf(X4))) & ! [X5] : (room(X5) => (predm(X5) => (predp(X5) <~> predh(X5)))) & ! [X6] : (room(X6) => (predk(X6) => predm(X6))) & (! [X7] : (room(X7) => (~predj(X7) | ~predf(X7))) => ! [X8] : (room(X8) => (~predj(X8) => ~(predh(X8) | predl(X8))))) & (! [X9] : (room(X9) => preda(X9)) => ! [X10] : (room(X10) => (~predj(X10) | ~predf(X10)))) & there_is_a_room [pure predicate removal 46] 48. ! [X0] : (room(X0) => (preda(X0) => predl(X0))) & ~? [X1] : (~room(X1) => preda(X1)) & ! [X2] : (room(X2) => (predn(X2) => ~predg(X2))) & ! [X3] : (room(X3) => (~predj(X3) => ~(predh(X3) | predl(X3)))) & ! [X4] : (room(X4) => (~predj(X4) | ~predf(X4))) & ! [X5] : (room(X5) => (predm(X5) => (predp(X5) <~> predh(X5)))) & (! [X7] : (room(X7) => (~predj(X7) | ~predf(X7))) => ! [X8] : (room(X8) => (~predj(X8) => ~(predh(X8) | predl(X8))))) & (! [X9] : (room(X9) => preda(X9)) => ! [X10] : (room(X10) => (~predj(X10) | ~predf(X10)))) & there_is_a_room [pure predicate removal 47] 49. ! [X0] : (room(X0) => (preda(X0) => predl(X0))) & ~? [X1] : (~room(X1) => preda(X1)) & ! [X3] : (room(X3) => (~predj(X3) => ~(predh(X3) | predl(X3)))) & ! [X4] : (room(X4) => (~predj(X4) | ~predf(X4))) & ! [X5] : (room(X5) => (predm(X5) => (predp(X5) <~> predh(X5)))) & (! [X7] : (room(X7) => (~predj(X7) | ~predf(X7))) => ! [X8] : (room(X8) => (~predj(X8) => ~(predh(X8) | predl(X8))))) & (! [X9] : (room(X9) => preda(X9)) => ! [X10] : (room(X10) => (~predj(X10) | ~predf(X10)))) & there_is_a_room [pure predicate removal 48] 50. ~? [X1] : ~~room(X1) & ! [X3] : (room(X3) => (~predj(X3) => ~(predh(X3) | predl(X3)))) & ! [X4] : (room(X4) => (~predj(X4) | ~predf(X4))) & ! [X5] : (room(X5) => (predm(X5) => (predp(X5) <~> predh(X5)))) & (! [X7] : (room(X7) => (~predj(X7) | ~predf(X7))) => ! [X8] : (room(X8) => (~predj(X8) => ~(predh(X8) | predl(X8))))) & (! [X9] : ~room(X9) => ! [X10] : (room(X10) => (~predj(X10) | ~predf(X10)))) & there_is_a_room [pure predicate removal 49] 51. ~? [X1] : ~~room(X1) & ! [X3] : (room(X3) => (~predj(X3) => ~predh(X3))) & ! [X4] : (room(X4) => (~predj(X4) | ~predf(X4))) & ! [X5] : (room(X5) => (predm(X5) => (predp(X5) <~> predh(X5)))) & (! [X7] : (room(X7) => (~predj(X7) | ~predf(X7))) => ! [X8] : (room(X8) => (~predj(X8) => ~predh(X8)))) & (! [X9] : ~room(X9) => ! [X10] : (room(X10) => (~predj(X10) | ~predf(X10)))) & there_is_a_room [pure predicate removal 50] 124. ! [X1] : ~room(X1) & ! [X3] : ((~predh(X3) | predj(X3)) | ~room(X3)) & ! [X4] : ((~predj(X4) | ~predf(X4)) | ~room(X4)) & ! [X5] : (((predp(X5) <~> predh(X5)) | ~predm(X5)) | ~room(X5)) & (! [X8] : ((~predh(X8) | predj(X8)) | ~room(X8)) | ? [X7] : ((predj(X7) & predf(X7)) & room(X7))) & (! [X10] : ((~predj(X10) | ~predf(X10)) | ~room(X10)) | ? [X9] : room(X9)) & there_is_a_room [ennf transformation 51] 125. ! [X1] : ~room(X1) & ! [X3] : (~predh(X3) | predj(X3) | ~room(X3)) & ! [X4] : (~predj(X4) | ~predf(X4) | ~room(X4)) & ! [X5] : ((predp(X5) <~> predh(X5)) | ~predm(X5) | ~room(X5)) & (! [X8] : (~predh(X8) | predj(X8) | ~room(X8)) | ? [X7] : (predj(X7) & predf(X7) & room(X7))) & (! [X10] : (~predj(X10) | ~predf(X10) | ~room(X10)) | ? [X9] : room(X9)) & there_is_a_room [flattening 124] 126. ? [X0] : ((~predm(X0) & predm(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 45] 127. ? [X0] : (~predm(X0) & predm(X0) & room(X0)) | ~there_is_a_room [flattening 126] 129. ! [X1] : ~room(X1) & ! [X3] : (~predh(X3) | predj(X3) | ~room(X3)) & ! [X4] : (~predj(X4) | ~predf(X4) | ~room(X4)) & ! [X5] : (((~predh(X5) | ~predp(X5)) & (predh(X5) | predp(X5))) | ~predm(X5) | ~room(X5)) & (! [X8] : (~predh(X8) | predj(X8) | ~room(X8)) | ? [X7] : (predj(X7) & predf(X7) & room(X7))) & (! [X10] : (~predj(X10) | ~predf(X10) | ~room(X10)) | ? [X9] : room(X9)) & there_is_a_room [nnf transformation 125] 130. ! [X0] : ~room(X0) & ! [X1] : (~predh(X1) | predj(X1) | ~room(X1)) & ! [X2] : (~predj(X2) | ~predf(X2) | ~room(X2)) & ! [X3] : (((~predh(X3) | ~predp(X3)) & (predh(X3) | predp(X3))) | ~predm(X3) | ~room(X3)) & (! [X4] : (~predh(X4) | predj(X4) | ~room(X4)) | ? [X5] : (predj(X5) & predf(X5) & room(X5))) & (! [X6] : (~predj(X6) | ~predf(X6) | ~room(X6)) | ? [X7] : room(X7)) & there_is_a_room [rectify 129] 131. ? [X5] : (predj(X5) & predf(X5) & room(X5)) => (predj(sK0) & predf(sK0) & room(sK0)) [choice axiom] 132. ? [X7] : room(X7) => room(sK1) [choice axiom] 133. ! [X0] : ~room(X0) & ! [X1] : (~predh(X1) | predj(X1) | ~room(X1)) & ! [X2] : (~predj(X2) | ~predf(X2) | ~room(X2)) & ! [X3] : (((~predh(X3) | ~predp(X3)) & (predh(X3) | predp(X3))) | ~predm(X3) | ~room(X3)) & (! [X4] : (~predh(X4) | predj(X4) | ~room(X4)) | (predj(sK0) & predf(sK0) & room(sK0))) & (! [X6] : (~predj(X6) | ~predf(X6) | ~room(X6)) | room(sK1)) & there_is_a_room [skolemisation 130,132,131] 134. ? [X0] : (~predm(X0) & predm(X0) & room(X0)) => (~predm(sK2) & predm(sK2) & room(sK2)) [choice axiom] 135. (~predm(sK2) & predm(sK2) & room(sK2)) | ~there_is_a_room [skolemisation 127,134] 216. there_is_a_room [cnf transformation 133] 227. predm(sK2) | ~there_is_a_room [cnf transformation 135] 228. ~predm(sK2) | ~there_is_a_room [cnf transformation 135] 229. ~predm(sK2) [subsumption resolution 228,216] 230. ~there_is_a_room [subsumption resolution 227,229] 231. $false [subsumption resolution 230,216] % SZS output end Proof for 2430407833598879498192039 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark is the only person in the room. “Mark is an avid hiker” if “everyone in the room is a client of Meta or does not collect rare minerals” and vice versa. Everyone in the room who hosts themed dinner parties featuring gourmet home-cooked meals practices tai chi. Mark develops open-source software projects in their free time. If someone is an avid hiker then he/she plays eSports competitively. Mark enjoys stand-up paddleboarding. Everyone in the room practices tai chi or does not play eSports competitively.

Mark is an avid hiker.

neutral

room(mark)&(![X]:(room(X)=>(X='mark')))& ((![X]:(room(X)=>(((does_not_collect_rare_minerals(X))|(is_a_client_of_Meta(X))))))<=>(is_an_avid_hiker(mark)))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(practices_tai_chi(X))))))& (develops_open-source_software_projects_in_their_free_time(mark))& ((![X]:((is_an_avid_hiker(X))=>(plays_eSports_competitively(X)))))& (enjoys_stand-up_paddleboarding(mark))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(practices_tai_chi(X))))))

room(mark)&(![X]:(room(X)=>(X='mark')))& is_an_avid_hiker(mark)

Jesse, Christine, Harvey are the only persons in the room. It is true that “Jesse does not regularly contributes to tech forums and online communities, is not a coffee connoisseur or does not practice archery”. Christine enjoys origami, is an amateur astronomer who builds and uses custom telescopes and does not create large-scale murals for public art installations.

Christine neither regularly contributes to tech forums and online communities nor practices and performs acrobatic dance routines.

neutral

room(jesse)&room(christine)&room(harvey)&(![X]:(room(X)=>(X='jesse'|X='christine'|X='harvey')))& (((does_not_regularly_contributes_to_tech_forums_and_online_communities(jesse))|(is_not_a_coffee_connoisseur(jesse))|(does_not_practice_archery(jesse))))& (((enjoys_origami(christine))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(christine))&(does_not_create_large-scale_murals_for_public_art_installations(christine))))& (((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(jesse))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(jesse))|(can_play_the_flute(jesse))))& (((is_not_a_coffee_connoisseur(harvey))&(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(harvey))&(travels_domestically_frequently(harvey))))& (((does_not_enjoy_kayaking_and_exploring_remote_waterways(harvey))|(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(harvey))))& (does_not_collect_limited-edition_art_prints_from_contemporary_artists(christine))& (does_not_collect_limited-edition_art_prints_from_contemporary_artists(jesse))& (((does_not_create_large-scale_murals_for_public_art_installations(jesse))|(does_not_regularly_contributes_to_tech_forums_and_online_communities(jesse))|(does_not_enjoy_snowboarding(jesse))))& ((((does_not_practice_and_performs_acrobatic_dance_routines(harvey))|(does_not_collect_first_edition_books(harvey))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(harvey))))&(((does_not_enjoy_kayaking_and_exploring_remote_waterways(harvey))|(does_not_own_a_telescope(harvey))|(does_not_practice_and_performs_acrobatic_dance_routines(harvey)))))& (~((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(harvey))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(harvey))))& (does_not_collect_first_edition_books(jesse))& ((~((does_not_use_an_ios_phone(jesse))|(does_not_travel_domestically_frequently(jesse))))&(((creates_YouTube_content(jesse))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(jesse))|(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(jesse)))))& (((does_not_enjoy_snowboarding(christine))|(does_not_own_a_telescope(christine))))& ((![X]:((practices_archery(X))<=>(~((does_not_practice_zumba(X))|(collects_first_edition_books(X)))))))& ((![X]:((((cannot_play_the_flute(X))&(practices_archery(X))&(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))<=>(((does_not_collect_foreign_coins(X))<~>(can_play_the_flute(X)))))))& ((does_not_use_an_ios_phone(christine))&(does_not_collect_foreign_coins(christine)))& (~((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(christine))|(does_not_enjoy_snowboarding(christine))))& (((cannot_play_the_flute(christine))|(creates_YouTube_content(christine))|(regularly_contributes_to_tech_forums_and_online_communities(christine))))& (((does_not_regularly_contributes_to_tech_forums_and_online_communities(jesse))&(cannot_play_the_flute(jesse))&(does_not_own_a_telescope(jesse))))& ((((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(jesse))|(does_not_create_YouTube_content(jesse))|(uses_an_ios_phone(jesse))))&(((practices_and_performs_acrobatic_dance_routines(jesse))&(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(jesse))&(does_not_regularly_contributes_to_tech_forums_and_online_communities(jesse)))))& ((![X]:((does_not_own_a_telescope(X))<=>(~((does_not_enjoy_origami(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X)))))))& (~((creates_large-scale_murals_for_public_art_installations(jesse))|(does_not_travel_domestically_frequently(jesse))))& ((jesse_dream=>(~((collects_first_edition_books(jesse))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(jesse))))))

room(jesse)&room(christine)&room(harvey)&(![X]:(room(X)=>(X='jesse'|X='christine'|X='harvey')))& ~((regularly_contributes_to_tech_forums_and_online_communities(christine))|(practices_and_performs_acrobatic_dance_routines(christine)))

Christine, Carol, Aaron, Gloria are the only persons in the room. If no one in the room is a dedicated advocate for digital privacy and encryption then everyone in the room either does not play the drums or is a wine connoisseur but not both if they does not collect rare minerals, collects classic novels or does not play the violin.

It is not the case that Carol plays the drums.

neutral

room(christine)&room(carol)&room(aaron)&room(gloria)&(![X]:(room(X)=>(X='christine'|X='carol'|X='aaron'|X='gloria')))& ((~?[X]:(room(X)=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))=>(![X]:(room(X)=>(((((does_not_collect_rare_minerals(X))|(collects_classic_novels(X))|(does_not_play_the_violin(X))))=>(((does_not_play_the_drums(X))<~>(is_a_wine_connoisseur(X)))))))))& ((![X]:(room(X)=>(((streams_on_Twitch(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))))=>(![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))=>(enjoys_stargazing(X)))))))& ((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(carol))&(((is_a_wine_connoisseur(carol))<~>(streams_on_Twitch(carol)))))& (![X]:(anywhere(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(((plays_the_violin(X))&(collects_rare_minerals(X))&(is_not_a_wine_connoisseur(X))))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((((does_not_collect_rare_minerals(X))|(collects_classic_novels(X))|(does_not_play_the_violin(X))))=>(((does_not_play_the_drums(X))<~>(is_a_wine_connoisseur(X))))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(writes_and_illustrates_their_own_graphic_novels(X)&writes_and_illustrates_their_own_graphic_novels(Y))&(X!=Y))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(is_a_wine_connoisseur(X))))))& (?[X]:(anywhere(X)&(collects_rare_minerals(X))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(enjoys_stargazing(X))))))& ((((does_not_collect_rare_minerals(aaron))|(collects_classic_novels(aaron))|(does_not_play_the_violin(aaron))))&(plays_the_violin(aaron)))& ((?[X,Y]:(room(X)&room(Y)&(watches_fantasy_movies(X)&watches_fantasy_movies(Y))&(X!=Y))))& (![X]:(room(X)=>(((((plays_the_violin(X))|(collects_classic_novels(X))|(enjoys_kayaking(X))))=>(collects_rare_minerals(X))))))& (~![X]:(room(X)=>(((collects_rare_minerals(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (~![X]:(anywhere(X)=>(((does_not_collect_rare_minerals(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (((?[X]:(room(X)&writes_and_illustrates_their_own_graphic_novels(X)))&(![X,Y]:((room(X)&room(Y)&(writes_and_illustrates_their_own_graphic_novels(X))&(writes_and_illustrates_their_own_graphic_novels(Y)))=>(X=Y)))))& (((?[X]:(room(X)&does_not_play_the_drums(X)))))& (?[X]:(room(X)&(enjoys_stargazing(X))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(enjoys_stargazing(X))))))& (((?[X]:(room(X)&enjoys_kayaking(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_kayaking(X))&(enjoys_kayaking(Y)))=>(X=Y)))))& (![X]:(~room(X)=>(((plays_the_drums(X))<=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(watches_fantasy_movies(X))))))& ((plays_the_violin(carol))&(writes_and_illustrates_their_own_graphic_novels(carol)))& (~![X]:(room(X)=>(((plays_the_violin(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))

room(christine)&room(carol)&room(aaron)&room(gloria)&(![X]:(room(X)=>(X='christine'|X='carol'|X='aaron'|X='gloria')))& ~(plays_the_drums(carol))

Jean is the only person in the room. If “Jean hosts a YouTube channel dedicated to art tutorials, has lived in exactly three countries or enjoys deep-sea diving and exploring underwater caves” then “Jean is an enthusiastic bird watcher who travels for rare sightings” otherwise “it is not the case that “Jean is a dedicated advocate for digital privacy and encryption””. If “it is not the case that “Jean hosts a YouTube channel dedicated to art tutorials”” then “Jean enjoys deep-sea diving and exploring underwater caves, is a tea enthusiast and is a chess master who participates in national tournaments”. “If someone writes in-depth travel guides for off-the-beaten-path destinations then he/she is a client of Costco” if “at least one person in the room can play the flute”. Either “Jean enjoys skydiving, hosts a YouTube channel dedicated to art tutorials and can play the flute” or “Jean collects luxury watches” but not both. If “Jean enjoys fishing, owns a smartwatch and is a chess master who participates in national tournaments” then “it is not the case that “Jean either does not enjoy fishing or competes in national level swimming championships but not both”” otherwise “Jean writes and illustrates their own graphic novels”. If “Jean is a client of Costco” then “Jean either develops open-source software projects in their free time or is a client of Costco but not both”. Jean is a dedicated advocate for digital privacy and encryption. If someone hosts a YouTube channel dedicated to art tutorials then he/she writes in-depth travel guides for off-the-beaten-path destinations. At least one person outside the room can play the flute. At least one person in the room is a dedicated volunteer for local community service projects. Jean does not enjoy skydiving. If someone is right-handed then he/she writes and illustrates their own graphic novels and vice versa. If someone writes in-depth travel guides for off-the-beaten-path destinations then he/she enjoys deep-sea diving and exploring underwater caves and vice versa. Jean works on fridays. Jean is right-handed. Someone in the room is a chess master who participates in national tournaments. It is not the case that “it is not the case that “Jean is a chess master who participates in national tournaments””. Jean is a night owl.

Jean enjoys deep-sea diving and exploring underwater caves.

entailment

room(jean)&(![X]:(room(X)=>(X='jean')))& (((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(jean))|(has_lived_in_exactly_three_countries(jean))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(jean))))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jean)))&((~(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(jean))|(has_lived_in_exactly_three_countries(jean))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(jean)))))=>(~(is_a_dedicated_advocate_for_digital_privacy_and_encryption(jean)))))& ((~(hosts_a_YouTube_channel_dedicated_to_art_tutorials(jean)))=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(jean))&(is_a_tea_enthusiast(jean))&(is_a_chess_master_who_participates_in_national_tournaments(jean)))))& ((((?[X]:(room(X)&can_play_the_flute(X)))))=>((![X]:((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(is_a_client_of_Costco(X))))))& ((((enjoys_skydiving(jean))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(jean))&(can_play_the_flute(jean))))<~>(collects_luxury_watches(jean)))& (((((enjoys_fishing(jean))&(owns_a_smartwatch(jean))&(is_a_chess_master_who_participates_in_national_tournaments(jean))))=>(~(((does_not_enjoy_fishing(jean))<~>(competes_in_national_level_swimming_championships(jean))))))&((~(((enjoys_fishing(jean))&(owns_a_smartwatch(jean))&(is_a_chess_master_who_participates_in_national_tournaments(jean)))))=>(writes_and_illustrates_their_own_graphic_novels(jean))))& ((is_a_client_of_Costco(jean))=>(((develops_open-source_software_projects_in_their_free_time(jean))<~>(is_a_client_of_Costco(jean)))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(jean))& ((![X]:((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))& (((?[X]:(~room(X)&can_play_the_flute(X)))))& (((?[X]:(room(X)&is_a_dedicated_volunteer_for_local_community_service_projects(X)))))& (does_not_enjoy_skydiving(jean))& ((![X]:((is_right-handed(X))<=>(writes_and_illustrates_their_own_graphic_novels(X)))))& ((![X]:((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))& (works_on_fridays(jean))& (is_right-handed(jean))& (?[X]:(room(X)&(is_a_chess_master_who_participates_in_national_tournaments(X))))& (~(~(is_a_chess_master_who_participates_in_national_tournaments(jean))))& (is_a_night_owl(jean))

room(jean)&(![X]:(room(X)=>(X='jean')))& enjoys_deep-sea_diving_and_exploring_underwater_caves(jean)

% SZS status Unsatisfiable for 6937275903086055913912706 % SZS output start Proof for 6937275903086055913912706 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ~predj(mary) => (predn(mary) & predq(mary) & predm(mary)) [input p2] 52. ! [X0] : (predj(X0) => predg(X0)) [input p8] 57. ! [X0] : (predg(X0) <=> predm(X0)) [input p13] 63. ~(predm(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 69. ~predj(mary) => (predq(mary) & predm(mary)) [pure predicate removal 46] 76. ~predj(mary) => predm(mary) [pure predicate removal 69] 152. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 153. predm(mary) | predj(mary) [ennf transformation 76] 156. ! [X0] : (predg(X0) | ~predj(X0)) [ennf transformation 52] 157. ~predm(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 63] 167. ! [X0] : ((predg(X0) | ~predm(X0)) & (predm(X0) | ~predg(X0))) [nnf transformation 57] 170. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 171. ~predm(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 157,170] 252. room(mary) [cnf transformation 152] 253. ~room(X0) | mary = X0 [cnf transformation 152] 254. predm(mary) | predj(mary) [cnf transformation 153] 262. ~predj(X0) | predg(X0) [cnf transformation 156] 267. ~predg(X0) | predm(X0) [cnf transformation 167] 270. ~predm(mary) | room(sK3) | ~room(mary) [cnf transformation 171] 271. ~predm(mary) | mary != sK3 | ~room(mary) [cnf transformation 171] 274. 1 <=> predj(mary) [avatar definition] 276. predj(mary) <- (1) [avatar component clause 274] 278. 2 <=> predm(mary) [avatar definition] 279. ~predm(mary) <- (~2) [avatar component clause 278] 281. 1 | 2 [avatar split clause 254,278,274] 315. ~predm(mary) | mary != sK3 [subsumption resolution 271,252] 317. 10 <=> mary = sK3 [avatar definition] 319. mary != sK3 <- (~10) [avatar component clause 317] 320. ~10 | ~2 [avatar split clause 315,278,317] 321. ~predm(mary) | room(sK3) [subsumption resolution 270,252] 323. 11 <=> room(sK3) [avatar definition] 325. room(sK3) <- (11) [avatar component clause 323] 326. 11 | ~2 [avatar split clause 321,278,323] 333. mary = sK3 <- (11) [resolution 253,325] 336. $false <- (~10, 11) [subsumption resolution 333,319] 337. 10 | ~11 [avatar contradiction clause 336] 338. predg(mary) <- (1) [resolution 276,262] 339. predm(mary) <- (1) [resolution 338,267] 340. $false <- (1, ~2) [subsumption resolution 339,279] 341. ~1 | 2 [avatar contradiction clause 340] 342. $false [avatar sat refutation 281,320,326,337,341] % SZS output end Proof for 6937275903086055913912706 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

Eric is the only person in the room. If 'Eric is older than Heidi' then 'Eric is quieter than Beth'. If 'Eric is richer than Beth' then 'no quiet person is old'. If 'Eric neither is quieter than Beth nor is older than Heidi' then 'someone in the room is older than Heidi'. 'Eric is the richest in the room' unless 'Eric is older than Elliot'. If 'Eric is richer than Linda' then 'Heidi is quieter than Eric'.

Elliot is older than Eric.

neutral

room(eric)&(![X]:(room(X)=>(X='eric')))& ((older(heidi,eric))=>(quieter(beth,eric)))& ((richer(beth,eric))=>(~?[X]:(quiet(X)=>old(X))))& ((~((quieter(beth,eric))|(older(heidi,eric))))=>(?[X]:(room(X)&(older(heidi,X)))))& (~(older(elliot,eric))=>(![X]:((room(X)&(X!=eric))=>richer(X,eric))))& ((richer(linda,eric))=>(quieter(eric,heidi)))& ((richer(heidi,eric))=>(quieter(eric,linda)))& ((richer(elliot,eric))=>((![X]:((~((older(elliot,X))|(quieter(beth,X))))<=>(older(elliot,X))))))& (~?[X]:(old(X)=>tall(X)))& (?[X]:(room(X)&(richer(heidi,X))))& (richer(elliot,eric))& (?[X]:(room(X)&(richer(linda,X))))& (richer(linda,eric))& (quieter(elliot,eric))& ((![X]:((richer(heidi,X))=>(quieter(elliot,X)))))& (older(heidi,eric))& ((![X]:((quieter(linda,X))=>(quieter(elliot,X)))))

room(eric)&(![X]:(room(X)=>(X='eric')))& older(eric,elliot)

There is a room. Someone who is not hated by Ross hate someone who is liked by Donald, does not hate Donald or is hated by Ross. Everyone in the room does not hate Ross, hates Ross and does not like Sadie if they does not like Ross. Everyone in the room does not like Dorothy and likes Daisy if they does not hate Ross, hates Ross and does not like Sadie. Someone who either likes Dorothy or does not hate Sadie but not both like someone who does not hate Donald and does not like Dorothy. Someone who hates Dorothy and does not like Dorothy like someone who does not like Donald, hates Dorothy and is not hated by Dorothy. Everyone in the room who is not hated by Daisy, does not like Sadie and is not hated by Donald does not hate Sadie, does not hate Dorothy or is hated by Sadie. Everyone in the room is not liked by Dorothy and does not hate Donald if they is not liked by Ross. Not everyone in the room who is not liked by Dorothy and does not hate Donald hates Ross. Everyone in the room who is not hated by Donald, is not liked by Dorothy and does not like Sadie either does not hate Donald or is not hated by Donald but not both. Everyone in the room does not like Dorothy if they either does not hate Donald or is not hated by Donald but not both. Everyone in the room who does not like Dorothy hates Ross, does not hate Ross or is liked by Dorothy. Everyone in the room who is liked by Daisy does not like Dorothy.

Everyone in the room hates Sadie.

neutral

(there_is_a_room)& (?[X,Y]:((~hate(X,ross))&(((like(Y,donald))|(~hate(donald,Y))|(hate(Y,ross))))&(hate(X,Y))))& (![X]:(room(X)=>(((~like(ross,X))=>(((~hate(ross,X))&(hate(ross,X))&(~like(sadie,X))))))))& (![X]:(room(X)=>(((((~hate(ross,X))&(hate(ross,X))&(~like(sadie,X))))=>(((~like(dorothy,X))&(like(daisy,X))))))))& (?[X,Y]:((((like(dorothy,X))<~>(~hate(sadie,X))))&(((~hate(donald,Y))&(~like(dorothy,Y))))&(like(X,Y))))& (?[X,Y]:((((hate(dorothy,X))&(~like(dorothy,X))))&(((~like(donald,Y))&(hate(dorothy,Y))&(~hate(Y,dorothy))))&(like(X,Y))))& (![X]:(room(X)=>(((((~hate(X,daisy))&(~like(sadie,X))&(~hate(X,donald))))=>(((~hate(sadie,X))|(~hate(dorothy,X))|(hate(X,sadie))))))))& (![X]:(room(X)=>(((~like(X,ross))=>(((~like(X,dorothy))&(~hate(donald,X))))))))& (~![X]:(room(X)=>(((((~like(X,dorothy))&(~hate(donald,X))))=>(hate(ross,X))))))& (![X]:(room(X)=>(((((~hate(X,donald))&(~like(X,dorothy))&(~like(sadie,X))))=>(((~hate(donald,X))<~>(~hate(X,donald))))))))& (![X]:(room(X)=>(((((~hate(donald,X))<~>(~hate(X,donald))))=>(~like(dorothy,X))))))& (![X]:(room(X)=>(((~like(dorothy,X))=>(((hate(ross,X))|(~hate(ross,X))|(like(X,dorothy))))))))& (![X]:(room(X)=>(((like(X,daisy))=>(~like(dorothy,X))))))

(there_is_a_room)& ![X]:(room(X)=>(hate(sadie,X)))

There is a room. If someone is a quiet person then he/she is a tall person and vice versa. Someone who is a old person is older than someone who is quiet. Someone in the room is a quiet person. Someone outside the room is a quiet person. Someone in the room is quiet and is a tall person.

Everyone in the room is a tall person.

neutral

(there_is_a_room)& ((![X]:((quiet(X)&person(X))<=>(tall(X)&person(X)))))& (?[X,Y]:((old(X)&person(X))&(quiet(Y))&(older(X,Y))))& (?[X]:(room(X)&(quiet(X)&person(X))))& (?[X]:(~room(X)&(quiet(X)&person(X))))& (?[X]:(room(X)&(((quiet(X))&(tall(X)&person(X))))))

(there_is_a_room)& ![X]:(room(X)=>(tall(X)&person(X)))

Barbara is the only person in the room. If “no one in the room does not enjoy snowboarding or enjoys snowboarding” then “everyone in the room does not enjoy snowboarding if they is a night owl and vice versa”. Everyone in the room who is a night owl collects limited-edition art prints from contemporary artists. Everyone outside the room enjoys snowboarding if they collects limited-edition art prints from contemporary artists and vice versa. If someone collects limited-edition art prints from contemporary artists then he/she creates YouTube content. Everyone in the room does not enjoy snowboarding if they is a night owl and vice versa. Everyone in the room creates YouTube content if they is a night owl and vice versa. Barbara who is a night owl is a night owl or enjoys snowboarding or both. Everyone in the room who enjoys snowboarding collects limited-edition art prints from contemporary artists. Everyone in the room who collects limited-edition art prints from contemporary artists creates YouTube content.

Not everyone in the room collects limited-edition art prints from contemporary artists.

contradiction

room(barbara)&(![X]:(room(X)=>(X='barbara')))& ((~?[X]:(room(X)=>(((enjoys_snowboarding(X))|(does_not_enjoy_snowboarding(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))<=>(is_a_night_owl(X)))))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(~room(X)=>(((enjoys_snowboarding(X))<=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& ((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(creates_YouTube_content(X)))))& (![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))<=>(is_a_night_owl(X))))))& (![X]:(room(X)=>(((creates_YouTube_content(X))<=>(is_a_night_owl(X))))))& ((is_a_night_owl(barbara))&(((is_a_night_owl(barbara))|(enjoys_snowboarding(barbara)))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(creates_YouTube_content(X))))))

room(barbara)&(![X]:(room(X)=>(X='barbara')))& ~![X]:(room(X)=>(collects_limited-edition_art_prints_from_contemporary_artists(X)))

% SZS status Unsatisfiable for 1436184524226022426905651 % SZS output start Proof for 1436184524226022426905651 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (predb(X0) => predd(X0))) [input p2] 51. (predc(mary) | predb(mary)) & predb(mary) [input p7] 54. ~! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 56. ~! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => mary = X1) & room(mary) [rectify 54] 129. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 132. ! [X0] : ((predd(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 46] 133. ! [X0] : (predd(X0) | ~predb(X0) | ~room(X0)) [flattening 132] 142. ? [X0] : (~predd(X0) & room(X0)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [ennf transformation 56] 151. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK1) & room(sK1)) [choice axiom] 152. (~predd(sK1) & room(sK1)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [skolemisation 142,151] 233. room(mary) [cnf transformation 129] 234. ~room(X0) | mary = X0 [cnf transformation 129] 237. ~predb(X0) | predd(X0) | ~room(X0) [cnf transformation 133] 245. predb(mary) [cnf transformation 51] 251. room(sK1) [cnf transformation 152] 252. ~predd(sK1) [cnf transformation 152] 254. 1 <=> predb(mary) [avatar definition] 256. predb(mary) <- (1) [avatar component clause 254] 262. 1 [avatar split clause 245,254] 265. mary = sK1 [resolution 234,251] 267. ~predd(mary) [backward demodulation 252,265] 268. predd(mary) | ~room(mary) <- (1) [resolution 237,256] 269. ~room(mary) <- (1) [subsumption resolution 268,267] 270. $false <- (1) [subsumption resolution 269,233] 271. ~1 [avatar contradiction clause 270] 272. $false [avatar sat refutation 262,271] % SZS output end Proof for 1436184524226022426905651 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jeffrey is the only person in the room. If “at least one person in the room is a coffee connoisseur” then “Jeffrey competes in national level swimming championships”. Either “Jeffrey has a saltwater aquarium” or “Jeffrey is not an active member of a local robotics club” but not both. If someone uses contact lenses then he/she creates large-scale murals for public art installations and vice versa. At least one person anywhere travels domestically frequently. Everyone in the room who is a coffee connoisseur has a pet dog. Jeffrey creates YouTube content. Everyone in the room who uses contact lenses creates large-scale murals for public art installations. Jeffrey maintains a personal blog focused on cybersecurity tips. Jeffrey creates augmented reality experiences for mobile applications. If someone volunteers for local environmental conservation projects then he/she hosts a YouTube channel dedicated to art tutorials, has a tattoo or practices archery. Jeffrey practices and performs acrobatic dance routines. Jeffrey uses an ios phone. Jeffrey uses a Windows laptop. If someone maintains a personal blog focused on cybersecurity tips then he/she creates augmented reality experiences for mobile applications. Jeffrey develops open-source software projects in their free time.

Jeffrey has a saltwater aquarium.

neutral

room(jeffrey)&(![X]:(room(X)=>(X='jeffrey')))& ((((?[X]:(room(X)&is_a_coffee_connoisseur(X)))))=>(competes_in_national_level_swimming_championships(jeffrey)))& ((has_a_saltwater_aquarium(jeffrey))<~>(is_not_an_active_member_of_a_local_robotics_club(jeffrey)))& ((![X]:((uses_contact_lenses(X))<=>(creates_large-scale_murals_for_public_art_installations(X)))))& (((?[X]:(anywhere(X)&travels_domestically_frequently(X)))))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(has_a_pet_dog(X))))))& (creates_YouTube_content(jeffrey))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(jeffrey))& (creates_augmented_reality_experiences_for_mobile_applications(jeffrey))& ((![X]:((volunteers_for_local_environmental_conservation_projects(X))=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(has_a_tattoo(X))|(practices_archery(X)))))))& (practices_and_performs_acrobatic_dance_routines(jeffrey))& (uses_an_ios_phone(jeffrey))& (uses_a_Windows_laptop(jeffrey))& ((![X]:((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))& (develops_open-source_software_projects_in_their_free_time(jeffrey))

room(jeffrey)&(![X]:(room(X)=>(X='jeffrey')))& has_a_saltwater_aquarium(jeffrey)

Sophia, Carol are the only persons in the room. Not everyone in the room who is a night owl practices archery. Everyone anywhere who plays the drums enjoys landscape photography. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations if they enjoys landscape photography. If someone collects foreign coins then he/she is passionate about collecting and restoring classic cars and vice versa. If someone enjoys landscape photography then he/she enjoys deep-sea diving and exploring underwater caves, practices kickboxing and has a vast collection of first-edition science fiction novels and vice versa. Everyone outside the room does not enjoy watercolor painting and collects foreign coins if they does not collect limited-edition art prints from contemporary artists. Everyone in the room collects limited-edition art prints from contemporary artists, practices archery or drives a hybrid car. Everyone in the room builds model airplanes if they has a vast collection of first-edition science fiction novels. Everyone anywhere who plays the drums is passionate about collecting and restoring classic cars. Everyone in the room enjoys watercolor painting if they collects limited-edition art prints from contemporary artists, practices kickboxing or enjoys watercolor painting. Everyone in the room drives a hybrid car if they enjoys watercolor painting. Everyone anywhere collects foreign coins if they drives a hybrid car. Everyone in the room is a craft beer aficionado if they owns a high-end gaming PC with custom-built components. No one anywhere enjoys stargazing. Everyone in the room collects limited-edition art prints from contemporary artists if they enjoys landscape photography.

Everyone in the room is not passionate about collecting and restoring classic cars.

contradiction

room(sophia)&room(carol)&(![X]:(room(X)=>(X='sophia'|X='carol')))& (~![X]:(room(X)=>(((is_a_night_owl(X))=>(practices_archery(X))))))& (![X]:(anywhere(X)=>(((plays_the_drums(X))=>(enjoys_landscape_photography(X))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& ((![X]:((collects_foreign_coins(X))<=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))& ((![X]:((enjoys_landscape_photography(X))<=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(practices_kickboxing(X))&(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))& (![X]:(~room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))=>(((does_not_enjoy_watercolor_painting(X))&(collects_foreign_coins(X))))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(practices_archery(X))|(drives_a_hybrid_car(X))))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(builds_model_airplanes(X))))))& (![X]:(anywhere(X)=>(((plays_the_drums(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((((collects_limited-edition_art_prints_from_contemporary_artists(X))|(practices_kickboxing(X))|(enjoys_watercolor_painting(X))))=>(enjoys_watercolor_painting(X))))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(drives_a_hybrid_car(X))))))& (![X]:(anywhere(X)=>(((drives_a_hybrid_car(X))=>(collects_foreign_coins(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_a_craft_beer_aficionado(X))))))& (~?[X]:(anywhere(X)=>(enjoys_stargazing(X))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))

room(sophia)&room(carol)&(![X]:(room(X)=>(X='sophia'|X='carol')))& ![X]:(room(X)=>(is_not_passionate_about_collecting_and_restoring_classic_cars(X)))

% SZS status Unsatisfiable for 5426005319585528287883016 % SZS output start Proof for 5426005319585528287883016 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~! [X0] : (room(X0) => (predx(X0) => predj(X0))) [input p1] 48. ! [X0] : (predf(X0) <=> predn(X0)) [input p4] 51. ! [X0] : (room(X0) => (predv(X0) | predj(X0) | predu(X0))) [input p7] 54. ! [X0] : (room(X0) => ((predb(X0) | predd(X0) | predu(X0)) => predb(X0))) [input p10] 55. ! [X0] : (room(X0) => (predb(X0) => predv(X0))) [input p11] 56. ! [X0] : (anywhere(X0) => (predv(X0) => predf(X0))) [input p12] 60. ! [X0] : (room(X0) => ~predn(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 61. ! [X0] : (room(X0) => ~predn(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 60] 62. ! [X0] : (predf(X0) => predn(X0)) [unused predicate definition removal 48] 69. ~! [X0] : (room(X0) => predj(X0)) [pure predicate removal 45] 77. ! [X0] : (room(X0) => ((predb(X0) | predu(X0)) => predb(X0))) [pure predicate removal 54] 145. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 146. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 145] 147. ? [X0] : (~predj(X0) & room(X0)) [ennf transformation 69] 148. ! [X0] : (predn(X0) | ~predf(X0)) [ennf transformation 62] 151. ! [X0] : ((predv(X0) | predj(X0) | predu(X0)) | ~room(X0)) [ennf transformation 51] 152. ! [X0] : (predv(X0) | predj(X0) | predu(X0) | ~room(X0)) [flattening 151] 153. ! [X0] : ((predb(X0) | (~predb(X0) & ~predu(X0))) | ~room(X0)) [ennf transformation 77] 154. ! [X0] : (predb(X0) | (~predb(X0) & ~predu(X0)) | ~room(X0)) [flattening 153] 155. ! [X0] : ((predv(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 55] 156. ! [X0] : (predv(X0) | ~predb(X0) | ~room(X0)) [flattening 155] 157. ! [X0] : ((predf(X0) | ~predv(X0)) | ~anywhere(X0)) [ennf transformation 56] 158. ! [X0] : (predf(X0) | ~predv(X0) | ~anywhere(X0)) [flattening 157] 160. ! [X0] : (~predn(X0) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 61] 161. ! [X0] : (~predn(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 160] 163. ? [X0] : (~predj(X0) & room(X0)) => (~predj(sK0) & room(sK0)) [choice axiom] 164. ~predj(sK0) & room(sK0) [skolemisation 147,163] 165. anywhere(X0) [cnf transformation 5] 246. room(mary) [cnf transformation 146] 247. room(paul) [cnf transformation 146] 248. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 146] 249. room(sK0) [cnf transformation 164] 250. ~predj(sK0) [cnf transformation 164] 251. ~predf(X0) | predn(X0) [cnf transformation 148] 254. ~room(X0) | predj(X0) | predu(X0) | predv(X0) [cnf transformation 152] 255. ~predu(X0) | predb(X0) | ~room(X0) [cnf transformation 154] 257. ~predb(X0) | predv(X0) | ~room(X0) [cnf transformation 156] 258. predf(X0) | ~predv(X0) | ~anywhere(X0) [cnf transformation 158] 263. ~predn(X0) | ~room(X0) [cnf transformation 161] 264. ~predv(X0) | predf(X0) [subsumption resolution 258,165] 268. mary = sK0 | paul = sK0 [resolution 248,249] 270. 1 <=> paul = sK0 [avatar definition] 272. paul = sK0 <- (1) [avatar component clause 270] 274. 2 <=> mary = sK0 [avatar definition] 276. mary = sK0 <- (2) [avatar component clause 274] 277. 1 | 2 [avatar split clause 268,274,270] 279. ~predj(mary) <- (2) [backward demodulation 250,276] 280. predj(mary) | predu(mary) | predv(mary) [resolution 254,246] 281. predj(paul) | predu(paul) | predv(paul) [resolution 254,247] 282. predu(mary) | predv(mary) <- (2) [subsumption resolution 280,279] 284. 3 <=> predv(mary) [avatar definition] 285. ~predv(mary) <- (~3) [avatar component clause 284] 286. predv(mary) <- (3) [avatar component clause 284] 288. 4 <=> predu(mary) [avatar definition] 290. predu(mary) <- (4) [avatar component clause 288] 291. 3 | 4 | ~2 [avatar split clause 282,274,288,284] 293. 5 <=> predv(paul) [avatar definition] 294. ~predv(paul) <- (~5) [avatar component clause 293] 295. predv(paul) <- (5) [avatar component clause 293] 297. 6 <=> predu(paul) [avatar definition] 299. predu(paul) <- (6) [avatar component clause 297] 301. 7 <=> predj(paul) [avatar definition] 304. 5 | 6 | 7 [avatar split clause 281,301,297,293] 305. predf(mary) <- (3) [resolution 286,264] 306. predf(paul) <- (5) [resolution 295,264] 307. predn(mary) <- (3) [resolution 305,251] 308. predn(paul) <- (5) [resolution 306,251] 309. ~room(mary) <- (3) [resolution 307,263] 310. $false <- (3) [subsumption resolution 309,246] 311. ~3 [avatar contradiction clause 310] 312. predb(mary) | ~room(mary) <- (4) [resolution 290,255] 313. predb(mary) <- (4) [subsumption resolution 312,246] 314. predv(mary) | ~room(mary) <- (4) [resolution 313,257] 316. ~room(mary) <- (~3, 4) [subsumption resolution 314,285] 317. $false <- (~3, 4) [subsumption resolution 316,246] 318. 3 | ~4 [avatar contradiction clause 317] 326. ~predj(paul) <- (1) [backward demodulation 250,272] 327. ~7 | ~1 [avatar split clause 326,270,301] 329. ~room(paul) <- (5) [resolution 308,263] 330. $false <- (5) [subsumption resolution 329,247] 331. ~5 [avatar contradiction clause 330] 332. predb(paul) | ~room(paul) <- (6) [resolution 299,255] 333. predb(paul) <- (6) [subsumption resolution 332,247] 334. predv(paul) | ~room(paul) <- (6) [resolution 333,257] 336. ~room(paul) <- (~5, 6) [subsumption resolution 334,294] 337. $false <- (~5, 6) [subsumption resolution 336,247] 338. 5 | ~6 [avatar contradiction clause 337] 339. $false [avatar sat refutation 277,291,304,311,318,327,331,338] % SZS output end Proof for 5426005319585528287883016 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Heidi, Christopher are the only persons in the room. Everyone in the room does not maintain a large, organic vegetable garden year-round. Everyone outside the room neither does not participate in citizen science projects related to wildlife monitoring nor does not frequently participates in hackathons and coding competitions. Heidi either is not a wine connoisseur with a private cellar of vintage wines or does not maintain a large, organic vegetable garden year-round but not both. Everyone in the room does not collect limited-edition art prints from contemporary artists. Everyone in the room does not participate in citizen science projects related to wildlife monitoring. Christopher does not maintain a large, organic vegetable garden year-round. Christopher does not participate in citizen science projects related to wildlife monitoring. Heidi does not collect limited-edition art prints from contemporary artists, collects limited-edition art prints from contemporary artists or does not frequently participates in hackathons and coding competitions. Everyone anywhere collects limited-edition art prints from contemporary artists, does not enjoy writing detailed reviews of new and classic board games or does not maintain a large, organic vegetable garden year-round. Everyone anywhere does not maintain a large, organic vegetable garden year-round. Everyone in the room does not frequently participates in hackathons and coding competitions. Heidi does not frequently participates in hackathons and coding competitions. Heidi does not enjoy writing detailed reviews of new and classic board games.

Christopher enjoys writing detailed reviews of new and classic board games.

neutral

room(heidi)&room(christopher)&(![X]:(room(X)=>(X='heidi'|X='christopher')))& (![X]:(room(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))& (![X]:(~room(X)=>(~((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))& (((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(heidi))<~>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(heidi))))& (![X]:(room(X)=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))& (![X]:(room(X)=>(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))& (does_not_maintain_a_large,_organic_vegetable_garden_year-round(christopher))& (does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(christopher))& (((does_not_collect_limited-edition_art_prints_from_contemporary_artists(heidi))|(collects_limited-edition_art_prints_from_contemporary_artists(heidi))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(heidi))))& (![X]:(anywhere(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(anywhere(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))& (![X]:(room(X)=>(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))& (does_not_frequently_participates_in_hackathons_and_coding_competitions(heidi))& (does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(heidi))

room(heidi)&room(christopher)&(![X]:(room(X)=>(X='heidi'|X='christopher')))& enjoys_writing_detailed_reviews_of_new_and_classic_board_games(christopher)

Gladys is the only person in the room. Either 'everyone in the room plays as a goalkeeper for a local amateur soccer team or does not enjoy mountain biking' or 'Gladys owns a smart tv' but not both. If 'not everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or is passionate about collecting and restoring classic cars' then 'everyone in the room who is not an enthusiastic bird watcher who travels for rare sightings writes and illustrates their own graphic novels'. 'Gladys plays as a goalkeeper for a local amateur soccer team' if 'everyone in the room does not practice digital art or practices digital art' and vice versa. Not everyone outside the room either bakes bread at home or collects luxury watches but not both if they trains for and competes in international triathlons. Gladys is an enthusiastic bird watcher who travels for rare sightings. Gladys does not have completed a triathlon.

Gladys is an avid collector of autographed memorabilia from famous musicians, has completed a triathlon and is a client of Meta.

contradiction

room(gladys)&(![X]:(room(X)=>(X='gladys')))& ((![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))<~>(owns_a_smart_tv(gladys)))& ((~![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>(![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(writes_and_illustrates_their_own_graphic_novels(X)))))))& ((![X]:(room(X)=>(((practices_digital_art(X))|(does_not_practice_digital_art(X))))))<=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(gladys)))& (~![X]:(~room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(((bakes_bread_at_home(X))<~>(collects_luxury_watches(X))))))))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(gladys))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (does_not_have_completed_a_triathlon(gladys))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(~room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(is_not_a_chess_master_who_participates_in_national_tournaments(X))&(creates_YouTube_content(X))))))))& (((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(gladys))&(collects_first_edition_books(gladys))&(collects_luxury_watches(gladys))))& (~![X]:(~room(X)=>(((is_a_client_of_Meta(X))=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(trains_for_and_competes_in_international_triathlons(X))|(collects_vintage_stamps(X))))))))& (![X]:(room(X)=>(((practices_digital_art(X))=>(uses_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))<=>(((bakes_bread_at_home(X))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(creates_YouTube_content(X))))))))& ((![X]:((((reads_mystery_novels(X))<~>(does_not_collect_first_edition_books(X))))=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))<~>(owns_a_smart_tv(X)))))))

room(gladys)&(![X]:(room(X)=>(X='gladys')))& ((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(gladys))&(has_completed_a_triathlon(gladys))&(is_a_client_of_Meta(gladys)))

% SZS status Unsatisfiable for 2032090829314138891117313 % SZS output start Proof for 2032090829314138891117313 51. ~preda(mary) [input p7] 59. predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 62. preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [pure predicate removal 59] 65. preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [pure predicate removal 62] 157. preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 65] 270. ~preda(mary) [cnf transformation 51] 286. preda(mary) [cnf transformation 157] 335. $false [subsumption resolution 286,270] % SZS output end Proof for 2032090829314138891117313 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ellen, Christopher are the only persons in the room. “If someone enjoys virtual reality gaming then he/she collects vintage vinyl records or enjoys stargazing or both” if “it is not the case that “it is not the case that “Ellen either practices digital art or enjoys stargazing but not both”””. “At least one person in the room is an avid collector of autographed memorabilia from famous musicians” if “Christopher owns an Android phone”. “Only one person in the room owns a smartwatch” if “Ellen enjoys kayaking”. If “it is not the case that “Christopher hosts a popular podcast about emerging technologies”” then “only one person in the room does not host a popular podcast about emerging technologies”. “It is not the case that “it is not the case that “Ellen collects vintage vinyl records””” if “Christopher enjoys virtual reality gaming” and vice versa. “Ellen collects vintage vinyl records” if “Ellen hosts a popular podcast about emerging technologies” and vice versa. “Christopher enjoys virtual reality gaming or practices digital art or both” if “Christopher uses contact lenses” and vice versa. If “someone anywhere does practice yoga or does not make homemade pastries or both” then “if someone owns a smart tv then he/she is a chess master who participates in national tournaments and vice versa”. Someone anywhere does practice yoga or does not make homemade pastries or both. Only one person anywhere does not own an Android phone. If someone writes poetry then he/she trains for and competes in international triathlons and vice versa. More than one person in the room practices digital art. More than one person in the room either uses contact lenses or hosts a popular podcast about emerging technologies but not both.

Ellen hosts a popular podcast about emerging technologies.

entailment

room(ellen)&room(christopher)&(![X]:(room(X)=>(X='ellen'|X='christopher')))& ((~(~(((practices_digital_art(ellen))<~>(enjoys_stargazing(ellen))))))=>((![X]:((enjoys_virtual_reality_gaming(X))=>(((collects_vintage_vinyl_records(X))|(enjoys_stargazing(X))))))))& ((owns_an_Android_phone(christopher))=>(((?[X]:(room(X)&is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& ((enjoys_kayaking(ellen))=>(((?[X]:(room(X)&owns_a_smartwatch(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_smartwatch(X))&(owns_a_smartwatch(Y)))=>(X=Y))))))& ((~(hosts_a_popular_podcast_about_emerging_technologies(christopher)))=>(((?[X]:(room(X)&does_not_host_a_popular_podcast_about_emerging_technologies(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_host_a_popular_podcast_about_emerging_technologies(X))&(does_not_host_a_popular_podcast_about_emerging_technologies(Y)))=>(X=Y))))))& ((enjoys_virtual_reality_gaming(christopher))<=>(~(~(collects_vintage_vinyl_records(ellen)))))& ((hosts_a_popular_podcast_about_emerging_technologies(ellen))<=>(collects_vintage_vinyl_records(ellen)))& ((uses_contact_lenses(christopher))<=>(((enjoys_virtual_reality_gaming(christopher))|(practices_digital_art(christopher)))))& ((?[X]:(anywhere(X)&(((does_practice_yoga(X))|(does_not_make_homemade_pastries(X))))))=>((![X]:((owns_a_smart_tv(X))<=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (?[X]:(anywhere(X)&(((does_practice_yoga(X))|(does_not_make_homemade_pastries(X))))))& (((?[X]:(anywhere(X)&does_not_own_an_Android_phone(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(does_not_own_an_Android_phone(X))&(does_not_own_an_Android_phone(Y)))=>(X=Y)))))& ((![X]:((writes_poetry(X))<=>(trains_for_and_competes_in_international_triathlons(X)))))& ((![X]:((owns_a_smart_tv(X))<=>(is_a_chess_master_who_participates_in_national_tournaments(X)))))& ((?[X,Y]:(room(X)&room(Y)&(practices_digital_art(X)&practices_digital_art(Y))&(X!=Y))))& ((?[X,Y]:(room(X)&room(Y)&(((uses_contact_lenses(X))<~>(hosts_a_popular_podcast_about_emerging_technologies(X)))&((uses_contact_lenses(Y))<~>(hosts_a_popular_podcast_about_emerging_technologies(Y))))&(X!=Y))))& ((![X]:((((does_not_practice_graffiti_art(X))|(travels_domestically_frequently(X))))=>(practices_digital_art(X)))))& ((![X]:((((can_play_the_guitar(X))|(does_not_enjoy_virtual_reality_gaming(X))))<=>(((owns_an_Android_phone(X))|(collects_vintage_vinyl_records(X)))))))& (((?[X]:(anywhere(X)&does_not_enjoy_kayaking(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(does_not_enjoy_kayaking(X))&(does_not_enjoy_kayaking(Y)))=>(X=Y)))))& (((?[X]:(room(X)&owns_a_smartwatch(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_smartwatch(X))&(owns_a_smartwatch(Y)))=>(X=Y)))))

room(ellen)&room(christopher)&(![X]:(room(X)=>(X='ellen'|X='christopher')))& hosts_a_popular_podcast_about_emerging_technologies(ellen)

% SZS status Unsatisfiable for 1581124854000053194662661 % SZS output start Proof for 1581124854000053194662661 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. ~predu(paul) => (! [X0,X1] : ((~predu(X1) & ~predu(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~predu(X0) & room(X0))) [input p4] 51. predt(paul) <=> (predq(paul) | predo(paul)) [input p7] 57. ? [X0,X1] : (X0 != X1 & predq(X1) & predq(X0) & room(X1) & room(X0)) [input p13] 58. ? [X0,X1] : (X0 != X1 & (predt(X1) <~> predu(X1)) & (predt(X0) <~> predu(X0)) & room(X1) & room(X0)) [input p14] 63. ~(predu(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 66. ~predu(paul) => (! [X0,X1] : ((~predu(X1) & ~predu(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~predu(X2) & room(X2))) [rectify 48] 145. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 146. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 145] 152. (! [X0,X1] : (X0 = X1 | (predu(X1) | predu(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (~predu(X2) & room(X2))) | predu(paul) [ennf transformation 66] 153. (! [X0,X1] : (X0 = X1 | predu(X1) | predu(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~predu(X2) & room(X2))) | predu(paul) [flattening 152] 161. ~predu(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 63] 162. ~predu(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 161] 169. ? [X2] : (~predu(X2) & room(X2)) => (~predu(sK2) & room(sK2)) [choice axiom] 170. (! [X0,X1] : (X0 = X1 | predu(X1) | predu(X0) | ~room(X1) | ~room(X0)) & (~predu(sK2) & room(sK2))) | predu(paul) [skolemisation 153,169] 173. (predt(paul) | (~predq(paul) & ~predo(paul))) & ((predq(paul) | predo(paul)) | ~predt(paul)) [nnf transformation 51] 174. (predt(paul) | (~predq(paul) & ~predo(paul))) & (predq(paul) | predo(paul) | ~predt(paul)) [flattening 173] 182. ? [X0,X1] : (X0 != X1 & predq(X1) & predq(X0) & room(X1) & room(X0)) => (sK5 != sK6 & predq(sK6) & predq(sK5) & room(sK6) & room(sK5)) [choice axiom] 183. sK5 != sK6 & predq(sK6) & predq(sK5) & room(sK6) & room(sK5) [skolemisation 57,182] 184. ? [X0,X1] : (X0 != X1 & ((~predu(X1) | ~predt(X1)) & (predu(X1) | predt(X1))) & ((~predu(X0) | ~predt(X0)) & (predu(X0) | predt(X0))) & room(X1) & room(X0)) [nnf transformation 58] 185. ? [X0,X1] : (X0 != X1 & (~predu(X1) | ~predt(X1)) & (predu(X1) | predt(X1)) & (~predu(X0) | ~predt(X0)) & (predu(X0) | predt(X0)) & room(X1) & room(X0)) [flattening 184] 186. ? [X0,X1] : (X0 != X1 & (~predu(X1) | ~predt(X1)) & (predu(X1) | predt(X1)) & (~predu(X0) | ~predt(X0)) & (predu(X0) | predt(X0)) & room(X1) & room(X0)) => (sK7 != sK8 & (~predu(sK8) | ~predt(sK8)) & (predu(sK8) | predt(sK8)) & (~predu(sK7) | ~predt(sK7)) & (predu(sK7) | predt(sK7)) & room(sK8) & room(sK7)) [choice axiom] 187. sK7 != sK8 & (~predu(sK8) | ~predt(sK8)) & (predu(sK8) | predt(sK8)) & (~predu(sK7) | ~predt(sK7)) & (predu(sK7) | predt(sK7)) & room(sK8) & room(sK7) [skolemisation 185,186] 194. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK11 & mary != sK11 & room(sK11)) [choice axiom] 195. ~predu(mary) | (paul != sK11 & mary != sK11 & room(sK11)) | ~room(paul) | ~room(mary) [skolemisation 162,194] 241. mary != paul [cnf transformation 43] 277. room(mary) [cnf transformation 146] 278. room(paul) [cnf transformation 146] 279. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 146] 288. X0 = X1 | predu(X1) | predu(X0) | ~room(X1) | ~room(X0) | predu(paul) [cnf transformation 170] 295. predt(paul) | ~predq(paul) [cnf transformation 174] 307. room(sK5) [cnf transformation 183] 308. room(sK6) [cnf transformation 183] 309. predq(sK5) [cnf transformation 183] 310. predq(sK6) [cnf transformation 183] 311. sK5 != sK6 [cnf transformation 183] 312. room(sK7) [cnf transformation 187] 313. room(sK8) [cnf transformation 187] 315. ~predu(sK7) | ~predt(sK7) [cnf transformation 187] 317. ~predu(sK8) | ~predt(sK8) [cnf transformation 187] 318. sK7 != sK8 [cnf transformation 187] 329. ~predu(mary) | room(sK11) | ~room(paul) | ~room(mary) [cnf transformation 195] 330. ~predu(mary) | mary != sK11 | ~room(paul) | ~room(mary) [cnf transformation 195] 331. ~predu(mary) | paul != sK11 | ~room(paul) | ~room(mary) [cnf transformation 195] 373. 10 <=> predu(paul) [avatar definition] 375. predu(paul) <- (10) [avatar component clause 373] 377. 11 <=> ! [X0,X1] : (X0 = X1 | ~room(X0) | ~room(X1) | predu(X0) | predu(X1)) [avatar definition] 378. ~room(X1) | ~room(X0) | X0 = X1 | predu(X0) | predu(X1) <- (11) [avatar component clause 377] 379. 10 | 11 [avatar split clause 288,377,373] 401. 16 <=> predu(mary) [avatar definition] 402. ~predu(mary) <- (~16) [avatar component clause 401] 407. 17 <=> predq(paul) [avatar definition] 409. ~predq(paul) <- (~17) [avatar component clause 407] 411. 18 <=> predt(paul) [avatar definition] 413. predt(paul) <- (18) [avatar component clause 411] 414. ~17 | 18 [avatar split clause 295,411,407] 451. 25 <=> predt(sK8) [avatar definition] 453. ~predt(sK8) <- (~25) [avatar component clause 451] 455. 26 <=> predu(sK8) [avatar definition] 456. predu(sK8) <- (26) [avatar component clause 455] 457. ~predu(sK8) <- (~26) [avatar component clause 455] 458. ~25 | ~26 [avatar split clause 317,455,451] 461. 27 <=> predt(sK7) [avatar definition] 463. ~predt(sK7) <- (~27) [avatar component clause 461] 465. 28 <=> predu(sK7) [avatar definition] 467. ~predu(sK7) <- (~28) [avatar component clause 465] 468. ~27 | ~28 [avatar split clause 315,465,461] 473. ~predu(mary) | paul != sK11 | ~room(mary) [subsumption resolution 331,278] 474. ~predu(mary) | paul != sK11 [subsumption resolution 473,277] 476. 29 <=> paul = sK11 [avatar definition] 479. ~29 | ~16 [avatar split clause 474,401,476] 480. ~predu(mary) | mary != sK11 | ~room(mary) [subsumption resolution 330,278] 481. ~predu(mary) | mary != sK11 [subsumption resolution 480,277] 483. 30 <=> mary = sK11 [avatar definition] 485. mary != sK11 <- (~30) [avatar component clause 483] 486. ~30 | ~16 [avatar split clause 481,401,483] 487. ~predu(mary) | room(sK11) | ~room(mary) [subsumption resolution 329,278] 488. ~predu(mary) | room(sK11) [subsumption resolution 487,277] 490. 31 <=> room(sK11) [avatar definition] 492. room(sK11) <- (31) [avatar component clause 490] 493. 31 | ~16 [avatar split clause 488,401,490] 536. mary = sK5 | paul = sK5 [resolution 279,307] 537. mary = sK6 | paul = sK6 [resolution 279,308] 538. mary = sK7 | paul = sK7 [resolution 279,312] 539. mary = sK8 | paul = sK8 [resolution 279,313] 551. 36 <=> paul = sK5 [avatar definition] 553. paul = sK5 <- (36) [avatar component clause 551] 555. 37 <=> mary = sK5 [avatar definition] 557. mary = sK5 <- (37) [avatar component clause 555] 558. 36 | 37 [avatar split clause 536,555,551] 560. 38 <=> paul = sK6 [avatar definition] 562. paul = sK6 <- (38) [avatar component clause 560] 564. 39 <=> mary = sK6 [avatar definition] 567. 38 | 39 [avatar split clause 537,564,560] 569. 40 <=> paul = sK7 [avatar definition] 571. paul = sK7 <- (40) [avatar component clause 569] 573. 41 <=> mary = sK7 [avatar definition] 576. 40 | 41 [avatar split clause 538,573,569] 578. 42 <=> paul = sK8 [avatar definition] 580. paul = sK8 <- (42) [avatar component clause 578] 582. 43 <=> mary = sK8 [avatar definition] 584. mary = sK8 <- (43) [avatar component clause 582] 585. 42 | 43 [avatar split clause 539,582,578] 606. ~predu(paul) <- (~28, 40) [backward demodulation 467,571] 609. $false <- (10, ~28, 40) [subsumption resolution 606,375] 610. ~10 | 28 | ~40 [avatar contradiction clause 609] 618. predq(paul) <- (36) [backward demodulation 309,553] 619. $false <- (~17, 36) [subsumption resolution 618,409] 620. 17 | ~36 [avatar contradiction clause 619] 652. ~predt(paul) <- (~25, 42) [forward demodulation 453,580] 661. ~18 | 25 | ~42 [avatar split clause 652,578,451,411] 663. mary != sK6 <- (37) [forward demodulation 311,557] 664. ~39 | ~37 [avatar split clause 663,555,564] 670. predq(paul) <- (38) [backward demodulation 310,562] 671. 17 | ~38 [avatar split clause 670,560,407] 674. ~predu(paul) <- (~26, 42) [forward demodulation 457,580] 675. ~10 | 26 | ~42 [avatar split clause 674,578,455,373] 679. mary = sK11 | paul = sK11 <- (31) [resolution 492,279] 680. paul = sK11 <- (~30, 31) [subsumption resolution 679,485] 683. 29 | 30 | ~31 [avatar split clause 680,490,483,476] 743. ~room(X0) | mary = X0 | predu(X0) | predu(mary) <- (11) [resolution 378,277] 745. ~room(X0) | mary = X0 | predu(X0) <- (11, ~16) [subsumption resolution 743,402] 748. mary = paul | predu(paul) <- (11, ~16) [resolution 745,278] 749. predu(paul) <- (11, ~16) [subsumption resolution 748,241] 752. 10 | ~11 | 16 [avatar split clause 749,401,377,373] 761. predu(mary) <- (26, 43) [forward demodulation 456,584] 762. $false <- (~16, 26, 43) [subsumption resolution 761,402] 763. 16 | ~26 | ~43 [avatar contradiction clause 762] 767. mary != sK7 <- (43) [forward demodulation 318,584] 768. ~41 | ~43 [avatar split clause 767,582,573] 771. ~predt(paul) <- (~27, 40) [forward demodulation 463,571] 772. $false <- (18, ~27, 40) [subsumption resolution 771,413] 773. ~18 | 27 | ~40 [avatar contradiction clause 772] 776. $false [avatar sat refutation 379,414,458,468,479,486,493,558,567,576,585,610,620,661,664,671,675,683,752,763,768,773] % SZS output end Proof for 1581124854000053194662661 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s % ------------------------------ % ------------------------------

There is a room. No one in the room makes homemade pastries or is not an active member of a local robotics club. Everyone anywhere who is an active member of a local robotics club develops open-source software projects in their free time. Everyone in the room frequently participates in hackathons and coding competitions or does not develop open-source software projects in their free time. Everyone in the room who frequently participates in hackathons and coding competitions is a culinary enthusiast who experiments with international cuisines, is an active member of a local robotics club and is a client of Costco.

Everyone outside the room is a culinary enthusiast who experiments with international cuisines.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((is_right-handed(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(~![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))))& ((![X]:(~room(X)=>(((knows_morse_code(X))|(is_not_a_coffee_connoisseur(X))))))=>(![X]:(~room(X)=>(((has_a_saltwater_aquarium(X))<=(is_not_a_coffee_connoisseur(X)))))))& (![X]:(anywhere(X)=>(((has_a_saltwater_aquarium(X))=>(~((does_not_collect_action_figures(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))))& (![X]:(room(X)=>(((~((does_not_collect_action_figures(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))=>(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(is_an_avid_hiker(X))))))& (~?[X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))|(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(~room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(anywhere(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(is_an_avid_hiker(X))))))& (![X]:(room(X)=>(((is_an_avid_hiker(X))=>(creates_YouTube_content(X))))))& (((?[X]:(room(X)&is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<=(enjoys_skydiving(X))))))& (![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(is_an_active_member_of_a_local_robotics_club(X))&(is_a_client_of_Costco(X))))))))& (?[X]:(room(X)&(can_play_the_harmonica(X))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<~>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))))& (![X]:(anywhere(X)=>(((is_an_avid_hiker(X))=>(is_a_coffee_connoisseur(X))))))& (![X]:(anywhere(X)=>(((makes_homemade_pastries(X))=>(knows_morse_code(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(~((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(is_a_coffee_connoisseur(X))))))))& (![X]:(~room(X)=>(((~((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(is_a_coffee_connoisseur(X))))|(does_not_enjoy_trail_running(X))))))

(there_is_a_room)& ![X]:(~room(X)=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))

% SZS status Unsatisfiable for 1352251389946469991837110 % SZS output start Proof for 1352251389946469991837110 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 52. ~? [X0] : (room(X0) => (predo(X0) | ~predl(X0))) [input p8] 55. ! [X0] : (anywhere(X0) => (predl(X0) => preds(X0))) [input p11] 60. ! [X0] : (room(X0) => (predi(X0) | ~preds(X0))) [input p16] 61. ! [X0] : (room(X0) => (predi(X0) => (predx(X0) & predl(X0) & predc(X0)))) [input p17] 68. ~(! [X0] : (~room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 78. ~? [X0] : (room(X0) => ~predl(X0)) [pure predicate removal 52] 91. ! [X0] : (room(X0) => (predi(X0) => (predl(X0) & predc(X0)))) [pure predicate removal 61] 166. ! [X0] : (predl(X0) & room(X0)) [ennf transformation 78] 167. ! [X0] : ((preds(X0) | ~predl(X0)) | ~anywhere(X0)) [ennf transformation 55] 168. ! [X0] : (preds(X0) | ~predl(X0) | ~anywhere(X0)) [flattening 167] 169. ! [X0] : ((predi(X0) | ~preds(X0)) | ~room(X0)) [ennf transformation 60] 170. ! [X0] : (predi(X0) | ~preds(X0) | ~room(X0)) [flattening 169] 171. ! [X0] : (((predl(X0) & predc(X0)) | ~predi(X0)) | ~room(X0)) [ennf transformation 91] 172. ! [X0] : ((predl(X0) & predc(X0)) | ~predi(X0) | ~room(X0)) [flattening 171] 175. ? [X0] : (~predc(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 68] 186. ? [X0] : (~predc(X0) & ~room(X0)) => (~predc(sK4) & ~room(sK4)) [choice axiom] 187. (~predc(sK4) & ~room(sK4)) | ~there_is_a_room [skolemisation 175,186] 188. anywhere(X0) [cnf transformation 5] 269. there_is_a_room [cnf transformation 44] 274. room(X0) [cnf transformation 166] 275. predl(X0) [cnf transformation 166] 276. preds(X0) | ~predl(X0) | ~anywhere(X0) [cnf transformation 168] 278. predi(X0) | ~preds(X0) | ~room(X0) [cnf transformation 170] 279. predc(X0) | ~predi(X0) | ~room(X0) [cnf transformation 172] 285. ~predc(sK4) | ~there_is_a_room [cnf transformation 187] 306. preds(X0) | ~anywhere(X0) [subsumption resolution 276,275] 307. preds(X0) [subsumption resolution 306,188] 308. predi(X0) | ~room(X0) [subsumption resolution 278,307] 309. predi(X0) [subsumption resolution 308,274] 310. predc(X0) | ~room(X0) [subsumption resolution 279,309] 311. predc(X0) [subsumption resolution 310,274] 315. ~there_is_a_room [subsumption resolution 285,311] 316. $false [subsumption resolution 315,269] % SZS output end Proof for 1352251389946469991837110 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Bonnie is the only person in the room. Bonnie is a client of LVMH. Not everyone in the room collect rare sneakers only if they competes in national level swimming championships. At least one person in the room collect rare sneakers. If someone collect rare sneakers then he/she maintains a personal blog focused on cybersecurity tips and vice versa. Everyone anywhere who is a skilled home brewer experimenting with craft beer recipes enjoys stand-up paddleboarding. It is not the case that “at least one person in the room competes in national level swimming championships”. Someone in the room does not own a smartwatch. If someone collects vintage stamps then he/she builds model airplanes and vice versa. Only one person in the room collects antique clocks. Someone in the room maintains a personal blog focused on cybersecurity tips. Bonnie is right-handed or enjoys stand-up paddleboarding or both.

It is not the case that “it is not the case that “Bonnie uses a Windows laptop””.

neutral

room(bonnie)&(![X]:(room(X)=>(X='bonnie')))& (is_a_client_of_LVMH(bonnie))& (~![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))<=(collect_rare_sneakers(X))))))& (((?[X]:(room(X)&collect_rare_sneakers(X)))))& ((![X]:((collect_rare_sneakers(X))<=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))& (![X]:(anywhere(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(enjoys_stand-up_paddleboarding(X))))))& (~(((?[X]:(room(X)&competes_in_national_level_swimming_championships(X))))))& (?[X]:(room(X)&(does_not_own_a_smartwatch(X))))& ((![X]:((collects_vintage_stamps(X))<=>(builds_model_airplanes(X)))))& (((?[X]:(room(X)&collects_antique_clocks(X)))&(![X,Y]:((room(X)&room(Y)&(collects_antique_clocks(X))&(collects_antique_clocks(Y)))=>(X=Y)))))& (?[X]:(room(X)&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))& (((is_right-handed(bonnie))|(enjoys_stand-up_paddleboarding(bonnie))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(does_not_collect_rare_and_antique_scientific_instruments(X))))))& ((bonnie_dream=>(~(((?[X]:(room(X)&is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))))& (?[X]:(room(X)&(collects_vintage_stamps(X))))& (?[X]:(room(X)&(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(is_a_client_of_LVMH(X))))))& (~(?[X]:(room(X)&(does_not_collect_antique_clocks(X)))))& (enjoys_stand-up_paddleboarding(bonnie))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(bonnie))& (~(?[X]:(room(X)&(collects_rare_and_antique_scientific_instruments(X)))))& ((bonnie_dream=>((![X]:((enjoys_stand-up_paddleboarding(X))<=>(collect_rare_sneakers(X)))))))& (((?[X]:(room(X)&maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))&(![X,Y]:((room(X)&room(Y)&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(Y)))=>(X=Y)))))& (?[X]:(room(X)&(enjoys_stand-up_paddleboarding(X))))

room(bonnie)&(![X]:(room(X)=>(X='bonnie')))& ~(~(uses_a_Windows_laptop(bonnie)))

Daniel, Heidi, Kent are the only persons in the room. Everyone in the room is not a creative european only if they is not a old funny wise european. Everyone in the room is not a calm person or is not a brave happy strong european or both only if they neither is wise nor is not a quiet calm wise tourist. Everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations only if they is not a wine connoisseur. Everyone in the room is calm. It is true that "it is true that "everyone in the room is kind only if they is not a curious european"". Not everyone in the room is not a patient tourist only if they is not a quiet funny humble european. Everyone in the room does not enjoy writing detailed reviews of new and classic board games and does not practice yoga only if they is creative. Daniel and Heidi are kind. Kent is the least old outside the room. Everyone outside the room is not a tall curious person only if they is kind. Everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations if and only if they does not have a vast collection of first-edition science fiction novels. Daniel is not a humble tourist. Everyone outside the room neither does not enjoy stand-up paddleboarding nor hates Bertha only if they is not a quiet european. Everyone in the room is not a curious tourist. Everyone in the room is not a generous funny strong european only if they is not a humble curious kind tourist. Everyone outside the room does not enjoy stargazing or does not enjoy stand-up paddleboarding or both only if they is not dedicated to sustainable living and zero-waste practices.

Heidi and Daniel are not a funny quiet tall generous wise persons.

neutral

room(daniel)&room(heidi)&room(kent)&(![X]:(room(X)=>(X='daniel'|X='heidi'|X='kent')))& (![X]:(room(X)=>(((~(old(X)&funny(X)&wise(X)&european(X)))<=(~(creative(X)&european(X)))))))& (![X]:(room(X)=>(((~((wise(X))|(~(quiet(X)&calm(X)&wise(X)&tourist(X)))))<=(((~(calm(X)&person(X)))|(~(brave(X)&happy(X)&strong(X)&european(X)))))))))& (![X]:(room(X)=>(((is_not_a_wine_connoisseur(X))<=(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(calm(X))))& (![X]:(room(X)=>(((~(curious(X)&european(X)))<=(kind(X))))))& (~![X]:(room(X)=>(((~(quiet(X)&funny(X)&humble(X)&european(X)))<=(~(patient(X)&tourist(X)))))))& (![X]:(room(X)=>(((creative(X))<=(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))&(does_not_practice_yoga(X))))))))& (kind(daniel)&kind(heidi))& (![X]:((~room(X)&(X!=kent))=>older(kent,X)))& (![X]:(~room(X)=>(((kind(X))<=(~(tall(X)&curious(X)&person(X)))))))& (![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=>(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (~(humble(daniel)&tourist(daniel)))& (![X]:(~room(X)=>(((~(quiet(X)&european(X)))<=(~((does_not_enjoy_stand-up_paddleboarding(X))|(hate(bertha,X))))))))& (![X]:(room(X)=>(~(curious(X)&tourist(X)))))& (![X]:(room(X)=>(((~(humble(X)&curious(X)&kind(X)&tourist(X)))<=(~(generous(X)&funny(X)&strong(X)&european(X)))))))& (![X]:(~room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))<=(((does_not_enjoy_stargazing(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))))

room(daniel)&room(heidi)&room(kent)&(![X]:(room(X)=>(X='daniel'|X='heidi'|X='kent')))& ~(funny(heidi)&quiet(heidi)&tall(heidi)&generous(heidi)&wise(heidi)&person(heidi))&~(funny(daniel)&quiet(daniel)&tall(daniel)&generous(daniel)&wise(daniel)&person(daniel))

There is a room. If 'everyone in the room is not a client of Costco or is a wine connoisseur with a private cellar of vintage wines' then 'someone in the room can play the harmonica'. 'Everyone in the room who can play the harmonica, plays video games or uses contact lenses uses contact lenses' if 'someone anywhere enjoys skydiving, can play the harmonica or creates bespoke furniture pieces from reclaimed wood'. 'Everyone outside the room is not a client of Costco if they can play the harmonica and vice versa' if 'everyone in the room is not a client of Costco or uses contact lenses'. Everyone in the room who can play the harmonica is a wine connoisseur with a private cellar of vintage wines. Everyone outside the room is not a client of Costco if they can play the harmonica and vice versa. Everyone in the room who uses contact lenses, can play the harmonica and is a client of Costco is a client of Costco. No one in the room who is a client of Costco practices zumba. Everyone anywhere practices zumba only if they volunteers for local environmental conservation projects. Everyone in the room who volunteers for local environmental conservation projects either is a drone photographer or uses contact lenses but not both. No one in the room is a client of Costco only if they either practices zumba or creates bespoke furniture pieces from reclaimed wood but not both. Everyone in the room either practices zumba or creates bespoke furniture pieces from reclaimed wood but not both only if they enjoys skydiving, uses contact lenses or enjoys camping and organizing outdoor survival workshops.

Everyone in the room does not play video games or practices zumba.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(is_not_a_client_of_Costco(X))))))=>(?[X]:(room(X)&(can_play_the_harmonica(X)))))& ((?[X]:(anywhere(X)&(((enjoys_skydiving(X))|(can_play_the_harmonica(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>(![X]:(room(X)=>(((((can_play_the_harmonica(X))|(plays_video_games(X))|(uses_contact_lenses(X))))=>(uses_contact_lenses(X)))))))& ((![X]:(room(X)=>(((uses_contact_lenses(X))|(is_not_a_client_of_Costco(X))))))=>(![X]:(~room(X)=>(((is_not_a_client_of_Costco(X))<=>(can_play_the_harmonica(X)))))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(~room(X)=>(((is_not_a_client_of_Costco(X))<=>(can_play_the_harmonica(X))))))& (![X]:(room(X)=>(((((uses_contact_lenses(X))&(can_play_the_harmonica(X))&(is_a_client_of_Costco(X))))=>(is_a_client_of_Costco(X))))))& (~?[X]:(room(X)=>(((is_a_client_of_Costco(X))=>(practices_zumba(X))))))& (![X]:(anywhere(X)=>(((volunteers_for_local_environmental_conservation_projects(X))<=(practices_zumba(X))))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(((is_a_drone_photographer(X))<~>(uses_contact_lenses(X))))))))& (~?[X]:(room(X)=>(((((practices_zumba(X))<~>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))<=(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((((enjoys_skydiving(X))|(uses_contact_lenses(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))<=(((practices_zumba(X))<~>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))& (![X]:(room(X)=>(((((enjoys_skydiving(X))|(uses_contact_lenses(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))|(does_not_use_contact_lenses(X))))))& (?[X]:(room(X)&(((plays_video_games(X))|(uses_contact_lenses(X))|(can_play_the_harmonica(X))))))& (?[X]:(anywhere(X)&(is_a_client_of_Costco(X))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))<=(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))<=(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))|(is_not_a_client_of_Costco(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((practices_zumba(X))|(does_not_play_video_games(X)))))

Rena, Daniel, Jacob, Kathryn are the only persons in the room. “No one in the room is older than Dawn” only if “Rena who is richer than Dawn neither is a old person nor is calm”. If “someone anywhere is older than Dawn, is tall or is richer than Dawn” then “only one person outside the room is richer than Dawn” otherwise “Rena is the richest in the room”. “Rena and Kathryn are richer than Dawn, are not kind and are tall” if “Jacob is older than Dawn” and vice versa. If “it is not the case that “Jacob is wise”” then “at least one person in the room is richer than Dawn”. If “at least one person in the room is richer than Dawn” then “Kathryn is a funny person and is quieter than Dawn”. “Rena is a generous kind quiet person” if “Jacob is not funny” and vice versa. If “Daniel is happy” then “Rena is a curious quiet person”. Jacob is not a kind creative old funny strong person. Everyone in the room is a patient calm wise person. All strong persons are patient. Daniel is a brave calm person. Everyone in the room who is a kind person is older than Dawn. Someone in the room is not not generous. Rena is a old quiet funny curious patient calm person or is a calm quiet happy old person or both. All brave persons are creative. All kind persons are happy. If someone is a brave person then he/she is older than Dawn. Everyone outside the room is richer than Dawn only if they neither is kind nor is older than Dawn.

Everyone anywhere neither is a happy person nor is a kind happy person.

neutral

room(rena)&room(daniel)&room(jacob)&room(kathryn)&(![X]:(room(X)=>(X='rena'|X='daniel'|X='jacob'|X='kathryn')))& ((~?[X]:(room(X)=>(older(dawn,X))))=>((richer(dawn,rena))&(~((old(rena)&person(rena))|(calm(rena))))))& (((?[X]:(anywhere(X)&(((older(dawn,X))|(tall(X))|(richer(dawn,X))))))=>(((?[X]:(~room(X)&richer(dawn,X)))&(![X,Y]:((~room(X)&~room(Y)&(richer(dawn,X))&(richer(dawn,Y)))=>(X=Y))))))&((~(?[X]:(anywhere(X)&(((older(dawn,X))|(tall(X))|(richer(dawn,X)))))))=>(![X]:((room(X)&(X!=rena))=>richer(X,rena)))))& ((older(dawn,jacob))<=>(((richer(dawn,rena))&(~kind(rena))&(tall(rena)))&((richer(dawn,kathryn))&(~kind(kathryn))&(tall(kathryn)))))& (((~(wise(jacob)))=>(((?[X]:(room(X)&richer(dawn,X))))))& ((((?[X]:(room(X)&richer(dawn,X)))))=>(((funny(kathryn)&person(kathryn))&(quieter(dawn,kathryn))))))& ((~funny(jacob))<=>(generous(rena)&kind(rena)&quiet(rena)&person(rena)))& ((happy(daniel))=>(curious(rena)&quiet(rena)&person(rena)))& (~(kind(jacob)&creative(jacob)&old(jacob)&funny(jacob)&strong(jacob)&person(jacob)))& (![X]:(room(X)=>(patient(X)&calm(X)&wise(X)&person(X))))& (![X]:(strong(X)=>patient(X)))& (brave(daniel)&calm(daniel)&person(daniel))& (![X]:(room(X)=>(((kind(X)&person(X))=>(older(dawn,X))))))& (?[X]:(room(X)&(~~generous(X))))& (((old(rena)&quiet(rena)&funny(rena)&curious(rena)&patient(rena)&calm(rena)&person(rena))|(calm(rena)&quiet(rena)&happy(rena)&old(rena)&person(rena))))& (![X]:(brave(X)=>creative(X)))& (![X]:(kind(X)=>happy(X)))& ((![X]:((brave(X)&person(X))=>(older(dawn,X)))))& (![X]:(~room(X)=>(((~((kind(X))|(older(dawn,X))))<=(richer(dawn,X))))))

room(rena)&room(daniel)&room(jacob)&room(kathryn)&(![X]:(room(X)=>(X='rena'|X='daniel'|X='jacob'|X='kathryn')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

Marian, Howard, James are the only persons in the room. Everyone in the room is humble if and only if they is happy. All calm persons are kind. If someone is a old wise calm humble person then he/she is a kind european and vice versa. All calm persons are patient. Everyone anywhere is a wine connoisseur. Everyone outside the room is not a patient person or is not dedicated to sustainable living and zero-waste practices. Howard and Lori hate each other. "A city has not outlawed the use of round tables." and "A clock measures time in various colors." and "A book can be opened only at midnight.". James who enjoys making ceramics is a patient old person. "A book can be opened only at midnight." and "A clock measures time in various colors.". James is humble. Everyone in the room plays the drums if they frequently participates in hackathons and coding competitions. Everyone in the room either is curious or is not old, not kind, not brave but not both. Everyone in the room does not enjoy virtual reality gaming or is patient. Someone who is not patient, not happy, not brave and is a tea enthusiast is younger than someone who does practice yoga.

James is a wine connoisseur.

entailment

room(marian)&room(howard)&room(james)&(![X]:(room(X)=>(X='marian'|X='howard'|X='james')))& (![X]:(room(X)=>(((humble(X))<=>(happy(X))))))& (![X]:(calm(X)=>kind(X)))& ((![X]:((old(X)&wise(X)&calm(X)&humble(X)&person(X))<=>(kind(X)&european(X)))))& (![X]:(calm(X)=>patient(X)))& (![X]:(anywhere(X)=>(is_a_wine_connoisseur(X))))& (![X]:(~room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(~(patient(X)&person(X)))))))& ((hate(howard,lori) & hate(lori,howard)))& (((A_city_has_not_outlawed_the_use_of_round_tables.)&(A_clock_measures_time_in_various_colors.)&(A_book_can_be_opened_only_at_midnight.)))& ((enjoys_making_ceramics(james))&(patient(james)&old(james)&person(james)))& (((A_book_can_be_opened_only_at_midnight.)&(A_clock_measures_time_in_various_colors.)))& (humble(james))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((curious(X))<~>(~old(X)&~kind(X)&~brave(X))))))& (![X]:(room(X)=>(((patient(X))|(does_not_enjoy_virtual_reality_gaming(X))))))& (?[X,Y]:((((~patient(X)&~happy(X)&~brave(X))&(is_a_tea_enthusiast(X))))&(does_practice_yoga(Y))&(younger(X,Y))))

room(marian)&room(howard)&room(james)&(![X]:(room(X)=>(X='marian'|X='howard'|X='james')))& is_a_wine_connoisseur(james)

% SZS status Unsatisfiable for 7490798453738148289234160 % SZS output start Proof for 7490798453738148289234160 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0] : (anywhere(X0) => prede(X0)) [input p5] 60. ~(prede(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 144. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 144] 149. ! [X0] : (prede(X0) | ~anywhere(X0)) [ennf transformation 49] 151. ~prede(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60] 152. ~prede(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 151] 161. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 162. ~prede(fred) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 152,161] 164. anywhere(X0) [cnf transformation 5] 245. room(mary) [cnf transformation 145] 246. room(paul) [cnf transformation 145] 247. room(fred) [cnf transformation 145] 248. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 145] 260. prede(X0) | ~anywhere(X0) [cnf transformation 149] 273. ~prede(fred) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 274. ~prede(fred) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 275. ~prede(fred) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 276. ~prede(fred) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 277. prede(X0) [subsumption resolution 260,164] 278. fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,277] 279. fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 278,247] 280. fred != sK2 | ~room(mary) [subsumption resolution 279,246] 281. fred != sK2 [subsumption resolution 280,245] 282. paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,277] 283. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 282,247] 284. paul != sK2 | ~room(mary) [subsumption resolution 283,246] 285. paul != sK2 [subsumption resolution 284,245] 286. mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,277] 287. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 286,247] 288. mary != sK2 | ~room(mary) [subsumption resolution 287,246] 289. mary != sK2 [subsumption resolution 288,245] 290. room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,277] 291. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 290,247] 292. room(sK2) | ~room(mary) [subsumption resolution 291,246] 293. room(sK2) [subsumption resolution 292,245] 393. paul = sK2 | mary = sK2 | fred = sK2 [resolution 248,293] 394. mary = sK2 | fred = sK2 [subsumption resolution 393,285] 395. fred = sK2 [subsumption resolution 394,289] 396. $false [subsumption resolution 395,281] % SZS output end Proof for 7490798453738148289234160 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Henry is the only person in the room. If “everyone in the room has a specialized collection of handmade artisan pottery or is not passionate about collecting and restoring classic cars” then “if someone does not create large-scale murals for public art installations then he/she enjoys watercolor painting and vice versa”. If “it is not the case that “Henry enjoys spelunking”” then “Henry practices digital art”. If “everyone in the room hosts a YouTube channel dedicated to art tutorials or does not enjoy watercolor painting” then “Henry collects rare minerals”. Everyone in the room is an avid collector of autographed memorabilia from famous musicians if they enjoys spelunking. Henry is an avid mountain climber who has scaled several peaks. Henry does not collect historical artifacts related to ancient civilizations.

Henry practices digital art.

neutral

room(henry)&(![X]:(room(X)=>(X='henry')))& ((![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))=>((![X]:((does_not_create_large-scale_murals_for_public_art_installations(X))<=>(enjoys_watercolor_painting(X))))))& ((~(enjoys_spelunking(henry)))=>(practices_digital_art(henry)))& ((![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))=>(collects_rare_minerals(henry)))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(henry))& (does_not_collect_historical_artifacts_related_to_ancient_civilizations(henry))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=(can_play_the_harmonica(X))))))& (![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(~room(X)=>(((collects_vintage_stamps(X))<=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((((enjoys_spelunking(X))|(writes_a_travel_blog(X))))<=(is_a_drone_photographer(X))))))& (can_play_the_flute(henry))& (is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(henry))& ((![X]:((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))& ((![X]:((is_not_a_Linux_enthusiast(X))<=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))& (?[X]:(room(X)&(can_play_the_harmonica(X))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(henry))& ((![X]:((does_not_create_large-scale_murals_for_public_art_installations(X))<=>(enjoys_watercolor_painting(X)))))& (hosts_regular_game_nights_featuring_complex_strategy_games(henry))

room(henry)&(![X]:(room(X)=>(X='henry')))& practices_digital_art(henry)

There is a room. Either “everyone in the room is not a cybersecurity expert or does not play the violin” or “everyone outside the room is not a professional photographer specializing in portrait photography or is not dedicated to sustainable living and zero-waste practices” but not both. Everyone anywhere is not a professional photographer specializing in portrait photography if and only if they collects rare and antique scientific instruments. Everyone outside the room is not a professional photographer specializing in portrait photography or is not dedicated to sustainable living and zero-waste practices. At least one person in the room practices calligraphy. Everyone in the room who either collects rare and antique scientific instruments or is a certified yoga instructor teaching classes weekly but not both neither is a Linux enthusiast nor is an avid collector of autographed memorabilia from famous musicians. Everyone in the room is an avid collector of autographed memorabilia from famous musicians if and only if they collects rare and antique scientific instruments. Not everyone in the room who collects rare and antique scientific instruments does enjoy trail running, frequently participates in hackathons and coding competitions and reads mystery novels. If someone is a Linux enthusiast then he/she does not make homemade pastries. If someone enjoys salsa dancing then he/she writes and illustrates their own graphic novels and vice versa. Everyone in the room who enjoys virtual reality gaming, enjoys salsa dancing or is dedicated to sustainable living and zero-waste practices collects vintage stamps. Everyone in the room plays the violin, is an enthusiastic bird watcher who travels for rare sightings and is a tea enthusiast only if they makes homemade pastries or writes in-depth travel guides for off-the-beaten-path destinations or both. Everyone in the room enjoys virtual reality gaming. Everyone anywhere practices calligraphy or does not enjoy trail running. It is true that “everyone in the room enjoys spelunking or collects rare and antique scientific instruments or both if they practices calligraphy”. More than one person in the room writes in-depth travel guides for off-the-beaten-path destinations. If someone can play the piano then he/she makes homemade pastries. If someone is a cybersecurity expert then he/she is a professional photographer specializing in portrait photography. Everyone outside the room is a Linux enthusiast if they is passionate about collecting and restoring classic cars. Everyone in the room is a Linux enthusiast only if they collects rare and antique scientific instruments. Everyone anywhere is not a professional photographer specializing in portrait photography if they collects rare and antique scientific instruments.

Everyone in the room does not collect rare and antique scientific instruments.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_play_the_violin(X))|(is_not_a_cybersecurity_expert(X))))))<~>(![X]:(~room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))))& (![X]:(anywhere(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))<=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(~room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& (((?[X]:(room(X)&practices_calligraphy(X)))))& (![X]:(room(X)=>(((((collects_rare_and_antique_scientific_instruments(X))<~>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))=>(~((is_a_Linux_enthusiast(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))<=>(collects_rare_and_antique_scientific_instruments(X))))))& (~![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(((does_enjoy_trail_running(X))&(frequently_participates_in_hackathons_and_coding_competitions(X))&(reads_mystery_novels(X))))))))& ((![X]:((is_a_Linux_enthusiast(X))=>(does_not_make_homemade_pastries(X)))))& ((![X]:((enjoys_salsa_dancing(X))<=>(writes_and_illustrates_their_own_graphic_novels(X)))))& (![X]:(room(X)=>(((((enjoys_virtual_reality_gaming(X))|(enjoys_salsa_dancing(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((((makes_homemade_pastries(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))<=(((plays_the_violin(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(enjoys_virtual_reality_gaming(X))))& (![X]:(anywhere(X)=>(((does_not_enjoy_trail_running(X))|(practices_calligraphy(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(((enjoys_spelunking(X))|(collects_rare_and_antique_scientific_instruments(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)&writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(Y))&(X!=Y))))& ((![X]:((can_play_the_piano(X))=>(makes_homemade_pastries(X)))))& ((![X]:((is_a_cybersecurity_expert(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))& (![X]:(~room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(is_a_Linux_enthusiast(X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))<=(is_a_Linux_enthusiast(X))))))& (![X]:(anywhere(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((((does_not_write_a_travel_blog(X))|(does_not_enjoy_trail_running(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (~![X]:(anywhere(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(does_not_collect_rare_and_antique_scientific_instruments(X))))))

(there_is_a_room)& ![X]:(room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X)))

% SZS status Unsatisfiable for 8676552245129248693299677 % SZS output start Proof for 8676552245129248693299677 51. ~! [X0] : (room(X0) => (predm(X0) => (predy(X0) & prede(X0) & preds(X0)))) [input p7] 67. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 85. ~! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 51] 88. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 67] 168. ? [X0] : (predm(X0) & room(X0)) [ennf transformation 85] 176. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 88] 188. ? [X0] : (predm(X0) & room(X0)) => (predm(sK3) & room(sK3)) [choice axiom] 189. predm(sK3) & room(sK3) [skolemisation 168,188] 293. room(sK3) [cnf transformation 189] 294. predm(sK3) [cnf transformation 189] 304. ~predm(X0) | ~room(X0) [cnf transformation 176] 348. ~room(sK3) [resolution 304,294] 350. $false [subsumption resolution 348,293] % SZS output end Proof for 8676552245129248693299677 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Douglas, Kathy are the only persons in the room. If “Douglas does not have a tattoo” then “no one in the room designs and sews custom cosplay costumes for conventions if they hosts themed dinner parties featuring gourmet home-cooked meals”. Everyone in the room does not watche fantasy movies, is a client of Costco and does not enjoy origami. Everyone anywhere either hosts themed dinner parties featuring gourmet home-cooked meals or does not enjoy origami but not both. More than one person outside the room hosts themed dinner parties featuring gourmet home-cooked meals. Everyone in the room does not build model airplanes only if they hosts themed dinner parties featuring gourmet home-cooked meals or does not have a tattoo or both.

It is true that “Douglas does not build model airplanes”.

contradiction

room(douglas)&room(kathy)&(![X]:(room(X)=>(X='douglas'|X='kathy')))& ((does_not_have_a_tattoo(douglas))=>(~?[X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))))& ((![X]:(~room(X)=>(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))<~>(((enjoys_windsurfing(douglas))<~>(plays_video_games(douglas)))))& ((((?[X]:(room(X)&((is_not_a_client_of_Costco(X))<~>(does_not_make_homemade_pastries(X)))))))<~>(![X]:(room(X)=>(((does_not_make_homemade_pastries(X))|(does_not_have_a_tattoo(X)))))))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))&(is_a_client_of_Costco(X))&(does_not_enjoy_origami(X))))))& ((![X]:((collects_historical_artifacts_related_to_ancient_civilizations(X))<=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))& (((?[X]:(room(X)&~((does_not_enjoy_fishing(X))|(does_not_stream_on_Twitch(X)))))&(![X,Y]:((room(X)&room(Y)&(~((does_not_enjoy_fishing(X))|(does_not_stream_on_Twitch(X))))&(~((does_not_enjoy_fishing(Y))|(does_not_stream_on_Twitch(Y)))))=>(X=Y)))))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))=>(does_not_enjoy_windsurfing(X))))))& (![X]:(room(X)=>(practices_urban_gardening(X))))& (((?[X]:(room(X)&collects_luxury_watches(X)))))& (does_not_enjoy_fishing(douglas))& (![X]:(room(X)=>(((does_not_enjoy_origami(X))<=(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (does_not_participate_in_long-distance_cycling_events_across_the_country(douglas))& (![X]:(anywhere(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<~>(does_not_enjoy_origami(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)&hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(Y))&(X!=Y))))& (practices_digital_art(douglas))& (designs_and_sews_custom_cosplay_costumes_for_conventions(douglas))& (![X]:(room(X)=>(((does_not_make_homemade_pastries(X))=>(does_not_watche_fantasy_movies(X))))))& (((?[X]:(anywhere(X)&hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& (![X]:(room(X)=>(((((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_have_a_tattoo(X))))<=(does_not_build_model_airplanes(X))))))& (((?[X]:(~room(X)&does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))

room(douglas)&room(kathy)&(![X]:(room(X)=>(X='douglas'|X='kathy')))& does_not_build_model_airplanes(douglas)

% SZS status Unsatisfiable for 8780813054515672086161030 % SZS output start Proof for 8780813054515672086161030 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~prede(mary) => ~? [X0] : (room(X0) => (predl(X0) => predt(X0))) [input p1] 48. ! [X0] : (room(X0) => (~predg(X0) & predw(X0) & ~predz(X0))) [input p4] 57. ! [X0] : (anywhere(X0) => (predl(X0) <~> ~predg(X0))) [input p13] 58. ? [X0,X1] : (X0 != X1 & predl(X1) & predl(X0) & ~room(X1) & ~room(X0)) [input p14] 63. ! [X0] : (room(X0) => (~predk(X0) => (~prede(X0) | predl(X0)))) [input p19] 65. ~predk(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 147. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 148. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 147] 149. ! [X0] : ((~predt(X0) & predl(X0)) & room(X0)) | prede(mary) [ennf transformation 45] 150. ! [X0] : (~predt(X0) & predl(X0) & room(X0)) | prede(mary) [flattening 149] 154. ! [X0] : ((~predg(X0) & predw(X0) & ~predz(X0)) | ~room(X0)) [ennf transformation 48] 159. ! [X0] : ((predl(X0) <~> ~predg(X0)) | ~anywhere(X0)) [ennf transformation 57] 162. ! [X0] : (((~prede(X0) | predl(X0)) | predk(X0)) | ~room(X0)) [ennf transformation 63] 163. ! [X0] : (~prede(X0) | predl(X0) | predk(X0) | ~room(X0)) [flattening 162] 164. ~predk(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 65] 165. ~predk(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 164] 186. ! [X0] : (((predg(X0) | ~predl(X0)) & (~predg(X0) | predl(X0))) | ~anywhere(X0)) [nnf transformation 159] 187. ? [X0,X1] : (X0 != X1 & predl(X1) & predl(X0) & ~room(X1) & ~room(X0)) => (sK6 != sK7 & predl(sK7) & predl(sK6) & ~room(sK7) & ~room(sK6)) [choice axiom] 188. sK6 != sK7 & predl(sK7) & predl(sK6) & ~room(sK7) & ~room(sK6) [skolemisation 58,187] 193. anywhere(X0) [cnf transformation 5] 274. room(mary) [cnf transformation 148] 277. room(X0) | prede(mary) [cnf transformation 150] 297. ~predg(X0) | ~room(X0) [cnf transformation 154] 306. predg(X0) | ~predl(X0) | ~anywhere(X0) [cnf transformation 186] 307. ~room(sK6) [cnf transformation 188] 316. ~prede(X0) | predl(X0) | predk(X0) | ~room(X0) [cnf transformation 163] 321. ~predk(mary) [cnf transformation 165] 323. 1 <=> prede(mary) [avatar definition] 325. prede(mary) <- (1) [avatar component clause 323] 335. 4 <=> ! [X0] : room(X0) [avatar definition] 336. room(X0) <- (4) [avatar component clause 335] 337. 1 | 4 [avatar split clause 277,335,323] 410. ~predl(X0) | predg(X0) [subsumption resolution 306,193] 414. $false <- (4) [resolution 336,307] 419. ~4 [avatar contradiction clause 414] 485. predl(mary) | predk(mary) | ~room(mary) <- (1) [resolution 316,325] 493. predl(mary) | ~room(mary) <- (1) [subsumption resolution 485,321] 494. predl(mary) <- (1) [subsumption resolution 493,274] 523. predg(mary) <- (1) [resolution 494,410] 526. ~room(mary) <- (1) [resolution 523,297] 527. $false <- (1) [subsumption resolution 526,274] 528. ~1 [avatar contradiction clause 527] 529. $false [avatar sat refutation 337,419,528] % SZS output end Proof for 8780813054515672086161030 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s % ------------------------------ % ------------------------------

Wilbert, Cyril, Evelyn, Lauren are the only persons in the room. Either "Cyril does not enjoy origami" or "everyone anywhere does not collect classic novels or creates augmented reality experiences for mobile applications" but not both. "Wilbert creates augmented reality experiences for mobile applications" if "Cyril collects classic novels". "Cyril does not collect classic novels" if "everyone outside the room does not collect classic novels or creates augmented reality experiences for mobile applications" and vice versa. Everyone in the room neither collects classic novels nor enjoys origami if they creates augmented reality experiences for mobile applications. Wilbert dreamt that "everyone outside the room neither collects classic novels nor enjoys origami only if they collects classic novels". Cyril creates augmented reality experiences for mobile applications.

Cyril collects classic novels.

contradiction

room(wilbert)&room(cyril)&room(evelyn)&room(lauren)&(![X]:(room(X)=>(X='wilbert'|X='cyril'|X='evelyn'|X='lauren')))& ((does_not_enjoy_origami(cyril))<~>(![X]:(anywhere(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_collect_classic_novels(X)))))))& ((collects_classic_novels(cyril))=>(creates_augmented_reality_experiences_for_mobile_applications(wilbert)))& ((![X]:(~room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_collect_classic_novels(X))))))<=>(does_not_collect_classic_novels(cyril)))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(~((collects_classic_novels(X))|(enjoys_origami(X))))))))& ((wilbert_dream=>(![X]:(~room(X)=>(((collects_classic_novels(X))<=(~((collects_classic_novels(X))|(enjoys_origami(X))))))))))& (creates_augmented_reality_experiences_for_mobile_applications(cyril))& (creates_augmented_reality_experiences_for_mobile_applications(wilbert))

room(wilbert)&room(cyril)&room(evelyn)&room(lauren)&(![X]:(room(X)=>(X='wilbert'|X='cyril'|X='evelyn'|X='lauren')))& collects_classic_novels(cyril)

% SZS status Unsatisfiable for 4606002072022177448911981 % SZS output start Proof for 4606002072022177448911981 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (preda(X0) => ~(predc(X0) | predb(X0)))) [input p4] 50. preda(paul) [input p6] 52. predb(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 125. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 126. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 125] 132. ! [X0] : (((~predc(X0) & ~predb(X0)) | ~preda(X0)) | ~room(X0)) [ennf transformation 48] 133. ! [X0] : ((~predc(X0) & ~predb(X0)) | ~preda(X0) | ~room(X0)) [flattening 132] 134. predb(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 52] 135. predb(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134] 227. room(paul) [cnf transformation 126] 240. ~predb(X0) | ~preda(X0) | ~room(X0) [cnf transformation 133] 242. preda(paul) [cnf transformation 50] 249. predb(paul) [cnf transformation 135] 270. 5 <=> predb(paul) [avatar definition] 271. predb(paul) <- (5) [avatar component clause 270] 298. 5 [avatar split clause 249,270] 300. ~preda(paul) | ~room(paul) <- (5) [resolution 240,271] 302. ~room(paul) <- (5) [subsumption resolution 300,242] 303. $false <- (5) [subsumption resolution 302,227] 304. ~5 [avatar contradiction clause 303] 305. $false [avatar sat refutation 298,304] % SZS output end Proof for 4606002072022177448911981 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Diane, Tami, Patrick, Ronald are the only persons in the room. "Ronald is poorer than Jamie" unless "everyone in the room is not a dedicated volunteer for local community service projects or is a dedicated volunteer for local community service projects". "Ronald is older than Jamie" only if "all calm persons are happy". If "Tami and Ronald are respectively old and happy" then "Tami who collects vintage stamps is not old". If "no one in the room is not a dedicated volunteer for local community service projects or collects vintage stamps" then "it is true that "everyone in the room is a dedicated volunteer for local community service projects or does not collect vintage stamps"". If "it is true that "everyone in the room is a dedicated volunteer for local community service projects or does not collect vintage stamps"" then "no calm person is generous". If "everyone in the room is not a dedicated volunteer for local community service projects or does not like Jamie" then "everyone in the room who is not a dedicated volunteer for local community service projects is a generous person". If "everyone in the room is old" then "Ronald is a dedicated volunteer for local community service projects". If "Patrick is old" then "Diane is a dedicated volunteer for local community service projects". "Tami is older than Jamie" if "everyone outside the room is not a dedicated volunteer for local community service projects or is liked by Jamie" and vice versa. If "everyone in the room collects vintage stamps or is not a dedicated volunteer for local community service projects" then "Diane and Jamie like each other" otherwise "it is not the case that "Jamie is older than Ronald"". If "everyone in the room does not collect vintage stamps or does not like Jamie" then "Diane dreamt that "no one in the room is a old person"". "Diane who does not collect vintage stamps is calm" unless "Jamie and Tami like each other". Everyone outside the room collects vintage stamps if they is calm. All old persons are happy. More than one person in the room is poorer than Jamie. Everyone in the room does not collect vintage stamps or collects vintage stamps. Tami is older than Jamie. Tami and Ronald are respectively calm and generous.

Diane is a dedicated volunteer for local community service projects.

neutral

room(diane)&room(tami)&room(patrick)&room(ronald)&(![X]:(room(X)=>(X='diane'|X='tami'|X='patrick'|X='ronald')))& (~(![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))=>(poorer(jamie,ronald)))& ((older(jamie,ronald))=>(![X]:(calm(X)=>happy(X))))& (((old(tami))&(happy(ronald)))=>((collects_vintage_stamps(tami))&(~old(tami))))& (((~?[X]:(room(X)=>(((collects_vintage_stamps(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))=>(![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))))& ((![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))=>(~?[X]:(calm(X)=>generous(X)))))& ((![X]:(room(X)=>(((~like(jamie,X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))=>(![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))=>(generous(X)&person(X)))))))& ((![X]:(room(X)=>(old(X))))=>(is_a_dedicated_volunteer_for_local_community_service_projects(ronald)))& ((old(patrick))=>(is_a_dedicated_volunteer_for_local_community_service_projects(diane)))& ((![X]:(~room(X)=>(((like(X,jamie))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))<=>(older(jamie,tami)))& (((![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(collects_vintage_stamps(X))))))=>((like(diane,jamie) & like(jamie,diane))))&((~(![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(collects_vintage_stamps(X)))))))=>(~(older(ronald,jamie)))))& ((![X]:(room(X)=>(((~like(jamie,X))|(does_not_collect_vintage_stamps(X))))))=>((diane_dream=>(~?[X]:(room(X)=>(old(X)&person(X)))))))& (~((like(jamie,tami) & like(tami,jamie)))=>((does_not_collect_vintage_stamps(diane))&(calm(diane))))& (![X]:(~room(X)=>(((calm(X))=>(collects_vintage_stamps(X))))))& (![X]:(old(X)=>happy(X)))& ((?[X,Y]:(room(X)&room(Y)&(poorer(jamie,X)&poorer(jamie,Y))&(X!=Y))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))|(does_not_collect_vintage_stamps(X))))))& (older(jamie,tami))& ((calm(tami))&(generous(ronald)))& (old(diane))& (![X]:(room(X)=>(((((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(calm(X)&person(X))&(~(happy(X)&calm(X)&generous(X)&person(X)))))=>(older(jamie,X))))))& (?[X]:(anywhere(X)&(~like(jamie,X))))& (collects_vintage_stamps(diane))& (poorer(jamie,ronald)&poorer(jamie,patrick))& (older(jamie,diane))& ((old(ronald))&(calm(diane)))& (((collects_vintage_stamps(ronald))<~>(is_not_a_dedicated_volunteer_for_local_community_service_projects(ronald))))

room(diane)&room(tami)&room(patrick)&room(ronald)&(![X]:(room(X)=>(X='diane'|X='tami'|X='patrick'|X='ronald')))& is_a_dedicated_volunteer_for_local_community_service_projects(diane)

There is a room. If “someone in the room builds model airplanes” then “if someone is a Linux enthusiast then he/she is right-handed and vice versa”. If someone is not a wine connoisseur then he/she practices digital art. At least one person in the room composes and performs experimental electronic music. If someone own a television then he/she trains for and competes in international triathlons, enjoys stand-up paddleboarding or is right-handed and vice versa. It is true that “it is true that “someone in the room composes and performs experimental electronic music””. At least one person in the room writes a travel blog. If someone collects rare minerals then he/she maintains a personal blog focused on cybersecurity tips. At least one person in the room collects vintage vinyl records. It is not the case that “at least one person in the room enjoys spelunking”. If someone enjoys cross-country skiing then he/she owns a smart tv and vice versa. At least one person in the room does not compose and performs experimental electronic music. If someone owns a smart tv then he/she trains for and competes in international triathlons. If someone does not enjoy stand-up paddleboarding then he/she enjoys skydiving. At least one person in the room hosts a popular podcast about emerging technologies. It is not the case that “at least one person outside the room either owns a smart tv or is a certified yoga instructor teaching classes weekly but not both”. At least one person in the room collects luxury watches. Someone anywhere maintains a large, organic vegetable garden year-round. If someone enjoys stand-up paddleboarding then he/she own a television and vice versa. Someone in the room builds model airplanes. It is true that “if someone is a wine connoisseur and builds model airplanes then he/she collects rare minerals”.

Everyone in the room is not a certified yoga instructor teaching classes weekly.

neutral

(there_is_a_room)& ((?[X]:(room(X)&(builds_model_airplanes(X))))=>((![X]:((is_a_Linux_enthusiast(X))<=>(is_right-handed(X))))))& ((![X]:((is_not_a_wine_connoisseur(X))=>(practices_digital_art(X)))))& (((?[X]:(room(X)&composes_and_performs_experimental_electronic_music(X)))))& ((![X]:((own_a_television(X))<=>(((trains_for_and_competes_in_international_triathlons(X))|(enjoys_stand-up_paddleboarding(X))|(is_right-handed(X)))))))& (?[X]:(room(X)&(composes_and_performs_experimental_electronic_music(X))))& (((?[X]:(room(X)&writes_a_travel_blog(X)))))& ((![X]:((collects_rare_minerals(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))& (((?[X]:(room(X)&collects_vintage_vinyl_records(X)))))& (~(((?[X]:(room(X)&enjoys_spelunking(X))))))& ((![X]:((enjoys_cross-country_skiing(X))<=>(owns_a_smart_tv(X)))))& (((?[X]:(room(X)&does_not_compose_and_performs_experimental_electronic_music(X)))))& ((![X]:((owns_a_smart_tv(X))=>(trains_for_and_competes_in_international_triathlons(X)))))& ((![X]:((does_not_enjoy_stand-up_paddleboarding(X))=>(enjoys_skydiving(X)))))& (((?[X]:(room(X)&hosts_a_popular_podcast_about_emerging_technologies(X)))))& (~(((?[X]:(~room(X)&((owns_a_smart_tv(X))<~>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))& (((?[X]:(room(X)&collects_luxury_watches(X)))))& (?[X]:(anywhere(X)&(maintains_a_large,_organic_vegetable_garden_year-round(X))))& ((![X]:((enjoys_stand-up_paddleboarding(X))<=>(own_a_television(X)))))& (?[X]:(room(X)&(builds_model_airplanes(X))))& ((![X]:((((is_a_wine_connoisseur(X))&(builds_model_airplanes(X))))=>(collects_rare_minerals(X)))))

(there_is_a_room)& ![X]:(room(X)=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))

Jerry, Jose, Bernard, Kim are the only persons in the room. If “at least one person in the room composes and performs experimental electronic music” then “everyone in the room is an avid hiker or does not compose and performs experimental electronic music”. Either “Jose does not collect vintage vinyl records” or “someone in the room enjoys wildlife photography” but not both. Jose is a tea enthusiast. Everyone outside the room is a client of Costco if they is a client of LVMH. Everyone in the room participates in citizen science projects related to wildlife monitoring if they is a client of Costco. Jose collects first edition books. Everyone outside the room who is dedicated to sustainable living and zero-waste practices is an avid hiker. Someone in the room is a certified yoga instructor teaching classes weekly. Everyone in the room uses an ios phone or does not use an ios phone. Someone in the room enjoys wildlife photography. Not everyone outside the room who collects rare minerals neither collects classic novels nor enjoys bird watching. Jose either enjoys bird watching or collects classic novels but not both. Everyone in the room who is a member of a local theater group specializing in improv does not maintain a large, organic vegetable garden year-round. Everyone in the room is a client of Costco. Bernard does not collect first edition books. Bernard is a member of a local theater group specializing in improv. Everyone in the room collects rare minerals if and only if they is a member of a local theater group specializing in improv. Everyone in the room uses an ios phone if they is a member of a local theater group specializing in improv.

Jose collects vintage vinyl records.

entailment

room(jerry)&room(jose)&room(bernard)&room(kim)&(![X]:(room(X)=>(X='jerry'|X='jose'|X='bernard'|X='kim')))& ((((?[X]:(room(X)&composes_and_performs_experimental_electronic_music(X)))))=>(![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(is_an_avid_hiker(X)))))))& ((does_not_collect_vintage_vinyl_records(jose))<~>(?[X]:(room(X)&(enjoys_wildlife_photography(X)))))& (is_a_tea_enthusiast(jose))& (![X]:(~room(X)=>(((is_a_client_of_LVMH(X))=>(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (collects_first_edition_books(jose))& (![X]:(~room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(is_an_avid_hiker(X))))))& (?[X]:(room(X)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))& (![X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(uses_an_ios_phone(X))))))& (?[X]:(room(X)&(enjoys_wildlife_photography(X))))& (~![X]:(~room(X)=>(((collects_rare_minerals(X))=>(~((collects_classic_novels(X))|(enjoys_bird_watching(X))))))))& (((enjoys_bird_watching(jose))<~>(collects_classic_novels(jose))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(is_a_client_of_Costco(X))))& (does_not_collect_first_edition_books(bernard))& (is_a_member_of_a_local_theater_group_specializing_in_improv(bernard))& (![X]:(room(X)=>(((collects_rare_minerals(X))<=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(uses_an_ios_phone(X))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(((enjoys_wildlife_photography(X))&(is_a_client_of_Costco(X))&(is_not_a_wine_connoisseur(X))))))))& (~![X]:(anywhere(X)=>(((((enjoys_wildlife_photography(X))&(is_a_client_of_Costco(X))&(is_not_a_wine_connoisseur(X))))=>(~((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(is_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(can_play_the_harmonica(X))&(does_not_collect_vintage_vinyl_records(X))))))))& (practices_urban_gardening(bernard))& (((?[X]:(room(X)&composes_and_performs_experimental_electronic_music(X)))))& (![X]:(room(X)=>(creates_large-scale_murals_for_public_art_installations(X))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(does_not_have_a_saltwater_aquarium(X))))))& (((is_a_wine_connoisseur(jose))<~>(creates_large-scale_murals_for_public_art_installations(jose))))& (collects_first_edition_books(kim))

room(jerry)&room(jose)&room(bernard)&room(kim)&(![X]:(room(X)=>(X='jerry'|X='jose'|X='bernard'|X='kim')))& collects_vintage_vinyl_records(jose)

% SZS status Unsatisfiable for 549951623658152929842597 % SZS output start Proof for 549951623658152929842597 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ~predf(paul) <~> ? [X0] : (prede(X0) & room(X0)) [input p2] 54. ? [X0] : (prede(X0) & room(X0)) [input p10] 73. ~(predf(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 164. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 165. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 164] 179. ~predf(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 73] 180. ~predf(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 179] 182. (! [X0] : (~prede(X0) | ~room(X0)) | predf(paul)) & (? [X0] : (prede(X0) & room(X0)) | ~predf(paul)) [nnf transformation 46] 183. (! [X0] : (~prede(X0) | ~room(X0)) | predf(paul)) & (? [X1] : (prede(X1) & room(X1)) | ~predf(paul)) [rectify 182] 184. ? [X1] : (prede(X1) & room(X1)) => (prede(sK0) & room(sK0)) [choice axiom] 185. (! [X0] : (~prede(X0) | ~room(X0)) | predf(paul)) & ((prede(sK0) & room(sK0)) | ~predf(paul)) [skolemisation 183,184] 188. ? [X0] : (prede(X0) & room(X0)) => (prede(sK2) & room(sK2)) [choice axiom] 189. prede(sK2) & room(sK2) [skolemisation 54,188] 199. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 200. ~predf(paul) | (alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 180,199] 281. room(mary) [cnf transformation 165] 282. room(paul) [cnf transformation 165] 283. room(fred) [cnf transformation 165] 284. room(alice) [cnf transformation 165] 285. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 165] 288. ~prede(X0) | ~room(X0) | predf(paul) [cnf transformation 185] 292. room(sK2) [cnf transformation 189] 293. prede(sK2) [cnf transformation 189] 315. ~predf(paul) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 316. ~predf(paul) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 317. ~predf(paul) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 318. ~predf(paul) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 319. ~predf(paul) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 321. 1 <=> predf(paul) [avatar definition] 325. 2 <=> ! [X0] : (~prede(X0) | ~room(X0)) [avatar definition] 326. ~prede(X0) | ~room(X0) <- (2) [avatar component clause 325] 327. 1 | 2 [avatar split clause 288,325,321] 367. ~predf(paul) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,284] 368. ~predf(paul) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 367,283] 369. ~predf(paul) | alice != sK6 | ~room(mary) [subsumption resolution 368,282] 370. ~predf(paul) | alice != sK6 [subsumption resolution 369,281] 372. 11 <=> alice = sK6 [avatar definition] 374. alice != sK6 <- (~11) [avatar component clause 372] 375. ~11 | ~1 [avatar split clause 370,321,372] 376. ~predf(paul) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,284] 377. ~predf(paul) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 376,283] 378. ~predf(paul) | fred != sK6 | ~room(mary) [subsumption resolution 377,282] 379. ~predf(paul) | fred != sK6 [subsumption resolution 378,281] 381. 12 <=> fred = sK6 [avatar definition] 383. fred != sK6 <- (~12) [avatar component clause 381] 384. ~12 | ~1 [avatar split clause 379,321,381] 385. ~predf(paul) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,284] 386. ~predf(paul) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 385,283] 387. ~predf(paul) | paul != sK6 | ~room(mary) [subsumption resolution 386,282] 388. ~predf(paul) | paul != sK6 [subsumption resolution 387,281] 390. 13 <=> paul = sK6 [avatar definition] 392. paul != sK6 <- (~13) [avatar component clause 390] 393. ~13 | ~1 [avatar split clause 388,321,390] 394. ~predf(paul) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,284] 395. ~predf(paul) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 394,283] 396. ~predf(paul) | mary != sK6 | ~room(mary) [subsumption resolution 395,282] 397. ~predf(paul) | mary != sK6 [subsumption resolution 396,281] 399. 14 <=> mary = sK6 [avatar definition] 401. mary != sK6 <- (~14) [avatar component clause 399] 402. ~14 | ~1 [avatar split clause 397,321,399] 403. ~predf(paul) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,284] 404. ~predf(paul) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 403,283] 405. ~predf(paul) | room(sK6) | ~room(mary) [subsumption resolution 404,282] 406. ~predf(paul) | room(sK6) [subsumption resolution 405,281] 408. 15 <=> room(sK6) [avatar definition] 410. room(sK6) <- (15) [avatar component clause 408] 411. 15 | ~1 [avatar split clause 406,321,408] 422. ~room(sK2) <- (2) [resolution 326,293] 424. $false <- (2) [subsumption resolution 422,292] 425. ~2 [avatar contradiction clause 424] 486. fred = sK6 | paul = sK6 | mary = sK6 | alice = sK6 <- (15) [resolution 285,410] 555. paul = sK6 | mary = sK6 | alice = sK6 <- (~12, 15) [subsumption resolution 486,383] 556. mary = sK6 | alice = sK6 <- (~12, ~13, 15) [subsumption resolution 555,392] 557. alice = sK6 <- (~12, ~13, ~14, 15) [subsumption resolution 556,401] 558. $false <- (~11, ~12, ~13, ~14, 15) [subsumption resolution 557,374] 559. 11 | 12 | 13 | 14 | ~15 [avatar contradiction clause 558] 560. $false [avatar sat refutation 327,375,384,393,402,411,425,559] % SZS output end Proof for 549951623658152929842597 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s % ------------------------------ % ------------------------------